Finite Group Databasebeta

← #8726579

Subgroups — #8726579

Order 512.

4467 conjugacy classes of subgroups.

The subgroup lattice has 1376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59832C211yesmaximal, characteristic, complemented
2#59663C212yesmaximal, complemented
3#59502C212yesmaximal, complemented
4#59113C212yesmaximal
5#59071C212yesmaximal, complemented
6#58969C214yesmaximal, complemented
7#58290C212yesmaximal, complemented
8#57282C214yesmaximal, complemented
9#56818C214yesmaximal, complemented
10#53100C211yesmaximal, characteristic, complemented
11#53002C212yesmaximal, complemented
12#52302C211yesmaximal, characteristic
13#47799C212yesmaximal
14#46583C214yesmaximal, complemented
15#45384C211yesmaximal, characteristic
16#44994C212yesmaximal, complemented
17#44894C214yesmaximal, complemented
18#44862C212yesmaximal
19#42825C212yesmaximal, complemented
20#42814C211yesmaximal, characteristic
21#42376C212yesmaximal, complemented
22#41354C214yesmaximal
23#40055C212yesmaximal
24#39660C212yesmaximal, complemented
25#39597C212yesmaximal, complemented
26#39368C212yesmaximal, complemented
27#39170C211yesmaximal, characteristic, complemented
28#35937C211yesmaximal, characteristic, complemented
29#35919C212yesmaximal, complemented
30C2×Q82C2212yes—
31C2×Q82C2211yescharacteristic
32C2×#557C2211yescharacteristic
33C2×#557C2211yescharacteristic
34C2×#554C2211yescharacteristic
35C2×#544C2214yes—
36C2×#533C2212yes—
37#2862C2211yescharacteristic
38#2857C2212yes—
39#2844C2214yes—
40#2839C2214yes—
41#2839C2214yes—
42#2835C2214yes—
43#2833C2214yes—
44#2833C2214yes—
45#2833C2212yes—
46#2822C2212yes—
47#2822C2212yes—
48#2809C2212yes—
49#2805C2214yes—
50#2802C2214yes—
51#2802C2214yes—
52#2799C2211yescharacteristic
53#2799C2212yes—
54#2799C2214yes—
55#2794C2211yescharacteristic
56#2794C2214yes—
57#2789C2212yes—
58#2787C2214yes—
59#2776C2212yes—
60#2774C2214yes—
61#2770C2212yes—
62#2769C2212yes—
63#2767C2214yes—
64#2763C2214yes—
65#2762C2214yes—
66#2758C2214yes—
67#2755C2214yes—
68#2755C2214yes—
69#2745C2212yes—
70#2745C2214yes—
71#2744C2214yes—
72#2739C2214yes—
73#2734C2214yes—
74#2734C2212yes—
75#2734C2214yes—
76#2734C2212yes—
77#2729C2214yes—
78#2729C2212yes—
79#2729C2214yes—
80#2728C2211yescharacteristic
81#2726C2214yes—
82#2726C2214yes—
83#2720C2214yes—
84#2719C2214yes—
85#2719C2214yes—
86#2719C2214yes—
87#2719C2214yes—
88#2719C2214yes—
89#2713C2214yes—
90#2713C2214yes—
91#2713C2214yes—
92#2713C2214yes—
93#2713C2214yes—
94#2713C2214yes—
95#2713C2214yes—
96#2698C2214yes—
97#2695C2212yes—
98#2690C2214yes—
99#2690C2214yes—
100#2689C2212yes—
101#2687C2214yes—
102#2680C2211yescharacteristic
103#2677C2214yes—
104#2677C2214yes—
105#2677C2214yes—
106#2666C2214yes—
107#2666C2214yes—
108#2666C2214yes—
109#2660C2211yescharacteristic
110#2660C2211yescharacteristic
111#2660C2212yes—
112#2655C2214yes—
113#2655C2214yes—
114#2645C2212yes—
115#2642C2212yes—
116#2634C2212yes—
117#2633C2212yes—
118#2628C2214yes—
119#2627C2214yes—
120#2611C2214yes—
121#2609C2212yes—
122#2590C2214yes—
123#2588C2214yes—
124#2588C2214yes—
125#2584C2211yescharacteristic
126#2584C2214yes—
127#2584C2212yes—
128#2582C2212yes—
129#2582C2212yes—
130#2581C2214yes—
131#2575C2214yes—
132#2575C2214yes—
133#2572C2212yes—
134#2570C2212yes—
135#2568C2211yescharacteristic
136#2568C2212yes—
137#2567C2212yes—
138#2565C2212yes—
139#2565C2214yes—
140#2562C2211yescharacteristic
141#2551C2212yes—
142#2551C2212yes—
143#2551C2212yes—
144#2551C2214yes—
145#2551C2212yes—
146#2550C2214yes—
147#2550C2212yes—
148#2550C2214yes—
149#2549C2214yes—
150#2546C2212yes—
151#2546C2211yescharacteristic
152#2546C2211yescharacteristic
153#2546C2211yescharacteristic
154#2546C2214yes—
155#2546C2212yes—
156#2546C2212yes—
157#2536C2212yes—
158#2528C2214yes—
159#2528C2214yes—
160#2527C2214yes—
161#2524C2214yes—
162#2520C2214yes—
163#2511C2212yes—
164#2511C2212yes—
165#2509C2212yes—
166#2506C2212yes—
167#2506C2212yes—
168#2506C2212yes—
169#2506C2212yes—
170#2505C2214yes—
171#2502C2212yes—
172#2494C2212yes—
173#2492C2212yes—
174#2492C2212yes—
175#2492C2212yes—
176#2489C2214yes—
177#2477C2214yes—
178#2475C2214yes—
179#2475C2214yes—
180#2475C2214yes—
181#2473C2214yes—
182#2465C2214yes—
183#2465C2214yes—
184#2462C2214yes—
185#2462C2214yes—
186#2462C2214yes—
187#2453C2212yes—
188#2453C2212yes—
189#2453C2214yes—
190#2453C2214yes—
191#2451C2212yes—
192#2451C2212yes—
193#2451C2212yes—
194#2451C2214yes—
195#2451C2214yes—
196#2451C2214yes—
197#2449C2214yes—
198#2446C2212yes—
199#2446C2212yes—
200#2446C2212yes—
201#2446C2212yes—
202#2442C2212yes—
203#2440C2212yes—
204#2440C2212yes—
205#2440C2212yes—
206#2440C2214yes—
207#2439C2214yes—
208#2438C2214yes—
209#2438C2214yes—
210#2438C2214yes—
211#2429C2212yes—
212#2429C2212yes—
213#2429C2214yes—
214#2429C2214yes—
215#2423C2212yes—
216#2423C2212yes—
217#2421C2212yes—
218#2421C2212yes—
219#2417C2212yes—
220#2402C2212yes—
221#2401C2212yes—
222#2399C2212yes—
223#2399C2211yescharacteristic
224#2398C2211yescharacteristic
225#2396C2214yes—
226#2365C2212yes—
227#2365C2212yes—
228#2365C2214yes—
229#2365C2212yes—
230#2362C2214yes—
231#2360C2212yes—
232#2360C2214yes—
233#2360C2212yes—
234#2360C2212yes—
235#2359C2214yes—
236#2355C2212yes—
237#2355C2212yes—
238#2351C2212yes—
239#2351C2212yes—
240Q8×C4⋊C4C2212yes—
241#2344C2212yes—
242#2344C2212yes—
243#2334C2214yes—
244#2327C2212yes—
245#2323C2214yes—
246#2323C2214yes—
247#2320C2211yescharacteristic
248#2320C2212yes—
249C4×C4⋊Q8C2211yescharacteristic
250C4×C4⋊Q8C2212yes—
251C4×#126C2212yes—
252C4×C22⋊Q8C2212yes—
253C4×C22⋊Q8C2212yes—
254C4×C22⋊Q8C2212yes—
255C4×#123C2212yes—
256#2295C2211yescharacteristic
257C2×#389C2212yes—
258#2276C2211yescharacteristic
259Q82—44no—
260Q82—48no—
261#557—44no—
262#557—44no—
263#554—44no—
264#544—416no—
265#533—48no—
266C2×C4⋊Q8C2312yes—
267C2×C4⋊Q8C2311yescharacteristic
268C2×C4⋊Q8C2312yes—
269C2×C4⋊Q8C2312yes—
270C2×C4⋊Q8C2314yes—
271C2×C4⋊Q8C2312yes—
272C2×C4⋊Q8C2311yescharacteristic
273C2×C4⋊Q8C2312yes—
274C2×C4⋊Q8C2311yescharacteristic
275C2×C4⋊Q8C2314yes—
276C2×C4⋊Q8C2312yes—
277C2×C4⋊Q8C2312yes—
278C2×C4⋊Q8C2311yescharacteristic
279C2×C4⋊Q8C2311yescharacteristic
280C2×C4⋊Q8C2312yes—
281C2×C4⋊Q8C2314yes—
282C2×C4⋊Q8C2314yes—
283C2×C4⋊Q8C2314yes—
284C2×C4⋊Q8C2314yes—
285C2×C4⋊Q8C2312yes—
286C2×#126C2312yes—
287C2×#125C2311yescharacteristic
288C2×#125C2314yes—
289C2×#125C2312yes—
290C2×#125C2314yes—
291C2×#125C2312yes—
292C2×#125C2312yes—
293C2×#125C2312yes—
294C2×#125C2311yescharacteristic
295C2×#125C2314yes—
296C2×#125C2314yes—
297C2×#125C2314yes—
298C2×#125C2314yes—
299C2×#123C2312yes—
300C2×C22⋊Q8C2312yes—
301C2×C22⋊Q8C2314yes—
302C2×C22⋊Q8C2312yes—
303C2×C22⋊Q8C2312yes—
304C2×C22⋊Q8C2312yes—
305C2×C22⋊Q8C2314yes—
306C2×C22⋊Q8C2312yes—
307C2×C22⋊Q8C2314yes—
308C2×C22⋊Q8C2314yes—
309C2×C22⋊Q8C2314yes—
310C2×C22⋊Q8C2314yes—
311C2×C4×Q8C2311yescharacteristic
312C2×C4×Q8C2312yes—
313C2×C4×Q8C2312yes—
314C2×C4×Q8C2312yes—
315C2×C4×Q8C2311yescharacteristic
316C2×C4×Q8C2311yescharacteristic
317C2×C4×Q8C2311yescharacteristic
318C2×C4×Q8C2314yes—
319C2×C4×Q8C2311yescharacteristic
320C2×C4×Q8C2314yes—
321C2×C4×Q8C2312yes—
322C2×C4×Q8C2312yes—
323C2×C4×Q8C2312yes—
324C2×C4×Q8C2312yes—
325C2×C4×Q8C2314yes—
326C2×C4×Q8C2311yescharacteristic
327C2×C4×Q8C2312yes—
328C2×C4×Q8C2314yes—
329C2×C4×D4C2311yescharacteristic
330C2×C4×D4C2312yes—
331C2×#117C2314yes—
332C2×#117C2314yes—
333C2×#117C2314yes—
334C22×C4⋊C4C2312yes—
335C22×C4⋊C4C2314yes—
336C22×C4⋊C4C2312yes—
337C22×C42C2312yes—
338#401C2314yes—
339#401C2312yes—
340#401C2314yes—
341#400C2312yes—
342#400C2311yescharacteristic
343#400C2314yes—
344#400C2314yes—
345#400C2314yes—
346#400C2312yes—
347#400C2314yes—
348#400C2312yes—
349#400C2314yes—
350#400C2314yes—
351#400C2314yes—
352#400C2314yes—
353#400C2314yes—
354#400C2312yes—
355#400C2314yes—
356#400C2314yes—
357#400C2314yes—
358#400C2314yes—
359#400C2314yes—
360#400C2314yes—
361#400C2314yes—
362#400C2314yes—
363#400C2314yes—
364#400C2314yes—
365#400C2312yes—
366#400C2314yes—
367#400C2314yes—
368#400C2312yes—
369#400C2314yes—
370#400C2314yes—
371#400C2314yes—
372#400C2314yes—
373#400C2314yes—
374#400C2311yescharacteristic
375#400C2314yes—
376#400C2314yes—
377#400C2312yes—
378#400C2312yes—
379#400C2312yes—
380#400C2312yes—
381#399C2314yes—
382#399C2314yes—
383#398C2312yes—
384#398C2314yes—
385#398C2314yes—
386#398C2314yes—
387#398C2314yes—
388#398C2314yes—
389#398C2311yescharacteristic
390#398C2314yes—
391#398C2314yes—
392#398C2312yes—
393#398C2312yes—
394#398C2314yes—
395#398C2314yes—
396#398C2312yes—
397#398C2314yes—
398#398C2314yes—
399#398C2314yes—
400#398C2311yescharacteristic
401#398C2312yes—
402#398C2314yes—
403#398C2314yes—
404#398C2314yes—
405#398C2312yes—
406#398C2314yes—
407#398C2312yes—
408#398C2312yes—
409#398C2314yes—
410#398C2314yes—
411#398C2312yes—
412#398C2312yes—
413#398C2314yes—
414#398C2314yes—
415#398C2314yes—
416#398C2314yes—
417#398C2314yes—
418#398C2314yes—
419#398C2312yes—
420#398C2314yes—
421#398C2314yes—
422#398C2314yes—
423#398C2312yes—
424#398C2312yes—
425#398C2312yes—
426#398C2314yes—
427#398C2314yes—
428#398C2314yes—
429#398C2314yes—
430#397C2312yes—
431#397C2314yes—
432#397C2314yes—
433#397C2314yes—
434#397C2312yes—
435#397C2312yes—
436#397C2312yes—
437#396C2314yes—
438#396C2312yes—
439#396C2314yes—
440#396C2314yes—
441#395C2314yes—
442#395C2314yes—
443#395C2314yes—
444#395C2314yes—
445#395C2314yes—
446#395C2314yes—
447#395C2314yes—
448#395C2314yes—
449#395C2312yes—
450#395C2311yescharacteristic
451#395C2314yes—
452#395C2314yes—
453#395C2314yes—
454#395C2314yes—
455#395C2314yes—
456#395C2314yes—
457#395C2314yes—
458#395C2314yes—
459#395C2314yes—
460#395C2311yescharacteristic
461#395C2314yes—
462#395C2312yes—
463#395C2314yes—
464#394C2312yes—
465#394C2311yescharacteristic
466#394C2311yescharacteristic
467#393C2314yes—
468#393C2314yes—
469#393C2314yes—
470#393C2312yes—
471#391C2311yescharacteristic
472#391C2311yescharacteristic
473#391C2314yes—
474#391C2312yes—
475#391C2314yes—
476#391C2314yes—
477#391C2312yes—
478#391C2312yes—
479#391C2312yes—
480#391C2312yes—
481#391C2314yes—
482#391C2312yes—
483#391C2312yes—
484#391C2312yes—
485#391C2314yes—
486#391C2312yes—
487#391C2312yes—
488#391C2312yes—
489#391C2314yes—
490#391C2314yes—
491#391C2314yes—
492#391C2312yes—
493#391C2314yes—
494#391C2314yes—
495#391C2312yes—
496#391C2312yes—
497#391C2314yes—
498#391C2312yes—
499#391C2312yes—
500#391C2312yes—
501#391C2312yes—
502#391C2314yes—
503#391C2314yes—
504#391C2314yes—
505#391C2314yes—
506#389C2312yes—
507#389C2314yes—
508#389C2312yes—
509#389C2312yes—
510#389C2312yes—
511#389C2314yes—
512#389C2314yes—
513#389C2312yes—
514#389C2312yes—
515#389C2312yes—
516#389C2312yes—
517#389C2312yes—
518#389C2314yes—
519#389C2314yes—
520#389C2314yes—
521#389C2314yes—
522#389C2314yes—
523#389C2314yes—
524#389C2314yes—
525#389C2312yes—
526#389C2312yes—
527#389C2314yes—
528#389C2312yes—
529#389C2314yes—
530#389C2314yes—
531#389C2314yes—
532#389C2314yes—
533#389C2312yes—
534#389C2314yes—
535#389C2312yes—
536#389C2314yes—
537#389C2314yes—
538#389C2314yes—
539#389C2314yes—
540#389C2314yes—
541#389C2312yes—
542#389C2312yes—
543#389C2312yes—
544#389C2314yes—
545#389C2314yes—
546#389C2312yes—
547#389C2314yes—
548#389C2314yes—
549#389C2314yes—
550#389C2314yes—
551#389C2312yes—
552#389C2312yes—
553#389C2314yes—
554#388C2312yes—
555#388C2312yes—
556#388C2312yes—
557#388C2314yes—
558#388C2314yes—
559#388C2314yes—
560#388C2314yes—
561#388C2314yes—
562#388C2314yes—
563#388C2312yes—
564#388C2314yes—
565#388C2314yes—
566#388C2314yes—
567#388C2314yes—
568#388C2314yes—
569#388C2312yes—
570#387C2312yes—
571#387C2312yes—
572#387C2312yes—
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#387C2314yes—
603#387C2314yes—
604#387C2314yes—
605#387C2314yes—
606#387C2314yes—
607#387C2314yes—
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#387C2312yes—
624#387C2312yes—
625#387C2312yes—
626#387C2312yes—
627#387C2312yes—
628#387C2314yes—
629#387C2312yes—
630#386C2314yes—
631#386C2312yes—
632#385C2314yes—
633#385C2314yes—
634#385C2314yes—
635#385C2314yes—
636#385C2314yes—
637#385C2314yes—
638#385C2314yes—
639#385C2314yes—
640#385C2312yes—
641#385C2314yes—
642#385C2312yes—
643#385C2312yes—
644#385C2314yes—
645#385C2312yes—
646#385C2312yes—
647#384C2311yescharacteristic
648#384C2312yes—
649#384C2314yes—
650#384C2312yes—
651#384C2312yes—
652#384C2312yes—
653#383C2312yes—
654#383C2314yes—
655#383C2312yes—
656#382C2312yes—
657#382C2314yes—
658#382C2312yes—
659#382C2312yes—
660#382C2312yes—
661#382C2314yes—
662#382C2314yes—
663#382C2314yes—
664#382C2314yes—
665#382C2314yes—
666#381C2314yes—
667#381C2314yes—
668#381C2312yes—
669#380C2312yes—
670#380C2312yes—
671#380C2314yes—
672#380C2314yes—
673#380C2312yes—
674#380C2312yes—
675#380C2312yes—
676#380C2314yes—
677C4×C4⋊C4C2312yes—
678C4×C4⋊C4C2312yes—
679C4×C4⋊C4C2312yes—
680C4×C4⋊C4C2311yescharacteristic
681C4×C4⋊C4C2314yes—
682C4×C4⋊C4C2312yes—
683C4×C4⋊C4C2312yes—
684C4×C4⋊C4C2312yes—
685C4×C4⋊C4C2312yes—
686C4×C4⋊C4C2312yes—
687C4×C4⋊C4C2314yes—
688C4×C4⋊C4C2311yescharacteristic
689C4×C4⋊C4C2312yes—
690C4×C4⋊C4C2312yes—
691C4×C4⋊C4C2314yes—
692C4×C4⋊C4C2314yes—
693C4×C4⋊C4C2314yes—
694C4×C4⋊C4C2312yes—
695C4×C4⋊C4C2311yescharacteristic
696C4×C4⋊C4C2314yes—
697C4×C4⋊C4C2314yes—
698C4×C4⋊C4C2312yes—
699C4×C4⋊C4C2312yes—
700C4×C4⋊C4C2314yes—
701C4×C4⋊C4C2312yes—
702C4×C4⋊C4C2314yes—
703C4×C4⋊C4C2312yes—
704C4×C22⋊C4C2312yes—
705C4×C22⋊C4C2312yes—
706C4×C22⋊C4C2312yes—
707C4×C22⋊C4C2314yes—
708C4×C22⋊C4C2314yes—
709C4×C22⋊C4C2314yes—
710C4×C22⋊C4C2312yes—
711C4×C22⋊C4C2312yes—
712C4×C22⋊C4C2314yes—
713#376C2311yescharacteristic
714#376C2312yes—
715#376C2311yescharacteristic
716#376C2312yes—
717C2×#95C2314yes—
718C43C2311yescharacteristic
719C22×Q8C2412yes—
720C22×Q8C2411yescharacteristic
721C22×Q8C2414yes—
722C22×Q8C2411yescharacteristic
723C22×Q8C2414yes—
724C22×Q8C2412yes—
725C22×Q8C2411yescharacteristic
726C22×Q8C2412yes—
727C22×Q8C2414yes—
728C22×Q8C2412yes—
729C22×Q8C2411yescharacteristic
730C22×D4C2411yescharacteristic
731C23×C4C2412yes—
732C23×C4C2414yes—
733C23×C4C2412yes—
734C23×C4C2412yes—
735C23×C4C2414yes—
736C4⋊Q8—28no—
737C4⋊Q8—28no—
738C4⋊Q8—216no—
739C4⋊Q8—24no—
740C4⋊Q8—28no—
741C4⋊Q8—44no—
742C4⋊Q8—42no—
743C4⋊Q8—44no—
744C4⋊Q8—42no—
745C4⋊Q8—44no—
746C4⋊Q8—48no—
747C4⋊Q8—44no—
748C4⋊Q8—42no—
749C4⋊Q8—42no—
750C4⋊Q8—48no—
751C4⋊Q8—48no—
752C4⋊Q8—48no—
753C4⋊Q8—44no—
754C4⋊Q8—48no—
755C4⋊Q8—44no—
756#126—28no—
757#125—48no—
758#125—48no—
759#125—44no—
760#125—44no—
761#125—42no—
762#125—42no—
763#125—44no—
764#125—44no—
765#125—48no—
766#125—48no—
767#125—48no—
768#125—48no—
769#123—28no—
770C22⋊Q8—28no—
771C22⋊Q8—28no—
772C22⋊Q8—28no—
773C22⋊Q8—28no—
774C22⋊Q8—216no—
775C22⋊Q8—48no—
776C22⋊Q8—48no—
777C22⋊Q8—48no—
778C22⋊Q8—48no—
779C22⋊Q8—48no—
780C22⋊Q8—44no—
781C4×Q8—28no—
782C4×Q8—24no—
783C4×Q8—24no—
784C4×Q8—24no—
785C4×Q8—28no—
786C4×Q8—28no—
787C4×Q8—42no—
788C4×Q8—44no—
789C4×Q8—42no—
790C4×Q8—42no—
791C4×Q8—44no—
792C4×Q8—48no—
793C4×Q8—44no—
794C4×Q8—48no—
795C4×Q8—48no—
796C4×Q8—48no—
797C4×Q8—44no—
798C4×Q8—44no—
799C4×D4—44no—
800C4×D4—42no—
801#117—48no—
802#117—48no—
803#117—48no—
804C2×C4⋊C4—28no—
805C2×C4⋊C4—48no—
806C2×C4⋊C4—44no—
807C2×C4⋊C4C2411yescharacteristic
808C2×C4⋊C4C2412yes—
809C2×C4⋊C4C2414yes—
810C2×C4⋊C4C2414yes—
811C2×C4⋊C4C2412yes—
812C2×C4⋊C4C2414yes—
813C2×C4⋊C4C2414yes—
814C2×C4⋊C4C2414yes—
815C2×C4⋊C4C2414yes—
816C2×C4⋊C4C2411yescharacteristic
817C2×C4⋊C4C2414yes—
818C2×C4⋊C4C2412yes—
819C2×C4⋊C4C2412yes—
820C2×C4⋊C4C2414yes—
821C2×C4⋊C4C2412yes—
822C2×C4⋊C4C2414yes—
823C2×C4⋊C4C2414yes—
824C2×C4⋊C4C2414yes—
825C2×C4⋊C4C2412yes—
826C2×C4⋊C4C2412yes—
827C2×C4⋊C4C2411yescharacteristic
828C2×C4⋊C4C2412yes—
829C2×C4⋊C4C2414yes—
830C2×C4⋊C4C2414yes—
831C2×C4⋊C4C2412yes—
832C2×C4⋊C4C2412yes—
833C2×C4⋊C4C2412yes—
834C2×C4⋊C4C2414yes—
835C2×C4⋊C4C2412yes—
836C2×C4⋊C4C2414yes—
837C2×C4⋊C4C2414yes—
838C2×C4⋊C4C2412yes—
839C2×C4⋊C4C2412yes—
840C2×C4⋊C4C2414yes—
841C2×C4⋊C4C2412yes—
842C2×C4⋊C4C2412yes—
843C2×C4⋊C4C2412yes—
844C2×C4⋊C4C2412yes—
845C2×C4⋊C4C2412yes—
846C2×C4⋊C4C2412yes—
847C2×C4⋊C4C2414yes—
848C2×C4⋊C4C2414yes—
849C2×C4⋊C4C2414yes—
850C2×C4⋊C4C2414yes—
851C2×C4⋊C4C2414yes—
852C2×C4⋊C4C2414yes—
853C2×C4⋊C4C2414yes—
854C2×C4⋊C4C2411yescharacteristic
855C2×C4⋊C4C2412yes—
856C2×C4⋊C4C2411yescharacteristic
857C2×C4⋊C4C2414yes—
858C2×C4⋊C4C2414yes—
859C2×C4⋊C4C2412yes—
860C2×C4⋊C4C2412yes—
861C2×C4⋊C4C2414yes—
862C2×C4⋊C4C2411yescharacteristic
863C2×C4⋊C4C2412yes—
864C2×C4⋊C4C2411yescharacteristic
865C2×C4⋊C4C2411yescharacteristic
866C2×C4⋊C4C2412yes—
867C2×C4⋊C4C2414yes—
868C2×C4⋊C4C2412yes—
869C2×C4⋊C4C2414yes—
870C2×C4⋊C4C2414yes—
871C2×C4⋊C4C2411yescharacteristic
872C2×C4⋊C4C2414yes—
873C2×C4⋊C4C2412yes—
874C2×C4⋊C4C2414yes—
875C2×C4⋊C4C2414yes—
876C2×C4⋊C4C2414yes—
877C2×C4⋊C4C2414yes—
878C2×C4⋊C4C2414yes—
879C2×C4⋊C4C2412yes—
880C2×C4⋊C4C2412yes—
881C2×C4⋊C4C2412yes—
882C2×C4⋊C4C2412yes—
883C2×C4⋊C4C2412yes—
884C2×C4⋊C4C2412yes—
885C2×C4⋊C4C2414yes—
886C2×C4⋊C4C2414yes—
887C2×C4⋊C4C2412yes—
888C2×C4⋊C4C2414yes—
889C2×C4⋊C4C2412yes—
890C2×C22⋊C4C2412yes—
891C2×C22⋊C4C2412yes—
892C2×C22⋊C4C2414yes—
893C2×C22⋊C4C2414yes—
894C2×C22⋊C4C2412yes—
895C2×C22⋊C4C2414yes—
896C2×C22⋊C4C2412yes—
897C2×C22⋊C4C2412yes—
898C2×C22⋊C4C2412yes—
899C2×C22⋊C4C2412yes—
900C2×C22⋊C4C2414yes—
901C2×C22⋊C4C2414yes—
902C2×C22⋊C4C2414yes—
903C2×C22⋊C4C2412yes—
904C2×C22⋊C4C2412yes—
905C2×C22⋊C4C2412yes—
906C2×C22⋊C4C2412yes—
907C2×C42—44no—
908C2×C42C2412yes—
909C2×C42C2414yes—
910C2×C42C2414yes—
911C2×C42C2412yes—
912C2×C42C2411yescharacteristic
913C2×C42C2411yescharacteristic
914C2×C42C2411yescharacteristic
915C2×C42C2412yes—
916C2×C42C2412yes—
917C2×C42C2411yescharacteristic
918C2×C42C2412yes—
919C2×C42C2412yes—
920C2×C42C2412yes—
921C2×C42C2412yes—
922C2×C42C2414yes—
923C2×C42C2414yes—
924C2×C42C2412yes—
925C2×C42C2412yes—
926C2×C42C2414yes—
927C2×C42C2414yes—
928C2×C42C2414yes—
929C2×C42C2414yes—
930C2×C42C2412yes—
931C2×C42C2414yes—
932C2×C42C2414yes—
933C2×C42C2412yes—
934C2×C42C2412yes—
935C2×C42C2412yes—
936C2×C42C2411yescharacteristic
937#95C2414yes—
938#95C2414yes—
939#95C2414yes—
940#95C2414yes—
941#95C2411yescharacteristic
942#95C2414yes—
943#95C2412yes—
944#95C2412yes—
945#95C2411yescharacteristic
946#95C2412yes—
947#95C2411yescharacteristic
948#95C2414yes—
949#95C2411yescharacteristic
950#95C2414yes—
951#95C2414yes—
952#95C2414yes—
953#95C2412yes—
954#95C2412yes—
955#95C2414yes—
956#95C2414yes—
957#95C2412yes—
958#95C2412yes—
959#95C2412yes—
960#95C2412yes—
961#95C2414yes—
962#95C2412yes—
963#95C2412yes—
964#95C2412yes—
965#95C2414yes—
966#95C2412yes—
967#95C2414yes—
968#95C2412yes—
969#95C2412yes—
970#95C2412yes—
971#95C2412yes—
972#95C2414yes—
973#95C2412yes—
974#95C2412yes—
975#95C2414yes—
976#95C2414yes—
977#95C2414yes—
978#95C2412yes—
979#95C2412yes—
980#95C2414yes—
981#95C2414yes—
982#95C2414yes—
983#95C2412yes—
984#95C2414yes—
985#95C2414yes—
986#95C2414yes—
987#95C2414yes—
988#95C2412yes—
989#95C2414yes—
990#95C2412yes—
991#95C2412yes—
992#95C2414yes—
993#95C2412yes—
994#95C2412yes—
995#95C2412yes—
996#95C2414yes—
997#95C2414yes—
998#95C2412yes—
999#95C2412yes—
1000#95C2412yes—
1001#95C2414yes—
1002#95C2414yes—
1003#95C2414yes—
1004#95C2414yes—
1005#95C2414yes—
1006#95C2414yes—
1007#95C2414yes—
1008#95C2414yes—
1009#95C2414yes—
1010#95C2414yes—
1011#95C2414yes—
1012#95C2414yes—
1013#95C2414yes—
1014#95C2414yes—
1015#95C2414yes—
1016#95C2414yes—
1017#95C2414yes—
1018#95C2414yes—
1019#95C2414yes—
1020C24C2512yes—
1021C2×Q8—24no—
1022C2×Q8—24no—
1023C2×Q8—28no—
1024C2×Q8—22no—
1025C2×Q8—24no—
1026C2×Q8—24no—
1027C2×Q8—28no—
1028C2×Q8—24no—
1029C2×Q8—24no—
1030C2×Q8—28no—
1031C2×Q8—41no—
1032C2×Q8—41no—
1033C2×Q8—44no—
1034C2×Q8—41no—
1035C2×Q8—44no—
1036C2×Q8—41no—
1037C2×Q8—42no—
1038C2×Q8—41no—
1039C2×Q8—42no—
1040C2×Q8—44no—
1041C2×Q8—42no—
1042C2×Q8—44no—
1043C2×Q8—44no—
1044C2×Q8—42no—
1045C2×Q8—42no—
1046C2×Q8—42no—
1047C2×Q8—42no—
1048C2×Q8—44no—
1049C2×Q8—42no—
1050C2×Q8H(5,𝔽2)14yes—
1051C2×Q8H(5,𝔽2)14yes—
1052C2×D4—24no—
1053C2×D4—41no—
1054C22×C4—28no—
1055C22×C4—24no—
1056C22×C4—24no—
1057C22×C4—28no—
1058C22×C4—24no—
1059C22×C4—24no—
1060C22×C4—24no—
1061C22×C4—24no—
1062C22×C4—42no—
1063C22×C4—44no—
1064C22×C4—42no—
1065C22×C4—42no—
1066C22×C4—44no—
1067C22×C4—44no—
1068C22×C4—44no—
1069C22×C4C2512yes—
1070C22×C4C2512yes—
1071C22×C4C2512yes—
1072C22×C4C2511yescharacteristic
1073C22×C4C2514yes—
1074C22×C4C2514yes—
1075C22×C4C2511yescharacteristic
1076C22×C4C2514yes—
1077C22×C4C2512yes—
1078C22×C4C2512yes—
1079C22×C4C2512yes—
1080C22×C4C2511yescharacteristic
1081C22×C4C2512yes—
1082C22×C4C2512yes—
1083C22×C4C2511yescharacteristic
1084C22×C4C2514yes—
1085C22×C4C2512yes—
1086C22×C4C2511yescharacteristic
1087C22×C4C2512yes—
1088C22×C4C2514yes—
1089C22×C4C2512yes—
1090C22×C4C2512yes—
1091C22×C4C2511yescharacteristic
1092C22×C4C2512yes—
1093C22×C4C2512yes—
1094C22×C4C2512yes—
1095C22×C4C2514yes—
1096C22×C4C2511yescharacteristic
1097C4⋊C4—22no—
1098C4⋊C4—24no—
1099C4⋊C4—28no—
1100C4⋊C4—28no—
1101C4⋊C4—28no—
1102C4⋊C4—28no—
1103C4⋊C4—28no—
1104C4⋊C4—22no—
1105C4⋊C4—24no—
1106C4⋊C4—28no—
1107C4⋊C4—24no—
1108C4⋊C4—24no—
1109C4⋊C4—24no—
1110C4⋊C4—22no—
1111C4⋊C4—28no—
1112C4⋊C4—24no—
1113C4⋊C4—24no—
1114C4⋊C4—28no—
1115C4⋊C4—28no—
1116C4⋊C4—28no—
1117C4⋊C4—24no—
1118C4⋊C4—24no—
1119C4⋊C4—24no—
1120C4⋊C4—28no—
1121C4⋊C4—24no—
1122C4⋊C4—28no—
1123C4⋊C4—28no—
1124C4⋊C4—24no—
1125C4⋊C4—28no—
1126C4⋊C4—28no—
1127C4⋊C4—24no—
1128C4⋊C4—28no—
1129C4⋊C4—24no—
1130C4⋊C4—28no—
1131C4⋊C4—24no—
1132C4⋊C4—24no—
1133C4⋊C4—24no—
1134C4⋊C4—24no—
1135C4⋊C4—24no—
1136C4⋊C4—28no—
1137C4⋊C4—24no—
1138C4⋊C4—44no—
1139C4⋊C4—44no—
1140C4⋊C4—44no—
1141C4⋊C4—42no—
1142C4⋊C4—42no—
1143C4⋊C4—44no—
1144C4⋊C4—44no—
1145C4⋊C4—42no—
1146C4⋊C4—44no—
1147C4⋊C4—44no—
1148C4⋊C4—44no—
1149C4⋊C4—44no—
1150C4⋊C4—41no—
1151C4⋊C4—42no—
1152C4⋊C4—41no—
1153C4⋊C4—44no—
1154C4⋊C4—44no—
1155C4⋊C4—41no—
1156C4⋊C4—42no—
1157C4⋊C4—42no—
1158C4⋊C4—41no—
1159C4⋊C4—42no—
1160C4⋊C4—41no—
1161C4⋊C4—44no—
1162C4⋊C4—42no—
1163C4⋊C4—42no—
1164C4⋊C4—44no—
1165C4⋊C4—44no—
1166C4⋊C4—44no—
1167C4⋊C4—41no—
1168C4⋊C4—42no—
1169C4⋊C4—44no—
1170C4⋊C4—44no—
1171C4⋊C4—44no—
1172C4⋊C4—44no—
1173C4⋊C4—44no—
1174C4⋊C4—44no—
1175C4⋊C4—42no—
1176C4⋊C4—42no—
1177C4⋊C4—42no—
1178C4⋊C4—42no—
1179C4⋊C42−1+418yes—
1180C22⋊C4—24no—
1181C22⋊C4—28no—
1182C22⋊C4—24no—
1183C22⋊C4—24no—
1184C22⋊C4—24no—
1185C22⋊C4—24no—
1186C22⋊C4—24no—
1187C22⋊C4—28no—
1188C22⋊C4—28no—
1189C22⋊C4—24no—
1190C22⋊C4—42no—
1191C22⋊C4—42no—
1192C22⋊C4—44no—
1193C22⋊C4—44no—
1194C22⋊C4—44no—
1195C22⋊C4—42no—
1196C22⋊C42−1+418yes—
1197C42—24no—
1198C42—24no—
1199C42—24no—
1200C42—28no—
1201C42—28no—
1202C42—24no—
1203C42—22no—
1204C42—24no—
1205C42—24no—
1206C42—22no—
1207C42—22no—
1208C42—22no—
1209C42—28no—
1210C42—24no—
1211C42—24no—
1212C42—28no—
1213C42—24no—
1214C42—24no—
1215C42—42no—
1216C42—42no—
1217C42—41no—
1218C42—44no—
1219C42—44no—
1220C42—44no—
1221C42—44no—
1222C42—44no—
1223C42—44no—
1224C42—42no—
1225C42—42no—
1226C23—22no—
1227C23—22no—
1228C23—22no—
1229C23—22no—
1230C23—22no—
1231C23—22no—
1232C23C2×2−1+414yes—
1233C23C2611yescharacteristic
1234Q8—28no—
1235Q8—44no—
1236Q8—44no—
1237Q8—416no—
1238Q8—48no—
1239Q8—88no—
1240Q8—84no—
1241Q8—82no—
1242Q8—164no—
1243Q8—162no—
1244Q8—162no—
1245D4—44no—
1246C2×C4—22no—
1247C2×C4—21no—
1248C2×C4—22no—
1249C2×C4—24no—
1250C2×C4—22no—
1251C2×C4—24no—
1252C2×C4—22no—
1253C2×C4—24no—
1254C2×C4—22no—
1255C2×C4—21no—
1256C2×C4—22no—
1257C2×C4—21no—
1258C2×C4—21no—
1259C2×C4—24no—
1260C2×C4—22no—
1261C2×C4—24no—
1262C2×C4—22no—
1263C2×C4—22no—
1264C2×C4—21no—
1265C2×C4—24no—
1266C2×C4—21no—
1267C2×C4—22no—
1268C2×C4—22no—
1269C2×C4—21no—
1270C2×C4—22no—
1271C2×C4—22no—
1272C2×C4—22no—
1273C2×C4—22no—
1274C2×C4—24no—
1275C2×C4—24no—
1276C2×C4—21no—
1277C2×C4—21no—
1278C2×C4—24no—
1279C2×C4—24no—
1280C2×C4—22no—
1281C2×C4—22no—
1282C2×C4—22no—
1283C2×C4—22no—
1284C2×C4—22no—
1285C2×C4—22no—
1286C2×C4—22no—
1287C2×C4—22no—
1288C2×C4—22no—
1289C2×C4—24no—
1290C2×C4—22no—
1291C2×C4—22no—
1292C2×C4—24no—
1293C2×C4—22no—
1294C2×C4—22no—
1295C2×C4—22no—
1296C2×C4—24no—
1297C2×C4—24no—
1298C2×C4—22no—
1299C2×C4—22no—
1300C2×C4—22no—
1301C2×C4—24no—
1302C2×C4—24no—
1303C2×C4—22no—
1304C2×C4—22no—
1305C2×C4—24no—
1306C2×C4—22no—
1307C2×C4—21no—
1308C2×C4—22no—
1309C2×C4—22no—
1310C2×C4—22no—
1311C2×C4—22no—
1312C2×C4—24no—
1313C2×C4—21no—
1314C2×C4—24no—
1315C2×C4—22no—
1316C2×C4—416no—
1317C2×C4—48no—
1318C2×C4—48no—
1319C2×C4—84no—
1320C2×C4—164no—
1321C2×C4C2×H(5,𝔽2)14yes—
1322C2×C4C2×H(5,𝔽2)12yes—
1323C2×C4C2×H(5,𝔽2)14yes—
1324C2×C4C2×H(5,𝔽2)12yes—
1325C2×C4C2×2−1+418yes—
1326C2×C4C2×2−1+414yes—
1327C2×C4C2×2−1+414yes—
1328C2×C4C2×2−1+414yes—
1329C22—24no—
1330C22—24no—
1331C22—24no—
1332C22—42no—
1333C22—42no—
1334C22—42no—
1335C22—42no—
1336C22C22×H(5,𝔽2)11yescharacteristic
1337C22C22×H(5,𝔽2)11yescharacteristic
1338C22C22×2−1+412yes—
1339C22C22×2−1+412yes—
1340C222−1+611yescharacteristic
1341C4—24no—
1342C4—28no—
1343C4—24no—
1344C4—24no—
1345C4—24no—
1346C4—22no—
1347C4—42no—
1348C4—44no—
1349C4—42no—
1350C4—42no—
1351C4—42no—
1352C4—41no—
1353C4—44no—
1354C4—42no—
1355C4—41no—
1356C4—44no—
1357C4—41no—
1358C4—42no—
1359C4—42no—
1360C4—44no—
1361C4—41no—
1362C4—44no—
1363C4—42no—
1364C4—41no—
1365C4—42no—
1366C4—42no—
1367C4—42no—
1368C4#354414yes—
1369C2—44no—
1370C2C2×#354411yescharacteristic
1371C2#6289511yescharacteristic
1372C2#6294712yes—
1373C2#6301612yes—
1374C2#6301611yescharacteristic
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. #59832C2semidirect
2. #59663C2semidirect
3. #59502C2semidirect
5. #59071C2semidirect
6. #58969C2semidirect
7. #58290C2semidirect
8. #57282C2semidirect
9. #56818C2semidirect
10. #53100C2semidirect
11. #53002C2semidirect
14. #46583C2semidirect
16. #44994C2semidirect
17. #44894C2semidirect
19. #42825C2semidirect
21. #42376C2semidirect
24. #39660C2semidirect
25. #39597C2semidirect
26. #39368C2semidirect
27. #39170C2semidirect
28. #35937C2semidirect
29. #35919C2semidirect

Maximal subgroups

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

subgroupindex
#598322
#596632
#595022
#591132
#590712
#589692
#582902
#572822
#568182
#531002
#530022
#523022
#477992
#465832
#453842
#449942
#448942
#448622
#428252
#428142
#423762
#413542
#400552
#396602
#395972
#393682
#391702
#359372
#359192