Finite Group Databasebeta

← #7685882

Subgroups — #7685882

Order 512.

5398 conjugacy classes of subgroups.

The subgroup lattice has 1357 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59867C213yesmaximal, complemented
2#59752C213yesmaximal, complemented
3#59481C213yesmaximal, complemented
4#59271C213yesmaximal, complemented
5#59204C213yesmaximal
6#45351C213yesmaximal, complemented
7#45340C213yesmaximal, complemented
8#45327C213yesmaximal, complemented
9#45149C213yesmaximal, complemented
10#38251C213yesmaximal, complemented
11#38203C213yesmaximal, complemented
12#38113C213yesmaximal, complemented
13#37850C213yesmaximal, complemented
14Q8×#123C211yesmaximal, characteristic, complemented
15Q8×#120C211yesmaximal, characteristic
16#36448C211yesmaximal, characteristic, complemented
17#36446C211yesmaximal, characteristic, complemented
18#36435C211yesmaximal, characteristic, complemented
19#36279C213yesmaximal, complemented
20#36207C213yesmaximal, complemented
21#35920C211yesmaximal, characteristic, complemented
22#35786C211yesmaximal, characteristic, complemented
23#35723C211yesmaximal, characteristic, complemented
24#35723C211yesmaximal, characteristic, complemented
25#34806C213yesmaximal
26#34311C211yesmaximal, characteristic, complemented
27#34291C211yesmaximal, characteristic, complemented
28#34262C211yesmaximal, characteristic, complemented
29#34173C211yesmaximal, characteristic, complemented
30Q8×#117C211yesmaximal, characteristic, complemented
31C2×Q8×C22⋊C4C211yesmaximal, characteristic, complemented
32C24×Q8C2211yescharacteristic
33C2×#557C2211yescharacteristic, complemented
34C2×D4×Q8C2211yescharacteristic
35C2×D4×Q8C2211yescharacteristic
36C2×D4×Q8C2211yescharacteristic
37C2×#519C2211yescharacteristic
38C2×#519C2211yescharacteristic
39C2×#519C2211yescharacteristic, complemented
40C22×C4×Q8C2211yescharacteristic
41C22×C4×Q8C2211yescharacteristic
42#2863C2213yescomplemented
43#2862C2213yescomplemented
44#2855C2213yes—
45#2851C2213yes—
46#2848C2213yes—
47#2799C2216yescomplemented
48#2798C2216yescomplemented
49#2789C2216yescomplemented
50#2762C2216yescomplemented
51#2758C2216yescomplemented
52#2755C2216yescomplemented
53#2754C2216yescomplemented
54#2754C2216yescomplemented
55#2747C2216yes—
56#2745C2216yes—
57#2744C2216yes—
58#2740C2216yes—
59#2739C2216yes—
60#2722C2216yes—
61#2645C2213yescomplemented
62#2629C2213yes—
63#2625C2213yes—
64#2625C2213yescomplemented
65#2612C2216yescomplemented
66#2605C2216yescomplemented
67#2588C2216yescomplemented
68#2586C2216yescomplemented
69#2582C2213yescomplemented
70#2581C2213yescomplemented
71#2577C2216yes—
72#2575C2216yes—
73#2569C2216yes—
74#2568C2213yescomplemented
75#2565C2213yescomplemented
76#2565C2213yescomplemented
77#2547C2213yes—
78#2532C2216yescomplemented
79#2531C2213yes—
80#2530C2213yes—
81#2527C2213yes—
82#2526C2213yes—
83#2522C2213yes—
84#2521C2213yes—
85#2521C2216yes—
86#2520C2216yescomplemented
87#2520C2216yescomplemented
88#2520C2216yescomplemented
89#2517C2216yes—
90#2516C2213yes—
91#2515C2216yes—
92#2515C2213yes—
93#2514C2213yescomplemented
94#2514C2213yescomplemented
95#2511C2213yescomplemented
96#2511C2213yescomplemented
97#2511C2213yescomplemented
98#2511C2213yescomplemented
99#2510C2216yes—
100#2510C2213yes—
101#2505C2216yes—
102#2505C2216yes—
103#2505C2213yes—
104#2502C2213yes—
105#2499C2213yes—
106#2499C2213yescomplemented
107#2498C2213yes—
108#2496C2213yes—
109#2496C2213yes—
110#2496C2213yes—
111#2496C2213yes—
112#2495C2213yes—
113#2494C2213yes—
114#2489C2213yes—
115#2489C2213yes—
116#2489C2213yescomplemented
117#2489C2213yescomplemented
118#2487C2213yes—
119#2485C2213yes—
120#2485C2213yes—
121#2482C2213yes—
122#2480C2216yes—
123#2480C2213yes—
124#2472C2213yes—
125#2453C2213yescomplemented
126#2453C2213yescomplemented
127#2451C2213yescomplemented
128#2451C2213yescomplemented
129#2446C2213yescomplemented
130#2446C2213yescomplemented
131#2446C2213yescomplemented
132#2446C2213yescomplemented
133#2446C2213yescomplemented
134#2446C2213yescomplemented
135#2442C2213yes—
136#2441C2213yes—
137#2440C2213yes—
138#2439C2213yes—
139#2438C2213yes—
140#2434C2213yes—
141#2434C2213yes—
142#2434C2213yes—
143#2423C2213yes—
144#2423C2213yescomplemented
145#2423C2213yescomplemented
146#2423C2213yescomplemented
147#2421C2213yes—
148#2421C2213yescomplemented
149#2411C2211yescharacteristic
150#2409C2213yes—
151#2409C2213yes—
152#2409C2213yes—
153#2401C2213yes—
154#2396C2213yes—
155#2395C2213yes—
156#2395C2213yes—
157#2373C2216yes—
158#2368C2216yes—
159#2365C2213yescomplemented
160#2365C2213yescomplemented
161#2362C2213yes—
162#2362C2213yescomplemented
163#2362C2213yescomplemented
164#2360C2213yes—
165#2356C2213yescomplemented
166#2355C2213yescomplemented
167#2355C2213yescomplemented
168#2355C2213yescomplemented
169#2354C2213yes—
170#2352C2213yes—
171#2351C2211yescharacteristic, complemented
172#2351C2211yescharacteristic, complemented
173#2351C2211yescharacteristic, complemented
174Q8×C4⋊C4C2211yescharacteristic, complemented
175Q8×C4⋊C4C2211yescharacteristic, complemented
176Q8×C4⋊C4C2211yescharacteristic, complemented
177Q8×C4⋊C4C2211yescharacteristic, complemented
178Q8×C4⋊C4C2211yescharacteristic, complemented
179#2347C2213yes—
180#2346C2213yes—
181#2345C2213yes—
182#2345C2213yes—
183#2343C2216yes—
184Q8×C22⋊C4C2211yescharacteristic
185Q8×C22⋊C4C2213yes—
186Q8×C22⋊C4C2213yes—
187Q8×C22⋊C4C2213yes—
188Q8×C22⋊C4C2213yes—
189Q8×C22⋊C4C2213yes—
190Q8×C22⋊C4C2211yescharacteristic
191Q8×C22⋊C4C2213yes—
192Q8×C22⋊C4C2211yescharacteristic
193Q8×C22⋊C4C2211yescharacteristic
194Q8×C22⋊C4C2211yescharacteristic
195Q8×C22⋊C4C2211yescharacteristic
196Q8×C22⋊C4C2211yescharacteristic
197Q8×C22⋊C4C2211yescharacteristic
198Q8×C22⋊C4C2211yescharacteristic
199Q8×C22⋊C4C2211yescharacteristic
200Q8×C22⋊C4C2213yes—
201Q8×C22⋊C4C2213yes—
202Q8×C22⋊C4C2211yescharacteristic
203Q8×C22⋊C4C2211yescharacteristic, complemented
204Q8×C22⋊C4C2211yescharacteristic, complemented
205Q8×C22⋊C4C2211yescharacteristic, complemented
206#2327C2213yescomplemented
207#2323C2213yes—
208#2323C2213yescomplemented
209#2323C2213yescomplemented
210#2320C2213yescomplemented
211#2314C2213yes—
212#2310C2213yes—
213#2310C2213yes—
214C4×C4⋊Q8C2213yescomplemented
215C4×#126C2213yes—
216C4×#124C2213yes—
217C4×C22⋊Q8C2213yes—
218C4×C22⋊Q8C2213yes—
219C4×#123C2213yes—
220C4×#120C2213yes—
221#2298C2213yes—
222#2295C2213yescomplemented
223#2295C2213yescomplemented
224#2295C2213yescomplemented
225C2×#391C2213yes—
226C2×#391C2213yes—
227#2293C2213yes—
228#2290C2213yes—
229#2285C2213yes—
230#2280C2213yes—
231#2280C2213yes—
232C2×#380C2213yes—
233#2276C2211yescharacteristic, complemented
234C42×Q8C2211yescharacteristic, complemented
235C42×Q8C2211yescharacteristic, complemented
236C4×#117C2213yes—
237C2×C4×C22⋊C4C2213yes—
238C23×Q8—28no—
239C23×Q8—28no—
240C23×Q8—44no—
241C23×Q8C2311yescharacteristic
242C23×Q8C2311yescharacteristic
243C23×Q8C2313yes—
244C23×Q8C2313yes—
245C23×Q8C2313yes—
246C23×Q8C2311yescharacteristic
247C23×Q8C2311yescharacteristic
248C24×C4C2313yes—
249#557—44no—
250D4×Q8—28no—
251D4×Q8—28no—
252D4×Q8—44no—
253C2×C4⋊Q8C2313yes—
254C2×C4⋊Q8C2313yes—
255C2×C4⋊Q8C2313yes—
256C2×C4⋊Q8C2313yes—
257C2×#126C2313yes—
258C2×#126C2316yes—
259C2×#125C2313yes—
260C2×#125C2313yes—
261C2×#124C2313yes—
262C2×#123C2311yescharacteristic
263C2×C22⋊Q8C2313yes—
264C2×C22⋊Q8C2313yes—
265C2×C22⋊Q8C2313yes—
266C2×C22⋊Q8C2313yes—
267C2×C22⋊Q8C2313yes—
268C2×C22⋊Q8C2313yes—
269C2×C22⋊Q8C2313yes—
270C2×#120C2311yescharacteristic
271#519—28no—
272#519—44no—
273#519—44no—
274C2×C4×Q8—28no—
275C2×C4×Q8—44no—
276C2×C4×Q8C2313yes—
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×D4C2313yes—
299C2×C4×D4C2313yes—
300C2×C4×D4C2313yes—
301C2×#117C2313yes—
302C2×#117C2313yes—
303C2×#117C2313yes—
304C2×#117C2311yescharacteristic
305C2×#117C2313yes—
306C2×#117C2313yes—
307C2×#117C2313yes—
308C2×#117C2313yes—
309C22×C4⋊C4C2313yes—
310C22×C4⋊C4C2313yes—
311C22×C22⋊C4C2311yescharacteristic
312C22×C22⋊C4C2313yes—
313C22×C42C2313yes—
314C22×C42C2313yes—
315#401C2313yes—
316#401C2316yes—
317#400C2316yes—
318#400C2316yes—
319#400C2316yes—
320#400C2316yes—
321#400C2316yes—
322#400C2316yes—
323#400C2313yes—
324#400C2316yes—
325#400C2316yes—
326#400C2316yes—
327#400C2316yes—
328#400C2316yes—
329#400C2313yes—
330#400C2313yes—
331#400C2313yes—
332#400C2313yes—
333#400C2313yes—
334#399C2313yes—
335#399C2313yes—
336#399C2313yes—
337#399C2316yes—
338#398C2313yes—
339#398C2316yes—
340#398C2316yes—
341#398C2316yes—
342#398C2316yes—
343#398C2313yes—
344#398C2313yes—
345#398C2316yes—
346#398C2316yes—
347#398C2316yes—
348#398C2313yes—
349#398C2316yes—
350#397C2313yes—
351#397C2313yes—
352#397C2316yes—
353#397C2313yes—
354#397C2316yes—
355#397C2313yes—
356#397C2316yes—
357#397C2313yes—
358#397C2313yes—
359#397C2313yes—
360#397C2313yes—
361#397C2313yes—
362#397C2316yes—
363#397C2316yes—
364#396C2313yes—
365#396C2316yes—
366#396C2311yescharacteristic
367#396C2311yescharacteristic
368#395C2316yes—
369#395C2313yes—
370#395C2316yes—
371#395C2316yes—
372#395C2316yes—
373#394C2311yescharacteristic
374#394C2311yescharacteristic
375#394C2313yes—
376#394C2313yes—
377#393C2313yes—
378#393C2316yes—
379#391C2313yes—
380#391C2313yes—
381#391C2313yes—
382#391C2313yes—
383#391C2313yes—
384#391C2313yes—
385#391C2313yes—
386#391C2313yes—
387#391C2313yes—
388#391C2313yes—
389#391C2316yes—
390#391C2316yes—
391#391C2316yes—
392#391C2313yes—
393#391C2313yes—
394#391C2313yes—
395#391C2316yes—
396#391C2313yes—
397#391C2316yes—
398#391C2313yes—
399#391C2313yes—
400#391C2313yes—
401#391C2313yes—
402#391C2313yes—
403#391C2313yes—
404#391C2316yes—
405#391C2313yes—
406#391C2316yes—
407#391C2316yes—
408#391C2316yes—
409#391C2313yes—
410#391C2313yes—
411#391C2313yes—
412#391C2316yes—
413#391C2313yes—
414#391C2313yes—
415#391C2313yes—
416#391C2313yes—
417#391C2313yes—
418#391C2313yes—
419#390C2313yes—
420#390C2311yescharacteristic
421#390C2311yescharacteristic
422#389C2313yes—
423#389C2316yes—
424#389C2313yes—
425#389C2313yes—
426#389C2313yes—
427#389C2316yes—
428#389C2313yes—
429#389C2313yes—
430#389C2313yes—
431#389C2316yes—
432#389C2313yes—
433#389C2313yes—
434#389C2313yes—
435#389C2313yes—
436#389C2313yes—
437#389C2313yes—
438#389C2313yes—
439#389C2313yes—
440#389C2313yes—
441#389C2313yes—
442#389C2313yes—
443#389C2313yes—
444#388C2311yescharacteristic
445#388C2313yes—
446#388C2313yes—
447#388C2313yes—
448#388C2316yes—
449#388C2316yes—
450#388C2316yes—
451#388C2313yes—
452#388C2313yes—
453#388C2313yes—
454#388C2316yes—
455#388C2316yes—
456#388C2313yes—
457#388C2313yes—
458#388C2313yes—
459#388C2313yes—
460#388C2313yes—
461#388C2313yes—
462#388C2311yescharacteristic
463#388C2316yes—
464#388C2313yes—
465#388C2313yes—
466#388C2313yes—
467#388C2313yes—
468#388C2313yes—
469#387C2313yes—
470#387C2313yes—
471#387C2313yes—
472#387C2313yes—
473#387C2316yes—
474#387C2316yes—
475#387C2316yes—
476#387C2316yes—
477#387C2316yes—
478#387C2316yes—
479#387C2316yes—
480#387C2316yes—
481#387C2316yes—
482#387C2316yes—
483#387C2316yes—
484#387C2313yes—
485#387C2316yes—
486#387C2316yes—
487#387C2316yes—
488#387C2316yes—
489#387C2316yes—
490#387C2313yes—
491#387C2313yes—
492#387C2316yes—
493#387C2316yes—
494#387C2316yes—
495#387C2316yes—
496#387C2316yes—
497#387C2316yes—
498#387C2316yes—
499#387C2316yes—
500#387C2316yes—
501#387C2313yes—
502#387C2316yes—
503#387C2316yes—
504#387C2313yes—
505#387C2313yes—
506#387C2313yes—
507#387C2316yes—
508#387C2313yes—
509#387C2313yes—
510#386C2313yes—
511#386C2313yes—
512#386C2313yes—
513#386C2313yes—
514#386C2311yescharacteristic
515#386C2313yes—
516#385C2313yes—
517#385C2316yes—
518#385C2316yes—
519#385C2313yes—
520#385C2316yes—
521#385C2313yes—
522#385C2316yes—
523#385C2316yes—
524#385C2313yes—
525#385C2313yes—
526#385C2311yescharacteristic
527#385C2313yes—
528#385C2313yes—
529#384C2313yes—
530#384C2313yes—
531#384C2313yes—
532#384C2313yes—
533#384C2313yes—
534#383C2313yes—
535#383C2316yes—
536#383C2316yes—
537#382C2313yes—
538#382C2313yes—
539#382C2313yes—
540#382C2316yes—
541#382C2316yes—
542#382C2313yes—
543#382C2316yes—
544#382C2316yes—
545#381C2316yes—
546#381C2313yes—
547#381C2313yes—
548#381C2313yes—
549#380C2313yes—
550#380C2313yes—
551#380C2316yes—
552#380C2313yes—
553#380C2313yes—
554#380C2316yes—
555#380C2313yes—
556#380C2313yes—
557#380C2313yes—
558#380C2313yes—
559#380C2313yes—
560#380C2313yes—
561#380C2313yes—
562#380C2313yes—
563#380C2313yes—
564#380C2313yes—
565#380C2313yes—
566#380C2316yes—
567#380C2313yes—
568#380C2313yes—
569#380C2313yes—
570#380C2313yes—
571#379C2313yes—
572#379C2311yescharacteristic
573#379C2313yes—
574C4×C4⋊C4C2313yes—
575C4×C4⋊C4C2313yes—
576C4×C4⋊C4C2313yes—
577C4×C4⋊C4C2316yes—
578C4×C4⋊C4C2316yes—
579C4×C4⋊C4C2313yes—
580C4×C4⋊C4C2313yes—
581C4×C4⋊C4C2313yes—
582C4×C4⋊C4C2313yes—
583C4×C4⋊C4C2316yes—
584C4×C4⋊C4C2313yes—
585C4×C4⋊C4C2313yes—
586C4×C4⋊C4C2313yes—
587C4×C4⋊C4C2316yes—
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⋊C4C2316yes—
598C4×C22⋊C4C2313yes—
599C4×C22⋊C4C2313yes—
600C4×C22⋊C4C2313yes—
601C4×C22⋊C4C2316yes—
602C4×C22⋊C4C2313yes—
603C4×C22⋊C4C2316yes—
604C4×C22⋊C4C2316yes—
605C4×C22⋊C4C2313yes—
606C4×C22⋊C4C2313yes—
607C4×C22⋊C4C2313yes—
608C4×C22⋊C4C2313yes—
609C4×C22⋊C4C2313yes—
610C4×C22⋊C4C2313yes—
611C4×C22⋊C4C2313yes—
612C4×C22⋊C4C2313yes—
613C4×C22⋊C4C2313yes—
614C4×C22⋊C4C2313yes—
615C4×C22⋊C4C2313yes—
616C4×C22⋊C4C2313yes—
617C4×C22⋊C4C2313yes—
618C4×C22⋊C4C2313yes—
619C4×C22⋊C4C2313yes—
620C4×C22⋊C4C2313yes—
621#376C2313yes—
622#376C2316yes—
623#376C2313yes—
624#376C2313yes—
625C2×#95C2316yes—
626C2×#95C2313yes—
627C2×#95C2313yes—
628C43C2313yes—
629C43C2313yes—
630C25C2411yescharacteristic
631C22×Q8—24no—
632C22×Q8—24no—
633C22×Q8—24no—
634C22×Q8—24no—
635C22×Q8—24no—
636C22×Q8—24no—
637C22×Q8—212no—
638C22×Q8—212no—
639C22×Q8—212no—
640C22×Q8—212no—
641C22×Q8—24no—
642C22×Q8—24no—
643C22×Q8—24no—
644C22×Q8—24no—
645C22×Q8—212no—
646C22×Q8—212no—
647C22×Q8—46no—
648C22×Q8—46no—
649C22×Q8—46no—
650C22×Q8—464no—
651C22×Q8#4118yes—
652C22×Q8#4118yes—
653C22×Q8C2413yes—
654C22×Q8C2413yes—
655C22×Q8C2416yes—
656C22×Q8C2413yes—
657C22×Q8C2413yes—
658C22×Q8C2413yes—
659C22×Q8C2411yescharacteristic
660C22×D4C2411yescharacteristic
661C22×D4C2411yescharacteristic
662C22×D4C2411yescharacteristic
663C23×C4—212no—
664C23×C4—212no—
665C23×C4—46no—
666C23×C4C2413yes—
667C23×C4C2413yes—
668C23×C4C2413yes—
669C23×C4C2413yes—
670C23×C4C2413yes—
671C23×C4C2413yes—
672C23×C4C2413yes—
673C23×C4C2411yescharacteristic
674C23×C4C2413yes—
675C23×C4C2413yes—
676C23×C4C2411yescharacteristic
677C4⋊Q8—212no—
678C4⋊Q8—212no—
679C4⋊Q8—46no—
680C4⋊Q8—46no—
681#126—46no—
682#126—412no—
683#125—46no—
684#125—46no—
685#124—46no—
686#123—24no—
687C22⋊Q8—212no—
688C22⋊Q8—212no—
689C22⋊Q8—212no—
690C22⋊Q8—212no—
691C22⋊Q8—212no—
692C22⋊Q8—46no—
693C22⋊Q8—46no—
694#120—24no—
695C4×Q8—212no—
696C4×Q8—212no—
697C4×Q8—24no—
698C4×Q8—24no—
699C4×Q8—212no—
700C4×Q8—212no—
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—46no—
711C4×Q8—46no—
712C4×Q8—46no—
713C4×Q8—46no—
714C4×Q8—46no—
715C4×Q8—46no—
716C4×Q8—46no—
717C4×D4—212no—
718C4×D4—212no—
719C4×D4—46no—
720#117—212no—
721#117—212no—
722#117—212no—
723#117—24no—
724#117—46no—
725#117—46no—
726#117—46no—
727#117—46no—
728C2×C4⋊C4—212no—
729C2×C4⋊C4—46no—
730C2×C4⋊C4C2413yes—
731C2×C4⋊C4C2413yes—
732C2×C4⋊C4C2413yes—
733C2×C4⋊C4C2413yes—
734C2×C4⋊C4C2416yes—
735C2×C4⋊C4C2413yes—
736C2×C4⋊C4C2413yes—
737C2×C4⋊C4C2413yes—
738C2×C4⋊C4C2413yes—
739C2×C4⋊C4C2413yes—
740C2×C4⋊C4C2413yes—
741C2×C4⋊C4C2411yescharacteristic
742C2×C4⋊C4C2411yescharacteristic
743C2×C4⋊C4C2413yes—
744C2×C4⋊C4C2413yes—
745C2×C4⋊C4C2413yes—
746C2×C4⋊C4C2413yes—
747C2×C4⋊C4C2413yes—
748C2×C4⋊C4C2413yes—
749C2×C4⋊C4C2413yes—
750C2×C4⋊C4C2416yes—
751C2×C4⋊C4C2416yes—
752C2×C4⋊C4C2413yes—
753C2×C4⋊C4C2413yes—
754C2×C4⋊C4C2413yes—
755C2×C4⋊C4C2411yescharacteristic
756C2×C4⋊C4C2411yescharacteristic
757C2×C4⋊C4C2416yes—
758C2×C4⋊C4C2413yes—
759C2×C4⋊C4C2413yes—
760C2×C4⋊C4C2413yes—
761C2×C4⋊C4C2413yes—
762C2×C4⋊C4C2413yes—
763C2×C4⋊C4C2411yescharacteristic
764C2×C4⋊C4C2413yes—
765C2×C4⋊C4C2413yes—
766C2×C4⋊C4C2416yes—
767C2×C4⋊C4C2416yes—
768C2×C4⋊C4C2416yes—
769C2×C4⋊C4C2413yes—
770C2×C4⋊C4C2413yes—
771C2×C4⋊C4C2416yes—
772C2×C4⋊C4C2413yes—
773C2×C4⋊C4C2416yes—
774C2×C4⋊C4C2413yes—
775C2×C4⋊C4C2411yescharacteristic
776C2×C4⋊C4C2416yes—
777C2×C4⋊C4C2413yes—
778C2×C4⋊C4C2416yes—
779C2×C4⋊C4C2413yes—
780C2×C22⋊C4—24no—
781C2×C22⋊C4—46no—
782C2×C22⋊C4C2413yes—
783C2×C22⋊C4C2413yes—
784C2×C22⋊C4C2411yescharacteristic
785C2×C22⋊C4C2411yescharacteristic
786C2×C22⋊C4C2411yescharacteristic
787C2×C22⋊C4C2411yescharacteristic
788C2×C22⋊C4C2411yescharacteristic
789C2×C22⋊C4C2413yes—
790C2×C22⋊C4C2413yes—
791C2×C22⋊C4C2411yescharacteristic
792C2×C22⋊C4C2413yes—
793C2×C22⋊C4C2413yes—
794C2×C22⋊C4C2413yes—
795C2×C22⋊C4C2413yes—
796C2×C22⋊C4C2413yes—
797C2×C22⋊C4C2411yescharacteristic
798C2×C22⋊C4C2411yescharacteristic
799C2×C22⋊C4C2413yes—
800C2×C22⋊C4C2411yescharacteristic
801C2×C22⋊C4C2411yescharacteristic
802C2×C22⋊C4C2411yescharacteristic
803C2×C22⋊C4C2413yes—
804C2×C22⋊C4C2411yescharacteristic
805C2×C22⋊C4C2413yes—
806C2×C22⋊C4C2413yes—
807C2×C22⋊C4C2413yes—
808C2×C22⋊C4C2413yes—
809C2×C22⋊C4C2411yescharacteristic
810C2×C22⋊C4C2411yescharacteristic
811C2×C22⋊C4C2413yes—
812C2×C22⋊C4C2413yes—
813C2×C22⋊C4C2413yes—
814C2×C22⋊C4C2413yes—
815C2×C22⋊C4C2413yes—
816C2×C22⋊C4C2413yes—
817C2×C22⋊C4C2411yescharacteristic
818C2×C22⋊C4C2411yescharacteristic
819C2×C22⋊C4C2413yes—
820C2×C22⋊C4C2413yes—
821C2×C22⋊C4C2411yescharacteristic
822C2×C42—212no—
823C2×C42—46no—
824C2×C42C2413yes—
825C2×C42C2413yes—
826C2×C42C2413yes—
827C2×C42C2413yes—
828C2×C42C2416yes—
829C2×C42C2413yes—
830C2×C42C2411yescharacteristic
831C2×C42C2411yescharacteristic
832C2×C42C2413yes—
833C2×C42C2413yes—
834C2×C42C2413yes—
835C2×C42C2413yes—
836C2×C42C2413yes—
837C2×C42C2413yes—
838C2×C42C2413yes—
839C2×C42C2413yes—
840C2×C42C2413yes—
841C2×C42C2413yes—
842C2×C42C2416yes—
843C2×C42C2416yes—
844C2×C42C2413yes—
845C2×C42C2413yes—
846C2×C42C2413yes—
847C2×C42C2413yes—
848C2×C42C2416yes—
849C2×C42C2413yes—
850C2×C42C2413yes—
851#95C2413yes—
852#95C2413yes—
853#95C2413yes—
854#95C2413yes—
855#95C2413yes—
856#95C2413yes—
857#95C2413yes—
858#95C2413yes—
859#95C2416yes—
860#95C2416yes—
861#95C2416yes—
862#95C2416yes—
863#95C2411yescharacteristic
864#95C2413yes—
865#95C2413yes—
866#95C2413yes—
867#95C2413yes—
868#95C2413yes—
869#95C2413yes—
870#95C2413yes—
871#95C2413yes—
872#95C2413yes—
873#95C2413yes—
874#95C2413yes—
875#95C2413yes—
876#95C2416yes—
877#95C2416yes—
878#95C2416yes—
879#95C2413yes—
880#95C2413yes—
881#95C2413yes—
882#95C2413yes—
883#95C2413yes—
884#95C2416yes—
885#95C2413yes—
886#95C2416yes—
887#95C2416yes—
888#95C2413yes—
889#95C2413yes—
890#95C2413yes—
891#95C2416yes—
892#95C2413yes—
893#95C2413yes—
894#95C2416yes—
895#95C2413yes—
896#95C2413yes—
897#95C2413yes—
898#95C2413yes—
899#95C2413yes—
900#95C2416yes—
901#95C2416yes—
902#95C2411yescharacteristic
903#95C2411yescharacteristic
904#95C2411yescharacteristic
905#95C2413yes—
906#95C2416yes—
907#95C2416yes—
908#95C2413yes—
909#95C2413yes—
910#95C2413yes—
911#95C2413yes—
912#95C2413yes—
913#95C2413yes—
914#95C2413yes—
915#95C2416yes—
916#95C2416yes—
917#95C2416yes—
918C24—22no—
919C24—22no—
920C24—22no—
921C24—22no—
922C24—22no—
923C24—41no—
924C24—41no—
925C24C2511yescharacteristic
926C24C2511yescharacteristic
927C24C2511yescharacteristic
928C24C2511yescharacteristic
929C2×Q8—232no—
930C2×Q8—232no—
931C2×Q8—26no—
932C2×Q8—26no—
933C2×Q8—26no—
934C2×Q8—26no—
935C2×Q8—212no—
936C2×Q8—212no—
937C2×Q8—26no—
938C2×Q8—26no—
939C2×Q8—26no—
940C2×Q8—26no—
941C2×Q8—26no—
942C2×Q8—26no—
943C2×Q8—26no—
944C2×Q8—46no—
945C2×Q8—43no—
946C2×Q8—43no—
947C2×Q8—448no—
948C2×Q8—448no—
949C2×Q8—448no—
950C2×Q8—416no—
951C2×Q8—416no—
952C2×Q8C2×#41112yes—
953C2×Q8C2×#41112yes—
954C2×Q8C2×#4114yes—
955C2×Q8C2×#4114yes—
956C2×Q8H(5,𝔽2)14yes—
957C2×D4—22no—
958C2×D4—22no—
959C2×D4—22no—
960C2×D4—22no—
961C2×D4—22no—
962C2×D4—22no—
963C2×D4—22no—
964C2×D4—41no—
965C2×D4—41no—
966C22×C4—22no—
967C22×C4—22no—
968C22×C4—26no—
969C22×C4—26no—
970C22×C4—26no—
971C22×C4—26no—
972C22×C4—26no—
973C22×C4—26no—
974C22×C4—22no—
975C22×C4—26no—
976C22×C4—26no—
977C22×C4—26no—
978C22×C4—26no—
979C22×C4—26no—
980C22×C4—26no—
981C22×C4—26no—
982C22×C4—26no—
983C22×C4—26no—
984C22×C4—26no—
985C22×C4—26no—
986C22×C4—26no—
987C22×C4—41no—
988C22×C4—43no—
989C22×C4—43no—
990C22×C4—43no—
991C22×C4—41no—
992C22×C4—448no—
993C22×C4—43no—
994C22×C4—43no—
995C22×C4—43no—
996C22×C4—43no—
997C22×C4C2×#41112yes—
998C22×C4C2×#41112yes—
999C22×C42−1+414yes—
1000C22×C4C2511yescharacteristic
1001C22×C4C2513yes—
1002C22×C4C2511yescharacteristic
1003C22×C4C2513yes—
1004C22×C4C2513yes—
1005C22×C4C2513yes—
1006C22×C4C2511yescharacteristic
1007C22×C4C2511yescharacteristic
1008C22×C4C2511yescharacteristic
1009C22×C4C2513yes—
1010C22×C4C2513yes—
1011C22×C4C2513yes—
1012C22×C4C2513yes—
1013C22×C4C2513yes—
1014C22×C4C2513yes—
1015C22×C4C2511yescharacteristic
1016C22×C4C2513yes—
1017C22×C4C2513yes—
1018C22×C4C2513yes—
1019C22×C4C2511yescharacteristic
1020C22×C4C2513yes—
1021C22×C4C2513yes—
1022C22×C4C2511yescharacteristic
1023C22×C4C2511yescharacteristic
1024C22×C4C2511yescharacteristic
1025C22×C4C2511yescharacteristic
1026C22×C4C2513yes—
1027C4⋊C4—212no—
1028C4⋊C4—26no—
1029C4⋊C4—26no—
1030C4⋊C4—26no—
1031C4⋊C4—26no—
1032C4⋊C4—26no—
1033C4⋊C4—26no—
1034C4⋊C4—26no—
1035C4⋊C4—26no—
1036C4⋊C4—26no—
1037C4⋊C4—26no—
1038C4⋊C4—212no—
1039C4⋊C4—212no—
1040C4⋊C4—26no—
1041C4⋊C4—26no—
1042C4⋊C4—26no—
1043C4⋊C4—26no—
1044C4⋊C4—26no—
1045C4⋊C4—22no—
1046C4⋊C4—22no—
1047C4⋊C4—26no—
1048C4⋊C4—26no—
1049C4⋊C4—26no—
1050C4⋊C4—26no—
1051C4⋊C4—26no—
1052C4⋊C4—22no—
1053C4⋊C4—22no—
1054C4⋊C4—46no—
1055C4⋊C4—41no—
1056C4⋊C4—46no—
1057C4⋊C4—46no—
1058C4⋊C4—43no—
1059C4⋊C4—43no—
1060C4⋊C4—43no—
1061C4⋊C4—43no—
1062C4⋊C4—43no—
1063C4⋊C4—43no—
1064C4⋊C4—43no—
1065C4⋊C4—43no—
1066C4⋊C4—41no—
1067C4⋊C4—43no—
1068C4⋊C4—43no—
1069C4⋊C4—46no—
1070C4⋊C4—46no—
1071C4⋊C4—46no—
1072C4⋊C4—43no—
1073C4⋊C4—43no—
1074C4⋊C4—46no—
1075C4⋊C4—46no—
1076C4⋊C4—43no—
1077C22⋊C4—22no—
1078C22⋊C4—26no—
1079C22⋊C4—26no—
1080C22⋊C4—26no—
1081C22⋊C4—26no—
1082C22⋊C4—26no—
1083C22⋊C4—22no—
1084C22⋊C4—26no—
1085C22⋊C4—22no—
1086C22⋊C4—26no—
1087C22⋊C4—26no—
1088C22⋊C4—26no—
1089C22⋊C4—22no—
1090C22⋊C4—26no—
1091C22⋊C4—26no—
1092C22⋊C4—26no—
1093C22⋊C4—22no—
1094C22⋊C4—22no—
1095C22⋊C4—22no—
1096C22⋊C4—22no—
1097C22⋊C4—22no—
1098C22⋊C4—22no—
1099C22⋊C4—22no—
1100C22⋊C4—22no—
1101C22⋊C4—43no—
1102C22⋊C4—43no—
1103C22⋊C4—41no—
1104C22⋊C4—41no—
1105C22⋊C4—43no—
1106C22⋊C4—43no—
1107C22⋊C4—43no—
1108C22⋊C4—41no—
1109C22⋊C4—41no—
1110C22⋊C4—43no—
1111C22⋊C4—43no—
1112C22⋊C4—43no—
1113C22⋊C4—43no—
1114C22⋊C4—43no—
1115C22⋊C4—43no—
1116C22⋊C42−1+414yes—
1117C42—26no—
1118C42—26no—
1119C42—26no—
1120C42—26no—
1121C42—212no—
1122C42—26no—
1123C42—26no—
1124C42—26no—
1125C42—26no—
1126C42—26no—
1127C42—26no—
1128C42—26no—
1129C42—26no—
1130C42—26no—
1131C42—22no—
1132C42—22no—
1133C42—26no—
1134C42—26no—
1135C42—43no—
1136C42—43no—
1137C42—43no—
1138C42—43no—
1139C42—46no—
1140C42—46no—
1141C42—43no—
1142C42—46no—
1143C42—43no—
1144C23—21no—
1145C23—21no—
1146C23—21no—
1147C23—21no—
1148C23—28no—
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—21no—
1164C23—21no—
1165C23—21no—
1166C23—21no—
1167C23—21no—
1168C23—44no—
1169C23—44no—
1170C23—44no—
1171C23—44no—
1172C23—44no—
1173C23—44no—
1174C23C22×#4112yes—
1175C23C22×#4112yes—
1176C23C2×2−1+412yes—
1177C23C2×2−1+412yes—
1178C23#58512yes—
1179C23C2611yescharacteristic
1180Q8—224no—
1181Q8—224no—
1182Q8—424no—
1183Q8—412no—
1184Q8—412no—
1185Q8—86no—
1186Q8#551116yes—
1187D4—44no—
1188D4—44no—
1189D4—44no—
1190C2×C4—21no—
1191C2×C4—21no—
1192C2×C4—21no—
1193C2×C4—23no—
1194C2×C4—23no—
1195C2×C4—21no—
1196C2×C4—23no—
1197C2×C4—23no—
1198C2×C4—21no—
1199C2×C4—21no—
1200C2×C4—21no—
1201C2×C4—21no—
1202C2×C4—28no—
1203C2×C4—224no—
1204C2×C4—224no—
1205C2×C4—21no—
1206C2×C4—23no—
1207C2×C4—23no—
1208C2×C4—21no—
1209C2×C4—21no—
1210C2×C4—23no—
1211C2×C4—23no—
1212C2×C4—23no—
1213C2×C4—23no—
1214C2×C4—23no—
1215C2×C4—23no—
1216C2×C4—23no—
1217C2×C4—23no—
1218C2×C4—21no—
1219C2×C4—21no—
1220C2×C4—21no—
1221C2×C4—21no—
1222C2×C4—23no—
1223C2×C4—23no—
1224C2×C4—23no—
1225C2×C4—23no—
1226C2×C4—23no—
1227C2×C4—23no—
1228C2×C4—23no—
1229C2×C4—21no—
1230C2×C4—21no—
1231C2×C4—23no—
1232C2×C4—23no—
1233C2×C4—23no—
1234C2×C4—23no—
1235C2×C4—21no—
1236C2×C4—21no—
1237C2×C4—21no—
1238C2×C4—21no—
1239C2×C4—21no—
1240C2×C4—23no—
1241C2×C4—23no—
1242C2×C4—23no—
1243C2×C4—21no—
1244C2×C4—23no—
1245C2×C4—23no—
1246C2×C4—21no—
1247C2×C4—23no—
1248C2×C4—23no—
1249C2×C4—23no—
1250C2×C4—23no—
1251C2×C4—23no—
1252C2×C4—23no—
1253C2×C4—23no—
1254C2×C4—21no—
1255C2×C4—21no—
1256C2×C4—23no—
1257C2×C4—23no—
1258C2×C4—23no—
1259C2×C4—23no—
1260C2×C4—23no—
1261C2×C4—21no—
1262C2×C4—23no—
1263C2×C4—21no—
1264C2×C4—21no—
1265C2×C4—412no—
1266C2×C4—412no—
1267C2×C4—412no—
1268C2×C4—44no—
1269C2×C4—412no—
1270C2×C4—412no—
1271C2×C4—86no—
1272C2×C4—86no—
1273C2×C4C22×#4116yes—
1274C2×C4C22×#4116yes—
1275C2×C4C22×#4116yes—
1276C2×C4C22×#4116yes—
1277C2×C4C2×H(5,𝔽2)16yes—
1278C2×C4C2×2−1+412yes—
1279C2×C4C2×2−1+412yes—
1280C2×C4C2×2−1+412yes—
1281C2×C4C2×2−1+412yes—
1282C22—22no—
1283C22—22no—
1284C22—22no—
1285C22—22no—
1286C22—22no—
1287C22—22no—
1288C22—22no—
1289C22—22no—
1290C22—22no—
1291C22—22no—
1292C22—22no—
1293C22—22no—
1294C22—416no—
1295C22—41no—
1296C22—41no—
1297C22—41no—
1298C22—41no—
1299C22—41no—
1300C22—41no—
1301C22—41no—
1302C22—41no—
1303C22—41no—
1304C22—41no—
1305C22—41no—
1306C22—41no—
1307C22—41no—
1308C22—41no—
1309C22—41no—
1310C22#352314yes—
1311C22C23×#4111yescharacteristic
1312C22C23×#4111yescharacteristic
1313C22C22×H(5,𝔽2)11yescharacteristic
1314C22C22×2−1+411yescharacteristic
1315C22C22×2−1+411yescharacteristic
1316C22C2×#58511yescharacteristic
1317C222−1+611yescharacteristic
1318C4—22no—
1319C4—22no—
1320C4—22no—
1321C4—22no—
1322C4—26no—
1323C4—26no—
1324C4—41no—
1325C4—43no—
1326C4—43no—
1327C4—43no—
1328C4—43no—
1329C4—41no—
1330C4—43no—
1331C4—43no—
1332C4—43no—
1333C4—41no—
1334C4—43no—
1335C4—41no—
1336C4—43no—
1337C4—41no—
1338C4—43no—
1339C4—43no—
1340C4—41no—
1341C4—41no—
1342C4—43no—
1343C4—43no—
1344C4C2×#551112yes—
1345C2—24no—
1346C2—42no—
1347C2—42no—
1348C2—81no—
1349C2C22×#55111yescharacteristic
1350C2C2×#352311yescharacteristic
1351C2#6278811yescharacteristic
1352C2#6291311yescharacteristic
1353C2#6299811yescharacteristic
1354C2#6300511yescharacteristic
1355C2#6301511yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#120C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59867C2semidirect
2. #59752C2semidirect
3. #59481C2semidirect
4. #59271C2semidirect
6. #45351C2semidirect
7. #45340C2semidirect
8. #45327C2semidirect
9. #45149C2semidirect
10. #38251C2semidirect
11. #38203C2semidirect
12. #38113C2semidirect
13. #37850C2semidirect
14. Q8×#123C2semidirect
16. #36448C2semidirect
17. #36446C2semidirect
18. #36435C2semidirect
19. #36279C2semidirect
20. #36207C2semidirect
21. #35920C2semidirect
22. #35786C2semidirect
23. #35723C2semidirect
24. #35723C2semidirect
26. #34311C2semidirect
27. #34291C2semidirect
28. #34262C2semidirect
29. #34173C2semidirect
30. Q8×#117C2semidirect
31. C2×Q8×C22⋊C4C2semidirect
33. C2×#557C22semidirect
39. C2×#519C22semidirect
42. #2863C22semidirect
43. #2862C22semidirect
47. #2799C22semidirect
48. #2798C22semidirect
49. #2789C22semidirect
50. #2762C22semidirect
51. #2758C22semidirect
52. #2755C22semidirect
53. #2754C22semidirect
54. #2754C22semidirect
61. #2645C22semidirect
64. #2625C22semidirect
65. #2612C22semidirect
66. #2605C22semidirect
67. #2588C22semidirect
68. #2586C22semidirect
69. #2582C22semidirect
70. #2581C22semidirect
74. #2568C22semidirect
75. #2565C22semidirect
76. #2565C22semidirect
78. #2532C22semidirect
86. #2520C22semidirect
87. #2520C22semidirect
88. #2520C22semidirect
93. #2514C22semidirect
94. #2514C22semidirect
95. #2511C22semidirect
96. #2511C22semidirect
97. #2511C22semidirect
98. #2511C22semidirect
106. #2499C22semidirect
116. #2489C22semidirect
117. #2489C22semidirect
125. #2453C22semidirect
126. #2453C22semidirect
127. #2451C22semidirect
128. #2451C22semidirect
129. #2446C22semidirect
130. #2446C22semidirect
131. #2446C22semidirect
132. #2446C22semidirect
133. #2446C22semidirect
134. #2446C22semidirect
144. #2423C22semidirect
145. #2423C22semidirect
146. #2423C22semidirect
148. #2421C22semidirect
159. #2365C22semidirect
160. #2365C22semidirect
162. #2362C22semidirect
163. #2362C22semidirect
165. #2356C22semidirect
166. #2355C22semidirect
167. #2355C22semidirect
168. #2355C22semidirect
171. #2351C22semidirect
172. #2351C22semidirect
173. #2351C22semidirect
174. Q8×C4⋊C4C22semidirect
175. Q8×C4⋊C4C22semidirect
176. Q8×C4⋊C4C22semidirect
177. Q8×C4⋊C4C22semidirect
178. Q8×C4⋊C4C22semidirect
203. Q8×C22⋊C4C22semidirect
204. Q8×C22⋊C4C22semidirect
205. Q8×C22⋊C4C22semidirect
206. #2327C22semidirect
208. #2323C22semidirect
209. #2323C22semidirect
210. #2320C22semidirect
214. C4×C4⋊Q8C22semidirect
222. #2295C22semidirect
223. #2295C22semidirect
224. #2295C22semidirect
233. #2276C22semidirect
234. C42×Q8C22semidirect
235. C42×Q8C22semidirect

Maximal subgroups

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

subgroupindex
#598672
#597522
#594812
#592712
#592042
#453512
#453402
#453272
#451492
#382512
#382032
#381132
#378502
Q8×#1232
Q8×#1202
#364482
#364462
#364352
#362792
#362072
#359202
#357862
#357232
#348062
#343112
#342912
#342622
#341732
Q8×#1172
C2×Q8×C22⋊C42