Finite Group Databasebeta

← #7898428

Subgroups — #7898428

Order 512.

4375 conjugacy classes of subgroups.

The subgroup lattice has 1369 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59828C211yesmaximal, characteristic, complemented
2#59460C212yesmaximal
3#52274C211yesmaximal, characteristic, complemented
4#51078C214yesmaximal, complemented
5#50904C214yesmaximal, complemented
6#47972C214yesmaximal, complemented
7#47732C214yesmaximal, complemented
8#45794C212yesmaximal, complemented
9#45424C212yesmaximal
10#45279C212yesmaximal, complemented
11#45059C212yesmaximal
12#44211C214yesmaximal, complemented
13#42825C212yesmaximal, complemented
14#42498C212yesmaximal
15#42005C214yesmaximal, complemented
16#39749C211yesmaximal, characteristic, complemented
17#39639C212yesmaximal, complemented
18#39626C212yesmaximal, complemented
19#39613C212yesmaximal
20#39612C211yesmaximal, characteristic, complemented
21#39183C212yesmaximal, complemented
22#38447C212yesmaximal, complemented
23#37309C212yesmaximal, complemented
24#36261C211yesmaximal, characteristic
25#35957C212yesmaximal, complemented
26#35582C212yesmaximal, complemented
27#35177C211yesmaximal, characteristic
28#34499C212yesmaximal
29#34324C211yesmaximal, characteristic
30C2×#557C2212yes—
31C2×#557C2212yes—
32C2×#556C2211yescharacteristic
33C2×#554C2212yes—
34#2859C2212yes—
35#2859C2211yescharacteristic
36#2857C2212yes—
37#2857C2212yes—
38#2855C2212yes—
39#2844C2214yes—
40#2841C2214yes—
41#2809C2211yescharacteristic
42#2809C2212yes—
43#2806C2214yes—
44#2806C2211yescharacteristic
45#2806C2212yes—
46#2806C2214yes—
47#2806C2214yes—
48#2805C2212yes—
49#2805C2211yescharacteristic
50#2805C2214yes—
51#2802C2214yes—
52#2802C2214yes—
53#2802C2214yes—
54#2802C2212yes—
55#2802C2214yes—
56#2799C2212yes—
57#2792C2214yes—
58#2792C2214yes—
59#2791C2214yes—
60#2791C2214yes—
61#2791C2212yes—
62#2791C2214yes—
63#2790C2214yes—
64#2790C2214yes—
65#2790C2214yes—
66#2790C2214yes—
67#2788C2214yes—
68#2788C2214yes—
69#2774C2212yes—
70#2763C2214yes—
71#2755C2212yes—
72#2755C2214yes—
73#2734C2212yes—
74#2734C2214yes—
75#2734C2212yes—
76#2729C2214yes—
77#2729C2214yes—
78#2726C2212yes—
79#2726C2212yes—
80#2726C2211yescharacteristic
81#2726C2212yes—
82#2726C2212yes—
83#2726C2212yes—
84#2720C2214yes—
85#2720C2214yes—
86#2713C2212yes—
87#2713C2214yes—
88#2704C2214yes—
89#2704C2214yes—
90#2704C2214yes—
91#2704C2214yes—
92#2704C2214yes—
93#2704C2214yes—
94#2677C2214yes—
95#2666C2214yes—
96#2666C2214yes—
97#2665C2214yes—
98#2660C2212yes—
99#2660C2214yes—
100#2660C2212yes—
101#2660C2212yes—
102#2647C2214yes—
103#2646C2214yes—
104#2629C2214yes—
105#2612C2214yes—
106#2606C2214yes—
107#2605C2214yes—
108#2590C2214yes—
109#2590C2214yes—
110#2589C2214yes—
111#2588C2214yes—
112#2587C2214yes—
113#2587C2214yes—
114#2586C2214yes—
115#2586C2214yes—
116#2584C2214yes—
117#2584C2212yes—
118#2583C2214yes—
119#2583C2214yes—
120#2582C2214yes—
121#2582C2212yes—
122#2574C2214yes—
123#2570C2212yes—
124#2570C2214yes—
125#2570C2212yes—
126#2568C2212yes—
127#2567C2212yes—
128#2567C2214yes—
129#2567C2211yescharacteristic
130#2567C2214yes—
131#2566C2212yes—
132#2566C2212yes—
133#2565C2212yes—
134#2565C2212yes—
135#2565C2212yes—
136#2563C2211yescharacteristic
137#2552C2212yes—
138#2552C2212yes—
139#2552C2212yes—
140#2552C2212yes—
141#2552C2211yescharacteristic
142#2552C2212yes—
143#2552C2214yes—
144#2552C2214yes—
145#2552C2214yes—
146#2551C2211yescharacteristic
147#2551C2212yes—
148#2551C2211yescharacteristic
149#2550C2212yes—
150#2550C2214yes—
151#2550C2212yes—
152#2550C2214yes—
153#2550C2214yes—
154#2550C2214yes—
155#2550C2212yes—
156#2549C2214yes—
157#2546C2212yes—
158#2538C2211yescharacteristic
159#2522C2214yes—
160#2520C2214yes—
161#2511C2214yes—
162#2509C2212yes—
163#2509C2212yes—
164#2507C2214yes—
165#2506C2212yes—
166#2506C2214yes—
167#2502C2214yes—
168#2497C2212yes—
169#2492C2212yes—
170#2473C2214yes—
171#2473C2214yes—
172#2473C2214yes—
173#2473C2214yes—
174#2465C2214yes—
175#2465C2214yes—
176#2465C2214yes—
177#2465C2214yes—
178#2465C2214yes—
179#2462C2214yes—
180#2462C2214yes—
181#2462C2214yes—
182#2462C2214yes—
183#2454C2212yes—
184#2453C2212yes—
185#2453C2212yes—
186#2453C2212yes—
187#2452C2212yes—
188#2452C2212yes—
189#2451C2212yes—
190#2451C2212yes—
191#2451C2212yes—
192#2451C2214yes—
193#2446C2214yes—
194#2446C2214yes—
195#2440C2214yes—
196#2440C2212yes—
197#2440C2212yes—
198#2438C2214yes—
199#2429C2214yes—
200#2402C2212yes—
201#2402C2212yes—
202#2399C2214yes—
203#2399C2212yes—
204#2383C2214yes—
205#2378C2214yes—
206#2373C2214yes—
207#2373C2214yes—
208#2367C2212yes—
209#2367C2212yes—
210#2367C2212yes—
211#2365C2211yescharacteristic
212#2365C2212yes—
213#2362C2212yes—
214#2360C2214yes—
215#2355C2212yes—
216#2355C2212yes—
217#2354C2211yescharacteristic
218#2351C2212yes—
219#2351C2212yes—
220Q8×C4⋊C4C2212yes—
221Q8×C4⋊C4C2212yes—
222Q8×C4⋊C4C2211yescharacteristic
223Q8×C4⋊C4C2212yes—
224#2349C2212yes—
225D4×C4⋊C4C2211yescharacteristic
226D4×C4⋊C4C2211yescharacteristic
227#2346C2212yes—
228#2343C2214yes—
229#2334C2214yes—
230#2334C2214yes—
231#2334C2214yes—
232#2331C2212yes—
233#2331C2212yes—
234#2330C2214yes—
235#2330C2212yes—
236#2329C2214yes—
237#2327C2212yes—
238#2326C2212yes—
239#2326C2212yes—
240#2320C2212yes—
241#2319C2212yes—
242#2314C2214yes—
243C4×C4⋊Q8C2211yescharacteristic
244C4×C4⋊Q8C2211yescharacteristic
245C4×C4⋊Q8C2212yes—
246C4×C4⋊Q8C2211yescharacteristic
247C4×#125C2212yes—
248C4×#124C2212yes—
249C4×C22⋊Q8C2212yes—
250#2296C2212yes—
251#2295C2212yes—
252#2295C2211yescharacteristic
253#2295C2211yescharacteristic
254#2295C2212yes—
255#2295C2212yes—
256C2×#389C2212yes—
257#2276C2212yes—
258C42×D4C2211yescharacteristic
259#557—48no—
260#557—48no—
261#556Q8116yescomplemented
262#554—48no—
263C2×C4⋊Q8C2311yescharacteristic
264C2×C4⋊Q8C2312yes—
265C2×C4⋊Q8C2311yescharacteristic
266C2×C4⋊Q8C2314yes—
267C2×C4⋊Q8C2312yes—
268C2×C4⋊Q8C2312yes—
269C2×C4⋊Q8C2314yes—
270C2×C4⋊Q8C2314yes—
271C2×C4⋊Q8C2312yes—
272C2×C4⋊Q8C2312yes—
273C2×C4⋊Q8C2311yescharacteristic
274C2×#126C2314yes—
275C2×#125C2312yes—
276C2×#125C2312yes—
277C2×#125C2312yes—
278C2×#125C2312yes—
279C2×#125C2312yes—
280C2×#125C2312yes—
281C2×#125C2314yes—
282C2×#125C2314yes—
283C2×#125C2314yes—
284C2×#125C2314yes—
285C2×#125C2314yes—
286C2×#125C2314yes—
287C2×#124C2312yes—
288C2×C22⋊Q8C2314yes—
289C2×C22⋊Q8C2314yes—
290C2×C22⋊Q8C2314yes—
291C2×C22⋊Q8C2314yes—
292C2×C22⋊Q8C2314yes—
293C2×C22⋊Q8C2312yes—
294C2×C22⋊Q8C2312yes—
295C2×C4×Q8C2312yes—
296C2×C4×Q8C2312yes—
297C2×C4×Q8C2311yescharacteristic
298C2×C4×Q8C2312yes—
299C2×C4×Q8C2312yes—
300C2×C4×Q8C2312yes—
301C2×C4×Q8C2312yes—
302C2×C4×Q8C2312yes—
303C2×C4×Q8C2314yes—
304C2×C4×Q8C2312yes—
305C2×C4×Q8C2314yes—
306C2×C4×Q8C2314yes—
307C2×C4×Q8C2312yes—
308C2×C4×Q8C2312yes—
309C2×C4×Q8C2311yescharacteristic
310C2×C4×D4C2311yescharacteristic
311C2×C4×D4C2311yescharacteristic
312C2×C4×D4C2312yes—
313C2×C4×D4C2312yes—
314C2×C4×D4C2311yescharacteristic
315C2×#117C2312yes—
316C2×#117C2312yes—
317C22×C4⋊C4C2314yes—
318C22×C4⋊C4C2312yes—
319C22×C4⋊C4C2312yes—
320C22×C42C2312yes—
321#400C2314yes—
322#400C2314yes—
323#400C2314yes—
324#400C2314yes—
325#400C2314yes—
326#400C2314yes—
327#400C2314yes—
328#400C2314yes—
329#400C2312yes—
330#400C2314yes—
331#400C2312yes—
332#400C2314yes—
333#400C2314yes—
334#400C2312yes—
335#400C2314yes—
336#400C2312yes—
337#400C2312yes—
338#400C2312yes—
339#400C2312yes—
340#400C2312yes—
341#399C2314yes—
342#398C2314yes—
343#398C2314yes—
344#398C2314yes—
345#398C2314yes—
346#398C2314yes—
347#398C2314yes—
348#398C2314yes—
349#398C2314yes—
350#398C2314yes—
351#398C2314yes—
352#398C2314yes—
353#398C2314yes—
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#398C2312yes—
367#398C2314yes—
368#398C2314yes—
369#398C2314yes—
370#398C2314yes—
371#398C2314yes—
372#398C2314yes—
373#398C2312yes—
374#398C2314yes—
375#398C2314yes—
376#398C2312yes—
377#398C2312yes—
378#398C2314yes—
379#398C2312yes—
380#398C2312yes—
381#398C2312yes—
382#398C2312yes—
383#398C2312yes—
384#398C2312yes—
385#398C2314yes—
386#398C2314yes—
387#398C2314yes—
388#398C2314yes—
389#398C2314yes—
390#398C2314yes—
391#398C2314yes—
392#396C2314yes—
393#396C2314yes—
394#396C2314yes—
395#396C2314yes—
396#396C2314yes—
397#396C2314yes—
398#396C2314yes—
399#396C2314yes—
400#395C2314yes—
401#395C2312yes—
402#395C2314yes—
403#395C2314yes—
404#395C2314yes—
405#395C2314yes—
406#395C2314yes—
407#395C2314yes—
408#395C2314yes—
409#395C2314yes—
410#395C2314yes—
411#395C2314yes—
412#395C2314yes—
413#395C2314yes—
414#395C2314yes—
415#395C2314yes—
416#395C2314yes—
417#395C2314yes—
418#395C2312yes—
419#395C2314yes—
420#395C2312yes—
421#395C2312yes—
422#395C2314yes—
423#395C2314yes—
424#393C2314yes—
425#393C2314yes—
426#393C2314yes—
427#391C2312yes—
428#391C2314yes—
429#391C2312yes—
430#391C2312yes—
431#391C2312yes—
432#391C2312yes—
433#391C2312yes—
434#391C2314yes—
435#391C2314yes—
436#391C2314yes—
437#391C2312yes—
438#391C2314yes—
439#391C2314yes—
440#391C2314yes—
441#391C2312yes—
442#391C2312yes—
443#391C2314yes—
444#391C2314yes—
445#391C2314yes—
446#391C2314yes—
447#391C2312yes—
448#391C2312yes—
449#391C2314yes—
450#391C2314yes—
451#391C2314yes—
452#391C2311yescharacteristic
453#391C2314yes—
454#391C2312yes—
455#391C2311yescharacteristic
456#391C2312yes—
457#391C2311yescharacteristic
458#391C2311yescharacteristic
459#390C2312yes—
460#390C2312yes—
461#390C2312yes—
462#389C2312yes—
463#389C2312yes—
464#389C2312yes—
465#389C2312yes—
466#389C2312yes—
467#389C2314yes—
468#389C2312yes—
469#389C2312yes—
470#389C2312yes—
471#389C2311yescharacteristic
472#389C2312yes—
473#389C2311yescharacteristic
474#389C2312yes—
475#389C2312yes—
476#389C2314yes—
477#389C2314yes—
478#389C2314yes—
479#389C2312yes—
480#389C2314yes—
481#389C2314yes—
482#389C2314yes—
483#389C2314yes—
484#389C2314yes—
485#389C2314yes—
486#389C2312yes—
487#389C2312yes—
488#389C2314yes—
489#389C2314yes—
490#389C2312yes—
491#389C2312yes—
492#389C2314yes—
493#389C2312yes—
494#389C2314yes—
495#389C2314yes—
496#389C2314yes—
497#389C2312yes—
498#389C2314yes—
499#389C2314yes—
500#389C2314yes—
501#389C2314yes—
502#389C2314yes—
503#389C2314yes—
504#389C2312yes—
505#389C2314yes—
506#389C2314yes—
507#389C2312yes—
508#389C2314yes—
509#389C2312yes—
510#389C2314yes—
511#389C2314yes—
512#389C2314yes—
513#389C2314yes—
514#389C2314yes—
515#389C2312yes—
516#389C2314yes—
517#389C2312yes—
518#389C2312yes—
519#389C2311yescharacteristic
520#389C2312yes—
521#389C2314yes—
522#389C2311yescharacteristic
523#389C2312yes—
524#389C2312yes—
525#389C2314yes—
526#389C2312yes—
527#389C2314yes—
528#389C2312yes—
529#389C2312yes—
530#389C2314yes—
531#389C2312yes—
532#389C2312yes—
533#389C2311yescharacteristic
534#389C2311yescharacteristic
535#389C2314yes—
536#388C2314yes—
537#388C2314yes—
538#388C2314yes—
539#388C2314yes—
540#388C2314yes—
541#388C2314yes—
542#388C2314yes—
543#388C2314yes—
544#388C2314yes—
545#388C2314yes—
546#388C2314yes—
547#388C2314yes—
548#388C2314yes—
549#388C2314yes—
550#388C2314yes—
551#387C2312yes—
552#387C2312yes—
553#387C2312yes—
554#387C2312yes—
555#387C2314yes—
556#387C2314yes—
557#387C2314yes—
558#387C2314yes—
559#387C2314yes—
560#387C2314yes—
561#387C2312yes—
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#387C2312yes—
594#387C2314yes—
595#387C2314yes—
596#387C2312yes—
597#387C2312yes—
598#387C2314yes—
599#387C2312yes—
600#387C2312yes—
601#387C2312yes—
602#387C2312yes—
603#387C2314yes—
604#387C2312yes—
605#387C2312yes—
606#387C2312yes—
607#385C2314yes—
608#385C2314yes—
609#385C2314yes—
610#385C2314yes—
611#385C2314yes—
612#385C2314yes—
613#385C2314yes—
614#385C2314yes—
615#385C2314yes—
616#385C2314yes—
617#385C2314yes—
618#385C2314yes—
619#385C2314yes—
620#385C2314yes—
621#385C2314yes—
622#385C2314yes—
623#385C2314yes—
624#385C2314yes—
625#384C2312yes—
626#384C2311yescharacteristic
627#384C2311yescharacteristic
628#384C2311yescharacteristic
629#384C2311yescharacteristic
630#384C2312yes—
631#384C2311yescharacteristic
632#384C2314yes—
633#384C2314yes—
634#384C2312yes—
635#384C2314yes—
636#384C2314yes—
637#384C2314yes—
638#384C2312yes—
639#384C2312yes—
640#384C2312yes—
641#384C2314yes—
642#383C2314yes—
643#382C2312yes—
644#382C2312yes—
645#382C2312yes—
646#382C2312yes—
647#382C2314yes—
648#382C2312yes—
649#382C2314yes—
650#382C2312yes—
651#382C2314yes—
652#382C2314yes—
653#381C2314yes—
654#380C2312yes—
655#380C2312yes—
656#380C2314yes—
657#380C2314yes—
658#380C2312yes—
659#380C2312yes—
660#380C2312yes—
661#380C2312yes—
662#380C2314yes—
663C4×C4⋊C4C2311yescharacteristic
664C4×C4⋊C4C2312yes—
665C4×C4⋊C4C2312yes—
666C4×C4⋊C4C2312yes—
667C4×C4⋊C4C2312yes—
668C4×C4⋊C4C2312yes—
669C4×C4⋊C4C2312yes—
670C4×C4⋊C4C2312yes—
671C4×C4⋊C4C2314yes—
672C4×C4⋊C4C2312yes—
673C4×C4⋊C4C2312yes—
674C4×C4⋊C4C2312yes—
675C4×C4⋊C4C2311yescharacteristic
676C4×C4⋊C4C2312yes—
677C4×C4⋊C4C2312yes—
678C4×C4⋊C4C2311yescharacteristic
679C4×C4⋊C4C2312yes—
680C4×C4⋊C4C2311yescharacteristic
681C4×C4⋊C4C2314yes—
682C4×C4⋊C4C2314yes—
683C4×C4⋊C4C2314yes—
684C4×C4⋊C4C2314yes—
685C4×C4⋊C4C2311yescharacteristic
686C4×C4⋊C4C2314yes—
687C4×C4⋊C4C2312yes—
688C4×C4⋊C4C2314yes—
689C4×C4⋊C4C2314yes—
690C4×C4⋊C4C2314yes—
691C4×C4⋊C4C2311yescharacteristic
692C4×C4⋊C4C2314yes—
693C4×C4⋊C4C2314yes—
694C4×C4⋊C4C2314yes—
695C4×C4⋊C4C2312yes—
696C4×C4⋊C4C2312yes—
697C4×C4⋊C4C2312yes—
698C4×C4⋊C4C2312yes—
699C4×C4⋊C4C2311yescharacteristic
700C4×C22⋊C4C2314yes—
701C4×C22⋊C4C2312yes—
702C4×C22⋊C4C2314yes—
703C4×C22⋊C4C2314yes—
704C4×C22⋊C4C2314yes—
705C4×C22⋊C4C2314yes—
706C4×C22⋊C4C2312yes—
707C4×C22⋊C4C2312yes—
708#376C2312yes—
709#376C2312yes—
710#376C2312yes—
711#376C2314yes—
712#376C2314yes—
713C2×#95C2314yes—
714C43C2312yes—
715C43C2311yescharacteristic
716C22×Q8C2412yes—
717C22×Q8C2412yes—
718C22×Q8C2411yescharacteristic
719C22×Q8C2412yes—
720C22×Q8C2414yes—
721C22×Q8C2414yes—
722C22×Q8C2414yes—
723C22×Q8C2411yescharacteristic
724C22×D4C2411yescharacteristic
725C23×C4C2412yes—
726C23×C4C2412yes—
727C23×C4C2414yes—
728C23×C4C2414yes—
729C23×C4C2412yes—
730C4⋊Q8—28no—
731C4⋊Q8—24no—
732C4⋊Q8—42no—
733C4⋊Q8—44no—
734C4⋊Q8—44no—
735C4⋊Q8—48no—
736C4⋊Q8—48no—
737C4⋊Q8—82no—
738C4⋊Q8—82no—
739C4⋊Q8—84no—
740C4⋊Q8C2×Q818yes—
741#126C2×Q8132yes—
742#125—28no—
743#125—44no—
744#125—44no—
745#125—44no—
746#125—44no—
747#125—48no—
748#125—48no—
749#125—44no—
750#125—48no—
751#125—48no—
752#125—48no—
753#125—84no—
754#124C2×Q8116yes—
755C22⋊Q8—48no—
756C22⋊Q8—48no—
757C22⋊Q8—48no—
758C22⋊Q8—48no—
759C22⋊Q8—84no—
760C22⋊Q8—82no—
761C22⋊Q8C2×Q8116yes—
762C4×Q8—28no—
763C4×Q8—28no—
764C4×Q8—24no—
765C4×Q8—28no—
766C4×Q8—44no—
767C4×Q8—48no—
768C4×Q8—44no—
769C4×Q8—44no—
770C4×Q8—44no—
771C4×Q8—48no—
772C4×Q8—44no—
773C4×Q8—82no—
774C4×Q8—84no—
775C4×Q8C2×Q8116yes—
776C4×Q8C2×Q818yes—
777C4×D4—24no—
778C4×D4—24no—
779C4×D4—44no—
780C4×D4—44no—
781C4×D4C2×Q818yes—
782#117—82no—
783#117C2×Q8116yes—
784C2×C4⋊C4—44no—
785C2×C4⋊C4—48no—
786C2×C4⋊C4—82no—
787C2×C4⋊C4C2412yes—
788C2×C4⋊C4C2411yescharacteristic
789C2×C4⋊C4C2414yes—
790C2×C4⋊C4C2412yes—
791C2×C4⋊C4C2412yes—
792C2×C4⋊C4C2412yes—
793C2×C4⋊C4C2411yescharacteristic
794C2×C4⋊C4C2412yes—
795C2×C4⋊C4C2412yes—
796C2×C4⋊C4C2412yes—
797C2×C4⋊C4C2414yes—
798C2×C4⋊C4C2412yes—
799C2×C4⋊C4C2414yes—
800C2×C4⋊C4C2411yescharacteristic
801C2×C4⋊C4C2412yes—
802C2×C4⋊C4C2414yes—
803C2×C4⋊C4C2414yes—
804C2×C4⋊C4C2412yes—
805C2×C4⋊C4C2412yes—
806C2×C4⋊C4C2412yes—
807C2×C4⋊C4C2411yescharacteristic
808C2×C4⋊C4C2412yes—
809C2×C4⋊C4C2414yes—
810C2×C4⋊C4C2411yescharacteristic
811C2×C4⋊C4C2414yes—
812C2×C4⋊C4C2414yes—
813C2×C4⋊C4C2414yes—
814C2×C4⋊C4C2412yes—
815C2×C4⋊C4C2414yes—
816C2×C4⋊C4C2411yescharacteristic
817C2×C4⋊C4C2412yes—
818C2×C4⋊C4C2414yes—
819C2×C4⋊C4C2414yes—
820C2×C4⋊C4C2414yes—
821C2×C4⋊C4C2414yes—
822C2×C4⋊C4C2414yes—
823C2×C4⋊C4C2414yes—
824C2×C4⋊C4C2414yes—
825C2×C4⋊C4C2414yes—
826C2×C4⋊C4C2414yes—
827C2×C4⋊C4C2414yes—
828C2×C4⋊C4C2412yes—
829C2×C4⋊C4C2414yes—
830C2×C4⋊C4C2412yes—
831C2×C4⋊C4C2414yes—
832C2×C4⋊C4C2412yes—
833C2×C4⋊C4C2414yes—
834C2×C4⋊C4C2414yes—
835C2×C4⋊C4C2414yes—
836C2×C4⋊C4C2414yes—
837C2×C4⋊C4C2414yes—
838C2×C4⋊C4C2414yes—
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⋊C4C2414yes—
848C2×C4⋊C4C2414yes—
849C2×C4⋊C4C2411yescharacteristic
850C2×C4⋊C4C2411yescharacteristic
851C2×C4⋊C4C2412yes—
852C2×C4⋊C4C2412yes—
853C2×C4⋊C4C2411yescharacteristic
854C2×C4⋊C4C2412yes—
855C2×C4⋊C4C2412yes—
856C2×C4⋊C4C2412yes—
857C2×C4⋊C4C2411yescharacteristic
858C2×C4⋊C4C2414yes—
859C2×C4⋊C4C2414yes—
860C2×C4⋊C4C2412yes—
861C2×C4⋊C4C2414yes—
862C2×C4⋊C4C2412yes—
863C2×C4⋊C4C2412yes—
864C2×C4⋊C4C2412yes—
865C2×C4⋊C4C2414yes—
866C2×C4⋊C4C2414yes—
867C2×C4⋊C4C2414yes—
868C2×C4⋊C4C2412yes—
869C2×C4⋊C4C2412yes—
870C2×C4⋊C4C2412yes—
871C2×C4⋊C4C2412yes—
872C2×C4⋊C4C2412yes—
873C2×C4⋊C4C2411yescharacteristic
874C2×C4⋊C4C2412yes—
875C2×C4⋊C4C2411yescharacteristic
876C2×C4⋊C4C2414yes—
877C2×C4⋊C4C2412yes—
878C2×C4⋊C4C2412yes—
879C2×C4⋊C4C2411yescharacteristic
880C2×C22⋊C4C2412yes—
881C2×C22⋊C4C2412yes—
882C2×C22⋊C4C2414yes—
883C2×C22⋊C4C2414yes—
884C2×C22⋊C4C2414yes—
885C2×C22⋊C4C2414yes—
886C2×C22⋊C4C2414yes—
887C2×C22⋊C4C2414yes—
888C2×C22⋊C4C2414yes—
889C2×C22⋊C4C2414yes—
890C2×C22⋊C4C2414yes—
891C2×C22⋊C4C2412yes—
892C2×C22⋊C4C2414yes—
893C2×C42—82no—
894C2×C42C2412yes—
895C2×C42C2412yes—
896C2×C42C2411yescharacteristic
897C2×C42C2412yes—
898C2×C42C2414yes—
899C2×C42C2411yescharacteristic
900C2×C42C2414yes—
901C2×C42C2412yes—
902C2×C42C2412yes—
903C2×C42C2414yes—
904C2×C42C2414yes—
905C2×C42C2414yes—
906C2×C42C2414yes—
907C2×C42C2414yes—
908C2×C42C2412yes—
909C2×C42C2414yes—
910C2×C42C2414yes—
911C2×C42C2412yes—
912C2×C42C2414yes—
913C2×C42C2412yes—
914C2×C42C2414yes—
915C2×C42C2412yes—
916C2×C42C2412yes—
917C2×C42C2412yes—
918C2×C42C2411yescharacteristic
919C2×C42C2411yescharacteristic
920C2×C42C2412yes—
921C2×C42C2411yescharacteristic
922C2×C42C2414yes—
923C2×C42C2411yescharacteristic
924C2×C42C2412yes—
925C2×C42C2411yescharacteristic
926#95C2412yes—
927#95C2414yes—
928#95C2414yes—
929#95C2414yes—
930#95C2412yes—
931#95C2412yes—
932#95C2414yes—
933#95C2414yes—
934#95C2412yes—
935#95C2412yes—
936#95C2414yes—
937#95C2412yes—
938#95C2412yes—
939#95C2412yes—
940#95C2414yes—
941#95C2412yes—
942#95C2412yes—
943#95C2412yes—
944#95C2414yes—
945#95C2412yes—
946#95C2412yes—
947#95C2412yes—
948#95C2412yes—
949#95C2412yes—
950#95C2412yes—
951#95C2412yes—
952#95C2412yes—
953#95C2414yes—
954#95C2414yes—
955#95C2414yes—
956#95C2414yes—
957#95C2414yes—
958#95C2414yes—
959#95C2412yes—
960#95C2412yes—
961#95C2412yes—
962#95C2412yes—
963#95C2414yes—
964#95C2414yes—
965#95C2414yes—
966#95C2414yes—
967#95C2412yes—
968#95C2414yes—
969#95C2414yes—
970#95C2414yes—
971#95C2412yes—
972#95C2412yes—
973#95C2414yes—
974#95C2414yes—
975#95C2414yes—
976#95C2412yes—
977#95C2414yes—
978#95C2412yes—
979#95C2412yes—
980#95C2412yes—
981#95C2412yes—
982#95C2412yes—
983#95C2414yes—
984#95C2414yes—
985#95C2414yes—
986#95C2412yes—
987#95C2412yes—
988#95C2412yes—
989#95C2414yes—
990#95C2412yes—
991#95C2414yes—
992#95C2414yes—
993#95C2412yes—
994#95C2414yes—
995#95C2414yes—
996#95C2414yes—
997#95C2414yes—
998#95C2414yes—
999#95C2414yes—
1000#95C2414yes—
1001#95C2414yes—
1002#95C2414yes—
1003C24C2512yes—
1004C2×Q8—24no—
1005C2×Q8—24no—
1006C2×Q8—24no—
1007C2×Q8—22no—
1008C2×Q8—24no—
1009C2×Q8—28no—
1010C2×Q8—42no—
1011C2×Q8—41no—
1012C2×Q8—41no—
1013C2×Q8—42no—
1014C2×Q8—44no—
1015C2×Q8—44no—
1016C2×Q8—44no—
1017C2×Q8—41no—
1018C2×Q8—44no—
1019C2×Q8—42no—
1020C2×Q8—41no—
1021C2×Q8—42no—
1022C2×Q8—44no—
1023C2×Q8—44no—
1024C2×Q8—44no—
1025C2×Q8—44no—
1026C2×Q8C22×Q818yes—
1027C2×Q8C22×Q814yes—
1028C2×D4—22no—
1029C2×D4—22no—
1030C2×D4C22×Q814yes—
1031C22×C4—24no—
1032C22×C4—24no—
1033C22×C4—24no—
1034C22×C4—42no—
1035C22×C4—42no—
1036C22×C4—42no—
1037C22×C4—42no—
1038C22×C4—44no—
1039C22×C4—44no—
1040C22×C4—42no—
1041C22×C4—44no—
1042C22×C4—44no—
1043C22×C4—44no—
1044C22×C4—44no—
1045C22×C4C22×Q818yes—
1046C22×C4C2512yes—
1047C22×C4C2511yescharacteristic
1048C22×C4C2512yes—
1049C22×C4C2512yes—
1050C22×C4C2514yes—
1051C22×C4C2512yes—
1052C22×C4C2512yes—
1053C22×C4C2512yes—
1054C22×C4C2514yes—
1055C22×C4C2512yes—
1056C22×C4C2512yes—
1057C22×C4C2512yes—
1058C22×C4C2514yes—
1059C22×C4C2512yes—
1060C22×C4C2514yes—
1061C22×C4C2512yes—
1062C22×C4C2514yes—
1063C22×C4C2511yescharacteristic
1064C22×C4C2511yescharacteristic
1065C22×C4C2512yes—
1066C22×C4C2514yes—
1067C22×C4C2512yes—
1068C22×C4C2512yes—
1069C22×C4C2511yescharacteristic
1070C22×C4C2511yescharacteristic
1071C22×C4C2512yes—
1072C22×C4C2511yescharacteristic
1073C22×C4C2511yescharacteristic
1074C4⋊C4—24no—
1075C4⋊C4—28no—
1076C4⋊C4—22no—
1077C4⋊C4—24no—
1078C4⋊C4—24no—
1079C4⋊C4—24no—
1080C4⋊C4—24no—
1081C4⋊C4—24no—
1082C4⋊C4—22no—
1083C4⋊C4—28no—
1084C4⋊C4—24no—
1085C4⋊C4—24no—
1086C4⋊C4—28no—
1087C4⋊C4—24no—
1088C4⋊C4—28no—
1089C4⋊C4—28no—
1090C4⋊C4—24no—
1091C4⋊C4—22no—
1092C4⋊C4—24no—
1093C4⋊C4—28no—
1094C4⋊C4—24no—
1095C4⋊C4—24no—
1096C4⋊C4—22no—
1097C4⋊C4—44no—
1098C4⋊C4—44no—
1099C4⋊C4—44no—
1100C4⋊C4—41no—
1101C4⋊C4—44no—
1102C4⋊C4—42no—
1103C4⋊C4—42no—
1104C4⋊C4—42no—
1105C4⋊C4—42no—
1106C4⋊C4—42no—
1107C4⋊C4—44no—
1108C4⋊C4—44no—
1109C4⋊C4—42no—
1110C4⋊C4—41no—
1111C4⋊C4—41no—
1112C4⋊C4—44no—
1113C4⋊C4—44no—
1114C4⋊C4—42no—
1115C4⋊C4—42no—
1116C4⋊C4—42no—
1117C4⋊C4—44no—
1118C4⋊C4—42no—
1119C4⋊C4—42no—
1120C4⋊C4—42no—
1121C4⋊C4—44no—
1122C4⋊C4—42no—
1123C4⋊C4—41no—
1124C4⋊C4—42no—
1125C4⋊C4—42no—
1126C4⋊C4—44no—
1127C4⋊C4—44no—
1128C4⋊C4—44no—
1129C4⋊C4—44no—
1130C4⋊C4—44no—
1131C4⋊C4—44no—
1132C4⋊C4—44no—
1133C4⋊C4—44no—
1134C4⋊C4—44no—
1135C4⋊C4—44no—
1136C4⋊C4—44no—
1137C4⋊C4—44no—
1138C4⋊C4—42no—
1139C4⋊C4—44no—
1140C4⋊C4—42no—
1141C4⋊C4—44no—
1142C4⋊C4—44no—
1143C4⋊C4—42no—
1144C4⋊C4—44no—
1145C4⋊C4—42no—
1146C4⋊C4—44no—
1147C4⋊C4—42no—
1148C4⋊C4—44no—
1149C4⋊C4—44no—
1150C4⋊C4—44no—
1151C4⋊C4—44no—
1152C4⋊C4—42no—
1153C4⋊C4—44no—
1154C4⋊C4—44no—
1155C4⋊C4—44no—
1156C4⋊C4—42no—
1157C4⋊C4—42no—
1158C4⋊C4—41no—
1159C4⋊C4—41no—
1160C4⋊C4C22×Q814yes—
1161C4⋊C4C22×Q818yes—
1162C4⋊C4C22×Q814yes—
1163C4⋊C4C22×Q8116yes—
1164C4⋊C4C22×Q818yes—
1165C4⋊C4C22×Q818yes—
1166C4⋊C42−1+414yes—
1167C22⋊C4—24no—
1168C22⋊C4—24no—
1169C22⋊C4—44no—
1170C22⋊C4—44no—
1171C22⋊C4—44no—
1172C22⋊C4—44no—
1173C22⋊C4—44no—
1174C22⋊C4—44no—
1175C22⋊C4—44no—
1176C22⋊C4—44no—
1177C22⋊C4C22×Q8116yes—
1178C22⋊C4C22×Q818yes—
1179C22⋊C4C22×Q8116yes—
1180C42—24no—
1181C42—24no—
1182C42—28no—
1183C42—24no—
1184C42—22no—
1185C42—28no—
1186C42—24no—
1187C42—24no—
1188C42—22no—
1189C42—41no—
1190C42—42no—
1191C42—42no—
1192C42—42no—
1193C42—41no—
1194C42—42no—
1195C42—42no—
1196C42—41no—
1197C42—44no—
1198C42—44no—
1199C42—44no—
1200C42—44no—
1201C42—44no—
1202C42—44no—
1203C42—44no—
1204C42—42no—
1205C42—44no—
1206C42—44no—
1207C42—42no—
1208C42C22×Q8116yes—
1209C42C22×Q814yes—
1210C42C22×Q818yes—
1211C42H(5,𝔽2)14yes—
1212C23—22no—
1213C23—22no—
1214C23—22no—
1215C23—22no—
1216C23—22no—
1217C23—22no—
1218C23C23×Q814yes—
1219C23C2611yescharacteristic
1220Q8—216no—
1221Q8—44no—
1222Q8—48no—
1223Q8—82no—
1224Q8—84no—
1225Q8—88no—
1226Q8—88no—
1227Q8—164no—
1228D4—28no—
1229C2×C4—24no—
1230C2×C4—24no—
1231C2×C4—21no—
1232C2×C4—21no—
1233C2×C4—21no—
1234C2×C4—22no—
1235C2×C4—22no—
1236C2×C4—22no—
1237C2×C4—22no—
1238C2×C4—22no—
1239C2×C4—21no—
1240C2×C4—21no—
1241C2×C4—21no—
1242C2×C4—21no—
1243C2×C4—22no—
1244C2×C4—22no—
1245C2×C4—21no—
1246C2×C4—21no—
1247C2×C4—21no—
1248C2×C4—22no—
1249C2×C4—22no—
1250C2×C4—22no—
1251C2×C4—22no—
1252C2×C4—22no—
1253C2×C4—22no—
1254C2×C4—24no—
1255C2×C4—22no—
1256C2×C4—24no—
1257C2×C4—24no—
1258C2×C4—24no—
1259C2×C4—22no—
1260C2×C4—22no—
1261C2×C4—21no—
1262C2×C4—22no—
1263C2×C4—22no—
1264C2×C4—22no—
1265C2×C4—24no—
1266C2×C4—24no—
1267C2×C4—22no—
1268C2×C4—24no—
1269C2×C4—24no—
1270C2×C4—22no—
1271C2×C4—22no—
1272C2×C4—22no—
1273C2×C4—22no—
1274C2×C4—22no—
1275C2×C4—24no—
1276C2×C4—22no—
1277C2×C4—24no—
1278C2×C4—22no—
1279C2×C4—22no—
1280C2×C4—24no—
1281C2×C4—22no—
1282C2×C4—22no—
1283C2×C4—22no—
1284C2×C4—21no—
1285C2×C4—22no—
1286C2×C4—21no—
1287C2×C4—22no—
1288C2×C4—22no—
1289C2×C4—22no—
1290C2×C4—24no—
1291C2×C4—24no—
1292C2×C4—22no—
1293C2×C4—22no—
1294C2×C4—24no—
1295C2×C4—22no—
1296C2×C4—22no—
1297C2×C4—22no—
1298C2×C4—24no—
1299C2×C4—22no—
1300C2×C4—48no—
1301C2×C4—48no—
1302C2×C4—84no—
1303C2×C4—88no—
1304C2×C4—164no—
1305C2×C4C23×Q814yes—
1306C2×C4C23×Q814yes—
1307C2×C4C23×Q812yes—
1308C2×C4C23×Q818yes—
1309C2×C4C23×Q814yes—
1310C2×C4C23×Q812yes—
1311C2×C4C23×Q812yes—
1312C2×C4C2×H(5,𝔽2)12yes—
1313C2×C4C2×H(5,𝔽2)12yes—
1314C2×C4C2×H(5,𝔽2)12yes—
1315C2×C4C2×2−1+414yes—
1316C2×C4C2×2−1+412yes—
1317C2×C4#58512yes—
1318C22—24no—
1319C22—24no—
1320C22—24no—
1321C22—42no—
1322C22—42no—
1323C22—42no—
1324C22—42no—
1325C22C24×Q811yescharacteristic
1326C22C22×H(5,𝔽2)11yescharacteristic
1327C22C22×2−1+411yescharacteristic
1328C22C2×#58511yescharacteristic
1329C22H(7,𝔽2)11yescharacteristic
1330C222−1+611yescharacteristic
1331C222−1+611yescharacteristic
1332C4—22no—
1333C4—24no—
1334C4—28no—
1335C4—22no—
1336C4—24no—
1337C4—24no—
1338C4—22no—
1339C4—22no—
1340C4—22no—
1341C4—24no—
1342C4—42no—
1343C4—41no—
1344C4—42no—
1345C4—42no—
1346C4—42no—
1347C4—44no—
1348C4—44no—
1349C4—42no—
1350C4—42no—
1351C4—42no—
1352C4—44no—
1353C4—42no—
1354C4—44no—
1355C4—42no—
1356C4—42no—
1357C4—44no—
1358C4—42no—
1359C4#350314yes—
1360C2—44no—
1361C2C2×#350311yescharacteristic
1362C2#6285411yescharacteristic
1363C2#6287811yescharacteristic
1364C2#6292511yescharacteristic
1365C2#6294811yescharacteristic
1366C2#6300411yescharacteristic
1367C2#6305711yescharacteristic
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. #59828C2semidirect
3. #52274C2semidirect
4. #51078C2semidirect
5. #50904C2semidirect
6. #47972C2semidirect
7. #47732C2semidirect
8. #45794C2semidirect
10. #45279C2semidirect
12. #44211C2semidirect
13. #42825C2semidirect
15. #42005C2semidirect
16. #39749C2semidirect
17. #39639C2semidirect
18. #39626C2semidirect
20. #39612C2semidirect
21. #39183C2semidirect
22. #38447C2semidirect
23. #37309C2semidirect
25. #35957C2semidirect
26. #35582C2semidirect
261. #556Q8semidirect

Maximal subgroups

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

subgroupindex
#598282
#594602
#522742
#510782
#509042
#479722
#477322
#457942
#454242
#452792
#450592
#442112
#428252
#424982
#420052
#397492
#396392
#396262
#396132
#396122
#391832
#384472
#373092
#362612
#359572
#355822
#351772
#344992
#343242