Finite Group Databasebeta

← #7657438

Subgroups — #7657438

Order 512.

6812 conjugacy classes of subgroups.

The subgroup lattice has 1364 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#42799C214yesmaximal, complemented
4#42797C214yesmaximal, complemented
5#41942C218yesmaximal, complemented
6#40499C218yesmaximal, complemented
7#39745C211yesmaximal, characteristic, complemented
8#39741C212yesmaximal, complemented
9#39619C211yesmaximal, characteristic, complemented
10#39611C212yesmaximal, complemented
11#39174C211yesmaximal, characteristic, complemented
12#39168C211yesmaximal, characteristic, complemented
13#39163C212yesmaximal, complemented
14#39161C212yesmaximal, complemented
15#37640C211yesmaximal, characteristic, complemented
16#37616C212yesmaximal, complemented
17#37616C211yesmaximal, characteristic, complemented
18#37542C212yesmaximal, complemented
19#36595C211yesmaximal, characteristic, complemented
20#36562C211yesmaximal, characteristic, complemented
21#36538C211yesmaximal, characteristic, complemented
22#36496C211yesmaximal, characteristic, complemented
23#35787C214yesmaximal, complemented
24#35715C214yesmaximal, complemented
25#35343C212yesmaximal, complemented
26#35293C211yesmaximal, characteristic, complemented
27#34631C211yesmaximal, characteristic, complemented
28#34624C212yesmaximal, complemented
29Q8×#117C211yesmaximal, characteristic, complemented
30#3522—216no—
31#3507—216no—
32C2×#559C2211yescharacteristic
33C2×#559C2211yescharacteristic
34C2×#559C2212yes—
35C2×#559C2211yescharacteristic
36C2×Q82C2211yescharacteristic
37C2×#557C2211yescharacteristic
38C2×#557C2211yescharacteristic
39C2×#556C2212yes—
40C2×#556C2212yes—
41C2×#556C2212yes—
42C2×#554C2212yes—
43C2×#554C2211yescharacteristic
44C2×#554C2212yes—
45C2×#552C2214yes—
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×#529C2212yes—
59C2×#529C2212yes—
60C2×#529C2212yes—
61C2×#529C2211yescharacteristic
62C2×#520C2212yes—
63C2×#520C2212yes—
64C22×C4×Q8C2211yescharacteristic
65#2867C2211yescharacteristic
66#2862C2211yescharacteristic
67#2861C2212yes—
68#2861C2212yes—
69#2859C2212yes—
70#2858C2211yescharacteristic
71#2858C2211yescharacteristic
72#2858C2212yes—
73#2823C2218yes—
74#2820C2214yes—
75#2813C2218yes—
76#2813C2214yes—
77#2732C2218yes—
78#2730C2218yes—
79#2730C2218yes—
80#2728C2218yes—
81#2713C2218yes—
82#2711C2218yes—
83#2705C2218yes—
84#2702C2218yes—
85#2683C2218yes—
86#2681C2218yes—
87#2674C2218yes—
88#2673C2218yes—
89#2664C2214yes—
90#2663C2214yes—
91#2662C2218yes—
92#2661C2218yes—
93#2660C2212yes—
94#2660C2211yescharacteristic
95#2658C2211yescharacteristic
96#2657C2212yes—
97#2642C2211yescharacteristic
98#2641C2212yes—
99#2640C2212yes—
100#2640C2211yescharacteristic
101#2636C2218yes—
102#2636C2214yes—
103#2630C2218yes—
104#2630C2218yes—
105#2624C2214yes—
106#2621C2211yescharacteristic
107#2621C2211yescharacteristic
108#2620C2212yes—
109#2620C2212yes—
110#2620C2212yes—
111#2620C2214yes—
112#2620C2218yes—
113#2620C2211yescharacteristic
114#2620C2211yescharacteristic
115#2619C2212yes—
116#2619C2212yes—
117#2619C2212yes—
118#2616C2214yes—
119#2609C2218yes—
120#2602C2218yes—
121#2602C2218yes—
122#2601C2218yes—
123#2601C2218yes—
124#2568C2211yescharacteristic
125#2568C2212yes—
126#2567C2211yescharacteristic
127#2567C2211yescharacteristic
128#2566C2212yes—
129#2566C2212yes—
130#2566C2212yes—
131#2566C2212yes—
132#2566C2212yes—
133#2565C2212yes—
134#2565C2212yes—
135#2558C2218yes—
136#2556C2218yes—
137#2548C2211yescharacteristic
138#2548C2211yescharacteristic
139#2548C2212yes—
140#2548C2211yescharacteristic
141#2548C2214yes—
142#2547C2212yes—
143#2545C2212yes—
144#2545C2214yes—
145#2545C2212yes—
146#2544C2214yes—
147#2544C2212yes—
148#2544C2212yes—
149#2544C2212yes—
150#2544C2212yes—
151#2544C2214yes—
152#2544C2212yes—
153#2542C2212yes—
154#2542C2211yescharacteristic
155#2542C2212yes—
156#2541C2211yescharacteristic
157#2541C2212yes—
158#2538C2214yes—
159#2481C2218yes—
160#2477C2218yes—
161#2471C2218yes—
162#2467C2218yes—
163#2463C2218yes—
164#2461C2218yes—
165#2452C2214yes—
166#2451C2214yes—
167#2449C2218yes—
168#2449C2218yes—
169#2448C2214yes—
170#2446C2214yes—
171#2445C2218yes—
172#2443C2218yes—
173#2432C2214yes—
174#2431C2214yes—
175#2431C2214yes—
176#2431C2214yes—
177#2429C2214yes—
178#2428C2214yes—
179#2426C2214yes—
180#2426C2214yes—
181#2407C2214yes—
182#2407C2218yes—
183#2396C2214yes—
184#2395C2214yes—
185#2392C2218yes—
186#2388C2218yes—
187#2367C2214yes—
188#2366C2214yes—
189#2361C2214yes—
190#2360C2214yes—
191#2355C2212yes—
192#2355C2214yes—
193Q8×C4⋊C4C2212yes—
194#2345C2214yes—
195#2345C2212yes—
196Q8×C22⋊C4C2212yes—
197#2328C2212yes—
198#2328C2212yes—
199#2328C2212yes—
200#2327C2212yes—
201#2326C2212yes—
202#2326C2212yes—
203C4×C4⋊Q8C2211yescharacteristic
204C4×C4⋊Q8C2211yescharacteristic
205C4×#127C2212yes—
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—28no—
227#559—28no—
228#559—216no—
229#559—28no—
230Q82—28no—
231#557—28no—
232#557—28no—
233#556—216no—
234#556—216no—
235#556—216no—
236#554—216no—
237#554—216no—
238#554—28no—
239#552—232no—
240#550—28no—
241#548—216no—
242#547—216no—
243#547—232no—
244#542—232no—
245#542—216no—
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⋊Q8C2311yescharacteristic
258C2×C4⋊Q8C2314yes—
259C2×C4⋊Q8C2312yes—
260C2×C4⋊Q8C2312yes—
261C2×C4⋊Q8C2312yes—
262C2×C4⋊Q8C2311yescharacteristic
263C2×#127C2312yes—
264C2×#127C2311yescharacteristic
265C2×#127C2311yescharacteristic
266C2×#127C2312yes—
267C2×#127C2312yes—
268C2×#127C2312yes—
269C2×#127C2314yes—
270C2×#127C2314yes—
271#529—216no—
272#529—216no—
273#529—216no—
274#529—28no—
275C2×#126C2314yes—
276C2×#126C2314yes—
277C2×#126C2314yes—
278C2×#126C2312yes—
279C2×#126C2314yes—
280C2×#126C2314yes—
281C2×#125C2312yes—
282C2×#125C2312yes—
283C2×#125C2312yes—
284C2×#125C2312yes—
285C2×#125C2311yescharacteristic
286C2×#125C2314yes—
287C2×#125C2314yes—
288C2×#124C2312yes—
289C2×#124C2312yes—
290C2×#124C2312yes—
291C2×#124C2314yes—
292C2×#124C2312yes—
293C2×#124C2311yescharacteristic
294C2×#124C2312yes—
295C2×#124C2311yescharacteristic
296C2×#124C2312yes—
297C2×#124C2312yes—
298C2×#124C2314yes—
299C2×#124C2312yes—
300C2×#124C2312yes—
301C2×#124C2312yes—
302C2×#124C2314yes—
303C2×#124C2312yes—
304C2×#124C2311yescharacteristic
305C2×#124C2314yes—
306C2×#123C2314yes—
307C2×#123C2314yes—
308C2×#123C2314yes—
309C2×#123C2312yes—
310C2×#123C2314yes—
311C2×#123C2314yes—
312C2×#123C2314yes—
313C2×#123C2314yes—
314C2×#123C2314yes—
315C2×C22⋊Q8C2312yes—
316C2×C22⋊Q8C2311yescharacteristic
317C2×C22⋊Q8C2311yescharacteristic
318C2×C22⋊Q8C2311yescharacteristic
319C2×C22⋊Q8C2314yes—
320C2×C22⋊Q8C2314yes—
321C2×C22⋊Q8C2314yes—
322C2×C22⋊Q8C2312yes—
323C2×C22⋊Q8C2314yes—
324C2×C22⋊Q8C2314yes—
325C2×C22⋊Q8C2314yes—
326C2×C22⋊Q8C2314yes—
327C2×C22⋊Q8C2314yes—
328C2×C22⋊Q8C2314yes—
329C2×C22⋊Q8C2318yes—
330C2×C22⋊Q8C2318yes—
331C2×#121C2312yes—
332C2×#121C2312yes—
333C2×#121C2311yescharacteristic
334C2×#121C2312yes—
335C2×#121C2314yes—
336C2×#121C2314yes—
337C2×#121C2312yes—
338C2×#121C2312yes—
339C2×#121C2314yes—
340C2×#121C2318yes—
341#520—216no—
342#520—216no—
343C2×C4×Q8D4116yescomplemented
344C2×C4×Q8C2311yescharacteristic
345C2×C4×Q8C2311yescharacteristic
346C2×C4×Q8C2311yescharacteristic
347C2×C4×Q8C2312yes—
348C2×C4×Q8C2312yes—
349C2×C4×Q8C2312yes—
350C2×C4×Q8C2312yes—
351C2×C4×Q8C2312yes—
352C2×C4×Q8C2312yes—
353C2×C4×Q8C2312yes—
354C2×C4×Q8C2312yes—
355C2×C4×Q8C2312yes—
356C2×C4×Q8C2311yescharacteristic
357C2×C4×Q8C2311yescharacteristic
358C2×C4×Q8C2312yes—
359C2×C4×Q8C2311yescharacteristic
360C2×C4×Q8C2312yes—
361C2×C4×Q8C2311yescharacteristic
362C2×C4×D4C2312yes—
363C2×C4×D4C2312yes—
364C2×C4×D4C2312yes—
365C2×C4×D4C2312yes—
366C2×C4×D4C2312yes—
367C2×C4×D4C2312yes—
368C2×C4×D4C2312yes—
369C2×C4×D4C2314yes—
370C2×C4×D4C2314yes—
371C2×C4×D4C2312yes—
372C2×C4×D4C2312yes—
373C2×C4×D4C2314yes—
374C2×C4×D4C2314yes—
375C2×C4×D4C2312yes—
376C2×C4×D4C2312yes—
377C2×C4×D4C2312yes—
378C2×C4×D4C2312yes—
379C2×C4×D4C2314yes—
380C2×C4×D4C2311yescharacteristic
381C2×C4×D4C2318yes—
382C2×C4×D4C2318yes—
383C2×#117C2314yes—
384C2×#117C2314yes—
385C2×#117C2314yes—
386C2×#117C2311yescharacteristic
387C2×#117C2312yes—
388C2×#117C2312yes—
389C2×#117C2314yes—
390C2×#117C2311yescharacteristic
391C2×#117C2312yes—
392C22×C4⋊C4C2312yes—
393C22×C4⋊C4C2314yes—
394C22×C4⋊C4C2314yes—
395C22×C4⋊C4C2311yescharacteristic
396C22×C4⋊C4C2312yes—
397C22×C42C2312yes—
398C22×C42C2311yescharacteristic
399#400C2318yes—
400#400C2314yes—
401#400C2314yes—
402#400C2314yes—
403#399C2318yes—
404#399C2318yes—
405#399C2314yes—
406#399C2314yes—
407#399C2314yes—
408#398C2318yes—
409#398C2318yes—
410#398C2314yes—
411#398C2314yes—
412#398C2318yes—
413#398C2314yes—
414#397C2318yes—
415#397C2314yes—
416#397C2314yes—
417#397C2318yes—
418#397C2314yes—
419#396C2318yes—
420#396C2318yes—
421#396C2318yes—
422#396C2318yes—
423#396C2318yes—
424#396C2318yes—
425#396C2318yes—
426#396C2318yes—
427#396C2318yes—
428#396C2318yes—
429#396C2314yes—
430#396C2314yes—
431#395C2314yes—
432#395C2314yes—
433#395C2318yes—
434#395C2314yes—
435#394C2314yes—
436#394C2314yes—
437#394C2318yes—
438#394C2318yes—
439#394C2318yes—
440#394C2318yes—
441#394C2318yes—
442#394C2318yes—
443#394C2318yes—
444#394C2318yes—
445#394C2314yes—
446#394C2314yes—
447#394C2318yes—
448#394C2318yes—
449#394C2318yes—
450#394C2314yes—
451#394C2318yes—
452#394C2318yes—
453#394C2318yes—
454#393C2318yes—
455#393C2314yes—
456#392C2318yes—
457#392C2318yes—
458#392C2318yes—
459#392C2314yes—
460#392C2318yes—
461#392C2318yes—
462#392C2318yes—
463#391C2311yescharacteristic
464#391C2311yescharacteristic
465#391C2311yescharacteristic
466#391C2311yescharacteristic
467#391C2311yescharacteristic
468#391C2312yes—
469#391C2312yes—
470#391C2312yes—
471#391C2314yes—
472#391C2318yes—
473#391C2311yescharacteristic
474#391C2312yes—
475#391C2312yes—
476#391C2314yes—
477#391C2314yes—
478#391C2314yes—
479#391C2314yes—
480#390C2311yescharacteristic
481#390C2312yes—
482#390C2312yes—
483#390C2312yes—
484#390C2318yes—
485#390C2318yes—
486#390C2312yes—
487#390C2312yes—
488#390C2311yescharacteristic
489#390C2312yes—
490#390C2312yes—
491#390C2312yes—
492#390C2312yes—
493#390C2318yes—
494#390C2318yes—
495#390C2314yes—
496#390C2314yes—
497#390C2314yes—
498#390C2318yes—
499#390C2314yes—
500#390C2314yes—
501#389C2314yes—
502#389C2314yes—
503#389C2314yes—
504#389C2314yes—
505#389C2314yes—
506#389C2312yes—
507#389C2314yes—
508#389C2312yes—
509#389C2318yes—
510#389C2318yes—
511#388C2318yes—
512#388C2318yes—
513#388C2318yes—
514#388C2318yes—
515#388C2318yes—
516#388C2318yes—
517#388C2318yes—
518#388C2318yes—
519#388C2318yes—
520#388C2318yes—
521#388C2314yes—
522#388C2314yes—
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#386C2318yes—
540#386C2318yes—
541#386C2318yes—
542#386C2318yes—
543#386C2318yes—
544#385C2318yes—
545#385C2318yes—
546#385C2318yes—
547#385C2318yes—
548#385C2318yes—
549#385C2318yes—
550#385C2318yes—
551#384C2311yescharacteristic
552#384C2312yes—
553#384C2311yescharacteristic
554#384C2312yes—
555#384C2312yes—
556#384C2314yes—
557#384C2312yes—
558#382C2312yes—
559#382C2312yes—
560#382C2311yescharacteristic
561#382C2312yes—
562#382C2312yes—
563#382C2311yescharacteristic
564#382C2314yes—
565#380C2312yes—
566#380C2314yes—
567#380C2312yes—
568#380C2314yes—
569#380C2318yes—
570C4×C4⋊C4C2314yes—
571C4×C4⋊C4C2314yes—
572C4×C4⋊C4C2312yes—
573C4×C4⋊C4C2312yes—
574C4×C4⋊C4C2312yes—
575C4×C4⋊C4C2312yes—
576C4×C4⋊C4C2312yes—
577C4×C4⋊C4C2311yescharacteristic
578C4×C4⋊C4C2311yescharacteristic
579C4×C4⋊C4C2312yes—
580C4×C4⋊C4C2312yes—
581C4×C4⋊C4C2314yes—
582C4×C4⋊C4C2314yes—
583C4×C4⋊C4C2314yes—
584C4×C4⋊C4C2314yes—
585C4×C4⋊C4C2312yes—
586C4×C4⋊C4C2312yes—
587C4×C22⋊C4C2314yes—
588C4×C22⋊C4C2312yes—
589C4×C22⋊C4C2314yes—
590C4×C22⋊C4C2312yes—
591C4×C22⋊C4C2318yes—
592C4×C22⋊C4C2314yes—
593C4×C22⋊C4C2314yes—
594C4×C22⋊C4C2318yes—
595#376C2312yes—
596#376C2312yes—
597#376C2311yescharacteristic
598#376C2311yescharacteristic
599C43C2312yes—
600C43C2312yes—
601C43C2311yescharacteristic
602C43C2311yescharacteristic
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×Q8C2411yescharacteristic
615C22×Q8C2411yescharacteristic
616C22×Q8C2412yes—
617C22×Q8C2411yescharacteristic
618C22×Q8C2411yescharacteristic
619C22×Q8C2412yes—
620C22×Q8C2414yes—
621C22×Q8C2412yes—
622C22×Q8C2412yes—
623C22×D4C2412yes—
624C22×D4C2411yescharacteristic
625C22×D4C2412yes—
626C22×D4C2412yes—
627C22×D4C2412yes—
628C22×D4C2414yes—
629C22×D4C2414yes—
630C22×D4C2414yes—
631C22×D4C2412yes—
632C22×D4C2412yes—
633C22×D4C2418yes—
634C22×D4C2414yes—
635C22×D4C2412yes—
636C22×D4C2418yes—
637C22×D4C2418yes—
638C23×C4C2412yes—
639C23×C4C2411yescharacteristic
640C23×C4C2411yescharacteristic
641C23×C4C2414yes—
642C23×C4C2414yes—
643C23×C4C2414yes—
644C23×C4C2414yes—
645C23×C4C2414yes—
646C23×C4C2414yes—
647C23×C4C2414yes—
648C23×C4C2412yes—
649C23×C4C2411yescharacteristic
650C23×C4C2412yes—
651C4⋊Q8—28no—
652C4⋊Q8—28no—
653C4⋊Q8—28no—
654C4⋊Q8—216no—
655C4⋊Q8—28no—
656C4⋊Q8—24no—
657C4⋊Q8—24no—
658C4⋊Q8—24no—
659C4⋊Q8—24no—
660C4⋊Q8—24no—
661C4⋊Q8—42no—
662#127—28no—
663#127—24no—
664#127—24no—
665#127—28no—
666#127—44no—
667#127—44no—
668#127—48no—
669#127—84no—
670#126—216no—
671#126—216no—
672#126—216no—
673#126—28no—
674#126—216no—
675#126—216no—
676#125—216no—
677#125—216no—
678#125—24no—
679#125—28no—
680#125—28no—
681#125—28no—
682#125—28no—
683#124—28no—
684#124—28no—
685#124—28no—
686#124—216no—
687#124—28no—
688#124—28no—
689#124—24no—
690#124—28no—
691#124—216no—
692#124—28no—
693#124—28no—
694#124—24no—
695#124—44no—
696#124—44no—
697#124—44no—
698#124—42no—
699#124—48no—
700#124—84no—
701#123—216no—
702#123—216no—
703#123—216no—
704#123—28no—
705#123—216no—
706#123—216no—
707#123—216no—
708#123—216no—
709#123—216no—
710C22⋊Q8—216no—
711C22⋊Q8—216no—
712C22⋊Q8—28no—
713C22⋊Q8—216no—
714C22⋊Q8—24no—
715C22⋊Q8—24no—
716C22⋊Q8—24no—
717C22⋊Q8—28no—
718C22⋊Q8—216no—
719C22⋊Q8—216no—
720C22⋊Q8—216no—
721C22⋊Q8—216no—
722C22⋊Q8—216no—
723C22⋊Q8—48no—
724C22⋊Q8—88no—
725C22⋊Q8—88no—
726#121—28no—
727#121—28no—
728#121—24no—
729#121—28no—
730#121—28no—
731#121—216no—
732#121—28no—
733#121—216no—
734#121—48no—
735#121—88no—
736C4×Q8—28no—
737C4×Q8—28no—
738C4×Q8—28no—
739C4×Q8—28no—
740C4×Q8—28no—
741C4×Q8—28no—
742C4×Q8—24no—
743C4×Q8—28no—
744C4×Q8—24no—
745C4×Q8—24no—
746C4×Q8—44no—
747C4×Q8—44no—
748C4×Q8C2×D418yes—
749C4×Q8C2×D4116yes—
750C4×Q8C2×D418yes—
751C4×Q8C2×D418yes—
752C4×Q8C2×D4116yes—
753C4×Q8C2×D418yes—
754C4×D4—216no—
755C4×D4—216no—
756C4×D4—28no—
757C4×D4—216no—
758C4×D4—28no—
759C4×D4—216no—
760C4×D4—28no—
761C4×D4—28no—
762C4×D4—216no—
763C4×D4—28no—
764C4×D4—28no—
765C4×D4—24no—
766C4×D4—28no—
767C4×D4—28no—
768C4×D4—28no—
769C4×D4—28no—
770C4×D4—28no—
771C4×D4—28no—
772C4×D4—28no—
773C4×D4—88no—
774C4×D4—88no—
775#117—28no—
776#117—216no—
777#117—216no—
778#117—28no—
779#117—216no—
780#117—216no—
781#117—24no—
782#117—44no—
783#117—42no—
784C2×C4⋊C4—28no—
785C2×C4⋊C4—216no—
786C2×C4⋊C4—216no—
787C2×C4⋊C4C2×D418yes—
788C2×C4⋊C4C2×D4116yes—
789C2×C4⋊C4C2414yes—
790C2×C4⋊C4C2412yes—
791C2×C4⋊C4C2412yes—
792C2×C4⋊C4C2412yes—
793C2×C4⋊C4C2414yes—
794C2×C4⋊C4C2414yes—
795C2×C4⋊C4C2414yes—
796C2×C4⋊C4C2412yes—
797C2×C4⋊C4C2412yes—
798C2×C4⋊C4C2412yes—
799C2×C4⋊C4C2412yes—
800C2×C4⋊C4C2414yes—
801C2×C4⋊C4C2414yes—
802C2×C4⋊C4C2412yes—
803C2×C4⋊C4C2411yescharacteristic
804C2×C4⋊C4C2411yescharacteristic
805C2×C4⋊C4C2412yes—
806C2×C4⋊C4C2411yescharacteristic
807C2×C4⋊C4C2411yescharacteristic
808C2×C4⋊C4C2412yes—
809C2×C4⋊C4C2412yes—
810C2×C4⋊C4C2412yes—
811C2×C4⋊C4C2414yes—
812C2×C4⋊C4C2412yes—
813C2×C4⋊C4C2412yes—
814C2×C4⋊C4C2412yes—
815C2×C4⋊C4C2412yes—
816C2×C4⋊C4C2414yes—
817C2×C4⋊C4C2414yes—
818C2×C4⋊C4C2412yes—
819C2×C4⋊C4C2414yes—
820C2×C4⋊C4C2412yes—
821C2×C4⋊C4C2414yes—
822C2×C4⋊C4C2412yes—
823C2×C4⋊C4C2414yes—
824C2×C4⋊C4C2414yes—
825C2×C4⋊C4C2418yes—
826C2×C4⋊C4C2414yes—
827C2×C4⋊C4C2414yes—
828C2×C4⋊C4C2414yes—
829C2×C4⋊C4C2414yes—
830C2×C4⋊C4C2414yes—
831C2×C4⋊C4C2414yes—
832C2×C4⋊C4C2418yes—
833C2×C4⋊C4C2418yes—
834C2×C4⋊C4C2414yes—
835C2×C4⋊C4C2412yes—
836C2×C4⋊C4C2411yescharacteristic
837C2×C4⋊C4C2412yes—
838C2×C4⋊C4C2411yescharacteristic
839C2×C4⋊C4C2412yes—
840C2×C4⋊C4C2412yes—
841C2×C4⋊C4C2412yes—
842C2×C22⋊C4C2414yes—
843C2×C22⋊C4C2414yes—
844C2×C22⋊C4C2412yes—
845C2×C22⋊C4C2412yes—
846C2×C22⋊C4C2412yes—
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⋊C4C2414yes—
861C2×C22⋊C4C2414yes—
862C2×C22⋊C4C2414yes—
863C2×C22⋊C4C2412yes—
864C2×C22⋊C4C2414yes—
865C2×C22⋊C4C2414yes—
866C2×C22⋊C4C2412yes—
867C2×C22⋊C4C2414yes—
868C2×C22⋊C4C2414yes—
869C2×C22⋊C4C2418yes—
870C2×C22⋊C4C2418yes—
871C2×C22⋊C4C2418yes—
872C2×C22⋊C4C2414yes—
873C2×C22⋊C4C2418yes—
874C2×C22⋊C4C2418yes—
875C2×C22⋊C4C2418yes—
876C2×C22⋊C4C2418yes—
877C2×C22⋊C4C2418yes—
878C2×C22⋊C4C2418yes—
879C2×C22⋊C4C2414yes—
880C2×C22⋊C4C2418yes—
881C2×C22⋊C4C2418yes—
882C2×C22⋊C4C2418yes—
883C2×C42C2×D4116yes—
884C2×C42C2×D418yes—
885C2×C42C2414yes—
886C2×C42C2414yes—
887C2×C42C2412yes—
888C2×C42C2414yes—
889C2×C42C2412yes—
890C2×C42C2412yes—
891C2×C42C2412yes—
892C2×C42C2412yes—
893C2×C42C2411yescharacteristic
894C2×C42C2411yescharacteristic
895C2×C42C2411yescharacteristic
896C2×C42C2412yes—
897C2×C42C2412yes—
898C2×C42C2414yes—
899C2×C42C2414yes—
900C2×C42C2414yes—
901C2×C42C2414yes—
902C2×C42C2412yes—
903C2×C42C2412yes—
904C2×C42C2412yes—
905C2×C42C2411yescharacteristic
906C2×C42C2412yes—
907C2×C42C2411yescharacteristic
908C2×C42C2412yes—
909C2×C42C2412yes—
910C2×C42C2411yescharacteristic
911C2×C42C2411yescharacteristic
912C2×C42C2411yescharacteristic
913#95C2414yes—
914#95C2414yes—
915#95C2412yes—
916#95C2412yes—
917#95C2412yes—
918#95C2412yes—
919#95C2414yes—
920#95C2414yes—
921#95C2414yes—
922#95C2418yes—
923#95C2414yes—
924#95C2418yes—
925#95C2414yes—
926#95C2418yes—
927#95C2414yes—
928#95C2414yes—
929#95C2414yes—
930#95C2414yes—
931#95C2412yes—
932#95C2412yes—
933#95C2414yes—
934#95C2414yes—
935#95C2414yes—
936#95C2414yes—
937#95C2414yes—
938#95C2414yes—
939#95C2418yes—
940#95C2418yes—
941#95C2418yes—
942C24C2514yes—
943C24C2512yes—
944C24C2514yes—
945C24C2511yescharacteristic
946#41—432no—
947#41—432no—
948#41—832no—
949#41—816no—
950C2×Q8—22no—
951C2×Q8—22no—
952C2×Q8—22no—
953C2×Q8—24no—
954C2×Q8—24no—
955C2×Q8—28no—
956C2×Q8—24no—
957C2×Q8—22no—
958C2×Q8—22no—
959C2×Q8—22no—
960C2×Q8—24no—
961C2×Q8—24no—
962C2×Q8—28no—
963C2×Q8—22no—
964C2×Q8—22no—
965C2×Q8—22no—
966C2×Q8—44no—
967C2×Q8—44no—
968C2×Q8—48no—
969C2×Q8—44no—
970C2×Q8—416no—
971C2×Q8C22×D414yes—
972C2×Q8C22×D414yes—
973C2×Q8C22×D418yes—
974C2×D4—28no—
975C2×D4—24no—
976C2×D4—28no—
977C2×D4—24no—
978C2×D4—22no—
979C2×D4—24no—
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—24no—
989C2×D4—216no—
990C2×D4—28no—
991C2×D4—24no—
992C2×D4—24no—
993C2×D4—22no—
994C2×D4—28no—
995C2×D4—48no—
996C2×D4—48no—
997C2×D4—44no—
998C2×D4—48no—
999C2×D4—48no—
1000C2×D4—48no—
1001C2×D4—48no—
1002C2×D4—48no—
1003C2×D4—44no—
1004C2×D4—48no—
1005C2×D4—48no—
1006C2×D4—44no—
1007C2×D4—48no—
1008C2×D4—48no—
1009C2×D4—48no—
1010C22×C4—22no—
1011C22×C4—22no—
1012C22×C4—24no—
1013C22×C4—28no—
1014C22×C4—24no—
1015C22×C4—28no—
1016C22×C4—28no—
1017C22×C4—28no—
1018C22×C4—28no—
1019C22×C4—28no—
1020C22×C4—28no—
1021C22×C4—28no—
1022C22×C4—44no—
1023C22×C4—48no—
1024C22×C4—48no—
1025C22×C4—44no—
1026C22×C4—42no—
1027C22×C4—48no—
1028C22×C4—48no—
1029C22×C4—48no—
1030C22×C4—48no—
1031C22×C4—48no—
1032C22×C4C22×D414yes—
1033C22×C4C22×D414yes—
1034C22×C4C22×D418yes—
1035C22×C4C22×D414yes—
1036C22×C4C22×D418yes—
1037C22×C4C2512yes—
1038C22×C4C2512yes—
1039C22×C4C2514yes—
1040C22×C4C2514yes—
1041C22×C4C2512yes—
1042C22×C4C2512yes—
1043C22×C4C2512yes—
1044C22×C4C2512yes—
1045C22×C4C2514yes—
1046C22×C4C2512yes—
1047C22×C4C2514yes—
1048C22×C4C2512yes—
1049C22×C4C2512yes—
1050C22×C4C2512yes—
1051C22×C4C2512yes—
1052C22×C4C2511yescharacteristic
1053C22×C4C2512yes—
1054C22×C4C2511yescharacteristic
1055C22×C4C2512yes—
1056C22×C4C2511yescharacteristic
1057C22×C4C2511yescharacteristic
1058C22×C4C2512yes—
1059C22×C4C2512yes—
1060C22×C4C2511yescharacteristic
1061C22×C4C2511yescharacteristic
1062C4⋊C4—28no—
1063C4⋊C4—24no—
1064C4⋊C4—24no—
1065C4⋊C4—28no—
1066C4⋊C4—24no—
1067C4⋊C4—28no—
1068C4⋊C4—28no—
1069C4⋊C4—24no—
1070C4⋊C4—24no—
1071C4⋊C4—24no—
1072C4⋊C4—24no—
1073C4⋊C4—28no—
1074C4⋊C4—28no—
1075C4⋊C4—22no—
1076C4⋊C4—22no—
1077C4⋊C4—24no—
1078C4⋊C4—22no—
1079C4⋊C4—22no—
1080C4⋊C4—24no—
1081C4⋊C4—24no—
1082C4⋊C4—28no—
1083C4⋊C4—24no—
1084C4⋊C4—24no—
1085C4⋊C4—24no—
1086C4⋊C4—28no—
1087C4⋊C4—28no—
1088C4⋊C4—24no—
1089C4⋊C4—28no—
1090C4⋊C4—24no—
1091C4⋊C4—24no—
1092C4⋊C4—28no—
1093C4⋊C4—24no—
1094C4⋊C4—24no—
1095C4⋊C4—44no—
1096C4⋊C4—42no—
1097C4⋊C4—44no—
1098C4⋊C4—48no—
1099C4⋊C4—44no—
1100C4⋊C4—44no—
1101C4⋊C4—44no—
1102C4⋊C4—48no—
1103C4⋊C4—44no—
1104C4⋊C4—44no—
1105C4⋊C4—44no—
1106C4⋊C4—48no—
1107C4⋊C4—44no—
1108C4⋊C4C22×D418yes—
1109C4⋊C4C22×D414yes—
1110C4⋊C4C22×D418yes—
1111C4⋊C4C22×D414yes—
1112C4⋊C4C22×D418yes—
1113C4⋊C4C22×D418yes—
1114C4⋊C4C22×D418yes—
1115C22⋊C4—24no—
1116C22⋊C4—24no—
1117C22⋊C4—24no—
1118C22⋊C4—28no—
1119C22⋊C4—28no—
1120C22⋊C4—24no—
1121C22⋊C4—28no—
1122C22⋊C4—24no—
1123C22⋊C4—28no—
1124C22⋊C4—28no—
1125C22⋊C4—28no—
1126C22⋊C4—28no—
1127C22⋊C4—28no—
1128C22⋊C4—24no—
1129C22⋊C4—28no—
1130C22⋊C4—28no—
1131C22⋊C4—28no—
1132C22⋊C4—28no—
1133C22⋊C4—28no—
1134C22⋊C4—28no—
1135C22⋊C4—28no—
1136C22⋊C4—24no—
1137C22⋊C4—24no—
1138C22⋊C4—28no—
1139C22⋊C4—44no—
1140C22⋊C4—42no—
1141C22⋊C4—44no—
1142C22⋊C4—48no—
1143C22⋊C4—48no—
1144C22⋊C4—48no—
1145C22⋊C4—48no—
1146C22⋊C4—44no—
1147C22⋊C4—48no—
1148C22⋊C4—48no—
1149C22⋊C4—48no—
1150C22⋊C4—48no—
1151C22⋊C4—48no—
1152C22⋊C4—48no—
1153C22⋊C4—48no—
1154C22⋊C4—44no—
1155C22⋊C4—48no—
1156C42—28no—
1157C42—28no—
1158C42—28no—
1159C42—24no—
1160C42—24no—
1161C42—24no—
1162C42—22no—
1163C42—24no—
1164C42—24no—
1165C42—22no—
1166C42—22no—
1167C42—24no—
1168C42—24no—
1169C42—44no—
1170C42—44no—
1171C42—44no—
1172C42—44no—
1173C42—42no—
1174C42—42no—
1175C42C22×D418yes—
1176C42C22×D414yes—
1177C42C22×D418yes—
1178C42C22×D414yes—
1179C42C22×D418yes—
1180C42C22×D418yes—
1181C42C22×D414yes—
1182C42C22×D414yes—
1183C422−1+414yes—
1184C23—21no—
1185C23—21no—
1186C23—22no—
1187C23—22no—
1188C23—24no—
1189C23—22no—
1190C23—24no—
1191C23—22no—
1192C23—24no—
1193C23—24no—
1194C23—24no—
1195C23—24no—
1196C23—28no—
1197C23—22no—
1198C23—24no—
1199C23—28no—
1200C23—28no—
1201C23—28no—
1202C23—24no—
1203C23C23×D412yes—
1204C23C2611yescharacteristic
1205Q8—28no—
1206Q8—28no—
1207Q8—48no—
1208Q8—48no—
1209Q8—44no—
1210Q8—44no—
1211Q8—44no—
1212Q8—84no—
1213Q8—88no—
1214Q8—84no—
1215D4—416no—
1216D4—416no—
1217D4—48no—
1218D4—416no—
1219D4—48no—
1220D4—48no—
1221D4—48no—
1222D4—44no—
1223D4—48no—
1224D4—84no—
1225D4—816no—
1226D4—88no—
1227D4—84no—
1228D4—816no—
1229D4—168no—
1230C2×C4—21no—
1231C2×C4—22no—
1232C2×C4—24no—
1233C2×C4—21no—
1234C2×C4—22no—
1235C2×C4—24no—
1236C2×C4—22no—
1237C2×C4—24no—
1238C2×C4—22no—
1239C2×C4—22no—
1240C2×C4—24no—
1241C2×C4—28no—
1242C2×C4—28no—
1243C2×C4—22no—
1244C2×C4—22no—
1245C2×C4—22no—
1246C2×C4—24no—
1247C2×C4—22no—
1248C2×C4—22no—
1249C2×C4—24no—
1250C2×C4—22no—
1251C2×C4—22no—
1252C2×C4—22no—
1253C2×C4—22no—
1254C2×C4—22no—
1255C2×C4—22no—
1256C2×C4—22no—
1257C2×C4—24no—
1258C2×C4—22no—
1259C2×C4—22no—
1260C2×C4—24no—
1261C2×C4—22no—
1262C2×C4—22no—
1263C2×C4—24no—
1264C2×C4—24no—
1265C2×C4—22no—
1266C2×C4—22no—
1267C2×C4—22no—
1268C2×C4—28no—
1269C2×C4—24no—
1270C2×C4—22no—
1271C2×C4—24no—
1272C2×C4—22no—
1273C2×C4—24no—
1274C2×C4—22no—
1275C2×C4—24no—
1276C2×C4—24no—
1277C2×C4—24no—
1278C2×C4—28no—
1279C2×C4—48no—
1280C2×C4—48no—
1281C2×C4—44no—
1282C2×C4—416no—
1283C2×C4—416no—
1284C2×C4—48no—
1285C2×C4—88no—
1286C2×C4—88no—
1287C2×C4—88no—
1288C2×C4—88no—
1289C2×C4—88no—
1290C2×C4C23×D414yes—
1291C2×C4C23×D414yes—
1292C2×C4C23×D414yes—
1293C2×C4C23×D412yes—
1294C2×C4C23×D414yes—
1295C2×C4C23×D412yes—
1296C2×C4C23×D412yes—
1297C2×C4C23×D412yes—
1298C2×C4C23×D412yes—
1299C2×C4C23×D412yes—
1300C2×C4C2×2−1+414yes—
1301C2×C4C2×2−1+412yes—
1302C2×C4#58514yes—
1303C2×C4#58512yes—
1304C22—22no—
1305C22—22no—
1306C22—22no—
1307C22—42no—
1308C22—42no—
1309C22—44no—
1310C22—42no—
1311C22—44no—
1312C22—44no—
1313C22—42no—
1314C22—44no—
1315C22—44no—
1316C22—44no—
1317C22—42no—
1318C22—48no—
1319C22—48no—
1320C22—44no—
1321C22—44no—
1322C22—48no—
1323C22—48no—
1324C22C24×D411yescharacteristic
1325C22C22×2−1+411yescharacteristic
1326C22C2×#58511yescharacteristic
1327C22C2×#58512yes—
1328C22H(7,𝔽2)12yes—
1329C4—22no—
1330C4—24no—
1331C4—22no—
1332C4—24no—
1333C4—22no—
1334C4—22no—
1335C4—24no—
1336C4—24no—
1337C4—24no—
1338C4—42no—
1339C4—42no—
1340C4—42no—
1341C4—42no—
1342C4—44no—
1343C4—42no—
1344C4—42no—
1345C4—42no—
1346C4—44no—
1347C4—42no—
1348C4—44no—
1349C4—42no—
1350C4—44no—
1351C4—42no—
1352C4#344914yes—
1353C4#349714yes—
1354C2—42no—
1355C2—84no—
1356C2—82no—
1357C2—84no—
1358C2C2×#344911yescharacteristic
1359C2C2×#349711yescharacteristic
1360C2#6285211yescharacteristic
1361C2#6296212yes—
1362C2#6296912yes—
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. #42799C2semidirect
4. #42797C2semidirect
5. #41942C2semidirect
6. #40499C2semidirect
7. #39745C2semidirect
8. #39741C2semidirect
9. #39619C2semidirect
10. #39611C2semidirect
11. #39174C2semidirect
12. #39168C2semidirect
13. #39163C2semidirect
14. #39161C2semidirect
15. #37640C2semidirect
16. #37616C2semidirect
17. #37616C2semidirect
18. #37542C2semidirect
19. #36595C2semidirect
20. #36562C2semidirect
21. #36538C2semidirect
22. #36496C2semidirect
23. #35787C2semidirect
24. #35715C2semidirect
25. #35343C2semidirect
26. #35293C2semidirect
27. #34631C2semidirect
28. #34624C2semidirect
29. Q8×#117C2semidirect
343. 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
#427992
#427972
#419422
#404992
#397452
#397412
#396192
#396112
#391742
#391682
#391632
#391612
#376402
#376162
#375422
#365952
#365622
#365382
#364962
#357872
#357152
#353432
#352932
#346312
#346242
Q8×#1172