Finite Group Databasebeta

← #7657980

Subgroups — #7657980

Order 512.

4160 conjugacy classes of subgroups.

The subgroup lattice has 1390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42320C214yesmaximal, complemented
2#41685C214yesmaximal, complemented
3#41678C214yesmaximal, complemented
4#41670C214yesmaximal, complemented
5#41670C214yesmaximal, complemented
6#41399C214yesmaximal, complemented
7#39809C212yesmaximal, complemented
8#39757C211yesmaximal, characteristic, complemented
9#39683C212yesmaximal, complemented
10#39630C211yesmaximal, characteristic, complemented
11#38971C211yesmaximal, characteristic, complemented
12#38970C211yesmaximal, characteristic, complemented
13#38243C212yesmaximal, complemented
14#38237C212yesmaximal, complemented
15#37635C211yesmaximal, characteristic, complemented
16#37551C211yesmaximal, characteristic
17#37524C212yesmaximal
18#37522C212yesmaximal, complemented
19#36601C211yesmaximal, characteristic, complemented
20#36574C211yesmaximal, characteristic, complemented
21#36403C211yesmaximal, characteristic, complemented
22#36383C211yesmaximal, characteristic, complemented
23#35820C214yesmaximal, complemented
24#35805C214yesmaximal, complemented
25#35345C211yesmaximal, characteristic, complemented
26#35269C212yesmaximal
27#34631C211yesmaximal, characteristic
28#34629C212yesmaximal, complemented
29#34235C211yesmaximal, characteristic, complemented
30#34224C211yesmaximal, characteristic
31#34145C211yesmaximal, characteristic, complemented
32C2×#533C2211yescharacteristic
33C2×#533C2211yescharacteristic
34C2×#529C2211yescharacteristic
35#2864C2211yescharacteristic
36#2864C2211yescharacteristic
37#2863C2212yes—
38#2861C2212yes—
39#2860C2212yes—
40#2859C2212yes—
41#2859C2211yescharacteristic
42#2859C2211yescharacteristic
43#2839C2214yes—
44#2839C2214yes—
45#2827C2214yes—
46#2827C2214yes—
47#2821C2212yes—
48#2821C2212yes—
49#2817C2212yes—
50#2817C2212yes—
51#2810C2214yes—
52#2810C2214yes—
53#2807C2214yes—
54#2807C2214yes—
55#2805C2214yes—
56#2805C2214yes—
57#2798C2214yes—
58#2798C2214yes—
59#2793C2214yes—
60#2791C2214yes—
61#2788C2214yes—
62#2788C2214yes—
63#2776C2214yes—
64#2776C2214yes—
65#2774C2214yes—
66#2774C2214yes—
67#2773C2214yes—
68#2771C2214yes—
69#2771C2214yes—
70#2767C2214yes—
71#2758C2214yes—
72#2755C2214yes—
73#2745C2214yes—
74#2745C2214yes—
75#2667C2214yes—
76#2664C2214yes—
77#2664C2214yes—
78#2663C2214yes—
79#2663C2212yes—
80#2663C2212yes—
81#2660C2212yes—
82#2660C2211yescharacteristic
83#2658C2211yescharacteristic
84#2655C2214yes—
85#2655C2214yes—
86#2654C2214yes—
87#2652C2214yes—
88#2652C2214yes—
89#2652C2214yes—
90#2652C2214yes—
91#2652C2214yes—
92#2652C2214yes—
93#2652C2214yes—
94#2647C2212yes—
95#2645C2212yes—
96#2645C2212yes—
97#2642C2212yes—
98#2642C2212yes—
99#2642C2211yescharacteristic
100#2640C2211yescharacteristic
101#2638C2214yes—
102#2634C2214yes—
103#2629C2212yes—
104#2629C2212yes—
105#2625C2212yes—
106#2625C2212yes—
107#2625C2212yes—
108#2624C2212yes—
109#2621C2211yescharacteristic
110#2621C2211yescharacteristic
111#2620C2211yescharacteristic
112#2620C2211yescharacteristic
113#2611C2214yes—
114#2608C2214yes—
115#2608C2214yes—
116#2606C2214yes—
117#2606C2214yes—
118#2604C2214yes—
119#2604C2214yes—
120#2596C2214yes—
121#2596C2214yes—
122#2596C2214yes—
123#2596C2214yes—
124#2592C2212yes—
125#2589C2214yes—
126#2588C2214yes—
127#2588C2214yes—
128#2585C2214yes—
129#2585C2214yes—
130#2584C2212yes—
131#2584C2214yes—
132#2584C2214yes—
133#2581C2211yescharacteristic
134#2581C2211yescharacteristic
135#2581C2211yescharacteristic
136#2581C2211yescharacteristic
137#2581C2211yescharacteristic
138#2581C2211yescharacteristic
139#2580C2211yescharacteristic
140#2580C2211yescharacteristic
141#2575C2214yes—
142#2575C2214yes—
143#2573C2214yes—
144#2568C2212yes—
145#2567C2212yes—
146#2533C2214yes—
147#2533C2214yes—
148#2533C2214yes—
149#2533C2214yes—
150#2530C2214yes—
151#2528C2214yes—
152#2528C2214yes—
153#2527C2214yes—
154#2525C2214yes—
155#2524C2214yes—
156#2524C2214yes—
157#2522C2214yes—
158#2522C2214yes—
159#2519C2214yes—
160#2518C2214yes—
161#2518C2214yes—
162#2515C2214yes—
163#2512C2212yes—
164#2511C2212yes—
165#2511C2212yes—
166#2511C2212yes—
167#2509C2212yes—
168#2509C2212yes—
169#2509C2214yes—
170#2509C2214yes—
171#2508C2214yes—
172#2507C2212yes—
173#2506C2212yes—
174#2506C2214yes—
175#2505C2214yes—
176#2499C2214yes—
177#2496C2214yes—
178#2493C2214yes—
179#2469C2214yes—
180#2469C2214yes—
181#2466C2214yes—
182#2466C2214yes—
183#2462C2214yes—
184#2462C2214yes—
185#2460C2214yes—
186#2460C2214yes—
187#2454C2212yes—
188#2453C2212yes—
189#2453C2212yes—
190#2453C2212yes—
191#2448C2212yes—
192#2447C2212yes—
193#2446C2212yes—
194#2446C2212yes—
195#2402C2214yes—
196#2402C2214yes—
197#2401C2214yes—
198#2401C2214yes—
199#2396C2214yes—
200#2395C2214yes—
201#2373C2214yes—
202#2373C2214yes—
203#2373C2214yes—
204#2371C2214yes—
205#2370C2212yes—
206#2370C2212yes—
207#2370C2212yes—
208#2370C2214yes—
209#2369C2212yes—
210#2368C2212yes—
211#2368C2212yes—
212#2367C2212yes—
213#2365C2212yes—
214#2365C2212yes—
215#2365C2212yes—
216#2360C2212yes—
217#2360C2212yes—
218#2360C2214yes—
219#2357C2211yescharacteristic
220#2356C2211yescharacteristic
221#2356C2211yescharacteristic
222#2356C2211yescharacteristic
223#2351C2211yescharacteristic
224#2351C2211yescharacteristic
225#2351C2211yescharacteristic
226#2349C2211yescharacteristic
227#2347C2212yes—
228#2343C2212yes—
229#2343C2212yes—
230#2343C2212yes—
231#2336C2214yes—
232#2330C2212yes—
233#2330C2212yes—
234#2330C2212yes—
235#2326C2212yes—
236#2322C2214yes—
237#2320C2212yes—
238#2320C2212yes—
239#2319C2212yes—
240#2318C2212yes—
241C4×C4⋊Q8C2211yescharacteristic
242C4×C4⋊Q8C2212yes—
243C4×C4⋊Q8C2211yescharacteristic
244C4×#125C2212yes—
245C4×#124C2211yescharacteristic
246C4×#124C2211yescharacteristic
247C4×C22⋊Q8C2212yes—
248C4×C22⋊Q8C2212yes—
249C4×C22⋊Q8C2212yes—
250C4×#121C2212yes—
251#2296C2212yes—
252#2295C2212yes—
253#2295C2212yes—
254#2295C2212yes—
255#2295C2211yescharacteristic
256#2295C2211yescharacteristic
257#2295C2212yes—
258#2283C2211yescharacteristic
259#2283C2211yescharacteristic
260#2276C2212yes—
261#2275C2212yes—
262C42×Q8C2211yescharacteristic
263C42×Q8C2211yescharacteristic
264C4×#117C2211yescharacteristic
265C4×#117C2212yes—
266C2×C4×C4⋊C4C2211yescharacteristic
267#533—28no—
268#533—28no—
269C2×C4⋊Q8C2311yescharacteristic
270C2×C4⋊Q8C2311yescharacteristic
271C2×C4⋊Q8C2311yescharacteristic
272C2×C4⋊Q8C2311yescharacteristic
273C2×C4⋊Q8C2311yescharacteristic
274C2×C4⋊Q8C2311yescharacteristic
275#529—28no—
276C2×#126C2312yes—
277C2×#126C2314yes—
278C2×#126C2314yes—
279C2×#125C2312yes—
280C2×#125C2311yescharacteristic
281C2×#125C2312yes—
282C2×#125C2312yes—
283C2×#125C2314yes—
284C2×#125C2314yes—
285C2×#125C2312yes—
286C2×#124C2311yescharacteristic
287C2×#124C2311yescharacteristic
288C2×#124C2311yescharacteristic
289C2×#123C2312yes—
290C2×C22⋊Q8C2311yescharacteristic
291C2×C22⋊Q8C2311yescharacteristic
292C2×C22⋊Q8C2312yes—
293C2×C22⋊Q8C2311yescharacteristic
294C2×C22⋊Q8C2311yescharacteristic
295C2×C22⋊Q8C2311yescharacteristic
296C2×C22⋊Q8C2312yes—
297C2×#121C2311yescharacteristic
298C2×C4×Q8C2311yescharacteristic
299C2×C4×Q8C2311yescharacteristic
300C2×C4×Q8C2311yescharacteristic
301C2×C4×Q8C2312yes—
302C2×C4×Q8C2312yes—
303C2×C4×Q8C2311yescharacteristic
304C2×C4×Q8C2311yescharacteristic
305C2×C4×Q8C2312yes—
306C2×C4×Q8C2312yes—
307C2×C4×Q8C2312yes—
308C2×C4×Q8C2312yes—
309C2×C4×Q8C2314yes—
310C2×C4×Q8C2312yes—
311C2×C4×D4C2312yes—
312C2×C4×D4C2311yescharacteristic
313C2×C4×D4C2312yes—
314C2×C4×D4C2314yes—
315C2×#117C2312yes—
316C2×#117C2312yes—
317C2×#117C2311yescharacteristic
318C2×#117C2312yes—
319C2×#117C2311yescharacteristic
320C22×C4⋊C4C2312yes—
321C22×C42C2312yes—
322C22×C42C2311yescharacteristic
323#401C2314yes—
324#401C2314yes—
325#400C2314yes—
326#400C2314yes—
327#400C2312yes—
328#400C2312yes—
329#400C2312yes—
330#400C2312yes—
331#400C2312yes—
332#400C2312yes—
333#400C2314yes—
334#400C2314yes—
335#400C2314yes—
336#400C2314yes—
337#400C2314yes—
338#400C2314yes—
339#400C2314yes—
340#400C2314yes—
341#400C2314yes—
342#400C2314yes—
343#400C2314yes—
344#400C2314yes—
345#400C2314yes—
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#400C2314yes—
359#400C2314yes—
360#400C2314yes—
361#400C2314yes—
362#400C2314yes—
363#400C2314yes—
364#400C2314yes—
365#400C2314yes—
366#399C2312yes—
367#399C2312yes—
368#399C2314yes—
369#399C2314yes—
370#399C2314yes—
371#399C2314yes—
372#399C2314yes—
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#398C2314yes—
388#398C2314yes—
389#398C2314yes—
390#398C2314yes—
391#398C2314yes—
392#398C2314yes—
393#398C2314yes—
394#397C2314yes—
395#397C2314yes—
396#397C2314yes—
397#397C2314yes—
398#397C2314yes—
399#397C2314yes—
400#397C2314yes—
401#397C2314yes—
402#397C2314yes—
403#397C2314yes—
404#397C2314yes—
405#397C2314yes—
406#397C2314yes—
407#397C2314yes—
408#397C2314yes—
409#396C2314yes—
410#396C2314yes—
411#396C2314yes—
412#396C2314yes—
413#396C2314yes—
414#396C2314yes—
415#396C2314yes—
416#396C2314yes—
417#395C2314yes—
418#395C2314yes—
419#395C2312yes—
420#395C2312yes—
421#395C2312yes—
422#395C2312yes—
423#395C2312yes—
424#395C2312yes—
425#395C2314yes—
426#395C2314yes—
427#394C2314yes—
428#394C2314yes—
429#394C2314yes—
430#394C2314yes—
431#393C2312yes—
432#393C2312yes—
433#393C2314yes—
434#393C2314yes—
435#391C2312yes—
436#391C2311yescharacteristic
437#391C2312yes—
438#391C2311yescharacteristic
439#391C2311yescharacteristic
440#391C2311yescharacteristic
441#391C2314yes—
442#391C2312yes—
443#391C2312yes—
444#391C2312yes—
445#391C2314yes—
446#391C2314yes—
447#391C2312yes—
448#391C2312yes—
449#391C2312yes—
450#391C2312yes—
451#391C2312yes—
452#391C2312yes—
453#391C2312yes—
454#391C2312yes—
455#391C2311yescharacteristic
456#391C2311yescharacteristic
457#391C2312yes—
458#391C2312yes—
459#390C2311yescharacteristic
460#390C2312yes—
461#390C2312yes—
462#390C2312yes—
463#390C2311yescharacteristic
464#389C2312yes—
465#389C2312yes—
466#389C2314yes—
467#389C2314yes—
468#389C2314yes—
469#389C2314yes—
470#389C2312yes—
471#389C2312yes—
472#389C2312yes—
473#389C2314yes—
474#389C2312yes—
475#389C2312yes—
476#389C2312yes—
477#389C2314yes—
478#389C2314yes—
479#389C2314yes—
480#389C2312yes—
481#389C2312yes—
482#389C2312yes—
483#389C2312yes—
484#389C2312yes—
485#389C2314yes—
486#389C2314yes—
487#389C2314yes—
488#389C2314yes—
489#389C2314yes—
490#389C2314yes—
491#389C2314yes—
492#389C2314yes—
493#389C2314yes—
494#389C2314yes—
495#389C2314yes—
496#389C2314yes—
497#389C2312yes—
498#389C2312yes—
499#389C2314yes—
500#389C2314yes—
501#389C2314yes—
502#389C2314yes—
503#389C2312yes—
504#389C2312yes—
505#389C2314yes—
506#389C2314yes—
507#389C2314yes—
508#389C2312yes—
509#389C2314yes—
510#389C2312yes—
511#389C2312yes—
512#389C2312yes—
513#389C2312yes—
514#389C2312yes—
515#389C2312yes—
516#389C2312yes—
517#389C2312yes—
518#389C2314yes—
519#388C2314yes—
520#388C2314yes—
521#388C2314yes—
522#388C2314yes—
523#388C2314yes—
524#388C2314yes—
525#388C2314yes—
526#388C2314yes—
527#388C2314yes—
528#388C2314yes—
529#388C2314yes—
530#388C2314yes—
531#388C2314yes—
532#388C2314yes—
533#388C2314yes—
534#388C2314yes—
535#388C2314yes—
536#388C2314yes—
537#388C2314yes—
538#388C2314yes—
539#388C2314yes—
540#388C2314yes—
541#387C2314yes—
542#387C2314yes—
543#387C2314yes—
544#387C2314yes—
545#387C2312yes—
546#387C2314yes—
547#387C2314yes—
548#387C2314yes—
549#387C2314yes—
550#387C2314yes—
551#387C2314yes—
552#387C2314yes—
553#387C2314yes—
554#387C2314yes—
555#387C2314yes—
556#387C2314yes—
557#387C2314yes—
558#387C2314yes—
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#387C2314yes—
572#387C2314yes—
573#387C2314yes—
574#387C2314yes—
575#387C2314yes—
576#387C2314yes—
577#387C2314yes—
578#387C2314yes—
579#387C2314yes—
580#387C2314yes—
581#387C2314yes—
582#387C2314yes—
583#387C2314yes—
584#387C2314yes—
585#387C2314yes—
586#387C2314yes—
587#387C2314yes—
588#387C2314yes—
589#387C2314yes—
590#387C2312yes—
591#387C2314yes—
592#387C2314yes—
593#387C2314yes—
594#387C2314yes—
595#387C2314yes—
596#387C2312yes—
597#387C2312yes—
598#387C2312yes—
599#387C2312yes—
600#387C2312yes—
601#387C2312yes—
602#387C2312yes—
603#387C2312yes—
604#387C2312yes—
605#387C2312yes—
606#387C2314yes—
607#387C2314yes—
608#387C2314yes—
609#386C2314yes—
610#385C2314yes—
611#385C2312yes—
612#385C2312yes—
613#385C2314yes—
614#385C2314yes—
615#385C2314yes—
616#385C2314yes—
617#385C2314yes—
618#385C2314yes—
619#385C2314yes—
620#385C2314yes—
621#385C2314yes—
622#385C2312yes—
623#385C2312yes—
624#385C2314yes—
625#384C2312yes—
626#384C2311yescharacteristic
627#384C2311yescharacteristic
628#384C2314yes—
629#384C2312yes—
630#383C2312yes—
631#383C2312yes—
632#383C2312yes—
633#383C2312yes—
634#383C2314yes—
635#383C2312yes—
636#383C2314yes—
637#382C2311yescharacteristic
638#382C2314yes—
639#382C2312yes—
640#382C2312yes—
641#382C2312yes—
642#382C2314yes—
643#382C2311yescharacteristic
644#382C2311yescharacteristic
645#382C2311yescharacteristic
646#382C2311yescharacteristic
647#382C2314yes—
648#382C2311yescharacteristic
649#381C2312yes—
650#381C2312yes—
651#381C2314yes—
652#381C2314yes—
653#381C2312yes—
654#380C2312yes—
655#380C2314yes—
656#380C2312yes—
657#380C2312yes—
658#380C2314yes—
659C4×C4⋊C4C2314yes—
660C4×C4⋊C4C2312yes—
661C4×C4⋊C4C2312yes—
662C4×C4⋊C4C2314yes—
663C4×C4⋊C4C2314yes—
664C4×C4⋊C4C2314yes—
665C4×C4⋊C4C2314yes—
666C4×C4⋊C4C2314yes—
667C4×C4⋊C4C2312yes—
668C4×C4⋊C4C2312yes—
669C4×C4⋊C4C2312yes—
670C4×C4⋊C4C2312yes—
671C4×C4⋊C4C2311yescharacteristic
672C4×C4⋊C4C2312yes—
673C4×C4⋊C4C2312yes—
674C4×C4⋊C4C2314yes—
675C4×C4⋊C4C2314yes—
676C4×C4⋊C4C2314yes—
677C4×C4⋊C4C2314yes—
678C4×C4⋊C4C2312yes—
679C4×C4⋊C4C2314yes—
680C4×C4⋊C4C2314yes—
681C4×C4⋊C4C2312yes—
682C4×C4⋊C4C2312yes—
683C4×C4⋊C4C2312yes—
684C4×C4⋊C4C2312yes—
685C4×C4⋊C4C2311yescharacteristic
686C4×C4⋊C4C2312yes—
687C4×C4⋊C4C2311yescharacteristic
688C4×C4⋊C4C2312yes—
689C4×C4⋊C4C2312yes—
690C4×C4⋊C4C2311yescharacteristic
691C4×C4⋊C4C2312yes—
692C4×C4⋊C4C2312yes—
693C4×C4⋊C4C2312yes—
694C4×C4⋊C4C2312yes—
695C4×C4⋊C4C2312yes—
696C4×C4⋊C4C2312yes—
697C4×C4⋊C4C2312yes—
698C4×C4⋊C4C2314yes—
699C4×C4⋊C4C2312yes—
700C4×C4⋊C4C2312yes—
701C4×C4⋊C4C2312yes—
702C4×C4⋊C4C2312yes—
703C4×C22⋊C4C2314yes—
704C4×C22⋊C4C2312yes—
705C4×C22⋊C4C2314yes—
706C4×C22⋊C4C2314yes—
707C4×C22⋊C4C2314yes—
708C4×C22⋊C4C2314yes—
709C4×C22⋊C4C2314yes—
710C4×C22⋊C4C2314yes—
711C4×C22⋊C4C2312yes—
712C4×C22⋊C4C2312yes—
713C4×C22⋊C4C2312yes—
714C4×C22⋊C4C2312yes—
715C4×C22⋊C4C2312yes—
716C4×C22⋊C4C2312yes—
717C4×C22⋊C4C2312yes—
718C4×C22⋊C4C2312yes—
719#376C2312yes—
720#376C2312yes—
721#376C2312yes—
722#376C2311yescharacteristic
723#376C2311yescharacteristic
724#376C2312yes—
725#376C2312yes—
726#376C2312yes—
727#376C2314yes—
728#376C2314yes—
729#376C2312yes—
730C2×#95C2311yescharacteristic
731C2×#95C2311yescharacteristic
732C2×#95C2312yes—
733C43C2312yes—
734C43C2311yescharacteristic
735C43C2311yescharacteristic
736C43C2312yes—
737C22×Q8C2411yescharacteristic
738C22×Q8C2411yescharacteristic
739C22×Q8C2411yescharacteristic
740C22×Q8C2412yes—
741C22×Q8C2411yescharacteristic
742C22×Q8C2411yescharacteristic
743C22×Q8C2412yes—
744C22×D4C2411yescharacteristic
745C22×D4C2412yes—
746C23×C4C2411yescharacteristic
747C23×C4C2412yes—
748C23×C4C2412yes—
749C23×C4C2412yes—
750C23×C4C2414yes—
751C23×C4C2411yescharacteristic
752C23×C4C2411yescharacteristic
753C4⋊Q8—24no—
754C4⋊Q8—24no—
755C4⋊Q8—24no—
756C4⋊Q8—24no—
757C4⋊Q8—24no—
758C4⋊Q8—42no—
759#126—28no—
760#126—48no—
761#126—48no—
762#125—24no—
763#125—28no—
764#125—28no—
765#125—28no—
766#125—44no—
767#125—48no—
768#125—48no—
769#124—24no—
770#124—24no—
771#124—42no—
772#123—28no—
773C22⋊Q8—24no—
774C22⋊Q8—24no—
775C22⋊Q8—24no—
776C22⋊Q8—28no—
777C22⋊Q8—24no—
778C22⋊Q8—24no—
779C22⋊Q8—28no—
780#121—24no—
781C4×Q8—24no—
782C4×Q8—28no—
783C4×Q8—24no—
784C4×Q8—24no—
785C4×Q8—24no—
786C4×Q8—24no—
787C4×Q8—28no—
788C4×Q8—44no—
789C4×Q8—48no—
790C4×Q8—44no—
791C4×Q8—44no—
792C4×Q8—44no—
793C4×Q8—44no—
794C4×D4—28no—
795C4×D4—24no—
796C4×D4—44no—
797C4×D4—48no—
798#117—28no—
799#117—28no—
800#117—28no—
801#117—24no—
802#117—42no—
803C2×C4⋊C4—44no—
804C2×C4⋊C4C2412yes—
805C2×C4⋊C4C2412yes—
806C2×C4⋊C4C2412yes—
807C2×C4⋊C4C2412yes—
808C2×C4⋊C4C2412yes—
809C2×C4⋊C4C2412yes—
810C2×C4⋊C4C2412yes—
811C2×C4⋊C4C2412yes—
812C2×C4⋊C4C2412yes—
813C2×C4⋊C4C2412yes—
814C2×C4⋊C4C2411yescharacteristic
815C2×C4⋊C4C2414yes—
816C2×C4⋊C4C2412yes—
817C2×C4⋊C4C2412yes—
818C2×C4⋊C4C2411yescharacteristic
819C2×C4⋊C4C2412yes—
820C2×C4⋊C4C2412yes—
821C2×C4⋊C4C2412yes—
822C2×C4⋊C4C2412yes—
823C2×C4⋊C4C2412yes—
824C2×C4⋊C4C2412yes—
825C2×C4⋊C4C2412yes—
826C2×C4⋊C4C2412yes—
827C2×C4⋊C4C2411yescharacteristic
828C2×C4⋊C4C2411yescharacteristic
829C2×C4⋊C4C2412yes—
830C2×C4⋊C4C2411yescharacteristic
831C2×C4⋊C4C2411yescharacteristic
832C2×C4⋊C4C2412yes—
833C2×C4⋊C4C2412yes—
834C2×C4⋊C4C2412yes—
835C2×C4⋊C4C2414yes—
836C2×C4⋊C4C2412yes—
837C2×C4⋊C4C2412yes—
838C2×C4⋊C4C2412yes—
839C2×C4⋊C4C2414yes—
840C2×C4⋊C4C2414yes—
841C2×C4⋊C4C2414yes—
842C2×C4⋊C4C2412yes—
843C2×C4⋊C4C2412yes—
844C2×C4⋊C4C2412yes—
845C2×C4⋊C4C2412yes—
846C2×C4⋊C4C2414yes—
847C2×C4⋊C4C2412yes—
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⋊C4C2414yes—
857C2×C4⋊C4C2414yes—
858C2×C4⋊C4C2414yes—
859C2×C4⋊C4C2414yes—
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⋊C4C2412yes—
870C2×C4⋊C4C2412yes—
871C2×C4⋊C4C2412yes—
872C2×C4⋊C4C2412yes—
873C2×C4⋊C4C2414yes—
874C2×C4⋊C4C2414yes—
875C2×C4⋊C4C2414yes—
876C2×C4⋊C4C2414yes—
877C2×C22⋊C4C2412yes—
878C2×C22⋊C4C2412yes—
879C2×C22⋊C4C2412yes—
880C2×C22⋊C4C2412yes—
881C2×C22⋊C4C2412yes—
882C2×C22⋊C4C2412yes—
883C2×C22⋊C4C2412yes—
884C2×C22⋊C4C2412yes—
885C2×C22⋊C4C2412yes—
886C2×C22⋊C4C2412yes—
887C2×C22⋊C4C2414yes—
888C2×C22⋊C4C2414yes—
889C2×C22⋊C4C2412yes—
890C2×C22⋊C4C2414yes—
891C2×C22⋊C4C2414yes—
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×C42—44no—
902C2×C42#4118yes—
903C2×C42C2412yes—
904C2×C42C2412yes—
905C2×C42C2412yes—
906C2×C42C2412yes—
907C2×C42C2412yes—
908C2×C42C2411yescharacteristic
909C2×C42C2411yescharacteristic
910C2×C42C2411yescharacteristic
911C2×C42C2412yes—
912C2×C42C2412yes—
913C2×C42C2412yes—
914C2×C42C2414yes—
915C2×C42C2412yes—
916C2×C42C2414yes—
917C2×C42C2412yes—
918C2×C42C2412yes—
919C2×C42C2412yes—
920C2×C42C2412yes—
921C2×C42C2414yes—
922C2×C42C2414yes—
923C2×C42C2414yes—
924C2×C42C2414yes—
925C2×C42C2414yes—
926C2×C42C2412yes—
927C2×C42C2412yes—
928C2×C42C2412yes—
929C2×C42C2412yes—
930C2×C42C2412yes—
931C2×C42C2412yes—
932C2×C42C2414yes—
933C2×C42C2414yes—
934C2×C42C2412yes—
935C2×C42C2412yes—
936C2×C42C2411yescharacteristic
937C2×C42C2411yescharacteristic
938C2×C42C2411yescharacteristic
939C2×C42C2411yescharacteristic
940C2×C42C2411yescharacteristic
941#95C2411yescharacteristic
942#95C2411yescharacteristic
943#95C2411yescharacteristic
944#95C2412yes—
945#95C2412yes—
946#95C2414yes—
947#95C2411yescharacteristic
948#95C2412yes—
949#95C2412yes—
950#95C2412yes—
951#95C2414yes—
952#95C2412yes—
953#95C2414yes—
954#95C2412yes—
955#95C2412yes—
956#95C2412yes—
957#95C2412yes—
958#95C2412yes—
959#95C2412yes—
960#95C2412yes—
961#95C2412yes—
962#95C2412yes—
963#95C2412yes—
964#95C2412yes—
965#95C2414yes—
966#95C2414yes—
967#95C2412yes—
968#95C2414yes—
969#95C2414yes—
970#95C2414yes—
971#95C2412yes—
972#95C2412yes—
973#95C2414yes—
974#95C2414yes—
975#95C2414yes—
976#95C2414yes—
977#95C2414yes—
978#95C2414yes—
979#95C2414yes—
980#95C2414yes—
981#95C2414yes—
982#95C2414yes—
983#95C2414yes—
984#95C2412yes—
985#95C2412yes—
986#95C2414yes—
987#95C2414yes—
988#95C2414yes—
989#95C2412yes—
990#95C2412yes—
991#95C2412yes—
992#95C2412yes—
993#95C2412yes—
994#95C2414yes—
995#95C2412yes—
996#95C2414yes—
997#95C2414yes—
998#95C2414yes—
999#95C2414yes—
1000#95C2414yes—
1001#95C2414yes—
1002#95C2414yes—
1003#95C2414yes—
1004#95C2412yes—
1005#95C2412yes—
1006#95C2414yes—
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—
1025C24C2512yes—
1026C24C2511yescharacteristic
1027C2×Q8—22no—
1028C2×Q8—24no—
1029C2×Q8—22no—
1030C2×Q8—22no—
1031C2×Q8—22no—
1032C2×Q8—22no—
1033C2×Q8—24no—
1034C2×Q8—22no—
1035C2×Q8—22no—
1036C2×Q8—22no—
1037C2×Q8—22no—
1038C2×Q8—22no—
1039C2×Q8—22no—
1040C2×Q8—42no—
1041C2×Q8—44no—
1042C2×Q8—42no—
1043C2×Q8—42no—
1044C2×Q8—42no—
1045C2×D4—24no—
1046C2×D4—22no—
1047C2×D4—22no—
1048C2×D4—22no—
1049C2×D4—44no—
1050C22×C4—22no—
1051C22×C4—22no—
1052C22×C4—24no—
1053C22×C4—24no—
1054C22×C4—42no—
1055C22×C4—42no—
1056C22×C4—42no—
1057C22×C4—42no—
1058C22×C4—42no—
1059C22×C4—42no—
1060C22×C4—44no—
1061C22×C4—42no—
1062C22×C4—44no—
1063C22×C4—44no—
1064C22×C4—44no—
1065C22×C4C2×#4114yes—
1066C22×C4C2×#4114yes—
1067C22×C4C2×#4114yes—
1068C22×C4C2512yes—
1069C22×C4C2512yes—
1070C22×C4C2514yes—
1071C22×C4C2514yes—
1072C22×C4C2512yes—
1073C22×C4C2512yes—
1074C22×C4C2512yes—
1075C22×C4C2512yes—
1076C22×C4C2512yes—
1077C22×C4C2512yes—
1078C22×C4C2512yes—
1079C22×C4C2512yes—
1080C22×C4C2514yes—
1081C22×C4C2512yes—
1082C22×C4C2512yes—
1083C22×C4C2514yes—
1084C22×C4C2512yes—
1085C22×C4C2512yes—
1086C22×C4C2512yes—
1087C22×C4C2512yes—
1088C22×C4C2512yes—
1089C22×C4C2511yescharacteristic
1090C22×C4C2511yescharacteristic
1091C22×C4C2511yescharacteristic
1092C22×C4C2511yescharacteristic
1093C22×C4C2511yescharacteristic
1094C22×C4C2512yes—
1095C22×C4C2512yes—
1096C22×C4C2511yescharacteristic
1097C4⋊C4—24no—
1098C4⋊C4—24no—
1099C4⋊C4—24no—
1100C4⋊C4—24no—
1101C4⋊C4—24no—
1102C4⋊C4—24no—
1103C4⋊C4—22no—
1104C4⋊C4—24no—
1105C4⋊C4—22no—
1106C4⋊C4—24no—
1107C4⋊C4—24no—
1108C4⋊C4—24no—
1109C4⋊C4—24no—
1110C4⋊C4—24no—
1111C4⋊C4—24no—
1112C4⋊C4—24no—
1113C4⋊C4—24no—
1114C4⋊C4—24no—
1115C4⋊C4—22no—
1116C4⋊C4—22no—
1117C4⋊C4—24no—
1118C4⋊C4—22no—
1119C4⋊C4—22no—
1120C4⋊C4—24no—
1121C4⋊C4—24no—
1122C4⋊C4—28no—
1123C4⋊C4—28no—
1124C4⋊C4—24no—
1125C4⋊C4—24no—
1126C4⋊C4—28no—
1127C4⋊C4—24no—
1128C4⋊C4—24no—
1129C4⋊C4—24no—
1130C4⋊C4—28no—
1131C4⋊C4—24no—
1132C4⋊C4—24no—
1133C4⋊C4—28no—
1134C4⋊C4—24no—
1135C4⋊C4—42no—
1136C4⋊C4—42no—
1137C4⋊C4—44no—
1138C4⋊C4—44no—
1139C4⋊C4—44no—
1140C4⋊C4—44no—
1141C4⋊C4—42no—
1142C4⋊C4—42no—
1143C4⋊C4—42no—
1144C4⋊C4—42no—
1145C4⋊C4—44no—
1146C4⋊C4—44no—
1147C4⋊C4—44no—
1148C4⋊C4—42no—
1149C4⋊C4—44no—
1150C4⋊C4—44no—
1151C4⋊C4—44no—
1152C4⋊C4—42no—
1153C4⋊C4—44no—
1154C4⋊C4—42no—
1155C4⋊C4—44no—
1156C4⋊C4—44no—
1157C4⋊C4—44no—
1158C4⋊C4—44no—
1159C4⋊C4—44no—
1160C4⋊C4—44no—
1161C4⋊C4—44no—
1162C4⋊C4—44no—
1163C4⋊C4—44no—
1164C4⋊C4—44no—
1165C4⋊C4—44no—
1166C4⋊C4—44no—
1167C4⋊C4—44no—
1168C4⋊C4—44no—
1169C4⋊C4—44no—
1170C22⋊C4—24no—
1171C22⋊C4—24no—
1172C22⋊C4—24no—
1173C22⋊C4—24no—
1174C22⋊C4—24no—
1175C22⋊C4—24no—
1176C22⋊C4—24no—
1177C22⋊C4—24no—
1178C22⋊C4—24no—
1179C22⋊C4—24no—
1180C22⋊C4—28no—
1181C22⋊C4—28no—
1182C22⋊C4—44no—
1183C22⋊C4—44no—
1184C22⋊C4—44no—
1185C22⋊C4—44no—
1186C22⋊C4—42no—
1187C22⋊C4—44no—
1188C22⋊C4—44no—
1189C22⋊C4—44no—
1190C22⋊C4—44no—
1191C22⋊C4—44no—
1192C22⋊C4—44no—
1193C22⋊C4—44no—
1194C42—24no—
1195C42—24no—
1196C42—24no—
1197C42—24no—
1198C42—24no—
1199C42—22no—
1200C42—24no—
1201C42—24no—
1202C42—22no—
1203C42—22no—
1204C42—24no—
1205C42—28no—
1206C42—24no—
1207C42—42no—
1208C42—42no—
1209C42—42no—
1210C42—42no—
1211C42—44no—
1212C42—42no—
1213C42—42no—
1214C42—42no—
1215C42—44no—
1216C42—42no—
1217C42—44no—
1218C42—44no—
1219C42—44no—
1220C42—42no—
1221C42—42no—
1222C42—42no—
1223C42—44no—
1224C42—44no—
1225C42—42no—
1226C42—44no—
1227C42C2×#4114yes—
1228C42C2×#4114yes—
1229C42C2×#4114yes—
1230C42C2×#4114yes—
1231C422−1+414yes—
1232C23—21no—
1233C23—21no—
1234C23—22no—
1235C23—22no—
1236C23—22no—
1237C23—22no—
1238C23—24no—
1239C23—22no—
1240C23—24no—
1241C23C22×#4112yes—
1242C23C2611yescharacteristic
1243Q8—44no—
1244Q8—48no—
1245Q8—44no—
1246Q8—44no—
1247Q8—44no—
1248Q8—44no—
1249Q8—84no—
1250D4—48no—
1251D4—44no—
1252C2×C4—21no—
1253C2×C4—22no—
1254C2×C4—22no—
1255C2×C4—21no—
1256C2×C4—22no—
1257C2×C4—22no—
1258C2×C4—22no—
1259C2×C4—22no—
1260C2×C4—22no—
1261C2×C4—22no—
1262C2×C4—28no—
1263C2×C4—22no—
1264C2×C4—22no—
1265C2×C4—22no—
1266C2×C4—22no—
1267C2×C4—22no—
1268C2×C4—22no—
1269C2×C4—22no—
1270C2×C4—22no—
1271C2×C4—22no—
1272C2×C4—22no—
1273C2×C4—22no—
1274C2×C4—22no—
1275C2×C4—22no—
1276C2×C4—24no—
1277C2×C4—24no—
1278C2×C4—22no—
1279C2×C4—22no—
1280C2×C4—22no—
1281C2×C4—22no—
1282C2×C4—24no—
1283C2×C4—22no—
1284C2×C4—22no—
1285C2×C4—22no—
1286C2×C4—22no—
1287C2×C4—22no—
1288C2×C4—24no—
1289C2×C4—22no—
1290C2×C4—22no—
1291C2×C4—24no—
1292C2×C4—22no—
1293C2×C4—22no—
1294C2×C4—22no—
1295C2×C4—22no—
1296C2×C4—22no—
1297C2×C4—24no—
1298C2×C4—22no—
1299C2×C4—22no—
1300C2×C4—24no—
1301C2×C4—24no—
1302C2×C4—24no—
1303C2×C4—22no—
1304C2×C4—24no—
1305C2×C4—22no—
1306C2×C4—24no—
1307C2×C4—22no—
1308C2×C4—22no—
1309C2×C4—24no—
1310C2×C4—22no—
1311C2×C4—22no—
1312C2×C4—22no—
1313C2×C4—22no—
1314C2×C4—24no—
1315C2×C4—24no—
1316C2×C4—22no—
1317C2×C4—22no—
1318C2×C4—24no—
1319C2×C4—24no—
1320C2×C4—22no—
1321C2×C4—22no—
1322C2×C4—44no—
1323C2×C4—44no—
1324C2×C4—84no—
1325C2×C4—84no—
1326C2×C4—84no—
1327C2×C4—164no—
1328C2×C4C22×#4112yes—
1329C2×C4C22×#4112yes—
1330C2×C4C22×#4112yes—
1331C2×C4C22×#4112yes—
1332C2×C4C22×#4112yes—
1333C2×C4C22×#4112yes—
1334C2×C4C2×2−1+414yes—
1335C2×C4C2×2−1+412yes—
1336C2×C4#58514yes—
1337C2×C4#58512yes—
1338C22—22no—
1339C22—22no—
1340C22—22no—
1341C22—42no—
1342C22—42no—
1343C22—42no—
1344C22—42no—
1345C22—42no—
1346C22—44no—
1347C22—44no—
1348C22C23×#4111yescharacteristic
1349C22C22×2−1+411yescharacteristic
1350C22C2×#58511yescharacteristic
1351C22C2×#58512yes—
1352C222−1+612yes—
1353C4—22no—
1354C4—22no—
1355C4—22no—
1356C4—22no—
1357C4—22no—
1358C4—24no—
1359C4—24no—
1360C4—42no—
1361C4—42no—
1362C4—42no—
1363C4—42no—
1364C4—42no—
1365C4—42no—
1366C4—42no—
1367C4—42no—
1368C4—42no—
1369C4—42no—
1370C4—42no—
1371C4—42no—
1372C4—44no—
1373C4—44no—
1374C4—42no—
1375C4—42no—
1376C4—44no—
1377C4—42no—
1378C4—42no—
1379C4—42no—
1380C4—44no—
1381C4#350714yes—
1382C2—42no—
1383C2—82no—
1384C2#6268611yescharacteristic
1385C2C2×#350711yescharacteristic
1386C2#6286011yescharacteristic
1387C2#6295612yes—
1388C2#6297112yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#121C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #42320C2semidirect
2. #41685C2semidirect
3. #41678C2semidirect
4. #41670C2semidirect
5. #41670C2semidirect
6. #41399C2semidirect
7. #39809C2semidirect
8. #39757C2semidirect
9. #39683C2semidirect
10. #39630C2semidirect
11. #38971C2semidirect
12. #38970C2semidirect
13. #38243C2semidirect
14. #38237C2semidirect
15. #37635C2semidirect
18. #37522C2semidirect
19. #36601C2semidirect
20. #36574C2semidirect
21. #36403C2semidirect
22. #36383C2semidirect
23. #35820C2semidirect
24. #35805C2semidirect
25. #35345C2semidirect
28. #34629C2semidirect
29. #34235C2semidirect
31. #34145C2semidirect

Maximal subgroups

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

subgroupindex
#423202
#416852
#416782
#416702
#413992
#398092
#397572
#396832
#396302
#389712
#389702
#382432
#382372
#376352
#375512
#375242
#375222
#366012
#365742
#364032
#363832
#358202
#358052
#353452
#352692
#346312
#346292
#342352
#342242
#341452