Finite Group Databasebeta

← #7657635

Subgroups — #7657635

Order 512.

6937 conjugacy classes of subgroups.

The subgroup lattice has 1443 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3511C211yesmaximal, characteristic, complemented
2C2×#3480C211yesmaximal, characteristic, complemented
3#42909C212yesmaximal, complemented
4#42908C212yesmaximal, complemented
5#42891C212yesmaximal, complemented
6#42887C212yesmaximal, complemented
7#42156C214yesmaximal, complemented
8#41959C214yesmaximal, complemented
9#40607C214yesmaximal, complemented
10#40603C214yesmaximal, complemented
11#39469C212yesmaximal, complemented
12#39462C214yesmaximal, complemented
13#38922C212yesmaximal, complemented
14#38914C214yesmaximal, complemented
15#37632C211yesmaximal, characteristic, complemented
16#37621C211yesmaximal, characteristic, complemented
17#37560C212yesmaximal, complemented
18#37554C212yesmaximal, complemented
19#36544C212yesmaximal, complemented
20#36492C212yesmaximal, complemented
21#35923C212yesmaximal, complemented
22#35912C212yesmaximal, complemented
23#35759C212yesmaximal, complemented
24#35689C212yesmaximal, complemented
25#35334C212yesmaximal, complemented
26#35279C211yesmaximal, characteristic, complemented
27#34609C211yesmaximal, characteristic, complemented
28#34609C212yesmaximal, complemented
29#34191C211yesmaximal, characteristic, complemented
30#3511—216no—
31#3480—216no—
32C2×#559C2211yescharacteristic
33C2×#559C2212yes—
34C2×#557C2211yescharacteristic
35C2×#556C2212yes—
36C2×#556C2212yes—
37C2×#556C2211yescharacteristic
38C2×#555C2212yes—
39C2×#554C2212yes—
40C2×#553C2214yes—
41C2×#553C2211yescharacteristic
42C2×#553C2211yescharacteristic
43C2×#553C2212yes—
44C2×#553C2212yes—
45C2×#550C2211yescharacteristic
46C2×#548C2214yes—
47C2×#548C2211yescharacteristic
48C2×#548C2211yescharacteristic
49C2×#547C2212yes—
50C2×#542C2214yes—
51C2×#537C2212yes—
52C2×#533C2212yes—
53C2×#532C2212yes—
54C2×#532C2211yescharacteristic
55C2×#532C2212yes—
56C2×#532C2211yescharacteristic
57C22×C4⋊Q8C2211yescharacteristic
58C2×#529C2211yescharacteristic
59C2×#529C2212yes—
60C2×#529C2211yescharacteristic
61C2×#529C2212yes—
62C2×#520C2212yes—
63C2×C4×#41C2212yes—
64C2×C4×#41C2211yescharacteristic
65C2×C4×#41C2211yescharacteristic
66C2×C4×#41C2211yescharacteristic
67C22×C4×Q8C2211yescharacteristic
68#2857C2212yes—
69#2857C2212yes—
70#2851C2214yes—
71#2851C2214yes—
72#2821C2214yes—
73#2820C2214yes—
74#2819C2214yes—
75#2817C2214yes—
76#2816C2214yes—
77#2813C2214yes—
78#2723C2218yes—
79#2721C2218yes—
80#2716C2218yes—
81#2715C2218yes—
82#2714C2218yes—
83#2712C2218yes—
84#2688C2218yes—
85#2686C2218yes—
86#2676C2218yes—
87#2673C2218yes—
88#2672C2218yes—
89#2671C2218yes—
90#2663C2214yes—
91#2663C2214yes—
92#2662C2214yes—
93#2660C2212yes—
94#2656C2214yes—
95#2640C2212yes—
96#2639C2214yes—
97#2636C2214yes—
98#2636C2214yes—
99#2635C2212yes—
100#2635C2214yes—
101#2635C2214yes—
102#2635C2212yes—
103#2634C2214yes—
104#2632C2214yes—
105#2632C2212yes—
106#2632C2214yes—
107#2631C2214yes—
108#2631C2212yes—
109#2628C2212yes—
110#2628C2212yes—
111#2628C2211yescharacteristic
112#2628C2212yes—
113#2628C2212yes—
114#2628C2211yescharacteristic
115#2628C2212yes—
116#2624C2212yes—
117#2624C2214yes—
118#2619C2211yescharacteristic
119#2619C2211yescharacteristic
120#2619C2212yes—
121#2616C2212yes—
122#2615C2212yes—
123#2615C2214yes—
124#2615C2212yes—
125#2614C2214yes—
126#2604C2214yes—
127#2604C2214yes—
128#2584C2214yes—
129#2581C2214yes—
130#2581C2214yes—
131#2580C2214yes—
132#2580C2214yes—
133#2580C2214yes—
134#2568C2212yes—
135#2567C2212yes—
136#2567C2212yes—
137#2564C2214yes—
138#2564C2214yes—
139#2564C2214yes—
140#2564C2214yes—
141#2563C2212yes—
142#2563C2212yes—
143#2562C2214yes—
144#2562C2212yes—
145#2557C2218yes—
146#2553C2218yes—
147#2542C2212yes—
148#2540C2212yes—
149#2538C2212yes—
150#2537C2214yes—
151#2537C2212yes—
152#2535C2214yes—
153#2535C2214yes—
154#2503C2212yes—
155#2501C2212yes—
156#2487C2212yes—
157#2487C2212yes—
158#2486C2214yes—
159#2485C2214yes—
160#2485C2214yes—
161#2477C2218yes—
162#2466C2218yes—
163#2465C2218yes—
164#2464C2218yes—
165#2463C2218yes—
166#2459C2218yes—
167#2456C2218yes—
168#2455C2218yes—
169#2449C2218yes—
170#2441C2214yes—
171#2439C2214yes—
172#2430C2214yes—
173#2430C2214yes—
174#2428C2214yes—
175#2427C2214yes—
176#2423C2214yes—
177#2422C2218yes—
178#2421C2214yes—
179#2416C2214yes—
180#2416C2214yes—
181#2415C2214yes—
182#2414C2214yes—
183#2414C2214yes—
184#2409C2214yes—
185#2409C2212yes—
186#2409C2212yes—
187#2407C2214yes—
188#2398C2212yes—
189#2398C2214yes—
190#2397C2212yes—
191#2397C2214yes—
192#2388C2214yes—
193#2388C2214yes—
194#2388C2212yes—
195#2388C2212yes—
196#2361C2214yes—
197#2360C2214yes—
198#2355C2212yes—
199#2352C2214yes—
200#2352C2214yes—
201D4×C4⋊C4C2212yes—
202D4×C4⋊C4C2214yes—
203#2346C2212yes—
204#2343C2214yes—
205#2339C2212yes—
206#2320C2212yes—
207#2318C2214yes—
208#2317C2212yes—
209#2316C2214yes—
210#2311C2214yes—
211#2311C2212yes—
212C4×#121C2214yes—
213C4×#121C2212yes—
214C4×#121C2214yes—
215C4×#121C2212yes—
216#2285C2211yescharacteristic
217#2283C2211yescharacteristic
218#2283C2212yes—
219C2×#382C2212yes—
220#2275C2212yes—
221C22×#41C2312yes—
222C22×#41C2311yescharacteristic
223C22×#41C2312yes—
224C22×#41C2311yescharacteristic
225C22×#41C2314yes—
226C22×#41C2311yescharacteristic
227C23×Q8C2311yescharacteristic
228C23×Q8C2312yes—
229#559—28no—
230#559—216no—
231#557—28no—
232#556—216no—
233#556—28no—
234#556—216no—
235#555—216no—
236#554—216no—
237#553—28no—
238#553—216no—
239#553—232no—
240#553—28no—
241#553—216no—
242#550—28no—
243#548—28no—
244#548—28no—
245#548—232no—
246#547—216no—
247#542—232no—
248#537—216no—
249#533—216no—
250#532—216no—
251#532—28no—
252#532—28no—
253#532—216no—
254C2×C4⋊Q8—28no—
255C2×C4⋊Q8C2312yes—
256C2×C4⋊Q8C2312yes—
257C2×C4⋊Q8C2312yes—
258C2×C4⋊Q8C2312yes—
259C2×C4⋊Q8C2311yescharacteristic
260C2×C4⋊Q8C2311yescharacteristic
261C2×C4⋊Q8C2312yes—
262C2×#127C2311yescharacteristic
263C2×#127C2312yes—
264C2×#127C2311yescharacteristic
265#529—216no—
266#529—28no—
267#529—28no—
268#529—216no—
269C2×#126C2312yes—
270C2×#126C2312yes—
271C2×#126C2312yes—
272C2×#126C2312yes—
273C2×#126C2312yes—
274C2×#126C2312yes—
275C2×#126C2318yes—
276C2×#125C2311yescharacteristic
277C2×#125C2314yes—
278C2×#125C2312yes—
279C2×#125C2311yescharacteristic
280C2×#125C2312yes—
281C2×#124C2312yes—
282C2×#124C2314yes—
283C2×#124C2312yes—
284C2×#124C2311yescharacteristic
285C2×#124C2311yescharacteristic
286C2×#124C2312yes—
287C2×#124C2318yes—
288C2×#124C2312yes—
289C2×#124C2312yes—
290C2×#124C2312yes—
291C2×#123C2312yes—
292C2×#123C2312yes—
293C2×#123C2312yes—
294C2×#123C2312yes—
295C2×#123C2312yes—
296C2×#123C2312yes—
297C2×#123C2318yes—
298C2×#123C2318yes—
299C2×C22⋊Q8C2314yes—
300C2×C22⋊Q8C2312yes—
301C2×C22⋊Q8C2314yes—
302C2×C22⋊Q8C2311yescharacteristic
303C2×C22⋊Q8C2314yes—
304C2×C22⋊Q8C2311yescharacteristic
305C2×C22⋊Q8C2312yes—
306C2×C22⋊Q8C2318yes—
307C2×C22⋊Q8C2314yes—
308C2×C22⋊Q8C2314yes—
309C2×C22⋊Q8C2314yes—
310C2×#121C2312yes—
311C2×#121C2312yes—
312C2×#121C2311yescharacteristic
313C2×#121C2312yes—
314C2×#121C2314yes—
315C2×#121C2314yes—
316C2×#121C2312yes—
317C2×#121C2311yescharacteristic
318C2×#121C2312yes—
319C2×#121C2318yes—
320C2×#121C2311yescharacteristic
321C2×#121C2312yes—
322C2×#121C2312yes—
323C2×#121C2312yes—
324C2×#121C2311yescharacteristic
325C2×#121C2312yes—
326C2×#121C2312yes—
327C2×#121C2314yes—
328C2×#121C2314yes—
329C2×#121C2314yes—
330C2×#121C2312yes—
331C2×#121C2318yes—
332C2×#121C2318yes—
333#520—216no—
334C4×#41—28no—
335C4×#41—28no—
336C4×#41—216no—
337C4×#41D4116yescomplemented
338C2×C4×Q8—28no—
339C2×C4×Q8C2311yescharacteristic
340C2×C4×Q8C2311yescharacteristic
341C2×C4×Q8C2311yescharacteristic
342C2×C4×Q8C2312yes—
343C2×C4×Q8C2314yes—
344C2×C4×Q8C2314yes—
345C2×C4×Q8C2312yes—
346C2×C4×Q8C2312yes—
347C2×C4×Q8C2311yescharacteristic
348C2×C4×Q8C2311yescharacteristic
349C2×C4×Q8C2312yes—
350C2×C4×Q8C2311yescharacteristic
351C2×C4×Q8C2311yescharacteristic
352C2×C4×Q8C2311yescharacteristic
353C2×C4×D4C2312yes—
354C2×C4×D4C2312yes—
355C2×C4×D4C2311yescharacteristic
356C2×C4×D4C2311yescharacteristic
357C2×C4×D4C2312yes—
358C2×C4×D4C2312yes—
359C2×C4×D4C2312yes—
360C2×C4×D4C2312yes—
361C2×C4×D4C2312yes—
362C2×C4×D4C2312yes—
363C2×C4×D4C2314yes—
364C2×C4×D4C2311yescharacteristic
365C2×C4×D4C2311yescharacteristic
366C2×C4×D4C2311yescharacteristic
367C2×C4×D4C2311yescharacteristic
368C2×C4×D4C2314yes—
369C2×C4×D4C2311yescharacteristic
370C2×C4×D4C2311yescharacteristic
371C2×C4×D4C2312yes—
372C2×C4×D4C2318yes—
373C2×C4×D4C2312yes—
374C2×C4×D4C2312yes—
375C2×C4×D4C2312yes—
376C2×C4×D4C2312yes—
377C2×C4×D4C2314yes—
378C2×C4×D4C2314yes—
379C2×C4×D4C2314yes—
380C2×C4×D4C2318yes—
381C2×C4×D4C2318yes—
382C2×C4×D4C2312yes—
383C2×C4×D4C2311yescharacteristic
384C2×C4×D4C2312yes—
385C2×C4×D4C2311yescharacteristic
386C2×#117C2314yes—
387C2×#117C2312yes—
388C2×#117C2311yescharacteristic
389C2×#117C2311yescharacteristic
390C2×#117C2311yescharacteristic
391C2×#117C2311yescharacteristic
392C2×#117C2312yes—
393C2×#117C2312yes—
394C2×#117C2314yes—
395C2×#117C2312yes—
396C2×#117C2312yes—
397C2×#117C2311yescharacteristic
398C22×C4⋊C4C2312yes—
399C22×C4⋊C4C2311yescharacteristic
400C22×C4⋊C4C2314yes—
401C22×C4⋊C4C2312yes—
402C22×C4⋊C4C2312yes—
403C22×C4⋊C4C2314yes—
404C22×C42C2312yes—
405C22×C42C2312yes—
406C22×C42C2311yescharacteristic
407C22×C42C2311yescharacteristic
408C22×C42C2311yescharacteristic
409C22×C42C2312yes—
410#400C2318yes—
411#400C2314yes—
412#400C2314yes—
413#400C2314yes—
414#400C2312yes—
415#400C2314yes—
416#400C2314yes—
417#400C2312yes—
418#399C2314yes—
419#399C2314yes—
420#399C2312yes—
421#399C2314yes—
422#399C2314yes—
423#399C2314yes—
424#399C2318yes—
425#399C2318yes—
426#399C2314yes—
427#399C2312yes—
428#398C2318yes—
429#398C2318yes—
430#397C2318yes—
431#397C2318yes—
432#397C2318yes—
433#397C2318yes—
434#397C2318yes—
435#397C2314yes—
436#396C2318yes—
437#396C2318yes—
438#396C2318yes—
439#395C2312yes—
440#395C2314yes—
441#395C2318yes—
442#395C2312yes—
443#395C2314yes—
444#395C2314yes—
445#395C2314yes—
446#395C2318yes—
447#395C2314yes—
448#394C2318yes—
449#394C2318yes—
450#394C2318yes—
451#394C2314yes—
452#394C2318yes—
453#394C2318yes—
454#394C2312yes—
455#394C2314yes—
456#394C2318yes—
457#394C2312yes—
458#394C2312yes—
459#394C2312yes—
460#394C2314yes—
461#394C2318yes—
462#394C2318yes—
463#394C2314yes—
464#394C2318yes—
465#393C2312yes—
466#393C2314yes—
467#393C2314yes—
468#393C2314yes—
469#393C2318yes—
470#393C2314yes—
471#393C2318yes—
472#393C2312yes—
473#393C2314yes—
474#393C2318yes—
475#393C2314yes—
476#392C2312yes—
477#392C2314yes—
478#392C2318yes—
479#392C2314yes—
480#392C2318yes—
481#392C2314yes—
482#392C2314yes—
483#392C2318yes—
484#392C2318yes—
485#392C2314yes—
486#392C2318yes—
487#392C2312yes—
488#392C2312yes—
489#392C2312yes—
490#391C2314yes—
491#391C2318yes—
492#391C2314yes—
493#391C2314yes—
494#391C2314yes—
495#391C2314yes—
496#390C2314yes—
497#390C2314yes—
498#390C2318yes—
499#390C2312yes—
500#390C2314yes—
501#390C2312yes—
502#390C2318yes—
503#389C2314yes—
504#389C2314yes—
505#389C2314yes—
506#389C2314yes—
507#389C2312yes—
508#389C2314yes—
509#389C2318yes—
510#389C2318yes—
511#389C2314yes—
512#389C2314yes—
513#389C2314yes—
514#389C2312yes—
515#389C2318yes—
516#389C2318yes—
517#388C2318yes—
518#388C2318yes—
519#388C2318yes—
520#388C2318yes—
521#388C2318yes—
522#388C2318yes—
523#388C2318yes—
524#388C2318yes—
525#388C2314yes—
526#388C2314yes—
527#387C2318yes—
528#387C2318yes—
529#387C2318yes—
530#387C2318yes—
531#387C2318yes—
532#387C2318yes—
533#387C2318yes—
534#387C2318yes—
535#386C2318yes—
536#386C2318yes—
537#386C2314yes—
538#386C2314yes—
539#386C2318yes—
540#386C2318yes—
541#386C2318yes—
542#386C2318yes—
543#386C2318yes—
544#386C2314yes—
545#386C2314yes—
546#386C2318yes—
547#386C2318yes—
548#385C2318yes—
549#385C2318yes—
550#385C2318yes—
551#385C2318yes—
552#385C2314yes—
553#385C2314yes—
554#385C2318yes—
555#385C2318yes—
556#385C2318yes—
557#384C2314yes—
558#384C2314yes—
559#384C2312yes—
560#383C2312yes—
561#383C2314yes—
562#382C2314yes—
563#382C2314yes—
564#382C2314yes—
565#382C2314yes—
566#382C2314yes—
567#382C2311yescharacteristic
568#382C2312yes—
569#382C2311yescharacteristic
570#381C2314yes—
571#381C2312yes—
572#381C2318yes—
573#380C2312yes—
574#380C2314yes—
575#380C2314yes—
576#380C2314yes—
577#380C2314yes—
578#380C2314yes—
579#380C2314yes—
580#380C2314yes—
581#380C2314yes—
582#380C2318yes—
583#380C2318yes—
584#380C2312yes—
585#380C2314yes—
586#380C2312yes—
587#380C2312yes—
588#380C2314yes—
589#380C2312yes—
590C4×C4⋊C4C2312yes—
591C4×C4⋊C4C2314yes—
592C4×C4⋊C4C2312yes—
593C4×C4⋊C4C2312yes—
594C4×C4⋊C4C2314yes—
595C4×C22⋊C4C2314yes—
596C4×C22⋊C4C2312yes—
597C4×C22⋊C4C2318yes—
598C4×C22⋊C4C2318yes—
599C4×C22⋊C4C2314yes—
600C4×C22⋊C4C2318yes—
601C4×C22⋊C4C2314yes—
602#376C2312yes—
603#376C2314yes—
604C2×#95C2314yes—
605C2×#95C2314yes—
606C2×#41—24no—
607C2×#41—24no—
608C2×#41—28no—
609C2×#41—28no—
610C2×#41—216no—
611C2×#41—28no—
612C2×#41—24no—
613C2×#41—44no—
614C2×#41—42no—
615C2×#41—48no—
616C2×#41—44no—
617C2×#41—44no—
618C2×#41—88no—
619C2×#41C2×D418yes—
620C22×Q8—24no—
621C22×Q8—28no—
622C22×Q8—44no—
623C22×Q8—84no—
624C22×Q8C2411yescharacteristic
625C22×Q8C2411yescharacteristic
626C22×Q8C2412yes—
627C22×Q8C2411yescharacteristic
628C22×Q8C2412yes—
629C22×Q8C2412yes—
630C22×Q8C2414yes—
631C22×Q8C2414yes—
632C22×D4C2412yes—
633C22×D4C2411yescharacteristic
634C22×D4C2412yes—
635C22×D4C2411yescharacteristic
636C22×D4C2411yescharacteristic
637C22×D4C2412yes—
638C22×D4C2412yes—
639C22×D4C2411yescharacteristic
640C22×D4C2411yescharacteristic
641C22×D4C2414yes—
642C22×D4C2414yes—
643C22×D4C2412yes—
644C22×D4C2412yes—
645C22×D4C2412yes—
646C22×D4C2412yes—
647C22×D4C2412yes—
648C22×D4C2412yes—
649C22×D4C2418yes—
650C22×D4C2414yes—
651C22×D4C2418yes—
652C22×D4C2412yes—
653C23×C4C2414yes—
654C23×C4C2411yescharacteristic
655C23×C4C2411yescharacteristic
656C23×C4C2411yescharacteristic
657C23×C4C2412yes—
658C23×C4C2412yes—
659C23×C4C2411yescharacteristic
660C23×C4C2411yescharacteristic
661C23×C4C2411yescharacteristic
662C23×C4C2412yes—
663C23×C4C2411yescharacteristic
664C23×C4C2414yes—
665C23×C4C2418yes—
666C23×C4C2412yes—
667C23×C4C2412yes—
668C23×C4C2412yes—
669C23×C4C2411yescharacteristic
670C23×C4C2418yes—
671C23×C4C2412yes—
672C23×C4C2411yescharacteristic
673C23×C4C2412yes—
674C4⋊Q8—24no—
675C4⋊Q8—28no—
676C4⋊Q8—28no—
677C4⋊Q8—28no—
678C4⋊Q8—28no—
679C4⋊Q8—28no—
680C4⋊Q8—24no—
681#127—24no—
682#127—28no—
683#127—24no—
684#126—232no—
685#126—28no—
686#126—28no—
687#126—28no—
688#126—28no—
689#126—28no—
690#126—28no—
691#125—24no—
692#125—28no—
693#125—24no—
694#125—28no—
695#125—216no—
696#124—24no—
697#124—28no—
698#124—28no—
699#124—28no—
700#124—28no—
701#124—232no—
702#124—24no—
703#124—28no—
704#124—28no—
705#124—216no—
706#123—28no—
707#123—28no—
708#123—28no—
709#123—28no—
710#123—28no—
711#123—28no—
712#123—232no—
713#123—88no—
714C22⋊Q8—216no—
715C22⋊Q8—24no—
716C22⋊Q8—28no—
717C22⋊Q8—216no—
718C22⋊Q8—216no—
719C22⋊Q8—24no—
720C22⋊Q8—28no—
721C22⋊Q8—232no—
722C22⋊Q8—48no—
723C22⋊Q8—84no—
724C22⋊Q8—84no—
725#121—24no—
726#121—28no—
727#121—24no—
728#121—28no—
729#121—216no—
730#121—232no—
731#121—24no—
732#121—28no—
733#121—216no—
734#121—28no—
735#121—28no—
736#121—216no—
737#121—28no—
738#121—24no—
739#121—28no—
740#121—28no—
741#121—28no—
742#121—28no—
743#121—44no—
744#121—48no—
745#121—48no—
746#121—88no—
747#121—88no—
748C4×Q8—24no—
749C4×Q8—24no—
750C4×Q8—24no—
751C4×Q8—28no—
752C4×Q8—28no—
753C4×Q8—24no—
754C4×Q8—28no—
755C4×Q8—24no—
756C4×Q8—24no—
757C4×Q8—28no—
758C4×Q8—216no—
759C4×Q8—216no—
760C4×Q8C2×D418yes—
761C4×Q8C2×D418yes—
762C4×D4—24no—
763C4×D4—28no—
764C4×D4—24no—
765C4×D4—28no—
766C4×D4—24no—
767C4×D4—28no—
768C4×D4—24no—
769C4×D4—28no—
770C4×D4—28no—
771C4×D4—28no—
772C4×D4—28no—
773C4×D4—24no—
774C4×D4—28no—
775C4×D4—232no—
776C4×D4—28no—
777C4×D4—24no—
778C4×D4—24no—
779C4×D4—28no—
780C4×D4—28no—
781C4×D4—24no—
782C4×D4—216no—
783C4×D4—28no—
784C4×D4—216no—
785C4×D4—28no—
786C4×D4—48no—
787C4×D4—48no—
788C4×D4—48no—
789C4×D4—88no—
790C4×D4—88no—
791C4×D4C2×D4116yes—
792C4×D4C2×D418yes—
793C4×D4C2×D418yes—
794C4×D4C2×D4116yes—
795#117—24no—
796#117—28no—
797#117—216no—
798#117—24no—
799#117—28no—
800#117—216no—
801#117—24no—
802#117—24no—
803#117—28no—
804#117—44no—
805#117C2×D418yes—
806#117C2×D4116yes—
807C2×C4⋊C4—28no—
808C2×C4⋊C4—28no—
809C2×C4⋊C4—24no—
810C2×C4⋊C4—28no—
811C2×C4⋊C4—216no—
812C2×C4⋊C4—48no—
813C2×C4⋊C4C2414yes—
814C2×C4⋊C4C2412yes—
815C2×C4⋊C4C2414yes—
816C2×C4⋊C4C2414yes—
817C2×C4⋊C4C2414yes—
818C2×C4⋊C4C2418yes—
819C2×C4⋊C4C2411yescharacteristic
820C2×C4⋊C4C2412yes—
821C2×C4⋊C4C2412yes—
822C2×C4⋊C4C2412yes—
823C2×C4⋊C4C2412yes—
824C2×C4⋊C4C2414yes—
825C2×C4⋊C4C2412yes—
826C2×C4⋊C4C2411yescharacteristic
827C2×C4⋊C4C2411yescharacteristic
828C2×C4⋊C4C2411yescharacteristic
829C2×C4⋊C4C2412yes—
830C2×C4⋊C4C2411yescharacteristic
831C2×C4⋊C4C2412yes—
832C2×C4⋊C4C2412yes—
833C2×C4⋊C4C2411yescharacteristic
834C2×C4⋊C4C2411yescharacteristic
835C2×C4⋊C4C2412yes—
836C2×C4⋊C4C2412yes—
837C2×C4⋊C4C2411yescharacteristic
838C2×C4⋊C4C2412yes—
839C2×C4⋊C4C2414yes—
840C2×C4⋊C4C2412yes—
841C2×C4⋊C4C2412yes—
842C2×C4⋊C4C2412yes—
843C2×C4⋊C4C2418yes—
844C2×C4⋊C4C2412yes—
845C2×C4⋊C4C2418yes—
846C2×C4⋊C4C2418yes—
847C2×C4⋊C4C2418yes—
848C2×C4⋊C4C2414yes—
849C2×C4⋊C4C2414yes—
850C2×C4⋊C4C2418yes—
851C2×C4⋊C4C2418yes—
852C2×C4⋊C4C2414yes—
853C2×C4⋊C4C2418yes—
854C2×C4⋊C4C2411yescharacteristic
855C2×C4⋊C4C2412yes—
856C2×C4⋊C4C2411yescharacteristic
857C2×C4⋊C4C2412yes—
858C2×C22⋊C4C2411yescharacteristic
859C2×C22⋊C4C2411yescharacteristic
860C2×C22⋊C4C2412yes—
861C2×C22⋊C4C2411yescharacteristic
862C2×C22⋊C4C2412yes—
863C2×C22⋊C4C2411yescharacteristic
864C2×C22⋊C4C2412yes—
865C2×C22⋊C4C2412yes—
866C2×C22⋊C4C2412yes—
867C2×C22⋊C4C2418yes—
868C2×C22⋊C4C2412yes—
869C2×C22⋊C4C2411yescharacteristic
870C2×C22⋊C4C2411yescharacteristic
871C2×C22⋊C4C2412yes—
872C2×C22⋊C4C2418yes—
873C2×C22⋊C4C2418yes—
874C2×C22⋊C4C2414yes—
875C2×C22⋊C4C2412yes—
876C2×C22⋊C4C2412yes—
877C2×C22⋊C4C2412yes—
878C2×C22⋊C4C2412yes—
879C2×C22⋊C4C2412yes—
880C2×C22⋊C4C2412yes—
881C2×C22⋊C4C2414yes—
882C2×C22⋊C4C2414yes—
883C2×C22⋊C4C2414yes—
884C2×C22⋊C4C2414yes—
885C2×C22⋊C4C2418yes—
886C2×C22⋊C4C2418yes—
887C2×C22⋊C4C2418yes—
888C2×C22⋊C4C2418yes—
889C2×C22⋊C4C2414yes—
890C2×C22⋊C4C2414yes—
891C2×C22⋊C4C2414yes—
892C2×C22⋊C4C2414yes—
893C2×C22⋊C4C2414yes—
894C2×C22⋊C4C2418yes—
895C2×C22⋊C4C2418yes—
896C2×C22⋊C4C2418yes—
897C2×C22⋊C4C2414yes—
898C2×C22⋊C4C2418yes—
899C2×C22⋊C4C2418yes—
900C2×C22⋊C4C2414yes—
901C2×C22⋊C4C2412yes—
902C2×C22⋊C4C2412yes—
903C2×C22⋊C4C2412yes—
904C2×C42—28no—
905C2×C42—24no—
906C2×C42—28no—
907C2×C42—24no—
908C2×C42C2×D418yes—
909C2×C42C2×D4116yes—
910C2×C42C2411yescharacteristic
911C2×C42C2412yes—
912C2×C42C2411yescharacteristic
913C2×C42C2418yes—
914C2×C42C2412yes—
915C2×C42C2411yescharacteristic
916C2×C42C2414yes—
917C2×C42C2411yescharacteristic
918C2×C42C2412yes—
919C2×C42C2412yes—
920C2×C42C2411yescharacteristic
921C2×C42C2411yescharacteristic
922C2×C42C2412yes—
923C2×C42C2414yes—
924C2×C42C2418yes—
925C2×C42C2411yescharacteristic
926C2×C42C2412yes—
927C2×C42C2411yescharacteristic
928C2×C42C2411yescharacteristic
929C2×C42C2412yes—
930C2×C42C2411yescharacteristic
931C2×C42C2412yes—
932#95C2412yes—
933#95C2412yes—
934#95C2414yes—
935#95C2414yes—
936#95C2418yes—
937#95C2418yes—
938#95C2412yes—
939#95C2414yes—
940#95C2412yes—
941#95C2418yes—
942#95C2418yes—
943#95C2414yes—
944#95C2418yes—
945#95C2414yes—
946#95C2418yes—
947#95C2414yes—
948#95C2418yes—
949#95C2414yes—
950#95C2414yes—
951#95C2418yes—
952#95C2418yes—
953#95C2418yes—
954#95C2418yes—
955#95C2418yes—
956#95C2418yes—
957#95C2418yes—
958C24C2514yes—
959C24C2511yescharacteristic
960C24C2512yes—
961C24C2511yescharacteristic
962C24C2512yes—
963C24C2511yescharacteristic
964#41—432no—
965#41—416no—
966#41—416no—
967#41—432no—
968#41—416no—
969#41—832no—
970C2×Q8—24no—
971C2×Q8—22no—
972C2×Q8—24no—
973C2×Q8—24no—
974C2×Q8—22no—
975C2×Q8—28no—
976C2×Q8—28no—
977C2×Q8—22no—
978C2×Q8—24no—
979C2×Q8—24no—
980C2×Q8—24no—
981C2×Q8—44no—
982C2×Q8—48no—
983C2×Q8—41no—
984C2×Q8—42no—
985C2×Q8—44no—
986C2×Q8—44no—
987C2×Q8—44no—
988C2×Q8—416no—
989C2×Q8—816no—
990C2×Q8C22×D414yes—
991C2×D4—24no—
992C2×D4—22no—
993C2×D4—28no—
994C2×D4—24no—
995C2×D4—22no—
996C2×D4—28no—
997C2×D4—22no—
998C2×D4—24no—
999C2×D4—24no—
1000C2×D4—22no—
1001C2×D4—24no—
1002C2×D4—24no—
1003C2×D4—24no—
1004C2×D4—216no—
1005C2×D4—24no—
1006C2×D4—24no—
1007C2×D4—22no—
1008C2×D4—24no—
1009C2×D4—24no—
1010C2×D4—22no—
1011C2×D4—24no—
1012C2×D4—24no—
1013C2×D4—24no—
1014C2×D4—22no—
1015C2×D4—24no—
1016C2×D4—24no—
1017C2×D4—24no—
1018C2×D4—44no—
1019C2×D4—44no—
1020C2×D4—41no—
1021C2×D4—42no—
1022C2×D4—44no—
1023C2×D4—41no—
1024C2×D4—42no—
1025C2×D4—44no—
1026C2×D4—44no—
1027C2×D4—41no—
1028C2×D4—42no—
1029C2×D4—44no—
1030C2×D4—44no—
1031C2×D4—44no—
1032C2×D4—44no—
1033C2×D4—48no—
1034C2×D4—48no—
1035C2×D4—48no—
1036C2×D4—44no—
1037C2×D4—44no—
1038C2×D4—44no—
1039C2×D4—44no—
1040C2×D4—48no—
1041C2×D4—48no—
1042C2×D4—44no—
1043C2×D4C22×D414yes—
1044C2×D4C22×D418yes—
1045C22×C4—22no—
1046C22×C4—24no—
1047C22×C4—22no—
1048C22×C4—24no—
1049C22×C4—22no—
1050C22×C4—24no—
1051C22×C4—22no—
1052C22×C4—28no—
1053C22×C4—24no—
1054C22×C4—22no—
1055C22×C4—24no—
1056C22×C4—22no—
1057C22×C4—24no—
1058C22×C4—22no—
1059C22×C4—28no—
1060C22×C4—22no—
1061C22×C4—24no—
1062C22×C4—24no—
1063C22×C4—24no—
1064C22×C4—28no—
1065C22×C4—28no—
1066C22×C4—22no—
1067C22×C4—24no—
1068C22×C4—22no—
1069C22×C4—24no—
1070C22×C4—22no—
1071C22×C4—24no—
1072C22×C4—216no—
1073C22×C4—44no—
1074C22×C4—42no—
1075C22×C4—44no—
1076C22×C4—44no—
1077C22×C4—44no—
1078C22×C4—44no—
1079C22×C4—44no—
1080C22×C4—48no—
1081C22×C4—48no—
1082C22×C4—42no—
1083C22×C4—42no—
1084C22×C4—48no—
1085C22×C4—48no—
1086C22×C4—48no—
1087C22×C4—48no—
1088C22×C4C22×D414yes—
1089C22×C4C22×D414yes—
1090C22×C4C22×D418yes—
1091C22×C4C22×D418yes—
1092C22×C4C22×D414yes—
1093C22×C4C22×D418yes—
1094C22×C42−1+414yes—
1095C22×C4C2514yes—
1096C22×C4C2514yes—
1097C22×C4C2518yes—
1098C22×C4C2512yes—
1099C22×C4C2511yescharacteristic
1100C22×C4C2511yescharacteristic
1101C22×C4C2511yescharacteristic
1102C22×C4C2512yes—
1103C22×C4C2514yes—
1104C22×C4C2518yes—
1105C22×C4C2511yescharacteristic
1106C22×C4C2511yescharacteristic
1107C22×C4C2512yes—
1108C22×C4C2511yescharacteristic
1109C22×C4C2512yes—
1110C22×C4C2511yescharacteristic
1111C22×C4C2512yes—
1112C22×C4C2511yescharacteristic
1113C22×C4C2512yes—
1114C22×C4C2511yescharacteristic
1115C22×C4C2511yescharacteristic
1116C22×C4C2511yescharacteristic
1117C22×C4C2511yescharacteristic
1118C4⋊C4—28no—
1119C4⋊C4—28no—
1120C4⋊C4—28no—
1121C4⋊C4—216no—
1122C4⋊C4—24no—
1123C4⋊C4—22no—
1124C4⋊C4—24no—
1125C4⋊C4—24no—
1126C4⋊C4—24no—
1127C4⋊C4—28no—
1128C4⋊C4—24no—
1129C4⋊C4—22no—
1130C4⋊C4—22no—
1131C4⋊C4—24no—
1132C4⋊C4—22no—
1133C4⋊C4—24no—
1134C4⋊C4—22no—
1135C4⋊C4—24no—
1136C4⋊C4—22no—
1137C4⋊C4—24no—
1138C4⋊C4—22no—
1139C4⋊C4—24no—
1140C4⋊C4—22no—
1141C4⋊C4—24no—
1142C4⋊C4—24no—
1143C4⋊C4—24no—
1144C4⋊C4—24no—
1145C4⋊C4—216no—
1146C4⋊C4—24no—
1147C4⋊C4—24no—
1148C4⋊C4—28no—
1149C4⋊C4—28no—
1150C4⋊C4—48no—
1151C4⋊C4—44no—
1152C4⋊C4—44no—
1153C4⋊C4—48no—
1154C4⋊C4—48no—
1155C4⋊C4—48no—
1156C4⋊C4—48no—
1157C4⋊C4—48no—
1158C4⋊C4—44no—
1159C4⋊C4C22×D414yes—
1160C4⋊C4C22×D418yes—
1161C4⋊C4C22×D414yes—
1162C4⋊C4C22×D418yes—
1163C22⋊C4—24no—
1164C22⋊C4—22no—
1165C22⋊C4—24no—
1166C22⋊C4—22no—
1167C22⋊C4—216no—
1168C22⋊C4—24no—
1169C22⋊C4—24no—
1170C22⋊C4—24no—
1171C22⋊C4—22no—
1172C22⋊C4—22no—
1173C22⋊C4—24no—
1174C22⋊C4—22no—
1175C22⋊C4—24no—
1176C22⋊C4—24no—
1177C22⋊C4—24no—
1178C22⋊C4—216no—
1179C22⋊C4—22no—
1180C22⋊C4—24no—
1181C22⋊C4—216no—
1182C22⋊C4—28no—
1183C22⋊C4—24no—
1184C22⋊C4—24no—
1185C22⋊C4—24no—
1186C22⋊C4—28no—
1187C22⋊C4—28no—
1188C22⋊C4—44no—
1189C22⋊C4—48no—
1190C22⋊C4—44no—
1191C22⋊C4—44no—
1192C22⋊C4—44no—
1193C22⋊C4—44no—
1194C22⋊C4—44no—
1195C22⋊C4—48no—
1196C22⋊C4—48no—
1197C22⋊C4—48no—
1198C22⋊C4—48no—
1199C22⋊C4—44no—
1200C22⋊C4—48no—
1201C22⋊C4—44no—
1202C22⋊C4—48no—
1203C22⋊C4—48no—
1204C22⋊C4—48no—
1205C22⋊C4—44no—
1206C22⋊C4C22×D418yes—
1207C22⋊C4C22×D418yes—
1208C22⋊C4C22×D418yes—
1209C42—22no—
1210C42—24no—
1211C42—22no—
1212C42—22no—
1213C42—24no—
1214C42—24no—
1215C42—22no—
1216C42—22no—
1217C42—24no—
1218C42—24no—
1219C42—22no—
1220C42—216no—
1221C42—28no—
1222C42—44no—
1223C42—48no—
1224C42C22×D418yes—
1225C42C22×D414yes—
1226C42C22×D414yes—
1227C42C22×D418yes—
1228C42C22×D414yes—
1229C42C22×D414yes—
1230C42C22×D418yes—
1231C23—21no—
1232C23—21no—
1233C23—22no—
1234C23—21no—
1235C23—22no—
1236C23—24no—
1237C23—22no—
1238C23—21no—
1239C23—22no—
1240C23—22no—
1241C23—22no—
1242C23—24no—
1243C23—22no—
1244C23—21no—
1245C23—24no—
1246C23—24no—
1247C23—21no—
1248C23—22no—
1249C23—24no—
1250C23—24no—
1251C23—22no—
1252C23—24no—
1253C23—24no—
1254C23—21no—
1255C23—22no—
1256C23—24no—
1257C23—22no—
1258C23—24no—
1259C23—24no—
1260C23C23×D414yes—
1261C23C23×D412yes—
1262C23C2×2−1+412yes—
1263C23C2611yescharacteristic
1264Q8—28no—
1265Q8—44no—
1266Q8—48no—
1267Q8—48no—
1268Q8—416no—
1269Q8—48no—
1270Q8—44no—
1271Q8—88no—
1272D4—28no—
1273D4—48no—
1274D4—44no—
1275D4—48no—
1276D4—44no—
1277D4—48no—
1278D4—48no—
1279D4—48no—
1280D4—48no—
1281D4—44no—
1282D4—48no—
1283D4—416no—
1284D4—416no—
1285D4—44no—
1286D4—48no—
1287D4—84no—
1288D4—84no—
1289D4—84no—
1290D4—816no—
1291D4—88no—
1292D4—816no—
1293C2×C4—21no—
1294C2×C4—21no—
1295C2×C4—22no—
1296C2×C4—21no—
1297C2×C4—22no—
1298C2×C4—22no—
1299C2×C4—21no—
1300C2×C4—24no—
1301C2×C4—24no—
1302C2×C4—22no—
1303C2×C4—22no—
1304C2×C4—28no—
1305C2×C4—216no—
1306C2×C4—28no—
1307C2×C4—28no—
1308C2×C4—21no—
1309C2×C4—21no—
1310C2×C4—21no—
1311C2×C4—22no—
1312C2×C4—21no—
1313C2×C4—22no—
1314C2×C4—24no—
1315C2×C4—22no—
1316C2×C4—21no—
1317C2×C4—28no—
1318C2×C4—24no—
1319C2×C4—22no—
1320C2×C4—21no—
1321C2×C4—24no—
1322C2×C4—24no—
1323C2×C4—28no—
1324C2×C4—22no—
1325C2×C4—21no—
1326C2×C4—28no—
1327C2×C4—24no—
1328C2×C4—22no—
1329C2×C4—22no—
1330C2×C4—24no—
1331C2×C4—24no—
1332C2×C4—24no—
1333C2×C4—24no—
1334C2×C4—28no—
1335C2×C4—24no—
1336C2×C4—22no—
1337C2×C4—24no—
1338C2×C4—22no—
1339C2×C4—28no—
1340C2×C4—28no—
1341C2×C4—44no—
1342C2×C4—48no—
1343C2×C4—48no—
1344C2×C4—48no—
1345C2×C4—48no—
1346C2×C4—44no—
1347C2×C4—44no—
1348C2×C4—416no—
1349C2×C4—48no—
1350C2×C4—44no—
1351C2×C4—84no—
1352C2×C4—84no—
1353C2×C4—82no—
1354C2×C4—82no—
1355C2×C4—816no—
1356C2×C4—88no—
1357C2×C4—168no—
1358C2×C4C23×D414yes—
1359C2×C4C23×D412yes—
1360C2×C4C23×D414yes—
1361C2×C4C23×D414yes—
1362C2×C4C23×D412yes—
1363C2×C4C23×D412yes—
1364C2×C4C23×D412yes—
1365C2×C4C23×D412yes—
1366C2×C4C23×D412yes—
1367C2×C4C2×2−1+412yes—
1368C2×C4C2×2−1+412yes—
1369C2×C4#58514yes—
1370C2×C4#58512yes—
1371C22—22no—
1372C22—22no—
1373C22—24no—
1374C22—22no—
1375C22—24no—
1376C22—24no—
1377C22—22no—
1378C22—24no—
1379C22—41no—
1380C22—44no—
1381C22—42no—
1382C22—44no—
1383C22—42no—
1384C22—42no—
1385C22—41no—
1386C22—41no—
1387C22—42no—
1388C22—44no—
1389C22—44no—
1390C22—42no—
1391C22—41no—
1392C22—44no—
1393C22—44no—
1394C22—42no—
1395C22—44no—
1396C22—44no—
1397C22—42no—
1398C22—44no—
1399C22—44no—
1400C22—42no—
1401C22—41no—
1402C22—44no—
1403C22C24×D411yescharacteristic
1404C22C22×2−1+411yescharacteristic
1405C22C2×#58511yescharacteristic
1406C22C2×#58512yes—
1407C22H(7,𝔽2)12yes—
1408C4—22no—
1409C4—24no—
1410C4—22no—
1411C4—22no—
1412C4—24no—
1413C4—22no—
1414C4—22no—
1415C4—24no—
1416C4—41no—
1417C4—42no—
1418C4—41no—
1419C4—48no—
1420C4—42no—
1421C4—41no—
1422C4—44no—
1423C4—44no—
1424C4—48no—
1425C4—41no—
1426C4—44no—
1427C4—41no—
1428C4—42no—
1429C4#344914yes—
1430C4#348914yes—
1431C2—42no—
1432C2—42no—
1433C2—44no—
1434C2—81no—
1435C2—82no—
1436C2—84no—
1437C2C2×#344911yescharacteristic
1438C2C2×#348911yescharacteristic
1439C2#6285211yescharacteristic
1440C2#6292612yes—
1441C2#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×#3511C2semidirect
2. C2×#3480C2semidirect
3. #42909C2semidirect
4. #42908C2semidirect
5. #42891C2semidirect
6. #42887C2semidirect
7. #42156C2semidirect
8. #41959C2semidirect
9. #40607C2semidirect
10. #40603C2semidirect
11. #39469C2semidirect
12. #39462C2semidirect
13. #38922C2semidirect
14. #38914C2semidirect
15. #37632C2semidirect
16. #37621C2semidirect
17. #37560C2semidirect
18. #37554C2semidirect
19. #36544C2semidirect
20. #36492C2semidirect
21. #35923C2semidirect
22. #35912C2semidirect
23. #35759C2semidirect
24. #35689C2semidirect
25. #35334C2semidirect
26. #35279C2semidirect
27. #34609C2semidirect
28. #34609C2semidirect
29. #34191C2semidirect
337. C4×#41D4semidirect

Maximal subgroups

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

subgroupindex
C2×#35112
C2×#34802
#429092
#429082
#428912
#428872
#421562
#419592
#406072
#406032
#394692
#394622
#389222
#389142
#376322
#376212
#375602
#375542
#365442
#364922
#359232
#359122
#357592
#356892
#353342
#352792
#346092
#341912