Finite Group Databasebeta

← #8701489

Subgroups — #8701489

Order 512.

4207 conjugacy classes of subgroups.

The subgroup lattice has 1358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59946C212yesmaximal
2#59631C211yesmaximal, characteristic
3#59629C211yesmaximal, characteristic
4#59154C212yesmaximal, complemented
5#59144C212yesmaximal, complemented
6#58641C214yesmaximal, complemented
7#55262C214yesmaximal, complemented
8#55108C214yesmaximal, complemented
9#52304C211yesmaximal, characteristic
10#51074C212yesmaximal
11#50090C214yesmaximal, complemented
12#49699C214yesmaximal, complemented
13#49077C212yesmaximal
14#46190C211yesmaximal, characteristic
15#46045C212yesmaximal, complemented
16#45341C212yesmaximal, complemented
17#45174C212yesmaximal, complemented
18#44950C212yesmaximal, complemented
19#42811C212yesmaximal, complemented
20#42772C212yesmaximal, complemented
21#42747C212yesmaximal, complemented
22#40071C212yesmaximal, complemented
23#39592C211yesmaximal, characteristic
24#39122C211yesmaximal, characteristic
25#39007C212yesmaximal, complemented
26#37359C214yesmaximal, complemented
27#37162C212yesmaximal
28#36562C211yesmaximal, characteristic
29#36283C212yesmaximal, complemented
30C2×#557C2212yes—
31C2×#557C2211yescharacteristic
32C2×#554C2211yescharacteristic
33C22×C4⋊Q8C2211yescharacteristic
34C22×#125C2211yescharacteristic
35#2864C2212yes—
36#2863C2214yes—
37#2862C2211yescharacteristic
38#2859C2212yes—
39#2855C2211yescharacteristic
40#2855C2211yescharacteristic
41#2839C2214yes—
42#2839C2214yes—
43#2833C2212yes—
44#2833C2214yes—
45#2822C2214yes—
46#2807C2212yes—
47#2806C2214yes—
48#2806C2214yes—
49#2805C2212yes—
50#2804C2212yes—
51#2799C2214yes—
52#2792C2214yes—
53#2790C2214yes—
54#2789C2214yes—
55#2789C2214yes—
56#2789C2212yes—
57#2788C2214yes—
58#2787C2214yes—
59#2787C2214yes—
60#2776C2214yes—
61#2776C2214yes—
62#2774C2214yes—
63#2771C2212yes—
64#2770C2214yes—
65#2770C2214yes—
66#2769C2214yes—
67#2769C2212yes—
68#2767C2214yes—
69#2767C2214yes—
70#2766C2214yes—
71#2766C2214yes—
72#2766C2214yes—
73#2765C2212yes—
74#2765C2212yes—
75#2765C2214yes—
76#2764C2214yes—
77#2764C2214yes—
78#2762C2214yes—
79#2762C2214yes—
80#2762C2214yes—
81#2758C2214yes—
82#2758C2214yes—
83#2758C2214yes—
84#2755C2214yes—
85#2739C2214yes—
86#2738C2214yes—
87#2734C2214yes—
88#2729C2214yes—
89#2726C2214yes—
90#2724C2212yes—
91#2724C2211yescharacteristic
92#2719C2214yes—
93#2719C2214yes—
94#2719C2214yes—
95#2717C2211yescharacteristic
96#2717C2212yes—
97#2717C2211yescharacteristic
98#2713C2214yes—
99#2713C2214yes—
100#2713C2214yes—
101#2713C2214yes—
102#2713C2214yes—
103#2713C2214yes—
104#2713C2214yes—
105#2690C2212yes—
106#2690C2212yes—
107#2690C2214yes—
108#2683C2211yescharacteristic
109#2677C2214yes—
110#2665C2214yes—
111#2655C2214yes—
112#2655C2214yes—
113#2652C2214yes—
114#2647C2214yes—
115#2645C2214yes—
116#2642C2212yes—
117#2634C2214yes—
118#2634C2214yes—
119#2627C2212yes—
120#2627C2212yes—
121#2607C2212yes—
122#2606C2214yes—
123#2605C2214yes—
124#2589C2214yes—
125#2586C2214yes—
126#2586C2214yes—
127#2585C2214yes—
128#2584C2212yes—
129#2584C2212yes—
130#2581C2214yes—
131#2581C2214yes—
132#2577C2214yes—
133#2575C2214yes—
134#2570C2214yes—
135#2568C2212yes—
136#2568C2212yes—
137#2567C2214yes—
138#2567C2211yescharacteristic
139#2566C2212yes—
140#2565C2212yes—
141#2565C2212yes—
142#2556C2214yes—
143#2556C2214yes—
144#2552C2212yes—
145#2551C2212yes—
146#2550C2212yes—
147#2550C2212yes—
148#2550C2212yes—
149#2550C2212yes—
150#2546C2214yes—
151#2546C2212yes—
152#2542C2211yescharacteristic
153#2530C2214yes—
154#2530C2214yes—
155#2527C2214yes—
156#2527C2214yes—
157#2523C2214yes—
158#2523C2214yes—
159#2520C2214yes—
160#2517C2212yes—
161#2515C2214yes—
162#2514C2212yes—
163#2514C2214yes—
164#2514C2212yes—
165#2514C2212yes—
166#2511C2214yes—
167#2511C2212yes—
168#2507C2214yes—
169#2506C2214yes—
170#2503C2212yes—
171#2503C2211yescharacteristic
172#2502C2211yescharacteristic
173#2495C2212yes—
174#2494C2212yes—
175#2494C2214yes—
176#2492C2212yes—
177#2492C2212yes—
178#2492C2212yes—
179#2489C2212yes—
180#2489C2212yes—
181#2489C2212yes—
182#2487C2211yescharacteristic
183#2486C2212yes—
184#2486C2211yescharacteristic
185#2473C2214yes—
186#2473C2214yes—
187#2473C2214yes—
188#2473C2214yes—
189#2465C2214yes—
190#2465C2214yes—
191#2462C2214yes—
192#2462C2214yes—
193#2453C2212yes—
194#2453C2212yes—
195#2453C2212yes—
196#2453C2212yes—
197#2451C2212yes—
198#2451C2212yes—
199#2451C2214yes—
200#2451C2212yes—
201#2451C2212yes—
202#2446C2214yes—
203#2446C2212yes—
204#2446C2212yes—
205#2446C2212yes—
206#2446C2212yes—
207#2442C2212yes—
208#2442C2212yes—
209#2442C2212yes—
210#2440C2212yes—
211#2440C2214yes—
212#2434C2214yes—
213#2434C2212yes—
214#2429C2212yes—
215#2429C2212yes—
216#2421C2214yes—
217#2409C2212yes—
218#2401C2212yes—
219#2401C2212yes—
220#2399C2212yes—
221#2381C2214yes—
222#2376C2212yes—
223#2374C2212yes—
224#2374C2212yes—
225#2370C2212yes—
226#2370C2212yes—
227#2370C2212yes—
228#2369C2212yes—
229#2365C2212yes—
230#2365C2212yes—
231#2360C2212yes—
232#2360C2212yes—
233#2360C2212yes—
234#2360C2214yes—
235#2360C2212yes—
236#2356C2212yes—
237#2356C2212yes—
238#2345C2211yescharacteristic
239#2345C2211yescharacteristic
240Q8×C22⋊C4C2214yes—
241#2331C2212yes—
242#2331C2214yes—
243#2330C2212yes—
244#2322C2212yes—
245#2322C2212yes—
246#2320C2212yes—
247#2320C2214yes—
248C4×#125C2212yes—
249C4×#124C2212yes—
250C4×#124C2211yescharacteristic
251C4×C22⋊Q8C2212yes—
252C4×C22⋊Q8C2212yes—
253C4×C22⋊Q8C2212yes—
254C4×C22⋊Q8C2212yes—
255C4×#123C2211yescharacteristic
256C4×#123C2211yescharacteristic
257#2295C2214yes—
258C42×Q8C2211yescharacteristic
259C23×Q8C2312yes—
260#557—44no—
261#557—48no—
262#554—44no—
263C2×C4⋊Q8—44no—
264C2×C4⋊Q8C2312yes—
265C2×C4⋊Q8C2312yes—
266C2×C4⋊Q8C2314yes—
267C2×C4⋊Q8C2311yescharacteristic
268C2×C4⋊Q8C2312yes—
269C2×C4⋊Q8C2312yes—
270C2×C4⋊Q8C2311yescharacteristic
271C2×C4⋊Q8C2314yes—
272C2×C4⋊Q8C2314yes—
273C2×C4⋊Q8C2314yes—
274C2×#125—44no—
275C2×#125C2312yes—
276C2×#125C2312yes—
277C2×#125C2312yes—
278C2×#125C2312yes—
279C2×#125C2312yes—
280C2×#125C2312yes—
281C2×#125C2314yes—
282C2×#125C2314yes—
283C2×#125C2312yes—
284C2×#125C2314yes—
285C2×#125C2314yes—
286C2×#124C2311yescharacteristic
287C2×#123C2311yescharacteristic
288C2×#123C2312yes—
289C2×#123C2311yescharacteristic
290C2×C22⋊Q8C2312yes—
291C2×C22⋊Q8C2312yes—
292C2×C22⋊Q8C2311yescharacteristic
293C2×C22⋊Q8C2311yescharacteristic
294C2×C22⋊Q8C2314yes—
295C2×C22⋊Q8C2312yes—
296C2×C22⋊Q8C2312yes—
297C2×C22⋊Q8C2312yes—
298C2×C22⋊Q8C2312yes—
299C2×C4×Q8C2312yes—
300C2×C4×Q8C2312yes—
301C2×C4×Q8C2311yescharacteristic
302C2×C4×Q8C2312yes—
303C2×C4×Q8C2312yes—
304C2×C4×Q8C2314yes—
305C2×C4×Q8C2311yescharacteristic
306C2×C4×Q8C2312yes—
307C2×C4×Q8C2312yes—
308C2×C4×Q8C2314yes—
309C2×C4×Q8C2314yes—
310C2×C4×D4C2312yes—
311C2×C4×D4C2311yescharacteristic
312C22×C4⋊C4C2311yescharacteristic
313C22×C4⋊C4C2311yescharacteristic
314C22×C4⋊C4C2312yes—
315C22×C4⋊C4C2312yes—
316C22×C4⋊C4C2311yescharacteristic
317C22×C4⋊C4C2312yes—
318C22×C4⋊C4C2311yescharacteristic
319C22×C42C2311yescharacteristic
320C22×C42C2311yescharacteristic
321#401C2314yes—
322#401C2314yes—
323#401C2314yes—
324#401C2312yes—
325#401C2312yes—
326#401C2314yes—
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#400C2314yes—
342#400C2312yes—
343#400C2312yes—
344#400C2314yes—
345#400C2312yes—
346#400C2312yes—
347#400C2314yes—
348#400C2314yes—
349#400C2314yes—
350#400C2314yes—
351#400C2314yes—
352#400C2314yes—
353#400C2314yes—
354#400C2314yes—
355#400C2314yes—
356#400C2314yes—
357#400C2314yes—
358#400C2314yes—
359#400C2314yes—
360#400C2314yes—
361#400C2312yes—
362#400C2314yes—
363#400C2312yes—
364#400C2312yes—
365#400C2314yes—
366#399C2312yes—
367#399C2312yes—
368#399C2312yes—
369#398C2314yes—
370#398C2314yes—
371#398C2314yes—
372#398C2314yes—
373#398C2312yes—
374#398C2314yes—
375#398C2314yes—
376#398C2314yes—
377#398C2314yes—
378#398C2314yes—
379#398C2314yes—
380#398C2314yes—
381#398C2312yes—
382#398C2314yes—
383#398C2314yes—
384#398C2314yes—
385#398C2314yes—
386#398C2314yes—
387#398C2314yes—
388#398C2314yes—
389#398C2314yes—
390#398C2314yes—
391#398C2314yes—
392#398C2314yes—
393#398C2314yes—
394#398C2314yes—
395#398C2314yes—
396#398C2314yes—
397#398C2312yes—
398#398C2314yes—
399#398C2314yes—
400#398C2312yes—
401#398C2312yes—
402#398C2314yes—
403#398C2314yes—
404#398C2314yes—
405#397C2314yes—
406#397C2312yes—
407#397C2314yes—
408#397C2314yes—
409#397C2312yes—
410#397C2312yes—
411#397C2312yes—
412#397C2312yes—
413#397C2312yes—
414#397C2314yes—
415#397C2312yes—
416#397C2314yes—
417#396C2314yes—
418#396C2314yes—
419#396C2312yes—
420#396C2312yes—
421#395C2312yes—
422#395C2314yes—
423#395C2314yes—
424#395C2314yes—
425#395C2314yes—
426#395C2314yes—
427#395C2314yes—
428#395C2314yes—
429#395C2312yes—
430#395C2314yes—
431#395C2314yes—
432#395C2314yes—
433#395C2314yes—
434#395C2314yes—
435#395C2314yes—
436#395C2312yes—
437#395C2312yes—
438#395C2314yes—
439#393C2314yes—
440#393C2314yes—
441#393C2314yes—
442#391C2311yescharacteristic
443#391C2312yes—
444#391C2312yes—
445#391C2312yes—
446#391C2314yes—
447#391C2314yes—
448#391C2314yes—
449#391C2314yes—
450#391C2312yes—
451#391C2312yes—
452#391C2312yes—
453#391C2312yes—
454#391C2314yes—
455#391C2312yes—
456#391C2312yes—
457#391C2314yes—
458#391C2314yes—
459#391C2312yes—
460#391C2312yes—
461#391C2314yes—
462#391C2314yes—
463#391C2314yes—
464#391C2314yes—
465#391C2314yes—
466#391C2314yes—
467#391C2314yes—
468#391C2314yes—
469#391C2312yes—
470#391C2314yes—
471#391C2314yes—
472#391C2314yes—
473#391C2314yes—
474#391C2314yes—
475#391C2312yes—
476#391C2312yes—
477#391C2314yes—
478#391C2314yes—
479#391C2312yes—
480#390C2311yescharacteristic
481#390C2312yes—
482#389C2312yes—
483#389C2312yes—
484#389C2314yes—
485#389C2312yes—
486#389C2314yes—
487#389C2314yes—
488#389C2312yes—
489#389C2314yes—
490#389C2314yes—
491#389C2314yes—
492#389C2314yes—
493#389C2312yes—
494#389C2312yes—
495#389C2314yes—
496#389C2314yes—
497#389C2314yes—
498#389C2314yes—
499#389C2314yes—
500#389C2314yes—
501#389C2314yes—
502#389C2312yes—
503#389C2312yes—
504#389C2314yes—
505#389C2312yes—
506#389C2312yes—
507#389C2312yes—
508#389C2312yes—
509#389C2314yes—
510#389C2314yes—
511#389C2314yes—
512#389C2314yes—
513#389C2314yes—
514#389C2314yes—
515#389C2312yes—
516#389C2314yes—
517#389C2314yes—
518#389C2314yes—
519#389C2312yes—
520#389C2312yes—
521#389C2312yes—
522#389C2314yes—
523#389C2312yes—
524#389C2314yes—
525#389C2312yes—
526#388C2312yes—
527#388C2314yes—
528#388C2314yes—
529#388C2314yes—
530#388C2314yes—
531#388C2314yes—
532#388C2312yes—
533#388C2314yes—
534#388C2314yes—
535#388C2314yes—
536#388C2314yes—
537#388C2314yes—
538#388C2312yes—
539#388C2312yes—
540#387C2312yes—
541#387C2312yes—
542#387C2312yes—
543#387C2312yes—
544#387C2314yes—
545#387C2314yes—
546#387C2314yes—
547#387C2314yes—
548#387C2312yes—
549#387C2314yes—
550#387C2314yes—
551#387C2314yes—
552#387C2314yes—
553#387C2314yes—
554#387C2314yes—
555#387C2312yes—
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#387C2312yes—
601#387C2314yes—
602#387C2312yes—
603#387C2314yes—
604#387C2314yes—
605#387C2312yes—
606#387C2314yes—
607#387C2312yes—
608#386C2311yescharacteristic
609#386C2312yes—
610#386C2311yescharacteristic
611#385C2314yes—
612#385C2314yes—
613#385C2314yes—
614#385C2312yes—
615#385C2312yes—
616#385C2314yes—
617#385C2314yes—
618#385C2312yes—
619#385C2314yes—
620#385C2312yes—
621#385C2312yes—
622#385C2314yes—
623#385C2311yescharacteristic
624#385C2312yes—
625#385C2314yes—
626#385C2311yescharacteristic
627#385C2314yes—
628#385C2312yes—
629#385C2314yes—
630#385C2312yes—
631#385C2312yes—
632#384C2312yes—
633#384C2312yes—
634#384C2312yes—
635#384C2314yes—
636#383C2314yes—
637#383C2314yes—
638#383C2314yes—
639#383C2314yes—
640#383C2314yes—
641#383C2314yes—
642#383C2314yes—
643#382C2312yes—
644#382C2312yes—
645#382C2312yes—
646#382C2314yes—
647#382C2314yes—
648#382C2312yes—
649#382C2314yes—
650#382C2314yes—
651#382C2314yes—
652#382C2311yescharacteristic
653#382C2312yes—
654#382C2312yes—
655#381C2312yes—
656#381C2312yes—
657#381C2312yes—
658#381C2312yes—
659#381C2311yescharacteristic
660#381C2311yescharacteristic
661#381C2312yes—
662#380C2314yes—
663#380C2312yes—
664#380C2314yes—
665#380C2311yescharacteristic
666#380C2311yescharacteristic
667#380C2312yes—
668#380C2312yes—
669#380C2314yes—
670#380C2312yes—
671#380C2312yes—
672#380C2312yes—
673C4×C4⋊C4C2312yes—
674C4×C4⋊C4C2312yes—
675C4×C4⋊C4C2312yes—
676C4×C4⋊C4C2312yes—
677C4×C4⋊C4C2312yes—
678C4×C4⋊C4C2312yes—
679C4×C4⋊C4C2312yes—
680C4×C4⋊C4C2314yes—
681C4×C4⋊C4C2311yescharacteristic
682C4×C4⋊C4C2312yes—
683C4×C4⋊C4C2314yes—
684C4×C4⋊C4C2314yes—
685C4×C4⋊C4C2312yes—
686C4×C4⋊C4C2314yes—
687C4×C4⋊C4C2312yes—
688C4×C4⋊C4C2312yes—
689C4×C4⋊C4C2314yes—
690C4×C4⋊C4C2312yes—
691C4×C4⋊C4C2312yes—
692C4×C4⋊C4C2314yes—
693C4×C4⋊C4C2312yes—
694C4×C4⋊C4C2312yes—
695C4×C4⋊C4C2314yes—
696C4×C4⋊C4C2312yes—
697C4×C4⋊C4C2312yes—
698C4×C22⋊C4C2314yes—
699C4×C22⋊C4C2312yes—
700C4×C22⋊C4C2312yes—
701C4×C22⋊C4C2314yes—
702C4×C22⋊C4C2314yes—
703C4×C22⋊C4C2314yes—
704C4×C22⋊C4C2311yescharacteristic
705C4×C22⋊C4C2311yescharacteristic
706C4×C22⋊C4C2314yes—
707C4×C22⋊C4C2314yes—
708C4×C22⋊C4C2312yes—
709C4×C22⋊C4C2312yes—
710C4×C22⋊C4C2312yes—
711C4×C22⋊C4C2312yes—
712#376C2312yes—
713#376C2314yes—
714#376C2314yes—
715C43C2311yescharacteristic
716C43C2312yes—
717C22×Q8—44no—
718C22×Q8—48no—
719C22×Q8C2412yes—
720C22×Q8C2411yescharacteristic
721C22×Q8C2414yes—
722C22×Q8C2411yescharacteristic
723C22×Q8C2412yes—
724C22×Q8C2414yes—
725C22×Q8C2414yes—
726C22×Q8C2412yes—
727C22×D4C2411yescharacteristic
728C23×C4C2411yescharacteristic
729C23×C4C2411yescharacteristic
730C23×C4C2411yescharacteristic
731C23×C4C2412yes—
732C23×C4C2412yes—
733C23×C4C2412yes—
734C23×C4C2411yescharacteristic
735C23×C4C2411yescharacteristic
736C23×C4C2411yescharacteristic
737C23×C4C2412yes—
738C4⋊Q8—28no—
739C4⋊Q8—28no—
740C4⋊Q8—44no—
741C4⋊Q8—42no—
742C4⋊Q8—48no—
743C4⋊Q8—42no—
744C4⋊Q8—44no—
745C4⋊Q8—48no—
746C4⋊Q8—48no—
747C4⋊Q8—48no—
748#125—28no—
749#125—28no—
750#125—44no—
751#125—44no—
752#125—44no—
753#125—48no—
754#125—48no—
755#125—44no—
756#125—48no—
757#125—44no—
758#125—48no—
759#124—24no—
760#123—24no—
761#123—28no—
762#123—24no—
763C22⋊Q8—28no—
764C22⋊Q8—28no—
765C22⋊Q8—48no—
766C22⋊Q8—44no—
767C22⋊Q8—44no—
768C22⋊Q8—44no—
769C22⋊Q8—44no—
770C22⋊Q8—42no—
771C22⋊Q8—42no—
772C4×Q8—24no—
773C4×Q8—28no—
774C4×Q8—28no—
775C4×Q8—44no—
776C4×Q8—44no—
777C4×Q8—42no—
778C4×Q8—48no—
779C4×Q8—48no—
780C4×Q8—44no—
781C4×Q8—44no—
782C4×Q8—48no—
783C4×D4—44no—
784C4×D4—42no—
785C2×C4⋊C4—24no—
786C2×C4⋊C4—24no—
787C2×C4⋊C4—42no—
788C2×C4⋊C4—44no—
789C2×C4⋊C4—44no—
790C2×C4⋊C4—42no—
791C2×C4⋊C4—44no—
792C2×C4⋊C4C2412yes—
793C2×C4⋊C4C2414yes—
794C2×C4⋊C4C2412yes—
795C2×C4⋊C4C2412yes—
796C2×C4⋊C4C2411yescharacteristic
797C2×C4⋊C4C2412yes—
798C2×C4⋊C4C2411yescharacteristic
799C2×C4⋊C4C2414yes—
800C2×C4⋊C4C2414yes—
801C2×C4⋊C4C2412yes—
802C2×C4⋊C4C2412yes—
803C2×C4⋊C4C2412yes—
804C2×C4⋊C4C2414yes—
805C2×C4⋊C4C2414yes—
806C2×C4⋊C4C2414yes—
807C2×C4⋊C4C2412yes—
808C2×C4⋊C4C2414yes—
809C2×C4⋊C4C2414yes—
810C2×C4⋊C4C2412yes—
811C2×C4⋊C4C2412yes—
812C2×C4⋊C4C2414yes—
813C2×C4⋊C4C2412yes—
814C2×C4⋊C4C2412yes—
815C2×C4⋊C4C2414yes—
816C2×C4⋊C4C2414yes—
817C2×C4⋊C4C2412yes—
818C2×C4⋊C4C2414yes—
819C2×C4⋊C4C2414yes—
820C2×C4⋊C4C2414yes—
821C2×C4⋊C4C2412yes—
822C2×C4⋊C4C2412yes—
823C2×C4⋊C4C2414yes—
824C2×C4⋊C4C2411yescharacteristic
825C2×C4⋊C4C2412yes—
826C2×C4⋊C4C2412yes—
827C2×C4⋊C4C2412yes—
828C2×C4⋊C4C2414yes—
829C2×C4⋊C4C2412yes—
830C2×C4⋊C4C2411yescharacteristic
831C2×C4⋊C4C2414yes—
832C2×C4⋊C4C2412yes—
833C2×C4⋊C4C2412yes—
834C2×C4⋊C4C2414yes—
835C2×C4⋊C4C2414yes—
836C2×C4⋊C4C2414yes—
837C2×C4⋊C4C2414yes—
838C2×C4⋊C4C2414yes—
839C2×C4⋊C4C2412yes—
840C2×C4⋊C4C2412yes—
841C2×C4⋊C4C2414yes—
842C2×C4⋊C4C2412yes—
843C2×C4⋊C4C2412yes—
844C2×C4⋊C4C2412yes—
845C2×C4⋊C4C2414yes—
846C2×C4⋊C4C2414yes—
847C2×C4⋊C4C2414yes—
848C2×C4⋊C4C2412yes—
849C2×C4⋊C4C2412yes—
850C2×C4⋊C4C2412yes—
851C2×C4⋊C4C2412yes—
852C2×C4⋊C4C2414yes—
853C2×C4⋊C4C2414yes—
854C2×C4⋊C4C2414yes—
855C2×C4⋊C4C2414yes—
856C2×C4⋊C4C2414yes—
857C2×C4⋊C4C2414yes—
858C2×C4⋊C4C2412yes—
859C2×C4⋊C4C2412yes—
860C2×C4⋊C4C2414yes—
861C2×C4⋊C4C2412yes—
862C2×C4⋊C4C2412yes—
863C2×C4⋊C4C2414yes—
864C2×C4⋊C4C2414yes—
865C2×C4⋊C4C2411yescharacteristic
866C2×C4⋊C4C2412yes—
867C2×C22⋊C4C2412yes—
868C2×C22⋊C4C2414yes—
869C2×C22⋊C4C2414yes—
870C2×C22⋊C4C2412yes—
871C2×C22⋊C4C2411yescharacteristic
872C2×C22⋊C4C2414yes—
873C2×C22⋊C4C2412yes—
874C2×C22⋊C4C2411yescharacteristic
875C2×C22⋊C4C2412yes—
876C2×C22⋊C4C2412yes—
877C2×C22⋊C4C2412yes—
878C2×C22⋊C4C2412yes—
879C2×C22⋊C4C2411yescharacteristic
880C2×C22⋊C4C2412yes—
881C2×C22⋊C4C2411yescharacteristic
882C2×C22⋊C4C2414yes—
883C2×C22⋊C4C2412yes—
884C2×C22⋊C4C2412yes—
885C2×C22⋊C4C2412yes—
886C2×C22⋊C4C2411yescharacteristic
887C2×C22⋊C4C2412yes—
888C2×C22⋊C4C2411yescharacteristic
889C2×C42—42no—
890C2×C42—42no—
891C2×C42C2412yes—
892C2×C42C2411yescharacteristic
893C2×C42C2414yes—
894C2×C42C2412yes—
895C2×C42C2412yes—
896C2×C42C2412yes—
897C2×C42C2414yes—
898C2×C42C2414yes—
899C2×C42C2412yes—
900C2×C42C2411yescharacteristic
901C2×C42C2412yes—
902C2×C42C2412yes—
903C2×C42C2414yes—
904C2×C42C2414yes—
905C2×C42C2414yes—
906C2×C42C2414yes—
907C2×C42C2414yes—
908C2×C42C2414yes—
909C2×C42C2412yes—
910C2×C42C2412yes—
911C2×C42C2412yes—
912C2×C42C2414yes—
913C2×C42C2412yes—
914C2×C42C2411yescharacteristic
915C2×C42C2414yes—
916C2×C42C2414yes—
917#95C2412yes—
918#95C2412yes—
919#95C2414yes—
920#95C2414yes—
921#95C2414yes—
922#95C2412yes—
923#95C2414yes—
924#95C2412yes—
925#95C2414yes—
926#95C2414yes—
927#95C2412yes—
928#95C2412yes—
929#95C2414yes—
930#95C2414yes—
931#95C2412yes—
932#95C2412yes—
933#95C2412yes—
934#95C2412yes—
935#95C2412yes—
936#95C2414yes—
937#95C2414yes—
938#95C2414yes—
939#95C2414yes—
940#95C2412yes—
941#95C2414yes—
942#95C2414yes—
943#95C2412yes—
944#95C2414yes—
945#95C2414yes—
946#95C2412yes—
947#95C2412yes—
948#95C2412yes—
949#95C2414yes—
950#95C2414yes—
951#95C2412yes—
952#95C2414yes—
953#95C2412yes—
954#95C2412yes—
955#95C2412yes—
956#95C2414yes—
957#95C2414yes—
958#95C2412yes—
959#95C2414yes—
960#95C2412yes—
961#95C2412yes—
962#95C2414yes—
963#95C2414yes—
964#95C2412yes—
965#95C2412yes—
966#95C2412yes—
967#95C2414yes—
968#95C2414yes—
969#95C2412yes—
970#95C2412yes—
971#95C2414yes—
972#95C2414yes—
973#95C2414yes—
974#95C2414yes—
975#95C2414yes—
976#95C2412yes—
977#95C2412yes—
978#95C2414yes—
979#95C2412yes—
980#95C2414yes—
981#95C2414yes—
982#95C2412yes—
983#95C2414yes—
984#95C2412yes—
985#95C2414yes—
986#95C2414yes—
987#95C2414yes—
988#95C2414yes—
989#95C2414yes—
990#95C2414yes—
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—
1004C24C2511yescharacteristic
1005C24C2511yescharacteristic
1006C2×Q8—24no—
1007C2×Q8—22no—
1008C2×Q8—28no—
1009C2×Q8—24no—
1010C2×Q8—24no—
1011C2×Q8—24no—
1012C2×Q8—22no—
1013C2×Q8—28no—
1014C2×Q8—28no—
1015C2×Q8—24no—
1016C2×Q8—28no—
1017C2×Q8—41no—
1018C2×Q8—44no—
1019C2×Q8—41no—
1020C2×Q8—42no—
1021C2×Q8—44no—
1022C2×Q8—42no—
1023C2×Q8—44no—
1024C2×Q8—44no—
1025C2×Q8—44no—
1026C2×Q8—42no—
1027C2×Q8—44no—
1028C2×Q8—816no—
1029C2×D4—41no—
1030C2×D4—41no—
1031C2×D42−1+414yes—
1032C22×C4—22no—
1033C22×C4—24no—
1034C22×C4—22no—
1035C22×C4—22no—
1036C22×C4—22no—
1037C22×C4—24no—
1038C22×C4—24no—
1039C22×C4—24no—
1040C22×C4—24no—
1041C22×C4—24no—
1042C22×C4—41no—
1043C22×C4—41no—
1044C22×C4—41no—
1045C22×C4—41no—
1046C22×C4—41no—
1047C22×C4—42no—
1048C22×C4—42no—
1049C22×C4—44no—
1050C22×C4—42no—
1051C22×C4—41no—
1052C22×C4—42no—
1053C22×C4—44no—
1054C22×C4—44no—
1055C22×C4C2512yes—
1056C22×C4C2512yes—
1057C22×C4C2512yes—
1058C22×C4C2512yes—
1059C22×C4C2514yes—
1060C22×C4C2514yes—
1061C22×C4C2512yes—
1062C22×C4C2512yes—
1063C22×C4C2514yes—
1064C22×C4C2512yes—
1065C22×C4C2511yescharacteristic
1066C22×C4C2511yescharacteristic
1067C22×C4C2512yes—
1068C22×C4C2512yes—
1069C22×C4C2512yes—
1070C22×C4C2514yes—
1071C22×C4C2512yes—
1072C22×C4C2514yes—
1073C22×C4C2511yescharacteristic
1074C22×C4C2512yes—
1075C22×C4C2512yes—
1076C22×C4C2512yes—
1077C22×C4C2512yes—
1078C22×C4C2514yes—
1079C22×C4C2511yescharacteristic
1080C22×C4C2512yes—
1081C22×C4C2511yescharacteristic
1082C4⋊C4—24no—
1083C4⋊C4—22no—
1084C4⋊C4—24no—
1085C4⋊C4—22no—
1086C4⋊C4—28no—
1087C4⋊C4—24no—
1088C4⋊C4—24no—
1089C4⋊C4—28no—
1090C4⋊C4—28no—
1091C4⋊C4—24no—
1092C4⋊C4—28no—
1093C4⋊C4—28no—
1094C4⋊C4—28no—
1095C4⋊C4—28no—
1096C4⋊C4—24no—
1097C4⋊C4—24no—
1098C4⋊C4—28no—
1099C4⋊C4—28no—
1100C4⋊C4—28no—
1101C4⋊C4—24no—
1102C4⋊C4—28no—
1103C4⋊C4—24no—
1104C4⋊C4—24no—
1105C4⋊C4—24no—
1106C4⋊C4—28no—
1107C4⋊C4—24no—
1108C4⋊C4—24no—
1109C4⋊C4—44no—
1110C4⋊C4—44no—
1111C4⋊C4—42no—
1112C4⋊C4—44no—
1113C4⋊C4—42no—
1114C4⋊C4—44no—
1115C4⋊C4—42no—
1116C4⋊C4—42no—
1117C4⋊C4—42no—
1118C4⋊C4—44no—
1119C4⋊C4—44no—
1120C4⋊C4—42no—
1121C4⋊C4—41no—
1122C4⋊C4—42no—
1123C4⋊C4—44no—
1124C4⋊C4—44no—
1125C4⋊C4—44no—
1126C4⋊C4—42no—
1127C4⋊C4—41no—
1128C4⋊C4—42no—
1129C4⋊C4—42no—
1130C4⋊C4—44no—
1131C4⋊C4—42no—
1132C4⋊C4—44no—
1133C4⋊C4—42no—
1134C4⋊C4—44no—
1135C4⋊C4—44no—
1136C4⋊C4—44no—
1137C4⋊C4—42no—
1138C4⋊C4—42no—
1139C4⋊C4—44no—
1140C4⋊C4—42no—
1141C4⋊C4—42no—
1142C4⋊C4—42no—
1143C4⋊C4—42no—
1144C4⋊C4—42no—
1145C4⋊C4—42no—
1146C4⋊C4—42no—
1147C4⋊C4—44no—
1148C4⋊C4—44no—
1149C4⋊C4—44no—
1150C4⋊C4—44no—
1151C4⋊C4—44no—
1152C4⋊C4—44no—
1153C4⋊C4—44no—
1154C4⋊C4—44no—
1155C4⋊C4H(5,𝔽2)14yes—
1156C4⋊C42−1+418yes—
1157C22⋊C4—22no—
1158C22⋊C4—24no—
1159C22⋊C4—22no—
1160C22⋊C4—24no—
1161C22⋊C4—28no—
1162C22⋊C4—24no—
1163C22⋊C4—24no—
1164C22⋊C4—24no—
1165C22⋊C4—28no—
1166C22⋊C4—28no—
1167C22⋊C4—24no—
1168C22⋊C4—41no—
1169C22⋊C4—42no—
1170C22⋊C4—41no—
1171C22⋊C4—41no—
1172C22⋊C4—41no—
1173C22⋊C4—42no—
1174C22⋊C4—42no—
1175C22⋊C4—42no—
1176C22⋊C4—44no—
1177C22⋊C4—42no—
1178C22⋊C4—42no—
1179C42—24no—
1180C42—24no—
1181C42—24no—
1182C42—22no—
1183C42—28no—
1184C42—24no—
1185C42—24no—
1186C42—28no—
1187C42—22no—
1188C42—24no—
1189C42—24no—
1190C42—28no—
1191C42—42no—
1192C42—42no—
1193C42—42no—
1194C42—44no—
1195C42—44no—
1196C42—41no—
1197C42—44no—
1198C42—44no—
1199C42—44no—
1200C42—44no—
1201C42—44no—
1202C42—44no—
1203C42—42no—
1204C42—44no—
1205C23—21no—
1206C23—21no—
1207C23—22no—
1208C23—22no—
1209C23—22no—
1210C23—22no—
1211C23—21no—
1212C23—21no—
1213C23C2×2−1+412yes—
1214C23C2×2−1+412yes—
1215C23C2611yescharacteristic
1216Q8—416no—
1217Q8—44no—
1218Q8—48no—
1219Q8—44no—
1220Q8—84no—
1221Q8—88no—
1222Q8—88no—
1223Q8—162no—
1224D4—44no—
1225C2×C4—21no—
1226C2×C4—22no—
1227C2×C4—24no—
1228C2×C4—24no—
1229C2×C4—22no—
1230C2×C4—24no—
1231C2×C4—21no—
1232C2×C4—22no—
1233C2×C4—22no—
1234C2×C4—24no—
1235C2×C4—22no—
1236C2×C4—22no—
1237C2×C4—21no—
1238C2×C4—22no—
1239C2×C4—22no—
1240C2×C4—21no—
1241C2×C4—21no—
1242C2×C4—24no—
1243C2×C4—24no—
1244C2×C4—22no—
1245C2×C4—22no—
1246C2×C4—22no—
1247C2×C4—22no—
1248C2×C4—22no—
1249C2×C4—22no—
1250C2×C4—22no—
1251C2×C4—22no—
1252C2×C4—24no—
1253C2×C4—22no—
1254C2×C4—22no—
1255C2×C4—22no—
1256C2×C4—24no—
1257C2×C4—22no—
1258C2×C4—22no—
1259C2×C4—22no—
1260C2×C4—24no—
1261C2×C4—24no—
1262C2×C4—24no—
1263C2×C4—24no—
1264C2×C4—22no—
1265C2×C4—22no—
1266C2×C4—24no—
1267C2×C4—24no—
1268C2×C4—22no—
1269C2×C4—22no—
1270C2×C4—24no—
1271C2×C4—22no—
1272C2×C4—22no—
1273C2×C4—22no—
1274C2×C4—22no—
1275C2×C4—24no—
1276C2×C4—24no—
1277C2×C4—22no—
1278C2×C4—24no—
1279C2×C4—22no—
1280C2×C4—22no—
1281C2×C4—22no—
1282C2×C4—22no—
1283C2×C4—24no—
1284C2×C4—22no—
1285C2×C4—22no—
1286C2×C4—24no—
1287C2×C4—22no—
1288C2×C4—24no—
1289C2×C4—22no—
1290C2×C4—22no—
1291C2×C4—22no—
1292C2×C4—44no—
1293C2×C4—44no—
1294C2×C4—44no—
1295C2×C4—44no—
1296C2×C4—84no—
1297C2×C4—84no—
1298C2×C4—82no—
1299C2×C4—84no—
1300C2×C4—82no—
1301C2×C4—84no—
1302C2×C4C2×H(5,𝔽2)14yes—
1303C2×C4C2×H(5,𝔽2)12yes—
1304C2×C4C2×2−1+418yes—
1305C2×C4C2×2−1+412yes—
1306C2×C4C2×2−1+414yes—
1307C2×C4#58514yes—
1308C22—24no—
1309C22—24no—
1310C22—22no—
1311C22—22no—
1312C22—41no—
1313C22—41no—
1314C22—41no—
1315C22—41no—
1316C22—42no—
1317C22—42no—
1318C22C22×H(5,𝔽2)11yescharacteristic
1319C22C22×2−1+412yes—
1320C22C22×2−1+411yescharacteristic
1321C22C2×#58512yes—
1322C222−1+611yescharacteristic
1323C4—24no—
1324C4—24no—
1325C4—22no—
1326C4—28no—
1327C4—41no—
1328C4—41no—
1329C4—44no—
1330C4—42no—
1331C4—44no—
1332C4—42no—
1333C4—42no—
1334C4—42no—
1335C4—42no—
1336C4—41no—
1337C4—42no—
1338C4—42no—
1339C4—42no—
1340C4—44no—
1341C4—42no—
1342C4—42no—
1343C4—44no—
1344C4—42no—
1345C4—42no—
1346C4—42no—
1347C4—44no—
1348C4—42no—
1349C4#355014yes—
1350C2—42no—
1351C2—42no—
1352C2C2×#355011yescharacteristic
1353C2#6289311yescharacteristic
1354C2#6295012yes—
1355C2#6301711yescharacteristic
1356C2#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
4. #59154C2semidirect
5. #59144C2semidirect
6. #58641C2semidirect
7. #55262C2semidirect
8. #55108C2semidirect
11. #50090C2semidirect
12. #49699C2semidirect
15. #46045C2semidirect
16. #45341C2semidirect
17. #45174C2semidirect
18. #44950C2semidirect
19. #42811C2semidirect
20. #42772C2semidirect
21. #42747C2semidirect
22. #40071C2semidirect
25. #39007C2semidirect
26. #37359C2semidirect
29. #36283C2semidirect

Maximal subgroups

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

subgroupindex
#599462
#596312
#596292
#591542
#591442
#586412
#552622
#551082
#523042
#510742
#500902
#496992
#490772
#461902
#460452
#453412
#451742
#449502
#428112
#427722
#427472
#400712
#395922
#391222
#390072
#373592
#371622
#365622
#362832