Finite Group Databasebeta

← #8429479

Subgroups — #8429479

Order 512.

4805 conjugacy classes of subgroups.

The subgroup lattice has 1151 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59817C211yesmaximal, characteristic, complemented
2#59652C212yesmaximal, complemented
3#59302C212yesmaximal, complemented
4#59230C212yesmaximal, complemented
5#53755C218yesmaximal, complemented
6#53083C214yesmaximal, complemented
7#52975C214yesmaximal, complemented
8#52962C214yesmaximal, complemented
9#42936C214yesmaximal, complemented
10#42618C214yesmaximal, complemented
11#42590C214yesmaximal, complemented
12#39736C212yesmaximal, complemented
13#39618C212yesmaximal, complemented
14#39148C212yesmaximal, complemented
15#39124C212yesmaximal, complemented
16#38958C212yesmaximal, complemented
17#38911C212yesmaximal, complemented
18#37637C212yesmaximal, complemented
19#37624C212yesmaximal, complemented
20#37620C212yesmaximal, complemented
21#36598C211yesmaximal, characteristic, complemented
22#36187C211yesmaximal, characteristic, complemented
23#36180C211yesmaximal, characteristic, complemented
24#34945C211yesmaximal, characteristic, complemented
25#34934C211yesmaximal, characteristic, complemented
26#34932C211yesmaximal, characteristic, complemented
27C2×#555C2212yes—
28C2×#554C2212yes—
29C2×D4×Q8C2212yes—
30C2×D4×Q8C2212yes—
31C2×#529C2212yes—
32C2×#529C2212yes—
33#2868C2211yescharacteristic
34#2862C2212yes—
35#2857C2212yes—
36#2856C2212yes—
37#2841C2218yes—
38#2831C2218yes—
39#2831C2218yes—
40#2830C2218yes—
41#2827C2218yes—
42#2824C2218yes—
43#2823C2218yes—
44#2793C2218yes—
45#2784C2218yes—
46#2765C2218yes—
47#2761C2218yes—
48#2750C2218yes—
49#2749C2218yes—
50#2730C2218yes—
51#2723C2218yes—
52#2700C2218yes—
53#2700C2218yes—
54#2696C2218yes—
55#2692C2218yes—
56#2692C2218yes—
57#2691C2218yes—
58#2691C2218yes—
59#2689C2218yes—
60#2688C2218yes—
61#2687C2218yes—
62#2683C2214yes—
63#2666C2218yes—
64#2660C2214yes—
65#2653C2218yes—
66#2647C2214yes—
67#2644C2214yes—
68#2637C2218yes—
69#2629C2214yes—
70#2629C2214yes—
71#2628C2214yes—
72#2625C2214yes—
73#2620C2214yes—
74#2620C2214yes—
75#2618C2218yes—
76#2582C2212yes—
77#2574C2218yes—
78#2573C2214yes—
79#2571C2211yescharacteristic
80#2571C2212yes—
81#2570C2214yes—
82#2570C2214yes—
83#2568C2211yescharacteristic
84#2568C2212yes—
85#2567C2212yes—
86#2566C2214yes—
87#2563C2212yes—
88#2563C2214yes—
89#2563C2214yes—
90#2554C2214yes—
91#2553C2214yes—
92#2552C2211yescharacteristic
93#2552C2212yes—
94#2552C2212yes—
95#2552C2211yescharacteristic
96#2551C2212yes—
97#2550C2214yes—
98#2548C2211yescharacteristic
99#2547C2211yescharacteristic
100#2547C2211yescharacteristic
101#2542C2211yescharacteristic
102#2541C2211yescharacteristic
103#2540C2214yes—
104#2538C2212yes—
105#2538C2211yescharacteristic
106#2538C2211yescharacteristic
107#2538C2212yes—
108#2537C2211yescharacteristic
109#2537C2212yes—
110#2537C2212yes—
111#2535C2214yes—
112#2514C2212yes—
113#2512C2214yes—
114#2512C2214yes—
115#2512C2212yes—
116#2511C2214yes—
117#2508C2214yes—
118#2504C2214yes—
119#2502C2214yes—
120#2500C2214yes—
121#2499C2214yes—
122#2496C2214yes—
123#2496C2212yes—
124#2494C2212yes—
125#2492C2214yes—
126#2491C2214yes—
127#2491C2214yes—
128#2490C2214yes—
129#2490C2212yes—
130#2489C2214yes—
131#2489C2212yes—
132#2481C2218yes—
133#2452C2214yes—
134#2452C2214yes—
135#2447C2214yes—
136#2447C2212yes—
137#2446C2214yes—
138#2445C2212yes—
139#2441C2214yes—
140#2440C2214yes—
141#2440C2214yes—
142#2439C2214yes—
143#2439C2214yes—
144#2436C2214yes—
145#2428C2214yes—
146#2427C2212yes—
147#2426C2218yes—
148#2426C2212yes—
149#2422C2212yes—
150#2421C2212yes—
151#2420C2214yes—
152#2420C2214yes—
153#2420C2214yes—
154#2417C2214yes—
155#2417C2214yes—
156#2417C2214yes—
157#2416C2214yes—
158#2416C2214yes—
159#2415C2214yes—
160#2409C2214yes—
161#2409C2214yes—
162#2409C2214yes—
163#2401C2214yes—
164#2395C2214yes—
165#2392C2214yes—
166#2366C2212yes—
167#2365C2212yes—
168#2363C2214yes—
169#2355C2212yes—
170#2355C2212yes—
171#2354C2212yes—
172#2354C2212yes—
173#2352C2214yes—
174D4×C4⋊C4C2212yes—
175D4×C4⋊C4C2212yes—
176#2345C2214yes—
177#2328C2214yes—
178#2324C2214yes—
179#2310C2214yes—
180C4×C4⋊Q8C2212yes—
181C4×C4⋊Q8C2211yescharacteristic
182C4×C4⋊Q8C2211yescharacteristic
183C4×#127C2212yes—
184C4×#127C2211yescharacteristic
185C4×#124C2212yes—
186C4×C22⋊Q8C2212yes—
187C4×C22⋊Q8C2212yes—
188C4×#121C2212yes—
189C4×#121C2212yes—
190#2295C2212yes—
191#2293C2212yes—
192#2285C2212yes—
193#2285C2212yes—
194C2×#384C2212yes—
195#2283C2212yes—
196C42×Q8C2211yescharacteristic
197C42×D4C2211yescharacteristic
198C42×D4C2211yescharacteristic
199C23×Q8C2314yes—
200#555—48no—
201#554—48no—
202D4×Q8—48no—
203D4×Q8—48no—
204C2×C4⋊Q8C2312yes—
205C2×C4⋊Q8C2311yescharacteristic
206C2×C4⋊Q8C2311yescharacteristic
207C2×C4⋊Q8C2314yes—
208C2×C4⋊Q8C2314yes—
209C2×C4⋊Q8C2312yes—
210C2×C4⋊Q8C2312yes—
211C2×#127C2312yes—
212C2×#127C2311yescharacteristic
213#529—48no—
214#529—48no—
215C2×#126C2314yes—
216C2×#126C2314yes—
217C2×#126C2318yes—
218C2×#125C2314yes—
219C2×#125C2312yes—
220C2×#125C2312yes—
221C2×#124C2312yes—
222C2×#124C2312yes—
223C2×#124C2318yes—
224C2×#124C2312yes—
225C2×#123C2314yes—
226C2×#123C2314yes—
227C2×C22⋊Q8C2314yes—
228C2×C22⋊Q8C2312yes—
229C2×C22⋊Q8C2314yes—
230C2×C22⋊Q8C2314yes—
231C2×C22⋊Q8C2312yes—
232C2×C22⋊Q8C2312yes—
233C2×C22⋊Q8C2312yes—
234C2×C22⋊Q8C2318yes—
235C2×C22⋊Q8C2318yes—
236C2×C22⋊Q8C2318yes—
237C2×#121C2312yes—
238C2×#121C2314yes—
239C2×#121C2314yes—
240C2×#121C2314yes—
241C2×#121C2312yes—
242C2×#121C2312yes—
243C2×#121C2312yes—
244C2×#121C2314yes—
245C2×#121C2318yes—
246C2×C4×Q8C2312yes—
247C2×C4×Q8C2312yes—
248C2×C4×Q8C2311yescharacteristic
249C2×C4×Q8C2311yescharacteristic
250C2×C4×Q8C2311yescharacteristic
251C2×C4×Q8C2314yes—
252C2×C4×D4C2312yes—
253C2×C4×D4C2311yescharacteristic
254C2×C4×D4C2312yes—
255C2×C4×D4C2311yescharacteristic
256C2×C4×D4C2311yescharacteristic
257C2×C4×D4C2311yescharacteristic
258C2×C4×D4C2311yescharacteristic
259C2×C4×D4C2314yes—
260C2×C4×D4C2312yes—
261C2×C4×D4C2314yes—
262C2×C4×D4C2314yes—
263C2×C4×D4C2314yes—
264C2×C4×D4C2314yes—
265C2×C4×D4C2314yes—
266C2×C4×D4C2311yescharacteristic
267C2×#117C2314yes—
268C2×#117C2314yes—
269C2×#117C2314yes—
270C2×#117C2314yes—
271C22×C4⋊C4C2314yes—
272C22×C4⋊C4C2314yes—
273C22×C4⋊C4C2314yes—
274C22×C42C2312yes—
275C22×C42C2312yes—
276#401C2314yes—
277#400C2318yes—
278#400C2314yes—
279#400C2318yes—
280#400C2314yes—
281#400C2318yes—
282#400C2318yes—
283#400C2314yes—
284#400C2314yes—
285#400C2318yes—
286#399C2318yes—
287#399C2314yes—
288#398C2318yes—
289#398C2318yes—
290#398C2318yes—
291#398C2318yes—
292#398C2318yes—
293#398C2314yes—
294#398C2314yes—
295#398C2318yes—
296#398C2318yes—
297#398C2318yes—
298#397C2314yes—
299#397C2318yes—
300#397C2314yes—
301#397C2318yes—
302#397C2314yes—
303#397C2314yes—
304#397C2314yes—
305#397C2318yes—
306#397C2318yes—
307#397C2318yes—
308#397C2318yes—
309#397C2314yes—
310#397C2314yes—
311#397C2318yes—
312#396C2318yes—
313#396C2318yes—
314#396C2314yes—
315#396C2318yes—
316#396C2318yes—
317#396C2318yes—
318#396C2318yes—
319#396C2314yes—
320#396C2314yes—
321#396C2318yes—
322#396C2318yes—
323#396C2318yes—
324#395C2318yes—
325#395C2318yes—
326#395C2318yes—
327#395C2318yes—
328#394C2318yes—
329#394C2318yes—
330#394C2318yes—
331#394C2314yes—
332#394C2314yes—
333#394C2318yes—
334#394C2318yes—
335#394C2314yes—
336#394C2314yes—
337#394C2314yes—
338#394C2318yes—
339#393C2318yes—
340#393C2318yes—
341#393C2318yes—
342#393C2318yes—
343#393C2318yes—
344#393C2318yes—
345#392C2318yes—
346#392C2314yes—
347#391C2314yes—
348#391C2312yes—
349#391C2312yes—
350#391C2312yes—
351#391C2312yes—
352#391C2314yes—
353#391C2318yes—
354#391C2314yes—
355#391C2318yes—
356#391C2314yes—
357#391C2314yes—
358#391C2312yes—
359#391C2312yes—
360#391C2314yes—
361#391C2314yes—
362#391C2312yes—
363#390C2312yes—
364#390C2312yes—
365#390C2314yes—
366#390C2314yes—
367#390C2312yes—
368#390C2312yes—
369#390C2312yes—
370#390C2312yes—
371#390C2314yes—
372#390C2318yes—
373#390C2318yes—
374#390C2312yes—
375#390C2314yes—
376#390C2314yes—
377#390C2312yes—
378#390C2314yes—
379#390C2314yes—
380#390C2312yes—
381#390C2312yes—
382#389C2312yes—
383#389C2314yes—
384#389C2312yes—
385#389C2314yes—
386#389C2312yes—
387#389C2312yes—
388#389C2314yes—
389#389C2314yes—
390#389C2312yes—
391#389C2314yes—
392#389C2314yes—
393#389C2312yes—
394#389C2312yes—
395#389C2314yes—
396#389C2314yes—
397#389C2314yes—
398#389C2312yes—
399#389C2312yes—
400#389C2312yes—
401#389C2312yes—
402#389C2318yes—
403#389C2312yes—
404#388C2314yes—
405#388C2314yes—
406#388C2314yes—
407#388C2318yes—
408#388C2314yes—
409#388C2318yes—
410#388C2318yes—
411#388C2318yes—
412#388C2318yes—
413#388C2314yes—
414#388C2314yes—
415#387C2318yes—
416#387C2318yes—
417#387C2318yes—
418#387C2318yes—
419#387C2314yes—
420#387C2314yes—
421#387C2314yes—
422#387C2318yes—
423#387C2318yes—
424#387C2318yes—
425#387C2314yes—
426#386C2318yes—
427#386C2318yes—
428#386C2318yes—
429#386C2318yes—
430#386C2318yes—
431#386C2318yes—
432#386C2318yes—
433#386C2318yes—
434#386C2318yes—
435#386C2314yes—
436#386C2314yes—
437#385C2318yes—
438#385C2318yes—
439#385C2318yes—
440#385C2318yes—
441#385C2314yes—
442#385C2318yes—
443#385C2314yes—
444#384C2312yes—
445#384C2311yescharacteristic
446#384C2311yescharacteristic
447#384C2311yescharacteristic
448#384C2312yes—
449#384C2314yes—
450#384C2314yes—
451#384C2312yes—
452#384C2314yes—
453#384C2312yes—
454#384C2312yes—
455#384C2312yes—
456#384C2312yes—
457#383C2314yes—
458#382C2314yes—
459#382C2314yes—
460#382C2318yes—
461#382C2314yes—
462#382C2312yes—
463#382C2312yes—
464#382C2314yes—
465#382C2312yes—
466#382C2314yes—
467#381C2318yes—
468#381C2318yes—
469#381C2314yes—
470#380C2312yes—
471#380C2312yes—
472#380C2318yes—
473#380C2318yes—
474#380C2314yes—
475#380C2314yes—
476#380C2314yes—
477#380C2314yes—
478#380C2314yes—
479#380C2314yes—
480#380C2314yes—
481#380C2312yes—
482#380C2314yes—
483#380C2312yes—
484#380C2312yes—
485#380C2312yes—
486#380C2312yes—
487#380C2312yes—
488C4×C4⋊C4C2312yes—
489C4×C4⋊C4C2314yes—
490C4×C4⋊C4C2312yes—
491C4×C4⋊C4C2312yes—
492C4×C4⋊C4C2312yes—
493C4×C4⋊C4C2314yes—
494C4×C4⋊C4C2311yescharacteristic
495C4×C4⋊C4C2314yes—
496C4×C4⋊C4C2314yes—
497C4×C4⋊C4C2311yescharacteristic
498C4×C4⋊C4C2311yescharacteristic
499C4×C4⋊C4C2312yes—
500C4×C4⋊C4C2314yes—
501C4×C4⋊C4C2314yes—
502C4×C4⋊C4C2311yescharacteristic
503C4×C4⋊C4C2311yescharacteristic
504C4×C4⋊C4C2312yes—
505C4×C4⋊C4C2314yes—
506C4×C4⋊C4C2311yescharacteristic
507C4×C4⋊C4C2311yescharacteristic
508C4×C4⋊C4C2312yes—
509C4×C4⋊C4C2311yescharacteristic
510C4×C4⋊C4C2311yescharacteristic
511C4×C22⋊C4C2312yes—
512C4×C22⋊C4C2318yes—
513C4×C22⋊C4C2314yes—
514C4×C22⋊C4C2314yes—
515C4×C22⋊C4C2312yes—
516C4×C22⋊C4C2314yes—
517C4×C22⋊C4C2312yes—
518C4×C22⋊C4C2312yes—
519C4×C22⋊C4C2312yes—
520C4×C22⋊C4C2314yes—
521C4×C22⋊C4C2312yes—
522#376C2314yes—
523C43C2311yescharacteristic
524C43C2312yes—
525C22×Q8—48no—
526C22×Q8—48no—
527C22×Q8—48no—
528C22×Q8C2411yescharacteristic
529C22×Q8C2412yes—
530C22×Q8C2412yes—
531C22×Q8C2414yes—
532C22×Q8C2418yes—
533C22×D4C2411yescharacteristic
534C22×D4C2412yes—
535C22×D4C2412yes—
536C22×D4C2411yescharacteristic
537C22×D4C2414yes—
538C22×D4C2414yes—
539C22×D4C2412yes—
540C22×D4C2414yes—
541C22×D4C2418yes—
542C23×C4C2412yes—
543C23×C4C2412yes—
544C23×C4C2414yes—
545C23×C4C2412yes—
546C23×C4C2412yes—
547C23×C4C2412yes—
548C23×C4C2412yes—
549C23×C4C2418yes—
550C23×C4C2418yes—
551C4⋊Q8—24no—
552C4⋊Q8—24no—
553C4⋊Q8—28no—
554C4⋊Q8—44no—
555C4⋊Q8—48no—
556C4⋊Q8—48no—
557C4⋊Q8—82no—
558#127—28no—
559#127—24no—
560#126—48no—
561#126—48no—
562#126—88no—
563#125—44no—
564#125—44no—
565#125—48no—
566#124—44no—
567#124—44no—
568#124—44no—
569#124—416no—
570#123—48no—
571#123—48no—
572C22⋊Q8—416no—
573C22⋊Q8—416no—
574C22⋊Q8—416no—
575C22⋊Q8—44no—
576C22⋊Q8—44no—
577C22⋊Q8—44no—
578C22⋊Q8—44no—
579C22⋊Q8—48no—
580C22⋊Q8—48no—
581C22⋊Q8—48no—
582#121—28no—
583#121—48no—
584#121—44no—
585#121—44no—
586#121—44no—
587#121—48no—
588#121—48no—
589#121—88no—
590#121—84no—
591C4×Q8—24no—
592C4×Q8—28no—
593C4×Q8—28no—
594C4×Q8—24no—
595C4×Q8—42no—
596C4×Q8—84no—
597C4×D4—24no—
598C4×D4—24no—
599C4×D4—28no—
600C4×D4—28no—
601C4×D4—24no—
602C4×D4—24no—
603C4×D4—24no—
604C4×D4—42no—
605C4×D4—48no—
606C4×D4—48no—
607C4×D4—48no—
608C4×D4—44no—
609C4×D4—48no—
610C4×D4—48no—
611C4×D4—48no—
612#117—48no—
613#117—48no—
614#117—48no—
615#117—48no—
616C2×C4⋊C4—48no—
617C2×C4⋊C4—48no—
618C2×C4⋊C4—84no—
619C2×C4⋊C4C2412yes—
620C2×C4⋊C4C2412yes—
621C2×C4⋊C4C2414yes—
622C2×C4⋊C4C2414yes—
623C2×C4⋊C4C2411yescharacteristic
624C2×C4⋊C4C2412yes—
625C2×C4⋊C4C2414yes—
626C2×C4⋊C4C2412yes—
627C2×C4⋊C4C2412yes—
628C2×C4⋊C4C2411yescharacteristic
629C2×C4⋊C4C2411yescharacteristic
630C2×C4⋊C4C2412yes—
631C2×C4⋊C4C2411yescharacteristic
632C2×C4⋊C4C2411yescharacteristic
633C2×C4⋊C4C2411yescharacteristic
634C2×C4⋊C4C2411yescharacteristic
635C2×C4⋊C4C2411yescharacteristic
636C2×C4⋊C4C2412yes—
637C2×C4⋊C4C2414yes—
638C2×C4⋊C4C2414yes—
639C2×C4⋊C4C2412yes—
640C2×C4⋊C4C2411yescharacteristic
641C2×C4⋊C4C2412yes—
642C2×C4⋊C4C2412yes—
643C2×C4⋊C4C2412yes—
644C2×C4⋊C4C2412yes—
645C2×C4⋊C4C2412yes—
646C2×C4⋊C4C2418yes—
647C2×C4⋊C4C2418yes—
648C2×C4⋊C4C2414yes—
649C2×C4⋊C4C2418yes—
650C2×C4⋊C4C2414yes—
651C2×C4⋊C4C2414yes—
652C2×C4⋊C4C2414yes—
653C2×C4⋊C4C2414yes—
654C2×C4⋊C4C2414yes—
655C2×C4⋊C4C2414yes—
656C2×C4⋊C4C2412yes—
657C2×C4⋊C4C2414yes—
658C2×C4⋊C4C2412yes—
659C2×C4⋊C4C2418yes—
660C2×C4⋊C4C2412yes—
661C2×C4⋊C4C2414yes—
662C2×C4⋊C4C2418yes—
663C2×C4⋊C4C2418yes—
664C2×C4⋊C4C2418yes—
665C2×C4⋊C4C2414yes—
666C2×C4⋊C4C2414yes—
667C2×C4⋊C4C2414yes—
668C2×C4⋊C4C2414yes—
669C2×C4⋊C4C2414yes—
670C2×C22⋊C4C2412yes—
671C2×C22⋊C4C2414yes—
672C2×C22⋊C4C2414yes—
673C2×C22⋊C4C2412yes—
674C2×C22⋊C4C2412yes—
675C2×C22⋊C4C2412yes—
676C2×C22⋊C4C2412yes—
677C2×C22⋊C4C2414yes—
678C2×C22⋊C4C2418yes—
679C2×C22⋊C4C2418yes—
680C2×C22⋊C4C2414yes—
681C2×C22⋊C4C2414yes—
682C2×C22⋊C4C2414yes—
683C2×C22⋊C4C2414yes—
684C2×C22⋊C4C2418yes—
685C2×C22⋊C4C2418yes—
686C2×C22⋊C4C2418yes—
687C2×C22⋊C4C2414yes—
688C2×C22⋊C4C2414yes—
689C2×C22⋊C4C2414yes—
690C2×C22⋊C4C2414yes—
691C2×C22⋊C4C2414yes—
692C2×C22⋊C4C2412yes—
693C2×C22⋊C4C2414yes—
694C2×C22⋊C4C2414yes—
695C2×C22⋊C4C2414yes—
696C2×C22⋊C4C2418yes—
697C2×C22⋊C4C2418yes—
698C2×C22⋊C4C2414yes—
699C2×C22⋊C4C2418yes—
700C2×C22⋊C4C2414yes—
701C2×C22⋊C4C2414yes—
702C2×C22⋊C4C2414yes—
703C2×C22⋊C4C2414yes—
704C2×C22⋊C4C2414yes—
705C2×C42—28no—
706C2×C42—28no—
707C2×C42C2412yes—
708C2×C42C2412yes—
709C2×C42C2412yes—
710C2×C42C2414yes—
711C2×C42C2411yescharacteristic
712C2×C42C2414yes—
713C2×C42C2412yes—
714C2×C42C2411yescharacteristic
715C2×C42C2411yescharacteristic
716C2×C42C2412yes—
717C2×C42C2412yes—
718C2×C42C2412yes—
719C2×C42C2412yes—
720C2×C42C2412yes—
721C2×C42C2412yes—
722C2×C42C2418yes—
723C2×C42C2412yes—
724C2×C42C2418yes—
725C2×C42C2412yes—
726C2×C42C2411yescharacteristic
727C2×C42C2411yescharacteristic
728C2×C42C2411yescharacteristic
729C2×C42C2411yescharacteristic
730#95C2414yes—
731#95C2414yes—
732#95C2414yes—
733#95C2414yes—
734#95C2414yes—
735#95C2412yes—
736#95C2412yes—
737#95C2412yes—
738#95C2412yes—
739#95C2412yes—
740#95C2412yes—
741#95C2414yes—
742#95C2414yes—
743#95C2418yes—
744#95C2414yes—
745#95C2414yes—
746#95C2414yes—
747#95C2414yes—
748#95C2414yes—
749#95C2412yes—
750#95C2412yes—
751#95C2412yes—
752#95C2418yes—
753#95C2418yes—
754#95C2414yes—
755#95C2414yes—
756#95C2414yes—
757#95C2418yes—
758#95C2414yes—
759#95C2414yes—
760#95C2418yes—
761#95C2414yes—
762#95C2414yes—
763#95C2414yes—
764#95C2418yes—
765#95C2418yes—
766#95C2418yes—
767#95C2418yes—
768#95C2418yes—
769#95C2418yes—
770C24C2512yes—
771C24C2514yes—
772C24C2512yes—
773C2×Q8—22no—
774C2×Q8—24no—
775C2×Q8—24no—
776C2×Q8—24no—
777C2×Q8—24no—
778C2×Q8—28no—
779C2×Q8—22no—
780C2×Q8—22no—
781C2×Q8—24no—
782C2×Q8—24no—
783C2×Q8—44no—
784C2×Q8—48no—
785C2×Q8—48no—
786C2×Q8—44no—
787C2×Q8—48no—
788C2×Q8—832no—
789C2×D4—28no—
790C2×D4—28no—
791C2×D4—28no—
792C2×D4—22no—
793C2×D4—24no—
794C2×D4—24no—
795C2×D4—22no—
796C2×D4—22no—
797C2×D4—22no—
798C2×D4—24no—
799C2×D4—24no—
800C2×D4—24no—
801C2×D4—24no—
802C2×D4—22no—
803C2×D4—24no—
804C2×D4—44no—
805C2×D4—44no—
806C2×D4—42no—
807C2×D4—44no—
808C2×D4—44no—
809C2×D4—42no—
810C2×D4—44no—
811C2×D4—44no—
812C2×D4—48no—
813C2×D4—48no—
814C2×D4—48no—
815C2×D42−1+414yes—
816C22×C4—24no—
817C22×C4—24no—
818C22×C4—24no—
819C22×C4—24no—
820C22×C4—24no—
821C22×C4—24no—
822C22×C4—24no—
823C22×C4—28no—
824C22×C4—28no—
825C22×C4—24no—
826C22×C4—24no—
827C22×C4—24no—
828C22×C4—24no—
829C22×C4—24no—
830C22×C4—24no—
831C22×C4—28no—
832C22×C4—24no—
833C22×C4—24no—
834C22×C4—42no—
835C22×C4—48no—
836C22×C4—48no—
837C22×C4—42no—
838C22×C4—42no—
839C22×C4—48no—
840C22×C4—48no—
841C22×C4—48no—
842C22×C4—48no—
843C22×C4C2512yes—
844C22×C4C2512yes—
845C22×C4C2511yescharacteristic
846C22×C4C2512yes—
847C22×C4C2512yes—
848C22×C4C2512yes—
849C22×C4C2512yes—
850C22×C4C2512yes—
851C22×C4C2512yes—
852C22×C4C2514yes—
853C22×C4C2514yes—
854C22×C4C2514yes—
855C22×C4C2512yes—
856C22×C4C2518yes—
857C22×C4C2514yes—
858C22×C4C2514yes—
859C22×C4C2512yes—
860C22×C4C2511yescharacteristic
861C22×C4C2511yescharacteristic
862C22×C4C2511yescharacteristic
863C22×C4C2511yescharacteristic
864C22×C4C2511yescharacteristic
865C22×C4C2511yescharacteristic
866C4⋊C4—24no—
867C4⋊C4—28no—
868C4⋊C4—22no—
869C4⋊C4—24no—
870C4⋊C4—28no—
871C4⋊C4—22no—
872C4⋊C4—24no—
873C4⋊C4—22no—
874C4⋊C4—24no—
875C4⋊C4—24no—
876C4⋊C4—22no—
877C4⋊C4—24no—
878C4⋊C4—28no—
879C4⋊C4—28no—
880C4⋊C4—24no—
881C4⋊C4—24no—
882C4⋊C4—24no—
883C4⋊C4—22no—
884C4⋊C4—22no—
885C4⋊C4—22no—
886C4⋊C4—24no—
887C4⋊C4—24no—
888C4⋊C4—24no—
889C4⋊C4—28no—
890C4⋊C4—22no—
891C4⋊C4—22no—
892C4⋊C4—48no—
893C4⋊C4—48no—
894C4⋊C4—42no—
895C4⋊C4—48no—
896C4⋊C4—44no—
897C4⋊C4—44no—
898C4⋊C4—44no—
899C4⋊C4—44no—
900C4⋊C4—44no—
901C4⋊C4—42no—
902C4⋊C4—44no—
903C4⋊C4—44no—
904C4⋊C4—44no—
905C4⋊C4—42no—
906C4⋊C4—42no—
907C4⋊C4—48no—
908C4⋊C4—44no—
909C4⋊C4—44no—
910C4⋊C4—44no—
911C4⋊C4—48no—
912C4⋊C4—48no—
913C4⋊C4—48no—
914C4⋊C4—44no—
915C4⋊C4—44no—
916C4⋊C4—44no—
917C22⋊C4—24no—
918C22⋊C4—28no—
919C22⋊C4—24no—
920C22⋊C4—28no—
921C22⋊C4—28no—
922C22⋊C4—24no—
923C22⋊C4—24no—
924C22⋊C4—24no—
925C22⋊C4—48no—
926C22⋊C4—48no—
927C22⋊C4—44no—
928C22⋊C4—44no—
929C22⋊C4—44no—
930C22⋊C4—44no—
931C22⋊C4—42no—
932C22⋊C4—44no—
933C22⋊C4—44no—
934C22⋊C4—44no—
935C22⋊C4—48no—
936C22⋊C4—48no—
937C22⋊C4—48no—
938C22⋊C4—44no—
939C22⋊C4—44no—
940C22⋊C4—44no—
941C22⋊C4—44no—
942C22⋊C4—44no—
943C22⋊C4—48no—
944C22⋊C4—44no—
945C22⋊C4—48no—
946C22⋊C4—48no—
947C22⋊C4—44no—
948C22⋊C4—44no—
949C22⋊C4—44no—
950C22⋊C4—44no—
951C22⋊C4—44no—
952C42—24no—
953C42—24no—
954C42—24no—
955C42—24no—
956C42—28no—
957C42—28no—
958C42—24no—
959C42—24no—
960C42—24no—
961C42—22no—
962C42—24no—
963C42—24no—
964C42—22no—
965C42—24no—
966C42—22no—
967C42—48no—
968C42—42no—
969C42—42no—
970C42—48no—
971C42—41no—
972C42H(5,𝔽2)14yes—
973C42H(5,𝔽2)14yes—
974C422−1+414yes—
975C23—22no—
976C23—22no—
977C23—22no—
978C23—22no—
979C23—22no—
980C23—22no—
981C23—22no—
982C23—24no—
983C23—24no—
984C23—22no—
985C23—22no—
986C23—22no—
987C23—24no—
988C23—24no—
989C23—22no—
990C23—24no—
991C23—24no—
992C23—22no—
993C23—24no—
994C23—22no—
995C23C2×2−1+414yes—
996C23C2611yescharacteristic
997Q8—48no—
998Q8—48no—
999Q8—44no—
1000Q8—88no—
1001Q8—816no—
1002D4—28no—
1003D4—44no—
1004D4—48no—
1005D4—48no—
1006D4—84no—
1007D4—88no—
1008D4—88no—
1009D4—88no—
1010D4—168no—
1011C2×C4—21no—
1012C2×C4—21no—
1013C2×C4—21no—
1014C2×C4—21no—
1015C2×C4—21no—
1016C2×C4—21no—
1017C2×C4—22no—
1018C2×C4—22no—
1019C2×C4—22no—
1020C2×C4—22no—
1021C2×C4—24no—
1022C2×C4—24no—
1023C2×C4—24no—
1024C2×C4—22no—
1025C2×C4—24no—
1026C2×C4—22no—
1027C2×C4—24no—
1028C2×C4—28no—
1029C2×C4—22no—
1030C2×C4—24no—
1031C2×C4—22no—
1032C2×C4—24no—
1033C2×C4—24no—
1034C2×C4—22no—
1035C2×C4—22no—
1036C2×C4—22no—
1037C2×C4—21no—
1038C2×C4—22no—
1039C2×C4—22no—
1040C2×C4—22no—
1041C2×C4—22no—
1042C2×C4—22no—
1043C2×C4—22no—
1044C2×C4—22no—
1045C2×C4—24no—
1046C2×C4—21no—
1047C2×C4—22no—
1048C2×C4—22no—
1049C2×C4—21no—
1050C2×C4—22no—
1051C2×C4—22no—
1052C2×C4—22no—
1053C2×C4—22no—
1054C2×C4—22no—
1055C2×C4—22no—
1056C2×C4—24no—
1057C2×C4—24no—
1058C2×C4—24no—
1059C2×C4—28no—
1060C2×C4—24no—
1061C2×C4—22no—
1062C2×C4—24no—
1063C2×C4—22no—
1064C2×C4—28no—
1065C2×C4—22no—
1066C2×C4—24no—
1067C2×C4—22no—
1068C2×C4—48no—
1069C2×C4—48no—
1070C2×C4—416no—
1071C2×C4—48no—
1072C2×C4—48no—
1073C2×C4—48no—
1074C2×C4—84no—
1075C2×C4—816no—
1076C2×C4—168no—
1077C2×C4C2×H(5,𝔽2)12yes—
1078C2×C4C2×H(5,𝔽2)12yes—
1079C2×C4C2×H(5,𝔽2)12yes—
1080C2×C4C2×H(5,𝔽2)12yes—
1081C2×C4C2×H(5,𝔽2)12yes—
1082C2×C4C2×H(5,𝔽2)12yes—
1083C2×C4C2×2−1+412yes—
1084C2×C4C2×2−1+412yes—
1085C2×C4C2×2−1+412yes—
1086C2×C4C2×2−1+412yes—
1087C2×C4#58512yes—
1088C2×C4#58512yes—
1089C22—24no—
1090C22—24no—
1091C22—24no—
1092C22—42no—
1093C22—42no—
1094C22—42no—
1095C22—42no—
1096C22—42no—
1097C22—44no—
1098C22—44no—
1099C22—42no—
1100C22—42no—
1101C22—44no—
1102C22—44no—
1103C22—42no—
1104C22—42no—
1105C22—44no—
1106C22—42no—
1107C22—44no—
1108C22—42no—
1109C22—44no—
1110C22C22×H(5,𝔽2)11yescharacteristic
1111C22C22×H(5,𝔽2)11yescharacteristic
1112C22C22×2−1+411yescharacteristic
1113C22C22×2−1+411yescharacteristic
1114C22C2×#58511yescharacteristic
1115C22C2×#58511yescharacteristic
1116C22H(7,𝔽2)11yescharacteristic
1117C4—22no—
1118C4—22no—
1119C4—22no—
1120C4—42no—
1121C4—42no—
1122C4—44no—
1123C4—44no—
1124C4—44no—
1125C4—42no—
1126C4—42no—
1127C4—42no—
1128C4—41no—
1129C4—42no—
1130C4—42no—
1131C4—42no—
1132C4—42no—
1133C4—44no—
1134C4—42no—
1135C4—44no—
1136C4—48no—
1137C4#354614yes—
1138C4#354714yes—
1139C4#355214yes—
1140C2—44no—
1141C2—82no—
1142C2—84no—
1143C2C2×#355211yescharacteristic
1144C2C2×#354611yescharacteristic
1145C2C2×#354711yescharacteristic
1146C2#6292911yescharacteristic
1147C2#6294411yescharacteristic
1148C2#6296111yescharacteristic
1149C2#6302511yescharacteristic
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. #59817C2semidirect
2. #59652C2semidirect
3. #59302C2semidirect
4. #59230C2semidirect
5. #53755C2semidirect
6. #53083C2semidirect
7. #52975C2semidirect
8. #52962C2semidirect
9. #42936C2semidirect
10. #42618C2semidirect
11. #42590C2semidirect
12. #39736C2semidirect
13. #39618C2semidirect
14. #39148C2semidirect
15. #39124C2semidirect
16. #38958C2semidirect
17. #38911C2semidirect
18. #37637C2semidirect
19. #37624C2semidirect
20. #37620C2semidirect
21. #36598C2semidirect
22. #36187C2semidirect
23. #36180C2semidirect
24. #34945C2semidirect
25. #34934C2semidirect
26. #34932C2semidirect

Maximal subgroups

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

subgroupindex
#598172
#596522
#593022
#592302
#537552
#530832
#529752
#529622
#429362
#426182
#425902
#397362
#396182
#391482
#391242
#389582
#389112
#376372
#376242
#376202
#365982
#361872
#361802
#349452
#349342
#349322