Finite Group Databasebeta

← #7656611

Subgroups — #7656611

Order 512.

4600 conjugacy classes of subgroups.

The subgroup lattice has 1444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42705C212yesmaximal, complemented
2#42702C212yesmaximal, complemented
3#42701C212yesmaximal, complemented
4#42698C212yesmaximal, complemented
5#41764C214yesmaximal, complemented
6#41760C214yesmaximal, complemented
7#41759C214yesmaximal, complemented
8#41755C214yesmaximal, complemented
9#39798C212yesmaximal, complemented
10#39768C211yesmaximal, characteristic
11#39670C212yesmaximal, complemented
12#39640C211yesmaximal, characteristic, complemented
13#38983C212yesmaximal, complemented
14#38223C214yesmaximal, complemented
15#37617C212yesmaximal, complemented
16#37525C214yesmaximal, complemented
17#36580C211yesmaximal, characteristic
18#36545C211yesmaximal, characteristic, complemented
19#36233C212yesmaximal, complemented
20#35973C212yesmaximal, complemented
21#35959C212yesmaximal, complemented
22#35938C212yesmaximal, complemented
23#35870C212yesmaximal, complemented
24#35103C211yesmaximal, characteristic
25#35098C212yesmaximal, complemented
26#34595C211yesmaximal, characteristic, complemented
27#34584C212yesmaximal, complemented
28#34230C212yesmaximal, complemented
29C2×#2365C211yesmaximal, characteristic, complemented
30C2×#559C2211yescharacteristic
31C2×#557C2211yescharacteristic
32C2×#556C2212yes—
33C22×C4⋊Q8C2211yescharacteristic
34C2×#529C2212yes—
35C22×C4×Q8C2211yescharacteristic
36C22×C4×Q8C2211yescharacteristic
37#2857C2211yescharacteristic
38#2856C2211yescharacteristic
39#2852C2214yes—
40#2851C2212yes—
41#2850C2212yes—
42#2850C2212yes—
43#2839C2214yes—
44#2838C2214yes—
45#2837C2214yes—
46#2836C2214yes—
47#2821C2214yes—
48#2821C2214yes—
49#2808C2212yes—
50#2806C2212yes—
51#2805C2212yes—
52#2804C2212yes—
53#2788C2214yes—
54#2777C2214yes—
55#2775C2214yes—
56#2774C2214yes—
57#2774C2214yes—
58#2773C2214yes—
59#2768C2214yes—
60#2767C2214yes—
61#2766C2214yes—
62#2759C2214yes—
63#2758C2214yes—
64#2751C2214yes—
65#2748C2214yes—
66#2747C2214yes—
67#2745C2214yes—
68#2745C2214yes—
69#2743C2214yes—
70#2742C2214yes—
71#2741C2214yes—
72#2740C2214yes—
73#2738C2214yes—
74#2738C2214yes—
75#2667C2214yes—
76#2666C2212yes—
77#2666C2212yes—
78#2666C2212yes—
79#2666C2212yes—
80#2666C2214yes—
81#2664C2214yes—
82#2663C2214yes—
83#2659C2211yescharacteristic
84#2659C2211yescharacteristic
85#2658C2212yes—
86#2658C2212yes—
87#2655C2214yes—
88#2655C2214yes—
89#2654C2214yes—
90#2654C2214yes—
91#2652C2214yes—
92#2651C2214yes—
93#2650C2214yes—
94#2649C2214yes—
95#2646C2212yes—
96#2646C2212yes—
97#2643C2214yes—
98#2642C2212yes—
99#2642C2212yes—
100#2639C2212yes—
101#2628C2214yes—
102#2628C2214yes—
103#2627C2211yescharacteristic
104#2627C2211yescharacteristic
105#2627C2212yes—
106#2623C2214yes—
107#2623C2214yes—
108#2618C2212yes—
109#2618C2212yes—
110#2611C2214yes—
111#2604C2214yes—
112#2604C2214yes—
113#2601C2214yes—
114#2601C2214yes—
115#2599C2214yes—
116#2592C2212yes—
117#2592C2212yes—
118#2592C2212yes—
119#2590C2214yes—
120#2585C2214yes—
121#2584C2212yes—
122#2582C2211yescharacteristic
123#2582C2211yescharacteristic
124#2581C2212yes—
125#2581C2212yes—
126#2580C2212yes—
127#2577C2214yes—
128#2573C2214yes—
129#2568C2212yes—
130#2568C2212yes—
131#2566C2212yes—
132#2565C2212yes—
133#2564C2214yes—
134#2556C2214yes—
135#2556C2214yes—
136#2553C2214yes—
137#2553C2214yes—
138#2548C2211yescharacteristic
139#2547C2212yes—
140#2547C2212yes—
141#2547C2212yes—
142#2546C2212yes—
143#2546C2212yes—
144#2546C2212yes—
145#2546C2211yescharacteristic
146#2545C2212yes—
147#2545C2212yes—
148#2545C2212yes—
149#2544C2212yes—
150#2544C2212yes—
151#2533C2214yes—
152#2533C2214yes—
153#2530C2214yes—
154#2528C2214yes—
155#2525C2214yes—
156#2524C2214yes—
157#2522C2214yes—
158#2521C2214yes—
159#2521C2214yes—
160#2520C2214yes—
161#2519C2214yes—
162#2519C2214yes—
163#2516C2214yes—
164#2515C2214yes—
165#2514C2212yes—
166#2514C2212yes—
167#2511C2212yes—
168#2511C2212yes—
169#2510C2214yes—
170#2505C2214yes—
171#2505C2214yes—
172#2498C2214yes—
173#2493C2214yes—
174#2487C2214yes—
175#2487C2214yes—
176#2481C2214yes—
177#2473C2214yes—
178#2469C2214yes—
179#2465C2214yes—
180#2462C2214yes—
181#2458C2214yes—
182#2450C2214yes—
183#2449C2214yes—
184#2448C2212yes—
185#2448C2212yes—
186#2447C2212yes—
187#2447C2212yes—
188#2446C2212yes—
189#2446C2212yes—
190#2446C2212yes—
191#2446C2212yes—
192#2444C2214yes—
193#2443C2214yes—
194#2436C2212yes—
195#2436C2212yes—
196#2434C2212yes—
197#2434C2212yes—
198#2402C2214yes—
199#2402C2212yes—
200#2402C2212yes—
201#2401C2214yes—
202#2399C2212yes—
203#2399C2212yes—
204#2396C2214yes—
205#2395C2214yes—
206#2370C2212yes—
207#2370C2212yes—
208#2367C2212yes—
209#2367C2212yes—
210#2367C2212yes—
211#2367C2212yes—
212#2365C2214yes—
213#2365C2212yes—
214#2365C2212yes—
215#2365C2212yes—
216#2365C2214yes—
217#2365C2212yes—
218#2365C2212yes—
219#2365C2212yes—
220#2361C2212yes—
221#2361C2212yes—
222#2360C2212yes—
223#2360C2212yes—
224#2356C2212yes—
225#2355C2211yescharacteristic
226#2355C2211yescharacteristic
227#2353C2214yes—
228#2349C2214yes—
229#2347C2214yes—
230#2343C2214yes—
231#2334C2214yes—
232#2334C2214yes—
233#2329C2212yes—
234#2325C2212yes—
235#2325C2212yes—
236#2325C2212yes—
237#2320C2212yes—
238#2319C2212yes—
239#2318C2214yes—
240C4×C22⋊Q8C2212yes—
241C4×C22⋊Q8C2212yes—
242C4×C22⋊Q8C2211yescharacteristic
243C4×C22⋊Q8C2211yescharacteristic
244C4×#123C2214yes—
245C4×#123C2214yes—
246C4×#121C2212yes—
247C2×#391C2211yescharacteristic
248C2×#391C2211yescharacteristic
249C2×#389C2212yes—
250#2290C2214yes—
251C2×#387C2212yes—
252C2×#387C2212yes—
253#2283C2212yes—
254#2276C2212yes—
255#2275C2212yes—
256C2×C4×C4⋊C4C2212yes—
257C2×C4×C4⋊C4C2211yescharacteristic
258C2×C4×C4⋊C4C2211yescharacteristic
259C23×Q8C2311yescharacteristic
260C23×Q8C2311yescharacteristic
261#559—44no—
262#557—44no—
263#556—48no—
264C2×C4⋊Q8—28no—
265C2×C4⋊Q8C2314yes—
266C2×C4⋊Q8C2312yes—
267C2×C4⋊Q8C2312yes—
268C2×C4⋊Q8C2312yes—
269C2×C4⋊Q8C2312yes—
270C2×C4⋊Q8C2311yescharacteristic
271C2×C4⋊Q8C2312yes—
272C2×C4⋊Q8C2312yes—
273C2×#127C2311yescharacteristic
274#529—216no—
275C2×#126C2314yes—
276C2×#126C2314yes—
277C2×#126C2314yes—
278C2×#125C2312yes—
279C2×#125C2312yes—
280C2×#125C2314yes—
281C2×#124C2312yes—
282C2×#124C2312yes—
283C2×#124C2312yes—
284C2×#124C2312yes—
285C2×#124C2312yes—
286C2×#124C2312yes—
287C2×#124C2312yes—
288C2×#123C2314yes—
289C2×#123C2314yes—
290C2×C22⋊Q8C2311yescharacteristic
291C2×C22⋊Q8C2312yes—
292C2×C22⋊Q8C2311yescharacteristic
293C2×C22⋊Q8C2314yes—
294C2×C22⋊Q8C2312yes—
295C2×#121C2312yes—
296C2×#121C2312yes—
297C2×#121C2312yes—
298C2×C4×Q8—44no—
299C2×C4×Q8—44no—
300C2×C4×Q8C2312yes—
301C2×C4×Q8C2311yescharacteristic
302C2×C4×Q8C2311yescharacteristic
303C2×C4×Q8C2312yes—
304C2×C4×Q8C2312yes—
305C2×C4×Q8C2311yescharacteristic
306C2×C4×Q8C2312yes—
307C2×C4×Q8C2312yes—
308C2×C4×Q8C2312yes—
309C2×C4×Q8C2312yes—
310C2×C4×Q8C2312yes—
311C2×C4×Q8C2311yescharacteristic
312C2×C4×Q8C2311yescharacteristic
313C2×C4×Q8C2311yescharacteristic
314C2×C4×Q8C2314yes—
315C2×C4×Q8C2312yes—
316C2×C4×D4C2312yes—
317C2×C4×D4C2314yes—
318C2×C4×D4C2312yes—
319C2×C4×D4C2312yes—
320C2×C4×D4C2314yes—
321C2×C4×D4C2314yes—
322C2×C4×D4C2312yes—
323C2×#117C2314yes—
324C2×#117C2314yes—
325C22×C4⋊C4C2311yescharacteristic
326C22×C4⋊C4C2311yescharacteristic
327C22×C4⋊C4C2312yes—
328C22×C4⋊C4C2312yes—
329C22×C4⋊C4C2311yescharacteristic
330C22×C4⋊C4C2311yescharacteristic
331C22×C4⋊C4C2312yes—
332C22×C4⋊C4C2312yes—
333C22×C42C2311yescharacteristic
334C22×C42C2312yes—
335C22×C42C2312yes—
336C22×C42C2311yescharacteristic
337C22×C42C2312yes—
338C22×C42C2311yescharacteristic
339#401C2314yes—
340#401C2314yes—
341#400C2314yes—
342#400C2314yes—
343#400C2314yes—
344#400C2314yes—
345#400C2314yes—
346#400C2314yes—
347#400C2314yes—
348#400C2314yes—
349#400C2312yes—
350#400C2314yes—
351#400C2314yes—
352#400C2314yes—
353#400C2314yes—
354#400C2314yes—
355#400C2314yes—
356#400C2314yes—
357#400C2314yes—
358#400C2314yes—
359#400C2314yes—
360#400C2314yes—
361#400C2312yes—
362#400C2312yes—
363#400C2312yes—
364#400C2314yes—
365#400C2314yes—
366#400C2314yes—
367#400C2314yes—
368#400C2312yes—
369#400C2312yes—
370#400C2312yes—
371#400C2312yes—
372#399C2314yes—
373#399C2314yes—
374#399C2314yes—
375#399C2314yes—
376#399C2314yes—
377#399C2314yes—
378#399C2314yes—
379#399C2314yes—
380#399C2314yes—
381#399C2314yes—
382#398C2314yes—
383#398C2314yes—
384#398C2314yes—
385#398C2314yes—
386#398C2314yes—
387#398C2314yes—
388#398C2312yes—
389#398C2314yes—
390#398C2314yes—
391#398C2314yes—
392#398C2312yes—
393#398C2314yes—
394#398C2314yes—
395#398C2314yes—
396#398C2312yes—
397#398C2314yes—
398#398C2312yes—
399#398C2314yes—
400#398C2312yes—
401#398C2312yes—
402#398C2312yes—
403#398C2312yes—
404#398C2312yes—
405#398C2312yes—
406#398C2312yes—
407#398C2314yes—
408#398C2312yes—
409#398C2312yes—
410#398C2312yes—
411#398C2312yes—
412#398C2312yes—
413#397C2314yes—
414#397C2314yes—
415#397C2314yes—
416#397C2314yes—
417#397C2314yes—
418#397C2314yes—
419#397C2314yes—
420#397C2314yes—
421#397C2314yes—
422#397C2314yes—
423#397C2314yes—
424#397C2314yes—
425#397C2314yes—
426#397C2314yes—
427#396C2314yes—
428#396C2314yes—
429#396C2314yes—
430#396C2314yes—
431#396C2314yes—
432#396C2314yes—
433#396C2314yes—
434#396C2314yes—
435#395C2312yes—
436#395C2314yes—
437#395C2314yes—
438#395C2314yes—
439#395C2314yes—
440#395C2314yes—
441#395C2312yes—
442#395C2312yes—
443#395C2312yes—
444#395C2312yes—
445#395C2312yes—
446#395C2312yes—
447#395C2312yes—
448#394C2314yes—
449#394C2314yes—
450#394C2314yes—
451#394C2314yes—
452#394C2314yes—
453#393C2314yes—
454#393C2314yes—
455#393C2314yes—
456#393C2314yes—
457#393C2314yes—
458#393C2314yes—
459#391C2312yes—
460#391C2312yes—
461#391C2312yes—
462#391C2312yes—
463#391C2312yes—
464#391C2314yes—
465#391C2312yes—
466#391C2312yes—
467#391C2314yes—
468#391C2312yes—
469#391C2311yescharacteristic
470#391C2312yes—
471#391C2312yes—
472#391C2312yes—
473#391C2312yes—
474#391C2311yescharacteristic
475#391C2312yes—
476#391C2312yes—
477#391C2312yes—
478#391C2312yes—
479#391C2312yes—
480#391C2312yes—
481#391C2314yes—
482#391C2312yes—
483#391C2312yes—
484#391C2312yes—
485#390C2312yes—
486#390C2312yes—
487#390C2312yes—
488#390C2312yes—
489#390C2312yes—
490#390C2312yes—
491#390C2312yes—
492#390C2312yes—
493#389C2314yes—
494#389C2312yes—
495#389C2312yes—
496#389C2312yes—
497#389C2312yes—
498#389C2311yescharacteristic
499#389C2312yes—
500#389C2314yes—
501#389C2312yes—
502#389C2312yes—
503#389C2314yes—
504#389C2312yes—
505#389C2311yescharacteristic
506#389C2314yes—
507#389C2314yes—
508#389C2312yes—
509#389C2314yes—
510#389C2314yes—
511#389C2314yes—
512#389C2314yes—
513#389C2314yes—
514#389C2314yes—
515#389C2314yes—
516#389C2312yes—
517#389C2314yes—
518#389C2314yes—
519#389C2314yes—
520#389C2314yes—
521#389C2312yes—
522#388C2314yes—
523#388C2314yes—
524#388C2314yes—
525#388C2314yes—
526#388C2314yes—
527#388C2314yes—
528#388C2314yes—
529#388C2314yes—
530#388C2314yes—
531#388C2314yes—
532#388C2314yes—
533#388C2314yes—
534#388C2314yes—
535#388C2314yes—
536#388C2314yes—
537#388C2314yes—
538#388C2314yes—
539#388C2314yes—
540#388C2314yes—
541#388C2314yes—
542#388C2314yes—
543#388C2314yes—
544#388C2314yes—
545#388C2314yes—
546#388C2314yes—
547#388C2314yes—
548#388C2314yes—
549#388C2314yes—
550#387C2314yes—
551#387C2314yes—
552#387C2314yes—
553#387C2314yes—
554#387C2314yes—
555#387C2314yes—
556#387C2314yes—
557#387C2314yes—
558#387C2314yes—
559#387C2314yes—
560#387C2314yes—
561#387C2314yes—
562#387C2314yes—
563#387C2314yes—
564#387C2314yes—
565#387C2314yes—
566#387C2314yes—
567#387C2314yes—
568#387C2314yes—
569#387C2314yes—
570#387C2314yes—
571#387C2314yes—
572#387C2314yes—
573#387C2314yes—
574#387C2314yes—
575#387C2314yes—
576#387C2314yes—
577#387C2314yes—
578#387C2314yes—
579#387C2314yes—
580#387C2314yes—
581#387C2314yes—
582#387C2314yes—
583#387C2312yes—
584#387C2314yes—
585#387C2312yes—
586#387C2314yes—
587#387C2314yes—
588#387C2314yes—
589#387C2314yes—
590#387C2314yes—
591#387C2314yes—
592#387C2314yes—
593#387C2314yes—
594#387C2312yes—
595#387C2312yes—
596#386C2314yes—
597#386C2314yes—
598#386C2314yes—
599#386C2314yes—
600#386C2314yes—
601#386C2314yes—
602#386C2314yes—
603#386C2314yes—
604#386C2314yes—
605#386C2314yes—
606#386C2314yes—
607#386C2314yes—
608#385C2314yes—
609#385C2314yes—
610#385C2314yes—
611#385C2314yes—
612#385C2314yes—
613#385C2312yes—
614#385C2314yes—
615#385C2314yes—
616#385C2314yes—
617#385C2314yes—
618#385C2314yes—
619#385C2314yes—
620#385C2314yes—
621#385C2314yes—
622#385C2314yes—
623#385C2314yes—
624#385C2314yes—
625#385C2312yes—
626#385C2312yes—
627#385C2312yes—
628#384C2311yescharacteristic
629#384C2311yescharacteristic
630#383C2312yes—
631#383C2312yes—
632#383C2314yes—
633#383C2314yes—
634#383C2314yes—
635#383C2314yes—
636#382C2312yes—
637#382C2314yes—
638#382C2314yes—
639#382C2314yes—
640#382C2312yes—
641#382C2312yes—
642#382C2312yes—
643#382C2312yes—
644#381C2314yes—
645#381C2314yes—
646#381C2314yes—
647#381C2312yes—
648#381C2312yes—
649#380C2314yes—
650#380C2314yes—
651#380C2314yes—
652#380C2314yes—
653#380C2314yes—
654#380C2311yescharacteristic
655#380C2312yes—
656#380C2312yes—
657#380C2312yes—
658#380C2312yes—
659#380C2311yescharacteristic
660#380C2312yes—
661#380C2314yes—
662#380C2314yes—
663C4×C4⋊C4C2312yes—
664C4×C4⋊C4C2312yes—
665C4×C4⋊C4C2312yes—
666C4×C4⋊C4C2312yes—
667C4×C4⋊C4C2314yes—
668C4×C4⋊C4C2312yes—
669C4×C4⋊C4C2312yes—
670C4×C4⋊C4C2314yes—
671C4×C4⋊C4C2314yes—
672C4×C4⋊C4C2314yes—
673C4×C4⋊C4C2312yes—
674C4×C4⋊C4C2314yes—
675C4×C4⋊C4C2312yes—
676C4×C4⋊C4C2312yes—
677C4×C4⋊C4C2314yes—
678C4×C4⋊C4C2312yes—
679C4×C4⋊C4C2312yes—
680C4×C4⋊C4C2311yescharacteristic
681C4×C4⋊C4C2311yescharacteristic
682C4×C4⋊C4C2312yes—
683C4×C4⋊C4C2312yes—
684C4×C4⋊C4C2314yes—
685C4×C4⋊C4C2314yes—
686C4×C4⋊C4C2314yes—
687C4×C4⋊C4C2314yes—
688C4×C4⋊C4C2314yes—
689C4×C4⋊C4C2314yes—
690C4×C4⋊C4C2312yes—
691C4×C4⋊C4C2312yes—
692C4×C4⋊C4C2312yes—
693C4×C4⋊C4C2312yes—
694C4×C4⋊C4C2312yes—
695C4×C4⋊C4C2312yes—
696C4×C22⋊C4C2314yes—
697C4×C22⋊C4C2314yes—
698C4×C22⋊C4C2314yes—
699C4×C22⋊C4C2314yes—
700C4×C22⋊C4C2314yes—
701C4×C22⋊C4C2314yes—
702C4×C22⋊C4C2314yes—
703C4×C22⋊C4C2312yes—
704C4×C22⋊C4C2312yes—
705C4×C22⋊C4C2314yes—
706C4×C22⋊C4C2314yes—
707#376C2312yes—
708#376C2312yes—
709#376C2314yes—
710#376C2314yes—
711C2×#95C2314yes—
712C2×#95C2312yes—
713C2×#95C2311yescharacteristic
714C2×#95C2311yescharacteristic
715C2×#95C2312yes—
716C2×#95C2312yes—
717C2×#95C2312yes—
718C2×#95C2312yes—
719C22×Q8—24no—
720C22×Q8—24no—
721C22×Q8—42no—
722C22×Q8—42no—
723C22×Q8—42no—
724C22×Q8—42no—
725C22×Q8C2412yes—
726C22×Q8C2411yescharacteristic
727C22×Q8C2412yes—
728C22×Q8C2411yescharacteristic
729C22×Q8C2411yescharacteristic
730C22×Q8C2412yes—
731C22×Q8C2412yes—
732C22×Q8C2411yescharacteristic
733C22×Q8C2412yes—
734C22×D4C2414yes—
735C22×D4C2412yes—
736C22×D4C2412yes—
737C22×D4C2412yes—
738C23×C4C2412yes—
739C23×C4C2411yescharacteristic
740C23×C4C2411yescharacteristic
741C23×C4C2411yescharacteristic
742C23×C4C2411yescharacteristic
743C23×C4C2412yes—
744C23×C4C2412yes—
745C23×C4C2412yes—
746C23×C4C2411yescharacteristic
747C23×C4C2414yes—
748C23×C4C2414yes—
749C23×C4C2414yes—
750C23×C4C2411yescharacteristic
751C23×C4C2411yescharacteristic
752C4⋊Q8—216no—
753C4⋊Q8—28no—
754C4⋊Q8—28no—
755C4⋊Q8—44no—
756C4⋊Q8—44no—
757C4⋊Q8—44no—
758C4⋊Q8—42no—
759C4⋊Q8—44no—
760#127—42no—
761#126—216no—
762#126—48no—
763#126—48no—
764#125—28no—
765#125—44no—
766#125—48no—
767#124—28no—
768#124—44no—
769#124—44no—
770#124—44no—
771#124—44no—
772#124—44no—
773#124—44no—
774#123—216no—
775#123—48no—
776C22⋊Q8—28no—
777C22⋊Q8—24no—
778C22⋊Q8—24no—
779C22⋊Q8—44no—
780C22⋊Q8—48no—
781#121—28no—
782#121—28no—
783#121—44no—
784C4×Q8—28no—
785C4×Q8—24no—
786C4×Q8—24no—
787C4×Q8—28no—
788C4×Q8—28no—
789C4×Q8—44no—
790C4×Q8—44no—
791C4×Q8—42no—
792C4×Q8—42no—
793C4×Q8—48no—
794C4×Q8—44no—
795C4×Q8—44no—
796C4×Q8—44no—
797C4×Q8—42no—
798C4×Q8—42no—
799C4×Q8—44no—
800C4×D4—216no—
801C4×D4—28no—
802C4×D4—28no—
803C4×D4—44no—
804C4×D4—44no—
805C4×D4—48no—
806C4×D4—48no—
807#117—216no—
808#117—48no—
809C2×C4⋊C4—28no—
810C2×C4⋊C4—28no—
811C2×C4⋊C4—24no—
812C2×C4⋊C4—24no—
813C2×C4⋊C4—42no—
814C2×C4⋊C4—44no—
815C2×C4⋊C4—44no—
816C2×C4⋊C4—42no—
817C2×C4⋊C4C2412yes—
818C2×C4⋊C4C2412yes—
819C2×C4⋊C4C2411yescharacteristic
820C2×C4⋊C4C2414yes—
821C2×C4⋊C4C2412yes—
822C2×C4⋊C4C2412yes—
823C2×C4⋊C4C2414yes—
824C2×C4⋊C4C2414yes—
825C2×C4⋊C4C2414yes—
826C2×C4⋊C4C2414yes—
827C2×C4⋊C4C2412yes—
828C2×C4⋊C4C2412yes—
829C2×C4⋊C4C2414yes—
830C2×C4⋊C4C2414yes—
831C2×C4⋊C4C2412yes—
832C2×C4⋊C4C2414yes—
833C2×C4⋊C4C2412yes—
834C2×C4⋊C4C2414yes—
835C2×C4⋊C4C2414yes—
836C2×C4⋊C4C2412yes—
837C2×C4⋊C4C2412yes—
838C2×C4⋊C4C2411yescharacteristic
839C2×C4⋊C4C2411yescharacteristic
840C2×C4⋊C4C2412yes—
841C2×C4⋊C4C2412yes—
842C2×C4⋊C4C2414yes—
843C2×C4⋊C4C2412yes—
844C2×C4⋊C4C2412yes—
845C2×C4⋊C4C2412yes—
846C2×C4⋊C4C2412yes—
847C2×C4⋊C4C2412yes—
848C2×C4⋊C4C2414yes—
849C2×C4⋊C4C2411yescharacteristic
850C2×C4⋊C4C2414yes—
851C2×C4⋊C4C2414yes—
852C2×C4⋊C4C2412yes—
853C2×C4⋊C4C2411yescharacteristic
854C2×C4⋊C4C2412yes—
855C2×C4⋊C4C2412yes—
856C2×C4⋊C4C2414yes—
857C2×C4⋊C4C2412yes—
858C2×C4⋊C4C2412yes—
859C2×C4⋊C4C2414yes—
860C2×C4⋊C4C2412yes—
861C2×C4⋊C4C2412yes—
862C2×C4⋊C4C2412yes—
863C2×C4⋊C4C2412yes—
864C2×C4⋊C4C2412yes—
865C2×C4⋊C4C2414yes—
866C2×C4⋊C4C2414yes—
867C2×C4⋊C4C2414yes—
868C2×C4⋊C4C2414yes—
869C2×C4⋊C4C2414yes—
870C2×C4⋊C4C2414yes—
871C2×C4⋊C4C2411yescharacteristic
872C2×C4⋊C4C2412yes—
873C2×C4⋊C4C2412yes—
874C2×C4⋊C4C2412yes—
875C2×C4⋊C4C2412yes—
876C2×C4⋊C4C2412yes—
877C2×C4⋊C4C2412yes—
878C2×C4⋊C4C2411yescharacteristic
879C2×C4⋊C4C2412yes—
880C2×C4⋊C4C2414yes—
881C2×C4⋊C4C2414yes—
882C2×C4⋊C4C2412yes—
883C2×C4⋊C4C2412yes—
884C2×C4⋊C4C2412yes—
885C2×C4⋊C4C2412yes—
886C2×C4⋊C4C2411yescharacteristic
887C2×C22⋊C4C2414yes—
888C2×C22⋊C4C2414yes—
889C2×C22⋊C4C2412yes—
890C2×C22⋊C4C2412yes—
891C2×C22⋊C4C2414yes—
892C2×C22⋊C4C2414yes—
893C2×C22⋊C4C2414yes—
894C2×C22⋊C4C2414yes—
895C2×C22⋊C4C2414yes—
896C2×C22⋊C4C2412yes—
897C2×C22⋊C4C2412yes—
898C2×C22⋊C4C2414yes—
899C2×C22⋊C4C2414yes—
900C2×C22⋊C4C2414yes—
901C2×C22⋊C4C2414yes—
902C2×C22⋊C4C2414yes—
903C2×C22⋊C4C2414yes—
904C2×C22⋊C4C2414yes—
905C2×C22⋊C4C2414yes—
906C2×C22⋊C4C2414yes—
907C2×C22⋊C4C2414yes—
908C2×C22⋊C4C2414yes—
909C2×C22⋊C4C2414yes—
910C2×C22⋊C4C2414yes—
911C2×C22⋊C4C2414yes—
912C2×C22⋊C4C2414yes—
913C2×C22⋊C4C2414yes—
914C2×C22⋊C4C2414yes—
915C2×C22⋊C4C2414yes—
916C2×C42—44no—
917C2×C42—44no—
918C2×C42—42no—
919C2×C42—42no—
920C2×C42—44no—
921C2×C42#4118yes—
922C2×C42C2414yes—
923C2×C42C2414yes—
924C2×C42C2414yes—
925C2×C42C2412yes—
926C2×C42C2412yes—
927C2×C42C2412yes—
928C2×C42C2412yes—
929C2×C42C2412yes—
930C2×C42C2412yes—
931C2×C42C2411yescharacteristic
932C2×C42C2411yescharacteristic
933C2×C42C2412yes—
934C2×C42C2414yes—
935C2×C42C2414yes—
936C2×C42C2414yes—
937C2×C42C2412yes—
938C2×C42C2412yes—
939C2×C42C2412yes—
940C2×C42C2411yescharacteristic
941C2×C42C2411yescharacteristic
942C2×C42C2414yes—
943C2×C42C2414yes—
944C2×C42C2414yes—
945C2×C42C2414yes—
946C2×C42C2414yes—
947C2×C42C2412yes—
948C2×C42C2412yes—
949#95C2414yes—
950#95C2412yes—
951#95C2414yes—
952#95C2414yes—
953#95C2414yes—
954#95C2414yes—
955#95C2414yes—
956#95C2412yes—
957#95C2412yes—
958#95C2414yes—
959#95C2412yes—
960#95C2412yes—
961#95C2414yes—
962#95C2414yes—
963#95C2414yes—
964#95C2414yes—
965#95C2414yes—
966#95C2412yes—
967#95C2412yes—
968#95C2412yes—
969#95C2412yes—
970#95C2412yes—
971#95C2412yes—
972#95C2412yes—
973#95C2412yes—
974#95C2414yes—
975#95C2414yes—
976#95C2414yes—
977#95C2414yes—
978#95C2414yes—
979#95C2412yes—
980#95C2412yes—
981#95C2412yes—
982#95C2412yes—
983#95C2414yes—
984#95C2414yes—
985#95C2414yes—
986#95C2414yes—
987#95C2414yes—
988#95C2412yes—
989#95C2412yes—
990#95C2412yes—
991#95C2412yes—
992#95C2414yes—
993#95C2414yes—
994#95C2414yes—
995#95C2412yes—
996#95C2412yes—
997#95C2412yes—
998#95C2414yes—
999#95C2414yes—
1000#95C2412yes—
1001#95C2414yes—
1002#95C2412yes—
1003#95C2412yes—
1004#95C2412yes—
1005#95C2414yes—
1006#95C2414yes—
1007#95C2412yes—
1008#95C2414yes—
1009#95C2412yes—
1010#95C2412yes—
1011#95C2412yes—
1012#95C2414yes—
1013#95C2414yes—
1014#95C2414yes—
1015#95C2414yes—
1016#95C2414yes—
1017#95C2414yes—
1018#95C2414yes—
1019#95C2414yes—
1020#95C2414yes—
1021#95C2414yes—
1022#95C2414yes—
1023#95C2414yes—
1024#95C2414yes—
1025C24C2514yes—
1026C24C2511yescharacteristic
1027C2×Q8—24no—
1028C2×Q8—24no—
1029C2×Q8—24no—
1030C2×Q8—22no—
1031C2×Q8—24no—
1032C2×Q8—22no—
1033C2×Q8—22no—
1034C2×Q8—24no—
1035C2×Q8—22no—
1036C2×Q8—24no—
1037C2×Q8—22no—
1038C2×Q8—22no—
1039C2×Q8—24no—
1040C2×Q8—22no—
1041C2×Q8—24no—
1042C2×Q8—22no—
1043C2×Q8—41no—
1044C2×Q8—42no—
1045C2×Q8—42no—
1046C2×Q8—42no—
1047C2×Q8—42no—
1048C2×Q8—41no—
1049C2×Q8—42no—
1050C2×Q8—41no—
1051C2×Q8—42no—
1052C2×Q8—41no—
1053C2×Q8—42no—
1054C2×Q8—416no—
1055C2×Q8—416no—
1056C2×D4—28no—
1057C2×D4—28no—
1058C2×D4—28no—
1059C2×D4—24no—
1060C2×D4—24no—
1061C2×D4—24no—
1062C2×D4—24no—
1063C2×D4—42no—
1064C2×D4—42no—
1065C2×D4—42no—
1066C2×D4—42no—
1067C2×D4—42no—
1068C22×C4—22no—
1069C22×C4—22no—
1070C22×C4—22no—
1071C22×C4—22no—
1072C22×C4—24no—
1073C22×C4—24no—
1074C22×C4—22no—
1075C22×C4—24no—
1076C22×C4—24no—
1077C22×C4—22no—
1078C22×C4—22no—
1079C22×C4—24no—
1080C22×C4—28no—
1081C22×C4—28no—
1082C22×C4—41no—
1083C22×C4—41no—
1084C22×C4—42no—
1085C22×C4—42no—
1086C22×C4—42no—
1087C22×C4—41no—
1088C22×C4—41no—
1089C22×C4—41no—
1090C22×C4—41no—
1091C22×C4—42no—
1092C22×C4—42no—
1093C22×C4—41no—
1094C22×C4—41no—
1095C22×C4—42no—
1096C22×C4—44no—
1097C22×C4—44no—
1098C22×C4—44no—
1099C22×C4—44no—
1100C22×C4—42no—
1101C22×C4—41no—
1102C22×C4—41no—
1103C22×C4—44no—
1104C22×C4—44no—
1105C22×C4—44no—
1106C22×C4C2×#4114yes—
1107C22×C4C2×#4114yes—
1108C22×C4C2×#4114yes—
1109C22×C42−1+414yes—
1110C22×C4C2514yes—
1111C22×C4C2512yes—
1112C22×C4C2512yes—
1113C22×C4C2514yes—
1114C22×C4C2514yes—
1115C22×C4C2512yes—
1116C22×C4C2512yes—
1117C22×C4C2512yes—
1118C22×C4C2512yes—
1119C22×C4C2511yescharacteristic
1120C22×C4C2512yes—
1121C22×C4C2512yes—
1122C22×C4C2512yes—
1123C22×C4C2512yes—
1124C22×C4C2514yes—
1125C22×C4C2512yes—
1126C22×C4C2512yes—
1127C22×C4C2512yes—
1128C22×C4C2511yescharacteristic
1129C22×C4C2514yes—
1130C22×C4C2512yes—
1131C22×C4C2512yes—
1132C22×C4C2511yescharacteristic
1133C22×C4C2512yes—
1134C22×C4C2511yescharacteristic
1135C22×C4C2511yescharacteristic
1136C22×C4C2511yescharacteristic
1137C4⋊C4—28no—
1138C4⋊C4—28no—
1139C4⋊C4—28no—
1140C4⋊C4—28no—
1141C4⋊C4—28no—
1142C4⋊C4—28no—
1143C4⋊C4—24no—
1144C4⋊C4—28no—
1145C4⋊C4—24no—
1146C4⋊C4—28no—
1147C4⋊C4—24no—
1148C4⋊C4—22no—
1149C4⋊C4—28no—
1150C4⋊C4—24no—
1151C4⋊C4—24no—
1152C4⋊C4—28no—
1153C4⋊C4—24no—
1154C4⋊C4—24no—
1155C4⋊C4—24no—
1156C4⋊C4—22no—
1157C4⋊C4—22no—
1158C4⋊C4—24no—
1159C4⋊C4—24no—
1160C4⋊C4—24no—
1161C4⋊C4—42no—
1162C4⋊C4—42no—
1163C4⋊C4—42no—
1164C4⋊C4—42no—
1165C4⋊C4—44no—
1166C4⋊C4—42no—
1167C4⋊C4—42no—
1168C4⋊C4—41no—
1169C4⋊C4—42no—
1170C4⋊C4—42no—
1171C4⋊C4—42no—
1172C4⋊C4—42no—
1173C4⋊C4—41no—
1174C4⋊C4—42no—
1175C4⋊C4—42no—
1176C4⋊C4—42no—
1177C4⋊C4—42no—
1178C4⋊C4—44no—
1179C4⋊C4—44no—
1180C4⋊C4—42no—
1181C4⋊C4—42no—
1182C4⋊C4—42no—
1183C4⋊C4—44no—
1184C4⋊C4—44no—
1185C4⋊C4—44no—
1186C4⋊C4—41no—
1187C4⋊C4—44no—
1188C4⋊C4—42no—
1189C4⋊C4—41no—
1190C4⋊C4—42no—
1191C4⋊C4—42no—
1192C4⋊C4—44no—
1193C4⋊C4—42no—
1194C4⋊C4—42no—
1195C4⋊C4—42no—
1196C4⋊C4—42no—
1197C4⋊C4—42no—
1198C4⋊C4—42no—
1199C4⋊C4—42no—
1200C4⋊C4—44no—
1201C4⋊C4—44no—
1202C4⋊C4—44no—
1203C4⋊C4—44no—
1204C4⋊C4—44no—
1205C4⋊C4—44no—
1206C4⋊C4H(5,𝔽2)14yes—
1207C22⋊C4—28no—
1208C22⋊C4—24no—
1209C22⋊C4—24no—
1210C22⋊C4—24no—
1211C22⋊C4—24no—
1212C22⋊C4—28no—
1213C22⋊C4—28no—
1214C22⋊C4—28no—
1215C22⋊C4—28no—
1216C22⋊C4—28no—
1217C22⋊C4—28no—
1218C22⋊C4—44no—
1219C22⋊C4—44no—
1220C22⋊C4—44no—
1221C22⋊C4—44no—
1222C22⋊C4—44no—
1223C22⋊C4—44no—
1224C22⋊C4—44no—
1225C22⋊C4—44no—
1226C22⋊C4—44no—
1227C22⋊C4—44no—
1228C22⋊C4—44no—
1229C22⋊C4—44no—
1230C22⋊C4—44no—
1231C22⋊C4—44no—
1232C22⋊C4—44no—
1233C22⋊C4—44no—
1234C22⋊C4—44no—
1235C22⋊C4—44no—
1236C42—28no—
1237C42—28no—
1238C42—24no—
1239C42—24no—
1240C42—24no—
1241C42—22no—
1242C42—22no—
1243C42—28no—
1244C42—24no—
1245C42—24no—
1246C42—24no—
1247C42—24no—
1248C42—44no—
1249C42—44no—
1250C42—41no—
1251C42—42no—
1252C42—41no—
1253C42—42no—
1254C42—42no—
1255C42—44no—
1256C42—44no—
1257C42—44no—
1258C42—44no—
1259C42—44no—
1260C42—44no—
1261C42C2×#4118yes—
1262C42C2×#4118yes—
1263C23—21no—
1264C23—21no—
1265C23—21no—
1266C23—21no—
1267C23—24no—
1268C23—24no—
1269C23—24no—
1270C23—24no—
1271C23—24no—
1272C23—24no—
1273C23—24no—
1274C23C22×#4112yes—
1275C23C2×2−1+412yes—
1276C23#58512yes—
1277C23C2611yescharacteristic
1278Q8—44no—
1279Q8—48no—
1280Q8—48no—
1281Q8—48no—
1282Q8—44no—
1283Q8—48no—
1284Q8—44no—
1285Q8—82no—
1286Q8—84no—
1287D4—416no—
1288D4—48no—
1289D4—84no—
1290D4—162no—
1291C2×C4—21no—
1292C2×C4—21no—
1293C2×C4—21no—
1294C2×C4—22no—
1295C2×C4—22no—
1296C2×C4—22no—
1297C2×C4—21no—
1298C2×C4—22no—
1299C2×C4—21no—
1300C2×C4—22no—
1301C2×C4—22no—
1302C2×C4—21no—
1303C2×C4—28no—
1304C2×C4—28no—
1305C2×C4—24no—
1306C2×C4—24no—
1307C2×C4—24no—
1308C2×C4—22no—
1309C2×C4—24no—
1310C2×C4—22no—
1311C2×C4—22no—
1312C2×C4—22no—
1313C2×C4—22no—
1314C2×C4—22no—
1315C2×C4—24no—
1316C2×C4—21no—
1317C2×C4—21no—
1318C2×C4—22no—
1319C2×C4—22no—
1320C2×C4—22no—
1321C2×C4—24no—
1322C2×C4—22no—
1323C2×C4—22no—
1324C2×C4—22no—
1325C2×C4—22no—
1326C2×C4—24no—
1327C2×C4—22no—
1328C2×C4—22no—
1329C2×C4—22no—
1330C2×C4—22no—
1331C2×C4—22no—
1332C2×C4—22no—
1333C2×C4—22no—
1334C2×C4—24no—
1335C2×C4—22no—
1336C2×C4—22no—
1337C2×C4—22no—
1338C2×C4—24no—
1339C2×C4—24no—
1340C2×C4—24no—
1341C2×C4—22no—
1342C2×C4—22no—
1343C2×C4—21no—
1344C2×C4—22no—
1345C2×C4—24no—
1346C2×C4—22no—
1347C2×C4—21no—
1348C2×C4—22no—
1349C2×C4—22no—
1350C2×C4—22no—
1351C2×C4—24no—
1352C2×C4—24no—
1353C2×C4—24no—
1354C2×C4—22no—
1355C2×C4—22no—
1356C2×C4—22no—
1357C2×C4—22no—
1358C2×C4—22no—
1359C2×C4—22no—
1360C2×C4—21no—
1361C2×C4—22no—
1362C2×C4—22no—
1363C2×C4—22no—
1364C2×C4—21no—
1365C2×C4—44no—
1366C2×C4—44no—
1367C2×C4—48no—
1368C2×C4—44no—
1369C2×C4—48no—
1370C2×C4—48no—
1371C2×C4—88no—
1372C2×C4—88no—
1373C2×C4—82no—
1374C2×C4—82no—
1375C2×C4—84no—
1376C2×C4—164no—
1377C2×C4C22×#4114yes—
1378C2×C4C22×#4114yes—
1379C2×C4C22×#4112yes—
1380C2×C4C22×#4112yes—
1381C2×C4C2×H(5,𝔽2)14yes—
1382C2×C4C2×H(5,𝔽2)12yes—
1383C2×C4C2×2−1+412yes—
1384C2×C4C2×2−1+412yes—
1385C2×C4#58512yes—
1386C22—22no—
1387C22—22no—
1388C22—22no—
1389C22—22no—
1390C22—22no—
1391C22—22no—
1392C22—44no—
1393C22—44no—
1394C22—44no—
1395C22—44no—
1396C22—44no—
1397C22—44no—
1398C22—44no—
1399C22#350714yes—
1400C22C23×#4111yescharacteristic
1401C22C22×H(5,𝔽2)11yescharacteristic
1402C22C22×2−1+411yescharacteristic
1403C22C2×#58511yescharacteristic
1404C22C2×#58511yescharacteristic
1405C222−1+611yescharacteristic
1406C222−1+611yescharacteristic
1407C4—24no—
1408C4—24no—
1409C4—22no—
1410C4—22no—
1411C4—24no—
1412C4—22no—
1413C4—44no—
1414C4—44no—
1415C4—42no—
1416C4—42no—
1417C4—42no—
1418C4—42no—
1419C4—41no—
1420C4—42no—
1421C4—41no—
1422C4—42no—
1423C4—42no—
1424C4—42no—
1425C4—44no—
1426C4—42no—
1427C4—44no—
1428C4—42no—
1429C4—42no—
1430C4—42no—
1431C4—44no—
1432C4—42no—
1433C4#346014yes—
1434C2—24no—
1435C2—84no—
1436C2C2×#346011yescharacteristic
1437C2C2×#350711yescharacteristic
1438C2#6286011yescharacteristic
1439C2#6289311yescharacteristic
1440C2#6289811yescharacteristic
1441C2#6295611yescharacteristic
1442C2#6296411yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#2856C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #42705C2semidirect
2. #42702C2semidirect
3. #42701C2semidirect
4. #42698C2semidirect
5. #41764C2semidirect
6. #41760C2semidirect
7. #41759C2semidirect
8. #41755C2semidirect
9. #39798C2semidirect
11. #39670C2semidirect
12. #39640C2semidirect
13. #38983C2semidirect
14. #38223C2semidirect
15. #37617C2semidirect
16. #37525C2semidirect
18. #36545C2semidirect
19. #36233C2semidirect
20. #35973C2semidirect
21. #35959C2semidirect
22. #35938C2semidirect
23. #35870C2semidirect
25. #35098C2semidirect
26. #34595C2semidirect
27. #34584C2semidirect
28. #34230C2semidirect
29. C2×#2365C2semidirect

Maximal subgroups

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

subgroupindex
#427052
#427022
#427012
#426982
#417642
#417602
#417592
#417552
#397982
#397682
#396702
#396402
#389832
#382232
#376172
#375252
#365802
#365452
#362332
#359732
#359592
#359382
#358702
#351032
#350982
#345952
#345842
#342302
C2×#23652