Finite Group Databasebeta

← #8461321

Subgroups — #8461321

Order 512.

3945 conjugacy classes of subgroups.

The subgroup lattice has 1523 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59870C211yesmaximal, characteristic, complemented
2#59445C211yesmaximal, characteristic, complemented
3#59445C211yesmaximal, characteristic, complemented
4#58689C214yesmaximal, complemented
5#58230C214yesmaximal, complemented
6#54072C214yesmaximal, complemented
7#53156C212yesmaximal, complemented
8#53140C212yesmaximal, complemented
9#48618C214yesmaximal, complemented
10#46191C212yesmaximal, complemented
11#45674C212yesmaximal, complemented
12#45329C212yesmaximal, complemented
13#45202C212yesmaximal, complemented
14#42755C212yesmaximal
15#42713C212yesmaximal, complemented
16#42530C212yesmaximal
17#42455C212yesmaximal, complemented
18#40199C212yesmaximal, complemented
19#39780C212yesmaximal
20#39754C211yesmaximal, characteristic, complemented
21#39681C212yesmaximal, complemented
22#39506C211yesmaximal, characteristic
23#39478C212yesmaximal, complemented
24#39192C211yesmaximal, characteristic
25#39182C211yesmaximal, characteristic, complemented
26#37637C211yesmaximal, characteristic
27#37382C212yesmaximal, complemented
28#37367C212yesmaximal
29#36574C211yesmaximal, characteristic, complemented
30#36497C211yesmaximal, characteristic, complemented
31#36477C211yesmaximal, characteristic
32#35185C211yesmaximal, characteristic
33#35177C211yesmaximal, characteristic
34#34951C211yesmaximal, characteristic, complemented
35#34941C211yesmaximal, characteristic
36#2864C2212yes—
37#2864C2212yes—
38#2860C2212yes—
39#2859C2211yescharacteristic
40#2859C2211yescharacteristic
41#2859C2211yescharacteristic
42#2857C2212yes—
43#2855C2212yes—
44#2855C2212yes—
45#2839C2214yes—
46#2839C2214yes—
47#2839C2214yes—
48#2839C2214yes—
49#2839C2214yes—
50#2831C2214yes—
51#2831C2214yes—
52#2831C2214yes—
53#2810C2214yes—
54#2806C2214yes—
55#2805C2214yes—
56#2805C2214yes—
57#2802C2214yes—
58#2802C2214yes—
59#2799C2214yes—
60#2798C2214yes—
61#2798C2214yes—
62#2791C2214yes—
63#2791C2214yes—
64#2783C2214yes—
65#2783C2214yes—
66#2783C2214yes—
67#2774C2214yes—
68#2774C2214yes—
69#2774C2214yes—
70#2774C2214yes—
71#2774C2214yes—
72#2772C2214yes—
73#2772C2214yes—
74#2772C2214yes—
75#2772C2214yes—
76#2767C2214yes—
77#2767C2214yes—
78#2767C2214yes—
79#2767C2214yes—
80#2767C2214yes—
81#2767C2214yes—
82#2767C2214yes—
83#2767C2214yes—
84#2755C2214yes—
85#2755C2214yes—
86#2747C2214yes—
87#2747C2214yes—
88#2744C2214yes—
89#2744C2214yes—
90#2739C2214yes—
91#2739C2214yes—
92#2739C2214yes—
93#2725C2214yes—
94#2725C2214yes—
95#2725C2214yes—
96#2722C2214yes—
97#2719C2214yes—
98#2698C2214yes—
99#2698C2214yes—
100#2690C2214yes—
101#2689C2214yes—
102#2665C2214yes—
103#2664C2214yes—
104#2660C2212yes—
105#2654C2214yes—
106#2652C2214yes—
107#2650C2214yes—
108#2650C2214yes—
109#2647C2212yes—
110#2647C2212yes—
111#2644C2212yes—
112#2637C2214yes—
113#2637C2214yes—
114#2629C2212yes—
115#2625C2212yes—
116#2625C2212yes—
117#2621C2212yes—
118#2608C2214yes—
119#2588C2214yes—
120#2587C2214yes—
121#2585C2212yes—
122#2585C2212yes—
123#2584C2212yes—
124#2584C2212yes—
125#2584C2212yes—
126#2582C2211yescharacteristic
127#2581C2214yes—
128#2581C2212yes—
129#2581C2212yes—
130#2581C2214yes—
131#2574C2212yes—
132#2574C2212yes—
133#2571C2212yes—
134#2571C2212yes—
135#2571C2211yescharacteristic
136#2571C2212yes—
137#2570C2212yes—
138#2570C2212yes—
139#2570C2212yes—
140#2570C2212yes—
141#2570C2212yes—
142#2568C2211yescharacteristic
143#2568C2212yes—
144#2568C2212yes—
145#2567C2211yescharacteristic
146#2567C2211yescharacteristic
147#2567C2211yescharacteristic
148#2567C2211yescharacteristic
149#2566C2212yes—
150#2565C2214yes—
151#2563C2211yescharacteristic
152#2563C2211yescharacteristic
153#2552C2211yescharacteristic
154#2552C2212yes—
155#2552C2212yes—
156#2552C2211yescharacteristic
157#2552C2211yescharacteristic
158#2551C2211yescharacteristic
159#2550C2212yes—
160#2550C2212yes—
161#2550C2212yes—
162#2546C2211yescharacteristic
163#2538C2211yescharacteristic
164#2538C2211yescharacteristic
165#2538C2211yescharacteristic
166#2538C2211yescharacteristic
167#2520C2214yes—
168#2520C2214yes—
169#2513C2212yes—
170#2513C2212yes—
171#2513C2212yes—
172#2513C2212yes—
173#2512C2212yes—
174#2512C2212yes—
175#2511C2212yes—
176#2511C2212yes—
177#2511C2212yes—
178#2511C2211yescharacteristic
179#2511C2212yes—
180#2511C2211yescharacteristic
181#2511C2214yes—
182#2509C2212yes—
183#2509C2214yes—
184#2509C2212yes—
185#2509C2212yes—
186#2509C2212yes—
187#2509C2212yes—
188#2509C2212yes—
189#2509C2212yes—
190#2509C2212yes—
191#2508C2212yes—
192#2508C2212yes—
193#2508C2212yes—
194#2508C2212yes—
195#2508C2212yes—
196#2508C2212yes—
197#2508C2212yes—
198#2508C2212yes—
199#2508C2212yes—
200#2508C2211yescharacteristic
201#2508C2211yescharacteristic
202#2508C2214yes—
203#2507C2212yes—
204#2506C2212yes—
205#2506C2212yes—
206#2497C2212yes—
207#2497C2212yes—
208#2497C2212yes—
209#2496C2212yes—
210#2496C2212yes—
211#2496C2212yes—
212#2492C2212yes—
213#2489C2214yes—
214#2489C2212yes—
215#2489C2212yes—
216#2489C2212yes—
217#2469C2214yes—
218#2469C2214yes—
219#2469C2214yes—
220#2465C2214yes—
221#2462C2214yes—
222#2462C2214yes—
223#2462C2214yes—
224#2462C2214yes—
225#2454C2211yescharacteristic
226#2454C2211yescharacteristic
227#2453C2212yes—
228#2453C2212yes—
229#2453C2212yes—
230#2453C2212yes—
231#2453C2212yes—
232#2453C2212yes—
233#2452C2212yes—
234#2451C2212yes—
235#2446C2211yescharacteristic
236#2446C2212yes—
237#2446C2212yes—
238#2446C2211yescharacteristic
239#2429C2212yes—
240#2429C2212yes—
241#2423C2212yes—
242#2421C2214yes—
243#2421C2212yes—
244#2402C2212yes—
245#2402C2212yes—
246#2396C2212yes—
247#2396C2212yes—
248#2382C2214yes—
249#2370C2212yes—
250#2370C2212yes—
251#2370C2212yes—
252#2370C2212yes—
253#2370C2212yes—
254#2370C2212yes—
255#2365C2212yes—
256#2365C2212yes—
257#2357C2212yes—
258#2355C2212yes—
259#2355C2211yescharacteristic
260#2355C2212yes—
261#2355C2211yescharacteristic
262#2355C2211yescharacteristic
263#2355C2211yescharacteristic
264#2351C2212yes—
265Q8×C4⋊C4C2211yescharacteristic
266Q8×C4⋊C4C2212yes—
267Q8×C4⋊C4C2211yescharacteristic
268#2334C2214yes—
269#2331C2212yes—
270#2331C2212yes—
271#2330C2212yes—
272#2323C2212yes—
273#2323C2212yes—
274#2319C2212yes—
275#2314C2212yes—
276#2314C2212yes—
277C4×C4⋊Q8C2212yes—
278C4×C4⋊Q8C2211yescharacteristic
279C4×C4⋊Q8C2211yescharacteristic
280C4×C4⋊Q8C2211yescharacteristic
281C4×C4⋊Q8C2211yescharacteristic
282C4×C4⋊Q8C2211yescharacteristic
283C4×C4⋊Q8C2211yescharacteristic
284C4×C4⋊Q8C2211yescharacteristic
285C4×#125C2211yescharacteristic
286C4×#125C2211yescharacteristic
287C4×#125C2212yes—
288C4×C22⋊Q8C2212yes—
289C4×C22⋊Q8C2212yes—
290#2295C2212yes—
291#2295C2211yescharacteristic
292#2295C2211yescharacteristic
293#2293C2211yescharacteristic
294#2293C2211yescharacteristic
295#2285C2212yes—
296C42×Q8C2211yescharacteristic
297C42×Q8C2211yescharacteristic
298C42×D4C2211yescharacteristic
299C2×C4⋊Q8C2311yescharacteristic
300C2×C4⋊Q8C2311yescharacteristic
301C2×C4⋊Q8C2312yes—
302C2×C4⋊Q8C2311yescharacteristic
303C2×C4⋊Q8C2311yescharacteristic
304C2×C4⋊Q8C2311yescharacteristic
305C2×C4⋊Q8C2312yes—
306C2×#126C2314yes—
307C2×#126C2314yes—
308C2×#126C2314yes—
309C2×#125C2311yescharacteristic
310C2×#125C2311yescharacteristic
311C2×#125C2312yes—
312C2×#125C2312yes—
313C2×#125C2312yes—
314C2×#125C2312yes—
315C2×#125C2314yes—
316C2×#125C2314yes—
317C2×#125C2312yes—
318C2×C22⋊Q8C2312yes—
319C2×C22⋊Q8C2312yes—
320C2×C22⋊Q8C2312yes—
321C2×C22⋊Q8C2312yes—
322C2×C22⋊Q8C2314yes—
323C2×C4×Q8C2311yescharacteristic
324C2×C4×Q8C2311yescharacteristic
325C2×C4×Q8C2311yescharacteristic
326C2×C4×Q8C2311yescharacteristic
327C2×C4×Q8C2312yes—
328C2×C4×Q8C2312yes—
329C2×C4×Q8C2311yescharacteristic
330C2×C4×Q8C2312yes—
331C2×C4×Q8C2311yescharacteristic
332C2×C4×Q8C2312yes—
333C2×C4×Q8C2311yescharacteristic
334C2×C4×Q8C2311yescharacteristic
335C2×C4×Q8C2314yes—
336C2×C4×Q8C2312yes—
337C2×C4×Q8C2312yes—
338C2×C4×Q8C2314yes—
339C2×C4×D4C2311yescharacteristic
340C2×C4×D4C2311yescharacteristic
341C2×C4×D4C2311yescharacteristic
342C2×#117C2312yes—
343C2×#117C2312yes—
344C22×C42C2312yes—
345#400C2314yes—
346#400C2314yes—
347#400C2314yes—
348#400C2314yes—
349#400C2312yes—
350#400C2312yes—
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#400C2314yes—
367#400C2314yes—
368#400C2314yes—
369#400C2314yes—
370#400C2312yes—
371#400C2314yes—
372#400C2314yes—
373#400C2314yes—
374#400C2314yes—
375#400C2314yes—
376#400C2314yes—
377#400C2314yes—
378#400C2314yes—
379#400C2314yes—
380#400C2312yes—
381#400C2314yes—
382#400C2312yes—
383#400C2312yes—
384#400C2314yes—
385#400C2312yes—
386#400C2312yes—
387#400C2312yes—
388#400C2312yes—
389#400C2314yes—
390#400C2314yes—
391#399C2312yes—
392#399C2312yes—
393#398C2314yes—
394#398C2314yes—
395#398C2314yes—
396#398C2314yes—
397#398C2314yes—
398#398C2314yes—
399#398C2314yes—
400#398C2314yes—
401#398C2314yes—
402#398C2312yes—
403#398C2312yes—
404#398C2312yes—
405#398C2312yes—
406#398C2314yes—
407#398C2314yes—
408#398C2314yes—
409#398C2312yes—
410#398C2312yes—
411#398C2312yes—
412#398C2312yes—
413#398C2312yes—
414#398C2312yes—
415#398C2314yes—
416#398C2314yes—
417#398C2314yes—
418#398C2314yes—
419#398C2314yes—
420#398C2314yes—
421#398C2314yes—
422#398C2314yes—
423#398C2314yes—
424#398C2312yes—
425#398C2314yes—
426#398C2312yes—
427#398C2314yes—
428#398C2314yes—
429#398C2314yes—
430#397C2314yes—
431#397C2314yes—
432#397C2314yes—
433#397C2314yes—
434#397C2314yes—
435#397C2314yes—
436#397C2314yes—
437#397C2314yes—
438#397C2314yes—
439#397C2314yes—
440#397C2314yes—
441#397C2314yes—
442#397C2314yes—
443#396C2314yes—
444#396C2314yes—
445#396C2312yes—
446#396C2312yes—
447#396C2312yes—
448#396C2314yes—
449#396C2314yes—
450#396C2314yes—
451#396C2314yes—
452#396C2314yes—
453#396C2312yes—
454#396C2314yes—
455#396C2314yes—
456#395C2312yes—
457#395C2312yes—
458#395C2314yes—
459#395C2314yes—
460#395C2314yes—
461#395C2314yes—
462#395C2314yes—
463#395C2314yes—
464#395C2314yes—
465#395C2314yes—
466#395C2314yes—
467#393C2312yes—
468#393C2312yes—
469#393C2314yes—
470#393C2314yes—
471#391C2311yescharacteristic
472#391C2311yescharacteristic
473#391C2312yes—
474#391C2312yes—
475#391C2311yescharacteristic
476#391C2312yes—
477#391C2311yescharacteristic
478#391C2311yescharacteristic
479#391C2311yescharacteristic
480#391C2312yes—
481#391C2314yes—
482#391C2314yes—
483#391C2314yes—
484#391C2312yes—
485#391C2312yes—
486#391C2312yes—
487#391C2312yes—
488#391C2312yes—
489#391C2311yescharacteristic
490#391C2314yes—
491#391C2311yescharacteristic
492#391C2312yes—
493#391C2314yes—
494#391C2312yes—
495#391C2311yescharacteristic
496#391C2311yescharacteristic
497#391C2314yes—
498#391C2314yes—
499#391C2312yes—
500#391C2312yes—
501#391C2314yes—
502#391C2312yes—
503#390C2312yes—
504#390C2311yescharacteristic
505#390C2311yescharacteristic
506#390C2312yes—
507#390C2312yes—
508#390C2312yes—
509#390C2311yescharacteristic
510#390C2311yescharacteristic
511#389C2311yescharacteristic
512#389C2311yescharacteristic
513#389C2312yes—
514#389C2312yes—
515#389C2311yescharacteristic
516#389C2311yescharacteristic
517#389C2311yescharacteristic
518#389C2311yescharacteristic
519#389C2312yes—
520#389C2312yes—
521#389C2312yes—
522#389C2312yes—
523#389C2312yes—
524#389C2312yes—
525#389C2312yes—
526#389C2312yes—
527#389C2312yes—
528#389C2312yes—
529#389C2312yes—
530#389C2312yes—
531#389C2312yes—
532#389C2312yes—
533#389C2314yes—
534#389C2312yes—
535#389C2312yes—
536#389C2312yes—
537#389C2312yes—
538#389C2312yes—
539#389C2312yes—
540#389C2311yescharacteristic
541#389C2311yescharacteristic
542#389C2312yes—
543#389C2312yes—
544#389C2312yes—
545#389C2312yes—
546#389C2312yes—
547#389C2312yes—
548#389C2314yes—
549#389C2314yes—
550#389C2312yes—
551#389C2312yes—
552#389C2314yes—
553#389C2314yes—
554#389C2314yes—
555#389C2312yes—
556#389C2312yes—
557#389C2314yes—
558#389C2312yes—
559#389C2312yes—
560#389C2312yes—
561#389C2311yescharacteristic
562#389C2311yescharacteristic
563#389C2314yes—
564#389C2314yes—
565#389C2314yes—
566#389C2311yescharacteristic
567#389C2314yes—
568#389C2312yes—
569#389C2314yes—
570#389C2312yes—
571#389C2312yes—
572#389C2312yes—
573#389C2314yes—
574#389C2314yes—
575#389C2314yes—
576#389C2312yes—
577#389C2314yes—
578#389C2314yes—
579#389C2312yes—
580#389C2312yes—
581#389C2312yes—
582#389C2312yes—
583#389C2314yes—
584#389C2314yes—
585#389C2314yes—
586#389C2314yes—
587#389C2314yes—
588#389C2314yes—
589#389C2311yescharacteristic
590#389C2312yes—
591#389C2312yes—
592#389C2311yescharacteristic
593#389C2311yescharacteristic
594#389C2312yes—
595#388C2314yes—
596#388C2314yes—
597#388C2314yes—
598#388C2314yes—
599#388C2312yes—
600#388C2312yes—
601#388C2312yes—
602#388C2312yes—
603#388C2314yes—
604#388C2314yes—
605#388C2314yes—
606#388C2314yes—
607#388C2314yes—
608#388C2314yes—
609#388C2314yes—
610#388C2314yes—
611#388C2314yes—
612#388C2314yes—
613#388C2314yes—
614#388C2314yes—
615#388C2314yes—
616#387C2312yes—
617#387C2312yes—
618#387C2312yes—
619#387C2312yes—
620#387C2312yes—
621#387C2312yes—
622#387C2312yes—
623#387C2312yes—
624#387C2312yes—
625#387C2314yes—
626#387C2314yes—
627#387C2314yes—
628#387C2314yes—
629#387C2314yes—
630#387C2314yes—
631#387C2314yes—
632#387C2314yes—
633#387C2314yes—
634#387C2314yes—
635#387C2314yes—
636#387C2314yes—
637#387C2314yes—
638#387C2314yes—
639#387C2314yes—
640#387C2312yes—
641#387C2312yes—
642#387C2312yes—
643#387C2314yes—
644#387C2314yes—
645#387C2314yes—
646#387C2314yes—
647#387C2312yes—
648#387C2314yes—
649#387C2314yes—
650#387C2314yes—
651#387C2314yes—
652#387C2314yes—
653#387C2314yes—
654#387C2314yes—
655#387C2314yes—
656#387C2314yes—
657#387C2314yes—
658#387C2314yes—
659#387C2314yes—
660#387C2312yes—
661#387C2312yes—
662#387C2312yes—
663#387C2312yes—
664#387C2312yes—
665#387C2314yes—
666#387C2314yes—
667#387C2314yes—
668#387C2314yes—
669#387C2314yes—
670#387C2314yes—
671#387C2314yes—
672#387C2314yes—
673#387C2314yes—
674#387C2314yes—
675#387C2314yes—
676#387C2314yes—
677#387C2314yes—
678#387C2314yes—
679#387C2314yes—
680#387C2314yes—
681#387C2314yes—
682#387C2314yes—
683#387C2314yes—
684#387C2314yes—
685#387C2314yes—
686#387C2314yes—
687#385C2314yes—
688#385C2314yes—
689#385C2312yes—
690#385C2312yes—
691#385C2314yes—
692#384C2311yescharacteristic
693#384C2312yes—
694#384C2311yescharacteristic
695#384C2311yescharacteristic
696#384C2311yescharacteristic
697#384C2311yescharacteristic
698#384C2311yescharacteristic
699#384C2311yescharacteristic
700#384C2312yes—
701#384C2312yes—
702#384C2312yes—
703#384C2312yes—
704#384C2312yes—
705#384C2312yes—
706#384C2312yes—
707#382C2311yescharacteristic
708#382C2311yescharacteristic
709#382C2312yes—
710#382C2312yes—
711#382C2314yes—
712#382C2312yes—
713#382C2312yes—
714#382C2312yes—
715#382C2314yes—
716#382C2312yes—
717#382C2312yes—
718#382C2312yes—
719#382C2312yes—
720#382C2312yes—
721#382C2314yes—
722#382C2314yes—
723#382C2312yes—
724#382C2312yes—
725#382C2312yes—
726#382C2314yes—
727#382C2314yes—
728#382C2314yes—
729#382C2314yes—
730#382C2314yes—
731#381C2314yes—
732#381C2314yes—
733#380C2312yes—
734#380C2312yes—
735#380C2312yes—
736#380C2312yes—
737#380C2312yes—
738#380C2312yes—
739#380C2312yes—
740#380C2312yes—
741#380C2314yes—
742#380C2312yes—
743#380C2312yes—
744C4×C4⋊C4C2311yescharacteristic
745C4×C4⋊C4C2311yescharacteristic
746C4×C4⋊C4C2311yescharacteristic
747C4×C4⋊C4C2311yescharacteristic
748C4×C4⋊C4C2312yes—
749C4×C4⋊C4C2312yes—
750C4×C4⋊C4C2312yes—
751C4×C4⋊C4C2312yes—
752C4×C4⋊C4C2312yes—
753C4×C4⋊C4C2312yes—
754C4×C4⋊C4C2312yes—
755C4×C4⋊C4C2312yes—
756C4×C4⋊C4C2312yes—
757C4×C4⋊C4C2312yes—
758C4×C4⋊C4C2312yes—
759C4×C4⋊C4C2312yes—
760C4×C4⋊C4C2312yes—
761C4×C4⋊C4C2312yes—
762C4×C4⋊C4C2312yes—
763C4×C4⋊C4C2312yes—
764C4×C4⋊C4C2312yes—
765C4×C4⋊C4C2312yes—
766C4×C4⋊C4C2314yes—
767C4×C4⋊C4C2312yes—
768C4×C4⋊C4C2312yes—
769C4×C4⋊C4C2312yes—
770C4×C4⋊C4C2311yescharacteristic
771C4×C4⋊C4C2311yescharacteristic
772C4×C4⋊C4C2314yes—
773C4×C4⋊C4C2311yescharacteristic
774C4×C4⋊C4C2311yescharacteristic
775C4×C4⋊C4C2311yescharacteristic
776C4×C4⋊C4C2312yes—
777C4×C4⋊C4C2312yes—
778C4×C4⋊C4C2311yescharacteristic
779C4×C4⋊C4C2312yes—
780C4×C4⋊C4C2312yes—
781C4×C4⋊C4C2312yes—
782C4×C4⋊C4C2312yes—
783C4×C4⋊C4C2311yescharacteristic
784C4×C4⋊C4C2311yescharacteristic
785C4×C4⋊C4C2312yes—
786C4×C4⋊C4C2312yes—
787C4×C4⋊C4C2311yescharacteristic
788C4×C4⋊C4C2312yes—
789C4×C4⋊C4C2314yes—
790C4×C4⋊C4C2314yes—
791C4×C4⋊C4C2312yes—
792C4×C4⋊C4C2314yes—
793C4×C4⋊C4C2311yescharacteristic
794C4×C4⋊C4C2311yescharacteristic
795C4×C4⋊C4C2311yescharacteristic
796C4×C4⋊C4C2311yescharacteristic
797C4×C4⋊C4C2312yes—
798C4×C22⋊C4C2312yes—
799C4×C22⋊C4C2312yes—
800C4×C22⋊C4C2314yes—
801C4×C22⋊C4C2312yes—
802C4×C22⋊C4C2312yes—
803C4×C22⋊C4C2312yes—
804#376C2312yes—
805#376C2312yes—
806C43C2311yescharacteristic
807C43C2311yescharacteristic
808C43C2312yes—
809C43C2311yescharacteristic
810C22×Q8C2411yescharacteristic
811C22×Q8C2411yescharacteristic
812C22×Q8C2411yescharacteristic
813C22×Q8C2411yescharacteristic
814C22×Q8C2412yes—
815C22×Q8C2412yes—
816C22×Q8C2414yes—
817C22×D4C2411yescharacteristic
818C23×C4C2412yes—
819C23×C4C2412yes—
820C23×C4C2412yes—
821C4⋊Q8—28no—
822C4⋊Q8—24no—
823C4⋊Q8—24no—
824C4⋊Q8—44no—
825C4⋊Q8—42no—
826C4⋊Q8—42no—
827C4⋊Q8—42no—
828#126—48no—
829#126—84no—
830#126—84no—
831#125—24no—
832#125—24no—
833#125—28no—
834#125—44no—
835#125—44no—
836#125—44no—
837#125—48no—
838#125—84no—
839#125—82no—
840C22⋊Q8—44no—
841C22⋊Q8—44no—
842C22⋊Q8—44no—
843C22⋊Q8—44no—
844C22⋊Q8—84no—
845C4×Q8—24no—
846C4×Q8—24no—
847C4×Q8—24no—
848C4×Q8—24no—
849C4×Q8—42no—
850C4×Q8—44no—
851C4×Q8—44no—
852C4×Q8—44no—
853C4×Q8—42no—
854C4×Q8—44no—
855C4×Q8—42no—
856C4×Q8—42no—
857C4×Q8—82no—
858C4×Q8—84no—
859C4×Q8—84no—
860C4×Q8—82no—
861C4×D4—24no—
862C4×D4—24no—
863C4×D4—24no—
864#117—44no—
865#117—44no—
866C2×C4⋊C4C2411yescharacteristic
867C2×C4⋊C4C2411yescharacteristic
868C2×C4⋊C4C2412yes—
869C2×C4⋊C4C2412yes—
870C2×C4⋊C4C2411yescharacteristic
871C2×C4⋊C4C2411yescharacteristic
872C2×C4⋊C4C2414yes—
873C2×C4⋊C4C2411yescharacteristic
874C2×C4⋊C4C2411yescharacteristic
875C2×C4⋊C4C2411yescharacteristic
876C2×C4⋊C4C2411yescharacteristic
877C2×C4⋊C4C2411yescharacteristic
878C2×C4⋊C4C2412yes—
879C2×C4⋊C4C2411yescharacteristic
880C2×C4⋊C4C2411yescharacteristic
881C2×C4⋊C4C2412yes—
882C2×C4⋊C4C2412yes—
883C2×C4⋊C4C2412yes—
884C2×C4⋊C4C2412yes—
885C2×C4⋊C4C2412yes—
886C2×C4⋊C4C2412yes—
887C2×C4⋊C4C2412yes—
888C2×C4⋊C4C2412yes—
889C2×C4⋊C4C2411yescharacteristic
890C2×C4⋊C4C2411yescharacteristic
891C2×C4⋊C4C2412yes—
892C2×C4⋊C4C2412yes—
893C2×C4⋊C4C2414yes—
894C2×C4⋊C4C2412yes—
895C2×C4⋊C4C2414yes—
896C2×C4⋊C4C2412yes—
897C2×C4⋊C4C2411yescharacteristic
898C2×C4⋊C4C2411yescharacteristic
899C2×C4⋊C4C2412yes—
900C2×C4⋊C4C2412yes—
901C2×C4⋊C4C2412yes—
902C2×C4⋊C4C2414yes—
903C2×C4⋊C4C2412yes—
904C2×C4⋊C4C2412yes—
905C2×C4⋊C4C2412yes—
906C2×C4⋊C4C2412yes—
907C2×C4⋊C4C2412yes—
908C2×C4⋊C4C2412yes—
909C2×C4⋊C4C2414yes—
910C2×C4⋊C4C2412yes—
911C2×C4⋊C4C2412yes—
912C2×C4⋊C4C2414yes—
913C2×C4⋊C4C2414yes—
914C2×C4⋊C4C2414yes—
915C2×C4⋊C4C2414yes—
916C2×C4⋊C4C2414yes—
917C2×C4⋊C4C2411yescharacteristic
918C2×C4⋊C4C2411yescharacteristic
919C2×C4⋊C4C2411yescharacteristic
920C2×C4⋊C4C2411yescharacteristic
921C2×C4⋊C4C2411yescharacteristic
922C2×C4⋊C4C2412yes—
923C2×C4⋊C4C2412yes—
924C2×C4⋊C4C2412yes—
925C2×C4⋊C4C2414yes—
926C2×C4⋊C4C2414yes—
927C2×C4⋊C4C2412yes—
928C2×C4⋊C4C2412yes—
929C2×C4⋊C4C2412yes—
930C2×C4⋊C4C2412yes—
931C2×C4⋊C4C2414yes—
932C2×C4⋊C4C2412yes—
933C2×C4⋊C4C2412yes—
934C2×C4⋊C4C2414yes—
935C2×C4⋊C4C2414yes—
936C2×C4⋊C4C2414yes—
937C2×C4⋊C4C2412yes—
938C2×C4⋊C4C2412yes—
939C2×C4⋊C4C2414yes—
940C2×C4⋊C4C2414yes—
941C2×C4⋊C4C2412yes—
942C2×C4⋊C4C2414yes—
943C2×C4⋊C4C2412yes—
944C2×C4⋊C4C2414yes—
945C2×C4⋊C4C2412yes—
946C2×C4⋊C4C2412yes—
947C2×C4⋊C4C2414yes—
948C2×C4⋊C4C2414yes—
949C2×C4⋊C4C2414yes—
950C2×C4⋊C4C2414yes—
951C2×C4⋊C4C2414yes—
952C2×C4⋊C4C2412yes—
953C2×C4⋊C4C2412yes—
954C2×C4⋊C4C2414yes—
955C2×C4⋊C4C2414yes—
956C2×C4⋊C4C2412yes—
957C2×C4⋊C4C2412yes—
958C2×C4⋊C4C2412yes—
959C2×C4⋊C4C2412yes—
960C2×C4⋊C4C2412yes—
961C2×C4⋊C4C2412yes—
962C2×C4⋊C4C2414yes—
963C2×C4⋊C4C2411yescharacteristic
964C2×C22⋊C4C2412yes—
965C2×C22⋊C4C2412yes—
966C2×C22⋊C4C2412yes—
967C2×C22⋊C4C2412yes—
968C2×C22⋊C4C2412yes—
969C2×C22⋊C4C2412yes—
970C2×C22⋊C4C2412yes—
971C2×C22⋊C4C2412yes—
972C2×C22⋊C4C2414yes—
973C2×C22⋊C4C2414yes—
974C2×C22⋊C4C2414yes—
975C2×C22⋊C4C2412yes—
976C2×C22⋊C4C2414yes—
977C2×C22⋊C4C2414yes—
978C2×C22⋊C4C2412yes—
979C2×C22⋊C4C2412yes—
980C2×C22⋊C4C2414yes—
981C2×C22⋊C4C2414yes—
982C2×C22⋊C4C2414yes—
983C2×C42—44no—
984C2×C42C2411yescharacteristic
985C2×C42C2411yescharacteristic
986C2×C42C2412yes—
987C2×C42C2412yes—
988C2×C42C2411yescharacteristic
989C2×C42C2411yescharacteristic
990C2×C42C2411yescharacteristic
991C2×C42C2411yescharacteristic
992C2×C42C2411yescharacteristic
993C2×C42C2412yes—
994C2×C42C2411yescharacteristic
995C2×C42C2411yescharacteristic
996C2×C42C2412yes—
997C2×C42C2411yescharacteristic
998C2×C42C2412yes—
999C2×C42C2412yes—
1000C2×C42C2412yes—
1001C2×C42C2411yescharacteristic
1002C2×C42C2411yescharacteristic
1003C2×C42C2412yes—
1004C2×C42C2411yescharacteristic
1005C2×C42C2412yes—
1006C2×C42C2411yescharacteristic
1007C2×C42C2414yes—
1008C2×C42C2414yes—
1009C2×C42C2414yes—
1010C2×C42C2414yes—
1011C2×C42C2414yes—
1012C2×C42C2411yescharacteristic
1013C2×C42C2412yes—
1014C2×C42C2411yescharacteristic
1015C2×C42C2412yes—
1016C2×C42C2414yes—
1017C2×C42C2414yes—
1018C2×C42C2414yes—
1019C2×C42C2411yescharacteristic
1020C2×C42C2414yes—
1021C2×C42C2412yes—
1022C2×C42C2412yes—
1023C2×C42C2411yescharacteristic
1024C2×C42C2411yescharacteristic
1025#95C2412yes—
1026#95C2412yes—
1027#95C2412yes—
1028#95C2412yes—
1029#95C2412yes—
1030#95C2412yes—
1031#95C2412yes—
1032#95C2412yes—
1033#95C2412yes—
1034#95C2412yes—
1035#95C2412yes—
1036#95C2412yes—
1037#95C2414yes—
1038#95C2412yes—
1039#95C2412yes—
1040#95C2412yes—
1041#95C2412yes—
1042#95C2411yescharacteristic
1043#95C2411yescharacteristic
1044#95C2411yescharacteristic
1045#95C2412yes—
1046#95C2412yes—
1047#95C2412yes—
1048#95C2411yescharacteristic
1049#95C2412yes—
1050#95C2412yes—
1051#95C2411yescharacteristic
1052#95C2412yes—
1053#95C2412yes—
1054#95C2411yescharacteristic
1055#95C2414yes—
1056#95C2412yes—
1057#95C2412yes—
1058#95C2412yes—
1059#95C2412yes—
1060#95C2412yes—
1061#95C2414yes—
1062#95C2412yes—
1063#95C2412yes—
1064#95C2412yes—
1065#95C2412yes—
1066#95C2414yes—
1067#95C2414yes—
1068#95C2412yes—
1069#95C2412yes—
1070#95C2414yes—
1071#95C2412yes—
1072#95C2412yes—
1073#95C2414yes—
1074#95C2414yes—
1075#95C2414yes—
1076#95C2412yes—
1077#95C2414yes—
1078#95C2414yes—
1079#95C2414yes—
1080#95C2414yes—
1081#95C2414yes—
1082#95C2412yes—
1083#95C2414yes—
1084#95C2412yes—
1085#95C2412yes—
1086#95C2412yes—
1087#95C2412yes—
1088#95C2412yes—
1089#95C2412yes—
1090#95C2414yes—
1091#95C2414yes—
1092#95C2414yes—
1093#95C2414yes—
1094#95C2414yes—
1095#95C2414yes—
1096#95C2414yes—
1097#95C2412yes—
1098#95C2412yes—
1099#95C2414yes—
1100#95C2414yes—
1101#95C2414yes—
1102#95C2414yes—
1103#95C2414yes—
1104#95C2414yes—
1105#95C2414yes—
1106#95C2414yes—
1107#95C2414yes—
1108#95C2414yes—
1109#95C2414yes—
1110#95C2414yes—
1111#95C2414yes—
1112#95C2414yes—
1113#95C2414yes—
1114#95C2414yes—
1115#95C2414yes—
1116#95C2414yes—
1117#95C2414yes—
1118#95C2414yes—
1119C24C2512yes—
1120C2×Q8—22no—
1121C2×Q8—22no—
1122C2×Q8—22no—
1123C2×Q8—22no—
1124C2×Q8—24no—
1125C2×Q8—24no—
1126C2×Q8—28no—
1127C2×Q8—22no—
1128C2×Q8—22no—
1129C2×Q8—22no—
1130C2×Q8—22no—
1131C2×Q8—22no—
1132C2×Q8—22no—
1133C2×Q8—22no—
1134C2×Q8—41no—
1135C2×Q8—42no—
1136C2×Q8—42no—
1137C2×Q8—42no—
1138C2×Q8—42no—
1139C2×Q8—44no—
1140C2×Q8—44no—
1141C2×D4—22no—
1142C2×D4—22no—
1143C2×D4—22no—
1144C22×C4—24no—
1145C22×C4—24no—
1146C22×C4—24no—
1147C22×C4—24no—
1148C22×C4—24no—
1149C22×C4—42no—
1150C22×C4—42no—
1151C22×C4—42no—
1152C22×C4—42no—
1153C22×C4C2511yescharacteristic
1154C22×C4C2511yescharacteristic
1155C22×C4C2512yes—
1156C22×C4C2512yes—
1157C22×C4C2512yes—
1158C22×C4C2512yes—
1159C22×C4C2512yes—
1160C22×C4C2512yes—
1161C22×C4C2511yescharacteristic
1162C22×C4C2511yescharacteristic
1163C22×C4C2512yes—
1164C22×C4C2511yescharacteristic
1165C22×C4C2512yes—
1166C22×C4C2512yes—
1167C22×C4C2514yes—
1168C22×C4C2512yes—
1169C22×C4C2512yes—
1170C22×C4C2514yes—
1171C22×C4C2514yes—
1172C22×C4C2511yescharacteristic
1173C22×C4C2512yes—
1174C22×C4C2511yescharacteristic
1175C22×C4C2511yescharacteristic
1176C22×C4C2511yescharacteristic
1177C22×C4C2512yes—
1178C22×C4C2512yes—
1179C22×C4C2514yes—
1180C22×C4C2511yescharacteristic
1181C22×C4C2512yes—
1182C22×C4C2511yescharacteristic
1183C22×C4C2511yescharacteristic
1184C22×C4C2511yescharacteristic
1185C22×C4C2511yescharacteristic
1186C22×C4C2511yescharacteristic
1187C4⋊C4—22no—
1188C4⋊C4—22no—
1189C4⋊C4—22no—
1190C4⋊C4—22no—
1191C4⋊C4—22no—
1192C4⋊C4—22no—
1193C4⋊C4—22no—
1194C4⋊C4—24no—
1195C4⋊C4—22no—
1196C4⋊C4—24no—
1197C4⋊C4—24no—
1198C4⋊C4—24no—
1199C4⋊C4—24no—
1200C4⋊C4—24no—
1201C4⋊C4—24no—
1202C4⋊C4—28no—
1203C4⋊C4—28no—
1204C4⋊C4—22no—
1205C4⋊C4—22no—
1206C4⋊C4—24no—
1207C4⋊C4—24no—
1208C4⋊C4—28no—
1209C4⋊C4—24no—
1210C4⋊C4—24no—
1211C4⋊C4—24no—
1212C4⋊C4—22no—
1213C4⋊C4—22no—
1214C4⋊C4—24no—
1215C4⋊C4—24no—
1216C4⋊C4—24no—
1217C4⋊C4—22no—
1218C4⋊C4—22no—
1219C4⋊C4—28no—
1220C4⋊C4—22no—
1221C4⋊C4—24no—
1222C4⋊C4—24no—
1223C4⋊C4—24no—
1224C4⋊C4—42no—
1225C4⋊C4—42no—
1226C4⋊C4—42no—
1227C4⋊C4—42no—
1228C4⋊C4—41no—
1229C4⋊C4—42no—
1230C4⋊C4—41no—
1231C4⋊C4—42no—
1232C4⋊C4—41no—
1233C4⋊C4—41no—
1234C4⋊C4—42no—
1235C4⋊C4—41no—
1236C4⋊C4—44no—
1237C4⋊C4—42no—
1238C4⋊C4—42no—
1239C4⋊C4—44no—
1240C4⋊C4—42no—
1241C4⋊C4—42no—
1242C4⋊C4—42no—
1243C4⋊C4—44no—
1244C4⋊C4—42no—
1245C4⋊C4—42no—
1246C4⋊C4—44no—
1247C4⋊C4—44no—
1248C4⋊C4—44no—
1249C4⋊C4—44no—
1250C4⋊C4—44no—
1251C4⋊C4—42no—
1252C4⋊C4—44no—
1253C4⋊C4—44no—
1254C4⋊C4—42no—
1255C4⋊C4—44no—
1256C4⋊C4—42no—
1257C4⋊C4—44no—
1258C4⋊C4—42no—
1259C4⋊C4—42no—
1260C4⋊C4—42no—
1261C4⋊C4—42no—
1262C4⋊C4—44no—
1263C4⋊C4—44no—
1264C4⋊C4—44no—
1265C4⋊C4—44no—
1266C4⋊C4—44no—
1267C4⋊C4—44no—
1268C4⋊C4—44no—
1269C4⋊C4—42no—
1270C4⋊C4—42no—
1271C4⋊C4—44no—
1272C4⋊C4—44no—
1273C4⋊C4—44no—
1274C4⋊C4—44no—
1275C4⋊C4—42no—
1276C4⋊C4—42no—
1277C4⋊C4—42no—
1278C4⋊C4—42no—
1279C4⋊C4—44no—
1280C4⋊C4—42no—
1281C4⋊C4—42no—
1282C4⋊C4—42no—
1283C4⋊C4—42no—
1284C4⋊C42−1+414yes—
1285C22⋊C4—24no—
1286C22⋊C4—24no—
1287C22⋊C4—24no—
1288C22⋊C4—24no—
1289C22⋊C4—42no—
1290C22⋊C4—42no—
1291C22⋊C4—42no—
1292C22⋊C4—42no—
1293C22⋊C4—42no—
1294C22⋊C4—44no—
1295C22⋊C4—44no—
1296C22⋊C4—44no—
1297C22⋊C4—44no—
1298C22⋊C4—44no—
1299C22⋊C4—44no—
1300C22⋊C4—44no—
1301C22⋊C4—42no—
1302C22⋊C4—44no—
1303C22⋊C4—42no—
1304C42—22no—
1305C42—22no—
1306C42—24no—
1307C42—24no—
1308C42—24no—
1309C42—22no—
1310C42—22no—
1311C42—22no—
1312C42—24no—
1313C42—22no—
1314C42—24no—
1315C42—22no—
1316C42—22no—
1317C42—24no—
1318C42—24no—
1319C42—22no—
1320C42—22no—
1321C42—22no—
1322C42—22no—
1323C42—24no—
1324C42—42no—
1325C42—42no—
1326C42—44no—
1327C42—42no—
1328C42—41no—
1329C42—41no—
1330C42—44no—
1331C42—42no—
1332C42—44no—
1333C42—41no—
1334C42—44no—
1335C42—41no—
1336C42—44no—
1337C42—42no—
1338C42—44no—
1339C42—44no—
1340C42—44no—
1341C42—44no—
1342C42—41no—
1343C422−1+414yes—
1344C422−1+414yes—
1345C23—22no—
1346C23—22no—
1347C23—22no—
1348C23—22no—
1349C23—22no—
1350C23—22no—
1351C23—22no—
1352C23C2611yescharacteristic
1353Q8—44no—
1354Q8—48no—
1355Q8—48no—
1356Q8—44no—
1357Q8—44no—
1358Q8—44no—
1359Q8—88no—
1360D4—44no—
1361C2×C4—21no—
1362C2×C4—22no—
1363C2×C4—21no—
1364C2×C4—21no—
1365C2×C4—21no—
1366C2×C4—21no—
1367C2×C4—21no—
1368C2×C4—21no—
1369C2×C4—21no—
1370C2×C4—22no—
1371C2×C4—21no—
1372C2×C4—21no—
1373C2×C4—21no—
1374C2×C4—22no—
1375C2×C4—22no—
1376C2×C4—22no—
1377C2×C4—22no—
1378C2×C4—21no—
1379C2×C4—21no—
1380C2×C4—21no—
1381C2×C4—21no—
1382C2×C4—22no—
1383C2×C4—22no—
1384C2×C4—22no—
1385C2×C4—21no—
1386C2×C4—21no—
1387C2×C4—22no—
1388C2×C4—22no—
1389C2×C4—22no—
1390C2×C4—22no—
1391C2×C4—22no—
1392C2×C4—24no—
1393C2×C4—24no—
1394C2×C4—24no—
1395C2×C4—22no—
1396C2×C4—22no—
1397C2×C4—24no—
1398C2×C4—21no—
1399C2×C4—21no—
1400C2×C4—22no—
1401C2×C4—21no—
1402C2×C4—22no—
1403C2×C4—21no—
1404C2×C4—21no—
1405C2×C4—22no—
1406C2×C4—21no—
1407C2×C4—22no—
1408C2×C4—22no—
1409C2×C4—22no—
1410C2×C4—22no—
1411C2×C4—21no—
1412C2×C4—21no—
1413C2×C4—21no—
1414C2×C4—21no—
1415C2×C4—22no—
1416C2×C4—24no—
1417C2×C4—22no—
1418C2×C4—22no—
1419C2×C4—22no—
1420C2×C4—22no—
1421C2×C4—22no—
1422C2×C4—21no—
1423C2×C4—24no—
1424C2×C4—24no—
1425C2×C4—24no—
1426C2×C4—22no—
1427C2×C4—21no—
1428C2×C4—21no—
1429C2×C4—22no—
1430C2×C4—22no—
1431C2×C4—22no—
1432C2×C4—22no—
1433C2×C4—22no—
1434C2×C4—24no—
1435C2×C4—22no—
1436C2×C4—22no—
1437C2×C4—22no—
1438C2×C4—21no—
1439C2×C4—22no—
1440C2×C4—24no—
1441C2×C4—21no—
1442C2×C4—22no—
1443C2×C4—24no—
1444C2×C4—22no—
1445C2×C4—24no—
1446C2×C4—22no—
1447C2×C4—21no—
1448C2×C4—22no—
1449C2×C4—21no—
1450C2×C4—21no—
1451C2×C4—22no—
1452C2×C4—48no—
1453C2×C4—84no—
1454C2×C4—84no—
1455C2×C4C2×2−1+412yes—
1456C2×C4C2×2−1+412yes—
1457C2×C4C2×2−1+412yes—
1458C2×C4C2×2−1+414yes—
1459C2×C4C2×2−1+412yes—
1460C2×C4C2×2−1+412yes—
1461C2×C4C2×2−1+412yes—
1462C2×C4C2×2−1+412yes—
1463C2×C4#58512yes—
1464C2×C4#58512yes—
1465C2×C4#58512yes—
1466C22—42no—
1467C22—42no—
1468C22—42no—
1469C22—42no—
1470C22—42no—
1471C22—42no—
1472C22—42no—
1473C22C22×2−1+411yescharacteristic
1474C22C22×2−1+411yescharacteristic
1475C22C22×2−1+411yescharacteristic
1476C22C2×#58511yescharacteristic
1477C22C2×#58511yescharacteristic
1478C22C2×#58511yescharacteristic
1479C22H(7,𝔽2)11yescharacteristic
1480C4—22no—
1481C4—22no—
1482C4—22no—
1483C4—22no—
1484C4—24no—
1485C4—42no—
1486C4—42no—
1487C4—42no—
1488C4—42no—
1489C4—41no—
1490C4—41no—
1491C4—41no—
1492C4—42no—
1493C4—42no—
1494C4—42no—
1495C4—44no—
1496C4—42no—
1497C4—41no—
1498C4—41no—
1499C4—42no—
1500C4—41no—
1501C4—42no—
1502C4—42no—
1503C4—44no—
1504C4—42no—
1505C4—42no—
1506C4—44no—
1507C4—41no—
1508C4—41no—
1509C4—41no—
1510C4—44no—
1511C4—42no—
1512C4#355614yes—
1513C4#356514yes—
1514C2—82no—
1515C2C2×#356511yescharacteristic
1516C2C2×#355611yescharacteristic
1517C2#6283111yescharacteristic
1518C2#6292611yescharacteristic
1519C2#6292611yescharacteristic
1520C2#6295111yescharacteristic
1521C2#6303411yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC22×D4C24
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59870C2semidirect
2. #59445C2semidirect
3. #59445C2semidirect
4. #58689C2semidirect
5. #58230C2semidirect
6. #54072C2semidirect
7. #53156C2semidirect
8. #53140C2semidirect
9. #48618C2semidirect
10. #46191C2semidirect
11. #45674C2semidirect
12. #45329C2semidirect
13. #45202C2semidirect
15. #42713C2semidirect
17. #42455C2semidirect
18. #40199C2semidirect
20. #39754C2semidirect
21. #39681C2semidirect
23. #39478C2semidirect
25. #39182C2semidirect
27. #37382C2semidirect
29. #36574C2semidirect
30. #36497C2semidirect
34. #34951C2semidirect

Maximal subgroups

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

subgroupindex
#598702
#594452
#586892
#582302
#540722
#531562
#531402
#486182
#461912
#456742
#453292
#452022
#427552
#427132
#425302
#424552
#401992
#397802
#397542
#396812
#395062
#394782
#391922
#391822
#376372
#373822
#373672
#365742
#364972
#364772
#351852
#351772
#349512
#349412