Finite Group Databasebeta

← #7645690

Subgroups — #7645690

Order 512.

5002 conjugacy classes of subgroups.

The subgroup lattice has 1502 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#41115C214yesmaximal, complemented
2#41099C214yesmaximal, complemented
3#40996C214yesmaximal, complemented
4#40985C214yesmaximal, complemented
5#39691C212yesmaximal, complemented
6#39674C212yesmaximal, complemented
7#39287C212yesmaximal, complemented
8#39259C212yesmaximal, complemented
9#38273C212yesmaximal, complemented
10#38225C212yesmaximal, complemented
11#37797C212yesmaximal, complemented
12#37767C212yesmaximal, complemented
13#37561C211yesmaximal, characteristic, complemented
14#37554C211yesmaximal, characteristic
15#37502C212yesmaximal, complemented
16#36976C212yesmaximal, complemented
17#36975C212yesmaximal, complemented
18#36823C214yesmaximal, complemented
19#35363C214yesmaximal, complemented
20#35249C211yesmaximal, characteristic, complemented
21#35247C211yesmaximal, characteristic, complemented
22#35243C212yesmaximal, complemented
23#35042C212yesmaximal, complemented
24#35008C212yesmaximal, complemented
25#35004C212yesmaximal, complemented
26#34708C212yesmaximal, complemented
27#34206C211yesmaximal, characteristic, complemented
28C2×#2351C211yesmaximal, characteristic, complemented
29#34083C211yesmaximal, characteristic, complemented
30C2×#542C2212yes—
31C2×#539C2214yes—
32C2×#532C2211yescharacteristic
33C2×#529C2211yescharacteristic
34C2×#529C2212yes—
35C2×#520C2212yes—
36C22×C4×Q8C2211yescharacteristic
37C22×C4×Q8C2211yescharacteristic
38C22×C4×Q8C2211yescharacteristic
39#2860C2212yes—
40#2859C2212yes—
41#2857C2212yes—
42#2855C2212yes—
43#2854C2212yes—
44#2854C2212yes—
45#2854C2212yes—
46#2854C2212yes—
47#2852C2214yes—
48#2850C2214yes—
49#2845C2212yes—
50#2844C2212yes—
51#2837C2214yes—
52#2836C2214yes—
53#2820C2212yes—
54#2819C2212yes—
55#2806C2214yes—
56#2803C2214yes—
57#2800C2214yes—
58#2788C2214yes—
59#2788C2214yes—
60#2780C2214yes—
61#2779C2214yes—
62#2775C2214yes—
63#2774C2214yes—
64#2774C2214yes—
65#2773C2214yes—
66#2773C2214yes—
67#2772C2214yes—
68#2770C2214yes—
69#2768C2214yes—
70#2768C2214yes—
71#2768C2214yes—
72#2768C2214yes—
73#2767C2214yes—
74#2763C2214yes—
75#2761C2214yes—
76#2754C2214yes—
77#2753C2214yes—
78#2753C2214yes—
79#2727C2214yes—
80#2723C2214yes—
81#2715C2214yes—
82#2710C2214yes—
83#2706C2214yes—
84#2706C2214yes—
85#2698C2214yes—
86#2695C2214yes—
87#2667C2214yes—
88#2666C2214yes—
89#2664C2214yes—
90#2663C2214yes—
91#2660C2212yes—
92#2659C2212yes—
93#2656C2212yes—
94#2649C2214yes—
95#2647C2212yes—
96#2647C2212yes—
97#2646C2212yes—
98#2644C2212yes—
99#2639C2212yes—
100#2637C2214yes—
101#2637C2214yes—
102#2636C2214yes—
103#2632C2214yes—
104#2632C2214yes—
105#2629C2212yes—
106#2628C2212yes—
107#2624C2212yes—
108#2623C2214yes—
109#2619C2212yes—
110#2618C2214yes—
111#2611C2214yes—
112#2604C2214yes—
113#2602C2214yes—
114#2601C2214yes—
115#2597C2214yes—
116#2596C2214yes—
117#2592C2212yes—
118#2590C2214yes—
119#2589C2214yes—
120#2584C2214yes—
121#2584C2212yes—
122#2583C2214yes—
123#2582C2211yescharacteristic
124#2582C2211yescharacteristic
125#2580C2212yes—
126#2580C2212yes—
127#2580C2212yes—
128#2570C2212yes—
129#2567C2211yescharacteristic
130#2567C2211yescharacteristic
131#2556C2214yes—
132#2556C2214yes—
133#2556C2214yes—
134#2554C2214yes—
135#2554C2214yes—
136#2553C2214yes—
137#2550C2212yes—
138#2548C2211yescharacteristic
139#2548C2211yescharacteristic
140#2538C2211yescharacteristic
141#2538C2211yescharacteristic
142#2535C2212yes—
143#2533C2214yes—
144#2532C2214yes—
145#2519C2214yes—
146#2519C2214yes—
147#2507C2212yes—
148#2506C2212yes—
149#2501C2212yes—
150#2497C2212yes—
151#2496C2212yes—
152#2488C2214yes—
153#2486C2212yes—
154#2481C2214yes—
155#2479C2214yes—
156#2478C2214yes—
157#2478C2214yes—
158#2473C2214yes—
159#2470C2214yes—
160#2469C2214yes—
161#2466C2214yes—
162#2465C2214yes—
163#2465C2214yes—
164#2462C2214yes—
165#2461C2214yes—
166#2461C2214yes—
167#2458C2214yes—
168#2458C2214yes—
169#2455C2214yes—
170#2454C2212yes—
171#2453C2212yes—
172#2452C2212yes—
173#2451C2212yes—
174#2449C2214yes—
175#2449C2214yes—
176#2448C2212yes—
177#2448C2212yes—
178#2443C2214yes—
179#2443C2214yes—
180#2442C2212yes—
181#2440C2212yes—
182#2438C2214yes—
183#2436C2212yes—
184#2430C2214yes—
185#2426C2212yes—
186#2426C2212yes—
187#2425C2214yes—
188#2425C2214yes—
189#2423C2212yes—
190#2422C2212yes—
191#2421C2212yes—
192#2420C2212yes—
193#2419C2214yes—
194#2416C2212yes—
195#2416C2212yes—
196#2415C2214yes—
197#2413C2214yes—
198#2413C2214yes—
199#2409C2212yes—
200#2406C2214yes—
201#2398C2214yes—
202#2396C2214yes—
203#2367C2214yes—
204#2366C2212yes—
205#2365C2212yes—
206#2354C2212yes—
207#2352C2214yes—
208#2351C2212yes—
209#2351C2214yes—
210#2351C2212yes—
211#2351C2212yes—
212#2351C2212yes—
213#2351C2214yes—
214D4×C4⋊C4C2212yes—
215#2337C2212yes—
216#2336C2212yes—
217#2334C2212yes—
218#2334C2212yes—
219#2329C2211yescharacteristic
220#2329C2211yescharacteristic
221#2326C2212yes—
222#2326C2212yes—
223#2326C2212yes—
224#2325C2211yescharacteristic
225#2325C2211yescharacteristic
226#2325C2212yes—
227#2325C2212yes—
228#2323C2212yes—
229#2323C2212yes—
230#2323C2212yes—
231#2322C2212yes—
232#2322C2212yes—
233#2322C2214yes—
234#2320C2212yes—
235#2311C2212yes—
236C4×#124C2212yes—
237C4×C22⋊Q8C2212yes—
238C4×#121C2214yes—
239C4×#121C2212yes—
240C4×#121C2212yes—
241#2298C2212yes—
242#2296C2212yes—
243#2295C2212yes—
244#2295C2212yes—
245C2×#389C2212yes—
246C2×#389C2211yescharacteristic
247C2×#389C2211yescharacteristic
248C2×#389C2212yes—
249#2290C2212yes—
250#2290C2212yes—
251#2290C2214yes—
252#2285C2211yescharacteristic
253#2283C2211yescharacteristic
254C2×#382C2212yes—
255C2×#382C2211yescharacteristic
256C42×D4C2212yes—
257C2×C4×C4⋊C4C2211yescharacteristic
258C2×C4×C4⋊C4C2212yes—
259C22×#41C2312yes—
260C23×Q8C2311yescharacteristic
261#542—48no—
262#539—416no—
263#532—28no—
264C2×C4⋊Q8C2311yescharacteristic
265C2×C4⋊Q8C2312yes—
266C2×#127C2311yescharacteristic
267#529—28no—
268#529—48no—
269C2×#126C2312yes—
270C2×#126C2314yes—
271C2×#126C2314yes—
272C2×#126C2314yes—
273C2×#126C2314yes—
274C2×#125C2311yescharacteristic
275C2×#125C2314yes—
276C2×#125C2314yes—
277C2×#125C2312yes—
278C2×#124C2311yescharacteristic
279C2×#124C2312yes—
280C2×#124C2312yes—
281C2×#124C2312yes—
282C2×#124C2314yes—
283C2×#123C2312yes—
284C2×#123C2314yes—
285C2×#123C2314yes—
286C2×#123C2314yes—
287C2×#123C2314yes—
288C2×#123C2314yes—
289C2×#123C2314yes—
290C2×#123C2314yes—
291C2×C22⋊Q8C2312yes—
292C2×C22⋊Q8C2312yes—
293C2×C22⋊Q8C2311yescharacteristic
294C2×C22⋊Q8C2314yes—
295C2×C22⋊Q8C2314yes—
296C2×C22⋊Q8C2314yes—
297C2×C22⋊Q8C2314yes—
298C2×#121C2312yes—
299C2×#121C2311yescharacteristic
300C2×#121C2312yes—
301C2×#121C2314yes—
302C2×#121C2312yes—
303C2×#121C2314yes—
304C2×#121C2312yes—
305#520—48no—
306C2×C4×Q8—28no—
307C2×C4×Q8—44no—
308C2×C4×Q8—44no—
309C2×C4×Q8C2311yescharacteristic
310C2×C4×Q8C2311yescharacteristic
311C2×C4×Q8C2312yes—
312C2×C4×Q8C2311yescharacteristic
313C2×C4×Q8C2312yes—
314C2×C4×Q8C2311yescharacteristic
315C2×C4×Q8C2311yescharacteristic
316C2×C4×Q8C2312yes—
317C2×C4×Q8C2312yes—
318C2×C4×Q8C2312yes—
319C2×C4×Q8C2314yes—
320C2×C4×Q8C2314yes—
321C2×C4×Q8C2314yes—
322C2×C4×Q8C2312yes—
323C2×C4×D4C2314yes—
324C2×C4×D4C2312yes—
325C2×C4×D4C2312yes—
326C2×C4×D4C2312yes—
327C2×C4×D4C2312yes—
328C2×C4×D4C2311yescharacteristic
329C2×C4×D4C2312yes—
330C2×C4×D4C2314yes—
331C2×C4×D4C2312yes—
332C2×C4×D4C2314yes—
333C2×C4×D4C2312yes—
334C2×C4×D4C2314yes—
335C2×#117C2312yes—
336C2×#117C2312yes—
337C2×#117C2312yes—
338C2×#117C2314yes—
339C2×#117C2314yes—
340C22×C4⋊C4C2311yescharacteristic
341C22×C4⋊C4C2312yes—
342C22×C4⋊C4C2312yes—
343C22×C4⋊C4C2311yescharacteristic
344C22×C4⋊C4C2311yescharacteristic
345C22×C4⋊C4C2314yes—
346C22×C4⋊C4C2312yes—
347C22×C4⋊C4C2311yescharacteristic
348C22×C4⋊C4C2311yescharacteristic
349C22×C4⋊C4C2312yes—
350C22×C4⋊C4C2312yes—
351C22×C42C2312yes—
352C22×C42C2312yes—
353C22×C42C2312yes—
354C22×C42C2311yescharacteristic
355C22×C42C2311yescharacteristic
356C22×C42C2312yes—
357C22×C42C2311yescharacteristic
358#400C2314yes—
359#400C2314yes—
360#400C2314yes—
361#400C2314yes—
362#400C2314yes—
363#400C2314yes—
364#400C2314yes—
365#400C2314yes—
366#400C2314yes—
367#400C2314yes—
368#400C2314yes—
369#400C2314yes—
370#399C2314yes—
371#399C2314yes—
372#399C2314yes—
373#399C2314yes—
374#399C2314yes—
375#399C2314yes—
376#399C2314yes—
377#399C2314yes—
378#399C2314yes—
379#398C2314yes—
380#398C2314yes—
381#398C2314yes—
382#398C2314yes—
383#398C2314yes—
384#398C2314yes—
385#398C2314yes—
386#398C2314yes—
387#398C2314yes—
388#398C2314yes—
389#398C2314yes—
390#398C2314yes—
391#398C2314yes—
392#398C2314yes—
393#398C2314yes—
394#398C2314yes—
395#398C2314yes—
396#398C2314yes—
397#398C2314yes—
398#398C2314yes—
399#398C2314yes—
400#397C2314yes—
401#397C2314yes—
402#397C2314yes—
403#397C2314yes—
404#397C2314yes—
405#397C2314yes—
406#397C2314yes—
407#397C2314yes—
408#397C2314yes—
409#397C2314yes—
410#397C2314yes—
411#397C2314yes—
412#396C2314yes—
413#396C2314yes—
414#396C2314yes—
415#396C2314yes—
416#396C2314yes—
417#396C2314yes—
418#396C2314yes—
419#396C2314yes—
420#396C2314yes—
421#396C2314yes—
422#396C2314yes—
423#396C2314yes—
424#395C2314yes—
425#395C2314yes—
426#395C2314yes—
427#395C2314yes—
428#395C2314yes—
429#395C2314yes—
430#395C2314yes—
431#395C2314yes—
432#395C2314yes—
433#394C2314yes—
434#394C2314yes—
435#394C2314yes—
436#394C2314yes—
437#394C2314yes—
438#394C2314yes—
439#394C2314yes—
440#394C2314yes—
441#394C2314yes—
442#394C2314yes—
443#394C2314yes—
444#394C2314yes—
445#393C2314yes—
446#393C2314yes—
447#393C2314yes—
448#393C2314yes—
449#393C2314yes—
450#393C2314yes—
451#392C2314yes—
452#392C2314yes—
453#392C2314yes—
454#391C2314yes—
455#391C2312yes—
456#391C2312yes—
457#391C2312yes—
458#391C2312yes—
459#391C2312yes—
460#391C2312yes—
461#391C2312yes—
462#391C2312yes—
463#391C2314yes—
464#391C2314yes—
465#391C2314yes—
466#390C2314yes—
467#390C2312yes—
468#390C2312yes—
469#390C2312yes—
470#390C2312yes—
471#390C2312yes—
472#390C2312yes—
473#390C2312yes—
474#390C2312yes—
475#390C2312yes—
476#390C2312yes—
477#390C2314yes—
478#390C2312yes—
479#390C2314yes—
480#390C2312yes—
481#389C2312yes—
482#389C2312yes—
483#389C2312yes—
484#389C2312yes—
485#389C2312yes—
486#389C2312yes—
487#389C2312yes—
488#389C2312yes—
489#389C2314yes—
490#389C2312yes—
491#389C2314yes—
492#389C2312yes—
493#389C2312yes—
494#389C2312yes—
495#389C2312yes—
496#389C2314yes—
497#389C2314yes—
498#389C2314yes—
499#389C2312yes—
500#389C2312yes—
501#389C2314yes—
502#389C2312yes—
503#389C2312yes—
504#389C2314yes—
505#389C2314yes—
506#389C2312yes—
507#389C2312yes—
508#389C2314yes—
509#389C2314yes—
510#389C2314yes—
511#389C2312yes—
512#389C2312yes—
513#389C2312yes—
514#389C2312yes—
515#389C2312yes—
516#389C2314yes—
517#389C2312yes—
518#389C2314yes—
519#389C2314yes—
520#389C2312yes—
521#389C2312yes—
522#389C2314yes—
523#389C2314yes—
524#389C2314yes—
525#389C2314yes—
526#389C2314yes—
527#389C2312yes—
528#388C2312yes—
529#388C2312yes—
530#388C2312yes—
531#388C2312yes—
532#388C2314yes—
533#388C2314yes—
534#388C2314yes—
535#388C2314yes—
536#388C2314yes—
537#388C2314yes—
538#388C2314yes—
539#388C2314yes—
540#388C2314yes—
541#388C2312yes—
542#388C2312yes—
543#388C2314yes—
544#388C2314yes—
545#388C2312yes—
546#388C2314yes—
547#388C2314yes—
548#388C2314yes—
549#388C2314yes—
550#388C2314yes—
551#388C2314yes—
552#388C2312yes—
553#388C2314yes—
554#388C2314yes—
555#388C2314yes—
556#388C2314yes—
557#388C2314yes—
558#388C2314yes—
559#388C2314yes—
560#388C2314yes—
561#388C2314yes—
562#388C2314yes—
563#388C2314yes—
564#388C2314yes—
565#388C2314yes—
566#388C2314yes—
567#388C2314yes—
568#387C2314yes—
569#387C2314yes—
570#387C2314yes—
571#387C2314yes—
572#387C2312yes—
573#387C2312yes—
574#387C2314yes—
575#387C2312yes—
576#387C2312yes—
577#387C2314yes—
578#387C2314yes—
579#387C2314yes—
580#387C2314yes—
581#387C2312yes—
582#387C2314yes—
583#387C2312yes—
584#387C2312yes—
585#387C2314yes—
586#387C2312yes—
587#387C2312yes—
588#387C2312yes—
589#387C2312yes—
590#387C2314yes—
591#387C2314yes—
592#387C2312yes—
593#387C2314yes—
594#387C2314yes—
595#387C2314yes—
596#387C2314yes—
597#387C2314yes—
598#387C2314yes—
599#387C2314yes—
600#386C2314yes—
601#386C2314yes—
602#386C2312yes—
603#386C2312yes—
604#386C2314yes—
605#386C2312yes—
606#386C2312yes—
607#386C2314yes—
608#386C2314yes—
609#386C2314yes—
610#386C2314yes—
611#386C2314yes—
612#386C2314yes—
613#386C2314yes—
614#386C2314yes—
615#386C2314yes—
616#386C2314yes—
617#385C2312yes—
618#385C2312yes—
619#385C2314yes—
620#385C2312yes—
621#385C2312yes—
622#385C2312yes—
623#385C2312yes—
624#385C2314yes—
625#385C2314yes—
626#385C2314yes—
627#385C2314yes—
628#385C2314yes—
629#385C2314yes—
630#385C2314yes—
631#385C2314yes—
632#385C2314yes—
633#385C2312yes—
634#385C2312yes—
635#385C2314yes—
636#385C2314yes—
637#385C2314yes—
638#385C2314yes—
639#385C2314yes—
640#385C2314yes—
641#385C2314yes—
642#384C2312yes—
643#384C2312yes—
644#384C2312yes—
645#384C2311yescharacteristic
646#384C2311yescharacteristic
647#383C2314yes—
648#383C2312yes—
649#382C2312yes—
650#382C2312yes—
651#382C2312yes—
652#382C2314yes—
653#382C2311yescharacteristic
654#382C2311yescharacteristic
655#382C2312yes—
656#382C2312yes—
657#382C2312yes—
658#382C2314yes—
659#382C2314yes—
660#382C2314yes—
661#382C2314yes—
662#382C2314yes—
663#381C2312yes—
664#381C2314yes—
665#381C2314yes—
666#380C2314yes—
667#380C2314yes—
668#380C2312yes—
669#380C2312yes—
670#380C2312yes—
671#380C2312yes—
672#380C2311yescharacteristic
673#380C2311yescharacteristic
674#380C2314yes—
675#380C2314yes—
676#380C2312yes—
677#380C2312yes—
678#380C2314yes—
679C4×C4⋊C4C2311yescharacteristic
680C4×C4⋊C4C2311yescharacteristic
681C4×C4⋊C4C2312yes—
682C4×C4⋊C4C2312yes—
683C4×C4⋊C4C2314yes—
684C4×C4⋊C4C2312yes—
685C4×C4⋊C4C2314yes—
686C4×C4⋊C4C2312yes—
687C4×C4⋊C4C2312yes—
688C4×C4⋊C4C2312yes—
689C4×C4⋊C4C2314yes—
690C4×C4⋊C4C2312yes—
691C4×C4⋊C4C2312yes—
692C4×C4⋊C4C2312yes—
693C4×C4⋊C4C2314yes—
694C4×C4⋊C4C2314yes—
695C4×C4⋊C4C2312yes—
696C4×C4⋊C4C2314yes—
697C4×C4⋊C4C2312yes—
698C4×C4⋊C4C2312yes—
699C4×C22⋊C4C2312yes—
700C4×C22⋊C4C2312yes—
701C4×C22⋊C4C2314yes—
702C4×C22⋊C4C2312yes—
703C4×C22⋊C4C2312yes—
704C4×C22⋊C4C2314yes—
705C4×C22⋊C4C2314yes—
706C4×C22⋊C4C2314yes—
707C4×C22⋊C4C2314yes—
708C4×C22⋊C4C2312yes—
709C4×C22⋊C4C2312yes—
710C4×C22⋊C4C2312yes—
711#376C2312yes—
712#376C2312yes—
713#376C2314yes—
714C2×#95C2311yescharacteristic
715C2×#95C2311yescharacteristic
716C2×#95C2312yes—
717C2×#95C2312yes—
718C2×#95C2312yes—
719C2×#95C2312yes—
720C43C2312yes—
721C2×#41—28no—
722C2×#41—44no—
723C2×#41—44no—
724C22×Q8—24no—
725C22×Q8—24no—
726C22×Q8—24no—
727C22×Q8C2412yes—
728C22×Q8C2411yescharacteristic
729C22×Q8C2411yescharacteristic
730C22×Q8C2412yes—
731C22×Q8C2411yescharacteristic
732C22×Q8C2414yes—
733C22×D4C2412yes—
734C22×D4C2412yes—
735C22×D4C2414yes—
736C22×D4C2412yes—
737C22×D4C2411yescharacteristic
738C22×D4C2412yes—
739C22×D4C2414yes—
740C22×D4C2414yes—
741C23×C4C2412yes—
742C23×C4C2412yes—
743C23×C4C2412yes—
744C23×C4C2411yescharacteristic
745C23×C4C2411yescharacteristic
746C23×C4C2411yescharacteristic
747C23×C4C2411yescharacteristic
748C23×C4C2412yes—
749C23×C4C2412yes—
750C23×C4C2411yescharacteristic
751C23×C4C2414yes—
752C23×C4C2414yes—
753C23×C4C2412yes—
754C23×C4C2414yes—
755C23×C4C2412yes—
756C23×C4C2411yescharacteristic
757C23×C4C2411yescharacteristic
758C4⋊Q8—24no—
759C4⋊Q8—44no—
760#127—24no—
761#126—28no—
762#126—48no—
763#126—48no—
764#126—48no—
765#126—48no—
766#125—24no—
767#125—44no—
768#125—48no—
769#125—48no—
770#124—28no—
771#124—28no—
772#124—24no—
773#124—28no—
774#124—48no—
775#123—28no—
776#123—48no—
777#123—48no—
778#123—48no—
779#123—48no—
780#123—48no—
781#123—48no—
782#123—48no—
783C22⋊Q8—28no—
784C22⋊Q8—28no—
785C22⋊Q8—24no—
786C22⋊Q8—48no—
787C22⋊Q8—48no—
788C22⋊Q8—48no—
789C22⋊Q8—48no—
790#121—24no—
791#121—28no—
792#121—28no—
793#121—44no—
794#121—44no—
795#121—48no—
796#121—48no—
797C4×Q8—28no—
798C4×Q8—28no—
799C4×Q8—24no—
800C4×Q8—24no—
801C4×Q8—24no—
802C4×Q8—24no—
803C4×Q8—28no—
804C4×Q8—28no—
805C4×Q8—24no—
806C4×Q8—48no—
807C4×Q8—44no—
808C4×Q8—44no—
809C4×Q8—48no—
810C4×Q8—48no—
811C4×D4—28no—
812C4×D4—216no—
813C4×D4—28no—
814C4×D4—24no—
815C4×D4—28no—
816C4×D4—28no—
817C4×D4—48no—
818C4×D4—44no—
819C4×D4—44no—
820C4×D4—48no—
821C4×D4—44no—
822C4×D4—48no—
823#117—28no—
824#117—44no—
825#117—48no—
826#117—48no—
827#117—44no—
828C2×C4⋊C4—28no—
829C2×C4⋊C4—24no—
830C2×C4⋊C4—24no—
831C2×C4⋊C4—28no—
832C2×C4⋊C4—42no—
833C2×C4⋊C4—42no—
834C2×C4⋊C4—44no—
835C2×C4⋊C4—44no—
836C2×C4⋊C4—48no—
837C2×C4⋊C4—42no—
838C2×C4⋊C4—44no—
839C2×C4⋊C4C2412yes—
840C2×C4⋊C4C2412yes—
841C2×C4⋊C4C2414yes—
842C2×C4⋊C4C2412yes—
843C2×C4⋊C4C2412yes—
844C2×C4⋊C4C2414yes—
845C2×C4⋊C4C2414yes—
846C2×C4⋊C4C2411yescharacteristic
847C2×C4⋊C4C2411yescharacteristic
848C2×C4⋊C4C2412yes—
849C2×C4⋊C4C2412yes—
850C2×C4⋊C4C2412yes—
851C2×C4⋊C4C2412yes—
852C2×C4⋊C4C2412yes—
853C2×C4⋊C4C2414yes—
854C2×C4⋊C4C2414yes—
855C2×C4⋊C4C2414yes—
856C2×C4⋊C4C2412yes—
857C2×C4⋊C4C2412yes—
858C2×C4⋊C4C2412yes—
859C2×C4⋊C4C2412yes—
860C2×C4⋊C4C2412yes—
861C2×C4⋊C4C2412yes—
862C2×C4⋊C4C2411yescharacteristic
863C2×C4⋊C4C2412yes—
864C2×C4⋊C4C2411yescharacteristic
865C2×C4⋊C4C2412yes—
866C2×C4⋊C4C2412yes—
867C2×C4⋊C4C2414yes—
868C2×C4⋊C4C2412yes—
869C2×C4⋊C4C2414yes—
870C2×C4⋊C4C2414yes—
871C2×C4⋊C4C2414yes—
872C2×C4⋊C4C2412yes—
873C2×C4⋊C4C2412yes—
874C2×C4⋊C4C2412yes—
875C2×C4⋊C4C2412yes—
876C2×C4⋊C4C2414yes—
877C2×C4⋊C4C2414yes—
878C2×C4⋊C4C2412yes—
879C2×C4⋊C4C2412yes—
880C2×C4⋊C4C2414yes—
881C2×C4⋊C4C2412yes—
882C2×C4⋊C4C2414yes—
883C2×C4⋊C4C2412yes—
884C2×C4⋊C4C2414yes—
885C2×C4⋊C4C2414yes—
886C2×C4⋊C4C2414yes—
887C2×C4⋊C4C2414yes—
888C2×C4⋊C4C2414yes—
889C2×C4⋊C4C2414yes—
890C2×C4⋊C4C2414yes—
891C2×C4⋊C4C2414yes—
892C2×C4⋊C4C2414yes—
893C2×C4⋊C4C2414yes—
894C2×C4⋊C4C2414yes—
895C2×C4⋊C4C2414yes—
896C2×C4⋊C4C2411yescharacteristic
897C2×C4⋊C4C2411yescharacteristic
898C2×C4⋊C4C2411yescharacteristic
899C2×C4⋊C4C2411yescharacteristic
900C2×C4⋊C4C2412yes—
901C2×C4⋊C4C2412yes—
902C2×C4⋊C4C2414yes—
903C2×C4⋊C4C2412yes—
904C2×C4⋊C4C2412yes—
905C2×C4⋊C4C2414yes—
906C2×C4⋊C4C2414yes—
907C2×C22⋊C4C2414yes—
908C2×C22⋊C4C2414yes—
909C2×C22⋊C4C2412yes—
910C2×C22⋊C4C2414yes—
911C2×C22⋊C4C2412yes—
912C2×C22⋊C4C2414yes—
913C2×C22⋊C4C2414yes—
914C2×C22⋊C4C2412yes—
915C2×C22⋊C4C2414yes—
916C2×C22⋊C4C2412yes—
917C2×C22⋊C4C2414yes—
918C2×C22⋊C4C2412yes—
919C2×C22⋊C4C2412yes—
920C2×C22⋊C4C2412yes—
921C2×C22⋊C4C2412yes—
922C2×C22⋊C4C2414yes—
923C2×C22⋊C4C2414yes—
924C2×C22⋊C4C2414yes—
925C2×C22⋊C4C2414yes—
926C2×C22⋊C4C2414yes—
927C2×C22⋊C4C2412yes—
928C2×C22⋊C4C2412yes—
929C2×C22⋊C4C2414yes—
930C2×C22⋊C4C2414yes—
931C2×C22⋊C4C2412yes—
932C2×C22⋊C4C2414yes—
933C2×C22⋊C4C2414yes—
934C2×C22⋊C4C2414yes—
935C2×C22⋊C4C2414yes—
936C2×C22⋊C4C2414yes—
937C2×C22⋊C4C2414yes—
938C2×C22⋊C4C2414yes—
939C2×C22⋊C4C2414yes—
940C2×C22⋊C4C2414yes—
941C2×C22⋊C4C2414yes—
942C2×C22⋊C4C2414yes—
943C2×C22⋊C4C2414yes—
944C2×C22⋊C4C2414yes—
945C2×C22⋊C4C2414yes—
946C2×C22⋊C4C2412yes—
947C2×C22⋊C4C2412yes—
948C2×C22⋊C4C2414yes—
949C2×C42—28no—
950C2×C42—42no—
951C2×C42—44no—
952C2×C42—42no—
953C2×C42—44no—
954C2×C42—44no—
955C2×C42#4118yes—
956C2×C42C2412yes—
957C2×C42C2414yes—
958C2×C42C2414yes—
959C2×C42C2412yes—
960C2×C42C2412yes—
961C2×C42C2412yes—
962C2×C42C2412yes—
963C2×C42C2414yes—
964C2×C42C2412yes—
965C2×C42C2412yes—
966C2×C42C2412yes—
967C2×C42C2412yes—
968C2×C42C2412yes—
969C2×C42C2412yes—
970C2×C42C2414yes—
971C2×C42C2414yes—
972C2×C42C2412yes—
973C2×C42C2412yes—
974C2×C42C2414yes—
975C2×C42C2412yes—
976C2×C42C2414yes—
977C2×C42C2412yes—
978C2×C42C2412yes—
979C2×C42C2412yes—
980C2×C42C2411yescharacteristic
981C2×C42C2411yescharacteristic
982C2×C42C2411yescharacteristic
983C2×C42C2411yescharacteristic
984#95C2412yes—
985#95C2412yes—
986#95C2412yes—
987#95C2412yes—
988#95C2414yes—
989#95C2414yes—
990#95C2414yes—
991#95C2414yes—
992#95C2414yes—
993#95C2414yes—
994#95C2414yes—
995#95C2414yes—
996#95C2412yes—
997#95C2412yes—
998#95C2412yes—
999#95C2412yes—
1000#95C2412yes—
1001#95C2412yes—
1002#95C2414yes—
1003#95C2414yes—
1004#95C2412yes—
1005#95C2412yes—
1006#95C2414yes—
1007#95C2414yes—
1008#95C2414yes—
1009#95C2412yes—
1010#95C2412yes—
1011#95C2412yes—
1012#95C2412yes—
1013#95C2412yes—
1014#95C2412yes—
1015#95C2414yes—
1016#95C2414yes—
1017#95C2414yes—
1018#95C2414yes—
1019#95C2412yes—
1020#95C2414yes—
1021#95C2414yes—
1022#95C2414yes—
1023#95C2414yes—
1024#95C2412yes—
1025#95C2412yes—
1026#95C2414yes—
1027#95C2414yes—
1028#95C2414yes—
1029#95C2414yes—
1030#95C2412yes—
1031#95C2412yes—
1032#95C2414yes—
1033#95C2414yes—
1034#95C2414yes—
1035#95C2412yes—
1036#95C2414yes—
1037#95C2414yes—
1038#95C2414yes—
1039#95C2414yes—
1040#95C2414yes—
1041#95C2414yes—
1042#95C2414yes—
1043#95C2414yes—
1044C24C2512yes—
1045C24C2514yes—
1046C24C2511yescharacteristic
1047#41—432no—
1048C2×Q8—232no—
1049C2×Q8—24no—
1050C2×Q8—22no—
1051C2×Q8—22no—
1052C2×Q8—24no—
1053C2×Q8—22no—
1054C2×Q8—24no—
1055C2×Q8—22no—
1056C2×Q8—24no—
1057C2×Q8—22no—
1058C2×Q8—42no—
1059C2×Q8—42no—
1060C2×Q8—41no—
1061C2×Q8—41no—
1062C2×Q8—44no—
1063C2×Q8—44no—
1064C2×Q8—44no—
1065C2×Q8H(5,𝔽2)14yes—
1066C2×Q82−1+414yes—
1067C2×D4—24no—
1068C2×D4—28no—
1069C2×D4—28no—
1070C2×D4—24no—
1071C2×D4—24no—
1072C2×D4—28no—
1073C2×D4—24no—
1074C2×D4—24no—
1075C2×D4—22no—
1076C2×D4—24no—
1077C2×D4—24no—
1078C2×D4—24no—
1079C2×D4—42no—
1080C2×D4—42no—
1081C2×D4—44no—
1082C2×D4—44no—
1083C2×D4—42no—
1084C2×D4—42no—
1085C2×D4—41no—
1086C2×D4—41no—
1087C2×D4—44no—
1088C2×D4—44no—
1089C2×D4—44no—
1090C2×D4—44no—
1091C22×C4—24no—
1092C22×C4—22no—
1093C22×C4—22no—
1094C22×C4—24no—
1095C22×C4—22no—
1096C22×C4—24no—
1097C22×C4—22no—
1098C22×C4—24no—
1099C22×C4—24no—
1100C22×C4—22no—
1101C22×C4—24no—
1102C22×C4—22no—
1103C22×C4—24no—
1104C22×C4—22no—
1105C22×C4—24no—
1106C22×C4—24no—
1107C22×C4—28no—
1108C22×C4—24no—
1109C22×C4—24no—
1110C22×C4—28no—
1111C22×C4—24no—
1112C22×C4—41no—
1113C22×C4—41no—
1114C22×C4—44no—
1115C22×C4—41no—
1116C22×C4—41no—
1117C22×C4—41no—
1118C22×C4—41no—
1119C22×C4—44no—
1120C22×C4—41no—
1121C22×C4—42no—
1122C22×C4—41no—
1123C22×C4—42no—
1124C22×C4—42no—
1125C22×C4—42no—
1126C22×C4—44no—
1127C22×C4—42no—
1128C22×C4—44no—
1129C22×C4—42no—
1130C22×C4—41no—
1131C22×C4—42no—
1132C22×C4—42no—
1133C22×C4—41no—
1134C22×C4—42no—
1135C22×C4—44no—
1136C22×C4—44no—
1137C22×C4—44no—
1138C22×C4C2×#4114yes—
1139C22×C4C2×#4114yes—
1140C22×C4C2×#4114yes—
1141C22×C4H(5,𝔽2)14yes—
1142C22×C4C2512yes—
1143C22×C4C2512yes—
1144C22×C4C2512yes—
1145C22×C4C2514yes—
1146C22×C4C2512yes—
1147C22×C4C2512yes—
1148C22×C4C2514yes—
1149C22×C4C2514yes—
1150C22×C4C2512yes—
1151C22×C4C2512yes—
1152C22×C4C2512yes—
1153C22×C4C2512yes—
1154C22×C4C2514yes—
1155C22×C4C2514yes—
1156C22×C4C2512yes—
1157C22×C4C2512yes—
1158C22×C4C2512yes—
1159C22×C4C2511yescharacteristic
1160C22×C4C2511yescharacteristic
1161C22×C4C2511yescharacteristic
1162C22×C4C2511yescharacteristic
1163C22×C4C2511yescharacteristic
1164C22×C4C2512yes—
1165C22×C4C2512yes—
1166C22×C4C2512yes—
1167C22×C4C2511yescharacteristic
1168C4⋊C4—24no—
1169C4⋊C4—24no—
1170C4⋊C4—24no—
1171C4⋊C4—24no—
1172C4⋊C4—24no—
1173C4⋊C4—22no—
1174C4⋊C4—22no—
1175C4⋊C4—24no—
1176C4⋊C4—24no—
1177C4⋊C4—24no—
1178C4⋊C4—24no—
1179C4⋊C4—22no—
1180C4⋊C4—24no—
1181C4⋊C4—22no—
1182C4⋊C4—24no—
1183C4⋊C4—24no—
1184C4⋊C4—24no—
1185C4⋊C4—28no—
1186C4⋊C4—28no—
1187C4⋊C4—28no—
1188C4⋊C4—24no—
1189C4⋊C4—24no—
1190C4⋊C4—28no—
1191C4⋊C4—28no—
1192C4⋊C4—28no—
1193C4⋊C4—24no—
1194C4⋊C4—24no—
1195C4⋊C4—24no—
1196C4⋊C4—28no—
1197C4⋊C4—42no—
1198C4⋊C4—42no—
1199C4⋊C4—42no—
1200C4⋊C4—44no—
1201C4⋊C4—44no—
1202C4⋊C4—44no—
1203C4⋊C4—44no—
1204C4⋊C4—42no—
1205C4⋊C4—44no—
1206C4⋊C4—42no—
1207C4⋊C4—41no—
1208C4⋊C4—41no—
1209C4⋊C4—41no—
1210C4⋊C4—41no—
1211C4⋊C4—42no—
1212C4⋊C4—42no—
1213C4⋊C4—42no—
1214C4⋊C4—42no—
1215C4⋊C4—44no—
1216C4⋊C4—44no—
1217C4⋊C4—44no—
1218C4⋊C4—42no—
1219C4⋊C4—42no—
1220C4⋊C4—44no—
1221C4⋊C4—42no—
1222C4⋊C4—42no—
1223C4⋊C4—44no—
1224C4⋊C4—44no—
1225C4⋊C4—44no—
1226C4⋊C4—44no—
1227C4⋊C4—44no—
1228C4⋊C4—44no—
1229C4⋊C4—44no—
1230C4⋊C4—44no—
1231C4⋊C4—44no—
1232C4⋊C4—44no—
1233C4⋊C4—44no—
1234C4⋊C4—44no—
1235C4⋊C4—44no—
1236C22⋊C4—24no—
1237C22⋊C4—28no—
1238C22⋊C4—24no—
1239C22⋊C4—24no—
1240C22⋊C4—24no—
1241C22⋊C4—24no—
1242C22⋊C4—28no—
1243C22⋊C4—28no—
1244C22⋊C4—24no—
1245C22⋊C4—24no—
1246C22⋊C4—28no—
1247C22⋊C4—28no—
1248C22⋊C4—24no—
1249C22⋊C4—28no—
1250C22⋊C4—28no—
1251C22⋊C4—28no—
1252C22⋊C4—28no—
1253C22⋊C4—28no—
1254C22⋊C4—44no—
1255C22⋊C4—44no—
1256C22⋊C4—44no—
1257C22⋊C4—42no—
1258C22⋊C4—42no—
1259C22⋊C4—44no—
1260C22⋊C4—44no—
1261C22⋊C4—44no—
1262C22⋊C4—42no—
1263C22⋊C4—42no—
1264C22⋊C4—42no—
1265C22⋊C4—44no—
1266C22⋊C4—44no—
1267C22⋊C4—44no—
1268C22⋊C4—44no—
1269C22⋊C4—44no—
1270C22⋊C4—44no—
1271C22⋊C4—44no—
1272C22⋊C4—44no—
1273C22⋊C4—44no—
1274C22⋊C4—44no—
1275C22⋊C4—44no—
1276C22⋊C4—44no—
1277C22⋊C4—44no—
1278C42—24no—
1279C42—24no—
1280C42—24no—
1281C42—24no—
1282C42—24no—
1283C42—24no—
1284C42—28no—
1285C42—24no—
1286C42—24no—
1287C42—28no—
1288C42—28no—
1289C42—24no—
1290C42—24no—
1291C42—42no—
1292C42—42no—
1293C42—44no—
1294C42—42no—
1295C42—44no—
1296C42—42no—
1297C42—42no—
1298C42—42no—
1299C42—44no—
1300C42—44no—
1301C42—42no—
1302C42C2×#4114yes—
1303C42C2×#4114yes—
1304C42C2×#4114yes—
1305C42C2×#4114yes—
1306C23—21no—
1307C23—21no—
1308C23—21no—
1309C23—21no—
1310C23—22no—
1311C23—24no—
1312C23—24no—
1313C23—22no—
1314C23—22no—
1315C23—24no—
1316C23—22no—
1317C23—24no—
1318C23—22no—
1319C23—24no—
1320C23—24no—
1321C23—24no—
1322C23—22no—
1323C23—22no—
1324C23C22×#4112yes—
1325C23C2×H(5,𝔽2)12yes—
1326C23#58512yes—
1327C23C2611yescharacteristic
1328Q8—216no—
1329Q8—28no—
1330Q8—28no—
1331Q8—48no—
1332Q8—82no—
1333Q8—164no—
1334D4—48no—
1335D4—48no—
1336D4—416no—
1337D4—48no—
1338D4—84no—
1339D4—82no—
1340D4—88no—
1341D4—164no—
1342C2×C4—216no—
1343C2×C4—22no—
1344C2×C4—22no—
1345C2×C4—22no—
1346C2×C4—21no—
1347C2×C4—21no—
1348C2×C4—22no—
1349C2×C4—21no—
1350C2×C4—21no—
1351C2×C4—22no—
1352C2×C4—21no—
1353C2×C4—21no—
1354C2×C4—22no—
1355C2×C4—21no—
1356C2×C4—21no—
1357C2×C4—21no—
1358C2×C4—21no—
1359C2×C4—28no—
1360C2×C4—28no—
1361C2×C4—22no—
1362C2×C4—22no—
1363C2×C4—22no—
1364C2×C4—22no—
1365C2×C4—22no—
1366C2×C4—24no—
1367C2×C4—22no—
1368C2×C4—24no—
1369C2×C4—22no—
1370C2×C4—22no—
1371C2×C4—22no—
1372C2×C4—24no—
1373C2×C4—22no—
1374C2×C4—24no—
1375C2×C4—24no—
1376C2×C4—22no—
1377C2×C4—22no—
1378C2×C4—22no—
1379C2×C4—22no—
1380C2×C4—24no—
1381C2×C4—24no—
1382C2×C4—22no—
1383C2×C4—22no—
1384C2×C4—22no—
1385C2×C4—24no—
1386C2×C4—22no—
1387C2×C4—22no—
1388C2×C4—24no—
1389C2×C4—22no—
1390C2×C4—22no—
1391C2×C4—22no—
1392C2×C4—22no—
1393C2×C4—22no—
1394C2×C4—22no—
1395C2×C4—22no—
1396C2×C4—24no—
1397C2×C4—24no—
1398C2×C4—22no—
1399C2×C4—22no—
1400C2×C4—22no—
1401C2×C4—22no—
1402C2×C4—22no—
1403C2×C4—22no—
1404C2×C4—22no—
1405C2×C4—24no—
1406C2×C4—24no—
1407C2×C4—22no—
1408C2×C4—24no—
1409C2×C4—22no—
1410C2×C4—24no—
1411C2×C4—22no—
1412C2×C4—44no—
1413C2×C4—44no—
1414C2×C4—416no—
1415C2×C4—44no—
1416C2×C4—48no—
1417C2×C4—48no—
1418C2×C4—88no—
1419C2×C4—84no—
1420C2×C4—82no—
1421C2×C4—84no—
1422C2×C4—82no—
1423C2×C4—84no—
1424C2×C4—84no—
1425C2×C4—164no—
1426C2×C4C22×#4112yes—
1427C2×C4C22×#4112yes—
1428C2×C4C22×#4112yes—
1429C2×C4C22×#4112yes—
1430C2×C4C22×#4112yes—
1431C2×C4C22×#4112yes—
1432C2×C4C2×H(5,𝔽2)14yes—
1433C2×C4C2×H(5,𝔽2)14yes—
1434C2×C4C2×H(5,𝔽2)12yes—
1435C2×C4C2×2−1+414yes—
1436C2×C4C2×2−1+412yes—
1437C22—22no—
1438C22—22no—
1439C22—22no—
1440C22—22no—
1441C22—22no—
1442C22—22no—
1443C22—42no—
1444C22—44no—
1445C22—42no—
1446C22—44no—
1447C22—44no—
1448C22—42no—
1449C22—42no—
1450C22—44no—
1451C22—44no—
1452C22—42no—
1453C22—42no—
1454C22—44no—
1455C22—42no—
1456C22—44no—
1457C22#346014yes—
1458C22C23×#4111yescharacteristic
1459C22C22×H(5,𝔽2)11yescharacteristic
1460C22C22×H(5,𝔽2)11yescharacteristic
1461C22C22×2−1+411yescharacteristic
1462C22C2×#58511yescharacteristic
1463C222−1+611yescharacteristic
1464C222−1+611yescharacteristic
1465C4—22no—
1466C4—24no—
1467C4—24no—
1468C4—22no—
1469C4—22no—
1470C4—24no—
1471C4—22no—
1472C4—22no—
1473C4—42no—
1474C4—42no—
1475C4—42no—
1476C4—44no—
1477C4—44no—
1478C4—42no—
1479C4—42no—
1480C4—42no—
1481C4—42no—
1482C4—44no—
1483C4—42no—
1484C4—42no—
1485C4—44no—
1486C4—42no—
1487C4—44no—
1488C4—42no—
1489C4—42no—
1490C4#349214yes—
1491C2—24no—
1492C2—82no—
1493C2—84no—
1494C2C2×#346011yescharacteristic
1495C2C2×#349211yescharacteristic
1496C2#6286011yescharacteristic
1497C2#6289511yescharacteristic
1498C2#6289711yescharacteristic
1499C2#6294611yescharacteristic
1500C2#6294911yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#37554C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #41115C2semidirect
2. #41099C2semidirect
3. #40996C2semidirect
4. #40985C2semidirect
5. #39691C2semidirect
6. #39674C2semidirect
7. #39287C2semidirect
8. #39259C2semidirect
9. #38273C2semidirect
10. #38225C2semidirect
11. #37797C2semidirect
12. #37767C2semidirect
13. #37561C2semidirect
15. #37502C2semidirect
16. #36976C2semidirect
17. #36975C2semidirect
18. #36823C2semidirect
19. #35363C2semidirect
20. #35249C2semidirect
21. #35247C2semidirect
22. #35243C2semidirect
23. #35042C2semidirect
24. #35008C2semidirect
25. #35004C2semidirect
26. #34708C2semidirect
27. #34206C2semidirect
28. C2×#2351C2semidirect
29. #34083C2semidirect

Maximal subgroups

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

subgroupindex
#411152
#410992
#409962
#409852
#396912
#396742
#392872
#392592
#382732
#382252
#377972
#377672
#375612
#375542
#375022
#369762
#369752
#368232
#353632
#352492
#352472
#352432
#350422
#350082
#350042
#347082
#342062
C2×#23512
#340832