Finite Group Databasebeta

← #8096749

Subgroups — #8096749

Order 512.

4566 conjugacy classes of subgroups.

The subgroup lattice has 1426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#53155C212yesmaximal, complemented
2#53104C212yesmaximal, complemented
3#53031C211yesmaximal, characteristic, complemented
4#53017C211yesmaximal, characteristic, complemented
5#52603C212yesmaximal, complemented
6#52430C214yesmaximal, complemented
7#52396C212yesmaximal, complemented
8#52349C214yesmaximal, complemented
9#52300C211yesmaximal, characteristic, complemented
10C2×#2764C212yesmaximal, complemented
11#46348C214yesmaximal, complemented
12#46343C212yesmaximal, complemented
13#46085C214yesmaximal, complemented
14#46060C212yesmaximal, complemented
15#46049C212yesmaximal, complemented
16#45983C214yesmaximal, complemented
17#45696C211yesmaximal, characteristic, complemented
18#45690C212yesmaximal, complemented
19#45531C214yesmaximal, complemented
20#45474C212yesmaximal, complemented
21#36276C212yesmaximal, complemented
22#36240C212yesmaximal, complemented
23#36215C212yesmaximal, complemented
24#36166C212yesmaximal, complemented
25#36155C211yesmaximal, characteristic
26#35976C211yesmaximal, characteristic
27#35961C212yesmaximal, complemented
28#35939C211yesmaximal, characteristic
29#35806C212yesmaximal, complemented
30C2×#554C2212yes—
31C2×D4×Q8C2211yescharacteristic
32C2×#546C2211yescharacteristic
33C2×#520C2211yescharacteristic
34C22×C4×D4C2211yescharacteristic
35#2863C2212yescomplemented
36#2862C2212yescomplemented
37#2860C2212yes—
38#2857C2214yescomplemented
39#2855C2211yescharacteristic
40#2852C2214yes—
41#2852C2214yescomplemented
42#2851C2212yes—
43#2849C2212yes—
44#2848C2214yes—
45#2843C2214yescomplemented
46#2841C2212yes—
47#2839C2214yescomplemented
48#2838C2214yescomplemented
49#2838C2214yescomplemented
50#2837C2214yescomplemented
51#2836C2214yescomplemented
52#2836C2214yescomplemented
53#2835C2212yes—
54#2834C2214yescomplemented
55#2833C2214yescomplemented
56#2831C2214yescomplemented
57#2831C2214yescomplemented
58#2831C2214yescomplemented
59#2827C2214yescomplemented
60#2822C2212yescomplemented
61#2821C2214yescomplemented
62#2817C2212yes—
63#2817C2212yescomplemented
64#2809C2214yescomplemented
65#2791C2212yescomplemented
66#2787C2214yes—
67#2777C2214yescomplemented
68#2777C2212yescomplemented
69#2776C2214yescomplemented
70#2775C2214yescomplemented
71#2771C2211yescharacteristic
72#2770C2214yescomplemented
73#2769C2212yescomplemented
74#2766C2214yescomplemented
75#2765C2214yes—
76#2764C2214yes—
77#2764C2212yes—
78#2764C2212yes—
79#2764C2211yescharacteristic
80#2764C2214yes—
81#2764C2212yes—
82#2764C2214yescomplemented
83#2764C2212yescomplemented
84#2764C2214yescomplemented
85#2764C2214yescomplemented
86#2764C2214yescomplemented
87#2762C2214yescomplemented
88#2762C2214yescomplemented
89#2759C2214yescomplemented
90#2758C2212yescomplemented
91#2758C2214yescomplemented
92#2745C2214yes—
93#2745C2214yescomplemented
94#2745C2214yescomplemented
95#2738C2214yescomplemented
96#2731C2214yescomplemented
97#2729C2214yes—
98#2728C2214yescomplemented
99#2724C2212yes—
100#2722C2211yescharacteristic
101#2721C2214yescomplemented
102#2720C2214yescomplemented
103#2718C2212yes—
104#2716C2214yescomplemented
105#2716C2212yescomplemented
106#2715C2214yescomplemented
107#2715C2214yescomplemented
108#2707C2214yes—
109#2702C2212yes—
110#2702C2214yescomplemented
111#2698C2214yes—
112#2698C2214yescomplemented
113#2689C2214yescomplemented
114#2680C2214yes—
115#2677C2211yescharacteristic
116#2647C2212yescomplemented
117#2646C2214yescomplemented
118#2640C2211yescharacteristic
119#2639C2212yes—
120#2629C2212yescomplemented
121#2627C2214yescomplemented
122#2624C2211yescharacteristic
123#2623C2212yes—
124#2592C2211yescharacteristic
125#2582C2212yescomplemented
126#2580C2212yes—
127#2579C2214yes—
128#2579C2214yescomplemented
129#2571C2212yescomplemented
130#2570C2212yescomplemented
131#2569C2214yescomplemented
132#2567C2212yescomplemented
133#2566C2212yes—
134#2565C2212yescomplemented
135#2564C2214yes—
136#2563C2211yescharacteristic
137#2561C2212yes—
138#2550C2212yescomplemented
139#2550C2212yescomplemented
140#2550C2212yescomplemented
141#2550C2212yescomplemented
142#2549C2214yescomplemented
143#2549C2214yescomplemented
144#2549C2214yescomplemented
145#2549C2214yescomplemented
146#2546C2212yescomplemented
147#2514C2212yescomplemented
148#2514C2212yescomplemented
149#2514C2212yescomplemented
150#2513C2212yes—
151#2513C2212yes—
152#2512C2212yes—
153#2510C2214yes—
154#2510C2214yes—
155#2510C2214yescomplemented
156#2510C2214yescomplemented
157#2510C2214yescomplemented
158#2509C2212yescomplemented
159#2509C2212yescomplemented
160#2508C2212yescomplemented
161#2506C2212yescomplemented
162#2505C2214yescomplemented
163#2505C2214yescomplemented
164#2505C2214yescomplemented
165#2504C2211yescharacteristic
166#2503C2211yescharacteristic
167#2502C2214yescomplemented
168#2498C2212yes—
169#2497C2212yes—
170#2495C2212yes—
171#2495C2212yescomplemented
172#2495C2212yescomplemented
173#2495C2212yescomplemented
174#2494C2212yes—
175#2493C2214yescomplemented
176#2493C2214yescomplemented
177#2493C2214yescomplemented
178#2492C2212yes—
179#2491C2212yes—
180#2488C2214yes—
181#2486C2211yescharacteristic
182#2486C2211yescharacteristic
183#2483C2212yes—
184#2482C2212yes—
185#2481C2214yes—
186#2480C2214yes—
187#2480C2214yes—
188#2480C2214yes—
189#2473C2214yescomplemented
190#2472C2214yes—
191#2454C2212yes—
192#2453C2212yescomplemented
193#2452C2212yes—
194#2451C2212yescomplemented
195#2450C2214yes—
196#2450C2214yescomplemented
197#2449C2214yes—
198#2449C2214yescomplemented
199#2448C2212yes—
200#2447C2212yes—
201#2444C2214yes—
202#2444C2214yes—
203#2442C2212yes—
204#2442C2214yescomplemented
205#2442C2212yescomplemented
206#2440C2212yes—
207#2440C2212yescomplemented
208#2438C2214yescomplemented
209#2438C2214yescomplemented
210#2437C2214yes—
211#2437C2214yes—
212#2436C2212yes—
213#2434C2214yescomplemented
214#2421C2212yes—
215#2420C2212yes—
216#2419C2214yes—
217#2418C2214yes—
218#2417C2214yescomplemented
219#2412C2212yes—
220#2402C2212yescomplemented
221#2398C2211yescharacteristic
222#2396C2212yescomplemented
223#2395C2211yescharacteristic
224C2×#400C2214yescomplemented
225C2×#398C2214yescomplemented
226C2×#397C2212yes—
227C2×#393C2212yes—
228#2383C2214yescomplemented
229#2381C2214yescomplemented
230#2379C2214yescomplemented
231#2378C2214yes—
232#2376C2212yes—
233#2349C2212yes—
234#2349C2212yes—
235#2349C2212yes—
236#2349C2212yes—
237#2349C2212yes—
238#2349C2212yes—
239D4×C4⋊C4C2212yes—
240D4×C4⋊C4C2212yes—
241#2339C2212yes—
242#2339C2211yescharacteristic
243#2339C2212yes—
244D4×C22⋊C4C2211yescharacteristic
245D4×C22⋊C4C2212yes—
246D4×C22⋊C4C2212yes—
247C4×C4⋊Q8C2212yescomplemented
248C4×#126C2212yes—
249C4×#126C2212yescomplemented
250C4×C22⋊Q8C2212yes—
251C4×#123C2211yescharacteristic
252C2×#391C2214yescomplemented
253C2×#388C2214yes—
254C2×#385C2214yes—
255C2×#383C2214yescomplemented
256C2×#381C2212yes—
257#2275C2211yescharacteristic
258C42×D4C2212yes—
259C22×#41C2311yescharacteristic
260C23×Q8C2312yes—
261C23×D4C2311yescharacteristic
262C24×C4C2312yes—
263#554—48no—
264D4×Q8—44no—
265#546—44no—
266C2×C4⋊Q8C2312yes—
267C2×C4⋊Q8C2311yescharacteristic
268C2×C4⋊Q8C2314yes—
269C2×C4⋊Q8C2312yes—
270C2×C4⋊Q8C2312yes—
271C2×#126C2312yes—
272C2×#126C2312yes—
273C2×#126C2314yes—
274C2×#126C2314yes—
275C2×#125C2312yes—
276C2×#125C2312yes—
277C2×#125C2314yes—
278C2×#124C2311yescharacteristic
279C2×#124C2314yes—
280C2×#123C2311yescharacteristic
281C2×#123C2312yes—
282C2×#123C2312yes—
283C2×#123C2312yes—
284C2×C22⋊Q8C2312yes—
285C2×C22⋊Q8C2314yes—
286C2×C22⋊Q8C2314yes—
287C2×C22⋊Q8C2311yescharacteristic
288C2×C22⋊Q8C2314yes—
289C2×C22⋊Q8C2314yes—
290C2×C22⋊Q8C2314yes—
291C2×C22⋊Q8C2312yes—
292C2×C22⋊Q8C2314yes—
293C2×C22⋊Q8C2314yes—
294C2×#121C2311yescharacteristic
295C2×#121C2312yes—
296C2×#120C2312yes—
297#520—44no—
298C2×C4×Q8C2311yescharacteristic
299C2×C4×Q8C2312yes—
300C2×C4×Q8C2312yes—
301C2×C4×D4—44no—
302C2×C4×D4C2312yes—
303C2×C4×D4C2312yes—
304C2×C4×D4C2312yes—
305C2×C4×D4C2312yes—
306C2×C4×D4C2312yes—
307C2×C4×D4C2312yes—
308C2×C4×D4C2311yescharacteristic
309C2×C4×D4C2311yescharacteristic
310C2×C4×D4C2314yes—
311C2×C4×D4C2312yes—
312C2×C4×D4C2314yes—
313C2×#117C2311yescharacteristic
314C2×#117C2312yes—
315C22×C4⋊C4C2314yes—
316C22×C4⋊C4C2312yes—
317C22×C4⋊C4C2311yescharacteristic
318C22×C4⋊C4C2311yescharacteristic
319C22×C4⋊C4C2314yes—
320C22×C4⋊C4C2314yes—
321C22×C22⋊C4C2312yes—
322C22×C22⋊C4C2314yes—
323C22×C22⋊C4C2314yes—
324C22×C22⋊C4C2312yes—
325C22×C22⋊C4C2312yes—
326C22×C42C2311yescharacteristic
327C22×C42C2314yes—
328#401C2314yes—
329#401C2314yes—
330#401C2314yes—
331#401C2314yes—
332#400C2314yes—
333#400C2314yes—
334#400C2314yes—
335#400C2314yes—
336#400C2314yes—
337#400C2314yes—
338#400C2314yes—
339#400C2314yes—
340#400C2314yes—
341#400C2312yes—
342#400C2314yes—
343#400C2314yes—
344#400C2314yes—
345#400C2314yes—
346#400C2314yes—
347#400C2314yes—
348#400C2314yes—
349#400C2314yes—
350#400C2314yes—
351#400C2314yes—
352#400C2314yes—
353#400C2314yes—
354#400C2314yes—
355#400C2314yes—
356#400C2312yes—
357#400C2312yes—
358#400C2314yes—
359#400C2314yes—
360#400C2311yescharacteristic
361#400C2312yes—
362#400C2312yes—
363#400C2312yes—
364#399C2314yes—
365#399C2312yes—
366#399C2312yes—
367#399C2314yes—
368#399C2314yes—
369#399C2311yescharacteristic
370#398C2314yes—
371#398C2314yes—
372#398C2314yes—
373#398C2314yes—
374#398C2311yescharacteristic
375#398C2314yes—
376#398C2314yes—
377#398C2314yes—
378#398C2312yes—
379#398C2314yes—
380#398C2314yes—
381#398C2314yes—
382#398C2312yes—
383#398C2314yes—
384#398C2314yes—
385#398C2314yes—
386#398C2312yes—
387#398C2314yes—
388#398C2314yes—
389#398C2314yes—
390#398C2314yes—
391#398C2314yes—
392#398C2312yes—
393#398C2312yes—
394#398C2314yes—
395#398C2314yes—
396#398C2312yes—
397#398C2314yes—
398#398C2312yes—
399#398C2312yes—
400#398C2314yes—
401#398C2314yes—
402#397C2311yescharacteristic
403#397C2312yes—
404#397C2312yes—
405#397C2314yes—
406#397C2311yescharacteristic
407#397C2314yes—
408#397C2312yes—
409#397C2314yes—
410#397C2314yes—
411#397C2314yes—
412#397C2312yes—
413#397C2312yes—
414#397C2314yes—
415#397C2314yes—
416#397C2314yes—
417#397C2314yes—
418#397C2314yes—
419#397C2314yes—
420#397C2314yes—
421#397C2312yes—
422#397C2314yes—
423#397C2314yes—
424#397C2314yes—
425#397C2311yescharacteristic
426#397C2314yes—
427#397C2312yes—
428#396C2314yes—
429#396C2314yes—
430#396C2314yes—
431#396C2314yes—
432#396C2314yes—
433#396C2314yes—
434#396C2314yes—
435#396C2312yes—
436#396C2312yes—
437#396C2314yes—
438#395C2314yes—
439#395C2314yes—
440#395C2314yes—
441#395C2312yes—
442#395C2314yes—
443#395C2314yes—
444#395C2314yes—
445#395C2314yes—
446#395C2314yes—
447#395C2314yes—
448#394C2314yes—
449#394C2314yes—
450#394C2314yes—
451#394C2312yes—
452#394C2312yes—
453#393C2312yes—
454#393C2312yes—
455#393C2312yes—
456#393C2314yes—
457#393C2314yes—
458#393C2314yes—
459#393C2312yes—
460#393C2312yes—
461#393C2311yescharacteristic
462#393C2314yes—
463#393C2312yes—
464#393C2311yescharacteristic
465#391C2312yes—
466#391C2312yes—
467#391C2312yes—
468#391C2312yes—
469#391C2314yes—
470#391C2314yes—
471#391C2314yes—
472#391C2314yes—
473#391C2312yes—
474#391C2312yes—
475#391C2314yes—
476#391C2312yes—
477#391C2314yes—
478#391C2314yes—
479#391C2314yes—
480#391C2314yes—
481#391C2312yes—
482#391C2314yes—
483#391C2314yes—
484#391C2314yes—
485#391C2314yes—
486#390C2312yes—
487#390C2312yes—
488#390C2312yes—
489#390C2312yes—
490#390C2312yes—
491#390C2312yes—
492#389C2312yes—
493#389C2312yes—
494#389C2312yes—
495#389C2312yes—
496#389C2312yes—
497#389C2312yes—
498#389C2312yes—
499#389C2312yes—
500#389C2312yes—
501#389C2312yes—
502#389C2312yes—
503#389C2312yes—
504#389C2314yes—
505#389C2312yes—
506#389C2314yes—
507#389C2314yes—
508#389C2314yes—
509#389C2312yes—
510#389C2314yes—
511#389C2314yes—
512#389C2312yes—
513#389C2312yes—
514#389C2314yes—
515#389C2314yes—
516#389C2312yes—
517#389C2312yes—
518#389C2312yes—
519#389C2312yes—
520#389C2312yes—
521#389C2314yes—
522#388C2312yes—
523#388C2312yes—
524#388C2312yes—
525#388C2312yes—
526#388C2312yes—
527#388C2312yes—
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#388C2312yes—
546#388C2314yes—
547#388C2314yes—
548#388C2314yes—
549#387C2312yes—
550#387C2312yes—
551#387C2312yes—
552#387C2312yes—
553#387C2312yes—
554#387C2312yes—
555#387C2312yes—
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#387C2312yes—
569#387C2314yes—
570#387C2314yes—
571#387C2314yes—
572#387C2314yes—
573#387C2314yes—
574#387C2314yes—
575#387C2314yes—
576#387C2314yes—
577#387C2314yes—
578#387C2314yes—
579#387C2312yes—
580#386C2314yes—
581#386C2314yes—
582#386C2314yes—
583#386C2314yes—
584#386C2314yes—
585#386C2314yes—
586#386C2314yes—
587#386C2314yes—
588#386C2314yes—
589#386C2314yes—
590#386C2314yes—
591#386C2311yescharacteristic
592#386C2314yes—
593#385C2314yes—
594#385C2314yes—
595#385C2314yes—
596#385C2314yes—
597#385C2314yes—
598#385C2314yes—
599#385C2314yes—
600#385C2314yes—
601#385C2314yes—
602#385C2314yes—
603#385C2314yes—
604#385C2314yes—
605#385C2314yes—
606#385C2314yes—
607#385C2311yescharacteristic
608#385C2314yes—
609#385C2312yes—
610#385C2314yes—
611#385C2314yes—
612#385C2314yes—
613#385C2314yes—
614#385C2314yes—
615#385C2312yes—
616#385C2314yes—
617#385C2314yes—
618#385C2314yes—
619#385C2314yes—
620#385C2314yes—
621#385C2314yes—
622#385C2314yes—
623#385C2314yes—
624#385C2314yes—
625#385C2312yes—
626#384C2312yes—
627#384C2312yes—
628#384C2314yes—
629#384C2312yes—
630#383C2312yes—
631#383C2312yes—
632#383C2314yes—
633#383C2314yes—
634#383C2314yes—
635#383C2314yes—
636#383C2314yes—
637#383C2314yes—
638#383C2314yes—
639#383C2314yes—
640#382C2312yes—
641#382C2312yes—
642#382C2312yes—
643#382C2312yes—
644#382C2312yes—
645#382C2312yes—
646#382C2312yes—
647#382C2314yes—
648#382C2314yes—
649#381C2314yes—
650#381C2312yes—
651#381C2312yes—
652#381C2312yes—
653#381C2312yes—
654#381C2312yes—
655#381C2314yes—
656#381C2312yes—
657#381C2314yes—
658#381C2314yes—
659#381C2311yescharacteristic
660#380C2312yes—
661#380C2312yes—
662#380C2314yes—
663#380C2314yes—
664#380C2314yes—
665#380C2314yes—
666#380C2314yes—
667#380C2314yes—
668#380C2314yes—
669#380C2314yes—
670#380C2312yes—
671#380C2311yescharacteristic
672#380C2311yescharacteristic
673#380C2312yes—
674#380C2314yes—
675#380C2314yes—
676#380C2314yes—
677#380C2312yes—
678#379C2314yes—
679#379C2314yes—
680#379C2312yes—
681C4×C4⋊C4C2312yes—
682C4×C4⋊C4C2312yes—
683C4×C4⋊C4C2312yes—
684C4×C4⋊C4C2312yes—
685C4×C4⋊C4C2312yes—
686C4×C4⋊C4C2312yes—
687C4×C4⋊C4C2312yes—
688C4×C4⋊C4C2311yescharacteristic
689C4×C4⋊C4C2312yes—
690C4×C4⋊C4C2312yes—
691C4×C4⋊C4C2312yes—
692C4×C4⋊C4C2312yes—
693C4×C4⋊C4C2312yes—
694C4×C22⋊C4C2311yescharacteristic
695C4×C22⋊C4C2312yes—
696C4×C22⋊C4C2312yes—
697C4×C22⋊C4C2311yescharacteristic
698C4×C22⋊C4C2312yes—
699C4×C22⋊C4C2312yes—
700C4×C22⋊C4C2312yes—
701C4×C22⋊C4C2314yes—
702C4×C22⋊C4C2314yes—
703C4×C22⋊C4C2314yes—
704C4×C22⋊C4C2314yes—
705#376C2311yescharacteristic
706C2×#95C2314yes—
707C2×#95C2314yes—
708C2×#95C2314yes—
709C2×#95C2312yes—
710C2×#95C2314yes—
711C2×#95C2314yes—
712C2×#95C2314yes—
713C2×#95C2314yes—
714C2×#95C2314yes—
715C2×#95C2312yes—
716C43C2312yes—
717C25C2412yes—
718C2×#41—24no—
719C2×#41—28no—
720C22×Q8—44no—
721C22×Q8—48no—
722C22×Q8C2411yescharacteristic
723C22×Q8C2411yescharacteristic
724C22×Q8C2412yes—
725C22×Q8C2414yes—
726C22×Q8C2414yes—
727C22×Q8C2412yes—
728C22×D4—24no—
729C22×D4—28no—
730C22×D4C2412yes—
731C22×D4C2412yes—
732C22×D4C2411yescharacteristic
733C22×D4C2411yescharacteristic
734C22×D4C2412yes—
735C22×D4C2411yescharacteristic
736C23×C4—44no—
737C23×C4—44no—
738C23×C4—82no—
739C23×C4C2412yes—
740C23×C4C2411yescharacteristic
741C23×C4C2411yescharacteristic
742C23×C4C2414yes—
743C23×C4C2414yes—
744C23×C4C2414yes—
745C23×C4C2414yes—
746C23×C4C2412yes—
747C23×C4C2412yes—
748C23×C4C2414yes—
749C23×C4C2414yes—
750C23×C4C2411yescharacteristic
751C23×C4C2411yescharacteristic
752C23×C4C2412yes—
753C23×C4C2414yes—
754C4⋊Q8—42no—
755C4⋊Q8—44no—
756C4⋊Q8—44no—
757C4⋊Q8—48no—
758C4⋊Q8—44no—
759#126—44no—
760#126—48no—
761#126—44no—
762#126—84no—
763#125—44no—
764#125—44no—
765#125—84no—
766#124—42no—
767#124—48no—
768#123—44no—
769#123—42no—
770#123—44no—
771#123—82no—
772C22⋊Q8—48no—
773C22⋊Q8—48no—
774C22⋊Q8—44no—
775C22⋊Q8—48no—
776C22⋊Q8—48no—
777C22⋊Q8—48no—
778C22⋊Q8—44no—
779C22⋊Q8—42no—
780C22⋊Q8—84no—
781C22⋊Q8—84no—
782#121—42no—
783#121—44no—
784#120—44no—
785C4×Q8—42no—
786C4×Q8—44no—
787C4×Q8—44no—
788C4×D4—28no—
789C4×D4—28no—
790C4×D4—24no—
791C4×D4—28no—
792C4×D4—28no—
793C4×D4—28no—
794C4×D4—28no—
795C4×D4—44no—
796C4×D4—42no—
797C4×D4—48no—
798C4×D4—48no—
799#117—42no—
800#117—44no—
801C2×C4⋊C4—42no—
802C2×C4⋊C4—42no—
803C2×C4⋊C4—44no—
804C2×C4⋊C4—48no—
805C2×C4⋊C4—84no—
806C2×C4⋊C4—84no—
807C2×C4⋊C4C2412yes—
808C2×C4⋊C4C2412yes—
809C2×C4⋊C4C2411yescharacteristic
810C2×C4⋊C4C2412yes—
811C2×C4⋊C4C2412yes—
812C2×C4⋊C4C2412yes—
813C2×C4⋊C4C2412yes—
814C2×C4⋊C4C2412yes—
815C2×C4⋊C4C2412yes—
816C2×C4⋊C4C2412yes—
817C2×C4⋊C4C2411yescharacteristic
818C2×C4⋊C4C2412yes—
819C2×C4⋊C4C2412yes—
820C2×C4⋊C4C2412yes—
821C2×C4⋊C4C2412yes—
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⋊C4C2414yes—
831C2×C4⋊C4C2414yes—
832C2×C4⋊C4C2411yescharacteristic
833C2×C4⋊C4C2411yescharacteristic
834C2×C4⋊C4C2412yes—
835C2×C4⋊C4C2412yes—
836C2×C4⋊C4C2412yes—
837C2×C4⋊C4C2411yescharacteristic
838C2×C4⋊C4C2412yes—
839C2×C4⋊C4C2414yes—
840C2×C4⋊C4C2414yes—
841C2×C4⋊C4C2412yes—
842C2×C4⋊C4C2414yes—
843C2×C4⋊C4C2412yes—
844C2×C4⋊C4C2414yes—
845C2×C4⋊C4C2414yes—
846C2×C4⋊C4C2412yes—
847C2×C4⋊C4C2412yes—
848C2×C4⋊C4C2414yes—
849C2×C4⋊C4C2414yes—
850C2×C4⋊C4C2414yes—
851C2×C4⋊C4C2414yes—
852C2×C4⋊C4C2412yes—
853C2×C4⋊C4C2414yes—
854C2×C4⋊C4C2412yes—
855C2×C4⋊C4C2414yes—
856C2×C4⋊C4C2412yes—
857C2×C4⋊C4C2412yes—
858C2×C4⋊C4C2412yes—
859C2×C4⋊C4C2412yes—
860C2×C4⋊C4C2412yes—
861C2×C4⋊C4C2414yes—
862C2×C4⋊C4C2414yes—
863C2×C4⋊C4C2412yes—
864C2×C4⋊C4C2412yes—
865C2×C4⋊C4C2414yes—
866C2×C4⋊C4C2414yes—
867C2×C4⋊C4C2414yes—
868C2×C4⋊C4C2414yes—
869C2×C22⋊C4—48no—
870C2×C22⋊C4—48no—
871C2×C22⋊C4—44no—
872C2×C22⋊C4—44no—
873C2×C22⋊C4—82no—
874C2×C22⋊C4C2412yes—
875C2×C22⋊C4C2412yes—
876C2×C22⋊C4C2414yes—
877C2×C22⋊C4C2414yes—
878C2×C22⋊C4C2414yes—
879C2×C22⋊C4C2414yes—
880C2×C22⋊C4C2412yes—
881C2×C22⋊C4C2414yes—
882C2×C22⋊C4C2414yes—
883C2×C22⋊C4C2414yes—
884C2×C22⋊C4C2414yes—
885C2×C22⋊C4C2412yes—
886C2×C22⋊C4C2411yescharacteristic
887C2×C22⋊C4C2412yes—
888C2×C22⋊C4C2411yescharacteristic
889C2×C22⋊C4C2411yescharacteristic
890C2×C22⋊C4C2414yes—
891C2×C22⋊C4C2412yes—
892C2×C22⋊C4C2412yes—
893C2×C22⋊C4C2412yes—
894C2×C22⋊C4C2412yes—
895C2×C22⋊C4C2414yes—
896C2×C22⋊C4C2414yes—
897C2×C22⋊C4C2414yes—
898C2×C22⋊C4C2414yes—
899C2×C22⋊C4C2414yes—
900C2×C22⋊C4C2412yes—
901C2×C22⋊C4C2411yescharacteristic
902C2×C22⋊C4C2412yes—
903C2×C22⋊C4C2412yes—
904C2×C22⋊C4C2414yes—
905C2×C22⋊C4C2414yes—
906C2×C22⋊C4C2414yes—
907C2×C22⋊C4C2412yes—
908C2×C22⋊C4C2412yes—
909C2×C22⋊C4C2412yes—
910C2×C22⋊C4C2414yes—
911C2×C22⋊C4C2414yes—
912C2×C22⋊C4C2412yes—
913C2×C22⋊C4C2412yes—
914C2×C22⋊C4C2414yes—
915C2×C22⋊C4C2414yes—
916C2×C42—42no—
917C2×C42—48no—
918C2×C42C2412yes—
919C2×C42C2411yescharacteristic
920C2×C42C2412yes—
921C2×C42C2412yes—
922C2×C42C2412yes—
923C2×C42C2412yes—
924C2×C42C2412yes—
925C2×C42C2414yes—
926C2×C42C2412yes—
927C2×C42C2414yes—
928C2×C42C2412yes—
929C2×C42C2414yes—
930C2×C42C2412yes—
931C2×C42C2412yes—
932C2×C42C2412yes—
933C2×C42C2412yes—
934C2×C42C2414yes—
935C2×C42C2414yes—
936#95C2411yescharacteristic
937#95C2412yes—
938#95C2411yescharacteristic
939#95C2412yes—
940#95C2412yes—
941#95C2412yes—
942#95C2412yes—
943#95C2412yes—
944#95C2412yes—
945#95C2412yes—
946#95C2412yes—
947#95C2414yes—
948#95C2414yes—
949#95C2414yes—
950#95C2414yes—
951#95C2414yes—
952#95C2412yes—
953#95C2414yes—
954#95C2414yes—
955#95C2414yes—
956#95C2414yes—
957#95C2414yes—
958#95C2414yes—
959#95C2414yes—
960#95C2414yes—
961#95C2414yes—
962#95C2414yes—
963#95C2414yes—
964#95C2414yes—
965#95C2414yes—
966#95C2414yes—
967#95C2414yes—
968#95C2414yes—
969#95C2414yes—
970#95C2414yes—
971#95C2414yes—
972#95C2414yes—
973#95C2414yes—
974#95C2411yescharacteristic
975#95C2412yes—
976#95C2414yes—
977#95C2414yes—
978#95C2414yes—
979#95C2412yes—
980#95C2411yescharacteristic
981#95C2412yes—
982#95C2412yes—
983#95C2412yes—
984#95C2412yes—
985#95C2412yes—
986#95C2412yes—
987#95C2412yes—
988#95C2412yes—
989#95C2412yes—
990#95C2412yes—
991#95C2412yes—
992#95C2412yes—
993#95C2412yes—
994#95C2412yes—
995#95C2412yes—
996#95C2412yes—
997#95C2414yes—
998#95C2414yes—
999#95C2414yes—
1000#95C2414yes—
1001#95C2414yes—
1002#95C2414yes—
1003#95C2414yes—
1004#95C2412yes—
1005#95C2414yes—
1006#95C2414yes—
1007#95C2414yes—
1008#95C2414yes—
1009#95C2414yes—
1010#95C2414yes—
1011#95C2414yes—
1012#95C2414yes—
1013#95C2414yes—
1014#95C2414yes—
1015C24—24no—
1016C24—24no—
1017C24—28no—
1018C24—44no—
1019C24—42no—
1020C24C2512yes—
1021C24C2511yescharacteristic
1022C24C2511yescharacteristic
1023C24C2512yes—
1024#41—416no—
1025C2×Q8—22no—
1026C2×Q8—24no—
1027C2×Q8—24no—
1028C2×Q8—24no—
1029C2×Q8—28no—
1030C2×Q8—41no—
1031C2×Q8—42no—
1032C2×Q8—44no—
1033C2×Q8—42no—
1034C2×Q8—42no—
1035C2×Q8—44no—
1036C2×Q8—44no—
1037C2×Q8—44no—
1038C2×Q8—44no—
1039C2×Q8—44no—
1040C2×Q8—816no—
1041C2×D4—24no—
1042C2×D4—24no—
1043C2×D4—28no—
1044C2×D4—28no—
1045C2×D4—22no—
1046C2×D4—22no—
1047C2×D4—24no—
1048C2×D4—41no—
1049C2×D4—41no—
1050C2×D4—42no—
1051C2×D4—44no—
1052C2×D4—416no—
1053C2×D4H(5,𝔽2)14yes—
1054C2×D42−1+418yes—
1055C22×C4—24no—
1056C22×C4—28no—
1057C22×C4—28no—
1058C22×C4—22no—
1059C22×C4—24no—
1060C22×C4—28no—
1061C22×C4—28no—
1062C22×C4—28no—
1063C22×C4—28no—
1064C22×C4—28no—
1065C22×C4—24no—
1066C22×C4—22no—
1067C22×C4—22no—
1068C22×C4—24no—
1069C22×C4—24no—
1070C22×C4—28no—
1071C22×C4—41no—
1072C22×C4—41no—
1073C22×C4—44no—
1074C22×C4—41no—
1075C22×C4—44no—
1076C22×C4—44no—
1077C22×C4—42no—
1078C22×C4—44no—
1079C22×C4—44no—
1080C22×C4—44no—
1081C22×C4—44no—
1082C22×C4—44no—
1083C22×C4—44no—
1084C22×C4—44no—
1085C22×C4—44no—
1086C22×C4—42no—
1087C22×C4—44no—
1088C22×C4—42no—
1089C22×C4—44no—
1090C22×C4—44no—
1091C22×C4—44no—
1092C22×C4—42no—
1093C22×C4—42no—
1094C22×C4—42no—
1095C22×C4—816no—
1096C22×C4C2512yes—
1097C22×C4C2511yescharacteristic
1098C22×C4C2511yescharacteristic
1099C22×C4C2512yes—
1100C22×C4C2512yes—
1101C22×C4C2514yes—
1102C22×C4C2512yes—
1103C22×C4C2511yescharacteristic
1104C22×C4C2512yes—
1105C22×C4C2512yes—
1106C22×C4C2514yes—
1107C22×C4C2514yes—
1108C22×C4C2512yes—
1109C22×C4C2512yes—
1110C22×C4C2512yes—
1111C22×C4C2514yes—
1112C22×C4C2514yes—
1113C22×C4C2512yes—
1114C22×C4C2514yes—
1115C22×C4C2512yes—
1116C22×C4C2512yes—
1117C22×C4C2512yes—
1118C22×C4C2511yescharacteristic
1119C22×C4C2512yes—
1120C22×C4C2511yescharacteristic
1121C4⋊C4—24no—
1122C4⋊C4—24no—
1123C4⋊C4—22no—
1124C4⋊C4—24no—
1125C4⋊C4—24no—
1126C4⋊C4—24no—
1127C4⋊C4—24no—
1128C4⋊C4—24no—
1129C4⋊C4—24no—
1130C4⋊C4—41no—
1131C4⋊C4—42no—
1132C4⋊C4—42no—
1133C4⋊C4—42no—
1134C4⋊C4—44no—
1135C4⋊C4—44no—
1136C4⋊C4—44no—
1137C4⋊C4—44no—
1138C4⋊C4—42no—
1139C4⋊C4—42no—
1140C4⋊C4—44no—
1141C4⋊C4—44no—
1142C4⋊C4—44no—
1143C4⋊C4—44no—
1144C4⋊C4—44no—
1145C4⋊C4—44no—
1146C4⋊C4—41no—
1147C4⋊C4—41no—
1148C4⋊C4—42no—
1149C4⋊C4—42no—
1150C4⋊C4—42no—
1151C4⋊C4—41no—
1152C4⋊C4—42no—
1153C4⋊C4—44no—
1154C4⋊C4—42no—
1155C4⋊C4—44no—
1156C4⋊C4—42no—
1157C4⋊C4—44no—
1158C4⋊C4—44no—
1159C4⋊C4—44no—
1160C4⋊C4—42no—
1161C4⋊C4—44no—
1162C4⋊C4—42no—
1163C4⋊C4—44no—
1164C4⋊C4—44no—
1165C4⋊C4—42no—
1166C4⋊C4—44no—
1167C4⋊C4—44no—
1168C4⋊C4—42no—
1169C4⋊C4—44no—
1170C4⋊C4—42no—
1171C4⋊C4—42no—
1172C4⋊C4—44no—
1173C4⋊C4—44no—
1174C4⋊C4—42no—
1175C4⋊C4—42no—
1176C4⋊C4—42no—
1177C4⋊C4—44no—
1178C4⋊C4—44no—
1179C4⋊C4—44no—
1180C4⋊C4—44no—
1181C4⋊C4—42no—
1182C4⋊C4—42no—
1183C22⋊C4—28no—
1184C22⋊C4—28no—
1185C22⋊C4—24no—
1186C22⋊C4—28no—
1187C22⋊C4—28no—
1188C22⋊C4—28no—
1189C22⋊C4—28no—
1190C22⋊C4—24no—
1191C22⋊C4—28no—
1192C22⋊C4—24no—
1193C22⋊C4—22no—
1194C22⋊C4—24no—
1195C22⋊C4—28no—
1196C22⋊C4—24no—
1197C22⋊C4—41no—
1198C22⋊C4—44no—
1199C22⋊C4—44no—
1200C22⋊C4—44no—
1201C22⋊C4—44no—
1202C22⋊C4—44no—
1203C22⋊C4—42no—
1204C22⋊C4—42no—
1205C22⋊C4—42no—
1206C22⋊C4—41no—
1207C22⋊C4—42no—
1208C22⋊C4—44no—
1209C22⋊C4—42no—
1210C22⋊C4—41no—
1211C22⋊C4—42no—
1212C22⋊C4—42no—
1213C22⋊C4—42no—
1214C22⋊C4—44no—
1215C22⋊C4—44no—
1216C22⋊C4—44no—
1217C22⋊C4—42no—
1218C22⋊C4—42no—
1219C22⋊C4—44no—
1220C22⋊C4—44no—
1221C22⋊C4—42no—
1222C22⋊C4—42no—
1223C22⋊C4—44no—
1224C22⋊C4—44no—
1225C42—24no—
1226C42—24no—
1227C42—22no—
1228C42—24no—
1229C42—24no—
1230C42—24no—
1231C42—24no—
1232C42—24no—
1233C42—28no—
1234C42—44no—
1235C42—44no—
1236C42—42no—
1237C42—44no—
1238C42—44no—
1239C42—42no—
1240C42—42no—
1241C42—42no—
1242C42—42no—
1243C23—24no—
1244C23—22no—
1245C23—22no—
1246C23—21no—
1247C23—22no—
1248C23—22no—
1249C23—21no—
1250C23—22no—
1251C23—21no—
1252C23—22no—
1253C23—24no—
1254C23—22no—
1255C23—24no—
1256C23—21no—
1257C23—22no—
1258C23—21no—
1259C23—22no—
1260C23—48no—
1261C23—416no—
1262C23—48no—
1263C23—84no—
1264C23—88no—
1265C23C2×H(5,𝔽2)14yes—
1266C23C2×2−1+418yes—
1267C23#58512yes—
1268C23C2611yescharacteristic
1269Q8—44no—
1270Q8—44no—
1271Q8—84no—
1272Q8—88no—
1273Q8—84no—
1274Q8—164no—
1275D4—48no—
1276D4—48no—
1277D4—44no—
1278D4—82no—
1279D4—162no—
1280D4#563116yes—
1281C2×C4—22no—
1282C2×C4—22no—
1283C2×C4—22no—
1284C2×C4—22no—
1285C2×C4—22no—
1286C2×C4—21no—
1287C2×C4—22no—
1288C2×C4—21no—
1289C2×C4—22no—
1290C2×C4—22no—
1291C2×C4—21no—
1292C2×C4—24no—
1293C2×C4—22no—
1294C2×C4—24no—
1295C2×C4—24no—
1296C2×C4—21no—
1297C2×C4—22no—
1298C2×C4—22no—
1299C2×C4—22no—
1300C2×C4—22no—
1301C2×C4—22no—
1302C2×C4—22no—
1303C2×C4—24no—
1304C2×C4—24no—
1305C2×C4—24no—
1306C2×C4—22no—
1307C2×C4—22no—
1308C2×C4—24no—
1309C2×C4—22no—
1310C2×C4—22no—
1311C2×C4—24no—
1312C2×C4—24no—
1313C2×C4—22no—
1314C2×C4—24no—
1315C2×C4—24no—
1316C2×C4—22no—
1317C2×C4—22no—
1318C2×C4—22no—
1319C2×C4—22no—
1320C2×C4—22no—
1321C2×C4—24no—
1322C2×C4—24no—
1323C2×C4—22no—
1324C2×C4—22no—
1325C2×C4—24no—
1326C2×C4—22no—
1327C2×C4—22no—
1328C2×C4—24no—
1329C2×C4—22no—
1330C2×C4—22no—
1331C2×C4—22no—
1332C2×C4—21no—
1333C2×C4—22no—
1334C2×C4—24no—
1335C2×C4—22no—
1336C2×C4—21no—
1337C2×C4—22no—
1338C2×C4—22no—
1339C2×C4—22no—
1340C2×C4—24no—
1341C2×C4—24no—
1342C2×C4—22no—
1343C2×C4—24no—
1344C2×C4—24no—
1345C2×C4—22no—
1346C2×C4—22no—
1347C2×C4—416no—
1348C2×C4—44no—
1349C2×C4—48no—
1350C2×C4—44no—
1351C2×C4—44no—
1352C2×C4—88no—
1353C2×C4—88no—
1354C2×C4—88no—
1355C2×C4—88no—
1356C2×C4—88no—
1357C2×C4—84no—
1358C2×C4—84no—
1359C2×C4—82no—
1360C2×C4—88no—
1361C2×C4—162no—
1362C2×C4C2×H(5,𝔽2)12yes—
1363C2×C4C2×2−1+414yes—
1364C2×C4#58514yes—
1365C22—24no—
1366C22—28no—
1367C22—24no—
1368C22—28no—
1369C22—24no—
1370C22—22no—
1371C22—41no—
1372C22—41no—
1373C22—42no—
1374C22—41no—
1375C22—42no—
1376C22—42no—
1377C22—44no—
1378C22—42no—
1379C22—41no—
1380C22—41no—
1381C22—42no—
1382C22—42no—
1383C22—44no—
1384C22—816no—
1385C22C2×#56318yes—
1386C22C22×H(5,𝔽2)11yescharacteristic
1387C22C22×2−1+412yes—
1388C22C2×#58512yes—
1389C22C2×#58511yescharacteristic
1390C22H(7,𝔽2)11yescharacteristic
1391C4—24no—
1392C4—44no—
1393C4—41no—
1394C4—42no—
1395C4—42no—
1396C4—42no—
1397C4—42no—
1398C4—42no—
1399C4—44no—
1400C4—42no—
1401C4—42no—
1402C4—42no—
1403C4—44no—
1404C4—44no—
1405C4—41no—
1406C4—42no—
1407C4—41no—
1408C4—41no—
1409C4—42no—
1410C4—42no—
1411C4—44no—
1412C4—44no—
1413C4—42no—
1414C4—42no—
1415C4C2×#56314yes—
1416C2—28no—
1417C2—42no—
1418C2—81no—
1419C2—82no—
1420C2C22×#56311yescharacteristic
1421C2#6291811yescharacteristic
1422C2#6295112yes—
1423C2#6301711yescharacteristic
1424C2#6302312yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#546C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #53155C2semidirect
2. #53104C2semidirect
3. #53031C2semidirect
4. #53017C2semidirect
5. #52603C2semidirect
6. #52430C2semidirect
7. #52396C2semidirect
8. #52349C2semidirect
9. #52300C2semidirect
10. C2×#2764C2semidirect
11. #46348C2semidirect
12. #46343C2semidirect
13. #46085C2semidirect
14. #46060C2semidirect
15. #46049C2semidirect
16. #45983C2semidirect
17. #45696C2semidirect
18. #45690C2semidirect
19. #45531C2semidirect
20. #45474C2semidirect
21. #36276C2semidirect
22. #36240C2semidirect
23. #36215C2semidirect
24. #36166C2semidirect
27. #35961C2semidirect
29. #35806C2semidirect
35. #2863C22semidirect
36. #2862C22semidirect
38. #2857C22semidirect
41. #2852C22semidirect
45. #2843C22semidirect
47. #2839C22semidirect
48. #2838C22semidirect
49. #2838C22semidirect
50. #2837C22semidirect
51. #2836C22semidirect
52. #2836C22semidirect
54. #2834C22semidirect
55. #2833C22semidirect
56. #2831C22semidirect
57. #2831C22semidirect
58. #2831C22semidirect
59. #2827C22semidirect
60. #2822C22semidirect
61. #2821C22semidirect
63. #2817C22semidirect
64. #2809C22semidirect
65. #2791C22semidirect
67. #2777C22semidirect
68. #2777C22semidirect
69. #2776C22semidirect
70. #2775C22semidirect
72. #2770C22semidirect
73. #2769C22semidirect
74. #2766C22semidirect
82. #2764C22semidirect
83. #2764C22semidirect
84. #2764C22semidirect
85. #2764C22semidirect
86. #2764C22semidirect
87. #2762C22semidirect
88. #2762C22semidirect
89. #2759C22semidirect
90. #2758C22semidirect
91. #2758C22semidirect
93. #2745C22semidirect
94. #2745C22semidirect
95. #2738C22semidirect
96. #2731C22semidirect
98. #2728C22semidirect
101. #2721C22semidirect
102. #2720C22semidirect
104. #2716C22semidirect
105. #2716C22semidirect
106. #2715C22semidirect
107. #2715C22semidirect
110. #2702C22semidirect
112. #2698C22semidirect
113. #2689C22semidirect
116. #2647C22semidirect
117. #2646C22semidirect
120. #2629C22semidirect
121. #2627C22semidirect
125. #2582C22semidirect
128. #2579C22semidirect
129. #2571C22semidirect
130. #2570C22semidirect
131. #2569C22semidirect
132. #2567C22semidirect
134. #2565C22semidirect
138. #2550C22semidirect
139. #2550C22semidirect
140. #2550C22semidirect
141. #2550C22semidirect
142. #2549C22semidirect
143. #2549C22semidirect
144. #2549C22semidirect
145. #2549C22semidirect
146. #2546C22semidirect
147. #2514C22semidirect
148. #2514C22semidirect
149. #2514C22semidirect
155. #2510C22semidirect
156. #2510C22semidirect
157. #2510C22semidirect
158. #2509C22semidirect
159. #2509C22semidirect
160. #2508C22semidirect
161. #2506C22semidirect
162. #2505C22semidirect
163. #2505C22semidirect
164. #2505C22semidirect
167. #2502C22semidirect
171. #2495C22semidirect
172. #2495C22semidirect
173. #2495C22semidirect
175. #2493C22semidirect
176. #2493C22semidirect
177. #2493C22semidirect
189. #2473C22semidirect
192. #2453C22semidirect
194. #2451C22semidirect
196. #2450C22semidirect
198. #2449C22semidirect
204. #2442C22semidirect
205. #2442C22semidirect
207. #2440C22semidirect
208. #2438C22semidirect
209. #2438C22semidirect
213. #2434C22semidirect
218. #2417C22semidirect
220. #2402C22semidirect
222. #2396C22semidirect
224. C2×#400C22semidirect
225. C2×#398C22semidirect
228. #2383C22semidirect
229. #2381C22semidirect
230. #2379C22semidirect
247. C4×C4⋊Q8C22semidirect
249. C4×#126C22semidirect
252. C2×#391C22semidirect
255. C2×#383C22semidirect

Maximal subgroups

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

subgroupindex
#531552
#531042
#530312
#530172
#526032
#524302
#523962
#523492
#523002
C2×#27642
#463482
#463432
#460852
#460602
#460492
#459832
#456962
#456902
#455312
#454742
#362762
#362402
#362152
#361662
#361552
#359762
#359612
#359392
#358062