Finite Group Databasebeta

← #7653565

Subgroups — #7653565

Order 512.

6660 conjugacy classes of subgroups.

The subgroup lattice has 1328 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3507C211yesmaximal, characteristic, complemented
2C2×Q8×#41C211yesmaximal, characteristic, complemented
3#42787C214yesmaximal, complemented
4#40523C218yesmaximal, complemented
5#39879C214yesmaximal, complemented
6#39619C211yesmaximal, characteristic, complemented
7#39616C211yesmaximal, characteristic, complemented
8#39613C212yesmaximal, complemented
9#39611C212yesmaximal, complemented
10#39171C211yesmaximal, characteristic, complemented
11#39168C211yesmaximal, characteristic, complemented
12#39163C212yesmaximal, complemented
13#39162C212yesmaximal, complemented
14#38374C218yesmaximal, complemented
15#37635C211yesmaximal, characteristic, complemented
16#37545C212yesmaximal, complemented
17#36562C211yesmaximal, characteristic, complemented
18#36560C211yesmaximal, characteristic, complemented
19#36538C211yesmaximal, characteristic, complemented
20#36496C211yesmaximal, characteristic, complemented
21#36233C214yesmaximal, complemented
22#35724C214yesmaximal, complemented
23#35298C211yesmaximal, characteristic, complemented
24#35211C212yesmaximal, complemented
25#35201C212yesmaximal, complemented
26#35190C211yesmaximal, characteristic
27#34979C211yesmaximal, characteristic, complemented
28#34910C212yesmaximal, complemented
29#34128C211yesmaximal, characteristic, complemented
30#3507—216no—
31C2×#559C2211yescharacteristic
32C2×#559C2211yescharacteristic
33Q8×#41—216no—
34C2×Q82C2211yescharacteristic
35C2×#557C2211yescharacteristic
36C2×#557C2211yescharacteristic
37C2×#557C2211yescharacteristic
38C2×#557C2212yes—
39C2×#556C2212yes—
40C2×#556C2212yes—
41C2×#556C2212yes—
42C2×#554C2212yes—
43C2×#554C2214yes—
44C2×#554C2212yes—
45C2×#554C2211yescharacteristic
46C2×#554C2212yes—
47C2×#552C2214yes—
48C2×D4×Q8C2211yescharacteristic
49C2×D4×Q8C2212yes—
50C2×#539C2214yes—
51C2×#536C2212yes—
52C2×#533C2211yescharacteristic
53C2×#533C2211yescharacteristic
54C2×#533C2212yes—
55C2×#533C2212yes—
56C2×#533C2214yes—
57C2×#532C2211yescharacteristic
58C2×#529C2212yes—
59C2×#529C2212yes—
60C2×#520C2212yes—
61C2×C4×#41C2212yes—
62C2×C4×#41C2211yescharacteristic
63C22×C4×Q8C2212yes—
64C22×C4×Q8C2211yescharacteristic
65#2868C2211yescharacteristic
66#2862C2211yescharacteristic
67#2861C2212yes—
68#2861C2212yes—
69#2859C2212yes—
70#2859C2212yes—
71#2858C2211yescharacteristic
72#2858C2211yescharacteristic
73#2852C2218yes—
74#2850C2214yes—
75#2817C2214yes—
76#2814C2218yes—
77#2732C2218yes—
78#2729C2218yes—
79#2729C2218yes—
80#2728C2218yes—
81#2725C2218yes—
82#2720C2218yes—
83#2713C2218yes—
84#2704C2218yes—
85#2702C2218yes—
86#2696C2218yes—
87#2683C2218yes—
88#2674C2218yes—
89#2663C2218yes—
90#2660C2212yes—
91#2660C2212yes—
92#2660C2212yes—
93#2642C2212yes—
94#2640C2212yes—
95#2640C2212yes—
96#2638C2218yes—
97#2637C2218yes—
98#2635C2214yes—
99#2634C2214yes—
100#2630C2218yes—
101#2625C2214yes—
102#2620C2214yes—
103#2611C2214yes—
104#2609C2218yes—
105#2604C2218yes—
106#2602C2218yes—
107#2601C2218yes—
108#2600C2218yes—
109#2599C2218yes—
110#2598C2214yes—
111#2581C2214yes—
112#2568C2211yescharacteristic
113#2568C2211yescharacteristic
114#2568C2211yescharacteristic
115#2568C2212yes—
116#2568C2211yescharacteristic
117#2567C2211yescharacteristic
118#2567C2211yescharacteristic
119#2567C2212yes—
120#2566C2212yes—
121#2566C2212yes—
122#2566C2212yes—
123#2566C2212yes—
124#2566C2212yes—
125#2566C2212yes—
126#2565C2212yes—
127#2565C2212yes—
128#2565C2212yes—
129#2565C2212yes—
130#2563C2212yes—
131#2558C2218yes—
132#2556C2218yes—
133#2548C2211yescharacteristic
134#2547C2211yescharacteristic
135#2546C2214yes—
136#2546C2211yescharacteristic
137#2545C2212yes—
138#2545C2214yes—
139#2545C2214yes—
140#2545C2212yes—
141#2544C2212yes—
142#2544C2212yes—
143#2542C2212yes—
144#2542C2211yescharacteristic
145#2542C2211yescharacteristic
146#2541C2211yescharacteristic
147#2506C2218yes—
148#2500C2212yes—
149#2500C2212yes—
150#2500C2212yes—
151#2499C2212yes—
152#2499C2212yes—
153#2499C2211yescharacteristic
154#2499C2211yescharacteristic
155#2481C2218yes—
156#2477C2218yes—
157#2475C2218yes—
158#2473C2218yes—
159#2469C2218yes—
160#2465C2218yes—
161#2461C2218yes—
162#2452C2214yes—
163#2451C2214yes—
164#2449C2218yes—
165#2449C2218yes—
166#2448C2214yes—
167#2446C2214yes—
168#2436C2214yes—
169#2434C2214yes—
170#2432C2214yes—
171#2432C2211yescharacteristic
172#2432C2211yescharacteristic
173#2431C2212yes—
174#2429C2214yes—
175#2429C2214yes—
176#2427C2214yes—
177#2426C2214yes—
178#2415C2214yes—
179#2415C2218yes—
180#2407C2214yes—
181#2395C2214yes—
182#2392C2218yes—
183#2367C2214yes—
184#2365C2214yes—
185#2361C2214yes—
186#2360C2214yes—
187#2356C2212yes—
188#2356C2214yes—
189#2351C2212yes—
190#2344C2214yes—
191#2344C2212yes—
192Q8×C22⋊C4C2212yes—
193#2328C2212yes—
194#2328C2212yes—
195#2327C2212yes—
196#2326C2212yes—
197#2326C2212yes—
198#2326C2212yes—
199#2326C2214yes—
200#2323C2218yes—
201C4×C4⋊Q8C2211yescharacteristic
202C4×C4⋊Q8C2212yes—
203C4×C4⋊Q8C2211yescharacteristic
204C4×#127C2212yes—
205C4×#124C2211yescharacteristic
206C4×#124C2212yes—
207C4×#124C2212yes—
208C4×#124C2211yescharacteristic
209C4×C22⋊Q8C2214yes—
210#2295C2211yescharacteristic
211#2295C2211yescharacteristic
212#2295C2212yes—
213#2295C2212yes—
214#2290C2218yes—
215#2283C2211yescharacteristic
216#2283C2212yes—
217C42×Q8C2211yescharacteristic
218C42×Q8C2211yescharacteristic
219C4×#117C2212yes—
220C4×#117C2211yescharacteristic
221C22×#41C2311yescharacteristic
222C22×#41C2312yes—
223C23×Q8C2312yes—
224C23×Q8C2311yescharacteristic
225#559—28no—
226#559—28no—
227Q82—28no—
228#557—216no—
229#557—28no—
230#557—28no—
231#557—28no—
232#556—216no—
233#556—216no—
234#556—216no—
235#554—216no—
236#554—28no—
237#554—216no—
238#554—216no—
239#554—232no—
240#552—232no—
241D4×Q8—216no—
242D4×Q8—28no—
243#539—232no—
244#536—216no—
245#533—232no—
246#533—216no—
247#533—216no—
248#533—28no—
249#533—28no—
250#532—28no—
251C2×C4⋊Q8C2311yescharacteristic
252C2×C4⋊Q8C2311yescharacteristic
253C2×C4⋊Q8C2312yes—
254C2×C4⋊Q8C2311yescharacteristic
255C2×C4⋊Q8C2311yescharacteristic
256C2×C4⋊Q8C2311yescharacteristic
257C2×C4⋊Q8C2312yes—
258C2×C4⋊Q8C2311yescharacteristic
259C2×C4⋊Q8C2311yescharacteristic
260C2×C4⋊Q8C2314yes—
261C2×C4⋊Q8C2314yes—
262C2×C4⋊Q8C2312yes—
263C2×C4⋊Q8C2312yes—
264C2×C4⋊Q8C2312yes—
265C2×C4⋊Q8C2312yes—
266C2×C4⋊Q8C2314yes—
267C2×#127C2312yes—
268C2×#127C2311yescharacteristic
269#529—216no—
270#529—216no—
271C2×#126C2314yes—
272C2×#126C2314yes—
273C2×#126C2314yes—
274C2×#126C2314yes—
275C2×#125C2312yes—
276C2×#125C2312yes—
277C2×#125C2312yes—
278C2×#125C2312yes—
279C2×#125C2312yes—
280C2×#125C2312yes—
281C2×#125C2314yes—
282C2×#125C2314yes—
283C2×#125C2314yes—
284C2×#125C2314yes—
285C2×#125C2314yes—
286C2×#124C2312yes—
287C2×#124C2311yescharacteristic
288C2×#124C2312yes—
289C2×#124C2312yes—
290C2×#124C2312yes—
291C2×#124C2312yes—
292C2×#124C2312yes—
293C2×#124C2311yescharacteristic
294C2×#124C2314yes—
295C2×#124C2314yes—
296C2×#123C2314yes—
297C2×#123C2314yes—
298C2×#123C2314yes—
299C2×#123C2314yes—
300C2×C22⋊Q8C2312yes—
301C2×C22⋊Q8C2312yes—
302C2×C22⋊Q8C2312yes—
303C2×C22⋊Q8C2314yes—
304C2×C22⋊Q8C2314yes—
305C2×C22⋊Q8C2311yescharacteristic
306C2×C22⋊Q8C2311yescharacteristic
307C2×C22⋊Q8C2312yes—
308C2×C22⋊Q8C2312yes—
309C2×C22⋊Q8C2314yes—
310C2×C22⋊Q8C2314yes—
311C2×C22⋊Q8C2314yes—
312C2×C22⋊Q8C2314yes—
313C2×C22⋊Q8C2314yes—
314C2×C22⋊Q8C2314yes—
315C2×C22⋊Q8C2314yes—
316C2×C22⋊Q8C2314yes—
317C2×C22⋊Q8C2314yes—
318C2×C22⋊Q8C2318yes—
319C2×C22⋊Q8C2314yes—
320C2×C22⋊Q8C2314yes—
321C2×#121C2312yes—
322C2×#121C2312yes—
323C2×#121C2314yes—
324#520—216no—
325C4×#41—216no—
326C4×#41—28no—
327C2×C4×Q8—216no—
328C2×C4×Q8D4116yescomplemented
329C2×C4×Q8C2311yescharacteristic
330C2×C4×Q8C2312yes—
331C2×C4×Q8C2312yes—
332C2×C4×Q8C2311yescharacteristic
333C2×C4×Q8C2311yescharacteristic
334C2×C4×Q8C2312yes—
335C2×C4×Q8C2312yes—
336C2×C4×Q8C2311yescharacteristic
337C2×C4×Q8C2314yes—
338C2×C4×Q8C2312yes—
339C2×C4×Q8C2312yes—
340C2×C4×Q8C2312yes—
341C2×C4×Q8C2314yes—
342C2×C4×Q8C2312yes—
343C2×C4×Q8C2312yes—
344C2×C4×Q8C2312yes—
345C2×C4×Q8C2314yes—
346C2×C4×Q8C2312yes—
347C2×C4×Q8C2312yes—
348C2×C4×Q8C2312yes—
349C2×C4×Q8C2311yescharacteristic
350C2×C4×Q8C2311yescharacteristic
351C2×C4×Q8C2312yes—
352C2×C4×Q8C2311yescharacteristic
353C2×C4×Q8C2312yes—
354C2×C4×Q8C2311yescharacteristic
355C2×C4×D4C2312yes—
356C2×C4×D4C2312yes—
357C2×C4×D4C2312yes—
358C2×C4×D4C2312yes—
359C2×C4×D4C2312yes—
360C2×C4×D4C2312yes—
361C2×C4×D4C2311yescharacteristic
362C2×C4×D4C2314yes—
363C2×C4×D4C2314yes—
364C2×C4×D4C2314yes—
365C2×C4×D4C2312yes—
366C2×C4×D4C2312yes—
367C2×C4×D4C2314yes—
368C2×C4×D4C2312yes—
369C2×C4×D4C2311yescharacteristic
370C2×C4×D4C2312yes—
371C2×C4×D4C2318yes—
372C2×#117C2314yes—
373C2×#117C2312yes—
374C2×#117C2314yes—
375C2×#117C2314yes—
376C2×#117C2312yes—
377C2×#117C2312yes—
378C2×#117C2311yescharacteristic
379C2×#117C2314yes—
380C2×#117C2312yes—
381C2×#117C2314yes—
382C22×C4⋊C4C2312yes—
383C22×C4⋊C4C2314yes—
384C22×C4⋊C4C2314yes—
385C22×C4⋊C4C2311yescharacteristic
386C22×C4⋊C4C2312yes—
387C22×C42C2312yes—
388C22×C42C2314yes—
389C22×C42C2312yes—
390C22×C42C2311yescharacteristic
391#400C2314yes—
392#400C2314yes—
393#400C2318yes—
394#400C2314yes—
395#400C2318yes—
396#400C2314yes—
397#400C2318yes—
398#399C2314yes—
399#399C2318yes—
400#399C2314yes—
401#398C2318yes—
402#398C2318yes—
403#398C2318yes—
404#398C2318yes—
405#398C2318yes—
406#398C2314yes—
407#398C2318yes—
408#398C2318yes—
409#397C2318yes—
410#397C2318yes—
411#397C2318yes—
412#397C2314yes—
413#397C2318yes—
414#397C2314yes—
415#397C2314yes—
416#396C2318yes—
417#396C2318yes—
418#396C2318yes—
419#396C2318yes—
420#396C2318yes—
421#396C2318yes—
422#396C2318yes—
423#396C2318yes—
424#395C2314yes—
425#395C2314yes—
426#395C2318yes—
427#395C2318yes—
428#395C2318yes—
429#395C2318yes—
430#394C2314yes—
431#394C2314yes—
432#394C2318yes—
433#394C2318yes—
434#394C2314yes—
435#394C2318yes—
436#394C2318yes—
437#394C2318yes—
438#393C2318yes—
439#393C2318yes—
440#393C2318yes—
441#392C2314yes—
442#392C2318yes—
443#391C2311yescharacteristic
444#391C2312yes—
445#391C2311yescharacteristic
446#391C2311yescharacteristic
447#391C2312yes—
448#391C2311yescharacteristic
449#391C2311yescharacteristic
450#391C2312yes—
451#391C2311yescharacteristic
452#391C2312yes—
453#391C2312yes—
454#391C2318yes—
455#391C2314yes—
456#391C2314yes—
457#391C2314yes—
458#391C2314yes—
459#391C2314yes—
460#391C2312yes—
461#391C2312yes—
462#391C2314yes—
463#391C2314yes—
464#391C2314yes—
465#390C2311yescharacteristic
466#390C2312yes—
467#390C2318yes—
468#390C2312yes—
469#390C2312yes—
470#390C2312yes—
471#390C2312yes—
472#390C2311yescharacteristic
473#390C2312yes—
474#390C2312yes—
475#390C2314yes—
476#390C2314yes—
477#390C2314yes—
478#389C2318yes—
479#389C2314yes—
480#389C2314yes—
481#389C2318yes—
482#389C2314yes—
483#389C2314yes—
484#389C2318yes—
485#389C2318yes—
486#389C2312yes—
487#389C2314yes—
488#389C2312yes—
489#389C2314yes—
490#389C2318yes—
491#389C2318yes—
492#389C2314yes—
493#388C2318yes—
494#388C2318yes—
495#388C2318yes—
496#388C2318yes—
497#388C2318yes—
498#388C2318yes—
499#388C2318yes—
500#388C2318yes—
501#388C2318yes—
502#388C2318yes—
503#388C2318yes—
504#388C2318yes—
505#388C2318yes—
506#388C2318yes—
507#388C2314yes—
508#388C2314yes—
509#387C2318yes—
510#387C2318yes—
511#387C2318yes—
512#387C2318yes—
513#387C2314yes—
514#387C2318yes—
515#387C2318yes—
516#387C2318yes—
517#387C2318yes—
518#387C2314yes—
519#387C2314yes—
520#387C2314yes—
521#387C2314yes—
522#387C2314yes—
523#387C2314yes—
524#387C2314yes—
525#386C2318yes—
526#386C2318yes—
527#386C2318yes—
528#386C2318yes—
529#386C2318yes—
530#386C2318yes—
531#386C2318yes—
532#385C2318yes—
533#385C2318yes—
534#385C2318yes—
535#385C2318yes—
536#385C2318yes—
537#385C2318yes—
538#385C2318yes—
539#385C2318yes—
540#385C2318yes—
541#385C2314yes—
542#385C2314yes—
543#384C2312yes—
544#384C2312yes—
545#384C2311yescharacteristic
546#384C2311yescharacteristic
547#384C2312yes—
548#384C2312yes—
549#384C2312yes—
550#384C2314yes—
551#383C2314yes—
552#383C2312yes—
553#382C2311yescharacteristic
554#382C2312yes—
555#382C2312yes—
556#382C2312yes—
557#382C2312yes—
558#382C2312yes—
559#382C2311yescharacteristic
560#382C2312yes—
561#382C2314yes—
562#381C2312yes—
563#381C2314yes—
564#380C2318yes—
565#380C2312yes—
566#380C2314yes—
567#380C2314yes—
568C4×C4⋊C4C2318yes—
569C4×C4⋊C4C2314yes—
570C4×C4⋊C4C2314yes—
571C4×C4⋊C4C2312yes—
572C4×C4⋊C4C2312yes—
573C4×C4⋊C4C2312yes—
574C4×C4⋊C4C2311yescharacteristic
575C4×C4⋊C4C2311yescharacteristic
576C4×C4⋊C4C2312yes—
577C4×C4⋊C4C2311yescharacteristic
578C4×C4⋊C4C2311yescharacteristic
579C4×C4⋊C4C2314yes—
580C4×C4⋊C4C2312yes—
581C4×C4⋊C4C2312yes—
582C4×C4⋊C4C2314yes—
583C4×C4⋊C4C2314yes—
584C4×C4⋊C4C2312yes—
585C4×C22⋊C4C2314yes—
586C4×C22⋊C4C2312yes—
587C4×C22⋊C4C2318yes—
588C4×C22⋊C4C2314yes—
589C4×C22⋊C4C2314yes—
590C4×C22⋊C4C2318yes—
591C4×C22⋊C4C2312yes—
592C4×C22⋊C4C2311yescharacteristic
593C4×C22⋊C4C2311yescharacteristic
594#376C2312yes—
595#376C2312yes—
596#376C2312yes—
597#376C2312yes—
598#376C2314yes—
599C43C2312yes—
600C43C2311yescharacteristic
601C43C2311yescharacteristic
602C43C2312yes—
603C2×#41—24no—
604C2×#41—24no—
605C2×#41—24no—
606C2×#41—28no—
607C2×#41—48no—
608C22×Q8—28no—
609C22×Q8—44no—
610C22×Q8—48no—
611C22×Q8C2×D418yes—
612C22×Q8C2411yescharacteristic
613C22×Q8C2411yescharacteristic
614C22×Q8C2412yes—
615C22×Q8C2412yes—
616C22×Q8C2411yescharacteristic
617C22×Q8C2411yescharacteristic
618C22×Q8C2411yescharacteristic
619C22×Q8C2414yes—
620C22×Q8C2412yes—
621C22×Q8C2414yes—
622C22×Q8C2412yes—
623C22×Q8C2412yes—
624C22×D4C2412yes—
625C22×D4C2412yes—
626C22×D4C2412yes—
627C22×D4C2411yescharacteristic
628C22×D4C2414yes—
629C22×D4C2412yes—
630C22×D4C2418yes—
631C23×C4C2412yes—
632C23×C4C2412yes—
633C23×C4C2411yescharacteristic
634C23×C4C2411yescharacteristic
635C23×C4C2414yes—
636C23×C4C2412yes—
637C23×C4C2414yes—
638C23×C4C2414yes—
639C23×C4C2414yes—
640C23×C4C2414yes—
641C23×C4C2412yes—
642C23×C4C2411yescharacteristic
643C23×C4C2412yes—
644C4⋊Q8—28no—
645C4⋊Q8—216no—
646C4⋊Q8—28no—
647C4⋊Q8—28no—
648C4⋊Q8—24no—
649C4⋊Q8—24no—
650C4⋊Q8—28no—
651C4⋊Q8—216no—
652C4⋊Q8—24no—
653C4⋊Q8—28no—
654C4⋊Q8—24no—
655C4⋊Q8—24no—
656C4⋊Q8—28no—
657C4⋊Q8—24no—
658C4⋊Q8—24no—
659C4⋊Q8—48no—
660#127—28no—
661#127—24no—
662#126—216no—
663#126—216no—
664#126—216no—
665#126—216no—
666#125—216no—
667#125—216no—
668#125—216no—
669#125—216no—
670#125—216no—
671#125—28no—
672#125—28no—
673#125—28no—
674#125—28no—
675#125—28no—
676#125—28no—
677#124—28no—
678#124—28no—
679#124—28no—
680#124—24no—
681#124—24no—
682#124—28no—
683#124—28no—
684#124—28no—
685#124—48no—
686#124—48no—
687#123—216no—
688#123—216no—
689#123—216no—
690#123—216no—
691C22⋊Q8—28no—
692C22⋊Q8—216no—
693C22⋊Q8—216no—
694C22⋊Q8—216no—
695C22⋊Q8—24no—
696C22⋊Q8—24no—
697C22⋊Q8—28no—
698C22⋊Q8—28no—
699C22⋊Q8—216no—
700C22⋊Q8—216no—
701C22⋊Q8—28no—
702C22⋊Q8—28no—
703C22⋊Q8—216no—
704C22⋊Q8—216no—
705C22⋊Q8—216no—
706C22⋊Q8—216no—
707C22⋊Q8—216no—
708C22⋊Q8—216no—
709C22⋊Q8—48no—
710C22⋊Q8—416no—
711C22⋊Q8—48no—
712#121—28no—
713#121—28no—
714#121—48no—
715C4×Q8—28no—
716C4×Q8—28no—
717C4×Q8—216no—
718C4×Q8—28no—
719C4×Q8—28no—
720C4×Q8—216no—
721C4×Q8—28no—
722C4×Q8—24no—
723C4×Q8—28no—
724C4×Q8—28no—
725C4×Q8—24no—
726C4×Q8—28no—
727C4×Q8—28no—
728C4×Q8—216no—
729C4×Q8—28no—
730C4×Q8—28no—
731C4×Q8—24no—
732C4×Q8—24no—
733C4×Q8—44no—
734C4×Q8—44no—
735C4×Q8C2×D418yes—
736C4×Q8C2×D4116yes—
737C4×Q8C2×D418yes—
738C4×Q8C2×D418yes—
739C4×Q8C2×D4116yes—
740C4×Q8C2×D418yes—
741C4×D4—28no—
742C4×D4—216no—
743C4×D4—216no—
744C4×D4—28no—
745C4×D4—216no—
746C4×D4—216no—
747C4×D4—28no—
748C4×D4—28no—
749C4×D4—28no—
750C4×D4—24no—
751C4×D4—24no—
752C4×D4—28no—
753C4×D4—28no—
754C4×D4—28no—
755C4×D4—28no—
756C4×D4—28no—
757C4×D4—416no—
758#117—28no—
759#117—24no—
760#117—28no—
761#117—216no—
762#117—216no—
763#117—28no—
764#117—216no—
765#117—216no—
766#117—48no—
767#117—44no—
768C2×C4⋊C4—28no—
769C2×C4⋊C4—216no—
770C2×C4⋊C4—216no—
771C2×C4⋊C4C2×D418yes—
772C2×C4⋊C4C2×D4116yes—
773C2×C4⋊C4C2412yes—
774C2×C4⋊C4C2414yes—
775C2×C4⋊C4C2414yes—
776C2×C4⋊C4C2414yes—
777C2×C4⋊C4C2414yes—
778C2×C4⋊C4C2414yes—
779C2×C4⋊C4C2412yes—
780C2×C4⋊C4C2414yes—
781C2×C4⋊C4C2412yes—
782C2×C4⋊C4C2412yes—
783C2×C4⋊C4C2412yes—
784C2×C4⋊C4C2412yes—
785C2×C4⋊C4C2412yes—
786C2×C4⋊C4C2411yescharacteristic
787C2×C4⋊C4C2411yescharacteristic
788C2×C4⋊C4C2412yes—
789C2×C4⋊C4C2414yes—
790C2×C4⋊C4C2414yes—
791C2×C4⋊C4C2412yes—
792C2×C4⋊C4C2414yes—
793C2×C4⋊C4C2414yes—
794C2×C4⋊C4C2412yes—
795C2×C4⋊C4C2414yes—
796C2×C4⋊C4C2411yescharacteristic
797C2×C4⋊C4C2411yescharacteristic
798C2×C4⋊C4C2412yes—
799C2×C4⋊C4C2412yes—
800C2×C4⋊C4C2412yes—
801C2×C4⋊C4C2414yes—
802C2×C4⋊C4C2412yes—
803C2×C4⋊C4C2414yes—
804C2×C4⋊C4C2414yes—
805C2×C4⋊C4C2414yes—
806C2×C4⋊C4C2412yes—
807C2×C4⋊C4C2412yes—
808C2×C4⋊C4C2412yes—
809C2×C4⋊C4C2414yes—
810C2×C4⋊C4C2414yes—
811C2×C4⋊C4C2412yes—
812C2×C4⋊C4C2414yes—
813C2×C4⋊C4C2414yes—
814C2×C4⋊C4C2414yes—
815C2×C4⋊C4C2414yes—
816C2×C4⋊C4C2412yes—
817C2×C4⋊C4C2418yes—
818C2×C4⋊C4C2414yes—
819C2×C4⋊C4C2414yes—
820C2×C4⋊C4C2414yes—
821C2×C4⋊C4C2418yes—
822C2×C4⋊C4C2418yes—
823C2×C4⋊C4C2418yes—
824C2×C4⋊C4C2418yes—
825C2×C4⋊C4C2412yes—
826C2×C4⋊C4C2411yescharacteristic
827C2×C4⋊C4C2412yes—
828C2×C4⋊C4C2411yescharacteristic
829C2×C4⋊C4C2412yes—
830C2×C4⋊C4C2412yes—
831C2×C4⋊C4C2412yes—
832C2×C22⋊C4C2412yes—
833C2×C22⋊C4C2414yes—
834C2×C22⋊C4C2412yes—
835C2×C22⋊C4C2414yes—
836C2×C22⋊C4C2412yes—
837C2×C22⋊C4C2414yes—
838C2×C22⋊C4C2414yes—
839C2×C22⋊C4C2412yes—
840C2×C22⋊C4C2412yes—
841C2×C22⋊C4C2412yes—
842C2×C22⋊C4C2414yes—
843C2×C22⋊C4C2414yes—
844C2×C22⋊C4C2414yes—
845C2×C22⋊C4C2414yes—
846C2×C22⋊C4C2414yes—
847C2×C22⋊C4C2414yes—
848C2×C22⋊C4C2414yes—
849C2×C22⋊C4C2414yes—
850C2×C22⋊C4C2418yes—
851C2×C22⋊C4C2414yes—
852C2×C22⋊C4C2414yes—
853C2×C22⋊C4C2418yes—
854C2×C22⋊C4C2414yes—
855C2×C22⋊C4C2412yes—
856C2×C22⋊C4C2418yes—
857C2×C22⋊C4C2414yes—
858C2×C22⋊C4C2418yes—
859C2×C22⋊C4C2418yes—
860C2×C22⋊C4C2418yes—
861C2×C22⋊C4C2418yes—
862C2×C22⋊C4C2418yes—
863C2×C42—216no—
864C2×C42—28no—
865C2×C42C2×D4116yes—
866C2×C42C2×D418yes—
867C2×C42C2414yes—
868C2×C42C2414yes—
869C2×C42C2412yes—
870C2×C42C2414yes—
871C2×C42C2414yes—
872C2×C42C2412yes—
873C2×C42C2412yes—
874C2×C42C2412yes—
875C2×C42C2414yes—
876C2×C42C2412yes—
877C2×C42C2412yes—
878C2×C42C2414yes—
879C2×C42C2412yes—
880C2×C42C2412yes—
881C2×C42C2411yescharacteristic
882C2×C42C2412yes—
883C2×C42C2411yescharacteristic
884C2×C42C2412yes—
885C2×C42C2411yescharacteristic
886C2×C42C2411yescharacteristic
887C2×C42C2414yes—
888C2×C42C2412yes—
889C2×C42C2414yes—
890C2×C42C2414yes—
891C2×C42C2412yes—
892C2×C42C2411yescharacteristic
893C2×C42C2412yes—
894C2×C42C2411yescharacteristic
895C2×C42C2412yes—
896C2×C42C2412yes—
897C2×C42C2411yescharacteristic
898C2×C42C2411yescharacteristic
899#95C2412yes—
900#95C2412yes—
901#95C2414yes—
902#95C2412yes—
903#95C2412yes—
904#95C2414yes—
905#95C2414yes—
906#95C2414yes—
907#95C2414yes—
908#95C2414yes—
909#95C2414yes—
910#95C2414yes—
911#95C2414yes—
912#95C2414yes—
913#95C2414yes—
914#95C2414yes—
915#95C2418yes—
916#95C2418yes—
917#95C2414yes—
918#95C2418yes—
919#95C2414yes—
920#95C2414yes—
921#95C2414yes—
922#95C2412yes—
923#95C2412yes—
924#95C2414yes—
925#95C2414yes—
926#95C2414yes—
927#95C2418yes—
928#95C2418yes—
929#95C2418yes—
930#95C2418yes—
931#95C2418yes—
932#95C2418yes—
933#95C2418yes—
934C24C2514yes—
935C24C2511yescharacteristic
936C24C2512yes—
937#41—232no—
938#41—432no—
939C2×Q8—22no—
940C2×Q8—22no—
941C2×Q8—22no—
942C2×Q8—28no—
943C2×Q8—24no—
944C2×Q8—24no—
945C2×Q8—24no—
946C2×Q8—28no—
947C2×Q8—24no—
948C2×Q8—22no—
949C2×Q8—22no—
950C2×Q8—22no—
951C2×Q8—22no—
952C2×Q8—22no—
953C2×Q8—24no—
954C2×Q8—24no—
955C2×Q8—28no—
956C2×Q8—28no—
957C2×Q8—44no—
958C2×Q8—48no—
959C2×Q8—48no—
960C2×Q8—44no—
961C2×Q8—44no—
962C2×Q8—416no—
963C2×Q8—432no—
964C2×Q8C22×D414yes—
965C2×Q8C22×D414yes—
966C2×Q8C22×D418yes—
967C2×Q82−1+414yes—
968C2×D4—24no—
969C2×D4—24no—
970C2×D4—28no—
971C2×D4—216no—
972C2×D4—22no—
973C2×D4—24no—
974C2×D4—24no—
975C2×D4—24no—
976C2×D4—24no—
977C2×D4—22no—
978C2×D4—24no—
979C2×D4—24no—
980C2×D4—28no—
981C2×D4—48no—
982C2×D4—48no—
983C2×D4—48no—
984C2×D4—44no—
985C2×D42−1+414yes—
986C22×C4—24no—
987C22×C4—24no—
988C22×C4—24no—
989C22×C4—22no—
990C22×C4—22no—
991C22×C4—24no—
992C22×C4—28no—
993C22×C4—24no—
994C22×C4—28no—
995C22×C4—28no—
996C22×C4—28no—
997C22×C4—24no—
998C22×C4—28no—
999C22×C4—28no—
1000C22×C4—44no—
1001C22×C4—42no—
1002C22×C4—44no—
1003C22×C4—48no—
1004C22×C4—48no—
1005C22×C4—48no—
1006C22×C4—48no—
1007C22×C4—44no—
1008C22×C4—48no—
1009C22×C4C22×D414yes—
1010C22×C4C22×D414yes—
1011C22×C4C22×D418yes—
1012C22×C4C22×D414yes—
1013C22×C4C22×D418yes—
1014C22×C4C2514yes—
1015C22×C4C2512yes—
1016C22×C4C2512yes—
1017C22×C4C2514yes—
1018C22×C4C2512yes—
1019C22×C4C2512yes—
1020C22×C4C2512yes—
1021C22×C4C2514yes—
1022C22×C4C2512yes—
1023C22×C4C2512yes—
1024C22×C4C2514yes—
1025C22×C4C2514yes—
1026C22×C4C2512yes—
1027C22×C4C2512yes—
1028C22×C4C2511yescharacteristic
1029C22×C4C2512yes—
1030C22×C4C2511yescharacteristic
1031C22×C4C2512yes—
1032C22×C4C2511yescharacteristic
1033C22×C4C2512yes—
1034C22×C4C2511yescharacteristic
1035C22×C4C2512yes—
1036C22×C4C2512yes—
1037C22×C4C2512yes—
1038C22×C4C2511yescharacteristic
1039C22×C4C2511yescharacteristic
1040C4⋊C4—24no—
1041C4⋊C4—28no—
1042C4⋊C4—28no—
1043C4⋊C4—28no—
1044C4⋊C4—28no—
1045C4⋊C4—28no—
1046C4⋊C4—28no—
1047C4⋊C4—24no—
1048C4⋊C4—24no—
1049C4⋊C4—24no—
1050C4⋊C4—24no—
1051C4⋊C4—28no—
1052C4⋊C4—28no—
1053C4⋊C4—24no—
1054C4⋊C4—24no—
1055C4⋊C4—24no—
1056C4⋊C4—22no—
1057C4⋊C4—24no—
1058C4⋊C4—22no—
1059C4⋊C4—28no—
1060C4⋊C4—28no—
1061C4⋊C4—22no—
1062C4⋊C4—22no—
1063C4⋊C4—24no—
1064C4⋊C4—24no—
1065C4⋊C4—28no—
1066C4⋊C4—28no—
1067C4⋊C4—28no—
1068C4⋊C4—24no—
1069C4⋊C4—28no—
1070C4⋊C4—24no—
1071C4⋊C4—24no—
1072C4⋊C4—28no—
1073C4⋊C4—28no—
1074C4⋊C4—24no—
1075C4⋊C4—28no—
1076C4⋊C4—28no—
1077C4⋊C4—24no—
1078C4⋊C4—28no—
1079C4⋊C4—24no—
1080C4⋊C4—24no—
1081C4⋊C4—28no—
1082C4⋊C4—42no—
1083C4⋊C4—44no—
1084C4⋊C4—48no—
1085C4⋊C4—44no—
1086C4⋊C4—44no—
1087C4⋊C4—48no—
1088C4⋊C4—44no—
1089C4⋊C4—48no—
1090C4⋊C4—48no—
1091C4⋊C4—48no—
1092C4⋊C4C22×D418yes—
1093C4⋊C4C22×D414yes—
1094C4⋊C4C22×D418yes—
1095C4⋊C4C22×D414yes—
1096C4⋊C4C22×D418yes—
1097C4⋊C4C22×D418yes—
1098C4⋊C4C22×D418yes—
1099C22⋊C4—28no—
1100C22⋊C4—24no—
1101C22⋊C4—24no—
1102C22⋊C4—24no—
1103C22⋊C4—28no—
1104C22⋊C4—28no—
1105C22⋊C4—28no—
1106C22⋊C4—28no—
1107C22⋊C4—28no—
1108C22⋊C4—24no—
1109C22⋊C4—24no—
1110C22⋊C4—28no—
1111C22⋊C4—28no—
1112C22⋊C4—28no—
1113C22⋊C4—28no—
1114C22⋊C4—28no—
1115C22⋊C4—28no—
1116C22⋊C4—28no—
1117C22⋊C4—216no—
1118C22⋊C4—24no—
1119C22⋊C4—28no—
1120C22⋊C4—216no—
1121C22⋊C4—42no—
1122C22⋊C4—44no—
1123C22⋊C4—48no—
1124C22⋊C4—48no—
1125C22⋊C4—44no—
1126C22⋊C4—48no—
1127C22⋊C4—48no—
1128C22⋊C4—48no—
1129C22⋊C4—48no—
1130C42—28no—
1131C42—24no—
1132C42—28no—
1133C42—24no—
1134C42—28no—
1135C42—24no—
1136C42—28no—
1137C42—28no—
1138C42—24no—
1139C42—24no—
1140C42—24no—
1141C42—22no—
1142C42—22no—
1143C42—24no—
1144C42—22no—
1145C42—22no—
1146C42—28no—
1147C42—24no—
1148C42—24no—
1149C42—24no—
1150C42—44no—
1151C42—42no—
1152C42—44no—
1153C42—44no—
1154C42C22×D418yes—
1155C42C22×D414yes—
1156C42C22×D418yes—
1157C42C22×D414yes—
1158C42C22×D414yes—
1159C42C22×D418yes—
1160C42C22×D418yes—
1161C42C22×D414yes—
1162C23—22no—
1163C23—21no—
1164C23—21no—
1165C23—22no—
1166C23—22no—
1167C23—24no—
1168C23—24no—
1169C23—22no—
1170C23—24no—
1171C23—24no—
1172C23—24no—
1173C23—28no—
1174C23—28no—
1175C23C23×D412yes—
1176C23C2×2−1+414yes—
1177C23C2611yescharacteristic
1178Q8—28no—
1179Q8—28no—
1180Q8—28no—
1181Q8—48no—
1182Q8—416no—
1183Q8—48no—
1184Q8—48no—
1185Q8—44no—
1186Q8—44no—
1187Q8—84no—
1188Q8—88no—
1189Q8—84no—
1190D4—216no—
1191D4—28no—
1192D4—416no—
1193D4—48no—
1194D4—48no—
1195D4—84no—
1196D4—816no—
1197C2×C4—216no—
1198C2×C4—22no—
1199C2×C4—22no—
1200C2×C4—21no—
1201C2×C4—21no—
1202C2×C4—22no—
1203C2×C4—22no—
1204C2×C4—24no—
1205C2×C4—22no—
1206C2×C4—24no—
1207C2×C4—22no—
1208C2×C4—24no—
1209C2×C4—22no—
1210C2×C4—24no—
1211C2×C4—28no—
1212C2×C4—28no—
1213C2×C4—22no—
1214C2×C4—22no—
1215C2×C4—24no—
1216C2×C4—24no—
1217C2×C4—22no—
1218C2×C4—22no—
1219C2×C4—24no—
1220C2×C4—22no—
1221C2×C4—22no—
1222C2×C4—22no—
1223C2×C4—22no—
1224C2×C4—24no—
1225C2×C4—22no—
1226C2×C4—24no—
1227C2×C4—22no—
1228C2×C4—22no—
1229C2×C4—22no—
1230C2×C4—22no—
1231C2×C4—22no—
1232C2×C4—22no—
1233C2×C4—22no—
1234C2×C4—24no—
1235C2×C4—22no—
1236C2×C4—22no—
1237C2×C4—24no—
1238C2×C4—22no—
1239C2×C4—24no—
1240C2×C4—24no—
1241C2×C4—28no—
1242C2×C4—24no—
1243C2×C4—24no—
1244C2×C4—24no—
1245C2×C4—28no—
1246C2×C4—24no—
1247C2×C4—28no—
1248C2×C4—48no—
1249C2×C4—44no—
1250C2×C4—48no—
1251C2×C4—416no—
1252C2×C4—416no—
1253C2×C4—48no—
1254C2×C4—88no—
1255C2×C4—88no—
1256C2×C4—88no—
1257C2×C4—84no—
1258C2×C4C23×D412yes—
1259C2×C4C23×D414yes—
1260C2×C4C23×D412yes—
1261C2×C4C23×D414yes—
1262C2×C4C23×D414yes—
1263C2×C4C23×D414yes—
1264C2×C4C23×D412yes—
1265C2×C4C23×D412yes—
1266C2×C4C23×D412yes—
1267C2×C4C23×D412yes—
1268C2×C4C2×2−1+414yes—
1269C2×C4C2×2−1+412yes—
1270C2×C4C2×2−1+412yes—
1271C2×C4#58514yes—
1272C2×C4#58514yes—
1273C22—28no—
1274C22—22no—
1275C22—24no—
1276C22—22no—
1277C22—22no—
1278C22—42no—
1279C22—42no—
1280C22—44no—
1281C22—42no—
1282C22—42no—
1283C22—48no—
1284C22—48no—
1285C22—44no—
1286C22—44no—
1287C22—44no—
1288C22C24×D411yescharacteristic
1289C22C22×2−1+411yescharacteristic
1290C22C22×2−1+411yescharacteristic
1291C22C2×#58512yes—
1292C22C2×#58512yes—
1293C4—24no—
1294C4—22no—
1295C4—24no—
1296C4—24no—
1297C4—24no—
1298C4—22no—
1299C4—22no—
1300C4—22no—
1301C4—24no—
1302C4—24no—
1303C4—42no—
1304C4—42no—
1305C4—44no—
1306C4—44no—
1307C4—42no—
1308C4—42no—
1309C4—42no—
1310C4—42no—
1311C4—42no—
1312C4—44no—
1313C4—42no—
1314C4—44no—
1315C4—42no—
1316C4—44no—
1317C4#344914yes—
1318C4#348614yes—
1319C2—44no—
1320C2—42no—
1321C2—84no—
1322C2C2×#344911yescharacteristic
1323C2C2×#348611yescharacteristic
1324C2#6281211yescharacteristic
1325C2#6302512yes—
1326C2#6303312yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#35190C2
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×#3507C2semidirect
2. C2×Q8×#41C2semidirect
3. #42787C2semidirect
4. #40523C2semidirect
5. #39879C2semidirect
6. #39619C2semidirect
7. #39616C2semidirect
8. #39613C2semidirect
9. #39611C2semidirect
10. #39171C2semidirect
11. #39168C2semidirect
12. #39163C2semidirect
13. #39162C2semidirect
14. #38374C2semidirect
15. #37635C2semidirect
16. #37545C2semidirect
17. #36562C2semidirect
18. #36560C2semidirect
19. #36538C2semidirect
20. #36496C2semidirect
21. #36233C2semidirect
22. #35724C2semidirect
23. #35298C2semidirect
24. #35211C2semidirect
25. #35201C2semidirect
27. #34979C2semidirect
28. #34910C2semidirect
29. #34128C2semidirect
328. C2×C4×Q8D4semidirect

Maximal subgroups

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

subgroupindex
C2×#35072
C2×Q8×#412
#427872
#405232
#398792
#396192
#396162
#396132
#396112
#391712
#391682
#391632
#391622
#383742
#376352
#375452
#365622
#365602
#365382
#364962
#362332
#357242
#352982
#352112
#352012
#351902
#349792
#349102
#341282