Finite Group Databasebeta

← #7683923

Subgroups — #7683923

Order 512.

4857 conjugacy classes of subgroups.

The subgroup lattice has 1500 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59991C214yesmaximal, complemented
2#59928C212yesmaximal, complemented
3#59537C212yesmaximal, complemented
4#59501C214yesmaximal, complemented
5#59361C212yesmaximal, complemented
6#59262C212yesmaximal, complemented
7#59237C212yesmaximal, complemented
8#59231C212yesmaximal, complemented
9#59055C212yesmaximal, complemented
10#59052C212yesmaximal, complemented
11#45436C211yesmaximal, characteristic, complemented
12#45410C211yesmaximal, characteristic, complemented
13#45384C211yesmaximal, characteristic, complemented
14#45364C211yesmaximal, characteristic, complemented
15#45170C212yesmaximal, complemented
16#45138C212yesmaximal, complemented
17#44716C212yesmaximal, complemented
18#44657C212yesmaximal, complemented
19#44591C214yesmaximal, complemented
20#43883C212yesmaximal, complemented
21#43832C214yesmaximal, complemented
22#43788C212yesmaximal, complemented
23#35637C212yesmaximal, complemented
24#35637C212yesmaximal, complemented
25#35635C212yesmaximal, complemented
26#34979C211yesmaximal, characteristic, complemented
27#34947C211yesmaximal, characteristic, complemented
28#34876C211yesmaximal, characteristic
29#34307C212yesmaximal, complemented
30#34299C212yesmaximal, complemented
31#34221C212yesmaximal, complemented
32C2×#556C2212yes—
33C2×#554C2212yes—
34C2×#541C2212yes—
35C2×#533C2212yes—
36C2×#533C2211yescharacteristic
37C2×#533C2211yescharacteristic
38C2×#529C2211yescharacteristic
39C2×C4×#41C2211yescharacteristic
40#2811C2212yes—
41#2809C2212yes—
42#2806C2214yes—
43#2795C2212yes—
44#2792C2212yes—
45#2785C2212yes—
46#2783C2214yes—
47#2781C2214yes—
48#2775C2214yes—
49#2775C2214yes—
50#2769C2214yes—
51#2769C2214yes—
52#2769C2212yes—
53#2769C2214yes—
54#2769C2212yes—
55#2769C2212yes—
56#2744C2214yes—
57#2744C2214yes—
58#2737C2214yes—
59#2732C2214yes—
60#2732C2214yes—
61#2730C2214yes—
62#2730C2214yes—
63#2721C2214yes—
64#2721C2214yes—
65#2721C2214yes—
66#2721C2214yes—
67#2686C2214yes—
68#2612C2212yes—
69#2612C2212yes—
70#2612C2214yes—
71#2612C2214yes—
72#2612C2212yes—
73#2611C2214yes—
74#2611C2214yes—
75#2611C2212yes—
76#2611C2211yescharacteristic
77#2611C2211yescharacteristic
78#2611C2212yes—
79#2610C2211yescharacteristic
80#2610C2211yescharacteristic
81#2609C2212yes—
82#2604C2214yes—
83#2604C2214yes—
84#2604C2212yes—
85#2603C2212yes—
86#2601C2214yes—
87#2601C2214yes—
88#2586C2212yes—
89#2584C2212yes—
90#2582C2212yes—
91#2574C2214yes—
92#2574C2214yes—
93#2572C2212yes—
94#2572C2214yes—
95#2571C2212yes—
96#2568C2212yes—
97#2568C2211yescharacteristic
98#2568C2211yescharacteristic
99#2567C2211yescharacteristic
100#2566C2212yes—
101#2565C2214yes—
102#2565C2214yes—
103#2565C2212yes—
104#2564C2211yescharacteristic
105#2564C2212yes—
106#2564C2212yes—
107#2564C2211yescharacteristic
108#2563C2211yescharacteristic
109#2562C2212yes—
110#2560C2214yes—
111#2560C2214yes—
112#2559C2214yes—
113#2558C2214yes—
114#2556C2214yes—
115#2556C2214yes—
116#2556C2214yes—
117#2553C2214yes—
118#2552C2214yes—
119#2550C2212yes—
120#2550C2212yes—
121#2547C2211yescharacteristic
122#2546C2211yescharacteristic
123#2546C2212yes—
124#2546C2212yes—
125#2543C2211yescharacteristic
126#2543C2211yescharacteristic
127#2542C2212yes—
128#2542C2212yes—
129#2542C2212yes—
130#2542C2211yescharacteristic
131#2542C2211yescharacteristic
132#2536C2212yes—
133#2536C2212yes—
134#2532C2214yes—
135#2532C2214yes—
136#2532C2214yes—
137#2531C2214yes—
138#2526C2214yes—
139#2521C2214yes—
140#2519C2214yes—
141#2519C2214yes—
142#2519C2214yes—
143#2518C2214yes—
144#2518C2214yes—
145#2508C2214yes—
146#2506C2214yes—
147#2506C2214yes—
148#2506C2214yes—
149#2499C2212yes—
150#2498C2212yes—
151#2496C2214yes—
152#2495C2214yes—
153#2495C2214yes—
154#2492C2212yes—
155#2492C2212yes—
156#2489C2212yes—
157#2489C2212yes—
158#2479C2214yes—
159#2479C2214yes—
160#2476C2214yes—
161#2467C2214yes—
162#2467C2214yes—
163#2454C2214yes—
164#2451C2214yes—
165#2448C2214yes—
166#2441C2214yes—
167#2439C2214yes—
168#2432C2212yes—
169#2430C2212yes—
170#2429C2212yes—
171#2429C2212yes—
172#2429C2212yes—
173#2429C2212yes—
174#2426C2214yes—
175#2423C2214yes—
176#2423C2214yes—
177#2423C2214yes—
178#2423C2214yes—
179#2423C2214yes—
180#2417C2212yes—
181#2417C2212yes—
182#2417C2212yes—
183#2417C2212yes—
184#2415C2212yes—
185#2415C2212yes—
186#2415C2212yes—
187#2415C2212yes—
188#2399C2211yescharacteristic
189#2398C2211yescharacteristic
190#2398C2211yescharacteristic
191#2397C2211yescharacteristic
192#2396C2212yes—
193#2396C2212yes—
194#2395C2212yes—
195#2395C2212yes—
196#2373C2214yes—
197#2373C2214yes—
198#2372C2214yes—
199#2372C2214yes—
200#2371C2214yes—
201#2371C2214yes—
202#2371C2214yes—
203#2369C2212yes—
204#2368C2214yes—
205#2368C2214yes—
206#2368C2214yes—
207#2365C2212yes—
208#2363C2214yes—
209#2362C2212yes—
210#2362C2212yes—
211#2362C2214yes—
212#2360C2212yes—
213#2360C2212yes—
214#2356C2214yes—
215#2356C2212yes—
216#2356C2214yes—
217#2356C2214yes—
218#2356C2212yes—
219#2353C2214yes—
220#2352C2212yes—
221#2352C2212yes—
222Q8×C4⋊C4C2214yes—
223#2347C2212yes—
224#2346C2212yes—
225#2346C2214yes—
226#2345C2212yes—
227#2344C2212yes—
228#2343C2214yes—
229#2343C2214yes—
230#2337C2214yes—
231#2336C2214yes—
232#2334C2214yes—
233#2332C2214yes—
234#2331C2212yes—
235#2331C2212yes—
236#2327C2212yes—
237#2327C2212yes—
238#2323C2212yes—
239#2323C2212yes—
240#2320C2212yes—
241#2320C2212yes—
242C4×C4⋊Q8C2212yes—
243C4×#126C2214yes—
244C4×#124C2212yes—
245C4×C22⋊Q8C2212yes—
246C4×C22⋊Q8C2212yes—
247C4×C22⋊Q8C2212yes—
248C4×C22⋊Q8C2212yes—
249C4×C22⋊Q8C2214yes—
250C4×C22⋊Q8C2212yes—
251C4×C22⋊Q8C2212yes—
252C4×#121C2212yes—
253C4×#121C2212yes—
254#2297C2212yes—
255#2295C2214yes—
256#2290C2212yes—
257#2290C2212yes—
258#2290C2214yes—
259#2285C2212yes—
260#2283C2212yes—
261#2276C2212yes—
262#2276C2212yes—
263#2274C2212yes—
264C4×#117C2211yescharacteristic
265C2×C4×C4⋊C4C2211yescharacteristic
266C2×#376C2211yescharacteristic
267C22×#41C2311yescharacteristic
268#556—216no—
269#554—216no—
270#541—48no—
271#533—216no—
272#533—44no—
273#533—44no—
274C2×C4⋊Q8C2312yes—
275C2×C4⋊Q8C2312yes—
276C2×C4⋊Q8C2311yescharacteristic
277C2×C4⋊Q8C2311yescharacteristic
278C2×C4⋊Q8C2311yescharacteristic
279C2×C4⋊Q8C2312yes—
280C2×C4⋊Q8C2311yescharacteristic
281C2×C4⋊Q8C2312yes—
282#529—44no—
283C2×#126C2314yes—
284C2×#126C2314yes—
285C2×#126C2314yes—
286C2×#126C2314yes—
287C2×#126C2312yes—
288C2×#125C2314yes—
289C2×#125C2314yes—
290C2×#125C2312yes—
291C2×#125C2312yes—
292C2×#125C2314yes—
293C2×#125C2314yes—
294C2×#125C2311yescharacteristic
295C2×#125C2312yes—
296C2×#124C2314yes—
297C2×#124C2312yes—
298C2×#124C2311yescharacteristic
299C2×#123C2312yes—
300C2×C22⋊Q8C2312yes—
301C2×C22⋊Q8C2312yes—
302C2×C22⋊Q8C2314yes—
303C2×C22⋊Q8C2312yes—
304C2×C22⋊Q8C2312yes—
305C2×C22⋊Q8C2314yes—
306C2×C22⋊Q8C2314yes—
307C2×C22⋊Q8C2312yes—
308C2×C22⋊Q8C2312yes—
309C2×C22⋊Q8C2312yes—
310C2×C22⋊Q8C2312yes—
311C2×C22⋊Q8C2311yescharacteristic
312C2×C22⋊Q8C2312yes—
313C2×C22⋊Q8C2312yes—
314C2×C22⋊Q8C2312yes—
315C2×C22⋊Q8C2312yes—
316C2×#121C2312yes—
317C2×#121C2311yescharacteristic
318C2×#121C2312yes—
319C4×#41—44no—
320C2×C4×Q8C2312yes—
321C2×C4×Q8C2312yes—
322C2×C4×Q8C2312yes—
323C2×C4×Q8C2312yes—
324C2×C4×Q8C2312yes—
325C2×C4×Q8C2312yes—
326C2×C4×Q8C2314yes—
327C2×C4×Q8C2314yes—
328C2×C4×Q8C2311yescharacteristic
329C2×C4×Q8C2312yes—
330C2×C4×Q8C2312yes—
331C2×C4×Q8C2311yescharacteristic
332C2×C4×Q8C2311yescharacteristic
333C2×C4×Q8C2314yes—
334C2×C4×D4C2312yes—
335C2×C4×D4C2312yes—
336C2×C4×D4C2314yes—
337C2×C4×D4C2312yes—
338C2×C4×D4C2311yescharacteristic
339C2×C4×D4C2311yescharacteristic
340C2×C4×D4C2311yescharacteristic
341C2×C4×D4C2311yescharacteristic
342C2×C4×D4C2311yescharacteristic
343C2×C4×D4C2311yescharacteristic
344C2×C4×D4C2311yescharacteristic
345C2×#117C2312yes—
346C2×#117C2314yes—
347C2×#117C2312yes—
348C2×#117C2312yes—
349C2×#117C2314yes—
350C2×#117C2312yes—
351C2×#117C2312yes—
352C2×#117C2311yescharacteristic
353C2×#117C2311yescharacteristic
354C2×#117C2311yescharacteristic
355C22×C4⋊C4C2312yes—
356C22×C4⋊C4C2312yes—
357C22×C42C2311yescharacteristic
358C22×C42C2311yescharacteristic
359C22×C42C2311yescharacteristic
360C22×C42C2312yes—
361C22×C42C2312yes—
362#400C2314yes—
363#400C2312yes—
364#400C2312yes—
365#400C2311yescharacteristic
366#400C2311yescharacteristic
367#400C2312yes—
368#400C2312yes—
369#400C2314yes—
370#400C2314yes—
371#400C2314yes—
372#400C2314yes—
373#400C2312yes—
374#400C2314yes—
375#400C2314yes—
376#399C2311yescharacteristic
377#399C2311yescharacteristic
378#399C2312yes—
379#399C2312yes—
380#399C2312yes—
381#399C2314yes—
382#399C2314yes—
383#399C2312yes—
384#399C2312yes—
385#399C2314yes—
386#399C2314yes—
387#399C2314yes—
388#399C2314yes—
389#398C2314yes—
390#398C2314yes—
391#398C2314yes—
392#398C2314yes—
393#398C2314yes—
394#398C2314yes—
395#398C2314yes—
396#398C2314yes—
397#398C2314yes—
398#398C2314yes—
399#398C2311yescharacteristic
400#398C2312yes—
401#398C2314yes—
402#398C2314yes—
403#398C2311yescharacteristic
404#398C2314yes—
405#398C2314yes—
406#398C2312yes—
407#398C2312yes—
408#398C2314yes—
409#398C2314yes—
410#398C2314yes—
411#397C2314yes—
412#397C2314yes—
413#397C2312yes—
414#397C2312yes—
415#397C2312yes—
416#397C2311yescharacteristic
417#397C2311yescharacteristic
418#397C2314yes—
419#397C2314yes—
420#397C2314yes—
421#397C2314yes—
422#396C2314yes—
423#396C2314yes—
424#396C2314yes—
425#396C2314yes—
426#396C2314yes—
427#396C2314yes—
428#396C2314yes—
429#396C2314yes—
430#395C2312yes—
431#395C2312yes—
432#395C2311yescharacteristic
433#395C2311yescharacteristic
434#395C2314yes—
435#395C2314yes—
436#395C2314yes—
437#395C2312yes—
438#394C2314yes—
439#394C2314yes—
440#394C2314yes—
441#394C2311yescharacteristic
442#394C2312yes—
443#394C2311yescharacteristic
444#394C2314yes—
445#394C2314yes—
446#394C2314yes—
447#394C2314yes—
448#393C2314yes—
449#393C2314yes—
450#393C2312yes—
451#393C2312yes—
452#393C2311yescharacteristic
453#393C2311yescharacteristic
454#393C2312yes—
455#392C2312yes—
456#392C2311yescharacteristic
457#392C2311yescharacteristic
458#391C2314yes—
459#391C2314yes—
460#391C2312yes—
461#391C2312yes—
462#391C2312yes—
463#391C2312yes—
464#391C2314yes—
465#391C2314yes—
466#391C2312yes—
467#391C2312yes—
468#391C2314yes—
469#391C2312yes—
470#391C2312yes—
471#391C2312yes—
472#391C2312yes—
473#391C2312yes—
474#391C2312yes—
475#391C2312yes—
476#391C2314yes—
477#391C2314yes—
478#391C2314yes—
479#391C2314yes—
480#391C2314yes—
481#391C2314yes—
482#391C2314yes—
483#390C2314yes—
484#390C2314yes—
485#390C2312yes—
486#390C2312yes—
487#390C2312yes—
488#390C2312yes—
489#390C2312yes—
490#390C2314yes—
491#389C2314yes—
492#389C2314yes—
493#389C2312yes—
494#389C2312yes—
495#389C2314yes—
496#389C2314yes—
497#389C2312yes—
498#389C2312yes—
499#389C2312yes—
500#389C2312yes—
501#389C2312yes—
502#389C2314yes—
503#389C2314yes—
504#389C2314yes—
505#389C2314yes—
506#389C2314yes—
507#389C2314yes—
508#389C2314yes—
509#389C2312yes—
510#389C2314yes—
511#389C2312yes—
512#389C2314yes—
513#389C2312yes—
514#389C2314yes—
515#389C2314yes—
516#389C2314yes—
517#389C2314yes—
518#389C2314yes—
519#389C2314yes—
520#389C2314yes—
521#389C2314yes—
522#388C2312yes—
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#388C2312yes—
539#388C2314yes—
540#388C2314yes—
541#388C2314yes—
542#388C2314yes—
543#388C2314yes—
544#388C2314yes—
545#388C2314yes—
546#388C2314yes—
547#388C2314yes—
548#388C2314yes—
549#388C2314yes—
550#388C2312yes—
551#388C2312yes—
552#388C2312yes—
553#388C2312yes—
554#388C2312yes—
555#388C2314yes—
556#388C2312yes—
557#388C2314yes—
558#388C2314yes—
559#388C2314yes—
560#388C2314yes—
561#388C2314yes—
562#387C2314yes—
563#387C2314yes—
564#387C2314yes—
565#387C2314yes—
566#387C2314yes—
567#387C2312yes—
568#387C2314yes—
569#387C2312yes—
570#387C2312yes—
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#387C2314yes—
591#387C2314yes—
592#387C2314yes—
593#387C2314yes—
594#387C2314yes—
595#387C2314yes—
596#387C2314yes—
597#387C2314yes—
598#387C2314yes—
599#387C2314yes—
600#387C2312yes—
601#387C2314yes—
602#387C2314yes—
603#387C2314yes—
604#387C2314yes—
605#387C2314yes—
606#386C2312yes—
607#386C2312yes—
608#386C2314yes—
609#386C2312yes—
610#386C2314yes—
611#386C2312yes—
612#386C2312yes—
613#386C2314yes—
614#386C2314yes—
615#386C2312yes—
616#386C2314yes—
617#386C2312yes—
618#386C2314yes—
619#386C2312yes—
620#385C2314yes—
621#385C2314yes—
622#385C2312yes—
623#385C2312yes—
624#385C2314yes—
625#385C2314yes—
626#385C2314yes—
627#385C2314yes—
628#385C2314yes—
629#385C2314yes—
630#385C2312yes—
631#385C2312yes—
632#384C2312yes—
633#384C2312yes—
634#384C2314yes—
635#384C2314yes—
636#384C2312yes—
637#384C2314yes—
638#383C2314yes—
639#383C2314yes—
640#383C2314yes—
641#383C2314yes—
642#383C2314yes—
643#383C2314yes—
644#382C2312yes—
645#382C2314yes—
646#382C2314yes—
647#382C2312yes—
648#382C2312yes—
649#382C2314yes—
650#382C2314yes—
651#382C2314yes—
652#382C2314yes—
653#382C2312yes—
654#382C2312yes—
655#381C2314yes—
656#381C2314yes—
657#380C2312yes—
658#380C2312yes—
659#380C2312yes—
660#380C2312yes—
661#380C2312yes—
662#380C2312yes—
663#380C2314yes—
664#380C2314yes—
665#380C2312yes—
666#380C2312yes—
667#380C2314yes—
668#380C2314yes—
669#380C2314yes—
670C4×C4⋊C4C2314yes—
671C4×C4⋊C4C2314yes—
672C4×C4⋊C4C2314yes—
673C4×C4⋊C4C2314yes—
674C4×C4⋊C4C2312yes—
675C4×C4⋊C4C2314yes—
676C4×C4⋊C4C2314yes—
677C4×C4⋊C4C2311yescharacteristic
678C4×C4⋊C4C2312yes—
679C4×C4⋊C4C2314yes—
680C4×C4⋊C4C2314yes—
681C4×C4⋊C4C2311yescharacteristic
682C4×C4⋊C4C2311yescharacteristic
683C4×C4⋊C4C2314yes—
684C4×C4⋊C4C2314yes—
685C4×C4⋊C4C2312yes—
686C4×C4⋊C4C2312yes—
687C4×C4⋊C4C2312yes—
688C4×C4⋊C4C2312yes—
689C4×C4⋊C4C2312yes—
690C4×C4⋊C4C2312yes—
691C4×C4⋊C4C2312yes—
692C4×C4⋊C4C2312yes—
693C4×C4⋊C4C2314yes—
694C4×C4⋊C4C2314yes—
695C4×C4⋊C4C2314yes—
696C4×C4⋊C4C2314yes—
697C4×C4⋊C4C2314yes—
698C4×C4⋊C4C2314yes—
699C4×C4⋊C4C2312yes—
700C4×C4⋊C4C2312yes—
701C4×C4⋊C4C2314yes—
702C4×C4⋊C4C2314yes—
703C4×C4⋊C4C2311yescharacteristic
704C4×C22⋊C4C2314yes—
705C4×C22⋊C4C2314yes—
706C4×C22⋊C4C2314yes—
707C4×C22⋊C4C2314yes—
708C4×C22⋊C4C2314yes—
709C4×C22⋊C4C2314yes—
710C4×C22⋊C4C2314yes—
711C4×C22⋊C4C2314yes—
712C4×C22⋊C4C2314yes—
713C4×C22⋊C4C2312yes—
714C4×C22⋊C4C2314yes—
715C4×C22⋊C4C2314yes—
716C4×C22⋊C4C2314yes—
717C4×C22⋊C4C2312yes—
718C4×C22⋊C4C2312yes—
719C4×C22⋊C4C2312yes—
720C4×C22⋊C4C2312yes—
721C4×C22⋊C4C2314yes—
722C4×C22⋊C4C2314yes—
723C4×C22⋊C4C2312yes—
724#376C2311yescharacteristic
725#376C2311yescharacteristic
726#376C2312yes—
727#376C2314yes—
728#376C2314yes—
729#376C2314yes—
730#376C2314yes—
731#376C2314yes—
732#376C2312yes—
733#376C2311yescharacteristic
734#376C2311yescharacteristic
735#376C2312yes—
736#376C2314yes—
737C2×#95C2312yes—
738C2×#95C2311yescharacteristic
739C2×#95C2311yescharacteristic
740C2×#95C2312yes—
741C43C2312yes—
742C2×#41—24no—
743C2×#41—42no—
744C2×#41—42no—
745C22×Q8C2412yes—
746C22×Q8C2412yes—
747C22×Q8C2411yescharacteristic
748C22×Q8C2412yes—
749C22×Q8C2411yescharacteristic
750C22×Q8C2412yes—
751C22×Q8C2414yes—
752C22×D4C2412yes—
753C22×D4C2411yescharacteristic
754C22×D4C2411yescharacteristic
755C22×D4C2412yes—
756C22×D4C2412yes—
757C22×D4C2411yescharacteristic
758C22×D4C2411yescharacteristic
759C23×C4C2411yescharacteristic
760C23×C4C2412yes—
761C23×C4C2411yescharacteristic
762C23×C4C2411yescharacteristic
763C23×C4C2411yescharacteristic
764C23×C4C2412yes—
765C23×C4C2411yescharacteristic
766C23×C4C2411yescharacteristic
767C23×C4C2414yes—
768C23×C4C2414yes—
769C23×C4C2411yescharacteristic
770C23×C4C2411yescharacteristic
771C23×C4C2411yescharacteristic
772C23×C4C2412yes—
773C4⋊Q8—28no—
774C4⋊Q8—42no—
775C4⋊Q8—42no—
776C4⋊Q8—42no—
777C4⋊Q8—42no—
778C4⋊Q8—44no—
779C4⋊Q8—44no—
780C4⋊Q8#41116yescomplemented
781#126—216no—
782#126—216no—
783#126—44no—
784#126—48no—
785#126—48no—
786#125—216no—
787#125—216no—
788#125—42no—
789#125—44no—
790#125—44no—
791#125—44no—
792#125—48no—
793#125—48no—
794#124—216no—
795#124—28no—
796#124—42no—
797#123—44no—
798C22⋊Q8—216no—
799C22⋊Q8—216no—
800C22⋊Q8—216no—
801C22⋊Q8—28no—
802C22⋊Q8—28no—
803C22⋊Q8—28no—
804C22⋊Q8—28no—
805C22⋊Q8—28no—
806C22⋊Q8—28no—
807C22⋊Q8—42no—
808C22⋊Q8—44no—
809C22⋊Q8—44no—
810C22⋊Q8—44no—
811C22⋊Q8—44no—
812C22⋊Q8—44no—
813C22⋊Q8—44no—
814#121—28no—
815#121—42no—
816#121—44no—
817C4×Q8—216no—
818C4×Q8—216no—
819C4×Q8—28no—
820C4×Q8—28no—
821C4×Q8—28no—
822C4×Q8—28no—
823C4×Q8—28no—
824C4×Q8—28no—
825C4×Q8—42no—
826C4×Q8—42no—
827C4×Q8—42no—
828C4×Q8—44no—
829C4×Q8—44no—
830C4×Q8—48no—
831C4×D4—216no—
832C4×D4—28no—
833C4×D4—28no—
834C4×D4—42no—
835C4×D4—42no—
836C4×D4—42no—
837C4×D4—42no—
838C4×D4—42no—
839C4×D4—42no—
840C4×D4—42no—
841C4×D4—44no—
842#117—216no—
843#117—28no—
844#117—28no—
845#117—28no—
846#117—42no—
847#117—42no—
848#117—42no—
849#117—44no—
850#117—44no—
851#117—48no—
852C2×C4⋊C4—28no—
853C2×C4⋊C4—28no—
854C2×C4⋊C4C2412yes—
855C2×C4⋊C4C2414yes—
856C2×C4⋊C4C2414yes—
857C2×C4⋊C4C2412yes—
858C2×C4⋊C4C2414yes—
859C2×C4⋊C4C2412yes—
860C2×C4⋊C4C2412yes—
861C2×C4⋊C4C2414yes—
862C2×C4⋊C4C2412yes—
863C2×C4⋊C4C2412yes—
864C2×C4⋊C4C2412yes—
865C2×C4⋊C4C2412yes—
866C2×C4⋊C4C2412yes—
867C2×C4⋊C4C2414yes—
868C2×C4⋊C4C2414yes—
869C2×C4⋊C4C2414yes—
870C2×C4⋊C4C2414yes—
871C2×C4⋊C4C2414yes—
872C2×C4⋊C4C2414yes—
873C2×C4⋊C4C2414yes—
874C2×C4⋊C4C2414yes—
875C2×C4⋊C4C2414yes—
876C2×C4⋊C4C2414yes—
877C2×C4⋊C4C2414yes—
878C2×C4⋊C4C2412yes—
879C2×C4⋊C4C2414yes—
880C2×C4⋊C4C2414yes—
881C2×C4⋊C4C2411yescharacteristic
882C2×C4⋊C4C2411yescharacteristic
883C2×C4⋊C4C2411yescharacteristic
884C2×C4⋊C4C2411yescharacteristic
885C2×C4⋊C4C2411yescharacteristic
886C2×C4⋊C4C2411yescharacteristic
887C2×C4⋊C4C2412yes—
888C2×C4⋊C4C2412yes—
889C2×C4⋊C4C2412yes—
890C2×C4⋊C4C2412yes—
891C2×C4⋊C4C2414yes—
892C2×C4⋊C4C2411yescharacteristic
893C2×C4⋊C4C2412yes—
894C2×C4⋊C4C2411yescharacteristic
895C2×C4⋊C4C2414yes—
896C2×C4⋊C4C2414yes—
897C2×C4⋊C4C2412yes—
898C2×C4⋊C4C2412yes—
899C2×C4⋊C4C2412yes—
900C2×C4⋊C4C2414yes—
901C2×C4⋊C4C2414yes—
902C2×C4⋊C4C2414yes—
903C2×C4⋊C4C2414yes—
904C2×C4⋊C4C2414yes—
905C2×C4⋊C4C2414yes—
906C2×C4⋊C4C2414yes—
907C2×C4⋊C4C2414yes—
908C2×C4⋊C4C2414yes—
909C2×C4⋊C4C2414yes—
910C2×C4⋊C4C2414yes—
911C2×C4⋊C4C2412yes—
912C2×C4⋊C4C2412yes—
913C2×C4⋊C4C2414yes—
914C2×C4⋊C4C2412yes—
915C2×C4⋊C4C2412yes—
916C2×C4⋊C4C2414yes—
917C2×C22⋊C4C2412yes—
918C2×C22⋊C4C2412yes—
919C2×C22⋊C4C2414yes—
920C2×C22⋊C4C2414yes—
921C2×C22⋊C4C2412yes—
922C2×C22⋊C4C2414yes—
923C2×C22⋊C4C2414yes—
924C2×C22⋊C4C2412yes—
925C2×C22⋊C4C2414yes—
926C2×C22⋊C4C2412yes—
927C2×C22⋊C4C2414yes—
928C2×C22⋊C4C2412yes—
929C2×C22⋊C4C2412yes—
930C2×C22⋊C4C2412yes—
931C2×C22⋊C4C2412yes—
932C2×C22⋊C4C2414yes—
933C2×C22⋊C4C2414yes—
934C2×C22⋊C4C2414yes—
935C2×C22⋊C4C2414yes—
936C2×C22⋊C4C2411yescharacteristic
937C2×C22⋊C4C2411yescharacteristic
938C2×C22⋊C4C2411yescharacteristic
939C2×C22⋊C4C2411yescharacteristic
940C2×C22⋊C4C2411yescharacteristic
941C2×C22⋊C4C2411yescharacteristic
942C2×C22⋊C4C2414yes—
943C2×C22⋊C4C2414yes—
944C2×C22⋊C4C2414yes—
945C2×C22⋊C4C2412yes—
946C2×C22⋊C4C2412yes—
947C2×C22⋊C4C2412yes—
948C2×C22⋊C4C2412yes—
949C2×C22⋊C4C2414yes—
950C2×C22⋊C4C2414yes—
951C2×C22⋊C4C2414yes—
952C2×C22⋊C4C2412yes—
953C2×C22⋊C4C2414yes—
954C2×C22⋊C4C2414yes—
955C2×C22⋊C4C2412yes—
956C2×C22⋊C4C2412yes—
957C2×C22⋊C4C2412yes—
958C2×C42—28no—
959C2×C42—24no—
960C2×C42—24no—
961C2×C42—24no—
962C2×C42—44no—
963C2×C42C2411yescharacteristic
964C2×C42C2411yescharacteristic
965C2×C42C2411yescharacteristic
966C2×C42C2412yes—
967C2×C42C2412yes—
968C2×C42C2414yes—
969C2×C42C2414yes—
970C2×C42C2414yes—
971C2×C42C2414yes—
972C2×C42C2414yes—
973C2×C42C2414yes—
974C2×C42C2411yescharacteristic
975C2×C42C2411yescharacteristic
976C2×C42C2411yescharacteristic
977C2×C42C2414yes—
978C2×C42C2411yescharacteristic
979C2×C42C2411yescharacteristic
980C2×C42C2411yescharacteristic
981C2×C42C2414yes—
982C2×C42C2412yes—
983C2×C42C2412yes—
984C2×C42C2412yes—
985C2×C42C2412yes—
986C2×C42C2412yes—
987C2×C42C2414yes—
988C2×C42C2414yes—
989C2×C42C2414yes—
990C2×C42C2412yes—
991C2×C42C2414yes—
992C2×C42C2414yes—
993C2×C42C2414yes—
994C2×C42C2414yes—
995C2×C42C2414yes—
996C2×C42C2412yes—
997C2×C42C2411yescharacteristic
998#95C2412yes—
999#95C2412yes—
1000#95C2412yes—
1001#95C2412yes—
1002#95C2411yescharacteristic
1003#95C2412yes—
1004#95C2411yescharacteristic
1005#95C2411yescharacteristic
1006#95C2412yes—
1007#95C2411yescharacteristic
1008#95C2414yes—
1009#95C2412yes—
1010#95C2412yes—
1011#95C2414yes—
1012#95C2414yes—
1013#95C2412yes—
1014#95C2412yes—
1015#95C2412yes—
1016#95C2414yes—
1017#95C2414yes—
1018#95C2414yes—
1019#95C2412yes—
1020#95C2412yes—
1021#95C2414yes—
1022#95C2414yes—
1023#95C2414yes—
1024#95C2414yes—
1025#95C2414yes—
1026#95C2414yes—
1027#95C2414yes—
1028#95C2414yes—
1029#95C2414yes—
1030#95C2414yes—
1031#95C2414yes—
1032#95C2414yes—
1033#95C2414yes—
1034#95C2414yes—
1035#95C2412yes—
1036#95C2414yes—
1037#95C2412yes—
1038#95C2412yes—
1039#95C2414yes—
1040#95C2414yes—
1041#95C2412yes—
1042#95C2414yes—
1043#95C2412yes—
1044#95C2412yes—
1045#95C2414yes—
1046#95C2412yes—
1047#95C2414yes—
1048#95C2414yes—
1049#95C2414yes—
1050#95C2414yes—
1051#95C2414yes—
1052#95C2414yes—
1053#95C2414yes—
1054#95C2414yes—
1055#95C2414yes—
1056#95C2414yes—
1057#95C2414yes—
1058#95C2414yes—
1059#95C2414yes—
1060#95C2414yes—
1061#95C2414yes—
1062#95C2412yes—
1063#95C2412yes—
1064#95C2414yes—
1065#95C2414yes—
1066C24C2511yescharacteristic
1067C24C2512yes—
1068C24C2511yescharacteristic
1069C24C2511yescharacteristic
1070#41—416no—
1071C2×Q8—24no—
1072C2×Q8—24no—
1073C2×Q8—24no—
1074C2×Q8—24no—
1075C2×Q8—24no—
1076C2×Q8—24no—
1077C2×Q8—22no—
1078C2×Q8—24no—
1079C2×Q8—22no—
1080C2×Q8—41no—
1081C2×Q8—44no—
1082C2×Q8—44no—
1083C2×Q8—41no—
1084C2×Q8—42no—
1085C2×Q8—42no—
1086C2×Q8—42no—
1087C2×Q8—44no—
1088C2×Q8—42no—
1089C2×Q8C2×#41116yes—
1090C2×D4—24no—
1091C2×D4—22no—
1092C2×D4—22no—
1093C2×D4—24no—
1094C2×D4—24no—
1095C2×D4—24no—
1096C2×D4—22no—
1097C2×D4—41no—
1098C2×D4—41no—
1099C2×D4—41no—
1100C2×D4—42no—
1101C2×D4—41no—
1102C2×D4—41no—
1103C2×D4—42no—
1104C2×D4—41no—
1105C2×D4—42no—
1106C2×D4—42no—
1107C2×D4—42no—
1108C2×D4—42no—
1109C2×D42−1+414yes—
1110C22×C4—22no—
1111C22×C4—22no—
1112C22×C4—22no—
1113C22×C4—24no—
1114C22×C4—22no—
1115C22×C4—24no—
1116C22×C4—24no—
1117C22×C4—24no—
1118C22×C4—24no—
1119C22×C4—24no—
1120C22×C4—24no—
1121C22×C4—22no—
1122C22×C4—22no—
1123C22×C4—22no—
1124C22×C4—22no—
1125C22×C4—22no—
1126C22×C4—22no—
1127C22×C4—24no—
1128C22×C4—22no—
1129C22×C4—24no—
1130C22×C4—28no—
1131C22×C4—28no—
1132C22×C4—22no—
1133C22×C4—22no—
1134C22×C4—42no—
1135C22×C4—42no—
1136C22×C4—41no—
1137C22×C4—41no—
1138C22×C4—44no—
1139C22×C4—44no—
1140C22×C4—42no—
1141C22×C4—44no—
1142C22×C4—42no—
1143C22×C4—42no—
1144C22×C4—44no—
1145C22×C4—42no—
1146C22×C4C2512yes—
1147C22×C4C2514yes—
1148C22×C4C2514yes—
1149C22×C4C2511yescharacteristic
1150C22×C4C2511yescharacteristic
1151C22×C4C2511yescharacteristic
1152C22×C4C2512yes—
1153C22×C4C2512yes—
1154C22×C4C2514yes—
1155C22×C4C2514yes—
1156C22×C4C2512yes—
1157C22×C4C2511yescharacteristic
1158C22×C4C2511yescharacteristic
1159C22×C4C2511yescharacteristic
1160C22×C4C2514yes—
1161C22×C4C2514yes—
1162C22×C4C2512yes—
1163C22×C4C2511yescharacteristic
1164C22×C4C2512yes—
1165C22×C4C2512yes—
1166C22×C4C2514yes—
1167C22×C4C2514yes—
1168C22×C4C2511yescharacteristic
1169C22×C4C2511yescharacteristic
1170C22×C4C2511yescharacteristic
1171C22×C4C2511yescharacteristic
1172C22×C4C2511yescharacteristic
1173C4⋊C4—24no—
1174C4⋊C4—28no—
1175C4⋊C4—28no—
1176C4⋊C4—24no—
1177C4⋊C4—28no—
1178C4⋊C4—24no—
1179C4⋊C4—24no—
1180C4⋊C4—28no—
1181C4⋊C4—28no—
1182C4⋊C4—28no—
1183C4⋊C4—28no—
1184C4⋊C4—28no—
1185C4⋊C4—28no—
1186C4⋊C4—28no—
1187C4⋊C4—28no—
1188C4⋊C4—28no—
1189C4⋊C4—28no—
1190C4⋊C4—28no—
1191C4⋊C4—24no—
1192C4⋊C4—24no—
1193C4⋊C4—24no—
1194C4⋊C4—24no—
1195C4⋊C4—28no—
1196C4⋊C4—28no—
1197C4⋊C4—24no—
1198C4⋊C4—28no—
1199C4⋊C4—24no—
1200C4⋊C4—42no—
1201C4⋊C4—44no—
1202C4⋊C4—44no—
1203C4⋊C4—44no—
1204C4⋊C4—44no—
1205C4⋊C4—42no—
1206C4⋊C4—44no—
1207C4⋊C4—41no—
1208C4⋊C4—41no—
1209C4⋊C4—41no—
1210C4⋊C4—41no—
1211C4⋊C4—41no—
1212C4⋊C4—41no—
1213C4⋊C4—42no—
1214C4⋊C4—42no—
1215C4⋊C4—42no—
1216C4⋊C4—42no—
1217C4⋊C4—41no—
1218C4⋊C4—42no—
1219C4⋊C4—44no—
1220C4⋊C4—41no—
1221C4⋊C4—44no—
1222C4⋊C4—44no—
1223C4⋊C4—42no—
1224C4⋊C4—42no—
1225C4⋊C4—42no—
1226C4⋊C4—44no—
1227C4⋊C4—44no—
1228C4⋊C4—44no—
1229C4⋊C4—44no—
1230C4⋊C4—44no—
1231C4⋊C4—44no—
1232C4⋊C4—44no—
1233C4⋊C4C2×#4118yes—
1234C4⋊C4C2×#4118yes—
1235C4⋊C4C2×#41116yes—
1236C22⋊C4—24no—
1237C22⋊C4—28no—
1238C22⋊C4—28no—
1239C22⋊C4—28no—
1240C22⋊C4—28no—
1241C22⋊C4—28no—
1242C22⋊C4—28no—
1243C22⋊C4—28no—
1244C22⋊C4—28no—
1245C22⋊C4—24no—
1246C22⋊C4—24no—
1247C22⋊C4—24no—
1248C22⋊C4—24no—
1249C22⋊C4—28no—
1250C22⋊C4—28no—
1251C22⋊C4—24no—
1252C22⋊C4—24no—
1253C22⋊C4—24no—
1254C22⋊C4—24no—
1255C22⋊C4—44no—
1256C22⋊C4—42no—
1257C22⋊C4—42no—
1258C22⋊C4—44no—
1259C22⋊C4—44no—
1260C22⋊C4—42no—
1261C22⋊C4—42no—
1262C22⋊C4—44no—
1263C22⋊C4—41no—
1264C22⋊C4—41no—
1265C22⋊C4—41no—
1266C22⋊C4—41no—
1267C22⋊C4—41no—
1268C22⋊C4—41no—
1269C22⋊C4—44no—
1270C22⋊C4—44no—
1271C22⋊C4—42no—
1272C22⋊C4—42no—
1273C22⋊C4—42no—
1274C22⋊C4—42no—
1275C22⋊C4—44no—
1276C22⋊C4—44no—
1277C42—24no—
1278C42—24no—
1279C42—24no—
1280C42—28no—
1281C42—28no—
1282C42—28no—
1283C42—28no—
1284C42—28no—
1285C42—28no—
1286C42—22no—
1287C42—22no—
1288C42—22no—
1289C42—22no—
1290C42—22no—
1291C42—22no—
1292C42—22no—
1293C42—22no—
1294C42—22no—
1295C42—24no—
1296C42—28no—
1297C42—28no—
1298C42—24no—
1299C42—24no—
1300C42—24no—
1301C42—44no—
1302C42—44no—
1303C42—44no—
1304C42—44no—
1305C42—44no—
1306C42—44no—
1307C42—44no—
1308C42—44no—
1309C42—42no—
1310C42C2×#4118yes—
1311C42H(5,𝔽2)14yes—
1312C23—22no—
1313C23—22no—
1314C23—21no—
1315C23—21no—
1316C23—21no—
1317C23—21no—
1318C23—22no—
1319C23—22no—
1320C23—22no—
1321C23—22no—
1322C23—22no—
1323C23—22no—
1324C23—21no—
1325C23—22no—
1326C23—21no—
1327C23—22no—
1328C23—21no—
1329C23—22no—
1330C23—22no—
1331C23—22no—
1332C23C2×2−1+412yes—
1333C23C2×2−1+412yes—
1334C23C2611yescharacteristic
1335Q8—416no—
1336Q8—44no—
1337Q8—48no—
1338Q8—48no—
1339Q8—84no—
1340Q8—82no—
1341Q8—84no—
1342D4—44no—
1343D4—48no—
1344D4—44no—
1345D4—44no—
1346D4—84no—
1347D4—84no—
1348D4—82no—
1349C2×C4—28no—
1350C2×C4—21no—
1351C2×C4—21no—
1352C2×C4—22no—
1353C2×C4—21no—
1354C2×C4—21no—
1355C2×C4—24no—
1356C2×C4—21no—
1357C2×C4—24no—
1358C2×C4—22no—
1359C2×C4—21no—
1360C2×C4—22no—
1361C2×C4—24no—
1362C2×C4—22no—
1363C2×C4—24no—
1364C2×C4—22no—
1365C2×C4—22no—
1366C2×C4—24no—
1367C2×C4—22no—
1368C2×C4—22no—
1369C2×C4—22no—
1370C2×C4—22no—
1371C2×C4—24no—
1372C2×C4—24no—
1373C2×C4—24no—
1374C2×C4—24no—
1375C2×C4—24no—
1376C2×C4—22no—
1377C2×C4—22no—
1378C2×C4—21no—
1379C2×C4—21no—
1380C2×C4—21no—
1381C2×C4—21no—
1382C2×C4—21no—
1383C2×C4—21no—
1384C2×C4—21no—
1385C2×C4—22no—
1386C2×C4—22no—
1387C2×C4—24no—
1388C2×C4—24no—
1389C2×C4—24no—
1390C2×C4—24no—
1391C2×C4—22no—
1392C2×C4—24no—
1393C2×C4—22no—
1394C2×C4—24no—
1395C2×C4—22no—
1396C2×C4—21no—
1397C2×C4—24no—
1398C2×C4—22no—
1399C2×C4—22no—
1400C2×C4—24no—
1401C2×C4—21no—
1402C2×C4—24no—
1403C2×C4—22no—
1404C2×C4—24no—
1405C2×C4—22no—
1406C2×C4—24no—
1407C2×C4—22no—
1408C2×C4—22no—
1409C2×C4—24no—
1410C2×C4—22no—
1411C2×C4—22no—
1412C2×C4—22no—
1413C2×C4—44no—
1414C2×C4—48no—
1415C2×C4—44no—
1416C2×C4—44no—
1417C2×C4—44no—
1418C2×C4—44no—
1419C2×C4—48no—
1420C2×C4—44no—
1421C2×C4—84no—
1422C2×C4—88no—
1423C2×C4—88no—
1424C2×C4—82no—
1425C2×C4—82no—
1426C2×C4C22×#4114yes—
1427C2×C4C22×#4114yes—
1428C2×C4C22×#4118yes—
1429C2×C4C22×#4118yes—
1430C2×C4C22×#4114yes—
1431C2×C4C2×H(5,𝔽2)12yes—
1432C2×C4C2×H(5,𝔽2)12yes—
1433C2×C4C2×H(5,𝔽2)12yes—
1434C2×C4C2×2−1+412yes—
1435C2×C4#58512yes—
1436C22—24no—
1437C22—24no—
1438C22—22no—
1439C22—22no—
1440C22—42no—
1441C22—42no—
1442C22—41no—
1443C22—41no—
1444C22—41no—
1445C22—41no—
1446C22—42no—
1447C22—42no—
1448C22—42no—
1449C22—42no—
1450C22—42no—
1451C22—42no—
1452C22—41no—
1453C22—42no—
1454C22—41no—
1455C22—42no—
1456C22—41no—
1457C22—42no—
1458C22C23×#4112yes—
1459C22C22×H(5,𝔽2)11yescharacteristic
1460C22C22×2−1+411yescharacteristic
1461C22C2×#58511yescharacteristic
1462C222−1+612yes—
1463C4—24no—
1464C4—28no—
1465C4—28no—
1466C4—24no—
1467C4—22no—
1468C4—22no—
1469C4—22no—
1470C4—22no—
1471C4—42no—
1472C4—44no—
1473C4—44no—
1474C4—42no—
1475C4—41no—
1476C4—42no—
1477C4—44no—
1478C4—41no—
1479C4—41no—
1480C4—41no—
1481C4—42no—
1482C4—44no—
1483C4—41no—
1484C4—42no—
1485C4—41no—
1486C4—41no—
1487C4—44no—
1488C4—44no—
1489C4#348314yes—
1490C2—42no—
1491C2—42no—
1492C2—82no—
1493C2—81no—
1494C2C2×#348311yescharacteristic
1495C2#6281911yescharacteristic
1496C2#6288611yescharacteristic
1497C2#6299112yes—
1498C2#6299812yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#34876C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59991C2semidirect
2. #59928C2semidirect
3. #59537C2semidirect
4. #59501C2semidirect
5. #59361C2semidirect
6. #59262C2semidirect
7. #59237C2semidirect
8. #59231C2semidirect
9. #59055C2semidirect
10. #59052C2semidirect
11. #45436C2semidirect
12. #45410C2semidirect
13. #45384C2semidirect
14. #45364C2semidirect
15. #45170C2semidirect
16. #45138C2semidirect
17. #44716C2semidirect
18. #44657C2semidirect
19. #44591C2semidirect
20. #43883C2semidirect
21. #43832C2semidirect
22. #43788C2semidirect
23. #35637C2semidirect
24. #35637C2semidirect
25. #35635C2semidirect
26. #34979C2semidirect
27. #34947C2semidirect
29. #34307C2semidirect
30. #34299C2semidirect
31. #34221C2semidirect
780. C4⋊Q8#41semidirect

Maximal subgroups

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

subgroupindex
#599912
#599282
#595372
#595012
#593612
#592622
#592372
#592312
#590552
#590522
#454362
#454102
#453842
#453642
#451702
#451382
#447162
#446572
#445912
#438832
#438322
#437882
#356372
#356352
#349792
#349472
#348762
#343072
#342992
#342212