Finite Group Databasebeta

← #7717496

Subgroups — #7717496

Order 512.

6438 conjugacy classes of subgroups.

The subgroup lattice has 1465 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3564C212yesmaximal, complemented
2#51331C214yesmaximal, complemented
3#51330C214yesmaximal, complemented
4#51329C214yesmaximal, complemented
5#51328C214yesmaximal, complemented
6#44775C214yesmaximal, complemented
7#44773C214yesmaximal, complemented
8#44364C214yesmaximal, complemented
9#44204C214yesmaximal, complemented
10#39610C212yesmaximal, complemented
11#39487C212yesmaximal, complemented
12#39482C212yesmaximal, complemented
13#39482C212yesmaximal, complemented
14#37867C212yesmaximal, complemented
15#37861C212yesmaximal, complemented
16#36742C212yesmaximal, complemented
17#36740C212yesmaximal, complemented
18#36561C212yesmaximal, complemented
19#36183C212yesmaximal, complemented
20#35326C212yesmaximal, complemented
21#35173C211yesmaximal, characteristic, complemented
22#35167C211yesmaximal, characteristic, complemented
23#35004C211yesmaximal, characteristic, complemented
24#35003C211yesmaximal, characteristic
25#35002C211yesmaximal, characteristic, complemented
26#34594C211yesmaximal, characteristic, complemented
27C2×#2373C211yesmaximal, characteristic, complemented
28#3564—232no—
29C2×#563C2214yes—
30C2×#563C2214yes—
31C2×#556C2214yes—
32C2×#554C2214yes—
33C2×#552C2214yes—
34C2×#552C2214yes—
35C2×#551C2214yes—
36C2×#551C2214yes—
37C2×#544C2212yes—
38C2×#543C2212yes—
39C2×#542C2214yes—
40C2×#541C2214yes—
41C2×#541C2214yes—
42C2×#539C2214yes—
43C2×#539C2212yes—
44C2×#538C2212yes—
45C2×#533C2212yes—
46C2×#529C2212yes—
47C22×#126C2211yescharacteristic
48#2857C2212yes—
49#2857C2212yes—
50#2857C2212yes—
51#2857C2212yes—
52#2857C2212yes—
53#2857C2212yes—
54#2854C2212yes—
55#2850C2212yes—
56#2850C2212yes—
57#2847C2212yes—
58#2727C2214yescomplemented
59#2726C2214yescomplemented
60#2725C2214yescomplemented
61#2725C2214yescomplemented
62#2723C2214yescomplemented
63#2722C2214yes—
64#2721C2214yescomplemented
65#2721C2214yescomplemented
66#2720C2214yescomplemented
67#2720C2214yescomplemented
68#2719C2214yescomplemented
69#2719C2214yescomplemented
70#2718C2214yes—
71#2718C2214yes—
72#2716C2214yescomplemented
73#2715C2214yes—
74#2713C2214yescomplemented
75#2713C2214yescomplemented
76#2710C2214yes—
77#2710C2214yes—
78#2700C2214yes—
79#2698C2214yes—
80#2695C2214yes—
81#2694C2214yescomplemented
82#2692C2214yescomplemented
83#2690C2214yescomplemented
84#2689C2214yes—
85#2689C2214yes—
86#2689C2214yes—
87#2687C2214yes—
88#2681C2214yes—
89#2680C2214yes—
90#2677C2214yescomplemented
91#2677C2214yescomplemented
92#2674C2214yes—
93#2674C2214yes—
94#2674C2214yes—
95#2674C2214yescomplemented
96#2672C2214yes—
97#2672C2214yes—
98#2664C2214yescomplemented
99#2662C2214yescomplemented
100#2660C2212yescomplemented
101#2659C2211yescharacteristic
102#2659C2211yescharacteristic
103#2659C2212yes—
104#2659C2212yes—
105#2659C2211yescharacteristic
106#2659C2212yes—
107#2658C2212yescomplemented
108#2656C2211yescharacteristic
109#2642C2212yescomplemented
110#2640C2212yescomplemented
111#2639C2212yes—
112#2618C2212yes—
113#2618C2212yes—
114#2618C2212yes—
115#2617C2212yes—
116#2611C2214yescomplemented
117#2611C2214yescomplemented
118#2604C2214yescomplemented
119#2604C2214yescomplemented
120#2584C2214yescomplemented
121#2584C2214yescomplemented
122#2567C2214yescomplemented
123#2564C2214yes—
124#2564C2214yes—
125#2564C2214yes—
126#2564C2214yes—
127#2556C2214yescomplemented
128#2556C2214yescomplemented
129#2556C2214yescomplemented
130#2555C2214yes—
131#2554C2214yescomplemented
132#2553C2214yes—
133#2553C2214yes—
134#2552C2214yescomplemented
135#2551C2214yescomplemented
136#2551C2212yescomplemented
137#2550C2214yescomplemented
138#2550C2214yescomplemented
139#2549C2214yes—
140#2549C2214yes—
141#2546C2214yescomplemented
142#2542C2212yescomplemented
143#2521C2214yes—
144#2521C2214yes—
145#2519C2214yescomplemented
146#2506C2212yescomplemented
147#2506C2212yescomplemented
148#2501C2212yes—
149#2498C2214yes—
150#2498C2214yes—
151#2498C2214yes—
152#2498C2214yes—
153#2496C2212yes—
154#2496C2212yes—
155#2492C2214yescomplemented
156#2491C2212yes—
157#2488C2214yes—
158#2479C2214yescomplemented
159#2478C2214yes—
160#2478C2214yes—
161#2475C2214yescomplemented
162#2473C2214yescomplemented
163#2470C2214yes—
164#2470C2214yes—
165#2469C2214yescomplemented
166#2466C2214yes—
167#2466C2214yes—
168#2465C2214yescomplemented
169#2464C2214yes—
170#2462C2214yescomplemented
171#2462C2214yescomplemented
172#2461C2214yescomplemented
173#2455C2214yes—
174#2455C2214yes—
175#2453C2214yescomplemented
176#2452C2212yescomplemented
177#2452C2212yescomplemented
178#2449C2214yes—
179#2449C2214yescomplemented
180#2441C2214yescomplemented
181#2440C2214yes—
182#2440C2212yes—
183#2440C2214yes—
184#2438C2214yes—
185#2429C2214yescomplemented
186#2425C2214yes—
187#2422C2212yes—
188#2417C2214yes—
189#2417C2214yes—
190#2415C2214yescomplemented
191#2413C2214yes—
192#2412C2214yes—
193#2412C2214yes—
194#2396C2214yescomplemented
195#2392C2214yescomplemented
196#2373C2214yes—
197#2373C2214yes—
198#2373C2214yes—
199#2373C2214yes—
200#2365C2212yescomplemented
201#2361C2212yes—
202#2360C2214yescomplemented
203#2359C2214yes—
204D4×C4⋊C4C2212yescomplemented
205#2344C2212yes—
206#2327C2212yescomplemented
207#2327C2212yescomplemented
208#2326C2212yescomplemented
209#2326C2212yescomplemented
210#2325C2212yes—
211#2325C2212yes—
212#2316C2212yes—
213#2316C2212yes—
214#2316C2212yes—
215#2315C2212yes—
216C4×#121C2212yes—
217C4×#121C2212yes—
218C4×#121C2212yes—
219C4×#121C2212yes—
220C2×#389C2211yescharacteristic
221C2×#388C2211yescharacteristic
222C2×#388C2211yescharacteristic
223C2×#388C2211yescharacteristic
224C2×#387C2211yescharacteristic
225C2×#387C2211yescharacteristic
226C2×#387C2211yescharacteristic
227C2×#385C2211yescharacteristic
228#2285C2212yes—
229C2×#380C2212yes—
230C2×C4×C4⋊C4C2211yescharacteristic
231C2×C4×C4⋊C4C2211yescharacteristic
232C2×C4×C4⋊C4C2211yescharacteristic
233C2×C4×C22⋊C4C2211yescharacteristic
234C2×C4×C22⋊C4C2211yescharacteristic
235C2×#376C2211yescharacteristic
236C24×C4C2311yescharacteristic
237#563—232no—
238#563—232no—
239#556—232no—
240#554—232no—
241#552—232no—
242#552—232no—
243#551—232no—
244#551—232no—
245#544—216no—
246#543—216no—
247#542—232no—
248#541—232no—
249#541—232no—
250#539—232no—
251#539—216no—
252#538—216no—
253#533—216no—
254C2×C4⋊Q8C2312yes—
255C2×C4⋊Q8C2312yes—
256C2×C4⋊Q8C2314yes—
257C2×C4⋊Q8C2314yes—
258C2×C4⋊Q8C2314yes—
259C2×C4⋊Q8C2312yes—
260C2×C4⋊Q8C2312yes—
261C2×C4⋊Q8C2312yes—
262C2×C4⋊Q8C2312yes—
263C2×C4⋊Q8C2312yes—
264C2×C4⋊Q8C2312yes—
265#529—216no—
266C2×#126D4116yescomplemented
267C2×#126C2314yes—
268C2×#126C2314yes—
269C2×#126C2314yes—
270C2×#126C2314yes—
271C2×#126C2314yes—
272C2×#126C2314yes—
273C2×#126C2314yes—
274C2×#126C2314yes—
275C2×#126C2314yes—
276C2×#126C2314yes—
277C2×#126C2314yes—
278C2×#125C2314yes—
279C2×#125C2312yes—
280C2×#125C2314yes—
281C2×#125C2314yes—
282C2×#125C2314yes—
283C2×#125C2314yes—
284C2×#125C2314yes—
285C2×#125C2314yes—
286C2×#125C2314yes—
287C2×#125C2314yes—
288C2×#124C2312yes—
289C2×#124C2314yes—
290C2×#124C2314yes—
291C2×#124C2314yes—
292C2×#124C2312yes—
293C2×#124C2312yes—
294C2×#123C2314yes—
295C2×#123C2314yes—
296C2×#123C2314yes—
297C2×#123C2314yes—
298C2×#123C2314yes—
299C2×#123C2314yes—
300C2×#123C2314yes—
301C2×#123C2314yes—
302C2×#123C2314yes—
303C2×#123C2314yes—
304C2×C22⋊Q8C2314yes—
305C2×C22⋊Q8C2314yes—
306C2×C22⋊Q8C2314yes—
307C2×C22⋊Q8C2312yes—
308C2×C22⋊Q8C2312yes—
309C2×C22⋊Q8C2312yes—
310C2×C22⋊Q8C2314yes—
311C2×C22⋊Q8C2314yes—
312C2×C22⋊Q8C2314yes—
313C2×C22⋊Q8C2314yes—
314C2×C22⋊Q8C2314yes—
315C2×C22⋊Q8C2314yes—
316C2×C22⋊Q8C2314yes—
317C2×C22⋊Q8C2314yes—
318C2×C22⋊Q8C2314yes—
319C2×C22⋊Q8C2314yes—
320C2×C22⋊Q8C2314yes—
321C2×C22⋊Q8C2314yes—
322C2×C22⋊Q8C2314yes—
323C2×#121C2312yes—
324C2×#121C2312yes—
325C2×#121C2312yes—
326C2×#121C2314yes—
327C2×#121C2312yes—
328C2×#121C2312yes—
329C2×#120C2314yes—
330C2×C4×Q8C2314yes—
331C2×C4×Q8C2312yes—
332C2×C4×Q8C2312yes—
333C2×C4×Q8C2312yes—
334C2×C4×Q8C2314yes—
335C2×C4×Q8C2314yes—
336C2×C4×D4C2314yes—
337C2×C4×D4C2314yes—
338C2×C4×D4C2314yes—
339C2×C4×D4C2312yes—
340C2×C4×D4C2314yes—
341C2×C4×D4C2314yes—
342C2×C4×D4C2312yes—
343C2×C4×D4C2312yes—
344C2×C4×D4C2312yes—
345C2×C4×D4C2312yes—
346C2×#117C2314yes—
347C2×#117C2314yes—
348C2×#117C2314yes—
349C2×#117C2314yes—
350C2×#117C2314yes—
351C2×#117C2314yes—
352C22×C4⋊C4C2311yescharacteristic
353C22×C4⋊C4C2311yescharacteristic
354C22×C4⋊C4C2311yescharacteristic
355C22×C4⋊C4C2314yes—
356C22×C4⋊C4C2312yes—
357C22×C4⋊C4C2311yescharacteristic
358C22×C4⋊C4C2312yes—
359C22×C4⋊C4C2311yescharacteristic
360C22×C4⋊C4C2311yescharacteristic
361C22×C4⋊C4C2311yescharacteristic
362C22×C4⋊C4C2311yescharacteristic
363C22×C22⋊C4C2311yescharacteristic
364C22×C22⋊C4C2314yes—
365C22×C22⋊C4C2311yescharacteristic
366C22×C22⋊C4C2311yescharacteristic
367C22×C22⋊C4C2311yescharacteristic
368C22×C22⋊C4C2311yescharacteristic
369C22×C22⋊C4C2311yescharacteristic
370C22×C42C2311yescharacteristic
371C22×C42C2311yescharacteristic
372C22×C42C2311yescharacteristic
373C22×C42C2311yescharacteristic
374C22×C42C2311yescharacteristic
375C22×C42C2311yescharacteristic
376C22×C42C2311yescharacteristic
377C22×C42C2311yescharacteristic
378#400C2314yes—
379#400C2314yes—
380#400C2314yes—
381#400C2314yes—
382#400C2314yes—
383#400C2314yes—
384#400C2314yes—
385#400C2314yes—
386#400C2314yes—
387#399C2314yes—
388#399C2314yes—
389#399C2314yes—
390#399C2314yes—
391#399C2314yes—
392#399C2314yes—
393#399C2314yes—
394#399C2314yes—
395#399C2314yes—
396#398C2314yes—
397#398C2314yes—
398#398C2314yes—
399#398C2314yes—
400#398C2314yes—
401#398C2314yes—
402#398C2314yes—
403#398C2314yes—
404#398C2314yes—
405#398C2314yes—
406#398C2314yes—
407#398C2314yes—
408#398C2314yes—
409#398C2314yes—
410#398C2314yes—
411#398C2314yes—
412#398C2314yes—
413#398C2314yes—
414#398C2314yes—
415#398C2314yes—
416#397C2314yes—
417#397C2314yes—
418#397C2314yes—
419#397C2314yes—
420#397C2314yes—
421#397C2314yes—
422#397C2314yes—
423#397C2314yes—
424#397C2314yes—
425#397C2314yes—
426#396C2314yes—
427#396C2314yes—
428#396C2314yes—
429#396C2314yes—
430#396C2314yes—
431#396C2314yes—
432#396C2314yes—
433#396C2314yes—
434#396C2314yes—
435#396C2314yes—
436#395C2314yes—
437#395C2314yes—
438#395C2314yes—
439#395C2314yes—
440#395C2314yes—
441#395C2314yes—
442#395C2314yes—
443#395C2314yes—
444#395C2314yes—
445#395C2314yes—
446#395C2314yes—
447#395C2314yes—
448#395C2314yes—
449#394C2314yes—
450#394C2314yes—
451#394C2314yes—
452#394C2314yes—
453#394C2314yes—
454#394C2314yes—
455#394C2314yes—
456#394C2314yes—
457#394C2314yes—
458#394C2314yes—
459#393C2314yes—
460#393C2314yes—
461#393C2314yes—
462#393C2314yes—
463#393C2314yes—
464#392C2314yes—
465#392C2314yes—
466#391C2314yes—
467#391C2314yes—
468#391C2312yes—
469#391C2312yes—
470#391C2312yes—
471#391C2312yes—
472#391C2312yes—
473#391C2312yes—
474#391C2314yes—
475#391C2314yes—
476#391C2314yes—
477#391C2314yes—
478#390C2312yes—
479#390C2312yes—
480#390C2312yes—
481#390C2312yes—
482#390C2312yes—
483#390C2312yes—
484#390C2312yes—
485#390C2312yes—
486#389C2314yes—
487#389C2314yes—
488#389C2314yes—
489#389C2314yes—
490#389C2314yes—
491#389C2314yes—
492#389C2314yes—
493#389C2314yes—
494#389C2314yes—
495#389C2314yes—
496#389C2314yes—
497#389C2314yes—
498#389C2312yes—
499#389C2312yes—
500#389C2314yes—
501#389C2314yes—
502#389C2312yes—
503#389C2312yes—
504#389C2312yes—
505#389C2312yes—
506#389C2312yes—
507#389C2314yes—
508#389C2314yes—
509#389C2314yes—
510#389C2314yes—
511#389C2314yes—
512#389C2312yes—
513#389C2312yes—
514#389C2312yes—
515#389C2314yes—
516#389C2314yes—
517#389C2314yes—
518#389C2314yes—
519#389C2312yes—
520#389C2312yes—
521#389C2314yes—
522#389C2312yes—
523#389C2312yes—
524#388C2314yes—
525#388C2314yes—
526#388C2314yes—
527#388C2314yes—
528#388C2314yes—
529#388C2314yes—
530#388C2314yes—
531#388C2314yes—
532#388C2314yes—
533#388C2314yes—
534#388C2314yes—
535#388C2314yes—
536#388C2314yes—
537#388C2314yes—
538#388C2314yes—
539#388C2314yes—
540#388C2314yes—
541#388C2314yes—
542#388C2314yes—
543#388C2314yes—
544#388C2314yes—
545#388C2314yes—
546#388C2314yes—
547#388C2314yes—
548#388C2314yes—
549#388C2314yes—
550#387C2314yes—
551#387C2314yes—
552#387C2314yes—
553#387C2314yes—
554#387C2314yes—
555#387C2314yes—
556#387C2314yes—
557#387C2314yes—
558#387C2314yes—
559#387C2314yes—
560#387C2314yes—
561#387C2314yes—
562#387C2314yes—
563#387C2314yes—
564#387C2314yes—
565#387C2314yes—
566#387C2314yes—
567#387C2314yes—
568#387C2314yes—
569#387C2314yes—
570#387C2314yes—
571#387C2314yes—
572#387C2314yes—
573#387C2314yes—
574#386C2314yes—
575#386C2314yes—
576#386C2314yes—
577#386C2314yes—
578#386C2314yes—
579#386C2314yes—
580#386C2314yes—
581#386C2314yes—
582#386C2314yes—
583#386C2314yes—
584#386C2314yes—
585#386C2314yes—
586#385C2314yes—
587#385C2314yes—
588#385C2314yes—
589#385C2314yes—
590#385C2314yes—
591#385C2314yes—
592#385C2314yes—
593#385C2314yes—
594#385C2314yes—
595#385C2314yes—
596#385C2314yes—
597#385C2314yes—
598#385C2314yes—
599#385C2314yes—
600#385C2314yes—
601#385C2314yes—
602#385C2314yes—
603#385C2314yes—
604#384C2312yes—
605#384C2312yes—
606#384C2312yes—
607#384C2312yes—
608#384C2312yes—
609#384C2312yes—
610#384C2312yes—
611#384C2312yes—
612#382C2312yes—
613#382C2312yes—
614#382C2314yes—
615#381C2314yes—
616#381C2314yes—
617#380C2314yes—
618#380C2314yes—
619#380C2314yes—
620#380C2314yes—
621#380C2314yes—
622#380C2314yes—
623#380C2312yes—
624#380C2312yes—
625#380C2312yes—
626#380C2312yes—
627#380C2312yes—
628#380C2312yes—
629#380C2312yes—
630#380C2314yes—
631#380C2312yes—
632#380C2314yes—
633#380C2314yes—
634#380C2312yes—
635#380C2312yes—
636C4×C4⋊C4C2314yes—
637C4×C4⋊C4C2314yes—
638C4×C4⋊C4C2312yes—
639C4×C4⋊C4C2312yes—
640C4×C4⋊C4C2312yes—
641C4×C4⋊C4C2314yes—
642C4×C4⋊C4C2312yes—
643C4×C4⋊C4C2312yes—
644C4×C4⋊C4C2312yes—
645C4×C4⋊C4C2312yes—
646C4×C4⋊C4C2312yes—
647C4×C4⋊C4C2312yes—
648C4×C4⋊C4C2314yes—
649C4×C4⋊C4C2312yes—
650C4×C4⋊C4C2314yes—
651C4×C22⋊C4C2312yes—
652C4×C22⋊C4C2312yes—
653C4×C22⋊C4C2314yes—
654C4×C22⋊C4C2314yes—
655C4×C22⋊C4C2314yes—
656C4×C22⋊C4C2314yes—
657C4×C22⋊C4C2314yes—
658C4×C22⋊C4C2312yes—
659C4×C22⋊C4C2314yes—
660C4×C22⋊C4C2312yes—
661#376C2312yes—
662#376C2312yes—
663#376C2312yes—
664#376C2312yes—
665C2×#95C2311yescharacteristic
666C2×#95C2311yescharacteristic
667C2×#95C2311yescharacteristic
668C2×#95C2311yescharacteristic
669C2×#95C2311yescharacteristic
670C2×#95C2311yescharacteristic
671C2×#95C2314yes—
672C2×#95C2311yescharacteristic
673C2×#95C2311yescharacteristic
674C2×#95C2311yescharacteristic
675C2×#95C2311yescharacteristic
676C2×#95C2311yescharacteristic
677C2×#95C2311yescharacteristic
678C25C2411yescharacteristic
679C22×Q8C2414yes—
680C22×Q8C2412yes—
681C22×Q8C2414yes—
682C22×Q8C2412yes—
683C22×Q8C2414yes—
684C22×Q8C2412yes—
685C22×D4C2414yes—
686C22×D4C2412yes—
687C22×D4C2414yes—
688C22×D4C2414yes—
689C22×D4C2412yes—
690C22×D4C2412yes—
691C23×C4—24no—
692C23×C4—42no—
693C23×C4—81no—
694C23×C4C2411yescharacteristic
695C23×C4C2412yes—
696C23×C4C2411yescharacteristic
697C23×C4C2411yescharacteristic
698C23×C4C2411yescharacteristic
699C23×C4C2411yescharacteristic
700C23×C4C2411yescharacteristic
701C23×C4C2411yescharacteristic
702C23×C4C2414yes—
703C23×C4C2414yes—
704C23×C4C2411yescharacteristic
705C23×C4C2414yes—
706C23×C4C2414yes—
707C23×C4C2414yes—
708C23×C4C2412yes—
709C23×C4C2411yescharacteristic
710C23×C4C2411yescharacteristic
711C23×C4C2411yescharacteristic
712C23×C4C2411yescharacteristic
713C23×C4C2411yescharacteristic
714C23×C4C2411yescharacteristic
715C4⋊Q8—216no—
716C4⋊Q8—216no—
717C4⋊Q8—216no—
718C4⋊Q8—28no—
719C4⋊Q8—28no—
720C4⋊Q8—44no—
721C4⋊Q8—44no—
722C4⋊Q8—44no—
723C4⋊Q8—82no—
724C4⋊Q8—82no—
725C4⋊Q8—82no—
726#126—216no—
727#126—216no—
728#126—216no—
729#126—216no—
730#126—216no—
731#126—216no—
732#126—216no—
733#126—216no—
734#126—216no—
735#126C2×D4132yes—
736#126C2×D4132yes—
737#125—216no—
738#125—216no—
739#125—216no—
740#125—216no—
741#125—216no—
742#125—216no—
743#125—216no—
744#125—216no—
745#125—28no—
746#125—216no—
747#124—216no—
748#124—216no—
749#124—216no—
750#124—28no—
751#124—44no—
752#124—44no—
753#123—216no—
754#123—216no—
755#123—216no—
756#123—216no—
757#123—216no—
758#123—216no—
759#123—216no—
760#123—216no—
761#123—48no—
762#123—84no—
763C22⋊Q8—28no—
764C22⋊Q8—28no—
765C22⋊Q8—28no—
766C22⋊Q8—216no—
767C22⋊Q8—216no—
768C22⋊Q8—216no—
769C22⋊Q8—216no—
770C22⋊Q8—216no—
771C22⋊Q8—216no—
772C22⋊Q8—216no—
773C22⋊Q8—216no—
774C22⋊Q8—216no—
775C22⋊Q8—216no—
776C22⋊Q8—216no—
777C22⋊Q8—216no—
778C22⋊Q8—216no—
779C22⋊Q8—216no—
780C22⋊Q8—48no—
781C22⋊Q8—84no—
782#121—28no—
783#121—28no—
784#121—28no—
785#121—216no—
786#121—44no—
787#121—82no—
788#120—216no—
789C4×Q8—216no—
790C4×Q8—216no—
791C4×Q8—28no—
792C4×Q8—216no—
793C4×Q8—28no—
794C4×Q8—28no—
795C4×D4—216no—
796C4×D4—216no—
797C4×D4—216no—
798C4×D4—216no—
799C4×D4—216no—
800C4×D4—28no—
801C4×D4—44no—
802C4×D4—82no—
803C4×D4—82no—
804C4×D4—82no—
805#117—216no—
806#117—216no—
807#117—216no—
808#117—216no—
809#117—216no—
810#117—216no—
811C2×C4⋊C4—24no—
812C2×C4⋊C4—24no—
813C2×C4⋊C4—24no—
814C2×C4⋊C4—216no—
815C2×C4⋊C4—42no—
816C2×C4⋊C4—44no—
817C2×C4⋊C4—82no—
818C2×C4⋊C4—81no—
819C2×C4⋊C4C2×D418yes—
820C2×C4⋊C4C2×D418yes—
821C2×C4⋊C4C2×D418yes—
822C2×C4⋊C4C2414yes—
823C2×C4⋊C4C2414yes—
824C2×C4⋊C4C2412yes—
825C2×C4⋊C4C2414yes—
826C2×C4⋊C4C2414yes—
827C2×C4⋊C4C2414yes—
828C2×C4⋊C4C2414yes—
829C2×C4⋊C4C2414yes—
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⋊C4C2414yes—
839C2×C4⋊C4C2414yes—
840C2×C4⋊C4C2412yes—
841C2×C4⋊C4C2414yes—
842C2×C4⋊C4C2414yes—
843C2×C4⋊C4C2414yes—
844C2×C4⋊C4C2414yes—
845C2×C4⋊C4C2414yes—
846C2×C4⋊C4C2412yes—
847C2×C4⋊C4C2414yes—
848C2×C4⋊C4C2414yes—
849C2×C4⋊C4C2412yes—
850C2×C4⋊C4C2414yes—
851C2×C4⋊C4C2412yes—
852C2×C4⋊C4C2414yes—
853C2×C4⋊C4C2414yes—
854C2×C4⋊C4C2412yes—
855C2×C4⋊C4C2412yes—
856C2×C4⋊C4C2414yes—
857C2×C4⋊C4C2412yes—
858C2×C4⋊C4C2414yes—
859C2×C4⋊C4C2414yes—
860C2×C4⋊C4C2412yes—
861C2×C4⋊C4C2412yes—
862C2×C4⋊C4C2412yes—
863C2×C4⋊C4C2412yes—
864C2×C4⋊C4C2412yes—
865C2×C4⋊C4C2412yes—
866C2×C4⋊C4C2412yes—
867C2×C4⋊C4C2412yes—
868C2×C4⋊C4C2412yes—
869C2×C4⋊C4C2414yes—
870C2×C4⋊C4C2414yes—
871C2×C4⋊C4C2414yes—
872C2×C4⋊C4C2414yes—
873C2×C4⋊C4C2414yes—
874C2×C4⋊C4C2412yes—
875C2×C4⋊C4C2412yes—
876C2×C4⋊C4C2412yes—
877C2×C4⋊C4C2414yes—
878C2×C4⋊C4C2414yes—
879C2×C4⋊C4C2414yes—
880C2×C4⋊C4C2414yes—
881C2×C4⋊C4C2412yes—
882C2×C4⋊C4C2414yes—
883C2×C4⋊C4C2412yes—
884C2×C4⋊C4C2414yes—
885C2×C22⋊C4—216no—
886C2×C22⋊C4—24no—
887C2×C22⋊C4—42no—
888C2×C22⋊C4—81no—
889C2×C22⋊C4C2×D418yes—
890C2×C22⋊C4C2×D418yes—
891C2×C22⋊C4C2×D418yes—
892C2×C22⋊C4C2414yes—
893C2×C22⋊C4C2414yes—
894C2×C22⋊C4C2414yes—
895C2×C22⋊C4C2414yes—
896C2×C22⋊C4C2412yes—
897C2×C22⋊C4C2414yes—
898C2×C22⋊C4C2414yes—
899C2×C22⋊C4C2414yes—
900C2×C22⋊C4C2414yes—
901C2×C22⋊C4C2414yes—
902C2×C22⋊C4C2414yes—
903C2×C22⋊C4C2414yes—
904C2×C22⋊C4C2414yes—
905C2×C22⋊C4C2414yes—
906C2×C22⋊C4C2414yes—
907C2×C22⋊C4C2414yes—
908C2×C22⋊C4C2414yes—
909C2×C22⋊C4C2414yes—
910C2×C22⋊C4C2414yes—
911C2×C22⋊C4C2414yes—
912C2×C22⋊C4C2414yes—
913C2×C22⋊C4C2414yes—
914C2×C22⋊C4C2412yes—
915C2×C22⋊C4C2414yes—
916C2×C22⋊C4C2414yes—
917C2×C22⋊C4C2414yes—
918C2×C22⋊C4C2414yes—
919C2×C22⋊C4C2414yes—
920C2×C22⋊C4C2414yes—
921C2×C22⋊C4C2414yes—
922C2×C22⋊C4C2414yes—
923C2×C22⋊C4C2414yes—
924C2×C22⋊C4C2414yes—
925C2×C22⋊C4C2412yes—
926C2×C22⋊C4C2414yes—
927C2×C22⋊C4C2414yes—
928C2×C22⋊C4C2412yes—
929C2×C42—24no—
930C2×C42—42no—
931C2×C42—42no—
932C2×C42—42no—
933C2×C42—81no—
934C2×C42—81no—
935C2×C42—81no—
936C2×C42C2×D418yes—
937C2×C42C2414yes—
938C2×C42C2414yes—
939C2×C42C2414yes—
940C2×C42C2414yes—
941C2×C42C2414yes—
942C2×C42C2414yes—
943C2×C42C2414yes—
944C2×C42C2412yes—
945C2×C42C2412yes—
946C2×C42C2412yes—
947C2×C42C2412yes—
948C2×C42C2412yes—
949C2×C42C2412yes—
950C2×C42C2412yes—
951C2×C42C2412yes—
952C2×C42C2412yes—
953C2×C42C2412yes—
954C2×C42C2412yes—
955C2×C42C2412yes—
956C2×C42C2412yes—
957C2×C42C2412yes—
958C2×C42C2412yes—
959C2×C42C2412yes—
960#95C2411yescharacteristic
961#95C2411yescharacteristic
962#95C2411yescharacteristic
963#95C2411yescharacteristic
964#95C2412yes—
965#95C2412yes—
966#95C2412yes—
967#95C2412yes—
968#95C2412yes—
969#95C2412yes—
970#95C2414yes—
971#95C2414yes—
972#95C2412yes—
973#95C2412yes—
974#95C2414yes—
975#95C2414yes—
976#95C2412yes—
977#95C2412yes—
978#95C2414yes—
979#95C2414yes—
980#95C2414yes—
981#95C2414yes—
982#95C2414yes—
983#95C2414yes—
984#95C2414yes—
985#95C2414yes—
986#95C2414yes—
987#95C2414yes—
988#95C2414yes—
989#95C2414yes—
990#95C2414yes—
991#95C2414yes—
992#95C2414yes—
993#95C2414yes—
994#95C2414yes—
995#95C2414yes—
996#95C2414yes—
997#95C2414yes—
998#95C2414yes—
999#95C2414yes—
1000#95C2414yes—
1001#95C2414yes—
1002#95C2414yes—
1003#95C2414yes—
1004#95C2414yes—
1005#95C2414yes—
1006#95C2414yes—
1007#95C2414yes—
1008#95C2414yes—
1009#95C2414yes—
1010C24—22no—
1011C24—22no—
1012C24—41no—
1013C24—41no—
1014C24—41no—
1015C24—41no—
1016C24C22×D414yes—
1017C24C2514yes—
1018C24C2512yes—
1019C24C2511yescharacteristic
1020C2×Q8—28no—
1021C2×Q8—24no—
1022C2×Q8—28no—
1023C2×Q8—24no—
1024C2×Q8—28no—
1025C2×Q8—24no—
1026C2×Q8—44no—
1027C2×Q8—44no—
1028C2×Q8—42no—
1029C2×Q8—42no—
1030C2×Q8—44no—
1031C2×Q8—42no—
1032C2×Q8—42no—
1033C2×Q8—42no—
1034C2×Q8—42no—
1035C2×Q8—44no—
1036C2×Q8—44no—
1037C2×Q8—44no—
1038C2×D4—28no—
1039C2×D4—28no—
1040C2×D4—28no—
1041C2×D4—28no—
1042C2×D4—28no—
1043C2×D4—24no—
1044C2×D4—24no—
1045C2×D4—24no—
1046C2×D4—42no—
1047C2×D4—42no—
1048C2×D4—42no—
1049C2×D4—42no—
1050C2×D4—44no—
1051C2×D4—44no—
1052C2×D4—44no—
1053C2×D4—42no—
1054C2×D4—42no—
1055C2×D4—44no—
1056C22×C4—22no—
1057C22×C4—22no—
1058C22×C4—22no—
1059C22×C4—22no—
1060C22×C4—22no—
1061C22×C4—22no—
1062C22×C4—28no—
1063C22×C4—28no—
1064C22×C4—22no—
1065C22×C4—22no—
1066C22×C4—22no—
1067C22×C4—22no—
1068C22×C4—24no—
1069C22×C4—22no—
1070C22×C4—22no—
1071C22×C4—24no—
1072C22×C4—28no—
1073C22×C4—28no—
1074C22×C4—28no—
1075C22×C4—24no—
1076C22×C4—41no—
1077C22×C4—41no—
1078C22×C4—41no—
1079C22×C4—41no—
1080C22×C4—41no—
1081C22×C4—41no—
1082C22×C4—41no—
1083C22×C4—41no—
1084C22×C4—41no—
1085C22×C4—41no—
1086C22×C4—42no—
1087C22×C4—41no—
1088C22×C4—41no—
1089C22×C4—41no—
1090C22×C4—41no—
1091C22×C4—41no—
1092C22×C4—41no—
1093C22×C4—41no—
1094C22×C4—41no—
1095C22×C4—41no—
1096C22×C4—41no—
1097C22×C4—41no—
1098C22×C4—44no—
1099C22×C4—44no—
1100C22×C4—44no—
1101C22×C4—44no—
1102C22×C4—44no—
1103C22×C4—42no—
1104C22×C4—44no—
1105C22×C4—44no—
1106C22×C4—42no—
1107C22×C4—44no—
1108C22×C4—44no—
1109C22×C4—41no—
1110C22×C4—44no—
1111C22×C4—88no—
1112C22×C4C22×D414yes—
1113C22×C4C22×D414yes—
1114C22×C4C22×D414yes—
1115C22×C4C22×D414yes—
1116C22×C4C22×D414yes—
1117C22×C4C22×D414yes—
1118C22×C42−1+414yes—
1119C22×C42−1+414yes—
1120C22×C4C2511yescharacteristic
1121C22×C4C2511yescharacteristic
1122C22×C4C2512yes—
1123C22×C4C2512yes—
1124C22×C4C2512yes—
1125C22×C4C2512yes—
1126C22×C4C2514yes—
1127C22×C4C2514yes—
1128C22×C4C2514yes—
1129C22×C4C2514yes—
1130C22×C4C2514yes—
1131C22×C4C2514yes—
1132C22×C4C2514yes—
1133C22×C4C2511yescharacteristic
1134C22×C4C2512yes—
1135C22×C4C2512yes—
1136C22×C4C2511yescharacteristic
1137C22×C4C2512yes—
1138C22×C4C2512yes—
1139C22×C4C2512yes—
1140C22×C4C2512yes—
1141C22×C4C2512yes—
1142C22×C4C2511yescharacteristic
1143C22×C4C2511yescharacteristic
1144C4⋊C4—28no—
1145C4⋊C4—28no—
1146C4⋊C4—28no—
1147C4⋊C4—28no—
1148C4⋊C4—28no—
1149C4⋊C4—28no—
1150C4⋊C4—28no—
1151C4⋊C4—28no—
1152C4⋊C4—28no—
1153C4⋊C4—28no—
1154C4⋊C4—28no—
1155C4⋊C4—28no—
1156C4⋊C4—28no—
1157C4⋊C4—24no—
1158C4⋊C4—28no—
1159C4⋊C4—28no—
1160C4⋊C4—28no—
1161C4⋊C4—28no—
1162C4⋊C4—28no—
1163C4⋊C4—24no—
1164C4⋊C4—28no—
1165C4⋊C4—28no—
1166C4⋊C4—24no—
1167C4⋊C4—28no—
1168C4⋊C4—24no—
1169C4⋊C4—28no—
1170C4⋊C4—28no—
1171C4⋊C4—28no—
1172C4⋊C4—28no—
1173C4⋊C4—28no—
1174C4⋊C4—24no—
1175C4⋊C4—24no—
1176C4⋊C4—24no—
1177C4⋊C4—28no—
1178C4⋊C4—28no—
1179C4⋊C4—42no—
1180C4⋊C4—42no—
1181C4⋊C4—42no—
1182C4⋊C4—42no—
1183C4⋊C4—44no—
1184C4⋊C4—44no—
1185C4⋊C4—42no—
1186C4⋊C4—44no—
1187C4⋊C4—44no—
1188C4⋊C4—42no—
1189C4⋊C4—42no—
1190C4⋊C4—42no—
1191C4⋊C4—42no—
1192C4⋊C4—42no—
1193C4⋊C4—44no—
1194C4⋊C4—44no—
1195C4⋊C4—44no—
1196C4⋊C4—44no—
1197C4⋊C4—44no—
1198C4⋊C4—42no—
1199C4⋊C4—42no—
1200C4⋊C4—44no—
1201C4⋊C4—44no—
1202C4⋊C4—42no—
1203C4⋊C4C22×D418yes—
1204C4⋊C4C22×D4116yes—
1205C4⋊C4C22×D418yes—
1206C4⋊C4C22×D4116yes—
1207C22⋊C4—28no—
1208C22⋊C4—28no—
1209C22⋊C4—28no—
1210C22⋊C4—28no—
1211C22⋊C4—28no—
1212C22⋊C4—28no—
1213C22⋊C4—28no—
1214C22⋊C4—28no—
1215C22⋊C4—28no—
1216C22⋊C4—28no—
1217C22⋊C4—28no—
1218C22⋊C4—28no—
1219C22⋊C4—28no—
1220C22⋊C4—28no—
1221C22⋊C4—28no—
1222C22⋊C4—28no—
1223C22⋊C4—28no—
1224C22⋊C4—28no—
1225C22⋊C4—24no—
1226C22⋊C4—28no—
1227C22⋊C4—28no—
1228C22⋊C4—42no—
1229C22⋊C4—44no—
1230C22⋊C4—44no—
1231C22⋊C4—44no—
1232C22⋊C4—44no—
1233C22⋊C4—44no—
1234C22⋊C4—44no—
1235C22⋊C4—44no—
1236C22⋊C4—44no—
1237C22⋊C4—44no—
1238C22⋊C4—44no—
1239C22⋊C4—44no—
1240C22⋊C4C22×D418yes—
1241C22⋊C4C22×D4116yes—
1242C22⋊C4C22×D4116yes—
1243C22⋊C4C22×D418yes—
1244C42—28no—
1245C42—28no—
1246C42—28no—
1247C42—28no—
1248C42—28no—
1249C42—28no—
1250C42—28no—
1251C42—24no—
1252C42—24no—
1253C42—24no—
1254C42—24no—
1255C42—24no—
1256C42—42no—
1257C42—42no—
1258C42—42no—
1259C42—42no—
1260C42—42no—
1261C42—42no—
1262C42—42no—
1263C42—42no—
1264C42—42no—
1265C42C22×D418yes—
1266C42C22×D418yes—
1267C23—21no—
1268C23—21no—
1269C23—21no—
1270C23—21no—
1271C23—22no—
1272C23—22no—
1273C23—22no—
1274C23—22no—
1275C23—22no—
1276C23—22no—
1277C23—28no—
1278C23—24no—
1279C23—24no—
1280C23—24no—
1281C23—24no—
1282C23—24no—
1283C23—24no—
1284C23—24no—
1285C23—44no—
1286C23—44no—
1287C23—82no—
1288C23—82no—
1289C23—82no—
1290C23—82no—
1291C23C23×D414yes—
1292C23C23×D412yes—
1293C23C2×2−1+412yes—
1294C23C2×2−1+412yes—
1295C23C2611yescharacteristic
1296Q8—88no—
1297Q8—84no—
1298Q8—84no—
1299Q8—84no—
1300Q8—88no—
1301Q8—88no—
1302D4—48no—
1303D4—416no—
1304D4—84no—
1305D4—84no—
1306D4—88no—
1307D4—88no—
1308C2×C4—22no—
1309C2×C4—21no—
1310C2×C4—22no—
1311C2×C4—22no—
1312C2×C4—22no—
1313C2×C4—21no—
1314C2×C4—22no—
1315C2×C4—22no—
1316C2×C4—22no—
1317C2×C4—22no—
1318C2×C4—22no—
1319C2×C4—22no—
1320C2×C4—22no—
1321C2×C4—21no—
1322C2×C4—21no—
1323C2×C4—21no—
1324C2×C4—22no—
1325C2×C4—22no—
1326C2×C4—21no—
1327C2×C4—21no—
1328C2×C4—22no—
1329C2×C4—21no—
1330C2×C4—28no—
1331C2×C4—28no—
1332C2×C4—24no—
1333C2×C4—24no—
1334C2×C4—24no—
1335C2×C4—24no—
1336C2×C4—24no—
1337C2×C4—24no—
1338C2×C4—24no—
1339C2×C4—21no—
1340C2×C4—22no—
1341C2×C4—24no—
1342C2×C4—24no—
1343C2×C4—22no—
1344C2×C4—22no—
1345C2×C4—22no—
1346C2×C4—21no—
1347C2×C4—22no—
1348C2×C4—22no—
1349C2×C4—21no—
1350C2×C4—21no—
1351C2×C4—22no—
1352C2×C4—24no—
1353C2×C4—24no—
1354C2×C4—22no—
1355C2×C4—24no—
1356C2×C4—24no—
1357C2×C4—24no—
1358C2×C4—24no—
1359C2×C4—22no—
1360C2×C4—21no—
1361C2×C4—22no—
1362C2×C4—22no—
1363C2×C4—24no—
1364C2×C4—24no—
1365C2×C4—24no—
1366C2×C4—21no—
1367C2×C4—22no—
1368C2×C4—24no—
1369C2×C4—24no—
1370C2×C4—24no—
1371C2×C4—44no—
1372C2×C4—44no—
1373C2×C4—44no—
1374C2×C4—44no—
1375C2×C4—44no—
1376C2×C4—44no—
1377C2×C4—48no—
1378C2×C4—44no—
1379C2×C4—44no—
1380C2×C4—88no—
1381C2×C4—88no—
1382C2×C4—88no—
1383C2×C4—84no—
1384C2×C4—88no—
1385C2×C4—88no—
1386C2×C4—82no—
1387C2×C4—82no—
1388C2×C4—82no—
1389C2×C4—82no—
1390C2×C4C23×D414yes—
1391C2×C4C23×D412yes—
1392C2×C4C23×D414yes—
1393C2×C4C23×D414yes—
1394C2×C4C23×D414yes—
1395C2×C4C23×D412yes—
1396C2×C4C23×D414yes—
1397C2×C4C2×2−1+414yes—
1398C2×C4C2×2−1+414yes—
1399C2×C4#58512yes—
1400C2×C4#58512yes—
1401C22—22no—
1402C22—22no—
1403C22—22no—
1404C22—22no—
1405C22—22no—
1406C22—22no—
1407C22—24no—
1408C22—24no—
1409C22—24no—
1410C22—42no—
1411C22—42no—
1412C22—42no—
1413C22—42no—
1414C22—44no—
1415C22—44no—
1416C22—44no—
1417C22—44no—
1418C22—44no—
1419C22—44no—
1420C22—44no—
1421C22—88no—
1422C22#349914yes—
1423C22C24×D411yescharacteristic
1424C22C22×2−1+411yescharacteristic
1425C22C22×2−1+411yescharacteristic
1426C22C2×#58511yescharacteristic
1427C22C2×#58511yescharacteristic
1428C22H(7,𝔽2)11yescharacteristic
1429C222−1+611yescharacteristic
1430C4—24no—
1431C4—24no—
1432C4—24no—
1433C4—24no—
1434C4—22no—
1435C4—24no—
1436C4—22no—
1437C4—24no—
1438C4—22no—
1439C4—24no—
1440C4—22no—
1441C4—44no—
1442C4—44no—
1443C4—44no—
1444C4—44no—
1445C4—44no—
1446C4—44no—
1447C4—44no—
1448C4—42no—
1449C4—42no—
1450C4—41no—
1451C4—42no—
1452C4—41no—
1453C4—42no—
1454C2—24no—
1455C2—44no—
1456C2—84no—
1457C2C2×#349911yescharacteristic
1458C2#6281211yescharacteristic
1459C2#6285311yescharacteristic
1460C2#6290211yescharacteristic
1461C2#6290311yescharacteristic
1462C2#6292811yescharacteristic
1463C2#6293211yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#35003C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#3564C2semidirect
2. #51331C2semidirect
3. #51330C2semidirect
4. #51329C2semidirect
5. #51328C2semidirect
6. #44775C2semidirect
7. #44773C2semidirect
8. #44364C2semidirect
9. #44204C2semidirect
10. #39610C2semidirect
11. #39487C2semidirect
12. #39482C2semidirect
13. #39482C2semidirect
14. #37867C2semidirect
15. #37861C2semidirect
16. #36742C2semidirect
17. #36740C2semidirect
18. #36561C2semidirect
19. #36183C2semidirect
20. #35326C2semidirect
21. #35173C2semidirect
22. #35167C2semidirect
23. #35004C2semidirect
25. #35002C2semidirect
26. #34594C2semidirect
27. C2×#2373C2semidirect
58. #2727C22semidirect
59. #2726C22semidirect
60. #2725C22semidirect
61. #2725C22semidirect
62. #2723C22semidirect
64. #2721C22semidirect
65. #2721C22semidirect
66. #2720C22semidirect
67. #2720C22semidirect
68. #2719C22semidirect
69. #2719C22semidirect
72. #2716C22semidirect
74. #2713C22semidirect
75. #2713C22semidirect
81. #2694C22semidirect
82. #2692C22semidirect
83. #2690C22semidirect
90. #2677C22semidirect
91. #2677C22semidirect
95. #2674C22semidirect
98. #2664C22semidirect
99. #2662C22semidirect
100. #2660C22semidirect
107. #2658C22semidirect
109. #2642C22semidirect
110. #2640C22semidirect
116. #2611C22semidirect
117. #2611C22semidirect
118. #2604C22semidirect
119. #2604C22semidirect
120. #2584C22semidirect
121. #2584C22semidirect
122. #2567C22semidirect
127. #2556C22semidirect
128. #2556C22semidirect
129. #2556C22semidirect
131. #2554C22semidirect
134. #2552C22semidirect
135. #2551C22semidirect
136. #2551C22semidirect
137. #2550C22semidirect
138. #2550C22semidirect
141. #2546C22semidirect
142. #2542C22semidirect
145. #2519C22semidirect
146. #2506C22semidirect
147. #2506C22semidirect
155. #2492C22semidirect
158. #2479C22semidirect
161. #2475C22semidirect
162. #2473C22semidirect
165. #2469C22semidirect
168. #2465C22semidirect
170. #2462C22semidirect
171. #2462C22semidirect
172. #2461C22semidirect
175. #2453C22semidirect
176. #2452C22semidirect
177. #2452C22semidirect
179. #2449C22semidirect
180. #2441C22semidirect
185. #2429C22semidirect
190. #2415C22semidirect
194. #2396C22semidirect
195. #2392C22semidirect
200. #2365C22semidirect
202. #2360C22semidirect
204. D4×C4⋊C4C22semidirect
206. #2327C22semidirect
207. #2327C22semidirect
208. #2326C22semidirect
209. #2326C22semidirect
266. C2×#126D4semidirect

Maximal subgroups

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

subgroupindex
C2×#35642
#513312
#513302
#513292
#513282
#447752
#447732
#443642
#442042
#396102
#394872
#394822
#378672
#378612
#367422
#367402
#365612
#361832
#353262
#351732
#351672
#350042
#350032
#350022
#345942
C2×#23732