Finite Group Databasebeta

← #8757183

Subgroups — #8757183

Order 512.

5176 conjugacy classes of subgroups.

The subgroup lattice has 1402 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#58878C214yesmaximal, complemented
2#57488C214yesmaximal, complemented
3#56309C214yesmaximal, complemented
4#55322C214yesmaximal, complemented
5#54197C214yesmaximal, complemented
6#53636C214yesmaximal, complemented
7#51317C212yesmaximal, complemented
8#50690C214yesmaximal, complemented
9#49562C212yesmaximal, complemented
10#48218C214yesmaximal, complemented
11#47497C214yesmaximal, complemented
12#46428C212yesmaximal, complemented
13#46357C212yesmaximal, complemented
14#46356C214yesmaximal, complemented
15#46228C211yesmaximal, characteristic, complemented
16#46225C211yesmaximal, characteristic, complemented
17#46016C212yesmaximal, complemented
18#46013C212yesmaximal, complemented
19#46000C212yesmaximal, complemented
20#45999C212yesmaximal, complemented
21#45976C212yesmaximal, complemented
22#35329C211yesmaximal, characteristic, complemented
23#35137C212yesmaximal, complemented
24C2×#563C2211yescharacteristic, complemented
25C2×#562C2212yes—
26C2×H(3,𝔽4)C2212yescomplemented
27C2×H(3,𝔽4)C2211yescharacteristic, complemented
28C2×#559C2212yes—
29C2×#543C2212yescomplemented
30C2×#537C2212yes—
31C2×#536C2211yescharacteristic
32C2×#536C2211yescharacteristic, complemented
33C2×#535C2211yescharacteristic
34C2×#535C2211yescharacteristic, complemented
35C2×#532C2211yescharacteristic
36C22×#124C2211yescharacteristic, complemented
37#2862C2212yescomplemented
38#2861C2212yescomplemented
39#2858C2212yes—
40#2858C2212yescomplemented
41#2851C2212yescomplemented
42#2850C2212yes—
43#2838C2214yescomplemented
44#2837C2214yescomplemented
45#2829C2214yescomplemented
46#2825C2214yescomplemented
47#2820C2212yescomplemented
48#2820C2212yescomplemented
49#2819C2212yes—
50#2819C2212yescomplemented
51#2817C2212yescomplemented
52#2816C2214yescomplemented
53#2815C2212yes—
54#2812C2214yescomplemented
55#2808C2214yescomplemented
56#2804C2214yescomplemented
57#2778C2214yescomplemented
58#2761C2214yescomplemented
59#2761C2214yescomplemented
60#2753C2214yescomplemented
61#2753C2214yescomplemented
62#2752C2214yescomplemented
63#2749C2214yescomplemented
64#2746C2214yescomplemented
65#2740C2214yescomplemented
66#2738C2214yescomplemented
67#2734C2212yescomplemented
68#2733C2214yescomplemented
69#2733C2214yescomplemented
70#2732C2214yescomplemented
71#2732C2214yescomplemented
72#2731C2212yescomplemented
73#2730C2214yescomplemented
74#2730C2214yescomplemented
75#2728C2214yescomplemented
76#2724C2212yescomplemented
77#2714C2214yescomplemented
78#2712C2214yescomplemented
79#2712C2214yescomplemented
80#2712C2214yescomplemented
81#2710C2214yescomplemented
82#2710C2214yescomplemented
83#2710C2214yescomplemented
84#2710C2214yescomplemented
85#2709C2212yes—
86#2709C2212yescomplemented
87#2705C2214yescomplemented
88#2700C2214yescomplemented
89#2700C2214yescomplemented
90#2700C2214yescomplemented
91#2700C2214yescomplemented
92#2699C2214yescomplemented
93#2696C2214yes—
94#2692C2214yescomplemented
95#2692C2214yescomplemented
96#2692C2214yescomplemented
97#2691C2214yescomplemented
98#2688C2214yescomplemented
99#2688C2214yescomplemented
100#2687C2214yescomplemented
101#2686C2214yescomplemented
102#2686C2214yescomplemented
103#2684C2212yescomplemented
104#2681C2214yescomplemented
105#2681C2214yescomplemented
106#2679C2212yescomplemented
107#2678C2214yescomplemented
108#2678C2214yescomplemented
109#2678C2214yescomplemented
110#2677C2214yescomplemented
111#2676C2214yes—
112#2676C2214yes—
113#2676C2214yes—
114#2676C2214yescomplemented
115#2676C2214yescomplemented
116#2674C2214yescomplemented
117#2673C2214yescomplemented
118#2672C2214yescomplemented
119#2672C2214yescomplemented
120#2672C2214yescomplemented
121#2670C2214yes—
122#2670C2214yescomplemented
123#2669C2214yes—
124#2669C2214yes—
125#2669C2214yes—
126#2669C2212yescomplemented
127#2658C2212yescomplemented
128#2657C2212yes—
129#2653C2214yescomplemented
130#2650C2214yescomplemented
131#2649C2214yescomplemented
132#2635C2214yescomplemented
133#2632C2214yescomplemented
134#2631C2214yescomplemented
135#2630C2214yescomplemented
136#2617C2214yes—
137#2607C2214yescomplemented
138#2592C2214yescomplemented
139#2591C2212yescomplemented
140#2561C2212yescomplemented
141#2560C2214yescomplemented
142#2557C2214yescomplemented
143#2555C2214yes—
144#2555C2214yes—
145#2554C2214yescomplemented
146#2545C2214yescomplemented
147#2544C2214yes—
148#2540C2214yescomplemented
149#2540C2214yescomplemented
150#2540C2214yescomplemented
151#2539C2214yescomplemented
152#2539C2214yescomplemented
153#2539C2214yescomplemented
154#2532C2214yescomplemented
155#2527C2214yescomplemented
156#2522C2214yescomplemented
157#2514C2212yescomplemented
158#2513C2212yescomplemented
159#2492C2214yescomplemented
160#2492C2212yescomplemented
161#2491C2212yes—
162#2491C2214yescomplemented
163#2491C2214yescomplemented
164#2477C2214yescomplemented
165#2474C2214yescomplemented
166#2472C2214yescomplemented
167#2472C2214yescomplemented
168#2466C2214yescomplemented
169#2465C2214yescomplemented
170#2461C2214yes—
171#2461C2214yescomplemented
172#2461C2214yescomplemented
173#2459C2214yescomplemented
174#2452C2212yescomplemented
175#2452C2214yescomplemented
176#2451C2212yescomplemented
177#2451C2214yescomplemented
178#2449C2214yescomplemented
179#2449C2214yescomplemented
180#2448C2214yescomplemented
181#2448C2214yescomplemented
182#2447C2214yescomplemented
183#2437C2214yescomplemented
184#2432C2212yes—
185#2432C2214yescomplemented
186#2431C2212yes—
187#2431C2214yescomplemented
188#2426C2214yescomplemented
189#2424C2214yes—
190#2424C2214yescomplemented
191#2424C2214yescomplemented
192#2424C2214yescomplemented
193#2424C2214yescomplemented
194#2421C2212yescomplemented
195#2420C2212yes—
196#2418C2214yescomplemented
197#2418C2214yescomplemented
198#2412C2214yescomplemented
199#2410C2214yescomplemented
200#2409C2214yescomplemented
201#2407C2214yescomplemented
202#2407C2214yescomplemented
203#2406C2212yescomplemented
204#2404C2212yes—
205#2404C2214yescomplemented
206#2404C2214yescomplemented
207#2379C2211yescharacteristic, complemented
208#2379C2211yescharacteristic, complemented
209#2379C2212yescomplemented
210#2376C2212yescomplemented
211#2358C2212yescomplemented
212#2337C2214yescomplemented
213#2333C2212yescomplemented
214#2332C2214yescomplemented
215#2332C2212yescomplemented
216C4×#125C2212yescomplemented
217C4×#124C2212yescomplemented
218C4×#117C2211yescharacteristic, complemented
219C22×#41C2311yescharacteristic
220C22×#41C2311yescharacteristic
221C22×#41C2314yes—
222C23×Q8C2311yescharacteristic
223C23×D4C2311yescharacteristic
224#563—44no—
225#562—48no—
226H(3,𝔽4)—48no—
227H(3,𝔽4)—44no—
228#559—48no—
229#543—48no—
230#537—48no—
231#536—44no—
232#536—44no—
233#535—44no—
234#535—44no—
235#532—44no—
236C2×C4⋊Q8C2312yes—
237C2×C4⋊Q8C2312yes—
238C2×C4⋊Q8C2311yescharacteristic
239C2×C4⋊Q8C2312yes—
240C2×C4⋊Q8C2312yes—
241C2×C4⋊Q8C2312yes—
242C2×#127C2312yes—
243C2×#127C2312yes—
244C2×#127C2311yescharacteristic
245C2×#127C2312yes—
246C2×#126C2314yes—
247C2×#125C2312yes—
248C2×#124—44no—
249C2×#124C2312yes—
250C2×#124C2312yes—
251C2×#124C2311yescharacteristic
252C2×#124C2311yescharacteristic
253C2×#124C2314yes—
254C2×#124C2312yes—
255C2×#124C2312yes—
256C2×#124C2312yes—
257C2×#124C2312yes—
258C2×#124C2314yes—
259C2×#124C2314yes—
260C2×#124C2312yes—
261C2×#124C2314yes—
262C2×#124C2314yes—
263C2×#124C2312yes—
264C2×#124C2312yes—
265C2×#124C2314yes—
266C2×#124C2314yes—
267C2×#124C2314yes—
268C2×#124C2314yes—
269C2×#123C2312yes—
270C2×#123C2312yes—
271C2×#123C2312yes—
272C2×#123C2312yes—
273C2×#123C2314yes—
274C2×#123C2314yes—
275C2×#123C2314yes—
276C2×#123C2314yes—
277C2×C22⋊Q8C2314yes—
278C2×C22⋊Q8C2312yes—
279C2×C22⋊Q8C2314yes—
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⋊Q8C2314yes—
289C2×C22⋊Q8C2314yes—
290C2×C22⋊Q8C2312yes—
291C2×#121C2312yes—
292C2×#121C2314yes—
293C2×#121C2312yes—
294C2×#121C2314yes—
295C2×#121C2314yes—
296C2×#121C2314yes—
297C2×#121C2314yes—
298C2×#121C2314yes—
299C2×#121C2314yes—
300C2×#121C2312yes—
301C2×#121C2312yes—
302C2×#121C2314yes—
303C2×#121C2314yes—
304C2×#121C2314yes—
305C2×#120C2312yes—
306C2×#120C2312yes—
307C2×#120C2314yes—
308C2×#120C2312yes—
309C2×#120C2312yes—
310C2×#120C2314yes—
311C2×#120C2314yes—
312C2×#120C2314yes—
313C2×#120C2314yes—
314C2×#120C2314yes—
315C2×#120C2314yes—
316C2×C4×Q8C2314yes—
317C2×C4×Q8C2312yes—
318C2×C4×D4C2314yes—
319C2×C4×D4C2314yes—
320C2×C4×D4C2314yes—
321C2×C4×D4C2314yes—
322C2×C4×D4C2312yes—
323C2×#117C2311yescharacteristic
324C2×#117C2311yescharacteristic
325C22×C4⋊C4C2312yes—
326C22×C22⋊C4C2312yes—
327C22×C22⋊C4C2314yes—
328C22×C22⋊C4C2314yes—
329C22×C22⋊C4C2314yes—
330C22×C42C2311yescharacteristic
331#401C2314yes—
332#400C2314yes—
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#398C2314yes—
347#398C2314yes—
348#398C2314yes—
349#398C2314yes—
350#398C2314yes—
351#398C2314yes—
352#397C2314yes—
353#397C2314yes—
354#397C2314yes—
355#397C2314yes—
356#397C2314yes—
357#397C2314yes—
358#397C2314yes—
359#397C2314yes—
360#397C2314yes—
361#397C2314yes—
362#397C2314yes—
363#397C2314yes—
364#397C2314yes—
365#397C2314yes—
366#397C2314yes—
367#397C2314yes—
368#396C2314yes—
369#396C2314yes—
370#396C2314yes—
371#396C2314yes—
372#396C2314yes—
373#396C2314yes—
374#396C2314yes—
375#396C2314yes—
376#396C2314yes—
377#396C2314yes—
378#396C2314yes—
379#395C2314yes—
380#395C2314yes—
381#395C2314yes—
382#395C2314yes—
383#395C2314yes—
384#395C2314yes—
385#394C2314yes—
386#394C2314yes—
387#394C2314yes—
388#394C2314yes—
389#394C2314yes—
390#394C2314yes—
391#394C2314yes—
392#394C2314yes—
393#394C2314yes—
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#393C2314yes—
418#393C2314yes—
419#393C2314yes—
420#393C2314yes—
421#393C2314yes—
422#393C2314yes—
423#393C2314yes—
424#393C2314yes—
425#393C2314yes—
426#393C2314yes—
427#393C2314yes—
428#393C2314yes—
429#393C2314yes—
430#392C2314yes—
431#392C2314yes—
432#392C2314yes—
433#392C2314yes—
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#391C2312yes—
452#391C2314yes—
453#391C2314yes—
454#391C2314yes—
455#391C2314yes—
456#391C2314yes—
457#391C2314yes—
458#391C2312yes—
459#391C2312yes—
460#391C2314yes—
461#391C2314yes—
462#391C2314yes—
463#391C2314yes—
464#391C2312yes—
465#391C2312yes—
466#391C2312yes—
467#390C2314yes—
468#390C2314yes—
469#390C2314yes—
470#390C2312yes—
471#390C2314yes—
472#390C2314yes—
473#390C2314yes—
474#390C2314yes—
475#390C2314yes—
476#390C2314yes—
477#390C2312yes—
478#390C2312yes—
479#390C2312yes—
480#390C2312yes—
481#390C2314yes—
482#390C2314yes—
483#390C2314yes—
484#390C2314yes—
485#390C2314yes—
486#390C2314yes—
487#390C2312yes—
488#390C2314yes—
489#389C2312yes—
490#389C2312yes—
491#389C2314yes—
492#389C2314yes—
493#389C2312yes—
494#389C2312yes—
495#389C2314yes—
496#389C2314yes—
497#388C2314yes—
498#388C2314yes—
499#388C2314yes—
500#388C2314yes—
501#388C2314yes—
502#388C2314yes—
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#387C2314yes—
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#386C2314yes—
544#386C2314yes—
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#386C2314yes—
560#386C2312yes—
561#386C2312yes—
562#386C2312yes—
563#386C2314yes—
564#386C2314yes—
565#386C2314yes—
566#386C2314yes—
567#386C2314yes—
568#386C2314yes—
569#386C2314yes—
570#386C2314yes—
571#386C2314yes—
572#386C2314yes—
573#386C2314yes—
574#386C2314yes—
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#385C2314yes—
590#385C2314yes—
591#383C2314yes—
592#382C2312yes—
593#382C2312yes—
594#382C2312yes—
595#382C2312yes—
596#381C2314yes—
597#381C2314yes—
598#381C2312yes—
599#381C2312yes—
600#381C2314yes—
601#381C2314yes—
602#380C2312yes—
603#380C2312yes—
604#380C2314yes—
605#380C2314yes—
606#380C2314yes—
607#380C2314yes—
608#379C2314yes—
609#379C2314yes—
610C4×C4⋊C4C2314yes—
611C4×C4⋊C4C2312yes—
612C4×C4⋊C4C2312yes—
613C4×C4⋊C4C2314yes—
614C4×C4⋊C4C2312yes—
615C4×C4⋊C4C2314yes—
616C4×C4⋊C4C2312yes—
617C4×C22⋊C4C2314yes—
618C4×C22⋊C4C2312yes—
619C4×C22⋊C4C2314yes—
620C4×C22⋊C4C2312yes—
621C4×C22⋊C4C2314yes—
622C4×C22⋊C4C2312yes—
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—
635C2×#41—48no—
636C2×#41—84no—
637C2×#41—84no—
638C22×Q8—42no—
639C22×Q8—42no—
640C22×Q8—42no—
641C22×Q8C2412yes—
642C22×Q8C2414yes—
643C22×Q8C2412yes—
644C22×Q8C2414yes—
645C22×Q8C2412yes—
646C22×Q8C2411yescharacteristic
647C22×Q8C2411yescharacteristic
648C22×Q8C2412yes—
649C22×D4—42no—
650C22×D4—42no—
651C22×D4—42no—
652C22×D4C2414yes—
653C22×D4C2412yes—
654C22×D4C2414yes—
655C22×D4C2412yes—
656C22×D4C2412yes—
657C22×D4C2411yescharacteristic
658C22×D4C2414yes—
659C22×D4C2412yes—
660C22×D4C2412yes—
661C22×D4C2411yescharacteristic
662C22×D4C2414yes—
663C22×D4C2414yes—
664C22×D4C2414yes—
665C22×D4C2412yes—
666C22×D4C2414yes—
667C22×D4C2414yes—
668C22×D4C2414yes—
669C22×D4C2414yes—
670C22×D4C2414yes—
671C22×D4C2414yes—
672C22×D4C2414yes—
673C23×C4C2411yescharacteristic
674C23×C4C2412yes—
675C23×C4C2412yes—
676C23×C4C2412yes—
677C23×C4C2414yes—
678C23×C4C2412yes—
679C23×C4C2412yes—
680C23×C4C2414yes—
681C23×C4C2414yes—
682C23×C4C2414yes—
683C23×C4C2412yes—
684C23×C4C2412yes—
685C4⋊Q8—44no—
686C4⋊Q8—44no—
687C4⋊Q8—42no—
688C4⋊Q8—44no—
689C4⋊Q8—82no—
690C4⋊Q8—82no—
691#127—42no—
692#127—44no—
693#127—44no—
694#127—44no—
695#126—48no—
696#125—28no—
697#124—216no—
698#124—28no—
699#124—24no—
700#124—24no—
701#124—28no—
702#124—48no—
703#124—44no—
704#124—44no—
705#124—44no—
706#124—44no—
707#124—48no—
708#124—44no—
709#124—48no—
710#124—44no—
711#124—48no—
712#124—48no—
713#124—48no—
714#124—44no—
715#124—84no—
716#124—84no—
717#123—28no—
718#123—48no—
719#123—48no—
720#123—48no—
721#123—48no—
722#123—44no—
723#123—44no—
724#123—44no—
725C22⋊Q8—28no—
726C22⋊Q8—216no—
727C22⋊Q8—48no—
728C22⋊Q8—48no—
729C22⋊Q8—48no—
730C22⋊Q8—48no—
731C22⋊Q8—48no—
732C22⋊Q8—48no—
733C22⋊Q8—48no—
734C22⋊Q8—48no—
735C22⋊Q8—44no—
736C22⋊Q8—44no—
737C22⋊Q8—48no—
738C22⋊Q8—82no—
739#121—28no—
740#121—48no—
741#121—44no—
742#121—48no—
743#121—48no—
744#121—48no—
745#121—48no—
746#121—48no—
747#121—48no—
748#121—44no—
749#121—82no—
750#121—84no—
751#121—84no—
752#121—84no—
753#120—28no—
754#120—48no—
755#120—48no—
756#120—48no—
757#120—44no—
758#120—44no—
759#120—48no—
760#120—44no—
761#120—84no—
762#120—84no—
763#120—84no—
764C4×Q8—48no—
765C4×Q8—82no—
766C4×D4—48no—
767C4×D4—48no—
768C4×D4—48no—
769C4×D4—82no—
770C4×D4—84no—
771#117—24no—
772#117—24no—
773C2×C4⋊C4—44no—
774C2×C4⋊C4C2414yes—
775C2×C4⋊C4C2412yes—
776C2×C4⋊C4C2411yescharacteristic
777C2×C4⋊C4C2414yes—
778C2×C4⋊C4C2414yes—
779C2×C4⋊C4C2414yes—
780C2×C4⋊C4C2414yes—
781C2×C4⋊C4C2414yes—
782C2×C4⋊C4C2412yes—
783C2×C4⋊C4C2412yes—
784C2×C4⋊C4C2414yes—
785C2×C4⋊C4C2414yes—
786C2×C4⋊C4C2414yes—
787C2×C4⋊C4C2412yes—
788C2×C4⋊C4C2414yes—
789C2×C4⋊C4C2414yes—
790C2×C4⋊C4C2414yes—
791C2×C4⋊C4C2412yes—
792C2×C4⋊C4C2412yes—
793C2×C4⋊C4C2414yes—
794C2×C4⋊C4C2414yes—
795C2×C4⋊C4C2412yes—
796C2×C4⋊C4C2414yes—
797C2×C4⋊C4C2414yes—
798C2×C4⋊C4C2412yes—
799C2×C4⋊C4C2414yes—
800C2×C4⋊C4C2414yes—
801C2×C4⋊C4C2414yes—
802C2×C4⋊C4C2414yes—
803C2×C4⋊C4C2414yes—
804C2×C4⋊C4C2412yes—
805C2×C4⋊C4C2414yes—
806C2×C4⋊C4C2414yes—
807C2×C4⋊C4C2411yescharacteristic
808C2×C22⋊C4—48no—
809C2×C22⋊C4—44no—
810C2×C22⋊C4—48no—
811C2×C22⋊C4—84no—
812C2×C22⋊C4C2414yes—
813C2×C22⋊C4C2414yes—
814C2×C22⋊C4C2414yes—
815C2×C22⋊C4C2414yes—
816C2×C22⋊C4C2414yes—
817C2×C22⋊C4C2412yes—
818C2×C22⋊C4C2411yescharacteristic
819C2×C22⋊C4C2414yes—
820C2×C22⋊C4C2414yes—
821C2×C22⋊C4C2414yes—
822C2×C22⋊C4C2414yes—
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⋊C4C2412yes—
850C2×C22⋊C4C2412yes—
851C2×C22⋊C4C2414yes—
852C2×C22⋊C4C2414yes—
853C2×C22⋊C4C2414yes—
854C2×C22⋊C4C2414yes—
855C2×C22⋊C4C2414yes—
856C2×C22⋊C4C2414yes—
857C2×C22⋊C4C2414yes—
858C2×C22⋊C4C2414yes—
859C2×C22⋊C4C2414yes—
860C2×C22⋊C4C2414yes—
861C2×C22⋊C4C2414yes—
862C2×C22⋊C4C2414yes—
863C2×C22⋊C4C2414yes—
864C2×C22⋊C4C2414yes—
865C2×C22⋊C4C2412yes—
866C2×C22⋊C4C2412yes—
867C2×C22⋊C4C2414yes—
868C2×C22⋊C4C2414yes—
869C2×C22⋊C4C2414yes—
870C2×C22⋊C4C2414yes—
871C2×C22⋊C4C2414yes—
872C2×C22⋊C4C2411yescharacteristic
873C2×C42—24no—
874C2×C42C2412yes—
875C2×C42C2412yes—
876C2×C42C2412yes—
877C2×C42C2414yes—
878C2×C42C2411yescharacteristic
879C2×C42C2414yes—
880C2×C42C2412yes—
881C2×C42C2414yes—
882C2×C42C2412yes—
883C2×C42C2414yes—
884C2×C42C2412yes—
885C2×C42C2412yes—
886C2×C42C2412yes—
887C2×C42C2412yes—
888C2×C42C2412yes—
889C2×C42C2412yes—
890C2×C42C2411yescharacteristic
891#95C2412yes—
892#95C2412yes—
893#95C2412yes—
894#95C2412yes—
895#95C2414yes—
896#95C2414yes—
897#95C2414yes—
898#95C2414yes—
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—44no—
934C24—42no—
935C24—44no—
936C24—44no—
937C24—42no—
938C24—42no—
939C24—42no—
940C24—44no—
941C24C2512yes—
942C24C2514yes—
943C24C2514yes—
944C24C2512yes—
945C24C2511yescharacteristic
946#41—88no—
947#41—88no—
948#41—832no—
949C2×Q8—28no—
950C2×Q8—24no—
951C2×Q8—28no—
952C2×Q8—24no—
953C2×Q8—24no—
954C2×Q8—22no—
955C2×Q8—22no—
956C2×Q8—42no—
957C2×Q8—42no—
958C2×Q8—42no—
959C2×Q8—41no—
960C2×Q8—41no—
961C2×Q8—42no—
962C2×Q8—42no—
963C2×Q8—44no—
964C2×Q8—44no—
965C2×Q8—41no—
966C2×Q8—41no—
967C2×Q8—44no—
968C2×Q8—42no—
969C2×Q8—44no—
970C2×Q8—42no—
971C2×Q8—42no—
972C2×Q8—42no—
973C2×Q8—88no—
974C2×D4—28no—
975C2×D4—24no—
976C2×D4—24no—
977C2×D4—28no—
978C2×D4—24no—
979C2×D4—22no—
980C2×D4—28no—
981C2×D4—24no—
982C2×D4—24no—
983C2×D4—22no—
984C2×D4—44no—
985C2×D4—44no—
986C2×D4—42no—
987C2×D4—44no—
988C2×D4—42no—
989C2×D4—44no—
990C2×D4—44no—
991C2×D4—44no—
992C2×D4—44no—
993C2×D4—44no—
994C2×D4—44no—
995C2×D4—42no—
996C2×D4—42no—
997C2×D4—42no—
998C2×D4—44no—
999C2×D4—44no—
1000C2×D4—44no—
1001C2×D4—44no—
1002C2×D4—42no—
1003C2×D4—42no—
1004C2×D4—41no—
1005C2×D4—41no—
1006C2×D4—42no—
1007C2×D4—42no—
1008C2×D4—44no—
1009C2×D4—41no—
1010C2×D4—41no—
1011C2×D4—42no—
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—44no—
1021C2×D4—44no—
1022C2×D4—44no—
1023C2×D4—44no—
1024C2×D4—42no—
1025C2×D4—44no—
1026C2×D4—44no—
1027C2×D4—44no—
1028C2×D4—44no—
1029C2×D4—44no—
1030C2×D4—42no—
1031C2×D4—44no—
1032C2×D4—44no—
1033C2×D4—44no—
1034C2×D4—44no—
1035C2×D4—44no—
1036C2×D4—44no—
1037C2×D4—88no—
1038C22×C4—22no—
1039C22×C4—22no—
1040C22×C4—22no—
1041C22×C4—24no—
1042C22×C4—24no—
1043C22×C4—28no—
1044C22×C4—24no—
1045C22×C4—24no—
1046C22×C4—42no—
1047C22×C4—44no—
1048C22×C4—42no—
1049C22×C4—44no—
1050C22×C4—42no—
1051C22×C4—42no—
1052C22×C4—44no—
1053C22×C4—44no—
1054C22×C4—42no—
1055C22×C4—44no—
1056C22×C4—42no—
1057C22×C4—44no—
1058C22×C4—42no—
1059C22×C4—42no—
1060C22×C4—42no—
1061C22×C4—44no—
1062C22×C4—42no—
1063C22×C4—44no—
1064C22×C4—42no—
1065C22×C4—42no—
1066C22×C4—44no—
1067C22×C4—44no—
1068C22×C4—44no—
1069C22×C4—44no—
1070C22×C4—42no—
1071C22×C4—44no—
1072C22×C4C2512yes—
1073C22×C4C2514yes—
1074C22×C4C2514yes—
1075C22×C4C2512yes—
1076C22×C4C2514yes—
1077C22×C4C2514yes—
1078C22×C4C2512yes—
1079C22×C4C2514yes—
1080C22×C4C2514yes—
1081C22×C4C2512yes—
1082C22×C4C2512yes—
1083C22×C4C2514yes—
1084C22×C4C2514yes—
1085C22×C4C2511yescharacteristic
1086C22×C4C2511yescharacteristic
1087C22×C4C2512yes—
1088C22×C4C2512yes—
1089C22×C4C2512yes—
1090C4⋊C4—28no—
1091C4⋊C4—24no—
1092C4⋊C4—22no—
1093C4⋊C4—28no—
1094C4⋊C4—28no—
1095C4⋊C4—28no—
1096C4⋊C4—28no—
1097C4⋊C4—28no—
1098C4⋊C4—24no—
1099C4⋊C4—24no—
1100C4⋊C4—44no—
1101C4⋊C4—44no—
1102C4⋊C4—44no—
1103C4⋊C4—44no—
1104C4⋊C4—44no—
1105C4⋊C4—44no—
1106C4⋊C4—42no—
1107C4⋊C4—44no—
1108C4⋊C4—44no—
1109C4⋊C4—42no—
1110C4⋊C4—42no—
1111C4⋊C4—44no—
1112C4⋊C4—42no—
1113C4⋊C4—44no—
1114C4⋊C4—44no—
1115C4⋊C4—44no—
1116C4⋊C4—42no—
1117C4⋊C4—44no—
1118C4⋊C4—44no—
1119C4⋊C4—44no—
1120C4⋊C4—44no—
1121C4⋊C4—44no—
1122C4⋊C4—42no—
1123C4⋊C4H(5,𝔽2)14yes—
1124C22⋊C4—22no—
1125C22⋊C4—28no—
1126C22⋊C4—28no—
1127C22⋊C4—28no—
1128C22⋊C4—28no—
1129C22⋊C4—28no—
1130C22⋊C4—28no—
1131C22⋊C4—24no—
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—28no—
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—42no—
1160C22⋊C4—44no—
1161C22⋊C4—44no—
1162C22⋊C4—44no—
1163C22⋊C4—44no—
1164C22⋊C4—42no—
1165C22⋊C4—44no—
1166C22⋊C4—44no—
1167C22⋊C4—44no—
1168C22⋊C4—44no—
1169C22⋊C4—44no—
1170C22⋊C4—44no—
1171C22⋊C4—44no—
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—42no—
1182C22⋊C4—42no—
1183C22⋊C4—44no—
1184C22⋊C4H(5,𝔽2)14yes—
1185C42—24no—
1186C42—22no—
1187C42—24no—
1188C42—24no—
1189C42—28no—
1190C42—42no—
1191C42—42no—
1192C42—44no—
1193C42—42no—
1194C42—44no—
1195C42—42no—
1196C42—44no—
1197C42—42no—
1198C42—42no—
1199C42—42no—
1200C42—42no—
1201C42H(5,𝔽2)14yes—
1202C23—21no—
1203C23—21no—
1204C23—22no—
1205C23—22no—
1206C23—22no—
1207C23—22no—
1208C23—22no—
1209C23—24no—
1210C23—24no—
1211C23—24no—
1212C23—24no—
1213C23—22no—
1214C23—24no—
1215C23—24no—
1216C23—22no—
1217C23—22no—
1218C23—24no—
1219C23—24no—
1220C23—24no—
1221C23—24no—
1222C23—24no—
1223C23—24no—
1224C23—24no—
1225C23—24no—
1226C23—24no—
1227C23—24no—
1228C23—24no—
1229C23—24no—
1230C23—48no—
1231C23—84no—
1232C23—88no—
1233C23—88no—
1234C23—162no—
1235C23—162no—
1236C23—162no—
1237C23—164no—
1238C23—162no—
1239C23—164no—
1240C23C2×H(5,𝔽2)12yes—
1241C23C2611yescharacteristic
1242Q8—88no—
1243Q8—84no—
1244Q8—84no—
1245Q8—84no—
1246Q8—88no—
1247Q8—82no—
1248Q8—82no—
1249Q8—162no—
1250D4—88no—
1251D4—84no—
1252D4—84no—
1253D4—84no—
1254D4—88no—
1255D4—82no—
1256D4—82no—
1257D4—88no—
1258D4—84no—
1259D4—84no—
1260D4—88no—
1261D4—88no—
1262D4—88no—
1263D4—88no—
1264D4—164no—
1265D4—164no—
1266D4—164no—
1267D4—162no—
1268D4—164no—
1269D4—164no—
1270D4—164no—
1271C2×C4—28no—
1272C2×C4—21no—
1273C2×C4—21no—
1274C2×C4—21no—
1275C2×C4—21no—
1276C2×C4—22no—
1277C2×C4—22no—
1278C2×C4—22no—
1279C2×C4—22no—
1280C2×C4—22no—
1281C2×C4—22no—
1282C2×C4—22no—
1283C2×C4—24no—
1284C2×C4—24no—
1285C2×C4—22no—
1286C2×C4—22no—
1287C2×C4—24no—
1288C2×C4—22no—
1289C2×C4—24no—
1290C2×C4—22no—
1291C2×C4—22no—
1292C2×C4—24no—
1293C2×C4—24no—
1294C2×C4—22no—
1295C2×C4—24no—
1296C2×C4—22no—
1297C2×C4—24no—
1298C2×C4—24no—
1299C2×C4—24no—
1300C2×C4—24no—
1301C2×C4—22no—
1302C2×C4—24no—
1303C2×C4—24no—
1304C2×C4—22no—
1305C2×C4—24no—
1306C2×C4—24no—
1307C2×C4—24no—
1308C2×C4—22no—
1309C2×C4—24no—
1310C2×C4—24no—
1311C2×C4—24no—
1312C2×C4—24no—
1313C2×C4—22no—
1314C2×C4—22no—
1315C2×C4—22no—
1316C2×C4—24no—
1317C2×C4—24no—
1318C2×C4—24no—
1319C2×C4—24no—
1320C2×C4—22no—
1321C2×C4—48no—
1322C2×C4—84no—
1323C2×C4—88no—
1324C2×C4—84no—
1325C2×C4—84no—
1326C2×C4—84no—
1327C2×C4—88no—
1328C2×C4—162no—
1329C2×C4—164no—
1330C2×C4—162no—
1331C2×C4—164no—
1332C2×C4C2×H(5,𝔽2)14yes—
1333C2×C4C2×H(5,𝔽2)14yes—
1334C2×C4C2×H(5,𝔽2)12yes—
1335C2×C4C2×H(5,𝔽2)14yes—
1336C2×C4C2×H(5,𝔽2)12yes—
1337C22—24no—
1338C22—22no—
1339C22—41no—
1340C22—41no—
1341C22—42no—
1342C22—42no—
1343C22—44no—
1344C22—44no—
1345C22—42no—
1346C22—42no—
1347C22—44no—
1348C22—42no—
1349C22—44no—
1350C22—44no—
1351C22—44no—
1352C22—44no—
1353C22—44no—
1354C22—44no—
1355C22—44no—
1356C22—42no—
1357C22—42no—
1358C22—44no—
1359C22—44no—
1360C22—44no—
1361C22—44no—
1362C22—44no—
1363C22—44no—
1364C22—44no—
1365C22—44no—
1366C22—168no—
1367C22—168no—
1368C22C22×H(5,𝔽2)11yescharacteristic
1369C22C22×H(5,𝔽2)11yescharacteristic
1370C22C22×H(5,𝔽2)11yescharacteristic
1371C22H(7,𝔽2)12yes—
1372C222−1+612yes—
1373C4—24no—
1374C4—24no—
1375C4—22no—
1376C4—22no—
1377C4—24no—
1378C4—44no—
1379C4—44no—
1380C4—42no—
1381C4—44no—
1382C4—42no—
1383C4—44no—
1384C4—44no—
1385C4—42no—
1386C4—42no—
1387C4—44no—
1388C4—42no—
1389C4—44no—
1390C4—44no—
1391C2—42no—
1392C2—82no—
1393C2—84no—
1394C2—84no—
1395C2—82no—
1396C2#6283211yescharacteristic
1397C2#6287812yes—
1398C2#6304511yescharacteristic
1399C2#6304811yescharacteristic
1400C2#6304912yes—
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. #58878C2semidirect
2. #57488C2semidirect
3. #56309C2semidirect
4. #55322C2semidirect
5. #54197C2semidirect
6. #53636C2semidirect
7. #51317C2semidirect
8. #50690C2semidirect
9. #49562C2semidirect
10. #48218C2semidirect
11. #47497C2semidirect
12. #46428C2semidirect
13. #46357C2semidirect
14. #46356C2semidirect
15. #46228C2semidirect
16. #46225C2semidirect
17. #46016C2semidirect
18. #46013C2semidirect
19. #46000C2semidirect
20. #45999C2semidirect
21. #45976C2semidirect
22. #35329C2semidirect
23. #35137C2semidirect
24. C2×#563C22semidirect
26. C2×H(3,𝔽4)C22semidirect
27. C2×H(3,𝔽4)C22semidirect
29. C2×#543C22semidirect
32. C2×#536C22semidirect
34. C2×#535C22semidirect
36. C22×#124C22semidirect
37. #2862C22semidirect
38. #2861C22semidirect
40. #2858C22semidirect
41. #2851C22semidirect
43. #2838C22semidirect
44. #2837C22semidirect
45. #2829C22semidirect
46. #2825C22semidirect
47. #2820C22semidirect
48. #2820C22semidirect
50. #2819C22semidirect
51. #2817C22semidirect
52. #2816C22semidirect
54. #2812C22semidirect
55. #2808C22semidirect
56. #2804C22semidirect
57. #2778C22semidirect
58. #2761C22semidirect
59. #2761C22semidirect
60. #2753C22semidirect
61. #2753C22semidirect
62. #2752C22semidirect
63. #2749C22semidirect
64. #2746C22semidirect
65. #2740C22semidirect
66. #2738C22semidirect
67. #2734C22semidirect
68. #2733C22semidirect
69. #2733C22semidirect
70. #2732C22semidirect
71. #2732C22semidirect
72. #2731C22semidirect
73. #2730C22semidirect
74. #2730C22semidirect
75. #2728C22semidirect
76. #2724C22semidirect
77. #2714C22semidirect
78. #2712C22semidirect
79. #2712C22semidirect
80. #2712C22semidirect
81. #2710C22semidirect
82. #2710C22semidirect
83. #2710C22semidirect
84. #2710C22semidirect
86. #2709C22semidirect
87. #2705C22semidirect
88. #2700C22semidirect
89. #2700C22semidirect
90. #2700C22semidirect
91. #2700C22semidirect
92. #2699C22semidirect
94. #2692C22semidirect
95. #2692C22semidirect
96. #2692C22semidirect
97. #2691C22semidirect
98. #2688C22semidirect
99. #2688C22semidirect
100. #2687C22semidirect
101. #2686C22semidirect
102. #2686C22semidirect
103. #2684C22semidirect
104. #2681C22semidirect
105. #2681C22semidirect
106. #2679C22semidirect
107. #2678C22semidirect
108. #2678C22semidirect
109. #2678C22semidirect
110. #2677C22semidirect
114. #2676C22semidirect
115. #2676C22semidirect
116. #2674C22semidirect
117. #2673C22semidirect
118. #2672C22semidirect
119. #2672C22semidirect
120. #2672C22semidirect
122. #2670C22semidirect
126. #2669C22semidirect
127. #2658C22semidirect
129. #2653C22semidirect
130. #2650C22semidirect
131. #2649C22semidirect
132. #2635C22semidirect
133. #2632C22semidirect
134. #2631C22semidirect
135. #2630C22semidirect
137. #2607C22semidirect
138. #2592C22semidirect
139. #2591C22semidirect
140. #2561C22semidirect
141. #2560C22semidirect
142. #2557C22semidirect
145. #2554C22semidirect
146. #2545C22semidirect
148. #2540C22semidirect
149. #2540C22semidirect
150. #2540C22semidirect
151. #2539C22semidirect
152. #2539C22semidirect
153. #2539C22semidirect
154. #2532C22semidirect
155. #2527C22semidirect
156. #2522C22semidirect
157. #2514C22semidirect
158. #2513C22semidirect
159. #2492C22semidirect
160. #2492C22semidirect
162. #2491C22semidirect
163. #2491C22semidirect
164. #2477C22semidirect
165. #2474C22semidirect
166. #2472C22semidirect
167. #2472C22semidirect
168. #2466C22semidirect
169. #2465C22semidirect
171. #2461C22semidirect
172. #2461C22semidirect
173. #2459C22semidirect
174. #2452C22semidirect
175. #2452C22semidirect
176. #2451C22semidirect
177. #2451C22semidirect
178. #2449C22semidirect
179. #2449C22semidirect
180. #2448C22semidirect
181. #2448C22semidirect
182. #2447C22semidirect
183. #2437C22semidirect
185. #2432C22semidirect
187. #2431C22semidirect
188. #2426C22semidirect
190. #2424C22semidirect
191. #2424C22semidirect
192. #2424C22semidirect
193. #2424C22semidirect
194. #2421C22semidirect
196. #2418C22semidirect
197. #2418C22semidirect
198. #2412C22semidirect
199. #2410C22semidirect
200. #2409C22semidirect
201. #2407C22semidirect
202. #2407C22semidirect
203. #2406C22semidirect
205. #2404C22semidirect
206. #2404C22semidirect
207. #2379C22semidirect
208. #2379C22semidirect
209. #2379C22semidirect
210. #2376C22semidirect
211. #2358C22semidirect
212. #2337C22semidirect
213. #2333C22semidirect
214. #2332C22semidirect
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
#588782
#574882
#563092
#553222
#541972
#536362
#513172
#506902
#495622
#482182
#474972
#464282
#463572
#463562
#462282
#462252
#460162
#460132
#460002
#459992
#459762
#353292
#351372