Finite Group Databasebeta

← #7654860

Subgroups — #7654860

Order 512.

5722 conjugacy classes of subgroups.

The subgroup lattice has 1241 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42974C214yesmaximal, complemented
2#42051C218yesmaximal, complemented
3#39736C212yesmaximal, complemented
4#39416C214yesmaximal, complemented
5#39352C212yesmaximal, complemented
6#39147C212yesmaximal, complemented
7#39046C214yesmaximal, complemented
8#38942C212yesmaximal, complemented
9#38202C214yesmaximal, complemented
10#37751C214yesmaximal, complemented
11#37643C211yesmaximal, characteristic, complemented
12#37625C212yesmaximal, complemented
13#36596C212yesmaximal, complemented
14#36472C212yesmaximal, complemented
15#36302C212yesmaximal, complemented
16#36117C212yesmaximal, complemented
17#35823C214yesmaximal, complemented
18#35272C211yesmaximal, characteristic, complemented
19#35272C211yesmaximal, characteristic, complemented
20#35186C212yesmaximal, complemented
21#35171C212yesmaximal, complemented
22#34976C211yesmaximal, characteristic, complemented
23#34934C212yesmaximal, complemented
24#34210C211yesmaximal, characteristic, complemented
25#34129C211yesmaximal, characteristic, complemented
26#34127C211yesmaximal, characteristic, complemented
27C2×#553C2214yescomplemented
28C2×#540C2214yescomplemented
29C2×#535C2212yes—
30C2×#535C2212yes—
31C22×#127C2211yescharacteristic
32C2×#529C2214yescomplemented
33C2×#518C2212yes—
34C2×C4×#41C2211yescharacteristic
35C2×C4×#41C2211yescharacteristic
36#2861C2214yescomplemented
37#2860C2214yescomplemented
38#2856C2212yes—
39#2856C2212yes—
40#2856C2212yes—
41#2856C2212yes—
42#2856C2214yescomplemented
43#2854C2214yescomplemented
44#2845C2214yescomplemented
45#2829C2218yescomplemented
46#2761C2218yescomplemented
47#2757C2218yescomplemented
48#2756C2218yescomplemented
49#2735C2218yes—
50#2706C2218yescomplemented
51#2701C2218yescomplemented
52#2699C2218yescomplemented
53#2697C2218yes—
54#2691C2218yescomplemented
55#2685C2218yes—
56#2678C2218yes—
57#2671C2218yescomplemented
58#2661C2218yescomplemented
59#2651C2218yescomplemented
60#2644C2214yescomplemented
61#2641C2214yescomplemented
62#2630C2218yescomplemented
63#2629C2214yes—
64#2629C2214yes—
65#2629C2214yes—
66#2624C2214yescomplemented
67#2620C2214yescomplemented
68#2619C2214yes—
69#2619C2214yes—
70#2609C2214yescomplemented
71#2603C2218yescomplemented
72#2582C2211yescharacteristic, complemented
73#2566C2214yescomplemented
74#2554C2218yescomplemented
75#2554C2218yescomplemented
76#2552C2212yescomplemented
77#2552C2212yescomplemented
78#2552C2212yescomplemented
79#2552C2212yescomplemented
80#2552C2212yescomplemented
81#2552C2212yescomplemented
82#2548C2212yes—
83#2548C2212yes—
84#2548C2212yes—
85#2548C2212yes—
86#2543C2218yescomplemented
87#2541C2212yes—
88#2541C2212yes—
89#2541C2212yes—
90#2541C2212yes—
91#2538C2211yescharacteristic, complemented
92#2538C2211yescharacteristic, complemented
93#2537C2214yescomplemented
94#2537C2211yescharacteristic, complemented
95#2534C2218yes—
96#2531C2218yescomplemented
97#2513C2214yescomplemented
98#2512C2214yescomplemented
99#2512C2214yescomplemented
100#2512C2214yescomplemented
101#2501C2214yescomplemented
102#2500C2214yescomplemented
103#2490C2214yescomplemented
104#2490C2214yescomplemented
105#2490C2214yescomplemented
106#2490C2214yescomplemented
107#2485C2212yes—
108#2485C2212yes—
109#2480C2218yes—
110#2479C2218yescomplemented
111#2476C2218yescomplemented
112#2468C2218yescomplemented
113#2464C2218yescomplemented
114#2464C2218yescomplemented
115#2454C2214yescomplemented
116#2454C2214yescomplemented
117#2448C2214yescomplemented
118#2447C2214yescomplemented
119#2445C2214yescomplemented
120#2445C2214yescomplemented
121#2428C2214yescomplemented
122#2428C2214yescomplemented
123#2427C2214yescomplemented
124#2426C2214yescomplemented
125#2425C2218yescomplemented
126#2424C2218yes—
127#2422C2214yescomplemented
128#2422C2214yescomplemented
129#2422C2214yescomplemented
130#2420C2214yescomplemented
131#2416C2214yescomplemented
132#2414C2214yescomplemented
133#2411C2218yes—
134#2408C2214yes—
135#2408C2214yes—
136#2408C2214yes—
137#2408C2214yes—
138#2407C2212yes—
139#2407C2212yes—
140#2392C2214yes—
141#2392C2218yescomplemented
142#2366C2212yes—
143#2366C2212yes—
144#2366C2212yes—
145#2366C2212yes—
146#2363C2214yescomplemented
147#2361C2214yescomplemented
148#2355C2211yescharacteristic, complemented
149#2355C2211yescharacteristic, complemented
150#2354C2212yes—
151#2354C2212yes—
152#2354C2214yescomplemented
153#2354C2211yescharacteristic, complemented
154#2354C2211yescharacteristic, complemented
155#2352C2212yes—
156#2352C2212yes—
157Q8×C4⋊C4C2211yescharacteristic, complemented
158Q8×C4⋊C4C2211yescharacteristic, complemented
159D4×C4⋊C4C2211yescharacteristic, complemented
160D4×C4⋊C4C2211yescharacteristic, complemented
161#2347C2212yes—
162#2346C2212yes—
163#2346C2214yescomplemented
164#2343C2214yescomplemented
165#2341C2212yes—
166#2339C2212yes—
167D4×C22⋊C4C2214yes—
168D4×C22⋊C4C2214yes—
169#2328C2214yes—
170#2326C2214yescomplemented
171#2324C2214yescomplemented
172#2319C2214yescomplemented
173#2309C2212yes—
174#2309C2212yes—
175#2309C2212yes—
176C4×#127C2212yes—
177C4×#127C2212yes—
178C4×#127C2214yescomplemented
179C4×C22⋊Q8C2212yescomplemented
180C4×C22⋊Q8C2212yescomplemented
181C4×#121C2212yescomplemented
182C4×#121C2214yescomplemented
183C4×#121C2212yescomplemented
184#2295C2212yescomplemented
185#2293C2214yes—
186#2293C2214yescomplemented
187#2293C2212yescomplemented
188#2290C2214yes—
189#2285C2211yescharacteristic
190#2285C2211yescharacteristic
191#2285C2211yescharacteristic
192#2285C2212yescomplemented
193#2283C2212yescomplemented
194C42×Q8C2212yescomplemented
195C42×D4C2212yescomplemented
196C4×#117C2211yescharacteristic
197C4×#117C2212yescomplemented
198C2×C4×C4⋊C4C2212yescomplemented
199C22×#41C2311yescharacteristic
200C22×#41C2311yescharacteristic
201C23×D4C2312yes—
202C23×D4C2312yes—
203C23×D4C2312yes—
204#553—416no—
205#540—416no—
206#535—48no—
207#535—48no—
208C2×#127—28no—
209C2×#127C2312yes—
210C2×#127C2314yes—
211C2×#127C2312yes—
212C2×#127C2312yes—
213C2×#127C2312yes—
214C2×#127C2314yes—
215#529—416no—
216C2×#126C2318yes—
217C2×#126C2318yes—
218C2×#125C2314yes—
219C2×#125C2314yes—
220C2×#125C2314yes—
221C2×#124C2314yes—
222C2×#124C2314yes—
223C2×#123C2318yes—
224C2×#123C2318yes—
225C2×#123C2318yes—
226C2×#123C2318yes—
227C2×C22⋊Q8C2312yes—
228C2×C22⋊Q8C2312yes—
229C2×#121C2312yes—
230C2×#121C2314yes—
231C2×#121C2314yes—
232C2×#121C2314yes—
233C2×#121C2314yes—
234C2×#121C2314yes—
235C2×#121C2314yes—
236C2×#121C2314yes—
237C2×#121C2314yes—
238C2×#121C2314yes—
239C2×#121C2314yes—
240C2×#121C2314yes—
241C2×#121C2314yes—
242C2×#121C2312yes—
243C2×#121C2318yes—
244C2×#121C2318yes—
245C2×#121C2318yes—
246C2×#120C2318yes—
247C2×#120C2318yes—
248#518—48no—
249C4×#41—28no—
250C4×#41—28no—
251C2×C4×Q8C2311yescharacteristic
252C2×C4×Q8C2311yescharacteristic
253C2×C4×Q8C2312yes—
254C2×C4×Q8C2311yescharacteristic
255C2×C4×Q8C2311yescharacteristic
256C2×C4×Q8C2312yes—
257C2×C4×D4C2312yes—
258C2×C4×D4C2311yescharacteristic
259C2×C4×D4C2312yes—
260C2×C4×D4C2312yes—
261C2×C4×D4C2311yescharacteristic
262C2×C4×D4C2314yes—
263C2×C4×D4C2312yes—
264C2×C4×D4C2312yes—
265C2×C4×D4C2311yescharacteristic
266C2×C4×D4C2311yescharacteristic
267C2×C4×D4C2314yes—
268C2×C4×D4C2314yes—
269C2×C4×D4C2314yes—
270C2×C4×D4C2314yes—
271C2×C4×D4C2314yes—
272C2×C4×D4C2314yes—
273C2×C4×D4C2312yes—
274C2×C4×D4C2318yes—
275C2×C4×D4C2318yes—
276C2×C4×D4C2314yes—
277C2×C4×D4C2314yes—
278C2×#117C2311yescharacteristic
279C2×#117C2311yescharacteristic
280C2×#117C2312yes—
281C2×#117C2312yes—
282C2×#117C2311yescharacteristic
283C2×#117C2312yes—
284C2×#117C2311yescharacteristic
285C2×#117C2312yes—
286C2×#117C2312yes—
287C2×#117C2312yes—
288C2×#117C2314yes—
289C2×#117C2312yes—
290C2×#117C2318yes—
291C22×C4⋊C4C2312yes—
292C22×C4⋊C4C2312yes—
293C22×C22⋊C4C2318yes—
294C22×C42C2312yes—
295C22×C42C2312yes—
296C22×C42C2314yes—
297C22×C42C2311yescharacteristic
298#399C2318yes—
299#399C2318yes—
300#398C2318yes—
301#398C2314yes—
302#398C2318yes—
303#398C2318yes—
304#398C2318yes—
305#398C2318yes—
306#398C2318yes—
307#397C2318yes—
308#397C2318yes—
309#397C2318yes—
310#397C2314yes—
311#397C2318yes—
312#397C2318yes—
313#397C2318yes—
314#397C2318yes—
315#396C2318yes—
316#396C2318yes—
317#396C2314yes—
318#396C2318yes—
319#396C2314yes—
320#396C2318yes—
321#396C2318yes—
322#396C2318yes—
323#394C2318yes—
324#394C2318yes—
325#394C2318yes—
326#394C2318yes—
327#394C2318yes—
328#394C2318yes—
329#394C2314yes—
330#394C2318yes—
331#394C2318yes—
332#394C2318yes—
333#394C2318yes—
334#394C2318yes—
335#394C2314yes—
336#394C2314yes—
337#394C2318yes—
338#394C2318yes—
339#394C2318yes—
340#392C2318yes—
341#392C2318yes—
342#392C2318yes—
343#392C2318yes—
344#392C2314yes—
345#392C2318yes—
346#391C2312yes—
347#391C2312yes—
348#391C2312yes—
349#391C2312yes—
350#390C2314yes—
351#390C2314yes—
352#390C2314yes—
353#390C2314yes—
354#390C2314yes—
355#390C2314yes—
356#390C2312yes—
357#390C2314yes—
358#390C2318yes—
359#390C2318yes—
360#390C2314yes—
361#390C2314yes—
362#390C2314yes—
363#390C2314yes—
364#390C2314yes—
365#390C2314yes—
366#390C2314yes—
367#390C2314yes—
368#390C2314yes—
369#390C2314yes—
370#390C2314yes—
371#390C2314yes—
372#390C2314yes—
373#390C2318yes—
374#390C2314yes—
375#390C2312yes—
376#390C2314yes—
377#390C2314yes—
378#390C2312yes—
379#390C2314yes—
380#390C2314yes—
381#390C2314yes—
382#390C2318yes—
383#390C2312yes—
384#389C2312yes—
385#389C2314yes—
386#389C2314yes—
387#389C2312yes—
388#389C2312yes—
389#389C2312yes—
390#389C2314yes—
391#389C2314yes—
392#389C2312yes—
393#389C2312yes—
394#389C2314yes—
395#389C2314yes—
396#389C2314yes—
397#389C2314yes—
398#389C2312yes—
399#389C2312yes—
400#388C2314yes—
401#388C2318yes—
402#388C2318yes—
403#388C2318yes—
404#388C2318yes—
405#388C2318yes—
406#388C2318yes—
407#388C2314yes—
408#388C2314yes—
409#388C2314yes—
410#388C2314yes—
411#388C2314yes—
412#388C2314yes—
413#388C2314yes—
414#388C2314yes—
415#388C2318yes—
416#388C2318yes—
417#388C2318yes—
418#388C2314yes—
419#388C2318yes—
420#388C2318yes—
421#388C2318yes—
422#387C2314yes—
423#387C2314yes—
424#387C2314yes—
425#387C2314yes—
426#387C2314yes—
427#387C2314yes—
428#386C2318yes—
429#386C2318yes—
430#386C2318yes—
431#386C2318yes—
432#386C2318yes—
433#386C2314yes—
434#386C2314yes—
435#386C2318yes—
436#386C2314yes—
437#386C2314yes—
438#386C2318yes—
439#386C2318yes—
440#385C2318yes—
441#385C2318yes—
442#385C2318yes—
443#385C2314yes—
444#385C2314yes—
445#385C2318yes—
446#385C2314yes—
447#385C2314yes—
448#384C2311yescharacteristic
449#384C2311yescharacteristic
450#384C2314yes—
451#384C2312yes—
452#384C2314yes—
453#384C2311yescharacteristic
454#384C2311yescharacteristic
455#384C2311yescharacteristic
456#384C2311yescharacteristic
457#384C2312yes—
458#384C2314yes—
459#383C2314yes—
460#382C2312yes—
461#382C2312yes—
462#382C2312yes—
463#382C2312yes—
464#382C2314yes—
465#382C2312yes—
466#381C2318yes—
467#381C2314yes—
468#380C2318yes—
469#380C2312yes—
470#380C2312yes—
471#380C2312yes—
472#380C2312yes—
473#380C2312yes—
474#380C2314yes—
475#380C2312yes—
476#380C2312yes—
477#380C2312yes—
478#380C2312yes—
479#380C2312yes—
480#380C2312yes—
481#380C2312yes—
482#380C2318yes—
483#380C2312yes—
484#380C2312yes—
485#379C2318yes—
486#379C2318yes—
487#379C2318yes—
488C4×C4⋊C4C2314yes—
489C4×C4⋊C4C2312yes—
490C4×C4⋊C4C2312yes—
491C4×C4⋊C4C2314yes—
492C4×C4⋊C4C2312yes—
493C4×C4⋊C4C2314yes—
494C4×C4⋊C4C2314yes—
495C4×C4⋊C4C2312yes—
496C4×C4⋊C4C2311yescharacteristic
497C4×C4⋊C4C2311yescharacteristic
498C4×C4⋊C4C2312yes—
499C4×C4⋊C4C2312yes—
500C4×C4⋊C4C2311yescharacteristic
501C4×C4⋊C4C2311yescharacteristic
502C4×C4⋊C4C2312yes—
503C4×C4⋊C4C2312yes—
504C4×C4⋊C4C2312yes—
505C4×C4⋊C4C2312yes—
506C4×C4⋊C4C2314yes—
507C4×C4⋊C4C2314yes—
508C4×C4⋊C4C2312yes—
509C4×C4⋊C4C2312yes—
510C4×C4⋊C4C2312yes—
511C4×C4⋊C4C2312yes—
512C4×C22⋊C4C2312yes—
513C4×C22⋊C4C2312yes—
514C4×C22⋊C4C2314yes—
515C4×C22⋊C4C2314yes—
516C4×C22⋊C4C2314yes—
517C4×C22⋊C4C2314yes—
518C4×C22⋊C4C2314yes—
519C4×C22⋊C4C2318yes—
520C4×C22⋊C4C2314yes—
521C4×C22⋊C4C2314yes—
522#376C2314yes—
523#376C2312yes—
524#376C2314yes—
525C2×#95C2314yes—
526C43C2312yes—
527C43C2314yes—
528C25C2414yes—
529C2×#41—24no—
530C2×#41—24no—
531C2×#41—24no—
532C2×#41—24no—
533C2×#41—42no—
534C2×#41—42no—
535C22×Q8C2411yescharacteristic
536C22×Q8C2411yescharacteristic
537C22×D4—28no—
538C22×D4—28no—
539C22×D4—28no—
540C22×D4—44no—
541C22×D4—44no—
542C22×D4—44no—
543C22×D4—44no—
544C22×D4—44no—
545C22×D4—44no—
546C22×D4C2414yes—
547C22×D4C2414yes—
548C22×D4C2414yes—
549C22×D4C2411yescharacteristic
550C22×D4C2412yes—
551C22×D4C2412yes—
552C22×D4C2411yescharacteristic
553C22×D4C2414yes—
554C22×D4C2418yes—
555C22×D4C2418yes—
556C22×D4C2414yes—
557C22×D4C2414yes—
558C22×D4C2414yes—
559C22×D4C2418yes—
560C22×D4C2418yes—
561C23×C4C2412yes—
562C23×C4C2412yes—
563C23×C4C2412yes—
564C23×C4C2412yes—
565C23×C4C2412yes—
566C23×C4C2412yes—
567C23×C4C2411yescharacteristic
568C23×C4C2411yescharacteristic
569C23×C4C2411yescharacteristic
570C23×C4C2418yes—
571C23×C4C2414yes—
572C23×C4C2414yes—
573C23×C4C2418yes—
574#127—216no—
575#127—28no—
576#127—28no—
577#127—28no—
578#127—28no—
579#127—48no—
580#126—416no—
581#126—416no—
582#125—48no—
583#125—48no—
584#125—48no—
585#124—216no—
586#124—48no—
587#123—416no—
588#123—416no—
589#123—416no—
590#123—416no—
591C22⋊Q8—28no—
592C22⋊Q8—44no—
593#121—28no—
594#121—48no—
595#121—48no—
596#121—416no—
597#121—416no—
598#121—48no—
599#121—48no—
600#121—44no—
601#121—48no—
602#121—48no—
603#121—48no—
604#121—48no—
605#121—48no—
606#121—48no—
607#121—48no—
608#121—48no—
609#121—416no—
610#120—416no—
611#120—416no—
612C4×Q8—28no—
613C4×Q8—24no—
614C4×Q8—24no—
615C4×Q8—24no—
616C4×Q8—24no—
617C4×Q8—44no—
618C4×D4—28no—
619C4×D4—28no—
620C4×D4—28no—
621C4×D4—28no—
622C4×D4—28no—
623C4×D4—216no—
624C4×D4—24no—
625C4×D4—24no—
626C4×D4—24no—
627C4×D4—24no—
628C4×D4—48no—
629C4×D4—416no—
630C4×D4—48no—
631C4×D4—44no—
632C4×D4—48no—
633C4×D4—48no—
634C4×D4—48no—
635C4×D4—48no—
636C4×D4—48no—
637C4×D4—416no—
638C4×D4—48no—
639#117—24no—
640#117—24no—
641#117—24no—
642#117—28no—
643#117—28no—
644#117—28no—
645#117—44no—
646#117—44no—
647#117—44no—
648#117—48no—
649#117—416no—
650#117—42no—
651#117—44no—
652C2×C4⋊C4—28no—
653C2×C4⋊C4—44no—
654C2×C4⋊C4C2411yescharacteristic
655C2×C4⋊C4C2412yes—
656C2×C4⋊C4C2412yes—
657C2×C4⋊C4C2414yes—
658C2×C4⋊C4C2411yescharacteristic
659C2×C4⋊C4C2414yes—
660C2×C4⋊C4C2411yescharacteristic
661C2×C4⋊C4C2411yescharacteristic
662C2×C4⋊C4C2411yescharacteristic
663C2×C4⋊C4C2412yes—
664C2×C4⋊C4C2411yescharacteristic
665C2×C4⋊C4C2411yescharacteristic
666C2×C4⋊C4C2412yes—
667C2×C4⋊C4C2412yes—
668C2×C4⋊C4C2412yes—
669C2×C4⋊C4C2412yes—
670C2×C4⋊C4C2412yes—
671C2×C4⋊C4C2412yes—
672C2×C4⋊C4C2412yes—
673C2×C4⋊C4C2412yes—
674C2×C4⋊C4C2412yes—
675C2×C4⋊C4C2412yes—
676C2×C4⋊C4C2412yes—
677C2×C4⋊C4C2412yes—
678C2×C4⋊C4C2412yes—
679C2×C4⋊C4C2414yes—
680C2×C4⋊C4C2414yes—
681C2×C4⋊C4C2412yes—
682C2×C4⋊C4C2412yes—
683C2×C4⋊C4C2412yes—
684C2×C4⋊C4C2412yes—
685C2×C4⋊C4C2412yes—
686C2×C4⋊C4C2412yes—
687C2×C4⋊C4C2414yes—
688C2×C4⋊C4C2414yes—
689C2×C4⋊C4C2418yes—
690C2×C4⋊C4C2418yes—
691C2×C4⋊C4C2418yes—
692C2×C4⋊C4C2414yes—
693C2×C4⋊C4C2414yes—
694C2×C4⋊C4C2418yes—
695C2×C4⋊C4C2418yes—
696C2×C4⋊C4C2418yes—
697C2×C4⋊C4C2414yes—
698C2×C4⋊C4C2411yescharacteristic
699C2×C22⋊C4—416no—
700C2×C22⋊C4C2412yes—
701C2×C22⋊C4C2418yes—
702C2×C22⋊C4C2412yes—
703C2×C22⋊C4C2412yes—
704C2×C22⋊C4C2412yes—
705C2×C22⋊C4C2412yes—
706C2×C22⋊C4C2412yes—
707C2×C22⋊C4C2412yes—
708C2×C22⋊C4C2418yes—
709C2×C22⋊C4C2414yes—
710C2×C22⋊C4C2414yes—
711C2×C22⋊C4C2418yes—
712C2×C22⋊C4C2414yes—
713C2×C22⋊C4C2414yes—
714C2×C22⋊C4C2414yes—
715C2×C22⋊C4C2418yes—
716C2×C22⋊C4C2414yes—
717C2×C22⋊C4C2414yes—
718C2×C22⋊C4C2414yes—
719C2×C22⋊C4C2414yes—
720C2×C22⋊C4C2418yes—
721C2×C22⋊C4C2412yes—
722C2×C22⋊C4C2414yes—
723C2×C22⋊C4C2414yes—
724C2×C22⋊C4C2418yes—
725C2×C22⋊C4C2418yes—
726C2×C22⋊C4C2414yes—
727C2×C22⋊C4C2418yes—
728C2×C22⋊C4C2414yes—
729C2×C22⋊C4C2418yes—
730C2×C22⋊C4C2418yes—
731C2×C22⋊C4C2418yes—
732C2×C22⋊C4C2418yes—
733C2×C22⋊C4C2418yes—
734C2×C22⋊C4C2418yes—
735C2×C22⋊C4C2418yes—
736C2×C22⋊C4C2418yes—
737C2×C22⋊C4C2414yes—
738C2×C22⋊C4C2418yes—
739C2×C22⋊C4C2418yes—
740C2×C22⋊C4C2414yes—
741C2×C42—28no—
742C2×C42—28no—
743C2×C42—48no—
744C2×C42#4118yes—
745C2×C42C2412yes—
746C2×C42C2414yes—
747C2×C42C2414yes—
748C2×C42C2412yes—
749C2×C42C2412yes—
750C2×C42C2412yes—
751C2×C42C2414yes—
752C2×C42C2414yes—
753C2×C42C2414yes—
754C2×C42C2412yes—
755C2×C42C2412yes—
756C2×C42C2412yes—
757C2×C42C2412yes—
758C2×C42C2412yes—
759C2×C42C2412yes—
760C2×C42C2412yes—
761C2×C42C2414yes—
762C2×C42C2412yes—
763C2×C42C2414yes—
764C2×C42C2414yes—
765C2×C42C2414yes—
766C2×C42C2411yescharacteristic
767C2×C42C2411yescharacteristic
768C2×C42C2411yescharacteristic
769C2×C42C2411yescharacteristic
770#95C2412yes—
771#95C2414yes—
772#95C2414yes—
773#95C2414yes—
774#95C2412yes—
775#95C2412yes—
776#95C2414yes—
777#95C2414yes—
778#95C2412yes—
779#95C2414yes—
780#95C2414yes—
781#95C2414yes—
782#95C2414yes—
783#95C2414yes—
784#95C2414yes—
785#95C2414yes—
786#95C2414yes—
787#95C2414yes—
788#95C2414yes—
789#95C2414yes—
790#95C2414yes—
791#95C2418yes—
792#95C2414yes—
793#95C2414yes—
794#95C2414yes—
795#95C2414yes—
796#95C2414yes—
797#95C2414yes—
798#95C2414yes—
799#95C2418yes—
800C24—28no—
801C24—44no—
802C24—44no—
803C24—44no—
804C24—44no—
805C24—44no—
806C24—44no—
807C24C2518yes—
808C24C2512yes—
809C24C2511yescharacteristic
810C24C2512yes—
811#41—416no—
812#41—416no—
813C2×Q8—22no—
814C2×Q8—22no—
815C2×Q8—22no—
816C2×Q8—22no—
817C2×Q8—22no—
818C2×Q8H(5,𝔽2)14yes—
819C2×D4—24no—
820C2×D4—24no—
821C2×D4—24no—
822C2×D4—216no—
823C2×D4—216no—
824C2×D4—28no—
825C2×D4—22no—
826C2×D4—22no—
827C2×D4—28no—
828C2×D4—28no—
829C2×D4—28no—
830C2×D4—28no—
831C2×D4—28no—
832C2×D4—28no—
833C2×D4—28no—
834C2×D4—28no—
835C2×D4—28no—
836C2×D4—24no—
837C2×D4—22no—
838C2×D4—22no—
839C2×D4—28no—
840C2×D4—28no—
841C2×D4—28no—
842C2×D4—22no—
843C2×D4—44no—
844C2×D4—44no—
845C2×D4—42no—
846C2×D4—42no—
847C2×D4—432no—
848C2×D4—44no—
849C2×D4—48no—
850C2×D4—48no—
851C2×D4—44no—
852C2×D4—44no—
853C2×D4—48no—
854C2×D4—48no—
855C2×D4—44no—
856C2×D4—44no—
857C2×D4—44no—
858C2×D4—48no—
859C2×D4—48no—
860C2×D4—48no—
861C2×D4—48no—
862C2×D4—48no—
863C2×D4—48no—
864C2×D4—816no—
865C2×D4—816no—
866C2×D4H(5,𝔽2)14yes—
867C22×C4—22no—
868C22×C4—22no—
869C22×C4—22no—
870C22×C4—22no—
871C22×C4—22no—
872C22×C4—22no—
873C22×C4—24no—
874C22×C4—28no—
875C22×C4—24no—
876C22×C4—24no—
877C22×C4—24no—
878C22×C4—24no—
879C22×C4—24no—
880C22×C4—24no—
881C22×C4—24no—
882C22×C4—24no—
883C22×C4—24no—
884C22×C4—24no—
885C22×C4—24no—
886C22×C4—24no—
887C22×C4—24no—
888C22×C4—24no—
889C22×C4—24no—
890C22×C4—216no—
891C22×C4—28no—
892C22×C4—42no—
893C22×C4—42no—
894C22×C4—44no—
895C22×C4—44no—
896C22×C4—44no—
897C22×C4—48no—
898C22×C4—48no—
899C22×C4—44no—
900C22×C4—48no—
901C22×C4—48no—
902C22×C4—48no—
903C22×C4C2×#4114yes—
904C22×C4C2×#4114yes—
905C22×C4C2×#4114yes—
906C22×C4C2512yes—
907C22×C4C2512yes—
908C22×C4C2512yes—
909C22×C4C2512yes—
910C22×C4C2512yes—
911C22×C4C2512yes—
912C22×C4C2512yes—
913C22×C4C2514yes—
914C22×C4C2514yes—
915C22×C4C2514yes—
916C22×C4C2512yes—
917C22×C4C2514yes—
918C22×C4C2514yes—
919C22×C4C2514yes—
920C22×C4C2511yescharacteristic
921C22×C4C2511yescharacteristic
922C22×C4C2511yescharacteristic
923C22×C4C2512yes—
924C22×C4C2512yes—
925C22×C4C2511yescharacteristic
926C22×C4C2511yescharacteristic
927C22×C4C2511yescharacteristic
928C4⋊C4—24no—
929C4⋊C4—24no—
930C4⋊C4—22no—
931C4⋊C4—22no—
932C4⋊C4—22no—
933C4⋊C4—22no—
934C4⋊C4—24no—
935C4⋊C4—24no—
936C4⋊C4—24no—
937C4⋊C4—28no—
938C4⋊C4—22no—
939C4⋊C4—24no—
940C4⋊C4—28no—
941C4⋊C4—24no—
942C4⋊C4—24no—
943C4⋊C4—24no—
944C4⋊C4—24no—
945C4⋊C4—28no—
946C4⋊C4—22no—
947C4⋊C4—24no—
948C4⋊C4—22no—
949C4⋊C4—24no—
950C4⋊C4—24no—
951C4⋊C4—24no—
952C4⋊C4—24no—
953C4⋊C4—24no—
954C4⋊C4—44no—
955C4⋊C4—42no—
956C4⋊C4—42no—
957C4⋊C4—42no—
958C4⋊C4—42no—
959C4⋊C4—42no—
960C4⋊C4—42no—
961C4⋊C4—44no—
962C4⋊C4—44no—
963C4⋊C4—48no—
964C4⋊C4—48no—
965C4⋊C4—48no—
966C4⋊C4—44no—
967C4⋊C4—44no—
968C4⋊C4—48no—
969C4⋊C4—48no—
970C4⋊C4—48no—
971C4⋊C4—44no—
972C4⋊C4H(5,𝔽2)14yes—
973C22⋊C4—24no—
974C22⋊C4—24no—
975C22⋊C4—28no—
976C22⋊C4—28no—
977C22⋊C4—24no—
978C22⋊C4—24no—
979C22⋊C4—24no—
980C22⋊C4—24no—
981C22⋊C4—24no—
982C22⋊C4—216no—
983C22⋊C4—28no—
984C22⋊C4—216no—
985C22⋊C4—28no—
986C22⋊C4—216no—
987C22⋊C4—44no—
988C22⋊C4—48no—
989C22⋊C4—44no—
990C22⋊C4—42no—
991C22⋊C4—44no—
992C22⋊C4—44no—
993C22⋊C4—44no—
994C22⋊C4—44no—
995C22⋊C4—48no—
996C22⋊C4—48no—
997C22⋊C4—48no—
998C22⋊C4—44no—
999C22⋊C4—44no—
1000C22⋊C4—48no—
1001C22⋊C4—48no—
1002C22⋊C4—44no—
1003C22⋊C4—48no—
1004C22⋊C4—48no—
1005C22⋊C4—48no—
1006C22⋊C4—48no—
1007C22⋊C4—48no—
1008C22⋊C4—48no—
1009C22⋊C4—44no—
1010C22⋊C4—48no—
1011C22⋊C4—48no—
1012C22⋊C4—48no—
1013C22⋊C4—44no—
1014C42—24no—
1015C42—24no—
1016C42—24no—
1017C42—24no—
1018C42—24no—
1019C42—24no—
1020C42—24no—
1021C42—28no—
1022C42—24no—
1023C42—28no—
1024C42—24no—
1025C42—28no—
1026C42—28no—
1027C42—28no—
1028C42—24no—
1029C42—24no—
1030C42—44no—
1031C42—44no—
1032C42—42no—
1033C42—44no—
1034C42—44no—
1035C42C2×#4114yes—
1036C42C2×#4114yes—
1037C42C2×#4114yes—
1038C42C2×#4114yes—
1039C23—22no—
1040C23—21no—
1041C23—22no—
1042C23—21no—
1043C23—21no—
1044C23—22no—
1045C23—21no—
1046C23—22no—
1047C23—22no—
1048C23—22no—
1049C23—21no—
1050C23—21no—
1051C23—22no—
1052C23—28no—
1053C23—22no—
1054C23—28no—
1055C23—28no—
1056C23—22no—
1057C23—28no—
1058C23—22no—
1059C23—22no—
1060C23—22no—
1061C23—22no—
1062C23—28no—
1063C23—28no—
1064C23—28no—
1065C23—416no—
1066C23—88no—
1067C23—88no—
1068C23—164no—
1069C23—164no—
1070C23—164no—
1071C23—164no—
1072C23C22×#4112yes—
1073C23C2×H(5,𝔽2)14yes—
1074C23C2611yescharacteristic
1075Q8—28no—
1076Q8—44no—
1077D4—28no—
1078D4—48no—
1079D4—416no—
1080D4—48no—
1081D4—416no—
1082D4—416no—
1083D4—416no—
1084D4—44no—
1085D4—88no—
1086D4—88no—
1087D4—88no—
1088D4—816no—
1089D4—816no—
1090D4—168no—
1091D4—168no—
1092C2×C4—22no—
1093C2×C4—22no—
1094C2×C4—21no—
1095C2×C4—21no—
1096C2×C4—21no—
1097C2×C4—22no—
1098C2×C4—22no—
1099C2×C4—21no—
1100C2×C4—21no—
1101C2×C4—21no—
1102C2×C4—28no—
1103C2×C4—28no—
1104C2×C4—28no—
1105C2×C4—22no—
1106C2×C4—22no—
1107C2×C4—22no—
1108C2×C4—22no—
1109C2×C4—22no—
1110C2×C4—22no—
1111C2×C4—22no—
1112C2×C4—24no—
1113C2×C4—24no—
1114C2×C4—22no—
1115C2×C4—24no—
1116C2×C4—22no—
1117C2×C4—24no—
1118C2×C4—22no—
1119C2×C4—24no—
1120C2×C4—24no—
1121C2×C4—24no—
1122C2×C4—24no—
1123C2×C4—22no—
1124C2×C4—22no—
1125C2×C4—24no—
1126C2×C4—24no—
1127C2×C4—24no—
1128C2×C4—22no—
1129C2×C4—22no—
1130C2×C4—24no—
1131C2×C4—22no—
1132C2×C4—22no—
1133C2×C4—22no—
1134C2×C4—22no—
1135C2×C4—22no—
1136C2×C4—24no—
1137C2×C4—24no—
1138C2×C4—22no—
1139C2×C4—22no—
1140C2×C4—22no—
1141C2×C4—22no—
1142C2×C4—24no—
1143C2×C4—24no—
1144C2×C4—24no—
1145C2×C4—24no—
1146C2×C4—22no—
1147C2×C4—48no—
1148C2×C4—48no—
1149C2×C4—48no—
1150C2×C4—48no—
1151C2×C4—48no—
1152C2×C4—48no—
1153C2×C4—816no—
1154C2×C4—88no—
1155C2×C4—88no—
1156C2×C4—168no—
1157C2×C4C22×#4112yes—
1158C2×C4C22×#4112yes—
1159C2×C4C22×#4112yes—
1160C2×C4C22×#4112yes—
1161C2×C4C22×#4112yes—
1162C2×C4C22×#4112yes—
1163C2×C4C2×H(5,𝔽2)14yes—
1164C2×C4C2×H(5,𝔽2)14yes—
1165C2×C4C2×H(5,𝔽2)12yes—
1166C2×C4C2×H(5,𝔽2)12yes—
1167C2×C4C2×H(5,𝔽2)12yes—
1168C2×C4#58512yes—
1169C2×C4#58512yes—
1170C2×C4#58512yes—
1171C22—24no—
1172C22—24no—
1173C22—22no—
1174C22—22no—
1175C22—24no—
1176C22—22no—
1177C22—42no—
1178C22—41no—
1179C22—41no—
1180C22—41no—
1181C22—42no—
1182C22—41no—
1183C22—42no—
1184C22—42no—
1185C22—48no—
1186C22—48no—
1187C22—42no—
1188C22—48no—
1189C22—42no—
1190C22—42no—
1191C22—42no—
1192C22—48no—
1193C22—42no—
1194C22—42no—
1195C22—48no—
1196C22—48no—
1197C22—42no—
1198C22—48no—
1199C22—1616no—
1200C22C23×#4111yescharacteristic
1201C22C22×H(5,𝔽2)11yescharacteristic
1202C22C22×H(5,𝔽2)11yescharacteristic
1203C22C22×H(5,𝔽2)11yescharacteristic
1204C22C2×#58511yescharacteristic
1205C22C2×#58511yescharacteristic
1206C22C2×#58511yescharacteristic
1207C4—24no—
1208C4—22no—
1209C4—22no—
1210C4—24no—
1211C4—22no—
1212C4—44no—
1213C4—42no—
1214C4—44no—
1215C4—44no—
1216C4—42no—
1217C4—44no—
1218C4—44no—
1219C4—44no—
1220C4—42no—
1221C4—42no—
1222C4—42no—
1223C4—42no—
1224C4—42no—
1225C4—42no—
1226C4#346014yes—
1227C4#349414yes—
1228C4#349414yes—
1229C2—44no—
1230C2—42no—
1231C2—82no—
1232C2—88no—
1233C2C2×#346011yescharacteristic
1234C2C2×#349411yescharacteristic
1235C2C2×#349411yescharacteristic
1236C2#6301411yescharacteristic
1237C2#6301411yescharacteristic
1238C2#6301411yescharacteristic
1239C2#6303611yescharacteristic
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. #42974C2semidirect
2. #42051C2semidirect
3. #39736C2semidirect
4. #39416C2semidirect
5. #39352C2semidirect
6. #39147C2semidirect
7. #39046C2semidirect
8. #38942C2semidirect
9. #38202C2semidirect
10. #37751C2semidirect
11. #37643C2semidirect
12. #37625C2semidirect
13. #36596C2semidirect
14. #36472C2semidirect
15. #36302C2semidirect
16. #36117C2semidirect
17. #35823C2semidirect
18. #35272C2semidirect
19. #35272C2semidirect
20. #35186C2semidirect
21. #35171C2semidirect
22. #34976C2semidirect
23. #34934C2semidirect
24. #34210C2semidirect
25. #34129C2semidirect
26. #34127C2semidirect
27. C2×#553C22semidirect
28. C2×#540C22semidirect
32. C2×#529C22semidirect
36. #2861C22semidirect
37. #2860C22semidirect
42. #2856C22semidirect
43. #2854C22semidirect
44. #2845C22semidirect
45. #2829C22semidirect
46. #2761C22semidirect
47. #2757C22semidirect
48. #2756C22semidirect
50. #2706C22semidirect
51. #2701C22semidirect
52. #2699C22semidirect
54. #2691C22semidirect
57. #2671C22semidirect
58. #2661C22semidirect
59. #2651C22semidirect
60. #2644C22semidirect
61. #2641C22semidirect
62. #2630C22semidirect
66. #2624C22semidirect
67. #2620C22semidirect
70. #2609C22semidirect
71. #2603C22semidirect
72. #2582C22semidirect
73. #2566C22semidirect
74. #2554C22semidirect
75. #2554C22semidirect
76. #2552C22semidirect
77. #2552C22semidirect
78. #2552C22semidirect
79. #2552C22semidirect
80. #2552C22semidirect
81. #2552C22semidirect
86. #2543C22semidirect
91. #2538C22semidirect
92. #2538C22semidirect
93. #2537C22semidirect
94. #2537C22semidirect
96. #2531C22semidirect
97. #2513C22semidirect
98. #2512C22semidirect
99. #2512C22semidirect
100. #2512C22semidirect
101. #2501C22semidirect
102. #2500C22semidirect
103. #2490C22semidirect
104. #2490C22semidirect
105. #2490C22semidirect
106. #2490C22semidirect
110. #2479C22semidirect
111. #2476C22semidirect
112. #2468C22semidirect
113. #2464C22semidirect
114. #2464C22semidirect
115. #2454C22semidirect
116. #2454C22semidirect
117. #2448C22semidirect
118. #2447C22semidirect
119. #2445C22semidirect
120. #2445C22semidirect
121. #2428C22semidirect
122. #2428C22semidirect
123. #2427C22semidirect
124. #2426C22semidirect
125. #2425C22semidirect
127. #2422C22semidirect
128. #2422C22semidirect
129. #2422C22semidirect
130. #2420C22semidirect
131. #2416C22semidirect
132. #2414C22semidirect
141. #2392C22semidirect
146. #2363C22semidirect
147. #2361C22semidirect
148. #2355C22semidirect
149. #2355C22semidirect
152. #2354C22semidirect
153. #2354C22semidirect
154. #2354C22semidirect
157. Q8×C4⋊C4C22semidirect
158. Q8×C4⋊C4C22semidirect
159. D4×C4⋊C4C22semidirect
160. D4×C4⋊C4C22semidirect
163. #2346C22semidirect
164. #2343C22semidirect
170. #2326C22semidirect
171. #2324C22semidirect
172. #2319C22semidirect
178. C4×#127C22semidirect
179. C4×C22⋊Q8C22semidirect
180. C4×C22⋊Q8C22semidirect
181. C4×#121C22semidirect
182. C4×#121C22semidirect
183. C4×#121C22semidirect
184. #2295C22semidirect
186. #2293C22semidirect
187. #2293C22semidirect
192. #2285C22semidirect
193. #2283C22semidirect
194. C42×Q8C22semidirect
195. C42×D4C22semidirect
197. C4×#117C22semidirect
198. C2×C4×C4⋊C4C22semidirect

Maximal subgroups

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

subgroupindex
#429742
#420512
#397362
#394162
#393522
#391472
#390462
#389422
#382022
#377512
#376432
#376252
#365962
#364722
#363022
#361172
#358232
#352722
#351862
#351712
#349762
#349342
#342102
#341292
#341272