Finite Group Databasebeta

← #8402656

Subgroups — #8402656

Order 512.

4435 conjugacy classes of subgroups.

The subgroup lattice has 1465 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59644C212yesmaximal, complemented
2#59239C212yesmaximal, complemented
3#54910C214yesmaximal, complemented
4#54417C214yesmaximal, complemented
5#50482C214yesmaximal, complemented
6#49335C214yesmaximal, complemented
7#48610C214yesmaximal, complemented
8#47892C214yesmaximal, complemented
9#46004C212yesmaximal, complemented
10#45669C212yesmaximal, complemented
11#45431C211yesmaximal, characteristic, complemented
12#45337C211yesmaximal, characteristic, complemented
13#45336C211yesmaximal, characteristic, complemented
14#45151C211yesmaximal, characteristic, complemented
15#44233C214yesmaximal, complemented
16#43652C214yesmaximal, complemented
17#42788C211yesmaximal, characteristic
18#42427C211yesmaximal, characteristic, complemented
19#40098C212yesmaximal, complemented
20#39660C212yesmaximal, complemented
21#39159C212yesmaximal, complemented
22#38983C212yesmaximal, complemented
23#37396C211yesmaximal, characteristic, complemented
24#36608C211yesmaximal, characteristic, complemented
25#36446C211yesmaximal, characteristic, complemented
26#36276C211yesmaximal, characteristic, complemented
27#36195C211yesmaximal, characteristic, complemented
28#35749C211yesmaximal, characteristic, complemented
29#35738C211yesmaximal, characteristic, complemented
30#35669C211yesmaximal, characteristic, complemented
31#34968C211yesmaximal, characteristic, complemented
32C2×#557C2211yescharacteristic
33C2×#554C2211yescharacteristic
34C2×D4×Q8C2211yescharacteristic
35C2×D4×Q8C2211yescharacteristic
36C2×#542C2211yescharacteristic
37C2×#519C2211yescharacteristic
38#2862C2211yescharacteristic
39#2862C2212yes—
40#2862C2211yescharacteristic
41#2862C2212yes—
42#2857C2212yes—
43#2850C2212yes—
44#2844C2214yes—
45#2838C2214yes—
46#2821C2212yes—
47#2817C2212yes—
48#2811C2214yes—
49#2804C2214yes—
50#2799C2214yes—
51#2788C2214yes—
52#2784C2214yes—
53#2781C2214yes—
54#2778C2214yes—
55#2775C2214yes—
56#2775C2214yes—
57#2775C2214yes—
58#2774C2214yes—
59#2763C2214yes—
60#2763C2214yes—
61#2763C2214yes—
62#2763C2214yes—
63#2763C2214yes—
64#2762C2214yes—
65#2762C2214yes—
66#2762C2214yes—
67#2759C2214yes—
68#2759C2214yes—
69#2759C2214yes—
70#2759C2214yes—
71#2758C2214yes—
72#2758C2214yes—
73#2758C2214yes—
74#2757C2214yes—
75#2755C2214yes—
76#2754C2214yes—
77#2754C2214yes—
78#2745C2214yes—
79#2745C2214yes—
80#2745C2214yes—
81#2744C2214yes—
82#2742C2214yes—
83#2737C2214yes—
84#2729C2214yes—
85#2728C2214yes—
86#2715C2214yes—
87#2713C2214yes—
88#2712C2214yes—
89#2696C2214yes—
90#2693C2214yes—
91#2692C2214yes—
92#2690C2214yes—
93#2690C2214yes—
94#2689C2214yes—
95#2674C2214yes—
96#2666C2214yes—
97#2665C2214yes—
98#2663C2212yes—
99#2645C2214yes—
100#2643C2214yes—
101#2640C2212yes—
102#2634C2212yes—
103#2634C2212yes—
104#2631C2212yes—
105#2628C2211yescharacteristic
106#2621C2211yescharacteristic
107#2614C2212yes—
108#2611C2212yes—
109#2611C2212yes—
110#2605C2214yes—
111#2605C2214yes—
112#2603C2212yes—
113#2602C2214yes—
114#2599C2212yes—
115#2598C2212yes—
116#2595C2214yes—
117#2593C2214yes—
118#2592C2212yes—
119#2589C2214yes—
120#2581C2214yes—
121#2581C2211yescharacteristic
122#2581C2211yescharacteristic
123#2576C2214yes—
124#2574C2214yes—
125#2574C2214yes—
126#2572C2214yes—
127#2568C2212yes—
128#2568C2211yescharacteristic
129#2568C2212yes—
130#2568C2211yescharacteristic
131#2568C2212yes—
132#2567C2211yescharacteristic
133#2567C2211yescharacteristic
134#2551C2212yes—
135#2550C2214yes—
136#2549C2214yes—
137#2549C2214yes—
138#2547C2211yescharacteristic
139#2547C2212yes—
140#2546C2211yescharacteristic
141#2545C2211yescharacteristic
142#2545C2211yescharacteristic
143#2545C2212yes—
144#2540C2212yes—
145#2536C2211yescharacteristic
146#2535C2211yescharacteristic
147#2532C2214yes—
148#2532C2214yes—
149#2529C2214yes—
150#2528C2214yes—
151#2525C2212yes—
152#2521C2212yes—
153#2520C2212yes—
154#2515C2212yes—
155#2514C2212yes—
156#2514C2212yes—
157#2514C2214yes—
158#2514C2214yes—
159#2514C2212yes—
160#2514C2212yes—
161#2511C2212yes—
162#2510C2214yes—
163#2510C2214yes—
164#2502C2212yes—
165#2500C2211yescharacteristic
166#2499C2211yescharacteristic
167#2495C2214yes—
168#2493C2214yes—
169#2492C2212yes—
170#2492C2212yes—
171#2492C2212yes—
172#2492C2212yes—
173#2492C2212yes—
174#2492C2214yes—
175#2491C2212yes—
176#2489C2214yes—
177#2489C2214yes—
178#2489C2214yes—
179#2488C2214yes—
180#2477C2214yes—
181#2475C2214yes—
182#2474C2214yes—
183#2470C2214yes—
184#2469C2214yes—
185#2468C2212yes—
186#2465C2214yes—
187#2465C2214yes—
188#2465C2214yes—
189#2465C2214yes—
190#2465C2212yes—
191#2463C2214yes—
192#2462C2214yes—
193#2461C2212yes—
194#2460C2214yes—
195#2459C2214yes—
196#2458C2212yes—
197#2458C2214yes—
198#2451C2212yes—
199#2451C2214yes—
200#2450C2214yes—
201#2447C2212yes—
202#2446C2212yes—
203#2440C2212yes—
204#2436C2212yes—
205#2436C2211yescharacteristic
206#2434C2212yes—
207#2434C2211yescharacteristic
208#2434C2212yes—
209#2434C2212yes—
210#2434C2212yes—
211#2429C2212yes—
212#2427C2212yes—
213#2422C2212yes—
214#2421C2212yes—
215#2421C2212yes—
216#2421C2212yes—
217#2409C2214yes—
218#2409C2212yes—
219#2409C2212yes—
220#2399C2211yescharacteristic
221#2399C2212yes—
222#2398C2211yescharacteristic
223#2398C2212yes—
224#2396C2211yescharacteristic
225#2392C2211yescharacteristic
226#2379C2214yes—
227#2376C2214yes—
228#2372C2214yes—
229#2368C2214yes—
230#2367C2214yes—
231#2365C2212yes—
232#2362C2212yes—
233#2361C2212yes—
234#2360C2212yes—
235#2357C2211yescharacteristic
236#2356C2211yescharacteristic
237#2356C2214yes—
238#2356C2211yescharacteristic
239#2356C2211yescharacteristic
240#2355C2212yes—
241#2355C2212yes—
242#2352C2212yes—
243#2349C2214yes—
244Q8×C22⋊C4C2214yes—
245Q8×C22⋊C4C2212yes—
246#2337C2214yes—
247#2334C2214yes—
248#2331C2211yescharacteristic
249#2331C2214yes—
250#2327C2211yescharacteristic
251#2327C2211yescharacteristic
252#2326C2211yescharacteristic
253#2318C2214yes—
254C4×C4⋊Q8C2211yescharacteristic
255C4×C4⋊Q8C2212yes—
256C4×#126C2212yes—
257C4×#124C2211yescharacteristic
258C4×#124C2212yes—
259C4×#124C2212yes—
260C4×C22⋊Q8C2212yes—
261C4×#123C2212yes—
262#2298C2211yescharacteristic
263C2×#391C2212yes—
264#2283C2212yes—
265C42×Q8C2211yescharacteristic
266C42×D4C2211yescharacteristic
267C23×Q8C2312yes—
268C23×Q8C2312yes—
269C23×Q8C2311yescharacteristic
270#557—44no—
271#554—44no—
272D4×Q8—44no—
273D4×Q8—44no—
274#542—44no—
275C2×C4⋊Q8C2311yescharacteristic
276C2×C4⋊Q8C2311yescharacteristic
277C2×C4⋊Q8C2311yescharacteristic
278C2×C4⋊Q8C2312yes—
279C2×C4⋊Q8C2312yes—
280C2×C4⋊Q8C2311yescharacteristic
281C2×C4⋊Q8C2311yescharacteristic
282C2×C4⋊Q8C2312yes—
283C2×C4⋊Q8C2312yes—
284C2×C4⋊Q8C2314yes—
285C2×C4⋊Q8C2312yes—
286C2×#126C2312yes—
287C2×#126C2312yes—
288C2×#125C2312yes—
289C2×#125C2312yes—
290C2×#125C2314yes—
291C2×#124C2314yes—
292C2×#124C2312yes—
293C2×#124C2311yescharacteristic
294C2×#124C2312yes—
295C2×#124C2311yescharacteristic
296C2×#124C2312yes—
297C2×#124C2311yescharacteristic
298C2×#123C2314yes—
299C2×#123C2312yes—
300C2×#123C2312yes—
301C2×C22⋊Q8C2312yes—
302C2×C22⋊Q8C2312yes—
303C2×C22⋊Q8C2312yes—
304C2×C22⋊Q8C2312yes—
305C2×C22⋊Q8C2312yes—
306C2×C22⋊Q8C2312yes—
307C2×C22⋊Q8C2314yes—
308C2×C22⋊Q8C2311yescharacteristic
309C2×C22⋊Q8C2314yes—
310C2×C22⋊Q8C2314yes—
311C2×C22⋊Q8C2314yes—
312C2×C22⋊Q8C2312yes—
313C2×#121C2312yes—
314C2×#121C2311yescharacteristic
315#519—44no—
316C2×C4×Q8C2311yescharacteristic
317C2×C4×Q8C2311yescharacteristic
318C2×C4×Q8C2311yescharacteristic
319C2×C4×Q8C2311yescharacteristic
320C2×C4×Q8C2314yes—
321C2×C4×Q8C2311yescharacteristic
322C2×C4×Q8C2312yes—
323C2×C4×Q8C2312yes—
324C2×C4×Q8C2311yescharacteristic
325C2×C4×Q8C2312yes—
326C2×C4×Q8C2312yes—
327C2×C4×Q8C2312yes—
328C2×C4×Q8C2312yes—
329C2×C4×Q8C2312yes—
330C2×C4×D4C2311yescharacteristic
331C2×C4×D4C2312yes—
332C2×C4×D4C2311yescharacteristic
333C2×C4×D4C2314yes—
334C2×C4×D4C2312yes—
335C2×C4×D4C2312yes—
336C2×C4×D4C2312yes—
337C2×C4×D4C2312yes—
338C2×#117C2311yescharacteristic
339C2×#117C2312yes—
340C2×#117C2312yes—
341C2×#117C2311yescharacteristic
342C22×C4⋊C4C2312yes—
343C22×C42C2312yes—
344#401C2314yes—
345#401C2314yes—
346#401C2314yes—
347#401C2314yes—
348#400C2311yescharacteristic
349#400C2312yes—
350#400C2314yes—
351#400C2314yes—
352#400C2314yes—
353#400C2314yes—
354#400C2312yes—
355#400C2314yes—
356#400C2312yes—
357#400C2314yes—
358#400C2314yes—
359#400C2314yes—
360#400C2314yes—
361#400C2314yes—
362#400C2314yes—
363#400C2312yes—
364#400C2314yes—
365#400C2314yes—
366#400C2314yes—
367#400C2314yes—
368#400C2314yes—
369#400C2314yes—
370#400C2314yes—
371#400C2312yes—
372#400C2314yes—
373#400C2314yes—
374#400C2314yes—
375#400C2312yes—
376#400C2314yes—
377#399C2314yes—
378#399C2312yes—
379#399C2311yescharacteristic
380#398C2311yescharacteristic
381#398C2312yes—
382#398C2312yes—
383#398C2314yes—
384#398C2314yes—
385#398C2314yes—
386#398C2312yes—
387#398C2312yes—
388#398C2312yes—
389#398C2312yes—
390#398C2314yes—
391#398C2312yes—
392#398C2312yes—
393#398C2314yes—
394#398C2314yes—
395#397C2314yes—
396#397C2314yes—
397#397C2312yes—
398#397C2312yes—
399#397C2314yes—
400#397C2314yes—
401#397C2314yes—
402#397C2314yes—
403#397C2314yes—
404#397C2312yes—
405#397C2312yes—
406#397C2311yescharacteristic
407#397C2312yes—
408#397C2312yes—
409#397C2314yes—
410#397C2314yes—
411#397C2314yes—
412#397C2314yes—
413#396C2314yes—
414#396C2314yes—
415#396C2314yes—
416#396C2314yes—
417#396C2312yes—
418#396C2312yes—
419#396C2314yes—
420#395C2312yes—
421#395C2312yes—
422#395C2314yes—
423#395C2314yes—
424#395C2312yes—
425#395C2314yes—
426#395C2312yes—
427#395C2314yes—
428#395C2312yes—
429#395C2312yes—
430#395C2314yes—
431#395C2314yes—
432#395C2314yes—
433#395C2314yes—
434#395C2314yes—
435#395C2314yes—
436#395C2314yes—
437#395C2311yescharacteristic
438#395C2314yes—
439#395C2312yes—
440#395C2314yes—
441#395C2314yes—
442#394C2314yes—
443#394C2314yes—
444#394C2314yes—
445#394C2312yes—
446#394C2311yescharacteristic
447#394C2312yes—
448#394C2312yes—
449#394C2314yes—
450#393C2314yes—
451#393C2314yes—
452#393C2314yes—
453#393C2314yes—
454#393C2314yes—
455#393C2314yes—
456#393C2311yescharacteristic
457#393C2312yes—
458#393C2314yes—
459#393C2314yes—
460#393C2314yes—
461#393C2312yes—
462#393C2314yes—
463#393C2314yes—
464#393C2314yes—
465#392C2311yescharacteristic
466#392C2314yes—
467#392C2312yes—
468#391C2311yescharacteristic
469#391C2314yes—
470#391C2311yescharacteristic
471#391C2312yes—
472#391C2311yescharacteristic
473#391C2311yescharacteristic
474#391C2311yescharacteristic
475#391C2312yes—
476#391C2312yes—
477#391C2314yes—
478#391C2312yes—
479#391C2314yes—
480#391C2314yes—
481#391C2312yes—
482#391C2314yes—
483#391C2314yes—
484#391C2312yes—
485#391C2314yes—
486#391C2312yes—
487#391C2312yes—
488#391C2314yes—
489#391C2314yes—
490#391C2314yes—
491#391C2312yes—
492#391C2312yes—
493#391C2311yescharacteristic
494#391C2314yes—
495#391C2314yes—
496#391C2314yes—
497#391C2312yes—
498#391C2314yes—
499#391C2312yes—
500#391C2314yes—
501#391C2314yes—
502#391C2314yes—
503#391C2314yes—
504#391C2314yes—
505#391C2314yes—
506#391C2314yes—
507#391C2312yes—
508#391C2314yes—
509#391C2314yes—
510#391C2312yes—
511#391C2314yes—
512#391C2314yes—
513#391C2312yes—
514#391C2314yes—
515#390C2311yescharacteristic
516#390C2312yes—
517#390C2314yes—
518#390C2314yes—
519#390C2312yes—
520#390C2311yescharacteristic
521#389C2314yes—
522#389C2312yes—
523#389C2312yes—
524#389C2314yes—
525#389C2314yes—
526#389C2314yes—
527#389C2314yes—
528#389C2312yes—
529#389C2314yes—
530#389C2312yes—
531#389C2314yes—
532#389C2314yes—
533#389C2314yes—
534#389C2314yes—
535#389C2312yes—
536#389C2314yes—
537#388C2312yes—
538#388C2312yes—
539#388C2312yes—
540#388C2314yes—
541#388C2314yes—
542#388C2314yes—
543#388C2314yes—
544#388C2314yes—
545#388C2314yes—
546#388C2314yes—
547#388C2314yes—
548#388C2314yes—
549#388C2314yes—
550#388C2314yes—
551#388C2314yes—
552#388C2314yes—
553#388C2314yes—
554#388C2314yes—
555#388C2312yes—
556#388C2314yes—
557#388C2314yes—
558#388C2314yes—
559#388C2314yes—
560#388C2314yes—
561#388C2314yes—
562#388C2312yes—
563#388C2314yes—
564#388C2314yes—
565#388C2314yes—
566#388C2312yes—
567#388C2312yes—
568#388C2314yes—
569#388C2314yes—
570#388C2314yes—
571#388C2314yes—
572#388C2312yes—
573#388C2312yes—
574#388C2314yes—
575#388C2312yes—
576#388C2312yes—
577#387C2312yes—
578#387C2312yes—
579#387C2312yes—
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#387C2312yes—
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#387C2312yes—
607#387C2314yes—
608#387C2314yes—
609#387C2314yes—
610#387C2314yes—
611#387C2314yes—
612#387C2314yes—
613#387C2314yes—
614#387C2312yes—
615#387C2312yes—
616#387C2312yes—
617#387C2312yes—
618#386C2314yes—
619#386C2314yes—
620#386C2314yes—
621#386C2314yes—
622#386C2314yes—
623#386C2314yes—
624#386C2314yes—
625#386C2314yes—
626#386C2314yes—
627#386C2314yes—
628#386C2314yes—
629#386C2312yes—
630#385C2312yes—
631#385C2314yes—
632#385C2314yes—
633#385C2314yes—
634#385C2314yes—
635#385C2314yes—
636#385C2314yes—
637#385C2314yes—
638#385C2314yes—
639#385C2314yes—
640#385C2314yes—
641#385C2314yes—
642#385C2314yes—
643#385C2314yes—
644#385C2314yes—
645#385C2314yes—
646#385C2312yes—
647#385C2314yes—
648#385C2314yes—
649#385C2312yes—
650#384C2311yescharacteristic
651#384C2311yescharacteristic
652#384C2312yes—
653#383C2312yes—
654#383C2312yes—
655#383C2312yes—
656#383C2314yes—
657#383C2314yes—
658#383C2314yes—
659#383C2312yes—
660#383C2314yes—
661#383C2314yes—
662#382C2311yescharacteristic
663#382C2312yes—
664#382C2314yes—
665#382C2314yes—
666#382C2311yescharacteristic
667#382C2314yes—
668#382C2311yescharacteristic
669#382C2311yescharacteristic
670#382C2312yes—
671#382C2314yes—
672#382C2314yes—
673#382C2314yes—
674#382C2312yes—
675#382C2314yes—
676#382C2314yes—
677#381C2312yes—
678#381C2314yes—
679#381C2314yes—
680#381C2312yes—
681#380C2314yes—
682#380C2314yes—
683#380C2314yes—
684#380C2312yes—
685#380C2314yes—
686#380C2314yes—
687#380C2314yes—
688#380C2314yes—
689#380C2312yes—
690#380C2312yes—
691#380C2312yes—
692C4×C4⋊C4C2311yescharacteristic
693C4×C4⋊C4C2312yes—
694C4×C4⋊C4C2312yes—
695C4×C4⋊C4C2314yes—
696C4×C4⋊C4C2312yes—
697C4×C4⋊C4C2314yes—
698C4×C4⋊C4C2312yes—
699C4×C4⋊C4C2311yescharacteristic
700C4×C4⋊C4C2312yes—
701C4×C4⋊C4C2312yes—
702C4×C4⋊C4C2311yescharacteristic
703C4×C4⋊C4C2312yes—
704C4×C4⋊C4C2311yescharacteristic
705C4×C4⋊C4C2314yes—
706C4×C4⋊C4C2314yes—
707C4×C4⋊C4C2314yes—
708C4×C4⋊C4C2314yes—
709C4×C4⋊C4C2312yes—
710C4×C4⋊C4C2312yes—
711C4×C4⋊C4C2312yes—
712C4×C4⋊C4C2312yes—
713C4×C4⋊C4C2312yes—
714C4×C22⋊C4C2312yes—
715C4×C22⋊C4C2312yes—
716C4×C22⋊C4C2312yes—
717C4×C22⋊C4C2312yes—
718C4×C22⋊C4C2314yes—
719C4×C22⋊C4C2314yes—
720C4×C22⋊C4C2312yes—
721C4×C22⋊C4C2314yes—
722C4×C22⋊C4C2314yes—
723C4×C22⋊C4C2314yes—
724C4×C22⋊C4C2314yes—
725C4×C22⋊C4C2312yes—
726C4×C22⋊C4C2312yes—
727C4×C22⋊C4C2314yes—
728C4×C22⋊C4C2312yes—
729C4×C22⋊C4C2311yescharacteristic
730C4×C22⋊C4C2311yescharacteristic
731#376C2311yescharacteristic
732#376C2314yes—
733#376C2312yes—
734#376C2312yes—
735#376C2312yes—
736C2×#95C2314yes—
737C2×#95C2314yes—
738C43C2312yes—
739C43C2311yescharacteristic
740C22×Q8—42no—
741C22×Q8—42no—
742C22×Q8—42no—
743C22×Q8—44no—
744C22×Q8—44no—
745C22×Q8—44no—
746C22×Q8—44no—
747C22×Q8—48no—
748C22×Q8C2411yescharacteristic
749C22×Q8C2411yescharacteristic
750C22×Q8C2411yescharacteristic
751C22×Q8C2412yes—
752C22×Q8C2411yescharacteristic
753C22×Q8C2412yes—
754C22×Q8C2414yes—
755C22×Q8C2412yes—
756C22×Q8C2414yes—
757C22×Q8C2412yes—
758C22×Q8C2412yes—
759C22×Q8C2414yes—
760C22×D4C2411yescharacteristic
761C22×D4C2411yescharacteristic
762C22×D4C2414yes—
763C22×D4C2412yes—
764C22×D4C2412yes—
765C23×C4C2412yes—
766C23×C4C2411yescharacteristic
767C23×C4C2414yes—
768C23×C4C2412yes—
769C23×C4C2412yes—
770C23×C4C2412yes—
771C23×C4C2414yes—
772C23×C4C2412yes—
773C23×C4C2414yes—
774C4⋊Q8—24no—
775C4⋊Q8—24no—
776C4⋊Q8—44no—
777C4⋊Q8—42no—
778C4⋊Q8—44no—
779C4⋊Q8—44no—
780C4⋊Q8—44no—
781C4⋊Q8—42no—
782C4⋊Q8—42no—
783C4⋊Q8—44no—
784C4⋊Q8—48no—
785#126—28no—
786#126—44no—
787#125—44no—
788#125—44no—
789#125—48no—
790#124—216no—
791#124—28no—
792#124—44no—
793#124—42no—
794#124—44no—
795#124—42no—
796#124—42no—
797#123—44no—
798#123—48no—
799#123—44no—
800C22⋊Q8—44no—
801C22⋊Q8—48no—
802C22⋊Q8—48no—
803C22⋊Q8—48no—
804C22⋊Q8—48no—
805C22⋊Q8—44no—
806C22⋊Q8—44no—
807C22⋊Q8—44no—
808C22⋊Q8—42no—
809C22⋊Q8—44no—
810C22⋊Q8—44no—
811C22⋊Q8—44no—
812#121—44no—
813#121—42no—
814C4×Q8—24no—
815C4×Q8—24no—
816C4×Q8—24no—
817C4×Q8—24no—
818C4×Q8—44no—
819C4×Q8—48no—
820C4×Q8—44no—
821C4×Q8—44no—
822C4×Q8—44no—
823C4×Q8—44no—
824C4×Q8—42no—
825C4×Q8—42no—
826C4×Q8—44no—
827C4×Q8—44no—
828C4×D4—28no—
829C4×D4—24no—
830C4×D4—24no—
831C4×D4—44no—
832C4×D4—44no—
833C4×D4—44no—
834C4×D4—44no—
835C4×D4—48no—
836#117—24no—
837#117—44no—
838#117—44no—
839#117—42no—
840C2×C4⋊C4—44no—
841C2×C4⋊C4C2411yescharacteristic
842C2×C4⋊C4C2412yes—
843C2×C4⋊C4C2411yescharacteristic
844C2×C4⋊C4C2412yes—
845C2×C4⋊C4C2411yescharacteristic
846C2×C4⋊C4C2412yes—
847C2×C4⋊C4C2411yescharacteristic
848C2×C4⋊C4C2414yes—
849C2×C4⋊C4C2412yes—
850C2×C4⋊C4C2411yescharacteristic
851C2×C4⋊C4C2411yescharacteristic
852C2×C4⋊C4C2412yes—
853C2×C4⋊C4C2412yes—
854C2×C4⋊C4C2411yescharacteristic
855C2×C4⋊C4C2412yes—
856C2×C4⋊C4C2412yes—
857C2×C4⋊C4C2411yescharacteristic
858C2×C4⋊C4C2412yes—
859C2×C4⋊C4C2412yes—
860C2×C4⋊C4C2412yes—
861C2×C4⋊C4C2414yes—
862C2×C4⋊C4C2412yes—
863C2×C4⋊C4C2412yes—
864C2×C4⋊C4C2412yes—
865C2×C4⋊C4C2412yes—
866C2×C4⋊C4C2412yes—
867C2×C4⋊C4C2414yes—
868C2×C4⋊C4C2412yes—
869C2×C4⋊C4C2412yes—
870C2×C4⋊C4C2412yes—
871C2×C4⋊C4C2414yes—
872C2×C4⋊C4C2414yes—
873C2×C4⋊C4C2412yes—
874C2×C4⋊C4C2412yes—
875C2×C4⋊C4C2412yes—
876C2×C4⋊C4C2414yes—
877C2×C4⋊C4C2414yes—
878C2×C4⋊C4C2412yes—
879C2×C4⋊C4C2412yes—
880C2×C4⋊C4C2414yes—
881C2×C4⋊C4C2412yes—
882C2×C4⋊C4C2414yes—
883C2×C4⋊C4C2414yes—
884C2×C4⋊C4C2414yes—
885C2×C4⋊C4C2412yes—
886C2×C4⋊C4C2414yes—
887C2×C4⋊C4C2414yes—
888C2×C4⋊C4C2414yes—
889C2×C4⋊C4C2412yes—
890C2×C4⋊C4C2412yes—
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×C22⋊C4C2411yescharacteristic
901C2×C22⋊C4C2411yescharacteristic
902C2×C22⋊C4C2412yes—
903C2×C22⋊C4C2412yes—
904C2×C22⋊C4C2412yes—
905C2×C22⋊C4C2412yes—
906C2×C22⋊C4C2412yes—
907C2×C22⋊C4C2412yes—
908C2×C22⋊C4C2414yes—
909C2×C22⋊C4C2414yes—
910C2×C22⋊C4C2412yes—
911C2×C22⋊C4C2412yes—
912C2×C22⋊C4C2414yes—
913C2×C22⋊C4C2412yes—
914C2×C22⋊C4C2412yes—
915C2×C22⋊C4C2412yes—
916C2×C22⋊C4C2412yes—
917C2×C22⋊C4C2414yes—
918C2×C22⋊C4C2414yes—
919C2×C22⋊C4C2414yes—
920C2×C22⋊C4C2412yes—
921C2×C22⋊C4C2414yes—
922C2×C22⋊C4C2412yes—
923C2×C22⋊C4C2412yes—
924C2×C22⋊C4C2414yes—
925C2×C22⋊C4C2412yes—
926C2×C22⋊C4C2412yes—
927C2×C22⋊C4C2414yes—
928C2×C22⋊C4C2414yes—
929C2×C22⋊C4C2412yes—
930C2×C22⋊C4C2414yes—
931C2×C22⋊C4C2412yes—
932C2×C22⋊C4C2412yes—
933C2×C22⋊C4C2414yes—
934C2×C22⋊C4C2414yes—
935C2×C22⋊C4C2414yes—
936C2×C22⋊C4C2414yes—
937C2×C22⋊C4C2414yes—
938C2×C22⋊C4C2414yes—
939C2×C22⋊C4C2412yes—
940C2×C42—44no—
941C2×C42C2412yes—
942C2×C42C2412yes—
943C2×C42C2411yescharacteristic
944C2×C42C2412yes—
945C2×C42C2412yes—
946C2×C42C2412yes—
947C2×C42C2412yes—
948C2×C42C2412yes—
949C2×C42C2411yescharacteristic
950C2×C42C2411yescharacteristic
951C2×C42C2412yes—
952C2×C42C2411yescharacteristic
953C2×C42C2412yes—
954C2×C42C2414yes—
955C2×C42C2412yes—
956C2×C42C2411yescharacteristic
957C2×C42C2412yes—
958C2×C42C2412yes—
959C2×C42C2412yes—
960C2×C42C2414yes—
961C2×C42C2414yes—
962C2×C42C2412yes—
963C2×C42C2412yes—
964C2×C42C2414yes—
965C2×C42C2414yes—
966C2×C42C2414yes—
967C2×C42C2414yes—
968C2×C42C2412yes—
969C2×C42C2412yes—
970C2×C42C2411yescharacteristic
971#95C2414yes—
972#95C2414yes—
973#95C2414yes—
974#95C2414yes—
975#95C2414yes—
976#95C2414yes—
977#95C2414yes—
978#95C2411yescharacteristic
979#95C2411yescharacteristic
980#95C2414yes—
981#95C2414yes—
982#95C2414yes—
983#95C2414yes—
984#95C2414yes—
985#95C2414yes—
986#95C2412yes—
987#95C2412yes—
988#95C2412yes—
989#95C2412yes—
990#95C2414yes—
991#95C2412yes—
992#95C2411yescharacteristic
993#95C2412yes—
994#95C2414yes—
995#95C2412yes—
996#95C2412yes—
997#95C2412yes—
998#95C2414yes—
999#95C2414yes—
1000#95C2414yes—
1001#95C2414yes—
1002#95C2412yes—
1003#95C2412yes—
1004#95C2414yes—
1005#95C2412yes—
1006#95C2414yes—
1007#95C2414yes—
1008#95C2414yes—
1009#95C2414yes—
1010#95C2414yes—
1011#95C2412yes—
1012#95C2412yes—
1013#95C2412yes—
1014#95C2412yes—
1015#95C2412yes—
1016#95C2412yes—
1017#95C2412yes—
1018#95C2411yescharacteristic
1019#95C2412yes—
1020#95C2414yes—
1021#95C2414yes—
1022#95C2414yes—
1023#95C2412yes—
1024#95C2414yes—
1025#95C2412yes—
1026#95C2414yes—
1027#95C2412yes—
1028#95C2414yes—
1029#95C2414yes—
1030#95C2412yes—
1031#95C2414yes—
1032#95C2412yes—
1033#95C2412yes—
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—
1047#95C2414yes—
1048#95C2414yes—
1049#95C2414yes—
1050#95C2414yes—
1051C24C2511yescharacteristic
1052C24C2512yes—
1053C24C2512yes—
1054C2×Q8—22no—
1055C2×Q8—22no—
1056C2×Q8—22no—
1057C2×Q8—22no—
1058C2×Q8—24no—
1059C2×Q8—24no—
1060C2×Q8—28no—
1061C2×Q8—24no—
1062C2×Q8—24no—
1063C2×Q8—24no—
1064C2×Q8—22no—
1065C2×Q8—22no—
1066C2×Q8—24no—
1067C2×Q8—22no—
1068C2×Q8—22no—
1069C2×Q8—22no—
1070C2×Q8—22no—
1071C2×Q8—28no—
1072C2×Q8—42no—
1073C2×Q8—42no—
1074C2×Q8—42no—
1075C2×Q8—44no—
1076C2×Q8—42no—
1077C2×Q8—44no—
1078C2×Q8—44no—
1079C2×Q8—42no—
1080C2×Q8—44no—
1081C2×Q8—44no—
1082C2×Q8—44no—
1083C2×Q8—44no—
1084C2×Q8—44no—
1085C2×Q8—42no—
1086C2×Q8—44no—
1087C2×Q8—416no—
1088C2×Q8—816no—
1089C2×Q8—816no—
1090C2×D4—24no—
1091C2×D4—28no—
1092C2×D4—24no—
1093C2×D4—22no—
1094C2×D4—22no—
1095C2×D4—22no—
1096C2×D4—22no—
1097C2×D4—42no—
1098C2×D4—44no—
1099C2×D4—44no—
1100C2×D4—42no—
1101C2×D4—42no—
1102C2×D4—44no—
1103C22×C4—24no—
1104C22×C4—24no—
1105C22×C4—22no—
1106C22×C4—24no—
1107C22×C4—22no—
1108C22×C4—24no—
1109C22×C4—22no—
1110C22×C4—24no—
1111C22×C4—24no—
1112C22×C4—28no—
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—42no—
1122C22×C4—44no—
1123C22×C4—44no—
1124C22×C4—44no—
1125C22×C4—44no—
1126C22×C4—44no—
1127C22×C4—44no—
1128C22×C4—44no—
1129C22×C4C2512yes—
1130C22×C4C2512yes—
1131C22×C4C2514yes—
1132C22×C4C2512yes—
1133C22×C4C2514yes—
1134C22×C4C2512yes—
1135C22×C4C2512yes—
1136C22×C4C2512yes—
1137C22×C4C2512yes—
1138C22×C4C2511yescharacteristic
1139C22×C4C2512yes—
1140C22×C4C2512yes—
1141C22×C4C2512yes—
1142C22×C4C2514yes—
1143C22×C4C2512yes—
1144C22×C4C2512yes—
1145C22×C4C2511yescharacteristic
1146C22×C4C2514yes—
1147C22×C4C2512yes—
1148C22×C4C2512yes—
1149C22×C4C2511yescharacteristic
1150C22×C4C2512yes—
1151C22×C4C2511yescharacteristic
1152C22×C4C2511yescharacteristic
1153C22×C4C2512yes—
1154C22×C4C2512yes—
1155C22×C4C2512yes—
1156C22×C4C2511yescharacteristic
1157C4⋊C4—22no—
1158C4⋊C4—24no—
1159C4⋊C4—22no—
1160C4⋊C4—22no—
1161C4⋊C4—22no—
1162C4⋊C4—24no—
1163C4⋊C4—24no—
1164C4⋊C4—22no—
1165C4⋊C4—22no—
1166C4⋊C4—24no—
1167C4⋊C4—24no—
1168C4⋊C4—22no—
1169C4⋊C4—24no—
1170C4⋊C4—24no—
1171C4⋊C4—22no—
1172C4⋊C4—24no—
1173C4⋊C4—24no—
1174C4⋊C4—24no—
1175C4⋊C4—24no—
1176C4⋊C4—24no—
1177C4⋊C4—28no—
1178C4⋊C4—24no—
1179C4⋊C4—24no—
1180C4⋊C4—28no—
1181C4⋊C4—24no—
1182C4⋊C4—24no—
1183C4⋊C4—44no—
1184C4⋊C4—42no—
1185C4⋊C4—42no—
1186C4⋊C4—42no—
1187C4⋊C4—44no—
1188C4⋊C4—42no—
1189C4⋊C4—42no—
1190C4⋊C4—42no—
1191C4⋊C4—44no—
1192C4⋊C4—42no—
1193C4⋊C4—42no—
1194C4⋊C4—44no—
1195C4⋊C4—44no—
1196C4⋊C4—42no—
1197C4⋊C4—44no—
1198C4⋊C4—44no—
1199C4⋊C4—44no—
1200C4⋊C4—44no—
1201C4⋊C4—44no—
1202C4⋊C4—42no—
1203C4⋊C4—44no—
1204C4⋊C4—44no—
1205C4⋊C4—42no—
1206C4⋊C4—44no—
1207C4⋊C4—42no—
1208C4⋊C4—44no—
1209C4⋊C4—44no—
1210C4⋊C4—44no—
1211C4⋊C4—44no—
1212C4⋊C4—44no—
1213C4⋊C4—44no—
1214C4⋊C4—44no—
1215C4⋊C4—44no—
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—28no—
1226C22⋊C4—24no—
1227C22⋊C4—24no—
1228C22⋊C4—28no—
1229C22⋊C4—24no—
1230C22⋊C4—24no—
1231C22⋊C4—24no—
1232C22⋊C4—42no—
1233C22⋊C4—42no—
1234C22⋊C4—42no—
1235C22⋊C4—44no—
1236C22⋊C4—44no—
1237C22⋊C4—44no—
1238C22⋊C4—44no—
1239C22⋊C4—44no—
1240C22⋊C4—42no—
1241C22⋊C4—44no—
1242C22⋊C4—44no—
1243C22⋊C4—42no—
1244C22⋊C4—44no—
1245C22⋊C4—42no—
1246C22⋊C4—42no—
1247C22⋊C4—44no—
1248C22⋊C4—44no—
1249C22⋊C4—42no—
1250C22⋊C4—42no—
1251C22⋊C4—44no—
1252C22⋊C4—44no—
1253C22⋊C4—44no—
1254C22⋊C4—44no—
1255C22⋊C42−1+418yes—
1256C42—22no—
1257C42—24no—
1258C42—24no—
1259C42—24no—
1260C42—24no—
1261C42—24no—
1262C42—24no—
1263C42—28no—
1264C42—24no—
1265C42—22no—
1266C42—24no—
1267C42—24no—
1268C42—24no—
1269C42—22no—
1270C42—22no—
1271C42—22no—
1272C42—42no—
1273C42—42no—
1274C42—42no—
1275C42—42no—
1276C42—42no—
1277C42—44no—
1278C42—42no—
1279C42—42no—
1280C42—44no—
1281C42—44no—
1282C42—44no—
1283C42—44no—
1284C42—44no—
1285C42H(5,𝔽2)14yes—
1286C23—22no—
1287C23—22no—
1288C23—22no—
1289C23—22no—
1290C23—22no—
1291C23—22no—
1292C23—21no—
1293C23—22no—
1294C23—22no—
1295C23—24no—
1296C23—22no—
1297C23—22no—
1298C23—21no—
1299C23—22no—
1300C23—21no—
1301C23—24no—
1302C23C2×2−1+414yes—
1303C23C2611yescharacteristic
1304Q8—28no—
1305Q8—48no—
1306Q8—44no—
1307Q8—44no—
1308Q8—48no—
1309Q8—44no—
1310Q8—84no—
1311Q8—88no—
1312Q8—84no—
1313Q8—88no—
1314Q8—88no—
1315Q8—162no—
1316D4—28no—
1317D4—44no—
1318D4—84no—
1319D4—88no—
1320D4—162no—
1321C2×C4—22no—
1322C2×C4—22no—
1323C2×C4—22no—
1324C2×C4—22no—
1325C2×C4—22no—
1326C2×C4—22no—
1327C2×C4—22no—
1328C2×C4—22no—
1329C2×C4—22no—
1330C2×C4—21no—
1331C2×C4—21no—
1332C2×C4—22no—
1333C2×C4—22no—
1334C2×C4—22no—
1335C2×C4—22no—
1336C2×C4—22no—
1337C2×C4—22no—
1338C2×C4—21no—
1339C2×C4—24no—
1340C2×C4—22no—
1341C2×C4—22no—
1342C2×C4—24no—
1343C2×C4—24no—
1344C2×C4—22no—
1345C2×C4—22no—
1346C2×C4—22no—
1347C2×C4—22no—
1348C2×C4—22no—
1349C2×C4—24no—
1350C2×C4—22no—
1351C2×C4—24no—
1352C2×C4—22no—
1353C2×C4—22no—
1354C2×C4—22no—
1355C2×C4—22no—
1356C2×C4—22no—
1357C2×C4—22no—
1358C2×C4—22no—
1359C2×C4—22no—
1360C2×C4—22no—
1361C2×C4—22no—
1362C2×C4—22no—
1363C2×C4—24no—
1364C2×C4—24no—
1365C2×C4—22no—
1366C2×C4—24no—
1367C2×C4—22no—
1368C2×C4—24no—
1369C2×C4—22no—
1370C2×C4—24no—
1371C2×C4—24no—
1372C2×C4—24no—
1373C2×C4—24no—
1374C2×C4—22no—
1375C2×C4—22no—
1376C2×C4—24no—
1377C2×C4—21no—
1378C2×C4—22no—
1379C2×C4—22no—
1380C2×C4—22no—
1381C2×C4—22no—
1382C2×C4—24no—
1383C2×C4—22no—
1384C2×C4—21no—
1385C2×C4—22no—
1386C2×C4—24no—
1387C2×C4—22no—
1388C2×C4—22no—
1389C2×C4—48no—
1390C2×C4—44no—
1391C2×C4—48no—
1392C2×C4—84no—
1393C2×C4—84no—
1394C2×C4—88no—
1395C2×C4—84no—
1396C2×C4—88no—
1397C2×C4—164no—
1398C2×C4C2×H(5,𝔽2)12yes—
1399C2×C4C2×H(5,𝔽2)12yes—
1400C2×C4C2×H(5,𝔽2)12yes—
1401C2×C4C2×2−1+414yes—
1402C2×C4C2×2−1+414yes—
1403C2×C4#58514yes—
1404C2×C4#58512yes—
1405C2×C4#58512yes—
1406C22—24no—
1407C22—24no—
1408C22—24no—
1409C22—42no—
1410C22—42no—
1411C22—42no—
1412C22—42no—
1413C22—41no—
1414C22—42no—
1415C22—42no—
1416C22—44no—
1417C22—42no—
1418C22—44no—
1419C22—42no—
1420C22—41no—
1421C22—41no—
1422C22—42no—
1423C22C22×H(5,𝔽2)11yescharacteristic
1424C22C22×2−1+412yes—
1425C22C2×#58511yescharacteristic
1426C22C2×#58511yescharacteristic
1427C22C2×#58512yes—
1428C4—24no—
1429C4—24no—
1430C4—22no—
1431C4—24no—
1432C4—22no—
1433C4—42no—
1434C4—42no—
1435C4—41no—
1436C4—42no—
1437C4—42no—
1438C4—44no—
1439C4—42no—
1440C4—42no—
1441C4—42no—
1442C4—42no—
1443C4—42no—
1444C4—44no—
1445C4—42no—
1446C4—44no—
1447C4—44no—
1448C4—42no—
1449C4—42no—
1450C4—42no—
1451C4—41no—
1452C4—42no—
1453C4—41no—
1454C4—42no—
1455C4#354014yes—
1456C2—44no—
1457C2—81no—
1458C2—82no—
1459C2C2×#354011yescharacteristic
1460C2#6282411yescharacteristic
1461C2#6283311yescharacteristic
1462C2#6302512yes—
1463C2#6302512yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#42788C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59644C2semidirect
2. #59239C2semidirect
3. #54910C2semidirect
4. #54417C2semidirect
5. #50482C2semidirect
6. #49335C2semidirect
7. #48610C2semidirect
8. #47892C2semidirect
9. #46004C2semidirect
10. #45669C2semidirect
11. #45431C2semidirect
12. #45337C2semidirect
13. #45336C2semidirect
14. #45151C2semidirect
15. #44233C2semidirect
16. #43652C2semidirect
18. #42427C2semidirect
19. #40098C2semidirect
20. #39660C2semidirect
21. #39159C2semidirect
22. #38983C2semidirect
23. #37396C2semidirect
24. #36608C2semidirect
25. #36446C2semidirect
26. #36276C2semidirect
27. #36195C2semidirect
28. #35749C2semidirect
29. #35738C2semidirect
30. #35669C2semidirect
31. #34968C2semidirect

Maximal subgroups

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

subgroupindex
#596442
#592392
#549102
#544172
#504822
#493352
#486102
#478922
#460042
#456692
#454312
#453372
#453362
#451512
#442332
#436522
#427882
#424272
#400982
#396602
#391592
#389832
#373962
#366082
#364462
#362762
#361952
#357492
#357382
#356692
#349682