Finite Group Databasebeta

← #15634402

Subgroups — #15634402

Order 2816.

1818 conjugacy classes of subgroups.

The subgroup lattice has 786 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082417C211yesmaximal, characteristic, complemented
2#13081570C214yesmaximal, complemented
3#13081515C212yesmaximal, complemented
4#13081511C212yesmaximal, complemented
5#13081479C212yesmaximal, complemented
6#13081479C214yesmaximal, complemented
7Q8×#4323C212yesmaximal, complemented
8#13079150C212yesmaximal, complemented
9#13079126C211yesmaximal, characteristic, complemented
10#13078447C212yesmaximal, complemented
11#13078441C212yesmaximal, complemented
12#13078413C211yesmaximal, characteristic, complemented
13#13078409C211yesmaximal, characteristic, complemented
14#13077551C211yesmaximal, characteristic, complemented
15#13077466C212yesmaximal
16C2×C4×#4323C211yesmaximal, characteristic
17C11×#3501C211yesmaximal, characteristic, complemented
18C11×#554—21no—
19C11×#554—22no—
20C11×#554C2212yescomplemented
21C11×#554C2214yescomplemented
22D4×Q8×C11—21no—
23D4×Q8×C11C2212yescomplemented
24C11×#544C2212yes—
25C11×#543—22no—
26C11×#533C2211yescharacteristic
27C11×#533C2211yescharacteristic
28C2×C11×C22⋊Q8—22no—
29C11×#518C2212yes—
30C2×C4×D4×C11C2211yescharacteristic
31C22×#4323C2211yescharacteristic
32#10623261—21no—
33#10623258—21no—
34#10623221—22no—
35#10623165—22no—
36D11×C22⋊Q8—22no—
37#10623110C2212yescomplemented
38#10623110C2214yescomplemented
39Q8×D44C2212yescomplemented
40#10623052C2212yes—
41#10623050C2212yes—
42C2×C4×D44C2211yescharacteristic
43#10623001C2211yescharacteristic
44#10622828C2212yes—
45C2×#66896C2211yescharacteristic
46#10622700C2212yescomplemented
47#10622700C2214yescomplemented
48#10622697C2212yescomplemented
49#10622697C2214yescomplemented
50#10622693C2214yescomplemented
51#10622692C2211yescharacteristic, complemented
52#10622692C2211yescharacteristic, complemented
53#10622691C2211yescharacteristic, complemented
54#10622691C2211yescharacteristic, complemented
55#10622691C2214yescomplemented
56#10622679C2214yescomplemented
57#10622679C2214yescomplemented
58#10622679C2214yescomplemented
59#10622678C2214yescomplemented
60#10622677C2212yescomplemented
61#10622677C2212yescomplemented
62#10622677C2214yescomplemented
63#10622637C2212yescomplemented
64#10622637C2212yescomplemented
65Q8×C11⋊C8C2212yescomplemented
66Q8×C11⋊C8C2212yescomplemented
67#10622627C2214yes—
68#10622627C2214yes—
69C4×#4323C2212yes—
70C4×#4323C2212yes—
71C4×#4323C2212yes—
72C4×#4323C2212yes—
73C4×#4323C2214yes—
74C4×#4323C2214yes—
75#10622622C2214yescomplemented
76#10622622C2214yescomplemented
77#10622622C2214yescomplemented
78#10622621C2212yescomplemented
79#10622621C2214yescomplemented
80#10622620C2212yescomplemented
81#10622620C2214yescomplemented
82#10622614C2212yes—
83#10622612C2212yes—
84#10622611C2212yes—
85#10622611C2212yes—
86#10622610C2212yes—
87#10622608C2212yes—
88C2×#66873C2211yescharacteristic
89#10622577C2212yes—
90C2×#66871C2211yescharacteristic
91#10622537C2211yescharacteristic
92C2×C4×C11⋊C8C2211yescharacteristic
93C22×Q8×C11—22no—
94C22×D4×C11C2311yescharacteristic
95C23×C4×C11—21no—
96C2×Q8×D11—22no—
97C22×D44C2311yescharacteristic
98C22×C4×D11—21no—
99C11×C4⋊Q8—22no—
100C11×C4⋊Q8D411yescharacteristic
101C11×C4⋊Q8D411yescharacteristic
102C11×C4⋊Q8C2311yescharacteristic
103C11×C4⋊Q8C2311yescharacteristic
104C11×C4⋊Q8C2314yes—
105C11×#125—22no—
106C11×#125D412yes—
107C11×#125C2312yes—
108C11×#125C2314yes—
109C11×C22⋊Q8—22no—
110C11×C22⋊Q8—24no—
111C11×C22⋊Q8—21no—
112C11×C22⋊Q8—21no—
113C11×C22⋊Q8—22no—
114C11×C22⋊Q8—24no—
115C11×C22⋊Q8—24no—
116C11×C22⋊Q8—24no—
117C11×C22⋊Q8—24no—
118C11×C22⋊Q8—24no—
119C11×C22⋊Q8D412yes—
120C11×C22⋊Q8D412yes—
121C4×Q8×C11—21no—
122C4×Q8×C11—21no—
123C4×Q8×C11C2312yes—
124C4×Q8×C11C2312yes—
125C4×D4×C11—22no—
126C4×D4×C11—22no—
127C4×D4×C11—21no—
128C4×D4×C11—21no—
129C4×D4×C11C2312yes—
130C4×D4×C11C2312yes—
131C4×D4×C11C2314yes—
132C4×D4×C11C2314yes—
133C11×#117C2312yes—
134C11×#117C2312yes—
135C2×C11×C4⋊C4—24no—
136C2×C11×C4⋊C4—22no—
137C2×C11×C4⋊C4C2311yescharacteristic
138C2×C11×C22⋊C4—21no—
139C2×C11×C22⋊C4—24no—
140C2×C42×C11C2311yescharacteristic
141#66999—22no—
142#66999—24no—
143C2×#4323Q818yescomplemented
144C2×#4323C2312yes—
145C2×#4323C2312yes—
146C2×(C2×D11)⋊C4—21no—
147#66979C2312yes—
148C2×C4⋊Dic11C2311yescharacteristic
149#66977—21no—
150#66977—21no—
151C2×#4318C2312yes—
152C22×C11⋊C8C2311yescharacteristic
153C22×C11⋊C8C2311yescharacteristic
154#66950—22no—
155#66950—24no—
156#66949—24no—
157#66949—24no—
158#66949—24no—
159#66946—22no—
160#66946—22no—
161C4⋊C4×D11—22no—
162C4⋊C4×D11—24no—
163#66943—22no—
164#66941—22no—
165C22⋊C4×D11—24no—
166#66931—24no—
167C4×D44—21no—
168C4×D44—21no—
169C4×D44C2312yes—
170C4×D44C2312yes—
171C4×D44C2314yes—
172C4×D44C2314yes—
173#66923C2312yes—
174#66923C2314yes—
175#66922C2311yescharacteristic
176#66922C2311yescharacteristic
177#66922C2314yes—
178C4×Dic22—21no—
179C4×Dic22—21no—
180#66896C2312yes—
181#66896C2312yes—
182#66896C2314yes—
183#66896C2314yes—
184#66873C2312yes—
185#66873C2312yes—
186#66873C2314yes—
187#66873C2314yes—
188#66872C2314yes—
189#66872C2314yes—
190#66872C2312yes—
191#66872C2312yes—
192#66872C2312yes—
193#66872C2312yes—
194#66871C2312yes—
195#66871C2312yes—
196#66871C2314yes—
197#66871C2314yes—
198#66871C2312yes—
199#66871C2312yes—
200#66871C2312yes—
201#66871C2312yes—
202C4⋊(C11⋊C8)C2312yes—
203C4⋊(C11⋊C8)C2312yes—
204C4⋊(C11⋊C8)C2314yes—
205C4⋊(C11⋊C8)C2314yes—
206#66867C2314yes—
207C4×C11⋊C8C2311yescharacteristic
208C4×C11⋊C8C2311yescharacteristic
209C4×C11⋊C8C2311yescharacteristic
210C4×C11⋊C8C2311yescharacteristic
211C4×C11⋊C8C2314yes—
212#61370—111nomaximal, Sylow
213C24×C11—21no—
214C23×D11—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×C11C2×Q814yescomplemented
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
234C22×Dic11—21no—
235Q8×D11—84no—
236C2×D44—21no—
237C2×D44—22no—
238C2×D44C2×Q814yescomplemented
239C2×D44C2412yes—
240C2×C4×D11—22no—
241C2×C4×D11—22no—
242C2×C4×D11—24no—
243C2×C4×D11—24no—
244C2×C4×D11—82no—
245C2×Dic22—21no—
246C2×Dic22—21no—
247C2×Dic22—24no—
248C11×C4⋊C4—22no—
249C11×C4⋊C4—21no—
250C11×C4⋊C4—24no—
251C11×C4⋊C4—24no—
252C11×C4⋊C4—24no—
253C11×C4⋊C4—21no—
254C11×C4⋊C4—22no—
255C11×C4⋊C4—21no—
256C11×C4⋊C4C2×D412yes—
257C11×C4⋊C4C2×D412yes—
258C11×C4⋊C4C2×D414yes—
259C11×C4⋊C4C2×D412yes—
260C11×C4⋊C4C2×D412yes—
261C11×C4⋊C4C2×D414yes—
262C11×C4⋊C4C2412yes—
263C11×C4⋊C4C2412yes—
264C11×C4⋊C4C2412yes—
265C11×C22⋊C4—22no—
266C11×C22⋊C4—24no—
267C11×C22⋊C4—24no—
268C11×C22⋊C4—22no—
269C11×C22⋊C4—22no—
270C11×C22⋊C4C2×D414yes—
271C42×C11—22no—
272C42×C11C2×D411yescharacteristic
273C42×C11C2×D411yescharacteristic
274C42×C11C2411yescharacteristic
275C42×C11C2411yescharacteristic
276C42×C11C2414yes—
277C22⋊Dic11—22no—
278#4323C2×Q818yescomplemented
279#4323C2×Q818yescomplemented
280(C2×D11)⋊C4—22no—
281(C2×D11)⋊C4—22no—
282(C2×D11)⋊C4—24no—
283(C2×D11)⋊C4—24no—
284C4⋊Dic11—21no—
285C4⋊Dic11—21no—
286C4⋊Dic11—24no—
287C4⋊Dic11—21no—
288C4⋊Dic11C2412yes—
289C4⋊Dic11C2412yes—
290C4⋊Dic11C2412yes—
291Dic11⋊C4—22no—
292Dic11⋊C4—22no—
293Dic11⋊C4—24no—
294Dic11⋊C4—24no—
295C4×Dic11—22no—
296#4318—24no—
297C2×C11⋊C8—22no—
298C2×C11⋊C8C2×Q814yescomplemented
299C2×C11⋊C8C2411yescharacteristic
300C2×C11⋊C8C2411yescharacteristic
301C2×C11⋊C8C2414yes—
302C2×C11⋊C8C2411yescharacteristic
303C2×C11⋊C8C2411yescharacteristic
304#3501—111no—
305#3501D1111yescharacteristic, complemented
306#3389—114no—
307#3384—112no—
308#3384—112no—
309#3380—112no—
310#3380—114no—
311Q8×D8—112no—
312#3164—112no—
313#3160—111no—
314#3081—112no—
315#3081—112no—
316#3077—111no—
317#3077—111no—
318#2960—111no—
319#2948—112no—
320C2×C4×D8—111no—
321C23×C11—22no—
322C23×C11—24no—
323C23×C11—81no—
324C23×C11—81no—
325C23×C11C22×D411yescharacteristic
326C22×D11—22no—
327C22×D11—24no—
328C22×D11—81no—
329C22×D11—81no—
330Q8×C11—24no—
331Q8×C11—42no—
332Q8×C11—42no—
333Q8×C11—81no—
334Q8×C11—84no—
335D4×C11—24no—
336D4×C11—22no—
337D4×C11C22×Q814yes—
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×D411yescharacteristic
350C2×C4×C11C22×D414yes—
351C2×C4×C11C22×D414yes—
352C2×C4×C11C22×D411yescharacteristic
353C2×C4×C11C22×D411yescharacteristic
354C2×C4×C11C22×D411yescharacteristic
355C2×C4×C11C22×Q812yes—
356C2×C4×C112−1+412yes—
357C2×C4×C11C2511yescharacteristic
358C2×Dic11—22no—
359C2×Dic11—22no—
360C2×Dic11—22no—
361C2×Dic11—81no—
362D44—24no—
363D44—22no—
364D44C22×Q814yes—
365C4×D11—44no—
366C4×D11—84no—
367C4×D11—82no—
368C4×D11—84no—
369Dic22—42no—
370Dic22—81no—
371Dic22—84no—
372C11⋊C8—21no—
373C11⋊C8—21no—
374C11⋊C8—24no—
375C11⋊C8C22×Q812yes—
376C11⋊C8C22×Q812yes—
377C22×D8—111no—
378#554—21no—
379#554—22no—
380#554—112no—
381#554—114no—
382#554—221no—
383#554—222no—
384#554C2×D1112yescomplemented
385#554C2×D1114yescomplemented
386D4×Q8—21no—
387D4×Q8—112no—
388D4×Q8—221no—
389D4×Q8C2×D1112yescomplemented
390#544—112no—
391#544C2×D1112yes—
392#543—22no—
393#543—222no—
394#533—111no—
395#533C2×D1111yescharacteristic
396#533C2×D1111yescharacteristic
397C2×C22⋊Q8—22no—
398C2×C22⋊Q8—222no—
399#518—112no—
400#518C2×D1112yes—
401C2×C4×D4—111no—
402C2×C4×D4C2×D1111yescharacteristic
403#501—114no—
404#501—114no—
405#500—111no—
406#500—114no—
407#500—111no—
408#499—112no—
409#499—114no—
410#499—112no—
411#498—111no—
412#498—111no—
413#478—114no—
414#478—114no—
415#478—114no—
416#478—114no—
417#478—114no—
418#478—114no—
419#476—112no—
420#476—114no—
421#476—112no—
422#476—114no—
423#474—112no—
424#474—114no—
425#474—112no—
426#474—114no—
427#446—112no—
428#446—112no—
429C8×Q8—112no—
430C8×Q8—112no—
431#442—114no—
432#442—114no—
433C4×D8—112no—
434C4×D8—114no—
435C4×D8—112no—
436C4×D8—114no—
437C4×D8—112no—
438C4×D8—112no—
439#428—112no—
440#428—112no—
441#427—112no—
442#427—112no—
443C2×#107—111no—
444#424—112no—
445#423—111no—
446#418—112no—
447#418—112no—
448C2×#102—111no—
449C2×#102—111no—
450#405—112no—
451C2×C4×C8—111no—
452C22×C11—21no—
453C22×C11—21no—
454C22×C11—24no—
455C22×C11—42no—
456C22×C11—42no—
457C22×C11—84no—
458C22×C11D4×Q812yes—
459C22×C11C23×D411yescharacteristic
460C2×D11—24no—
461C2×D11—42no—
462C2×D11—42no—
463C2×D11—84no—
464C4×C11—21no—
465C4×C11—21no—
466C4×C11—24no—
467C4×C11—21no—
468C4×C11—24no—
469C4×C11—42no—
470C4×C11—42no—
471C4×C11—42no—
472C4×C11D4×Q812yes—
473C4×C11#57612yes—
474C4×C11C23×Q811yescharacteristic
475C4×C11C2×2−1+411yescharacteristic
476Dic11—42no—
477Dic11—42no—
478Dic11—42no—
479C22×Q8—22no—
480C22×Q8—222no—
481C22×D4—111no—
482C22×D4C22×D1111yescharacteristic
483C23×C4—21no—
484C23×C4—221no—
485C2×D8—118no—
486C2×D8—112no—
487C2×D8—112no—
488C2×M16—112no—
489C22×C8—111no—
490C22×C8—111no—
491C4⋊Q8—22no—
492C4⋊Q8—111no—
493C4⋊Q8—111no—
494C4⋊Q8—114no—
495C4⋊Q8—222no—
496C4⋊Q8C22⋊D1111yescharacteristic
497C4⋊Q8C22⋊D1111yescharacteristic
498C4⋊Q8C22×D1111yescharacteristic
499C4⋊Q8C22×D1111yescharacteristic
500C4⋊Q8C22×D1114yes—
501#125—22no—
502#125—112no—
503#125—114no—
504#125—222no—
505#125C22⋊D1112yes—
506#125C22×D1112yes—
507#125C22×D1114yes—
508C22⋊Q8—22no—
509C22⋊Q8—24no—
510C22⋊Q8—21no—
511C22⋊Q8—21no—
512C22⋊Q8—22no—
513C22⋊Q8—24no—
514C22⋊Q8—24no—
515C22⋊Q8—24no—
516C22⋊Q8—24no—
517C22⋊Q8—24no—
518C22⋊Q8—222no—
519C22⋊Q8—224no—
520C22⋊Q8—221no—
521C22⋊Q8—221no—
522C22⋊Q8—222no—
523C22⋊Q8—224no—
524C22⋊Q8—224no—
525C22⋊Q8—224no—
526C22⋊Q8—224no—
527C22⋊Q8—224no—
528C22⋊Q8C22⋊D1112yes—
529C22⋊Q8C22⋊D1112yes—
530C4×Q8—21no—
531C4×Q8—21no—
532C4×Q8—221no—
533C4×Q8—221no—
534C4×Q8C22×D1112yes—
535C4×Q8C22×D1112yes—
536C4×D4—22no—
537C4×D4—22no—
538C4×D4—21no—
539C4×D4—21no—
540C4×D4—112no—
541C4×D4—112no—
542C4×D4—114no—
543C4×D4—114no—
544C4×D4—222no—
545C4×D4—222no—
546C4×D4—221no—
547C4×D4—221no—
548C4×D4C22×D1112yes—
549C4×D4C22×D1112yes—
550C4×D4C22×D1114yes—
551C4×D4C22×D1114yes—
552#117—112no—
553#117C22×D1112yes—
554#117C22×D1112yes—
555C2×C4⋊C4—24no—
556C2×C4⋊C4—22no—
557C2×C4⋊C4—111no—
558C2×C4⋊C4—224no—
559C2×C4⋊C4—222no—
560C2×C4⋊C4C22×D1111yescharacteristic
561C2×C22⋊C4—21no—
562C2×C22⋊C4—24no—
563C2×C22⋊C4—221no—
564C2×C22⋊C4—224no—
565C2×C42C22×D1111yescharacteristic
566#107—112no—
567#107—112no—
568#107—112no—
569#107—112no—
570#107—112no—
571#107—112no—
572#107—114no—
573#107—114no—
574#106—112no—
575#106—112no—
576#106—112no—
577#106—112no—
578#106—114no—
579#106—114no—
580C4⋊C8—112no—
581C4⋊C8—112no—
582C4⋊C8—114no—
583C4⋊C8—114no—
584#102—112no—
585#102—112no—
586#102—114no—
587#102—114no—
588#102—112no—
589#102—112no—
590#102—114no—
591#102—114no—
592#97—114no—
593C4×C8—111no—
594C4×C8—111no—
595C4×C8—111no—
596C4×C8—111no—
597C4×C8—114no—
598C2×C11—22no—
599C2×C11—44no—
600C2×C11C2×D4×Q811yescharacteristic
601C2×C11C2×#57611yescharacteristic
602C2×C11#358411yescharacteristic
603D11—44no—
604C24—21no—
605C24—221no—
606C2×Q8—21no—
607C2×Q8—21no—
608C2×Q8—24no—
609C2×Q8—84no—
610C2×Q8—221no—
611C2×Q8—221no—
612C2×Q8—224no—
613C2×Q8—884no—
614C2×Q8C2×C22⋊D1112yes—
615C2×Q8C2×C22⋊D1112yes—
616C2×D4—22no—
617C2×D4—21no—
618C2×D4—114no—
619C2×D4—112no—
620C2×D4—222no—
621C2×D4—221no—
622C2×D4Q8×D1114yescomplemented
623C2×D4C23×D1112yes—
624C22×C4—21no—
625C22×C4—22no—
626C22×C4—24no—
627C22×C4—24no—
628C22×C4—22no—
629C22×C4—82no—
630C22×C4—221no—
631C22×C4—222no—
632C22×C4—224no—
633C22×C4—224no—
634C22×C4—222no—
635C22×C4—882no—
636C22×C4C2×C22⋊D1111yescharacteristic
637C22×C4C2×C22⋊D1111yescharacteristic
638C22×C4C23×D1111yescharacteristic
639D8—118no—
640D8—118no—
641M16—224no—
642C2×C8—114no—
643C2×C8—111no—
644C2×C8—111no—
645C2×C8—111no—
646C2×C8—111no—
647C2×C8—114no—
648C2×C8—222no—
649C4⋊C4—22no—
650C4⋊C4—21no—
651C4⋊C4—24no—
652C4⋊C4—24no—
653C4⋊C4—24no—
654C4⋊C4—21no—
655C4⋊C4—22no—
656C4⋊C4—21no—
657C4⋊C4—112no—
658C4⋊C4—112no—
659C4⋊C4—112no—
660C4⋊C4—221no—
661C4⋊C4—222no—
662C4⋊C4—221no—
663C4⋊C4—224no—
664C4⋊C4—224no—
665C4⋊C4—224no—
666C4⋊C4—222no—
667C4⋊C4—221no—
668C4⋊C4C2×C22⋊D1114yes—
669C4⋊C4C2×C22⋊D1112yes—
670C4⋊C4C2×C22⋊D1112yes—
671C4⋊C4C2×C22⋊D1112yes—
672C4⋊C4C2×C22⋊D1114yes—
673C4⋊C4C2×C22⋊D1112yes—
674C4⋊C4C23×D1112yes—
675C4⋊C4C23×D1112yes—
676C4⋊C4C23×D1112yes—
677C22⋊C4—22no—
678C22⋊C4—24no—
679C22⋊C4—24no—
680C22⋊C4—22no—
681C22⋊C4—22no—
682C22⋊C4—222no—
683C22⋊C4—224no—
684C22⋊C4—224no—
685C22⋊C4—222no—
686C22⋊C4—222no—
687C22⋊C4C2×C22⋊D1114yes—
688C42—22no—
689C42—222no—
690C42C2×C22⋊D1111yescharacteristic
691C42C2×C22⋊D1111yescharacteristic
692C42C23×D1111yescharacteristic
693C42C23×D1111yescharacteristic
694C42C23×D1114yes—
695C11#6137011yescharacteristic, complemented, Sylow
696C23—22no—
697C23—24no—
698C23—81no—
699C23—81no—
700C23—222no—
701C23—224no—
702C23—881no—
703C23—881no—
704C23C22×C22⋊D1111yescharacteristic
705Q8—24no—
706Q8—42no—
707Q8—42no—
708Q8—81no—
709Q8—84no—
710Q8—442no—
711Q8—884no—
712Q8—881no—
713D4—24no—
714D4—22no—
715D4—114no—
716D4—224no—
717D4—222no—
718D4C2×Q8×D1114yes—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—41no—
724C2×C4—44no—
725C2×C4—84no—
726C2×C4—82no—
727C2×C4—84no—
728C2×C4—81no—
729C2×C4—222no—
730C2×C4—222no—
731C2×C4—222no—
732C2×C4—444no—
733C2×C4—882no—
734C2×C4—884no—
735C2×C4—884no—
736C2×C4—881no—
737C2×C4C2×Q8×D1112yes—
738C2×C4#6704012yes—
739C2×C4C22×C22⋊D1111yescharacteristic
740C2×C4C22×C22⋊D1111yescharacteristic
741C2×C4C22×C22⋊D1111yescharacteristic
742C2×C4C22×C22⋊D1114yes—
743C2×C4C22×C22⋊D1114yes—
744C2×C4C22×C22⋊D1111yescharacteristic
745C2×C4C22×C22⋊D1111yescharacteristic
746C2×C4C24×D1111yescharacteristic
747C8—112no—
748C8—112no—
749C8—221no—
750C8—221no—
751C8—224no—
752C22—21no—
753C22—21no—
754C22—24no—
755C22—42no—
756C22—42no—
757C22—84no—
758C22—224no—
759C22—442no—
760C22—442no—
761C22—884no—
762C22Q8×C22⋊D1112yes—
763C22C23×C22⋊D1111yescharacteristic
764C4—21no—
765C4—24no—
766C4—21no—
767C4—21no—
768C4—24no—
769C4—42no—
770C4—42no—
771C4—42no—
772C4—442no—
773C4—442no—
774C4—442no—
775C4Q8×C22⋊D1112yes—
776C4#1062336612yes—
777C4C22×Q8×D1111yescharacteristic
778C4C2×#6704011yescharacteristic
779C2—22no—
780C2—44no—
781C2—444no—
782C2C2×Q8×C22⋊D1111yescharacteristic
783C2C2×#1062336611yescharacteristic
784C2#1308338711yescharacteristic
subgroupG/H
centerC22C23×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#3501C2
socleC22×C11C23×D4
prime radicalC22×#4323C22
hypercenter#3501D11
hypocenterC11#61370
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. #13082417C2semidirect
2. #13081570C2semidirect
3. #13081515C2semidirect
4. #13081511C2semidirect
5. #13081479C2semidirect
6. #13081479C2semidirect
7. Q8×#4323C2semidirect
8. #13079150C2semidirect
9. #13079126C2semidirect
10. #13078447C2semidirect
11. #13078441C2semidirect
12. #13078413C2semidirect
13. #13078409C2semidirect
14. #13077551C2semidirect
17. C11×#3501C2semidirect
20. C11×#554C22semidirect
21. C11×#554C22semidirect
23. D4×Q8×C11C22semidirect
37. #10623110C22semidirect
38. #10623110C22semidirect
39. Q8×D44C22semidirect
46. #10622700C22semidirect
47. #10622700C22semidirect
48. #10622697C22semidirect
49. #10622697C22semidirect
50. #10622693C22semidirect
51. #10622692C22semidirect
52. #10622692C22semidirect
53. #10622691C22semidirect
54. #10622691C22semidirect
55. #10622691C22semidirect
56. #10622679C22semidirect
57. #10622679C22semidirect
58. #10622679C22semidirect
59. #10622678C22semidirect
60. #10622677C22semidirect
61. #10622677C22semidirect
62. #10622677C22semidirect
63. #10622637C22semidirect
64. #10622637C22semidirect
65. Q8×C11⋊C8C22semidirect
66. Q8×C11⋊C8C22semidirect
75. #10622622C22semidirect
76. #10622622C22semidirect
77. #10622622C22semidirect
78. #10622621C22semidirect
79. #10622621C22semidirect
80. #10622620C22semidirect
81. #10622620C22semidirect
143. C2×#4323Q8semidirect
223. C2×D4×C11C2×Q8semidirect
238. C2×D44C2×Q8semidirect
278. #4323C2×Q8semidirect
279. #4323C2×Q8semidirect
298. C2×C11⋊C8C2×Q8semidirect
305. #3501D11semidirect
384. #554C2×D11semidirect
385. #554C2×D11semidirect
389. D4×Q8C2×D11semidirect
622. C2×D4Q8×D11semidirect
695. C11#61370semidirect

Maximal subgroups

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

subgroupindex
#130824172
#130815702
#130815152
#130815112
#130814792
Q8×#43232
#130791502
#130791262
#130784472
#130784412
#130784132
#130784092
#130775512
#130774662
C2×C4×#43232
C11×#35012
#6137011