Finite Group Databasebeta

← #7654348

Subgroups — #7654348

Order 512.

6826 conjugacy classes of subgroups.

The subgroup lattice has 1386 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3507C211yesmaximal, characteristic, complemented
2C2×#3480C211yesmaximal, characteristic, complemented
3#42796C214yesmaximal, complemented
4#40527C218yesmaximal, complemented
5#39883C214yesmaximal, complemented
6#39747C211yesmaximal, characteristic, complemented
7#39744C211yesmaximal, characteristic, complemented
8#39741C212yesmaximal, complemented
9#39739C212yesmaximal, complemented
10#39173C211yesmaximal, characteristic, complemented
11#39169C211yesmaximal, characteristic, complemented
12#39164C212yesmaximal, complemented
13#39162C212yesmaximal, complemented
14#38379C218yesmaximal, complemented
15#37618C211yesmaximal, characteristic, complemented
16#37544C212yesmaximal, complemented
17#36597C211yesmaximal, characteristic, complemented
18#36594C211yesmaximal, characteristic, complemented
19#36534C211yesmaximal, characteristic, complemented
20#36496C211yesmaximal, characteristic, complemented
21#36228C214yesmaximal, complemented
22#35752C214yesmaximal, complemented
23#35298C211yesmaximal, characteristic, complemented
24#35211C212yesmaximal, complemented
25#35200C211yesmaximal, characteristic, complemented
26#35191C212yesmaximal, complemented
27#34977C211yesmaximal, characteristic, complemented
28#34910C212yesmaximal, complemented
29#34128C211yesmaximal, characteristic, complemented
30#3507—216no—
31#3480—216no—
32C2×#559C2212yes—
33C2×#559C2212yes—
34C2×#559C2211yescharacteristic
35C2×#557C2211yescharacteristic
36C2×#557C2212yes—
37C2×#556C2211yescharacteristic
38C2×#556C2214yes—
39C2×#556C2211yescharacteristic
40C2×#556C2212yes—
41C2×#556C2211yescharacteristic
42C2×#554C2211yescharacteristic
43C2×#554C2211yescharacteristic
44C2×#553C2214yes—
45C2×#553C2212yes—
46C2×#552C2212yes—
47C2×#552C2212yes—
48C2×#550C2211yescharacteristic
49C2×#548C2212yes—
50C2×#539C2214yes—
51C2×#536C2212yes—
52C2×#533C2211yescharacteristic
53C2×#532C2211yescharacteristic
54C2×#532C2212yes—
55C2×#532C2211yescharacteristic
56C2×#529C2212yes—
57C2×#529C2212yes—
58C2×#529C2212yes—
59C2×#529C2214yes—
60C2×#520C2212yes—
61C2×C4×#41C2212yes—
62C2×C4×#41C2211yescharacteristic
63C2×C4×#41C2212yes—
64C22×C4×Q8C2211yescharacteristic
65#2868C2211yescharacteristic
66#2862C2211yescharacteristic
67#2861C2212yes—
68#2861C2212yes—
69#2858C2211yescharacteristic
70#2858C2212yes—
71#2858C2212yes—
72#2858C2211yescharacteristic
73#2852C2218yes—
74#2851C2214yes—
75#2815C2214yes—
76#2813C2218yes—
77#2733C2218yes—
78#2731C2218yes—
79#2730C2218yes—
80#2729C2218yes—
81#2725C2218yes—
82#2721C2218yes—
83#2714C2218yes—
84#2707C2218yes—
85#2705C2218yes—
86#2690C2218yes—
87#2682C2218yes—
88#2676C2218yes—
89#2661C2218yes—
90#2658C2212yes—
91#2657C2212yes—
92#2657C2212yes—
93#2642C2212yes—
94#2641C2212yes—
95#2640C2212yes—
96#2638C2214yes—
97#2636C2218yes—
98#2635C2218yes—
99#2631C2214yes—
100#2630C2218yes—
101#2620C2214yes—
102#2615C2214yes—
103#2610C2214yes—
104#2609C2218yes—
105#2603C2218yes—
106#2602C2218yes—
107#2601C2218yes—
108#2600C2218yes—
109#2599C2214yes—
110#2598C2218yes—
111#2567C2211yescharacteristic
112#2567C2211yescharacteristic
113#2566C2212yes—
114#2566C2214yes—
115#2566C2212yes—
116#2565C2212yes—
117#2565C2212yes—
118#2563C2211yescharacteristic
119#2563C2211yescharacteristic
120#2560C2218yes—
121#2554C2218yes—
122#2548C2211yescharacteristic
123#2548C2212yes—
124#2547C2212yes—
125#2547C2211yescharacteristic
126#2547C2211yescharacteristic
127#2547C2211yescharacteristic
128#2546C2212yes—
129#2546C2211yescharacteristic
130#2545C2212yes—
131#2545C2212yes—
132#2545C2212yes—
133#2545C2212yes—
134#2545C2212yes—
135#2545C2212yes—
136#2544C2212yes—
137#2544C2212yes—
138#2544C2212yes—
139#2544C2212yes—
140#2541C2212yes—
141#2541C2211yescharacteristic
142#2541C2211yescharacteristic
143#2541C2211yescharacteristic
144#2538C2214yes—
145#2536C2214yes—
146#2535C2214yes—
147#2512C2218yes—
148#2500C2214yes—
149#2500C2211yescharacteristic
150#2500C2211yescharacteristic
151#2499C2212yes—
152#2485C2214yes—
153#2475C2218yes—
154#2471C2218yes—
155#2469C2218yes—
156#2467C2218yes—
157#2461C2218yes—
158#2460C2218yes—
159#2458C2218yes—
160#2456C2218yes—
161#2456C2218yes—
162#2442C2214yes—
163#2441C2214yes—
164#2432C2212yes—
165#2432C2212yes—
166#2432C2212yes—
167#2431C2212yes—
168#2431C2211yescharacteristic
169#2431C2212yes—
170#2431C2211yescharacteristic
171#2426C2214yes—
172#2426C2214yes—
173#2423C2214yes—
174#2421C2214yes—
175#2416C2214yes—
176#2414C2214yes—
177#2414C2214yes—
178#2414C2218yes—
179#2407C2214yes—
180#2407C2214yes—
181#2392C2218yes—
182#2388C2214yes—
183#2363C2214yes—
184#2361C2214yes—
185#2356C2212yes—
186#2356C2214yes—
187#2354C2214yes—
188#2352C2214yes—
189#2351C2212yes—
190#2344C2214yes—
191#2344C2212yes—
192Q8×C22⋊C4C2212yes—
193#2328C2212yes—
194#2327C2212yes—
195#2327C2212yes—
196#2326C2212yes—
197#2326C2212yes—
198#2326C2212yes—
199#2326C2214yes—
200#2324C2218yes—
201C4×C4⋊Q8C2212yes—
202C4×#127C2211yescharacteristic
203C4×#127C2212yes—
204C4×#127C2211yescharacteristic
205C4×#124C2211yescharacteristic
206C4×#124C2212yes—
207C4×#124C2211yescharacteristic
208C4×#124C2212yes—
209C4×#121C2214yes—
210#2295C2211yescharacteristic
211#2295C2211yescharacteristic
212#2295C2212yes—
213#2295C2212yes—
214#2290C2218yes—
215#2283C2211yescharacteristic
216#2283C2212yes—
217C42×Q8C2211yescharacteristic
218C42×Q8C2211yescharacteristic
219C4×#117C2212yes—
220C4×#117C2211yescharacteristic
221C22×#41C2312yes—
222C22×#41C2312yes—
223C22×#41C2312yes—
224C22×#41C2311yescharacteristic
225C23×Q8C2311yescharacteristic
226#559—28no—
227#559—216no—
228#559—216no—
229#557—28no—
230#557—216no—
231#556—28no—
232#556—216no—
233#556—28no—
234#556—28no—
235#556—232no—
236#554—28no—
237#554—28no—
238#553—216no—
239#553—232no—
240#552—216no—
241#552—216no—
242#550—28no—
243#548—216no—
244#539—232no—
245#536—216no—
246#533—28no—
247#532—216no—
248#532—28no—
249#532—28no—
250C2×C4⋊Q8C2311yescharacteristic
251C2×C4⋊Q8C2311yescharacteristic
252C2×C4⋊Q8C2311yescharacteristic
253C2×C4⋊Q8C2311yescharacteristic
254C2×C4⋊Q8C2312yes—
255C2×C4⋊Q8C2314yes—
256C2×C4⋊Q8C2312yes—
257C2×C4⋊Q8C2312yes—
258C2×C4⋊Q8C2312yes—
259C2×#127C2311yescharacteristic
260C2×#127C2312yes—
261C2×#127C2311yescharacteristic
262C2×#127C2311yescharacteristic
263C2×#127C2312yes—
264C2×#127C2311yescharacteristic
265C2×#127C2312yes—
266#529—216no—
267#529—232no—
268#529—216no—
269#529—216no—
270C2×#126C2314yes—
271C2×#126C2314yes—
272C2×#126C2314yes—
273C2×#126C2314yes—
274C2×#126C2314yes—
275C2×#126C2314yes—
276C2×#126C2314yes—
277C2×#125C2312yes—
278C2×#125C2312yes—
279C2×#125C2312yes—
280C2×#125C2314yes—
281C2×#125C2312yes—
282C2×#125C2314yes—
283C2×#125C2314yes—
284C2×#124C2312yes—
285C2×#124C2312yes—
286C2×#124C2312yes—
287C2×#124C2312yes—
288C2×#124C2312yes—
289C2×#124C2312yes—
290C2×#124C2312yes—
291C2×#124C2314yes—
292C2×#124C2314yes—
293C2×#124C2314yes—
294C2×#124C2312yes—
295C2×#124C2312yes—
296C2×#124C2312yes—
297C2×#124C2311yescharacteristic
298C2×#124C2312yes—
299C2×#124C2312yes—
300C2×#124C2311yescharacteristic
301C2×#123C2314yes—
302C2×#123C2314yes—
303C2×#123C2314yes—
304C2×#123C2314yes—
305C2×#123C2314yes—
306C2×#123C2314yes—
307C2×#123C2314yes—
308C2×C22⋊Q8C2314yes—
309C2×C22⋊Q8C2312yes—
310C2×C22⋊Q8C2312yes—
311C2×C22⋊Q8C2312yes—
312C2×C22⋊Q8C2312yes—
313C2×C22⋊Q8C2314yes—
314C2×C22⋊Q8C2312yes—
315C2×C22⋊Q8C2314yes—
316C2×C22⋊Q8C2312yes—
317C2×C22⋊Q8C2312yes—
318C2×#121C2312yes—
319C2×#121C2312yes—
320C2×#121C2314yes—
321C2×#121C2314yes—
322C2×#121C2312yes—
323C2×#121C2312yes—
324C2×#121C2311yescharacteristic
325C2×#121C2311yescharacteristic
326C2×#121C2314yes—
327C2×#121C2318yes—
328C2×#121C2314yes—
329C2×#121C2314yes—
330C2×#121C2314yes—
331#520—216no—
332C4×#41—216no—
333C4×#41—216no—
334C4×#41—28no—
335C2×C4×Q8D4116yescomplemented
336C2×C4×Q8C2312yes—
337C2×C4×Q8C2312yes—
338C2×C4×Q8C2312yes—
339C2×C4×Q8C2311yescharacteristic
340C2×C4×Q8C2311yescharacteristic
341C2×C4×Q8C2312yes—
342C2×C4×Q8C2312yes—
343C2×C4×Q8C2312yes—
344C2×C4×Q8C2312yes—
345C2×C4×Q8C2314yes—
346C2×C4×Q8C2312yes—
347C2×C4×Q8C2312yes—
348C2×C4×Q8C2311yescharacteristic
349C2×C4×Q8C2311yescharacteristic
350C2×C4×Q8C2312yes—
351C2×C4×Q8C2311yescharacteristic
352C2×C4×Q8C2311yescharacteristic
353C2×C4×Q8C2312yes—
354C2×C4×D4C2311yescharacteristic
355C2×C4×D4C2312yes—
356C2×C4×D4C2312yes—
357C2×C4×D4C2311yescharacteristic
358C2×C4×D4C2311yescharacteristic
359C2×C4×D4C2311yescharacteristic
360C2×C4×D4C2312yes—
361C2×C4×D4C2312yes—
362C2×C4×D4C2314yes—
363C2×C4×D4C2312yes—
364C2×C4×D4C2312yes—
365C2×C4×D4C2314yes—
366C2×C4×D4C2314yes—
367C2×C4×D4C2314yes—
368C2×C4×D4C2314yes—
369C2×C4×D4C2312yes—
370C2×C4×D4C2314yes—
371C2×C4×D4C2312yes—
372C2×C4×D4C2312yes—
373C2×C4×D4C2314yes—
374C2×C4×D4C2314yes—
375C2×C4×D4C2312yes—
376C2×C4×D4C2314yes—
377C2×C4×D4C2314yes—
378C2×C4×D4C2318yes—
379C2×#117C2314yes—
380C2×#117C2314yes—
381C2×#117C2312yes—
382C2×#117C2314yes—
383C2×#117C2312yes—
384C2×#117C2312yes—
385C2×#117C2311yescharacteristic
386C2×#117C2314yes—
387C2×#117C2312yes—
388C2×#117C2312yes—
389C2×#117C2312yes—
390C2×#117C2314yes—
391C22×C4⋊C4C2312yes—
392C22×C4⋊C4C2312yes—
393C22×C4⋊C4C2311yescharacteristic
394C22×C4⋊C4C2312yes—
395C22×C42C2312yes—
396C22×C42C2314yes—
397C22×C42C2312yes—
398C22×C42C2311yescharacteristic
399#400C2318yes—
400#400C2318yes—
401#399C2318yes—
402#399C2318yes—
403#398C2318yes—
404#398C2318yes—
405#398C2314yes—
406#398C2318yes—
407#397C2314yes—
408#397C2314yes—
409#397C2318yes—
410#397C2318yes—
411#397C2314yes—
412#397C2318yes—
413#396C2318yes—
414#396C2318yes—
415#396C2318yes—
416#396C2318yes—
417#396C2318yes—
418#396C2318yes—
419#396C2318yes—
420#396C2318yes—
421#395C2314yes—
422#395C2314yes—
423#394C2318yes—
424#394C2318yes—
425#394C2314yes—
426#394C2318yes—
427#394C2318yes—
428#394C2314yes—
429#394C2318yes—
430#394C2318yes—
431#394C2318yes—
432#394C2314yes—
433#394C2318yes—
434#394C2318yes—
435#394C2318yes—
436#393C2314yes—
437#393C2314yes—
438#393C2318yes—
439#392C2318yes—
440#392C2318yes—
441#392C2318yes—
442#392C2318yes—
443#392C2314yes—
444#392C2318yes—
445#392C2314yes—
446#392C2314yes—
447#392C2314yes—
448#392C2318yes—
449#392C2314yes—
450#392C2318yes—
451#391C2314yes—
452#391C2312yes—
453#391C2312yes—
454#391C2312yes—
455#391C2312yes—
456#391C2312yes—
457#391C2312yes—
458#391C2311yescharacteristic
459#391C2311yescharacteristic
460#391C2312yes—
461#391C2312yes—
462#391C2312yes—
463#391C2314yes—
464#391C2314yes—
465#390C2314yes—
466#390C2311yescharacteristic
467#390C2311yescharacteristic
468#390C2311yescharacteristic
469#390C2312yes—
470#390C2311yescharacteristic
471#390C2318yes—
472#390C2314yes—
473#390C2311yescharacteristic
474#390C2312yes—
475#390C2312yes—
476#390C2312yes—
477#390C2314yes—
478#390C2314yes—
479#390C2312yes—
480#390C2318yes—
481#390C2318yes—
482#390C2318yes—
483#390C2311yescharacteristic
484#390C2314yes—
485#390C2318yes—
486#390C2318yes—
487#390C2314yes—
488#389C2318yes—
489#389C2314yes—
490#389C2314yes—
491#389C2318yes—
492#389C2314yes—
493#389C2312yes—
494#389C2312yes—
495#389C2314yes—
496#389C2314yes—
497#388C2318yes—
498#388C2318yes—
499#388C2318yes—
500#388C2318yes—
501#388C2318yes—
502#388C2318yes—
503#388C2318yes—
504#388C2318yes—
505#388C2318yes—
506#388C2314yes—
507#388C2318yes—
508#388C2318yes—
509#388C2318yes—
510#388C2314yes—
511#388C2318yes—
512#388C2318yes—
513#388C2318yes—
514#388C2314yes—
515#388C2314yes—
516#387C2318yes—
517#387C2318yes—
518#387C2318yes—
519#387C2318yes—
520#387C2318yes—
521#387C2318yes—
522#387C2318yes—
523#387C2314yes—
524#387C2314yes—
525#387C2314yes—
526#387C2314yes—
527#387C2314yes—
528#387C2314yes—
529#386C2318yes—
530#386C2314yes—
531#386C2318yes—
532#386C2318yes—
533#386C2318yes—
534#386C2318yes—
535#386C2314yes—
536#386C2318yes—
537#386C2318yes—
538#386C2318yes—
539#385C2318yes—
540#385C2318yes—
541#385C2318yes—
542#385C2318yes—
543#385C2318yes—
544#385C2318yes—
545#385C2318yes—
546#385C2318yes—
547#384C2311yescharacteristic
548#384C2311yescharacteristic
549#384C2312yes—
550#384C2314yes—
551#384C2314yes—
552#383C2314yes—
553#383C2312yes—
554#382C2311yescharacteristic
555#382C2312yes—
556#382C2311yescharacteristic
557#382C2314yes—
558#382C2312yes—
559#382C2314yes—
560#381C2314yes—
561#381C2312yes—
562#380C2314yes—
563#380C2314yes—
564#380C2318yes—
565#380C2314yes—
566#380C2312yes—
567#380C2314yes—
568#380C2314yes—
569#380C2314yes—
570C4×C4⋊C4C2314yes—
571C4×C4⋊C4C2318yes—
572C4×C4⋊C4C2311yescharacteristic
573C4×C4⋊C4C2311yescharacteristic
574C4×C4⋊C4C2312yes—
575C4×C4⋊C4C2312yes—
576C4×C4⋊C4C2312yes—
577C4×C4⋊C4C2312yes—
578C4×C4⋊C4C2312yes—
579C4×C4⋊C4C2311yescharacteristic
580C4×C4⋊C4C2311yescharacteristic
581C4×C4⋊C4C2314yes—
582C4×C4⋊C4C2312yes—
583C4×C4⋊C4C2312yes—
584C4×C4⋊C4C2314yes—
585C4×C22⋊C4C2318yes—
586C4×C22⋊C4C2314yes—
587C4×C22⋊C4C2312yes—
588C4×C22⋊C4C2314yes—
589C4×C22⋊C4C2314yes—
590C4×C22⋊C4C2318yes—
591C4×C22⋊C4C2312yes—
592C4×C22⋊C4C2311yescharacteristic
593C4×C22⋊C4C2311yescharacteristic
594#376C2312yes—
595#376C2312yes—
596#376C2312yes—
597#376C2312yes—
598#376C2314yes—
599C43C2312yes—
600C43C2311yescharacteristic
601C43C2311yescharacteristic
602C43C2312yes—
603C2×#41—28no—
604C2×#41—28no—
605C2×#41—24no—
606C2×#41—28no—
607C2×#41—48no—
608C2×#41—42no—
609C2×#41—44no—
610C2×#41—44no—
611C2×#41—42no—
612C2×#41—48no—
613C22×Q8—44no—
614C22×Q8C2×D418yes—
615C22×Q8C2412yes—
616C22×Q8C2411yescharacteristic
617C22×Q8C2412yes—
618C22×Q8C2411yescharacteristic
619C22×Q8C2411yescharacteristic
620C22×Q8C2412yes—
621C22×Q8C2412yes—
622C22×Q8C2412yes—
623C22×D4C2411yescharacteristic
624C22×D4C2411yescharacteristic
625C22×D4C2412yes—
626C22×D4C2411yescharacteristic
627C22×D4C2412yes—
628C22×D4C2414yes—
629C22×D4C2412yes—
630C22×D4C2412yes—
631C22×D4C2412yes—
632C22×D4C2414yes—
633C22×D4C2412yes—
634C22×D4C2414yes—
635C22×D4C2412yes—
636C22×D4C2412yes—
637C22×D4C2414yes—
638C22×D4C2414yes—
639C22×D4C2418yes—
640C22×D4C2418yes—
641C23×C4C2412yes—
642C23×C4C2412yes—
643C23×C4C2412yes—
644C23×C4C2411yescharacteristic
645C23×C4C2411yescharacteristic
646C23×C4C2414yes—
647C23×C4C2414yes—
648C23×C4C2412yes—
649C23×C4C2414yes—
650C23×C4C2414yes—
651C23×C4C2414yes—
652C23×C4C2412yes—
653C23×C4C2412yes—
654C23×C4C2411yescharacteristic
655C23×C4C2412yes—
656C4⋊Q8—216no—
657C4⋊Q8—24no—
658C4⋊Q8—28no—
659C4⋊Q8—24no—
660C4⋊Q8—24no—
661C4⋊Q8—24no—
662C4⋊Q8—44no—
663C4⋊Q8—44no—
664C4⋊Q8—44no—
665#127—24no—
666#127—28no—
667#127—24no—
668#127—42no—
669#127—44no—
670#127—44no—
671#127—42no—
672#126—216no—
673#126—216no—
674#126—216no—
675#126—216no—
676#126—216no—
677#126—216no—
678#126—216no—
679#125—28no—
680#125—216no—
681#125—216no—
682#125—216no—
683#125—28no—
684#125—28no—
685#125—28no—
686#124—28no—
687#124—216no—
688#124—216no—
689#124—28no—
690#124—28no—
691#124—28no—
692#124—28no—
693#124—28no—
694#124—28no—
695#124—48no—
696#124—42no—
697#124—44no—
698#124—44no—
699#124—44no—
700#124—44no—
701#124—44no—
702#124—42no—
703#123—216no—
704#123—216no—
705#123—216no—
706#123—216no—
707#123—216no—
708#123—216no—
709#123—216no—
710C22⋊Q8—28no—
711C22⋊Q8—216no—
712C22⋊Q8—28no—
713C22⋊Q8—28no—
714C22⋊Q8—28no—
715C22⋊Q8—28no—
716C22⋊Q8—28no—
717C22⋊Q8—28no—
718C22⋊Q8—216no—
719C22⋊Q8—216no—
720#121—24no—
721#121—24no—
722#121—28no—
723#121—28no—
724#121—216no—
725#121—216no—
726#121—28no—
727#121—28no—
728#121—216no—
729#121—48no—
730#121—416no—
731#121—48no—
732#121—48no—
733C4×Q8—28no—
734C4×Q8—216no—
735C4×Q8—28no—
736C4×Q8—24no—
737C4×Q8—24no—
738C4×Q8—28no—
739C4×Q8—28no—
740C4×Q8—28no—
741C4×Q8—28no—
742C4×Q8—28no—
743C4×Q8—44no—
744C4×Q8—44no—
745C4×Q8C2×D418yes—
746C4×Q8C2×D418yes—
747C4×Q8C2×D4116yes—
748C4×Q8C2×D418yes—
749C4×Q8C2×D418yes—
750C4×Q8C2×D4116yes—
751C4×D4—28no—
752C4×D4—216no—
753C4×D4—216no—
754C4×D4—28no—
755C4×D4—216no—
756C4×D4—216no—
757C4×D4—28no—
758C4×D4—216no—
759C4×D4—216no—
760C4×D4—216no—
761C4×D4—28no—
762C4×D4—24no—
763C4×D4—28no—
764C4×D4—28no—
765C4×D4—24no—
766C4×D4—216no—
767C4×D4—28no—
768C4×D4—28no—
769C4×D4—28no—
770C4×D4—28no—
771C4×D4—24no—
772C4×D4—24no—
773C4×D4—416no—
774C4×D4—48no—
775C4×D4—48no—
776#117—24no—
777#117—28no—
778#117—28no—
779#117—216no—
780#117—28no—
781#117—28no—
782#117—216no—
783#117—28no—
784#117—216no—
785#117—216no—
786#117—48no—
787#117—44no—
788C2×C4⋊C4—28no—
789C2×C4⋊C4—28no—
790C2×C4⋊C4C2×D418yes—
791C2×C4⋊C4C2×D4116yes—
792C2×C4⋊C4C2412yes—
793C2×C4⋊C4C2414yes—
794C2×C4⋊C4C2414yes—
795C2×C4⋊C4C2412yes—
796C2×C4⋊C4C2414yes—
797C2×C4⋊C4C2411yescharacteristic
798C2×C4⋊C4C2411yescharacteristic
799C2×C4⋊C4C2412yes—
800C2×C4⋊C4C2414yes—
801C2×C4⋊C4C2412yes—
802C2×C4⋊C4C2414yes—
803C2×C4⋊C4C2414yes—
804C2×C4⋊C4C2412yes—
805C2×C4⋊C4C2412yes—
806C2×C4⋊C4C2414yes—
807C2×C4⋊C4C2414yes—
808C2×C4⋊C4C2414yes—
809C2×C4⋊C4C2412yes—
810C2×C4⋊C4C2411yescharacteristic
811C2×C4⋊C4C2411yescharacteristic
812C2×C4⋊C4C2412yes—
813C2×C4⋊C4C2414yes—
814C2×C4⋊C4C2412yes—
815C2×C4⋊C4C2412yes—
816C2×C4⋊C4C2412yes—
817C2×C4⋊C4C2414yes—
818C2×C4⋊C4C2414yes—
819C2×C4⋊C4C2414yes—
820C2×C4⋊C4C2412yes—
821C2×C4⋊C4C2414yes—
822C2×C4⋊C4C2412yes—
823C2×C4⋊C4C2414yes—
824C2×C4⋊C4C2418yes—
825C2×C4⋊C4C2414yes—
826C2×C4⋊C4C2414yes—
827C2×C4⋊C4C2414yes—
828C2×C4⋊C4C2418yes—
829C2×C4⋊C4C2418yes—
830C2×C4⋊C4C2418yes—
831C2×C4⋊C4C2411yescharacteristic
832C2×C4⋊C4C2411yescharacteristic
833C2×C4⋊C4C2412yes—
834C2×C4⋊C4C2412yes—
835C2×C4⋊C4C2412yes—
836C2×C4⋊C4C2412yes—
837C2×C4⋊C4C2412yes—
838C2×C22⋊C4C2412yes—
839C2×C22⋊C4C2412yes—
840C2×C22⋊C4C2412yes—
841C2×C22⋊C4C2412yes—
842C2×C22⋊C4C2414yes—
843C2×C22⋊C4C2412yes—
844C2×C22⋊C4C2414yes—
845C2×C22⋊C4C2414yes—
846C2×C22⋊C4C2414yes—
847C2×C22⋊C4C2414yes—
848C2×C22⋊C4C2412yes—
849C2×C22⋊C4C2414yes—
850C2×C22⋊C4C2414yes—
851C2×C22⋊C4C2414yes—
852C2×C22⋊C4C2414yes—
853C2×C22⋊C4C2414yes—
854C2×C22⋊C4C2414yes—
855C2×C22⋊C4C2412yes—
856C2×C22⋊C4C2412yes—
857C2×C22⋊C4C2414yes—
858C2×C22⋊C4C2414yes—
859C2×C22⋊C4C2414yes—
860C2×C22⋊C4C2418yes—
861C2×C22⋊C4C2414yes—
862C2×C22⋊C4C2414yes—
863C2×C22⋊C4C2414yes—
864C2×C22⋊C4C2412yes—
865C2×C22⋊C4C2414yes—
866C2×C22⋊C4C2414yes—
867C2×C22⋊C4C2414yes—
868C2×C22⋊C4C2414yes—
869C2×C22⋊C4C2414yes—
870C2×C22⋊C4C2418yes—
871C2×C22⋊C4C2418yes—
872C2×C22⋊C4C2418yes—
873C2×C22⋊C4C2414yes—
874C2×C22⋊C4C2418yes—
875C2×C22⋊C4C2418yes—
876C2×C22⋊C4C2414yes—
877C2×C22⋊C4C2418yes—
878C2×C22⋊C4C2418yes—
879C2×C22⋊C4C2418yes—
880C2×C22⋊C4C2418yes—
881C2×C42—216no—
882C2×C42—28no—
883C2×C42C2×D4116yes—
884C2×C42C2×D418yes—
885C2×C42C2412yes—
886C2×C42C2414yes—
887C2×C42C2414yes—
888C2×C42C2414yes—
889C2×C42C2412yes—
890C2×C42C2414yes—
891C2×C42C2414yes—
892C2×C42C2412yes—
893C2×C42C2412yes—
894C2×C42C2414yes—
895C2×C42C2412yes—
896C2×C42C2412yes—
897C2×C42C2411yescharacteristic
898C2×C42C2412yes—
899C2×C42C2411yescharacteristic
900C2×C42C2412yes—
901C2×C42C2411yescharacteristic
902C2×C42C2411yescharacteristic
903C2×C42C2414yes—
904C2×C42C2412yes—
905C2×C42C2414yes—
906C2×C42C2414yes—
907C2×C42C2412yes—
908C2×C42C2411yescharacteristic
909C2×C42C2412yes—
910C2×C42C2411yescharacteristic
911C2×C42C2411yescharacteristic
912C2×C42C2412yes—
913C2×C42C2412yes—
914C2×C42C2411yescharacteristic
915#95C2412yes—
916#95C2412yes—
917#95C2414yes—
918#95C2414yes—
919#95C2414yes—
920#95C2412yes—
921#95C2412yes—
922#95C2414yes—
923#95C2414yes—
924#95C2414yes—
925#95C2414yes—
926#95C2414yes—
927#95C2414yes—
928#95C2414yes—
929#95C2414yes—
930#95C2418yes—
931#95C2418yes—
932#95C2418yes—
933#95C2414yes—
934#95C2414yes—
935#95C2414yes—
936#95C2414yes—
937#95C2412yes—
938#95C2412yes—
939#95C2418yes—
940#95C2418yes—
941#95C2418yes—
942#95C2418yes—
943#95C2418yes—
944C24C2512yes—
945C24C2512yes—
946C24C2514yes—
947C24C2512yes—
948C24C2511yescharacteristic
949#41—432no—
950#41—416no—
951#41—432no—
952#41—432no—
953C2×Q8—24no—
954C2×Q8—22no—
955C2×Q8—24no—
956C2×Q8—24no—
957C2×Q8—24no—
958C2×Q8—24no—
959C2×Q8—24no—
960C2×Q8—24no—
961C2×Q8—22no—
962C2×Q8—24no—
963C2×Q8—24no—
964C2×Q8—24no—
965C2×Q8—22no—
966C2×Q8—44no—
967C2×Q8—44no—
968C2×Q8—44no—
969C2×Q8—416no—
970C2×Q8C22×D414yes—
971C2×Q8C22×D414yes—
972C2×Q8C22×D418yes—
973C2×D4—24no—
974C2×D4—28no—
975C2×D4—24no—
976C2×D4—24no—
977C2×D4—22no—
978C2×D4—22no—
979C2×D4—28no—
980C2×D4—24no—
981C2×D4—24no—
982C2×D4—22no—
983C2×D4—24no—
984C2×D4—28no—
985C2×D4—24no—
986C2×D4—24no—
987C2×D4—28no—
988C2×D4—22no—
989C2×D4—22no—
990C2×D4—22no—
991C2×D4—22no—
992C2×D4—24no—
993C2×D4—24no—
994C2×D4—22no—
995C2×D4—22no—
996C2×D4—28no—
997C2×D4—44no—
998C2×D4—48no—
999C2×D4—42no—
1000C2×D4—44no—
1001C2×D4—44no—
1002C2×D4—44no—
1003C2×D4—44no—
1004C2×D4—42no—
1005C2×D4—44no—
1006C2×D4—48no—
1007C2×D4—44no—
1008C2×D4—48no—
1009C2×D4—44no—
1010C2×D4—44no—
1011C2×D4—48no—
1012C2×D4—44no—
1013C2×D4—44no—
1014C2×D4—44no—
1015C2×D4—48no—
1016C2×D4—48no—
1017C2×D4—48no—
1018C2×D4—48no—
1019C22×C4—24no—
1020C22×C4—22no—
1021C22×C4—22no—
1022C22×C4—28no—
1023C22×C4—24no—
1024C22×C4—28no—
1025C22×C4—24no—
1026C22×C4—24no—
1027C22×C4—24no—
1028C22×C4—28no—
1029C22×C4—28no—
1030C22×C4—28no—
1031C22×C4—28no—
1032C22×C4—24no—
1033C22×C4—28no—
1034C22×C4—28no—
1035C22×C4—44no—
1036C22×C4—42no—
1037C22×C4—44no—
1038C22×C4—42no—
1039C22×C4—44no—
1040C22×C4—44no—
1041C22×C4—42no—
1042C22×C4—48no—
1043C22×C4—48no—
1044C22×C4—48no—
1045C22×C4—48no—
1046C22×C4—44no—
1047C22×C4C22×D414yes—
1048C22×C4C22×D414yes—
1049C22×C4C22×D418yes—
1050C22×C4C22×D414yes—
1051C22×C4C22×D418yes—
1052C22×C4C2514yes—
1053C22×C4C2512yes—
1054C22×C4C2514yes—
1055C22×C4C2512yes—
1056C22×C4C2512yes—
1057C22×C4C2512yes—
1058C22×C4C2512yes—
1059C22×C4C2512yes—
1060C22×C4C2514yes—
1061C22×C4C2512yes—
1062C22×C4C2512yes—
1063C22×C4C2514yes—
1064C22×C4C2514yes—
1065C22×C4C2511yescharacteristic
1066C22×C4C2511yescharacteristic
1067C22×C4C2512yes—
1068C22×C4C2512yes—
1069C22×C4C2511yescharacteristic
1070C22×C4C2511yescharacteristic
1071C22×C4C2512yes—
1072C22×C4C2512yes—
1073C22×C4C2512yes—
1074C22×C4C2511yescharacteristic
1075C22×C4C2511yescharacteristic
1076C4⋊C4—24no—
1077C4⋊C4—28no—
1078C4⋊C4—28no—
1079C4⋊C4—24no—
1080C4⋊C4—28no—
1081C4⋊C4—22no—
1082C4⋊C4—22no—
1083C4⋊C4—28no—
1084C4⋊C4—24no—
1085C4⋊C4—24no—
1086C4⋊C4—28no—
1087C4⋊C4—28no—
1088C4⋊C4—24no—
1089C4⋊C4—28no—
1090C4⋊C4—28no—
1091C4⋊C4—24no—
1092C4⋊C4—22no—
1093C4⋊C4—22no—
1094C4⋊C4—24no—
1095C4⋊C4—28no—
1096C4⋊C4—24no—
1097C4⋊C4—28no—
1098C4⋊C4—28no—
1099C4⋊C4—28no—
1100C4⋊C4—24no—
1101C4⋊C4—24no—
1102C4⋊C4—28no—
1103C4⋊C4—24no—
1104C4⋊C4—24no—
1105C4⋊C4—42no—
1106C4⋊C4—44no—
1107C4⋊C4—44no—
1108C4⋊C4—48no—
1109C4⋊C4—44no—
1110C4⋊C4—44no—
1111C4⋊C4—44no—
1112C4⋊C4—48no—
1113C4⋊C4—48no—
1114C4⋊C4—48no—
1115C4⋊C4C22×D414yes—
1116C4⋊C4C22×D414yes—
1117C4⋊C4C22×D418yes—
1118C4⋊C4C22×D418yes—
1119C4⋊C4C22×D418yes—
1120C4⋊C4C22×D418yes—
1121C4⋊C4C22×D418yes—
1122C22⋊C4—24no—
1123C22⋊C4—28no—
1124C22⋊C4—24no—
1125C22⋊C4—24no—
1126C22⋊C4—28no—
1127C22⋊C4—24no—
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—24no—
1138C22⋊C4—24no—
1139C22⋊C4—28no—
1140C22⋊C4—28no—
1141C22⋊C4—28no—
1142C22⋊C4—28no—
1143C22⋊C4—28no—
1144C22⋊C4—24no—
1145C22⋊C4—28no—
1146C22⋊C4—216no—
1147C22⋊C4—42no—
1148C22⋊C4—44no—
1149C22⋊C4—44no—
1150C22⋊C4—44no—
1151C22⋊C4—44no—
1152C22⋊C4—44no—
1153C22⋊C4—48no—
1154C22⋊C4—44no—
1155C22⋊C4—48no—
1156C22⋊C4—48no—
1157C22⋊C4—48no—
1158C22⋊C4—44no—
1159C22⋊C4—48no—
1160C22⋊C4—48no—
1161C22⋊C4—48no—
1162C22⋊C4—48no—
1163C22⋊C4—44no—
1164C22⋊C4—48no—
1165C42—24no—
1166C42—28no—
1167C42—24no—
1168C42—28no—
1169C42—24no—
1170C42—28no—
1171C42—28no—
1172C42—28no—
1173C42—28no—
1174C42—24no—
1175C42—24no—
1176C42—24no—
1177C42—22no—
1178C42—22no—
1179C42—24no—
1180C42—24no—
1181C42—22no—
1182C42—22no—
1183C42—44no—
1184C42—42no—
1185C42—44no—
1186C42—44no—
1187C42C22×D418yes—
1188C42C22×D414yes—
1189C42C22×D418yes—
1190C42C22×D414yes—
1191C42C22×D414yes—
1192C42C22×D418yes—
1193C42C22×D418yes—
1194C42C22×D414yes—
1195C23—22no—
1196C23—22no—
1197C23—21no—
1198C23—21no—
1199C23—22no—
1200C23—22no—
1201C23—22no—
1202C23—24no—
1203C23—28no—
1204C23—24no—
1205C23—22no—
1206C23—22no—
1207C23—22no—
1208C23—24no—
1209C23—24no—
1210C23—24no—
1211C23—28no—
1212C23—24no—
1213C23—22no—
1214C23—24no—
1215C23—24no—
1216C23—24no—
1217C23—22no—
1218C23—22no—
1219C23C23×D412yes—
1220C23C2611yescharacteristic
1221Q8—28no—
1222Q8—28no—
1223Q8—48no—
1224Q8—48no—
1225Q8—48no—
1226Q8—44no—
1227Q8—48no—
1228Q8—84no—
1229D4—48no—
1230D4—416no—
1231D4—48no—
1232D4—416no—
1233D4—48no—
1234D4—48no—
1235D4—48no—
1236D4—44no—
1237D4—44no—
1238D4—44no—
1239D4—48no—
1240D4—88no—
1241D4—84no—
1242D4—88no—
1243D4—84no—
1244D4—88no—
1245D4—816no—
1246D4—168no—
1247C2×C4—22no—
1248C2×C4—24no—
1249C2×C4—22no—
1250C2×C4—22no—
1251C2×C4—24no—
1252C2×C4—22no—
1253C2×C4—24no—
1254C2×C4—21no—
1255C2×C4—21no—
1256C2×C4—22no—
1257C2×C4—24no—
1258C2×C4—28no—
1259C2×C4—28no—
1260C2×C4—22no—
1261C2×C4—22no—
1262C2×C4—24no—
1263C2×C4—22no—
1264C2×C4—24no—
1265C2×C4—22no—
1266C2×C4—22no—
1267C2×C4—24no—
1268C2×C4—22no—
1269C2×C4—22no—
1270C2×C4—22no—
1271C2×C4—22no—
1272C2×C4—22no—
1273C2×C4—24no—
1274C2×C4—22no—
1275C2×C4—24no—
1276C2×C4—24no—
1277C2×C4—22no—
1278C2×C4—22no—
1279C2×C4—22no—
1280C2×C4—24no—
1281C2×C4—24no—
1282C2×C4—24no—
1283C2×C4—28no—
1284C2×C4—24no—
1285C2×C4—24no—
1286C2×C4—22no—
1287C2×C4—24no—
1288C2×C4—24no—
1289C2×C4—24no—
1290C2×C4—24no—
1291C2×C4—24no—
1292C2×C4—24no—
1293C2×C4—22no—
1294C2×C4—48no—
1295C2×C4—44no—
1296C2×C4—48no—
1297C2×C4—48no—
1298C2×C4—416no—
1299C2×C4—416no—
1300C2×C4—48no—
1301C2×C4—48no—
1302C2×C4—48no—
1303C2×C4—88no—
1304C2×C4—88no—
1305C2×C4—84no—
1306C2×C4—88no—
1307C2×C4C23×D414yes—
1308C2×C4C23×D412yes—
1309C2×C4C23×D412yes—
1310C2×C4C23×D412yes—
1311C2×C4C23×D414yes—
1312C2×C4C23×D414yes—
1313C2×C4C23×D414yes—
1314C2×C4C23×D412yes—
1315C2×C4C23×D412yes—
1316C2×C4C23×D412yes—
1317C2×C4#58514yes—
1318C2×C4#58514yes—
1319C2×C4#58512yes—
1320C2×C4#58512yes—
1321C22—22no—
1322C22—22no—
1323C22—22no—
1324C22—42no—
1325C22—42no—
1326C22—44no—
1327C22—44no—
1328C22—44no—
1329C22—48no—
1330C22—44no—
1331C22—48no—
1332C22—44no—
1333C22—44no—
1334C22—42no—
1335C22—44no—
1336C22—42no—
1337C22—42no—
1338C22—42no—
1339C22—42no—
1340C22—44no—
1341C22—42no—
1342C22—44no—
1343C22—42no—
1344C22—42no—
1345C22—42no—
1346C22C24×D411yescharacteristic
1347C22C2×#58511yescharacteristic
1348C22C2×#58512yes—
1349C22C2×#58512yes—
1350C22C2×#58511yescharacteristic
1351C4—24no—
1352C4—22no—
1353C4—24no—
1354C4—24no—
1355C4—22no—
1356C4—22no—
1357C4—22no—
1358C4—24no—
1359C4—24no—
1360C4—42no—
1361C4—44no—
1362C4—42no—
1363C4—42no—
1364C4—44no—
1365C4—42no—
1366C4—44no—
1367C4—44no—
1368C4—42no—
1369C4—44no—
1370C4—42no—
1371C4—42no—
1372C4—42no—
1373C4#344914yes—
1374C4#348714yes—
1375C2—42no—
1376C2—82no—
1377C2—82no—
1378C2—82no—
1379C2—84no—
1380C2C2×#344911yescharacteristic
1381C2C2×#348711yescharacteristic
1382C2#6281211yescharacteristic
1383C2#6302912yes—
1384C2#6303112yes—
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. C2×#3507C2semidirect
2. C2×#3480C2semidirect
3. #42796C2semidirect
4. #40527C2semidirect
5. #39883C2semidirect
6. #39747C2semidirect
7. #39744C2semidirect
8. #39741C2semidirect
9. #39739C2semidirect
10. #39173C2semidirect
11. #39169C2semidirect
12. #39164C2semidirect
13. #39162C2semidirect
14. #38379C2semidirect
15. #37618C2semidirect
16. #37544C2semidirect
17. #36597C2semidirect
18. #36594C2semidirect
19. #36534C2semidirect
20. #36496C2semidirect
21. #36228C2semidirect
22. #35752C2semidirect
23. #35298C2semidirect
24. #35211C2semidirect
25. #35200C2semidirect
26. #35191C2semidirect
27. #34977C2semidirect
28. #34910C2semidirect
29. #34128C2semidirect
335. C2×C4×Q8D4semidirect

Maximal subgroups

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

subgroupindex
C2×#35072
C2×#34802
#427962
#405272
#398832
#397472
#397442
#397412
#397392
#391732
#391692
#391642
#391622
#383792
#376182
#375442
#365972
#365942
#365342
#364962
#362282
#357522
#352982
#352112
#352002
#351912
#349772
#349102
#341282