Finite Group Databasebeta

← #8636148

Subgroups — #8636148

Order 512.

4994 conjugacy classes of subgroups.

The subgroup lattice has 1465 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59430C212yesmaximal, complemented
2#57966C212yesmaximal, complemented
3#55192C214yesmaximal, complemented
4#53524C214yesmaximal, complemented
5#53009C211yesmaximal, characteristic, complemented
6#49557C214yesmaximal, complemented
7#49098C214yesmaximal, complemented
8#48902C214yesmaximal, complemented
9#47766C214yesmaximal, complemented
10#46847C212yesmaximal, complemented
11#45648C212yesmaximal, complemented
12#45502C211yesmaximal, characteristic, complemented
13#45375C211yesmaximal, characteristic, complemented
14#45321C212yesmaximal, complemented
15#44984C212yesmaximal, complemented
16#42914C211yesmaximal, characteristic, complemented
17#42514C212yesmaximal, complemented
18#40974C212yesmaximal, complemented
19#39720C211yesmaximal, characteristic, complemented
20#39625C212yesmaximal, complemented
21#39377C212yesmaximal, complemented
22#39337C212yesmaximal, complemented
23#37686C212yesmaximal, complemented
24#37340C212yesmaximal, complemented
25D4×C4⋊Q8C212yesmaximal, complemented
26#35923C211yesmaximal, characteristic
27#35581C212yesmaximal, complemented
28#35107C212yesmaximal, complemented
29#34921C211yesmaximal, characteristic, complemented
30C2×#553C2211yescharacteristic
31C2×D4×Q8C2214yes—
32C2×#547C2211yescharacteristic
33C2×#544C2211yescharacteristic
34C2×#542C2214yes—
35C2×#536C2214yes—
36C22×C4⋊Q8C2211yescharacteristic
37C22×C4⋊Q8C2212yes—
38#2868C2212yes—
39#2857C2212yes—
40#2857C2212yes—
41#2854C2211yescharacteristic
42#2854C2212yes—
43#2851C2212yes—
44#2844C2212yes—
45#2841C2212yes—
46#2838C2214yes—
47#2835C2212yes—
48#2833C2214yes—
49#2821C2214yes—
50#2821C2212yes—
51#2807C2212yes—
52#2807C2212yes—
53#2805C2214yes—
54#2801C2214yes—
55#2792C2214yes—
56#2792C2214yes—
57#2791C2214yes—
58#2787C2214yes—
59#2787C2214yes—
60#2779C2214yes—
61#2776C2214yes—
62#2774C2214yes—
63#2771C2214yes—
64#2769C2212yes—
65#2765C2214yes—
66#2762C2214yes—
67#2746C2214yes—
68#2745C2214yes—
69#2742C2214yes—
70#2734C2214yes—
71#2734C2214yes—
72#2734C2214yes—
73#2731C2214yes—
74#2729C2214yes—
75#2729C2214yes—
76#2723C2214yes—
77#2718C2214yes—
78#2718C2214yes—
79#2717C2214yes—
80#2716C2214yes—
81#2713C2214yes—
82#2700C2214yes—
83#2698C2214yes—
84#2695C2214yes—
85#2692C2214yes—
86#2689C2214yes—
87#2687C2214yes—
88#2686C2214yes—
89#2683C2212yes—
90#2681C2214yes—
91#2680C2214yes—
92#2680C2214yes—
93#2677C2212yes—
94#2677C2212yes—
95#2677C2214yes—
96#2677C2214yes—
97#2677C2214yes—
98#2674C2214yes—
99#2674C2214yes—
100#2674C2214yes—
101#2674C2214yes—
102#2674C2214yes—
103#2674C2214yes—
104#2672C2214yes—
105#2664C2212yes—
106#2663C2212yes—
107#2660C2212yes—
108#2660C2211yescharacteristic
109#2654C2214yes—
110#2650C2214yes—
111#2633C2212yes—
112#2630C2214yes—
113#2630C2214yes—
114#2628C2212yes—
115#2628C2214yes—
116#2624C2211yescharacteristic
117#2618C2212yes—
118#2614C2214yes—
119#2608C2214yes—
120#2607C2211yescharacteristic
121#2602C2212yes—
122#2601C2214yes—
123#2600C2214yes—
124#2600C2211yescharacteristic
125#2599C2214yes—
126#2596C2212yes—
127#2594C2214yes—
128#2589C2212yes—
129#2588C2214yes—
130#2587C2214yes—
131#2584C2212yes—
132#2575C2212yes—
133#2574C2214yes—
134#2573C2214yes—
135#2567C2214yes—
136#2566C2212yes—
137#2564C2212yes—
138#2563C2211yescharacteristic
139#2562C2212yes—
140#2562C2212yes—
141#2562C2211yescharacteristic
142#2557C2212yes—
143#2553C2214yes—
144#2552C2212yes—
145#2551C2214yes—
146#2551C2212yes—
147#2551C2214yes—
148#2551C2212yes—
149#2551C2212yes—
150#2551C2212yes—
151#2550C2212yes—
152#2550C2212yes—
153#2549C2214yes—
154#2546C2214yes—
155#2542C2212yes—
156#2538C2212yes—
157#2537C2212yes—
158#2535C2212yes—
159#2525C2214yes—
160#2517C2211yescharacteristic
161#2508C2212yes—
162#2507C2214yes—
163#2507C2212yes—
164#2504C2211yescharacteristic
165#2501C2212yes—
166#2501C2211yescharacteristic
167#2497C2212yes—
168#2497C2212yes—
169#2497C2212yes—
170#2496C2212yes—
171#2496C2212yes—
172#2495C2212yes—
173#2494C2212yes—
174#2494C2212yes—
175#2491C2212yes—
176#2491C2212yes—
177#2491C2212yes—
178#2490C2212yes—
179#2487C2211yescharacteristic
180#2487C2211yescharacteristic
181#2486C2212yes—
182#2477C2214yes—
183#2473C2214yes—
184#2470C2214yes—
185#2469C2214yes—
186#2466C2214yes—
187#2465C2214yes—
188#2465C2214yes—
189#2464C2214yes—
190#2461C2214yes—
191#2461C2214yes—
192#2459C2212yes—
193#2455C2211yescharacteristic
194#2455C2212yes—
195#2455C2212yes—
196#2452C2212yes—
197#2452C2212yes—
198#2451C2214yes—
199#2449C2214yes—
200#2442C2212yes—
201#2440C2214yes—
202#2440C2212yes—
203#2440C2212yes—
204#2440C2212yes—
205#2440C2214yes—
206#2440C2212yes—
207#2440C2212yes—
208#2440C2212yes—
209#2439C2212yes—
210#2439C2214yes—
211#2438C2214yes—
212#2436C2212yes—
213#2434C2214yes—
214#2434C2214yes—
215#2434C2214yes—
216#2430C2212yes—
217#2429C2214yes—
218#2423C2214yes—
219#2422C2214yes—
220#2415C2214yes—
221#2413C2214yes—
222#2409C2212yes—
223#2409C2214yes—
224#2406C2214yes—
225#2398C2212yes—
226#2397C2211yescharacteristic
227#2395C2211yescharacteristic
228#2388C2212yes—
229#2378C2214yes—
230#2376C2212yes—
231#2362C2214yes—
232#2355C2212yes—
233#2352C2212yes—
234Q8×C4⋊C4C2212yes—
235D4×C4⋊C4C2214yes—
236D4×C4⋊C4C2212yes—
237D4×C4⋊C4C2212yes—
238D4×C4⋊C4C2212yes—
239#2347C2211yescharacteristic
240#2345C2211yescharacteristic
241#2344C2212yes—
242#2337C2214yes—
243#2335C2214yes—
244#2331C2212yes—
245#2330C2212yes—
246#2330C2212yes—
247#2322C2212yes—
248#2319C2212yes—
249C4×C4⋊Q8C2212yes—
250C4×#125C2212yes—
251C4×#124C2212yes—
252C4×#123C2211yescharacteristic
253C4×#123C2212yes—
254#2295C2212yes—
255#2293C2212yes—
256#2290C2212yes—
257#2275C2211yescharacteristic
258C42×D4C2212yes—
259C22×#41C2312yes—
260C23×Q8C2314yes—
261C23×Q8C2312yes—
262#553—44no—
263D4×Q8—416no—
264#547—44no—
265#544—44no—
266#542—416no—
267#536—416no—
268C2×C4⋊Q8—48no—
269C2×C4⋊Q8—44no—
270C2×C4⋊Q8C2312yes—
271C2×C4⋊Q8C2312yes—
272C2×C4⋊Q8C2311yescharacteristic
273C2×C4⋊Q8C2314yes—
274C2×C4⋊Q8C2312yes—
275C2×C4⋊Q8C2312yes—
276C2×C4⋊Q8C2312yes—
277C2×C4⋊Q8C2314yes—
278C2×C4⋊Q8C2314yes—
279C2×C4⋊Q8C2312yes—
280C2×C4⋊Q8C2314yes—
281C2×C4⋊Q8C2314yes—
282C2×C4⋊Q8C2314yes—
283C2×C4⋊Q8C2314yes—
284C2×C4⋊Q8C2314yes—
285C2×C4⋊Q8C2314yes—
286C2×#126C2314yes—
287C2×#126C2312yes—
288C2×#126C2314yes—
289C2×#125C2312yes—
290C2×#125C2311yescharacteristic
291C2×#125C2312yes—
292C2×#125C2312yes—
293C2×#124C2314yes—
294C2×#124C2312yes—
295C2×#124C2314yes—
296C2×#124C2314yes—
297C2×#123C2312yes—
298C2×#123C2311yescharacteristic
299C2×#123C2312yes—
300C2×#123C2314yes—
301C2×#123C2314yes—
302C2×#123C2314yes—
303C2×#123C2314yes—
304C2×#123C2312yes—
305C2×#123C2314yes—
306C2×#123C2314yes—
307C2×C22⋊Q8C2314yes—
308C2×C22⋊Q8C2314yes—
309C2×C22⋊Q8C2312yes—
310C2×C22⋊Q8C2314yes—
311C2×C22⋊Q8C2314yes—
312C2×C22⋊Q8C2314yes—
313C2×C22⋊Q8C2314yes—
314C2×C22⋊Q8C2314yes—
315C2×C22⋊Q8C2314yes—
316C2×C22⋊Q8C2314yes—
317C2×C22⋊Q8C2314yes—
318C2×C22⋊Q8C2314yes—
319C2×C22⋊Q8C2314yes—
320C2×#121C2312yes—
321C2×#121C2311yescharacteristic
322C2×#121C2312yes—
323C2×#121C2311yescharacteristic
324C2×#121C2314yes—
325C2×C4×Q8C2312yes—
326C2×C4×Q8C2314yes—
327C2×C4×Q8C2314yes—
328C2×C4×D4C2312yes—
329C2×C4×D4C2312yes—
330C2×C4×D4C2312yes—
331C2×C4×D4C2312yes—
332C2×C4×D4C2311yescharacteristic
333C2×C4×D4C2312yes—
334C2×C4×D4C2311yescharacteristic
335C2×C4×D4C2311yescharacteristic
336C2×C4×D4C2312yes—
337C2×C4×D4C2314yes—
338C2×C4×D4C2314yes—
339C2×C4×D4C2314yes—
340C2×#117C2311yescharacteristic
341C2×#117C2314yes—
342C2×#117C2311yescharacteristic
343C2×#117C2314yes—
344C22×C4⋊C4C2312yes—
345C22×C4⋊C4C2311yescharacteristic
346C22×C4⋊C4C2312yes—
347C22×C4⋊C4C2311yescharacteristic
348C22×C4⋊C4C2312yes—
349C22×C4⋊C4C2311yescharacteristic
350C22×C4⋊C4C2314yes—
351C22×C42C2312yes—
352C22×C42C2311yescharacteristic
353#401C2314yes—
354#401C2314yes—
355#400C2312yes—
356#400C2314yes—
357#400C2314yes—
358#400C2311yescharacteristic
359#400C2314yes—
360#400C2314yes—
361#400C2312yes—
362#400C2314yes—
363#400C2314yes—
364#400C2312yes—
365#400C2314yes—
366#400C2314yes—
367#400C2314yes—
368#400C2314yes—
369#400C2314yes—
370#400C2312yes—
371#400C2312yes—
372#399C2311yescharacteristic
373#399C2312yes—
374#399C2312yes—
375#399C2312yes—
376#399C2314yes—
377#399C2312yes—
378#399C2314yes—
379#399C2312yes—
380#399C2311yescharacteristic
381#399C2311yescharacteristic
382#399C2314yes—
383#399C2312yes—
384#398C2314yes—
385#398C2314yes—
386#398C2314yes—
387#398C2314yes—
388#398C2314yes—
389#398C2314yes—
390#398C2314yes—
391#398C2314yes—
392#398C2314yes—
393#398C2314yes—
394#398C2314yes—
395#398C2311yescharacteristic
396#398C2314yes—
397#398C2314yes—
398#398C2314yes—
399#398C2314yes—
400#398C2314yes—
401#398C2314yes—
402#398C2314yes—
403#398C2314yes—
404#397C2312yes—
405#397C2314yes—
406#397C2314yes—
407#397C2314yes—
408#397C2312yes—
409#397C2311yescharacteristic
410#397C2314yes—
411#397C2314yes—
412#397C2314yes—
413#397C2314yes—
414#397C2314yes—
415#397C2312yes—
416#397C2312yes—
417#397C2314yes—
418#396C2314yes—
419#396C2314yes—
420#396C2314yes—
421#396C2314yes—
422#396C2314yes—
423#396C2314yes—
424#396C2314yes—
425#396C2314yes—
426#396C2314yes—
427#396C2314yes—
428#395C2312yes—
429#395C2314yes—
430#395C2314yes—
431#395C2314yes—
432#395C2314yes—
433#395C2314yes—
434#395C2314yes—
435#395C2314yes—
436#395C2314yes—
437#395C2314yes—
438#395C2314yes—
439#395C2314yes—
440#395C2314yes—
441#395C2314yes—
442#395C2314yes—
443#395C2314yes—
444#395C2314yes—
445#395C2314yes—
446#395C2312yes—
447#395C2314yes—
448#395C2314yes—
449#395C2314yes—
450#394C2314yes—
451#394C2314yes—
452#394C2312yes—
453#394C2312yes—
454#394C2312yes—
455#394C2312yes—
456#394C2314yes—
457#394C2314yes—
458#394C2314yes—
459#394C2314yes—
460#394C2314yes—
461#394C2314yes—
462#394C2314yes—
463#393C2312yes—
464#393C2312yes—
465#393C2314yes—
466#393C2314yes—
467#393C2314yes—
468#393C2312yes—
469#393C2312yes—
470#393C2314yes—
471#393C2314yes—
472#393C2314yes—
473#393C2314yes—
474#392C2312yes—
475#392C2311yescharacteristic
476#392C2314yes—
477#392C2311yescharacteristic
478#391C2314yes—
479#391C2312yes—
480#391C2314yes—
481#391C2314yes—
482#391C2314yes—
483#391C2314yes—
484#391C2312yes—
485#391C2312yes—
486#391C2314yes—
487#391C2314yes—
488#391C2314yes—
489#391C2314yes—
490#390C2312yes—
491#390C2312yes—
492#390C2312yes—
493#390C2312yes—
494#390C2314yes—
495#390C2312yes—
496#390C2312yes—
497#389C2312yes—
498#389C2312yes—
499#389C2312yes—
500#389C2314yes—
501#389C2312yes—
502#389C2314yes—
503#389C2314yes—
504#389C2314yes—
505#389C2314yes—
506#389C2314yes—
507#389C2312yes—
508#389C2312yes—
509#389C2314yes—
510#389C2312yes—
511#389C2314yes—
512#389C2312yes—
513#389C2314yes—
514#389C2312yes—
515#389C2312yes—
516#389C2314yes—
517#389C2312yes—
518#389C2312yes—
519#389C2312yes—
520#389C2314yes—
521#389C2312yes—
522#389C2312yes—
523#389C2312yes—
524#389C2314yes—
525#389C2314yes—
526#389C2314yes—
527#389C2314yes—
528#389C2314yes—
529#389C2314yes—
530#389C2314yes—
531#389C2314yes—
532#389C2314yes—
533#389C2314yes—
534#389C2314yes—
535#389C2314yes—
536#388C2314yes—
537#388C2314yes—
538#388C2314yes—
539#388C2314yes—
540#388C2314yes—
541#388C2312yes—
542#388C2314yes—
543#388C2314yes—
544#388C2314yes—
545#388C2312yes—
546#388C2314yes—
547#388C2312yes—
548#388C2312yes—
549#388C2314yes—
550#388C2314yes—
551#388C2314yes—
552#388C2314yes—
553#388C2314yes—
554#388C2314yes—
555#388C2312yes—
556#388C2314yes—
557#388C2314yes—
558#388C2314yes—
559#388C2312yes—
560#388C2312yes—
561#388C2312yes—
562#388C2312yes—
563#388C2314yes—
564#388C2314yes—
565#388C2314yes—
566#388C2314yes—
567#388C2314yes—
568#388C2314yes—
569#387C2314yes—
570#387C2314yes—
571#387C2314yes—
572#387C2314yes—
573#387C2314yes—
574#387C2312yes—
575#387C2314yes—
576#387C2314yes—
577#387C2312yes—
578#387C2312yes—
579#387C2312yes—
580#387C2312yes—
581#387C2314yes—
582#387C2314yes—
583#387C2314yes—
584#387C2314yes—
585#387C2314yes—
586#387C2314yes—
587#387C2312yes—
588#387C2314yes—
589#387C2314yes—
590#387C2314yes—
591#387C2314yes—
592#387C2312yes—
593#387C2314yes—
594#387C2314yes—
595#387C2312yes—
596#387C2314yes—
597#387C2314yes—
598#387C2314yes—
599#387C2314yes—
600#387C2314yes—
601#387C2314yes—
602#387C2312yes—
603#387C2314yes—
604#386C2314yes—
605#386C2312yes—
606#386C2314yes—
607#386C2314yes—
608#386C2312yes—
609#386C2312yes—
610#386C2312yes—
611#386C2312yes—
612#386C2314yes—
613#386C2312yes—
614#386C2312yes—
615#386C2312yes—
616#386C2311yescharacteristic
617#385C2314yes—
618#385C2314yes—
619#385C2314yes—
620#385C2314yes—
621#385C2312yes—
622#385C2312yes—
623#385C2314yes—
624#385C2314yes—
625#385C2314yes—
626#385C2312yes—
627#385C2312yes—
628#385C2314yes—
629#385C2314yes—
630#385C2314yes—
631#385C2314yes—
632#385C2314yes—
633#385C2314yes—
634#385C2314yes—
635#385C2314yes—
636#385C2314yes—
637#385C2314yes—
638#385C2314yes—
639#385C2311yescharacteristic
640#385C2312yes—
641#385C2314yes—
642#384C2312yes—
643#384C2314yes—
644#384C2314yes—
645#384C2312yes—
646#384C2312yes—
647#384C2314yes—
648#384C2312yes—
649#384C2312yes—
650#384C2312yes—
651#383C2312yes—
652#383C2314yes—
653#382C2312yes—
654#382C2312yes—
655#382C2312yes—
656#382C2314yes—
657#382C2312yes—
658#382C2312yes—
659#381C2314yes—
660#381C2314yes—
661#381C2312yes—
662#381C2311yescharacteristic
663#381C2314yes—
664#380C2312yes—
665#380C2311yescharacteristic
666#380C2311yescharacteristic
667#380C2312yes—
668#380C2312yes—
669#380C2312yes—
670#380C2312yes—
671#380C2312yes—
672#380C2312yes—
673#380C2312yes—
674#380C2312yes—
675#380C2314yes—
676#380C2314yes—
677#380C2314yes—
678#380C2314yes—
679#380C2312yes—
680#380C2314yes—
681#380C2314yes—
682C4×C4⋊C4C2314yes—
683C4×C4⋊C4C2312yes—
684C4×C4⋊C4C2312yes—
685C4×C4⋊C4C2314yes—
686C4×C4⋊C4C2312yes—
687C4×C4⋊C4C2311yescharacteristic
688C4×C4⋊C4C2312yes—
689C4×C4⋊C4C2314yes—
690C4×C4⋊C4C2312yes—
691C4×C4⋊C4C2312yes—
692C4×C4⋊C4C2312yes—
693C4×C4⋊C4C2312yes—
694C4×C4⋊C4C2312yes—
695C4×C4⋊C4C2312yes—
696C4×C4⋊C4C2312yes—
697C4×C4⋊C4C2314yes—
698C4×C4⋊C4C2312yes—
699C4×C4⋊C4C2312yes—
700C4×C22⋊C4C2314yes—
701C4×C22⋊C4C2314yes—
702C4×C22⋊C4C2312yes—
703C4×C22⋊C4C2312yes—
704C4×C22⋊C4C2312yes—
705C4×C22⋊C4C2312yes—
706C4×C22⋊C4C2312yes—
707C4×C22⋊C4C2314yes—
708C4×C22⋊C4C2312yes—
709C4×C22⋊C4C2311yescharacteristic
710C4×C22⋊C4C2311yescharacteristic
711C4×C22⋊C4C2312yes—
712C4×C22⋊C4C2312yes—
713C4×C22⋊C4C2312yes—
714C4×C22⋊C4C2312yes—
715C4×C22⋊C4C2312yes—
716#376C2312yes—
717#376C2311yescharacteristic
718C2×#95C2312yes—
719C43C2312yes—
720C2×#41—44no—
721C2×#41—48no—
722C22×Q8—48no—
723C22×Q8—48no—
724C22×Q8—44no—
725C22×Q8—48no—
726C22×Q8—48no—
727C22×Q8C2412yes—
728C22×Q8C2414yes—
729C22×Q8C2414yes—
730C22×Q8C2414yes—
731C22×Q8C2414yes—
732C22×Q8C2414yes—
733C22×Q8C2412yes—
734C22×D4C2412yes—
735C22×D4C2411yescharacteristic
736C22×D4C2412yes—
737C22×D4C2411yescharacteristic
738C22×D4C2411yescharacteristic
739C22×D4C2412yes—
740C22×D4C2414yes—
741C22×D4C2412yes—
742C23×C4C2412yes—
743C23×C4C2411yescharacteristic
744C23×C4C2411yescharacteristic
745C23×C4C2414yes—
746C23×C4C2411yescharacteristic
747C23×C4C2412yes—
748C23×C4C2412yes—
749C23×C4C2414yes—
750C23×C4C2412yes—
751C23×C4C2414yes—
752C23×C4C2412yes—
753C23×C4C2412yes—
754C23×C4C2412yes—
755C23×C4C2411yescharacteristic
756C4⋊Q8—28no—
757C4⋊Q8—28no—
758C4⋊Q8—44no—
759C4⋊Q8—44no—
760C4⋊Q8—44no—
761C4⋊Q8—48no—
762C4⋊Q8—42no—
763C4⋊Q8—48no—
764C4⋊Q8—48no—
765C4⋊Q8—44no—
766C4⋊Q8—48no—
767C4⋊Q8—48no—
768C4⋊Q8—48no—
769C4⋊Q8—48no—
770C4⋊Q8—48no—
771C4⋊Q8—48no—
772#126—48no—
773#126—44no—
774#126—48no—
775#125—28no—
776#125—44no—
777#125—44no—
778#125—42no—
779#124—216no—
780#124—28no—
781#124—48no—
782#124—48no—
783#123—28no—
784#123—24no—
785#123—28no—
786#123—48no—
787#123—48no—
788#123—48no—
789#123—48no—
790#123—48no—
791#123—44no—
792#123—48no—
793C22⋊Q8—216no—
794C22⋊Q8—216no—
795C22⋊Q8—48no—
796C22⋊Q8—48no—
797C22⋊Q8—48no—
798C22⋊Q8—48no—
799C22⋊Q8—48no—
800C22⋊Q8—48no—
801C22⋊Q8—48no—
802C22⋊Q8—48no—
803C22⋊Q8—48no—
804C22⋊Q8—44no—
805C22⋊Q8—48no—
806#121—44no—
807#121—48no—
808#121—44no—
809#121—42no—
810#121—42no—
811C4×Q8—28no—
812C4×Q8—48no—
813C4×Q8—48no—
814C4×D4—28no—
815C4×D4—24no—
816C4×D4—28no—
817C4×D4—28no—
818C4×D4—28no—
819C4×D4—28no—
820C4×D4—42no—
821C4×D4—44no—
822C4×D4—42no—
823C4×D4—48no—
824C4×D4—48no—
825C4×D4—48no—
826#117—24no—
827#117—42no—
828#117—48no—
829#117—48no—
830C2×C4⋊C4—28no—
831C2×C4⋊C4—24no—
832C2×C4⋊C4—44no—
833C2×C4⋊C4—42no—
834C2×C4⋊C4—44no—
835C2×C4⋊C4—48no—
836C2×C4⋊C4—42no—
837C2×C4⋊C4C2412yes—
838C2×C4⋊C4C2412yes—
839C2×C4⋊C4C2414yes—
840C2×C4⋊C4C2411yescharacteristic
841C2×C4⋊C4C2412yes—
842C2×C4⋊C4C2414yes—
843C2×C4⋊C4C2414yes—
844C2×C4⋊C4C2412yes—
845C2×C4⋊C4C2414yes—
846C2×C4⋊C4C2411yescharacteristic
847C2×C4⋊C4C2414yes—
848C2×C4⋊C4C2412yes—
849C2×C4⋊C4C2412yes—
850C2×C4⋊C4C2412yes—
851C2×C4⋊C4C2412yes—
852C2×C4⋊C4C2412yes—
853C2×C4⋊C4C2414yes—
854C2×C4⋊C4C2414yes—
855C2×C4⋊C4C2412yes—
856C2×C4⋊C4C2412yes—
857C2×C4⋊C4C2412yes—
858C2×C4⋊C4C2414yes—
859C2×C4⋊C4C2412yes—
860C2×C4⋊C4C2412yes—
861C2×C4⋊C4C2414yes—
862C2×C4⋊C4C2414yes—
863C2×C4⋊C4C2412yes—
864C2×C4⋊C4C2412yes—
865C2×C4⋊C4C2412yes—
866C2×C4⋊C4C2414yes—
867C2×C4⋊C4C2414yes—
868C2×C4⋊C4C2412yes—
869C2×C4⋊C4C2414yes—
870C2×C4⋊C4C2414yes—
871C2×C4⋊C4C2412yes—
872C2×C4⋊C4C2414yes—
873C2×C4⋊C4C2414yes—
874C2×C4⋊C4C2414yes—
875C2×C4⋊C4C2411yescharacteristic
876C2×C4⋊C4C2414yes—
877C2×C4⋊C4C2411yescharacteristic
878C2×C4⋊C4C2411yescharacteristic
879C2×C4⋊C4C2414yes—
880C2×C4⋊C4C2412yes—
881C2×C4⋊C4C2411yescharacteristic
882C2×C4⋊C4C2414yes—
883C2×C4⋊C4C2414yes—
884C2×C4⋊C4C2414yes—
885C2×C4⋊C4C2414yes—
886C2×C4⋊C4C2414yes—
887C2×C4⋊C4C2412yes—
888C2×C4⋊C4C2414yes—
889C2×C4⋊C4C2414yes—
890C2×C4⋊C4C2414yes—
891C2×C4⋊C4C2414yes—
892C2×C4⋊C4C2414yes—
893C2×C4⋊C4C2414yes—
894C2×C4⋊C4C2414yes—
895C2×C4⋊C4C2414yes—
896C2×C4⋊C4C2414yes—
897C2×C4⋊C4C2412yes—
898C2×C4⋊C4C2414yes—
899C2×C4⋊C4C2414yes—
900C2×C4⋊C4C2414yes—
901C2×C4⋊C4C2412yes—
902C2×C4⋊C4C2414yes—
903C2×C4⋊C4C2411yescharacteristic
904C2×C22⋊C4C2412yes—
905C2×C22⋊C4C2412yes—
906C2×C22⋊C4C2414yes—
907C2×C22⋊C4C2414yes—
908C2×C22⋊C4C2412yes—
909C2×C22⋊C4C2412yes—
910C2×C22⋊C4C2414yes—
911C2×C22⋊C4C2414yes—
912C2×C22⋊C4C2412yes—
913C2×C22⋊C4C2412yes—
914C2×C22⋊C4C2412yes—
915C2×C22⋊C4C2412yes—
916C2×C22⋊C4C2412yes—
917C2×C22⋊C4C2414yes—
918C2×C22⋊C4C2412yes—
919C2×C22⋊C4C2414yes—
920C2×C22⋊C4C2412yes—
921C2×C22⋊C4C2412yes—
922C2×C22⋊C4C2412yes—
923C2×C22⋊C4C2412yes—
924C2×C22⋊C4C2412yes—
925C2×C22⋊C4C2411yescharacteristic
926C2×C22⋊C4C2414yes—
927C2×C22⋊C4C2412yes—
928C2×C22⋊C4C2412yes—
929C2×C22⋊C4C2414yes—
930C2×C22⋊C4C2414yes—
931C2×C22⋊C4C2411yescharacteristic
932C2×C22⋊C4C2412yes—
933C2×C22⋊C4C2414yes—
934C2×C22⋊C4C2414yes—
935C2×C22⋊C4C2412yes—
936C2×C22⋊C4C2411yescharacteristic
937C2×C22⋊C4C2414yes—
938C2×C22⋊C4C2414yes—
939C2×C22⋊C4C2414yes—
940C2×C22⋊C4C2412yes—
941C2×C22⋊C4C2414yes—
942C2×C22⋊C4C2414yes—
943C2×C22⋊C4C2414yes—
944C2×C22⋊C4C2411yescharacteristic
945C2×C22⋊C4C2414yes—
946C2×C22⋊C4C2412yes—
947C2×C22⋊C4C2412yes—
948C2×C22⋊C4C2414yes—
949C2×C22⋊C4C2412yes—
950C2×C42—42no—
951C2×C42—44no—
952C2×C42C2412yes—
953C2×C42C2412yes—
954C2×C42C2414yes—
955C2×C42C2412yes—
956C2×C42C2411yescharacteristic
957C2×C42C2412yes—
958C2×C42C2412yes—
959C2×C42C2412yes—
960C2×C42C2412yes—
961C2×C42C2412yes—
962C2×C42C2414yes—
963C2×C42C2414yes—
964C2×C42C2414yes—
965C2×C42C2414yes—
966C2×C42C2414yes—
967C2×C42C2412yes—
968C2×C42C2412yes—
969C2×C42C2412yes—
970C2×C42C2412yes—
971C2×C42C2412yes—
972C2×C42C2414yes—
973C2×C42C2412yes—
974#95C2411yescharacteristic
975#95C2414yes—
976#95C2412yes—
977#95C2412yes—
978#95C2411yescharacteristic
979#95C2412yes—
980#95C2412yes—
981#95C2412yes—
982#95C2412yes—
983#95C2412yes—
984#95C2412yes—
985#95C2412yes—
986#95C2412yes—
987#95C2412yes—
988#95C2412yes—
989#95C2414yes—
990#95C2411yescharacteristic
991#95C2414yes—
992#95C2414yes—
993#95C2414yes—
994#95C2412yes—
995#95C2412yes—
996#95C2411yescharacteristic
997#95C2412yes—
998#95C2412yes—
999#95C2414yes—
1000#95C2412yes—
1001#95C2412yes—
1002#95C2412yes—
1003#95C2414yes—
1004#95C2414yes—
1005#95C2412yes—
1006#95C2414yes—
1007#95C2414yes—
1008#95C2412yes—
1009#95C2414yes—
1010#95C2412yes—
1011#95C2412yes—
1012#95C2414yes—
1013#95C2414yes—
1014#95C2414yes—
1015#95C2414yes—
1016#95C2414yes—
1017#95C2412yes—
1018#95C2414yes—
1019#95C2414yes—
1020#95C2414yes—
1021#95C2414yes—
1022#95C2414yes—
1023#95C2414yes—
1024#95C2414yes—
1025#95C2414yes—
1026#95C2412yes—
1027#95C2414yes—
1028#95C2414yes—
1029#95C2414yes—
1030#95C2414yes—
1031#95C2414yes—
1032#95C2414yes—
1033#95C2414yes—
1034#95C2414yes—
1035#95C2414yes—
1036#95C2414yes—
1037#95C2414yes—
1038#95C2414yes—
1039C24C2511yescharacteristic
1040C24C2512yes—
1041C24C2512yes—
1042C24C2511yescharacteristic
1043#41—816no—
1044C2×Q8—24no—
1045C2×Q8—28no—
1046C2×Q8—28no—
1047C2×Q8—28no—
1048C2×Q8—28no—
1049C2×Q8—28no—
1050C2×Q8—24no—
1051C2×Q8—44no—
1052C2×Q8—42no—
1053C2×Q8—44no—
1054C2×Q8—44no—
1055C2×Q8—44no—
1056C2×Q8—44no—
1057C2×Q8—44no—
1058C2×Q8—42no—
1059C2×Q8—44no—
1060C2×Q8—44no—
1061C2×Q8—44no—
1062C2×Q8—44no—
1063C2×Q8—44no—
1064C2×Q8—832no—
1065C2×Q8—816no—
1066C2×D4—24no—
1067C2×D4—24no—
1068C2×D4—24no—
1069C2×D4—24no—
1070C2×D4—28no—
1071C2×D4—24no—
1072C2×D4—22no—
1073C2×D4—22no—
1074C2×D4—24no—
1075C2×D4—24no—
1076C2×D4—24no—
1077C2×D4—41no—
1078C2×D4—42no—
1079C2×D4—41no—
1080C2×D4—42no—
1081C2×D4—44no—
1082C2×D4—44no—
1083C2×D4—42no—
1084C2×D4—41no—
1085C2×D4—42no—
1086C2×D4—44no—
1087C22×C4—24no—
1088C22×C4—28no—
1089C22×C4—28no—
1090C22×C4—24no—
1091C22×C4—22no—
1092C22×C4—28no—
1093C22×C4—22no—
1094C22×C4—24no—
1095C22×C4—24no—
1096C22×C4—24no—
1097C22×C4—24no—
1098C22×C4—24no—
1099C22×C4—24no—
1100C22×C4—24no—
1101C22×C4—24no—
1102C22×C4—24no—
1103C22×C4—28no—
1104C22×C4—41no—
1105C22×C4—42no—
1106C22×C4—41no—
1107C22×C4—42no—
1108C22×C4—44no—
1109C22×C4—41no—
1110C22×C4—42no—
1111C22×C4—44no—
1112C22×C4—42no—
1113C22×C4—44no—
1114C22×C4—44no—
1115C22×C4—44no—
1116C22×C4—44no—
1117C22×C4—44no—
1118C22×C4—44no—
1119C22×C4—42no—
1120C22×C4—44no—
1121C22×C42−1+414yes—
1122C22×C4C2511yescharacteristic
1123C22×C4C2512yes—
1124C22×C4C2511yescharacteristic
1125C22×C4C2514yes—
1126C22×C4C2512yes—
1127C22×C4C2512yes—
1128C22×C4C2512yes—
1129C22×C4C2511yescharacteristic
1130C22×C4C2512yes—
1131C22×C4C2512yes—
1132C22×C4C2514yes—
1133C22×C4C2514yes—
1134C22×C4C2512yes—
1135C22×C4C2514yes—
1136C22×C4C2514yes—
1137C22×C4C2511yescharacteristic
1138C22×C4C2512yes—
1139C22×C4C2514yes—
1140C22×C4C2512yes—
1141C22×C4C2512yes—
1142C22×C4C2512yes—
1143C22×C4C2512yes—
1144C22×C4C2512yes—
1145C22×C4C2512yes—
1146C22×C4C2511yescharacteristic
1147C4⋊C4—22no—
1148C4⋊C4—24no—
1149C4⋊C4—28no—
1150C4⋊C4—24no—
1151C4⋊C4—24no—
1152C4⋊C4—28no—
1153C4⋊C4—24no—
1154C4⋊C4—28no—
1155C4⋊C4—22no—
1156C4⋊C4—28no—
1157C4⋊C4—28no—
1158C4⋊C4—24no—
1159C4⋊C4—28no—
1160C4⋊C4—28no—
1161C4⋊C4—28no—
1162C4⋊C4—28no—
1163C4⋊C4—24no—
1164C4⋊C4—24no—
1165C4⋊C4—24no—
1166C4⋊C4—24no—
1167C4⋊C4—24no—
1168C4⋊C4—24no—
1169C4⋊C4—24no—
1170C4⋊C4—24no—
1171C4⋊C4—24no—
1172C4⋊C4—28no—
1173C4⋊C4—24no—
1174C4⋊C4—28no—
1175C4⋊C4—28no—
1176C4⋊C4—24no—
1177C4⋊C4—24no—
1178C4⋊C4—42no—
1179C4⋊C4—44no—
1180C4⋊C4—44no—
1181C4⋊C4—44no—
1182C4⋊C4—44no—
1183C4⋊C4—42no—
1184C4⋊C4—42no—
1185C4⋊C4—44no—
1186C4⋊C4—44no—
1187C4⋊C4—44no—
1188C4⋊C4—41no—
1189C4⋊C4—44no—
1190C4⋊C4—41no—
1191C4⋊C4—41no—
1192C4⋊C4—44no—
1193C4⋊C4—42no—
1194C4⋊C4—41no—
1195C4⋊C4—44no—
1196C4⋊C4—44no—
1197C4⋊C4—44no—
1198C4⋊C4—44no—
1199C4⋊C4—44no—
1200C4⋊C4—42no—
1201C4⋊C4—44no—
1202C4⋊C4—44no—
1203C4⋊C4—44no—
1204C4⋊C4—44no—
1205C4⋊C4—44no—
1206C4⋊C4—44no—
1207C4⋊C4—44no—
1208C4⋊C4—44no—
1209C4⋊C4—44no—
1210C4⋊C4—42no—
1211C4⋊C4—44no—
1212C4⋊C4—44no—
1213C4⋊C4H(5,𝔽2)14yes—
1214C22⋊C4—28no—
1215C22⋊C4—28no—
1216C22⋊C4—28no—
1217C22⋊C4—24no—
1218C22⋊C4—24no—
1219C22⋊C4—24no—
1220C22⋊C4—24no—
1221C22⋊C4—22no—
1222C22⋊C4—24no—
1223C22⋊C4—24no—
1224C22⋊C4—28no—
1225C22⋊C4—24no—
1226C22⋊C4—24no—
1227C22⋊C4—28no—
1228C22⋊C4—24no—
1229C22⋊C4—24no—
1230C22⋊C4—24no—
1231C22⋊C4—24no—
1232C22⋊C4—28no—
1233C22⋊C4—24no—
1234C22⋊C4—24no—
1235C22⋊C4—24no—
1236C22⋊C4—28no—
1237C22⋊C4—24no—
1238C22⋊C4—44no—
1239C22⋊C4—42no—
1240C22⋊C4—44no—
1241C22⋊C4—42no—
1242C22⋊C4—41no—
1243C22⋊C4—42no—
1244C22⋊C4—44no—
1245C22⋊C4—44no—
1246C22⋊C4—41no—
1247C22⋊C4—42no—
1248C22⋊C4—44no—
1249C22⋊C4—44no—
1250C22⋊C4—42no—
1251C22⋊C4—41no—
1252C22⋊C4—44no—
1253C22⋊C4—44no—
1254C22⋊C4—44no—
1255C22⋊C4—42no—
1256C22⋊C4—44no—
1257C22⋊C4—44no—
1258C22⋊C4—44no—
1259C22⋊C4H(5,𝔽2)18yes—
1260C42—24no—
1261C42—24no—
1262C42—24no—
1263C42—24no—
1264C42—28no—
1265C42—22no—
1266C42—24no—
1267C42—24no—
1268C42—24no—
1269C42—24no—
1270C42—42no—
1271C42—42no—
1272C42—42no—
1273C42—42no—
1274C42—44no—
1275C42—42no—
1276C42—44no—
1277C42—44no—
1278C42—44no—
1279C42—44no—
1280C42—44no—
1281C422−1+418yes—
1282C23—22no—
1283C23—22no—
1284C23—22no—
1285C23—21no—
1286C23—22no—
1287C23—22no—
1288C23—22no—
1289C23—22no—
1290C23—22no—
1291C23—21no—
1292C23—24no—
1293C23—22no—
1294C23—21no—
1295C23—22no—
1296C23—21no—
1297C23—22no—
1298C23—22no—
1299C23—24no—
1300C23—22no—
1301C23—21no—
1302C23C2×H(5,𝔽2)14yes—
1303C23C2×2−1+412yes—
1304C23C2611yescharacteristic
1305Q8—48no—
1306Q8—416no—
1307Q8—88no—
1308Q8—88no—
1309Q8—88no—
1310Q8—88no—
1311Q8—84no—
1312D4—216no—
1313D4—48no—
1314D4—44no—
1315D4—44no—
1316D4—82no—
1317D4—84no—
1318D4—88no—
1319D4—162no—
1320C2×C4—22no—
1321C2×C4—22no—
1322C2×C4—22no—
1323C2×C4—22no—
1324C2×C4—22no—
1325C2×C4—24no—
1326C2×C4—22no—
1327C2×C4—22no—
1328C2×C4—22no—
1329C2×C4—22no—
1330C2×C4—22no—
1331C2×C4—21no—
1332C2×C4—24no—
1333C2×C4—22no—
1334C2×C4—24no—
1335C2×C4—22no—
1336C2×C4—22no—
1337C2×C4—21no—
1338C2×C4—22no—
1339C2×C4—21no—
1340C2×C4—22no—
1341C2×C4—22no—
1342C2×C4—24no—
1343C2×C4—22no—
1344C2×C4—21no—
1345C2×C4—24no—
1346C2×C4—24no—
1347C2×C4—24no—
1348C2×C4—24no—
1349C2×C4—24no—
1350C2×C4—22no—
1351C2×C4—24no—
1352C2×C4—22no—
1353C2×C4—22no—
1354C2×C4—24no—
1355C2×C4—24no—
1356C2×C4—24no—
1357C2×C4—22no—
1358C2×C4—24no—
1359C2×C4—22no—
1360C2×C4—22no—
1361C2×C4—22no—
1362C2×C4—22no—
1363C2×C4—24no—
1364C2×C4—22no—
1365C2×C4—22no—
1366C2×C4—22no—
1367C2×C4—22no—
1368C2×C4—22no—
1369C2×C4—22no—
1370C2×C4—24no—
1371C2×C4—24no—
1372C2×C4—24no—
1373C2×C4—21no—
1374C2×C4—22no—
1375C2×C4—22no—
1376C2×C4—21no—
1377C2×C4—24no—
1378C2×C4—24no—
1379C2×C4—22no—
1380C2×C4—22no—
1381C2×C4—44no—
1382C2×C4—44no—
1383C2×C4—48no—
1384C2×C4—416no—
1385C2×C4—48no—
1386C2×C4—48no—
1387C2×C4—44no—
1388C2×C4—44no—
1389C2×C4—88no—
1390C2×C4—84no—
1391C2×C4—84no—
1392C2×C4—88no—
1393C2×C4—84no—
1394C2×C4—162no—
1395C2×C4C2×H(5,𝔽2)14yes—
1396C2×C4C2×H(5,𝔽2)14yes—
1397C2×C4C2×H(5,𝔽2)14yes—
1398C2×C4C2×H(5,𝔽2)12yes—
1399C2×C4C2×2−1+414yes—
1400C2×C4C2×2−1+414yes—
1401C2×C4C2×2−1+414yes—
1402C2×C4C2×2−1+414yes—
1403C22—24no—
1404C22—24no—
1405C22—24no—
1406C22—22no—
1407C22—24no—
1408C22—41no—
1409C22—42no—
1410C22—41no—
1411C22—42no—
1412C22—42no—
1413C22—42no—
1414C22—42no—
1415C22—42no—
1416C22—41no—
1417C22—41no—
1418C22—42no—
1419C22—44no—
1420C22—42no—
1421C22—41no—
1422C22—42no—
1423C22—44no—
1424C22—42no—
1425C22C22×H(5,𝔽2)11yescharacteristic
1426C22C22×H(5,𝔽2)12yes—
1427C22C22×2−1+412yes—
1428C22C22×2−1+411yescharacteristic
1429C222−1+611yescharacteristic
1430C4—24no—
1431C4—24no—
1432C4—24no—
1433C4—24no—
1434C4—24no—
1435C4—24no—
1436C4—44no—
1437C4—42no—
1438C4—41no—
1439C4—44no—
1440C4—44no—
1441C4—42no—
1442C4—41no—
1443C4—42no—
1444C4—41no—
1445C4—44no—
1446C4—42no—
1447C4—42no—
1448C4—42no—
1449C4—41no—
1450C4—42no—
1451C4—44no—
1452C4—44no—
1453C4—42no—
1454C4#355014yes—
1455C2—44no—
1456C2—42no—
1457C2—82no—
1458C2—81no—
1459C2C2×#355011yescharacteristic
1460C2#6283312yes—
1461C2#6289311yescharacteristic
1462C2#6291512yes—
1463C2#6301111yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#35923C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59430C2semidirect
2. #57966C2semidirect
3. #55192C2semidirect
4. #53524C2semidirect
5. #53009C2semidirect
6. #49557C2semidirect
7. #49098C2semidirect
8. #48902C2semidirect
9. #47766C2semidirect
10. #46847C2semidirect
11. #45648C2semidirect
12. #45502C2semidirect
13. #45375C2semidirect
14. #45321C2semidirect
15. #44984C2semidirect
16. #42914C2semidirect
17. #42514C2semidirect
18. #40974C2semidirect
19. #39720C2semidirect
20. #39625C2semidirect
21. #39377C2semidirect
22. #39337C2semidirect
23. #37686C2semidirect
24. #37340C2semidirect
25. D4×C4⋊Q8C2semidirect
27. #35581C2semidirect
28. #35107C2semidirect
29. #34921C2semidirect

Maximal subgroups

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

subgroupindex
#594302
#579662
#551922
#535242
#530092
#495572
#490982
#489022
#477662
#468472
#456482
#455022
#453752
#453212
#449842
#429142
#425142
#409742
#397202
#396252
#393772
#393372
#376862
#373402
D4×C4⋊Q82
#359232
#355812
#351072
#349212