Finite Group Databasebeta

← #8678561

Subgroups — #8678561

Order 512.

5237 conjugacy classes of subgroups.

The subgroup lattice has 1546 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59677C212yesmaximal, complemented
2#59112C212yesmaximal, complemented
3#59039C212yesmaximal, complemented
4#58193C214yesmaximal, complemented
5#55552C214yesmaximal, complemented
6#53509C214yesmaximal, complemented
7#53195C212yesmaximal, complemented
8#52303C211yesmaximal, characteristic, complemented
9#51537C214yesmaximal, complemented
10#48565C214yesmaximal, complemented
11#47936C214yesmaximal, complemented
12#46152C211yesmaximal, characteristic, complemented
13#45998C211yesmaximal, characteristic, complemented
14#45995C211yesmaximal, characteristic, complemented
15#45046C212yesmaximal, complemented
16#44940C212yesmaximal, complemented
17#44928C212yesmaximal, complemented
18#42946C212yesmaximal, complemented
19#42608C212yesmaximal, complemented
20#42556C212yesmaximal, complemented
21#40077C212yesmaximal, complemented
22#39623C212yesmaximal, complemented
23#39359C212yesmaximal, complemented
24#39340C212yesmaximal, complemented
25#38780C212yesmaximal, complemented
26#38445C212yesmaximal, complemented
27#36453C211yesmaximal, characteristic, complemented
28#36412C211yesmaximal, characteristic, complemented
29#36290C211yesmaximal, characteristic, complemented
30C2×#563C2212yes—
31C2×#562C2212yes—
32C2×#555C2211yescharacteristic
33C2×#550C2211yescharacteristic
34C2×#547C2214yes—
35C2×#547C2212yes—
36C2×#537C2214yes—
37C2×#532C2212yes—
38#2859C2211yescharacteristic
39#2859C2211yescharacteristic
40#2858C2211yescharacteristic
41#2857C2212yes—
42#2856C2212yes—
43#2855C2212yes—
44#2851C2212yes—
45#2844C2212yes—
46#2838C2214yes—
47#2829C2214yes—
48#2827C2214yes—
49#2820C2212yes—
50#2820C2212yes—
51#2809C2212yes—
52#2808C2211yescharacteristic
53#2806C2211yescharacteristic
54#2806C2214yes—
55#2800C2214yes—
56#2797C2214yes—
57#2792C2214yes—
58#2792C2214yes—
59#2787C2214yes—
60#2786C2214yes—
61#2783C2212yes—
62#2781C2212yes—
63#2780C2214yes—
64#2780C2214yes—
65#2779C2214yes—
66#2779C2214yes—
67#2746C2214yes—
68#2744C2212yes—
69#2742C2214yes—
70#2734C2214yes—
71#2732C2212yes—
72#2732C2211yescharacteristic
73#2730C2212yes—
74#2729C2214yes—
75#2727C2212yes—
76#2723C2214yes—
77#2723C2214yes—
78#2720C2214yes—
79#2720C2214yes—
80#2717C2214yes—
81#2709C2214yes—
82#2708C2214yes—
83#2708C2214yes—
84#2707C2214yes—
85#2706C2214yes—
86#2705C2214yes—
87#2701C2214yes—
88#2695C2214yes—
89#2694C2212yes—
90#2692C2214yes—
91#2691C2214yes—
92#2687C2214yes—
93#2686C2214yes—
94#2686C2212yes—
95#2686C2214yes—
96#2683C2212yes—
97#2683C2212yes—
98#2682C2211yescharacteristic
99#2682C2212yes—
100#2681C2214yes—
101#2681C2214yes—
102#2681C2214yes—
103#2674C2214yes—
104#2674C2214yes—
105#2674C2214yes—
106#2672C2214yes—
107#2672C2214yes—
108#2672C2214yes—
109#2672C2214yes—
110#2672C2214yes—
111#2671C2214yes—
112#2671C2214yes—
113#2671C2214yes—
114#2671C2214yes—
115#2667C2214yes—
116#2663C2214yes—
117#2659C2214yes—
118#2653C2214yes—
119#2648C2214yes—
120#2630C2214yes—
121#2630C2214yes—
122#2624C2212yes—
123#2618C2214yes—
124#2616C2214yes—
125#2608C2214yes—
126#2579C2214yes—
127#2576C2214yes—
128#2571C2211yescharacteristic
129#2567C2211yescharacteristic
130#2567C2212yes—
131#2564C2214yes—
132#2563C2212yes—
133#2559C2214yes—
134#2555C2214yes—
135#2555C2214yes—
136#2553C2214yes—
137#2552C2211yescharacteristic
138#2551C2212yes—
139#2551C2212yes—
140#2549C2214yes—
141#2542C2212yes—
142#2541C2211yescharacteristic
143#2538C2211yescharacteristic
144#2538C2212yes—
145#2537C2214yes—
146#2537C2211yescharacteristic
147#2537C2212yes—
148#2537C2212yes—
149#2522C2214yes—
150#2512C2212yes—
151#2512C2212yes—
152#2509C2212yes—
153#2507C2212yes—
154#2507C2212yes—
155#2507C2212yes—
156#2507C2212yes—
157#2505C2214yes—
158#2501C2212yes—
159#2500C2212yes—
160#2497C2212yes—
161#2497C2212yes—
162#2494C2212yes—
163#2494C2212yes—
164#2487C2212yes—
165#2485C2212yes—
166#2481C2214yes—
167#2473C2214yes—
168#2470C2214yes—
169#2467C2214yes—
170#2464C2214yes—
171#2460C2214yes—
172#2460C2214yes—
173#2455C2214yes—
174#2452C2214yes—
175#2452C2212yes—
176#2449C2214yes—
177#2449C2214yes—
178#2445C2212yes—
179#2445C2212yes—
180#2444C2214yes—
181#2442C2212yes—
182#2442C2212yes—
183#2440C2214yes—
184#2440C2212yes—
185#2440C2212yes—
186#2440C2214yes—
187#2440C2212yes—
188#2440C2212yes—
189#2439C2212yes—
190#2438C2214yes—
191#2432C2214yes—
192#2431C2212yes—
193#2430C2214yes—
194#2430C2214yes—
195#2430C2214yes—
196#2430C2214yes—
197#2428C2212yes—
198#2428C2212yes—
199#2428C2212yes—
200#2428C2214yes—
201#2428C2212yes—
202#2427C2212yes—
203#2425C2214yes—
204#2425C2214yes—
205#2422C2214yes—
206#2422C2212yes—
207#2422C2212yes—
208#2422C2212yes—
209#2420C2212yes—
210#2420C2212yes—
211#2417C2214yes—
212#2416C2214yes—
213#2416C2214yes—
214#2416C2212yes—
215#2416C2212yes—
216#2416C2212yes—
217#2416C2212yes—
218#2407C2214yes—
219#2407C2214yes—
220#2406C2214yes—
221#2396C2212yes—
222#2395C2212yes—
223#2392C2212yes—
224#2379C2212yes—
225#2366C2212yes—
226#2364C2214yes—
227#2363C2212yes—
228#2363C2212yes—
229#2361C2212yes—
230#2361C2212yes—
231#2355C2211yescharacteristic
232#2352C2212yes—
233#2349C2212yes—
234#2349C2212yes—
235D4×C4⋊C4C2211yescharacteristic
236D4×C4⋊C4C2212yes—
237D4×C4⋊C4C2211yescharacteristic
238D4×C4⋊C4C2211yescharacteristic
239#2345C2212yes—
240#2345C2212yes—
241#2339C2214yes—
242#2329C2214yes—
243#2329C2214yes—
244#2324C2212yes—
245#2324C2212yes—
246#2317C2212yes—
247C4×#125C2211yescharacteristic
248C4×#124C2211yescharacteristic
249C4×#124C2211yescharacteristic
250C4×C22⋊Q8C2212yes—
251C4×#123C2212yes—
252C4×#121C2212yes—
253C4×#121C2212yes—
254C4×#121C2212yes—
255#2297C2212yes—
256C2×#389C2212yes—
257C2×#389C2212yes—
258C42×D4C2211yescharacteristic
259C22×#41C2312yes—
260C22×#41C2314yes—
261C22×#41C2314yes—
262#563—48no—
263#562—48no—
264#555—44no—
265#550—44no—
266#547—416no—
267#547—48no—
268#537—416no—
269#532—48no—
270C2×C4⋊Q8C2312yes—
271C2×C4⋊Q8C2311yescharacteristic
272C2×C4⋊Q8C2312yes—
273C2×C4⋊Q8C2314yes—
274C2×C4⋊Q8C2314yes—
275C2×#127C2312yes—
276C2×#127C2311yescharacteristic
277C2×#127C2312yes—
278C2×#126C2314yes—
279C2×#126C2314yes—
280C2×#125C2311yescharacteristic
281C2×#125C2312yes—
282C2×#125C2312yes—
283C2×#125C2312yes—
284C2×#124C2311yescharacteristic
285C2×#124C2311yescharacteristic
286C2×#124C2312yes—
287C2×#124C2312yes—
288C2×#124C2314yes—
289C2×#124C2314yes—
290C2×#123C2312yes—
291C2×#123C2314yes—
292C2×#123C2314yes—
293C2×#123C2314yes—
294C2×#123C2314yes—
295C2×#123C2314yes—
296C2×#123C2314yes—
297C2×#123C2314yes—
298C2×#123C2314yes—
299C2×#123C2314yes—
300C2×C22⋊Q8C2312yes—
301C2×C22⋊Q8C2314yes—
302C2×C22⋊Q8C2314yes—
303C2×C22⋊Q8C2314yes—
304C2×C22⋊Q8C2314yes—
305C2×C22⋊Q8C2314yes—
306C2×C22⋊Q8C2314yes—
307C2×C22⋊Q8C2314yes—
308C2×C22⋊Q8C2314yes—
309C2×C22⋊Q8C2314yes—
310C2×C22⋊Q8C2314yes—
311C2×C22⋊Q8C2312yes—
312C2×#121C2312yes—
313C2×#121C2312yes—
314C2×#121C2312yes—
315C2×#121C2314yes—
316C2×#121C2312yes—
317C2×#121C2312yes—
318C2×#121C2314yes—
319C2×#121C2314yes—
320C2×#121C2312yes—
321C2×#121C2312yes—
322C2×#121C2312yes—
323C2×#121C2314yes—
324C2×#121C2314yes—
325C2×#121C2314yes—
326C2×#121C2314yes—
327C2×#121C2314yes—
328C2×#121C2314yes—
329C2×#121C2312yes—
330C2×#121C2312yes—
331C2×#121C2314yes—
332C2×#121C2314yes—
333C2×#121C2314yes—
334C2×C4×Q8C2311yescharacteristic
335C2×C4×Q8C2311yescharacteristic
336C2×C4×D4C2312yes—
337C2×C4×D4C2311yescharacteristic
338C2×C4×D4C2311yescharacteristic
339C2×C4×D4C2312yes—
340C2×C4×D4C2314yes—
341C2×C4×D4C2312yes—
342C2×C4×D4C2312yes—
343C2×C4×D4C2314yes—
344C2×C4×D4C2311yescharacteristic
345C2×C4×D4C2311yescharacteristic
346C2×C4×D4C2312yes—
347C2×C4×D4C2312yes—
348C2×C4×D4C2314yes—
349C2×C4×D4C2311yescharacteristic
350C2×C4×D4C2312yes—
351C2×C4×D4C2314yes—
352C2×C4×D4C2312yes—
353C2×C4×D4C2314yes—
354C2×#117C2312yes—
355C2×#117C2312yes—
356C2×#117C2312yes—
357C22×C4⋊C4C2312yes—
358C22×C4⋊C4C2312yes—
359C22×C4⋊C4C2312yes—
360C22×C4⋊C4C2314yes—
361C22×C4⋊C4C2312yes—
362C22×C4⋊C4C2314yes—
363C22×C4⋊C4C2312yes—
364C22×C42C2312yes—
365C22×C42C2312yes—
366#401C2314yes—
367#400C2314yes—
368#400C2314yes—
369#400C2312yes—
370#400C2314yes—
371#400C2312yes—
372#400C2314yes—
373#400C2314yes—
374#400C2314yes—
375#399C2312yes—
376#399C2314yes—
377#399C2314yes—
378#399C2314yes—
379#399C2314yes—
380#399C2312yes—
381#399C2314yes—
382#399C2314yes—
383#398C2314yes—
384#398C2314yes—
385#398C2314yes—
386#398C2312yes—
387#398C2314yes—
388#398C2314yes—
389#398C2314yes—
390#398C2314yes—
391#398C2312yes—
392#398C2312yes—
393#398C2312yes—
394#398C2314yes—
395#398C2314yes—
396#398C2314yes—
397#398C2314yes—
398#398C2314yes—
399#398C2314yes—
400#397C2314yes—
401#397C2314yes—
402#397C2314yes—
403#397C2314yes—
404#397C2312yes—
405#397C2314yes—
406#397C2314yes—
407#397C2314yes—
408#397C2314yes—
409#397C2312yes—
410#397C2312yes—
411#397C2312yes—
412#397C2314yes—
413#397C2314yes—
414#396C2314yes—
415#396C2314yes—
416#396C2314yes—
417#396C2314yes—
418#396C2314yes—
419#396C2314yes—
420#396C2314yes—
421#396C2314yes—
422#396C2314yes—
423#396C2314yes—
424#396C2312yes—
425#396C2314yes—
426#396C2312yes—
427#396C2312yes—
428#396C2312yes—
429#396C2314yes—
430#396C2314yes—
431#395C2314yes—
432#395C2314yes—
433#395C2314yes—
434#395C2314yes—
435#395C2314yes—
436#395C2314yes—
437#395C2314yes—
438#395C2314yes—
439#395C2314yes—
440#395C2312yes—
441#395C2314yes—
442#395C2314yes—
443#394C2314yes—
444#394C2314yes—
445#394C2314yes—
446#394C2314yes—
447#394C2314yes—
448#394C2314yes—
449#394C2314yes—
450#394C2314yes—
451#394C2314yes—
452#394C2314yes—
453#394C2314yes—
454#394C2314yes—
455#394C2314yes—
456#394C2314yes—
457#394C2314yes—
458#394C2314yes—
459#394C2314yes—
460#394C2312yes—
461#394C2312yes—
462#394C2312yes—
463#394C2314yes—
464#394C2314yes—
465#394C2312yes—
466#394C2312yes—
467#394C2314yes—
468#394C2314yes—
469#394C2314yes—
470#394C2314yes—
471#394C2314yes—
472#394C2314yes—
473#393C2314yes—
474#393C2314yes—
475#393C2314yes—
476#393C2312yes—
477#393C2314yes—
478#392C2314yes—
479#392C2314yes—
480#392C2312yes—
481#392C2314yes—
482#392C2314yes—
483#392C2314yes—
484#391C2312yes—
485#391C2314yes—
486#391C2314yes—
487#391C2314yes—
488#391C2312yes—
489#391C2311yescharacteristic
490#391C2312yes—
491#391C2311yescharacteristic
492#390C2312yes—
493#390C2312yes—
494#390C2314yes—
495#390C2312yes—
496#390C2314yes—
497#390C2311yescharacteristic
498#390C2312yes—
499#390C2314yes—
500#390C2314yes—
501#390C2312yes—
502#390C2312yes—
503#390C2312yes—
504#390C2312yes—
505#390C2314yes—
506#390C2312yes—
507#390C2312yes—
508#390C2312yes—
509#390C2311yescharacteristic
510#389C2311yescharacteristic
511#389C2311yescharacteristic
512#389C2312yes—
513#389C2312yes—
514#389C2312yes—
515#389C2312yes—
516#389C2312yes—
517#389C2312yes—
518#389C2312yes—
519#389C2312yes—
520#389C2314yes—
521#389C2314yes—
522#389C2312yes—
523#389C2312yes—
524#389C2312yes—
525#389C2314yes—
526#389C2314yes—
527#389C2314yes—
528#389C2312yes—
529#389C2312yes—
530#389C2312yes—
531#389C2312yes—
532#389C2314yes—
533#389C2312yes—
534#389C2312yes—
535#389C2312yes—
536#389C2312yes—
537#389C2312yes—
538#389C2312yes—
539#389C2312yes—
540#389C2314yes—
541#389C2314yes—
542#389C2314yes—
543#389C2314yes—
544#389C2314yes—
545#389C2312yes—
546#389C2312yes—
547#389C2314yes—
548#388C2314yes—
549#388C2312yes—
550#388C2314yes—
551#388C2314yes—
552#388C2314yes—
553#388C2314yes—
554#388C2314yes—
555#388C2314yes—
556#388C2314yes—
557#388C2314yes—
558#388C2314yes—
559#388C2314yes—
560#388C2312yes—
561#388C2314yes—
562#388C2312yes—
563#388C2312yes—
564#388C2312yes—
565#388C2312yes—
566#388C2314yes—
567#388C2314yes—
568#388C2312yes—
569#388C2312yes—
570#387C2312yes—
571#387C2312yes—
572#387C2314yes—
573#387C2314yes—
574#387C2314yes—
575#387C2314yes—
576#387C2314yes—
577#387C2314yes—
578#387C2314yes—
579#387C2312yes—
580#387C2314yes—
581#387C2314yes—
582#387C2314yes—
583#387C2314yes—
584#387C2314yes—
585#387C2314yes—
586#387C2314yes—
587#387C2314yes—
588#387C2312yes—
589#387C2312yes—
590#387C2312yes—
591#387C2314yes—
592#386C2314yes—
593#386C2314yes—
594#386C2314yes—
595#386C2314yes—
596#386C2314yes—
597#386C2314yes—
598#386C2314yes—
599#386C2314yes—
600#386C2314yes—
601#386C2314yes—
602#386C2314yes—
603#386C2314yes—
604#386C2314yes—
605#386C2314yes—
606#386C2312yes—
607#386C2314yes—
608#386C2314yes—
609#386C2314yes—
610#386C2314yes—
611#386C2314yes—
612#386C2314yes—
613#386C2314yes—
614#386C2312yes—
615#386C2314yes—
616#386C2314yes—
617#386C2312yes—
618#385C2314yes—
619#385C2314yes—
620#385C2314yes—
621#385C2314yes—
622#385C2314yes—
623#385C2314yes—
624#385C2314yes—
625#385C2314yes—
626#385C2314yes—
627#385C2314yes—
628#385C2314yes—
629#385C2314yes—
630#385C2314yes—
631#385C2314yes—
632#385C2314yes—
633#385C2314yes—
634#385C2314yes—
635#385C2314yes—
636#385C2314yes—
637#385C2314yes—
638#385C2314yes—
639#385C2314yes—
640#385C2314yes—
641#385C2314yes—
642#385C2312yes—
643#385C2312yes—
644#385C2312yes—
645#384C2312yes—
646#384C2314yes—
647#384C2311yescharacteristic
648#384C2312yes—
649#384C2312yes—
650#384C2312yes—
651#384C2311yescharacteristic
652#384C2311yescharacteristic
653#384C2311yescharacteristic
654#382C2311yescharacteristic
655#382C2312yes—
656#382C2312yes—
657#382C2311yescharacteristic
658#382C2312yes—
659#382C2312yes—
660#382C2311yescharacteristic
661#382C2312yes—
662#381C2314yes—
663#381C2314yes—
664#381C2312yes—
665#380C2314yes—
666#380C2314yes—
667#380C2314yes—
668#380C2314yes—
669#380C2312yes—
670#380C2312yes—
671#380C2314yes—
672#380C2314yes—
673#380C2312yes—
674#380C2312yes—
675#380C2312yes—
676#380C2312yes—
677#380C2312yes—
678#380C2314yes—
679#380C2314yes—
680#380C2312yes—
681#380C2314yes—
682#380C2314yes—
683#380C2314yes—
684#380C2312yes—
685#380C2312yes—
686#380C2312yes—
687#380C2312yes—
688C4×C4⋊C4C2311yescharacteristic
689C4×C4⋊C4C2312yes—
690C4×C4⋊C4C2311yescharacteristic
691C4×C4⋊C4C2312yes—
692C4×C4⋊C4C2312yes—
693C4×C4⋊C4C2311yescharacteristic
694C4×C4⋊C4C2312yes—
695C4×C4⋊C4C2311yescharacteristic
696C4×C4⋊C4C2312yes—
697C4×C4⋊C4C2312yes—
698C4×C4⋊C4C2311yescharacteristic
699C4×C4⋊C4C2312yes—
700C4×C4⋊C4C2312yes—
701C4×C22⋊C4C2312yes—
702C4×C22⋊C4C2314yes—
703C4×C22⋊C4C2314yes—
704C4×C22⋊C4C2314yes—
705C4×C22⋊C4C2314yes—
706C4×C22⋊C4C2312yes—
707C4×C22⋊C4C2312yes—
708C4×C22⋊C4C2314yes—
709C4×C22⋊C4C2314yes—
710C4×C22⋊C4C2312yes—
711C4×C22⋊C4C2312yes—
712C4×C22⋊C4C2312yes—
713C4×C22⋊C4C2312yes—
714C4×C22⋊C4C2312yes—
715C4×C22⋊C4C2312yes—
716C2×#95C2314yes—
717C2×#95C2314yes—
718C2×#95C2314yes—
719C43C2311yescharacteristic
720C2×#41—28no—
721C2×#41—48no—
722C2×#41—48no—
723C2×#41—48no—
724C2×#41—48no—
725C2×#41—48no—
726C2×#41—44no—
727C2×#41—48no—
728C2×#41—82no—
729C22×Q8C2411yescharacteristic
730C22×Q8C2414yes—
731C22×Q8C2414yes—
732C22×Q8C2412yes—
733C22×Q8C2411yescharacteristic
734C22×D4C2412yes—
735C22×D4C2414yes—
736C22×D4C2414yes—
737C22×D4C2412yes—
738C22×D4C2411yescharacteristic
739C22×D4C2412yes—
740C22×D4C2414yes—
741C22×D4C2414yes—
742C22×D4C2411yescharacteristic
743C22×D4C2414yes—
744C22×D4C2414yes—
745C22×D4C2414yes—
746C22×D4C2412yes—
747C22×D4C2412yes—
748C22×D4C2414yes—
749C22×D4C2411yescharacteristic
750C23×C4C2412yes—
751C23×C4C2412yes—
752C23×C4C2412yes—
753C23×C4C2414yes—
754C23×C4C2412yes—
755C23×C4C2412yes—
756C23×C4C2414yes—
757C23×C4C2412yes—
758C23×C4C2414yes—
759C23×C4C2414yes—
760C23×C4C2412yes—
761C23×C4C2414yes—
762C23×C4C2414yes—
763C23×C4C2414yes—
764C23×C4C2414yes—
765C4⋊Q8—44no—
766C4⋊Q8—44no—
767C4⋊Q8—42no—
768C4⋊Q8—48no—
769C4⋊Q8—48no—
770#127—28no—
771#127—42no—
772#127—82no—
773#126—48no—
774#126—48no—
775#125—24no—
776#125—44no—
777#125—44no—
778#125—82no—
779#124—24no—
780#124—24no—
781#124—44no—
782#124—44no—
783#124—48no—
784#124—48no—
785#123—28no—
786#123—48no—
787#123—48no—
788#123—48no—
789#123—48no—
790#123—48no—
791#123—48no—
792#123—48no—
793#123—48no—
794#123—84no—
795C22⋊Q8—28no—
796C22⋊Q8—216no—
797C22⋊Q8—48no—
798C22⋊Q8—48no—
799C22⋊Q8—48no—
800C22⋊Q8—48no—
801C22⋊Q8—48no—
802C22⋊Q8—48no—
803C22⋊Q8—48no—
804C22⋊Q8—48no—
805C22⋊Q8—48no—
806C22⋊Q8—82no—
807#121—28no—
808#121—28no—
809#121—28no—
810#121—216no—
811#121—28no—
812#121—28no—
813#121—48no—
814#121—48no—
815#121—48no—
816#121—48no—
817#121—48no—
818#121—48no—
819#121—48no—
820#121—48no—
821#121—48no—
822#121—48no—
823#121—44no—
824#121—44no—
825#121—44no—
826#121—44no—
827#121—44no—
828#121—84no—
829C4×Q8—42no—
830C4×Q8—42no—
831C4×D4—28no—
832C4×D4—24no—
833C4×D4—24no—
834C4×D4—44no—
835C4×D4—44no—
836C4×D4—42no—
837C4×D4—44no—
838C4×D4—44no—
839C4×D4—44no—
840C4×D4—42no—
841C4×D4—44no—
842C4×D4—42no—
843C4×D4—48no—
844C4×D4—48no—
845C4×D4—48no—
846C4×D4—82no—
847C4×D4—84no—
848C4×D4—84no—
849#117—44no—
850#117—44no—
851#117—44no—
852C2×C4⋊C4—28no—
853C2×C4⋊C4—28no—
854C2×C4⋊C4—48no—
855C2×C4⋊C4—48no—
856C2×C4⋊C4—44no—
857C2×C4⋊C4—44no—
858C2×C4⋊C4—82no—
859C2×C4⋊C4C2412yes—
860C2×C4⋊C4C2414yes—
861C2×C4⋊C4C2412yes—
862C2×C4⋊C4C2412yes—
863C2×C4⋊C4C2412yes—
864C2×C4⋊C4C2414yes—
865C2×C4⋊C4C2412yes—
866C2×C4⋊C4C2414yes—
867C2×C4⋊C4C2412yes—
868C2×C4⋊C4C2414yes—
869C2×C4⋊C4C2411yescharacteristic
870C2×C4⋊C4C2412yes—
871C2×C4⋊C4C2411yescharacteristic
872C2×C4⋊C4C2414yes—
873C2×C4⋊C4C2412yes—
874C2×C4⋊C4C2412yes—
875C2×C4⋊C4C2412yes—
876C2×C4⋊C4C2412yes—
877C2×C4⋊C4C2412yes—
878C2×C4⋊C4C2412yes—
879C2×C4⋊C4C2412yes—
880C2×C4⋊C4C2411yescharacteristic
881C2×C4⋊C4C2411yescharacteristic
882C2×C4⋊C4C2414yes—
883C2×C4⋊C4C2414yes—
884C2×C4⋊C4C2414yes—
885C2×C4⋊C4C2414yes—
886C2×C4⋊C4C2414yes—
887C2×C4⋊C4C2414yes—
888C2×C4⋊C4C2414yes—
889C2×C4⋊C4C2412yes—
890C2×C4⋊C4C2411yescharacteristic
891C2×C4⋊C4C2412yes—
892C2×C4⋊C4C2412yes—
893C2×C4⋊C4C2412yes—
894C2×C4⋊C4C2412yes—
895C2×C4⋊C4C2414yes—
896C2×C4⋊C4C2412yes—
897C2×C4⋊C4C2412yes—
898C2×C4⋊C4C2414yes—
899C2×C4⋊C4C2411yescharacteristic
900C2×C4⋊C4C2412yes—
901C2×C4⋊C4C2412yes—
902C2×C4⋊C4C2411yescharacteristic
903C2×C4⋊C4C2411yescharacteristic
904C2×C4⋊C4C2412yes—
905C2×C4⋊C4C2414yes—
906C2×C4⋊C4C2414yes—
907C2×C4⋊C4C2414yes—
908C2×C4⋊C4C2414yes—
909C2×C4⋊C4C2414yes—
910C2×C4⋊C4C2414yes—
911C2×C4⋊C4C2412yes—
912C2×C4⋊C4C2414yes—
913C2×C4⋊C4C2414yes—
914C2×C4⋊C4C2412yes—
915C2×C4⋊C4C2412yes—
916C2×C4⋊C4C2414yes—
917C2×C4⋊C4C2414yes—
918C2×C4⋊C4C2414yes—
919C2×C4⋊C4C2414yes—
920C2×C4⋊C4C2411yescharacteristic
921C2×C4⋊C4C2412yes—
922C2×C4⋊C4C2411yescharacteristic
923C2×C4⋊C4C2411yescharacteristic
924C2×C22⋊C4C2414yes—
925C2×C22⋊C4C2412yes—
926C2×C22⋊C4C2412yes—
927C2×C22⋊C4C2412yes—
928C2×C22⋊C4C2414yes—
929C2×C22⋊C4C2414yes—
930C2×C22⋊C4C2412yes—
931C2×C22⋊C4C2414yes—
932C2×C22⋊C4C2412yes—
933C2×C22⋊C4C2412yes—
934C2×C22⋊C4C2414yes—
935C2×C22⋊C4C2412yes—
936C2×C22⋊C4C2412yes—
937C2×C22⋊C4C2414yes—
938C2×C22⋊C4C2414yes—
939C2×C22⋊C4C2414yes—
940C2×C22⋊C4C2414yes—
941C2×C22⋊C4C2412yes—
942C2×C22⋊C4C2412yes—
943C2×C22⋊C4C2412yes—
944C2×C22⋊C4C2412yes—
945C2×C22⋊C4C2412yes—
946C2×C22⋊C4C2414yes—
947C2×C22⋊C4C2412yes—
948C2×C22⋊C4C2412yes—
949C2×C22⋊C4C2414yes—
950C2×C22⋊C4C2414yes—
951C2×C22⋊C4C2414yes—
952C2×C22⋊C4C2414yes—
953C2×C22⋊C4C2414yes—
954C2×C22⋊C4C2414yes—
955C2×C22⋊C4C2414yes—
956C2×C22⋊C4C2414yes—
957C2×C22⋊C4C2412yes—
958C2×C22⋊C4C2412yes—
959C2×C22⋊C4C2414yes—
960C2×C22⋊C4C2412yes—
961C2×C22⋊C4C2412yes—
962C2×C22⋊C4C2412yes—
963C2×C22⋊C4C2414yes—
964C2×C22⋊C4C2412yes—
965C2×C22⋊C4C2414yes—
966C2×C22⋊C4C2412yes—
967C2×C22⋊C4C2414yes—
968C2×C22⋊C4C2414yes—
969C2×C22⋊C4C2414yes—
970C2×C22⋊C4C2414yes—
971C2×C22⋊C4C2414yes—
972C2×C22⋊C4C2414yes—
973C2×C22⋊C4C2414yes—
974C2×C22⋊C4C2414yes—
975C2×C22⋊C4C2414yes—
976C2×C22⋊C4C2414yes—
977C2×C22⋊C4C2412yes—
978C2×C22⋊C4C2414yes—
979C2×C42—44no—
980C2×C42—82no—
981C2×C42C2412yes—
982C2×C42C2412yes—
983C2×C42C2412yes—
984C2×C42C2411yescharacteristic
985C2×C42C2411yescharacteristic
986C2×C42C2412yes—
987C2×C42C2411yescharacteristic
988C2×C42C2411yescharacteristic
989C2×C42C2411yescharacteristic
990C2×C42C2411yescharacteristic
991C2×C42C2414yes—
992C2×C42C2414yes—
993C2×C42C2414yes—
994C2×C42C2412yes—
995C2×C42C2412yes—
996C2×C42C2412yes—
997C2×C42C2412yes—
998C2×C42C2414yes—
999C2×C42C2412yes—
1000C2×C42C2411yescharacteristic
1001#95C2414yes—
1002#95C2412yes—
1003#95C2412yes—
1004#95C2414yes—
1005#95C2414yes—
1006#95C2414yes—
1007#95C2414yes—
1008#95C2414yes—
1009#95C2414yes—
1010#95C2414yes—
1011#95C2414yes—
1012#95C2412yes—
1013#95C2412yes—
1014#95C2412yes—
1015#95C2412yes—
1016#95C2412yes—
1017#95C2414yes—
1018#95C2414yes—
1019#95C2412yes—
1020#95C2414yes—
1021#95C2414yes—
1022#95C2414yes—
1023#95C2412yes—
1024#95C2414yes—
1025#95C2412yes—
1026#95C2412yes—
1027#95C2414yes—
1028#95C2412yes—
1029#95C2412yes—
1030#95C2412yes—
1031#95C2412yes—
1032#95C2412yes—
1033#95C2412yes—
1034#95C2412yes—
1035#95C2412yes—
1036#95C2414yes—
1037#95C2414yes—
1038#95C2414yes—
1039#95C2414yes—
1040#95C2412yes—
1041#95C2412yes—
1042#95C2412yes—
1043#95C2412yes—
1044#95C2412yes—
1045#95C2412yes—
1046#95C2414yes—
1047#95C2414yes—
1048#95C2414yes—
1049#95C2414yes—
1050#95C2414yes—
1051#95C2414yes—
1052#95C2414yes—
1053#95C2414yes—
1054C24C2514yes—
1055C24C2512yes—
1056C24C2512yes—
1057C24C2512yes—
1058#41—832no—
1059#41—816no—
1060#41—832no—
1061C2×Q8—28no—
1062C2×Q8—22no—
1063C2×Q8—41no—
1064C2×Q8—41no—
1065C2×Q8—41no—
1066C2×Q8—44no—
1067C2×Q8—44no—
1068C2×Q8—44no—
1069C2×Q8—44no—
1070C2×Q8—41no—
1071C2×Q8—44no—
1072C2×Q8—42no—
1073C2×Q8—42no—
1074C2×Q8—42no—
1075C2×Q82−1+414yes—
1076C2×D4—28no—
1077C2×D4—24no—
1078C2×D4—28no—
1079C2×D4—28no—
1080C2×D4—24no—
1081C2×D4—28no—
1082C2×D4—28no—
1083C2×D4—28no—
1084C2×D4—28no—
1085C2×D4—24no—
1086C2×D4—24no—
1087C2×D4—22no—
1088C2×D4—24no—
1089C2×D4—28no—
1090C2×D4—28no—
1091C2×D4—22no—
1092C2×D4—24no—
1093C2×D4—22no—
1094C2×D4—24no—
1095C2×D4—41no—
1096C2×D4—42no—
1097C2×D4—44no—
1098C2×D4—41no—
1099C2×D4—44no—
1100C2×D4—41no—
1101C2×D4—44no—
1102C2×D4—42no—
1103C2×D4—44no—
1104C2×D4—44no—
1105C2×D4—44no—
1106C2×D4—44no—
1107C2×D4—44no—
1108C2×D4—44no—
1109C2×D4—44no—
1110C2×D4—42no—
1111C2×D4—44no—
1112C2×D4—42no—
1113C2×D4—44no—
1114C2×D4—41no—
1115C2×D4—42no—
1116C2×D4—44no—
1117C2×D4—42no—
1118C2×D4—42no—
1119C2×D4—44no—
1120C2×D4—42no—
1121C2×D4—44no—
1122C2×D4H(5,𝔽2)14yes—
1123C2×D4H(5,𝔽2)14yes—
1124C22×C4—24no—
1125C22×C4—28no—
1126C22×C4—24no—
1127C22×C4—28no—
1128C22×C4—24no—
1129C22×C4—24no—
1130C22×C4—28no—
1131C22×C4—24no—
1132C22×C4—24no—
1133C22×C4—24no—
1134C22×C4—24no—
1135C22×C4—24no—
1136C22×C4—24no—
1137C22×C4—24no—
1138C22×C4—24no—
1139C22×C4—24no—
1140C22×C4—28no—
1141C22×C4—28no—
1142C22×C4—24no—
1143C22×C4—28no—
1144C22×C4—42no—
1145C22×C4—42no—
1146C22×C4—42no—
1147C22×C4—44no—
1148C22×C4—42no—
1149C22×C4—42no—
1150C22×C4—44no—
1151C22×C4—44no—
1152C22×C4—44no—
1153C22×C4—44no—
1154C22×C4—44no—
1155C22×C4—44no—
1156C22×C4—44no—
1157C22×C4—42no—
1158C22×C4—42no—
1159C22×C4—44no—
1160C22×C4—44no—
1161C22×C4—44no—
1162C22×C4—44no—
1163C22×C4—44no—
1164C22×C4—44no—
1165C22×C4—44no—
1166C22×C4—44no—
1167C22×C4—44no—
1168C22×C4—44no—
1169C22×C4C2512yes—
1170C22×C4C2511yescharacteristic
1171C22×C4C2512yes—
1172C22×C4C2512yes—
1173C22×C4C2511yescharacteristic
1174C22×C4C2512yes—
1175C22×C4C2512yes—
1176C22×C4C2512yes—
1177C22×C4C2514yes—
1178C22×C4C2512yes—
1179C22×C4C2512yes—
1180C22×C4C2512yes—
1181C22×C4C2514yes—
1182C22×C4C2512yes—
1183C22×C4C2514yes—
1184C22×C4C2514yes—
1185C22×C4C2511yescharacteristic
1186C22×C4C2514yes—
1187C22×C4C2512yes—
1188C22×C4C2511yescharacteristic
1189C22×C4C2511yescharacteristic
1190C22×C4C2511yescharacteristic
1191C22×C4C2512yes—
1192C22×C4C2512yes—
1193C22×C4C2511yescharacteristic
1194C4⋊C4—28no—
1195C4⋊C4—24no—
1196C4⋊C4—24no—
1197C4⋊C4—24no—
1198C4⋊C4—24no—
1199C4⋊C4—24no—
1200C4⋊C4—28no—
1201C4⋊C4—28no—
1202C4⋊C4—22no—
1203C4⋊C4—28no—
1204C4⋊C4—24no—
1205C4⋊C4—24no—
1206C4⋊C4—24no—
1207C4⋊C4—24no—
1208C4⋊C4—22no—
1209C4⋊C4—28no—
1210C4⋊C4—24no—
1211C4⋊C4—24no—
1212C4⋊C4—24no—
1213C4⋊C4—24no—
1214C4⋊C4—24no—
1215C4⋊C4—22no—
1216C4⋊C4—44no—
1217C4⋊C4—44no—
1218C4⋊C4—44no—
1219C4⋊C4—44no—
1220C4⋊C4—44no—
1221C4⋊C4—44no—
1222C4⋊C4—41no—
1223C4⋊C4—44no—
1224C4⋊C4—42no—
1225C4⋊C4—42no—
1226C4⋊C4—42no—
1227C4⋊C4—41no—
1228C4⋊C4—42no—
1229C4⋊C4—41no—
1230C4⋊C4—42no—
1231C4⋊C4—44no—
1232C4⋊C4—42no—
1233C4⋊C4—42no—
1234C4⋊C4—42no—
1235C4⋊C4—44no—
1236C4⋊C4—41no—
1237C4⋊C4—42no—
1238C4⋊C4—42no—
1239C4⋊C4—41no—
1240C4⋊C4—44no—
1241C4⋊C4—44no—
1242C4⋊C4—44no—
1243C4⋊C4—44no—
1244C4⋊C4—44no—
1245C4⋊C4—44no—
1246C4⋊C4—42no—
1247C4⋊C4—44no—
1248C4⋊C4—44no—
1249C4⋊C4—42no—
1250C4⋊C4—42no—
1251C4⋊C4—44no—
1252C4⋊C4—44no—
1253C4⋊C4—44no—
1254C4⋊C4—44no—
1255C4⋊C4—42no—
1256C4⋊C4—41no—
1257C4⋊C4H(5,𝔽2)14yes—
1258C4⋊C42−1+414yes—
1259C22⋊C4—28no—
1260C22⋊C4—24no—
1261C22⋊C4—28no—
1262C22⋊C4—28no—
1263C22⋊C4—28no—
1264C22⋊C4—24no—
1265C22⋊C4—28no—
1266C22⋊C4—24no—
1267C22⋊C4—24no—
1268C22⋊C4—24no—
1269C22⋊C4—24no—
1270C22⋊C4—24no—
1271C22⋊C4—28no—
1272C22⋊C4—24no—
1273C22⋊C4—28no—
1274C22⋊C4—28no—
1275C22⋊C4—24no—
1276C22⋊C4—28no—
1277C22⋊C4—24no—
1278C22⋊C4—24no—
1279C22⋊C4—24no—
1280C22⋊C4—24no—
1281C22⋊C4—42no—
1282C22⋊C4—42no—
1283C22⋊C4—44no—
1284C22⋊C4—42no—
1285C22⋊C4—44no—
1286C22⋊C4—42no—
1287C22⋊C4—42no—
1288C22⋊C4—42no—
1289C22⋊C4—44no—
1290C22⋊C4—44no—
1291C22⋊C4—44no—
1292C22⋊C4—44no—
1293C22⋊C4—42no—
1294C22⋊C4—42no—
1295C22⋊C4—44no—
1296C22⋊C4—44no—
1297C22⋊C4—42no—
1298C22⋊C4—44no—
1299C22⋊C4—44no—
1300C22⋊C4—44no—
1301C22⋊C4—44no—
1302C22⋊C4—44no—
1303C22⋊C4—44no—
1304C22⋊C4—44no—
1305C22⋊C4—44no—
1306C22⋊C4—44no—
1307C22⋊C4—44no—
1308C22⋊C4—44no—
1309C22⋊C4—44no—
1310C22⋊C4—44no—
1311C22⋊C4—44no—
1312C22⋊C4—44no—
1313C22⋊C4—42no—
1314C42—24no—
1315C42—24no—
1316C42—22no—
1317C42—22no—
1318C42—22no—
1319C42—22no—
1320C42—22no—
1321C42—24no—
1322C42—24no—
1323C42—22no—
1324C42—42no—
1325C42—42no—
1326C42—41no—
1327C42—42no—
1328C42—42no—
1329C42—42no—
1330C42—44no—
1331C42—44no—
1332C42—44no—
1333C42—44no—
1334C23—22no—
1335C23—22no—
1336C23—22no—
1337C23—22no—
1338C23—22no—
1339C23—22no—
1340C23—22no—
1341C23—22no—
1342C23—22no—
1343C23—22no—
1344C23—22no—
1345C23—22no—
1346C23—24no—
1347C23—22no—
1348C23—24no—
1349C23—22no—
1350C23—22no—
1351C23—24no—
1352C23—22no—
1353C23—24no—
1354C23—22no—
1355C23—24no—
1356C23—22no—
1357C23—24no—
1358C23—22no—
1359C23—24no—
1360C23C2×H(5,𝔽2)14yes—
1361C23C2×H(5,𝔽2)14yes—
1362C23C2611yescharacteristic
1363Q8—44no—
1364Q8—82no—
1365Q8—88no—
1366Q8—88no—
1367Q8—162no—
1368D4—28no—
1369D4—44no—
1370D4—416no—
1371D4—48no—
1372D4—416no—
1373D4—48no—
1374D4—82no—
1375D4—88no—
1376D4—84no—
1377D4—88no—
1378D4—84no—
1379D4—88no—
1380D4—88no—
1381D4—88no—
1382D4—162no—
1383D4—164no—
1384C2×C4—22no—
1385C2×C4—22no—
1386C2×C4—21no—
1387C2×C4—22no—
1388C2×C4—22no—
1389C2×C4—21no—
1390C2×C4—21no—
1391C2×C4—21no—
1392C2×C4—21no—
1393C2×C4—21no—
1394C2×C4—22no—
1395C2×C4—22no—
1396C2×C4—22no—
1397C2×C4—22no—
1398C2×C4—21no—
1399C2×C4—21no—
1400C2×C4—21no—
1401C2×C4—21no—
1402C2×C4—21no—
1403C2×C4—22no—
1404C2×C4—22no—
1405C2×C4—22no—
1406C2×C4—22no—
1407C2×C4—22no—
1408C2×C4—24no—
1409C2×C4—24no—
1410C2×C4—24no—
1411C2×C4—24no—
1412C2×C4—22no—
1413C2×C4—24no—
1414C2×C4—22no—
1415C2×C4—22no—
1416C2×C4—22no—
1417C2×C4—24no—
1418C2×C4—24no—
1419C2×C4—24no—
1420C2×C4—24no—
1421C2×C4—22no—
1422C2×C4—24no—
1423C2×C4—24no—
1424C2×C4—21no—
1425C2×C4—21no—
1426C2×C4—21no—
1427C2×C4—22no—
1428C2×C4—22no—
1429C2×C4—22no—
1430C2×C4—22no—
1431C2×C4—22no—
1432C2×C4—24no—
1433C2×C4—22no—
1434C2×C4—22no—
1435C2×C4—21no—
1436C2×C4—22no—
1437C2×C4—22no—
1438C2×C4—22no—
1439C2×C4—22no—
1440C2×C4—24no—
1441C2×C4—22no—
1442C2×C4—22no—
1443C2×C4—22no—
1444C2×C4—22no—
1445C2×C4—24no—
1446C2×C4—24no—
1447C2×C4—22no—
1448C2×C4—22no—
1449C2×C4—22no—
1450C2×C4—48no—
1451C2×C4—48no—
1452C2×C4—416no—
1453C2×C4—48no—
1454C2×C4—48no—
1455C2×C4—48no—
1456C2×C4—84no—
1457C2×C4—84no—
1458C2×C4—88no—
1459C2×C4—88no—
1460C2×C4—88no—
1461C2×C4—88no—
1462C2×C4—88no—
1463C2×C4—164no—
1464C2×C4—164no—
1465C2×C4C2×H(5,𝔽2)12yes—
1466C2×C4C2×H(5,𝔽2)12yes—
1467C2×C4C2×H(5,𝔽2)14yes—
1468C2×C4C2×H(5,𝔽2)12yes—
1469C2×C4C2×2−1+412yes—
1470C2×C4C2×2−1+414yes—
1471C2×C4C2×2−1+414yes—
1472C2×C4C2×2−1+412yes—
1473C2×C4#58512yes—
1474C22—24no—
1475C22—24no—
1476C22—24no—
1477C22—24no—
1478C22—24no—
1479C22—24no—
1480C22—42no—
1481C22—42no—
1482C22—42no—
1483C22—42no—
1484C22—42no—
1485C22—42no—
1486C22—42no—
1487C22—42no—
1488C22—42no—
1489C22—44no—
1490C22—42no—
1491C22—44no—
1492C22—44no—
1493C22—42no—
1494C22—44no—
1495C22—42no—
1496C22—44no—
1497C22—42no—
1498C22—44no—
1499C22—42no—
1500C22—42no—
1501C22—44no—
1502C22C22×H(5,𝔽2)11yescharacteristic
1503C22C22×H(5,𝔽2)11yescharacteristic
1504C22C22×H(5,𝔽2)11yescharacteristic
1505C22C22×2−1+411yescharacteristic
1506C22C22×2−1+411yescharacteristic
1507C22C2×#58511yescharacteristic
1508C22H(7,𝔽2)11yescharacteristic
1509C4—24no—
1510C4—22no—
1511C4—24no—
1512C4—22no—
1513C4—22no—
1514C4—24no—
1515C4—42no—
1516C4—42no—
1517C4—44no—
1518C4—42no—
1519C4—44no—
1520C4—44no—
1521C4—41no—
1522C4—41no—
1523C4—41no—
1524C4—42no—
1525C4—42no—
1526C4—42no—
1527C4—42no—
1528C4—42no—
1529C4—42no—
1530C4—44no—
1531C4—42no—
1532C4—44no—
1533C4#355914yes—
1534C2—44no—
1535C2—44no—
1536C2—82no—
1537C2—84no—
1538C2C2×#355911yescharacteristic
1539C2#6289411yescharacteristic
1540C2#6290511yescharacteristic
1541C2#6294411yescharacteristic
1542C2#6301111yescharacteristic
1543C2#6303711yescharacteristic
1544C2#6303911yescharacteristic
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. #59677C2semidirect
2. #59112C2semidirect
3. #59039C2semidirect
4. #58193C2semidirect
5. #55552C2semidirect
6. #53509C2semidirect
7. #53195C2semidirect
8. #52303C2semidirect
9. #51537C2semidirect
10. #48565C2semidirect
11. #47936C2semidirect
12. #46152C2semidirect
13. #45998C2semidirect
14. #45995C2semidirect
15. #45046C2semidirect
16. #44940C2semidirect
17. #44928C2semidirect
18. #42946C2semidirect
19. #42608C2semidirect
20. #42556C2semidirect
21. #40077C2semidirect
22. #39623C2semidirect
23. #39359C2semidirect
24. #39340C2semidirect
25. #38780C2semidirect
26. #38445C2semidirect
27. #36453C2semidirect
28. #36412C2semidirect
29. #36290C2semidirect

Maximal subgroups

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

subgroupindex
#596772
#591122
#590392
#581932
#555522
#535092
#531952
#523032
#515372
#485652
#479362
#461522
#459982
#459952
#450462
#449402
#449282
#429462
#426082
#425562
#400772
#396232
#393592
#393402
#387802
#384452
#364532
#364122
#362902