Finite Group Databasebeta

← #15626812

Subgroups — #15626812

Order 2816.

1822 conjugacy classes of subgroups.

The subgroup lattice has 852 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623065C211yesmaximal, characteristic, complemented
2#13080081C214yesmaximal, complemented
3#13080072C214yesmaximal, complemented
4#13080036C214yesmaximal, complemented
5#13080021C214yesmaximal, complemented
6#13078431C212yesmaximal, complemented
7#13078417C211yesmaximal, characteristic, complemented
8#13078409C211yesmaximal, characteristic, complemented
9#13078248C212yesmaximal, complemented
10#13078237C212yesmaximal, complemented
11#13078110C212yesmaximal, complemented
12#13078084C211yesmaximal, characteristic, complemented
13#13078076C211yesmaximal, characteristic, complemented
14#13077180C211yesmaximal, characteristic, complemented
15C11×#3455C211yesmaximal, characteristic, complemented
16C11×#542C2212yescomplemented
17C11×#542C2212yescomplemented
18C11×#541C2212yescomplemented
19C11×#540C2212yescomplemented
20C11×#539—21no—
21C11×#539—21no—
22C11×#538—21no—
23C11×#538—21no—
24C11×#533C2211yescharacteristic
25C11×#532C2211yescharacteristic
26C11×#529—22no—
27C11×#529—22no—
28C11×#525C2212yes—
29C4×C11×#41C2212yes—
30C2×C11×#117C2211yescharacteristic
31C2×#67004C2212yes—
32C2×#67002C2212yes—
33C2×#66983C2211yescharacteristic
34C2×#66977C2211yescharacteristic
35C22×#4318C2212yes—
36#10623065—22no—
37#10623065—22no—
38#10623065C2214yes—
39#10623065C2214yes—
40C2×#66951—21no—
41C2×#66949—21no—
42C2×#66938—21no—
43C2×#66936—21no—
44C2×#66928C2211yescharacteristic
45C2×C4×D44C2211yescharacteristic
46C2×#66922C2211yescharacteristic
47C2×C4×Dic22C2211yescharacteristic
48#10622845C2212yes—
49#10622845C2212yes—
50#10622707C2212yescomplemented
51#10622704C2212yescomplemented
52#10622703C2212yescomplemented
53#10622700C2212yescomplemented
54#10622697C2212yescomplemented
55#10622696C2212yescomplemented
56#10622688C2212yescomplemented
57#10622685C2212yescomplemented
58#10622679C2214yescomplemented
59#10622676C2214yescomplemented
60#10622670C2214yescomplemented
61#10622667C2214yescomplemented
62#10622665C2214yescomplemented
63#10622664C2214yescomplemented
64#10622662C2214yes—
65#10622661C2214yes—
66#10622655C2214yescomplemented
67#10622654C2214yescomplemented
68#10622652C2214yes—
69#10622651C2214yes—
70#10622641C2214yescomplemented
71#10622641C2214yescomplemented
72#10622634C2214yescomplemented
73#10622633C2214yescomplemented
74#10622629C2214yescomplemented
75#10622629C2214yescomplemented
76#10622621C2214yescomplemented
77#10622620C2214yescomplemented
78#10622617C2212yes—
79#10622614C2212yes—
80#10622612C2214yescomplemented
81#10622612C2214yescomplemented
82#10622608C2212yes—
83#10622608C2212yes—
84#10622537C2211yescharacteristic
85#10622537C2211yescharacteristic
86#10622537C2212yes—
87C2×C11×#41C2312yes—
88C23×C4×C11C2311yescharacteristic
89C22×C22⋊D11—21no—
90C22×D44C2311yescharacteristic
91C22×C4×D11—21no—
92C22×Dic22—21no—
93C22×Dic22C2311yescharacteristic
94C11×C4⋊Q8C2311yescharacteristic
95C11×C4⋊Q8C2311yescharacteristic
96C11×C4⋊Q8C2311yescharacteristic
97C11×#127C2311yescharacteristic
98C11×#126—22no—
99C11×#126—22no—
100C11×#126—22no—
101C11×#126—22no—
102C11×#125—22no—
103C11×#125—22no—
104C11×#125C2312yes—
105C11×#124—22no—
106C11×#124—22no—
107C11×#124C2312yes—
108C11×#123—22no—
109C11×#123—22no—
110C11×#123—22no—
111C11×#123—22no—
112C11×#123—22no—
113C11×C22⋊Q8—21no—
114C11×C22⋊Q8—21no—
115C11×C22⋊Q8—22no—
116C11×C22⋊Q8—22no—
117C11×C22⋊Q8C2312yes—
118C11×C22⋊Q8C2312yes—
119C11×#121—21no—
120C11×#121—21no—
121C11×#121—22no—
122C11×#121—22no—
123C11×#121C2312yes—
124C11×#121C2312yes—
125C11×#120—22no—
126C4×Q8×C11—21no—
127C4×Q8×C11—21no—
128C4×Q8×C11C2312yes—
129C4×Q8×C11C2312yes—
130C4×D4×C11—22no—
131C4×D4×C11—22no—
132C4×D4×C11—22no—
133C4×D4×C11—22no—
134C4×D4×C11—21no—
135C4×D4×C11—21no—
136C4×D4×C11C2312yes—
137C4×D4×C11C2312yes—
138C11×#117—22no—
139C11×#117D412yes—
140C11×#117D412yes—
141C11×#117C2312yes—
142C11×#117C2312yes—
143C11×#117C2312yes—
144C2×C11×C4⋊C4D411yescharacteristic
145C2×C11×C4⋊C4D411yescharacteristic
146C2×C11×C22⋊C4D411yescharacteristic
147C2×C11×C22⋊C4D411yescharacteristic
148C2×C42×C11—22no—
149C2×C42×C11C2311yescharacteristic
150C2×C42×C11C2311yescharacteristic
151C2×C22⋊Dic11—21no—
152#67004—44no—
153#67002—44no—
154C2×#4326C2314yes—
155C2×#4325C2314yes—
156C2×#4324C2314yes—
157C2×#4323C2314yes—
158#66983—22no—
159#66983C2314yes—
160C2×(C2×D11)⋊C4—21no—
161C2×(C2×D11)⋊C4—21no—
162C2×(C2×D11)⋊C4—21no—
163C2×(C2×D11)⋊C4—21no—
164C2×C4⋊Dic11—21no—
165C2×C4⋊Dic11C2311yescharacteristic
166C2×C4⋊Dic11C2311yescharacteristic
167#66977—22no—
168#66977C2314yes—
169C2×Dic11⋊C4—21no—
170C2×Dic11⋊C4—21no—
171C2×C4×Dic11—21no—
172C2×#4318—44no—
173C2×#4318C2312yes—
174C2×#4318C2312yes—
175C2×#4318C2314yes—
176C22×C11⋊C8C2314yes—
177#66951—24no—
178#66951—24no—
179#66949—24no—
180#66949—24no—
181#66938—24no—
182#66938—24no—
183#66936—24no—
184#66936—24no—
185#66928—22no—
186#66928C2314yes—
187C4×D44—21no—
188C4×D44—21no—
189C4×D44C2312yes—
190C4×D44C2312yes—
191#66922—22no—
192#66922C2314yes—
193C4×Dic22—21no—
194C4×Dic22—21no—
195C4×Dic22C2312yes—
196C4×Dic22C2312yes—
197#66899C2314yes—
198#66899C2314yes—
199#66896C2314yes—
200#66896C2314yes—
201#66874C2314yes—
202#66874C2314yes—
203#66873C2314yes—
204#66873C2314yes—
205#66872C2314yes—
206#66872C2314yes—
207#66871C2314yes—
208#66871C2314yes—
209C4⋊(C11⋊C8)C2314yes—
210C4⋊(C11⋊C8)C2314yes—
211C4⋊(C11⋊C8)C2312yes—
212C4⋊(C11⋊C8)C2312yes—
213C4⋊(C11⋊C8)C2312yes—
214C4⋊(C11⋊C8)C2312yes—
215#60919—111nomaximal, Sylow
216C24×C11C2×D411yescharacteristic
217C23×D11—21no—
218C11×#41—24no—
219C11×#41—24no—
220C2×Q8×C11—21no—
221C2×Q8×C11—21no—
222C2×Q8×C11C2412yes—
223C2×D4×C11—22no—
224C2×D4×C11—22no—
225C2×D4×C11—22no—
226C2×D4×C11—21no—
227C2×D4×C11—21no—
228C2×D4×C11C2412yes—
229C22×C4×C11—22no—
230C22×C4×C11—22no—
231C22×C4×C11—22no—
232C22×C4×C11—22no—
233C22×C4×C11—22no—
234C22×C4×C11C2×D411yescharacteristic
235C22×C4×C11C2×D412yes—
236C22×C4×C11C2×D411yescharacteristic
237C22×C4×C11C2×D411yescharacteristic
238C22×C4×C11C2×D411yescharacteristic
239C22×C4×C11C2×D411yescharacteristic
240C22×C4×C11C2412yes—
241C22×C4×C11C2411yescharacteristic
242C2×C22⋊D11—24no—
243C2×C22⋊D11—82no—
244C22×Dic11—21no—
245C22×Dic11—21no—
246C22×Dic11—21no—
247C2×D44—21no—
248C2×D44—22no—
249C2×D44—22no—
250C2×D44C2412yes—
251C2×C4×D11—22no—
252C2×C4×D11—22no—
253C2×C4×D11—82no—
254C2×Dic22—21no—
255C2×Dic22—24no—
256C2×Dic22—22no—
257C2×Dic22—22no—
258C2×Dic22—82no—
259C2×Dic22C2412yes—
260C11×C4⋊C4—22no—
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—21no—
269C11×C4⋊C4—21no—
270C11×C4⋊C4C2×D412yes—
271C11×C4⋊C4C2×D412yes—
272C11×C4⋊C4C2×D412yes—
273C11×C4⋊C4C2×D412yes—
274C11×C4⋊C4C2412yes—
275C11×C4⋊C4C2412yes—
276C11×C22⋊C4—22no—
277C11×C22⋊C4—22no—
278C11×C22⋊C4—22no—
279C11×C22⋊C4—22no—
280C11×C22⋊C4—22no—
281C11×C22⋊C4—22no—
282C11×C22⋊C4—22no—
283C11×C22⋊C4—22no—
284C11×C22⋊C4—22no—
285C11×C22⋊C4C2×D412yes—
286C11×C22⋊C4C2×D412yes—
287C11×C22⋊C4C2×D412yes—
288C11×C22⋊C4C2×D412yes—
289C42×C11—22no—
290C42×C11—22no—
291C42×C11—22no—
292C42×C11C2×D411yescharacteristic
293C42×C11C2×D411yescharacteristic
294C42×C11C2×D412yes—
295C42×C11C2411yescharacteristic
296C42×C11C2411yescharacteristic
297C42×C11C2412yes—
298C22⋊Dic11—24no—
299#4326—44no—
300#4325—44no—
301#4324—44no—
302#4323—44no—
303(C2×D11)⋊C4—22no—
304(C2×D11)⋊C4—22no—
305(C2×D11)⋊C4—24no—
306(C2×D11)⋊C4—24no—
307(C2×D11)⋊C4—24no—
308C4⋊Dic11—21no—
309C4⋊Dic11—21no—
310C4⋊Dic11—24no—
311C4⋊Dic11C2412yes—
312C4⋊Dic11C2412yes—
313Dic11⋊C4—22no—
314Dic11⋊C4—22no—
315Dic11⋊C4—24no—
316C4×Dic11—22no—
317C4×Dic11—22no—
318#4318—24no—
319#4318—24no—
320#4318—44no—
321C2×C11⋊C8—44no—
322C2×C11⋊C8C2414yes—
323C2×C11⋊C8C2414yes—
324#3455D1111yescharacteristic, complemented
325C2×#542—111no—
326#3263—114no—
327#3262—114no—
328#3258—114no—
329#3257—114no—
330#3079—112no—
331#3078—111no—
332#3077—111no—
333#3056—112no—
334#3055—112no—
335#3040—112no—
336#3037—111no—
337#3036—111no—
338#2905—111no—
339C23×C11—22no—
340C23×C11—22no—
341C23×C11—41no—
342C23×C11—41no—
343C23×C11C22×D412yes—
344C23×C11C22×D411yescharacteristic
345C22×D11—22no—
346C22×D11—42no—
347C22×D11—42no—
348C22×D11—42no—
349Q8×C11—22no—
350Q8×C11—22no—
351Q8×C11—81no—
352Q8×C11—81no—
353D4×C11—22no—
354D4×C11—22no—
355D4×C11—44no—
356D4×C11—81no—
357D4×C11—81no—
358D4×C11—82no—
359D4×C11—82no—
360C2×C4×C11—22no—
361C2×C4×C11—24no—
362C2×C4×C11—22no—
363C2×C4×C11—22no—
364C2×C4×C11—22no—
365C2×C4×C11—22no—
366C2×C4×C11—22no—
367C2×C4×C11—41no—
368C2×C4×C11—41no—
369C2×C4×C11—41no—
370C2×C4×C11—41no—
371C2×C4×C11—44no—
372C2×C4×C11—82no—
373C2×C4×C11—82no—
374C2×C4×C11C22×D411yescharacteristic
375C2×C4×C11C22×D411yescharacteristic
376C2×C4×C11C22×D412yes—
377C2×C4×C11C22×D411yescharacteristic
378C2×C4×C11C22×D411yescharacteristic
379C2×C4×C11C22×D412yes—
380C2×C4×C11C22×D412yes—
381C2×C4×C11C22×D411yescharacteristic
382C2×C4×C11H(5,𝔽2)12yes—
383C2×C4×C112−1+412yes—
384C2×C4×C11C2511yescharacteristic
385C22⋊D11—84no—
386C2×Dic11—22no—
387C2×Dic11—22no—
388C2×Dic11—22no—
389C2×Dic11—42no—
390C2×Dic11—42no—
391C2×Dic11—42no—
392D44—22no—
393D44—22no—
394D44—42no—
395C4×D11—82no—
396C4×D11—82no—
397Dic22—22no—
398Dic22—22no—
399Dic22—42no—
400Dic22—84no—
401C11⋊C8—24no—
402C11⋊C8—24no—
403C2×#137—112no—
404C2×AGL(1,ℤ/8)—112no—
405C22×M16—112no—
406#542—114no—
407#542—114no—
408#542—222no—
409#542—222no—
410#542C2×D1112yescomplemented
411#542C2×D1112yescomplemented
412#541C2×D1112yescomplemented
413#540C2×D1112yescomplemented
414#539—21no—
415#539—21no—
416#538—21no—
417#538—21no—
418#533C2×D1111yescharacteristic
419#532C2×D1111yescharacteristic
420C2×C4⋊Q8—111no—
421#529—22no—
422#529—22no—
423C2×#126—221no—
424C2×#124—111no—
425C2×#124—221no—
426#525C2×D1112yes—
427C2×#123—221no—
428C2×C22⋊Q8—111no—
429C2×C22⋊Q8—221no—
430C2×#121—111no—
431C4×#41C2×D1112yes—
432C2×C4×Q8—111no—
433C2×C4×D4—111no—
434C2×#117C2×D1111yescharacteristic
435#479—114no—
436#478—114no—
437#477—112no—
438#477—114no—
439#476—112no—
440#476—114no—
441#475—112no—
442#475—114no—
443#474—112no—
444#474—114no—
445#470—114no—
446#469—114no—
447#468—114no—
448#468—114no—
449#467—114no—
450#466—114no—
451#465—114no—
452#465—114no—
453#464—114no—
454#464—114no—
455#464—114no—
456#463—114no—
457#463—114no—
458#463—114no—
459#462—112no—
460#461—112no—
461#460—112no—
462#459—112no—
463#428—112no—
464#428—112no—
465#424—114no—
466#424—114no—
467#423—111no—
468#423—111no—
469#423—112no—
470#419—112no—
471#418—112no—
472#417—112no—
473#417—112no—
474C22×C11—21no—
475C22×C11—21no—
476C22×C11—22no—
477C22×C11—22no—
478C22×C11—22no—
479C22×C11—42no—
480C22×C11—42no—
481C22×C11—42no—
482C22×C11—82no—
483C22×C11#53712yes—
484C22×C11C23×D411yescharacteristic
485C2×D11—42no—
486C2×D11—42no—
487C2×D11—42no—
488C2×D11—84no—
489C4×C11—22no—
490C4×C11—21no—
491C4×C11—21no—
492C4×C11—22no—
493C4×C11—21no—
494C4×C11—21no—
495C4×C11—22no—
496C4×C11—42no—
497C4×C11—42no—
498C4×C11—42no—
499C4×C11#53712yes—
500C4×C11C2×H(5,𝔽2)11yescharacteristic
501C4×C11C2×2−1+411yescharacteristic
502Dic11—42no—
503Dic11—42no—
504Dic11—42no—
505C2×#41C22×D1112yes—
506C22×Q8—111no—
507C22×Q8—221no—
508C22×D4—111no—
509C22×D4—221no—
510C23×C4—221no—
511C23×C4C22×D1111yescharacteristic
512#137—444no—
513AGL(1,ℤ/8)—444no—
514C2×Q16—114no—
515C2×SD16—114no—
516C2×SD16—114no—
517C2×D8—114no—
518C2×M16—112no—
519C2×M16—112no—
520C2×M16—114no—
521C2×M16—444no—
522C22×C8—114no—
523C4⋊Q8—114no—
524C4⋊Q8—222no—
525C4⋊Q8C22×D1111yescharacteristic
526C4⋊Q8C22×D1111yescharacteristic
527C4⋊Q8C22×D1111yescharacteristic
528#127C22×D1111yescharacteristic
529#126—22no—
530#126—22no—
531#126—22no—
532#126—22no—
533#126—224no—
534#126—224no—
535#125—22no—
536#125—22no—
537#125C22×D1112yes—
538#124—22no—
539#124—22no—
540#124—114no—
541#124—224no—
542#124—224no—
543#124—222no—
544#124C22×D1112yes—
545#123—22no—
546#123—22no—
547#123—22no—
548#123—22no—
549#123—22no—
550#123—224no—
551#123—224no—
552C22⋊Q8—21no—
553C22⋊Q8—21no—
554C22⋊Q8—22no—
555C22⋊Q8—22no—
556C22⋊Q8—114no—
557C22⋊Q8—222no—
558C22⋊Q8—224no—
559C22⋊Q8—224no—
560C22⋊Q8C22×D1112yes—
561C22⋊Q8C22×D1112yes—
562#121—21no—
563#121—21no—
564#121—22no—
565#121—22no—
566#121—114no—
567#121—222no—
568#121C22×D1112yes—
569#121C22×D1112yes—
570#120—22no—
571C4×Q8—21no—
572C4×Q8—21no—
573C4×Q8—112no—
574C4×Q8—112no—
575C4×Q8—221no—
576C4×Q8—221no—
577C4×Q8C22×D1112yes—
578C4×Q8C22×D1112yes—
579C4×D4—22no—
580C4×D4—22no—
581C4×D4—22no—
582C4×D4—22no—
583C4×D4—21no—
584C4×D4—21no—
585C4×D4—112no—
586C4×D4—112no—
587C4×D4—221no—
588C4×D4—221no—
589C4×D4C22×D1112yes—
590C4×D4C22×D1112yes—
591#117—22no—
592#117C22⋊D1112yes—
593#117C22⋊D1112yes—
594#117C22×D1112yes—
595#117C22×D1112yes—
596#117C22×D1112yes—
597C2×C4⋊C4—111no—
598C2×C4⋊C4—111no—
599C2×C4⋊C4—221no—
600C2×C4⋊C4—221no—
601C2×C4⋊C4—221no—
602C2×C4⋊C4C22⋊D1111yescharacteristic
603C2×C4⋊C4C22⋊D1111yescharacteristic
604C2×C22⋊C4—221no—
605C2×C22⋊C4—221no—
606C2×C22⋊C4—221no—
607C2×C22⋊C4—221no—
608C2×C22⋊C4—221no—
609C2×C22⋊C4C22⋊D1111yescharacteristic
610C2×C22⋊C4C22⋊D1111yescharacteristic
611C2×C42—22no—
612C2×C42—221no—
613C2×C42C22×D1111yescharacteristic
614C2×C42C22×D1111yescharacteristic
615#107—114no—
616#107—114no—
617#106—114no—
618#106—114no—
619C4⋊C8—112no—
620C4⋊C8—112no—
621C4⋊C8—112no—
622C4⋊C8—114no—
623C4⋊C8—114no—
624C4⋊C8—112no—
625#103—114no—
626#103—114no—
627#103—114no—
628#103—114no—
629#102—114no—
630#102—114no—
631#102—114no—
632#102—114no—
633C2×C11—22no—
634C2×C11—42no—
635C2×C11—82no—
636C2×C11C2×#53711yescharacteristic
637C2×C11#358511yescharacteristic
638C2×C11#358611yescharacteristic
639D11—82no—
640C24—221no—
641C24C2×C22⋊D1111yescharacteristic
642#41—24no—
643#41—24no—
644C2×Q8—21no—
645C2×Q8—21no—
646C2×Q8—112no—
647C2×Q8—221no—
648C2×Q8—224no—
649C2×Q8—222no—
650C2×Q8—222no—
651C2×Q8—882no—
652C2×Q8C23×D1112yes—
653C2×D4—22no—
654C2×D4—22no—
655C2×D4—22no—
656C2×D4—21no—
657C2×D4—21no—
658C2×D4—112no—
659C2×D4—224no—
660C2×D4—222no—
661C2×D4—222no—
662C2×D4—221no—
663C2×D4—882no—
664C2×D4C23×D1112yes—
665C22×C4—22no—
666C22×C4—22no—
667C22×C4—22no—
668C22×C4—22no—
669C22×C4—22no—
670C22×C4—221no—
671C22×C4—221no—
672C22×C4—221no—
673C22×C4—222no—
674C22×C4—222no—
675C22×C4—882no—
676C22×C4C2×C22⋊D1111yescharacteristic
677C22×C4C2×C22⋊D1112yes—
678C22×C4C2×C22⋊D1111yescharacteristic
679C22×C4C2×C22⋊D1111yescharacteristic
680C22×C4C2×C22⋊D1111yescharacteristic
681C22×C4C2×C22⋊D1111yescharacteristic
682C22×C4C23×D1112yes—
683C22×C4C23×D1111yescharacteristic
684Q16—444no—
685SD16—444no—
686SD16—444no—
687D8—444no—
688M16—224no—
689M16—224no—
690M16—444no—
691C2×C8—114no—
692C2×C8—114no—
693C2×C8—444no—
694C4⋊C4—22no—
695C4⋊C4—22no—
696C4⋊C4—21no—
697C4⋊C4—21no—
698C4⋊C4—22no—
699C4⋊C4—22no—
700C4⋊C4—22no—
701C4⋊C4—22no—
702C4⋊C4—21no—
703C4⋊C4—21no—
704C4⋊C4—112no—
705C4⋊C4—112no—
706C4⋊C4—221no—
707C4⋊C4—221no—
708C4⋊C4—222no—
709C4⋊C4—222no—
710C4⋊C4—224no—
711C4⋊C4—224no—
712C4⋊C4C2×C22⋊D1112yes—
713C4⋊C4C2×C22⋊D1112yes—
714C4⋊C4C2×C22⋊D1112yes—
715C4⋊C4C2×C22⋊D1112yes—
716C4⋊C4C23×D1112yes—
717C4⋊C4C23×D1112yes—
718C22⋊C4—22no—
719C22⋊C4—22no—
720C22⋊C4—22no—
721C22⋊C4—22no—
722C22⋊C4—22no—
723C22⋊C4—22no—
724C22⋊C4—22no—
725C22⋊C4—22no—
726C22⋊C4—22no—
727C22⋊C4—224no—
728C22⋊C4—222no—
729C22⋊C4—222no—
730C22⋊C4—224no—
731C22⋊C4—224no—
732C22⋊C4—224no—
733C22⋊C4C2×C22⋊D1112yes—
734C22⋊C4C2×C22⋊D1112yes—
735C22⋊C4C2×C22⋊D1112yes—
736C22⋊C4C2×C22⋊D1112yes—
737C42—22no—
738C42—22no—
739C42—22no—
740C42—222no—
741C42—222no—
742C42C2×C22⋊D1112yes—
743C42C2×C22⋊D1111yescharacteristic
744C42C2×C22⋊D1111yescharacteristic
745C42C23×D1111yescharacteristic
746C42C23×D1111yescharacteristic
747C42C23×D1112yes—
748C11#6091911yescharacteristic, complemented, Sylow
749C23—22no—
750C23—22no—
751C23—41no—
752C23—41no—
753C23—222no—
754C23—442no—
755C23—442no—
756C23—442no—
757C23C22×C22⋊D1112yes—
758C23C22×C22⋊D1111yescharacteristic
759Q8—22no—
760Q8—22no—
761Q8—81no—
762Q8—81no—
763Q8—222no—
764Q8—222no—
765Q8—442no—
766Q8—884no—
767D4—22no—
768D4—22no—
769D4—44no—
770D4—81no—
771D4—81no—
772D4—82no—
773D4—82no—
774D4—222no—
775D4—222no—
776D4—442no—
777D4—884no—
778C2×C4—22no—
779C2×C4—24no—
780C2×C4—22no—
781C2×C4—22no—
782C2×C4—22no—
783C2×C4—22no—
784C2×C4—22no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—44no—
790C2×C4—82no—
791C2×C4—82no—
792C2×C4—222no—
793C2×C4—222no—
794C2×C4—222no—
795C2×C4—442no—
796C2×C4—442no—
797C2×C4—442no—
798C2×C4—882no—
799C2×C4—882no—
800C2×C4#6704212yes—
801C2×C4#6704312yes—
802C2×C4C22×C22⋊D1112yes—
803C2×C4C22×C22⋊D1112yes—
804C2×C4C22×C22⋊D1111yescharacteristic
805C2×C4C22×C22⋊D1111yescharacteristic
806C2×C4C22×C22⋊D1111yescharacteristic
807C2×C4C22×C22⋊D1111yescharacteristic
808C2×C4C22×C22⋊D1112yes—
809C2×C4C22×C22⋊D1111yescharacteristic
810C2×C4C24×D1111yescharacteristic
811C8—224no—
812C8—224no—
813C22—21no—
814C22—21no—
815C22—22no—
816C22—22no—
817C22—22no—
818C22—42no—
819C22—42no—
820C22—42no—
821C22—82no—
822C22—442no—
823C22—442no—
824C22—442no—
825C22—884no—
826C22#1062336412yes—
827C22C23×C22⋊D1111yescharacteristic
828C4—22no—
829C4—21no—
830C4—21no—
831C4—22no—
832C4—21no—
833C4—21no—
834C4—22no—
835C4—42no—
836C4—42no—
837C4—42no—
838C4—442no—
839C4—442no—
840C4—442no—
841C4#1062336412yes—
842C4C2×#6704211yescharacteristic
843C4C2×#6704311yescharacteristic
844C2—22no—
845C2—42no—
846C2—82no—
847C2—882no—
848C2C2×#1062336411yescharacteristic
849C2#1308339511yescharacteristic
850C2#1308340211yescharacteristic
subgroupG/H
centerC22C23×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#3455C2
socleC22×C11C23×D4
hypercenter#3455D11
hypocenterC11#60919
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×#117 ◁ #3455

Complements

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

NH ≅ G/Ntype
1. C2×#10623065C2semidirect
2. #13080081C2semidirect
3. #13080072C2semidirect
4. #13080036C2semidirect
5. #13080021C2semidirect
6. #13078431C2semidirect
7. #13078417C2semidirect
8. #13078409C2semidirect
9. #13078248C2semidirect
10. #13078237C2semidirect
11. #13078110C2semidirect
12. #13078084C2semidirect
13. #13078076C2semidirect
14. #13077180C2semidirect
15. C11×#3455C2semidirect
16. C11×#542C22semidirect
17. C11×#542C22semidirect
18. C11×#541C22semidirect
19. C11×#540C22semidirect
50. #10622707C22semidirect
51. #10622704C22semidirect
52. #10622703C22semidirect
53. #10622700C22semidirect
54. #10622697C22semidirect
55. #10622696C22semidirect
56. #10622688C22semidirect
57. #10622685C22semidirect
58. #10622679C22semidirect
59. #10622676C22semidirect
60. #10622670C22semidirect
61. #10622667C22semidirect
62. #10622665C22semidirect
63. #10622664C22semidirect
66. #10622655C22semidirect
67. #10622654C22semidirect
70. #10622641C22semidirect
71. #10622641C22semidirect
72. #10622634C22semidirect
73. #10622633C22semidirect
74. #10622629C22semidirect
75. #10622629C22semidirect
76. #10622621C22semidirect
77. #10622620C22semidirect
80. #10622612C22semidirect
81. #10622612C22semidirect
324. #3455D11semidirect
410. #542C2×D11semidirect
411. #542C2×D11semidirect
412. #541C2×D11semidirect
413. #540C2×D11semidirect
748. C11#60919semidirect

Maximal subgroups

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

subgroupindex
C2×#106230652
#130800812
#130800722
#130800362
#130800212
#130784312
#130784172
#130784092
#130782482
#130782372
#130781102
#130780842
#130780762
#130771802
C11×#34552
#6091911