Finite Group Databasebeta

← #8115438

Subgroups — #8115438

Order 512.

4314 conjugacy classes of subgroups.

The subgroup lattice has 1372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#58940C214yesmaximal, complemented
2#58938C214yesmaximal, complemented
3#58202C214yesmaximal, complemented
4#57671C214yesmaximal, complemented
5#56799C214yesmaximal, complemented
6#55746C214yesmaximal, complemented
7#54688C214yesmaximal, complemented
8#54191C214yesmaximal, complemented
9#53127C212yesmaximal, complemented
10#52998C212yesmaximal, complemented
11#45116C212yesmaximal, complemented
12#44901C212yesmaximal, complemented
13#42982C211yesmaximal, characteristic
14#42937C211yesmaximal, characteristic, complemented
15#42818C211yesmaximal, characteristic, complemented
16#42737C212yesmaximal, complemented
17#42574C212yesmaximal, complemented
18#42487C211yesmaximal, characteristic, complemented
19#39801C212yesmaximal, complemented
20#39424C212yesmaximal, complemented
21#37696C212yesmaximal, complemented
22#37690C212yesmaximal, complemented
23#37423C212yesmaximal, complemented
24#37327C212yesmaximal, complemented
25#35338C211yesmaximal, characteristic, complemented
26#35283C211yesmaximal, characteristic, complemented
27#34640C211yesmaximal, characteristic, complemented
28C2×#544C2212yescomplemented
29C2×#542C2212yes—
30C2×#533C2211yescharacteristic
31C22×#124C2211yescharacteristic
32#2868C2211yescharacteristic, complemented
33#2862C2211yescharacteristic, complemented
34#2861C2212yes—
35#2861C2212yes—
36#2857C2212yes—
37#2841C2212yes—
38#2840C2212yes—
39#2838C2214yescomplemented
40#2836C2214yescomplemented
41#2836C2214yescomplemented
42#2835C2214yescomplemented
43#2832C2212yescomplemented
44#2832C2214yescomplemented
45#2831C2214yescomplemented
46#2831C2214yescomplemented
47#2830C2212yes—
48#2830C2214yescomplemented
49#2827C2214yescomplemented
50#2816C2214yescomplemented
51#2809C2212yescomplemented
52#2806C2214yescomplemented
53#2804C2212yes—
54#2799C2214yescomplemented
55#2799C2212yescomplemented
56#2797C2214yes—
57#2795C2214yescomplemented
58#2793C2214yescomplemented
59#2790C2214yescomplemented
60#2788C2214yescomplemented
61#2788C2214yescomplemented
62#2787C2214yescomplemented
63#2784C2212yes—
64#2777C2214yescomplemented
65#2771C2212yes—
66#2771C2214yescomplemented
67#2759C2214yescomplemented
68#2759C2214yescomplemented
69#2759C2214yescomplemented
70#2758C2214yescomplemented
71#2757C2214yescomplemented
72#2752C2212yes—
73#2751C2214yes—
74#2751C2214yescomplemented
75#2747C2214yescomplemented
76#2743C2214yes—
77#2739C2214yes—
78#2737C2214yescomplemented
79#2735C2214yes—
80#2735C2212yes—
81#2731C2214yescomplemented
82#2731C2214yescomplemented
83#2729C2214yescomplemented
84#2729C2214yescomplemented
85#2728C2214yescomplemented
86#2725C2214yescomplemented
87#2718C2214yescomplemented
88#2716C2214yescomplemented
89#2716C2214yescomplemented
90#2716C2214yescomplemented
91#2716C2214yescomplemented
92#2716C2214yescomplemented
93#2715C2214yes—
94#2715C2214yescomplemented
95#2712C2214yes—
96#2710C2214yes—
97#2705C2214yes—
98#2704C2214yes—
99#2701C2214yescomplemented
100#2700C2214yes—
101#2700C2214yescomplemented
102#2700C2214yescomplemented
103#2692C2214yes—
104#2692C2214yes—
105#2692C2214yescomplemented
106#2690C2214yescomplemented
107#2690C2214yescomplemented
108#2689C2214yescomplemented
109#2687C2214yescomplemented
110#2687C2214yescomplemented
111#2687C2214yescomplemented
112#2685C2214yes—
113#2684C2214yes—
114#2683C2214yes—
115#2681C2214yescomplemented
116#2677C2214yes—
117#2674C2214yescomplemented
118#2668C2212yes—
119#2667C2214yes—
120#2665C2214yescomplemented
121#2660C2212yescomplemented
122#2655C2212yescomplemented
123#2654C2212yescomplemented
124#2653C2212yes—
125#2653C2214yescomplemented
126#2652C2212yes—
127#2651C2212yescomplemented
128#2650C2212yescomplemented
129#2650C2214yescomplemented
130#2649C2212yes—
131#2648C2214yes—
132#2648C2212yes—
133#2647C2212yescomplemented
134#2640C2212yes—
135#2640C2212yes—
136#2640C2212yes—
137#2640C2214yescomplemented
138#2629C2212yescomplemented
139#2628C2211yescharacteristic
140#2628C2211yescharacteristic
141#2626C2214yes—
142#2625C2214yescomplemented
143#2620C2212yes—
144#2607C2212yes—
145#2607C2214yescomplemented
146#2604C2214yescomplemented
147#2601C2214yes—
148#2599C2214yescomplemented
149#2595C2214yes—
150#2592C2214yes—
151#2592C2214yes—
152#2586C2212yescomplemented
153#2582C2212yescomplemented
154#2580C2212yes—
155#2572C2214yes—
156#2568C2212yescomplemented
157#2566C2212yes—
158#2565C2212yescomplemented
159#2563C2212yes—
160#2561C2214yes—
161#2561C2214yes—
162#2560C2214yescomplemented
163#2558C2214yescomplemented
164#2555C2212yes—
165#2551C2212yescomplemented
166#2550C2212yescomplemented
167#2532C2214yescomplemented
168#2530C2214yescomplemented
169#2527C2214yes—
170#2527C2214yescomplemented
171#2514C2212yescomplemented
172#2513C2212yes—
173#2512C2212yes—
174#2512C2212yes—
175#2511C2212yescomplemented
176#2511C2212yescomplemented
177#2511C2214yescomplemented
178#2504C2212yes—
179#2503C2212yescomplemented
180#2500C2212yes—
181#2499C2212yescomplemented
182#2492C2214yes—
183#2492C2212yescomplemented
184#2492C2212yescomplemented
185#2491C2212yes—
186#2490C2212yes—
187#2480C2214yes—
188#2480C2214yes—
189#2478C2214yescomplemented
190#2477C2214yescomplemented
191#2472C2214yes—
192#2465C2214yescomplemented
193#2462C2214yescomplemented
194#2453C2212yescomplemented
195#2452C2212yes—
196#2452C2212yes—
197#2451C2214yescomplemented
198#2451C2214yescomplemented
199#2451C2212yescomplemented
200#2448C2212yes—
201#2447C2212yes—
202#2441C2212yes—
203#2440C2212yescomplemented
204#2439C2212yes—
205#2439C2212yescomplemented
206#2437C2214yes—
207#2437C2212yes—
208#2429C2214yescomplemented
209#2429C2214yescomplemented
210#2427C2212yes—
211#2426C2212yes—
212#2426C2214yescomplemented
213#2423C2214yes—
214#2423C2212yescomplemented
215#2422C2212yes—
216#2416C2212yes—
217#2415C2212yescomplemented
218#2412C2214yes—
219#2411C2214yes—
220#2409C2212yes—
221#2408C2212yes—
222#2402C2211yescharacteristic, complemented
223#2401C2212yescomplemented
224#2398C2211yescharacteristic, complemented
225#2396C2211yescharacteristic
226#2395C2212yes—
227#2392C2211yescharacteristic
228#2363C2212yes—
229#2360C2212yescomplemented
230#2356C2212yescomplemented
231#2354C2212yes—
232#2354C2212yes—
233#2352C2212yes—
234Q8×C22⋊C4C2212yes—
235D4×C22⋊C4C2212yes—
236#2331C2211yescharacteristic, complemented
237#2331C2211yescharacteristic, complemented
238#2330C2212yescomplemented
239#2326C2212yes—
240#2314C2212yes—
241#2310C2211yescharacteristic
242#2310C2211yescharacteristic
243#2309C2211yescharacteristic
244#2309C2211yescharacteristic
245C4×C4⋊Q8C2212yescomplemented
246#2298C2212yescomplemented
247#2295C2211yescharacteristic, complemented
248#2293C2211yescharacteristic, complemented
249#2290C2212yes—
250C4×#117C2211yescharacteristic
251C23×Q8C2311yescharacteristic
252C23×D4C2311yescharacteristic
253#544—48no—
254#542—48no—
255#533—44no—
256C2×C4⋊Q8C2312yes—
257C2×C4⋊Q8C2312yes—
258C2×C4⋊Q8C2311yescharacteristic
259C2×C4⋊Q8C2311yescharacteristic
260C2×C4⋊Q8C2312yes—
261C2×C4⋊Q8C2314yes—
262C2×C4⋊Q8C2314yes—
263C2×C4⋊Q8C2314yes—
264C2×#126C2314yes—
265C2×#126C2314yes—
266C2×#126C2314yes—
267C2×#125C2312yes—
268C2×#125C2312yes—
269C2×#125C2314yes—
270C2×#124—44no—
271C2×#124C2312yes—
272C2×#124C2314yes—
273C2×#124C2312yes—
274C2×#124C2314yes—
275C2×#124C2314yes—
276C2×#123C2314yes—
277C2×#123C2314yes—
278C2×C22⋊Q8C2314yes—
279C2×C22⋊Q8C2314yes—
280C2×C22⋊Q8C2312yes—
281C2×C22⋊Q8C2312yes—
282C2×C22⋊Q8C2314yes—
283C2×C22⋊Q8C2314yes—
284C2×C22⋊Q8C2314yes—
285C2×C22⋊Q8C2314yes—
286C2×C22⋊Q8C2314yes—
287C2×C22⋊Q8C2314yes—
288C2×#121C2312yes—
289C2×#121C2312yes—
290C2×#121C2314yes—
291C2×#120C2314yes—
292C2×C4×Q8C2312yes—
293C2×C4×Q8C2311yescharacteristic
294C2×C4×Q8C2312yes—
295C2×C4×Q8C2314yes—
296C2×C4×Q8C2314yes—
297C2×C4×D4C2312yes—
298C2×C4×D4C2312yes—
299C2×C4×D4C2312yes—
300C2×C4×D4C2311yescharacteristic
301C2×#117C2311yescharacteristic
302C2×#117C2312yes—
303C2×#117C2311yescharacteristic
304C2×#117C2311yescharacteristic
305C2×#117C2311yescharacteristic
306C2×#117C2312yes—
307C2×#117C2314yes—
308C22×C4⋊C4C2312yes—
309C22×C22⋊C4C2314yes—
310C22×C22⋊C4C2314yes—
311C22×C42C2311yescharacteristic
312#401C2314yes—
313#401C2312yes—
314#400C2314yes—
315#400C2314yes—
316#400C2314yes—
317#400C2314yes—
318#400C2314yes—
319#400C2312yes—
320#400C2314yes—
321#400C2314yes—
322#400C2314yes—
323#400C2314yes—
324#400C2312yes—
325#400C2314yes—
326#400C2314yes—
327#400C2312yes—
328#400C2312yes—
329#400C2314yes—
330#400C2312yes—
331#400C2312yes—
332#400C2314yes—
333#400C2312yes—
334#400C2312yes—
335#400C2311yescharacteristic
336#400C2312yes—
337#400C2314yes—
338#399C2314yes—
339#399C2314yes—
340#399C2314yes—
341#399C2311yescharacteristic
342#399C2314yes—
343#399C2312yes—
344#399C2312yes—
345#399C2312yes—
346#398C2314yes—
347#398C2314yes—
348#398C2314yes—
349#398C2314yes—
350#398C2314yes—
351#398C2314yes—
352#398C2314yes—
353#398C2311yescharacteristic
354#398C2314yes—
355#398C2312yes—
356#398C2314yes—
357#398C2314yes—
358#398C2314yes—
359#398C2312yes—
360#398C2314yes—
361#398C2312yes—
362#398C2314yes—
363#398C2312yes—
364#398C2314yes—
365#398C2314yes—
366#397C2314yes—
367#397C2314yes—
368#397C2314yes—
369#397C2314yes—
370#397C2314yes—
371#397C2312yes—
372#397C2314yes—
373#397C2314yes—
374#397C2312yes—
375#397C2314yes—
376#397C2314yes—
377#397C2314yes—
378#397C2314yes—
379#397C2314yes—
380#397C2314yes—
381#397C2314yes—
382#397C2314yes—
383#397C2314yes—
384#397C2314yes—
385#397C2314yes—
386#397C2314yes—
387#397C2314yes—
388#397C2312yes—
389#397C2314yes—
390#397C2311yescharacteristic
391#397C2312yes—
392#397C2312yes—
393#397C2312yes—
394#397C2312yes—
395#396C2314yes—
396#396C2314yes—
397#396C2314yes—
398#396C2314yes—
399#396C2314yes—
400#396C2314yes—
401#396C2314yes—
402#396C2314yes—
403#396C2314yes—
404#396C2314yes—
405#396C2314yes—
406#396C2314yes—
407#396C2312yes—
408#396C2314yes—
409#396C2314yes—
410#396C2314yes—
411#396C2312yes—
412#396C2312yes—
413#395C2312yes—
414#395C2314yes—
415#395C2314yes—
416#395C2314yes—
417#395C2312yes—
418#395C2314yes—
419#395C2314yes—
420#395C2314yes—
421#395C2314yes—
422#395C2314yes—
423#395C2311yescharacteristic
424#394C2314yes—
425#394C2312yes—
426#394C2314yes—
427#394C2314yes—
428#394C2314yes—
429#394C2314yes—
430#394C2314yes—
431#394C2314yes—
432#394C2312yes—
433#394C2314yes—
434#394C2314yes—
435#394C2311yescharacteristic
436#394C2314yes—
437#394C2314yes—
438#394C2312yes—
439#394C2312yes—
440#394C2314yes—
441#393C2314yes—
442#393C2314yes—
443#393C2314yes—
444#393C2314yes—
445#393C2314yes—
446#393C2314yes—
447#393C2314yes—
448#393C2314yes—
449#393C2314yes—
450#393C2314yes—
451#393C2314yes—
452#393C2312yes—
453#393C2314yes—
454#393C2314yes—
455#393C2314yes—
456#393C2311yescharacteristic
457#393C2312yes—
458#393C2314yes—
459#393C2312yes—
460#393C2314yes—
461#393C2314yes—
462#392C2311yescharacteristic
463#392C2314yes—
464#391C2314yes—
465#391C2314yes—
466#391C2312yes—
467#391C2312yes—
468#391C2312yes—
469#391C2312yes—
470#391C2312yes—
471#391C2314yes—
472#391C2312yes—
473#391C2312yes—
474#391C2314yes—
475#391C2314yes—
476#391C2312yes—
477#391C2314yes—
478#391C2314yes—
479#391C2312yes—
480#391C2314yes—
481#391C2314yes—
482#391C2314yes—
483#391C2314yes—
484#391C2312yes—
485#391C2314yes—
486#391C2314yes—
487#391C2314yes—
488#391C2314yes—
489#391C2314yes—
490#391C2314yes—
491#391C2312yes—
492#391C2314yes—
493#390C2314yes—
494#390C2312yes—
495#390C2312yes—
496#390C2312yes—
497#390C2312yes—
498#390C2312yes—
499#390C2314yes—
500#390C2312yes—
501#390C2312yes—
502#390C2312yes—
503#390C2312yes—
504#390C2312yes—
505#390C2314yes—
506#390C2314yes—
507#390C2312yes—
508#390C2314yes—
509#389C2312yes—
510#389C2312yes—
511#389C2314yes—
512#389C2312yes—
513#389C2314yes—
514#389C2314yes—
515#389C2312yes—
516#389C2314yes—
517#389C2314yes—
518#389C2314yes—
519#389C2314yes—
520#389C2312yes—
521#389C2312yes—
522#389C2314yes—
523#389C2314yes—
524#389C2312yes—
525#389C2312yes—
526#389C2314yes—
527#389C2312yes—
528#389C2312yes—
529#389C2314yes—
530#388C2312yes—
531#388C2314yes—
532#388C2314yes—
533#388C2314yes—
534#388C2314yes—
535#388C2314yes—
536#388C2314yes—
537#388C2314yes—
538#388C2314yes—
539#388C2314yes—
540#388C2314yes—
541#388C2314yes—
542#388C2314yes—
543#388C2314yes—
544#388C2314yes—
545#388C2314yes—
546#388C2314yes—
547#388C2314yes—
548#388C2314yes—
549#388C2314yes—
550#388C2314yes—
551#388C2314yes—
552#388C2314yes—
553#388C2314yes—
554#388C2314yes—
555#388C2314yes—
556#388C2314yes—
557#388C2314yes—
558#388C2312yes—
559#388C2312yes—
560#388C2314yes—
561#388C2314yes—
562#388C2312yes—
563#388C2312yes—
564#388C2312yes—
565#388C2314yes—
566#388C2314yes—
567#388C2312yes—
568#388C2312yes—
569#388C2314yes—
570#388C2314yes—
571#387C2314yes—
572#387C2314yes—
573#387C2314yes—
574#387C2314yes—
575#387C2314yes—
576#387C2314yes—
577#387C2314yes—
578#387C2314yes—
579#387C2314yes—
580#387C2314yes—
581#387C2314yes—
582#387C2314yes—
583#387C2314yes—
584#387C2314yes—
585#387C2314yes—
586#387C2314yes—
587#387C2312yes—
588#387C2312yes—
589#387C2314yes—
590#387C2314yes—
591#387C2314yes—
592#387C2312yes—
593#387C2312yes—
594#387C2312yes—
595#387C2314yes—
596#387C2314yes—
597#387C2312yes—
598#387C2312yes—
599#387C2312yes—
600#387C2314yes—
601#387C2314yes—
602#387C2314yes—
603#387C2314yes—
604#386C2314yes—
605#386C2314yes—
606#386C2314yes—
607#386C2314yes—
608#386C2314yes—
609#386C2314yes—
610#386C2314yes—
611#386C2312yes—
612#386C2312yes—
613#386C2314yes—
614#386C2314yes—
615#385C2314yes—
616#385C2314yes—
617#385C2314yes—
618#385C2314yes—
619#385C2314yes—
620#385C2314yes—
621#385C2314yes—
622#385C2314yes—
623#385C2314yes—
624#385C2314yes—
625#385C2314yes—
626#385C2312yes—
627#385C2312yes—
628#385C2314yes—
629#385C2314yes—
630#384C2312yes—
631#384C2312yes—
632#384C2312yes—
633#384C2312yes—
634#384C2314yes—
635#383C2314yes—
636#383C2314yes—
637#382C2311yescharacteristic
638#382C2312yes—
639#382C2311yescharacteristic
640#382C2312yes—
641#382C2312yes—
642#381C2314yes—
643#381C2314yes—
644#381C2312yes—
645#381C2312yes—
646#381C2314yes—
647#381C2314yes—
648#380C2314yes—
649#380C2314yes—
650#380C2312yes—
651#380C2312yes—
652#380C2314yes—
653#380C2314yes—
654#380C2312yes—
655#380C2312yes—
656#380C2314yes—
657#380C2314yes—
658#379C2312yes—
659#379C2312yes—
660#379C2314yes—
661#379C2314yes—
662#379C2314yes—
663C4×C4⋊C4C2314yes—
664C4×C4⋊C4C2312yes—
665C4×C4⋊C4C2312yes—
666C4×C4⋊C4C2312yes—
667C4×C4⋊C4C2312yes—
668C4×C4⋊C4C2312yes—
669C4×C4⋊C4C2312yes—
670C4×C4⋊C4C2314yes—
671C4×C4⋊C4C2312yes—
672C4×C4⋊C4C2312yes—
673C4×C4⋊C4C2312yes—
674C4×C4⋊C4C2311yescharacteristic
675C4×C4⋊C4C2311yescharacteristic
676C4×C4⋊C4C2312yes—
677C4×C22⋊C4C2314yes—
678C4×C22⋊C4C2312yes—
679C4×C22⋊C4C2312yes—
680C4×C22⋊C4C2314yes—
681C4×C22⋊C4C2312yes—
682C4×C22⋊C4C2314yes—
683C4×C22⋊C4C2314yes—
684C4×C22⋊C4C2312yes—
685C4×C22⋊C4C2312yes—
686C4×C22⋊C4C2312yes—
687C4×C22⋊C4C2312yes—
688#376C2312yes—
689#376C2311yescharacteristic
690#376C2314yes—
691#376C2311yescharacteristic
692C43C2311yescharacteristic
693C43C2311yescharacteristic
694C25C2412yes—
695C22×Q8—24no—
696C22×Q8—42no—
697C22×Q8—42no—
698C22×Q8C2412yes—
699C22×Q8C2414yes—
700C22×Q8C2412yes—
701C22×Q8C2414yes—
702C22×Q8C2411yescharacteristic
703C22×Q8C2412yes—
704C22×Q8C2414yes—
705C22×Q8C2412yes—
706C22×D4—24no—
707C22×D4—42no—
708C22×D4—42no—
709C22×D4C2412yes—
710C22×D4C2412yes—
711C22×D4C2412yes—
712C22×D4C2411yescharacteristic
713C22×D4C2414yes—
714C22×D4C2414yes—
715C23×C4C2412yes—
716C23×C4C2411yescharacteristic
717C23×C4C2412yes—
718C23×C4C2412yes—
719C23×C4C2414yes—
720C23×C4C2414yes—
721C23×C4C2414yes—
722C4⋊Q8—28no—
723C4⋊Q8—42no—
724C4⋊Q8—42no—
725C4⋊Q8—44no—
726C4⋊Q8—44no—
727C4⋊Q8—48no—
728C4⋊Q8—84no—
729C4⋊Q8—84no—
730#126—48no—
731#126—84no—
732#126—84no—
733#125—28no—
734#125—44no—
735#125—48no—
736#124—28no—
737#124—48no—
738#124—44no—
739#124—48no—
740#124—84no—
741#123—48no—
742#123—84no—
743C22⋊Q8—48no—
744C22⋊Q8—48no—
745C22⋊Q8—48no—
746C22⋊Q8—48no—
747C22⋊Q8—44no—
748C22⋊Q8—44no—
749C22⋊Q8—84no—
750C22⋊Q8—84no—
751C22⋊Q8—84no—
752C22⋊Q8—84no—
753#121—44no—
754#121—44no—
755#121—84no—
756#120—84no—
757C4×Q8—42no—
758C4×Q8—48no—
759C4×Q8—44no—
760C4×Q8—44no—
761C4×Q8—84no—
762C4×D4—28no—
763C4×D4—44no—
764C4×D4—44no—
765C4×D4—42no—
766#117—24no—
767#117—28no—
768#117—42no—
769#117—42no—
770#117—42no—
771#117—44no—
772#117—84no—
773C2×C4⋊C4—44no—
774C2×C4⋊C4C2412yes—
775C2×C4⋊C4C2412yes—
776C2×C4⋊C4C2412yes—
777C2×C4⋊C4C2412yes—
778C2×C4⋊C4C2412yes—
779C2×C4⋊C4C2412yes—
780C2×C4⋊C4C2412yes—
781C2×C4⋊C4C2412yes—
782C2×C4⋊C4C2412yes—
783C2×C4⋊C4C2412yes—
784C2×C4⋊C4C2414yes—
785C2×C4⋊C4C2414yes—
786C2×C4⋊C4C2414yes—
787C2×C4⋊C4C2414yes—
788C2×C4⋊C4C2412yes—
789C2×C4⋊C4C2414yes—
790C2×C4⋊C4C2411yescharacteristic
791C2×C4⋊C4C2411yescharacteristic
792C2×C4⋊C4C2411yescharacteristic
793C2×C4⋊C4C2414yes—
794C2×C4⋊C4C2414yes—
795C2×C4⋊C4C2414yes—
796C2×C4⋊C4C2414yes—
797C2×C4⋊C4C2414yes—
798C2×C4⋊C4C2414yes—
799C2×C4⋊C4C2411yescharacteristic
800C2×C4⋊C4C2412yes—
801C2×C4⋊C4C2414yes—
802C2×C4⋊C4C2412yes—
803C2×C4⋊C4C2412yes—
804C2×C4⋊C4C2414yes—
805C2×C4⋊C4C2414yes—
806C2×C4⋊C4C2414yes—
807C2×C4⋊C4C2414yes—
808C2×C4⋊C4C2414yes—
809C2×C4⋊C4C2414yes—
810C2×C4⋊C4C2414yes—
811C2×C4⋊C4C2414yes—
812C2×C4⋊C4C2414yes—
813C2×C4⋊C4C2414yes—
814C2×C4⋊C4C2414yes—
815C2×C4⋊C4C2412yes—
816C2×C4⋊C4C2412yes—
817C2×C4⋊C4C2414yes—
818C2×C4⋊C4C2414yes—
819C2×C4⋊C4C2414yes—
820C2×C4⋊C4C2412yes—
821C2×C4⋊C4C2412yes—
822C2×C4⋊C4C2412yes—
823C2×C4⋊C4C2412yes—
824C2×C4⋊C4C2414yes—
825C2×C4⋊C4C2412yes—
826C2×C4⋊C4C2412yes—
827C2×C4⋊C4C2412yes—
828C2×C4⋊C4C2414yes—
829C2×C22⋊C4—48no—
830C2×C22⋊C4—84no—
831C2×C22⋊C4C2414yes—
832C2×C22⋊C4C2414yes—
833C2×C22⋊C4C2412yes—
834C2×C22⋊C4C2412yes—
835C2×C22⋊C4C2412yes—
836C2×C22⋊C4C2412yes—
837C2×C22⋊C4C2412yes—
838C2×C22⋊C4C2412yes—
839C2×C22⋊C4C2414yes—
840C2×C22⋊C4C2414yes—
841C2×C22⋊C4C2414yes—
842C2×C22⋊C4C2414yes—
843C2×C22⋊C4C2414yes—
844C2×C22⋊C4C2414yes—
845C2×C22⋊C4C2412yes—
846C2×C22⋊C4C2412yes—
847C2×C22⋊C4C2414yes—
848C2×C22⋊C4C2414yes—
849C2×C22⋊C4C2411yescharacteristic
850C2×C22⋊C4C2411yescharacteristic
851C2×C22⋊C4C2414yes—
852C2×C22⋊C4C2414yes—
853C2×C22⋊C4C2412yes—
854C2×C22⋊C4C2414yes—
855C2×C22⋊C4C2414yes—
856C2×C22⋊C4C2414yes—
857C2×C22⋊C4C2414yes—
858C2×C22⋊C4C2414yes—
859C2×C22⋊C4C2414yes—
860C2×C22⋊C4C2412yes—
861C2×C22⋊C4C2414yes—
862C2×C22⋊C4C2414yes—
863C2×C22⋊C4C2414yes—
864C2×C22⋊C4C2414yes—
865C2×C22⋊C4C2414yes—
866C2×C22⋊C4C2412yes—
867C2×C22⋊C4C2414yes—
868C2×C22⋊C4C2412yes—
869C2×C22⋊C4C2414yes—
870C2×C22⋊C4C2412yes—
871C2×C22⋊C4C2412yes—
872C2×C22⋊C4C2414yes—
873C2×C22⋊C4C2412yes—
874C2×C22⋊C4C2412yes—
875C2×C22⋊C4C2412yes—
876C2×C22⋊C4C2412yes—
877C2×C22⋊C4C2414yes—
878C2×C22⋊C4C2414yes—
879C2×C22⋊C4C2414yes—
880C2×C22⋊C4C2414yes—
881C2×C22⋊C4C2414yes—
882C2×C42—24no—
883C2×C42C2412yes—
884C2×C42C2411yescharacteristic
885C2×C42C2411yescharacteristic
886C2×C42C2411yescharacteristic
887C2×C42C2411yescharacteristic
888C2×C42C2412yes—
889C2×C42C2412yes—
890C2×C42C2412yes—
891C2×C42C2411yescharacteristic
892C2×C42C2412yes—
893C2×C42C2412yes—
894C2×C42C2414yes—
895C2×C42C2414yes—
896C2×C42C2414yes—
897C2×C42C2412yes—
898C2×C42C2414yes—
899C2×C42C2414yes—
900C2×C42C2414yes—
901C2×C42C2414yes—
902C2×C42C2412yes—
903C2×C42C2412yes—
904C2×C42C2412yes—
905C2×C42C2411yescharacteristic
906#95C2412yes—
907#95C2412yes—
908#95C2412yes—
909#95C2412yes—
910#95C2412yes—
911#95C2414yes—
912#95C2414yes—
913#95C2412yes—
914#95C2412yes—
915#95C2414yes—
916#95C2412yes—
917#95C2412yes—
918#95C2412yes—
919#95C2412yes—
920#95C2414yes—
921#95C2414yes—
922#95C2414yes—
923#95C2414yes—
924#95C2412yes—
925#95C2412yes—
926#95C2414yes—
927#95C2412yes—
928#95C2412yes—
929#95C2414yes—
930#95C2412yes—
931#95C2412yes—
932#95C2412yes—
933#95C2412yes—
934#95C2414yes—
935#95C2414yes—
936#95C2414yes—
937#95C2414yes—
938#95C2414yes—
939#95C2412yes—
940#95C2412yes—
941#95C2414yes—
942#95C2414yes—
943#95C2411yescharacteristic
944#95C2412yes—
945#95C2412yes—
946#95C2412yes—
947#95C2414yes—
948#95C2412yes—
949#95C2414yes—
950#95C2411yescharacteristic
951#95C2411yescharacteristic
952#95C2412yes—
953#95C2411yescharacteristic
954#95C2414yes—
955#95C2412yes—
956#95C2412yes—
957#95C2414yes—
958#95C2414yes—
959#95C2414yes—
960#95C2414yes—
961#95C2414yes—
962#95C2414yes—
963#95C2414yes—
964#95C2414yes—
965#95C2414yes—
966#95C2414yes—
967#95C2414yes—
968#95C2414yes—
969#95C2414yes—
970#95C2414yes—
971#95C2414yes—
972#95C2412yes—
973#95C2412yes—
974#95C2414yes—
975#95C2414yes—
976#95C2414yes—
977#95C2414yes—
978C24—24no—
979C24—42no—
980C24—44no—
981C24—44no—
982C24—42no—
983C24C2514yes—
984C24C2512yes—
985C24C2511yescharacteristic
986C2×Q8—24no—
987C2×Q8—28no—
988C2×Q8—24no—
989C2×Q8—24no—
990C2×Q8—24no—
991C2×Q8—44no—
992C2×Q8—41no—
993C2×Q8—44no—
994C2×Q8—44no—
995C2×Q8—42no—
996C2×Q8—42no—
997C2×Q8—44no—
998C2×Q8—42no—
999C2×Q8—44no—
1000C2×Q8—44no—
1001C2×Q8—44no—
1002C2×Q8—44no—
1003C2×Q8—44no—
1004C2×Q8—42no—
1005C2×Q8—42no—
1006C2×Q8—44no—
1007C2×Q8—88no—
1008C2×D4—24no—
1009C2×D4—24no—
1010C2×D4—24no—
1011C2×D4—24no—
1012C2×D4—24no—
1013C2×D4—41no—
1014C2×D4—42no—
1015C2×D4—42no—
1016C2×D4—42no—
1017C2×D4—42no—
1018C2×D4—42no—
1019C2×D4—44no—
1020C2×D4—44no—
1021C2×D4—44no—
1022C2×D4—44no—
1023C2×D4—44no—
1024C2×D4—44no—
1025C2×D4—88no—
1026C22×C4—22no—
1027C22×C4—22no—
1028C22×C4—24no—
1029C22×C4—24no—
1030C22×C4—24no—
1031C22×C4—24no—
1032C22×C4—24no—
1033C22×C4—42no—
1034C22×C4—44no—
1035C22×C4—44no—
1036C22×C4—44no—
1037C22×C4—42no—
1038C22×C4—42no—
1039C22×C4—42no—
1040C22×C4—44no—
1041C22×C4—44no—
1042C22×C4—44no—
1043C22×C4—44no—
1044C22×C4—44no—
1045C22×C4—44no—
1046C22×C42−1+414yes—
1047C22×C4C2512yes—
1048C22×C4C2511yescharacteristic
1049C22×C4C2512yes—
1050C22×C4C2514yes—
1051C22×C4C2512yes—
1052C22×C4C2512yes—
1053C22×C4C2512yes—
1054C22×C4C2511yescharacteristic
1055C22×C4C2511yescharacteristic
1056C22×C4C2512yes—
1057C22×C4C2512yes—
1058C22×C4C2514yes—
1059C22×C4C2514yes—
1060C22×C4C2514yes—
1061C22×C4C2512yes—
1062C22×C4C2514yes—
1063C22×C4C2514yes—
1064C22×C4C2512yes—
1065C22×C4C2512yes—
1066C22×C4C2514yes—
1067C22×C4C2511yescharacteristic
1068C22×C4C2512yes—
1069C22×C4C2511yescharacteristic
1070C22×C4C2511yescharacteristic
1071C4⋊C4—24no—
1072C4⋊C4—24no—
1073C4⋊C4—24no—
1074C4⋊C4—24no—
1075C4⋊C4—24no—
1076C4⋊C4—24no—
1077C4⋊C4—28no—
1078C4⋊C4—28no—
1079C4⋊C4—28no—
1080C4⋊C4—24no—
1081C4⋊C4—24no—
1082C4⋊C4—24no—
1083C4⋊C4—24no—
1084C4⋊C4—44no—
1085C4⋊C4—42no—
1086C4⋊C4—42no—
1087C4⋊C4—42no—
1088C4⋊C4—42no—
1089C4⋊C4—44no—
1090C4⋊C4—44no—
1091C4⋊C4—41no—
1092C4⋊C4—41no—
1093C4⋊C4—42no—
1094C4⋊C4—44no—
1095C4⋊C4—41no—
1096C4⋊C4—42no—
1097C4⋊C4—41no—
1098C4⋊C4—44no—
1099C4⋊C4—44no—
1100C4⋊C4—44no—
1101C4⋊C4—44no—
1102C4⋊C4—44no—
1103C4⋊C4—44no—
1104C4⋊C4—44no—
1105C4⋊C4—44no—
1106C4⋊C4—44no—
1107C4⋊C4—44no—
1108C4⋊C4—44no—
1109C4⋊C4—44no—
1110C4⋊C4—44no—
1111C4⋊C4—42no—
1112C4⋊C4—42no—
1113C4⋊C4—44no—
1114C4⋊C4—44no—
1115C4⋊C4—44no—
1116C4⋊C4—44no—
1117C4⋊C4—44no—
1118C4⋊C4—42no—
1119C4⋊C4—42no—
1120C4⋊C4—44no—
1121C4⋊C4—44no—
1122C4⋊C4—44no—
1123C4⋊C4—42no—
1124C4⋊C4—42no—
1125C4⋊C4—42no—
1126C22⋊C4—24no—
1127C22⋊C4—24no—
1128C22⋊C4—28no—
1129C22⋊C4—28no—
1130C22⋊C4—24no—
1131C22⋊C4—24no—
1132C22⋊C4—24no—
1133C22⋊C4—44no—
1134C22⋊C4—44no—
1135C22⋊C4—42no—
1136C22⋊C4—44no—
1137C22⋊C4—44no—
1138C22⋊C4—44no—
1139C22⋊C4—44no—
1140C22⋊C4—42no—
1141C22⋊C4—42no—
1142C22⋊C4—42no—
1143C22⋊C4—44no—
1144C22⋊C4—44no—
1145C22⋊C4—42no—
1146C22⋊C4—44no—
1147C22⋊C4—44no—
1148C22⋊C4—42no—
1149C22⋊C4—44no—
1150C22⋊C4—42no—
1151C22⋊C4—41no—
1152C22⋊C4—41no—
1153C22⋊C4—42no—
1154C22⋊C4—44no—
1155C22⋊C4—42no—
1156C22⋊C4—44no—
1157C22⋊C4—44no—
1158C22⋊C4—44no—
1159C22⋊C4—42no—
1160C22⋊C4—44no—
1161C22⋊C4—44no—
1162C22⋊C4—44no—
1163C22⋊C4—44no—
1164C22⋊C4—44no—
1165C22⋊C4—44no—
1166C22⋊C4—44no—
1167C22⋊C4—44no—
1168C22⋊C4—44no—
1169C22⋊C4—42no—
1170C22⋊C4—44no—
1171C22⋊C4—44no—
1172C22⋊C4—44no—
1173C22⋊C4—42no—
1174C22⋊C4—44no—
1175C22⋊C4—42no—
1176C22⋊C4—44no—
1177C42—24no—
1178C42—22no—
1179C42—24no—
1180C42—22no—
1181C42—22no—
1182C42—24no—
1183C42—22no—
1184C42—22no—
1185C42—24no—
1186C42—42no—
1187C42—42no—
1188C42—42no—
1189C42—42no—
1190C42—44no—
1191C42—44no—
1192C42—44no—
1193C42—44no—
1194C42—44no—
1195C42—42no—
1196C42—44no—
1197C42—44no—
1198C42—42no—
1199C42H(5,𝔽2)14yes—
1200C23—21no—
1201C23—21no—
1202C23—22no—
1203C23—22no—
1204C23—22no—
1205C23—24no—
1206C23—22no—
1207C23—24no—
1208C23—22no—
1209C23—24no—
1210C23—24no—
1211C23—22no—
1212C23—24no—
1213C23—22no—
1214C23—24no—
1215C23—22no—
1216C23—22no—
1217C23—24no—
1218C23—84no—
1219C23—88no—
1220C23—88no—
1221C23—162no—
1222C23—162no—
1223C23C2×2−1+412yes—
1224C23C2611yescharacteristic
1225Q8—48no—
1226Q8—88no—
1227Q8—84no—
1228Q8—88no—
1229Q8—82no—
1230Q8—164no—
1231Q8—162no—
1232Q8—162no—
1233D4—48no—
1234D4—84no—
1235D4—84no—
1236D4—82no—
1237D4—164no—
1238D4—164no—
1239C2×C4—21no—
1240C2×C4—21no—
1241C2×C4—22no—
1242C2×C4—22no—
1243C2×C4—28no—
1244C2×C4—22no—
1245C2×C4—22no—
1246C2×C4—22no—
1247C2×C4—24no—
1248C2×C4—22no—
1249C2×C4—24no—
1250C2×C4—24no—
1251C2×C4—24no—
1252C2×C4—24no—
1253C2×C4—22no—
1254C2×C4—22no—
1255C2×C4—22no—
1256C2×C4—22no—
1257C2×C4—22no—
1258C2×C4—24no—
1259C2×C4—22no—
1260C2×C4—21no—
1261C2×C4—21no—
1262C2×C4—21no—
1263C2×C4—21no—
1264C2×C4—22no—
1265C2×C4—24no—
1266C2×C4—24no—
1267C2×C4—22no—
1268C2×C4—24no—
1269C2×C4—22no—
1270C2×C4—22no—
1271C2×C4—22no—
1272C2×C4—24no—
1273C2×C4—22no—
1274C2×C4—24no—
1275C2×C4—24no—
1276C2×C4—22no—
1277C2×C4—22no—
1278C2×C4—24no—
1279C2×C4—24no—
1280C2×C4—24no—
1281C2×C4—24no—
1282C2×C4—22no—
1283C2×C4—22no—
1284C2×C4—24no—
1285C2×C4—22no—
1286C2×C4—22no—
1287C2×C4—22no—
1288C2×C4—22no—
1289C2×C4—22no—
1290C2×C4—22no—
1291C2×C4—22no—
1292C2×C4—22no—
1293C2×C4—22no—
1294C2×C4—24no—
1295C2×C4—22no—
1296C2×C4—24no—
1297C2×C4—22no—
1298C2×C4—22no—
1299C2×C4—22no—
1300C2×C4—24no—
1301C2×C4—22no—
1302C2×C4—24no—
1303C2×C4—48no—
1304C2×C4—84no—
1305C2×C4—84no—
1306C2×C4—88no—
1307C2×C4—164no—
1308C2×C4—164no—
1309C2×C4C2×H(5,𝔽2)14yes—
1310C2×C4C2×H(5,𝔽2)12yes—
1311C2×C4C2×2−1+412yes—
1312C2×C4C2×2−1+412yes—
1313C2×C4#58512yes—
1314C22—22no—
1315C22—24no—
1316C22—42no—
1317C22—41no—
1318C22—41no—
1319C22—42no—
1320C22—44no—
1321C22—42no—
1322C22—44no—
1323C22—42no—
1324C22—44no—
1325C22—42no—
1326C22—42no—
1327C22—44no—
1328C22—44no—
1329C22—44no—
1330C22—42no—
1331C22—42no—
1332C22—44no—
1333C22—168no—
1334C22C22×H(5,𝔽2)11yescharacteristic
1335C22C22×2−1+411yescharacteristic
1336C22C2×#58511yescharacteristic
1337C22H(7,𝔽2)12yes—
1338C222−1+612yes—
1339C4—22no—
1340C4—24no—
1341C4—42no—
1342C4—44no—
1343C4—42no—
1344C4—42no—
1345C4—44no—
1346C4—44no—
1347C4—44no—
1348C4—44no—
1349C4—42no—
1350C4—42no—
1351C4—42no—
1352C4—42no—
1353C4—42no—
1354C4—42no—
1355C4—44no—
1356C4—41no—
1357C4—44no—
1358C4—41no—
1359C4—41no—
1360C4—42no—
1361C4—41no—
1362C4#356114yes—
1363C2—42no—
1364C2—82no—
1365C2—84no—
1366C2C2×#356111yescharacteristic
1367C2#6287812yes—
1368C2#6287912yes—
1369C2#6288511yescharacteristic
1370C2#6289111yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#42982C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #58940C2semidirect
2. #58938C2semidirect
3. #58202C2semidirect
4. #57671C2semidirect
5. #56799C2semidirect
6. #55746C2semidirect
7. #54688C2semidirect
8. #54191C2semidirect
9. #53127C2semidirect
10. #52998C2semidirect
11. #45116C2semidirect
12. #44901C2semidirect
14. #42937C2semidirect
15. #42818C2semidirect
16. #42737C2semidirect
17. #42574C2semidirect
18. #42487C2semidirect
19. #39801C2semidirect
20. #39424C2semidirect
21. #37696C2semidirect
22. #37690C2semidirect
23. #37423C2semidirect
24. #37327C2semidirect
25. #35338C2semidirect
26. #35283C2semidirect
27. #34640C2semidirect
28. C2×#544C22semidirect
32. #2868C22semidirect
33. #2862C22semidirect
39. #2838C22semidirect
40. #2836C22semidirect
41. #2836C22semidirect
42. #2835C22semidirect
43. #2832C22semidirect
44. #2832C22semidirect
45. #2831C22semidirect
46. #2831C22semidirect
48. #2830C22semidirect
49. #2827C22semidirect
50. #2816C22semidirect
51. #2809C22semidirect
52. #2806C22semidirect
54. #2799C22semidirect
55. #2799C22semidirect
57. #2795C22semidirect
58. #2793C22semidirect
59. #2790C22semidirect
60. #2788C22semidirect
61. #2788C22semidirect
62. #2787C22semidirect
64. #2777C22semidirect
66. #2771C22semidirect
67. #2759C22semidirect
68. #2759C22semidirect
69. #2759C22semidirect
70. #2758C22semidirect
71. #2757C22semidirect
74. #2751C22semidirect
75. #2747C22semidirect
78. #2737C22semidirect
81. #2731C22semidirect
82. #2731C22semidirect
83. #2729C22semidirect
84. #2729C22semidirect
85. #2728C22semidirect
86. #2725C22semidirect
87. #2718C22semidirect
88. #2716C22semidirect
89. #2716C22semidirect
90. #2716C22semidirect
91. #2716C22semidirect
92. #2716C22semidirect
94. #2715C22semidirect
99. #2701C22semidirect
101. #2700C22semidirect
102. #2700C22semidirect
105. #2692C22semidirect
106. #2690C22semidirect
107. #2690C22semidirect
108. #2689C22semidirect
109. #2687C22semidirect
110. #2687C22semidirect
111. #2687C22semidirect
115. #2681C22semidirect
117. #2674C22semidirect
120. #2665C22semidirect
121. #2660C22semidirect
122. #2655C22semidirect
123. #2654C22semidirect
125. #2653C22semidirect
127. #2651C22semidirect
128. #2650C22semidirect
129. #2650C22semidirect
133. #2647C22semidirect
137. #2640C22semidirect
138. #2629C22semidirect
142. #2625C22semidirect
145. #2607C22semidirect
146. #2604C22semidirect
148. #2599C22semidirect
152. #2586C22semidirect
153. #2582C22semidirect
156. #2568C22semidirect
158. #2565C22semidirect
162. #2560C22semidirect
163. #2558C22semidirect
165. #2551C22semidirect
166. #2550C22semidirect
167. #2532C22semidirect
168. #2530C22semidirect
170. #2527C22semidirect
171. #2514C22semidirect
175. #2511C22semidirect
176. #2511C22semidirect
177. #2511C22semidirect
179. #2503C22semidirect
181. #2499C22semidirect
183. #2492C22semidirect
184. #2492C22semidirect
189. #2478C22semidirect
190. #2477C22semidirect
192. #2465C22semidirect
193. #2462C22semidirect
194. #2453C22semidirect
197. #2451C22semidirect
198. #2451C22semidirect
199. #2451C22semidirect
203. #2440C22semidirect
205. #2439C22semidirect
208. #2429C22semidirect
209. #2429C22semidirect
212. #2426C22semidirect
214. #2423C22semidirect
217. #2415C22semidirect
222. #2402C22semidirect
223. #2401C22semidirect
224. #2398C22semidirect
229. #2360C22semidirect
230. #2356C22semidirect
236. #2331C22semidirect
237. #2331C22semidirect
238. #2330C22semidirect
245. C4×C4⋊Q8C22semidirect
246. #2298C22semidirect
247. #2295C22semidirect
248. #2293C22semidirect

Maximal subgroups

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

subgroupindex
#589402
#589382
#582022
#576712
#567992
#557462
#546882
#541912
#531272
#529982
#451162
#449012
#429822
#429372
#428182
#427372
#425742
#424872
#398012
#394242
#376962
#376902
#374232
#373272
#353382
#352832
#346402