Finite Group Databasebeta

← #15634387

Subgroups — #15634387

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
1#41×Dic22C211yesmaximal, characteristic
2C2×#10623101C211yesmaximal, characteristic, complemented
3#13081584C214yesmaximal, complemented
4#13081562C214yesmaximal, complemented
5#13081546C212yesmaximal, complemented
6#13081535C212yesmaximal, complemented
7#13081505C212yesmaximal, complemented
8#13081489C212yesmaximal, complemented
9#13079166C212yesmaximal, complemented
10#13079162C211yesmaximal, characteristic, complemented
11#13078436C212yesmaximal
12#13078431C211yesmaximal, characteristic
13#13078421C211yesmaximal, characteristic, complemented
14#13078418C212yesmaximal, complemented
15M16×Dic22C211yesmaximal, characteristic, complemented
16#137×Dic11C212yesmaximal
17C4×C11×#137C211yesmaximal, characteristic
18C2×C11×#137C2211yescharacteristic
19C4×C11×#41C2211yescharacteristic
20C2×C4×Q8×C11C2211yescharacteristic
21#41×Dic11C2212yes—
22C2×Q8×Dic11C2212yes—
23#10623101—21no—
24#10623101—21no—
25#10623101—22no—
26#10623101C2212yes—
27#10623101C2212yes—
28#10623101C2214yes—
29#10623101C2211yescharacteristic
30#10623100C2212yes—
31Q8×Dic22C2211yescharacteristic
32#10623074—21no—
33#10623074C2211yescharacteristic
34#10623070—22no—
35#10623070C2212yes—
36D4×Dic22—21no—
37D4×Dic22C2211yescharacteristic
38#10623048—22no—
39#10623048C2212yes—
40C2×#66943—22no—
41C2×#66943C2212yes—
42#10623001—21no—
43#10623001C2211yescharacteristic
44C2×#66922—21no—
45C2×#66922C2211yescharacteristic
46C2×C4×Dic22—21no—
47C2×C4×Dic22—21no—
48C2×C4×Dic22C2211yescharacteristic
49C11×#441C2212yes—
50C11×#440C2212yes—
51C4×C11×Q16C2212yes—
52C4×C11×SD16C2212yes—
53C11×#428C2211yescharacteristic
54C11×#419C2211yescharacteristic
55C11×#417C2211yescharacteristic
56C4×C11×M16C2211yescharacteristic
57#10622845C2212yes—
58#10622838C2212yes—
59#10622797C2214yes—
60Q16×Dic11C2214yes—
61#10622777C2214yes—
62SD16×Dic11C2214yes—
63#10622734C2212yes—
64#10622734C2212yes—
65#10622731C2212yes—
66M16×Dic11C2212yes—
67#10622635C2214yes—
68#10622634C2212yes—
69#10622634C2212yes—
70#10622633C2212yes—
71#10622633C2212yes—
72#10622621C2212yes—
73#10622620C2212yes—
74#10622608C2212yes—
75#10622577C2212yes—
76#10622537C2211yescharacteristic
77#10622491C2214yes—
78#10622489C2214yes—
79#10622471C2214yes—
80#10622469C2214yes—
81#10622412C2214yes—
82#10622412C2214yes—
83#10622409C2214yes—
84#10622409C2214yes—
85#10622407C2214yes—
86#10622404C2214yes—
87#10622379C2214yes—
88#10622376C2214yes—
89#10622315C2214yes—
90#10622314C2214yes—
91#10622295C2212yes—
92#10622293C2212yes—
93#10622292C2212yes—
94C8×Dic22C2212yes—
95C2×C11×#41C2311yescharacteristic
96C22×Q8×C11C2311yescharacteristic
97C22×Dic22—21no—
98C22×Dic22—21no—
99C22×Dic22D411yescharacteristic
100C11×#137Q818yescomplemented
101C2×C11×Q16C2312yes—
102C2×C11×SD16C2312yes—
103C2×C11×M16C2311yescharacteristic
104C2×C11×M16C2311yescharacteristic
105C4×Q8×C11—21no—
106C4×Q8×C11—21no—
107C4×Q8×C11C2311yescharacteristic
108C4×Q8×C11C2311yescharacteristic
109C4×Q8×C11C2312yes—
110C4×Q8×C11C2312yes—
111C4×D4×C11—21no—
112C4×D4×C11—21no—
113C4×D4×C11C2311yescharacteristic
114C4×D4×C11C2311yescharacteristic
115C11×#117—21no—
116C11×#117C2311yescharacteristic
117C2×C11×C4⋊C4—21no—
118C2×C11×C4⋊C4C2311yescharacteristic
119C2×C42×C11—21no—
120C2×C42×C11—21no—
121C2×C42×C11C2311yescharacteristic
122Q8×Dic11—22no—
123Q8×Dic11—22no—
124Q8×Dic11C2314yes—
125Q8×Dic11C2314yes—
126Q8×Dic11C2312yes—
127Q8×Dic11C2312yes—
128D4×Dic11—22no—
129D4×Dic11—22no—
130D4×Dic11C2312yes—
131D4×Dic11C2312yes—
132#66979—22no—
133#66979C2312yes—
134C2×C4⋊Dic11—21no—
135C2×C4⋊Dic11—22no—
136C2×C4⋊Dic11—22no—
137C2×C4⋊Dic11—21no—
138C2×C4⋊Dic11D411yescharacteristic
139C2×C4⋊Dic11C2312yes—
140#66977—21no—
141#66977—21no—
142#66977—21no—
143#66977—21no—
144#66977—22no—
145C2×Dic11⋊C4—22no—
146C2×Dic11⋊C4—22no—
147C2×Dic11⋊C4D412yes—
148C2×C4×Dic11—22no—
149C2×C4×Dic11—22no—
150C2×C4×Dic11C2312yes—
151C2×#4318C2312yes—
152#66943—22no—
153#66943—24no—
154#66943—24no—
155#66943—24no—
156#66943—24no—
157#66943—22no—
158#66943—22no—
159#66943—22no—
160#66943C2314yes—
161#66943C2312yes—
162#66943C2314yes—
163#66943C2312yes—
164#66941—22no—
165#66941—22no—
166#66941C2312yes—
167#66941C2312yes—
168#66931—22no—
169#66931—22no—
170#66931—22no—
171#66931—22no—
172#66931—22no—
173#66931—22no—
174#66923—22no—
175#66923C2312yes—
176#66922—22no—
177#66922—22no—
178#66922—24no—
179#66922—21no—
180#66922—21no—
181#66922—21no—
182#66922—21no—
183#66922C2312yes—
184#66922C2312yes—
185#66922C2311yescharacteristic
186#66922C2311yescharacteristic
187C4×Dic22—21no—
188C4×Dic22—21no—
189C4×Dic22—21no—
190C4×Dic22—21no—
191C4×Dic22—22no—
192C4×Dic22—22no—
193C4×Dic22—24no—
194C4×Dic22—22no—
195C4×Dic22—22no—
196C4×Dic22—22no—
197C4×Dic22D411yescharacteristic
198C4×Dic22D411yescharacteristic
199C4×Dic22D412yes—
200C4×Dic22C2311yescharacteristic
201C4×Dic22C2311yescharacteristic
202C4×Dic22C2312yes—
203C11×#107C2312yes—
204C11×#106C2312yes—
205C11×#103C2312yes—
206C11×#103C2312yes—
207C11×#103C2312yes—
208C11×#102C2312yes—
209C11×#97C2312yes—
210C4×C8×C11C2312yes—
211#66899C2314yes—
212#66899C2314yes—
213#66899C2314yes—
214#66896C2314yes—
215#66882C2314yes—
216#66882C2314yes—
217#66881C2314yes—
218#66881C2314yes—
219#66879C2314yes—
220Dic11⋊C8C2314yes—
221Dic11⋊C8C2314yes—
222C8×Dic11C2314yes—
223#66872C2314yes—
224#66872C2314yes—
225#66871C2314yes—
226#66871C2314yes—
227C4⋊(C11⋊C8)C2312yes—
228C4⋊(C11⋊C8)C2312yes—
229#61369—111nomaximal, Sylow
230C11×#41—22no—
231C11×#41C2×Q814yes—
232C2×Q8×C11—21no—
233C2×Q8×C11—22no—
234C2×Q8×C11C2×Q814yescomplemented
235C2×Q8×C11C2412yes—
236C2×Q8×C11C2411yescharacteristic
237C2×D4×C11—21no—
238C2×D4×C11C2411yescharacteristic
239C22×C4×C11—21no—
240C22×C4×C11—21no—
241C22×C4×C11—21no—
242C22×C4×C11—21no—
243C22×C4×C11—21no—
244C22×C4×C11C2×D411yescharacteristic
245C22×C4×C11C2×D411yescharacteristic
246C22×C4×C11C2411yescharacteristic
247C22×Dic11—22no—
248C22×Dic11—22no—
249C22×Dic11—22no—
250C22×Dic11C2×D412yes—
251C22×Dic11C2×D412yes—
252C2×Dic22—22no—
253C2×Dic22—22no—
254C2×Dic22—22no—
255C2×Dic22—22no—
256C2×Dic22—21no—
257C2×Dic22—21no—
258C2×Dic22—42no—
259C2×Dic22—44no—
260C2×Dic22—44no—
261C2×Dic22C2×D411yescharacteristic
262C2×Dic22C2×D411yescharacteristic
263C2×Dic22C2×D412yes—
264C11×Q16C2×Q818yescomplemented
265C11×SD16C2×Q818yescomplemented
266C11×M16—22no—
267C11×M16C2×Q814yescomplemented
268C2×C8×C11C2412yes—
269C2×C8×C11C2412yes—
270C11×C4⋊C4—21no—
271C11×C4⋊C4—21no—
272C11×C4⋊C4—22no—
273C11×C4⋊C4—22no—
274C11×C4⋊C4—21no—
275C11×C4⋊C4C2411yescharacteristic
276C11×C4⋊C4C2412yes—
277C11×C4⋊C4C2411yescharacteristic
278C11×C22⋊C4—21no—
279C11×C22⋊C4—21no—
280C11×C22⋊C4—21no—
281C42×C11—21no—
282C42×C11—21no—
283C42×C11—22no—
284C42×C11—22no—
285C42×C11—21no—
286C42×C11C2×D411yescharacteristic
287C42×C11C2×D411yescharacteristic
288C42×C11C2411yescharacteristic
289C42×C11C2411yescharacteristic
290C22⋊Dic11—22no—
291C22⋊Dic11—22no—
292C22⋊Dic11—22no—
293C4⋊Dic11—22no—
294C4⋊Dic11—22no—
295C4⋊Dic11—24no—
296C4⋊Dic11—24no—
297C4⋊Dic11—24no—
298C4⋊Dic11—24no—
299C4⋊Dic11—22no—
300C4⋊Dic11—22no—
301C4⋊Dic11—21no—
302C4⋊Dic11—21no—
303C4⋊Dic11—22no—
304C4⋊Dic11—22no—
305C4⋊Dic11—22no—
306C4⋊Dic11C2×D411yescharacteristic
307C4⋊Dic11C2×D411yescharacteristic
308C4⋊Dic11C2×D412yes—
309C4⋊Dic11C2412yes—
310C4⋊Dic11C2414yes—
311C4⋊Dic11C2412yes—
312Dic11⋊C4—22no—
313Dic11⋊C4—22no—
314Dic11⋊C4—24no—
315Dic11⋊C4—24no—
316Dic11⋊C4—22no—
317Dic11⋊C4—22no—
318Dic11⋊C4—22no—
319Dic11⋊C4—22no—
320Dic11⋊C4C2×D412yes—
321Dic11⋊C4C2×D412yes—
322Dic11⋊C4C2×D412yes—
323Dic11⋊C4C2×D412yes—
324C4×Dic11—22no—
325C4×Dic11—22no—
326C4×Dic11—24no—
327C4×Dic11—24no—
328C4×Dic11—22no—
329C4×Dic11C2×D412yes—
330C4×Dic11C2×D412yes—
331C4×Dic11C2412yes—
332C4×Dic11C2412yes—
333#4318—24no—
334C2×C11⋊C8C2414yes—
335Q8×#41—111no—
336C2×#557—111no—
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—112no—
348#3078—111no—
349Q8×M16—111no—
350C4×#137—112no—
351C4×#137D1111yescharacteristic
352C23×C11—21no—
353C23×C11C22×D411yescharacteristic
354Q8×C11—24no—
355Q8×C11—22no—
356Q8×C11—21no—
357Q8×C11C22×Q814yes—
358Q8×C11C22×Q812yes—
359D4×C11—24no—
360D4×C11—21no—
361D4×C11C22×Q812yes—
362C2×C4×C11—24no—
363C2×C4×C11—21no—
364C2×C4×C11—22no—
365C2×C4×C11—24no—
366C2×C4×C11—22no—
367C2×C4×C11—22no—
368C2×C4×C11—21no—
369C2×C4×C11—21no—
370C2×C4×C11—41no—
371C2×C4×C11—42no—
372C2×C4×C11—42no—
373C2×C4×C11—81no—
374C2×C4×C11C22×D411yescharacteristic
375C2×C4×C11C22×D411yescharacteristic
376C2×C4×C11C22×D411yescharacteristic
377C2×C4×C11C22×D411yescharacteristic
378C2×C4×C11C22×D411yescharacteristic
379C2×C4×C11C22×Q812yes—
380C2×C4×C112−1+412yes—
381C2×C4×C11C2511yescharacteristic
382C2×Dic11—22no—
383C2×Dic11—22no—
384C2×Dic11—24no—
385C2×Dic11—42no—
386C2×Dic11—42no—
387C2×Dic11—44no—
388C2×Dic11—44no—
389C2×Dic11—82no—
390C2×Dic11C22×D412yes—
391C2×Dic11C22×D412yes—
392C2×Dic11C22×D412yes—
393C2×Dic11C22×D412yes—
394Dic22—22no—
395Dic22—22no—
396Dic22—42no—
397Dic22—44no—
398Dic22—44no—
399Dic22—44no—
400Dic22—42no—
401Dic22—82no—
402Dic22—81no—
403C8×C11—22no—
404C8×C11C22×Q814yes—
405C11⋊C8—24no—
406C2×#137C2×D1111yescharacteristic
407Q82—111no—
408#557—112no—
409#557—111no—
410#557—112no—
411#557—114no—
412#557—112no—
413#557—221no—
414#557—221no—
415#557—222no—
416#554—111no—
417#554—112no—
418#554—222no—
419#554—221no—
420D4×Q8—111no—
421D4×Q8—221no—
422#533—112no—
423#533—111no—
424#533—221no—
425#533—222no—
426C2×C4⋊Q8—111no—
427C2×C4⋊Q8—221no—
428C2×#125—112no—
429C2×#125—222no—
430C4×#41—112no—
431C4×#41C2×D1111yescharacteristic
432C2×C4×Q8—111no—
433C2×C4×Q8—112no—
434C2×C4×Q8—221no—
435C2×C4×Q8—221no—
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—114no—
460#446—112no—
461C8×Q8—112no—
462#441—114no—
463#441C2×D1112yes—
464#440—114no—
465#440C2×D1112yes—
466C4×Q16—114no—
467C4×Q16C2×D1112yes—
468C4×SD16—114no—
469C4×SD16C2×D1112yes—
470#428—112no—
471#428—112no—
472#428—112no—
473#428—112no—
474#428C2×D1111yescharacteristic
475#423—112no—
476#423—111no—
477#419—112no—
478#419C2×D1111yescharacteristic
479#417—112no—
480#417C2×D1111yescharacteristic
481C4×M16—112no—
482C4×M16C2×D1111yescharacteristic
483C22×C11—21no—
484C22×C11—21no—
485C22×C11—22no—
486C22×C11—41no—
487C22×C11—41no—
488C22×C11D4×Q812yes—
489C22×C11C23×D411yescharacteristic
490C4×C11—21no—
491C4×C11—21no—
492C4×C11—22no—
493C4×C11—24no—
494C4×C11—21no—
495C4×C11—42no—
496C4×C11—41no—
497C4×C11—41no—
498C4×C11D4×Q812yes—
499C4×C11#57512yes—
500C4×C11C23×Q811yescharacteristic
501C4×C11C2×2−1+411yescharacteristic
502Dic11—22no—
503Dic11—22no—
504Dic11—22no—
505Dic11—22no—
506Dic11—42no—
507Dic11—42no—
508Dic11—44no—
509C2×#41C22×D1111yescharacteristic
510C22×Q8—111no—
511C22×Q8—221no—
512C22×Q8—221no—
513C22×Q8C22×D1111yescharacteristic
514#137Dic2218yescomplemented
515C2×Q16C22×D1112yes—
516C2×SD16C22×D1112yes—
517C2×M16—112no—
518C2×M16C22×D1111yescharacteristic
519C2×M16C22×D1111yescharacteristic
520C4⋊Q8—112no—
521C4⋊Q8—112no—
522C4⋊Q8—112no—
523C4⋊Q8—112no—
524C4⋊Q8—111no—
525C4⋊Q8—111no—
526C4⋊Q8—221no—
527C4⋊Q8—222no—
528C4⋊Q8—222no—
529C4⋊Q8—224no—
530C4⋊Q8—221no—
531C4⋊Q8—222no—
532C4⋊Q8—222no—
533C4⋊Q8—221no—
534C4⋊Q8—221no—
535#125—114no—
536#125—114no—
537#125—112no—
538#125—112no—
539#125—112no—
540#125—222no—
541#125—222no—
542#125—222no—
543#125—224no—
544#125—224no—
545#125—224no—
546#125—224no—
547#125—222no—
548#125—222no—
549C22⋊Q8—222no—
550C22⋊Q8—222no—
551C22⋊Q8—222no—
552C22⋊Q8—222no—
553C22⋊Q8—222no—
554C22⋊Q8—222no—
555C22⋊Q8—221no—
556C22⋊Q8—222no—
557C22⋊Q8—221no—
558C22⋊Q8—221no—
559C22⋊Q8—221no—
560C4×Q8—21no—
561C4×Q8—21no—
562C4×Q8—111no—
563C4×Q8—112no—
564C4×Q8—111no—
565C4×Q8—111no—
566C4×Q8—111no—
567C4×Q8—112no—
568C4×Q8—114no—
569C4×Q8—114no—
570C4×Q8—112no—
571C4×Q8—112no—
572C4×Q8—222no—
573C4×Q8—222no—
574C4×Q8—222no—
575C4×Q8—221no—
576C4×Q8—222no—
577C4×Q8—224no—
578C4×Q8—222no—
579C4×Q8—221no—
580C4×Q8—222no—
581C4×Q8—222no—
582C4×Q8—221no—
583C4×Q8—221no—
584C4×Q8C22×D1112yes—
585C4×Q8C22×D1112yes—
586C4×Q8C22×D1111yescharacteristic
587C4×Q8C22×D1111yescharacteristic
588C4×D4—21no—
589C4×D4—21no—
590C4×D4—112no—
591C4×D4—112no—
592C4×D4—222no—
593C4×D4—222no—
594C4×D4C22×D1111yescharacteristic
595C4×D4C22×D1111yescharacteristic
596#117—21no—
597#117—112no—
598#117—222no—
599#117C22×D1111yescharacteristic
600C2×C4⋊C4—21no—
601C2×C4⋊C4—111no—
602C2×C4⋊C4—112no—
603C2×C4⋊C4—112no—
604C2×C4⋊C4—222no—
605C2×C4⋊C4—221no—
606C2×C4⋊C4—222no—
607C2×C4⋊C4—222no—
608C2×C4⋊C4—222no—
609C2×C4⋊C4—221no—
610C2×C4⋊C4C22×D1111yescharacteristic
611C2×C42—21no—
612C2×C42—21no—
613C2×C42—112no—
614C2×C42—222no—
615C2×C42—222no—
616C2×C42C22×D1111yescharacteristic
617#107—114no—
618#107—114no—
619#107—114no—
620#107—114no—
621#107C22×D1112yes—
622#106—114no—
623#106—114no—
624#106—114no—
625#106—114no—
626#106C22×D1112yes—
627C4⋊C8—114no—
628C4⋊C8—114no—
629C4⋊C8—112no—
630C4⋊C8—112no—
631#103—114no—
632#103—114no—
633#103—114no—
634#103C22×D1112yes—
635#103C22×D1112yes—
636#103C22×D1112yes—
637#102—114no—
638#102C22×D1112yes—
639#97—114no—
640#97C22×D1112yes—
641C4×C8—114no—
642C4×C8C22×D1112yes—
643C2×C11—22no—
644C2×C11—42no—
645C2×C11C2×D4×Q811yescharacteristic
646C2×C11C2×#57511yescharacteristic
647C2×C11#358611yescharacteristic
648#41—22no—
649#41C2×Dic2214yes—
650C2×Q8—21no—
651C2×Q8—22no—
652C2×Q8—111no—
653C2×Q8—111no—
654C2×Q8—112no—
655C2×Q8—222no—
656C2×Q8—222no—
657C2×Q8—221no—
658C2×Q8—222no—
659C2×Q8—222no—
660C2×Q8—221no—
661C2×Q8—442no—
662C2×Q8—444no—
663C2×Q8—444no—
664C2×Q8C2×Dic2214yescomplemented
665C2×Q8C23×D1112yes—
666C2×Q8C23×D1111yescharacteristic
667C2×D4—21no—
668C2×D4C23×D1111yescharacteristic
669C22×C4—21no—
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—112no—
675C22×C4—112no—
676C22×C4—222no—
677C22×C4—222no—
678C22×C4—222no—
679C22×C4D4×D1111yescharacteristic
680C22×C4D4×D1111yescharacteristic
681C22×C4C23×D1111yescharacteristic
682Q16C2×Dic2218yescomplemented
683SD16C2×Dic2218yescomplemented
684M16—22no—
685M16—224no—
686M16C2×Dic2214yescomplemented
687C2×C8—114no—
688C2×C8C23×D1112yes—
689C2×C8C23×D1112yes—
690C4⋊C4—22no—
691C4⋊C4—22no—
692C4⋊C4—21no—
693C4⋊C4—21no—
694C4⋊C4—21no—
695C4⋊C4—111no—
696C4⋊C4—112no—
697C4⋊C4—112no—
698C4⋊C4—111no—
699C4⋊C4—112no—
700C4⋊C4—112no—
701C4⋊C4—112no—
702C4⋊C4—114no—
703C4⋊C4—112no—
704C4⋊C4—112no—
705C4⋊C4—224no—
706C4⋊C4—224no—
707C4⋊C4—222no—
708C4⋊C4—222no—
709C4⋊C4—222no—
710C4⋊C4—224no—
711C4⋊C4—224no—
712C4⋊C4—224no—
713C4⋊C4—224no—
714C4⋊C4—222no—
715C4⋊C4—222no—
716C4⋊C4—222no—
717C4⋊C4—222no—
718C4⋊C4—222no—
719C4⋊C4—222no—
720C4⋊C4—222no—
721C4⋊C4—221no—
722C4⋊C4—222no—
723C4⋊C4—222no—
724C4⋊C4—222no—
725C4⋊C4—221no—
726C4⋊C4C23×D1112yes—
727C4⋊C4C23×D1111yescharacteristic
728C4⋊C4C23×D1111yescharacteristic
729C22⋊C4—21no—
730C22⋊C4—21no—
731C22⋊C4—21no—
732C22⋊C4—222no—
733C22⋊C4—222no—
734C22⋊C4—222no—
735C42—21no—
736C42—21no—
737C42—21no—
738C42—22no—
739C42—22no—
740C42—112no—
741C42—112no—
742C42—112no—
743C42—112no—
744C42—222no—
745C42—222no—
746C42—224no—
747C42—224no—
748C42—222no—
749C42D4×D1111yescharacteristic
750C42D4×D1111yescharacteristic
751C42C23×D1111yescharacteristic
752C42C23×D1111yescharacteristic
753C11#6136911yescharacteristic, complemented, Sylow
754C23—21no—
755C23C2×D4×D1111yescharacteristic
756Q8—24no—
757Q8—22no—
758Q8—21no—
759Q8—222no—
760Q8—222no—
761Q8—442no—
762Q8—444no—
763Q8—444no—
764Q8—442no—
765Q8—444no—
766Q8—881no—
767Q8—882no—
768Q8C22×Dic2214yes—
769Q8C22×Dic2212yes—
770D4—24no—
771D4—21no—
772D4C22×Dic2212yes—
773C2×C4—24no—
774C2×C4—21no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—24no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—22no—
781C2×C4—41no—
782C2×C4—42no—
783C2×C4—42no—
784C2×C4—81no—
785C2×C4—112no—
786C2×C4—112no—
787C2×C4—112no—
788C2×C4—112no—
789C2×C4—222no—
790C2×C4—222no—
791C2×C4—224no—
792C2×C4—442no—
793C2×C4—442no—
794C2×C4—444no—
795C2×C4—444no—
796C2×C4—882no—
797C2×C4C22×Dic2212yes—
798C2×C4C2×D4×D1111yescharacteristic
799C2×C4C2×D4×D1111yescharacteristic
800C2×C4C2×D4×D1111yescharacteristic
801C2×C4C2×D4×D1111yescharacteristic
802C2×C4C2×D4×D1111yescharacteristic
803C2×C4#6704312yes—
804C2×C4C24×D1111yescharacteristic
805C8—22no—
806C8—224no—
807C8C22×Dic2214yes—
808C22—21no—
809C22—21no—
810C22—22no—
811C22—41no—
812C22—41no—
813C22D4×Dic2212yes—
814C22C22×D4×D1111yescharacteristic
815C4—21no—
816C4—21no—
817C4—21no—
818C4—22no—
819C4—24no—
820C4—42no—
821C4—41no—
822C4—41no—
823C4—222no—
824C4—222no—
825C4—222no—
826C4—222no—
827C4—442no—
828C4—442no—
829C4—444no—
830C4D4×Dic2212yes—
831C4#1062330812yes—
832C4C23×Dic2211yescharacteristic
833C4C2×#6704311yescharacteristic
834C2—22no—
835C2—42no—
836C2C2×D4×Dic2211yescharacteristic
837C2C2×#1062330811yescharacteristic
838C2#1308340011yescharacteristic
subgroupG/H
centerC22C22×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC4×C11×#137C2
socleC22×C11C23×D4
prime radicalC2×C11×#41C23
hypercenterC4×#137D11
hypocenterC11#61369
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ C4×#137

Complements

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

NH ≅ G/Ntype
2. C2×#10623101C2semidirect
3. #13081584C2semidirect
4. #13081562C2semidirect
5. #13081546C2semidirect
6. #13081535C2semidirect
7. #13081505C2semidirect
8. #13081489C2semidirect
9. #13079166C2semidirect
10. #13079162C2semidirect
13. #13078421C2semidirect
14. #13078418C2semidirect
15. M16×Dic22C2semidirect
100. C11×#137Q8semidirect
234. C2×Q8×C11C2×Q8semidirect
264. C11×Q16C2×Q8semidirect
265. C11×SD16C2×Q8semidirect
267. C11×M16C2×Q8semidirect
514. #137Dic22semidirect
664. C2×Q8C2×Dic22semidirect
682. Q16C2×Dic22semidirect
683. SD16C2×Dic22semidirect
686. M16C2×Dic22semidirect
753. C11#61369semidirect

Maximal subgroups

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

subgroupindex
#41×Dic222
C2×#106231012
#130815842
#130815622
#130815462
#130815352
#130815052
#130814892
#130791662
#130791622
#130784362
#130784312
#130784212
#130784182
M16×Dic222
#137×Dic112
C4×C11×#1372
#6136911