Finite Group Databasebeta

← #28271014

Subgroups — #28271014

Order 13568.

2160 conjugacy classes of subgroups.

The subgroup lattice has 1952 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20289117C211yesmaximal, characteristic, complemented
2#20288501C211yesmaximal, characteristic, complemented
3#20286908C211yesmaximal, characteristic, complemented
4#20286907C211yesmaximal, characteristic, complemented
5#20286903C211yesmaximal, characteristic, complemented
6#20286896C211yesmaximal, characteristic, complemented
7#20286876C211yesmaximal, characteristic, complemented
8#20286875C211yesmaximal, characteristic, complemented
9#20286871C211yesmaximal, characteristic, complemented
10#20286864C211yesmaximal, characteristic, complemented
11#20286214C211yesmaximal, characteristic, complemented
12#20286209C211yesmaximal, characteristic, complemented
13#20286208C211yesmaximal, characteristic, complemented
14#20286206C211yesmaximal, characteristic, complemented
15#20286195C211yesmaximal, characteristic, complemented
16#20286190C211yesmaximal, characteristic, complemented
17#20286189C211yesmaximal, characteristic, complemented
18#20285700C211yesmaximal, characteristic, complemented
19#20285697C211yesmaximal, characteristic, complemented
20#20285584C211yesmaximal, characteristic, complemented
21#20285581C211yesmaximal, characteristic, complemented
22#20285578C211yesmaximal, characteristic, complemented
23#20285577C211yesmaximal, characteristic, complemented
24#20284863C211yesmaximal, characteristic, complemented
25#20284862C211yesmaximal, characteristic, complemented
26#20284000C211yesmaximal, characteristic, complemented
27#20283998C211yesmaximal, characteristic, complemented
28#20283979C211yesmaximal, characteristic, complemented
29#20283978C211yesmaximal, characteristic, complemented
30#20283783C211yesmaximal, characteristic, complemented
31C53×#3264C211yesmaximal, characteristic, complemented
32C2×#13133264C2211yescharacteristic, complemented
33C2×#13133262C2211yescharacteristic, complemented
34C2×#13133243C2211yescharacteristic, complemented
35C2×#13133241C2211yescharacteristic, complemented
36C2×#13133241C2211yescharacteristic, complemented
37C22×#11719923C2211yescharacteristic, complemented
38C2×SD16×D53C2211yescharacteristic, complemented
39C2×D8×D53C2211yescharacteristic, complemented
40#16811366—21no—
41#16811366—21no—
42#16811338C2211yescharacteristic, complemented
43#16811338C2211yescharacteristic, complemented
44#16811337—21no—
45#16811337C2211yescharacteristic, complemented
46#16811337C2211yescharacteristic, complemented
47#16811283C2211yescharacteristic, complemented
48#16811282C2211yescharacteristic, complemented
49#16811281C2211yescharacteristic, complemented
50#16811279C2211yescharacteristic, complemented
51#16811268C2211yescharacteristic, complemented
52#16811267C2211yescharacteristic, complemented
53#16811265—21no—
54#16811263—21no—
55#16811262—21no—
56#16811261C2211yescharacteristic, complemented
57#16811260—21no—
58#16811258C2211yescharacteristic, complemented
59D4×C22⋊D53—21no—
60D4×C22⋊D53C2211yescharacteristic, complemented
61D4×C22⋊D53C2211yescharacteristic, complemented
62#16811196C2211yescharacteristic, complemented
63#16811195—21no—
64#16811190—21no—
65#16811190C2211yescharacteristic
66#16811190C2211yescharacteristic, complemented
67#16811189—21no—
68#16811189C2211yescharacteristic
69#16811189C2211yescharacteristic, complemented
70#16811189C2211yescharacteristic, complemented
71#16811188—21no—
72#16811188—21no—
73#16811188—21no—
74#16811171C2211yescharacteristic, complemented
75#16811170C2211yescharacteristic
76#16811170C2211yescharacteristic, complemented
77#16811168—21no—
78C2×#13133203—21no—
79#124×D53C2211yescharacteristic, complemented
80C4×#11719947C2211yescharacteristic, complemented
81#16811011C2211yescharacteristic, complemented
82#16811010C2211yescharacteristic, complemented
83#16811009C2211yescharacteristic, complemented
84#16810984C2211yescharacteristic, complemented
85#16810983C2211yescharacteristic, complemented
86#16810982C2211yescharacteristic, complemented
87#16810981C2211yescharacteristic, complemented
88#16810967C2211yescharacteristic, complemented
89#16810965C2211yescharacteristic, complemented
90#16810962C2211yescharacteristic, complemented
91#16810961C2211yescharacteristic, complemented
92#16810949C2211yescharacteristic, complemented
93#16810949C2211yescharacteristic, complemented
94#16810948C2211yescharacteristic, complemented
95#16810946C2211yescharacteristic, complemented
96#16810946C2211yescharacteristic, complemented
97#16810946C2211yescharacteristic, complemented
98#16810945C2211yescharacteristic, complemented
99#16810944C2211yescharacteristic, complemented
100#16810909C2211yescharacteristic, complemented
101#16810907C2211yescharacteristic, complemented
102#16810903C2211yescharacteristic, complemented
103#16810901C2211yescharacteristic, complemented
104#16810876C2211yescharacteristic, complemented
105#16810875C2211yescharacteristic, complemented
106#16810873C2211yescharacteristic, complemented
107#16810871C2211yescharacteristic, complemented
108#16810868C2211yescharacteristic, complemented
109#16810867C2211yescharacteristic, complemented
110#16810866C2211yescharacteristic, complemented
111#16810858C2211yescharacteristic, complemented
112#16810857C2211yescharacteristic, complemented
113#16810857C2211yescharacteristic, complemented
114#16810856C2211yescharacteristic, complemented
115#16810852C2211yescharacteristic, complemented
116#16810851C2211yescharacteristic, complemented
117#16810849C2211yescharacteristic, complemented
118#16810840C2211yescharacteristic, complemented
119#16810840C2211yescharacteristic, complemented
120#16810839C2211yescharacteristic, complemented
121#16810838C2211yescharacteristic, complemented
122#16810836C2211yescharacteristic, complemented
123#16810836C2211yescharacteristic, complemented
124#16810835C2211yescharacteristic, complemented
125#16810822C2211yescharacteristic, complemented
126#16810820C2211yescharacteristic, complemented
127#16810816C2211yescharacteristic, complemented
128#16810775C2211yescharacteristic, complemented
129#16810774C2211yescharacteristic, complemented
130#16810772C2211yescharacteristic, complemented
131#16810770C2211yescharacteristic, complemented
132#16810769C2211yescharacteristic, complemented
133#16810768C2211yescharacteristic, complemented
134#16810766C2211yescharacteristic, complemented
135#16810765C2211yescharacteristic, complemented
136#16810765C2211yescharacteristic, complemented
137#16810765C2211yescharacteristic, complemented
138#16810765C2211yescharacteristic, complemented
139#16810765C2211yescharacteristic, complemented
140#16810765C2211yescharacteristic, complemented
141#16810765C2211yescharacteristic, complemented
142#16810764C2211yescharacteristic, complemented
143#16810763C2211yescharacteristic, complemented
144#16810761C2211yescharacteristic, complemented
145#16810760C2211yescharacteristic, complemented
146#16810760C2211yescharacteristic, complemented
147#16810760C2211yescharacteristic, complemented
148#16810760C2211yescharacteristic, complemented
149#16810760C2211yescharacteristic, complemented
150#16810758C2211yescharacteristic, complemented
151#16810758C2211yescharacteristic, complemented
152#16810757C2211yescharacteristic, complemented
153#16810757C2211yescharacteristic, complemented
154#16810755C2211yescharacteristic, complemented
155#16810755C2211yescharacteristic, complemented
156#16810755C2211yescharacteristic, complemented
157#16810755C2211yescharacteristic, complemented
158#16810755C2211yescharacteristic, complemented
159#16810755C2211yescharacteristic, complemented
160#16810735C2211yescharacteristic, complemented
161#16810735C2211yescharacteristic, complemented
162#16810733C2211yescharacteristic, complemented
163#16810725C2211yescharacteristic, complemented
164#16810723C2211yescharacteristic, complemented
165#16810720C2211yescharacteristic, complemented
166#16810720C2211yescharacteristic, complemented
167#16810697C2211yescharacteristic, complemented
168#16810696C2211yescharacteristic, complemented
169#16810695C2211yescharacteristic, complemented
170#16810694C2211yescharacteristic, complemented
171#16810693C2211yescharacteristic, complemented
172#16810692C2211yescharacteristic, complemented
173#16810691C2211yescharacteristic, complemented
174#16810679C2211yescharacteristic, complemented
175#16810678C2211yescharacteristic, complemented
176#16810633C2211yescharacteristic, complemented
177#16810630C2211yescharacteristic, complemented
178#16810628C2211yescharacteristic, complemented
179#16810626C2211yescharacteristic, complemented
180#16810620C2211yescharacteristic, complemented
181#16810619C2211yescharacteristic, complemented
182#16810616C2211yescharacteristic, complemented
183#16810616C2211yescharacteristic, complemented
184#16810591C2211yescharacteristic, complemented
185#16810589C2211yescharacteristic, complemented
186#16810588C2211yescharacteristic, complemented
187#16810588C2211yescharacteristic, complemented
188C2×AGL(1,ℤ/8)×C53C2211yescharacteristic, complemented
189C22×D8×C53C2211yescharacteristic, complemented
190C53×#546C2211yescharacteristic, complemented
191D42×C53C2211yescharacteristic, complemented
192C53×#496C2211yescharacteristic, complemented
193C53×#469C2211yescharacteristic, complemented
194C53×#465C2211yescharacteristic, complemented
195C53×#463C2211yescharacteristic, complemented
196C53×#459C2211yescharacteristic, complemented
197C53×#450C2211yescharacteristic, complemented
198C53×#449C2211yescharacteristic, complemented
199C53×#447C2211yescharacteristic, complemented
200C53×#447C2211yescharacteristic, complemented
201C53×#442C2211yescharacteristic, complemented
202C53×#435C2211yescharacteristic, complemented
203#13133264—42no—
204#13133264—42no—
205#13133262—42no—
206#13133262—42no—
207C2×#11719945—21no—
208C2×#11719945—21no—
209C2×#11719945C2311yescharacteristic
210C2×#11719945C2311yescharacteristic
211C2×#11719945C2311yescharacteristic
212C2×#11719947—21no—
213C2×#11719947—21no—
214C2×#11719947—21no—
215C2×#11719947—21no—
216C2×#11719947C2311yescharacteristic
217C2×#11719947C2311yescharacteristic
218C2×#11719947C2311yescharacteristic
219C22×Dic106—21no—
220C22×Dic106C2311yescharacteristic
221C2×Q8×D53C2311yescharacteristic
222C2×Q8×D53C2311yescharacteristic
223C22×C22⋊D53—21no—
224C22×C22⋊D53—21no—
225C22×C22⋊D53—21no—
226C22×C22⋊D53—21no—
227C2×D4×D53—21no—
228C2×D4×D53—21no—
229C2×D4×D53C2311yescharacteristic
230C2×D4×D53C2311yescharacteristic
231C2×D4×D53C2311yescharacteristic
232C2×D4×D53C2311yescharacteristic
233#13133243—42no—
234#13133241—42no—
235#13133241—42no—
236C2×#11719913C2311yescharacteristic
237C2×#11719913C2311yescharacteristic
238C2×#11719923—42no—
239C2×#11719923C2311yescharacteristic
240C2×#11719923C2311yescharacteristic
241C2×#11719923C2311yescharacteristic
242C2×#11719923C2311yescharacteristic
243C2×#11719923C2311yescharacteristic
244C2×#11719923C2311yescharacteristic
245C2×#11719924C2311yescharacteristic
246SD16×D53—42no—
247C2×D424C2311yescharacteristic
248C2×#11719922C2311yescharacteristic
249C2×#11719922C2311yescharacteristic
250C2×#11719922C2311yescharacteristic
251C2×#11719922C2311yescharacteristic
252C2×#11719922C2311yescharacteristic
253D8×D53—42no—
254C2×#11719917C2311yescharacteristic
255C2×#11719912C2311yescharacteristic
256C2×#11719912C2311yescharacteristic
257C22×#88322C2311yescharacteristic
258C2×C8×D53C2311yescharacteristic
259C2×C8×D53C2311yescharacteristic
260#13133217C2311yescharacteristic
261#13133216—21no—
262#13133216D411yescharacteristic
263#13133216C2311yescharacteristic
264#13133213—21no—
265#13133213—21no—
266#13133213—21no—
267#13133213—21no—
268#13133213—21no—
269#13133213D411yescharacteristic
270#13133213C2311yescharacteristic
271#13133206C2311yescharacteristic
272#13133205C2311yescharacteristic
273#13133204—21no—
274#13133204—21no—
275#13133204—21no—
276#13133204—21no—
277#13133204—21no—
278#13133204C2311yescharacteristic
279#13133203—21no—
280#13133203—21no—
281#13133203—21no—
282#13133203—21no—
283#13133203—21no—
284#13133203—21no—
285#13133203—21no—
286#13133203—21no—
287#13133203—21no—
288#13133203—21no—
289#13133203—21no—
290#13133203—21no—
291#13133203—21no—
292#13133203—21no—
293#13133203—21no—
294#13133203—21no—
295#13133203—21no—
296#13133203D411yescharacteristic
297#13133203D411yescharacteristic
298#13133202—21no—
299#13133201—21no—
300#13133200—21no—
301#13133199—21no—
302#13133198—21no—
303#13133197C2311yescharacteristic
304#13133196C2311yescharacteristic
305#13133195—21no—
306#13133195—21no—
307#13133194—21no—
308#13133194—21no—
309#13133193C2311yescharacteristic
310#13133192D411yescharacteristic
311#13133192C2311yescharacteristic
312#13133192C2311yescharacteristic
313#13133191—21no—
314#13133191—21no—
315#13133191C2311yescharacteristic
316#13133191C2311yescharacteristic
317#13133191C2311yescharacteristic
318#13133190—21no—
319#13133190—21no—
320#13133190—21no—
321#13133190D411yescharacteristic
322#13133190D411yescharacteristic
323#13133189—21no—
324#13133189—21no—
325#13133189—21no—
326#13133189—21no—
327#13133189—21no—
328#13133189—21no—
329#13133189—21no—
330#13133189—21no—
331#13133188—21no—
332#13133188—21no—
333#13133188—21no—
334#13133188D411yescharacteristic
335#13133188C2311yescharacteristic
336#13133188C2311yescharacteristic
337#13133188C2311yescharacteristic
338#13133188C2311yescharacteristic
339#13133188C2311yescharacteristic
340#13133188C2311yescharacteristic
341#13133188C2311yescharacteristic
342#13133188C2311yescharacteristic
343#13133187—21no—
344#13133187—21no—
345#13133187—21no—
346#13133187—21no—
347#13133186—21no—
348#13133186—21no—
349#13133186—21no—
350#13133186—21no—
351#13133186—21no—
352#13133186—21no—
353#13133186—21no—
354#13133185—21no—
355#13133185—21no—
356#13133185—21no—
357#13133185—21no—
358#13133185—21no—
359#13133185—21no—
360#13133185—21no—
361#13133185—21no—
362C4×Dic106C2311yescharacteristic
363#13133182C2311yescharacteristic
364C4×D212C2311yescharacteristic
365C4×D212C2311yescharacteristic
366D4×Dic53—21no—
367D4×Dic53—21no—
368D4×Dic53C2311yescharacteristic
369D4×Dic53C2311yescharacteristic
370D4×Dic53C2311yescharacteristic
371#13133179—21no—
372C4×C22⋊D53—21no—
373C4×C22⋊D53—21no—
374C4×C22⋊D53C2311yescharacteristic
375C4×C22⋊D53C2311yescharacteristic
376#13133177—21no—
377#13133177—21no—
378#13133177—21no—
379#13133176—21no—
380#13133176C2311yescharacteristic
381#13133176C2311yescharacteristic
382#13133175—21no—
383#13133175C2311yescharacteristic
384#13133175C2311yescharacteristic
385#13133175C2311yescharacteristic
386#13133173—21no—
387#13133173—21no—
388#13133173—21no—
389C2×C22⋊Dic53—21no—
390C2×#11719921—21no—
391C2×#11719921—21no—
392C22⋊C4×D53—21no—
393C22⋊C4×D53—21no—
394C2×C4×Dic53—21no—
395C42×D53C2311yescharacteristic
396#13133151C2311yescharacteristic
397#13133150C2311yescharacteristic
398#13133150C2311yescharacteristic
399#13133150C2311yescharacteristic
400#13133149C2311yescharacteristic
401#13133149C2311yescharacteristic
402#13133148C2311yescharacteristic
403C4⋊#88322C2311yescharacteristic
404#13133146C2311yescharacteristic
405#13133146C2311yescharacteristic
406#13133142C2311yescharacteristic
407#13133142C2311yescharacteristic
408#13133142C2311yescharacteristic
409#13133142C2311yescharacteristic
410#13133142C2311yescharacteristic
411#13133142C2311yescharacteristic
412#13133141C2311yescharacteristic
413#13133141C2311yescharacteristic
414#13133141C2311yescharacteristic
415#13133140C2311yescharacteristic
416#13133140C2311yescharacteristic
417#13133139C2311yescharacteristic
418#13133139C2311yescharacteristic
419#13133139C2311yescharacteristic
420#13133139C2311yescharacteristic
421#13133138C2311yescharacteristic
422#13133138C2311yescharacteristic
423#13133138C2311yescharacteristic
424#13133138C2311yescharacteristic
425#13133138C2311yescharacteristic
426#13133138C2311yescharacteristic
427#13133138C2311yescharacteristic
428#13133138C2311yescharacteristic
429#13133138C2311yescharacteristic
430#13133137C2311yescharacteristic
431#13133137C2311yescharacteristic
432C22⋊#88322C2311yescharacteristic
433C22⋊#88322C2311yescharacteristic
434#13133129C2311yescharacteristic
435#13133129C2311yescharacteristic
436#13133129C2311yescharacteristic
437#13133129C2311yescharacteristic
438#13133129C2311yescharacteristic
439#13133129C2311yescharacteristic
440#13133129C2311yescharacteristic
441#13133129C2311yescharacteristic
442#13133128C2311yescharacteristic
443#13133127C2311yescharacteristic
444#13133127C2311yescharacteristic
445C2×#41×C53C2311yescharacteristic
446C22×D4×C53—21no—
447C22×D4×C53C2311yescharacteristic
448C22×D4×C53C2311yescharacteristic
449C22×D4×C53C2311yescharacteristic
450AGL(1,ℤ/8)×C53—42no—
451C2×SD16×C53C2311yescharacteristic
452C2×SD16×C53C2311yescharacteristic
453C2×SD16×C53C2311yescharacteristic
454C2×D8×C53—42no—
455C2×D8×C53C2311yescharacteristic
456C2×D8×C53C2311yescharacteristic
457C2×D8×C53C2311yescharacteristic
458C2×D8×C53C2311yescharacteristic
459C2×D8×C53C2311yescharacteristic
460C2×D8×C53C2311yescharacteristic
461C2×M16×C53C2311yescharacteristic
462C22×C8×C53C2311yescharacteristic
463#127×C53C2311yescharacteristic
464#124×C53C2311yescharacteristic
465#123×C53—21no—
466C22⋊Q8×C53C2311yescharacteristic
467#121×C53—21no—
468#121×C53—21no—
469#121×C53C2311yescharacteristic
470#121×C53C2311yescharacteristic
471#121×C53C2311yescharacteristic
472#120×C53—21no—
473#120×C53—21no—
474#120×C53—21no—
475C4×D4×C53C2311yescharacteristic
476C4×D4×C53C2311yescharacteristic
477C4×D4×C53C2311yescharacteristic
478C2×C22⋊C4×C53—21no—
479#106×C53C2311yescharacteristic
480C4⋊C8×C53C2311yescharacteristic
481#103×C53C2311yescharacteristic
482#102×C53C2311yescharacteristic
483#102×C53C2311yescharacteristic
484#102×C53C2311yescharacteristic
485#102×C53C2311yescharacteristic
486#102×C53C2311yescharacteristic
487C22⋊C8×C53C2311yescharacteristic
488C22⋊C8×C53C2311yescharacteristic
489#97×C53C2311yescharacteristic
490C24×C53—21no—
491C24×C53—21no—
492C24×C53—21no—
493C23×D53—21no—
494C23×D53—21no—
495C23×D53—21no—
496C23×D53—21no—
497#41×C53—22no—
498#41×C53—41no—
499C2×Q8×C53C2411yescharacteristic
500C2×D4×C53—22no—
501C2×D4×C53—21no—
502C2×D4×C53—21no—
503C2×D4×C53—21no—
504C2×D4×C53—21no—
505C2×D4×C53—21no—
506C2×D4×C53—21no—
507C2×D4×C53—21no—
508C2×D4×C53—21no—
509C2×D4×C53—21no—
510C2×D4×C53—41no—
511C2×D4×C53—41no—
512C2×D4×C53—41no—
513C2×D4×C53—41no—
514C2×D4×C53—41no—
515C2×D4×C53—82no—
516C2×D4×C53C2×D411yescharacteristic
517C2×D4×C53C2411yescharacteristic
518C2×D4×C53C2411yescharacteristic
519C2×D4×C53C2411yescharacteristic
520C2×D4×C53C2411yescharacteristic
521C2×D4×C53C2411yescharacteristic
522C22×C4×C53—21no—
523C22×C4×C53—21no—
524C22×C4×C53—21no—
525C22×C4×C53C2411yescharacteristic
526C22×C4×C53C2411yescharacteristic
527C2×C22⋊D53—21no—
528C2×C22⋊D53—21no—
529C2×C22⋊D53—21no—
530C2×C22⋊D53—21no—
531C2×C22⋊D53—21no—
532C2×C22⋊D53—21no—
533C2×C22⋊D53—21no—
534C2×C22⋊D53—21no—
535C2×C22⋊D53—21no—
536C2×C22⋊D53—21no—
537C2×C22⋊D53—21no—
538C2×C22⋊D53—21no—
539C2×C22⋊D53—21no—
540C2×C22⋊D53—21no—
541C2×C22⋊D53—21no—
542C2×C22⋊D53—21no—
543C2×C22⋊D53—21no—
544C2×C22⋊D53—21no—
545C2×C22⋊D53—21no—
546C2×C22⋊D53—21no—
547C2×C22⋊D53—21no—
548C2×C22⋊D53—44no—
549C2×C22⋊D53—44no—
550C2×C22⋊D53—82no—
551C2×C22⋊D53—82no—
552C2×C22⋊D53C2×D411yescharacteristic
553C2×C22⋊D53C2×D411yescharacteristic
554C2×C22⋊D53C2×D411yescharacteristic
555C2×C22⋊D53C2×D411yescharacteristic
556C2×C22⋊D53C2×D411yescharacteristic
557C2×C22⋊D53C2×D411yescharacteristic
558C22×Dic53—21no—
559C22×Dic53—21no—
560C22×Dic53—21no—
561C22×Dic53—21no—
562C22×Dic53—21no—
563C22×Dic53—21no—
564C22×Dic53—21no—
565Q8×D53—22no—
566Q8×D53—41no—
567Q8×D53—41no—
568Q8×D53—41no—
569#11719947—22no—
570#11719947—22no—
571#11719947—22no—
572#11719947—22no—
573#11719947—41no—
574#11719947—41no—
575#11719947—44no—
576#11719947—44no—
577#11719947—44no—
578#11719947—82no—
579D4×D53—22no—
580D4×D53—41no—
581D4×D53—41no—
582D4×D53—41no—
583D4×D53—41no—
584D4×D53—41no—
585D4×D53—41no—
586D4×D53—41no—
587D4×D53—44no—
588D4×D53—82no—
589#11719945—22no—
590#11719945—41no—
591#11719945—41no—
592#11719945—41no—
593#11719945—41no—
594#11719945—41no—
595#11719945—44no—
596#11719945—82no—
597C2×D212—21no—
598C2×D212—21no—
599C2×D212C2×D411yescharacteristic
600C2×D212C2×D411yescharacteristic
601C2×D212C2×D411yescharacteristic
602C2×D212C2411yescharacteristic
603C2×D212C2411yescharacteristic
604C2×C4×D53—21no—
605C2×C4×D53—21no—
606C2×C4×D53—21no—
607C2×C4×D53—21no—
608C2×C4×D53C2×D411yescharacteristic
609C2×C4×D53C2×D411yescharacteristic
610C2×C4×D53C2411yescharacteristic
611C2×C4×D53C2411yescharacteristic
612C2×C4×D53C2411yescharacteristic
613C2×Dic106—22no—
614C2×Dic106—21no—
615C2×Dic106—21no—
616C2×Dic106—21no—
617C2×Dic106—21no—
618C2×Dic106—21no—
619C2×Dic106—41no—
620C2×Dic106—44no—
621C2×Dic106C2×D411yescharacteristic
622C2×Dic106C2×D411yescharacteristic
623C2×Dic106C2411yescharacteristic
624C2×Dic106C2411yescharacteristic
625SD16×C53—41no—
626SD16×C53—41no—
627SD16×C53—41no—
628D8×C53—22no—
629D8×C53—22no—
630D8×C53—22no—
631D8×C53—41no—
632D8×C53—41no—
633D8×C53—41no—
634M16×C53—41no—
635C2×C8×C53—41no—
636C2×C8×C53C2411yescharacteristic
637C2×C8×C53C2411yescharacteristic
638C2×C8×C53C2411yescharacteristic
639C2×C8×C53C2411yescharacteristic
640C4⋊C4×C53—21no—
641C4⋊C4×C53C2×D411yescharacteristic
642C4⋊C4×C53C2411yescharacteristic
643C4⋊C4×C53C2411yescharacteristic
644C22⋊C4×C53—21no—
645C22⋊C4×C53—21no—
646C22⋊C4×C53—21no—
647C22⋊C4×C53—21no—
648C22⋊C4×C53—21no—
649C22⋊C4×C53—21no—
650C22⋊C4×C53—21no—
651C22⋊C4×C53—21no—
652C22⋊C4×C53C2×D411yescharacteristic
653C22⋊C4×C53C2×D411yescharacteristic
654C42×C53C2411yescharacteristic
655C22⋊Dic53—21no—
656C22⋊Dic53—21no—
657C22⋊Dic53—21no—
658C22⋊Dic53—21no—
659C22⋊Dic53—21no—
660C22⋊Dic53—21no—
661C22⋊Dic53—21no—
662C22⋊Dic53—21no—
663C22⋊Dic53—21no—
664C22⋊Dic53—21no—
665C22⋊Dic53—21no—
666C22⋊Dic53—21no—
667C22⋊Dic53—21no—
668C22⋊Dic53—21no—
669C22⋊Dic53—21no—
670C22⋊Dic53—21no—
671C22⋊Dic53C2×D411yescharacteristic
672C22⋊Dic53C2×D411yescharacteristic
673#11719924—41no—
674#11719923—22no—
675#11719923—22no—
676#11719923—22no—
677#11719923—41no—
678#11719923—41no—
679#11719923—41no—
680#11719922—22no—
681#11719922—41no—
682#11719922—41no—
683#11719922—41no—
684#11719922—41no—
685#11719921—21no—
686#11719921—21no—
687#11719921—21no—
688#11719921—21no—
689#11719921—21no—
690#11719921—21no—
691#11719921—21no—
692#11719921—21no—
693#11719921—21no—
694#11719921—21no—
695#11719921—21no—
696#11719921—21no—
697#11719921—21no—
698#11719921—21no—
699#11719921—21no—
700#11719921C2×D411yescharacteristic
701#11719921C2×D411yescharacteristic
702#11719921C2×D411yescharacteristic
703#11719921C2×D411yescharacteristic
704C4⋊Dic53—21no—
705C4⋊Dic53—21no—
706C4⋊Dic53C2×D411yescharacteristic
707C4⋊Dic53C2411yescharacteristic
708C4⋊Dic53C2411yescharacteristic
709C4⋊Dic53C2411yescharacteristic
710C4⋊Dic53C2411yescharacteristic
711#11719919—21no—
712#11719919—21no—
713#11719919—21no—
714#11719919—21no—
715#11719919—21no—
716#11719919C2×D411yescharacteristic
717#11719919C2×D411yescharacteristic
718C4×Dic53—21no—
719C4×Dic53—21no—
720C4×Dic53—21no—
721C4×Dic53—21no—
722C4×Dic53—21no—
723C4×Dic53—21no—
724C4×Dic53—21no—
725C4×Dic53C2×D411yescharacteristic
726C4×Dic53C2×D411yescharacteristic
727C4×Dic53C2411yescharacteristic
728#11719917—41no—
729C2×#88322—41no—
730C2×#88322C2411yescharacteristic
731C2×#88322C2411yescharacteristic
732C2×#88322C2411yescharacteristic
733C2×#88322C2411yescharacteristic
734D424—41no—
735#11719913—22no—
736#11719913—41no—
737#11719912—41no—
738#11719912—41no—
739C8×D53—41no—
740C8×D53—41no—
741C23×C53—21no—
742C23×C53—21no—
743C23×C53—21no—
744C23×C53—21no—
745C23×C53—21no—
746C23×C53—42no—
747C23×C53—81no—
748C23×C53—81no—
749C23×C53—81no—
750C23×C53—81no—
751C23×C53—81no—
752C23×C53—81no—
753C23×C53—81no—
754C23×C53—81no—
755C23×C53C22×D411yescharacteristic
756C23×C53C22×D411yescharacteristic
757C22×D53—21no—
758C22×D53—21no—
759C22×D53—42no—
760C22×D53—42no—
761C22×D53—81no—
762C22×D53—81no—
763C22×D53—81no—
764C22×D53—81no—
765C22×D53—81no—
766C22×D53—81no—
767C22×D53—81no—
768C22×D53—81no—
769C22×D53—81no—
770C22×D53—81no—
771C22×D53C22×D411yescharacteristic
772C22×D53C22×D411yescharacteristic
773C22×D53C22×D411yescharacteristic
774Q8×C53—21no—
775Q8×C53—21no—
776D4×C53—21no—
777D4×C53—21no—
778D4×C53—21no—
779D4×C53—21no—
780D4×C53—21no—
781D4×C53—21no—
782D4×C53—21no—
783D4×C53—21no—
784D4×C53—21no—
785D4×C53—41no—
786D4×C53—42no—
787D4×C53—42no—
788D4×C53—42no—
789D4×C53—81no—
790D4×C53—81no—
791D4×C53—81no—
792D4×C53—81no—
793D4×C53—81no—
794D4×C53—81no—
795D4×C53H(5,𝔽2)12yes—
796C2×C4×C53—21no—
797C2×C4×C53—21no—
798C2×C4×C53—21no—
799C2×C4×C53—21no—
800C2×C4×C53—21no—
801C2×C4×C53—21no—
802C2×C4×C53—21no—
803C2×C4×C53—42no—
804C2×C4×C53—42no—
805C2×C4×C53—81no—
806C2×C4×C53C22×D411yescharacteristic
807C2×C4×C53C22×D411yescharacteristic
808C2×C4×C53C22×D411yescharacteristic
809C2×C4×C53C22×D411yescharacteristic
810C2×C4×C53C2511yescharacteristic
811C22⋊D53—24no—
812C22⋊D53—41no—
813C22⋊D53—41no—
814C22⋊D53—41no—
815C22⋊D53—41no—
816C22⋊D53—41no—
817C22⋊D53—41no—
818C22⋊D53—42no—
819C22⋊D53—42no—
820C22⋊D53—42no—
821C22⋊D53—42no—
822C22⋊D53—42no—
823C22⋊D53—42no—
824C22⋊D53—81no—
825C22⋊D53—81no—
826C22⋊D53—81no—
827C22⋊D53—81no—
828C22⋊D53—81no—
829C22⋊D53—81no—
830C22⋊D53—81no—
831C22⋊D53—81no—
832C22⋊D53—81no—
833C22⋊D53—81no—
834C22⋊D53—81no—
835C22⋊D53—81no—
836C22⋊D53—81no—
837C22⋊D53—81no—
838C2×Dic53—24no—
839C2×Dic53—21no—
840C2×Dic53—21no—
841C2×Dic53—21no—
842C2×Dic53—21no—
843C2×Dic53—21no—
844C2×Dic53—21no—
845C2×Dic53—42no—
846C2×Dic53—42no—
847C2×Dic53—42no—
848C2×Dic53—42no—
849C2×Dic53—42no—
850C2×Dic53—81no—
851C2×Dic53C22×D411yescharacteristic
852C2×Dic53C22×D411yescharacteristic
853C2×Dic53C22×D411yescharacteristic
854C2×Dic53C22×D411yescharacteristic
855C2×Dic53C22×D411yescharacteristic
856D212—21no—
857D212—21no—
858D212—21no—
859D212—21no—
860D212—41no—
861D212—41no—
862D212—41no—
863D212—81no—
864D212—81no—
865C4×D53—21no—
866C4×D53—21no—
867C4×D53—21no—
868C4×D53—21no—
869C4×D53—21no—
870C4×D53—21no—
871C4×D53—41no—
872C4×D53—41no—
873C4×D53—42no—
874C4×D53—42no—
875C4×D53—42no—
876C4×D53—42no—
877Dic106—21no—
878Dic106—21no—
879Dic106—21no—
880Dic106—41no—
881Dic106—41no—
882Dic106—42no—
883Dic106—42no—
884Dic106—42no—
885Dic106—81no—
886Dic106—81no—
887Dic106H(5,𝔽2)12yes—
888C8×C53—21no—
889C8×C53—21no—
890C8×C53—21no—
891C8×C53—21no—
892#88322—21no—
893#88322—21no—
894#88322—21no—
895#88322—21no—
896#61673—531nomaximal, Sylow
897C22×C53—21no—
898C22×C53—21no—
899C22×C53—21no—
900C22×C53—21no—
901C22×C53—22no—
902C22×C53—21no—
903C22×C53—21no—
904C22×C53—41no—
905C22×C53—41no—
906C22×C53—41no—
907C22×C53—41no—
908C22×C53—41no—
909C22×C53—41no—
910C22×C53—41no—
911C22×C53—41no—
912C22×C53—41no—
913C22×C53—41no—
914C22×C53—41no—
915C22×C53—41no—
916C22×C53—41no—
917C22×C53—41no—
918C22×C53—162no—
919C22×C53—162no—
920C22×C53—162no—
921C22×C53C23×D411yescharacteristic
922C2×D53—21no—
923C2×D53—21no—
924C2×D53—21no—
925C2×D53—21no—
926C2×D53—21no—
927C2×D53—21no—
928C2×D53—21no—
929C2×D53—21no—
930C2×D53—21no—
931C2×D53—41no—
932C2×D53—41no—
933C2×D53—41no—
934C2×D53—41no—
935C2×D53—41no—
936C2×D53—41no—
937C2×D53—162no—
938C2×D53—162no—
939C2×D53—162no—
940C2×D53—162no—
941C4×C53—21no—
942C4×C53—21no—
943C4×C53—21no—
944C4×C53—21no—
945C4×C53—41no—
946C4×C53—41no—
947C4×C53—41no—
948C4×C53C2×H(5,𝔽2)11yescharacteristic
949C4×C53C2×H(5,𝔽2)11yescharacteristic
950Dic53—21no—
951Dic53—21no—
952Dic53—22no—
953Dic53—21no—
954Dic53—21no—
955Dic53—21no—
956Dic53—41no—
957Dic53—41no—
958Dic53—41no—
959Dic53—41no—
960Dic53—41no—
961#3549—531no—
962#3500—531no—
963#3321—531no—
964#3321—531no—
965#3321—531no—
966#3321—531no—
967#3319—531no—
968#3319—531no—
969#3319—531no—
970#3319—531no—
971#3265—531no—
972#3265—531no—
973#3265—531no—
974#3265—531no—
975#3264—531no—
976#3264—531no—
977#3264—531no—
978#3264D5311yescharacteristic, complemented
979#3213—531no—
980#3213—531no—
981#3200—531no—
982#3200—531no—
983#3199—531no—
984#3199—531no—
985#3115—531no—
986#3115—531no—
987#3010—531no—
988#3010—531no—
989#3008—531no—
990#3008—531no—
991#2980—531no—
992C2×C53—42no—
993C2×C53—41no—
994C2×C53—41no—
995C2×C53—81no—
996C2×C53—81no—
997C2×C53—81no—
998C2×C53—81no—
999C2×C53#348411yescharacteristic
1000C2×C53#358511yescharacteristic
1001C2×C53#358511yescharacteristic
1002D53—41no—
1003D53—41no—
1004D53—41no—
1005D53—81no—
1006D53—81no—
1007C2×2−1+4—531no—
1008C2×H(5,𝔽2)—531no—
1009C2×AGL(1,ℤ/8)—531no—
1010C2×AGL(1,ℤ/8)—531no—
1011C2×AGL(1,ℤ/8)—531no—
1012C2×AGL(1,ℤ/8)C2×D5311yescharacteristic, complemented
1013C22×SD16—531no—
1014C22×SD16—531no—
1015C22×D8—531no—
1016C22×D8C2×D5311yescharacteristic, complemented
1017H(3,𝔽4)—1061no—
1018H(3,𝔽4)—1061no—
1019#555—531no—
1020#555—531no—
1021#555—531no—
1022#555—531no—
1023#555—1061no—
1024#548—531no—
1025#548—531no—
1026#548—531no—
1027#548—531no—
1028#546—531no—
1029#546—531no—
1030#546—531no—
1031#546—1061no—
1032#546—1061no—
1033#546—1061no—
1034#546—1061no—
1035#546C2×D5311yescharacteristic, complemented
1036D42—531no—
1037D42—531no—
1038D42—531no—
1039D42—1061no—
1040D42C2×D5311yescharacteristic, complemented
1041#536—531no—
1042#536—1061no—
1043#535—531no—
1044#535—531no—
1045#535—531no—
1046#535—531no—
1047#535—531no—
1048#535—1061no—
1049#535—1061no—
1050#535—1061no—
1051#535—1061no—
1052#535—1061no—
1053#532—531no—
1054#532—531no—
1055#532—531no—
1056#532—1061no—
1057C2×#124—531no—
1058C2×#124—1061no—
1059C4×#41—531no—
1060#496—531no—
1061#496—531no—
1062#496—531no—
1063#496C2×D5311yescharacteristic, complemented
1064#489—531no—
1065#489—531no—
1066#489—531no—
1067#489—531no—
1068#485—531no—
1069#485—531no—
1070#485—531no—
1071#485—531no—
1072#482—531no—
1073#482—531no—
1074#482—531no—
1075#482—531no—
1076#482—531no—
1077#482—531no—
1078#482—531no—
1079#482—531no—
1080#475—531no—
1081#475—531no—
1082#474—531no—
1083#474—531no—
1084#469—531no—
1085#469—531no—
1086#469—531no—
1087#469C2×D5311yescharacteristic, complemented
1088#468—531no—
1089#468—531no—
1090#468—531no—
1091#468—531no—
1092#466—531no—
1093#466—531no—
1094#466—531no—
1095#466—531no—
1096#465—531no—
1097#465—531no—
1098#465—531no—
1099#465C2×D5311yescharacteristic, complemented
1100#463—531no—
1101#463—531no—
1102#463—531no—
1103#463—531no—
1104#463—531no—
1105#463—531no—
1106#463—531no—
1107#463C2×D5311yescharacteristic, complemented
1108#460—531no—
1109#460—531no—
1110#459—531no—
1111#459C2×D5311yescharacteristic, complemented
1112#450—531no—
1113#450—531no—
1114#450—531no—
1115#450C2×D5311yescharacteristic, complemented
1116#449—531no—
1117#449—531no—
1118#449—531no—
1119#449—531no—
1120#449—531no—
1121#449—531no—
1122#449—531no—
1123#449—531no—
1124#449—531no—
1125#449—531no—
1126#449—531no—
1127#449C2×D5311yescharacteristic, complemented
1128#448—531no—
1129#448—531no—
1130#448—531no—
1131#448—531no—
1132#448—531no—
1133#448—531no—
1134#448—531no—
1135#448—531no—
1136#447—531no—
1137#447—531no—
1138#447—531no—
1139#447—531no—
1140#447—531no—
1141#447—531no—
1142#447—531no—
1143#447—531no—
1144#447—531no—
1145#447—531no—
1146#447C2×D5311yescharacteristic, complemented
1147#447C2×D5311yescharacteristic, complemented
1148#442—531no—
1149#442—531no—
1150#442—531no—
1151#442C2×D5311yescharacteristic, complemented
1152#440—531no—
1153#440—531no—
1154#440—531no—
1155#440—531no—
1156#435—531no—
1157#435—531no—
1158#435—531no—
1159#435—531no—
1160#435—531no—
1161#435—531no—
1162#435—531no—
1163#435C2×D5311yescharacteristic, complemented
1164#432—531no—
1165#432—531no—
1166#419—531no—
1167#419—531no—
1168#418—531no—
1169#418—531no—
1170#416—531no—
1171#416—531no—
1172#416—531no—
1173#416—531no—
1174#408—531no—
1175#408—531no—
1176#408—531no—
1177#408—531no—
1178C53#6167311yescharacteristic, complemented, Sylow
11792−1+4—2122no—
11802−1+4—2122no—
1181H(5,𝔽2)—2122no—
1182H(5,𝔽2)—2122no—
1183C2×#41—531no—
1184C2×#41—531no—
1185C2×#41—531no—
1186C2×#41—531no—
1187C2×#41—531no—
1188C2×#41—531no—
1189C2×#41—1061no—
1190C2×#41—1061no—
1191C2×#41—1061no—
1192C2×#41—1061no—
1193C2×#41—1061no—
1194C2×#41—1061no—
1195C2×#41C22×D5311yescharacteristic
1196C22×Q8—531no—
1197C22×Q8—531no—
1198C22×Q8—531no—
1199C22×Q8—1061no—
1200C22×D4—21no—
1201C22×D4—531no—
1202C22×D4—531no—
1203C22×D4—531no—
1204C22×D4—531no—
1205C22×D4—1061no—
1206C22×D4—1061no—
1207C22×D4—1061no—
1208C22×D4—1061no—
1209C22×D4—1061no—
1210C22×D4—1061no—
1211C22×D4C22×D5311yescharacteristic
1212C22×D4C22×D5311yescharacteristic
1213C22×D4C22×D5311yescharacteristic
1214AGL(1,ℤ/8)—42no—
1215AGL(1,ℤ/8)—2122no—
1216AGL(1,ℤ/8)—2122no—
1217AGL(1,ℤ/8)—2122no—
1218C2×SD16—531no—
1219C2×SD16—531no—
1220C2×SD16—531no—
1221C2×SD16—531no—
1222C2×SD16—531no—
1223C2×SD16—531no—
1224C2×SD16—531no—
1225C2×SD16—531no—
1226C2×SD16—531no—
1227C2×SD16—2122no—
1228C2×SD16—2122no—
1229C2×SD16C22×D5311yescharacteristic
1230C2×SD16C22×D5311yescharacteristic
1231C2×SD16C22×D5311yescharacteristic
1232C2×D8—42no—
1233C2×D8—531no—
1234C2×D8—531no—
1235C2×D8—531no—
1236C2×D8—531no—
1237C2×D8—531no—
1238C2×D8—531no—
1239C2×D8—2122no—
1240C2×D8C22×D5311yescharacteristic
1241C2×D8C22×D5311yescharacteristic
1242C2×D8C22×D5311yescharacteristic
1243C2×D8C22×D5311yescharacteristic
1244C2×D8C22×D5311yescharacteristic
1245C2×D8C22×D5311yescharacteristic
1246C2×M16—531no—
1247C2×M16—531no—
1248C2×M16—531no—
1249C2×M16C22×D5311yescharacteristic
1250C22×C8—531no—
1251C22×C8—531no—
1252C22×C8—531no—
1253C22×C8C22×D5311yescharacteristic
1254C4⋊Q8—531no—
1255C4⋊Q8—531no—
1256C4⋊Q8—531no—
1257C4⋊Q8—1061no—
1258#127—531no—
1259#127—531no—
1260#127—1061no—
1261#127—1061no—
1262#127—1061no—
1263#127—1061no—
1264#127—1061no—
1265#127C22×D5311yescharacteristic
1266#124—531no—
1267#124—531no—
1268#124—531no—
1269#124—531no—
1270#124—531no—
1271#124—1061no—
1272#124—1061no—
1273#124—1061no—
1274#124—1061no—
1275#124—1061no—
1276#124—1061no—
1277#124—1061no—
1278#124—1061no—
1279#124—1061no—
1280#124—1061no—
1281#124—1061no—
1282#124—1061no—
1283#124—1061no—
1284#124—1061no—
1285#124—1061no—
1286#124—1061no—
1287#124—1061no—
1288#124—1061no—
1289#124—1061no—
1290#124—1061no—
1291#124—1061no—
1292#124—1061no—
1293#124C22×D5311yescharacteristic
1294#123—21no—
1295#123—1061no—
1296#123—1061no—
1297#123—1061no—
1298#123—1061no—
1299#123—1061no—
1300C22⋊Q8—531no—
1301C22⋊Q8—531no—
1302C22⋊Q8—531no—
1303C22⋊Q8—1061no—
1304C22⋊Q8—1061no—
1305C22⋊Q8—1061no—
1306C22⋊Q8—1061no—
1307C22⋊Q8C22×D5311yescharacteristic
1308#121—21no—
1309#121—21no—
1310#121—531no—
1311#121—531no—
1312#121—531no—
1313#121—531no—
1314#121—531no—
1315#121—531no—
1316#121—531no—
1317#121—531no—
1318#121—531no—
1319#121—531no—
1320#121—531no—
1321#121—531no—
1322#121—531no—
1323#121—531no—
1324#121—531no—
1325#121—531no—
1326#121—531no—
1327#121—1061no—
1328#121—1061no—
1329#121—1061no—
1330#121—1061no—
1331#121—1061no—
1332#121—1061no—
1333#121—1061no—
1334#121—1061no—
1335#121—1061no—
1336#121—1061no—
1337#121—1061no—
1338#121—1061no—
1339#121—1061no—
1340#121—1061no—
1341#121—1061no—
1342#121—1061no—
1343#121C22×D5311yescharacteristic
1344#121C22×D5311yescharacteristic
1345#121C22×D5311yescharacteristic
1346#120—21no—
1347#120—21no—
1348#120—21no—
1349#120—1061no—
1350#120—1061no—
1351#120—1061no—
1352#120—1061no—
1353#120—1061no—
1354#120—1061no—
1355#120—1061no—
1356#120—1061no—
1357#120—1061no—
1358#120—1061no—
1359#120—1061no—
1360#120—1061no—
1361#120—1061no—
1362#120—1061no—
1363#120—1061no—
1364#120—1061no—
1365#120—1061no—
1366#120—1061no—
1367#120—1061no—
1368C4×Q8—531no—
1369C4×Q8—531no—
1370C4×D4—531no—
1371C4×D4—531no—
1372C4×D4—531no—
1373C4×D4—531no—
1374C4×D4—531no—
1375C4×D4—531no—
1376C4×D4—531no—
1377C4×D4—1061no—
1378C4×D4—1061no—
1379C4×D4—1061no—
1380C4×D4—1061no—
1381C4×D4—1061no—
1382C4×D4—1061no—
1383C4×D4—1061no—
1384C4×D4—1061no—
1385C4×D4C22×D5311yescharacteristic
1386C4×D4C22×D5311yescharacteristic
1387C4×D4C22×D5311yescharacteristic
1388#117—531no—
1389#117—531no—
1390#117—531no—
1391#117—531no—
1392#117—531no—
1393#117—1061no—
1394#117—1061no—
1395#117—1061no—
1396#117—1061no—
1397#117—1061no—
1398C2×C22⋊C4—21no—
1399C2×C22⋊C4—1061no—
1400C2×C22⋊C4—1061no—
1401C2×C22⋊C4—1061no—
1402C2×C22⋊C4—1061no—
1403C2×C22⋊C4—1061no—
1404C2×C42—531no—
1405C2×C42—1061no—
1406#107—531no—
1407#107—531no—
1408#107—531no—
1409#107—531no—
1410#106—531no—
1411#106—531no—
1412#106—531no—
1413#106C22×D5311yescharacteristic
1414C4⋊C8—531no—
1415C4⋊C8—531no—
1416C4⋊C8—531no—
1417C4⋊C8C22×D5311yescharacteristic
1418#103—531no—
1419#103—531no—
1420#103—531no—
1421#103—531no—
1422#103—531no—
1423#103—531no—
1424#103—531no—
1425#103—531no—
1426#103—531no—
1427#103—531no—
1428#103—531no—
1429#103C22×D5311yescharacteristic
1430#102—531no—
1431#102—531no—
1432#102—531no—
1433#102—531no—
1434#102—531no—
1435#102—531no—
1436#102—531no—
1437#102—531no—
1438#102—531no—
1439#102—531no—
1440#102—531no—
1441#102—531no—
1442#102—531no—
1443#102—531no—
1444#102—531no—
1445#102C22×D5311yescharacteristic
1446#102C22×D5311yescharacteristic
1447#102C22×D5311yescharacteristic
1448#102C22×D5311yescharacteristic
1449#102C22×D5311yescharacteristic
1450C22⋊C8—531no—
1451C22⋊C8—531no—
1452C22⋊C8—531no—
1453C22⋊C8—531no—
1454C22⋊C8—531no—
1455C22⋊C8—531no—
1456C22⋊C8—531no—
1457C22⋊C8—531no—
1458C22⋊C8—531no—
1459C22⋊C8—531no—
1460C22⋊C8C22×D5311yescharacteristic
1461C22⋊C8C22×D5311yescharacteristic
1462#97—531no—
1463#97—531no—
1464#97—531no—
1465#97C22×D5311yescharacteristic
1466C24—21no—
1467C24—21no—
1468C24—21no—
1469C24—1061no—
1470C24—1061no—
1471C24—1061no—
1472C24—1061no—
1473#41—22no—
1474#41—41no—
1475#41—1062no—
1476#41—1062no—
1477#41—1062no—
1478#41—1062no—
1479#41—1062no—
1480#41—4242no—
1481#41—4242no—
1482#41—2121no—
1483#41—2121no—
1484#41—2121no—
1485#41—2121no—
1486#41—2121no—
1487#41—2124no—
1488#41—2121no—
1489#41—2121no—
1490#41—2124no—
1491#41—2124no—
1492#41—2124no—
1493C2×Q8—531no—
1494C2×Q8—531no—
1495C2×Q8—531no—
1496C2×Q8—531no—
1497C2×Q8—1061no—
1498C2×Q8—1061no—
1499C2×Q8—1061no—
1500C2×Q8—1062no—
1501C2×Q8—1061no—
1502C2×Q8—1061no—
1503C2×Q8—1062no—
1504C2×Q8—2121no—
1505C2×Q8—2124no—
1506C2×Q8—2121no—
1507C2×Q8—2121no—
1508C2×Q8—2121no—
1509C2×Q8C23×D5311yescharacteristic
1510C2×D4—22no—
1511C2×D4—21no—
1512C2×D4—21no—
1513C2×D4—21no—
1514C2×D4—21no—
1515C2×D4—21no—
1516C2×D4—21no—
1517C2×D4—21no—
1518C2×D4—21no—
1519C2×D4—21no—
1520C2×D4—41no—
1521C2×D4—41no—
1522C2×D4—41no—
1523C2×D4—41no—
1524C2×D4—41no—
1525C2×D4—82no—
1526C2×D4—531no—
1527C2×D4—531no—
1528C2×D4—531no—
1529C2×D4—531no—
1530C2×D4—531no—
1531C2×D4—531no—
1532C2×D4—531no—
1533C2×D4—531no—
1534C2×D4—531no—
1535C2×D4—531no—
1536C2×D4—531no—
1537C2×D4—1061no—
1538C2×D4—1061no—
1539C2×D4—1061no—
1540C2×D4—1061no—
1541C2×D4—1061no—
1542C2×D4—1061no—
1543C2×D4—1061no—
1544C2×D4—1061no—
1545C2×D4—1061no—
1546C2×D4—1062no—
1547C2×D4—1061no—
1548C2×D4—1061no—
1549C2×D4—1061no—
1550C2×D4—1061no—
1551C2×D4—1061no—
1552C2×D4—1061no—
1553C2×D4—1061no—
1554C2×D4—1061no—
1555C2×D4—1061no—
1556C2×D4—1061no—
1557C2×D4—1061no—
1558C2×D4—1061no—
1559C2×D4—1061no—
1560C2×D4—1061no—
1561C2×D4—4242no—
1562C2×D4—4242no—
1563C2×D4—4242no—
1564C2×D4—2121no—
1565C2×D4—2121no—
1566C2×D4—2121no—
1567C2×D4—2121no—
1568C2×D4—2121no—
1569C2×D4—2121no—
1570C2×D4—2121no—
1571C2×D4—2124no—
1572C2×D4—2124no—
1573C2×D4—2124no—
1574C2×D4D4×D5311yescharacteristic
1575C2×D4C23×D5311yescharacteristic
1576C2×D4C23×D5311yescharacteristic
1577C2×D4C23×D5311yescharacteristic
1578C2×D4C23×D5311yescharacteristic
1579C2×D4C23×D5311yescharacteristic
1580C22×C4—21no—
1581C22×C4—21no—
1582C22×C4—21no—
1583C22×C4—531no—
1584C22×C4—531no—
1585C22×C4—531no—
1586C22×C4—531no—
1587C22×C4—531no—
1588C22×C4—1061no—
1589C22×C4—1061no—
1590C22×C4—1061no—
1591C22×C4—1061no—
1592C22×C4—1061no—
1593C22×C4—1061no—
1594C22×C4—1061no—
1595C22×C4—1061no—
1596C22×C4—1061no—
1597C22×C4—1061no—
1598C22×C4—1061no—
1599C22×C4C23×D5311yescharacteristic
1600C22×C4C23×D5311yescharacteristic
1601SD16—41no—
1602SD16—41no—
1603SD16—41no—
1604SD16—1062no—
1605SD16—1062no—
1606SD16—1062no—
1607SD16—1062no—
1608SD16—2121no—
1609SD16—2121no—
1610SD16—2121no—
1611SD16—2121no—
1612SD16—2121no—
1613D8—22no—
1614D8—22no—
1615D8—22no—
1616D8—41no—
1617D8—41no—
1618D8—41no—
1619D8—1062no—
1620D8—2121no—
1621D8—2121no—
1622D8—2121no—
1623D8—2121no—
1624D8—2121no—
1625M16—41no—
1626M16—2121no—
1627M16—2121no—
1628M16—2121no—
1629C2×C8—41no—
1630C2×C8—531no—
1631C2×C8—531no—
1632C2×C8—531no—
1633C2×C8—531no—
1634C2×C8—2121no—
1635C2×C8—2121no—
1636C2×C8—2121no—
1637C2×C8C23×D5311yescharacteristic
1638C2×C8C23×D5311yescharacteristic
1639C2×C8C23×D5311yescharacteristic
1640C2×C8C23×D5311yescharacteristic
1641C4⋊C4—21no—
1642C4⋊C4—531no—
1643C4⋊C4—531no—
1644C4⋊C4—531no—
1645C4⋊C4—531no—
1646C4⋊C4—531no—
1647C4⋊C4—531no—
1648C4⋊C4—531no—
1649C4⋊C4—1061no—
1650C4⋊C4—1061no—
1651C4⋊C4—1061no—
1652C4⋊C4—1061no—
1653C4⋊C4—1061no—
1654C4⋊C4—1061no—
1655C4⋊C4—1061no—
1656C4⋊C4D4×D5311yescharacteristic
1657C4⋊C4C23×D5311yescharacteristic
1658C4⋊C4C23×D5311yescharacteristic
1659C22⋊C4—21no—
1660C22⋊C4—21no—
1661C22⋊C4—21no—
1662C22⋊C4—21no—
1663C22⋊C4—21no—
1664C22⋊C4—21no—
1665C22⋊C4—21no—
1666C22⋊C4—21no—
1667C22⋊C4—531no—
1668C22⋊C4—531no—
1669C22⋊C4—531no—
1670C22⋊C4—531no—
1671C22⋊C4—531no—
1672C22⋊C4—531no—
1673C22⋊C4—1061no—
1674C22⋊C4—1061no—
1675C22⋊C4—1061no—
1676C22⋊C4—1061no—
1677C22⋊C4—1061no—
1678C22⋊C4—1061no—
1679C22⋊C4—1061no—
1680C22⋊C4—1061no—
1681C22⋊C4—1061no—
1682C22⋊C4—1061no—
1683C22⋊C4—1061no—
1684C22⋊C4—1061no—
1685C22⋊C4—1061no—
1686C22⋊C4—1061no—
1687C22⋊C4—1061no—
1688C22⋊C4—1061no—
1689C22⋊C4—1061no—
1690C22⋊C4—1061no—
1691C22⋊C4—1061no—
1692C22⋊C4—1061no—
1693C22⋊C4—1061no—
1694C22⋊C4—1061no—
1695C22⋊C4—1061no—
1696C22⋊C4—1061no—
1697C22⋊C4—1061no—
1698C22⋊C4—1061no—
1699C22⋊C4—1061no—
1700C22⋊C4—1061no—
1701C22⋊C4—1061no—
1702C22⋊C4—1061no—
1703C22⋊C4—1061no—
1704C22⋊C4D4×D5311yescharacteristic
1705C22⋊C4D4×D5311yescharacteristic
1706C42—531no—
1707C42—531no—
1708C42—531no—
1709C42—1061no—
1710C42—1061no—
1711C42—1061no—
1712C42—1061no—
1713C42—1061no—
1714C42—1061no—
1715C42—1061no—
1716C42C23×D5311yescharacteristic
1717C23—21no—
1718C23—21no—
1719C23—21no—
1720C23—21no—
1721C23—21no—
1722C23—42no—
1723C23—81no—
1724C23—81no—
1725C23—81no—
1726C23—81no—
1727C23—81no—
1728C23—81no—
1729C23—81no—
1730C23—81no—
1731C23—531no—
1732C23—531no—
1733C23—531no—
1734C23—1061no—
1735C23—1061no—
1736C23—4241no—
1737C23—4241no—
1738C23—4241no—
1739C23—4241no—
1740C23—4241no—
1741C23—4241no—
1742C23—4241no—
1743C23—4241no—
1744C23—4241no—
1745C23—4241no—
1746C23—2122no—
1747C23—2122no—
1748C23C2×D4×D5311yescharacteristic
1749C23C2×D4×D5311yescharacteristic
1750Q8—21no—
1751Q8—21no—
1752Q8—532no—
1753Q8—1061no—
1754Q8—1061no—
1755Q8—1061no—
1756Q8—4241no—
1757Q8—4241no—
1758Q8—2121no—
1759Q8—2121no—
1760Q8—2122no—
1761Q8—2122no—
1762Q8—2122no—
1763D4—21no—
1764D4—21no—
1765D4—21no—
1766D4—21no—
1767D4—21no—
1768D4—21no—
1769D4—21no—
1770D4—21no—
1771D4—21no—
1772D4—41no—
1773D4—42no—
1774D4—42no—
1775D4—42no—
1776D4—81no—
1777D4—81no—
1778D4—81no—
1779D4—81no—
1780D4—81no—
1781D4—81no—
1782D4—1064no—
1783D4—1061no—
1784D4—1061no—
1785D4—1061no—
1786D4—1061no—
1787D4—4241no—
1788D4—4241no—
1789D4—4241no—
1790D4—4241no—
1791D4—4241no—
1792D4—4241no—
1793D4—4241no—
1794D4—4241no—
1795D4—4241no—
1796D4—4241no—
1797D4—4241no—
1798D4—4241no—
1799D4—4241no—
1800D4—4241no—
1801D4—4241no—
1802D4—4241no—
1803D4—2121no—
1804D4—2121no—
1805D4—2121no—
1806D4—2121no—
1807D4—2121no—
1808D4—2121no—
1809D4—2121no—
1810D4—2121no—
1811D4—2121no—
1812D4—2122no—
1813D4—2122no—
1814D4—2122no—
1815D4—2122no—
1816D4—2122no—
1817D4—2122no—
1818D4#1313326212yes—
1819C2×C4—21no—
1820C2×C4—21no—
1821C2×C4—21no—
1822C2×C4—21no—
1823C2×C4—21no—
1824C2×C4—21no—
1825C2×C4—21no—
1826C2×C4—42no—
1827C2×C4—42no—
1828C2×C4—81no—
1829C2×C4—531no—
1830C2×C4—531no—
1831C2×C4—531no—
1832C2×C4—531no—
1833C2×C4—531no—
1834C2×C4—1064no—
1835C2×C4—1061no—
1836C2×C4—1061no—
1837C2×C4—1061no—
1838C2×C4—1061no—
1839C2×C4—1061no—
1840C2×C4—1061no—
1841C2×C4—1061no—
1842C2×C4—1061no—
1843C2×C4—1061no—
1844C2×C4—1061no—
1845C2×C4—1061no—
1846C2×C4—1061no—
1847C2×C4—4241no—
1848C2×C4—2121no—
1849C2×C4—2121no—
1850C2×C4—2122no—
1851C2×C4—2122no—
1852C2×C4—2122no—
1853C2×C4—2122no—
1854C2×C4—2122no—
1855C2×C4—2122no—
1856C2×C4—2122no—
1857C2×C4—2122no—
1858C2×C4—2122no—
1859C2×C4C2×D4×D5311yescharacteristic
1860C2×C4C2×D4×D5311yescharacteristic
1861C2×C4C2×D4×D5311yescharacteristic
1862C2×C4C2×D4×D5311yescharacteristic
1863C2×C4C24×D5311yescharacteristic
1864C8—21no—
1865C8—21no—
1866C8—21no—
1867C8—21no—
1868C8—1061no—
1869C8—1061no—
1870C8—1061no—
1871C8—1061no—
1872C22—21no—
1873C22—21no—
1874C22—22no—
1875C22—21no—
1876C22—21no—
1877C22—21no—
1878C22—21no—
1879C22—41no—
1880C22—41no—
1881C22—41no—
1882C22—41no—
1883C22—41no—
1884C22—41no—
1885C22—41no—
1886C22—41no—
1887C22—41no—
1888C22—41no—
1889C22—41no—
1890C22—41no—
1891C22—41no—
1892C22—41no—
1893C22—162no—
1894C22—162no—
1895C22—162no—
1896C22—8482no—
1897C22—8482no—
1898C22—8482no—
1899C22—8482no—
1900C22—1061no—
1901C22—1061no—
1902C22—1061no—
1903C22—1061no—
1904C22—1061no—
1905C22—1061no—
1906C22—1061no—
1907C22—1061no—
1908C22—1061no—
1909C22—2121no—
1910C22—2121no—
1911C22—2121no—
1912C22—2121no—
1913C22—2121no—
1914C22—2121no—
1915C22C22×D4×D5311yescharacteristic
1916C4—21no—
1917C4—21no—
1918C4—21no—
1919C4—21no—
1920C4—41no—
1921C4—41no—
1922C4—41no—
1923C4—1061no—
1924C4—1061no—
1925C4—1061no—
1926C4—1062no—
1927C4—1061no—
1928C4—1061no—
1929C4—2121no—
1930C4—2121no—
1931C4—2121no—
1932C4—2121no—
1933C4—2121no—
1934C4H(5,𝔽2)×D5311yescharacteristic
1935C4C2×#1313326211yescharacteristic
1936C2—41no—
1937C2—41no—
1938C2—42no—
1939C2—81no—
1940C2—81no—
1941C2—81no—
1942C2—81no—
1943C2—4241no—
1944C2—4241no—
1945C2—2121no—
1946C2—2121no—
1947C2—2121no—
1948C2#2028834311yescharacteristic
1949C2#2028949011yescharacteristic
1950C2#2028949111yescharacteristic
subgroupG/H
centerC22C22×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC53×#3264C2
socleC22×C53C23×D4
hypercenter#3264D53
hypocenterC53#61673
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C22 ◁ C4×D4 ◁ #3264

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #20289117C2semidirect
2. #20288501C2semidirect
3. #20286908C2semidirect
4. #20286907C2semidirect
5. #20286903C2semidirect
6. #20286896C2semidirect
7. #20286876C2semidirect
8. #20286875C2semidirect
9. #20286871C2semidirect
10. #20286864C2semidirect
11. #20286214C2semidirect
12. #20286209C2semidirect
13. #20286208C2semidirect
14. #20286206C2semidirect
15. #20286195C2semidirect
16. #20286190C2semidirect
17. #20286189C2semidirect
18. #20285700C2semidirect
19. #20285697C2semidirect
20. #20285584C2semidirect
21. #20285581C2semidirect
22. #20285578C2semidirect
23. #20285577C2semidirect
24. #20284863C2semidirect
25. #20284862C2semidirect
26. #20284000C2semidirect
27. #20283998C2semidirect
28. #20283979C2semidirect
29. #20283978C2semidirect
30. #20283783C2semidirect
31. C53×#3264C2semidirect
32. C2×#13133264C22semidirect
33. C2×#13133262C22semidirect
34. C2×#13133243C22semidirect
35. C2×#13133241C22semidirect
36. C2×#13133241C22semidirect
37. C22×#11719923C22semidirect
38. C2×SD16×D53C22semidirect
39. C2×D8×D53C22semidirect
42. #16811338C22semidirect
43. #16811338C22semidirect
45. #16811337C22semidirect
46. #16811337C22semidirect
47. #16811283C22semidirect
48. #16811282C22semidirect
49. #16811281C22semidirect
50. #16811279C22semidirect
51. #16811268C22semidirect
52. #16811267C22semidirect
56. #16811261C22semidirect
58. #16811258C22semidirect
60. D4×C22⋊D53C22semidirect
61. D4×C22⋊D53C22semidirect
62. #16811196C22semidirect
66. #16811190C22semidirect
69. #16811189C22semidirect
70. #16811189C22semidirect
74. #16811171C22semidirect
76. #16811170C22semidirect
79. #124×D53C22semidirect
80. C4×#11719947C22semidirect
81. #16811011C22semidirect
82. #16811010C22semidirect
83. #16811009C22semidirect
84. #16810984C22semidirect
85. #16810983C22semidirect
86. #16810982C22semidirect
87. #16810981C22semidirect
88. #16810967C22semidirect
89. #16810965C22semidirect
90. #16810962C22semidirect
91. #16810961C22semidirect
92. #16810949C22semidirect
93. #16810949C22semidirect
94. #16810948C22semidirect
95. #16810946C22semidirect
96. #16810946C22semidirect
97. #16810946C22semidirect
98. #16810945C22semidirect
99. #16810944C22semidirect
100. #16810909C22semidirect
101. #16810907C22semidirect
102. #16810903C22semidirect
103. #16810901C22semidirect
104. #16810876C22semidirect
105. #16810875C22semidirect
106. #16810873C22semidirect
107. #16810871C22semidirect
108. #16810868C22semidirect
109. #16810867C22semidirect
110. #16810866C22semidirect
111. #16810858C22semidirect
112. #16810857C22semidirect
113. #16810857C22semidirect
114. #16810856C22semidirect
115. #16810852C22semidirect
116. #16810851C22semidirect
117. #16810849C22semidirect
118. #16810840C22semidirect
119. #16810840C22semidirect
120. #16810839C22semidirect
121. #16810838C22semidirect
122. #16810836C22semidirect
123. #16810836C22semidirect
124. #16810835C22semidirect
125. #16810822C22semidirect
126. #16810820C22semidirect
127. #16810816C22semidirect
128. #16810775C22semidirect
129. #16810774C22semidirect
130. #16810772C22semidirect
131. #16810770C22semidirect
132. #16810769C22semidirect
133. #16810768C22semidirect
134. #16810766C22semidirect
135. #16810765C22semidirect
136. #16810765C22semidirect
137. #16810765C22semidirect
138. #16810765C22semidirect
139. #16810765C22semidirect
140. #16810765C22semidirect
141. #16810765C22semidirect
142. #16810764C22semidirect
143. #16810763C22semidirect
144. #16810761C22semidirect
145. #16810760C22semidirect
146. #16810760C22semidirect
147. #16810760C22semidirect
148. #16810760C22semidirect
149. #16810760C22semidirect
150. #16810758C22semidirect
151. #16810758C22semidirect
152. #16810757C22semidirect
153. #16810757C22semidirect
154. #16810755C22semidirect
155. #16810755C22semidirect
156. #16810755C22semidirect
157. #16810755C22semidirect
158. #16810755C22semidirect
159. #16810755C22semidirect
160. #16810735C22semidirect
161. #16810735C22semidirect
162. #16810733C22semidirect
163. #16810725C22semidirect
164. #16810723C22semidirect
165. #16810720C22semidirect
166. #16810720C22semidirect
167. #16810697C22semidirect
168. #16810696C22semidirect
169. #16810695C22semidirect
170. #16810694C22semidirect
171. #16810693C22semidirect
172. #16810692C22semidirect
173. #16810691C22semidirect
174. #16810679C22semidirect
175. #16810678C22semidirect
176. #16810633C22semidirect
177. #16810630C22semidirect
178. #16810628C22semidirect
179. #16810626C22semidirect
180. #16810620C22semidirect
181. #16810619C22semidirect
182. #16810616C22semidirect
183. #16810616C22semidirect
184. #16810591C22semidirect
185. #16810589C22semidirect
186. #16810588C22semidirect
187. #16810588C22semidirect
188. C2×AGL(1,ℤ/8)×C53C22semidirect
189. C22×D8×C53C22semidirect
190. C53×#546C22semidirect
191. D42×C53C22semidirect
192. C53×#496C22semidirect
193. C53×#469C22semidirect
194. C53×#465C22semidirect
195. C53×#463C22semidirect
196. C53×#459C22semidirect
197. C53×#450C22semidirect
198. C53×#449C22semidirect
199. C53×#447C22semidirect
200. C53×#447C22semidirect
201. C53×#442C22semidirect
202. C53×#435C22semidirect
978. #3264D53semidirect
1012. C2×AGL(1,ℤ/8)C2×D53semidirect
1016. C22×D8C2×D53semidirect
1035. #546C2×D53semidirect
1040. D42C2×D53semidirect
1063. #496C2×D53semidirect
1087. #469C2×D53semidirect
1099. #465C2×D53semidirect
1107. #463C2×D53semidirect
1111. #459C2×D53semidirect
1115. #450C2×D53semidirect
1127. #449C2×D53semidirect
1146. #447C2×D53semidirect
1147. #447C2×D53semidirect
1151. #442C2×D53semidirect
1163. #435C2×D53semidirect
1178. C53#61673semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#202891172
#202885012
#202869082
#202869072
#202869032
#202868962
#202868762
#202868752
#202868712
#202868642
#202862142
#202862092
#202862082
#202862062
#202861952
#202861902
#202861892
#202857002
#202856972
#202855842
#202855812
#202855782
#202855772
#202848632
#202848622
#202840002
#202839982
#202839792
#202839782
#202837832
C53×#32642
#6167353