Finite Group Databasebeta

← #7656070

Subgroups — #7656070

Order 512.

4716 conjugacy classes of subgroups.

The subgroup lattice has 1301 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42870C213yesmaximal, complemented
2#42868C213yesmaximal, complemented
3#42856C213yesmaximal, complemented
4#42848C213yesmaximal, complemented
5#42846C213yesmaximal, complemented
6#42845C213yesmaximal, complemented
7#42837C213yesmaximal, complemented
8#42836C213yesmaximal, complemented
9#39732C213yesmaximal, complemented
10#39604C213yesmaximal, complemented
11#38982C213yesmaximal, complemented
12#38973C213yesmaximal, complemented
13#37505C213yesmaximal, complemented
14#37504C213yesmaximal, complemented
15#36578C211yesmaximal, characteristic, complemented
16Q8×#123C211yesmaximal, characteristic, complemented
17#36435C211yesmaximal, characteristic, complemented
18#36434C211yesmaximal, characteristic
19#35996C211yesmaximal, characteristic, complemented
20#35971C211yesmaximal, characteristic, complemented
21#35898C211yesmaximal, characteristic, complemented
22#35883C211yesmaximal, characteristic, complemented
23#35868C211yesmaximal, characteristic, complemented
24#35845C211yesmaximal, characteristic, complemented
25#35816C211yesmaximal, characteristic, complemented
26#35801C211yesmaximal, characteristic, complemented
27#35024C213yesmaximal, complemented
28#34584C213yesmaximal, complemented
29#34294C211yesmaximal, characteristic, complemented
30#34291C211yesmaximal, characteristic, complemented
31C2×Q8×C4⋊C4C211yesmaximal, characteristic, complemented
32C2×#557C2211yescharacteristic
33C2×D4×Q8C2211yescharacteristic
34C2×#548C2211yescharacteristic
35C2×#548C2211yescharacteristic
36C2×#520C2211yescharacteristic
37C2×#519C2211yescharacteristic
38C22×C4×Q8C2211yescharacteristic
39C22×C4×Q8C2211yescharacteristic
40C22×C4×Q8C2211yescharacteristic
41#2855C2213yes—
42#2854C2213yes—
43#2851C2213yes—
44#2850C2213yes—
45#2839C2216yes—
46#2838C2216yes—
47#2837C2216yes—
48#2836C2216yes—
49#2795C2216yes—
50#2793C2216yes—
51#2792C2216yes—
52#2791C2216yes—
53#2790C2216yes—
54#2790C2216yes—
55#2787C2216yes—
56#2783C2216yes—
57#2777C2216yes—
58#2776C2216yes—
59#2773C2216yes—
60#2771C2216yes—
61#2720C2216yes—
62#2718C2216yes—
63#2694C2216yes—
64#2689C2216yes—
65#2664C2216yes—
66#2663C2216yes—
67#2655C2213yes—
68#2655C2213yes—
69#2655C2216yes—
70#2654C2213yes—
71#2654C2213yes—
72#2652C2216yes—
73#2651C2213yes—
74#2651C2213yes—
75#2650C2213yes—
76#2650C2213yes—
77#2647C2213yes—
78#2647C2213yes—
79#2646C2213yes—
80#2645C2213yes—
81#2644C2213yes—
82#2643C2213yes—
83#2643C2213yes—
84#2643C2216yes—
85#2639C2213yes—
86#2629C2213yes—
87#2628C2213yes—
88#2627C2213yes—
89#2625C2213yes—
90#2624C2213yes—
91#2623C2211yescharacteristic
92#2623C2213yes—
93#2618C2213yes—
94#2596C2216yes—
95#2594C2216yes—
96#2581C2213yes—
97#2581C2213yes—
98#2577C2216yes—
99#2575C2216yes—
100#2571C2213yes—
101#2570C2213yes—
102#2570C2213yes—
103#2567C2213yes—
104#2566C2213yes—
105#2565C2213yes—
106#2552C2213yes—
107#2545C2213yes—
108#2538C2213yes—
109#2536C2213yes—
110#2514C2213yes—
111#2514C2213yes—
112#2513C2213yes—
113#2512C2213yes—
114#2512C2213yes—
115#2511C2213yes—
116#2509C2213yes—
117#2509C2213yes—
118#2508C2213yes—
119#2508C2213yes—
120#2507C2213yes—
121#2507C2213yes—
122#2506C2213yes—
123#2506C2213yes—
124#2504C2213yes—
125#2502C2213yes—
126#2502C2213yes—
127#2500C2213yes—
128#2497C2213yes—
129#2497C2213yes—
130#2496C2213yes—
131#2495C2213yes—
132#2494C2213yes—
133#2494C2213yes—
134#2487C2213yes—
135#2487C2213yes—
136#2486C2213yes—
137#2485C2213yes—
138#2481C2216yes—
139#2473C2216yes—
140#2454C2213yes—
141#2453C2213yes—
142#2453C2213yes—
143#2453C2213yes—
144#2452C2213yes—
145#2451C2213yes—
146#2449C2216yes—
147#2448C2213yes—
148#2448C2213yes—
149#2448C2213yes—
150#2448C2213yes—
151#2447C2213yes—
152#2447C2213yes—
153#2446C2213yes—
154#2446C2213yes—
155#2443C2216yes—
156#2442C2213yes—
157#2442C2213yes—
158#2441C2213yes—
159#2441C2213yes—
160#2440C2213yes—
161#2440C2213yes—
162#2429C2213yes—
163#2426C2213yes—
164#2423C2213yes—
165#2423C2213yes—
166#2423C2213yes—
167#2422C2213yes—
168#2422C2213yes—
169#2421C2213yes—
170#2421C2213yes—
171#2421C2213yes—
172#2417C2213yes—
173#2416C2213yes—
174#2402C2213yes—
175#2402C2213yes—
176#2401C2213yes—
177#2401C2213yes—
178#2396C2213yes—
179#2396C2213yes—
180#2395C2213yes—
181#2395C2213yes—
182#2367C2213yes—
183#2365C2213yes—
184#2362C2213yes—
185#2361C2213yes—
186#2360C2213yes—
187#2360C2213yes—
188#2352C2213yes—
189#2351C2211yescharacteristic
190#2351C2211yescharacteristic
191#2351C2211yescharacteristic
192#2351C2211yescharacteristic
193#2351C2211yescharacteristic
194#2351C2211yescharacteristic
195Q8×C4⋊C4C2211yescharacteristic
196Q8×C4⋊C4C2211yescharacteristic
197Q8×C4⋊C4C2211yescharacteristic
198Q8×C4⋊C4C2211yescharacteristic
199Q8×C4⋊C4C2211yescharacteristic
200Q8×C4⋊C4C2211yescharacteristic
201Q8×C4⋊C4C2211yescharacteristic
202Q8×C4⋊C4C2213yes—
203Q8×C4⋊C4C2213yes—
204Q8×C4⋊C4C2213yes—
205Q8×C4⋊C4C2213yes—
206Q8×C4⋊C4C2211yescharacteristic
207D4×C4⋊C4C2213yes—
208#2341C2211yescharacteristic
209#2341C2211yescharacteristic
210#2341C2211yescharacteristic
211#2341C2211yescharacteristic
212Q8×C22⋊C4C2211yescharacteristic
213Q8×C22⋊C4C2211yescharacteristic
214Q8×C22⋊C4C2211yescharacteristic
215Q8×C22⋊C4C2211yescharacteristic
216Q8×C22⋊C4C2211yescharacteristic
217Q8×C22⋊C4C2211yescharacteristic
218#2327C2213yes—
219#2326C2213yes—
220#2323C2213yes—
221#2323C2213yes—
222#2322C2216yes—
223#2318C2216yes—
224C4×C22⋊Q8C2213yes—
225C4×C22⋊Q8C2213yes—
226C4×#123C2213yes—
227C4×#123C2213yes—
228C4×#121C2213yes—
229C4×#121C2213yes—
230C2×#389C2213yes—
231C2×#389C2213yes—
232#2290C2213yes—
233#2290C2213yes—
234C2×#384C2213yes—
235#2276C2211yescharacteristic
236#2276C2211yescharacteristic
237C2×C4×C4⋊C4C2213yes—
238C22×#41C2311yescharacteristic
239C23×Q8C2311yescharacteristic
240C23×Q8C2311yescharacteristic
241#557—44no—
242D4×Q8—28no—
243#548—28no—
244#548—44no—
245C2×C4⋊Q8C2313yes—
246C2×C4⋊Q8C2313yes—
247C2×#126C2316yes—
248C2×#125C2313yes—
249C2×#125C2313yes—
250C2×#125C2316yes—
251C2×#124C2313yes—
252C2×#124C2313yes—
253C2×#123C2313yes—
254C2×#123C2311yescharacteristic
255C2×#123C2316yes—
256C2×C22⋊Q8C2313yes—
257C2×C22⋊Q8C2313yes—
258C2×C22⋊Q8C2313yes—
259C2×C22⋊Q8C2313yes—
260C2×C22⋊Q8C2313yes—
261C2×C22⋊Q8C2316yes—
262C2×#121C2313yes—
263C2×#121C2313yes—
264C2×#121C2313yes—
265#520—44no—
266#519—44no—
267C2×C4×Q8—28no—
268C2×C4×Q8—44no—
269C2×C4×Q8—44no—
270C2×C4×Q8C2311yescharacteristic
271C2×C4×Q8C2311yescharacteristic
272C2×C4×Q8C2311yescharacteristic
273C2×C4×Q8C2311yescharacteristic
274C2×C4×Q8C2311yescharacteristic
275C2×C4×Q8C2311yescharacteristic
276C2×C4×Q8C2311yescharacteristic
277C2×C4×Q8C2311yescharacteristic
278C2×C4×Q8C2311yescharacteristic
279C2×C4×Q8C2311yescharacteristic
280C2×C4×Q8C2311yescharacteristic
281C2×C4×Q8C2311yescharacteristic
282C2×C4×Q8C2313yes—
283C2×C4×Q8C2313yes—
284C2×C4×Q8C2313yes—
285C2×C4×Q8C2313yes—
286C2×C4×Q8C2313yes—
287C2×C4×Q8C2313yes—
288C2×C4×Q8C2313yes—
289C2×C4×Q8C2313yes—
290C2×C4×Q8C2313yes—
291C2×C4×D4C2313yes—
292C2×C4×D4C2313yes—
293C2×C4×D4C2313yes—
294C2×C4×D4C2316yes—
295C2×C4×D4C2313yes—
296C2×C4×D4C2313yes—
297C2×#117C2313yes—
298C2×#117C2313yes—
299C2×#117C2313yes—
300C22×C4⋊C4C2311yescharacteristic
301C22×C4⋊C4C2313yes—
302C22×C4⋊C4C2313yes—
303C22×C4⋊C4C2313yes—
304C22×C4⋊C4C2313yes—
305C22×C4⋊C4C2313yes—
306C22×C4⋊C4C2316yes—
307C22×C42C2313yes—
308C22×C42C2313yes—
309C22×C42C2313yes—
310#401C2316yes—
311#401C2313yes—
312#401C2313yes—
313#400C2313yes—
314#400C2316yes—
315#400C2313yes—
316#400C2313yes—
317#400C2316yes—
318#400C2316yes—
319#400C2316yes—
320#400C2316yes—
321#400C2313yes—
322#400C2316yes—
323#400C2313yes—
324#400C2316yes—
325#400C2313yes—
326#400C2313yes—
327#400C2316yes—
328#400C2316yes—
329#400C2313yes—
330#400C2311yescharacteristic
331#400C2311yescharacteristic
332#400C2313yes—
333#400C2313yes—
334#400C2313yes—
335#400C2313yes—
336#400C2313yes—
337#400C2313yes—
338#400C2313yes—
339#400C2313yes—
340#399C2313yes—
341#399C2316yes—
342#399C2316yes—
343#399C2316yes—
344#399C2316yes—
345#399C2313yes—
346#399C2311yescharacteristic
347#399C2311yescharacteristic
348#398C2316yes—
349#398C2316yes—
350#398C2313yes—
351#398C2316yes—
352#398C2313yes—
353#398C2313yes—
354#398C2313yes—
355#398C2316yes—
356#398C2316yes—
357#398C2316yes—
358#398C2316yes—
359#398C2316yes—
360#398C2316yes—
361#398C2316yes—
362#398C2313yes—
363#398C2313yes—
364#398C2311yescharacteristic
365#398C2311yescharacteristic
366#398C2313yes—
367#398C2313yes—
368#398C2313yes—
369#398C2313yes—
370#398C2313yes—
371#398C2313yes—
372#397C2316yes—
373#397C2313yes—
374#397C2316yes—
375#397C2316yes—
376#397C2313yes—
377#397C2316yes—
378#397C2316yes—
379#397C2316yes—
380#397C2316yes—
381#397C2313yes—
382#397C2311yescharacteristic
383#397C2311yescharacteristic
384#397C2313yes—
385#397C2313yes—
386#397C2313yes—
387#397C2313yes—
388#397C2313yes—
389#397C2313yes—
390#397C2313yes—
391#396C2313yes—
392#396C2316yes—
393#396C2316yes—
394#396C2316yes—
395#396C2316yes—
396#396C2316yes—
397#396C2313yes—
398#396C2313yes—
399#396C2313yes—
400#396C2313yes—
401#396C2313yes—
402#395C2313yes—
403#395C2316yes—
404#395C2316yes—
405#395C2313yes—
406#394C2313yes—
407#394C2316yes—
408#394C2316yes—
409#394C2313yes—
410#394C2313yes—
411#394C2313yes—
412#393C2313yes—
413#393C2313yes—
414#391C2313yes—
415#391C2313yes—
416#391C2313yes—
417#391C2313yes—
418#391C2313yes—
419#391C2313yes—
420#391C2313yes—
421#391C2313yes—
422#391C2313yes—
423#391C2313yes—
424#391C2313yes—
425#391C2313yes—
426#391C2313yes—
427#390C2313yes—
428#390C2313yes—
429#390C2313yes—
430#390C2313yes—
431#390C2313yes—
432#390C2313yes—
433#390C2313yes—
434#390C2313yes—
435#390C2313yes—
436#389C2316yes—
437#389C2316yes—
438#389C2313yes—
439#389C2313yes—
440#389C2313yes—
441#389C2313yes—
442#389C2313yes—
443#389C2313yes—
444#389C2316yes—
445#389C2316yes—
446#389C2316yes—
447#389C2316yes—
448#389C2316yes—
449#389C2313yes—
450#389C2313yes—
451#389C2313yes—
452#389C2316yes—
453#389C2313yes—
454#389C2313yes—
455#389C2313yes—
456#389C2313yes—
457#389C2313yes—
458#389C2313yes—
459#389C2313yes—
460#389C2313yes—
461#389C2313yes—
462#389C2316yes—
463#389C2316yes—
464#389C2313yes—
465#389C2313yes—
466#389C2313yes—
467#389C2313yes—
468#389C2313yes—
469#389C2313yes—
470#389C2313yes—
471#389C2313yes—
472#389C2313yes—
473#389C2313yes—
474#389C2313yes—
475#389C2313yes—
476#388C2316yes—
477#388C2316yes—
478#388C2316yes—
479#388C2316yes—
480#388C2316yes—
481#388C2316yes—
482#388C2316yes—
483#388C2316yes—
484#388C2313yes—
485#388C2316yes—
486#388C2316yes—
487#388C2316yes—
488#388C2313yes—
489#388C2313yes—
490#388C2313yes—
491#388C2313yes—
492#388C2313yes—
493#388C2313yes—
494#388C2313yes—
495#388C2313yes—
496#388C2313yes—
497#388C2316yes—
498#388C2316yes—
499#387C2313yes—
500#387C2316yes—
501#387C2316yes—
502#387C2316yes—
503#387C2316yes—
504#387C2316yes—
505#387C2316yes—
506#387C2316yes—
507#387C2316yes—
508#387C2316yes—
509#387C2316yes—
510#387C2316yes—
511#387C2313yes—
512#387C2313yes—
513#387C2316yes—
514#387C2313yes—
515#387C2313yes—
516#387C2316yes—
517#387C2316yes—
518#387C2313yes—
519#387C2313yes—
520#387C2313yes—
521#387C2316yes—
522#387C2313yes—
523#387C2313yes—
524#387C2316yes—
525#387C2316yes—
526#386C2313yes—
527#386C2316yes—
528#386C2316yes—
529#386C2313yes—
530#386C2313yes—
531#386C2311yescharacteristic
532#386C2313yes—
533#386C2311yescharacteristic
534#386C2313yes—
535#386C2313yes—
536#385C2316yes—
537#385C2316yes—
538#385C2313yes—
539#385C2316yes—
540#385C2316yes—
541#385C2316yes—
542#385C2316yes—
543#385C2316yes—
544#385C2313yes—
545#385C2313yes—
546#385C2311yescharacteristic
547#385C2313yes—
548#385C2311yescharacteristic
549#385C2313yes—
550#385C2313yes—
551#385C2316yes—
552#384C2313yes—
553#384C2313yes—
554#384C2313yes—
555#384C2313yes—
556#384C2313yes—
557#384C2313yes—
558#384C2313yes—
559#384C2313yes—
560#384C2316yes—
561#384C2316yes—
562#383C2316yes—
563#382C2313yes—
564#382C2313yes—
565#382C2313yes—
566#382C2313yes—
567#382C2316yes—
568#382C2313yes—
569#382C2313yes—
570#381C2316yes—
571#381C2313yes—
572#381C2311yescharacteristic
573#380C2316yes—
574#380C2313yes—
575#380C2313yes—
576#380C2313yes—
577#380C2313yes—
578#380C2313yes—
579#380C2313yes—
580#380C2313yes—
581#380C2313yes—
582#380C2313yes—
583#380C2313yes—
584#380C2313yes—
585#380C2313yes—
586C4×C4⋊C4C2313yes—
587C4×C4⋊C4C2313yes—
588C4×C4⋊C4C2313yes—
589C4×C4⋊C4C2313yes—
590C4×C4⋊C4C2313yes—
591C4×C4⋊C4C2313yes—
592C4×C4⋊C4C2313yes—
593C4×C4⋊C4C2313yes—
594C4×C4⋊C4C2313yes—
595C4×C4⋊C4C2313yes—
596C4×C4⋊C4C2313yes—
597C4×C4⋊C4C2313yes—
598C4×C4⋊C4C2313yes—
599C4×C4⋊C4C2316yes—
600C4×C4⋊C4C2313yes—
601C4×C4⋊C4C2313yes—
602C4×C4⋊C4C2313yes—
603C4×C4⋊C4C2313yes—
604C4×C4⋊C4C2313yes—
605C4×C4⋊C4C2313yes—
606C4×C4⋊C4C2313yes—
607C4×C4⋊C4C2313yes—
608C4×C4⋊C4C2313yes—
609C4×C4⋊C4C2313yes—
610C4×C4⋊C4C2313yes—
611C4×C22⋊C4C2316yes—
612C4×C22⋊C4C2316yes—
613C4×C22⋊C4C2313yes—
614C4×C22⋊C4C2313yes—
615C4×C22⋊C4C2313yes—
616C4×C22⋊C4C2313yes—
617C4×C22⋊C4C2313yes—
618C4×C22⋊C4C2313yes—
619C4×C22⋊C4C2313yes—
620C4×C22⋊C4C2313yes—
621C4×C22⋊C4C2313yes—
622C4×C22⋊C4C2313yes—
623#376C2313yes—
624#376C2313yes—
625C2×#95C2313yes—
626C2×#95C2313yes—
627C2×#41—24no—
628C2×#41—24no—
629C2×#41—24no—
630C22×Q8—24no—
631C22×Q8—24no—
632C22×Q8—24no—
633C22×Q8—24no—
634C22×Q8—24no—
635C22×Q8#4118yes—
636C22×Q8C2413yes—
637C22×Q8C2413yes—
638C22×Q8C2413yes—
639C22×Q8C2411yescharacteristic
640C22×D4C2411yescharacteristic
641C22×D4C2413yes—
642C22×D4C2413yes—
643C22×D4C2413yes—
644C23×C4C2413yes—
645C23×C4C2413yes—
646C23×C4C2413yes—
647C23×C4C2411yescharacteristic
648C23×C4C2413yes—
649C23×C4C2413yes—
650C23×C4C2413yes—
651C23×C4C2411yescharacteristic
652C23×C4C2411yescharacteristic
653C23×C4C2416yes—
654C4⋊Q8—212no—
655C4⋊Q8—46no—
656#126—86no—
657#125—46no—
658#125—46no—
659#125—86no—
660#124—212no—
661#124—46no—
662#123—212no—
663#123—24no—
664#123—86no—
665C22⋊Q8—212no—
666C22⋊Q8—212no—
667C22⋊Q8—212no—
668C22⋊Q8—46no—
669C22⋊Q8—46no—
670C22⋊Q8—86no—
671#121—212no—
672#121—46no—
673#121—46no—
674C4×Q8—212no—
675C4×Q8—212no—
676C4×Q8—24no—
677C4×Q8—24no—
678C4×Q8—24no—
679C4×Q8—24no—
680C4×Q8—24no—
681C4×Q8—24no—
682C4×Q8—24no—
683C4×Q8—24no—
684C4×Q8—24no—
685C4×Q8—24no—
686C4×Q8—24no—
687C4×Q8—24no—
688C4×Q8—46no—
689C4×Q8—46no—
690C4×Q8—46no—
691C4×Q8—46no—
692C4×Q8—46no—
693C4×Q8—46no—
694C4×Q8—46no—
695C4×D4—212no—
696C4×D4—212no—
697C4×D4—46no—
698C4×D4—46no—
699C4×D4—46no—
700C4×D4—412no—
701#117—46no—
702#117—46no—
703#117—46no—
704C2×C4⋊C4—212no—
705C2×C4⋊C4—24no—
706C2×C4⋊C4—46no—
707C2×C4⋊C4—46no—
708C2×C4⋊C4—46no—
709C2×C4⋊C4—46no—
710C2×C4⋊C4—86no—
711C2×C4⋊C4C2413yes—
712C2×C4⋊C4C2413yes—
713C2×C4⋊C4C2413yes—
714C2×C4⋊C4C2413yes—
715C2×C4⋊C4C2413yes—
716C2×C4⋊C4C2413yes—
717C2×C4⋊C4C2413yes—
718C2×C4⋊C4C2416yes—
719C2×C4⋊C4C2411yescharacteristic
720C2×C4⋊C4C2411yescharacteristic
721C2×C4⋊C4C2411yescharacteristic
722C2×C4⋊C4C2411yescharacteristic
723C2×C4⋊C4C2413yes—
724C2×C4⋊C4C2413yes—
725C2×C4⋊C4C2413yes—
726C2×C4⋊C4C2413yes—
727C2×C4⋊C4C2413yes—
728C2×C4⋊C4C2413yes—
729C2×C4⋊C4C2413yes—
730C2×C4⋊C4C2416yes—
731C2×C4⋊C4C2411yescharacteristic
732C2×C4⋊C4C2411yescharacteristic
733C2×C4⋊C4C2413yes—
734C2×C4⋊C4C2413yes—
735C2×C4⋊C4C2413yes—
736C2×C4⋊C4C2416yes—
737C2×C4⋊C4C2416yes—
738C2×C4⋊C4C2416yes—
739C2×C4⋊C4C2416yes—
740C2×C4⋊C4C2416yes—
741C2×C4⋊C4C2416yes—
742C2×C4⋊C4C2413yes—
743C2×C4⋊C4C2413yes—
744C2×C4⋊C4C2413yes—
745C2×C4⋊C4C2413yes—
746C2×C4⋊C4C2411yescharacteristic
747C2×C4⋊C4C2413yes—
748C2×C4⋊C4C2413yes—
749C2×C4⋊C4C2413yes—
750C2×C4⋊C4C2416yes—
751C2×C4⋊C4C2411yescharacteristic
752C2×C4⋊C4C2413yes—
753C2×C4⋊C4C2413yes—
754C2×C4⋊C4C2413yes—
755C2×C4⋊C4C2413yes—
756C2×C4⋊C4C2416yes—
757C2×C4⋊C4C2413yes—
758C2×C4⋊C4C2413yes—
759C2×C4⋊C4C2413yes—
760C2×C4⋊C4C2416yes—
761C2×C4⋊C4C2416yes—
762C2×C4⋊C4C2413yes—
763C2×C4⋊C4C2413yes—
764C2×C4⋊C4C2413yes—
765C2×C4⋊C4C2413yes—
766C2×C4⋊C4C2413yes—
767C2×C4⋊C4C2411yescharacteristic
768C2×C4⋊C4C2413yes—
769C2×C4⋊C4C2411yescharacteristic
770C2×C4⋊C4C2413yes—
771C2×C4⋊C4C2413yes—
772C2×C4⋊C4C2413yes—
773C2×C4⋊C4C2416yes—
774C2×C22⋊C4C2411yescharacteristic
775C2×C22⋊C4C2413yes—
776C2×C22⋊C4C2413yes—
777C2×C22⋊C4C2413yes—
778C2×C22⋊C4C2413yes—
779C2×C22⋊C4C2416yes—
780C2×C22⋊C4C2411yescharacteristic
781C2×C22⋊C4C2413yes—
782C2×C22⋊C4C2411yescharacteristic
783C2×C22⋊C4C2411yescharacteristic
784C2×C22⋊C4C2411yescharacteristic
785C2×C22⋊C4C2413yes—
786C2×C22⋊C4C2413yes—
787C2×C22⋊C4C2411yescharacteristic
788C2×C22⋊C4C2413yes—
789C2×C22⋊C4C2413yes—
790C2×C22⋊C4C2413yes—
791C2×C22⋊C4C2411yescharacteristic
792C2×C22⋊C4C2413yes—
793C2×C22⋊C4C2416yes—
794C2×C22⋊C4C2416yes—
795C2×C22⋊C4C2413yes—
796C2×C22⋊C4C2413yes—
797C2×C22⋊C4C2413yes—
798C2×C22⋊C4C2416yes—
799C2×C22⋊C4C2413yes—
800C2×C22⋊C4C2413yes—
801C2×C22⋊C4C2416yes—
802C2×C22⋊C4C2413yes—
803C2×C22⋊C4C2411yescharacteristic
804C2×C22⋊C4C2413yes—
805C2×C22⋊C4C2411yescharacteristic
806C2×C22⋊C4C2413yes—
807C2×C22⋊C4C2413yes—
808C2×C22⋊C4C2413yes—
809C2×C22⋊C4C2416yes—
810C2×C42—212no—
811C2×C42—46no—
812C2×C42—46no—
813C2×C42C2413yes—
814C2×C42C2413yes—
815C2×C42C2413yes—
816C2×C42C2413yes—
817C2×C42C2413yes—
818C2×C42C2413yes—
819C2×C42C2413yes—
820C2×C42C2413yes—
821C2×C42C2413yes—
822C2×C42C2413yes—
823C2×C42C2413yes—
824C2×C42C2413yes—
825C2×C42C2413yes—
826C2×C42C2413yes—
827C2×C42C2416yes—
828C2×C42C2416yes—
829C2×C42C2413yes—
830C2×C42C2413yes—
831C2×C42C2413yes—
832C2×C42C2413yes—
833C2×C42C2416yes—
834#95C2413yes—
835#95C2413yes—
836#95C2413yes—
837#95C2413yes—
838#95C2413yes—
839#95C2413yes—
840#95C2413yes—
841#95C2413yes—
842#95C2411yescharacteristic
843#95C2411yescharacteristic
844#95C2413yes—
845#95C2413yes—
846#95C2413yes—
847#95C2413yes—
848#95C2413yes—
849#95C2413yes—
850#95C2411yescharacteristic
851#95C2411yescharacteristic
852#95C2411yescharacteristic
853#95C2411yescharacteristic
854#95C2413yes—
855#95C2413yes—
856#95C2413yes—
857#95C2413yes—
858#95C2413yes—
859#95C2413yes—
860#95C2416yes—
861#95C2416yes—
862#95C2416yes—
863#95C2413yes—
864#95C2413yes—
865#95C2413yes—
866#95C2413yes—
867#95C2413yes—
868#95C2413yes—
869#95C2413yes—
870#95C2413yes—
871#95C2413yes—
872#95C2413yes—
873#95C2413yes—
874#95C2411yescharacteristic
875#95C2411yescharacteristic
876#95C2411yescharacteristic
877#95C2411yescharacteristic
878#95C2411yescharacteristic
879#95C2411yescharacteristic
880#95C2413yes—
881#95C2416yes—
882#95C2413yes—
883#95C2413yes—
884#95C2413yes—
885#95C2413yes—
886#95C2413yes—
887#95C2413yes—
888#95C2413yes—
889#95C2413yes—
890#95C2413yes—
891#95C2413yes—
892#95C2413yes—
893#95C2413yes—
894#95C2416yes—
895#95C2416yes—
896#95C2416yes—
897#95C2416yes—
898#95C2416yes—
899#95C2416yes—
900#95C2416yes—
901#95C2416yes—
902C24C2511yescharacteristic
903C24C2513yes—
904C24C2511yescharacteristic
905#41—416no—
906C2×Q8—232no—
907C2×Q8—26no—
908C2×Q8—26no—
909C2×Q8—26no—
910C2×Q8—26no—
911C2×Q8—26no—
912C2×Q8—43no—
913C2×Q8—43no—
914C2×Q8—43no—
915C2×Q8—416no—
916C2×Q8C2×#41112yes—
917C2×Q8C2×#4114yes—
918C2×Q8H(5,𝔽2)14yes—
919C2×Q82−1+414yes—
920C2×D4—22no—
921C2×D4—26no—
922C2×D4—22no—
923C2×D4—26no—
924C2×D4—26no—
925C2×D4—22no—
926C2×D4—26no—
927C2×D4—26no—
928C2×D4—26no—
929C2×D4—43no—
930C2×D4—43no—
931C2×D4—43no—
932C22×C4—22no—
933C22×C4—22no—
934C22×C4—26no—
935C22×C4—26no—
936C22×C4—26no—
937C22×C4—22no—
938C22×C4—22no—
939C22×C4—26no—
940C22×C4—26no—
941C22×C4—26no—
942C22×C4—26no—
943C22×C4—26no—
944C22×C4—26no—
945C22×C4—26no—
946C22×C4—26no—
947C22×C4—41no—
948C22×C4—41no—
949C22×C4—43no—
950C22×C4—41no—
951C22×C4—43no—
952C22×C4—41no—
953C22×C4—43no—
954C22×C4—43no—
955C22×C4—43no—
956C22×C4—43no—
957C22×C4—46no—
958C22×C4—46no—
959C22×C4—46no—
960C22×C4C2×#41112yes—
961C22×C42−1+414yes—
962C22×C4C2511yescharacteristic
963C22×C4C2511yescharacteristic
964C22×C4C2513yes—
965C22×C4C2513yes—
966C22×C4C2511yescharacteristic
967C22×C4C2513yes—
968C22×C4C2513yes—
969C22×C4C2511yescharacteristic
970C22×C4C2511yescharacteristic
971C22×C4C2511yescharacteristic
972C22×C4C2511yescharacteristic
973C22×C4C2511yescharacteristic
974C22×C4C2511yescharacteristic
975C22×C4C2513yes—
976C22×C4C2513yes—
977C22×C4C2513yes—
978C22×C4C2513yes—
979C22×C4C2511yescharacteristic
980C22×C4C2513yes—
981C22×C4C2511yescharacteristic
982C22×C4C2513yes—
983C22×C4C2513yes—
984C22×C4C2513yes—
985C22×C4C2513yes—
986C22×C4C2513yes—
987C22×C4C2511yescharacteristic
988C22×C4C2511yescharacteristic
989C22×C4C2513yes—
990C4⋊C4—212no—
991C4⋊C4—26no—
992C4⋊C4—26no—
993C4⋊C4—26no—
994C4⋊C4—26no—
995C4⋊C4—26no—
996C4⋊C4—26no—
997C4⋊C4—212no—
998C4⋊C4—26no—
999C4⋊C4—26no—
1000C4⋊C4—26no—
1001C4⋊C4—26no—
1002C4⋊C4—26no—
1003C4⋊C4—26no—
1004C4⋊C4—22no—
1005C4⋊C4—22no—
1006C4⋊C4—22no—
1007C4⋊C4—22no—
1008C4⋊C4—26no—
1009C4⋊C4—26no—
1010C4⋊C4—22no—
1011C4⋊C4—22no—
1012C4⋊C4—26no—
1013C4⋊C4—26no—
1014C4⋊C4—43no—
1015C4⋊C4—43no—
1016C4⋊C4—43no—
1017C4⋊C4—43no—
1018C4⋊C4—43no—
1019C4⋊C4—46no—
1020C4⋊C4—46no—
1021C4⋊C4—46no—
1022C4⋊C4—46no—
1023C4⋊C4—46no—
1024C4⋊C4—46no—
1025C4⋊C4—41no—
1026C4⋊C4—41no—
1027C4⋊C4—43no—
1028C4⋊C4—43no—
1029C4⋊C4—43no—
1030C4⋊C4—43no—
1031C4⋊C4—46no—
1032C4⋊C4—41no—
1033C4⋊C4—43no—
1034C4⋊C4—43no—
1035C4⋊C4—46no—
1036C4⋊C4—43no—
1037C4⋊C4—41no—
1038C4⋊C4—43no—
1039C4⋊C4—43no—
1040C4⋊C4—43no—
1041C4⋊C4—43no—
1042C4⋊C4—43no—
1043C4⋊C4—43no—
1044C4⋊C4—43no—
1045C4⋊C4—46no—
1046C4⋊C4—46no—
1047C4⋊C4—46no—
1048C4⋊C4—43no—
1049C4⋊C4—43no—
1050C4⋊C4—43no—
1051C4⋊C4—43no—
1052C4⋊C4—43no—
1053C22⋊C4—22no—
1054C22⋊C4—26no—
1055C22⋊C4—26no—
1056C22⋊C4—22no—
1057C22⋊C4—26no—
1058C22⋊C4—22no—
1059C22⋊C4—26no—
1060C22⋊C4—26no—
1061C22⋊C4—212no—
1062C22⋊C4—22no—
1063C22⋊C4—22no—
1064C22⋊C4—26no—
1065C22⋊C4—26no—
1066C22⋊C4—41no—
1067C22⋊C4—43no—
1068C22⋊C4—41no—
1069C22⋊C4—43no—
1070C22⋊C4—43no—
1071C22⋊C4—43no—
1072C22⋊C4—46no—
1073C22⋊C4—41no—
1074C22⋊C4—43no—
1075C22⋊C4—43no—
1076C22⋊C4—43no—
1077C22⋊C4—46no—
1078C22⋊C4—41no—
1079C22⋊C4—43no—
1080C22⋊C4—43no—
1081C22⋊C4—43no—
1082C22⋊C4—46no—
1083C22⋊C4—43no—
1084C22⋊C4—46no—
1085C22⋊C4—43no—
1086C22⋊C4—43no—
1087C22⋊C4—46no—
1088C22⋊C4—43no—
1089C42—26no—
1090C42—26no—
1091C42—26no—
1092C42—26no—
1093C42—26no—
1094C42—26no—
1095C42—26no—
1096C42—26no—
1097C42—26no—
1098C42—26no—
1099C42—26no—
1100C42—26no—
1101C42—26no—
1102C42—26no—
1103C42—43no—
1104C42—43no—
1105C42—43no—
1106C42—43no—
1107C42—46no—
1108C42—46no—
1109C42—46no—
1110C23—21no—
1111C23—21no—
1112C23—21no—
1113C23—21no—
1114C23—21no—
1115C23—23no—
1116C23—21no—
1117C23—23no—
1118C23—21no—
1119C23—23no—
1120C23—21no—
1121C23—23no—
1122C23—23no—
1123C23—21no—
1124C23—23no—
1125C23—21no—
1126C23—21no—
1127C23—23no—
1128C23C22×#4112yes—
1129C23C2×2−1+412yes—
1130C23#58512yes—
1131C23C2611yescharacteristic
1132Q8—224no—
1133Q8—412no—
1134Q8—86no—
1135Q8#539116yes—
1136D4—44no—
1137D4—412no—
1138D4—412no—
1139D4—86no—
1140C2×C4—21no—
1141C2×C4—21no—
1142C2×C4—23no—
1143C2×C4—23no—
1144C2×C4—21no—
1145C2×C4—21no—
1146C2×C4—28no—
1147C2×C4—224no—
1148C2×C4—21no—
1149C2×C4—21no—
1150C2×C4—23no—
1151C2×C4—23no—
1152C2×C4—23no—
1153C2×C4—23no—
1154C2×C4—21no—
1155C2×C4—23no—
1156C2×C4—21no—
1157C2×C4—21no—
1158C2×C4—21no—
1159C2×C4—21no—
1160C2×C4—21no—
1161C2×C4—21no—
1162C2×C4—23no—
1163C2×C4—23no—
1164C2×C4—23no—
1165C2×C4—23no—
1166C2×C4—23no—
1167C2×C4—23no—
1168C2×C4—23no—
1169C2×C4—21no—
1170C2×C4—21no—
1171C2×C4—21no—
1172C2×C4—23no—
1173C2×C4—23no—
1174C2×C4—21no—
1175C2×C4—23no—
1176C2×C4—21no—
1177C2×C4—23no—
1178C2×C4—21no—
1179C2×C4—21no—
1180C2×C4—21no—
1181C2×C4—21no—
1182C2×C4—21no—
1183C2×C4—23no—
1184C2×C4—21no—
1185C2×C4—23no—
1186C2×C4—23no—
1187C2×C4—23no—
1188C2×C4—23no—
1189C2×C4—21no—
1190C2×C4—23no—
1191C2×C4—21no—
1192C2×C4—21no—
1193C2×C4—23no—
1194C2×C4—23no—
1195C2×C4—23no—
1196C2×C4—23no—
1197C2×C4—23no—
1198C2×C4—23no—
1199C2×C4—21no—
1200C2×C4—23no—
1201C2×C4—21no—
1202C2×C4—23no—
1203C2×C4—23no—
1204C2×C4—23no—
1205C2×C4—23no—
1206C2×C4—21no—
1207C2×C4—23no—
1208C2×C4—21no—
1209C2×C4—21no—
1210C2×C4—23no—
1211C2×C4—21no—
1212C2×C4—23no—
1213C2×C4—23no—
1214C2×C4—21no—
1215C2×C4—23no—
1216C2×C4—23no—
1217C2×C4—21no—
1218C2×C4—21no—
1219C2×C4—21no—
1220C2×C4—412no—
1221C2×C4—44no—
1222C2×C4—44no—
1223C2×C4—412no—
1224C2×C4—412no—
1225C2×C4—86no—
1226C2×C4—86no—
1227C2×C4—166no—
1228C2×C4C22×#4116yes—
1229C2×C4C22×#4116yes—
1230C2×C4C2×H(5,𝔽2)16yes—
1231C2×C4C2×2−1+412yes—
1232C2×C4C2×2−1+412yes—
1233C2×C4C2×2−1+416yes—
1234C22—22no—
1235C22—22no—
1236C22—22no—
1237C22—22no—
1238C22—22no—
1239C22—22no—
1240C22—41no—
1241C22—43no—
1242C22—41no—
1243C22—43no—
1244C22—43no—
1245C22—41no—
1246C22—41no—
1247C22—43no—
1248C22—41no—
1249C22—43no—
1250C22—41no—
1251C22—43no—
1252C22—41no—
1253C22—43no—
1254C22#351614yes—
1255C22C23×#4111yescharacteristic
1256C22C22×H(5,𝔽2)11yescharacteristic
1257C22C22×2−1+411yescharacteristic
1258C22C22×2−1+411yescharacteristic
1259C22C2×#58511yescharacteristic
1260C22H(7,𝔽2)11yescharacteristic
1261C222−1+611yescharacteristic
1262C4—22no—
1263C4—22no—
1264C4—26no—
1265C4—41no—
1266C4—43no—
1267C4—41no—
1268C4—43no—
1269C4—43no—
1270C4—43no—
1271C4—43no—
1272C4—43no—
1273C4—43no—
1274C4—43no—
1275C4—43no—
1276C4—41no—
1277C4—41no—
1278C4—43no—
1279C4—41no—
1280C4—41no—
1281C4—41no—
1282C4—41no—
1283C4—41no—
1284C4—43no—
1285C4—41no—
1286C4—43no—
1287C4—41no—
1288C4—43no—
1289C4C2×#539112yes—
1290C2—24no—
1291C2—83no—
1292C2—81no—
1293C2C22×#53911yescharacteristic
1294C2C2×#351611yescharacteristic
1295C2#6285111yescharacteristic
1296C2#6289911yescharacteristic
1297C2#6291311yescharacteristic
1298C2#6294311yescharacteristic
1299C2#6294911yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#36434C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #42870C2semidirect
2. #42868C2semidirect
3. #42856C2semidirect
4. #42848C2semidirect
5. #42846C2semidirect
6. #42845C2semidirect
7. #42837C2semidirect
8. #42836C2semidirect
9. #39732C2semidirect
10. #39604C2semidirect
11. #38982C2semidirect
12. #38973C2semidirect
13. #37505C2semidirect
14. #37504C2semidirect
15. #36578C2semidirect
16. Q8×#123C2semidirect
17. #36435C2semidirect
19. #35996C2semidirect
20. #35971C2semidirect
21. #35898C2semidirect
22. #35883C2semidirect
23. #35868C2semidirect
24. #35845C2semidirect
25. #35816C2semidirect
26. #35801C2semidirect
27. #35024C2semidirect
28. #34584C2semidirect
29. #34294C2semidirect
30. #34291C2semidirect
31. C2×Q8×C4⋊C4C2semidirect

Maximal subgroups

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

subgroupindex
#428702
#428682
#428562
#428482
#428462
#428452
#428372
#428362
#397322
#396042
#389822
#389732
#375052
#375042
#365782
Q8×#1232
#364352
#364342
#359962
#359712
#358982
#358832
#358682
#358452
#358162
#358012
#350242
#345842
#342942
#342912
C2×Q8×C4⋊C42