Finite Group Databasebeta

← #8125437

Subgroups — #8125437

Order 512.

4259 conjugacy classes of subgroups.

The subgroup lattice has 1350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#58700C214yesmaximal, complemented
2#58266C214yesmaximal, complemented
3#55661C214yesmaximal, complemented
4#54092C214yesmaximal, complemented
5#53067C212yesmaximal, complemented
6#53024C212yesmaximal, complemented
7#47803C214yesmaximal, complemented
8#47755C214yesmaximal, complemented
9#47478C214yesmaximal, complemented
10#47146C214yesmaximal, complemented
11#45253C212yesmaximal, complemented
12#45238C212yesmaximal, complemented
13#40195C212yesmaximal, complemented
14#39914C212yesmaximal, complemented
15#39693C212yesmaximal, complemented
16#39463C212yesmaximal
17#39022C212yesmaximal, complemented
18#38919C212yesmaximal, complemented
19#37971C212yesmaximal, complemented
20#37971C212yesmaximal, complemented
21#37425C211yesmaximal, characteristic, complemented
22#37393C211yesmaximal, characteristic, complemented
23#35333C211yesmaximal, characteristic, complemented
24#35309C211yesmaximal, characteristic, complemented
25#35181C211yesmaximal, characteristic, complemented
26#35087C211yesmaximal, characteristic, complemented
27#34744C211yesmaximal, characteristic
28C2×#552C2212yes—
29C2×#541C2211yescharacteristic
30C2×#532C2211yescharacteristic
31C22×#125C2211yescharacteristic
32C2×C4×#41C2211yescharacteristic
33#2857C2211yescharacteristic
34#2855C2212yes—
35#2855C2212yes—
36#2851C2211yescharacteristic
37#2851C2211yescharacteristic
38#2851C2211yescharacteristic
39#2851C2211yescharacteristic
40#2851C2212yes—
41#2851C2211yescharacteristic
42#2845C2214yes—
43#2839C2214yes—
44#2839C2214yes—
45#2837C2214yes—
46#2836C2214yes—
47#2836C2214yes—
48#2827C2214yes—
49#2823C2214yes—
50#2809C2214yes—
51#2802C2214yes—
52#2800C2214yes—
53#2794C2214yes—
54#2794C2214yes—
55#2793C2214yes—
56#2791C2214yes—
57#2791C2214yes—
58#2790C2214yes—
59#2790C2214yes—
60#2790C2214yes—
61#2783C2214yes—
62#2781C2214yes—
63#2781C2214yes—
64#2780C2214yes—
65#2780C2214yes—
66#2779C2214yes—
67#2774C2214yes—
68#2772C2214yes—
69#2771C2214yes—
70#2771C2214yes—
71#2768C2214yes—
72#2767C2214yes—
73#2767C2214yes—
74#2761C2214yes—
75#2761C2214yes—
76#2755C2214yes—
77#2755C2214yes—
78#2748C2214yes—
79#2747C2214yes—
80#2746C2214yes—
81#2746C2214yes—
82#2744C2214yes—
83#2743C2214yes—
84#2743C2214yes—
85#2743C2214yes—
86#2740C2214yes—
87#2740C2214yes—
88#2738C2214yes—
89#2738C2214yes—
90#2725C2214yes—
91#2721C2214yes—
92#2721C2214yes—
93#2721C2214yes—
94#2721C2214yes—
95#2719C2214yes—
96#2719C2214yes—
97#2719C2214yes—
98#2718C2214yes—
99#2718C2214yes—
100#2718C2214yes—
101#2713C2214yes—
102#2711C2214yes—
103#2709C2214yes—
104#2708C2214yes—
105#2695C2214yes—
106#2655C2214yes—
107#2655C2214yes—
108#2655C2214yes—
109#2649C2214yes—
110#2646C2214yes—
111#2629C2212yes—
112#2629C2212yes—
113#2629C2212yes—
114#2629C2211yescharacteristic
115#2623C2214yes—
116#2621C2211yescharacteristic
117#2616C2212yes—
118#2616C2212yes—
119#2609C2214yes—
120#2609C2214yes—
121#2609C2214yes—
122#2601C2214yes—
123#2601C2214yes—
124#2596C2214yes—
125#2590C2214yes—
126#2587C2214yes—
127#2587C2214yes—
128#2585C2214yes—
129#2585C2214yes—
130#2579C2214yes—
131#2579C2214yes—
132#2577C2214yes—
133#2575C2214yes—
134#2571C2212yes—
135#2571C2212yes—
136#2570C2214yes—
137#2570C2214yes—
138#2566C2214yes—
139#2565C2214yes—
140#2565C2212yes—
141#2562C2212yes—
142#2559C2214yes—
143#2552C2212yes—
144#2552C2212yes—
145#2552C2212yes—
146#2552C2214yes—
147#2536C2212yes—
148#2521C2214yes—
149#2520C2214yes—
150#2520C2214yes—
151#2519C2214yes—
152#2515C2214yes—
153#2514C2212yes—
154#2509C2212yes—
155#2507C2214yes—
156#2507C2212yes—
157#2506C2212yes—
158#2502C2212yes—
159#2502C2212yes—
160#2497C2212yes—
161#2497C2212yes—
162#2497C2212yes—
163#2496C2212yes—
164#2496C2212yes—
165#2493C2214yes—
166#2489C2212yes—
167#2489C2212yes—
168#2489C2212yes—
169#2487C2212yes—
170#2485C2212yes—
171#2484C2214yes—
172#2479C2214yes—
173#2479C2214yes—
174#2478C2214yes—
175#2478C2214yes—
176#2476C2214yes—
177#2475C2214yes—
178#2474C2214yes—
179#2473C2214yes—
180#2470C2214yes—
181#2468C2214yes—
182#2466C2214yes—
183#2462C2214yes—
184#2460C2214yes—
185#2453C2212yes—
186#2453C2212yes—
187#2453C2212yes—
188#2448C2212yes—
189#2447C2212yes—
190#2446C2212yes—
191#2446C2212yes—
192#2445C2212yes—
193#2444C2212yes—
194#2444C2212yes—
195#2443C2212yes—
196#2443C2212yes—
197#2442C2212yes—
198#2442C2212yes—
199#2441C2212yes—
200#2441C2212yes—
201#2441C2212yes—
202#2441C2212yes—
203#2441C2214yes—
204#2429C2212yes—
205#2423C2212yes—
206#2423C2212yes—
207#2421C2212yes—
208#2417C2212yes—
209#2415C2212yes—
210#2413C2214yes—
211#2395C2212yes—
212#2395C2212yes—
213#2370C2212yes—
214#2362C2212yes—
215#2362C2212yes—
216#2352C2212yes—
217Q8×C4⋊C4C2212yes—
218#2344C2212yes—
219#2344C2212yes—
220#2336C2214yes—
221#2334C2214yes—
222#2334C2214yes—
223#2323C2212yes—
224#2323C2212yes—
225#2317C2212yes—
226#2317C2214yes—
227#2317C2214yes—
228#2314C2214yes—
229#2314C2211yescharacteristic
230#2311C2212yes—
231#2311C2212yes—
232C4×C22⋊Q8C2212yes—
233C4×C22⋊Q8C2212yes—
234C4×#123C2212yes—
235C4×#123C2212yes—
236#2297C2211yescharacteristic
237#2297C2211yescharacteristic
238#2297C2211yescharacteristic
239#2296C2211yescharacteristic
240#2285C2211yescharacteristic
241#2285C2212yes—
242C2×C4×C4⋊C4C2211yescharacteristic
243C22×#41C2311yescharacteristic
244C22×#41C2311yescharacteristic
245#552—48no—
246#541—44no—
247#532—44no—
248C2×C4⋊Q8C2311yescharacteristic
249C2×C4⋊Q8C2311yescharacteristic
250C2×#127C2311yescharacteristic
251C2×#126C2314yes—
252C2×#126C2314yes—
253C2×#126C2314yes—
254C2×#126C2314yes—
255C2×#125—44no—
256C2×#125C2312yes—
257C2×#125C2314yes—
258C2×#125C2312yes—
259C2×#125C2314yes—
260C2×#125C2311yescharacteristic
261C2×#125C2311yescharacteristic
262C2×#125C2311yescharacteristic
263C2×#125C2312yes—
264C2×#125C2314yes—
265C2×#125C2314yes—
266C2×#124C2311yescharacteristic
267C2×#124C2311yescharacteristic
268C2×#123C2314yes—
269C2×#123C2312yes—
270C2×#123C2312yes—
271C2×C22⋊Q8C2312yes—
272C2×C22⋊Q8C2312yes—
273C2×C22⋊Q8C2312yes—
274C2×C22⋊Q8C2312yes—
275C2×C22⋊Q8C2312yes—
276C2×#121C2312yes—
277C2×#121C2312yes—
278C4×#41—44no—
279C2×C4×Q8C2312yes—
280C2×C4×Q8C2312yes—
281C2×C4×Q8C2312yes—
282C2×C4×Q8C2312yes—
283C2×C4×D4C2312yes—
284C2×C4×D4C2312yes—
285C2×C4×D4C2312yes—
286C2×C4×D4C2312yes—
287C2×C4×D4C2312yes—
288C2×#117C2311yescharacteristic
289C2×#117C2312yes—
290C2×#117C2312yes—
291C2×#117C2314yes—
292C2×#117C2314yes—
293C2×#117C2314yes—
294C2×#117C2314yes—
295C2×#117C2311yescharacteristic
296C2×#117C2311yescharacteristic
297C2×#117C2311yescharacteristic
298C22×C4⋊C4C2312yes—
299C22×C4⋊C4C2312yes—
300C22×C4⋊C4C2312yes—
301C22×C4⋊C4C2314yes—
302C22×C42C2311yescharacteristic
303C22×C42C2311yescharacteristic
304C22×C42C2311yescharacteristic
305C22×C42C2311yescharacteristic
306C22×C42C2311yescharacteristic
307#401C2314yes—
308#400C2314yes—
309#400C2314yes—
310#400C2314yes—
311#400C2314yes—
312#400C2314yes—
313#400C2314yes—
314#400C2314yes—
315#400C2314yes—
316#400C2314yes—
317#400C2314yes—
318#400C2314yes—
319#400C2312yes—
320#400C2314yes—
321#400C2314yes—
322#400C2314yes—
323#400C2314yes—
324#400C2314yes—
325#400C2314yes—
326#400C2314yes—
327#400C2314yes—
328#400C2314yes—
329#400C2314yes—
330#400C2312yes—
331#400C2314yes—
332#400C2314yes—
333#400C2314yes—
334#400C2314yes—
335#399C2314yes—
336#399C2314yes—
337#399C2314yes—
338#399C2314yes—
339#399C2314yes—
340#399C2312yes—
341#399C2312yes—
342#399C2314yes—
343#399C2314yes—
344#398C2314yes—
345#398C2314yes—
346#398C2314yes—
347#398C2314yes—
348#398C2314yes—
349#398C2314yes—
350#398C2314yes—
351#398C2314yes—
352#398C2314yes—
353#398C2314yes—
354#398C2314yes—
355#398C2314yes—
356#398C2314yes—
357#398C2314yes—
358#398C2314yes—
359#398C2314yes—
360#398C2314yes—
361#398C2314yes—
362#398C2314yes—
363#398C2314yes—
364#398C2314yes—
365#398C2314yes—
366#398C2314yes—
367#398C2314yes—
368#398C2314yes—
369#398C2314yes—
370#398C2312yes—
371#398C2314yes—
372#398C2314yes—
373#398C2314yes—
374#398C2314yes—
375#398C2314yes—
376#398C2314yes—
377#398C2312yes—
378#398C2314yes—
379#398C2314yes—
380#397C2314yes—
381#397C2314yes—
382#397C2314yes—
383#397C2312yes—
384#397C2314yes—
385#397C2314yes—
386#397C2312yes—
387#397C2312yes—
388#397C2314yes—
389#397C2314yes—
390#397C2314yes—
391#397C2312yes—
392#397C2312yes—
393#397C2312yes—
394#397C2314yes—
395#396C2314yes—
396#396C2314yes—
397#396C2314yes—
398#396C2314yes—
399#396C2314yes—
400#396C2314yes—
401#396C2314yes—
402#396C2314yes—
403#396C2314yes—
404#396C2314yes—
405#396C2314yes—
406#396C2314yes—
407#396C2314yes—
408#396C2314yes—
409#396C2314yes—
410#396C2314yes—
411#395C2314yes—
412#395C2314yes—
413#394C2314yes—
414#394C2312yes—
415#394C2314yes—
416#394C2312yes—
417#394C2314yes—
418#394C2314yes—
419#394C2314yes—
420#394C2312yes—
421#394C2314yes—
422#394C2314yes—
423#394C2314yes—
424#394C2314yes—
425#394C2312yes—
426#394C2314yes—
427#391C2314yes—
428#391C2312yes—
429#391C2312yes—
430#391C2314yes—
431#391C2312yes—
432#391C2312yes—
433#391C2312yes—
434#391C2312yes—
435#391C2312yes—
436#391C2312yes—
437#391C2312yes—
438#390C2314yes—
439#390C2314yes—
440#390C2312yes—
441#390C2312yes—
442#390C2312yes—
443#389C2314yes—
444#389C2314yes—
445#389C2314yes—
446#389C2314yes—
447#389C2312yes—
448#389C2312yes—
449#389C2312yes—
450#389C2312yes—
451#389C2314yes—
452#389C2314yes—
453#389C2314yes—
454#389C2312yes—
455#389C2312yes—
456#389C2312yes—
457#389C2314yes—
458#389C2312yes—
459#389C2312yes—
460#389C2314yes—
461#389C2314yes—
462#389C2314yes—
463#389C2314yes—
464#389C2314yes—
465#389C2314yes—
466#389C2312yes—
467#389C2314yes—
468#389C2314yes—
469#389C2314yes—
470#389C2314yes—
471#389C2314yes—
472#389C2314yes—
473#389C2314yes—
474#389C2314yes—
475#389C2312yes—
476#389C2312yes—
477#389C2312yes—
478#389C2312yes—
479#389C2312yes—
480#389C2312yes—
481#388C2314yes—
482#388C2314yes—
483#388C2312yes—
484#388C2314yes—
485#388C2314yes—
486#388C2314yes—
487#388C2314yes—
488#388C2314yes—
489#388C2312yes—
490#388C2314yes—
491#388C2314yes—
492#388C2314yes—
493#388C2314yes—
494#388C2314yes—
495#388C2314yes—
496#388C2314yes—
497#388C2312yes—
498#388C2314yes—
499#388C2314yes—
500#388C2314yes—
501#388C2312yes—
502#388C2314yes—
503#388C2314yes—
504#388C2314yes—
505#388C2314yes—
506#388C2314yes—
507#388C2314yes—
508#388C2314yes—
509#388C2314yes—
510#388C2314yes—
511#387C2314yes—
512#387C2314yes—
513#387C2314yes—
514#387C2314yes—
515#387C2314yes—
516#387C2314yes—
517#387C2314yes—
518#387C2314yes—
519#387C2314yes—
520#387C2314yes—
521#387C2314yes—
522#387C2314yes—
523#387C2314yes—
524#387C2314yes—
525#387C2314yes—
526#387C2314yes—
527#387C2314yes—
528#387C2314yes—
529#387C2314yes—
530#387C2314yes—
531#387C2314yes—
532#387C2314yes—
533#387C2314yes—
534#387C2314yes—
535#387C2314yes—
536#387C2312yes—
537#387C2314yes—
538#387C2314yes—
539#387C2314yes—
540#387C2314yes—
541#387C2314yes—
542#387C2314yes—
543#387C2314yes—
544#387C2312yes—
545#387C2314yes—
546#387C2314yes—
547#387C2314yes—
548#387C2314yes—
549#387C2314yes—
550#387C2314yes—
551#387C2314yes—
552#387C2314yes—
553#387C2314yes—
554#387C2314yes—
555#387C2314yes—
556#387C2314yes—
557#387C2312yes—
558#387C2312yes—
559#387C2314yes—
560#387C2314yes—
561#387C2314yes—
562#387C2314yes—
563#387C2314yes—
564#386C2314yes—
565#386C2314yes—
566#386C2314yes—
567#386C2314yes—
568#386C2314yes—
569#386C2311yescharacteristic
570#386C2312yes—
571#386C2314yes—
572#386C2311yescharacteristic
573#386C2314yes—
574#386C2312yes—
575#386C2312yes—
576#386C2312yes—
577#386C2312yes—
578#386C2311yescharacteristic
579#386C2312yes—
580#386C2311yescharacteristic
581#385C2314yes—
582#385C2314yes—
583#385C2314yes—
584#385C2314yes—
585#385C2314yes—
586#385C2314yes—
587#385C2312yes—
588#385C2314yes—
589#385C2314yes—
590#385C2314yes—
591#385C2314yes—
592#385C2314yes—
593#385C2314yes—
594#385C2314yes—
595#385C2314yes—
596#385C2312yes—
597#385C2312yes—
598#385C2312yes—
599#385C2314yes—
600#385C2314yes—
601#385C2314yes—
602#385C2314yes—
603#385C2314yes—
604#385C2314yes—
605#384C2314yes—
606#384C2312yes—
607#384C2314yes—
608#384C2314yes—
609#384C2311yescharacteristic
610#384C2312yes—
611#384C2314yes—
612#384C2312yes—
613#384C2314yes—
614#384C2312yes—
615#383C2314yes—
616#382C2314yes—
617#382C2312yes—
618#382C2311yescharacteristic
619#382C2314yes—
620#382C2314yes—
621#382C2314yes—
622#382C2314yes—
623#382C2311yescharacteristic
624#382C2314yes—
625#382C2314yes—
626#382C2311yescharacteristic
627#381C2314yes—
628#381C2314yes—
629#381C2314yes—
630#381C2314yes—
631#381C2312yes—
632#381C2312yes—
633#380C2312yes—
634#380C2312yes—
635#380C2312yes—
636#380C2312yes—
637#380C2312yes—
638#380C2312yes—
639#380C2312yes—
640#380C2312yes—
641#380C2312yes—
642#380C2314yes—
643#380C2312yes—
644#380C2314yes—
645#380C2314yes—
646#380C2314yes—
647#380C2312yes—
648#380C2314yes—
649#380C2314yes—
650C4×C4⋊C4C2312yes—
651C4×C4⋊C4C2314yes—
652C4×C4⋊C4C2312yes—
653C4×C4⋊C4C2314yes—
654C4×C4⋊C4C2312yes—
655C4×C4⋊C4C2314yes—
656C4×C4⋊C4C2312yes—
657C4×C4⋊C4C2312yes—
658C4×C4⋊C4C2314yes—
659C4×C4⋊C4C2312yes—
660C4×C4⋊C4C2312yes—
661C4×C4⋊C4C2312yes—
662C4×C4⋊C4C2312yes—
663C4×C4⋊C4C2312yes—
664C4×C4⋊C4C2314yes—
665C4×C4⋊C4C2314yes—
666C4×C4⋊C4C2314yes—
667C4×C4⋊C4C2314yes—
668C4×C4⋊C4C2312yes—
669C4×C22⋊C4C2314yes—
670C4×C22⋊C4C2314yes—
671C4×C22⋊C4C2314yes—
672C4×C22⋊C4C2312yes—
673C4×C22⋊C4C2312yes—
674C4×C22⋊C4C2312yes—
675C4×C22⋊C4C2312yes—
676C4×C22⋊C4C2312yes—
677C4×C22⋊C4C2312yes—
678C2×#95C2312yes—
679C2×#41—24no—
680C2×#41—24no—
681C2×#41—24no—
682C2×#41—42no—
683C2×#41—42no—
684C2×#41—42no—
685C22×Q8C2412yes—
686C22×Q8C2411yescharacteristic
687C22×Q8C2411yescharacteristic
688C22×D4C2411yescharacteristic
689C22×D4C2411yescharacteristic
690C22×D4C2411yescharacteristic
691C22×D4C2412yes—
692C22×D4C2412yes—
693C22×D4C2411yescharacteristic
694C22×D4C2412yes—
695C23×C4C2411yescharacteristic
696C23×C4C2412yes—
697C23×C4C2411yescharacteristic
698C23×C4C2411yescharacteristic
699C23×C4C2411yescharacteristic
700C23×C4C2414yes—
701C23×C4C2412yes—
702C23×C4C2411yescharacteristic
703C23×C4C2414yes—
704C23×C4C2412yes—
705C23×C4C2412yes—
706C23×C4C2412yes—
707C4⋊Q8—42no—
708C4⋊Q8—42no—
709#127—42no—
710#126—48no—
711#126—48no—
712#126—48no—
713#126—48no—
714#125—42no—
715#125—42no—
716#125—44no—
717#125—48no—
718#125—44no—
719#125—42no—
720#125—44no—
721#125—48no—
722#125—48no—
723#125—48no—
724#124—42no—
725#124—42no—
726#123—44no—
727#123—44no—
728#123—48no—
729C22⋊Q8—28no—
730C22⋊Q8—28no—
731C22⋊Q8—44no—
732C22⋊Q8—44no—
733C22⋊Q8—44no—
734#121—44no—
735#121—44no—
736C4×Q8—44no—
737C4×Q8—44no—
738C4×Q8—44no—
739C4×Q8—44no—
740C4×D4—28no—
741C4×D4—44no—
742C4×D4—44no—
743C4×D4—44no—
744C4×D4—44no—
745#117—24no—
746#117—48no—
747#117—42no—
748#117—42no—
749#117—42no—
750#117—48no—
751#117—48no—
752#117—48no—
753#117—44no—
754#117—44no—
755C2×C4⋊C4—28no—
756C2×C4⋊C4—44no—
757C2×C4⋊C4—44no—
758C2×C4⋊C4—48no—
759C2×C4⋊C4C2412yes—
760C2×C4⋊C4C2412yes—
761C2×C4⋊C4C2412yes—
762C2×C4⋊C4C2412yes—
763C2×C4⋊C4C2412yes—
764C2×C4⋊C4C2414yes—
765C2×C4⋊C4C2412yes—
766C2×C4⋊C4C2412yes—
767C2×C4⋊C4C2412yes—
768C2×C4⋊C4C2412yes—
769C2×C4⋊C4C2414yes—
770C2×C4⋊C4C2414yes—
771C2×C4⋊C4C2412yes—
772C2×C4⋊C4C2414yes—
773C2×C4⋊C4C2412yes—
774C2×C4⋊C4C2414yes—
775C2×C4⋊C4C2414yes—
776C2×C4⋊C4C2414yes—
777C2×C4⋊C4C2414yes—
778C2×C4⋊C4C2414yes—
779C2×C4⋊C4C2412yes—
780C2×C4⋊C4C2412yes—
781C2×C4⋊C4C2414yes—
782C2×C4⋊C4C2412yes—
783C2×C4⋊C4C2412yes—
784C2×C4⋊C4C2414yes—
785C2×C4⋊C4C2414yes—
786C2×C4⋊C4C2414yes—
787C2×C4⋊C4C2414yes—
788C2×C4⋊C4C2414yes—
789C2×C4⋊C4C2414yes—
790C2×C4⋊C4C2412yes—
791C2×C4⋊C4C2412yes—
792C2×C4⋊C4C2414yes—
793C2×C4⋊C4C2414yes—
794C2×C4⋊C4C2414yes—
795C2×C4⋊C4C2414yes—
796C2×C4⋊C4C2414yes—
797C2×C4⋊C4C2414yes—
798C2×C4⋊C4C2412yes—
799C2×C4⋊C4C2412yes—
800C2×C4⋊C4C2414yes—
801C2×C4⋊C4C2414yes—
802C2×C4⋊C4C2414yes—
803C2×C4⋊C4C2414yes—
804C2×C4⋊C4C2414yes—
805C2×C4⋊C4C2414yes—
806C2×C4⋊C4C2414yes—
807C2×C4⋊C4C2414yes—
808C2×C4⋊C4C2414yes—
809C2×C4⋊C4C2414yes—
810C2×C4⋊C4C2414yes—
811C2×C4⋊C4C2412yes—
812C2×C4⋊C4C2414yes—
813C2×C4⋊C4C2414yes—
814C2×C4⋊C4C2414yes—
815C2×C4⋊C4C2414yes—
816C2×C4⋊C4C2414yes—
817C2×C4⋊C4C2414yes—
818C2×C4⋊C4C2412yes—
819C2×C4⋊C4C2414yes—
820C2×C4⋊C4C2414yes—
821C2×C4⋊C4C2414yes—
822C2×C4⋊C4C2414yes—
823C2×C22⋊C4C2412yes—
824C2×C22⋊C4C2412yes—
825C2×C22⋊C4C2412yes—
826C2×C22⋊C4C2412yes—
827C2×C22⋊C4C2414yes—
828C2×C22⋊C4C2412yes—
829C2×C22⋊C4C2414yes—
830C2×C22⋊C4C2412yes—
831C2×C22⋊C4C2412yes—
832C2×C22⋊C4C2412yes—
833C2×C22⋊C4C2412yes—
834C2×C22⋊C4C2414yes—
835C2×C22⋊C4C2414yes—
836C2×C22⋊C4C2414yes—
837C2×C22⋊C4C2414yes—
838C2×C22⋊C4C2414yes—
839C2×C22⋊C4C2414yes—
840C2×C22⋊C4C2411yescharacteristic
841C2×C22⋊C4C2411yescharacteristic
842C2×C22⋊C4C2412yes—
843C2×C22⋊C4C2412yes—
844C2×C22⋊C4C2414yes—
845C2×C22⋊C4C2414yes—
846C2×C22⋊C4C2414yes—
847C2×C22⋊C4C2412yes—
848C2×C22⋊C4C2412yes—
849C2×C22⋊C4C2414yes—
850C2×C22⋊C4C2414yes—
851C2×C22⋊C4C2414yes—
852C2×C22⋊C4C2414yes—
853C2×C22⋊C4C2412yes—
854C2×C22⋊C4C2414yes—
855C2×C22⋊C4C2412yes—
856C2×C22⋊C4C2412yes—
857C2×C22⋊C4C2412yes—
858C2×C22⋊C4C2412yes—
859C2×C22⋊C4C2412yes—
860C2×C22⋊C4C2414yes—
861C2×C22⋊C4C2414yes—
862C2×C42—24no—
863C2×C42—24no—
864C2×C42—42no—
865C2×C42—42no—
866C2×C42—42no—
867C2×C42C2414yes—
868C2×C42C2411yescharacteristic
869C2×C42C2411yescharacteristic
870C2×C42C2411yescharacteristic
871C2×C42C2412yes—
872C2×C42C2414yes—
873C2×C42C2412yes—
874C2×C42C2412yes—
875C2×C42C2411yescharacteristic
876C2×C42C2412yes—
877C2×C42C2412yes—
878C2×C42C2414yes—
879C2×C42C2414yes—
880C2×C42C2414yes—
881C2×C42C2414yes—
882C2×C42C2414yes—
883C2×C42C2412yes—
884C2×C42C2412yes—
885C2×C42C2414yes—
886C2×C42C2414yes—
887C2×C42C2411yescharacteristic
888C2×C42C2414yes—
889C2×C42C2411yescharacteristic
890#95C2412yes—
891#95C2412yes—
892#95C2412yes—
893#95C2412yes—
894#95C2412yes—
895#95C2412yes—
896#95C2414yes—
897#95C2414yes—
898#95C2412yes—
899#95C2414yes—
900#95C2412yes—
901#95C2412yes—
902#95C2412yes—
903#95C2412yes—
904#95C2414yes—
905#95C2412yes—
906#95C2412yes—
907#95C2412yes—
908#95C2412yes—
909#95C2414yes—
910#95C2414yes—
911#95C2412yes—
912#95C2412yes—
913#95C2414yes—
914#95C2414yes—
915#95C2414yes—
916#95C2414yes—
917#95C2414yes—
918#95C2414yes—
919#95C2414yes—
920#95C2414yes—
921#95C2414yes—
922#95C2414yes—
923#95C2414yes—
924#95C2414yes—
925#95C2412yes—
926#95C2414yes—
927#95C2414yes—
928#95C2414yes—
929#95C2414yes—
930#95C2414yes—
931#95C2412yes—
932#95C2414yes—
933#95C2412yes—
934#95C2414yes—
935#95C2414yes—
936#95C2414yes—
937#95C2414yes—
938#95C2414yes—
939#95C2414yes—
940#95C2414yes—
941#95C2414yes—
942#95C2414yes—
943#95C2414yes—
944#95C2414yes—
945#95C2414yes—
946#95C2414yes—
947#95C2414yes—
948#95C2414yes—
949#95C2414yes—
950#95C2414yes—
951#95C2414yes—
952#95C2414yes—
953#95C2414yes—
954#95C2414yes—
955#95C2414yes—
956#95C2414yes—
957C24C2512yes—
958C24C2511yescharacteristic
959C24C2511yescharacteristic
960C24C2511yescharacteristic
961#41—416no—
962#41—88no—
963C2×Q8—24no—
964C2×Q8—22no—
965C2×Q8—24no—
966C2×Q8—22no—
967C2×Q8—22no—
968C2×Q8—24no—
969C2×Q8—41no—
970C2×Q8—41no—
971C2×Q8—41no—
972C2×D4—22no—
973C2×D4—22no—
974C2×D4—22no—
975C2×D4—22no—
976C2×D4—24no—
977C2×D4—24no—
978C2×D4—22no—
979C2×D4—22no—
980C2×D4—22no—
981C2×D4—41no—
982C2×D4—41no—
983C2×D4—41no—
984C2×D4—42no—
985C2×D4—42no—
986C2×D4—42no—
987C2×D4—42no—
988C2×D4—41no—
989C2×D4—42no—
990C2×D4—42no—
991C2×D4—41no—
992C2×D4—42no—
993C22×C4—22no—
994C22×C4—22no—
995C22×C4—22no—
996C22×C4—24no—
997C22×C4—22no—
998C22×C4—22no—
999C22×C4—28no—
1000C22×C4—24no—
1001C22×C4—22no—
1002C22×C4—22no—
1003C22×C4—24no—
1004C22×C4—22no—
1005C22×C4—24no—
1006C22×C4—24no—
1007C22×C4—22no—
1008C22×C4—44no—
1009C22×C4—44no—
1010C22×C4—42no—
1011C22×C4—42no—
1012C22×C4—42no—
1013C22×C4—42no—
1014C22×C4—44no—
1015C22×C4—42no—
1016C22×C4—44no—
1017C22×C4—42no—
1018C22×C4—42no—
1019C22×C4—42no—
1020C22×C4—44no—
1021C22×C4—42no—
1022C22×C4—42no—
1023C22×C4—42no—
1024C22×C4—42no—
1025C22×C4H(5,𝔽2)14yes—
1026C22×C42−1+414yes—
1027C22×C4C2512yes—
1028C22×C4C2512yes—
1029C22×C4C2511yescharacteristic
1030C22×C4C2512yes—
1031C22×C4C2514yes—
1032C22×C4C2514yes—
1033C22×C4C2514yes—
1034C22×C4C2512yes—
1035C22×C4C2512yes—
1036C22×C4C2514yes—
1037C22×C4C2512yes—
1038C22×C4C2514yes—
1039C22×C4C2512yes—
1040C22×C4C2512yes—
1041C22×C4C2512yes—
1042C22×C4C2512yes—
1043C22×C4C2514yes—
1044C22×C4C2514yes—
1045C22×C4C2514yes—
1046C22×C4C2511yescharacteristic
1047C22×C4C2511yescharacteristic
1048C22×C4C2512yes—
1049C22×C4C2511yescharacteristic
1050C4⋊C4—24no—
1051C4⋊C4—24no—
1052C4⋊C4—28no—
1053C4⋊C4—24no—
1054C4⋊C4—24no—
1055C4⋊C4—24no—
1056C4⋊C4—28no—
1057C4⋊C4—24no—
1058C4⋊C4—28no—
1059C4⋊C4—24no—
1060C4⋊C4—24no—
1061C4⋊C4—24no—
1062C4⋊C4—24no—
1063C4⋊C4—24no—
1064C4⋊C4—28no—
1065C4⋊C4—28no—
1066C4⋊C4—42no—
1067C4⋊C4—42no—
1068C4⋊C4—44no—
1069C4⋊C4—44no—
1070C4⋊C4—44no—
1071C4⋊C4—44no—
1072C4⋊C4—44no—
1073C4⋊C4—44no—
1074C4⋊C4—44no—
1075C4⋊C4—42no—
1076C4⋊C4—42no—
1077C4⋊C4—44no—
1078C4⋊C4—44no—
1079C4⋊C4—44no—
1080C4⋊C4—44no—
1081C4⋊C4—44no—
1082C4⋊C4—44no—
1083C4⋊C4—44no—
1084C4⋊C4—44no—
1085C4⋊C4—44no—
1086C4⋊C4—44no—
1087C4⋊C4—42no—
1088C4⋊C4—44no—
1089C4⋊C4—44no—
1090C4⋊C4—42no—
1091C4⋊C4—42no—
1092C4⋊C4—44no—
1093C4⋊C4—44no—
1094C4⋊C4—42no—
1095C4⋊C4—44no—
1096C4⋊C4—44no—
1097C4⋊C4—44no—
1098C4⋊C4—44no—
1099C4⋊C4—44no—
1100C4⋊C4—42no—
1101C4⋊C4—42no—
1102C4⋊C4—44no—
1103C4⋊C4—44no—
1104C4⋊C4—44no—
1105C4⋊C4—44no—
1106C4⋊C4—44no—
1107C4⋊C4—44no—
1108C4⋊C4—44no—
1109C4⋊C4—44no—
1110C4⋊C4—44no—
1111C4⋊C4—44no—
1112C4⋊C4—44no—
1113C4⋊C4—44no—
1114C22⋊C4—24no—
1115C22⋊C4—24no—
1116C22⋊C4—28no—
1117C22⋊C4—28no—
1118C22⋊C4—24no—
1119C22⋊C4—24no—
1120C22⋊C4—24no—
1121C22⋊C4—24no—
1122C22⋊C4—24no—
1123C22⋊C4—42no—
1124C22⋊C4—42no—
1125C22⋊C4—42no—
1126C22⋊C4—42no—
1127C22⋊C4—44no—
1128C22⋊C4—42no—
1129C22⋊C4—44no—
1130C22⋊C4—44no—
1131C22⋊C4—42no—
1132C22⋊C4—41no—
1133C22⋊C4—44no—
1134C22⋊C4—44no—
1135C22⋊C4—44no—
1136C22⋊C4—44no—
1137C22⋊C4—41no—
1138C22⋊C4—44no—
1139C22⋊C4—42no—
1140C22⋊C4—42no—
1141C22⋊C4—44no—
1142C22⋊C4—42no—
1143C22⋊C4—42no—
1144C22⋊C4—44no—
1145C22⋊C4—44no—
1146C22⋊C4—44no—
1147C22⋊C4—42no—
1148C22⋊C4—42no—
1149C22⋊C4—44no—
1150C22⋊C4—44no—
1151C22⋊C4—44no—
1152C22⋊C4—44no—
1153C42—22no—
1154C42—22no—
1155C42—24no—
1156C42—22no—
1157C42—22no—
1158C42—24no—
1159C42—24no—
1160C42—24no—
1161C42—28no—
1162C42—24no—
1163C42—28no—
1164C42—42no—
1165C42—42no—
1166C42—41no—
1167C42—41no—
1168C42—44no—
1169C42—44no—
1170C42—44no—
1171C42—44no—
1172C42—44no—
1173C42—44no—
1174C42—44no—
1175C42—44no—
1176C23—21no—
1177C23—21no—
1178C23—22no—
1179C23—22no—
1180C23—21no—
1181C23—21no—
1182C23—22no—
1183C23—22no—
1184C23—22no—
1185C23—21no—
1186C23—21no—
1187C23—22no—
1188C23—22no—
1189C23—22no—
1190C23—22no—
1191C23—21no—
1192C23—22no—
1193C23—22no—
1194C23—22no—
1195C23—22no—
1196C23C2×H(5,𝔽2)12yes—
1197C23C2×2−1+412yes—
1198C23C2611yescharacteristic
1199Q8—44no—
1200Q8—48no—
1201Q8—82no—
1202D4—44no—
1203D4—44no—
1204D4—44no—
1205D4—82no—
1206D4—84no—
1207D4—84no—
1208D4—84no—
1209C2×C4—28no—
1210C2×C4—21no—
1211C2×C4—22no—
1212C2×C4—21no—
1213C2×C4—21no—
1214C2×C4—22no—
1215C2×C4—21no—
1216C2×C4—28no—
1217C2×C4—28no—
1218C2×C4—22no—
1219C2×C4—22no—
1220C2×C4—22no—
1221C2×C4—22no—
1222C2×C4—22no—
1223C2×C4—22no—
1224C2×C4—24no—
1225C2×C4—24no—
1226C2×C4—22no—
1227C2×C4—21no—
1228C2×C4—24no—
1229C2×C4—24no—
1230C2×C4—22no—
1231C2×C4—24no—
1232C2×C4—24no—
1233C2×C4—21no—
1234C2×C4—22no—
1235C2×C4—22no—
1236C2×C4—24no—
1237C2×C4—24no—
1238C2×C4—24no—
1239C2×C4—24no—
1240C2×C4—22no—
1241C2×C4—22no—
1242C2×C4—22no—
1243C2×C4—24no—
1244C2×C4—24no—
1245C2×C4—22no—
1246C2×C4—24no—
1247C2×C4—24no—
1248C2×C4—24no—
1249C2×C4—24no—
1250C2×C4—22no—
1251C2×C4—22no—
1252C2×C4—22no—
1253C2×C4—24no—
1254C2×C4—24no—
1255C2×C4—22no—
1256C2×C4—22no—
1257C2×C4—21no—
1258C2×C4—22no—
1259C2×C4—22no—
1260C2×C4—22no—
1261C2×C4—22no—
1262C2×C4—22no—
1263C2×C4—24no—
1264C2×C4—22no—
1265C2×C4—24no—
1266C2×C4—24no—
1267C2×C4—22no—
1268C2×C4—22no—
1269C2×C4—24no—
1270C2×C4—24no—
1271C2×C4—24no—
1272C2×C4—22no—
1273C2×C4—22no—
1274C2×C4—22no—
1275C2×C4—416no—
1276C2×C4—44no—
1277C2×C4—48no—
1278C2×C4—82no—
1279C2×C4—84no—
1280C2×C4—84no—
1281C2×C4—84no—
1282C2×C4—84no—
1283C2×C4—88no—
1284C2×C4C2×H(5,𝔽2)12yes—
1285C2×C4C2×H(5,𝔽2)12yes—
1286C2×C4C2×2−1+412yes—
1287C2×C4C2×2−1+412yes—
1288C2×C4#58514yes—
1289C2×C4#58512yes—
1290C22—22no—
1291C22—22no—
1292C22—22no—
1293C22—22no—
1294C22—24no—
1295C22—41no—
1296C22—41no—
1297C22—42no—
1298C22—42no—
1299C22—42no—
1300C22—41no—
1301C22—42no—
1302C22—42no—
1303C22—41no—
1304C22—42no—
1305C22—41no—
1306C22—42no—
1307C22—42no—
1308C22—42no—
1309C22—42no—
1310C22—42no—
1311C22—42no—
1312C22C22×H(5,𝔽2)11yescharacteristic
1313C22C22×2−1+411yescharacteristic
1314C22C2×#58511yescharacteristic
1315C22C2×#58512yes—
1316C222−1+612yes—
1317C4—22no—
1318C4—22no—
1319C4—24no—
1320C4—41no—
1321C4—42no—
1322C4—44no—
1323C4—44no—
1324C4—42no—
1325C4—44no—
1326C4—44no—
1327C4—44no—
1328C4—42no—
1329C4—42no—
1330C4—42no—
1331C4—42no—
1332C4—42no—
1333C4—42no—
1334C4—42no—
1335C4—44no—
1336C4—42no—
1337C4—44no—
1338C4—44no—
1339C4#353514yes—
1340C2—42no—
1341C2—42no—
1342C2—81no—
1343C2—82no—
1344C2C2×#353511yescharacteristic
1345C2#6282511yescharacteristic
1346C2#6288911yescharacteristic
1347C2#6292512yes—
1348C2#6293912yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#532C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #58700C2semidirect
2. #58266C2semidirect
3. #55661C2semidirect
4. #54092C2semidirect
5. #53067C2semidirect
6. #53024C2semidirect
7. #47803C2semidirect
8. #47755C2semidirect
9. #47478C2semidirect
10. #47146C2semidirect
11. #45253C2semidirect
12. #45238C2semidirect
13. #40195C2semidirect
14. #39914C2semidirect
15. #39693C2semidirect
17. #39022C2semidirect
18. #38919C2semidirect
19. #37971C2semidirect
20. #37971C2semidirect
21. #37425C2semidirect
22. #37393C2semidirect
23. #35333C2semidirect
24. #35309C2semidirect
25. #35181C2semidirect
26. #35087C2semidirect

Maximal subgroups

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

subgroupindex
#587002
#582662
#556612
#540922
#530672
#530242
#478032
#477552
#474782
#471462
#452532
#452382
#401952
#399142
#396932
#394632
#390222
#389192
#379712
#374252
#373932
#353332
#353092
#351812
#350872
#347442