Finite Group Databasebeta

← #7692822

Subgroups — #7692822

Order 512.

5407 conjugacy classes of subgroups.

The subgroup lattice has 1355 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59752C213yesmaximal, complemented
2#59481C213yesmaximal, complemented
3#59477C213yesmaximal, complemented
4#59279C213yesmaximal, complemented
5#59276C213yesmaximal, complemented
6#45391C213yesmaximal, complemented
7#45320C213yesmaximal, complemented
8#44962C213yesmaximal, complemented
9#44900C213yesmaximal, complemented
10#38205C213yesmaximal, complemented
11#38201C213yesmaximal, complemented
12#37974C213yesmaximal, complemented
13#37971C213yesmaximal, complemented
14Q8×#123C211yesmaximal, characteristic, complemented
15#36482C211yesmaximal, characteristic, complemented
16#36467C211yesmaximal, characteristic, complemented
17#36458C211yesmaximal, characteristic, complemented
18#36458C211yesmaximal, characteristic, complemented
19#36379C213yesmaximal, complemented
20#36379C213yesmaximal, complemented
21#35845C211yesmaximal, characteristic, complemented
22#35801C211yesmaximal, characteristic, complemented
23#35786C211yesmaximal, characteristic, complemented
24#35687C211yesmaximal, characteristic
25#34871C213yesmaximal, complemented
26#34311C211yesmaximal, characteristic, complemented
27#34311C211yesmaximal, characteristic, complemented
28#34257C211yesmaximal, characteristic, complemented
29#34257C211yesmaximal, characteristic, complemented
30#34128C211yesmaximal, characteristic, complemented
31Q8×#117C211yesmaximal, characteristic, complemented
32C22×2−1+4C2211yescharacteristic
33C2×#557C2211yescharacteristic
34C2×D4×Q8C2211yescharacteristic
35C2×D4×Q8C2211yescharacteristic
36C2×#548C2211yescharacteristic
37C2×#519C2211yescharacteristic
38C2×#519C2211yescharacteristic
39C2×#519C2211yescharacteristic
40C22×C4×Q8C2211yescharacteristic
41C22×C4×Q8C2211yescharacteristic
42#2861C2213yes—
43#2860C2213yes—
44#2860C2213yes—
45#2855C2213yes—
46#2855C2213yes—
47#2798C2216yes—
48#2761C2216yes—
49#2758C2216yes—
50#2755C2216yes—
51#2752C2216yes—
52#2751C2216yes—
53#2747C2216yes—
54#2743C2216yes—
55#2742C2216yes—
56#2741C2216yes—
57#2740C2216yes—
58#2737C2216yes—
59#2722C2216yes—
60#2705C2216yes—
61#2629C2213yes—
62#2628C2213yes—
63#2624C2213yes—
64#2616C2213yes—
65#2612C2213yes—
66#2610C2213yes—
67#2610C2213yes—
68#2609C2213yes—
69#2605C2216yes—
70#2601C2216yes—
71#2601C2216yes—
72#2592C2213yes—
73#2588C2216yes—
74#2586C2213yes—
75#2582C2213yes—
76#2581C2213yes—
77#2577C2216yes—
78#2574C2216yes—
79#2572C2213yes—
80#2567C2213yes—
81#2565C2213yes—
82#2562C2213yes—
83#2554C2213yes—
84#2554C2213yes—
85#2532C2213yes—
86#2532C2213yes—
87#2531C2216yes—
88#2530C2216yes—
89#2530C2216yes—
90#2526C2213yes—
91#2526C2216yes—
92#2526C2213yes—
93#2522C2216yes—
94#2522C2216yes—
95#2521C2216yes—
96#2520C2216yes—
97#2518C2216yes—
98#2516C2216yes—
99#2516C2216yes—
100#2513C2213yes—
101#2513C2213yes—
102#2512C2213yes—
103#2512C2213yes—
104#2512C2213yes—
105#2512C2213yes—
106#2503C2213yes—
107#2502C2213yes—
108#2500C2213yes—
109#2497C2213yes—
110#2497C2213yes—
111#2496C2213yes—
112#2496C2213yes—
113#2495C2213yes—
114#2495C2213yes—
115#2492C2213yes—
116#2491C2213yes—
117#2490C2213yes—
118#2489C2213yes—
119#2487C2213yes—
120#2486C2213yes—
121#2485C2213yes—
122#2479C2213yes—
123#2479C2216yes—
124#2479C2213yes—
125#2471C2211yescharacteristic
126#2471C2213yes—
127#2453C2213yes—
128#2453C2213yes—
129#2453C2213yes—
130#2451C2213yes—
131#2448C2213yes—
132#2448C2213yes—
133#2446C2213yes—
134#2446C2213yes—
135#2446C2213yes—
136#2446C2213yes—
137#2441C2213yes—
138#2441C2213yes—
139#2441C2213yes—
140#2439C2213yes—
141#2434C2213yes—
142#2432C2213yes—
143#2432C2213yes—
144#2423C2213yes—
145#2423C2213yes—
146#2423C2213yes—
147#2421C2213yes—
148#2421C2213yes—
149#2421C2213yes—
150#2409C2213yes—
151#2407C2213yes—
152#2407C2213yes—
153#2396C2213yes—
154#2396C2213yes—
155#2395C2213yes—
156#2388C2213yes—
157#2373C2216yes—
158#2373C2216yes—
159#2373C2216yes—
160#2365C2213yes—
161#2365C2213yes—
162#2362C2213yes—
163#2362C2213yes—
164#2362C2213yes—
165#2362C2213yes—
166#2356C2213yes—
167#2356C2213yes—
168#2355C2213yes—
169#2355C2213yes—
170#2354C2213yes—
171#2354C2213yes—
172#2351C2211yescharacteristic
173#2351C2211yescharacteristic
174#2351C2211yescharacteristic
175Q8×C4⋊C4C2211yescharacteristic
176Q8×C4⋊C4C2211yescharacteristic
177Q8×C4⋊C4C2211yescharacteristic
178Q8×C4⋊C4C2211yescharacteristic
179Q8×C4⋊C4C2211yescharacteristic
180#2345C2213yes—
181#2345C2213yes—
182#2344C2213yes—
183#2344C2213yes—
184#2341C2213yes—
185#2341C2213yes—
186#2341C2213yes—
187#2341C2211yescharacteristic
188#2341C2211yescharacteristic
189#2341C2211yescharacteristic
190#2341C2211yescharacteristic
191#2341C2211yescharacteristic
192#2341C2213yes—
193Q8×C22⋊C4C2211yescharacteristic
194Q8×C22⋊C4C2211yescharacteristic
195Q8×C22⋊C4C2211yescharacteristic
196Q8×C22⋊C4C2211yescharacteristic
197Q8×C22⋊C4C2211yescharacteristic
198Q8×C22⋊C4C2211yescharacteristic
199Q8×C22⋊C4C2213yes—
200Q8×C22⋊C4C2213yes—
201Q8×C22⋊C4C2211yescharacteristic
202Q8×C22⋊C4C2213yes—
203Q8×C22⋊C4C2213yes—
204Q8×C22⋊C4C2211yescharacteristic
205Q8×C22⋊C4C2211yescharacteristic
206#2323C2213yes—
207#2323C2213yes—
208#2323C2213yes—
209#2323C2213yes—
210#2311C2213yes—
211#2311C2213yes—
212#2311C2213yes—
213#2311C2213yes—
214C4×C4⋊Q8C2213yes—
215C4×C4⋊Q8C2213yes—
216C4×#126C2213yes—
217C4×#126C2213yes—
218C4×#124C2213yes—
219C4×#123C2213yes—
220C4×#123C2213yes—
221#2297C2213yes—
222#2297C2213yes—
223#2297C2213yes—
224#2297C2213yes—
225#2295C2213yes—
226#2295C2213yes—
227#2295C2213yes—
228#2295C2213yes—
229#2293C2213yes—
230#2293C2213yes—
231#2285C2213yes—
232#2283C2213yes—
233C42×Q8C2211yescharacteristic
234C42×Q8C2211yescharacteristic
235C42×Q8C2211yescharacteristic
236C4×#117C2213yes—
237C4×#117C2213yes—
238C2×2−1+4—28no—
239C2×2−1+4—28no—
240C2×2−1+4—44no—
241C22×#41C2311yescharacteristic
242C22×#41C2313yes—
243C22×#41C2313yes—
244C22×#41C2313yes—
245C23×Q8C2311yescharacteristic
246C23×Q8C2313yes—
247C23×Q8C2311yescharacteristic
248C23×Q8C2311yescharacteristic
249#557—44no—
250D4×Q8—28no—
251D4×Q8—28no—
252#548—44no—
253C2×C4⋊Q8C2313yes—
254C2×C4⋊Q8C2313yes—
255C2×C4⋊Q8C2313yes—
256C2×#126C2313yes—
257C2×#126C2313yes—
258C2×#126C2316yes—
259C2×#126C2316yes—
260C2×#125C2313yes—
261C2×#125C2313yes—
262C2×#124C2313yes—
263C2×#124C2313yes—
264C2×#123C2311yescharacteristic
265C2×#123C2313yes—
266C2×C22⋊Q8C2313yes—
267C2×C22⋊Q8C2313yes—
268C2×C22⋊Q8C2313yes—
269C2×C22⋊Q8C2313yes—
270C2×C22⋊Q8C2313yes—
271C2×#121C2313yes—
272#519—44no—
273#519—44no—
274#519—44no—
275C2×C4×Q8—28no—
276C2×C4×Q8—28no—
277C2×C4×Q8C2311yescharacteristic
278C2×C4×Q8C2311yescharacteristic
279C2×C4×Q8C2311yescharacteristic
280C2×C4×Q8C2311yescharacteristic
281C2×C4×Q8C2311yescharacteristic
282C2×C4×Q8C2311yescharacteristic
283C2×C4×Q8C2311yescharacteristic
284C2×C4×Q8C2311yescharacteristic
285C2×C4×Q8C2311yescharacteristic
286C2×C4×Q8C2311yescharacteristic
287C2×C4×Q8C2311yescharacteristic
288C2×C4×Q8C2313yes—
289C2×C4×Q8C2313yes—
290C2×C4×Q8C2313yes—
291C2×C4×Q8C2313yes—
292C2×C4×Q8C2313yes—
293C2×C4×Q8C2313yes—
294C2×C4×Q8C2313yes—
295C2×C4×Q8C2313yes—
296C2×C4×Q8C2313yes—
297C2×C4×Q8C2313yes—
298C2×C4×Q8C2313yes—
299C2×C4×D4C2313yes—
300C2×C4×D4C2313yes—
301C2×C4×D4C2313yes—
302C2×#117C2311yescharacteristic
303C2×#117C2313yes—
304C2×#117C2313yes—
305C2×#117C2313yes—
306C2×#117C2313yes—
307C2×#117C2313yes—
308C2×#117C2313yes—
309C2×#117C2313yes—
310C2×#117C2313yes—
311C2×#117C2313yes—
312C22×C4⋊C4C2313yes—
313C22×C4⋊C4C2313yes—
314C22×C42C2313yes—
315C22×C42C2313yes—
316#400C2316yes—
317#400C2313yes—
318#400C2316yes—
319#400C2313yes—
320#400C2316yes—
321#400C2316yes—
322#400C2316yes—
323#400C2316yes—
324#400C2313yes—
325#400C2316yes—
326#399C2316yes—
327#399C2316yes—
328#399C2313yes—
329#399C2311yescharacteristic
330#399C2313yes—
331#399C2316yes—
332#398C2313yes—
333#398C2316yes—
334#398C2316yes—
335#398C2313yes—
336#398C2313yes—
337#398C2316yes—
338#398C2313yes—
339#398C2316yes—
340#398C2313yes—
341#398C2316yes—
342#397C2316yes—
343#397C2316yes—
344#397C2316yes—
345#397C2311yescharacteristic
346#397C2313yes—
347#397C2313yes—
348#397C2316yes—
349#397C2316yes—
350#397C2316yes—
351#397C2316yes—
352#396C2316yes—
353#396C2313yes—
354#396C2316yes—
355#396C2316yes—
356#396C2313yes—
357#396C2313yes—
358#396C2311yescharacteristic
359#395C2313yes—
360#395C2316yes—
361#395C2313yes—
362#395C2313yes—
363#395C2316yes—
364#394C2316yes—
365#394C2313yes—
366#394C2313yes—
367#394C2316yes—
368#394C2313yes—
369#394C2313yes—
370#394C2316yes—
371#394C2316yes—
372#394C2313yes—
373#393C2313yes—
374#393C2313yes—
375#393C2316yes—
376#393C2313yes—
377#392C2313yes—
378#392C2313yes—
379#392C2311yescharacteristic
380#391C2313yes—
381#391C2313yes—
382#391C2313yes—
383#391C2313yes—
384#391C2313yes—
385#391C2313yes—
386#391C2313yes—
387#391C2313yes—
388#391C2313yes—
389#391C2313yes—
390#391C2316yes—
391#391C2316yes—
392#391C2313yes—
393#391C2313yes—
394#391C2313yes—
395#391C2316yes—
396#391C2313yes—
397#391C2313yes—
398#391C2313yes—
399#391C2313yes—
400#391C2313yes—
401#391C2313yes—
402#391C2313yes—
403#391C2313yes—
404#391C2313yes—
405#391C2313yes—
406#390C2313yes—
407#390C2313yes—
408#390C2316yes—
409#390C2316yes—
410#390C2313yes—
411#390C2313yes—
412#390C2313yes—
413#390C2313yes—
414#390C2313yes—
415#390C2313yes—
416#390C2313yes—
417#390C2313yes—
418#390C2313yes—
419#390C2313yes—
420#390C2313yes—
421#390C2313yes—
422#390C2313yes—
423#390C2313yes—
424#390C2311yescharacteristic
425#390C2311yescharacteristic
426#390C2313yes—
427#389C2313yes—
428#389C2313yes—
429#389C2316yes—
430#389C2316yes—
431#389C2316yes—
432#389C2316yes—
433#389C2313yes—
434#389C2313yes—
435#389C2313yes—
436#389C2313yes—
437#389C2313yes—
438#389C2313yes—
439#389C2316yes—
440#389C2313yes—
441#389C2313yes—
442#389C2313yes—
443#389C2313yes—
444#389C2313yes—
445#389C2313yes—
446#389C2313yes—
447#389C2313yes—
448#389C2313yes—
449#389C2313yes—
450#389C2313yes—
451#389C2313yes—
452#388C2313yes—
453#388C2313yes—
454#388C2313yes—
455#388C2313yes—
456#388C2313yes—
457#388C2313yes—
458#388C2313yes—
459#388C2316yes—
460#388C2313yes—
461#388C2313yes—
462#388C2316yes—
463#388C2316yes—
464#388C2313yes—
465#388C2313yes—
466#388C2313yes—
467#388C2316yes—
468#388C2316yes—
469#388C2316yes—
470#388C2316yes—
471#388C2313yes—
472#388C2316yes—
473#388C2316yes—
474#388C2316yes—
475#388C2316yes—
476#388C2316yes—
477#388C2316yes—
478#388C2313yes—
479#388C2316yes—
480#388C2313yes—
481#388C2313yes—
482#388C2313yes—
483#388C2313yes—
484#388C2313yes—
485#388C2313yes—
486#388C2313yes—
487#388C2311yescharacteristic
488#387C2311yescharacteristic
489#387C2311yescharacteristic
490#387C2313yes—
491#387C2313yes—
492#387C2313yes—
493#387C2313yes—
494#387C2316yes—
495#387C2316yes—
496#387C2313yes—
497#387C2316yes—
498#387C2316yes—
499#387C2313yes—
500#387C2316yes—
501#387C2316yes—
502#387C2316yes—
503#387C2316yes—
504#387C2316yes—
505#387C2316yes—
506#387C2313yes—
507#387C2316yes—
508#387C2316yes—
509#387C2316yes—
510#387C2316yes—
511#387C2316yes—
512#387C2316yes—
513#387C2316yes—
514#387C2316yes—
515#387C2316yes—
516#387C2316yes—
517#387C2316yes—
518#387C2313yes—
519#386C2313yes—
520#386C2316yes—
521#386C2313yes—
522#386C2313yes—
523#386C2316yes—
524#386C2313yes—
525#386C2311yescharacteristic
526#386C2313yes—
527#386C2311yescharacteristic
528#386C2311yescharacteristic
529#386C2313yes—
530#386C2316yes—
531#386C2313yes—
532#385C2316yes—
533#385C2316yes—
534#385C2313yes—
535#385C2316yes—
536#385C2313yes—
537#385C2316yes—
538#384C2313yes—
539#384C2313yes—
540#384C2313yes—
541#384C2313yes—
542#384C2313yes—
543#383C2313yes—
544#383C2313yes—
545#383C2316yes—
546#382C2313yes—
547#382C2316yes—
548#382C2313yes—
549#382C2313yes—
550#382C2313yes—
551#381C2313yes—
552#381C2313yes—
553#381C2316yes—
554#381C2316yes—
555#380C2313yes—
556#380C2313yes—
557#380C2313yes—
558#380C2313yes—
559#380C2316yes—
560#380C2316yes—
561#380C2313yes—
562#380C2313yes—
563#380C2313yes—
564#380C2313yes—
565#380C2313yes—
566#380C2313yes—
567#380C2316yes—
568#380C2316yes—
569#380C2313yes—
570#380C2313yes—
571#380C2313yes—
572#380C2313yes—
573#380C2316yes—
574C4×C4⋊C4C2313yes—
575C4×C4⋊C4C2313yes—
576C4×C4⋊C4C2313yes—
577C4×C4⋊C4C2313yes—
578C4×C4⋊C4C2313yes—
579C4×C4⋊C4C2313yes—
580C4×C4⋊C4C2313yes—
581C4×C4⋊C4C2316yes—
582C4×C4⋊C4C2316yes—
583C4×C4⋊C4C2316yes—
584C4×C4⋊C4C2316yes—
585C4×C4⋊C4C2313yes—
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×C22⋊C4C2313yes—
601C4×C22⋊C4C2313yes—
602C4×C22⋊C4C2313yes—
603C4×C22⋊C4C2313yes—
604C4×C22⋊C4C2313yes—
605C4×C22⋊C4C2313yes—
606C4×C22⋊C4C2313yes—
607C4×C22⋊C4C2316yes—
608C4×C22⋊C4C2316yes—
609C4×C22⋊C4C2313yes—
610C4×C22⋊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⋊C4C2311yescharacteristic
622#376C2316yes—
623#376C2313yes—
624#376C2313yes—
625#376C2313yes—
626#376C2313yes—
627C43C2313yes—
628C43C2313yes—
629C43C2313yes—
6302−1+4—464no—
631C2×#41—212no—
632C2×#41—212no—
633C2×#41—24no—
634C2×#41—24no—
635C2×#41—24no—
636C2×#41—212no—
637C2×#41—212no—
638C2×#41—212no—
639C2×#41—212no—
640C2×#41—46no—
641C2×#41—46no—
642C2×#41—46no—
643C22×Q8—24no—
644C22×Q8—24no—
645C22×Q8—24no—
646C22×Q8—24no—
647C22×Q8—24no—
648C22×Q8—24no—
649C22×Q8—212no—
650C22×Q8—212no—
651C22×Q8—24no—
652C22×Q8—46no—
653C22×Q8#4118yes—
654C22×Q8#4118yes—
655C22×Q8C2413yes—
656C22×Q8C2413yes—
657C22×Q8C2413yes—
658C22×Q8C2413yes—
659C22×Q8C2413yes—
660C22×Q8C2411yescharacteristic
661C22×D4C2413yes—
662C22×D4C2411yescharacteristic
663C22×D4C2411yescharacteristic
664C22×D4C2411yescharacteristic
665C22×D4C2413yes—
666C22×D4C2413yes—
667C22×D4C2413yes—
668C23×C4C2411yescharacteristic
669C23×C4C2413yes—
670C23×C4C2413yes—
671C23×C4C2411yescharacteristic
672C23×C4C2416yes—
673C23×C4C2413yes—
674C23×C4C2413yes—
675C23×C4C2413yes—
676C23×C4C2413yes—
677C4⋊Q8—212no—
678C4⋊Q8—212no—
679C4⋊Q8—46no—
680#126—212no—
681#126—412no—
682#126—412no—
683#126—46no—
684#125—46no—
685#125—46no—
686#124—46no—
687#124—46no—
688#123—24no—
689#123—46no—
690C22⋊Q8—212no—
691C22⋊Q8—212no—
692C22⋊Q8—212no—
693C22⋊Q8—212no—
694C22⋊Q8—46no—
695#121—46no—
696C4×Q8—212no—
697C4×Q8—212no—
698C4×Q8—212no—
699C4×Q8—212no—
700C4×Q8—24no—
701C4×Q8—24no—
702C4×Q8—24no—
703C4×Q8—24no—
704C4×Q8—24no—
705C4×Q8—24no—
706C4×Q8—24no—
707C4×Q8—24no—
708C4×Q8—24no—
709C4×Q8—24no—
710C4×Q8—24no—
711C4×Q8—46no—
712C4×Q8—46no—
713C4×Q8—46no—
714C4×Q8—46no—
715C4×Q8—46no—
716C4×Q8—46no—
717C4×Q8—46no—
718C4×D4—212no—
719C4×D4—212no—
720C4×D4—46no—
721#117—24no—
722#117—46no—
723#117—46no—
724#117—46no—
725#117—46no—
726#117—46no—
727#117—46no—
728#117—46no—
729#117—46no—
730#117—46no—
731C2×C4⋊C4—212no—
732C2×C4⋊C4—212no—
733C2×C4⋊C4C2413yes—
734C2×C4⋊C4C2413yes—
735C2×C4⋊C4C2413yes—
736C2×C4⋊C4C2413yes—
737C2×C4⋊C4C2416yes—
738C2×C4⋊C4C2416yes—
739C2×C4⋊C4C2413yes—
740C2×C4⋊C4C2413yes—
741C2×C4⋊C4C2413yes—
742C2×C4⋊C4C2413yes—
743C2×C4⋊C4C2413yes—
744C2×C4⋊C4C2413yes—
745C2×C4⋊C4C2411yescharacteristic
746C2×C4⋊C4C2413yes—
747C2×C4⋊C4C2413yes—
748C2×C4⋊C4C2413yes—
749C2×C4⋊C4C2413yes—
750C2×C4⋊C4C2413yes—
751C2×C4⋊C4C2416yes—
752C2×C4⋊C4C2416yes—
753C2×C4⋊C4C2413yes—
754C2×C4⋊C4C2411yescharacteristic
755C2×C4⋊C4C2411yescharacteristic
756C2×C4⋊C4C2413yes—
757C2×C4⋊C4C2413yes—
758C2×C4⋊C4C2413yes—
759C2×C4⋊C4C2413yes—
760C2×C4⋊C4C2413yes—
761C2×C4⋊C4C2413yes—
762C2×C4⋊C4C2413yes—
763C2×C4⋊C4C2413yes—
764C2×C4⋊C4C2413yes—
765C2×C4⋊C4C2413yes—
766C2×C4⋊C4C2413yes—
767C2×C4⋊C4C2413yes—
768C2×C4⋊C4C2413yes—
769C2×C4⋊C4C2411yescharacteristic
770C2×C4⋊C4C2413yes—
771C2×C4⋊C4C2413yes—
772C2×C4⋊C4C2416yes—
773C2×C4⋊C4C2416yes—
774C2×C4⋊C4C2413yes—
775C2×C4⋊C4C2416yes—
776C2×C4⋊C4C2416yes—
777C2×C4⋊C4C2416yes—
778C2×C4⋊C4C2413yes—
779C2×C4⋊C4C2411yescharacteristic
780C2×C4⋊C4C2416yes—
781C2×C4⋊C4C2411yescharacteristic
782C2×C22⋊C4C2411yescharacteristic
783C2×C22⋊C4C2411yescharacteristic
784C2×C22⋊C4C2411yescharacteristic
785C2×C22⋊C4C2411yescharacteristic
786C2×C22⋊C4C2413yes—
787C2×C22⋊C4C2413yes—
788C2×C22⋊C4C2413yes—
789C2×C22⋊C4C2413yes—
790C2×C22⋊C4C2411yescharacteristic
791C2×C22⋊C4C2411yescharacteristic
792C2×C22⋊C4C2411yescharacteristic
793C2×C22⋊C4C2411yescharacteristic
794C2×C22⋊C4C2413yes—
795C2×C22⋊C4C2413yes—
796C2×C22⋊C4C2413yes—
797C2×C22⋊C4C2413yes—
798C2×C22⋊C4C2413yes—
799C2×C22⋊C4C2411yescharacteristic
800C2×C22⋊C4C2413yes—
801C2×C22⋊C4C2411yescharacteristic
802C2×C22⋊C4C2413yes—
803C2×C22⋊C4C2411yescharacteristic
804C2×C22⋊C4C2413yes—
805C2×C22⋊C4C2413yes—
806C2×C22⋊C4C2413yes—
807C2×C22⋊C4C2413yes—
808C2×C22⋊C4C2413yes—
809C2×C22⋊C4C2411yescharacteristic
810C2×C22⋊C4C2413yes—
811C2×C22⋊C4C2416yes—
812C2×C22⋊C4C2413yes—
813C2×C22⋊C4C2413yes—
814C2×C22⋊C4C2413yes—
815C2×C22⋊C4C2413yes—
816C2×C22⋊C4C2413yes—
817C2×C22⋊C4C2416yes—
818C2×C22⋊C4C2416yes—
819C2×C22⋊C4C2416yes—
820C2×C22⋊C4C2413yes—
821C2×C22⋊C4C2413yes—
822C2×C22⋊C4C2416yes—
823C2×C22⋊C4C2411yescharacteristic
824C2×C22⋊C4C2413yes—
825C2×C22⋊C4C2413yes—
826C2×C22⋊C4C2416yes—
827C2×C22⋊C4C2413yes—
828C2×C42—212no—
829C2×C42—212no—
830C2×C42C2413yes—
831C2×C42C2413yes—
832C2×C42C2413yes—
833C2×C42C2413yes—
834C2×C42C2413yes—
835C2×C42C2413yes—
836C2×C42C2413yes—
837C2×C42C2411yescharacteristic
838C2×C42C2411yescharacteristic
839C2×C42C2413yes—
840C2×C42C2413yes—
841C2×C42C2413yes—
842C2×C42C2413yes—
843C2×C42C2413yes—
844C2×C42C2413yes—
845C2×C42C2413yes—
846C2×C42C2413yes—
847C2×C42C2413yes—
848C2×C42C2413yes—
849C2×C42C2413yes—
850C2×C42C2413yes—
851C2×C42C2416yes—
852C2×C42C2416yes—
853C2×C42C2416yes—
854C2×C42C2413yes—
855C2×C42C2413yes—
856C2×C42C2413yes—
857C2×C42C2411yescharacteristic
858C2×C42C2413yes—
859C2×C42C2413yes—
860#95C2411yescharacteristic
861#95C2411yescharacteristic
862#95C2413yes—
863#95C2413yes—
864#95C2416yes—
865#95C2413yes—
866#95C2413yes—
867#95C2413yes—
868#95C2413yes—
869#95C2413yes—
870#95C2413yes—
871#95C2413yes—
872#95C2413yes—
873#95C2413yes—
874#95C2413yes—
875#95C2413yes—
876#95C2413yes—
877#95C2416yes—
878#95C2416yes—
879#95C2416yes—
880#95C2411yescharacteristic
881#95C2411yescharacteristic
882#95C2411yescharacteristic
883#95C2411yescharacteristic
884#95C2413yes—
885#95C2413yes—
886#95C2411yescharacteristic
887#95C2416yes—
888#95C2413yes—
889#95C2413yes—
890#95C2413yes—
891#95C2413yes—
892#95C2413yes—
893#95C2413yes—
894#95C2413yes—
895#95C2413yes—
896#95C2416yes—
897#95C2416yes—
898#95C2413yes—
899#95C2413yes—
900#95C2413yes—
901#95C2413yes—
902#95C2413yes—
903#95C2416yes—
904#95C2416yes—
905#95C2416yes—
906#95C2411yescharacteristic
907#95C2416yes—
908#95C2416yes—
909#95C2416yes—
910#95C2413yes—
911#95C2413yes—
912#95C2413yes—
913#95C2413yes—
914#95C2413yes—
915#95C2413yes—
916#95C2413yes—
917#95C2416yes—
918#95C2416yes—
919C24C2511yescharacteristic
920C24C2513yes—
921C24C2511yescharacteristic
922C24C2511yescharacteristic
923#41—448no—
924#41—448no—
925#41—448no—
926#41—416no—
927C2×Q8—232no—
928C2×Q8—232no—
929C2×Q8—26no—
930C2×Q8—26no—
931C2×Q8—26no—
932C2×Q8—26no—
933C2×Q8—26no—
934C2×Q8—26no—
935C2×Q8—26no—
936C2×Q8—26no—
937C2×Q8—26no—
938C2×Q8—43no—
939C2×Q8—43no—
940C2×Q8—43no—
941C2×Q8—43no—
942C2×Q8—448no—
943C2×Q8—416no—
944C2×Q8C2×#41112yes—
945C2×Q8C2×#41112yes—
946C2×Q8C2×#4114yes—
947C2×Q8C2×#4114yes—
948C2×Q8H(5,𝔽2)14yes—
949C2×D4—22no—
950C2×D4—22no—
951C2×D4—26no—
952C2×D4—26no—
953C2×D4—22no—
954C2×D4—22no—
955C2×D4—26no—
956C2×D4—26no—
957C2×D4—26no—
958C2×D4—26no—
959C2×D4—26no—
960C2×D4—22no—
961C2×D4—22no—
962C2×D4—41no—
963C2×D4—41no—
964C2×D4—43no—
965C2×D4—43no—
966C2×D4—41no—
967C2×D4—43no—
968C2×D4—43no—
969C2×D4—43no—
970C22×C4—22no—
971C22×C4—26no—
972C22×C4—26no—
973C22×C4—26no—
974C22×C4—26no—
975C22×C4—22no—
976C22×C4—22no—
977C22×C4—22no—
978C22×C4—26no—
979C22×C4—26no—
980C22×C4—26no—
981C22×C4—26no—
982C22×C4—212no—
983C22×C4—212no—
984C22×C4—26no—
985C22×C4—26no—
986C22×C4—26no—
987C22×C4—26no—
988C22×C4—22no—
989C22×C4—43no—
990C22×C4—43no—
991C22×C4—41no—
992C22×C4—46no—
993C22×C4—43no—
994C22×C4—43no—
995C22×C4C2×#41112yes—
996C22×C4C2×#41112yes—
997C22×C4C2511yescharacteristic
998C22×C4C2511yescharacteristic
999C22×C4C2513yes—
1000C22×C4C2513yes—
1001C22×C4C2511yescharacteristic
1002C22×C4C2513yes—
1003C22×C4C2513yes—
1004C22×C4C2513yes—
1005C22×C4C2513yes—
1006C22×C4C2513yes—
1007C22×C4C2511yescharacteristic
1008C22×C4C2511yescharacteristic
1009C22×C4C2513yes—
1010C22×C4C2513yes—
1011C22×C4C2511yescharacteristic
1012C22×C4C2513yes—
1013C22×C4C2513yes—
1014C22×C4C2511yescharacteristic
1015C22×C4C2513yes—
1016C22×C4C2513yes—
1017C22×C4C2513yes—
1018C22×C4C2511yescharacteristic
1019C22×C4C2511yescharacteristic
1020C22×C4C2511yescharacteristic
1021C22×C4C2511yescharacteristic
1022C22×C4C2511yescharacteristic
1023C22×C4C2513yes—
1024C4⋊C4—212no—
1025C4⋊C4—212no—
1026C4⋊C4—26no—
1027C4⋊C4—26no—
1028C4⋊C4—26no—
1029C4⋊C4—26no—
1030C4⋊C4—26no—
1031C4⋊C4—26no—
1032C4⋊C4—26no—
1033C4⋊C4—26no—
1034C4⋊C4—212no—
1035C4⋊C4—212no—
1036C4⋊C4—26no—
1037C4⋊C4—26no—
1038C4⋊C4—26no—
1039C4⋊C4—26no—
1040C4⋊C4—26no—
1041C4⋊C4—22no—
1042C4⋊C4—22no—
1043C4⋊C4—26no—
1044C4⋊C4—26no—
1045C4⋊C4—26no—
1046C4⋊C4—26no—
1047C4⋊C4—26no—
1048C4⋊C4—22no—
1049C4⋊C4—41no—
1050C4⋊C4—43no—
1051C4⋊C4—46no—
1052C4⋊C4—43no—
1053C4⋊C4—43no—
1054C4⋊C4—43no—
1055C4⋊C4—43no—
1056C4⋊C4—43no—
1057C4⋊C4—43no—
1058C4⋊C4—43no—
1059C4⋊C4—43no—
1060C4⋊C4—43no—
1061C4⋊C4—43no—
1062C4⋊C4—43no—
1063C4⋊C4—41no—
1064C4⋊C4—43no—
1065C4⋊C4—43no—
1066C4⋊C4—46no—
1067C4⋊C4—46no—
1068C4⋊C4—46no—
1069C4⋊C4—46no—
1070C4⋊C4—46no—
1071C4⋊C4—43no—
1072C4⋊C42−1+414yescomplemented
1073C22⋊C4—26no—
1074C22⋊C4—26no—
1075C22⋊C4—26no—
1076C22⋊C4—26no—
1077C22⋊C4—22no—
1078C22⋊C4—22no—
1079C22⋊C4—22no—
1080C22⋊C4—22no—
1081C22⋊C4—22no—
1082C22⋊C4—26no—
1083C22⋊C4—26no—
1084C22⋊C4—26no—
1085C22⋊C4—22no—
1086C22⋊C4—22no—
1087C22⋊C4—22no—
1088C22⋊C4—26no—
1089C22⋊C4—26no—
1090C22⋊C4—46no—
1091C22⋊C4—43no—
1092C22⋊C4—43no—
1093C22⋊C4—41no—
1094C22⋊C4—43no—
1095C22⋊C4—43no—
1096C22⋊C4—43no—
1097C22⋊C4—43no—
1098C22⋊C4—43no—
1099C22⋊C4—41no—
1100C22⋊C4—41no—
1101C22⋊C4—41no—
1102C22⋊C4—43no—
1103C22⋊C4—43no—
1104C22⋊C4—43no—
1105C22⋊C4—41no—
1106C22⋊C4—43no—
1107C22⋊C4—46no—
1108C22⋊C4—43no—
1109C22⋊C4—43no—
1110C22⋊C4—43no—
1111C22⋊C4—43no—
1112C22⋊C4—43no—
1113C22⋊C4—46no—
1114C22⋊C4—46no—
1115C22⋊C4—46no—
1116C22⋊C4—46no—
1117C22⋊C4—43no—
1118C22⋊C4—43no—
1119C42—26no—
1120C42—26no—
1121C42—26no—
1122C42—26no—
1123C42—26no—
1124C42—26no—
1125C42—26no—
1126C42—26no—
1127C42—26no—
1128C42—26no—
1129C42—26no—
1130C42—26no—
1131C42—26no—
1132C42—26no—
1133C42—26no—
1134C42—22no—
1135C42—22no—
1136C42—26no—
1137C42—26no—
1138C42—26no—
1139C42—26no—
1140C42—41no—
1141C42—43no—
1142C42—43no—
1143C42—43no—
1144C42—43no—
1145C42—46no—
1146C42—46no—
1147C42—46no—
1148C42—43no—
1149C23—21no—
1150C23—21no—
1151C23—21no—
1152C23—21no—
1153C23—21no—
1154C23—21no—
1155C23—21no—
1156C23—21no—
1157C23—21no—
1158C23—21no—
1159C23—21no—
1160C23—21no—
1161C23—21no—
1162C23—21no—
1163C23—23no—
1164C23—23no—
1165C23—21no—
1166C23—23no—
1167C23—23no—
1168C23—21no—
1169C23—23no—
1170C23—23no—
1171C23—21no—
1172C23—21no—
1173C23—23no—
1174C23—21no—
1175C23C22×#4112yes—
1176C23C22×#4112yes—
1177C23C2611yescharacteristic
1178Q8—224no—
1179Q8—224no—
1180Q8—412no—
1181Q8—412no—
1182Q8—86no—
1183Q8#551116yes—
1184D4—44no—
1185D4—44no—
1186D4—412no—
1187D4—412no—
1188D4—44no—
1189D4—412no—
1190D4—86no—
1191C2×C4—28no—
1192C2×C4—21no—
1193C2×C4—21no—
1194C2×C4—21no—
1195C2×C4—21no—
1196C2×C4—21no—
1197C2×C4—23no—
1198C2×C4—23no—
1199C2×C4—23no—
1200C2×C4—23no—
1201C2×C4—21no—
1202C2×C4—21no—
1203C2×C4—21no—
1204C2×C4—21no—
1205C2×C4—21no—
1206C2×C4—224no—
1207C2×C4—224no—
1208C2×C4—21no—
1209C2×C4—23no—
1210C2×C4—23no—
1211C2×C4—23no—
1212C2×C4—23no—
1213C2×C4—23no—
1214C2×C4—23no—
1215C2×C4—23no—
1216C2×C4—23no—
1217C2×C4—21no—
1218C2×C4—21no—
1219C2×C4—21no—
1220C2×C4—21no—
1221C2×C4—21no—
1222C2×C4—21no—
1223C2×C4—21no—
1224C2×C4—23no—
1225C2×C4—23no—
1226C2×C4—23no—
1227C2×C4—23no—
1228C2×C4—23no—
1229C2×C4—23no—
1230C2×C4—21no—
1231C2×C4—21no—
1232C2×C4—21no—
1233C2×C4—23no—
1234C2×C4—23no—
1235C2×C4—21no—
1236C2×C4—23no—
1237C2×C4—21no—
1238C2×C4—23no—
1239C2×C4—23no—
1240C2×C4—23no—
1241C2×C4—23no—
1242C2×C4—23no—
1243C2×C4—23no—
1244C2×C4—21no—
1245C2×C4—21no—
1246C2×C4—21no—
1247C2×C4—23no—
1248C2×C4—23no—
1249C2×C4—23no—
1250C2×C4—21no—
1251C2×C4—23no—
1252C2×C4—23no—
1253C2×C4—21no—
1254C2×C4—23no—
1255C2×C4—23no—
1256C2×C4—23no—
1257C2×C4—23no—
1258C2×C4—21no—
1259C2×C4—23no—
1260C2×C4—23no—
1261C2×C4—21no—
1262C2×C4—23no—
1263C2×C4—23no—
1264C2×C4—21no—
1265C2×C4—424no—
1266C2×C4—44no—
1267C2×C4—412no—
1268C2×C4—412no—
1269C2×C4—412no—
1270C2×C4—86no—
1271C2×C4C22×#4116yes—
1272C2×C4C22×#4116yes—
1273C2×C4C22×#4116yes—
1274C2×C4C22×#4116yes—
1275C2×C4C2×H(5,𝔽2)16yes—
1276C2×C4C2×2−1+412yes—
1277C2×C4C2×2−1+412yes—
1278C2×C4C2×2−1+412yes—
1279C2×C4#58512yes—
1280C2×C4#58512yes—
1281C22—22no—
1282C22—22no—
1283C22—22no—
1284C22—22no—
1285C22—22no—
1286C22—22no—
1287C22—41no—
1288C22—41no—
1289C22—41no—
1290C22—41no—
1291C22—41no—
1292C22—41no—
1293C22—41no—
1294C22—41no—
1295C22—41no—
1296C22—43no—
1297C22—41no—
1298C22—43no—
1299C22—41no—
1300C22—43no—
1301C22—41no—
1302C22—43no—
1303C22—41no—
1304C22—43no—
1305C22—41no—
1306C22—43no—
1307C22—43no—
1308C22—41no—
1309C22C23×#4111yescharacteristic
1310C22C23×#4111yescharacteristic
1311C22C22×H(5,𝔽2)11yescharacteristic
1312C22C22×2−1+411yescharacteristic
1313C22C2×#58511yescharacteristic
1314C22C2×#58511yescharacteristic
1315C222−1+611yescharacteristic
1316C4—22no—
1317C4—22no—
1318C4—22no—
1319C4—22no—
1320C4—22no—
1321C4—26no—
1322C4—26no—
1323C4—41no—
1324C4—43no—
1325C4—43no—
1326C4—41no—
1327C4—41no—
1328C4—41no—
1329C4—43no—
1330C4—43no—
1331C4—43no—
1332C4—43no—
1333C4—43no—
1334C4—43no—
1335C4—41no—
1336C4—43no—
1337C4—43no—
1338C4—43no—
1339C4—41no—
1340C4—41no—
1341C4—43no—
1342C4C2×#551112yes—
1343C2—42no—
1344C2—42no—
1345C2—81no—
1346C2—83no—
1347C2C22×#55111yescharacteristic
1348C2#6278811yescharacteristic
1349C2#6279311yescharacteristic
1350C2#6292211yescharacteristic
1351C2#6299811yescharacteristic
1352C2#6300511yescharacteristic
1353C2#6303911yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#35687C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59752C2semidirect
2. #59481C2semidirect
3. #59477C2semidirect
4. #59279C2semidirect
5. #59276C2semidirect
6. #45391C2semidirect
7. #45320C2semidirect
8. #44962C2semidirect
9. #44900C2semidirect
10. #38205C2semidirect
11. #38201C2semidirect
12. #37974C2semidirect
13. #37971C2semidirect
14. Q8×#123C2semidirect
15. #36482C2semidirect
16. #36467C2semidirect
17. #36458C2semidirect
18. #36458C2semidirect
19. #36379C2semidirect
20. #36379C2semidirect
21. #35845C2semidirect
22. #35801C2semidirect
23. #35786C2semidirect
25. #34871C2semidirect
26. #34311C2semidirect
27. #34311C2semidirect
28. #34257C2semidirect
29. #34257C2semidirect
30. #34128C2semidirect
31. Q8×#117C2semidirect
1072. C4⋊C42−1+4semidirect

Maximal subgroups

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

subgroupindex
#597522
#594812
#594772
#592792
#592762
#453912
#453202
#449622
#449002
#382052
#382012
#379742
#379712
Q8×#1232
#364822
#364672
#364582
#363792
#358452
#358012
#357862
#356872
#348712
#343112
#342572
#341282
Q8×#1172