Finite Group Databasebeta

← #7644184

Subgroups — #7644184

Order 512.

4374 conjugacy classes of subgroups.

The subgroup lattice has 1379 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42500C212yesmaximal, complemented
2#42497C212yesmaximal, complemented
3#42496C212yesmaximal, complemented
4#42493C212yesmaximal, complemented
5#42492C212yesmaximal, complemented
6#42488C212yesmaximal, complemented
7#42487C212yesmaximal
8#42486C212yesmaximal
9#42184C214yesmaximal, complemented
10#42001C214yesmaximal, complemented
11#40627C214yesmaximal, complemented
12#40626C214yesmaximal, complemented
13#37480C212yesmaximal, complemented
14#37479C212yesmaximal, complemented
15#37478C212yesmaximal, complemented
16#37476C212yesmaximal, complemented
17#37138C214yesmaximal, complemented
18#37136C214yesmaximal, complemented
19#35602C212yesmaximal, complemented
20#35602C212yesmaximal, complemented
21#35581C212yesmaximal, complemented
22#35580C212yesmaximal, complemented
23#35213C211yesmaximal, characteristic, complemented
24#35192C211yesmaximal, characteristic, complemented
25#34644C211yesmaximal, characteristic, complemented
26#34625C211yesmaximal, characteristic, complemented
27#34194C211yesmaximal, characteristic
28#34190C211yesmaximal, characteristic
29#34058C211yesmaximal, characteristic
30C22×C4×D4C2211yescharacteristic
31#2864C2212yescomplemented
32#2863C2214yescomplemented
33#2862C2212yescomplemented
34#2842C2214yes—
35#2841C2214yes—
36#2841C2214yes—
37#2841C2214yescomplemented
38#2841C2214yescomplemented
39#2841C2214yescomplemented
40#2841C2214yescomplemented
41#2840C2214yes—
42#2807C2214yescomplemented
43#2806C2214yescomplemented
44#2804C2214yes—
45#2802C2214yescomplemented
46#2791C2214yescomplemented
47#2790C2214yescomplemented
48#2788C2214yescomplemented
49#2788C2214yescomplemented
50#2784C2214yes—
51#2780C2214yes—
52#2774C2214yescomplemented
53#2768C2214yescomplemented
54#2768C2214yescomplemented
55#2768C2214yescomplemented
56#2763C2214yescomplemented
57#2763C2214yescomplemented
58#2755C2214yescomplemented
59#2755C2214yescomplemented
60#2748C2214yes—
61#2742C2214yescomplemented
62#2734C2214yescomplemented
63#2732C2214yes—
64#2729C2214yescomplemented
65#2729C2214yescomplemented
66#2729C2214yescomplemented
67#2713C2214yescomplemented
68#2704C2214yescomplemented
69#2692C2214yes—
70#2692C2214yes—
71#2692C2214yes—
72#2677C2214yescomplemented
73#2677C2214yescomplemented
74#2667C2212yes—
75#2667C2211yescharacteristic
76#2667C2211yescharacteristic
77#2667C2212yes—
78#2667C2212yes—
79#2667C2214yes—
80#2666C2212yescomplemented
81#2666C2214yescomplemented
82#2666C2212yescomplemented
83#2666C2212yescomplemented
84#2666C2212yescomplemented
85#2665C2212yes—
86#2665C2211yescharacteristic
87#2665C2211yescharacteristic
88#2665C2212yes—
89#2665C2212yes—
90#2665C2212yes—
91#2665C2212yes—
92#2665C2214yes—
93#2665C2214yescomplemented
94#2665C2214yescomplemented
95#2660C2212yescomplemented
96#2659C2214yescomplemented
97#2647C2212yescomplemented
98#2646C2214yescomplemented
99#2629C2212yes—
100#2629C2214yes—
101#2628C2212yes—
102#2628C2214yes—
103#2628C2214yescomplemented
104#2628C2214yescomplemented
105#2627C2214yescomplemented
106#2627C2214yescomplemented
107#2626C2214yes—
108#2626C2214yes—
109#2626C2214yes—
110#2626C2214yes—
111#2612C2214yescomplemented
112#2608C2212yes—
113#2608C2214yescomplemented
114#2607C2212yes—
115#2607C2214yescomplemented
116#2607C2214yescomplemented
117#2607C2214yescomplemented
118#2605C2214yescomplemented
119#2589C2214yescomplemented
120#2589C2214yescomplemented
121#2589C2214yescomplemented
122#2587C2214yescomplemented
123#2584C2212yescomplemented
124#2580C2212yes—
125#2580C2212yes—
126#2580C2212yes—
127#2574C2214yescomplemented
128#2574C2214yescomplemented
129#2574C2214yescomplemented
130#2571C2212yescomplemented
131#2570C2212yescomplemented
132#2569C2214yescomplemented
133#2569C2214yescomplemented
134#2567C2212yescomplemented
135#2566C2212yes—
136#2563C2212yes—
137#2563C2212yes—
138#2556C2214yescomplemented
139#2551C2212yescomplemented
140#2551C2212yescomplemented
141#2550C2212yescomplemented
142#2550C2212yescomplemented
143#2550C2212yescomplemented
144#2550C2212yescomplemented
145#2549C2214yescomplemented
146#2549C2214yescomplemented
147#2546C2212yescomplemented
148#2546C2212yescomplemented
149#2542C2212yes—
150#2538C2212yes—
151#2522C2214yescomplemented
152#2522C2214yescomplemented
153#2509C2212yescomplemented
154#2509C2212yescomplemented
155#2508C2212yescomplemented
156#2508C2212yescomplemented
157#2508C2212yescomplemented
158#2507C2212yescomplemented
159#2507C2212yescomplemented
160#2506C2212yescomplemented
161#2492C2214yescomplemented
162#2492C2214yescomplemented
163#2465C2214yescomplemented
164#2465C2214yescomplemented
165#2454C2212yes—
166#2454C2212yes—
167#2454C2212yes—
168#2452C2212yes—
169#2452C2212yes—
170#2452C2212yes—
171#2452C2212yes—
172#2452C2212yes—
173#2442C2214yescomplemented
174#2441C2212yes—
175#2441C2214yescomplemented
176#2440C2214yescomplemented
177#2439C2214yes—
178#2439C2214yes—
179#2439C2214yes—
180#2439C2212yes—
181#2439C2212yes—
182#2439C2212yes—
183#2439C2214yescomplemented
184#2439C2214yescomplemented
185#2439C2214yescomplemented
186#2438C2214yescomplemented
187#2438C2214yescomplemented
188#2438C2214yescomplemented
189#2438C2214yescomplemented
190#2438C2214yescomplemented
191#2438C2214yescomplemented
192#2437C2214yes—
193#2437C2214yes—
194#2429C2214yescomplemented
195#2423C2214yescomplemented
196#2402C2212yescomplemented
197#2402C2212yescomplemented
198#2399C2212yescomplemented
199#2399C2212yescomplemented
200#2396C2214yes—
201#2396C2212yes—
202#2396C2212yes—
203#2357C2212yes—
204#2354C2212yes—
205#2353C2214yes—
206#2352C2214yes—
207#2349C2212yes—
208D4×C4⋊C4C2212yes—
209#2345C2211yescharacteristic
210#2345C2211yescharacteristic
211#2344C2212yes—
212#2342C2214yes—
213#2342C2212yes—
214#2342C2212yes—
215D4×C22⋊C4C2212yes—
216D4×C22⋊C4C2211yescharacteristic
217D4×C22⋊C4C2211yescharacteristic
218#2331C2212yescomplemented
219#2331C2212yescomplemented
220#2331C2212yescomplemented
221#2330C2212yescomplemented
222#2319C2211yescharacteristic
223#2319C2211yescharacteristic
224#2319C2211yescharacteristic
225#2319C2212yes—
226#2319C2212yes—
227#2319C2211yescharacteristic
228#2319C2211yescharacteristic
229#2319C2212yes—
230#2319C2211yescharacteristic
231#2318C2212yes—
232#2318C2214yes—
233#2318C2212yes—
234#2316C2212yes—
235#2312C2214yes—
236#2309C2212yes—
237C4×C4⋊Q8C2212yescomplemented
238C4×#125C2212yescomplemented
239#2295C2212yescomplemented
240#2295C2212yescomplemented
241#2293C2214yes—
242#2293C2212yes—
243#2293C2212yes—
244#2285C2211yescharacteristic
245#2283C2211yescharacteristic
246#2283C2211yescharacteristic
247#2283C2211yescharacteristic
248#2280C2212yes—
249#2280C2212yes—
250#2280C2212yes—
251#2280C2212yes—
252C2×#381C2212yes—
253C2×#380C2212yes—
254#2275C2211yescharacteristic
255#2275C2212yes—
256#2275C2211yescharacteristic
257C4×#117C2211yescharacteristic
258C4×#117C2211yescharacteristic
259C23×D4C2311yescharacteristic
260C24×C4C2312yes—
261C2×C4⋊Q8C2312yes—
262C2×C4⋊Q8C2312yes—
263C2×C4⋊Q8C2312yes—
264C2×C4⋊Q8C2312yes—
265C2×C4⋊Q8C2314yes—
266C2×C4⋊Q8C2314yes—
267C2×C4⋊Q8C2314yes—
268C2×C4⋊Q8C2314yes—
269C2×#125C2312yes—
270C2×#125C2312yes—
271C2×#125C2314yes—
272C2×C22⋊Q8C2314yes—
273C2×C22⋊Q8C2314yes—
274C2×C22⋊Q8C2314yes—
275C2×C22⋊Q8C2314yes—
276C2×C22⋊Q8C2314yes—
277C2×C22⋊Q8C2314yes—
278C2×C22⋊Q8C2314yes—
279C2×C22⋊Q8C2314yes—
280C2×C4×Q8C2312yes—
281C2×C4×Q8C2312yes—
282C2×C4×Q8C2314yes—
283C2×C4×D4Q8116yescomplemented
284C2×C4×D4C2312yes—
285C2×C4×D4C2312yes—
286C2×C4×D4C2312yes—
287C2×C4×D4C2312yes—
288C2×C4×D4C2312yes—
289C2×C4×D4C2311yescharacteristic
290C2×C4×D4C2311yescharacteristic
291C2×C4×D4C2312yes—
292C2×C4×D4C2311yescharacteristic
293C2×C4×D4C2311yescharacteristic
294C2×#117C2312yes—
295C2×#117C2312yes—
296C2×#117C2312yes—
297C2×#117C2314yes—
298C2×#117C2314yes—
299C2×#117C2314yes—
300C2×#117C2314yes—
301C22×C4⋊C4C2314yes—
302C22×C4⋊C4C2311yescharacteristic
303C22×C22⋊C4C2312yes—
304C22×C22⋊C4C2312yes—
305C22×C22⋊C4C2314yes—
306C22×C22⋊C4C2312yes—
307C22×C42C2311yescharacteristic
308#400C2314yes—
309#400C2314yes—
310#400C2314yes—
311#400C2314yes—
312#400C2314yes—
313#400C2314yes—
314#400C2314yes—
315#400C2314yes—
316#400C2314yes—
317#400C2312yes—
318#400C2314yes—
319#400C2314yes—
320#400C2314yes—
321#400C2314yes—
322#400C2312yes—
323#400C2314yes—
324#400C2312yes—
325#400C2312yes—
326#400C2312yes—
327#400C2312yes—
328#399C2314yes—
329#399C2314yes—
330#399C2314yes—
331#399C2312yes—
332#399C2314yes—
333#399C2314yes—
334#399C2314yes—
335#399C2314yes—
336#399C2314yes—
337#399C2314yes—
338#399C2314yes—
339#399C2312yes—
340#398C2314yes—
341#398C2314yes—
342#398C2314yes—
343#398C2314yes—
344#398C2314yes—
345#398C2314yes—
346#398C2314yes—
347#398C2314yes—
348#398C2314yes—
349#398C2314yes—
350#398C2314yes—
351#398C2314yes—
352#398C2312yes—
353#398C2314yes—
354#398C2312yes—
355#398C2314yes—
356#398C2314yes—
357#398C2314yes—
358#398C2314yes—
359#398C2314yes—
360#398C2314yes—
361#398C2314yes—
362#398C2312yes—
363#398C2312yes—
364#398C2314yes—
365#398C2314yes—
366#398C2314yes—
367#398C2314yes—
368#398C2312yes—
369#398C2312yes—
370#398C2312yes—
371#398C2312yes—
372#398C2312yes—
373#398C2312yes—
374#398C2312yes—
375#398C2312yes—
376#396C2314yes—
377#396C2314yes—
378#396C2314yes—
379#396C2314yes—
380#396C2314yes—
381#396C2312yes—
382#396C2314yes—
383#396C2314yes—
384#396C2314yes—
385#396C2314yes—
386#396C2314yes—
387#396C2314yes—
388#396C2314yes—
389#396C2314yes—
390#396C2312yes—
391#396C2314yes—
392#396C2314yes—
393#396C2314yes—
394#396C2314yes—
395#396C2312yes—
396#396C2314yes—
397#396C2312yes—
398#395C2314yes—
399#395C2314yes—
400#395C2314yes—
401#395C2314yes—
402#395C2314yes—
403#395C2314yes—
404#395C2314yes—
405#395C2314yes—
406#395C2312yes—
407#395C2314yes—
408#395C2314yes—
409#395C2314yes—
410#395C2314yes—
411#395C2314yes—
412#395C2312yes—
413#395C2314yes—
414#395C2312yes—
415#395C2312yes—
416#395C2312yes—
417#395C2312yes—
418#393C2314yes—
419#393C2314yes—
420#393C2314yes—
421#393C2314yes—
422#393C2314yes—
423#393C2314yes—
424#393C2314yes—
425#393C2314yes—
426#393C2314yes—
427#393C2314yes—
428#393C2312yes—
429#393C2314yes—
430#393C2314yes—
431#393C2314yes—
432#393C2314yes—
433#393C2314yes—
434#393C2314yes—
435#393C2312yes—
436#391C2314yes—
437#391C2314yes—
438#391C2314yes—
439#391C2314yes—
440#391C2314yes—
441#391C2314yes—
442#391C2314yes—
443#391C2314yes—
444#391C2312yes—
445#391C2314yes—
446#391C2314yes—
447#391C2314yes—
448#391C2314yes—
449#391C2314yes—
450#391C2312yes—
451#391C2314yes—
452#391C2314yes—
453#391C2314yes—
454#391C2314yes—
455#391C2312yes—
456#391C2312yes—
457#390C2312yes—
458#390C2312yes—
459#390C2312yes—
460#390C2312yes—
461#390C2312yes—
462#390C2312yes—
463#390C2314yes—
464#390C2314yes—
465#390C2312yes—
466#390C2312yes—
467#389C2312yes—
468#389C2312yes—
469#389C2312yes—
470#389C2312yes—
471#389C2314yes—
472#389C2312yes—
473#389C2312yes—
474#389C2312yes—
475#389C2312yes—
476#389C2312yes—
477#389C2312yes—
478#389C2314yes—
479#389C2312yes—
480#389C2314yes—
481#389C2314yes—
482#389C2312yes—
483#389C2312yes—
484#389C2312yes—
485#389C2312yes—
486#389C2312yes—
487#389C2312yes—
488#389C2312yes—
489#389C2312yes—
490#389C2314yes—
491#389C2314yes—
492#389C2314yes—
493#389C2314yes—
494#389C2312yes—
495#389C2314yes—
496#389C2314yes—
497#389C2314yes—
498#389C2314yes—
499#389C2314yes—
500#389C2314yes—
501#389C2312yes—
502#389C2314yes—
503#389C2314yes—
504#389C2314yes—
505#389C2314yes—
506#389C2314yes—
507#389C2312yes—
508#389C2312yes—
509#389C2312yes—
510#388C2314yes—
511#388C2314yes—
512#388C2314yes—
513#388C2314yes—
514#388C2314yes—
515#388C2314yes—
516#388C2314yes—
517#388C2314yes—
518#388C2314yes—
519#388C2314yes—
520#388C2314yes—
521#388C2314yes—
522#388C2314yes—
523#388C2314yes—
524#388C2314yes—
525#388C2314yes—
526#387C2314yes—
527#387C2314yes—
528#387C2314yes—
529#387C2312yes—
530#387C2312yes—
531#387C2314yes—
532#387C2314yes—
533#387C2314yes—
534#387C2314yes—
535#387C2314yes—
536#387C2314yes—
537#387C2314yes—
538#387C2314yes—
539#387C2312yes—
540#387C2312yes—
541#387C2314yes—
542#387C2314yes—
543#387C2314yes—
544#387C2314yes—
545#387C2314yes—
546#387C2314yes—
547#387C2314yes—
548#387C2314yes—
549#387C2312yes—
550#387C2312yes—
551#387C2314yes—
552#387C2314yes—
553#387C2312yes—
554#387C2312yes—
555#387C2314yes—
556#387C2314yes—
557#387C2314yes—
558#387C2314yes—
559#387C2314yes—
560#387C2314yes—
561#387C2314yes—
562#386C2314yes—
563#386C2314yes—
564#386C2314yes—
565#386C2314yes—
566#385C2314yes—
567#385C2314yes—
568#385C2314yes—
569#385C2314yes—
570#385C2314yes—
571#385C2314yes—
572#385C2314yes—
573#385C2314yes—
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#384C2312yes—
587#384C2314yes—
588#384C2312yes—
589#384C2312yes—
590#383C2312yes—
591#383C2312yes—
592#383C2312yes—
593#382C2312yes—
594#382C2312yes—
595#382C2312yes—
596#382C2312yes—
597#382C2312yes—
598#382C2314yes—
599#382C2311yescharacteristic
600#382C2312yes—
601#382C2311yescharacteristic
602#382C2314yes—
603#382C2314yes—
604#382C2314yes—
605#382C2312yes—
606#381C2312yes—
607#381C2314yes—
608#381C2312yes—
609#381C2312yes—
610#381C2312yes—
611#381C2312yes—
612#381C2312yes—
613#381C2314yes—
614#381C2314yes—
615#381C2311yescharacteristic
616#381C2311yescharacteristic
617#381C2311yescharacteristic
618#381C2311yescharacteristic
619#381C2312yes—
620#380C2314yes—
621#380C2314yes—
622#380C2314yes—
623#380C2314yes—
624#380C2314yes—
625#380C2314yes—
626#380C2312yes—
627#380C2314yes—
628#380C2314yes—
629#380C2314yes—
630#380C2312yes—
631#380C2314yes—
632#380C2312yes—
633#380C2312yes—
634#380C2312yes—
635#380C2312yes—
636#380C2312yes—
637#380C2312yes—
638#380C2314yes—
639#380C2314yes—
640#380C2314yes—
641#380C2312yes—
642#380C2311yescharacteristic
643#380C2311yescharacteristic
644#380C2312yes—
645#380C2314yes—
646#380C2312yes—
647#380C2311yescharacteristic
648#380C2311yescharacteristic
649#379C2314yes—
650#379C2314yes—
651#379C2312yes—
652#379C2314yes—
653#379C2312yes—
654C4×C4⋊C4C2311yescharacteristic
655C4×C4⋊C4C2312yes—
656C4×C4⋊C4C2314yes—
657C4×C4⋊C4C2314yes—
658C4×C4⋊C4C2311yescharacteristic
659C4×C4⋊C4C2314yes—
660C4×C4⋊C4C2312yes—
661C4×C4⋊C4C2312yes—
662C4×C4⋊C4C2312yes—
663C4×C4⋊C4C2312yes—
664C4×C4⋊C4C2311yescharacteristic
665C4×C4⋊C4C2312yes—
666C4×C4⋊C4C2311yescharacteristic
667C4×C4⋊C4C2312yes—
668C4×C4⋊C4C2311yescharacteristic
669C4×C4⋊C4C2311yescharacteristic
670C4×C4⋊C4C2312yes—
671C4×C4⋊C4C2312yes—
672C4×C4⋊C4C2312yes—
673C4×C4⋊C4C2312yes—
674C4×C4⋊C4C2312yes—
675C4×C4⋊C4C2312yes—
676C4×C4⋊C4C2312yes—
677C4×C4⋊C4C2312yes—
678C4×C4⋊C4C2312yes—
679C4×C22⋊C4C2312yes—
680C4×C22⋊C4C2312yes—
681C4×C22⋊C4C2314yes—
682C4×C22⋊C4C2314yes—
683C4×C22⋊C4C2312yes—
684C4×C22⋊C4C2312yes—
685C4×C22⋊C4C2314yes—
686C4×C22⋊C4C2314yes—
687C4×C22⋊C4C2314yes—
688C4×C22⋊C4C2314yes—
689C4×C22⋊C4C2314yes—
690C4×C22⋊C4C2312yes—
691C4×C22⋊C4C2311yescharacteristic
692C4×C22⋊C4C2311yescharacteristic
693C4×C22⋊C4C2312yes—
694C4×C22⋊C4C2312yes—
695C4×C22⋊C4C2312yes—
696C4×C22⋊C4C2314yes—
697C4×C22⋊C4C2311yescharacteristic
698C4×C22⋊C4C2312yes—
699C4×C22⋊C4C2311yescharacteristic
700#376C2312yes—
701#376C2311yescharacteristic
702#376C2311yescharacteristic
703#376C2312yes—
704#376C2311yescharacteristic
705#376C2311yescharacteristic
706#376C2312yes—
707C2×#95C2312yes—
708C2×#95C2314yes—
709C2×#95C2312yes—
710C2×#95C2314yes—
711C43C2312yes—
712C43C2312yes—
713C25C2412yes—
714C22×Q8C2412yes—
715C22×Q8C2414yes—
716C22×Q8C2412yes—
717C22×Q8C2414yes—
718C22×Q8C2414yes—
719C22×Q8C2414yes—
720C22×D4—44no—
721C22×D4C2×Q818yes—
722C22×D4C2411yescharacteristic
723C22×D4C2411yescharacteristic
724C22×D4C2412yes—
725C23×C4—84no—
726C23×C4C2×Q8116yes—
727C23×C4C2411yescharacteristic
728C23×C4C2414yes—
729C23×C4C2414yes—
730C23×C4C2414yes—
731C23×C4C2414yes—
732C23×C4C2411yescharacteristic
733C23×C4C2412yes—
734C23×C4C2412yes—
735C23×C4C2412yes—
736C23×C4C2412yes—
737C23×C4C2412yes—
738C23×C4C2411yescharacteristic
739C4⋊Q8—44no—
740C4⋊Q8—44no—
741C4⋊Q8—44no—
742C4⋊Q8—44no—
743C4⋊Q8—84no—
744C4⋊Q8—84no—
745C4⋊Q8—84no—
746C4⋊Q8—84no—
747#125—44no—
748#125—44no—
749#125—84no—
750C22⋊Q8—84no—
751C22⋊Q8—84no—
752C22⋊Q8—84no—
753C22⋊Q8—84no—
754C22⋊Q8—84no—
755C22⋊Q8—84no—
756C22⋊Q8—84no—
757C22⋊Q8—84no—
758C4×Q8—44no—
759C4×Q8—44no—
760C4×Q8—84no—
761C4×D4—44no—
762C4×D4—44no—
763C4×D4—44no—
764C4×D4—44no—
765C4×D4C2×Q818yes—
766C4×D4C2×Q818yes—
767C4×D4C2×Q818yes—
768C4×D4C2×Q818yes—
769C4×D4C2×Q8116yes—
770C4×D4C2×Q8116yes—
771#117—44no—
772#117—44no—
773#117—84no—
774#117—84no—
775#117—82no—
776#117—84no—
777#117—84no—
778C2×C4⋊C4—84no—
779C2×C4⋊C4C2×Q818yes—
780C2×C4⋊C4C2412yes—
781C2×C4⋊C4C2412yes—
782C2×C4⋊C4C2412yes—
783C2×C4⋊C4C2412yes—
784C2×C4⋊C4C2412yes—
785C2×C4⋊C4C2412yes—
786C2×C4⋊C4C2412yes—
787C2×C4⋊C4C2414yes—
788C2×C4⋊C4C2414yes—
789C2×C4⋊C4C2414yes—
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⋊C4C2412yes—
799C2×C4⋊C4C2412yes—
800C2×C4⋊C4C2414yes—
801C2×C4⋊C4C2414yes—
802C2×C4⋊C4C2414yes—
803C2×C4⋊C4C2412yes—
804C2×C4⋊C4C2412yes—
805C2×C4⋊C4C2412yes—
806C2×C4⋊C4C2412yes—
807C2×C4⋊C4C2412yes—
808C2×C4⋊C4C2412yes—
809C2×C4⋊C4C2412yes—
810C2×C4⋊C4C2412yes—
811C2×C4⋊C4C2412yes—
812C2×C4⋊C4C2412yes—
813C2×C4⋊C4C2412yes—
814C2×C4⋊C4C2412yes—
815C2×C4⋊C4C2412yes—
816C2×C4⋊C4C2414yes—
817C2×C4⋊C4C2414yes—
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⋊C4C2412yes—
828C2×C4⋊C4C2414yes—
829C2×C4⋊C4C2414yes—
830C2×C4⋊C4C2414yes—
831C2×C4⋊C4C2414yes—
832C2×C4⋊C4C2414yes—
833C2×C4⋊C4C2412yes—
834C2×C4⋊C4C2412yes—
835C2×C4⋊C4C2414yes—
836C2×C4⋊C4C2414yes—
837C2×C4⋊C4C2414yes—
838C2×C4⋊C4C2414yes—
839C2×C4⋊C4C2412yes—
840C2×C4⋊C4C2412yes—
841C2×C4⋊C4C2412yes—
842C2×C4⋊C4C2412yes—
843C2×C4⋊C4C2414yes—
844C2×C4⋊C4C2411yescharacteristic
845C2×C4⋊C4C2411yescharacteristic
846C2×C4⋊C4C2412yes—
847C2×C22⋊C4—82no—
848C2×C22⋊C4—82no—
849C2×C22⋊C4—84no—
850C2×C22⋊C4C2×Q8116yes—
851C2×C22⋊C4C2411yescharacteristic
852C2×C22⋊C4C2411yescharacteristic
853C2×C22⋊C4C2412yes—
854C2×C22⋊C4C2412yes—
855C2×C22⋊C4C2412yes—
856C2×C22⋊C4C2414yes—
857C2×C22⋊C4C2414yes—
858C2×C22⋊C4C2414yes—
859C2×C22⋊C4C2414yes—
860C2×C22⋊C4C2414yes—
861C2×C22⋊C4C2412yes—
862C2×C22⋊C4C2414yes—
863C2×C22⋊C4C2414yes—
864C2×C22⋊C4C2414yes—
865C2×C22⋊C4C2414yes—
866C2×C22⋊C4C2414yes—
867C2×C22⋊C4C2414yes—
868C2×C22⋊C4C2412yes—
869C2×C22⋊C4C2414yes—
870C2×C22⋊C4C2412yes—
871C2×C22⋊C4C2414yes—
872C2×C22⋊C4C2414yes—
873C2×C22⋊C4C2414yes—
874C2×C22⋊C4C2414yes—
875C2×C22⋊C4C2414yes—
876C2×C22⋊C4C2414yes—
877C2×C22⋊C4C2414yes—
878C2×C22⋊C4C2411yescharacteristic
879C2×C22⋊C4C2411yescharacteristic
880C2×C22⋊C4C2414yes—
881C2×C22⋊C4C2414yes—
882C2×C22⋊C4C2414yes—
883C2×C22⋊C4C2412yes—
884C2×C22⋊C4C2412yes—
885C2×C22⋊C4C2412yes—
886C2×C22⋊C4C2412yes—
887C2×C42C2×Q818yes—
888C2×C42C2412yes—
889C2×C42C2412yes—
890C2×C42C2412yes—
891C2×C42C2412yes—
892C2×C42C2412yes—
893C2×C42C2412yes—
894C2×C42C2412yes—
895C2×C42C2412yes—
896C2×C42C2414yes—
897C2×C42C2414yes—
898C2×C42C2414yes—
899C2×C42C2414yes—
900C2×C42C2414yes—
901C2×C42C2414yes—
902C2×C42C2414yes—
903C2×C42C2412yes—
904C2×C42C2412yes—
905C2×C42C2412yes—
906C2×C42C2412yes—
907C2×C42C2412yes—
908C2×C42C2412yes—
909C2×C42C2411yescharacteristic
910C2×C42C2411yescharacteristic
911C2×C42C2411yescharacteristic
912C2×C42C2411yescharacteristic
913#95C2412yes—
914#95C2411yescharacteristic
915#95C2411yescharacteristic
916#95C2412yes—
917#95C2414yes—
918#95C2414yes—
919#95C2414yes—
920#95C2414yes—
921#95C2412yes—
922#95C2412yes—
923#95C2414yes—
924#95C2414yes—
925#95C2414yes—
926#95C2414yes—
927#95C2411yescharacteristic
928#95C2411yescharacteristic
929#95C2412yes—
930#95C2412yes—
931#95C2412yes—
932#95C2412yes—
933#95C2412yes—
934#95C2412yes—
935#95C2411yescharacteristic
936#95C2411yescharacteristic
937#95C2412yes—
938#95C2411yescharacteristic
939#95C2411yescharacteristic
940#95C2414yes—
941#95C2412yes—
942#95C2412yes—
943#95C2414yes—
944#95C2412yes—
945#95C2414yes—
946#95C2414yes—
947#95C2414yes—
948#95C2414yes—
949#95C2414yes—
950#95C2414yes—
951#95C2414yes—
952#95C2412yes—
953#95C2412yes—
954#95C2412yes—
955#95C2412yes—
956#95C2414yes—
957#95C2414yes—
958#95C2412yes—
959#95C2412yes—
960#95C2412yes—
961#95C2414yes—
962#95C2412yes—
963#95C2412yes—
964#95C2412yes—
965#95C2412yes—
966#95C2412yes—
967#95C2412yes—
968#95C2412yes—
969#95C2412yes—
970#95C2412yes—
971#95C2414yes—
972#95C2414yes—
973#95C2414yes—
974#95C2412yes—
975#95C2412yes—
976#95C2412yes—
977#95C2412yes—
978#95C2414yes—
979#95C2414yes—
980#95C2414yes—
981#95C2414yes—
982#95C2414yes—
983#95C2414yes—
984#95C2414yes—
985#95C2414yes—
986#95C2414yes—
987#95C2414yes—
988#95C2414yes—
989#95C2414yes—
990#95C2414yes—
991#95C2414yes—
992C24—42no—
993C24—44no—
994C24—44no—
995C24—42no—
996C24C22×Q818yes—
997C24C2511yescharacteristic
998C24C2512yes—
999C24C2512yes—
1000C2×Q8—42no—
1001C2×Q8—42no—
1002C2×Q8—44no—
1003C2×Q8—42no—
1004C2×Q8—44no—
1005C2×Q8—44no—
1006C2×Q8—42no—
1007C2×Q8—42no—
1008C2×Q8—42no—
1009C2×Q8—44no—
1010C2×Q8—44no—
1011C2×Q8—44no—
1012C2×Q8—44no—
1013C2×Q8—44no—
1014C2×Q8—44no—
1015C2×Q8—44no—
1016C2×Q8—44no—
1017C2×Q8—44no—
1018C2×D4—24no—
1019C2×D4—24no—
1020C2×D4—416no—
1021C2×D4—44no—
1022C2×D4C22×Q814yes—
1023C2×D4C22×Q814yes—
1024C2×D4C22×Q818yes—
1025C22×C4—24no—
1026C22×C4—44no—
1027C22×C4—41no—
1028C22×C4—44no—
1029C22×C4—44no—
1030C22×C4—44no—
1031C22×C4—44no—
1032C22×C4—42no—
1033C22×C4—41no—
1034C22×C4—44no—
1035C22×C4—44no—
1036C22×C4—44no—
1037C22×C4—44no—
1038C22×C4—44no—
1039C22×C4—44no—
1040C22×C4—44no—
1041C22×C4—44no—
1042C22×C4—44no—
1043C22×C4—44no—
1044C22×C4—44no—
1045C22×C4—44no—
1046C22×C4—816no—
1047C22×C4C22×Q814yes—
1048C22×C4C22×Q814yes—
1049C22×C4C22×Q814yes—
1050C22×C4C22×Q818yes—
1051C22×C4C22×Q818yes—
1052C22×C4C22×Q818yes—
1053C22×C4C22×Q818yes—
1054C22×C4C22×Q818yes—
1055C22×C4C2512yes—
1056C22×C4C2514yes—
1057C22×C4C2512yes—
1058C22×C4C2512yes—
1059C22×C4C2512yes—
1060C22×C4C2512yes—
1061C22×C4C2514yes—
1062C22×C4C2512yes—
1063C22×C4C2514yes—
1064C22×C4C2512yes—
1065C22×C4C2512yes—
1066C22×C4C2512yes—
1067C22×C4C2512yes—
1068C22×C4C2514yes—
1069C22×C4C2514yes—
1070C22×C4C2514yes—
1071C22×C4C2512yes—
1072C22×C4C2512yes—
1073C22×C4C2511yescharacteristic
1074C22×C4C2511yescharacteristic
1075C22×C4C2511yescharacteristic
1076C22×C4C2511yescharacteristic
1077C22×C4C2511yescharacteristic
1078C22×C4C2512yes—
1079C22×C4C2512yes—
1080C22×C4C2511yescharacteristic
1081C4⋊C4—24no—
1082C4⋊C4—24no—
1083C4⋊C4—24no—
1084C4⋊C4—24no—
1085C4⋊C4—24no—
1086C4⋊C4—24no—
1087C4⋊C4—42no—
1088C4⋊C4—44no—
1089C4⋊C4—44no—
1090C4⋊C4—44no—
1091C4⋊C4—42no—
1092C4⋊C4—42no—
1093C4⋊C4—42no—
1094C4⋊C4—44no—
1095C4⋊C4—42no—
1096C4⋊C4—42no—
1097C4⋊C4—42no—
1098C4⋊C4—42no—
1099C4⋊C4—44no—
1100C4⋊C4—44no—
1101C4⋊C4—44no—
1102C4⋊C4—44no—
1103C4⋊C4—44no—
1104C4⋊C4—44no—
1105C4⋊C4—44no—
1106C4⋊C4—42no—
1107C4⋊C4—42no—
1108C4⋊C4—42no—
1109C4⋊C4—42no—
1110C4⋊C4—42no—
1111C4⋊C4—42no—
1112C4⋊C4—44no—
1113C4⋊C4—44no—
1114C4⋊C4—44no—
1115C4⋊C4—42no—
1116C4⋊C4—42no—
1117C4⋊C4—44no—
1118C4⋊C4—42no—
1119C4⋊C4—42no—
1120C4⋊C4—44no—
1121C4⋊C4—44no—
1122C4⋊C4—42no—
1123C4⋊C4—42no—
1124C4⋊C4—42no—
1125C4⋊C4—44no—
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—42no—
1138C4⋊C4—44no—
1139C4⋊C4—44no—
1140C4⋊C4—44no—
1141C4⋊C4—44no—
1142C4⋊C4—44no—
1143C4⋊C4—42no—
1144C4⋊C4—42no—
1145C4⋊C4C22×Q818yes—
1146C4⋊C4C22×Q814yes—
1147C4⋊C4C22×Q814yes—
1148C22⋊C4—41no—
1149C22⋊C4—42no—
1150C22⋊C4—41no—
1151C22⋊C4—42no—
1152C22⋊C4—44no—
1153C22⋊C4—42no—
1154C22⋊C4—44no—
1155C22⋊C4—44no—
1156C22⋊C4—44no—
1157C22⋊C4—44no—
1158C22⋊C4—44no—
1159C22⋊C4—44no—
1160C22⋊C4—44no—
1161C22⋊C4—41no—
1162C22⋊C4—41no—
1163C22⋊C4—42no—
1164C22⋊C4—42no—
1165C22⋊C4—44no—
1166C22⋊C4—42no—
1167C22⋊C4—44no—
1168C22⋊C4—44no—
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⋊C4—44no—
1178C22⋊C4—44no—
1179C22⋊C4—44no—
1180C22⋊C4C22×Q818yes—
1181C22⋊C4C22×Q818yes—
1182C22⋊C4C22×Q818yes—
1183C22⋊C4C22×Q818yes—
1184C42—24no—
1185C42—24no—
1186C42—24no—
1187C42—24no—
1188C42—24no—
1189C42—24no—
1190C42—42no—
1191C42—42no—
1192C42—42no—
1193C42—44no—
1194C42—42no—
1195C42—42no—
1196C42—44no—
1197C42—44no—
1198C42—44no—
1199C42—44no—
1200C42—44no—
1201C42—44no—
1202C42—42no—
1203C42—42no—
1204C42—42no—
1205C42C22×Q814yes—
1206C42C22×Q814yes—
1207C42C22×Q814yes—
1208C42C22×Q814yes—
1209C23—22no—
1210C23—24no—
1211C23—24no—
1212C23—22no—
1213C23—21no—
1214C23—24no—
1215C23—24no—
1216C23—22no—
1217C23—22no—
1218C23—22no—
1219C23—22no—
1220C23—21no—
1221C23—48no—
1222C23—48no—
1223C23—48no—
1224C23—88no—
1225C23—88no—
1226C23C23×Q814yes—
1227C23C23×Q814yes—
1228C23C23×Q812yes—
1229C23C2611yescharacteristic
1230Q8—84no—
1231Q8—84no—
1232Q8—88no—
1233Q8—164no—
1234Q8—164no—
1235Q8—164no—
1236D4—28no—
1237D4—28no—
1238D4—48no—
1239C2×C4—22no—
1240C2×C4—21no—
1241C2×C4—22no—
1242C2×C4—21no—
1243C2×C4—24no—
1244C2×C4—24no—
1245C2×C4—22no—
1246C2×C4—21no—
1247C2×C4—21no—
1248C2×C4—28no—
1249C2×C4—22no—
1250C2×C4—22no—
1251C2×C4—22no—
1252C2×C4—22no—
1253C2×C4—22no—
1254C2×C4—22no—
1255C2×C4—22no—
1256C2×C4—22no—
1257C2×C4—22no—
1258C2×C4—22no—
1259C2×C4—22no—
1260C2×C4—22no—
1261C2×C4—24no—
1262C2×C4—24no—
1263C2×C4—24no—
1264C2×C4—24no—
1265C2×C4—24no—
1266C2×C4—24no—
1267C2×C4—22no—
1268C2×C4—22no—
1269C2×C4—22no—
1270C2×C4—22no—
1271C2×C4—22no—
1272C2×C4—22no—
1273C2×C4—24no—
1274C2×C4—22no—
1275C2×C4—22no—
1276C2×C4—24no—
1277C2×C4—24no—
1278C2×C4—24no—
1279C2×C4—22no—
1280C2×C4—22no—
1281C2×C4—24no—
1282C2×C4—24no—
1283C2×C4—24no—
1284C2×C4—24no—
1285C2×C4—24no—
1286C2×C4—24no—
1287C2×C4—22no—
1288C2×C4—22no—
1289C2×C4—22no—
1290C2×C4—22no—
1291C2×C4—22no—
1292C2×C4—22no—
1293C2×C4—22no—
1294C2×C4—22no—
1295C2×C4—22no—
1296C2×C4—22no—
1297C2×C4—24no—
1298C2×C4—24no—
1299C2×C4—22no—
1300C2×C4—22no—
1301C2×C4—22no—
1302C2×C4—22no—
1303C2×C4—44no—
1304C2×C4—48no—
1305C2×C4—48no—
1306C2×C4—48no—
1307C2×C4—48no—
1308C2×C4—48no—
1309C2×C4—44no—
1310C2×C4—164no—
1311C2×C4—164no—
1312C2×C4—164no—
1313C2×C4—164no—
1314C2×C4C23×Q812yes—
1315C2×C4C23×Q812yes—
1316C2×C4C23×Q812yes—
1317C2×C4C23×Q812yes—
1318C2×C4C23×Q812yes—
1319C2×C4C23×Q814yes—
1320C2×C4C23×Q814yes—
1321C2×C4C23×Q812yes—
1322C2×C4#58514yes—
1323C22—22no—
1324C22—24no—
1325C22—24no—
1326C22—22no—
1327C22—24no—
1328C22—24no—
1329C22—22no—
1330C22—24no—
1331C22—24no—
1332C22—44no—
1333C22—44no—
1334C22—42no—
1335C22—44no—
1336C22—44no—
1337C22—42no—
1338C22—816no—
1339C22C24×Q811yescharacteristic
1340C22C2×#58512yes—
1341C22H(7,𝔽2)12yes—
1342C22H(7,𝔽2)11yescharacteristic
1343C222−1+611yescharacteristic
1344C4—22no—
1345C4—22no—
1346C4—24no—
1347C4—24no—
1348C4—22no—
1349C4—22no—
1350C4—22no—
1351C4—42no—
1352C4—42no—
1353C4—42no—
1354C4—44no—
1355C4—42no—
1356C4—42no—
1357C4—42no—
1358C4—44no—
1359C4—42no—
1360C4—42no—
1361C4—42no—
1362C4—44no—
1363C4—44no—
1364C4—44no—
1365C4—42no—
1366C4—42no—
1367C4—42no—
1368C4—44no—
1369C4#345814yes—
1370C2—44no—
1371C2—44no—
1372C2—42no—
1373C2C2×#345811yescharacteristic
1374C2#6284311yescharacteristic
1375C2#6285411yescharacteristic
1376C2#6288212yes—
1377C2#6288512yes—
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. #42500C2semidirect
2. #42497C2semidirect
3. #42496C2semidirect
4. #42493C2semidirect
5. #42492C2semidirect
6. #42488C2semidirect
9. #42184C2semidirect
10. #42001C2semidirect
11. #40627C2semidirect
12. #40626C2semidirect
13. #37480C2semidirect
14. #37479C2semidirect
15. #37478C2semidirect
16. #37476C2semidirect
17. #37138C2semidirect
18. #37136C2semidirect
19. #35602C2semidirect
20. #35602C2semidirect
21. #35581C2semidirect
22. #35580C2semidirect
23. #35213C2semidirect
24. #35192C2semidirect
25. #34644C2semidirect
26. #34625C2semidirect
31. #2864C22semidirect
32. #2863C22semidirect
33. #2862C22semidirect
37. #2841C22semidirect
38. #2841C22semidirect
39. #2841C22semidirect
40. #2841C22semidirect
42. #2807C22semidirect
43. #2806C22semidirect
45. #2802C22semidirect
46. #2791C22semidirect
47. #2790C22semidirect
48. #2788C22semidirect
49. #2788C22semidirect
52. #2774C22semidirect
53. #2768C22semidirect
54. #2768C22semidirect
55. #2768C22semidirect
56. #2763C22semidirect
57. #2763C22semidirect
58. #2755C22semidirect
59. #2755C22semidirect
61. #2742C22semidirect
62. #2734C22semidirect
64. #2729C22semidirect
65. #2729C22semidirect
66. #2729C22semidirect
67. #2713C22semidirect
68. #2704C22semidirect
72. #2677C22semidirect
73. #2677C22semidirect
80. #2666C22semidirect
81. #2666C22semidirect
82. #2666C22semidirect
83. #2666C22semidirect
84. #2666C22semidirect
93. #2665C22semidirect
94. #2665C22semidirect
95. #2660C22semidirect
96. #2659C22semidirect
97. #2647C22semidirect
98. #2646C22semidirect
103. #2628C22semidirect
104. #2628C22semidirect
105. #2627C22semidirect
106. #2627C22semidirect
111. #2612C22semidirect
113. #2608C22semidirect
115. #2607C22semidirect
116. #2607C22semidirect
117. #2607C22semidirect
118. #2605C22semidirect
119. #2589C22semidirect
120. #2589C22semidirect
121. #2589C22semidirect
122. #2587C22semidirect
123. #2584C22semidirect
127. #2574C22semidirect
128. #2574C22semidirect
129. #2574C22semidirect
130. #2571C22semidirect
131. #2570C22semidirect
132. #2569C22semidirect
133. #2569C22semidirect
134. #2567C22semidirect
138. #2556C22semidirect
139. #2551C22semidirect
140. #2551C22semidirect
141. #2550C22semidirect
142. #2550C22semidirect
143. #2550C22semidirect
144. #2550C22semidirect
145. #2549C22semidirect
146. #2549C22semidirect
147. #2546C22semidirect
148. #2546C22semidirect
151. #2522C22semidirect
152. #2522C22semidirect
153. #2509C22semidirect
154. #2509C22semidirect
155. #2508C22semidirect
156. #2508C22semidirect
157. #2508C22semidirect
158. #2507C22semidirect
159. #2507C22semidirect
160. #2506C22semidirect
161. #2492C22semidirect
162. #2492C22semidirect
163. #2465C22semidirect
164. #2465C22semidirect
173. #2442C22semidirect
175. #2441C22semidirect
176. #2440C22semidirect
183. #2439C22semidirect
184. #2439C22semidirect
185. #2439C22semidirect
186. #2438C22semidirect
187. #2438C22semidirect
188. #2438C22semidirect
189. #2438C22semidirect
190. #2438C22semidirect
191. #2438C22semidirect
194. #2429C22semidirect
195. #2423C22semidirect
196. #2402C22semidirect
197. #2402C22semidirect
198. #2399C22semidirect
199. #2399C22semidirect
218. #2331C22semidirect
219. #2331C22semidirect
220. #2331C22semidirect
221. #2330C22semidirect
237. C4×C4⋊Q8C22semidirect
238. C4×#125C22semidirect
239. #2295C22semidirect
240. #2295C22semidirect
283. C2×C4×D4Q8semidirect

Maximal subgroups

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

subgroupindex
#425002
#424972
#424962
#424932
#424922
#424882
#424872
#424862
#421842
#420012
#406272
#406262
#374802
#374792
#374782
#374762
#371382
#371362
#356022
#355812
#355802
#352132
#351922
#346442
#346252
#341942
#341902
#340582