Finite Group Databasebeta

← #15625943

Subgroups — #15625943

Order 2816.

1780 conjugacy classes of subgroups.

The subgroup lattice has 820 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623001C211yesmaximal, characteristic, complemented
2#13079852C214yesmaximal, complemented
3#13079843C212yesmaximal, complemented
4#13079834C212yesmaximal, complemented
5#13079826C212yesmaximal, complemented
6#13079818C212yesmaximal, complemented
7#13079810C212yesmaximal, complemented
8#13079802C212yesmaximal, complemented
9#13079138C212yesmaximal, complemented
10#13078961C212yesmaximal, complemented
11#13078525C214yesmaximal, complemented
12#13078404C214yesmaximal, complemented
13C2×#10622539C211yesmaximal, characteristic, complemented
14C11×#3444C211yesmaximal, characteristic
15C11×#533C2211yescharacteristic
16C11×#533C2211yescharacteristic
17C11×#533C2211yescharacteristic
18C11×#532C2211yescharacteristic
19C11×#532C2211yescharacteristic
20C11×#532C2211yescharacteristic
21C11×#529—21no—
22C11×#529—21no—
23C11×#529—21no—
24C11×#529—21no—
25C11×#529C2212yes—
26C11×#529C2212yes—
27C11×#525—21no—
28C11×#525—21no—
29C11×#525C2212yes—
30C4×C11×#41—21no—
31C4×C11×#41—21no—
32C4×C11×#41C2212yes—
33C22×C42×C11C2211yescharacteristic
34C2×#66979C2212yes—
35C2×#66977—21no—
36C2×#66977—21no—
37#10623001—21no—
38#10623001—21no—
39#10623001—21no—
40#10623001—21no—
41#10623001C2212yes—
42#10623001C2212yes—
43#10623001C2212yes—
44#10623001C2212yes—
45C2×#66923C2212yes—
46C2×#66922C2211yescharacteristic
47C2×#66922C2211yescharacteristic
48C2×C4×Dic22—21no—
49C2×C4×Dic22—21no—
50#10622846C2218yes—
51C2×C22⋊(C11⋊C8)C2212yes—
52#10622695C2214yescomplemented
53#10622693C2214yescomplemented
54#10622693C2214yescomplemented
55#10622684C2214yescomplemented
56#10622678C2214yescomplemented
57#10622678C2214yescomplemented
58#10622668C2214yescomplemented
59#10622668C2214yescomplemented
60#10622658C2218yes—
61#10622657C2214yes—
62#10622656C2214yes—
63#10622648C2218yes—
64#10622647C2214yes—
65#10622646C2214yes—
66#10622635C2218yescomplemented
67#10622634C2214yescomplemented
68#10622633C2214yescomplemented
69#10622622C2218yescomplemented
70#10622621C2214yescomplemented
71#10622620C2214yescomplemented
72#10622611C2218yes—
73#10622539C2212yes—
74#10622539C2212yes—
75#10622539C2212yes—
76#10622539C2212yes—
77C2×C4⋊(C11⋊C8)C2212yes—
78C2×#66867C2212yes—
79C2×C11×#41—21no—
80C2×C11×#41—21no—
81C2×C11×#41C2312yes—
82C23×C4×C11D411yescharacteristic
83C23×C4×C11D411yescharacteristic
84C23×C4×C11C2311yescharacteristic
85C22×Dic22—21no—
86C22×Dic22—21no—
87C11×C4⋊Q8C2311yescharacteristic
88C11×C4⋊Q8C2311yescharacteristic
89C11×C4⋊Q8C2311yescharacteristic
90C11×#127C2311yescharacteristic
91C11×#126—22no—
92C11×#126—22no—
93C11×#125—21no—
94C11×#125—21no—
95C11×#125C2312yes—
96C11×#124—21no—
97C11×#124—21no—
98C11×#124C2312yes—
99C11×#123—22no—
100C11×#123—22no—
101C11×#123—22no—
102C11×C22⋊Q8—21no—
103C11×C22⋊Q8—21no—
104C11×C22⋊Q8—21no—
105C11×C22⋊Q8—21no—
106C11×C22⋊Q8C2312yes—
107C11×C22⋊Q8C2312yes—
108C11×#121—21no—
109C11×#121—21no—
110C11×#121—21no—
111C11×#121—21no—
112C11×#121C2312yes—
113C11×#121C2312yes—
114C11×#120—22no—
115C4×Q8×C11—21no—
116C4×Q8×C11—21no—
117C4×Q8×C11—21no—
118C4×Q8×C11—21no—
119C4×Q8×C11C2312yes—
120C4×Q8×C11C2312yes—
121C4×D4×C11—22no—
122C4×D4×C11—22no—
123C4×D4×C11—22no—
124C4×D4×C11—22no—
125C4×D4×C11—22no—
126C4×D4×C11—22no—
127C4×D4×C11—21no—
128C4×D4×C11—21no—
129C4×D4×C11—21no—
130C4×D4×C11—21no—
131C4×D4×C11C2312yes—
132C4×D4×C11C2312yes—
133C11×#117—21no—
134C11×#117—21no—
135C11×#117—22no—
136C11×#117—22no—
137C11×#117—22no—
138C11×#117C2312yes—
139C2×C42×C11—22no—
140C2×C42×C11D411yescharacteristic
141C2×C42×C11D411yescharacteristic
142C2×C42×C11D411yescharacteristic
143C2×C42×C11D411yescharacteristic
144C2×C42×C11D411yescharacteristic
145C2×C42×C11D411yescharacteristic
146C2×C42×C11C2311yescharacteristic
147C2×C42×C11C2311yescharacteristic
148C2×C42×C11C2311yescharacteristic
149C2×C42×C11C2311yescharacteristic
150C2×C42×C11C2311yescharacteristic
151C2×C42×C11C2311yescharacteristic
152C2×C22⋊Dic11—22no—
153#66979—22no—
154#66979—22no—
155#66979C2314yes—
156#66979C2314yes—
157C2×C4⋊Dic11—21no—
158C2×C4⋊Dic11—21no—
159C2×C4⋊Dic11C2312yes—
160C2×C4⋊Dic11C2312yes—
161#66977—22no—
162#66977—22no—
163#66977—22no—
164#66977—22no—
165#66977—22no—
166#66977—22no—
167#66977—22no—
168#66977—22no—
169C2×Dic11⋊C4—22no—
170C2×Dic11⋊C4—22no—
171C2×C4×Dic11—22no—
172C22×C11⋊C8C2314yes—
173#66923—22no—
174#66923—22no—
175#66923C2314yes—
176#66923C2314yes—
177#66922—21no—
178#66922—21no—
179#66922—21no—
180#66922—21no—
181#66922C2312yes—
182#66922C2312yes—
183#66922C2312yes—
184#66922C2312yes—
185C4×Dic22—22no—
186C4×Dic22—22no—
187C4×Dic22—22no—
188C4×Dic22—22no—
189C4×Dic22—22no—
190C4×Dic22—22no—
191C4×Dic22—22no—
192C4×Dic22—22no—
193#66899C2318yes—
194#66899C2318yes—
195#66896C2318yes—
196#66896C2318yes—
197C22⋊(C11⋊C8)C2314yes—
198C22⋊(C11⋊C8)C2314yes—
199#66872C2318yes—
200#66872C2318yes—
201#66871C2318yes—
202#66871C2318yes—
203C4⋊(C11⋊C8)C2314yes—
204C4⋊(C11⋊C8)C2314yes—
205#66867C2314yes—
206#66867C2314yes—
207#60854—111nomaximal, Sylow
208C24×C11C2×D411yescharacteristic
209C11×#41—28no—
210C11×#41—44no—
211C11×#41—44no—
212C2×Q8×C11—21no—
213C2×Q8×C11—21no—
214C2×Q8×C11C2412yes—
215C2×D4×C11—22no—
216C2×D4×C11—22no—
217C2×D4×C11—22no—
218C2×D4×C11—21no—
219C2×D4×C11—21no—
220C2×D4×C11C2412yes—
221C22×C4×C11—24no—
222C22×C4×C11—22no—
223C22×C4×C11—22no—
224C22×C4×C11—22no—
225C22×C4×C11—42no—
226C22×C4×C11—42no—
227C22×C4×C11C2×D411yescharacteristic
228C22×C4×C11C2×D411yescharacteristic
229C22×C4×C11C2×D411yescharacteristic
230C22×C4×C11C2×D411yescharacteristic
231C22×C4×C11C2×D411yescharacteristic
232C22×C4×C11C2×D411yescharacteristic
233C22×C4×C11C2×D411yescharacteristic
234C22×C4×C11C2×D411yescharacteristic
235C22×C4×C11C2×D411yescharacteristic
236C22×C4×C11C2×D411yescharacteristic
237C22×C4×C11C2×D411yescharacteristic
238C22×C4×C11C2×D411yescharacteristic
239C22×C4×C11C2×D411yescharacteristic
240C22×C4×C11C2×D411yescharacteristic
241C22×C4×C11C2×D411yescharacteristic
242C22×C4×C11C2411yescharacteristic
243C22×C4×C11C2411yescharacteristic
244C22×C4×C11C2411yescharacteristic
245C22×Dic11—22no—
246C22×Dic11—22no—
247C2×Dic22—22no—
248C2×Dic22—22no—
249C2×Dic22—22no—
250C2×Dic22—22no—
251C2×Dic22—44no—
252C2×Dic22—44no—
253C11×C4⋊C4—21no—
254C11×C4⋊C4—21no—
255C11×C4⋊C4—21no—
256C11×C4⋊C4—21no—
257C11×C4⋊C4—22no—
258C11×C4⋊C4—22no—
259C11×C4⋊C4—22no—
260C11×C4⋊C4—22no—
261C11×C4⋊C4—22no—
262C11×C4⋊C4—22no—
263C11×C4⋊C4C2412yes—
264C11×C4⋊C4C2412yes—
265C11×C22⋊C4—22no—
266C11×C22⋊C4—22no—
267C11×C22⋊C4—22no—
268C11×C22⋊C4—22no—
269C11×C22⋊C4—22no—
270C11×C22⋊C4—22no—
271C11×C22⋊C4—22no—
272C11×C22⋊C4—22no—
273C11×C22⋊C4—22no—
274C42×C11—22no—
275C42×C11—22no—
276C42×C11—22no—
277C42×C11C2×D411yescharacteristic
278C42×C11C2×D411yescharacteristic
279C42×C11C2×D411yescharacteristic
280C42×C11C2×D411yescharacteristic
281C42×C11C2×D411yescharacteristic
282C42×C11C2×D411yescharacteristic
283C42×C11C2×D411yescharacteristic
284C42×C11C2×D411yescharacteristic
285C42×C11C2×D411yescharacteristic
286C42×C11C2×D411yescharacteristic
287C42×C11C2×D411yescharacteristic
288C42×C11C2×D411yescharacteristic
289C42×C11C2411yescharacteristic
290C42×C11C2411yescharacteristic
291C42×C11C2411yescharacteristic
292C42×C11C2411yescharacteristic
293C22⋊Dic11—24no—
294C22⋊Dic11—24no—
295C4⋊Dic11—22no—
296C4⋊Dic11—22no—
297C4⋊Dic11—22no—
298C4⋊Dic11—22no—
299C4⋊Dic11—22no—
300C4⋊Dic11—22no—
301C4⋊Dic11C2414yes—
302C4⋊Dic11C2414yes—
303Dic11⋊C4—24no—
304Dic11⋊C4—24no—
305Dic11⋊C4—24no—
306Dic11⋊C4—24no—
307C4×Dic11—24no—
308C4×Dic11—24no—
309C2×C11⋊C8—28no—
310C2×C11⋊C8C2418yes—
311#3444D1111yescharacteristic
312C2×#533—111no—
313#3240—114no—
314#3239—112no—
315#3238—112no—
316#3237—112no—
317#3236—112no—
318#3235—112no—
319#3234—112no—
320#3162—112no—
321#3135—112no—
322#3091—114no—
323#3076—114no—
324C2×#432—111no—
325C23×C11—22no—
326C23×C11—22no—
327C23×C11—22no—
328C23×C11—41no—
329C23×C11C22×D411yescharacteristic
330C23×C11C22×D411yescharacteristic
331C23×C11C22×D411yescharacteristic
332Q8×C11—24no—
333Q8×C11—42no—
334Q8×C11—42no—
335D4×C11—24no—
336D4×C11—42no—
337D4×C11—42no—
338D4×C11—44no—
339D4×C11—44no—
340D4×C11—44no—
341C2×C4×C11—22no—
342C2×C4×C11—22no—
343C2×C4×C11—22no—
344C2×C4×C11—22no—
345C2×C4×C11—22no—
346C2×C4×C11—22no—
347C2×C4×C11—22no—
348C2×C4×C11—22no—
349C2×C4×C11—22no—
350C2×C4×C11—22no—
351C2×C4×C11—22no—
352C2×C4×C11—22no—
353C2×C4×C11—22no—
354C2×C4×C11—41no—
355C2×C4×C11—41no—
356C2×C4×C11—41no—
357C2×C4×C11—41no—
358C2×C4×C11—41no—
359C2×C4×C11—41no—
360C2×C4×C11—41no—
361C2×C4×C11—44no—
362C2×C4×C11—44no—
363C2×C4×C11—44no—
364C2×C4×C11C22×D411yescharacteristic
365C2×C4×C11C22×D411yescharacteristic
366C2×C4×C11C22×D411yescharacteristic
367C2×C4×C11C22×D411yescharacteristic
368C2×C4×C11C22×D411yescharacteristic
369C2×C4×C11C22×D411yescharacteristic
370C2×C4×C11C22×D411yescharacteristic
371C2×C4×C11C22×D411yescharacteristic
372C2×C4×C11C22×D411yescharacteristic
373C2×C4×C11C22×D411yescharacteristic
374C2×C4×C11C22×D411yescharacteristic
375C2×C4×C112−1+414yes—
376C2×C4×C11C2511yescharacteristic
377C2×Dic11—24no—
378C2×Dic11—24no—
379C2×Dic11—44no—
380C2×Dic11—44no—
381Dic22—44no—
382Dic22—44no—
383Dic22—44no—
384Dic22—44no—
385C11⋊C8—28no—
386#533—112no—
387#533—112no—
388#533—112no—
389#533—112no—
390#533—221no—
391#533—221no—
392#533—221no—
393#533—221no—
394#533C2×D1111yescharacteristic
395#533C2×D1111yescharacteristic
396#533C2×D1111yescharacteristic
397#532C2×D1111yescharacteristic
398#532C2×D1111yescharacteristic
399#532C2×D1111yescharacteristic
400C2×C4⋊Q8—111no—
401C2×C4⋊Q8—111no—
402#529—21no—
403#529—21no—
404#529—21no—
405#529—21no—
406#529C2×D1112yes—
407#529C2×D1112yes—
408C2×#125—112no—
409#525—21no—
410#525—21no—
411#525C2×D1112yes—
412C2×C22⋊Q8—221no—
413C2×C22⋊Q8—221no—
414C4×#41—21no—
415C4×#41—21no—
416C4×#41C2×D1112yes—
417C2×C4×Q8—221no—
418C2×C4×Q8—221no—
419C2×#117—112no—
420C22×C42C2×D1111yescharacteristic
421#501—114no—
422#501—114no—
423#501—114no—
424#501—114no—
425#491—114no—
426#490—114no—
427#489—114no—
428#489—114no—
429#485—118no—
430#484—114no—
431#483—114no—
432#482—118no—
433#481—114no—
434#480—114no—
435#479—118no—
436#478—118no—
437#477—114no—
438#476—114no—
439#475—114no—
440#474—114no—
441#432—112no—
442#432—112no—
443#432—112no—
444#432—112no—
445#427—118no—
446C2×C4⋊C8—112no—
447#416—118no—
448C2×C22⋊C8—112no—
449C2×#97—112no—
450C22×C11—21no—
451C22×C11—21no—
452C22×C11—21no—
453C22×C11—21no—
454C22×C11—21no—
455C22×C11—21no—
456C22×C11—21no—
457C22×C11—44no—
458C22×C11—42no—
459C22×C11—42no—
460C22×C11—42no—
461C22×C11#53612yes—
462C22×C11#57512yes—
463C22×C11C23×D411yescharacteristic
464C4×C11—21no—
465C4×C11—21no—
466C4×C11—21no—
467C4×C11—21no—
468C4×C11—21no—
469C4×C11—21no—
470C4×C11—21no—
471C4×C11—21no—
472C4×C11—21no—
473C4×C11—42no—
474C4×C11—42no—
475C4×C11—42no—
476C4×C11#53612yes—
477C4×C11#57512yes—
478C4×C11C2×2−1+412yes—
479Dic11—44no—
480Dic11—44no—
481C2×#41—21no—
482C2×#41—21no—
483C2×#41C22×D1112yes—
484C22×Q8—221no—
485C22×Q8—221no—
486C23×C4C22⋊D1111yescharacteristic
487C23×C4C22⋊D1111yescharacteristic
488C23×C4C22×D1111yescharacteristic
489C22×C8—114no—
490C4⋊Q8—112no—
491C4⋊Q8—112no—
492C4⋊Q8—112no—
493C4⋊Q8—112no—
494C4⋊Q8—221no—
495C4⋊Q8—221no—
496C4⋊Q8—221no—
497C4⋊Q8—221no—
498C4⋊Q8C22×D1111yescharacteristic
499C4⋊Q8C22×D1111yescharacteristic
500C4⋊Q8C22×D1111yescharacteristic
501#127C22×D1111yescharacteristic
502#126—22no—
503#126—22no—
504#125—21no—
505#125—21no—
506#125—114no—
507#125—114no—
508#125—222no—
509#125—222no—
510#125C22×D1112yes—
511#124—21no—
512#124—21no—
513#124C22×D1112yes—
514#123—22no—
515#123—22no—
516#123—22no—
517C22⋊Q8—21no—
518C22⋊Q8—21no—
519C22⋊Q8—21no—
520C22⋊Q8—21no—
521C22⋊Q8—222no—
522C22⋊Q8—222no—
523C22⋊Q8—222no—
524C22⋊Q8—222no—
525C22⋊Q8—222no—
526C22⋊Q8—222no—
527C22⋊Q8—222no—
528C22⋊Q8—222no—
529C22⋊Q8C22×D1112yes—
530C22⋊Q8C22×D1112yes—
531#121—21no—
532#121—21no—
533#121—21no—
534#121—21no—
535#121C22×D1112yes—
536#121C22×D1112yes—
537#120—22no—
538C4×Q8—21no—
539C4×Q8—21no—
540C4×Q8—21no—
541C4×Q8—21no—
542C4×Q8—222no—
543C4×Q8—222no—
544C4×Q8—222no—
545C4×Q8—222no—
546C4×Q8—222no—
547C4×Q8—222no—
548C4×Q8—222no—
549C4×Q8—222no—
550C4×Q8C22×D1112yes—
551C4×Q8C22×D1112yes—
552C4×D4—22no—
553C4×D4—22no—
554C4×D4—22no—
555C4×D4—22no—
556C4×D4—22no—
557C4×D4—22no—
558C4×D4—21no—
559C4×D4—21no—
560C4×D4—21no—
561C4×D4—21no—
562C4×D4C22×D1112yes—
563C4×D4C22×D1112yes—
564#117—21no—
565#117—21no—
566#117—22no—
567#117—22no—
568#117—22no—
569#117—114no—
570#117—114no—
571#117—222no—
572#117—222no—
573#117C22×D1112yes—
574C2×C4⋊C4—112no—
575C2×C4⋊C4—112no—
576C2×C4⋊C4—222no—
577C2×C4⋊C4—222no—
578C2×C4⋊C4—221no—
579C2×C4⋊C4—221no—
580C2×C22⋊C4—222no—
581C2×C42—22no—
582C2×C42—222no—
583C2×C42C22⋊D1111yescharacteristic
584C2×C42C22⋊D1111yescharacteristic
585C2×C42C22⋊D1111yescharacteristic
586C2×C42C22⋊D1111yescharacteristic
587C2×C42C22⋊D1111yescharacteristic
588C2×C42C22⋊D1111yescharacteristic
589C2×C42C22×D1111yescharacteristic
590C2×C42C22×D1111yescharacteristic
591C2×C42C22×D1111yescharacteristic
592C2×C42C22×D1111yescharacteristic
593C2×C42C22×D1111yescharacteristic
594C2×C42C22×D1111yescharacteristic
595#107—118no—
596#107—118no—
597#106—118no—
598#106—118no—
599C4⋊C8—114no—
600C4⋊C8—114no—
601#103—118no—
602#103—118no—
603#102—118no—
604#102—118no—
605C22⋊C8—114no—
606C22⋊C8—114no—
607#97—114no—
608#97—114no—
609C2×C11—22no—
610C2×C11—22no—
611C2×C11—41no—
612C2×C11—82no—
613C2×C11C2×#53611yescharacteristic
614C2×C11C2×#57511yescharacteristic
615C2×C11C2×#57511yescharacteristic
616C24C2×C22⋊D1111yescharacteristic
617#41—28no—
618#41—44no—
619#41—44no—
620C2×Q8—21no—
621C2×Q8—21no—
622C2×Q8—222no—
623C2×Q8—222no—
624C2×Q8—222no—
625C2×Q8—222no—
626C2×Q8—444no—
627C2×Q8—444no—
628C2×Q8C23×D1112yes—
629C2×D4—22no—
630C2×D4—22no—
631C2×D4—22no—
632C2×D4—21no—
633C2×D4—21no—
634C2×D4C23×D1112yes—
635C22×C4—24no—
636C22×C4—22no—
637C22×C4—22no—
638C22×C4—22no—
639C22×C4—42no—
640C22×C4—42no—
641C22×C4—222no—
642C22×C4—222no—
643C22×C4C2×C22⋊D1111yescharacteristic
644C22×C4C2×C22⋊D1111yescharacteristic
645C22×C4C2×C22⋊D1111yescharacteristic
646C22×C4C2×C22⋊D1111yescharacteristic
647C22×C4C2×C22⋊D1111yescharacteristic
648C22×C4C2×C22⋊D1111yescharacteristic
649C22×C4C2×C22⋊D1111yescharacteristic
650C22×C4C2×C22⋊D1111yescharacteristic
651C22×C4C2×C22⋊D1111yescharacteristic
652C22×C4C2×C22⋊D1111yescharacteristic
653C22×C4C2×C22⋊D1111yescharacteristic
654C22×C4C2×C22⋊D1111yescharacteristic
655C22×C4C2×C22⋊D1111yescharacteristic
656C22×C4C2×C22⋊D1111yescharacteristic
657C22×C4C2×C22⋊D1111yescharacteristic
658C22×C4C23×D1111yescharacteristic
659C22×C4C23×D1111yescharacteristic
660C22×C4C23×D1111yescharacteristic
661C2×C8—118no—
662C2×C8—228no—
663C4⋊C4—21no—
664C4⋊C4—21no—
665C4⋊C4—21no—
666C4⋊C4—21no—
667C4⋊C4—22no—
668C4⋊C4—22no—
669C4⋊C4—22no—
670C4⋊C4—22no—
671C4⋊C4—22no—
672C4⋊C4—22no—
673C4⋊C4—114no—
674C4⋊C4—114no—
675C4⋊C4—222no—
676C4⋊C4—222no—
677C4⋊C4—224no—
678C4⋊C4—224no—
679C4⋊C4—224no—
680C4⋊C4—224no—
681C4⋊C4—222no—
682C4⋊C4—222no—
683C4⋊C4—222no—
684C4⋊C4—222no—
685C4⋊C4C23×D1112yes—
686C4⋊C4C23×D1112yes—
687C22⋊C4—22no—
688C22⋊C4—22no—
689C22⋊C4—22no—
690C22⋊C4—22no—
691C22⋊C4—22no—
692C22⋊C4—22no—
693C22⋊C4—22no—
694C22⋊C4—22no—
695C22⋊C4—22no—
696C22⋊C4—224no—
697C22⋊C4—224no—
698C42—22no—
699C42—22no—
700C42—22no—
701C42—224no—
702C42—224no—
703C42C2×C22⋊D1111yescharacteristic
704C42C2×C22⋊D1111yescharacteristic
705C42C2×C22⋊D1111yescharacteristic
706C42C2×C22⋊D1111yescharacteristic
707C42C2×C22⋊D1111yescharacteristic
708C42C2×C22⋊D1111yescharacteristic
709C42C2×C22⋊D1111yescharacteristic
710C42C2×C22⋊D1111yescharacteristic
711C42C2×C22⋊D1111yescharacteristic
712C42C2×C22⋊D1111yescharacteristic
713C42C2×C22⋊D1111yescharacteristic
714C42C2×C22⋊D1111yescharacteristic
715C42C23×D1111yescharacteristic
716C42C23×D1111yescharacteristic
717C42C23×D1111yescharacteristic
718C42C23×D1111yescharacteristic
719C11#6085411yescharacteristic, complemented, Sylow
720C23—22no—
721C23—22no—
722C23—22no—
723C23—41no—
724C23C22×C22⋊D1111yescharacteristic
725C23C22×C22⋊D1111yescharacteristic
726C23C22×C22⋊D1111yescharacteristic
727Q8—24no—
728Q8—42no—
729Q8—42no—
730Q8—444no—
731Q8—444no—
732Q8—444no—
733Q8—444no—
734D4—24no—
735D4—42no—
736D4—42no—
737D4—44no—
738D4—44no—
739D4—44no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—22no—
753C2×C4—41no—
754C2×C4—41no—
755C2×C4—41no—
756C2×C4—41no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—44no—
761C2×C4—44no—
762C2×C4—44no—
763C2×C4—224no—
764C2×C4—224no—
765C2×C4—444no—
766C2×C4—444no—
767C2×C4#6704314yes—
768C2×C4C22×C22⋊D1111yescharacteristic
769C2×C4C22×C22⋊D1111yescharacteristic
770C2×C4C22×C22⋊D1111yescharacteristic
771C2×C4C22×C22⋊D1111yescharacteristic
772C2×C4C22×C22⋊D1111yescharacteristic
773C2×C4C22×C22⋊D1111yescharacteristic
774C2×C4C22×C22⋊D1111yescharacteristic
775C2×C4C22×C22⋊D1111yescharacteristic
776C2×C4C22×C22⋊D1111yescharacteristic
777C2×C4C22×C22⋊D1111yescharacteristic
778C2×C4C22×C22⋊D1111yescharacteristic
779C2×C4C24×D1111yescharacteristic
780C8—228no—
781C22—21no—
782C22—21no—
783C22—21no—
784C22—21no—
785C22—21no—
786C22—21no—
787C22—21no—
788C22—44no—
789C22—42no—
790C22—42no—
791C22—42no—
792C22#1062335312yes—
793C22#1062335612yes—
794C22C23×C22⋊D1111yescharacteristic
795C4—21no—
796C4—21no—
797C4—21no—
798C4—21no—
799C4—21no—
800C4—21no—
801C4—21no—
802C4—21no—
803C4—21no—
804C4—42no—
805C4—42no—
806C4—42no—
807C4—444no—
808C4—444no—
809C4#1062335312yes—
810C4#1062335612yes—
811C4C2×#6704312yes—
812C2—22no—
813C2—22no—
814C2—41no—
815C2—82no—
816C2C2×#1062335611yescharacteristic
817C2C2×#1062335311yescharacteristic
818C2C2×#1062335311yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
Fitting, prime radicalC11×#3444C2
socleC22×C11C23×D4
hypercenter#3444D11
hypocenterC11#60854
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C22×C42 ◁ #3444

Complements

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

NH ≅ G/Ntype
1. C2×#10623001C2semidirect
2. #13079852C2semidirect
3. #13079843C2semidirect
4. #13079834C2semidirect
5. #13079826C2semidirect
6. #13079818C2semidirect
7. #13079810C2semidirect
8. #13079802C2semidirect
9. #13079138C2semidirect
10. #13078961C2semidirect
11. #13078525C2semidirect
12. #13078404C2semidirect
13. C2×#10622539C2semidirect
52. #10622695C22semidirect
53. #10622693C22semidirect
54. #10622693C22semidirect
55. #10622684C22semidirect
56. #10622678C22semidirect
57. #10622678C22semidirect
58. #10622668C22semidirect
59. #10622668C22semidirect
66. #10622635C22semidirect
67. #10622634C22semidirect
68. #10622633C22semidirect
69. #10622622C22semidirect
70. #10622621C22semidirect
71. #10622620C22semidirect
719. C11#60854semidirect

Maximal subgroups

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

subgroupindex
C2×#106230012
#130798522
#130798432
#130798342
#130798262
#130798182
#130798102
#130798022
#130791382
#130789612
#130785252
#130784042
C2×#106225392
C11×#34442
#6085411