Finite Group Databasebeta

← #8751318

Subgroups — #8751318

Order 512.

4620 conjugacy classes of subgroups.

The subgroup lattice has 1482 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59198C211yesmaximal, characteristic, complemented
2#59014C212yesmaximal, complemented
3#57069C214yesmaximal, complemented
4#54138C214yesmaximal, complemented
5#54058C214yesmaximal, complemented
6#53858C212yesmaximal, complemented
7#53806C214yesmaximal, complemented
8#53127C212yesmaximal, complemented
9#52991C211yesmaximal, characteristic, complemented
10#52942C212yesmaximal, complemented
11#52606C214yesmaximal, complemented
12#46812C212yesmaximal, complemented
13#45419C212yesmaximal, complemented
14#45382C212yesmaximal, complemented
15#45115C211yesmaximal, characteristic, complemented
16#45022C212yesmaximal, complemented
17#44913C212yesmaximal, complemented
18#42984C211yesmaximal, characteristic, complemented
19#42813C212yesmaximal, complemented
20#42693C212yesmaximal, complemented
21#42512C212yesmaximal, complemented
22#42446C212yesmaximal, complemented
23#41616C212yesmaximal, complemented
24#41378C214yesmaximal, complemented
25#39723C211yesmaximal, characteristic, complemented
26#39349C212yesmaximal, complemented
27#36675C211yesmaximal, characteristic, complemented
28#35948C211yesmaximal, characteristic, complemented
29#35911C212yesmaximal, complemented
30C2×Q82C2211yescharacteristic, complemented
31C2×#552C2212yes—
32C2×#551C2212yes—
33C2×#548C2211yescharacteristic
34C2×#538C2214yes—
35C2×#537C2211yescharacteristic, complemented
36C22×C22⋊Q8C2211yescharacteristic
37#2847C2211yescharacteristic
38#2841C2212yescomplemented
39#2840C2211yescharacteristic
40#2839C2214yescomplemented
41#2839C2214yescomplemented
42#2836C2214yescomplemented
43#2835C2212yes—
44#2835C2211yescharacteristic
45#2835C2212yes—
46#2832C2214yescomplemented
47#2832C2214yescomplemented
48#2827C2214yescomplemented
49#2827C2214yescomplemented
50#2824C2212yes—
51#2824C2212yes—
52#2824C2212yes—
53#2824C2211yescharacteristic
54#2824C2212yes—
55#2821C2214yescomplemented
56#2816C2214yes—
57#2816C2212yescomplemented
58#2812C2212yes—
59#2812C2211yescharacteristic
60#2806C2214yescomplemented
61#2800C2214yescomplemented
62#2799C2212yescomplemented
63#2788C2214yescomplemented
64#2784C2214yescomplemented
65#2783C2214yescomplemented
66#2771C2212yescomplemented
67#2770C2214yescomplemented
68#2764C2214yes—
69#2764C2214yescomplemented
70#2763C2214yescomplemented
71#2757C2214yescomplemented
72#2755C2214yescomplemented
73#2755C2214yescomplemented
74#2751C2214yes—
75#2751C2214yescomplemented
76#2747C2214yescomplemented
77#2745C2214yes—
78#2745C2214yescomplemented
79#2744C2214yescomplemented
80#2740C2214yescomplemented
81#2738C2214yescomplemented
82#2737C2214yes—
83#2730C2214yes—
84#2728C2214yes—
85#2722C2212yes—
86#2722C2214yes—
87#2722C2212yes—
88#2717C2212yes—
89#2715C2214yes—
90#2713C2214yescomplemented
91#2713C2214yescomplemented
92#2711C2214yescomplemented
93#2710C2214yes—
94#2708C2214yes—
95#2706C2214yes—
96#2704C2214yescomplemented
97#2702C2214yes—
98#2701C2214yes—
99#2698C2214yes—
100#2695C2214yes—
101#2695C2214yes—
102#2693C2212yes—
103#2691C2214yes—
104#2691C2214yescomplemented
105#2690C2214yes—
106#2687C2214yes—
107#2686C2214yes—
108#2686C2214yes—
109#2686C2214yescomplemented
110#2674C2214yes—
111#2674C2214yes—
112#2671C2214yes—
113#2671C2214yes—
114#2666C2214yescomplemented
115#2660C2212yescomplemented
116#2659C2212yescomplemented
117#2655C2214yescomplemented
118#2653C2214yes—
119#2653C2214yescomplemented
120#2651C2214yescomplemented
121#2647C2212yescomplemented
122#2640C2212yescomplemented
123#2640C2211yescharacteristic, complemented
124#2638C2214yes—
125#2638C2212yes—
126#2637C2214yescomplemented
127#2630C2214yes—
128#2622C2214yes—
129#2621C2214yes—
130#2617C2212yes—
131#2616C2211yescharacteristic, complemented
132#2607C2214yescomplemented
133#2602C2214yes—
134#2599C2214yes—
135#2592C2211yescharacteristic, complemented
136#2592C2212yescomplemented
137#2591C2212yes—
138#2589C2214yescomplemented
139#2585C2214yescomplemented
140#2584C2212yescomplemented
141#2582C2212yescomplemented
142#2582C2212yescomplemented
143#2580C2212yescomplemented
144#2579C2212yes—
145#2572C2214yes—
146#2572C2212yescomplemented
147#2559C2214yescomplemented
148#2557C2214yes—
149#2553C2214yes—
150#2553C2214yes—
151#2547C2211yescharacteristic
152#2547C2212yes—
153#2547C2212yes—
154#2543C2212yes—
155#2537C2212yes—
156#2536C2212yes—
157#2536C2212yes—
158#2530C2214yescomplemented
159#2527C2214yes—
160#2523C2214yes—
161#2523C2212yes—
162#2521C2214yes—
163#2518C2214yescomplemented
164#2505C2214yescomplemented
165#2504C2211yescharacteristic
166#2503C2212yes—
167#2502C2211yescharacteristic, complemented
168#2500C2212yescomplemented
169#2497C2212yescomplemented
170#2496C2212yes—
171#2496C2212yes—
172#2496C2212yes—
173#2495C2212yescomplemented
174#2494C2212yescomplemented
175#2492C2212yescomplemented
176#2492C2214yescomplemented
177#2491C2214yes—
178#2491C2212yes—
179#2490C2212yescomplemented
180#2489C2212yes—
181#2488C2214yes—
182#2487C2211yescharacteristic
183#2486C2212yes—
184#2486C2212yes—
185#2486C2211yescharacteristic
186#2485C2214yes—
187#2483C2212yes—
188#2481C2214yes—
189#2478C2214yes—
190#2477C2214yes—
191#2476C2214yes—
192#2468C2214yes—
193#2468C2214yes—
194#2464C2214yes—
195#2459C2214yes—
196#2450C2214yes—
197#2444C2214yes—
198#2442C2214yes—
199#2442C2212yes—
200#2442C2212yescomplemented
201#2440C2212yes—
202#2440C2212yes—
203#2439C2212yescomplemented
204#2439C2212yescomplemented
205#2438C2214yes—
206#2438C2214yes—
207#2427C2212yescomplemented
208#2426C2212yes—
209#2423C2212yescomplemented
210#2423C2212yescomplemented
211#2423C2212yescomplemented
212#2422C2212yes—
213#2421C2212yes—
214#2421C2212yes—
215#2420C2214yes—
216#2419C2214yes—
217#2419C2214yes—
218#2417C2212yes—
219#2416C2212yes—
220#2416C2212yes—
221#2415C2212yes—
222#2414C2214yes—
223#2412C2214yes—
224#2409C2212yes—
225#2407C2212yes—
226#2398C2212yes—
227#2398C2212yes—
228#2398C2212yes—
229#2398C2212yes—
230#2398C2211yescharacteristic
231#2398C2212yes—
232#2395C2214yes—
233#2388C2211yescharacteristic
234#2388C2212yes—
235#2361C2212yes—
236#2360C2212yes—
237#2360C2212yescomplemented
238#2360C2212yescomplemented
239#2355C2212yescomplemented
240#2352C2212yes—
241D4×C4⋊C4C2212yes—
242D4×C4⋊C4C2212yes—
243#2345C2212yescomplemented
244#2344C2212yes—
245#2342C2214yes—
246#2341C2212yescomplemented
247Q8×C22⋊C4C2211yescharacteristic
248Q8×C22⋊C4C2212yes—
249#2339C2211yescharacteristic, complemented
250#2321C2212yes—
251#2320C2212yescomplemented
252#2320C2212yescomplemented
253#2319C2212yescomplemented
254#2311C2212yescomplemented
255C4×#120C2211yescharacteristic
256C4×#120C2212yes—
257C2×#380C2212yes—
258#2276C2211yescharacteristic, complemented
259C22×#41C2311yescharacteristic
260C22×#41C2311yescharacteristic
261C23×Q8C2311yescharacteristic
262C24×C4C2311yescharacteristic
263Q82—44no—
264#552—48no—
265#551—48no—
266#548—44no—
267#538—416no—
268#537—44no—
269C2×C4⋊Q8C2314yes—
270C2×C4⋊Q8C2312yes—
271C2×C4⋊Q8C2311yescharacteristic
272C2×C4⋊Q8C2312yes—
273C2×#126C2314yes—
274C2×#126C2314yes—
275C2×#126C2314yes—
276C2×#126C2314yes—
277C2×#125C2312yes—
278C2×#125C2314yes—
279C2×#124C2311yescharacteristic
280C2×#124C2312yes—
281C2×#124C2314yes—
282C2×#124C2314yes—
283C2×#124C2312yes—
284C2×#123C2314yes—
285C2×#123C2314yes—
286C2×#123C2312yes—
287C2×#123C2314yes—
288C2×#123C2314yes—
289C2×C22⋊Q8—44no—
290C2×C22⋊Q8C2312yes—
291C2×C22⋊Q8C2312yes—
292C2×C22⋊Q8C2314yes—
293C2×C22⋊Q8C2312yes—
294C2×C22⋊Q8C2312yes—
295C2×C22⋊Q8C2311yescharacteristic
296C2×C22⋊Q8C2314yes—
297C2×C22⋊Q8C2312yes—
298C2×C22⋊Q8C2312yes—
299C2×C22⋊Q8C2314yes—
300C2×#121C2314yes—
301C2×#121C2312yes—
302C2×#121C2312yes—
303C2×#121C2312yes—
304C2×#121C2311yescharacteristic
305C2×#121C2314yes—
306C2×#121C2314yes—
307C2×#121C2314yes—
308C2×#121C2312yes—
309C2×#120C2312yes—
310C2×#120C2311yescharacteristic
311C2×#120C2312yes—
312C2×C4×Q8C2312yes—
313C2×C4×Q8C2311yescharacteristic
314C2×C4×Q8C2312yes—
315C2×C4×Q8C2312yes—
316C2×C4×Q8C2312yes—
317C2×C4×Q8C2311yescharacteristic
318C2×C4×Q8C2312yes—
319C2×C4×D4C2312yes—
320C2×C4×D4C2312yes—
321C2×C4×D4C2314yes—
322C2×C4×D4C2314yes—
323C2×C4×D4C2314yes—
324C2×C4×D4C2312yes—
325C2×C4×D4C2312yes—
326C2×C4×D4C2312yes—
327C2×C4×D4C2312yes—
328C2×C4×D4C2311yescharacteristic
329C2×#117C2312yes—
330C2×#117C2314yes—
331C2×#117C2314yes—
332C22×C4⋊C4C2312yes—
333C22×C4⋊C4C2312yes—
334C22×C4⋊C4C2312yes—
335C22×C4⋊C4C2311yescharacteristic
336C22×C4⋊C4C2312yes—
337C22×C4⋊C4C2311yescharacteristic
338C22×C22⋊C4C2314yes—
339C22×C22⋊C4C2312yes—
340#401C2314yes—
341#400C2314yes—
342#400C2314yes—
343#400C2312yes—
344#400C2312yes—
345#400C2312yes—
346#400C2312yes—
347#400C2312yes—
348#400C2312yes—
349#400C2312yes—
350#400C2312yes—
351#400C2312yes—
352#400C2314yes—
353#400C2314yes—
354#400C2314yes—
355#400C2314yes—
356#400C2312yes—
357#400C2314yes—
358#400C2314yes—
359#400C2314yes—
360#400C2314yes—
361#400C2314yes—
362#400C2314yes—
363#400C2314yes—
364#400C2314yes—
365#400C2314yes—
366#399C2314yes—
367#399C2314yes—
368#399C2314yes—
369#399C2314yes—
370#399C2312yes—
371#398C2314yes—
372#398C2314yes—
373#398C2312yes—
374#398C2312yes—
375#398C2314yes—
376#398C2314yes—
377#398C2314yes—
378#398C2314yes—
379#398C2314yes—
380#398C2314yes—
381#398C2314yes—
382#398C2314yes—
383#398C2314yes—
384#398C2314yes—
385#398C2312yes—
386#398C2314yes—
387#398C2314yes—
388#398C2314yes—
389#398C2314yes—
390#398C2314yes—
391#398C2314yes—
392#398C2314yes—
393#398C2314yes—
394#398C2314yes—
395#397C2312yes—
396#397C2314yes—
397#397C2312yes—
398#397C2311yescharacteristic
399#397C2312yes—
400#397C2312yes—
401#397C2314yes—
402#397C2312yes—
403#397C2314yes—
404#397C2314yes—
405#397C2314yes—
406#397C2312yes—
407#397C2314yes—
408#397C2312yes—
409#397C2312yes—
410#397C2312yes—
411#397C2312yes—
412#397C2311yescharacteristic
413#397C2312yes—
414#397C2314yes—
415#397C2312yes—
416#397C2312yes—
417#397C2314yes—
418#397C2314yes—
419#397C2314yes—
420#397C2314yes—
421#397C2314yes—
422#397C2314yes—
423#397C2314yes—
424#397C2314yes—
425#397C2314yes—
426#397C2314yes—
427#397C2312yes—
428#396C2314yes—
429#396C2314yes—
430#396C2314yes—
431#396C2314yes—
432#396C2314yes—
433#396C2314yes—
434#396C2314yes—
435#395C2314yes—
436#395C2314yes—
437#395C2314yes—
438#395C2311yescharacteristic
439#395C2312yes—
440#395C2314yes—
441#395C2312yes—
442#395C2314yes—
443#395C2314yes—
444#394C2312yes—
445#394C2314yes—
446#394C2314yes—
447#394C2314yes—
448#394C2314yes—
449#394C2314yes—
450#394C2311yescharacteristic
451#394C2312yes—
452#394C2314yes—
453#394C2312yes—
454#394C2312yes—
455#394C2312yes—
456#394C2312yes—
457#394C2312yes—
458#394C2312yes—
459#394C2312yes—
460#394C2312yes—
461#394C2312yes—
462#394C2312yes—
463#394C2312yes—
464#394C2312yes—
465#394C2314yes—
466#394C2314yes—
467#394C2314yes—
468#394C2314yes—
469#394C2314yes—
470#394C2314yes—
471#394C2314yes—
472#394C2314yes—
473#394C2314yes—
474#394C2314yes—
475#393C2314yes—
476#393C2314yes—
477#393C2314yes—
478#393C2314yes—
479#393C2312yes—
480#393C2312yes—
481#393C2311yescharacteristic
482#393C2312yes—
483#393C2312yes—
484#393C2312yes—
485#393C2311yescharacteristic
486#393C2312yes—
487#393C2312yes—
488#393C2312yes—
489#393C2314yes—
490#393C2314yes—
491#393C2311yescharacteristic
492#393C2312yes—
493#393C2312yes—
494#393C2314yes—
495#392C2312yes—
496#392C2312yes—
497#392C2312yes—
498#392C2311yescharacteristic
499#392C2312yes—
500#392C2314yes—
501#391C2314yes—
502#391C2314yes—
503#391C2312yes—
504#391C2312yes—
505#391C2312yes—
506#391C2312yes—
507#391C2312yes—
508#391C2314yes—
509#391C2314yes—
510#391C2312yes—
511#391C2314yes—
512#391C2314yes—
513#391C2314yes—
514#391C2314yes—
515#391C2314yes—
516#391C2314yes—
517#391C2314yes—
518#390C2314yes—
519#390C2312yes—
520#390C2312yes—
521#390C2314yes—
522#390C2312yes—
523#390C2314yes—
524#390C2314yes—
525#390C2314yes—
526#389C2312yes—
527#389C2312yes—
528#389C2312yes—
529#389C2312yes—
530#389C2312yes—
531#389C2312yes—
532#389C2312yes—
533#389C2314yes—
534#389C2314yes—
535#389C2312yes—
536#389C2314yes—
537#389C2314yes—
538#389C2314yes—
539#389C2312yes—
540#389C2312yes—
541#389C2314yes—
542#389C2314yes—
543#389C2314yes—
544#389C2314yes—
545#389C2314yes—
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#388C2314yes—
559#388C2314yes—
560#388C2314yes—
561#388C2314yes—
562#388C2314yes—
563#388C2314yes—
564#388C2314yes—
565#388C2314yes—
566#388C2314yes—
567#388C2314yes—
568#388C2314yes—
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#387C2314yes—
588#387C2314yes—
589#387C2314yes—
590#387C2314yes—
591#387C2314yes—
592#387C2314yes—
593#387C2314yes—
594#387C2314yes—
595#387C2314yes—
596#387C2314yes—
597#386C2314yes—
598#386C2314yes—
599#386C2311yescharacteristic
600#386C2312yes—
601#386C2312yes—
602#386C2312yes—
603#386C2312yes—
604#386C2314yes—
605#386C2314yes—
606#386C2314yes—
607#386C2312yes—
608#386C2312yes—
609#386C2312yes—
610#386C2312yes—
611#386C2314yes—
612#386C2314yes—
613#386C2314yes—
614#386C2314yes—
615#386C2314yes—
616#386C2314yes—
617#386C2314yes—
618#385C2311yescharacteristic
619#385C2312yes—
620#385C2312yes—
621#385C2312yes—
622#385C2312yes—
623#385C2314yes—
624#385C2314yes—
625#385C2314yes—
626#385C2314yes—
627#385C2312yes—
628#385C2314yes—
629#385C2314yes—
630#385C2314yes—
631#385C2314yes—
632#385C2314yes—
633#385C2314yes—
634#385C2314yes—
635#385C2314yes—
636#385C2314yes—
637#385C2314yes—
638#385C2314yes—
639#385C2314yes—
640#385C2314yes—
641#385C2314yes—
642#384C2312yes—
643#384C2312yes—
644#384C2312yes—
645#383C2314yes—
646#383C2314yes—
647#383C2314yes—
648#382C2314yes—
649#382C2314yes—
650#382C2312yes—
651#382C2312yes—
652#382C2312yes—
653#382C2314yes—
654#381C2314yes—
655#381C2312yes—
656#381C2314yes—
657#381C2314yes—
658#381C2314yes—
659#381C2312yes—
660#381C2314yes—
661#381C2314yes—
662#380C2312yes—
663#380C2312yes—
664#380C2312yes—
665#380C2312yes—
666#380C2314yes—
667#380C2312yes—
668#380C2314yes—
669#380C2311yescharacteristic
670#380C2312yes—
671#380C2311yescharacteristic
672#380C2312yes—
673#380C2314yes—
674#380C2314yes—
675#380C2314yes—
676#380C2312yes—
677#380C2314yes—
678#380C2312yes—
679#380C2314yes—
680#380C2314yes—
681#380C2312yes—
682#380C2314yes—
683#380C2312yes—
684#380C2314yes—
685#380C2314yes—
686#379C2311yescharacteristic
687#379C2312yes—
688C4×C4⋊C4C2312yes—
689C4×C4⋊C4C2312yes—
690C4×C4⋊C4C2312yes—
691C4×C4⋊C4C2312yes—
692C4×C4⋊C4C2314yes—
693C4×C4⋊C4C2314yes—
694C4×C4⋊C4C2311yescharacteristic
695C4×C4⋊C4C2312yes—
696C4×C22⋊C4C2314yes—
697C4×C22⋊C4C2314yes—
698C4×C22⋊C4C2314yes—
699C4×C22⋊C4C2312yes—
700C4×C22⋊C4C2311yescharacteristic
701C4×C22⋊C4C2314yes—
702C4×C22⋊C4C2312yes—
703C4×C22⋊C4C2311yescharacteristic
704C4×C22⋊C4C2312yes—
705C4×C22⋊C4C2314yes—
706C4×C22⋊C4C2312yes—
707C4×C22⋊C4C2312yes—
708C4×C22⋊C4C2314yes—
709C4×C22⋊C4C2314yes—
710C4×C22⋊C4C2312yes—
711C4×C22⋊C4C2312yes—
712C4×C22⋊C4C2312yes—
713C4×C22⋊C4C2312yes—
714#376C2312yes—
715#376C2311yescharacteristic
716#376C2312yes—
717C2×#95C2312yes—
718C2×#95C2314yes—
719C25C2411yescharacteristic
720C2×#41—24no—
721C2×#41—42no—
722C2×#41—44no—
723C2×#41—44no—
724C22×Q8—24no—
725C22×Q8—44no—
726C22×Q8C2411yescharacteristic
727C22×Q8C2411yescharacteristic
728C22×Q8C2412yes—
729C22×Q8C2411yescharacteristic
730C22×Q8C2412yes—
731C22×Q8C2412yes—
732C22×Q8C2411yescharacteristic
733C22×Q8C2414yes—
734C22×D4C2411yescharacteristic
735C22×D4C2412yes—
736C22×D4C2412yes—
737C22×D4C2412yes—
738C22×D4C2414yes—
739C22×D4C2412yes—
740C22×D4C2411yescharacteristic
741C22×D4C2412yes—
742C22×D4C2412yes—
743C22×D4C2414yes—
744C22×D4C2411yescharacteristic
745C22×D4C2412yes—
746C23×C4—42no—
747C23×C4—44no—
748C23×C4C2412yes—
749C23×C4C2412yes—
750C23×C4C2411yescharacteristic
751C23×C4C2411yescharacteristic
752C23×C4C2414yes—
753C23×C4C2414yes—
754C23×C4C2412yes—
755C23×C4C2412yes—
756C23×C4C2412yes—
757C23×C4C2411yescharacteristic
758C23×C4C2412yes—
759C23×C4C2414yes—
760C23×C4C2414yes—
761C23×C4C2412yes—
762C4⋊Q8—48no—
763C4⋊Q8—42no—
764C4⋊Q8—44no—
765C4⋊Q8—44no—
766#126—48no—
767#126—48no—
768#126—48no—
769#126—48no—
770#125—44no—
771#125—48no—
772#124—42no—
773#124—44no—
774#124—48no—
775#124—48no—
776#124—44no—
777#123—48no—
778#123—48no—
779#123—48no—
780#123—44no—
781#123—48no—
782C22⋊Q8—28no—
783C22⋊Q8—28no—
784C22⋊Q8—48no—
785C22⋊Q8—48no—
786C22⋊Q8—48no—
787C22⋊Q8—44no—
788C22⋊Q8—44no—
789C22⋊Q8—44no—
790C22⋊Q8—42no—
791C22⋊Q8—44no—
792#121—44no—
793#121—48no—
794#121—48no—
795#121—48no—
796#121—44no—
797#121—44no—
798#121—42no—
799#121—44no—
800#121—48no—
801#120—28no—
802#120—28no—
803#120—24no—
804C4×Q8—24no—
805C4×Q8—28no—
806C4×Q8—44no—
807C4×Q8—44no—
808C4×Q8—42no—
809C4×Q8—44no—
810C4×Q8—44no—
811C4×D4—44no—
812C4×D4—44no—
813C4×D4—44no—
814C4×D4—44no—
815C4×D4—42no—
816C4×D4—44no—
817C4×D4—44no—
818C4×D4—48no—
819C4×D4—48no—
820C4×D4—48no—
821#117—48no—
822#117—48no—
823#117—44no—
824C2×C4⋊C4—44no—
825C2×C4⋊C4—44no—
826C2×C4⋊C4—42no—
827C2×C4⋊C4—44no—
828C2×C4⋊C4—42no—
829C2×C4⋊C4—44no—
830C2×C4⋊C4C2412yes—
831C2×C4⋊C4C2412yes—
832C2×C4⋊C4C2412yes—
833C2×C4⋊C4C2412yes—
834C2×C4⋊C4C2412yes—
835C2×C4⋊C4C2412yes—
836C2×C4⋊C4C2414yes—
837C2×C4⋊C4C2414yes—
838C2×C4⋊C4C2411yescharacteristic
839C2×C4⋊C4C2412yes—
840C2×C4⋊C4C2414yes—
841C2×C4⋊C4C2412yes—
842C2×C4⋊C4C2414yes—
843C2×C4⋊C4C2412yes—
844C2×C4⋊C4C2414yes—
845C2×C4⋊C4C2414yes—
846C2×C4⋊C4C2414yes—
847C2×C4⋊C4C2414yes—
848C2×C4⋊C4C2414yes—
849C2×C4⋊C4C2414yes—
850C2×C4⋊C4C2411yescharacteristic
851C2×C4⋊C4C2412yes—
852C2×C4⋊C4C2414yes—
853C2×C4⋊C4C2414yes—
854C2×C4⋊C4C2414yes—
855C2×C4⋊C4C2412yes—
856C2×C4⋊C4C2412yes—
857C2×C4⋊C4C2412yes—
858C2×C4⋊C4C2412yes—
859C2×C4⋊C4C2412yes—
860C2×C4⋊C4C2414yes—
861C2×C4⋊C4C2412yes—
862C2×C4⋊C4C2411yescharacteristic
863C2×C4⋊C4C2414yes—
864C2×C4⋊C4C2412yes—
865C2×C4⋊C4C2414yes—
866C2×C4⋊C4C2412yes—
867C2×C4⋊C4C2412yes—
868C2×C4⋊C4C2414yes—
869C2×C4⋊C4C2414yes—
870C2×C4⋊C4C2414yes—
871C2×C4⋊C4C2414yes—
872C2×C4⋊C4C2414yes—
873C2×C4⋊C4C2414yes—
874C2×C4⋊C4C2414yes—
875C2×C4⋊C4C2414yes—
876C2×C4⋊C4C2414yes—
877C2×C4⋊C4C2414yes—
878C2×C4⋊C4C2414yes—
879C2×C4⋊C4C2414yes—
880C2×C4⋊C4C2414yes—
881C2×C22⋊C4—216no—
882C2×C22⋊C4—44no—
883C2×C22⋊C4C2414yes—
884C2×C22⋊C4C2414yes—
885C2×C22⋊C4C2414yes—
886C2×C22⋊C4C2414yes—
887C2×C22⋊C4C2414yes—
888C2×C22⋊C4C2412yes—
889C2×C22⋊C4C2412yes—
890C2×C22⋊C4C2414yes—
891C2×C22⋊C4C2412yes—
892C2×C22⋊C4C2412yes—
893C2×C22⋊C4C2412yes—
894C2×C22⋊C4C2411yescharacteristic
895C2×C22⋊C4C2414yes—
896C2×C22⋊C4C2414yes—
897C2×C22⋊C4C2412yes—
898C2×C22⋊C4C2414yes—
899C2×C22⋊C4C2411yescharacteristic
900C2×C22⋊C4C2414yes—
901C2×C22⋊C4C2414yes—
902C2×C22⋊C4C2414yes—
903C2×C22⋊C4C2411yescharacteristic
904C2×C22⋊C4C2412yes—
905C2×C22⋊C4C2412yes—
906C2×C22⋊C4C2412yes—
907C2×C22⋊C4C2412yes—
908C2×C22⋊C4C2412yes—
909C2×C22⋊C4C2412yes—
910C2×C22⋊C4C2414yes—
911C2×C22⋊C4C2412yes—
912C2×C22⋊C4C2412yes—
913C2×C22⋊C4C2414yes—
914C2×C22⋊C4C2412yes—
915C2×C22⋊C4C2412yes—
916C2×C22⋊C4C2412yes—
917C2×C22⋊C4C2414yes—
918C2×C22⋊C4C2414yes—
919C2×C22⋊C4C2414yes—
920C2×C22⋊C4C2414yes—
921C2×C22⋊C4C2412yes—
922C2×C22⋊C4C2412yes—
923C2×C22⋊C4C2412yes—
924C2×C22⋊C4C2411yescharacteristic
925C2×C22⋊C4C2412yes—
926C2×C22⋊C4C2412yes—
927C2×C22⋊C4C2412yes—
928C2×C22⋊C4C2412yes—
929C2×C22⋊C4C2412yes—
930C2×C22⋊C4C2414yes—
931C2×C22⋊C4C2412yes—
932C2×C22⋊C4C2412yes—
933C2×C22⋊C4C2414yes—
934C2×C22⋊C4C2412yes—
935C2×C22⋊C4C2414yes—
936C2×C22⋊C4C2412yes—
937C2×C22⋊C4C2412yes—
938C2×C22⋊C4C2412yes—
939C2×C22⋊C4C2414yes—
940C2×C22⋊C4C2414yes—
941C2×C22⋊C4C2414yes—
942C2×C42C2414yes—
943C2×C42C2412yes—
944C2×C42C2411yescharacteristic
945C2×C42C2412yes—
946C2×C42C2412yes—
947C2×C42C2412yes—
948C2×C42C2412yes—
949C2×C42C2412yes—
950C2×C42C2414yes—
951C2×C42C2414yes—
952C2×C42C2414yes—
953C2×C42C2414yes—
954C2×C42C2414yes—
955C2×C42C2414yes—
956C2×C42C2414yes—
957#95C2411yescharacteristic
958#95C2414yes—
959#95C2414yes—
960#95C2414yes—
961#95C2414yes—
962#95C2412yes—
963#95C2414yes—
964#95C2411yescharacteristic
965#95C2412yes—
966#95C2414yes—
967#95C2412yes—
968#95C2411yescharacteristic
969#95C2412yes—
970#95C2412yes—
971#95C2412yes—
972#95C2412yes—
973#95C2412yes—
974#95C2414yes—
975#95C2414yes—
976#95C2412yes—
977#95C2412yes—
978#95C2414yes—
979#95C2414yes—
980#95C2414yes—
981#95C2414yes—
982#95C2411yescharacteristic
983#95C2414yes—
984#95C2414yes—
985#95C2414yes—
986#95C2414yes—
987#95C2412yes—
988#95C2414yes—
989#95C2412yes—
990#95C2412yes—
991#95C2414yes—
992#95C2412yes—
993#95C2412yes—
994#95C2412yes—
995#95C2414yes—
996#95C2412yes—
997#95C2412yes—
998#95C2412yes—
999#95C2414yes—
1000#95C2412yes—
1001#95C2412yes—
1002#95C2412yes—
1003#95C2412yes—
1004#95C2412yes—
1005#95C2414yes—
1006#95C2414yes—
1007#95C2414yes—
1008#95C2414yes—
1009#95C2414yes—
1010#95C2414yes—
1011#95C2412yes—
1012#95C2414yes—
1013#95C2414yes—
1014#95C2414yes—
1015#95C2414yes—
1016#95C2414yes—
1017#95C2414yes—
1018#95C2414yes—
1019#95C2414yes—
1020#95C2414yes—
1021#95C2414yes—
1022#95C2414yes—
1023#95C2414yes—
1024#95C2414yes—
1025#95C2414yes—
1026C24—41no—
1027C24—42no—
1028C24—41no—
1029C24—42no—
1030C24H(5,𝔽2)14yes—
1031C24C2512yes—
1032C24C2511yescharacteristic
1033C24C2512yes—
1034C24C2512yes—
1035C24C2511yescharacteristic
1036#41—88no—
1037#41—88no—
1038C2×Q8—22no—
1039C2×Q8—24no—
1040C2×Q8—24no—
1041C2×Q8—24no—
1042C2×Q8—41no—
1043C2×Q8—42no—
1044C2×Q8—42no—
1045C2×Q8—41no—
1046C2×Q8—44no—
1047C2×Q8—42no—
1048C2×Q8—42no—
1049C2×Q8—42no—
1050C2×Q8—42no—
1051C2×Q8—44no—
1052C2×Q8—42no—
1053C2×Q8—44no—
1054C2×Q8—42no—
1055C2×Q8—44no—
1056C2×Q8—88no—
1057C2×Q8H(5,𝔽2)14yes—
1058C2×D4—24no—
1059C2×D4—24no—
1060C2×D4—28no—
1061C2×D4—24no—
1062C2×D4—24no—
1063C2×D4—24no—
1064C2×D4—22no—
1065C2×D4—22no—
1066C2×D4—24no—
1067C2×D4—24no—
1068C2×D4—42no—
1069C2×D4—42no—
1070C2×D4—42no—
1071C2×D4—42no—
1072C2×D4—42no—
1073C2×D4—41no—
1074C2×D4—42no—
1075C2×D4—42no—
1076C2×D4—42no—
1077C2×D4—41no—
1078C2×D4—44no—
1079C2×D4—42no—
1080C2×D4—42no—
1081C2×D4—41no—
1082C2×D4—44no—
1083C2×D4—42no—
1084C2×D4—44no—
1085C2×D4—42no—
1086C2×D4—42no—
1087C2×D4—42no—
1088C2×D4—44no—
1089C2×D4—44no—
1090C2×D4—44no—
1091C22×C4—28no—
1092C22×C4—28no—
1093C22×C4—22no—
1094C22×C4—24no—
1095C22×C4—22no—
1096C22×C4—24no—
1097C22×C4—24no—
1098C22×C4—24no—
1099C22×C4—24no—
1100C22×C4—24no—
1101C22×C4—24no—
1102C22×C4—24no—
1103C22×C4—24no—
1104C22×C4—24no—
1105C22×C4—42no—
1106C22×C4—41no—
1107C22×C4—44no—
1108C22×C4—44no—
1109C22×C4—42no—
1110C22×C4—42no—
1111C22×C4—42no—
1112C22×C4—42no—
1113C22×C4—44no—
1114C22×C4—44no—
1115C22×C4—44no—
1116C22×C4—44no—
1117C22×C4—44no—
1118C22×C4—42no—
1119C22×C4—44no—
1120C22×C4—42no—
1121C22×C4—44no—
1122C22×C4—44no—
1123C22×C4—44no—
1124C22×C4—44no—
1125C22×C4—44no—
1126C22×C4—42no—
1127C22×C4—88no—
1128C22×C4C2512yes—
1129C22×C4C2512yes—
1130C22×C4C2512yes—
1131C22×C4C2511yescharacteristic
1132C22×C4C2511yescharacteristic
1133C22×C4C2512yes—
1134C22×C4C2514yes—
1135C22×C4C2511yescharacteristic
1136C22×C4C2512yes—
1137C22×C4C2514yes—
1138C22×C4C2512yes—
1139C22×C4C2514yes—
1140C22×C4C2512yes—
1141C22×C4C2514yes—
1142C22×C4C2512yes—
1143C22×C4C2512yes—
1144C22×C4C2512yes—
1145C22×C4C2512yes—
1146C22×C4C2511yescharacteristic
1147C22×C4C2512yes—
1148C22×C4C2514yes—
1149C22×C4C2514yes—
1150C22×C4C2512yes—
1151C22×C4C2511yescharacteristic
1152C4⋊C4—24no—
1153C4⋊C4—24no—
1154C4⋊C4—24no—
1155C4⋊C4—28no—
1156C4⋊C4—28no—
1157C4⋊C4—24no—
1158C4⋊C4—22no—
1159C4⋊C4—28no—
1160C4⋊C4—24no—
1161C4⋊C4—24no—
1162C4⋊C4—24no—
1163C4⋊C4—44no—
1164C4⋊C4—44no—
1165C4⋊C4—42no—
1166C4⋊C4—42no—
1167C4⋊C4—44no—
1168C4⋊C4—44no—
1169C4⋊C4—44no—
1170C4⋊C4—44no—
1171C4⋊C4—44no—
1172C4⋊C4—44no—
1173C4⋊C4—44no—
1174C4⋊C4—44no—
1175C4⋊C4—44no—
1176C4⋊C4—44no—
1177C4⋊C4—44no—
1178C4⋊C4—42no—
1179C4⋊C4—42no—
1180C4⋊C4—42no—
1181C4⋊C4—42no—
1182C4⋊C4—41no—
1183C4⋊C4—44no—
1184C4⋊C4—44no—
1185C4⋊C4—44no—
1186C4⋊C4—42no—
1187C4⋊C4—44no—
1188C4⋊C4—42no—
1189C4⋊C4—42no—
1190C4⋊C4—42no—
1191C4⋊C4—44no—
1192C4⋊C4—42no—
1193C4⋊C4—41no—
1194C4⋊C4—44no—
1195C4⋊C4—42no—
1196C4⋊C4—44no—
1197C4⋊C4—44no—
1198C4⋊C4—44no—
1199C4⋊C4—44no—
1200C4⋊C4—44no—
1201C4⋊C4—44no—
1202C4⋊C4—44no—
1203C22⋊C4—28no—
1204C22⋊C4—28no—
1205C22⋊C4—28no—
1206C22⋊C4—28no—
1207C22⋊C4—24no—
1208C22⋊C4—24no—
1209C22⋊C4—28no—
1210C22⋊C4—24no—
1211C22⋊C4—24no—
1212C22⋊C4—24no—
1213C22⋊C4—22no—
1214C22⋊C4—28no—
1215C22⋊C4—28no—
1216C22⋊C4—44no—
1217C22⋊C4—42no—
1218C22⋊C4—42no—
1219C22⋊C4—44no—
1220C22⋊C4—44no—
1221C22⋊C4—44no—
1222C22⋊C4—42no—
1223C22⋊C4—42no—
1224C22⋊C4—44no—
1225C22⋊C4—42no—
1226C22⋊C4—42no—
1227C22⋊C4—42no—
1228C22⋊C4—42no—
1229C22⋊C4—42no—
1230C22⋊C4—42no—
1231C22⋊C4—44no—
1232C22⋊C4—44no—
1233C22⋊C4—41no—
1234C22⋊C4—42no—
1235C22⋊C4—42no—
1236C22⋊C4—42no—
1237C22⋊C4—42no—
1238C22⋊C4—44no—
1239C22⋊C4—42no—
1240C22⋊C4—42no—
1241C22⋊C4—42no—
1242C22⋊C4—42no—
1243C22⋊C4—44no—
1244C22⋊C4—42no—
1245C22⋊C4—42no—
1246C22⋊C4—41no—
1247C22⋊C4—44no—
1248C22⋊C4—44no—
1249C22⋊C4—44no—
1250C22⋊C4—42no—
1251C22⋊C4—41no—
1252C22⋊C4—42no—
1253C22⋊C4—44no—
1254C22⋊C4—44no—
1255C22⋊C4—42no—
1256C22⋊C4—42no—
1257C22⋊C4—42no—
1258C22⋊C4—44no—
1259C22⋊C4—44no—
1260C22⋊C4—44no—
1261C22⋊C4—42no—
1262C42—28no—
1263C42—24no—
1264C42—22no—
1265C42—24no—
1266C42—24no—
1267C42—24no—
1268C42—24no—
1269C42—44no—
1270C42—42no—
1271C42—44no—
1272C42—44no—
1273C42—44no—
1274C42—44no—
1275C42—44no—
1276C42—44no—
1277C23—22no—
1278C23—21no—
1279C23—22no—
1280C23—22no—
1281C23—22no—
1282C23—22no—
1283C23—22no—
1284C23—22no—
1285C23—21no—
1286C23—22no—
1287C23—22no—
1288C23—21no—
1289C23—22no—
1290C23—22no—
1291C23—22no—
1292C23—21no—
1293C23—22no—
1294C23—24no—
1295C23—22no—
1296C23—22no—
1297C23—22no—
1298C23—22no—
1299C23—24no—
1300C23—22no—
1301C23—21no—
1302C23—22no—
1303C23—22no—
1304C23—44no—
1305C23—48no—
1306C23—82no—
1307C23—82no—
1308C23—84no—
1309C23C2×H(5,𝔽2)12yes—
1310C23C2×H(5,𝔽2)14yes—
1311C23C2611yescharacteristic
1312Q8—28no—
1313Q8—44no—
1314Q8—44no—
1315Q8—84no—
1316Q8—84no—
1317Q8—82no—
1318Q8—162no—
1319Q8—164no—
1320D4—48no—
1321D4—48no—
1322D4—44no—
1323D4—84no—
1324D4—84no—
1325D4—82no—
1326D4—84no—
1327D4—84no—
1328D4—88no—
1329D4—82no—
1330D4—84no—
1331D4—164no—
1332C2×C4—24no—
1333C2×C4—21no—
1334C2×C4—22no—
1335C2×C4—24no—
1336C2×C4—22no—
1337C2×C4—21no—
1338C2×C4—22no—
1339C2×C4—24no—
1340C2×C4—22no—
1341C2×C4—22no—
1342C2×C4—22no—
1343C2×C4—22no—
1344C2×C4—21no—
1345C2×C4—22no—
1346C2×C4—24no—
1347C2×C4—24no—
1348C2×C4—24no—
1349C2×C4—24no—
1350C2×C4—24no—
1351C2×C4—22no—
1352C2×C4—24no—
1353C2×C4—22no—
1354C2×C4—21no—
1355C2×C4—22no—
1356C2×C4—21no—
1357C2×C4—22no—
1358C2×C4—22no—
1359C2×C4—22no—
1360C2×C4—22no—
1361C2×C4—22no—
1362C2×C4—22no—
1363C2×C4—24no—
1364C2×C4—24no—
1365C2×C4—24no—
1366C2×C4—22no—
1367C2×C4—24no—
1368C2×C4—22no—
1369C2×C4—22no—
1370C2×C4—22no—
1371C2×C4—22no—
1372C2×C4—22no—
1373C2×C4—22no—
1374C2×C4—24no—
1375C2×C4—24no—
1376C2×C4—22no—
1377C2×C4—22no—
1378C2×C4—22no—
1379C2×C4—22no—
1380C2×C4—24no—
1381C2×C4—22no—
1382C2×C4—22no—
1383C2×C4—22no—
1384C2×C4—22no—
1385C2×C4—22no—
1386C2×C4—22no—
1387C2×C4—22no—
1388C2×C4—21no—
1389C2×C4—22no—
1390C2×C4—24no—
1391C2×C4—24no—
1392C2×C4—24no—
1393C2×C4—24no—
1394C2×C4—22no—
1395C2×C4—48no—
1396C2×C4—44no—
1397C2×C4—48no—
1398C2×C4—44no—
1399C2×C4—84no—
1400C2×C4—84no—
1401C2×C4—88no—
1402C2×C4—88no—
1403C2×C4—84no—
1404C2×C4—82no—
1405C2×C4—84no—
1406C2×C4—162no—
1407C2×C4—164no—
1408C2×C4—164no—
1409C2×C4C2×H(5,𝔽2)14yes—
1410C2×C4C2×H(5,𝔽2)12yes—
1411C2×C4#58514yes—
1412C22—24no—
1413C22—22no—
1414C22—24no—
1415C22—24no—
1416C22—24no—
1417C22—41no—
1418C22—42no—
1419C22—41no—
1420C22—42no—
1421C22—42no—
1422C22—42no—
1423C22—42no—
1424C22—41no—
1425C22—42no—
1426C22—42no—
1427C22—42no—
1428C22—42no—
1429C22—41no—
1430C22—42no—
1431C22—44no—
1432C22—42no—
1433C22—42no—
1434C22—41no—
1435C22—42no—
1436C22—42no—
1437C22—42no—
1438C22—44no—
1439C22—42no—
1440C22—42no—
1441C22—88no—
1442C22C22×H(5,𝔽2)11yescharacteristic
1443C22C22×H(5,𝔽2)11yescharacteristic
1444C22C2×#58512yes—
1445C222−1+612yes—
1446C222−1+611yescharacteristic
1447C4—24no—
1448C4—42no—
1449C4—41no—
1450C4—41no—
1451C4—42no—
1452C4—42no—
1453C4—44no—
1454C4—41no—
1455C4—42no—
1456C4—42no—
1457C4—42no—
1458C4—42no—
1459C4—44no—
1460C4—44no—
1461C4—42no—
1462C4—41no—
1463C4—42no—
1464C4—44no—
1465C4—44no—
1466C4—42no—
1467C4—44no—
1468C4—42no—
1469C4—42no—
1470C4#354514yes—
1471C2—44no—
1472C2—42no—
1473C2—81no—
1474C2—82no—
1475C2—82no—
1476C2C2×#354511yescharacteristic
1477C2#6289511yescharacteristic
1478C2#6290112yes—
1479C2#6304411yescharacteristic
1480C2#6305312yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59198C2semidirect
2. #59014C2semidirect
3. #57069C2semidirect
4. #54138C2semidirect
5. #54058C2semidirect
6. #53858C2semidirect
7. #53806C2semidirect
8. #53127C2semidirect
9. #52991C2semidirect
10. #52942C2semidirect
11. #52606C2semidirect
12. #46812C2semidirect
13. #45419C2semidirect
14. #45382C2semidirect
15. #45115C2semidirect
16. #45022C2semidirect
17. #44913C2semidirect
18. #42984C2semidirect
19. #42813C2semidirect
20. #42693C2semidirect
21. #42512C2semidirect
22. #42446C2semidirect
23. #41616C2semidirect
24. #41378C2semidirect
25. #39723C2semidirect
26. #39349C2semidirect
27. #36675C2semidirect
28. #35948C2semidirect
29. #35911C2semidirect
30. C2×Q82C22semidirect
35. C2×#537C22semidirect
38. #2841C22semidirect
40. #2839C22semidirect
41. #2839C22semidirect
42. #2836C22semidirect
46. #2832C22semidirect
47. #2832C22semidirect
48. #2827C22semidirect
49. #2827C22semidirect
55. #2821C22semidirect
57. #2816C22semidirect
60. #2806C22semidirect
61. #2800C22semidirect
62. #2799C22semidirect
63. #2788C22semidirect
64. #2784C22semidirect
65. #2783C22semidirect
66. #2771C22semidirect
67. #2770C22semidirect
69. #2764C22semidirect
70. #2763C22semidirect
71. #2757C22semidirect
72. #2755C22semidirect
73. #2755C22semidirect
75. #2751C22semidirect
76. #2747C22semidirect
78. #2745C22semidirect
79. #2744C22semidirect
80. #2740C22semidirect
81. #2738C22semidirect
90. #2713C22semidirect
91. #2713C22semidirect
92. #2711C22semidirect
96. #2704C22semidirect
104. #2691C22semidirect
109. #2686C22semidirect
114. #2666C22semidirect
115. #2660C22semidirect
116. #2659C22semidirect
117. #2655C22semidirect
119. #2653C22semidirect
120. #2651C22semidirect
121. #2647C22semidirect
122. #2640C22semidirect
123. #2640C22semidirect
126. #2637C22semidirect
131. #2616C22semidirect
132. #2607C22semidirect
135. #2592C22semidirect
136. #2592C22semidirect
138. #2589C22semidirect
139. #2585C22semidirect
140. #2584C22semidirect
141. #2582C22semidirect
142. #2582C22semidirect
143. #2580C22semidirect
146. #2572C22semidirect
147. #2559C22semidirect
158. #2530C22semidirect
163. #2518C22semidirect
164. #2505C22semidirect
167. #2502C22semidirect
168. #2500C22semidirect
169. #2497C22semidirect
173. #2495C22semidirect
174. #2494C22semidirect
175. #2492C22semidirect
176. #2492C22semidirect
179. #2490C22semidirect
200. #2442C22semidirect
203. #2439C22semidirect
204. #2439C22semidirect
207. #2427C22semidirect
209. #2423C22semidirect
210. #2423C22semidirect
211. #2423C22semidirect
237. #2360C22semidirect
238. #2360C22semidirect
239. #2355C22semidirect
243. #2345C22semidirect
246. #2341C22semidirect
249. #2339C22semidirect
251. #2320C22semidirect
252. #2320C22semidirect
253. #2319C22semidirect
254. #2311C22semidirect
258. #2276C22semidirect

Maximal subgroups

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

subgroupindex
#591982
#590142
#570692
#541382
#540582
#538582
#538062
#531272
#529912
#529422
#526062
#468122
#454192
#453822
#451152
#450222
#449132
#429842
#428132
#426932
#425122
#424462
#416162
#413782
#397232
#393492
#366752
#359482
#359112