Finite Group Databasebeta

← #8701609

Subgroups — #8701609

Order 512.

3959 conjugacy classes of subgroups.

The subgroup lattice has 1330 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59866C212yesmaximal, complemented
2#59461C212yesmaximal
3#59445C212yesmaximal, complemented
4#59437C212yesmaximal
5#58698C214yesmaximal, complemented
6#55995C214yesmaximal, complemented
7#55884C214yesmaximal, complemented
8#52305C211yesmaximal, characteristic, complemented
9#51369C214yesmaximal, complemented
10#49048C214yesmaximal, complemented
11#48961C214yesmaximal, complemented
12#46022C211yesmaximal, characteristic, complemented
13#46007C211yesmaximal, characteristic, complemented
14#46006C211yesmaximal, characteristic, complemented
15#45221C212yesmaximal
16#45154C212yesmaximal, complemented
17#45086C212yesmaximal
18#42850C212yesmaximal, complemented
19#42639C212yesmaximal
20#42553C212yesmaximal, complemented
21#40143C212yesmaximal, complemented
22#39655C212yesmaximal, complemented
23#39025C212yesmaximal
24#37212C212yesmaximal, complemented
25#37168C212yesmaximal, complemented
26#37135C212yesmaximal, complemented
27#36454C211yesmaximal, characteristic
28#36454C211yesmaximal, characteristic
29#36290C211yesmaximal, characteristic
30#2863C2212yes—
31#2862C2211yescharacteristic
32#2862C2211yescharacteristic
33#2859C2211yescharacteristic
34#2855C2212yes—
35#2855C2212yes—
36#2851C2212yes—
37#2845C2212yes—
38#2844C2212yes—
39#2839C2214yes—
40#2839C2214yes—
41#2835C2214yes—
42#2822C2212yes—
43#2810C2214yes—
44#2810C2211yescharacteristic
45#2809C2212yes—
46#2807C2214yes—
47#2806C2212yes—
48#2806C2212yes—
49#2805C2212yes—
50#2805C2212yes—
51#2805C2214yes—
52#2802C2214yes—
53#2802C2214yes—
54#2794C2214yes—
55#2794C2214yes—
56#2792C2214yes—
57#2791C2214yes—
58#2791C2214yes—
59#2791C2214yes—
60#2789C2214yes—
61#2787C2214yes—
62#2787C2214yes—
63#2787C2214yes—
64#2774C2214yes—
65#2774C2214yes—
66#2774C2214yes—
67#2770C2214yes—
68#2770C2214yes—
69#2770C2214yes—
70#2769C2214yes—
71#2768C2214yes—
72#2767C2212yes—
73#2767C2212yes—
74#2767C2212yes—
75#2767C2214yes—
76#2766C2214yes—
77#2766C2214yes—
78#2766C2214yes—
79#2762C2214yes—
80#2762C2214yes—
81#2758C2214yes—
82#2755C2214yes—
83#2755C2214yes—
84#2755C2214yes—
85#2747C2214yes—
86#2747C2214yes—
87#2747C2214yes—
88#2745C2214yes—
89#2744C2214yes—
90#2742C2214yes—
91#2739C2214yes—
92#2738C2214yes—
93#2734C2212yes—
94#2729C2214yes—
95#2726C2211yescharacteristic
96#2726C2211yescharacteristic
97#2726C2211yescharacteristic
98#2720C2214yes—
99#2720C2214yes—
100#2719C2214yes—
101#2719C2212yes—
102#2719C2212yes—
103#2719C2212yes—
104#2713C2214yes—
105#2713C2214yes—
106#2690C2214yes—
107#2666C2214yes—
108#2655C2214yes—
109#2655C2214yes—
110#2655C2214yes—
111#2652C2214yes—
112#2652C2214yes—
113#2645C2212yes—
114#2634C2214yes—
115#2634C2214yes—
116#2627C2214yes—
117#2590C2214yes—
118#2589C2214yes—
119#2588C2214yes—
120#2585C2214yes—
121#2585C2214yes—
122#2583C2214yes—
123#2577C2214yes—
124#2577C2214yes—
125#2575C2214yes—
126#2575C2214yes—
127#2571C2211yescharacteristic
128#2570C2214yes—
129#2570C2212yes—
130#2569C2214yes—
131#2569C2214yes—
132#2567C2212yes—
133#2567C2212yes—
134#2565C2212yes—
135#2565C2212yes—
136#2556C2214yes—
137#2552C2212yes—
138#2552C2211yescharacteristic
139#2551C2212yes—
140#2550C2212yes—
141#2549C2214yes—
142#2547C2211yescharacteristic
143#2547C2212yes—
144#2547C2212yes—
145#2547C2211yescharacteristic
146#2546C2212yes—
147#2546C2212yes—
148#2542C2211yescharacteristic
149#2542C2211yescharacteristic
150#2533C2214yes—
151#2530C2214yes—
152#2530C2214yes—
153#2528C2214yes—
154#2528C2214yes—
155#2524C2214yes—
156#2522C2214yes—
157#2522C2214yes—
158#2517C2214yes—
159#2517C2214yes—
160#2517C2214yes—
161#2514C2212yes—
162#2514C2212yes—
163#2511C2212yes—
164#2511C2212yes—
165#2511C2212yes—
166#2511C2212yes—
167#2511C2212yes—
168#2511C2212yes—
169#2509C2212yes—
170#2508C2214yes—
171#2508C2212yes—
172#2507C2212yes—
173#2506C2214yes—
174#2506C2212yes—
175#2505C2214yes—
176#2495C2214yes—
177#2494C2214yes—
178#2489C2212yes—
179#2489C2212yes—
180#2473C2214yes—
181#2473C2214yes—
182#2473C2214yes—
183#2465C2214yes—
184#2462C2214yes—
185#2462C2214yes—
186#2462C2214yes—
187#2454C2212yes—
188#2453C2212yes—
189#2453C2214yes—
190#2453C2212yes—
191#2452C2212yes—
192#2451C2212yes—
193#2451C2212yes—
194#2451C2212yes—
195#2451C2212yes—
196#2447C2212yes—
197#2447C2212yes—
198#2446C2212yes—
199#2446C2212yes—
200#2446C2212yes—
201#2446C2212yes—
202#2446C2212yes—
203#2446C2212yes—
204#2446C2212yes—
205#2446C2212yes—
206#2442C2214yes—
207#2442C2212yes—
208#2442C2212yes—
209#2440C2214yes—
210#2423C2214yes—
211#2421C2212yes—
212#2421C2212yes—
213#2402C2212yes—
214#2402C2212yes—
215#2402C2212yes—
216#2382C2212yes—
217#2382C2212yes—
218#2382C2212yes—
219#2370C2214yes—
220#2368C2214yes—
221#2367C2212yes—
222#2367C2212yes—
223#2367C2212yes—
224#2367C2212yes—
225#2365C2211yescharacteristic
226#2365C2211yescharacteristic
227#2365C2211yescharacteristic
228#2365C2211yescharacteristic
229#2356C2212yes—
230#2355C2212yes—
231#2355C2212yes—
232#2355C2212yes—
233Q8×C4⋊C4C2212yes—
234Q8×C4⋊C4C2212yes—
235#2349C2212yes—
236D4×C4⋊C4C2212yes—
237D4×C4⋊C4C2211yescharacteristic
238D4×C4⋊C4C2211yescharacteristic
239#2345C2214yes—
240#2336C2214yes—
241#2330C2212yes—
242#2327C2214yes—
243#2327C2212yes—
244#2326C2212yes—
245#2313C2214yes—
246C4×C4⋊Q8C2212yes—
247C4×C4⋊Q8C2212yes—
248C4×#125C2212yes—
249C4×#125C2212yes—
250C4×#125C2212yes—
251C4×#125C2211yescharacteristic
252C4×#125C2211yescharacteristic
253C4×#125C2211yescharacteristic
254C4×#124C2212yes—
255C4×C22⋊Q8C2212yes—
256C4×C22⋊Q8C2212yes—
257C2×#389C2212yes—
258C42×D4C2211yescharacteristic
259C2×C4⋊Q8C2312yes—
260C2×C4⋊Q8C2312yes—
261C2×C4⋊Q8C2314yes—
262C2×C4⋊Q8C2312yes—
263C2×C4⋊Q8C2311yescharacteristic
264C2×C4⋊Q8C2311yescharacteristic
265C2×C4⋊Q8C2311yescharacteristic
266C2×C4⋊Q8C2311yescharacteristic
267C2×#125C2312yes—
268C2×#125C2312yes—
269C2×#125C2311yescharacteristic
270C2×#125C2311yescharacteristic
271C2×#125C2311yescharacteristic
272C2×#125C2312yes—
273C2×#125C2312yes—
274C2×#125C2312yes—
275C2×#125C2312yes—
276C2×#125C2314yes—
277C2×#125C2314yes—
278C2×#124C2312yes—
279C2×#124C2312yes—
280C2×C22⋊Q8C2312yes—
281C2×C22⋊Q8C2312yes—
282C2×C22⋊Q8C2312yes—
283C2×C22⋊Q8C2312yes—
284C2×C22⋊Q8C2314yes—
285C2×C4×Q8C2312yes—
286C2×C4×Q8C2312yes—
287C2×C4×Q8C2312yes—
288C2×C4×Q8C2312yes—
289C2×C4×Q8C2312yes—
290C2×C4×Q8C2312yes—
291C2×C4×Q8C2314yes—
292C2×C4×Q8C2312yes—
293C2×C4×Q8C2312yes—
294C2×C4×D4C2311yescharacteristic
295C2×C4×D4C2312yes—
296C2×C4×D4C2312yes—
297C2×C4×D4C2311yescharacteristic
298C2×C4×D4C2311yescharacteristic
299C22×C4⋊C4C2312yes—
300C22×C4⋊C4C2314yes—
301C22×C4⋊C4C2312yes—
302C22×C42C2312yes—
303#401C2314yes—
304#401C2314yes—
305#401C2314yes—
306#400C2314yes—
307#400C2314yes—
308#400C2314yes—
309#400C2314yes—
310#400C2314yes—
311#400C2314yes—
312#400C2314yes—
313#400C2314yes—
314#400C2314yes—
315#400C2314yes—
316#400C2314yes—
317#400C2314yes—
318#400C2314yes—
319#400C2314yes—
320#400C2312yes—
321#400C2314yes—
322#400C2314yes—
323#400C2314yes—
324#400C2314yes—
325#400C2312yes—
326#400C2312yes—
327#400C2314yes—
328#400C2314yes—
329#400C2314yes—
330#400C2314yes—
331#400C2314yes—
332#400C2314yes—
333#400C2314yes—
334#400C2314yes—
335#400C2314yes—
336#400C2314yes—
337#400C2314yes—
338#400C2314yes—
339#400C2314yes—
340#400C2314yes—
341#400C2312yes—
342#400C2312yes—
343#400C2312yes—
344#400C2314yes—
345#400C2312yes—
346#400C2312yes—
347#400C2312yes—
348#400C2312yes—
349#400C2312yes—
350#400C2312yes—
351#399C2314yes—
352#399C2314yes—
353#399C2314yes—
354#398C2314yes—
355#398C2314yes—
356#398C2314yes—
357#398C2314yes—
358#398C2314yes—
359#398C2314yes—
360#398C2314yes—
361#398C2314yes—
362#398C2312yes—
363#398C2312yes—
364#398C2314yes—
365#398C2314yes—
366#398C2314yes—
367#398C2314yes—
368#398C2314yes—
369#398C2312yes—
370#398C2314yes—
371#398C2314yes—
372#398C2314yes—
373#398C2314yes—
374#398C2314yes—
375#398C2314yes—
376#398C2314yes—
377#398C2312yes—
378#398C2314yes—
379#398C2314yes—
380#398C2314yes—
381#398C2314yes—
382#398C2314yes—
383#398C2314yes—
384#398C2314yes—
385#398C2312yes—
386#398C2312yes—
387#398C2312yes—
388#398C2314yes—
389#398C2314yes—
390#398C2312yes—
391#398C2312yes—
392#398C2312yes—
393#398C2312yes—
394#398C2312yes—
395#398C2314yes—
396#398C2314yes—
397#397C2314yes—
398#397C2314yes—
399#397C2314yes—
400#397C2314yes—
401#397C2314yes—
402#397C2314yes—
403#397C2314yes—
404#397C2314yes—
405#397C2314yes—
406#397C2314yes—
407#396C2314yes—
408#396C2314yes—
409#395C2314yes—
410#395C2314yes—
411#395C2314yes—
412#395C2314yes—
413#395C2314yes—
414#395C2314yes—
415#395C2314yes—
416#395C2314yes—
417#395C2314yes—
418#395C2314yes—
419#395C2314yes—
420#393C2314yes—
421#391C2314yes—
422#391C2312yes—
423#391C2312yes—
424#391C2312yes—
425#391C2312yes—
426#391C2312yes—
427#391C2312yes—
428#391C2312yes—
429#391C2312yes—
430#391C2312yes—
431#391C2312yes—
432#391C2314yes—
433#391C2312yes—
434#391C2312yes—
435#391C2314yes—
436#391C2314yes—
437#391C2312yes—
438#391C2312yes—
439#391C2312yes—
440#391C2312yes—
441#391C2312yes—
442#391C2312yes—
443#391C2312yes—
444#391C2312yes—
445#391C2312yes—
446#391C2312yes—
447#391C2314yes—
448#391C2314yes—
449#390C2312yes—
450#390C2312yes—
451#389C2312yes—
452#389C2311yescharacteristic
453#389C2311yescharacteristic
454#389C2311yescharacteristic
455#389C2312yes—
456#389C2312yes—
457#389C2312yes—
458#389C2311yescharacteristic
459#389C2311yescharacteristic
460#389C2312yes—
461#389C2312yes—
462#389C2311yescharacteristic
463#389C2312yes—
464#389C2314yes—
465#389C2312yes—
466#389C2314yes—
467#389C2314yes—
468#389C2314yes—
469#389C2314yes—
470#389C2314yes—
471#389C2314yes—
472#389C2312yes—
473#389C2312yes—
474#389C2312yes—
475#389C2312yes—
476#389C2314yes—
477#389C2314yes—
478#389C2314yes—
479#389C2314yes—
480#389C2314yes—
481#389C2314yes—
482#389C2314yes—
483#389C2314yes—
484#389C2314yes—
485#389C2314yes—
486#389C2314yes—
487#389C2312yes—
488#389C2312yes—
489#389C2312yes—
490#389C2312yes—
491#389C2312yes—
492#389C2312yes—
493#389C2312yes—
494#389C2312yes—
495#389C2312yes—
496#389C2314yes—
497#389C2314yes—
498#389C2312yes—
499#389C2312yes—
500#389C2312yes—
501#389C2314yes—
502#389C2314yes—
503#389C2314yes—
504#389C2314yes—
505#388C2314yes—
506#388C2314yes—
507#388C2314yes—
508#388C2314yes—
509#388C2314yes—
510#388C2314yes—
511#388C2314yes—
512#388C2314yes—
513#388C2314yes—
514#388C2314yes—
515#388C2314yes—
516#388C2314yes—
517#387C2312yes—
518#387C2312yes—
519#387C2312yes—
520#387C2312yes—
521#387C2312yes—
522#387C2312yes—
523#387C2312yes—
524#387C2312yes—
525#387C2312yes—
526#387C2312yes—
527#387C2312yes—
528#387C2312yes—
529#387C2312yes—
530#387C2312yes—
531#387C2312yes—
532#387C2312yes—
533#387C2312yes—
534#387C2312yes—
535#387C2314yes—
536#387C2314yes—
537#387C2314yes—
538#387C2314yes—
539#387C2314yes—
540#387C2314yes—
541#387C2314yes—
542#387C2314yes—
543#387C2314yes—
544#387C2314yes—
545#387C2314yes—
546#387C2314yes—
547#387C2314yes—
548#387C2314yes—
549#387C2314yes—
550#387C2314yes—
551#387C2314yes—
552#387C2314yes—
553#387C2314yes—
554#387C2314yes—
555#387C2314yes—
556#387C2314yes—
557#387C2314yes—
558#387C2314yes—
559#387C2314yes—
560#387C2314yes—
561#387C2314yes—
562#387C2314yes—
563#387C2314yes—
564#387C2314yes—
565#387C2314yes—
566#387C2314yes—
567#387C2314yes—
568#387C2314yes—
569#387C2314yes—
570#387C2314yes—
571#387C2314yes—
572#387C2314yes—
573#387C2314yes—
574#387C2314yes—
575#387C2314yes—
576#387C2314yes—
577#387C2314yes—
578#387C2314yes—
579#387C2314yes—
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#387C2314yes—
594#387C2314yes—
595#387C2314yes—
596#387C2314yes—
597#387C2314yes—
598#387C2314yes—
599#387C2314yes—
600#387C2314yes—
601#387C2314yes—
602#385C2314yes—
603#385C2314yes—
604#385C2314yes—
605#385C2314yes—
606#385C2314yes—
607#385C2314yes—
608#385C2314yes—
609#385C2314yes—
610#385C2314yes—
611#385C2314yes—
612#385C2314yes—
613#385C2314yes—
614#385C2314yes—
615#385C2314yes—
616#385C2314yes—
617#385C2314yes—
618#384C2312yes—
619#384C2312yes—
620#384C2311yescharacteristic
621#384C2311yescharacteristic
622#384C2312yes—
623#384C2312yes—
624#384C2314yes—
625#384C2314yes—
626#383C2314yes—
627#383C2314yes—
628#383C2314yes—
629#383C2314yes—
630#382C2312yes—
631#382C2311yescharacteristic
632#382C2311yescharacteristic
633#382C2311yescharacteristic
634#382C2312yes—
635#382C2312yes—
636#382C2312yes—
637#382C2312yes—
638#382C2312yes—
639#382C2314yes—
640#382C2312yes—
641#382C2312yes—
642#382C2312yes—
643#382C2314yes—
644#382C2312yes—
645#382C2312yes—
646#382C2314yes—
647#382C2314yes—
648#381C2314yes—
649#381C2314yes—
650#380C2314yes—
651#380C2314yes—
652#380C2312yes—
653#380C2312yes—
654#380C2314yes—
655#380C2314yes—
656#380C2314yes—
657#380C2312yes—
658#380C2312yes—
659#380C2312yes—
660#380C2312yes—
661#380C2314yes—
662#380C2314yes—
663C4×C4⋊C4C2311yescharacteristic
664C4×C4⋊C4C2311yescharacteristic
665C4×C4⋊C4C2311yescharacteristic
666C4×C4⋊C4C2312yes—
667C4×C4⋊C4C2312yes—
668C4×C4⋊C4C2312yes—
669C4×C4⋊C4C2312yes—
670C4×C4⋊C4C2312yes—
671C4×C4⋊C4C2312yes—
672C4×C4⋊C4C2312yes—
673C4×C4⋊C4C2312yes—
674C4×C4⋊C4C2312yes—
675C4×C4⋊C4C2312yes—
676C4×C4⋊C4C2311yescharacteristic
677C4×C4⋊C4C2312yes—
678C4×C4⋊C4C2311yescharacteristic
679C4×C4⋊C4C2311yescharacteristic
680C4×C4⋊C4C2312yes—
681C4×C4⋊C4C2314yes—
682C4×C4⋊C4C2312yes—
683C4×C4⋊C4C2314yes—
684C4×C4⋊C4C2314yes—
685C4×C4⋊C4C2312yes—
686C4×C4⋊C4C2311yescharacteristic
687C4×C4⋊C4C2314yes—
688C4×C4⋊C4C2314yes—
689C4×C4⋊C4C2312yes—
690C4×C4⋊C4C2312yes—
691C4×C4⋊C4C2312yes—
692C4×C4⋊C4C2314yes—
693C4×C4⋊C4C2314yes—
694C4×C4⋊C4C2312yes—
695C4×C4⋊C4C2314yes—
696C4×C4⋊C4C2311yescharacteristic
697C4×C4⋊C4C2311yescharacteristic
698C4×C22⋊C4C2314yes—
699C4×C22⋊C4C2314yes—
700C4×C22⋊C4C2314yes—
701C4×C22⋊C4C2312yes—
702C4×C22⋊C4C2314yes—
703C4×C22⋊C4C2314yes—
704C4×C22⋊C4C2314yes—
705C4×C22⋊C4C2312yes—
706C4×C22⋊C4C2312yes—
707#376C2312yes—
708#376C2314yes—
709C2×#95C2314yes—
710C43C2312yes—
711C43C2311yescharacteristic
712C22×Q8C2412yes—
713C22×Q8C2412yes—
714C22×Q8C2412yes—
715C22×Q8C2412yes—
716C22×Q8C2414yes—
717C22×D4C2411yescharacteristic
718C23×C4C2412yes—
719C23×C4C2412yes—
720C23×C4C2414yes—
721C23×C4C2412yes—
722C23×C4C2414yes—
723C4⋊Q8—42no—
724C4⋊Q8—42no—
725C4⋊Q8—44no—
726C4⋊Q8—44no—
727C4⋊Q8—44no—
728C4⋊Q8—42no—
729C4⋊Q8—42no—
730C4⋊Q8—48no—
731#125—28no—
732#125—24no—
733#125—28no—
734#125—24no—
735#125—44no—
736#125—44no—
737#125—42no—
738#125—44no—
739#125—82no—
740#125—84no—
741#125—84no—
742#124—28no—
743#124—28no—
744C22⋊Q8—28no—
745C22⋊Q8—44no—
746C22⋊Q8—82no—
747C22⋊Q8—82no—
748C22⋊Q8—84no—
749C4×Q8—44no—
750C4×Q8—44no—
751C4×Q8—44no—
752C4×Q8—44no—
753C4×Q8—44no—
754C4×Q8—44no—
755C4×Q8—82no—
756C4×Q8—82no—
757C4×Q8—84no—
758C4×D4—24no—
759C4×D4—44no—
760C4×D4—44no—
761C4×D4—42no—
762C4×D4—42no—
763C2×C4⋊C4—28no—
764C2×C4⋊C4—48no—
765C2×C4⋊C4—82no—
766C2×C4⋊C4C2412yes—
767C2×C4⋊C4C2414yes—
768C2×C4⋊C4C2412yes—
769C2×C4⋊C4C2414yes—
770C2×C4⋊C4C2411yescharacteristic
771C2×C4⋊C4C2411yescharacteristic
772C2×C4⋊C4C2412yes—
773C2×C4⋊C4C2412yes—
774C2×C4⋊C4C2411yescharacteristic
775C2×C4⋊C4C2412yes—
776C2×C4⋊C4C2412yes—
777C2×C4⋊C4C2411yescharacteristic
778C2×C4⋊C4C2414yes—
779C2×C4⋊C4C2411yescharacteristic
780C2×C4⋊C4C2412yes—
781C2×C4⋊C4C2412yes—
782C2×C4⋊C4C2412yes—
783C2×C4⋊C4C2412yes—
784C2×C4⋊C4C2412yes—
785C2×C4⋊C4C2412yes—
786C2×C4⋊C4C2411yescharacteristic
787C2×C4⋊C4C2412yes—
788C2×C4⋊C4C2411yescharacteristic
789C2×C4⋊C4C2412yes—
790C2×C4⋊C4C2412yes—
791C2×C4⋊C4C2412yes—
792C2×C4⋊C4C2412yes—
793C2×C4⋊C4C2412yes—
794C2×C4⋊C4C2412yes—
795C2×C4⋊C4C2412yes—
796C2×C4⋊C4C2412yes—
797C2×C4⋊C4C2411yescharacteristic
798C2×C4⋊C4C2412yes—
799C2×C4⋊C4C2414yes—
800C2×C4⋊C4C2414yes—
801C2×C4⋊C4C2414yes—
802C2×C4⋊C4C2411yescharacteristic
803C2×C4⋊C4C2411yescharacteristic
804C2×C4⋊C4C2414yes—
805C2×C4⋊C4C2414yes—
806C2×C4⋊C4C2414yes—
807C2×C4⋊C4C2414yes—
808C2×C4⋊C4C2414yes—
809C2×C4⋊C4C2414yes—
810C2×C4⋊C4C2414yes—
811C2×C4⋊C4C2414yes—
812C2×C4⋊C4C2414yes—
813C2×C4⋊C4C2414yes—
814C2×C4⋊C4C2414yes—
815C2×C4⋊C4C2411yescharacteristic
816C2×C4⋊C4C2411yescharacteristic
817C2×C4⋊C4C2412yes—
818C2×C4⋊C4C2414yes—
819C2×C4⋊C4C2414yes—
820C2×C4⋊C4C2414yes—
821C2×C4⋊C4C2414yes—
822C2×C4⋊C4C2411yescharacteristic
823C2×C4⋊C4C2412yes—
824C2×C4⋊C4C2414yes—
825C2×C4⋊C4C2412yes—
826C2×C4⋊C4C2414yes—
827C2×C4⋊C4C2412yes—
828C2×C4⋊C4C2412yes—
829C2×C4⋊C4C2412yes—
830C2×C4⋊C4C2412yes—
831C2×C4⋊C4C2412yes—
832C2×C4⋊C4C2414yes—
833C2×C4⋊C4C2414yes—
834C2×C4⋊C4C2412yes—
835C2×C4⋊C4C2412yes—
836C2×C4⋊C4C2414yes—
837C2×C4⋊C4C2414yes—
838C2×C4⋊C4C2412yes—
839C2×C4⋊C4C2412yes—
840C2×C4⋊C4C2414yes—
841C2×C4⋊C4C2414yes—
842C2×C4⋊C4C2414yes—
843C2×C4⋊C4C2414yes—
844C2×C4⋊C4C2412yes—
845C2×C4⋊C4C2412yes—
846C2×C4⋊C4C2412yes—
847C2×C4⋊C4C2412yes—
848C2×C4⋊C4C2414yes—
849C2×C4⋊C4C2414yes—
850C2×C4⋊C4C2411yescharacteristic
851C2×C4⋊C4C2411yescharacteristic
852C2×C22⋊C4C2412yes—
853C2×C22⋊C4C2414yes—
854C2×C22⋊C4C2414yes—
855C2×C22⋊C4C2414yes—
856C2×C22⋊C4C2414yes—
857C2×C22⋊C4C2414yes—
858C2×C22⋊C4C2412yes—
859C2×C22⋊C4C2412yes—
860C2×C22⋊C4C2414yes—
861C2×C22⋊C4C2414yes—
862C2×C22⋊C4C2414yes—
863C2×C22⋊C4C2414yes—
864C2×C22⋊C4C2414yes—
865C2×C42—82no—
866C2×C42C2412yes—
867C2×C42C2412yes—
868C2×C42C2411yescharacteristic
869C2×C42C2411yescharacteristic
870C2×C42C2411yescharacteristic
871C2×C42C2412yes—
872C2×C42C2412yes—
873C2×C42C2412yes—
874C2×C42C2412yes—
875C2×C42C2411yescharacteristic
876C2×C42C2412yes—
877C2×C42C2411yescharacteristic
878C2×C42C2411yescharacteristic
879C2×C42C2412yes—
880C2×C42C2412yes—
881C2×C42C2414yes—
882C2×C42C2414yes—
883C2×C42C2414yes—
884C2×C42C2414yes—
885C2×C42C2414yes—
886C2×C42C2414yes—
887C2×C42C2414yes—
888C2×C42C2414yes—
889C2×C42C2412yes—
890C2×C42C2412yes—
891C2×C42C2414yes—
892C2×C42C2412yes—
893C2×C42C2412yes—
894C2×C42C2414yes—
895C2×C42C2411yescharacteristic
896#95C2412yes—
897#95C2414yes—
898#95C2414yes—
899#95C2414yes—
900#95C2412yes—
901#95C2414yes—
902#95C2414yes—
903#95C2414yes—
904#95C2412yes—
905#95C2412yes—
906#95C2412yes—
907#95C2412yes—
908#95C2412yes—
909#95C2412yes—
910#95C2412yes—
911#95C2412yes—
912#95C2412yes—
913#95C2412yes—
914#95C2412yes—
915#95C2414yes—
916#95C2414yes—
917#95C2414yes—
918#95C2414yes—
919#95C2414yes—
920#95C2414yes—
921#95C2414yes—
922#95C2414yes—
923#95C2414yes—
924#95C2412yes—
925#95C2412yes—
926#95C2414yes—
927#95C2414yes—
928#95C2414yes—
929#95C2414yes—
930#95C2414yes—
931#95C2414yes—
932#95C2414yes—
933#95C2412yes—
934#95C2412yes—
935#95C2414yes—
936#95C2414yes—
937#95C2412yes—
938#95C2414yes—
939#95C2412yes—
940#95C2412yes—
941#95C2412yes—
942#95C2412yes—
943#95C2414yes—
944#95C2412yes—
945#95C2412yes—
946#95C2412yes—
947#95C2414yes—
948#95C2412yes—
949#95C2412yes—
950#95C2412yes—
951#95C2412yes—
952#95C2412yes—
953#95C2414yes—
954#95C2414yes—
955#95C2414yes—
956#95C2412yes—
957#95C2412yes—
958#95C2414yes—
959#95C2414yes—
960#95C2412yes—
961#95C2412yes—
962#95C2412yes—
963#95C2412yes—
964#95C2412yes—
965#95C2414yes—
966#95C2414yes—
967#95C2414yes—
968#95C2414yes—
969#95C2414yes—
970#95C2414yes—
971#95C2414yes—
972#95C2414yes—
973#95C2414yes—
974#95C2414yes—
975#95C2414yes—
976#95C2414yes—
977#95C2414yes—
978#95C2414yes—
979#95C2414yes—
980#95C2414yes—
981#95C2414yes—
982#95C2414yes—
983#95C2414yes—
984#95C2414yes—
985C24C2512yes—
986C2×Q8—24no—
987C2×Q8—24no—
988C2×Q8—24no—
989C2×Q8—24no—
990C2×Q8—24no—
991C2×Q8—24no—
992C2×Q8—24no—
993C2×Q8—24no—
994C2×Q8—42no—
995C2×Q8—42no—
996C2×Q8—44no—
997C2×Q8—42no—
998C2×Q8—42no—
999C2×Q8—44no—
1000C2×Q8—44no—
1001C2×D4—22no—
1002C2×D4—22no—
1003C2×D42−1+414yes—
1004C22×C4—24no—
1005C22×C4—24no—
1006C22×C4—28no—
1007C22×C4—24no—
1008C22×C4—24no—
1009C22×C4—42no—
1010C22×C4—42no—
1011C22×C4—42no—
1012C22×C4—44no—
1013C22×C4—44no—
1014C22×C4—42no—
1015C22×C4—42no—
1016C22×C4—44no—
1017C22×C4—44no—
1018C22×C4—44no—
1019C22×C4C2511yescharacteristic
1020C22×C4C2512yes—
1021C22×C4C2512yes—
1022C22×C4C2511yescharacteristic
1023C22×C4C2512yes—
1024C22×C4C2512yes—
1025C22×C4C2512yes—
1026C22×C4C2512yes—
1027C22×C4C2514yes—
1028C22×C4C2514yes—
1029C22×C4C2514yes—
1030C22×C4C2512yes—
1031C22×C4C2511yescharacteristic
1032C22×C4C2512yes—
1033C22×C4C2514yes—
1034C22×C4C2512yes—
1035C22×C4C2512yes—
1036C22×C4C2512yes—
1037C22×C4C2514yes—
1038C22×C4C2514yes—
1039C22×C4C2512yes—
1040C22×C4C2512yes—
1041C22×C4C2511yescharacteristic
1042C22×C4C2511yescharacteristic
1043C22×C4C2512yes—
1044C22×C4C2512yes—
1045C22×C4C2511yescharacteristic
1046C22×C4C2511yescharacteristic
1047C4⋊C4—24no—
1048C4⋊C4—28no—
1049C4⋊C4—22no—
1050C4⋊C4—28no—
1051C4⋊C4—24no—
1052C4⋊C4—24no—
1053C4⋊C4—24no—
1054C4⋊C4—24no—
1055C4⋊C4—24no—
1056C4⋊C4—24no—
1057C4⋊C4—24no—
1058C4⋊C4—24no—
1059C4⋊C4—24no—
1060C4⋊C4—24no—
1061C4⋊C4—24no—
1062C4⋊C4—24no—
1063C4⋊C4—24no—
1064C4⋊C4—22no—
1065C4⋊C4—24no—
1066C4⋊C4—22no—
1067C4⋊C4—24no—
1068C4⋊C4—28no—
1069C4⋊C4—22no—
1070C4⋊C4—22no—
1071C4⋊C4—24no—
1072C4⋊C4—24no—
1073C4⋊C4—24no—
1074C4⋊C4—24no—
1075C4⋊C4—22no—
1076C4⋊C4—22no—
1077C4⋊C4—24no—
1078C4⋊C4—44no—
1079C4⋊C4—44no—
1080C4⋊C4—41no—
1081C4⋊C4—42no—
1082C4⋊C4—44no—
1083C4⋊C4—44no—
1084C4⋊C4—44no—
1085C4⋊C4—44no—
1086C4⋊C4—44no—
1087C4⋊C4—44no—
1088C4⋊C4—44no—
1089C4⋊C4—41no—
1090C4⋊C4—41no—
1091C4⋊C4—44no—
1092C4⋊C4—44no—
1093C4⋊C4—44no—
1094C4⋊C4—44no—
1095C4⋊C4—44no—
1096C4⋊C4—44no—
1097C4⋊C4—41no—
1098C4⋊C4—41no—
1099C4⋊C4—42no—
1100C4⋊C4—44no—
1101C4⋊C4—44no—
1102C4⋊C4—44no—
1103C4⋊C4—42no—
1104C4⋊C4—44no—
1105C4⋊C4—44no—
1106C4⋊C4—42no—
1107C4⋊C4—42no—
1108C4⋊C4—42no—
1109C4⋊C4—44no—
1110C4⋊C4—42no—
1111C4⋊C4—42no—
1112C4⋊C4—42no—
1113C4⋊C4—41no—
1114C4⋊C4—42no—
1115C4⋊C4—44no—
1116C4⋊C4—44no—
1117C4⋊C4—42no—
1118C4⋊C4—44no—
1119C4⋊C4—44no—
1120C4⋊C4—42no—
1121C4⋊C4—42no—
1122C4⋊C4—44no—
1123C4⋊C4—44no—
1124C4⋊C4—42no—
1125C4⋊C4—42no—
1126C4⋊C4—42no—
1127C4⋊C4—42no—
1128C4⋊C4—44no—
1129C4⋊C4—44no—
1130C4⋊C4—44no—
1131C4⋊C42−1+414yes—
1132C4⋊C42−1+414yes—
1133C22⋊C4—24no—
1134C22⋊C4—28no—
1135C22⋊C4—28no—
1136C22⋊C4—28no—
1137C22⋊C4—28no—
1138C22⋊C4—28no—
1139C22⋊C4—44no—
1140C22⋊C4—42no—
1141C22⋊C4—42no—
1142C22⋊C4—44no—
1143C22⋊C4—44no—
1144C22⋊C4—44no—
1145C22⋊C4—44no—
1146C42—22no—
1147C42—24no—
1148C42—24no—
1149C42—24no—
1150C42—24no—
1151C42—22no—
1152C42—22no—
1153C42—24no—
1154C42—24no—
1155C42—22no—
1156C42—22no—
1157C42—24no—
1158C42—24no—
1159C42—22no—
1160C42—41no—
1161C42—42no—
1162C42—42no—
1163C42—42no—
1164C42—44no—
1165C42—44no—
1166C42—44no—
1167C42—44no—
1168C42—44no—
1169C42—44no—
1170C42—44no—
1171C42—42no—
1172C42—44no—
1173C42—44no—
1174C42—42no—
1175C42—44no—
1176C23—22no—
1177C23—22no—
1178C23—22no—
1179C23—22no—
1180C23—22no—
1181C23—22no—
1182C23C2×2−1+414yes—
1183C23C2611yescharacteristic
1184Q8—48no—
1185Q8—48no—
1186Q8—84no—
1187Q8—84no—
1188Q8—88no—
1189D4—28no—
1190C2×C4—22no—
1191C2×C4—21no—
1192C2×C4—22no—
1193C2×C4—22no—
1194C2×C4—21no—
1195C2×C4—21no—
1196C2×C4—22no—
1197C2×C4—21no—
1198C2×C4—21no—
1199C2×C4—21no—
1200C2×C4—21no—
1201C2×C4—22no—
1202C2×C4—22no—
1203C2×C4—22no—
1204C2×C4—22no—
1205C2×C4—21no—
1206C2×C4—21no—
1207C2×C4—21no—
1208C2×C4—21no—
1209C2×C4—22no—
1210C2×C4—22no—
1211C2×C4—22no—
1212C2×C4—24no—
1213C2×C4—24no—
1214C2×C4—22no—
1215C2×C4—24no—
1216C2×C4—22no—
1217C2×C4—22no—
1218C2×C4—22no—
1219C2×C4—22no—
1220C2×C4—22no—
1221C2×C4—22no—
1222C2×C4—24no—
1223C2×C4—22no—
1224C2×C4—22no—
1225C2×C4—22no—
1226C2×C4—22no—
1227C2×C4—22no—
1228C2×C4—21no—
1229C2×C4—21no—
1230C2×C4—22no—
1231C2×C4—21no—
1232C2×C4—21no—
1233C2×C4—22no—
1234C2×C4—22no—
1235C2×C4—22no—
1236C2×C4—22no—
1237C2×C4—22no—
1238C2×C4—24no—
1239C2×C4—24no—
1240C2×C4—24no—
1241C2×C4—24no—
1242C2×C4—24no—
1243C2×C4—22no—
1244C2×C4—24no—
1245C2×C4—24no—
1246C2×C4—24no—
1247C2×C4—22no—
1248C2×C4—24no—
1249C2×C4—24no—
1250C2×C4—22no—
1251C2×C4—22no—
1252C2×C4—24no—
1253C2×C4—22no—
1254C2×C4—22no—
1255C2×C4—22no—
1256C2×C4—22no—
1257C2×C4—24no—
1258C2×C4—22no—
1259C2×C4—22no—
1260C2×C4—22no—
1261C2×C4—24no—
1262C2×C4—22no—
1263C2×C4—24no—
1264C2×C4—22no—
1265C2×C4—22no—
1266C2×C4—48no—
1267C2×C4—88no—
1268C2×C4—84no—
1269C2×C4—84no—
1270C2×C4—164no—
1271C2×C4C2×2−1+414yes—
1272C2×C4C2×2−1+414yes—
1273C2×C4C2×2−1+412yes—
1274C2×C4C2×2−1+412yes—
1275C2×C4C2×2−1+412yes—
1276C2×C4#58512yes—
1277C2×C4#58512yes—
1278C2×C4#58512yes—
1279C22—24no—
1280C22—24no—
1281C22—24no—
1282C22—42no—
1283C22—42no—
1284C22—42no—
1285C22—42no—
1286C22C22×2−1+411yescharacteristic
1287C22C22×2−1+411yescharacteristic
1288C22C22×2−1+411yescharacteristic
1289C22C2×#58511yescharacteristic
1290C22C2×#58511yescharacteristic
1291C22C2×#58511yescharacteristic
1292C22H(7,𝔽2)11yescharacteristic
1293C4—24no—
1294C4—24no—
1295C4—22no—
1296C4—22no—
1297C4—22no—
1298C4—44no—
1299C4—44no—
1300C4—41no—
1301C4—42no—
1302C4—44no—
1303C4—41no—
1304C4—42no—
1305C4—41no—
1306C4—42no—
1307C4—42no—
1308C4—42no—
1309C4—42no—
1310C4—42no—
1311C4—42no—
1312C4—42no—
1313C4—42no—
1314C4—44no—
1315C4—42no—
1316C4—42no—
1317C4—44no—
1318C4—42no—
1319C4—44no—
1320C4#355314yes—
1321C2—44no—
1322C2C2×#355311yescharacteristic
1323C2#6294511yescharacteristic
1324C2#6296211yescharacteristic
1325C2#6296511yescharacteristic
1326C2#6302511yescharacteristic
1327C2#6303211yescharacteristic
1328C2#6303211yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC22×D4C24
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59866C2semidirect
3. #59445C2semidirect
5. #58698C2semidirect
6. #55995C2semidirect
7. #55884C2semidirect
8. #52305C2semidirect
9. #51369C2semidirect
10. #49048C2semidirect
11. #48961C2semidirect
12. #46022C2semidirect
13. #46007C2semidirect
14. #46006C2semidirect
16. #45154C2semidirect
18. #42850C2semidirect
20. #42553C2semidirect
21. #40143C2semidirect
22. #39655C2semidirect
24. #37212C2semidirect
25. #37168C2semidirect
26. #37135C2semidirect

Maximal subgroups

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

subgroupindex
#598662
#594612
#594452
#594372
#586982
#559952
#558842
#523052
#513692
#490482
#489612
#460222
#460072
#460062
#452212
#451542
#450862
#428502
#426392
#425532
#401432
#396552
#390252
#372122
#371682
#371352
#364542
#362902