Finite Group Databasebeta

← #15633741

Subgroups — #15633741

Order 2816.

1806 conjugacy classes of subgroups.

The subgroup lattice has 790 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082483C211yesmaximal, characteristic, complemented
2#13081443C214yesmaximal, complemented
3#13081408C212yesmaximal, complemented
4#13081397C212yesmaximal, complemented
5#13081276C212yesmaximal, complemented
6#13081265C214yesmaximal, complemented
7#13081258C212yesmaximal, complemented
8#13078986C212yesmaximal, complemented
9#13078941C211yesmaximal, characteristic, complemented
10#13078474C212yesmaximal, complemented
11#13078417C211yesmaximal, characteristic, complemented
12#13078128C212yesmaximal, complemented
13#13078080C211yesmaximal, characteristic
14#13077551C211yesmaximal, characteristic, complemented
15#13077448C212yesmaximal, complemented
16C2×C4×#4324C211yesmaximal, characteristic, complemented
17C11×#3501C211yesmaximal, characteristic, complemented
18C11×#554—21no—
19C11×#554—22no—
20C11×#554C2212yes—
21C11×#554C2214yes—
22D4×Q8×C11—21no—
23D4×Q8×C11C2212yes—
24C11×#544C2212yes—
25C11×#543—22no—
26C11×#533C2211yescharacteristic
27C11×#533C2211yescharacteristic
28C2×C11×C22⋊Q8—22no—
29C11×#518C2212yes—
30C2×C4×D4×C11C2211yescharacteristic
31C22×#4324C2211yescharacteristic
32C2×#66985C2212yes—
33#10623263—21no—
34#10623261—21no—
35#10623225—22no—
36#10623176—22no—
37#10623155—22no—
38#10623116C2212yescomplemented
39#10623115C2214yescomplemented
40#10623101C2212yescomplemented
41#10623057C2212yes—
42#10623054C2212yes—
43#10623008C2211yescharacteristic
44C2×C4×Dic22C2211yescharacteristic
45C2×#66896C2211yescharacteristic
46#10622707C2212yescomplemented
47#10622707C2214yescomplemented
48#10622706C2211yescharacteristic, complemented
49#10622706C2211yescharacteristic, complemented
50#10622706C2214yescomplemented
51#10622704C2212yescomplemented
52#10622702C2214yescomplemented
53#10622701C2211yescharacteristic, complemented
54#10622701C2211yescharacteristic, complemented
55#10622697C2214yescomplemented
56#10622682C2214yescomplemented
57#10622681C2212yescomplemented
58#10622681C2212yescomplemented
59#10622681C2214yescomplemented
60#10622679C2214yescomplemented
61#10622676C2214yescomplemented
62#10622676C2214yescomplemented
63#10622637C2212yescomplemented
64#10622637C2212yescomplemented
65Q8×C11⋊C8C2212yescomplemented
66Q8×C11⋊C8C2212yescomplemented
67#10622632C2212yes—
68#10622632C2214yes—
69#10622632C2214yes—
70#10622631C2214yes—
71C4×#4324C2212yes—
72C4×#4324C2212yes—
73C4×#4324C2212yes—
74C4×#4324C2212yes—
75C4×#4324C2214yes—
76#10622629C2214yes—
77#10622629C2214yes—
78#10622629C2214yes—
79#10622628C2212yes—
80#10622627C2214yes—
81C4×#4323C2214yes—
82#10622617C2212yes—
83#10622615C2212yes—
84#10622615C2212yes—
85#10622612C2212yes—
86#10622610C2212yes—
87#10622608C2212yes—
88C2×#66874C2211yescharacteristic
89#10622579C2212yes—
90C2×#66872C2211yescharacteristic
91#10622537C2211yescharacteristic
92C2×C4×C11⋊C8C2211yescharacteristic
93C22×Q8×C11—22no—
94C22×D4×C11C2311yescharacteristic
95C23×C4×C11—21no—
96C2×#4339C2312yes—
97C22×Dic22C2311yescharacteristic
98C11×C4⋊Q8—22no—
99C11×C4⋊Q8D411yescharacteristic
100C11×C4⋊Q8D411yescharacteristic
101C11×C4⋊Q8C2311yescharacteristic
102C11×C4⋊Q8C2311yescharacteristic
103C11×C4⋊Q8C2314yes—
104C11×#125—22no—
105C11×#125D412yes—
106C11×#125C2312yes—
107C11×#125C2314yes—
108C11×C22⋊Q8—22no—
109C11×C22⋊Q8—24no—
110C11×C22⋊Q8—21no—
111C11×C22⋊Q8—21no—
112C11×C22⋊Q8—22no—
113C11×C22⋊Q8—24no—
114C11×C22⋊Q8—24no—
115C11×C22⋊Q8—24no—
116C11×C22⋊Q8—24no—
117C11×C22⋊Q8—24no—
118C11×C22⋊Q8D412yes—
119C11×C22⋊Q8D412yes—
120C4×Q8×C11—21no—
121C4×Q8×C11—21no—
122C4×Q8×C11C2312yes—
123C4×Q8×C11C2312yes—
124C4×D4×C11—22no—
125C4×D4×C11—22no—
126C4×D4×C11—21no—
127C4×D4×C11—21no—
128C4×D4×C11C2312yes—
129C4×D4×C11C2312yes—
130C4×D4×C11C2314yes—
131C4×D4×C11C2314yes—
132C11×#117C2312yes—
133C11×#117C2312yes—
134C2×C11×C4⋊C4—24no—
135C2×C11×C4⋊C4—22no—
136C2×C11×C4⋊C4C2311yescharacteristic
137C2×C11×C22⋊C4—21no—
138C2×C11×C22⋊C4—24no—
139C2×C42×C11C2311yescharacteristic
140#67000—22no—
141#66999—24no—
142Q8×Dic11—22no—
143C2×#4324—24no—
144C2×#4324C2314yes—
145C2×#4324C2312yes—
146C2×#4324C2312yes—
147#66985—28no—
148C2×#4323C2314yes—
149#66983—21no—
150#66983—21no—
151C2×C4⋊Dic11C2311yescharacteristic
152C2×Dic11⋊C4—21no—
153C2×C4×Dic11—21no—
154C2×#4318C2312yes—
155C22×C11⋊C8C2311yescharacteristic
156C22×C11⋊C8C2311yescharacteristic
157#66951—24no—
158#66951—24no—
159#66950—22no—
160#66950—22no—
161#66947—24no—
162#66946—22no—
163#66945—22no—
164#66945—24no—
165C4⋊C4×D11—22no—
166#66943—22no—
167#66943—24no—
168#66939—24no—
169(C22⋊D11)⋊C4—24no—
170#66928C2312yes—
171#66928C2314yes—
172#66927C2311yescharacteristic
173C4×D44—21no—
174C4×D44—21no—
175C4×D44C2314yes—
176#66922C2311yescharacteristic
177#66922C2314yes—
178C4×Dic22—21no—
179C4×Dic22—21no—
180C4×Dic22C2312yes—
181C4×Dic22C2312yes—
182C4×Dic22C2314yes—
183#66896C2312yes—
184#66896C2312yes—
185#66874C2314yes—
186#66874C2312yes—
187#66874C2312yes—
188#66874C2312yes—
189#66874C2312yes—
190#66874C2312yes—
191#66874C2312yes—
192#66874C2314yes—
193#66874C2314yes—
194#66873C2314yes—
195#66873C2312yes—
196#66873C2312yes—
197#66873C2312yes—
198#66873C2312yes—
199#66872C2312yes—
200#66872C2312yes—
201#66872C2314yes—
202#66871C2314yes—
203C4⋊(C11⋊C8)C2312yes—
204C4⋊(C11⋊C8)C2312yes—
205C4⋊(C11⋊C8)C2314yes—
206C4⋊(C11⋊C8)C2314yes—
207#66867C2314yes—
208C4×C11⋊C8C2311yescharacteristic
209C4×C11⋊C8C2311yescharacteristic
210C4×C11⋊C8C2311yescharacteristic
211C4×C11⋊C8C2311yescharacteristic
212C4×C11⋊C8C2314yes—
213#61326—111nomaximal, Sylow
214C24×C11—21no—
215C2×Q8×C11—21no—
216C2×Q8×C11—21no—
217C2×Q8×C11—24no—
218C2×Q8×C11—84no—
219C2×Q8×C11C2×D412yes—
220C2×Q8×C11C2×D412yes—
221C2×D4×C11—21no—
222C2×D4×C11—22no—
223C2×D4×C11#4114yes—
224C2×D4×C11C2412yes—
225C22×C4×C11—21no—
226C22×C4×C11—22no—
227C22×C4×C11—24no—
228C22×C4×C11—24no—
229C22×C4×C11—22no—
230C22×C4×C11—82no—
231C22×C4×C11C2×D411yescharacteristic
232C22×C4×C11C2×D411yescharacteristic
233C22×C4×C11C2411yescharacteristic
234C2×C22⋊D11—22no—
235C22×Dic11—21no—
236C22×Dic11—21no—
237#4339—24no—
238#4339—24no—
239C2×D44—21no—
240C2×D44—21no—
241C2×D44C2412yes—
242C2×C4×D11—22no—
243C2×C4×D11—24no—
244C2×Dic22—21no—
245C2×Dic22—22no—
246C2×Dic22—22no—
247C2×Dic22C2412yes—
248C2×Dic22C2412yes—
249C11×C4⋊C4—22no—
250C11×C4⋊C4—21no—
251C11×C4⋊C4—24no—
252C11×C4⋊C4—24no—
253C11×C4⋊C4—24no—
254C11×C4⋊C4—21no—
255C11×C4⋊C4—22no—
256C11×C4⋊C4—21no—
257C11×C4⋊C4C2×D412yes—
258C11×C4⋊C4C2×D414yes—
259C11×C4⋊C4C2×D412yes—
260C11×C4⋊C4C2×D412yes—
261C11×C4⋊C4C2×D414yes—
262C11×C4⋊C4C2×D412yes—
263C11×C4⋊C4C2412yes—
264C11×C4⋊C4C2412yes—
265C11×C4⋊C4C2412yes—
266C11×C22⋊C4—22no—
267C11×C22⋊C4—24no—
268C11×C22⋊C4—24no—
269C11×C22⋊C4—22no—
270C11×C22⋊C4—22no—
271C11×C22⋊C4C2×D414yes—
272C42×C11—22no—
273C42×C11C2×D411yescharacteristic
274C42×C11C2×D411yescharacteristic
275C42×C11C2411yescharacteristic
276C42×C11C2411yescharacteristic
277C42×C11C2414yes—
278#4324—28no—
279#4324—24no—
280#4324—24no—
281#4323—28no—
282(C2×D11)⋊C4—22no—
283(C2×D11)⋊C4—22no—
284(C2×D11)⋊C4—24no—
285(C2×D11)⋊C4—24no—
286(C2×D11)⋊C4—24no—
287C4⋊Dic11—21no—
288C4⋊Dic11—21no—
289C4⋊Dic11—21no—
290C4⋊Dic11—24no—
291C4⋊Dic11—24no—
292C4⋊Dic11C2412yes—
293Dic11⋊C4—22no—
294Dic11⋊C4—22no—
295Dic11⋊C4—24no—
296C4×Dic11—22no—
297C4×Dic11—22no—
298C4×Dic11—24no—
299#4318—24no—
300C2×C11⋊C8—22no—
301C2×C11⋊C8—22no—
302C2×C11⋊C8C2411yescharacteristic
303C2×C11⋊C8C2411yescharacteristic
304C2×C11⋊C8C2411yescharacteristic
305C2×C11⋊C8C2411yescharacteristic
306C2×C11⋊C8C2414yes—
307#3507—111no—
308#3501D1111yescharacteristic, complemented
309#3376—114no—
310#3373—112no—
311#3372—112no—
312#3361—112no—
313#3360—114no—
314#3359—112no—
315#3137—112no—
316#3131—111no—
317#3084—112no—
318#3078—111no—
319#3042—112no—
320#3036—111no—
321#2960—111no—
322#2946—112no—
323C2×C4×SD16—111no—
324C23×C11—22no—
325C23×C11—24no—
326C23×C11—81no—
327C23×C11—81no—
328C23×C11C22×D411yescharacteristic
329C22×D11—22no—
330Q8×C11—24no—
331Q8×C11—42no—
332Q8×C11—42no—
333Q8×C11—81no—
334Q8×C11—84no—
335D4×C11—24no—
336D4×C11—22no—
337D4×C11C2×#4114yes—
338C2×C4×C11—22no—
339C2×C4×C11—22no—
340C2×C4×C11—22no—
341C2×C4×C11—22no—
342C2×C4×C11—41no—
343C2×C4×C11—44no—
344C2×C4×C11—84no—
345C2×C4×C11—82no—
346C2×C4×C11—84no—
347C2×C4×C11—81no—
348C2×C4×C11C22×D411yescharacteristic
349C2×C4×C11C22×D414yes—
350C2×C4×C11C22×D411yescharacteristic
351C2×C4×C11C22×D411yescharacteristic
352C2×C4×C11C22×D414yes—
353C2×C4×C11C22×D411yescharacteristic
354C2×C4×C11C22×D411yescharacteristic
355C2×C4×C11C2×#4112yes—
356C2×C4×C112−1+412yes—
357C2×C4×C11C2511yescharacteristic
358C22⋊D11—44no—
359C2×Dic11—22no—
360C2×Dic11—22no—
361C2×Dic11—22no—
362C2×Dic11—42no—
363C2×Dic11—81no—
364D44—22no—
365D44—22no—
366D44—42no—
367D44—81no—
368C4×D11—44no—
369C4×D11—84no—
370Dic22—22no—
371Dic22—22no—
372Dic22—22no—
373Dic22—22no—
374Dic22—42no—
375C11⋊C8—21no—
376C11⋊C8—21no—
377C11⋊C8—24no—
378C11⋊C8—21no—
379C11⋊C8—21no—
380C2×AGL(1,ℤ/8)—112no—
381C22×SD16—111no—
382#559—112no—
383#557—112no—
384#556—114no—
385#556—221no—
386#554—21no—
387#554—22no—
388#554—221no—
389#554C2×D1114yes—
390#554C2×D1112yes—
391#552—222no—
392D4×Q8—21no—
393D4×Q8C2×D1112yes—
394#544C2×D1112yes—
395#543—22no—
396#539—222no—
397#536—112no—
398#533C2×D1111yescharacteristic
399#533C2×D1111yescharacteristic
400#532—111no—
401#529—222no—
402C2×C22⋊Q8—22no—
403#520—112no—
404#518C2×D1112yes—
405C2×C4×Q8—111no—
406C2×C4×D4C2×D1111yescharacteristic
407#491—114no—
408#489—114no—
409#488—112no—
410#488—114no—
411#488—112no—
412#487—111no—
413#487—114no—
414#487—111no—
415#486—111no—
416#486—111no—
417#479—114no—
418#479—114no—
419#478—114no—
420#477—112no—
421#476—114no—
422#475—112no—
423#475—114no—
424#463—114no—
425#463—114no—
426#463—114no—
427#461—112no—
428#461—114no—
429#461—114no—
430#459—112no—
431#446—112no—
432#446—112no—
433C8×Q8—112no—
434C8×Q8—112no—
435#442—114no—
436#440—114no—
437C4×SD16—114no—
438C4×SD16—112no—
439C4×SD16—112no—
440C4×SD16—112no—
441C4×SD16—112no—
442C4×D8—114no—
443#428—112no—
444C2×#106—111no—
445#424—112no—
446#423—111no—
447#419—112no—
448#417—112no—
449#416—112no—
450#416—112no—
451C2×#103—111no—
452C2×#102—111no—
453#405—112no—
454C2×C4×C8—111no—
455C22×C11—21no—
456C22×C11—21no—
457C22×C11—24no—
458C22×C11—42no—
459C22×C11—42no—
460C22×C11—84no—
461C22×C11#54812yes—
462C22×C11C23×D411yescharacteristic
463C2×D11—42no—
464C2×D11—42no—
465C2×D11—42no—
466C4×C11—21no—
467C4×C11—21no—
468C4×C11—24no—
469C4×C11—21no—
470C4×C11—24no—
471C4×C11—42no—
472C4×C11—42no—
473C4×C11—42no—
474C4×C11#54812yes—
475C4×C11#57712yes—
476C4×C11C22×#4111yescharacteristic
477C4×C11C2×2−1+411yescharacteristic
478Dic11—42no—
479Dic11—42no—
480Dic11—42no—
481C2×#41—112no—
482C22×Q8—22no—
483C22×Q8—111no—
484C22×D4C22×D1111yescharacteristic
485C23×C4—21no—
486AGL(1,ℤ/8)—228no—
487C2×SD16—112no—
488C2×SD16—112no—
489C2×SD16—114no—
490C2×SD16—224no—
491C2×D8—114no—
492C2×M16—112no—
493C22×C8—111no—
494C22×C8—111no—
495C4⋊Q8—22no—
496C4⋊Q8—111no—
497C4⋊Q8—114no—
498C4⋊Q8C22⋊D1111yescharacteristic
499C4⋊Q8C22⋊D1111yescharacteristic
500C4⋊Q8C22×D1111yescharacteristic
501C4⋊Q8C22×D1111yescharacteristic
502C4⋊Q8C22×D1114yes—
503#127—111no—
504#126—224no—
505#126—224no—
506#125—22no—
507#125—222no—
508#125—224no—
509#125C22⋊D1112yes—
510#125C22×D1112yes—
511#125C22×D1114yes—
512#124—112no—
513#124—114no—
514#124—222no—
515#123—224no—
516#123—224no—
517C22⋊Q8—22no—
518C22⋊Q8—24no—
519C22⋊Q8—21no—
520C22⋊Q8—21no—
521C22⋊Q8—22no—
522C22⋊Q8—24no—
523C22⋊Q8—24no—
524C22⋊Q8—24no—
525C22⋊Q8—24no—
526C22⋊Q8—24no—
527C22⋊Q8—224no—
528C22⋊Q8—222no—
529C22⋊Q8—222no—
530C22⋊Q8C22⋊D1112yes—
531C22⋊Q8C22⋊D1112yes—
532#121—221no—
533#121—221no—
534C4×Q8—21no—
535C4×Q8—21no—
536C4×Q8—112no—
537C4×Q8—112no—
538C4×Q8—114no—
539C4×Q8—222no—
540C4×Q8—221no—
541C4×Q8—221no—
542C4×Q8C22×D1112yes—
543C4×Q8C22×D1112yes—
544C4×D4—22no—
545C4×D4—22no—
546C4×D4—21no—
547C4×D4—21no—
548C4×D4—114no—
549C4×D4—222no—
550C4×D4—224no—
551C4×D4—221no—
552C4×D4—221no—
553C4×D4C22×D1112yes—
554C4×D4C22×D1112yes—
555C4×D4C22×D1114yes—
556C4×D4C22×D1114yes—
557#117—222no—
558#117—224no—
559#117C22×D1112yes—
560#117C22×D1112yes—
561C2×C4⋊C4—24no—
562C2×C4⋊C4—22no—
563C2×C4⋊C4—111no—
564C2×C4⋊C4—221no—
565C2×C4⋊C4—222no—
566C2×C4⋊C4C22×D1111yescharacteristic
567C2×C22⋊C4—21no—
568C2×C22⋊C4—24no—
569C2×C42—221no—
570C2×C42C22×D1111yescharacteristic
571#107—114no—
572#106—112no—
573#106—112no—
574#106—114no—
575C4⋊C8—112no—
576C4⋊C8—112no—
577C4⋊C8—114no—
578C4⋊C8—114no—
579#103—112no—
580#103—112no—
581#103—112no—
582#103—112no—
583#103—112no—
584#103—112no—
585#103—114no—
586#103—114no—
587#103—114no—
588#102—112no—
589#102—112no—
590#102—112no—
591#102—112no—
592#102—112no—
593#102—112no—
594#102—114no—
595#97—114no—
596C4×C8—111no—
597C4×C8—111no—
598C4×C8—111no—
599C4×C8—111no—
600C4×C8—114no—
601C2×C11—22no—
602C2×C11—44no—
603C2×C11C2×#54811yescharacteristic
604C2×C11C2×#57711yescharacteristic
605C2×C11#358411yescharacteristic
606D11—82no—
607C24—21no—
608#41—224no—
609#41—224no—
610C2×Q8—21no—
611C2×Q8—21no—
612C2×Q8—24no—
613C2×Q8—84no—
614C2×Q8—112no—
615C2×Q8—112no—
616C2×Q8—221no—
617C2×Q8—222no—
618C2×Q8—222no—
619C2×Q8C2×C22⋊D1112yes—
620C2×Q8C2×C22⋊D1112yes—
621C2×D4—22no—
622C2×D4—21no—
623C2×D4—112no—
624C2×D4—222no—
625C2×D4—221no—
626C2×D4—221no—
627C2×D4#434314yes—
628C2×D4C23×D1112yes—
629C22×C4—21no—
630C22×C4—22no—
631C22×C4—24no—
632C22×C4—24no—
633C22×C4—22no—
634C22×C4—82no—
635C22×C4—221no—
636C22×C4—221no—
637C22×C4—222no—
638C22×C4—224no—
639C22×C4C2×C22⋊D1111yescharacteristic
640C22×C4C2×C22⋊D1111yescharacteristic
641C22×C4C23×D1111yescharacteristic
642SD16—224no—
643SD16—224no—
644SD16—228no—
645D8—228no—
646M16—224no—
647C2×C8—111no—
648C2×C8—111no—
649C2×C8—111no—
650C2×C8—111no—
651C2×C8—114no—
652C2×C8—222no—
653C2×C8—222no—
654C4⋊C4—22no—
655C4⋊C4—21no—
656C4⋊C4—24no—
657C4⋊C4—24no—
658C4⋊C4—24no—
659C4⋊C4—21no—
660C4⋊C4—22no—
661C4⋊C4—21no—
662C4⋊C4—112no—
663C4⋊C4—221no—
664C4⋊C4—224no—
665C4⋊C4—222no—
666C4⋊C4—222no—
667C4⋊C4—224no—
668C4⋊C4—221no—
669C4⋊C4—221no—
670C4⋊C4—224no—
671C4⋊C4C2×C22⋊D1114yes—
672C4⋊C4C2×C22⋊D1112yes—
673C4⋊C4C2×C22⋊D1112yes—
674C4⋊C4C2×C22⋊D1112yes—
675C4⋊C4C2×C22⋊D1114yes—
676C4⋊C4C2×C22⋊D1112yes—
677C4⋊C4C23×D1112yes—
678C4⋊C4C23×D1112yes—
679C4⋊C4C23×D1112yes—
680C22⋊C4—22no—
681C22⋊C4—24no—
682C22⋊C4—24no—
683C22⋊C4—22no—
684C22⋊C4—22no—
685C22⋊C4—222no—
686C22⋊C4—224no—
687C22⋊C4—224no—
688C22⋊C4—222no—
689C22⋊C4—224no—
690C22⋊C4C2×C22⋊D1114yes—
691C42—22no—
692C42—222no—
693C42—222no—
694C42—224no—
695C42C2×C22⋊D1111yescharacteristic
696C42C2×C22⋊D1111yescharacteristic
697C42C23×D1111yescharacteristic
698C42C23×D1111yescharacteristic
699C42C23×D1114yes—
700C11#6132611yescharacteristic, complemented, Sylow
701C23—22no—
702C23—24no—
703C23—81no—
704C23—81no—
705C23—222no—
706C23C22×C22⋊D1111yescharacteristic
707Q8—24no—
708Q8—42no—
709Q8—42no—
710Q8—81no—
711Q8—84no—
712Q8—222no—
713Q8—222no—
714Q8—222no—
715Q8—222no—
716Q8—442no—
717D4—24no—
718D4—22no—
719D4—222no—
720D4—222no—
721D4—444no—
722D4—442no—
723D4—881no—
724D4C2×#434314yes—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—41no—
730C2×C4—44no—
731C2×C4—84no—
732C2×C4—82no—
733C2×C4—84no—
734C2×C4—81no—
735C2×C4—222no—
736C2×C4—222no—
737C2×C4—222no—
738C2×C4—442no—
739C2×C4—444no—
740C2×C4—884no—
741C2×C4—881no—
742C2×C4C2×#434312yes—
743C2×C4#6704012yes—
744C2×C4C22×C22⋊D1111yescharacteristic
745C2×C4C22×C22⋊D1114yes—
746C2×C4C22×C22⋊D1111yescharacteristic
747C2×C4C22×C22⋊D1111yescharacteristic
748C2×C4C22×C22⋊D1114yes—
749C2×C4C22×C22⋊D1111yescharacteristic
750C2×C4C22×C22⋊D1111yescharacteristic
751C2×C4C24×D1111yescharacteristic
752C8—221no—
753C8—221no—
754C8—224no—
755C8—221no—
756C8—221no—
757C22—21no—
758C22—21no—
759C22—24no—
760C22—42no—
761C22—42no—
762C22—84no—
763C22—442no—
764C22—442no—
765C22—442no—
766C22#1062334812yes—
767C22C23×C22⋊D1111yescharacteristic
768C4—21no—
769C4—24no—
770C4—21no—
771C4—21no—
772C4—24no—
773C4—42no—
774C4—42no—
775C4—42no—
776C4—442no—
777C4—442no—
778C4—442no—
779C4#1062334812yes—
780C4#1062336712yes—
781C4C22×#434311yescharacteristic
782C4C2×#6704011yescharacteristic
783C2—22no—
784C2—44no—
785C2—882no—
786C2C2×#1062334811yescharacteristic
787C2C2×#1062336711yescharacteristic
788C2#1308338711yescharacteristic
subgroupG/H
centerC22C23×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#3501C2
socleC22×C11C23×D4
prime radical#13078080C2
hypercenter#3501D11
hypocenterC11#61326
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ #533 ◁ #3501

Complements

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

NH ≅ G/Ntype
1. #13082483C2semidirect
2. #13081443C2semidirect
3. #13081408C2semidirect
4. #13081397C2semidirect
5. #13081276C2semidirect
6. #13081265C2semidirect
7. #13081258C2semidirect
8. #13078986C2semidirect
9. #13078941C2semidirect
10. #13078474C2semidirect
11. #13078417C2semidirect
12. #13078128C2semidirect
14. #13077551C2semidirect
15. #13077448C2semidirect
16. C2×C4×#4324C2semidirect
17. C11×#3501C2semidirect
38. #10623116C22semidirect
39. #10623115C22semidirect
40. #10623101C22semidirect
46. #10622707C22semidirect
47. #10622707C22semidirect
48. #10622706C22semidirect
49. #10622706C22semidirect
50. #10622706C22semidirect
51. #10622704C22semidirect
52. #10622702C22semidirect
53. #10622701C22semidirect
54. #10622701C22semidirect
55. #10622697C22semidirect
56. #10622682C22semidirect
57. #10622681C22semidirect
58. #10622681C22semidirect
59. #10622681C22semidirect
60. #10622679C22semidirect
61. #10622676C22semidirect
62. #10622676C22semidirect
63. #10622637C22semidirect
64. #10622637C22semidirect
65. Q8×C11⋊C8C22semidirect
66. Q8×C11⋊C8C22semidirect
308. #3501D11semidirect
700. C11#61326semidirect

Maximal subgroups

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

subgroupindex
#130824832
#130814432
#130814082
#130813972
#130812762
#130812652
#130812582
#130789862
#130789412
#130784742
#130784172
#130781282
#130780802
#130775512
#130774482
C2×C4×#43242
C11×#35012
#6132611