Finite Group Databasebeta

← #7715526

Subgroups — #7715526

Order 512.

4570 conjugacy classes of subgroups.

The subgroup lattice has 1435 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#49807C214yesmaximal, complemented
2#49757C214yesmaximal, complemented
3#48257C214yesmaximal, complemented
4#48188C214yesmaximal, complemented
5#47514C214yesmaximal, complemented
6#47446C214yesmaximal, complemented
7#47284C214yesmaximal, complemented
8#46914C214yesmaximal, complemented
9#39762C211yesmaximal, characteristic, complemented
10#39756C211yesmaximal, characteristic, complemented
11#39674C212yesmaximal, complemented
12#39554C212yesmaximal, complemented
13#39378C211yesmaximal, characteristic, complemented
14#39373C211yesmaximal, characteristic, complemented
15#37952C212yesmaximal, complemented
16#37945C212yesmaximal, complemented
17#37710C211yesmaximal, characteristic, complemented
18#37709C211yesmaximal, characteristic, complemented
19#37706C211yesmaximal, characteristic, complemented
20#37705C211yesmaximal, characteristic, complemented
21#37588C212yesmaximal, complemented
22#37293C212yesmaximal, complemented
23#37280C212yesmaximal, complemented
24#35335C211yesmaximal, characteristic, complemented
25#35332C211yesmaximal, characteristic, complemented
26#35332C211yesmaximal, characteristic, complemented
27#35294C211yesmaximal, characteristic, complemented
28#35284C211yesmaximal, characteristic, complemented
29#35277C211yesmaximal, characteristic, complemented
30#34428C212yesmaximal, complemented
31#34081C211yesmaximal, characteristic, complemented
32C2×#542C2212yes—
33C2×#541C2211yescharacteristic
34C2×#541C2211yescharacteristic
35C2×#540C2211yescharacteristic
36C2×#540C2211yescharacteristic
37C2×#533C2211yescharacteristic
38C2×#529C2211yescharacteristic
39C22×#125C2211yescharacteristic
40#2868C2211yescharacteristic
41#2859C2211yescharacteristic
42#2859C2211yescharacteristic
43#2859C2211yescharacteristic
44#2859C2211yescharacteristic
45#2859C2212yes—
46#2858C2211yescharacteristic
47#2857C2211yescharacteristic
48#2857C2212yes—
49#2856C2211yescharacteristic
50#2850C2212yes—
51#2850C2212yes—
52#2838C2214yes—
53#2837C2214yes—
54#2808C2214yes—
55#2801C2214yes—
56#2788C2214yes—
57#2785C2214yes—
58#2781C2214yes—
59#2781C2214yes—
60#2780C2214yes—
61#2778C2214yes—
62#2776C2214yes—
63#2776C2214yes—
64#2772C2214yes—
65#2768C2214yes—
66#2768C2214yes—
67#2765C2214yes—
68#2764C2214yes—
69#2763C2214yes—
70#2759C2214yes—
71#2757C2214yes—
72#2746C2214yes—
73#2744C2214yes—
74#2737C2214yes—
75#2727C2214yes—
76#2727C2214yes—
77#2727C2214yes—
78#2726C2214yes—
79#2725C2214yes—
80#2725C2214yes—
81#2719C2214yes—
82#2712C2214yes—
83#2711C2214yes—
84#2711C2214yes—
85#2707C2214yes—
86#2704C2214yes—
87#2702C2214yes—
88#2702C2214yes—
89#2702C2214yes—
90#2701C2214yes—
91#2701C2214yes—
92#2698C2214yes—
93#2695C2214yes—
94#2692C2214yes—
95#2690C2214yes—
96#2686C2214yes—
97#2681C2214yes—
98#2681C2214yes—
99#2676C2214yes—
100#2672C2214yes—
101#2671C2214yes—
102#2665C2214yes—
103#2660C2212yes—
104#2660C2212yes—
105#2653C2214yes—
106#2647C2212yes—
107#2642C2211yescharacteristic
108#2642C2211yescharacteristic
109#2641C2211yescharacteristic
110#2641C2211yescharacteristic
111#2640C2212yes—
112#2637C2214yes—
113#2632C2214yes—
114#2629C2211yescharacteristic
115#2629C2211yescharacteristic
116#2629C2211yescharacteristic
117#2629C2211yescharacteristic
118#2628C2212yes—
119#2620C2212yes—
120#2620C2212yes—
121#2620C2212yes—
122#2608C2214yes—
123#2601C2214yes—
124#2598C2214yes—
125#2593C2214yes—
126#2589C2214yes—
127#2584C2214yes—
128#2584C2214yes—
129#2583C2214yes—
130#2583C2214yes—
131#2583C2214yes—
132#2582C2212yes—
133#2580C2212yes—
134#2576C2214yes—
135#2574C2214yes—
136#2570C2214yes—
137#2559C2214yes—
138#2559C2214yes—
139#2559C2214yes—
140#2559C2214yes—
141#2559C2214yes—
142#2558C2214yes—
143#2558C2214yes—
144#2558C2214yes—
145#2558C2214yes—
146#2556C2214yes—
147#2550C2214yes—
148#2537C2212yes—
149#2536C2212yes—
150#2525C2214yes—
151#2521C2214yes—
152#2519C2214yes—
153#2519C2214yes—
154#2518C2214yes—
155#2515C2214yes—
156#2514C2212yes—
157#2514C2214yes—
158#2514C2212yes—
159#2512C2212yes—
160#2512C2212yes—
161#2512C2214yes—
162#2509C2214yes—
163#2507C2214yes—
164#2497C2214yes—
165#2492C2212yes—
166#2491C2214yes—
167#2491C2212yes—
168#2490C2212yes—
169#2489C2212yes—
170#2486C2214yes—
171#2481C2214yes—
172#2476C2214yes—
173#2474C2214yes—
174#2473C2214yes—
175#2469C2214yes—
176#2468C2214yes—
177#2466C2214yes—
178#2466C2214yes—
179#2458C2214yes—
180#2454C2212yes—
181#2453C2212yes—
182#2453C2214yes—
183#2452C2212yes—
184#2452C2214yes—
185#2451C2212yes—
186#2446C2214yes—
187#2443C2214yes—
188#2442C2214yes—
189#2441C2214yes—
190#2439C2214yes—
191#2429C2214yes—
192#2426C2214yes—
193#2423C2212yes—
194#2423C2212yes—
195#2422C2214yes—
196#2420C2212yes—
197#2420C2212yes—
198#2417C2212yes—
199#2416C2214yes—
200#2416C2212yes—
201#2416C2214yes—
202#2415C2212yes—
203#2414C2212yes—
204#2379C2214yes—
205#2378C2214yes—
206#2367C2214yes—
207#2363C2212yes—
208#2362C2212yes—
209#2361C2212yes—
210#2360C2212yes—
211#2360C2214yes—
212#2357C2212yes—
213#2355C2212yes—
214#2351C2212yes—
215D4×C4⋊C4C2212yes—
216#2337C2212yes—
217#2336C2212yes—
218#2335C2212yes—
219#2335C2212yes—
220#2335C2214yes—
221#2334C2212yes—
222#2334C2212yes—
223#2334C2214yes—
224#2334C2214yes—
225#2333C2212yes—
226#2332C2212yes—
227#2331C2212yes—
228#2330C2211yescharacteristic
229#2330C2211yescharacteristic
230#2330C2211yescharacteristic
231#2330C2211yescharacteristic
232#2326C2212yes—
233#2326C2212yes—
234#2326C2212yes—
235#2322C2214yes—
236#2317C2212yes—
237#2317C2212yes—
238#2314C2212yes—
239C4×C4⋊Q8C2211yescharacteristic
240C4×C4⋊Q8C2212yes—
241C4×#127C2211yescharacteristic
242C4×#124C2212yes—
243C4×#124C2212yes—
244#2298C2211yescharacteristic
245#2298C2211yescharacteristic
246#2295C2211yescharacteristic
247#2295C2211yescharacteristic
248#2293C2211yescharacteristic
249#2293C2211yescharacteristic
250#2290C2211yescharacteristic
251#2290C2211yescharacteristic
252#2290C2211yescharacteristic
253#2290C2211yescharacteristic
254#2285C2212yes—
255#2283C2211yescharacteristic
256C4×#117C2211yescharacteristic
257C4×#117C2211yescharacteristic
258C4×#117C2211yescharacteristic
259#542—216no—
260#541—44no—
261#541—44no—
262#540—44no—
263#540—44no—
264#533—44no—
265C2×C4⋊Q8C2312yes—
266C2×C4⋊Q8C2311yescharacteristic
267C2×C4⋊Q8C2312yes—
268C2×C4⋊Q8C2314yes—
269C2×#127C2311yescharacteristic
270#529—28no—
271C2×#126C2311yescharacteristic
272C2×#126C2311yescharacteristic
273C2×#126C2314yes—
274C2×#126C2314yes—
275C2×#126C2314yes—
276C2×#126C2314yes—
277C2×#126C2314yes—
278C2×#125—44no—
279C2×#125C2311yescharacteristic
280C2×#125C2311yescharacteristic
281C2×#125C2311yescharacteristic
282C2×#125C2311yescharacteristic
283C2×#125C2311yescharacteristic
284C2×#125C2314yes—
285C2×#125C2312yes—
286C2×#125C2314yes—
287C2×#125C2314yes—
288C2×#125C2314yes—
289C2×#124C2312yes—
290C2×#124C2312yes—
291C2×#124C2311yescharacteristic
292C2×#124C2314yes—
293C2×#124C2314yes—
294C2×#123C2314yes—
295C2×#123C2311yescharacteristic
296C2×#123C2311yescharacteristic
297C2×#123C2314yes—
298C2×#123C2314yes—
299C2×C22⋊Q8C2311yescharacteristic
300C2×C22⋊Q8C2312yes—
301C2×C22⋊Q8C2314yes—
302C2×C22⋊Q8C2314yes—
303C2×C22⋊Q8C2312yes—
304C2×C22⋊Q8C2312yes—
305C2×C22⋊Q8C2314yes—
306C2×C22⋊Q8C2314yes—
307C2×#121C2311yescharacteristic
308C2×#121C2312yes—
309C2×#121C2312yes—
310C2×#121C2312yes—
311C2×#121C2314yes—
312C2×#121C2314yes—
313C2×#121C2314yes—
314C2×#121C2314yes—
315C2×#121C2314yes—
316C2×C4×Q8C2312yes—
317C2×C4×Q8C2311yescharacteristic
318C2×C4×Q8C2312yes—
319C2×C4×Q8C2312yes—
320C2×C4×Q8C2314yes—
321C2×C4×Q8C2314yes—
322C2×C4×D4C2312yes—
323C2×C4×D4C2311yescharacteristic
324C2×C4×D4C2311yescharacteristic
325C2×C4×D4C2311yescharacteristic
326C2×C4×D4C2312yes—
327C2×C4×D4C2312yes—
328C2×C4×D4C2314yes—
329C2×C4×D4C2314yes—
330C2×#117C2311yescharacteristic
331C2×#117C2311yescharacteristic
332C2×#117C2311yescharacteristic
333C2×#117C2311yescharacteristic
334C2×#117C2311yescharacteristic
335C2×#117C2312yes—
336C2×#117C2314yes—
337C2×#117C2311yescharacteristic
338C22×C4⋊C4C2312yes—
339C22×C4⋊C4C2314yes—
340C22×C4⋊C4C2314yes—
341C22×C42C2311yescharacteristic
342C22×C42C2311yescharacteristic
343C22×C42C2311yescharacteristic
344#401C2314yes—
345#401C2314yes—
346#400C2314yes—
347#400C2314yes—
348#400C2314yes—
349#400C2314yes—
350#400C2314yes—
351#400C2314yes—
352#400C2314yes—
353#400C2314yes—
354#400C2314yes—
355#400C2314yes—
356#400C2314yes—
357#400C2314yes—
358#399C2314yes—
359#399C2314yes—
360#399C2314yes—
361#399C2314yes—
362#399C2314yes—
363#398C2314yes—
364#398C2314yes—
365#398C2314yes—
366#398C2314yes—
367#398C2314yes—
368#398C2314yes—
369#398C2314yes—
370#398C2314yes—
371#398C2314yes—
372#398C2314yes—
373#398C2314yes—
374#398C2314yes—
375#398C2314yes—
376#398C2314yes—
377#398C2314yes—
378#398C2314yes—
379#398C2314yes—
380#398C2314yes—
381#397C2314yes—
382#397C2314yes—
383#397C2314yes—
384#397C2314yes—
385#397C2314yes—
386#397C2314yes—
387#397C2314yes—
388#397C2314yes—
389#397C2314yes—
390#396C2314yes—
391#396C2314yes—
392#396C2314yes—
393#396C2314yes—
394#396C2314yes—
395#396C2314yes—
396#396C2314yes—
397#396C2314yes—
398#396C2314yes—
399#396C2314yes—
400#396C2314yes—
401#396C2314yes—
402#396C2314yes—
403#396C2314yes—
404#396C2314yes—
405#396C2314yes—
406#395C2314yes—
407#395C2314yes—
408#395C2314yes—
409#395C2314yes—
410#395C2314yes—
411#395C2314yes—
412#394C2314yes—
413#394C2314yes—
414#394C2314yes—
415#394C2314yes—
416#394C2314yes—
417#394C2314yes—
418#394C2314yes—
419#394C2314yes—
420#394C2314yes—
421#394C2314yes—
422#394C2314yes—
423#394C2314yes—
424#394C2314yes—
425#394C2314yes—
426#394C2314yes—
427#394C2314yes—
428#394C2314yes—
429#394C2314yes—
430#394C2314yes—
431#394C2314yes—
432#393C2314yes—
433#393C2314yes—
434#393C2314yes—
435#393C2314yes—
436#393C2314yes—
437#393C2314yes—
438#393C2314yes—
439#392C2314yes—
440#391C2312yes—
441#391C2314yes—
442#391C2314yes—
443#391C2312yes—
444#391C2312yes—
445#391C2312yes—
446#391C2314yes—
447#391C2312yes—
448#391C2314yes—
449#391C2314yes—
450#391C2312yes—
451#391C2312yes—
452#391C2314yes—
453#391C2312yes—
454#391C2314yes—
455#390C2312yes—
456#390C2314yes—
457#390C2312yes—
458#390C2312yes—
459#390C2312yes—
460#390C2312yes—
461#390C2312yes—
462#390C2312yes—
463#390C2314yes—
464#390C2314yes—
465#390C2314yes—
466#390C2314yes—
467#390C2314yes—
468#390C2314yes—
469#390C2312yes—
470#389C2314yes—
471#389C2312yes—
472#389C2312yes—
473#389C2314yes—
474#389C2314yes—
475#389C2314yes—
476#389C2314yes—
477#389C2314yes—
478#389C2314yes—
479#389C2314yes—
480#389C2314yes—
481#389C2312yes—
482#389C2312yes—
483#389C2312yes—
484#389C2312yes—
485#389C2314yes—
486#389C2312yes—
487#389C2314yes—
488#389C2314yes—
489#389C2314yes—
490#389C2314yes—
491#389C2314yes—
492#389C2314yes—
493#389C2314yes—
494#389C2314yes—
495#389C2314yes—
496#389C2314yes—
497#389C2314yes—
498#389C2314yes—
499#389C2314yes—
500#389C2312yes—
501#389C2312yes—
502#389C2312yes—
503#389C2312yes—
504#389C2312yes—
505#389C2314yes—
506#389C2314yes—
507#389C2314yes—
508#389C2314yes—
509#389C2314yes—
510#388C2314yes—
511#388C2314yes—
512#388C2314yes—
513#388C2314yes—
514#388C2312yes—
515#388C2314yes—
516#388C2312yes—
517#388C2314yes—
518#388C2312yes—
519#388C2314yes—
520#388C2314yes—
521#388C2314yes—
522#388C2314yes—
523#388C2314yes—
524#388C2314yes—
525#388C2314yes—
526#388C2312yes—
527#388C2312yes—
528#388C2312yes—
529#388C2312yes—
530#388C2312yes—
531#388C2312yes—
532#388C2312yes—
533#388C2314yes—
534#388C2314yes—
535#388C2314yes—
536#388C2314yes—
537#388C2312yes—
538#388C2312yes—
539#388C2314yes—
540#388C2314yes—
541#388C2314yes—
542#388C2314yes—
543#388C2314yes—
544#388C2314yes—
545#388C2314yes—
546#388C2314yes—
547#388C2314yes—
548#388C2314yes—
549#388C2314yes—
550#388C2314yes—
551#388C2314yes—
552#388C2314yes—
553#388C2314yes—
554#388C2314yes—
555#388C2314yes—
556#387C2314yes—
557#387C2314yes—
558#387C2314yes—
559#387C2314yes—
560#387C2314yes—
561#387C2314yes—
562#387C2312yes—
563#387C2314yes—
564#387C2314yes—
565#387C2312yes—
566#387C2314yes—
567#387C2314yes—
568#387C2312yes—
569#387C2312yes—
570#387C2312yes—
571#387C2312yes—
572#387C2312yes—
573#387C2314yes—
574#387C2314yes—
575#387C2312yes—
576#387C2312yes—
577#387C2312yes—
578#387C2314yes—
579#387C2314yes—
580#387C2312yes—
581#387C2312yes—
582#387C2314yes—
583#387C2314yes—
584#387C2314yes—
585#387C2314yes—
586#386C2314yes—
587#386C2314yes—
588#386C2312yes—
589#386C2312yes—
590#386C2312yes—
591#386C2312yes—
592#386C2314yes—
593#386C2314yes—
594#386C2314yes—
595#386C2314yes—
596#386C2314yes—
597#386C2314yes—
598#386C2314yes—
599#386C2314yes—
600#385C2314yes—
601#385C2314yes—
602#385C2314yes—
603#385C2314yes—
604#385C2314yes—
605#385C2314yes—
606#385C2314yes—
607#385C2314yes—
608#385C2314yes—
609#385C2314yes—
610#385C2314yes—
611#385C2314yes—
612#385C2314yes—
613#385C2314yes—
614#385C2314yes—
615#385C2314yes—
616#385C2312yes—
617#385C2312yes—
618#385C2312yes—
619#385C2312yes—
620#385C2314yes—
621#385C2314yes—
622#384C2311yescharacteristic
623#384C2312yes—
624#384C2311yescharacteristic
625#384C2312yes—
626#384C2314yes—
627#384C2312yes—
628#384C2312yes—
629#384C2312yes—
630#383C2312yes—
631#383C2314yes—
632#383C2314yes—
633#382C2312yes—
634#382C2314yes—
635#382C2314yes—
636#382C2312yes—
637#382C2312yes—
638#382C2312yes—
639#382C2314yes—
640#382C2312yes—
641#382C2314yes—
642#382C2314yes—
643#381C2314yes—
644#381C2314yes—
645#381C2312yes—
646#381C2314yes—
647#380C2312yes—
648#380C2312yes—
649#380C2314yes—
650#380C2312yes—
651#380C2314yes—
652#380C2314yes—
653#380C2314yes—
654#380C2312yes—
655#380C2312yes—
656#380C2314yes—
657#380C2314yes—
658#380C2314yes—
659C4×C4⋊C4C2312yes—
660C4×C4⋊C4C2312yes—
661C4×C4⋊C4C2314yes—
662C4×C4⋊C4C2314yes—
663C4×C4⋊C4C2312yes—
664C4×C4⋊C4C2314yes—
665C4×C4⋊C4C2312yes—
666C4×C4⋊C4C2312yes—
667C4×C4⋊C4C2312yes—
668C4×C4⋊C4C2312yes—
669C4×C4⋊C4C2314yes—
670C4×C4⋊C4C2312yes—
671C4×C4⋊C4C2314yes—
672C4×C4⋊C4C2314yes—
673C4×C4⋊C4C2312yes—
674C4×C4⋊C4C2312yes—
675C4×C4⋊C4C2311yescharacteristic
676C4×C4⋊C4C2311yescharacteristic
677C4×C4⋊C4C2311yescharacteristic
678C4×C4⋊C4C2311yescharacteristic
679C4×C4⋊C4C2311yescharacteristic
680C4×C4⋊C4C2311yescharacteristic
681C4×C22⋊C4C2314yes—
682C4×C22⋊C4C2314yes—
683C4×C22⋊C4C2314yes—
684C4×C22⋊C4C2314yes—
685C4×C22⋊C4C2312yes—
686C4×C22⋊C4C2312yes—
687C4×C22⋊C4C2312yes—
688C4×C22⋊C4C2312yes—
689C4×C22⋊C4C2314yes—
690C4×C22⋊C4C2312yes—
691C4×C22⋊C4C2312yes—
692C4×C22⋊C4C2314yes—
693C4×C22⋊C4C2311yescharacteristic
694C4×C22⋊C4C2314yes—
695C4×C22⋊C4C2311yescharacteristic
696C4×C22⋊C4C2311yescharacteristic
697C4×C22⋊C4C2311yescharacteristic
698C4×C22⋊C4C2311yescharacteristic
699C4×C22⋊C4C2311yescharacteristic
700#376C2311yescharacteristic
701#376C2311yescharacteristic
702#376C2311yescharacteristic
703#376C2311yescharacteristic
704#376C2311yescharacteristic
705#376C2311yescharacteristic
706C43C2311yescharacteristic
707C43C2311yescharacteristic
708C43C2311yescharacteristic
709C43C2311yescharacteristic
710C22×Q8C2412yes—
711C22×Q8C2414yes—
712C22×Q8C2411yescharacteristic
713C22×Q8C2414yes—
714C22×D4C2412yes—
715C22×D4C2411yescharacteristic
716C22×D4C2411yescharacteristic
717C22×D4C2414yes—
718C22×D4C2414yes—
719C22×D4C2411yescharacteristic
720C22×D4C2414yes—
721C22×D4C2414yes—
722C23×C4C2411yescharacteristic
723C23×C4C2411yescharacteristic
724C23×C4C2411yescharacteristic
725C23×C4C2412yes—
726C23×C4C2414yes—
727C23×C4C2412yes—
728C23×C4C2411yescharacteristic
729C23×C4C2411yescharacteristic
730C23×C4C2414yes—
731C23×C4C2414yes—
732C23×C4C2414yes—
733C4⋊Q8—28no—
734C4⋊Q8—24no—
735C4⋊Q8—44no—
736C4⋊Q8—84no—
737#127—24no—
738#126—24no—
739#126—216no—
740#126—24no—
741#126—48no—
742#126—48no—
743#126—84no—
744#126—84no—
745#125—24no—
746#125—24no—
747#125—24no—
748#125—24no—
749#125—24no—
750#125—48no—
751#125—44no—
752#125—48no—
753#125—48no—
754#125—84no—
755#124—24no—
756#124—216no—
757#124—28no—
758#124—28no—
759#124—84no—
760#123—24no—
761#123—24no—
762#123—216no—
763#123—48no—
764#123—48no—
765C22⋊Q8—28no—
766C22⋊Q8—24no—
767C22⋊Q8—216no—
768C22⋊Q8—48no—
769C22⋊Q8—44no—
770C22⋊Q8—44no—
771C22⋊Q8—84no—
772C22⋊Q8—84no—
773#121—28no—
774#121—24no—
775#121—48no—
776#121—48no—
777#121—44no—
778#121—44no—
779#121—84no—
780#121—84no—
781#121—84no—
782C4×Q8—24no—
783C4×Q8—28no—
784C4×Q8—48no—
785C4×Q8—44no—
786C4×Q8—44no—
787C4×Q8—84no—
788C4×D4—24no—
789C4×D4—24no—
790C4×D4—24no—
791C4×D4—28no—
792C4×D4—44no—
793C4×D4—44no—
794C4×D4—84no—
795C4×D4—84no—
796#117—24no—
797#117—24no—
798#117—24no—
799#117—24no—
800#117—24no—
801#117—44no—
802#117—84no—
803#117#4118yes—
804C2×C4⋊C4—44no—
805C2×C4⋊C4—48no—
806C2×C4⋊C4—84no—
807C2×C4⋊C4C2412yes—
808C2×C4⋊C4C2412yes—
809C2×C4⋊C4C2414yes—
810C2×C4⋊C4C2414yes—
811C2×C4⋊C4C2412yes—
812C2×C4⋊C4C2412yes—
813C2×C4⋊C4C2411yescharacteristic
814C2×C4⋊C4C2412yes—
815C2×C4⋊C4C2412yes—
816C2×C4⋊C4C2411yescharacteristic
817C2×C4⋊C4C2412yes—
818C2×C4⋊C4C2412yes—
819C2×C4⋊C4C2411yescharacteristic
820C2×C4⋊C4C2412yes—
821C2×C4⋊C4C2411yescharacteristic
822C2×C4⋊C4C2411yescharacteristic
823C2×C4⋊C4C2414yes—
824C2×C4⋊C4C2411yescharacteristic
825C2×C4⋊C4C2412yes—
826C2×C4⋊C4C2414yes—
827C2×C4⋊C4C2414yes—
828C2×C4⋊C4C2411yescharacteristic
829C2×C4⋊C4C2411yescharacteristic
830C2×C4⋊C4C2414yes—
831C2×C4⋊C4C2414yes—
832C2×C4⋊C4C2414yes—
833C2×C4⋊C4C2412yes—
834C2×C4⋊C4C2414yes—
835C2×C4⋊C4C2414yes—
836C2×C4⋊C4C2414yes—
837C2×C4⋊C4C2414yes—
838C2×C4⋊C4C2414yes—
839C2×C4⋊C4C2414yes—
840C2×C4⋊C4C2414yes—
841C2×C4⋊C4C2414yes—
842C2×C4⋊C4C2414yes—
843C2×C4⋊C4C2414yes—
844C2×C4⋊C4C2414yes—
845C2×C4⋊C4C2414yes—
846C2×C4⋊C4C2414yes—
847C2×C4⋊C4C2414yes—
848C2×C4⋊C4C2414yes—
849C2×C4⋊C4C2414yes—
850C2×C4⋊C4C2412yes—
851C2×C4⋊C4C2414yes—
852C2×C4⋊C4C2414yes—
853C2×C4⋊C4C2414yes—
854C2×C4⋊C4C2414yes—
855C2×C4⋊C4C2414yes—
856C2×C4⋊C4C2414yes—
857C2×C4⋊C4C2414yes—
858C2×C4⋊C4C2412yes—
859C2×C4⋊C4C2412yes—
860C2×C4⋊C4C2414yes—
861C2×C4⋊C4C2412yes—
862C2×C4⋊C4C2414yes—
863C2×C4⋊C4C2414yes—
864C2×C4⋊C4C2414yes—
865C2×C4⋊C4C2412yes—
866C2×C4⋊C4C2414yes—
867C2×C4⋊C4C2411yescharacteristic
868C2×C4⋊C4C2411yescharacteristic
869C2×C22⋊C4C2412yes—
870C2×C22⋊C4C2412yes—
871C2×C22⋊C4C2411yescharacteristic
872C2×C22⋊C4C2411yescharacteristic
873C2×C22⋊C4C2412yes—
874C2×C22⋊C4C2412yes—
875C2×C22⋊C4C2411yescharacteristic
876C2×C22⋊C4C2411yescharacteristic
877C2×C22⋊C4C2411yescharacteristic
878C2×C22⋊C4C2411yescharacteristic
879C2×C22⋊C4C2411yescharacteristic
880C2×C22⋊C4C2411yescharacteristic
881C2×C22⋊C4C2414yes—
882C2×C22⋊C4C2414yes—
883C2×C22⋊C4C2414yes—
884C2×C22⋊C4C2414yes—
885C2×C22⋊C4C2414yes—
886C2×C22⋊C4C2414yes—
887C2×C22⋊C4C2414yes—
888C2×C22⋊C4C2414yes—
889C2×C22⋊C4C2414yes—
890C2×C22⋊C4C2414yes—
891C2×C22⋊C4C2412yes—
892C2×C22⋊C4C2414yes—
893C2×C22⋊C4C2414yes—
894C2×C22⋊C4C2414yes—
895C2×C22⋊C4C2414yes—
896C2×C22⋊C4C2414yes—
897C2×C22⋊C4C2414yes—
898C2×C22⋊C4C2414yes—
899C2×C22⋊C4C2414yes—
900C2×C22⋊C4C2414yes—
901C2×C22⋊C4C2414yes—
902C2×C22⋊C4C2414yes—
903C2×C22⋊C4C2414yes—
904C2×C22⋊C4C2414yes—
905C2×C22⋊C4C2414yes—
906C2×C22⋊C4C2414yes—
907C2×C22⋊C4C2412yes—
908C2×C22⋊C4C2414yes—
909C2×C22⋊C4C2412yes—
910C2×C22⋊C4C2414yes—
911C2×C22⋊C4C2412yes—
912C2×C22⋊C4C2412yes—
913C2×C22⋊C4C2414yes—
914C2×C22⋊C4C2414yes—
915C2×C22⋊C4C2412yes—
916C2×C22⋊C4C2414yes—
917C2×C22⋊C4C2411yescharacteristic
918C2×C22⋊C4C2411yescharacteristic
919C2×C42—24no—
920C2×C42—24no—
921C2×C42—24no—
922C2×C42C2411yescharacteristic
923C2×C42C2411yescharacteristic
924C2×C42C2411yescharacteristic
925C2×C42C2411yescharacteristic
926C2×C42C2411yescharacteristic
927C2×C42C2411yescharacteristic
928C2×C42C2412yes—
929C2×C42C2414yes—
930C2×C42C2411yescharacteristic
931C2×C42C2411yescharacteristic
932C2×C42C2411yescharacteristic
933C2×C42C2411yescharacteristic
934C2×C42C2412yes—
935C2×C42C2414yes—
936C2×C42C2414yes—
937C2×C42C2414yes—
938C2×C42C2412yes—
939C2×C42C2412yes—
940C2×C42C2414yes—
941C2×C42C2414yes—
942C2×C42C2414yes—
943C2×C42C2414yes—
944C2×C42C2412yes—
945C2×C42C2412yes—
946C2×C42C2412yes—
947C2×C42C2412yes—
948C2×C42C2412yes—
949C2×C42C2412yes—
950C2×C42C2411yescharacteristic
951C2×C42C2411yescharacteristic
952C2×C42C2411yescharacteristic
953C2×C42C2411yescharacteristic
954#95C2412yes—
955#95C2412yes—
956#95C2412yes—
957#95C2412yes—
958#95C2412yes—
959#95C2412yes—
960#95C2412yes—
961#95C2412yes—
962#95C2412yes—
963#95C2412yes—
964#95C2412yes—
965#95C2412yes—
966#95C2412yes—
967#95C2412yes—
968#95C2414yes—
969#95C2412yes—
970#95C2414yes—
971#95C2412yes—
972#95C2412yes—
973#95C2414yes—
974#95C2414yes—
975#95C2412yes—
976#95C2414yes—
977#95C2412yes—
978#95C2414yes—
979#95C2414yes—
980#95C2414yes—
981#95C2414yes—
982#95C2414yes—
983#95C2414yes—
984#95C2412yes—
985#95C2414yes—
986#95C2412yes—
987#95C2414yes—
988#95C2414yes—
989#95C2414yes—
990#95C2414yes—
991#95C2414yes—
992#95C2412yes—
993#95C2412yes—
994#95C2414yes—
995#95C2414yes—
996#95C2414yes—
997#95C2414yes—
998#95C2412yes—
999#95C2414yes—
1000#95C2414yes—
1001#95C2414yes—
1002#95C2414yes—
1003#95C2414yes—
1004#95C2414yes—
1005#95C2414yes—
1006#95C2414yes—
1007#95C2414yes—
1008#95C2414yes—
1009#95C2414yes—
1010#95C2414yes—
1011#95C2414yes—
1012#95C2414yes—
1013#95C2414yes—
1014C24C2511yescharacteristic
1015C24C2514yes—
1016C24C2511yescharacteristic
1017C24C2511yescharacteristic
1018C2×Q8—24no—
1019C2×Q8—22no—
1020C2×Q8—28no—
1021C2×Q8—24no—
1022C2×Q8—24no—
1023C2×Q8—44no—
1024C2×Q8—44no—
1025C2×Q8—44no—
1026C2×Q8—44no—
1027C2×Q8—42no—
1028C2×Q8—44no—
1029C2×D4—22no—
1030C2×D4—22no—
1031C2×D4—28no—
1032C2×D4—24no—
1033C2×D4—22no—
1034C2×D4—24no—
1035C2×D4—28no—
1036C2×D4—24no—
1037C2×D4—44no—
1038C2×D4—44no—
1039C2×D4—42no—
1040C2×D4—42no—
1041C2×D4—44no—
1042C2×D4—44no—
1043C2×D4—42no—
1044C2×D4—44no—
1045C2×D4—44no—
1046C2×D4—44no—
1047C2×D4—44no—
1048C2×D4—44no—
1049C2×D4—44no—
1050C22×C4—22no—
1051C22×C4—22no—
1052C22×C4—22no—
1053C22×C4—22no—
1054C22×C4—22no—
1055C22×C4—22no—
1056C22×C4—24no—
1057C22×C4—22no—
1058C22×C4—22no—
1059C22×C4—22no—
1060C22×C4—22no—
1061C22×C4—28no—
1062C22×C4—24no—
1063C22×C4—42no—
1064C22×C4—42no—
1065C22×C4—44no—
1066C22×C4—44no—
1067C22×C4—44no—
1068C22×C4—44no—
1069C22×C4—42no—
1070C22×C4—42no—
1071C22×C4—42no—
1072C22×C4—42no—
1073C22×C4—44no—
1074C22×C4—44no—
1075C22×C4—44no—
1076C22×C4—44no—
1077C22×C4—44no—
1078C22×C4—44no—
1079C22×C4—44no—
1080C22×C4C2×#4114yes—
1081C22×C4C2511yescharacteristic
1082C22×C4C2512yes—
1083C22×C4C2511yescharacteristic
1084C22×C4C2512yes—
1085C22×C4C2512yes—
1086C22×C4C2514yes—
1087C22×C4C2511yescharacteristic
1088C22×C4C2511yescharacteristic
1089C22×C4C2512yes—
1090C22×C4C2514yes—
1091C22×C4C2514yes—
1092C22×C4C2512yes—
1093C22×C4C2512yes—
1094C22×C4C2514yes—
1095C22×C4C2514yes—
1096C22×C4C2514yes—
1097C22×C4C2511yescharacteristic
1098C22×C4C2511yescharacteristic
1099C22×C4C2514yes—
1100C22×C4C2511yescharacteristic
1101C22×C4C2511yescharacteristic
1102C22×C4C2511yescharacteristic
1103C22×C4C2511yescharacteristic
1104C22×C4C2511yescharacteristic
1105C22×C4C2512yes—
1106C22×C4C2512yes—
1107C22×C4C2511yescharacteristic
1108C4⋊C4—22no—
1109C4⋊C4—22no—
1110C4⋊C4—22no—
1111C4⋊C4—24no—
1112C4⋊C4—22no—
1113C4⋊C4—22no—
1114C4⋊C4—22no—
1115C4⋊C4—24no—
1116C4⋊C4—28no—
1117C4⋊C4—22no—
1118C4⋊C4—22no—
1119C4⋊C4—28no—
1120C4⋊C4—28no—
1121C4⋊C4—24no—
1122C4⋊C4—24no—
1123C4⋊C4—28no—
1124C4⋊C4—28no—
1125C4⋊C4—24no—
1126C4⋊C4—24no—
1127C4⋊C4—24no—
1128C4⋊C4—24no—
1129C4⋊C4—28no—
1130C4⋊C4—28no—
1131C4⋊C4—28no—
1132C4⋊C4—24no—
1133C4⋊C4—24no—
1134C4⋊C4—44no—
1135C4⋊C4—44no—
1136C4⋊C4—44no—
1137C4⋊C4—42no—
1138C4⋊C4—44no—
1139C4⋊C4—44no—
1140C4⋊C4—44no—
1141C4⋊C4—44no—
1142C4⋊C4—44no—
1143C4⋊C4—42no—
1144C4⋊C4—44no—
1145C4⋊C4—44no—
1146C4⋊C4—42no—
1147C4⋊C4—44no—
1148C4⋊C4—44no—
1149C4⋊C4—44no—
1150C4⋊C4—44no—
1151C4⋊C4—44no—
1152C4⋊C4—44no—
1153C4⋊C4—44no—
1154C4⋊C4—44no—
1155C4⋊C4—44no—
1156C4⋊C4—44no—
1157C4⋊C4—44no—
1158C4⋊C4—44no—
1159C4⋊C4—44no—
1160C4⋊C4—42no—
1161C4⋊C4—44no—
1162C4⋊C4—44no—
1163C4⋊C4—44no—
1164C4⋊C4—44no—
1165C4⋊C4—42no—
1166C4⋊C4—42no—
1167C4⋊C4—44no—
1168C4⋊C4C2×#4114yes—
1169C4⋊C4C2×#4114yes—
1170C22⋊C4—22no—
1171C22⋊C4—22no—
1172C22⋊C4—28no—
1173C22⋊C4—22no—
1174C22⋊C4—22no—
1175C22⋊C4—22no—
1176C22⋊C4—22no—
1177C22⋊C4—22no—
1178C22⋊C4—22no—
1179C22⋊C4—28no—
1180C22⋊C4—28no—
1181C22⋊C4—28no—
1182C22⋊C4—28no—
1183C22⋊C4—24no—
1184C22⋊C4—24no—
1185C22⋊C4—24no—
1186C22⋊C4—24no—
1187C22⋊C4—28no—
1188C22⋊C4—28no—
1189C22⋊C4—42no—
1190C22⋊C4—44no—
1191C22⋊C4—42no—
1192C22⋊C4—42no—
1193C22⋊C4—44no—
1194C22⋊C4—44no—
1195C22⋊C4—42no—
1196C22⋊C4—44no—
1197C22⋊C4—44no—
1198C22⋊C4—44no—
1199C22⋊C4—44no—
1200C22⋊C4—44no—
1201C22⋊C4—44no—
1202C22⋊C4—42no—
1203C22⋊C4—44no—
1204C22⋊C4—44no—
1205C22⋊C4—44no—
1206C22⋊C4—44no—
1207C22⋊C4—44no—
1208C22⋊C4—44no—
1209C22⋊C4—44no—
1210C22⋊C4—44no—
1211C22⋊C4—44no—
1212C22⋊C4—44no—
1213C22⋊C4—44no—
1214C22⋊C4—44no—
1215C22⋊C4—44no—
1216C22⋊C4—42no—
1217C22⋊C4—44no—
1218C22⋊C4C2×#4114yes—
1219C22⋊C4C2×#4114yes—
1220C42—22no—
1221C42—22no—
1222C42—22no—
1223C42—22no—
1224C42—28no—
1225C42—24no—
1226C42—22no—
1227C42—22no—
1228C42—22no—
1229C42—24no—
1230C42—22no—
1231C42—22no—
1232C42—22no—
1233C42—42no—
1234C42—42no—
1235C42—42no—
1236C42—42no—
1237C42—44no—
1238C42—44no—
1239C42—44no—
1240C42—42no—
1241C42—44no—
1242C42—44no—
1243C42—42no—
1244C42—44no—
1245C42—44no—
1246C42—42no—
1247C42—42no—
1248C42C2×#4114yes—
1249C42C2×#4114yes—
1250C42H(5,𝔽2)14yes—
1251C422−1+414yes—
1252C23—21no—
1253C23—21no—
1254C23—22no—
1255C23—22no—
1256C23—21no—
1257C23—24no—
1258C23—21no—
1259C23—21no—
1260C23—21no—
1261C23—24no—
1262C23—21no—
1263C23—24no—
1264C23—21no—
1265C23—22no—
1266C23—24no—
1267C23—22no—
1268C23—24no—
1269C23—24no—
1270C23—22no—
1271C23—24no—
1272C23—22no—
1273C23C22×#4112yes—
1274C23C2611yescharacteristic
1275Q8—48no—
1276Q8—88no—
1277Q8—82no—
1278Q8—88no—
1279D4—48no—
1280D4—82no—
1281D4—88no—
1282D4—82no—
1283D4—88no—
1284D4—82no—
1285D4—164no—
1286D4—164no—
1287C2×C4—21no—
1288C2×C4—21no—
1289C2×C4—22no—
1290C2×C4—22no—
1291C2×C4—22no—
1292C2×C4—22no—
1293C2×C4—22no—
1294C2×C4—22no—
1295C2×C4—22no—
1296C2×C4—22no—
1297C2×C4—28no—
1298C2×C4—21no—
1299C2×C4—21no—
1300C2×C4—21no—
1301C2×C4—24no—
1302C2×C4—21no—
1303C2×C4—21no—
1304C2×C4—24no—
1305C2×C4—21no—
1306C2×C4—24no—
1307C2×C4—22no—
1308C2×C4—22no—
1309C2×C4—22no—
1310C2×C4—24no—
1311C2×C4—24no—
1312C2×C4—24no—
1313C2×C4—24no—
1314C2×C4—21no—
1315C2×C4—21no—
1316C2×C4—24no—
1317C2×C4—21no—
1318C2×C4—22no—
1319C2×C4—22no—
1320C2×C4—22no—
1321C2×C4—24no—
1322C2×C4—21no—
1323C2×C4—22no—
1324C2×C4—22no—
1325C2×C4—24no—
1326C2×C4—22no—
1327C2×C4—24no—
1328C2×C4—24no—
1329C2×C4—24no—
1330C2×C4—22no—
1331C2×C4—22no—
1332C2×C4—24no—
1333C2×C4—24no—
1334C2×C4—24no—
1335C2×C4—22no—
1336C2×C4—22no—
1337C2×C4—22no—
1338C2×C4—24no—
1339C2×C4—22no—
1340C2×C4—22no—
1341C2×C4—22no—
1342C2×C4—22no—
1343C2×C4—22no—
1344C2×C4—22no—
1345C2×C4—24no—
1346C2×C4—24no—
1347C2×C4—22no—
1348C2×C4—22no—
1349C2×C4—24no—
1350C2×C4—24no—
1351C2×C4—48no—
1352C2×C4—44no—
1353C2×C4—44no—
1354C2×C4—88no—
1355C2×C4—82no—
1356C2×C4—82no—
1357C2×C4—84no—
1358C2×C4—88no—
1359C2×C4—164no—
1360C2×C4—164no—
1361C2×C4C22×#4112yes—
1362C2×C4C22×#4112yes—
1363C2×C4C22×#4112yes—
1364C2×C4C22×#4112yes—
1365C2×C4C22×#4112yes—
1366C2×C4C22×#4112yes—
1367C2×C4C2×H(5,𝔽2)14yes—
1368C2×C4C2×H(5,𝔽2)12yes—
1369C2×C4C2×2−1+414yes—
1370C2×C4C2×2−1+412yes—
1371C22—22no—
1372C22—22no—
1373C22—22no—
1374C22—42no—
1375C22—42no—
1376C22—41no—
1377C22—41no—
1378C22—44no—
1379C22—41no—
1380C22—44no—
1381C22—41no—
1382C22—41no—
1383C22—41no—
1384C22—44no—
1385C22—42no—
1386C22—42no—
1387C22—44no—
1388C22—44no—
1389C22—44no—
1390C22—44no—
1391C22—42no—
1392C22—42no—
1393C22C23×#4111yescharacteristic
1394C22C22×H(5,𝔽2)11yescharacteristic
1395C22C22×2−1+411yescharacteristic
1396C22H(7,𝔽2)12yes—
1397C222−1+612yes—
1398C4—22no—
1399C4—22no—
1400C4—22no—
1401C4—22no—
1402C4—22no—
1403C4—24no—
1404C4—24no—
1405C4—41no—
1406C4—41no—
1407C4—44no—
1408C4—41no—
1409C4—44no—
1410C4—41no—
1411C4—44no—
1412C4—41no—
1413C4—41no—
1414C4—42no—
1415C4—42no—
1416C4—42no—
1417C4—44no—
1418C4—44no—
1419C4—42no—
1420C4—42no—
1421C4—42no—
1422C4—44no—
1423C4—44no—
1424C4#351114yes—
1425C2—42no—
1426C2—81no—
1427C2—81no—
1428C2—84no—
1429C2C2×#351111yescharacteristic
1430C2#6285811yescharacteristic
1431C2#6286111yescharacteristic
1432C2#6287712yes—
1433C2#6287812yes—
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. #49807C2semidirect
2. #49757C2semidirect
3. #48257C2semidirect
4. #48188C2semidirect
5. #47514C2semidirect
6. #47446C2semidirect
7. #47284C2semidirect
8. #46914C2semidirect
9. #39762C2semidirect
10. #39756C2semidirect
11. #39674C2semidirect
12. #39554C2semidirect
13. #39378C2semidirect
14. #39373C2semidirect
15. #37952C2semidirect
16. #37945C2semidirect
17. #37710C2semidirect
18. #37709C2semidirect
19. #37706C2semidirect
20. #37705C2semidirect
21. #37588C2semidirect
22. #37293C2semidirect
23. #37280C2semidirect
24. #35335C2semidirect
25. #35332C2semidirect
26. #35332C2semidirect
27. #35294C2semidirect
28. #35284C2semidirect
29. #35277C2semidirect
30. #34428C2semidirect
31. #34081C2semidirect

Maximal subgroups

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

subgroupindex
#498072
#497572
#482572
#481882
#475142
#474462
#472842
#469142
#397622
#397562
#396742
#395542
#393782
#393732
#379522
#379452
#377102
#377092
#377062
#377052
#375882
#372932
#372802
#353352
#353322
#352942
#352842
#352772
#344282
#340812