Finite Group Databasebeta

← #7655058

Subgroups — #7655058

Order 512.

4488 conjugacy classes of subgroups.

The subgroup lattice has 1412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#41746C214yesmaximal, complemented
2#41394C212yesmaximal, complemented
3#41098C214yesmaximal, complemented
4#40544C212yesmaximal
5#40322C214yesmaximal, complemented
6#39274C212yesmaximal, complemented
7#39271C212yesmaximal, complemented
8#38706C214yesmaximal, complemented
9#38469C214yesmaximal, complemented
10#37963C212yesmaximal, complemented
11#37960C212yesmaximal, complemented
12#37853C212yesmaximal, complemented
13#37850C212yesmaximal, complemented
14#37582C212yesmaximal, complemented
15#37540C211yesmaximal, characteristic, complemented
16#36344C214yesmaximal, complemented
17#36190C212yesmaximal, complemented
18#36167C212yesmaximal, complemented
19#36035C212yesmaximal, complemented
20#35731C212yesmaximal
21#35240C211yesmaximal, characteristic
22#35235C211yesmaximal, characteristic, complemented
23#35183C212yesmaximal, complemented
24#35110C212yesmaximal, complemented
25#34898C212yesmaximal, complemented
26C2×#2562C211yesmaximal, characteristic
27#34239C211yesmaximal, characteristic, complemented
28#34145C211yesmaximal, characteristic, complemented
29#34126C211yesmaximal, characteristic
30C2×#533C2211yescharacteristic
31C22×#125C2211yescharacteristic
32C22×C4×D4C2211yescharacteristic
33#2866C2214yescomplemented
34#2865C2214yescomplemented
35#2857C2212yescomplemented
36#2855C2214yes—
37#2855C2212yescomplemented
38#2855C2212yescomplemented
39#2851C2212yescomplemented
40#2848C2212yes—
41#2848C2212yes—
42#2839C2214yescomplemented
43#2830C2214yes—
44#2822C2214yescomplemented
45#2807C2214yescomplemented
46#2798C2214yescomplemented
47#2796C2214yes—
48#2794C2214yescomplemented
49#2794C2214yescomplemented
50#2789C2214yescomplemented
51#2787C2214yescomplemented
52#2783C2214yescomplemented
53#2777C2214yescomplemented
54#2773C2214yescomplemented
55#2771C2214yescomplemented
56#2758C2214yescomplemented
57#2751C2214yes—
58#2747C2214yescomplemented
59#2747C2214yescomplemented
60#2745C2214yescomplemented
61#2744C2214yescomplemented
62#2742C2214yescomplemented
63#2739C2214yescomplemented
64#2738C2214yescomplemented
65#2722C2214yescomplemented
66#2715C2214yes—
67#2700C2214yes—
68#2689C2214yescomplemented
69#2666C2214yescomplemented
70#2666C2214yescomplemented
71#2660C2211yescharacteristic, complemented
72#2660C2211yescharacteristic, complemented
73#2655C2214yescomplemented
74#2655C2214yescomplemented
75#2654C2214yescomplemented
76#2651C2214yes—
77#2651C2214yes—
78#2650C2214yescomplemented
79#2642C2211yescharacteristic, complemented
80#2642C2211yescharacteristic, complemented
81#2638C2214yes—
82#2634C2212yescomplemented
83#2634C2212yescomplemented
84#2633C2212yes—
85#2633C2212yes—
86#2629C2212yescomplemented
87#2628C2212yescomplemented
88#2627C2212yes—
89#2627C2212yes—
90#2625C2212yescomplemented
91#2625C2212yescomplemented
92#2606C2212yescomplemented
93#2605C2212yescomplemented
94#2605C2214yescomplemented
95#2596C2214yescomplemented
96#2596C2214yescomplemented
97#2596C2214yescomplemented
98#2595C2214yes—
99#2594C2214yescomplemented
100#2594C2214yescomplemented
101#2593C2214yes—
102#2589C2214yescomplemented
103#2588C2214yescomplemented
104#2585C2214yescomplemented
105#2577C2214yescomplemented
106#2577C2214yescomplemented
107#2577C2214yescomplemented
108#2575C2214yescomplemented
109#2575C2214yescomplemented
110#2574C2214yescomplemented
111#2570C2212yescomplemented
112#2570C2214yescomplemented
113#2569C2212yes—
114#2569C2214yes—
115#2569C2214yescomplemented
116#2565C2212yescomplemented
117#2565C2212yescomplemented
118#2562C2212yes—
119#2562C2211yescharacteristic
120#2562C2214yes—
121#2562C2212yes—
122#2562C2212yes—
123#2562C2211yescharacteristic
124#2562C2211yescharacteristic
125#2562C2212yes—
126#2562C2211yescharacteristic
127#2561C2214yes—
128#2550C2212yescomplemented
129#2549C2212yes—
130#2547C2212yes—
131#2542C2212yes—
132#2536C2212yes—
133#2536C2212yes—
134#2532C2214yescomplemented
135#2532C2214yescomplemented
136#2530C2214yescomplemented
137#2530C2214yescomplemented
138#2529C2214yescomplemented
139#2527C2214yescomplemented
140#2524C2214yescomplemented
141#2522C2214yescomplemented
142#2521C2214yes—
143#2520C2214yescomplemented
144#2516C2214yes—
145#2511C2214yescomplemented
146#2505C2214yes—
147#2505C2214yes—
148#2505C2214yescomplemented
149#2503C2212yes—
150#2502C2212yes—
151#2502C2212yes—
152#2497C2212yescomplemented
153#2497C2212yescomplemented
154#2496C2212yescomplemented
155#2496C2212yescomplemented
156#2495C2212yescomplemented
157#2495C2212yescomplemented
158#2494C2212yescomplemented
159#2494C2212yescomplemented
160#2493C2214yes—
161#2493C2214yes—
162#2493C2214yescomplemented
163#2492C2212yescomplemented
164#2492C2212yescomplemented
165#2489C2212yescomplemented
166#2489C2212yescomplemented
167#2484C2214yes—
168#2483C2214yes—
169#2482C2214yes—
170#2482C2214yes—
171#2480C2214yes—
172#2480C2214yes—
173#2478C2214yescomplemented
174#2474C2214yes—
175#2468C2214yes—
176#2468C2214yes—
177#2442C2212yes—
178#2440C2212yes—
179#2438C2214yes—
180#2438C2214yescomplemented
181#2437C2214yes—
182#2435C2212yes—
183#2423C2212yescomplemented
184#2423C2212yescomplemented
185#2421C2212yescomplemented
186#2421C2212yescomplemented
187#2402C2214yescomplemented
188#2395C2214yes—
189C2×#400C2212yes—
190C2×#394C2212yes—
191#2371C2214yescomplemented
192#2370C2214yescomplemented
193#2370C2212yescomplemented
194#2370C2212yescomplemented
195#2369C2212yescomplemented
196#2368C2214yes—
197#2368C2212yes—
198#2368C2212yes—
199#2365C2212yescomplemented
200#2360C2212yes—
201#2360C2212yes—
202#2357C2212yes—
203#2353C2212yes—
204#2353C2212yes—
205#2349C2212yes—
206#2345C2211yescharacteristic
207#2345C2211yescharacteristic
208#2345C2211yescharacteristic
209#2345C2211yescharacteristic
210#2344C2212yes—
211#2344C2211yescharacteristic
212#2344C2211yescharacteristic
213#2344C2212yes—
214#2343C2214yes—
215#2342C2212yes—
216#2342C2214yes—
217#2342C2212yes—
218#2342C2214yes—
219D4×C22⋊C4C2211yescharacteristic
220D4×C22⋊C4C2211yescharacteristic
221#2336C2214yescomplemented
222#2334C2214yescomplemented
223#2332C2214yescomplemented
224#2331C2212yescomplemented
225#2330C2212yescomplemented
226#2326C2214yes—
227#2323C2212yescomplemented
228#2323C2212yescomplemented
229#2314C2212yescomplemented
230#2314C2212yescomplemented
231#2313C2212yes—
232C4×#125C2212yescomplemented
233C4×#125C2212yescomplemented
234C4×#126C2214yescomplemented
235C4×C22⋊Q8C2212yescomplemented
236C4×C22⋊Q8C2212yescomplemented
237#2298C2214yescomplemented
238#2296C2212yes—
239#2295C2212yescomplemented
240#2295C2214yescomplemented
241#2293C2212yes—
242#2290C2212yes—
243#2290C2212yes—
244C2×#388C2214yes—
245#2285C2212yescomplemented
246#2283C2211yescharacteristic
247#2283C2211yescharacteristic
248#2283C2212yescomplemented
249#2280C2212yes—
250C2×#380C2212yes—
251C2×#380C2212yes—
252#2274C2212yes—
253C42×Q8C2212yescomplemented
254C42×D4C2212yes—
255C4×#117C2211yescharacteristic
256C4×#117C2212yes—
257C2×C4×C4⋊C4C2211yescharacteristic
258C2×C4×C22⋊C4C2212yes—
259C23×D4C2311yescharacteristic
260C24×C4C2312yes—
261#533—28no—
262C2×C4⋊Q8C2311yescharacteristic
263C2×C4⋊Q8C2311yescharacteristic
264C2×C4⋊Q8C2312yes—
265C2×#126C2314yes—
266C2×#126C2314yes—
267C2×#125—28no—
268C2×#125C2311yescharacteristic
269C2×#125C2311yescharacteristic
270C2×#125C2312yes—
271C2×#125C2311yescharacteristic
272C2×#125C2311yescharacteristic
273C2×#125C2312yes—
274C2×#125C2312yes—
275C2×#125C2312yes—
276C2×#124C2314yes—
277C2×C22⋊Q8C2312yes—
278C2×C22⋊Q8C2312yes—
279C2×C22⋊Q8C2314yes—
280C2×C22⋊Q8C2312yes—
281C2×C22⋊Q8C2312yes—
282C2×C22⋊Q8C2314yes—
283C2×C22⋊Q8C2312yes—
284C2×C22⋊Q8C2312yes—
285C2×C4×Q8C2312yes—
286C2×C4×Q8C2312yes—
287C2×C4×Q8C2312yes—
288C2×C4×Q8C2312yes—
289C2×C4×D4—28no—
290C2×C4×D4C2312yes—
291C2×C4×D4C2311yescharacteristic
292C2×C4×D4C2311yescharacteristic
293C2×C4×D4C2311yescharacteristic
294C2×C4×D4C2311yescharacteristic
295C2×C4×D4C2312yes—
296C2×C4×D4C2312yes—
297C2×C4×D4C2312yes—
298C2×#117C2312yes—
299C2×#117C2311yescharacteristic
300C2×#117C2312yes—
301C2×#117C2312yes—
302C2×#117C2312yes—
303C2×#117C2311yescharacteristic
304C2×#117C2314yes—
305C2×#117C2312yes—
306C22×C4⋊C4C2312yes—
307C22×C4⋊C4C2312yes—
308C22×C4⋊C4C2311yescharacteristic
309C22×C4⋊C4C2311yescharacteristic
310C22×C4⋊C4C2311yescharacteristic
311C22×C4⋊C4C2312yes—
312C22×C22⋊C4C2312yes—
313C22×C22⋊C4C2312yes—
314C22×C22⋊C4C2314yes—
315C22×C22⋊C4C2312yes—
316C22×C22⋊C4C2314yes—
317C22×C42C2312yes—
318C22×C42C2312yes—
319C22×C42C2312yes—
320C22×C42C2311yescharacteristic
321#401C2314yes—
322#401C2314yes—
323#400C2314yes—
324#400C2312yes—
325#400C2312yes—
326#400C2314yes—
327#400C2312yes—
328#400C2312yes—
329#400C2314yes—
330#400C2314yes—
331#400C2314yes—
332#400C2314yes—
333#400C2314yes—
334#400C2314yes—
335#400C2314yes—
336#400C2314yes—
337#400C2314yes—
338#400C2312yes—
339#400C2314yes—
340#400C2314yes—
341#400C2314yes—
342#400C2314yes—
343#400C2314yes—
344#400C2314yes—
345#400C2314yes—
346#400C2314yes—
347#400C2312yes—
348#400C2314yes—
349#400C2314yes—
350#400C2314yes—
351#400C2314yes—
352#400C2312yes—
353#400C2312yes—
354#399C2314yes—
355#399C2314yes—
356#399C2314yes—
357#399C2314yes—
358#399C2314yes—
359#398C2314yes—
360#398C2314yes—
361#398C2314yes—
362#398C2314yes—
363#398C2314yes—
364#398C2314yes—
365#398C2314yes—
366#398C2314yes—
367#398C2314yes—
368#398C2314yes—
369#398C2314yes—
370#398C2314yes—
371#398C2314yes—
372#398C2314yes—
373#398C2314yes—
374#398C2314yes—
375#398C2314yes—
376#398C2314yes—
377#398C2314yes—
378#398C2314yes—
379#397C2314yes—
380#397C2314yes—
381#397C2314yes—
382#397C2314yes—
383#397C2314yes—
384#397C2314yes—
385#397C2314yes—
386#397C2314yes—
387#397C2314yes—
388#397C2314yes—
389#397C2314yes—
390#397C2314yes—
391#397C2314yes—
392#397C2314yes—
393#397C2314yes—
394#397C2314yes—
395#396C2314yes—
396#396C2314yes—
397#396C2314yes—
398#396C2314yes—
399#395C2314yes—
400#395C2314yes—
401#395C2312yes—
402#395C2312yes—
403#395C2314yes—
404#395C2312yes—
405#395C2312yes—
406#394C2312yes—
407#394C2312yes—
408#394C2314yes—
409#394C2312yes—
410#394C2312yes—
411#394C2314yes—
412#394C2314yes—
413#394C2314yes—
414#393C2314yes—
415#393C2314yes—
416#393C2314yes—
417#391C2312yes—
418#391C2312yes—
419#391C2312yes—
420#391C2312yes—
421#391C2314yes—
422#391C2314yes—
423#391C2314yes—
424#391C2314yes—
425#391C2314yes—
426#391C2314yes—
427#391C2314yes—
428#391C2314yes—
429#391C2312yes—
430#391C2312yes—
431#391C2314yes—
432#390C2312yes—
433#390C2314yes—
434#390C2312yes—
435#389C2312yes—
436#389C2312yes—
437#389C2312yes—
438#389C2312yes—
439#389C2314yes—
440#389C2312yes—
441#389C2312yes—
442#389C2314yes—
443#389C2314yes—
444#389C2312yes—
445#389C2312yes—
446#389C2314yes—
447#389C2312yes—
448#389C2312yes—
449#389C2314yes—
450#389C2314yes—
451#389C2314yes—
452#389C2314yes—
453#389C2312yes—
454#389C2312yes—
455#389C2314yes—
456#389C2314yes—
457#389C2314yes—
458#389C2314yes—
459#388C2314yes—
460#388C2314yes—
461#388C2314yes—
462#388C2314yes—
463#388C2314yes—
464#388C2314yes—
465#388C2314yes—
466#388C2314yes—
467#388C2314yes—
468#388C2314yes—
469#388C2314yes—
470#388C2314yes—
471#388C2314yes—
472#388C2314yes—
473#388C2314yes—
474#388C2314yes—
475#388C2314yes—
476#388C2314yes—
477#388C2314yes—
478#388C2314yes—
479#388C2314yes—
480#388C2314yes—
481#388C2314yes—
482#388C2314yes—
483#388C2314yes—
484#388C2314yes—
485#388C2314yes—
486#388C2314yes—
487#388C2314yes—
488#388C2314yes—
489#388C2314yes—
490#388C2314yes—
491#388C2312yes—
492#388C2312yes—
493#388C2314yes—
494#388C2312yes—
495#388C2312yes—
496#388C2314yes—
497#388C2312yes—
498#388C2312yes—
499#388C2312yes—
500#388C2312yes—
501#387C2314yes—
502#387C2314yes—
503#387C2314yes—
504#387C2314yes—
505#387C2314yes—
506#387C2314yes—
507#387C2314yes—
508#387C2314yes—
509#387C2314yes—
510#387C2314yes—
511#387C2314yes—
512#387C2314yes—
513#387C2314yes—
514#387C2314yes—
515#387C2314yes—
516#387C2314yes—
517#387C2314yes—
518#387C2314yes—
519#387C2314yes—
520#387C2314yes—
521#387C2314yes—
522#387C2314yes—
523#387C2314yes—
524#387C2314yes—
525#387C2312yes—
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#387C2312yes—
552#387C2312yes—
553#387C2312yes—
554#387C2314yes—
555#387C2314yes—
556#387C2314yes—
557#386C2312yes—
558#386C2312yes—
559#386C2312yes—
560#386C2312yes—
561#385C2314yes—
562#385C2314yes—
563#385C2314yes—
564#385C2314yes—
565#385C2314yes—
566#385C2314yes—
567#385C2312yes—
568#385C2314yes—
569#385C2312yes—
570#385C2314yes—
571#385C2314yes—
572#385C2314yes—
573#385C2314yes—
574#385C2314yes—
575#385C2314yes—
576#385C2314yes—
577#385C2312yes—
578#385C2312yes—
579#385C2314yes—
580#385C2314yes—
581#385C2314yes—
582#385C2314yes—
583#384C2312yes—
584#384C2312yes—
585#384C2312yes—
586#384C2314yes—
587#383C2314yes—
588#383C2314yes—
589#383C2314yes—
590#383C2312yes—
591#383C2311yescharacteristic
592#383C2311yescharacteristic
593#382C2312yes—
594#382C2312yes—
595#382C2312yes—
596#382C2312yes—
597#382C2312yes—
598#382C2314yes—
599#382C2314yes—
600#382C2314yes—
601#381C2312yes—
602#381C2314yes—
603#381C2312yes—
604#381C2314yes—
605#381C2314yes—
606#381C2314yes—
607#381C2312yes—
608#381C2314yes—
609#381C2312yes—
610#381C2312yes—
611#381C2312yes—
612#380C2314yes—
613#380C2312yes—
614#380C2312yes—
615#380C2314yes—
616#380C2314yes—
617#380C2312yes—
618#380C2312yes—
619#380C2312yes—
620#380C2312yes—
621#380C2312yes—
622#380C2312yes—
623#380C2314yes—
624#380C2312yes—
625#380C2312yes—
626#380C2311yescharacteristic
627#380C2314yes—
628#380C2312yes—
629#380C2314yes—
630#380C2314yes—
631#380C2312yes—
632#380C2312yes—
633#380C2311yescharacteristic
634#380C2311yescharacteristic
635#380C2312yes—
636#380C2312yes—
637#380C2311yescharacteristic
638#380C2312yes—
639#380C2312yes—
640#380C2312yes—
641#379C2312yes—
642#379C2314yes—
643#379C2314yes—
644#379C2312yes—
645C4×C4⋊C4C2314yes—
646C4×C4⋊C4C2314yes—
647C4×C4⋊C4C2314yes—
648C4×C4⋊C4C2312yes—
649C4×C4⋊C4C2312yes—
650C4×C4⋊C4C2314yes—
651C4×C4⋊C4C2314yes—
652C4×C4⋊C4C2314yes—
653C4×C4⋊C4C2312yes—
654C4×C4⋊C4C2312yes—
655C4×C4⋊C4C2311yescharacteristic
656C4×C4⋊C4C2312yes—
657C4×C4⋊C4C2312yes—
658C4×C4⋊C4C2312yes—
659C4×C4⋊C4C2311yescharacteristic
660C4×C4⋊C4C2312yes—
661C4×C4⋊C4C2312yes—
662C4×C4⋊C4C2314yes—
663C4×C4⋊C4C2314yes—
664C4×C4⋊C4C2314yes—
665C4×C4⋊C4C2314yes—
666C4×C4⋊C4C2314yes—
667C4×C4⋊C4C2314yes—
668C4×C4⋊C4C2312yes—
669C4×C4⋊C4C2314yes—
670C4×C4⋊C4C2314yes—
671C4×C4⋊C4C2312yes—
672C4×C4⋊C4C2312yes—
673C4×C4⋊C4C2312yes—
674C4×C4⋊C4C2312yes—
675C4×C4⋊C4C2312yes—
676C4×C4⋊C4C2314yes—
677C4×C22⋊C4C2312yes—
678C4×C22⋊C4C2314yes—
679C4×C22⋊C4C2314yes—
680C4×C22⋊C4C2314yes—
681C4×C22⋊C4C2311yescharacteristic
682C4×C22⋊C4C2312yes—
683C4×C22⋊C4C2312yes—
684C4×C22⋊C4C2312yes—
685C4×C22⋊C4C2314yes—
686C4×C22⋊C4C2312yes—
687C4×C22⋊C4C2312yes—
688C4×C22⋊C4C2311yescharacteristic
689C4×C22⋊C4C2314yes—
690C4×C22⋊C4C2312yes—
691C4×C22⋊C4C2312yes—
692C4×C22⋊C4C2312yes—
693C4×C22⋊C4C2312yes—
694C4×C22⋊C4C2311yescharacteristic
695C4×C22⋊C4C2311yescharacteristic
696C4×C22⋊C4C2312yes—
697C4×C22⋊C4C2312yes—
698C4×C22⋊C4C2312yes—
699C4×C22⋊C4C2312yes—
700C4×C22⋊C4C2312yes—
701C4×C22⋊C4C2312yes—
702#376C2312yes—
703#376C2311yescharacteristic
704#376C2311yescharacteristic
705#376C2314yes—
706#376C2312yes—
707#376C2314yes—
708C2×#95C2312yes—
709C2×#95C2314yes—
710C2×#95C2312yes—
711C2×#95C2314yes—
712C2×#95C2312yes—
713C43C2314yes—
714C43C2312yes—
715C25C2412yes—
716C22×Q8C2412yes—
717C22×Q8C2412yes—
718C22×Q8C2414yes—
719C22×D4—24no—
720C22×D4—44no—
721C22×D4C2411yescharacteristic
722C22×D4C2412yes—
723C22×D4C2411yescharacteristic
724C23×C4—28no—
725C23×C4—44no—
726C23×C4—44no—
727C23×C4C2412yes—
728C23×C4C2412yes—
729C23×C4C2412yes—
730C23×C4C2412yes—
731C23×C4C2411yescharacteristic
732C23×C4C2411yescharacteristic
733C23×C4C2412yes—
734C23×C4C2414yes—
735C23×C4C2412yes—
736C23×C4C2412yes—
737C23×C4C2412yes—
738C23×C4C2412yes—
739C23×C4C2412yes—
740C23×C4C2412yes—
741C23×C4C2411yescharacteristic
742C4⋊Q8—24no—
743C4⋊Q8—24no—
744C4⋊Q8—44no—
745#126—48no—
746#126—48no—
747#125—24no—
748#125—24no—
749#125—28no—
750#125—28no—
751#125—24no—
752#125—24no—
753#125—28no—
754#125—44no—
755#124—48no—
756C22⋊Q8—28no—
757C22⋊Q8—28no—
758C22⋊Q8—48no—
759C22⋊Q8—48no—
760C22⋊Q8—44no—
761C22⋊Q8—44no—
762C22⋊Q8—44no—
763C22⋊Q8—44no—
764C4×Q8—28no—
765C4×Q8—28no—
766C4×Q8—44no—
767C4×Q8—44no—
768C4×D4—24no—
769C4×D4—24no—
770C4×D4—28no—
771C4×D4—24no—
772C4×D4—24no—
773C4×D4—28no—
774C4×D4—44no—
775C4×D4—44no—
776#117—28no—
777#117—24no—
778#117—28no—
779#117—44no—
780#117—44no—
781#117—42no—
782#117—48no—
783#117—44no—
784C2×C4⋊C4—24no—
785C2×C4⋊C4—24no—
786C2×C4⋊C4—28no—
787C2×C4⋊C4—28no—
788C2×C4⋊C4—24no—
789C2×C4⋊C4—44no—
790C2×C4⋊C4C2411yescharacteristic
791C2×C4⋊C4C2412yes—
792C2×C4⋊C4C2411yescharacteristic
793C2×C4⋊C4C2412yes—
794C2×C4⋊C4C2411yescharacteristic
795C2×C4⋊C4C2411yescharacteristic
796C2×C4⋊C4C2411yescharacteristic
797C2×C4⋊C4C2411yescharacteristic
798C2×C4⋊C4C2412yes—
799C2×C4⋊C4C2412yes—
800C2×C4⋊C4C2412yes—
801C2×C4⋊C4C2412yes—
802C2×C4⋊C4C2412yes—
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⋊C4C2414yes—
813C2×C4⋊C4C2414yes—
814C2×C4⋊C4C2414yes—
815C2×C4⋊C4C2412yes—
816C2×C4⋊C4C2412yes—
817C2×C4⋊C4C2412yes—
818C2×C4⋊C4C2412yes—
819C2×C4⋊C4C2414yes—
820C2×C4⋊C4C2412yes—
821C2×C4⋊C4C2414yes—
822C2×C4⋊C4C2412yes—
823C2×C4⋊C4C2412yes—
824C2×C4⋊C4C2412yes—
825C2×C4⋊C4C2412yes—
826C2×C4⋊C4C2414yes—
827C2×C4⋊C4C2414yes—
828C2×C4⋊C4C2412yes—
829C2×C4⋊C4C2412yes—
830C2×C4⋊C4C2414yes—
831C2×C4⋊C4C2414yes—
832C2×C4⋊C4C2414yes—
833C2×C4⋊C4C2414yes—
834C2×C4⋊C4C2414yes—
835C2×C4⋊C4C2414yes—
836C2×C4⋊C4C2414yes—
837C2×C4⋊C4C2414yes—
838C2×C4⋊C4C2414yes—
839C2×C4⋊C4C2414yes—
840C2×C4⋊C4C2414yes—
841C2×C4⋊C4C2414yes—
842C2×C4⋊C4C2414yes—
843C2×C4⋊C4C2414yes—
844C2×C4⋊C4C2414yes—
845C2×C4⋊C4C2414yes—
846C2×C4⋊C4C2414yes—
847C2×C4⋊C4C2414yes—
848C2×C4⋊C4C2414yes—
849C2×C4⋊C4C2414yes—
850C2×C4⋊C4C2414yes—
851C2×C22⋊C4—28no—
852C2×C22⋊C4—28no—
853C2×C22⋊C4—44no—
854C2×C22⋊C4—48no—
855C2×C22⋊C4—48no—
856C2×C22⋊C4C2411yescharacteristic
857C2×C22⋊C4C2414yes—
858C2×C22⋊C4C2412yes—
859C2×C22⋊C4C2412yes—
860C2×C22⋊C4C2412yes—
861C2×C22⋊C4C2412yes—
862C2×C22⋊C4C2412yes—
863C2×C22⋊C4C2414yes—
864C2×C22⋊C4C2412yes—
865C2×C22⋊C4C2412yes—
866C2×C22⋊C4C2412yes—
867C2×C22⋊C4C2411yescharacteristic
868C2×C22⋊C4C2412yes—
869C2×C22⋊C4C2414yes—
870C2×C22⋊C4C2414yes—
871C2×C22⋊C4C2411yescharacteristic
872C2×C22⋊C4C2412yes—
873C2×C22⋊C4C2412yes—
874C2×C22⋊C4C2412yes—
875C2×C22⋊C4C2414yes—
876C2×C22⋊C4C2414yes—
877C2×C22⋊C4C2412yes—
878C2×C22⋊C4C2412yes—
879C2×C22⋊C4C2414yes—
880C2×C22⋊C4C2414yes—
881C2×C22⋊C4C2414yes—
882C2×C22⋊C4C2414yes—
883C2×C22⋊C4C2414yes—
884C2×C22⋊C4C2412yes—
885C2×C22⋊C4C2412yes—
886C2×C22⋊C4C2412yes—
887C2×C22⋊C4C2412yes—
888C2×C22⋊C4C2412yes—
889C2×C22⋊C4C2412yes—
890C2×C22⋊C4C2414yes—
891C2×C22⋊C4C2414yes—
892C2×C22⋊C4C2414yes—
893C2×C22⋊C4C2414yes—
894C2×C22⋊C4C2414yes—
895C2×C22⋊C4C2414yes—
896C2×C22⋊C4C2411yescharacteristic
897C2×C42—44no—
898C2×C42—44no—
899C2×C42—44no—
900C2×C42#4118yes—
901C2×C42C2412yes—
902C2×C42C2414yes—
903C2×C42C2412yes—
904C2×C42C2412yes—
905C2×C42C2412yes—
906C2×C42C2414yes—
907C2×C42C2412yes—
908C2×C42C2412yes—
909C2×C42C2414yes—
910C2×C42C2414yes—
911C2×C42C2414yes—
912C2×C42C2412yes—
913C2×C42C2412yes—
914C2×C42C2414yes—
915C2×C42C2414yes—
916C2×C42C2414yes—
917C2×C42C2414yes—
918C2×C42C2414yes—
919C2×C42C2412yes—
920C2×C42C2412yes—
921C2×C42C2412yes—
922C2×C42C2412yes—
923C2×C42C2412yes—
924C2×C42C2412yes—
925C2×C42C2414yes—
926C2×C42C2411yescharacteristic
927C2×C42C2411yescharacteristic
928C2×C42C2411yescharacteristic
929C2×C42C2411yescharacteristic
930#95C2412yes—
931#95C2414yes—
932#95C2412yes—
933#95C2412yes—
934#95C2412yes—
935#95C2412yes—
936#95C2412yes—
937#95C2412yes—
938#95C2412yes—
939#95C2414yes—
940#95C2414yes—
941#95C2412yes—
942#95C2414yes—
943#95C2414yes—
944#95C2414yes—
945#95C2414yes—
946#95C2414yes—
947#95C2414yes—
948#95C2412yes—
949#95C2412yes—
950#95C2414yes—
951#95C2414yes—
952#95C2412yes—
953#95C2414yes—
954#95C2414yes—
955#95C2414yes—
956#95C2412yes—
957#95C2412yes—
958#95C2414yes—
959#95C2411yescharacteristic
960#95C2411yescharacteristic
961#95C2411yescharacteristic
962#95C2411yescharacteristic
963#95C2414yes—
964#95C2412yes—
965#95C2412yes—
966#95C2414yes—
967#95C2412yes—
968#95C2412yes—
969#95C2412yes—
970#95C2412yes—
971#95C2412yes—
972#95C2412yes—
973#95C2414yes—
974#95C2414yes—
975#95C2414yes—
976#95C2414yes—
977#95C2414yes—
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—
992#95C2414yes—
993#95C2414yes—
994#95C2414yes—
995#95C2414yes—
996#95C2414yes—
997#95C2414yes—
998#95C2414yes—
999#95C2414yes—
1000#95C2414yes—
1001#95C2414yes—
1002#95C2414yes—
1003#95C2414yes—
1004#95C2414yes—
1005#95C2414yes—
1006C24—24no—
1007C24—24no—
1008C24—24no—
1009C24—24no—
1010C24—42no—
1011C24—42no—
1012C24—42no—
1013C24C2512yes—
1014C24C2512yes—
1015C24C2511yescharacteristic
1016C2×Q8—24no—
1017C2×Q8—24no—
1018C2×Q8—24no—
1019C2×Q8—24no—
1020C2×Q8—44no—
1021C2×Q8—44no—
1022C2×Q8—44no—
1023C2×Q8—44no—
1024C2×D4—24no—
1025C2×D4—24no—
1026C2×D4—22no—
1027C2×D4—22no—
1028C2×D4—24no—
1029C2×D4—42no—
1030C2×D4—42no—
1031C2×D4—416no—
1032C22×C4—22no—
1033C22×C4—22no—
1034C22×C4—24no—
1035C22×C4—24no—
1036C22×C4—24no—
1037C22×C4—24no—
1038C22×C4—24no—
1039C22×C4—24no—
1040C22×C4—24no—
1041C22×C4—28no—
1042C22×C4—24no—
1043C22×C4—24no—
1044C22×C4—24no—
1045C22×C4—24no—
1046C22×C4—24no—
1047C22×C4—24no—
1048C22×C4—24no—
1049C22×C4—24no—
1050C22×C4—24no—
1051C22×C4—24no—
1052C22×C4—24no—
1053C22×C4—42no—
1054C22×C4—42no—
1055C22×C4—42no—
1056C22×C4—42no—
1057C22×C4—42no—
1058C22×C4—44no—
1059C22×C4—42no—
1060C22×C4—42no—
1061C22×C4—44no—
1062C22×C4—44no—
1063C22×C4—42no—
1064C22×C4—42no—
1065C22×C4—42no—
1066C22×C4—42no—
1067C22×C4—42no—
1068C22×C4—42no—
1069C22×C4—42no—
1070C22×C4—42no—
1071C22×C4—816no—
1072C22×C4C2×#4114yes—
1073C22×C4C2×#4114yes—
1074C22×C4C2×#4114yes—
1075C22×C4C2512yes—
1076C22×C4C2512yes—
1077C22×C4C2512yes—
1078C22×C4C2512yes—
1079C22×C4C2512yes—
1080C22×C4C2512yes—
1081C22×C4C2512yes—
1082C22×C4C2512yes—
1083C22×C4C2512yes—
1084C22×C4C2514yes—
1085C22×C4C2514yes—
1086C22×C4C2514yes—
1087C22×C4C2514yes—
1088C22×C4C2514yes—
1089C22×C4C2514yes—
1090C22×C4C2512yes—
1091C22×C4C2512yes—
1092C22×C4C2512yes—
1093C22×C4C2512yes—
1094C22×C4C2511yescharacteristic
1095C22×C4C2511yescharacteristic
1096C22×C4C2511yescharacteristic
1097C22×C4C2511yescharacteristic
1098C22×C4C2511yescharacteristic
1099C22×C4C2512yes—
1100C22×C4C2511yescharacteristic
1101C4⋊C4—22no—
1102C4⋊C4—22no—
1103C4⋊C4—24no—
1104C4⋊C4—24no—
1105C4⋊C4—24no—
1106C4⋊C4—24no—
1107C4⋊C4—24no—
1108C4⋊C4—24no—
1109C4⋊C4—24no—
1110C4⋊C4—24no—
1111C4⋊C4—24no—
1112C4⋊C4—24no—
1113C4⋊C4—24no—
1114C4⋊C4—22no—
1115C4⋊C4—22no—
1116C4⋊C4—22no—
1117C4⋊C4—22no—
1118C4⋊C4—24no—
1119C4⋊C4—24no—
1120C4⋊C4—28no—
1121C4⋊C4—28no—
1122C4⋊C4—24no—
1123C4⋊C4—24no—
1124C4⋊C4—24no—
1125C4⋊C4—28no—
1126C4⋊C4—24no—
1127C4⋊C4—24no—
1128C4⋊C4—24no—
1129C4⋊C4—24no—
1130C4⋊C4—44no—
1131C4⋊C4—42no—
1132C4⋊C4—42no—
1133C4⋊C4—42no—
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—44no—
1143C4⋊C4—44no—
1144C4⋊C4—44no—
1145C4⋊C4—44no—
1146C4⋊C4—44no—
1147C4⋊C4—44no—
1148C4⋊C4—44no—
1149C4⋊C4—44no—
1150C4⋊C4—44no—
1151C4⋊C4—44no—
1152C4⋊C4—44no—
1153C4⋊C4—44no—
1154C4⋊C4—44no—
1155C4⋊C4—44no—
1156C4⋊C4—44no—
1157C4⋊C4—44no—
1158C4⋊C4—44no—
1159C4⋊C4—44no—
1160C4⋊C4—44no—
1161C4⋊C4—44no—
1162C22⋊C4—28no—
1163C22⋊C4—24no—
1164C22⋊C4—22no—
1165C22⋊C4—24no—
1166C22⋊C4—22no—
1167C22⋊C4—28no—
1168C22⋊C4—24no—
1169C22⋊C4—28no—
1170C22⋊C4—22no—
1171C22⋊C4—24no—
1172C22⋊C4—28no—
1173C22⋊C4—24no—
1174C22⋊C4—24no—
1175C22⋊C4—28no—
1176C22⋊C4—24no—
1177C22⋊C4—24no—
1178C22⋊C4—24no—
1179C22⋊C4—24no—
1180C22⋊C4—24no—
1181C22⋊C4—24no—
1182C22⋊C4—44no—
1183C22⋊C4—44no—
1184C22⋊C4—44no—
1185C22⋊C4—44no—
1186C22⋊C4—44no—
1187C22⋊C4—42no—
1188C22⋊C4—42no—
1189C22⋊C4—44no—
1190C22⋊C4—42no—
1191C22⋊C4—42no—
1192C22⋊C4—42no—
1193C22⋊C4—42no—
1194C22⋊C4—42no—
1195C22⋊C4—42no—
1196C22⋊C4—44no—
1197C22⋊C4—44no—
1198C22⋊C4—44no—
1199C22⋊C4—44no—
1200C22⋊C4—44no—
1201C22⋊C4—44no—
1202C22⋊C42−1+414yes—
1203C42—28no—
1204C42—24no—
1205C42—28no—
1206C42—24no—
1207C42—24no—
1208C42—24no—
1209C42—24no—
1210C42—42no—
1211C42—42no—
1212C42—42no—
1213C42—42no—
1214C42—44no—
1215C42—42no—
1216C42—42no—
1217C42—42no—
1218C42—44no—
1219C42—44no—
1220C42—44no—
1221C42—42no—
1222C42—42no—
1223C42—44no—
1224C42—44no—
1225C42—44no—
1226C42—44no—
1227C42—44no—
1228C42C2×#4114yes—
1229C42C2×#4114yes—
1230C42C2×#4114yes—
1231C42C2×#4114yes—
1232C23—22no—
1233C23—22no—
1234C23—22no—
1235C23—22no—
1236C23—22no—
1237C23—22no—
1238C23—22no—
1239C23—22no—
1240C23—22no—
1241C23—22no—
1242C23—22no—
1243C23—22no—
1244C23—22no—
1245C23—22no—
1246C23—22no—
1247C23—48no—
1248C23—48no—
1249C23—48no—
1250C23—48no—
1251C23—84no—
1252C23—84no—
1253C23—84no—
1254C23C22×#4112yes—
1255C23C2×2−1+412yes—
1256C23#58514yes—
1257C23#58512yes—
1258C23C2611yescharacteristic
1259Q8—48no—
1260Q8—84no—
1261Q8—164no—
1262D4—28no—
1263D4—48no—
1264D4—44no—
1265C2×C4—21no—
1266C2×C4—21no—
1267C2×C4—22no—
1268C2×C4—21no—
1269C2×C4—22no—
1270C2×C4—21no—
1271C2×C4—22no—
1272C2×C4—22no—
1273C2×C4—22no—
1274C2×C4—28no—
1275C2×C4—28no—
1276C2×C4—24no—
1277C2×C4—24no—
1278C2×C4—22no—
1279C2×C4—22no—
1280C2×C4—22no—
1281C2×C4—22no—
1282C2×C4—22no—
1283C2×C4—22no—
1284C2×C4—22no—
1285C2×C4—22no—
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—22no—
1298C2×C4—22no—
1299C2×C4—22no—
1300C2×C4—24no—
1301C2×C4—24no—
1302C2×C4—24no—
1303C2×C4—22no—
1304C2×C4—24no—
1305C2×C4—24no—
1306C2×C4—24no—
1307C2×C4—22no—
1308C2×C4—22no—
1309C2×C4—22no—
1310C2×C4—24no—
1311C2×C4—24no—
1312C2×C4—24no—
1313C2×C4—24no—
1314C2×C4—24no—
1315C2×C4—24no—
1316C2×C4—24no—
1317C2×C4—22no—
1318C2×C4—22no—
1319C2×C4—24no—
1320C2×C4—22no—
1321C2×C4—22no—
1322C2×C4—22no—
1323C2×C4—22no—
1324C2×C4—24no—
1325C2×C4—24no—
1326C2×C4—22no—
1327C2×C4—22no—
1328C2×C4—24no—
1329C2×C4—22no—
1330C2×C4—22no—
1331C2×C4—44no—
1332C2×C4—48no—
1333C2×C4—48no—
1334C2×C4—48no—
1335C2×C4—48no—
1336C2×C4—84no—
1337C2×C4—84no—
1338C2×C4—84no—
1339C2×C4—88no—
1340C2×C4—84no—
1341C2×C4—84no—
1342C2×C4—84no—
1343C2×C4—84no—
1344C2×C4C22×#4112yes—
1345C2×C4C22×#4112yes—
1346C2×C4C22×#4112yes—
1347C2×C4C22×#4112yes—
1348C2×C4C22×#4112yes—
1349C2×C4C22×#4112yes—
1350C2×C4C2×2−1+414yes—
1351C2×C4#58514yes—
1352C22—24no—
1353C22—24no—
1354C22—22no—
1355C22—22no—
1356C22—24no—
1357C22—24no—
1358C22—24no—
1359C22—42no—
1360C22—42no—
1361C22—42no—
1362C22—42no—
1363C22—42no—
1364C22—42no—
1365C22—42no—
1366C22—42no—
1367C22—42no—
1368C22—42no—
1369C22—42no—
1370C22—816no—
1371C22#346114yes—
1372C22C23×#4111yescharacteristic
1373C22C22×2−1+411yescharacteristic
1374C22C2×#58512yes—
1375C22C2×#58512yes—
1376C22C2×#58511yescharacteristic
1377C4—24no—
1378C4—22no—
1379C4—22no—
1380C4—22no—
1381C4—22no—
1382C4—22no—
1383C4—42no—
1384C4—44no—
1385C4—42no—
1386C4—42no—
1387C4—42no—
1388C4—42no—
1389C4—44no—
1390C4—42no—
1391C4—44no—
1392C4—42no—
1393C4—44no—
1394C4—42no—
1395C4—42no—
1396C4—44no—
1397C4—42no—
1398C4—42no—
1399C4—44no—
1400C4—42no—
1401C4—42no—
1402C4#351014yes—
1403C2—24no—
1404C2—44no—
1405C2—82no—
1406C2C2×#346111yescharacteristic
1407C2C2×#351011yescharacteristic
1408C2#6281411yescharacteristic
1409C2#6302312yes—
1410C2#6302712yes—
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. #41746C2semidirect
2. #41394C2semidirect
3. #41098C2semidirect
5. #40322C2semidirect
6. #39274C2semidirect
7. #39271C2semidirect
8. #38706C2semidirect
9. #38469C2semidirect
10. #37963C2semidirect
11. #37960C2semidirect
12. #37853C2semidirect
13. #37850C2semidirect
14. #37582C2semidirect
15. #37540C2semidirect
16. #36344C2semidirect
17. #36190C2semidirect
18. #36167C2semidirect
19. #36035C2semidirect
22. #35235C2semidirect
23. #35183C2semidirect
24. #35110C2semidirect
25. #34898C2semidirect
27. #34239C2semidirect
28. #34145C2semidirect
33. #2866C22semidirect
34. #2865C22semidirect
35. #2857C22semidirect
37. #2855C22semidirect
38. #2855C22semidirect
39. #2851C22semidirect
42. #2839C22semidirect
44. #2822C22semidirect
45. #2807C22semidirect
46. #2798C22semidirect
48. #2794C22semidirect
49. #2794C22semidirect
50. #2789C22semidirect
51. #2787C22semidirect
52. #2783C22semidirect
53. #2777C22semidirect
54. #2773C22semidirect
55. #2771C22semidirect
56. #2758C22semidirect
58. #2747C22semidirect
59. #2747C22semidirect
60. #2745C22semidirect
61. #2744C22semidirect
62. #2742C22semidirect
63. #2739C22semidirect
64. #2738C22semidirect
65. #2722C22semidirect
68. #2689C22semidirect
69. #2666C22semidirect
70. #2666C22semidirect
71. #2660C22semidirect
72. #2660C22semidirect
73. #2655C22semidirect
74. #2655C22semidirect
75. #2654C22semidirect
78. #2650C22semidirect
79. #2642C22semidirect
80. #2642C22semidirect
82. #2634C22semidirect
83. #2634C22semidirect
86. #2629C22semidirect
87. #2628C22semidirect
90. #2625C22semidirect
91. #2625C22semidirect
92. #2606C22semidirect
93. #2605C22semidirect
94. #2605C22semidirect
95. #2596C22semidirect
96. #2596C22semidirect
97. #2596C22semidirect
99. #2594C22semidirect
100. #2594C22semidirect
102. #2589C22semidirect
103. #2588C22semidirect
104. #2585C22semidirect
105. #2577C22semidirect
106. #2577C22semidirect
107. #2577C22semidirect
108. #2575C22semidirect
109. #2575C22semidirect
110. #2574C22semidirect
111. #2570C22semidirect
112. #2570C22semidirect
115. #2569C22semidirect
116. #2565C22semidirect
117. #2565C22semidirect
128. #2550C22semidirect
134. #2532C22semidirect
135. #2532C22semidirect
136. #2530C22semidirect
137. #2530C22semidirect
138. #2529C22semidirect
139. #2527C22semidirect
140. #2524C22semidirect
141. #2522C22semidirect
143. #2520C22semidirect
145. #2511C22semidirect
148. #2505C22semidirect
152. #2497C22semidirect
153. #2497C22semidirect
154. #2496C22semidirect
155. #2496C22semidirect
156. #2495C22semidirect
157. #2495C22semidirect
158. #2494C22semidirect
159. #2494C22semidirect
162. #2493C22semidirect
163. #2492C22semidirect
164. #2492C22semidirect
165. #2489C22semidirect
166. #2489C22semidirect
173. #2478C22semidirect
180. #2438C22semidirect
183. #2423C22semidirect
184. #2423C22semidirect
185. #2421C22semidirect
186. #2421C22semidirect
187. #2402C22semidirect
191. #2371C22semidirect
192. #2370C22semidirect
193. #2370C22semidirect
194. #2370C22semidirect
195. #2369C22semidirect
199. #2365C22semidirect
221. #2336C22semidirect
222. #2334C22semidirect
223. #2332C22semidirect
224. #2331C22semidirect
225. #2330C22semidirect
227. #2323C22semidirect
228. #2323C22semidirect
229. #2314C22semidirect
230. #2314C22semidirect
232. C4×#125C22semidirect
233. C4×#125C22semidirect
234. C4×#126C22semidirect
235. C4×C22⋊Q8C22semidirect
236. C4×C22⋊Q8C22semidirect
237. #2298C22semidirect
239. #2295C22semidirect
240. #2295C22semidirect
245. #2285C22semidirect
248. #2283C22semidirect
253. C42×Q8C22semidirect

Maximal subgroups

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

subgroupindex
#417462
#413942
#410982
#405442
#403222
#392742
#392712
#387062
#384692
#379632
#379602
#378532
#378502
#375822
#375402
#363442
#361902
#361672
#360352
#357312
#352402
#352352
#351832
#351102
#348982
C2×#25622
#342392
#341452
#341262