Finite Group Databasebeta

← #7669578

Subgroups — #7669578

Order 512.

5541 conjugacy classes of subgroups.

The subgroup lattice has 1392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#52295C214yesmaximal, complemented
2#52169C214yesmaximal, complemented
3#45050C212yesmaximal, complemented
4#45034C212yesmaximal, complemented
5#45007C212yesmaximal, complemented
6#44991C212yesmaximal, complemented
7#44982C211yesmaximal, characteristic, complemented
8#44965C211yesmaximal, characteristic, complemented
9#44948C211yesmaximal, characteristic, complemented
10#44931C211yesmaximal, characteristic, complemented
11#44911C212yesmaximal, complemented
12#44880C212yesmaximal, complemented
13#44438C214yesmaximal, complemented
14#44156C214yesmaximal, complemented
15#43840C214yesmaximal, complemented
16#43423C214yesmaximal, complemented
17#34970C212yesmaximal, complemented
18#34964C214yesmaximal, complemented
19#34934C212yesmaximal, complemented
20#34914C212yesmaximal, complemented
21#34893C212yesmaximal, complemented
22#34735C214yesmaximal, complemented
23#34552C211yesmaximal, characteristic, complemented
24C4×#554C212yesmaximal, complemented
25C4×#550C212yesmaximal, complemented
26C4×#540C211yesmaximal, characteristic, complemented
27C4×#540C211yesmaximal, characteristic, complemented
28C2×#554C2212yes—
29C2×#550C2212yes—
30C2×#540C2211yescharacteristic
31C2×#540C2211yescharacteristic
32C2×#529C2214yes—
33C2×#529C2214yes—
34C2×C4×#41C2214yes—
35#2802C2214yes—
36#2798C2214yes—
37#2788C2214yes—
38#2786C2214yes—
39#2779C2214yes—
40#2751C2214yes—
41#2747C2214yes—
42#2743C2214yes—
43#2739C2214yes—
44#2727C2214yes—
45#2726C2214yes—
46#2715C2214yes—
47#2715C2214yes—
48#2708C2214yes—
49#2707C2214yes—
50#2707C2214yes—
51#2702C2214yes—
52#2702C2214yes—
53#2701C2214yes—
54#2696C2214yes—
55#2695C2214yes—
56#2695C2214yes—
57#2692C2214yes—
58#2687C2214yes—
59#2683C2214yes—
60#2682C2214yes—
61#2681C2214yes—
62#2676C2214yes—
63#2676C2214yes—
64#2671C2214yes—
65#2671C2214yes—
66#2671C2214yes—
67#2601C2214yes—
68#2601C2214yes—
69#2601C2214yes—
70#2601C2214yes—
71#2592C2214yes—
72#2589C2214yes—
73#2587C2214yes—
74#2584C2212yes—
75#2584C2214yes—
76#2580C2212yes—
77#2566C2212yes—
78#2562C2214yes—
79#2560C2214yes—
80#2559C2214yes—
81#2558C2214yes—
82#2557C2214yes—
83#2554C2214yes—
84#2554C2214yes—
85#2552C2212yes—
86#2550C2212yes—
87#2548C2212yes—
88#2541C2212yes—
89#2540C2214yes—
90#2538C2212yes—
91#2531C2214yes—
92#2526C2214yes—
93#2522C2214yes—
94#2513C2212yes—
95#2512C2212yes—
96#2512C2212yes—
97#2512C2212yes—
98#2509C2212yes—
99#2507C2212yes—
100#2507C2212yes—
101#2506C2212yes—
102#2498C2214yes—
103#2498C2214yes—
104#2497C2212yes—
105#2496C2212yes—
106#2491C2212yes—
107#2490C2214yes—
108#2490C2212yes—
109#2479C2214yes—
110#2478C2214yes—
111#2476C2214yes—
112#2475C2214yes—
113#2474C2214yes—
114#2471C2214yes—
115#2469C2214yes—
116#2468C2214yes—
117#2465C2214yes—
118#2462C2214yes—
119#2461C2214yes—
120#2454C2212yes—
121#2454C2212yes—
122#2452C2212yes—
123#2452C2212yes—
124#2449C2214yes—
125#2445C2212yes—
126#2445C2212yes—
127#2445C2212yes—
128#2445C2212yes—
129#2443C2214yes—
130#2438C2214yes—
131#2430C2214yes—
132#2430C2214yes—
133#2430C2214yes—
134#2428C2212yes—
135#2428C2212yes—
136#2426C2214yes—
137#2425C2214yes—
138#2422C2212yes—
139#2420C2212yes—
140#2419C2214yes—
141#2417C2214yes—
142#2417C2214yes—
143#2416C2214yes—
144#2416C2214yes—
145#2413C2214yes—
146#2406C2214yes—
147#2402C2212yes—
148#2402C2212yes—
149#2402C2211yescharacteristic
150#2402C2211yescharacteristic
151#2399C2211yescharacteristic
152#2399C2211yescharacteristic
153#2399C2212yes—
154#2399C2212yes—
155#2398C2214yes—
156#2396C2214yes—
157#2396C2214yes—
158#2396C2212yes—
159#2396C2212yes—
160#2396C2212yes—
161#2396C2212yes—
162#2396C2212yes—
163#2396C2212yes—
164#2395C2214yes—
165#2392C2214yes—
166#2392C2214yes—
167#2392C2214yes—
168#2392C2214yes—
169#2370C2212yes—
170#2370C2212yes—
171#2369C2212yes—
172#2368C2214yes—
173#2368C2214yes—
174#2366C2212yes—
175#2366C2212yes—
176#2366C2212yes—
177#2363C2214yes—
178#2363C2214yes—
179#2363C2214yes—
180#2360C2214yes—
181#2355C2212yes—
182#2354C2212yes—
183#2354C2212yes—
184#2354C2212yes—
185Q8×C4⋊C4C2212yes—
186#2349C2212yes—
187#2349C2212yes—
188D4×C4⋊C4C2212yes—
189#2345C2214yes—
190#2341C2214yes—
191#2335C2214yes—
192#2335C2214yes—
193#2333C2214yes—
194#2333C2214yes—
195#2330C2211yescharacteristic
196#2330C2211yescharacteristic
197#2328C2211yescharacteristic
198#2328C2211yescharacteristic
199#2324C2212yes—
200#2324C2212yes—
201#2319C2212yes—
202#2319C2212yes—
203#2314C2211yescharacteristic
204#2314C2211yescharacteristic
205C4×C4⋊Q8C2212yes—
206C4×#127C2211yescharacteristic
207C4×#127C2211yescharacteristic
208C4×#127C2212yes—
209C4×#127C2212yes—
210C4×#125C2211yescharacteristic
211C4×#125C2211yescharacteristic
212C4×#125C2212yes—
213C4×C22⋊Q8C2214yes—
214C4×C22⋊Q8C2214yes—
215C4×C22⋊Q8C2214yes—
216C4×C22⋊Q8C2214yes—
217C4×#123C2214yes—
218C4×#123C2214yes—
219C4×#123C2214yes—
220C4×#121C2212yes—
221C4×#121C2212yes—
222C4×#121C2214yes—
223C4×#121C2214yes—
224C4×#121C2214yes—
225C4×#121C2214yes—
226C4×#121C2214yes—
227C4×#121C2214yes—
228C4×#121C2214yes—
229#2296C2214yes—
230#2293C2212yes—
231#2293C2212yes—
232#2290C2214yes—
233C42×Q8C2212yes—
234C42×Q8C2212yes—
235C42×D4C2212yes—
236C42×D4C2212yes—
237C42×D4C2212yes—
238C42×D4C2212yes—
239C4×#117C2211yescharacteristic
240C4×#117C2211yescharacteristic
241C4×#117C2211yescharacteristic
242C2×C4×C4⋊C4C2214yes—
243C22×#41C2314yes—
244#554—216no—
245#550—216no—
246#540—28no—
247#540—28no—
248C2×C4⋊Q8C2312yes—
249C2×#127C2311yescharacteristic
250C2×#127C2312yes—
251C2×#127C2312yes—
252C2×#127C2311yescharacteristic
253#529—416no—
254#529—416no—
255C2×#126C2314yes—
256C2×#126C2314yes—
257C2×#126C2314yes—
258C2×#126C2314yes—
259C2×#125C2311yescharacteristic
260C2×#125C2312yes—
261C2×#125C2314yes—
262C2×#125C2314yes—
263C2×#125C2311yescharacteristic
264C2×#124C2314yes—
265C2×#124C2314yes—
266C2×#123C2314yes—
267C2×#123C2314yes—
268C2×#123C2314yes—
269C2×#123C2314yes—
270C2×#123C2314yes—
271C2×#123C2314yes—
272C2×#123C2314yes—
273C2×C22⋊Q8C2314yes—
274C2×C22⋊Q8C2314yes—
275C2×C22⋊Q8C2314yes—
276C2×C22⋊Q8C2314yes—
277C2×C22⋊Q8C2314yes—
278C2×C22⋊Q8C2314yes—
279C2×#121C2312yes—
280C2×#121C2312yes—
281C2×#121C2314yes—
282C2×#121C2314yes—
283C2×#121C2314yes—
284C2×#121C2314yes—
285C2×#121C2314yes—
286C2×#121C2314yes—
287C2×#121C2314yes—
288C2×#121C2314yes—
289C2×#121C2314yes—
290C4×#41—416no—
291C2×C4×Q8C2312yes—
292C2×C4×Q8C2312yes—
293C2×C4×Q8C2312yes—
294C2×C4×Q8C2312yes—
295C2×C4×Q8C2314yes—
296C2×C4×Q8C2314yes—
297C2×C4×Q8C2312yes—
298C2×C4×Q8C2312yes—
299C2×C4×D4C2312yes—
300C2×C4×D4C2312yes—
301C2×C4×D4C2314yes—
302C2×C4×D4C2312yes—
303C2×C4×D4C2312yes—
304C2×C4×D4C2312yes—
305C2×C4×D4C2312yes—
306C2×C4×D4C2312yes—
307C2×C4×D4C2312yes—
308C2×C4×D4C2312yes—
309C2×C4×D4C2312yes—
310C2×C4×D4C2314yes—
311C2×C4×D4C2314yes—
312C2×C4×D4C2314yes—
313C2×C4×D4C2314yes—
314C2×C4×D4C2314yes—
315C2×C4×D4C2314yes—
316C2×C4×D4C2314yes—
317C2×C4×D4C2314yes—
318C2×C4×D4C2314yes—
319C2×C4×D4C2314yes—
320C2×#117C2311yescharacteristic
321C2×#117C2311yescharacteristic
322C2×#117C2312yes—
323C2×#117C2314yes—
324C2×#117C2314yes—
325C2×#117C2314yes—
326C2×#117C2314yes—
327C2×#117C2314yes—
328C2×#117C2312yes—
329C22×C4⋊C4C2314yes—
330C22×C4⋊C4C2314yes—
331C22×C42C2314yes—
332C22×C42C2311yescharacteristic
333C22×C42C2314yes—
334C22×C42C2314yes—
335C22×C42C2314yes—
336#400C2312yes—
337#400C2314yes—
338#400C2314yes—
339#400C2314yes—
340#400C2312yes—
341#400C2312yes—
342#400C2312yes—
343#400C2312yes—
344#400C2312yes—
345#400C2314yes—
346#400C2314yes—
347#399C2314yes—
348#399C2314yes—
349#399C2314yes—
350#399C2312yes—
351#399C2312yes—
352#398C2314yes—
353#398C2314yes—
354#398C2314yes—
355#398C2314yes—
356#398C2314yes—
357#398C2312yes—
358#398C2312yes—
359#398C2314yes—
360#398C2314yes—
361#398C2314yes—
362#398C2314yes—
363#398C2312yes—
364#398C2312yes—
365#398C2312yes—
366#398C2312yes—
367#398C2312yes—
368#398C2312yes—
369#398C2312yes—
370#398C2312yes—
371#398C2312yes—
372#398C2312yes—
373#397C2314yes—
374#397C2314yes—
375#397C2314yes—
376#397C2314yes—
377#397C2314yes—
378#397C2314yes—
379#397C2314yes—
380#397C2314yes—
381#397C2314yes—
382#396C2314yes—
383#396C2314yes—
384#396C2314yes—
385#396C2314yes—
386#396C2312yes—
387#396C2312yes—
388#396C2314yes—
389#396C2314yes—
390#396C2314yes—
391#396C2314yes—
392#396C2314yes—
393#396C2314yes—
394#396C2314yes—
395#396C2314yes—
396#396C2312yes—
397#396C2312yes—
398#395C2312yes—
399#395C2314yes—
400#395C2312yes—
401#395C2312yes—
402#395C2312yes—
403#395C2312yes—
404#395C2312yes—
405#395C2314yes—
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#393C2314yes—
423#393C2314yes—
424#393C2314yes—
425#393C2312yes—
426#393C2312yes—
427#393C2314yes—
428#392C2314yes—
429#392C2314yes—
430#392C2314yes—
431#392C2314yes—
432#391C2314yes—
433#391C2314yes—
434#391C2314yes—
435#391C2314yes—
436#391C2314yes—
437#390C2314yes—
438#390C2312yes—
439#390C2312yes—
440#390C2314yes—
441#390C2314yes—
442#390C2314yes—
443#390C2312yes—
444#390C2312yes—
445#390C2312yes—
446#390C2312yes—
447#390C2314yes—
448#390C2314yes—
449#390C2312yes—
450#390C2312yes—
451#390C2312yes—
452#390C2312yes—
453#390C2314yes—
454#390C2314yes—
455#390C2312yes—
456#390C2312yes—
457#390C2314yes—
458#390C2314yes—
459#390C2314yes—
460#390C2314yes—
461#390C2314yes—
462#389C2312yes—
463#389C2312yes—
464#389C2312yes—
465#389C2312yes—
466#389C2312yes—
467#389C2312yes—
468#389C2314yes—
469#389C2312yes—
470#389C2312yes—
471#389C2314yes—
472#389C2314yes—
473#389C2314yes—
474#389C2314yes—
475#389C2314yes—
476#389C2314yes—
477#389C2314yes—
478#389C2314yes—
479#389C2312yes—
480#389C2312yes—
481#389C2314yes—
482#389C2314yes—
483#389C2314yes—
484#389C2314yes—
485#389C2314yes—
486#389C2314yes—
487#389C2314yes—
488#389C2312yes—
489#389C2312yes—
490#388C2314yes—
491#388C2314yes—
492#388C2314yes—
493#388C2314yes—
494#388C2314yes—
495#388C2314yes—
496#388C2314yes—
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#387C2314yes—
519#387C2314yes—
520#387C2314yes—
521#387C2314yes—
522#387C2314yes—
523#387C2314yes—
524#387C2314yes—
525#387C2314yes—
526#387C2314yes—
527#387C2314yes—
528#387C2314yes—
529#387C2314yes—
530#387C2314yes—
531#387C2314yes—
532#387C2314yes—
533#387C2314yes—
534#387C2314yes—
535#387C2314yes—
536#387C2314yes—
537#387C2314yes—
538#386C2314yes—
539#386C2314yes—
540#386C2314yes—
541#386C2314yes—
542#386C2314yes—
543#386C2314yes—
544#386C2314yes—
545#386C2314yes—
546#386C2314yes—
547#386C2314yes—
548#386C2314yes—
549#386C2314yes—
550#386C2314yes—
551#386C2314yes—
552#386C2314yes—
553#386C2314yes—
554#386C2314yes—
555#386C2314yes—
556#386C2314yes—
557#386C2314yes—
558#386C2314yes—
559#385C2314yes—
560#385C2314yes—
561#385C2314yes—
562#385C2314yes—
563#385C2314yes—
564#385C2314yes—
565#385C2314yes—
566#385C2314yes—
567#385C2314yes—
568#385C2314yes—
569#385C2314yes—
570#385C2314yes—
571#385C2314yes—
572#385C2314yes—
573#385C2314yes—
574#385C2314yes—
575#385C2314yes—
576#384C2311yescharacteristic
577#384C2311yescharacteristic
578#384C2312yes—
579#384C2312yes—
580#384C2312yes—
581#382C2312yes—
582#382C2311yescharacteristic
583#382C2311yescharacteristic
584#381C2314yes—
585#381C2314yes—
586#381C2314yes—
587#380C2314yes—
588#380C2314yes—
589#380C2314yes—
590#380C2314yes—
591#380C2312yes—
592#380C2312yes—
593#380C2314yes—
594#380C2314yes—
595#380C2314yes—
596#380C2314yes—
597#380C2314yes—
598#380C2314yes—
599#380C2314yes—
600C4×C4⋊C4C2312yes—
601C4×C4⋊C4C2312yes—
602C4×C4⋊C4C2312yes—
603C4×C4⋊C4C2314yes—
604C4×C4⋊C4C2314yes—
605C4×C4⋊C4C2314yes—
606C4×C4⋊C4C2314yes—
607C4×C4⋊C4C2314yes—
608C4×C4⋊C4C2314yes—
609C4×C4⋊C4C2312yes—
610C4×C4⋊C4C2312yes—
611C4×C4⋊C4C2312yes—
612C4×C4⋊C4C2312yes—
613C4×C4⋊C4C2312yes—
614C4×C4⋊C4C2314yes—
615C4×C4⋊C4C2312yes—
616C4×C4⋊C4C2312yes—
617C4×C4⋊C4C2312yes—
618C4×C4⋊C4C2312yes—
619C4×C4⋊C4C2314yes—
620C4×C4⋊C4C2314yes—
621C4×C4⋊C4C2312yes—
622C4×C4⋊C4C2312yes—
623C4×C4⋊C4C2312yes—
624C4×C4⋊C4C2312yes—
625C4×C4⋊C4C2312yes—
626C4×C4⋊C4C2312yes—
627C4×C4⋊C4C2312yes—
628C4×C4⋊C4C2312yes—
629C4×C4⋊C4C2312yes—
630C4×C4⋊C4C2312yes—
631C4×C4⋊C4C2312yes—
632C4×C4⋊C4C2312yes—
633C4×C4⋊C4C2312yes—
634C4×C4⋊C4C2312yes—
635C4×C4⋊C4C2312yes—
636C4×C4⋊C4C2312yes—
637C4×C4⋊C4C2312yes—
638C4×C4⋊C4C2312yes—
639C4×C4⋊C4C2312yes—
640C4×C4⋊C4C2311yescharacteristic
641C4×C4⋊C4C2311yescharacteristic
642C4×C4⋊C4C2311yescharacteristic
643C4×C4⋊C4C2311yescharacteristic
644C4×C4⋊C4C2312yes—
645C4×C22⋊C4C2314yes—
646C4×C22⋊C4C2314yes—
647C4×C22⋊C4C2312yes—
648C4×C22⋊C4C2314yes—
649C4×C22⋊C4C2314yes—
650C4×C22⋊C4C2314yes—
651C4×C22⋊C4C2314yes—
652C4×C22⋊C4C2314yes—
653C4×C22⋊C4C2314yes—
654C4×C22⋊C4C2311yescharacteristic
655C4×C22⋊C4C2314yes—
656C4×C22⋊C4C2314yes—
657C4×C22⋊C4C2314yes—
658C4×C22⋊C4C2314yes—
659C4×C22⋊C4C2314yes—
660C4×C22⋊C4C2314yes—
661C4×C22⋊C4C2314yes—
662C4×C22⋊C4C2312yes—
663C4×C22⋊C4C2312yes—
664C4×C22⋊C4C2311yescharacteristic
665C4×C22⋊C4C2312yes—
666C4×C22⋊C4C2311yescharacteristic
667C4×C22⋊C4C2311yescharacteristic
668C4×C22⋊C4C2314yes—
669#376C2311yescharacteristic
670#376C2311yescharacteristic
671#376C2311yescharacteristic
672#376C2311yescharacteristic
673#376C2311yescharacteristic
674#376C2311yescharacteristic
675C2×#95C2314yes—
676C2×#95C2314yes—
677C43C2311yescharacteristic
678C43C2311yescharacteristic
679C43C2312yes—
680C43C2312yes—
681C2×#41—216no—
682C2×#41—48no—
683C2×#41—48no—
684C22×Q8C2412yes—
685C22×Q8C2412yes—
686C22×Q8C2414yes—
687C22×D4C2412yes—
688C22×D4C2414yes—
689C22×D4C2414yes—
690C22×D4C2412yes—
691C22×D4C2414yes—
692C22×D4C2414yes—
693C22×D4C2414yes—
694C22×D4C2414yes—
695C22×D4C2414yes—
696C22×D4C2414yes—
697C23×C4C2411yescharacteristic
698C23×C4C2414yes—
699C23×C4C2411yescharacteristic
700C23×C4C2414yes—
701C23×C4C2414yes—
702C23×C4C2414yes—
703C23×C4C2414yes—
704C23×C4C2414yes—
705C23×C4C2414yes—
706C23×C4C2414yes—
707C23×C4C2411yescharacteristic
708C23×C4C2414yes—
709C23×C4C2414yes—
710C4⋊Q8—28no—
711#127—28no—
712#127—28no—
713#127—24no—
714#127#4118yes—
715#126—48no—
716#126—48no—
717#126—48no—
718#126—48no—
719#125—28no—
720#125—24no—
721#125—48no—
722#125—48no—
723#125#4118yescomplemented
724#124—48no—
725#124—48no—
726#123—216no—
727#123—216no—
728#123—48no—
729#123—48no—
730#123—48no—
731#123—48no—
732#123—48no—
733C22⋊Q8—216no—
734C22⋊Q8—216no—
735C22⋊Q8—216no—
736C22⋊Q8—48no—
737C22⋊Q8—48no—
738C22⋊Q8—48no—
739#121—216no—
740#121—28no—
741#121—216no—
742#121—216no—
743#121—216no—
744#121—216no—
745#121—28no—
746#121—48no—
747#121—48no—
748#121—48no—
749#121—48no—
750C4×Q8—28no—
751C4×Q8—28no—
752C4×Q8—28no—
753C4×Q8—28no—
754C4×Q8—48no—
755C4×Q8—44no—
756C4×Q8—44no—
757C4×Q8—48no—
758C4×D4—28no—
759C4×D4—28no—
760C4×D4—28no—
761C4×D4—28no—
762C4×D4—28no—
763C4×D4—28no—
764C4×D4—28no—
765C4×D4—28no—
766C4×D4—216no—
767C4×D4—28no—
768C4×D4—28no—
769C4×D4—48no—
770C4×D4—48no—
771C4×D4—48no—
772C4×D4—48no—
773C4×D4—48no—
774C4×D4—48no—
775C4×D4—48no—
776C4×D4—48no—
777C4×D4—48no—
778C4×D4—48no—
779#117—24no—
780#117—24no—
781#117—216no—
782#117—28no—
783#117—48no—
784#117—44no—
785#117—48no—
786#117—48no—
787#117—48no—
788C2×C4⋊C4—216no—
789C2×C4⋊C4—48no—
790C2×C4⋊C4C2412yes—
791C2×C4⋊C4C2412yes—
792C2×C4⋊C4C2414yes—
793C2×C4⋊C4C2414yes—
794C2×C4⋊C4C2414yes—
795C2×C4⋊C4C2412yes—
796C2×C4⋊C4C2412yes—
797C2×C4⋊C4C2412yes—
798C2×C4⋊C4C2414yes—
799C2×C4⋊C4C2412yes—
800C2×C4⋊C4C2414yes—
801C2×C4⋊C4C2412yes—
802C2×C4⋊C4C2414yes—
803C2×C4⋊C4C2412yes—
804C2×C4⋊C4C2412yes—
805C2×C4⋊C4C2412yes—
806C2×C4⋊C4C2412yes—
807C2×C4⋊C4C2412yes—
808C2×C4⋊C4C2412yes—
809C2×C4⋊C4C2412yes—
810C2×C4⋊C4C2412yes—
811C2×C4⋊C4C2412yes—
812C2×C4⋊C4C2412yes—
813C2×C4⋊C4C2412yes—
814C2×C4⋊C4C2412yes—
815C2×C4⋊C4C2412yes—
816C2×C4⋊C4C2412yes—
817C2×C4⋊C4C2412yes—
818C2×C4⋊C4C2412yes—
819C2×C4⋊C4C2412yes—
820C2×C4⋊C4C2412yes—
821C2×C4⋊C4C2414yes—
822C2×C4⋊C4C2414yes—
823C2×C4⋊C4C2414yes—
824C2×C4⋊C4C2414yes—
825C2×C4⋊C4C2414yes—
826C2×C4⋊C4C2414yes—
827C2×C4⋊C4C2414yes—
828C2×C4⋊C4C2414yes—
829C2×C4⋊C4C2412yes—
830C2×C4⋊C4C2414yes—
831C2×C4⋊C4C2414yes—
832C2×C4⋊C4C2414yes—
833C2×C4⋊C4C2414yes—
834C2×C4⋊C4C2414yes—
835C2×C4⋊C4C2414yes—
836C2×C4⋊C4C2414yes—
837C2×C4⋊C4C2414yes—
838C2×C4⋊C4C2412yes—
839C2×C4⋊C4C2412yes—
840C2×C4⋊C4C2412yes—
841C2×C4⋊C4C2414yes—
842C2×C4⋊C4C2414yes—
843C2×C4⋊C4C2414yes—
844C2×C4⋊C4C2412yes—
845C2×C22⋊C4C2414yes—
846C2×C22⋊C4C2414yes—
847C2×C22⋊C4C2412yes—
848C2×C22⋊C4C2412yes—
849C2×C22⋊C4C2412yes—
850C2×C22⋊C4C2412yes—
851C2×C22⋊C4C2414yes—
852C2×C22⋊C4C2414yes—
853C2×C22⋊C4C2412yes—
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⋊C4C2414yes—
866C2×C22⋊C4C2414yes—
867C2×C22⋊C4C2414yes—
868C2×C22⋊C4C2414yes—
869C2×C22⋊C4C2414yes—
870C2×C22⋊C4C2414yes—
871C2×C22⋊C4C2414yes—
872C2×C22⋊C4C2414yes—
873C2×C22⋊C4C2412yes—
874C2×C22⋊C4C2414yes—
875C2×C22⋊C4C2414yes—
876C2×C22⋊C4C2414yes—
877C2×C22⋊C4C2414yes—
878C2×C22⋊C4C2414yes—
879C2×C22⋊C4C2414yes—
880C2×C22⋊C4C2414yes—
881C2×C22⋊C4C2414yes—
882C2×C22⋊C4C2414yes—
883C2×C22⋊C4C2414yes—
884C2×C22⋊C4C2414yes—
885C2×C22⋊C4C2414yes—
886C2×C22⋊C4C2414yes—
887C2×C22⋊C4C2414yes—
888C2×C22⋊C4C2414yes—
889C2×C42—216no—
890C2×C42—24no—
891C2×C42—48no—
892C2×C42—48no—
893C2×C42—48no—
894C2×C42C2414yes—
895C2×C42C2411yescharacteristic
896C2×C42C2411yescharacteristic
897C2×C42C2412yes—
898C2×C42C2414yes—
899C2×C42C2412yes—
900C2×C42C2412yes—
901C2×C42C2412yes—
902C2×C42C2412yes—
903C2×C42C2411yescharacteristic
904C2×C42C2411yescharacteristic
905C2×C42C2412yes—
906C2×C42C2414yes—
907C2×C42C2412yes—
908C2×C42C2412yes—
909C2×C42C2412yes—
910C2×C42C2412yes—
911C2×C42C2414yes—
912C2×C42C2411yescharacteristic
913C2×C42C2414yes—
914C2×C42C2414yes—
915C2×C42C2412yes—
916C2×C42C2414yes—
917C2×C42C2414yes—
918C2×C42C2412yes—
919C2×C42C2412yes—
920C2×C42C2412yes—
921C2×C42C2412yes—
922C2×C42C2414yes—
923C2×C42C2414yes—
924C2×C42C2411yescharacteristic
925C2×C42C2411yescharacteristic
926C2×C42C2412yes—
927C2×C42C2411yescharacteristic
928#95C2412yes—
929#95C2412yes—
930#95C2414yes—
931#95C2414yes—
932#95C2414yes—
933#95C2414yes—
934#95C2414yes—
935#95C2414yes—
936#95C2412yes—
937#95C2411yescharacteristic
938#95C2412yes—
939#95C2412yes—
940#95C2411yescharacteristic
941#95C2412yes—
942#95C2412yes—
943#95C2411yescharacteristic
944#95C2412yes—
945#95C2411yescharacteristic
946#95C2412yes—
947#95C2411yescharacteristic
948#95C2412yes—
949#95C2411yescharacteristic
950#95C2411yescharacteristic
951#95C2411yescharacteristic
952#95C2414yes—
953#95C2414yes—
954#95C2414yes—
955#95C2414yes—
956#95C2414yes—
957#95C2414yes—
958#95C2414yes—
959#95C2414yes—
960#95C2414yes—
961#95C2414yes—
962#95C2414yes—
963#95C2414yes—
964#95C2414yes—
965#95C2414yes—
966#95C2414yes—
967#95C2414yes—
968#95C2414yes—
969#95C2414yes—
970#95C2412yes—
971#95C2412yes—
972#95C2412yes—
973#95C2412yes—
974#95C2412yes—
975#95C2412yes—
976#95C2412yes—
977#95C2412yes—
978#95C2412yes—
979#95C2412yes—
980#95C2414yes—
981#95C2414yes—
982#95C2414yes—
983#95C2414yes—
984C24C2511yescharacteristic
985C24C2514yes—
986C24C2514yes—
987#41—464no—
988C2×Q8—24no—
989C2×Q8—24no—
990C2×Q8—28no—
991C2×Q8—24no—
992C2×Q8—24no—
993C2×Q8—24no—
994C2×Q8—42no—
995C2×Q8—44no—
996C2×Q8—44no—
997C2×D4—28no—
998C2×D4—28no—
999C2×D4—28no—
1000C2×D4—28no—
1001C2×D4—28no—
1002C2×D4—24no—
1003C2×D4—24no—
1004C2×D4—24no—
1005C2×D4—28no—
1006C2×D4—28no—
1007C2×D4—28no—
1008C2×D4—24no—
1009C2×D4—24no—
1010C2×D4—28no—
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—44no—
1020C2×D4—44no—
1021C2×D4—44no—
1022C2×D4—44no—
1023C2×D4—44no—
1024C2×D4—44no—
1025C2×D4C2×#4118yes—
1026C2×D4C2×#41116yes—
1027C22×C4—28no—
1028C22×C4—28no—
1029C22×C4—28no—
1030C22×C4—28no—
1031C22×C4—22no—
1032C22×C4—22no—
1033C22×C4—28no—
1034C22×C4—28no—
1035C22×C4—28no—
1036C22×C4—28no—
1037C22×C4—28no—
1038C22×C4—28no—
1039C22×C4—28no—
1040C22×C4—24no—
1041C22×C4—22no—
1042C22×C4—22no—
1043C22×C4—22no—
1044C22×C4—28no—
1045C22×C4—28no—
1046C22×C4—28no—
1047C22×C4—28no—
1048C22×C4—28no—
1049C22×C4—28no—
1050C22×C4—44no—
1051C22×C4—44no—
1052C22×C4—44no—
1053C22×C4—42no—
1054C22×C4—44no—
1055C22×C4—44no—
1056C22×C4—44no—
1057C22×C4—44no—
1058C22×C4—44no—
1059C22×C4—44no—
1060C22×C4—44no—
1061C22×C4—44no—
1062C22×C4—44no—
1063C22×C4—44no—
1064C22×C4C2511yescharacteristic
1065C22×C4C2511yescharacteristic
1066C22×C4C2514yes—
1067C22×C4C2512yes—
1068C22×C4C2512yes—
1069C22×C4C2512yes—
1070C22×C4C2512yes—
1071C22×C4C2512yes—
1072C22×C4C2512yes—
1073C22×C4C2514yes—
1074C22×C4C2514yes—
1075C22×C4C2514yes—
1076C22×C4C2512yes—
1077C22×C4C2514yes—
1078C22×C4C2511yescharacteristic
1079C22×C4C2512yes—
1080C22×C4C2512yes—
1081C22×C4C2514yes—
1082C22×C4C2512yes—
1083C22×C4C2512yes—
1084C22×C4C2511yescharacteristic
1085C22×C4C2512yes—
1086C22×C4C2511yescharacteristic
1087C22×C4C2511yescharacteristic
1088C4⋊C4—24no—
1089C4⋊C4—28no—
1090C4⋊C4—28no—
1091C4⋊C4—24no—
1092C4⋊C4—24no—
1093C4⋊C4—24no—
1094C4⋊C4—24no—
1095C4⋊C4—24no—
1096C4⋊C4—24no—
1097C4⋊C4—24no—
1098C4⋊C4—24no—
1099C4⋊C4—24no—
1100C4⋊C4—24no—
1101C4⋊C4—28no—
1102C4⋊C4—28no—
1103C4⋊C4—28no—
1104C4⋊C4—24no—
1105C4⋊C4—28no—
1106C4⋊C4—24no—
1107C4⋊C4—24no—
1108C4⋊C4—24no—
1109C4⋊C4—24no—
1110C4⋊C4—28no—
1111C4⋊C4—24no—
1112C4⋊C4—24no—
1113C4⋊C4—24no—
1114C4⋊C4—24no—
1115C4⋊C4—24no—
1116C4⋊C4—24no—
1117C4⋊C4—28no—
1118C4⋊C4—24no—
1119C4⋊C4—24no—
1120C4⋊C4—24no—
1121C4⋊C4—44no—
1122C4⋊C4—44no—
1123C4⋊C4—42no—
1124C4⋊C4—44no—
1125C4⋊C4—44no—
1126C4⋊C4—44no—
1127C4⋊C4—44no—
1128C4⋊C4—44no—
1129C4⋊C4—44no—
1130C4⋊C4—44no—
1131C4⋊C4—44no—
1132C4⋊C4—44no—
1133C4⋊C4—42no—
1134C4⋊C4—42no—
1135C4⋊C4—42no—
1136C4⋊C4—44no—
1137C4⋊C4—44no—
1138C4⋊C4—44no—
1139C4⋊C4—44no—
1140C4⋊C4—44no—
1141C4⋊C4C2×#41116yes—
1142C4⋊C4C2×#4118yes—
1143C22⋊C4—28no—
1144C22⋊C4—28no—
1145C22⋊C4—28no—
1146C22⋊C4—28no—
1147C22⋊C4—24no—
1148C22⋊C4—24no—
1149C22⋊C4—28no—
1150C22⋊C4—28no—
1151C22⋊C4—28no—
1152C22⋊C4—28no—
1153C22⋊C4—28no—
1154C22⋊C4—28no—
1155C22⋊C4—24no—
1156C22⋊C4—28no—
1157C22⋊C4—28no—
1158C22⋊C4—24no—
1159C22⋊C4—28no—
1160C22⋊C4—28no—
1161C22⋊C4—28no—
1162C22⋊C4—28no—
1163C22⋊C4—24no—
1164C22⋊C4—28no—
1165C22⋊C4—42no—
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—44no—
1182C22⋊C4—44no—
1183C22⋊C4—44no—
1184C22⋊C4—44no—
1185C22⋊C4—44no—
1186C22⋊C4—44no—
1187C42—22no—
1188C42—22no—
1189C42—24no—
1190C42—24no—
1191C42—24no—
1192C42—24no—
1193C42—28no—
1194C42—28no—
1195C42—28no—
1196C42—24no—
1197C42—24no—
1198C42—24no—
1199C42—28no—
1200C42—24no—
1201C42—24no—
1202C42—22no—
1203C42—22no—
1204C42—22no—
1205C42—24no—
1206C42—44no—
1207C42—44no—
1208C42—44no—
1209C42—44no—
1210C42—44no—
1211C42—44no—
1212C42—42no—
1213C42—42no—
1214C42—42no—
1215C42—42no—
1216C42—42no—
1217C42C2×#4114yes—
1218C42C2×#4114yes—
1219C42H(5,𝔽2)18yes—
1220C422−1+414yes—
1221C23—24no—
1222C23—24no—
1223C23—24no—
1224C23—24no—
1225C23—24no—
1226C23—24no—
1227C23—21no—
1228C23—24no—
1229C23—21no—
1230C23—24no—
1231C23—22no—
1232C23—24no—
1233C23—24no—
1234C23—24no—
1235C23—21no—
1236C23—24no—
1237C23—22no—
1238C23—24no—
1239C23C22×#4118yes—
1240C23C2611yescharacteristic
1241Q8—216no—
1242Q8—48no—
1243Q8—88no—
1244D4—216no—
1245D4—416no—
1246D4—416no—
1247D4—416no—
1248D4—48no—
1249D4—88no—
1250D4—88no—
1251D4—88no—
1252D4—88no—
1253D4—88no—
1254C2×C4—22no—
1255C2×C4—22no—
1256C2×C4—22no—
1257C2×C4—24no—
1258C2×C4—22no—
1259C2×C4—22no—
1260C2×C4—22no—
1261C2×C4—22no—
1262C2×C4—22no—
1263C2×C4—22no—
1264C2×C4—22no—
1265C2×C4—22no—
1266C2×C4—24no—
1267C2×C4—22no—
1268C2×C4—22no—
1269C2×C4—22no—
1270C2×C4—22no—
1271C2×C4—22no—
1272C2×C4—22no—
1273C2×C4—22no—
1274C2×C4—21no—
1275C2×C4—21no—
1276C2×C4—24no—
1277C2×C4—24no—
1278C2×C4—24no—
1279C2×C4—24no—
1280C2×C4—24no—
1281C2×C4—22no—
1282C2×C4—22no—
1283C2×C4—22no—
1284C2×C4—24no—
1285C2×C4—24no—
1286C2×C4—22no—
1287C2×C4—22no—
1288C2×C4—22no—
1289C2×C4—22no—
1290C2×C4—24no—
1291C2×C4—24no—
1292C2×C4—24no—
1293C2×C4—22no—
1294C2×C4—21no—
1295C2×C4—21no—
1296C2×C4—21no—
1297C2×C4—24no—
1298C2×C4—24no—
1299C2×C4—22no—
1300C2×C4—22no—
1301C2×C4—22no—
1302C2×C4—22no—
1303C2×C4—22no—
1304C2×C4—22no—
1305C2×C4—22no—
1306C2×C4—24no—
1307C2×C4—22no—
1308C2×C4—24no—
1309C2×C4—24no—
1310C2×C4—416no—
1311C2×C4—416no—
1312C2×C4—416no—
1313C2×C4—44no—
1314C2×C4—416no—
1315C2×C4—44no—
1316C2×C4—416no—
1317C2×C4—416no—
1318C2×C4—44no—
1319C2×C4—88no—
1320C2×C4—88no—
1321C2×C4—88no—
1322C2×C4—88no—
1323C2×C4C22×#4114yes—
1324C2×C4C22×#4114yes—
1325C2×C4C22×#4118yes—
1326C2×C4C22×#4112yes—
1327C2×C4C22×#4112yes—
1328C2×C4C2×H(5,𝔽2)14yes—
1329C2×C4C2×H(5,𝔽2)14yes—
1330C2×C4C2×H(5,𝔽2)14yes—
1331C2×C4C2×2−1+412yes—
1332C2×C4C2×2−1+412yes—
1333C2×C4C2×2−1+412yes—
1334C2×C4#58514yes—
1335C22—28no—
1336C22—28no—
1337C22—28no—
1338C22—44no—
1339C22—44no—
1340C22—44no—
1341C22—44no—
1342C22—41no—
1343C22—44no—
1344C22—41no—
1345C22—44no—
1346C22—44no—
1347C22—42no—
1348C22—44no—
1349C22—44no—
1350C22—42no—
1351C22—44no—
1352C22—41no—
1353C22—44no—
1354C22C23×#4111yescharacteristic
1355C22C23×#4111yescharacteristic
1356C22C22×H(5,𝔽2)12yes—
1357C22C22×2−1+411yescharacteristic
1358C22C2×#58512yes—
1359C4—22no—
1360C4—24no—
1361C4—24no—
1362C4—24no—
1363C4—24no—
1364C4—28no—
1365C4—24no—
1366C4—44no—
1367C4—44no—
1368C4—41no—
1369C4—41no—
1370C4—44no—
1371C4—42no—
1372C4—44no—
1373C4—42no—
1374C4—42no—
1375C4—42no—
1376C4—42no—
1377C4—44no—
1378C4—42no—
1379C4—42no—
1380C4—41no—
1381C4#348214yes—
1382C4#354814yes—
1383C2—48no—
1384C2—81no—
1385C2—84no—
1386C2C2×#348211yescharacteristic
1387C2C2×#354811yescharacteristic
1388C2#6276111yescharacteristic
1389C2#6277312yes—
1390C2#6280012yes—
subgroupG/H
centerC22×C4C25
commutator, Frattini, socle, cosocleC23C26
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C22×C4 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #52295C2semidirect
2. #52169C2semidirect
3. #45050C2semidirect
4. #45034C2semidirect
5. #45007C2semidirect
6. #44991C2semidirect
7. #44982C2semidirect
8. #44965C2semidirect
9. #44948C2semidirect
10. #44931C2semidirect
11. #44911C2semidirect
12. #44880C2semidirect
13. #44438C2semidirect
14. #44156C2semidirect
15. #43840C2semidirect
16. #43423C2semidirect
17. #34970C2semidirect
18. #34964C2semidirect
19. #34934C2semidirect
20. #34914C2semidirect
21. #34893C2semidirect
22. #34735C2semidirect
23. #34552C2semidirect
24. C4×#554C2semidirect
25. C4×#550C2semidirect
26. C4×#540C2semidirect
27. C4×#540C2semidirect
723. #125#41semidirect

Maximal subgroups

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

subgroupindex
#522952
#521692
#450502
#450342
#450072
#449912
#449822
#449652
#449482
#449312
#449112
#448802
#444382
#441562
#438402
#434232
#349702
#349642
#349342
#349142
#348932
#347352
#345522
C4×#5542
C4×#5502
C4×#5402