Finite Group Databasebeta

← #8749951

Subgroups — #8749951

Order 512.

4691 conjugacy classes of subgroups.

The subgroup lattice has 1451 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59842C212yesmaximal, complemented
2#59841C211yesmaximal, characteristic, complemented
3#58012C214yesmaximal, complemented
4#57482C214yesmaximal, complemented
5#56358C214yesmaximal, complemented
6#55001C214yesmaximal, complemented
7#53490C212yesmaximal, complemented
8#53099C211yesmaximal, characteristic, complemented
9#53089C212yesmaximal, complemented
10#52549C212yesmaximal, complemented
11#52503C214yesmaximal, complemented
12#47802C212yesmaximal, complemented
13#45364C211yesmaximal, characteristic, complemented
14#45027C212yesmaximal, complemented
15#44943C212yesmaximal, complemented
16#44888C212yesmaximal, complemented
17#44880C212yesmaximal, complemented
18#42970C214yesmaximal, complemented
19#42618C212yesmaximal, complemented
20#42588C212yesmaximal, complemented
21#42489C212yesmaximal, complemented
22#42479C211yesmaximal, characteristic, complemented
23#42439C212yesmaximal, complemented
24#42167C212yesmaximal, complemented
25#39497C212yesmaximal, complemented
26#39489C211yesmaximal, characteristic, complemented
27#36698C211yesmaximal, characteristic, complemented
28#35950C211yesmaximal, characteristic, complemented
29#35916C212yesmaximal, complemented
30C2×#555C2211yescharacteristic
31C2×#555C2212yes—
32C2×#554C2211yescharacteristic
33C2×#554C2211yescharacteristic
34C2×#552C2214yes—
35C2×#550C2211yescharacteristic
36C2×#540C2212yes—
37#2868C2211yescharacteristic
38#2844C2211yescharacteristic
39#2841C2214yes—
40#2838C2214yes—
41#2838C2212yes—
42#2838C2212yes—
43#2837C2214yes—
44#2836C2212yes—
45#2836C2212yes—
46#2833C2212yes—
47#2830C2214yes—
48#2830C2212yes—
49#2830C2211yescharacteristic
50#2830C2211yescharacteristic
51#2829C2214yes—
52#2827C2214yes—
53#2823C2212yes—
54#2822C2211yescharacteristic
55#2820C2214yes—
56#2820C2212yes—
57#2816C2212yes—
58#2814C2214yes—
59#2814C2214yes—
60#2811C2212yes—
61#2806C2214yes—
62#2802C2214yes—
63#2795C2214yes—
64#2792C2212yes—
65#2792C2214yes—
66#2791C2214yes—
67#2790C2214yes—
68#2790C2214yes—
69#2788C2214yes—
70#2787C2214yes—
71#2780C2214yes—
72#2765C2214yes—
73#2765C2214yes—
74#2765C2214yes—
75#2745C2214yes—
76#2745C2214yes—
77#2731C2212yes—
78#2729C2214yes—
79#2729C2214yes—
80#2726C2214yes—
81#2725C2214yes—
82#2715C2214yes—
83#2715C2214yes—
84#2710C2214yes—
85#2710C2214yes—
86#2708C2214yes—
87#2707C2214yes—
88#2704C2214yes—
89#2702C2214yes—
90#2702C2214yes—
91#2701C2214yes—
92#2700C2214yes—
93#2699C2212yes—
94#2692C2214yes—
95#2692C2214yes—
96#2691C2214yes—
97#2691C2214yes—
98#2687C2214yes—
99#2687C2214yes—
100#2686C2214yes—
101#2683C2212yes—
102#2682C2214yes—
103#2681C2214yes—
104#2681C2214yes—
105#2680C2212yes—
106#2680C2214yes—
107#2674C2214yes—
108#2674C2214yes—
109#2672C2214yes—
110#2672C2214yes—
111#2672C2214yes—
112#2671C2214yes—
113#2671C2214yes—
114#2667C2214yes—
115#2660C2211yescharacteristic
116#2659C2212yes—
117#2653C2214yes—
118#2653C2214yes—
119#2653C2214yes—
120#2644C2212yes—
121#2641C2211yescharacteristic
122#2637C2214yes—
123#2629C2214yes—
124#2629C2212yes—
125#2629C2214yes—
126#2620C2214yes—
127#2620C2212yes—
128#2620C2214yes—
129#2618C2214yes—
130#2618C2212yes—
131#2616C2212yes—
132#2609C2214yes—
133#2609C2212yes—
134#2609C2214yes—
135#2595C2214yes—
136#2586C2212yes—
137#2584C2212yes—
138#2584C2211yescharacteristic
139#2584C2211yescharacteristic
140#2583C2212yes—
141#2583C2214yes—
142#2582C2212yes—
143#2571C2212yes—
144#2567C2211yescharacteristic
145#2566C2212yes—
146#2566C2212yes—
147#2563C2211yescharacteristic
148#2557C2214yes—
149#2552C2212yes—
150#2552C2212yes—
151#2550C2212yes—
152#2550C2212yes—
153#2550C2212yes—
154#2549C2214yes—
155#2548C2211yescharacteristic
156#2546C2211yescharacteristic
157#2538C2212yes—
158#2522C2214yes—
159#2512C2212yes—
160#2512C2212yes—
161#2507C2212yes—
162#2507C2212yes—
163#2507C2212yes—
164#2506C2212yes—
165#2506C2212yes—
166#2502C2212yes—
167#2501C2212yes—
168#2500C2212yes—
169#2499C2212yes—
170#2494C2212yes—
171#2491C2212yes—
172#2491C2212yes—
173#2490C2212yes—
174#2481C2214yes—
175#2477C2214yes—
176#2476C2214yes—
177#2470C2214yes—
178#2470C2214yes—
179#2470C2214yes—
180#2460C2214yes—
181#2459C2214yes—
182#2458C2214yes—
183#2454C2214yes—
184#2454C2212yes—
185#2452C2212yes—
186#2452C2212yes—
187#2452C2212yes—
188#2452C2212yes—
189#2451C2214yes—
190#2450C2214yes—
191#2445C2212yes—
192#2445C2212yes—
193#2445C2212yes—
194#2445C2212yes—
195#2441C2214yes—
196#2441C2212yes—
197#2441C2212yes—
198#2441C2212yes—
199#2440C2214yes—
200#2440C2214yes—
201#2440C2212yes—
202#2439C2214yes—
203#2438C2214yes—
204#2430C2214yes—
205#2428C2212yes—
206#2428C2212yes—
207#2427C2214yes—
208#2427C2214yes—
209#2426C2214yes—
210#2425C2214yes—
211#2425C2214yes—
212#2422C2212yes—
213#2422C2212yes—
214#2420C2212yes—
215#2420C2212yes—
216#2419C2214yes—
217#2417C2214yes—
218#2416C2214yes—
219#2416C2214yes—
220#2416C2212yes—
221#2415C2214yes—
222#2413C2214yes—
223#2413C2214yes—
224#2406C2212yes—
225#2406C2214yes—
226#2401C2212yes—
227#2401C2212yes—
228#2399C2211yescharacteristic
229#2399C2211yescharacteristic
230#2396C2212yes—
231#2396C2212yes—
232#2395C2212yes—
233#2392C2214yes—
234C2×#398C2212yes—
235#2369C2212yes—
236#2366C2212yes—
237#2365C2212yes—
238#2363C2212yes—
239#2361C2212yes—
240#2361C2212yes—
241#2354C2212yes—
242#2354C2212yes—
243#2349C2212yes—
244D4×C4⋊C4C2212yes—
245D4×C4⋊C4C2212yes—
246#2345C2212yes—
247#2344C2212yes—
248#2331C2212yes—
249#2324C2212yes—
250#2319C2211yescharacteristic
251#2317C2212yes—
252#2317C2214yes—
253#2316C2212yes—
254C4×#125C2212yes—
255C4×#124C2211yescharacteristic
256#2293C2211yescharacteristic
257#2293C2212yes—
258#2275C2211yescharacteristic
259C22×#41C2312yes—
260#555—48no—
261#555—44no—
262#554—44no—
263#554—44no—
264#552—416no—
265#550—44no—
266#540—48no—
267C2×C4⋊Q8C2312yes—
268C2×C4⋊Q8C2311yescharacteristic
269C2×C4⋊Q8C2311yescharacteristic
270C2×C4⋊Q8C2311yescharacteristic
271C2×C4⋊Q8C2312yes—
272C2×C4⋊Q8C2314yes—
273C2×#127C2312yes—
274C2×#127C2311yescharacteristic
275C2×#126C2314yes—
276C2×#126C2314yes—
277C2×#125C2312yes—
278C2×#125C2314yes—
279C2×#125C2312yes—
280C2×#125C2312yes—
281C2×#125C2311yescharacteristic
282C2×#125C2311yescharacteristic
283C2×#125C2314yes—
284C2×#124C2311yescharacteristic
285C2×#124C2314yes—
286C2×#124C2312yes—
287C2×#124C2314yes—
288C2×#124C2314yes—
289C2×#123C2314yes—
290C2×#123C2314yes—
291C2×#123C2314yes—
292C2×#123C2314yes—
293C2×#123C2314yes—
294C2×#123C2314yes—
295C2×#123C2314yes—
296C2×#123C2314yes—
297C2×C22⋊Q8C2312yes—
298C2×C22⋊Q8C2312yes—
299C2×C22⋊Q8C2312yes—
300C2×C22⋊Q8C2314yes—
301C2×C22⋊Q8C2314yes—
302C2×C22⋊Q8C2312yes—
303C2×C22⋊Q8C2314yes—
304C2×C22⋊Q8C2314yes—
305C2×C22⋊Q8C2314yes—
306C2×C22⋊Q8C2314yes—
307C2×C22⋊Q8C2314yes—
308C2×#121C2312yes—
309C2×#121C2312yes—
310C2×#121C2312yes—
311C2×#121C2314yes—
312C2×#121C2312yes—
313C2×#121C2314yes—
314C2×#121C2314yes—
315C2×#121C2314yes—
316C2×#121C2314yes—
317C2×#121C2312yes—
318C2×#121C2314yes—
319C2×C4×Q8C2311yescharacteristic
320C2×C4×Q8C2314yes—
321C2×C4×Q8C2311yescharacteristic
322C2×C4×Q8C2311yescharacteristic
323C2×C4×D4C2311yescharacteristic
324C2×C4×D4C2311yescharacteristic
325C2×C4×D4C2312yes—
326C2×C4×D4C2312yes—
327C2×C4×D4C2312yes—
328C2×C4×D4C2311yescharacteristic
329C2×C4×D4C2311yescharacteristic
330C2×C4×D4C2312yes—
331C2×C4×D4C2312yes—
332C2×C4×D4C2314yes—
333C2×C4×D4C2314yes—
334C2×C4×D4C2314yes—
335C2×#117C2312yes—
336C2×#117C2314yes—
337C2×#117C2312yes—
338C2×#117C2312yes—
339C2×#117C2312yes—
340C2×#117C2314yes—
341C2×#117C2314yes—
342C2×#117C2314yes—
343C22×C4⋊C4C2312yes—
344C22×C4⋊C4C2312yes—
345C22×C4⋊C4C2314yes—
346C22×C4⋊C4C2312yes—
347C22×C4⋊C4C2314yes—
348#401C2312yes—
349#401C2312yes—
350#401C2314yes—
351#400C2312yes—
352#400C2312yes—
353#400C2314yes—
354#400C2314yes—
355#400C2314yes—
356#400C2312yes—
357#400C2312yes—
358#400C2312yes—
359#400C2312yes—
360#400C2312yes—
361#400C2312yes—
362#400C2312yes—
363#400C2314yes—
364#399C2314yes—
365#399C2312yes—
366#399C2312yes—
367#399C2314yes—
368#399C2314yes—
369#399C2314yes—
370#399C2312yes—
371#398C2311yescharacteristic
372#398C2312yes—
373#398C2311yescharacteristic
374#398C2311yescharacteristic
375#398C2312yes—
376#398C2312yes—
377#398C2312yes—
378#398C2314yes—
379#398C2312yes—
380#398C2314yes—
381#398C2314yes—
382#398C2311yescharacteristic
383#398C2314yes—
384#398C2312yes—
385#398C2312yes—
386#398C2312yes—
387#398C2312yes—
388#398C2312yes—
389#398C2314yes—
390#398C2312yes—
391#398C2314yes—
392#398C2314yes—
393#398C2314yes—
394#398C2312yes—
395#398C2314yes—
396#398C2314yes—
397#398C2314yes—
398#398C2314yes—
399#398C2314yes—
400#398C2314yes—
401#398C2314yes—
402#398C2314yes—
403#398C2312yes—
404#398C2314yes—
405#398C2314yes—
406#398C2314yes—
407#397C2314yes—
408#397C2312yes—
409#397C2312yes—
410#397C2314yes—
411#397C2312yes—
412#397C2314yes—
413#397C2312yes—
414#397C2312yes—
415#397C2312yes—
416#397C2314yes—
417#397C2314yes—
418#397C2312yes—
419#397C2314yes—
420#397C2314yes—
421#397C2312yes—
422#397C2312yes—
423#397C2314yes—
424#397C2314yes—
425#397C2314yes—
426#397C2314yes—
427#396C2312yes—
428#396C2314yes—
429#396C2312yes—
430#396C2312yes—
431#396C2312yes—
432#396C2314yes—
433#396C2314yes—
434#396C2314yes—
435#396C2314yes—
436#396C2314yes—
437#396C2314yes—
438#396C2314yes—
439#396C2314yes—
440#396C2314yes—
441#396C2314yes—
442#396C2312yes—
443#396C2312yes—
444#396C2314yes—
445#396C2314yes—
446#396C2314yes—
447#396C2314yes—
448#396C2314yes—
449#396C2314yes—
450#396C2314yes—
451#396C2314yes—
452#396C2314yes—
453#395C2312yes—
454#395C2312yes—
455#395C2314yes—
456#395C2314yes—
457#395C2312yes—
458#395C2312yes—
459#395C2311yescharacteristic
460#395C2311yescharacteristic
461#395C2314yes—
462#395C2311yescharacteristic
463#395C2311yescharacteristic
464#395C2312yes—
465#395C2312yes—
466#395C2312yes—
467#395C2312yes—
468#395C2314yes—
469#395C2314yes—
470#395C2314yes—
471#394C2312yes—
472#394C2314yes—
473#394C2312yes—
474#394C2314yes—
475#394C2314yes—
476#394C2312yes—
477#394C2312yes—
478#394C2314yes—
479#394C2314yes—
480#394C2312yes—
481#394C2314yes—
482#394C2314yes—
483#394C2314yes—
484#394C2314yes—
485#394C2314yes—
486#394C2314yes—
487#394C2314yes—
488#394C2314yes—
489#394C2312yes—
490#394C2314yes—
491#394C2314yes—
492#394C2314yes—
493#394C2314yes—
494#394C2314yes—
495#394C2314yes—
496#394C2314yes—
497#394C2314yes—
498#393C2314yes—
499#393C2314yes—
500#393C2312yes—
501#393C2312yes—
502#393C2314yes—
503#393C2314yes—
504#393C2314yes—
505#393C2314yes—
506#393C2314yes—
507#392C2314yes—
508#392C2314yes—
509#391C2312yes—
510#391C2311yescharacteristic
511#391C2314yes—
512#391C2314yes—
513#391C2314yes—
514#391C2312yes—
515#391C2314yes—
516#391C2314yes—
517#391C2314yes—
518#391C2314yes—
519#391C2314yes—
520#390C2312yes—
521#390C2312yes—
522#390C2312yes—
523#390C2312yes—
524#390C2314yes—
525#390C2311yescharacteristic
526#390C2314yes—
527#390C2312yes—
528#390C2312yes—
529#390C2312yes—
530#390C2314yes—
531#390C2312yes—
532#390C2312yes—
533#390C2312yes—
534#390C2314yes—
535#390C2312yes—
536#390C2312yes—
537#389C2312yes—
538#389C2312yes—
539#389C2312yes—
540#389C2312yes—
541#389C2312yes—
542#389C2312yes—
543#389C2314yes—
544#389C2314yes—
545#389C2312yes—
546#389C2312yes—
547#389C2312yes—
548#389C2314yes—
549#389C2312yes—
550#389C2314yes—
551#389C2314yes—
552#389C2314yes—
553#389C2314yes—
554#389C2314yes—
555#389C2314yes—
556#389C2312yes—
557#389C2314yes—
558#389C2314yes—
559#389C2314yes—
560#389C2314yes—
561#389C2314yes—
562#389C2312yes—
563#389C2312yes—
564#389C2312yes—
565#389C2314yes—
566#389C2314yes—
567#389C2314yes—
568#389C2312yes—
569#389C2312yes—
570#389C2312yes—
571#389C2314yes—
572#389C2314yes—
573#389C2312yes—
574#388C2314yes—
575#388C2314yes—
576#388C2314yes—
577#388C2312yes—
578#388C2312yes—
579#388C2314yes—
580#388C2314yes—
581#388C2314yes—
582#388C2314yes—
583#388C2314yes—
584#388C2314yes—
585#388C2314yes—
586#388C2314yes—
587#388C2314yes—
588#388C2314yes—
589#388C2314yes—
590#388C2314yes—
591#388C2314yes—
592#388C2314yes—
593#388C2314yes—
594#388C2314yes—
595#388C2314yes—
596#387C2312yes—
597#387C2312yes—
598#387C2312yes—
599#387C2312yes—
600#387C2314yes—
601#387C2314yes—
602#387C2314yes—
603#387C2314yes—
604#387C2314yes—
605#387C2314yes—
606#387C2314yes—
607#387C2314yes—
608#387C2314yes—
609#387C2314yes—
610#387C2314yes—
611#387C2314yes—
612#387C2314yes—
613#387C2314yes—
614#387C2314yes—
615#387C2314yes—
616#387C2314yes—
617#386C2314yes—
618#386C2314yes—
619#386C2314yes—
620#386C2314yes—
621#386C2314yes—
622#386C2314yes—
623#386C2314yes—
624#386C2314yes—
625#386C2314yes—
626#386C2314yes—
627#386C2314yes—
628#386C2314yes—
629#386C2314yes—
630#386C2314yes—
631#386C2314yes—
632#385C2314yes—
633#385C2314yes—
634#385C2314yes—
635#385C2314yes—
636#385C2314yes—
637#385C2314yes—
638#385C2314yes—
639#385C2314yes—
640#385C2314yes—
641#385C2314yes—
642#385C2314yes—
643#385C2314yes—
644#385C2314yes—
645#385C2314yes—
646#385C2314yes—
647#385C2314yes—
648#385C2314yes—
649#385C2314yes—
650#385C2314yes—
651#385C2314yes—
652#385C2314yes—
653#384C2312yes—
654#384C2312yes—
655#384C2312yes—
656#384C2312yes—
657#384C2314yes—
658#384C2312yes—
659#384C2312yes—
660#384C2312yes—
661#384C2314yes—
662#382C2312yes—
663#382C2312yes—
664#382C2314yes—
665#382C2312yes—
666#382C2312yes—
667#382C2311yescharacteristic
668#381C2312yes—
669#381C2314yes—
670#381C2314yes—
671#381C2314yes—
672#380C2312yes—
673#380C2312yes—
674#380C2314yes—
675#380C2314yes—
676#380C2312yes—
677#380C2314yes—
678#380C2312yes—
679#380C2314yes—
680#380C2314yes—
681#380C2314yes—
682#380C2314yes—
683#380C2314yes—
684#380C2314yes—
685#380C2314yes—
686C4×C4⋊C4C2312yes—
687C4×C4⋊C4C2312yes—
688C4×C4⋊C4C2312yes—
689C4×C4⋊C4C2312yes—
690C4×C4⋊C4C2312yes—
691C4×C4⋊C4C2312yes—
692C4×C4⋊C4C2311yescharacteristic
693C4×C4⋊C4C2312yes—
694C4×C4⋊C4C2311yescharacteristic
695C4×C4⋊C4C2312yes—
696C4×C4⋊C4C2311yescharacteristic
697C4×C4⋊C4C2314yes—
698C4×C4⋊C4C2312yes—
699C4×C4⋊C4C2312yes—
700C4×C4⋊C4C2312yes—
701C4×C4⋊C4C2312yes—
702C4×C4⋊C4C2312yes—
703C4×C22⋊C4C2314yes—
704C4×C22⋊C4C2312yes—
705C4×C22⋊C4C2314yes—
706C4×C22⋊C4C2312yes—
707C4×C22⋊C4C2314yes—
708C4×C22⋊C4C2312yes—
709C4×C22⋊C4C2312yes—
710C4×C22⋊C4C2312yes—
711C4×C22⋊C4C2312yes—
712C4×C22⋊C4C2314yes—
713C4×C22⋊C4C2312yes—
714#376C2311yescharacteristic
715#376C2311yescharacteristic
716C2×#95C2314yes—
717C2×#95C2312yes—
718C43C2311yescharacteristic
719C2×#41—44no—
720C2×#41—84no—
721C22×Q8C2414yes—
722C22×Q8C2411yescharacteristic
723C22×Q8C2411yescharacteristic
724C22×Q8C2411yescharacteristic
725C22×Q8C2412yes—
726C22×Q8C2412yes—
727C22×Q8C2412yes—
728C22×D4C2412yes—
729C22×D4C2411yescharacteristic
730C22×D4C2411yescharacteristic
731C22×D4C2414yes—
732C22×D4C2414yes—
733C22×D4C2414yes—
734C22×D4C2414yes—
735C22×D4C2414yes—
736C22×D4C2412yes—
737C22×D4C2412yes—
738C23×C4C2412yes—
739C23×C4C2412yes—
740C23×C4C2414yes—
741C23×C4C2414yes—
742C23×C4C2412yes—
743C23×C4C2414yes—
744C23×C4C2414yes—
745C23×C4C2412yes—
746C23×C4C2414yes—
747C23×C4C2414yes—
748C4⋊Q8—28no—
749C4⋊Q8—42no—
750C4⋊Q8—42no—
751C4⋊Q8—42no—
752C4⋊Q8—44no—
753C4⋊Q8—84no—
754#127—28no—
755#127—42no—
756#126—48no—
757#126—48no—
758#125—28no—
759#125—44no—
760#125—48no—
761#125—44no—
762#125—42no—
763#125—42no—
764#125—48no—
765#124—24no—
766#124—48no—
767#124—48no—
768#124—44no—
769#124—84no—
770#123—48no—
771#123—48no—
772#123—48no—
773#123—48no—
774#123—84no—
775#123—84no—
776#123—84no—
777#123—84no—
778C22⋊Q8—44no—
779C22⋊Q8—44no—
780C22⋊Q8—44no—
781C22⋊Q8—48no—
782C22⋊Q8—44no—
783C22⋊Q8—48no—
784C22⋊Q8—48no—
785C22⋊Q8—84no—
786C22⋊Q8—84no—
787C22⋊Q8—84no—
788C22⋊Q8—84no—
789#121—28no—
790#121—28no—
791#121—48no—
792#121—48no—
793#121—48no—
794#121—48no—
795#121—44no—
796#121—48no—
797#121—44no—
798#121—44no—
799#121—84no—
800C4×Q8—42no—
801C4×Q8—42no—
802C4×Q8—42no—
803C4×Q8—48no—
804C4×D4—28no—
805C4×D4—24no—
806C4×D4—24no—
807C4×D4—24no—
808C4×D4—28no—
809C4×D4—28no—
810C4×D4—44no—
811C4×D4—44no—
812C4×D4—42no—
813C4×D4—48no—
814C4×D4—48no—
815C4×D4—84no—
816#117—28no—
817#117—216no—
818#117—44no—
819#117—48no—
820#117—48no—
821#117—44no—
822#117—44no—
823#117—84no—
824C2×C4⋊C4—28no—
825C2×C4⋊C4—48no—
826C2×C4⋊C4—44no—
827C2×C4⋊C4—44no—
828C2×C4⋊C4—84no—
829C2×C4⋊C4C2412yes—
830C2×C4⋊C4C2414yes—
831C2×C4⋊C4C2412yes—
832C2×C4⋊C4C2414yes—
833C2×C4⋊C4C2414yes—
834C2×C4⋊C4C2411yescharacteristic
835C2×C4⋊C4C2412yes—
836C2×C4⋊C4C2412yes—
837C2×C4⋊C4C2414yes—
838C2×C4⋊C4C2411yescharacteristic
839C2×C4⋊C4C2412yes—
840C2×C4⋊C4C2412yes—
841C2×C4⋊C4C2411yescharacteristic
842C2×C4⋊C4C2412yes—
843C2×C4⋊C4C2412yes—
844C2×C4⋊C4C2412yes—
845C2×C4⋊C4C2412yes—
846C2×C4⋊C4C2414yes—
847C2×C4⋊C4C2411yescharacteristic
848C2×C4⋊C4C2411yescharacteristic
849C2×C4⋊C4C2412yes—
850C2×C4⋊C4C2414yes—
851C2×C4⋊C4C2414yes—
852C2×C4⋊C4C2414yes—
853C2×C4⋊C4C2412yes—
854C2×C4⋊C4C2412yes—
855C2×C4⋊C4C2412yes—
856C2×C4⋊C4C2412yes—
857C2×C4⋊C4C2414yes—
858C2×C4⋊C4C2414yes—
859C2×C4⋊C4C2414yes—
860C2×C4⋊C4C2411yescharacteristic
861C2×C4⋊C4C2412yes—
862C2×C4⋊C4C2414yes—
863C2×C4⋊C4C2412yes—
864C2×C4⋊C4C2412yes—
865C2×C4⋊C4C2412yes—
866C2×C4⋊C4C2414yes—
867C2×C4⋊C4C2414yes—
868C2×C4⋊C4C2414yes—
869C2×C4⋊C4C2412yes—
870C2×C4⋊C4C2411yescharacteristic
871C2×C4⋊C4C2412yes—
872C2×C4⋊C4C2411yescharacteristic
873C2×C4⋊C4C2411yescharacteristic
874C2×C4⋊C4C2414yes—
875C2×C4⋊C4C2414yes—
876C2×C4⋊C4C2414yes—
877C2×C4⋊C4C2412yes—
878C2×C4⋊C4C2412yes—
879C2×C4⋊C4C2414yes—
880C2×C4⋊C4C2412yes—
881C2×C4⋊C4C2412yes—
882C2×C4⋊C4C2414yes—
883C2×C4⋊C4C2414yes—
884C2×C4⋊C4C2414yes—
885C2×C4⋊C4C2414yes—
886C2×C4⋊C4C2414yes—
887C2×C4⋊C4C2414yes—
888C2×C4⋊C4C2412yes—
889C2×C4⋊C4C2412yes—
890C2×C4⋊C4C2414yes—
891C2×C4⋊C4C2414yes—
892C2×C4⋊C4C2414yes—
893C2×C4⋊C4C2414yes—
894C2×C4⋊C4C2412yes—
895C2×C4⋊C4C2412yes—
896C2×C4⋊C4C2412yes—
897C2×C4⋊C4C2412yes—
898C2×C4⋊C4C2414yes—
899C2×C4⋊C4C2412yes—
900C2×C22⋊C4C2414yes—
901C2×C22⋊C4C2412yes—
902C2×C22⋊C4C2414yes—
903C2×C22⋊C4C2414yes—
904C2×C22⋊C4C2414yes—
905C2×C22⋊C4C2412yes—
906C2×C22⋊C4C2412yes—
907C2×C22⋊C4C2414yes—
908C2×C22⋊C4C2412yes—
909C2×C22⋊C4C2412yes—
910C2×C22⋊C4C2414yes—
911C2×C22⋊C4C2414yes—
912C2×C22⋊C4C2414yes—
913C2×C22⋊C4C2412yes—
914C2×C22⋊C4C2412yes—
915C2×C22⋊C4C2414yes—
916C2×C22⋊C4C2414yes—
917C2×C22⋊C4C2414yes—
918C2×C22⋊C4C2414yes—
919C2×C22⋊C4C2414yes—
920C2×C22⋊C4C2412yes—
921C2×C22⋊C4C2414yes—
922C2×C22⋊C4C2414yes—
923C2×C22⋊C4C2414yes—
924C2×C22⋊C4C2414yes—
925C2×C22⋊C4C2412yes—
926C2×C22⋊C4C2414yes—
927C2×C22⋊C4C2412yes—
928C2×C22⋊C4C2414yes—
929C2×C22⋊C4C2414yes—
930C2×C22⋊C4C2412yes—
931C2×C22⋊C4C2414yes—
932C2×C22⋊C4C2414yes—
933C2×C22⋊C4C2414yes—
934C2×C22⋊C4C2414yes—
935C2×C22⋊C4C2414yes—
936C2×C22⋊C4C2414yes—
937C2×C22⋊C4C2414yes—
938C2×C22⋊C4C2414yes—
939C2×C22⋊C4C2412yes—
940C2×C22⋊C4C2412yes—
941C2×C22⋊C4C2414yes—
942C2×C22⋊C4C2414yes—
943C2×C22⋊C4C2412yes—
944C2×C22⋊C4C2412yes—
945C2×C22⋊C4C2412yes—
946C2×C22⋊C4C2414yes—
947C2×C22⋊C4C2414yes—
948C2×C42C2414yes—
949C2×C42C2412yes—
950C2×C42C2412yes—
951C2×C42C2412yes—
952C2×C42C2411yescharacteristic
953C2×C42C2411yescharacteristic
954C2×C42C2411yescharacteristic
955C2×C42C2412yes—
956C2×C42C2412yes—
957C2×C42C2412yes—
958C2×C42C2414yes—
959C2×C42C2412yes—
960C2×C42C2414yes—
961C2×C42C2414yes—
962C2×C42C2414yes—
963C2×C42C2412yes—
964C2×C42C2414yes—
965C2×C42C2412yes—
966C2×C42C2411yescharacteristic
967C2×C42C2411yescharacteristic
968#95C2411yescharacteristic
969#95C2412yes—
970#95C2414yes—
971#95C2412yes—
972#95C2414yes—
973#95C2414yes—
974#95C2414yes—
975#95C2412yes—
976#95C2411yescharacteristic
977#95C2411yescharacteristic
978#95C2411yescharacteristic
979#95C2412yes—
980#95C2412yes—
981#95C2414yes—
982#95C2414yes—
983#95C2412yes—
984#95C2412yes—
985#95C2414yes—
986#95C2412yes—
987#95C2412yes—
988#95C2412yes—
989#95C2412yes—
990#95C2414yes—
991#95C2412yes—
992#95C2414yes—
993#95C2414yes—
994#95C2412yes—
995#95C2412yes—
996#95C2414yes—
997#95C2412yes—
998#95C2412yes—
999#95C2412yes—
1000#95C2414yes—
1001#95C2414yes—
1002#95C2414yes—
1003#95C2414yes—
1004#95C2414yes—
1005#95C2412yes—
1006#95C2412yes—
1007#95C2412yes—
1008#95C2412yes—
1009#95C2412yes—
1010#95C2412yes—
1011#95C2412yes—
1012#95C2412yes—
1013#95C2412yes—
1014#95C2412yes—
1015#95C2412yes—
1016#95C2412yes—
1017#95C2412yes—
1018#95C2412yes—
1019#95C2414yes—
1020#95C2414yes—
1021#95C2414yes—
1022#95C2414yes—
1023#95C2414yes—
1024#95C2414yes—
1025#95C2414yes—
1026#95C2414yes—
1027#95C2414yes—
1028#95C2414yes—
1029#95C2414yes—
1030#95C2414yes—
1031C24C2514yes—
1032C24C2512yes—
1033C24C2512yes—
1034#41—816no—
1035C2×Q8—22no—
1036C2×Q8—28no—
1037C2×Q8—41no—
1038C2×Q8—42no—
1039C2×Q8—41no—
1040C2×Q8—44no—
1041C2×Q8—41no—
1042C2×Q8—42no—
1043C2×Q8—44no—
1044C2×Q8—41no—
1045C2×Q8—42no—
1046C2×Q8—42no—
1047C2×Q8—44no—
1048C2×Q8—44no—
1049C2×Q8—42no—
1050C2×Q8—42no—
1051C2×Q8—42no—
1052C2×D4—28no—
1053C2×D4—28no—
1054C2×D4—28no—
1055C2×D4—24no—
1056C2×D4—22no—
1057C2×D4—24no—
1058C2×D4—24no—
1059C2×D4—24no—
1060C2×D4—28no—
1061C2×D4—41no—
1062C2×D4—44no—
1063C2×D4—44no—
1064C2×D4—44no—
1065C2×D4—42no—
1066C2×D4—44no—
1067C2×D4—44no—
1068C2×D4—44no—
1069C2×D4—44no—
1070C2×D4—44no—
1071C2×D4—41no—
1072C2×D4—44no—
1073C2×D4—44no—
1074C2×D4—44no—
1075C2×D4—42no—
1076C2×D4—42no—
1077C2×D4—44no—
1078C2×D4—42no—
1079C2×D4H(5,𝔽2)14yes—
1080C22×C4—24no—
1081C22×C4—24no—
1082C22×C4—28no—
1083C22×C4—24no—
1084C22×C4—24no—
1085C22×C4—28no—
1086C22×C4—24no—
1087C22×C4—24no—
1088C22×C4—28no—
1089C22×C4—24no—
1090C22×C4—28no—
1091C22×C4—28no—
1092C22×C4—44no—
1093C22×C4—42no—
1094C22×C4—44no—
1095C22×C4—44no—
1096C22×C4—44no—
1097C22×C4—44no—
1098C22×C4—44no—
1099C22×C4—44no—
1100C22×C4—44no—
1101C22×C4—44no—
1102C22×C4—44no—
1103C22×C4—44no—
1104C22×C4—44no—
1105C22×C4—44no—
1106C22×C4—44no—
1107C22×C4—44no—
1108C22×C4C2512yes—
1109C22×C4C2512yes—
1110C22×C4C2512yes—
1111C22×C4C2512yes—
1112C22×C4C2512yes—
1113C22×C4C2512yes—
1114C22×C4C2512yes—
1115C22×C4C2511yescharacteristic
1116C22×C4C2514yes—
1117C22×C4C2511yescharacteristic
1118C22×C4C2511yescharacteristic
1119C22×C4C2511yescharacteristic
1120C22×C4C2514yes—
1121C22×C4C2514yes—
1122C22×C4C2512yes—
1123C22×C4C2512yes—
1124C22×C4C2514yes—
1125C22×C4C2512yes—
1126C22×C4C2512yes—
1127C22×C4C2511yescharacteristic
1128C22×C4C2512yes—
1129C22×C4C2512yes—
1130C22×C4C2512yes—
1131C22×C4C2511yescharacteristic
1132C22×C4C2514yes—
1133C22×C4C2511yescharacteristic
1134C4⋊C4—24no—
1135C4⋊C4—28no—
1136C4⋊C4—28no—
1137C4⋊C4—28no—
1138C4⋊C4—22no—
1139C4⋊C4—24no—
1140C4⋊C4—24no—
1141C4⋊C4—22no—
1142C4⋊C4—24no—
1143C4⋊C4—22no—
1144C4⋊C4—24no—
1145C4⋊C4—24no—
1146C4⋊C4—24no—
1147C4⋊C4—24no—
1148C4⋊C4—28no—
1149C4⋊C4—24no—
1150C4⋊C4—28no—
1151C4⋊C4—24no—
1152C4⋊C4—41no—
1153C4⋊C4—41no—
1154C4⋊C4—44no—
1155C4⋊C4—44no—
1156C4⋊C4—42no—
1157C4⋊C4—42no—
1158C4⋊C4—42no—
1159C4⋊C4—42no—
1160C4⋊C4—44no—
1161C4⋊C4—42no—
1162C4⋊C4—44no—
1163C4⋊C4—44no—
1164C4⋊C4—44no—
1165C4⋊C4—42no—
1166C4⋊C4—42no—
1167C4⋊C4—42no—
1168C4⋊C4—44no—
1169C4⋊C4—42no—
1170C4⋊C4—41no—
1171C4⋊C4—42no—
1172C4⋊C4—44no—
1173C4⋊C4—42no—
1174C4⋊C4—42no—
1175C4⋊C4—44no—
1176C4⋊C4—42no—
1177C4⋊C4—44no—
1178C4⋊C4—44no—
1179C4⋊C4—42no—
1180C4⋊C4—41no—
1181C4⋊C4—41no—
1182C4⋊C4—41no—
1183C4⋊C4—42no—
1184C4⋊C4—44no—
1185C4⋊C4—44no—
1186C4⋊C4—44no—
1187C4⋊C4—44no—
1188C4⋊C4—42no—
1189C4⋊C4—42no—
1190C4⋊C4—44no—
1191C4⋊C4—42no—
1192C4⋊C4—42no—
1193C4⋊C4—44no—
1194C4⋊C4—44no—
1195C4⋊C4—44no—
1196C4⋊C4—44no—
1197C4⋊C4—44no—
1198C4⋊C4—44no—
1199C4⋊C4—42no—
1200C4⋊C4—42no—
1201C4⋊C4—44no—
1202C4⋊C4—44no—
1203C4⋊C4—44no—
1204C4⋊C42−1+418yes—
1205C22⋊C4—28no—
1206C22⋊C4—24no—
1207C22⋊C4—28no—
1208C22⋊C4—24no—
1209C22⋊C4—24no—
1210C22⋊C4—28no—
1211C22⋊C4—28no—
1212C22⋊C4—28no—
1213C22⋊C4—24no—
1214C22⋊C4—24no—
1215C22⋊C4—28no—
1216C22⋊C4—28no—
1217C22⋊C4—28no—
1218C22⋊C4—44no—
1219C22⋊C4—44no—
1220C22⋊C4—42no—
1221C22⋊C4—42no—
1222C22⋊C4—42no—
1223C22⋊C4—42no—
1224C22⋊C4—44no—
1225C22⋊C4—44no—
1226C22⋊C4—44no—
1227C22⋊C4—44no—
1228C22⋊C4—44no—
1229C22⋊C4—44no—
1230C22⋊C4—44no—
1231C22⋊C4—44no—
1232C22⋊C4—42no—
1233C22⋊C4—44no—
1234C22⋊C4—42no—
1235C22⋊C4—44no—
1236C22⋊C4—44no—
1237C22⋊C4—42no—
1238C22⋊C4—44no—
1239C22⋊C4—44no—
1240C22⋊C4—44no—
1241C22⋊C4—44no—
1242C22⋊C4—42no—
1243C22⋊C4—44no—
1244C22⋊C4—44no—
1245C22⋊C4—44no—
1246C22⋊C4—44no—
1247C22⋊C4—44no—
1248C22⋊C4—42no—
1249C22⋊C4—42no—
1250C22⋊C4—44no—
1251C22⋊C4—44no—
1252C22⋊C4—42no—
1253C42—28no—
1254C42—24no—
1255C42—24no—
1256C42—24no—
1257C42—22no—
1258C42—22no—
1259C42—22no—
1260C42—24no—
1261C42—24no—
1262C42—24no—
1263C42—41no—
1264C42—42no—
1265C42—44no—
1266C42—44no—
1267C42—44no—
1268C42—44no—
1269C42—42no—
1270C42—44no—
1271C42—42no—
1272C42H(5,𝔽2)14yes—
1273C23—22no—
1274C23—24no—
1275C23—24no—
1276C23—22no—
1277C23—24no—
1278C23—22no—
1279C23—22no—
1280C23—24no—
1281C23—24no—
1282C23—24no—
1283C23—22no—
1284C23—22no—
1285C23—22no—
1286C23—22no—
1287C23—24no—
1288C23—24no—
1289C23—24no—
1290C23—22no—
1291C23C2×H(5,𝔽2)14yes—
1292C23C2611yescharacteristic
1293Q8—44no—
1294Q8—82no—
1295Q8—88no—
1296Q8—82no—
1297Q8—162no—
1298Q8—162no—
1299Q8—162no—
1300D4—28no—
1301D4—48no—
1302D4—82no—
1303D4—88no—
1304D4—88no—
1305D4—88no—
1306D4—88no—
1307D4—84no—
1308D4—164no—
1309D4—162no—
1310C2×C4—21no—
1311C2×C4—24no—
1312C2×C4—22no—
1313C2×C4—24no—
1314C2×C4—22no—
1315C2×C4—21no—
1316C2×C4—24no—
1317C2×C4—24no—
1318C2×C4—24no—
1319C2×C4—21no—
1320C2×C4—22no—
1321C2×C4—21no—
1322C2×C4—21no—
1323C2×C4—22no—
1324C2×C4—22no—
1325C2×C4—22no—
1326C2×C4—21no—
1327C2×C4—21no—
1328C2×C4—21no—
1329C2×C4—22no—
1330C2×C4—21no—
1331C2×C4—22no—
1332C2×C4—22no—
1333C2×C4—22no—
1334C2×C4—24no—
1335C2×C4—22no—
1336C2×C4—24no—
1337C2×C4—22no—
1338C2×C4—22no—
1339C2×C4—22no—
1340C2×C4—22no—
1341C2×C4—22no—
1342C2×C4—22no—
1343C2×C4—22no—
1344C2×C4—22no—
1345C2×C4—22no—
1346C2×C4—22no—
1347C2×C4—22no—
1348C2×C4—24no—
1349C2×C4—24no—
1350C2×C4—22no—
1351C2×C4—22no—
1352C2×C4—22no—
1353C2×C4—24no—
1354C2×C4—22no—
1355C2×C4—24no—
1356C2×C4—24no—
1357C2×C4—22no—
1358C2×C4—22no—
1359C2×C4—24no—
1360C2×C4—22no—
1361C2×C4—22no—
1362C2×C4—22no—
1363C2×C4—24no—
1364C2×C4—24no—
1365C2×C4—22no—
1366C2×C4—22no—
1367C2×C4—22no—
1368C2×C4—22no—
1369C2×C4—22no—
1370C2×C4—22no—
1371C2×C4—22no—
1372C2×C4—22no—
1373C2×C4—22no—
1374C2×C4—24no—
1375C2×C4—21no—
1376C2×C4—21no—
1377C2×C4—416no—
1378C2×C4—48no—
1379C2×C4—48no—
1380C2×C4—88no—
1381C2×C4—88no—
1382C2×C4—84no—
1383C2×C4—88no—
1384C2×C4—84no—
1385C2×C4—88no—
1386C2×C4—164no—
1387C2×C4C2×H(5,𝔽2)14yes—
1388C2×C4C2×H(5,𝔽2)12yes—
1389C2×C4C2×H(5,𝔽2)12yes—
1390C2×C4C2×2−1+418yes—
1391C2×C4C2×2−1+414yes—
1392C22—24no—
1393C22—24no—
1394C22—24no—
1395C22—44no—
1396C22—44no—
1397C22—42no—
1398C22—44no—
1399C22—44no—
1400C22—42no—
1401C22—44no—
1402C22—44no—
1403C22—42no—
1404C22—42no—
1405C22—42no—
1406C22—44no—
1407C22—44no—
1408C22—42no—
1409C22—42no—
1410C22—44no—
1411C22C22×H(5,𝔽2)11yescharacteristic
1412C22C22×H(5,𝔽2)11yescharacteristic
1413C22C22×2−1+412yes—
1414C22H(7,𝔽2)12yes—
1415C222−1+611yescharacteristic
1416C4—22no—
1417C4—24no—
1418C4—28no—
1419C4—42no—
1420C4—42no—
1421C4—42no—
1422C4—41no—
1423C4—41no—
1424C4—42no—
1425C4—42no—
1426C4—44no—
1427C4—41no—
1428C4—42no—
1429C4—42no—
1430C4—42no—
1431C4—42no—
1432C4—42no—
1433C4—44no—
1434C4—42no—
1435C4—41no—
1436C4—41no—
1437C4—44no—
1438C4—42no—
1439C4—44no—
1440C4—42no—
1441C4#354414yes—
1442C2—44no—
1443C2—82no—
1444C2—84no—
1445C2C2×#354411yescharacteristic
1446C2#6291411yescharacteristic
1447C2#6294412yes—
1448C2#6304111yescharacteristic
1449C2#6306112yes—
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. #59842C2semidirect
2. #59841C2semidirect
3. #58012C2semidirect
4. #57482C2semidirect
5. #56358C2semidirect
6. #55001C2semidirect
7. #53490C2semidirect
8. #53099C2semidirect
9. #53089C2semidirect
10. #52549C2semidirect
11. #52503C2semidirect
12. #47802C2semidirect
13. #45364C2semidirect
14. #45027C2semidirect
15. #44943C2semidirect
16. #44888C2semidirect
17. #44880C2semidirect
18. #42970C2semidirect
19. #42618C2semidirect
20. #42588C2semidirect
21. #42489C2semidirect
22. #42479C2semidirect
23. #42439C2semidirect
24. #42167C2semidirect
25. #39497C2semidirect
26. #39489C2semidirect
27. #36698C2semidirect
28. #35950C2semidirect
29. #35916C2semidirect

Maximal subgroups

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

subgroupindex
#598422
#598412
#580122
#574822
#563582
#550012
#534902
#530992
#530892
#525492
#525032
#478022
#453642
#450272
#449432
#448882
#448802
#429702
#426182
#425882
#424892
#424792
#424392
#421672
#394972
#394892
#366982
#359502
#359162