Finite Group Databasebeta

← #8757392

Subgroups — #8757392

Order 512.

5112 conjugacy classes of subgroups.

The subgroup lattice has 1399 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#58584C214yesmaximal, complemented
2#57222C214yesmaximal, complemented
3#56618C214yesmaximal, complemented
4#55028C214yesmaximal, complemented
5#54922C214yesmaximal, complemented
6#53486C214yesmaximal, complemented
7#51409C212yesmaximal, complemented
8#49786C214yesmaximal, complemented
9#49564C212yesmaximal, complemented
10#48830C214yesmaximal, complemented
11#47685C214yesmaximal, complemented
12#47303C214yesmaximal, complemented
13#46424C212yesmaximal, complemented
14#46361C212yesmaximal, complemented
15#46228C211yesmaximal, characteristic, complemented
16#46225C211yesmaximal, characteristic, complemented
17#46015C212yesmaximal, complemented
18#46014C212yesmaximal, complemented
19#46000C212yesmaximal, complemented
20#45999C212yesmaximal, complemented
21#45976C212yesmaximal, complemented
22#35329C211yesmaximal, characteristic, complemented
23#35135C212yesmaximal, complemented
24C2×#563C2211yescharacteristic, complemented
25C2×#562C2212yes—
26C2×H(3,𝔽4)C2211yescharacteristic, complemented
27C2×#560C2212yes—
28C2×#551C2212yescomplemented
29C2×#539C2212yescomplemented
30C2×#538C2212yescomplemented
31C2×#536C2211yescharacteristic
32C2×#536C2211yescharacteristic, complemented
33C2×#535C2211yescharacteristic
34C2×#535C2211yescharacteristic, complemented
35C2×#532C2211yescharacteristic
36C22×#124C2211yescharacteristic, complemented
37#2861C2212yescomplemented
38#2859C2212yescomplemented
39#2858C2212yes—
40#2858C2212yescomplemented
41#2851C2212yescomplemented
42#2850C2212yes—
43#2837C2214yescomplemented
44#2829C2214yescomplemented
45#2828C2214yescomplemented
46#2826C2214yescomplemented
47#2820C2214yescomplemented
48#2820C2212yescomplemented
49#2820C2212yescomplemented
50#2819C2212yes—
51#2819C2212yescomplemented
52#2816C2212yescomplemented
53#2816C2212yescomplemented
54#2813C2214yescomplemented
55#2808C2214yescomplemented
56#2780C2214yescomplemented
57#2773C2214yescomplemented
58#2753C2214yescomplemented
59#2752C2214yescomplemented
60#2748C2214yescomplemented
61#2742C2214yescomplemented
62#2734C2212yescomplemented
63#2732C2214yescomplemented
64#2731C2212yescomplemented
65#2730C2214yescomplemented
66#2730C2214yescomplemented
67#2727C2214yescomplemented
68#2724C2214yescomplemented
69#2723C2214yescomplemented
70#2723C2214yescomplemented
71#2717C2212yescomplemented
72#2715C2214yescomplemented
73#2715C2214yescomplemented
74#2714C2214yes—
75#2714C2214yescomplemented
76#2714C2214yescomplemented
77#2714C2214yescomplemented
78#2711C2214yescomplemented
79#2711C2214yescomplemented
80#2710C2214yescomplemented
81#2710C2214yescomplemented
82#2710C2214yescomplemented
83#2710C2214yescomplemented
84#2709C2212yescomplemented
85#2707C2214yescomplemented
86#2707C2214yescomplemented
87#2706C2214yes—
88#2706C2214yescomplemented
89#2706C2214yescomplemented
90#2705C2214yescomplemented
91#2700C2214yescomplemented
92#2698C2214yescomplemented
93#2697C2212yescomplemented
94#2697C2212yescomplemented
95#2694C2214yescomplemented
96#2694C2214yescomplemented
97#2692C2214yescomplemented
98#2691C2214yescomplemented
99#2688C2214yescomplemented
100#2688C2214yescomplemented
101#2686C2214yescomplemented
102#2683C2214yescomplemented
103#2682C2214yescomplemented
104#2681C2214yescomplemented
105#2679C2214yescomplemented
106#2678C2214yescomplemented
107#2678C2214yescomplemented
108#2678C2214yescomplemented
109#2678C2214yescomplemented
110#2678C2214yescomplemented
111#2677C2214yescomplemented
112#2676C2214yes—
113#2676C2214yes—
114#2675C2214yes—
115#2674C2214yescomplemented
116#2673C2214yescomplemented
117#2672C2214yescomplemented
118#2672C2214yescomplemented
119#2672C2214yescomplemented
120#2671C2214yes—
121#2671C2214yescomplemented
122#2670C2214yes—
123#2669C2214yes—
124#2669C2214yes—
125#2669C2212yes—
126#2669C2212yescomplemented
127#2667C2214yescomplemented
128#2658C2212yescomplemented
129#2657C2212yes—
130#2654C2214yescomplemented
131#2649C2214yescomplemented
132#2630C2214yes—
133#2630C2214yescomplemented
134#2624C2214yescomplemented
135#2617C2214yescomplemented
136#2617C2214yescomplemented
137#2583C2212yescomplemented
138#2580C2214yescomplemented
139#2566C2214yescomplemented
140#2560C2214yescomplemented
141#2559C2214yescomplemented
142#2557C2214yescomplemented
143#2555C2214yes—
144#2554C2214yescomplemented
145#2550C2214yescomplemented
146#2540C2214yescomplemented
147#2540C2214yescomplemented
148#2540C2214yescomplemented
149#2539C2214yes—
150#2539C2214yescomplemented
151#2539C2214yescomplemented
152#2539C2214yescomplemented
153#2539C2212yescomplemented
154#2535C2214yescomplemented
155#2530C2214yescomplemented
156#2529C2214yescomplemented
157#2517C2214yescomplemented
158#2516C2214yescomplemented
159#2513C2214yescomplemented
160#2512C2212yescomplemented
161#2512C2214yescomplemented
162#2511C2212yescomplemented
163#2500C2214yescomplemented
164#2491C2214yescomplemented
165#2490C2212yes—
166#2489C2212yescomplemented
167#2479C2214yescomplemented
168#2479C2214yescomplemented
169#2477C2214yescomplemented
170#2472C2214yescomplemented
171#2470C2214yescomplemented
172#2466C2214yescomplemented
173#2461C2214yescomplemented
174#2461C2214yescomplemented
175#2459C2214yescomplemented
176#2456C2214yescomplemented
177#2455C2214yescomplemented
178#2454C2212yescomplemented
179#2454C2214yescomplemented
180#2453C2212yescomplemented
181#2449C2214yescomplemented
182#2445C2214yes—
183#2445C2214yes—
184#2439C2214yescomplemented
185#2437C2214yescomplemented
186#2437C2214yescomplemented
187#2432C2212yes—
188#2431C2212yes—
189#2428C2214yescomplemented
190#2426C2214yescomplemented
191#2424C2214yes—
192#2424C2214yescomplemented
193#2424C2214yescomplemented
194#2424C2214yescomplemented
195#2423C2212yescomplemented
196#2422C2212yes—
197#2422C2214yescomplemented
198#2418C2214yescomplemented
199#2418C2214yescomplemented
200#2416C2214yescomplemented
201#2414C2214yescomplemented
202#2412C2214yescomplemented
203#2410C2214yescomplemented
204#2409C2214yescomplemented
205#2406C2212yescomplemented
206#2404C2212yes—
207#2379C2211yescharacteristic, complemented
208#2379C2211yescharacteristic, complemented
209#2379C2212yescomplemented
210#2376C2212yescomplemented
211#2358C2212yescomplemented
212#2335C2214yescomplemented
213#2334C2214yescomplemented
214#2333C2212yescomplemented
215#2332C2212yescomplemented
216C4×#125C2212yescomplemented
217C4×#124C2212yescomplemented
218C4×#117C2211yescharacteristic, complemented
219C22×#41C2311yescharacteristic
220C22×#41C2311yescharacteristic
221C23×Q8C2311yescharacteristic
222C23×D4C2311yescharacteristic
223#563—44no—
224#562—48no—
225H(3,𝔽4)—44no—
226#560—48no—
227#551—48no—
228#539—48no—
229#538—48no—
230#536—44no—
231#536—44no—
232#535—44no—
233#535—44no—
234#532—44no—
235C2×C4⋊Q8C2312yes—
236C2×C4⋊Q8C2312yes—
237C2×C4⋊Q8C2311yescharacteristic
238C2×C4⋊Q8C2312yes—
239C2×#127C2312yes—
240C2×#127C2312yes—
241C2×#127C2311yescharacteristic
242C2×#127C2312yes—
243C2×#126C2314yes—
244C2×#126C2314yes—
245C2×#126C2314yes—
246C2×#126C2314yes—
247C2×#125C2312yes—
248C2×#125C2314yes—
249C2×#125C2312yes—
250C2×#125C2312yes—
251C2×#124—44no—
252C2×#124C2312yes—
253C2×#124C2312yes—
254C2×#124C2311yescharacteristic
255C2×#124C2311yescharacteristic
256C2×#124C2314yes—
257C2×#124C2312yes—
258C2×#124C2312yes—
259C2×#124C2312yes—
260C2×#124C2312yes—
261C2×#124C2312yes—
262C2×#124C2314yes—
263C2×#124C2312yes—
264C2×#124C2312yes—
265C2×#124C2314yes—
266C2×#123C2314yes—
267C2×#123C2312yes—
268C2×#123C2312yes—
269C2×#123C2312yes—
270C2×#123C2312yes—
271C2×#123C2314yes—
272C2×#123C2314yes—
273C2×#123C2314yes—
274C2×#123C2314yes—
275C2×#123C2314yes—
276C2×#123C2314yes—
277C2×#123C2314yes—
278C2×#123C2314yes—
279C2×C22⋊Q8C2312yes—
280C2×C22⋊Q8C2314yes—
281C2×C22⋊Q8C2312yes—
282C2×C22⋊Q8C2312yes—
283C2×C22⋊Q8C2314yes—
284C2×C22⋊Q8C2314yes—
285C2×C22⋊Q8C2314yes—
286C2×C22⋊Q8C2314yes—
287C2×C22⋊Q8C2314yes—
288C2×C22⋊Q8C2312yes—
289C2×#121C2312yes—
290C2×#121C2312yes—
291C2×#121C2312yes—
292C2×#121C2314yes—
293C2×#121C2314yes—
294C2×#121C2314yes—
295C2×#121C2314yes—
296C2×#121C2314yes—
297C2×#121C2314yes—
298C2×#121C2314yes—
299C2×#121C2314yes—
300C2×#121C2312yes—
301C2×#121C2314yes—
302C2×#121C2314yes—
303C2×#121C2314yes—
304C2×#121C2314yes—
305C2×#121C2314yes—
306C2×#120C2312yes—
307C2×#120C2312yes—
308C2×#120C2314yes—
309C2×#120C2312yes—
310C2×#120C2312yes—
311C2×#120C2314yes—
312C2×#120C2314yes—
313C2×#120C2314yes—
314C2×#120C2314yes—
315C2×#120C2314yes—
316C2×#120C2314yes—
317C2×C4×Q8C2312yes—
318C2×C4×D4C2314yes—
319C2×C4×D4C2314yes—
320C2×C4×D4C2314yes—
321C2×C4×D4C2314yes—
322C2×C4×D4C2314yes—
323C2×C4×D4C2312yes—
324C2×#117C2311yescharacteristic
325C2×#117C2311yescharacteristic
326C2×#117C2314yes—
327C22×C4⋊C4C2312yes—
328C22×C22⋊C4C2314yes—
329C22×C22⋊C4C2312yes—
330C22×C22⋊C4C2314yes—
331C22×C22⋊C4C2314yes—
332C22×C42C2311yescharacteristic
333#400C2314yes—
334#400C2314yes—
335#400C2314yes—
336#400C2314yes—
337#399C2314yes—
338#399C2314yes—
339#399C2314yes—
340#399C2314yes—
341#399C2314yes—
342#399C2314yes—
343#399C2314yes—
344#399C2314yes—
345#399C2314yes—
346#399C2314yes—
347#399C2314yes—
348#399C2314yes—
349#399C2314yes—
350#398C2314yes—
351#398C2314yes—
352#398C2314yes—
353#398C2314yes—
354#398C2314yes—
355#398C2314yes—
356#398C2314yes—
357#397C2314yes—
358#397C2314yes—
359#397C2314yes—
360#397C2314yes—
361#397C2314yes—
362#397C2314yes—
363#397C2314yes—
364#397C2314yes—
365#397C2314yes—
366#397C2314yes—
367#397C2314yes—
368#397C2314yes—
369#397C2314yes—
370#397C2314yes—
371#397C2314yes—
372#397C2314yes—
373#396C2314yes—
374#396C2314yes—
375#396C2314yes—
376#396C2314yes—
377#396C2314yes—
378#396C2314yes—
379#396C2314yes—
380#396C2314yes—
381#396C2314yes—
382#396C2314yes—
383#396C2314yes—
384#396C2314yes—
385#396C2314yes—
386#396C2314yes—
387#396C2314yes—
388#396C2314yes—
389#395C2314yes—
390#395C2314yes—
391#395C2314yes—
392#395C2314yes—
393#395C2314yes—
394#394C2314yes—
395#394C2314yes—
396#394C2314yes—
397#394C2314yes—
398#394C2314yes—
399#394C2314yes—
400#394C2314yes—
401#394C2314yes—
402#394C2314yes—
403#394C2314yes—
404#394C2314yes—
405#394C2314yes—
406#394C2314yes—
407#394C2314yes—
408#394C2314yes—
409#394C2314yes—
410#394C2314yes—
411#394C2314yes—
412#394C2314yes—
413#394C2314yes—
414#394C2314yes—
415#394C2314yes—
416#394C2314yes—
417#394C2314yes—
418#394C2314yes—
419#394C2314yes—
420#394C2314yes—
421#394C2314yes—
422#394C2314yes—
423#394C2314yes—
424#394C2314yes—
425#394C2314yes—
426#394C2314yes—
427#394C2314yes—
428#393C2314yes—
429#393C2314yes—
430#393C2314yes—
431#393C2314yes—
432#393C2314yes—
433#393C2314yes—
434#392C2314yes—
435#392C2314yes—
436#392C2314yes—
437#392C2314yes—
438#392C2314yes—
439#392C2314yes—
440#392C2314yes—
441#392C2314yes—
442#392C2314yes—
443#392C2314yes—
444#392C2314yes—
445#392C2314yes—
446#392C2314yes—
447#392C2314yes—
448#392C2314yes—
449#392C2314yes—
450#392C2314yes—
451#392C2314yes—
452#392C2314yes—
453#391C2312yes—
454#391C2314yes—
455#391C2312yes—
456#391C2312yes—
457#391C2314yes—
458#391C2312yes—
459#391C2312yes—
460#391C2312yes—
461#390C2314yes—
462#390C2314yes—
463#390C2314yes—
464#390C2314yes—
465#390C2314yes—
466#390C2314yes—
467#390C2314yes—
468#390C2314yes—
469#390C2312yes—
470#390C2314yes—
471#390C2314yes—
472#390C2314yes—
473#390C2314yes—
474#390C2314yes—
475#390C2312yes—
476#390C2312yes—
477#390C2312yes—
478#390C2314yes—
479#390C2314yes—
480#390C2312yes—
481#390C2314yes—
482#390C2314yes—
483#390C2314yes—
484#390C2312yes—
485#390C2314yes—
486#390C2314yes—
487#390C2314yes—
488#389C2312yes—
489#389C2312yes—
490#389C2314yes—
491#389C2314yes—
492#389C2314yes—
493#389C2314yes—
494#389C2314yes—
495#389C2314yes—
496#389C2312yes—
497#389C2312yes—
498#389C2314yes—
499#389C2314yes—
500#389C2314yes—
501#389C2314yes—
502#389C2314yes—
503#388C2314yes—
504#388C2314yes—
505#388C2314yes—
506#388C2314yes—
507#388C2314yes—
508#388C2314yes—
509#388C2314yes—
510#388C2314yes—
511#388C2314yes—
512#388C2314yes—
513#388C2314yes—
514#388C2314yes—
515#388C2314yes—
516#388C2314yes—
517#388C2314yes—
518#388C2314yes—
519#388C2314yes—
520#388C2314yes—
521#388C2314yes—
522#388C2314yes—
523#388C2314yes—
524#388C2314yes—
525#388C2314yes—
526#388C2314yes—
527#388C2314yes—
528#388C2314yes—
529#388C2314yes—
530#388C2314yes—
531#387C2314yes—
532#387C2314yes—
533#387C2314yes—
534#387C2314yes—
535#387C2314yes—
536#387C2314yes—
537#387C2314yes—
538#387C2314yes—
539#387C2314yes—
540#387C2314yes—
541#387C2314yes—
542#387C2314yes—
543#387C2314yes—
544#387C2314yes—
545#386C2314yes—
546#386C2314yes—
547#386C2314yes—
548#386C2314yes—
549#386C2314yes—
550#386C2314yes—
551#386C2314yes—
552#386C2312yes—
553#386C2314yes—
554#386C2314yes—
555#386C2314yes—
556#386C2314yes—
557#386C2314yes—
558#386C2314yes—
559#386C2312yes—
560#386C2312yes—
561#386C2312yes—
562#386C2314yes—
563#386C2314yes—
564#386C2314yes—
565#386C2314yes—
566#386C2314yes—
567#386C2314yes—
568#386C2314yes—
569#386C2314yes—
570#385C2314yes—
571#385C2314yes—
572#385C2314yes—
573#385C2314yes—
574#385C2314yes—
575#385C2314yes—
576#385C2314yes—
577#385C2314yes—
578#385C2314yes—
579#385C2314yes—
580#385C2314yes—
581#385C2314yes—
582#385C2314yes—
583#385C2314yes—
584#385C2314yes—
585#385C2314yes—
586#385C2314yes—
587#385C2314yes—
588#385C2314yes—
589#384C2312yes—
590#384C2312yes—
591#382C2312yes—
592#382C2312yes—
593#382C2314yes—
594#382C2314yes—
595#382C2314yes—
596#381C2312yes—
597#381C2312yes—
598#381C2314yes—
599#380C2314yes—
600#380C2312yes—
601#380C2312yes—
602#380C2314yes—
603#380C2314yes—
604#380C2314yes—
605#380C2314yes—
606#380C2314yes—
607#380C2314yes—
608#379C2314yes—
609#379C2314yes—
610C4×C4⋊C4C2314yes—
611C4×C4⋊C4C2314yes—
612C4×C4⋊C4C2312yes—
613C4×C4⋊C4C2312yes—
614C4×C4⋊C4C2314yes—
615C4×C4⋊C4C2312yes—
616C4×C4⋊C4C2312yes—
617C4×C22⋊C4C2314yes—
618C4×C22⋊C4C2312yes—
619C4×C22⋊C4C2312yes—
620C4×C22⋊C4C2314yes—
621C4×C22⋊C4C2312yes—
622C4×C22⋊C4C2314yes—
623C4×C22⋊C4C2312yes—
624C4×C22⋊C4C2314yes—
625#376C2312yes—
626C43C2312yes—
627C25C2412yes—
628C25C2412yes—
629C2×#41—42no—
630C2×#41—42no—
631C2×#41—42no—
632C2×#41—42no—
633C2×#41—42no—
634C2×#41—42no—
635C22×Q8—42no—
636C22×Q8—42no—
637C22×Q8—42no—
638C22×Q8C2412yes—
639C22×Q8C2412yes—
640C22×Q8C2412yes—
641C22×Q8C2411yescharacteristic
642C22×Q8C2411yescharacteristic
643C22×Q8C2412yes—
644C22×D4—42no—
645C22×D4—42no—
646C22×D4—42no—
647C22×D4C2414yes—
648C22×D4C2412yes—
649C22×D4C2414yes—
650C22×D4C2414yes—
651C22×D4C2412yes—
652C22×D4C2412yes—
653C22×D4C2411yescharacteristic
654C22×D4C2412yes—
655C22×D4C2412yes—
656C22×D4C2411yescharacteristic
657C22×D4C2414yes—
658C22×D4C2414yes—
659C22×D4C2414yes—
660C22×D4C2414yes—
661C22×D4C2412yes—
662C22×D4C2414yes—
663C22×D4C2414yes—
664C22×D4C2414yes—
665C22×D4C2414yes—
666C22×D4C2414yes—
667C22×D4C2414yes—
668C23×C4C2411yescharacteristic
669C23×C4C2412yes—
670C23×C4C2412yes—
671C23×C4C2414yes—
672C23×C4C2412yes—
673C23×C4C2412yes—
674C23×C4C2412yes—
675C23×C4C2414yes—
676C23×C4C2414yes—
677C23×C4C2414yes—
678C23×C4C2412yes—
679C23×C4C2412yes—
680C4⋊Q8—44no—
681C4⋊Q8—44no—
682C4⋊Q8—42no—
683C4⋊Q8—44no—
684#127—42no—
685#127—44no—
686#127—44no—
687#127—44no—
688#126—216no—
689#126—48no—
690#126—48no—
691#126—48no—
692#125—28no—
693#125—48no—
694#125—82no—
695#125—82no—
696#124—28no—
697#124—24no—
698#124—24no—
699#124—28no—
700#124—48no—
701#124—44no—
702#124—44no—
703#124—44no—
704#124—44no—
705#124—48no—
706#124—44no—
707#124—44no—
708#124—48no—
709#124—44no—
710#123—28no—
711#123—216no—
712#123—48no—
713#123—48no—
714#123—48no—
715#123—48no—
716#123—48no—
717#123—48no—
718#123—44no—
719#123—44no—
720#123—44no—
721#123—84no—
722#123—84no—
723C22⋊Q8—28no—
724C22⋊Q8—48no—
725C22⋊Q8—48no—
726C22⋊Q8—48no—
727C22⋊Q8—48no—
728C22⋊Q8—48no—
729C22⋊Q8—48no—
730C22⋊Q8—44no—
731C22⋊Q8—44no—
732C22⋊Q8—82no—
733#121—28no—
734#121—48no—
735#121—44no—
736#121—48no—
737#121—48no—
738#121—48no—
739#121—48no—
740#121—48no—
741#121—48no—
742#121—44no—
743#121—48no—
744#121—84no—
745#121—82no—
746#121—84no—
747#121—84no—
748#121—84no—
749#121—84no—
750#120—28no—
751#120—48no—
752#120—48no—
753#120—48no—
754#120—44no—
755#120—44no—
756#120—48no—
757#120—44no—
758#120—84no—
759#120—84no—
760#120—84no—
761C4×Q8—82no—
762C4×D4—48no—
763C4×D4—48no—
764C4×D4—48no—
765C4×D4—48no—
766C4×D4—84no—
767C4×D4—82no—
768#117—24no—
769#117—24no—
770#117—48no—
771C2×C4⋊C4—44no—
772C2×C4⋊C4C2414yes—
773C2×C4⋊C4C2412yes—
774C2×C4⋊C4C2411yescharacteristic
775C2×C4⋊C4C2414yes—
776C2×C4⋊C4C2414yes—
777C2×C4⋊C4C2414yes—
778C2×C4⋊C4C2414yes—
779C2×C4⋊C4C2414yes—
780C2×C4⋊C4C2414yes—
781C2×C4⋊C4C2412yes—
782C2×C4⋊C4C2414yes—
783C2×C4⋊C4C2412yes—
784C2×C4⋊C4C2414yes—
785C2×C4⋊C4C2414yes—
786C2×C4⋊C4C2414yes—
787C2×C4⋊C4C2414yes—
788C2×C4⋊C4C2414yes—
789C2×C4⋊C4C2412yes—
790C2×C4⋊C4C2414yes—
791C2×C4⋊C4C2412yes—
792C2×C4⋊C4C2414yes—
793C2×C4⋊C4C2414yes—
794C2×C4⋊C4C2412yes—
795C2×C4⋊C4C2412yes—
796C2×C4⋊C4C2414yes—
797C2×C4⋊C4C2414yes—
798C2×C4⋊C4C2414yes—
799C2×C4⋊C4C2414yes—
800C2×C4⋊C4C2412yes—
801C2×C4⋊C4C2414yes—
802C2×C4⋊C4C2414yes—
803C2×C4⋊C4C2414yes—
804C2×C4⋊C4C2412yes—
805C2×C4⋊C4C2414yes—
806C2×C4⋊C4C2414yes—
807C2×C4⋊C4C2414yes—
808C2×C4⋊C4C2414yes—
809C2×C4⋊C4C2414yes—
810C2×C4⋊C4C2414yes—
811C2×C4⋊C4C2411yescharacteristic
812C2×C22⋊C4—48no—
813C2×C22⋊C4—44no—
814C2×C22⋊C4—48no—
815C2×C22⋊C4—84no—
816C2×C22⋊C4C2414yes—
817C2×C22⋊C4C2414yes—
818C2×C22⋊C4C2414yes—
819C2×C22⋊C4C2414yes—
820C2×C22⋊C4C2414yes—
821C2×C22⋊C4C2412yes—
822C2×C22⋊C4C2411yescharacteristic
823C2×C22⋊C4C2414yes—
824C2×C22⋊C4C2414yes—
825C2×C22⋊C4C2414yes—
826C2×C22⋊C4C2414yes—
827C2×C22⋊C4C2414yes—
828C2×C22⋊C4C2414yes—
829C2×C22⋊C4C2414yes—
830C2×C22⋊C4C2414yes—
831C2×C22⋊C4C2414yes—
832C2×C22⋊C4C2414yes—
833C2×C22⋊C4C2414yes—
834C2×C22⋊C4C2414yes—
835C2×C22⋊C4C2414yes—
836C2×C22⋊C4C2414yes—
837C2×C22⋊C4C2414yes—
838C2×C22⋊C4C2414yes—
839C2×C22⋊C4C2414yes—
840C2×C22⋊C4C2414yes—
841C2×C22⋊C4C2414yes—
842C2×C22⋊C4C2414yes—
843C2×C22⋊C4C2414yes—
844C2×C22⋊C4C2414yes—
845C2×C22⋊C4C2414yes—
846C2×C22⋊C4C2414yes—
847C2×C22⋊C4C2414yes—
848C2×C22⋊C4C2414yes—
849C2×C22⋊C4C2414yes—
850C2×C22⋊C4C2414yes—
851C2×C22⋊C4C2414yes—
852C2×C22⋊C4C2414yes—
853C2×C22⋊C4C2414yes—
854C2×C22⋊C4C2414yes—
855C2×C22⋊C4C2414yes—
856C2×C22⋊C4C2414yes—
857C2×C22⋊C4C2414yes—
858C2×C22⋊C4C2412yes—
859C2×C22⋊C4C2414yes—
860C2×C22⋊C4C2412yes—
861C2×C22⋊C4C2412yes—
862C2×C22⋊C4C2414yes—
863C2×C22⋊C4C2414yes—
864C2×C22⋊C4C2414yes—
865C2×C22⋊C4C2414yes—
866C2×C22⋊C4C2414yes—
867C2×C22⋊C4C2414yes—
868C2×C22⋊C4C2414yes—
869C2×C22⋊C4C2414yes—
870C2×C22⋊C4C2414yes—
871C2×C22⋊C4C2414yes—
872C2×C22⋊C4C2412yes—
873C2×C22⋊C4C2414yes—
874C2×C22⋊C4C2414yes—
875C2×C22⋊C4C2414yes—
876C2×C22⋊C4C2411yescharacteristic
877C2×C42—24no—
878C2×C42C2412yes—
879C2×C42C2412yes—
880C2×C42C2412yes—
881C2×C42C2414yes—
882C2×C42C2411yescharacteristic
883C2×C42C2412yes—
884C2×C42C2414yes—
885C2×C42C2412yes—
886C2×C42C2414yes—
887C2×C42C2412yes—
888C2×C42C2412yes—
889C2×C42C2412yes—
890C2×C42C2412yes—
891C2×C42C2412yes—
892C2×C42C2412yes—
893C2×C42C2414yes—
894C2×C42C2411yescharacteristic
895#95C2412yes—
896#95C2412yes—
897#95C2412yes—
898#95C2412yes—
899#95C2414yes—
900#95C2414yes—
901#95C2414yes—
902#95C2414yes—
903#95C2414yes—
904#95C2414yes—
905#95C2414yes—
906#95C2414yes—
907#95C2414yes—
908#95C2414yes—
909#95C2414yes—
910#95C2414yes—
911#95C2414yes—
912#95C2414yes—
913#95C2414yes—
914#95C2414yes—
915#95C2414yes—
916#95C2414yes—
917#95C2414yes—
918#95C2414yes—
919#95C2414yes—
920#95C2414yes—
921#95C2414yes—
922#95C2414yes—
923#95C2414yes—
924#95C2414yes—
925#95C2414yes—
926#95C2414yes—
927#95C2414yes—
928#95C2414yes—
929#95C2414yes—
930#95C2414yes—
931C24—24no—
932C24—42no—
933C24—42no—
934C24—44no—
935C24—44no—
936C24—44no—
937C24—42no—
938C24—42no—
939C24—44no—
940C24—42no—
941C24C2514yes—
942C24C2512yes—
943C24C2514yes—
944C24C2512yes—
945C24C2511yescharacteristic
946#41—88no—
947#41—88no—
948C2×Q8—24no—
949C2×Q8—24no—
950C2×Q8—24no—
951C2×Q8—22no—
952C2×Q8—22no—
953C2×Q8—42no—
954C2×Q8—42no—
955C2×Q8—42no—
956C2×Q8—41no—
957C2×Q8—41no—
958C2×Q8—42no—
959C2×Q8—42no—
960C2×Q8—41no—
961C2×Q8—41no—
962C2×Q8—42no—
963C2×Q8—42no—
964C2×Q8—42no—
965C2×Q8—42no—
966C2×Q8—88no—
967C2×D4—28no—
968C2×D4—24no—
969C2×D4—24no—
970C2×D4—28no—
971C2×D4—28no—
972C2×D4—24no—
973C2×D4—22no—
974C2×D4—24no—
975C2×D4—24no—
976C2×D4—22no—
977C2×D4—44no—
978C2×D4—44no—
979C2×D4—44no—
980C2×D4—42no—
981C2×D4—42no—
982C2×D4—44no—
983C2×D4—44no—
984C2×D4—44no—
985C2×D4—42no—
986C2×D4—42no—
987C2×D4—42no—
988C2×D4—44no—
989C2×D4—42no—
990C2×D4—42no—
991C2×D4—41no—
992C2×D4—41no—
993C2×D4—42no—
994C2×D4—42no—
995C2×D4—41no—
996C2×D4—41no—
997C2×D4—44no—
998C2×D4—42no—
999C2×D4—44no—
1000C2×D4—44no—
1001C2×D4—44no—
1002C2×D4—44no—
1003C2×D4—44no—
1004C2×D4—42no—
1005C2×D4—44no—
1006C2×D4—44no—
1007C2×D4—44no—
1008C2×D4—44no—
1009C2×D4—44no—
1010C2×D4—44no—
1011C2×D4—44no—
1012C2×D4—44no—
1013C2×D4—44no—
1014C2×D4—44no—
1015C2×D4—44no—
1016C2×D4—44no—
1017C2×D4—44no—
1018C2×D4—44no—
1019C2×D4—42no—
1020C2×D4—42no—
1021C2×D4—44no—
1022C2×D4—44no—
1023C2×D4—44no—
1024C2×D4—44no—
1025C2×D4—44no—
1026C2×D4—44no—
1027C2×D4—44no—
1028C2×D4—44no—
1029C2×D4—44no—
1030C2×D4—88no—
1031C22×C4—22no—
1032C22×C4—22no—
1033C22×C4—22no—
1034C22×C4—24no—
1035C22×C4—24no—
1036C22×C4—28no—
1037C22×C4—24no—
1038C22×C4—24no—
1039C22×C4—42no—
1040C22×C4—42no—
1041C22×C4—42no—
1042C22×C4—42no—
1043C22×C4—44no—
1044C22×C4—44no—
1045C22×C4—42no—
1046C22×C4—42no—
1047C22×C4—42no—
1048C22×C4—42no—
1049C22×C4—42no—
1050C22×C4—44no—
1051C22×C4—42no—
1052C22×C4—44no—
1053C22×C4—44no—
1054C22×C4—44no—
1055C22×C4—42no—
1056C22×C4—44no—
1057C22×C4—44no—
1058C22×C4—44no—
1059C22×C4—42no—
1060C22×C4—44no—
1061C22×C4—44no—
1062C22×C4—44no—
1063C22×C4—42no—
1064C22×C4—44no—
1065C22×C4C2514yes—
1066C22×C4C2512yes—
1067C22×C4C2512yes—
1068C22×C4C2514yes—
1069C22×C4C2514yes—
1070C22×C4C2514yes—
1071C22×C4C2514yes—
1072C22×C4C2514yes—
1073C22×C4C2512yes—
1074C22×C4C2512yes—
1075C22×C4C2512yes—
1076C22×C4C2514yes—
1077C22×C4C2514yes—
1078C22×C4C2511yescharacteristic
1079C22×C4C2511yescharacteristic
1080C22×C4C2512yes—
1081C22×C4C2512yes—
1082C22×C4C2512yes—
1083C4⋊C4—28no—
1084C4⋊C4—24no—
1085C4⋊C4—22no—
1086C4⋊C4—28no—
1087C4⋊C4—28no—
1088C4⋊C4—28no—
1089C4⋊C4—28no—
1090C4⋊C4—28no—
1091C4⋊C4—28no—
1092C4⋊C4—28no—
1093C4⋊C4—24no—
1094C4⋊C4—24no—
1095C4⋊C4—44no—
1096C4⋊C4—44no—
1097C4⋊C4—44no—
1098C4⋊C4—44no—
1099C4⋊C4—44no—
1100C4⋊C4—44no—
1101C4⋊C4—44no—
1102C4⋊C4—42no—
1103C4⋊C4—44no—
1104C4⋊C4—42no—
1105C4⋊C4—44no—
1106C4⋊C4—42no—
1107C4⋊C4—44no—
1108C4⋊C4—42no—
1109C4⋊C4—44no—
1110C4⋊C4—44no—
1111C4⋊C4—44no—
1112C4⋊C4—44no—
1113C4⋊C4—42no—
1114C4⋊C4—44no—
1115C4⋊C4—44no—
1116C4⋊C4—44no—
1117C4⋊C4—44no—
1118C4⋊C4—42no—
1119C4⋊C4—44no—
1120C4⋊C4—44no—
1121C4⋊C4—44no—
1122C4⋊C4H(5,𝔽2)14yes—
1123C22⋊C4—22no—
1124C22⋊C4—28no—
1125C22⋊C4—28no—
1126C22⋊C4—28no—
1127C22⋊C4—28no—
1128C22⋊C4—28no—
1129C22⋊C4—28no—
1130C22⋊C4—24no—
1131C22⋊C4—28no—
1132C22⋊C4—28no—
1133C22⋊C4—28no—
1134C22⋊C4—28no—
1135C22⋊C4—28no—
1136C22⋊C4—28no—
1137C22⋊C4—28no—
1138C22⋊C4—28no—
1139C22⋊C4—28no—
1140C22⋊C4—44no—
1141C22⋊C4—44no—
1142C22⋊C4—44no—
1143C22⋊C4—44no—
1144C22⋊C4—44no—
1145C22⋊C4—44no—
1146C22⋊C4—44no—
1147C22⋊C4—44no—
1148C22⋊C4—44no—
1149C22⋊C4—44no—
1150C22⋊C4—44no—
1151C22⋊C4—44no—
1152C22⋊C4—44no—
1153C22⋊C4—44no—
1154C22⋊C4—44no—
1155C22⋊C4—44no—
1156C22⋊C4—44no—
1157C22⋊C4—44no—
1158C22⋊C4—44no—
1159C22⋊C4—44no—
1160C22⋊C4—44no—
1161C22⋊C4—42no—
1162C22⋊C4—44no—
1163C22⋊C4—42no—
1164C22⋊C4—44no—
1165C22⋊C4—44no—
1166C22⋊C4—44no—
1167C22⋊C4—44no—
1168C22⋊C4—44no—
1169C22⋊C4—44no—
1170C22⋊C4—44no—
1171C22⋊C4—42no—
1172C22⋊C4—44no—
1173C22⋊C4—44no—
1174C22⋊C4—44no—
1175C22⋊C4—44no—
1176C22⋊C4—44no—
1177C22⋊C4—44no—
1178C22⋊C4—44no—
1179C22⋊C4—44no—
1180C22⋊C4—44no—
1181C22⋊C4—44no—
1182C22⋊C4—42no—
1183C22⋊C4H(5,𝔽2)14yes—
1184C42—24no—
1185C42—22no—
1186C42—24no—
1187C42—24no—
1188C42—28no—
1189C42—42no—
1190C42—44no—
1191C42—42no—
1192C42—42no—
1193C42—44no—
1194C42—42no—
1195C42—44no—
1196C42—42no—
1197C42—42no—
1198C42—42no—
1199C42—42no—
1200C42H(5,𝔽2)14yes—
1201C23—21no—
1202C23—21no—
1203C23—22no—
1204C23—22no—
1205C23—24no—
1206C23—22no—
1207C23—22no—
1208C23—24no—
1209C23—22no—
1210C23—24no—
1211C23—22no—
1212C23—24no—
1213C23—24no—
1214C23—24no—
1215C23—22no—
1216C23—22no—
1217C23—24no—
1218C23—24no—
1219C23—24no—
1220C23—24no—
1221C23—24no—
1222C23—24no—
1223C23—24no—
1224C23—24no—
1225C23—24no—
1226C23—24no—
1227C23—24no—
1228C23—24no—
1229C23—84no—
1230C23—88no—
1231C23—88no—
1232C23—88no—
1233C23—84no—
1234C23—162no—
1235C23—162no—
1236C23—162no—
1237C23—162no—
1238C23—164no—
1239C23C2×H(5,𝔽2)12yes—
1240C23C2611yescharacteristic
1241Q8—84no—
1242Q8—84no—
1243Q8—84no—
1244Q8—82no—
1245Q8—82no—
1246Q8—162no—
1247D4—88no—
1248D4—88no—
1249D4—84no—
1250D4—84no—
1251D4—84no—
1252D4—82no—
1253D4—82no—
1254D4—88no—
1255D4—84no—
1256D4—84no—
1257D4—88no—
1258D4—88no—
1259D4—164no—
1260D4—164no—
1261D4—164no—
1262D4—164no—
1263D4—164no—
1264D4—162no—
1265D4—164no—
1266D4—164no—
1267D4—164no—
1268C2×C4—28no—
1269C2×C4—21no—
1270C2×C4—21no—
1271C2×C4—21no—
1272C2×C4—21no—
1273C2×C4—22no—
1274C2×C4—22no—
1275C2×C4—22no—
1276C2×C4—22no—
1277C2×C4—22no—
1278C2×C4—22no—
1279C2×C4—22no—
1280C2×C4—22no—
1281C2×C4—22no—
1282C2×C4—24no—
1283C2×C4—24no—
1284C2×C4—24no—
1285C2×C4—24no—
1286C2×C4—24no—
1287C2×C4—22no—
1288C2×C4—22no—
1289C2×C4—22no—
1290C2×C4—24no—
1291C2×C4—24no—
1292C2×C4—22no—
1293C2×C4—22no—
1294C2×C4—24no—
1295C2×C4—24no—
1296C2×C4—24no—
1297C2×C4—24no—
1298C2×C4—24no—
1299C2×C4—22no—
1300C2×C4—22no—
1301C2×C4—24no—
1302C2×C4—22no—
1303C2×C4—24no—
1304C2×C4—22no—
1305C2×C4—24no—
1306C2×C4—24no—
1307C2×C4—24no—
1308C2×C4—24no—
1309C2×C4—24no—
1310C2×C4—22no—
1311C2×C4—24no—
1312C2×C4—22no—
1313C2×C4—24no—
1314C2×C4—24no—
1315C2×C4—24no—
1316C2×C4—24no—
1317C2×C4—22no—
1318C2×C4—88no—
1319C2×C4—84no—
1320C2×C4—84no—
1321C2×C4—84no—
1322C2×C4—84no—
1323C2×C4—84no—
1324C2×C4—164no—
1325C2×C4—162no—
1326C2×C4—164no—
1327C2×C4—162no—
1328C2×C4—164no—
1329C2×C4C2×H(5,𝔽2)14yes—
1330C2×C4C2×H(5,𝔽2)14yes—
1331C2×C4C2×H(5,𝔽2)12yes—
1332C2×C4C2×H(5,𝔽2)14yes—
1333C2×C4C2×H(5,𝔽2)12yes—
1334C22—24no—
1335C22—22no—
1336C22—41no—
1337C22—41no—
1338C22—42no—
1339C22—44no—
1340C22—44no—
1341C22—44no—
1342C22—44no—
1343C22—44no—
1344C22—44no—
1345C22—42no—
1346C22—44no—
1347C22—42no—
1348C22—44no—
1349C22—42no—
1350C22—44no—
1351C22—42no—
1352C22—44no—
1353C22—42no—
1354C22—42no—
1355C22—44no—
1356C22—44no—
1357C22—44no—
1358C22—44no—
1359C22—44no—
1360C22—44no—
1361C22—44no—
1362C22—44no—
1363C22—168no—
1364C22—168no—
1365C22C22×H(5,𝔽2)11yescharacteristic
1366C22C22×H(5,𝔽2)11yescharacteristic
1367C22C22×H(5,𝔽2)11yescharacteristic
1368C22H(7,𝔽2)12yes—
1369C222−1+612yes—
1370C4—24no—
1371C4—24no—
1372C4—22no—
1373C4—22no—
1374C4—24no—
1375C4—44no—
1376C4—44no—
1377C4—42no—
1378C4—44no—
1379C4—44no—
1380C4—42no—
1381C4—44no—
1382C4—42no—
1383C4—42no—
1384C4—44no—
1385C4—42no—
1386C4—44no—
1387C4—44no—
1388C2—42no—
1389C2—82no—
1390C2—84no—
1391C2—84no—
1392C2—82no—
1393C2#6283211yescharacteristic
1394C2#6287812yes—
1395C2#6304912yes—
1396C2#6306311yescharacteristic
1397C2#6306611yescharacteristic
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. #58584C2semidirect
2. #57222C2semidirect
3. #56618C2semidirect
4. #55028C2semidirect
5. #54922C2semidirect
6. #53486C2semidirect
7. #51409C2semidirect
8. #49786C2semidirect
9. #49564C2semidirect
10. #48830C2semidirect
11. #47685C2semidirect
12. #47303C2semidirect
13. #46424C2semidirect
14. #46361C2semidirect
15. #46228C2semidirect
16. #46225C2semidirect
17. #46015C2semidirect
18. #46014C2semidirect
19. #46000C2semidirect
20. #45999C2semidirect
21. #45976C2semidirect
22. #35329C2semidirect
23. #35135C2semidirect
24. C2×#563C22semidirect
26. C2×H(3,𝔽4)C22semidirect
28. C2×#551C22semidirect
29. C2×#539C22semidirect
30. C2×#538C22semidirect
32. C2×#536C22semidirect
34. C2×#535C22semidirect
36. C22×#124C22semidirect
37. #2861C22semidirect
38. #2859C22semidirect
40. #2858C22semidirect
41. #2851C22semidirect
43. #2837C22semidirect
44. #2829C22semidirect
45. #2828C22semidirect
46. #2826C22semidirect
47. #2820C22semidirect
48. #2820C22semidirect
49. #2820C22semidirect
51. #2819C22semidirect
52. #2816C22semidirect
53. #2816C22semidirect
54. #2813C22semidirect
55. #2808C22semidirect
56. #2780C22semidirect
57. #2773C22semidirect
58. #2753C22semidirect
59. #2752C22semidirect
60. #2748C22semidirect
61. #2742C22semidirect
62. #2734C22semidirect
63. #2732C22semidirect
64. #2731C22semidirect
65. #2730C22semidirect
66. #2730C22semidirect
67. #2727C22semidirect
68. #2724C22semidirect
69. #2723C22semidirect
70. #2723C22semidirect
71. #2717C22semidirect
72. #2715C22semidirect
73. #2715C22semidirect
75. #2714C22semidirect
76. #2714C22semidirect
77. #2714C22semidirect
78. #2711C22semidirect
79. #2711C22semidirect
80. #2710C22semidirect
81. #2710C22semidirect
82. #2710C22semidirect
83. #2710C22semidirect
84. #2709C22semidirect
85. #2707C22semidirect
86. #2707C22semidirect
88. #2706C22semidirect
89. #2706C22semidirect
90. #2705C22semidirect
91. #2700C22semidirect
92. #2698C22semidirect
93. #2697C22semidirect
94. #2697C22semidirect
95. #2694C22semidirect
96. #2694C22semidirect
97. #2692C22semidirect
98. #2691C22semidirect
99. #2688C22semidirect
100. #2688C22semidirect
101. #2686C22semidirect
102. #2683C22semidirect
103. #2682C22semidirect
104. #2681C22semidirect
105. #2679C22semidirect
106. #2678C22semidirect
107. #2678C22semidirect
108. #2678C22semidirect
109. #2678C22semidirect
110. #2678C22semidirect
111. #2677C22semidirect
115. #2674C22semidirect
116. #2673C22semidirect
117. #2672C22semidirect
118. #2672C22semidirect
119. #2672C22semidirect
121. #2671C22semidirect
126. #2669C22semidirect
127. #2667C22semidirect
128. #2658C22semidirect
130. #2654C22semidirect
131. #2649C22semidirect
133. #2630C22semidirect
134. #2624C22semidirect
135. #2617C22semidirect
136. #2617C22semidirect
137. #2583C22semidirect
138. #2580C22semidirect
139. #2566C22semidirect
140. #2560C22semidirect
141. #2559C22semidirect
142. #2557C22semidirect
144. #2554C22semidirect
145. #2550C22semidirect
146. #2540C22semidirect
147. #2540C22semidirect
148. #2540C22semidirect
150. #2539C22semidirect
151. #2539C22semidirect
152. #2539C22semidirect
153. #2539C22semidirect
154. #2535C22semidirect
155. #2530C22semidirect
156. #2529C22semidirect
157. #2517C22semidirect
158. #2516C22semidirect
159. #2513C22semidirect
160. #2512C22semidirect
161. #2512C22semidirect
162. #2511C22semidirect
163. #2500C22semidirect
164. #2491C22semidirect
166. #2489C22semidirect
167. #2479C22semidirect
168. #2479C22semidirect
169. #2477C22semidirect
170. #2472C22semidirect
171. #2470C22semidirect
172. #2466C22semidirect
173. #2461C22semidirect
174. #2461C22semidirect
175. #2459C22semidirect
176. #2456C22semidirect
177. #2455C22semidirect
178. #2454C22semidirect
179. #2454C22semidirect
180. #2453C22semidirect
181. #2449C22semidirect
184. #2439C22semidirect
185. #2437C22semidirect
186. #2437C22semidirect
189. #2428C22semidirect
190. #2426C22semidirect
192. #2424C22semidirect
193. #2424C22semidirect
194. #2424C22semidirect
195. #2423C22semidirect
197. #2422C22semidirect
198. #2418C22semidirect
199. #2418C22semidirect
200. #2416C22semidirect
201. #2414C22semidirect
202. #2412C22semidirect
203. #2410C22semidirect
204. #2409C22semidirect
205. #2406C22semidirect
207. #2379C22semidirect
208. #2379C22semidirect
209. #2379C22semidirect
210. #2376C22semidirect
211. #2358C22semidirect
212. #2335C22semidirect
213. #2334C22semidirect
214. #2333C22semidirect
215. #2332C22semidirect
216. C4×#125C22semidirect
217. C4×#124C22semidirect
218. C4×#117C22semidirect

Maximal subgroups

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

subgroupindex
#585842
#572222
#566182
#550282
#549222
#534862
#514092
#497862
#495642
#488302
#476852
#473032
#464242
#463612
#462282
#462252
#460152
#460142
#460002
#459992
#459762
#353292
#351352