Finite Group Databasebeta

← #15626406

Subgroups — #15626406

Order 2816.

1678 conjugacy classes of subgroups.

The subgroup lattice has 824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082527C211yesmaximal, characteristic
2#13079914C214yesmaximal, complemented
3#13079899C214yesmaximal, complemented
4#13079830C212yesmaximal, complemented
5#13079822C212yesmaximal, complemented
6#13079814C212yesmaximal, complemented
7#13079806C212yesmaximal, complemented
8#13079163C211yesmaximal, characteristic, complemented
9C2×#10622678C211yesmaximal, characteristic, complemented
10#13079019C211yesmaximal, characteristic, complemented
11#13078964C211yesmaximal, characteristic, complemented
12#13078605C212yesmaximal, complemented
13#13078594C212yesmaximal, complemented
14#13078474C212yesmaximal, complemented
15#13078463C212yesmaximal, complemented
16#13077267C211yesmaximal, characteristic, complemented
17C11×#3504C211yesmaximal, characteristic, complemented
18C11×#557—21no—
19C11×#557—21no—
20C11×#554—21no—
21C11×#554—22no—
22C11×#554—21no—
23C11×#554—22no—
24C11×#544C2212yes—
25C11×#544C2212yes—
26C11×#544C2211yescharacteristic
27C11×#544C2211yescharacteristic
28C11×#533C2212yes—
29C11×#533C2211yescharacteristic
30C2×C11×#125C2212yes—
31C2×C11×#125C2211yescharacteristic
32C11×#520C2211yescharacteristic
33C11×#520C2211yescharacteristic
34C4×C11×#41C2211yescharacteristic
35#10623364C2212yes—
36#10623115—21no—
37#10623110—21no—
38#10623096—22no—
39#10623094—21no—
40#10623083—22no—
41#10623082—21no—
42#10623065C2214yes—
43#10623054C2212yes—
44#10623008C2211yescharacteristic
45#10623008C2212yes—
46#10623001C2212yes—
47C2×#66922C2211yescharacteristic
48#10622847C2212yes—
49#10622707C2214yes—
50#10622704C2214yes—
51#10622702C2212yes—
52#10622702C2212yes—
53#10622700C2214yes—
54#10622697C2214yes—
55#10622692C2212yes—
56#10622691C2212yes—
57#10622682C2211yescharacteristic
58#10622682C2212yes—
59#10622682C2211yescharacteristic
60#10622681C2214yes—
61#10622680C2211yescharacteristic
62#10622680C2212yes—
63#10622680C2211yescharacteristic
64#10622679C2214yes—
65#10622679C2214yes—
66#10622678C2212yes—
67#10622678C2212yes—
68#10622678C2212yes—
69#10622678C2212yes—
70#10622678C2214yes—
71#10622676C2214yes—
72#10622676C2214yes—
73#10622616C2214yes—
74#10622616C2214yes—
75#10622615C2212yes—
76#10622615C2212yes—
77#10622613C2214yes—
78#10622612C2212yes—
79#10622609C2214yes—
80#10622609C2214yes—
81#10622608C2212yes—
82#10622608C2212yes—
83#10622584C2214yes—
84#10622583C2214yes—
85#10622581C2214yes—
86#10622580C2214yes—
87#10622579C2212yes—
88#10622579C2212yes—
89C2×#66872C2212yes—
90C2×#66871C2212yes—
91#10622539C2212yes—
92#10622539C2212yes—
93C4×#4318C2211yescharacteristic
94C2×#66867C2211yescharacteristic
95C2×C11×#41C2311yescharacteristic
96C2×#4339—22no—
97C2×#4339C2312yes—
98C22×Dic22—21no—
99C11×C4⋊Q8—21no—
100C11×C4⋊Q8—21no—
101C11×C4⋊Q8—22no—
102C11×C4⋊Q8—22no—
103C11×C4⋊Q8C2311yescharacteristic
104C11×C4⋊Q8C2311yescharacteristic
105C11×C4⋊Q8C2312yes—
106C11×C4⋊Q8C2312yes—
107C11×#125—21no—
108C11×#125—21no—
109C11×#125—22no—
110C11×#125—22no—
111C11×#125—22no—
112C11×#125—21no—
113C11×#125—21no—
114C11×#125—22no—
115C11×#125C2311yescharacteristic
116C11×#125C2312yes—
117C11×#125C2312yes—
118C11×#125C2312yes—
119C11×#125C2312yes—
120C11×#125C2311yescharacteristic
121C11×C22⋊Q8—22no—
122C11×C22⋊Q8—21no—
123C11×C22⋊Q8—22no—
124C11×C22⋊Q8—21no—
125C11×C22⋊Q8—22no—
126C11×C22⋊Q8—22no—
127C11×C22⋊Q8—22no—
128C11×C22⋊Q8—22no—
129C11×C22⋊Q8—22no—
130C11×C22⋊Q8—22no—
131C4×Q8×C11—21no—
132C4×Q8×C11—21no—
133C4×Q8×C11—22no—
134C4×Q8×C11—21no—
135C4×Q8×C11—21no—
136C4×Q8×C11—22no—
137C4×Q8×C11D411yescharacteristic
138C4×Q8×C11D411yescharacteristic
139C4×D4×C11—21no—
140C4×D4×C11—21no—
141C4×D4×C11—22no—
142C4×D4×C11—22no—
143C4×D4×C11D411yescharacteristic
144C4×D4×C11D412yes—
145C4×D4×C11D411yescharacteristic
146C4×D4×C11D412yes—
147C11×#117C2311yescharacteristic
148C11×#117C2311yescharacteristic
149C11×#117C2312yes—
150C11×#117C2312yes—
151C11×#117C2311yescharacteristic
152C11×#117C2312yes—
153C2×C11×C4⋊C4—22no—
154C2×C11×C4⋊C4—21no—
155C2×C11×C4⋊C4—22no—
156C2×C11×C4⋊C4—21no—
157C2×C11×C4⋊C4C2311yescharacteristic
158C2×C11×C4⋊C4C2311yescharacteristic
159C2×C11×C4⋊C4C2312yes—
160C2×C11×C4⋊C4C2312yes—
161C2×C42×C11C2311yescharacteristic
162C2×C42×C11C2312yes—
163#66999—22no—
164#66992—24no—
165#66991—22no—
166#66983—21no—
167#66983—22no—
168#66983—21no—
169#66983C2314yes—
170#66979—22no—
171C2×C4⋊Dic11—21no—
172C2×C4⋊Dic11C2312yes—
173#66977—22no—
174#66977C2314yes—
175C2×#4318C2312yes—
176C22×C11⋊C8C2312yes—
177#66951—24no—
178#66949—24no—
179#66945—22no—
180C4⋊C4×D11—22no—
181#66938—24no—
182#66936—24no—
183(C22⋊D11)⋊C4—24no—
184#66928—22no—
185#66928C2312yes—
186#66927C2311yescharacteristic
187C4×D44—21no—
188C4×D44—21no—
189C4×D44—22no—
190C4×D44C2314yes—
191#66923—22no—
192#66922—21no—
193#66922—21no—
194#66922C2311yescharacteristic
195#66922C2312yes—
196#66922C2312yes—
197C4×Dic22—22no—
198C4×Dic22C2314yes—
199C22⋊(C11⋊C8)C2314yes—
200C22⋊(C11⋊C8)C2314yes—
201#66874C2314yes—
202#66874C2314yes—
203#66874C2312yes—
204#66874C2312yes—
205#66874C2312yes—
206#66874C2312yes—
207#66873C2314yes—
208#66873C2314yes—
209#66873C2312yes—
210#66873C2312yes—
211#66873C2312yes—
212#66873C2312yes—
213#66872C2314yes—
214#66872C2314yes—
215#66872C2314yes—
216#66872C2314yes—
217#66871C2314yes—
218#66871C2314yes—
219#66871C2314yes—
220#66871C2314yes—
221C4⋊(C11⋊C8)C2314yes—
222C4⋊(C11⋊C8)C2314yes—
223#66867C2311yescharacteristic
224#66867C2311yescharacteristic
225#66867C2312yes—
226#66867C2312yes—
227C4×C11⋊C8C2312yes—
228#60886—111nomaximal, Sylow
229C11×#41—24no—
230C2×Q8×C11—22no—
231C2×Q8×C11—22no—
232C2×Q8×C11—21no—
233C2×Q8×C11—21no—
234C2×Q8×C11C2×D411yescharacteristic
235C2×D4×C11C2×D411yescharacteristic
236C2×D4×C11C2×D412yes—
237C22×C4×C11—22no—
238C22×C4×C11—22no—
239C22×C4×C11—21no—
240C22×C4×C11—21no—
241C22×C4×C11C2×D412yes—
242C22×C4×C11C2×D411yescharacteristic
243C22×C4×C11C2×D412yes—
244C22×C4×C11C2×D411yescharacteristic
245C22×C4×C11C2412yes—
246C22×C4×C11C2411yescharacteristic
247C2×C22⋊D11—22no—
248C2×C22⋊D11—24no—
249C22×Dic11—22no—
250#4339—28no—
251#4339—84no—
252C2×D44—21no—
253C2×D44—21no—
254C2×D44C2412yes—
255C2×C4×D11—22no—
256C2×C4×D11—24no—
257C2×Dic22—22no—
258C2×Dic22—22no—
259C2×Dic22—82no—
260C2×Dic22C2412yes—
261C11×C4⋊C4—22no—
262C11×C4⋊C4—21no—
263C11×C4⋊C4—21no—
264C11×C4⋊C4—22no—
265C11×C4⋊C4—22no—
266C11×C4⋊C4—22no—
267C11×C4⋊C4—22no—
268C11×C4⋊C4—22no—
269C11×C4⋊C4—22no—
270C11×C4⋊C4—22no—
271C11×C4⋊C4—22no—
272C11×C4⋊C4—22no—
273C11×C4⋊C4—21no—
274C11×C4⋊C4—21no—
275C11×C4⋊C4—21no—
276C11×C4⋊C4—21no—
277C11×C4⋊C4—22no—
278C11×C4⋊C4—22no—
279C11×C4⋊C4—21no—
280C11×C4⋊C4—21no—
281C11×C4⋊C4C2×D411yescharacteristic
282C11×C4⋊C4C2×D411yescharacteristic
283C11×C4⋊C4C2×D412yes—
284C11×C4⋊C4C2×D412yes—
285C11×C4⋊C4C2412yes—
286C11×C4⋊C4C2411yescharacteristic
287C11×C4⋊C4C2411yescharacteristic
288C11×C4⋊C4C2412yes—
289C11×C4⋊C4C2411yescharacteristic
290C11×C4⋊C4C2411yescharacteristic
291C11×C22⋊C4—22no—
292C11×C22⋊C4—22no—
293C11×C22⋊C4—21no—
294C11×C22⋊C4—21no—
295C11×C22⋊C4C2×D412yes—
296C11×C22⋊C4C2×D412yes—
297C11×C22⋊C4C2×D412yes—
298C42×C11—22no—
299C42×C11—22no—
300C42×C11—21no—
301C42×C11—21no—
302C42×C11C2×D412yes—
303C42×C11C2×D411yescharacteristic
304C42×C11C2×D411yescharacteristic
305C42×C11C2×D412yes—
306C42×C11C2411yescharacteristic
307C42×C11C2411yescharacteristic
308C42×C11C2412yes—
309C22⋊Dic11—24no—
310(C2×D11)⋊C4—24no—
311(C2×D11)⋊C4—22no—
312(C2×D11)⋊C4—22no—
313(C2×D11)⋊C4—24no—
314C4⋊Dic11—21no—
315C4⋊Dic11—22no—
316C4⋊Dic11—22no—
317C4⋊Dic11—22no—
318C4⋊Dic11—21no—
319C4⋊Dic11C2414yes—
320Dic11⋊C4—24no—
321Dic11⋊C4—24no—
322C4×Dic11—24no—
323#4318—24no—
324C2×C11⋊C8—24no—
325C2×C11⋊C8C2414yes—
326C2×C11⋊C8C2412yes—
327C2×C11⋊C8C2412yes—
328#3511—111no—
329#3504D1111yescharacteristic, complemented
330#3244—114no—
331#3243—114no—
332#3237—112no—
333#3236—112no—
334#3235—112no—
335#3234—112no—
336#3165—111no—
337C2×#501—111no—
338#3142—111no—
339#3135—111no—
340#3099—112no—
341#3098—112no—
342#3084—112no—
343#3083—112no—
344#2923—111no—
345C23×C11C22×D412yes—
346C23×C11C22×D411yescharacteristic
347C22×D11—22no—
348Q8×C11—22no—
349Q8×C11—81no—
350Q8×C11—82no—
351Q8×C11—82no—
352Q8×C11—81no—
353D4×C11—24no—
354D4×C11—22no—
355C2×C4×C11—24no—
356C2×C4×C11—21no—
357C2×C4×C11—21no—
358C2×C4×C11—22no—
359C2×C4×C11—21no—
360C2×C4×C11—22no—
361C2×C4×C11—21no—
362C2×C4×C11—41no—
363C2×C4×C11—42no—
364C2×C4×C11—41no—
365C2×C4×C11—42no—
366C2×C4×C11—81no—
367C2×C4×C11—82no—
368C2×C4×C11—81no—
369C2×C4×C11—82no—
370C2×C4×C11C22×D412yes—
371C2×C4×C11C22×D412yes—
372C2×C4×C11C22×D412yes—
373C2×C4×C11C22×D411yescharacteristic
374C2×C4×C11C22×D411yescharacteristic
375C2×C4×C11C22×D411yescharacteristic
376C2×C4×C11C22×D411yescharacteristic
377C2×C4×C11C22×D411yescharacteristic
378C2×C4×C112−1+414yes—
379C2×C4×C11C2511yescharacteristic
380C22⋊D11—44no—
381C22⋊D11—84no—
382C2×Dic11—22no—
383C2×Dic11—24no—
384C2×Dic11—82no—
385D44—24no—
386D44—42no—
387D44—42no—
388C4×D11—44no—
389C4×D11—84no—
390Dic22—24no—
391Dic22—44no—
392Dic22—82no—
393C11⋊C8—22no—
394C11⋊C8—22no—
395C11⋊C8—24no—
396#557—21no—
397#557—21no—
398#556—221no—
399#555—221no—
400#554—21no—
401#554—22no—
402#554—22no—
403#554—21no—
404#554—221no—
405#553—222no—
406#548—222no—
407#547—221no—
408#544C2×D1111yescharacteristic
409#544C2×D1111yescharacteristic
410#544C2×D1112yes—
411#544C2×D1112yes—
412#542—114no—
413#537—112no—
414#533—112no—
415#533C2×D1111yescharacteristic
416#533C2×D1112yes—
417#532—112no—
418#532—111no—
419C2×C4⋊Q8—111no—
420C2×#125C2×D1111yescharacteristic
421C2×#125C2×D1112yes—
422#520—112no—
423#520C2×D1111yescharacteristic
424#520C2×D1111yescharacteristic
425C4×#41C2×D1111yescharacteristic
426#501—112no—
427#501—112no—
428#501—114no—
429#501—112no—
430#501—112no—
431#500—112no—
432#498—112no—
433#491—111no—
434#491—111no—
435#491—112no—
436#490—111no—
437#490—111no—
438#490—112no—
439#489—112no—
440#489—112no—
441#488—114no—
442#485—114no—
443#485—114no—
444#484—114no—
445#483—114no—
446#482—114no—
447#482—114no—
448#481—114no—
449#480—114no—
450#479—114no—
451#479—114no—
452#478—114no—
453#478—114no—
454#477—114no—
455#476—114no—
456#475—114no—
457#474—114no—
458#433—114no—
459#432—112no—
460#432—112no—
461#428—112no—
462#428—112no—
463C2×#107—112no—
464C2×#106—112no—
465#424—112no—
466#417—112no—
467#417—112no—
468#416—112no—
469#416—112no—
470#408—112no—
471C4×M16—111no—
472C2×#97—111no—
473C22×C11—21no—
474C22×C11—21no—
475C22×C11—22no—
476C22×C11—22no—
477C22×C11—22no—
478C22×C11#53612yes—
479C22×C11C23×D411yescharacteristic
480C2×D11—42no—
481C2×D11—42no—
482C2×D11—42no—
483C4×C11—21no—
484C4×C11—21no—
485C4×C11—22no—
486C4×C11—21no—
487C4×C11—22no—
488C4×C11—21no—
489C4×C11—22no—
490C4×C11—42no—
491C4×C11—41no—
492C4×C11—41no—
493C4×C11—42no—
494C4×C11—41no—
495C4×C11—41no—
496C4×C11#53612yes—
497C4×C11C2×2−1+412yes—
498Dic11—44no—
499Dic11—42no—
500C2×#41—112no—
501C2×#41—222no—
502C2×#41C22×D1111yescharacteristic
503C22×Q8—221no—
504C2×M16—112no—
505C22×C8—112no—
506C4⋊Q8—21no—
507C4⋊Q8—21no—
508C4⋊Q8—22no—
509C4⋊Q8—22no—
510C4⋊Q8—112no—
511C4⋊Q8—112no—
512C4⋊Q8—111no—
513C4⋊Q8—221no—
514C4⋊Q8—221no—
515C4⋊Q8C22×D1112yes—
516C4⋊Q8C22×D1112yes—
517C4⋊Q8C22×D1111yescharacteristic
518C4⋊Q8C22×D1111yescharacteristic
519#127—111no—
520#126—224no—
521#125—21no—
522#125—21no—
523#125—22no—
524#125—22no—
525#125—22no—
526#125—21no—
527#125—21no—
528#125—22no—
529#125—222no—
530#125C22×D1112yes—
531#125C22×D1111yescharacteristic
532#125C22×D1112yes—
533#125C22×D1112yes—
534#125C22×D1112yes—
535#125C22×D1111yescharacteristic
536#124—112no—
537#124—224no—
538#124—222no—
539#123—224no—
540C22⋊Q8—21no—
541C22⋊Q8—22no—
542C22⋊Q8—21no—
543C22⋊Q8—22no—
544C22⋊Q8—22no—
545C22⋊Q8—22no—
546C22⋊Q8—22no—
547C22⋊Q8—22no—
548C22⋊Q8—22no—
549C22⋊Q8—22no—
550C22⋊Q8—114no—
551C22⋊Q8—222no—
552C22⋊Q8—222no—
553C22⋊Q8—224no—
554#121—114no—
555#121—222no—
556#121—224no—
557#121—221no—
558#121—221no—
559#121—222no—
560C4×Q8—21no—
561C4×Q8—21no—
562C4×Q8—22no—
563C4×Q8—21no—
564C4×Q8—21no—
565C4×Q8—22no—
566C4×Q8—114no—
567C4×Q8—222no—
568C4×Q8C22⋊D1111yescharacteristic
569C4×Q8C22⋊D1111yescharacteristic
570C4×D4—22no—
571C4×D4—21no—
572C4×D4—22no—
573C4×D4—21no—
574C4×D4—114no—
575C4×D4—224no—
576C4×D4—221no—
577C4×D4—222no—
578C4×D4—221no—
579C4×D4C22⋊D1111yescharacteristic
580C4×D4C22⋊D1112yes—
581C4×D4C22⋊D1112yes—
582C4×D4C22⋊D1111yescharacteristic
583#117—222no—
584#117—222no—
585#117C22×D1111yescharacteristic
586#117C22×D1111yescharacteristic
587#117C22×D1112yes—
588#117C22×D1112yes—
589#117C22×D1111yescharacteristic
590#117C22×D1112yes—
591C2×C4⋊C4—21no—
592C2×C4⋊C4—22no—
593C2×C4⋊C4—21no—
594C2×C4⋊C4—22no—
595C2×C4⋊C4—112no—
596C2×C4⋊C4—221no—
597C2×C4⋊C4—222no—
598C2×C4⋊C4C22×D1111yescharacteristic
599C2×C4⋊C4C22×D1111yescharacteristic
600C2×C4⋊C4C22×D1112yes—
601C2×C4⋊C4C22×D1112yes—
602C2×C42C22×D1111yescharacteristic
603C2×C42C22×D1112yes—
604#107—114no—
605#107—114no—
606#107—114no—
607#107—114no—
608#106—114no—
609#106—114no—
610#106—114no—
611#106—114no—
612C4⋊C8—114no—
613C4⋊C8—114no—
614#103—112no—
615#103—112no—
616#103—112no—
617#103—112no—
618#103—114no—
619#103—114no—
620#102—112no—
621#102—112no—
622#102—112no—
623#102—112no—
624#102—114no—
625#102—114no—
626C22⋊C8—114no—
627C22⋊C8—114no—
628#97—111no—
629#97—111no—
630#97—112no—
631#97—112no—
632C4×C8—112no—
633C2×C11—22no—
634C2×C11—42no—
635C2×C11C2×#53611yescharacteristic
636C2×C11#358511yescharacteristic
637C2×C11#358611yescharacteristic
638D11—82no—
639#41—24no—
640#41—228no—
641#41—884no—
642C2×Q8—22no—
643C2×Q8—21no—
644C2×Q8—21no—
645C2×Q8—22no—
646C2×Q8—112no—
647C2×Q8—222no—
648C2×Q8—222no—
649C2×Q8—882no—
650C2×Q8C2×C22⋊D1111yescharacteristic
651C2×D4—112no—
652C2×D4—222no—
653C2×D4—224no—
654C2×D4—221no—
655C2×D4—221no—
656C2×D4C2×C22⋊D1112yes—
657C2×D4C2×C22⋊D1111yescharacteristic
658C22×C4—22no—
659C22×C4—22no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—222no—
663C22×C4—222no—
664C22×C4—224no—
665C22×C4C2×C22⋊D1111yescharacteristic
666C22×C4C2×C22⋊D1112yes—
667C22×C4C2×C22⋊D1111yescharacteristic
668C22×C4C2×C22⋊D1112yes—
669C22×C4C23×D1112yes—
670C22×C4C23×D1111yescharacteristic
671M16—224no—
672C2×C8—114no—
673C2×C8—112no—
674C2×C8—112no—
675C2×C8—224no—
676C4⋊C4—22no—
677C4⋊C4—21no—
678C4⋊C4—22no—
679C4⋊C4—21no—
680C4⋊C4—22no—
681C4⋊C4—22no—
682C4⋊C4—22no—
683C4⋊C4—22no—
684C4⋊C4—22no—
685C4⋊C4—22no—
686C4⋊C4—22no—
687C4⋊C4—22no—
688C4⋊C4—21no—
689C4⋊C4—21no—
690C4⋊C4—21no—
691C4⋊C4—21no—
692C4⋊C4—22no—
693C4⋊C4—21no—
694C4⋊C4—21no—
695C4⋊C4—22no—
696C4⋊C4—114no—
697C4⋊C4—222no—
698C4⋊C4—222no—
699C4⋊C4—224no—
700C4⋊C4—222no—
701C4⋊C4—221no—
702C4⋊C4—221no—
703C4⋊C4—224no—
704C4⋊C4C2×C22⋊D1111yescharacteristic
705C4⋊C4C2×C22⋊D1111yescharacteristic
706C4⋊C4C2×C22⋊D1112yes—
707C4⋊C4C2×C22⋊D1112yes—
708C4⋊C4C23×D1111yescharacteristic
709C4⋊C4C23×D1112yes—
710C4⋊C4C23×D1111yescharacteristic
711C4⋊C4C23×D1111yescharacteristic
712C4⋊C4C23×D1112yes—
713C4⋊C4C23×D1111yescharacteristic
714C22⋊C4—22no—
715C22⋊C4—22no—
716C22⋊C4—21no—
717C22⋊C4—21no—
718C22⋊C4—224no—
719C22⋊C4—224no—
720C22⋊C4—224no—
721C22⋊C4—222no—
722C22⋊C4—222no—
723C22⋊C4C2×C22⋊D1112yes—
724C22⋊C4C2×C22⋊D1112yes—
725C22⋊C4C2×C22⋊D1112yes—
726C42—22no—
727C42—22no—
728C42—21no—
729C42—21no—
730C42—224no—
731C42C2×C22⋊D1112yes—
732C42C2×C22⋊D1111yescharacteristic
733C42C2×C22⋊D1111yescharacteristic
734C42C2×C22⋊D1112yes—
735C42C23×D1111yescharacteristic
736C42C23×D1111yescharacteristic
737C42C23×D1112yes—
738C11#6088611yescharacteristic, complemented, Sylow
739C23—222no—
740C23C22×C22⋊D1112yes—
741C23C22×C22⋊D1111yescharacteristic
742Q8—22no—
743Q8—82no—
744Q8—81no—
745Q8—82no—
746Q8—81no—
747Q8—224no—
748Q8—444no—
749Q8—882no—
750D4—24no—
751D4—22no—
752D4—224no—
753D4—442no—
754D4—442no—
755D4—444no—
756D4—884no—
757C2×C4—24no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—22no—
761C2×C4—21no—
762C2×C4—22no—
763C2×C4—21no—
764C2×C4—41no—
765C2×C4—42no—
766C2×C4—41no—
767C2×C4—42no—
768C2×C4—81no—
769C2×C4—82no—
770C2×C4—81no—
771C2×C4—82no—
772C2×C4—222no—
773C2×C4—224no—
774C2×C4—444no—
775C2×C4—884no—
776C2×C4—882no—
777C2×C4#6704014yes—
778C2×C4C22×C22⋊D1112yes—
779C2×C4C22×C22⋊D1112yes—
780C2×C4C22×C22⋊D1111yescharacteristic
781C2×C4C22×C22⋊D1111yescharacteristic
782C2×C4C22×C22⋊D1111yescharacteristic
783C2×C4C22×C22⋊D1111yescharacteristic
784C2×C4C22×C22⋊D1112yes—
785C2×C4C22×C22⋊D1111yescharacteristic
786C2×C4C24×D1111yescharacteristic
787C8—222no—
788C8—222no—
789C8—224no—
790C22—21no—
791C22—21no—
792C22—22no—
793C22—22no—
794C22—22no—
795C22—442no—
796C22—442no—
797C22—442no—
798C22#1062334712yes—
799C22C23×C22⋊D1111yescharacteristic
800C4—21no—
801C4—22no—
802C4—21no—
803C4—21no—
804C4—22no—
805C4—21no—
806C4—22no—
807C4—42no—
808C4—41no—
809C4—41no—
810C4—42no—
811C4—41no—
812C4—41no—
813C4—444no—
814C4—442no—
815C4#1062334712yes—
816C4C2×#6704012yes—
817C2—22no—
818C2—42no—
819C2—882no—
820C2C2×#1062334711yescharacteristic
821C2#1308339511yescharacteristic
822C2#1308340211yescharacteristic
subgroupG/H
centerC22C23×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#3504C2
socleC22×C11C23×D4
prime radical#13082527C2
hypercenter#3504D11
hypocenterC11#60886
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4×#41 ◁ #3504

Complements

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

NH ≅ G/Ntype
2. #13079914C2semidirect
3. #13079899C2semidirect
4. #13079830C2semidirect
5. #13079822C2semidirect
6. #13079814C2semidirect
7. #13079806C2semidirect
8. #13079163C2semidirect
9. C2×#10622678C2semidirect
10. #13079019C2semidirect
11. #13078964C2semidirect
12. #13078605C2semidirect
13. #13078594C2semidirect
14. #13078474C2semidirect
15. #13078463C2semidirect
16. #13077267C2semidirect
17. C11×#3504C2semidirect
329. #3504D11semidirect
738. C11#60886semidirect

Maximal subgroups

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

subgroupindex
#130825272
#130799142
#130798992
#130798302
#130798222
#130798142
#130798062
#130791632
C2×#106226782
#130790192
#130789642
#130786052
#130785942
#130784742
#130784632
#130772672
C11×#35042
#6088611