Finite Group Databasebeta

← #7646563

Subgroups — #7646563

Order 512.

6678 conjugacy classes of subgroups.

The subgroup lattice has 1098 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3493C211yesmaximal, characteristic, complemented
2C22×#552C211yesmaximal, characteristic, complemented
3#42179C218yesmaximal, complemented
4#41996C218yesmaximal, complemented
5#38439C218yesmaximal, complemented
6#38436C218yesmaximal, complemented
7#37538C212yesmaximal, complemented
8#37443C212yesmaximal, complemented
9#36962C211yesmaximal, characteristic, complemented
10#36961C211yesmaximal, characteristic, complemented
11#36959C211yesmaximal, characteristic, complemented
12#36958C211yesmaximal, characteristic, complemented
13#36956C212yesmaximal, complemented
14#36716C212yesmaximal, complemented
15#35453C212yesmaximal, complemented
16#35357C212yesmaximal, complemented
17#35247C212yesmaximal, complemented
18#35139C212yesmaximal, complemented
19#35093C212yesmaximal, complemented
20#35057C212yesmaximal, complemented
21#34986C212yesmaximal, complemented
22#34877C212yesmaximal, complemented
23#34048C211yesmaximal, characteristic, complemented
24#3493—216no—
25C2×#556C2214yescomplemented
26C2×#555C2214yescomplemented
27C2×#553C2214yescomplemented
28C2×#552—216no—
29C2×#552C2218yes—
30C2×#552C2218yes—
31C2×#552C2214yescomplemented
32C2×#544C2211yescharacteristic
33C2×#538C2212yes—
34C2×#538C2212yes—
35C2×#537C2211yescharacteristic
36C2×#529C2212yes—
37C2×#529C2212yes—
38C22×#126C2211yescharacteristic
39C22×#126C2211yescharacteristic
40C22×#125C2211yescharacteristic
41C22×#125C2211yescharacteristic
42C22×#125C2211yescharacteristic
43C2×#525C2212yes—
44C22×#123C2211yescharacteristic
45C22×#123C2211yescharacteristic
46C22×C22⋊Q8C2211yescharacteristic
47C22×C22⋊Q8C2211yescharacteristic
48C2×#520C2212yes—
49C22×C4×Q8C2211yescharacteristic
50C22×C4×D4C2211yescharacteristic
51C22×#117C2211yescharacteristic
52C22×#117C2211yescharacteristic
53C22×#117C2211yescharacteristic
54C23×C4⋊C4C2211yescharacteristic
55#2861C2214yescomplemented
56#2859C2214yescomplemented
57#2855C2212yes—
58#2855C2212yes—
59#2854C2212yes—
60#2854C2212yes—
61#2849C2214yes—
62#2849C2214yes—
63#2823C2218yescomplemented
64#2814C2214yes—
65#2813C2214yes—
66#2723C2218yescomplemented
67#2721C2218yescomplemented
68#2720C2218yescomplemented
69#2719C2218yescomplemented
70#2718C2218yes—
71#2716C2218yescomplemented
72#2714C2218yescomplemented
73#2713C2218yescomplemented
74#2711C2218yescomplemented
75#2710C2218yes—
76#2706C2218yes—
77#2703C2218yes—
78#2700C2218yescomplemented
79#2698C2218yescomplemented
80#2681C2218yescomplemented
81#2680C2218yescomplemented
82#2664C2218yescomplemented
83#2664C2214yescomplemented
84#2663C2214yes—
85#2662C2214yescomplemented
86#2661C2214yes—
87#2637C2218yescomplemented
88#2637C2214yescomplemented
89#2636C2214yescomplemented
90#2630C2218yes—
91#2627C2212yes—
92#2627C2214yescomplemented
93#2626C2212yes—
94#2622C2214yes—
95#2618C2212yes—
96#2618C2214yescomplemented
97#2617C2212yes—
98#2613C2214yes—
99#2611C2214yescomplemented
100#2611C2218yescomplemented
101#2610C2214yescomplemented
102#2602C2218yes—
103#2601C2218yescomplemented
104#2601C2218yescomplemented
105#2592C2214yescomplemented
106#2591C2212yes—
107#2591C2214yescomplemented
108#2584C2214yescomplemented
109#2583C2212yes—
110#2583C2214yescomplemented
111#2582C2214yescomplemented
112#2579C2214yes—
113#2579C2218yescomplemented
114#2566C2214yescomplemented
115#2565C2214yescomplemented
116#2561C2212yes—
117#2539C2212yes—
118#2538C2214yescomplemented
119#2534C2214yes—
120#2504C2212yes—
121#2503C2212yes—
122#2502C2212yes—
123#2501C2212yes—
124#2486C2214yes—
125#2484C2212yes—
126#2484C2212yes—
127#2484C2212yes—
128#2482C2212yes—
129#2478C2218yescomplemented
130#2477C2218yescomplemented
131#2476C2218yescomplemented
132#2475C2218yescomplemented
133#2474C2218yescomplemented
134#2473C2218yescomplemented
135#2470C2218yescomplemented
136#2466C2218yes—
137#2465C2218yescomplemented
138#2463C2218yescomplemented
139#2462C2218yescomplemented
140#2460C2218yescomplemented
141#2459C2218yes—
142#2456C2218yes—
143#2455C2218yes—
144#2449C2218yescomplemented
145#2413C2214yes—
146#2413C2214yes—
147#2413C2214yes—
148#2411C2214yes—
149#2409C2214yes—
150#2406C2212yes—
151#2406C2212yes—
152#2406C2212yes—
153#2404C2212yes—
154#2396C2214yescomplemented
155#2392C2214yescomplemented
156#2323C2218yescomplemented
157#2322C2214yes—
158#2322C2214yes—
159#2322C2218yescomplemented
160#2314C2218yescomplemented
161#2313C2212yes—
162#2313C2211yescharacteristic
163#2313C2211yescharacteristic
164#2312C2212yes—
165#2312C2212yes—
166C4×#123C2214yes—
167C4×#120C2214yes—
168#2298C2218yescomplemented
169#2293C2218yescomplemented
170#2285C2212yes—
171#2280C2212yes—
172C4×#117C2212yes—
173C22×#41C2312yes—
174C23×Q8C2311yescharacteristic
175C23×D4C2311yescharacteristic
176C24×C4C2311yescharacteristic
177C24×C4C2311yescharacteristic
178C24×C4C2311yescharacteristic
179C24×C4C2311yescharacteristic
180#556—232no—
181#555—232no—
182#553—232no—
183#552—264no—
184#552—264no—
185#552—232no—
186#544—28no—
187#538—216no—
188#538—216no—
189#537—28no—
190C2×C4⋊Q8C2314yes—
191#529—216no—
192#529—216no—
193C2×#126—28no—
194C2×#126—28no—
195C2×#126C2314yes—
196C2×#126C2314yes—
197C2×#126C2314yes—
198C2×#126C2314yes—
199C2×#126C2318yes—
200C2×#126C2314yes—
201C2×#126C2314yes—
202C2×#125—28no—
203C2×#125—28no—
204C2×#125—28no—
205C2×#125C2314yes—
206C2×#125C2312yes—
207C2×#125C2312yes—
208C2×#125C2314yes—
209C2×#125C2318yes—
210C2×#125C2318yes—
211C2×#125C2314yes—
212C2×#124C2312yes—
213C2×#124C2312yes—
214C2×#124C2314yes—
215C2×#124C2314yes—
216#525—216no—
217C2×#123—28no—
218C2×#123—28no—
219C2×#123C2314yes—
220C2×#123C2314yes—
221C2×#123C2318yes—
222C2×#123C2314yes—
223C2×#123C2314yes—
224C2×#123C2314yes—
225C2×#123C2314yes—
226C2×#123C2314yes—
227C2×#123C2318yes—
228C2×#123C2314yes—
229C2×C22⋊Q8—28no—
230C2×C22⋊Q8—28no—
231C2×C22⋊Q8C2312yes—
232C2×C22⋊Q8C2312yes—
233C2×C22⋊Q8C2312yes—
234C2×C22⋊Q8C2312yes—
235C2×C22⋊Q8C2318yes—
236C2×C22⋊Q8C2318yes—
237C2×C22⋊Q8C2314yes—
238C2×C22⋊Q8C2318yes—
239C2×#121C2312yes—
240C2×#121C2312yes—
241C2×#121C2312yes—
242C2×#121C2312yes—
243C2×#121C2314yes—
244C2×#121C2314yes—
245C2×#121C2314yes—
246C2×#120C2314yes—
247C2×#120C2314yes—
248#520—216no—
249C2×C4×Q8—28no—
250C2×C4×Q8C2312yes—
251C2×C4×Q8C2314yes—
252C2×C4×Q8C2312yes—
253C2×C4×Q8C2314yes—
254C2×C4×Q8C2314yes—
255C2×C4×D4—28no—
256C2×C4×D4C2312yes—
257C2×C4×D4C2314yes—
258C2×C4×D4C2314yes—
259C2×C4×D4C2314yes—
260C2×C4×D4C2314yes—
261C2×C4×D4C2312yes—
262C2×C4×D4C2318yes—
263C2×C4×D4C2314yes—
264C2×C4×D4C2318yes—
265C2×#117—28no—
266C2×#117—28no—
267C2×#117D4116yescomplemented
268C2×#117C2314yes—
269C2×#117C2314yes—
270C2×#117C2314yes—
271C2×#117C2314yes—
272C2×#117C2318yes—
273C2×#117C2312yes—
274C2×#117C2314yes—
275C2×#117C2314yes—
276C2×#117C2314yes—
277C2×#117C2314yes—
278C22×C4⋊C4—28no—
279C22×C4⋊C4C2311yescharacteristic
280C22×C4⋊C4C2311yescharacteristic
281C22×C4⋊C4C2314yes—
282C22×C4⋊C4C2311yescharacteristic
283C22×C4⋊C4C2314yes—
284C22×C4⋊C4C2311yescharacteristic
285C22×C4⋊C4C2311yescharacteristic
286C22×C4⋊C4C2311yescharacteristic
287C22×C4⋊C4C2311yescharacteristic
288C22×C4⋊C4C2311yescharacteristic
289C22×C4⋊C4C2311yescharacteristic
290C22×C4⋊C4C2311yescharacteristic
291C22×C4⋊C4C2311yescharacteristic
292C22×C4⋊C4C2314yes—
293C22×C4⋊C4C2311yescharacteristic
294C22×C4⋊C4C2311yescharacteristic
295C22×C4⋊C4C2311yescharacteristic
296C22×C4⋊C4C2311yescharacteristic
297C22×C4⋊C4C2311yescharacteristic
298C22×C22⋊C4C2311yescharacteristic
299C22×C22⋊C4C2311yescharacteristic
300C22×C22⋊C4C2311yescharacteristic
301C22×C22⋊C4C2311yescharacteristic
302C22×C22⋊C4C2311yescharacteristic
303C22×C22⋊C4C2311yescharacteristic
304C22×C22⋊C4C2311yescharacteristic
305C22×C22⋊C4C2311yescharacteristic
306C22×C42C2311yescharacteristic
307C22×C42C2311yescharacteristic
308C22×C42C2311yescharacteristic
309C22×C42C2311yescharacteristic
310C22×C42C2311yescharacteristic
311#400C2314yes—
312#400C2314yes—
313#400C2314yes—
314#400C2318yes—
315#400C2314yes—
316#400C2314yes—
317#399C2314yes—
318#399C2318yes—
319#399C2314yes—
320#399C2314yes—
321#398C2318yes—
322#398C2318yes—
323#398C2318yes—
324#398C2318yes—
325#398C2318yes—
326#398C2314yes—
327#398C2314yes—
328#398C2314yes—
329#398C2318yes—
330#398C2318yes—
331#398C2314yes—
332#398C2314yes—
333#397C2314yes—
334#397C2318yes—
335#397C2318yes—
336#397C2318yes—
337#397C2314yes—
338#397C2318yes—
339#397C2314yes—
340#396C2318yes—
341#396C2318yes—
342#396C2318yes—
343#396C2318yes—
344#396C2318yes—
345#396C2318yes—
346#396C2318yes—
347#396C2318yes—
348#395C2314yes—
349#395C2314yes—
350#395C2314yes—
351#395C2318yes—
352#395C2314yes—
353#395C2314yes—
354#394C2318yes—
355#394C2318yes—
356#394C2318yes—
357#394C2314yes—
358#394C2314yes—
359#394C2314yes—
360#394C2318yes—
361#394C2318yes—
362#394C2318yes—
363#394C2314yes—
364#394C2318yes—
365#394C2314yes—
366#393C2314yes—
367#393C2318yes—
368#393C2314yes—
369#393C2314yes—
370#392C2318yes—
371#392C2314yes—
372#392C2318yes—
373#392C2314yes—
374#392C2314yes—
375#391C2314yes—
376#391C2314yes—
377#391C2318yes—
378#391C2314yes—
379#391C2314yes—
380#390C2314yes—
381#390C2314yes—
382#390C2314yes—
383#390C2314yes—
384#390C2318yes—
385#390C2318yes—
386#389C2318yes—
387#389C2318yes—
388#389C2318yes—
389#389C2318yes—
390#389C2318yes—
391#389C2318yes—
392#389C2314yes—
393#389C2314yes—
394#389C2318yes—
395#389C2314yes—
396#389C2314yes—
397#388C2318yes—
398#388C2318yes—
399#388C2318yes—
400#388C2318yes—
401#388C2318yes—
402#388C2318yes—
403#388C2318yes—
404#388C2318yes—
405#388C2318yes—
406#388C2318yes—
407#388C2318yes—
408#388C2318yes—
409#388C2318yes—
410#388C2318yes—
411#388C2318yes—
412#388C2318yes—
413#388C2318yes—
414#387C2318yes—
415#387C2318yes—
416#387C2318yes—
417#387C2318yes—
418#387C2318yes—
419#387C2318yes—
420#387C2318yes—
421#387C2318yes—
422#387C2318yes—
423#387C2318yes—
424#387C2318yes—
425#387C2318yes—
426#387C2318yes—
427#386C2314yes—
428#386C2314yes—
429#386C2318yes—
430#386C2314yes—
431#386C2318yes—
432#386C2318yes—
433#386C2314yes—
434#386C2318yes—
435#386C2318yes—
436#386C2318yes—
437#385C2318yes—
438#385C2318yes—
439#385C2314yes—
440#385C2314yes—
441#385C2318yes—
442#385C2318yes—
443#385C2318yes—
444#385C2314yes—
445#385C2318yes—
446#385C2318yes—
447#385C2318yes—
448#385C2314yes—
449#385C2318yes—
450#385C2318yes—
451#384C2314yes—
452#384C2314yes—
453#384C2314yes—
454#382C2314yes—
455#382C2314yes—
456#382C2314yes—
457#381C2314yes—
458#381C2312yes—
459#381C2312yes—
460#381C2314yes—
461#381C2314yes—
462#381C2318yes—
463#380C2314yes—
464#380C2312yes—
465#380C2312yes—
466#380C2314yes—
467#380C2314yes—
468#380C2318yes—
469#379C2314yes—
470#379C2314yes—
471C4×C4⋊C4C2314yes—
472C4×C4⋊C4C2314yes—
473C4×C4⋊C4C2314yes—
474C4×C4⋊C4C2314yes—
475C4×C4⋊C4C2318yes—
476C4×C22⋊C4C2312yes—
477C4×C22⋊C4C2314yes—
478C4×C22⋊C4C2312yes—
479C4×C22⋊C4C2314yes—
480C4×C22⋊C4C2314yes—
481C4×C22⋊C4C2318yes—
482C4×C22⋊C4C2318yes—
483#376C2314yes—
484C43C2314yes—
485C25C2411yescharacteristic
486C25C2411yescharacteristic
487C2×#41—28no—
488C2×#41—48no—
489C22×Q8—24no—
490C22×Q8—44no—
491C22×Q8C2414yes—
492C22×Q8C2412yes—
493C22×Q8C2412yes—
494C22×Q8C2412yes—
495C22×D4—24no—
496C22×D4—44no—
497C22×D4C2414yes—
498C22×D4C2412yes—
499C22×D4C2414yes—
500C22×D4C2414yes—
501C22×D4C2414yes—
502C22×D4C2412yes—
503C22×D4C2412yes—
504C22×D4C2418yes—
505C23×C4—24no—
506C23×C4—24no—
507C23×C4—24no—
508C23×C4—44no—
509C23×C4—44no—
510C23×C4—44no—
511C23×C4—44no—
512C23×C4C2×D418yes—
513C23×C4C2411yescharacteristic
514C23×C4C2411yescharacteristic
515C23×C4C2411yescharacteristic
516C23×C4C2411yescharacteristic
517C23×C4C2414yes—
518C23×C4C2414yes—
519C23×C4C2411yescharacteristic
520C23×C4C2411yescharacteristic
521C23×C4C2411yescharacteristic
522C23×C4C2411yescharacteristic
523C23×C4C2411yescharacteristic
524C23×C4C2414yes—
525C23×C4C2414yes—
526C23×C4C2414yes—
527C23×C4C2414yes—
528C23×C4C2411yescharacteristic
529C23×C4C2411yescharacteristic
530C23×C4C2411yescharacteristic
531C23×C4C2411yescharacteristic
532C23×C4C2412yes—
533C23×C4C2412yes—
534C4⋊Q8—216no—
535#126—232no—
536#126—216no—
537#126—216no—
538#126—216no—
539#126—216no—
540#126—216no—
541#126—216no—
542#125—232no—
543#125—232no—
544#125—216no—
545#125—216no—
546#125—216no—
547#125—28no—
548#125—28no—
549#124—216no—
550#124—216no—
551#124—28no—
552#124—28no—
553#123—216no—
554#123—216no—
555#123—216no—
556#123—232no—
557#123—216no—
558#123—216no—
559#123—416no—
560#123—48no—
561#123—48no—
562#123—48no—
563C22⋊Q8—28no—
564C22⋊Q8—28no—
565C22⋊Q8—28no—
566C22⋊Q8—28no—
567C22⋊Q8—232no—
568C22⋊Q8—216no—
569C22⋊Q8—232no—
570C22⋊Q8—416no—
571#121—28no—
572#121—28no—
573#121—28no—
574#121—28no—
575#121—216no—
576#121—216no—
577#121—216no—
578#120—216no—
579#120—48no—
580C4×Q8—216no—
581C4×Q8—216no—
582C4×Q8—216no—
583C4×Q8—28no—
584C4×Q8—28no—
585C4×D4—216no—
586C4×D4—216no—
587C4×D4—216no—
588C4×D4—216no—
589C4×D4—216no—
590C4×D4—232no—
591C4×D4—28no—
592C4×D4—28no—
593C4×D4—416no—
594#117—28no—
595#117—216no—
596#117—232no—
597#117—216no—
598#117—216no—
599#117—216no—
600#117—216no—
601#117—48no—
602#117C2×D4132yes—
603#117C2×D4132yes—
604C2×C4⋊C4—24no—
605C2×C4⋊C4—24no—
606C2×C4⋊C4—24no—
607C2×C4⋊C4—24no—
608C2×C4⋊C4—216no—
609C2×C4⋊C4—216no—
610C2×C4⋊C4—24no—
611C2×C4⋊C4—24no—
612C2×C4⋊C4—24no—
613C2×C4⋊C4—24no—
614C2×C4⋊C4—24no—
615C2×C4⋊C4—24no—
616C2×C4⋊C4—24no—
617C2×C4⋊C4—24no—
618C2×C4⋊C4—24no—
619C2×C4⋊C4—24no—
620C2×C4⋊C4—216no—
621C2×C4⋊C4C2×D418yes—
622C2×C4⋊C4C2×D418yes—
623C2×C4⋊C4C2412yes—
624C2×C4⋊C4C2412yes—
625C2×C4⋊C4C2414yes—
626C2×C4⋊C4C2414yes—
627C2×C4⋊C4C2412yes—
628C2×C4⋊C4C2412yes—
629C2×C4⋊C4C2412yes—
630C2×C4⋊C4C2414yes—
631C2×C4⋊C4C2414yes—
632C2×C4⋊C4C2414yes—
633C2×C4⋊C4C2414yes—
634C2×C4⋊C4C2414yes—
635C2×C4⋊C4C2414yes—
636C2×C4⋊C4C2414yes—
637C2×C4⋊C4C2412yes—
638C2×C4⋊C4C2412yes—
639C2×C4⋊C4C2414yes—
640C2×C4⋊C4C2414yes—
641C2×C4⋊C4C2414yes—
642C2×C4⋊C4C2414yes—
643C2×C4⋊C4C2412yes—
644C2×C4⋊C4C2414yes—
645C2×C4⋊C4C2414yes—
646C2×C4⋊C4C2414yes—
647C2×C4⋊C4C2414yes—
648C2×C4⋊C4C2412yes—
649C2×C4⋊C4C2412yes—
650C2×C4⋊C4C2418yes—
651C2×C4⋊C4C2412yes—
652C2×C4⋊C4C2412yes—
653C2×C4⋊C4C2418yes—
654C2×C4⋊C4C2418yes—
655C2×C4⋊C4C2418yes—
656C2×C4⋊C4C2418yes—
657C2×C4⋊C4C2418yes—
658C2×C4⋊C4C2418yes—
659C2×C4⋊C4C2418yes—
660C2×C4⋊C4C2414yes—
661C2×C4⋊C4C2414yes—
662C2×C4⋊C4C2418yes—
663C2×C4⋊C4C2414yes—
664C2×C4⋊C4C2414yes—
665C2×C22⋊C4—24no—
666C2×C22⋊C4—24no—
667C2×C22⋊C4—24no—
668C2×C22⋊C4—24no—
669C2×C22⋊C4—24no—
670C2×C22⋊C4—24no—
671C2×C22⋊C4C2×D418yes—
672C2×C22⋊C4C2×D418yes—
673C2×C22⋊C4C2414yes—
674C2×C22⋊C4C2412yes—
675C2×C22⋊C4C2414yes—
676C2×C22⋊C4C2412yes—
677C2×C22⋊C4C2414yes—
678C2×C22⋊C4C2414yes—
679C2×C22⋊C4C2414yes—
680C2×C22⋊C4C2414yes—
681C2×C22⋊C4C2414yes—
682C2×C22⋊C4C2414yes—
683C2×C22⋊C4C2414yes—
684C2×C22⋊C4C2414yes—
685C2×C22⋊C4C2414yes—
686C2×C22⋊C4C2414yes—
687C2×C22⋊C4C2414yes—
688C2×C22⋊C4C2414yes—
689C2×C22⋊C4C2414yes—
690C2×C22⋊C4C2414yes—
691C2×C22⋊C4C2418yes—
692C2×C22⋊C4C2418yes—
693C2×C22⋊C4C2418yes—
694C2×C22⋊C4C2418yes—
695C2×C22⋊C4C2418yes—
696C2×C22⋊C4C2418yes—
697C2×C22⋊C4C2418yes—
698C2×C22⋊C4C2418yes—
699C2×C22⋊C4C2418yes—
700C2×C22⋊C4C2418yes—
701C2×C22⋊C4C2418yes—
702C2×C22⋊C4C2418yes—
703C2×C22⋊C4C2414yes—
704C2×C22⋊C4C2414yes—
705C2×C42—24no—
706C2×C42—24no—
707C2×C42—24no—
708C2×C42C2×D418yes—
709C2×C42C2×D418yes—
710C2×C42C2414yes—
711C2×C42C2414yes—
712C2×C42C2414yes—
713C2×C42C2414yes—
714C2×C42C2414yes—
715C2×C42C2414yes—
716C2×C42C2418yes—
717C2×C42C2418yes—
718C2×C42C2414yes—
719C2×C42C2414yes—
720C2×C42C2412yes—
721C2×C42C2412yes—
722C2×C42C2412yes—
723C2×C42C2412yes—
724#95C2418yes—
725#95C2414yes—
726#95C2414yes—
727#95C2414yes—
728#95C2414yes—
729#95C2414yes—
730#95C2418yes—
731#95C2414yes—
732#95C2418yes—
733#95C2418yes—
734#95C2418yes—
735#95C2418yes—
736#95C2414yes—
737#95C2414yes—
738#95C2418yes—
739#95C2418yes—
740#95C2418yes—
741#95C2418yes—
742#95C2418yes—
743#95C2418yes—
744#95C2418yes—
745#95C2418yes—
746#95C2418yes—
747#95C2418yes—
748C24—24no—
749C24—22no—
750C24—24no—
751C24—42no—
752C24—42no—
753C24—42no—
754C24—42no—
755C24C22×D414yes—
756C24C2512yes—
757C24C2514yes—
758C24C2512yes—
759C24C2511yescharacteristic
760#41—432no—
761C2×Q8—28no—
762C2×Q8—24no—
763C2×Q8—24no—
764C2×Q8—24no—
765C2×Q8—28no—
766C2×Q8—44no—
767C2×Q8—44no—
768C2×Q8—44no—
769C2×Q8—44no—
770C2×Q8—416no—
771C2×D4—28no—
772C2×D4—28no—
773C2×D4—28no—
774C2×D4—28no—
775C2×D4—28no—
776C2×D4—28no—
777C2×D4—24no—
778C2×D4—24no—
779C2×D4—24no—
780C2×D4—48no—
781C2×D4—44no—
782C2×D4—48no—
783C2×D4—48no—
784C2×D4—48no—
785C2×D4—44no—
786C2×D4—44no—
787C2×D4—48no—
788C2×D4—48no—
789C2×D4—416no—
790C22×C4—22no—
791C22×C4—24no—
792C22×C4—24no—
793C22×C4—24no—
794C22×C4—22no—
795C22×C4—22no—
796C22×C4—22no—
797C22×C4—22no—
798C22×C4—22no—
799C22×C4—22no—
800C22×C4—28no—
801C22×C4—28no—
802C22×C4—24no—
803C22×C4—24no—
804C22×C4—24no—
805C22×C4—28no—
806C22×C4—28no—
807C22×C4—28no—
808C22×C4—28no—
809C22×C4—28no—
810C22×C4—28no—
811C22×C4—416no—
812C22×C4—44no—
813C22×C4—42no—
814C22×C4—44no—
815C22×C4—44no—
816C22×C4—44no—
817C22×C4—42no—
818C22×C4—48no—
819C22×C4—42no—
820C22×C4—42no—
821C22×C4—42no—
822C22×C4—42no—
823C22×C4—42no—
824C22×C4—44no—
825C22×C4—44no—
826C22×C4—48no—
827C22×C4—48no—
828C22×C4—416no—
829C22×C4—416no—
830C22×C4—416no—
831C22×C4C22×D414yes—
832C22×C4C22×D414yes—
833C22×C4C22×D414yes—
834C22×C4C22×D414yes—
835C22×C4C22×D414yes—
836C22×C4C22×D414yes—
837C22×C4C22×D418yes—
838C22×C4C22×D418yes—
839C22×C4C2518yes—
840C22×C4C2518yes—
841C22×C4C2514yes—
842C22×C4C2512yes—
843C22×C4C2512yes—
844C22×C4C2512yes—
845C22×C4C2514yes—
846C22×C4C2512yes—
847C22×C4C2514yes—
848C22×C4C2512yes—
849C22×C4C2512yes—
850C22×C4C2512yes—
851C22×C4C2512yes—
852C22×C4C2512yes—
853C22×C4C2512yes—
854C22×C4C2512yes—
855C22×C4C2511yescharacteristic
856C22×C4C2511yescharacteristic
857C22×C4C2512yes—
858C4⋊C4—24no—
859C4⋊C4—24no—
860C4⋊C4—28no—
861C4⋊C4—28no—
862C4⋊C4—24no—
863C4⋊C4—24no—
864C4⋊C4—24no—
865C4⋊C4—28no—
866C4⋊C4—28no—
867C4⋊C4—28no—
868C4⋊C4—28no—
869C4⋊C4—28no—
870C4⋊C4—28no—
871C4⋊C4—28no—
872C4⋊C4—24no—
873C4⋊C4—24no—
874C4⋊C4—28no—
875C4⋊C4—28no—
876C4⋊C4—28no—
877C4⋊C4—28no—
878C4⋊C4—24no—
879C4⋊C4—28no—
880C4⋊C4—28no—
881C4⋊C4—28no—
882C4⋊C4—28no—
883C4⋊C4—24no—
884C4⋊C4—24no—
885C4⋊C4—24no—
886C4⋊C4—24no—
887C4⋊C4—216no—
888C4⋊C4—44no—
889C4⋊C4—44no—
890C4⋊C4—48no—
891C4⋊C4—48no—
892C4⋊C4—48no—
893C4⋊C4—48no—
894C4⋊C4—48no—
895C4⋊C4—48no—
896C4⋊C4—48no—
897C4⋊C4—48no—
898C4⋊C4C22×D4116yes—
899C4⋊C4C22×D4116yes—
900C22⋊C4—28no—
901C22⋊C4—28no—
902C22⋊C4—28no—
903C22⋊C4—28no—
904C22⋊C4—28no—
905C22⋊C4—28no—
906C22⋊C4—28no—
907C22⋊C4—24no—
908C22⋊C4—24no—
909C22⋊C4—28no—
910C22⋊C4—28no—
911C22⋊C4—28no—
912C22⋊C4—28no—
913C22⋊C4—28no—
914C22⋊C4—28no—
915C22⋊C4—28no—
916C22⋊C4—28no—
917C22⋊C4—28no—
918C22⋊C4—216no—
919C22⋊C4—48no—
920C22⋊C4—48no—
921C22⋊C4—48no—
922C22⋊C4—48no—
923C22⋊C4—48no—
924C22⋊C4—48no—
925C22⋊C4—48no—
926C22⋊C4—48no—
927C22⋊C4—48no—
928C22⋊C4—48no—
929C22⋊C4—48no—
930C22⋊C4C22×D4116yes—
931C22⋊C4C22×D4116yes—
932C42—28no—
933C42—28no—
934C42—28no—
935C42—28no—
936C42—28no—
937C42—28no—
938C42—44no—
939C42—44no—
940C42—48no—
941C42—48no—
942C42C22×D418yes—
943C42C22×D418yes—
944C42C22×D418yes—
945C42C22×D418yes—
946C23—22no—
947C23—22no—
948C23—24no—
949C23—24no—
950C23—24no—
951C23—28no—
952C23—22no—
953C23—24no—
954C23—28no—
955C23—24no—
956C23—24no—
957C23—24no—
958C23—24no—
959C23—24no—
960C23—28no—
961C23—44no—
962C23—44no—
963C23—416no—
964C23—44no—
965C23—44no—
966C23—44no—
967C23—88no—
968C23C23×D414yes—
969C23C23×D412yes—
970C23#58514yes—
971C23C2611yescharacteristic
972Q8—416no—
973Q8—48no—
974Q8—84no—
975Q8—84no—
976D4—48no—
977D4—416no—
978D4—416no—
979D4—84no—
980D4—84no—
981D4—88no—
982D4—88no—
983D4—816no—
984C2×C4—28no—
985C2×C4—22no—
986C2×C4—22no—
987C2×C4—24no—
988C2×C4—22no—
989C2×C4—24no—
990C2×C4—24no—
991C2×C4—22no—
992C2×C4—24no—
993C2×C4—24no—
994C2×C4—28no—
995C2×C4—28no—
996C2×C4—22no—
997C2×C4—24no—
998C2×C4—22no—
999C2×C4—24no—
1000C2×C4—22no—
1001C2×C4—22no—
1002C2×C4—24no—
1003C2×C4—22no—
1004C2×C4—22no—
1005C2×C4—28no—
1006C2×C4—28no—
1007C2×C4—28no—
1008C2×C4—28no—
1009C2×C4—24no—
1010C2×C4—24no—
1011C2×C4—24no—
1012C2×C4—24no—
1013C2×C4—24no—
1014C2×C4—24no—
1015C2×C4—28no—
1016C2×C4—24no—
1017C2×C4—28no—
1018C2×C4—28no—
1019C2×C4—24no—
1020C2×C4—28no—
1021C2×C4—44no—
1022C2×C4—48no—
1023C2×C4—48no—
1024C2×C4—44no—
1025C2×C4—44no—
1026C2×C4—44no—
1027C2×C4—416no—
1028C2×C4—416no—
1029C2×C4—416no—
1030C2×C4—44no—
1031C2×C4—44no—
1032C2×C4—416no—
1033C2×C4—44no—
1034C2×C4—44no—
1035C2×C4—44no—
1036C2×C4—44no—
1037C2×C4—88no—
1038C2×C4—88no—
1039C2×C4C23×D414yes—
1040C2×C4C23×D414yes—
1041C2×C4C23×D414yes—
1042C2×C4C23×D414yes—
1043C2×C4C23×D412yes—
1044C2×C4C23×D412yes—
1045C2×C4C23×D414yes—
1046C2×C4#58514yes—
1047C22—22no—
1048C22—22no—
1049C22—28no—
1050C22—24no—
1051C22—24no—
1052C22—24no—
1053C22—416no—
1054C22—48no—
1055C22—42no—
1056C22—44no—
1057C22—44no—
1058C22—42no—
1059C22—48no—
1060C22—48no—
1061C22—48no—
1062C22—44no—
1063C22—42no—
1064C22—88no—
1065C22#344914yes—
1066C22C24×D411yescharacteristic
1067C22C2×#58512yes—
1068C22C2×#58512yes—
1069C222−1+612yes—
1070C4—24no—
1071C4—24no—
1072C4—24no—
1073C4—24no—
1074C4—24no—
1075C4—24no—
1076C4—22no—
1077C4—22no—
1078C4—42no—
1079C4—42no—
1080C4—44no—
1081C4—42no—
1082C4—44no—
1083C4—48no—
1084C4—48no—
1085C4—42no—
1086C4—42no—
1087C4—42no—
1088C4—44no—
1089C2—24no—
1090C2—44no—
1091C2—84no—
1092C2—82no—
1093C2C2×#344911yescharacteristic
1094C2#6281111yescharacteristic
1095C2#6285911yescharacteristic
1096C2#6290714yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#3493C2semidirect
2. C22×#552C2semidirect
3. #42179C2semidirect
4. #41996C2semidirect
5. #38439C2semidirect
6. #38436C2semidirect
7. #37538C2semidirect
8. #37443C2semidirect
9. #36962C2semidirect
10. #36961C2semidirect
11. #36959C2semidirect
12. #36958C2semidirect
13. #36956C2semidirect
14. #36716C2semidirect
15. #35453C2semidirect
16. #35357C2semidirect
17. #35247C2semidirect
18. #35139C2semidirect
19. #35093C2semidirect
20. #35057C2semidirect
21. #34986C2semidirect
22. #34877C2semidirect
23. #34048C2semidirect
25. C2×#556C22semidirect
26. C2×#555C22semidirect
27. C2×#553C22semidirect
31. C2×#552C22semidirect
55. #2861C22semidirect
56. #2859C22semidirect
63. #2823C22semidirect
66. #2723C22semidirect
67. #2721C22semidirect
68. #2720C22semidirect
69. #2719C22semidirect
71. #2716C22semidirect
72. #2714C22semidirect
73. #2713C22semidirect
74. #2711C22semidirect
78. #2700C22semidirect
79. #2698C22semidirect
80. #2681C22semidirect
81. #2680C22semidirect
82. #2664C22semidirect
83. #2664C22semidirect
85. #2662C22semidirect
87. #2637C22semidirect
88. #2637C22semidirect
89. #2636C22semidirect
92. #2627C22semidirect
96. #2618C22semidirect
99. #2611C22semidirect
100. #2611C22semidirect
101. #2610C22semidirect
103. #2601C22semidirect
104. #2601C22semidirect
105. #2592C22semidirect
107. #2591C22semidirect
108. #2584C22semidirect
110. #2583C22semidirect
111. #2582C22semidirect
113. #2579C22semidirect
114. #2566C22semidirect
115. #2565C22semidirect
118. #2538C22semidirect
129. #2478C22semidirect
130. #2477C22semidirect
131. #2476C22semidirect
132. #2475C22semidirect
133. #2474C22semidirect
134. #2473C22semidirect
135. #2470C22semidirect
137. #2465C22semidirect
138. #2463C22semidirect
139. #2462C22semidirect
140. #2460C22semidirect
144. #2449C22semidirect
154. #2396C22semidirect
155. #2392C22semidirect
156. #2323C22semidirect
159. #2322C22semidirect
160. #2314C22semidirect
168. #2298C22semidirect
169. #2293C22semidirect
267. C2×#117D4semidirect

Maximal subgroups

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

subgroupindex
C2×#34932
C22×#5522
#421792
#419962
#384392
#384362
#375382
#374432
#369622
#369612
#369592
#369582
#369562
#367162
#354532
#353572
#352472
#351392
#350932
#350572
#349862
#348772
#340482