Finite Group Databasebeta

← #7898462

Subgroups — #7898462

Order 512.

5211 conjugacy classes of subgroups.

The subgroup lattice has 1536 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59815C211yesmaximal, characteristic, complemented
2#59112C212yesmaximal, complemented
3#52273C211yesmaximal, characteristic, complemented
4#49490C214yesmaximal, complemented
5#48669C214yesmaximal, complemented
6#48639C214yesmaximal, complemented
7#47176C214yesmaximal, complemented
8#46090C212yesmaximal, complemented
9#45271C212yesmaximal, complemented
10#45072C212yesmaximal, complemented
11#44930C214yesmaximal, complemented
12#44888C212yesmaximal, complemented
13#42758C212yesmaximal, complemented
14#42515C212yesmaximal, complemented
15#40750C214yesmaximal, complemented
16#40171C212yesmaximal, complemented
17#39628C211yesmaximal, characteristic, complemented
18#39621C211yesmaximal, characteristic, complemented
19#38762C212yesmaximal, complemented
20#38425C212yesmaximal, complemented
21#38101C212yesmaximal, complemented
22#37764C212yesmaximal, complemented
23#37156C212yesmaximal, complemented
24#36415C211yesmaximal, characteristic, complemented
25#35905C212yesmaximal, complemented
26#35571C212yesmaximal, complemented
27#35197C211yesmaximal, characteristic, complemented
28#34460C212yesmaximal, complemented
29#34332C211yesmaximal, characteristic, complemented
30C2×#555C2211yescharacteristic
31C2×#554C2211yescharacteristic
32C2×#550C2212yes—
33C2×#547C2212yes—
34C2×#547C2214yes—
35C2×#547C2211yescharacteristic
36C2×#540C2212yes—
37C2×#532C2212yes—
38#2862C2211yescharacteristic
39#2854C2212yes—
40#2851C2212yes—
41#2850C2212yes—
42#2850C2212yes—
43#2837C2214yes—
44#2830C2214yes—
45#2811C2212yes—
46#2808C2211yescharacteristic
47#2808C2211yescharacteristic
48#2806C2212yes—
49#2806C2212yes—
50#2805C2214yes—
51#2804C2212yes—
52#2804C2211yescharacteristic
53#2804C2212yes—
54#2802C2214yes—
55#2796C2214yes—
56#2796C2214yes—
57#2796C2212yes—
58#2796C2212yes—
59#2794C2212yes—
60#2772C2214yes—
61#2768C2214yes—
62#2752C2214yes—
63#2751C2212yes—
64#2751C2212yes—
65#2751C2214yes—
66#2742C2214yes—
67#2742C2214yes—
68#2738C2214yes—
69#2737C2214yes—
70#2734C2212yes—
71#2732C2212yes—
72#2732C2212yes—
73#2729C2214yes—
74#2728C2214yes—
75#2728C2214yes—
76#2724C2211yescharacteristic
77#2717C2214yes—
78#2717C2214yes—
79#2710C2214yes—
80#2710C2214yes—
81#2709C2214yes—
82#2709C2212yes—
83#2708C2214yes—
84#2701C2214yes—
85#2701C2214yes—
86#2696C2214yes—
87#2696C2214yes—
88#2686C2214yes—
89#2686C2214yes—
90#2682C2212yes—
91#2682C2212yes—
92#2674C2214yes—
93#2672C2214yes—
94#2672C2214yes—
95#2672C2214yes—
96#2672C2214yes—
97#2671C2214yes—
98#2671C2214yes—
99#2663C2214yes—
100#2660C2212yes—
101#2652C2214yes—
102#2650C2214yes—
103#2649C2214yes—
104#2648C2214yes—
105#2647C2212yes—
106#2638C2214yes—
107#2632C2214yes—
108#2628C2212yes—
109#2602C2214yes—
110#2602C2214yes—
111#2586C2214yes—
112#2583C2214yes—
113#2580C2212yes—
114#2578C2214yes—
115#2573C2214yes—
116#2571C2211yescharacteristic
117#2563C2211yescharacteristic
118#2557C2214yes—
119#2557C2214yes—
120#2557C2214yes—
121#2557C2214yes—
122#2555C2214yes—
123#2551C2212yes—
124#2550C2212yes—
125#2550C2212yes—
126#2548C2211yescharacteristic
127#2547C2211yescharacteristic
128#2543C2214yes—
129#2541C2212yes—
130#2541C2211yescharacteristic
131#2538C2211yescharacteristic
132#2538C2212yes—
133#2537C2212yes—
134#2535C2212yes—
135#2535C2212yes—
136#2516C2214yes—
137#2515C2214yes—
138#2513C2212yes—
139#2505C2214yes—
140#2501C2212yes—
141#2500C2212yes—
142#2499C2212yes—
143#2497C2212yes—
144#2495C2212yes—
145#2491C2212yes—
146#2491C2214yes—
147#2490C2212yes—
148#2490C2212yes—
149#2490C2212yes—
150#2487C2214yes—
151#2477C2214yes—
152#2477C2214yes—
153#2470C2214yes—
154#2464C2214yes—
155#2458C2214yes—
156#2457C2214yes—
157#2457C2214yes—
158#2455C2214yes—
159#2452C2212yes—
160#2452C2212yes—
161#2451C2214yes—
162#2450C2214yes—
163#2450C2214yes—
164#2450C2214yes—
165#2450C2214yes—
166#2449C2214yes—
167#2445C2214yes—
168#2445C2214yes—
169#2445C2212yes—
170#2443C2214yes—
171#2443C2214yes—
172#2443C2214yes—
173#2442C2212yes—
174#2442C2212yes—
175#2441C2212yes—
176#2440C2212yes—
177#2431C2212yes—
178#2431C2214yes—
179#2430C2214yes—
180#2430C2214yes—
181#2430C2214yes—
182#2428C2214yes—
183#2428C2212yes—
184#2428C2212yes—
185#2427C2214yes—
186#2427C2212yes—
187#2425C2214yes—
188#2422C2212yes—
189#2422C2212yes—
190#2420C2212yes—
191#2420C2212yes—
192#2420C2212yes—
193#2419C2214yes—
194#2419C2214yes—
195#2416C2212yes—
196#2416C2214yes—
197#2416C2212yes—
198#2413C2214yes—
199#2407C2214yes—
200#2407C2214yes—
201#2407C2214yes—
202#2406C2214yes—
203#2406C2214yes—
204#2398C2212yes—
205#2398C2212yes—
206#2395C2212yes—
207#2392C2214yes—
208#2378C2214yes—
209#2376C2214yes—
210#2370C2212yes—
211#2369C2211yescharacteristic
212#2363C2212yes—
213#2361C2212yes—
214#2361C2212yes—
215#2361C2212yes—
216#2360C2214yes—
217#2360C2212yes—
218#2359C2214yes—
219#2355C2212yes—
220#2352C2212yes—
221#2352C2212yes—
222Q8×C4⋊C4C2211yescharacteristic
223#2349C2212yes—
224D4×C4⋊C4C2212yes—
225D4×C4⋊C4C2211yescharacteristic
226D4×C4⋊C4C2212yes—
227#2345C2212yes—
228#2345C2212yes—
229#2344C2212yes—
230#2339C2214yes—
231#2335C2214yes—
232#2331C2212yes—
233#2330C2212yes—
234#2329C2214yes—
235#2329C2214yes—
236#2328C2212yes—
237#2328C2212yes—
238#2324C2212yes—
239#2324C2214yes—
240#2322C2214yes—
241#2319C2212yes—
242#2316C2212yes—
243#2311C2214yes—
244C4×C4⋊Q8C2211yescharacteristic
245C4×#127C2211yescharacteristic
246C4×#127C2211yescharacteristic
247C4×C22⋊Q8C2212yes—
248C4×#123C2212yes—
249C4×#121C2212yes—
250#2297C2212yes—
251#2295C2211yescharacteristic
252#2295C2211yescharacteristic
253C2×#389C2212yes—
254C2×#389C2212yes—
255#2290C2212yes—
256#2290C2212yes—
257#2275C2212yes—
258C42×D4C2211yescharacteristic
259C22×#41C2314yes—
260C22×#41C2312yes—
261C22×#41C2314yes—
262#555—44no—
263#554—28no—
264#550—48no—
265#547—216no—
266#547—44no—
267#547—416no—
268#540—48no—
269#532—48no—
270C2×C4⋊Q8C2311yescharacteristic
271C2×C4⋊Q8C2311yescharacteristic
272C2×C4⋊Q8C2312yes—
273C2×C4⋊Q8C2314yes—
274C2×C4⋊Q8C2311yescharacteristic
275C2×#127C2311yescharacteristic
276C2×#127C2311yescharacteristic
277C2×#127C2312yes—
278C2×#127C2314yes—
279C2×#125C2312yes—
280C2×#125C2312yes—
281C2×#124C2314yes—
282C2×#124C2314yes—
283C2×#124C2312yes—
284C2×#124C2312yes—
285C2×#124C2314yes—
286C2×#123C2314yes—
287C2×#123C2314yes—
288C2×#123C2312yes—
289C2×#123C2314yes—
290C2×#123C2314yes—
291C2×#123C2314yes—
292C2×#123C2314yes—
293C2×#123C2314yes—
294C2×#123C2314yes—
295C2×#123C2314yes—
296C2×#123C2314yes—
297C2×C22⋊Q8C2314yes—
298C2×C22⋊Q8C2314yes—
299C2×C22⋊Q8C2312yes—
300C2×C22⋊Q8C2314yes—
301C2×C22⋊Q8C2312yes—
302C2×C22⋊Q8C2314yes—
303C2×C22⋊Q8C2312yes—
304C2×C22⋊Q8C2314yes—
305C2×#121C2312yes—
306C2×#121C2314yes—
307C2×#121C2312yes—
308C2×#121C2312yes—
309C2×#121C2312yes—
310C2×#121C2312yes—
311C2×#121C2314yes—
312C2×#121C2314yes—
313C2×#121C2314yes—
314C2×#121C2314yes—
315C2×#121C2314yes—
316C2×#121C2314yes—
317C2×#121C2312yes—
318C2×#121C2312yes—
319C2×#121C2312yes—
320C2×#121C2312yes—
321C2×#121C2314yes—
322C2×C4×Q8C2311yescharacteristic
323C2×C4×Q8C2311yescharacteristic
324C2×C4×Q8C2312yes—
325C2×C4×Q8C2312yes—
326C2×C4×D4C2312yes—
327C2×C4×D4C2312yes—
328C2×C4×D4C2312yes—
329C2×C4×D4C2311yescharacteristic
330C2×C4×D4C2312yes—
331C2×C4×D4C2311yescharacteristic
332C2×C4×D4C2312yes—
333C2×C4×D4C2311yescharacteristic
334C2×C4×D4C2311yescharacteristic
335C2×C4×D4C2311yescharacteristic
336C2×C4×D4C2312yes—
337C2×C4×D4C2314yes—
338C2×C4×D4C2312yes—
339C2×C4×D4C2312yes—
340C2×C4×D4C2314yes—
341C2×C4×D4C2314yes—
342C2×C4×D4C2314yes—
343C2×C4×D4C2312yes—
344C2×C4×D4C2314yes—
345C2×C4×D4C2314yes—
346C2×#117C2312yes—
347C2×#117C2312yes—
348C2×#117C2312yes—
349C2×#117C2314yes—
350C22×C4⋊C4C2312yes—
351C22×C4⋊C4C2312yes—
352C22×C4⋊C4C2312yes—
353C22×C4⋊C4C2314yes—
354C22×C4⋊C4C2314yes—
355C22×C4⋊C4C2312yes—
356C22×C4⋊C4C2312yes—
357C22×C42C2312yes—
358C22×C42C2312yes—
359#400C2314yes—
360#400C2312yes—
361#400C2314yes—
362#400C2314yes—
363#400C2314yes—
364#400C2314yes—
365#400C2314yes—
366#400C2312yes—
367#400C2314yes—
368#400C2312yes—
369#400C2312yes—
370#400C2312yes—
371#400C2314yes—
372#399C2314yes—
373#399C2314yes—
374#399C2314yes—
375#399C2314yes—
376#399C2314yes—
377#399C2312yes—
378#398C2314yes—
379#398C2314yes—
380#398C2314yes—
381#398C2314yes—
382#398C2314yes—
383#398C2314yes—
384#398C2312yes—
385#398C2314yes—
386#398C2314yes—
387#398C2314yes—
388#397C2314yes—
389#397C2312yes—
390#397C2314yes—
391#397C2314yes—
392#397C2314yes—
393#397C2312yes—
394#397C2314yes—
395#397C2312yes—
396#397C2314yes—
397#397C2312yes—
398#397C2314yes—
399#397C2314yes—
400#397C2314yes—
401#397C2312yes—
402#397C2312yes—
403#397C2314yes—
404#397C2312yes—
405#397C2314yes—
406#397C2314yes—
407#397C2314yes—
408#396C2314yes—
409#396C2314yes—
410#396C2314yes—
411#396C2314yes—
412#396C2314yes—
413#396C2314yes—
414#396C2314yes—
415#395C2314yes—
416#395C2314yes—
417#395C2314yes—
418#395C2314yes—
419#395C2314yes—
420#395C2314yes—
421#395C2314yes—
422#395C2314yes—
423#394C2314yes—
424#394C2314yes—
425#394C2314yes—
426#394C2314yes—
427#394C2314yes—
428#394C2314yes—
429#394C2314yes—
430#394C2314yes—
431#394C2314yes—
432#394C2314yes—
433#394C2314yes—
434#394C2314yes—
435#394C2312yes—
436#394C2314yes—
437#394C2314yes—
438#394C2314yes—
439#394C2314yes—
440#394C2314yes—
441#394C2312yes—
442#394C2312yes—
443#394C2312yes—
444#394C2312yes—
445#394C2312yes—
446#394C2314yes—
447#394C2314yes—
448#393C2314yes—
449#393C2314yes—
450#393C2314yes—
451#393C2314yes—
452#393C2312yes—
453#393C2314yes—
454#393C2312yes—
455#393C2312yes—
456#393C2312yes—
457#393C2314yes—
458#392C2314yes—
459#392C2314yes—
460#392C2314yes—
461#392C2314yes—
462#392C2314yes—
463#392C2314yes—
464#392C2314yes—
465#391C2312yes—
466#391C2314yes—
467#391C2314yes—
468#391C2312yes—
469#391C2314yes—
470#391C2314yes—
471#391C2314yes—
472#391C2311yescharacteristic
473#391C2312yes—
474#391C2312yes—
475#391C2312yes—
476#391C2314yes—
477#391C2311yescharacteristic
478#391C2312yes—
479#391C2311yescharacteristic
480#391C2311yescharacteristic
481#390C2311yescharacteristic
482#390C2312yes—
483#390C2312yes—
484#390C2312yes—
485#390C2312yes—
486#390C2311yescharacteristic
487#390C2312yes—
488#390C2312yes—
489#390C2314yes—
490#390C2314yes—
491#390C2312yes—
492#390C2312yes—
493#390C2314yes—
494#390C2314yes—
495#390C2312yes—
496#390C2312yes—
497#390C2312yes—
498#390C2312yes—
499#390C2312yes—
500#390C2314yes—
501#390C2314yes—
502#389C2312yes—
503#389C2312yes—
504#389C2312yes—
505#389C2312yes—
506#389C2314yes—
507#389C2312yes—
508#389C2312yes—
509#389C2312yes—
510#389C2314yes—
511#389C2314yes—
512#389C2312yes—
513#389C2312yes—
514#389C2312yes—
515#389C2314yes—
516#389C2312yes—
517#389C2312yes—
518#389C2312yes—
519#389C2314yes—
520#389C2314yes—
521#389C2314yes—
522#389C2314yes—
523#389C2312yes—
524#389C2314yes—
525#389C2314yes—
526#389C2314yes—
527#389C2311yescharacteristic
528#389C2311yescharacteristic
529#389C2312yes—
530#389C2314yes—
531#389C2314yes—
532#389C2311yescharacteristic
533#389C2311yescharacteristic
534#388C2314yes—
535#388C2314yes—
536#388C2314yes—
537#388C2314yes—
538#388C2314yes—
539#388C2314yes—
540#388C2314yes—
541#388C2314yes—
542#388C2314yes—
543#388C2314yes—
544#388C2312yes—
545#388C2314yes—
546#388C2314yes—
547#388C2314yes—
548#388C2314yes—
549#388C2314yes—
550#388C2314yes—
551#388C2314yes—
552#388C2314yes—
553#388C2312yes—
554#388C2312yes—
555#388C2314yes—
556#388C2314yes—
557#388C2312yes—
558#388C2312yes—
559#388C2312yes—
560#387C2314yes—
561#387C2314yes—
562#387C2314yes—
563#387C2314yes—
564#387C2314yes—
565#387C2314yes—
566#387C2314yes—
567#387C2314yes—
568#387C2312yes—
569#387C2312yes—
570#387C2314yes—
571#387C2314yes—
572#387C2314yes—
573#387C2314yes—
574#387C2312yes—
575#387C2314yes—
576#387C2314yes—
577#387C2314yes—
578#387C2314yes—
579#387C2312yes—
580#387C2314yes—
581#387C2312yes—
582#387C2312yes—
583#387C2312yes—
584#387C2314yes—
585#387C2312yes—
586#387C2312yes—
587#387C2312yes—
588#386C2312yes—
589#386C2314yes—
590#386C2314yes—
591#386C2314yes—
592#386C2314yes—
593#386C2314yes—
594#386C2312yes—
595#386C2314yes—
596#386C2314yes—
597#386C2314yes—
598#386C2314yes—
599#386C2314yes—
600#386C2314yes—
601#386C2314yes—
602#386C2314yes—
603#386C2314yes—
604#386C2314yes—
605#386C2314yes—
606#386C2314yes—
607#386C2314yes—
608#386C2312yes—
609#386C2314yes—
610#386C2314yes—
611#386C2314yes—
612#386C2314yes—
613#386C2314yes—
614#386C2314yes—
615#386C2314yes—
616#386C2314yes—
617#386C2314yes—
618#386C2312yes—
619#386C2312yes—
620#385C2314yes—
621#385C2312yes—
622#385C2314yes—
623#385C2314yes—
624#385C2314yes—
625#385C2314yes—
626#385C2314yes—
627#385C2314yes—
628#385C2314yes—
629#385C2312yes—
630#385C2314yes—
631#385C2314yes—
632#385C2314yes—
633#385C2314yes—
634#385C2314yes—
635#385C2314yes—
636#385C2314yes—
637#385C2314yes—
638#385C2314yes—
639#385C2312yes—
640#385C2314yes—
641#385C2314yes—
642#385C2312yes—
643#385C2314yes—
644#385C2314yes—
645#385C2314yes—
646#385C2312yes—
647#384C2311yescharacteristic
648#384C2311yescharacteristic
649#384C2311yescharacteristic
650#384C2312yes—
651#384C2312yes—
652#383C2314yes—
653#382C2312yes—
654#382C2312yes—
655#382C2312yes—
656#382C2312yes—
657#382C2312yes—
658#382C2312yes—
659#381C2314yes—
660#381C2314yes—
661#381C2314yes—
662#381C2314yes—
663#381C2312yes—
664#380C2312yes—
665#380C2312yes—
666#380C2314yes—
667#380C2314yes—
668#380C2314yes—
669#380C2314yes—
670#380C2314yes—
671#380C2312yes—
672#380C2312yes—
673#380C2314yes—
674#380C2314yes—
675#380C2312yes—
676#380C2312yes—
677#380C2312yes—
678#380C2312yes—
679#380C2314yes—
680#380C2314yes—
681C4×C4⋊C4C2312yes—
682C4×C4⋊C4C2312yes—
683C4×C4⋊C4C2311yescharacteristic
684C4×C4⋊C4C2311yescharacteristic
685C4×C4⋊C4C2311yescharacteristic
686C4×C4⋊C4C2314yes—
687C4×C4⋊C4C2311yescharacteristic
688C4×C4⋊C4C2312yes—
689C4×C4⋊C4C2314yes—
690C4×C4⋊C4C2312yes—
691C4×C4⋊C4C2312yes—
692C4×C4⋊C4C2312yes—
693C4×C4⋊C4C2311yescharacteristic
694C4×C4⋊C4C2312yes—
695C4×C4⋊C4C2312yes—
696C4×C4⋊C4C2312yes—
697C4×C22⋊C4C2314yes—
698C4×C22⋊C4C2314yes—
699C4×C22⋊C4C2314yes—
700C4×C22⋊C4C2314yes—
701C4×C22⋊C4C2314yes—
702C4×C22⋊C4C2312yes—
703C4×C22⋊C4C2314yes—
704C4×C22⋊C4C2314yes—
705C4×C22⋊C4C2312yes—
706C4×C22⋊C4C2314yes—
707C4×C22⋊C4C2312yes—
708C4×C22⋊C4C2312yes—
709C4×C22⋊C4C2312yes—
710C4×C22⋊C4C2312yes—
711C4×C22⋊C4C2312yes—
712C4×C22⋊C4C2312yes—
713C4×C22⋊C4C2312yes—
714#376C2312yes—
715#376C2312yes—
716C2×#95C2314yes—
717C2×#95C2314yes—
718C2×#95C2314yes—
719C43C2311yescharacteristic
720C2×#41—216no—
721C2×#41—28no—
722C2×#41—48no—
723C2×#41—48no—
724C2×#41—44no—
725C2×#41—48no—
726C2×#41—82no—
727C2×#41—84no—
728C2×#41—84no—
729C22×Q8C2411yescharacteristic
730C22×Q8C2411yescharacteristic
731C22×Q8C2412yes—
732C22×Q8C2412yes—
733C22×Q8C2414yes—
734C22×Q8C2412yes—
735C22×D4C2412yes—
736C22×D4C2412yes—
737C22×D4C2414yes—
738C22×D4C2414yes—
739C22×D4C2412yes—
740C22×D4C2411yescharacteristic
741C22×D4C2411yescharacteristic
742C22×D4C2414yes—
743C22×D4C2414yes—
744C22×D4C2412yes—
745C22×D4C2412yes—
746C22×D4C2414yes—
747C22×D4C2414yes—
748C22×D4C2414yes—
749C22×D4C2414yes—
750C22×D4C2411yescharacteristic
751C23×C4C2412yes—
752C23×C4C2412yes—
753C23×C4C2414yes—
754C23×C4C2412yes—
755C23×C4C2414yes—
756C23×C4C2414yes—
757C23×C4C2414yes—
758C23×C4C2412yes—
759C23×C4C2412yes—
760C23×C4C2414yes—
761C23×C4C2414yes—
762C23×C4C2412yes—
763C23×C4C2414yes—
764C23×C4C2412yes—
765C23×C4C2414yes—
766C4⋊Q8—44no—
767C4⋊Q8—42no—
768C4⋊Q8—42no—
769C4⋊Q8—48no—
770C4⋊Q8#4118yescomplemented
771#127—28no—
772#127—24no—
773#127—24no—
774#127—48no—
775#125—28no—
776#125—44no—
777#124—48no—
778#124—48no—
779#124—82no—
780#124—82no—
781#124—84no—
782#123—28no—
783#123—216no—
784#123—216no—
785#123—48no—
786#123—48no—
787#123—48no—
788#123—48no—
789#123—48no—
790#123—48no—
791#123—84no—
792#123—84no—
793C22⋊Q8—216no—
794C22⋊Q8—216no—
795C22⋊Q8—28no—
796C22⋊Q8—48no—
797C22⋊Q8—44no—
798C22⋊Q8—48no—
799C22⋊Q8—82no—
800C22⋊Q8—84no—
801#121—28no—
802#121—28no—
803#121—216no—
804#121—28no—
805#121—28no—
806#121—48no—
807#121—48no—
808#121—48no—
809#121—48no—
810#121—48no—
811#121—44no—
812#121—44no—
813#121—48no—
814#121—44no—
815#121—82no—
816#121—84no—
817#121—82no—
818C4×Q8—24no—
819C4×Q8—24no—
820C4×Q8—44no—
821C4×Q8—82no—
822C4×D4—28no—
823C4×D4—24no—
824C4×D4—28no—
825C4×D4—28no—
826C4×D4—28no—
827C4×D4—24no—
828C4×D4—28no—
829C4×D4—24no—
830C4×D4—44no—
831C4×D4—44no—
832C4×D4—44no—
833C4×D4—42no—
834C4×D4—42no—
835C4×D4—48no—
836C4×D4—48no—
837C4×D4—48no—
838C4×D4—48no—
839C4×D4—84no—
840C4×D4—84no—
841C4×D4—82no—
842#117—44no—
843#117—44no—
844#117—44no—
845#117—84no—
846C2×C4⋊C4—28no—
847C2×C4⋊C4—28no—
848C2×C4⋊C4—28no—
849C2×C4⋊C4—44no—
850C2×C4⋊C4—48no—
851C2×C4⋊C4—48no—
852C2×C4⋊C4—82no—
853C2×C4⋊C4C2411yescharacteristic
854C2×C4⋊C4C2412yes—
855C2×C4⋊C4C2411yescharacteristic
856C2×C4⋊C4C2412yes—
857C2×C4⋊C4C2412yes—
858C2×C4⋊C4C2414yes—
859C2×C4⋊C4C2414yes—
860C2×C4⋊C4C2414yes—
861C2×C4⋊C4C2414yes—
862C2×C4⋊C4C2412yes—
863C2×C4⋊C4C2412yes—
864C2×C4⋊C4C2412yes—
865C2×C4⋊C4C2411yescharacteristic
866C2×C4⋊C4C2411yescharacteristic
867C2×C4⋊C4C2412yes—
868C2×C4⋊C4C2412yes—
869C2×C4⋊C4C2412yes—
870C2×C4⋊C4C2411yescharacteristic
871C2×C4⋊C4C2414yes—
872C2×C4⋊C4C2412yes—
873C2×C4⋊C4C2414yes—
874C2×C4⋊C4C2411yescharacteristic
875C2×C4⋊C4C2412yes—
876C2×C4⋊C4C2414yes—
877C2×C4⋊C4C2414yes—
878C2×C4⋊C4C2414yes—
879C2×C4⋊C4C2414yes—
880C2×C4⋊C4C2414yes—
881C2×C4⋊C4C2414yes—
882C2×C4⋊C4C2411yescharacteristic
883C2×C4⋊C4C2412yes—
884C2×C4⋊C4C2414yes—
885C2×C4⋊C4C2414yes—
886C2×C4⋊C4C2412yes—
887C2×C4⋊C4C2412yes—
888C2×C4⋊C4C2412yes—
889C2×C4⋊C4C2414yes—
890C2×C4⋊C4C2414yes—
891C2×C4⋊C4C2411yescharacteristic
892C2×C4⋊C4C2414yes—
893C2×C4⋊C4C2412yes—
894C2×C4⋊C4C2414yes—
895C2×C4⋊C4C2412yes—
896C2×C4⋊C4C2414yes—
897C2×C4⋊C4C2411yescharacteristic
898C2×C4⋊C4C2411yescharacteristic
899C2×C4⋊C4C2414yes—
900C2×C4⋊C4C2414yes—
901C2×C4⋊C4C2412yes—
902C2×C4⋊C4C2414yes—
903C2×C4⋊C4C2412yes—
904C2×C4⋊C4C2414yes—
905C2×C4⋊C4C2411yescharacteristic
906C2×C4⋊C4C2412yes—
907C2×C4⋊C4C2412yes—
908C2×C4⋊C4C2412yes—
909C2×C22⋊C4C2414yes—
910C2×C22⋊C4C2412yes—
911C2×C22⋊C4C2412yes—
912C2×C22⋊C4C2414yes—
913C2×C22⋊C4C2414yes—
914C2×C22⋊C4C2414yes—
915C2×C22⋊C4C2414yes—
916C2×C22⋊C4C2412yes—
917C2×C22⋊C4C2414yes—
918C2×C22⋊C4C2412yes—
919C2×C22⋊C4C2412yes—
920C2×C22⋊C4C2414yes—
921C2×C22⋊C4C2412yes—
922C2×C22⋊C4C2412yes—
923C2×C22⋊C4C2412yes—
924C2×C22⋊C4C2412yes—
925C2×C22⋊C4C2412yes—
926C2×C22⋊C4C2414yes—
927C2×C22⋊C4C2414yes—
928C2×C22⋊C4C2412yes—
929C2×C22⋊C4C2414yes—
930C2×C22⋊C4C2412yes—
931C2×C22⋊C4C2412yes—
932C2×C22⋊C4C2414yes—
933C2×C22⋊C4C2412yes—
934C2×C22⋊C4C2414yes—
935C2×C22⋊C4C2414yes—
936C2×C22⋊C4C2414yes—
937C2×C22⋊C4C2414yes—
938C2×C22⋊C4C2414yes—
939C2×C22⋊C4C2414yes—
940C2×C22⋊C4C2414yes—
941C2×C22⋊C4C2414yes—
942C2×C22⋊C4C2412yes—
943C2×C22⋊C4C2414yes—
944C2×C22⋊C4C2412yes—
945C2×C22⋊C4C2412yes—
946C2×C22⋊C4C2414yes—
947C2×C22⋊C4C2414yes—
948C2×C22⋊C4C2414yes—
949C2×C22⋊C4C2414yes—
950C2×C22⋊C4C2412yes—
951C2×C22⋊C4C2412yes—
952C2×C22⋊C4C2414yes—
953C2×C22⋊C4C2414yes—
954C2×C22⋊C4C2414yes—
955C2×C22⋊C4C2414yes—
956C2×C22⋊C4C2414yes—
957C2×C22⋊C4C2412yes—
958C2×C22⋊C4C2412yes—
959C2×C22⋊C4C2414yes—
960C2×C22⋊C4C2412yes—
961C2×C22⋊C4C2412yes—
962C2×C22⋊C4C2414yes—
963C2×C22⋊C4C2414yes—
964C2×C42—44no—
965C2×C42—82no—
966C2×C42C2412yes—
967C2×C42C2412yes—
968C2×C42C2411yescharacteristic
969C2×C42C2411yescharacteristic
970C2×C42C2412yes—
971C2×C42C2412yes—
972C2×C42C2414yes—
973C2×C42C2414yes—
974C2×C42C2414yes—
975C2×C42C2414yes—
976C2×C42C2411yescharacteristic
977C2×C42C2412yes—
978C2×C42C2414yes—
979C2×C42C2414yes—
980C2×C42C2412yes—
981C2×C42C2412yes—
982C2×C42C2412yes—
983C2×C42C2412yes—
984C2×C42C2411yescharacteristic
985C2×C42C2411yescharacteristic
986C2×C42C2411yescharacteristic
987C2×C42C2411yescharacteristic
988#95C2412yes—
989#95C2414yes—
990#95C2412yes—
991#95C2414yes—
992#95C2414yes—
993#95C2414yes—
994#95C2414yes—
995#95C2414yes—
996#95C2414yes—
997#95C2414yes—
998#95C2414yes—
999#95C2412yes—
1000#95C2412yes—
1001#95C2412yes—
1002#95C2412yes—
1003#95C2412yes—
1004#95C2412yes—
1005#95C2412yes—
1006#95C2412yes—
1007#95C2412yes—
1008#95C2412yes—
1009#95C2412yes—
1010#95C2414yes—
1011#95C2414yes—
1012#95C2414yes—
1013#95C2414yes—
1014#95C2414yes—
1015#95C2412yes—
1016#95C2412yes—
1017#95C2412yes—
1018#95C2412yes—
1019#95C2414yes—
1020#95C2414yes—
1021#95C2412yes—
1022#95C2412yes—
1023#95C2412yes—
1024#95C2412yes—
1025#95C2412yes—
1026#95C2412yes—
1027#95C2412yes—
1028#95C2412yes—
1029#95C2414yes—
1030#95C2414yes—
1031#95C2414yes—
1032#95C2414yes—
1033#95C2412yes—
1034#95C2414yes—
1035#95C2412yes—
1036#95C2414yes—
1037#95C2412yes—
1038#95C2412yes—
1039#95C2414yes—
1040#95C2414yes—
1041#95C2414yes—
1042#95C2414yes—
1043#95C2414yes—
1044#95C2414yes—
1045#95C2414yes—
1046#95C2414yes—
1047C24C2514yes—
1048C24C2512yes—
1049C24C2512yes—
1050C24C2512yes—
1051#41—816no—
1052#41—832no—
1053#41—832no—
1054C2×Q8—22no—
1055C2×Q8—24no—
1056C2×Q8—22no—
1057C2×Q8—42no—
1058C2×Q8—41no—
1059C2×Q8—41no—
1060C2×Q8—42no—
1061C2×Q8—42no—
1062C2×Q8—44no—
1063C2×Q8—41no—
1064C2×Q8—44no—
1065C2×Q8—41no—
1066C2×Q8—42no—
1067C2×Q8—44no—
1068C2×Q8—42no—
1069C2×Q8—42no—
1070C2×Q8—42no—
1071C2×Q8C2×#4118yes—
1072C2×D4—24no—
1073C2×D4—28no—
1074C2×D4—28no—
1075C2×D4—28no—
1076C2×D4—24no—
1077C2×D4—28no—
1078C2×D4—28no—
1079C2×D4—28no—
1080C2×D4—28no—
1081C2×D4—22no—
1082C2×D4—24no—
1083C2×D4—24no—
1084C2×D4—28no—
1085C2×D4—28no—
1086C2×D4—24no—
1087C2×D4—22no—
1088C2×D4—22no—
1089C2×D4—24no—
1090C2×D4—24no—
1091C2×D4—24no—
1092C2×D4—24no—
1093C2×D4—41no—
1094C2×D4—44no—
1095C2×D4—42no—
1096C2×D4—41no—
1097C2×D4—42no—
1098C2×D4—44no—
1099C2×D4—41no—
1100C2×D4—42no—
1101C2×D4—42no—
1102C2×D4—44no—
1103C2×D4—44no—
1104C2×D4—44no—
1105C2×D4—44no—
1106C2×D4—44no—
1107C2×D4—42no—
1108C2×D4—44no—
1109C2×D4—44no—
1110C2×D4—44no—
1111C2×D4—41no—
1112C2×D4—42no—
1113C2×D4—44no—
1114C2×D4—44no—
1115C2×D4—44no—
1116C2×D4—44no—
1117C2×D4—44no—
1118C2×D4H(5,𝔽2)14yes—
1119C2×D4H(5,𝔽2)14yes—
1120C22×C4—24no—
1121C22×C4—28no—
1122C22×C4—24no—
1123C22×C4—28no—
1124C22×C4—28no—
1125C22×C4—24no—
1126C22×C4—24no—
1127C22×C4—24no—
1128C22×C4—28no—
1129C22×C4—24no—
1130C22×C4—24no—
1131C22×C4—24no—
1132C22×C4—24no—
1133C22×C4—24no—
1134C22×C4—28no—
1135C22×C4—28no—
1136C22×C4—28no—
1137C22×C4—24no—
1138C22×C4—42no—
1139C22×C4—42no—
1140C22×C4—42no—
1141C22×C4—44no—
1142C22×C4—42no—
1143C22×C4—42no—
1144C22×C4—42no—
1145C22×C4—42no—
1146C22×C4—44no—
1147C22×C4—44no—
1148C22×C4—44no—
1149C22×C4—44no—
1150C22×C4—44no—
1151C22×C4—44no—
1152C22×C4—44no—
1153C22×C4—44no—
1154C22×C4—42no—
1155C22×C4—44no—
1156C22×C4—44no—
1157C22×C4—44no—
1158C22×C4—42no—
1159C22×C4—44no—
1160C22×C4—44no—
1161C22×C4—42no—
1162C22×C4—44no—
1163C22×C4—44no—
1164C22×C4—44no—
1165C22×C4C2512yes—
1166C22×C4C2512yes—
1167C22×C4C2512yes—
1168C22×C4C2512yes—
1169C22×C4C2512yes—
1170C22×C4C2512yes—
1171C22×C4C2512yes—
1172C22×C4C2512yes—
1173C22×C4C2514yes—
1174C22×C4C2512yes—
1175C22×C4C2511yescharacteristic
1176C22×C4C2512yes—
1177C22×C4C2512yes—
1178C22×C4C2514yes—
1179C22×C4C2514yes—
1180C22×C4C2514yes—
1181C22×C4C2512yes—
1182C22×C4C2512yes—
1183C22×C4C2511yescharacteristic
1184C22×C4C2511yescharacteristic
1185C22×C4C2514yes—
1186C22×C4C2511yescharacteristic
1187C22×C4C2511yescharacteristic
1188C22×C4C2511yescharacteristic
1189C22×C4C2511yescharacteristic
1190C4⋊C4—24no—
1191C4⋊C4—22no—
1192C4⋊C4—28no—
1193C4⋊C4—28no—
1194C4⋊C4—28no—
1195C4⋊C4—24no—
1196C4⋊C4—22no—
1197C4⋊C4—24no—
1198C4⋊C4—28no—
1199C4⋊C4—22no—
1200C4⋊C4—24no—
1201C4⋊C4—24no—
1202C4⋊C4—28no—
1203C4⋊C4—24no—
1204C4⋊C4—24no—
1205C4⋊C4—24no—
1206C4⋊C4—24no—
1207C4⋊C4—22no—
1208C4⋊C4—22no—
1209C4⋊C4—24no—
1210C4⋊C4—44no—
1211C4⋊C4—44no—
1212C4⋊C4—44no—
1213C4⋊C4—44no—
1214C4⋊C4—44no—
1215C4⋊C4—44no—
1216C4⋊C4—41no—
1217C4⋊C4—42no—
1218C4⋊C4—44no—
1219C4⋊C4—41no—
1220C4⋊C4—42no—
1221C4⋊C4—41no—
1222C4⋊C4—42no—
1223C4⋊C4—42no—
1224C4⋊C4—42no—
1225C4⋊C4—44no—
1226C4⋊C4—44no—
1227C4⋊C4—42no—
1228C4⋊C4—44no—
1229C4⋊C4—41no—
1230C4⋊C4—44no—
1231C4⋊C4—44no—
1232C4⋊C4—42no—
1233C4⋊C4—44no—
1234C4⋊C4—42no—
1235C4⋊C4—44no—
1236C4⋊C4—44no—
1237C4⋊C4—44no—
1238C4⋊C4—41no—
1239C4⋊C4—41no—
1240C4⋊C4—42no—
1241C4⋊C4—42no—
1242C4⋊C4—44no—
1243C4⋊C4—44no—
1244C4⋊C4C2×#4118yes—
1245C4⋊C4C2×#4118yes—
1246C22⋊C4—28no—
1247C22⋊C4—28no—
1248C22⋊C4—24no—
1249C22⋊C4—24no—
1250C22⋊C4—24no—
1251C22⋊C4—28no—
1252C22⋊C4—28no—
1253C22⋊C4—24no—
1254C22⋊C4—28no—
1255C22⋊C4—24no—
1256C22⋊C4—24no—
1257C22⋊C4—24no—
1258C22⋊C4—28no—
1259C22⋊C4—28no—
1260C22⋊C4—28no—
1261C22⋊C4—28no—
1262C22⋊C4—24no—
1263C22⋊C4—24no—
1264C22⋊C4—24no—
1265C22⋊C4—44no—
1266C22⋊C4—42no—
1267C22⋊C4—42no—
1268C22⋊C4—44no—
1269C22⋊C4—44no—
1270C22⋊C4—42no—
1271C22⋊C4—42no—
1272C22⋊C4—42no—
1273C22⋊C4—44no—
1274C22⋊C4—42no—
1275C22⋊C4—44no—
1276C22⋊C4—44no—
1277C22⋊C4—44no—
1278C22⋊C4—44no—
1279C22⋊C4—44no—
1280C22⋊C4—42no—
1281C22⋊C4—44no—
1282C22⋊C4—44no—
1283C22⋊C4—42no—
1284C22⋊C4—42no—
1285C22⋊C4—44no—
1286C22⋊C4—44no—
1287C22⋊C4—44no—
1288C22⋊C4—44no—
1289C22⋊C4—44no—
1290C22⋊C4—42no—
1291C22⋊C4—44no—
1292C22⋊C4—44no—
1293C22⋊C4—42no—
1294C22⋊C4—42no—
1295C22⋊C4—44no—
1296C22⋊C4—44no—
1297C22⋊C4—44no—
1298C22⋊C4—44no—
1299C22⋊C4—44no—
1300C22⋊C4—42no—
1301C42—24no—
1302C42—24no—
1303C42—24no—
1304C42—22no—
1305C42—22no—
1306C42—24no—
1307C42—42no—
1308C42—42no—
1309C42—41no—
1310C42—42no—
1311C42—42no—
1312C42—42no—
1313C42—41no—
1314C42—44no—
1315C42—44no—
1316C42—44no—
1317C42—44no—
1318C42—44no—
1319C42—41no—
1320C42—44no—
1321C42C2×#4114yes—
1322C422−1+414yes—
1323C23—22no—
1324C23—22no—
1325C23—22no—
1326C23—22no—
1327C23—22no—
1328C23—22no—
1329C23—22no—
1330C23—22no—
1331C23—22no—
1332C23—22no—
1333C23—22no—
1334C23—22no—
1335C23—24no—
1336C23—22no—
1337C23—24no—
1338C23—22no—
1339C23—24no—
1340C23—22no—
1341C23—22no—
1342C23—24no—
1343C23—22no—
1344C23—24no—
1345C23—24no—
1346C23—22no—
1347C23—24no—
1348C23—22no—
1349C23C2×H(5,𝔽2)14yes—
1350C23C2×H(5,𝔽2)14yes—
1351C23C2611yescharacteristic
1352Q8—48no—
1353Q8—44no—
1354Q8—82no—
1355Q8—84no—
1356Q8—88no—
1357Q8—162no—
1358D4—28no—
1359D4—44no—
1360D4—48no—
1361D4—416no—
1362D4—48no—
1363D4—416no—
1364D4—48no—
1365D4—84no—
1366D4—82no—
1367D4—84no—
1368D4—88no—
1369D4—88no—
1370D4—88no—
1371D4—88no—
1372D4—88no—
1373D4—164no—
1374C2×C4—21no—
1375C2×C4—21no—
1376C2×C4—21no—
1377C2×C4—24no—
1378C2×C4—21no—
1379C2×C4—21no—
1380C2×C4—21no—
1381C2×C4—24no—
1382C2×C4—21no—
1383C2×C4—21no—
1384C2×C4—21no—
1385C2×C4—21no—
1386C2×C4—22no—
1387C2×C4—22no—
1388C2×C4—22no—
1389C2×C4—22no—
1390C2×C4—22no—
1391C2×C4—24no—
1392C2×C4—22no—
1393C2×C4—22no—
1394C2×C4—22no—
1395C2×C4—22no—
1396C2×C4—21no—
1397C2×C4—22no—
1398C2×C4—22no—
1399C2×C4—22no—
1400C2×C4—22no—
1401C2×C4—24no—
1402C2×C4—24no—
1403C2×C4—24no—
1404C2×C4—22no—
1405C2×C4—24no—
1406C2×C4—24no—
1407C2×C4—24no—
1408C2×C4—22no—
1409C2×C4—22no—
1410C2×C4—22no—
1411C2×C4—22no—
1412C2×C4—22no—
1413C2×C4—22no—
1414C2×C4—22no—
1415C2×C4—22no—
1416C2×C4—22no—
1417C2×C4—22no—
1418C2×C4—22no—
1419C2×C4—22no—
1420C2×C4—22no—
1421C2×C4—22no—
1422C2×C4—22no—
1423C2×C4—21no—
1424C2×C4—24no—
1425C2×C4—24no—
1426C2×C4—22no—
1427C2×C4—22no—
1428C2×C4—22no—
1429C2×C4—24no—
1430C2×C4—22no—
1431C2×C4—24no—
1432C2×C4—22no—
1433C2×C4—21no—
1434C2×C4—22no—
1435C2×C4—22no—
1436C2×C4—22no—
1437C2×C4—24no—
1438C2×C4—22no—
1439C2×C4—22no—
1440C2×C4—416no—
1441C2×C4—48no—
1442C2×C4—48no—
1443C2×C4—48no—
1444C2×C4—48no—
1445C2×C4—48no—
1446C2×C4—88no—
1447C2×C4—84no—
1448C2×C4—88no—
1449C2×C4—88no—
1450C2×C4—88no—
1451C2×C4—88no—
1452C2×C4—84no—
1453C2×C4—88no—
1454C2×C4—164no—
1455C2×C4C22×#4112yes—
1456C2×C4C22×#4112yes—
1457C2×C4C22×#4118yes—
1458C2×C4C22×#4112yes—
1459C2×C4C2×H(5,𝔽2)12yes—
1460C2×C4C2×H(5,𝔽2)12yes—
1461C2×C4C2×2−1+412yes—
1462C2×C4C2×2−1+412yes—
1463C2×C4C2×2−1+412yes—
1464C22—24no—
1465C22—24no—
1466C22—24no—
1467C22—24no—
1468C22—24no—
1469C22—24no—
1470C22—42no—
1471C22—42no—
1472C22—42no—
1473C22—42no—
1474C22—42no—
1475C22—42no—
1476C22—42no—
1477C22—42no—
1478C22—42no—
1479C22—44no—
1480C22—42no—
1481C22—44no—
1482C22—44no—
1483C22—42no—
1484C22—44no—
1485C22—42no—
1486C22—44no—
1487C22—42no—
1488C22—44no—
1489C22—42no—
1490C22—42no—
1491C22—44no—
1492C22C23×#4111yescharacteristic
1493C22C22×H(5,𝔽2)11yescharacteristic
1494C22C22×H(5,𝔽2)11yescharacteristic
1495C22C22×2−1+411yescharacteristic
1496C22H(7,𝔽2)11yescharacteristic
1497C22H(7,𝔽2)11yescharacteristic
1498C222−1+611yescharacteristic
1499C4—28no—
1500C4—22no—
1501C4—22no—
1502C4—22no—
1503C4—22no—
1504C4—22no—
1505C4—44no—
1506C4—42no—
1507C4—42no—
1508C4—42no—
1509C4—42no—
1510C4—42no—
1511C4—44no—
1512C4—41no—
1513C4—42no—
1514C4—42no—
1515C4—42no—
1516C4—42no—
1517C4—42no—
1518C4—42no—
1519C4—42no—
1520C4—44no—
1521C4—44no—
1522C4—42no—
1523C4#352214yes—
1524C2—44no—
1525C2—44no—
1526C2—82no—
1527C2—84no—
1528C2C2×#352211yescharacteristic
1529C2#6285111yescharacteristic
1530C2#6288111yescharacteristic
1531C2#6289211yescharacteristic
1532C2#6291511yescharacteristic
1533C2#6298311yescharacteristic
1534C2#6304911yescharacteristic
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. #59815C2semidirect
2. #59112C2semidirect
3. #52273C2semidirect
4. #49490C2semidirect
5. #48669C2semidirect
6. #48639C2semidirect
7. #47176C2semidirect
8. #46090C2semidirect
9. #45271C2semidirect
10. #45072C2semidirect
11. #44930C2semidirect
12. #44888C2semidirect
13. #42758C2semidirect
14. #42515C2semidirect
15. #40750C2semidirect
16. #40171C2semidirect
17. #39628C2semidirect
18. #39621C2semidirect
19. #38762C2semidirect
20. #38425C2semidirect
21. #38101C2semidirect
22. #37764C2semidirect
23. #37156C2semidirect
24. #36415C2semidirect
25. #35905C2semidirect
26. #35571C2semidirect
27. #35197C2semidirect
28. #34460C2semidirect
29. #34332C2semidirect
770. C4⋊Q8#41semidirect

Maximal subgroups

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

subgroupindex
#598152
#591122
#522732
#494902
#486692
#486392
#471762
#460902
#452712
#450722
#449302
#448882
#427582
#425152
#407502
#401712
#396282
#396212
#387622
#384252
#381012
#377642
#371562
#364152
#359052
#355712
#351972
#344602
#343322