Finite Group Databasebeta

← #7657345

Subgroups — #7657345

Order 512.

6820 conjugacy classes of subgroups.

The subgroup lattice has 1380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3522C211yesmaximal, characteristic, complemented
2C2×#3507C211yesmaximal, characteristic, complemented
3#42798C214yesmaximal, complemented
4#42796C214yesmaximal, complemented
5#41943C218yesmaximal, complemented
6#40497C218yesmaximal, complemented
7#39747C211yesmaximal, characteristic, complemented
8#39739C212yesmaximal, complemented
9#39617C211yesmaximal, characteristic, complemented
10#39613C212yesmaximal, complemented
11#39172C211yesmaximal, characteristic, complemented
12#39169C211yesmaximal, characteristic, complemented
13#39164C212yesmaximal, complemented
14#39161C212yesmaximal, complemented
15#37639C211yesmaximal, characteristic, complemented
16#37633C211yesmaximal, characteristic, complemented
17#37616C212yesmaximal, complemented
18#37542C212yesmaximal, complemented
19#36597C211yesmaximal, characteristic, complemented
20#36559C211yesmaximal, characteristic, complemented
21#36534C211yesmaximal, characteristic, complemented
22#36496C211yesmaximal, characteristic, complemented
23#35772C214yesmaximal, complemented
24#35682C214yesmaximal, complemented
25#35343C212yesmaximal, complemented
26#35298C211yesmaximal, characteristic, complemented
27#34624C211yesmaximal, characteristic, complemented
28#34624C212yesmaximal, complemented
29Q8×#117C211yesmaximal, characteristic, complemented
30#3522—216no—
31#3507—216no—
32C2×#559C2212yes—
33C2×#559C2212yes—
34C2×#559C2211yescharacteristic
35C2×Q82C2211yescharacteristic
36C2×#557C2212yes—
37C2×#556C2211yescharacteristic
38C2×#556C2211yescharacteristic
39C2×#556C2214yes—
40C2×#554C2211yescharacteristic
41C2×#554C2211yescharacteristic
42C2×#554C2211yescharacteristic
43C2×#554C2212yes—
44C2×#552C2212yes—
45C2×#552C2212yes—
46C2×#550C2211yescharacteristic
47C2×#548C2212yes—
48C2×#547C2214yes—
49C2×#547C2212yes—
50C2×#542C2212yes—
51C2×#542C2214yes—
52C2×#539C2214yes—
53C2×#536C2212yes—
54C2×#533C2211yescharacteristic
55C2×#532C2211yescharacteristic
56C2×#532C2211yescharacteristic
57C2×#532C2212yes—
58C2×#529C2211yescharacteristic
59C2×#529C2212yes—
60C2×#529C2212yes—
61C2×#529C2212yes—
62C2×#520C2212yes—
63C2×#520C2212yes—
64C22×C4×Q8C2211yescharacteristic
65#2868C2211yescharacteristic
66#2862C2211yescharacteristic
67#2861C2212yes—
68#2861C2212yes—
69#2859C2212yes—
70#2858C2211yescharacteristic
71#2858C2212yes—
72#2858C2211yescharacteristic
73#2823C2218yes—
74#2819C2214yes—
75#2814C2214yes—
76#2813C2218yes—
77#2733C2218yes—
78#2731C2218yes—
79#2730C2218yes—
80#2729C2218yes—
81#2716C2218yes—
82#2714C2218yes—
83#2707C2218yes—
84#2704C2218yes—
85#2682C2218yes—
86#2681C2218yes—
87#2677C2218yes—
88#2676C2218yes—
89#2662C2218yes—
90#2662C2214yes—
91#2661C2218yes—
92#2661C2214yes—
93#2660C2211yescharacteristic
94#2660C2212yes—
95#2657C2211yescharacteristic
96#2657C2212yes—
97#2641C2212yes—
98#2641C2211yescharacteristic
99#2640C2212yes—
100#2640C2211yescharacteristic
101#2637C2214yes—
102#2636C2218yes—
103#2630C2218yes—
104#2630C2218yes—
105#2629C2214yes—
106#2621C2212yes—
107#2620C2212yes—
108#2620C2211yescharacteristic
109#2620C2212yes—
110#2620C2218yes—
111#2620C2211yescharacteristic
112#2620C2212yes—
113#2619C2212yes—
114#2619C2212yes—
115#2619C2211yescharacteristic
116#2619C2211yescharacteristic
117#2615C2214yes—
118#2615C2214yes—
119#2609C2218yes—
120#2602C2218yes—
121#2602C2218yes—
122#2601C2218yes—
123#2601C2218yes—
124#2568C2212yes—
125#2567C2211yescharacteristic
126#2566C2212yes—
127#2566C2214yes—
128#2566C2212yes—
129#2566C2212yes—
130#2566C2212yes—
131#2565C2212yes—
132#2565C2212yes—
133#2565C2212yes—
134#2563C2211yescharacteristic
135#2563C2211yescharacteristic
136#2563C2211yescharacteristic
137#2563C2212yes—
138#2560C2218yes—
139#2554C2218yes—
140#2548C2212yes—
141#2547C2211yescharacteristic
142#2546C2211yescharacteristic
143#2545C2212yes—
144#2545C2212yes—
145#2545C2212yes—
146#2545C2214yes—
147#2544C2212yes—
148#2544C2212yes—
149#2544C2212yes—
150#2544C2212yes—
151#2542C2212yes—
152#2541C2211yescharacteristic
153#2541C2212yes—
154#2541C2212yes—
155#2541C2211yescharacteristic
156#2538C2214yes—
157#2537C2214yes—
158#2536C2214yes—
159#2500C2214yes—
160#2485C2214yes—
161#2473C2218yes—
162#2465C2218yes—
163#2463C2218yes—
164#2461C2218yes—
165#2460C2218yes—
166#2458C2218yes—
167#2456C2218yes—
168#2456C2218yes—
169#2452C2218yes—
170#2443C2218yes—
171#2440C2214yes—
172#2439C2214yes—
173#2432C2214yes—
174#2426C2214yes—
175#2426C2214yes—
176#2423C2214yes—
177#2421C2214yes—
178#2416C2214yes—
179#2414C2214yes—
180#2407C2214yes—
181#2407C2214yes—
182#2407C2218yes—
183#2392C2214yes—
184#2392C2218yes—
185#2388C2214yes—
186#2388C2218yes—
187#2363C2214yes—
188#2361C2214yes—
189#2355C2212yes—
190#2355C2214yes—
191#2352C2214yes—
192Q8×C4⋊C4C2212yes—
193D4×C4⋊C4C2214yes—
194#2345C2214yes—
195#2345C2212yes—
196Q8×C22⋊C4C2212yes—
197#2328C2212yes—
198#2327C2212yes—
199#2326C2212yes—
200#2326C2212yes—
201#2326C2212yes—
202#2326C2212yes—
203C4×#127C2211yescharacteristic
204C4×#127C2212yes—
205C4×#127C2211yescharacteristic
206C4×#127C2212yes—
207C4×#124C2211yescharacteristic
208C4×#124C2212yes—
209C4×#124C2212yes—
210C4×#124C2211yescharacteristic
211#2295C2211yescharacteristic
212#2295C2212yes—
213#2295C2211yescharacteristic
214#2295C2212yes—
215#2285C2211yescharacteristic
216#2285C2212yes—
217C42×Q8C2211yescharacteristic
218C42×Q8C2211yescharacteristic
219C4×#117C2212yes—
220C4×#117C2211yescharacteristic
221C22×#41C2312yes—
222C22×#41C2312yes—
223C22×#41C2312yes—
224C22×#41C2314yes—
225C23×Q8C2311yescharacteristic
226#559—216no—
227#559—28no—
228#559—216no—
229Q82—28no—
230#557—216no—
231#556—28no—
232#556—28no—
233#556—232no—
234#554—28no—
235#554—28no—
236#554—28no—
237#554—216no—
238#552—216no—
239#552—216no—
240#550—28no—
241#548—216no—
242#547—216no—
243#547—232no—
244#542—216no—
245#542—232no—
246#539—232no—
247#536—216no—
248#533—28no—
249#532—28no—
250#532—216no—
251#532—28no—
252C2×C4⋊Q8C2311yescharacteristic
253C2×C4⋊Q8C2311yescharacteristic
254C2×C4⋊Q8C2311yescharacteristic
255C2×C4⋊Q8C2312yes—
256C2×C4⋊Q8C2311yescharacteristic
257C2×C4⋊Q8C2314yes—
258C2×C4⋊Q8C2314yes—
259C2×C4⋊Q8C2312yes—
260C2×C4⋊Q8C2312yes—
261C2×C4⋊Q8C2314yes—
262C2×#127C2311yescharacteristic
263C2×#127C2311yescharacteristic
264C2×#127C2312yes—
265C2×#127C2311yescharacteristic
266C2×#127C2311yescharacteristic
267C2×#127C2312yes—
268C2×#127C2312yes—
269#529—216no—
270#529—216no—
271#529—216no—
272#529—28no—
273C2×#126C2314yes—
274C2×#126C2314yes—
275C2×#126C2314yes—
276C2×#126C2314yes—
277C2×#126C2312yes—
278C2×#126C2314yes—
279C2×#125C2311yescharacteristic
280C2×#125C2312yes—
281C2×#125C2312yes—
282C2×#125C2312yes—
283C2×#125C2312yes—
284C2×#125C2314yes—
285C2×#125C2314yes—
286C2×#124C2312yes—
287C2×#124C2312yes—
288C2×#124C2311yescharacteristic
289C2×#124C2312yes—
290C2×#124C2312yes—
291C2×#124C2312yes—
292C2×#124C2314yes—
293C2×#124C2312yes—
294C2×#124C2311yescharacteristic
295C2×#124C2314yes—
296C2×#124C2312yes—
297C2×#124C2314yes—
298C2×#124C2312yes—
299C2×#124C2311yescharacteristic
300C2×#124C2312yes—
301C2×#124C2314yes—
302C2×#123C2314yes—
303C2×#123C2314yes—
304C2×#123C2314yes—
305C2×#123C2312yes—
306C2×#123C2314yes—
307C2×#123C2314yes—
308C2×#123C2314yes—
309C2×#123C2314yes—
310C2×#123C2314yes—
311C2×C22⋊Q8C2314yes—
312C2×C22⋊Q8C2312yes—
313C2×C22⋊Q8C2311yescharacteristic
314C2×C22⋊Q8C2312yes—
315C2×C22⋊Q8C2312yes—
316C2×C22⋊Q8C2312yes—
317C2×C22⋊Q8C2314yes—
318C2×C22⋊Q8C2312yes—
319C2×C22⋊Q8C2312yes—
320C2×C22⋊Q8C2314yes—
321C2×C22⋊Q8C2314yes—
322C2×C22⋊Q8C2314yes—
323C2×C22⋊Q8C2314yes—
324C2×C22⋊Q8C2312yes—
325C2×C22⋊Q8C2318yes—
326C2×#121C2312yes—
327C2×#121C2312yes—
328C2×#121C2311yescharacteristic
329C2×#121C2311yescharacteristic
330C2×#121C2312yes—
331C2×#121C2311yescharacteristic
332C2×#121C2314yes—
333C2×#121C2312yes—
334C2×#121C2314yes—
335C2×#121C2314yes—
336C2×#121C2314yes—
337C2×#121C2318yes—
338C2×#121C2318yes—
339#520—216no—
340#520—216no—
341C2×C4×Q8D4116yescomplemented
342C2×C4×Q8C2312yes—
343C2×C4×Q8C2312yes—
344C2×C4×Q8C2312yes—
345C2×C4×Q8C2311yescharacteristic
346C2×C4×Q8C2312yes—
347C2×C4×Q8C2312yes—
348C2×C4×Q8C2312yes—
349C2×C4×Q8C2314yes—
350C2×C4×Q8C2312yes—
351C2×C4×Q8C2312yes—
352C2×C4×Q8C2311yescharacteristic
353C2×C4×Q8C2311yescharacteristic
354C2×C4×Q8C2312yes—
355C2×C4×Q8C2311yescharacteristic
356C2×C4×Q8C2311yescharacteristic
357C2×C4×Q8C2312yes—
358C2×C4×D4C2311yescharacteristic
359C2×C4×D4C2312yes—
360C2×C4×D4C2311yescharacteristic
361C2×C4×D4C2311yescharacteristic
362C2×C4×D4C2312yes—
363C2×C4×D4C2312yes—
364C2×C4×D4C2312yes—
365C2×C4×D4C2312yes—
366C2×C4×D4C2312yes—
367C2×C4×D4C2312yes—
368C2×C4×D4C2314yes—
369C2×C4×D4C2314yes—
370C2×C4×D4C2312yes—
371C2×C4×D4C2314yes—
372C2×C4×D4C2314yes—
373C2×C4×D4C2312yes—
374C2×C4×D4C2312yes—
375C2×C4×D4C2314yes—
376C2×C4×D4C2314yes—
377C2×C4×D4C2314yes—
378C2×C4×D4C2314yes—
379C2×C4×D4C2318yes—
380C2×C4×D4C2318yes—
381C2×#117C2314yes—
382C2×#117C2314yes—
383C2×#117C2312yes—
384C2×#117C2314yes—
385C2×#117C2311yescharacteristic
386C2×#117C2312yes—
387C2×#117C2312yes—
388C2×#117C2312yes—
389C2×#117C2312yes—
390C2×#117C2311yescharacteristic
391C22×C4⋊C4C2312yes—
392C22×C4⋊C4C2312yes—
393C22×C4⋊C4C2312yes—
394C22×C4⋊C4C2314yes—
395C22×C4⋊C4C2311yescharacteristic
396C22×C4⋊C4C2312yes—
397C22×C42C2312yes—
398C22×C42C2311yescharacteristic
399#400C2318yes—
400#399C2318yes—
401#398C2318yes—
402#398C2318yes—
403#398C2318yes—
404#398C2318yes—
405#398C2314yes—
406#398C2318yes—
407#398C2314yes—
408#397C2314yes—
409#397C2318yes—
410#397C2318yes—
411#397C2314yes—
412#396C2318yes—
413#396C2318yes—
414#396C2318yes—
415#396C2318yes—
416#396C2318yes—
417#396C2318yes—
418#396C2314yes—
419#396C2318yes—
420#396C2318yes—
421#396C2314yes—
422#396C2318yes—
423#396C2318yes—
424#395C2314yes—
425#395C2318yes—
426#395C2314yes—
427#394C2318yes—
428#394C2318yes—
429#394C2318yes—
430#394C2318yes—
431#394C2318yes—
432#394C2314yes—
433#394C2318yes—
434#394C2314yes—
435#394C2314yes—
436#394C2314yes—
437#394C2318yes—
438#394C2318yes—
439#394C2318yes—
440#394C2318yes—
441#394C2318yes—
442#394C2314yes—
443#394C2318yes—
444#394C2314yes—
445#393C2314yes—
446#393C2314yes—
447#393C2318yes—
448#393C2314yes—
449#393C2318yes—
450#393C2314yes—
451#392C2314yes—
452#392C2318yes—
453#392C2314yes—
454#392C2318yes—
455#392C2318yes—
456#392C2314yes—
457#392C2314yes—
458#392C2318yes—
459#392C2318yes—
460#392C2314yes—
461#392C2318yes—
462#392C2314yes—
463#391C2314yes—
464#391C2312yes—
465#391C2311yescharacteristic
466#391C2312yes—
467#391C2312yes—
468#391C2312yes—
469#391C2318yes—
470#391C2312yes—
471#391C2311yescharacteristic
472#391C2312yes—
473#391C2312yes—
474#391C2314yes—
475#391C2314yes—
476#390C2314yes—
477#390C2311yescharacteristic
478#390C2312yes—
479#390C2312yes—
480#390C2311yescharacteristic
481#390C2311yescharacteristic
482#390C2312yes—
483#390C2311yescharacteristic
484#390C2311yescharacteristic
485#390C2318yes—
486#390C2318yes—
487#390C2314yes—
488#390C2312yes—
489#390C2312yes—
490#390C2312yes—
491#390C2312yes—
492#390C2314yes—
493#390C2314yes—
494#390C2318yes—
495#390C2318yes—
496#390C2314yes—
497#390C2311yescharacteristic
498#390C2318yes—
499#389C2314yes—
500#389C2312yes—
501#389C2312yes—
502#389C2314yes—
503#389C2314yes—
504#389C2318yes—
505#389C2318yes—
506#389C2314yes—
507#388C2318yes—
508#388C2318yes—
509#388C2318yes—
510#388C2318yes—
511#388C2318yes—
512#388C2318yes—
513#388C2318yes—
514#388C2318yes—
515#388C2318yes—
516#388C2318yes—
517#388C2318yes—
518#388C2318yes—
519#388C2314yes—
520#388C2318yes—
521#388C2314yes—
522#387C2318yes—
523#387C2318yes—
524#387C2318yes—
525#387C2318yes—
526#387C2318yes—
527#387C2314yes—
528#387C2314yes—
529#387C2314yes—
530#387C2314yes—
531#387C2314yes—
532#387C2314yes—
533#386C2318yes—
534#386C2318yes—
535#386C2318yes—
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#384C2312yes—
549#384C2311yescharacteristic
550#384C2312yes—
551#384C2312yes—
552#384C2314yes—
553#384C2314yes—
554#384C2312yes—
555#382C2312yes—
556#382C2312yes—
557#382C2312yes—
558#382C2312yes—
559#382C2311yescharacteristic
560#382C2314yes—
561#382C2314yes—
562#382C2311yescharacteristic
563#380C2314yes—
564#380C2314yes—
565#380C2314yes—
566#380C2318yes—
567#380C2312yes—
568#380C2314yes—
569#380C2312yes—
570#380C2314yes—
571#380C2314yes—
572C4×C4⋊C4C2314yes—
573C4×C4⋊C4C2311yescharacteristic
574C4×C4⋊C4C2312yes—
575C4×C4⋊C4C2311yescharacteristic
576C4×C4⋊C4C2312yes—
577C4×C4⋊C4C2312yes—
578C4×C4⋊C4C2312yes—
579C4×C4⋊C4C2312yes—
580C4×C4⋊C4C2312yes—
581C4×C4⋊C4C2312yes—
582C4×C4⋊C4C2312yes—
583C4×C4⋊C4C2314yes—
584C4×C4⋊C4C2314yes—
585C4×C4⋊C4C2314yes—
586C4×C4⋊C4C2312yes—
587C4×C22⋊C4C2318yes—
588C4×C22⋊C4C2314yes—
589C4×C22⋊C4C2312yes—
590C4×C22⋊C4C2314yes—
591C4×C22⋊C4C2312yes—
592C4×C22⋊C4C2314yes—
593C4×C22⋊C4C2314yes—
594C4×C22⋊C4C2318yes—
595#376C2311yescharacteristic
596#376C2311yescharacteristic
597#376C2312yes—
598#376C2312yes—
599C43C2312yes—
600C43C2311yescharacteristic
601C43C2311yescharacteristic
602C43C2312yes—
603C2×#41—28no—
604C2×#41—28no—
605C2×#41—216no—
606C2×#41—28no—
607C2×#41—48no—
608C2×#41—48no—
609C2×#41—88no—
610C2×#41—84no—
611C22×Q8—44no—
612C22×Q8C2×D418yes—
613C22×Q8C2411yescharacteristic
614C22×Q8C2412yes—
615C22×Q8C2411yescharacteristic
616C22×Q8C2411yescharacteristic
617C22×Q8C2412yes—
618C22×Q8C2412yes—
619C22×Q8C2414yes—
620C22×Q8C2412yes—
621C22×Q8C2412yes—
622C22×D4C2411yescharacteristic
623C22×D4C2411yescharacteristic
624C22×D4C2412yes—
625C22×D4C2411yescharacteristic
626C22×D4C2412yes—
627C22×D4C2414yes—
628C22×D4C2412yes—
629C22×D4C2412yes—
630C22×D4C2414yes—
631C22×D4C2412yes—
632C22×D4C2412yes—
633C22×D4C2414yes—
634C22×D4C2412yes—
635C22×D4C2414yes—
636C22×D4C2412yes—
637C22×D4C2414yes—
638C22×D4C2418yes—
639C22×D4C2418yes—
640C23×C4C2412yes—
641C23×C4C2412yes—
642C23×C4C2412yes—
643C23×C4C2411yescharacteristic
644C23×C4C2411yescharacteristic
645C23×C4C2414yes—
646C23×C4C2414yes—
647C23×C4C2414yes—
648C23×C4C2414yes—
649C23×C4C2414yes—
650C23×C4C2414yes—
651C23×C4C2412yes—
652C23×C4C2411yescharacteristic
653C23×C4C2412yes—
654C4⋊Q8—216no—
655C4⋊Q8—28no—
656C4⋊Q8—216no—
657C4⋊Q8—24no—
658C4⋊Q8—28no—
659C4⋊Q8—24no—
660C4⋊Q8—24no—
661C4⋊Q8—24no—
662C4⋊Q8—44no—
663C4⋊Q8—84no—
664#127—24no—
665#127—28no—
666#127—24no—
667#127—24no—
668#127—42no—
669#127—44no—
670#127—44no—
671#126—216no—
672#126—216no—
673#126—216no—
674#126—28no—
675#126—216no—
676#126—216no—
677#125—216no—
678#125—216no—
679#125—28no—
680#125—24no—
681#125—28no—
682#125—28no—
683#125—28no—
684#124—216no—
685#124—28no—
686#124—216no—
687#124—28no—
688#124—28no—
689#124—28no—
690#124—24no—
691#124—216no—
692#124—28no—
693#124—28no—
694#124—24no—
695#124—28no—
696#124—44no—
697#124—44no—
698#124—42no—
699#124—84no—
700#123—216no—
701#123—216no—
702#123—216no—
703#123—28no—
704#123—216no—
705#123—216no—
706#123—216no—
707#123—216no—
708#123—216no—
709C22⋊Q8—28no—
710C22⋊Q8—28no—
711C22⋊Q8—28no—
712C22⋊Q8—28no—
713C22⋊Q8—28no—
714C22⋊Q8—216no—
715C22⋊Q8—24no—
716C22⋊Q8—28no—
717C22⋊Q8—28no—
718C22⋊Q8—216no—
719C22⋊Q8—216no—
720C22⋊Q8—216no—
721C22⋊Q8—216no—
722C22⋊Q8—216no—
723C22⋊Q8—88no—
724#121—24no—
725#121—24no—
726#121—28no—
727#121—24no—
728#121—28no—
729#121—28no—
730#121—216no—
731#121—28no—
732#121—216no—
733#121—48no—
734#121—48no—
735#121—88no—
736#121—88no—
737C4×Q8—28no—
738C4×Q8—216no—
739C4×Q8—28no—
740C4×Q8—28no—
741C4×Q8—24no—
742C4×Q8—28no—
743C4×Q8—28no—
744C4×Q8—28no—
745C4×Q8—44no—
746C4×Q8—44no—
747C4×Q8C2×D418yes—
748C4×Q8C2×D418yes—
749C4×Q8C2×D4116yes—
750C4×Q8C2×D418yes—
751C4×Q8C2×D418yes—
752C4×Q8C2×D4116yes—
753C4×D4—216no—
754C4×D4—216no—
755C4×D4—28no—
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—28no—
766C4×D4—28no—
767C4×D4—24no—
768C4×D4—24no—
769C4×D4—28no—
770C4×D4—28no—
771C4×D4—28no—
772C4×D4—48no—
773C4×D4—48no—
774C4×D4—88no—
775C4×D4—88no—
776#117—28no—
777#117—28no—
778#117—28no—
779#117—216no—
780#117—28no—
781#117—216no—
782#117—216no—
783#117—24no—
784#117—42no—
785#117—44no—
786C2×C4⋊C4—28no—
787C2×C4⋊C4—216no—
788C2×C4⋊C4—28no—
789C2×C4⋊C4—28no—
790C2×C4⋊C4C2×D418yes—
791C2×C4⋊C4C2×D4116yes—
792C2×C4⋊C4C2414yes—
793C2×C4⋊C4C2412yes—
794C2×C4⋊C4C2412yes—
795C2×C4⋊C4C2412yes—
796C2×C4⋊C4C2414yes—
797C2×C4⋊C4C2414yes—
798C2×C4⋊C4C2414yes—
799C2×C4⋊C4C2412yes—
800C2×C4⋊C4C2412yes—
801C2×C4⋊C4C2414yes—
802C2×C4⋊C4C2414yes—
803C2×C4⋊C4C2414yes—
804C2×C4⋊C4C2412yes—
805C2×C4⋊C4C2411yescharacteristic
806C2×C4⋊C4C2411yescharacteristic
807C2×C4⋊C4C2412yes—
808C2×C4⋊C4C2412yes—
809C2×C4⋊C4C2411yescharacteristic
810C2×C4⋊C4C2411yescharacteristic
811C2×C4⋊C4C2412yes—
812C2×C4⋊C4C2412yes—
813C2×C4⋊C4C2414yes—
814C2×C4⋊C4C2412yes—
815C2×C4⋊C4C2412yes—
816C2×C4⋊C4C2414yes—
817C2×C4⋊C4C2414yes—
818C2×C4⋊C4C2414yes—
819C2×C4⋊C4C2412yes—
820C2×C4⋊C4C2414yes—
821C2×C4⋊C4C2412yes—
822C2×C4⋊C4C2414yes—
823C2×C4⋊C4C2412yes—
824C2×C4⋊C4C2418yes—
825C2×C4⋊C4C2418yes—
826C2×C4⋊C4C2414yes—
827C2×C4⋊C4C2414yes—
828C2×C4⋊C4C2414yes—
829C2×C4⋊C4C2414yes—
830C2×C4⋊C4C2414yes—
831C2×C4⋊C4C2414yes—
832C2×C4⋊C4C2414yes—
833C2×C4⋊C4C2418yes—
834C2×C4⋊C4C2418yes—
835C2×C4⋊C4C2411yescharacteristic
836C2×C4⋊C4C2411yescharacteristic
837C2×C4⋊C4C2412yes—
838C2×C4⋊C4C2412yes—
839C2×C4⋊C4C2412yes—
840C2×C4⋊C4C2412yes—
841C2×C4⋊C4C2412yes—
842C2×C22⋊C4C2412yes—
843C2×C22⋊C4C2412yes—
844C2×C22⋊C4C2414yes—
845C2×C22⋊C4C2412yes—
846C2×C22⋊C4C2414yes—
847C2×C22⋊C4C2414yes—
848C2×C22⋊C4C2412yes—
849C2×C22⋊C4C2414yes—
850C2×C22⋊C4C2414yes—
851C2×C22⋊C4C2414yes—
852C2×C22⋊C4C2414yes—
853C2×C22⋊C4C2412yes—
854C2×C22⋊C4C2412yes—
855C2×C22⋊C4C2414yes—
856C2×C22⋊C4C2412yes—
857C2×C22⋊C4C2414yes—
858C2×C22⋊C4C2414yes—
859C2×C22⋊C4C2414yes—
860C2×C22⋊C4C2412yes—
861C2×C22⋊C4C2412yes—
862C2×C22⋊C4C2414yes—
863C2×C22⋊C4C2414yes—
864C2×C22⋊C4C2412yes—
865C2×C22⋊C4C2414yes—
866C2×C22⋊C4C2414yes—
867C2×C22⋊C4C2418yes—
868C2×C22⋊C4C2414yes—
869C2×C22⋊C4C2412yes—
870C2×C22⋊C4C2414yes—
871C2×C22⋊C4C2418yes—
872C2×C22⋊C4C2418yes—
873C2×C22⋊C4C2418yes—
874C2×C22⋊C4C2414yes—
875C2×C22⋊C4C2414yes—
876C2×C22⋊C4C2414yes—
877C2×C22⋊C4C2414yes—
878C2×C22⋊C4C2418yes—
879C2×C22⋊C4C2418yes—
880C2×C22⋊C4C2418yes—
881C2×C22⋊C4C2418yes—
882C2×C22⋊C4C2414yes—
883C2×C22⋊C4C2418yes—
884C2×C22⋊C4C2414yes—
885C2×C22⋊C4C2418yes—
886C2×C42C2×D4116yes—
887C2×C42C2×D418yes—
888C2×C42C2414yes—
889C2×C42C2414yes—
890C2×C42C2412yes—
891C2×C42C2414yes—
892C2×C42C2414yes—
893C2×C42C2411yescharacteristic
894C2×C42C2412yes—
895C2×C42C2411yescharacteristic
896C2×C42C2412yes—
897C2×C42C2411yescharacteristic
898C2×C42C2412yes—
899C2×C42C2412yes—
900C2×C42C2414yes—
901C2×C42C2414yes—
902C2×C42C2414yes—
903C2×C42C2414yes—
904C2×C42C2412yes—
905C2×C42C2412yes—
906C2×C42C2412yes—
907C2×C42C2411yescharacteristic
908C2×C42C2412yes—
909C2×C42C2412yes—
910C2×C42C2411yescharacteristic
911C2×C42C2411yescharacteristic
912C2×C42C2412yes—
913C2×C42C2411yescharacteristic
914C2×C42C2411yescharacteristic
915#95C2412yes—
916#95C2412yes—
917#95C2414yes—
918#95C2414yes—
919#95C2414yes—
920#95C2414yes—
921#95C2412yes—
922#95C2412yes—
923#95C2414yes—
924#95C2418yes—
925#95C2414yes—
926#95C2418yes—
927#95C2418yes—
928#95C2414yes—
929#95C2414yes—
930#95C2414yes—
931#95C2414yes—
932#95C2412yes—
933#95C2412yes—
934#95C2414yes—
935#95C2414yes—
936#95C2414yes—
937#95C2418yes—
938#95C2418yes—
939#95C2418yes—
940#95C2418yes—
941#95C2418yes—
942C24C2512yes—
943C24C2512yes—
944C24C2514yes—
945C24C2512yes—
946C24C2511yescharacteristic
947#41—432no—
948#41—432no—
949#41—832no—
950#41—816no—
951C2×Q8—22no—
952C2×Q8—24no—
953C2×Q8—24no—
954C2×Q8—24no—
955C2×Q8—28no—
956C2×Q8—24no—
957C2×Q8—22no—
958C2×Q8—24no—
959C2×Q8—24no—
960C2×Q8—24no—
961C2×Q8—24no—
962C2×Q8—22no—
963C2×Q8—44no—
964C2×Q8—44no—
965C2×Q8—48no—
966C2×Q8—44no—
967C2×Q8—44no—
968C2×Q8—416no—
969C2×Q8C22×D414yes—
970C2×Q8C22×D414yes—
971C2×Q8C22×D418yes—
972C2×D4—24no—
973C2×D4—24no—
974C2×D4—24no—
975C2×D4—28no—
976C2×D4—22no—
977C2×D4—22no—
978C2×D4—24no—
979C2×D4—22no—
980C2×D4—28no—
981C2×D4—24no—
982C2×D4—24no—
983C2×D4—24no—
984C2×D4—28no—
985C2×D4—24no—
986C2×D4—22no—
987C2×D4—24no—
988C2×D4—28no—
989C2×D4—22no—
990C2×D4—22no—
991C2×D4—28no—
992C2×D4—22no—
993C2×D4—22no—
994C2×D4—24no—
995C2×D4—22no—
996C2×D4—44no—
997C2×D4—44no—
998C2×D4—44no—
999C2×D4—48no—
1000C2×D4—44no—
1001C2×D4—44no—
1002C2×D4—44no—
1003C2×D4—48no—
1004C2×D4—44no—
1005C2×D4—48no—
1006C2×D4—48no—
1007C2×D4—44no—
1008C2×D4—44no—
1009C2×D4—48no—
1010C2×D4—44no—
1011C2×D4—44no—
1012C2×D4—48no—
1013C2×D4—48no—
1014C2×D4—48no—
1015C2×D4—48no—
1016C22×C4—22no—
1017C22×C4—22no—
1018C22×C4—24no—
1019C22×C4—28no—
1020C22×C4—24no—
1021C22×C4—24no—
1022C22×C4—24no—
1023C22×C4—28no—
1024C22×C4—28no—
1025C22×C4—28no—
1026C22×C4—28no—
1027C22×C4—28no—
1028C22×C4—28no—
1029C22×C4—28no—
1030C22×C4—28no—
1031C22×C4—44no—
1032C22×C4—48no—
1033C22×C4—44no—
1034C22×C4—42no—
1035C22×C4—48no—
1036C22×C4—48no—
1037C22×C4—48no—
1038C22×C4—48no—
1039C22×C4—48no—
1040C22×C4C22×D414yes—
1041C22×C4C22×D414yes—
1042C22×C4C22×D418yes—
1043C22×C4C22×D414yes—
1044C22×C4C22×D418yes—
1045C22×C4C2512yes—
1046C22×C4C2512yes—
1047C22×C4C2514yes—
1048C22×C4C2514yes—
1049C22×C4C2512yes—
1050C22×C4C2512yes—
1051C22×C4C2514yes—
1052C22×C4C2512yes—
1053C22×C4C2512yes—
1054C22×C4C2512yes—
1055C22×C4C2514yes—
1056C22×C4C2512yes—
1057C22×C4C2514yes—
1058C22×C4C2511yescharacteristic
1059C22×C4C2512yes—
1060C22×C4C2512yes—
1061C22×C4C2511yescharacteristic
1062C22×C4C2512yes—
1063C22×C4C2511yescharacteristic
1064C22×C4C2511yescharacteristic
1065C22×C4C2512yes—
1066C22×C4C2512yes—
1067C22×C4C2511yescharacteristic
1068C22×C4C2511yescharacteristic
1069C4⋊C4—28no—
1070C4⋊C4—24no—
1071C4⋊C4—24no—
1072C4⋊C4—28no—
1073C4⋊C4—24no—
1074C4⋊C4—28no—
1075C4⋊C4—28no—
1076C4⋊C4—24no—
1077C4⋊C4—24no—
1078C4⋊C4—28no—
1079C4⋊C4—28no—
1080C4⋊C4—28no—
1081C4⋊C4—22no—
1082C4⋊C4—22no—
1083C4⋊C4—24no—
1084C4⋊C4—24no—
1085C4⋊C4—22no—
1086C4⋊C4—22no—
1087C4⋊C4—24no—
1088C4⋊C4—24no—
1089C4⋊C4—28no—
1090C4⋊C4—28no—
1091C4⋊C4—28no—
1092C4⋊C4—28no—
1093C4⋊C4—24no—
1094C4⋊C4—28no—
1095C4⋊C4—24no—
1096C4⋊C4—24no—
1097C4⋊C4—24no—
1098C4⋊C4—24no—
1099C4⋊C4—42no—
1100C4⋊C4—44no—
1101C4⋊C4—44no—
1102C4⋊C4—44no—
1103C4⋊C4—48no—
1104C4⋊C4—48no—
1105C4⋊C4—44no—
1106C4⋊C4—44no—
1107C4⋊C4—44no—
1108C4⋊C4—44no—
1109C4⋊C4—44no—
1110C4⋊C4—48no—
1111C4⋊C4—48no—
1112C4⋊C4C22×D414yes—
1113C4⋊C4C22×D414yes—
1114C4⋊C4C22×D418yes—
1115C4⋊C4C22×D418yes—
1116C4⋊C4C22×D418yes—
1117C4⋊C4C22×D418yes—
1118C4⋊C4C22×D418yes—
1119C22⋊C4—28no—
1120C22⋊C4—24no—
1121C22⋊C4—24no—
1122C22⋊C4—24no—
1123C22⋊C4—28no—
1124C22⋊C4—24no—
1125C22⋊C4—28no—
1126C22⋊C4—24no—
1127C22⋊C4—28no—
1128C22⋊C4—28no—
1129C22⋊C4—28no—
1130C22⋊C4—28no—
1131C22⋊C4—28no—
1132C22⋊C4—24no—
1133C22⋊C4—28no—
1134C22⋊C4—28no—
1135C22⋊C4—28no—
1136C22⋊C4—24no—
1137C22⋊C4—24no—
1138C22⋊C4—28no—
1139C22⋊C4—28no—
1140C22⋊C4—24no—
1141C22⋊C4—28no—
1142C22⋊C4—24no—
1143C22⋊C4—28no—
1144C22⋊C4—216no—
1145C22⋊C4—42no—
1146C22⋊C4—44no—
1147C22⋊C4—44no—
1148C22⋊C4—44no—
1149C22⋊C4—44no—
1150C22⋊C4—44no—
1151C22⋊C4—44no—
1152C22⋊C4—48no—
1153C22⋊C4—48no—
1154C22⋊C4—48no—
1155C22⋊C4—48no—
1156C22⋊C4—48no—
1157C22⋊C4—48no—
1158C22⋊C4—48no—
1159C22⋊C4—44no—
1160C22⋊C4—48no—
1161C22⋊C4—48no—
1162C22⋊C4—44no—
1163C42—28no—
1164C42—28no—
1165C42—28no—
1166C42—24no—
1167C42—28no—
1168C42—22no—
1169C42—22no—
1170C42—24no—
1171C42—22no—
1172C42—24no—
1173C42—24no—
1174C42—24no—
1175C42—44no—
1176C42—44no—
1177C42—44no—
1178C42—44no—
1179C42—42no—
1180C42—42no—
1181C42C22×D418yes—
1182C42C22×D414yes—
1183C42C22×D418yes—
1184C42C22×D418yes—
1185C42C22×D414yes—
1186C42C22×D414yes—
1187C42C22×D418yes—
1188C42C22×D414yes—
1189C422−1+414yes—
1190C23—21no—
1191C23—21no—
1192C23—22no—
1193C23—22no—
1194C23—22no—
1195C23—22no—
1196C23—24no—
1197C23—22no—
1198C23—22no—
1199C23—24no—
1200C23—22no—
1201C23—22no—
1202C23—22no—
1203C23—24no—
1204C23—28no—
1205C23—22no—
1206C23—24no—
1207C23—24no—
1208C23—24no—
1209C23—22no—
1210C23—24no—
1211C23—24no—
1212C23—24no—
1213C23—28no—
1214C23C23×D412yes—
1215C23C2611yescharacteristic
1216Q8—28no—
1217Q8—28no—
1218Q8—48no—
1219Q8—48no—
1220Q8—44no—
1221Q8—48no—
1222Q8—84no—
1223Q8—88no—
1224Q8—84no—
1225D4—416no—
1226D4—48no—
1227D4—416no—
1228D4—48no—
1229D4—48no—
1230D4—48no—
1231D4—416no—
1232D4—48no—
1233D4—44no—
1234D4—44no—
1235D4—48no—
1236D4—44no—
1237D4—84no—
1238D4—88no—
1239D4—84no—
1240D4—816no—
1241D4—88no—
1242D4—168no—
1243C2×C4—21no—
1244C2×C4—22no—
1245C2×C4—24no—
1246C2×C4—21no—
1247C2×C4—22no—
1248C2×C4—24no—
1249C2×C4—22no—
1250C2×C4—24no—
1251C2×C4—22no—
1252C2×C4—22no—
1253C2×C4—24no—
1254C2×C4—28no—
1255C2×C4—28no—
1256C2×C4—22no—
1257C2×C4—24no—
1258C2×C4—22no—
1259C2×C4—22no—
1260C2×C4—24no—
1261C2×C4—24no—
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—24no—
1272C2×C4—24no—
1273C2×C4—22no—
1274C2×C4—24no—
1275C2×C4—24no—
1276C2×C4—24no—
1277C2×C4—24no—
1278C2×C4—24no—
1279C2×C4—22no—
1280C2×C4—24no—
1281C2×C4—22no—
1282C2×C4—22no—
1283C2×C4—24no—
1284C2×C4—22no—
1285C2×C4—24no—
1286C2×C4—28no—
1287C2×C4—24no—
1288C2×C4—28no—
1289C2×C4—48no—
1290C2×C4—48no—
1291C2×C4—44no—
1292C2×C4—416no—
1293C2×C4—48no—
1294C2×C4—48no—
1295C2×C4—48no—
1296C2×C4—88no—
1297C2×C4—88no—
1298C2×C4—88no—
1299C2×C4—88no—
1300C2×C4—88no—
1301C2×C4C23×D412yes—
1302C2×C4C23×D414yes—
1303C2×C4C23×D414yes—
1304C2×C4C23×D414yes—
1305C2×C4C23×D412yes—
1306C2×C4C23×D414yes—
1307C2×C4C23×D412yes—
1308C2×C4C23×D412yes—
1309C2×C4C23×D412yes—
1310C2×C4C23×D412yes—
1311C2×C4C2×2−1+414yes—
1312C2×C4C2×2−1+412yes—
1313C2×C4#58514yes—
1314C2×C4#58512yes—
1315C22—22no—
1316C22—22no—
1317C22—22no—
1318C22—42no—
1319C22—42no—
1320C22—42no—
1321C22—42no—
1322C22—44no—
1323C22—42no—
1324C22—42no—
1325C22—44no—
1326C22—42no—
1327C22—42no—
1328C22—44no—
1329C22—44no—
1330C22—48no—
1331C22—44no—
1332C22—44no—
1333C22—44no—
1334C22—48no—
1335C22—44no—
1336C22—44no—
1337C22—42no—
1338C22—42no—
1339C22—42no—
1340C22C24×D411yescharacteristic
1341C22C22×2−1+411yescharacteristic
1342C22C2×#58511yescharacteristic
1343C22C2×#58512yes—
1344C22H(7,𝔽2)12yes—
1345C4—22no—
1346C4—24no—
1347C4—22no—
1348C4—24no—
1349C4—22no—
1350C4—24no—
1351C4—22no—
1352C4—24no—
1353C4—24no—
1354C4—42no—
1355C4—44no—
1356C4—42no—
1357C4—44no—
1358C4—44no—
1359C4—42no—
1360C4—42no—
1361C4—42no—
1362C4—44no—
1363C4—44no—
1364C4—42no—
1365C4—42no—
1366C4—42no—
1367C4#344914yes—
1368C4#349714yes—
1369C2—42no—
1370C2—82no—
1371C2—84no—
1372C2—82no—
1373C2—82no—
1374C2C2×#344911yescharacteristic
1375C2C2×#349711yescharacteristic
1376C2#6285211yescharacteristic
1377C2#6292612yes—
1378C2#6293812yes—
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×#3522C2semidirect
2. C2×#3507C2semidirect
3. #42798C2semidirect
4. #42796C2semidirect
5. #41943C2semidirect
6. #40497C2semidirect
7. #39747C2semidirect
8. #39739C2semidirect
9. #39617C2semidirect
10. #39613C2semidirect
11. #39172C2semidirect
12. #39169C2semidirect
13. #39164C2semidirect
14. #39161C2semidirect
15. #37639C2semidirect
16. #37633C2semidirect
17. #37616C2semidirect
18. #37542C2semidirect
19. #36597C2semidirect
20. #36559C2semidirect
21. #36534C2semidirect
22. #36496C2semidirect
23. #35772C2semidirect
24. #35682C2semidirect
25. #35343C2semidirect
26. #35298C2semidirect
27. #34624C2semidirect
28. #34624C2semidirect
29. Q8×#117C2semidirect
341. C2×C4×Q8D4semidirect

Maximal subgroups

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

subgroupindex
C2×#35222
C2×#35072
#427982
#427962
#419432
#404972
#397472
#397392
#396172
#396132
#391722
#391692
#391642
#391612
#376392
#376332
#376162
#375422
#365972
#365592
#365342
#364962
#357722
#356822
#353432
#352982
#346242
Q8×#1172