Finite Group Databasebeta

← #28270656

Subgroups — #28270656

Order 13568.

2100 conjugacy classes of subgroups.

The subgroup lattice has 1902 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20289008C211yesmaximal, characteristic, complemented
2#20288376C211yesmaximal, characteristic, complemented
3#20287054C211yesmaximal, characteristic, complemented
4#20286985C211yesmaximal, characteristic, complemented
5#20286947C211yesmaximal, characteristic, complemented
6#20286918C211yesmaximal, characteristic, complemented
7#20286798C211yesmaximal, characteristic, complemented
8#20286783C211yesmaximal, characteristic, complemented
9#20286738C211yesmaximal, characteristic, complemented
10#20286723C211yesmaximal, characteristic, complemented
11#20286383C211yesmaximal, characteristic, complemented
12#20286373C211yesmaximal, characteristic, complemented
13#20286351C211yesmaximal, characteristic, complemented
14#20286317C211yesmaximal, characteristic, complemented
15#20286305C211yesmaximal, characteristic, complemented
16#20286275C211yesmaximal, characteristic, complemented
17#20286230C211yesmaximal, characteristic, complemented
18#20286215C211yesmaximal, characteristic, complemented
19#20285811C211yesmaximal, characteristic, complemented
20#20285789C211yesmaximal, characteristic, complemented
21#20285617C211yesmaximal, characteristic, complemented
22#20285599C211yesmaximal, characteristic, complemented
23#20285531C211yesmaximal, characteristic, complemented
24#20285522C211yesmaximal, characteristic, complemented
25#20284979C211yesmaximal, characteristic, complemented
26#20284931C211yesmaximal, characteristic, complemented
27#20284022C211yesmaximal, characteristic, complemented
28#20283994C211yesmaximal, characteristic, complemented
29#20283977C211yesmaximal, characteristic, complemented
30#20283960C211yesmaximal, characteristic, complemented
31C53×#2978C211yesmaximal, characteristic, complemented
32C2×#13133263C2211yescharacteristic
33C22×#11719945C2211yescharacteristic
34C2×#13133250C2211yescharacteristic, complemented
35C2×#13133250C2211yescharacteristic, complemented
36C2×#13133250C2211yescharacteristic, complemented
37C2×#13133250C2211yescharacteristic, complemented
38C2×#13133245C2211yescharacteristic, complemented
39C2×#13133245C2211yescharacteristic, complemented
40C2×#13133239C2211yescharacteristic, complemented
41C22×#11719913C2211yescharacteristic, complemented
42#16811374—21no—
43#16811368—21no—
44#16811343C2211yescharacteristic, complemented
45#16811330C2211yescharacteristic, complemented
46#16811327—21no—
47#16811319C2211yescharacteristic, complemented
48#16811316—21no—
49#16811313C2211yescharacteristic, complemented
50#16811294C2211yescharacteristic
51#16811294C2211yescharacteristic
52D4×Dic106C2211yescharacteristic, complemented
53#16811282C2211yescharacteristic
54#16811282C2211yescharacteristic
55#16811282C2211yescharacteristic, complemented
56#16811282C2211yescharacteristic, complemented
57#16811278C2211yescharacteristic, complemented
58#16811269C2211yescharacteristic
59#16811269C2211yescharacteristic
60#16811265—21no—
61#16811265—21no—
62D4×D212C2211yescharacteristic
63D4×D212C2211yescharacteristic
64#16811255—21no—
65#16811255—21no—
66#16811244C2211yescharacteristic, complemented
67#16811241—21no—
68#16811235C2211yescharacteristic, complemented
69#16811216—21no—
70#16811208—21no—
71#16811208—21no—
72#16811203—21no—
73#16811201C2211yescharacteristic
74#16811201C2211yescharacteristic, complemented
75#16811194C2211yescharacteristic, complemented
76#16811192C2211yescharacteristic
77#16811189—21no—
78#16811136—21no—
79#16811134C2211yescharacteristic, complemented
80C2×#13133196C2211yescharacteristic, complemented
81C2×#13133191C2211yescharacteristic
82#121×D53—21no—
83#16811103C2211yescharacteristic
84#16811017C2211yescharacteristic, complemented
85#16811012C2211yescharacteristic, complemented
86#16811007C2211yescharacteristic, complemented
87#16810996C2211yescharacteristic, complemented
88#16810988C2211yescharacteristic, complemented
89#16810983C2211yescharacteristic, complemented
90#16810978C2211yescharacteristic, complemented
91#16810970C2211yescharacteristic, complemented
92#16810965C2211yescharacteristic, complemented
93#16810959C2211yescharacteristic, complemented
94#16810959C2211yescharacteristic, complemented
95#16810959C2211yescharacteristic, complemented
96#16810954C2211yescharacteristic, complemented
97#16810948C2211yescharacteristic, complemented
98#16810948C2211yescharacteristic, complemented
99#16810948C2211yescharacteristic, complemented
100#16810937C2211yescharacteristic, complemented
101#16810937C2211yescharacteristic, complemented
102#16810937C2211yescharacteristic, complemented
103#16810937C2211yescharacteristic, complemented
104#16810931C2211yescharacteristic, complemented
105#16810924C2211yescharacteristic, complemented
106#16810919C2211yescharacteristic, complemented
107#16810904C2211yescharacteristic, complemented
108#16810881C2211yescharacteristic, complemented
109#16810876C2211yescharacteristic, complemented
110#16810876C2211yescharacteristic, complemented
111#16810869C2211yescharacteristic, complemented
112#16810869C2211yescharacteristic, complemented
113#16810869C2211yescharacteristic, complemented
114#16810869C2211yescharacteristic, complemented
115#16810869C2211yescharacteristic, complemented
116#16810869C2211yescharacteristic, complemented
117#16810869C2211yescharacteristic, complemented
118#16810869C2211yescharacteristic, complemented
119#16810869C2211yescharacteristic, complemented
120#16810864C2211yescharacteristic, complemented
121#16810864C2211yescharacteristic, complemented
122#16810859C2211yescharacteristic, complemented
123#16810852C2211yescharacteristic, complemented
124#16810846C2211yescharacteristic, complemented
125#16810846C2211yescharacteristic, complemented
126#16810846C2211yescharacteristic, complemented
127#16810846C2211yescharacteristic, complemented
128#16810839C2211yescharacteristic, complemented
129#16810839C2211yescharacteristic, complemented
130#16810834C2211yescharacteristic, complemented
131#16810829C2211yescharacteristic, complemented
132#16810824C2211yescharacteristic, complemented
133#16810824C2211yescharacteristic, complemented
134#16810824C2211yescharacteristic, complemented
135#16810819C2211yescharacteristic, complemented
136#16810787C2211yescharacteristic
137#16810787C2211yescharacteristic
138#16810787C2211yescharacteristic
139#16810787C2211yescharacteristic, complemented
140#16810787C2211yescharacteristic, complemented
141#16810787C2211yescharacteristic, complemented
142#16810787C2211yescharacteristic, complemented
143#16810787C2211yescharacteristic, complemented
144#16810787C2211yescharacteristic, complemented
145#16810787C2211yescharacteristic, complemented
146#16810787C2211yescharacteristic, complemented
147#16810787C2211yescharacteristic, complemented
148#16810781C2211yescharacteristic, complemented
149#16810781C2211yescharacteristic, complemented
150#16810781C2211yescharacteristic, complemented
151#16810776C2211yescharacteristic, complemented
152#16810776C2211yescharacteristic, complemented
153#16810776C2211yescharacteristic, complemented
154#16810776C2211yescharacteristic, complemented
155#16810776C2211yescharacteristic, complemented
156#16810776C2211yescharacteristic, complemented
157#16810776C2211yescharacteristic, complemented
158#16810776C2211yescharacteristic, complemented
159#16810770C2211yescharacteristic
160#16810770C2211yescharacteristic, complemented
161#16810770C2211yescharacteristic, complemented
162#16810770C2211yescharacteristic, complemented
163#16810770C2211yescharacteristic, complemented
164#16810770C2211yescharacteristic, complemented
165#16810770C2211yescharacteristic, complemented
166#16810770C2211yescharacteristic, complemented
167#16810764C2211yescharacteristic, complemented
168#16810764C2211yescharacteristic, complemented
169#16810764C2211yescharacteristic, complemented
170#16810759C2211yescharacteristic, complemented
171#16810759C2211yescharacteristic, complemented
172#16810731C2211yescharacteristic, complemented
173#16810725C2211yescharacteristic, complemented
174#16810725C2211yescharacteristic, complemented
175#16810725C2211yescharacteristic, complemented
176C4×Dic212C2211yescharacteristic, complemented
177C4×Dic212C2211yescharacteristic, complemented
178C4×#11719913C2211yescharacteristic, complemented
179C4×D424C2211yescharacteristic, complemented
180#16810633C2211yescharacteristic, complemented
181#16810629C2211yescharacteristic, complemented
182#16810629C2211yescharacteristic, complemented
183#16810625C2211yescharacteristic, complemented
184#16810625C2211yescharacteristic, complemented
185#16810625C2211yescharacteristic, complemented
186#16810620C2211yescharacteristic, complemented
187C2×#13133139C2211yescharacteristic, complemented
188C53×#525C2211yescharacteristic
189C53×#436C2211yescharacteristic, complemented
190C53×#436C2211yescharacteristic, complemented
191C53×#436C2211yescharacteristic, complemented
192C53×#436C2211yescharacteristic, complemented
193C53×#435C2211yescharacteristic, complemented
194C53×#435C2211yescharacteristic, complemented
195C53×#435C2211yescharacteristic, complemented
196C53×#435C2211yescharacteristic, complemented
197C53×#433C2211yescharacteristic, complemented
198C53×#433C2211yescharacteristic, complemented
199C53×#408C2211yescharacteristic, complemented
200C53×#408C2211yescharacteristic, complemented
201C53×#407C2211yescharacteristic, complemented
202C53×#407C2211yescharacteristic, complemented
203#13133263—42no—
204#13133263—42no—
205C2×#11719949—21no—
206C2×#11719945—21no—
207C2×#11719945—21no—
208C2×#11719945—42no—
209C2×#11719945—42no—
210C2×#11719945C2311yescharacteristic
211C2×#11719945C2311yescharacteristic
212C2×#11719945C2311yescharacteristic
213C2×#11719945C2311yescharacteristic
214C2×#11719945C2311yescharacteristic
215C2×#11719945C2311yescharacteristic
216C2×#11719945C2311yescharacteristic
217C2×#11719945C2311yescharacteristic
218C22×Dic106C2311yescharacteristic
219C22×Dic106C2311yescharacteristic
220C22×Dic106C2311yescharacteristic
221C22×D212C2311yescharacteristic
222C22×D212C2311yescharacteristic
223C22×D212C2311yescharacteristic
224C22×D212C2311yescharacteristic
225C22×C22⋊D53—21no—
226C22×C22⋊D53—21no—
227C2×D4×D53—21no—
228C2×D4×D53—21no—
229C2×D4×D53—21no—
230C2×D4×D53—21no—
231C2×D4×D53—21no—
232C22×C4×D53—21no—
233#13133250—42no—
234#13133250—42no—
235#13133250—42no—
236#13133250—42no—
237#13133245—42no—
238#13133245—42no—
239#13133239—42no—
240C2×Dic212C2311yescharacteristic
241C2×Dic212C2311yescharacteristic
242C2×Dic212C2311yescharacteristic
243C2×Dic212C2311yescharacteristic
244C2×Dic212C2311yescharacteristic
245C2×Dic212C2311yescharacteristic
246C2×#11719913—42no—
247C2×#11719913C2311yescharacteristic
248C2×#11719913C2311yescharacteristic
249C2×#11719913C2311yescharacteristic
250C2×#11719913C2311yescharacteristic
251C2×#11719913C2311yescharacteristic
252C2×#11719913C2311yescharacteristic
253C2×#11719913C2311yescharacteristic
254C2×#11719913C2311yescharacteristic
255C2×#11719913C2311yescharacteristic
256C2×#11719913C2311yescharacteristic
257C2×#11719913C2311yescharacteristic
258C2×#11719913C2311yescharacteristic
259C2×#11719913C2311yescharacteristic
260C2×#11719913C2311yescharacteristic
261C2×D424C2311yescharacteristic
262C2×D424C2311yescharacteristic
263C2×D424C2311yescharacteristic
264C2×D424C2311yescharacteristic
265#13133217C2311yescharacteristic
266#13133217C2311yescharacteristic
267#13133216—21no—
268#13133215—21no—
269#13133214C2311yescharacteristic
270#13133214C2311yescharacteristic
271#13133213—21no—
272#13133213—21no—
273#13133212—21no—
274#13133212—21no—
275#13133210—21no—
276#13133210—21no—
277#13133210—21no—
278#13133210—21no—
279#13133210—21no—
280#13133209C2311yescharacteristic
281#13133208—21no—
282#13133207—21no—
283#13133207—21no—
284#13133207—21no—
285#13133205C2311yescharacteristic
286#13133205C2311yescharacteristic
287#13133205C2311yescharacteristic
288#13133204—21no—
289#13133204—21no—
290#13133203—21no—
291#13133203—21no—
292#13133203—21no—
293#13133203—21no—
294#13133203—21no—
295#13133202—21no—
296#13133202—21no—
297#13133200—21no—
298#13133199—21no—
299#13133199—21no—
300#13133199—21no—
301#13133199—21no—
302#13133198—21no—
303#13133198—21no—
304#13133198—21no—
305#13133196—21no—
306#13133196—21no—
307#13133196C2311yescharacteristic
308#13133196C2311yescharacteristic
309#13133196C2311yescharacteristic
310#13133196C2311yescharacteristic
311#13133196C2311yescharacteristic
312#13133196C2311yescharacteristic
313#13133196C2311yescharacteristic
314#13133196C2311yescharacteristic
315#13133196C2311yescharacteristic
316#13133196C2311yescharacteristic
317#13133196C2311yescharacteristic
318#13133195—21no—
319#13133195—21no—
320#13133195—21no—
321#13133195—21no—
322#13133195—21no—
323#13133194—21no—
324#13133194—21no—
325#13133194—21no—
326#13133194—21no—
327#13133193—21no—
328#13133193—21no—
329#13133192—21no—
330#13133192—21no—
331#13133192—21no—
332#13133192—21no—
333#13133191—21no—
334#13133191—21no—
335#13133191C2311yescharacteristic
336#13133191C2311yescharacteristic
337#13133191C2311yescharacteristic
338#13133191C2311yescharacteristic
339#13133191C2311yescharacteristic
340#13133191C2311yescharacteristic
341#13133191C2311yescharacteristic
342#13133191C2311yescharacteristic
343#13133191C2311yescharacteristic
344#13133190—21no—
345#13133190—21no—
346#13133190—21no—
347#13133190—21no—
348#13133190—21no—
349#13133190—21no—
350#13133189—21no—
351#13133189—21no—
352#13133189—21no—
353#13133189—21no—
354#13133189—21no—
355#13133189—21no—
356#13133189—21no—
357#13133189—21no—
358#13133189—21no—
359#13133188—21no—
360#13133188—21no—
361#13133188—21no—
362#13133187—21no—
363#13133187—21no—
364#13133187—21no—
365#13133187—21no—
366#13133187—21no—
367#13133187—21no—
368#13133186—21no—
369#13133185—21no—
370#13133185—21no—
371C4×Dic106C2311yescharacteristic
372C4×Dic106C2311yescharacteristic
373C4×Dic106C2311yescharacteristic
374C4×Dic106C2311yescharacteristic
375C4×Dic106C2311yescharacteristic
376#13133182—21no—
377C4×D212C2311yescharacteristic
378C4×D212C2311yescharacteristic
379C4×D212C2311yescharacteristic
380D4×Dic53—21no—
381D4×Dic53—21no—
382#13133179—21no—
383#13133179—21no—
384C4×C22⋊D53—21no—
385C4×C22⋊D53—21no—
386#13133177—21no—
387#13133177—21no—
388#13133177—21no—
389#13133177—21no—
390#13133177—21no—
391#13133177—21no—
392#13133177—21no—
393#13133176C2311yescharacteristic
394#13133176C2311yescharacteristic
395#13133175—21no—
396#13133173—21no—
397C2×C4⋊Dic53C2311yescharacteristic
398C2×C4⋊Dic53C2311yescharacteristic
399C2×C4⋊Dic53C2311yescharacteristic
400C2×#11719919—21no—
401C4⋊C4×D53—21no—
402C4⋊C4×D53—21no—
403C2×C22⋊Dic53—21no—
404C2×#11719921—21no—
405C22⋊C4×D53—21no—
406C22⋊C4×D53—21no—
407#13133151C2311yescharacteristic
408#13133151C2311yescharacteristic
409#13133151C2311yescharacteristic
410#13133151C2311yescharacteristic
411#13133151C2311yescharacteristic
412#13133151C2311yescharacteristic
413#13133149C2311yescharacteristic
414#13133149C2311yescharacteristic
415#13133142C2311yescharacteristic
416#13133142C2311yescharacteristic
417#13133142C2311yescharacteristic
418#13133142C2311yescharacteristic
419#13133142C2311yescharacteristic
420#13133142C2311yescharacteristic
421#13133142C2311yescharacteristic
422#13133142C2311yescharacteristic
423#13133142C2311yescharacteristic
424#13133142C2311yescharacteristic
425#13133142C2311yescharacteristic
426#13133142C2311yescharacteristic
427#13133142C2311yescharacteristic
428#13133142C2311yescharacteristic
429#13133139C2311yescharacteristic
430#13133139C2311yescharacteristic
431#13133139C2311yescharacteristic
432#13133139C2311yescharacteristic
433#13133139C2311yescharacteristic
434#13133139C2311yescharacteristic
435#13133139C2311yescharacteristic
436#13133139C2311yescharacteristic
437#13133139C2311yescharacteristic
438#13133139C2311yescharacteristic
439#13133139C2311yescharacteristic
440#13133139C2311yescharacteristic
441#13133139C2311yescharacteristic
442#13133139C2311yescharacteristic
443#13133139C2311yescharacteristic
444#13133139C2311yescharacteristic
445#13133139C2311yescharacteristic
446#13133139C2311yescharacteristic
447C2×#41×C53C2311yescharacteristic
448C23×C4×C53C2311yescharacteristic
449C2×M16×C53C2311yescharacteristic
450C2×M16×C53C2311yescharacteristic
451C2×M16×C53C2311yescharacteristic
452C2×M16×C53C2311yescharacteristic
453C2×M16×C53C2311yescharacteristic
454C2×M16×C53C2311yescharacteristic
455C22×C8×C53C2311yescharacteristic
456C22×C8×C53C2311yescharacteristic
457#123×C53D411yescharacteristic
458#123×C53D411yescharacteristic
459C22⋊Q8×C53D411yescharacteristic
460C22⋊Q8×C53D411yescharacteristic
461#121×C53D411yescharacteristic
462#121×C53D411yescharacteristic
463#120×C53D411yescharacteristic
464#120×C53D411yescharacteristic
465C4×D4×C53C2311yescharacteristic
466C4×D4×C53C2311yescharacteristic
467C4×D4×C53C2311yescharacteristic
468C4×D4×C53C2311yescharacteristic
469#117×C53C2311yescharacteristic
470C4⋊C8×C53C2311yescharacteristic
471C4⋊C8×C53C2311yescharacteristic
472C4⋊C8×C53C2311yescharacteristic
473C4⋊C8×C53C2311yescharacteristic
474C22⋊C8×C53C2311yescharacteristic
475C22⋊C8×C53C2311yescharacteristic
476C22⋊C8×C53C2311yescharacteristic
477C22⋊C8×C53C2311yescharacteristic
478C22⋊C8×C53C2311yescharacteristic
479C22⋊C8×C53C2311yescharacteristic
480C22⋊C8×C53C2311yescharacteristic
481C22⋊C8×C53C2311yescharacteristic
482C22⋊C8×C53C2311yescharacteristic
483C22⋊C8×C53C2311yescharacteristic
484C22⋊C8×C53C2311yescharacteristic
485C22⋊C8×C53C2311yescharacteristic
486#97×C53C2311yescharacteristic
487#97×C53C2311yescharacteristic
488C4×C8×C53C2311yescharacteristic
489C4×C8×C53C2311yescharacteristic
490C24×C53C2×D411yescharacteristic
491C23×D53—21no—
492C23×D53—21no—
493C23×D53—21no—
494C23×D53—21no—
495#41×C53—41no—
496#41×C53—41no—
497C2×Q8×C53C2×D411yescharacteristic
498C2×D4×C53C2×D411yescharacteristic
499C2×D4×C53C2×D411yescharacteristic
500C2×D4×C53C2×D411yescharacteristic
501C2×D4×C53C2×D411yescharacteristic
502C2×D4×C53C2×D411yescharacteristic
503C2×D4×C53C2×D411yescharacteristic
504C2×D4×C53C2×D411yescharacteristic
505C22×C4×C53—41no—
506C22×C4×C53—41no—
507C22×C4×C53C2×D411yescharacteristic
508C22×C4×C53C2×D411yescharacteristic
509C22×C4×C53C2×D411yescharacteristic
510C22×C4×C53C2411yescharacteristic
511C22×C4×C53C2411yescharacteristic
512C22×C4×C53C2411yescharacteristic
513C22×C4×C53C2411yescharacteristic
514C22×C4×C53C2411yescharacteristic
515C2×C22⋊D53—21no—
516C2×C22⋊D53—21no—
517C2×C22⋊D53—21no—
518C2×C22⋊D53—21no—
519C2×C22⋊D53—21no—
520C2×C22⋊D53—21no—
521C2×C22⋊D53—21no—
522C2×C22⋊D53—21no—
523C2×C22⋊D53—21no—
524C2×C22⋊D53—21no—
525C2×C22⋊D53—21no—
526C2×C22⋊D53—21no—
527C2×C22⋊D53—21no—
528C2×C22⋊D53—21no—
529C2×C22⋊D53—21no—
530C2×C22⋊D53—21no—
531C2×C22⋊D53—21no—
532C2×C22⋊D53—44no—
533C2×C22⋊D53—82no—
534C22×Dic53—21no—
535C22×Dic53—21no—
536C22×Dic53—21no—
537C22×Dic53—21no—
538C22×Dic53—21no—
539C22×Dic53—21no—
540#11719949—44no—
541D4×D53—44no—
542D4×D53—44no—
543D4×D53—44no—
544D4×D53—82no—
545D4×D53—82no—
546#11719945—22no—
547#11719945—22no—
548#11719945—22no—
549#11719945—22no—
550#11719945—22no—
551#11719945—22no—
552#11719945—41no—
553#11719945—41no—
554#11719945—41no—
555#11719945—41no—
556#11719945—41no—
557#11719945—41no—
558#11719945—41no—
559#11719945—41no—
560#11719945—41no—
561#11719945—41no—
562#11719945—44no—
563#11719945—44no—
564C2×D212—22no—
565C2×D212—22no—
566C2×D212—22no—
567C2×D212—21no—
568C2×D212—21no—
569C2×D212—21no—
570C2×D212—21no—
571C2×D212—21no—
572C2×D212—21no—
573C2×D212—21no—
574C2×D212—21no—
575C2×D212—41no—
576C2×D212—41no—
577C2×D212—41no—
578C2×D212—41no—
579C2×D212—41no—
580C2×D212C2411yescharacteristic
581C2×D212C2411yescharacteristic
582C2×D212C2411yescharacteristic
583C2×D212C2411yescharacteristic
584C2×D212C2411yescharacteristic
585C2×C4×D53—21no—
586C2×C4×D53—21no—
587C2×C4×D53—21no—
588C2×C4×D53—21no—
589C2×C4×D53—21no—
590C2×C4×D53—21no—
591C2×C4×D53—21no—
592C2×C4×D53—21no—
593C2×C4×D53—21no—
594C2×C4×D53—21no—
595C2×C4×D53—21no—
596C2×C4×D53—44no—
597C2×Dic106—22no—
598C2×Dic106—21no—
599C2×Dic106—21no—
600C2×Dic106—21no—
601C2×Dic106—21no—
602C2×Dic106—41no—
603C2×Dic106—41no—
604C2×Dic106—41no—
605C2×Dic106—41no—
606C2×Dic106—41no—
607C2×Dic106C2411yescharacteristic
608C2×Dic106C2411yescharacteristic
609C2×Dic106C2411yescharacteristic
610C2×Dic106C2411yescharacteristic
611C2×Dic106C2411yescharacteristic
612M16×C53—41no—
613M16×C53—41no—
614M16×C53—41no—
615M16×C53—41no—
616M16×C53—41no—
617M16×C53—41no—
618C2×C8×C53—41no—
619C2×C8×C53—41no—
620C2×C8×C53C2411yescharacteristic
621C2×C8×C53C2411yescharacteristic
622C2×C8×C53C2411yescharacteristic
623C2×C8×C53C2411yescharacteristic
624C2×C8×C53C2411yescharacteristic
625C2×C8×C53C2411yescharacteristic
626C2×C8×C53C2411yescharacteristic
627C2×C8×C53C2411yescharacteristic
628C4⋊C4×C53C2×D411yescharacteristic
629C4⋊C4×C53C2×D411yescharacteristic
630C4⋊C4×C53C2×D411yescharacteristic
631C4⋊C4×C53C2×D411yescharacteristic
632C4⋊C4×C53C2×D411yescharacteristic
633C4⋊C4×C53C2×D411yescharacteristic
634C22⋊C4×C53C2×D411yescharacteristic
635C22⋊C4×C53C2×D411yescharacteristic
636C22⋊C4×C53C2×D411yescharacteristic
637C22⋊C4×C53C2×D411yescharacteristic
638C22⋊C4×C53C2×D411yescharacteristic
639C22⋊C4×C53C2×D411yescharacteristic
640C22⋊C4×C53C2×D411yescharacteristic
641C22⋊C4×C53C2×D411yescharacteristic
642C22⋊C4×C53C2×D411yescharacteristic
643C22⋊C4×C53C2×D411yescharacteristic
644C42×C53C2411yescharacteristic
645C42×C53C2411yescharacteristic
646C22⋊Dic53—21no—
647C22⋊Dic53—21no—
648C22⋊Dic53—21no—
649C22⋊Dic53—21no—
650C22⋊Dic53—21no—
651C22⋊Dic53—21no—
652C22⋊Dic53—21no—
653C22⋊Dic53—21no—
654C22⋊Dic53—21no—
655C22⋊Dic53—21no—
656C22⋊Dic53—21no—
657C22⋊Dic53—21no—
658C22⋊Dic53—21no—
659#11719921—21no—
660#11719921—21no—
661#11719921—21no—
662#11719921—21no—
663#11719921—21no—
664#11719921—21no—
665#11719921—21no—
666#11719921—21no—
667#11719921—21no—
668#11719921—21no—
669#11719921—21no—
670#11719921—21no—
671#11719921—21no—
672#11719921—21no—
673#11719921—21no—
674#11719921—21no—
675#11719921—21no—
676#11719921—21no—
677C4⋊Dic53—21no—
678C4⋊Dic53—21no—
679C4⋊Dic53—21no—
680C4⋊Dic53—21no—
681C4⋊Dic53—21no—
682C4⋊Dic53—21no—
683C4⋊Dic53C2411yescharacteristic
684C4⋊Dic53C2411yescharacteristic
685C4⋊Dic53C2411yescharacteristic
686C4⋊Dic53C2411yescharacteristic
687C4⋊Dic53C2411yescharacteristic
688C4⋊Dic53C2411yescharacteristic
689#11719919—21no—
690#11719919—21no—
691#11719919—21no—
692#11719919—21no—
693#11719919—21no—
694#11719919—21no—
695#11719919—21no—
696#11719919—21no—
697#11719919—21no—
698#11719919—21no—
699#11719919—21no—
700#11719919—21no—
701#11719919—21no—
702#11719919—21no—
703#11719919—21no—
704#11719919—21no—
705#11719919—21no—
706#11719919—21no—
707C4×Dic53—21no—
708C4×Dic53—21no—
709C4×Dic53—21no—
710C4×Dic53—21no—
711C4×Dic53—21no—
712C4×Dic53—21no—
713C4×Dic53—21no—
714Dic212—22no—
715Dic212—22no—
716Dic212—22no—
717Dic212—41no—
718Dic212—41no—
719Dic212—41no—
720D424—22no—
721D424—41no—
722D424—41no—
723D424—41no—
724#11719913—22no—
725#11719913—22no—
726#11719913—22no—
727#11719913—22no—
728#11719913—41no—
729#11719913—41no—
730#11719913—41no—
731#11719913—41no—
732#11719913—41no—
733#11719913—41no—
734#11719913—41no—
735#11719913—41no—
736#11719913—41no—
737#11719913—41no—
738C23×C53—41no—
739C23×C53—41no—
740C23×C53—41no—
741C23×C53C22×D411yescharacteristic
742C23×C53C22×D411yescharacteristic
743C23×C53C22×D411yescharacteristic
744C23×C53C22×D411yescharacteristic
745C23×C53C22×D411yescharacteristic
746C22×D53—21no—
747C22×D53—21no—
748C22×D53—21no—
749C22×D53—21no—
750C22×D53—21no—
751C22×D53—42no—
752C22×D53—42no—
753C22×D53—42no—
754C22×D53—42no—
755C22×D53—42no—
756C22×D53—81no—
757C22×D53—81no—
758C22×D53—81no—
759C22×D53—81no—
760C22×D53—81no—
761C22×D53—81no—
762C22×D53—81no—
763Q8×C53—41no—
764D4×C53—41no—
765D4×C53—41no—
766D4×C53—41no—
767D4×C53—41no—
768D4×C53—41no—
769D4×C53—41no—
770D4×C53—41no—
771C2×C4×C53—21no—
772C2×C4×C53—21no—
773C2×C4×C53—21no—
774C2×C4×C53—21no—
775C2×C4×C53—21no—
776C2×C4×C53—21no—
777C2×C4×C53—21no—
778C2×C4×C53—21no—
779C2×C4×C53—21no—
780C2×C4×C53—21no—
781C2×C4×C53—41no—
782C2×C4×C53—41no—
783C2×C4×C53—41no—
784C2×C4×C53C22×D411yescharacteristic
785C2×C4×C53C22×D411yescharacteristic
786C2×C4×C53C22×D411yescharacteristic
787C2×C4×C53C22×D411yescharacteristic
788C2×C4×C53C22×D411yescharacteristic
789C2×C4×C53C22×D411yescharacteristic
790C2×C4×C53C22×D411yescharacteristic
791C2×C4×C53C22×D411yescharacteristic
792C2×C4×C53C22×D411yescharacteristic
793C2×C4×C53C2511yescharacteristic
794C22⋊D53—24no—
795C22⋊D53—42no—
796C22⋊D53—42no—
797C22⋊D53—42no—
798C22⋊D53—42no—
799C22⋊D53—42no—
800C22⋊D53—42no—
801C22⋊D53—42no—
802C22⋊D53—42no—
803C22⋊D53—81no—
804C22⋊D53—81no—
805C22⋊D53—81no—
806C22⋊D53—81no—
807C22⋊D53—81no—
808C22⋊D53—81no—
809C22⋊D53—81no—
810C22⋊D53—81no—
811C2×Dic53—21no—
812C2×Dic53—21no—
813C2×Dic53—21no—
814C2×Dic53—21no—
815C2×Dic53—21no—
816C2×Dic53—21no—
817C2×Dic53—21no—
818C2×Dic53—21no—
819C2×Dic53—21no—
820C2×Dic53—21no—
821C2×Dic53—21no—
822C2×Dic53—42no—
823C2×Dic53—81no—
824C2×Dic53—81no—
825C2×Dic53—81no—
826C2×Dic53—81no—
827C2×Dic53—81no—
828D212—21no—
829D212—21no—
830D212—21no—
831D212—21no—
832D212—21no—
833D212—21no—
834D212—21no—
835D212—21no—
836D212—21no—
837D212—42no—
838D212—42no—
839D212—42no—
840D212—42no—
841D212—81no—
842D212—81no—
843D212—81no—
844D212—81no—
845D212H(5,𝔽2)12yes—
846C4×D53—24no—
847C4×D53—42no—
848C4×D53—42no—
849C4×D53—42no—
850C4×D53—42no—
851C4×D53—42no—
852C4×D53—81no—
853C4×D53—81no—
854C4×D53—81no—
855C4×D53—81no—
856C4×D53—81no—
857Dic106—21no—
858Dic106—21no—
859Dic106—21no—
860Dic106—21no—
861Dic106—21no—
862Dic106—21no—
863Dic106—21no—
864Dic106—21no—
865Dic106—21no—
866Dic106—42no—
867Dic106—81no—
868Dic106—81no—
869Dic106—81no—
870Dic106H(5,𝔽2)12yes—
871C8×C53—21no—
872C8×C53—21no—
873C8×C53—21no—
874C8×C53—21no—
875C8×C53—21no—
876C8×C53—21no—
877C8×C53—21no—
878C8×C53—21no—
879#61654—531nomaximal, Sylow
880C22×C53—21no—
881C22×C53—21no—
882C22×C53—21no—
883C22×C53—21no—
884C22×C53—21no—
885C22×C53—21no—
886C22×C53—21no—
887C22×C53—21no—
888C22×C53—21no—
889C22×C53—21no—
890C22×C53—21no—
891C22×C53—21no—
892C22×C53—21no—
893C22×C53—21no—
894C22×C53—21no—
895C22×C53—82no—
896C22×C53C23×D411yescharacteristic
897C2×D53—22no—
898C2×D53—41no—
899C2×D53—41no—
900C2×D53—41no—
901C2×D53—41no—
902C2×D53—41no—
903C2×D53—41no—
904C2×D53—41no—
905C2×D53—41no—
906C2×D53—41no—
907C2×D53—41no—
908C2×D53—41no—
909C2×D53—41no—
910C2×D53—41no—
911C2×D53—41no—
912C2×D53—84no—
913C2×D53—162no—
914C2×D53—162no—
915C2×D53—162no—
916C4×C53—21no—
917C4×C53—21no—
918C4×C53—21no—
919C4×C53—21no—
920C4×C53—21no—
921C4×C53—21no—
922C4×C53—21no—
923C4×C53—21no—
924C4×C53—21no—
925C4×C53C2×H(5,𝔽2)11yescharacteristic
926C4×C53C2×H(5,𝔽2)11yescharacteristic
927Dic53—22no—
928Dic53—41no—
929Dic53—41no—
930Dic53—41no—
931Dic53—41no—
932Dic53—41no—
933Dic53—41no—
934Dic53—41no—
935Dic53—41no—
936Dic53—41no—
937Dic53—41no—
938#3541—531no—
939#3488—531no—
940#3333—531no—
941#3327—531no—
942#3324—531no—
943#3322—531no—
944#3314—531no—
945#3313—531no—
946#3310—531no—
947#3309—531no—
948#3278—531no—
949#3277—531no—
950#3275—531no—
951#3272—531no—
952#3271—531no—
953#3269—531no—
954#3266—531no—
955#3265—531no—
956#3224—531no—
957#3222—531no—
958#3203—531no—
959#3201—531no—
960#3194—531no—
961#3193—531no—
962#3124—531no—
963#3120—531no—
964#3012—531no—
965#3009—531no—
966#3007—531no—
967#3005—531no—
968#2978D5311yescharacteristic, complemented
969C2×C53—41no—
970C2×C53—41no—
971C2×C53—41no—
972C2×C53—41no—
973C2×C53—41no—
974C2×C53#348411yescharacteristic
975C2×C53#358511yescharacteristic
976C2×C53#358611yescharacteristic
977D53—42no—
978D53—81no—
979D53—81no—
980D53—81no—
981D53—81no—
982C2×H(5,𝔽2)—531no—
983C22×#41—531no—
984C2×#137—531no—
985C2×#137—531no—
986C2×#137—531no—
987C2×#137—531no—
988C2×AGL(1,ℤ/8)—531no—
989C2×AGL(1,ℤ/8)—531no—
990C2×#135—531no—
991C22×SD16—531no—
992#563—1061no—
993#562—1061no—
994#556—531no—
995#554—531no—
996#554—1061no—
997#553—531no—
998#553—1061no—
999#552—531no—
1000#550—531no—
1001#550—531no—
1002D4×Q8—531no—
1003#548—531no—
1004#548—531no—
1005#548—531no—
1006#548—531no—
1007#547—531no—
1008#546—531no—
1009#546—531no—
1010#546—1061no—
1011#546—1061no—
1012D42—531no—
1013D42—531no—
1014D42—1061no—
1015D42—1061no—
1016#542—531no—
1017#542—1061no—
1018#541—531no—
1019#539—1061no—
1020#538—1061no—
1021#538—1061no—
1022#537—531no—
1023#537—531no—
1024#537—1061no—
1025#536—531no—
1026#535—531no—
1027#535—1061no—
1028#525—531no—
1029#525—1061no—
1030#525C2×D5311yescharacteristic
1031C2×C22⋊Q8—531no—
1032C2×#121—531no—
1033C2×#121—1061no—
1034#520—531no—
1035#497—531no—
1036#496—531no—
1037#495—531no—
1038#492—531no—
1039#490—531no—
1040#489—531no—
1041#488—531no—
1042#486—531no—
1043#485—531no—
1044#484—531no—
1045#484—531no—
1046#484—531no—
1047#483—531no—
1048#482—531no—
1049#482—531no—
1050#482—531no—
1051#480—531no—
1052#480—531no—
1053#480—531no—
1054#480—531no—
1055#479—531no—
1056#478—531no—
1057#477—531no—
1058#474—531no—
1059#470—531no—
1060#469—531no—
1061#469—531no—
1062#468—531no—
1063#468—531no—
1064#468—531no—
1065#468—531no—
1066#468—531no—
1067#468—531no—
1068#468—531no—
1069#468—531no—
1070#468—531no—
1071#467—531no—
1072#467—531no—
1073#466—531no—
1074#465—531no—
1075#464—531no—
1076#464—531no—
1077#464—531no—
1078#464—531no—
1079#463—531no—
1080#463—531no—
1081#462—531no—
1082#461—531no—
1083#460—531no—
1084#460—531no—
1085#460—531no—
1086#459—531no—
1087#452—531no—
1088#452—531no—
1089#452—531no—
1090#452—531no—
1091#452—531no—
1092#452—531no—
1093#452—531no—
1094#452—531no—
1095#452—531no—
1096#452—531no—
1097#452—531no—
1098#452—531no—
1099#451—531no—
1100#451—531no—
1101#451—531no—
1102#450—531no—
1103#450—531no—
1104#450—531no—
1105#450—531no—
1106#450—531no—
1107#450—531no—
1108#450—531no—
1109#450—531no—
1110#449—531no—
1111#449—531no—
1112#449—531no—
1113#449—531no—
1114#449—531no—
1115#449—531no—
1116#449—531no—
1117#449—531no—
1118#448—531no—
1119#448—531no—
1120#448—531no—
1121#447—531no—
1122#447—531no—
1123#441—531no—
1124#440—531no—
1125#440—531no—
1126#440—531no—
1127C4×Q16—531no—
1128C4×Q16—531no—
1129C4×SD16—531no—
1130C4×D8—531no—
1131#436C2×D5311yescharacteristic, complemented
1132#436C2×D5311yescharacteristic, complemented
1133#436C2×D5311yescharacteristic, complemented
1134#436C2×D5311yescharacteristic, complemented
1135#435C2×D5311yescharacteristic, complemented
1136#435C2×D5311yescharacteristic, complemented
1137#435C2×D5311yescharacteristic, complemented
1138#435C2×D5311yescharacteristic, complemented
1139#433C2×D5311yescharacteristic, complemented
1140#433C2×D5311yescharacteristic, complemented
1141#419—531no—
1142#418—531no—
1143#418—531no—
1144#417—531no—
1145#417—531no—
1146#417—531no—
1147#416—531no—
1148C2×#102—531no—
1149#408C2×D5311yescharacteristic, complemented
1150#408C2×D5311yescharacteristic, complemented
1151#407C2×D5311yescharacteristic, complemented
1152#407C2×D5311yescharacteristic, complemented
1153C53#6165411yescharacteristic, complemented, Sylow
1154H(5,𝔽2)—2122no—
1155H(5,𝔽2)—2122no—
1156C2×#41—531no—
1157C2×#41—531no—
1158C2×#41—531no—
1159C2×#41—531no—
1160C2×#41—531no—
1161C2×#41—531no—
1162C2×#41—531no—
1163C2×#41—531no—
1164C2×#41—1061no—
1165C2×#41—1061no—
1166C2×#41—1061no—
1167C2×#41—2122no—
1168C2×#41—2122no—
1169C2×#41C22×D5311yescharacteristic
1170C22×Q8—531no—
1171C22×Q8—531no—
1172C22×Q8—531no—
1173C22×D4—531no—
1174C22×D4—531no—
1175C22×D4—531no—
1176C22×D4—531no—
1177C22×D4—1061no—
1178C22×D4—1061no—
1179C22×D4—1061no—
1180C22×D4—1061no—
1181C22×D4—1061no—
1182C22×D4—1061no—
1183C22×D4—1061no—
1184C23×C4—1061no—
1185C23×C4C22×D5311yescharacteristic
1186#137—2122no—
1187#137—2122no—
1188#137—2122no—
1189#137—2122no—
1190AGL(1,ℤ/8)—2122no—
1191AGL(1,ℤ/8)—2122no—
1192#135—2122no—
1193C2×Q16—531no—
1194C2×Q16—531no—
1195C2×Q16—531no—
1196C2×Q16—531no—
1197C2×Q16—531no—
1198C2×Q16—531no—
1199C2×SD16—531no—
1200C2×SD16—531no—
1201C2×SD16—531no—
1202C2×SD16—531no—
1203C2×SD16—531no—
1204C2×SD16—531no—
1205C2×SD16—531no—
1206C2×SD16—531no—
1207C2×SD16—531no—
1208C2×SD16—531no—
1209C2×SD16—531no—
1210C2×SD16—531no—
1211C2×SD16—531no—
1212C2×SD16—531no—
1213C2×SD16—2122no—
1214C2×D8—531no—
1215C2×D8—531no—
1216C2×D8—531no—
1217C2×D8—531no—
1218C2×M16C22×D5311yescharacteristic
1219C2×M16C22×D5311yescharacteristic
1220C2×M16C22×D5311yescharacteristic
1221C2×M16C22×D5311yescharacteristic
1222C2×M16C22×D5311yescharacteristic
1223C2×M16C22×D5311yescharacteristic
1224C22×C8C22×D5311yescharacteristic
1225C22×C8C22×D5311yescharacteristic
1226C4⋊Q8—531no—
1227C4⋊Q8—531no—
1228C4⋊Q8—1061no—
1229C4⋊Q8—1061no—
1230#127—531no—
1231#127—531no—
1232#127—1061no—
1233#127—1061no—
1234#126—1061no—
1235#126—1061no—
1236#126—1061no—
1237#126—1061no—
1238#126—1061no—
1239#126—1061no—
1240#126—1061no—
1241#125—531no—
1242#125—1061no—
1243#125—1061no—
1244#125—1061no—
1245#125—1061no—
1246#124—531no—
1247#124—531no—
1248#124—531no—
1249#124—1061no—
1250#124—1061no—
1251#124—1061no—
1252#124—1061no—
1253#124—1061no—
1254#124—1061no—
1255#124—1061no—
1256#123—1061no—
1257#123—1061no—
1258#123—1061no—
1259#123—1061no—
1260#123—1061no—
1261#123—1061no—
1262#123—1061no—
1263#123—1061no—
1264#123—1061no—
1265#123—1061no—
1266#123D21211yescharacteristic
1267#123D21211yescharacteristic
1268C22⋊Q8—531no—
1269C22⋊Q8—531no—
1270C22⋊Q8—531no—
1271C22⋊Q8—531no—
1272C22⋊Q8—531no—
1273C22⋊Q8—531no—
1274C22⋊Q8—531no—
1275C22⋊Q8—531no—
1276C22⋊Q8—531no—
1277C22⋊Q8—531no—
1278C22⋊Q8—531no—
1279C22⋊Q8—1061no—
1280C22⋊Q8—1061no—
1281C22⋊Q8—1061no—
1282C22⋊Q8—1061no—
1283C22⋊Q8—1061no—
1284C22⋊Q8—1061no—
1285C22⋊Q8—1061no—
1286C22⋊Q8—1061no—
1287C22⋊Q8—1061no—
1288C22⋊Q8—1061no—
1289C22⋊Q8—1061no—
1290C22⋊Q8—1061no—
1291C22⋊Q8—1061no—
1292C22⋊Q8D21211yescharacteristic
1293C22⋊Q8D21211yescharacteristic
1294#121—531no—
1295#121—531no—
1296#121—531no—
1297#121—531no—
1298#121—531no—
1299#121—531no—
1300#121—531no—
1301#121—531no—
1302#121—531no—
1303#121—1061no—
1304#121—1061no—
1305#121—1061no—
1306#121—1061no—
1307#121—1061no—
1308#121—1061no—
1309#121—1061no—
1310#121—1061no—
1311#121—1061no—
1312#121—1061no—
1313#121—1061no—
1314#121—1061no—
1315#121—1061no—
1316#121—1061no—
1317#121—1061no—
1318#121—1061no—
1319#121—1061no—
1320#121—1061no—
1321#121—1061no—
1322#121—1061no—
1323#121—1061no—
1324#121—1061no—
1325#121—1061no—
1326#121—1061no—
1327#121D21211yescharacteristic
1328#121D21211yescharacteristic
1329#120—1061no—
1330#120—1061no—
1331#120—1061no—
1332#120—1061no—
1333#120—1061no—
1334#120—1061no—
1335#120—1061no—
1336#120—1061no—
1337#120—1061no—
1338#120D21211yescharacteristic
1339#120D21211yescharacteristic
1340C4×Q8—531no—
1341C4×Q8—531no—
1342C4×Q8—531no—
1343C4×Q8—531no—
1344C4×Q8—531no—
1345C4×Q8—1061no—
1346C4×D4—531no—
1347C4×D4—531no—
1348C4×D4—531no—
1349C4×D4—1061no—
1350C4×D4—1061no—
1351C4×D4—1061no—
1352C4×D4—1061no—
1353C4×D4—1061no—
1354C4×D4—1061no—
1355C4×D4—1061no—
1356C4×D4—1061no—
1357C4×D4—1061no—
1358C4×D4—1061no—
1359C4×D4—1061no—
1360C4×D4—1061no—
1361C4×D4—1061no—
1362C4×D4C22×D5311yescharacteristic
1363C4×D4C22×D5311yescharacteristic
1364C4×D4C22×D5311yescharacteristic
1365C4×D4C22×D5311yescharacteristic
1366#117—531no—
1367#117—531no—
1368#117—1061no—
1369#117—1061no—
1370#117C22×D5311yescharacteristic
1371C2×C4⋊C4—531no—
1372C2×C4⋊C4—531no—
1373C2×C4⋊C4—531no—
1374C2×C4⋊C4—1061no—
1375C2×C4⋊C4—1061no—
1376C2×C4⋊C4—1061no—
1377C2×C22⋊C4—1061no—
1378C2×C22⋊C4—1061no—
1379C2×C22⋊C4—1061no—
1380C2×C22⋊C4—1061no—
1381#107—531no—
1382#107—531no—
1383#107—531no—
1384#107—531no—
1385#107—531no—
1386#107—531no—
1387#106—531no—
1388#106—531no—
1389C4⋊C8C22×D5311yescharacteristic
1390C4⋊C8C22×D5311yescharacteristic
1391C4⋊C8C22×D5311yescharacteristic
1392C4⋊C8C22×D5311yescharacteristic
1393#103—531no—
1394#103—531no—
1395#103—531no—
1396#103—531no—
1397#103—531no—
1398#103—531no—
1399#103—531no—
1400#103—531no—
1401#103—531no—
1402#103—531no—
1403#103—531no—
1404#103—531no—
1405#103—531no—
1406#103—531no—
1407#102—531no—
1408#102—531no—
1409#102—531no—
1410#102—531no—
1411#102—531no—
1412#102—531no—
1413#102—531no—
1414#102—531no—
1415#102—531no—
1416#102—531no—
1417#102—531no—
1418#102—531no—
1419#102—531no—
1420#102—531no—
1421#102—531no—
1422#102—531no—
1423#102—531no—
1424#102—531no—
1425C22⋊C8C22×D5311yescharacteristic
1426C22⋊C8C22×D5311yescharacteristic
1427C22⋊C8C22×D5311yescharacteristic
1428C22⋊C8C22×D5311yescharacteristic
1429C22⋊C8C22×D5311yescharacteristic
1430C22⋊C8C22×D5311yescharacteristic
1431C22⋊C8C22×D5311yescharacteristic
1432C22⋊C8C22×D5311yescharacteristic
1433C22⋊C8C22×D5311yescharacteristic
1434C22⋊C8C22×D5311yescharacteristic
1435C22⋊C8C22×D5311yescharacteristic
1436C22⋊C8C22×D5311yescharacteristic
1437#97C22×D5311yescharacteristic
1438#97C22×D5311yescharacteristic
1439C4×C8C22×D5311yescharacteristic
1440C4×C8C22×D5311yescharacteristic
1441C24—1061no—
1442C24—1061no—
1443C24—1061no—
1444C24—1061no—
1445C24C2×D21211yescharacteristic
1446#41—41no—
1447#41—41no—
1448#41—1062no—
1449#41—1062no—
1450#41—1062no—
1451#41—1062no—
1452#41—1062no—
1453#41—1062no—
1454#41—2121no—
1455#41—2121no—
1456#41—2121no—
1457#41—2121no—
1458#41—2121no—
1459#41—2121no—
1460#41—2121no—
1461#41—2121no—
1462#41—2121no—
1463#41—2121no—
1464#41—2124no—
1465#41—2124no—
1466#41—2124no—
1467C2×Q8—531no—
1468C2×Q8—531no—
1469C2×Q8—531no—
1470C2×Q8—531no—
1471C2×Q8—531no—
1472C2×Q8—1062no—
1473C2×Q8—1061no—
1474C2×Q8—1061no—
1475C2×Q8—1061no—
1476C2×Q8—1061no—
1477C2×Q8—2121no—
1478C2×Q8—2121no—
1479C2×Q8—2121no—
1480C2×Q8—2121no—
1481C2×Q8—2121no—
1482C2×Q8C2×D21211yescharacteristic
1483C2×D4—531no—
1484C2×D4—531no—
1485C2×D4—531no—
1486C2×D4—531no—
1487C2×D4—531no—
1488C2×D4—1062no—
1489C2×D4—1062no—
1490C2×D4—1062no—
1491C2×D4—1061no—
1492C2×D4—1061no—
1493C2×D4—1061no—
1494C2×D4—1061no—
1495C2×D4—1061no—
1496C2×D4—1061no—
1497C2×D4—1061no—
1498C2×D4—1061no—
1499C2×D4—1061no—
1500C2×D4—1061no—
1501C2×D4—1061no—
1502C2×D4—1061no—
1503C2×D4—1061no—
1504C2×D4—1061no—
1505C2×D4—1061no—
1506C2×D4—1061no—
1507C2×D4—1061no—
1508C2×D4—1061no—
1509C2×D4—1061no—
1510C2×D4—1061no—
1511C2×D4—1061no—
1512C2×D4—1061no—
1513C2×D4—1061no—
1514C2×D4—1061no—
1515C2×D4—1061no—
1516C2×D4—4242no—
1517C2×D4—4242no—
1518C2×D4—4242no—
1519C2×D4—2121no—
1520C2×D4—2121no—
1521C2×D4—2121no—
1522C2×D4—2121no—
1523C2×D4—2121no—
1524C2×D4—2124no—
1525C2×D4—2124no—
1526C2×D4—2124no—
1527C2×D4—2124no—
1528C2×D4C2×D21211yescharacteristic
1529C2×D4C2×D21211yescharacteristic
1530C2×D4C2×D21211yescharacteristic
1531C2×D4C2×D21211yescharacteristic
1532C2×D4C2×D21211yescharacteristic
1533C2×D4C2×D21211yescharacteristic
1534C2×D4C2×D21211yescharacteristic
1535C22×C4—41no—
1536C22×C4—41no—
1537C22×C4—1061no—
1538C22×C4—1061no—
1539C22×C4—1061no—
1540C22×C4—1061no—
1541C22×C4—1061no—
1542C22×C4—1061no—
1543C22×C4—1061no—
1544C22×C4—1061no—
1545C22×C4—1061no—
1546C22×C4—1061no—
1547C22×C4—1061no—
1548C22×C4—1061no—
1549C22×C4—1061no—
1550C22×C4—1061no—
1551C22×C4—1061no—
1552C22×C4—1061no—
1553C22×C4—1061no—
1554C22×C4—2124no—
1555C22×C4C2×D21211yescharacteristic
1556C22×C4C2×D21211yescharacteristic
1557C22×C4C2×D21211yescharacteristic
1558C22×C4C23×D5311yescharacteristic
1559C22×C4C23×D5311yescharacteristic
1560C22×C4C23×D5311yescharacteristic
1561C22×C4C23×D5311yescharacteristic
1562C22×C4C23×D5311yescharacteristic
1563Q16—1062no—
1564Q16—1062no—
1565Q16—1062no—
1566Q16—2121no—
1567Q16—2121no—
1568Q16—2121no—
1569SD16—1062no—
1570SD16—1062no—
1571SD16—1062no—
1572SD16—1062no—
1573SD16—2121no—
1574SD16—2121no—
1575SD16—2121no—
1576SD16—2121no—
1577SD16—2121no—
1578SD16—2121no—
1579SD16—2121no—
1580SD16—2121no—
1581SD16—2121no—
1582SD16—2121no—
1583D8—1062no—
1584D8—2121no—
1585D8—2121no—
1586D8—2121no—
1587M16—41no—
1588M16—41no—
1589M16—41no—
1590M16—41no—
1591M16—41no—
1592M16—41no—
1593C2×C8—41no—
1594C2×C8—41no—
1595C2×C8C23×D5311yescharacteristic
1596C2×C8C23×D5311yescharacteristic
1597C2×C8C23×D5311yescharacteristic
1598C2×C8C23×D5311yescharacteristic
1599C2×C8C23×D5311yescharacteristic
1600C2×C8C23×D5311yescharacteristic
1601C2×C8C23×D5311yescharacteristic
1602C2×C8C23×D5311yescharacteristic
1603C4⋊C4—531no—
1604C4⋊C4—531no—
1605C4⋊C4—531no—
1606C4⋊C4—531no—
1607C4⋊C4—531no—
1608C4⋊C4—531no—
1609C4⋊C4—1061no—
1610C4⋊C4—1061no—
1611C4⋊C4—1061no—
1612C4⋊C4—1061no—
1613C4⋊C4—1061no—
1614C4⋊C4—1061no—
1615C4⋊C4—1061no—
1616C4⋊C4—1061no—
1617C4⋊C4—1061no—
1618C4⋊C4—1061no—
1619C4⋊C4—1061no—
1620C4⋊C4—1061no—
1621C4⋊C4—1061no—
1622C4⋊C4—1061no—
1623C4⋊C4—1061no—
1624C4⋊C4—1061no—
1625C4⋊C4—1061no—
1626C4⋊C4—1061no—
1627C4⋊C4—1061no—
1628C4⋊C4—1061no—
1629C4⋊C4—1061no—
1630C4⋊C4—1061no—
1631C4⋊C4—1061no—
1632C4⋊C4—1061no—
1633C4⋊C4C2×D21211yescharacteristic
1634C4⋊C4C2×D21211yescharacteristic
1635C4⋊C4C2×D21211yescharacteristic
1636C4⋊C4C2×D21211yescharacteristic
1637C4⋊C4C2×D21211yescharacteristic
1638C4⋊C4C2×D21211yescharacteristic
1639C22⋊C4—1061no—
1640C22⋊C4—1061no—
1641C22⋊C4—1061no—
1642C22⋊C4—1061no—
1643C22⋊C4—1061no—
1644C22⋊C4—1061no—
1645C22⋊C4—1061no—
1646C22⋊C4—1061no—
1647C22⋊C4—1061no—
1648C22⋊C4—1061no—
1649C22⋊C4—1061no—
1650C22⋊C4—1061no—
1651C22⋊C4—1061no—
1652C22⋊C4—1061no—
1653C22⋊C4—1061no—
1654C22⋊C4—1061no—
1655C22⋊C4—1061no—
1656C22⋊C4—1061no—
1657C22⋊C4—1061no—
1658C22⋊C4—1061no—
1659C22⋊C4—1061no—
1660C22⋊C4—1061no—
1661C22⋊C4—1061no—
1662C22⋊C4—1061no—
1663C22⋊C4—1061no—
1664C22⋊C4—1061no—
1665C22⋊C4—1061no—
1666C22⋊C4—1061no—
1667C22⋊C4—1061no—
1668C22⋊C4—1061no—
1669C22⋊C4—1061no—
1670C22⋊C4C2×D21211yescharacteristic
1671C22⋊C4C2×D21211yescharacteristic
1672C22⋊C4C2×D21211yescharacteristic
1673C22⋊C4C2×D21211yescharacteristic
1674C22⋊C4C2×D21211yescharacteristic
1675C22⋊C4C2×D21211yescharacteristic
1676C22⋊C4C2×D21211yescharacteristic
1677C22⋊C4C2×D21211yescharacteristic
1678C22⋊C4C2×D21211yescharacteristic
1679C22⋊C4C2×D21211yescharacteristic
1680C42—1061no—
1681C42—1061no—
1682C42—1061no—
1683C42—1061no—
1684C42—1061no—
1685C42—1061no—
1686C42—1061no—
1687C42C23×D5311yescharacteristic
1688C42C23×D5311yescharacteristic
1689C23—41no—
1690C23—41no—
1691C23—41no—
1692C23—1061no—
1693C23—1061no—
1694C23—1061no—
1695C23—1061no—
1696C23—1061no—
1697C23—4241no—
1698C23—4241no—
1699C23—4241no—
1700C23—4241no—
1701C23—4241no—
1702C23—4241no—
1703C23—4241no—
1704C23—2122no—
1705C23—2122no—
1706C23—2122no—
1707C23—2122no—
1708C23—2122no—
1709C23C22×D21211yescharacteristic
1710C23C22×D21211yescharacteristic
1711C23C22×D21211yescharacteristic
1712C23C22×D21211yescharacteristic
1713C23C22×D21211yescharacteristic
1714Q8—41no—
1715Q8—532no—
1716Q8—1061no—
1717Q8—1061no—
1718Q8—1061no—
1719Q8—1061no—
1720Q8—1061no—
1721Q8—1061no—
1722Q8—1061no—
1723Q8—1061no—
1724Q8—1061no—
1725Q8—4241no—
1726Q8—4241no—
1727Q8—4241no—
1728Q8—2122no—
1729D4—41no—
1730D4—41no—
1731D4—41no—
1732D4—41no—
1733D4—41no—
1734D4—41no—
1735D4—41no—
1736D4—532no—
1737D4—1064no—
1738D4—1061no—
1739D4—1061no—
1740D4—1061no—
1741D4—1061no—
1742D4—1061no—
1743D4—1061no—
1744D4—1061no—
1745D4—1061no—
1746D4—1061no—
1747D4—4241no—
1748D4—4241no—
1749D4—4241no—
1750D4—4241no—
1751D4—4241no—
1752D4—4241no—
1753D4—4241no—
1754D4—4241no—
1755D4—4241no—
1756D4—4241no—
1757D4—4241no—
1758D4—4241no—
1759D4—2122no—
1760D4—2122no—
1761D4—2122no—
1762D4—2122no—
1763D4—2122no—
1764D4—2122no—
1765D4—2122no—
1766D4—2122no—
1767D4—2122no—
1768D4—2122no—
1769D4—2122no—
1770D4—2122no—
1771C2×C4—21no—
1772C2×C4—21no—
1773C2×C4—21no—
1774C2×C4—21no—
1775C2×C4—21no—
1776C2×C4—21no—
1777C2×C4—21no—
1778C2×C4—21no—
1779C2×C4—21no—
1780C2×C4—21no—
1781C2×C4—41no—
1782C2×C4—41no—
1783C2×C4—41no—
1784C2×C4—1064no—
1785C2×C4—1061no—
1786C2×C4—1061no—
1787C2×C4—1061no—
1788C2×C4—1061no—
1789C2×C4—1061no—
1790C2×C4—1061no—
1791C2×C4—1061no—
1792C2×C4—1061no—
1793C2×C4—1061no—
1794C2×C4—1061no—
1795C2×C4—1061no—
1796C2×C4—4241no—
1797C2×C4—4241no—
1798C2×C4—4241no—
1799C2×C4—4241no—
1800C2×C4—4241no—
1801C2×C4—4241no—
1802C2×C4—4241no—
1803C2×C4—4241no—
1804C2×C4—4241no—
1805C2×C4—4241no—
1806C2×C4—2122no—
1807C2×C4—2122no—
1808C2×C4—2122no—
1809C2×C4—2122no—
1810C2×C4—2122no—
1811C2×C4—2122no—
1812C2×C4C22×D21211yescharacteristic
1813C2×C4C22×D21211yescharacteristic
1814C2×C4C22×D21211yescharacteristic
1815C2×C4C22×D21211yescharacteristic
1816C2×C4C22×D21211yescharacteristic
1817C2×C4C22×D21211yescharacteristic
1818C2×C4C22×D21211yescharacteristic
1819C2×C4C22×D21211yescharacteristic
1820C2×C4C22×D21211yescharacteristic
1821C2×C4C24×D5311yescharacteristic
1822C8—21no—
1823C8—21no—
1824C8—21no—
1825C8—21no—
1826C8—21no—
1827C8—21no—
1828C8—21no—
1829C8—21no—
1830C22—21no—
1831C22—21no—
1832C22—21no—
1833C22—21no—
1834C22—21no—
1835C22—21no—
1836C22—21no—
1837C22—21no—
1838C22—21no—
1839C22—21no—
1840C22—21no—
1841C22—21no—
1842C22—21no—
1843C22—21no—
1844C22—21no—
1845C22—82no—
1846C22—8482no—
1847C22—8482no—
1848C22—8482no—
1849C22—1062no—
1850C22—4244no—
1851C22—2121no—
1852C22—2121no—
1853C22—2121no—
1854C22—2121no—
1855C22—2121no—
1856C22—2121no—
1857C22—2121no—
1858C22—2121no—
1859C22—2121no—
1860C22—2121no—
1861C22—2121no—
1862C22—2121no—
1863C22—2121no—
1864C22—2121no—
1865C22C23×D21211yescharacteristic
1866C4—21no—
1867C4—21no—
1868C4—21no—
1869C4—21no—
1870C4—21no—
1871C4—21no—
1872C4—21no—
1873C4—21no—
1874C4—21no—
1875C4—1062no—
1876C4—2121no—
1877C4—2121no—
1878C4—2121no—
1879C4—2121no—
1880C4—2121no—
1881C4—2121no—
1882C4—2121no—
1883C4—2121no—
1884C4—2121no—
1885C4—2121no—
1886C4H(5,𝔽2)×D5311yescharacteristic
1887C4H(5,𝔽2)×D5311yescharacteristic
1888C2—41no—
1889C2—41no—
1890C2—41no—
1891C2—41no—
1892C2—41no—
1893C2—4241no—
1894C2—4241no—
1895C2—4241no—
1896C2—4241no—
1897C2—2122no—
1898C2#2028835111yescharacteristic
1899C2#2028949611yescharacteristic
1900C2#2028950311yescharacteristic
subgroupG/H
centerC22C23×D212
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC53×#2978C2
socleC22×C53C23×D4
hypercenter#2978D53
hypocenterC53#61654
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C22 ◁ #525 ◁ #2978

Complements

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

NH ≅ G/Ntype
1. #20289008C2semidirect
2. #20288376C2semidirect
3. #20287054C2semidirect
4. #20286985C2semidirect
5. #20286947C2semidirect
6. #20286918C2semidirect
7. #20286798C2semidirect
8. #20286783C2semidirect
9. #20286738C2semidirect
10. #20286723C2semidirect
11. #20286383C2semidirect
12. #20286373C2semidirect
13. #20286351C2semidirect
14. #20286317C2semidirect
15. #20286305C2semidirect
16. #20286275C2semidirect
17. #20286230C2semidirect
18. #20286215C2semidirect
19. #20285811C2semidirect
20. #20285789C2semidirect
21. #20285617C2semidirect
22. #20285599C2semidirect
23. #20285531C2semidirect
24. #20285522C2semidirect
25. #20284979C2semidirect
26. #20284931C2semidirect
27. #20284022C2semidirect
28. #20283994C2semidirect
29. #20283977C2semidirect
30. #20283960C2semidirect
31. C53×#2978C2semidirect
34. C2×#13133250C22semidirect
35. C2×#13133250C22semidirect
36. C2×#13133250C22semidirect
37. C2×#13133250C22semidirect
38. C2×#13133245C22semidirect
39. C2×#13133245C22semidirect
40. C2×#13133239C22semidirect
41. C22×#11719913C22semidirect
44. #16811343C22semidirect
45. #16811330C22semidirect
47. #16811319C22semidirect
49. #16811313C22semidirect
52. D4×Dic106C22semidirect
55. #16811282C22semidirect
56. #16811282C22semidirect
57. #16811278C22semidirect
66. #16811244C22semidirect
68. #16811235C22semidirect
74. #16811201C22semidirect
75. #16811194C22semidirect
79. #16811134C22semidirect
80. C2×#13133196C22semidirect
84. #16811017C22semidirect
85. #16811012C22semidirect
86. #16811007C22semidirect
87. #16810996C22semidirect
88. #16810988C22semidirect
89. #16810983C22semidirect
90. #16810978C22semidirect
91. #16810970C22semidirect
92. #16810965C22semidirect
93. #16810959C22semidirect
94. #16810959C22semidirect
95. #16810959C22semidirect
96. #16810954C22semidirect
97. #16810948C22semidirect
98. #16810948C22semidirect
99. #16810948C22semidirect
100. #16810937C22semidirect
101. #16810937C22semidirect
102. #16810937C22semidirect
103. #16810937C22semidirect
104. #16810931C22semidirect
105. #16810924C22semidirect
106. #16810919C22semidirect
107. #16810904C22semidirect
108. #16810881C22semidirect
109. #16810876C22semidirect
110. #16810876C22semidirect
111. #16810869C22semidirect
112. #16810869C22semidirect
113. #16810869C22semidirect
114. #16810869C22semidirect
115. #16810869C22semidirect
116. #16810869C22semidirect
117. #16810869C22semidirect
118. #16810869C22semidirect
119. #16810869C22semidirect
120. #16810864C22semidirect
121. #16810864C22semidirect
122. #16810859C22semidirect
123. #16810852C22semidirect
124. #16810846C22semidirect
125. #16810846C22semidirect
126. #16810846C22semidirect
127. #16810846C22semidirect
128. #16810839C22semidirect
129. #16810839C22semidirect
130. #16810834C22semidirect
131. #16810829C22semidirect
132. #16810824C22semidirect
133. #16810824C22semidirect
134. #16810824C22semidirect
135. #16810819C22semidirect
139. #16810787C22semidirect
140. #16810787C22semidirect
141. #16810787C22semidirect
142. #16810787C22semidirect
143. #16810787C22semidirect
144. #16810787C22semidirect
145. #16810787C22semidirect
146. #16810787C22semidirect
147. #16810787C22semidirect
148. #16810781C22semidirect
149. #16810781C22semidirect
150. #16810781C22semidirect
151. #16810776C22semidirect
152. #16810776C22semidirect
153. #16810776C22semidirect
154. #16810776C22semidirect
155. #16810776C22semidirect
156. #16810776C22semidirect
157. #16810776C22semidirect
158. #16810776C22semidirect
160. #16810770C22semidirect
161. #16810770C22semidirect
162. #16810770C22semidirect
163. #16810770C22semidirect
164. #16810770C22semidirect
165. #16810770C22semidirect
166. #16810770C22semidirect
167. #16810764C22semidirect
168. #16810764C22semidirect
169. #16810764C22semidirect
170. #16810759C22semidirect
171. #16810759C22semidirect
172. #16810731C22semidirect
173. #16810725C22semidirect
174. #16810725C22semidirect
175. #16810725C22semidirect
176. C4×Dic212C22semidirect
177. C4×Dic212C22semidirect
178. C4×#11719913C22semidirect
179. C4×D424C22semidirect
180. #16810633C22semidirect
181. #16810629C22semidirect
182. #16810629C22semidirect
183. #16810625C22semidirect
184. #16810625C22semidirect
185. #16810625C22semidirect
186. #16810620C22semidirect
187. C2×#13133139C22semidirect
189. C53×#436C22semidirect
190. C53×#436C22semidirect
191. C53×#436C22semidirect
192. C53×#436C22semidirect
193. C53×#435C22semidirect
194. C53×#435C22semidirect
195. C53×#435C22semidirect
196. C53×#435C22semidirect
197. C53×#433C22semidirect
198. C53×#433C22semidirect
199. C53×#408C22semidirect
200. C53×#408C22semidirect
201. C53×#407C22semidirect
202. C53×#407C22semidirect
968. #2978D53semidirect
1131. #436C2×D53semidirect
1132. #436C2×D53semidirect
1133. #436C2×D53semidirect
1134. #436C2×D53semidirect
1135. #435C2×D53semidirect
1136. #435C2×D53semidirect
1137. #435C2×D53semidirect
1138. #435C2×D53semidirect
1139. #433C2×D53semidirect
1140. #433C2×D53semidirect
1149. #408C2×D53semidirect
1150. #408C2×D53semidirect
1151. #407C2×D53semidirect
1152. #407C2×D53semidirect
1153. C53#61654semidirect

Maximal subgroups

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

subgroupindex
#202890082
#202883762
#202870542
#202869852
#202869472
#202869182
#202867982
#202867832
#202867382
#202867232
#202863832
#202863732
#202863512
#202863172
#202863052
#202862752
#202862302
#202862152
#202858112
#202857892
#202856172
#202855992
#202855312
#202855222
#202849792
#202849312
#202840222
#202839942
#202839772
#202839602
C53×#29782
#6165453