Finite Group Databasebeta

← #7732052

Subgroups — #7732052

Order 512.

7844 conjugacy classes of subgroups.

The subgroup lattice has 1451 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3499C211yesmaximal, characteristic, complemented
2C2×#3547C211yesmaximal, characteristic, complemented
3#48822C218yesmaximal, complemented
4#47766C218yesmaximal, complemented
5#45255C214yesmaximal, complemented
6#44928C214yesmaximal, complemented
7#39360C211yesmaximal, characteristic, complemented
8#39360C211yesmaximal, characteristic, complemented
9#38958C211yesmaximal, characteristic, complemented
10#38955C211yesmaximal, characteristic, complemented
11#38088C212yesmaximal, complemented
12#38081C212yesmaximal, complemented
13#37764C214yesmaximal, complemented
14#37686C214yesmaximal, complemented
15#37680C212yesmaximal, complemented
16#37675C212yesmaximal, complemented
17#37617C211yesmaximal, characteristic, complemented
18#37388C212yesmaximal, complemented
19#37386C212yesmaximal, complemented
20#36415C211yesmaximal, characteristic, complemented
21#36276C211yesmaximal, characteristic, complemented
22#36127C211yesmaximal, characteristic, complemented
23D4×C4⋊Q8C211yesmaximal, characteristic, complemented
24#35666C212yesmaximal, complemented
25#35660C212yesmaximal, complemented
26#35281C211yesmaximal, characteristic, complemented
27#35200C211yesmaximal, characteristic, complemented
28#34910C211yesmaximal, characteristic, complemented
29#34086C211yesmaximal, characteristic, complemented
30C22×2−1+4C2212yes—
31#3547—216no—
32C2×#562C2214yes—
33#3499—216no—
34C2×#555C2211yescharacteristic
35C2×#555C2212yes—
36C2×#554C2211yescharacteristic
37C2×#553C2212yes—
38C2×#552C2212yes—
39C2×D4×Q8C2211yescharacteristic
40C2×D4×Q8C2211yescharacteristic
41C2×D4×Q8C2212yes—
42C2×D4×Q8C2211yescharacteristic
43C2×#548C2212yes—
44C2×#547C2211yescharacteristic
45C2×#547C2211yescharacteristic
46C2×#547C2212yes—
47C2×#547C2211yescharacteristic
48C2×#547C2212yes—
49C2×#547C2214yes—
50C2×#547C2212yes—
51C2×#544C2212yes—
52C2×#542C2214yes—
53C2×#540C2212yes—
54C2×#537C2212yes—
55C2×#536C2212yes—
56C2×#536C2212yes—
57C2×#536C2214yes—
58C2×#536C2212yes—
59C2×#536C2212yes—
60C2×#533C2211yescharacteristic
61C2×#532C2212yes—
62C2×#532C2212yes—
63C2×#532C2211yescharacteristic
64C22×C4⋊Q8C2212yes—
65C22×C4⋊Q8C2211yescharacteristic
66C22×C4⋊Q8C2212yes—
67C2×#529C2211yescharacteristic
68C2×C4×#41C2211yescharacteristic
69#2868C2211yescharacteristic
70#2868C2211yescharacteristic
71#2862C2211yescharacteristic
72#2862C2211yescharacteristic
73#2857C2212yes—
74#2857C2212yes—
75#2857C2212yes—
76#2851C2214yes—
77#2850C2212yes—
78#2821C2214yes—
79#2734C2218yes—
80#2729C2218yes—
81#2724C2218yes—
82#2717C2218yes—
83#2717C2218yes—
84#2713C2218yes—
85#2708C2218yes—
86#2708C2218yes—
87#2701C2218yes—
88#2700C2218yes—
89#2695C2218yes—
90#2689C2218yes—
91#2687C2218yes—
92#2686C2218yes—
93#2680C2218yes—
94#2680C2218yes—
95#2677C2218yes—
96#2674C2218yes—
97#2672C2218yes—
98#2671C2218yes—
99#2660C2214yes—
100#2658C2212yes—
101#2642C2212yes—
102#2638C2214yes—
103#2628C2214yes—
104#2623C2214yes—
105#2621C2212yes—
106#2621C2212yes—
107#2621C2212yes—
108#2620C2212yes—
109#2602C2214yes—
110#2601C2214yes—
111#2599C2214yes—
112#2567C2211yescharacteristic
113#2567C2214yes—
114#2566C2211yescharacteristic
115#2565C2211yescharacteristic
116#2563C2211yescharacteristic
117#2557C2218yes—
118#2551C2214yes—
119#2550C2214yes—
120#2549C2218yes—
121#2547C2211yescharacteristic
122#2547C2211yescharacteristic
123#2547C2211yescharacteristic
124#2546C2211yescharacteristic
125#2546C2211yescharacteristic
126#2546C2212yes—
127#2546C2212yes—
128#2546C2211yescharacteristic
129#2545C2211yescharacteristic
130#2544C2211yescharacteristic
131#2537C2214yes—
132#2535C2214yes—
133#2503C2212yes—
134#2502C2212yes—
135#2502C2214yes—
136#2500C2211yescharacteristic
137#2499C2211yescharacteristic
138#2499C2212yes—
139#2499C2212yes—
140#2499C2212yes—
141#2487C2214yes—
142#2485C2214yes—
143#2473C2218yes—
144#2470C2218yes—
145#2455C2218yes—
146#2449C2218yes—
147#2449C2218yes—
148#2443C2218yes—
149#2442C2214yes—
150#2440C2218yes—
151#2440C2214yes—
152#2440C2214yes—
153#2439C2214yes—
154#2438C2218yes—
155#2436C2212yes—
156#2436C2212yes—
157#2434C2212yes—
158#2434C2212yes—
159#2434C2212yes—
160#2434C2212yes—
161#2434C2212yes—
162#2434C2212yes—
163#2434C2212yes—
164#2434C2218yes—
165#2434C2212yes—
166#2432C2212yes—
167#2432C2212yes—
168#2432C2212yes—
169#2432C2212yes—
170#2432C2212yes—
171#2432C2212yes—
172#2432C2211yescharacteristic
173#2432C2218yes—
174#2431C2212yes—
175#2431C2211yescharacteristic
176#2430C2218yes—
177#2430C2218yes—
178#2422C2218yes—
179#2422C2214yes—
180#2422C2214yes—
181#2420C2214yes—
182#2420C2214yes—
183#2419C2218yes—
184#2409C2218yes—
185#2407C2218yes—
186#2406C2218yes—
187#2406C2218yes—
188#2392C2214yes—
189#2352C2214yes—
190#2349C2214yes—
191D4×C4⋊C4C2214yes—
192D4×C4⋊C4C2214yes—
193#2337C2214yes—
194#2333C2214yes—
195#2331C2212yes—
196#2328C2212yes—
197#2327C2212yes—
198#2326C2212yes—
199#2324C2212yes—
200#2324C2212yes—
201#2317C2214yes—
202#2311C2212yes—
203#2310C2212yes—
204C4×C4⋊Q8C2211yescharacteristic
205C4×#127C2211yescharacteristic
206C4×#124C2211yescharacteristic
207C4×#124C2211yescharacteristic
208#2297C2212yes—
209#2297C2212yes—
210#2297C2212yes—
211C2×#391C2212yes—
212#2293C2211yescharacteristic
213#2293C2211yescharacteristic
214#2290C2212yes—
215#2290C2212yes—
216#2290C2214yes—
217#2283C2211yescharacteristic
218C42×D4C2211yescharacteristic
219C42×D4C2211yescharacteristic
220C4×#117C2211yescharacteristic
221C2×2−1+4—216no—
222C2×2−1+4—48no—
223C2×2−1+4—48no—
224C22×#41C2311yescharacteristic
225C22×#41C2312yes—
226C22×#41C2312yes—
227C22×#41C2314yes—
228C22×#41C2314yes—
229C22×#41C2314yes—
230C22×#41C2312yes—
231C22×#41C2312yes—
232C23×Q8C2312yes—
233C23×Q8C2312yes—
234C23×Q8C2314yes—
235C23×Q8C2312yes—
236C23×Q8C2312yes—
237#562—232no—
238#555—216no—
239#555—28no—
240#554—28no—
241#553—216no—
242#552—216no—
243D4×Q8—28no—
244D4×Q8—216no—
245D4×Q8—28no—
246D4×Q8—28no—
247#548—216no—
248#547—216no—
249#547—216no—
250#547—232no—
251#547—28no—
252#547—216no—
253#547—28no—
254#547—28no—
255#544—216no—
256#542—232no—
257#540—216no—
258#537—216no—
259#536—216no—
260#536—216no—
261#536—232no—
262#536—48no—
263#536—48no—
264#533—28no—
265#532—216no—
266#532—48no—
267#532D4116yescomplemented
268C2×C4⋊Q8—216no—
269C2×C4⋊Q8—28no—
270C2×C4⋊Q8—48no—
271C2×C4⋊Q8C2311yescharacteristic
272C2×C4⋊Q8C2311yescharacteristic
273C2×C4⋊Q8C2312yes—
274C2×C4⋊Q8C2312yes—
275C2×C4⋊Q8C2311yescharacteristic
276C2×C4⋊Q8C2311yescharacteristic
277C2×C4⋊Q8C2311yescharacteristic
278C2×C4⋊Q8C2312yes—
279C2×C4⋊Q8C2312yes—
280C2×C4⋊Q8C2314yes—
281C2×C4⋊Q8C2314yes—
282C2×C4⋊Q8C2312yes—
283C2×C4⋊Q8C2312yes—
284C2×C4⋊Q8C2314yes—
285C2×C4⋊Q8C2312yes—
286C2×C4⋊Q8C2312yes—
287C2×C4⋊Q8C2312yes—
288C2×C4⋊Q8C2312yes—
289C2×C4⋊Q8C2312yes—
290C2×C4⋊Q8C2312yes—
291C2×C4⋊Q8C2312yes—
292C2×C4⋊Q8C2318yes—
293C2×C4⋊Q8C2311yescharacteristic
294C2×#127C2311yescharacteristic
295C2×#127C2311yescharacteristic
296#529—28no—
297C2×#126C2312yes—
298C2×#126C2314yes—
299C2×#125C2311yescharacteristic
300C2×#125C2312yes—
301C2×#125C2312yes—
302C2×#125C2314yes—
303C2×#124C2312yes—
304C2×#124C2311yescharacteristic
305C2×#124C2314yes—
306C2×#124C2314yes—
307C2×#124C2311yescharacteristic
308C2×#124C2311yescharacteristic
309C2×#124C2314yes—
310C2×#124C2314yes—
311C2×#124C2312yes—
312C2×#124C2312yes—
313C2×#124C2312yes—
314C2×#123C2312yes—
315C2×#123C2314yes—
316C2×#123C2314yes—
317C2×#123C2314yes—
318C2×#123C2314yes—
319C2×#123C2314yes—
320C2×#123C2314yes—
321C2×#123C2314yes—
322C2×#123C2314yes—
323C2×#123C2314yes—
324C2×#123C2314yes—
325C2×#123C2318yes—
326C2×#123C2318yes—
327C2×C22⋊Q8C2312yes—
328C2×C22⋊Q8C2312yes—
329C2×C22⋊Q8C2312yes—
330C2×C22⋊Q8C2312yes—
331C2×C22⋊Q8C2312yes—
332C2×C22⋊Q8C2312yes—
333C2×C22⋊Q8C2312yes—
334C2×C22⋊Q8C2312yes—
335C2×C22⋊Q8C2314yes—
336C2×C22⋊Q8C2311yescharacteristic
337C2×C22⋊Q8C2314yes—
338C2×C22⋊Q8C2312yes—
339C2×C22⋊Q8C2314yes—
340C2×C22⋊Q8C2314yes—
341C2×C22⋊Q8C2314yes—
342C2×C22⋊Q8C2314yes—
343C2×C22⋊Q8C2314yes—
344C2×C22⋊Q8C2314yes—
345C2×C22⋊Q8C2318yes—
346C2×C22⋊Q8C2318yes—
347C2×#121C2312yes—
348C2×#121C2314yes—
349C2×#121C2314yes—
350C2×#121C2314yes—
351C2×#121C2311yescharacteristic
352C2×#121C2312yes—
353C2×#121C2312yes—
354C2×#121C2312yes—
355C2×#121C2312yes—
356C2×#121C2314yes—
357C2×#121C2314yes—
358C2×#121C2318yes—
359C2×#121C2311yescharacteristic
360C2×#121C2311yescharacteristic
361C2×#121C2312yes—
362C4×#41—28no—
363C2×C4×Q8C2311yescharacteristic
364C2×C4×Q8C2311yescharacteristic
365C2×C4×Q8C2311yescharacteristic
366C2×C4×Q8C2312yes—
367C2×C4×Q8C2312yes—
368C2×C4×D4C2311yescharacteristic
369C2×C4×D4C2314yes—
370C2×C4×D4C2311yescharacteristic
371C2×C4×D4C2311yescharacteristic
372C2×C4×D4C2312yes—
373C2×C4×D4C2312yes—
374C2×C4×D4C2312yes—
375C2×C4×D4C2312yes—
376C2×C4×D4C2312yes—
377C2×C4×D4C2312yes—
378C2×C4×D4C2312yes—
379C2×C4×D4C2312yes—
380C2×C4×D4C2312yes—
381C2×C4×D4C2314yes—
382C2×C4×D4C2314yes—
383C2×C4×D4C2318yes—
384C2×C4×D4C2311yescharacteristic
385C2×C4×D4C2312yes—
386C2×C4×D4C2311yescharacteristic
387C2×#117C2312yes—
388C2×#117C2312yes—
389C2×#117C2312yes—
390C2×#117C2312yes—
391C2×#117C2312yes—
392C2×#117C2312yes—
393C2×#117C2311yescharacteristic
394C2×#117C2314yes—
395C2×#117C2312yes—
396C2×#117C2312yes—
397C22×C4⋊C4C2312yes—
398C22×C4⋊C4C2312yes—
399C22×C4⋊C4C2312yes—
400C22×C4⋊C4C2312yes—
401C22×C4⋊C4C2312yes—
402C22×C4⋊C4C2312yes—
403C22×C4⋊C4C2314yes—
404C22×C4⋊C4C2318yes—
405C22×C42C2312yes—
406C22×C42C2312yes—
407C22×C42C2312yes—
408C22×C42C2311yescharacteristic
409#400C2318yes—
410#400C2318yes—
411#400C2318yes—
412#399C2318yes—
413#399C2318yes—
414#398C2314yes—
415#398C2314yes—
416#398C2314yes—
417#398C2314yes—
418#398C2318yes—
419#398C2318yes—
420#398C2318yes—
421#398C2318yes—
422#398C2318yes—
423#398C2318yes—
424#397C2314yes—
425#397C2314yes—
426#397C2314yes—
427#397C2314yes—
428#397C2318yes—
429#397C2318yes—
430#397C2318yes—
431#397C2318yes—
432#397C2318yes—
433#397C2318yes—
434#396C2314yes—
435#396C2314yes—
436#396C2318yes—
437#395C2318yes—
438#395C2314yes—
439#395C2318yes—
440#395C2318yes—
441#395C2318yes—
442#395C2318yes—
443#395C2318yes—
444#395C2318yes—
445#395C2318yes—
446#394C2314yes—
447#394C2314yes—
448#394C2314yes—
449#394C2318yes—
450#394C2318yes—
451#394C2318yes—
452#394C2318yes—
453#394C2318yes—
454#394C2318yes—
455#394C2318yes—
456#393C2314yes—
457#393C2318yes—
458#393C2318yes—
459#392C2314yes—
460#392C2318yes—
461#391C2311yescharacteristic
462#391C2311yescharacteristic
463#391C2311yescharacteristic
464#391C2312yes—
465#391C2312yes—
466#391C2312yes—
467#391C2318yes—
468#391C2312yes—
469#391C2312yes—
470#391C2314yes—
471#391C2314yes—
472#391C2312yes—
473#391C2312yes—
474#391C2314yes—
475#391C2314yes—
476#391C2312yes—
477#391C2312yes—
478#391C2311yescharacteristic
479#391C2312yes—
480#391C2312yes—
481#391C2318yes—
482#390C2311yescharacteristic
483#390C2311yescharacteristic
484#390C2314yes—
485#390C2312yes—
486#390C2311yescharacteristic
487#390C2312yes—
488#390C2312yes—
489#390C2314yes—
490#390C2314yes—
491#390C2311yescharacteristic
492#389C2314yes—
493#389C2318yes—
494#389C2318yes—
495#389C2314yes—
496#389C2312yes—
497#389C2312yes—
498#389C2314yes—
499#389C2318yes—
500#389C2318yes—
501#389C2318yes—
502#389C2314yes—
503#389C2314yes—
504#388C2314yes—
505#388C2314yes—
506#388C2318yes—
507#388C2314yes—
508#388C2314yes—
509#388C2318yes—
510#388C2314yes—
511#388C2314yes—
512#388C2314yes—
513#388C2314yes—
514#387C2314yes—
515#387C2318yes—
516#387C2318yes—
517#387C2314yes—
518#387C2314yes—
519#387C2318yes—
520#387C2314yes—
521#387C2318yes—
522#387C2318yes—
523#386C2318yes—
524#386C2314yes—
525#386C2314yes—
526#386C2314yes—
527#386C2314yes—
528#386C2314yes—
529#386C2314yes—
530#386C2318yes—
531#386C2314yes—
532#386C2314yes—
533#386C2318yes—
534#386C2318yes—
535#386C2318yes—
536#386C2318yes—
537#385C2314yes—
538#385C2318yes—
539#385C2318yes—
540#385C2314yes—
541#385C2314yes—
542#385C2318yes—
543#385C2318yes—
544#385C2314yes—
545#385C2318yes—
546#385C2318yes—
547#385C2318yes—
548#385C2318yes—
549#385C2318yes—
550#385C2318yes—
551#385C2318yes—
552#385C2318yes—
553#385C2318yes—
554#385C2318yes—
555#385C2318yes—
556#385C2318yes—
557#384C2311yescharacteristic
558#384C2311yescharacteristic
559#384C2312yes—
560#384C2314yes—
561#384C2314yes—
562#384C2314yes—
563#384C2314yes—
564#383C2312yes—
565#382C2312yes—
566#382C2311yescharacteristic
567#382C2311yescharacteristic
568#382C2314yes—
569#382C2314yes—
570#382C2312yes—
571#381C2318yes—
572#381C2312yes—
573#381C2318yes—
574#380C2314yes—
575#380C2318yes—
576#380C2312yes—
577#380C2314yes—
578#380C2318yes—
579#380C2318yes—
580#380C2318yes—
581#380C2314yes—
582#380C2314yes—
583C4×C4⋊C4C2314yes—
584C4×C4⋊C4C2311yescharacteristic
585C4×C4⋊C4C2311yescharacteristic
586C4×C4⋊C4C2311yescharacteristic
587C4×C4⋊C4C2312yes—
588C4×C4⋊C4C2311yescharacteristic
589C4×C4⋊C4C2312yes—
590C4×C4⋊C4C2312yes—
591C4×C22⋊C4C2312yes—
592C4×C22⋊C4C2314yes—
593C4×C22⋊C4C2314yes—
594C4×C22⋊C4C2318yes—
595C4×C22⋊C4C2314yes—
596C4×C22⋊C4C2314yes—
597C4×C22⋊C4C2311yescharacteristic
598C4×C22⋊C4C2312yes—
599C4×C22⋊C4C2312yes—
600C4×C22⋊C4C2312yes—
601C4×C22⋊C4C2311yescharacteristic
602C4×C22⋊C4C2312yes—
603C4×C22⋊C4C2312yes—
604#376C2312yes—
605#376C2312yes—
606C2×#95C2318yes—
607C43C2311yescharacteristic
608C43C2311yescharacteristic
6092−1+4—4128no—
610C2×#41—24no—
611C2×#41—216no—
612C2×#41—216no—
613C2×#41—216no—
614C2×#41—24no—
615C2×#41—28no—
616C2×#41—28no—
617C2×#41—24no—
618C2×#41—28no—
619C2×#41—28no—
620C2×#41—28no—
621C2×#41—44no—
622C2×#41—44no—
623C2×#41—48no—
624C2×#41—48no—
625C2×#41—48no—
626C2×#41—48no—
627C2×#41—44no—
628C2×#41—44no—
629C2×#41—48no—
630C2×#41—48no—
631C2×#41—44no—
632C2×#41—44no—
633C2×#41C2×D4116yes—
634C22×Q8—216no—
635C22×Q8—28no—
636C22×Q8—28no—
637C22×Q8—28no—
638C22×Q8—28no—
639C22×Q8—28no—
640C22×Q8—28no—
641C22×Q8—48no—
642C22×Q8—44no—
643C22×Q8—44no—
644C22×Q8—48no—
645C22×Q8—44no—
646C22×Q8—44no—
647C22×Q8—44no—
648C22×Q8—44no—
649C22×Q8C2411yescharacteristic
650C22×Q8C2412yes—
651C22×Q8C2412yes—
652C22×Q8C2412yes—
653C22×Q8C2414yes—
654C22×Q8C2414yes—
655C22×Q8C2411yescharacteristic
656C22×Q8C2412yes—
657C22×Q8C2414yes—
658C22×Q8C2414yes—
659C22×Q8C2412yes—
660C22×D4C2412yes—
661C22×D4C2411yescharacteristic
662C22×D4C2414yes—
663C22×D4C2414yes—
664C22×D4C2414yes—
665C22×D4C2411yescharacteristic
666C22×D4C2411yescharacteristic
667C22×D4C2411yescharacteristic
668C22×D4C2412yes—
669C22×D4C2414yes—
670C22×D4C2414yes—
671C22×D4C2412yes—
672C22×D4C2412yes—
673C22×D4C2412yes—
674C22×D4C2412yes—
675C23×C4C2412yes—
676C23×C4C2412yes—
677C23×C4C2412yes—
678C23×C4C2414yes—
679C23×C4C2414yes—
680C23×C4C2414yes—
681C23×C4C2414yes—
682C23×C4C2411yescharacteristic
683C23×C4C2412yes—
684C23×C4C2412yes—
685C23×C4C2411yescharacteristic
686C23×C4C2412yes—
687C23×C4C2414yes—
688C23×C4C2414yes—
689C23×C4C2414yes—
690C23×C4C2414yes—
691C23×C4C2414yes—
692C23×C4C2414yes—
693C23×C4C2411yescharacteristic
694C4⋊Q8—216no—
695C4⋊Q8—216no—
696C4⋊Q8—24no—
697C4⋊Q8—28no—
698C4⋊Q8—28no—
699C4⋊Q8—28no—
700C4⋊Q8—216no—
701C4⋊Q8—28no—
702C4⋊Q8—28no—
703C4⋊Q8—28no—
704C4⋊Q8—24no—
705C4⋊Q8—24no—
706C4⋊Q8—28no—
707C4⋊Q8—24no—
708C4⋊Q8—24no—
709C4⋊Q8—44no—
710C4⋊Q8—44no—
711C4⋊Q8—44no—
712C4⋊Q8—44no—
713C4⋊Q8—44no—
714C4⋊Q8—44no—
715C4⋊Q8—416no—
716C4⋊Q8C2×D418yes—
717#127—24no—
718#127C2×D418yes—
719#126—216no—
720#126—28no—
721#125—216no—
722#125—28no—
723#125—24no—
724#125—28no—
725#124—24no—
726#124—216no—
727#124—216no—
728#124—28no—
729#124—24no—
730#124—216no—
731#124—216no—
732#124—24no—
733#124—44no—
734#124—44no—
735#124C2×D4116yes—
736#123—216no—
737#123—216no—
738#123—216no—
739#123—216no—
740#123—216no—
741#123—28no—
742#123—216no—
743#123—216no—
744#123—216no—
745#123—216no—
746#123—216no—
747#123—416no—
748#123—416no—
749C22⋊Q8—216no—
750C22⋊Q8—24no—
751C22⋊Q8—28no—
752C22⋊Q8—28no—
753C22⋊Q8—28no—
754C22⋊Q8—28no—
755C22⋊Q8—28no—
756C22⋊Q8—28no—
757C22⋊Q8—28no—
758C22⋊Q8—28no—
759C22⋊Q8—28no—
760C22⋊Q8—216no—
761C22⋊Q8—216no—
762C22⋊Q8—216no—
763C22⋊Q8—216no—
764C22⋊Q8—216no—
765C22⋊Q8—216no—
766C22⋊Q8—216no—
767C22⋊Q8—416no—
768C22⋊Q8—416no—
769#121—28no—
770#121—28no—
771#121—216no—
772#121—216no—
773#121—216no—
774#121—216no—
775#121—28no—
776#121—216no—
777#121—28no—
778#121—24no—
779#121—28no—
780#121—416no—
781#121C2×D418yes—
782#121C2×D418yes—
783#121C2×D4116yes—
784C4×Q8—24no—
785C4×Q8—24no—
786C4×Q8—24no—
787C4×Q8—28no—
788C4×Q8—28no—
789C4×D4—28no—
790C4×D4—28no—
791C4×D4—216no—
792C4×D4—28no—
793C4×D4—28no—
794C4×D4—28no—
795C4×D4—28no—
796C4×D4—28no—
797C4×D4—216no—
798C4×D4—24no—
799C4×D4—24no—
800C4×D4—24no—
801C4×D4—28no—
802C4×D4—216no—
803C4×D4—28no—
804C4×D4—416no—
805C4×D4C2×D418yes—
806C4×D4C2×D4116yes—
807C4×D4C2×D418yes—
808#117—24no—
809#117—28no—
810#117—28no—
811#117—28no—
812#117—216no—
813#117—28no—
814#117—28no—
815#117—28no—
816#117—44no—
817#117—44no—
818C2×C4⋊C4—28no—
819C2×C4⋊C4—28no—
820C2×C4⋊C4—28no—
821C2×C4⋊C4—28no—
822C2×C4⋊C4—28no—
823C2×C4⋊C4—216no—
824C2×C4⋊C4—28no—
825C2×C4⋊C4—416no—
826C2×C4⋊C4C2412yes—
827C2×C4⋊C4C2412yes—
828C2×C4⋊C4C2414yes—
829C2×C4⋊C4C2411yescharacteristic
830C2×C4⋊C4C2414yes—
831C2×C4⋊C4C2412yes—
832C2×C4⋊C4C2412yes—
833C2×C4⋊C4C2414yes—
834C2×C4⋊C4C2412yes—
835C2×C4⋊C4C2412yes—
836C2×C4⋊C4C2414yes—
837C2×C4⋊C4C2414yes—
838C2×C4⋊C4C2414yes—
839C2×C4⋊C4C2414yes—
840C2×C4⋊C4C2414yes—
841C2×C4⋊C4C2414yes—
842C2×C4⋊C4C2418yes—
843C2×C4⋊C4C2412yes—
844C2×C4⋊C4C2411yescharacteristic
845C2×C4⋊C4C2412yes—
846C2×C4⋊C4C2411yescharacteristic
847C2×C4⋊C4C2411yescharacteristic
848C2×C4⋊C4C2412yes—
849C2×C4⋊C4C2412yes—
850C2×C4⋊C4C2414yes—
851C2×C4⋊C4C2412yes—
852C2×C4⋊C4C2412yes—
853C2×C4⋊C4C2412yes—
854C2×C4⋊C4C2412yes—
855C2×C4⋊C4C2414yes—
856C2×C4⋊C4C2412yes—
857C2×C4⋊C4C2412yes—
858C2×C4⋊C4C2414yes—
859C2×C4⋊C4C2414yes—
860C2×C4⋊C4C2414yes—
861C2×C4⋊C4C2412yes—
862C2×C4⋊C4C2412yes—
863C2×C4⋊C4C2418yes—
864C2×C4⋊C4C2418yes—
865C2×C4⋊C4C2414yes—
866C2×C4⋊C4C2414yes—
867C2×C4⋊C4C2418yes—
868C2×C4⋊C4C2418yes—
869C2×C4⋊C4C2418yes—
870C2×C4⋊C4C2418yes—
871C2×C4⋊C4C2414yes—
872C2×C4⋊C4C2418yes—
873C2×C4⋊C4C2411yescharacteristic
874C2×C4⋊C4C2411yescharacteristic
875C2×C4⋊C4C2412yes—
876C2×C22⋊C4C2412yes—
877C2×C22⋊C4C2412yes—
878C2×C22⋊C4C2412yes—
879C2×C22⋊C4C2412yes—
880C2×C22⋊C4C2414yes—
881C2×C22⋊C4C2412yes—
882C2×C22⋊C4C2414yes—
883C2×C22⋊C4C2414yes—
884C2×C22⋊C4C2414yes—
885C2×C22⋊C4C2412yes—
886C2×C22⋊C4C2412yes—
887C2×C22⋊C4C2412yes—
888C2×C22⋊C4C2414yes—
889C2×C22⋊C4C2414yes—
890C2×C22⋊C4C2414yes—
891C2×C22⋊C4C2414yes—
892C2×C22⋊C4C2414yes—
893C2×C22⋊C4C2414yes—
894C2×C22⋊C4C2418yes—
895C2×C22⋊C4C2412yes—
896C2×C22⋊C4C2412yes—
897C2×C22⋊C4C2414yes—
898C2×C22⋊C4C2414yes—
899C2×C22⋊C4C2414yes—
900C2×C22⋊C4C2414yes—
901C2×C22⋊C4C2414yes—
902C2×C22⋊C4C2414yes—
903C2×C22⋊C4C2414yes—
904C2×C22⋊C4C2414yes—
905C2×C22⋊C4C2418yes—
906C2×C22⋊C4C2418yes—
907C2×C22⋊C4C2418yes—
908C2×C22⋊C4C2414yes—
909C2×C22⋊C4C2414yes—
910C2×C22⋊C4C2414yes—
911C2×C22⋊C4C2414yes—
912C2×C22⋊C4C2414yes—
913C2×C22⋊C4C2412yes—
914C2×C22⋊C4C2412yes—
915C2×C22⋊C4C2412yes—
916C2×C22⋊C4C2412yes—
917C2×C42—28no—
918C2×C42—44no—
919C2×C42—44no—
920C2×C42C2×D418yes—
921C2×C42C2414yes—
922C2×C42C2414yes—
923C2×C42C2412yes—
924C2×C42C2411yescharacteristic
925C2×C42C2411yescharacteristic
926C2×C42C2412yes—
927C2×C42C2412yes—
928C2×C42C2412yes—
929C2×C42C2412yes—
930C2×C42C2412yes—
931C2×C42C2412yes—
932C2×C42C2411yescharacteristic
933C2×C42C2411yescharacteristic
934C2×C42C2414yes—
935C2×C42C2414yes—
936C2×C42C2412yes—
937C2×C42C2412yes—
938C2×C42C2411yescharacteristic
939C2×C42C2411yescharacteristic
940C2×C42C2411yescharacteristic
941C2×C42C2411yescharacteristic
942C2×C42C2412yes—
943#95C2414yes—
944#95C2418yes—
945#95C2418yes—
946#95C2418yes—
947#95C2412yes—
948#95C2412yes—
949#95C2412yes—
950#95C2412yes—
951#95C2414yes—
952#95C2414yes—
953#95C2412yes—
954#95C2412yes—
955#95C2414yes—
956#95C2414yes—
957#95C2418yes—
958#95C2414yes—
959#95C2414yes—
960#95C2414yes—
961#95C2418yes—
962#95C2414yes—
963#95C2414yes—
964#95C2414yes—
965#95C2414yes—
966#95C2414yes—
967#95C2418yes—
968#95C2418yes—
969#95C2418yes—
970#95C2418yes—
971#95C2418yes—
972#95C2418yes—
973#95C2418yes—
974C24C2512yes—
975C24C2512yes—
976C24C2512yes—
977C24C2511yescharacteristic
978C24C2512yes—
979#41—232no—
980#41—432no—
981#41—432no—
982#41—432no—
983#41—464no—
984#41—464no—
985#41—464no—
986#41—816no—
987C2×Q8—22no—
988C2×Q8—22no—
989C2×Q8—24no—
990C2×Q8—28no—
991C2×Q8—28no—
992C2×Q8—24no—
993C2×Q8—24no—
994C2×Q8—28no—
995C2×Q8—24no—
996C2×Q8—28no—
997C2×Q8—22no—
998C2×Q8—28no—
999C2×Q8—22no—
1000C2×Q8—24no—
1001C2×Q8—24no—
1002C2×Q8—24no—
1003C2×Q8—22no—
1004C2×Q8—24no—
1005C2×Q8—28no—
1006C2×Q8—24no—
1007C2×Q8—24no—
1008C2×Q8—42no—
1009C2×Q8—44no—
1010C2×Q8—42no—
1011C2×Q8—44no—
1012C2×Q8—44no—
1013C2×Q8—44no—
1014C2×Q8—44no—
1015C2×Q8—44no—
1016C2×Q8—44no—
1017C2×Q8—432no—
1018C2×Q8—432no—
1019C2×Q8—464no—
1020C2×Q8—432no—
1021C2×Q8—816no—
1022C2×Q8C22×D418yes—
1023C2×Q8H(5,𝔽2)14yes—
1024C2×D4—24no—
1025C2×D4—24no—
1026C2×D4—28no—
1027C2×D4—28no—
1028C2×D4—28no—
1029C2×D4—28no—
1030C2×D4—28no—
1031C2×D4—24no—
1032C2×D4—28no—
1033C2×D4—28no—
1034C2×D4—22no—
1035C2×D4—22no—
1036C2×D4—24no—
1037C2×D4—22no—
1038C2×D4—22no—
1039C2×D4—22no—
1040C2×D4—24no—
1041C2×D4—24no—
1042C2×D4—28no—
1043C2×D4—44no—
1044C2×D4—44no—
1045C2×D4—42no—
1046C2×D4—42no—
1047C2×D4—42no—
1048C2×D4—42no—
1049C2×D4—42no—
1050C2×D4—42no—
1051C2×D4—44no—
1052C2×D4—44no—
1053C2×D4—44no—
1054C2×D4—44no—
1055C2×D4—44no—
1056C2×D4—48no—
1057C2×D4C22×D414yes—
1058C2×D4C22×D414yes—
1059C2×D4C22×D418yes—
1060C2×D4C22×D418yes—
1061C2×D4C22×D418yes—
1062C2×D4C22×D418yes—
1063C2×D4H(5,𝔽2)14yes—
1064C22×C4—24no—
1065C22×C4—24no—
1066C22×C4—24no—
1067C22×C4—24no—
1068C22×C4—24no—
1069C22×C4—24no—
1070C22×C4—24no—
1071C22×C4—22no—
1072C22×C4—22no—
1073C22×C4—24no—
1074C22×C4—28no—
1075C22×C4—28no—
1076C22×C4—28no—
1077C22×C4—28no—
1078C22×C4—28no—
1079C22×C4—28no—
1080C22×C4—28no—
1081C22×C4—24no—
1082C22×C4—24no—
1083C22×C4—28no—
1084C22×C4—28no—
1085C22×C4—24no—
1086C22×C4—28no—
1087C22×C4—28no—
1088C22×C4—28no—
1089C22×C4—28no—
1090C22×C4—28no—
1091C22×C4—28no—
1092C22×C4—28no—
1093C22×C4—44no—
1094C22×C4—42no—
1095C22×C4—44no—
1096C22×C4—44no—
1097C22×C4—44no—
1098C22×C4—44no—
1099C22×C4—44no—
1100C22×C4—44no—
1101C22×C4—44no—
1102C22×C4—44no—
1103C22×C4—44no—
1104C22×C4—44no—
1105C22×C4—44no—
1106C22×C4—44no—
1107C22×C4—44no—
1108C22×C4—44no—
1109C22×C4—48no—
1110C22×C4C22×D414yes—
1111C22×C4C22×D414yes—
1112C22×C4C22×D418yes—
1113C22×C4C22×D418yes—
1114C22×C4C22×D414yes—
1115C22×C4C2514yes—
1116C22×C4C2514yes—
1117C22×C4C2512yes—
1118C22×C4C2512yes—
1119C22×C4C2512yes—
1120C22×C4C2512yes—
1121C22×C4C2514yes—
1122C22×C4C2512yes—
1123C22×C4C2512yes—
1124C22×C4C2514yes—
1125C22×C4C2514yes—
1126C22×C4C2512yes—
1127C22×C4C2514yes—
1128C22×C4C2511yescharacteristic
1129C22×C4C2511yescharacteristic
1130C22×C4C2511yescharacteristic
1131C22×C4C2511yescharacteristic
1132C22×C4C2512yes—
1133C22×C4C2512yes—
1134C22×C4C2512yes—
1135C22×C4C2512yes—
1136C22×C4C2512yes—
1137C22×C4C2511yescharacteristic
1138C22×C4C2511yescharacteristic
1139C4⋊C4—28no—
1140C4⋊C4—24no—
1141C4⋊C4—24no—
1142C4⋊C4—22no—
1143C4⋊C4—24no—
1144C4⋊C4—24no—
1145C4⋊C4—28no—
1146C4⋊C4—28no—
1147C4⋊C4—28no—
1148C4⋊C4—28no—
1149C4⋊C4—28no—
1150C4⋊C4—28no—
1151C4⋊C4—24no—
1152C4⋊C4—24no—
1153C4⋊C4—28no—
1154C4⋊C4—24no—
1155C4⋊C4—22no—
1156C4⋊C4—24no—
1157C4⋊C4—24no—
1158C4⋊C4—24no—
1159C4⋊C4—22no—
1160C4⋊C4—22no—
1161C4⋊C4—28no—
1162C4⋊C4—24no—
1163C4⋊C4—24no—
1164C4⋊C4—28no—
1165C4⋊C4—28no—
1166C4⋊C4—28no—
1167C4⋊C4—24no—
1168C4⋊C4—24no—
1169C4⋊C4—28no—
1170C4⋊C4—216no—
1171C4⋊C4—24no—
1172C4⋊C4—24no—
1173C4⋊C4—28no—
1174C4⋊C4—24no—
1175C4⋊C4—24no—
1176C4⋊C4—48no—
1177C4⋊C4—48no—
1178C4⋊C4—44no—
1179C4⋊C4—48no—
1180C4⋊C4—44no—
1181C4⋊C4—44no—
1182C4⋊C4—48no—
1183C4⋊C4—48no—
1184C4⋊C4—48no—
1185C4⋊C4—48no—
1186C4⋊C4C22×D414yes—
1187C4⋊C4C22×D414yes—
1188C4⋊C4C22×D418yes—
1189C22⋊C4—24no—
1190C22⋊C4—28no—
1191C22⋊C4—28no—
1192C22⋊C4—28no—
1193C22⋊C4—28no—
1194C22⋊C4—28no—
1195C22⋊C4—28no—
1196C22⋊C4—28no—
1197C22⋊C4—28no—
1198C22⋊C4—28no—
1199C22⋊C4—24no—
1200C22⋊C4—216no—
1201C22⋊C4—28no—
1202C22⋊C4—24no—
1203C22⋊C4—24no—
1204C22⋊C4—24no—
1205C22⋊C4—24no—
1206C22⋊C4—28no—
1207C22⋊C4—24no—
1208C22⋊C4—24no—
1209C22⋊C4—28no—
1210C22⋊C4—24no—
1211C22⋊C4—24no—
1212C22⋊C4—28no—
1213C22⋊C4—28no—
1214C22⋊C4—28no—
1215C22⋊C4—28no—
1216C22⋊C4—44no—
1217C22⋊C4—44no—
1218C22⋊C4—44no—
1219C22⋊C4—44no—
1220C22⋊C4—44no—
1221C22⋊C4—48no—
1222C22⋊C4—44no—
1223C22⋊C4—44no—
1224C22⋊C4—48no—
1225C22⋊C4—48no—
1226C22⋊C4C22×D418yes—
1227C22⋊C4C22×D418yes—
1228C22⋊C4C22×D418yes—
1229C22⋊C4C22×D418yes—
1230C42—24no—
1231C42—24no—
1232C42—24no—
1233C42—28no—
1234C42—28no—
1235C42—24no—
1236C42—22no—
1237C42—22no—
1238C42—24no—
1239C42—24no—
1240C42—22no—
1241C42—22no—
1242C42—24no—
1243C42—44no—
1244C42—44no—
1245C42—42no—
1246C42—42no—
1247C42C22×D414yes—
1248C42C22×D414yes—
1249C42C22×D414yes—
1250C42C22×D414yes—
1251C422−1+418yescomplemented
1252C23—22no—
1253C23—22no—
1254C23—22no—
1255C23—22no—
1256C23—21no—
1257C23—21no—
1258C23—22no—
1259C23—22no—
1260C23—22no—
1261C23—24no—
1262C23—24no—
1263C23—24no—
1264C23—24no—
1265C23—22no—
1266C23—24no—
1267C23—24no—
1268C23—22no—
1269C23—22no—
1270C23—22no—
1271C23—24no—
1272C23—24no—
1273C23C23×D414yes—
1274C23C23×D414yes—
1275C23C23×D412yes—
1276C23C2×H(5,𝔽2)14yes—
1277C23C2611yescharacteristic
1278Q8—28no—
1279Q8—48no—
1280Q8—416no—
1281Q8—416no—
1282Q8—416no—
1283Q8—48no—
1284Q8—48no—
1285Q8—44no—
1286Q8—48no—
1287Q8—84no—
1288Q8—88no—
1289D4—216no—
1290D4—28no—
1291D4—28no—
1292D4—28no—
1293D4—48no—
1294D4—48no—
1295D4—48no—
1296D4—48no—
1297D4—416no—
1298D4—416no—
1299D4—416no—
1300D4—44no—
1301D4—84no—
1302D4—88no—
1303D4—88no—
1304C2×C4—216no—
1305C2×C4—22no—
1306C2×C4—22no—
1307C2×C4—22no—
1308C2×C4—22no—
1309C2×C4—22no—
1310C2×C4—22no—
1311C2×C4—22no—
1312C2×C4—21no—
1313C2×C4—21no—
1314C2×C4—22no—
1315C2×C4—22no—
1316C2×C4—22no—
1317C2×C4—22no—
1318C2×C4—22no—
1319C2×C4—22no—
1320C2×C4—28no—
1321C2×C4—216no—
1322C2×C4—216no—
1323C2×C4—28no—
1324C2×C4—22no—
1325C2×C4—22no—
1326C2×C4—22no—
1327C2×C4—24no—
1328C2×C4—22no—
1329C2×C4—22no—
1330C2×C4—24no—
1331C2×C4—24no—
1332C2×C4—24no—
1333C2×C4—24no—
1334C2×C4—24no—
1335C2×C4—22no—
1336C2×C4—22no—
1337C2×C4—24no—
1338C2×C4—22no—
1339C2×C4—24no—
1340C2×C4—24no—
1341C2×C4—24no—
1342C2×C4—22no—
1343C2×C4—24no—
1344C2×C4—24no—
1345C2×C4—22no—
1346C2×C4—22no—
1347C2×C4—24no—
1348C2×C4—24no—
1349C2×C4—24no—
1350C2×C4—24no—
1351C2×C4—22no—
1352C2×C4—22no—
1353C2×C4—24no—
1354C2×C4—24no—
1355C2×C4—24no—
1356C2×C4—24no—
1357C2×C4—28no—
1358C2×C4—44no—
1359C2×C4—416no—
1360C2×C4—416no—
1361C2×C4—416no—
1362C2×C4—416no—
1363C2×C4—48no—
1364C2×C4—416no—
1365C2×C4—416no—
1366C2×C4—48no—
1367C2×C4—48no—
1368C2×C4—88no—
1369C2×C4—88no—
1370C2×C4—88no—
1371C2×C4—88no—
1372C2×C4C23×D412yes—
1373C2×C4C23×D412yes—
1374C2×C4C23×D412yes—
1375C2×C4C23×D414yes—
1376C2×C4C23×D412yes—
1377C2×C4C23×D414yes—
1378C2×C4C23×D412yes—
1379C2×C4C23×D412yes—
1380C2×C4C2×H(5,𝔽2)14yes—
1381C2×C4C2×H(5,𝔽2)12yes—
1382C2×C4C2×H(5,𝔽2)12yes—
1383C2×C4C2×2−1+414yes—
1384C2×C4C2×2−1+414yes—
1385C2×C4C2×2−1+414yes—
1386C22—22no—
1387C22—24no—
1388C22—24no—
1389C22—24no—
1390C22—22no—
1391C22—24no—
1392C22—24no—
1393C22—22no—
1394C22—24no—
1395C22—24no—
1396C22—28no—
1397C22—42no—
1398C22—42no—
1399C22—44no—
1400C22—44no—
1401C22—42no—
1402C22—44no—
1403C22—44no—
1404C22—44no—
1405C22—42no—
1406C22—42no—
1407C22—42no—
1408C22—42no—
1409C22—44no—
1410C22—44no—
1411C22C24×D411yescharacteristic
1412C22C22×H(5,𝔽2)11yescharacteristic
1413C22C22×H(5,𝔽2)11yescharacteristic
1414C22C22×2−1+412yes—
1415C222−1+612yes—
1416C4—22no—
1417C4—24no—
1418C4—24no—
1419C4—24no—
1420C4—22no—
1421C4—22no—
1422C4—22no—
1423C4—24no—
1424C4—24no—
1425C4—44no—
1426C4—44no—
1427C4—44no—
1428C4—42no—
1429C4—42no—
1430C4—42no—
1431C4—42no—
1432C4—42no—
1433C4—44no—
1434C4—42no—
1435C4—44no—
1436C4—42no—
1437C4—44no—
1438C4#348414yes—
1439C4#349914yes—
1440C2—42no—
1441C2—44no—
1442C2—44no—
1443C2—44no—
1444C2—82no—
1445C2C2×#348411yescharacteristic
1446C2C2×#349911yescharacteristic
1447C2#6285911yescharacteristic
1448C2#6291312yes—
1449C2#6291512yes—
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×#3499C2semidirect
2. C2×#3547C2semidirect
3. #48822C2semidirect
4. #47766C2semidirect
5. #45255C2semidirect
6. #44928C2semidirect
7. #39360C2semidirect
8. #39360C2semidirect
9. #38958C2semidirect
10. #38955C2semidirect
11. #38088C2semidirect
12. #38081C2semidirect
13. #37764C2semidirect
14. #37686C2semidirect
15. #37680C2semidirect
16. #37675C2semidirect
17. #37617C2semidirect
18. #37388C2semidirect
19. #37386C2semidirect
20. #36415C2semidirect
21. #36276C2semidirect
22. #36127C2semidirect
23. D4×C4⋊Q8C2semidirect
24. #35666C2semidirect
25. #35660C2semidirect
26. #35281C2semidirect
27. #35200C2semidirect
28. #34910C2semidirect
29. #34086C2semidirect
267. #532D4semidirect
1251. C422−1+4semidirect

Maximal subgroups

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

subgroupindex
C2×#34992
C2×#35472
#488222
#477662
#452552
#449282
#393602
#389582
#389552
#380882
#380812
#377642
#376862
#376802
#376752
#376172
#373882
#373862
#364152
#362762
#361272
D4×C4⋊Q82
#356662
#356602
#352812
#352002
#349102
#340862