Finite Group Databasebeta

← #8726299

Subgroups — #8726299

Order 512.

4235 conjugacy classes of subgroups.

The subgroup lattice has 1357 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59869C211yesmaximal, characteristic, complemented
2#59481C212yesmaximal, complemented
3#59383C212yesmaximal
4#59144C212yesmaximal, complemented
5#59144C212yesmaximal, complemented
6#58703C212yesmaximal, complemented
7#58405C214yesmaximal, complemented
8#55995C214yesmaximal, complemented
9#54237C214yesmaximal, complemented
10#53146C212yesmaximal, complemented
11#53032C211yesmaximal, characteristic
12#52302C211yesmaximal, characteristic
13#47817C212yesmaximal, complemented
14#46925C214yesmaximal
15#45436C211yesmaximal, characteristic, complemented
16#45340C212yesmaximal, complemented
17#44597C214yesmaximal, complemented
18#43803C212yesmaximal
19#42853C212yesmaximal, complemented
20#42811C211yesmaximal, characteristic, complemented
21#42419C212yesmaximal
22#41777C214yesmaximal, complemented
23#40199C212yesmaximal, complemented
24#40071C212yesmaximal, complemented
25#39663C212yesmaximal, complemented
26#39593C212yesmaximal
27#39170C211yesmaximal, characteristic, complemented
28#35910C211yesmaximal, characteristic
29#35870C212yesmaximal, complemented
30C2×#557C2211yescharacteristic
31C2×#557C2211yescharacteristic
32C2×#557C2211yescharacteristic
33C2×D4×Q8C2211yescharacteristic
34C22×C4⋊Q8C2212yes—
35#2862C2211yescharacteristic
36#2855C2212yes—
37#2844C2212yes—
38#2844C2212yes—
39#2839C2214yes—
40#2839C2214yes—
41#2839C2214yes—
42#2839C2214yes—
43#2835C2214yes—
44#2833C2214yes—
45#2822C2212yes—
46#2809C2212yes—
47#2809C2212yes—
48#2806C2214yes—
49#2805C2214yes—
50#2802C2214yes—
51#2802C2214yes—
52#2802C2214yes—
53#2802C2214yes—
54#2799C2211yescharacteristic
55#2794C2211yescharacteristic
56#2789C2214yes—
57#2788C2214yes—
58#2787C2214yes—
59#2782C2212yes—
60#2782C2212yes—
61#2776C2212yes—
62#2774C2214yes—
63#2774C2214yes—
64#2770C2214yes—
65#2770C2214yes—
66#2770C2212yes—
67#2769C2214yes—
68#2769C2212yes—
69#2769C2212yes—
70#2768C2214yes—
71#2767C2214yes—
72#2767C2214yes—
73#2766C2214yes—
74#2763C2214yes—
75#2762C2214yes—
76#2762C2214yes—
77#2762C2214yes—
78#2758C2214yes—
79#2755C2214yes—
80#2747C2214yes—
81#2747C2214yes—
82#2745C2212yes—
83#2739C2214yes—
84#2734C2214yes—
85#2734C2214yes—
86#2729C2214yes—
87#2729C2212yes—
88#2729C2214yes—
89#2729C2214yes—
90#2728C2211yescharacteristic
91#2722C2214yes—
92#2719C2214yes—
93#2719C2214yes—
94#2719C2214yes—
95#2713C2214yes—
96#2713C2214yes—
97#2713C2214yes—
98#2713C2214yes—
99#2713C2214yes—
100#2698C2214yes—
101#2695C2212yes—
102#2689C2212yes—
103#2680C2211yescharacteristic
104#2666C2214yes—
105#2666C2214yes—
106#2655C2214yes—
107#2655C2214yes—
108#2652C2214yes—
109#2652C2214yes—
110#2642C2212yes—
111#2642C2212yes—
112#2642C2212yes—
113#2642C2211yescharacteristic
114#2642C2211yescharacteristic
115#2634C2212yes—
116#2634C2212yes—
117#2627C2214yes—
118#2612C2212yes—
119#2612C2212yes—
120#2612C2214yes—
121#2612C2214yes—
122#2590C2214yes—
123#2589C2214yes—
124#2589C2214yes—
125#2588C2214yes—
126#2588C2214yes—
127#2587C2214yes—
128#2586C2214yes—
129#2585C2214yes—
130#2584C2211yescharacteristic
131#2583C2214yes—
132#2581C2212yes—
133#2579C2214yes—
134#2578C2214yes—
135#2577C2214yes—
136#2577C2214yes—
137#2571C2212yes—
138#2568C2211yescharacteristic
139#2568C2212yes—
140#2568C2212yes—
141#2568C2211yescharacteristic
142#2568C2212yes—
143#2568C2211yescharacteristic
144#2565C2212yes—
145#2565C2212yes—
146#2562C2212yes—
147#2562C2211yescharacteristic
148#2553C2214yes—
149#2550C2214yes—
150#2550C2214yes—
151#2546C2212yes—
152#2546C2211yescharacteristic
153#2546C2212yes—
154#2546C2212yes—
155#2546C2212yes—
156#2546C2212yes—
157#2546C2212yes—
158#2546C2212yes—
159#2546C2212yes—
160#2533C2214yes—
161#2533C2214yes—
162#2530C2214yes—
163#2528C2214yes—
164#2527C2214yes—
165#2527C2214yes—
166#2524C2214yes—
167#2522C2214yes—
168#2520C2214yes—
169#2520C2214yes—
170#2520C2214yes—
171#2517C2214yes—
172#2515C2214yes—
173#2514C2212yes—
174#2511C2212yes—
175#2509C2214yes—
176#2508C2214yes—
177#2508C2214yes—
178#2496C2212yes—
179#2494C2212yes—
180#2492C2214yes—
181#2492C2212yes—
182#2489C2212yes—
183#2489C2212yes—
184#2489C2212yes—
185#2489C2214yes—
186#2473C2214yes—
187#2473C2214yes—
188#2473C2214yes—
189#2473C2214yes—
190#2453C2212yes—
191#2453C2212yes—
192#2453C2212yes—
193#2453C2212yes—
194#2453C2212yes—
195#2451C2214yes—
196#2451C2214yes—
197#2451C2212yes—
198#2446C2212yes—
199#2446C2212yes—
200#2446C2212yes—
201#2446C2212yes—
202#2446C2212yes—
203#2446C2212yes—
204#2446C2212yes—
205#2446C2212yes—
206#2442C2214yes—
207#2442C2214yes—
208#2434C2212yes—
209#2434C2212yes—
210#2434C2212yes—
211#2434C2212yes—
212#2434C2212yes—
213#2429C2212yes—
214#2429C2212yes—
215#2423C2212yes—
216#2421C2212yes—
217#2409C2212yes—
218#2402C2214yes—
219#2402C2212yes—
220#2401C2212yes—
221#2399C2211yescharacteristic
222#2398C2212yes—
223#2398C2211yescharacteristic
224#2373C2214yes—
225#2373C2214yes—
226#2370C2212yes—
227#2369C2212yes—
228#2365C2212yes—
229#2365C2212yes—
230#2365C2212yes—
231#2360C2214yes—
232#2360C2214yes—
233#2356C2212yes—
234#2356C2212yes—
235#2355C2212yes—
236#2355C2212yes—
237Q8×C22⋊C4C2212yes—
238Q8×C22⋊C4C2212yes—
239Q8×C22⋊C4C2212yes—
240Q8×C22⋊C4C2212yes—
241Q8×C22⋊C4C2212yes—
242#2334C2214yes—
243#2334C2214yes—
244#2331C2214yes—
245#2327C2212yes—
246#2327C2212yes—
247#2322C2214yes—
248#2320C2211yescharacteristic
249C4×C4⋊Q8C2211yescharacteristic
250C4×C4⋊Q8C2212yes—
251C4×#126C2212yes—
252C4×C22⋊Q8C2212yes—
253C4×C22⋊Q8C2212yes—
254C4×C22⋊Q8C2212yes—
255C4×C22⋊Q8C2212yes—
256C4×#123C2212yes—
257#2295C2211yescharacteristic
258#2276C2211yescharacteristic
259C23×Q8C2312yes—
260C23×Q8C2312yes—
261#557—44no—
262#557—44no—
263#557—44no—
264D4×Q8—44no—
265C2×C4⋊Q8—48no—
266C2×C4⋊Q8C2311yescharacteristic
267C2×C4⋊Q8C2312yes—
268C2×C4⋊Q8C2312yes—
269C2×C4⋊Q8C2312yes—
270C2×C4⋊Q8C2312yes—
271C2×C4⋊Q8C2311yescharacteristic
272C2×C4⋊Q8C2311yescharacteristic
273C2×C4⋊Q8C2312yes—
274C2×C4⋊Q8C2311yescharacteristic
275C2×C4⋊Q8C2312yes—
276C2×C4⋊Q8C2312yes—
277C2×C4⋊Q8C2312yes—
278C2×C4⋊Q8C2311yescharacteristic
279C2×C4⋊Q8C2312yes—
280C2×C4⋊Q8C2312yes—
281C2×C4⋊Q8C2314yes—
282C2×C4⋊Q8C2314yes—
283C2×#126C2312yes—
284C2×#126C2314yes—
285C2×#125C2311yescharacteristic
286C2×#125C2312yes—
287C2×#125C2312yes—
288C2×#125C2312yes—
289C2×#125C2312yes—
290C2×#125C2312yes—
291C2×#125C2311yescharacteristic
292C2×#125C2314yes—
293C2×#125C2314yes—
294C2×#123C2312yes—
295C2×C22⋊Q8C2312yes—
296C2×C22⋊Q8C2312yes—
297C2×C22⋊Q8C2314yes—
298C2×C22⋊Q8C2312yes—
299C2×C22⋊Q8C2312yes—
300C2×C22⋊Q8C2312yes—
301C2×C4×Q8C2311yescharacteristic
302C2×C4×Q8C2311yescharacteristic
303C2×C4×Q8C2311yescharacteristic
304C2×C4×Q8C2311yescharacteristic
305C2×C4×Q8C2311yescharacteristic
306C2×C4×Q8C2312yes—
307C2×C4×Q8C2312yes—
308C2×C4×Q8C2312yes—
309C2×C4×Q8C2312yes—
310C2×C4×Q8C2311yescharacteristic
311C2×C4×Q8C2312yes—
312C2×C4×Q8C2312yes—
313C2×C4×Q8C2312yes—
314C2×C4×Q8C2312yes—
315C2×C4×Q8C2312yes—
316C2×C4×Q8C2312yes—
317C2×C4×D4C2312yes—
318C2×C4×D4C2311yescharacteristic
319C22×C4⋊C4C2314yes—
320C22×C4⋊C4C2314yes—
321C22×C42C2312yes—
322#401C2312yes—
323#401C2314yes—
324#401C2314yes—
325#400C2312yes—
326#400C2312yes—
327#400C2312yes—
328#400C2312yes—
329#400C2314yes—
330#400C2312yes—
331#400C2312yes—
332#400C2311yescharacteristic
333#400C2312yes—
334#400C2314yes—
335#400C2312yes—
336#400C2312yes—
337#400C2314yes—
338#400C2314yes—
339#400C2314yes—
340#400C2314yes—
341#400C2314yes—
342#400C2314yes—
343#400C2314yes—
344#400C2314yes—
345#400C2314yes—
346#400C2314yes—
347#400C2314yes—
348#400C2314yes—
349#400C2314yes—
350#400C2314yes—
351#400C2312yes—
352#400C2314yes—
353#400C2314yes—
354#400C2314yes—
355#400C2312yes—
356#400C2312yes—
357#400C2312yes—
358#400C2312yes—
359#400C2314yes—
360#400C2314yes—
361#400C2314yes—
362#400C2314yes—
363#400C2314yes—
364#400C2311yescharacteristic
365#400C2314yes—
366#400C2314yes—
367#400C2314yes—
368#400C2314yes—
369#400C2312yes—
370#400C2314yes—
371#400C2314yes—
372#400C2314yes—
373#400C2314yes—
374#400C2312yes—
375#400C2312yes—
376#400C2312yes—
377#399C2314yes—
378#398C2314yes—
379#398C2314yes—
380#398C2314yes—
381#398C2314yes—
382#398C2311yescharacteristic
383#398C2314yes—
384#398C2314yes—
385#398C2312yes—
386#398C2314yes—
387#398C2314yes—
388#398C2314yes—
389#398C2314yes—
390#398C2314yes—
391#398C2314yes—
392#398C2314yes—
393#398C2314yes—
394#398C2314yes—
395#398C2314yes—
396#398C2314yes—
397#398C2314yes—
398#398C2314yes—
399#398C2314yes—
400#398C2314yes—
401#398C2314yes—
402#398C2314yes—
403#398C2314yes—
404#398C2312yes—
405#398C2314yes—
406#398C2314yes—
407#398C2314yes—
408#398C2314yes—
409#398C2312yes—
410#398C2314yes—
411#398C2311yescharacteristic
412#398C2314yes—
413#398C2312yes—
414#398C2314yes—
415#398C2314yes—
416#398C2312yes—
417#398C2312yes—
418#398C2314yes—
419#398C2314yes—
420#397C2312yes—
421#397C2314yes—
422#397C2314yes—
423#397C2314yes—
424#397C2314yes—
425#397C2312yes—
426#397C2314yes—
427#397C2312yes—
428#397C2312yes—
429#397C2314yes—
430#396C2314yes—
431#396C2314yes—
432#396C2312yes—
433#395C2314yes—
434#395C2314yes—
435#395C2314yes—
436#395C2314yes—
437#395C2311yescharacteristic
438#395C2312yes—
439#395C2314yes—
440#395C2314yes—
441#395C2314yes—
442#395C2314yes—
443#395C2314yes—
444#395C2314yes—
445#395C2314yes—
446#395C2311yescharacteristic
447#395C2312yes—
448#395C2314yes—
449#394C2312yes—
450#394C2311yescharacteristic
451#394C2311yescharacteristic
452#393C2314yes—
453#393C2314yes—
454#393C2312yes—
455#391C2312yes—
456#391C2312yes—
457#391C2311yescharacteristic
458#391C2311yescharacteristic
459#391C2312yes—
460#391C2312yes—
461#391C2312yes—
462#391C2312yes—
463#391C2312yes—
464#391C2312yes—
465#391C2314yes—
466#391C2314yes—
467#391C2312yes—
468#391C2312yes—
469#391C2314yes—
470#391C2314yes—
471#391C2312yes—
472#391C2312yes—
473#391C2312yes—
474#391C2312yes—
475#391C2314yes—
476#391C2312yes—
477#391C2312yes—
478#391C2312yes—
479#391C2314yes—
480#391C2314yes—
481#391C2312yes—
482#391C2314yes—
483#391C2312yes—
484#391C2314yes—
485#391C2314yes—
486#391C2314yes—
487#391C2314yes—
488#391C2312yes—
489#391C2314yes—
490#391C2312yes—
491#391C2312yes—
492#391C2312yes—
493#391C2314yes—
494#391C2312yes—
495#391C2312yes—
496#391C2312yes—
497#391C2312yes—
498#391C2312yes—
499#389C2314yes—
500#389C2312yes—
501#389C2312yes—
502#389C2314yes—
503#389C2314yes—
504#389C2314yes—
505#389C2312yes—
506#389C2314yes—
507#389C2314yes—
508#389C2314yes—
509#389C2314yes—
510#389C2314yes—
511#389C2314yes—
512#389C2314yes—
513#389C2314yes—
514#389C2314yes—
515#389C2312yes—
516#389C2312yes—
517#389C2314yes—
518#389C2314yes—
519#389C2314yes—
520#389C2314yes—
521#389C2314yes—
522#389C2314yes—
523#389C2314yes—
524#389C2314yes—
525#389C2314yes—
526#389C2314yes—
527#389C2314yes—
528#389C2314yes—
529#389C2314yes—
530#389C2314yes—
531#389C2312yes—
532#389C2314yes—
533#389C2312yes—
534#389C2312yes—
535#389C2312yes—
536#389C2312yes—
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#388C2312yes—
550#388C2314yes—
551#388C2312yes—
552#387C2312yes—
553#387C2312yes—
554#387C2312yes—
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#387C2312yes—
593#387C2314yes—
594#387C2314yes—
595#387C2314yes—
596#387C2314yes—
597#387C2314yes—
598#387C2314yes—
599#387C2314yes—
600#387C2314yes—
601#387C2314yes—
602#387C2314yes—
603#387C2314yes—
604#387C2314yes—
605#387C2314yes—
606#387C2314yes—
607#387C2314yes—
608#387C2314yes—
609#387C2314yes—
610#387C2314yes—
611#387C2312yes—
612#387C2312yes—
613#387C2314yes—
614#387C2314yes—
615#387C2312yes—
616#387C2312yes—
617#387C2312yes—
618#386C2314yes—
619#386C2312yes—
620#385C2314yes—
621#385C2314yes—
622#385C2314yes—
623#385C2314yes—
624#385C2314yes—
625#385C2314yes—
626#385C2314yes—
627#385C2314yes—
628#385C2314yes—
629#385C2314yes—
630#385C2314yes—
631#385C2312yes—
632#385C2314yes—
633#385C2314yes—
634#385C2312yes—
635#385C2312yes—
636#385C2312yes—
637#385C2312yes—
638#385C2314yes—
639#384C2311yescharacteristic
640#384C2312yes—
641#383C2312yes—
642#383C2312yes—
643#383C2314yes—
644#383C2314yes—
645#383C2314yes—
646#382C2312yes—
647#382C2312yes—
648#382C2312yes—
649#382C2312yes—
650#382C2314yes—
651#382C2312yes—
652#382C2314yes—
653#382C2314yes—
654#382C2314yes—
655#382C2314yes—
656#382C2314yes—
657#382C2314yes—
658#382C2314yes—
659#381C2314yes—
660#381C2312yes—
661#380C2314yes—
662#380C2312yes—
663#380C2312yes—
664#380C2314yes—
665#380C2314yes—
666#380C2314yes—
667#380C2312yes—
668#380C2314yes—
669#380C2312yes—
670#380C2312yes—
671C4×C4⋊C4C2312yes—
672C4×C4⋊C4C2312yes—
673C4×C4⋊C4C2312yes—
674C4×C4⋊C4C2312yes—
675C4×C4⋊C4C2311yescharacteristic
676C4×C4⋊C4C2314yes—
677C4×C4⋊C4C2314yes—
678C4×C4⋊C4C2312yes—
679C4×C4⋊C4C2312yes—
680C4×C4⋊C4C2312yes—
681C4×C4⋊C4C2311yescharacteristic
682C4×C4⋊C4C2312yes—
683C4×C4⋊C4C2312yes—
684C4×C4⋊C4C2311yescharacteristic
685C4×C4⋊C4C2314yes—
686C4×C4⋊C4C2314yes—
687C4×C4⋊C4C2314yes—
688C4×C4⋊C4C2314yes—
689C4×C4⋊C4C2314yes—
690C4×C4⋊C4C2314yes—
691C4×C4⋊C4C2314yes—
692C4×C4⋊C4C2314yes—
693C4×C4⋊C4C2314yes—
694C4×C4⋊C4C2312yes—
695C4×C4⋊C4C2312yes—
696C4×C4⋊C4C2312yes—
697C4×C4⋊C4C2312yes—
698C4×C22⋊C4C2312yes—
699C4×C22⋊C4C2312yes—
700C4×C22⋊C4C2312yes—
701C4×C22⋊C4C2314yes—
702C4×C22⋊C4C2314yes—
703C4×C22⋊C4C2314yes—
704C4×C22⋊C4C2314yes—
705C4×C22⋊C4C2314yes—
706C4×C22⋊C4C2314yes—
707C4×C22⋊C4C2312yes—
708C4×C22⋊C4C2312yes—
709C4×C22⋊C4C2314yes—
710#376C2311yescharacteristic
711#376C2312yes—
712#376C2314yes—
713#376C2314yes—
714#376C2311yescharacteristic
715#376C2312yes—
716C43C2311yescharacteristic
717C22×Q8—28no—
718C22×Q8—44no—
719C22×Q8—44no—
720C22×Q8—44no—
721C22×Q8—44no—
722C22×Q8—44no—
723C22×Q8C2412yes—
724C22×Q8C2412yes—
725C22×Q8C2412yes—
726C22×Q8C2411yescharacteristic
727C22×Q8C2411yescharacteristic
728C22×Q8C2411yescharacteristic
729C22×Q8C2412yes—
730C22×Q8C2414yes—
731C22×Q8C2414yes—
732C22×Q8C2411yescharacteristic
733C22×D4C2411yescharacteristic
734C23×C4C2412yes—
735C23×C4C2412yes—
736C23×C4C2414yes—
737C23×C4C2412yes—
738C23×C4C2414yes—
739C4⋊Q8—28no—
740C4⋊Q8—28no—
741C4⋊Q8—24no—
742C4⋊Q8—28no—
743C4⋊Q8—44no—
744C4⋊Q8—42no—
745C4⋊Q8—44no—
746C4⋊Q8—44no—
747C4⋊Q8—44no—
748C4⋊Q8—44no—
749C4⋊Q8—44no—
750C4⋊Q8—42no—
751C4⋊Q8—44no—
752C4⋊Q8—42no—
753C4⋊Q8—42no—
754C4⋊Q8—48no—
755C4⋊Q8—48no—
756#126—28no—
757#126—216no—
758#125—44no—
759#125—42no—
760#125—44no—
761#125—44no—
762#125—44no—
763#125—44no—
764#125—42no—
765#125—48no—
766#125—48no—
767#123—28no—
768C22⋊Q8—28no—
769C22⋊Q8—28no—
770C22⋊Q8—44no—
771C22⋊Q8—44no—
772C22⋊Q8—44no—
773C22⋊Q8—48no—
774C4×Q8—24no—
775C4×Q8—24no—
776C4×Q8—24no—
777C4×Q8—42no—
778C4×Q8—42no—
779C4×Q8—44no—
780C4×Q8—42no—
781C4×Q8—44no—
782C4×Q8—44no—
783C4×Q8—44no—
784C4×Q8—44no—
785C4×Q8—44no—
786C4×Q8—44no—
787C4×Q8—44no—
788C4×Q8—44no—
789C4×Q8—44no—
790C4×D4—42no—
791C4×D4—44no—
792C2×C4⋊C4—48no—
793C2×C4⋊C4—48no—
794C2×C4⋊C4C2414yes—
795C2×C4⋊C4C2414yes—
796C2×C4⋊C4C2414yes—
797C2×C4⋊C4C2414yes—
798C2×C4⋊C4C2411yescharacteristic
799C2×C4⋊C4C2411yescharacteristic
800C2×C4⋊C4C2412yes—
801C2×C4⋊C4C2411yescharacteristic
802C2×C4⋊C4C2412yes—
803C2×C4⋊C4C2412yes—
804C2×C4⋊C4C2412yes—
805C2×C4⋊C4C2412yes—
806C2×C4⋊C4C2412yes—
807C2×C4⋊C4C2412yes—
808C2×C4⋊C4C2412yes—
809C2×C4⋊C4C2412yes—
810C2×C4⋊C4C2412yes—
811C2×C4⋊C4C2412yes—
812C2×C4⋊C4C2412yes—
813C2×C4⋊C4C2412yes—
814C2×C4⋊C4C2412yes—
815C2×C4⋊C4C2414yes—
816C2×C4⋊C4C2412yes—
817C2×C4⋊C4C2412yes—
818C2×C4⋊C4C2412yes—
819C2×C4⋊C4C2414yes—
820C2×C4⋊C4C2414yes—
821C2×C4⋊C4C2412yes—
822C2×C4⋊C4C2412yes—
823C2×C4⋊C4C2414yes—
824C2×C4⋊C4C2414yes—
825C2×C4⋊C4C2414yes—
826C2×C4⋊C4C2414yes—
827C2×C4⋊C4C2414yes—
828C2×C4⋊C4C2414yes—
829C2×C4⋊C4C2411yescharacteristic
830C2×C4⋊C4C2412yes—
831C2×C4⋊C4C2411yescharacteristic
832C2×C4⋊C4C2412yes—
833C2×C4⋊C4C2412yes—
834C2×C4⋊C4C2414yes—
835C2×C4⋊C4C2414yes—
836C2×C4⋊C4C2412yes—
837C2×C4⋊C4C2411yescharacteristic
838C2×C4⋊C4C2411yescharacteristic
839C2×C4⋊C4C2411yescharacteristic
840C2×C4⋊C4C2411yescharacteristic
841C2×C4⋊C4C2412yes—
842C2×C4⋊C4C2412yes—
843C2×C4⋊C4C2412yes—
844C2×C4⋊C4C2414yes—
845C2×C4⋊C4C2414yes—
846C2×C4⋊C4C2414yes—
847C2×C4⋊C4C2414yes—
848C2×C4⋊C4C2414yes—
849C2×C4⋊C4C2414yes—
850C2×C4⋊C4C2412yes—
851C2×C4⋊C4C2414yes—
852C2×C4⋊C4C2414yes—
853C2×C4⋊C4C2412yes—
854C2×C4⋊C4C2412yes—
855C2×C4⋊C4C2412yes—
856C2×C4⋊C4C2412yes—
857C2×C4⋊C4C2412yes—
858C2×C4⋊C4C2414yes—
859C2×C4⋊C4C2414yes—
860C2×C4⋊C4C2414yes—
861C2×C4⋊C4C2414yes—
862C2×C4⋊C4C2414yes—
863C2×C4⋊C4C2414yes—
864C2×C4⋊C4C2414yes—
865C2×C4⋊C4C2414yes—
866C2×C4⋊C4C2412yes—
867C2×C4⋊C4C2414yes—
868C2×C4⋊C4C2412yes—
869C2×C4⋊C4C2412yes—
870C2×C4⋊C4C2414yes—
871C2×C4⋊C4C2414yes—
872C2×C22⋊C4C2412yes—
873C2×C22⋊C4C2412yes—
874C2×C22⋊C4C2412yes—
875C2×C22⋊C4C2412yes—
876C2×C22⋊C4C2412yes—
877C2×C22⋊C4C2414yes—
878C2×C22⋊C4C2412yes—
879C2×C22⋊C4C2412yes—
880C2×C22⋊C4C2414yes—
881C2×C22⋊C4C2412yes—
882C2×C22⋊C4C2414yes—
883C2×C22⋊C4C2414yes—
884C2×C22⋊C4C2414yes—
885C2×C22⋊C4C2414yes—
886C2×C22⋊C4C2412yes—
887C2×C22⋊C4C2412yes—
888C2×C22⋊C4C2412yes—
889C2×C42—44no—
890C2×C42C2411yescharacteristic
891C2×C42C2412yes—
892C2×C42C2412yes—
893C2×C42C2411yescharacteristic
894C2×C42C2412yes—
895C2×C42C2411yescharacteristic
896C2×C42C2412yes—
897C2×C42C2412yes—
898C2×C42C2412yes—
899C2×C42C2412yes—
900C2×C42C2412yes—
901C2×C42C2412yes—
902C2×C42C2414yes—
903C2×C42C2411yescharacteristic
904C2×C42C2412yes—
905C2×C42C2414yes—
906C2×C42C2414yes—
907C2×C42C2414yes—
908C2×C42C2414yes—
909C2×C42C2414yes—
910C2×C42C2414yes—
911C2×C42C2414yes—
912C2×C42C2412yes—
913C2×C42C2412yes—
914C2×C42C2411yescharacteristic
915C2×C42C2412yes—
916C2×C42C2414yes—
917C2×C42C2414yes—
918C2×C42C2412yes—
919#95C2411yescharacteristic
920#95C2412yes—
921#95C2412yes—
922#95C2414yes—
923#95C2414yes—
924#95C2412yes—
925#95C2414yes—
926#95C2412yes—
927#95C2411yescharacteristic
928#95C2414yes—
929#95C2414yes—
930#95C2411yescharacteristic
931#95C2414yes—
932#95C2414yes—
933#95C2411yescharacteristic
934#95C2414yes—
935#95C2412yes—
936#95C2414yes—
937#95C2414yes—
938#95C2414yes—
939#95C2414yes—
940#95C2414yes—
941#95C2412yes—
942#95C2412yes—
943#95C2414yes—
944#95C2412yes—
945#95C2412yes—
946#95C2412yes—
947#95C2414yes—
948#95C2414yes—
949#95C2412yes—
950#95C2412yes—
951#95C2412yes—
952#95C2412yes—
953#95C2412yes—
954#95C2414yes—
955#95C2414yes—
956#95C2414yes—
957#95C2414yes—
958#95C2414yes—
959#95C2412yes—
960#95C2412yes—
961#95C2414yes—
962#95C2414yes—
963#95C2414yes—
964#95C2412yes—
965#95C2414yes—
966#95C2414yes—
967#95C2412yes—
968#95C2414yes—
969#95C2412yes—
970#95C2412yes—
971#95C2414yes—
972#95C2414yes—
973#95C2414yes—
974#95C2414yes—
975#95C2414yes—
976#95C2414yes—
977#95C2412yes—
978#95C2412yes—
979#95C2412yes—
980#95C2412yes—
981#95C2414yes—
982#95C2412yes—
983#95C2414yes—
984#95C2412yes—
985#95C2412yes—
986#95C2412yes—
987#95C2414yes—
988#95C2414yes—
989#95C2412yes—
990#95C2412yes—
991#95C2414yes—
992#95C2414yes—
993#95C2414yes—
994#95C2414yes—
995#95C2414yes—
996#95C2414yes—
997#95C2414yes—
998#95C2414yes—
999#95C2414yes—
1000#95C2414yes—
1001#95C2414yes—
1002#95C2414yes—
1003#95C2414yes—
1004#95C2414yes—
1005#95C2414yes—
1006#95C2414yes—
1007#95C2414yes—
1008C24C2512yes—
1009C2×Q8—24no—
1010C2×Q8—24no—
1011C2×Q8—24no—
1012C2×Q8—28no—
1013C2×Q8—24no—
1014C2×Q8—22no—
1015C2×Q8—24no—
1016C2×Q8—24no—
1017C2×Q8—24no—
1018C2×Q8—24no—
1019C2×Q8—24no—
1020C2×Q8—24no—
1021C2×Q8—24no—
1022C2×Q8—24no—
1023C2×Q8—41no—
1024C2×Q8—41no—
1025C2×Q8—41no—
1026C2×Q8—42no—
1027C2×Q8—41no—
1028C2×Q8—44no—
1029C2×Q8—44no—
1030C2×Q8—44no—
1031C2×Q8—44no—
1032C2×Q8—44no—
1033C2×Q8—41no—
1034C2×Q8—42no—
1035C2×Q8—816no—
1036C2×Q8—816no—
1037C2×Q8H(5,𝔽2)14yes—
1038C2×Q82−1+414yes—
1039C2×D4—24no—
1040C2×D4—41no—
1041C22×C4—24no—
1042C22×C4—24no—
1043C22×C4—24no—
1044C22×C4—24no—
1045C22×C4—24no—
1046C22×C4—24no—
1047C22×C4—28no—
1048C22×C4—42no—
1049C22×C4—42no—
1050C22×C4—42no—
1051C22×C4—44no—
1052C22×C4—44no—
1053C22×C4—44no—
1054C22×C4—44no—
1055C22×C4—44no—
1056C22×C4C2514yes—
1057C22×C4C2512yes—
1058C22×C4C2512yes—
1059C22×C4C2514yes—
1060C22×C4C2512yes—
1061C22×C4C2512yes—
1062C22×C4C2512yes—
1063C22×C4C2514yes—
1064C22×C4C2511yescharacteristic
1065C22×C4C2511yescharacteristic
1066C22×C4C2512yes—
1067C22×C4C2512yes—
1068C22×C4C2512yes—
1069C22×C4C2511yescharacteristic
1070C22×C4C2512yes—
1071C22×C4C2511yescharacteristic
1072C22×C4C2512yes—
1073C22×C4C2511yescharacteristic
1074C22×C4C2512yes—
1075C22×C4C2514yes—
1076C22×C4C2514yes—
1077C22×C4C2514yes—
1078C22×C4C2512yes—
1079C22×C4C2511yescharacteristic
1080C22×C4C2512yes—
1081C22×C4C2512yes—
1082C22×C4C2512yes—
1083C22×C4C2511yescharacteristic
1084C4⋊C4—28no—
1085C4⋊C4—28no—
1086C4⋊C4—28no—
1087C4⋊C4—28no—
1088C4⋊C4—22no—
1089C4⋊C4—22no—
1090C4⋊C4—24no—
1091C4⋊C4—22no—
1092C4⋊C4—24no—
1093C4⋊C4—24no—
1094C4⋊C4—24no—
1095C4⋊C4—24no—
1096C4⋊C4—24no—
1097C4⋊C4—24no—
1098C4⋊C4—24no—
1099C4⋊C4—24no—
1100C4⋊C4—24no—
1101C4⋊C4—24no—
1102C4⋊C4—24no—
1103C4⋊C4—24no—
1104C4⋊C4—28no—
1105C4⋊C4—28no—
1106C4⋊C4—28no—
1107C4⋊C4—24no—
1108C4⋊C4—24no—
1109C4⋊C4—24no—
1110C4⋊C4—28no—
1111C4⋊C4—28no—
1112C4⋊C4—24no—
1113C4⋊C4—24no—
1114C4⋊C4—24no—
1115C4⋊C4—44no—
1116C4⋊C4—44no—
1117C4⋊C4—44no—
1118C4⋊C4—44no—
1119C4⋊C4—42no—
1120C4⋊C4—44no—
1121C4⋊C4—42no—
1122C4⋊C4—44no—
1123C4⋊C4—44no—
1124C4⋊C4—42no—
1125C4⋊C4—41no—
1126C4⋊C4—42no—
1127C4⋊C4—44no—
1128C4⋊C4—44no—
1129C4⋊C4—44no—
1130C4⋊C4—44no—
1131C4⋊C4—44no—
1132C4⋊C4—41no—
1133C4⋊C4—41no—
1134C4⋊C4—42no—
1135C4⋊C4—42no—
1136C4⋊C4—42no—
1137C4⋊C4—41no—
1138C4⋊C4—42no—
1139C4⋊C4—41no—
1140C4⋊C4—41no—
1141C4⋊C4—44no—
1142C4⋊C4—44no—
1143C4⋊C4—42no—
1144C4⋊C4—42no—
1145C4⋊C4—44no—
1146C4⋊C4—44no—
1147C4⋊C4—44no—
1148C4⋊C4—42no—
1149C4⋊C4—44no—
1150C4⋊C4—44no—
1151C4⋊C4—42no—
1152C4⋊C4—42no—
1153C4⋊C4—42no—
1154C4⋊C4—42no—
1155C4⋊C4—42no—
1156C4⋊C4—44no—
1157C4⋊C4—44no—
1158C4⋊C4—44no—
1159C4⋊C4—44no—
1160C4⋊C4—44no—
1161C4⋊C4—44no—
1162C22⋊C4—24no—
1163C22⋊C4—24no—
1164C22⋊C4—28no—
1165C22⋊C4—24no—
1166C22⋊C4—28no—
1167C22⋊C4—24no—
1168C22⋊C4—24no—
1169C22⋊C4—24no—
1170C22⋊C4—24no—
1171C22⋊C4—44no—
1172C22⋊C4—42no—
1173C22⋊C4—42no—
1174C22⋊C4—42no—
1175C22⋊C4—44no—
1176C22⋊C4—44no—
1177C22⋊C4—44no—
1178C22⋊C42−1+418yes—
1179C42—24no—
1180C42—24no—
1181C42—24no—
1182C42—22no—
1183C42—24no—
1184C42—24no—
1185C42—22no—
1186C42—22no—
1187C42—28no—
1188C42—24no—
1189C42—22no—
1190C42—24no—
1191C42—24no—
1192C42—24no—
1193C42—24no—
1194C42—42no—
1195C42—42no—
1196C42—44no—
1197C42—41no—
1198C42—42no—
1199C42—44no—
1200C42—42no—
1201C42—44no—
1202C42—44no—
1203C42—44no—
1204C42—44no—
1205C42—44no—
1206C42—44no—
1207C42—44no—
1208C23—22no—
1209C23—22no—
1210C23—22no—
1211C23—22no—
1212C23—22no—
1213C23—22no—
1214C23C2×2−1+414yes—
1215C23C2611yescharacteristic
1216Q8—28no—
1217Q8—44no—
1218Q8—44no—
1219Q8—48no—
1220Q8—48no—
1221Q8—48no—
1222Q8—84no—
1223Q8—82no—
1224Q8—88no—
1225Q8—88no—
1226D4—44no—
1227C2×C4—21no—
1228C2×C4—22no—
1229C2×C4—22no—
1230C2×C4—22no—
1231C2×C4—22no—
1232C2×C4—22no—
1233C2×C4—24no—
1234C2×C4—22no—
1235C2×C4—21no—
1236C2×C4—21no—
1237C2×C4—21no—
1238C2×C4—22no—
1239C2×C4—22no—
1240C2×C4—22no—
1241C2×C4—22no—
1242C2×C4—22no—
1243C2×C4—21no—
1244C2×C4—21no—
1245C2×C4—21no—
1246C2×C4—22no—
1247C2×C4—24no—
1248C2×C4—24no—
1249C2×C4—24no—
1250C2×C4—22no—
1251C2×C4—24no—
1252C2×C4—24no—
1253C2×C4—22no—
1254C2×C4—24no—
1255C2×C4—22no—
1256C2×C4—24no—
1257C2×C4—22no—
1258C2×C4—22no—
1259C2×C4—22no—
1260C2×C4—22no—
1261C2×C4—22no—
1262C2×C4—24no—
1263C2×C4—22no—
1264C2×C4—22no—
1265C2×C4—22no—
1266C2×C4—22no—
1267C2×C4—22no—
1268C2×C4—22no—
1269C2×C4—21no—
1270C2×C4—22no—
1271C2×C4—21no—
1272C2×C4—22no—
1273C2×C4—22no—
1274C2×C4—22no—
1275C2×C4—22no—
1276C2×C4—22no—
1277C2×C4—24no—
1278C2×C4—24no—
1279C2×C4—24no—
1280C2×C4—24no—
1281C2×C4—24no—
1282C2×C4—24no—
1283C2×C4—24no—
1284C2×C4—24no—
1285C2×C4—24no—
1286C2×C4—22no—
1287C2×C4—22no—
1288C2×C4—24no—
1289C2×C4—21no—
1290C2×C4—22no—
1291C2×C4—24no—
1292C2×C4—21no—
1293C2×C4—22no—
1294C2×C4—22no—
1295C2×C4—22no—
1296C2×C4—22no—
1297C2×C4—22no—
1298C2×C4—48no—
1299C2×C4—48no—
1300C2×C4—48no—
1301C2×C4—88no—
1302C2×C4—88no—
1303C2×C4C2×H(5,𝔽2)14yes—
1304C2×C4C2×H(5,𝔽2)12yes—
1305C2×C4C2×2−1+412yes—
1306C2×C4C2×2−1+414yes—
1307C2×C4C2×2−1+414yes—
1308C2×C4C2×2−1+414yes—
1309C2×C4#58514yes—
1310C22—24no—
1311C22—24no—
1312C22—24no—
1313C22—42no—
1314C22—42no—
1315C22—42no—
1316C22—42no—
1317C22C22×H(5,𝔽2)11yescharacteristic
1318C22C22×2−1+412yes—
1319C22C22×2−1+411yescharacteristic
1320C22C2×#58512yes—
1321C222−1+611yescharacteristic
1322C4—24no—
1323C4—24no—
1324C4—24no—
1325C4—24no—
1326C4—22no—
1327C4—42no—
1328C4—44no—
1329C4—44no—
1330C4—44no—
1331C4—42no—
1332C4—41no—
1333C4—42no—
1334C4—41no—
1335C4—41no—
1336C4—44no—
1337C4—42no—
1338C4—42no—
1339C4—42no—
1340C4—42no—
1341C4—42no—
1342C4—41no—
1343C4—41no—
1344C4—42no—
1345C4—44no—
1346C4—42no—
1347C4—42no—
1348C4—44no—
1349C4#354514yes—
1350C2—44no—
1351C2C2×#354511yescharacteristic
1352C2#6289311yescharacteristic
1353C2#6295612yes—
1354C2#6301611yescharacteristic
1355C2#6303212yes—
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. #59869C2semidirect
2. #59481C2semidirect
4. #59144C2semidirect
5. #59144C2semidirect
6. #58703C2semidirect
7. #58405C2semidirect
8. #55995C2semidirect
9. #54237C2semidirect
10. #53146C2semidirect
13. #47817C2semidirect
15. #45436C2semidirect
16. #45340C2semidirect
17. #44597C2semidirect
19. #42853C2semidirect
20. #42811C2semidirect
22. #41777C2semidirect
23. #40199C2semidirect
24. #40071C2semidirect
25. #39663C2semidirect
27. #39170C2semidirect
29. #35870C2semidirect

Maximal subgroups

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

subgroupindex
#598692
#594812
#593832
#591442
#587032
#584052
#559952
#542372
#531462
#530322
#523022
#478172
#469252
#454362
#453402
#445972
#438032
#428532
#428112
#424192
#417772
#401992
#400712
#396632
#395932
#391702
#359102
#358702