Finite Group Databasebeta

← #7657708

Subgroups — #7657708

Order 512.

6770 conjugacy classes of subgroups.

The subgroup lattice has 1468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3511C211yesmaximal, characteristic, complemented
2C2×#3515C211yesmaximal, characteristic, complemented
3#42314C214yesmaximal, complemented
4#42312C214yesmaximal, complemented
5#41948C214yesmaximal, complemented
6#41937C214yesmaximal, complemented
7#40504C214yesmaximal, complemented
8#40493C214yesmaximal, complemented
9#39613C212yesmaximal, complemented
10#39611C212yesmaximal, complemented
11#37871C212yesmaximal, complemented
12#37869C212yesmaximal, complemented
13#37864C212yesmaximal, complemented
14#37862C212yesmaximal, complemented
15#37634C211yesmaximal, characteristic, complemented
16#37615C211yesmaximal, characteristic, complemented
17#37545C211yesmaximal, characteristic, complemented
18#37545C211yesmaximal, characteristic, complemented
19#37539C211yesmaximal, characteristic, complemented
20#37539C211yesmaximal, characteristic, complemented
21#36184C212yesmaximal, complemented
22#36182C212yesmaximal, complemented
23#36001C214yesmaximal, complemented
24#35740C214yesmaximal, complemented
25#35335C211yesmaximal, characteristic, complemented
26#35303C211yesmaximal, characteristic, complemented
27#35303C211yesmaximal, characteristic, complemented
28#34642C211yesmaximal, characteristic, complemented
29#34624C211yesmaximal, characteristic, complemented
30C2×#2660C211yesmaximal, characteristic, complemented
31#34123C211yesmaximal, characteristic, complemented
32#3515—216no—
33#3511—216no—
34C2×#557C2211yescharacteristic
35C2×#556C2212yes—
36C2×#555C2212yes—
37C2×#554C2211yescharacteristic
38C2×#554C2211yescharacteristic
39C2×#554C2212yes—
40C2×#553C2211yescharacteristic
41C2×#553C2211yescharacteristic
42C2×#553C2212yes—
43C2×#553C2212yes—
44C2×#552C2212yes—
45C2×#552C2211yescharacteristic
46C2×#552C2212yes—
47C2×#552C2212yes—
48C2×#552C2211yescharacteristic
49C2×#548C2212yes—
50C2×#548C2212yes—
51C2×#547C2212yes—
52C2×#547C2212yes—
53C2×#547C2211yescharacteristic
54C2×#542C2212yes—
55C2×#542C2212yes—
56C2×#541C2212yes—
57C2×#539C2212yes—
58C2×#539C2212yes—
59C2×#537C2212yes—
60C2×#533C2211yescharacteristic
61C2×#533C2211yescharacteristic
62C2×#533C2211yescharacteristic
63C2×#532C2211yescharacteristic
64C2×#532C2211yescharacteristic
65C2×#532C2211yescharacteristic
66C22×C4⋊Q8C2211yescharacteristic
67C2×#529C2211yescharacteristic
68C2×#529C2211yescharacteristic
69C2×#529C2211yescharacteristic
70C22×#125C2211yescharacteristic
71C22×#125C2211yescharacteristic
72C2×#520C2212yes—
73C2×#520C2212yes—
74C2×C4×#41C2211yescharacteristic
75#2859C2212yes—
76#2859C2212yes—
77#2856C2212yes—
78#2856C2212yes—
79#2850C2212yes—
80#2850C2212yes—
81#2821C2214yes—
82#2820C2214yes—
83#2820C2214yes—
84#2816C2214yes—
85#2814C2214yes—
86#2814C2214yes—
87#2732C2218yes—
88#2729C2218yes—
89#2723C2218yes—
90#2721C2218yes—
91#2715C2218yes—
92#2708C2218yes—
93#2706C2218yes—
94#2704C2218yes—
95#2683C2218yes—
96#2680C2218yes—
97#2672C2218yes—
98#2671C2218yes—
99#2662C2214yes—
100#2661C2214yes—
101#2660C2211yescharacteristic
102#2660C2211yescharacteristic
103#2660C2211yescharacteristic
104#2660C2211yescharacteristic
105#2660C2211yescharacteristic
106#2660C2214yes—
107#2660C2211yescharacteristic
108#2660C2214yes—
109#2660C2211yescharacteristic
110#2660C2212yes—
111#2660C2212yes—
112#2660C2211yescharacteristic
113#2660C2211yescharacteristic
114#2660C2212yes—
115#2660C2212yes—
116#2659C2214yes—
117#2659C2214yes—
118#2657C2211yescharacteristic
119#2641C2211yescharacteristic
120#2641C2211yescharacteristic
121#2641C2211yescharacteristic
122#2640C2211yescharacteristic
123#2640C2211yescharacteristic
124#2640C2211yescharacteristic
125#2638C2214yes—
126#2638C2214yes—
127#2637C2214yes—
128#2637C2214yes—
129#2633C2214yes—
130#2633C2214yes—
131#2632C2214yes—
132#2623C2214yes—
133#2621C2214yes—
134#2620C2212yes—
135#2619C2212yes—
136#2618C2214yes—
137#2618C2214yes—
138#2616C2214yes—
139#2610C2214yes—
140#2610C2214yes—
141#2603C2214yes—
142#2603C2214yes—
143#2599C2214yes—
144#2599C2214yes—
145#2584C2214yes—
146#2584C2214yes—
147#2583C2214yes—
148#2583C2214yes—
149#2568C2212yes—
150#2566C2212yes—
151#2566C2212yes—
152#2566C2212yes—
153#2566C2212yes—
154#2566C2212yes—
155#2566C2212yes—
156#2565C2212yes—
157#2565C2212yes—
158#2563C2212yes—
159#2553C2218yes—
160#2543C2214yes—
161#2543C2214yes—
162#2542C2212yes—
163#2542C2212yes—
164#2536C2214yes—
165#2519C2218yes—
166#2512C2218yes—
167#2504C2212yes—
168#2504C2212yes—
169#2504C2212yes—
170#2502C2212yes—
171#2501C2212yes—
172#2501C2212yes—
173#2500C2212yes—
174#2500C2212yes—
175#2500C2212yes—
176#2500C2212yes—
177#2499C2212yes—
178#2499C2212yes—
179#2479C2218yes—
180#2475C2218yes—
181#2474C2218yes—
182#2473C2218yes—
183#2465C2218yes—
184#2461C2218yes—
185#2449C2218yes—
186#2449C2218yes—
187#2449C2218yes—
188#2443C2218yes—
189#2430C2214yes—
190#2430C2218yes—
191#2430C2214yes—
192#2425C2218yes—
193#2425C2218yes—
194#2422C2218yes—
195#2416C2218yes—
196#2409C2214yes—
197#2406C2214yes—
198#2406C2214yes—
199#2399C2214yes—
200#2399C2214yes—
201#2392C2214yes—
202C2×#398C2214yes—
203#2388C2214yes—
204C2×#395C2214yes—
205#2361C2218yes—
206#2359C2218yes—
207#2356C2212yes—
208#2353C2212yes—
209#2353C2212yes—
210#2349C2212yes—
211#2346C2212yes—
212#2343C2212yes—
213#2343C2212yes—
214#2339C2212yes—
215#2328C2212yes—
216#2328C2212yes—
217#2326C2212yes—
218#2326C2212yes—
219#2317C2212yes—
220#2317C2212yes—
221C4×#127C2212yes—
222C4×#124C2212yes—
223#2295C2212yes—
224#2290C2212yes—
225#2290C2212yes—
226#2285C2212yes—
227#2285C2212yes—
228C2×#384C2212yes—
229#2283C2211yescharacteristic
230#2283C2211yescharacteristic
231#2283C2211yescharacteristic
232C2×#382C2212yes—
233C42×D4C2212yes—
234C4×#117C2211yescharacteristic
235C2×#376C2211yescharacteristic
236C2×#376C2211yescharacteristic
237C22×#41C2312yes—
238C22×#41C2312yes—
239C22×#41C2312yes—
240C22×#41C2312yes—
241C22×#41C2311yescharacteristic
242C23×Q8C2312yes—
243#557—28no—
244#556—216no—
245#555—216no—
246#554—216no—
247#554—28no—
248#554—28no—
249#553—216no—
250#553—216no—
251#553—28no—
252#553—28no—
253#552—28no—
254#552—28no—
255#552—216no—
256#552—216no—
257#552—216no—
258#548—216no—
259#548—216no—
260#547—216no—
261#547—216no—
262#547—28no—
263#542—216no—
264#542—216no—
265#541—216no—
266#539—216no—
267#539—216no—
268#537—216no—
269#533—28no—
270#533—28no—
271#533—28no—
272#532—28no—
273#532—28no—
274#532—28no—
275C2×C4⋊Q8—28no—
276C2×C4⋊Q8C2311yescharacteristic
277C2×C4⋊Q8C2312yes—
278C2×C4⋊Q8C2312yes—
279C2×C4⋊Q8C2312yes—
280C2×C4⋊Q8C2311yescharacteristic
281C2×C4⋊Q8C2311yescharacteristic
282C2×C4⋊Q8C2311yescharacteristic
283C2×C4⋊Q8C2311yescharacteristic
284C2×C4⋊Q8C2312yes—
285C2×#127C2312yes—
286C2×#127C2311yescharacteristic
287#529—28no—
288#529—28no—
289#529—28no—
290C2×#126C2312yes—
291C2×#126C2312yes—
292C2×#126C2312yes—
293C2×#126C2312yes—
294C2×#126C2312yes—
295C2×#126C2312yes—
296C2×#126C2312yes—
297C2×#126C2314yes—
298C2×#126C2314yes—
299C2×#125—28no—
300C2×#125—28no—
301C2×#125C2312yes—
302C2×#125C2312yes—
303C2×#125C2312yes—
304C2×#125C2312yes—
305C2×#125C2311yescharacteristic
306C2×#125C2311yescharacteristic
307C2×#125C2311yescharacteristic
308C2×#125C2311yescharacteristic
309C2×#125C2312yes—
310C2×#125C2312yes—
311C2×#125C2311yescharacteristic
312C2×#125C2311yescharacteristic
313C2×#125C2311yescharacteristic
314C2×#125C2312yes—
315C2×#125C2312yes—
316C2×#125C2312yes—
317C2×#125C2312yes—
318C2×#125C2312yes—
319C2×#124C2312yes—
320C2×#124C2312yes—
321C2×#124C2312yes—
322C2×#124C2312yes—
323C2×#124C2311yescharacteristic
324C2×#124C2314yes—
325C2×#124C2314yes—
326C2×#123C2312yes—
327C2×#123C2312yes—
328C2×#123C2312yes—
329C2×#123C2312yes—
330C2×#123C2312yes—
331C2×#123C2314yes—
332C2×#123C2314yes—
333C2×#123C2312yes—
334C2×#123C2312yes—
335C2×#123C2312yes—
336C2×#123C2312yes—
337C2×#123C2318yes—
338C2×#123C2318yes—
339C2×C22⋊Q8C2312yes—
340C2×C22⋊Q8C2312yes—
341C2×C22⋊Q8C2312yes—
342C2×C22⋊Q8C2311yescharacteristic
343C2×C22⋊Q8C2311yescharacteristic
344C2×C22⋊Q8C2312yes—
345C2×C22⋊Q8C2311yescharacteristic
346C2×C22⋊Q8C2312yes—
347C2×C22⋊Q8C2312yes—
348C2×C22⋊Q8C2312yes—
349C2×C22⋊Q8C2314yes—
350C2×C22⋊Q8C2312yes—
351C2×C22⋊Q8C2314yes—
352C2×C22⋊Q8C2312yes—
353C2×C22⋊Q8C2312yes—
354C2×C22⋊Q8C2312yes—
355C2×C22⋊Q8C2312yes—
356C2×C22⋊Q8C2314yes—
357C2×C22⋊Q8C2318yes—
358C2×C22⋊Q8C2318yes—
359C2×#121C2312yes—
360C2×#121C2312yes—
361C2×#121C2312yes—
362C2×#121C2311yescharacteristic
363C2×#121C2311yescharacteristic
364C2×#121C2312yes—
365C2×#121C2312yes—
366C2×#121C2311yescharacteristic
367C2×#121C2312yes—
368C2×#121C2312yes—
369C2×#121C2314yes—
370C2×#121C2312yes—
371C2×#121C2314yes—
372C2×#121C2314yes—
373C2×#121C2318yes—
374C2×#121C2318yes—
375#520—216no—
376#520—216no—
377C4×#41D4116yescomplemented
378C2×C4×Q8C2311yescharacteristic
379C2×C4×Q8C2311yescharacteristic
380C2×C4×Q8C2311yescharacteristic
381C2×C4×Q8C2312yes—
382C2×C4×Q8C2312yes—
383C2×C4×Q8C2312yes—
384C2×C4×Q8C2312yes—
385C2×C4×Q8C2312yes—
386C2×C4×Q8C2312yes—
387C2×C4×Q8C2312yes—
388C2×C4×Q8C2311yescharacteristic
389C2×C4×Q8C2311yescharacteristic
390C2×C4×D4C2311yescharacteristic
391C2×C4×D4C2312yes—
392C2×C4×D4C2312yes—
393C2×C4×D4C2312yes—
394C2×C4×D4C2311yescharacteristic
395C2×C4×D4C2311yescharacteristic
396C2×C4×D4C2312yes—
397C2×C4×D4C2312yes—
398C2×C4×D4C2314yes—
399C2×C4×D4C2312yes—
400C2×C4×D4C2312yes—
401C2×C4×D4C2312yes—
402C2×C4×D4C2312yes—
403C2×C4×D4C2312yes—
404C2×C4×D4C2314yes—
405C2×C4×D4C2312yes—
406C2×C4×D4C2312yes—
407C2×C4×D4C2314yes—
408C2×C4×D4C2318yes—
409C2×C4×D4C2311yescharacteristic
410C2×C4×D4C2311yescharacteristic
411C2×C4×D4C2311yescharacteristic
412C2×C4×D4C2311yescharacteristic
413C2×C4×D4C2311yescharacteristic
414C2×C4×D4C2311yescharacteristic
415C2×#117C2312yes—
416C2×#117C2312yes—
417C2×#117C2312yes—
418C2×#117C2312yes—
419C2×#117C2312yes—
420C2×#117C2312yes—
421C2×#117C2312yes—
422C2×#117C2314yes—
423C2×#117C2311yescharacteristic
424C2×#117C2311yescharacteristic
425C2×#117C2312yes—
426C2×#117C2311yescharacteristic
427C2×#117C2311yescharacteristic
428C2×#117C2311yescharacteristic
429C22×C4⋊C4C2311yescharacteristic
430C22×C4⋊C4C2311yescharacteristic
431C22×C4⋊C4C2312yes—
432C22×C4⋊C4C2312yes—
433C22×C4⋊C4C2312yes—
434C22×C4⋊C4C2312yes—
435C22×C4⋊C4C2312yes—
436C22×C4⋊C4C2314yes—
437C22×C4⋊C4C2312yes—
438C22×C4⋊C4C2311yescharacteristic
439C22×C4⋊C4C2311yescharacteristic
440C22×C4⋊C4C2312yes—
441C22×C4⋊C4C2318yes—
442C22×C42C2312yes—
443C22×C42C2312yes—
444C22×C42C2311yescharacteristic
445C22×C42C2311yescharacteristic
446C22×C42C2311yescharacteristic
447#400C2318yes—
448#399C2318yes—
449#399C2318yes—
450#399C2318yes—
451#399C2318yes—
452#398C2314yes—
453#398C2314yes—
454#398C2318yes—
455#398C2318yes—
456#398C2318yes—
457#398C2314yes—
458#398C2314yes—
459#398C2314yes—
460#398C2314yes—
461#398C2314yes—
462#398C2314yes—
463#398C2314yes—
464#398C2318yes—
465#398C2318yes—
466#398C2318yes—
467#398C2318yes—
468#397C2318yes—
469#397C2318yes—
470#397C2318yes—
471#397C2314yes—
472#397C2314yes—
473#397C2314yes—
474#397C2318yes—
475#397C2318yes—
476#396C2318yes—
477#396C2318yes—
478#396C2318yes—
479#396C2318yes—
480#396C2318yes—
481#396C2318yes—
482#396C2318yes—
483#395C2314yes—
484#395C2314yes—
485#395C2314yes—
486#395C2314yes—
487#395C2314yes—
488#395C2314yes—
489#395C2314yes—
490#395C2314yes—
491#395C2314yes—
492#395C2318yes—
493#395C2318yes—
494#395C2318yes—
495#395C2318yes—
496#394C2314yes—
497#394C2314yes—
498#394C2318yes—
499#394C2318yes—
500#394C2314yes—
501#394C2314yes—
502#394C2314yes—
503#394C2314yes—
504#394C2318yes—
505#394C2318yes—
506#394C2318yes—
507#394C2318yes—
508#393C2318yes—
509#393C2314yes—
510#393C2314yes—
511#393C2314yes—
512#392C2314yes—
513#392C2314yes—
514#392C2318yes—
515#391C2312yes—
516#391C2312yes—
517#391C2312yes—
518#391C2318yes—
519#391C2314yes—
520#390C2312yes—
521#390C2312yes—
522#390C2318yes—
523#390C2312yes—
524#390C2312yes—
525#390C2312yes—
526#390C2312yes—
527#390C2312yes—
528#390C2312yes—
529#390C2312yes—
530#390C2318yes—
531#390C2318yes—
532#389C2318yes—
533#389C2318yes—
534#389C2318yes—
535#389C2318yes—
536#389C2318yes—
537#389C2318yes—
538#389C2314yes—
539#388C2318yes—
540#388C2318yes—
541#388C2318yes—
542#388C2318yes—
543#388C2318yes—
544#388C2318yes—
545#388C2314yes—
546#388C2314yes—
547#388C2318yes—
548#388C2318yes—
549#388C2318yes—
550#387C2318yes—
551#387C2318yes—
552#387C2314yes—
553#387C2314yes—
554#387C2314yes—
555#387C2314yes—
556#387C2318yes—
557#387C2318yes—
558#386C2318yes—
559#386C2318yes—
560#386C2318yes—
561#386C2318yes—
562#386C2318yes—
563#386C2318yes—
564#386C2314yes—
565#386C2314yes—
566#386C2318yes—
567#386C2318yes—
568#386C2318yes—
569#385C2318yes—
570#385C2318yes—
571#385C2318yes—
572#385C2318yes—
573#385C2318yes—
574#385C2318yes—
575#385C2318yes—
576#385C2318yes—
577#385C2318yes—
578#385C2318yes—
579#385C2314yes—
580#385C2314yes—
581#385C2318yes—
582#384C2312yes—
583#384C2312yes—
584#384C2312yes—
585#384C2312yes—
586#384C2312yes—
587#384C2312yes—
588#384C2312yes—
589#384C2312yes—
590#384C2312yes—
591#384C2318yes—
592#383C2312yes—
593#383C2312yes—
594#383C2312yes—
595#382C2312yes—
596#382C2312yes—
597#382C2312yes—
598#382C2312yes—
599#382C2312yes—
600#382C2312yes—
601#382C2312yes—
602#382C2312yes—
603#382C2312yes—
604#382C2312yes—
605#382C2312yes—
606#382C2312yes—
607#382C2318yes—
608#381C2312yes—
609#381C2312yes—
610#381C2312yes—
611#380C2318yes—
612#380C2312yes—
613#380C2312yes—
614#380C2312yes—
615#380C2318yes—
616#380C2318yes—
617C4×C4⋊C4C2312yes—
618C4×C4⋊C4C2312yes—
619C4×C4⋊C4C2312yes—
620C4×C4⋊C4C2312yes—
621C4×C4⋊C4C2312yes—
622C4×C4⋊C4C2314yes—
623C4×C4⋊C4C2318yes—
624C4×C4⋊C4C2318yes—
625C4×C22⋊C4C2312yes—
626C4×C22⋊C4C2312yes—
627C4×C22⋊C4C2314yes—
628C4×C22⋊C4C2314yes—
629C4×C22⋊C4C2318yes—
630C4×C22⋊C4C2312yes—
631C4×C22⋊C4C2312yes—
632C4×C22⋊C4C2312yes—
633#376C2312yes—
634#376C2312yes—
635#376C2312yes—
636#376C2312yes—
637#376C2312yes—
638#376C2312yes—
639#376C2311yescharacteristic
640#376C2311yescharacteristic
641#376C2311yescharacteristic
642#376C2311yescharacteristic
643C2×#95C2312yes—
644C2×#95C2312yes—
645C2×#95C2312yes—
646C2×#95C2312yes—
647C2×#95C2318yes—
648C43C2312yes—
649C2×#41—28no—
650C2×#41—28no—
651C2×#41—28no—
652C2×#41—28no—
653C2×#41—44no—
654C2×#41—48no—
655C2×#41—48no—
656C2×#41—84no—
657C2×#41—84no—
658C2×#41C2×D418yes—
659C22×Q8—28no—
660C22×Q8—84no—
661C22×Q8C2411yescharacteristic
662C22×Q8C2412yes—
663C22×Q8C2412yes—
664C22×Q8C2412yes—
665C22×Q8C2412yes—
666C22×Q8C2412yes—
667C22×Q8C2414yes—
668C22×Q8C2411yescharacteristic
669C22×D4C2411yescharacteristic
670C22×D4C2412yes—
671C22×D4C2414yes—
672C22×D4C2412yes—
673C22×D4C2411yescharacteristic
674C22×D4C2411yescharacteristic
675C22×D4C2412yes—
676C22×D4C2412yes—
677C22×D4C2412yes—
678C22×D4C2418yes—
679C22×D4C2412yes—
680C22×D4C2414yes—
681C22×D4C2414yes—
682C22×D4C2411yescharacteristic
683C23×C4C2412yes—
684C23×C4C2414yes—
685C23×C4C2411yescharacteristic
686C23×C4C2411yescharacteristic
687C23×C4C2411yescharacteristic
688C23×C4C2411yescharacteristic
689C23×C4C2412yes—
690C23×C4C2414yes—
691C23×C4C2412yes—
692C23×C4C2412yes—
693C23×C4C2412yes—
694C23×C4C2412yes—
695C23×C4C2414yes—
696C23×C4C2412yes—
697C23×C4C2414yes—
698C23×C4C2414yes—
699C23×C4C2414yes—
700C23×C4C2411yescharacteristic
701C23×C4C2411yescharacteristic
702C23×C4C2411yescharacteristic
703C23×C4C2411yescharacteristic
704C23×C4C2411yescharacteristic
705C4⋊Q8—28no—
706C4⋊Q8—24no—
707C4⋊Q8—24no—
708C4⋊Q8—28no—
709C4⋊Q8—28no—
710C4⋊Q8—28no—
711C4⋊Q8—24no—
712C4⋊Q8—24no—
713C4⋊Q8—24no—
714#127—24no—
715#127—28no—
716#126—28no—
717#126—28no—
718#126—216no—
719#126—216no—
720#126—28no—
721#126—28no—
722#126—28no—
723#126—28no—
724#126—28no—
725#125—28no—
726#125—28no—
727#125—28no—
728#125—28no—
729#125—28no—
730#125—24no—
731#125—24no—
732#125—24no—
733#125—28no—
734#125—28no—
735#125—28no—
736#125—28no—
737#125—24no—
738#125—24no—
739#125—24no—
740#125—24no—
741#125—28no—
742#125—28no—
743#124—216no—
744#124—216no—
745#124—24no—
746#124—28no—
747#124—28no—
748#124—28no—
749#124—28no—
750#123—28no—
751#123—28no—
752#123—28no—
753#123—28no—
754#123—28no—
755#123—28no—
756#123—28no—
757#123—28no—
758#123—28no—
759#123—216no—
760#123—216no—
761#123—416no—
762#123—88no—
763C22⋊Q8—216no—
764C22⋊Q8—28no—
765C22⋊Q8—24no—
766C22⋊Q8—24no—
767C22⋊Q8—24no—
768C22⋊Q8—28no—
769C22⋊Q8—28no—
770C22⋊Q8—28no—
771C22⋊Q8—28no—
772C22⋊Q8—28no—
773C22⋊Q8—28no—
774C22⋊Q8—28no—
775C22⋊Q8—28no—
776C22⋊Q8—28no—
777C22⋊Q8—216no—
778C22⋊Q8—216no—
779C22⋊Q8—28no—
780C22⋊Q8—28no—
781C22⋊Q8—88no—
782C22⋊Q8—88no—
783#121—216no—
784#121—216no—
785#121—216no—
786#121—28no—
787#121—28no—
788#121—24no—
789#121—24no—
790#121—24no—
791#121—28no—
792#121—28no—
793#121—28no—
794#121—28no—
795#121—28no—
796#121—28no—
797#121—416no—
798#121—88no—
799C4×Q8—28no—
800C4×Q8—28no—
801C4×Q8—28no—
802C4×Q8—28no—
803C4×Q8—24no—
804C4×Q8—24no—
805C4×Q8—24no—
806C4×Q8—28no—
807C4×Q8—28no—
808C4×Q8—28no—
809C4×Q8C2×D418yes—
810C4×Q8C2×D418yes—
811C4×D4—28no—
812C4×D4—28no—
813C4×D4—28no—
814C4×D4—28no—
815C4×D4—216no—
816C4×D4—216no—
817C4×D4—28no—
818C4×D4—28no—
819C4×D4—28no—
820C4×D4—28no—
821C4×D4—24no—
822C4×D4—24no—
823C4×D4—24no—
824C4×D4—28no—
825C4×D4—28no—
826C4×D4—28no—
827C4×D4—28no—
828C4×D4—48no—
829C4×D4—88no—
830C4×D4C2×D418yes—
831C4×D4C2×D418yes—
832C4×D4C2×D418yes—
833C4×D4C2×D418yes—
834C4×D4C2×D418yes—
835C4×D4C2×D418yes—
836#117—24no—
837#117—24no—
838#117—28no—
839#117—28no—
840#117—216no—
841#117—28no—
842#117—28no—
843#117—28no—
844#117—28no—
845#117—28no—
846#117—28no—
847#117C2×D418yes—
848#117C2×D418yes—
849#117C2×D418yes—
850C2×C4⋊C4—28no—
851C2×C4⋊C4—28no—
852C2×C4⋊C4—28no—
853C2×C4⋊C4—24no—
854C2×C4⋊C4—24no—
855C2×C4⋊C4—28no—
856C2×C4⋊C4—28no—
857C2×C4⋊C4—24no—
858C2×C4⋊C4—24no—
859C2×C4⋊C4—28no—
860C2×C4⋊C4—216no—
861C2×C4⋊C4—28no—
862C2×C4⋊C4—88no—
863C2×C4⋊C4C2414yes—
864C2×C4⋊C4C2412yes—
865C2×C4⋊C4C2412yes—
866C2×C4⋊C4C2412yes—
867C2×C4⋊C4C2411yescharacteristic
868C2×C4⋊C4C2412yes—
869C2×C4⋊C4C2411yescharacteristic
870C2×C4⋊C4C2412yes—
871C2×C4⋊C4C2412yes—
872C2×C4⋊C4C2411yescharacteristic
873C2×C4⋊C4C2411yescharacteristic
874C2×C4⋊C4C2411yescharacteristic
875C2×C4⋊C4C2411yescharacteristic
876C2×C4⋊C4C2412yes—
877C2×C4⋊C4C2412yes—
878C2×C4⋊C4C2412yes—
879C2×C4⋊C4C2412yes—
880C2×C4⋊C4C2414yes—
881C2×C4⋊C4C2414yes—
882C2×C4⋊C4C2412yes—
883C2×C4⋊C4C2412yes—
884C2×C4⋊C4C2412yes—
885C2×C4⋊C4C2412yes—
886C2×C4⋊C4C2412yes—
887C2×C4⋊C4C2412yes—
888C2×C4⋊C4C2412yes—
889C2×C4⋊C4C2412yes—
890C2×C4⋊C4C2412yes—
891C2×C4⋊C4C2412yes—
892C2×C4⋊C4C2412yes—
893C2×C4⋊C4C2412yes—
894C2×C4⋊C4C2412yes—
895C2×C4⋊C4C2414yes—
896C2×C4⋊C4C2412yes—
897C2×C4⋊C4C2412yes—
898C2×C4⋊C4C2412yes—
899C2×C4⋊C4C2412yes—
900C2×C4⋊C4C2414yes—
901C2×C4⋊C4C2412yes—
902C2×C4⋊C4C2414yes—
903C2×C4⋊C4C2414yes—
904C2×C4⋊C4C2412yes—
905C2×C4⋊C4C2412yes—
906C2×C4⋊C4C2412yes—
907C2×C4⋊C4C2412yes—
908C2×C4⋊C4C2418yes—
909C2×C4⋊C4C2418yes—
910C2×C4⋊C4C2418yes—
911C2×C4⋊C4C2418yes—
912C2×C4⋊C4C2414yes—
913C2×C4⋊C4C2418yes—
914C2×C4⋊C4C2414yes—
915C2×C4⋊C4C2414yes—
916C2×C4⋊C4C2418yes—
917C2×C4⋊C4C2418yes—
918C2×C4⋊C4C2418yes—
919C2×C4⋊C4C2418yes—
920C2×C4⋊C4C2411yescharacteristic
921C2×C4⋊C4C2411yescharacteristic
922C2×C4⋊C4C2411yescharacteristic
923C2×C4⋊C4C2411yescharacteristic
924C2×C4⋊C4C2411yescharacteristic
925C2×C4⋊C4C2411yescharacteristic
926C2×C22⋊C4C2412yes—
927C2×C22⋊C4C2414yes—
928C2×C22⋊C4C2414yes—
929C2×C22⋊C4C2412yes—
930C2×C22⋊C4C2412yes—
931C2×C22⋊C4C2412yes—
932C2×C22⋊C4C2412yes—
933C2×C22⋊C4C2414yes—
934C2×C22⋊C4C2414yes—
935C2×C22⋊C4C2412yes—
936C2×C22⋊C4C2412yes—
937C2×C22⋊C4C2412yes—
938C2×C22⋊C4C2412yes—
939C2×C22⋊C4C2414yes—
940C2×C22⋊C4C2414yes—
941C2×C22⋊C4C2414yes—
942C2×C22⋊C4C2412yes—
943C2×C22⋊C4C2412yes—
944C2×C22⋊C4C2414yes—
945C2×C22⋊C4C2414yes—
946C2×C22⋊C4C2412yes—
947C2×C22⋊C4C2412yes—
948C2×C22⋊C4C2414yes—
949C2×C22⋊C4C2418yes—
950C2×C22⋊C4C2418yes—
951C2×C22⋊C4C2418yes—
952C2×C22⋊C4C2414yes—
953C2×C22⋊C4C2418yes—
954C2×C22⋊C4C2418yes—
955C2×C22⋊C4C2418yes—
956C2×C22⋊C4C2418yes—
957C2×C22⋊C4C2418yes—
958C2×C22⋊C4C2414yes—
959C2×C22⋊C4C2418yes—
960C2×C22⋊C4C2418yes—
961C2×C22⋊C4C2411yescharacteristic
962C2×C22⋊C4C2411yescharacteristic
963C2×C22⋊C4C2411yescharacteristic
964C2×C22⋊C4C2411yescharacteristic
965C2×C22⋊C4C2411yescharacteristic
966C2×C22⋊C4C2411yescharacteristic
967C2×C42—28no—
968C2×C42—28no—
969C2×C42C2×D418yes—
970C2×C42C2×D418yes—
971C2×C42C2×D418yes—
972C2×C42C2414yes—
973C2×C42C2414yes—
974C2×C42C2412yes—
975C2×C42C2412yes—
976C2×C42C2412yes—
977C2×C42C2412yes—
978C2×C42C2412yes—
979C2×C42C2412yes—
980C2×C42C2412yes—
981C2×C42C2412yes—
982C2×C42C2414yes—
983C2×C42C2414yes—
984C2×C42C2414yes—
985C2×C42C2414yes—
986C2×C42C2411yescharacteristic
987C2×C42C2411yescharacteristic
988C2×C42C2411yescharacteristic
989C2×C42C2411yescharacteristic
990C2×C42C2411yescharacteristic
991C2×C42C2411yescharacteristic
992C2×C42C2411yescharacteristic
993C2×C42C2411yescharacteristic
994C2×C42C2411yescharacteristic
995C2×C42C2411yescharacteristic
996C2×C42C2412yes—
997#95C2412yes—
998#95C2412yes—
999#95C2412yes—
1000#95C2412yes—
1001#95C2412yes—
1002#95C2412yes—
1003#95C2414yes—
1004#95C2414yes—
1005#95C2414yes—
1006#95C2414yes—
1007#95C2418yes—
1008#95C2418yes—
1009#95C2418yes—
1010#95C2418yes—
1011#95C2412yes—
1012#95C2412yes—
1013#95C2414yes—
1014#95C2414yes—
1015#95C2414yes—
1016#95C2414yes—
1017#95C2418yes—
1018#95C2418yes—
1019#95C2418yes—
1020#95C2418yes—
1021#95C2414yes—
1022#95C2414yes—
1023#95C2418yes—
1024#95C2418yes—
1025#95C2418yes—
1026#95C2418yes—
1027C24C2512yes—
1028C24C2514yes—
1029C24C2511yescharacteristic
1030C24C2511yescharacteristic
1031C24C2511yescharacteristic
1032#41—416no—
1033#41—432no—
1034#41—432no—
1035#41—816no—
1036#41—816no—
1037C2×Q8—22no—
1038C2×Q8—24no—
1039C2×Q8—24no—
1040C2×Q8—24no—
1041C2×Q8—24no—
1042C2×Q8—24no—
1043C2×Q8—28no—
1044C2×Q8—24no—
1045C2×Q8—44no—
1046C2×Q8—44no—
1047C2×Q8—42no—
1048C2×Q8—44no—
1049C2×Q8—44no—
1050C2×Q8—44no—
1051C2×Q8—48no—
1052C2×Q8—816no—
1053C2×Q8C22×D414yes—
1054C2×D4—24no—
1055C2×D4—24no—
1056C2×D4—28no—
1057C2×D4—24no—
1058C2×D4—24no—
1059C2×D4—28no—
1060C2×D4—216no—
1061C2×D4—24no—
1062C2×D4—28no—
1063C2×D4—28no—
1064C2×D4—22no—
1065C2×D4—24no—
1066C2×D4—24no—
1067C2×D4—24no—
1068C2×D4—24no—
1069C2×D4—24no—
1070C2×D4—24no—
1071C2×D4—216no—
1072C2×D4—42no—
1073C2×D4—44no—
1074C2×D4—44no—
1075C2×D4—44no—
1076C2×D4—48no—
1077C2×D4—48no—
1078C2×D4—44no—
1079C2×D4—48no—
1080C2×D4—48no—
1081C2×D4C22×D414yes—
1082C2×D4C22×D414yes—
1083C2×D4C22×D414yes—
1084C22×C4—24no—
1085C22×C4—24no—
1086C22×C4—24no—
1087C22×C4—24no—
1088C22×C4—24no—
1089C22×C4—24no—
1090C22×C4—28no—
1091C22×C4—28no—
1092C22×C4—24no—
1093C22×C4—24no—
1094C22×C4—28no—
1095C22×C4—28no—
1096C22×C4—24no—
1097C22×C4—28no—
1098C22×C4—24no—
1099C22×C4—24no—
1100C22×C4—28no—
1101C22×C4—28no—
1102C22×C4—28no—
1103C22×C4—44no—
1104C22×C4—42no—
1105C22×C4—42no—
1106C22×C4—48no—
1107C22×C4—42no—
1108C22×C4—44no—
1109C22×C4—44no—
1110C22×C4—42no—
1111C22×C4—42no—
1112C22×C4—44no—
1113C22×C4—48no—
1114C22×C4—44no—
1115C22×C4—44no—
1116C22×C4—48no—
1117C22×C4—44no—
1118C22×C4—44no—
1119C22×C4—48no—
1120C22×C4—44no—
1121C22×C4C22×D414yes—
1122C22×C4C22×D414yes—
1123C22×C4C22×D414yes—
1124C22×C4C22×D414yes—
1125C22×C4C22×D414yes—
1126C22×C4C22×D414yes—
1127C22×C4C22×D414yes—
1128C22×C4C22×D414yes—
1129C22×C4C22×D414yes—
1130C22×C4C2514yes—
1131C22×C4C2514yes—
1132C22×C4C2514yes—
1133C22×C4C2512yes—
1134C22×C4C2514yes—
1135C22×C4C2512yes—
1136C22×C4C2512yes—
1137C22×C4C2514yes—
1138C22×C4C2514yes—
1139C22×C4C2512yes—
1140C22×C4C2512yes—
1141C22×C4C2512yes—
1142C22×C4C2512yes—
1143C22×C4C2511yescharacteristic
1144C22×C4C2511yescharacteristic
1145C22×C4C2511yescharacteristic
1146C22×C4C2511yescharacteristic
1147C22×C4C2511yescharacteristic
1148C22×C4C2511yescharacteristic
1149C22×C4C2511yescharacteristic
1150C22×C4C2511yescharacteristic
1151C22×C4C2511yescharacteristic
1152C22×C4C2511yescharacteristic
1153C22×C4C2511yescharacteristic
1154C22×C4C2514yes—
1155C22×C4C2511yescharacteristic
1156C4⋊C4—28no—
1157C4⋊C4—24no—
1158C4⋊C4—24no—
1159C4⋊C4—24no—
1160C4⋊C4—22no—
1161C4⋊C4—24no—
1162C4⋊C4—22no—
1163C4⋊C4—24no—
1164C4⋊C4—24no—
1165C4⋊C4—22no—
1166C4⋊C4—22no—
1167C4⋊C4—22no—
1168C4⋊C4—22no—
1169C4⋊C4—24no—
1170C4⋊C4—24no—
1171C4⋊C4—24no—
1172C4⋊C4—24no—
1173C4⋊C4—28no—
1174C4⋊C4—28no—
1175C4⋊C4—24no—
1176C4⋊C4—24no—
1177C4⋊C4—24no—
1178C4⋊C4—24no—
1179C4⋊C4—24no—
1180C4⋊C4—24no—
1181C4⋊C4—24no—
1182C4⋊C4—24no—
1183C4⋊C4—24no—
1184C4⋊C4—24no—
1185C4⋊C4—24no—
1186C4⋊C4—24no—
1187C4⋊C4—24no—
1188C4⋊C4—28no—
1189C4⋊C4—24no—
1190C4⋊C4—24no—
1191C4⋊C4—24no—
1192C4⋊C4—24no—
1193C4⋊C4—24no—
1194C4⋊C4—28no—
1195C4⋊C4—28no—
1196C4⋊C4—24no—
1197C4⋊C4—24no—
1198C4⋊C4—24no—
1199C4⋊C4—24no—
1200C4⋊C4—28no—
1201C4⋊C4—48no—
1202C4⋊C4—48no—
1203C4⋊C4—48no—
1204C4⋊C4—48no—
1205C4⋊C4—44no—
1206C4⋊C4—48no—
1207C4⋊C4—44no—
1208C4⋊C4—44no—
1209C4⋊C4—48no—
1210C4⋊C4—48no—
1211C4⋊C4—48no—
1212C4⋊C4—48no—
1213C4⋊C4C22×D414yes—
1214C4⋊C4C22×D414yes—
1215C4⋊C4C22×D414yes—
1216C4⋊C4C22×D414yes—
1217C4⋊C4C22×D414yes—
1218C4⋊C4C22×D414yes—
1219C22⋊C4—24no—
1220C22⋊C4—24no—
1221C22⋊C4—28no—
1222C22⋊C4—28no—
1223C22⋊C4—24no—
1224C22⋊C4—24no—
1225C22⋊C4—24no—
1226C22⋊C4—28no—
1227C22⋊C4—24no—
1228C22⋊C4—28no—
1229C22⋊C4—28no—
1230C22⋊C4—24no—
1231C22⋊C4—24no—
1232C22⋊C4—24no—
1233C22⋊C4—24no—
1234C22⋊C4—28no—
1235C22⋊C4—28no—
1236C22⋊C4—24no—
1237C22⋊C4—24no—
1238C22⋊C4—28no—
1239C22⋊C4—28no—
1240C22⋊C4—24no—
1241C22⋊C4—28no—
1242C22⋊C4—216no—
1243C22⋊C4—44no—
1244C22⋊C4—48no—
1245C22⋊C4—48no—
1246C22⋊C4—48no—
1247C22⋊C4—48no—
1248C22⋊C4—48no—
1249C22⋊C4—48no—
1250C22⋊C4—48no—
1251C22⋊C4—48no—
1252C22⋊C4—48no—
1253C22⋊C4—44no—
1254C22⋊C4C22×D414yes—
1255C22⋊C4C22×D414yes—
1256C22⋊C4C22×D414yes—
1257C22⋊C4C22×D414yes—
1258C22⋊C4C22×D414yes—
1259C22⋊C4C22×D414yes—
1260C42—28no—
1261C42—28no—
1262C42—24no—
1263C42—24no—
1264C42—24no—
1265C42—24no—
1266C42—24no—
1267C42—28no—
1268C42—28no—
1269C42—24no—
1270C42—24no—
1271C42—24no—
1272C42—44no—
1273C42—44no—
1274C42C22×D414yes—
1275C42C22×D414yes—
1276C42C22×D414yes—
1277C42C22×D414yes—
1278C42C22×D414yes—
1279C42C22×D414yes—
1280C42C22×D414yes—
1281C42C22×D414yes—
1282C42C22×D414yes—
1283C42C22×D414yes—
1284C422−1+418yes—
1285C23—22no—
1286C23—22no—
1287C23—22no—
1288C23—22no—
1289C23—22no—
1290C23—22no—
1291C23—22no—
1292C23—22no—
1293C23—22no—
1294C23—24no—
1295C23—24no—
1296C23—24no—
1297C23—24no—
1298C23—28no—
1299C23—24no—
1300C23—24no—
1301C23—28no—
1302C23C23×D412yes—
1303C23C23×D412yes—
1304C23C23×D412yes—
1305C23#58514yes—
1306C23C2611yescharacteristic
1307Q8—44no—
1308Q8—48no—
1309Q8—48no—
1310Q8—48no—
1311Q8—48no—
1312Q8—44no—
1313Q8—84no—
1314Q8—88no—
1315D4—28no—
1316D4—28no—
1317D4—44no—
1318D4—48no—
1319D4—48no—
1320D4—48no—
1321D4—416no—
1322D4—48no—
1323D4—44no—
1324D4—48no—
1325D4—816no—
1326D4—84no—
1327D4—88no—
1328D4—88no—
1329C2×C4—22no—
1330C2×C4—22no—
1331C2×C4—22no—
1332C2×C4—22no—
1333C2×C4—24no—
1334C2×C4—22no—
1335C2×C4—22no—
1336C2×C4—22no—
1337C2×C4—22no—
1338C2×C4—24no—
1339C2×C4—22no—
1340C2×C4—22no—
1341C2×C4—22no—
1342C2×C4—28no—
1343C2×C4—28no—
1344C2×C4—28no—
1345C2×C4—28no—
1346C2×C4—22no—
1347C2×C4—24no—
1348C2×C4—22no—
1349C2×C4—22no—
1350C2×C4—22no—
1351C2×C4—22no—
1352C2×C4—24no—
1353C2×C4—24no—
1354C2×C4—22no—
1355C2×C4—22no—
1356C2×C4—24no—
1357C2×C4—24no—
1358C2×C4—24no—
1359C2×C4—24no—
1360C2×C4—24no—
1361C2×C4—24no—
1362C2×C4—24no—
1363C2×C4—24no—
1364C2×C4—24no—
1365C2×C4—24no—
1366C2×C4—28no—
1367C2×C4—24no—
1368C2×C4—24no—
1369C2×C4—24no—
1370C2×C4—24no—
1371C2×C4—24no—
1372C2×C4—24no—
1373C2×C4—28no—
1374C2×C4—28no—
1375C2×C4—44no—
1376C2×C4—44no—
1377C2×C4—44no—
1378C2×C4—44no—
1379C2×C4—44no—
1380C2×C4—416no—
1381C2×C4—416no—
1382C2×C4—48no—
1383C2×C4—48no—
1384C2×C4—48no—
1385C2×C4—84no—
1386C2×C4—84no—
1387C2×C4—88no—
1388C2×C4—88no—
1389C2×C4—88no—
1390C2×C4—84no—
1391C2×C4—84no—
1392C2×C4—88no—
1393C2×C4C23×D412yes—
1394C2×C4C23×D412yes—
1395C2×C4C23×D412yes—
1396C2×C4C23×D412yes—
1397C2×C4C23×D412yes—
1398C2×C4C23×D412yes—
1399C2×C4C23×D412yes—
1400C2×C4C23×D412yes—
1401C2×C4C23×D412yes—
1402C2×C4C23×D412yes—
1403C2×C4C23×D412yes—
1404C2×C4C23×D412yes—
1405C2×C4C2×2−1+418yes—
1406C2×C4C2×2−1+414yes—
1407C22—22no—
1408C22—22no—
1409C22—28no—
1410C22—22no—
1411C22—22no—
1412C22—22no—
1413C22—22no—
1414C22—22no—
1415C22—22no—
1416C22—44no—
1417C22—44no—
1418C22—42no—
1419C22—44no—
1420C22—44no—
1421C22—42no—
1422C22—44no—
1423C22—42no—
1424C22—48no—
1425C22—48no—
1426C22—48no—
1427C22#344914yes—
1428C22C24×D411yescharacteristic
1429C22C22×2−1+412yes—
1430C22C2×#58512yes—
1431C22H(7,𝔽2)12yes—
1432C4—22no—
1433C4—22no—
1434C4—22no—
1435C4—22no—
1436C4—22no—
1437C4—22no—
1438C4—22no—
1439C4—22no—
1440C4—22no—
1441C4—22no—
1442C4—22no—
1443C4—28no—
1444C4—42no—
1445C4—42no—
1446C4—44no—
1447C4—44no—
1448C4—42no—
1449C4—42no—
1450C4—42no—
1451C4—44no—
1452C4—42no—
1453C4—42no—
1454C4—44no—
1455C4—44no—
1456C4—44no—
1457C4#349914yes—
1458C2—24no—
1459C2—42no—
1460C2—42no—
1461C2—84no—
1462C2—82no—
1463C2C2×#344911yescharacteristic
1464C2C2×#349911yescharacteristic
1465C2#6285211yescharacteristic
1466C2#6295814yes—
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×#3515C2semidirect
3. #42314C2semidirect
4. #42312C2semidirect
5. #41948C2semidirect
6. #41937C2semidirect
7. #40504C2semidirect
8. #40493C2semidirect
9. #39613C2semidirect
10. #39611C2semidirect
11. #37871C2semidirect
12. #37869C2semidirect
13. #37864C2semidirect
14. #37862C2semidirect
15. #37634C2semidirect
16. #37615C2semidirect
17. #37545C2semidirect
18. #37545C2semidirect
19. #37539C2semidirect
20. #37539C2semidirect
21. #36184C2semidirect
22. #36182C2semidirect
23. #36001C2semidirect
24. #35740C2semidirect
25. #35335C2semidirect
26. #35303C2semidirect
27. #35303C2semidirect
28. #34642C2semidirect
29. #34624C2semidirect
30. C2×#2660C2semidirect
31. #34123C2semidirect
377. 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×#35152
#423142
#423122
#419482
#419372
#405042
#404932
#396132
#396112
#378712
#378692
#378642
#378622
#376342
#376152
#375452
#375392
#361842
#361822
#360012
#357402
#353352
#353032
#346422
#346242
C2×#26602
#341232