Finite Group Databasebeta

← #137×Dic22 #15634376

Subgroups — #137×Dic22 #15634376

Order 2816.

1782 conjugacy classes of subgroups.

The subgroup lattice has 846 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#41×Dic22C211yesmaximal, characteristic
2C2×Q8×Dic22C211yesmaximal, characteristic, complemented
3#13081549C214yesmaximal, complemented
4#13081546C212yesmaximal, complemented
5#13081527C214yesmaximal, complemented
6#13081524C212yesmaximal, complemented
7Q16×Dic22C212yesmaximal, complemented
8SD16×Dic22C212yesmaximal, complemented
9#13079162C211yesmaximal, characteristic, complemented
10#13079160C212yesmaximal, complemented
11#13078431C211yesmaximal, characteristic
12#13078427C212yesmaximal
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#10623101C2211yescharacteristic
24#10623100C2212yes—
25Q8×Dic22—21no—
26Q8×Dic22—21no—
27Q8×Dic22—22no—
28Q8×Dic22C2212yes—
29Q8×Dic22C2212yes—
30Q8×Dic22C2214yes—
31Q8×Dic22C2211yescharacteristic
32#10623074—21no—
33#10623074C2211yescharacteristic
34#10623070—22no—
35#10623070C2212yes—
36D4×Dic22—21no—
37D4×Dic22C2211yescharacteristic
38#10623048—22no—
39#10623048C2212yes—
40C2×#66941—22no—
41C2×#66941C2212yes—
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#10622489C2214yes—
78#10622487C2214yes—
79#10622469C2214yes—
80#10622468C2214yes—
81#10622412C2214yes—
82#10622409C2214yes—
83#10622407C2214yes—
84#10622407C2214yes—
85#10622404C2214yes—
86#10622404C2214yes—
87#10622374C2214yes—
88#10622372C2214yes—
89#10622315C2214yes—
90#10622314C2214yes—
91#10622295C2212yes—
92#10622293C2212yes—
93#10622292C2212yes—
94C8×Dic22C2212yes—
95C2×C11×#41C2311yescharacteristic
96C22×Q8×C11C2311yescharacteristic
97C22×Dic22—21no—
98C22×Dic22—22no—
99C22×Dic22—21no—
100C22×Dic22D411yescharacteristic
101C11×#137Q818yescomplemented
102C2×C11×Q16C2312yes—
103C2×C11×SD16C2312yes—
104C2×C11×M16C2311yescharacteristic
105C2×C11×M16C2311yescharacteristic
106C4×Q8×C11—21no—
107C4×Q8×C11—21no—
108C4×Q8×C11C2312yes—
109C4×Q8×C11C2312yes—
110C4×Q8×C11C2311yescharacteristic
111C4×Q8×C11C2311yescharacteristic
112C4×D4×C11—21no—
113C4×D4×C11—21no—
114C4×D4×C11C2311yescharacteristic
115C4×D4×C11C2311yescharacteristic
116C11×#117—21no—
117C11×#117C2311yescharacteristic
118C2×C11×C4⋊C4—21no—
119C2×C11×C4⋊C4C2311yescharacteristic
120C2×C42×C11—21no—
121C2×C42×C11—21no—
122C2×C42×C11C2311yescharacteristic
123Q8×Dic11—22no—
124Q8×Dic11—22no—
125Q8×Dic11C2314yes—
126Q8×Dic11C2314yes—
127Q8×Dic11C2312yes—
128Q8×Dic11C2312yes—
129D4×Dic11—22no—
130D4×Dic11—22no—
131D4×Dic11C2312yes—
132D4×Dic11C2312yes—
133#66979—22no—
134#66979C2312yes—
135C2×C4⋊Dic11—21no—
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—22no—
154#66943C2312yes—
155#66943C2312yes—
156#66941—22no—
157#66941—24no—
158#66941—24no—
159#66941—24no—
160#66941—24no—
161#66941—22no—
162#66941—22no—
163#66941—22no—
164#66941C2312yes—
165#66941C2314yes—
166#66941C2314yes—
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—21no—
177#66922—21no—
178#66922—21no—
179#66922—22no—
180#66922—22no—
181#66922—24no—
182#66922—21no—
183#66922C2312yes—
184#66922C2312yes—
185#66922C2311yescharacteristic
186#66922C2311yescharacteristic
187C4×Dic22—21no—
188C4×Dic22—22no—
189C4×Dic22—24no—
190C4×Dic22—22no—
191C4×Dic22—21no—
192C4×Dic22—21no—
193C4×Dic22—21no—
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—
229Q8×#137—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—24no—
253C2×Dic22—22no—
254C2×Dic22—22no—
255C2×Dic22—24no—
256C2×Dic22—24no—
257C2×Dic22—21no—
258C2×Dic22—21no—
259C2×Dic22—22no—
260C2×Dic22—22no—
261C2×Dic22—44no—
262C2×Dic22—82no—
263C2×Dic22—84no—
264C2×Dic22C2×D411yescharacteristic
265C2×Dic22C2×D412yes—
266C2×Dic22C2×D411yescharacteristic
267C11×Q16C2×Q818yescomplemented
268C11×SD16C2×Q818yescomplemented
269C11×M16—22no—
270C11×M16C2×Q814yescomplemented
271C2×C8×C11C2412yes—
272C2×C8×C11C2412yes—
273C11×C4⋊C4—22no—
274C11×C4⋊C4—22no—
275C11×C4⋊C4—21no—
276C11×C4⋊C4—21no—
277C11×C4⋊C4—21no—
278C11×C4⋊C4C2411yescharacteristic
279C11×C4⋊C4C2412yes—
280C11×C4⋊C4C2411yescharacteristic
281C11×C22⋊C4—21no—
282C11×C22⋊C4—21no—
283C11×C22⋊C4—21no—
284C42×C11—21no—
285C42×C11—21no—
286C42×C11—22no—
287C42×C11—22no—
288C42×C11—21no—
289C42×C11C2×D411yescharacteristic
290C42×C11C2×D411yescharacteristic
291C42×C11C2411yescharacteristic
292C42×C11C2411yescharacteristic
293C22⋊Dic11—22no—
294C22⋊Dic11—22no—
295C22⋊Dic11—22no—
296C4⋊Dic11—22no—
297C4⋊Dic11—22no—
298C4⋊Dic11—24no—
299C4⋊Dic11—24no—
300C4⋊Dic11—22no—
301C4⋊Dic11—22no—
302C4⋊Dic11—22no—
303C4⋊Dic11—22no—
304C4⋊Dic11—21no—
305C4⋊Dic11—21no—
306C4⋊Dic11—22no—
307C4⋊Dic11C2×D411yescharacteristic
308C4⋊Dic11C2×D411yescharacteristic
309C4⋊Dic11C2×D412yes—
310C4⋊Dic11C2412yes—
311C4⋊Dic11C2414yes—
312C4⋊Dic11C2412yes—
313Dic11⋊C4—22no—
314Dic11⋊C4—22no—
315Dic11⋊C4—24no—
316Dic11⋊C4—24no—
317Dic11⋊C4—22no—
318Dic11⋊C4—22no—
319Dic11⋊C4—22no—
320Dic11⋊C4—22no—
321Dic11⋊C4C2×D412yes—
322Dic11⋊C4C2×D412yes—
323Dic11⋊C4C2×D412yes—
324Dic11⋊C4C2×D412yes—
325C4×Dic11—22no—
326C4×Dic11—24no—
327C4×Dic11—24no—
328C4×Dic11—22no—
329C4×Dic11—22no—
330C4×Dic11C2×D412yes—
331C4×Dic11C2×D412yes—
332C4×Dic11C2412yes—
333C4×Dic11C2412yes—
334#4318—24no—
335C2×C11⋊C8C2414yes—
336Q8×#41—111no—
337C2×Q82—111no—
338#3387—114no—
339#3387—112no—
340#3385—114no—
341#3385—112no—
342Q8×Q16—112no—
343Q8×SD16—112no—
344#3165—112no—
345#3165—111no—
346#3079—112no—
347#3079—111no—
348#3078—112no—
349#3078—111no—
350Q8×M16—111no—
351C4×#137—112no—
352C4×#137D1111yescharacteristic
353C23×C11—21no—
354C23×C11C22×D411yescharacteristic
355Q8×C11—24no—
356Q8×C11—22no—
357Q8×C11—21no—
358Q8×C11C22×Q814yes—
359Q8×C11C22×Q812yes—
360D4×C11—24no—
361D4×C11—21no—
362D4×C11C22×Q812yes—
363C2×C4×C11—24no—
364C2×C4×C11—21no—
365C2×C4×C11—22no—
366C2×C4×C11—24no—
367C2×C4×C11—22no—
368C2×C4×C11—21no—
369C2×C4×C11—21no—
370C2×C4×C11—22no—
371C2×C4×C11—41no—
372C2×C4×C11—42no—
373C2×C4×C11—42no—
374C2×C4×C11—81no—
375C2×C4×C11C22×D411yescharacteristic
376C2×C4×C11C22×D411yescharacteristic
377C2×C4×C11C22×D411yescharacteristic
378C2×C4×C11C22×D411yescharacteristic
379C2×C4×C11C22×D411yescharacteristic
380C2×C4×C11C22×Q812yes—
381C2×C4×C112−1+412yes—
382C2×C4×C11C2511yescharacteristic
383C2×Dic11—24no—
384C2×Dic11—22no—
385C2×Dic11—22no—
386C2×Dic11—24no—
387C2×Dic11—42no—
388C2×Dic11—44no—
389C2×Dic11—44no—
390C2×Dic11—82no—
391C2×Dic11C22×D412yes—
392C2×Dic11C22×D412yes—
393C2×Dic11C22×D412yes—
394C2×Dic11C22×D412yes—
395Dic22—22no—
396Dic22—24no—
397Dic22—42no—
398Dic22—44no—
399Dic22—82no—
400Dic22—84no—
401Dic22—84no—
402Dic22—81no—
403Dic22—82no—
404Dic22—82no—
405Dic22#13714yesdirect product factor
406C8×C11—22no—
407C8×C11C22×Q814yes—
408C11⋊C8—24no—
409C2×#137C2×D1111yescharacteristic
410Q82—112no—
411Q82—111no—
412Q82—114no—
413Q82—112no—
414Q82—221no—
415Q82—221no—
416Q82—222no—
417#557—112no—
418#557—111no—
419#554—112no—
420#554—111no—
421#554—222no—
422#554—221no—
423D4×Q8—111no—
424D4×Q8—221no—
425#533—112no—
426#533—111no—
427#533—221no—
428#533—222no—
429C2×C4⋊Q8—112no—
430C2×C4⋊Q8—111no—
431C2×C4⋊Q8—221no—
432C2×C4⋊Q8—222no—
433C4×#41—112no—
434C4×#41C2×D1111yescharacteristic
435C2×C4×Q8—111no—
436C2×C4×Q8—112no—
437C2×C4×Q8—221no—
438C2×C4×Q8—221no—
439C2×C4×Q8C2×D1111yescharacteristic
440#501—114no—
441#501—114no—
442#501—114no—
443#500—114no—
444#500—112no—
445#498—114no—
446#498—112no—
447#479—114no—
448#479—114no—
449#479—114no—
450#477—112no—
451#477—112no—
452#477—114no—
453#477—114no—
454#476—112no—
455#476—114no—
456#475—112no—
457#475—112no—
458#475—114no—
459#475—114no—
460#474—112no—
461#474—114no—
462#446—114no—
463#446—112no—
464C8×Q8—112no—
465#441—114no—
466#441C2×D1112yes—
467#440—114no—
468#440C2×D1112yes—
469C4×Q16—114no—
470C4×Q16C2×D1112yes—
471C4×SD16—114no—
472C4×SD16C2×D1112yes—
473#428—112no—
474#428—112no—
475#428—112no—
476#428—112no—
477#428C2×D1111yescharacteristic
478#423—112no—
479#423—111no—
480#419—112no—
481#419C2×D1111yescharacteristic
482#417—112no—
483#417C2×D1111yescharacteristic
484C4×M16—112no—
485C4×M16C2×D1111yescharacteristic
486C22×C11—21no—
487C22×C11—21no—
488C22×C11—22no—
489C22×C11—41no—
490C22×C11—41no—
491C22×C11D4×Q812yes—
492C22×C11C23×D411yescharacteristic
493C4×C11—21no—
494C4×C11—21no—
495C4×C11—22no—
496C4×C11—24no—
497C4×C11—21no—
498C4×C11—42no—
499C4×C11—41no—
500C4×C11—41no—
501C4×C11D4×Q812yes—
502C4×C11C2×#13712yes—
503C4×C11C23×Q811yescharacteristic
504C4×C11C2×2−1+411yescharacteristic
505Dic11—22no—
506Dic11—22no—
507Dic11—22no—
508Dic11—44no—
509Dic11—42no—
510Dic11—42no—
511Dic11C2×#13714yes—
512C2×#41C22×D1111yescharacteristic
513C22×Q8—111no—
514C22×Q8—222no—
515C22×Q8—221no—
516C22×Q8—221no—
517C22×Q8C22×D1111yescharacteristic
518#137Dic2218yesdirect product factor
519C2×Q16C22×D1112yes—
520C2×SD16C22×D1112yes—
521C2×M16—112no—
522C2×M16C22×D1111yescharacteristic
523C2×M16C22×D1111yescharacteristic
524C4⋊Q8—114no—
525C4⋊Q8—114no—
526C4⋊Q8—112no—
527C4⋊Q8—112no—
528C4⋊Q8—112no—
529C4⋊Q8—112no—
530C4⋊Q8—111no—
531C4⋊Q8—111no—
532C4⋊Q8—222no—
533C4⋊Q8—224no—
534C4⋊Q8—222no—
535C4⋊Q8—221no—
536C4⋊Q8—221no—
537C4⋊Q8—222no—
538C4⋊Q8—222no—
539C4⋊Q8—224no—
540C4⋊Q8—224no—
541C4⋊Q8—224no—
542C4⋊Q8—224no—
543C4⋊Q8—222no—
544C4⋊Q8—222no—
545C4⋊Q8—221no—
546C4⋊Q8—221no—
547#125—112no—
548#125—112no—
549#125—112no—
550#125—222no—
551#125—222no—
552#125—222no—
553C22⋊Q8—222no—
554C22⋊Q8—222no—
555C22⋊Q8—222no—
556C22⋊Q8—222no—
557C22⋊Q8—222no—
558C22⋊Q8—222no—
559C22⋊Q8—221no—
560C22⋊Q8—222no—
561C22⋊Q8—221no—
562C22⋊Q8—221no—
563C22⋊Q8—221no—
564C4×Q8—21no—
565C4×Q8—21no—
566C4×Q8—111no—
567C4×Q8—112no—
568C4×Q8—111no—
569C4×Q8—111no—
570C4×Q8—112no—
571C4×Q8—111no—
572C4×Q8—114no—
573C4×Q8—114no—
574C4×Q8—112no—
575C4×Q8—112no—
576C4×Q8—222no—
577C4×Q8—222no—
578C4×Q8—222no—
579C4×Q8—221no—
580C4×Q8—221no—
581C4×Q8—222no—
582C4×Q8—224no—
583C4×Q8—222no—
584C4×Q8—222no—
585C4×Q8—222no—
586C4×Q8—221no—
587C4×Q8—221no—
588C4×Q8C22×D1112yes—
589C4×Q8C22×D1112yes—
590C4×Q8C22×D1111yescharacteristic
591C4×Q8C22×D1111yescharacteristic
592C4×D4—21no—
593C4×D4—21no—
594C4×D4—112no—
595C4×D4—112no—
596C4×D4—222no—
597C4×D4—222no—
598C4×D4C22×D1111yescharacteristic
599C4×D4C22×D1111yescharacteristic
600#117—21no—
601#117—112no—
602#117—222no—
603#117C22×D1111yescharacteristic
604C2×C4⋊C4—21no—
605C2×C4⋊C4—112no—
606C2×C4⋊C4—111no—
607C2×C4⋊C4—112no—
608C2×C4⋊C4—222no—
609C2×C4⋊C4—221no—
610C2×C4⋊C4—222no—
611C2×C4⋊C4—222no—
612C2×C4⋊C4—221no—
613C2×C4⋊C4C22×D1111yescharacteristic
614C2×C42—21no—
615C2×C42—21no—
616C2×C42—112no—
617C2×C42—222no—
618C2×C42—222no—
619C2×C42C22×D1111yescharacteristic
620#107—114no—
621#107—114no—
622#107—114no—
623#107—114no—
624#107C22×D1112yes—
625#106—114no—
626#106—114no—
627#106—114no—
628#106—114no—
629#106C22×D1112yes—
630C4⋊C8—114no—
631C4⋊C8—114no—
632C4⋊C8—112no—
633C4⋊C8—112no—
634#103—114no—
635#103—114no—
636#103—114no—
637#103C22×D1112yes—
638#103C22×D1112yes—
639#103C22×D1112yes—
640#102—114no—
641#102C22×D1112yes—
642#97—114no—
643#97C22×D1112yes—
644C4×C8—114no—
645C4×C8C22×D1112yes—
646C2×C11—22no—
647C2×C11—42no—
648C2×C11C2×D4×Q811yescharacteristic
649C2×C11C22×#13711yescharacteristic
650C2×C11#358511yescharacteristic
651#41—22no—
652#41C2×Dic2214yes—
653C2×Q8—21no—
654C2×Q8—22no—
655C2×Q8—111no—
656C2×Q8—112no—
657C2×Q8—111no—
658C2×Q8—222no—
659C2×Q8—222no—
660C2×Q8—224no—
661C2×Q8—224no—
662C2×Q8—224no—
663C2×Q8—221no—
664C2×Q8—221no—
665C2×Q8—222no—
666C2×Q8—222no—
667C2×Q8—444no—
668C2×Q8—882no—
669C2×Q8—884no—
670C2×Q8C2×Dic2214yescomplemented
671C2×Q8C23×D1112yes—
672C2×Q8C23×D1111yescharacteristic
673C2×D4—21no—
674C2×D4C23×D1111yescharacteristic
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—112no—
681C22×C4—112no—
682C22×C4—222no—
683C22×C4—222no—
684C22×C4—222no—
685C22×C4D4×D1111yescharacteristic
686C22×C4D4×D1111yescharacteristic
687C22×C4C23×D1111yescharacteristic
688Q16C2×Dic2218yescomplemented
689SD16C2×Dic2218yescomplemented
690M16—22no—
691M16—224no—
692M16C2×Dic2214yescomplemented
693C2×C8—114no—
694C2×C8C23×D1112yes—
695C2×C8C23×D1112yes—
696C4⋊C4—22no—
697C4⋊C4—22no—
698C4⋊C4—21no—
699C4⋊C4—21no—
700C4⋊C4—21no—
701C4⋊C4—112no—
702C4⋊C4—111no—
703C4⋊C4—112no—
704C4⋊C4—112no—
705C4⋊C4—112no—
706C4⋊C4—112no—
707C4⋊C4—111no—
708C4⋊C4—114no—
709C4⋊C4—112no—
710C4⋊C4—112no—
711C4⋊C4—224no—
712C4⋊C4—224no—
713C4⋊C4—222no—
714C4⋊C4—222no—
715C4⋊C4—222no—
716C4⋊C4—224no—
717C4⋊C4—224no—
718C4⋊C4—222no—
719C4⋊C4—222no—
720C4⋊C4—222no—
721C4⋊C4—222no—
722C4⋊C4—222no—
723C4⋊C4—222no—
724C4⋊C4—222no—
725C4⋊C4—221no—
726C4⋊C4—222no—
727C4⋊C4—222no—
728C4⋊C4—222no—
729C4⋊C4—221no—
730C4⋊C4C23×D1112yes—
731C4⋊C4C23×D1111yescharacteristic
732C4⋊C4C23×D1111yescharacteristic
733C22⋊C4—21no—
734C22⋊C4—21no—
735C22⋊C4—21no—
736C22⋊C4—222no—
737C22⋊C4—222no—
738C22⋊C4—222no—
739C42—21no—
740C42—21no—
741C42—21no—
742C42—22no—
743C42—22no—
744C42—112no—
745C42—112no—
746C42—112no—
747C42—112no—
748C42—222no—
749C42—222no—
750C42—224no—
751C42—224no—
752C42—222no—
753C42D4×D1111yescharacteristic
754C42D4×D1111yescharacteristic
755C42C23×D1111yescharacteristic
756C42C23×D1111yescharacteristic
757C11Q8×#13711yescharacteristic, complemented, Sylow
758C23—21no—
759C23C2×D4×D1111yescharacteristic
760Q8—24no—
761Q8—22no—
762Q8—21no—
763Q8—114no—
764Q8—224no—
765Q8—222no—
766Q8—444no—
767Q8—442no—
768Q8—882no—
769Q8—882no—
770Q8—881no—
771Q8—884no—
772Q8—884no—
773Q8—882no—
774Q8C22×Dic2214yes—
775Q8C22×Dic2212yes—
776D4—24no—
777D4—21no—
778D4C22×Dic2212yes—
779C2×C4—24no—
780C2×C4—21no—
781C2×C4—22no—
782C2×C4—22no—
783C2×C4—24no—
784C2×C4—21no—
785C2×C4—21no—
786C2×C4—22no—
787C2×C4—41no—
788C2×C4—42no—
789C2×C4—42no—
790C2×C4—81no—
791C2×C4—112no—
792C2×C4—112no—
793C2×C4—112no—
794C2×C4—112no—
795C2×C4—224no—
796C2×C4—222no—
797C2×C4—222no—
798C2×C4—224no—
799C2×C4—444no—
800C2×C4—442no—
801C2×C4—444no—
802C2×C4—882no—
803C2×C4C22×Dic2212yes—
804C2×C4C2×D4×D1111yescharacteristic
805C2×C4C2×D4×D1111yescharacteristic
806C2×C4C2×D4×D1111yescharacteristic
807C2×C4C2×D4×D1111yescharacteristic
808C2×C4C2×D4×D1111yescharacteristic
809C2×C4#6704312yes—
810C2×C4C24×D1111yescharacteristic
811C8—22no—
812C8—224no—
813C8C22×Dic2214yes—
814C22—21no—
815C22—21no—
816C22—22no—
817C22—41no—
818C22—41no—
819C22D4×Dic2212yes—
820C22C22×D4×D1111yescharacteristic
821C4—21no—
822C4—21no—
823C4—21no—
824C4—22no—
825C4—24no—
826C4—42no—
827C4—41no—
828C4—41no—
829C4—114no—
830C4—222no—
831C4—222no—
832C4—222no—
833C4—444no—
834C4—442no—
835C4—442no—
836C4D4×Dic2212yes—
837C4D11×#13712yes—
838C4C23×Dic2211yescharacteristic
839C4C2×#6704311yescharacteristic
840C2—22no—
841C2—42no—
842C2C2×D4×Dic2211yescharacteristic
843C2C2×D11×#13711yescharacteristic
844C2#1308339311yescharacteristic
subgroupG/H
centerC22C22×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC4×C11×#137C2
socleC22×C11C23×D4
prime radicalC2×C11×#41C23
hypercenterC4×#137D11
hypocenterC11Q8×#137
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×Q8×Dic22C2semidirect
3. #13081549C2semidirect
4. #13081546C2semidirect
5. #13081527C2semidirect
6. #13081524C2semidirect
7. Q16×Dic22C2semidirect
8. SD16×Dic22C2semidirect
9. #13079162C2semidirect
10. #13079160C2semidirect
13. #13078421C2semidirect
14. #13078418C2semidirect
15. M16×Dic22C2semidirect
101. C11×#137Q8semidirect
234. C2×Q8×C11C2×Q8semidirect
267. C11×Q16C2×Q8semidirect
268. C11×SD16C2×Q8semidirect
270. C11×M16C2×Q8semidirect
405. Dic22#137direct (N × H)
518. #137Dic22direct (N × H)
670. C2×Q8C2×Dic22semidirect
688. Q16C2×Dic22semidirect
689. SD16C2×Dic22semidirect
692. M16C2×Dic22semidirect
757. C11Q8×#137semidirect

Maximal subgroups

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

subgroupindex
#41×Dic222
C2×Q8×Dic222
#130815492
#130815462
#130815272
#130815242
Q16×Dic222
SD16×Dic222
#130791622
#130791602
#130784312
#130784272
#130784212
#130784182
M16×Dic222
#137×Dic112
C4×C11×#1372
Q8×#13711