Finite Group Databasebeta

← #7656389

Subgroups — #7656389

Order 512.

4450 conjugacy classes of subgroups.

The subgroup lattice has 1386 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42497C212yesmaximal, complemented
2#42493C212yesmaximal, complemented
3#42487C212yesmaximal
4#42486C212yesmaximal
5#40634C214yesmaximal, complemented
6#40630C214yesmaximal, complemented
7#40627C214yesmaximal, complemented
8#40626C214yesmaximal, complemented
9#39977C212yesmaximal, complemented
10#39972C212yesmaximal, complemented
11#39967C214yesmaximal, complemented
12#39964C214yesmaximal, complemented
13#37567C211yesmaximal, characteristic, complemented
14#37565C211yesmaximal, characteristic, complemented
15#37480C212yesmaximal, complemented
16#37479C212yesmaximal, complemented
17#36479C212yesmaximal, complemented
18#36476C212yesmaximal, complemented
19#35952C212yesmaximal, complemented
20#35871C212yesmaximal, complemented
21#35843C212yesmaximal, complemented
22#35788C212yesmaximal, complemented
23#35192C211yesmaximal, characteristic, complemented
24#35065C212yesmaximal, complemented
25#34625C211yesmaximal, characteristic, complemented
26#34578C212yesmaximal, complemented
27#34190C211yesmaximal, characteristic
28#34186C211yesmaximal, characteristic
29#34126C211yesmaximal, characteristic
30C22×C4×D4C2211yescharacteristic
31#2864C2212yescomplemented
32#2862C2212yescomplemented
33#2855C2214yescomplemented
34#2855C2214yescomplemented
35#2843C2214yescomplemented
36#2842C2214yes—
37#2841C2214yes—
38#2841C2214yescomplemented
39#2841C2214yescomplemented
40#2840C2214yes—
41#2807C2214yescomplemented
42#2804C2214yes—
43#2790C2214yescomplemented
44#2788C2214yescomplemented
45#2788C2214yescomplemented
46#2784C2214yes—
47#2780C2214yes—
48#2768C2214yescomplemented
49#2768C2214yescomplemented
50#2768C2214yescomplemented
51#2763C2214yescomplemented
52#2763C2214yescomplemented
53#2748C2214yes—
54#2742C2214yescomplemented
55#2732C2214yes—
56#2729C2214yescomplemented
57#2729C2214yescomplemented
58#2729C2214yescomplemented
59#2704C2214yescomplemented
60#2692C2214yes—
61#2692C2214yes—
62#2692C2214yes—
63#2677C2214yescomplemented
64#2677C2214yescomplemented
65#2667C2211yescharacteristic
66#2667C2212yes—
67#2667C2211yescharacteristic
68#2667C2214yes—
69#2667C2212yes—
70#2667C2212yes—
71#2667C2214yescomplemented
72#2666C2212yescomplemented
73#2666C2212yescomplemented
74#2666C2214yescomplemented
75#2665C2214yes—
76#2665C2212yes—
77#2665C2212yes—
78#2665C2211yescharacteristic
79#2665C2211yescharacteristic
80#2665C2212yes—
81#2665C2212yes—
82#2665C2212yes—
83#2665C2214yescomplemented
84#2665C2214yescomplemented
85#2665C2214yescomplemented
86#2660C2212yescomplemented
87#2660C2212yescomplemented
88#2659C2214yescomplemented
89#2647C2212yescomplemented
90#2647C2212yescomplemented
91#2646C2214yescomplemented
92#2629C2212yes—
93#2629C2212yes—
94#2628C2212yes—
95#2628C2212yes—
96#2628C2214yescomplemented
97#2628C2214yescomplemented
98#2626C2214yes—
99#2626C2214yes—
100#2626C2214yes—
101#2626C2214yes—
102#2612C2214yescomplemented
103#2608C2214yes—
104#2608C2214yescomplemented
105#2607C2214yes—
106#2607C2214yescomplemented
107#2607C2214yescomplemented
108#2607C2214yescomplemented
109#2606C2212yescomplemented
110#2605C2212yescomplemented
111#2605C2212yescomplemented
112#2605C2212yescomplemented
113#2590C2214yescomplemented
114#2589C2214yescomplemented
115#2589C2214yescomplemented
116#2589C2214yescomplemented
117#2588C2214yescomplemented
118#2587C2214yescomplemented
119#2586C2214yescomplemented
120#2585C2214yescomplemented
121#2584C2212yescomplemented
122#2580C2212yes—
123#2580C2212yes—
124#2580C2212yes—
125#2574C2214yescomplemented
126#2574C2214yescomplemented
127#2574C2214yescomplemented
128#2571C2212yescomplemented
129#2570C2212yescomplemented
130#2570C2212yescomplemented
131#2570C2212yescomplemented
132#2569C2214yescomplemented
133#2566C2212yes—
134#2563C2212yes—
135#2563C2212yes—
136#2556C2214yescomplemented
137#2551C2212yescomplemented
138#2551C2212yescomplemented
139#2550C2212yescomplemented
140#2550C2212yescomplemented
141#2550C2212yescomplemented
142#2550C2212yescomplemented
143#2549C2214yescomplemented
144#2546C2212yescomplemented
145#2542C2212yes—
146#2538C2212yes—
147#2522C2214yescomplemented
148#2522C2214yescomplemented
149#2520C2214yescomplemented
150#2520C2214yescomplemented
151#2509C2212yescomplemented
152#2508C2212yescomplemented
153#2508C2212yescomplemented
154#2507C2212yescomplemented
155#2492C2214yescomplemented
156#2492C2214yescomplemented
157#2465C2214yescomplemented
158#2465C2214yescomplemented
159#2454C2212yes—
160#2454C2212yes—
161#2454C2212yes—
162#2452C2212yes—
163#2452C2212yes—
164#2452C2212yes—
165#2452C2212yes—
166#2452C2212yes—
167#2451C2214yescomplemented
168#2446C2214yescomplemented
169#2441C2212yes—
170#2439C2214yes—
171#2439C2212yes—
172#2439C2212yes—
173#2439C2214yes—
174#2439C2214yes—
175#2439C2212yes—
176#2439C2214yescomplemented
177#2439C2214yescomplemented
178#2438C2214yescomplemented
179#2438C2214yescomplemented
180#2438C2214yescomplemented
181#2438C2214yescomplemented
182#2438C2214yescomplemented
183#2438C2214yescomplemented
184#2437C2214yes—
185#2437C2214yes—
186#2429C2214yescomplemented
187#2423C2214yescomplemented
188#2402C2212yescomplemented
189#2399C2212yescomplemented
190#2396C2214yes—
191#2396C2212yes—
192#2396C2214yes—
193#2396C2212yes—
194#2396C2214yescomplemented
195#2396C2214yescomplemented
196#2370C2212yescomplemented
197#2370C2212yescomplemented
198#2369C2212yescomplemented
199#2369C2212yescomplemented
200#2365C2212yescomplemented
201#2365C2212yescomplemented
202#2357C2214yes—
203#2357C2211yescharacteristic
204#2357C2212yes—
205#2357C2211yescharacteristic
206#2357C2211yescharacteristic
207#2357C2212yes—
208#2357C2211yescharacteristic
209#2355C2212yescomplemented
210#2355C2212yescomplemented
211#2354C2212yes—
212#2354C2212yes—
213#2354C2214yes—
214#2353C2212yes—
215#2353C2212yes—
216#2353C2212yes—
217#2353C2212yes—
218#2349C2211yescharacteristic
219#2349C2211yescharacteristic
220#2349C2211yescharacteristic
221#2349C2211yescharacteristic
222#2345C2212yes—
223#2344C2212yes—
224#2342C2214yes—
225#2342C2214yes—
226D4×C22⋊C4C2212yes—
227D4×C22⋊C4C2212yes—
228#2331C2214yescomplemented
229#2329C2214yescomplemented
230#2329C2214yescomplemented
231#2319C2212yes—
232#2318C2214yes—
233#2312C2212yes—
234#2312C2212yes—
235#2309C2211yescharacteristic
236#2309C2211yescharacteristic
237C4×C4⋊Q8C2212yescomplemented
238C4×#125C2212yescomplemented
239C4×C22⋊Q8C2214yescomplemented
240C4×C22⋊Q8C2214yescomplemented
241#2293C2212yes—
242#2290C2214yes—
243#2285C2211yescharacteristic
244#2285C2211yescharacteristic
245#2283C2211yescharacteristic
246#2283C2211yescharacteristic
247#2283C2211yescharacteristic
248#2280C2212yes—
249#2280C2212yes—
250#2280C2212yes—
251#2280C2212yes—
252C2×#381C2212yes—
253#2275C2212yes—
254#2274C2211yescharacteristic
255#2274C2211yescharacteristic
256C42×D4C2212yes—
257C4×#117C2211yescharacteristic
258C2×C4×C22⋊C4C2212yes—
259C23×D4C2311yescharacteristic
260C24×C4C2312yes—
261C2×C4⋊Q8C2312yes—
262C2×C4⋊Q8C2312yes—
263C2×C4⋊Q8C2312yes—
264C2×C4⋊Q8C2314yes—
265C2×C4⋊Q8C2312yes—
266C2×C4⋊Q8C2312yes—
267C2×C4⋊Q8C2314yes—
268C2×C4⋊Q8C2314yes—
269C2×#125C2312yes—
270C2×#125C2312yes—
271C2×#125C2312yes—
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×Q8C2314yes—
284C2×C4×D4Q8116yescomplemented
285C2×C4×D4C2312yes—
286C2×C4×D4C2312yes—
287C2×C4×D4C2312yes—
288C2×C4×D4C2312yes—
289C2×C4×D4C2312yes—
290C2×C4×D4C2311yescharacteristic
291C2×C4×D4C2311yescharacteristic
292C2×C4×D4C2312yes—
293C2×C4×D4C2311yescharacteristic
294C2×C4×D4C2311yescharacteristic
295C2×#117C2311yescharacteristic
296C2×#117C2311yescharacteristic
297C2×#117C2311yescharacteristic
298C2×#117C2311yescharacteristic
299C2×#117C2312yes—
300C2×#117C2314yes—
301C2×#117C2314yes—
302C2×#117C2314yes—
303C2×#117C2314yes—
304C22×C4⋊C4C2311yescharacteristic
305C22×C22⋊C4C2314yes—
306C22×C22⋊C4C2314yes—
307C22×C22⋊C4C2312yes—
308C22×C42C2314yes—
309C22×C42C2311yescharacteristic
310#400C2314yes—
311#400C2314yes—
312#400C2314yes—
313#400C2314yes—
314#400C2314yes—
315#400C2314yes—
316#400C2314yes—
317#400C2312yes—
318#400C2314yes—
319#400C2314yes—
320#400C2312yes—
321#400C2314yes—
322#400C2312yes—
323#400C2312yes—
324#400C2312yes—
325#400C2314yes—
326#400C2314yes—
327#400C2312yes—
328#399C2314yes—
329#399C2314yes—
330#399C2314yes—
331#399C2314yes—
332#399C2314yes—
333#399C2314yes—
334#399C2314yes—
335#399C2314yes—
336#399C2314yes—
337#399C2312yes—
338#399C2312yes—
339#399C2314yes—
340#398C2312yes—
341#398C2314yes—
342#398C2314yes—
343#398C2314yes—
344#398C2314yes—
345#398C2312yes—
346#398C2314yes—
347#398C2314yes—
348#398C2314yes—
349#398C2312yes—
350#398C2314yes—
351#398C2314yes—
352#398C2314yes—
353#398C2314yes—
354#398C2314yes—
355#398C2314yes—
356#398C2314yes—
357#398C2314yes—
358#398C2314yes—
359#398C2312yes—
360#398C2314yes—
361#398C2314yes—
362#398C2312yes—
363#398C2314yes—
364#398C2312yes—
365#398C2312yes—
366#398C2312yes—
367#398C2312yes—
368#398C2314yes—
369#398C2312yes—
370#398C2312yes—
371#398C2312yes—
372#396C2314yes—
373#396C2314yes—
374#396C2314yes—
375#396C2314yes—
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#396C2312yes—
389#396C2314yes—
390#396C2312yes—
391#396C2314yes—
392#396C2312yes—
393#396C2314yes—
394#395C2312yes—
395#395C2314yes—
396#395C2314yes—
397#395C2314yes—
398#395C2314yes—
399#395C2312yes—
400#395C2314yes—
401#395C2314yes—
402#395C2312yes—
403#395C2314yes—
404#395C2314yes—
405#395C2314yes—
406#395C2314yes—
407#395C2312yes—
408#395C2312yes—
409#395C2314yes—
410#395C2314yes—
411#395C2312yes—
412#393C2314yes—
413#393C2314yes—
414#393C2314yes—
415#393C2314yes—
416#393C2314yes—
417#393C2314yes—
418#393C2314yes—
419#393C2314yes—
420#393C2312yes—
421#393C2314yes—
422#393C2314yes—
423#393C2314yes—
424#393C2314yes—
425#393C2314yes—
426#393C2314yes—
427#393C2314yes—
428#393C2312yes—
429#393C2314yes—
430#391C2312yes—
431#391C2312yes—
432#391C2314yes—
433#391C2314yes—
434#391C2314yes—
435#391C2314yes—
436#391C2314yes—
437#391C2314yes—
438#391C2314yes—
439#391C2314yes—
440#391C2314yes—
441#391C2314yes—
442#391C2314yes—
443#391C2314yes—
444#391C2314yes—
445#391C2314yes—
446#391C2314yes—
447#391C2314yes—
448#391C2314yes—
449#391C2314yes—
450#391C2314yes—
451#391C2314yes—
452#390C2312yes—
453#390C2312yes—
454#390C2312yes—
455#390C2312yes—
456#390C2312yes—
457#390C2312yes—
458#390C2314yes—
459#390C2314yes—
460#390C2312yes—
461#390C2312yes—
462#389C2312yes—
463#389C2312yes—
464#389C2312yes—
465#389C2312yes—
466#389C2312yes—
467#389C2312yes—
468#389C2312yes—
469#389C2312yes—
470#389C2312yes—
471#389C2312yes—
472#389C2312yes—
473#389C2312yes—
474#389C2312yes—
475#389C2314yes—
476#389C2312yes—
477#389C2312yes—
478#389C2312yes—
479#389C2314yes—
480#389C2314yes—
481#389C2312yes—
482#389C2314yes—
483#389C2314yes—
484#389C2314yes—
485#389C2314yes—
486#389C2314yes—
487#389C2314yes—
488#389C2314yes—
489#389C2314yes—
490#389C2314yes—
491#389C2314yes—
492#389C2314yes—
493#389C2312yes—
494#389C2314yes—
495#389C2314yes—
496#389C2312yes—
497#389C2312yes—
498#389C2312yes—
499#389C2312yes—
500#388C2314yes—
501#388C2314yes—
502#388C2314yes—
503#388C2314yes—
504#388C2314yes—
505#388C2314yes—
506#388C2314yes—
507#388C2314yes—
508#388C2314yes—
509#388C2314yes—
510#388C2314yes—
511#388C2314yes—
512#388C2314yes—
513#388C2314yes—
514#388C2314yes—
515#388C2314yes—
516#387C2312yes—
517#387C2312yes—
518#387C2312yes—
519#387C2312yes—
520#387C2314yes—
521#387C2314yes—
522#387C2314yes—
523#387C2314yes—
524#387C2314yes—
525#387C2314yes—
526#387C2314yes—
527#387C2314yes—
528#387C2314yes—
529#387C2314yes—
530#387C2314yes—
531#387C2314yes—
532#387C2314yes—
533#387C2314yes—
534#387C2314yes—
535#387C2314yes—
536#387C2314yes—
537#387C2314yes—
538#387C2314yes—
539#387C2314yes—
540#387C2314yes—
541#387C2314yes—
542#387C2314yes—
543#387C2314yes—
544#387C2314yes—
545#387C2314yes—
546#387C2314yes—
547#387C2314yes—
548#387C2314yes—
549#387C2314yes—
550#387C2314yes—
551#387C2314yes—
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#385C2314yes—
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#384C2312yes—
579#384C2312yes—
580#384C2312yes—
581#384C2312yes—
582#384C2312yes—
583#383C2312yes—
584#383C2312yes—
585#383C2311yescharacteristic
586#383C2311yescharacteristic
587#382C2312yes—
588#382C2312yes—
589#382C2312yes—
590#382C2312yes—
591#382C2312yes—
592#382C2311yescharacteristic
593#382C2311yescharacteristic
594#382C2312yes—
595#382C2314yes—
596#382C2312yes—
597#382C2311yescharacteristic
598#382C2311yescharacteristic
599#382C2312yes—
600#382C2314yes—
601#382C2314yes—
602#381C2314yes—
603#381C2312yes—
604#381C2314yes—
605#381C2312yes—
606#381C2314yes—
607#381C2312yes—
608#381C2312yes—
609#381C2312yes—
610#381C2314yes—
611#381C2312yes—
612#381C2311yescharacteristic
613#381C2311yescharacteristic
614#380C2314yes—
615#380C2314yes—
616#380C2314yes—
617#380C2314yes—
618#380C2312yes—
619#380C2311yescharacteristic
620#380C2311yescharacteristic
621#380C2314yes—
622#380C2314yes—
623#380C2314yes—
624#380C2314yes—
625#380C2312yes—
626#380C2312yes—
627#380C2312yes—
628#380C2314yes—
629#380C2312yes—
630#380C2312yes—
631#380C2314yes—
632#380C2314yes—
633#380C2312yes—
634#380C2312yes—
635#380C2314yes—
636#380C2311yescharacteristic
637#380C2312yes—
638#380C2311yescharacteristic
639#379C2312yes—
640#379C2312yes—
641#379C2312yes—
642#379C2312yes—
643#379C2314yes—
644#379C2314yes—
645C4×C4⋊C4C2311yescharacteristic
646C4×C4⋊C4C2312yes—
647C4×C4⋊C4C2312yes—
648C4×C4⋊C4C2312yes—
649C4×C4⋊C4C2312yes—
650C4×C4⋊C4C2312yes—
651C4×C4⋊C4C2311yescharacteristic
652C4×C4⋊C4C2312yes—
653C4×C4⋊C4C2312yes—
654C4×C4⋊C4C2312yes—
655C4×C4⋊C4C2312yes—
656C4×C4⋊C4C2312yes—
657C4×C4⋊C4C2311yescharacteristic
658C4×C4⋊C4C2314yes—
659C4×C4⋊C4C2314yes—
660C4×C4⋊C4C2314yes—
661C4×C4⋊C4C2312yes—
662C4×C4⋊C4C2314yes—
663C4×C4⋊C4C2314yes—
664C4×C4⋊C4C2314yes—
665C4×C4⋊C4C2312yes—
666C4×C4⋊C4C2312yes—
667C4×C4⋊C4C2314yes—
668C4×C4⋊C4C2314yes—
669C4×C4⋊C4C2312yes—
670C4×C4⋊C4C2312yes—
671C4×C4⋊C4C2312yes—
672C4×C4⋊C4C2312yes—
673C4×C4⋊C4C2311yescharacteristic
674C4×C4⋊C4C2312yes—
675C4×C4⋊C4C2312yes—
676C4×C4⋊C4C2312yes—
677C4×C4⋊C4C2312yes—
678C4×C22⋊C4C2312yes—
679C4×C22⋊C4C2312yes—
680C4×C22⋊C4C2312yes—
681C4×C22⋊C4C2312yes—
682C4×C22⋊C4C2312yes—
683C4×C22⋊C4C2314yes—
684C4×C22⋊C4C2314yes—
685C4×C22⋊C4C2314yes—
686C4×C22⋊C4C2314yes—
687C4×C22⋊C4C2314yes—
688C4×C22⋊C4C2314yes—
689C4×C22⋊C4C2314yes—
690C4×C22⋊C4C2312yes—
691C4×C22⋊C4C2312yes—
692C4×C22⋊C4C2312yes—
693C4×C22⋊C4C2314yes—
694C4×C22⋊C4C2314yes—
695C4×C22⋊C4C2312yes—
696C4×C22⋊C4C2312yes—
697C4×C22⋊C4C2314yes—
698C4×C22⋊C4C2312yes—
699C4×C22⋊C4C2311yescharacteristic
700C4×C22⋊C4C2311yescharacteristic
701C4×C22⋊C4C2312yes—
702#376C2312yes—
703#376C2312yes—
704#376C2311yescharacteristic
705#376C2311yescharacteristic
706#376C2312yes—
707C2×#95C2314yes—
708C2×#95C2312yes—
709C2×#95C2312yes—
710C2×#95C2312yes—
711C2×#95C2312yes—
712C43C2312yes—
713C25C2412yes—
714C22×Q8C2414yes—
715C22×Q8C2412yes—
716C22×Q8C2414yes—
717C22×Q8C2412yes—
718C22×Q8C2414yes—
719C22×Q8C2414yes—
720C22×D4—42no—
721C22×D4—42no—
722C22×D4C2×Q818yes—
723C22×D4C2411yescharacteristic
724C22×D4C2411yescharacteristic
725C22×D4C2412yes—
726C23×C4—84no—
727C23×C4C2×Q8116yes—
728C23×C4C2411yescharacteristic
729C23×C4C2414yes—
730C23×C4C2414yes—
731C23×C4C2414yes—
732C23×C4C2414yes—
733C23×C4C2411yescharacteristic
734C23×C4C2412yes—
735C23×C4C2412yes—
736C23×C4C2412yes—
737C23×C4C2412yes—
738C23×C4C2412yes—
739C23×C4C2411yescharacteristic
740C4⋊Q8—44no—
741C4⋊Q8—44no—
742C4⋊Q8—44no—
743C4⋊Q8—44no—
744C4⋊Q8—44no—
745C4⋊Q8—48no—
746C4⋊Q8—84no—
747C4⋊Q8—84no—
748#125—44no—
749#125—44no—
750#125—44no—
751C22⋊Q8—48no—
752C22⋊Q8—48no—
753C22⋊Q8—48no—
754C22⋊Q8—48no—
755C22⋊Q8—84no—
756C22⋊Q8—84no—
757C22⋊Q8—84no—
758C22⋊Q8—84no—
759C4×Q8—44no—
760C4×Q8—44no—
761C4×Q8—84no—
762C4×Q8—84no—
763C4×D4—44no—
764C4×D4—44no—
765C4×D4—44no—
766C4×D4—44no—
767C4×D4C2×Q818yes—
768C4×D4C2×Q818yes—
769C4×D4C2×Q818yes—
770C4×D4C2×Q818yes—
771C4×D4C2×Q8116yes—
772C4×D4C2×Q8116yes—
773#117—42no—
774#117—42no—
775#117—44no—
776#117—42no—
777#117—42no—
778#117—84no—
779#117—84no—
780#117—84no—
781#117—84no—
782C2×C4⋊C4C2×Q818yes—
783C2×C4⋊C4C2412yes—
784C2×C4⋊C4C2412yes—
785C2×C4⋊C4C2412yes—
786C2×C4⋊C4C2412yes—
787C2×C4⋊C4C2412yes—
788C2×C4⋊C4C2412yes—
789C2×C4⋊C4C2412yes—
790C2×C4⋊C4C2412yes—
791C2×C4⋊C4C2412yes—
792C2×C4⋊C4C2412yes—
793C2×C4⋊C4C2412yes—
794C2×C4⋊C4C2414yes—
795C2×C4⋊C4C2412yes—
796C2×C4⋊C4C2414yes—
797C2×C4⋊C4C2412yes—
798C2×C4⋊C4C2414yes—
799C2×C4⋊C4C2414yes—
800C2×C4⋊C4C2414yes—
801C2×C4⋊C4C2414yes—
802C2×C4⋊C4C2412yes—
803C2×C4⋊C4C2412yes—
804C2×C4⋊C4C2412yes—
805C2×C4⋊C4C2412yes—
806C2×C4⋊C4C2412yes—
807C2×C4⋊C4C2414yes—
808C2×C4⋊C4C2414yes—
809C2×C4⋊C4C2414yes—
810C2×C4⋊C4C2414yes—
811C2×C4⋊C4C2412yes—
812C2×C4⋊C4C2412yes—
813C2×C4⋊C4C2412yes—
814C2×C4⋊C4C2412yes—
815C2×C4⋊C4C2412yes—
816C2×C4⋊C4C2412yes—
817C2×C4⋊C4C2412yes—
818C2×C4⋊C4C2412yes—
819C2×C4⋊C4C2412yes—
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⋊C4C2414yes—
829C2×C4⋊C4C2414yes—
830C2×C4⋊C4C2412yes—
831C2×C4⋊C4C2412yes—
832C2×C4⋊C4C2412yes—
833C2×C4⋊C4C2414yes—
834C2×C4⋊C4C2414yes—
835C2×C4⋊C4C2412yes—
836C2×C4⋊C4C2414yes—
837C2×C4⋊C4C2414yes—
838C2×C4⋊C4C2412yes—
839C2×C4⋊C4C2414yes—
840C2×C4⋊C4C2412yes—
841C2×C4⋊C4C2412yes—
842C2×C4⋊C4C2414yes—
843C2×C4⋊C4C2414yes—
844C2×C4⋊C4C2414yes—
845C2×C4⋊C4C2414yes—
846C2×C4⋊C4C2414yes—
847C2×C4⋊C4C2411yescharacteristic
848C2×C4⋊C4C2412yes—
849C2×C4⋊C4C2411yescharacteristic
850C2×C22⋊C4—48no—
851C2×C22⋊C4—84no—
852C2×C22⋊C4C2×Q8116yes—
853C2×C22⋊C4C2412yes—
854C2×C22⋊C4C2414yes—
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⋊C4C2411yescharacteristic
869C2×C22⋊C4C2412yes—
870C2×C22⋊C4C2412yes—
871C2×C22⋊C4C2411yescharacteristic
872C2×C22⋊C4C2412yes—
873C2×C22⋊C4C2411yescharacteristic
874C2×C22⋊C4C2411yescharacteristic
875C2×C22⋊C4C2414yes—
876C2×C22⋊C4C2414yes—
877C2×C22⋊C4C2414yes—
878C2×C22⋊C4C2414yes—
879C2×C22⋊C4C2414yes—
880C2×C22⋊C4C2414yes—
881C2×C22⋊C4C2414yes—
882C2×C22⋊C4C2414yes—
883C2×C22⋊C4C2414yes—
884C2×C22⋊C4C2414yes—
885C2×C22⋊C4C2412yes—
886C2×C22⋊C4C2412yes—
887C2×C22⋊C4C2412yes—
888C2×C22⋊C4C2412yes—
889C2×C42—84no—
890C2×C42C2×Q818yes—
891C2×C42C2412yes—
892C2×C42C2412yes—
893C2×C42C2412yes—
894C2×C42C2412yes—
895C2×C42C2412yes—
896C2×C42C2412yes—
897C2×C42C2412yes—
898C2×C42C2412yes—
899C2×C42C2414yes—
900C2×C42C2414yes—
901C2×C42C2414yes—
902C2×C42C2414yes—
903C2×C42C2414yes—
904C2×C42C2414yes—
905C2×C42C2412yes—
906C2×C42C2414yes—
907C2×C42C2412yes—
908C2×C42C2412yes—
909C2×C42C2414yes—
910C2×C42C2414yes—
911C2×C42C2414yes—
912C2×C42C2412yes—
913C2×C42C2411yescharacteristic
914C2×C42C2411yescharacteristic
915C2×C42C2411yescharacteristic
916C2×C42C2411yescharacteristic
917#95C2411yescharacteristic
918#95C2411yescharacteristic
919#95C2412yes—
920#95C2411yescharacteristic
921#95C2411yescharacteristic
922#95C2412yes—
923#95C2412yes—
924#95C2412yes—
925#95C2412yes—
926#95C2414yes—
927#95C2414yes—
928#95C2414yes—
929#95C2414yes—
930#95C2414yes—
931#95C2414yes—
932#95C2414yes—
933#95C2412yes—
934#95C2412yes—
935#95C2412yes—
936#95C2411yescharacteristic
937#95C2411yescharacteristic
938#95C2412yes—
939#95C2412yes—
940#95C2414yes—
941#95C2414yes—
942#95C2412yes—
943#95C2412yes—
944#95C2411yescharacteristic
945#95C2411yescharacteristic
946#95C2412yes—
947#95C2412yes—
948#95C2414yes—
949#95C2414yes—
950#95C2414yes—
951#95C2414yes—
952#95C2414yes—
953#95C2414yes—
954#95C2414yes—
955#95C2414yes—
956#95C2412yes—
957#95C2412yes—
958#95C2412yes—
959#95C2412yes—
960#95C2412yes—
961#95C2412yes—
962#95C2414yes—
963#95C2414yes—
964#95C2412yes—
965#95C2412yes—
966#95C2414yes—
967#95C2414yes—
968#95C2412yes—
969#95C2412yes—
970#95C2414yes—
971#95C2414yes—
972#95C2412yes—
973#95C2412yes—
974#95C2412yes—
975#95C2414yes—
976#95C2412yes—
977#95C2414yes—
978#95C2412yes—
979#95C2412yes—
980#95C2414yes—
981#95C2414yes—
982#95C2414yes—
983#95C2412yes—
984#95C2412yes—
985#95C2414yes—
986#95C2414yes—
987#95C2414yes—
988#95C2414yes—
989#95C2414yes—
990#95C2414yes—
991#95C2414yes—
992#95C2414yes—
993#95C2414yes—
994#95C2414yes—
995C24—44no—
996C24—44no—
997C24—42no—
998C24—42no—
999C24C22×Q818yes—
1000C24C2511yescharacteristic
1001C24C2512yes—
1002C24C2512yes—
1003C2×Q8—28no—
1004C2×Q8—42no—
1005C2×Q8—42no—
1006C2×Q8—44no—
1007C2×Q8—44no—
1008C2×Q8—44no—
1009C2×Q8—42no—
1010C2×Q8—44no—
1011C2×Q8—44no—
1012C2×Q8—42no—
1013C2×Q8—42no—
1014C2×Q8—42no—
1015C2×Q8—44no—
1016C2×Q8—44no—
1017C2×Q8—44no—
1018C2×Q8—44no—
1019C2×Q8—44no—
1020C2×Q8—44no—
1021C2×D4—22no—
1022C2×D4—22no—
1023C2×D4—22no—
1024C2×D4—22no—
1025C2×D4—416no—
1026C2×D4—42no—
1027C2×D4—42no—
1028C2×D4C22×Q814yes—
1029C2×D4C22×Q814yes—
1030C2×D4C22×Q818yes—
1031C22×C4—22no—
1032C22×C4—22no—
1033C22×C4—28no—
1034C22×C4—44no—
1035C22×C4—42no—
1036C22×C4—44no—
1037C22×C4—44no—
1038C22×C4—44no—
1039C22×C4—44no—
1040C22×C4—42no—
1041C22×C4—44no—
1042C22×C4—44no—
1043C22×C4—44no—
1044C22×C4—44no—
1045C22×C4—44no—
1046C22×C4—44no—
1047C22×C4—44no—
1048C22×C4—44no—
1049C22×C4—44no—
1050C22×C4—44no—
1051C22×C4—44no—
1052C22×C4—816no—
1053C22×C4C22×Q814yes—
1054C22×C4C22×Q814yes—
1055C22×C4C22×Q814yes—
1056C22×C4C22×Q818yes—
1057C22×C4C22×Q818yes—
1058C22×C4C22×Q818yes—
1059C22×C4C22×Q818yes—
1060C22×C4C22×Q818yes—
1061C22×C4C2512yes—
1062C22×C4C2514yes—
1063C22×C4C2512yes—
1064C22×C4C2512yes—
1065C22×C4C2512yes—
1066C22×C4C2512yes—
1067C22×C4C2512yes—
1068C22×C4C2514yes—
1069C22×C4C2514yes—
1070C22×C4C2514yes—
1071C22×C4C2514yes—
1072C22×C4C2512yes—
1073C22×C4C2512yes—
1074C22×C4C2512yes—
1075C22×C4C2514yes—
1076C22×C4C2512yes—
1077C22×C4C2512yes—
1078C22×C4C2511yescharacteristic
1079C22×C4C2511yescharacteristic
1080C22×C4C2511yescharacteristic
1081C22×C4C2512yes—
1082C22×C4C2511yescharacteristic
1083C22×C4C2511yescharacteristic
1084C22×C4C2512yes—
1085C22×C4C2512yes—
1086C22×C4C2511yescharacteristic
1087C4⋊C4—24no—
1088C4⋊C4—24no—
1089C4⋊C4—24no—
1090C4⋊C4—24no—
1091C4⋊C4—24no—
1092C4⋊C4—24no—
1093C4⋊C4—24no—
1094C4⋊C4—24no—
1095C4⋊C4—24no—
1096C4⋊C4—28no—
1097C4⋊C4—24no—
1098C4⋊C4—24no—
1099C4⋊C4—42no—
1100C4⋊C4—42no—
1101C4⋊C4—42no—
1102C4⋊C4—42no—
1103C4⋊C4—42no—
1104C4⋊C4—44no—
1105C4⋊C4—44no—
1106C4⋊C4—44no—
1107C4⋊C4—44no—
1108C4⋊C4—44no—
1109C4⋊C4—42no—
1110C4⋊C4—42no—
1111C4⋊C4—42no—
1112C4⋊C4—42no—
1113C4⋊C4—42no—
1114C4⋊C4—42no—
1115C4⋊C4—42no—
1116C4⋊C4—42no—
1117C4⋊C4—44no—
1118C4⋊C4—44no—
1119C4⋊C4—44no—
1120C4⋊C4—44no—
1121C4⋊C4—44no—
1122C4⋊C4—44no—
1123C4⋊C4—44no—
1124C4⋊C4—44no—
1125C4⋊C4—44no—
1126C4⋊C4—44no—
1127C4⋊C4—42no—
1128C4⋊C4—42no—
1129C4⋊C4—42no—
1130C4⋊C4—44no—
1131C4⋊C4—44no—
1132C4⋊C4—44no—
1133C4⋊C4—44no—
1134C4⋊C4—42no—
1135C4⋊C4—42no—
1136C4⋊C4—44no—
1137C4⋊C4—44no—
1138C4⋊C4—44no—
1139C4⋊C4—42no—
1140C4⋊C4—42no—
1141C4⋊C4—44no—
1142C4⋊C4—42no—
1143C4⋊C4—42no—
1144C4⋊C4—44no—
1145C4⋊C4—44no—
1146C4⋊C4—44no—
1147C4⋊C4—44no—
1148C4⋊C4—44no—
1149C4⋊C4—44no—
1150C4⋊C4—42no—
1151C4⋊C4C22×Q818yes—
1152C4⋊C4C22×Q814yes—
1153C4⋊C4C22×Q814yes—
1154C22⋊C4—24no—
1155C22⋊C4—28no—
1156C22⋊C4—44no—
1157C22⋊C4—44no—
1158C22⋊C4—42no—
1159C22⋊C4—44no—
1160C22⋊C4—44no—
1161C22⋊C4—44no—
1162C22⋊C4—41no—
1163C22⋊C4—41no—
1164C22⋊C4—41no—
1165C22⋊C4—42no—
1166C22⋊C4—41no—
1167C22⋊C4—42no—
1168C22⋊C4—42no—
1169C22⋊C4—42no—
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⋊C4—44no—
1181C22⋊C4—44no—
1182C22⋊C4—44no—
1183C22⋊C4—44no—
1184C22⋊C4—44no—
1185C22⋊C4—44no—
1186C22⋊C4C22×Q818yes—
1187C22⋊C4C22×Q818yes—
1188C22⋊C4C22×Q818yes—
1189C22⋊C4C22×Q818yes—
1190C42—24no—
1191C42—24no—
1192C42—24no—
1193C42—24no—
1194C42—24no—
1195C42—24no—
1196C42—24no—
1197C42—42no—
1198C42—44no—
1199C42—44no—
1200C42—44no—
1201C42—42no—
1202C42—42no—
1203C42—42no—
1204C42—42no—
1205C42—44no—
1206C42—44no—
1207C42—44no—
1208C42—44no—
1209C42—44no—
1210C42—44no—
1211C42—44no—
1212C42C22×Q814yes—
1213C42C22×Q814yes—
1214C42C22×Q814yes—
1215C42C22×Q814yes—
1216C23—24no—
1217C23—22no—
1218C23—24no—
1219C23—21no—
1220C23—21no—
1221C23—22no—
1222C23—22no—
1223C23—22no—
1224C23—22no—
1225C23—24no—
1226C23—24no—
1227C23—22no—
1228C23—48no—
1229C23—48no—
1230C23—48no—
1231C23—88no—
1232C23—88no—
1233C23C23×Q814yes—
1234C23C23×Q814yes—
1235C23C23×Q812yes—
1236C23C2611yescharacteristic
1237Q8—88no—
1238Q8—84no—
1239Q8—84no—
1240Q8—88no—
1241Q8—164no—
1242Q8—164no—
1243D4—28no—
1244D4—28no—
1245D4—48no—
1246C2×C4—22no—
1247C2×C4—22no—
1248C2×C4—21no—
1249C2×C4—22no—
1250C2×C4—21no—
1251C2×C4—24no—
1252C2×C4—22no—
1253C2×C4—22no—
1254C2×C4—24no—
1255C2×C4—22no—
1256C2×C4—28no—
1257C2×C4—22no—
1258C2×C4—22no—
1259C2×C4—22no—
1260C2×C4—22no—
1261C2×C4—22no—
1262C2×C4—22no—
1263C2×C4—22no—
1264C2×C4—22no—
1265C2×C4—22no—
1266C2×C4—22no—
1267C2×C4—22no—
1268C2×C4—22no—
1269C2×C4—22no—
1270C2×C4—24no—
1271C2×C4—24no—
1272C2×C4—24no—
1273C2×C4—22no—
1274C2×C4—24no—
1275C2×C4—24no—
1276C2×C4—22no—
1277C2×C4—22no—
1278C2×C4—22no—
1279C2×C4—22no—
1280C2×C4—22no—
1281C2×C4—24no—
1282C2×C4—22no—
1283C2×C4—24no—
1284C2×C4—24no—
1285C2×C4—24no—
1286C2×C4—24no—
1287C2×C4—24no—
1288C2×C4—24no—
1289C2×C4—22no—
1290C2×C4—22no—
1291C2×C4—22no—
1292C2×C4—22no—
1293C2×C4—22no—
1294C2×C4—22no—
1295C2×C4—24no—
1296C2×C4—24no—
1297C2×C4—22no—
1298C2×C4—22no—
1299C2×C4—24no—
1300C2×C4—24no—
1301C2×C4—22no—
1302C2×C4—24no—
1303C2×C4—22no—
1304C2×C4—22no—
1305C2×C4—24no—
1306C2×C4—22no—
1307C2×C4—22no—
1308C2×C4—44no—
1309C2×C4—48no—
1310C2×C4—48no—
1311C2×C4—48no—
1312C2×C4—48no—
1313C2×C4—48no—
1314C2×C4—44no—
1315C2×C4—88no—
1316C2×C4—88no—
1317C2×C4—164no—
1318C2×C4—164no—
1319C2×C4C23×Q812yes—
1320C2×C4C23×Q812yes—
1321C2×C4C23×Q812yes—
1322C2×C4C23×Q812yes—
1323C2×C4C23×Q812yes—
1324C2×C4C23×Q814yes—
1325C2×C4C23×Q814yes—
1326C2×C4C23×Q812yes—
1327C2×C4#58514yes—
1328C2×C4#58512yes—
1329C2×C4#58512yes—
1330C22—22no—
1331C22—24no—
1332C22—24no—
1333C22—22no—
1334C22—24no—
1335C22—24no—
1336C22—22no—
1337C22—24no—
1338C22—24no—
1339C22—44no—
1340C22—44no—
1341C22—42no—
1342C22—44no—
1343C22—44no—
1344C22—42no—
1345C22—816no—
1346C22C24×Q811yescharacteristic
1347C22C2×#58512yes—
1348C22C2×#58511yescharacteristic
1349C22C2×#58511yescharacteristic
1350C22H(7,𝔽2)12yes—
1351C4—22no—
1352C4—22no—
1353C4—22no—
1354C4—22no—
1355C4—24no—
1356C4—24no—
1357C4—22no—
1358C4—24no—
1359C4—42no—
1360C4—42no—
1361C4—42no—
1362C4—44no—
1363C4—42no—
1364C4—44no—
1365C4—42no—
1366C4—42no—
1367C4—42no—
1368C4—42no—
1369C4—44no—
1370C4—42no—
1371C4—44no—
1372C4—44no—
1373C4—42no—
1374C4—44no—
1375C4—42no—
1376C4#345814yes—
1377C2—44no—
1378C2—44no—
1379C2—42no—
1380C2C2×#345811yescharacteristic
1381C2#6281311yescharacteristic
1382C2#6284311yescharacteristic
1383C2#6293812yes—
1384C2#6296512yes—
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. #42497C2semidirect
2. #42493C2semidirect
5. #40634C2semidirect
6. #40630C2semidirect
7. #40627C2semidirect
8. #40626C2semidirect
9. #39977C2semidirect
10. #39972C2semidirect
11. #39967C2semidirect
12. #39964C2semidirect
13. #37567C2semidirect
14. #37565C2semidirect
15. #37480C2semidirect
16. #37479C2semidirect
17. #36479C2semidirect
18. #36476C2semidirect
19. #35952C2semidirect
20. #35871C2semidirect
21. #35843C2semidirect
22. #35788C2semidirect
23. #35192C2semidirect
24. #35065C2semidirect
25. #34625C2semidirect
26. #34578C2semidirect
31. #2864C22semidirect
32. #2862C22semidirect
33. #2855C22semidirect
34. #2855C22semidirect
35. #2843C22semidirect
38. #2841C22semidirect
39. #2841C22semidirect
41. #2807C22semidirect
43. #2790C22semidirect
44. #2788C22semidirect
45. #2788C22semidirect
48. #2768C22semidirect
49. #2768C22semidirect
50. #2768C22semidirect
51. #2763C22semidirect
52. #2763C22semidirect
54. #2742C22semidirect
56. #2729C22semidirect
57. #2729C22semidirect
58. #2729C22semidirect
59. #2704C22semidirect
63. #2677C22semidirect
64. #2677C22semidirect
71. #2667C22semidirect
72. #2666C22semidirect
73. #2666C22semidirect
74. #2666C22semidirect
83. #2665C22semidirect
84. #2665C22semidirect
85. #2665C22semidirect
86. #2660C22semidirect
87. #2660C22semidirect
88. #2659C22semidirect
89. #2647C22semidirect
90. #2647C22semidirect
91. #2646C22semidirect
96. #2628C22semidirect
97. #2628C22semidirect
102. #2612C22semidirect
104. #2608C22semidirect
106. #2607C22semidirect
107. #2607C22semidirect
108. #2607C22semidirect
109. #2606C22semidirect
110. #2605C22semidirect
111. #2605C22semidirect
112. #2605C22semidirect
113. #2590C22semidirect
114. #2589C22semidirect
115. #2589C22semidirect
116. #2589C22semidirect
117. #2588C22semidirect
118. #2587C22semidirect
119. #2586C22semidirect
120. #2585C22semidirect
121. #2584C22semidirect
125. #2574C22semidirect
126. #2574C22semidirect
127. #2574C22semidirect
128. #2571C22semidirect
129. #2570C22semidirect
130. #2570C22semidirect
131. #2570C22semidirect
132. #2569C22semidirect
136. #2556C22semidirect
137. #2551C22semidirect
138. #2551C22semidirect
139. #2550C22semidirect
140. #2550C22semidirect
141. #2550C22semidirect
142. #2550C22semidirect
143. #2549C22semidirect
144. #2546C22semidirect
147. #2522C22semidirect
148. #2522C22semidirect
149. #2520C22semidirect
150. #2520C22semidirect
151. #2509C22semidirect
152. #2508C22semidirect
153. #2508C22semidirect
154. #2507C22semidirect
155. #2492C22semidirect
156. #2492C22semidirect
157. #2465C22semidirect
158. #2465C22semidirect
167. #2451C22semidirect
168. #2446C22semidirect
176. #2439C22semidirect
177. #2439C22semidirect
178. #2438C22semidirect
179. #2438C22semidirect
180. #2438C22semidirect
181. #2438C22semidirect
182. #2438C22semidirect
183. #2438C22semidirect
186. #2429C22semidirect
187. #2423C22semidirect
188. #2402C22semidirect
189. #2399C22semidirect
194. #2396C22semidirect
195. #2396C22semidirect
196. #2370C22semidirect
197. #2370C22semidirect
198. #2369C22semidirect
199. #2369C22semidirect
200. #2365C22semidirect
201. #2365C22semidirect
209. #2355C22semidirect
210. #2355C22semidirect
228. #2331C22semidirect
229. #2329C22semidirect
230. #2329C22semidirect
237. C4×C4⋊Q8C22semidirect
238. C4×#125C22semidirect
239. C4×C22⋊Q8C22semidirect
240. C4×C22⋊Q8C22semidirect
284. C2×C4×D4Q8semidirect

Maximal subgroups

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

subgroupindex
#424972
#424932
#424872
#424862
#406342
#406302
#406272
#406262
#399772
#399722
#399672
#399642
#375672
#375652
#374802
#374792
#364792
#364762
#359522
#358712
#358432
#357882
#351922
#350652
#346252
#345782
#341902
#341862
#341262