Finite Group Databasebeta

← #7660761

Subgroups — #7660761

Order 512.

4740 conjugacy classes of subgroups.

The subgroup lattice has 1463 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#52291C212yesmaximal, complemented
2#52279C211yesmaximal, characteristic, complemented
3#42864C212yesmaximal, complemented
4#42847C212yesmaximal, complemented
5#42787C212yesmaximal, complemented
6#42126C214yesmaximal, complemented
7#42088C214yesmaximal, complemented
8#42046C214yesmaximal, complemented
9#40269C214yesmaximal, complemented
10#40119C212yesmaximal, complemented
11#39711C212yesmaximal, complemented
12#39659C212yesmaximal, complemented
13#39624C211yesmaximal, characteristic, complemented
14#39615C211yesmaximal, characteristic, complemented
15#38800C212yesmaximal, complemented
16#38700C214yesmaximal, complemented
17#37338C212yesmaximal, complemented
18#37323C211yesmaximal, characteristic, complemented
19#37212C212yesmaximal, complemented
20#37206C214yesmaximal, complemented
21#36545C212yesmaximal, complemented
22#36505C211yesmaximal, characteristic, complemented
23#36422C212yesmaximal, complemented
24#36404C211yesmaximal, characteristic
25#35993C212yesmaximal, complemented
26#35919C212yesmaximal, complemented
27#35869C212yesmaximal, complemented
28#34291C212yesmaximal, complemented
29#34268C211yesmaximal, characteristic, complemented
30C2×#557C2211yescharacteristic
31C2×D4×Q8C2212yes—
32C2×#547C2211yescharacteristic
33C2×#536C2211yescharacteristic
34C2×#519C2211yescharacteristic
35C2×C4×#41C2211yescharacteristic
36C22×C4×Q8C2212yes—
37#2857C2211yescharacteristic
38#2857C2211yescharacteristic
39#2857C2212yes—
40#2855C2212yes—
41#2854C2212yes—
42#2853C2214yes—
43#2851C2214yes—
44#2851C2212yes—
45#2839C2214yes—
46#2831C2214yes—
47#2814C2214yes—
48#2811C2212yes—
49#2810C2211yescharacteristic
50#2810C2212yes—
51#2809C2211yescharacteristic
52#2809C2214yes—
53#2809C2212yes—
54#2806C2214yes—
55#2806C2212yes—
56#2805C2212yes—
57#2805C2214yes—
58#2789C2214yes—
59#2788C2214yes—
60#2788C2214yes—
61#2788C2214yes—
62#2787C2212yes—
63#2787C2212yes—
64#2787C2214yes—
65#2786C2214yes—
66#2784C2214yes—
67#2784C2214yes—
68#2784C2214yes—
69#2783C2214yes—
70#2781C2214yes—
71#2779C2214yes—
72#2778C2214yes—
73#2776C2214yes—
74#2771C2212yes—
75#2767C2214yes—
76#2759C2214yes—
77#2750C2212yes—
78#2747C2214yes—
79#2745C2214yes—
80#2744C2214yes—
81#2734C2212yes—
82#2732C2214yes—
83#2732C2211yescharacteristic
84#2732C2214yes—
85#2732C2212yes—
86#2729C2214yes—
87#2729C2214yes—
88#2729C2214yes—
89#2728C2214yes—
90#2728C2212yes—
91#2726C2212yes—
92#2724C2211yescharacteristic
93#2708C2212yes—
94#2702C2214yes—
95#2696C2214yes—
96#2695C2214yes—
97#2690C2214yes—
98#2666C2214yes—
99#2665C2214yes—
100#2665C2214yes—
101#2664C2214yes—
102#2663C2214yes—
103#2659C2212yes—
104#2659C2212yes—
105#2655C2214yes—
106#2655C2214yes—
107#2655C2214yes—
108#2653C2214yes—
109#2650C2214yes—
110#2645C2212yes—
111#2640C2212yes—
112#2630C2214yes—
113#2625C2212yes—
114#2602C2214yes—
115#2596C2214yes—
116#2588C2214yes—
117#2588C2214yes—
118#2587C2214yes—
119#2586C2214yes—
120#2584C2214yes—
121#2582C2212yes—
122#2581C2214yes—
123#2578C2214yes—
124#2577C2214yes—
125#2576C2214yes—
126#2575C2214yes—
127#2574C2214yes—
128#2568C2211yescharacteristic
129#2567C2212yes—
130#2564C2214yes—
131#2562C2212yes—
132#2558C2214yes—
133#2553C2214yes—
134#2549C2214yes—
135#2547C2211yescharacteristic
136#2546C2212yes—
137#2545C2212yes—
138#2538C2211yescharacteristic
139#2538C2211yescharacteristic
140#2536C2212yes—
141#2530C2214yes—
142#2529C2214yes—
143#2528C2214yes—
144#2527C2214yes—
145#2520C2214yes—
146#2515C2214yes—
147#2514C2212yes—
148#2512C2212yes—
149#2511C2212yes—
150#2508C2212yes—
151#2506C2212yes—
152#2497C2212yes—
153#2492C2212yes—
154#2492C2212yes—
155#2478C2214yes—
156#2477C2214yes—
157#2475C2214yes—
158#2475C2214yes—
159#2473C2214yes—
160#2473C2214yes—
161#2470C2214yes—
162#2469C2214yes—
163#2465C2214yes—
164#2465C2214yes—
165#2462C2214yes—
166#2462C2214yes—
167#2460C2214yes—
168#2458C2214yes—
169#2458C2214yes—
170#2457C2214yes—
171#2453C2214yes—
172#2451C2212yes—
173#2451C2212yes—
174#2451C2212yes—
175#2448C2212yes—
176#2446C2212yes—
177#2446C2212yes—
178#2446C2212yes—
179#2446C2212yes—
180#2446C2212yes—
181#2440C2212yes—
182#2436C2212yes—
183#2434C2212yes—
184#2434C2212yes—
185#2432C2212yes—
186#2429C2212yes—
187#2426C2212yes—
188#2426C2212yes—
189#2423C2212yes—
190#2421C2214yes—
191#2420C2212yes—
192#2417C2212yes—
193#2415C2212yes—
194#2413C2214yes—
195#2409C2212yes—
196#2407C2212yes—
197#2407C2212yes—
198#2406C2214yes—
199#2402C2212yes—
200#2401C2212yes—
201#2396C2214yes—
202#2396C2214yes—
203#2396C2214yes—
204#2395C2212yes—
205#2367C2212yes—
206#2367C2212yes—
207#2367C2212yes—
208#2365C2212yes—
209#2365C2212yes—
210#2365C2214yes—
211#2365C2212yes—
212#2365C2212yes—
213#2362C2214yes—
214#2362C2212yes—
215#2360C2212yes—
216#2360C2212yes—
217#2360C2212yes—
218#2360C2214yes—
219#2359C2214yes—
220#2359C2214yes—
221#2355C2212yes—
222#2355C2211yescharacteristic
223#2354C2211yescharacteristic
224#2352C2214yes—
225#2352C2212yes—
226#2351C2212yes—
227#2344C2212yes—
228Q8×C22⋊C4C2212yes—
229Q8×C22⋊C4C2212yes—
230#2335C2214yes—
231#2332C2214yes—
232#2329C2212yes—
233#2327C2214yes—
234#2327C2212yes—
235#2325C2212yes—
236#2323C2214yes—
237#2323C2212yes—
238#2323C2212yes—
239#2323C2212yes—
240#2311C2211yescharacteristic
241C4×C22⋊Q8C2212yes—
242C4×C22⋊Q8C2212yes—
243C4×C22⋊Q8C2211yescharacteristic
244C4×C22⋊Q8C2212yes—
245C4×C22⋊Q8C2214yes—
246C4×C22⋊Q8C2214yes—
247C4×C22⋊Q8C2212yes—
248C4×C22⋊Q8C2212yes—
249C4×#123C2212yes—
250C4×#121C2211yescharacteristic
251#2297C2214yes—
252#2297C2212yes—
253#2296C2211yescharacteristic
254C2×#391C2211yescharacteristic
255#2290C2214yes—
256#2290C2212yes—
257#2276C2212yes—
258#2274C2211yescharacteristic
259C22×#41C2311yescharacteristic
260C22×#41C2312yes—
261C23×Q8C2312yes—
262C23×Q8C2311yescharacteristic
263#557—44no—
264D4×Q8—216no—
265#547—44no—
266#536—28no—
267C2×C4⋊Q8C2312yes—
268C2×C4⋊Q8C2314yes—
269C2×C4⋊Q8C2312yes—
270C2×C4⋊Q8C2312yes—
271C2×C4⋊Q8C2311yescharacteristic
272C2×C4⋊Q8C2312yes—
273C2×C4⋊Q8C2311yescharacteristic
274C2×#126C2314yes—
275C2×#125C2312yes—
276C2×#125C2314yes—
277C2×#125C2314yes—
278C2×#124C2312yes—
279C2×#124C2312yes—
280C2×#123C2312yes—
281C2×#123C2314yes—
282C2×#123C2314yes—
283C2×#123C2314yes—
284C2×C22⋊Q8C2314yes—
285C2×C22⋊Q8C2312yes—
286C2×C22⋊Q8C2312yes—
287C2×C22⋊Q8C2312yes—
288C2×C22⋊Q8C2311yescharacteristic
289C2×C22⋊Q8C2312yes—
290C2×C22⋊Q8C2312yes—
291C2×C22⋊Q8C2314yes—
292C2×C22⋊Q8C2312yes—
293C2×C22⋊Q8C2312yes—
294C2×C22⋊Q8C2312yes—
295C2×C22⋊Q8C2312yes—
296C2×C22⋊Q8C2312yes—
297C2×C22⋊Q8C2314yes—
298C2×#121C2311yescharacteristic
299C2×#121C2312yes—
300#519—44no—
301C4×#41—44no—
302C2×C4×Q8—48no—
303C2×C4×Q8C2312yes—
304C2×C4×Q8C2311yescharacteristic
305C2×C4×Q8C2312yes—
306C2×C4×Q8C2312yes—
307C2×C4×Q8C2312yes—
308C2×C4×Q8C2311yescharacteristic
309C2×C4×Q8C2312yes—
310C2×C4×Q8C2312yes—
311C2×C4×Q8C2314yes—
312C2×C4×Q8C2312yes—
313C2×C4×Q8C2312yes—
314C2×C4×Q8C2314yes—
315C2×C4×Q8C2311yescharacteristic
316C2×C4×Q8C2312yes—
317C2×C4×Q8C2312yes—
318C2×C4×Q8C2314yes—
319C2×C4×D4C2314yes—
320C2×C4×D4C2312yes—
321C2×C4×D4C2311yescharacteristic
322C2×C4×D4C2312yes—
323C2×C4×D4C2312yes—
324C2×C4×D4C2311yescharacteristic
325C2×C4×D4C2311yescharacteristic
326C2×#117C2311yescharacteristic
327C2×#117C2311yescharacteristic
328C2×#117C2311yescharacteristic
329C2×#117C2312yes—
330C2×#117C2314yes—
331C2×#117C2314yes—
332C2×#117C2312yes—
333C22×C4⋊C4C2312yes—
334C22×C4⋊C4C2311yescharacteristic
335C22×C4⋊C4C2314yes—
336C22×C42C2314yes—
337C22×C42C2312yes—
338C22×C42C2312yes—
339C22×C42C2311yescharacteristic
340#401C2314yes—
341#401C2314yes—
342#401C2312yes—
343#400C2314yes—
344#400C2314yes—
345#400C2314yes—
346#400C2314yes—
347#400C2314yes—
348#400C2312yes—
349#400C2314yes—
350#400C2314yes—
351#400C2314yes—
352#400C2314yes—
353#400C2312yes—
354#400C2314yes—
355#400C2314yes—
356#400C2312yes—
357#400C2312yes—
358#400C2314yes—
359#400C2314yes—
360#400C2312yes—
361#400C2314yes—
362#400C2312yes—
363#400C2314yes—
364#400C2314yes—
365#400C2314yes—
366#400C2314yes—
367#400C2312yes—
368#400C2312yes—
369#399C2314yes—
370#399C2314yes—
371#399C2312yes—
372#398C2312yes—
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#398C2312yes—
387#398C2312yes—
388#398C2314yes—
389#398C2314yes—
390#398C2314yes—
391#398C2314yes—
392#398C2314yes—
393#398C2312yes—
394#398C2312yes—
395#398C2314yes—
396#397C2312yes—
397#397C2314yes—
398#397C2314yes—
399#397C2314yes—
400#397C2314yes—
401#397C2312yes—
402#397C2314yes—
403#397C2314yes—
404#397C2314yes—
405#397C2314yes—
406#397C2312yes—
407#397C2312yes—
408#397C2312yes—
409#397C2312yes—
410#396C2314yes—
411#396C2314yes—
412#396C2314yes—
413#396C2314yes—
414#396C2314yes—
415#396C2314yes—
416#396C2312yes—
417#396C2314yes—
418#396C2314yes—
419#396C2314yes—
420#396C2314yes—
421#395C2314yes—
422#395C2314yes—
423#395C2314yes—
424#395C2314yes—
425#395C2314yes—
426#395C2314yes—
427#395C2314yes—
428#395C2314yes—
429#395C2314yes—
430#395C2314yes—
431#395C2314yes—
432#394C2314yes—
433#394C2312yes—
434#394C2314yes—
435#394C2314yes—
436#394C2312yes—
437#394C2314yes—
438#394C2314yes—
439#394C2314yes—
440#393C2314yes—
441#393C2314yes—
442#393C2314yes—
443#393C2314yes—
444#393C2314yes—
445#393C2314yes—
446#393C2314yes—
447#392C2314yes—
448#391C2312yes—
449#391C2312yes—
450#391C2312yes—
451#391C2312yes—
452#391C2312yes—
453#391C2312yes—
454#391C2314yes—
455#391C2314yes—
456#391C2312yes—
457#391C2312yes—
458#391C2312yes—
459#391C2314yes—
460#391C2312yes—
461#391C2312yes—
462#391C2314yes—
463#391C2312yes—
464#391C2314yes—
465#391C2314yes—
466#391C2314yes—
467#391C2314yes—
468#391C2314yes—
469#391C2312yes—
470#391C2312yes—
471#391C2312yes—
472#391C2312yes—
473#391C2312yes—
474#391C2312yes—
475#391C2314yes—
476#391C2314yes—
477#391C2312yes—
478#391C2311yescharacteristic
479#390C2312yes—
480#390C2312yes—
481#390C2312yes—
482#390C2314yes—
483#390C2312yes—
484#390C2314yes—
485#390C2311yescharacteristic
486#389C2314yes—
487#389C2314yes—
488#389C2311yescharacteristic
489#389C2311yescharacteristic
490#389C2314yes—
491#389C2314yes—
492#389C2314yes—
493#389C2314yes—
494#389C2312yes—
495#389C2314yes—
496#389C2314yes—
497#389C2314yes—
498#389C2314yes—
499#389C2314yes—
500#389C2312yes—
501#389C2312yes—
502#389C2312yes—
503#389C2314yes—
504#389C2314yes—
505#389C2314yes—
506#389C2312yes—
507#389C2314yes—
508#389C2311yescharacteristic
509#389C2312yes—
510#389C2311yescharacteristic
511#389C2312yes—
512#389C2312yes—
513#389C2314yes—
514#389C2312yes—
515#389C2312yes—
516#389C2312yes—
517#389C2314yes—
518#389C2312yes—
519#389C2312yes—
520#389C2311yescharacteristic
521#389C2311yescharacteristic
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#388C2312yes—
535#388C2314yes—
536#388C2314yes—
537#388C2314yes—
538#388C2314yes—
539#388C2314yes—
540#388C2312yes—
541#388C2314yes—
542#388C2314yes—
543#388C2314yes—
544#388C2314yes—
545#388C2314yes—
546#388C2314yes—
547#388C2314yes—
548#388C2314yes—
549#388C2312yes—
550#388C2314yes—
551#388C2312yes—
552#388C2312yes—
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#387C2312yes—
576#387C2314yes—
577#387C2314yes—
578#387C2314yes—
579#387C2314yes—
580#387C2314yes—
581#387C2314yes—
582#387C2312yes—
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#387C2312yes—
598#387C2314yes—
599#387C2314yes—
600#387C2312yes—
601#387C2312yes—
602#387C2312yes—
603#387C2312yes—
604#386C2312yes—
605#386C2314yes—
606#386C2314yes—
607#386C2314yes—
608#386C2314yes—
609#386C2314yes—
610#386C2314yes—
611#386C2314yes—
612#386C2312yes—
613#386C2314yes—
614#386C2314yes—
615#386C2312yes—
616#386C2312yes—
617#385C2314yes—
618#385C2314yes—
619#385C2314yes—
620#385C2314yes—
621#385C2314yes—
622#385C2314yes—
623#385C2314yes—
624#385C2314yes—
625#385C2314yes—
626#385C2314yes—
627#385C2314yes—
628#385C2314yes—
629#385C2312yes—
630#385C2314yes—
631#385C2312yes—
632#385C2312yes—
633#385C2314yes—
634#385C2312yes—
635#385C2314yes—
636#385C2312yes—
637#385C2312yes—
638#385C2312yes—
639#385C2314yes—
640#385C2312yes—
641#384C2311yescharacteristic
642#384C2312yes—
643#384C2311yescharacteristic
644#383C2314yes—
645#382C2312yes—
646#382C2314yes—
647#382C2312yes—
648#382C2314yes—
649#382C2314yes—
650#381C2314yes—
651#381C2314yes—
652#381C2312yes—
653#380C2311yescharacteristic
654#380C2312yes—
655#380C2312yes—
656#380C2312yes—
657#380C2314yes—
658#380C2312yes—
659#380C2312yes—
660#380C2312yes—
661#380C2312yes—
662#380C2312yes—
663#380C2314yes—
664#380C2312yes—
665#380C2312yes—
666#380C2314yes—
667#380C2312yes—
668#380C2314yes—
669#380C2312yes—
670#380C2314yes—
671#380C2312yes—
672#380C2311yescharacteristic
673C4×C4⋊C4C2312yes—
674C4×C4⋊C4C2312yes—
675C4×C4⋊C4C2311yescharacteristic
676C4×C4⋊C4C2314yes—
677C4×C4⋊C4C2314yes—
678C4×C4⋊C4C2314yes—
679C4×C4⋊C4C2314yes—
680C4×C4⋊C4C2312yes—
681C4×C4⋊C4C2312yes—
682C4×C4⋊C4C2312yes—
683C4×C4⋊C4C2314yes—
684C4×C4⋊C4C2314yes—
685C4×C4⋊C4C2314yes—
686C4×C4⋊C4C2312yes—
687C4×C4⋊C4C2312yes—
688C4×C4⋊C4C2312yes—
689C4×C4⋊C4C2312yes—
690C4×C4⋊C4C2312yes—
691C4×C4⋊C4C2311yescharacteristic
692C4×C4⋊C4C2314yes—
693C4×C4⋊C4C2314yes—
694C4×C4⋊C4C2314yes—
695C4×C4⋊C4C2312yes—
696C4×C4⋊C4C2312yes—
697C4×C4⋊C4C2312yes—
698C4×C4⋊C4C2312yes—
699C4×C22⋊C4C2314yes—
700C4×C22⋊C4C2314yes—
701C4×C22⋊C4C2314yes—
702C4×C22⋊C4C2314yes—
703C4×C22⋊C4C2314yes—
704C4×C22⋊C4C2314yes—
705C4×C22⋊C4C2314yes—
706C4×C22⋊C4C2314yes—
707C4×C22⋊C4C2312yes—
708C4×C22⋊C4C2312yes—
709C4×C22⋊C4C2312yes—
710C4×C22⋊C4C2314yes—
711C4×C22⋊C4C2314yes—
712C4×C22⋊C4C2314yes—
713C4×C22⋊C4C2312yes—
714C4×C22⋊C4C2312yes—
715#376C2312yes—
716#376C2314yes—
717C2×#95C2312yes—
718C2×#95C2312yes—
719C2×#41—28no—
720C2×#41—24no—
721C2×#41—44no—
722C2×#41—42no—
723C2×#41—42no—
724C2×#41—82no—
725C22×Q8—28no—
726C22×Q8—44no—
727C22×Q8—42no—
728C22×Q8—42no—
729C22×Q8—44no—
730C22×Q8#4118yescomplemented
731C22×Q8C2412yes—
732C22×Q8C2411yescharacteristic
733C22×Q8C2412yes—
734C22×Q8C2414yes—
735C22×Q8C2412yes—
736C22×Q8C2414yes—
737C22×Q8C2412yes—
738C22×Q8C2411yescharacteristic
739C22×D4C2411yescharacteristic
740C22×D4C2412yes—
741C22×D4C2412yes—
742C22×D4C2414yes—
743C22×D4C2411yescharacteristic
744C23×C4C2412yes—
745C23×C4C2414yes—
746C23×C4C2412yes—
747C23×C4C2411yescharacteristic
748C23×C4C2412yes—
749C23×C4C2414yes—
750C23×C4C2412yes—
751C23×C4C2411yescharacteristic
752C23×C4C2411yescharacteristic
753C23×C4C2412yes—
754C23×C4C2412yes—
755C23×C4C2412yes—
756C23×C4C2412yes—
757C4⋊Q8—28no—
758C4⋊Q8—28no—
759C4⋊Q8—216no—
760C4⋊Q8—44no—
761C4⋊Q8—42no—
762C4⋊Q8—42no—
763C4⋊Q8—44no—
764#126—84no—
765#125—44no—
766#125—48no—
767#125—84no—
768#124—28no—
769#124—44no—
770#123—28no—
771#123—216no—
772#123—48no—
773#123—84no—
774C22⋊Q8—28no—
775C22⋊Q8—28no—
776C22⋊Q8—28no—
777C22⋊Q8—216no—
778C22⋊Q8—28no—
779C22⋊Q8—24no—
780C22⋊Q8—28no—
781C22⋊Q8—28no—
782C22⋊Q8—216no—
783C22⋊Q8—44no—
784C22⋊Q8—44no—
785C22⋊Q8—44no—
786C22⋊Q8—84no—
787C22⋊Q8—82no—
788#121—24no—
789#121—44no—
790C4×Q8—28no—
791C4×Q8—28no—
792C4×Q8—28no—
793C4×Q8—24no—
794C4×Q8—44no—
795C4×Q8—44no—
796C4×Q8—42no—
797C4×Q8—48no—
798C4×Q8—48no—
799C4×Q8—44no—
800C4×Q8—44no—
801C4×Q8—44no—
802C4×Q8—44no—
803C4×Q8—42no—
804C4×Q8—44no—
805C4×Q8—84no—
806C4×D4—28no—
807C4×D4—216no—
808C4×D4—24no—
809C4×D4—44no—
810C4×D4—42no—
811C4×D4—42no—
812C4×D4—44no—
813#117—24no—
814#117—24no—
815#117—42no—
816#117—44no—
817#117—48no—
818#117—84no—
819#117—82no—
820C2×C4⋊C4—28no—
821C2×C4⋊C4—42no—
822C2×C4⋊C4—48no—
823C2×C4⋊C4C2414yes—
824C2×C4⋊C4C2412yes—
825C2×C4⋊C4C2414yes—
826C2×C4⋊C4C2414yes—
827C2×C4⋊C4C2412yes—
828C2×C4⋊C4C2411yescharacteristic
829C2×C4⋊C4C2412yes—
830C2×C4⋊C4C2411yescharacteristic
831C2×C4⋊C4C2411yescharacteristic
832C2×C4⋊C4C2412yes—
833C2×C4⋊C4C2414yes—
834C2×C4⋊C4C2412yes—
835C2×C4⋊C4C2414yes—
836C2×C4⋊C4C2412yes—
837C2×C4⋊C4C2411yescharacteristic
838C2×C4⋊C4C2414yes—
839C2×C4⋊C4C2414yes—
840C2×C4⋊C4C2414yes—
841C2×C4⋊C4C2414yes—
842C2×C4⋊C4C2414yes—
843C2×C4⋊C4C2412yes—
844C2×C4⋊C4C2414yes—
845C2×C4⋊C4C2412yes—
846C2×C4⋊C4C2412yes—
847C2×C4⋊C4C2411yescharacteristic
848C2×C4⋊C4C2412yes—
849C2×C4⋊C4C2412yes—
850C2×C4⋊C4C2412yes—
851C2×C4⋊C4C2412yes—
852C2×C4⋊C4C2414yes—
853C2×C4⋊C4C2414yes—
854C2×C4⋊C4C2412yes—
855C2×C4⋊C4C2411yescharacteristic
856C2×C4⋊C4C2412yes—
857C2×C4⋊C4C2411yescharacteristic
858C2×C4⋊C4C2411yescharacteristic
859C2×C4⋊C4C2414yes—
860C2×C4⋊C4C2412yes—
861C2×C4⋊C4C2414yes—
862C2×C4⋊C4C2414yes—
863C2×C4⋊C4C2411yescharacteristic
864C2×C4⋊C4C2412yes—
865C2×C4⋊C4C2411yescharacteristic
866C2×C4⋊C4C2412yes—
867C2×C4⋊C4C2412yes—
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⋊C4C2412yes—
878C2×C4⋊C4C2414yes—
879C2×C4⋊C4C2414yes—
880C2×C4⋊C4C2412yes—
881C2×C4⋊C4C2412yes—
882C2×C4⋊C4C2412yes—
883C2×C4⋊C4C2412yes—
884C2×C4⋊C4C2414yes—
885C2×C4⋊C4C2411yescharacteristic
886C2×C4⋊C4C2412yes—
887C2×C4⋊C4C2414yes—
888C2×C4⋊C4C2412yes—
889C2×C4⋊C4C2412yes—
890C2×C4⋊C4C2412yes—
891C2×C4⋊C4C2411yescharacteristic
892C2×C22⋊C4C2412yes—
893C2×C22⋊C4C2412yes—
894C2×C22⋊C4C2412yes—
895C2×C22⋊C4C2412yes—
896C2×C22⋊C4C2414yes—
897C2×C22⋊C4C2414yes—
898C2×C22⋊C4C2412yes—
899C2×C22⋊C4C2412yes—
900C2×C22⋊C4C2414yes—
901C2×C22⋊C4C2414yes—
902C2×C22⋊C4C2412yes—
903C2×C22⋊C4C2412yes—
904C2×C22⋊C4C2412yes—
905C2×C22⋊C4C2414yes—
906C2×C22⋊C4C2412yes—
907C2×C22⋊C4C2412yes—
908C2×C22⋊C4C2412yes—
909C2×C22⋊C4C2412yes—
910C2×C22⋊C4C2412yes—
911C2×C22⋊C4C2412yes—
912C2×C22⋊C4C2414yes—
913C2×C22⋊C4C2414yes—
914C2×C22⋊C4C2412yes—
915C2×C22⋊C4C2414yes—
916C2×C22⋊C4C2414yes—
917C2×C22⋊C4C2412yes—
918C2×C22⋊C4C2414yes—
919C2×C22⋊C4C2414yes—
920C2×C22⋊C4C2414yes—
921C2×C22⋊C4C2414yes—
922C2×C22⋊C4C2414yes—
923C2×C22⋊C4C2414yes—
924C2×C22⋊C4C2414yes—
925C2×C22⋊C4C2412yes—
926C2×C22⋊C4C2414yes—
927C2×C22⋊C4C2414yes—
928C2×C42—48no—
929C2×C42—44no—
930C2×C42—44no—
931C2×C42—42no—
932C2×C42C2412yes—
933C2×C42C2414yes—
934C2×C42C2412yes—
935C2×C42C2412yes—
936C2×C42C2411yescharacteristic
937C2×C42C2412yes—
938C2×C42C2411yescharacteristic
939C2×C42C2412yes—
940C2×C42C2414yes—
941C2×C42C2414yes—
942C2×C42C2412yes—
943C2×C42C2412yes—
944C2×C42C2411yescharacteristic
945C2×C42C2414yes—
946C2×C42C2414yes—
947C2×C42C2414yes—
948C2×C42C2414yes—
949C2×C42C2412yes—
950C2×C42C2414yes—
951C2×C42C2412yes—
952C2×C42C2414yes—
953C2×C42C2412yes—
954C2×C42C2414yes—
955C2×C42C2414yes—
956C2×C42C2414yes—
957C2×C42C2411yescharacteristic
958#95C2414yes—
959#95C2414yes—
960#95C2414yes—
961#95C2414yes—
962#95C2412yes—
963#95C2414yes—
964#95C2414yes—
965#95C2412yes—
966#95C2414yes—
967#95C2412yes—
968#95C2412yes—
969#95C2412yes—
970#95C2412yes—
971#95C2412yes—
972#95C2414yes—
973#95C2412yes—
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#95C2412yes—
987#95C2412yes—
988#95C2414yes—
989#95C2414yes—
990#95C2412yes—
991#95C2414yes—
992#95C2414yes—
993#95C2412yes—
994#95C2412yes—
995#95C2414yes—
996#95C2414yes—
997#95C2412yes—
998#95C2412yes—
999#95C2412yes—
1000#95C2414yes—
1001#95C2414yes—
1002#95C2414yes—
1003#95C2414yes—
1004#95C2414yes—
1005#95C2412yes—
1006#95C2412yes—
1007#95C2414yes—
1008#95C2412yes—
1009#95C2414yes—
1010#95C2412yes—
1011#95C2412yes—
1012#95C2412yes—
1013#95C2412yes—
1014#95C2414yes—
1015#95C2414yes—
1016#95C2412yes—
1017#95C2412yes—
1018#95C2412yes—
1019#95C2414yes—
1020#95C2414yes—
1021#95C2414yes—
1022#95C2414yes—
1023#95C2414yes—
1024#95C2414yes—
1025#95C2414yes—
1026#95C2414yes—
1027#95C2414yes—
1028#95C2414yes—
1029#95C2414yes—
1030C24C2512yes—
1031C24C2511yescharacteristic
1032C24C2512yes—
1033#41—416no—
1034#41—816no—
1035C2×Q8—28no—
1036C2×Q8—24no—
1037C2×Q8—22no—
1038C2×Q8—24no—
1039C2×Q8—24no—
1040C2×Q8—22no—
1041C2×Q8—24no—
1042C2×Q8—24no—
1043C2×Q8—22no—
1044C2×Q8—24no—
1045C2×Q8—41no—
1046C2×Q8—42no—
1047C2×Q8—44no—
1048C2×Q8—42no—
1049C2×Q8—44no—
1050C2×Q8—41no—
1051C2×Q8—44no—
1052C2×Q8—42no—
1053C2×Q8—42no—
1054C2×Q8—44no—
1055C2×Q8—44no—
1056C2×Q8—416no—
1057C2×Q8—432no—
1058C2×Q8C2×#4118yes—
1059C2×Q8C2×#4118yes—
1060C2×Q82−1+414yes—
1061C2×D4—24no—
1062C2×D4—24no—
1063C2×D4—24no—
1064C2×D4—28no—
1065C2×D4—22no—
1066C2×D4—22no—
1067C2×D4—22no—
1068C2×D4—42no—
1069C2×D4—41no—
1070C2×D4—42no—
1071C2×D4—42no—
1072C2×D4—41no—
1073C2×D4—44no—
1074C2×D4—44no—
1075C2×D42−1+414yes—
1076C22×C4—22no—
1077C22×C4—22no—
1078C22×C4—28no—
1079C22×C4—24no—
1080C22×C4—28no—
1081C22×C4—24no—
1082C22×C4—24no—
1083C22×C4—28no—
1084C22×C4—24no—
1085C22×C4—24no—
1086C22×C4—24no—
1087C22×C4—24no—
1088C22×C4—24no—
1089C22×C4—22no—
1090C22×C4—22no—
1091C22×C4—24no—
1092C22×C4—42no—
1093C22×C4—44no—
1094C22×C4—42no—
1095C22×C4—42no—
1096C22×C4—42no—
1097C22×C4—44no—
1098C22×C4—42no—
1099C22×C4—42no—
1100C22×C4—44no—
1101C22×C4—42no—
1102C22×C4—42no—
1103C22×C4—42no—
1104C22×C4—41no—
1105C22×C4—41no—
1106C22×C4—41no—
1107C22×C4—42no—
1108C22×C4—42no—
1109C22×C4—41no—
1110C22×C4—42no—
1111C22×C4—42no—
1112C22×C4—42no—
1113C22×C4C2×#4114yes—
1114C22×C4C2×#4118yes—
1115C22×C4C2512yes—
1116C22×C4C2512yes—
1117C22×C4C2512yes—
1118C22×C4C2512yes—
1119C22×C4C2512yes—
1120C22×C4C2512yes—
1121C22×C4C2511yescharacteristic
1122C22×C4C2514yes—
1123C22×C4C2514yes—
1124C22×C4C2512yes—
1125C22×C4C2514yes—
1126C22×C4C2512yes—
1127C22×C4C2514yes—
1128C22×C4C2514yes—
1129C22×C4C2512yes—
1130C22×C4C2512yes—
1131C22×C4C2512yes—
1132C22×C4C2511yescharacteristic
1133C22×C4C2512yes—
1134C22×C4C2514yes—
1135C22×C4C2511yescharacteristic
1136C22×C4C2512yes—
1137C22×C4C2511yescharacteristic
1138C22×C4C2511yescharacteristic
1139C22×C4C2512yes—
1140C22×C4C2511yescharacteristic
1141C4⋊C4—22no—
1142C4⋊C4—22no—
1143C4⋊C4—28no—
1144C4⋊C4—24no—
1145C4⋊C4—28no—
1146C4⋊C4—24no—
1147C4⋊C4—28no—
1148C4⋊C4—28no—
1149C4⋊C4—28no—
1150C4⋊C4—28no—
1151C4⋊C4—28no—
1152C4⋊C4—24no—
1153C4⋊C4—28no—
1154C4⋊C4—28no—
1155C4⋊C4—28no—
1156C4⋊C4—22no—
1157C4⋊C4—24no—
1158C4⋊C4—22no—
1159C4⋊C4—24no—
1160C4⋊C4—22no—
1161C4⋊C4—24no—
1162C4⋊C4—24no—
1163C4⋊C4—28no—
1164C4⋊C4—24no—
1165C4⋊C4—24no—
1166C4⋊C4—24no—
1167C4⋊C4—24no—
1168C4⋊C4—24no—
1169C4⋊C4—24no—
1170C4⋊C4—42no—
1171C4⋊C4—44no—
1172C4⋊C4—44no—
1173C4⋊C4—42no—
1174C4⋊C4—44no—
1175C4⋊C4—41no—
1176C4⋊C4—42no—
1177C4⋊C4—42no—
1178C4⋊C4—42no—
1179C4⋊C4—42no—
1180C4⋊C4—41no—
1181C4⋊C4—41no—
1182C4⋊C4—44no—
1183C4⋊C4—41no—
1184C4⋊C4—42no—
1185C4⋊C4—44no—
1186C4⋊C4—44no—
1187C4⋊C4—41no—
1188C4⋊C4—44no—
1189C4⋊C4—42no—
1190C4⋊C4—41no—
1191C4⋊C4—44no—
1192C4⋊C4—42no—
1193C4⋊C4—42no—
1194C4⋊C4—44no—
1195C4⋊C4—44no—
1196C4⋊C4—44no—
1197C4⋊C4—44no—
1198C4⋊C4—44no—
1199C4⋊C4—44no—
1200C4⋊C4—44no—
1201C4⋊C4—42no—
1202C4⋊C4—44no—
1203C4⋊C4—42no—
1204C4⋊C4—44no—
1205C4⋊C4—42no—
1206C4⋊C4—42no—
1207C4⋊C4—42no—
1208C4⋊C4—44no—
1209C4⋊C4H(5,𝔽2)14yes—
1210C22⋊C4—24no—
1211C22⋊C4—28no—
1212C22⋊C4—24no—
1213C22⋊C4—24no—
1214C22⋊C4—24no—
1215C22⋊C4—24no—
1216C22⋊C4—24no—
1217C22⋊C4—28no—
1218C22⋊C4—24no—
1219C22⋊C4—28no—
1220C22⋊C4—28no—
1221C22⋊C4—24no—
1222C22⋊C4—24no—
1223C22⋊C4—24no—
1224C22⋊C4—24no—
1225C22⋊C4—28no—
1226C22⋊C4—24no—
1227C22⋊C4—44no—
1228C22⋊C4—44no—
1229C22⋊C4—42no—
1230C22⋊C4—44no—
1231C22⋊C4—42no—
1232C22⋊C4—42no—
1233C22⋊C4—42no—
1234C22⋊C4—44no—
1235C22⋊C4—44no—
1236C22⋊C4—42no—
1237C22⋊C4—44no—
1238C22⋊C4—44no—
1239C22⋊C4—44no—
1240C22⋊C4—44no—
1241C22⋊C4—42no—
1242C22⋊C4—44no—
1243C22⋊C4—44no—
1244C22⋊C4—44no—
1245C22⋊C4—44no—
1246C42—24no—
1247C42—28no—
1248C42—24no—
1249C42—24no—
1250C42—28no—
1251C42—24no—
1252C42—22no—
1253C42—24no—
1254C42—22no—
1255C42—28no—
1256C42—24no—
1257C42—24no—
1258C42—41no—
1259C42—41no—
1260C42—42no—
1261C42—44no—
1262C42—42no—
1263C42—42no—
1264C42—44no—
1265C42—44no—
1266C42—44no—
1267C42—44no—
1268C42—44no—
1269C42—44no—
1270C42—44no—
1271C42—44no—
1272C23—22no—
1273C23—21no—
1274C23—22no—
1275C23—21no—
1276C23—22no—
1277C23—21no—
1278C23—22no—
1279C23—21no—
1280C23—21no—
1281C23—22no—
1282C23—22no—
1283C23—21no—
1284C23—22no—
1285C23—22no—
1286C23—22no—
1287C23—22no—
1288C23—22no—
1289C23—22no—
1290C23—22no—
1291C23C22×#4112yes—
1292C23C2×2−1+414yes—
1293C23C2611yescharacteristic
1294Q8—216no—
1295Q8—48no—
1296Q8—44no—
1297Q8—416no—
1298Q8—48no—
1299Q8—44no—
1300Q8—84no—
1301Q8—88no—
1302D4—44no—
1303D4—48no—
1304D4—48no—
1305D4—44no—
1306D4—88no—
1307C2×C4—22no—
1308C2×C4—21no—
1309C2×C4—21no—
1310C2×C4—21no—
1311C2×C4—24no—
1312C2×C4—22no—
1313C2×C4—24no—
1314C2×C4—21no—
1315C2×C4—22no—
1316C2×C4—21no—
1317C2×C4—22no—
1318C2×C4—21no—
1319C2×C4—28no—
1320C2×C4—22no—
1321C2×C4—22no—
1322C2×C4—22no—
1323C2×C4—24no—
1324C2×C4—22no—
1325C2×C4—24no—
1326C2×C4—22no—
1327C2×C4—22no—
1328C2×C4—22no—
1329C2×C4—22no—
1330C2×C4—22no—
1331C2×C4—21no—
1332C2×C4—21no—
1333C2×C4—22no—
1334C2×C4—22no—
1335C2×C4—24no—
1336C2×C4—22no—
1337C2×C4—24no—
1338C2×C4—22no—
1339C2×C4—22no—
1340C2×C4—21no—
1341C2×C4—22no—
1342C2×C4—24no—
1343C2×C4—22no—
1344C2×C4—22no—
1345C2×C4—22no—
1346C2×C4—22no—
1347C2×C4—22no—
1348C2×C4—22no—
1349C2×C4—22no—
1350C2×C4—21no—
1351C2×C4—24no—
1352C2×C4—22no—
1353C2×C4—22no—
1354C2×C4—24no—
1355C2×C4—24no—
1356C2×C4—22no—
1357C2×C4—24no—
1358C2×C4—22no—
1359C2×C4—22no—
1360C2×C4—24no—
1361C2×C4—22no—
1362C2×C4—24no—
1363C2×C4—22no—
1364C2×C4—22no—
1365C2×C4—24no—
1366C2×C4—22no—
1367C2×C4—24no—
1368C2×C4—21no—
1369C2×C4—22no—
1370C2×C4—22no—
1371C2×C4—24no—
1372C2×C4—22no—
1373C2×C4—22no—
1374C2×C4—24no—
1375C2×C4—22no—
1376C2×C4—21no—
1377C2×C4—48no—
1378C2×C4—48no—
1379C2×C4—416no—
1380C2×C4—48no—
1381C2×C4—416no—
1382C2×C4—48no—
1383C2×C4—48no—
1384C2×C4—82no—
1385C2×C4—84no—
1386C2×C4—82no—
1387C2×C4—84no—
1388C2×C4—162no—
1389C2×C4C22×#4118yes—
1390C2×C4C22×#4112yes—
1391C2×C4C22×#4112yes—
1392C2×C4C2×H(5,𝔽2)14yes—
1393C2×C4C2×H(5,𝔽2)12yes—
1394C2×C4C2×2−1+414yes—
1395C2×C4C2×2−1+412yes—
1396C2×C4C2×2−1+412yes—
1397C2×C4#58512yes—
1398C22—22no—
1399C22—24no—
1400C22—22no—
1401C22—24no—
1402C22—24no—
1403C22—22no—
1404C22—42no—
1405C22—41no—
1406C22—41no—
1407C22—42no—
1408C22—42no—
1409C22—41no—
1410C22—41no—
1411C22—42no—
1412C22—42no—
1413C22—42no—
1414C22—42no—
1415C22—42no—
1416C22—42no—
1417C22—42no—
1418C22—42no—
1419C22C23×#4111yescharacteristic
1420C22C22×H(5,𝔽2)11yescharacteristic
1421C22C22×2−1+411yescharacteristic
1422C22C22×2−1+411yescharacteristic
1423C22C2×#58511yescharacteristic
1424C22H(7,𝔽2)11yescharacteristic
1425C222−1+611yescharacteristic
1426C4—24no—
1427C4—22no—
1428C4—24no—
1429C4—22no—
1430C4—22no—
1431C4—28no—
1432C4—42no—
1433C4—42no—
1434C4—42no—
1435C4—42no—
1436C4—44no—
1437C4—42no—
1438C4—44no—
1439C4—44no—
1440C4—42no—
1441C4—42no—
1442C4—42no—
1443C4—41no—
1444C4—44no—
1445C4—42no—
1446C4—41no—
1447C4—42no—
1448C4—42no—
1449C4—44no—
1450C4—42no—
1451C4#345914yes—
1452C2—42no—
1453C2—44no—
1454C2—82no—
1455C2C2×#345911yescharacteristic
1456C2#6289311yescharacteristic
1457C2#6289411yescharacteristic
1458C2#6299811yescharacteristic
1459C2#6299911yescharacteristic
1460C2#6303211yescharacteristic
1461C2#6305611yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#36404C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #52291C2semidirect
2. #52279C2semidirect
3. #42864C2semidirect
4. #42847C2semidirect
5. #42787C2semidirect
6. #42126C2semidirect
7. #42088C2semidirect
8. #42046C2semidirect
9. #40269C2semidirect
10. #40119C2semidirect
11. #39711C2semidirect
12. #39659C2semidirect
13. #39624C2semidirect
14. #39615C2semidirect
15. #38800C2semidirect
16. #38700C2semidirect
17. #37338C2semidirect
18. #37323C2semidirect
19. #37212C2semidirect
20. #37206C2semidirect
21. #36545C2semidirect
22. #36505C2semidirect
23. #36422C2semidirect
25. #35993C2semidirect
26. #35919C2semidirect
27. #35869C2semidirect
28. #34291C2semidirect
29. #34268C2semidirect
730. C22×Q8#41semidirect

Maximal subgroups

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

subgroupindex
#522912
#522792
#428642
#428472
#427872
#421262
#420882
#420462
#402692
#401192
#397112
#396592
#396242
#396152
#388002
#387002
#373382
#373232
#372122
#372062
#365452
#365052
#364222
#364042
#359932
#359192
#358692
#342912
#342682