Finite Group Databasebeta

← #7680438

Subgroups — #7680438

Order 512.

6944 conjugacy classes of subgroups.

The subgroup lattice has 1377 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3517C211yesmaximal, characteristic
2C2×#3523C211yesmaximal, characteristic, complemented
3#59146C214yesmaximal, complemented
4#59101C214yesmaximal, complemented
5#59098C214yesmaximal, complemented
6#59085C214yesmaximal, complemented
7#44785C218yesmaximal, complemented
8#44452C218yesmaximal, complemented
9#39488C211yesmaximal, characteristic, complemented
10#39485C212yesmaximal, complemented
11#39363C211yesmaximal, characteristic, complemented
12#39363C212yesmaximal, complemented
13#39174C211yesmaximal, characteristic, complemented
14#39170C211yesmaximal, characteristic, complemented
15#38093C212yesmaximal, complemented
16#38085C212yesmaximal, complemented
17#36583C211yesmaximal, characteristic, complemented
18#36560C211yesmaximal, characteristic, complemented
19#36419C211yesmaximal, characteristic, complemented
20#36303C211yesmaximal, characteristic, complemented
21#35678C212yesmaximal, complemented
22#35622C212yesmaximal, complemented
23#35332C212yesmaximal, complemented
24#35298C211yesmaximal, characteristic, complemented
25#34979C211yesmaximal, characteristic, complemented
26#34955C211yesmaximal, characteristic, complemented
27#34276C212yesmaximal, complemented
28#34151C211yesmaximal, characteristic, complemented
29C4×#536C211yesmaximal, characteristic, complemented
30#3523—216no—
31#3517—216no—
32C2×#557C2211yescharacteristic
33C2×#557C2211yescharacteristic
34C2×#557C2211yescharacteristic
35C2×#557C2212yes—
36C2×#556C2212yes—
37C2×#556C2211yescharacteristic
38C2×#553C2212yes—
39C2×#553C2214yes—
40C2×#552C2212yes—
41C2×#552C2214yes—
42C2×#550C2211yescharacteristic
43C2×#550C2211yescharacteristic
44C2×#550C2212yes—
45C2×#550C2212yes—
46C2×D4×Q8C2212yes—
47C2×D4×Q8C2211yescharacteristic
48C2×#547C2211yescharacteristic
49C2×#547C2212yes—
50C2×#541C2212yes—
51C2×#541C2214yes—
52C2×#540C2212yes—
53C2×#540C2214yes—
54C2×#536C2211yescharacteristic
55C2×#536C2212yes—
56C2×#533C2211yescharacteristic
57C2×#533C2212yes—
58C2×#532C2212yes—
59C2×#532C2211yescharacteristic
60C2×#529C2212yes—
61C2×#529C2212yes—
62C2×#529C2211yescharacteristic
63C2×#520C2212yes—
64C2×#519C2212yes—
65C2×C4×#41C2211yescharacteristic
66C22×C4×Q8C2211yescharacteristic
67#2868C2211yescharacteristic
68#2862C2211yescharacteristic
69#2859C2212yes—
70#2858C2212yes—
71#2858C2211yescharacteristic
72#2858C2211yescharacteristic
73#2850C2212yes—
74#2850C2212yes—
75#2725C2218yes—
76#2719C2218yes—
77#2718C2218yes—
78#2716C2218yes—
79#2711C2218yes—
80#2709C2218yes—
81#2701C2218yes—
82#2691C2218yes—
83#2687C2218yes—
84#2681C2218yes—
85#2681C2218yes—
86#2681C2218yes—
87#2642C2212yes—
88#2641C2212yes—
89#2620C2212yes—
90#2620C2212yes—
91#2620C2212yes—
92#2620C2212yes—
93#2611C2214yes—
94#2592C2214yes—
95#2591C2214yes—
96#2568C2211yescharacteristic
97#2568C2211yescharacteristic
98#2568C2211yescharacteristic
99#2566C2212yes—
100#2566C2214yes—
101#2565C2212yes—
102#2565C2212yes—
103#2565C2212yes—
104#2559C2218yes—
105#2559C2218yes—
106#2559C2218yes—
107#2558C2218yes—
108#2558C2218yes—
109#2548C2212yes—
110#2548C2211yescharacteristic
111#2548C2211yescharacteristic
112#2548C2212yes—
113#2547C2212yes—
114#2547C2211yescharacteristic
115#2546C2212yes—
116#2546C2211yescharacteristic
117#2546C2214yes—
118#2545C2214yes—
119#2544C2214yes—
120#2542C2211yescharacteristic
121#2506C2218yes—
122#2504C2212yes—
123#2503C2212yes—
124#2502C2212yes—
125#2500C2212yes—
126#2500C2212yes—
127#2500C2214yes—
128#2499C2212yes—
129#2492C2214yes—
130#2490C2218yes—
131#2490C2214yes—
132#2488C2218yes—
133#2476C2218yes—
134#2476C2218yes—
135#2476C2218yes—
136#2475C2218yes—
137#2473C2218yes—
138#2470C2218yes—
139#2468C2218yes—
140#2466C2218yes—
141#2466C2218yes—
142#2460C2218yes—
143#2458C2218yes—
144#2458C2218yes—
145#2453C2214yes—
146#2452C2214yes—
147#2452C2218yes—
148#2450C2218yes—
149#2446C2214yes—
150#2445C2214yes—
151#2445C2218yes—
152#2444C2218yes—
153#2436C2212yes—
154#2436C2212yes—
155#2436C2212yes—
156#2432C2214yes—
157#2432C2214yes—
158#2432C2212yes—
159#2432C2212yes—
160#2432C2212yes—
161#2432C2214yes—
162#2429C2214yes—
163#2426C2214yes—
164#2415C2214yes—
165#2398C2214yes—
166#2395C2214yes—
167#2374C2214yes—
168#2373C2214yes—
169#2370C2212yes—
170#2367C2212yes—
171#2367C2214yes—
172#2365C2214yes—
173#2363C2212yes—
174#2362C2212yes—
175#2362C2218yes—
176#2360C2218yes—
177#2359C2218yes—
178#2359C2218yes—
179#2341C2214yes—
180#2339C2214yes—
181#2327C2212yes—
182#2327C2211yescharacteristic
183#2327C2211yescharacteristic
184#2326C2211yescharacteristic
185#2326C2212yes—
186#2326C2212yes—
187#2326C2212yes—
188#2326C2211yescharacteristic
189#2323C2214yes—
190#2322C2214yes—
191#2317C2211yescharacteristic
192#2317C2212yes—
193#2311C2211yescharacteristic
194#2310C2211yescharacteristic
195C4×C4⋊Q8C2211yescharacteristic
196C4×C4⋊Q8C2212yes—
197C4×C4⋊Q8C2211yescharacteristic
198C4×C4⋊Q8C2212yes—
199C4×#124C2212yes—
200C4×#124C2212yes—
201C4×#124C2211yescharacteristic
202C4×#124C2211yescharacteristic
203C4×#124C2212yes—
204C4×#124C2212yes—
205C4×C22⋊Q8C2214yes—
206C4×C22⋊Q8C2214yes—
207C4×#123C2214yes—
208#2298C2212yes—
209#2297C2212yes—
210#2297C2214yes—
211#2295C2211yescharacteristic
212C2×#391C2212yes—
213#2293C2212yes—
214#2293C2211yescharacteristic
215#2290C2212yes—
216C42×Q8C2211yescharacteristic
217C42×D4C2211yescharacteristic
218C4×#117C2212yes—
219C4×#117C2211yescharacteristic
220C4×#117C2211yescharacteristic
221C22×#41C2311yescharacteristic
222C22×#41C2312yes—
223C22×#41C2312yes—
224C22×#41C2312yes—
225C22×#41C2312yes—
226C23×Q8C2311yescharacteristic
227C23×Q8C2312yes—
228#557—216no—
229#557—28no—
230#557—28no—
231#557—28no—
232#556—216no—
233#556—28no—
234#553—232no—
235#553—216no—
236#552—232no—
237#552—216no—
238#550—216no—
239#550—28no—
240#550—28no—
241#550—216no—
242D4×Q8—216no—
243D4×Q8—28no—
244#547—216no—
245#547—28no—
246#541—232no—
247#541—216no—
248#540—232no—
249#540—216no—
250#536—28no—
251#536—216no—
252#533—216no—
253#533—28no—
254#532—216no—
255#532—28no—
256C2×C4⋊Q8C2311yescharacteristic
257C2×C4⋊Q8C2312yes—
258C2×C4⋊Q8C2311yescharacteristic
259C2×C4⋊Q8C2311yescharacteristic
260C2×C4⋊Q8C2311yescharacteristic
261C2×C4⋊Q8C2312yes—
262C2×C4⋊Q8C2312yes—
263C2×C4⋊Q8C2312yes—
264C2×C4⋊Q8C2312yes—
265C2×C4⋊Q8C2314yes—
266C2×C4⋊Q8C2314yes—
267C2×C4⋊Q8C2311yescharacteristic
268C2×#127C2311yescharacteristic
269C2×#127C2312yes—
270C2×#127C2312yes—
271C2×#127C2314yes—
272#529—216no—
273#529—216no—
274#529D4116yes—
275C2×#126C2314yes—
276C2×#126C2314yes—
277C2×#126C2314yes—
278C2×#126C2314yes—
279C2×#126C2314yes—
280C2×#126C2312yes—
281C2×#125C2312yes—
282C2×#125C2312yes—
283C2×#125C2312yes—
284C2×#125C2312yes—
285C2×#125C2314yes—
286C2×#125C2314yes—
287C2×#125C2314yes—
288C2×#125C2314yes—
289C2×#125C2314yes—
290C2×#125C2314yes—
291C2×#125C2311yescharacteristic
292C2×#124C2311yescharacteristic
293C2×#124C2312yes—
294C2×#124C2312yes—
295C2×#124C2311yescharacteristic
296C2×#124C2312yes—
297C2×#124C2312yes—
298C2×#124C2312yes—
299C2×#124C2312yes—
300C2×#124C2312yes—
301C2×#124C2314yes—
302C2×#124C2311yescharacteristic
303C2×#123C2314yes—
304C2×#123C2318yes—
305C2×#123C2314yes—
306C2×#123C2314yes—
307C2×#123C2314yes—
308C2×#123C2314yes—
309C2×#123C2314yes—
310C2×#123C2312yes—
311C2×C22⋊Q8C2314yes—
312C2×C22⋊Q8C2312yes—
313C2×C22⋊Q8C2312yes—
314C2×C22⋊Q8C2318yes—
315C2×C22⋊Q8C2312yes—
316C2×C22⋊Q8C2312yes—
317C2×C22⋊Q8C2312yes—
318C2×C22⋊Q8C2314yes—
319C2×C22⋊Q8C2314yes—
320C2×C22⋊Q8C2314yes—
321C2×C22⋊Q8C2314yes—
322C2×C22⋊Q8C2311yescharacteristic
323C2×#121C2312yes—
324C2×#121C2312yes—
325C2×#121C2312yes—
326C2×#121C2312yes—
327C2×#121C2312yes—
328C2×#121C2314yes—
329C2×#121C2314yes—
330C2×#121C2314yes—
331C2×#121C2314yes—
332C2×#121C2314yes—
333C2×#121C2314yes—
334C2×#121C2314yes—
335C2×#121C2311yescharacteristic
336#520—216no—
337#519—216no—
338C4×#41—28no—
339C2×C4×Q8—28no—
340C2×C4×Q8C2311yescharacteristic
341C2×C4×Q8C2311yescharacteristic
342C2×C4×Q8C2312yes—
343C2×C4×Q8C2312yes—
344C2×C4×Q8C2311yescharacteristic
345C2×C4×Q8C2311yescharacteristic
346C2×C4×Q8C2312yes—
347C2×C4×Q8C2312yes—
348C2×C4×Q8C2312yes—
349C2×C4×Q8C2311yescharacteristic
350C2×C4×Q8C2311yescharacteristic
351C2×C4×Q8C2312yes—
352C2×C4×Q8C2312yes—
353C2×C4×Q8C2314yes—
354C2×C4×Q8C2314yes—
355C2×C4×Q8C2312yes—
356C2×C4×Q8C2312yes—
357C2×C4×Q8C2312yes—
358C2×C4×Q8C2312yes—
359C2×C4×Q8C2312yes—
360C2×C4×Q8C2311yescharacteristic
361C2×C4×D4C2312yes—
362C2×C4×D4C2312yes—
363C2×C4×D4C2312yes—
364C2×C4×D4C2311yescharacteristic
365C2×C4×D4C2312yes—
366C2×C4×D4C2312yes—
367C2×C4×D4C2314yes—
368C2×C4×D4C2314yes—
369C2×C4×D4C2312yes—
370C2×C4×D4C2312yes—
371C2×C4×D4C2311yescharacteristic
372C2×C4×D4C2314yes—
373C2×C4×D4C2314yes—
374C2×C4×D4C2314yes—
375C2×C4×D4C2312yes—
376C2×C4×D4C2311yescharacteristic
377C2×C4×D4C2312yes—
378C2×#117C2311yescharacteristic
379C2×#117C2311yescharacteristic
380C2×#117C2312yes—
381C2×#117C2312yes—
382C2×#117C2312yes—
383C2×#117C2314yes—
384C2×#117C2314yes—
385C2×#117C2314yes—
386C2×#117C2312yes—
387C2×#117C2314yes—
388C2×#117C2311yescharacteristic
389C2×#117C2312yes—
390C2×#117C2312yes—
391C22×C4⋊C4C2311yescharacteristic
392C22×C4⋊C4C2312yes—
393C22×C4⋊C4C2312yes—
394C22×C4⋊C4C2314yes—
395C22×C42C2312yes—
396C22×C42C2312yes—
397C22×C42C2312yes—
398C22×C42C2311yescharacteristic
399#400C2314yes—
400#400C2314yes—
401#400C2314yes—
402#400C2318yes—
403#400C2318yes—
404#400C2318yes—
405#399C2314yes—
406#398C2318yes—
407#398C2318yes—
408#398C2318yes—
409#398C2314yes—
410#398C2318yes—
411#398C2318yes—
412#397C2318yes—
413#397C2314yes—
414#397C2318yes—
415#397C2318yes—
416#396C2318yes—
417#396C2318yes—
418#396C2318yes—
419#396C2318yes—
420#396C2318yes—
421#394C2314yes—
422#394C2314yes—
423#394C2318yes—
424#394C2318yes—
425#394C2318yes—
426#394C2318yes—
427#394C2318yes—
428#394C2318yes—
429#394C2318yes—
430#394C2318yes—
431#394C2318yes—
432#394C2318yes—
433#394C2318yes—
434#394C2318yes—
435#394C2318yes—
436#393C2318yes—
437#393C2318yes—
438#393C2318yes—
439#391C2312yes—
440#391C2311yescharacteristic
441#391C2311yescharacteristic
442#391C2312yes—
443#391C2311yescharacteristic
444#391C2311yescharacteristic
445#391C2312yes—
446#391C2312yes—
447#391C2312yes—
448#391C2314yes—
449#391C2311yescharacteristic
450#391C2311yescharacteristic
451#391C2314yes—
452#391C2314yes—
453#391C2312yes—
454#391C2314yes—
455#391C2312yes—
456#391C2314yes—
457#391C2318yes—
458#391C2312yes—
459#390C2312yes—
460#390C2314yes—
461#390C2314yes—
462#390C2312yes—
463#390C2311yescharacteristic
464#390C2311yescharacteristic
465#390C2312yes—
466#390C2314yes—
467#390C2314yes—
468#390C2318yes—
469#390C2314yes—
470#390C2318yes—
471#390C2318yes—
472#390C2312yes—
473#390C2314yes—
474#390C2312yes—
475#390C2318yes—
476#390C2312yes—
477#389C2314yes—
478#389C2314yes—
479#389C2318yes—
480#389C2318yes—
481#389C2314yes—
482#389C2318yes—
483#389C2318yes—
484#389C2318yes—
485#389C2312yes—
486#389C2312yes—
487#389C2314yes—
488#389C2314yes—
489#389C2318yes—
490#388C2314yes—
491#388C2314yes—
492#388C2314yes—
493#388C2314yes—
494#388C2318yes—
495#388C2318yes—
496#388C2318yes—
497#388C2318yes—
498#388C2318yes—
499#388C2318yes—
500#388C2318yes—
501#388C2318yes—
502#388C2318yes—
503#388C2314yes—
504#388C2314yes—
505#388C2314yes—
506#388C2314yes—
507#388C2314yes—
508#388C2318yes—
509#388C2314yes—
510#388C2318yes—
511#387C2318yes—
512#387C2318yes—
513#387C2318yes—
514#387C2314yes—
515#387C2314yes—
516#387C2314yes—
517#387C2314yes—
518#387C2318yes—
519#387C2318yes—
520#387C2318yes—
521#387C2314yes—
522#387C2314yes—
523#387C2314yes—
524#387C2314yes—
525#386C2314yes—
526#386C2318yes—
527#386C2318yes—
528#386C2318yes—
529#386C2318yes—
530#386C2318yes—
531#386C2318yes—
532#386C2314yes—
533#386C2318yes—
534#385C2318yes—
535#385C2318yes—
536#385C2318yes—
537#385C2314yes—
538#385C2318yes—
539#385C2314yes—
540#385C2314yes—
541#385C2318yes—
542#385C2318yes—
543#385C2314yes—
544#385C2318yes—
545#385C2318yes—
546#385C2318yes—
547#384C2311yescharacteristic
548#384C2312yes—
549#384C2311yescharacteristic
550#384C2312yes—
551#384C2312yes—
552#384C2314yes—
553#382C2312yes—
554#382C2312yes—
555#382C2312yes—
556#382C2311yescharacteristic
557#382C2314yes—
558#382C2311yescharacteristic
559#381C2314yes—
560#381C2318yes—
561#380C2314yes—
562#380C2314yes—
563#380C2318yes—
564C4×C4⋊C4C2318yes—
565C4×C4⋊C4C2318yes—
566C4×C4⋊C4C2314yes—
567C4×C4⋊C4C2314yes—
568C4×C4⋊C4C2312yes—
569C4×C4⋊C4C2312yes—
570C4×C4⋊C4C2312yes—
571C4×C4⋊C4C2311yescharacteristic
572C4×C4⋊C4C2311yescharacteristic
573C4×C4⋊C4C2312yes—
574C4×C4⋊C4C2314yes—
575C4×C4⋊C4C2314yes—
576C4×C4⋊C4C2312yes—
577C4×C4⋊C4C2312yes—
578C4×C4⋊C4C2312yes—
579C4×C4⋊C4C2314yes—
580C4×C22⋊C4C2312yes—
581C4×C22⋊C4C2312yes—
582C4×C22⋊C4C2314yes—
583C4×C22⋊C4C2318yes—
584C4×C22⋊C4C2314yes—
585C4×C22⋊C4C2314yes—
586C4×C22⋊C4C2314yes—
587C4×C22⋊C4C2318yes—
588C4×C22⋊C4C2318yes—
589C4×C22⋊C4C2312yes—
590C4×C22⋊C4C2314yes—
591C4×C22⋊C4C2318yes—
592C4×C22⋊C4C2318yes—
593C4×C22⋊C4C2312yes—
594C4×C22⋊C4C2312yes—
595C4×C22⋊C4C2312yes—
596#376C2311yescharacteristic
597#376C2311yescharacteristic
598#376C2312yes—
599#376C2312yes—
600C2×#95C2318yes—
601C43C2312yes—
602C43C2311yescharacteristic
603C43C2311yescharacteristic
604C43C2312yes—
605C2×#41—28no—
606C2×#41—24no—
607C2×#41—28no—
608C2×#41—28no—
609C2×#41—24no—
610C2×#41—28no—
611C2×#41—28no—
612C2×#41—44no—
613C2×#41—42no—
614C2×#41—48no—
615C2×#41—48no—
616C2×#41—48no—
617C22×Q8—24no—
618C22×Q8—28no—
619C22×Q8—24no—
620C22×Q8—28no—
621C22×Q8—44no—
622C22×Q8—42no—
623C22×Q8C2412yes—
624C22×Q8C2411yescharacteristic
625C22×Q8C2412yes—
626C22×Q8C2412yes—
627C22×Q8C2412yes—
628C22×Q8C2414yes—
629C22×Q8C2411yescharacteristic
630C22×Q8C2411yescharacteristic
631C22×Q8C2411yescharacteristic
632C22×D4C2412yes—
633C22×D4C2411yescharacteristic
634C22×D4C2412yes—
635C22×D4C2412yes—
636C22×D4C2414yes—
637C22×D4C2411yescharacteristic
638C22×D4C2414yes—
639C22×D4C2412yes—
640C22×D4C2414yes—
641C22×D4C2414yes—
642C22×D4C2414yes—
643C22×D4C2414yes—
644C22×D4C2412yes—
645C23×C4C2412yes—
646C23×C4C2414yes—
647C23×C4C2412yes—
648C23×C4C2414yes—
649C23×C4C2412yes—
650C23×C4C2412yes—
651C23×C4C2411yescharacteristic
652C23×C4C2411yescharacteristic
653C23×C4C2412yes—
654C23×C4C2414yes—
655C23×C4C2414yes—
656C23×C4C2414yes—
657C23×C4C2412yes—
658C23×C4C2414yes—
659C23×C4C2411yescharacteristic
660C4⋊Q8—28no—
661C4⋊Q8—28no—
662C4⋊Q8—24no—
663C4⋊Q8—28no—
664C4⋊Q8—28no—
665C4⋊Q8—216no—
666C4⋊Q8—24no—
667C4⋊Q8—24no—
668C4⋊Q8—24no—
669C4⋊Q8—28no—
670C4⋊Q8—48no—
671C4⋊Q8#4118yescomplemented
672#127—28no—
673#127—216no—
674#127—24no—
675#127—28no—
676#126—216no—
677#126—216no—
678#126—216no—
679#126—216no—
680#126—216no—
681#126C2×D4116yes—
682#125—28no—
683#125—216no—
684#125—216no—
685#125—216no—
686#125—216no—
687#125—216no—
688#125—216no—
689#125—28no—
690#125—28no—
691#125—28no—
692#125C2×D418yes—
693#124—28no—
694#124—24no—
695#124—28no—
696#124—28no—
697#124—24no—
698#124—28no—
699#124—44no—
700#124—44no—
701#124—44no—
702#124—48no—
703#124C2×D418yes—
704#123—216no—
705#123—216no—
706#123—216no—
707#123—216no—
708#123—232no—
709#123—216no—
710#123—216no—
711#123C2×D4116yes—
712C22⋊Q8—28no—
713C22⋊Q8—28no—
714C22⋊Q8—28no—
715C22⋊Q8—28no—
716C22⋊Q8—28no—
717C22⋊Q8—216no—
718C22⋊Q8—232no—
719C22⋊Q8—216no—
720C22⋊Q8—216no—
721C22⋊Q8—216no—
722C22⋊Q8—48no—
723C22⋊Q8C2×D418yes—
724#121—216no—
725#121—28no—
726#121—28no—
727#121—28no—
728#121—28no—
729#121—28no—
730#121—216no—
731#121—216no—
732#121—216no—
733#121—216no—
734#121—216no—
735#121—216no—
736#121C2×D418yes—
737C4×Q8—28no—
738C4×Q8—216no—
739C4×Q8—216no—
740C4×Q8—28no—
741C4×Q8—28no—
742C4×Q8—28no—
743C4×Q8—24no—
744C4×Q8—28no—
745C4×Q8—24no—
746C4×Q8—24no—
747C4×Q8—28no—
748C4×Q8—24no—
749C4×Q8—24no—
750C4×Q8—24no—
751C4×Q8—28no—
752C4×Q8—28no—
753C4×Q8—28no—
754C4×Q8—28no—
755C4×Q8—28no—
756C4×Q8—44no—
757C4×Q8C2×D418yes—
758C4×D4—216no—
759C4×D4—28no—
760C4×D4—28no—
761C4×D4—28no—
762C4×D4—28no—
763C4×D4—216no—
764C4×D4—216no—
765C4×D4—216no—
766C4×D4—216no—
767C4×D4—24no—
768C4×D4—24no—
769C4×D4—28no—
770C4×D4—28no—
771C4×D4—28no—
772C4×D4—44no—
773C4×D4C2×D418yes—
774C4×D4C2×D4116yes—
775#117—24no—
776#117—28no—
777#117—28no—
778#117—216no—
779#117—216no—
780#117—216no—
781#117—216no—
782#117—28no—
783#117—24no—
784#117—28no—
785#117—42no—
786#117—44no—
787#117C2×D4116yes—
788C2×C4⋊C4—24no—
789C2×C4⋊C4—28no—
790C2×C4⋊C4—28no—
791C2×C4⋊C4—216no—
792C2×C4⋊C4C2411yescharacteristic
793C2×C4⋊C4C2412yes—
794C2×C4⋊C4C2414yes—
795C2×C4⋊C4C2411yescharacteristic
796C2×C4⋊C4C2412yes—
797C2×C4⋊C4C2412yes—
798C2×C4⋊C4C2414yes—
799C2×C4⋊C4C2411yescharacteristic
800C2×C4⋊C4C2412yes—
801C2×C4⋊C4C2412yes—
802C2×C4⋊C4C2412yes—
803C2×C4⋊C4C2412yes—
804C2×C4⋊C4C2411yescharacteristic
805C2×C4⋊C4C2412yes—
806C2×C4⋊C4C2412yes—
807C2×C4⋊C4C2412yes—
808C2×C4⋊C4C2414yes—
809C2×C4⋊C4C2414yes—
810C2×C4⋊C4C2414yes—
811C2×C4⋊C4C2412yes—
812C2×C4⋊C4C2414yes—
813C2×C4⋊C4C2412yes—
814C2×C4⋊C4C2414yes—
815C2×C4⋊C4C2412yes—
816C2×C4⋊C4C2412yes—
817C2×C4⋊C4C2414yes—
818C2×C4⋊C4C2412yes—
819C2×C4⋊C4C2412yes—
820C2×C4⋊C4C2414yes—
821C2×C4⋊C4C2414yes—
822C2×C4⋊C4C2414yes—
823C2×C4⋊C4C2414yes—
824C2×C4⋊C4C2414yes—
825C2×C4⋊C4C2414yes—
826C2×C4⋊C4C2414yes—
827C2×C4⋊C4C2414yes—
828C2×C4⋊C4C2418yes—
829C2×C4⋊C4C2412yes—
830C2×C4⋊C4C2414yes—
831C2×C4⋊C4C2418yes—
832C2×C4⋊C4C2418yes—
833C2×C4⋊C4C2418yes—
834C2×C4⋊C4C2414yes—
835C2×C4⋊C4C2414yes—
836C2×C4⋊C4C2414yes—
837C2×C4⋊C4C2412yes—
838C2×C4⋊C4C2412yes—
839C2×C4⋊C4C2411yescharacteristic
840C2×C4⋊C4C2412yes—
841C2×C4⋊C4C2411yescharacteristic
842C2×C4⋊C4C2412yes—
843C2×C4⋊C4C2414yes—
844C2×C22⋊C4C2414yes—
845C2×C22⋊C4C2414yes—
846C2×C22⋊C4C2414yes—
847C2×C22⋊C4C2412yes—
848C2×C22⋊C4C2412yes—
849C2×C22⋊C4C2412yes—
850C2×C22⋊C4C2414yes—
851C2×C22⋊C4C2412yes—
852C2×C22⋊C4C2414yes—
853C2×C22⋊C4C2414yes—
854C2×C22⋊C4C2414yes—
855C2×C22⋊C4C2414yes—
856C2×C22⋊C4C2414yes—
857C2×C22⋊C4C2414yes—
858C2×C22⋊C4C2414yes—
859C2×C22⋊C4C2418yes—
860C2×C22⋊C4C2414yes—
861C2×C22⋊C4C2418yes—
862C2×C22⋊C4C2412yes—
863C2×C22⋊C4C2414yes—
864C2×C22⋊C4C2414yes—
865C2×C22⋊C4C2418yes—
866C2×C22⋊C4C2418yes—
867C2×C22⋊C4C2418yes—
868C2×C22⋊C4C2418yes—
869C2×C22⋊C4C2418yes—
870C2×C22⋊C4C2418yes—
871C2×C22⋊C4C2418yes—
872C2×C22⋊C4C2414yes—
873C2×C22⋊C4C2414yes—
874C2×C22⋊C4C2414yes—
875C2×C22⋊C4C2418yes—
876C2×C22⋊C4C2412yes—
877C2×C22⋊C4C2412yes—
878C2×C22⋊C4C2412yes—
879C2×C22⋊C4C2412yes—
880C2×C22⋊C4C2412yes—
881C2×C42—28no—
882C2×C42—28no—
883C2×C42—44no—
884C2×C42C2×D418yes—
885C2×C42C2412yes—
886C2×C42C2412yes—
887C2×C42C2412yes—
888C2×C42C2414yes—
889C2×C42C2414yes—
890C2×C42C2414yes—
891C2×C42C2414yes—
892C2×C42C2414yes—
893C2×C42C2411yescharacteristic
894C2×C42C2411yescharacteristic
895C2×C42C2412yes—
896C2×C42C2411yescharacteristic
897C2×C42C2412yes—
898C2×C42C2412yes—
899C2×C42C2412yes—
900C2×C42C2412yes—
901C2×C42C2412yes—
902C2×C42C2412yes—
903C2×C42C2412yes—
904C2×C42C2414yes—
905C2×C42C2414yes—
906C2×C42C2414yes—
907C2×C42C2412yes—
908C2×C42C2414yes—
909C2×C42C2412yes—
910C2×C42C2414yes—
911C2×C42C2411yescharacteristic
912C2×C42C2411yescharacteristic
913C2×C42C2412yes—
914C2×C42C2411yescharacteristic
915C2×C42C2411yescharacteristic
916C2×C42C2411yescharacteristic
917#95C2414yes—
918#95C2418yes—
919#95C2418yes—
920#95C2418yes—
921#95C2412yes—
922#95C2412yes—
923#95C2412yes—
924#95C2412yes—
925#95C2414yes—
926#95C2414yes—
927#95C2412yes—
928#95C2414yes—
929#95C2412yes—
930#95C2414yes—
931#95C2414yes—
932#95C2414yes—
933#95C2418yes—
934#95C2414yes—
935#95C2414yes—
936#95C2418yes—
937#95C2418yes—
938#95C2418yes—
939#95C2414yes—
940#95C2418yes—
941#95C2418yes—
942#95C2414yes—
943#95C2414yes—
944#95C2414yes—
945#95C2414yes—
946#95C2414yes—
947#95C2418yes—
948C24C2512yes—
949C24C2514yes—
950C24C2511yescharacteristic
951C24C2512yes—
952#41—416no—
953#41—432no—
954#41—816no—
955#41—816no—
956#41—816no—
957C2×Q8—22no—
958C2×Q8—22no—
959C2×Q8—24no—
960C2×Q8—24no—
961C2×Q8—28no—
962C2×Q8—22no—
963C2×Q8—24no—
964C2×Q8—24no—
965C2×Q8—24no—
966C2×Q8—28no—
967C2×Q8—22no—
968C2×Q8—24no—
969C2×Q8—24no—
970C2×Q8—22no—
971C2×Q8—22no—
972C2×Q8—28no—
973C2×Q8—22no—
974C2×Q8—24no—
975C2×Q8—28no—
976C2×Q8—44no—
977C2×Q8—42no—
978C2×Q8—416no—
979C2×Q8—432no—
980C2×Q8C22×D414yes—
981C2×Q8C2×#4114yes—
982C2×Q8C2×#4114yes—
983C2×D4—28no—
984C2×D4—24no—
985C2×D4—28no—
986C2×D4—28no—
987C2×D4—28no—
988C2×D4—22no—
989C2×D4—24no—
990C2×D4—24no—
991C2×D4—24no—
992C2×D4—28no—
993C2×D4—28no—
994C2×D4—24no—
995C2×D4—28no—
996C2×D4—24no—
997C2×D4—22no—
998C2×D4—24no—
999C2×D4—22no—
1000C2×D4—24no—
1001C2×D4—28no—
1002C2×D4—44no—
1003C2×D4—42no—
1004C2×D4—44no—
1005C2×D4—44no—
1006C2×D4—48no—
1007C2×D4—48no—
1008C2×D4—48no—
1009C2×D4—48no—
1010C2×D4—48no—
1011C2×D4C22×D414yes—
1012C2×D4C22×D418yes—
1013C22×C4—24no—
1014C22×C4—22no—
1015C22×C4—24no—
1016C22×C4—22no—
1017C22×C4—24no—
1018C22×C4—24no—
1019C22×C4—24no—
1020C22×C4—28no—
1021C22×C4—28no—
1022C22×C4—24no—
1023C22×C4—24no—
1024C22×C4—28no—
1025C22×C4—28no—
1026C22×C4—24no—
1027C22×C4—24no—
1028C22×C4—28no—
1029C22×C4—28no—
1030C22×C4—24no—
1031C22×C4—28no—
1032C22×C4—28no—
1033C22×C4—42no—
1034C22×C4—44no—
1035C22×C4—42no—
1036C22×C4—44no—
1037C22×C4—44no—
1038C22×C4—42no—
1039C22×C4—44no—
1040C22×C4—44no—
1041C22×C4—44no—
1042C22×C4—44no—
1043C22×C4—48no—
1044C22×C4—48no—
1045C22×C4—48no—
1046C22×C4C22×D414yes—
1047C22×C4C22×D414yes—
1048C22×C4C22×D418yes—
1049C22×C4C22×D414yes—
1050C22×C4C2512yes—
1051C22×C4C2514yes—
1052C22×C4C2512yes—
1053C22×C4C2514yes—
1054C22×C4C2512yes—
1055C22×C4C2512yes—
1056C22×C4C2512yes—
1057C22×C4C2514yes—
1058C22×C4C2512yes—
1059C22×C4C2512yes—
1060C22×C4C2514yes—
1061C22×C4C2512yes—
1062C22×C4C2514yes—
1063C22×C4C2511yescharacteristic
1064C22×C4C2511yescharacteristic
1065C22×C4C2512yes—
1066C22×C4C2511yescharacteristic
1067C22×C4C2512yes—
1068C22×C4C2512yes—
1069C22×C4C2511yescharacteristic
1070C22×C4C2512yes—
1071C22×C4C2512yes—
1072C22×C4C2512yes—
1073C22×C4C2511yescharacteristic
1074C22×C4C2511yescharacteristic
1075C4⋊C4—24no—
1076C4⋊C4—22no—
1077C4⋊C4—28no—
1078C4⋊C4—24no—
1079C4⋊C4—22no—
1080C4⋊C4—28no—
1081C4⋊C4—24no—
1082C4⋊C4—24no—
1083C4⋊C4—22no—
1084C4⋊C4—24no—
1085C4⋊C4—24no—
1086C4⋊C4—24no—
1087C4⋊C4—24no—
1088C4⋊C4—22no—
1089C4⋊C4—28no—
1090C4⋊C4—24no—
1091C4⋊C4—28no—
1092C4⋊C4—28no—
1093C4⋊C4—28no—
1094C4⋊C4—24no—
1095C4⋊C4—24no—
1096C4⋊C4—28no—
1097C4⋊C4—24no—
1098C4⋊C4—28no—
1099C4⋊C4—24no—
1100C4⋊C4—28no—
1101C4⋊C4—28no—
1102C4⋊C4—28no—
1103C4⋊C4—28no—
1104C4⋊C4—28no—
1105C4⋊C4—28no—
1106C4⋊C4—24no—
1107C4⋊C4—28no—
1108C4⋊C4—28no—
1109C4⋊C4—216no—
1110C4⋊C4—24no—
1111C4⋊C4—24no—
1112C4⋊C4—44no—
1113C4⋊C4—44no—
1114C4⋊C4—44no—
1115C4⋊C4—42no—
1116C4⋊C4—44no—
1117C4⋊C4—48no—
1118C4⋊C4—48no—
1119C4⋊C4—48no—
1120C4⋊C4C22×D418yes—
1121C4⋊C4C22×D418yes—
1122C4⋊C4C22×D414yes—
1123C4⋊C4C22×D418yes—
1124C4⋊C4C22×D414yes—
1125C4⋊C4C22×D418yes—
1126C4⋊C4C2×#41116yes—
1127C22⋊C4—28no—
1128C22⋊C4—28no—
1129C22⋊C4—24no—
1130C22⋊C4—28no—
1131C22⋊C4—28no—
1132C22⋊C4—28no—
1133C22⋊C4—24no—
1134C22⋊C4—24no—
1135C22⋊C4—28no—
1136C22⋊C4—28no—
1137C22⋊C4—28no—
1138C22⋊C4—28no—
1139C22⋊C4—24no—
1140C22⋊C4—28no—
1141C22⋊C4—28no—
1142C22⋊C4—216no—
1143C22⋊C4—28no—
1144C22⋊C4—216no—
1145C22⋊C4—48no—
1146C22⋊C4—44no—
1147C22⋊C4—44no—
1148C22⋊C4—48no—
1149C22⋊C4—44no—
1150C22⋊C4—42no—
1151C22⋊C4—44no—
1152C22⋊C4—44no—
1153C22⋊C4—48no—
1154C22⋊C4—48no—
1155C22⋊C4—48no—
1156C22⋊C4—48no—
1157C22⋊C4—48no—
1158C22⋊C4—48no—
1159C22⋊C4C22×D418yes—
1160C22⋊C4C22×D418yes—
1161C22⋊C4C22×D418yes—
1162C22⋊C4C22×D418yes—
1163C22⋊C4C22×D418yes—
1164C42—24no—
1165C42—24no—
1166C42—24no—
1167C42—24no—
1168C42—24no—
1169C42—24no—
1170C42—24no—
1171C42—28no—
1172C42—28no—
1173C42—28no—
1174C42—28no—
1175C42—28no—
1176C42—22no—
1177C42—24no—
1178C42—22no—
1179C42—24no—
1180C42—22no—
1181C42—24no—
1182C42—24no—
1183C42—44no—
1184C42—42no—
1185C42—44no—
1186C42—44no—
1187C42—42no—
1188C42—44no—
1189C42—44no—
1190C42C22×D414yes—
1191C42C22×D414yes—
1192C42C22×D414yes—
1193C42C22×D414yes—
1194C42C22×D418yes—
1195C42C2×#4114yes—
1196C23—21no—
1197C23—22no—
1198C23—21no—
1199C23—22no—
1200C23—24no—
1201C23—22no—
1202C23—24no—
1203C23—22no—
1204C23—22no—
1205C23—24no—
1206C23—22no—
1207C23—24no—
1208C23—22no—
1209C23—24no—
1210C23—24no—
1211C23—28no—
1212C23—24no—
1213C23—28no—
1214C23C23×D414yes—
1215C23C23×D412yes—
1216C23C2611yescharacteristic
1217Q8—28no—
1218Q8—28no—
1219Q8—28no—
1220Q8—416no—
1221Q8—48no—
1222Q8—44no—
1223Q8—48no—
1224Q8—48no—
1225Q8—48no—
1226D4—28no—
1227D4—48no—
1228D4—48no—
1229D4—416no—
1230D4—44no—
1231D4—48no—
1232D4—48no—
1233D4—84no—
1234D4—88no—
1235D4—88no—
1236D4—88no—
1237D4—88no—
1238D4—88no—
1239C2×C4—22no—
1240C2×C4—22no—
1241C2×C4—22no—
1242C2×C4—21no—
1243C2×C4—22no—
1244C2×C4—22no—
1245C2×C4—22no—
1246C2×C4—24no—
1247C2×C4—21no—
1248C2×C4—22no—
1249C2×C4—22no—
1250C2×C4—22no—
1251C2×C4—22no—
1252C2×C4—22no—
1253C2×C4—24no—
1254C2×C4—216no—
1255C2×C4—28no—
1256C2×C4—28no—
1257C2×C4—22no—
1258C2×C4—24no—
1259C2×C4—22no—
1260C2×C4—22no—
1261C2×C4—22no—
1262C2×C4—22no—
1263C2×C4—24no—
1264C2×C4—24no—
1265C2×C4—22no—
1266C2×C4—24no—
1267C2×C4—22no—
1268C2×C4—24no—
1269C2×C4—22no—
1270C2×C4—24no—
1271C2×C4—22no—
1272C2×C4—22no—
1273C2×C4—22no—
1274C2×C4—22no—
1275C2×C4—24no—
1276C2×C4—24no—
1277C2×C4—22no—
1278C2×C4—24no—
1279C2×C4—28no—
1280C2×C4—24no—
1281C2×C4—28no—
1282C2×C4—24no—
1283C2×C4—22no—
1284C2×C4—24no—
1285C2×C4—22no—
1286C2×C4—22no—
1287C2×C4—24no—
1288C2×C4—24no—
1289C2×C4—24no—
1290C2×C4—44no—
1291C2×C4—48no—
1292C2×C4—416no—
1293C2×C4—48no—
1294C2×C4—416no—
1295C2×C4—48no—
1296C2×C4—48no—
1297C2×C4—84no—
1298C2×C4—88no—
1299C2×C4—88no—
1300C2×C4—88no—
1301C2×C4—88no—
1302C2×C4C23×D412yes—
1303C2×C4C23×D412yes—
1304C2×C4C23×D414yes—
1305C2×C4C23×D412yes—
1306C2×C4C23×D414yes—
1307C2×C4C23×D414yes—
1308C2×C4C23×D412yes—
1309C2×C4C23×D412yes—
1310C2×C4C23×D412yes—
1311C2×C4C22×#4114yes—
1312C2×C4C22×#4114yes—
1313C2×C4C22×#4114yes—
1314C2×C4C22×#4112yes—
1315C2×C4#58512yes—
1316C2×C4#58514yes—
1317C22—22no—
1318C22—24no—
1319C22—22no—
1320C22—24no—
1321C22—22no—
1322C22—24no—
1323C22—42no—
1324C22—44no—
1325C22—44no—
1326C22—42no—
1327C22—44no—
1328C22—48no—
1329C22—42no—
1330C22—44no—
1331C22—42no—
1332C22—44no—
1333C22—42no—
1334C22—44no—
1335C22—44no—
1336C22—48no—
1337C22C24×D411yescharacteristic
1338C22C23×#4111yescharacteristic
1339C22C2×#58512yes—
1340C22C2×#58511yescharacteristic
1341C222−1+612yes—
1342C4—24no—
1343C4—22no—
1344C4—24no—
1345C4—22no—
1346C4—22no—
1347C4—24no—
1348C4—24no—
1349C4—22no—
1350C4—24no—
1351C4—24no—
1352C4—42no—
1353C4—44no—
1354C4—42no—
1355C4—44no—
1356C4—44no—
1357C4—42no—
1358C4—42no—
1359C4—42no—
1360C4—42no—
1361C4—44no—
1362C4—42no—
1363C4—44no—
1364C4—42no—
1365C4D4×#4114yes—
1366C4#350014yes—
1367C2—42no—
1368C2—44no—
1369C2—82no—
1370C2—84no—
1371C2C2×D4×#4111yescharacteristic
1372C2C2×#350011yescharacteristic
1373C2#6285911yescharacteristic
1374C2#6296712yes—
1375C2#6300712yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#3517C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C2×#3523C2semidirect
3. #59146C2semidirect
4. #59101C2semidirect
5. #59098C2semidirect
6. #59085C2semidirect
7. #44785C2semidirect
8. #44452C2semidirect
9. #39488C2semidirect
10. #39485C2semidirect
11. #39363C2semidirect
12. #39363C2semidirect
13. #39174C2semidirect
14. #39170C2semidirect
15. #38093C2semidirect
16. #38085C2semidirect
17. #36583C2semidirect
18. #36560C2semidirect
19. #36419C2semidirect
20. #36303C2semidirect
21. #35678C2semidirect
22. #35622C2semidirect
23. #35332C2semidirect
24. #35298C2semidirect
25. #34979C2semidirect
26. #34955C2semidirect
27. #34276C2semidirect
28. #34151C2semidirect
29. C4×#536C2semidirect
671. C4⋊Q8#41semidirect

Maximal subgroups

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

subgroupindex
C2×#35172
C2×#35232
#591462
#591012
#590982
#590852
#447852
#444522
#394882
#394852
#393632
#391742
#391702
#380932
#380852
#365832
#365602
#364192
#363032
#356782
#356222
#353322
#352982
#349792
#349552
#342762
#341512
C4×#5362