Finite Group Databasebeta

← #7680456

Subgroups — #7680456

Order 512.

7320 conjugacy classes of subgroups.

The subgroup lattice has 1422 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3517C211yesmaximal, characteristic, complemented
2C2×#3522C211yesmaximal, characteristic, complemented
3#59145C214yesmaximal, complemented
4#59102C214yesmaximal, complemented
5#59097C214yesmaximal, complemented
6#59086C214yesmaximal, complemented
7#44783C218yesmaximal, complemented
8#43897C218yesmaximal, complemented
9#39745C211yesmaximal, characteristic, complemented
10#39619C211yesmaximal, characteristic, complemented
11#38956C211yesmaximal, characteristic, complemented
12#38956C212yesmaximal, complemented
13#38952C211yesmaximal, characteristic, complemented
14#38948C212yesmaximal, complemented
15#37864C212yesmaximal, complemented
16#37683C212yesmaximal, complemented
17#36538C211yesmaximal, characteristic, complemented
18#36457C211yesmaximal, characteristic, complemented
19#36164C211yesmaximal, characteristic, complemented
20#36128C211yesmaximal, characteristic, complemented
21#35623C212yesmaximal, complemented
22#35534C212yesmaximal, complemented
23#35293C211yesmaximal, characteristic, complemented
24#35276C212yesmaximal, complemented
25#34977C211yesmaximal, characteristic, complemented
26#34955C211yesmaximal, characteristic, complemented
27#34208C212yesmaximal, complemented
28#34151C211yesmaximal, characteristic, complemented
29C4×#536C211yesmaximal, characteristic, complemented
30#3522—216no—
31#3517—216no—
32C2×#559C2212yes—
33C2×#559C2211yescharacteristic
34C2×Q82C2211yescharacteristic
35C2×#557C2211yescharacteristic
36C2×#554C2211yescharacteristic
37C2×#554C2212yes—
38C2×#553C2212yes—
39C2×#553C2214yes—
40C2×#550C2211yescharacteristic
41C2×#550C2211yescharacteristic
42C2×#550C2212yes—
43C2×#550C2211yescharacteristic
44C2×#550C2212yes—
45C2×#548C2212yes—
46C2×#547C2212yes—
47C2×#547C2211yescharacteristic
48C2×#547C2214yes—
49C2×#547C2212yes—
50C2×#542C2212yes—
51C2×#542C2214yes—
52C2×#540C2214yes—
53C2×#540C2212yes—
54C2×#536C2211yescharacteristic
55C2×#532C2212yes—
56C2×#532C2212yes—
57C2×#532C2211yescharacteristic
58C2×#532C2212yes—
59C2×#532C2211yescharacteristic
60C2×#529C2212yes—
61C2×#529C2212yes—
62C2×#529C2211yescharacteristic
63C2×#520C2212yes—
64C2×#520C2212yes—
65C2×C4×#41C2211yescharacteristic
66C22×C4×Q8C2211yescharacteristic
67#2867C2211yescharacteristic
68#2862C2211yescharacteristic
69#2861C2212yes—
70#2858C2211yescharacteristic
71#2858C2212yes—
72#2858C2211yescharacteristic
73#2856C2212yes—
74#2850C2212yes—
75#2723C2218yes—
76#2713C2218yes—
77#2706C2218yes—
78#2703C2218yes—
79#2703C2218yes—
80#2703C2218yes—
81#2702C2218yes—
82#2699C2218yes—
83#2676C2218yes—
84#2673C2218yes—
85#2673C2218yes—
86#2672C2218yes—
87#2660C2212yes—
88#2657C2212yes—
89#2620C2212yes—
90#2619C2212yes—
91#2619C2212yes—
92#2619C2212yes—
93#2610C2214yes—
94#2592C2214yes—
95#2591C2214yes—
96#2568C2212yes—
97#2568C2211yescharacteristic
98#2568C2211yescharacteristic
99#2567C2211yescharacteristic
100#2566C2212yes—
101#2565C2212yes—
102#2563C2212yes—
103#2563C2211yescharacteristic
104#2558C2218yes—
105#2555C2218yes—
106#2554C2218yes—
107#2548C2211yescharacteristic
108#2548C2211yescharacteristic
109#2548C2211yescharacteristic
110#2548C2212yes—
111#2545C2214yes—
112#2545C2212yes—
113#2544C2214yes—
114#2544C2212yes—
115#2544C2214yes—
116#2541C2214yes—
117#2541C2211yescharacteristic
118#2541C2212yes—
119#2504C2212yes—
120#2504C2212yes—
121#2504C2212yes—
122#2503C2212yes—
123#2501C2212yes—
124#2500C2212yes—
125#2491C2218yes—
126#2491C2214yes—
127#2489C2214yes—
128#2488C2218yes—
129#2481C2218yes—
130#2477C2218yes—
131#2471C2218yes—
132#2464C2218yes—
133#2464C2218yes—
134#2463C2218yes—
135#2461C2218yes—
136#2459C2218yes—
137#2459C2218yes—
138#2457C2218yes—
139#2457C2218yes—
140#2456C2218yes—
141#2456C2218yes—
142#2454C2214yes—
143#2451C2214yes—
144#2446C2214yes—
145#2445C2214yes—
146#2443C2218yes—
147#2436C2212yes—
148#2432C2212yes—
149#2431C2214yes—
150#2431C2214yes—
151#2431C2212yes—
152#2431C2212yes—
153#2431C2212yes—
154#2431C2212yes—
155#2431C2218yes—
156#2431C2214yes—
157#2431C2214yes—
158#2430C2218yes—
159#2428C2218yes—
160#2428C2214yes—
161#2427C2214yes—
162#2427C2218yes—
163#2425C2218yes—
164#2414C2214yes—
165#2398C2214yes—
166#2388C2214yes—
167#2374C2214yes—
168#2373C2214yes—
169#2370C2212yes—
170#2367C2212yes—
171#2367C2214yes—
172#2366C2214yes—
173#2364C2218yes—
174#2364C2218yes—
175#2363C2212yes—
176#2362C2212yes—
177#2352C2218yes—
178#2352C2218yes—
179#2341C2214yes—
180#2339C2214yes—
181#2328C2212yes—
182#2328C2212yes—
183#2328C2212yes—
184#2327C2211yescharacteristic
185#2327C2211yescharacteristic
186#2327C2212yes—
187#2326C2211yescharacteristic
188#2326C2211yescharacteristic
189#2323C2214yes—
190#2322C2214yes—
191#2317C2211yescharacteristic
192#2311C2212yes—
193#2311C2212yes—
194#2311C2211yescharacteristic
195#2310C2211yescharacteristic
196C4×C4⋊Q8C2211yescharacteristic
197C4×C4⋊Q8C2211yescharacteristic
198C4×#127C2212yes—
199C4×#124C2212yes—
200C4×#124C2212yes—
201C4×#124C2212yes—
202C4×#124C2211yescharacteristic
203C4×#124C2211yescharacteristic
204C4×#124C2212yes—
205C4×#124C2212yes—
206C4×C22⋊Q8C2214yes—
207C4×#123C2214yes—
208C4×#121C2214yes—
209#2298C2212yes—
210#2297C2214yes—
211#2295C2211yescharacteristic
212#2293C2212yes—
213#2293C2211yescharacteristic
214#2290C2212yes—
215C2×#382C2212yes—
216C42×Q8C2211yescharacteristic
217C42×D4C2211yescharacteristic
218C4×#117C2211yescharacteristic
219C4×#117C2211yescharacteristic
220C4×#117C2212yes—
221C22×#41C2311yescharacteristic
222C22×#41C2312yes—
223C22×#41C2312yes—
224C22×#41C2312yes—
225C22×#41C2312yes—
226C22×#41C2312yes—
227C22×#41C2312yes—
228C22×#41C2314yes—
229C23×Q8C2311yescharacteristic
230#559—216no—
231#559—28no—
232Q82—28no—
233#557—28no—
234#554—216no—
235#554—28no—
236#553—232no—
237#553—216no—
238#550—216no—
239#550—28no—
240#550—28no—
241#550—216no—
242#550—28no—
243#548—216no—
244#547—232no—
245#547—216no—
246#547—28no—
247#547—216no—
248#542—232no—
249#542—216no—
250#540—232no—
251#540—216no—
252#536—28no—
253#532—216no—
254#532—216no—
255#532—216no—
256#532—28no—
257#532—28no—
258C2×C4⋊Q8C2311yescharacteristic
259C2×C4⋊Q8C2311yescharacteristic
260C2×C4⋊Q8C2312yes—
261C2×C4⋊Q8C2311yescharacteristic
262C2×C4⋊Q8C2312yes—
263C2×C4⋊Q8C2312yes—
264C2×C4⋊Q8C2314yes—
265C2×C4⋊Q8C2311yescharacteristic
266C2×#127C2312yes—
267C2×#127C2311yescharacteristic
268C2×#127C2311yescharacteristic
269C2×#127C2312yes—
270C2×#127C2314yes—
271C2×#127C2312yes—
272C2×#127C2312yes—
273C2×#127C2312yes—
274C2×#127C2312yes—
275C2×#127C2314yes—
276C2×#127C2314yes—
277#529—216no—
278#529—216no—
279#529D4116yescomplemented
280C2×#126C2314yes—
281C2×#126C2314yes—
282C2×#126C2312yes—
283C2×#125C2312yes—
284C2×#125C2312yes—
285C2×#125C2314yes—
286C2×#125C2311yescharacteristic
287C2×#124C2311yescharacteristic
288C2×#124C2311yescharacteristic
289C2×#124C2312yes—
290C2×#124C2312yes—
291C2×#124C2312yes—
292C2×#124C2312yes—
293C2×#124C2314yes—
294C2×#124C2312yes—
295C2×#124C2312yes—
296C2×#124C2314yes—
297C2×#124C2314yes—
298C2×#124C2312yes—
299C2×#124C2314yes—
300C2×#124C2318yes—
301C2×#124C2311yescharacteristic
302C2×#123C2314yes—
303C2×#123C2314yes—
304C2×#123C2314yes—
305C2×#123C2314yes—
306C2×#123C2314yes—
307C2×#123C2314yes—
308C2×#123C2314yes—
309C2×#123C2314yes—
310C2×#123C2314yes—
311C2×#123C2318yes—
312C2×#123C2312yes—
313C2×C22⋊Q8C2314yes—
314C2×C22⋊Q8C2312yes—
315C2×C22⋊Q8C2312yes—
316C2×C22⋊Q8C2314yes—
317C2×C22⋊Q8C2314yes—
318C2×C22⋊Q8C2314yes—
319C2×C22⋊Q8C2314yes—
320C2×C22⋊Q8C2311yescharacteristic
321C2×#121C2312yes—
322C2×#121C2312yes—
323C2×#121C2312yes—
324C2×#121C2312yes—
325C2×#121C2312yes—
326C2×#121C2312yes—
327C2×#121C2318yes—
328C2×#121C2312yes—
329C2×#121C2312yes—
330C2×#121C2314yes—
331C2×#121C2314yes—
332C2×#121C2314yes—
333C2×#121C2314yes—
334C2×#121C2314yes—
335C2×#121C2314yes—
336C2×#121C2314yes—
337C2×#121C2314yes—
338C2×#121C2314yes—
339C2×#121C2314yes—
340C2×#121C2318yes—
341C2×#121C2318yes—
342C2×#121C2311yescharacteristic
343#520—216no—
344#520—216no—
345C4×#41—28no—
346C2×C4×Q8—28no—
347C2×C4×Q8C2311yescharacteristic
348C2×C4×Q8C2311yescharacteristic
349C2×C4×Q8C2311yescharacteristic
350C2×C4×Q8C2312yes—
351C2×C4×Q8C2312yes—
352C2×C4×Q8C2312yes—
353C2×C4×Q8C2311yescharacteristic
354C2×C4×Q8C2311yescharacteristic
355C2×C4×Q8C2311yescharacteristic
356C2×C4×Q8C2312yes—
357C2×C4×Q8C2312yes—
358C2×C4×Q8C2312yes—
359C2×C4×Q8C2312yes—
360C2×C4×Q8C2311yescharacteristic
361C2×C4×D4C2311yescharacteristic
362C2×C4×D4C2312yes—
363C2×C4×D4C2312yes—
364C2×C4×D4C2311yescharacteristic
365C2×C4×D4C2312yes—
366C2×C4×D4C2312yes—
367C2×C4×D4C2312yes—
368C2×C4×D4C2312yes—
369C2×C4×D4C2318yes—
370C2×C4×D4C2314yes—
371C2×C4×D4C2314yes—
372C2×C4×D4C2314yes—
373C2×C4×D4C2314yes—
374C2×C4×D4C2312yes—
375C2×C4×D4C2312yes—
376C2×C4×D4C2312yes—
377C2×C4×D4C2312yes—
378C2×C4×D4C2312yes—
379C2×C4×D4C2314yes—
380C2×C4×D4C2314yes—
381C2×C4×D4C2314yes—
382C2×C4×D4C2312yes—
383C2×C4×D4C2312yes—
384C2×C4×D4C2318yes—
385C2×C4×D4C2312yes—
386C2×C4×D4C2311yescharacteristic
387C2×#117C2311yescharacteristic
388C2×#117C2311yescharacteristic
389C2×#117C2312yes—
390C2×#117C2314yes—
391C2×#117C2314yes—
392C2×#117C2311yescharacteristic
393C2×#117C2312yes—
394C2×#117C2312yes—
395C2×#117C2312yes—
396C22×C4⋊C4C2311yescharacteristic
397C22×C4⋊C4C2312yes—
398C22×C4⋊C4C2312yes—
399C22×C4⋊C4C2312yes—
400C22×C4⋊C4C2314yes—
401C22×C4⋊C4C2314yes—
402C22×C42C2312yes—
403C22×C42C2312yes—
404C22×C42C2312yes—
405C22×C42C2311yescharacteristic
406#400C2314yes—
407#400C2314yes—
408#400C2318yes—
409#400C2318yes—
410#399C2318yes—
411#398C2318yes—
412#398C2318yes—
413#397C2318yes—
414#397C2318yes—
415#397C2318yes—
416#396C2318yes—
417#396C2318yes—
418#396C2318yes—
419#395C2314yes—
420#395C2318yes—
421#394C2314yes—
422#394C2314yes—
423#394C2314yes—
424#394C2318yes—
425#394C2318yes—
426#394C2318yes—
427#394C2318yes—
428#394C2318yes—
429#394C2318yes—
430#394C2318yes—
431#394C2318yes—
432#393C2314yes—
433#393C2318yes—
434#393C2318yes—
435#392C2314yes—
436#392C2318yes—
437#392C2318yes—
438#392C2318yes—
439#392C2318yes—
440#392C2318yes—
441#392C2318yes—
442#392C2318yes—
443#392C2318yes—
444#392C2318yes—
445#392C2318yes—
446#391C2311yescharacteristic
447#391C2311yescharacteristic
448#391C2311yescharacteristic
449#391C2311yescharacteristic
450#391C2312yes—
451#391C2311yescharacteristic
452#391C2314yes—
453#391C2311yescharacteristic
454#391C2312yes—
455#391C2314yes—
456#391C2314yes—
457#391C2312yes—
458#391C2318yes—
459#391C2314yes—
460#391C2314yes—
461#391C2312yes—
462#390C2312yes—
463#390C2312yes—
464#390C2318yes—
465#390C2312yes—
466#390C2312yes—
467#390C2312yes—
468#390C2311yescharacteristic
469#390C2311yescharacteristic
470#390C2312yes—
471#390C2312yes—
472#390C2312yes—
473#390C2312yes—
474#390C2314yes—
475#390C2314yes—
476#390C2314yes—
477#390C2318yes—
478#390C2318yes—
479#390C2318yes—
480#390C2314yes—
481#390C2312yes—
482#390C2314yes—
483#390C2314yes—
484#389C2314yes—
485#389C2314yes—
486#389C2314yes—
487#389C2314yes—
488#389C2312yes—
489#389C2312yes—
490#389C2314yes—
491#388C2314yes—
492#388C2314yes—
493#388C2314yes—
494#388C2314yes—
495#388C2318yes—
496#388C2318yes—
497#388C2318yes—
498#388C2318yes—
499#388C2318yes—
500#388C2318yes—
501#388C2318yes—
502#388C2318yes—
503#388C2318yes—
504#388C2314yes—
505#388C2314yes—
506#388C2314yes—
507#388C2314yes—
508#388C2314yes—
509#388C2318yes—
510#388C2314yes—
511#387C2318yes—
512#387C2314yes—
513#387C2314yes—
514#387C2314yes—
515#387C2314yes—
516#387C2318yes—
517#387C2318yes—
518#387C2314yes—
519#387C2314yes—
520#387C2314yes—
521#387C2314yes—
522#386C2314yes—
523#386C2318yes—
524#386C2318yes—
525#386C2318yes—
526#386C2318yes—
527#386C2318yes—
528#386C2318yes—
529#386C2318yes—
530#386C2318yes—
531#386C2318yes—
532#386C2318yes—
533#386C2318yes—
534#386C2318yes—
535#386C2318yes—
536#386C2314yes—
537#386C2318yes—
538#386C2318yes—
539#386C2318yes—
540#386C2318yes—
541#386C2318yes—
542#385C2318yes—
543#385C2314yes—
544#385C2314yes—
545#385C2314yes—
546#385C2314yes—
547#385C2318yes—
548#384C2312yes—
549#384C2311yescharacteristic
550#384C2311yescharacteristic
551#382C2311yescharacteristic
552#382C2312yes—
553#382C2312yes—
554#382C2312yes—
555#382C2312yes—
556#382C2311yescharacteristic
557#382C2312yes—
558#382C2318yes—
559#381C2314yes—
560#381C2318yes—
561#380C2314yes—
562#380C2318yes—
563#380C2314yes—
564#380C2318yes—
565#380C2318yes—
566C4×C4⋊C4C2314yes—
567C4×C4⋊C4C2314yes—
568C4×C4⋊C4C2312yes—
569C4×C4⋊C4C2311yescharacteristic
570C4×C4⋊C4C2312yes—
571C4×C4⋊C4C2311yescharacteristic
572C4×C4⋊C4C2312yes—
573C4×C4⋊C4C2312yes—
574C4×C4⋊C4C2314yes—
575C4×C4⋊C4C2314yes—
576C4×C4⋊C4C2312yes—
577C4×C4⋊C4C2312yes—
578C4×C4⋊C4C2312yes—
579C4×C4⋊C4C2314yes—
580C4×C22⋊C4C2312yes—
581C4×C22⋊C4C2312yes—
582C4×C22⋊C4C2314yes—
583C4×C22⋊C4C2318yes—
584C4×C22⋊C4C2314yes—
585C4×C22⋊C4C2318yes—
586C4×C22⋊C4C2318yes—
587C4×C22⋊C4C2318yes—
588C4×C22⋊C4C2312yes—
589C4×C22⋊C4C2314yes—
590C4×C22⋊C4C2314yes—
591C4×C22⋊C4C2314yes—
592C4×C22⋊C4C2318yes—
593C4×C22⋊C4C2312yes—
594C4×C22⋊C4C2312yes—
595C4×C22⋊C4C2312yes—
596#376C2311yescharacteristic
597#376C2311yescharacteristic
598#376C2312yes—
599#376C2312yes—
600C2×#95C2318yes—
601C43C2312yes—
602C43C2311yescharacteristic
603C43C2311yescharacteristic
604C43C2312yes—
605C2×#41—28no—
606C2×#41—28no—
607C2×#41—28no—
608C2×#41—24no—
609C2×#41—216no—
610C2×#41—28no—
611C2×#41—24no—
612C2×#41—28no—
613C2×#41—28no—
614C2×#41—28no—
615C2×#41—28no—
616C2×#41—42no—
617C2×#41—44no—
618C2×#41—44no—
619C2×#41—48no—
620C2×#41—48no—
621C2×#41—48no—
622C2×#41—84no—
623C2×#41—88no—
624C22×Q8—24no—
625C22×Q8—24no—
626C22×Q8—42no—
627C22×Q8C2411yescharacteristic
628C22×Q8C2412yes—
629C22×Q8C2412yes—
630C22×Q8C2411yescharacteristic
631C22×Q8C2411yescharacteristic
632C22×Q8C2411yescharacteristic
633C22×Q8C2414yes—
634C22×Q8C2412yes—
635C22×D4C2412yes—
636C22×D4C2412yes—
637C22×D4C2411yescharacteristic
638C22×D4C2412yes—
639C22×D4C2412yes—
640C22×D4C2414yes—
641C22×D4C2414yes—
642C22×D4C2412yes—
643C22×D4C2411yescharacteristic
644C22×D4C2414yes—
645C22×D4C2414yes—
646C22×D4C2412yes—
647C22×D4C2414yes—
648C22×D4C2418yes—
649C22×D4C2414yes—
650C22×D4C2414yes—
651C22×D4C2414yes—
652C22×D4C2414yes—
653C22×D4C2412yes—
654C22×D4C2418yes—
655C22×D4C2418yes—
656C22×D4C2412yes—
657C23×C4C2412yes—
658C23×C4C2414yes—
659C23×C4C2414yes—
660C23×C4C2412yes—
661C23×C4C2412yes—
662C23×C4C2412yes—
663C23×C4C2411yescharacteristic
664C23×C4C2411yescharacteristic
665C23×C4C2412yes—
666C23×C4C2414yes—
667C23×C4C2414yes—
668C23×C4C2414yes—
669C23×C4C2414yes—
670C23×C4C2414yes—
671C23×C4C2414yes—
672C23×C4C2412yes—
673C23×C4C2414yes—
674C23×C4C2411yescharacteristic
675C4⋊Q8—28no—
676C4⋊Q8—24no—
677C4⋊Q8—28no—
678C4⋊Q8—216no—
679C4⋊Q8—24no—
680C4⋊Q8—24no—
681C4⋊Q8—28no—
682C4⋊Q8#4118yescomplemented
683#127—28no—
684#127—28no—
685#127—216no—
686#127—24no—
687#127—24no—
688#127—28no—
689#127—28no—
690#127—44no—
691#127—44no—
692#127—48no—
693#127—84no—
694#126—216no—
695#126—216no—
696#126C2×D4116yes—
697#125—28no—
698#125—216no—
699#125—28no—
700#125C2×D418yes—
701#124—28no—
702#124—28no—
703#124—28no—
704#124—24no—
705#124—216no—
706#124—216no—
707#124—28no—
708#124—28no—
709#124—28no—
710#124—24no—
711#124—44no—
712#124—48no—
713#124—88no—
714#124—84no—
715#124C2×D418yes—
716#123—216no—
717#123—216no—
718#123—216no—
719#123—216no—
720#123—216no—
721#123—216no—
722#123—216no—
723#123—216no—
724#123—216no—
725#123—88no—
726#123C2×D4116yes—
727C22⋊Q8—28no—
728C22⋊Q8—28no—
729C22⋊Q8—216no—
730C22⋊Q8—216no—
731C22⋊Q8—216no—
732C22⋊Q8—216no—
733C22⋊Q8—216no—
734C22⋊Q8C2×D418yes—
735#121—216no—
736#121—216no—
737#121—28no—
738#121—28no—
739#121—28no—
740#121—28no—
741#121—28no—
742#121—28no—
743#121—28no—
744#121—28no—
745#121—216no—
746#121—232no—
747#121—216no—
748#121—216no—
749#121—216no—
750#121—216no—
751#121—216no—
752#121—216no—
753#121—48no—
754#121—88no—
755#121—88no—
756#121C2×D418yes—
757C4×Q8—28no—
758C4×Q8—28no—
759C4×Q8—24no—
760C4×Q8—28no—
761C4×Q8—24no—
762C4×Q8—24no—
763C4×Q8—24no—
764C4×Q8—28no—
765C4×Q8—24no—
766C4×Q8—24no—
767C4×Q8—28no—
768C4×Q8—28no—
769C4×Q8—44no—
770C4×Q8C2×D418yes—
771C4×D4—28no—
772C4×D4—28no—
773C4×D4—28no—
774C4×D4—28no—
775C4×D4—216no—
776C4×D4—28no—
777C4×D4—28no—
778C4×D4—232no—
779C4×D4—216no—
780C4×D4—216no—
781C4×D4—216no—
782C4×D4—216no—
783C4×D4—216no—
784C4×D4—216no—
785C4×D4—24no—
786C4×D4—24no—
787C4×D4—28no—
788C4×D4—28no—
789C4×D4—28no—
790C4×D4—28no—
791C4×D4—28no—
792C4×D4—28no—
793C4×D4—44no—
794C4×D4—88no—
795C4×D4C2×D4116yes—
796C4×D4C2×D418yes—
797#117—24no—
798#117—216no—
799#117—216no—
800#117—28no—
801#117—24no—
802#117—44no—
803#117—42no—
804#117—44no—
805#117C2×D4116yes—
806C2×C4⋊C4—24no—
807C2×C4⋊C4—28no—
808C2×C4⋊C4—28no—
809C2×C4⋊C4—28no—
810C2×C4⋊C4—216no—
811C2×C4⋊C4—216no—
812C2×C4⋊C4C2411yescharacteristic
813C2×C4⋊C4C2412yes—
814C2×C4⋊C4C2411yescharacteristic
815C2×C4⋊C4C2412yes—
816C2×C4⋊C4C2414yes—
817C2×C4⋊C4C2414yes—
818C2×C4⋊C4C2412yes—
819C2×C4⋊C4C2414yes—
820C2×C4⋊C4C2412yes—
821C2×C4⋊C4C2414yes—
822C2×C4⋊C4C2411yescharacteristic
823C2×C4⋊C4C2412yes—
824C2×C4⋊C4C2412yes—
825C2×C4⋊C4C2412yes—
826C2×C4⋊C4C2412yes—
827C2×C4⋊C4C2411yescharacteristic
828C2×C4⋊C4C2412yes—
829C2×C4⋊C4C2412yes—
830C2×C4⋊C4C2412yes—
831C2×C4⋊C4C2412yes—
832C2×C4⋊C4C2412yes—
833C2×C4⋊C4C2414yes—
834C2×C4⋊C4C2412yes—
835C2×C4⋊C4C2414yes—
836C2×C4⋊C4C2414yes—
837C2×C4⋊C4C2414yes—
838C2×C4⋊C4C2414yes—
839C2×C4⋊C4C2414yes—
840C2×C4⋊C4C2412yes—
841C2×C4⋊C4C2418yes—
842C2×C4⋊C4C2414yes—
843C2×C4⋊C4C2414yes—
844C2×C4⋊C4C2414yes—
845C2×C4⋊C4C2414yes—
846C2×C4⋊C4C2412yes—
847C2×C4⋊C4C2412yes—
848C2×C4⋊C4C2411yescharacteristic
849C2×C4⋊C4C2412yes—
850C2×C4⋊C4C2411yescharacteristic
851C2×C4⋊C4C2412yes—
852C2×C4⋊C4C2414yes—
853C2×C22⋊C4C2414yes—
854C2×C22⋊C4C2412yes—
855C2×C22⋊C4C2412yes—
856C2×C22⋊C4C2412yes—
857C2×C22⋊C4C2414yes—
858C2×C22⋊C4C2414yes—
859C2×C22⋊C4C2414yes—
860C2×C22⋊C4C2412yes—
861C2×C22⋊C4C2414yes—
862C2×C22⋊C4C2414yes—
863C2×C22⋊C4C2414yes—
864C2×C22⋊C4C2414yes—
865C2×C22⋊C4C2414yes—
866C2×C22⋊C4C2414yes—
867C2×C22⋊C4C2414yes—
868C2×C22⋊C4C2418yes—
869C2×C22⋊C4C2418yes—
870C2×C22⋊C4C2414yes—
871C2×C22⋊C4C2414yes—
872C2×C22⋊C4C2414yes—
873C2×C22⋊C4C2412yes—
874C2×C22⋊C4C2414yes—
875C2×C22⋊C4C2414yes—
876C2×C22⋊C4C2418yes—
877C2×C22⋊C4C2418yes—
878C2×C22⋊C4C2414yes—
879C2×C22⋊C4C2414yes—
880C2×C22⋊C4C2418yes—
881C2×C22⋊C4C2418yes—
882C2×C22⋊C4C2418yes—
883C2×C22⋊C4C2414yes—
884C2×C22⋊C4C2418yes—
885C2×C22⋊C4C2414yes—
886C2×C22⋊C4C2418yes—
887C2×C22⋊C4C2418yes—
888C2×C22⋊C4C2418yes—
889C2×C22⋊C4C2418yes—
890C2×C22⋊C4C2412yes—
891C2×C22⋊C4C2412yes—
892C2×C22⋊C4C2412yes—
893C2×C22⋊C4C2412yes—
894C2×C22⋊C4C2412yes—
895C2×C42—28no—
896C2×C42—28no—
897C2×C42—28no—
898C2×C42C2×D418yes—
899C2×C42C2411yescharacteristic
900C2×C42C2412yes—
901C2×C42C2412yes—
902C2×C42C2412yes—
903C2×C42C2414yes—
904C2×C42C2414yes—
905C2×C42C2412yes—
906C2×C42C2411yescharacteristic
907C2×C42C2411yescharacteristic
908C2×C42C2412yes—
909C2×C42C2412yes—
910C2×C42C2414yes—
911C2×C42C2412yes—
912C2×C42C2412yes—
913C2×C42C2412yes—
914C2×C42C2412yes—
915C2×C42C2412yes—
916C2×C42C2414yes—
917C2×C42C2414yes—
918C2×C42C2414yes—
919C2×C42C2414yes—
920C2×C42C2412yes—
921C2×C42C2412yes—
922C2×C42C2411yescharacteristic
923C2×C42C2411yescharacteristic
924C2×C42C2412yes—
925C2×C42C2411yescharacteristic
926C2×C42C2411yescharacteristic
927C2×C42C2411yescharacteristic
928#95C2414yes—
929#95C2418yes—
930#95C2418yes—
931#95C2418yes—
932#95C2412yes—
933#95C2412yes—
934#95C2412yes—
935#95C2412yes—
936#95C2414yes—
937#95C2414yes—
938#95C2412yes—
939#95C2414yes—
940#95C2412yes—
941#95C2414yes—
942#95C2414yes—
943#95C2414yes—
944#95C2414yes—
945#95C2418yes—
946#95C2418yes—
947#95C2414yes—
948#95C2418yes—
949#95C2418yes—
950#95C2414yes—
951#95C2414yes—
952#95C2414yes—
953#95C2414yes—
954#95C2414yes—
955#95C2414yes—
956#95C2418yes—
957C24C2514yes—
958C24C2512yes—
959C24C2514yes—
960C24C2511yescharacteristic
961C24C2512yes—
962#41—416no—
963#41—432no—
964#41—432no—
965#41—816no—
966#41—816no—
967#41—816no—
968#41—832no—
969#41—816no—
970C2×Q8—22no—
971C2×Q8—22no—
972C2×Q8—24no—
973C2×Q8—22no—
974C2×Q8—24no—
975C2×Q8—28no—
976C2×Q8—24no—
977C2×Q8—24no—
978C2×Q8—22no—
979C2×Q8—24no—
980C2×Q8—22no—
981C2×Q8—22no—
982C2×Q8—22no—
983C2×Q8—28no—
984C2×Q8—42no—
985C2×Q8—44no—
986C2×Q8—48no—
987C2×Q8—416no—
988C2×Q8C22×D414yes—
989C2×Q8C2×#4114yes—
990C2×Q8C2×#4114yes—
991C2×D4—28no—
992C2×D4—28no—
993C2×D4—24no—
994C2×D4—28no—
995C2×D4—28no—
996C2×D4—28no—
997C2×D4—28no—
998C2×D4—28no—
999C2×D4—24no—
1000C2×D4—24no—
1001C2×D4—22no—
1002C2×D4—24no—
1003C2×D4—24no—
1004C2×D4—24no—
1005C2×D4—28no—
1006C2×D4—28no—
1007C2×D4—24no—
1008C2×D4—28no—
1009C2×D4—28no—
1010C2×D4—24no—
1011C2×D4—22no—
1012C2×D4—24no—
1013C2×D4—24no—
1014C2×D4—216no—
1015C2×D4—24no—
1016C2×D4—28no—
1017C2×D4—24no—
1018C2×D4—24no—
1019C2×D4—22no—
1020C2×D4—28no—
1021C2×D4—42no—
1022C2×D4—44no—
1023C2×D4—44no—
1024C2×D4—44no—
1025C2×D4—48no—
1026C2×D4—48no—
1027C2×D4—48no—
1028C2×D4—48no—
1029C2×D4—48no—
1030C2×D4—48no—
1031C2×D4—48no—
1032C2×D4—44no—
1033C2×D4—48no—
1034C2×D4—48no—
1035C2×D4—44no—
1036C2×D4—48no—
1037C2×D4—48no—
1038C2×D4—48no—
1039C2×D4—48no—
1040C2×D4—48no—
1041C2×D4—48no—
1042C2×D4C22×D414yes—
1043C2×D4C22×D418yes—
1044C22×C4—24no—
1045C22×C4—22no—
1046C22×C4—22no—
1047C22×C4—24no—
1048C22×C4—24no—
1049C22×C4—24no—
1050C22×C4—24no—
1051C22×C4—28no—
1052C22×C4—28no—
1053C22×C4—24no—
1054C22×C4—24no—
1055C22×C4—28no—
1056C22×C4—28no—
1057C22×C4—28no—
1058C22×C4—28no—
1059C22×C4—24no—
1060C22×C4—24no—
1061C22×C4—28no—
1062C22×C4—24no—
1063C22×C4—28no—
1064C22×C4—28no—
1065C22×C4—28no—
1066C22×C4—28no—
1067C22×C4—28no—
1068C22×C4—42no—
1069C22×C4—44no—
1070C22×C4—44no—
1071C22×C4—42no—
1072C22×C4—42no—
1073C22×C4—44no—
1074C22×C4—44no—
1075C22×C4—44no—
1076C22×C4—48no—
1077C22×C4—44no—
1078C22×C4—48no—
1079C22×C4—48no—
1080C22×C4—48no—
1081C22×C4—48no—
1082C22×C4—48no—
1083C22×C4C22×D414yes—
1084C22×C4C22×D414yes—
1085C22×C4C22×D418yes—
1086C22×C4C22×D414yes—
1087C22×C4C2512yes—
1088C22×C4C2514yes—
1089C22×C4C2512yes—
1090C22×C4C2514yes—
1091C22×C4C2514yes—
1092C22×C4C2512yes—
1093C22×C4C2512yes—
1094C22×C4C2512yes—
1095C22×C4C2512yes—
1096C22×C4C2512yes—
1097C22×C4C2514yes—
1098C22×C4C2512yes—
1099C22×C4C2511yescharacteristic
1100C22×C4C2511yescharacteristic
1101C22×C4C2511yescharacteristic
1102C22×C4C2512yes—
1103C22×C4C2512yes—
1104C22×C4C2511yescharacteristic
1105C22×C4C2512yes—
1106C22×C4C2512yes—
1107C22×C4C2512yes—
1108C22×C4C2512yes—
1109C22×C4C2511yescharacteristic
1110C22×C4C2511yescharacteristic
1111C4⋊C4—24no—
1112C4⋊C4—22no—
1113C4⋊C4—24no—
1114C4⋊C4—22no—
1115C4⋊C4—28no—
1116C4⋊C4—28no—
1117C4⋊C4—28no—
1118C4⋊C4—24no—
1119C4⋊C4—28no—
1120C4⋊C4—24no—
1121C4⋊C4—24no—
1122C4⋊C4—22no—
1123C4⋊C4—24no—
1124C4⋊C4—24no—
1125C4⋊C4—24no—
1126C4⋊C4—24no—
1127C4⋊C4—22no—
1128C4⋊C4—24no—
1129C4⋊C4—28no—
1130C4⋊C4—24no—
1131C4⋊C4—28no—
1132C4⋊C4—28no—
1133C4⋊C4—28no—
1134C4⋊C4—24no—
1135C4⋊C4—28no—
1136C4⋊C4—24no—
1137C4⋊C4—24no—
1138C4⋊C4—44no—
1139C4⋊C4—42no—
1140C4⋊C4—48no—
1141C4⋊C4—44no—
1142C4⋊C4—44no—
1143C4⋊C4—44no—
1144C4⋊C4—44no—
1145C4⋊C4C22×D418yes—
1146C4⋊C4C22×D418yes—
1147C4⋊C4C22×D414yes—
1148C4⋊C4C22×D418yes—
1149C4⋊C4C22×D414yes—
1150C4⋊C4C22×D418yes—
1151C4⋊C4C2×#41116yes—
1152C22⋊C4—24no—
1153C22⋊C4—28no—
1154C22⋊C4—28no—
1155C22⋊C4—24no—
1156C22⋊C4—24no—
1157C22⋊C4—28no—
1158C22⋊C4—28no—
1159C22⋊C4—28no—
1160C22⋊C4—28no—
1161C22⋊C4—28no—
1162C22⋊C4—28no—
1163C22⋊C4—28no—
1164C22⋊C4—28no—
1165C22⋊C4—28no—
1166C22⋊C4—28no—
1167C22⋊C4—24no—
1168C22⋊C4—216no—
1169C22⋊C4—216no—
1170C22⋊C4—28no—
1171C22⋊C4—28no—
1172C22⋊C4—44no—
1173C22⋊C4—42no—
1174C22⋊C4—44no—
1175C22⋊C4—44no—
1176C22⋊C4—48no—
1177C22⋊C4—48no—
1178C22⋊C4—48no—
1179C22⋊C4—44no—
1180C22⋊C4—48no—
1181C22⋊C4—48no—
1182C22⋊C4—44no—
1183C22⋊C4—48no—
1184C22⋊C4—48no—
1185C22⋊C4—48no—
1186C22⋊C4—48no—
1187C22⋊C4—48no—
1188C22⋊C4—44no—
1189C22⋊C4C22×D418yes—
1190C22⋊C4C22×D418yes—
1191C22⋊C4C22×D418yes—
1192C22⋊C4C22×D418yes—
1193C22⋊C4C22×D418yes—
1194C42—24no—
1195C42—24no—
1196C42—24no—
1197C42—24no—
1198C42—24no—
1199C42—24no—
1200C42—24no—
1201C42—28no—
1202C42—28no—
1203C42—28no—
1204C42—24no—
1205C42—22no—
1206C42—22no—
1207C42—24no—
1208C42—22no—
1209C42—24no—
1210C42—24no—
1211C42—44no—
1212C42—44no—
1213C42—44no—
1214C42—42no—
1215C42—44no—
1216C42—42no—
1217C42C22×D414yes—
1218C42C22×D414yes—
1219C42C22×D414yes—
1220C42C22×D414yes—
1221C42C22×D418yes—
1222C42C2×#4114yes—
1223C23—21no—
1224C23—22no—
1225C23—21no—
1226C23—22no—
1227C23—22no—
1228C23—24no—
1229C23—24no—
1230C23—22no—
1231C23—24no—
1232C23—22no—
1233C23—24no—
1234C23—22no—
1235C23—24no—
1236C23—24no—
1237C23—28no—
1238C23—24no—
1239C23—24no—
1240C23—28no—
1241C23—22no—
1242C23—24no—
1243C23—24no—
1244C23—28no—
1245C23—28no—
1246C23C23×D414yes—
1247C23C23×D412yes—
1248C23C2611yescharacteristic
1249Q8—28no—
1250Q8—28no—
1251Q8—28no—
1252Q8—48no—
1253Q8—44no—
1254Q8—48no—
1255Q8—84no—
1256Q8—88no—
1257D4—28no—
1258D4—48no—
1259D4—48no—
1260D4—416no—
1261D4—416no—
1262D4—416no—
1263D4—48no—
1264D4—44no—
1265D4—48no—
1266D4—48no—
1267D4—48no—
1268D4—816no—
1269D4—84no—
1270D4—88no—
1271D4—88no—
1272D4—84no—
1273D4—88no—
1274D4—88no—
1275D4—88no—
1276D4—88no—
1277D4—816no—
1278D4—168no—
1279C2×C4—22no—
1280C2×C4—22no—
1281C2×C4—22no—
1282C2×C4—21no—
1283C2×C4—22no—
1284C2×C4—22no—
1285C2×C4—24no—
1286C2×C4—22no—
1287C2×C4—21no—
1288C2×C4—22no—
1289C2×C4—22no—
1290C2×C4—22no—
1291C2×C4—22no—
1292C2×C4—22no—
1293C2×C4—24no—
1294C2×C4—28no—
1295C2×C4—216no—
1296C2×C4—28no—
1297C2×C4—22no—
1298C2×C4—22no—
1299C2×C4—22no—
1300C2×C4—22no—
1301C2×C4—22no—
1302C2×C4—24no—
1303C2×C4—24no—
1304C2×C4—24no—
1305C2×C4—22no—
1306C2×C4—22no—
1307C2×C4—22no—
1308C2×C4—22no—
1309C2×C4—22no—
1310C2×C4—24no—
1311C2×C4—22no—
1312C2×C4—22no—
1313C2×C4—24no—
1314C2×C4—24no—
1315C2×C4—22no—
1316C2×C4—24no—
1317C2×C4—28no—
1318C2×C4—22no—
1319C2×C4—24no—
1320C2×C4—22no—
1321C2×C4—24no—
1322C2×C4—22no—
1323C2×C4—24no—
1324C2×C4—28no—
1325C2×C4—24no—
1326C2×C4—24no—
1327C2×C4—44no—
1328C2×C4—416no—
1329C2×C4—416no—
1330C2×C4—48no—
1331C2×C4—48no—
1332C2×C4—48no—
1333C2×C4—48no—
1334C2×C4—88no—
1335C2×C4—84no—
1336C2×C4—88no—
1337C2×C4—88no—
1338C2×C4—88no—
1339C2×C4—88no—
1340C2×C4—88no—
1341C2×C4—88no—
1342C2×C4C23×D412yes—
1343C2×C4C23×D412yes—
1344C2×C4C23×D412yes—
1345C2×C4C23×D414yes—
1346C2×C4C23×D414yes—
1347C2×C4C23×D412yes—
1348C2×C4C23×D414yes—
1349C2×C4C23×D412yes—
1350C2×C4C23×D412yes—
1351C2×C4C22×#4114yes—
1352C2×C4C22×#4114yes—
1353C2×C4C22×#4114yes—
1354C2×C4C22×#4112yes—
1355C2×C4#58512yes—
1356C2×C4#58514yes—
1357C22—22no—
1358C22—24no—
1359C22—22no—
1360C22—24no—
1361C22—22no—
1362C22—24no—
1363C22—44no—
1364C22—42no—
1365C22—42no—
1366C22—44no—
1367C22—48no—
1368C22—48no—
1369C22—44no—
1370C22—42no—
1371C22—44no—
1372C22—44no—
1373C22—44no—
1374C22—42no—
1375C22—44no—
1376C22—44no—
1377C22—42no—
1378C22—44no—
1379C22—44no—
1380C22—48no—
1381C22—48no—
1382C22C24×D411yescharacteristic
1383C22C23×#4111yescharacteristic
1384C22C2×#58512yes—
1385C22C2×#58511yescharacteristic
1386C22H(7,𝔽2)12yes—
1387C4—24no—
1388C4—22no—
1389C4—24no—
1390C4—22no—
1391C4—22no—
1392C4—24no—
1393C4—24no—
1394C4—22no—
1395C4—24no—
1396C4—24no—
1397C4—42no—
1398C4—44no—
1399C4—42no—
1400C4—44no—
1401C4—42no—
1402C4—42no—
1403C4—44no—
1404C4—42no—
1405C4—42no—
1406C4—42no—
1407C4—44no—
1408C4—42no—
1409C4D4×#4114yes—
1410C4#350014yes—
1411C2—42no—
1412C2—44no—
1413C2—84no—
1414C2—84no—
1415C2—82no—
1416C2C2×D4×#4111yescharacteristic
1417C2C2×#350011yescharacteristic
1418C2#6285211yescharacteristic
1419C2#6296912yes—
1420C2#6300612yes—
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×#3517C2semidirect
2. C2×#3522C2semidirect
3. #59145C2semidirect
4. #59102C2semidirect
5. #59097C2semidirect
6. #59086C2semidirect
7. #44783C2semidirect
8. #43897C2semidirect
9. #39745C2semidirect
10. #39619C2semidirect
11. #38956C2semidirect
12. #38956C2semidirect
13. #38952C2semidirect
14. #38948C2semidirect
15. #37864C2semidirect
16. #37683C2semidirect
17. #36538C2semidirect
18. #36457C2semidirect
19. #36164C2semidirect
20. #36128C2semidirect
21. #35623C2semidirect
22. #35534C2semidirect
23. #35293C2semidirect
24. #35276C2semidirect
25. #34977C2semidirect
26. #34955C2semidirect
27. #34208C2semidirect
28. #34151C2semidirect
29. C4×#536C2semidirect
279. #529D4semidirect
682. C4⋊Q8#41semidirect

Maximal subgroups

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

subgroupindex
C2×#35172
C2×#35222
#591452
#591022
#590972
#590862
#447832
#438972
#397452
#396192
#389562
#389522
#389482
#378642
#376832
#365382
#364572
#361642
#361282
#356232
#355342
#352932
#352762
#349772
#349552
#342082
#341512
C4×#5362