Finite Group Databasebeta

← #8402572

Subgroups — #8402572

Order 512.

4971 conjugacy classes of subgroups.

The subgroup lattice has 1494 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59479C212yesmaximal, complemented
2#59478C212yesmaximal
3#55195C214yesmaximal, complemented
4#54854C214yesmaximal, complemented
5#51543C214yesmaximal, complemented
6#49902C214yesmaximal, complemented
7#48622C214yesmaximal, complemented
8#47945C214yesmaximal, complemented
9#46001C212yesmaximal, complemented
10#45993C212yesmaximal, complemented
11#45350C211yesmaximal, characteristic, complemented
12#45083C211yesmaximal, characteristic, complemented
13#44934C211yesmaximal, characteristic, complemented
14#44934C211yesmaximal, characteristic, complemented
15#44308C214yesmaximal, complemented
16#43891C214yesmaximal, complemented
17#42789C211yesmaximal, characteristic, complemented
18#42427C211yesmaximal, characteristic, complemented
19#40191C212yesmaximal, complemented
20#40165C212yesmaximal, complemented
21#39625C212yesmaximal, complemented
22#39369C212yesmaximal, complemented
23#37320C211yesmaximal, characteristic, complemented
24Q8×C4⋊Q8C211yesmaximal, characteristic, complemented
25Q8×#127C211yesmaximal, characteristic, complemented
26#36383C211yesmaximal, characteristic, complemented
27#36370C211yesmaximal, characteristic, complemented
28#35748C211yesmaximal, characteristic, complemented
29#35739C211yesmaximal, characteristic, complemented
30#35535C211yesmaximal, characteristic
31#34973C211yesmaximal, characteristic, complemented
32C2×#563C2214yes—
33C2×Q82C2211yescharacteristic
34C2×Q82C2211yescharacteristic
35C2×D4×Q8C2214yes—
36C2×D4×Q8C2211yescharacteristic
37C2×D4×Q8C2211yescharacteristic
38C2×#544C2214yes—
39C2×#542C2211yescharacteristic
40C2×#520C2211yescharacteristic
41#2868C2212yes—
42#2868C2212yes—
43#2868C2211yescharacteristic
44#2864C2211yescharacteristic
45#2863C2212yes—
46#2860C2212yes—
47#2843C2214yes—
48#2821C2212yes—
49#2821C2214yes—
50#2817C2212yes—
51#2794C2214yes—
52#2792C2214yes—
53#2792C2214yes—
54#2791C2214yes—
55#2773C2214yes—
56#2773C2214yes—
57#2757C2214yes—
58#2738C2214yes—
59#2738C2214yes—
60#2737C2214yes—
61#2737C2214yes—
62#2734C2214yes—
63#2734C2214yes—
64#2734C2214yes—
65#2729C2214yes—
66#2729C2214yes—
67#2729C2214yes—
68#2723C2214yes—
69#2723C2214yes—
70#2721C2214yes—
71#2721C2214yes—
72#2721C2214yes—
73#2720C2214yes—
74#2720C2214yes—
75#2720C2214yes—
76#2720C2214yes—
77#2720C2214yes—
78#2718C2214yes—
79#2716C2214yes—
80#2713C2214yes—
81#2713C2214yes—
82#2707C2214yes—
83#2705C2214yes—
84#2698C2214yes—
85#2690C2214yes—
86#2689C2214yes—
87#2689C2214yes—
88#2680C2214yes—
89#2677C2214yes—
90#2677C2214yes—
91#2677C2214yes—
92#2677C2214yes—
93#2677C2214yes—
94#2677C2214yes—
95#2677C2214yes—
96#2674C2214yes—
97#2674C2214yes—
98#2674C2214yes—
99#2663C2212yes—
100#2660C2214yes—
101#2658C2212yes—
102#2654C2214yes—
103#2638C2214yes—
104#2632C2212yes—
105#2628C2211yescharacteristic
106#2628C2212yes—
107#2628C2214yes—
108#2628C2211yescharacteristic
109#2627C2212yes—
110#2614C2212yes—
111#2611C2214yes—
112#2610C2214yes—
113#2604C2212yes—
114#2602C2214yes—
115#2596C2214yes—
116#2581C2211yescharacteristic
117#2581C2211yescharacteristic
118#2580C2211yescharacteristic
119#2580C2211yescharacteristic
120#2580C2212yes—
121#2575C2214yes—
122#2567C2211yescharacteristic
123#2567C2211yescharacteristic
124#2567C2212yes—
125#2567C2212yes—
126#2567C2211yescharacteristic
127#2564C2214yes—
128#2564C2212yes—
129#2560C2214yes—
130#2556C2214yes—
131#2556C2214yes—
132#2552C2212yes—
133#2552C2212yes—
134#2551C2212yes—
135#2551C2214yes—
136#2551C2214yes—
137#2551C2214yes—
138#2551C2214yes—
139#2551C2212yes—
140#2551C2212yes—
141#2551C2212yes—
142#2550C2214yes—
143#2545C2211yescharacteristic
144#2544C2211yescharacteristic
145#2542C2214yes—
146#2542C2211yescharacteristic
147#2542C2211yescharacteristic
148#2542C2214yes—
149#2542C2212yes—
150#2542C2212yes—
151#2542C2214yes—
152#2542C2212yes—
153#2542C2211yescharacteristic
154#2533C2214yes—
155#2526C2214yes—
156#2524C2214yes—
157#2524C2212yes—
158#2524C2212yes—
159#2519C2214yes—
160#2519C2212yes—
161#2519C2212yes—
162#2516C2214yes—
163#2512C2212yes—
164#2511C2212yes—
165#2507C2212yes—
166#2507C2212yes—
167#2506C2212yes—
168#2506C2212yes—
169#2502C2211yescharacteristic
170#2501C2211yescharacteristic
171#2497C2212yes—
172#2496C2212yes—
173#2492C2212yes—
174#2491C2212yes—
175#2479C2214yes—
176#2479C2214yes—
177#2479C2214yes—
178#2469C2212yes—
179#2469C2212yes—
180#2468C2214yes—
181#2466C2214yes—
182#2465C2214yes—
183#2465C2214yes—
184#2462C2212yes—
185#2462C2214yes—
186#2462C2212yes—
187#2461C2214yes—
188#2461C2214yes—
189#2458C2214yes—
190#2455C2214yes—
191#2452C2214yes—
192#2452C2212yes—
193#2452C2212yes—
194#2452C2212yes—
195#2451C2212yes—
196#2451C2212yes—
197#2451C2212yes—
198#2449C2214yes—
199#2449C2214yes—
200#2449C2214yes—
201#2448C2212yes—
202#2448C2212yes—
203#2447C2212yes—
204#2447C2212yes—
205#2446C2212yes—
206#2445C2212yes—
207#2441C2214yes—
208#2440C2214yes—
209#2440C2214yes—
210#2440C2212yes—
211#2440C2212yes—
212#2438C2214yes—
213#2438C2214yes—
214#2438C2214yes—
215#2434C2214yes—
216#2434C2214yes—
217#2434C2212yes—
218#2432C2211yescharacteristic
219#2431C2211yescharacteristic
220#2423C2212yes—
221#2422C2212yes—
222#2409C2212yes—
223#2402C2211yescharacteristic
224#2399C2211yescharacteristic
225#2396C2212yes—
226#2396C2211yescharacteristic
227#2396C2211yescharacteristic
228C2×#395C2212yes—
229#2383C2214yes—
230#2371C2214yes—
231#2368C2214yes—
232#2367C2212yes—
233#2367C2212yes—
234#2359C2214yes—
235#2359C2214yes—
236#2357C2211yescharacteristic
237#2356C2211yescharacteristic
238#2355C2212yes—
239#2354C2212yes—
240#2351C2211yescharacteristic
241Q8×C4⋊C4C2214yes—
242Q8×C4⋊C4C2212yes—
243#2349C2211yescharacteristic
244D4×C4⋊C4C2212yes—
245#2341C2212yes—
246#2339C2212yes—
247#2332C2214yes—
248#2331C2211yescharacteristic
249#2331C2211yescharacteristic
250#2330C2214yes—
251#2326C2211yescharacteristic
252#2326C2211yescharacteristic
253#2322C2214yes—
254C4×C4⋊Q8C2211yescharacteristic
255C4×C4⋊Q8C2212yes—
256C4×#127C2211yescharacteristic
257C4×#127C2212yes—
258C4×#125C2212yes—
259C4×#125C2212yes—
260C4×#126C2212yes—
261C4×#126C2212yes—
262#2298C2211yescharacteristic
263#2295C2212yes—
264#2293C2212yes—
265C42×Q8C2211yescharacteristic
266C42×Q8C2211yescharacteristic
267C22×#41C2311yescharacteristic
268C23×Q8C2312yes—
269C23×Q8C2312yes—
270#563—416no—
271Q82—44no—
272Q82—44no—
273D4×Q8—44no—
274D4×Q8—44no—
275D4×Q8—416no—
276#544—416no—
277#542—44no—
278C2×C4⋊Q8C2311yescharacteristic
279C2×C4⋊Q8C2311yescharacteristic
280C2×C4⋊Q8C2311yescharacteristic
281C2×C4⋊Q8C2314yes—
282C2×C4⋊Q8C2312yes—
283C2×C4⋊Q8C2312yes—
284C2×C4⋊Q8C2312yes—
285C2×C4⋊Q8C2311yescharacteristic
286C2×C4⋊Q8C2314yes—
287C2×C4⋊Q8C2314yes—
288C2×C4⋊Q8C2312yes—
289C2×C4⋊Q8C2312yes—
290C2×C4⋊Q8C2314yes—
291C2×C4⋊Q8C2314yes—
292C2×C4⋊Q8C2312yes—
293C2×C4⋊Q8C2314yes—
294C2×C4⋊Q8C2314yes—
295C2×C4⋊Q8C2314yes—
296C2×C4⋊Q8C2314yes—
297C2×C4⋊Q8C2314yes—
298C2×C4⋊Q8C2314yes—
299C2×#127C2311yescharacteristic
300C2×#126C2312yes—
301C2×#126C2312yes—
302C2×#126C2314yes—
303C2×#126C2312yes—
304C2×#126C2314yes—
305C2×#126C2314yes—
306C2×#125C2312yes—
307C2×#125C2312yes—
308C2×#125C2314yes—
309C2×#125C2314yes—
310C2×#125C2314yes—
311C2×#125C2314yes—
312C2×#124C2311yescharacteristic
313C2×#124C2311yescharacteristic
314C2×#124C2314yes—
315C2×#124C2312yes—
316C2×#124C2311yescharacteristic
317C2×#123C2314yes—
318C2×#123C2314yes—
319C2×#123C2312yes—
320C2×#123C2314yes—
321C2×C22⋊Q8C2314yes—
322C2×C22⋊Q8C2314yes—
323C2×C22⋊Q8C2314yes—
324C2×C22⋊Q8C2312yes—
325C2×C22⋊Q8C2312yes—
326C2×C22⋊Q8C2312yes—
327C2×C22⋊Q8C2314yes—
328C2×C22⋊Q8C2314yes—
329C2×C22⋊Q8C2314yes—
330C2×C22⋊Q8C2314yes—
331C2×C22⋊Q8C2314yes—
332C2×C22⋊Q8C2314yes—
333C2×C22⋊Q8C2314yes—
334C2×C22⋊Q8C2314yes—
335C2×C22⋊Q8C2314yes—
336C2×C22⋊Q8C2314yes—
337C2×C22⋊Q8C2311yescharacteristic
338C2×C22⋊Q8C2314yes—
339C2×#121C2311yescharacteristic
340#520—44no—
341C2×C4×Q8C2311yescharacteristic
342C2×C4×Q8C2311yescharacteristic
343C2×C4×Q8C2311yescharacteristic
344C2×C4×Q8C2311yescharacteristic
345C2×C4×Q8C2312yes—
346C2×C4×Q8C2312yes—
347C2×C4×Q8C2312yes—
348C2×C4×Q8C2312yes—
349C2×C4×Q8C2312yes—
350C2×C4×Q8C2311yescharacteristic
351C2×C4×Q8C2312yes—
352C2×C4×Q8C2312yes—
353C2×C4×D4C2311yescharacteristic
354C2×C4×D4C2311yescharacteristic
355C2×C4×D4C2312yes—
356C2×C4×D4C2314yes—
357C2×C4×D4C2312yes—
358C2×C4×D4C2314yes—
359C2×C4×D4C2314yes—
360C2×C4×D4C2312yes—
361C2×C4×D4C2312yes—
362C2×C4×D4C2312yes—
363C2×C4×D4C2311yescharacteristic
364C2×#117C2311yescharacteristic
365C2×#117C2314yes—
366C2×#117C2314yes—
367C2×#117C2312yes—
368C22×C4⋊C4C2314yes—
369C22×C4⋊C4C2312yes—
370C22×C4⋊C4C2311yescharacteristic
371#400C2311yescharacteristic
372#400C2314yes—
373#400C2312yes—
374#400C2312yes—
375#400C2314yes—
376#400C2311yescharacteristic
377#400C2314yes—
378#400C2312yes—
379#400C2314yes—
380#400C2314yes—
381#400C2314yes—
382#400C2314yes—
383#400C2312yes—
384#400C2314yes—
385#400C2312yes—
386#400C2312yes—
387#399C2311yescharacteristic
388#399C2314yes—
389#399C2312yes—
390#399C2312yes—
391#399C2314yes—
392#399C2314yes—
393#399C2314yes—
394#399C2312yes—
395#399C2312yes—
396#399C2312yes—
397#399C2314yes—
398#399C2312yes—
399#399C2312yes—
400#399C2312yes—
401#399C2314yes—
402#399C2314yes—
403#399C2311yescharacteristic
404#399C2314yes—
405#399C2314yes—
406#398C2314yes—
407#398C2314yes—
408#398C2314yes—
409#398C2314yes—
410#398C2314yes—
411#398C2314yes—
412#398C2314yes—
413#398C2314yes—
414#398C2312yes—
415#398C2314yes—
416#398C2314yes—
417#398C2312yes—
418#398C2312yes—
419#398C2314yes—
420#398C2314yes—
421#398C2312yes—
422#398C2312yes—
423#398C2312yes—
424#398C2314yes—
425#398C2314yes—
426#398C2314yes—
427#398C2314yes—
428#398C2314yes—
429#398C2314yes—
430#397C2314yes—
431#397C2314yes—
432#397C2314yes—
433#397C2314yes—
434#397C2314yes—
435#397C2314yes—
436#397C2314yes—
437#397C2314yes—
438#397C2314yes—
439#396C2312yes—
440#396C2312yes—
441#396C2314yes—
442#396C2314yes—
443#396C2314yes—
444#396C2314yes—
445#396C2314yes—
446#396C2314yes—
447#395C2312yes—
448#395C2312yes—
449#395C2314yes—
450#395C2314yes—
451#395C2312yes—
452#395C2314yes—
453#395C2314yes—
454#395C2314yes—
455#395C2314yes—
456#395C2312yes—
457#395C2314yes—
458#395C2314yes—
459#395C2312yes—
460#395C2314yes—
461#395C2312yes—
462#395C2312yes—
463#395C2314yes—
464#395C2311yescharacteristic
465#395C2314yes—
466#395C2312yes—
467#395C2314yes—
468#395C2311yescharacteristic
469#395C2314yes—
470#395C2314yes—
471#395C2312yes—
472#395C2312yes—
473#395C2314yes—
474#395C2314yes—
475#395C2314yes—
476#395C2314yes—
477#394C2314yes—
478#394C2314yes—
479#394C2314yes—
480#394C2314yes—
481#394C2314yes—
482#394C2314yes—
483#393C2314yes—
484#393C2314yes—
485#393C2312yes—
486#393C2314yes—
487#393C2311yescharacteristic
488#393C2312yes—
489#393C2312yes—
490#393C2314yes—
491#393C2311yescharacteristic
492#393C2312yes—
493#393C2314yes—
494#392C2314yes—
495#391C2314yes—
496#391C2311yescharacteristic
497#391C2312yes—
498#391C2311yescharacteristic
499#391C2312yes—
500#391C2311yescharacteristic
501#391C2312yes—
502#391C2312yes—
503#391C2311yescharacteristic
504#391C2314yes—
505#391C2314yes—
506#391C2314yes—
507#391C2314yes—
508#391C2312yes—
509#391C2314yes—
510#390C2314yes—
511#390C2312yes—
512#390C2311yescharacteristic
513#390C2314yes—
514#390C2311yescharacteristic
515#390C2312yes—
516#390C2314yes—
517#390C2314yes—
518#390C2312yes—
519#390C2312yes—
520#390C2311yescharacteristic
521#390C2311yescharacteristic
522#390C2314yes—
523#390C2312yes—
524#389C2312yes—
525#389C2312yes—
526#389C2312yes—
527#389C2312yes—
528#389C2314yes—
529#389C2314yes—
530#389C2314yes—
531#389C2314yes—
532#389C2314yes—
533#389C2314yes—
534#389C2314yes—
535#389C2314yes—
536#389C2314yes—
537#389C2314yes—
538#389C2314yes—
539#389C2312yes—
540#389C2314yes—
541#389C2312yes—
542#389C2312yes—
543#389C2312yes—
544#389C2314yes—
545#389C2314yes—
546#389C2314yes—
547#389C2314yes—
548#389C2312yes—
549#389C2312yes—
550#389C2312yes—
551#389C2312yes—
552#389C2312yes—
553#389C2314yes—
554#389C2312yes—
555#389C2312yes—
556#389C2314yes—
557#389C2312yes—
558#389C2314yes—
559#389C2314yes—
560#389C2314yes—
561#388C2312yes—
562#388C2312yes—
563#388C2312yes—
564#388C2312yes—
565#388C2312yes—
566#388C2312yes—
567#388C2314yes—
568#388C2314yes—
569#388C2314yes—
570#388C2314yes—
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#388C2312yes—
592#388C2312yes—
593#387C2312yes—
594#387C2312yes—
595#387C2312yes—
596#387C2312yes—
597#387C2312yes—
598#387C2312yes—
599#387C2314yes—
600#387C2312yes—
601#387C2312yes—
602#387C2312yes—
603#387C2312yes—
604#387C2312yes—
605#387C2312yes—
606#387C2312yes—
607#387C2312yes—
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#387C2312yes—
635#387C2314yes—
636#387C2312yes—
637#386C2314yes—
638#386C2314yes—
639#386C2314yes—
640#386C2314yes—
641#386C2314yes—
642#385C2314yes—
643#385C2314yes—
644#385C2314yes—
645#385C2314yes—
646#385C2314yes—
647#385C2314yes—
648#385C2314yes—
649#385C2314yes—
650#385C2314yes—
651#385C2314yes—
652#385C2314yes—
653#385C2314yes—
654#385C2314yes—
655#385C2314yes—
656#385C2314yes—
657#385C2314yes—
658#385C2314yes—
659#385C2314yes—
660#385C2314yes—
661#384C2312yes—
662#384C2311yescharacteristic
663#384C2312yes—
664#384C2311yescharacteristic
665#384C2312yes—
666#384C2312yes—
667#384C2311yescharacteristic
668#384C2311yescharacteristic
669#384C2314yes—
670#384C2314yes—
671#384C2314yes—
672#384C2314yes—
673#384C2312yes—
674#384C2314yes—
675#384C2314yes—
676#384C2312yes—
677#383C2312yes—
678#383C2312yes—
679#383C2312yes—
680#383C2314yes—
681#382C2312yes—
682#382C2312yes—
683#382C2314yes—
684#382C2311yescharacteristic
685#382C2311yescharacteristic
686#382C2312yes—
687#381C2312yes—
688#381C2314yes—
689#381C2314yes—
690#381C2314yes—
691#380C2314yes—
692#380C2314yes—
693#380C2314yes—
694#380C2312yes—
695#380C2312yes—
696#380C2312yes—
697C4×C4⋊C4C2312yes—
698C4×C4⋊C4C2312yes—
699C4×C4⋊C4C2312yes—
700C4×C4⋊C4C2312yes—
701C4×C4⋊C4C2312yes—
702C4×C4⋊C4C2312yes—
703C4×C4⋊C4C2314yes—
704C4×C4⋊C4C2311yescharacteristic
705C4×C4⋊C4C2312yes—
706C4×C4⋊C4C2312yes—
707C4×C4⋊C4C2311yescharacteristic
708C4×C4⋊C4C2314yes—
709C4×C4⋊C4C2314yes—
710C4×C4⋊C4C2311yescharacteristic
711C4×C4⋊C4C2314yes—
712C4×C4⋊C4C2314yes—
713C4×C4⋊C4C2312yes—
714C4×C4⋊C4C2312yes—
715C4×C4⋊C4C2311yescharacteristic
716C4×C4⋊C4C2312yes—
717C4×C4⋊C4C2312yes—
718C4×C4⋊C4C2312yes—
719C4×C4⋊C4C2312yes—
720C4×C4⋊C4C2314yes—
721C4×C4⋊C4C2312yes—
722C4×C4⋊C4C2312yes—
723C4×C4⋊C4C2312yes—
724C4×C4⋊C4C2312yes—
725C4×C4⋊C4C2312yes—
726C4×C22⋊C4C2312yes—
727C4×C22⋊C4C2312yes—
728C4×C22⋊C4C2311yescharacteristic
729C4×C22⋊C4C2311yescharacteristic
730C4×C22⋊C4C2314yes—
731C4×C22⋊C4C2314yes—
732C4×C22⋊C4C2314yes—
733C4×C22⋊C4C2312yes—
734C4×C22⋊C4C2314yes—
735#376C2311yescharacteristic
736#376C2314yes—
737#376C2312yes—
738C2×#95C2314yes—
739C2×#95C2312yes—
740C43C2312yes—
741C43C2312yes—
742C43C2311yescharacteristic
743C2×#41—24no—
744C2×#41—24no—
745C2×#41—42no—
746C22×Q8—44no—
747C22×Q8—48no—
748C22×Q8—44no—
749C22×Q8—48no—
750C22×Q8C2411yescharacteristic
751C22×Q8C2411yescharacteristic
752C22×Q8C2411yescharacteristic
753C22×Q8C2411yescharacteristic
754C22×Q8C2414yes—
755C22×Q8C2414yes—
756C22×Q8C2412yes—
757C22×Q8C2412yes—
758C22×Q8C2412yes—
759C22×Q8C2414yes—
760C22×Q8C2414yes—
761C22×D4C2411yescharacteristic
762C22×D4C2414yes—
763C22×D4C2412yes—
764C22×D4C2411yescharacteristic
765C22×D4C2412yes—
766C23×C4C2411yescharacteristic
767C23×C4C2414yes—
768C23×C4C2412yes—
769C23×C4C2412yes—
770C23×C4C2414yes—
771C23×C4C2412yes—
772C23×C4C2414yes—
773C23×C4C2412yes—
774C23×C4C2412yes—
775C4⋊Q8—24no—
776C4⋊Q8—24no—
777C4⋊Q8—24no—
778C4⋊Q8—42no—
779C4⋊Q8—48no—
780C4⋊Q8—48no—
781C4⋊Q8—44no—
782C4⋊Q8—44no—
783C4⋊Q8—48no—
784C4⋊Q8—48no—
785C4⋊Q8—44no—
786C4⋊Q8—44no—
787C4⋊Q8—44no—
788C4⋊Q8—44no—
789C4⋊Q8—48no—
790C4⋊Q8—48no—
791C4⋊Q8—48no—
792C4⋊Q8—48no—
793C4⋊Q8—48no—
794C4⋊Q8—48no—
795C4⋊Q8—48no—
796#127—24no—
797#126—28no—
798#126—28no—
799#126—44no—
800#126—48no—
801#126—48no—
802#126—48no—
803#125—28no—
804#125—216no—
805#125—28no—
806#125—48no—
807#125—48no—
808#125—48no—
809#124—24no—
810#124—24no—
811#124—44no—
812#124—48no—
813#124—42no—
814#123—216no—
815#123—48no—
816#123—44no—
817#123—48no—
818C22⋊Q8—216no—
819C22⋊Q8—216no—
820C22⋊Q8—48no—
821C22⋊Q8—48no—
822C22⋊Q8—48no—
823C22⋊Q8—48no—
824C22⋊Q8—48no—
825C22⋊Q8—48no—
826C22⋊Q8—48no—
827C22⋊Q8—48no—
828C22⋊Q8—48no—
829C22⋊Q8—48no—
830C22⋊Q8—44no—
831C22⋊Q8—48no—
832C22⋊Q8—48no—
833C22⋊Q8—42no—
834C22⋊Q8—44no—
835C22⋊Q8—44no—
836#121—42no—
837C4×Q8—28no—
838C4×Q8—28no—
839C4×Q8—28no—
840C4×Q8—24no—
841C4×Q8—24no—
842C4×Q8—24no—
843C4×Q8—24no—
844C4×Q8—42no—
845C4×Q8—44no—
846C4×Q8—44no—
847C4×Q8—44no—
848C4×Q8—44no—
849C4×D4—28no—
850C4×D4—24no—
851C4×D4—24no—
852C4×D4—44no—
853C4×D4—48no—
854C4×D4—48no—
855C4×D4—42no—
856C4×D4—44no—
857C4×D4—44no—
858C4×D4—48no—
859C4×D4—44no—
860#117—24no—
861#117—44no—
862#117—48no—
863#117—48no—
864C2×C4⋊C4—44no—
865C2×C4⋊C4—42no—
866C2×C4⋊C4—48no—
867C2×C4⋊C4C2411yescharacteristic
868C2×C4⋊C4C2412yes—
869C2×C4⋊C4C2411yescharacteristic
870C2×C4⋊C4C2411yescharacteristic
871C2×C4⋊C4C2412yes—
872C2×C4⋊C4C2414yes—
873C2×C4⋊C4C2411yescharacteristic
874C2×C4⋊C4C2412yes—
875C2×C4⋊C4C2414yes—
876C2×C4⋊C4C2412yes—
877C2×C4⋊C4C2412yes—
878C2×C4⋊C4C2411yescharacteristic
879C2×C4⋊C4C2412yes—
880C2×C4⋊C4C2411yescharacteristic
881C2×C4⋊C4C2412yes—
882C2×C4⋊C4C2412yes—
883C2×C4⋊C4C2412yes—
884C2×C4⋊C4C2411yescharacteristic
885C2×C4⋊C4C2412yes—
886C2×C4⋊C4C2412yes—
887C2×C4⋊C4C2412yes—
888C2×C4⋊C4C2412yes—
889C2×C4⋊C4C2411yescharacteristic
890C2×C4⋊C4C2412yes—
891C2×C4⋊C4C2412yes—
892C2×C4⋊C4C2412yes—
893C2×C4⋊C4C2414yes—
894C2×C4⋊C4C2414yes—
895C2×C4⋊C4C2412yes—
896C2×C4⋊C4C2414yes—
897C2×C4⋊C4C2414yes—
898C2×C4⋊C4C2412yes—
899C2×C4⋊C4C2414yes—
900C2×C4⋊C4C2412yes—
901C2×C4⋊C4C2414yes—
902C2×C4⋊C4C2412yes—
903C2×C4⋊C4C2414yes—
904C2×C4⋊C4C2414yes—
905C2×C4⋊C4C2414yes—
906C2×C4⋊C4C2412yes—
907C2×C4⋊C4C2412yes—
908C2×C4⋊C4C2412yes—
909C2×C4⋊C4C2412yes—
910C2×C4⋊C4C2412yes—
911C2×C4⋊C4C2412yes—
912C2×C4⋊C4C2412yes—
913C2×C4⋊C4C2412yes—
914C2×C4⋊C4C2414yes—
915C2×C4⋊C4C2412yes—
916C2×C4⋊C4C2412yes—
917C2×C4⋊C4C2414yes—
918C2×C4⋊C4C2414yes—
919C2×C4⋊C4C2414yes—
920C2×C4⋊C4C2414yes—
921C2×C4⋊C4C2414yes—
922C2×C4⋊C4C2414yes—
923C2×C4⋊C4C2414yes—
924C2×C4⋊C4C2414yes—
925C2×C4⋊C4C2414yes—
926C2×C4⋊C4C2414yes—
927C2×C4⋊C4C2414yes—
928C2×C4⋊C4C2412yes—
929C2×C4⋊C4C2414yes—
930C2×C4⋊C4C2414yes—
931C2×C4⋊C4C2414yes—
932C2×C4⋊C4C2414yes—
933C2×C4⋊C4C2414yes—
934C2×C4⋊C4C2414yes—
935C2×C4⋊C4C2414yes—
936C2×C4⋊C4C2414yes—
937C2×C4⋊C4C2414yes—
938C2×C4⋊C4C2414yes—
939C2×C4⋊C4C2414yes—
940C2×C4⋊C4C2414yes—
941C2×C4⋊C4C2414yes—
942C2×C4⋊C4C2412yes—
943C2×C4⋊C4C2412yes—
944C2×C4⋊C4C2412yes—
945C2×C22⋊C4C2412yes—
946C2×C22⋊C4C2411yescharacteristic
947C2×C22⋊C4C2411yescharacteristic
948C2×C22⋊C4C2414yes—
949C2×C22⋊C4C2414yes—
950C2×C22⋊C4C2414yes—
951C2×C22⋊C4C2412yes—
952C2×C22⋊C4C2414yes—
953C2×C22⋊C4C2414yes—
954C2×C22⋊C4C2412yes—
955C2×C22⋊C4C2412yes—
956C2×C22⋊C4C2412yes—
957C2×C22⋊C4C2414yes—
958C2×C22⋊C4C2414yes—
959C2×C22⋊C4C2414yes—
960C2×C22⋊C4C2414yes—
961C2×C22⋊C4C2414yes—
962C2×C22⋊C4C2412yes—
963C2×C22⋊C4C2412yes—
964C2×C22⋊C4C2412yes—
965C2×C22⋊C4C2412yes—
966C2×C22⋊C4C2414yes—
967C2×C22⋊C4C2414yes—
968C2×C22⋊C4C2414yes—
969C2×C22⋊C4C2414yes—
970C2×C22⋊C4C2414yes—
971C2×C22⋊C4C2414yes—
972C2×C22⋊C4C2412yes—
973C2×C22⋊C4C2412yes—
974C2×C22⋊C4C2414yes—
975C2×C22⋊C4C2414yes—
976C2×C22⋊C4C2412yes—
977C2×C22⋊C4C2414yes—
978C2×C22⋊C4C2414yes—
979C2×C22⋊C4C2412yes—
980C2×C22⋊C4C2414yes—
981C2×C42C2412yes—
982C2×C42C2412yes—
983C2×C42C2411yescharacteristic
984C2×C42C2414yes—
985C2×C42C2412yes—
986C2×C42C2412yes—
987C2×C42C2412yes—
988C2×C42C2412yes—
989C2×C42C2412yes—
990C2×C42C2412yes—
991C2×C42C2412yes—
992C2×C42C2412yes—
993C2×C42C2412yes—
994C2×C42C2412yes—
995C2×C42C2412yes—
996C2×C42C2414yes—
997C2×C42C2411yescharacteristic
998C2×C42C2411yescharacteristic
999C2×C42C2412yes—
1000C2×C42C2412yes—
1001C2×C42C2412yes—
1002C2×C42C2411yescharacteristic
1003C2×C42C2411yescharacteristic
1004C2×C42C2412yes—
1005C2×C42C2414yes—
1006C2×C42C2414yes—
1007C2×C42C2414yes—
1008C2×C42C2414yes—
1009C2×C42C2414yes—
1010C2×C42C2411yescharacteristic
1011#95C2411yescharacteristic
1012#95C2412yes—
1013#95C2414yes—
1014#95C2414yes—
1015#95C2414yes—
1016#95C2412yes—
1017#95C2414yes—
1018#95C2411yescharacteristic
1019#95C2414yes—
1020#95C2414yes—
1021#95C2412yes—
1022#95C2414yes—
1023#95C2412yes—
1024#95C2414yes—
1025#95C2412yes—
1026#95C2414yes—
1027#95C2412yes—
1028#95C2412yes—
1029#95C2412yes—
1030#95C2412yes—
1031#95C2414yes—
1032#95C2412yes—
1033#95C2412yes—
1034#95C2414yes—
1035#95C2412yes—
1036#95C2412yes—
1037#95C2414yes—
1038#95C2414yes—
1039#95C2411yescharacteristic
1040#95C2411yescharacteristic
1041#95C2412yes—
1042#95C2412yes—
1043#95C2412yes—
1044#95C2412yes—
1045#95C2414yes—
1046#95C2414yes—
1047#95C2412yes—
1048#95C2412yes—
1049#95C2414yes—
1050#95C2414yes—
1051#95C2414yes—
1052#95C2414yes—
1053#95C2414yes—
1054#95C2412yes—
1055#95C2412yes—
1056#95C2412yes—
1057#95C2414yes—
1058#95C2412yes—
1059#95C2414yes—
1060#95C2412yes—
1061#95C2412yes—
1062#95C2412yes—
1063#95C2414yes—
1064#95C2412yes—
1065#95C2412yes—
1066#95C2412yes—
1067#95C2414yes—
1068#95C2412yes—
1069#95C2414yes—
1070#95C2414yes—
1071#95C2414yes—
1072#95C2414yes—
1073#95C2414yes—
1074#95C2414yes—
1075#95C2414yes—
1076#95C2414yes—
1077C24C2511yescharacteristic
1078C24C2512yes—
1079C24C2512yes—
1080#41—416no—
1081C2×Q8—22no—
1082C2×Q8—22no—
1083C2×Q8—24no—
1084C2×Q8—22no—
1085C2×Q8—22no—
1086C2×Q8—28no—
1087C2×Q8—28no—
1088C2×Q8—24no—
1089C2×Q8—24no—
1090C2×Q8—24no—
1091C2×Q8—22no—
1092C2×Q8—22no—
1093C2×Q8—22no—
1094C2×Q8—44no—
1095C2×Q8—44no—
1096C2×Q8—44no—
1097C2×Q8—44no—
1098C2×Q8—44no—
1099C2×Q8—44no—
1100C2×Q8—44no—
1101C2×Q8—42no—
1102C2×Q8—44no—
1103C2×Q8—44no—
1104C2×Q8—44no—
1105C2×Q8—44no—
1106C2×Q8—44no—
1107C2×Q8—44no—
1108C2×Q8—816no—
1109C2×Q8—816no—
1110C2×Q82−1+414yes—
1111C2×D4—28no—
1112C2×D4—24no—
1113C2×D4—22no—
1114C2×D4—22no—
1115C2×D4—22no—
1116C2×D4—28no—
1117C2×D4—22no—
1118C2×D4—22no—
1119C2×D4—24no—
1120C2×D4—44no—
1121C2×D4—42no—
1122C2×D4—42no—
1123C2×D4—44no—
1124C2×D42−1+414yes—
1125C22×C4—28no—
1126C22×C4—24no—
1127C22×C4—22no—
1128C22×C4—28no—
1129C22×C4—24no—
1130C22×C4—22no—
1131C22×C4—22no—
1132C22×C4—24no—
1133C22×C4—28no—
1134C22×C4—24no—
1135C22×C4—28no—
1136C22×C4—44no—
1137C22×C4—42no—
1138C22×C4—44no—
1139C22×C4—44no—
1140C22×C4—44no—
1141C22×C4—44no—
1142C22×C4—44no—
1143C22×C4—44no—
1144C22×C4—42no—
1145C22×C4—42no—
1146C22×C4—44no—
1147C22×C4—44no—
1148C22×C4C2511yescharacteristic
1149C22×C4C2512yes—
1150C22×C4C2514yes—
1151C22×C4C2511yescharacteristic
1152C22×C4C2512yes—
1153C22×C4C2512yes—
1154C22×C4C2512yes—
1155C22×C4C2512yes—
1156C22×C4C2514yes—
1157C22×C4C2512yes—
1158C22×C4C2512yes—
1159C22×C4C2512yes—
1160C22×C4C2514yes—
1161C22×C4C2512yes—
1162C22×C4C2514yes—
1163C22×C4C2511yescharacteristic
1164C22×C4C2512yes—
1165C22×C4C2512yes—
1166C22×C4C2511yescharacteristic
1167C22×C4C2512yes—
1168C22×C4C2511yescharacteristic
1169C22×C4C2512yes—
1170C22×C4C2512yes—
1171C22×C4C2512yes—
1172C22×C4C2512yes—
1173C22×C4C2512yes—
1174C22×C4C2512yes—
1175C22×C4C2511yescharacteristic
1176C4⋊C4—22no—
1177C4⋊C4—24no—
1178C4⋊C4—22no—
1179C4⋊C4—24no—
1180C4⋊C4—22no—
1181C4⋊C4—28no—
1182C4⋊C4—22no—
1183C4⋊C4—24no—
1184C4⋊C4—28no—
1185C4⋊C4—22no—
1186C4⋊C4—24no—
1187C4⋊C4—24no—
1188C4⋊C4—22no—
1189C4⋊C4—24no—
1190C4⋊C4—24no—
1191C4⋊C4—24no—
1192C4⋊C4—22no—
1193C4⋊C4—24no—
1194C4⋊C4—24no—
1195C4⋊C4—22no—
1196C4⋊C4—24no—
1197C4⋊C4—24no—
1198C4⋊C4—28no—
1199C4⋊C4—28no—
1200C4⋊C4—28no—
1201C4⋊C4—28no—
1202C4⋊C4—24no—
1203C4⋊C4—28no—
1204C4⋊C4—24no—
1205C4⋊C4—24no—
1206C4⋊C4—24no—
1207C4⋊C4—28no—
1208C4⋊C4—28no—
1209C4⋊C4—24no—
1210C4⋊C4—24no—
1211C4⋊C4—24no—
1212C4⋊C4—24no—
1213C4⋊C4—28no—
1214C4⋊C4—24no—
1215C4⋊C4—28no—
1216C4⋊C4—24no—
1217C4⋊C4—24no—
1218C4⋊C4—24no—
1219C4⋊C4—24no—
1220C4⋊C4—24no—
1221C4⋊C4—24no—
1222C4⋊C4—24no—
1223C4⋊C4—28no—
1224C4⋊C4—42no—
1225C4⋊C4—42no—
1226C4⋊C4—44no—
1227C4⋊C4—44no—
1228C4⋊C4—44no—
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—42no—
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—44no—
1248C4⋊C4—44no—
1249C4⋊C4—44no—
1250C4⋊C4—44no—
1251C4⋊C4—42no—
1252C4⋊C4H(5,𝔽2)18yes—
1253C4⋊C42−1+418yes—
1254C22⋊C4—28no—
1255C22⋊C4—28no—
1256C22⋊C4—22no—
1257C22⋊C4—22no—
1258C22⋊C4—24no—
1259C22⋊C4—28no—
1260C22⋊C4—28no—
1261C22⋊C4—24no—
1262C22⋊C4—28no—
1263C22⋊C4—28no—
1264C22⋊C4—24no—
1265C22⋊C4—24no—
1266C22⋊C4—24no—
1267C22⋊C4—28no—
1268C22⋊C4—28no—
1269C22⋊C4—28no—
1270C22⋊C4—28no—
1271C22⋊C4—24no—
1272C22⋊C4—24no—
1273C22⋊C4—24no—
1274C22⋊C4—42no—
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—44no—
1284C22⋊C4—44no—
1285C22⋊C4—42no—
1286C22⋊C4—44no—
1287C22⋊C4—44no—
1288C22⋊C4—42no—
1289C22⋊C4—44no—
1290C42—22no—
1291C42—24no—
1292C42—24no—
1293C42—28no—
1294C42—24no—
1295C42—24no—
1296C42—24no—
1297C42—24no—
1298C42—24no—
1299C42—24no—
1300C42—24no—
1301C42—24no—
1302C42—24no—
1303C42—24no—
1304C42—28no—
1305C42—24no—
1306C42—24no—
1307C42—22no—
1308C42—22no—
1309C42—24no—
1310C42—24no—
1311C42—22no—
1312C42—22no—
1313C42—42no—
1314C42—44no—
1315C42—44no—
1316C42—44no—
1317C42—44no—
1318C42—44no—
1319C42H(5,𝔽2)14yes—
1320C23—24no—
1321C23—22no—
1322C23—24no—
1323C23—22no—
1324C23—22no—
1325C23—24no—
1326C23—21no—
1327C23—22no—
1328C23—22no—
1329C23—22no—
1330C23—24no—
1331C23—21no—
1332C23—21no—
1333C23—22no—
1334C23C2×2−1+414yes—
1335C23C2611yescharacteristic
1336Q8—28no—
1337Q8—28no—
1338Q8—28no—
1339Q8—44no—
1340Q8—88no—
1341Q8—88no—
1342Q8—84no—
1343Q8—84no—
1344Q8—162no—
1345Q8—164no—
1346Q8—164no—
1347D4—28no—
1348D4—416no—
1349D4—48no—
1350D4—44no—
1351D4—162no—
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—22no—
1364C2×C4—22no—
1365C2×C4—22no—
1366C2×C4—22no—
1367C2×C4—22no—
1368C2×C4—21no—
1369C2×C4—22no—
1370C2×C4—24no—
1371C2×C4—22no—
1372C2×C4—21no—
1373C2×C4—22no—
1374C2×C4—22no—
1375C2×C4—22no—
1376C2×C4—22no—
1377C2×C4—22no—
1378C2×C4—22no—
1379C2×C4—24no—
1380C2×C4—22no—
1381C2×C4—22no—
1382C2×C4—24no—
1383C2×C4—22no—
1384C2×C4—24no—
1385C2×C4—22no—
1386C2×C4—24no—
1387C2×C4—24no—
1388C2×C4—24no—
1389C2×C4—24no—
1390C2×C4—22no—
1391C2×C4—24no—
1392C2×C4—21no—
1393C2×C4—24no—
1394C2×C4—24no—
1395C2×C4—24no—
1396C2×C4—22no—
1397C2×C4—22no—
1398C2×C4—22no—
1399C2×C4—22no—
1400C2×C4—22no—
1401C2×C4—22no—
1402C2×C4—22no—
1403C2×C4—22no—
1404C2×C4—24no—
1405C2×C4—22no—
1406C2×C4—24no—
1407C2×C4—22no—
1408C2×C4—22no—
1409C2×C4—24no—
1410C2×C4—24no—
1411C2×C4—22no—
1412C2×C4—22no—
1413C2×C4—22no—
1414C2×C4—21no—
1415C2×C4—21no—
1416C2×C4—416no—
1417C2×C4—48no—
1418C2×C4—44no—
1419C2×C4—84no—
1420C2×C4—88no—
1421C2×C4—84no—
1422C2×C4—88no—
1423C2×C4—162no—
1424C2×C4—162no—
1425C2×C4C2×H(5,𝔽2)12yes—
1426C2×C4C2×H(5,𝔽2)14yes—
1427C2×C4C2×H(5,𝔽2)14yes—
1428C2×C4C2×H(5,𝔽2)14yes—
1429C2×C4C2×H(5,𝔽2)12yes—
1430C2×C4C2×H(5,𝔽2)12yes—
1431C2×C4C2×2−1+414yes—
1432C2×C4C2×2−1+414yes—
1433C2×C4C2×2−1+414yes—
1434C2×C4C2×2−1+414yes—
1435C2×C4C2×2−1+412yes—
1436C2×C4C2×2−1+412yes—
1437C22—24no—
1438C22—28no—
1439C22—44no—
1440C22—42no—
1441C22—42no—
1442C22—41no—
1443C22—42no—
1444C22—44no—
1445C22—42no—
1446C22—42no—
1447C22—44no—
1448C22—42no—
1449C22—41no—
1450C22—41no—
1451C22—42no—
1452C22C22×H(5,𝔽2)11yescharacteristic
1453C22C22×H(5,𝔽2)12yes—
1454C22C22×2−1+411yescharacteristic
1455C22C22×2−1+411yescharacteristic
1456C22C22×2−1+412yes—
1457C4—24no—
1458C4—24no—
1459C4—24no—
1460C4—24no—
1461C4—24no—
1462C4—24no—
1463C4—22no—
1464C4—22no—
1465C4—24no—
1466C4—41no—
1467C4—42no—
1468C4—42no—
1469C4—42no—
1470C4—44no—
1471C4—42no—
1472C4—44no—
1473C4—42no—
1474C4—42no—
1475C4—44no—
1476C4—42no—
1477C4—44no—
1478C4—41no—
1479C4—42no—
1480C4—42no—
1481C4—42no—
1482C4—41no—
1483C4—42no—
1484C4#353814yes—
1485C2—44no—
1486C2—81no—
1487C2—82no—
1488C2C2×#353811yescharacteristic
1489C2#6283211yescharacteristic
1490C2#6283311yescharacteristic
1491C2#6301612yes—
1492C2#6303712yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#2431C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59479C2semidirect
3. #55195C2semidirect
4. #54854C2semidirect
5. #51543C2semidirect
6. #49902C2semidirect
7. #48622C2semidirect
8. #47945C2semidirect
9. #46001C2semidirect
10. #45993C2semidirect
11. #45350C2semidirect
12. #45083C2semidirect
13. #44934C2semidirect
14. #44934C2semidirect
15. #44308C2semidirect
16. #43891C2semidirect
17. #42789C2semidirect
18. #42427C2semidirect
19. #40191C2semidirect
20. #40165C2semidirect
21. #39625C2semidirect
22. #39369C2semidirect
23. #37320C2semidirect
24. Q8×C4⋊Q8C2semidirect
25. Q8×#127C2semidirect
26. #36383C2semidirect
27. #36370C2semidirect
28. #35748C2semidirect
29. #35739C2semidirect
31. #34973C2semidirect

Maximal subgroups

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

subgroupindex
#594792
#594782
#551952
#548542
#515432
#499022
#486222
#479452
#460012
#459932
#453502
#450832
#449342
#443082
#438912
#427892
#424272
#401912
#401652
#396252
#393692
#373202
Q8×C4⋊Q82
Q8×#1272
#363832
#363702
#357482
#357392
#355352
#349732