Finite Group Databasebeta

← #7715028

Subgroups — #7715028

Order 512.

4716 conjugacy classes of subgroups.

The subgroup lattice has 1418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#51969C214yesmaximal, complemented
2#51954C214yesmaximal, complemented
3#51732C214yesmaximal, complemented
4#51702C214yesmaximal, complemented
5#46700C214yesmaximal, complemented
6#46687C214yesmaximal, complemented
7#46684C214yesmaximal, complemented
8#46581C214yesmaximal, complemented
9#39515C212yesmaximal, complemented
10#39502C212yesmaximal, complemented
11#39381C212yesmaximal, complemented
12#39377C212yesmaximal, complemented
13#39273C212yesmaximal, complemented
14#39272C212yesmaximal, complemented
15#39257C212yesmaximal, complemented
16#39256C212yesmaximal, complemented
17#37519C211yesmaximal, characteristic, complemented
18#37515C211yesmaximal, characteristic, complemented
19#37380C211yesmaximal, characteristic, complemented
20#37283C211yesmaximal, characteristic, complemented
21#37271C212yesmaximal, complemented
22#35331C211yesmaximal, characteristic, complemented
23#35284C211yesmaximal, characteristic, complemented
24#35260C212yesmaximal, complemented
25#35258C212yesmaximal, complemented
26#34422C212yesmaximal, complemented
27#34065C211yesmaximal, characteristic, complemented
28C2×#542C2212yes—
29C2×#542C2212yes—
30C2×#542C2212yescomplemented
31C2×#525C2211yescharacteristic
32C2×C4×#41C2211yescharacteristic
33C22×#117C2211yescharacteristic
34#2868C2211yescharacteristic, complemented
35#2862C2211yescharacteristic, complemented
36#2859C2211yescharacteristic, complemented
37#2858C2211yescharacteristic, complemented
38#2857C2212yes—
39#2855C2212yescomplemented
40#2854C2212yescomplemented
41#2850C2212yes—
42#2848C2212yes—
43#2847C2212yes—
44#2827C2214yes—
45#2825C2214yes—
46#2808C2214yes—
47#2803C2214yes—
48#2803C2214yes—
49#2798C2214yes—
50#2798C2214yescomplemented
51#2796C2214yes—
52#2793C2214yes—
53#2790C2214yescomplemented
54#2787C2214yes—
55#2783C2214yescomplemented
56#2783C2214yescomplemented
57#2778C2214yescomplemented
58#2776C2214yescomplemented
59#2773C2214yescomplemented
60#2768C2214yes—
61#2765C2214yes—
62#2759C2214yes—
63#2759C2214yescomplemented
64#2757C2214yes—
65#2756C2214yes—
66#2756C2214yes—
67#2754C2214yescomplemented
68#2752C2214yes—
69#2751C2214yescomplemented
70#2749C2214yes—
71#2746C2214yescomplemented
72#2735C2214yes—
73#2733C2214yes—
74#2732C2214yescomplemented
75#2727C2214yescomplemented
76#2724C2214yescomplemented
77#2723C2214yes—
78#2718C2214yes—
79#2718C2214yescomplemented
80#2714C2214yes—
81#2710C2214yes—
82#2710C2214yes—
83#2708C2214yes—
84#2706C2214yes—
85#2692C2214yes—
86#2688C2214yes—
87#2682C2214yes—
88#2678C2214yes—
89#2678C2214yes—
90#2676C2214yes—
91#2674C2214yes—
92#2674C2214yescomplemented
93#2670C2214yes—
94#2666C2214yescomplemented
95#2661C2214yescomplemented
96#2653C2214yescomplemented
97#2651C2214yescomplemented
98#2647C2212yescomplemented
99#2640C2212yescomplemented
100#2629C2211yescharacteristic
101#2629C2211yescharacteristic
102#2628C2212yes—
103#2628C2212yescomplemented
104#2625C2212yes—
105#2624C2212yes—
106#2621C2211yescharacteristic
107#2620C2212yes—
108#2620C2212yescomplemented
109#2619C2211yescharacteristic
110#2616C2212yes—
111#2615C2212yes—
112#2606C2214yescomplemented
113#2602C2214yes—
114#2597C2214yescomplemented
115#2594C2214yes—
116#2592C2214yes—
117#2591C2214yes—
118#2589C2214yescomplemented
119#2581C2214yescomplemented
120#2580C2214yescomplemented
121#2578C2214yescomplemented
122#2573C2214yescomplemented
123#2563C2212yes—
124#2560C2214yescomplemented
125#2560C2214yescomplemented
126#2557C2214yes—
127#2557C2214yes—
128#2557C2214yes—
129#2554C2214yes—
130#2554C2214yescomplemented
131#2547C2212yes—
132#2540C2212yes—
133#2540C2212yes—
134#2538C2212yes—
135#2537C2212yes—
136#2536C2212yes—
137#2535C2212yes—
138#2526C2214yes—
139#2526C2214yes—
140#2526C2214yescomplemented
141#2518C2214yes—
142#2518C2214yes—
143#2518C2214yescomplemented
144#2517C2214yescomplemented
145#2514C2214yescomplemented
146#2513C2214yes—
147#2507C2214yescomplemented
148#2501C2214yes—
149#2497C2214yes—
150#2496C2214yescomplemented
151#2495C2212yes—
152#2495C2212yescomplemented
153#2494C2212yes—
154#2494C2212yescomplemented
155#2491C2214yes—
156#2490C2212yes—
157#2490C2212yescomplemented
158#2489C2212yes—
159#2489C2212yescomplemented
160#2481C2214yes—
161#2479C2214yes—
162#2477C2214yes—
163#2474C2214yes—
164#2472C2214yes—
165#2470C2214yes—
166#2469C2214yescomplemented
167#2467C2214yes—
168#2465C2214yescomplemented
169#2464C2214yes—
170#2463C2214yes—
171#2461C2214yes—
172#2459C2214yescomplemented
173#2458C2214yes—
174#2457C2214yes—
175#2456C2214yes—
176#2455C2214yescomplemented
177#2449C2214yes—
178#2448C2214yes—
179#2446C2214yescomplemented
180#2443C2214yescomplemented
181#2440C2214yescomplemented
182#2429C2212yes—
183#2429C2214yes—
184#2429C2212yescomplemented
185#2428C2212yes—
186#2428C2212yescomplemented
187#2426C2214yes—
188#2426C2214yescomplemented
189#2423C2212yes—
190#2423C2212yescomplemented
191#2422C2212yes—
192#2422C2212yescomplemented
193#2418C2214yes—
194#2383C2214yescomplemented
195#2378C2214yescomplemented
196#2373C2214yescomplemented
197#2369C2212yescomplemented
198#2367C2212yescomplemented
199#2367C2212yescomplemented
200#2365C2212yescomplemented
201#2360C2214yescomplemented
202#2357C2212yescomplemented
203#2356C2212yescomplemented
204Q8×C4⋊C4C2212yescomplemented
205D4×C4⋊C4C2212yescomplemented
206#2337C2214yes—
207#2335C2214yes—
208#2330C2211yescharacteristic, complemented
209#2330C2211yescharacteristic, complemented
210#2328C2211yescharacteristic, complemented
211#2327C2211yescharacteristic, complemented
212#2326C2214yes—
213#2324C2212yes—
214#2324C2212yes—
215#2324C2212yes—
216#2324C2212yes—
217#2323C2212yes—
218#2323C2212yes—
219#2323C2212yes—
220#2323C2212yes—
221#2322C2212yes—
222#2322C2212yes—
223#2322C2214yes—
224#2321C2212yes—
225#2321C2212yes—
226#2314C2212yes—
227#2314C2212yes—
228#2314C2212yescomplemented
229C4×C4⋊Q8C2212yescomplemented
230C4×#124C2212yescomplemented
231C4×C22⋊Q8C2212yes—
232C4×C22⋊Q8C2212yescomplemented
233C4×#121C2212yes—
234C4×#121C2212yescomplemented
235#2297C2211yescharacteristic
236#2296C2211yescharacteristic
237#2293C2212yes—
238#2293C2212yes—
239#2290C2212yes—
240#2290C2212yes—
241#2280C2211yescharacteristic
242C4×#117C2211yescharacteristic
243C22×#41C2311yescharacteristic
244C24×C4C2311yescharacteristic
245#542—216no—
246#542—48no—
247#542—48no—
248C2×C4⋊Q8C2312yes—
249C2×C4⋊Q8C2312yes—
250C2×C4⋊Q8C2311yescharacteristic
251C2×C4⋊Q8C2314yes—
252C2×#127C2311yescharacteristic
253C2×#126C2314yes—
254C2×#126C2314yes—
255C2×#126C2314yes—
256C2×#125C2311yescharacteristic
257C2×#125C2311yescharacteristic
258C2×#124C2314yes—
259C2×#124C2312yes—
260C2×#124C2312yes—
261C2×#124C2314yes—
262C2×#124C2314yes—
263C2×#124C2314yes—
264#525—28no—
265C2×#123C2312yes—
266C2×#123C2314yes—
267C2×#123C2314yes—
268C2×#123C2314yes—
269C2×#123C2314yes—
270C2×#123C2314yes—
271C2×#123C2314yes—
272C2×C22⋊Q8C2314yes—
273C2×C22⋊Q8C2312yes—
274C2×C22⋊Q8C2312yes—
275C2×C22⋊Q8C2312yes—
276C2×C22⋊Q8C2312yes—
277C2×C22⋊Q8C2312yes—
278C2×C22⋊Q8C2312yes—
279C2×C22⋊Q8C2314yes—
280C2×C22⋊Q8C2314yes—
281C2×C22⋊Q8C2314yes—
282C2×#121C2312yes—
283C2×#121C2312yes—
284C2×#121C2312yes—
285C2×#121C2312yes—
286C2×#121C2312yes—
287C2×#121C2312yes—
288C2×#121C2314yes—
289C2×#121C2314yes—
290C2×#121C2314yes—
291C2×#120C2312yes—
292C2×#120C2314yes—
293C4×#41—44no—
294C2×C4×Q8C2312yes—
295C2×C4×Q8C2311yescharacteristic
296C2×C4×Q8C2311yescharacteristic
297C2×C4×Q8C2312yes—
298C2×C4×Q8C2312yes—
299C2×C4×Q8C2314yes—
300C2×C4×Q8C2314yes—
301C2×C4×D4C2312yes—
302C2×C4×D4C2312yes—
303C2×C4×D4C2312yes—
304C2×C4×D4C2312yes—
305C2×C4×D4C2312yes—
306C2×C4×D4C2311yescharacteristic
307C2×C4×D4C2311yescharacteristic
308C2×C4×D4C2312yes—
309C2×C4×D4C2312yes—
310C2×C4×D4C2314yes—
311C2×C4×D4C2314yes—
312C2×#117—44no—
313C2×#117C2312yes—
314C2×#117C2312yes—
315C2×#117C2311yescharacteristic
316C2×#117C2312yes—
317C2×#117C2312yes—
318C2×#117C2312yes—
319C2×#117C2311yescharacteristic
320C2×#117C2311yescharacteristic
321C22×C4⋊C4C2311yescharacteristic
322C22×C4⋊C4C2311yescharacteristic
323C22×C4⋊C4C2314yes—
324C22×C22⋊C4C2311yescharacteristic
325C22×C22⋊C4C2311yescharacteristic
326C22×C42C2311yescharacteristic
327C22×C42C2312yes—
328C22×C42C2311yescharacteristic
329#401C2314yes—
330#401C2314yes—
331#400C2314yes—
332#400C2314yes—
333#400C2314yes—
334#400C2314yes—
335#400C2314yes—
336#400C2314yes—
337#400C2314yes—
338#400C2314yes—
339#400C2314yes—
340#399C2314yes—
341#399C2314yes—
342#399C2314yes—
343#399C2314yes—
344#399C2314yes—
345#399C2314yes—
346#399C2314yes—
347#398C2314yes—
348#398C2314yes—
349#398C2314yes—
350#398C2314yes—
351#398C2314yes—
352#398C2314yes—
353#398C2314yes—
354#398C2314yes—
355#398C2314yes—
356#398C2314yes—
357#398C2314yes—
358#397C2314yes—
359#397C2314yes—
360#397C2314yes—
361#397C2314yes—
362#397C2314yes—
363#397C2314yes—
364#397C2314yes—
365#397C2314yes—
366#397C2314yes—
367#397C2314yes—
368#397C2314yes—
369#397C2314yes—
370#397C2314yes—
371#397C2314yes—
372#397C2314yes—
373#397C2314yes—
374#397C2314yes—
375#397C2314yes—
376#397C2314yes—
377#396C2314yes—
378#396C2314yes—
379#396C2314yes—
380#396C2314yes—
381#396C2314yes—
382#396C2314yes—
383#396C2314yes—
384#396C2314yes—
385#396C2314yes—
386#396C2314yes—
387#395C2314yes—
388#395C2314yes—
389#395C2314yes—
390#394C2314yes—
391#394C2314yes—
392#394C2314yes—
393#394C2314yes—
394#394C2314yes—
395#394C2314yes—
396#394C2314yes—
397#394C2314yes—
398#394C2314yes—
399#394C2314yes—
400#394C2314yes—
401#394C2314yes—
402#394C2314yes—
403#394C2314yes—
404#394C2314yes—
405#394C2314yes—
406#394C2314yes—
407#394C2314yes—
408#394C2314yes—
409#393C2314yes—
410#393C2314yes—
411#393C2314yes—
412#393C2314yes—
413#393C2314yes—
414#393C2314yes—
415#393C2314yes—
416#392C2314yes—
417#392C2314yes—
418#392C2314yes—
419#392C2314yes—
420#392C2314yes—
421#392C2314yes—
422#392C2314yes—
423#392C2314yes—
424#392C2314yes—
425#391C2314yes—
426#391C2314yes—
427#391C2314yes—
428#391C2312yes—
429#391C2312yes—
430#391C2312yes—
431#391C2314yes—
432#391C2314yes—
433#391C2314yes—
434#391C2314yes—
435#391C2314yes—
436#391C2312yes—
437#391C2312yes—
438#390C2314yes—
439#390C2314yes—
440#390C2314yes—
441#390C2312yes—
442#390C2312yes—
443#390C2312yes—
444#390C2312yes—
445#390C2312yes—
446#390C2314yes—
447#390C2312yes—
448#390C2312yes—
449#390C2314yes—
450#390C2314yes—
451#390C2314yes—
452#390C2314yes—
453#390C2312yes—
454#390C2312yes—
455#390C2314yes—
456#390C2314yes—
457#390C2314yes—
458#390C2314yes—
459#389C2312yes—
460#389C2312yes—
461#389C2314yes—
462#389C2314yes—
463#389C2312yes—
464#389C2312yes—
465#389C2312yes—
466#389C2312yes—
467#389C2314yes—
468#389C2314yes—
469#389C2312yes—
470#389C2312yes—
471#389C2314yes—
472#389C2312yes—
473#389C2312yes—
474#389C2314yes—
475#389C2312yes—
476#389C2312yes—
477#389C2314yes—
478#389C2314yes—
479#389C2314yes—
480#389C2314yes—
481#389C2314yes—
482#389C2314yes—
483#389C2314yes—
484#389C2312yes—
485#389C2312yes—
486#389C2314yes—
487#388C2314yes—
488#388C2314yes—
489#388C2314yes—
490#388C2314yes—
491#388C2314yes—
492#388C2314yes—
493#388C2314yes—
494#388C2314yes—
495#388C2314yes—
496#388C2314yes—
497#388C2314yes—
498#388C2314yes—
499#388C2312yes—
500#388C2312yes—
501#388C2312yes—
502#388C2312yes—
503#388C2312yes—
504#388C2312yes—
505#388C2312yes—
506#388C2312yes—
507#388C2314yes—
508#388C2312yes—
509#388C2312yes—
510#388C2312yes—
511#388C2312yes—
512#388C2314yes—
513#388C2314yes—
514#388C2314yes—
515#388C2314yes—
516#388C2314yes—
517#388C2314yes—
518#388C2314yes—
519#388C2314yes—
520#388C2314yes—
521#388C2314yes—
522#388C2314yes—
523#388C2314yes—
524#388C2314yes—
525#388C2314yes—
526#388C2314yes—
527#388C2314yes—
528#388C2314yes—
529#388C2314yes—
530#388C2314yes—
531#388C2314yes—
532#388C2314yes—
533#388C2314yes—
534#388C2314yes—
535#388C2314yes—
536#388C2314yes—
537#388C2314yes—
538#388C2314yes—
539#387C2314yes—
540#387C2314yes—
541#387C2314yes—
542#387C2314yes—
543#387C2314yes—
544#387C2314yes—
545#387C2314yes—
546#387C2314yes—
547#387C2314yes—
548#387C2314yes—
549#387C2312yes—
550#387C2312yes—
551#387C2312yes—
552#387C2312yes—
553#387C2314yes—
554#387C2314yes—
555#387C2314yes—
556#387C2314yes—
557#387C2314yes—
558#387C2314yes—
559#387C2314yes—
560#387C2314yes—
561#387C2314yes—
562#387C2314yes—
563#387C2314yes—
564#387C2314yes—
565#387C2314yes—
566#387C2314yes—
567#386C2314yes—
568#386C2314yes—
569#386C2312yes—
570#386C2314yes—
571#386C2312yes—
572#386C2312yes—
573#386C2312yes—
574#386C2312yes—
575#386C2312yes—
576#386C2314yes—
577#386C2314yes—
578#386C2314yes—
579#386C2314yes—
580#386C2314yes—
581#386C2314yes—
582#386C2314yes—
583#386C2314yes—
584#386C2314yes—
585#386C2314yes—
586#386C2314yes—
587#386C2314yes—
588#386C2314yes—
589#385C2314yes—
590#385C2312yes—
591#385C2312yes—
592#385C2312yes—
593#385C2312yes—
594#385C2312yes—
595#385C2312yes—
596#385C2314yes—
597#385C2314yes—
598#385C2314yes—
599#385C2314yes—
600#385C2314yes—
601#385C2314yes—
602#385C2314yes—
603#385C2314yes—
604#385C2314yes—
605#385C2314yes—
606#385C2314yes—
607#385C2314yes—
608#385C2314yes—
609#384C2312yes—
610#384C2312yes—
611#384C2314yes—
612#384C2311yescharacteristic
613#384C2311yescharacteristic
614#384C2314yes—
615#383C2314yes—
616#383C2314yes—
617#383C2314yes—
618#382C2314yes—
619#382C2312yes—
620#382C2312yes—
621#382C2314yes—
622#382C2311yescharacteristic
623#382C2311yescharacteristic
624#382C2314yes—
625#381C2314yes—
626#381C2312yes—
627#381C2314yes—
628#380C2312yes—
629#380C2312yes—
630#380C2312yes—
631#380C2312yes—
632#380C2312yes—
633#380C2312yes—
634#380C2312yes—
635#380C2312yes—
636#380C2314yes—
637#380C2312yes—
638#380C2312yes—
639#380C2312yes—
640#380C2314yes—
641#380C2314yes—
642#380C2312yes—
643#379C2312yes—
644#379C2314yes—
645C4×C4⋊C4C2312yes—
646C4×C4⋊C4C2312yes—
647C4×C4⋊C4C2312yes—
648C4×C4⋊C4C2312yes—
649C4×C4⋊C4C2314yes—
650C4×C4⋊C4C2312yes—
651C4×C4⋊C4C2312yes—
652C4×C4⋊C4C2312yes—
653C4×C4⋊C4C2312yes—
654C4×C4⋊C4C2314yes—
655C4×C4⋊C4C2314yes—
656C4×C4⋊C4C2314yes—
657C4×C4⋊C4C2312yes—
658C4×C4⋊C4C2314yes—
659C4×C4⋊C4C2312yes—
660C4×C22⋊C4C2314yes—
661C4×C22⋊C4C2314yes—
662C4×C22⋊C4C2314yes—
663C4×C22⋊C4C2312yes—
664C4×C22⋊C4C2312yes—
665C4×C22⋊C4C2314yes—
666C4×C22⋊C4C2314yes—
667C4×C22⋊C4C2314yes—
668C4×C22⋊C4C2314yes—
669C4×C22⋊C4C2314yes—
670C4×C22⋊C4C2314yes—
671C4×C22⋊C4C2312yes—
672C4×C22⋊C4C2312yes—
673C4×C22⋊C4C2312yes—
674C4×C22⋊C4C2312yes—
675#376C2314yes—
676#376C2311yescharacteristic
677#376C2311yescharacteristic
678C43C2311yescharacteristic
679C43C2311yescharacteristic
680C25C2411yescharacteristic
681C2×#41—24no—
682C2×#41—42no—
683C2×#41—42no—
684C22×Q8C2412yes—
685C22×Q8C2411yescharacteristic
686C22×Q8C2414yes—
687C22×Q8C2414yes—
688C22×D4C2412yes—
689C22×D4C2412yes—
690C22×D4C2411yescharacteristic
691C22×D4C2412yes—
692C22×D4C2414yes—
693C22×D4C2412yes—
694C22×D4C2414yes—
695C22×D4C2414yes—
696C22×D4C2414yes—
697C22×D4C2414yes—
698C22×D4C2414yes—
699C23×C4—24no—
700C23×C4—42no—
701C23×C4—42no—
702C23×C4C2412yes—
703C23×C4C2412yes—
704C23×C4C2411yescharacteristic
705C23×C4C2411yescharacteristic
706C23×C4C2411yescharacteristic
707C23×C4C2411yescharacteristic
708C23×C4C2414yes—
709C23×C4C2412yes—
710C23×C4C2411yescharacteristic
711C23×C4C2411yescharacteristic
712C23×C4C2414yes—
713C23×C4C2414yes—
714C23×C4C2412yes—
715C23×C4C2412yes—
716C4⋊Q8—28no—
717C4⋊Q8—28no—
718C4⋊Q8—42no—
719C4⋊Q8—84no—
720#127—42no—
721#126—216no—
722#126—48no—
723#126—48no—
724#125—42no—
725#125—42no—
726#124—216no—
727#124—28no—
728#124—28no—
729#124—48no—
730#124—48no—
731#124—84no—
732#123—28no—
733#123—216no—
734#123—48no—
735#123—48no—
736#123—84no—
737#123—84no—
738#123—84no—
739C22⋊Q8—28no—
740C22⋊Q8—28no—
741C22⋊Q8—216no—
742C22⋊Q8—48no—
743C22⋊Q8—48no—
744C22⋊Q8—44no—
745C22⋊Q8—44no—
746C22⋊Q8—44no—
747C22⋊Q8—44no—
748C22⋊Q8—84no—
749#121—28no—
750#121—28no—
751#121—44no—
752#121—44no—
753#121—44no—
754#121—44no—
755#121—84no—
756#121—84no—
757#121—84no—
758#120—28no—
759#120—84no—
760C4×Q8—28no—
761C4×Q8—42no—
762C4×Q8—42no—
763C4×Q8—44no—
764C4×Q8—44no—
765C4×Q8—84no—
766C4×Q8—84no—
767C4×D4—28no—
768C4×D4—28no—
769C4×D4—28no—
770C4×D4—42no—
771C4×D4—42no—
772C4×D4—44no—
773C4×D4—44no—
774C4×D4—44no—
775C4×D4—44no—
776C4×D4—84no—
777C4×D4—84no—
778#117—28no—
779#117—28no—
780#117—44no—
781#117—42no—
782#117—42no—
783#117—44no—
784#117—44no—
785#117#4118yes—
786C2×C4⋊C4—42no—
787C2×C4⋊C4—42no—
788C2×C4⋊C4—84no—
789C2×C4⋊C4C2412yes—
790C2×C4⋊C4C2412yes—
791C2×C4⋊C4C2412yes—
792C2×C4⋊C4C2412yes—
793C2×C4⋊C4C2412yes—
794C2×C4⋊C4C2412yes—
795C2×C4⋊C4C2412yes—
796C2×C4⋊C4C2412yes—
797C2×C4⋊C4C2412yes—
798C2×C4⋊C4C2412yes—
799C2×C4⋊C4C2414yes—
800C2×C4⋊C4C2412yes—
801C2×C4⋊C4C2412yes—
802C2×C4⋊C4C2414yes—
803C2×C4⋊C4C2414yes—
804C2×C4⋊C4C2414yes—
805C2×C4⋊C4C2412yes—
806C2×C4⋊C4C2412yes—
807C2×C4⋊C4C2412yes—
808C2×C4⋊C4C2414yes—
809C2×C4⋊C4C2414yes—
810C2×C4⋊C4C2414yes—
811C2×C4⋊C4C2411yescharacteristic
812C2×C4⋊C4C2411yescharacteristic
813C2×C4⋊C4C2412yes—
814C2×C4⋊C4C2414yes—
815C2×C4⋊C4C2414yes—
816C2×C4⋊C4C2412yes—
817C2×C4⋊C4C2414yes—
818C2×C4⋊C4C2414yes—
819C2×C4⋊C4C2414yes—
820C2×C4⋊C4C2414yes—
821C2×C4⋊C4C2414yes—
822C2×C4⋊C4C2414yes—
823C2×C4⋊C4C2414yes—
824C2×C4⋊C4C2414yes—
825C2×C4⋊C4C2414yes—
826C2×C4⋊C4C2414yes—
827C2×C4⋊C4C2414yes—
828C2×C4⋊C4C2414yes—
829C2×C4⋊C4C2414yes—
830C2×C4⋊C4C2414yes—
831C2×C4⋊C4C2414yes—
832C2×C4⋊C4C2414yes—
833C2×C4⋊C4C2414yes—
834C2×C4⋊C4C2412yes—
835C2×C4⋊C4C2412yes—
836C2×C4⋊C4C2414yes—
837C2×C4⋊C4C2412yes—
838C2×C22⋊C4—42no—
839C2×C22⋊C4—42no—
840C2×C22⋊C4C2412yes—
841C2×C22⋊C4C2412yes—
842C2×C22⋊C4C2412yes—
843C2×C22⋊C4C2412yes—
844C2×C22⋊C4C2412yes—
845C2×C22⋊C4C2412yes—
846C2×C22⋊C4C2412yes—
847C2×C22⋊C4C2412yes—
848C2×C22⋊C4C2414yes—
849C2×C22⋊C4C2414yes—
850C2×C22⋊C4C2414yes—
851C2×C22⋊C4C2414yes—
852C2×C22⋊C4C2414yes—
853C2×C22⋊C4C2414yes—
854C2×C22⋊C4C2414yes—
855C2×C22⋊C4C2412yes—
856C2×C22⋊C4C2412yes—
857C2×C22⋊C4C2412yes—
858C2×C22⋊C4C2412yes—
859C2×C22⋊C4C2414yes—
860C2×C22⋊C4C2414yes—
861C2×C22⋊C4C2414yes—
862C2×C22⋊C4C2414yes—
863C2×C22⋊C4C2414yes—
864C2×C22⋊C4C2414yes—
865C2×C22⋊C4C2414yes—
866C2×C22⋊C4C2414yes—
867C2×C22⋊C4C2414yes—
868C2×C22⋊C4C2412yes—
869C2×C22⋊C4C2412yes—
870C2×C22⋊C4C2414yes—
871C2×C22⋊C4C2414yes—
872C2×C22⋊C4C2414yes—
873C2×C22⋊C4C2414yes—
874C2×C22⋊C4C2414yes—
875C2×C22⋊C4C2414yes—
876C2×C22⋊C4C2414yes—
877C2×C22⋊C4C2414yes—
878C2×C22⋊C4C2414yes—
879C2×C22⋊C4C2414yes—
880C2×C22⋊C4C2412yes—
881C2×C22⋊C4C2412yes—
882C2×C22⋊C4C2414yes—
883C2×C22⋊C4C2414yes—
884C2×C22⋊C4C2414yes—
885C2×C22⋊C4C2414yes—
886C2×C22⋊C4C2412yes—
887C2×C22⋊C4C2412yes—
888C2×C22⋊C4C2414yes—
889C2×C22⋊C4C2414yes—
890C2×C22⋊C4C2412yes—
891C2×C22⋊C4C2412yes—
892C2×C22⋊C4C2414yes—
893C2×C22⋊C4C2414yes—
894C2×C22⋊C4C2414yes—
895C2×C22⋊C4C2412yes—
896C2×C42—24no—
897C2×C42—42no—
898C2×C42—44no—
899C2×C42C2412yes—
900C2×C42C2412yes—
901C2×C42C2411yescharacteristic
902C2×C42C2411yescharacteristic
903C2×C42C2411yescharacteristic
904C2×C42C2411yescharacteristic
905C2×C42C2411yescharacteristic
906C2×C42C2414yes—
907C2×C42C2412yes—
908C2×C42C2414yes—
909C2×C42C2414yes—
910C2×C42C2412yes—
911C2×C42C2412yes—
912C2×C42C2412yes—
913C2×C42C2414yes—
914C2×C42C2414yes—
915C2×C42C2414yes—
916C2×C42C2414yes—
917C2×C42C2412yes—
918C2×C42C2412yes—
919C2×C42C2412yes—
920C2×C42C2414yes—
921C2×C42C2414yes—
922C2×C42C2411yescharacteristic
923C2×C42C2411yescharacteristic
924C2×C42C2411yescharacteristic
925#95C2412yes—
926#95C2414yes—
927#95C2412yes—
928#95C2412yes—
929#95C2412yes—
930#95C2412yes—
931#95C2414yes—
932#95C2414yes—
933#95C2412yes—
934#95C2412yes—
935#95C2412yes—
936#95C2414yes—
937#95C2414yes—
938#95C2412yes—
939#95C2412yes—
940#95C2412yes—
941#95C2412yes—
942#95C2414yes—
943#95C2414yes—
944#95C2414yes—
945#95C2414yes—
946#95C2414yes—
947#95C2414yes—
948#95C2412yes—
949#95C2414yes—
950#95C2414yes—
951#95C2414yes—
952#95C2414yes—
953#95C2414yes—
954#95C2414yes—
955#95C2412yes—
956#95C2412yes—
957#95C2412yes—
958#95C2414yes—
959#95C2414yes—
960#95C2414yes—
961#95C2414yes—
962#95C2414yes—
963#95C2414yes—
964#95C2414yes—
965#95C2414yes—
966#95C2414yes—
967#95C2414yes—
968#95C2414yes—
969#95C2414yes—
970#95C2414yes—
971#95C2414yes—
972#95C2414yes—
973#95C2414yes—
974#95C2414yes—
975#95C2414yes—
976#95C2414yes—
977#95C2414yes—
978#95C2414yes—
979C24—22no—
980C24—41no—
981C24—41no—
982C24—42no—
983C24—42no—
984C24C2512yes—
985C24C2514yes—
986C24C2512yes—
987C24C2511yescharacteristic
988#41—416no—
989C2×Q8—24no—
990C2×Q8—22no—
991C2×Q8—28no—
992C2×Q8—24no—
993C2×Q8—28no—
994C2×Q8—24no—
995C2×Q8—41no—
996C2×Q8—41no—
997C2×Q8—44no—
998C2×Q8—44no—
999C2×Q8—44no—
1000C2×Q8—44no—
1001C2×D4—24no—
1002C2×D4—28no—
1003C2×D4—24no—
1004C2×D4—22no—
1005C2×D4—24no—
1006C2×D4—24no—
1007C2×D4—24no—
1008C2×D4—24no—
1009C2×D4—41no—
1010C2×D4—42no—
1011C2×D4—41no—
1012C2×D4—42no—
1013C2×D4—44no—
1014C2×D4—44no—
1015C2×D4—44no—
1016C2×D4—42no—
1017C2×D4—42no—
1018C2×D4—42no—
1019C2×D4—42no—
1020C2×D4—44no—
1021C2×D4—44no—
1022C2×D4—44no—
1023C2×D4—44no—
1024C2×D4—44no—
1025C2×D4—44no—
1026C2×D4—44no—
1027C2×D4—44no—
1028C2×D4—44no—
1029C2×D4—44no—
1030C2×D4—44no—
1031C2×D4—44no—
1032C2×D4—44no—
1033C2×D4—44no—
1034C22×C4—22no—
1035C22×C4—22no—
1036C22×C4—22no—
1037C22×C4—24no—
1038C22×C4—24no—
1039C22×C4—24no—
1040C22×C4—24no—
1041C22×C4—24no—
1042C22×C4—24no—
1043C22×C4—24no—
1044C22×C4—28no—
1045C22×C4—22no—
1046C22×C4—22no—
1047C22×C4—41no—
1048C22×C4—42no—
1049C22×C4—42no—
1050C22×C4—41no—
1051C22×C4—41no—
1052C22×C4—41no—
1053C22×C4—42no—
1054C22×C4—42no—
1055C22×C4—44no—
1056C22×C4—42no—
1057C22×C4—42no—
1058C22×C4—42no—
1059C22×C4—42no—
1060C22×C4—42no—
1061C22×C4—44no—
1062C22×C4—42no—
1063C22×C4—42no—
1064C22×C4—42no—
1065C22×C4—44no—
1066C22×C4—44no—
1067C22×C4—44no—
1068C22×C4—44no—
1069C22×C4—44no—
1070C22×C4—44no—
1071C22×C4—416no—
1072C22×C4C2×#4114yes—
1073C22×C4C2511yescharacteristic
1074C22×C4C2514yes—
1075C22×C4C2512yes—
1076C22×C4C2514yes—
1077C22×C4C2512yes—
1078C22×C4C2512yes—
1079C22×C4C2514yes—
1080C22×C4C2514yes—
1081C22×C4C2512yes—
1082C22×C4C2512yes—
1083C22×C4C2512yes—
1084C22×C4C2511yescharacteristic
1085C22×C4C2512yes—
1086C22×C4C2512yes—
1087C22×C4C2514yes—
1088C22×C4C2514yes—
1089C22×C4C2514yes—
1090C22×C4C2512yes—
1091C22×C4C2512yes—
1092C22×C4C2511yescharacteristic
1093C22×C4C2511yescharacteristic
1094C22×C4C2511yescharacteristic
1095C22×C4C2511yescharacteristic
1096C4⋊C4—24no—
1097C4⋊C4—24no—
1098C4⋊C4—24no—
1099C4⋊C4—24no—
1100C4⋊C4—28no—
1101C4⋊C4—28no—
1102C4⋊C4—28no—
1103C4⋊C4—24no—
1104C4⋊C4—24no—
1105C4⋊C4—24no—
1106C4⋊C4—24no—
1107C4⋊C4—24no—
1108C4⋊C4—24no—
1109C4⋊C4—28no—
1110C4⋊C4—24no—
1111C4⋊C4—24no—
1112C4⋊C4—42no—
1113C4⋊C4—42no—
1114C4⋊C4—42no—
1115C4⋊C4—44no—
1116C4⋊C4—44no—
1117C4⋊C4—44no—
1118C4⋊C4—44no—
1119C4⋊C4—42no—
1120C4⋊C4—42no—
1121C4⋊C4—42no—
1122C4⋊C4—41no—
1123C4⋊C4—41no—
1124C4⋊C4—44no—
1125C4⋊C4—44no—
1126C4⋊C4—44no—
1127C4⋊C4—44no—
1128C4⋊C4—42no—
1129C4⋊C4—44no—
1130C4⋊C4—44no—
1131C4⋊C4—44no—
1132C4⋊C4—44no—
1133C4⋊C4—44no—
1134C4⋊C4—44no—
1135C4⋊C4—44no—
1136C4⋊C4—44no—
1137C4⋊C4—44no—
1138C4⋊C4—44no—
1139C4⋊C4—44no—
1140C4⋊C4—44no—
1141C4⋊C4—44no—
1142C4⋊C4—44no—
1143C4⋊C4—44no—
1144C4⋊C4C2×#4118yes—
1145C22⋊C4—28no—
1146C22⋊C4—24no—
1147C22⋊C4—24no—
1148C22⋊C4—24no—
1149C22⋊C4—24no—
1150C22⋊C4—28no—
1151C22⋊C4—28no—
1152C22⋊C4—28no—
1153C22⋊C4—28no—
1154C22⋊C4—24no—
1155C22⋊C4—24no—
1156C22⋊C4—24no—
1157C22⋊C4—24no—
1158C22⋊C4—28no—
1159C22⋊C4—28no—
1160C22⋊C4—42no—
1161C22⋊C4—42no—
1162C22⋊C4—42no—
1163C22⋊C4—42no—
1164C22⋊C4—42no—
1165C22⋊C4—44no—
1166C22⋊C4—44no—
1167C22⋊C4—42no—
1168C22⋊C4—44no—
1169C22⋊C4—44no—
1170C22⋊C4—44no—
1171C22⋊C4—44no—
1172C22⋊C4—42no—
1173C22⋊C4—42no—
1174C22⋊C4—44no—
1175C22⋊C4—44no—
1176C22⋊C4—44no—
1177C22⋊C4—44no—
1178C22⋊C4—44no—
1179C22⋊C4—44no—
1180C22⋊C4—44no—
1181C22⋊C4—44no—
1182C22⋊C4—44no—
1183C22⋊C4—44no—
1184C22⋊C4—44no—
1185C22⋊C4—44no—
1186C22⋊C4—44no—
1187C22⋊C4—42no—
1188C22⋊C4—42no—
1189C22⋊C4—44no—
1190C22⋊C4—44no—
1191C22⋊C4—44no—
1192C22⋊C4—44no—
1193C22⋊C4—44no—
1194C22⋊C4—44no—
1195C22⋊C4—42no—
1196C22⋊C4—44no—
1197C22⋊C4—42no—
1198C22⋊C4—44no—
1199C22⋊C4—44no—
1200C22⋊C4C2×#4118yes—
1201C42—28no—
1202C42—22no—
1203C42—22no—
1204C42—22no—
1205C42—24no—
1206C42—24no—
1207C42—22no—
1208C42—22no—
1209C42—42no—
1210C42—42no—
1211C42—42no—
1212C42—42no—
1213C42—42no—
1214C42—44no—
1215C42—44no—
1216C42—44no—
1217C42—44no—
1218C42—44no—
1219C42—44no—
1220C42—42no—
1221C42—44no—
1222C42—44no—
1223C42—42no—
1224C42C2×#4114yes—
1225C42C2×#4114yes—
1226C42H(5,𝔽2)14yes—
1227C23—21no—
1228C23—21no—
1229C23—22no—
1230C23—22no—
1231C23—24no—
1232C23—22no—
1233C23—22no—
1234C23—22no—
1235C23—24no—
1236C23—22no—
1237C23—22no—
1238C23—22no—
1239C23—24no—
1240C23—22no—
1241C23—22no—
1242C23—22no—
1243C23—24no—
1244C23—22no—
1245C23—24no—
1246C23—22no—
1247C23—22no—
1248C23—24no—
1249C23—24no—
1250C23—22no—
1251C23—22no—
1252C23—44no—
1253C23—84no—
1254C23—82no—
1255C23—84no—
1256C23—82no—
1257C23C22×#4112yes—
1258C23C2611yescharacteristic
1259Q8—44no—
1260Q8—48no—
1261Q8—88no—
1262Q8—88no—
1263D4—44no—
1264D4—48no—
1265D4—48no—
1266D4—84no—
1267D4—84no—
1268D4—88no—
1269D4—88no—
1270D4—164no—
1271D4—164no—
1272D4—164no—
1273D4—164no—
1274C2×C4—21no—
1275C2×C4—21no—
1276C2×C4—22no—
1277C2×C4—22no—
1278C2×C4—22no—
1279C2×C4—22no—
1280C2×C4—22no—
1281C2×C4—22no—
1282C2×C4—28no—
1283C2×C4—24no—
1284C2×C4—24no—
1285C2×C4—24no—
1286C2×C4—22no—
1287C2×C4—22no—
1288C2×C4—21no—
1289C2×C4—21no—
1290C2×C4—22no—
1291C2×C4—22no—
1292C2×C4—22no—
1293C2×C4—22no—
1294C2×C4—24no—
1295C2×C4—22no—
1296C2×C4—24no—
1297C2×C4—24no—
1298C2×C4—22no—
1299C2×C4—22no—
1300C2×C4—22no—
1301C2×C4—24no—
1302C2×C4—24no—
1303C2×C4—24no—
1304C2×C4—22no—
1305C2×C4—22no—
1306C2×C4—24no—
1307C2×C4—22no—
1308C2×C4—22no—
1309C2×C4—22no—
1310C2×C4—24no—
1311C2×C4—24no—
1312C2×C4—24no—
1313C2×C4—22no—
1314C2×C4—24no—
1315C2×C4—24no—
1316C2×C4—22no—
1317C2×C4—22no—
1318C2×C4—24no—
1319C2×C4—22no—
1320C2×C4—24no—
1321C2×C4—22no—
1322C2×C4—22no—
1323C2×C4—24no—
1324C2×C4—22no—
1325C2×C4—24no—
1326C2×C4—22no—
1327C2×C4—24no—
1328C2×C4—22no—
1329C2×C4—24no—
1330C2×C4—22no—
1331C2×C4—22no—
1332C2×C4—48no—
1333C2×C4—44no—
1334C2×C4—48no—
1335C2×C4—48no—
1336C2×C4—88no—
1337C2×C4—82no—
1338C2×C4—82no—
1339C2×C4—84no—
1340C2×C4—82no—
1341C2×C4—82no—
1342C2×C4—84no—
1343C2×C4—164no—
1344C2×C4—164no—
1345C2×C4C22×#4114yes—
1346C2×C4C22×#4114yes—
1347C2×C4C22×#4112yes—
1348C2×C4C22×#4112yes—
1349C2×C4C2×H(5,𝔽2)12yes—
1350C2×C4C2×H(5,𝔽2)12yes—
1351C2×C4C2×H(5,𝔽2)12yes—
1352C2×C4#58512yes—
1353C22—22no—
1354C22—24no—
1355C22—41no—
1356C22—42no—
1357C22—41no—
1358C22—42no—
1359C22—42no—
1360C22—44no—
1361C22—44no—
1362C22—42no—
1363C22—42no—
1364C22—42no—
1365C22—44no—
1366C22—42no—
1367C22—42no—
1368C22—44no—
1369C22—42no—
1370C22—42no—
1371C22—44no—
1372C22—44no—
1373C22—42no—
1374C22—42no—
1375C22—42no—
1376C22—42no—
1377C22—44no—
1378C22—42no—
1379C22—88no—
1380C22C23×#4111yescharacteristic
1381C22C22×H(5,𝔽2)11yescharacteristic
1382C22C2×#58511yescharacteristic
1383C22H(7,𝔽2)12yes—
1384C222−1+612yes—
1385C4—22no—
1386C4—24no—
1387C4—24no—
1388C4—22no—
1389C4—22no—
1390C4—42no—
1391C4—42no—
1392C4—44no—
1393C4—44no—
1394C4—44no—
1395C4—41no—
1396C4—42no—
1397C4—42no—
1398C4—44no—
1399C4—44no—
1400C4—42no—
1401C4—44no—
1402C4—44no—
1403C4—42no—
1404C4—42no—
1405C4—42no—
1406C4—41no—
1407C4#350614yes—
1408C2—42no—
1409C2—82no—
1410C2—84no—
1411C2—82no—
1412C2C2×#350611yescharacteristic
1413C2#6285712yes—
1414C2#6288011yescharacteristic
1415C2#6288212yes—
1416C2#6288811yescharacteristic
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. #51969C2semidirect
2. #51954C2semidirect
3. #51732C2semidirect
4. #51702C2semidirect
5. #46700C2semidirect
6. #46687C2semidirect
7. #46684C2semidirect
8. #46581C2semidirect
9. #39515C2semidirect
10. #39502C2semidirect
11. #39381C2semidirect
12. #39377C2semidirect
13. #39273C2semidirect
14. #39272C2semidirect
15. #39257C2semidirect
16. #39256C2semidirect
17. #37519C2semidirect
18. #37515C2semidirect
19. #37380C2semidirect
20. #37283C2semidirect
21. #37271C2semidirect
22. #35331C2semidirect
23. #35284C2semidirect
24. #35260C2semidirect
25. #35258C2semidirect
26. #34422C2semidirect
27. #34065C2semidirect
30. C2×#542C22semidirect
34. #2868C22semidirect
35. #2862C22semidirect
36. #2859C22semidirect
37. #2858C22semidirect
39. #2855C22semidirect
40. #2854C22semidirect
50. #2798C22semidirect
53. #2790C22semidirect
55. #2783C22semidirect
56. #2783C22semidirect
57. #2778C22semidirect
58. #2776C22semidirect
59. #2773C22semidirect
63. #2759C22semidirect
67. #2754C22semidirect
69. #2751C22semidirect
71. #2746C22semidirect
74. #2732C22semidirect
75. #2727C22semidirect
76. #2724C22semidirect
79. #2718C22semidirect
92. #2674C22semidirect
94. #2666C22semidirect
95. #2661C22semidirect
96. #2653C22semidirect
97. #2651C22semidirect
98. #2647C22semidirect
99. #2640C22semidirect
103. #2628C22semidirect
108. #2620C22semidirect
112. #2606C22semidirect
114. #2597C22semidirect
118. #2589C22semidirect
119. #2581C22semidirect
120. #2580C22semidirect
121. #2578C22semidirect
122. #2573C22semidirect
124. #2560C22semidirect
125. #2560C22semidirect
130. #2554C22semidirect
140. #2526C22semidirect
143. #2518C22semidirect
144. #2517C22semidirect
145. #2514C22semidirect
147. #2507C22semidirect
150. #2496C22semidirect
152. #2495C22semidirect
154. #2494C22semidirect
157. #2490C22semidirect
159. #2489C22semidirect
166. #2469C22semidirect
168. #2465C22semidirect
172. #2459C22semidirect
176. #2455C22semidirect
179. #2446C22semidirect
180. #2443C22semidirect
181. #2440C22semidirect
184. #2429C22semidirect
186. #2428C22semidirect
188. #2426C22semidirect
190. #2423C22semidirect
192. #2422C22semidirect
194. #2383C22semidirect
195. #2378C22semidirect
196. #2373C22semidirect
197. #2369C22semidirect
198. #2367C22semidirect
199. #2367C22semidirect
200. #2365C22semidirect
201. #2360C22semidirect
202. #2357C22semidirect
203. #2356C22semidirect
204. Q8×C4⋊C4C22semidirect
205. D4×C4⋊C4C22semidirect
208. #2330C22semidirect
209. #2330C22semidirect
210. #2328C22semidirect
211. #2327C22semidirect
228. #2314C22semidirect
229. C4×C4⋊Q8C22semidirect
230. C4×#124C22semidirect
232. C4×C22⋊Q8C22semidirect
234. C4×#121C22semidirect

Maximal subgroups

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

subgroupindex
#519692
#519542
#517322
#517022
#467002
#466872
#466842
#465812
#395152
#395022
#393812
#393772
#392732
#392722
#392572
#392562
#375192
#375152
#373802
#372832
#372712
#353312
#352842
#352602
#352582
#344222
#340652