Finite Group Databasebeta

← #7715608

Subgroups — #7715608

Order 512.

4754 conjugacy classes of subgroups.

The subgroup lattice has 1516 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#49083C214yesmaximal, complemented
2#49024C214yesmaximal, complemented
3#48242C214yesmaximal, complemented
4#48175C214yesmaximal, complemented
5#47542C214yesmaximal, complemented
6#47536C214yesmaximal, complemented
7#46973C214yesmaximal, complemented
8#46967C214yesmaximal, complemented
9#39057C212yesmaximal, complemented
10#39056C212yesmaximal, complemented
11#39041C212yesmaximal, complemented
12#39040C212yesmaximal, complemented
13#37898C211yesmaximal, characteristic, complemented
14#37897C211yesmaximal, characteristic, complemented
15#37883C211yesmaximal, characteristic, complemented
16#37882C211yesmaximal, characteristic, complemented
17#37706C211yesmaximal, characteristic, complemented
18#37705C211yesmaximal, characteristic, complemented
19#37701C211yesmaximal, characteristic, complemented
20#37700C211yesmaximal, characteristic, complemented
21#37512C212yesmaximal, complemented
22#37288C212yesmaximal, complemented
23#37272C212yesmaximal, complemented
24#35333C211yesmaximal, characteristic, complemented
25#35315C211yesmaximal, characteristic, complemented
26#35309C211yesmaximal, characteristic, complemented
27#35273C211yesmaximal, characteristic, complemented
28#35271C211yesmaximal, characteristic, complemented
29#35259C211yesmaximal, characteristic, complemented
30#34410C212yesmaximal, complemented
31#34070C211yesmaximal, characteristic, complemented
32C2×#541C2211yescharacteristic
33C2×#540C2211yescharacteristic
34C2×#537C2212yes—
35C2×#532C2211yescharacteristic
36C2×#532C2211yescharacteristic
37C22×#125C2211yescharacteristic
38C2×C4×#41C2211yescharacteristic
39C2×C4×#41C2211yescharacteristic
40#2857C2211yescharacteristic
41#2857C2211yescharacteristic
42#2856C2211yescharacteristic
43#2856C2211yescharacteristic
44#2855C2212yes—
45#2855C2212yes—
46#2854C2212yes—
47#2854C2212yes—
48#2851C2211yescharacteristic
49#2851C2211yescharacteristic
50#2851C2211yescharacteristic
51#2851C2211yescharacteristic
52#2831C2214yes—
53#2829C2214yes—
54#2794C2214yes—
55#2793C2214yes—
56#2793C2214yes—
57#2791C2214yes—
58#2790C2214yes—
59#2783C2214yes—
60#2781C2214yes—
61#2772C2214yes—
62#2761C2214yes—
63#2761C2214yes—
64#2749C2214yes—
65#2749C2214yes—
66#2748C2214yes—
67#2747C2214yes—
68#2747C2214yes—
69#2746C2214yes—
70#2746C2214yes—
71#2744C2214yes—
72#2744C2214yes—
73#2743C2214yes—
74#2743C2214yes—
75#2741C2214yes—
76#2740C2214yes—
77#2730C2214yes—
78#2729C2214yes—
79#2725C2214yes—
80#2721C2214yes—
81#2721C2214yes—
82#2719C2214yes—
83#2718C2214yes—
84#2714C2214yes—
85#2711C2214yes—
86#2711C2214yes—
87#2708C2214yes—
88#2708C2214yes—
89#2707C2214yes—
90#2707C2214yes—
91#2703C2214yes—
92#2699C2214yes—
93#2695C2214yes—
94#2693C2214yes—
95#2691C2214yes—
96#2688C2214yes—
97#2688C2214yes—
98#2686C2214yes—
99#2682C2214yes—
100#2673C2214yes—
101#2671C2214yes—
102#2648C2214yes—
103#2648C2214yes—
104#2647C2211yescharacteristic
105#2647C2211yescharacteristic
106#2645C2212yes—
107#2644C2212yes—
108#2642C2211yescharacteristic
109#2641C2211yescharacteristic
110#2636C2214yes—
111#2630C2214yes—
112#2629C2212yes—
113#2629C2212yes—
114#2629C2211yescharacteristic
115#2629C2211yescharacteristic
116#2621C2211yescharacteristic
117#2620C2212yes—
118#2620C2212yes—
119#2619C2211yescharacteristic
120#2616C2212yes—
121#2615C2212yes—
122#2601C2214yes—
123#2600C2214yes—
124#2597C2214yes—
125#2597C2214yes—
126#2596C2214yes—
127#2585C2214yes—
128#2579C2214yes—
129#2579C2214yes—
130#2577C2214yes—
131#2576C2214yes—
132#2576C2214yes—
133#2574C2214yes—
134#2569C2214yes—
135#2566C2214yes—
136#2566C2214yes—
137#2565C2214yes—
138#2559C2214yes—
139#2554C2214yes—
140#2554C2214yes—
141#2553C2214yes—
142#2538C2214yes—
143#2537C2214yes—
144#2533C2214yes—
145#2531C2214yes—
146#2528C2214yes—
147#2526C2214yes—
148#2515C2214yes—
149#2512C2212yes—
150#2511C2212yes—
151#2507C2212yes—
152#2506C2212yes—
153#2505C2214yes—
154#2497C2214yes—
155#2497C2212yes—
156#2496C2212yes—
157#2493C2214yes—
158#2490C2212yes—
159#2489C2212yes—
160#2487C2212yes—
161#2486C2212yes—
162#2484C2214yes—
163#2481C2214yes—
164#2481C2214yes—
165#2473C2214yes—
166#2471C2214yes—
167#2468C2214yes—
168#2467C2214yes—
169#2466C2214yes—
170#2464C2214yes—
171#2462C2214yes—
172#2460C2214yes—
173#2460C2214yes—
174#2460C2214yes—
175#2458C2214yes—
176#2457C2214yes—
177#2456C2214yes—
178#2456C2214yes—
179#2454C2212yes—
180#2453C2212yes—
181#2448C2212yes—
182#2447C2212yes—
183#2444C2214yes—
184#2444C2214yes—
185#2443C2214yes—
186#2442C2214yes—
187#2427C2212yes—
188#2426C2212yes—
189#2425C2214yes—
190#2423C2212yes—
191#2422C2212yes—
192#2419C2214yes—
193#2419C2214yes—
194#2417C2212yes—
195#2416C2214yes—
196#2416C2212yes—
197#2416C2214yes—
198#2416C2214yes—
199#2415C2212yes—
200#2414C2212yes—
201#2413C2214yes—
202#2407C2212yes—
203#2407C2212yes—
204#2377C2214yes—
205#2377C2214yes—
206#2364C2214yes—
207#2363C2212yes—
208#2363C2214yes—
209#2362C2212yes—
210#2361C2212yes—
211#2360C2212yes—
212#2345C2212yes—
213#2344C2212yes—
214#2341C2212yes—
215#2339C2212yes—
216#2333C2214yes—
217#2332C2214yes—
218#2330C2211yescharacteristic
219#2330C2211yescharacteristic
220#2329C2214yes—
221#2328C2211yescharacteristic
222#2328C2212yes—
223#2327C2211yescharacteristic
224#2327C2212yes—
225#2326C2212yes—
226#2326C2212yes—
227#2325C2212yes—
228#2325C2212yes—
229#2325C2212yes—
230#2325C2212yes—
231#2324C2212yes—
232#2324C2214yes—
233#2323C2212yes—
234#2320C2212yes—
235#2319C2212yes—
236#2317C2212yes—
237#2314C2211yescharacteristic
238#2314C2211yescharacteristic
239#2311C2212yes—
240#2311C2212yes—
241C4×C22⋊Q8C2212yes—
242C4×C22⋊Q8C2212yes—
243C4×#121C2212yes—
244C4×#121C2212yes—
245#2297C2211yescharacteristic
246#2297C2211yescharacteristic
247#2290C2211yescharacteristic
248#2290C2211yescharacteristic
249#2290C2211yescharacteristic
250#2290C2211yescharacteristic
251#2290C2211yescharacteristic
252#2290C2211yescharacteristic
253#2290C2211yescharacteristic
254#2290C2211yescharacteristic
255#2285C2211yescharacteristic
256#2285C2211yescharacteristic
257C2×#384C2211yescharacteristic
258C2×#376C2211yescharacteristic
259C22×#41C2312yes—
260C22×#41C2311yescharacteristic
261C22×#41C2311yescharacteristic
262#541—44no—
263#540—44no—
264#537—216no—
265#532—28no—
266#532—44no—
267C2×C4⋊Q8C2311yescharacteristic
268C2×C4⋊Q8C2311yescharacteristic
269C2×#127C2311yescharacteristic
270C2×#127C2311yescharacteristic
271C2×#126C2314yes—
272C2×#126C2314yes—
273C2×#126C2314yes—
274C2×#125—44no—
275C2×#125C2311yescharacteristic
276C2×#125C2311yescharacteristic
277C2×#125C2314yes—
278C2×#125C2312yes—
279C2×#125C2314yes—
280C2×#125C2314yes—
281C2×#124C2311yescharacteristic
282C2×#124C2311yescharacteristic
283C2×#124C2312yes—
284C2×#123C2314yes—
285C2×#123C2314yes—
286C2×#123C2314yes—
287C2×#123C2314yes—
288C2×#123C2314yes—
289C2×C22⋊Q8C2312yes—
290C2×C22⋊Q8C2314yes—
291C2×C22⋊Q8C2312yes—
292C2×C22⋊Q8C2312yes—
293C2×C22⋊Q8C2312yes—
294C2×#121C2314yes—
295C2×#121C2312yes—
296C2×#121C2311yescharacteristic
297C2×#121C2311yescharacteristic
298C2×#121C2311yescharacteristic
299C2×#121C2311yescharacteristic
300C2×#121C2312yes—
301C2×#121C2314yes—
302C2×#121C2314yes—
303C2×#121C2312yes—
304C2×#121C2312yes—
305C2×#121C2314yes—
306C2×#121C2314yes—
307C2×#121C2314yes—
308C2×#121C2314yes—
309C2×#121C2314yes—
310C4×#41—44no—
311C4×#41—44no—
312C2×C4×Q8C2312yes—
313C2×C4×Q8C2312yes—
314C2×C4×Q8C2312yes—
315C2×C4×Q8C2312yes—
316C2×C4×D4C2311yescharacteristic
317C2×C4×D4C2311yescharacteristic
318C2×C4×D4C2311yescharacteristic
319C2×C4×D4C2311yescharacteristic
320C2×C4×D4C2312yes—
321C2×C4×D4C2312yes—
322C2×C4×D4C2312yes—
323C2×C4×D4C2312yes—
324C2×C4×D4C2312yes—
325C2×C4×D4C2312yes—
326C2×C4×D4C2312yes—
327C2×C4×D4C2312yes—
328C2×C4×D4C2314yes—
329C2×C4×D4C2314yes—
330C2×C4×D4C2314yes—
331C2×C4×D4C2314yes—
332C2×#117C2311yescharacteristic
333C2×#117C2311yescharacteristic
334C2×#117C2311yescharacteristic
335C2×#117C2312yes—
336C2×#117C2311yescharacteristic
337C2×#117C2311yescharacteristic
338C2×#117C2311yescharacteristic
339C2×#117C2314yes—
340C22×C4⋊C4C2312yes—
341C22×C4⋊C4C2312yes—
342C22×C4⋊C4C2314yes—
343C22×C4⋊C4C2314yes—
344C22×C42C2311yescharacteristic
345C22×C42C2311yescharacteristic
346C22×C42C2311yescharacteristic
347C22×C42C2311yescharacteristic
348C22×C42C2311yescharacteristic
349C22×C42C2311yescharacteristic
350C22×C42C2311yescharacteristic
351#401C2314yes—
352#400C2314yes—
353#400C2314yes—
354#400C2314yes—
355#400C2314yes—
356#400C2314yes—
357#400C2314yes—
358#400C2314yes—
359#400C2314yes—
360#400C2314yes—
361#400C2314yes—
362#400C2314yes—
363#400C2314yes—
364#400C2314yes—
365#400C2314yes—
366#400C2314yes—
367#399C2314yes—
368#399C2314yes—
369#399C2314yes—
370#399C2314yes—
371#398C2314yes—
372#398C2314yes—
373#398C2314yes—
374#398C2314yes—
375#398C2314yes—
376#398C2314yes—
377#398C2314yes—
378#398C2314yes—
379#398C2314yes—
380#398C2314yes—
381#398C2314yes—
382#398C2314yes—
383#398C2314yes—
384#398C2314yes—
385#398C2314yes—
386#398C2314yes—
387#397C2314yes—
388#397C2314yes—
389#397C2314yes—
390#397C2314yes—
391#397C2314yes—
392#397C2314yes—
393#397C2314yes—
394#397C2314yes—
395#397C2314yes—
396#397C2314yes—
397#397C2314yes—
398#397C2314yes—
399#397C2314yes—
400#397C2314yes—
401#397C2314yes—
402#396C2314yes—
403#396C2314yes—
404#396C2314yes—
405#396C2314yes—
406#396C2314yes—
407#396C2314yes—
408#396C2314yes—
409#396C2314yes—
410#396C2314yes—
411#396C2314yes—
412#396C2314yes—
413#396C2314yes—
414#396C2314yes—
415#396C2314yes—
416#396C2314yes—
417#396C2314yes—
418#396C2314yes—
419#395C2314yes—
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#394C2314yes—
433#394C2314yes—
434#394C2314yes—
435#394C2314yes—
436#394C2314yes—
437#394C2314yes—
438#394C2314yes—
439#393C2314yes—
440#392C2314yes—
441#392C2314yes—
442#392C2314yes—
443#392C2314yes—
444#392C2314yes—
445#392C2314yes—
446#392C2314yes—
447#391C2314yes—
448#391C2312yes—
449#391C2312yes—
450#391C2312yes—
451#391C2312yes—
452#391C2312yes—
453#391C2312yes—
454#391C2312yes—
455#391C2312yes—
456#390C2314yes—
457#390C2314yes—
458#390C2314yes—
459#390C2312yes—
460#390C2312yes—
461#390C2312yes—
462#390C2312yes—
463#390C2312yes—
464#390C2312yes—
465#390C2314yes—
466#390C2314yes—
467#390C2314yes—
468#390C2312yes—
469#390C2314yes—
470#390C2312yes—
471#390C2314yes—
472#390C2314yes—
473#390C2314yes—
474#389C2312yes—
475#389C2312yes—
476#389C2312yes—
477#389C2312yes—
478#389C2312yes—
479#389C2312yes—
480#389C2314yes—
481#389C2312yes—
482#389C2312yes—
483#389C2314yes—
484#389C2314yes—
485#389C2314yes—
486#389C2312yes—
487#389C2312yes—
488#389C2314yes—
489#389C2314yes—
490#389C2312yes—
491#389C2312yes—
492#389C2314yes—
493#389C2314yes—
494#389C2314yes—
495#388C2314yes—
496#388C2314yes—
497#388C2314yes—
498#388C2314yes—
499#388C2314yes—
500#388C2314yes—
501#388C2314yes—
502#388C2312yes—
503#388C2314yes—
504#388C2314yes—
505#388C2314yes—
506#388C2314yes—
507#388C2314yes—
508#388C2314yes—
509#388C2314yes—
510#388C2314yes—
511#388C2312yes—
512#388C2312yes—
513#388C2312yes—
514#388C2312yes—
515#388C2312yes—
516#388C2312yes—
517#388C2312yes—
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#387C2314yes—
531#387C2314yes—
532#387C2314yes—
533#387C2314yes—
534#387C2312yes—
535#387C2314yes—
536#387C2314yes—
537#387C2314yes—
538#387C2314yes—
539#387C2314yes—
540#387C2314yes—
541#387C2314yes—
542#387C2314yes—
543#387C2314yes—
544#387C2314yes—
545#387C2314yes—
546#387C2314yes—
547#387C2314yes—
548#387C2314yes—
549#387C2312yes—
550#387C2314yes—
551#387C2314yes—
552#387C2314yes—
553#387C2312yes—
554#387C2312yes—
555#387C2312yes—
556#387C2312yes—
557#387C2312yes—
558#387C2312yes—
559#387C2314yes—
560#387C2314yes—
561#387C2314yes—
562#387C2314yes—
563#387C2314yes—
564#387C2314yes—
565#387C2314yes—
566#387C2314yes—
567#387C2314yes—
568#387C2314yes—
569#387C2314yes—
570#387C2314yes—
571#386C2314yes—
572#386C2314yes—
573#386C2314yes—
574#386C2314yes—
575#386C2314yes—
576#386C2314yes—
577#386C2314yes—
578#386C2314yes—
579#386C2312yes—
580#386C2312yes—
581#386C2312yes—
582#386C2312yes—
583#386C2312yes—
584#386C2312yes—
585#386C2312yes—
586#386C2312yes—
587#386C2312yes—
588#386C2312yes—
589#386C2312yes—
590#386C2312yes—
591#386C2314yes—
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#385C2312yes—
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#385C2314yes—
618#385C2314yes—
619#385C2314yes—
620#385C2314yes—
621#385C2312yes—
622#385C2312yes—
623#385C2312yes—
624#385C2312yes—
625#385C2312yes—
626#385C2312yes—
627#385C2314yes—
628#385C2314yes—
629#385C2314yes—
630#385C2314yes—
631#384C2314yes—
632#384C2311yescharacteristic
633#384C2311yescharacteristic
634#384C2312yes—
635#384C2312yes—
636#384C2312yes—
637#384C2314yes—
638#383C2314yes—
639#382C2314yes—
640#382C2314yes—
641#382C2311yescharacteristic
642#382C2311yescharacteristic
643#382C2314yes—
644#382C2312yes—
645#381C2314yes—
646#381C2314yes—
647#381C2314yes—
648#381C2314yes—
649#381C2314yes—
650#381C2314yes—
651#381C2314yes—
652#380C2314yes—
653#380C2314yes—
654#380C2312yes—
655#380C2312yes—
656#380C2312yes—
657#380C2312yes—
658#380C2314yes—
659#380C2314yes—
660#380C2312yes—
661#380C2312yes—
662#380C2314yes—
663#380C2314yes—
664#380C2314yes—
665#380C2312yes—
666#380C2312yes—
667#380C2314yes—
668#380C2314yes—
669#380C2314yes—
670#380C2312yes—
671#380C2312yes—
672#380C2314yes—
673C4×C4⋊C4C2314yes—
674C4×C4⋊C4C2314yes—
675C4×C4⋊C4C2312yes—
676C4×C4⋊C4C2312yes—
677C4×C4⋊C4C2314yes—
678C4×C4⋊C4C2312yes—
679C4×C4⋊C4C2312yes—
680C4×C4⋊C4C2314yes—
681C4×C4⋊C4C2311yescharacteristic
682C4×C4⋊C4C2311yescharacteristic
683C4×C4⋊C4C2311yescharacteristic
684C4×C4⋊C4C2311yescharacteristic
685C4×C22⋊C4C2314yes—
686C4×C22⋊C4C2314yes—
687C4×C22⋊C4C2314yes—
688C4×C22⋊C4C2314yes—
689C4×C22⋊C4C2314yes—
690C4×C22⋊C4C2314yes—
691C4×C22⋊C4C2314yes—
692C4×C22⋊C4C2311yescharacteristic
693C4×C22⋊C4C2311yescharacteristic
694C4×C22⋊C4C2311yescharacteristic
695C4×C22⋊C4C2311yescharacteristic
696C4×C22⋊C4C2314yes—
697C4×C22⋊C4C2311yescharacteristic
698C4×C22⋊C4C2311yescharacteristic
699C4×C22⋊C4C2311yescharacteristic
700C4×C22⋊C4C2311yescharacteristic
701#376C2311yescharacteristic
702#376C2311yescharacteristic
703#376C2312yes—
704#376C2312yes—
705#376C2311yescharacteristic
706#376C2311yescharacteristic
707C2×#95C2314yes—
708C2×#95C2312yes—
709C2×#95C2312yes—
710C2×#41—24no—
711C2×#41—28no—
712C2×#41—42no—
713C2×#41—42no—
714C2×#41—42no—
715C2×#41—42no—
716C2×#41—44no—
717C2×#41—44no—
718C2×#41#4118yes—
719C22×Q8C2412yes—
720C22×Q8C2411yescharacteristic
721C22×Q8C2411yescharacteristic
722C22×D4C2412yes—
723C22×D4C2411yescharacteristic
724C22×D4C2411yescharacteristic
725C22×D4C2411yescharacteristic
726C22×D4C2414yes—
727C22×D4C2414yes—
728C22×D4C2411yescharacteristic
729C22×D4C2414yes—
730C22×D4C2411yescharacteristic
731C22×D4C2411yescharacteristic
732C22×D4C2411yescharacteristic
733C22×D4C2414yes—
734C22×D4C2414yes—
735C22×D4C2414yes—
736C22×D4C2411yescharacteristic
737C22×D4C2411yescharacteristic
738C22×D4C2411yescharacteristic
739C23×C4C2411yescharacteristic
740C23×C4C2411yescharacteristic
741C23×C4C2411yescharacteristic
742C23×C4C2411yescharacteristic
743C23×C4C2411yescharacteristic
744C23×C4C2414yes—
745C23×C4C2412yes—
746C23×C4C2412yes—
747C23×C4C2412yes—
748C23×C4C2414yes—
749C23×C4C2411yescharacteristic
750C23×C4C2411yescharacteristic
751C23×C4C2414yes—
752C23×C4C2412yes—
753C23×C4C2414yes—
754C23×C4C2412yes—
755C23×C4C2414yes—
756C23×C4C2412yes—
757C4⋊Q8—24no—
758C4⋊Q8—24no—
759#127—24no—
760#127—24no—
761#126—48no—
762#126—84no—
763#126—84no—
764#125—24no—
765#125—24no—
766#125—44no—
767#125—48no—
768#125—48no—
769#125—84no—
770#124—24no—
771#124—24no—
772#124—44no—
773#123—48no—
774#123—84no—
775#123—84no—
776#123—84no—
777#123—84no—
778C22⋊Q8—216no—
779C22⋊Q8—28no—
780C22⋊Q8—28no—
781C22⋊Q8—44no—
782C22⋊Q8—44no—
783#121—24no—
784#121—24no—
785#121—24no—
786#121—24no—
787#121—216no—
788#121—216no—
789#121—216no—
790#121—28no—
791#121—28no—
792#121—48no—
793#121—44no—
794#121—48no—
795#121—44no—
796#121—84no—
797#121—84no—
798#121—84no—
799C4×Q8—44no—
800C4×Q8—44no—
801C4×Q8—44no—
802C4×Q8—44no—
803C4×D4—24no—
804C4×D4—24no—
805C4×D4—24no—
806C4×D4—24no—
807C4×D4—44no—
808C4×D4—44no—
809C4×D4—48no—
810C4×D4—44no—
811C4×D4—44no—
812C4×D4—44no—
813C4×D4—44no—
814C4×D4—44no—
815C4×D4—44no—
816C4×D4—84no—
817C4×D4—84no—
818C4×D4—84no—
819#117—24no—
820#117—24no—
821#117—42no—
822#117—42no—
823#117—42no—
824#117—42no—
825#117—44no—
826#117—84no—
827C2×C4⋊C4—28no—
828C2×C4⋊C4—44no—
829C2×C4⋊C4—48no—
830C2×C4⋊C4—84no—
831C2×C4⋊C4C2412yes—
832C2×C4⋊C4C2412yes—
833C2×C4⋊C4C2412yes—
834C2×C4⋊C4C2412yes—
835C2×C4⋊C4C2414yes—
836C2×C4⋊C4C2414yes—
837C2×C4⋊C4C2414yes—
838C2×C4⋊C4C2412yes—
839C2×C4⋊C4C2412yes—
840C2×C4⋊C4C2412yes—
841C2×C4⋊C4C2412yes—
842C2×C4⋊C4C2414yes—
843C2×C4⋊C4C2411yescharacteristic
844C2×C4⋊C4C2411yescharacteristic
845C2×C4⋊C4C2411yescharacteristic
846C2×C4⋊C4C2411yescharacteristic
847C2×C4⋊C4C2414yes—
848C2×C4⋊C4C2414yes—
849C2×C4⋊C4C2414yes—
850C2×C4⋊C4C2414yes—
851C2×C4⋊C4C2414yes—
852C2×C4⋊C4C2414yes—
853C2×C4⋊C4C2414yes—
854C2×C4⋊C4C2414yes—
855C2×C4⋊C4C2414yes—
856C2×C4⋊C4C2412yes—
857C2×C4⋊C4C2412yes—
858C2×C4⋊C4C2412yes—
859C2×C4⋊C4C2412yes—
860C2×C4⋊C4C2414yes—
861C2×C4⋊C4C2414yes—
862C2×C4⋊C4C2414yes—
863C2×C4⋊C4C2414yes—
864C2×C4⋊C4C2414yes—
865C2×C4⋊C4C2414yes—
866C2×C4⋊C4C2414yes—
867C2×C4⋊C4C2414yes—
868C2×C4⋊C4C2414yes—
869C2×C4⋊C4C2414yes—
870C2×C4⋊C4C2414yes—
871C2×C4⋊C4C2414yes—
872C2×C4⋊C4C2414yes—
873C2×C4⋊C4C2412yes—
874C2×C4⋊C4C2414yes—
875C2×C4⋊C4C2414yes—
876C2×C4⋊C4C2412yes—
877C2×C4⋊C4C2412yes—
878C2×C4⋊C4C2414yes—
879C2×C4⋊C4C2412yes—
880C2×C4⋊C4C2414yes—
881C2×C4⋊C4C2414yes—
882C2×C22⋊C4C2412yes—
883C2×C22⋊C4C2412yes—
884C2×C22⋊C4C2411yescharacteristic
885C2×C22⋊C4C2411yescharacteristic
886C2×C22⋊C4C2411yescharacteristic
887C2×C22⋊C4C2411yescharacteristic
888C2×C22⋊C4C2411yescharacteristic
889C2×C22⋊C4C2411yescharacteristic
890C2×C22⋊C4C2411yescharacteristic
891C2×C22⋊C4C2411yescharacteristic
892C2×C22⋊C4C2414yes—
893C2×C22⋊C4C2414yes—
894C2×C22⋊C4C2414yes—
895C2×C22⋊C4C2414yes—
896C2×C22⋊C4C2412yes—
897C2×C22⋊C4C2412yes—
898C2×C22⋊C4C2412yes—
899C2×C22⋊C4C2412yes—
900C2×C22⋊C4C2412yes—
901C2×C22⋊C4C2414yes—
902C2×C22⋊C4C2414yes—
903C2×C22⋊C4C2412yes—
904C2×C22⋊C4C2414yes—
905C2×C22⋊C4C2414yes—
906C2×C22⋊C4C2414yes—
907C2×C22⋊C4C2414yes—
908C2×C22⋊C4C2414yes—
909C2×C22⋊C4C2414yes—
910C2×C22⋊C4C2414yes—
911C2×C22⋊C4C2414yes—
912C2×C22⋊C4C2414yes—
913C2×C22⋊C4C2414yes—
914C2×C22⋊C4C2414yes—
915C2×C22⋊C4C2414yes—
916C2×C22⋊C4C2414yes—
917C2×C22⋊C4C2414yes—
918C2×C22⋊C4C2414yes—
919C2×C22⋊C4C2414yes—
920C2×C22⋊C4C2414yes—
921C2×C22⋊C4C2412yes—
922C2×C22⋊C4C2414yes—
923C2×C22⋊C4C2414yes—
924C2×C22⋊C4C2414yes—
925C2×C22⋊C4C2414yes—
926C2×C22⋊C4C2412yes—
927C2×C22⋊C4C2412yes—
928C2×C22⋊C4C2412yes—
929C2×C22⋊C4C2414yes—
930C2×C22⋊C4C2414yes—
931C2×C22⋊C4C2414yes—
932C2×C22⋊C4C2414yes—
933C2×C22⋊C4C2412yes—
934C2×C22⋊C4C2412yes—
935C2×C22⋊C4C2414yes—
936C2×C22⋊C4C2414yes—
937C2×C42—24no—
938C2×C42—24no—
939C2×C42—24no—
940C2×C42—24no—
941C2×C42—42no—
942C2×C42—42no—
943C2×C42—42no—
944C2×C42C2411yescharacteristic
945C2×C42C2411yescharacteristic
946C2×C42C2411yescharacteristic
947C2×C42C2411yescharacteristic
948C2×C42C2411yescharacteristic
949C2×C42C2412yes—
950C2×C42C2412yes—
951C2×C42C2411yescharacteristic
952C2×C42C2411yescharacteristic
953C2×C42C2411yescharacteristic
954C2×C42C2412yes—
955C2×C42C2411yescharacteristic
956C2×C42C2411yescharacteristic
957C2×C42C2411yescharacteristic
958C2×C42C2414yes—
959C2×C42C2414yes—
960C2×C42C2414yes—
961C2×C42C2412yes—
962C2×C42C2412yes—
963C2×C42C2414yes—
964C2×C42C2414yes—
965C2×C42C2414yes—
966C2×C42C2414yes—
967C2×C42C2412yes—
968C2×C42C2411yescharacteristic
969#95C2412yes—
970#95C2412yes—
971#95C2412yes—
972#95C2412yes—
973#95C2412yes—
974#95C2412yes—
975#95C2412yes—
976#95C2412yes—
977#95C2412yes—
978#95C2414yes—
979#95C2414yes—
980#95C2414yes—
981#95C2412yes—
982#95C2412yes—
983#95C2414yes—
984#95C2412yes—
985#95C2414yes—
986#95C2414yes—
987#95C2414yes—
988#95C2412yes—
989#95C2414yes—
990#95C2414yes—
991#95C2414yes—
992#95C2414yes—
993#95C2414yes—
994#95C2412yes—
995#95C2414yes—
996#95C2412yes—
997#95C2412yes—
998#95C2412yes—
999#95C2414yes—
1000#95C2414yes—
1001#95C2412yes—
1002#95C2414yes—
1003#95C2414yes—
1004#95C2414yes—
1005#95C2412yes—
1006#95C2412yes—
1007#95C2414yes—
1008#95C2414yes—
1009#95C2414yes—
1010#95C2414yes—
1011#95C2414yes—
1012#95C2414yes—
1013#95C2414yes—
1014#95C2414yes—
1015#95C2414yes—
1016#95C2414yes—
1017#95C2414yes—
1018#95C2414yes—
1019#95C2414yes—
1020#95C2414yes—
1021#95C2414yes—
1022#95C2414yes—
1023#95C2414yes—
1024#95C2414yes—
1025#95C2414yes—
1026#95C2414yes—
1027C24C2511yescharacteristic
1028C24C2511yescharacteristic
1029C24C2514yes—
1030C24C2511yescharacteristic
1031C24C2511yescharacteristic
1032C24C2511yescharacteristic
1033#41—416no—
1034#41—416no—
1035#41—816no—
1036C2×Q8—24no—
1037C2×Q8—22no—
1038C2×Q8—24no—
1039C2×Q8—24no—
1040C2×Q8—41no—
1041C2×Q8—41no—
1042C2×Q8—41no—
1043C2×Q8—41no—
1044C2×Q8C2×#4114yes—
1045C2×D4—22no—
1046C2×D4—22no—
1047C2×D4—22no—
1048C2×D4—22no—
1049C2×D4—22no—
1050C2×D4—22no—
1051C2×D4—28no—
1052C2×D4—28no—
1053C2×D4—28no—
1054C2×D4—24no—
1055C2×D4—22no—
1056C2×D4—24no—
1057C2×D4—28no—
1058C2×D4—24no—
1059C2×D4—41no—
1060C2×D4—41no—
1061C2×D4—41no—
1062C2×D4—41no—
1063C2×D4—41no—
1064C2×D4—41no—
1065C2×D4—41no—
1066C2×D4—41no—
1067C2×D4—41no—
1068C2×D4—41no—
1069C2×D4—41no—
1070C2×D4—41no—
1071C2×D4—44no—
1072C2×D4—44no—
1073C2×D4—44no—
1074C2×D4—44no—
1075C2×D4—44no—
1076C2×D4—44no—
1077C2×D4—44no—
1078C2×D4—42no—
1079C2×D4—44no—
1080C2×D4—42no—
1081C2×D4—44no—
1082C2×D4—44no—
1083C2×D4—42no—
1084C2×D4—42no—
1085C2×D4—44no—
1086C2×D4—44no—
1087C2×D4—44no—
1088C2×D4—44no—
1089C2×D4C2×#4114yes—
1090C2×D4C2×#4114yes—
1091C2×D4C2×#4114yes—
1092C22×C4—22no—
1093C22×C4—22no—
1094C22×C4—22no—
1095C22×C4—22no—
1096C22×C4—22no—
1097C22×C4—22no—
1098C22×C4—22no—
1099C22×C4—22no—
1100C22×C4—28no—
1101C22×C4—22no—
1102C22×C4—22no—
1103C22×C4—24no—
1104C22×C4—22no—
1105C22×C4—22no—
1106C22×C4—22no—
1107C22×C4—22no—
1108C22×C4—28no—
1109C22×C4—24no—
1110C22×C4—24no—
1111C22×C4—42no—
1112C22×C4—42no—
1113C22×C4—42no—
1114C22×C4—42no—
1115C22×C4—42no—
1116C22×C4—44no—
1117C22×C4—44no—
1118C22×C4—44no—
1119C22×C4—44no—
1120C22×C4—42no—
1121C22×C4—42no—
1122C22×C4—44no—
1123C22×C4—42no—
1124C22×C4—42no—
1125C22×C4—42no—
1126C22×C4—42no—
1127C22×C4—42no—
1128C22×C4—42no—
1129C22×C4—42no—
1130C22×C4—44no—
1131C22×C4—42no—
1132C22×C4—42no—
1133C22×C4—42no—
1134C22×C4—44no—
1135C22×C4—44no—
1136C22×C4—44no—
1137C22×C4—44no—
1138C22×C4—44no—
1139C22×C4—44no—
1140C22×C4—44no—
1141C22×C4C2×#4114yes—
1142C22×C4C2×#4114yes—
1143C22×C4C2×#4114yes—
1144C22×C4C2511yescharacteristic
1145C22×C4C2512yes—
1146C22×C4C2511yescharacteristic
1147C22×C4C2512yes—
1148C22×C4C2512yes—
1149C22×C4C2512yes—
1150C22×C4C2514yes—
1151C22×C4C2514yes—
1152C22×C4C2511yescharacteristic
1153C22×C4C2511yescharacteristic
1154C22×C4C2514yes—
1155C22×C4C2511yescharacteristic
1156C22×C4C2514yes—
1157C22×C4C2514yes—
1158C22×C4C2514yes—
1159C22×C4C2512yes—
1160C22×C4C2511yescharacteristic
1161C22×C4C2512yes—
1162C22×C4C2512yes—
1163C22×C4C2514yes—
1164C22×C4C2511yescharacteristic
1165C22×C4C2511yescharacteristic
1166C22×C4C2511yescharacteristic
1167C22×C4C2512yes—
1168C22×C4C2511yescharacteristic
1169C4⋊C4—28no—
1170C4⋊C4—24no—
1171C4⋊C4—24no—
1172C4⋊C4—22no—
1173C4⋊C4—22no—
1174C4⋊C4—22no—
1175C4⋊C4—22no—
1176C4⋊C4—28no—
1177C4⋊C4—28no—
1178C4⋊C4—24no—
1179C4⋊C4—24no—
1180C4⋊C4—28no—
1181C4⋊C4—28no—
1182C4⋊C4—24no—
1183C4⋊C4—24no—
1184C4⋊C4—28no—
1185C4⋊C4—24no—
1186C4⋊C4—24no—
1187C4⋊C4—44no—
1188C4⋊C4—44no—
1189C4⋊C4—44no—
1190C4⋊C4—44no—
1191C4⋊C4—44no—
1192C4⋊C4—44no—
1193C4⋊C4—44no—
1194C4⋊C4—42no—
1195C4⋊C4—44no—
1196C4⋊C4—44no—
1197C4⋊C4—42no—
1198C4⋊C4—44no—
1199C4⋊C4—42no—
1200C4⋊C4—42no—
1201C4⋊C4—42no—
1202C4⋊C4—42no—
1203C4⋊C4—44no—
1204C4⋊C4—44no—
1205C4⋊C4—44no—
1206C4⋊C4—44no—
1207C4⋊C4—44no—
1208C4⋊C4—44no—
1209C4⋊C4—44no—
1210C4⋊C4—44no—
1211C4⋊C4—44no—
1212C4⋊C4—44no—
1213C4⋊C4—44no—
1214C4⋊C4—44no—
1215C4⋊C4—44no—
1216C4⋊C4—42no—
1217C4⋊C4—44no—
1218C4⋊C4—44no—
1219C4⋊C4—42no—
1220C22⋊C4—22no—
1221C22⋊C4—22no—
1222C22⋊C4—22no—
1223C22⋊C4—22no—
1224C22⋊C4—28no—
1225C22⋊C4—28no—
1226C22⋊C4—22no—
1227C22⋊C4—22no—
1228C22⋊C4—22no—
1229C22⋊C4—22no—
1230C22⋊C4—28no—
1231C22⋊C4—28no—
1232C22⋊C4—24no—
1233C22⋊C4—24no—
1234C22⋊C4—44no—
1235C22⋊C4—42no—
1236C22⋊C4—42no—
1237C22⋊C4—44no—
1238C22⋊C4—44no—
1239C22⋊C4—44no—
1240C22⋊C4—42no—
1241C22⋊C4—44no—
1242C22⋊C4—42no—
1243C22⋊C4—44no—
1244C22⋊C4—44no—
1245C22⋊C4—42no—
1246C22⋊C4—42no—
1247C22⋊C4—42no—
1248C22⋊C4—42no—
1249C22⋊C4—42no—
1250C22⋊C4—44no—
1251C22⋊C4—44no—
1252C22⋊C4—44no—
1253C22⋊C4—44no—
1254C22⋊C4—44no—
1255C22⋊C4—42no—
1256C22⋊C4—44no—
1257C22⋊C4—44no—
1258C22⋊C4—44no—
1259C22⋊C4—44no—
1260C22⋊C4—44no—
1261C22⋊C4—44no—
1262C22⋊C4—44no—
1263C22⋊C4—44no—
1264C22⋊C4—44no—
1265C22⋊C4—44no—
1266C22⋊C4—44no—
1267C22⋊C4—44no—
1268C22⋊C4—44no—
1269C22⋊C4—42no—
1270C22⋊C4—44no—
1271C22⋊C4—44no—
1272C22⋊C4—44no—
1273C22⋊C4—44no—
1274C22⋊C4—42no—
1275C42—22no—
1276C42—22no—
1277C42—22no—
1278C42—22no—
1279C42—22no—
1280C42—22no—
1281C42—22no—
1282C42—24no—
1283C42—24no—
1284C42—24no—
1285C42—22no—
1286C42—22no—
1287C42—22no—
1288C42—22no—
1289C42—42no—
1290C42—42no—
1291C42—42no—
1292C42—44no—
1293C42—44no—
1294C42—44no—
1295C42—44no—
1296C42—44no—
1297C42—44no—
1298C42—44no—
1299C42H(5,𝔽2)14yes—
1300C23—21no—
1301C23—21no—
1302C23—21no—
1303C23—21no—
1304C23—21no—
1305C23—21no—
1306C23—22no—
1307C23—22no—
1308C23—22no—
1309C23—22no—
1310C23—22no—
1311C23—22no—
1312C23—21no—
1313C23—21no—
1314C23—24no—
1315C23—21no—
1316C23—21no—
1317C23—24no—
1318C23—21no—
1319C23—24no—
1320C23—21no—
1321C23—22no—
1322C23—22no—
1323C23—24no—
1324C23—24no—
1325C23—24no—
1326C23—22no—
1327C23—22no—
1328C23—24no—
1329C23C22×#4112yes—
1330C23C22×#4112yes—
1331C23C22×#4112yes—
1332C23C2611yescharacteristic
1333Q8—44no—
1334Q8—44no—
1335Q8—48no—
1336D4—44no—
1337D4—44no—
1338D4—44no—
1339D4—44no—
1340D4—44no—
1341D4—44no—
1342D4—48no—
1343D4—88no—
1344D4—88no—
1345D4—88no—
1346D4—82no—
1347D4—82no—
1348D4—82no—
1349D4—82no—
1350D4—88no—
1351D4—88no—
1352D4—164no—
1353C2×C4—21no—
1354C2×C4—21no—
1355C2×C4—21no—
1356C2×C4—21no—
1357C2×C4—21no—
1358C2×C4—21no—
1359C2×C4—22no—
1360C2×C4—22no—
1361C2×C4—28no—
1362C2×C4—28no—
1363C2×C4—28no—
1364C2×C4—21no—
1365C2×C4—21no—
1366C2×C4—21no—
1367C2×C4—21no—
1368C2×C4—24no—
1369C2×C4—24no—
1370C2×C4—21no—
1371C2×C4—21no—
1372C2×C4—24no—
1373C2×C4—22no—
1374C2×C4—22no—
1375C2×C4—22no—
1376C2×C4—22no—
1377C2×C4—22no—
1378C2×C4—21no—
1379C2×C4—21no—
1380C2×C4—24no—
1381C2×C4—24no—
1382C2×C4—24no—
1383C2×C4—22no—
1384C2×C4—22no—
1385C2×C4—24no—
1386C2×C4—24no—
1387C2×C4—24no—
1388C2×C4—21no—
1389C2×C4—21no—
1390C2×C4—22no—
1391C2×C4—22no—
1392C2×C4—22no—
1393C2×C4—24no—
1394C2×C4—22no—
1395C2×C4—24no—
1396C2×C4—24no—
1397C2×C4—24no—
1398C2×C4—24no—
1399C2×C4—24no—
1400C2×C4—24no—
1401C2×C4—22no—
1402C2×C4—22no—
1403C2×C4—24no—
1404C2×C4—22no—
1405C2×C4—22no—
1406C2×C4—22no—
1407C2×C4—22no—
1408C2×C4—22no—
1409C2×C4—24no—
1410C2×C4—24no—
1411C2×C4—22no—
1412C2×C4—22no—
1413C2×C4—22no—
1414C2×C4—22no—
1415C2×C4—22no—
1416C2×C4—24no—
1417C2×C4—22no—
1418C2×C4—24no—
1419C2×C4—22no—
1420C2×C4—48no—
1421C2×C4—44no—
1422C2×C4—44no—
1423C2×C4—84no—
1424C2×C4—84no—
1425C2×C4—88no—
1426C2×C4—82no—
1427C2×C4—88no—
1428C2×C4—82no—
1429C2×C4—84no—
1430C2×C4—88no—
1431C2×C4—84no—
1432C2×C4—84no—
1433C2×C4—164no—
1434C2×C4—164no—
1435C2×C4C22×#4112yes—
1436C2×C4C22×#4112yes—
1437C2×C4C22×#4112yes—
1438C2×C4C22×#4112yes—
1439C2×C4C2×H(5,𝔽2)14yes—
1440C2×C4C2×H(5,𝔽2)12yes—
1441C2×C4#58512yes—
1442C22—22no—
1443C22—22no—
1444C22—22no—
1445C22—22no—
1446C22—22no—
1447C22—22no—
1448C22—22no—
1449C22—22no—
1450C22—22no—
1451C22—42no—
1452C22—42no—
1453C22—42no—
1454C22—42no—
1455C22—42no—
1456C22—42no—
1457C22—41no—
1458C22—41no—
1459C22—44no—
1460C22—44no—
1461C22—41no—
1462C22—41no—
1463C22—41no—
1464C22—41no—
1465C22—44no—
1466C22—42no—
1467C22—42no—
1468C22—44no—
1469C22—44no—
1470C22—44no—
1471C22—42no—
1472C22—42no—
1473C22—44no—
1474C22C23×#4111yescharacteristic
1475C22C22×H(5,𝔽2)11yescharacteristic
1476C22C2×#58511yescharacteristic
1477C22H(7,𝔽2)12yes—
1478C222−1+612yes—
1479C4—22no—
1480C4—22no—
1481C4—22no—
1482C4—24no—
1483C4—41no—
1484C4—41no—
1485C4—44no—
1486C4—41no—
1487C4—44no—
1488C4—44no—
1489C4—41no—
1490C4—41no—
1491C4—41no—
1492C4—42no—
1493C4—42no—
1494C4—42no—
1495C4—44no—
1496C4—42no—
1497C4—42no—
1498C4—44no—
1499C4—42no—
1500C4—42no—
1501C4—44no—
1502C4—44no—
1503C4#350514yes—
1504C2—42no—
1505C2—42no—
1506C2—42no—
1507C2—81no—
1508C2—81no—
1509C2—84no—
1510C2C2×#350511yescharacteristic
1511C2#6285811yescharacteristic
1512C2#6286111yescharacteristic
1513C2#6287512yes—
1514C2#6288412yes—
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. #49083C2semidirect
2. #49024C2semidirect
3. #48242C2semidirect
4. #48175C2semidirect
5. #47542C2semidirect
6. #47536C2semidirect
7. #46973C2semidirect
8. #46967C2semidirect
9. #39057C2semidirect
10. #39056C2semidirect
11. #39041C2semidirect
12. #39040C2semidirect
13. #37898C2semidirect
14. #37897C2semidirect
15. #37883C2semidirect
16. #37882C2semidirect
17. #37706C2semidirect
18. #37705C2semidirect
19. #37701C2semidirect
20. #37700C2semidirect
21. #37512C2semidirect
22. #37288C2semidirect
23. #37272C2semidirect
24. #35333C2semidirect
25. #35315C2semidirect
26. #35309C2semidirect
27. #35273C2semidirect
28. #35271C2semidirect
29. #35259C2semidirect
30. #34410C2semidirect
31. #34070C2semidirect

Maximal subgroups

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

subgroupindex
#490832
#490242
#482422
#481752
#475422
#475362
#469732
#469672
#390572
#390562
#390412
#390402
#378982
#378972
#378832
#378822
#377062
#377052
#377012
#377002
#375122
#372882
#372722
#353332
#353152
#353092
#352732
#352712
#352592
#344102
#340702