Finite Group Databasebeta

← #8372133

Subgroups — #8372133

Order 512.

4375 conjugacy classes of subgroups.

The subgroup lattice has 1477 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59253C212yesmaximal, complemented
2#57415C214yesmaximal, complemented
3#56949C214yesmaximal, complemented
4#56470C214yesmaximal, complemented
5#54640C214yesmaximal, complemented
6#53144C212yesmaximal, complemented
7#48925C214yesmaximal, complemented
8#48683C214yesmaximal, complemented
9#45708C212yesmaximal, complemented
10#45431C211yesmaximal, characteristic, complemented
11#45428C211yesmaximal, characteristic, complemented
12#45336C211yesmaximal, characteristic, complemented
13#45271C211yesmaximal, characteristic, complemented
14#45168C212yesmaximal, complemented
15#42872C212yesmaximal, complemented
16#42788C211yesmaximal, characteristic, complemented
17#42747C212yesmaximal, complemented
18#42647C211yesmaximal, characteristic, complemented
19#41457C214yesmaximal, complemented
20#40646C214yesmaximal, complemented
21#39905C212yesmaximal, complemented
22#39758C211yesmaximal, characteristic, complemented
23#39173C211yesmaximal, characteristic, complemented
24#38983C212yesmaximal, complemented
25#37396C211yesmaximal, characteristic, complemented
26#36303C211yesmaximal, characteristic, complemented
27#36195C211yesmaximal, characteristic, complemented
28#35712C211yesmaximal, characteristic, complemented
29#35693C211yesmaximal, characteristic, complemented
30#35623C211yesmaximal, characteristic, complemented
31#34596C211yesmaximal, characteristic, complemented
32C2×#557C2211yescharacteristic
33C2×#554C2211yescharacteristic
34C2×D4×Q8C2211yescharacteristic
35C2×#547C2211yescharacteristic
36C2×#542C2211yescharacteristic
37C2×#520C2211yescharacteristic
38#2862C2211yescharacteristic
39#2862C2211yescharacteristic
40#2850C2212yes—
41#2850C2212yes—
42#2839C2214yes—
43#2835C2214yes—
44#2832C2214yes—
45#2832C2214yes—
46#2832C2214yes—
47#2825C2214yes—
48#2824C2214yes—
49#2821C2212yes—
50#2817C2212yes—
51#2804C2214yes—
52#2804C2214yes—
53#2804C2214yes—
54#2803C2214yes—
55#2799C2214yes—
56#2799C2214yes—
57#2798C2214yes—
58#2798C2214yes—
59#2796C2214yes—
60#2788C2214yes—
61#2782C2214yes—
62#2775C2214yes—
63#2771C2214yes—
64#2770C2214yes—
65#2764C2214yes—
66#2764C2214yes—
67#2763C2214yes—
68#2762C2214yes—
69#2762C2214yes—
70#2759C2214yes—
71#2759C2214yes—
72#2759C2214yes—
73#2759C2214yes—
74#2758C2214yes—
75#2758C2214yes—
76#2758C2214yes—
77#2756C2214yes—
78#2754C2214yes—
79#2753C2214yes—
80#2751C2214yes—
81#2751C2214yes—
82#2749C2214yes—
83#2746C2214yes—
84#2745C2214yes—
85#2739C2214yes—
86#2737C2214yes—
87#2737C2214yes—
88#2737C2214yes—
89#2728C2214yes—
90#2713C2214yes—
91#2708C2214yes—
92#2703C2214yes—
93#2700C2214yes—
94#2698C2214yes—
95#2696C2214yes—
96#2696C2214yes—
97#2692C2214yes—
98#2690C2214yes—
99#2690C2214yes—
100#2690C2214yes—
101#2687C2214yes—
102#2686C2214yes—
103#2665C2212yes—
104#2665C2214yes—
105#2663C2212yes—
106#2663C2212yes—
107#2655C2212yes—
108#2653C2214yes—
109#2653C2212yes—
110#2653C2214yes—
111#2652C2212yes—
112#2650C2212yes—
113#2648C2214yes—
114#2645C2214yes—
115#2643C2214yes—
116#2642C2212yes—
117#2640C2212yes—
118#2640C2212yes—
119#2638C2212yes—
120#2638C2212yes—
121#2633C2212yes—
122#2631C2212yes—
123#2630C2212yes—
124#2628C2211yescharacteristic
125#2623C2212yes—
126#2621C2211yescharacteristic
127#2612C2214yes—
128#2611C2212yes—
129#2605C2214yes—
130#2603C2212yes—
131#2600C2214yes—
132#2599C2212yes—
133#2597C2214yes—
134#2592C2212yes—
135#2592C2212yes—
136#2583C2212yes—
137#2581C2211yescharacteristic
138#2580C2211yescharacteristic
139#2572C2214yes—
140#2568C2211yescharacteristic
141#2568C2212yes—
142#2568C2211yescharacteristic
143#2567C2211yescharacteristic
144#2565C2212yes—
145#2563C2211yescharacteristic
146#2557C2214yes—
147#2550C2212yes—
148#2548C2212yes—
149#2547C2211yescharacteristic
150#2547C2212yes—
151#2547C2211yescharacteristic
152#2545C2211yescharacteristic
153#2544C2211yescharacteristic
154#2540C2212yes—
155#2536C2211yescharacteristic
156#2535C2211yescharacteristic
157#2532C2214yes—
158#2532C2214yes—
159#2531C2214yes—
160#2531C2214yes—
161#2530C2214yes—
162#2528C2214yes—
163#2527C2214yes—
164#2527C2214yes—
165#2527C2214yes—
166#2523C2214yes—
167#2514C2212yes—
168#2514C2212yes—
169#2514C2212yes—
170#2513C2212yes—
171#2511C2212yes—
172#2510C2214yes—
173#2505C2214yes—
174#2504C2211yescharacteristic
175#2503C2212yes—
176#2503C2211yescharacteristic
177#2503C2212yes—
178#2493C2214yes—
179#2492C2212yes—
180#2492C2212yes—
181#2492C2214yes—
182#2492C2212yes—
183#2491C2212yes—
184#2490C2212yes—
185#2489C2212yes—
186#2488C2214yes—
187#2488C2214yes—
188#2481C2214yes—
189#2477C2214yes—
190#2473C2214yes—
191#2470C2214yes—
192#2465C2214yes—
193#2460C2214yes—
194#2460C2214yes—
195#2459C2214yes—
196#2459C2214yes—
197#2459C2214yes—
198#2457C2214yes—
199#2455C2214yes—
200#2451C2212yes—
201#2450C2214yes—
202#2447C2214yes—
203#2447C2212yes—
204#2446C2212yes—
205#2443C2214yes—
206#2442C2214yes—
207#2442C2212yes—
208#2436C2212yes—
209#2436C2212yes—
210#2434C2212yes—
211#2432C2211yescharacteristic
212#2432C2212yes—
213#2431C2211yescharacteristic
214#2429C2212yes—
215#2428C2212yes—
216#2422C2212yes—
217#2421C2214yes—
218#2421C2212yes—
219#2421C2212yes—
220#2420C2212yes—
221#2419C2214yes—
222#2409C2212yes—
223#2407C2214yes—
224#2407C2212yes—
225#2406C2212yes—
226#2401C2212yes—
227#2399C2211yescharacteristic
228#2398C2211yescharacteristic
229#2398C2212yes—
230#2398C2212yes—
231#2396C2211yescharacteristic
232#2392C2211yescharacteristic
233#2388C2212yes—
234#2377C2214yes—
235#2372C2214yes—
236#2367C2212yes—
237#2361C2212yes—
238#2360C2212yes—
239#2360C2212yes—
240#2357C2211yescharacteristic
241#2357C2211yescharacteristic
242#2356C2211yescharacteristic
243#2356C2211yescharacteristic
244#2356C2212yes—
245#2355C2212yes—
246#2353C2214yes—
247D4×C4⋊C4C2212yes—
248Q8×C22⋊C4C2212yes—
249#2339C2214yes—
250#2335C2214yes—
251#2331C2211yescharacteristic
252#2331C2212yes—
253#2328C2211yescharacteristic
254#2327C2211yescharacteristic
255#2327C2211yescharacteristic
256#2326C2212yes—
257#2318C2214yes—
258C4×#124C2211yescharacteristic
259C4×#124C2211yescharacteristic
260C4×C22⋊Q8C2212yes—
261C4×#123C2212yes—
262#2298C2211yescharacteristic
263#2295C2211yescharacteristic
264C2×#391C2212yes—
265#2283C2212yes—
266C42×D4C2211yescharacteristic
267C22×#41C2312yes—
268C22×#41C2311yescharacteristic
269C23×Q8C2312yes—
270#557—44no—
271#554—44no—
272D4×Q8—44no—
273#547—44no—
274#542—44no—
275C2×C4⋊Q8C2311yescharacteristic
276C2×C4⋊Q8C2311yescharacteristic
277C2×C4⋊Q8C2311yescharacteristic
278C2×C4⋊Q8C2312yes—
279C2×C4⋊Q8C2311yescharacteristic
280C2×C4⋊Q8C2312yes—
281C2×C4⋊Q8C2312yes—
282C2×#127C2311yescharacteristic
283C2×#126C2312yes—
284C2×#125C2312yes—
285C2×#125C2312yes—
286C2×#125C2314yes—
287C2×#124C2312yes—
288C2×#124C2312yes—
289C2×#124C2311yescharacteristic
290C2×#124C2314yes—
291C2×#124C2312yes—
292C2×#124C2311yescharacteristic
293C2×#124C2311yescharacteristic
294C2×#123C2314yes—
295C2×#123C2312yes—
296C2×#123C2312yes—
297C2×#123C2314yes—
298C2×C22⋊Q8C2312yes—
299C2×C22⋊Q8C2312yes—
300C2×C22⋊Q8C2312yes—
301C2×C22⋊Q8C2312yes—
302C2×C22⋊Q8C2312yes—
303C2×C22⋊Q8C2312yes—
304C2×C22⋊Q8C2312yes—
305C2×C22⋊Q8C2314yes—
306C2×C22⋊Q8C2311yescharacteristic
307C2×C22⋊Q8C2314yes—
308C2×#121C2312yes—
309C2×#121C2312yes—
310C2×#121C2314yes—
311C2×#121C2311yescharacteristic
312#520—44no—
313C2×C4×Q8C2311yescharacteristic
314C2×C4×Q8C2311yescharacteristic
315C2×C4×Q8C2311yescharacteristic
316C2×C4×Q8C2312yes—
317C2×C4×Q8C2312yes—
318C2×C4×Q8C2311yescharacteristic
319C2×C4×Q8C2312yes—
320C2×C4×Q8C2312yes—
321C2×C4×D4C2311yescharacteristic
322C2×C4×D4C2311yescharacteristic
323C2×C4×D4C2311yescharacteristic
324C2×C4×D4C2311yescharacteristic
325C2×C4×D4C2314yes—
326C2×C4×D4C2312yes—
327C2×C4×D4C2312yes—
328C2×C4×D4C2312yes—
329C2×C4×D4C2314yes—
330C2×C4×D4C2312yes—
331C2×C4×D4C2312yes—
332C2×C4×D4C2312yes—
333C2×#117C2311yescharacteristic
334C2×#117C2312yes—
335C22×C4⋊C4C2312yes—
336C22×C4⋊C4C2311yescharacteristic
337C22×C4⋊C4C2312yes—
338C22×C4⋊C4C2312yes—
339C22×C42C2312yes—
340#401C2314yes—
341#401C2314yes—
342#401C2312yes—
343#401C2314yes—
344#400C2312yes—
345#400C2314yes—
346#400C2312yes—
347#400C2314yes—
348#400C2314yes—
349#400C2314yes—
350#400C2314yes—
351#400C2312yes—
352#400C2314yes—
353#400C2314yes—
354#400C2312yes—
355#400C2314yes—
356#400C2314yes—
357#400C2314yes—
358#400C2312yes—
359#400C2314yes—
360#400C2314yes—
361#400C2312yes—
362#400C2312yes—
363#400C2314yes—
364#400C2314yes—
365#400C2314yes—
366#400C2311yescharacteristic
367#400C2314yes—
368#400C2314yes—
369#400C2314yes—
370#400C2314yes—
371#400C2314yes—
372#400C2312yes—
373#400C2312yes—
374#400C2312yes—
375#400C2314yes—
376#400C2314yes—
377#400C2314yes—
378#399C2314yes—
379#399C2312yes—
380#399C2311yescharacteristic
381#399C2312yes—
382#398C2314yes—
383#398C2314yes—
384#398C2311yescharacteristic
385#398C2312yes—
386#398C2312yes—
387#398C2314yes—
388#398C2314yes—
389#398C2314yes—
390#398C2314yes—
391#398C2314yes—
392#398C2312yes—
393#398C2312yes—
394#398C2312yes—
395#398C2312yes—
396#397C2314yes—
397#397C2314yes—
398#397C2312yes—
399#397C2312yes—
400#397C2314yes—
401#397C2314yes—
402#397C2314yes—
403#397C2314yes—
404#397C2314yes—
405#397C2312yes—
406#397C2314yes—
407#397C2314yes—
408#397C2314yes—
409#397C2314yes—
410#397C2314yes—
411#397C2312yes—
412#397C2314yes—
413#397C2312yes—
414#397C2312yes—
415#397C2312yes—
416#397C2312yes—
417#397C2312yes—
418#397C2311yescharacteristic
419#397C2312yes—
420#397C2312yes—
421#397C2312yes—
422#397C2314yes—
423#397C2314yes—
424#397C2312yes—
425#397C2314yes—
426#397C2314yes—
427#396C2314yes—
428#396C2312yes—
429#396C2312yes—
430#396C2314yes—
431#396C2312yes—
432#395C2311yescharacteristic
433#395C2312yes—
434#395C2314yes—
435#395C2314yes—
436#395C2312yes—
437#395C2312yes—
438#395C2314yes—
439#395C2314yes—
440#395C2314yes—
441#395C2312yes—
442#395C2312yes—
443#395C2312yes—
444#394C2312yes—
445#394C2314yes—
446#394C2314yes—
447#394C2314yes—
448#394C2314yes—
449#394C2314yes—
450#394C2314yes—
451#394C2314yes—
452#394C2314yes—
453#394C2314yes—
454#394C2314yes—
455#394C2314yes—
456#394C2311yescharacteristic
457#394C2312yes—
458#394C2312yes—
459#394C2314yes—
460#394C2312yes—
461#394C2312yes—
462#393C2314yes—
463#393C2314yes—
464#393C2314yes—
465#393C2314yes—
466#393C2314yes—
467#393C2314yes—
468#393C2314yes—
469#393C2314yes—
470#393C2314yes—
471#393C2312yes—
472#393C2314yes—
473#393C2314yes—
474#393C2314yes—
475#393C2312yes—
476#393C2314yes—
477#393C2312yes—
478#393C2314yes—
479#393C2312yes—
480#393C2311yescharacteristic
481#393C2312yes—
482#392C2314yes—
483#392C2314yes—
484#392C2314yes—
485#392C2314yes—
486#392C2312yes—
487#392C2311yescharacteristic
488#391C2312yes—
489#391C2312yes—
490#391C2312yes—
491#391C2312yes—
492#391C2314yes—
493#391C2311yescharacteristic
494#391C2312yes—
495#391C2314yes—
496#391C2312yes—
497#391C2311yescharacteristic
498#391C2314yes—
499#391C2314yes—
500#391C2314yes—
501#391C2314yes—
502#391C2312yes—
503#391C2312yes—
504#391C2312yes—
505#391C2311yescharacteristic
506#391C2314yes—
507#391C2314yes—
508#391C2314yes—
509#391C2312yes—
510#391C2314yes—
511#391C2314yes—
512#391C2314yes—
513#391C2314yes—
514#391C2314yes—
515#391C2312yes—
516#391C2314yes—
517#391C2314yes—
518#391C2312yes—
519#391C2312yes—
520#391C2314yes—
521#391C2314yes—
522#391C2314yes—
523#391C2311yescharacteristic
524#390C2311yescharacteristic
525#390C2311yescharacteristic
526#390C2312yes—
527#390C2311yescharacteristic
528#390C2311yescharacteristic
529#390C2314yes—
530#390C2312yes—
531#390C2312yes—
532#390C2314yes—
533#390C2314yes—
534#390C2314yes—
535#390C2314yes—
536#389C2314yes—
537#389C2312yes—
538#389C2312yes—
539#389C2314yes—
540#389C2314yes—
541#389C2312yes—
542#389C2314yes—
543#389C2314yes—
544#389C2312yes—
545#389C2314yes—
546#389C2312yes—
547#389C2312yes—
548#388C2314yes—
549#388C2314yes—
550#388C2314yes—
551#388C2314yes—
552#388C2314yes—
553#388C2314yes—
554#388C2314yes—
555#388C2314yes—
556#388C2314yes—
557#388C2314yes—
558#388C2314yes—
559#388C2314yes—
560#388C2314yes—
561#388C2314yes—
562#388C2314yes—
563#388C2314yes—
564#388C2314yes—
565#388C2314yes—
566#388C2314yes—
567#388C2314yes—
568#388C2314yes—
569#388C2314yes—
570#388C2314yes—
571#388C2314yes—
572#388C2314yes—
573#388C2314yes—
574#388C2312yes—
575#388C2314yes—
576#388C2314yes—
577#388C2312yes—
578#388C2312yes—
579#388C2312yes—
580#388C2314yes—
581#388C2314yes—
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#387C2314yes—
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#387C2312yes—
608#387C2314yes—
609#387C2314yes—
610#387C2312yes—
611#387C2312yes—
612#387C2312yes—
613#387C2314yes—
614#387C2312yes—
615#387C2312yes—
616#387C2312yes—
617#387C2312yes—
618#386C2314yes—
619#386C2314yes—
620#386C2312yes—
621#386C2314yes—
622#386C2314yes—
623#386C2314yes—
624#386C2314yes—
625#386C2314yes—
626#386C2314yes—
627#386C2314yes—
628#386C2314yes—
629#386C2314yes—
630#386C2314yes—
631#386C2314yes—
632#386C2314yes—
633#386C2314yes—
634#386C2314yes—
635#386C2314yes—
636#386C2314yes—
637#386C2314yes—
638#385C2314yes—
639#385C2312yes—
640#385C2314yes—
641#385C2314yes—
642#385C2314yes—
643#385C2314yes—
644#385C2314yes—
645#385C2314yes—
646#385C2314yes—
647#385C2312yes—
648#385C2314yes—
649#385C2314yes—
650#385C2314yes—
651#385C2314yes—
652#385C2314yes—
653#385C2314yes—
654#385C2314yes—
655#385C2314yes—
656#385C2314yes—
657#385C2312yes—
658#385C2314yes—
659#385C2314yes—
660#384C2312yes—
661#383C2312yes—
662#383C2312yes—
663#383C2314yes—
664#383C2314yes—
665#383C2314yes—
666#383C2314yes—
667#383C2314yes—
668#382C2311yescharacteristic
669#382C2311yescharacteristic
670#382C2314yes—
671#382C2311yescharacteristic
672#382C2311yescharacteristic
673#382C2312yes—
674#382C2311yescharacteristic
675#382C2311yescharacteristic
676#382C2312yes—
677#382C2314yes—
678#382C2314yes—
679#381C2312yes—
680#381C2314yes—
681#381C2314yes—
682#381C2314yes—
683#381C2314yes—
684#381C2314yes—
685#381C2312yes—
686#381C2314yes—
687#381C2312yes—
688#380C2314yes—
689#380C2314yes—
690#380C2314yes—
691#380C2312yes—
692#380C2314yes—
693#380C2312yes—
694#380C2314yes—
695#380C2312yes—
696#380C2314yes—
697#380C2312yes—
698#380C2314yes—
699C4×C4⋊C4C2311yescharacteristic
700C4×C4⋊C4C2312yes—
701C4×C4⋊C4C2311yescharacteristic
702C4×C4⋊C4C2312yes—
703C4×C4⋊C4C2311yescharacteristic
704C4×C4⋊C4C2311yescharacteristic
705C4×C4⋊C4C2312yes—
706C4×C4⋊C4C2312yes—
707C4×C4⋊C4C2314yes—
708C4×C4⋊C4C2312yes—
709C4×C4⋊C4C2312yes—
710C4×C4⋊C4C2312yes—
711C4×C4⋊C4C2312yes—
712C4×C4⋊C4C2312yes—
713C4×C22⋊C4C2312yes—
714C4×C22⋊C4C2314yes—
715C4×C22⋊C4C2314yes—
716C4×C22⋊C4C2312yes—
717C4×C22⋊C4C2314yes—
718C4×C22⋊C4C2314yes—
719C4×C22⋊C4C2314yes—
720C4×C22⋊C4C2314yes—
721C4×C22⋊C4C2312yes—
722C4×C22⋊C4C2314yes—
723C4×C22⋊C4C2312yes—
724C4×C22⋊C4C2312yes—
725C4×C22⋊C4C2312yes—
726C4×C22⋊C4C2312yes—
727C4×C22⋊C4C2312yes—
728C4×C22⋊C4C2311yescharacteristic
729C4×C22⋊C4C2312yes—
730C4×C22⋊C4C2311yescharacteristic
731#376C2312yes—
732#376C2311yescharacteristic
733#376C2312yes—
734#376C2314yes—
735#376C2312yes—
736#376C2314yes—
737C2×#95C2314yes—
738C2×#95C2314yes—
739C43C2311yescharacteristic
740C2×#41—48no—
741C2×#41—42no—
742C2×#41—42no—
743C2×#41—42no—
744C2×#41—44no—
745C22×Q8—44no—
746C22×Q8—44no—
747C22×Q8—44no—
748C22×Q8C2412yes—
749C22×Q8C2411yescharacteristic
750C22×Q8C2411yescharacteristic
751C22×Q8C2411yescharacteristic
752C22×Q8C2412yes—
753C22×Q8C2412yes—
754C22×Q8C2412yes—
755C22×Q8C2414yes—
756C22×Q8C2414yes—
757C22×D4C2411yescharacteristic
758C22×D4C2411yescharacteristic
759C22×D4C2411yescharacteristic
760C22×D4C2412yes—
761C22×D4C2414yes—
762C22×D4C2414yes—
763C22×D4C2412yes—
764C22×D4C2412yes—
765C22×D4C2414yes—
766C23×C4C2411yescharacteristic
767C23×C4C2412yes—
768C23×C4C2412yes—
769C23×C4C2414yes—
770C23×C4C2412yes—
771C23×C4C2412yes—
772C23×C4C2412yes—
773C23×C4C2412yes—
774C23×C4C2414yes—
775C23×C4C2412yes—
776C23×C4C2414yes—
777C23×C4C2412yes—
778C4⋊Q8—24no—
779C4⋊Q8—24no—
780C4⋊Q8—44no—
781C4⋊Q8—42no—
782C4⋊Q8—44no—
783C4⋊Q8—42no—
784C4⋊Q8—44no—
785#127—42no—
786#126—44no—
787#125—44no—
788#125—44no—
789#125—48no—
790#124—44no—
791#124—42no—
792#124—44no—
793#124—44no—
794#124—42no—
795#124—42no—
796#124—48no—
797#123—48no—
798#123—48no—
799#123—44no—
800#123—44no—
801C22⋊Q8—44no—
802C22⋊Q8—48no—
803C22⋊Q8—48no—
804C22⋊Q8—44no—
805C22⋊Q8—44no—
806C22⋊Q8—44no—
807C22⋊Q8—42no—
808C22⋊Q8—44no—
809C22⋊Q8—44no—
810C22⋊Q8—44no—
811#121—48no—
812#121—44no—
813#121—42no—
814#121—44no—
815C4×Q8—24no—
816C4×Q8—24no—
817C4×Q8—24no—
818C4×Q8—44no—
819C4×Q8—44no—
820C4×Q8—42no—
821C4×Q8—44no—
822C4×Q8—44no—
823C4×D4—24no—
824C4×D4—24no—
825C4×D4—24no—
826C4×D4—44no—
827C4×D4—42no—
828C4×D4—44no—
829C4×D4—44no—
830C4×D4—44no—
831C4×D4—44no—
832C4×D4—48no—
833C4×D4—48no—
834C4×D4—44no—
835#117—24no—
836#117—44no—
837C2×C4⋊C4—42no—
838C2×C4⋊C4—44no—
839C2×C4⋊C4—44no—
840C2×C4⋊C4—44no—
841C2×C4⋊C4C2411yescharacteristic
842C2×C4⋊C4C2411yescharacteristic
843C2×C4⋊C4C2411yescharacteristic
844C2×C4⋊C4C2411yescharacteristic
845C2×C4⋊C4C2412yes—
846C2×C4⋊C4C2412yes—
847C2×C4⋊C4C2412yes—
848C2×C4⋊C4C2411yescharacteristic
849C2×C4⋊C4C2411yescharacteristic
850C2×C4⋊C4C2411yescharacteristic
851C2×C4⋊C4C2412yes—
852C2×C4⋊C4C2411yescharacteristic
853C2×C4⋊C4C2412yes—
854C2×C4⋊C4C2412yes—
855C2×C4⋊C4C2412yes—
856C2×C4⋊C4C2412yes—
857C2×C4⋊C4C2412yes—
858C2×C4⋊C4C2412yes—
859C2×C4⋊C4C2412yes—
860C2×C4⋊C4C2414yes—
861C2×C4⋊C4C2414yes—
862C2×C4⋊C4C2412yes—
863C2×C4⋊C4C2414yes—
864C2×C4⋊C4C2414yes—
865C2×C4⋊C4C2412yes—
866C2×C4⋊C4C2414yes—
867C2×C4⋊C4C2414yes—
868C2×C4⋊C4C2412yes—
869C2×C4⋊C4C2414yes—
870C2×C4⋊C4C2412yes—
871C2×C4⋊C4C2412yes—
872C2×C4⋊C4C2414yes—
873C2×C4⋊C4C2414yes—
874C2×C4⋊C4C2412yes—
875C2×C4⋊C4C2414yes—
876C2×C4⋊C4C2412yes—
877C2×C4⋊C4C2412yes—
878C2×C4⋊C4C2412yes—
879C2×C4⋊C4C2414yes—
880C2×C4⋊C4C2414yes—
881C2×C4⋊C4C2412yes—
882C2×C4⋊C4C2412yes—
883C2×C4⋊C4C2414yes—
884C2×C4⋊C4C2412yes—
885C2×C4⋊C4C2414yes—
886C2×C4⋊C4C2414yes—
887C2×C4⋊C4C2414yes—
888C2×C4⋊C4C2414yes—
889C2×C4⋊C4C2412yes—
890C2×C4⋊C4C2412yes—
891C2×C4⋊C4C2412yes—
892C2×C4⋊C4C2412yes—
893C2×C4⋊C4C2414yes—
894C2×C22⋊C4C2412yes—
895C2×C22⋊C4C2411yescharacteristic
896C2×C22⋊C4C2411yescharacteristic
897C2×C22⋊C4C2412yes—
898C2×C22⋊C4C2412yes—
899C2×C22⋊C4C2412yes—
900C2×C22⋊C4C2414yes—
901C2×C22⋊C4C2412yes—
902C2×C22⋊C4C2412yes—
903C2×C22⋊C4C2412yes—
904C2×C22⋊C4C2412yes—
905C2×C22⋊C4C2414yes—
906C2×C22⋊C4C2414yes—
907C2×C22⋊C4C2412yes—
908C2×C22⋊C4C2414yes—
909C2×C22⋊C4C2412yes—
910C2×C22⋊C4C2412yes—
911C2×C22⋊C4C2414yes—
912C2×C22⋊C4C2414yes—
913C2×C22⋊C4C2412yes—
914C2×C22⋊C4C2414yes—
915C2×C22⋊C4C2414yes—
916C2×C22⋊C4C2412yes—
917C2×C22⋊C4C2412yes—
918C2×C22⋊C4C2414yes—
919C2×C22⋊C4C2414yes—
920C2×C22⋊C4C2412yes—
921C2×C22⋊C4C2412yes—
922C2×C22⋊C4C2412yes—
923C2×C22⋊C4C2414yes—
924C2×C22⋊C4C2414yes—
925C2×C22⋊C4C2414yes—
926C2×C22⋊C4C2414yes—
927C2×C22⋊C4C2414yes—
928C2×C22⋊C4C2414yes—
929C2×C22⋊C4C2414yes—
930C2×C22⋊C4C2414yes—
931C2×C22⋊C4C2414yes—
932C2×C22⋊C4C2412yes—
933C2×C22⋊C4C2412yes—
934C2×C22⋊C4C2412yes—
935C2×C22⋊C4C2414yes—
936C2×C22⋊C4C2412yes—
937C2×C22⋊C4C2414yes—
938C2×C22⋊C4C2414yes—
939C2×C22⋊C4C2414yes—
940C2×C22⋊C4C2412yes—
941C2×C22⋊C4C2414yes—
942C2×C22⋊C4C2414yes—
943C2×C42—44no—
944C2×C42C2412yes—
945C2×C42C2411yescharacteristic
946C2×C42C2412yes—
947C2×C42C2412yes—
948C2×C42C2412yes—
949C2×C42C2411yescharacteristic
950C2×C42C2411yescharacteristic
951C2×C42C2412yes—
952C2×C42C2411yescharacteristic
953C2×C42C2411yescharacteristic
954C2×C42C2412yes—
955C2×C42C2412yes—
956C2×C42C2414yes—
957C2×C42C2414yes—
958C2×C42C2414yes—
959C2×C42C2414yes—
960C2×C42C2414yes—
961C2×C42C2412yes—
962C2×C42C2414yes—
963C2×C42C2412yes—
964C2×C42C2414yes—
965C2×C42C2412yes—
966C2×C42C2411yescharacteristic
967#95C2414yes—
968#95C2414yes—
969#95C2414yes—
970#95C2414yes—
971#95C2414yes—
972#95C2414yes—
973#95C2414yes—
974#95C2411yescharacteristic
975#95C2411yescharacteristic
976#95C2412yes—
977#95C2414yes—
978#95C2414yes—
979#95C2414yes—
980#95C2414yes—
981#95C2414yes—
982#95C2414yes—
983#95C2412yes—
984#95C2412yes—
985#95C2414yes—
986#95C2412yes—
987#95C2412yes—
988#95C2414yes—
989#95C2412yes—
990#95C2412yes—
991#95C2412yes—
992#95C2412yes—
993#95C2411yescharacteristic
994#95C2411yescharacteristic
995#95C2412yes—
996#95C2412yes—
997#95C2412yes—
998#95C2414yes—
999#95C2414yes—
1000#95C2414yes—
1001#95C2412yes—
1002#95C2414yes—
1003#95C2412yes—
1004#95C2412yes—
1005#95C2414yes—
1006#95C2412yes—
1007#95C2412yes—
1008#95C2414yes—
1009#95C2414yes—
1010#95C2412yes—
1011#95C2412yes—
1012#95C2412yes—
1013#95C2414yes—
1014#95C2414yes—
1015#95C2412yes—
1016#95C2412yes—
1017#95C2412yes—
1018#95C2412yes—
1019#95C2414yes—
1020#95C2412yes—
1021#95C2412yes—
1022#95C2414yes—
1023#95C2414yes—
1024#95C2412yes—
1025#95C2412yes—
1026#95C2414yes—
1027#95C2414yes—
1028#95C2412yes—
1029#95C2414yes—
1030#95C2414yes—
1031#95C2412yes—
1032#95C2414yes—
1033#95C2414yes—
1034#95C2414yes—
1035#95C2414yes—
1036#95C2414yes—
1037#95C2414yes—
1038#95C2414yes—
1039#95C2414yes—
1040#95C2414yes—
1041#95C2414yes—
1042#95C2414yes—
1043#95C2414yes—
1044#95C2414yes—
1045#95C2414yes—
1046#95C2414yes—
1047C24C2511yescharacteristic
1048C24C2512yes—
1049C24C2512yes—
1050C24C2512yes—
1051#41—416no—
1052#41—816no—
1053C2×Q8—22no—
1054C2×Q8—22no—
1055C2×Q8—22no—
1056C2×Q8—24no—
1057C2×Q8—24no—
1058C2×Q8—24no—
1059C2×Q8—22no—
1060C2×Q8—24no—
1061C2×Q8—22no—
1062C2×Q8—22no—
1063C2×Q8—22no—
1064C2×Q8—42no—
1065C2×Q8—42no—
1066C2×Q8—44no—
1067C2×Q8—42no—
1068C2×Q8—44no—
1069C2×Q8—44no—
1070C2×Q8—42no—
1071C2×Q8—44no—
1072C2×Q8—42no—
1073C2×Q8—44no—
1074C2×Q8—44no—
1075C2×Q8—44no—
1076C2×Q8—44no—
1077C2×Q8—816no—
1078C2×D4—24no—
1079C2×D4—24no—
1080C2×D4—28no—
1081C2×D4—28no—
1082C2×D4—22no—
1083C2×D4—22no—
1084C2×D4—22no—
1085C2×D4—22no—
1086C2×D4—22no—
1087C2×D4—22no—
1088C2×D4—22no—
1089C2×D4—42no—
1090C2×D4—42no—
1091C2×D4—42no—
1092C2×D4—42no—
1093C2×D4—42no—
1094C2×D4—44no—
1095C2×D4—44no—
1096C2×D4—44no—
1097C2×D4—44no—
1098C2×D4—42no—
1099C2×D4—44no—
1100C2×D4—44no—
1101C2×D4—44no—
1102C2×D4—44no—
1103C22×C4—28no—
1104C22×C4—24no—
1105C22×C4—22no—
1106C22×C4—24no—
1107C22×C4—24no—
1108C22×C4—22no—
1109C22×C4—24no—
1110C22×C4—22no—
1111C22×C4—24no—
1112C22×C4—24no—
1113C22×C4—42no—
1114C22×C4—42no—
1115C22×C4—42no—
1116C22×C4—42no—
1117C22×C4—42no—
1118C22×C4—44no—
1119C22×C4—44no—
1120C22×C4—42no—
1121C22×C4—44no—
1122C22×C4—42no—
1123C22×C4—42no—
1124C22×C4—44no—
1125C22×C4—44no—
1126C22×C4—44no—
1127C22×C4—44no—
1128C22×C4—42no—
1129C22×C4—42no—
1130C22×C4—44no—
1131C22×C4—44no—
1132C22×C4—44no—
1133C22×C4—44no—
1134C22×C4—44no—
1135C22×C4C2512yes—
1136C22×C4C2512yes—
1137C22×C4C2514yes—
1138C22×C4C2512yes—
1139C22×C4C2512yes—
1140C22×C4C2512yes—
1141C22×C4C2512yes—
1142C22×C4C2512yes—
1143C22×C4C2512yes—
1144C22×C4C2514yes—
1145C22×C4C2511yescharacteristic
1146C22×C4C2512yes—
1147C22×C4C2512yes—
1148C22×C4C2512yes—
1149C22×C4C2512yes—
1150C22×C4C2514yes—
1151C22×C4C2512yes—
1152C22×C4C2514yes—
1153C22×C4C2512yes—
1154C22×C4C2512yes—
1155C22×C4C2511yescharacteristic
1156C22×C4C2512yes—
1157C22×C4C2511yescharacteristic
1158C22×C4C2512yes—
1159C22×C4C2511yescharacteristic
1160C22×C4C2511yescharacteristic
1161C22×C4C2511yescharacteristic
1162C4⋊C4—22no—
1163C4⋊C4—22no—
1164C4⋊C4—22no—
1165C4⋊C4—22no—
1166C4⋊C4—24no—
1167C4⋊C4—24no—
1168C4⋊C4—24no—
1169C4⋊C4—22no—
1170C4⋊C4—22no—
1171C4⋊C4—22no—
1172C4⋊C4—24no—
1173C4⋊C4—22no—
1174C4⋊C4—24no—
1175C4⋊C4—24no—
1176C4⋊C4—24no—
1177C4⋊C4—24no—
1178C4⋊C4—24no—
1179C4⋊C4—42no—
1180C4⋊C4—42no—
1181C4⋊C4—44no—
1182C4⋊C4—44no—
1183C4⋊C4—42no—
1184C4⋊C4—42no—
1185C4⋊C4—44no—
1186C4⋊C4—42no—
1187C4⋊C4—42no—
1188C4⋊C4—42no—
1189C4⋊C4—42no—
1190C4⋊C4—44no—
1191C4⋊C4—44no—
1192C4⋊C4—44no—
1193C4⋊C4—42no—
1194C4⋊C4—42no—
1195C4⋊C4—42no—
1196C4⋊C4—44no—
1197C4⋊C4—44no—
1198C4⋊C4—44no—
1199C4⋊C4—42no—
1200C4⋊C4—44no—
1201C4⋊C4—42no—
1202C4⋊C4—44no—
1203C4⋊C4—42no—
1204C4⋊C4—44no—
1205C4⋊C4—42no—
1206C4⋊C4—44no—
1207C4⋊C4—42no—
1208C4⋊C4—42no—
1209C4⋊C4—44no—
1210C4⋊C4—44no—
1211C4⋊C4—42no—
1212C4⋊C4—44no—
1213C4⋊C4—44no—
1214C4⋊C4—44no—
1215C22⋊C4—24no—
1216C22⋊C4—28no—
1217C22⋊C4—24no—
1218C22⋊C4—24no—
1219C22⋊C4—24no—
1220C22⋊C4—22no—
1221C22⋊C4—22no—
1222C22⋊C4—24no—
1223C22⋊C4—24no—
1224C22⋊C4—24no—
1225C22⋊C4—42no—
1226C22⋊C4—44no—
1227C22⋊C4—44no—
1228C22⋊C4—44no—
1229C22⋊C4—44no—
1230C22⋊C4—44no—
1231C22⋊C4—44no—
1232C22⋊C4—42no—
1233C22⋊C4—42no—
1234C22⋊C4—42no—
1235C22⋊C4—42no—
1236C22⋊C4—42no—
1237C22⋊C4—42no—
1238C22⋊C4—42no—
1239C22⋊C4—44no—
1240C22⋊C4—44no—
1241C22⋊C4—42no—
1242C22⋊C4—44no—
1243C22⋊C4—44no—
1244C22⋊C4—44no—
1245C22⋊C4—44no—
1246C22⋊C4—44no—
1247C22⋊C4—42no—
1248C22⋊C4—44no—
1249C22⋊C4—44no—
1250C22⋊C4—42no—
1251C22⋊C4—42no—
1252C22⋊C4—44no—
1253C22⋊C4—42no—
1254C22⋊C4—42no—
1255C22⋊C4—42no—
1256C22⋊C4—44no—
1257C22⋊C4—44no—
1258C22⋊C4—44no—
1259C22⋊C4—44no—
1260C22⋊C4—44no—
1261C22⋊C4—44no—
1262C22⋊C4—44no—
1263C22⋊C4—44no—
1264C42—22no—
1265C42—24no—
1266C42—24no—
1267C42—24no—
1268C42—22no—
1269C42—24no—
1270C42—24no—
1271C42—22no—
1272C42—22no—
1273C42—22no—
1274C42—42no—
1275C42—42no—
1276C42—42no—
1277C42—44no—
1278C42—44no—
1279C42—42no—
1280C42—42no—
1281C42—44no—
1282C42—44no—
1283C42—44no—
1284C42—44no—
1285C42—44no—
1286C42H(5,𝔽2)14yes—
1287C23—22no—
1288C23—22no—
1289C23—22no—
1290C23—22no—
1291C23—22no—
1292C23—22no—
1293C23—21no—
1294C23—22no—
1295C23—22no—
1296C23—22no—
1297C23—21no—
1298C23—22no—
1299C23—22no—
1300C23—24no—
1301C23—21no—
1302C23—24no—
1303C23—22no—
1304C23—22no—
1305C23—24no—
1306C23—22no—
1307C23—24no—
1308C23#58514yes—
1309C23C2611yescharacteristic
1310Q8—44no—
1311Q8—48no—
1312Q8—44no—
1313Q8—44no—
1314Q8—84no—
1315Q8—84no—
1316Q8—88no—
1317Q8—162no—
1318Q8—164no—
1319D4—28no—
1320D4—48no—
1321D4—48no—
1322D4—44no—
1323D4—44no—
1324D4—88no—
1325D4—88no—
1326D4—162no—
1327D4—164no—
1328C2×C4—22no—
1329C2×C4—22no—
1330C2×C4—21no—
1331C2×C4—22no—
1332C2×C4—22no—
1333C2×C4—22no—
1334C2×C4—21no—
1335C2×C4—22no—
1336C2×C4—22no—
1337C2×C4—22no—
1338C2×C4—22no—
1339C2×C4—24no—
1340C2×C4—22no—
1341C2×C4—22no—
1342C2×C4—21no—
1343C2×C4—24no—
1344C2×C4—22no—
1345C2×C4—22no—
1346C2×C4—22no—
1347C2×C4—22no—
1348C2×C4—22no—
1349C2×C4—22no—
1350C2×C4—22no—
1351C2×C4—22no—
1352C2×C4—22no—
1353C2×C4—22no—
1354C2×C4—24no—
1355C2×C4—22no—
1356C2×C4—22no—
1357C2×C4—24no—
1358C2×C4—22no—
1359C2×C4—24no—
1360C2×C4—24no—
1361C2×C4—22no—
1362C2×C4—24no—
1363C2×C4—24no—
1364C2×C4—24no—
1365C2×C4—22no—
1366C2×C4—22no—
1367C2×C4—22no—
1368C2×C4—22no—
1369C2×C4—22no—
1370C2×C4—24no—
1371C2×C4—24no—
1372C2×C4—22no—
1373C2×C4—21no—
1374C2×C4—22no—
1375C2×C4—22no—
1376C2×C4—22no—
1377C2×C4—22no—
1378C2×C4—21no—
1379C2×C4—24no—
1380C2×C4—22no—
1381C2×C4—22no—
1382C2×C4—22no—
1383C2×C4—24no—
1384C2×C4—22no—
1385C2×C4—24no—
1386C2×C4—24no—
1387C2×C4—24no—
1388C2×C4—22no—
1389C2×C4—22no—
1390C2×C4—22no—
1391C2×C4—22no—
1392C2×C4—22no—
1393C2×C4—22no—
1394C2×C4—22no—
1395C2×C4—22no—
1396C2×C4—48no—
1397C2×C4—48no—
1398C2×C4—44no—
1399C2×C4—84no—
1400C2×C4—84no—
1401C2×C4—84no—
1402C2×C4—88no—
1403C2×C4—84no—
1404C2×C4—88no—
1405C2×C4—162no—
1406C2×C4—164no—
1407C2×C4—162no—
1408C2×C4C2×H(5,𝔽2)12yes—
1409C2×C4C2×H(5,𝔽2)12yes—
1410C2×C4C2×H(5,𝔽2)12yes—
1411C2×C4#58512yes—
1412C2×C4#58512yes—
1413C22—24no—
1414C22—24no—
1415C22—24no—
1416C22—42no—
1417C22—42no—
1418C22—42no—
1419C22—42no—
1420C22—42no—
1421C22—41no—
1422C22—42no—
1423C22—42no—
1424C22—41no—
1425C22—42no—
1426C22—42no—
1427C22—41no—
1428C22—42no—
1429C22—42no—
1430C22—44no—
1431C22—44no—
1432C22—44no—
1433C22—44no—
1434C22—42no—
1435C22C22×H(5,𝔽2)11yescharacteristic
1436C22C2×#58511yescharacteristic
1437C22C2×#58511yescharacteristic
1438C22C2×#58512yes—
1439C222−1+612yes—
1440C4—22no—
1441C4—22no—
1442C4—41no—
1443C4—42no—
1444C4—42no—
1445C4—42no—
1446C4—44no—
1447C4—42no—
1448C4—44no—
1449C4—42no—
1450C4—41no—
1451C4—42no—
1452C4—42no—
1453C4—42no—
1454C4—42no—
1455C4—41no—
1456C4—42no—
1457C4—42no—
1458C4—42no—
1459C4—42no—
1460C4—42no—
1461C4—42no—
1462C4—44no—
1463C4—42no—
1464C4—44no—
1465C4—42no—
1466C4#354014yes—
1467C2—44no—
1468C2—82no—
1469C2—81no—
1470C2—82no—
1471C2C2×#354011yescharacteristic
1472C2#6282411yescharacteristic
1473C2#6288711yescharacteristic
1474C2#6290712yes—
1475C2#6296412yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59253C2semidirect
2. #57415C2semidirect
3. #56949C2semidirect
4. #56470C2semidirect
5. #54640C2semidirect
6. #53144C2semidirect
7. #48925C2semidirect
8. #48683C2semidirect
9. #45708C2semidirect
10. #45431C2semidirect
11. #45428C2semidirect
12. #45336C2semidirect
13. #45271C2semidirect
14. #45168C2semidirect
15. #42872C2semidirect
16. #42788C2semidirect
17. #42747C2semidirect
18. #42647C2semidirect
19. #41457C2semidirect
20. #40646C2semidirect
21. #39905C2semidirect
22. #39758C2semidirect
23. #39173C2semidirect
24. #38983C2semidirect
25. #37396C2semidirect
26. #36303C2semidirect
27. #36195C2semidirect
28. #35712C2semidirect
29. #35693C2semidirect
30. #35623C2semidirect
31. #34596C2semidirect

Maximal subgroups

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

subgroupindex
#592532
#574152
#569492
#564702
#546402
#531442
#489252
#486832
#457082
#454312
#454282
#453362
#452712
#451682
#428722
#427882
#427472
#426472
#414572
#406462
#399052
#397582
#391732
#389832
#373962
#363032
#361952
#357122
#356932
#356232
#345962