Finite Group Databasebeta

← #15634390

Subgroups — #15634390

Order 2816.

1750 conjugacy classes of subgroups.

The subgroup lattice has 840 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1Q8×#4339C211yesmaximal, characteristic
2#13081579C214yesmaximal, complemented
3#13081555C214yesmaximal, complemented
4#13081548C212yesmaximal, complemented
5#13081533C212yesmaximal, complemented
6#13081503C212yesmaximal, complemented
7#13081487C212yesmaximal, complemented
8#13079165C212yesmaximal, complemented
9#13079158C211yesmaximal, characteristic, complemented
10#13078434C212yesmaximal
11#13078425C211yesmaximal, characteristic
12#13078421C211yesmaximal, characteristic, complemented
13#13078421C212yesmaximal, complemented
14Q8×#4318C211yesmaximal, characteristic, complemented
15C4×#66995C211yesmaximal, characteristic
16C4×#66995C212yesmaximal
17C2×C11×#557C211yesmaximal, characteristic, complemented
18C11×#557—21no—
19C11×#557—21no—
20C11×#557—22no—
21C11×#557C2212yes—
22C11×#557C2212yes—
23C11×#557C2214yes—
24C2×C11×C4⋊Q8—21no—
25C2×C11×C4⋊Q8C2211yescharacteristic
26C2×C11×#125—22no—
27C2×C11×#125C2212yes—
28C2×C4×Q8×C11—21no—
29C2×C4×Q8×C11C2212yes—
30C2×C4×Q8×C11C2211yescharacteristic
31C2×C4×Q8×C11C2211yescharacteristic
32Q8×C22⋊D11—21no—
33C2×#66995C2211yescharacteristic
34#10623110C2211yescharacteristic
35#10623110C2212yes—
36#10623109—22no—
37#10623109—21no—
38Q8×D44C2211yescharacteristic
39C4×Q8×D11—21no—
40#10623098C2211yescharacteristic
41#10623098C2212yes—
42Q8×Dic22C2211yescharacteristic
43#10623042—21no—
44#10623042—22no—
45C4×#4339C2211yescharacteristic
46C4×#4339C2212yes—
47#10623001C2211yescharacteristic
48#10623001C2212yes—
49#10622838C2211yescharacteristic
50#10622838C2212yes—
51#10622707C2212yes—
52#10622704C2212yes—
53#10622700C2212yes—
54#10622697C2212yes—
55#10622693C2214yes—
56#10622692C2212yes—
57#10622691C2212yes—
58#10622679C2214yes—
59#10622679C2214yes—
60#10622678C2214yes—
61#10622678C2214yes—
62#10622677C2214yes—
63#10622677C2214yes—
64#10622676C2214yes—
65#10622676C2214yes—
66#10622643C2214yes—
67#10622643C2212yes—
68C4×#4326C2212yes—
69C4×#4326C2214yes—
70#10622639C2214yes—
71#10622639C2212yes—
72C4×#4325C2212yes—
73C4×#4325C2214yes—
74#10622637C2212yes—
75#10622637C2214yes—
76Q8×C11⋊C8C2212yes—
77#10622635C2214yes—
78#10622635C2214yes—
79#10622635C2214yes—
80#10622634C2212yes—
81#10622634C2214yes—
82#10622633C2212yes—
83#10622633C2214yes—
84#10622579C2212yes—
85#10622579C2211yescharacteristic
86#10622577C2212yes—
87#10622577C2212yes—
88#10622577C2211yescharacteristic
89#10622577C2212yes—
90#10622577C2212yes—
91#10622537C2211yescharacteristic
92#10622537C2212yes—
93C4×#4318C2211yescharacteristic
94C4×#4318C2212yes—
95C22×Q8×C11—21no—
96C22×Q8×C11D411yescharacteristic
97C22×Q8×C11C2311yescharacteristic
98C2×Q8×D11—21no—
99C2×#4339C2311yescharacteristic
100C11×C4⋊Q8—22no—
101C11×C4⋊Q8—22no—
102C11×C4⋊Q8—24no—
103C11×C4⋊Q8—21no—
104C11×C4⋊Q8—21no—
105C11×C4⋊Q8C2312yes—
106C11×C4⋊Q8C2312yes—
107C11×#125—24no—
108C11×#125—24no—
109C11×#125—24no—
110C11×#125—24no—
111C11×#125—22no—
112C11×#125—22no—
113C11×#125C2314yes—
114C11×#125C2314yes—
115C4×Q8×C11—22no—
116C4×Q8×C11—22no—
117C4×Q8×C11—24no—
118C4×Q8×C11—22no—
119C4×Q8×C11—22no—
120C4×Q8×C11—21no—
121C4×Q8×C11—21no—
122C4×Q8×C11D411yescharacteristic
123C4×Q8×C11D412yes—
124C4×Q8×C11D411yescharacteristic
125C4×Q8×C11C2312yes—
126C4×Q8×C11C2314yes—
127C4×Q8×C11C2314yes—
128C4×Q8×C11C2312yes—
129C4×Q8×C11C2311yescharacteristic
130C4×Q8×C11C2311yescharacteristic
131C4×Q8×C11C2312yes—
132C2×C11×C4⋊C4—22no—
133C2×C11×C4⋊C4—21no—
134C2×C11×C4⋊C4—22no—
135C2×C11×C4⋊C4—21no—
136C2×C11×C4⋊C4—22no—
137C2×C11×C4⋊C4D411yescharacteristic
138C2×C11×C4⋊C4D412yes—
139C2×C11×C4⋊C4C2311yescharacteristic
140C2×C11×C4⋊C4C2312yes—
141C2×C42×C11—22no—
142C2×C42×C11—21no—
143C2×C42×C11C2312yes—
144C2×C42×C11C2311yescharacteristic
145#66999—21no—
146#66999—22no—
147Q8×Dic11—21no—
148#66997—21no—
149#66997—22no—
150C2×#4326C2312yes—
151#66995Q818yescomplemented
152C2×#4325C2312yes—
153C4×C22⋊D11—22no—
154C4×C22⋊D11—21no—
155C4×C22⋊D11—21no—
156C4×C22⋊D11—22no—
157#66979C2312yes—
158#66979C2311yescharacteristic
159#66977—22no—
160#66977—21no—
161#66977—21no—
162#66977—22no—
163C2×#4318C2311yescharacteristic
164C2×#4318C2312yes—
165C2×#4318C2311yescharacteristic
166#66950—21no—
167#66950—22no—
168#66949—22no—
169#66949—22no—
170#66949—22no—
171C4⋊C4×D11—21no—
172C4⋊C4×D11—22no—
173#66942—22no—
174#66942—22no—
175#66942—22no—
176#66941—21no—
177#66941—22no—
178#66940—21no—
179#66940—22no—
180C4×D44C2311yescharacteristic
181C4×D44C2312yes—
182C4×D44C2312yes—
183C4×D44C2311yescharacteristic
184#66925—22no—
185#66925—21no—
186C42×D11—22no—
187C42×D11—21no—
188#66923C2312yes—
189#66923C2312yes—
190#66923C2312yes—
191#66922C2312yes—
192#66922C2311yescharacteristic
193#66922C2311yescharacteristic
194#66922C2312yes—
195C4×Dic22—22no—
196C4×Dic22—21no—
197C4×Dic22—22no—
198C4×Dic22—21no—
199C4×Dic22C2311yescharacteristic
200C4×Dic22C2312yes—
201C4×Dic22C2312yes—
202C4×Dic22C2311yescharacteristic
203#66899C2312yes—
204#66899C2314yes—
205#66899C2314yes—
206#66899C2312yes—
207#66874C2312yes—
208#66874C2314yes—
209#66873C2312yes—
210#66873C2314yes—
211#66872C2314yes—
212#66872C2314yes—
213#66872C2314yes—
214#66872C2312yes—
215#66872C2314yes—
216#66871C2314yes—
217#66871C2314yes—
218#66871C2314yes—
219#66871C2312yes—
220#66871C2314yes—
221C4⋊(C11⋊C8)C2312yes—
222C4⋊(C11⋊C8)C2314yes—
223C4⋊(C11⋊C8)C2314yes—
224C4⋊(C11⋊C8)C2312yes—
225#66867C2314yes—
226#66867C2312yes—
227C4×C11⋊C8C2314yes—
228C4×C11⋊C8C2312yes—
229#61369—111nomaximal, Sylow
230C2×Q8×C11—21no—
231C2×Q8×C11—22no—
232C2×Q8×C11—22no—
233C2×Q8×C11—22no—
234C2×Q8×C11—42no—
235C2×Q8×C11—44no—
236C2×Q8×C11C2×D411yescharacteristic
237C2×Q8×C11C2×D411yescharacteristic
238C2×Q8×C11C2×D412yes—
239C2×Q8×C11C2×Q814yescomplemented
240C2×Q8×C11C2412yes—
241C22×C4×C11—21no—
242C22×C4×C11—21no—
243C22×C4×C11—22no—
244C22×C4×C11C2×D411yescharacteristic
245C22×C4×C11C2×D412yes—
246C22×C4×C11C2×D411yescharacteristic
247C22×C4×C11C2×D412yes—
248C22×C4×C11C2411yescharacteristic
249C2×C22⋊D11—21no—
250Q8×D11—44no—
251#4339—22no—
252#4339C2×Q814yes—
253C2×D44C2411yescharacteristic
254C2×C4×D11—21no—
255C2×C4×D11—22no—
256C2×C4×D11—21no—
257C2×C4×D11—22no—
258C2×C4×D11—21no—
259C2×Dic22—22no—
260C2×Dic22—21no—
261C2×Dic22—22no—
262C2×Dic22—21no—
263C2×Dic22C2411yescharacteristic
264C11×C4⋊C4—24no—
265C11×C4⋊C4—24no—
266C11×C4⋊C4—22no—
267C11×C4⋊C4—22no—
268C11×C4⋊C4—24no—
269C11×C4⋊C4—24no—
270C11×C4⋊C4—22no—
271C11×C4⋊C4—22no—
272C11×C4⋊C4—24no—
273C11×C4⋊C4—24no—
274C11×C4⋊C4—21no—
275C11×C4⋊C4—22no—
276C11×C4⋊C4C2×D411yescharacteristic
277C11×C4⋊C4C2×D412yes—
278C11×C4⋊C4C2×D411yescharacteristic
279C11×C4⋊C4C2×D412yes—
280C11×C4⋊C4C2×D412yes—
281C11×C4⋊C4C2×D412yes—
282C11×C4⋊C4C2×D412yes—
283C11×C4⋊C4C2412yes—
284C11×C4⋊C4C2414yes—
285C42×C11—24no—
286C42×C11—24no—
287C42×C11—22no—
288C42×C11—22no—
289C42×C11C2×D412yes—
290C42×C11C2×D411yescharacteristic
291C42×C11C2×D412yes—
292C42×C11C2×D411yescharacteristic
293C42×C11C2411yescharacteristic
294C42×C11C2412yes—
295C42×C11C2412yes—
296C42×C11C2411yescharacteristic
297C22⋊Dic11—21no—
298C22⋊Dic11—22no—
299#4326C2×Q818yescomplemented
300#4325C2×Q818yescomplemented
301(C2×D11)⋊C4—22no—
302(C2×D11)⋊C4—21no—
303(C2×D11)⋊C4—21no—
304(C2×D11)⋊C4—22no—
305C4⋊Dic11—22no—
306C4⋊Dic11—21no—
307C4⋊Dic11—22no—
308C4⋊Dic11—21no—
309C4⋊Dic11C2412yes—
310C4⋊Dic11C2411yescharacteristic
311C4⋊Dic11C2412yes—
312C4⋊Dic11C2411yescharacteristic
313Dic11⋊C4—22no—
314Dic11⋊C4—22no—
315Dic11⋊C4—22no—
316Dic11⋊C4—22no—
317Dic11⋊C4—22no—
318Dic11⋊C4—22no—
319Dic11⋊C4—22no—
320Dic11⋊C4—21no—
321Dic11⋊C4—21no—
322Dic11⋊C4—22no—
323C4×Dic11—21no—
324C4×Dic11—22no—
325C4×Dic11—22no—
326C4×Dic11—21no—
327C4×Dic11—22no—
328C4×Dic11—21no—
329#4318—22no—
330#4318—24no—
331#4318C2×Q814yescomplemented
332C2×C11⋊C8C2414yes—
333C2×C11⋊C8C2412yes—
334C2×C11⋊C8C2412yes—
335Q8×#41—111no—
336C2×#557D1111yescharacteristic, complemented
337#3390—114no—
338#3388—114no—
339#3387—112no—
340#3386—112no—
341#3383—112no—
342#3381—112no—
343#3166—112no—
344#3165—111no—
345#3080—112no—
346#3079—111no—
347#3078—111no—
348#3078—112no—
349Q8×M16—111no—
350C4×#137—111no—
351C4×#137—112no—
352C23×C11C22×D411yescharacteristic
353C22×D11—21no—
354Q8×C11—24no—
355Q8×C11—22no—
356Q8×C11—22no—
357Q8×C11—22no—
358Q8×C11—42no—
359Q8×C11—44no—
360Q8×C11—44no—
361Q8×C11C22×Q814yes—
362C2×C4×C11—24no—
363C2×C4×C11—22no—
364C2×C4×C11—22no—
365C2×C4×C11—22no—
366C2×C4×C11—24no—
367C2×C4×C11—42no—
368C2×C4×C11—41no—
369C2×C4×C11—42no—
370C2×C4×C11—42no—
371C2×C4×C11—44no—
372C2×C4×C11C22×D412yes—
373C2×C4×C11C22×D411yescharacteristic
374C2×C4×C11C22×D412yes—
375C2×C4×C11C22×D411yescharacteristic
376C2×C4×C11C22×D412yes—
377C2×C4×C11C22×D412yes—
378C2×C4×C11C22×D411yescharacteristic
379C2×C4×C11C22×D411yescharacteristic
380C2×C4×C11C22×D411yescharacteristic
381C2×C4×C11C22×Q812yes—
382C2×C4×C112−1+412yes—
383C2×C4×C11C2511yescharacteristic
384C22⋊D11—24no—
385C2×Dic11—21no—
386C2×Dic11—22no—
387C2×Dic11—21no—
388C2×Dic11—21no—
389C2×Dic11—22no—
390D44—21no—
391D44C22×Q812yes—
392C4×D11—24no—
393C4×D11—44no—
394C4×D11—42no—
395C4×D11—82no—
396C4×D11—81no—
397Dic22—21no—
398Dic22—44no—
399Dic22—42no—
400Dic22—82no—
401Dic22—81no—
402Dic22C22×Q812yes—
403C11⋊C8—24no—
404C11⋊C8—22no—
405C11⋊C8C22×Q814yes—
406C2×#137—111no—
407Q82—111no—
408#557—21no—
409#557—22no—
410#557—21no—
411#557—111no—
412#557—112no—
413#557C2×D1112yes—
414#557C2×D1112yes—
415#557C2×D1114yes—
416#554—111no—
417#554—112no—
418#554—221no—
419#554—222no—
420D4×Q8—111no—
421D4×Q8—221no—
422#533—111no—
423#533—112no—
424#533—222no—
425#533—221no—
426C2×C4⋊Q8—21no—
427C2×C4⋊Q8C2×D1111yescharacteristic
428C2×#125—22no—
429C2×#125C2×D1112yes—
430C4×#41—111no—
431C4×#41—112no—
432C2×C4×Q8—21no—
433C2×C4×Q8—221no—
434C2×C4×Q8C2×D1112yes—
435C2×C4×Q8C2×D1111yescharacteristic
436C2×C4×Q8C2×D1111yescharacteristic
437#501—114no—
438#501—114no—
439#501—114no—
440#500—112no—
441#499—114no—
442#499—114no—
443#498—112no—
444#479—114no—
445#479—114no—
446#479—114no—
447#479—114no—
448#479—114no—
449#478—114no—
450#478—114no—
451#477—112no—
452#477—112no—
453#477—114no—
454#476—112no—
455#475—112no—
456#475—112no—
457#475—114no—
458#474—112no—
459#446—112no—
460#446—114no—
461C8×Q8—112no—
462#441—114no—
463#441—112no—
464#440—114no—
465#440—112no—
466C4×Q16—112no—
467C4×Q16—114no—
468C4×SD16—112no—
469C4×SD16—114no—
470#428—112no—
471#428—112no—
472#428—112no—
473#428—112no—
474#428—111no—
475#423—111no—
476#423—112no—
477#419—112no—
478#419—111no—
479#417—112no—
480#417—111no—
481C4×M16—111no—
482C4×M16—112no—
483C22×C11—21no—
484C22×C11—21no—
485C22×C11D4×Q812yes—
486C22×C11C23×D411yescharacteristic
487C2×D11—22no—
488C2×D11—41no—
489C2×D11—41no—
490C4×C11—22no—
491C4×C11—21no—
492C4×C11—22no—
493C4×C11—21no—
494C4×C11—24no—
495C4×C11—21no—
496C4×C11—22no—
497C4×C11—22no—
498C4×C11—42no—
499C4×C11—44no—
500C4×C11D4×Q812yes—
501C4×C11#57512yes—
502C4×C11C23×Q811yescharacteristic
503C4×C11C2×2−1+411yescharacteristic
504Dic11—22no—
505Dic11—41no—
506Dic11—42no—
507Dic11—41no—
508Dic11—42no—
509C2×#41—111no—
510C22×Q8—21no—
511C22×Q8—221no—
512C22×Q8C22⋊D1111yescharacteristic
513C22×Q8C22×D1111yescharacteristic
514#137—118no—
515C2×Q16—112no—
516C2×SD16—112no—
517C2×M16—111no—
518C2×M16—111no—
519C2×M16—112no—
520C4⋊Q8—22no—
521C4⋊Q8—22no—
522C4⋊Q8—24no—
523C4⋊Q8—21no—
524C4⋊Q8—21no—
525C4⋊Q8—111no—
526C4⋊Q8—112no—
527C4⋊Q8—112no—
528C4⋊Q8—111no—
529C4⋊Q8—221no—
530C4⋊Q8—222no—
531C4⋊Q8—221no—
532C4⋊Q8—222no—
533C4⋊Q8C22×D1112yes—
534C4⋊Q8C22×D1112yes—
535#125—24no—
536#125—24no—
537#125—24no—
538#125—24no—
539#125—22no—
540#125—22no—
541#125—112no—
542#125—112no—
543#125—112no—
544#125—222no—
545#125—222no—
546#125—222no—
547#125C22×D1114yes—
548#125C22×D1114yes—
549C22⋊Q8—221no—
550C22⋊Q8—222no—
551C22⋊Q8—221no—
552C22⋊Q8—222no—
553C22⋊Q8—222no—
554C22⋊Q8—221no—
555C22⋊Q8—221no—
556C22⋊Q8—222no—
557C22⋊Q8—222no—
558C22⋊Q8—222no—
559C22⋊Q8—222no—
560C4×Q8—22no—
561C4×Q8—24no—
562C4×Q8—22no—
563C4×Q8—22no—
564C4×Q8—22no—
565C4×Q8—21no—
566C4×Q8—21no—
567C4×Q8—112no—
568C4×Q8—111no—
569C4×Q8—111no—
570C4×Q8—112no—
571C4×Q8—221no—
572C4×Q8—221no—
573C4×Q8—222no—
574C4×Q8—222no—
575C4×Q8—221no—
576C4×Q8—222no—
577C4×Q8—221no—
578C4×Q8C22⋊D1111yescharacteristic
579C4×Q8C22⋊D1112yes—
580C4×Q8C22⋊D1111yescharacteristic
581C4×Q8C22×D1112yes—
582C4×Q8C22×D1114yes—
583C4×Q8C22×D1114yes—
584C4×Q8C22×D1112yes—
585C4×Q8C22×D1111yescharacteristic
586C4×Q8C22×D1111yescharacteristic
587C4×Q8C22×D1112yes—
588C4×D4—111no—
589C4×D4—112no—
590C4×D4—112no—
591C4×D4—111no—
592C4×D4—221no—
593C4×D4—222no—
594C4×D4—222no—
595C4×D4—221no—
596#117—111no—
597#117—112no—
598#117—222no—
599#117—221no—
600C2×C4⋊C4—22no—
601C2×C4⋊C4—21no—
602C2×C4⋊C4—22no—
603C2×C4⋊C4—21no—
604C2×C4⋊C4—22no—
605C2×C4⋊C4—221no—
606C2×C4⋊C4—222no—
607C2×C4⋊C4C22⋊D1111yescharacteristic
608C2×C4⋊C4C22⋊D1112yes—
609C2×C4⋊C4C22×D1111yescharacteristic
610C2×C4⋊C4C22×D1112yes—
611C2×C42—22no—
612C2×C42—21no—
613C2×C42—222no—
614C2×C42—221no—
615C2×C42C22×D1112yes—
616C2×C42C22×D1111yescharacteristic
617#107—112no—
618#107—114no—
619#107—114no—
620#107—114no—
621#107—114no—
622#106—114no—
623#106—112no—
624#106—114no—
625#106—114no—
626#106—114no—
627C4⋊C8—112no—
628C4⋊C8—114no—
629C4⋊C8—114no—
630C4⋊C8—112no—
631#103—114no—
632#103—112no—
633#103—112no—
634#103—114no—
635#103—114no—
636#103—112no—
637#102—114no—
638#102—112no—
639#97—112no—
640#97—114no—
641C4×C8—112no—
642C4×C8—114no—
643C2×C11—22no—
644C2×C11C2×D4×Q811yescharacteristic
645C2×C11C2×#57511yescharacteristic
646C2×C11#358611yescharacteristic
647D11—42no—
648#41—114no—
649#41—222no—
650C2×Q8—22no—
651C2×Q8—21no—
652C2×Q8—22no—
653C2×Q8—22no—
654C2×Q8—42no—
655C2×Q8—44no—
656C2×Q8—111no—
657C2×Q8—222no—
658C2×Q8—221no—
659C2×Q8—222no—
660C2×Q8—221no—
661C2×Q8—444no—
662C2×Q8Q8×D1114yescomplemented
663C2×Q8C2×C22⋊D1111yescharacteristic
664C2×Q8C2×C22⋊D1111yescharacteristic
665C2×Q8C2×C22⋊D1112yes—
666C2×Q8C23×D1112yes—
667C2×D4—111no—
668C2×D4—221no—
669C22×C4—21no—
670C22×C4—21no—
671C22×C4—22no—
672C22×C4—221no—
673C22×C4—222no—
674C22×C4—221no—
675C22×C4—222no—
676C22×C4—221no—
677C22×C4C2×C22⋊D1111yescharacteristic
678C22×C4C2×C22⋊D1112yes—
679C22×C4C2×C22⋊D1111yescharacteristic
680C22×C4C2×C22⋊D1112yes—
681C22×C4C23×D1111yescharacteristic
682Q16—118no—
683SD16—118no—
684M16—114no—
685M16—222no—
686M16—224no—
687C2×C8—112no—
688C2×C8—112no—
689C2×C8—114no—
690C4⋊C4—24no—
691C4⋊C4—24no—
692C4⋊C4—22no—
693C4⋊C4—22no—
694C4⋊C4—24no—
695C4⋊C4—24no—
696C4⋊C4—22no—
697C4⋊C4—22no—
698C4⋊C4—24no—
699C4⋊C4—24no—
700C4⋊C4—21no—
701C4⋊C4—22no—
702C4⋊C4—112no—
703C4⋊C4—111no—
704C4⋊C4—111no—
705C4⋊C4—112no—
706C4⋊C4—222no—
707C4⋊C4—222no—
708C4⋊C4—222no—
709C4⋊C4—222no—
710C4⋊C4—221no—
711C4⋊C4—222no—
712C4⋊C4—221no—
713C4⋊C4—222no—
714C4⋊C4—221no—
715C4⋊C4—222no—
716C4⋊C4—222no—
717C4⋊C4—222no—
718C4⋊C4—222no—
719C4⋊C4—221no—
720C4⋊C4C2×C22⋊D1111yescharacteristic
721C4⋊C4C2×C22⋊D1112yes—
722C4⋊C4C2×C22⋊D1112yes—
723C4⋊C4C2×C22⋊D1111yescharacteristic
724C4⋊C4C2×C22⋊D1112yes—
725C4⋊C4C2×C22⋊D1112yes—
726C4⋊C4C2×C22⋊D1112yes—
727C4⋊C4C23×D1112yes—
728C4⋊C4C23×D1114yes—
729C22⋊C4—221no—
730C22⋊C4—222no—
731C22⋊C4—222no—
732C22⋊C4—221no—
733C22⋊C4—222no—
734C22⋊C4—221no—
735C42—24no—
736C42—24no—
737C42—22no—
738C42—22no—
739C42—222no—
740C42—221no—
741C42—222no—
742C42—221no—
743C42—222no—
744C42—221no—
745C42C2×C22⋊D1112yes—
746C42C2×C22⋊D1111yescharacteristic
747C42C2×C22⋊D1112yes—
748C42C2×C22⋊D1111yescharacteristic
749C42C23×D1112yes—
750C42C23×D1111yescharacteristic
751C42C23×D1111yescharacteristic
752C42C23×D1112yes—
753C11#6136911yescharacteristic, complemented, Sylow
754C23—221no—
755C23C22×C22⋊D1111yescharacteristic
756Q8—24no—
757Q8—22no—
758Q8—22no—
759Q8—22no—
760Q8—42no—
761Q8—44no—
762Q8—44no—
763Q8—112no—
764Q8—221no—
765Q8—444no—
766Q8—442no—
767Q8—882no—
768Q8—881no—
769Q8C2×Q8×D1114yes—
770D4—112no—
771D4—224no—
772D4—221no—
773C2×C4—24no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—24no—
778C2×C4—42no—
779C2×C4—41no—
780C2×C4—42no—
781C2×C4—42no—
782C2×C4—44no—
783C2×C4—221no—
784C2×C4—224no—
785C2×C4—222no—
786C2×C4—221no—
787C2×C4—222no—
788C2×C4—221no—
789C2×C4—444no—
790C2×C4—442no—
791C2×C4—882no—
792C2×C4—881no—
793C2×C4C2×Q8×D1112yes—
794C2×C4#6704012yes—
795C2×C4C22×C22⋊D1112yes—
796C2×C4C22×C22⋊D1112yes—
797C2×C4C22×C22⋊D1111yescharacteristic
798C2×C4C22×C22⋊D1111yescharacteristic
799C2×C4C22×C22⋊D1112yes—
800C2×C4C22×C22⋊D1112yes—
801C2×C4C22×C22⋊D1111yescharacteristic
802C2×C4C22×C22⋊D1111yescharacteristic
803C2×C4C22×C22⋊D1111yescharacteristic
804C2×C4C24×D1111yescharacteristic
805C8—114no—
806C8—222no—
807C8—224no—
808C22—21no—
809C22—21no—
810C22—222no—
811C22—441no—
812C22—441no—
813C22Q8×C22⋊D1112yes—
814C22C23×C22⋊D1111yescharacteristic
815C4—22no—
816C4—21no—
817C4—22no—
818C4—21no—
819C4—21no—
820C4—22no—
821C4—22no—
822C4—24no—
823C4—42no—
824C4—44no—
825C4—222no—
826C4—442no—
827C4—441no—
828C4—442no—
829C4—441no—
830C4Q8×C22⋊D1112yes—
831C4#1062335312yes—
832C4C22×Q8×D1111yescharacteristic
833C4C2×#6704011yescharacteristic
834C2—22no—
835C2—442no—
836C2C2×Q8×C22⋊D1111yescharacteristic
837C2C2×#1062335311yescharacteristic
838C2#1308340311yescharacteristic
subgroupG/H
centerC22C23×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#557C2
socleC22×C11C23×D4
prime radicalC2×#4339C23
hypercenterC2×#557D11
hypocenterC11#61369
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C4×Q8 ◁ C2×#557

Complements

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

NH ≅ G/Ntype
2. #13081579C2semidirect
3. #13081555C2semidirect
4. #13081548C2semidirect
5. #13081533C2semidirect
6. #13081503C2semidirect
7. #13081487C2semidirect
8. #13079165C2semidirect
9. #13079158C2semidirect
12. #13078421C2semidirect
13. #13078421C2semidirect
14. Q8×#4318C2semidirect
17. C2×C11×#557C2semidirect
151. #66995Q8semidirect
239. C2×Q8×C11C2×Q8semidirect
299. #4326C2×Q8semidirect
300. #4325C2×Q8semidirect
331. #4318C2×Q8semidirect
336. C2×#557D11semidirect
662. C2×Q8Q8×D11semidirect
753. C11#61369semidirect

Maximal subgroups

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

subgroupindex
Q8×#43392
#130815792
#130815552
#130815482
#130815332
#130815032
#130814872
#130791652
#130791582
#130784342
#130784252
#130784212
Q8×#43182
C4×#669952
C2×C11×#5572
#6136911