Finite Group Databasebeta

← #7695688

Subgroups — #7695688

Order 512.

4835 conjugacy classes of subgroups.

The subgroup lattice has 1403 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59926C212yesmaximal, complemented
2#59817C211yesmaximal, characteristic
3#59460C212yesmaximal, complemented
4#59096C214yesmaximal, complemented
5#52274C211yesmaximal, characteristic, complemented
6#52162C212yesmaximal, complemented
7#45213C212yesmaximal, complemented
8#44952C212yesmaximal
9#44934C212yesmaximal, complemented
10#44233C214yesmaximal, complemented
11#43564C214yesmaximal, complemented
12#43137C214yesmaximal, complemented
13#39700C212yesmaximal, complemented
14#39675C212yesmaximal, complemented
15#39644C214yesmaximal, complemented
16#39628C211yesmaximal, characteristic
17#39621C211yesmaximal, characteristic, complemented
18#39181C212yesmaximal, complemented
19#38453C212yesmaximal, complemented
20#38440C214yesmaximal, complemented
21#36286C211yesmaximal, characteristic, complemented
22#36132C212yesmaximal, complemented
23#35952C212yesmaximal, complemented
24#35871C212yesmaximal, complemented
25#35867C212yesmaximal, complemented
26#34335C211yesmaximal, characteristic, complemented
27#34334C212yesmaximal, complemented
28#34331C211yesmaximal, characteristic
29#34329C212yesmaximal
30C2×#559C2211yescharacteristic
31C2×Q82C2211yescharacteristic
32C2×D4×Q8C2212yes—
33C2×D4×Q8C2212yes—
34C2×#533C2214yes—
35#2863C2212yes—
36#2862C2211yescharacteristic
37#2859C2212yes—
38#2851C2214yes—
39#2811C2212yes—
40#2809C2211yescharacteristic
41#2806C2212yes—
42#2806C2211yescharacteristic
43#2806C2212yes—
44#2805C2211yescharacteristic
45#2804C2212yes—
46#2804C2214yes—
47#2804C2212yes—
48#2802C2212yes—
49#2799C2212yes—
50#2791C2212yes—
51#2790C2214yes—
52#2788C2214yes—
53#2788C2214yes—
54#2784C2214yes—
55#2780C2214yes—
56#2774C2214yes—
57#2774C2214yes—
58#2774C2212yes—
59#2763C2214yes—
60#2763C2214yes—
61#2755C2212yes—
62#2742C2214yes—
63#2734C2212yes—
64#2732C2212yes—
65#2732C2212yes—
66#2729C2214yes—
67#2729C2214yes—
68#2729C2214yes—
69#2726C2211yescharacteristic
70#2720C2214yes—
71#2713C2214yes—
72#2713C2214yes—
73#2713C2212yes—
74#2704C2214yes—
75#2704C2214yes—
76#2692C2214yes—
77#2683C2212yes—
78#2683C2212yes—
79#2677C2214yes—
80#2677C2214yes—
81#2666C2214yes—
82#2665C2214yes—
83#2665C2214yes—
84#2660C2212yes—
85#2647C2212yes—
86#2647C2212yes—
87#2612C2214yes—
88#2605C2214yes—
89#2605C2214yes—
90#2590C2214yes—
91#2589C2214yes—
92#2588C2214yes—
93#2588C2214yes—
94#2587C2214yes—
95#2587C2214yes—
96#2587C2214yes—
97#2587C2214yes—
98#2586C2214yes—
99#2583C2214yes—
100#2581C2214yes—
101#2581C2212yes—
102#2580C2212yes—
103#2579C2214yes—
104#2574C2214yes—
105#2574C2214yes—
106#2574C2214yes—
107#2574C2214yes—
108#2574C2214yes—
109#2571C2212yes—
110#2570C2212yes—
111#2570C2212yes—
112#2569C2214yes—
113#2568C2211yescharacteristic
114#2567C2211yescharacteristic
115#2566C2212yes—
116#2563C2212yes—
117#2551C2212yes—
118#2551C2212yes—
119#2551C2212yes—
120#2551C2212yes—
121#2550C2212yes—
122#2550C2212yes—
123#2549C2214yes—
124#2549C2214yes—
125#2549C2214yes—
126#2546C2214yes—
127#2538C2212yes—
128#2538C2212yes—
129#2522C2214yes—
130#2511C2212yes—
131#2509C2214yes—
132#2505C2214yes—
133#2505C2214yes—
134#2492C2214yes—
135#2492C2214yes—
136#2465C2214yes—
137#2465C2214yes—
138#2465C2214yes—
139#2465C2214yes—
140#2465C2214yes—
141#2465C2214yes—
142#2465C2214yes—
143#2465C2214yes—
144#2454C2212yes—
145#2453C2212yes—
146#2452C2212yes—
147#2452C2212yes—
148#2452C2212yes—
149#2452C2212yes—
150#2452C2212yes—
151#2452C2212yes—
152#2452C2212yes—
153#2452C2214yes—
154#2451C2214yes—
155#2451C2214yes—
156#2451C2212yes—
157#2451C2212yes—
158#2451C2212yes—
159#2451C2214yes—
160#2451C2212yes—
161#2450C2214yes—
162#2450C2214yes—
163#2450C2214yes—
164#2450C2214yes—
165#2446C2214yes—
166#2439C2214yes—
167#2439C2214yes—
168#2438C2214yes—
169#2438C2214yes—
170#2434C2214yes—
171#2434C2214yes—
172#2429C2214yes—
173#2417C2214yes—
174#2409C2214yes—
175#2402C2212yes—
176#2402C2212yes—
177#2399C2214yes—
178#2399C2212yes—
179#2396C2214yes—
180#2396C2214yes—
181#2374C2214yes—
182#2372C2214yes—
183#2370C2212yes—
184#2369C2212yes—
185#2369C2211yescharacteristic
186#2369C2212yes—
187#2369C2211yescharacteristic
188#2368C2214yes—
189#2368C2214yes—
190#2367C2212yes—
191#2367C2212yes—
192#2367C2212yes—
193#2367C2212yes—
194#2366C2212yes—
195#2366C2211yescharacteristic
196#2365C2212yes—
197#2365C2212yes—
198#2365C2212yes—
199#2365C2214yes—
200#2365C2211yescharacteristic
201#2360C2214yes—
202#2360C2214yes—
203#2359C2214yes—
204#2359C2214yes—
205#2357C2212yes—
206#2356C2212yes—
207#2355C2212yes—
208#2355C2211yescharacteristic
209#2355C2212yes—
210#2355C2211yescharacteristic
211#2355C2212yes—
212#2354C2212yes—
213#2354C2212yes—
214#2353C2214yes—
215#2351C2212yes—
216Q8×C4⋊C4C2211yescharacteristic
217Q8×C4⋊C4C2211yescharacteristic
218#2349C2212yes—
219#2349C2212yes—
220#2349C2212yes—
221D4×C4⋊C4C2212yes—
222Q8×C22⋊C4C2214yes—
223#2337C2214yes—
224#2335C2214yes—
225#2335C2214yes—
226#2331C2212yes—
227#2331C2212yes—
228#2331C2212yes—
229#2331C2214yes—
230#2329C2214yes—
231#2329C2214yes—
232#2328C2212yes—
233#2326C2212yes—
234#2326C2212yes—
235C4×C4⋊Q8C2212yes—
236C4×C4⋊Q8C2212yes—
237C4×C4⋊Q8C2211yescharacteristic
238C4×C4⋊Q8C2211yescharacteristic
239C4×#127C2211yescharacteristic
240C4×#125C2212yes—
241C4×#124C2212yes—
242C4×#124C2212yes—
243C4×C22⋊Q8C2214yes—
244C4×#123C2214yes—
245#2295C2212yes—
246#2295C2212yes—
247#2295C2212yes—
248#2295C2211yescharacteristic
249#2295C2212yes—
250#2295C2211yescharacteristic
251C2×#391C2214yes—
252#2293C2212yes—
253#2290C2214yes—
254#2276C2212yes—
255#2275C2212yes—
256#2275C2212yes—
257C42×Q8C2211yescharacteristic
258C42×D4C2212yes—
259C23×Q8C2314yes—
260#559Q8116yescomplemented
261Q82—28no—
262D4×Q8—216no—
263D4×Q8—48no—
264#533—416no—
265C2×C4⋊Q8C2312yes—
266C2×C4⋊Q8C2312yes—
267C2×C4⋊Q8C2311yescharacteristic
268C2×C4⋊Q8C2314yes—
269C2×C4⋊Q8C2312yes—
270C2×C4⋊Q8C2312yes—
271C2×C4⋊Q8C2312yes—
272C2×C4⋊Q8C2311yescharacteristic
273C2×C4⋊Q8C2311yescharacteristic
274C2×C4⋊Q8C2314yes—
275C2×C4⋊Q8C2314yes—
276C2×C4⋊Q8C2314yes—
277C2×C4⋊Q8C2314yes—
278C2×C4⋊Q8C2311yescharacteristic
279C2×#127C2311yescharacteristic
280C2×#125C2312yes—
281C2×#125C2312yes—
282C2×#125C2314yes—
283C2×#124C2312yes—
284C2×#124C2312yes—
285C2×#123C2314yes—
286C2×C22⋊Q8C2314yes—
287C2×C22⋊Q8C2314yes—
288C2×C22⋊Q8C2314yes—
289C2×C22⋊Q8C2314yes—
290C2×C22⋊Q8C2314yes—
291C2×C22⋊Q8C2314yes—
292C2×C22⋊Q8C2314yes—
293C2×C22⋊Q8C2314yes—
294C2×C22⋊Q8C2314yes—
295C2×C22⋊Q8C2314yes—
296C2×C22⋊Q8C2314yes—
297C2×C4×Q8C2312yes—
298C2×C4×Q8C2311yescharacteristic
299C2×C4×Q8C2311yescharacteristic
300C2×C4×Q8C2312yes—
301C2×C4×Q8C2312yes—
302C2×C4×Q8C2312yes—
303C2×C4×Q8C2314yes—
304C2×C4×Q8C2312yes—
305C2×C4×Q8C2311yescharacteristic
306C2×C4×Q8C2312yes—
307C2×C4×Q8C2314yes—
308C2×C4×Q8C2314yes—
309C2×C4×Q8C2314yes—
310C2×C4×Q8C2312yes—
311C2×C4×Q8C2311yescharacteristic
312C2×C4×Q8C2311yescharacteristic
313C2×C4×D4C2312yes—
314C2×C4×D4C2312yes—
315C2×C4×D4C2312yes—
316C2×C4×D4C2312yes—
317C2×C4×D4C2312yes—
318C2×C4×D4C2312yes—
319C2×C4×D4C2312yes—
320C2×C4×D4C2314yes—
321C2×C4×D4C2312yes—
322C2×C4×D4C2312yes—
323C2×C4×D4C2312yes—
324C2×C4×D4C2312yes—
325C2×#117C2314yes—
326C2×#117C2314yes—
327C22×C4⋊C4C2314yes—
328C22×C42C2314yes—
329#400C2314yes—
330#400C2314yes—
331#400C2314yes—
332#400C2314yes—
333#400C2314yes—
334#400C2314yes—
335#400C2314yes—
336#400C2314yes—
337#400C2314yes—
338#400C2314yes—
339#400C2312yes—
340#400C2312yes—
341#400C2312yes—
342#400C2314yes—
343#400C2312yes—
344#400C2312yes—
345#400C2312yes—
346#400C2312yes—
347#400C2312yes—
348#399C2314yes—
349#399C2314yes—
350#398C2312yes—
351#398C2314yes—
352#398C2314yes—
353#398C2314yes—
354#398C2312yes—
355#398C2312yes—
356#398C2314yes—
357#398C2314yes—
358#398C2314yes—
359#398C2312yes—
360#398C2314yes—
361#398C2314yes—
362#398C2314yes—
363#398C2312yes—
364#398C2314yes—
365#398C2314yes—
366#398C2314yes—
367#398C2314yes—
368#398C2312yes—
369#398C2312yes—
370#398C2312yes—
371#398C2312yes—
372#398C2312yes—
373#398C2312yes—
374#398C2312yes—
375#398C2314yes—
376#396C2314yes—
377#396C2314yes—
378#396C2314yes—
379#396C2314yes—
380#396C2314yes—
381#396C2314yes—
382#396C2314yes—
383#396C2314yes—
384#396C2314yes—
385#396C2314yes—
386#396C2314yes—
387#396C2314yes—
388#395C2314yes—
389#395C2312yes—
390#395C2314yes—
391#395C2314yes—
392#395C2314yes—
393#395C2314yes—
394#395C2314yes—
395#395C2314yes—
396#395C2314yes—
397#395C2314yes—
398#395C2314yes—
399#395C2314yes—
400#395C2314yes—
401#395C2314yes—
402#395C2312yes—
403#395C2314yes—
404#395C2312yes—
405#395C2312yes—
406#395C2314yes—
407#395C2314yes—
408#395C2314yes—
409#393C2314yes—
410#393C2314yes—
411#393C2314yes—
412#393C2314yes—
413#393C2314yes—
414#393C2314yes—
415#393C2314yes—
416#393C2314yes—
417#393C2314yes—
418#393C2314yes—
419#391C2312yes—
420#391C2314yes—
421#391C2312yes—
422#391C2314yes—
423#391C2312yes—
424#391C2312yes—
425#391C2312yes—
426#391C2312yes—
427#391C2312yes—
428#391C2314yes—
429#391C2314yes—
430#391C2314yes—
431#391C2312yes—
432#391C2314yes—
433#391C2312yes—
434#391C2314yes—
435#391C2314yes—
436#391C2314yes—
437#391C2314yes—
438#391C2312yes—
439#391C2314yes—
440#391C2314yes—
441#391C2314yes—
442#391C2314yes—
443#391C2314yes—
444#391C2314yes—
445#391C2312yes—
446#391C2312yes—
447#391C2314yes—
448#391C2312yes—
449#391C2314yes—
450#391C2312yes—
451#391C2312yes—
452#391C2312yes—
453#391C2311yescharacteristic
454#391C2314yes—
455#391C2314yes—
456#391C2311yescharacteristic
457#391C2314yes—
458#391C2312yes—
459#391C2311yescharacteristic
460#391C2311yescharacteristic
461#390C2312yes—
462#390C2312yes—
463#390C2312yes—
464#390C2312yes—
465#390C2312yes—
466#390C2312yes—
467#390C2312yes—
468#390C2312yes—
469#390C2314yes—
470#390C2312yes—
471#389C2312yes—
472#389C2312yes—
473#389C2312yes—
474#389C2311yescharacteristic
475#389C2314yes—
476#389C2312yes—
477#389C2314yes—
478#389C2312yes—
479#389C2312yes—
480#389C2312yes—
481#389C2311yescharacteristic
482#389C2311yescharacteristic
483#389C2312yes—
484#389C2312yes—
485#389C2312yes—
486#389C2312yes—
487#389C2312yes—
488#389C2312yes—
489#389C2312yes—
490#389C2312yes—
491#389C2314yes—
492#389C2314yes—
493#389C2314yes—
494#389C2314yes—
495#389C2314yes—
496#389C2312yes—
497#389C2314yes—
498#389C2314yes—
499#389C2314yes—
500#389C2312yes—
501#389C2312yes—
502#389C2312yes—
503#389C2312yes—
504#389C2314yes—
505#389C2312yes—
506#389C2314yes—
507#389C2314yes—
508#389C2312yes—
509#389C2314yes—
510#389C2314yes—
511#389C2314yes—
512#389C2311yescharacteristic
513#389C2312yes—
514#389C2312yes—
515#389C2312yes—
516#389C2311yescharacteristic
517#389C2314yes—
518#389C2312yes—
519#389C2311yescharacteristic
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#387C2312yes—
539#387C2312yes—
540#387C2312yes—
541#387C2312yes—
542#387C2314yes—
543#387C2314yes—
544#387C2314yes—
545#387C2314yes—
546#387C2314yes—
547#387C2314yes—
548#387C2314yes—
549#387C2314yes—
550#387C2312yes—
551#387C2314yes—
552#387C2314yes—
553#387C2314yes—
554#387C2314yes—
555#387C2314yes—
556#387C2314yes—
557#387C2314yes—
558#387C2314yes—
559#387C2314yes—
560#387C2312yes—
561#387C2314yes—
562#387C2314yes—
563#387C2314yes—
564#387C2314yes—
565#387C2314yes—
566#387C2312yes—
567#387C2314yes—
568#387C2314yes—
569#387C2312yes—
570#387C2314yes—
571#387C2314yes—
572#387C2314yes—
573#387C2314yes—
574#387C2314yes—
575#387C2314yes—
576#387C2314yes—
577#387C2314yes—
578#387C2312yes—
579#387C2314yes—
580#387C2312yes—
581#387C2312yes—
582#387C2312yes—
583#387C2312yes—
584#387C2312yes—
585#387C2312yes—
586#387C2312yes—
587#386C2314yes—
588#386C2314yes—
589#386C2314yes—
590#386C2314yes—
591#386C2314yes—
592#386C2314yes—
593#386C2314yes—
594#385C2314yes—
595#385C2314yes—
596#385C2314yes—
597#385C2314yes—
598#385C2314yes—
599#385C2314yes—
600#385C2314yes—
601#385C2314yes—
602#385C2314yes—
603#385C2314yes—
604#385C2314yes—
605#385C2314yes—
606#385C2314yes—
607#385C2314yes—
608#385C2314yes—
609#385C2314yes—
610#385C2314yes—
611#385C2314yes—
612#385C2314yes—
613#385C2314yes—
614#385C2314yes—
615#385C2314yes—
616#385C2314yes—
617#385C2314yes—
618#385C2314yes—
619#384C2311yescharacteristic
620#384C2312yes—
621#384C2311yescharacteristic
622#384C2312yes—
623#384C2311yescharacteristic
624#384C2312yes—
625#384C2312yes—
626#383C2314yes—
627#382C2312yes—
628#382C2312yes—
629#382C2312yes—
630#382C2312yes—
631#382C2312yes—
632#382C2314yes—
633#382C2314yes—
634#382C2314yes—
635#382C2312yes—
636#382C2312yes—
637#381C2314yes—
638#380C2314yes—
639#380C2314yes—
640#380C2314yes—
641#380C2314yes—
642#380C2314yes—
643#380C2314yes—
644#380C2314yes—
645#380C2314yes—
646#380C2314yes—
647C4×C4⋊C4C2311yescharacteristic
648C4×C4⋊C4C2312yes—
649C4×C4⋊C4C2312yes—
650C4×C4⋊C4C2312yes—
651C4×C4⋊C4C2312yes—
652C4×C4⋊C4C2312yes—
653C4×C4⋊C4C2311yescharacteristic
654C4×C4⋊C4C2312yes—
655C4×C4⋊C4C2312yes—
656C4×C4⋊C4C2314yes—
657C4×C4⋊C4C2312yes—
658C4×C4⋊C4C2314yes—
659C4×C4⋊C4C2312yes—
660C4×C4⋊C4C2312yes—
661C4×C4⋊C4C2312yes—
662C4×C4⋊C4C2312yes—
663C4×C4⋊C4C2312yes—
664C4×C4⋊C4C2311yescharacteristic
665C4×C4⋊C4C2312yes—
666C4×C4⋊C4C2312yes—
667C4×C4⋊C4C2314yes—
668C4×C4⋊C4C2314yes—
669C4×C4⋊C4C2314yes—
670C4×C4⋊C4C2314yes—
671C4×C4⋊C4C2312yes—
672C4×C4⋊C4C2312yes—
673C4×C4⋊C4C2312yes—
674C4×C4⋊C4C2312yes—
675C4×C4⋊C4C2314yes—
676C4×C4⋊C4C2314yes—
677C4×C4⋊C4C2314yes—
678C4×C4⋊C4C2311yescharacteristic
679C4×C4⋊C4C2312yes—
680C4×C4⋊C4C2312yes—
681C4×C4⋊C4C2311yescharacteristic
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×C22⋊C4C2314yes—
691C4×C22⋊C4C2314yes—
692C4×C22⋊C4C2314yes—
693C4×C22⋊C4C2314yes—
694C4×C22⋊C4C2314yes—
695C4×C22⋊C4C2314yes—
696C4×C22⋊C4C2314yes—
697C4×C22⋊C4C2314yes—
698C4×C22⋊C4C2314yes—
699C4×C22⋊C4C2314yes—
700C4×C22⋊C4C2314yes—
701C4×C22⋊C4C2314yes—
702C4×C22⋊C4C2314yes—
703C4×C22⋊C4C2314yes—
704C4×C22⋊C4C2314yes—
705#376C2312yes—
706#376C2312yes—
707#376C2312yes—
708#376C2314yes—
709#376C2314yes—
710C2×#95C2314yes—
711C2×#95C2314yes—
712C2×#95C2314yes—
713C2×#95C2314yes—
714C43C2312yes—
715C43C2311yescharacteristic
716C43C2312yes—
717C22×Q8—216no—
718C22×Q8—48no—
719C22×Q8—84no—
720C22×Q8C2414yes—
721C22×Q8C2412yes—
722C22×Q8C2411yescharacteristic
723C22×Q8C2411yescharacteristic
724C22×Q8C2414yes—
725C22×Q8C2412yes—
726C22×Q8C2414yes—
727C22×Q8C2414yes—
728C22×Q8C2412yes—
729C22×Q8C2411yescharacteristic
730C22×Q8C2412yes—
731C22×D4C2412yes—
732C22×D4C2412yes—
733C22×D4C2412yes—
734C23×C4C2414yes—
735C23×C4C2414yes—
736C23×C4C2414yes—
737C23×C4C2414yes—
738C23×C4C2414yes—
739C23×C4C2414yes—
740C23×C4C2414yes—
741C4⋊Q8—216no—
742C4⋊Q8—28no—
743C4⋊Q8—28no—
744C4⋊Q8—28no—
745C4⋊Q8—28no—
746C4⋊Q8—24no—
747C4⋊Q8—44no—
748C4⋊Q8—42no—
749C4⋊Q8—42no—
750C4⋊Q8—48no—
751C4⋊Q8—48no—
752C4⋊Q8—48no—
753C4⋊Q8—84no—
754C4⋊Q8#4118yes—
755#127C2×Q818yes—
756#125—28no—
757#125—44no—
758#125—48no—
759#124C2×Q8116yescomplemented
760#124C2×Q8116yescomplemented
761#123C2×Q8132yescomplemented
762C22⋊Q8—216no—
763C22⋊Q8—216no—
764C22⋊Q8—216no—
765C22⋊Q8—216no—
766C22⋊Q8—48no—
767C22⋊Q8—48no—
768C22⋊Q8—48no—
769C22⋊Q8—48no—
770C22⋊Q8—48no—
771C22⋊Q8—84no—
772C22⋊Q8—84no—
773C4×Q8—28no—
774C4×Q8—28no—
775C4×Q8—28no—
776C4×Q8—28no—
777C4×Q8—24no—
778C4×Q8—24no—
779C4×Q8—48no—
780C4×Q8—48no—
781C4×Q8—44no—
782C4×Q8—44no—
783C4×Q8—42no—
784C4×Q8—48no—
785C4×Q8—82no—
786C4×Q8—84no—
787C4×Q8C2×Q818yescomplemented
788C4×Q8C2×Q818yescomplemented
789C4×D4—28no—
790C4×D4—28no—
791C4×D4—28no—
792C4×D4—44no—
793C4×D4—44no—
794C4×D4—44no—
795C4×D4—44no—
796C4×D4—48no—
797C4×D4—82no—
798C4×D4—82no—
799C4×D4C2×Q8116yescomplemented
800C4×D4C2×Q8116yescomplemented
801#117—48no—
802#117—48no—
803C2×C4⋊C4—84no—
804C2×C4⋊C4C2412yes—
805C2×C4⋊C4C2412yes—
806C2×C4⋊C4C2411yescharacteristic
807C2×C4⋊C4C2412yes—
808C2×C4⋊C4C2412yes—
809C2×C4⋊C4C2412yes—
810C2×C4⋊C4C2412yes—
811C2×C4⋊C4C2412yes—
812C2×C4⋊C4C2412yes—
813C2×C4⋊C4C2412yes—
814C2×C4⋊C4C2414yes—
815C2×C4⋊C4C2414yes—
816C2×C4⋊C4C2414yes—
817C2×C4⋊C4C2412yes—
818C2×C4⋊C4C2412yes—
819C2×C4⋊C4C2412yes—
820C2×C4⋊C4C2412yes—
821C2×C4⋊C4C2411yescharacteristic
822C2×C4⋊C4C2412yes—
823C2×C4⋊C4C2414yes—
824C2×C4⋊C4C2411yescharacteristic
825C2×C4⋊C4C2412yes—
826C2×C4⋊C4C2414yes—
827C2×C4⋊C4C2411yescharacteristic
828C2×C4⋊C4C2414yes—
829C2×C4⋊C4C2414yes—
830C2×C4⋊C4C2412yes—
831C2×C4⋊C4C2414yes—
832C2×C4⋊C4C2414yes—
833C2×C4⋊C4C2414yes—
834C2×C4⋊C4C2414yes—
835C2×C4⋊C4C2414yes—
836C2×C4⋊C4C2411yescharacteristic
837C2×C4⋊C4C2412yes—
838C2×C4⋊C4C2412yes—
839C2×C4⋊C4C2412yes—
840C2×C4⋊C4C2414yes—
841C2×C4⋊C4C2414yes—
842C2×C4⋊C4C2414yes—
843C2×C4⋊C4C2414yes—
844C2×C4⋊C4C2414yes—
845C2×C4⋊C4C2414yes—
846C2×C4⋊C4C2412yes—
847C2×C4⋊C4C2414yes—
848C2×C4⋊C4C2414yes—
849C2×C4⋊C4C2412yes—
850C2×C4⋊C4C2412yes—
851C2×C4⋊C4C2414yes—
852C2×C4⋊C4C2414yes—
853C2×C4⋊C4C2414yes—
854C2×C4⋊C4C2414yes—
855C2×C4⋊C4C2412yes—
856C2×C4⋊C4C2412yes—
857C2×C4⋊C4C2414yes—
858C2×C4⋊C4C2412yes—
859C2×C4⋊C4C2411yescharacteristic
860C2×C4⋊C4C2412yes—
861C2×C4⋊C4C2411yescharacteristic
862C2×C4⋊C4C2411yescharacteristic
863C2×C4⋊C4C2412yes—
864C2×C4⋊C4C2411yescharacteristic
865C2×C4⋊C4C2412yes—
866C2×C4⋊C4C2412yes—
867C2×C4⋊C4C2412yes—
868C2×C4⋊C4C2412yes—
869C2×C4⋊C4C2414yes—
870C2×C4⋊C4C2414yes—
871C2×C4⋊C4C2412yes—
872C2×C4⋊C4C2411yescharacteristic
873C2×C4⋊C4C2412yes—
874C2×C4⋊C4C2412yes—
875C2×C4⋊C4C2411yescharacteristic
876C2×C4⋊C4C2411yescharacteristic
877C2×C4⋊C4C2412yes—
878C2×C4⋊C4C2412yes—
879C2×C4⋊C4C2412yes—
880C2×C4⋊C4C2412yes—
881C2×C4⋊C4C2411yescharacteristic
882C2×C22⋊C4C2414yes—
883C2×C22⋊C4C2414yes—
884C2×C22⋊C4C2414yes—
885C2×C22⋊C4C2414yes—
886C2×C22⋊C4C2414yes—
887C2×C22⋊C4C2414yes—
888C2×C22⋊C4C2414yes—
889C2×C22⋊C4C2414yes—
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×C22⋊C4C2414yes—
902C2×C22⋊C4C2414yes—
903C2×C42—48no—
904C2×C42C2412yes—
905C2×C42C2414yes—
906C2×C42C2411yescharacteristic
907C2×C42C2412yes—
908C2×C42C2412yes—
909C2×C42C2412yes—
910C2×C42C2412yes—
911C2×C42C2412yes—
912C2×C42C2414yes—
913C2×C42C2412yes—
914C2×C42C2411yescharacteristic
915C2×C42C2412yes—
916C2×C42C2414yes—
917C2×C42C2414yes—
918C2×C42C2411yescharacteristic
919C2×C42C2414yes—
920C2×C42C2412yes—
921C2×C42C2412yes—
922C2×C42C2414yes—
923C2×C42C2414yes—
924C2×C42C2414yes—
925C2×C42C2412yes—
926C2×C42C2414yes—
927C2×C42C2414yes—
928C2×C42C2411yescharacteristic
929C2×C42C2412yes—
930C2×C42C2412yes—
931C2×C42C2412yes—
932C2×C42C2411yescharacteristic
933C2×C42C2414yes—
934C2×C42C2412yes—
935C2×C42C2412yes—
936C2×C42C2411yescharacteristic
937C2×C42C2411yescharacteristic
938#95C2412yes—
939#95C2412yes—
940#95C2412yes—
941#95C2412yes—
942#95C2412yes—
943#95C2414yes—
944#95C2414yes—
945#95C2414yes—
946#95C2414yes—
947#95C2414yes—
948#95C2414yes—
949#95C2414yes—
950#95C2414yes—
951#95C2414yes—
952#95C2414yes—
953#95C2414yes—
954#95C2412yes—
955#95C2412yes—
956#95C2412yes—
957#95C2412yes—
958#95C2412yes—
959#95C2414yes—
960#95C2412yes—
961#95C2412yes—
962#95C2412yes—
963#95C2414yes—
964#95C2412yes—
965#95C2412yes—
966#95C2414yes—
967#95C2412yes—
968#95C2414yes—
969#95C2414yes—
970#95C2414yes—
971#95C2412yes—
972#95C2414yes—
973#95C2414yes—
974#95C2412yes—
975#95C2412yes—
976#95C2412yes—
977#95C2414yes—
978#95C2414yes—
979#95C2414yes—
980#95C2414yes—
981#95C2412yes—
982#95C2412yes—
983#95C2412yes—
984#95C2412yes—
985#95C2412yes—
986#95C2414yes—
987#95C2414yes—
988#95C2414yes—
989#95C2414yes—
990#95C2414yes—
991#95C2414yes—
992#95C2412yes—
993#95C2412yes—
994#95C2412yes—
995#95C2414yes—
996#95C2412yes—
997#95C2414yes—
998#95C2414yes—
999#95C2412yes—
1000#95C2412yes—
1001#95C2412yes—
1002#95C2412yes—
1003#95C2412yes—
1004#95C2414yes—
1005#95C2414yes—
1006#95C2412yes—
1007#95C2412yes—
1008#95C2412yes—
1009#95C2414yes—
1010#95C2414yes—
1011#95C2414yes—
1012#95C2414yes—
1013C24C2514yes—
1014C2×Q8—22no—
1015C2×Q8—22no—
1016C2×Q8—24no—
1017C2×Q8—28no—
1018C2×Q8—28no—
1019C2×Q8—28no—
1020C2×Q8—28no—
1021C2×Q8—24no—
1022C2×Q8—24no—
1023C2×Q8—22no—
1024C2×Q8—42no—
1025C2×Q8—41no—
1026C2×Q8—44no—
1027C2×Q8—42no—
1028C2×Q8—42no—
1029C2×Q8—41no—
1030C2×Q8—41no—
1031C2×Q8—41no—
1032C2×Q8—44no—
1033C2×Q8—44no—
1034C2×Q8—44no—
1035C2×Q8—44no—
1036C2×Q8—42no—
1037C2×Q8—44no—
1038C2×Q8—44no—
1039C2×Q8—42no—
1040C2×Q8—44no—
1041C2×Q8—42no—
1042C2×Q8—42no—
1043C2×Q8—42no—
1044C2×Q8—832no—
1045C2×Q8C22×Q814yes—
1046C2×Q8C22×Q814yes—
1047C2×Q8C2×#4118yes—
1048C2×D4—24no—
1049C2×D4—24no—
1050C2×D4—42no—
1051C2×D4—42no—
1052C2×D4—42no—
1053C2×D4—42no—
1054C2×D4C22×Q818yes—
1055C2×D4C22×Q818yes—
1056C2×D4C22×Q818yes—
1057C22×C4—28no—
1058C22×C4—28no—
1059C22×C4—28no—
1060C22×C4—28no—
1061C22×C4—44no—
1062C22×C4—44no—
1063C22×C4—44no—
1064C22×C4—44no—
1065C22×C4—44no—
1066C22×C4—44no—
1067C22×C4—44no—
1068C22×C4—44no—
1069C22×C4—44no—
1070C22×C4—44no—
1071C22×C4—44no—
1072C22×C4—44no—
1073C22×C4—44no—
1074C22×C4—44no—
1075C22×C4—44no—
1076C22×C4—44no—
1077C22×C4C22×Q8116yes—
1078C22×C4C2512yes—
1079C22×C4C2512yes—
1080C22×C4C2512yes—
1081C22×C4C2512yes—
1082C22×C4C2512yes—
1083C22×C4C2511yescharacteristic
1084C22×C4C2514yes—
1085C22×C4C2514yes—
1086C22×C4C2512yes—
1087C22×C4C2512yes—
1088C22×C4C2512yes—
1089C22×C4C2512yes—
1090C22×C4C2514yes—
1091C22×C4C2514yes—
1092C22×C4C2512yes—
1093C22×C4C2512yes—
1094C22×C4C2511yescharacteristic
1095C22×C4C2512yes—
1096C22×C4C2512yes—
1097C22×C4C2512yes—
1098C22×C4C2511yescharacteristic
1099C22×C4C2512yes—
1100C22×C4C2511yescharacteristic
1101C22×C4C2511yescharacteristic
1102C22×C4C2514yes—
1103C22×C4C2512yes—
1104C22×C4C2511yescharacteristic
1105C22×C4C2511yescharacteristic
1106C4⋊C4—24no—
1107C4⋊C4—24no—
1108C4⋊C4—24no—
1109C4⋊C4—24no—
1110C4⋊C4—28no—
1111C4⋊C4—24no—
1112C4⋊C4—28no—
1113C4⋊C4—24no—
1114C4⋊C4—22no—
1115C4⋊C4—22no—
1116C4⋊C4—28no—
1117C4⋊C4—28no—
1118C4⋊C4—24no—
1119C4⋊C4—24no—
1120C4⋊C4—24no—
1121C4⋊C4—28no—
1122C4⋊C4—28no—
1123C4⋊C4—24no—
1124C4⋊C4—24no—
1125C4⋊C4—24no—
1126C4⋊C4—28no—
1127C4⋊C4—22no—
1128C4⋊C4—22no—
1129C4⋊C4—24no—
1130C4⋊C4—24no—
1131C4⋊C4—24no—
1132C4⋊C4—42no—
1133C4⋊C4—44no—
1134C4⋊C4—44no—
1135C4⋊C4—44no—
1136C4⋊C4—41no—
1137C4⋊C4—41no—
1138C4⋊C4—42no—
1139C4⋊C4—42no—
1140C4⋊C4—44no—
1141C4⋊C4—42no—
1142C4⋊C4—42no—
1143C4⋊C4—42no—
1144C4⋊C4—41no—
1145C4⋊C4—41no—
1146C4⋊C4—41no—
1147C4⋊C4—42no—
1148C4⋊C4—42no—
1149C4⋊C4—42no—
1150C4⋊C4—44no—
1151C4⋊C4—42no—
1152C4⋊C4—44no—
1153C4⋊C4—44no—
1154C4⋊C4—42no—
1155C4⋊C4—41no—
1156C4⋊C4—42no—
1157C4⋊C4—44no—
1158C4⋊C4—42no—
1159C4⋊C4—42no—
1160C4⋊C4—44no—
1161C4⋊C4—44no—
1162C4⋊C4—44no—
1163C4⋊C4—44no—
1164C4⋊C4—44no—
1165C4⋊C4—44no—
1166C4⋊C4—44no—
1167C4⋊C4—42no—
1168C4⋊C4—42no—
1169C4⋊C4—44no—
1170C4⋊C4—44no—
1171C4⋊C4—44no—
1172C4⋊C4—44no—
1173C4⋊C4—42no—
1174C4⋊C4—44no—
1175C4⋊C4—42no—
1176C4⋊C4—42no—
1177C4⋊C4C22×Q814yes—
1178C4⋊C4C22×Q814yes—
1179C4⋊C4C22×Q818yes—
1180C4⋊C4C22×Q818yes—
1181C4⋊C4C2×#4118yes—
1182C4⋊C4C2×#4118yes—
1183C4⋊C4H(5,𝔽2)14yes—
1184C22⋊C4—28no—
1185C22⋊C4—28no—
1186C22⋊C4—28no—
1187C22⋊C4—28no—
1188C22⋊C4—28no—
1189C22⋊C4—44no—
1190C22⋊C4—44no—
1191C22⋊C4—44no—
1192C22⋊C4—44no—
1193C22⋊C4—44no—
1194C22⋊C4—44no—
1195C22⋊C4—44no—
1196C22⋊C4—44no—
1197C22⋊C4—44no—
1198C22⋊C4—44no—
1199C22⋊C4—44no—
1200C22⋊C4—44no—
1201C22⋊C4—44no—
1202C22⋊C4C22×Q8116yes—
1203C22⋊C4C22×Q8116yes—
1204C22⋊C4C22×Q8116yes—
1205C42—24no—
1206C42—24no—
1207C42—28no—
1208C42—24no—
1209C42—24no—
1210C42—24no—
1211C42—28no—
1212C42—24no—
1213C42—22no—
1214C42—24no—
1215C42—24no—
1216C42—22no—
1217C42—44no—
1218C42—44no—
1219C42—42no—
1220C42—41no—
1221C42—44no—
1222C42—41no—
1223C42—42no—
1224C42—42no—
1225C42—44no—
1226C42—44no—
1227C42—44no—
1228C42—41no—
1229C42—42no—
1230C42—42no—
1231C42—44no—
1232C42—42no—
1233C42—44no—
1234C42—44no—
1235C42C22×Q818yes—
1236C42C22×Q818yes—
1237C42C22×Q814yes—
1238C42C2×#4114yes—
1239C23—24no—
1240C23—24no—
1241C23—24no—
1242C23—24no—
1243C23—24no—
1244C23—24no—
1245C23C23×Q818yes—
1246C23C2611yescharacteristic
1247Q8—28no—
1248Q8—48no—
1249Q8—44no—
1250Q8—416no—
1251Q8—48no—
1252Q8—44no—
1253Q8—88no—
1254Q8—84no—
1255Q8—88no—
1256Q8—88no—
1257Q8—162no—
1258D4—216no—
1259D4—48no—
1260D4—48no—
1261C2×C4—22no—
1262C2×C4—22no—
1263C2×C4—22no—
1264C2×C4—21no—
1265C2×C4—22no—
1266C2×C4—21no—
1267C2×C4—24no—
1268C2×C4—21no—
1269C2×C4—22no—
1270C2×C4—22no—
1271C2×C4—21no—
1272C2×C4—22no—
1273C2×C4—24no—
1274C2×C4—21no—
1275C2×C4—21no—
1276C2×C4—22no—
1277C2×C4—21no—
1278C2×C4—22no—
1279C2×C4—22no—
1280C2×C4—21no—
1281C2×C4—21no—
1282C2×C4—21no—
1283C2×C4—22no—
1284C2×C4—22no—
1285C2×C4—22no—
1286C2×C4—22no—
1287C2×C4—22no—
1288C2×C4—22no—
1289C2×C4—24no—
1290C2×C4—22no—
1291C2×C4—24no—
1292C2×C4—22no—
1293C2×C4—24no—
1294C2×C4—22no—
1295C2×C4—22no—
1296C2×C4—24no—
1297C2×C4—22no—
1298C2×C4—22no—
1299C2×C4—22no—
1300C2×C4—22no—
1301C2×C4—22no—
1302C2×C4—21no—
1303C2×C4—22no—
1304C2×C4—24no—
1305C2×C4—24no—
1306C2×C4—24no—
1307C2×C4—22no—
1308C2×C4—21no—
1309C2×C4—22no—
1310C2×C4—24no—
1311C2×C4—24no—
1312C2×C4—22no—
1313C2×C4—22no—
1314C2×C4—22no—
1315C2×C4—22no—
1316C2×C4—22no—
1317C2×C4—22no—
1318C2×C4—24no—
1319C2×C4—22no—
1320C2×C4—22no—
1321C2×C4—22no—
1322C2×C4—22no—
1323C2×C4—21no—
1324C2×C4—22no—
1325C2×C4—22no—
1326C2×C4—22no—
1327C2×C4—24no—
1328C2×C4—24no—
1329C2×C4—22no—
1330C2×C4—22no—
1331C2×C4—416no—
1332C2×C4—416no—
1333C2×C4—88no—
1334C2×C4—88no—
1335C2×C4—88no—
1336C2×C4—164no—
1337C2×C4—164no—
1338C2×C4C23×Q812yes—
1339C2×C4C23×Q814yes—
1340C2×C4C23×Q814yes—
1341C2×C4C23×Q814yes—
1342C2×C4C23×Q814yes—
1343C2×C4C23×Q812yes—
1344C2×C4C23×Q812yes—
1345C2×C4C22×#4112yes—
1346C2×C4C22×#4118yes—
1347C2×C4C22×#4112yes—
1348C2×C4C22×#4112yes—
1349C2×C4C2×H(5,𝔽2)12yes—
1350C2×C4C2×H(5,𝔽2)14yes—
1351C2×C4#58512yes—
1352C22—28no—
1353C22—28no—
1354C22—28no—
1355C22—44no—
1356C22—44no—
1357C22—44no—
1358C22—44no—
1359C22C24×Q811yescharacteristic
1360C22C23×#4111yescharacteristic
1361C22C22×H(5,𝔽2)11yescharacteristic
1362C22C2×#58511yescharacteristic
1363C22H(7,𝔽2)11yescharacteristic
1364C222−1+611yescharacteristic
1365C222−1+611yescharacteristic
1366C4—24no—
1367C4—24no—
1368C4—22no—
1369C4—24no—
1370C4—28no—
1371C4—22no—
1372C4—22no—
1373C4—22no—
1374C4—24no—
1375C4—22no—
1376C4—24no—
1377C4—42no—
1378C4—44no—
1379C4—42no—
1380C4—42no—
1381C4—42no—
1382C4—42no—
1383C4—42no—
1384C4—44no—
1385C4—41no—
1386C4—42no—
1387C4—42no—
1388C4—42no—
1389C4—42no—
1390C4—44no—
1391C4—44no—
1392C4—42no—
1393C4Q8×#4114yes—
1394C2—48no—
1395C2C2×Q8×#4111yescharacteristic
1396C2#6285011yescharacteristic
1397C2#6285411yescharacteristic
1398C2#6296011yescharacteristic
1399C2Q8×H(5,𝔽2)11yescharacteristic
1400C2#6298311yescharacteristic
1401C2#6306911yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#127C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59926C2semidirect
3. #59460C2semidirect
4. #59096C2semidirect
5. #52274C2semidirect
6. #52162C2semidirect
7. #45213C2semidirect
9. #44934C2semidirect
10. #44233C2semidirect
11. #43564C2semidirect
12. #43137C2semidirect
13. #39700C2semidirect
14. #39675C2semidirect
15. #39644C2semidirect
17. #39621C2semidirect
18. #39181C2semidirect
19. #38453C2semidirect
20. #38440C2semidirect
21. #36286C2semidirect
22. #36132C2semidirect
23. #35952C2semidirect
24. #35871C2semidirect
25. #35867C2semidirect
26. #34335C2semidirect
27. #34334C2semidirect
260. #559Q8semidirect
759. #124C2×Q8semidirect
760. #124C2×Q8semidirect
761. #123C2×Q8semidirect
787. C4×Q8C2×Q8semidirect
788. C4×Q8C2×Q8semidirect
799. C4×D4C2×Q8semidirect
800. C4×D4C2×Q8semidirect

Maximal subgroups

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

subgroupindex
#599262
#598172
#594602
#590962
#522742
#521622
#452132
#449522
#449342
#442332
#435642
#431372
#397002
#396752
#396442
#396282
#396212
#391812
#384532
#384402
#362862
#361322
#359522
#358712
#358672
#343352
#343342
#343312
#343292