Finite Group Databasebeta

← #7674368

Subgroups — #7674368

Order 512.

7010 conjugacy classes of subgroups.

The subgroup lattice has 1428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3493C211yesmaximal, characteristic, complemented
2C2×#3492C211yesmaximal, characteristic, complemented
3#45333C214yesmaximal, complemented
4#45264C214yesmaximal, complemented
5#45135C214yesmaximal, complemented
6#44928C214yesmaximal, complemented
7#39489C212yesmaximal, complemented
8#39488C212yesmaximal, complemented
9#39485C212yesmaximal, complemented
10#39485C212yesmaximal, complemented
11#37869C212yesmaximal, complemented
12#37868C212yesmaximal, complemented
13#37865C212yesmaximal, complemented
14#37864C212yesmaximal, complemented
15#37791C218yesmaximal, complemented
16#37789C218yesmaximal, complemented
17#35620C211yesmaximal, characteristic, complemented
18#35618C211yesmaximal, characteristic, complemented
19#35532C211yesmaximal, characteristic, complemented
20#35530C211yesmaximal, characteristic, complemented
21#35275C211yesmaximal, characteristic, complemented
22#35273C211yesmaximal, characteristic, complemented
23#35227C211yesmaximal, characteristic, complemented
24#35157C211yesmaximal, characteristic, complemented
25#34633C211yesmaximal, characteristic, complemented
26#34208C211yesmaximal, characteristic, complemented
27#34184C211yesmaximal, characteristic, complemented
28#34065C211yesmaximal, characteristic, complemented
29C2×#2317C211yesmaximal, characteristic, complemented
30#3493—216no—
31#3492—216no—
32C2×#556C2212yes—
33C2×#556C2212yes—
34C2×#555C2212yes—
35C2×#555C2212yes—
36C2×#554C2212yes—
37C2×#554C2212yes—
38C2×#553C2212yes—
39C2×#553C2212yes—
40C2×#553C2212yes—
41C2×#553C2212yes—
42C2×#552C2212yes—
43C2×#552C2212yes—
44C2×#552C2212yes—
45C2×#552C2212yes—
46C2×#547C2212yes—
47C2×#547C2212yes—
48C2×#544C2211yescharacteristic
49C2×#544C2211yescharacteristic
50C2×#539C2214yes—
51C2×#538C2214yes—
52C2×#537C2211yescharacteristic
53C2×#537C2211yescharacteristic
54C2×#532C2211yescharacteristic
55C2×#529C2214yes—
56C2×#525C2211yescharacteristic
57C2×#525C2214yes—
58C2×#525C2211yescharacteristic
59C2×#525C2211yescharacteristic
60C2×#520C2211yescharacteristic
61C2×#520C2211yescharacteristic
62C2×#520C2211yescharacteristic
63C2×#520C2211yescharacteristic
64C2×C4×#41C2211yescharacteristic
65C22×#117C2211yescharacteristic
66C22×#117C2211yescharacteristic
67C23×C4⋊C4C2211yescharacteristic
68#2868C2212yescomplemented
69#2859C2212yescomplemented
70#2857C2212yescomplemented
71#2856C2212yescomplemented
72#2853C2214yes—
73#2849C2214yes—
74#2725C2218yescomplemented
75#2725C2218yescomplemented
76#2723C2218yescomplemented
77#2722C2218yescomplemented
78#2719C2218yescomplemented
79#2718C2218yes—
80#2718C2218yescomplemented
81#2717C2218yes—
82#2706C2218yes—
83#2701C2218yes—
84#2701C2218yes—
85#2698C2218yes—
86#2674C2218yes—
87#2674C2218yescomplemented
88#2672C2218yescomplemented
89#2671C2218yes—
90#2660C2212yescomplemented
91#2660C2212yescomplemented
92#2623C2214yes—
93#2622C2214yes—
94#2621C2211yescharacteristic
95#2621C2211yescharacteristic
96#2620C2211yescharacteristic
97#2620C2211yescharacteristic
98#2620C2211yescharacteristic
99#2620C2211yescharacteristic
100#2620C2212yescomplemented
101#2620C2212yescomplemented
102#2619C2211yescharacteristic
103#2619C2211yescharacteristic
104#2618C2214yes—
105#2617C2214yes—
106#2568C2212yescomplemented
107#2567C2212yescomplemented
108#2566C2212yescomplemented
109#2566C2212yescomplemented
110#2565C2212yescomplemented
111#2565C2212yescomplemented
112#2563C2212yescomplemented
113#2552C2214yescomplemented
114#2551C2214yescomplemented
115#2542C2212yescomplemented
116#2538C2214yescomplemented
117#2537C2214yescomplemented
118#2504C2212yes—
119#2504C2212yescomplemented
120#2503C2212yes—
121#2503C2212yescomplemented
122#2502C2212yes—
123#2502C2212yescomplemented
124#2501C2212yes—
125#2501C2212yescomplemented
126#2500C2212yes—
127#2500C2212yes—
128#2500C2212yescomplemented
129#2500C2212yescomplemented
130#2499C2212yes—
131#2499C2212yes—
132#2499C2212yescomplemented
133#2499C2212yescomplemented
134#2487C2214yes—
135#2486C2214yes—
136#2485C2214yes—
137#2485C2214yes—
138#2479C2218yescomplemented
139#2478C2218yes—
140#2470C2218yes—
141#2470C2218yescomplemented
142#2466C2218yes—
143#2466C2218yescomplemented
144#2462C2218yescomplemented
145#2461C2218yes—
146#2450C2218yes—
147#2449C2218yes—
148#2444C2218yes—
149#2443C2218yes—
150#2442C2214yescomplemented
151#2441C2218yescomplemented
152#2441C2214yescomplemented
153#2440C2218yes—
154#2440C2214yescomplemented
155#2439C2214yescomplemented
156#2438C2218yescomplemented
157#2432C2218yes—
158#2430C2218yes—
159#2429C2218yescomplemented
160#2425C2218yescomplemented
161#2423C2214yescomplemented
162#2422C2218yes—
163#2422C2214yescomplemented
164#2421C2214yescomplemented
165#2420C2214yescomplemented
166#2419C2218yes—
167#2416C2218yes—
168#2392C2214yes—
169#2392C2214yes—
170#2364C2218yes—
171#2352C2214yescomplemented
172#2352C2214yescomplemented
173#2351C2214yescomplemented
174#2349C2218yes—
175#2349C2214yescomplemented
176#2328C2212yescomplemented
177#2327C2212yescomplemented
178#2324C2212yes—
179#2324C2212yes—
180#2323C2212yes—
181#2323C2212yes—
182#2322C2214yes—
183#2321C2214yes—
184#2317C2214yes—
185#2317C2212yes—
186#2317C2212yes—
187#2317C2214yes—
188#2317C2212yes—
189#2317C2212yes—
190#2317C2211yescharacteristic
191#2317C2211yescharacteristic
192#2317C2211yescharacteristic
193#2317C2211yescharacteristic
194#2317C2212yescomplemented
195#2317C2212yescomplemented
196#2311C2211yescharacteristic
197#2311C2211yescharacteristic
198#2311C2211yescharacteristic
199#2311C2211yescharacteristic
200C4×#124C2212yescomplemented
201C4×#124C2212yescomplemented
202#2297C2211yescharacteristic
203#2297C2211yescharacteristic
204#2297C2211yescharacteristic
205#2296C2211yescharacteristic
206#2293C2212yes—
207#2293C2212yes—
208C2×#389C2214yes—
209#2290C2212yes—
210#2290C2212yes—
211C2×#385C2214yes—
212#2285C2211yescharacteristic
213#2285C2212yescomplemented
214C2×#384C2211yescharacteristic
215C2×#384C2211yescharacteristic
216C2×#382C2211yescharacteristic
217C2×#382C2211yescharacteristic
218C2×#382C2212yescomplemented
219#2280C2211yescharacteristic
220C4×#117C2211yescharacteristic
221C22×#41C2311yescharacteristic
222C22×#41C2311yescharacteristic
223C22×#41C2311yescharacteristic
224C22×#41C2314yes—
225C24×C4C2311yescharacteristic
226C24×C4C2312yes—
227#556—216no—
228#556—216no—
229#555—216no—
230#555—216no—
231#554—216no—
232#554—216no—
233#553—216no—
234#553—216no—
235#553—216no—
236#553—216no—
237#552—216no—
238#552—216no—
239#552—216no—
240#552—216no—
241#547—216no—
242#547—216no—
243#544—28no—
244#544—28no—
245#539—232no—
246#538—232no—
247#537—28no—
248#537—28no—
249#532—28no—
250C2×C4⋊Q8C2312yes—
251C2×C4⋊Q8C2312yes—
252C2×C4⋊Q8C2311yescharacteristic
253C2×C4⋊Q8C2312yes—
254C2×C4⋊Q8C2312yes—
255C2×C4⋊Q8C2318yes—
256C2×#127C2311yescharacteristic
257#529—232no—
258C2×#126C2314yes—
259C2×#126C2314yes—
260C2×#126C2314yes—
261C2×#126C2314yes—
262C2×#126C2314yes—
263C2×#126C2314yes—
264C2×#125C2312yes—
265C2×#125C2312yes—
266C2×#125C2314yes—
267C2×#125C2314yes—
268C2×#125C2314yes—
269C2×#125C2312yes—
270C2×#125C2312yes—
271C2×#124C2311yescharacteristic
272C2×#124C2311yescharacteristic
273C2×#124C2314yes—
274C2×#124C2314yes—
275C2×#124C2314yes—
276#525—28no—
277#525—28no—
278#525—232no—
279#525D4116yescomplemented
280C2×#123C2312yes—
281C2×#123C2312yes—
282C2×#123C2314yes—
283C2×#123C2314yes—
284C2×#123C2314yes—
285C2×#123C2314yes—
286C2×#123C2314yes—
287C2×#123C2314yes—
288C2×#123C2318yes—
289C2×#123C2318yes—
290C2×#123C2312yes—
291C2×C22⋊Q8C2312yes—
292C2×C22⋊Q8C2312yes—
293C2×C22⋊Q8C2311yescharacteristic
294C2×C22⋊Q8C2311yescharacteristic
295C2×C22⋊Q8C2311yescharacteristic
296C2×C22⋊Q8C2311yescharacteristic
297C2×C22⋊Q8C2314yes—
298C2×C22⋊Q8C2314yes—
299C2×C22⋊Q8C2314yes—
300C2×C22⋊Q8C2314yes—
301C2×C22⋊Q8C2312yes—
302C2×C22⋊Q8C2312yes—
303C2×C22⋊Q8C2314yes—
304C2×C22⋊Q8C2318yes—
305C2×C22⋊Q8C2311yescharacteristic
306C2×C22⋊Q8C2311yescharacteristic
307C2×#121C2312yes—
308C2×#121C2312yes—
309C2×#121C2314yes—
310C2×#121C2311yescharacteristic
311C2×#121C2311yescharacteristic
312C2×#121C2311yescharacteristic
313C2×#121C2311yescharacteristic
314C2×#121C2314yes—
315C2×#121C2314yes—
316C2×#121C2314yes—
317C2×#121C2314yes—
318C2×#121C2312yes—
319C2×#121C2312yes—
320C2×#121C2314yes—
321C2×#121C2318yes—
322C2×#121C2311yescharacteristic
323C2×#121C2311yescharacteristic
324C2×#120C2312yes—
325C2×#120C2312yes—
326C2×#120C2312yes—
327#520—28no—
328#520—28no—
329#520—28no—
330#520—28no—
331C4×#41—28no—
332C2×C4×Q8C2312yes—
333C2×C4×Q8C2312yes—
334C2×C4×Q8C2312yes—
335C2×C4×Q8C2312yes—
336C2×C4×Q8C2312yes—
337C2×C4×Q8C2314yes—
338C2×C4×D4C2312yes—
339C2×C4×D4C2312yes—
340C2×C4×D4C2314yes—
341C2×C4×D4C2312yes—
342C2×C4×D4C2314yes—
343C2×C4×D4C2314yes—
344C2×C4×D4C2312yes—
345C2×C4×D4C2312yes—
346C2×C4×D4C2314yes—
347C2×C4×D4C2314yes—
348C2×C4×D4C2314yes—
349C2×C4×D4C2312yes—
350C2×C4×D4C2312yes—
351C2×C4×D4C2312yes—
352C2×C4×D4C2312yes—
353C2×C4×D4C2314yes—
354C2×C4×D4C2314yes—
355C2×C4×D4C2314yes—
356C2×C4×D4C2312yes—
357C2×C4×D4C2312yes—
358C2×#117—28no—
359C2×#117—28no—
360C2×#117C2311yescharacteristic
361C2×#117C2311yescharacteristic
362C2×#117C2312yes—
363C2×#117C2312yes—
364C2×#117C2311yescharacteristic
365C2×#117C2311yescharacteristic
366C2×#117C2311yescharacteristic
367C2×#117C2311yescharacteristic
368C2×#117C2312yes—
369C2×#117C2312yes—
370C2×#117C2312yes—
371C2×#117C2312yes—
372C2×#117C2311yescharacteristic
373C2×#117C2311yescharacteristic
374C2×#117C2312yes—
375C2×#117C2312yes—
376C2×#117C2312yes—
377C2×#117C2312yes—
378C2×#117C2312yes—
379C2×#117C2314yes—
380C2×#117C2314yes—
381C2×#117C2314yes—
382C2×#117C2311yescharacteristic
383C22×C4⋊C4—28no—
384C22×C4⋊C4C2311yescharacteristic
385C22×C4⋊C4C2311yescharacteristic
386C22×C4⋊C4C2311yescharacteristic
387C22×C4⋊C4C2311yescharacteristic
388C22×C4⋊C4C2312yes—
389C22×C4⋊C4C2312yes—
390C22×C4⋊C4C2312yes—
391C22×C4⋊C4C2312yes—
392C22×C4⋊C4C2312yes—
393C22×C4⋊C4C2312yes—
394C22×C4⋊C4C2312yes—
395C22×C4⋊C4C2312yes—
396C22×C4⋊C4C2312yes—
397C22×C4⋊C4C2312yes—
398C22×C4⋊C4C2314yes—
399C22×C4⋊C4C2314yes—
400C22×C22⋊C4C2312yes—
401C22×C22⋊C4C2312yes—
402C22×C42C2312yes—
403C22×C42C2312yes—
404C22×C42C2311yescharacteristic
405C22×C42C2311yescharacteristic
406#400C2318yes—
407#400C2318yes—
408#400C2318yes—
409#399C2318yes—
410#399C2318yes—
411#399C2318yes—
412#398C2318yes—
413#398C2318yes—
414#398C2314yes—
415#398C2314yes—
416#398C2318yes—
417#398C2318yes—
418#398C2318yes—
419#398C2318yes—
420#397C2314yes—
421#397C2314yes—
422#397C2318yes—
423#397C2318yes—
424#397C2318yes—
425#397C2318yes—
426#397C2318yes—
427#397C2318yes—
428#396C2318yes—
429#396C2318yes—
430#396C2314yes—
431#396C2314yes—
432#396C2314yes—
433#396C2314yes—
434#396C2318yes—
435#396C2318yes—
436#395C2318yes—
437#395C2318yes—
438#395C2318yes—
439#394C2314yes—
440#394C2314yes—
441#394C2314yes—
442#394C2314yes—
443#394C2314yes—
444#394C2314yes—
445#394C2318yes—
446#394C2318yes—
447#394C2318yes—
448#394C2318yes—
449#394C2318yes—
450#394C2318yes—
451#393C2318yes—
452#392C2314yes—
453#392C2314yes—
454#391C2311yescharacteristic
455#391C2311yescharacteristic
456#391C2312yes—
457#391C2312yes—
458#391C2312yes—
459#391C2312yes—
460#391C2311yescharacteristic
461#391C2311yescharacteristic
462#391C2318yes—
463#391C2312yes—
464#390C2311yescharacteristic
465#390C2312yes—
466#390C2311yescharacteristic
467#390C2311yescharacteristic
468#390C2312yes—
469#390C2312yes—
470#390C2312yes—
471#390C2314yes—
472#390C2314yes—
473#390C2312yes—
474#390C2318yes—
475#390C2311yescharacteristic
476#389C2318yes—
477#389C2318yes—
478#389C2318yes—
479#389C2318yes—
480#389C2318yes—
481#389C2314yes—
482#389C2314yes—
483#389C2314yes—
484#389C2314yes—
485#389C2318yes—
486#389C2318yes—
487#389C2314yes—
488#389C2314yes—
489#389C2312yes—
490#389C2312yes—
491#389C2318yes—
492#389C2318yes—
493#389C2318yes—
494#388C2314yes—
495#388C2314yes—
496#388C2314yes—
497#388C2314yes—
498#388C2314yes—
499#388C2314yes—
500#388C2318yes—
501#388C2318yes—
502#388C2318yes—
503#388C2318yes—
504#388C2318yes—
505#388C2318yes—
506#387C2318yes—
507#387C2318yes—
508#387C2314yes—
509#387C2314yes—
510#387C2318yes—
511#387C2318yes—
512#387C2318yes—
513#387C2318yes—
514#387C2318yes—
515#387C2318yes—
516#386C2314yes—
517#386C2314yes—
518#386C2314yes—
519#386C2314yes—
520#386C2314yes—
521#386C2314yes—
522#386C2314yes—
523#386C2318yes—
524#386C2318yes—
525#386C2318yes—
526#386C2314yes—
527#386C2314yes—
528#386C2318yes—
529#385C2318yes—
530#385C2318yes—
531#385C2318yes—
532#385C2318yes—
533#385C2318yes—
534#385C2318yes—
535#385C2314yes—
536#385C2314yes—
537#385C2314yes—
538#385C2314yes—
539#385C2318yes—
540#385C2318yes—
541#385C2314yes—
542#385C2314yes—
543#385C2314yes—
544#385C2318yes—
545#385C2318yes—
546#384C2312yes—
547#384C2312yes—
548#384C2312yes—
549#384C2312yes—
550#384C2312yes—
551#384C2312yes—
552#384C2314yes—
553#384C2314yes—
554#384C2312yes—
555#384C2312yes—
556#384C2311yescharacteristic
557#384C2311yescharacteristic
558#384C2318yes—
559#382C2312yes—
560#382C2312yes—
561#382C2312yes—
562#382C2312yes—
563#382C2312yes—
564#382C2312yes—
565#382C2314yes—
566#382C2314yes—
567#382C2312yes—
568#382C2312yes—
569#382C2318yes—
570#382C2311yescharacteristic
571#382C2311yescharacteristic
572#381C2312yes—
573#381C2318yes—
574#381C2318yes—
575#380C2318yes—
576#380C2314yes—
577#380C2314yes—
578#380C2314yes—
579#380C2314yes—
580#380C2312yes—
581#380C2312yes—
582#380C2318yes—
583#380C2314yes—
584#380C2318yes—
585#379C2312yes—
586C4×C4⋊C4C2312yes—
587C4×C4⋊C4C2312yes—
588C4×C4⋊C4C2312yes—
589C4×C4⋊C4C2312yes—
590C4×C4⋊C4C2318yes—
591C4×C4⋊C4C2314yes—
592C4×C22⋊C4C2314yes—
593C4×C22⋊C4C2318yes—
594C4×C22⋊C4C2318yes—
595C4×C22⋊C4C2314yes—
596C4×C22⋊C4C2314yes—
597C4×C22⋊C4C2312yes—
598C4×C22⋊C4C2312yes—
599C4×C22⋊C4C2312yes—
600C4×C22⋊C4C2312yes—
601#376C2312yes—
602C2×#95C2314yes—
603C2×#95C2318yes—
604C2×#95C2314yes—
605C43C2312yes—
606C25C2411yescharacteristic
607C2×#41—216no—
608C2×#41—24no—
609C2×#41—24no—
610C2×#41—24no—
611C2×#41—24no—
612C2×#41—24no—
613C2×#41—24no—
614C2×#41—24no—
615C2×#41—24no—
616C2×#41—88no—
617C2×#41C2×D418yes—
618C22×Q8C2411yescharacteristic
619C22×Q8C2411yescharacteristic
620C22×Q8C2411yescharacteristic
621C22×Q8C2414yes—
622C22×Q8C2414yes—
623C22×D4C2412yes—
624C22×D4C2412yes—
625C22×D4C2411yescharacteristic
626C22×D4C2411yescharacteristic
627C22×D4C2412yes—
628C22×D4C2411yescharacteristic
629C22×D4C2412yes—
630C22×D4C2412yes—
631C22×D4C2412yes—
632C22×D4C2412yes—
633C22×D4C2414yes—
634C22×D4C2414yes—
635C22×D4C2414yes—
636C22×D4C2412yes—
637C22×D4C2412yes—
638C23×C4—24no—
639C23×C4—24no—
640C23×C4—28no—
641C23×C4—84no—
642C23×C4C2×D418yes—
643C23×C4C2412yes—
644C23×C4C2412yes—
645C23×C4C2411yescharacteristic
646C23×C4C2411yescharacteristic
647C23×C4C2411yescharacteristic
648C23×C4C2411yescharacteristic
649C23×C4C2411yescharacteristic
650C23×C4C2412yes—
651C23×C4C2412yes—
652C23×C4C2412yes—
653C23×C4C2412yes—
654C23×C4C2412yes—
655C23×C4C2412yes—
656C23×C4C2414yes—
657C23×C4C2414yes—
658C23×C4C2414yes—
659C23×C4C2414yes—
660C23×C4C2414yes—
661C23×C4C2414yes—
662C23×C4C2414yes—
663C23×C4C2412yes—
664C23×C4C2411yescharacteristic
665C4⋊Q8—28no—
666C4⋊Q8—28no—
667C4⋊Q8—28no—
668C4⋊Q8—28no—
669C4⋊Q8—24no—
670C4⋊Q8—88no—
671#127—24no—
672#126—216no—
673#126—216no—
674#126—216no—
675#126—216no—
676#126—216no—
677#126—216no—
678#125—216no—
679#125—216no—
680#125—216no—
681#125—28no—
682#125—28no—
683#125—28no—
684#125—28no—
685#124—216no—
686#124—216no—
687#124—216no—
688#124—24no—
689#124—24no—
690#123—216no—
691#123—216no—
692#123—28no—
693#123—28no—
694#123—216no—
695#123—216no—
696#123—216no—
697#123—216no—
698#123—88no—
699#123—88no—
700#123C2×D4116yes—
701C22⋊Q8—28no—
702C22⋊Q8—28no—
703C22⋊Q8—24no—
704C22⋊Q8—24no—
705C22⋊Q8—24no—
706C22⋊Q8—24no—
707C22⋊Q8—28no—
708C22⋊Q8—28no—
709C22⋊Q8—216no—
710C22⋊Q8—216no—
711C22⋊Q8—216no—
712C22⋊Q8—216no—
713C22⋊Q8—216no—
714C22⋊Q8—88no—
715C22⋊Q8C2×D418yes—
716C22⋊Q8C2×D418yes—
717#121—216no—
718#121—216no—
719#121—216no—
720#121—28no—
721#121—28no—
722#121—216no—
723#121—216no—
724#121—24no—
725#121—24no—
726#121—24no—
727#121—24no—
728#121—28no—
729#121—28no—
730#121—216no—
731#121—88no—
732#121C2×D418yes—
733#121C2×D418yes—
734#120—28no—
735#120—28no—
736#120C2×D4116yes—
737C4×Q8—28no—
738C4×Q8—28no—
739C4×Q8—216no—
740C4×Q8—28no—
741C4×Q8—28no—
742C4×Q8—28no—
743C4×D4—216no—
744C4×D4—216no—
745C4×D4—28no—
746C4×D4—28no—
747C4×D4—216no—
748C4×D4—28no—
749C4×D4—28no—
750C4×D4—28no—
751C4×D4—28no—
752C4×D4—216no—
753C4×D4—216no—
754C4×D4—216no—
755C4×D4—216no—
756C4×D4—216no—
757C4×D4—28no—
758C4×D4—28no—
759C4×D4—28no—
760C4×D4—216no—
761C4×D4C2×D4116yes—
762C4×D4C2×D4116yes—
763#117—28no—
764#117—28no—
765#117—28no—
766#117—28no—
767#117—24no—
768#117—24no—
769#117—28no—
770#117—28no—
771#117—24no—
772#117—24no—
773#117—28no—
774#117—28no—
775#117—216no—
776#117—216no—
777#117—216no—
778#117—24no—
779#117—24no—
780#117—24no—
781#117—24no—
782#117—28no—
783#117—28no—
784#117—28no—
785#117C2×D418yes—
786C2×C4⋊C4—24no—
787C2×C4⋊C4—24no—
788C2×C4⋊C4—28no—
789C2×C4⋊C4—28no—
790C2×C4⋊C4—28no—
791C2×C4⋊C4—28no—
792C2×C4⋊C4—28no—
793C2×C4⋊C4—24no—
794C2×C4⋊C4—24no—
795C2×C4⋊C4—28no—
796C2×C4⋊C4—28no—
797C2×C4⋊C4—28no—
798C2×C4⋊C4—28no—
799C2×C4⋊C4—28no—
800C2×C4⋊C4—84no—
801C2×C4⋊C4—84no—
802C2×C4⋊C4C2412yes—
803C2×C4⋊C4C2412yes—
804C2×C4⋊C4C2412yes—
805C2×C4⋊C4C2412yes—
806C2×C4⋊C4C2414yes—
807C2×C4⋊C4C2414yes—
808C2×C4⋊C4C2412yes—
809C2×C4⋊C4C2412yes—
810C2×C4⋊C4C2411yescharacteristic
811C2×C4⋊C4C2411yescharacteristic
812C2×C4⋊C4C2412yes—
813C2×C4⋊C4C2412yes—
814C2×C4⋊C4C2412yes—
815C2×C4⋊C4C2412yes—
816C2×C4⋊C4C2412yes—
817C2×C4⋊C4C2412yes—
818C2×C4⋊C4C2414yes—
819C2×C4⋊C4C2414yes—
820C2×C4⋊C4C2414yes—
821C2×C4⋊C4C2414yes—
822C2×C4⋊C4C2411yescharacteristic
823C2×C4⋊C4C2411yescharacteristic
824C2×C4⋊C4C2412yes—
825C2×C4⋊C4C2412yes—
826C2×C4⋊C4C2414yes—
827C2×C4⋊C4C2414yes—
828C2×C4⋊C4C2414yes—
829C2×C4⋊C4C2414yes—
830C2×C4⋊C4C2414yes—
831C2×C4⋊C4C2412yes—
832C2×C4⋊C4C2412yes—
833C2×C4⋊C4C2414yes—
834C2×C4⋊C4C2412yes—
835C2×C4⋊C4C2414yes—
836C2×C4⋊C4C2414yes—
837C2×C4⋊C4C2414yes—
838C2×C4⋊C4C2412yes—
839C2×C4⋊C4C2414yes—
840C2×C4⋊C4C2418yes—
841C2×C4⋊C4C2418yes—
842C2×C4⋊C4C2418yes—
843C2×C4⋊C4C2418yes—
844C2×C4⋊C4C2414yes—
845C2×C4⋊C4C2418yes—
846C2×C4⋊C4C2418yes—
847C2×C4⋊C4C2418yes—
848C2×C4⋊C4C2414yes—
849C2×C4⋊C4C2414yes—
850C2×C4⋊C4C2418yes—
851C2×C4⋊C4C2414yes—
852C2×C4⋊C4C2411yescharacteristic
853C2×C4⋊C4C2411yescharacteristic
854C2×C4⋊C4C2412yes—
855C2×C4⋊C4C2412yes—
856C2×C22⋊C4—28no—
857C2×C22⋊C4—28no—
858C2×C22⋊C4C2414yes—
859C2×C22⋊C4C2414yes—
860C2×C22⋊C4C2412yes—
861C2×C22⋊C4C2412yes—
862C2×C22⋊C4C2412yes—
863C2×C22⋊C4C2412yes—
864C2×C22⋊C4C2412yes—
865C2×C22⋊C4C2412yes—
866C2×C22⋊C4C2412yes—
867C2×C22⋊C4C2412yes—
868C2×C22⋊C4C2414yes—
869C2×C22⋊C4C2414yes—
870C2×C22⋊C4C2414yes—
871C2×C22⋊C4C2414yes—
872C2×C22⋊C4C2412yes—
873C2×C22⋊C4C2414yes—
874C2×C22⋊C4C2414yes—
875C2×C22⋊C4C2414yes—
876C2×C22⋊C4C2412yes—
877C2×C22⋊C4C2412yes—
878C2×C22⋊C4C2412yes—
879C2×C22⋊C4C2412yes—
880C2×C22⋊C4C2412yes—
881C2×C22⋊C4C2414yes—
882C2×C22⋊C4C2414yes—
883C2×C22⋊C4C2412yes—
884C2×C22⋊C4C2412yes—
885C2×C22⋊C4C2414yes—
886C2×C22⋊C4C2414yes—
887C2×C22⋊C4C2418yes—
888C2×C22⋊C4C2418yes—
889C2×C22⋊C4C2414yes—
890C2×C22⋊C4C2414yes—
891C2×C22⋊C4C2414yes—
892C2×C22⋊C4C2418yes—
893C2×C22⋊C4C2414yes—
894C2×C22⋊C4C2414yes—
895C2×C22⋊C4C2418yes—
896C2×C22⋊C4C2414yes—
897C2×C22⋊C4C2414yes—
898C2×C22⋊C4C2414yes—
899C2×C22⋊C4C2412yes—
900C2×C22⋊C4C2412yes—
901C2×C22⋊C4C2412yes—
902C2×C22⋊C4C2412yes—
903C2×C22⋊C4C2412yes—
904C2×C42—28no—
905C2×C42—24no—
906C2×C42—28no—
907C2×C42#4118yescomplemented
908C2×C42C2414yes—
909C2×C42C2414yes—
910C2×C42C2414yes—
911C2×C42C2414yes—
912C2×C42C2414yes—
913C2×C42C2414yes—
914C2×C42C2412yes—
915C2×C42C2412yes—
916C2×C42C2411yescharacteristic
917C2×C42C2411yescharacteristic
918C2×C42C2412yes—
919C2×C42C2412yes—
920C2×C42C2412yes—
921C2×C42C2414yes—
922C2×C42C2414yes—
923C2×C42C2414yes—
924C2×C42C2412yes—
925C2×C42C2411yescharacteristic
926C2×C42C2412yes—
927C2×C42C2411yescharacteristic
928#95C2418yes—
929#95C2414yes—
930#95C2418yes—
931#95C2418yes—
932#95C2418yes—
933#95C2418yes—
934#95C2418yes—
935#95C2414yes—
936#95C2414yes—
937#95C2418yes—
938#95C2414yes—
939#95C2414yes—
940#95C2418yes—
941#95C2414yes—
942#95C2414yes—
943#95C2414yes—
944#95C2414yes—
945#95C2414yes—
946#95C2414yes—
947#95C2414yes—
948#95C2414yes—
949#95C2414yes—
950#95C2418yes—
951#95C2418yes—
952#95C2418yes—
953#95C2418yes—
954C24—22no—
955C24—22no—
956C24—42no—
957C24—42no—
958C24C22×D414yes—
959C24C2512yes—
960C24C2512yes—
961C24C2511yescharacteristic
962C24C2511yescharacteristic
963C24C2512yes—
964C24C2511yescharacteristic
965#41—232no—
966#41—416no—
967#41—416no—
968#41—832no—
969C2×Q8—22no—
970C2×Q8—22no—
971C2×Q8—28no—
972C2×Q8—28no—
973C2×Q8—22no—
974C2×Q8—22no—
975C2×Q8—22no—
976C2×Q8—22no—
977C2×Q8—22no—
978C2×Q8—22no—
979C2×Q8—48no—
980C2×Q8—48no—
981C2×Q8C22×D414yes—
982C2×D4—24no—
983C2×D4—24no—
984C2×D4—24no—
985C2×D4—24no—
986C2×D4—24no—
987C2×D4—24no—
988C2×D4—24no—
989C2×D4—24no—
990C2×D4—24no—
991C2×D4—24no—
992C2×D4—24no—
993C2×D4—24no—
994C2×D4—28no—
995C2×D4—28no—
996C2×D4—22no—
997C2×D4—22no—
998C2×D4—22no—
999C2×D4—22no—
1000C2×D4—22no—
1001C2×D4—28no—
1002C2×D4—22no—
1003C2×D4—22no—
1004C2×D4—22no—
1005C2×D4—44no—
1006C2×D4—44no—
1007C2×D4—44no—
1008C2×D4—44no—
1009C2×D4—44no—
1010C2×D4—48no—
1011C2×D4—48no—
1012C2×D4—44no—
1013C2×D4—44no—
1014C2×D4—44no—
1015C2×D4C22×D418yes—
1016C2×D4C22×D414yes—
1017C2×D4C22×D418yes—
1018C2×D4C22×D418yes—
1019C22×C4—22no—
1020C22×C4—22no—
1021C22×C4—232no—
1022C22×C4—24no—
1023C22×C4—22no—
1024C22×C4—22no—
1025C22×C4—22no—
1026C22×C4—22no—
1027C22×C4—22no—
1028C22×C4—22no—
1029C22×C4—22no—
1030C22×C4—22no—
1031C22×C4—24no—
1032C22×C4—28no—
1033C22×C4—24no—
1034C22×C4—24no—
1035C22×C4—24no—
1036C22×C4—24no—
1037C22×C4—28no—
1038C22×C4—24no—
1039C22×C4—28no—
1040C22×C4—28no—
1041C22×C4—24no—
1042C22×C4—24no—
1043C22×C4—24no—
1044C22×C4—24no—
1045C22×C4—24no—
1046C22×C4—24no—
1047C22×C4—28no—
1048C22×C4—28no—
1049C22×C4—28no—
1050C22×C4—42no—
1051C22×C4—42no—
1052C22×C4—48no—
1053C22×C4—42no—
1054C22×C4—42no—
1055C22×C4—44no—
1056C22×C4—44no—
1057C22×C4—44no—
1058C22×C4—44no—
1059C22×C4—48no—
1060C22×C4—48no—
1061C22×C4—48no—
1062C22×C4—48no—
1063C22×C4—44no—
1064C22×C4—44no—
1065C22×C4—48no—
1066C22×C4—816no—
1067C22×C4C22×D414yes—
1068C22×C4C22×D414yes—
1069C22×C4C22×D414yes—
1070C22×C4C22×D414yes—
1071C22×C4C22×D414yes—
1072C22×C4C22×D418yes—
1073C22×C4C22×D414yes—
1074C22×C4C2×#4118yes—
1075C22×C4C2×#4114yes—
1076C22×C42−1+414yes—
1077C22×C4C2514yes—
1078C22×C4C2514yes—
1079C22×C4C2514yes—
1080C22×C4C2512yes—
1081C22×C4C2512yes—
1082C22×C4C2512yes—
1083C22×C4C2512yes—
1084C22×C4C2512yes—
1085C22×C4C2512yes—
1086C22×C4C2514yes—
1087C22×C4C2512yes—
1088C22×C4C2514yes—
1089C22×C4C2512yes—
1090C22×C4C2514yes—
1091C22×C4C2512yes—
1092C22×C4C2512yes—
1093C22×C4C2512yes—
1094C22×C4C2511yescharacteristic
1095C22×C4C2511yescharacteristic
1096C22×C4C2512yes—
1097C22×C4C2512yes—
1098C22×C4C2511yescharacteristic
1099C22×C4C2511yescharacteristic
1100C4⋊C4—24no—
1101C4⋊C4—24no—
1102C4⋊C4—24no—
1103C4⋊C4—24no—
1104C4⋊C4—28no—
1105C4⋊C4—28no—
1106C4⋊C4—24no—
1107C4⋊C4—24no—
1108C4⋊C4—22no—
1109C4⋊C4—22no—
1110C4⋊C4—24no—
1111C4⋊C4—24no—
1112C4⋊C4—28no—
1113C4⋊C4—28no—
1114C4⋊C4—28no—
1115C4⋊C4—28no—
1116C4⋊C4—22no—
1117C4⋊C4—22no—
1118C4⋊C4—24no—
1119C4⋊C4—28no—
1120C4⋊C4—28no—
1121C4⋊C4—28no—
1122C4⋊C4—28no—
1123C4⋊C4—24no—
1124C4⋊C4—24no—
1125C4⋊C4—28no—
1126C4⋊C4—28no—
1127C4⋊C4—28no—
1128C4⋊C4—24no—
1129C4⋊C4—28no—
1130C4⋊C4—24no—
1131C4⋊C4—24no—
1132C4⋊C4—24no—
1133C4⋊C4—24no—
1134C4⋊C4—28no—
1135C4⋊C4—24no—
1136C4⋊C4—28no—
1137C4⋊C4—24no—
1138C4⋊C4—48no—
1139C4⋊C4—48no—
1140C4⋊C4—48no—
1141C4⋊C4—48no—
1142C4⋊C4—44no—
1143C4⋊C4—44no—
1144C4⋊C4—48no—
1145C4⋊C4—44no—
1146C4⋊C4—48no—
1147C4⋊C4—48no—
1148C4⋊C4—48no—
1149C4⋊C4—44no—
1150C4⋊C4C22×D414yes—
1151C4⋊C4C22×D414yes—
1152C4⋊C4C22×D418yes—
1153C4⋊C4C22×D418yes—
1154C22⋊C4—28no—
1155C22⋊C4—28no—
1156C22⋊C4—24no—
1157C22⋊C4—24no—
1158C22⋊C4—24no—
1159C22⋊C4—28no—
1160C22⋊C4—28no—
1161C22⋊C4—28no—
1162C22⋊C4—24no—
1163C22⋊C4—24no—
1164C22⋊C4—24no—
1165C22⋊C4—28no—
1166C22⋊C4—24no—
1167C22⋊C4—24no—
1168C22⋊C4—24no—
1169C22⋊C4—28no—
1170C22⋊C4—28no—
1171C22⋊C4—28no—
1172C22⋊C4—24no—
1173C22⋊C4—28no—
1174C22⋊C4—24no—
1175C22⋊C4—24no—
1176C22⋊C4—24no—
1177C22⋊C4—24no—
1178C22⋊C4—24no—
1179C22⋊C4—24no—
1180C22⋊C4—28no—
1181C22⋊C4—28no—
1182C22⋊C4—28no—
1183C22⋊C4—44no—
1184C22⋊C4—44no—
1185C22⋊C4—48no—
1186C22⋊C4—44no—
1187C22⋊C4—44no—
1188C22⋊C4—48no—
1189C22⋊C4—48no—
1190C22⋊C4—44no—
1191C22⋊C4—44no—
1192C22⋊C4—44no—
1193C22⋊C4—48no—
1194C22⋊C4—44no—
1195C22⋊C4C22×D418yes—
1196C22⋊C4C22×D418yes—
1197C22⋊C4C22×D418yes—
1198C22⋊C4C22×D418yes—
1199C22⋊C4C22×D418yes—
1200C42—28no—
1201C42—28no—
1202C42—28no—
1203C42—28no—
1204C42—28no—
1205C42—28no—
1206C42—24no—
1207C42—24no—
1208C42—22no—
1209C42—22no—
1210C42—24no—
1211C42—24no—
1212C42—28no—
1213C42—24no—
1214C42—44no—
1215C42—44no—
1216C42C22×D418yes—
1217C42C2×#4114yes—
1218C42C2×#4114yes—
1219C42C2×#4118yes—
1220C23—22no—
1221C23—22no—
1222C23—21no—
1223C23—21no—
1224C23—22no—
1225C23—21no—
1226C23—21no—
1227C23—22no—
1228C23—22no—
1229C23—24no—
1230C23—22no—
1231C23—22no—
1232C23—24no—
1233C23—22no—
1234C23—28no—
1235C23—22no—
1236C23—22no—
1237C23—22no—
1238C23—22no—
1239C23—22no—
1240C23—22no—
1241C23—24no—
1242C23—24no—
1243C23—24no—
1244C23—24no—
1245C23—44no—
1246C23—44no—
1247C23—48no—
1248C23—48no—
1249C23C23×D412yes—
1250C23C23×D412yes—
1251C23C23×D414yes—
1252C23C23×D412yes—
1253C23C22×#4112yes—
1254C23C2×2−1+412yes—
1255C23C2611yescharacteristic
1256Q8—28no—
1257Q8—44no—
1258Q8—44no—
1259Q8—88no—
1260Q8—88no—
1261D4—216no—
1262D4—28no—
1263D4—48no—
1264D4—48no—
1265D4—48no—
1266D4—48no—
1267D4—48no—
1268D4—48no—
1269D4—44no—
1270D4—44no—
1271D4—88no—
1272D4—88no—
1273D4—84no—
1274D4—84no—
1275D4—88no—
1276C2×C4—22no—
1277C2×C4—21no—
1278C2×C4—21no—
1279C2×C4—21no—
1280C2×C4—21no—
1281C2×C4—22no—
1282C2×C4—22no—
1283C2×C4—24no—
1284C2×C4—22no—
1285C2×C4—22no—
1286C2×C4—24no—
1287C2×C4—22no—
1288C2×C4—28no—
1289C2×C4—28no—
1290C2×C4—28no—
1291C2×C4—28no—
1292C2×C4—28no—
1293C2×C4—216no—
1294C2×C4—24no—
1295C2×C4—22no—
1296C2×C4—22no—
1297C2×C4—24no—
1298C2×C4—22no—
1299C2×C4—22no—
1300C2×C4—24no—
1301C2×C4—22no—
1302C2×C4—22no—
1303C2×C4—24no—
1304C2×C4—22no—
1305C2×C4—22no—
1306C2×C4—24no—
1307C2×C4—22no—
1308C2×C4—22no—
1309C2×C4—24no—
1310C2×C4—22no—
1311C2×C4—22no—
1312C2×C4—24no—
1313C2×C4—24no—
1314C2×C4—22no—
1315C2×C4—22no—
1316C2×C4—28no—
1317C2×C4—24no—
1318C2×C4—28no—
1319C2×C4—28no—
1320C2×C4—24no—
1321C2×C4—24no—
1322C2×C4—22no—
1323C2×C4—22no—
1324C2×C4—24no—
1325C2×C4—24no—
1326C2×C4—28no—
1327C2×C4—24no—
1328C2×C4—48no—
1329C2×C4—48no—
1330C2×C4—416no—
1331C2×C4—48no—
1332C2×C4—48no—
1333C2×C4—88no—
1334C2×C4—88no—
1335C2×C4—88no—
1336C2×C4—84no—
1337C2×C4—84no—
1338C2×C4—88no—
1339C2×C4—84no—
1340C2×C4—88no—
1341C2×C4—84no—
1342C2×C4—88no—
1343C2×C4#547116yes—
1344C2×C4C23×D412yes—
1345C2×C4C23×D412yes—
1346C2×C4C23×D414yes—
1347C2×C4C23×D414yes—
1348C2×C4C23×D414yes—
1349C2×C4C23×D412yes—
1350C2×C4C23×D412yes—
1351C2×C4C22×#4114yes—
1352C2×C4C22×#4114yes—
1353C2×C4C22×#4112yes—
1354C2×C4C22×#4112yes—
1355C2×C4C2×2−1+412yes—
1356C2×C4C2×2−1+412yes—
1357C22—22no—
1358C22—24no—
1359C22—22no—
1360C22—24no—
1361C22—22no—
1362C22—22no—
1363C22—24no—
1364C22—24no—
1365C22—22no—
1366C22—22no—
1367C22—22no—
1368C22—22no—
1369C22—24no—
1370C22—416no—
1371C22—44no—
1372C22—42no—
1373C22—42no—
1374C22—44no—
1375C22—42no—
1376C22—42no—
1377C22—42no—
1378C22—42no—
1379C22—44no—
1380C22—44no—
1381C22—42no—
1382C22—42no—
1383C22—44no—
1384C22—44no—
1385C22—42no—
1386C22—42no—
1387C22C2×#54714yes—
1388C22C24×D411yescharacteristic
1389C22C23×#4111yescharacteristic
1390C22C22×2−1+411yescharacteristic
1391C22H(7,𝔽2)12yes—
1392C222−1+612yes—
1393C4—24no—
1394C4—24no—
1395C4—24no—
1396C4—24no—
1397C4—22no—
1398C4—22no—
1399C4—24no—
1400C4—44no—
1401C4—44no—
1402C4—42no—
1403C4—44no—
1404C4—42no—
1405C4—42no—
1406C4—42no—
1407C4—44no—
1408C4—44no—
1409C4—42no—
1410C4—42no—
1411C4—44no—
1412C4—42no—
1413C4—42no—
1414C4C2×#54714yes—
1415C4C2×#54714yes—
1416C2—24no—
1417C2—44no—
1418C2—42no—
1419C2—42no—
1420C2—82no—
1421C2—82no—
1422C2C22×#54711yescharacteristic
1423C2#6285211yescharacteristic
1424C2#6285612yes—
1425C2#6285911yescharacteristic
1426C2#6287712yes—
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×#3493C2semidirect
2. C2×#3492C2semidirect
3. #45333C2semidirect
4. #45264C2semidirect
5. #45135C2semidirect
6. #44928C2semidirect
7. #39489C2semidirect
8. #39488C2semidirect
9. #39485C2semidirect
10. #39485C2semidirect
11. #37869C2semidirect
12. #37868C2semidirect
13. #37865C2semidirect
14. #37864C2semidirect
15. #37791C2semidirect
16. #37789C2semidirect
17. #35620C2semidirect
18. #35618C2semidirect
19. #35532C2semidirect
20. #35530C2semidirect
21. #35275C2semidirect
22. #35273C2semidirect
23. #35227C2semidirect
24. #35157C2semidirect
25. #34633C2semidirect
26. #34208C2semidirect
27. #34184C2semidirect
28. #34065C2semidirect
29. C2×#2317C2semidirect
68. #2868C22semidirect
69. #2859C22semidirect
70. #2857C22semidirect
71. #2856C22semidirect
74. #2725C22semidirect
75. #2725C22semidirect
76. #2723C22semidirect
77. #2722C22semidirect
78. #2719C22semidirect
80. #2718C22semidirect
87. #2674C22semidirect
88. #2672C22semidirect
90. #2660C22semidirect
91. #2660C22semidirect
100. #2620C22semidirect
101. #2620C22semidirect
106. #2568C22semidirect
107. #2567C22semidirect
108. #2566C22semidirect
109. #2566C22semidirect
110. #2565C22semidirect
111. #2565C22semidirect
112. #2563C22semidirect
113. #2552C22semidirect
114. #2551C22semidirect
115. #2542C22semidirect
116. #2538C22semidirect
117. #2537C22semidirect
119. #2504C22semidirect
121. #2503C22semidirect
123. #2502C22semidirect
125. #2501C22semidirect
128. #2500C22semidirect
129. #2500C22semidirect
132. #2499C22semidirect
133. #2499C22semidirect
138. #2479C22semidirect
141. #2470C22semidirect
143. #2466C22semidirect
144. #2462C22semidirect
150. #2442C22semidirect
151. #2441C22semidirect
152. #2441C22semidirect
154. #2440C22semidirect
155. #2439C22semidirect
156. #2438C22semidirect
159. #2429C22semidirect
160. #2425C22semidirect
161. #2423C22semidirect
163. #2422C22semidirect
164. #2421C22semidirect
165. #2420C22semidirect
171. #2352C22semidirect
172. #2352C22semidirect
173. #2351C22semidirect
175. #2349C22semidirect
176. #2328C22semidirect
177. #2327C22semidirect
194. #2317C22semidirect
195. #2317C22semidirect
200. C4×#124C22semidirect
201. C4×#124C22semidirect
213. #2285C22semidirect
218. C2×#382C22semidirect
279. #525D4semidirect
907. C2×C42#41semidirect

Maximal subgroups

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

subgroupindex
C2×#34932
C2×#34922
#453332
#452642
#451352
#449282
#394892
#394882
#394852
#378692
#378682
#378652
#378642
#377912
#377892
#356202
#356182
#355322
#355302
#352752
#352732
#352272
#351572
#346332
#342082
#341842
#340652
C2×#23172