Finite Group Databasebeta

← #8115414

Subgroups — #8115414

Order 512.

3999 conjugacy classes of subgroups.

The subgroup lattice has 1395 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#57751C214yesmaximal, complemented
2#57256C214yesmaximal, complemented
3#56903C214yesmaximal, complemented
4#56892C214yesmaximal, complemented
5#56084C214yesmaximal, complemented
6#56072C214yesmaximal, complemented
7#54534C214yesmaximal, complemented
8#54518C214yesmaximal, complemented
9#53140C212yesmaximal, complemented
10#53138C212yesmaximal
11#45436C211yesmaximal, characteristic, complemented
12#45425C211yesmaximal, characteristic, complemented
13#45394C211yesmaximal, characteristic, complemented
14#45389C211yesmaximal, characteristic, complemented
15#42875C211yesmaximal, characteristic
16#42824C212yesmaximal, complemented
17#42793C211yesmaximal, characteristic, complemented
18#42791C211yesmaximal, characteristic, complemented
19#42702C212yesmaximal, complemented
20#42649C211yesmaximal, characteristic
21#39172C211yesmaximal, characteristic, complemented
22#39170C211yesmaximal, characteristic, complemented
23#39149C212yesmaximal, complemented
24#38971C211yesmaximal, characteristic, complemented
25#38970C211yesmaximal, characteristic, complemented
26#38937C212yesmaximal
27#37405C212yesmaximal, complemented
28#37401C212yesmaximal, complemented
29#35318C211yesmaximal, characteristic
30#35314C211yesmaximal, characteristic, complemented
31#34644C211yesmaximal, characteristic, complemented
32C2×Q82C2211yescharacteristic
33C2×#557C2211yescharacteristic
34C2×#557C2211yescharacteristic
35C2×#556C2211yescharacteristic
36C2×#542C2211yescharacteristic
37C2×#541C2211yescharacteristic
38#2864C2211yescharacteristic
39#2863C2212yes—
40#2862C2211yescharacteristic
41#2862C2211yescharacteristic
42#2861C2211yescharacteristic
43#2857C2211yescharacteristic
44#2850C2211yescharacteristic
45#2843C2214yes—
46#2839C2214yes—
47#2839C2214yes—
48#2837C2214yes—
49#2836C2214yes—
50#2836C2214yes—
51#2831C2214yes—
52#2831C2214yes—
53#2831C2214yes—
54#2827C2214yes—
55#2822C2212yes—
56#2821C2212yes—
57#2821C2212yes—
58#2814C2212yes—
59#2808C2214yes—
60#2806C2214yes—
61#2806C2214yes—
62#2802C2214yes—
63#2799C2214yes—
64#2798C2214yes—
65#2798C2214yes—
66#2784C2214yes—
67#2781C2214yes—
68#2777C2214yes—
69#2776C2214yes—
70#2776C2214yes—
71#2776C2214yes—
72#2775C2214yes—
73#2774C2214yes—
74#2774C2214yes—
75#2774C2214yes—
76#2773C2214yes—
77#2773C2214yes—
78#2772C2214yes—
79#2771C2214yes—
80#2769C2214yes—
81#2769C2214yes—
82#2768C2214yes—
83#2768C2214yes—
84#2767C2214yes—
85#2767C2214yes—
86#2766C2214yes—
87#2763C2214yes—
88#2762C2214yes—
89#2761C2214yes—
90#2759C2214yes—
91#2758C2214yes—
92#2755C2214yes—
93#2755C2214yes—
94#2755C2214yes—
95#2754C2214yes—
96#2747C2214yes—
97#2745C2214yes—
98#2745C2214yes—
99#2744C2214yes—
100#2742C2214yes—
101#2742C2214yes—
102#2739C2214yes—
103#2739C2214yes—
104#2739C2214yes—
105#2738C2214yes—
106#2738C2214yes—
107#2734C2214yes—
108#2726C2214yes—
109#2725C2214yes—
110#2722C2214yes—
111#2721C2214yes—
112#2720C2214yes—
113#2719C2214yes—
114#2719C2214yes—
115#2716C2214yes—
116#2716C2214yes—
117#2716C2214yes—
118#2715C2214yes—
119#2713C2214yes—
120#2713C2214yes—
121#2694C2214yes—
122#2690C2214yes—
123#2667C2212yes—
124#2667C2214yes—
125#2667C2212yes—
126#2666C2212yes—
127#2666C2214yes—
128#2666C2212yes—
129#2666C2212yes—
130#2666C2212yes—
131#2665C2212yes—
132#2665C2212yes—
133#2664C2212yes—
134#2660C2211yescharacteristic
135#2659C2212yes—
136#2658C2211yescharacteristic
137#2654C2214yes—
138#2647C2214yes—
139#2645C2212yes—
140#2645C2212yes—
141#2642C2212yes—
142#2642C2212yes—
143#2640C2212yes—
144#2640C2212yes—
145#2637C2212yes—
146#2634C2212yes—
147#2632C2212yes—
148#2628C2211yescharacteristic
149#2625C2212yes—
150#2625C2212yes—
151#2621C2211yescharacteristic
152#2621C2211yescharacteristic
153#2620C2211yescharacteristic
154#2612C2214yes—
155#2612C2214yes—
156#2605C2214yes—
157#2604C2212yes—
158#2604C2212yes—
159#2589C2214yes—
160#2584C2212yes—
161#2581C2212yes—
162#2581C2211yescharacteristic
163#2581C2211yescharacteristic
164#2581C2211yescharacteristic
165#2580C2212yes—
166#2580C2211yescharacteristic
167#2572C2214yes—
168#2571C2212yes—
169#2570C2214yes—
170#2568C2211yescharacteristic
171#2568C2212yes—
172#2568C2212yes—
173#2568C2212yes—
174#2565C2212yes—
175#2563C2211yescharacteristic
176#2556C2214yes—
177#2553C2214yes—
178#2550C2212yes—
179#2550C2212yes—
180#2550C2212yes—
181#2547C2212yes—
182#2546C2211yescharacteristic
183#2546C2212yes—
184#2546C2211yescharacteristic
185#2546C2212yes—
186#2546C2212yes—
187#2545C2212yes—
188#2545C2212yes—
189#2532C2214yes—
190#2530C2214yes—
191#2528C2214yes—
192#2526C2214yes—
193#2524C2214yes—
194#2524C2214yes—
195#2523C2214yes—
196#2522C2214yes—
197#2521C2214yes—
198#2520C2214yes—
199#2519C2214yes—
200#2517C2214yes—
201#2509C2214yes—
202#2509C2212yes—
203#2507C2212yes—
204#2505C2214yes—
205#2498C2212yes—
206#2497C2214yes—
207#2495C2214yes—
208#2494C2214yes—
209#2493C2214yes—
210#2492C2212yes—
211#2490C2212yes—
212#2475C2214yes—
213#2469C2214yes—
214#2462C2214yes—
215#2453C2214yes—
216#2453C2212yes—
217#2453C2212yes—
218#2451C2212yes—
219#2451C2212yes—
220#2448C2212yes—
221#2448C2212yes—
222#2447C2212yes—
223#2446C2214yes—
224#2446C2212yes—
225#2446C2212yes—
226#2446C2212yes—
227#2446C2214yes—
228#2439C2214yes—
229#2429C2212yes—
230#2429C2212yes—
231#2429C2212yes—
232#2427C2212yes—
233#2421C2214yes—
234#2421C2212yes—
235#2421C2212yes—
236#2402C2212yes—
237#2399C2211yescharacteristic
238#2399C2211yescharacteristic
239#2396C2211yescharacteristic
240#2396C2211yescharacteristic
241#2396C2212yes—
242#2367C2212yes—
243#2365C2212yes—
244#2356C2212yes—
245#2356C2211yescharacteristic
246#2356C2211yescharacteristic
247#2351C2211yescharacteristic
248Q8×C4⋊C4C2212yes—
249#2349C2211yescharacteristic
250#2331C2211yescharacteristic
251#2327C2212yes—
252#2327C2212yes—
253#2327C2211yescharacteristic
254#2327C2211yescharacteristic
255#2326C2211yescharacteristic
256#2320C2212yes—
257#2320C2212yes—
258#2319C2212yes—
259C4×C4⋊Q8C2211yescharacteristic
260C4×#124C2211yescharacteristic
261C4×C22⋊Q8C2212yes—
262#2295C2211yescharacteristic
263#2295C2211yescharacteristic
264#2295C2212yes—
265#2283C2212yes—
266C4×#117C2211yescharacteristic
267Q82—44no—
268#557—44no—
269#557—44no—
270#556—44no—
271#542—44no—
272#541—44no—
273C2×C4⋊Q8C2311yescharacteristic
274C2×C4⋊Q8C2311yescharacteristic
275C2×C4⋊Q8C2311yescharacteristic
276C2×C4⋊Q8C2311yescharacteristic
277C2×C4⋊Q8C2312yes—
278C2×C4⋊Q8C2312yes—
279C2×C4⋊Q8C2312yes—
280C2×C4⋊Q8C2312yes—
281C2×C4⋊Q8C2312yes—
282C2×C4⋊Q8C2311yescharacteristic
283C2×C4⋊Q8C2311yescharacteristic
284C2×C4⋊Q8C2312yes—
285C2×C4⋊Q8C2314yes—
286C2×#126C2312yes—
287C2×#126C2312yes—
288C2×#126C2312yes—
289C2×#126C2314yes—
290C2×#125C2312yes—
291C2×#125C2312yes—
292C2×#125C2312yes—
293C2×#125C2311yescharacteristic
294C2×#125C2312yes—
295C2×#125C2314yes—
296C2×#125C2314yes—
297C2×#124C2311yescharacteristic
298C2×#124C2311yescharacteristic
299C2×#124C2311yescharacteristic
300C2×#124C2312yes—
301C2×#124C2312yes—
302C2×#123C2312yes—
303C2×C22⋊Q8C2311yescharacteristic
304C2×C22⋊Q8C2311yescharacteristic
305C2×C22⋊Q8C2311yescharacteristic
306C2×C22⋊Q8C2312yes—
307C2×C22⋊Q8C2312yes—
308C2×C22⋊Q8C2312yes—
309C2×#121C2311yescharacteristic
310C2×C4×Q8C2311yescharacteristic
311C2×C4×Q8C2311yescharacteristic
312C2×C4×Q8C2312yes—
313C2×C4×Q8C2311yescharacteristic
314C2×C4×Q8C2311yescharacteristic
315C2×C4×Q8C2311yescharacteristic
316C2×C4×Q8C2312yes—
317C2×C4×Q8C2312yes—
318C2×C4×Q8C2312yes—
319C2×C4×Q8C2312yes—
320C2×C4×Q8C2312yes—
321C2×C4×Q8C2312yes—
322C2×C4×Q8C2312yes—
323C2×C4×Q8C2312yes—
324C2×C4×Q8C2312yes—
325C2×C4×D4C2311yescharacteristic
326C2×C4×D4C2312yes—
327C2×#117C2311yescharacteristic
328C2×#117C2311yescharacteristic
329C2×#117C2312yes—
330C22×C42C2311yescharacteristic
331#401C2314yes—
332#401C2314yes—
333#400C2312yes—
334#400C2312yes—
335#400C2314yes—
336#400C2311yescharacteristic
337#400C2312yes—
338#400C2314yes—
339#400C2314yes—
340#400C2314yes—
341#400C2314yes—
342#400C2314yes—
343#400C2314yes—
344#400C2314yes—
345#400C2312yes—
346#400C2314yes—
347#400C2314yes—
348#400C2314yes—
349#400C2314yes—
350#400C2314yes—
351#400C2314yes—
352#400C2314yes—
353#400C2314yes—
354#400C2314yes—
355#400C2314yes—
356#400C2314yes—
357#400C2314yes—
358#400C2312yes—
359#400C2314yes—
360#400C2312yes—
361#400C2314yes—
362#400C2312yes—
363#400C2314yes—
364#400C2311yescharacteristic
365#400C2312yes—
366#400C2314yes—
367#400C2314yes—
368#400C2314yes—
369#400C2314yes—
370#400C2314yes—
371#400C2314yes—
372#400C2314yes—
373#400C2312yes—
374#400C2312yes—
375#400C2312yes—
376#399C2311yescharacteristic
377#399C2312yes—
378#399C2314yes—
379#399C2312yes—
380#399C2314yes—
381#399C2312yes—
382#399C2314yes—
383#399C2314yes—
384#399C2311yescharacteristic
385#399C2314yes—
386#398C2314yes—
387#398C2314yes—
388#398C2314yes—
389#398C2314yes—
390#398C2314yes—
391#398C2314yes—
392#398C2312yes—
393#398C2312yes—
394#398C2314yes—
395#398C2314yes—
396#398C2314yes—
397#398C2314yes—
398#398C2314yes—
399#398C2314yes—
400#398C2314yes—
401#398C2312yes—
402#398C2314yes—
403#398C2314yes—
404#398C2314yes—
405#398C2314yes—
406#398C2314yes—
407#398C2314yes—
408#398C2312yes—
409#398C2314yes—
410#398C2312yes—
411#398C2312yes—
412#398C2314yes—
413#398C2314yes—
414#398C2314yes—
415#398C2312yes—
416#398C2312yes—
417#398C2312yes—
418#398C2314yes—
419#398C2314yes—
420#398C2312yes—
421#398C2312yes—
422#398C2312yes—
423#398C2312yes—
424#398C2312yes—
425#398C2312yes—
426#398C2312yes—
427#398C2312yes—
428#398C2312yes—
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#397C2312yes—
443#397C2312yes—
444#397C2314yes—
445#397C2314yes—
446#397C2314yes—
447#396C2314yes—
448#396C2314yes—
449#396C2314yes—
450#396C2312yes—
451#396C2314yes—
452#396C2314yes—
453#396C2314yes—
454#396C2314yes—
455#396C2312yes—
456#396C2312yes—
457#396C2312yes—
458#396C2314yes—
459#395C2311yescharacteristic
460#395C2312yes—
461#395C2314yes—
462#395C2312yes—
463#395C2314yes—
464#395C2314yes—
465#395C2312yes—
466#395C2312yes—
467#395C2312yes—
468#395C2314yes—
469#395C2314yes—
470#395C2314yes—
471#395C2314yes—
472#395C2312yes—
473#395C2312yes—
474#395C2311yescharacteristic
475#395C2312yes—
476#395C2312yes—
477#394C2314yes—
478#394C2314yes—
479#394C2314yes—
480#393C2312yes—
481#393C2312yes—
482#393C2314yes—
483#393C2312yes—
484#393C2314yes—
485#393C2312yes—
486#393C2314yes—
487#393C2311yescharacteristic
488#393C2312yes—
489#393C2311yescharacteristic
490#393C2314yes—
491#391C2311yescharacteristic
492#391C2311yescharacteristic
493#391C2312yes—
494#391C2312yes—
495#391C2311yescharacteristic
496#391C2311yescharacteristic
497#391C2312yes—
498#391C2312yes—
499#391C2314yes—
500#391C2314yes—
501#391C2314yes—
502#391C2312yes—
503#391C2314yes—
504#391C2312yes—
505#391C2312yes—
506#391C2314yes—
507#391C2314yes—
508#391C2312yes—
509#391C2312yes—
510#391C2311yescharacteristic
511#391C2312yes—
512#391C2312yes—
513#391C2311yescharacteristic
514#391C2312yes—
515#391C2314yes—
516#391C2314yes—
517#391C2314yes—
518#391C2314yes—
519#391C2314yes—
520#391C2314yes—
521#391C2314yes—
522#391C2312yes—
523#391C2312yes—
524#391C2312yes—
525#391C2312yes—
526#391C2314yes—
527#390C2312yes—
528#390C2311yescharacteristic
529#390C2312yes—
530#390C2311yescharacteristic
531#390C2314yes—
532#389C2314yes—
533#389C2314yes—
534#389C2314yes—
535#389C2312yes—
536#389C2312yes—
537#389C2314yes—
538#389C2312yes—
539#389C2312yes—
540#389C2312yes—
541#389C2312yes—
542#389C2312yes—
543#389C2312yes—
544#389C2312yes—
545#389C2314yes—
546#389C2314yes—
547#389C2312yes—
548#389C2314yes—
549#389C2314yes—
550#389C2314yes—
551#389C2314yes—
552#389C2314yes—
553#389C2314yes—
554#389C2314yes—
555#389C2314yes—
556#389C2314yes—
557#389C2314yes—
558#389C2314yes—
559#389C2314yes—
560#389C2314yes—
561#389C2314yes—
562#389C2314yes—
563#389C2314yes—
564#389C2314yes—
565#389C2314yes—
566#389C2312yes—
567#389C2312yes—
568#389C2312yes—
569#389C2312yes—
570#389C2314yes—
571#388C2314yes—
572#388C2314yes—
573#388C2314yes—
574#388C2314yes—
575#388C2314yes—
576#388C2314yes—
577#388C2314yes—
578#388C2314yes—
579#388C2314yes—
580#388C2314yes—
581#388C2314yes—
582#388C2314yes—
583#388C2314yes—
584#388C2314yes—
585#388C2314yes—
586#388C2314yes—
587#388C2314yes—
588#388C2314yes—
589#388C2314yes—
590#388C2314yes—
591#388C2314yes—
592#388C2314yes—
593#388C2314yes—
594#388C2314yes—
595#387C2314yes—
596#387C2314yes—
597#387C2314yes—
598#387C2314yes—
599#387C2314yes—
600#387C2314yes—
601#387C2314yes—
602#387C2314yes—
603#387C2314yes—
604#387C2314yes—
605#387C2314yes—
606#387C2314yes—
607#387C2314yes—
608#387C2314yes—
609#387C2314yes—
610#387C2314yes—
611#387C2314yes—
612#387C2314yes—
613#387C2314yes—
614#387C2314yes—
615#387C2314yes—
616#387C2314yes—
617#387C2314yes—
618#387C2314yes—
619#387C2314yes—
620#387C2314yes—
621#387C2314yes—
622#387C2314yes—
623#387C2314yes—
624#387C2314yes—
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#387C2312yes—
644#387C2312yes—
645#387C2312yes—
646#387C2312yes—
647#387C2312yes—
648#387C2314yes—
649#387C2314yes—
650#387C2314yes—
651#387C2314yes—
652#387C2314yes—
653#386C2314yes—
654#386C2314yes—
655#385C2314yes—
656#385C2314yes—
657#385C2314yes—
658#385C2314yes—
659#385C2314yes—
660#385C2314yes—
661#385C2314yes—
662#385C2314yes—
663#384C2311yescharacteristic
664#384C2314yes—
665#384C2311yescharacteristic
666#383C2312yes—
667#383C2312yes—
668#383C2314yes—
669#383C2314yes—
670#383C2314yes—
671#383C2314yes—
672#383C2312yes—
673#383C2312yes—
674#382C2312yes—
675#382C2312yes—
676#382C2312yes—
677#382C2311yescharacteristic
678#382C2314yes—
679#382C2314yes—
680#382C2312yes—
681#382C2314yes—
682#382C2314yes—
683#382C2314yes—
684#382C2311yescharacteristic
685#382C2311yescharacteristic
686#382C2311yescharacteristic
687#382C2314yes—
688#382C2314yes—
689#382C2312yes—
690#381C2312yes—
691#381C2314yes—
692#381C2312yes—
693#381C2314yes—
694#380C2314yes—
695#380C2314yes—
696#380C2314yes—
697#380C2312yes—
698#380C2312yes—
699#380C2314yes—
700#380C2314yes—
701#380C2312yes—
702#380C2312yes—
703#380C2314yes—
704C4×C4⋊C4C2314yes—
705C4×C4⋊C4C2311yescharacteristic
706C4×C4⋊C4C2312yes—
707C4×C4⋊C4C2312yes—
708C4×C4⋊C4C2312yes—
709C4×C4⋊C4C2311yescharacteristic
710C4×C4⋊C4C2312yes—
711C4×C4⋊C4C2314yes—
712C4×C4⋊C4C2314yes—
713C4×C4⋊C4C2312yes—
714C4×C4⋊C4C2312yes—
715C4×C4⋊C4C2312yes—
716C4×C4⋊C4C2314yes—
717C4×C4⋊C4C2312yes—
718C4×C4⋊C4C2312yes—
719C4×C4⋊C4C2312yes—
720C4×C4⋊C4C2312yes—
721C4×C4⋊C4C2312yes—
722C4×C4⋊C4C2312yes—
723C4×C22⋊C4C2314yes—
724C4×C22⋊C4C2314yes—
725C4×C22⋊C4C2312yes—
726C4×C22⋊C4C2312yes—
727C4×C22⋊C4C2312yes—
728C4×C22⋊C4C2312yes—
729C4×C22⋊C4C2314yes—
730#376C2312yes—
731#376C2311yescharacteristic
732#376C2312yes—
733#376C2311yescharacteristic
734#376C2312yes—
735#376C2312yes—
736#376C2314yes—
737C2×#95C2312yes—
738C43C2311yescharacteristic
739C43C2311yescharacteristic
740C22×Q8C2411yescharacteristic
741C22×Q8C2411yescharacteristic
742C22×Q8C2411yescharacteristic
743C22×Q8C2412yes—
744C22×Q8C2411yescharacteristic
745C22×Q8C2411yescharacteristic
746C22×Q8C2412yes—
747C22×Q8C2412yes—
748C22×Q8C2412yes—
749C22×Q8C2414yes—
750C22×D4C2411yescharacteristic
751C22×D4C2412yes—
752C23×C4C2411yescharacteristic
753C23×C4C2412yes—
754C23×C4C2412yes—
755C23×C4C2414yes—
756C4⋊Q8—24no—
757C4⋊Q8—24no—
758C4⋊Q8—24no—
759C4⋊Q8—42no—
760C4⋊Q8—44no—
761C4⋊Q8—44no—
762C4⋊Q8—42no—
763C4⋊Q8—44no—
764C4⋊Q8—44no—
765C4⋊Q8—42no—
766C4⋊Q8—44no—
767C4⋊Q8—44no—
768C4⋊Q8—48no—
769#126—44no—
770#126—44no—
771#126—44no—
772#126—48no—
773#125—42no—
774#125—44no—
775#125—44no—
776#125—44no—
777#125—44no—
778#125—48no—
779#125—48no—
780#124—24no—
781#124—44no—
782#124—42no—
783#124—42no—
784#124—44no—
785#123—44no—
786C22⋊Q8—44no—
787C22⋊Q8—44no—
788C22⋊Q8—42no—
789C22⋊Q8—42no—
790C22⋊Q8—42no—
791C22⋊Q8—44no—
792#121—42no—
793C4×Q8—24no—
794C4×Q8—24no—
795C4×Q8—24no—
796C4×Q8—24no—
797C4×Q8—24no—
798C4×Q8—28no—
799C4×Q8—44no—
800C4×Q8—44no—
801C4×Q8—44no—
802C4×Q8—44no—
803C4×Q8—44no—
804C4×Q8—44no—
805C4×Q8—44no—
806C4×Q8—44no—
807C4×Q8—44no—
808C4×D4—24no—
809C4×D4—44no—
810#117—24no—
811#117—42no—
812#117—44no—
813C2×C4⋊C4C2411yescharacteristic
814C2×C4⋊C4C2411yescharacteristic
815C2×C4⋊C4C2412yes—
816C2×C4⋊C4C2411yescharacteristic
817C2×C4⋊C4C2411yescharacteristic
818C2×C4⋊C4C2412yes—
819C2×C4⋊C4C2411yescharacteristic
820C2×C4⋊C4C2411yescharacteristic
821C2×C4⋊C4C2412yes—
822C2×C4⋊C4C2411yescharacteristic
823C2×C4⋊C4C2412yes—
824C2×C4⋊C4C2411yescharacteristic
825C2×C4⋊C4C2412yes—
826C2×C4⋊C4C2412yes—
827C2×C4⋊C4C2412yes—
828C2×C4⋊C4C2412yes—
829C2×C4⋊C4C2412yes—
830C2×C4⋊C4C2412yes—
831C2×C4⋊C4C2412yes—
832C2×C4⋊C4C2414yes—
833C2×C4⋊C4C2414yes—
834C2×C4⋊C4C2412yes—
835C2×C4⋊C4C2414yes—
836C2×C4⋊C4C2414yes—
837C2×C4⋊C4C2414yes—
838C2×C4⋊C4C2414yes—
839C2×C4⋊C4C2414yes—
840C2×C4⋊C4C2414yes—
841C2×C4⋊C4C2414yes—
842C2×C4⋊C4C2412yes—
843C2×C4⋊C4C2412yes—
844C2×C4⋊C4C2414yes—
845C2×C4⋊C4C2412yes—
846C2×C4⋊C4C2412yes—
847C2×C4⋊C4C2412yes—
848C2×C4⋊C4C2412yes—
849C2×C4⋊C4C2414yes—
850C2×C4⋊C4C2412yes—
851C2×C4⋊C4C2412yes—
852C2×C4⋊C4C2412yes—
853C2×C4⋊C4C2414yes—
854C2×C4⋊C4C2414yes—
855C2×C4⋊C4C2412yes—
856C2×C4⋊C4C2412yes—
857C2×C4⋊C4C2414yes—
858C2×C4⋊C4C2414yes—
859C2×C4⋊C4C2414yes—
860C2×C4⋊C4C2414yes—
861C2×C4⋊C4C2414yes—
862C2×C4⋊C4C2412yes—
863C2×C4⋊C4C2412yes—
864C2×C4⋊C4C2412yes—
865C2×C4⋊C4C2412yes—
866C2×C4⋊C4C2412yes—
867C2×C4⋊C4C2412yes—
868C2×C4⋊C4C2414yes—
869C2×C4⋊C4C2414yes—
870C2×C4⋊C4C2412yes—
871C2×C4⋊C4C2414yes—
872C2×C4⋊C4C2412yes—
873C2×C4⋊C4C2412yes—
874C2×C4⋊C4C2414yes—
875C2×C4⋊C4C2412yes—
876C2×C4⋊C4C2412yes—
877C2×C4⋊C4C2412yes—
878C2×C4⋊C4C2412yes—
879C2×C4⋊C4C2412yes—
880C2×C4⋊C4C2412yes—
881C2×C4⋊C4C2412yes—
882C2×C4⋊C4C2414yes—
883C2×C4⋊C4C2414yes—
884C2×C4⋊C4C2414yes—
885C2×C4⋊C4C2414yes—
886C2×C4⋊C4C2414yes—
887C2×C4⋊C4C2414yes—
888C2×C4⋊C4C2414yes—
889C2×C4⋊C4C2414yes—
890C2×C22⋊C4C2411yescharacteristic
891C2×C22⋊C4C2411yescharacteristic
892C2×C22⋊C4C2412yes—
893C2×C22⋊C4C2414yes—
894C2×C22⋊C4C2414yes—
895C2×C22⋊C4C2412yes—
896C2×C22⋊C4C2414yes—
897C2×C22⋊C4C2412yes—
898C2×C22⋊C4C2412yes—
899C2×C22⋊C4C2412yes—
900C2×C22⋊C4C2414yes—
901C2×C22⋊C4C2412yes—
902C2×C22⋊C4C2412yes—
903C2×C22⋊C4C2414yes—
904C2×C22⋊C4C2412yes—
905C2×C22⋊C4C2414yes—
906C2×C22⋊C4C2412yes—
907C2×C22⋊C4C2414yes—
908C2×C22⋊C4C2412yes—
909C2×C22⋊C4C2412yes—
910C2×C22⋊C4C2412yes—
911C2×C22⋊C4C2414yes—
912C2×C22⋊C4C2414yes—
913C2×C22⋊C4C2414yes—
914C2×C22⋊C4C2414yes—
915C2×C22⋊C4C2414yes—
916C2×C22⋊C4C2414yes—
917C2×C42—24no—
918C2×C42C2411yescharacteristic
919C2×C42C2411yescharacteristic
920C2×C42C2411yescharacteristic
921C2×C42C2412yes—
922C2×C42C2412yes—
923C2×C42C2412yes—
924C2×C42C2412yes—
925C2×C42C2412yes—
926C2×C42C2412yes—
927C2×C42C2412yes—
928C2×C42C2414yes—
929C2×C42C2411yescharacteristic
930C2×C42C2412yes—
931C2×C42C2414yes—
932C2×C42C2414yes—
933C2×C42C2414yes—
934C2×C42C2414yes—
935C2×C42C2414yes—
936C2×C42C2412yes—
937C2×C42C2412yes—
938C2×C42C2412yes—
939C2×C42C2412yes—
940C2×C42C2414yes—
941C2×C42C2414yes—
942C2×C42C2414yes—
943C2×C42C2411yescharacteristic
944C2×C42C2411yescharacteristic
945#95C2411yescharacteristic
946#95C2412yes—
947#95C2414yes—
948#95C2411yescharacteristic
949#95C2412yes—
950#95C2411yescharacteristic
951#95C2412yes—
952#95C2412yes—
953#95C2412yes—
954#95C2412yes—
955#95C2412yes—
956#95C2412yes—
957#95C2412yes—
958#95C2412yes—
959#95C2412yes—
960#95C2412yes—
961#95C2412yes—
962#95C2412yes—
963#95C2412yes—
964#95C2414yes—
965#95C2412yes—
966#95C2414yes—
967#95C2414yes—
968#95C2414yes—
969#95C2414yes—
970#95C2412yes—
971#95C2412yes—
972#95C2414yes—
973#95C2414yes—
974#95C2412yes—
975#95C2412yes—
976#95C2412yes—
977#95C2414yes—
978#95C2414yes—
979#95C2414yes—
980#95C2411yescharacteristic
981#95C2414yes—
982#95C2414yes—
983#95C2414yes—
984#95C2414yes—
985#95C2412yes—
986#95C2412yes—
987#95C2412yes—
988#95C2414yes—
989#95C2412yes—
990#95C2414yes—
991#95C2414yes—
992#95C2414yes—
993#95C2414yes—
994#95C2414yes—
995#95C2412yes—
996#95C2412yes—
997#95C2412yes—
998#95C2412yes—
999#95C2412yes—
1000#95C2412yes—
1001#95C2414yes—
1002#95C2412yes—
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#95C2414yes—
1018#95C2414yes—
1019#95C2414yes—
1020#95C2414yes—
1021#95C2414yes—
1022#95C2414yes—
1023#95C2414yes—
1024#95C2414yes—
1025#95C2414yes—
1026#95C2414yes—
1027#95C2414yes—
1028#95C2414yes—
1029#95C2414yes—
1030#95C2414yes—
1031#95C2414yes—
1032#95C2414yes—
1033C24C2511yescharacteristic
1034C24C2512yes—
1035C2×Q8—22no—
1036C2×Q8—22no—
1037C2×Q8—22no—
1038C2×Q8—22no—
1039C2×Q8—22no—
1040C2×Q8—24no—
1041C2×Q8—24no—
1042C2×Q8—24no—
1043C2×Q8—22no—
1044C2×Q8—22no—
1045C2×Q8—22no—
1046C2×Q8—22no—
1047C2×Q8—24no—
1048C2×Q8—22no—
1049C2×Q8—22no—
1050C2×Q8—42no—
1051C2×Q8—42no—
1052C2×Q8—42no—
1053C2×Q8—44no—
1054C2×Q8—42no—
1055C2×Q8—42no—
1056C2×Q8—42no—
1057C2×Q8—44no—
1058C2×Q8—44no—
1059C2×Q8—44no—
1060C2×Q8—44no—
1061C2×D4—22no—
1062C2×D4—22no—
1063C2×D4—22no—
1064C2×D4—42no—
1065C2×D4—44no—
1066C22×C4—22no—
1067C22×C4—22no—
1068C22×C4—22no—
1069C22×C4—24no—
1070C22×C4—24no—
1071C22×C4—42no—
1072C22×C4—44no—
1073C22×C4—42no—
1074C22×C4—44no—
1075C22×C4—44no—
1076C22×C4—44no—
1077C22×C4C2512yes—
1078C22×C4C2514yes—
1079C22×C4C2512yes—
1080C22×C4C2512yes—
1081C22×C4C2512yes—
1082C22×C4C2512yes—
1083C22×C4C2514yes—
1084C22×C4C2512yes—
1085C22×C4C2512yes—
1086C22×C4C2512yes—
1087C22×C4C2511yescharacteristic
1088C22×C4C2512yes—
1089C22×C4C2514yes—
1090C22×C4C2512yes—
1091C22×C4C2512yes—
1092C22×C4C2512yes—
1093C22×C4C2512yes—
1094C22×C4C2512yes—
1095C22×C4C2512yes—
1096C22×C4C2512yes—
1097C22×C4C2514yes—
1098C22×C4C2511yescharacteristic
1099C22×C4C2512yes—
1100C22×C4C2512yes—
1101C22×C4C2511yescharacteristic
1102C22×C4C2511yescharacteristic
1103C22×C4C2511yescharacteristic
1104C22×C4C2512yes—
1105C22×C4C2511yescharacteristic
1106C4⋊C4—22no—
1107C4⋊C4—22no—
1108C4⋊C4—22no—
1109C4⋊C4—24no—
1110C4⋊C4—22no—
1111C4⋊C4—22no—
1112C4⋊C4—22no—
1113C4⋊C4—22no—
1114C4⋊C4—24no—
1115C4⋊C4—22no—
1116C4⋊C4—24no—
1117C4⋊C4—24no—
1118C4⋊C4—24no—
1119C4⋊C4—24no—
1120C4⋊C4—24no—
1121C4⋊C4—24no—
1122C4⋊C4—24no—
1123C4⋊C4—24no—
1124C4⋊C4—28no—
1125C4⋊C4—28no—
1126C4⋊C4—24no—
1127C4⋊C4—42no—
1128C4⋊C4—42no—
1129C4⋊C4—42no—
1130C4⋊C4—42no—
1131C4⋊C4—42no—
1132C4⋊C4—42no—
1133C4⋊C4—44no—
1134C4⋊C4—44no—
1135C4⋊C4—44no—
1136C4⋊C4—44no—
1137C4⋊C4—42no—
1138C4⋊C4—44no—
1139C4⋊C4—44no—
1140C4⋊C4—44no—
1141C4⋊C4—44no—
1142C4⋊C4—42no—
1143C4⋊C4—42no—
1144C4⋊C4—42no—
1145C4⋊C4—42no—
1146C4⋊C4—42no—
1147C4⋊C4—42no—
1148C4⋊C4—44no—
1149C4⋊C4—42no—
1150C4⋊C4—44no—
1151C4⋊C4—42no—
1152C4⋊C4—42no—
1153C4⋊C4—44no—
1154C4⋊C4—44no—
1155C4⋊C4—42no—
1156C4⋊C4—42no—
1157C4⋊C4—42no—
1158C4⋊C4—42no—
1159C4⋊C4—44no—
1160C4⋊C4—44no—
1161C4⋊C4—44no—
1162C4⋊C4—44no—
1163C4⋊C4—44no—
1164C4⋊C4—44no—
1165C4⋊C4—44no—
1166C4⋊C4—44no—
1167C4⋊C4—44no—
1168C4⋊C4—42no—
1169C4⋊C4—42no—
1170C4⋊C4—42no—
1171C4⋊C4—42no—
1172C4⋊C4—42no—
1173C4⋊C4—42no—
1174C4⋊C4—44no—
1175C4⋊C4—44no—
1176C4⋊C4—42no—
1177C4⋊C4—42no—
1178C4⋊C4—44no—
1179C4⋊C4—44no—
1180C4⋊C4—44no—
1181C4⋊C4—44no—
1182C4⋊C4—44no—
1183C22⋊C4—22no—
1184C22⋊C4—22no—
1185C22⋊C4—24no—
1186C22⋊C4—28no—
1187C22⋊C4—44no—
1188C22⋊C4—44no—
1189C22⋊C4—44no—
1190C22⋊C4—44no—
1191C22⋊C4—44no—
1192C22⋊C4—44no—
1193C22⋊C4—42no—
1194C22⋊C4—44no—
1195C22⋊C4—42no—
1196C22⋊C4—42no—
1197C22⋊C4—42no—
1198C22⋊C4—42no—
1199C22⋊C4—44no—
1200C22⋊C4—44no—
1201C22⋊C4—42no—
1202C22⋊C4—44no—
1203C22⋊C4—42no—
1204C22⋊C4—42no—
1205C22⋊C4—44no—
1206C22⋊C4—42no—
1207C22⋊C4—42no—
1208C22⋊C4—42no—
1209C22⋊C4—44no—
1210C42—22no—
1211C42—24no—
1212C42—24no—
1213C42—24no—
1214C42—24no—
1215C42—24no—
1216C42—24no—
1217C42—22no—
1218C42—28no—
1219C42—22no—
1220C42—22no—
1221C42—24no—
1222C42—24no—
1223C42—44no—
1224C42—42no—
1225C42—42no—
1226C42—42no—
1227C42—42no—
1228C42—44no—
1229C42—44no—
1230C42—44no—
1231C42—44no—
1232C42—44no—
1233C42—44no—
1234C42—44no—
1235C42H(5,𝔽2)14yes—
1236C422−1+414yes—
1237C23—21no—
1238C23—22no—
1239C23—22no—
1240C23—21no—
1241C23—21no—
1242C23—22no—
1243C23—22no—
1244C23—24no—
1245C23—24no—
1246C23—22no—
1247C23C2611yescharacteristic
1248Q8—44no—
1249Q8—44no—
1250Q8—44no—
1251Q8—44no—
1252Q8—44no—
1253Q8—48no—
1254Q8—84no—
1255Q8—84no—
1256Q8—162no—
1257Q8—164no—
1258D4—44no—
1259D4—162no—
1260C2×C4—22no—
1261C2×C4—22no—
1262C2×C4—22no—
1263C2×C4—22no—
1264C2×C4—22no—
1265C2×C4—22no—
1266C2×C4—22no—
1267C2×C4—22no—
1268C2×C4—22no—
1269C2×C4—22no—
1270C2×C4—22no—
1271C2×C4—21no—
1272C2×C4—21no—
1273C2×C4—22no—
1274C2×C4—22no—
1275C2×C4—22no—
1276C2×C4—22no—
1277C2×C4—24no—
1278C2×C4—24no—
1279C2×C4—21no—
1280C2×C4—21no—
1281C2×C4—22no—
1282C2×C4—24no—
1283C2×C4—24no—
1284C2×C4—22no—
1285C2×C4—22no—
1286C2×C4—22no—
1287C2×C4—22no—
1288C2×C4—22no—
1289C2×C4—22no—
1290C2×C4—22no—
1291C2×C4—22no—
1292C2×C4—22no—
1293C2×C4—22no—
1294C2×C4—24no—
1295C2×C4—22no—
1296C2×C4—24no—
1297C2×C4—21no—
1298C2×C4—22no—
1299C2×C4—22no—
1300C2×C4—22no—
1301C2×C4—22no—
1302C2×C4—22no—
1303C2×C4—24no—
1304C2×C4—22no—
1305C2×C4—24no—
1306C2×C4—24no—
1307C2×C4—24no—
1308C2×C4—22no—
1309C2×C4—22no—
1310C2×C4—22no—
1311C2×C4—24no—
1312C2×C4—22no—
1313C2×C4—24no—
1314C2×C4—22no—
1315C2×C4—22no—
1316C2×C4—22no—
1317C2×C4—22no—
1318C2×C4—22no—
1319C2×C4—24no—
1320C2×C4—24no—
1321C2×C4—22no—
1322C2×C4—22no—
1323C2×C4—22no—
1324C2×C4—22no—
1325C2×C4—22no—
1326C2×C4—22no—
1327C2×C4—22no—
1328C2×C4—24no—
1329C2×C4—22no—
1330C2×C4—22no—
1331C2×C4—24no—
1332C2×C4—22no—
1333C2×C4—44no—
1334C2×C4—84no—
1335C2×C4—84no—
1336C2×C4—164no—
1337C2×C4C2×H(5,𝔽2)12yes—
1338C2×C4C2×H(5,𝔽2)12yes—
1339C2×C4C2×H(5,𝔽2)12yes—
1340C2×C4C2×2−1+414yes—
1341C2×C4C2×2−1+412yes—
1342C2×C4#58512yes—
1343C22—41no—
1344C22—42no—
1345C22—42no—
1346C22—41no—
1347C22—41no—
1348C22—42no—
1349C22—42no—
1350C22—44no—
1351C22—44no—
1352C22—42no—
1353C22C22×H(5,𝔽2)11yescharacteristic
1354C22C22×2−1+411yescharacteristic
1355C22C2×#58511yescharacteristic
1356C222−1+612yes—
1357C222−1+612yes—
1358C4—22no—
1359C4—22no—
1360C4—24no—
1361C4—41no—
1362C4—42no—
1363C4—42no—
1364C4—42no—
1365C4—44no—
1366C4—42no—
1367C4—42no—
1368C4—41no—
1369C4—42no—
1370C4—42no—
1371C4—42no—
1372C4—42no—
1373C4—44no—
1374C4—42no—
1375C4—41no—
1376C4—42no—
1377C4—44no—
1378C4—42no—
1379C4—42no—
1380C4—42no—
1381C4—44no—
1382C4—42no—
1383C4—42no—
1384C4—42no—
1385C4—42no—
1386C4#354714yes—
1387C2—81no—
1388C2—82no—
1389C2C2×#354711yescharacteristic
1390C2#6288711yescharacteristic
1391C2#6288711yescharacteristic
1392C2#6288912yes—
1393C2#6289112yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#121C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #57751C2semidirect
2. #57256C2semidirect
3. #56903C2semidirect
4. #56892C2semidirect
5. #56084C2semidirect
6. #56072C2semidirect
7. #54534C2semidirect
8. #54518C2semidirect
9. #53140C2semidirect
11. #45436C2semidirect
12. #45425C2semidirect
13. #45394C2semidirect
14. #45389C2semidirect
16. #42824C2semidirect
17. #42793C2semidirect
18. #42791C2semidirect
19. #42702C2semidirect
21. #39172C2semidirect
22. #39170C2semidirect
23. #39149C2semidirect
24. #38971C2semidirect
25. #38970C2semidirect
27. #37405C2semidirect
28. #37401C2semidirect
30. #35314C2semidirect
31. #34644C2semidirect

Maximal subgroups

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

subgroupindex
#577512
#572562
#569032
#568922
#560842
#560722
#545342
#545182
#531402
#531382
#454362
#454252
#453942
#453892
#428752
#428242
#427932
#427912
#427022
#426492
#391722
#391702
#391492
#389712
#389702
#389372
#374052
#374012
#353182
#353142
#346442