Finite Group Databasebeta

← #7681226

Subgroups — #7681226

Order 512.

6730 conjugacy classes of subgroups.

The subgroup lattice has 1342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3523C211yesmaximal, characteristic, complemented
2C2×#3515C211yesmaximal, characteristic
3#59154C214yesmaximal, complemented
4#59121C214yesmaximal, complemented
5#59116C214yesmaximal, complemented
6#59069C214yesmaximal, complemented
7#44849C218yesmaximal, complemented
8#43499C218yesmaximal, complemented
9#39490C211yesmaximal, characteristic, complemented
10#39484C212yesmaximal, complemented
11#39360C212yesmaximal, complemented
12#39360C211yesmaximal, characteristic, complemented
13#39173C211yesmaximal, characteristic, complemented
14#39170C211yesmaximal, characteristic, complemented
15#38088C212yesmaximal, complemented
16#38081C212yesmaximal, complemented
17#36593C211yesmaximal, characteristic, complemented
18#36562C211yesmaximal, characteristic, complemented
19#36406C211yesmaximal, characteristic, complemented
20#36276C211yesmaximal, characteristic, complemented
21#35670C212yesmaximal, complemented
22#35622C212yesmaximal, complemented
23#35322C211yesmaximal, characteristic, complemented
24#35319C212yesmaximal, complemented
25#34979C211yesmaximal, characteristic, complemented
26#34953C211yesmaximal, characteristic, complemented
27#34276C212yesmaximal, complemented
28#34151C211yesmaximal, characteristic, complemented
29C4×#536C211yesmaximal, characteristic, complemented
30#3523—216no—
31#3515—216no—
32C2×#557C2211yescharacteristic
33C2×#557C2211yescharacteristic
34C2×#557C2211yescharacteristic
35C2×#557C2212yes—
36C2×#556C2211yescharacteristic
37C2×#556C2212yes—
38C2×#554C2211yescharacteristic
39C2×#554C2211yescharacteristic
40C2×#553C2212yes—
41C2×#552C2214yes—
42C2×#552C2212yes—
43C2×#552C2212yes—
44C2×#552C2212yes—
45C2×#552C2214yes—
46C2×D4×Q8C2211yescharacteristic
47C2×D4×Q8C2212yes—
48C2×#547C2211yescharacteristic
49C2×#547C2212yes—
50C2×#541C2212yes—
51C2×#541C2214yes—
52C2×#541C2212yes—
53C2×#539C2214yes—
54C2×#536C2211yescharacteristic
55C2×#536C2212yes—
56C2×#533C2211yescharacteristic
57C2×#533C2211yescharacteristic
58C2×#533C2212yes—
59C2×#529C2212yes—
60C2×#529C2212yes—
61C2×#529C2211yescharacteristic
62C22×#125C2212yes—
63C2×#520C2212yes—
64C2×#519C2212yes—
65C2×C4×#41C2211yescharacteristic
66C22×C4×Q8C2211yescharacteristic
67#2868C2212yes—
68#2868C2211yescharacteristic
69#2862C2211yescharacteristic
70#2862C2211yescharacteristic
71#2862C2211yescharacteristic
72#2859C2212yes—
73#2857C2212yes—
74#2857C2212yes—
75#2726C2218yes—
76#2724C2218yes—
77#2719C2218yes—
78#2713C2218yes—
79#2708C2218yes—
80#2695C2218yes—
81#2690C2218yes—
82#2689C2218yes—
83#2689C2218yes—
84#2680C2218yes—
85#2680C2218yes—
86#2680C2218yes—
87#2642C2212yes—
88#2642C2212yes—
89#2621C2212yes—
90#2621C2212yes—
91#2621C2212yes—
92#2621C2212yes—
93#2611C2214yes—
94#2584C2214yes—
95#2583C2214yes—
96#2568C2211yescharacteristic
97#2567C2211yescharacteristic
98#2567C2211yescharacteristic
99#2566C2212yes—
100#2565C2212yes—
101#2565C2212yes—
102#2565C2214yes—
103#2565C2214yes—
104#2565C2212yes—
105#2556C2218yes—
106#2553C2218yes—
107#2552C2214yes—
108#2552C2218yes—
109#2550C2214yes—
110#2549C2218yes—
111#2547C2212yes—
112#2547C2211yescharacteristic
113#2546C2212yes—
114#2546C2211yescharacteristic
115#2546C2212yes—
116#2546C2211yescharacteristic
117#2546C2212yes—
118#2546C2211yescharacteristic
119#2542C2211yescharacteristic
120#2506C2218yes—
121#2506C2218yes—
122#2503C2212yes—
123#2502C2212yes—
124#2502C2212yes—
125#2499C2212yes—
126#2499C2212yes—
127#2499C2212yes—
128#2499C2214yes—
129#2499C2214yes—
130#2496C2218yes—
131#2496C2218yes—
132#2478C2218yes—
133#2478C2218yes—
134#2478C2218yes—
135#2478C2218yes—
136#2475C2218yes—
137#2473C2218yes—
138#2473C2218yes—
139#2470C2218yes—
140#2468C2218yes—
141#2466C2218yes—
142#2462C2218yes—
143#2462C2218yes—
144#2453C2214yes—
145#2453C2214yes—
146#2447C2214yes—
147#2446C2214yes—
148#2442C2214yes—
149#2440C2218yes—
150#2440C2214yes—
151#2438C2218yes—
152#2434C2212yes—
153#2434C2212yes—
154#2434C2212yes—
155#2432C2212yes—
156#2432C2212yes—
157#2432C2212yes—
158#2429C2214yes—
159#2427C2214yes—
160#2422C2214yes—
161#2422C2218yes—
162#2421C2214yes—
163#2419C2218yes—
164#2415C2214yes—
165#2399C2214yes—
166#2395C2214yes—
167#2374C2214yes—
168#2373C2214yes—
169#2370C2212yes—
170#2367C2212yes—
171#2363C2212yes—
172#2362C2218yes—
173#2362C2212yes—
174#2360C2214yes—
175#2360C2214yes—
176#2360C2218yes—
177#2359C2218yes—
178#2359C2218yes—
179Q8×C4⋊C4C2214yes—
180#2349C2214yes—
181#2327C2212yes—
182#2327C2212yes—
183#2327C2211yescharacteristic
184#2327C2211yescharacteristic
185#2327C2212yes—
186#2326C2212yes—
187#2326C2211yescharacteristic
188#2326C2211yescharacteristic
189#2323C2214yes—
190#2322C2214yes—
191#2317C2211yescharacteristic
192#2317C2212yes—
193#2311C2211yescharacteristic
194#2310C2211yescharacteristic
195C4×C4⋊Q8C2211yescharacteristic
196C4×C4⋊Q8C2212yes—
197C4×C4⋊Q8C2211yescharacteristic
198C4×C4⋊Q8C2212yes—
199C4×C4⋊Q8C2212yes—
200C4×C4⋊Q8C2212yes—
201C4×#124C2211yescharacteristic
202C4×#124C2212yes—
203C4×#124C2211yescharacteristic
204C4×#124C2212yes—
205C4×C22⋊Q8C2214yes—
206C4×C22⋊Q8C2214yes—
207C4×#123C2214yes—
208#2298C2212yes—
209#2297C2212yes—
210#2296C2214yes—
211#2295C2211yescharacteristic
212C2×#391C2212yes—
213#2293C2212yes—
214#2293C2211yescharacteristic
215#2290C2212yes—
216C42×Q8C2211yescharacteristic
217C42×D4C2211yescharacteristic
218C4×#117C2211yescharacteristic
219C4×#117C2211yescharacteristic
220C4×#117C2212yes—
221C22×#41C2311yescharacteristic
222C22×#41C2312yes—
223C23×Q8C2311yescharacteristic
224C23×Q8C2312yes—
225#557—216no—
226#557—28no—
227#557—28no—
228#557—28no—
229#556—216no—
230#556—28no—
231#554—28no—
232#554—28no—
233#553—216no—
234#552—232no—
235#552—232no—
236#552—216no—
237#552—216no—
238#552—216no—
239D4×Q8—216no—
240D4×Q8—28no—
241#547—28no—
242#547—216no—
243#541—232no—
244#541—216no—
245#541—216no—
246#539—232no—
247#536—28no—
248#536—216no—
249#533—216no—
250#533—28no—
251#533—28no—
252C2×C4⋊Q8C2311yescharacteristic
253C2×C4⋊Q8C2312yes—
254C2×C4⋊Q8C2311yescharacteristic
255C2×C4⋊Q8C2312yes—
256C2×C4⋊Q8C2311yescharacteristic
257C2×C4⋊Q8C2311yescharacteristic
258C2×C4⋊Q8C2311yescharacteristic
259C2×C4⋊Q8C2311yescharacteristic
260C2×C4⋊Q8C2312yes—
261C2×C4⋊Q8C2312yes—
262C2×C4⋊Q8C2312yes—
263C2×C4⋊Q8C2312yes—
264C2×C4⋊Q8C2314yes—
265C2×C4⋊Q8C2312yes—
266C2×C4⋊Q8C2312yes—
267C2×C4⋊Q8C2312yes—
268#529—216no—
269#529—216no—
270#529D4116yes—
271C2×#126C2314yes—
272C2×#126C2314yes—
273C2×#126C2314yes—
274C2×#126C2314yes—
275C2×#126C2314yes—
276C2×#126C2314yes—
277C2×#126C2314yes—
278C2×#126C2312yes—
279C2×#125—216no—
280C2×#125C2312yes—
281C2×#125C2312yes—
282C2×#125C2312yes—
283C2×#125C2312yes—
284C2×#125C2314yes—
285C2×#125C2314yes—
286C2×#125C2312yes—
287C2×#125C2312yes—
288C2×#125C2312yes—
289C2×#125C2314yes—
290C2×#125C2314yes—
291C2×#125C2314yes—
292C2×#125C2314yes—
293C2×#125C2314yes—
294C2×#125C2314yes—
295C2×#125C2314yes—
296C2×#125C2311yescharacteristic
297C2×#124C2312yes—
298C2×#124C2311yescharacteristic
299C2×#124C2312yes—
300C2×#124C2311yescharacteristic
301C2×#124C2311yescharacteristic
302C2×#123C2314yes—
303C2×#123C2318yes—
304C2×#123C2314yes—
305C2×#123C2314yes—
306C2×#123C2314yes—
307C2×#123C2314yes—
308C2×#123C2314yes—
309C2×#123C2312yes—
310C2×C22⋊Q8C2314yes—
311C2×C22⋊Q8C2312yes—
312C2×C22⋊Q8C2312yes—
313C2×C22⋊Q8C2312yes—
314C2×C22⋊Q8C2312yes—
315C2×C22⋊Q8C2312yes—
316C2×C22⋊Q8C2314yes—
317C2×C22⋊Q8C2318yes—
318C2×C22⋊Q8C2312yes—
319C2×C22⋊Q8C2312yes—
320C2×C22⋊Q8C2312yes—
321C2×C22⋊Q8C2312yes—
322C2×C22⋊Q8C2314yes—
323C2×C22⋊Q8C2314yes—
324C2×C22⋊Q8C2314yes—
325C2×C22⋊Q8C2314yes—
326C2×C22⋊Q8C2314yes—
327C2×C22⋊Q8C2311yescharacteristic
328C2×#121C2312yes—
329C2×#121C2314yes—
330C2×#121C2311yescharacteristic
331#520—216no—
332#519—216no—
333C4×#41—28no—
334C2×C4×Q8—28no—
335C2×C4×Q8C2311yescharacteristic
336C2×C4×Q8C2311yescharacteristic
337C2×C4×Q8C2311yescharacteristic
338C2×C4×Q8C2311yescharacteristic
339C2×C4×Q8C2312yes—
340C2×C4×Q8C2312yes—
341C2×C4×Q8C2312yes—
342C2×C4×Q8C2311yescharacteristic
343C2×C4×Q8C2311yescharacteristic
344C2×C4×Q8C2312yes—
345C2×C4×Q8C2312yes—
346C2×C4×Q8C2312yes—
347C2×C4×Q8C2312yes—
348C2×C4×Q8C2312yes—
349C2×C4×Q8C2312yes—
350C2×C4×Q8C2312yes—
351C2×C4×Q8C2312yes—
352C2×C4×Q8C2312yes—
353C2×C4×Q8C2314yes—
354C2×C4×Q8C2312yes—
355C2×C4×Q8C2312yes—
356C2×C4×Q8C2314yes—
357C2×C4×Q8C2311yescharacteristic
358C2×C4×D4C2312yes—
359C2×C4×D4C2312yes—
360C2×C4×D4C2311yescharacteristic
361C2×C4×D4C2312yes—
362C2×C4×D4C2312yes—
363C2×C4×D4C2312yes—
364C2×C4×D4C2314yes—
365C2×C4×D4C2314yes—
366C2×C4×D4C2312yes—
367C2×C4×D4C2311yescharacteristic
368C2×C4×D4C2314yes—
369C2×C4×D4C2312yes—
370C2×C4×D4C2311yescharacteristic
371C2×#117C2311yescharacteristic
372C2×#117C2311yescharacteristic
373C2×#117C2312yes—
374C2×#117C2312yes—
375C2×#117C2312yes—
376C2×#117C2314yes—
377C2×#117C2314yes—
378C2×#117C2314yes—
379C2×#117C2312yes—
380C2×#117C2312yes—
381C2×#117C2314yes—
382C2×#117C2314yes—
383C2×#117C2312yes—
384C2×#117C2311yescharacteristic
385C2×#117C2312yes—
386C22×C4⋊C4C2311yescharacteristic
387C22×C4⋊C4C2312yes—
388C22×C4⋊C4C2312yes—
389C22×C4⋊C4C2314yes—
390C22×C4⋊C4C2312yes—
391C22×C4⋊C4C2312yes—
392C22×C4⋊C4C2314yes—
393C22×C42C2312yes—
394C22×C42C2312yes—
395C22×C42C2312yes—
396C22×C42C2311yescharacteristic
397#400C2314yes—
398#400C2318yes—
399#400C2318yes—
400#400C2318yes—
401#400C2318yes—
402#400C2318yes—
403#399C2314yes—
404#398C2318yes—
405#398C2318yes—
406#398C2318yes—
407#398C2318yes—
408#398C2318yes—
409#398C2314yes—
410#398C2314yes—
411#398C2318yes—
412#398C2314yes—
413#398C2318yes—
414#398C2318yes—
415#398C2318yes—
416#398C2318yes—
417#398C2318yes—
418#398C2318yes—
419#397C2314yes—
420#397C2318yes—
421#397C2318yes—
422#397C2318yes—
423#397C2318yes—
424#397C2318yes—
425#397C2318yes—
426#397C2318yes—
427#397C2318yes—
428#396C2318yes—
429#395C2314yes—
430#395C2314yes—
431#395C2318yes—
432#395C2318yes—
433#395C2318yes—
434#394C2318yes—
435#394C2318yes—
436#394C2318yes—
437#391C2312yes—
438#391C2312yes—
439#391C2312yes—
440#391C2312yes—
441#391C2311yescharacteristic
442#391C2311yescharacteristic
443#391C2311yescharacteristic
444#391C2311yescharacteristic
445#391C2312yes—
446#391C2312yes—
447#391C2312yes—
448#391C2311yescharacteristic
449#391C2312yes—
450#391C2312yes—
451#391C2314yes—
452#391C2314yes—
453#391C2314yes—
454#391C2314yes—
455#391C2314yes—
456#391C2311yescharacteristic
457#391C2314yes—
458#391C2312yes—
459#391C2312yes—
460#391C2318yes—
461#391C2312yes—
462#390C2311yescharacteristic
463#390C2312yes—
464#390C2311yescharacteristic
465#390C2312yes—
466#390C2314yes—
467#389C2314yes—
468#389C2314yes—
469#389C2318yes—
470#389C2318yes—
471#389C2318yes—
472#389C2318yes—
473#389C2314yes—
474#389C2314yes—
475#389C2314yes—
476#389C2318yes—
477#389C2314yes—
478#389C2314yes—
479#389C2318yes—
480#389C2318yes—
481#389C2318yes—
482#389C2318yes—
483#389C2314yes—
484#389C2318yes—
485#389C2318yes—
486#389C2312yes—
487#389C2312yes—
488#389C2314yes—
489#389C2318yes—
490#388C2314yes—
491#388C2314yes—
492#388C2314yes—
493#388C2314yes—
494#388C2318yes—
495#388C2318yes—
496#388C2318yes—
497#388C2314yes—
498#388C2314yes—
499#388C2314yes—
500#388C2314yes—
501#388C2314yes—
502#388C2314yes—
503#387C2318yes—
504#387C2318yes—
505#387C2318yes—
506#387C2318yes—
507#387C2318yes—
508#387C2318yes—
509#387C2318yes—
510#387C2314yes—
511#387C2314yes—
512#387C2314yes—
513#387C2314yes—
514#387C2318yes—
515#387C2318yes—
516#387C2318yes—
517#387C2318yes—
518#387C2314yes—
519#387C2314yes—
520#387C2314yes—
521#387C2314yes—
522#387C2318yes—
523#386C2314yes—
524#386C2318yes—
525#386C2314yes—
526#385C2318yes—
527#385C2314yes—
528#385C2318yes—
529#385C2314yes—
530#385C2314yes—
531#385C2318yes—
532#385C2318yes—
533#385C2318yes—
534#385C2318yes—
535#385C2318yes—
536#385C2318yes—
537#385C2318yes—
538#385C2314yes—
539#385C2318yes—
540#385C2318yes—
541#384C2311yescharacteristic
542#384C2311yescharacteristic
543#384C2312yes—
544#384C2312yes—
545#384C2312yes—
546#384C2314yes—
547#384C2314yes—
548#384C2318yes—
549#384C2318yes—
550#382C2311yescharacteristic
551#382C2312yes—
552#382C2312yes—
553#382C2314yes—
554#382C2314yes—
555#382C2311yescharacteristic
556#382C2312yes—
557#381C2314yes—
558#381C2318yes—
559#380C2314yes—
560#380C2318yes—
561#380C2318yes—
562#380C2314yes—
563#380C2318yes—
564C4×C4⋊C4C2314yes—
565C4×C4⋊C4C2318yes—
566C4×C4⋊C4C2314yes—
567C4×C4⋊C4C2318yes—
568C4×C4⋊C4C2318yes—
569C4×C4⋊C4C2318yes—
570C4×C4⋊C4C2312yes—
571C4×C4⋊C4C2312yes—
572C4×C4⋊C4C2312yes—
573C4×C4⋊C4C2312yes—
574C4×C4⋊C4C2311yescharacteristic
575C4×C4⋊C4C2311yescharacteristic
576C4×C4⋊C4C2312yes—
577C4×C4⋊C4C2312yes—
578C4×C4⋊C4C2312yes—
579C4×C4⋊C4C2314yes—
580C4×C4⋊C4C2314yes—
581C4×C4⋊C4C2314yes—
582C4×C22⋊C4C2312yes—
583C4×C22⋊C4C2312yes—
584C4×C22⋊C4C2314yes—
585C4×C22⋊C4C2314yes—
586C4×C22⋊C4C2318yes—
587C4×C22⋊C4C2318yes—
588C4×C22⋊C4C2318yes—
589C4×C22⋊C4C2314yes—
590C4×C22⋊C4C2314yes—
591C4×C22⋊C4C2312yes—
592C4×C22⋊C4C2314yes—
593C4×C22⋊C4C2312yes—
594C4×C22⋊C4C2312yes—
595C4×C22⋊C4C2312yes—
596#376C2311yescharacteristic
597#376C2311yescharacteristic
598#376C2312yes—
599#376C2312yes—
600C2×#95C2318yes—
601C43C2312yes—
602C43C2312yes—
603C43C2311yescharacteristic
604C43C2311yescharacteristic
605C2×#41—24no—
606C2×#41—28no—
607C2×#41—24no—
608C2×#41—28no—
609C2×#41—44no—
610C2×#41—42no—
611C22×Q8—24no—
612C22×Q8—28no—
613C22×Q8—24no—
614C22×Q8—28no—
615C22×Q8—44no—
616C22×Q8—42no—
617C22×Q8C2412yes—
618C22×Q8C2411yescharacteristic
619C22×Q8C2412yes—
620C22×Q8C2411yescharacteristic
621C22×Q8C2412yes—
622C22×Q8C2412yes—
623C22×Q8C2414yes—
624C22×Q8C2411yescharacteristic
625C22×Q8C2411yescharacteristic
626C22×Q8C2412yes—
627C22×D4C2412yes—
628C22×D4C2414yes—
629C22×D4C2411yescharacteristic
630C22×D4C2411yescharacteristic
631C22×D4C2412yes—
632C23×C4C2412yes—
633C23×C4C2414yes—
634C23×C4C2412yes—
635C23×C4C2412yes—
636C23×C4C2414yes—
637C23×C4C2412yes—
638C23×C4C2411yescharacteristic
639C23×C4C2411yescharacteristic
640C23×C4C2414yes—
641C23×C4C2412yes—
642C23×C4C2412yes—
643C23×C4C2414yes—
644C23×C4C2414yes—
645C23×C4C2411yescharacteristic
646C4⋊Q8—28no—
647C4⋊Q8—24no—
648C4⋊Q8—28no—
649C4⋊Q8—28no—
650C4⋊Q8—216no—
651C4⋊Q8—24no—
652C4⋊Q8—24no—
653C4⋊Q8—24no—
654C4⋊Q8—24no—
655C4⋊Q8—28no—
656C4⋊Q8—28no—
657C4⋊Q8—24no—
658C4⋊Q8—28no—
659C4⋊Q8—44no—
660C4⋊Q8—44no—
661C4⋊Q8—44no—
662#126—216no—
663#126—216no—
664#126—216no—
665#126—216no—
666#126—216no—
667#126—216no—
668#126—216no—
669#126C2×D4116yes—
670#125—216no—
671#125—216no—
672#125—28no—
673#125—28no—
674#125—28no—
675#125—216no—
676#125—216no—
677#125—216no—
678#125—216no—
679#125—216no—
680#125—216no—
681#125—216no—
682#125—28no—
683#125—28no—
684#125—28no—
685#125—28no—
686#125C2×D418yes—
687#124—28no—
688#124—28no—
689#124—24no—
690#124C2×D418yes—
691#124#4118yes—
692#123—216no—
693#123—216no—
694#123—216no—
695#123—216no—
696#123—216no—
697#123—216no—
698#123—232no—
699#123C2×D4116yes—
700C22⋊Q8—28no—
701C22⋊Q8—28no—
702C22⋊Q8—28no—
703C22⋊Q8—28no—
704C22⋊Q8—28no—
705C22⋊Q8—28no—
706C22⋊Q8—28no—
707C22⋊Q8—28no—
708C22⋊Q8—28no—
709C22⋊Q8—216no—
710C22⋊Q8—216no—
711C22⋊Q8—216no—
712C22⋊Q8—216no—
713C22⋊Q8—216no—
714C22⋊Q8—216no—
715C22⋊Q8—216no—
716C22⋊Q8—232no—
717C22⋊Q8C2×D418yes—
718#121—28no—
719#121—216no—
720#121C2×D418yes—
721C4×Q8—28no—
722C4×Q8—28no—
723C4×Q8—216no—
724C4×Q8—216no—
725C4×Q8—28no—
726C4×Q8—28no—
727C4×Q8—28no—
728C4×Q8—24no—
729C4×Q8—28no—
730C4×Q8—24no—
731C4×Q8—24no—
732C4×Q8—28no—
733C4×Q8—24no—
734C4×Q8—24no—
735C4×Q8—24no—
736C4×Q8—28no—
737C4×Q8—28no—
738C4×Q8—28no—
739C4×Q8—28no—
740C4×Q8—28no—
741C4×Q8—28no—
742C4×Q8—28no—
743C4×Q8C2×D418yes—
744C4×D4—216no—
745C4×D4—28no—
746C4×D4—28no—
747C4×D4—28no—
748C4×D4—28no—
749C4×D4—28no—
750C4×D4—216no—
751C4×D4—216no—
752C4×D4—24no—
753C4×D4—24no—
754C4×D4—28no—
755C4×D4C2×D4116yes—
756C4×D4C2×D418yes—
757#117—24no—
758#117—28no—
759#117—28no—
760#117—28no—
761#117—216no—
762#117—28no—
763#117—216no—
764#117—216no—
765#117—216no—
766#117—216no—
767#117—28no—
768#117—24no—
769#117—28no—
770#117—42no—
771#117C2×D4116yes—
772C2×C4⋊C4—24no—
773C2×C4⋊C4—28no—
774C2×C4⋊C4—28no—
775C2×C4⋊C4—216no—
776C2×C4⋊C4—28no—
777C2×C4⋊C4—216no—
778C2×C4⋊C4—28no—
779C2×C4⋊C4C2411yescharacteristic
780C2×C4⋊C4C2414yes—
781C2×C4⋊C4C2411yescharacteristic
782C2×C4⋊C4C2412yes—
783C2×C4⋊C4C2412yes—
784C2×C4⋊C4C2412yes—
785C2×C4⋊C4C2414yes—
786C2×C4⋊C4C2412yes—
787C2×C4⋊C4C2414yes—
788C2×C4⋊C4C2414yes—
789C2×C4⋊C4C2411yescharacteristic
790C2×C4⋊C4C2412yes—
791C2×C4⋊C4C2412yes—
792C2×C4⋊C4C2412yes—
793C2×C4⋊C4C2412yes—
794C2×C4⋊C4C2414yes—
795C2×C4⋊C4C2414yes—
796C2×C4⋊C4C2414yes—
797C2×C4⋊C4C2414yes—
798C2×C4⋊C4C2411yescharacteristic
799C2×C4⋊C4C2412yes—
800C2×C4⋊C4C2412yes—
801C2×C4⋊C4C2412yes—
802C2×C4⋊C4C2414yes—
803C2×C4⋊C4C2414yes—
804C2×C4⋊C4C2414yes—
805C2×C4⋊C4C2412yes—
806C2×C4⋊C4C2414yes—
807C2×C4⋊C4C2414yes—
808C2×C4⋊C4C2412yes—
809C2×C4⋊C4C2414yes—
810C2×C4⋊C4C2412yes—
811C2×C4⋊C4C2414yes—
812C2×C4⋊C4C2412yes—
813C2×C4⋊C4C2412yes—
814C2×C4⋊C4C2414yes—
815C2×C4⋊C4C2414yes—
816C2×C4⋊C4C2414yes—
817C2×C4⋊C4C2414yes—
818C2×C4⋊C4C2412yes—
819C2×C4⋊C4C2414yes—
820C2×C4⋊C4C2414yes—
821C2×C4⋊C4C2414yes—
822C2×C4⋊C4C2414yes—
823C2×C4⋊C4C2418yes—
824C2×C4⋊C4C2414yes—
825C2×C4⋊C4C2418yes—
826C2×C4⋊C4C2418yes—
827C2×C4⋊C4C2412yes—
828C2×C4⋊C4C2418yes—
829C2×C4⋊C4C2418yes—
830C2×C4⋊C4C2418yes—
831C2×C4⋊C4C2414yes—
832C2×C4⋊C4C2414yes—
833C2×C4⋊C4C2418yes—
834C2×C4⋊C4C2414yes—
835C2×C4⋊C4C2418yes—
836C2×C4⋊C4C2412yes—
837C2×C4⋊C4C2411yescharacteristic
838C2×C4⋊C4C2412yes—
839C2×C4⋊C4C2411yescharacteristic
840C2×C4⋊C4C2412yes—
841C2×C4⋊C4C2412yes—
842C2×C4⋊C4C2412yes—
843C2×C22⋊C4C2412yes—
844C2×C22⋊C4C2414yes—
845C2×C22⋊C4C2414yes—
846C2×C22⋊C4C2414yes—
847C2×C22⋊C4C2412yes—
848C2×C22⋊C4C2412yes—
849C2×C22⋊C4C2414yes—
850C2×C22⋊C4C2414yes—
851C2×C22⋊C4C2412yes—
852C2×C22⋊C4C2414yes—
853C2×C22⋊C4C2414yes—
854C2×C22⋊C4C2414yes—
855C2×C22⋊C4C2414yes—
856C2×C22⋊C4C2414yes—
857C2×C22⋊C4C2414yes—
858C2×C22⋊C4C2414yes—
859C2×C22⋊C4C2418yes—
860C2×C22⋊C4C2418yes—
861C2×C22⋊C4C2412yes—
862C2×C22⋊C4C2414yes—
863C2×C22⋊C4C2414yes—
864C2×C22⋊C4C2414yes—
865C2×C22⋊C4C2412yes—
866C2×C22⋊C4C2412yes—
867C2×C22⋊C4C2412yes—
868C2×C22⋊C4C2412yes—
869C2×C22⋊C4C2412yes—
870C2×C22⋊C4C2414yes—
871C2×C42—28no—
872C2×C42—28no—
873C2×C42—44no—
874C2×C42C2×D418yes—
875C2×C42C2412yes—
876C2×C42C2414yes—
877C2×C42C2414yes—
878C2×C42C2412yes—
879C2×C42C2414yes—
880C2×C42C2414yes—
881C2×C42C2414yes—
882C2×C42C2414yes—
883C2×C42C2412yes—
884C2×C42C2411yescharacteristic
885C2×C42C2411yescharacteristic
886C2×C42C2411yescharacteristic
887C2×C42C2414yes—
888C2×C42C2412yes—
889C2×C42C2412yes—
890C2×C42C2412yes—
891C2×C42C2412yes—
892C2×C42C2412yes—
893C2×C42C2412yes—
894C2×C42C2412yes—
895C2×C42C2414yes—
896C2×C42C2412yes—
897C2×C42C2414yes—
898C2×C42C2414yes—
899C2×C42C2412yes—
900C2×C42C2412yes—
901C2×C42C2414yes—
902C2×C42C2411yescharacteristic
903C2×C42C2411yescharacteristic
904C2×C42C2412yes—
905C2×C42C2411yescharacteristic
906C2×C42C2411yescharacteristic
907C2×C42C2411yescharacteristic
908#95C2414yes—
909#95C2418yes—
910#95C2418yes—
911#95C2418yes—
912#95C2412yes—
913#95C2412yes—
914#95C2412yes—
915#95C2414yes—
916#95C2414yes—
917#95C2412yes—
918#95C2414yes—
919#95C2412yes—
920#95C2412yes—
921#95C2414yes—
922#95C2418yes—
923#95C2414yes—
924#95C2418yes—
925#95C2418yes—
926#95C2414yes—
927#95C2414yes—
928#95C2414yes—
929#95C2418yes—
930#95C2414yes—
931#95C2414yes—
932#95C2414yes—
933#95C2418yes—
934#95C2418yes—
935#95C2414yes—
936#95C2414yes—
937#95C2418yes—
938#95C2418yes—
939#95C2414yes—
940#95C2418yes—
941#95C2418yes—
942#95C2418yes—
943C24C2511yescharacteristic
944C24C2512yes—
945C24C2512yes—
946#41—416no—
947#41—432no—
948C2×Q8—22no—
949C2×Q8—24no—
950C2×Q8—24no—
951C2×Q8—28no—
952C2×Q8—22no—
953C2×Q8—24no—
954C2×Q8—22no—
955C2×Q8—24no—
956C2×Q8—24no—
957C2×Q8—24no—
958C2×Q8—28no—
959C2×Q8—22no—
960C2×Q8—24no—
961C2×Q8—22no—
962C2×Q8—24no—
963C2×Q8—24no—
964C2×Q8—28no—
965C2×Q8—22no—
966C2×Q8—22no—
967C2×Q8—24no—
968C2×Q8—22no—
969C2×Q8—24no—
970C2×Q8—44no—
971C2×Q8—42no—
972C2×Q8—44no—
973C2×Q8—416no—
974C2×Q8—432no—
975C2×Q8C22×D414yes—
976C2×Q8C2×#4114yes—
977C2×D4—28no—
978C2×D4—24no—
979C2×D4—24no—
980C2×D4—28no—
981C2×D4—22no—
982C2×D4—24no—
983C2×D4—22no—
984C2×D4—44no—
985C2×D4—42no—
986C2×D4—44no—
987C2×D4C22×D414yes—
988C2×D4C22×D418yes—
989C2×D4C2×#4114yes—
990C22×C4—24no—
991C22×C4—22no—
992C22×C4—24no—
993C22×C4—24no—
994C22×C4—22no—
995C22×C4—24no—
996C22×C4—24no—
997C22×C4—28no—
998C22×C4—28no—
999C22×C4—24no—
1000C22×C4—28no—
1001C22×C4—24no—
1002C22×C4—24no—
1003C22×C4—28no—
1004C22×C4—24no—
1005C22×C4—28no—
1006C22×C4—28no—
1007C22×C4—24no—
1008C22×C4—28no—
1009C22×C4—28no—
1010C22×C4—42no—
1011C22×C4—44no—
1012C22×C4—42no—
1013C22×C4—44no—
1014C22×C4—44no—
1015C22×C4—42no—
1016C22×C4—44no—
1017C22×C4—44no—
1018C22×C4—44no—
1019C22×C4—48no—
1020C22×C4—48no—
1021C22×C4C22×D414yes—
1022C22×C4C22×D414yes—
1023C22×C4C22×D418yes—
1024C22×C4C22×D414yes—
1025C22×C4C2512yes—
1026C22×C4C2512yes—
1027C22×C4C2514yes—
1028C22×C4C2512yes—
1029C22×C4C2512yes—
1030C22×C4C2514yes—
1031C22×C4C2512yes—
1032C22×C4C2514yes—
1033C22×C4C2512yes—
1034C22×C4C2512yes—
1035C22×C4C2514yes—
1036C22×C4C2512yes—
1037C22×C4C2514yes—
1038C22×C4C2512yes—
1039C22×C4C2511yescharacteristic
1040C22×C4C2511yescharacteristic
1041C22×C4C2512yes—
1042C22×C4C2511yescharacteristic
1043C22×C4C2512yes—
1044C22×C4C2512yes—
1045C22×C4C2511yescharacteristic
1046C22×C4C2512yes—
1047C22×C4C2512yes—
1048C22×C4C2514yes—
1049C22×C4C2511yescharacteristic
1050C22×C4C2511yescharacteristic
1051C4⋊C4—22no—
1052C4⋊C4—28no—
1053C4⋊C4—24no—
1054C4⋊C4—22no—
1055C4⋊C4—24no—
1056C4⋊C4—24no—
1057C4⋊C4—28no—
1058C4⋊C4—24no—
1059C4⋊C4—28no—
1060C4⋊C4—28no—
1061C4⋊C4—24no—
1062C4⋊C4—22no—
1063C4⋊C4—24no—
1064C4⋊C4—24no—
1065C4⋊C4—24no—
1066C4⋊C4—28no—
1067C4⋊C4—28no—
1068C4⋊C4—28no—
1069C4⋊C4—28no—
1070C4⋊C4—24no—
1071C4⋊C4—22no—
1072C4⋊C4—24no—
1073C4⋊C4—28no—
1074C4⋊C4—24no—
1075C4⋊C4—28no—
1076C4⋊C4—28no—
1077C4⋊C4—28no—
1078C4⋊C4—24no—
1079C4⋊C4—28no—
1080C4⋊C4—24no—
1081C4⋊C4—28no—
1082C4⋊C4—24no—
1083C4⋊C4—28no—
1084C4⋊C4—28no—
1085C4⋊C4—28no—
1086C4⋊C4—28no—
1087C4⋊C4—24no—
1088C4⋊C4—28no—
1089C4⋊C4—28no—
1090C4⋊C4—24no—
1091C4⋊C4—28no—
1092C4⋊C4—28no—
1093C4⋊C4—216no—
1094C4⋊C4—28no—
1095C4⋊C4—216no—
1096C4⋊C4—24no—
1097C4⋊C4—28no—
1098C4⋊C4—216no—
1099C4⋊C4—44no—
1100C4⋊C4—48no—
1101C4⋊C4—44no—
1102C4⋊C4—48no—
1103C4⋊C4—44no—
1104C4⋊C4—42no—
1105C4⋊C4—48no—
1106C4⋊C4—48no—
1107C4⋊C4—48no—
1108C4⋊C4C22×D418yes—
1109C4⋊C4C22×D414yes—
1110C4⋊C4C22×D418yes—
1111C4⋊C4C22×D414yes—
1112C4⋊C4C22×D418yes—
1113C4⋊C4C22×D418yes—
1114C4⋊C42−1+418yes—
1115C22⋊C4—28no—
1116C22⋊C4—28no—
1117C22⋊C4—24no—
1118C22⋊C4—28no—
1119C22⋊C4—28no—
1120C22⋊C4—28no—
1121C22⋊C4—28no—
1122C22⋊C4—28no—
1123C22⋊C4—28no—
1124C22⋊C4—216no—
1125C22⋊C4—24no—
1126C22⋊C4—24no—
1127C22⋊C4—28no—
1128C22⋊C4—24no—
1129C22⋊C4—28no—
1130C22⋊C4—28no—
1131C22⋊C4—28no—
1132C22⋊C4—216no—
1133C22⋊C4—44no—
1134C22⋊C4—44no—
1135C22⋊C4—44no—
1136C22⋊C4—42no—
1137C22⋊C4C22×D418yes—
1138C22⋊C4C22×D418yes—
1139C22⋊C4C22×D418yes—
1140C22⋊C4C22×D418yes—
1141C22⋊C4C22×D418yes—
1142C22⋊C4C2×#41116yes—
1143C42—24no—
1144C42—24no—
1145C42—24no—
1146C42—24no—
1147C42—24no—
1148C42—24no—
1149C42—24no—
1150C42—28no—
1151C42—28no—
1152C42—28no—
1153C42—28no—
1154C42—28no—
1155C42—28no—
1156C42—24no—
1157C42—22no—
1158C42—28no—
1159C42—24no—
1160C42—28no—
1161C42—24no—
1162C42—22no—
1163C42—24no—
1164C42—22no—
1165C42—44no—
1166C42—44no—
1167C42—42no—
1168C42—44no—
1169C42—42no—
1170C42C22×D414yes—
1171C42C22×D414yes—
1172C42C22×D414yes—
1173C42C22×D414yes—
1174C42C22×D418yes—
1175C42C2×#4114yes—
1176C23—22no—
1177C23—21no—
1178C23—22no—
1179C23—24no—
1180C23—22no—
1181C23—24no—
1182C23—21no—
1183C23—22no—
1184C23—22no—
1185C23—24no—
1186C23—24no—
1187C23—22no—
1188C23C23×D414yes—
1189C23C23×D412yes—
1190C23C22×#4114yes—
1191C23C2611yescharacteristic
1192Q8—28no—
1193Q8—28no—
1194Q8—416no—
1195Q8—48no—
1196Q8—44no—
1197Q8—48no—
1198Q8—44no—
1199Q8—48no—
1200Q8—48no—
1201Q8—84no—
1202D4—28no—
1203D4—28no—
1204D4—48no—
1205D4—48no—
1206D4—416no—
1207C2×C4—22no—
1208C2×C4—22no—
1209C2×C4—21no—
1210C2×C4—22no—
1211C2×C4—22no—
1212C2×C4—24no—
1213C2×C4—24no—
1214C2×C4—22no—
1215C2×C4—21no—
1216C2×C4—22no—
1217C2×C4—22no—
1218C2×C4—24no—
1219C2×C4—22no—
1220C2×C4—22no—
1221C2×C4—24no—
1222C2×C4—216no—
1223C2×C4—28no—
1224C2×C4—28no—
1225C2×C4—22no—
1226C2×C4—22no—
1227C2×C4—24no—
1228C2×C4—22no—
1229C2×C4—22no—
1230C2×C4—22no—
1231C2×C4—24no—
1232C2×C4—22no—
1233C2×C4—24no—
1234C2×C4—24no—
1235C2×C4—22no—
1236C2×C4—24no—
1237C2×C4—22no—
1238C2×C4—24no—
1239C2×C4—24no—
1240C2×C4—22no—
1241C2×C4—22no—
1242C2×C4—24no—
1243C2×C4—22no—
1244C2×C4—22no—
1245C2×C4—28no—
1246C2×C4—24no—
1247C2×C4—22no—
1248C2×C4—22no—
1249C2×C4—22no—
1250C2×C4—24no—
1251C2×C4—22no—
1252C2×C4—24no—
1253C2×C4—22no—
1254C2×C4—22no—
1255C2×C4—24no—
1256C2×C4—22no—
1257C2×C4—24no—
1258C2×C4—24no—
1259C2×C4—24no—
1260C2×C4—28no—
1261C2×C4—44no—
1262C2×C4—48no—
1263C2×C4—416no—
1264C2×C4—48no—
1265C2×C4—416no—
1266C2×C4—48no—
1267C2×C4—48no—
1268C2×C4—84no—
1269C2×C4—88no—
1270C2×C4—88no—
1271C2×C4—88no—
1272C2×C4C23×D412yes—
1273C2×C4C23×D412yes—
1274C2×C4C23×D414yes—
1275C2×C4C23×D412yes—
1276C2×C4C23×D414yes—
1277C2×C4C23×D414yes—
1278C2×C4C23×D412yes—
1279C2×C4C23×D412yes—
1280C2×C4C23×D412yes—
1281C2×C4C22×#4114yes—
1282C2×C4C22×#4114yes—
1283C2×C4C22×#4112yes—
1284C2×C4C2×2−1+418yes—
1285C2×C4C2×2−1+414yes—
1286C2×C4#58512yes—
1287C22—28no—
1288C22—22no—
1289C22—24no—
1290C22—22no—
1291C22—24no—
1292C22—22no—
1293C22—24no—
1294C22—24no—
1295C22—42no—
1296C22—44no—
1297C22—42no—
1298C22—42no—
1299C22—44no—
1300C22—42no—
1301C22—44no—
1302C22C24×D411yescharacteristic
1303C22C23×#4111yescharacteristic
1304C22C22×2−1+412yes—
1305C22C2×#58511yescharacteristic
1306C222−1+612yes—
1307C4—24no—
1308C4—22no—
1309C4—24no—
1310C4—22no—
1311C4—22no—
1312C4—24no—
1313C4—28no—
1314C4—24no—
1315C4—22no—
1316C4—24no—
1317C4—42no—
1318C4—44no—
1319C4—42no—
1320C4—44no—
1321C4—42no—
1322C4—42no—
1323C4—42no—
1324C4—44no—
1325C4—42no—
1326C4—42no—
1327C4—42no—
1328C4—44no—
1329C4—42no—
1330C4—44no—
1331C4D4×#4114yes—
1332C4#349914yes—
1333C2—44no—
1334C2—42no—
1335C2—44no—
1336C2C2×D4×#4111yescharacteristic
1337C2C2×#349911yescharacteristic
1338C2#6285911yescharacteristic
1339C2#6295012yes—
1340C2#6300112yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#3515C2
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×#3523C2semidirect
3. #59154C2semidirect
4. #59121C2semidirect
5. #59116C2semidirect
6. #59069C2semidirect
7. #44849C2semidirect
8. #43499C2semidirect
9. #39490C2semidirect
10. #39484C2semidirect
11. #39360C2semidirect
12. #39360C2semidirect
13. #39173C2semidirect
14. #39170C2semidirect
15. #38088C2semidirect
16. #38081C2semidirect
17. #36593C2semidirect
18. #36562C2semidirect
19. #36406C2semidirect
20. #36276C2semidirect
21. #35670C2semidirect
22. #35622C2semidirect
23. #35322C2semidirect
24. #35319C2semidirect
25. #34979C2semidirect
26. #34953C2semidirect
27. #34276C2semidirect
28. #34151C2semidirect
29. C4×#536C2semidirect

Maximal subgroups

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

subgroupindex
C2×#35232
C2×#35152
#591542
#591212
#591162
#590692
#448492
#434992
#394902
#394842
#393602
#391732
#391702
#380882
#380812
#365932
#365622
#364062
#362762
#356702
#356222
#353222
#353192
#349792
#349532
#342762
#341512
C4×#5362