Finite Group Databasebeta

← #28267129

Subgroups — #28267129

Order 13568.

1800 conjugacy classes of subgroups.

The subgroup lattice has 1698 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20288787C211yesmaximal, characteristic, complemented
2#20287790C211yesmaximal, characteristic, complemented
3#20287669C211yesmaximal, characteristic, complemented
4#20287364C211yesmaximal, characteristic, complemented
5#20287360C211yesmaximal, characteristic, complemented
6#20287284C211yesmaximal, characteristic, complemented
7#20287260C211yesmaximal, characteristic, complemented
8#20287254C211yesmaximal, characteristic, complemented
9#20286632C211yesmaximal, characteristic, complemented
10#20286626C211yesmaximal, characteristic, complemented
11#20286565C211yesmaximal, characteristic, complemented
12#20286559C211yesmaximal, characteristic, complemented
13#20286550C211yesmaximal, characteristic, complemented
14#20286544C211yesmaximal, characteristic, complemented
15#20286322C211yesmaximal, characteristic, complemented
16#20286241C211yesmaximal, characteristic, complemented
17#20286236C211yesmaximal, characteristic, complemented
18#20285385C211yesmaximal, characteristic, complemented
19#20285377C211yesmaximal, characteristic, complemented
20#20285279C211yesmaximal, characteristic, complemented
21#20284929C211yesmaximal, characteristic, complemented
22#20284923C211yesmaximal, characteristic, complemented
23#20284899C211yesmaximal, characteristic, complemented
24#20284893C211yesmaximal, characteristic, complemented
25#20284824C211yesmaximal, characteristic, complemented
26#20284818C211yesmaximal, characteristic, complemented
27#20283691C211yesmaximal, characteristic, complemented
28#20283547C211yesmaximal, characteristic, complemented
29#20283543C211yesmaximal, characteristic, complemented
30C4×#13133237C211yesmaximal, characteristic, complemented
31C53×#3521C211yesmaximal, characteristic, complemented
32C2×#13133243C2211yescharacteristic
33C2×#13133242C2211yescharacteristic
34C2×#13133237C2211yescharacteristic
35#16811346C2211yescharacteristic, complemented
36#16811343C2211yescharacteristic, complemented
37#16811333C2211yescharacteristic, complemented
38#16811319C2211yescharacteristic
39#16811318—21no—
40#16811313C2211yescharacteristic
41#16811305—21no—
42#16811303—21no—
43#16811301—21no—
44#16811278C2211yescharacteristic
45#16811269C2211yescharacteristic
46#16811269C2211yescharacteristic, complemented
47#16811244C2211yescharacteristic
48#16811235C2211yescharacteristic, complemented
49#16811219—21no—
50#16811205—21no—
51#16811157C2211yescharacteristic, complemented
52#16811156—21no—
53#126×D53—21no—
54#16811103C2211yescharacteristic
55#16811097C2211yescharacteristic, complemented
56C4×#11719945C2211yescharacteristic, complemented
57#16811033C2211yescharacteristic, complemented
58#16811029C2211yescharacteristic, complemented
59#16811022C2211yescharacteristic, complemented
60#16811018C2211yescharacteristic, complemented
61#16811015C2211yescharacteristic, complemented
62#16811005C2211yescharacteristic
63#16810980C2211yescharacteristic, complemented
64#16810980C2211yescharacteristic, complemented
65#16810977C2211yescharacteristic, complemented
66#16810977C2211yescharacteristic, complemented
67#16810975C2211yescharacteristic, complemented
68#16810973C2211yescharacteristic, complemented
69#16810964C2211yescharacteristic, complemented
70#16810964C2211yescharacteristic, complemented
71#16810961C2211yescharacteristic, complemented
72#16810961C2211yescharacteristic, complemented
73#16810958C2211yescharacteristic, complemented
74#16810956C2211yescharacteristic, complemented
75#16810953C2211yescharacteristic, complemented
76#16810951C2211yescharacteristic, complemented
77#16810947C2211yescharacteristic
78#16810947C2211yescharacteristic, complemented
79#16810944C2211yescharacteristic
80#16810944C2211yescharacteristic, complemented
81#16810930C2211yescharacteristic, complemented
82#16810930C2211yescharacteristic, complemented
83#16810927C2211yescharacteristic, complemented
84#16810927C2211yescharacteristic, complemented
85#16810923C2211yescharacteristic, complemented
86#16810923C2211yescharacteristic, complemented
87#16810920C2211yescharacteristic, complemented
88#16810920C2211yescharacteristic, complemented
89#16810913C2211yescharacteristic, complemented
90#16810910C2211yescharacteristic, complemented
91#16810903C2211yescharacteristic, complemented
92#16810900C2211yescharacteristic, complemented
93#16810879C2211yescharacteristic, complemented
94#16810879C2211yescharacteristic, complemented
95#16810871C2211yescharacteristic
96#16810867C2211yescharacteristic
97#16810862C2211yescharacteristic, complemented
98#16810862C2211yescharacteristic, complemented
99#16810862C2211yescharacteristic, complemented
100#16810857C2211yescharacteristic
101#16810854C2211yescharacteristic
102#16810854C2211yescharacteristic, complemented
103#16810850C2211yescharacteristic
104#16810850C2211yescharacteristic, complemented
105#16810845C2211yescharacteristic, complemented
106#16810842C2211yescharacteristic, complemented
107#16810838C2211yescharacteristic
108#16810838C2211yescharacteristic
109#16810838C2211yescharacteristic
110#16810835C2211yescharacteristic
111#16810835C2211yescharacteristic
112#16810835C2211yescharacteristic
113#16810833C2211yescharacteristic, complemented
114#16810830C2211yescharacteristic, complemented
115#16810828C2211yescharacteristic, complemented
116#16810825C2211yescharacteristic, complemented
117#16810785C2211yescharacteristic
118#16810785C2211yescharacteristic
119#16810785C2211yescharacteristic, complemented
120#16810783C2211yescharacteristic
121#16810783C2211yescharacteristic
122#16810783C2211yescharacteristic, complemented
123#16810774C2211yescharacteristic, complemented
124#16810773C2211yescharacteristic, complemented
125#16810768C2211yescharacteristic
126#16810766C2211yescharacteristic
127#16810757C2211yescharacteristic
128#16810756C2211yescharacteristic
129#16810754C2211yescharacteristic, complemented
130Q8×#88322C2211yescharacteristic, complemented
131#16810733C2211yescharacteristic
132#16810733C2211yescharacteristic
133#16810733C2211yescharacteristic
134#16810733C2211yescharacteristic
135#16810728C2211yescharacteristic, complemented
136#16810728C2211yescharacteristic, complemented
137#16810723C2211yescharacteristic, complemented
138#16810723C2211yescharacteristic, complemented
139#16810723C2211yescharacteristic, complemented
140#16810721C2211yescharacteristic, complemented
141#16810721C2211yescharacteristic, complemented
142#16810721C2211yescharacteristic, complemented
143C4×#11719925C2211yescharacteristic, complemented
144C4×#11719925C2211yescharacteristic, complemented
145C4×#11719925C2211yescharacteristic, complemented
146C4×#11719924C2211yescharacteristic, complemented
147C4×#11719924C2211yescharacteristic, complemented
148C4×#11719924C2211yescharacteristic, complemented
149C4×#11719924C2211yescharacteristic, complemented
150C4×#11719923C2211yescharacteristic, complemented
151C4×#11719923C2211yescharacteristic, complemented
152C4×#11719923C2211yescharacteristic, complemented
153C4×#11719923C2211yescharacteristic, complemented
154C4×#11719922C2211yescharacteristic
155C4×#11719922C2211yescharacteristic
156C4×#11719922C2211yescharacteristic
157C4×#11719922C2211yescharacteristic
158C4×#11719922C2211yescharacteristic
159#16810701C2211yescharacteristic
160#16810695C2211yescharacteristic, complemented
161#16810695C2211yescharacteristic, complemented
162D4×#88322C2211yescharacteristic
163D4×#88322C2211yescharacteristic, complemented
164D4×#88322C2211yescharacteristic, complemented
165#16810684C2211yescharacteristic, complemented
166#16810684C2211yescharacteristic, complemented
167#16810680C2211yescharacteristic, complemented
168#16810666C2211yescharacteristic, complemented
169#16810663C2211yescharacteristic, complemented
170#16810659C2211yescharacteristic, complemented
171#16810619C2211yescharacteristic
172#16810619C2211yescharacteristic, complemented
173#16810617C2211yescharacteristic
174#16810617C2211yescharacteristic, complemented
175C2×#13133138C2211yescharacteristic, complemented
176C2×#13133137C2211yescharacteristic, complemented
177#16810579C2211yescharacteristic, complemented
178#16810579C2211yescharacteristic, complemented
179C2×C4×#88322C2211yescharacteristic, complemented
180C53×#556C2211yescharacteristic, complemented
181C53×#556C2211yescharacteristic, complemented
182C53×#554C2211yescharacteristic, complemented
183C53×#553—21no—
184C53×#553C2211yescharacteristic
185C53×#552—21no—
186C53×#552C2211yescharacteristic
187C53×#551—21no—
188C53×#551—21no—
189C53×#547C2211yescharacteristic
190C53×#546C2211yescharacteristic
191C53×#546C2211yescharacteristic, complemented
192C53×#542C2211yescharacteristic
193C53×#541C2211yescharacteristic, complemented
194C53×#539—21no—
195C53×#538—21no—
196C53×#529—21no—
197C53×#529C2211yescharacteristic
198C53×#529C2211yescharacteristic, complemented
199C2×#126×C53—21no—
200C53×#520C2211yescharacteristic
201C53×#518C2211yescharacteristic, complemented
202C4×#41×C53C2211yescharacteristic, complemented
203C2×#11719945C2311yescharacteristic
204C2×#11719945C2311yescharacteristic
205C22×D212C2311yescharacteristic
206#13133243—24no—
207#13133242—24no—
208#13133237—24no—
209C2×#11719925C2311yescharacteristic
210C2×#11719925C2311yescharacteristic
211C2×#11719925C2311yescharacteristic
212C2×#11719925C2311yescharacteristic
213C2×#11719923C2311yescharacteristic
214C2×#11719923C2311yescharacteristic
215C2×#11719923C2311yescharacteristic
216C2×#11719923C2311yescharacteristic
217C2×#11719924C2311yescharacteristic
218C2×#11719924C2311yescharacteristic
219C2×#11719924C2311yescharacteristic
220C2×#11719924C2311yescharacteristic
221C2×#11719922C2311yescharacteristic
222C2×#11719922C2311yescharacteristic
223C2×#11719922C2311yescharacteristic
224C2×#11719922C2311yescharacteristic
225C2×#11719917C2311yescharacteristic
226C2×#11719917C2311yescharacteristic
227C22×#88322C2311yescharacteristic
228C22×#88322C2311yescharacteristic
229C22×#88322C2311yescharacteristic
230C22×#88322C2311yescharacteristic
231#13133217C2311yescharacteristic
232#13133217C2311yescharacteristic
233#13133212—21no—
234#13133212—21no—
235#13133212—21no—
236#13133212—21no—
237#13133211—21no—
238#13133210—21no—
239#13133210—21no—
240#13133210—21no—
241#13133210—21no—
242#13133210—21no—
243#13133209C2311yescharacteristic
244#13133209C2311yescharacteristic
245#13133207—21no—
246#13133207—21no—
247#13133207—21no—
248#13133205C2311yescharacteristic
249#13133205C2311yescharacteristic
250#13133204—21no—
251#13133203—21no—
252#13133202—21no—
253#13133202—21no—
254#13133200—21no—
255#13133199—21no—
256#13133199—21no—
257#13133199—21no—
258#13133199—21no—
259#13133198—21no—
260#13133196C2311yescharacteristic
261#13133196C2311yescharacteristic
262#13133196C2311yescharacteristic
263#13133196C2311yescharacteristic
264#13133195—21no—
265#13133195—21no—
266#13133195—21no—
267#13133193—21no—
268#13133193—21no—
269#13133191C2311yescharacteristic
270#13133191C2311yescharacteristic
271#13133190—21no—
272#13133190—21no—
273#13133189—21no—
274#13133188—21no—
275#13133185—21no—
276#13133185—21no—
277C4×Dic106C2311yescharacteristic
278C4×Dic106C2311yescharacteristic
279C4×Dic106C2311yescharacteristic
280C4×Dic106C2311yescharacteristic
281#13133182—21no—
282C4×D212C2311yescharacteristic
283C4×D212C2311yescharacteristic
284C4×D212C2311yescharacteristic
285C4×D212C2311yescharacteristic
286C4×D212C2311yescharacteristic
287C4×D212C2311yescharacteristic
288#13133179—21no—
289#13133179—21no—
290C4×C22⋊D53—21no—
291C4×C22⋊D53—21no—
292C4×C22⋊D53—21no—
293#13133177—21no—
294#13133177—21no—
295#13133177—21no—
296#13133176C2311yescharacteristic
297#13133176C2311yescharacteristic
298#13133175—21no—
299#13133175—21no—
300#13133174—21no—
301#13133174—21no—
302#13133173—21no—
303C2×C4⋊Dic53C2311yescharacteristic
304C4⋊C4×D53—21no—
305C4⋊C4×D53—21no—
306C4⋊C4×D53—21no—
307C22⋊C4×D53—21no—
308C22⋊C4×D53—21no—
309C22⋊C4×D53—21no—
310C22⋊C4×D53—21no—
311C42×D53—21no—
312#13133150C2311yescharacteristic
313#13133150C2311yescharacteristic
314#13133150C2311yescharacteristic
315#13133150C2311yescharacteristic
316#13133150C2311yescharacteristic
317#13133150C2311yescharacteristic
318#13133150C2311yescharacteristic
319#13133150C2311yescharacteristic
320#13133148C2311yescharacteristic
321#13133148C2311yescharacteristic
322#13133148C2311yescharacteristic
323#13133148C2311yescharacteristic
324#13133148C2311yescharacteristic
325#13133148C2311yescharacteristic
326#13133148C2311yescharacteristic
327#13133148C2311yescharacteristic
328C4⋊#88322C2311yescharacteristic
329C4⋊#88322C2311yescharacteristic
330C4⋊#88322C2311yescharacteristic
331C4⋊#88322C2311yescharacteristic
332C4⋊#88322C2311yescharacteristic
333C4⋊#88322C2311yescharacteristic
334#13133141C2311yescharacteristic
335#13133141C2311yescharacteristic
336#13133141C2311yescharacteristic
337#13133141C2311yescharacteristic
338#13133141C2311yescharacteristic
339#13133141C2311yescharacteristic
340#13133141C2311yescharacteristic
341#13133141C2311yescharacteristic
342#13133140C2311yescharacteristic
343#13133140C2311yescharacteristic
344#13133140C2311yescharacteristic
345#13133140C2311yescharacteristic
346#13133140C2311yescharacteristic
347#13133140C2311yescharacteristic
348#13133140C2311yescharacteristic
349#13133140C2311yescharacteristic
350#13133138C2311yescharacteristic
351#13133138C2311yescharacteristic
352#13133138C2311yescharacteristic
353#13133138C2311yescharacteristic
354#13133138C2311yescharacteristic
355#13133138C2311yescharacteristic
356#13133138C2311yescharacteristic
357#13133138C2311yescharacteristic
358#13133137C2311yescharacteristic
359#13133137C2311yescharacteristic
360#13133137C2311yescharacteristic
361#13133137C2311yescharacteristic
362#13133137C2311yescharacteristic
363#13133137C2311yescharacteristic
364#13133137C2311yescharacteristic
365#13133137C2311yescharacteristic
366C22⋊#88322C2311yescharacteristic
367C22⋊#88322C2311yescharacteristic
368C22⋊#88322C2311yescharacteristic
369C22⋊#88322C2311yescharacteristic
370C22⋊#88322C2311yescharacteristic
371C22⋊#88322C2311yescharacteristic
372#13133128C2311yescharacteristic
373#13133128C2311yescharacteristic
374#13133128C2311yescharacteristic
375#13133128C2311yescharacteristic
376C4×#88322C2311yescharacteristic
377C4×#88322C2311yescharacteristic
378C4×#88322C2311yescharacteristic
379C4×#88322C2311yescharacteristic
380C4×#88322C2311yescharacteristic
381C4×#88322C2311yescharacteristic
382C2×#41×C53C2311yescharacteristic
383C2×#41×C53C2311yescharacteristic
384C22×D4×C53C2311yescharacteristic
385C4⋊Q8×C53C2311yescharacteristic
386C4⋊Q8×C53C2311yescharacteristic
387#126×C53—21no—
388#126×C53—21no—
389#126×C53—21no—
390#126×C53—21no—
391#126×C53—21no—
392#126×C53—21no—
393#126×C53—21no—
394#126×C53—21no—
395#126×C53—21no—
396#126×C53—21no—
397#126×C53D411yescharacteristic
398#126×C53D411yescharacteristic
399#125×C53—21no—
400#125×C53—21no—
401#125×C53—21no—
402#125×C53D411yescharacteristic
403#125×C53C2311yescharacteristic
404#125×C53C2311yescharacteristic
405#124×C53—21no—
406#124×C53—21no—
407#124×C53D411yescharacteristic
408#124×C53C2311yescharacteristic
409#124×C53C2311yescharacteristic
410#123×C53—21no—
411#123×C53—21no—
412#123×C53—21no—
413#123×C53—21no—
414#123×C53—21no—
415#123×C53—21no—
416#123×C53—21no—
417#123×C53—21no—
418#123×C53D411yescharacteristic
419#123×C53D411yescharacteristic
420C22⋊Q8×C53—21no—
421C22⋊Q8×C53—21no—
422C22⋊Q8×C53—21no—
423C22⋊Q8×C53—21no—
424C22⋊Q8×C53—21no—
425C22⋊Q8×C53D411yescharacteristic
426C22⋊Q8×C53C2311yescharacteristic
427C22⋊Q8×C53C2311yescharacteristic
428C22⋊Q8×C53C2311yescharacteristic
429C22⋊Q8×C53C2311yescharacteristic
430#121×C53—21no—
431#121×C53—21no—
432#121×C53—21no—
433#121×C53—21no—
434#121×C53D411yescharacteristic
435#121×C53C2311yescharacteristic
436#121×C53C2311yescharacteristic
437#120×C53—21no—
438#120×C53—21no—
439C4×Q8×C53—21no—
440C4×Q8×C53C2311yescharacteristic
441C4×Q8×C53C2311yescharacteristic
442C4×Q8×C53C2311yescharacteristic
443C4×Q8×C53C2311yescharacteristic
444C4×Q8×C53C2311yescharacteristic
445C4×D4×C53—21no—
446C4×D4×C53—21no—
447C4×D4×C53—21no—
448C4×D4×C53—21no—
449C4×D4×C53—21no—
450C4×D4×C53—21no—
451C4×D4×C53—21no—
452C4×D4×C53—21no—
453C4×D4×C53C2311yescharacteristic
454C4×D4×C53C2311yescharacteristic
455C4×D4×C53C2311yescharacteristic
456C4×D4×C53C2311yescharacteristic
457C4×D4×C53C2311yescharacteristic
458C4×D4×C53C2311yescharacteristic
459C4×D4×C53C2311yescharacteristic
460C4×D4×C53C2311yescharacteristic
461C4×D4×C53C2311yescharacteristic
462#117×C53—21no—
463#117×C53—21no—
464#117×C53—21no—
465#117×C53—21no—
466#117×C53—21no—
467#117×C53C2311yescharacteristic
468#117×C53C2311yescharacteristic
469#117×C53C2311yescharacteristic
470#117×C53C2311yescharacteristic
471C2×C4⋊C4×C53—21no—
472C2×C4⋊C4×C53—21no—
473C2×C4⋊C4×C53—21no—
474C2×C4⋊C4×C53C2311yescharacteristic
475C2×C22⋊C4×C53—21no—
476C2×C22⋊C4×C53—21no—
477C2×C22⋊C4×C53—21no—
478C2×C22⋊C4×C53—21no—
479C2×C42×C53—21no—
480C2×C42×C53C2311yescharacteristic
481C24×C53—21no—
482C23×D53—21no—
483#41×C53—22no—
484#41×C53—22no—
485#41×C53—41no—
486#41×C53—41no—
487C2×Q8×C53—21no—
488C2×Q8×C53C2×D411yescharacteristic
489C2×Q8×C53C2411yescharacteristic
490C2×Q8×C53C2411yescharacteristic
491C2×D4×C53—22no—
492C2×D4×C53—21no—
493C2×D4×C53—21no—
494C2×D4×C53—21no—
495C2×D4×C53—21no—
496C2×D4×C53—21no—
497C2×D4×C53—41no—
498C2×D4×C53C2×D411yescharacteristic
499C2×D4×C53C2×D411yescharacteristic
500C2×D4×C53C2×D411yescharacteristic
501C2×D4×C53C2411yescharacteristic
502C2×D4×C53C2411yescharacteristic
503C22×C4×C53—21no—
504C22×C4×C53—21no—
505C22×C4×C53—21no—
506C22×C4×C53—21no—
507C22×C4×C53—21no—
508C22×C4×C53—21no—
509C22×C4×C53—21no—
510C22×C4×C53—21no—
511C22×C4×C53—21no—
512C22×C4×C53C2×D411yescharacteristic
513C22×C4×C53C2×D411yescharacteristic
514C22×C4×C53C2411yescharacteristic
515C22×C4×C53C2411yescharacteristic
516C22×C4×C53C2411yescharacteristic
517C2×C22⋊D53—21no—
518C2×C22⋊D53—21no—
519C2×C22⋊D53—21no—
520C2×C22⋊D53—21no—
521C22×Dic53—21no—
522#11719945—22no—
523#11719945—22no—
524#11719945—41no—
525#11719945—41no—
526C2×D212—22no—
527C2×D212—21no—
528C2×D212—41no—
529C2×D212C2411yescharacteristic
530C2×D212C2411yescharacteristic
531C2×C4×D53—21no—
532C2×C4×D53—21no—
533C2×C4×D53—21no—
534C2×C4×D53—21no—
535C2×C4×D53—21no—
536C2×C4×D53—21no—
537C2×C4×D53—21no—
538C2×C4×D53—21no—
539C2×Dic106—21no—
540C2×Dic106C2411yescharacteristic
541C2×Dic106C2411yescharacteristic
542C4⋊C4×C53—21no—
543C4⋊C4×C53—21no—
544C4⋊C4×C53—21no—
545C4⋊C4×C53—21no—
546C4⋊C4×C53—21no—
547C4⋊C4×C53—21no—
548C4⋊C4×C53—21no—
549C4⋊C4×C53—21no—
550C4⋊C4×C53—21no—
551C4⋊C4×C53—21no—
552C4⋊C4×C53—21no—
553C4⋊C4×C53—21no—
554C4⋊C4×C53—21no—
555C4⋊C4×C53—21no—
556C4⋊C4×C53—21no—
557C4⋊C4×C53—21no—
558C4⋊C4×C53C2×D411yescharacteristic
559C4⋊C4×C53C2×D411yescharacteristic
560C4⋊C4×C53C2×D411yescharacteristic
561C4⋊C4×C53C2×D411yescharacteristic
562C4⋊C4×C53C2×D411yescharacteristic
563C4⋊C4×C53C2×D411yescharacteristic
564C4⋊C4×C53C2×D411yescharacteristic
565C4⋊C4×C53C2×D411yescharacteristic
566C4⋊C4×C53C2×D411yescharacteristic
567C4⋊C4×C53C2×D411yescharacteristic
568C4⋊C4×C53C2411yescharacteristic
569C4⋊C4×C53C2411yescharacteristic
570C4⋊C4×C53C2411yescharacteristic
571C4⋊C4×C53C2411yescharacteristic
572C22⋊C4×C53—21no—
573C22⋊C4×C53—21no—
574C22⋊C4×C53—21no—
575C22⋊C4×C53—21no—
576C22⋊C4×C53—21no—
577C22⋊C4×C53—21no—
578C22⋊C4×C53—21no—
579C22⋊C4×C53—21no—
580C22⋊C4×C53—21no—
581C22⋊C4×C53—21no—
582C22⋊C4×C53—21no—
583C22⋊C4×C53—21no—
584C22⋊C4×C53—21no—
585C22⋊C4×C53—21no—
586C22⋊C4×C53—21no—
587C22⋊C4×C53—21no—
588C22⋊C4×C53—21no—
589C22⋊C4×C53—21no—
590C22⋊C4×C53C2×D411yescharacteristic
591C22⋊C4×C53C2×D411yescharacteristic
592C22⋊C4×C53C2×D411yescharacteristic
593C22⋊C4×C53C2×D411yescharacteristic
594C22⋊C4×C53C2×D411yescharacteristic
595C22⋊C4×C53C2×D411yescharacteristic
596C22⋊C4×C53C2×D411yescharacteristic
597C22⋊C4×C53C2×D411yescharacteristic
598C22⋊C4×C53C2×D411yescharacteristic
599C22⋊C4×C53C2×D411yescharacteristic
600C42×C53—21no—
601C42×C53—21no—
602C42×C53—21no—
603C42×C53—21no—
604C42×C53—21no—
605C42×C53—21no—
606C42×C53C2×D411yescharacteristic
607C42×C53C2×D411yescharacteristic
608C42×C53C2411yescharacteristic
609C42×C53C2411yescharacteristic
610C42×C53C2411yescharacteristic
611C42×C53C2411yescharacteristic
612C22⋊Dic53—21no—
613C22⋊Dic53—21no—
614C22⋊Dic53—21no—
615C22⋊Dic53—21no—
616C22⋊Dic53—21no—
617C22⋊Dic53—21no—
618#11719925—22no—
619#11719925—41no—
620#11719925—41no—
621#11719925—41no—
622#11719924—22no—
623#11719924—22no—
624#11719924—22no—
625#11719924—41no—
626#11719923—22no—
627#11719923—22no—
628#11719923—22no—
629#11719923—41no—
630#11719922—22no—
631#11719922—22no—
632#11719922—41no—
633#11719922#4114yes—
634#11719921—21no—
635#11719921—21no—
636#11719921—21no—
637#11719921—21no—
638#11719921—21no—
639#11719921—21no—
640#11719921—21no—
641#11719921—21no—
642#11719921—21no—
643#11719921—21no—
644#11719921—21no—
645#11719921—21no—
646C4⋊Dic53—21no—
647C4⋊Dic53—21no—
648C4⋊Dic53—21no—
649C4⋊Dic53—21no—
650C4⋊Dic53C2411yescharacteristic
651C4⋊Dic53C2411yescharacteristic
652C4⋊Dic53C2411yescharacteristic
653C4⋊Dic53C2411yescharacteristic
654#11719919—21no—
655#11719919—21no—
656#11719919—21no—
657#11719919—21no—
658#11719919—21no—
659#11719919—21no—
660#11719919—21no—
661#11719919—21no—
662#11719919—21no—
663#11719919—21no—
664#11719919—21no—
665#11719919—21no—
666C4×Dic53—21no—
667C4×Dic53—21no—
668C4×Dic53—21no—
669C4×Dic53—21no—
670C4×Dic53—21no—
671C4×Dic53—21no—
672#11719917—22no—
673#11719917—22no—
674C2×#88322—22no—
675C2×#88322—41no—
676C2×#88322—41no—
677C2×#88322—41no—
678C2×#88322C2411yescharacteristic
679C2×#88322C2411yescharacteristic
680C2×#88322C2411yescharacteristic
681C2×#88322C2411yescharacteristic
682C2×#88322C2411yescharacteristic
683C2×#88322C2411yescharacteristic
684C2×#88322C2411yescharacteristic
685C2×#88322C2411yescharacteristic
686C23×C53—21no—
687C23×C53—21no—
688C23×C53—42no—
689C23×C53—81no—
690C23×C53—81no—
691C23×C53C22×D411yescharacteristic
692C23×C53C22×D411yescharacteristic
693C23×C53C22×D411yescharacteristic
694C22×D53—21no—
695C22×D53—21no—
696C22×D53—42no—
697C22×D53—81no—
698C22×D53—81no—
699Q8×C53—21no—
700Q8×C53—21no—
701Q8×C53—21no—
702Q8×C53—21no—
703Q8×C53—41no—
704Q8×C53—81no—
705D4×C53—21no—
706D4×C53—21no—
707D4×C53—21no—
708D4×C53—41no—
709D4×C53—41no—
710D4×C53—41no—
711D4×C53—42no—
712D4×C53—42no—
713D4×C53—42no—
714D4×C53—81no—
715D4×C53—81no—
716D4×C53C2×#4112yes—
717C2×C4×C53—21no—
718C2×C4×C53—21no—
719C2×C4×C53—21no—
720C2×C4×C53—21no—
721C2×C4×C53—21no—
722C2×C4×C53—21no—
723C2×C4×C53—21no—
724C2×C4×C53—21no—
725C2×C4×C53—21no—
726C2×C4×C53—21no—
727C2×C4×C53—21no—
728C2×C4×C53—21no—
729C2×C4×C53—41no—
730C2×C4×C53—41no—
731C2×C4×C53—42no—
732C2×C4×C53—42no—
733C2×C4×C53—81no—
734C2×C4×C53—81no—
735C2×C4×C53—81no—
736C2×C4×C53—81no—
737C2×C4×C53—81no—
738C2×C4×C53—81no—
739C2×C4×C53—81no—
740C2×C4×C53C22×D411yescharacteristic
741C2×C4×C53C22×D411yescharacteristic
742C2×C4×C53C22×D411yescharacteristic
743C2×C4×C53C22×D411yescharacteristic
744C2×C4×C53C22×D411yescharacteristic
745C2×C4×C53C22×D411yescharacteristic
746C2×C4×C53C22×D411yescharacteristic
747C2×C4×C53C22×D411yescharacteristic
748C2×C4×C53C22×D411yescharacteristic
749C2×C4×C53C22×D411yescharacteristic
750C2×C4×C53C22×D411yescharacteristic
751C2×C4×C53C2511yescharacteristic
752C22⋊D53—42no—
753C22⋊D53—42no—
754C22⋊D53—81no—
755C22⋊D53—81no—
756C2×Dic53—21no—
757C2×Dic53—21no—
758C2×Dic53—21no—
759C2×Dic53—21no—
760C2×Dic53—21no—
761C2×Dic53—21no—
762C2×Dic53—81no—
763D212—21no—
764D212—21no—
765D212—21no—
766D212—42no—
767D212C2×#4112yes—
768C4×D53—42no—
769C4×D53—42no—
770C4×D53—81no—
771C4×D53—81no—
772C4×D53—81no—
773C4×D53—81no—
774C4×D53—81no—
775C4×D53—81no—
776Dic106—21no—
777Dic106—21no—
778Dic106—21no—
779Dic106—21no—
780Dic106—81no—
781#88322—21no—
782#88322—21no—
783#88322—21no—
784#88322—21no—
785#88322—21no—
786#88322—21no—
787#88322—21no—
788#88322C2×#4112yes—
789#61501—531nomaximal, Sylow
790C22×C53—21no—
791C22×C53—21no—
792C22×C53—21no—
793C22×C53—21no—
794C22×C53—21no—
795C22×C53—21no—
796C22×C53—21no—
797C22×C53—21no—
798C22×C53—21no—
799C22×C53—22no—
800C22×C53—41no—
801C22×C53—41no—
802C22×C53—41no—
803C22×C53—41no—
804C22×C53—41no—
805C22×C53—162no—
806C22×C53C23×D411yescharacteristic
807C2×D53—22no—
808C2×D53—41no—
809C2×D53—41no—
810C2×D53—41no—
811C2×D53—41no—
812C2×D53—41no—
813C2×D53—162no—
814C4×C53—21no—
815C4×C53—21no—
816C4×C53—21no—
817C4×C53—21no—
818C4×C53—21no—
819C4×C53—21no—
820C4×C53—21no—
821C4×C53—21no—
822C4×C53—21no—
823C4×C53—21no—
824C4×C53—21no—
825C4×C53—41no—
826C4×C53—41no—
827C4×C53—41no—
828C4×C53—41no—
829C4×C53—41no—
830C4×C53—41no—
831C4×C53C22×#4111yescharacteristic
832C4×C53#58511yescharacteristic
833Dic53—41no—
834Dic53—41no—
835Dic53—41no—
836Dic53—41no—
837Dic53—41no—
838Dic53—41no—
839#3521—531no—
840#3521D5311yescharacteristic, complemented
841#3402—531no—
842#3389—531no—
843#3360—531no—
844#3360—531no—
845#3352—531no—
846#3350—531no—
847#3350—531no—
848#3302—531no—
849#3302—531no—
850#3297—531no—
851#3297—531no—
852#3296—531no—
853#3296—531no—
854#3273—531no—
855#3267—531no—
856#3267—531no—
857#3178—531no—
858#3178—531no—
859#3168—531no—
860#3120—531no—
861#3120—531no—
862#3118—531no—
863#3118—531no—
864#3111—531no—
865#3111—531no—
866#2966—531no—
867#2946—531no—
868#2946—531no—
869C4×#135—531no—
870C2×C53—41no—
871C2×C53—41no—
872C2×C53—41no—
873C2×C53—42no—
874C2×C53—81no—
875C2×C53D4×#4111yescharacteristic
876C2×C53#358411yescharacteristic
877C2×C53#358411yescharacteristic
878D53—42no—
879D53—81no—
880C2×AGL(1,ℤ/8)—531no—
881C2×AGL(1,ℤ/8)—531no—
882C2×#135—531no—
883#556—531no—
884#556—531no—
885#556C2×D5311yescharacteristic, complemented
886#556C2×D5311yescharacteristic, complemented
887#554—531no—
888#554C2×D5311yescharacteristic, complemented
889#553—21no—
890#553—531no—
891#553—1061no—
892#553C2×D5311yescharacteristic
893#552—21no—
894#552—531no—
895#552—1061no—
896#552C2×D5311yescharacteristic
897#551—21no—
898#551—21no—
899#551—1061no—
900#551—1061no—
901#547—531no—
902#547C2×D5311yescharacteristic
903#546—531no—
904#546—531no—
905#546C2×D5311yescharacteristic
906#546C2×D5311yescharacteristic, complemented
907#542—531no—
908#542C2×D5311yescharacteristic
909#541—531no—
910#541C2×D5311yescharacteristic, complemented
911#539—21no—
912#539—1061no—
913#538—21no—
914#538—1061no—
915#529—21no—
916#529—531no—
917#529—1061no—
918#529C2×D5311yescharacteristic
919#529C2×D5311yescharacteristic, complemented
920C2×#126—21no—
921C2×#126—1061no—
922#520—531no—
923#520C2×D5311yescharacteristic
924#518—531no—
925#518C2×D5311yescharacteristic, complemented
926C4×#41—531no—
927C4×#41C2×D5311yescharacteristic, complemented
928#501—531no—
929#501—531no—
930#499—531no—
931#497—531no—
932#497—531no—
933#495—531no—
934#488—531no—
935#488—531no—
936#488—531no—
937#488—531no—
938#487—531no—
939#487—531no—
940#485—531no—
941#485—531no—
942#485—531no—
943#485—531no—
944#484—531no—
945#484—531no—
946#483—531no—
947#483—531no—
948#482—531no—
949#482—531no—
950#482—531no—
951#482—531no—
952#479—531no—
953#479—531no—
954#479—531no—
955#479—531no—
956#478—531no—
957#478—531no—
958#478—531no—
959#478—531no—
960#476—531no—
961#476—531no—
962#474—531no—
963#474—531no—
964#470—531no—
965#470—531no—
966#468—531no—
967#468—531no—
968#467—531no—
969#467—531no—
970#467—531no—
971#466—531no—
972#465—531no—
973#465—531no—
974#465—531no—
975#465—531no—
976#464—531no—
977#464—531no—
978#463—531no—
979#463—531no—
980#463—531no—
981#463—531no—
982#463—531no—
983#463—531no—
984#462—531no—
985#462—531no—
986#461—531no—
987#461—531no—
988#452—531no—
989#452—531no—
990#452—531no—
991#452—531no—
992#452—531no—
993#452—531no—
994#450—531no—
995#450—531no—
996#449—531no—
997#449—531no—
998#447—531no—
999#447—531no—
1000#446—531no—
1001C8×Q8—531no—
1002#442—531no—
1003#442—531no—
1004#442—531no—
1005#442—531no—
1006#441—531no—
1007#441—531no—
1008#440—531no—
1009#440—531no—
1010#440—531no—
1011#440—531no—
1012#440—531no—
1013#440—531no—
1014C4×Q16—531no—
1015C4×Q16—531no—
1016C4×Q16—531no—
1017C4×SD16—531no—
1018C4×SD16—531no—
1019C4×SD16—531no—
1020C4×SD16—531no—
1021C4×SD16—531no—
1022C4×SD16—531no—
1023C4×SD16—531no—
1024C4×SD16—531no—
1025C4×D8—531no—
1026C4×D8—531no—
1027C4×D8—531no—
1028C4×D8—531no—
1029C4×D8—531no—
1030#436—531no—
1031#435—531no—
1032#435—531no—
1033C8×D4—531no—
1034C8×D4—531no—
1035C8×D4—531no—
1036#433—531no—
1037#433—531no—
1038#432—531no—
1039#428—531no—
1040#428—531no—
1041#427—531no—
1042#416—531no—
1043#416—531no—
1044#416—531no—
1045#416—531no—
1046C2×#102—531no—
1047C2×#102—531no—
1048#405—531no—
1049#405—531no—
1050C2×C4×C8—531no—
1051C53#6150111yescharacteristic, complemented, Sylow
1052C2×#41—531no—
1053C2×#41—531no—
1054C2×#41C22×D5311yescharacteristic
1055C2×#41C22×D5311yescharacteristic
1056C22×D4—531no—
1057C22×D4C22×D5311yescharacteristic
1058AGL(1,ℤ/8)—1064no—
1059AGL(1,ℤ/8)—1064no—
1060#135—1064no—
1061C2×Q16—531no—
1062C2×Q16—531no—
1063C2×Q16—531no—
1064C2×Q16—531no—
1065C2×SD16—531no—
1066C2×SD16—531no—
1067C2×SD16—531no—
1068C2×SD16—531no—
1069C2×SD16—531no—
1070C2×SD16—531no—
1071C2×SD16—531no—
1072C2×SD16—531no—
1073C2×D8—531no—
1074C2×D8—531no—
1075C2×D8—531no—
1076C2×D8—531no—
1077C2×M16—531no—
1078C2×M16—531no—
1079C22×C8—531no—
1080C22×C8—531no—
1081C22×C8—531no—
1082C22×C8—531no—
1083C4⋊Q8—531no—
1084C4⋊Q8—531no—
1085C4⋊Q8C22×D5311yescharacteristic
1086C4⋊Q8C22×D5311yescharacteristic
1087#126—21no—
1088#126—21no—
1089#126—21no—
1090#126—21no—
1091#126—21no—
1092#126—21no—
1093#126—21no—
1094#126—21no—
1095#126—21no—
1096#126—21no—
1097#126—1061no—
1098#126—1061no—
1099#126—1061no—
1100#126—1061no—
1101#126—1061no—
1102#126—1061no—
1103#126—1061no—
1104#126—1061no—
1105#126—1061no—
1106#126—1061no—
1107#126C22⋊D5311yescharacteristic
1108#126C22⋊D5311yescharacteristic
1109#125—21no—
1110#125—21no—
1111#125—21no—
1112#125—531no—
1113#125—531no—
1114#125—1061no—
1115#125—1061no—
1116#125—1061no—
1117#125C22⋊D5311yescharacteristic
1118#125C22×D5311yescharacteristic
1119#125C22×D5311yescharacteristic
1120#124—21no—
1121#124—21no—
1122#124—531no—
1123#124—531no—
1124#124—1061no—
1125#124—1061no—
1126#124C22⋊D5311yescharacteristic
1127#124C22×D5311yescharacteristic
1128#124C22×D5311yescharacteristic
1129#123—21no—
1130#123—21no—
1131#123—21no—
1132#123—21no—
1133#123—21no—
1134#123—21no—
1135#123—21no—
1136#123—21no—
1137#123—1061no—
1138#123—1061no—
1139#123—1061no—
1140#123—1061no—
1141#123—1061no—
1142#123—1061no—
1143#123—1061no—
1144#123—1061no—
1145#123C22⋊D5311yescharacteristic
1146#123C22⋊D5311yescharacteristic
1147C22⋊Q8—21no—
1148C22⋊Q8—21no—
1149C22⋊Q8—21no—
1150C22⋊Q8—21no—
1151C22⋊Q8—21no—
1152C22⋊Q8—531no—
1153C22⋊Q8—531no—
1154C22⋊Q8—531no—
1155C22⋊Q8—531no—
1156C22⋊Q8—1061no—
1157C22⋊Q8—1061no—
1158C22⋊Q8—1061no—
1159C22⋊Q8—1061no—
1160C22⋊Q8—1061no—
1161C22⋊Q8C22⋊D5311yescharacteristic
1162C22⋊Q8C22×D5311yescharacteristic
1163C22⋊Q8C22×D5311yescharacteristic
1164C22⋊Q8C22×D5311yescharacteristic
1165C22⋊Q8C22×D5311yescharacteristic
1166#121—21no—
1167#121—21no—
1168#121—21no—
1169#121—21no—
1170#121—531no—
1171#121—531no—
1172#121—1061no—
1173#121—1061no—
1174#121—1061no—
1175#121—1061no—
1176#121C22⋊D5311yescharacteristic
1177#121C22×D5311yescharacteristic
1178#121C22×D5311yescharacteristic
1179#120—21no—
1180#120—21no—
1181#120—1061no—
1182#120—1061no—
1183C4×Q8—21no—
1184C4×Q8—531no—
1185C4×Q8—531no—
1186C4×Q8—531no—
1187C4×Q8—531no—
1188C4×Q8—1061no—
1189C4×Q8C22×D5311yescharacteristic
1190C4×Q8C22×D5311yescharacteristic
1191C4×Q8C22×D5311yescharacteristic
1192C4×Q8C22×D5311yescharacteristic
1193C4×Q8C22×D5311yescharacteristic
1194C4×D4—21no—
1195C4×D4—21no—
1196C4×D4—21no—
1197C4×D4—21no—
1198C4×D4—21no—
1199C4×D4—21no—
1200C4×D4—21no—
1201C4×D4—21no—
1202C4×D4—531no—
1203C4×D4—531no—
1204C4×D4—531no—
1205C4×D4—531no—
1206C4×D4—531no—
1207C4×D4—531no—
1208C4×D4—1061no—
1209C4×D4—1061no—
1210C4×D4—1061no—
1211C4×D4—1061no—
1212C4×D4—1061no—
1213C4×D4—1061no—
1214C4×D4—1061no—
1215C4×D4—1061no—
1216C4×D4C22×D5311yescharacteristic
1217C4×D4C22×D5311yescharacteristic
1218C4×D4C22×D5311yescharacteristic
1219C4×D4C22×D5311yescharacteristic
1220C4×D4C22×D5311yescharacteristic
1221C4×D4C22×D5311yescharacteristic
1222C4×D4C22×D5311yescharacteristic
1223C4×D4C22×D5311yescharacteristic
1224C4×D4C22×D5311yescharacteristic
1225#117—21no—
1226#117—21no—
1227#117—21no—
1228#117—21no—
1229#117—21no—
1230#117—531no—
1231#117—531no—
1232#117—1061no—
1233#117—1061no—
1234#117—1061no—
1235#117—1061no—
1236#117—1061no—
1237#117C22×D5311yescharacteristic
1238#117C22×D5311yescharacteristic
1239#117C22×D5311yescharacteristic
1240#117C22×D5311yescharacteristic
1241C2×C4⋊C4—21no—
1242C2×C4⋊C4—21no—
1243C2×C4⋊C4—21no—
1244C2×C4⋊C4—531no—
1245C2×C4⋊C4—1061no—
1246C2×C4⋊C4—1061no—
1247C2×C4⋊C4—1061no—
1248C2×C4⋊C4C22×D5311yescharacteristic
1249C2×C22⋊C4—21no—
1250C2×C22⋊C4—21no—
1251C2×C22⋊C4—21no—
1252C2×C22⋊C4—21no—
1253C2×C22⋊C4—1061no—
1254C2×C22⋊C4—1061no—
1255C2×C22⋊C4—1061no—
1256C2×C22⋊C4—1061no—
1257C2×C42—21no—
1258C2×C42—1061no—
1259C2×C42C22×D5311yescharacteristic
1260#107—531no—
1261#107—531no—
1262#107—531no—
1263#107—531no—
1264#107—531no—
1265#107—531no—
1266#107—531no—
1267#107—531no—
1268#106—531no—
1269#106—531no—
1270#106—531no—
1271#106—531no—
1272#106—531no—
1273#106—531no—
1274#106—531no—
1275#106—531no—
1276C4⋊C8—531no—
1277C4⋊C8—531no—
1278C4⋊C8—531no—
1279C4⋊C8—531no—
1280C4⋊C8—531no—
1281C4⋊C8—531no—
1282#103—531no—
1283#103—531no—
1284#103—531no—
1285#103—531no—
1286#103—531no—
1287#103—531no—
1288#103—531no—
1289#103—531no—
1290#103—531no—
1291#103—531no—
1292#103—531no—
1293#103—531no—
1294#103—531no—
1295#103—531no—
1296#103—531no—
1297#103—531no—
1298#102—531no—
1299#102—531no—
1300#102—531no—
1301#102—531no—
1302#102—531no—
1303#102—531no—
1304#102—531no—
1305#102—531no—
1306#102—531no—
1307#102—531no—
1308#102—531no—
1309#102—531no—
1310#102—531no—
1311#102—531no—
1312#102—531no—
1313#102—531no—
1314C22⋊C8—531no—
1315C22⋊C8—531no—
1316C22⋊C8—531no—
1317C22⋊C8—531no—
1318C22⋊C8—531no—
1319C22⋊C8—531no—
1320#97—531no—
1321#97—531no—
1322#97—531no—
1323#97—531no—
1324C4×C8—531no—
1325C4×C8—531no—
1326C4×C8—531no—
1327C4×C8—531no—
1328C4×C8—531no—
1329C4×C8—531no—
1330C24—21no—
1331C24—1061no—
1332#41—22no—
1333#41—22no—
1334#41—41no—
1335#41—41no—
1336#41—1062no—
1337#41—1062no—
1338#41—2121no—
1339#41—2121no—
1340C2×Q8—21no—
1341C2×Q8—531no—
1342C2×Q8—531no—
1343C2×Q8—1061no—
1344C2×Q8C2×C22⋊D5311yescharacteristic
1345C2×Q8C23×D5311yescharacteristic
1346C2×Q8C23×D5311yescharacteristic
1347C2×D4—22no—
1348C2×D4—21no—
1349C2×D4—21no—
1350C2×D4—21no—
1351C2×D4—21no—
1352C2×D4—21no—
1353C2×D4—41no—
1354C2×D4—531no—
1355C2×D4—531no—
1356C2×D4—1062no—
1357C2×D4—1061no—
1358C2×D4—1061no—
1359C2×D4—1061no—
1360C2×D4—1061no—
1361C2×D4—1061no—
1362C2×D4—2121no—
1363C2×D4C2×C22⋊D5311yescharacteristic
1364C2×D4C2×C22⋊D5311yescharacteristic
1365C2×D4C2×C22⋊D5311yescharacteristic
1366C2×D4C23×D5311yescharacteristic
1367C2×D4C23×D5311yescharacteristic
1368C22×C4—21no—
1369C22×C4—21no—
1370C22×C4—21no—
1371C22×C4—21no—
1372C22×C4—21no—
1373C22×C4—21no—
1374C22×C4—21no—
1375C22×C4—21no—
1376C22×C4—21no—
1377C22×C4—1061no—
1378C22×C4—1061no—
1379C22×C4—1061no—
1380C22×C4—1061no—
1381C22×C4—1061no—
1382C22×C4—1061no—
1383C22×C4—1061no—
1384C22×C4—1061no—
1385C22×C4—1061no—
1386C22×C4C2×C22⋊D5311yescharacteristic
1387C22×C4C2×C22⋊D5311yescharacteristic
1388C22×C4C23×D5311yescharacteristic
1389C22×C4C23×D5311yescharacteristic
1390C22×C4C23×D5311yescharacteristic
1391Q16—1062no—
1392Q16—2121no—
1393Q16—2121no—
1394Q16—2121no—
1395SD16—1062no—
1396SD16—1062no—
1397SD16—1062no—
1398SD16—1062no—
1399SD16—1062no—
1400SD16—1062no—
1401SD16—2121no—
1402SD16—2121no—
1403D8—534no—
1404D8—1062no—
1405D8—1062no—
1406D8—2121no—
1407M16—1062no—
1408M16—1062no—
1409C2×C8—531no—
1410C2×C8—531no—
1411C2×C8—531no—
1412C2×C8—531no—
1413C2×C8—531no—
1414C2×C8—531no—
1415C2×C8—531no—
1416C2×C8—531no—
1417C2×C8—1062no—
1418C2×C8—2121no—
1419C2×C8—2121no—
1420C2×C8—2121no—
1421C4⋊C4—21no—
1422C4⋊C4—21no—
1423C4⋊C4—21no—
1424C4⋊C4—21no—
1425C4⋊C4—21no—
1426C4⋊C4—21no—
1427C4⋊C4—21no—
1428C4⋊C4—21no—
1429C4⋊C4—21no—
1430C4⋊C4—21no—
1431C4⋊C4—21no—
1432C4⋊C4—21no—
1433C4⋊C4—21no—
1434C4⋊C4—21no—
1435C4⋊C4—21no—
1436C4⋊C4—21no—
1437C4⋊C4—531no—
1438C4⋊C4—531no—
1439C4⋊C4—531no—
1440C4⋊C4—531no—
1441C4⋊C4—1061no—
1442C4⋊C4—1061no—
1443C4⋊C4—1061no—
1444C4⋊C4—1061no—
1445C4⋊C4—1061no—
1446C4⋊C4—1061no—
1447C4⋊C4—1061no—
1448C4⋊C4—1061no—
1449C4⋊C4—1061no—
1450C4⋊C4—1061no—
1451C4⋊C4—1061no—
1452C4⋊C4—1061no—
1453C4⋊C4—1061no—
1454C4⋊C4—1061no—
1455C4⋊C4—1061no—
1456C4⋊C4—1061no—
1457C4⋊C4C2×C22⋊D5311yescharacteristic
1458C4⋊C4C2×C22⋊D5311yescharacteristic
1459C4⋊C4C2×C22⋊D5311yescharacteristic
1460C4⋊C4C2×C22⋊D5311yescharacteristic
1461C4⋊C4C2×C22⋊D5311yescharacteristic
1462C4⋊C4C2×C22⋊D5311yescharacteristic
1463C4⋊C4C2×C22⋊D5311yescharacteristic
1464C4⋊C4C2×C22⋊D5311yescharacteristic
1465C4⋊C4C2×C22⋊D5311yescharacteristic
1466C4⋊C4C2×C22⋊D5311yescharacteristic
1467C4⋊C4C23×D5311yescharacteristic
1468C4⋊C4C23×D5311yescharacteristic
1469C4⋊C4C23×D5311yescharacteristic
1470C4⋊C4C23×D5311yescharacteristic
1471C22⋊C4—21no—
1472C22⋊C4—21no—
1473C22⋊C4—21no—
1474C22⋊C4—21no—
1475C22⋊C4—21no—
1476C22⋊C4—21no—
1477C22⋊C4—21no—
1478C22⋊C4—21no—
1479C22⋊C4—21no—
1480C22⋊C4—21no—
1481C22⋊C4—21no—
1482C22⋊C4—21no—
1483C22⋊C4—21no—
1484C22⋊C4—21no—
1485C22⋊C4—21no—
1486C22⋊C4—21no—
1487C22⋊C4—21no—
1488C22⋊C4—21no—
1489C22⋊C4—1061no—
1490C22⋊C4—1061no—
1491C22⋊C4—1061no—
1492C22⋊C4—1061no—
1493C22⋊C4—1061no—
1494C22⋊C4—1061no—
1495C22⋊C4—1061no—
1496C22⋊C4—1061no—
1497C22⋊C4—1061no—
1498C22⋊C4—1061no—
1499C22⋊C4—1061no—
1500C22⋊C4—1061no—
1501C22⋊C4—1061no—
1502C22⋊C4—1061no—
1503C22⋊C4—1061no—
1504C22⋊C4—1061no—
1505C22⋊C4—1061no—
1506C22⋊C4—1061no—
1507C22⋊C4C2×C22⋊D5311yescharacteristic
1508C22⋊C4C2×C22⋊D5311yescharacteristic
1509C22⋊C4C2×C22⋊D5311yescharacteristic
1510C22⋊C4C2×C22⋊D5311yescharacteristic
1511C22⋊C4C2×C22⋊D5311yescharacteristic
1512C22⋊C4C2×C22⋊D5311yescharacteristic
1513C22⋊C4C2×C22⋊D5311yescharacteristic
1514C22⋊C4C2×C22⋊D5311yescharacteristic
1515C22⋊C4C2×C22⋊D5311yescharacteristic
1516C22⋊C4C2×C22⋊D5311yescharacteristic
1517C42—21no—
1518C42—21no—
1519C42—21no—
1520C42—21no—
1521C42—21no—
1522C42—21no—
1523C42—1061no—
1524C42—1061no—
1525C42—1061no—
1526C42—1061no—
1527C42—1061no—
1528C42—1061no—
1529C42C2×C22⋊D5311yescharacteristic
1530C42C2×C22⋊D5311yescharacteristic
1531C42C23×D5311yescharacteristic
1532C42C23×D5311yescharacteristic
1533C42C23×D5311yescharacteristic
1534C42C23×D5311yescharacteristic
1535C23—21no—
1536C23—21no—
1537C23—42no—
1538C23—81no—
1539C23—81no—
1540C23—1061no—
1541C23—1061no—
1542C23—4241no—
1543C23—4241no—
1544C23—2122no—
1545C23C22×C22⋊D5311yescharacteristic
1546C23C22×C22⋊D5311yescharacteristic
1547C23C22×C22⋊D5311yescharacteristic
1548Q8—21no—
1549Q8—21no—
1550Q8—21no—
1551Q8—21no—
1552Q8—41no—
1553Q8—81no—
1554Q8—1061no—
1555Q8—1061no—
1556Q8—1061no—
1557Q8—1061no—
1558Q8—4241no—
1559D4—21no—
1560D4—21no—
1561D4—21no—
1562D4—41no—
1563D4—41no—
1564D4—41no—
1565D4—42no—
1566D4—42no—
1567D4—42no—
1568D4—81no—
1569D4—81no—
1570D4—532no—
1571D4—1061no—
1572D4—1061no—
1573D4—1061no—
1574D4—4241no—
1575D4—4241no—
1576D4—2122no—
1577D4—2122no—
1578D4—2122no—
1579D4#41×D5312yes—
1580C2×C4—21no—
1581C2×C4—21no—
1582C2×C4—21no—
1583C2×C4—21no—
1584C2×C4—21no—
1585C2×C4—21no—
1586C2×C4—21no—
1587C2×C4—21no—
1588C2×C4—21no—
1589C2×C4—21no—
1590C2×C4—21no—
1591C2×C4—21no—
1592C2×C4—41no—
1593C2×C4—41no—
1594C2×C4—42no—
1595C2×C4—42no—
1596C2×C4—81no—
1597C2×C4—81no—
1598C2×C4—81no—
1599C2×C4—81no—
1600C2×C4—81no—
1601C2×C4—81no—
1602C2×C4—81no—
1603C2×C4—1061no—
1604C2×C4—1061no—
1605C2×C4—1061no—
1606C2×C4—1061no—
1607C2×C4—1061no—
1608C2×C4—1061no—
1609C2×C4—4241no—
1610C2×C4—4241no—
1611C2×C4—4241no—
1612C2×C4—4241no—
1613C2×C4—4241no—
1614C2×C4—4241no—
1615C2×C4—4241no—
1616C2×C4—2122no—
1617C2×C4—2122no—
1618C2×C4C22×C22⋊D5311yescharacteristic
1619C2×C4C22×C22⋊D5311yescharacteristic
1620C2×C4C22×C22⋊D5311yescharacteristic
1621C2×C4C22×C22⋊D5311yescharacteristic
1622C2×C4C22×C22⋊D5311yescharacteristic
1623C2×C4C22×C22⋊D5311yescharacteristic
1624C2×C4C22×C22⋊D5311yescharacteristic
1625C2×C4C22×C22⋊D5311yescharacteristic
1626C2×C4C22×C22⋊D5311yescharacteristic
1627C2×C4C22×C22⋊D5311yescharacteristic
1628C2×C4C22×C22⋊D5311yescharacteristic
1629C2×C4C24×D5311yescharacteristic
1630C8—532no—
1631C8—1061no—
1632C8—1061no—
1633C8—1061no—
1634C8—1061no—
1635C8—1061no—
1636C8—1061no—
1637C8—1061no—
1638C22—21no—
1639C22—21no—
1640C22—21no—
1641C22—22no—
1642C22—21no—
1643C22—21no—
1644C22—21no—
1645C22—21no—
1646C22—21no—
1647C22—21no—
1648C22—41no—
1649C22—41no—
1650C22—41no—
1651C22—41no—
1652C22—41no—
1653C22—162no—
1654C22—8482no—
1655C22—1062no—
1656C22—2121no—
1657C22—2121no—
1658C22—2121no—
1659C22—2121no—
1660C22—2121no—
1661C22C23×C22⋊D5311yescharacteristic
1662C4—21no—
1663C4—21no—
1664C4—21no—
1665C4—21no—
1666C4—21no—
1667C4—21no—
1668C4—21no—
1669C4—21no—
1670C4—21no—
1671C4—21no—
1672C4—21no—
1673C4—41no—
1674C4—41no—
1675C4—41no—
1676C4—41no—
1677C4—41no—
1678C4—41no—
1679C4—2121no—
1680C4—2121no—
1681C4—2121no—
1682C4—2121no—
1683C4—2121no—
1684C4—2121no—
1685C4C2×#41×D5311yescharacteristic
1686C4#1681145911yescharacteristic
1687C2—41no—
1688C2—41no—
1689C2—41no—
1690C2—42no—
1691C2—81no—
1692C2—4241no—
1693C2—2122no—
1694C2#41×C22⋊D5311yescharacteristic
1695C2#2028948611yescharacteristic
1696C2#2028948611yescharacteristic
subgroupG/H
centerC22C23×C22⋊D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC53×#3521C2
socleC22×C53C23×D4
hypercenter#3521D53
hypocenterC53#61501
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C22 ◁ #529 ◁ #3521

Complements

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

NH ≅ G/Ntype
1. #20288787C2semidirect
2. #20287790C2semidirect
3. #20287669C2semidirect
4. #20287364C2semidirect
5. #20287360C2semidirect
6. #20287284C2semidirect
7. #20287260C2semidirect
8. #20287254C2semidirect
9. #20286632C2semidirect
10. #20286626C2semidirect
11. #20286565C2semidirect
12. #20286559C2semidirect
13. #20286550C2semidirect
14. #20286544C2semidirect
15. #20286322C2semidirect
16. #20286241C2semidirect
17. #20286236C2semidirect
18. #20285385C2semidirect
19. #20285377C2semidirect
20. #20285279C2semidirect
21. #20284929C2semidirect
22. #20284923C2semidirect
23. #20284899C2semidirect
24. #20284893C2semidirect
25. #20284824C2semidirect
26. #20284818C2semidirect
27. #20283691C2semidirect
28. #20283547C2semidirect
29. #20283543C2semidirect
30. C4×#13133237C2semidirect
31. C53×#3521C2semidirect
35. #16811346C22semidirect
36. #16811343C22semidirect
37. #16811333C22semidirect
46. #16811269C22semidirect
48. #16811235C22semidirect
51. #16811157C22semidirect
55. #16811097C22semidirect
56. C4×#11719945C22semidirect
57. #16811033C22semidirect
58. #16811029C22semidirect
59. #16811022C22semidirect
60. #16811018C22semidirect
61. #16811015C22semidirect
63. #16810980C22semidirect
64. #16810980C22semidirect
65. #16810977C22semidirect
66. #16810977C22semidirect
67. #16810975C22semidirect
68. #16810973C22semidirect
69. #16810964C22semidirect
70. #16810964C22semidirect
71. #16810961C22semidirect
72. #16810961C22semidirect
73. #16810958C22semidirect
74. #16810956C22semidirect
75. #16810953C22semidirect
76. #16810951C22semidirect
78. #16810947C22semidirect
80. #16810944C22semidirect
81. #16810930C22semidirect
82. #16810930C22semidirect
83. #16810927C22semidirect
84. #16810927C22semidirect
85. #16810923C22semidirect
86. #16810923C22semidirect
87. #16810920C22semidirect
88. #16810920C22semidirect
89. #16810913C22semidirect
90. #16810910C22semidirect
91. #16810903C22semidirect
92. #16810900C22semidirect
93. #16810879C22semidirect
94. #16810879C22semidirect
97. #16810862C22semidirect
98. #16810862C22semidirect
99. #16810862C22semidirect
102. #16810854C22semidirect
104. #16810850C22semidirect
105. #16810845C22semidirect
106. #16810842C22semidirect
113. #16810833C22semidirect
114. #16810830C22semidirect
115. #16810828C22semidirect
116. #16810825C22semidirect
119. #16810785C22semidirect
122. #16810783C22semidirect
123. #16810774C22semidirect
124. #16810773C22semidirect
129. #16810754C22semidirect
130. Q8×#88322C22semidirect
135. #16810728C22semidirect
136. #16810728C22semidirect
137. #16810723C22semidirect
138. #16810723C22semidirect
139. #16810723C22semidirect
140. #16810721C22semidirect
141. #16810721C22semidirect
142. #16810721C22semidirect
143. C4×#11719925C22semidirect
144. C4×#11719925C22semidirect
145. C4×#11719925C22semidirect
146. C4×#11719924C22semidirect
147. C4×#11719924C22semidirect
148. C4×#11719924C22semidirect
149. C4×#11719924C22semidirect
150. C4×#11719923C22semidirect
151. C4×#11719923C22semidirect
152. C4×#11719923C22semidirect
153. C4×#11719923C22semidirect
160. #16810695C22semidirect
161. #16810695C22semidirect
163. D4×#88322C22semidirect
164. D4×#88322C22semidirect
165. #16810684C22semidirect
166. #16810684C22semidirect
167. #16810680C22semidirect
168. #16810666C22semidirect
169. #16810663C22semidirect
170. #16810659C22semidirect
172. #16810619C22semidirect
174. #16810617C22semidirect
175. C2×#13133138C22semidirect
176. C2×#13133137C22semidirect
177. #16810579C22semidirect
178. #16810579C22semidirect
179. C2×C4×#88322C22semidirect
180. C53×#556C22semidirect
181. C53×#556C22semidirect
182. C53×#554C22semidirect
191. C53×#546C22semidirect
193. C53×#541C22semidirect
198. C53×#529C22semidirect
201. C53×#518C22semidirect
202. C4×#41×C53C22semidirect
840. #3521D53semidirect
885. #556C2×D53semidirect
886. #556C2×D53semidirect
888. #554C2×D53semidirect
906. #546C2×D53semidirect
910. #541C2×D53semidirect
919. #529C2×D53semidirect
925. #518C2×D53semidirect
927. C4×#41C2×D53semidirect
1051. C53#61501semidirect

Maximal subgroups

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

subgroupindex
#202887872
#202877902
#202876692
#202873642
#202873602
#202872842
#202872602
#202872542
#202866322
#202866262
#202865652
#202865592
#202865502
#202865442
#202863222
#202862412
#202862362
#202853852
#202853772
#202852792
#202849292
#202849232
#202848992
#202848932
#202848242
#202848182
#202836912
#202835472
#202835432
C4×#131332372
C53×#35212
#6150153