Finite Group Databasebeta

← #8746470

Subgroups — #8746470

Order 512.

4388 conjugacy classes of subgroups.

The subgroup lattice has 1466 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59201C211yesmaximal, characteristic, complemented
2#59025C212yesmaximal, complemented
3#58860C212yesmaximal, complemented
4#57465C214yesmaximal, complemented
5#55529C214yesmaximal, complemented
6#54536C214yesmaximal, complemented
7#54089C214yesmaximal, complemented
8#53079C212yesmaximal, complemented
9#53031C211yesmaximal, characteristic, complemented
10#52943C212yesmaximal, complemented
11#52923C214yesmaximal, complemented
12#46935C212yesmaximal, complemented
13#45420C212yesmaximal, complemented
14#45401C212yesmaximal, complemented
15#45258C212yesmaximal, complemented
16#45251C211yesmaximal, characteristic, complemented
17#45009C212yesmaximal, complemented
18#42984C211yesmaximal, characteristic, complemented
19#42891C212yesmaximal, complemented
20#42653C212yesmaximal, complemented
21#42515C212yesmaximal, complemented
22#42513C212yesmaximal, complemented
23#41879C214yesmaximal, complemented
24#41679C212yesmaximal, complemented
25#39910C212yesmaximal, complemented
26#39133C211yesmaximal, characteristic, complemented
27#36675C211yesmaximal, characteristic, complemented
28#35945C212yesmaximal, complemented
29#35854C211yesmaximal, characteristic, complemented
30C2×#557C2211yescharacteristic, complemented
31C2×#556C2212yes—
32C2×#548C2211yescharacteristic
33C2×#537C2211yescharacteristic, complemented
34C22×C22⋊Q8C2211yescharacteristic
35#2847C2211yescharacteristic
36#2843C2214yescomplemented
37#2840C2211yescharacteristic
38#2838C2214yes—
39#2837C2214yescomplemented
40#2835C2212yes—
41#2835C2211yescharacteristic
42#2832C2214yes—
43#2830C2214yescomplemented
44#2829C2214yes—
45#2826C2214yes—
46#2824C2212yes—
47#2824C2214yes—
48#2824C2211yescharacteristic
49#2824C2212yes—
50#2824C2212yes—
51#2824C2212yes—
52#2820C2214yes—
53#2817C2212yes—
54#2817C2212yescomplemented
55#2816C2212yescomplemented
56#2812C2212yes—
57#2812C2211yescharacteristic
58#2808C2214yes—
59#2805C2214yescomplemented
60#2803C2214yes—
61#2800C2214yescomplemented
62#2798C2214yescomplemented
63#2789C2212yescomplemented
64#2786C2214yes—
65#2775C2214yes—
66#2775C2214yescomplemented
67#2774C2214yescomplemented
68#2766C2214yescomplemented
69#2764C2212yes—
70#2764C2212yescomplemented
71#2763C2214yescomplemented
72#2760C2212yes—
73#2758C2214yescomplemented
74#2758C2214yescomplemented
75#2757C2214yes—
76#2753C2214yes—
77#2752C2214yes—
78#2751C2214yescomplemented
79#2751C2214yescomplemented
80#2749C2214yes—
81#2743C2214yes—
82#2742C2214yes—
83#2742C2214yescomplemented
84#2739C2214yescomplemented
85#2738C2214yescomplemented
86#2737C2214yes—
87#2737C2214yes—
88#2737C2214yescomplemented
89#2736C2212yes—
90#2732C2214yes—
91#2730C2214yes—
92#2723C2214yes—
93#2721C2214yes—
94#2721C2214yescomplemented
95#2716C2214yes—
96#2716C2214yescomplemented
97#2714C2214yes—
98#2702C2214yes—
99#2701C2214yes—
100#2700C2214yes—
101#2697C2212yes—
102#2691C2214yescomplemented
103#2689C2214yes—
104#2686C2214yes—
105#2686C2214yescomplemented
106#2685C2214yes—
107#2680C2214yes—
108#2676C2214yes—
109#2672C2214yes—
110#2671C2214yes—
111#2668C2214yes—
112#2663C2214yes—
113#2660C2212yescomplemented
114#2659C2212yescomplemented
115#2654C2214yes—
116#2652C2214yescomplemented
117#2649C2214yes—
118#2649C2214yescomplemented
119#2648C2214yes—
120#2647C2212yescomplemented
121#2640C2212yescomplemented
122#2640C2211yescharacteristic, complemented
123#2638C2212yes—
124#2637C2214yes—
125#2634C2214yescomplemented
126#2632C2214yes—
127#2632C2214yescomplemented
128#2618C2212yes—
129#2616C2211yescharacteristic, complemented
130#2609C2212yescomplemented
131#2607C2212yes—
132#2595C2214yescomplemented
133#2592C2211yescharacteristic, complemented
134#2592C2212yescomplemented
135#2590C2214yescomplemented
136#2581C2212yescomplemented
137#2581C2212yescomplemented
138#2581C2214yescomplemented
139#2580C2212yescomplemented
140#2578C2214yes—
141#2578C2214yes—
142#2578C2214yes—
143#2575C2214yescomplemented
144#2573C2214yescomplemented
145#2572C2214yes—
146#2572C2214yescomplemented
147#2567C2212yescomplemented
148#2563C2211yescharacteristic
149#2563C2212yes—
150#2562C2212yes—
151#2560C2214yes—
152#2559C2214yes—
153#2559C2214yescomplemented
154#2555C2214yes—
155#2543C2212yes—
156#2539C2212yes—
157#2538C2212yes—
158#2538C2212yes—
159#2537C2212yes—
160#2534C2212yes—
161#2533C2214yescomplemented
162#2526C2214yes—
163#2523C2212yes—
164#2523C2214yescomplemented
165#2518C2214yescomplemented
166#2517C2214yes—
167#2515C2214yes—
168#2510C2214yes—
169#2502C2211yescharacteristic, complemented
170#2501C2211yescharacteristic
171#2500C2214yes—
172#2500C2212yescomplemented
173#2499C2212yes—
174#2497C2212yescomplemented
175#2497C2214yescomplemented
176#2496C2212yes—
177#2495C2212yes—
178#2495C2212yes—
179#2495C2212yescomplemented
180#2494C2212yescomplemented
181#2493C2214yescomplemented
182#2492C2212yes—
183#2491C2212yescomplemented
184#2490C2212yes—
185#2490C2214yes—
186#2489C2212yescomplemented
187#2489C2214yescomplemented
188#2487C2212yes—
189#2486C2211yescharacteristic
190#2486C2211yescharacteristic
191#2485C2212yes—
192#2481C2214yes—
193#2480C2214yes—
194#2479C2214yes—
195#2474C2214yescomplemented
196#2472C2214yes—
197#2471C2214yes—
198#2469C2214yes—
199#2465C2214yes—
200#2465C2214yescomplemented
201#2465C2214yescomplemented
202#2458C2214yes—
203#2441C2212yes—
204#2441C2212yescomplemented
205#2440C2212yes—
206#2440C2212yescomplemented
207#2439C2212yes—
208#2439C2212yescomplemented
209#2427C2212yescomplemented
210#2426C2212yes—
211#2426C2214yescomplemented
212#2423C2212yes—
213#2423C2212yescomplemented
214#2421C2212yes—
215#2421C2212yescomplemented
216#2421C2212yescomplemented
217#2420C2212yes—
218#2416C2212yes—
219#2415C2212yes—
220#2415C2212yes—
221#2414C2212yes—
222#2409C2212yes—
223#2407C2212yes—
224#2398C2211yescharacteristic
225#2398C2212yes—
226#2398C2212yes—
227#2398C2212yes—
228#2398C2212yes—
229#2398C2212yes—
230#2396C2214yescomplemented
231#2388C2212yes—
232#2388C2211yescharacteristic
233#2374C2212yes—
234#2363C2212yes—
235#2362C2212yes—
236#2360C2214yes—
237#2360C2212yescomplemented
238#2360C2212yescomplemented
239#2352C2212yes—
240#2352C2212yes—
241#2352C2212yes—
242Q8×C4⋊C4C2212yescomplemented
243#2347C2212yes—
244#2344C2212yescomplemented
245#2341C2212yescomplemented
246Q8×C22⋊C4C2212yes—
247Q8×C22⋊C4C2211yescharacteristic
248#2339C2211yescharacteristic, complemented
249#2333C2214yes—
250#2322C2212yes—
251#2320C2212yescomplemented
252#2320C2212yescomplemented
253#2319C2212yescomplemented
254#2311C2212yescomplemented
255C4×#120C2211yescharacteristic
256C4×#120C2212yes—
257#2280C2212yes—
258#2276C2211yescharacteristic, complemented
259C22×#41C2311yescharacteristic
260C22×#41C2311yescharacteristic
261C23×Q8C2311yescharacteristic
262C24×C4C2311yescharacteristic
263#557—44no—
264#556—48no—
265#548—44no—
266#537—44no—
267C2×C4⋊Q8C2311yescharacteristic
268C2×C4⋊Q8C2312yes—
269C2×C4⋊Q8C2312yes—
270C2×#126C2314yes—
271C2×#126C2314yes—
272C2×#126C2314yes—
273C2×#125C2312yes—
274C2×#125C2314yes—
275C2×#124C2314yes—
276C2×#124C2311yescharacteristic
277C2×#124C2312yes—
278C2×#124C2314yes—
279C2×#123C2312yes—
280C2×#123C2312yes—
281C2×#123C2312yes—
282C2×#123C2312yes—
283C2×C22⋊Q8—44no—
284C2×C22⋊Q8C2312yes—
285C2×C22⋊Q8C2312yes—
286C2×C22⋊Q8C2314yes—
287C2×C22⋊Q8C2312yes—
288C2×C22⋊Q8C2314yes—
289C2×C22⋊Q8C2312yes—
290C2×C22⋊Q8C2311yescharacteristic
291C2×C22⋊Q8C2312yes—
292C2×C22⋊Q8C2312yes—
293C2×C22⋊Q8C2314yes—
294C2×#121C2312yes—
295C2×#121C2314yes—
296C2×#121C2312yes—
297C2×#121C2311yescharacteristic
298C2×#121C2312yes—
299C2×#121C2312yes—
300C2×#121C2314yes—
301C2×#121C2314yes—
302C2×#120C2312yes—
303C2×#120C2311yescharacteristic
304C2×#120C2312yes—
305C2×C4×Q8C2312yes—
306C2×C4×Q8C2311yescharacteristic
307C2×C4×Q8C2311yescharacteristic
308C2×C4×Q8C2312yes—
309C2×C4×Q8C2312yes—
310C2×C4×Q8C2312yes—
311C2×C4×Q8C2312yes—
312C2×C4×Q8C2314yes—
313C2×C4×Q8C2314yes—
314C2×C4×D4C2312yes—
315C2×C4×D4C2312yes—
316C2×C4×D4C2311yescharacteristic
317C2×C4×D4C2312yes—
318C2×C4×D4C2312yes—
319C2×C4×D4C2312yes—
320C2×C4×D4C2312yes—
321C2×#117C2312yes—
322C2×#117C2312yes—
323C2×#117C2312yes—
324C2×#117C2314yes—
325C22×C4⋊C4C2312yes—
326C22×C4⋊C4C2312yes—
327C22×C4⋊C4C2311yescharacteristic
328C22×C4⋊C4C2311yescharacteristic
329C22×C22⋊C4C2312yes—
330#401C2314yes—
331#400C2314yes—
332#400C2314yes—
333#400C2314yes—
334#400C2314yes—
335#400C2314yes—
336#400C2312yes—
337#400C2314yes—
338#400C2312yes—
339#400C2312yes—
340#400C2312yes—
341#400C2312yes—
342#400C2312yes—
343#400C2312yes—
344#400C2312yes—
345#400C2312yes—
346#400C2314yes—
347#400C2314yes—
348#400C2314yes—
349#400C2314yes—
350#400C2314yes—
351#400C2314yes—
352#400C2314yes—
353#400C2314yes—
354#400C2314yes—
355#400C2314yes—
356#399C2314yes—
357#399C2314yes—
358#399C2314yes—
359#399C2314yes—
360#399C2314yes—
361#399C2314yes—
362#399C2314yes—
363#398C2314yes—
364#398C2312yes—
365#398C2312yes—
366#398C2314yes—
367#398C2314yes—
368#398C2314yes—
369#398C2312yes—
370#398C2312yes—
371#398C2314yes—
372#398C2314yes—
373#398C2314yes—
374#398C2314yes—
375#397C2314yes—
376#397C2311yescharacteristic
377#397C2314yes—
378#397C2312yes—
379#397C2311yescharacteristic
380#397C2314yes—
381#397C2312yes—
382#397C2314yes—
383#397C2312yes—
384#397C2312yes—
385#397C2312yes—
386#397C2312yes—
387#397C2314yes—
388#397C2314yes—
389#397C2314yes—
390#397C2314yes—
391#397C2314yes—
392#397C2314yes—
393#397C2314yes—
394#397C2314yes—
395#397C2314yes—
396#397C2314yes—
397#397C2314yes—
398#397C2312yes—
399#397C2312yes—
400#397C2312yes—
401#397C2312yes—
402#397C2312yes—
403#397C2314yes—
404#397C2314yes—
405#397C2314yes—
406#396C2314yes—
407#396C2314yes—
408#396C2314yes—
409#396C2314yes—
410#396C2314yes—
411#396C2314yes—
412#396C2314yes—
413#396C2314yes—
414#396C2314yes—
415#396C2314yes—
416#396C2314yes—
417#395C2314yes—
418#395C2314yes—
419#395C2314yes—
420#395C2314yes—
421#395C2314yes—
422#395C2314yes—
423#395C2311yescharacteristic
424#395C2312yes—
425#395C2314yes—
426#395C2314yes—
427#395C2312yes—
428#395C2314yes—
429#394C2314yes—
430#394C2311yescharacteristic
431#394C2312yes—
432#394C2314yes—
433#394C2314yes—
434#394C2314yes—
435#394C2312yes—
436#394C2312yes—
437#394C2312yes—
438#394C2312yes—
439#394C2312yes—
440#394C2312yes—
441#394C2312yes—
442#394C2314yes—
443#394C2314yes—
444#394C2312yes—
445#394C2312yes—
446#394C2312yes—
447#394C2312yes—
448#394C2312yes—
449#394C2312yes—
450#394C2314yes—
451#394C2314yes—
452#394C2314yes—
453#394C2314yes—
454#394C2314yes—
455#394C2314yes—
456#394C2314yes—
457#394C2314yes—
458#394C2314yes—
459#394C2314yes—
460#394C2314yes—
461#393C2314yes—
462#393C2311yescharacteristic
463#393C2312yes—
464#393C2312yes—
465#393C2312yes—
466#393C2312yes—
467#393C2312yes—
468#393C2312yes—
469#393C2312yes—
470#393C2311yescharacteristic
471#393C2312yes—
472#393C2312yes—
473#393C2314yes—
474#393C2312yes—
475#393C2312yes—
476#393C2312yes—
477#393C2312yes—
478#393C2314yes—
479#393C2314yes—
480#393C2311yescharacteristic
481#393C2312yes—
482#393C2314yes—
483#393C2314yes—
484#392C2312yes—
485#392C2314yes—
486#392C2312yes—
487#392C2312yes—
488#392C2312yes—
489#392C2311yescharacteristic
490#392C2314yes—
491#391C2314yes—
492#391C2314yes—
493#391C2314yes—
494#391C2314yes—
495#391C2312yes—
496#391C2312yes—
497#391C2312yes—
498#391C2312yes—
499#391C2314yes—
500#391C2312yes—
501#391C2314yes—
502#391C2314yes—
503#391C2314yes—
504#390C2314yes—
505#390C2314yes—
506#390C2312yes—
507#390C2314yes—
508#390C2314yes—
509#390C2314yes—
510#390C2312yes—
511#390C2312yes—
512#390C2312yes—
513#390C2314yes—
514#390C2314yes—
515#390C2314yes—
516#390C2314yes—
517#389C2312yes—
518#389C2312yes—
519#389C2312yes—
520#389C2312yes—
521#389C2314yes—
522#389C2312yes—
523#389C2312yes—
524#389C2312yes—
525#389C2312yes—
526#389C2314yes—
527#389C2312yes—
528#389C2312yes—
529#389C2314yes—
530#389C2314yes—
531#389C2314yes—
532#389C2314yes—
533#389C2314yes—
534#389C2314yes—
535#389C2314yes—
536#389C2314yes—
537#389C2314yes—
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#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#388C2314yes—
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#387C2314yes—
598#387C2314yes—
599#387C2314yes—
600#387C2314yes—
601#387C2314yes—
602#387C2314yes—
603#386C2312yes—
604#386C2314yes—
605#386C2314yes—
606#386C2312yes—
607#386C2312yes—
608#386C2311yescharacteristic
609#386C2312yes—
610#386C2314yes—
611#386C2314yes—
612#386C2314yes—
613#386C2314yes—
614#386C2314yes—
615#386C2312yes—
616#386C2314yes—
617#386C2314yes—
618#386C2314yes—
619#386C2314yes—
620#386C2314yes—
621#386C2314yes—
622#386C2314yes—
623#385C2311yescharacteristic
624#385C2312yes—
625#385C2312yes—
626#385C2312yes—
627#385C2312yes—
628#385C2314yes—
629#385C2314yes—
630#385C2314yes—
631#385C2314yes—
632#385C2314yes—
633#385C2314yes—
634#385C2314yes—
635#385C2314yes—
636#385C2314yes—
637#385C2314yes—
638#384C2314yes—
639#384C2312yes—
640#384C2312yes—
641#384C2312yes—
642#383C2314yes—
643#383C2314yes—
644#383C2314yes—
645#383C2314yes—
646#383C2314yes—
647#383C2314yes—
648#382C2312yes—
649#382C2314yes—
650#382C2314yes—
651#382C2314yes—
652#382C2312yes—
653#382C2312yes—
654#382C2312yes—
655#381C2312yes—
656#381C2312yes—
657#381C2312yes—
658#381C2314yes—
659#381C2314yes—
660#381C2314yes—
661#381C2314yes—
662#380C2312yes—
663#380C2312yes—
664#380C2312yes—
665#380C2312yes—
666#380C2312yes—
667#380C2314yes—
668#380C2312yes—
669#380C2314yes—
670#380C2312yes—
671#380C2312yes—
672#380C2314yes—
673#380C2312yes—
674#380C2314yes—
675#380C2311yescharacteristic
676#380C2311yescharacteristic
677#380C2312yes—
678#380C2314yes—
679#380C2312yes—
680#379C2312yes—
681#379C2311yescharacteristic
682#379C2314yes—
683C4×C4⋊C4C2314yes—
684C4×C4⋊C4C2312yes—
685C4×C4⋊C4C2312yes—
686C4×C4⋊C4C2311yescharacteristic
687C4×C4⋊C4C2312yes—
688C4×C4⋊C4C2312yes—
689C4×C4⋊C4C2314yes—
690C4×C4⋊C4C2314yes—
691C4×C4⋊C4C2312yes—
692C4×C22⋊C4C2314yes—
693C4×C22⋊C4C2314yes—
694C4×C22⋊C4C2314yes—
695C4×C22⋊C4C2314yes—
696C4×C22⋊C4C2314yes—
697C4×C22⋊C4C2314yes—
698C4×C22⋊C4C2312yes—
699C4×C22⋊C4C2314yes—
700C4×C22⋊C4C2314yes—
701C4×C22⋊C4C2314yes—
702C4×C22⋊C4C2311yescharacteristic
703C4×C22⋊C4C2312yes—
704C4×C22⋊C4C2311yescharacteristic
705C4×C22⋊C4C2312yes—
706C4×C22⋊C4C2312yes—
707C4×C22⋊C4C2312yes—
708C4×C22⋊C4C2314yes—
709C4×C22⋊C4C2312yes—
710C4×C22⋊C4C2312yes—
711C4×C22⋊C4C2312yes—
712C4×C22⋊C4C2312yes—
713#376C2312yes—
714#376C2311yescharacteristic
715#376C2312yes—
716C2×#95C2312yes—
717C25C2411yescharacteristic
718C2×#41—24no—
719C2×#41—42no—
720C2×#41—44no—
721C2×#41—44no—
722C22×Q8—24no—
723C22×Q8—44no—
724C22×Q8C2411yescharacteristic
725C22×Q8C2411yescharacteristic
726C22×Q8C2412yes—
727C22×Q8C2412yes—
728C22×Q8C2414yes—
729C22×Q8C2411yescharacteristic
730C22×Q8C2412yes—
731C22×Q8C2411yescharacteristic
732C22×D4C2411yescharacteristic
733C22×D4C2412yes—
734C22×D4C2411yescharacteristic
735C22×D4C2412yes—
736C22×D4C2412yes—
737C22×D4C2412yes—
738C22×D4C2412yes—
739C22×D4C2412yes—
740C22×D4C2414yes—
741C22×D4C2414yes—
742C22×D4C2411yescharacteristic
743C22×D4C2412yes—
744C23×C4—42no—
745C23×C4—44no—
746C23×C4C2412yes—
747C23×C4C2411yescharacteristic
748C23×C4C2411yescharacteristic
749C23×C4C2412yes—
750C23×C4C2412yes—
751C23×C4C2412yes—
752C23×C4C2412yes—
753C23×C4C2411yescharacteristic
754C23×C4C2414yes—
755C23×C4C2412yes—
756C23×C4C2414yes—
757C23×C4C2412yes—
758C4⋊Q8—44no—
759C4⋊Q8—42no—
760C4⋊Q8—44no—
761#126—48no—
762#126—48no—
763#126—84no—
764#125—44no—
765#125—48no—
766#124—48no—
767#124—42no—
768#124—44no—
769#124—84no—
770#123—44no—
771#123—44no—
772#123—82no—
773#123—82no—
774C22⋊Q8—28no—
775C22⋊Q8—28no—
776C22⋊Q8—48no—
777C22⋊Q8—48no—
778C22⋊Q8—44no—
779C22⋊Q8—44no—
780C22⋊Q8—44no—
781C22⋊Q8—42no—
782C22⋊Q8—44no—
783C22⋊Q8—84no—
784#121—44no—
785#121—48no—
786#121—48no—
787#121—44no—
788#121—44no—
789#121—42no—
790#121—44no—
791#121—84no—
792#120—44no—
793#120—42no—
794#120—82no—
795C4×Q8—24no—
796C4×Q8—28no—
797C4×Q8—44no—
798C4×Q8—42no—
799C4×Q8—44no—
800C4×Q8—48no—
801C4×Q8—44no—
802C4×Q8—44no—
803C4×Q8—84no—
804C4×D4—44no—
805C4×D4—44no—
806C4×D4—44no—
807C4×D4—44no—
808C4×D4—42no—
809C4×D4—44no—
810C4×D4—44no—
811#117—44no—
812#117—44no—
813#117—44no—
814#117—84no—
815C2×C4⋊C4—44no—
816C2×C4⋊C4—42no—
817C2×C4⋊C4—44no—
818C2×C4⋊C4—42no—
819C2×C4⋊C4C2412yes—
820C2×C4⋊C4C2412yes—
821C2×C4⋊C4C2412yes—
822C2×C4⋊C4C2412yes—
823C2×C4⋊C4C2414yes—
824C2×C4⋊C4C2412yes—
825C2×C4⋊C4C2412yes—
826C2×C4⋊C4C2414yes—
827C2×C4⋊C4C2411yescharacteristic
828C2×C4⋊C4C2412yes—
829C2×C4⋊C4C2414yes—
830C2×C4⋊C4C2412yes—
831C2×C4⋊C4C2414yes—
832C2×C4⋊C4C2412yes—
833C2×C4⋊C4C2414yes—
834C2×C4⋊C4C2414yes—
835C2×C4⋊C4C2414yes—
836C2×C4⋊C4C2412yes—
837C2×C4⋊C4C2411yescharacteristic
838C2×C4⋊C4C2412yes—
839C2×C4⋊C4C2412yes—
840C2×C4⋊C4C2412yes—
841C2×C4⋊C4C2412yes—
842C2×C4⋊C4C2411yescharacteristic
843C2×C4⋊C4C2414yes—
844C2×C4⋊C4C2414yes—
845C2×C4⋊C4C2412yes—
846C2×C4⋊C4C2414yes—
847C2×C4⋊C4C2414yes—
848C2×C4⋊C4C2414yes—
849C2×C4⋊C4C2414yes—
850C2×C4⋊C4C2412yes—
851C2×C4⋊C4C2412yes—
852C2×C4⋊C4C2412yes—
853C2×C4⋊C4C2414yes—
854C2×C4⋊C4C2414yes—
855C2×C4⋊C4C2414yes—
856C2×C4⋊C4C2414yes—
857C2×C4⋊C4C2414yes—
858C2×C4⋊C4C2414yes—
859C2×C4⋊C4C2414yes—
860C2×C4⋊C4C2414yes—
861C2×C4⋊C4C2414yes—
862C2×C4⋊C4C2412yes—
863C2×C4⋊C4C2414yes—
864C2×C4⋊C4C2414yes—
865C2×C4⋊C4C2414yes—
866C2×C4⋊C4C2414yes—
867C2×C4⋊C4C2414yes—
868C2×C22⋊C4—44no—
869C2×C22⋊C4C2414yes—
870C2×C22⋊C4C2412yes—
871C2×C22⋊C4C2411yescharacteristic
872C2×C22⋊C4C2414yes—
873C2×C22⋊C4C2414yes—
874C2×C22⋊C4C2414yes—
875C2×C22⋊C4C2412yes—
876C2×C22⋊C4C2414yes—
877C2×C22⋊C4C2414yes—
878C2×C22⋊C4C2414yes—
879C2×C22⋊C4C2414yes—
880C2×C22⋊C4C2411yescharacteristic
881C2×C22⋊C4C2411yescharacteristic
882C2×C22⋊C4C2412yes—
883C2×C22⋊C4C2412yes—
884C2×C22⋊C4C2412yes—
885C2×C22⋊C4C2412yes—
886C2×C22⋊C4C2412yes—
887C2×C22⋊C4C2412yes—
888C2×C22⋊C4C2412yes—
889C2×C22⋊C4C2412yes—
890C2×C22⋊C4C2414yes—
891C2×C22⋊C4C2412yes—
892C2×C22⋊C4C2412yes—
893C2×C22⋊C4C2414yes—
894C2×C22⋊C4C2412yes—
895C2×C22⋊C4C2412yes—
896C2×C22⋊C4C2412yes—
897C2×C22⋊C4C2414yes—
898C2×C22⋊C4C2412yes—
899C2×C22⋊C4C2412yes—
900C2×C22⋊C4C2412yes—
901C2×C22⋊C4C2414yes—
902C2×C22⋊C4C2414yes—
903C2×C22⋊C4C2414yes—
904C2×C22⋊C4C2414yes—
905C2×C22⋊C4C2412yes—
906C2×C22⋊C4C2414yes—
907C2×C22⋊C4C2414yes—
908C2×C22⋊C4C2411yescharacteristic
909C2×C22⋊C4C2414yes—
910C2×C22⋊C4C2412yes—
911C2×C22⋊C4C2414yes—
912C2×C22⋊C4C2412yes—
913C2×C22⋊C4C2412yes—
914C2×C22⋊C4C2414yes—
915C2×C22⋊C4C2412yes—
916C2×C22⋊C4C2412yes—
917C2×C22⋊C4C2412yes—
918C2×C22⋊C4C2414yes—
919C2×C22⋊C4C2412yes—
920C2×C22⋊C4C2412yes—
921C2×C22⋊C4C2414yes—
922C2×C22⋊C4C2414yes—
923C2×C22⋊C4C2412yes—
924C2×C22⋊C4C2412yes—
925C2×C22⋊C4C2412yes—
926C2×C22⋊C4C2412yes—
927C2×C22⋊C4C2414yes—
928C2×C22⋊C4C2414yes—
929C2×C22⋊C4C2414yes—
930C2×C42C2412yes—
931C2×C42C2411yescharacteristic
932C2×C42C2412yes—
933C2×C42C2412yes—
934C2×C42C2412yes—
935C2×C42C2412yes—
936C2×C42C2414yes—
937C2×C42C2412yes—
938C2×C42C2414yes—
939C2×C42C2414yes—
940C2×C42C2414yes—
941C2×C42C2414yes—
942C2×C42C2414yes—
943C2×C42C2414yes—
944C2×C42C2414yes—
945C2×C42C2414yes—
946C2×C42C2414yes—
947#95C2411yescharacteristic
948#95C2412yes—
949#95C2414yes—
950#95C2411yescharacteristic
951#95C2412yes—
952#95C2414yes—
953#95C2411yescharacteristic
954#95C2412yes—
955#95C2412yes—
956#95C2412yes—
957#95C2412yes—
958#95C2412yes—
959#95C2412yes—
960#95C2412yes—
961#95C2414yes—
962#95C2412yes—
963#95C2412yes—
964#95C2414yes—
965#95C2412yes—
966#95C2414yes—
967#95C2412yes—
968#95C2414yes—
969#95C2414yes—
970#95C2414yes—
971#95C2414yes—
972#95C2414yes—
973#95C2414yes—
974#95C2412yes—
975#95C2411yescharacteristic
976#95C2414yes—
977#95C2414yes—
978#95C2414yes—
979#95C2414yes—
980#95C2414yes—
981#95C2414yes—
982#95C2414yes—
983#95C2412yes—
984#95C2412yes—
985#95C2412yes—
986#95C2414yes—
987#95C2412yes—
988#95C2412yes—
989#95C2412yes—
990#95C2412yes—
991#95C2412yes—
992#95C2414yes—
993#95C2412yes—
994#95C2412yes—
995#95C2414yes—
996#95C2414yes—
997#95C2414yes—
998#95C2414yes—
999#95C2414yes—
1000#95C2414yes—
1001#95C2414yes—
1002#95C2412yes—
1003#95C2414yes—
1004#95C2414yes—
1005#95C2414yes—
1006#95C2414yes—
1007#95C2414yes—
1008#95C2414yes—
1009#95C2414yes—
1010#95C2414yes—
1011#95C2414yes—
1012#95C2414yes—
1013#95C2414yes—
1014#95C2414yes—
1015#95C2414yes—
1016C24—22no—
1017C24—41no—
1018C24—42no—
1019C24—41no—
1020C24—42no—
1021C24C2512yes—
1022C24C2512yes—
1023C24C2512yes—
1024C24C2511yescharacteristic
1025C24C2511yescharacteristic
1026#41—88no—
1027#41—88no—
1028C2×Q8—22no—
1029C2×Q8—24no—
1030C2×Q8—24no—
1031C2×Q8—24no—
1032C2×Q8—42no—
1033C2×Q8—42no—
1034C2×Q8—42no—
1035C2×Q8—44no—
1036C2×Q8—42no—
1037C2×Q8—41no—
1038C2×Q8—41no—
1039C2×Q8—44no—
1040C2×Q8—44no—
1041C2×Q8—44no—
1042C2×Q8—42no—
1043C2×Q8—44no—
1044C2×Q8—42no—
1045C2×Q8—88no—
1046C2×Q8H(5,𝔽2)14yes—
1047C2×D4—24no—
1048C2×D4—22no—
1049C2×D4—24no—
1050C2×D4—22no—
1051C2×D4—24no—
1052C2×D4—24no—
1053C2×D4—42no—
1054C2×D4—41no—
1055C2×D4—42no—
1056C2×D4—42no—
1057C2×D4—42no—
1058C2×D4—42no—
1059C2×D4—42no—
1060C2×D4—42no—
1061C2×D4—42no—
1062C2×D4—42no—
1063C2×D4—42no—
1064C2×D4—41no—
1065C2×D4—42no—
1066C2×D4—41no—
1067C2×D4—42no—
1068C2×D4—42no—
1069C2×D4—42no—
1070C2×D4—44no—
1071C2×D4—42no—
1072C2×D4—42no—
1073C2×D4—42no—
1074C2×D4—44no—
1075C2×D4—44no—
1076C2×D4—44no—
1077C2×D4—44no—
1078C2×D4—44no—
1079C2×D4—44no—
1080C22×C4—24no—
1081C22×C4—22no—
1082C22×C4—22no—
1083C22×C4—24no—
1084C22×C4—24no—
1085C22×C4—24no—
1086C22×C4—24no—
1087C22×C4—24no—
1088C22×C4—24no—
1089C22×C4—24no—
1090C22×C4—24no—
1091C22×C4—24no—
1092C22×C4—24no—
1093C22×C4—42no—
1094C22×C4—41no—
1095C22×C4—44no—
1096C22×C4—44no—
1097C22×C4—42no—
1098C22×C4—42no—
1099C22×C4—42no—
1100C22×C4—42no—
1101C22×C4—42no—
1102C22×C4—44no—
1103C22×C4—44no—
1104C22×C4—44no—
1105C22×C4—42no—
1106C22×C4—44no—
1107C22×C4—44no—
1108C22×C4—42no—
1109C22×C4—42no—
1110C22×C4—44no—
1111C22×C4—88no—
1112C22×C4C2512yes—
1113C22×C4C2511yescharacteristic
1114C22×C4C2511yescharacteristic
1115C22×C4C2511yescharacteristic
1116C22×C4C2512yes—
1117C22×C4C2512yes—
1118C22×C4C2514yes—
1119C22×C4C2514yes—
1120C22×C4C2514yes—
1121C22×C4C2512yes—
1122C22×C4C2514yes—
1123C22×C4C2512yes—
1124C22×C4C2512yes—
1125C22×C4C2512yes—
1126C22×C4C2512yes—
1127C22×C4C2512yes—
1128C22×C4C2512yes—
1129C22×C4C2512yes—
1130C22×C4C2514yes—
1131C22×C4C2514yes—
1132C22×C4C2512yes—
1133C22×C4C2511yescharacteristic
1134C22×C4C2512yes—
1135C22×C4C2511yescharacteristic
1136C4⋊C4—24no—
1137C4⋊C4—24no—
1138C4⋊C4—28no—
1139C4⋊C4—24no—
1140C4⋊C4—24no—
1141C4⋊C4—22no—
1142C4⋊C4—28no—
1143C4⋊C4—28no—
1144C4⋊C4—24no—
1145C4⋊C4—24no—
1146C4⋊C4—24no—
1147C4⋊C4—44no—
1148C4⋊C4—42no—
1149C4⋊C4—44no—
1150C4⋊C4—42no—
1151C4⋊C4—44no—
1152C4⋊C4—44no—
1153C4⋊C4—44no—
1154C4⋊C4—44no—
1155C4⋊C4—44no—
1156C4⋊C4—42no—
1157C4⋊C4—42no—
1158C4⋊C4—42no—
1159C4⋊C4—42no—
1160C4⋊C4—42no—
1161C4⋊C4—41no—
1162C4⋊C4—44no—
1163C4⋊C4—42no—
1164C4⋊C4—42no—
1165C4⋊C4—42no—
1166C4⋊C4—44no—
1167C4⋊C4—41no—
1168C4⋊C4—44no—
1169C4⋊C4—42no—
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—44no—
1179C4⋊C4—44no—
1180C4⋊C4—44no—
1181C4⋊C4—44no—
1182C4⋊C4—42no—
1183C4⋊C4—44no—
1184C4⋊C4—44no—
1185C22⋊C4—24no—
1186C22⋊C4—22no—
1187C22⋊C4—28no—
1188C22⋊C4—28no—
1189C22⋊C4—28no—
1190C22⋊C4—44no—
1191C22⋊C4—42no—
1192C22⋊C4—42no—
1193C22⋊C4—44no—
1194C22⋊C4—44no—
1195C22⋊C4—42no—
1196C22⋊C4—44no—
1197C22⋊C4—44no—
1198C22⋊C4—44no—
1199C22⋊C4—44no—
1200C22⋊C4—42no—
1201C22⋊C4—42no—
1202C22⋊C4—42no—
1203C22⋊C4—44no—
1204C22⋊C4—42no—
1205C22⋊C4—42no—
1206C22⋊C4—42no—
1207C22⋊C4—44no—
1208C22⋊C4—44no—
1209C22⋊C4—44no—
1210C22⋊C4—42no—
1211C22⋊C4—44no—
1212C22⋊C4—44no—
1213C22⋊C4—42no—
1214C22⋊C4—42no—
1215C22⋊C4—42no—
1216C22⋊C4—42no—
1217C22⋊C4—42no—
1218C22⋊C4—42no—
1219C22⋊C4—41no—
1220C22⋊C4—42no—
1221C22⋊C4—41no—
1222C22⋊C4—42no—
1223C22⋊C4—42no—
1224C22⋊C4—42no—
1225C22⋊C4—42no—
1226C22⋊C4—42no—
1227C22⋊C4—42no—
1228C22⋊C4—44no—
1229C22⋊C4—44no—
1230C22⋊C4—44no—
1231C22⋊C4—44no—
1232C22⋊C4—42no—
1233C22⋊C4—42no—
1234C22⋊C4—42no—
1235C22⋊C4—44no—
1236C22⋊C4—44no—
1237C22⋊C4—44no—
1238C22⋊C4—42no—
1239C22⋊C4—44no—
1240C22⋊C4—44no—
1241C22⋊C4—42no—
1242C22⋊C4—41no—
1243C22⋊C4—44no—
1244C22⋊C4—42no—
1245C22⋊C4—42no—
1246C42—24no—
1247C42—22no—
1248C42—24no—
1249C42—28no—
1250C42—24no—
1251C42—24no—
1252C42—24no—
1253C42—44no—
1254C42—44no—
1255C42—44no—
1256C42—44no—
1257C42—42no—
1258C42—44no—
1259C42—44no—
1260C42—44no—
1261C42—44no—
1262C42—44no—
1263C23—21no—
1264C23—22no—
1265C23—21no—
1266C23—22no—
1267C23—22no—
1268C23—22no—
1269C23—22no—
1270C23—21no—
1271C23—22no—
1272C23—22no—
1273C23—22no—
1274C23—24no—
1275C23—21no—
1276C23—22no—
1277C23—22no—
1278C23—22no—
1279C23—22no—
1280C23—22no—
1281C23—21no—
1282C23—22no—
1283C23—22no—
1284C23—22no—
1285C23—22no—
1286C23—22no—
1287C23—24no—
1288C23—22no—
1289C23—22no—
1290C23—22no—
1291C23—44no—
1292C23—82no—
1293C23—84no—
1294C23—82no—
1295C23—84no—
1296C23#58512yes—
1297C23C2611yescharacteristic
1298Q8—28no—
1299Q8—48no—
1300Q8—44no—
1301Q8—84no—
1302Q8—84no—
1303Q8—82no—
1304Q8—88no—
1305Q8—82no—
1306D4—44no—
1307D4—84no—
1308D4—82no—
1309D4—84no—
1310D4—84no—
1311D4—84no—
1312D4—84no—
1313D4—84no—
1314D4—82no—
1315D4—84no—
1316D4—164no—
1317D4—164no—
1318C2×C4—24no—
1319C2×C4—21no—
1320C2×C4—22no—
1321C2×C4—24no—
1322C2×C4—22no—
1323C2×C4—21no—
1324C2×C4—22no—
1325C2×C4—22no—
1326C2×C4—22no—
1327C2×C4—24no—
1328C2×C4—24no—
1329C2×C4—22no—
1330C2×C4—21no—
1331C2×C4—21no—
1332C2×C4—22no—
1333C2×C4—22no—
1334C2×C4—22no—
1335C2×C4—22no—
1336C2×C4—22no—
1337C2×C4—22no—
1338C2×C4—24no—
1339C2×C4—22no—
1340C2×C4—24no—
1341C2×C4—24no—
1342C2×C4—24no—
1343C2×C4—22no—
1344C2×C4—24no—
1345C2×C4—22no—
1346C2×C4—22no—
1347C2×C4—24no—
1348C2×C4—22no—
1349C2×C4—21no—
1350C2×C4—22no—
1351C2×C4—22no—
1352C2×C4—24no—
1353C2×C4—22no—
1354C2×C4—22no—
1355C2×C4—22no—
1356C2×C4—22no—
1357C2×C4—24no—
1358C2×C4—22no—
1359C2×C4—21no—
1360C2×C4—22no—
1361C2×C4—22no—
1362C2×C4—22no—
1363C2×C4—24no—
1364C2×C4—24no—
1365C2×C4—22no—
1366C2×C4—24no—
1367C2×C4—22no—
1368C2×C4—24no—
1369C2×C4—24no—
1370C2×C4—22no—
1371C2×C4—22no—
1372C2×C4—24no—
1373C2×C4—22no—
1374C2×C4—24no—
1375C2×C4—22no—
1376C2×C4—22no—
1377C2×C4—22no—
1378C2×C4—24no—
1379C2×C4—22no—
1380C2×C4—22no—
1381C2×C4—48no—
1382C2×C4—44no—
1383C2×C4—48no—
1384C2×C4—44no—
1385C2×C4—84no—
1386C2×C4—84no—
1387C2×C4—84no—
1388C2×C4—88no—
1389C2×C4—82no—
1390C2×C4—84no—
1391C2×C4—162no—
1392C2×C4—164no—
1393C2×C4C2×H(5,𝔽2)14yes—
1394C2×C4C2×H(5,𝔽2)12yes—
1395C2×C4#58514yes—
1396C22—22no—
1397C22—24no—
1398C22—41no—
1399C22—42no—
1400C22—41no—
1401C22—42no—
1402C22—41no—
1403C22—42no—
1404C22—42no—
1405C22—42no—
1406C22—42no—
1407C22—44no—
1408C22—42no—
1409C22—42no—
1410C22—42no—
1411C22—42no—
1412C22—42no—
1413C22—41no—
1414C22—42no—
1415C22—41no—
1416C22—42no—
1417C22—42no—
1418C22—42no—
1419C22—44no—
1420C22—42no—
1421C22—42no—
1422C22—42no—
1423C22—42no—
1424C22—42no—
1425C22—88no—
1426C22C22×H(5,𝔽2)11yescharacteristic
1427C22C2×#58512yes—
1428C22C2×#58511yescharacteristic
1429C22H(7,𝔽2)11yescharacteristic
1430C222−1+612yes—
1431C4—24no—
1432C4—42no—
1433C4—41no—
1434C4—41no—
1435C4—42no—
1436C4—42no—
1437C4—44no—
1438C4—44no—
1439C4—42no—
1440C4—42no—
1441C4—42no—
1442C4—44no—
1443C4—42no—
1444C4—41no—
1445C4—44no—
1446C4—44no—
1447C4—41no—
1448C4—42no—
1449C4—42no—
1450C4—44no—
1451C4—42no—
1452C4—42no—
1453C4—42no—
1454C4#354514yes—
1455C2—42no—
1456C2—81no—
1457C2—82no—
1458C2—82no—
1459C2—82no—
1460C2C2×#354511yescharacteristic
1461C2#6289911yescharacteristic
1462C2#6291112yes—
1463C2#6304312yes—
1464C2#6304411yescharacteristic
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. #59201C2semidirect
2. #59025C2semidirect
3. #58860C2semidirect
4. #57465C2semidirect
5. #55529C2semidirect
6. #54536C2semidirect
7. #54089C2semidirect
8. #53079C2semidirect
9. #53031C2semidirect
10. #52943C2semidirect
11. #52923C2semidirect
12. #46935C2semidirect
13. #45420C2semidirect
14. #45401C2semidirect
15. #45258C2semidirect
16. #45251C2semidirect
17. #45009C2semidirect
18. #42984C2semidirect
19. #42891C2semidirect
20. #42653C2semidirect
21. #42515C2semidirect
22. #42513C2semidirect
23. #41879C2semidirect
24. #41679C2semidirect
25. #39910C2semidirect
26. #39133C2semidirect
27. #36675C2semidirect
28. #35945C2semidirect
29. #35854C2semidirect
30. C2×#557C22semidirect
33. C2×#537C22semidirect
36. #2843C22semidirect
39. #2837C22semidirect
43. #2830C22semidirect
54. #2817C22semidirect
55. #2816C22semidirect
59. #2805C22semidirect
61. #2800C22semidirect
62. #2798C22semidirect
63. #2789C22semidirect
66. #2775C22semidirect
67. #2774C22semidirect
68. #2766C22semidirect
70. #2764C22semidirect
71. #2763C22semidirect
73. #2758C22semidirect
74. #2758C22semidirect
78. #2751C22semidirect
79. #2751C22semidirect
83. #2742C22semidirect
84. #2739C22semidirect
85. #2738C22semidirect
88. #2737C22semidirect
94. #2721C22semidirect
96. #2716C22semidirect
102. #2691C22semidirect
105. #2686C22semidirect
113. #2660C22semidirect
114. #2659C22semidirect
116. #2652C22semidirect
118. #2649C22semidirect
120. #2647C22semidirect
121. #2640C22semidirect
122. #2640C22semidirect
125. #2634C22semidirect
127. #2632C22semidirect
129. #2616C22semidirect
130. #2609C22semidirect
132. #2595C22semidirect
133. #2592C22semidirect
134. #2592C22semidirect
135. #2590C22semidirect
136. #2581C22semidirect
137. #2581C22semidirect
138. #2581C22semidirect
139. #2580C22semidirect
143. #2575C22semidirect
144. #2573C22semidirect
146. #2572C22semidirect
147. #2567C22semidirect
153. #2559C22semidirect
161. #2533C22semidirect
164. #2523C22semidirect
165. #2518C22semidirect
169. #2502C22semidirect
172. #2500C22semidirect
174. #2497C22semidirect
175. #2497C22semidirect
179. #2495C22semidirect
180. #2494C22semidirect
181. #2493C22semidirect
183. #2491C22semidirect
186. #2489C22semidirect
187. #2489C22semidirect
195. #2474C22semidirect
200. #2465C22semidirect
201. #2465C22semidirect
204. #2441C22semidirect
206. #2440C22semidirect
208. #2439C22semidirect
209. #2427C22semidirect
211. #2426C22semidirect
213. #2423C22semidirect
215. #2421C22semidirect
216. #2421C22semidirect
230. #2396C22semidirect
237. #2360C22semidirect
238. #2360C22semidirect
242. Q8×C4⋊C4C22semidirect
244. #2344C22semidirect
245. #2341C22semidirect
248. #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
#592012
#590252
#588602
#574652
#555292
#545362
#540892
#530792
#530312
#529432
#529232
#469352
#454202
#454012
#452582
#452512
#450092
#429842
#428912
#426532
#425152
#425132
#418792
#416792
#399102
#391332
#366752
#359452
#358542