Finite Group Databasebeta

← #7650915

Subgroups — #7650915

Order 512.

4398 conjugacy classes of subgroups.

The subgroup lattice has 1336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42973C211yesmaximal, characteristic, complemented
2#42955C211yesmaximal, characteristic, complemented
3#42495C212yesmaximal, complemented
4#42494C212yesmaximal, complemented
5#42490C211yesmaximal, characteristic
6#42490C211yesmaximal, characteristic
7#40637C214yesmaximal, complemented
8#40631C214yesmaximal, complemented
9#40626C214yesmaximal, complemented
10#40622C214yesmaximal, complemented
11#39986C212yesmaximal, complemented
12#39977C212yesmaximal, complemented
13#39965C214yesmaximal, complemented
14#38966C212yesmaximal, complemented
15#38962C212yesmaximal
16#38959C214yesmaximal, complemented
17#37879C214yesmaximal, complemented
18#37876C214yesmaximal, complemented
19#35612C212yesmaximal, complemented
20#35581C212yesmaximal, complemented
21#35579C212yesmaximal, complemented
22#35337C211yesmaximal, characteristic, complemented
23#35175C212yesmaximal, complemented
24#34941C212yesmaximal, complemented
25#34882C211yesmaximal, characteristic, complemented
26#34261C212yesmaximal
27#34255C211yesmaximal, characteristic
28C2×#518C2211yescharacteristic
29#2862C2211yescharacteristic, complemented
30#2859C2211yescharacteristic, complemented
31#2855C2214yescomplemented
32#2851C2212yes—
33#2851C2214yescomplemented
34#2844C2212yescomplemented
35#2843C2212yescomplemented
36#2842C2212yes—
37#2842C2212yes—
38#2841C2214yescomplemented
39#2841C2214yescomplemented
40#2807C2214yes—
41#2790C2214yes—
42#2790C2214yescomplemented
43#2790C2214yescomplemented
44#2790C2214yescomplemented
45#2788C2214yescomplemented
46#2788C2214yescomplemented
47#2784C2214yes—
48#2784C2212yes—
49#2784C2212yes—
50#2780C2214yes—
51#2780C2214yes—
52#2780C2214yes—
53#2768C2214yes—
54#2768C2214yes—
55#2768C2214yescomplemented
56#2768C2214yescomplemented
57#2768C2214yescomplemented
58#2763C2212yes—
59#2763C2212yes—
60#2763C2214yescomplemented
61#2748C2214yes—
62#2742C2212yes—
63#2742C2214yescomplemented
64#2729C2214yescomplemented
65#2720C2214yes—
66#2720C2214yes—
67#2720C2214yescomplemented
68#2720C2214yescomplemented
69#2704C2214yescomplemented
70#2704C2214yescomplemented
71#2704C2214yescomplemented
72#2692C2214yes—
73#2683C2212yes—
74#2683C2212yes—
75#2677C2212yes—
76#2667C2214yescomplemented
77#2667C2214yescomplemented
78#2666C2214yescomplemented
79#2666C2214yescomplemented
80#2665C2214yescomplemented
81#2665C2214yescomplemented
82#2660C2214yescomplemented
83#2659C2214yescomplemented
84#2647C2212yescomplemented
85#2629C2214yescomplemented
86#2629C2214yescomplemented
87#2628C2211yescharacteristic
88#2628C2211yescharacteristic
89#2627C2214yescomplemented
90#2626C2214yes—
91#2626C2214yes—
92#2626C2214yes—
93#2612C2212yescomplemented
94#2608C2214yescomplemented
95#2608C2214yescomplemented
96#2606C2214yescomplemented
97#2589C2214yes—
98#2589C2214yes—
99#2589C2214yescomplemented
100#2588C2214yescomplemented
101#2588C2214yescomplemented
102#2588C2214yescomplemented
103#2587C2214yes—
104#2587C2214yescomplemented
105#2587C2214yescomplemented
106#2587C2214yescomplemented
107#2586C2212yescomplemented
108#2585C2214yescomplemented
109#2585C2212yescomplemented
110#2584C2212yescomplemented
111#2584C2212yescomplemented
112#2584C2212yescomplemented
113#2580C2212yes—
114#2574C2212yes—
115#2574C2214yescomplemented
116#2574C2214yescomplemented
117#2574C2214yescomplemented
118#2574C2214yescomplemented
119#2571C2212yescomplemented
120#2570C2212yescomplemented
121#2570C2214yescomplemented
122#2569C2214yescomplemented
123#2567C2212yescomplemented
124#2566C2212yes—
125#2566C2212yes—
126#2566C2212yes—
127#2563C2212yes—
128#2556C2212yes—
129#2556C2214yes—
130#2556C2214yescomplemented
131#2556C2214yescomplemented
132#2552C2212yescomplemented
133#2552C2212yescomplemented
134#2552C2212yescomplemented
135#2552C2212yescomplemented
136#2551C2212yescomplemented
137#2550C2212yescomplemented
138#2550C2212yescomplemented
139#2549C2214yescomplemented
140#2538C2212yes—
141#2538C2212yes—
142#2538C2212yes—
143#2522C2214yes—
144#2522C2212yes—
145#2522C2214yescomplemented
146#2520C2212yescomplemented
147#2509C2212yescomplemented
148#2508C2212yescomplemented
149#2508C2212yescomplemented
150#2508C2212yescomplemented
151#2508C2212yescomplemented
152#2507C2214yescomplemented
153#2507C2212yescomplemented
154#2506C2212yescomplemented
155#2506C2212yescomplemented
156#2497C2214yescomplemented
157#2497C2214yescomplemented
158#2465C2212yes—
159#2465C2214yescomplemented
160#2462C2212yescomplemented
161#2462C2214yescomplemented
162#2454C2212yes—
163#2454C2212yes—
164#2454C2212yes—
165#2454C2212yes—
166#2454C2212yes—
167#2452C2212yes—
168#2452C2212yes—
169#2452C2212yes—
170#2442C2212yes—
171#2442C2214yescomplemented
172#2442C2214yescomplemented
173#2441C2212yes—
174#2441C2212yes—
175#2441C2214yescomplemented
176#2441C2214yescomplemented
177#2440C2212yes—
178#2439C2214yescomplemented
179#2439C2214yescomplemented
180#2438C2214yescomplemented
181#2438C2214yescomplemented
182#2438C2214yescomplemented
183#2438C2214yescomplemented
184#2437C2212yes—
185#2437C2214yes—
186#2437C2214yes—
187#2437C2212yes—
188#2429C2214yescomplemented
189#2423C2214yes—
190#2423C2214yescomplemented
191#2399C2211yescharacteristic, complemented
192#2399C2211yescharacteristic, complemented
193#2396C2211yescharacteristic
194#2396C2211yescharacteristic
195#2396C2214yescomplemented
196#2396C2214yescomplemented
197#2357C2214yes—
198#2357C2212yes—
199#2354C2212yes—
200#2354C2214yes—
201#2353C2214yes—
202#2352C2214yes—
203#2349C2212yes—
204D4×C4⋊C4C2212yes—
205#2347C2212yes—
206#2346C2212yes—
207#2342C2214yes—
208#2342C2214yes—
209#2342C2214yes—
210#2342C2214yes—
211D4×C22⋊C4C2212yes—
212D4×C22⋊C4C2212yes—
213#2331C2211yescharacteristic, complemented
214#2331C2211yescharacteristic, complemented
215#2330C2212yescomplemented
216#2330C2212yescomplemented
217#2330C2214yescomplemented
218#2329C2214yescomplemented
219#2319C2212yes—
220#2319C2212yes—
221#2319C2212yes—
222#2318C2214yes—
223#2317C2211yescharacteristic
224#2317C2214yescomplemented
225#2315C2214yes—
226#2314C2212yes—
227#2312C2214yes—
228#2309C2211yescharacteristic
229C4×C4⋊Q8C2212yescomplemented
230C4×#125C2212yescomplemented
231C4×#125C2212yescomplemented
232C4×#125C2212yescomplemented
233C4×C22⋊Q8C2212yes—
234C4×C22⋊Q8C2214yescomplemented
235#2298C2212yes—
236#2296C2211yescharacteristic
237#2295C2211yescharacteristic, complemented
238#2295C2212yescomplemented
239#2293C2212yes—
240#2293C2212yes—
241#2293C2212yes—
242C2×#390C2211yescharacteristic
243#2290C2214yes—
244C2×#388C2214yes—
245#2285C2214yescomplemented
246#2275C2212yes—
247#2274C2211yescharacteristic
248C42×Q8C2211yescharacteristic, complemented
249C42×D4C2212yes—
250C4×#117C2211yescharacteristic
251C23×D4C2311yescharacteristic
252C2×C4⋊Q8C2312yes—
253C2×C4⋊Q8C2311yescharacteristic
254C2×C4⋊Q8C2311yescharacteristic
255C2×C4⋊Q8C2314yes—
256C2×#125C2312yes—
257C2×#125C2312yes—
258C2×#125C2312yes—
259C2×#125C2312yes—
260C2×#125C2312yes—
261C2×#125C2314yes—
262C2×#125C2314yes—
263C2×#125C2314yes—
264C2×C22⋊Q8C2314yes—
265C2×C22⋊Q8C2314yes—
266C2×C22⋊Q8C2312yes—
267C2×C22⋊Q8C2314yes—
268C2×C22⋊Q8C2314yes—
269C2×C22⋊Q8C2314yes—
270C2×C22⋊Q8C2314yes—
271C2×C22⋊Q8C2314yes—
272#518Q8116yescomplemented
273C2×C4×Q8C2311yescharacteristic
274C2×C4×Q8C2312yes—
275C2×C4×Q8C2311yescharacteristic
276C2×C4×Q8C2312yes—
277C2×C4×Q8C2314yes—
278C2×C4×D4C2312yes—
279C2×C4×D4C2312yes—
280C2×C4×D4C2312yes—
281C2×C4×D4C2312yes—
282C2×C4×D4C2314yes—
283C2×C4×D4C2312yes—
284C2×C4×D4C2312yes—
285C2×#117C2311yescharacteristic
286C2×#117C2311yescharacteristic
287C2×#117C2314yes—
288C2×#117C2314yes—
289C2×#117C2314yes—
290C2×#117C2314yes—
291C2×#117C2311yescharacteristic
292C2×#117C2311yescharacteristic
293C22×C4⋊C4C2311yescharacteristic
294C22×C4⋊C4C2314yes—
295C22×C22⋊C4C2314yes—
296C22×C22⋊C4C2314yes—
297C22×C22⋊C4C2314yes—
298C22×C22⋊C4C2314yes—
299C22×C42C2311yescharacteristic
300C22×C42C2314yes—
301#400C2314yes—
302#400C2314yes—
303#400C2314yes—
304#400C2314yes—
305#400C2311yescharacteristic
306#400C2314yes—
307#400C2312yes—
308#400C2314yes—
309#400C2314yes—
310#400C2314yes—
311#400C2314yes—
312#400C2312yes—
313#400C2311yescharacteristic
314#400C2314yes—
315#400C2314yes—
316#400C2314yes—
317#399C2314yes—
318#399C2314yes—
319#399C2314yes—
320#399C2311yescharacteristic
321#399C2311yescharacteristic
322#399C2312yes—
323#399C2312yes—
324#399C2314yes—
325#399C2314yes—
326#399C2314yes—
327#399C2314yes—
328#399C2314yes—
329#398C2314yes—
330#398C2314yes—
331#398C2314yes—
332#398C2314yes—
333#398C2314yes—
334#398C2312yes—
335#398C2314yes—
336#398C2314yes—
337#398C2314yes—
338#398C2312yes—
339#398C2314yes—
340#398C2312yes—
341#398C2314yes—
342#398C2314yes—
343#398C2312yes—
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#398C2312yes—
360#398C2312yes—
361#396C2314yes—
362#396C2314yes—
363#396C2314yes—
364#396C2314yes—
365#396C2314yes—
366#396C2314yes—
367#396C2312yes—
368#396C2314yes—
369#396C2314yes—
370#396C2314yes—
371#396C2314yes—
372#396C2314yes—
373#396C2314yes—
374#396C2314yes—
375#396C2314yes—
376#396C2314yes—
377#396C2314yes—
378#396C2314yes—
379#396C2314yes—
380#396C2314yes—
381#396C2314yes—
382#396C2314yes—
383#396C2312yes—
384#396C2314yes—
385#395C2314yes—
386#395C2314yes—
387#395C2312yes—
388#395C2314yes—
389#395C2314yes—
390#395C2314yes—
391#395C2314yes—
392#395C2312yes—
393#395C2314yes—
394#395C2311yescharacteristic
395#395C2312yes—
396#395C2312yes—
397#395C2314yes—
398#395C2314yes—
399#395C2311yescharacteristic
400#395C2312yes—
401#395C2312yes—
402#395C2314yes—
403#393C2314yes—
404#393C2314yes—
405#393C2311yescharacteristic
406#393C2314yes—
407#393C2314yes—
408#393C2314yes—
409#393C2312yes—
410#393C2312yes—
411#393C2314yes—
412#393C2311yescharacteristic
413#391C2314yes—
414#391C2314yes—
415#391C2312yes—
416#391C2312yes—
417#391C2314yes—
418#391C2314yes—
419#391C2314yes—
420#391C2312yes—
421#391C2314yes—
422#391C2314yes—
423#391C2314yes—
424#391C2312yes—
425#390C2312yes—
426#390C2312yes—
427#390C2312yes—
428#390C2312yes—
429#390C2312yes—
430#390C2312yes—
431#390C2312yes—
432#390C2312yes—
433#390C2312yes—
434#390C2312yes—
435#390C2314yes—
436#389C2312yes—
437#389C2312yes—
438#389C2312yes—
439#389C2312yes—
440#389C2312yes—
441#389C2312yes—
442#389C2312yes—
443#389C2314yes—
444#389C2312yes—
445#389C2312yes—
446#389C2312yes—
447#389C2312yes—
448#389C2314yes—
449#389C2314yes—
450#389C2314yes—
451#389C2314yes—
452#389C2312yes—
453#389C2314yes—
454#389C2314yes—
455#389C2314yes—
456#389C2312yes—
457#389C2312yes—
458#389C2312yes—
459#389C2312yes—
460#389C2312yes—
461#389C2314yes—
462#389C2314yes—
463#389C2312yes—
464#389C2312yes—
465#389C2312yes—
466#389C2314yes—
467#389C2314yes—
468#389C2314yes—
469#389C2314yes—
470#389C2312yes—
471#389C2314yes—
472#389C2314yes—
473#389C2312yes—
474#389C2314yes—
475#389C2314yes—
476#389C2314yes—
477#389C2314yes—
478#389C2314yes—
479#389C2312yes—
480#389C2312yes—
481#389C2314yes—
482#389C2314yes—
483#389C2314yes—
484#389C2312yes—
485#389C2312yes—
486#388C2312yes—
487#388C2314yes—
488#388C2314yes—
489#388C2314yes—
490#388C2314yes—
491#388C2314yes—
492#388C2314yes—
493#388C2314yes—
494#388C2314yes—
495#388C2314yes—
496#388C2312yes—
497#388C2312yes—
498#388C2314yes—
499#388C2314yes—
500#388C2314yes—
501#388C2314yes—
502#388C2314yes—
503#388C2314yes—
504#388C2314yes—
505#388C2312yes—
506#388C2314yes—
507#388C2314yes—
508#388C2314yes—
509#388C2314yes—
510#388C2314yes—
511#388C2314yes—
512#387C2314yes—
513#387C2312yes—
514#387C2314yes—
515#387C2314yes—
516#387C2314yes—
517#387C2312yes—
518#387C2312yes—
519#387C2312yes—
520#387C2312yes—
521#387C2314yes—
522#387C2314yes—
523#387C2314yes—
524#387C2314yes—
525#387C2312yes—
526#387C2314yes—
527#387C2314yes—
528#387C2314yes—
529#387C2314yes—
530#387C2314yes—
531#387C2312yes—
532#387C2312yes—
533#387C2312yes—
534#387C2312yes—
535#387C2314yes—
536#387C2314yes—
537#387C2314yes—
538#387C2314yes—
539#387C2314yes—
540#387C2314yes—
541#387C2312yes—
542#387C2314yes—
543#387C2312yes—
544#387C2312yes—
545#387C2314yes—
546#387C2314yes—
547#387C2312yes—
548#387C2312yes—
549#387C2314yes—
550#387C2314yes—
551#387C2312yes—
552#387C2314yes—
553#387C2314yes—
554#386C2314yes—
555#386C2314yes—
556#386C2314yes—
557#386C2314yes—
558#385C2314yes—
559#385C2314yes—
560#385C2314yes—
561#385C2314yes—
562#385C2314yes—
563#385C2314yes—
564#385C2314yes—
565#385C2312yes—
566#385C2314yes—
567#385C2314yes—
568#385C2314yes—
569#385C2314yes—
570#385C2314yes—
571#385C2314yes—
572#385C2312yes—
573#385C2312yes—
574#385C2314yes—
575#385C2314yes—
576#385C2314yes—
577#385C2314yes—
578#385C2314yes—
579#385C2314yes—
580#385C2314yes—
581#385C2314yes—
582#385C2314yes—
583#385C2314yes—
584#385C2314yes—
585#385C2314yes—
586#385C2312yes—
587#384C2312yes—
588#384C2312yes—
589#384C2312yes—
590#384C2314yes—
591#384C2312yes—
592#384C2314yes—
593#384C2312yes—
594#384C2314yes—
595#384C2314yes—
596#383C2314yes—
597#382C2312yes—
598#382C2312yes—
599#382C2312yes—
600#382C2311yescharacteristic
601#382C2311yescharacteristic
602#382C2312yes—
603#382C2314yes—
604#382C2314yes—
605#382C2314yes—
606#382C2314yes—
607#382C2312yes—
608#382C2314yes—
609#381C2314yes—
610#381C2314yes—
611#381C2314yes—
612#381C2314yes—
613#380C2314yes—
614#380C2314yes—
615#380C2314yes—
616#380C2314yes—
617#380C2314yes—
618#380C2314yes—
619#380C2314yes—
620#380C2312yes—
621#380C2312yes—
622#380C2314yes—
623#380C2314yes—
624#380C2314yes—
625#380C2314yes—
626#380C2312yes—
627#380C2314yes—
628#380C2314yes—
629#380C2314yes—
630#380C2314yes—
631#380C2314yes—
632#380C2314yes—
633#379C2312yes—
634#379C2312yes—
635#379C2314yes—
636#379C2314yes—
637C4×C4⋊C4C2312yes—
638C4×C4⋊C4C2312yes—
639C4×C4⋊C4C2312yes—
640C4×C4⋊C4C2312yes—
641C4×C4⋊C4C2312yes—
642C4×C4⋊C4C2312yes—
643C4×C4⋊C4C2312yes—
644C4×C4⋊C4C2312yes—
645C4×C4⋊C4C2314yes—
646C4×C4⋊C4C2314yes—
647C4×C4⋊C4C2314yes—
648C4×C4⋊C4C2314yes—
649C4×C4⋊C4C2312yes—
650C4×C4⋊C4C2314yes—
651C4×C4⋊C4C2312yes—
652C4×C4⋊C4C2314yes—
653C4×C4⋊C4C2312yes—
654C4×C4⋊C4C2314yes—
655C4×C4⋊C4C2312yes—
656C4×C4⋊C4C2312yes—
657C4×C4⋊C4C2312yes—
658C4×C4⋊C4C2312yes—
659C4×C4⋊C4C2312yes—
660C4×C4⋊C4C2312yes—
661C4×C4⋊C4C2314yes—
662C4×C4⋊C4C2312yes—
663C4×C4⋊C4C2312yes—
664C4×C4⋊C4C2311yescharacteristic
665C4×C4⋊C4C2311yescharacteristic
666C4×C4⋊C4C2312yes—
667C4×C22⋊C4C2314yes—
668C4×C22⋊C4C2314yes—
669C4×C22⋊C4C2314yes—
670C4×C22⋊C4C2312yes—
671C4×C22⋊C4C2314yes—
672C4×C22⋊C4C2314yes—
673C4×C22⋊C4C2314yes—
674C4×C22⋊C4C2314yes—
675C4×C22⋊C4C2314yes—
676C4×C22⋊C4C2314yes—
677C4×C22⋊C4C2314yes—
678C4×C22⋊C4C2312yes—
679C4×C22⋊C4C2312yes—
680C4×C22⋊C4C2312yes—
681C4×C22⋊C4C2314yes—
682#376C2311yescharacteristic
683#376C2311yescharacteristic
684#376C2312yes—
685#376C2314yes—
686C2×#95C2314yes—
687C2×#95C2314yes—
688C43C2311yescharacteristic
689C43C2311yescharacteristic
690C43C2312yes—
691C25C2412yes—
692C22×Q8C2411yescharacteristic
693C22×Q8C2411yescharacteristic
694C22×Q8C2412yes—
695C22×Q8C2414yes—
696C22×Q8C2412yes—
697C22×Q8C2412yes—
698C22×D4—42no—
699C22×D4—42no—
700C22×D4C2×Q818yes—
701C22×D4C2412yes—
702C22×D4C2412yes—
703C23×C4C2411yescharacteristic
704C23×C4C2414yes—
705C23×C4C2412yes—
706C23×C4C2412yes—
707C23×C4C2414yes—
708C23×C4C2414yes—
709C23×C4C2414yes—
710C23×C4C2414yes—
711C23×C4C2414yes—
712C4⋊Q8—42no—
713C4⋊Q8—42no—
714C4⋊Q8—44no—
715C4⋊Q8—84no—
716#125—48no—
717#125—44no—
718#125—44no—
719#125—44no—
720#125—44no—
721#125—44no—
722#125—84no—
723#125—84no—
724C22⋊Q8—44no—
725C22⋊Q8—48no—
726C22⋊Q8—48no—
727C22⋊Q8—84no—
728C22⋊Q8—84no—
729C22⋊Q8—84no—
730C22⋊Q8—84no—
731C22⋊Q8—84no—
732C4×Q8—44no—
733C4×Q8—42no—
734C4×Q8—42no—
735C4×Q8—44no—
736C4×Q8—84no—
737C4×D4—44no—
738C4×D4—44no—
739C4×D4—44no—
740C4×D4—44no—
741C4×D4C2×Q8116yes—
742C4×D4C2×Q8116yes—
743C4×D4C2×Q8132yes—
744#117—42no—
745#117—48no—
746#117—42no—
747#117—84no—
748#117—84no—
749#117—84no—
750#117C2×Q818yes—
751#117C2×Q818yes—
752C2×C4⋊C4—42no—
753C2×C4⋊C4—84no—
754C2×C4⋊C4C2412yes—
755C2×C4⋊C4C2412yes—
756C2×C4⋊C4C2412yes—
757C2×C4⋊C4C2412yes—
758C2×C4⋊C4C2412yes—
759C2×C4⋊C4C2412yes—
760C2×C4⋊C4C2412yes—
761C2×C4⋊C4C2412yes—
762C2×C4⋊C4C2414yes—
763C2×C4⋊C4C2412yes—
764C2×C4⋊C4C2412yes—
765C2×C4⋊C4C2412yes—
766C2×C4⋊C4C2414yes—
767C2×C4⋊C4C2414yes—
768C2×C4⋊C4C2414yes—
769C2×C4⋊C4C2412yes—
770C2×C4⋊C4C2414yes—
771C2×C4⋊C4C2414yes—
772C2×C4⋊C4C2414yes—
773C2×C4⋊C4C2414yes—
774C2×C4⋊C4C2411yescharacteristic
775C2×C4⋊C4C2411yescharacteristic
776C2×C4⋊C4C2414yes—
777C2×C4⋊C4C2414yes—
778C2×C4⋊C4C2414yes—
779C2×C4⋊C4C2414yes—
780C2×C4⋊C4C2412yes—
781C2×C4⋊C4C2412yes—
782C2×C4⋊C4C2412yes—
783C2×C4⋊C4C2411yescharacteristic
784C2×C4⋊C4C2412yes—
785C2×C4⋊C4C2412yes—
786C2×C4⋊C4C2412yes—
787C2×C4⋊C4C2412yes—
788C2×C4⋊C4C2411yescharacteristic
789C2×C4⋊C4C2412yes—
790C2×C4⋊C4C2412yes—
791C2×C4⋊C4C2414yes—
792C2×C4⋊C4C2414yes—
793C2×C4⋊C4C2414yes—
794C2×C4⋊C4C2414yes—
795C2×C4⋊C4C2414yes—
796C2×C4⋊C4C2414yes—
797C2×C4⋊C4C2414yes—
798C2×C4⋊C4C2414yes—
799C2×C4⋊C4C2414yes—
800C2×C4⋊C4C2414yes—
801C2×C4⋊C4C2414yes—
802C2×C4⋊C4C2412yes—
803C2×C4⋊C4C2414yes—
804C2×C4⋊C4C2412yes—
805C2×C4⋊C4C2412yes—
806C2×C4⋊C4C2412yes—
807C2×C4⋊C4C2414yes—
808C2×C4⋊C4C2414yes—
809C2×C4⋊C4C2414yes—
810C2×C4⋊C4C2414yes—
811C2×C4⋊C4C2414yes—
812C2×C4⋊C4C2414yes—
813C2×C4⋊C4C2412yes—
814C2×C4⋊C4C2412yes—
815C2×C4⋊C4C2414yes—
816C2×C4⋊C4C2414yes—
817C2×C4⋊C4C2414yes—
818C2×C4⋊C4C2414yes—
819C2×C4⋊C4C2414yes—
820C2×C4⋊C4C2414yes—
821C2×C4⋊C4C2412yes—
822C2×C4⋊C4C2414yes—
823C2×C4⋊C4C2412yes—
824C2×C4⋊C4C2412yes—
825C2×C4⋊C4C2412yes—
826C2×C4⋊C4C2412yes—
827C2×C22⋊C4—48no—
828C2×C22⋊C4—84no—
829C2×C22⋊C4—84no—
830C2×C22⋊C4C2×Q8132yes—
831C2×C22⋊C4C2412yes—
832C2×C22⋊C4C2414yes—
833C2×C22⋊C4C2412yes—
834C2×C22⋊C4C2414yes—
835C2×C22⋊C4C2414yes—
836C2×C22⋊C4C2414yes—
837C2×C22⋊C4C2414yes—
838C2×C22⋊C4C2414yes—
839C2×C22⋊C4C2414yes—
840C2×C22⋊C4C2414yes—
841C2×C22⋊C4C2414yes—
842C2×C22⋊C4C2414yes—
843C2×C22⋊C4C2414yes—
844C2×C22⋊C4C2414yes—
845C2×C22⋊C4C2414yes—
846C2×C22⋊C4C2411yescharacteristic
847C2×C22⋊C4C2411yescharacteristic
848C2×C22⋊C4C2412yes—
849C2×C22⋊C4C2414yes—
850C2×C22⋊C4C2414yes—
851C2×C22⋊C4C2414yes—
852C2×C22⋊C4C2414yes—
853C2×C22⋊C4C2414yes—
854C2×C22⋊C4C2412yes—
855C2×C22⋊C4C2414yes—
856C2×C22⋊C4C2412yes—
857C2×C22⋊C4C2414yes—
858C2×C22⋊C4C2414yes—
859C2×C22⋊C4C2414yes—
860C2×C22⋊C4C2412yes—
861C2×C22⋊C4C2412yes—
862C2×C22⋊C4C2414yes—
863C2×C22⋊C4C2414yes—
864C2×C42—48no—
865C2×C42—42no—
866C2×C42C2411yescharacteristic
867C2×C42C2414yes—
868C2×C42C2411yescharacteristic
869C2×C42C2412yes—
870C2×C42C2412yes—
871C2×C42C2412yes—
872C2×C42C2412yes—
873C2×C42C2411yescharacteristic
874C2×C42C2412yes—
875C2×C42C2411yescharacteristic
876C2×C42C2412yes—
877C2×C42C2412yes—
878C2×C42C2412yes—
879C2×C42C2414yes—
880C2×C42C2414yes—
881C2×C42C2414yes—
882C2×C42C2414yes—
883C2×C42C2412yes—
884C2×C42C2412yes—
885C2×C42C2412yes—
886C2×C42C2412yes—
887C2×C42C2414yes—
888C2×C42C2412yes—
889C2×C42C2414yes—
890C2×C42C2414yes—
891C2×C42C2412yes—
892C2×C42C2411yescharacteristic
893C2×C42C2411yescharacteristic
894C2×C42C2412yes—
895#95C2412yes—
896#95C2412yes—
897#95C2414yes—
898#95C2414yes—
899#95C2414yes—
900#95C2414yes—
901#95C2414yes—
902#95C2414yes—
903#95C2412yes—
904#95C2412yes—
905#95C2412yes—
906#95C2412yes—
907#95C2412yes—
908#95C2412yes—
909#95C2412yes—
910#95C2412yes—
911#95C2414yes—
912#95C2414yes—
913#95C2414yes—
914#95C2414yes—
915#95C2414yes—
916#95C2412yes—
917#95C2414yes—
918#95C2414yes—
919#95C2414yes—
920#95C2412yes—
921#95C2414yes—
922#95C2414yes—
923#95C2414yes—
924#95C2414yes—
925#95C2412yes—
926#95C2412yes—
927#95C2411yescharacteristic
928#95C2412yes—
929#95C2412yes—
930#95C2411yescharacteristic
931#95C2411yescharacteristic
932#95C2414yes—
933#95C2412yes—
934#95C2414yes—
935#95C2412yes—
936#95C2412yes—
937#95C2414yes—
938#95C2414yes—
939#95C2414yes—
940#95C2414yes—
941#95C2414yes—
942#95C2414yes—
943#95C2414yes—
944#95C2414yes—
945#95C2412yes—
946#95C2414yes—
947#95C2412yes—
948#95C2414yes—
949#95C2412yes—
950#95C2412yes—
951#95C2412yes—
952#95C2412yes—
953#95C2412yes—
954#95C2411yescharacteristic
955#95C2414yes—
956#95C2414yes—
957#95C2414yes—
958#95C2414yes—
959#95C2414yes—
960#95C2412yes—
961#95C2412yes—
962#95C2412yes—
963#95C2412yes—
964#95C2414yes—
965C24—44no—
966C24—44no—
967C24—42no—
968C24—42no—
969C24C22×Q818yes—
970C24C2511yescharacteristic
971C24C2514yes—
972C2×Q8—24no—
973C2×Q8—41no—
974C2×Q8—42no—
975C2×Q8—41no—
976C2×Q8—44no—
977C2×Q8—42no—
978C2×Q8—42no—
979C2×Q8—42no—
980C2×Q8—44no—
981C2×Q8—44no—
982C2×Q8—44no—
983C2×Q8—44no—
984C2×Q8—42no—
985C2×Q8—42no—
986C2×D4—24no—
987C2×D4—24no—
988C2×D4—416no—
989C2×D4—42no—
990C2×D4—42no—
991C2×D4C22×Q818yes—
992C2×D4C22×Q818yes—
993C22×C4—22no—
994C22×C4—22no—
995C22×C4—28no—
996C22×C4—44no—
997C22×C4—44no—
998C22×C4—44no—
999C22×C4—44no—
1000C22×C4—44no—
1001C22×C4—42no—
1002C22×C4—42no—
1003C22×C4—44no—
1004C22×C4—44no—
1005C22×C4—44no—
1006C22×C4—44no—
1007C22×C4—42no—
1008C22×C4—44no—
1009C22×C4—44no—
1010C22×C4—44no—
1011C22×C4—42no—
1012C22×C4—44no—
1013C22×C4—44no—
1014C22×C4—44no—
1015C22×C4—44no—
1016C22×C4C22×Q814yes—
1017C22×C4C22×Q8116yes—
1018C22×C4C22×Q8116yes—
1019C22×C4C2511yescharacteristic
1020C22×C4C2514yes—
1021C22×C4C2512yes—
1022C22×C4C2512yes—
1023C22×C4C2511yescharacteristic
1024C22×C4C2512yes—
1025C22×C4C2514yes—
1026C22×C4C2512yes—
1027C22×C4C2512yes—
1028C22×C4C2512yes—
1029C22×C4C2512yes—
1030C22×C4C2512yes—
1031C22×C4C2511yescharacteristic
1032C22×C4C2514yes—
1033C22×C4C2514yes—
1034C22×C4C2514yes—
1035C22×C4C2512yes—
1036C22×C4C2514yes—
1037C22×C4C2511yescharacteristic
1038C22×C4C2511yescharacteristic
1039C22×C4C2512yes—
1040C22×C4C2514yes—
1041C22×C4C2512yes—
1042C22×C4C2512yes—
1043C22×C4C2511yescharacteristic
1044C4⋊C4—24no—
1045C4⋊C4—24no—
1046C4⋊C4—24no—
1047C4⋊C4—24no—
1048C4⋊C4—24no—
1049C4⋊C4—24no—
1050C4⋊C4—24no—
1051C4⋊C4—24no—
1052C4⋊C4—24no—
1053C4⋊C4—28no—
1054C4⋊C4—24no—
1055C4⋊C4—42no—
1056C4⋊C4—42no—
1057C4⋊C4—44no—
1058C4⋊C4—44no—
1059C4⋊C4—44no—
1060C4⋊C4—44no—
1061C4⋊C4—41no—
1062C4⋊C4—41no—
1063C4⋊C4—44no—
1064C4⋊C4—44no—
1065C4⋊C4—44no—
1066C4⋊C4—44no—
1067C4⋊C4—42no—
1068C4⋊C4—42no—
1069C4⋊C4—42no—
1070C4⋊C4—42no—
1071C4⋊C4—42no—
1072C4⋊C4—42no—
1073C4⋊C4—41no—
1074C4⋊C4—42no—
1075C4⋊C4—41no—
1076C4⋊C4—44no—
1077C4⋊C4—44no—
1078C4⋊C4—44no—
1079C4⋊C4—44no—
1080C4⋊C4—44no—
1081C4⋊C4—42no—
1082C4⋊C4—44no—
1083C4⋊C4—44no—
1084C4⋊C4—42no—
1085C4⋊C4—42no—
1086C4⋊C4—44no—
1087C4⋊C4—44no—
1088C4⋊C4—44no—
1089C4⋊C4—44no—
1090C4⋊C4—44no—
1091C4⋊C4—44no—
1092C4⋊C4—44no—
1093C4⋊C4—44no—
1094C4⋊C4—44no—
1095C4⋊C4—44no—
1096C4⋊C4—42no—
1097C4⋊C4—44no—
1098C4⋊C4—44no—
1099C4⋊C4—44no—
1100C4⋊C4—44no—
1101C4⋊C4—44no—
1102C4⋊C4—44no—
1103C4⋊C4—44no—
1104C4⋊C4—44no—
1105C4⋊C4—44no—
1106C4⋊C4—44no—
1107C4⋊C4—42no—
1108C4⋊C4—42no—
1109C4⋊C4—42no—
1110C4⋊C4—42no—
1111C4⋊C4—44no—
1112C4⋊C4—42no—
1113C4⋊C4—42no—
1114C4⋊C4—42no—
1115C4⋊C4C22×Q818yes—
1116C4⋊C4C22×Q818yes—
1117C22⋊C4—24no—
1118C22⋊C4—28no—
1119C22⋊C4—44no—
1120C22⋊C4—44no—
1121C22⋊C4—42no—
1122C22⋊C4—44no—
1123C22⋊C4—44no—
1124C22⋊C4—44no—
1125C22⋊C4—44no—
1126C22⋊C4—44no—
1127C22⋊C4—44no—
1128C22⋊C4—44no—
1129C22⋊C4—44no—
1130C22⋊C4—41no—
1131C22⋊C4—41no—
1132C22⋊C4—42no—
1133C22⋊C4—44no—
1134C22⋊C4—44no—
1135C22⋊C4—44no—
1136C22⋊C4—44no—
1137C22⋊C4—44no—
1138C22⋊C4—44no—
1139C22⋊C4—44no—
1140C22⋊C4—44no—
1141C22⋊C4—44no—
1142C22⋊C4—42no—
1143C22⋊C4—44no—
1144C22⋊C4—42no—
1145C22⋊C4—44no—
1146C22⋊C4C22×Q818yes—
1147C22⋊C4C22×Q818yes—
1148C22⋊C4C22×Q8116yes—
1149C22⋊C4C22×Q8116yes—
1150C42—24no—
1151C42—28no—
1152C42—22no—
1153C42—22no—
1154C42—22no—
1155C42—22no—
1156C42—24no—
1157C42—24no—
1158C42—24no—
1159C42—24no—
1160C42—44no—
1161C42—44no—
1162C42—42no—
1163C42—44no—
1164C42—42no—
1165C42—42no—
1166C42—42no—
1167C42—42no—
1168C42—44no—
1169C42—44no—
1170C42—44no—
1171C42—42no—
1172C42—42no—
1173C42—42no—
1174C42—42no—
1175C42—44no—
1176C42C22×Q818yes—
1177C42C22×Q814yes—
1178C42C22×Q814yes—
1179C23—24no—
1180C23—22no—
1181C23—24no—
1182C23—21no—
1183C23—21no—
1184C23—24no—
1185C23—24no—
1186C23—24no—
1187C23—24no—
1188C23—22no—
1189C23—48no—
1190C23—416no—
1191C23—162no—
1192C23—162no—
1193C23—164no—
1194C23C23×Q812yes—
1195C23C23×Q818yes—
1196C23C2611yescharacteristic
1197Q8—44no—
1198Q8—82no—
1199Q8—88no—
1200Q8—84no—
1201Q8—162no—
1202Q8—162no—
1203D4—216no—
1204D4—48no—
1205C2×C4—22no—
1206C2×C4—24no—
1207C2×C4—22no—
1208C2×C4—21no—
1209C2×C4—22no—
1210C2×C4—22no—
1211C2×C4—21no—
1212C2×C4—22no—
1213C2×C4—22no—
1214C2×C4—24no—
1215C2×C4—28no—
1216C2×C4—22no—
1217C2×C4—24no—
1218C2×C4—22no—
1219C2×C4—22no—
1220C2×C4—22no—
1221C2×C4—22no—
1222C2×C4—22no—
1223C2×C4—22no—
1224C2×C4—21no—
1225C2×C4—21no—
1226C2×C4—21no—
1227C2×C4—21no—
1228C2×C4—22no—
1229C2×C4—22no—
1230C2×C4—22no—
1231C2×C4—22no—
1232C2×C4—24no—
1233C2×C4—22no—
1234C2×C4—24no—
1235C2×C4—22no—
1236C2×C4—22no—
1237C2×C4—24no—
1238C2×C4—22no—
1239C2×C4—22no—
1240C2×C4—22no—
1241C2×C4—24no—
1242C2×C4—22no—
1243C2×C4—24no—
1244C2×C4—24no—
1245C2×C4—24no—
1246C2×C4—24no—
1247C2×C4—24no—
1248C2×C4—24no—
1249C2×C4—22no—
1250C2×C4—22no—
1251C2×C4—24no—
1252C2×C4—22no—
1253C2×C4—22no—
1254C2×C4—22no—
1255C2×C4—22no—
1256C2×C4—24no—
1257C2×C4—24no—
1258C2×C4—22no—
1259C2×C4—22no—
1260C2×C4—24no—
1261C2×C4—24no—
1262C2×C4—22no—
1263C2×C4—24no—
1264C2×C4—22no—
1265C2×C4—22no—
1266C2×C4—24no—
1267C2×C4—22no—
1268C2×C4—22no—
1269C2×C4—416no—
1270C2×C4—416no—
1271C2×C4—88no—
1272C2×C4—88no—
1273C2×C4—84no—
1274C2×C4—164no—
1275C2×C4—162no—
1276C2×C4—164no—
1277C2×C4C23×Q812yes—
1278C2×C4C23×Q814yes—
1279C2×C4C23×Q818yes—
1280C2×C4C23×Q814yes—
1281C2×C4C23×Q812yes—
1282C2×C4#58514yes—
1283C2×C4#58512yes—
1284C2×C4#58512yes—
1285C22—28no—
1286C22—28no—
1287C22—24no—
1288C22—22no—
1289C22—28no—
1290C22—44no—
1291C22—41no—
1292C22—41no—
1293C22—44no—
1294C22—44no—
1295C22—42no—
1296C22—44no—
1297C22—168no—
1298C22C24×Q811yescharacteristic
1299C22C2×#58512yes—
1300C22C2×#58511yescharacteristic
1301C22C2×#58511yescharacteristic
1302C22H(7,𝔽2)12yes—
1303C4—24no—
1304C4—28no—
1305C4—24no—
1306C4—24no—
1307C4—22no—
1308C4—42no—
1309C4—44no—
1310C4—41no—
1311C4—41no—
1312C4—42no—
1313C4—44no—
1314C4—44no—
1315C4—41no—
1316C4—42no—
1317C4—41no—
1318C4—42no—
1319C4—44no—
1320C4—44no—
1321C4—42no—
1322C4—42no—
1323C4—42no—
1324C4—44no—
1325C4—42no—
1326C4—42no—
1327C4#345814yes—
1328C2—48no—
1329C2—42no—
1330C2C2×#345811yescharacteristic
1331C2#6282911yescharacteristic
1332C2#6288511yescharacteristic
1333C2#6293712yes—
1334C2#6298912yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC23×D4C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #42973C2semidirect
2. #42955C2semidirect
3. #42495C2semidirect
4. #42494C2semidirect
7. #40637C2semidirect
8. #40631C2semidirect
9. #40626C2semidirect
10. #40622C2semidirect
11. #39986C2semidirect
12. #39977C2semidirect
13. #39965C2semidirect
14. #38966C2semidirect
16. #38959C2semidirect
17. #37879C2semidirect
18. #37876C2semidirect
19. #35612C2semidirect
20. #35581C2semidirect
21. #35579C2semidirect
22. #35337C2semidirect
23. #35175C2semidirect
24. #34941C2semidirect
25. #34882C2semidirect
29. #2862C22semidirect
30. #2859C22semidirect
31. #2855C22semidirect
33. #2851C22semidirect
34. #2844C22semidirect
35. #2843C22semidirect
38. #2841C22semidirect
39. #2841C22semidirect
42. #2790C22semidirect
43. #2790C22semidirect
44. #2790C22semidirect
45. #2788C22semidirect
46. #2788C22semidirect
55. #2768C22semidirect
56. #2768C22semidirect
57. #2768C22semidirect
60. #2763C22semidirect
63. #2742C22semidirect
64. #2729C22semidirect
67. #2720C22semidirect
68. #2720C22semidirect
69. #2704C22semidirect
70. #2704C22semidirect
71. #2704C22semidirect
76. #2667C22semidirect
77. #2667C22semidirect
78. #2666C22semidirect
79. #2666C22semidirect
80. #2665C22semidirect
81. #2665C22semidirect
82. #2660C22semidirect
83. #2659C22semidirect
84. #2647C22semidirect
85. #2629C22semidirect
86. #2629C22semidirect
89. #2627C22semidirect
93. #2612C22semidirect
94. #2608C22semidirect
95. #2608C22semidirect
96. #2606C22semidirect
99. #2589C22semidirect
100. #2588C22semidirect
101. #2588C22semidirect
102. #2588C22semidirect
104. #2587C22semidirect
105. #2587C22semidirect
106. #2587C22semidirect
107. #2586C22semidirect
108. #2585C22semidirect
109. #2585C22semidirect
110. #2584C22semidirect
111. #2584C22semidirect
112. #2584C22semidirect
115. #2574C22semidirect
116. #2574C22semidirect
117. #2574C22semidirect
118. #2574C22semidirect
119. #2571C22semidirect
120. #2570C22semidirect
121. #2570C22semidirect
122. #2569C22semidirect
123. #2567C22semidirect
130. #2556C22semidirect
131. #2556C22semidirect
132. #2552C22semidirect
133. #2552C22semidirect
134. #2552C22semidirect
135. #2552C22semidirect
136. #2551C22semidirect
137. #2550C22semidirect
138. #2550C22semidirect
139. #2549C22semidirect
145. #2522C22semidirect
146. #2520C22semidirect
147. #2509C22semidirect
148. #2508C22semidirect
149. #2508C22semidirect
150. #2508C22semidirect
151. #2508C22semidirect
152. #2507C22semidirect
153. #2507C22semidirect
154. #2506C22semidirect
155. #2506C22semidirect
156. #2497C22semidirect
157. #2497C22semidirect
159. #2465C22semidirect
160. #2462C22semidirect
161. #2462C22semidirect
171. #2442C22semidirect
172. #2442C22semidirect
175. #2441C22semidirect
176. #2441C22semidirect
178. #2439C22semidirect
179. #2439C22semidirect
180. #2438C22semidirect
181. #2438C22semidirect
182. #2438C22semidirect
183. #2438C22semidirect
188. #2429C22semidirect
190. #2423C22semidirect
191. #2399C22semidirect
192. #2399C22semidirect
195. #2396C22semidirect
196. #2396C22semidirect
213. #2331C22semidirect
214. #2331C22semidirect
215. #2330C22semidirect
216. #2330C22semidirect
217. #2330C22semidirect
218. #2329C22semidirect
224. #2317C22semidirect
229. C4×C4⋊Q8C22semidirect
230. C4×#125C22semidirect
231. C4×#125C22semidirect
232. C4×#125C22semidirect
234. C4×C22⋊Q8C22semidirect
237. #2295C22semidirect
238. #2295C22semidirect
245. #2285C22semidirect
248. C42×Q8C22semidirect
272. #518Q8semidirect

Maximal subgroups

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

subgroupindex
#429732
#429552
#424952
#424942
#424902
#406372
#406312
#406262
#406222
#399862
#399772
#399652
#389662
#389622
#389592
#378792
#378762
#356122
#355812
#355792
#353372
#351752
#349412
#348822
#342612
#342552