Finite Group Databasebeta

← #7698559

Subgroups — #7698559

Order 512.

5463 conjugacy classes of subgroups.

The subgroup lattice has 1359 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59486C213yesmaximal, complemented
2#59479C213yesmaximal, complemented
3#59204C213yesmaximal, complemented
4#52178C213yesmaximal, complemented
5#45401C213yesmaximal, complemented
6#45391C213yesmaximal, complemented
7#45365C213yesmaximal, complemented
8#45259C213yesmaximal, complemented
9#45087C213yesmaximal, complemented
10#44903C213yesmaximal, complemented
11#39070C213yesmaximal, complemented
12#39065C213yesmaximal, complemented
13#38206C213yesmaximal, complemented
14#38201C213yesmaximal, complemented
15#37859C213yesmaximal, complemented
16#37853C213yesmaximal, complemented
17#36585C211yesmaximal, characteristic, complemented
18#36458C211yesmaximal, characteristic, complemented
19#36428C211yesmaximal, characteristic
20#35983C211yesmaximal, characteristic, complemented
21#35948C211yesmaximal, characteristic, complemented
22#35801C211yesmaximal, characteristic, complemented
23#35748C211yesmaximal, characteristic, complemented
24#35723C211yesmaximal, characteristic, complemented
25#35711C211yesmaximal, characteristic, complemented
26#34312C211yesmaximal, characteristic, complemented
27#34311C211yesmaximal, characteristic, complemented
28#34263C211yesmaximal, characteristic, complemented
29#34262C211yesmaximal, characteristic, complemented
30#34175C211yesmaximal, characteristic, complemented
31#34174C211yesmaximal, characteristic, complemented
32C23×#41C2211yescharacteristic
33C2×Q82C2211yescharacteristic, complemented
34C2×D4×Q8C2211yescharacteristic
35C2×#548C2211yescharacteristic
36C2×#548C2211yescharacteristic
37C2×#520C2211yescharacteristic
38C2×#520C2211yescharacteristic
39C2×#519C2211yescharacteristic
40C2×#519C2211yescharacteristic
41C2×#519C2211yescharacteristic, complemented
42#2860C2213yescomplemented
43#2860C2213yescomplemented
44#2848C2213yes—
45#2757C2216yescomplemented
46#2753C2216yescomplemented
47#2752C2216yescomplemented
48#2751C2216yescomplemented
49#2747C2216yescomplemented
50#2745C2216yes—
51#2742C2216yescomplemented
52#2742C2213yescomplemented
53#2741C2213yescomplemented
54#2741C2213yescomplemented
55#2740C2213yes—
56#2740C2213yescomplemented
57#2740C2216yescomplemented
58#2739C2213yes—
59#2739C2213yescomplemented
60#2738C2213yes—
61#2738C2213yescomplemented
62#2737C2211yescharacteristic
63#2737C2216yescomplemented
64#2737C2213yescomplemented
65#2736C2213yes—
66#2736C2216yes—
67#2735C2216yes—
68#2735C2213yes—
69#2730C2216yescomplemented
70#2723C2216yescomplemented
71#2722C2213yescomplemented
72#2685C2213yes—
73#2685C2213yes—
74#2640C2213yescomplemented
75#2628C2213yes—
76#2628C2213yescomplemented
77#2625C2213yes—
78#2625C2213yescomplemented
79#2624C2213yescomplemented
80#2610C2216yescomplemented
81#2597C2216yescomplemented
82#2595C2216yescomplemented
83#2592C2213yescomplemented
84#2581C2213yescomplemented
85#2580C2213yescomplemented
86#2577C2216yescomplemented
87#2575C2216yescomplemented
88#2574C2216yescomplemented
89#2568C2213yescomplemented
90#2561C2216yes—
91#2560C2216yescomplemented
92#2560C2216yescomplemented
93#2547C2213yescomplemented
94#2542C2213yescomplemented
95#2530C2216yescomplemented
96#2527C2216yescomplemented
97#2526C2216yescomplemented
98#2521C2216yescomplemented
99#2516C2216yescomplemented
100#2513C2213yescomplemented
101#2513C2213yescomplemented
102#2513C2213yescomplemented
103#2513C2213yescomplemented
104#2512C2213yescomplemented
105#2512C2213yescomplemented
106#2510C2216yescomplemented
107#2503C2213yescomplemented
108#2500C2213yescomplemented
109#2499C2213yes—
110#2497C2213yescomplemented
111#2496C2213yescomplemented
112#2495C2213yescomplemented
113#2494C2213yescomplemented
114#2494C2213yescomplemented
115#2494C2213yescomplemented
116#2493C2216yescomplemented
117#2492C2213yescomplemented
118#2492C2213yescomplemented
119#2491C2213yescomplemented
120#2491C2213yescomplemented
121#2487C2213yescomplemented
122#2485C2213yes—
123#2485C2213yescomplemented
124#2482C2216yes—
125#2480C2216yes—
126#2479C2216yescomplemented
127#2472C2216yes—
128#2452C2213yescomplemented
129#2452C2213yescomplemented
130#2451C2213yescomplemented
131#2451C2213yescomplemented
132#2448C2213yescomplemented
133#2448C2213yescomplemented
134#2447C2213yescomplemented
135#2447C2213yescomplemented
136#2446C2213yescomplemented
137#2446C2213yescomplemented
138#2440C2213yescomplemented
139#2440C2213yescomplemented
140#2439C2213yes—
141#2439C2213yes—
142#2438C2216yescomplemented
143#2435C2213yes—
144#2432C2213yes—
145#2432C2213yes—
146#2423C2213yescomplemented
147#2423C2213yescomplemented
148#2421C2213yescomplemented
149#2421C2213yescomplemented
150#2420C2213yescomplemented
151#2420C2213yescomplemented
152#2408C2213yes—
153#2407C2213yes—
154#2407C2213yes—
155#2398C2213yescomplemented
156#2396C2213yes—
157#2396C2213yescomplemented
158#2395C2213yes—
159#2395C2213yescomplemented
160#2395C2213yescomplemented
161#2368C2216yescomplemented
162#2367C2213yescomplemented
163#2365C2213yescomplemented
164#2363C2213yescomplemented
165#2362C2213yes—
166#2362C2213yescomplemented
167#2360C2213yescomplemented
168#2357C2213yescomplemented
169#2356C2213yescomplemented
170#2355C2213yescomplemented
171#2354C2213yes—
172#2354C2213yescomplemented
173#2352C2213yescomplemented
174#2351C2211yescharacteristic, complemented
175#2351C2211yescharacteristic, complemented
176#2351C2211yescharacteristic, complemented
177#2351C2211yescharacteristic, complemented
178#2351C2211yescharacteristic, complemented
179Q8×C4⋊C4C2211yescharacteristic, complemented
180Q8×C4⋊C4C2211yescharacteristic, complemented
181Q8×C4⋊C4C2211yescharacteristic, complemented
182#2347C2213yes—
183#2346C2213yes—
184#2345C2213yescomplemented
185#2344C2213yescomplemented
186#2341C2211yescharacteristic
187#2341C2213yes—
188#2341C2213yes—
189#2341C2211yescharacteristic
190#2341C2211yescharacteristic
191#2341C2213yes—
192#2341C2213yes—
193#2341C2211yescharacteristic
194#2341C2211yescharacteristic
195#2341C2211yescharacteristic
196#2341C2211yescharacteristic
197#2341C2211yescharacteristic
198Q8×C22⋊C4C2211yescharacteristic
199Q8×C22⋊C4C2211yescharacteristic
200Q8×C22⋊C4C2211yescharacteristic
201Q8×C22⋊C4C2211yescharacteristic, complemented
202Q8×C22⋊C4C2211yescharacteristic, complemented
203Q8×C22⋊C4C2211yescharacteristic, complemented
204#2339C2213yes—
205#2339C2213yes—
206D4×C22⋊C4C2213yes—
207D4×C22⋊C4C2213yes—
208#2324C2213yescomplemented
209#2323C2213yes—
210#2323C2213yescomplemented
211#2323C2213yescomplemented
212#2320C2213yescomplemented
213#2319C2213yescomplemented
214#2314C2213yes—
215#2314C2213yescomplemented
216#2311C2213yes—
217#2311C2213yes—
218#2309C2213yes—
219#2309C2213yes—
220C4×C4⋊Q8C2213yescomplemented
221C4×#126C2213yescomplemented
222C4×#126C2213yescomplemented
223C4×#124C2213yescomplemented
224C4×#120C2213yes—
225#2298C2213yes—
226#2298C2213yescomplemented
227#2295C2213yescomplemented
228#2293C2213yes—
229#2293C2213yescomplemented
230#2293C2213yescomplemented
231#2280C2213yes—
232#2280C2213yes—
233#2280C2213yes—
234C2×#380C2213yes—
235#2276C2211yescharacteristic, complemented
236C42×Q8C2211yescharacteristic, complemented
237C42×Q8C2211yescharacteristic, complemented
238C22×#41—28no—
239C22×#41—28no—
240C22×#41—44no—
241C22×#41C2311yescharacteristic
242C22×#41C2313yes—
243C22×#41C2313yes—
244C22×#41C2311yescharacteristic
245C23×Q8C2311yescharacteristic
246C23×Q8C2311yescharacteristic
247C23×D4C2313yes—
248C24×C4C2313yes—
249Q82—44no—
250D4×Q8—28no—
251#548—28no—
252#548—44no—
253C2×C4⋊Q8C2313yes—
254C2×C4⋊Q8C2313yes—
255C2×C4⋊Q8C2313yes—
256C2×C4⋊Q8C2313yes—
257C2×#126C2313yes—
258C2×#126C2313yes—
259C2×#126C2316yes—
260C2×#124C2313yes—
261C2×#124C2313yes—
262C2×#124C2316yes—
263C2×C22⋊Q8C2313yes—
264C2×C22⋊Q8C2313yes—
265C2×C22⋊Q8C2313yes—
266C2×C22⋊Q8C2316yes—
267C2×C22⋊Q8C2313yes—
268C2×C22⋊Q8C2316yes—
269C2×#121C2313yes—
270C2×#121C2313yes—
271C2×#120C2313yes—
272#520—28no—
273#520—44no—
274#519—28no—
275#519—44no—
276#519—44no—
277C2×C4×Q8C2313yes—
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×Q8C2311yescharacteristic
289C2×C4×Q8C2313yes—
290C2×C4×Q8C2313yes—
291C2×C4×Q8C2313yes—
292C2×C4×Q8C2313yes—
293C2×C4×Q8C2313yes—
294C2×C4×Q8C2313yes—
295C2×C4×D4C2313yes—
296C2×C4×D4C2313yes—
297C2×C4×D4C2313yes—
298C2×C4×D4C2313yes—
299C2×C4×D4C2313yes—
300C2×C4×D4C2313yes—
301C2×C4×D4C2313yes—
302C2×#117C2313yes—
303C2×#117C2313yes—
304C2×#117C2313yes—
305C2×#117C2313yes—
306C2×#117C2313yes—
307C2×#117C2313yes—
308C2×#117C2313yes—
309C2×#117C2313yes—
310C2×#117C2316yes—
311C22×C4⋊C4C2313yes—
312C22×C4⋊C4C2313yes—
313C22×C22⋊C4C2316yes—
314#401C2316yes—
315#400C2313yes—
316#400C2316yes—
317#400C2313yes—
318#400C2316yes—
319#400C2316yes—
320#400C2316yes—
321#400C2313yes—
322#400C2313yes—
323#400C2313yes—
324#400C2313yes—
325#400C2313yes—
326#399C2316yes—
327#399C2316yes—
328#399C2313yes—
329#399C2313yes—
330#399C2313yes—
331#399C2313yes—
332#399C2313yes—
333#398C2313yes—
334#398C2316yes—
335#398C2313yes—
336#398C2313yes—
337#398C2313yes—
338#398C2313yes—
339#398C2313yes—
340#398C2313yes—
341#397C2313yes—
342#397C2316yes—
343#397C2313yes—
344#397C2316yes—
345#397C2316yes—
346#397C2316yes—
347#397C2316yes—
348#397C2313yes—
349#397C2313yes—
350#397C2316yes—
351#397C2316yes—
352#397C2316yes—
353#397C2313yes—
354#397C2313yes—
355#397C2311yescharacteristic
356#397C2311yescharacteristic
357#397C2313yes—
358#397C2313yes—
359#397C2313yes—
360#397C2316yes—
361#397C2316yes—
362#396C2316yes—
363#396C2313yes—
364#396C2313yes—
365#396C2313yes—
366#396C2313yes—
367#395C2316yes—
368#395C2313yes—
369#395C2316yes—
370#395C2311yescharacteristic
371#394C2316yes—
372#394C2316yes—
373#394C2316yes—
374#394C2313yes—
375#394C2316yes—
376#394C2311yescharacteristic
377#394C2313yes—
378#394C2313yes—
379#394C2313yes—
380#394C2313yes—
381#394C2313yes—
382#394C2313yes—
383#393C2316yes—
384#393C2316yes—
385#393C2316yes—
386#393C2313yes—
387#393C2313yes—
388#393C2316yes—
389#393C2311yescharacteristic
390#393C2311yescharacteristic
391#392C2316yes—
392#391C2316yes—
393#391C2316yes—
394#391C2313yes—
395#391C2313yes—
396#391C2313yes—
397#391C2313yes—
398#391C2313yes—
399#391C2313yes—
400#391C2313yes—
401#391C2313yes—
402#391C2313yes—
403#391C2313yes—
404#391C2313yes—
405#391C2313yes—
406#391C2316yes—
407#390C2316yes—
408#390C2316yes—
409#390C2313yes—
410#390C2313yes—
411#390C2313yes—
412#390C2313yes—
413#390C2316yes—
414#390C2313yes—
415#390C2313yes—
416#390C2316yes—
417#390C2313yes—
418#390C2313yes—
419#390C2313yes—
420#390C2313yes—
421#390C2313yes—
422#390C2313yes—
423#390C2313yes—
424#390C2313yes—
425#390C2313yes—
426#390C2313yes—
427#390C2313yes—
428#390C2313yes—
429#390C2313yes—
430#390C2311yescharacteristic
431#389C2313yes—
432#389C2316yes—
433#389C2313yes—
434#389C2313yes—
435#389C2313yes—
436#389C2313yes—
437#389C2313yes—
438#389C2313yes—
439#389C2313yes—
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#388C2316yes—
461#388C2316yes—
462#388C2316yes—
463#388C2313yes—
464#388C2316yes—
465#388C2316yes—
466#388C2316yes—
467#388C2316yes—
468#388C2316yes—
469#388C2313yes—
470#388C2316yes—
471#388C2316yes—
472#388C2313yes—
473#388C2313yes—
474#388C2316yes—
475#388C2316yes—
476#388C2316yes—
477#388C2316yes—
478#388C2313yes—
479#388C2313yes—
480#388C2316yes—
481#388C2316yes—
482#388C2313yes—
483#388C2313yes—
484#388C2316yes—
485#388C2313yes—
486#388C2313yes—
487#388C2313yes—
488#388C2313yes—
489#388C2311yescharacteristic
490#388C2313yes—
491#388C2311yescharacteristic
492#387C2311yescharacteristic
493#387C2313yes—
494#387C2313yes—
495#387C2313yes—
496#387C2313yes—
497#387C2313yes—
498#387C2313yes—
499#387C2316yes—
500#387C2316yes—
501#387C2313yes—
502#387C2316yes—
503#387C2316yes—
504#387C2316yes—
505#387C2316yes—
506#387C2316yes—
507#387C2316yes—
508#387C2313yes—
509#387C2313yes—
510#387C2316yes—
511#387C2316yes—
512#387C2316yes—
513#387C2316yes—
514#387C2313yes—
515#387C2313yes—
516#387C2311yescharacteristic
517#387C2313yes—
518#386C2316yes—
519#386C2316yes—
520#386C2316yes—
521#386C2316yes—
522#386C2316yes—
523#386C2316yes—
524#386C2313yes—
525#386C2313yes—
526#386C2311yescharacteristic
527#385C2316yes—
528#385C2316yes—
529#385C2313yes—
530#385C2316yes—
531#385C2316yes—
532#385C2316yes—
533#385C2313yes—
534#385C2313yes—
535#385C2316yes—
536#384C2313yes—
537#384C2313yes—
538#384C2313yes—
539#383C2311yescharacteristic
540#383C2313yes—
541#383C2316yes—
542#382C2313yes—
543#382C2313yes—
544#382C2313yes—
545#382C2316yes—
546#382C2313yes—
547#382C2313yes—
548#381C2316yes—
549#381C2316yes—
550#381C2313yes—
551#381C2313yes—
552#381C2316yes—
553#381C2311yescharacteristic
554#381C2313yes—
555#380C2313yes—
556#380C2316yes—
557#380C2313yes—
558#380C2313yes—
559#380C2313yes—
560#380C2313yes—
561#380C2313yes—
562#380C2316yes—
563#380C2313yes—
564#380C2313yes—
565#380C2313yes—
566#380C2313yes—
567#380C2313yes—
568#380C2313yes—
569#380C2313yes—
570#380C2313yes—
571#380C2313yes—
572#380C2313yes—
573#380C2313yes—
574#380C2313yes—
575#380C2313yes—
576#380C2313yes—
577#380C2311yescharacteristic
578#380C2313yes—
579#379C2313yes—
580#379C2316yes—
581#379C2313yes—
582#379C2316yes—
583#379C2313yes—
584#379C2313yes—
585#379C2313yes—
586C4×C4⋊C4C2313yes—
587C4×C4⋊C4C2313yes—
588C4×C4⋊C4C2313yes—
589C4×C4⋊C4C2313yes—
590C4×C4⋊C4C2313yes—
591C4×C4⋊C4C2313yes—
592C4×C4⋊C4C2316yes—
593C4×C4⋊C4C2316yes—
594C4×C4⋊C4C2313yes—
595C4×C4⋊C4C2313yes—
596C4×C4⋊C4C2313yes—
597C4×C4⋊C4C2313yes—
598C4×C4⋊C4C2313yes—
599C4×C4⋊C4C2313yes—
600C4×C4⋊C4C2313yes—
601C4×C4⋊C4C2316yes—
602C4×C4⋊C4C2313yes—
603C4×C4⋊C4C2313yes—
604C4×C4⋊C4C2313yes—
605C4×C4⋊C4C2313yes—
606C4×C22⋊C4C2313yes—
607C4×C22⋊C4C2313yes—
608C4×C22⋊C4C2313yes—
609C4×C22⋊C4C2313yes—
610C4×C22⋊C4C2313yes—
611C4×C22⋊C4C2316yes—
612C4×C22⋊C4C2316yes—
613C4×C22⋊C4C2316yes—
614C4×C22⋊C4C2316yes—
615C4×C22⋊C4C2313yes—
616C4×C22⋊C4C2313yes—
617C4×C22⋊C4C2313yes—
618C4×C22⋊C4C2313yes—
619C4×C22⋊C4C2313yes—
620C4×C22⋊C4C2313yes—
621C4×C22⋊C4C2313yes—
622C4×C22⋊C4C2313yes—
623C4×C22⋊C4C2313yes—
624C4×C22⋊C4C2316yes—
625#376C2313yes—
626#376C2316yes—
627C2×#95C2316yes—
628C43C2313yes—
629C43C2313yes—
630C25C2413yes—
631C2×#41—24no—
632C2×#41—212no—
633C2×#41—212no—
634C2×#41—24no—
635C2×#41—24no—
636C2×#41—24no—
637C2×#41—24no—
638C2×#41—212no—
639C2×#41—212no—
640C2×#41—46no—
641C2×#41—46no—
642C2×#41—464no—
643C2×#41#4118yes—
644C22×Q8—24no—
645C22×Q8—24no—
646C22×Q8—24no—
647C22×Q8—24no—
648C22×Q8—24no—
649C22×Q8#4118yes—
650C22×Q8C2413yes—
651C22×Q8C2413yes—
652C22×Q8C2411yescharacteristic
653C22×Q8C2416yes—
654C22×Q8C2411yescharacteristic
655C22×D4—212no—
656C22×D4—212no—
657C22×D4—46no—
658C22×D4C2413yes—
659C22×D4C2411yescharacteristic
660C22×D4C2416yes—
661C22×D4C2413yes—
662C22×D4C2413yes—
663C22×D4C2413yes—
664C23×C4—212no—
665C23×C4—212no—
666C23×C4—46no—
667C23×C4C2413yes—
668C23×C4C2413yes—
669C23×C4C2411yescharacteristic
670C23×C4C2413yes—
671C23×C4C2413yes—
672C23×C4C2413yes—
673C23×C4C2413yes—
674C23×C4C2416yes—
675C23×C4C2416yes—
676C4⋊Q8—212no—
677C4⋊Q8—46no—
678C4⋊Q8—46no—
679C4⋊Q8—46no—
680#126—46no—
681#126—46no—
682#126—86no—
683#124—212no—
684#124—46no—
685#124—86no—
686C22⋊Q8—212no—
687C22⋊Q8—212no—
688C22⋊Q8—212no—
689C22⋊Q8—412no—
690C22⋊Q8—46no—
691C22⋊Q8—86no—
692#121—212no—
693#121—46no—
694#120—46no—
695C4×Q8—212no—
696C4×Q8—212no—
697C4×Q8—24no—
698C4×Q8—24no—
699C4×Q8—24no—
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—46no—
709C4×Q8—46no—
710C4×Q8—46no—
711C4×Q8—46no—
712C4×Q8—46no—
713C4×D4—212no—
714C4×D4—212no—
715C4×D4—212no—
716C4×D4—212no—
717C4×D4—46no—
718C4×D4—46no—
719C4×D4—46no—
720#117—212no—
721#117—212no—
722#117—212no—
723#117—46no—
724#117—46no—
725#117—46no—
726#117—46no—
727#117—46no—
728#117—86no—
729C2×C4⋊C4—212no—
730C2×C4⋊C4—46no—
731C2×C4⋊C4C2413yes—
732C2×C4⋊C4C2413yes—
733C2×C4⋊C4C2413yes—
734C2×C4⋊C4C2413yes—
735C2×C4⋊C4C2413yes—
736C2×C4⋊C4C2411yescharacteristic
737C2×C4⋊C4C2413yes—
738C2×C4⋊C4C2413yes—
739C2×C4⋊C4C2413yes—
740C2×C4⋊C4C2413yes—
741C2×C4⋊C4C2413yes—
742C2×C4⋊C4C2413yes—
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⋊C4C2411yescharacteristic
752C2×C4⋊C4C2413yes—
753C2×C4⋊C4C2411yescharacteristic
754C2×C4⋊C4C2413yes—
755C2×C4⋊C4C2413yes—
756C2×C4⋊C4C2413yes—
757C2×C4⋊C4C2413yes—
758C2×C4⋊C4C2413yes—
759C2×C4⋊C4C2416yes—
760C2×C4⋊C4C2413yes—
761C2×C4⋊C4C2413yes—
762C2×C4⋊C4C2413yes—
763C2×C4⋊C4C2413yes—
764C2×C4⋊C4C2413yes—
765C2×C4⋊C4C2413yes—
766C2×C4⋊C4C2416yes—
767C2×C4⋊C4C2416yes—
768C2×C4⋊C4C2413yes—
769C2×C4⋊C4C2413yes—
770C2×C4⋊C4C2413yes—
771C2×C4⋊C4C2413yes—
772C2×C4⋊C4C2413yes—
773C2×C4⋊C4C2411yescharacteristic
774C2×C4⋊C4C2411yescharacteristic
775C2×C4⋊C4C2413yes—
776C2×C4⋊C4C2413yes—
777C2×C4⋊C4C2413yes—
778C2×C22⋊C4—86no—
779C2×C22⋊C4C2411yescharacteristic
780C2×C22⋊C4C2413yes—
781C2×C22⋊C4C2413yes—
782C2×C22⋊C4C2413yes—
783C2×C22⋊C4C2411yescharacteristic
784C2×C22⋊C4C2413yes—
785C2×C22⋊C4C2413yes—
786C2×C22⋊C4C2413yes—
787C2×C22⋊C4C2413yes—
788C2×C22⋊C4C2413yes—
789C2×C22⋊C4C2416yes—
790C2×C22⋊C4C2413yes—
791C2×C22⋊C4C2413yes—
792C2×C22⋊C4C2416yes—
793C2×C22⋊C4C2416yes—
794C2×C22⋊C4C2413yes—
795C2×C22⋊C4C2411yescharacteristic
796C2×C22⋊C4C2413yes—
797C2×C22⋊C4C2411yescharacteristic
798C2×C22⋊C4C2413yes—
799C2×C22⋊C4C2413yes—
800C2×C22⋊C4C2413yes—
801C2×C22⋊C4C2416yes—
802C2×C22⋊C4C2411yescharacteristic
803C2×C22⋊C4C2413yes—
804C2×C22⋊C4C2413yes—
805C2×C22⋊C4C2416yes—
806C2×C22⋊C4C2413yes—
807C2×C22⋊C4C2416yes—
808C2×C22⋊C4C2413yes—
809C2×C22⋊C4C2413yes—
810C2×C22⋊C4C2416yes—
811C2×C22⋊C4C2413yes—
812C2×C22⋊C4C2413yes—
813C2×C22⋊C4C2413yes—
814C2×C22⋊C4C2413yes—
815C2×C22⋊C4C2413yes—
816C2×C22⋊C4C2411yescharacteristic
817C2×C22⋊C4C2411yescharacteristic
818C2×C22⋊C4C2411yescharacteristic
819C2×C22⋊C4C2416yes—
820C2×C22⋊C4C2413yes—
821C2×C22⋊C4C2411yescharacteristic
822C2×C22⋊C4C2411yescharacteristic
823C2×C22⋊C4C2411yescharacteristic
824C2×C22⋊C4C2413yes—
825C2×C22⋊C4C2413yes—
826C2×C22⋊C4C2413yes—
827C2×C22⋊C4C2413yes—
828C2×C22⋊C4C2413yes—
829C2×C22⋊C4C2416yes—
830C2×C22⋊C4C2413yes—
831C2×C22⋊C4C2413yes—
832C2×C22⋊C4C2416yes—
833C2×C42C2413yes—
834C2×C42C2413yes—
835C2×C42C2413yes—
836C2×C42C2413yes—
837C2×C42C2413yes—
838C2×C42C2413yes—
839C2×C42C2413yes—
840C2×C42C2416yes—
841C2×C42C2413yes—
842C2×C42C2413yes—
843C2×C42C2413yes—
844C2×C42C2413yes—
845C2×C42C2411yescharacteristic
846C2×C42C2413yes—
847C2×C42C2416yes—
848C2×C42C2416yes—
849C2×C42C2416yes—
850C2×C42C2413yes—
851C2×C42C2413yes—
852C2×C42C2411yescharacteristic
853C2×C42C2413yes—
854C2×C42C2413yes—
855C2×C42C2413yes—
856#95C2413yes—
857#95C2413yes—
858#95C2416yes—
859#95C2416yes—
860#95C2411yescharacteristic
861#95C2413yes—
862#95C2413yes—
863#95C2413yes—
864#95C2413yes—
865#95C2413yes—
866#95C2416yes—
867#95C2416yes—
868#95C2411yescharacteristic
869#95C2411yescharacteristic
870#95C2413yes—
871#95C2411yescharacteristic
872#95C2413yes—
873#95C2413yes—
874#95C2413yes—
875#95C2411yescharacteristic
876#95C2411yescharacteristic
877#95C2411yescharacteristic
878#95C2411yescharacteristic
879#95C2411yescharacteristic
880#95C2413yes—
881#95C2413yes—
882#95C2413yes—
883#95C2413yes—
884#95C2413yes—
885#95C2413yes—
886#95C2413yes—
887#95C2413yes—
888#95C2413yes—
889#95C2413yes—
890#95C2416yes—
891#95C2413yes—
892#95C2413yes—
893#95C2416yes—
894#95C2416yes—
895#95C2413yes—
896#95C2413yes—
897#95C2413yes—
898#95C2416yes—
899#95C2416yes—
900#95C2411yescharacteristic
901#95C2411yescharacteristic
902#95C2411yescharacteristic
903#95C2411yescharacteristic
904#95C2411yescharacteristic
905#95C2416yes—
906#95C2413yes—
907#95C2413yes—
908#95C2413yes—
909#95C2413yes—
910#95C2413yes—
911#95C2413yes—
912#95C2413yes—
913#95C2413yes—
914#95C2416yes—
915#95C2416yes—
916#95C2416yes—
917C24—26no—
918C24—26no—
919C24—43no—
920C24—43no—
921C24—43no—
922C24—43no—
923C24—43no—
924C24C2513yes—
925C24C2511yescharacteristic
926C24C2511yescharacteristic
927C24C2513yes—
928#41—232no—
929#41—448no—
930#41—448no—
931#41—416no—
932C2×Q8—232no—
933C2×Q8—26no—
934C2×Q8—26no—
935C2×Q8—26no—
936C2×Q8—26no—
937C2×Q8—26no—
938C2×Q8—41no—
939C2×Q8—41no—
940C2×Q8—41no—
941C2×Q8—46no—
942C2×Q8—46no—
943C2×Q8—46no—
944C2×Q8—416no—
945C2×Q8C2×#41112yes—
946C2×Q8C2×#4114yes—
947C2×Q8C2×#4114yes—
948C2×Q8H(5,𝔽2)14yes—
949C2×D4—22no—
950C2×D4—212no—
951C2×D4—26no—
952C2×D4—26no—
953C2×D4—212no—
954C2×D4—26no—
955C2×D4—26no—
956C2×D4—26no—
957C2×D4—26no—
958C2×D4—22no—
959C2×D4—448no—
960C2×D4—46no—
961C2×D4—41no—
962C2×D4—43no—
963C2×D4—43no—
964C2×D4—43no—
965C2×D4—43no—
966C2×D4—43no—
967C2×D4C2×#41112yes—
968C22×C4—26no—
969C22×C4—26no—
970C22×C4—26no—
971C22×C4—26no—
972C22×C4—22no—
973C22×C4—26no—
974C22×C4—212no—
975C22×C4—26no—
976C22×C4—26no—
977C22×C4—22no—
978C22×C4—26no—
979C22×C4—26no—
980C22×C4—26no—
981C22×C4—26no—
982C22×C4—26no—
983C22×C4—26no—
984C22×C4—26no—
985C22×C4—41no—
986C22×C4—43no—
987C22×C4—43no—
988C22×C4—448no—
989C22×C4—46no—
990C22×C4—46no—
991C22×C4—46no—
992C22×C4—46no—
993C22×C4—46no—
994C22×C4C2×#41112yes—
995C22×C4C2×#41112yes—
996C22×C4C2511yescharacteristic
997C22×C4C2513yes—
998C22×C4C2513yes—
999C22×C4C2513yes—
1000C22×C4C2511yescharacteristic
1001C22×C4C2511yescharacteristic
1002C22×C4C2511yescharacteristic
1003C22×C4C2513yes—
1004C22×C4C2511yescharacteristic
1005C22×C4C2511yescharacteristic
1006C22×C4C2511yescharacteristic
1007C22×C4C2513yes—
1008C22×C4C2513yes—
1009C22×C4C2511yescharacteristic
1010C22×C4C2513yes—
1011C22×C4C2511yescharacteristic
1012C22×C4C2513yes—
1013C22×C4C2511yescharacteristic
1014C22×C4C2513yes—
1015C22×C4C2513yes—
1016C22×C4C2513yes—
1017C22×C4C2513yes—
1018C22×C4C2511yescharacteristic
1019C22×C4C2513yes—
1020C22×C4C2511yescharacteristic
1021C22×C4C2511yescharacteristic
1022C22×C4C2513yes—
1023C4⋊C4—26no—
1024C4⋊C4—26no—
1025C4⋊C4—26no—
1026C4⋊C4—22no—
1027C4⋊C4—26no—
1028C4⋊C4—26no—
1029C4⋊C4—26no—
1030C4⋊C4—26no—
1031C4⋊C4—26no—
1032C4⋊C4—26no—
1033C4⋊C4—26no—
1034C4⋊C4—26no—
1035C4⋊C4—212no—
1036C4⋊C4—26no—
1037C4⋊C4—26no—
1038C4⋊C4—26no—
1039C4⋊C4—26no—
1040C4⋊C4—26no—
1041C4⋊C4—26no—
1042C4⋊C4—26no—
1043C4⋊C4—22no—
1044C4⋊C4—43no—
1045C4⋊C4—41no—
1046C4⋊C4—41no—
1047C4⋊C4—43no—
1048C4⋊C4—43no—
1049C4⋊C4—43no—
1050C4⋊C4—43no—
1051C4⋊C4—41no—
1052C4⋊C4—43no—
1053C4⋊C4—43no—
1054C4⋊C4—43no—
1055C4⋊C4—43no—
1056C4⋊C4—43no—
1057C4⋊C4—46no—
1058C4⋊C4—43no—
1059C4⋊C4—43no—
1060C4⋊C4—43no—
1061C4⋊C4—43no—
1062C4⋊C4—46no—
1063C4⋊C4—43no—
1064C4⋊C4—43no—
1065C4⋊C4—46no—
1066C4⋊C4—43no—
1067C4⋊C4—43no—
1068C4⋊C4—43no—
1069C4⋊C4—43no—
1070C22⋊C4—22no—
1071C22⋊C4—26no—
1072C22⋊C4—26no—
1073C22⋊C4—26no—
1074C22⋊C4—26no—
1075C22⋊C4—26no—
1076C22⋊C4—212no—
1077C22⋊C4—22no—
1078C22⋊C4—26no—
1079C22⋊C4—26no—
1080C22⋊C4—26no—
1081C22⋊C4—43no—
1082C22⋊C4—43no—
1083C22⋊C4—46no—
1084C22⋊C4—46no—
1085C22⋊C4—41no—
1086C22⋊C4—41no—
1087C22⋊C4—43no—
1088C22⋊C4—41no—
1089C22⋊C4—46no—
1090C22⋊C4—46no—
1091C22⋊C4—46no—
1092C22⋊C4—43no—
1093C22⋊C4—43no—
1094C22⋊C4—43no—
1095C22⋊C4—43no—
1096C22⋊C4—41no—
1097C22⋊C4—43no—
1098C22⋊C4—43no—
1099C22⋊C4—41no—
1100C22⋊C4—43no—
1101C22⋊C4—41no—
1102C22⋊C4—41no—
1103C22⋊C4—41no—
1104C22⋊C4—43no—
1105C22⋊C4—43no—
1106C22⋊C4—43no—
1107C22⋊C4—43no—
1108C22⋊C4—43no—
1109C22⋊C4—46no—
1110C22⋊C4—41no—
1111C22⋊C4—43no—
1112C22⋊C4—43no—
1113C22⋊C4—46no—
1114C22⋊C4—46no—
1115C22⋊C4—43no—
1116C22⋊C4—43no—
1117C22⋊C4—43no—
1118C22⋊C4—46no—
1119C22⋊C4—43no—
1120C22⋊C4—43no—
1121C22⋊C4—43no—
1122C22⋊C4—43no—
1123C22⋊C4—43no—
1124C42—26no—
1125C42—26no—
1126C42—212no—
1127C42—26no—
1128C42—26no—
1129C42—26no—
1130C42—26no—
1131C42—26no—
1132C42—26no—
1133C42—26no—
1134C42—26no—
1135C42—26no—
1136C42—22no—
1137C42—43no—
1138C42—43no—
1139C42—43no—
1140C42—41no—
1141C42—46no—
1142C42—46no—
1143C42—43no—
1144C42—46no—
1145C42—43no—
1146C42—43no—
1147C23—21no—
1148C23—23no—
1149C23—21no—
1150C23—23no—
1151C23—23no—
1152C23—21no—
1153C23—21no—
1154C23—23no—
1155C23—23no—
1156C23—23no—
1157C23—21no—
1158C23—21no—
1159C23—21no—
1160C23—21no—
1161C23—23no—
1162C23—23no—
1163C23—21no—
1164C23—23no—
1165C23—23no—
1166C23—21no—
1167C23—23no—
1168C23—21no—
1169C23—21no—
1170C23—23no—
1171C23—23no—
1172C23—21no—
1173C23—412no—
1174C23—412no—
1175C23—86no—
1176C23—86no—
1177C23—86no—
1178C23—86no—
1179C23—86no—
1180C23C22×#4112yes—
1181C23C22×#4116yes—
1182C23C2611yescharacteristic
1183Q8—224no—
1184Q8—44no—
1185Q8—412no—
1186Q8—166no—
1187Q8#551116yes—
1188D4—224no—
1189D4—44no—
1190D4—424no—
1191D4—412no—
1192D4—86no—
1193D4—86no—
1194C2×C4—21no—
1195C2×C4—21no—
1196C2×C4—23no—
1197C2×C4—23no—
1198C2×C4—21no—
1199C2×C4—21no—
1200C2×C4—224no—
1201C2×C4—224no—
1202C2×C4—21no—
1203C2×C4—21no—
1204C2×C4—21no—
1205C2×C4—21no—
1206C2×C4—23no—
1207C2×C4—23no—
1208C2×C4—21no—
1209C2×C4—23no—
1210C2×C4—23no—
1211C2×C4—23no—
1212C2×C4—23no—
1213C2×C4—23no—
1214C2×C4—23no—
1215C2×C4—21no—
1216C2×C4—21no—
1217C2×C4—21no—
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—21no—
1229C2×C4—21no—
1230C2×C4—21no—
1231C2×C4—21no—
1232C2×C4—23no—
1233C2×C4—23no—
1234C2×C4—23no—
1235C2×C4—23no—
1236C2×C4—21no—
1237C2×C4—23no—
1238C2×C4—23no—
1239C2×C4—23no—
1240C2×C4—23no—
1241C2×C4—21no—
1242C2×C4—21no—
1243C2×C4—23no—
1244C2×C4—23no—
1245C2×C4—23no—
1246C2×C4—23no—
1247C2×C4—23no—
1248C2×C4—21no—
1249C2×C4—23no—
1250C2×C4—21no—
1251C2×C4—21no—
1252C2×C4—21no—
1253C2×C4—21no—
1254C2×C4—23no—
1255C2×C4—23no—
1256C2×C4—23no—
1257C2×C4—23no—
1258C2×C4—23no—
1259C2×C4—21no—
1260C2×C4—23no—
1261C2×C4—23no—
1262C2×C4—21no—
1263C2×C4—21no—
1264C2×C4—21no—
1265C2×C4—21no—
1266C2×C4—21no—
1267C2×C4—21no—
1268C2×C4—23no—
1269C2×C4—21no—
1270C2×C4—21no—
1271C2×C4—412no—
1272C2×C4—44no—
1273C2×C4—412no—
1274C2×C4—412no—
1275C2×C4—412no—
1276C2×C4—812no—
1277C2×C4—166no—
1278C2×C4C22×#4116yes—
1279C2×C4C22×#4112yes—
1280C2×C4C22×#4116yes—
1281C2×C4C22×#4116yes—
1282C2×C4C2×H(5,𝔽2)16yes—
1283C2×C4#58512yes—
1284C22—22no—
1285C22—26no—
1286C22—22no—
1287C22—26no—
1288C22—22no—
1289C22—26no—
1290C22—43no—
1291C22—41no—
1292C22—43no—
1293C22—41no—
1294C22—43no—
1295C22—41no—
1296C22—43no—
1297C22—41no—
1298C22—41no—
1299C22—43no—
1300C22—41no—
1301C22—43no—
1302C22—41no—
1303C22—43no—
1304C22—41no—
1305C22—43no—
1306C22—41no—
1307C22—43no—
1308C22—41no—
1309C22—43no—
1310C22—41no—
1311C22—43no—
1312C22—824no—
1313C22C23×#4111yescharacteristic
1314C22C23×#4111yescharacteristic
1315C22C22×H(5,𝔽2)11yescharacteristic
1316C22C2×#58511yescharacteristic
1317C22H(7,𝔽2)11yescharacteristic
1318C222−1+611yescharacteristic
1319C222−1+611yescharacteristic
1320C4—22no—
1321C4—22no—
1322C4—26no—
1323C4—41no—
1324C4—43no—
1325C4—41no—
1326C4—41no—
1327C4—43no—
1328C4—41no—
1329C4—43no—
1330C4—41no—
1331C4—41no—
1332C4—41no—
1333C4—43no—
1334C4—41no—
1335C4—43no—
1336C4—41no—
1337C4—43no—
1338C4—43no—
1339C4—41no—
1340C4—43no—
1341C4—43no—
1342C4—43no—
1343C4—43no—
1344C4—41no—
1345C4—43no—
1346C4C2×#551112yes—
1347C2—46no—
1348C2—42no—
1349C2—81no—
1350C2—83no—
1351C2C22×#55111yescharacteristic
1352C2#6285111yescharacteristic
1353C2#6285711yescharacteristic
1354C2#6292311yescharacteristic
1355C2#6300511yescharacteristic
1356C2#6300911yescharacteristic
1357C2#6304411yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#36428C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59486C2semidirect
2. #59479C2semidirect
3. #59204C2semidirect
4. #52178C2semidirect
5. #45401C2semidirect
6. #45391C2semidirect
7. #45365C2semidirect
8. #45259C2semidirect
9. #45087C2semidirect
10. #44903C2semidirect
11. #39070C2semidirect
12. #39065C2semidirect
13. #38206C2semidirect
14. #38201C2semidirect
15. #37859C2semidirect
16. #37853C2semidirect
17. #36585C2semidirect
18. #36458C2semidirect
20. #35983C2semidirect
21. #35948C2semidirect
22. #35801C2semidirect
23. #35748C2semidirect
24. #35723C2semidirect
25. #35711C2semidirect
26. #34312C2semidirect
27. #34311C2semidirect
28. #34263C2semidirect
29. #34262C2semidirect
30. #34175C2semidirect
31. #34174C2semidirect
33. C2×Q82C22semidirect
41. C2×#519C22semidirect
42. #2860C22semidirect
43. #2860C22semidirect
45. #2757C22semidirect
46. #2753C22semidirect
47. #2752C22semidirect
48. #2751C22semidirect
49. #2747C22semidirect
51. #2742C22semidirect
52. #2742C22semidirect
53. #2741C22semidirect
54. #2741C22semidirect
56. #2740C22semidirect
57. #2740C22semidirect
59. #2739C22semidirect
61. #2738C22semidirect
63. #2737C22semidirect
64. #2737C22semidirect
69. #2730C22semidirect
70. #2723C22semidirect
71. #2722C22semidirect
74. #2640C22semidirect
76. #2628C22semidirect
78. #2625C22semidirect
79. #2624C22semidirect
80. #2610C22semidirect
81. #2597C22semidirect
82. #2595C22semidirect
83. #2592C22semidirect
84. #2581C22semidirect
85. #2580C22semidirect
86. #2577C22semidirect
87. #2575C22semidirect
88. #2574C22semidirect
89. #2568C22semidirect
91. #2560C22semidirect
92. #2560C22semidirect
93. #2547C22semidirect
94. #2542C22semidirect
95. #2530C22semidirect
96. #2527C22semidirect
97. #2526C22semidirect
98. #2521C22semidirect
99. #2516C22semidirect
100. #2513C22semidirect
101. #2513C22semidirect
102. #2513C22semidirect
103. #2513C22semidirect
104. #2512C22semidirect
105. #2512C22semidirect
106. #2510C22semidirect
107. #2503C22semidirect
108. #2500C22semidirect
110. #2497C22semidirect
111. #2496C22semidirect
112. #2495C22semidirect
113. #2494C22semidirect
114. #2494C22semidirect
115. #2494C22semidirect
116. #2493C22semidirect
117. #2492C22semidirect
118. #2492C22semidirect
119. #2491C22semidirect
120. #2491C22semidirect
121. #2487C22semidirect
123. #2485C22semidirect
126. #2479C22semidirect
128. #2452C22semidirect
129. #2452C22semidirect
130. #2451C22semidirect
131. #2451C22semidirect
132. #2448C22semidirect
133. #2448C22semidirect
134. #2447C22semidirect
135. #2447C22semidirect
136. #2446C22semidirect
137. #2446C22semidirect
138. #2440C22semidirect
139. #2440C22semidirect
142. #2438C22semidirect
146. #2423C22semidirect
147. #2423C22semidirect
148. #2421C22semidirect
149. #2421C22semidirect
150. #2420C22semidirect
151. #2420C22semidirect
155. #2398C22semidirect
157. #2396C22semidirect
159. #2395C22semidirect
160. #2395C22semidirect
161. #2368C22semidirect
162. #2367C22semidirect
163. #2365C22semidirect
164. #2363C22semidirect
166. #2362C22semidirect
167. #2360C22semidirect
168. #2357C22semidirect
169. #2356C22semidirect
170. #2355C22semidirect
172. #2354C22semidirect
173. #2352C22semidirect
174. #2351C22semidirect
175. #2351C22semidirect
176. #2351C22semidirect
177. #2351C22semidirect
178. #2351C22semidirect
179. Q8×C4⋊C4C22semidirect
180. Q8×C4⋊C4C22semidirect
181. Q8×C4⋊C4C22semidirect
184. #2345C22semidirect
185. #2344C22semidirect
201. Q8×C22⋊C4C22semidirect
202. Q8×C22⋊C4C22semidirect
203. Q8×C22⋊C4C22semidirect
208. #2324C22semidirect
210. #2323C22semidirect
211. #2323C22semidirect
212. #2320C22semidirect
213. #2319C22semidirect
215. #2314C22semidirect
220. C4×C4⋊Q8C22semidirect
221. C4×#126C22semidirect
222. C4×#126C22semidirect
223. C4×#124C22semidirect
226. #2298C22semidirect
227. #2295C22semidirect
229. #2293C22semidirect
230. #2293C22semidirect
235. #2276C22semidirect
236. C42×Q8C22semidirect
237. C42×Q8C22semidirect

Maximal subgroups

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

subgroupindex
#594862
#594792
#592042
#521782
#454012
#453912
#453652
#452592
#450872
#449032
#390702
#390652
#382062
#382012
#378592
#378532
#365852
#364582
#364282
#359832
#359482
#358012
#357482
#357232
#357112
#343122
#343112
#342632
#342622
#341752
#341742