Finite Group Databasebeta

← #7715643

Subgroups — #7715643

Order 512.

4596 conjugacy classes of subgroups.

The subgroup lattice has 1510 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#48844C214yesmaximal, complemented
2#48840C214yesmaximal, complemented
3#47969C214yesmaximal, complemented
4#47965C214yesmaximal, complemented
5#47819C212yesmaximal, complemented
6#47818C212yesmaximal, complemented
7#47817C212yesmaximal, complemented
8#47814C212yesmaximal, complemented
9#47773C212yesmaximal, complemented
10#47772C212yesmaximal, complemented
11#47726C212yesmaximal, complemented
12#47725C212yesmaximal, complemented
13#38106C212yesmaximal, complemented
14#38105C212yesmaximal, complemented
15#38101C212yesmaximal, complemented
16#38098C212yesmaximal, complemented
17#37879C212yesmaximal, complemented
18#37875C212yesmaximal, complemented
19#37690C212yesmaximal, complemented
20#37686C212yesmaximal, complemented
21#37642C211yesmaximal, characteristic, complemented
22#37565C211yesmaximal, characteristic, complemented
23#37426C211yesmaximal, characteristic, complemented
24#37310C212yesmaximal, complemented
25#37306C211yesmaximal, characteristic, complemented
26#35334C211yesmaximal, characteristic, complemented
27#35304C212yesmaximal, complemented
28#35279C211yesmaximal, characteristic, complemented
29#35257C212yesmaximal, complemented
30#34367C212yesmaximal
31#34070C211yesmaximal, characteristic
32C2×#544C2212yes—
33C2×#533C2211yescharacteristic
34C2×#532C2211yescharacteristic
35C22×C4⋊Q8C2211yescharacteristic
36C2×C4×#41C2211yescharacteristic
37C2×C4×#41C2211yescharacteristic
38#2857C2212yes—
39#2857C2212yes—
40#2857C2212yes—
41#2857C2212yes—
42#2851C2212yes—
43#2851C2212yes—
44#2851C2212yes—
45#2851C2212yes—
46#2844C2212yes—
47#2844C2212yes—
48#2843C2212yes—
49#2843C2212yes—
50#2811C2212yes—
51#2809C2212yes—
52#2807C2214yes—
53#2806C2214yes—
54#2805C2214yes—
55#2804C2214yes—
56#2804C2214yes—
57#2804C2212yes—
58#2802C2214yes—
59#2799C2212yes—
60#2799C2212yes—
61#2799C2214yes—
62#2792C2214yes—
63#2790C2214yes—
64#2788C2214yes—
65#2788C2214yes—
66#2784C2212yes—
67#2784C2212yes—
68#2784C2214yes—
69#2784C2214yes—
70#2784C2214yes—
71#2780C2214yes—
72#2780C2214yes—
73#2780C2214yes—
74#2780C2214yes—
75#2774C2214yes—
76#2774C2214yes—
77#2768C2214yes—
78#2768C2214yes—
79#2768C2214yes—
80#2763C2214yes—
81#2763C2214yes—
82#2755C2214yes—
83#2748C2214yes—
84#2742C2214yes—
85#2734C2214yes—
86#2732C2214yes—
87#2729C2214yes—
88#2729C2214yes—
89#2729C2214yes—
90#2713C2214yes—
91#2704C2214yes—
92#2692C2214yes—
93#2692C2214yes—
94#2692C2214yes—
95#2692C2214yes—
96#2692C2214yes—
97#2692C2214yes—
98#2683C2214yes—
99#2683C2212yes—
100#2677C2214yes—
101#2677C2214yes—
102#2667C2214yes—
103#2665C2214yes—
104#2660C2212yes—
105#2660C2212yes—
106#2647C2212yes—
107#2647C2212yes—
108#2629C2212yes—
109#2629C2212yes—
110#2628C2211yescharacteristic
111#2628C2211yescharacteristic
112#2628C2211yescharacteristic
113#2628C2211yescharacteristic
114#2628C2211yescharacteristic
115#2628C2214yes—
116#2628C2214yes—
117#2628C2212yes—
118#2628C2212yes—
119#2628C2211yescharacteristic
120#2628C2211yescharacteristic
121#2628C2211yescharacteristic
122#2612C2212yes—
123#2612C2212yes—
124#2612C2214yes—
125#2612C2214yes—
126#2606C2214yes—
127#2605C2214yes—
128#2589C2214yes—
129#2588C2214yes—
130#2588C2214yes—
131#2587C2214yes—
132#2586C2214yes—
133#2585C2214yes—
134#2583C2214yes—
135#2581C2212yes—
136#2581C2212yes—
137#2580C2212yes—
138#2580C2212yes—
139#2574C2214yes—
140#2574C2214yes—
141#2571C2212yes—
142#2571C2212yes—
143#2571C2212yes—
144#2570C2212yes—
145#2570C2212yes—
146#2569C2214yes—
147#2568C2212yes—
148#2567C2212yes—
149#2564C2212yes—
150#2564C2212yes—
151#2564C2212yes—
152#2564C2212yes—
153#2564C2214yes—
154#2564C2214yes—
155#2563C2212yes—
156#2551C2212yes—
157#2551C2212yes—
158#2551C2212yes—
159#2550C2212yes—
160#2550C2212yes—
161#2549C2214yes—
162#2549C2214yes—
163#2542C2212yes—
164#2522C2214yes—
165#2520C2214yes—
166#2511C2214yes—
167#2505C2214yes—
168#2505C2214yes—
169#2505C2214yes—
170#2492C2214yes—
171#2487C2214yes—
172#2487C2212yes—
173#2487C2212yes—
174#2473C2214yes—
175#2465C2214yes—
176#2462C2214yes—
177#2454C2214yes—
178#2453C2214yes—
179#2452C2214yes—
180#2451C2214yes—
181#2451C2214yes—
182#2450C2214yes—
183#2450C2214yes—
184#2450C2214yes—
185#2450C2214yes—
186#2449C2214yes—
187#2449C2214yes—
188#2449C2214yes—
189#2449C2214yes—
190#2442C2212yes—
191#2442C2212yes—
192#2442C2212yes—
193#2442C2212yes—
194#2441C2212yes—
195#2441C2212yes—
196#2440C2212yes—
197#2440C2212yes—
198#2440C2212yes—
199#2440C2214yes—
200#2440C2212yes—
201#2439C2212yes—
202#2439C2212yes—
203#2439C2212yes—
204#2439C2212yes—
205#2439C2212yes—
206#2439C2212yes—
207#2438C2214yes—
208#2438C2214yes—
209#2434C2214yes—
210#2429C2214yes—
211#2409C2214yes—
212#2409C2212yes—
213#2409C2212yes—
214#2377C2214yes—
215#2377C2214yes—
216#2363C2214yes—
217#2363C2214yes—
218#2354C2212yes—
219#2354C2212yes—
220#2352C2212yes—
221#2352C2212yes—
222#2352C2212yes—
223#2352C2212yes—
224D4×C4⋊C4C2212yes—
225D4×C4⋊C4C2212yes—
226#2337C2214yes—
227#2337C2214yes—
228#2331C2212yes—
229#2331C2214yes—
230#2331C2212yes—
231#2330C2212yes—
232#2330C2212yes—
233#2328C2211yescharacteristic
234#2328C2211yescharacteristic
235#2328C2214yes—
236#2327C2211yescharacteristic
237#2327C2211yescharacteristic
238#2326C2211yescharacteristic
239#2326C2211yescharacteristic
240#2326C2211yescharacteristic
241#2326C2211yescharacteristic
242#2325C2212yes—
243#2325C2212yes—
244#2325C2212yes—
245#2325C2212yes—
246#2317C2212yes—
247#2317C2212yes—
248#2316C2212yes—
249#2311C2212yes—
250#2311C2212yes—
251#2311C2212yes—
252#2311C2212yes—
253#2297C2211yescharacteristic
254#2297C2211yescharacteristic
255#2296C2212yes—
256C2×#389C2212yes—
257#2290C2212yes—
258#2290C2212yes—
259#2290C2212yes—
260#2290C2212yes—
261#2285C2211yescharacteristic
262#2285C2212yes—
263#2285C2211yescharacteristic
264#2283C2212yes—
265C2×#382C2211yescharacteristic
266C2×#376C2211yescharacteristic
267C22×#41C2311yescharacteristic
268C22×#41C2311yescharacteristic
269C23×Q8C2312yes—
270#544—48no—
271#533—44no—
272#532Q8116yescomplemented
273C2×C4⋊Q8—44no—
274C2×C4⋊Q8C2312yes—
275C2×C4⋊Q8C2312yes—
276C2×C4⋊Q8C2312yes—
277C2×C4⋊Q8C2312yes—
278C2×C4⋊Q8C2312yes—
279C2×C4⋊Q8C2311yescharacteristic
280C2×C4⋊Q8C2311yescharacteristic
281C2×C4⋊Q8C2311yescharacteristic
282C2×C4⋊Q8C2311yescharacteristic
283C2×C4⋊Q8C2314yes—
284C2×C4⋊Q8C2314yes—
285C2×C4⋊Q8C2314yes—
286C2×C4⋊Q8C2311yescharacteristic
287C2×#127C2311yescharacteristic
288C2×#125C2312yes—
289C2×#125C2312yes—
290C2×#125C2312yes—
291C2×#125C2314yes—
292C2×#124C2311yescharacteristic
293C2×#124C2311yescharacteristic
294C2×C22⋊Q8C2312yes—
295C2×C22⋊Q8C2312yes—
296C2×C22⋊Q8C2314yes—
297C2×C22⋊Q8C2314yes—
298C2×C22⋊Q8C2314yes—
299C2×C22⋊Q8C2314yes—
300C2×C22⋊Q8C2314yes—
301C2×C22⋊Q8C2314yes—
302C2×C22⋊Q8C2314yes—
303C2×C22⋊Q8C2314yes—
304C2×C22⋊Q8C2314yes—
305C2×C22⋊Q8C2314yes—
306C2×#121C2312yes—
307C2×#121C2312yes—
308C4×#41—44no—
309C4×#41—44no—
310C2×C4×Q8C2311yescharacteristic
311C2×C4×Q8C2311yescharacteristic
312C2×C4×Q8C2312yes—
313C2×C4×Q8C2312yes—
314C2×C4×Q8C2311yescharacteristic
315C2×C4×Q8C2311yescharacteristic
316C2×C4×D4C2311yescharacteristic
317C2×C4×D4C2311yescharacteristic
318C2×C4×D4C2311yescharacteristic
319C2×C4×D4C2311yescharacteristic
320C2×C4×D4C2311yescharacteristic
321C2×C4×D4C2311yescharacteristic
322C2×C4×D4C2312yes—
323C2×C4×D4C2312yes—
324C2×C4×D4C2311yescharacteristic
325C2×C4×D4C2311yescharacteristic
326C2×C4×D4C2314yes—
327C2×C4×D4C2314yes—
328C2×C4×D4C2312yes—
329C2×C4×D4C2312yes—
330C2×#117C2312yes—
331C2×#117C2312yes—
332C2×#117C2312yes—
333C2×#117C2312yes—
334C2×#117C2312yes—
335C2×#117C2311yescharacteristic
336C2×#117C2311yescharacteristic
337C2×#117C2311yescharacteristic
338C2×#117C2311yescharacteristic
339C2×#117C2314yes—
340C22×C4⋊C4C2312yes—
341C22×C4⋊C4C2312yes—
342C22×C4⋊C4C2312yes—
343C22×C4⋊C4C2312yes—
344C22×C4⋊C4C2312yes—
345C22×C4⋊C4C2314yes—
346C22×C42C2311yescharacteristic
347C22×C42C2311yescharacteristic
348C22×C42C2311yescharacteristic
349C22×C42C2311yescharacteristic
350C22×C42C2312yes—
351C22×C42C2311yescharacteristic
352#400C2312yes—
353#400C2314yes—
354#400C2312yes—
355#400C2312yes—
356#400C2312yes—
357#400C2314yes—
358#400C2312yes—
359#400C2312yes—
360#400C2312yes—
361#400C2312yes—
362#400C2314yes—
363#400C2314yes—
364#400C2314yes—
365#400C2314yes—
366#400C2314yes—
367#400C2314yes—
368#400C2314yes—
369#400C2314yes—
370#400C2314yes—
371#400C2314yes—
372#400C2314yes—
373#400C2314yes—
374#400C2314yes—
375#400C2314yes—
376#399C2312yes—
377#399C2312yes—
378#399C2312yes—
379#399C2312yes—
380#399C2314yes—
381#399C2314yes—
382#399C2314yes—
383#399C2312yes—
384#399C2312yes—
385#399C2312yes—
386#399C2312yes—
387#399C2314yes—
388#398C2314yes—
389#398C2314yes—
390#398C2314yes—
391#398C2314yes—
392#398C2314yes—
393#398C2314yes—
394#398C2314yes—
395#398C2314yes—
396#398C2314yes—
397#398C2314yes—
398#398C2314yes—
399#398C2314yes—
400#398C2314yes—
401#398C2314yes—
402#398C2314yes—
403#398C2314yes—
404#398C2314yes—
405#398C2314yes—
406#398C2314yes—
407#398C2314yes—
408#398C2314yes—
409#398C2314yes—
410#398C2314yes—
411#398C2314yes—
412#396C2314yes—
413#396C2314yes—
414#396C2314yes—
415#396C2314yes—
416#396C2314yes—
417#396C2314yes—
418#396C2314yes—
419#396C2314yes—
420#396C2314yes—
421#396C2314yes—
422#396C2314yes—
423#396C2314yes—
424#395C2312yes—
425#395C2312yes—
426#395C2312yes—
427#395C2312yes—
428#395C2314yes—
429#395C2314yes—
430#395C2312yes—
431#395C2312yes—
432#395C2312yes—
433#395C2312yes—
434#395C2314yes—
435#395C2314yes—
436#395C2314yes—
437#395C2314yes—
438#395C2314yes—
439#395C2314yes—
440#395C2314yes—
441#395C2314yes—
442#395C2314yes—
443#395C2314yes—
444#395C2314yes—
445#395C2314yes—
446#395C2314yes—
447#395C2314yes—
448#393C2312yes—
449#393C2312yes—
450#393C2312yes—
451#393C2312yes—
452#393C2312yes—
453#393C2312yes—
454#393C2312yes—
455#393C2312yes—
456#393C2314yes—
457#393C2314yes—
458#393C2314yes—
459#393C2314yes—
460#393C2314yes—
461#393C2314yes—
462#393C2314yes—
463#393C2314yes—
464#391C2314yes—
465#391C2314yes—
466#391C2314yes—
467#391C2314yes—
468#391C2314yes—
469#391C2314yes—
470#391C2314yes—
471#391C2314yes—
472#391C2311yescharacteristic
473#391C2311yescharacteristic
474#391C2311yescharacteristic
475#391C2311yescharacteristic
476#391C2314yes—
477#391C2314yes—
478#391C2314yes—
479#391C2314yes—
480#391C2314yes—
481#391C2314yes—
482#391C2314yes—
483#391C2314yes—
484#391C2314yes—
485#391C2314yes—
486#391C2314yes—
487#391C2314yes—
488#390C2314yes—
489#390C2314yes—
490#390C2314yes—
491#390C2314yes—
492#390C2311yescharacteristic
493#390C2311yescharacteristic
494#390C2311yescharacteristic
495#390C2311yescharacteristic
496#390C2314yes—
497#390C2314yes—
498#389C2314yes—
499#389C2314yes—
500#389C2312yes—
501#389C2312yes—
502#389C2312yes—
503#389C2312yes—
504#389C2312yes—
505#389C2312yes—
506#389C2314yes—
507#389C2314yes—
508#389C2312yes—
509#389C2312yes—
510#389C2314yes—
511#389C2314yes—
512#389C2314yes—
513#389C2314yes—
514#389C2312yes—
515#389C2312yes—
516#389C2314yes—
517#389C2312yes—
518#389C2312yes—
519#389C2314yes—
520#389C2314yes—
521#389C2314yes—
522#389C2314yes—
523#389C2314yes—
524#389C2314yes—
525#389C2312yes—
526#389C2312yes—
527#389C2314yes—
528#389C2314yes—
529#389C2312yes—
530#389C2312yes—
531#389C2314yes—
532#389C2314yes—
533#389C2314yes—
534#389C2314yes—
535#389C2314yes—
536#389C2314yes—
537#389C2314yes—
538#388C2312yes—
539#388C2312yes—
540#388C2314yes—
541#388C2314yes—
542#388C2312yes—
543#388C2312yes—
544#388C2312yes—
545#388C2312yes—
546#388C2312yes—
547#388C2312yes—
548#388C2314yes—
549#388C2314yes—
550#388C2314yes—
551#388C2314yes—
552#388C2314yes—
553#388C2314yes—
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#387C2312yes—
572#387C2312yes—
573#387C2312yes—
574#387C2312yes—
575#387C2312yes—
576#387C2312yes—
577#387C2312yes—
578#387C2312yes—
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#386C2314yes—
595#386C2314yes—
596#386C2312yes—
597#386C2312yes—
598#386C2314yes—
599#386C2314yes—
600#386C2314yes—
601#386C2314yes—
602#386C2314yes—
603#386C2314yes—
604#386C2314yes—
605#386C2314yes—
606#386C2312yes—
607#386C2312yes—
608#386C2312yes—
609#386C2312yes—
610#386C2312yes—
611#386C2312yes—
612#386C2312yes—
613#386C2312yes—
614#386C2312yes—
615#386C2312yes—
616#386C2314yes—
617#386C2314yes—
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#385C2312yes—
631#385C2312yes—
632#385C2312yes—
633#385C2312yes—
634#385C2312yes—
635#385C2312yes—
636#385C2312yes—
637#385C2314yes—
638#385C2314yes—
639#385C2314yes—
640#385C2314yes—
641#385C2314yes—
642#385C2314yes—
643#385C2314yes—
644#385C2314yes—
645#385C2314yes—
646#385C2314yes—
647#385C2314yes—
648#385C2314yes—
649#385C2314yes—
650#385C2314yes—
651#385C2314yes—
652#384C2314yes—
653#384C2312yes—
654#384C2311yescharacteristic
655#384C2312yes—
656#384C2312yes—
657#384C2311yescharacteristic
658#384C2312yes—
659#384C2312yes—
660#383C2314yes—
661#382C2314yes—
662#382C2312yes—
663#382C2311yescharacteristic
664#382C2311yescharacteristic
665#382C2312yes—
666#382C2314yes—
667#382C2314yes—
668#382C2311yescharacteristic
669#382C2311yescharacteristic
670#382C2312yes—
671#382C2312yes—
672#382C2312yes—
673#382C2311yescharacteristic
674#382C2311yescharacteristic
675#382C2314yes—
676#382C2312yes—
677#382C2312yes—
678#381C2314yes—
679#380C2314yes—
680#380C2314yes—
681#380C2314yes—
682#380C2314yes—
683#380C2314yes—
684#380C2314yes—
685#380C2314yes—
686#380C2312yes—
687#380C2312yes—
688#380C2312yes—
689#380C2312yes—
690#380C2312yes—
691#380C2312yes—
692#380C2312yes—
693#380C2312yes—
694#380C2312yes—
695#380C2312yes—
696#380C2312yes—
697#380C2312yes—
698#380C2314yes—
699#380C2314yes—
700#380C2314yes—
701#380C2314yes—
702#380C2312yes—
703#380C2312yes—
704#380C2312yes—
705#380C2312yes—
706C4×C4⋊C4C2312yes—
707C4×C4⋊C4C2312yes—
708C4×C4⋊C4C2312yes—
709C4×C4⋊C4C2312yes—
710C4×C4⋊C4C2312yes—
711C4×C4⋊C4C2312yes—
712C4×C4⋊C4C2312yes—
713C4×C4⋊C4C2312yes—
714C4×C4⋊C4C2314yes—
715C4×C4⋊C4C2314yes—
716C4×C4⋊C4C2314yes—
717C4×C4⋊C4C2314yes—
718C4×C4⋊C4C2314yes—
719C4×C22⋊C4C2314yes—
720C4×C22⋊C4C2314yes—
721C4×C22⋊C4C2314yes—
722C4×C22⋊C4C2314yes—
723C4×C22⋊C4C2314yes—
724C4×C22⋊C4C2312yes—
725C4×C22⋊C4C2312yes—
726C4×C22⋊C4C2312yes—
727C4×C22⋊C4C2312yes—
728#376C2311yescharacteristic
729#376C2311yescharacteristic
730#376C2311yescharacteristic
731#376C2311yescharacteristic
732#376C2314yes—
733#376C2312yes—
734#376C2312yes—
735C2×#95C2312yes—
736C2×#95C2312yes—
737C2×#95C2314yes—
738C2×#95C2312yes—
739C2×#95C2312yes—
740C2×#41—42no—
741C2×#41—42no—
742C2×#41—42no—
743C2×#41—42no—
744C2×#41C2×Q818yes—
745C2×#41C2×Q818yescomplemented
746C22×Q8—44no—
747C22×Q8—84no—
748C22×Q8C2414yes—
749C22×Q8C2412yes—
750C22×Q8C2412yes—
751C22×Q8C2414yes—
752C22×Q8C2412yes—
753C22×Q8C2414yes—
754C22×Q8C2412yes—
755C22×Q8C2411yescharacteristic
756C22×Q8C2411yescharacteristic
757C22×D4C2412yes—
758C22×D4C2412yes—
759C22×D4C2411yescharacteristic
760C22×D4C2412yes—
761C22×D4C2411yescharacteristic
762C22×D4C2411yescharacteristic
763C22×D4C2411yescharacteristic
764C23×C4C2411yescharacteristic
765C23×C4C2411yescharacteristic
766C23×C4C2412yes—
767C23×C4C2411yescharacteristic
768C23×C4C2411yescharacteristic
769C23×C4C2411yescharacteristic
770C23×C4C2411yescharacteristic
771C23×C4C2411yescharacteristic
772C23×C4C2411yescharacteristic
773C23×C4C2411yescharacteristic
774C23×C4C2412yes—
775C23×C4C2414yes—
776C23×C4C2414yes—
777C23×C4C2414yes—
778C23×C4C2414yes—
779C23×C4C2412yes—
780C23×C4C2412yes—
781C23×C4C2412yes—
782C4⋊Q8—28no—
783C4⋊Q8—42no—
784C4⋊Q8—42no—
785C4⋊Q8—44no—
786C4⋊Q8—44no—
787C4⋊Q8—42no—
788C4⋊Q8—42no—
789C4⋊Q8—44no—
790C4⋊Q8—44no—
791C4⋊Q8—48no—
792C4⋊Q8—84no—
793C4⋊Q8—84no—
794C4⋊Q8C2×Q818yescomplemented
795#127C2×Q818yes—
796#125—28no—
797#125—44no—
798#125—44no—
799#125—48no—
800#124C2×Q818yes—
801#124C2×Q818yescomplemented
802C22⋊Q8—48no—
803C22⋊Q8—48no—
804C22⋊Q8—44no—
805C22⋊Q8—44no—
806C22⋊Q8—84no—
807C22⋊Q8—84no—
808C22⋊Q8—84no—
809C22⋊Q8—84no—
810C22⋊Q8—84no—
811C22⋊Q8—84no—
812C22⋊Q8—84no—
813C22⋊Q8—84no—
814#121C2×Q8116yes—
815#121C2×Q8116yescomplemented
816C4×Q8—42no—
817C4×Q8—42no—
818C4×Q8—42no—
819C4×Q8—42no—
820C4×Q8—44no—
821C4×Q8—44no—
822C4×D4—42no—
823C4×D4—42no—
824C4×D4—42no—
825C4×D4—42no—
826C4×D4—42no—
827C4×D4—42no—
828C4×D4—42no—
829C4×D4—42no—
830C4×D4—44no—
831C4×D4—44no—
832C4×D4—84no—
833C4×D4—84no—
834C4×D4C2×Q8116yes—
835C4×D4C2×Q8116yescomplemented
836#117—28no—
837#117—42no—
838#117—42no—
839#117—42no—
840#117—42no—
841#117—44no—
842#117—44no—
843#117—44no—
844#117—44no—
845#117—84no—
846C2×C4⋊C4—44no—
847C2×C4⋊C4—44no—
848C2×C4⋊C4—44no—
849C2×C4⋊C4—44no—
850C2×C4⋊C4—44no—
851C2×C4⋊C4—84no—
852C2×C4⋊C4C2412yes—
853C2×C4⋊C4C2412yes—
854C2×C4⋊C4C2412yes—
855C2×C4⋊C4C2412yes—
856C2×C4⋊C4C2412yes—
857C2×C4⋊C4C2412yes—
858C2×C4⋊C4C2414yes—
859C2×C4⋊C4C2412yes—
860C2×C4⋊C4C2412yes—
861C2×C4⋊C4C2412yes—
862C2×C4⋊C4C2412yes—
863C2×C4⋊C4C2414yes—
864C2×C4⋊C4C2414yes—
865C2×C4⋊C4C2414yes—
866C2×C4⋊C4C2414yes—
867C2×C4⋊C4C2414yes—
868C2×C4⋊C4C2414yes—
869C2×C4⋊C4C2414yes—
870C2×C4⋊C4C2412yes—
871C2×C4⋊C4C2412yes—
872C2×C4⋊C4C2414yes—
873C2×C4⋊C4C2414yes—
874C2×C4⋊C4C2414yes—
875C2×C4⋊C4C2411yescharacteristic
876C2×C4⋊C4C2411yescharacteristic
877C2×C4⋊C4C2411yescharacteristic
878C2×C4⋊C4C2411yescharacteristic
879C2×C4⋊C4C2411yescharacteristic
880C2×C4⋊C4C2411yescharacteristic
881C2×C4⋊C4C2411yescharacteristic
882C2×C4⋊C4C2411yescharacteristic
883C2×C4⋊C4C2414yes—
884C2×C4⋊C4C2414yes—
885C2×C4⋊C4C2412yes—
886C2×C4⋊C4C2412yes—
887C2×C4⋊C4C2414yes—
888C2×C4⋊C4C2414yes—
889C2×C4⋊C4C2414yes—
890C2×C4⋊C4C2414yes—
891C2×C4⋊C4C2414yes—
892C2×C4⋊C4C2414yes—
893C2×C4⋊C4C2414yes—
894C2×C4⋊C4C2414yes—
895C2×C4⋊C4C2414yes—
896C2×C4⋊C4C2414yes—
897C2×C4⋊C4C2414yes—
898C2×C4⋊C4C2414yes—
899C2×C4⋊C4C2414yes—
900C2×C4⋊C4C2414yes—
901C2×C4⋊C4C2414yes—
902C2×C4⋊C4C2414yes—
903C2×C4⋊C4C2414yes—
904C2×C4⋊C4C2412yes—
905C2×C4⋊C4C2414yes—
906C2×C4⋊C4C2412yes—
907C2×C4⋊C4C2414yes—
908C2×C4⋊C4C2414yes—
909C2×C4⋊C4C2412yes—
910C2×C4⋊C4C2414yes—
911C2×C4⋊C4C2412yes—
912C2×C4⋊C4C2414yes—
913C2×C4⋊C4C2414yes—
914C2×C4⋊C4C2414yes—
915C2×C4⋊C4C2414yes—
916C2×C4⋊C4C2414yes—
917C2×C4⋊C4C2412yes—
918C2×C4⋊C4C2412yes—
919C2×C22⋊C4C2412yes—
920C2×C22⋊C4C2412yes—
921C2×C22⋊C4C2411yescharacteristic
922C2×C22⋊C4C2411yescharacteristic
923C2×C22⋊C4C2411yescharacteristic
924C2×C22⋊C4C2412yes—
925C2×C22⋊C4C2411yescharacteristic
926C2×C22⋊C4C2411yescharacteristic
927C2×C22⋊C4C2411yescharacteristic
928C2×C22⋊C4C2414yes—
929C2×C22⋊C4C2414yes—
930C2×C22⋊C4C2414yes—
931C2×C22⋊C4C2414yes—
932C2×C22⋊C4C2414yes—
933C2×C22⋊C4C2414yes—
934C2×C22⋊C4C2414yes—
935C2×C22⋊C4C2414yes—
936C2×C22⋊C4C2414yes—
937C2×C22⋊C4C2414yes—
938C2×C22⋊C4C2414yes—
939C2×C22⋊C4C2412yes—
940C2×C22⋊C4C2412yes—
941C2×C22⋊C4C2414yes—
942C2×C22⋊C4C2414yes—
943C2×C22⋊C4C2412yes—
944C2×C22⋊C4C2412yes—
945C2×C22⋊C4C2412yes—
946C2×C22⋊C4C2412yes—
947C2×C22⋊C4C2414yes—
948C2×C22⋊C4C2414yes—
949C2×C22⋊C4C2414yes—
950C2×C22⋊C4C2412yes—
951C2×C22⋊C4C2412yes—
952C2×C22⋊C4C2412yes—
953C2×C22⋊C4C2412yes—
954C2×C22⋊C4C2412yes—
955C2×C22⋊C4C2412yes—
956C2×C42—24no—
957C2×C42—24no—
958C2×C42—24no—
959C2×C42—44no—
960C2×C42—42no—
961C2×C42C2×Q818yescomplemented
962C2×C42C2412yes—
963C2×C42C2411yescharacteristic
964C2×C42C2411yescharacteristic
965C2×C42C2411yescharacteristic
966C2×C42C2411yescharacteristic
967C2×C42C2411yescharacteristic
968C2×C42C2411yescharacteristic
969C2×C42C2411yescharacteristic
970C2×C42C2411yescharacteristic
971C2×C42C2411yescharacteristic
972C2×C42C2412yes—
973C2×C42C2414yes—
974C2×C42C2414yes—
975C2×C42C2414yes—
976C2×C42C2414yes—
977C2×C42C2414yes—
978C2×C42C2414yes—
979C2×C42C2414yes—
980C2×C42C2412yes—
981C2×C42C2412yes—
982C2×C42C2411yescharacteristic
983C2×C42C2411yescharacteristic
984C2×C42C2414yes—
985C2×C42C2412yes—
986C2×C42C2411yescharacteristic
987C2×C42C2411yescharacteristic
988C2×C42C2411yescharacteristic
989#95C2412yes—
990#95C2412yes—
991#95C2412yes—
992#95C2412yes—
993#95C2412yes—
994#95C2412yes—
995#95C2412yes—
996#95C2412yes—
997#95C2412yes—
998#95C2414yes—
999#95C2414yes—
1000#95C2412yes—
1001#95C2414yes—
1002#95C2414yes—
1003#95C2412yes—
1004#95C2412yes—
1005#95C2414yes—
1006#95C2414yes—
1007#95C2414yes—
1008#95C2414yes—
1009#95C2414yes—
1010#95C2414yes—
1011#95C2414yes—
1012#95C2414yes—
1013#95C2414yes—
1014#95C2414yes—
1015#95C2414yes—
1016#95C2414yes—
1017#95C2412yes—
1018#95C2412yes—
1019#95C2412yes—
1020#95C2412yes—
1021#95C2412yes—
1022#95C2412yes—
1023#95C2412yes—
1024#95C2412yes—
1025#95C2412yes—
1026#95C2414yes—
1027#95C2414yes—
1028#95C2412yes—
1029#95C2412yes—
1030#95C2412yes—
1031#95C2414yes—
1032#95C2412yes—
1033#95C2414yes—
1034#95C2412yes—
1035#95C2414yes—
1036#95C2414yes—
1037#95C2412yes—
1038#95C2412yes—
1039#95C2414yes—
1040#95C2414yes—
1041#95C2414yes—
1042#95C2414yes—
1043#95C2414yes—
1044#95C2414yes—
1045#95C2414yes—
1046#95C2414yes—
1047#95C2414yes—
1048#95C2414yes—
1049#95C2414yes—
1050#95C2414yes—
1051#95C2414yes—
1052#95C2414yes—
1053#95C2414yes—
1054#95C2414yes—
1055#95C2414yes—
1056#95C2414yes—
1057#95C2414yes—
1058#95C2414yes—
1059C24C2512yes—
1060C24C2511yescharacteristic
1061C24C2511yescharacteristic
1062C24C2511yescharacteristic
1063#41—416no—
1064#41—416no—
1065C2×Q8—28no—
1066C2×Q8—41no—
1067C2×Q8—41no—
1068C2×Q8—41no—
1069C2×Q8—41no—
1070C2×Q8—42no—
1071C2×Q8—42no—
1072C2×Q8—44no—
1073C2×Q8—44no—
1074C2×Q8—44no—
1075C2×Q8—44no—
1076C2×Q8—42no—
1077C2×Q8—42no—
1078C2×Q8—44no—
1079C2×Q8—44no—
1080C2×Q8—44no—
1081C2×Q8—44no—
1082C2×Q8—44no—
1083C2×Q8—44no—
1084C2×Q8—44no—
1085C2×Q8—44no—
1086C2×Q8—816no—
1087C2×Q8C22×Q814yes—
1088C2×Q8C22×Q814yes—
1089C2×D4—41no—
1090C2×D4—41no—
1091C2×D4—41no—
1092C2×D4—41no—
1093C2×D4—42no—
1094C2×D4—42no—
1095C2×D4—42no—
1096C2×D4—42no—
1097C2×D4—42no—
1098C2×D4—41no—
1099C2×D4—42no—
1100C2×D4—41no—
1101C2×D4—41no—
1102C2×D4—41no—
1103C2×D4C22×Q818yes—
1104C2×D4C22×Q818yes—
1105C2×D4C22×Q814yes—
1106C2×D4C22×Q818yes—
1107C2×D4C22×Q814yes—
1108C2×D4C22×Q814yes—
1109C2×D4C22×Q814yes—
1110C22×C4—22no—
1111C22×C4—22no—
1112C22×C4—22no—
1113C22×C4—24no—
1114C22×C4—22no—
1115C22×C4—22no—
1116C22×C4—24no—
1117C22×C4—22no—
1118C22×C4—22no—
1119C22×C4—22no—
1120C22×C4—22no—
1121C22×C4—22no—
1122C22×C4—22no—
1123C22×C4—22no—
1124C22×C4—42no—
1125C22×C4—42no—
1126C22×C4—42no—
1127C22×C4—42no—
1128C22×C4—42no—
1129C22×C4—42no—
1130C22×C4—42no—
1131C22×C4—44no—
1132C22×C4—44no—
1133C22×C4—42no—
1134C22×C4—44no—
1135C22×C4—44no—
1136C22×C4—42no—
1137C22×C4—42no—
1138C22×C4—42no—
1139C22×C4—42no—
1140C22×C4—44no—
1141C22×C4—42no—
1142C22×C4—42no—
1143C22×C4—42no—
1144C22×C4—44no—
1145C22×C4—42no—
1146C22×C4—42no—
1147C22×C4—44no—
1148C22×C4—44no—
1149C22×C4—44no—
1150C22×C4—44no—
1151C22×C4—44no—
1152C22×C4—44no—
1153C22×C4C22×Q814yes—
1154C22×C4C22×Q814yes—
1155C22×C4C22×Q818yes—
1156C22×C4C22×Q814yes—
1157C22×C4C22×Q818yes—
1158C22×C4C2511yescharacteristic
1159C22×C4C2511yescharacteristic
1160C22×C4C2512yes—
1161C22×C4C2514yes—
1162C22×C4C2514yes—
1163C22×C4C2514yes—
1164C22×C4C2514yes—
1165C22×C4C2511yescharacteristic
1166C22×C4C2512yes—
1167C22×C4C2512yes—
1168C22×C4C2514yes—
1169C22×C4C2511yescharacteristic
1170C22×C4C2514yes—
1171C22×C4C2514yes—
1172C22×C4C2511yescharacteristic
1173C22×C4C2511yescharacteristic
1174C22×C4C2512yes—
1175C22×C4C2514yes—
1176C22×C4C2512yes—
1177C22×C4C2511yescharacteristic
1178C22×C4C2512yes—
1179C22×C4C2511yescharacteristic
1180C22×C4C2511yescharacteristic
1181C22×C4C2512yes—
1182C22×C4C2511yescharacteristic
1183C22×C4C2511yescharacteristic
1184C22×C4C2511yescharacteristic
1185C4⋊C4—24no—
1186C4⋊C4—24no—
1187C4⋊C4—24no—
1188C4⋊C4—28no—
1189C4⋊C4—24no—
1190C4⋊C4—24no—
1191C4⋊C4—24no—
1192C4⋊C4—28no—
1193C4⋊C4—28no—
1194C4⋊C4—24no—
1195C4⋊C4—24no—
1196C4⋊C4—24no—
1197C4⋊C4—24no—
1198C4⋊C4—44no—
1199C4⋊C4—44no—
1200C4⋊C4—44no—
1201C4⋊C4—44no—
1202C4⋊C4—42no—
1203C4⋊C4—42no—
1204C4⋊C4—44no—
1205C4⋊C4—44no—
1206C4⋊C4—44no—
1207C4⋊C4—44no—
1208C4⋊C4—42no—
1209C4⋊C4—44no—
1210C4⋊C4—42no—
1211C4⋊C4—44no—
1212C4⋊C4—44no—
1213C4⋊C4—44no—
1214C4⋊C4—44no—
1215C4⋊C4—44no—
1216C4⋊C4—44no—
1217C4⋊C4—41no—
1218C4⋊C4—41no—
1219C4⋊C4—41no—
1220C4⋊C4—41no—
1221C4⋊C4—41no—
1222C4⋊C4—41no—
1223C4⋊C4—41no—
1224C4⋊C4—41no—
1225C4⋊C4—44no—
1226C4⋊C4—44no—
1227C4⋊C4—42no—
1228C4⋊C4—42no—
1229C4⋊C4—44no—
1230C4⋊C4—44no—
1231C4⋊C4—44no—
1232C4⋊C4—44no—
1233C4⋊C4—44no—
1234C4⋊C4—44no—
1235C4⋊C4—44no—
1236C4⋊C4—44no—
1237C4⋊C4—44no—
1238C4⋊C4—44no—
1239C4⋊C4—44no—
1240C4⋊C4—44no—
1241C4⋊C4—44no—
1242C4⋊C4—44no—
1243C4⋊C4—44no—
1244C4⋊C4—44no—
1245C4⋊C4—44no—
1246C4⋊C4—44no—
1247C4⋊C4—42no—
1248C4⋊C4—44no—
1249C4⋊C4—42no—
1250C4⋊C4C22×Q818yes—
1251C4⋊C4C22×Q818yes—
1252C22⋊C4—24no—
1253C22⋊C4—24no—
1254C22⋊C4—44no—
1255C22⋊C4—44no—
1256C22⋊C4—44no—
1257C22⋊C4—42no—
1258C22⋊C4—42no—
1259C22⋊C4—42no—
1260C22⋊C4—42no—
1261C22⋊C4—44no—
1262C22⋊C4—44no—
1263C22⋊C4—41no—
1264C22⋊C4—41no—
1265C22⋊C4—41no—
1266C22⋊C4—41no—
1267C22⋊C4—41no—
1268C22⋊C4—41no—
1269C22⋊C4—42no—
1270C22⋊C4—44no—
1271C22⋊C4—44no—
1272C22⋊C4—44no—
1273C22⋊C4—44no—
1274C22⋊C4—44no—
1275C22⋊C4—44no—
1276C22⋊C4—44no—
1277C22⋊C4—44no—
1278C22⋊C4—44no—
1279C22⋊C4—44no—
1280C22⋊C4—44no—
1281C22⋊C4—42no—
1282C22⋊C4—42no—
1283C22⋊C4—42no—
1284C22⋊C4—42no—
1285C22⋊C4C22×Q818yes—
1286C22⋊C4C22×Q818yes—
1287C22⋊C4C22×Q818yes—
1288C22⋊C4C22×Q818yes—
1289C42—22no—
1290C42—22no—
1291C42—22no—
1292C42—22no—
1293C42—22no—
1294C42—22no—
1295C42—22no—
1296C42—22no—
1297C42—22no—
1298C42—24no—
1299C42—24no—
1300C42—41no—
1301C42—41no—
1302C42—42no—
1303C42—42no—
1304C42—44no—
1305C42—44no—
1306C42—44no—
1307C42—44no—
1308C42—44no—
1309C42—44no—
1310C42—44no—
1311C42—44no—
1312C42C22×Q818yes—
1313C42C22×Q814yes—
1314C42C22×Q814yes—
1315C42H(5,𝔽2)14yes—
1316C23—22no—
1317C23—21no—
1318C23—21no—
1319C23—21no—
1320C23—21no—
1321C23—22no—
1322C23—21no—
1323C23—21no—
1324C23—22no—
1325C23—22no—
1326C23—22no—
1327C23—22no—
1328C23—22no—
1329C23—22no—
1330C23—22no—
1331C23—22no—
1332C23—22no—
1333C23—22no—
1334C23C23×Q812yes—
1335C23C23×Q814yes—
1336C23C23×Q812yes—
1337C23C23×Q812yes—
1338C23C2611yescharacteristic
1339Q8—44no—
1340Q8—44no—
1341Q8—88no—
1342Q8—84no—
1343Q8—84no—
1344Q8—84no—
1345Q8—84no—
1346Q8—164no—
1347Q8—164no—
1348D4—48no—
1349D4—48no—
1350D4—44no—
1351D4—44no—
1352D4—44no—
1353D4—48no—
1354D4—44no—
1355C2×C4—21no—
1356C2×C4—21no—
1357C2×C4—21no—
1358C2×C4—22no—
1359C2×C4—21no—
1360C2×C4—22no—
1361C2×C4—21no—
1362C2×C4—21no—
1363C2×C4—22no—
1364C2×C4—22no—
1365C2×C4—22no—
1366C2×C4—22no—
1367C2×C4—22no—
1368C2×C4—22no—
1369C2×C4—28no—
1370C2×C4—28no—
1371C2×C4—216no—
1372C2×C4—28no—
1373C2×C4—21no—
1374C2×C4—21no—
1375C2×C4—21no—
1376C2×C4—21no—
1377C2×C4—21no—
1378C2×C4—21no—
1379C2×C4—22no—
1380C2×C4—22no—
1381C2×C4—24no—
1382C2×C4—24no—
1383C2×C4—24no—
1384C2×C4—24no—
1385C2×C4—22no—
1386C2×C4—22no—
1387C2×C4—24no—
1388C2×C4—24no—
1389C2×C4—24no—
1390C2×C4—24no—
1391C2×C4—24no—
1392C2×C4—24no—
1393C2×C4—24no—
1394C2×C4—24no—
1395C2×C4—24no—
1396C2×C4—24no—
1397C2×C4—24no—
1398C2×C4—22no—
1399C2×C4—22no—
1400C2×C4—22no—
1401C2×C4—22no—
1402C2×C4—22no—
1403C2×C4—24no—
1404C2×C4—24no—
1405C2×C4—24no—
1406C2×C4—22no—
1407C2×C4—22no—
1408C2×C4—24no—
1409C2×C4—24no—
1410C2×C4—24no—
1411C2×C4—22no—
1412C2×C4—22no—
1413C2×C4—24no—
1414C2×C4—22no—
1415C2×C4—22no—
1416C2×C4—22no—
1417C2×C4—24no—
1418C2×C4—24no—
1419C2×C4—22no—
1420C2×C4—22no—
1421C2×C4—48no—
1422C2×C4—44no—
1423C2×C4—44no—
1424C2×C4—82no—
1425C2×C4—82no—
1426C2×C4—82no—
1427C2×C4—82no—
1428C2×C4—84no—
1429C2×C4—88no—
1430C2×C4—84no—
1431C2×C4—84no—
1432C2×C4—88no—
1433C2×C4—164no—
1434C2×C4—164no—
1435C2×C4C23×Q814yes—
1436C2×C4C23×Q814yes—
1437C2×C4C23×Q812yes—
1438C2×C4C23×Q814yes—
1439C2×C4C23×Q812yes—
1440C2×C4C23×Q812yes—
1441C2×C4C23×Q812yes—
1442C2×C4C2×H(5,𝔽2)12yes—
1443C2×C4C2×H(5,𝔽2)12yes—
1444C2×C4C2×H(5,𝔽2)12yes—
1445C2×C4#58512yes—
1446C22—22no—
1447C22—24no—
1448C22—22no—
1449C22—22no—
1450C22—24no—
1451C22—24no—
1452C22—24no—
1453C22—24no—
1454C22—24no—
1455C22—41no—
1456C22—42no—
1457C22—41no—
1458C22—41no—
1459C22—42no—
1460C22—42no—
1461C22—42no—
1462C22—42no—
1463C22—42no—
1464C22—41no—
1465C22—41no—
1466C22—41no—
1467C22—42no—
1468C22C24×Q811yescharacteristic
1469C22C22×H(5,𝔽2)11yescharacteristic
1470C22C2×#58511yescharacteristic
1471C22H(7,𝔽2)12yes—
1472C222−1+612yes—
1473C4—22no—
1474C4—22no—
1475C4—22no—
1476C4—24no—
1477C4—24no—
1478C4—24no—
1479C4—22no—
1480C4—22no—
1481C4—41no—
1482C4—41no—
1483C4—44no—
1484C4—41no—
1485C4—44no—
1486C4—42no—
1487C4—44no—
1488C4—42no—
1489C4—44no—
1490C4—44no—
1491C4—42no—
1492C4—44no—
1493C4—44no—
1494C4—41no—
1495C4—42no—
1496C4—41no—
1497C4—41no—
1498C4—44no—
1499C4#350114yes—
1500C2—42no—
1501C2—42no—
1502C2—44no—
1503C2—42no—
1504C2C2×#350111yescharacteristic
1505C2#6285412yes—
1506C2#6287411yescharacteristic
1507C2#6288212yes—
1508C2#6288611yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#532C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #48844C2semidirect
2. #48840C2semidirect
3. #47969C2semidirect
4. #47965C2semidirect
5. #47819C2semidirect
6. #47818C2semidirect
7. #47817C2semidirect
8. #47814C2semidirect
9. #47773C2semidirect
10. #47772C2semidirect
11. #47726C2semidirect
12. #47725C2semidirect
13. #38106C2semidirect
14. #38105C2semidirect
15. #38101C2semidirect
16. #38098C2semidirect
17. #37879C2semidirect
18. #37875C2semidirect
19. #37690C2semidirect
20. #37686C2semidirect
21. #37642C2semidirect
22. #37565C2semidirect
23. #37426C2semidirect
24. #37310C2semidirect
25. #37306C2semidirect
26. #35334C2semidirect
27. #35304C2semidirect
28. #35279C2semidirect
29. #35257C2semidirect
272. #532Q8semidirect
745. C2×#41C2×Q8semidirect
794. C4⋊Q8C2×Q8semidirect
801. #124C2×Q8semidirect
815. #121C2×Q8semidirect
835. C4×D4C2×Q8semidirect
961. C2×C42C2×Q8semidirect

Maximal subgroups

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

subgroupindex
#488442
#488402
#479692
#479652
#478192
#478182
#478172
#478142
#477732
#477722
#477262
#477252
#381062
#381052
#381012
#380982
#378792
#378752
#376902
#376862
#376422
#375652
#374262
#373102
#373062
#353342
#353042
#352792
#352572
#343672
#340702