Finite Group Databasebeta

← #7657969

Subgroups — #7657969

Order 512.

6460 conjugacy classes of subgroups.

The subgroup lattice has 1241 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3523C211yesmaximal, characteristic, complemented
2C2×Q8×#41C211yesmaximal, characteristic, complemented
3#42807C214yesmaximal, complemented
4#42793C212yesmaximal, complemented
5#42792C212yesmaximal, complemented
6#42389C214yesmaximal, complemented
7#42313C214yesmaximal, complemented
8#41417C218yesmaximal, complemented
9#39724C212yesmaximal, complemented
10#39719C214yesmaximal, complemented
11#39596C212yesmaximal, complemented
12#39591C214yesmaximal, complemented
13#37641C211yesmaximal, characteristic, complemented
14#37635C212yesmaximal, complemented
15#37622C211yesmaximal, characteristic, complemented
16#37551C212yesmaximal, complemented
17#36579C212yesmaximal, complemented
18#36545C212yesmaximal, complemented
19#35773C214yesmaximal, complemented
20#35749C212yesmaximal, complemented
21#35738C212yesmaximal, complemented
22#35342C212yesmaximal
23#35297C211yesmaximal, characteristic, complemented
24#34627C212yesmaximal, complemented
25#34614C211yesmaximal, characteristic
26#34187C211yesmaximal, characteristic, complemented
27#3523—216no—
28Q8×#41—216no—
29C2×Q82C2211yescharacteristic
30C2×#557C2211yescharacteristic
31C2×#557C2212yes—
32C2×#557C2211yescharacteristic
33C2×#557C2212yes—
34C2×#557C2211yescharacteristic
35C2×#556C2212yes—
36C2×#556C2211yescharacteristic
37C2×#554C2212yes—
38C2×#554C2211yescharacteristic
39C2×#554C2212yes—
40C2×#554C2214yes—
41C2×#552C2212yes—
42C2×#552C2214yes—
43C2×D4×Q8C2211yescharacteristic
44C2×D4×Q8C2212yes—
45C2×D4×Q8C2212yes—
46C2×D4×Q8C2211yescharacteristic
47C2×#541C2212yes—
48C2×#541C2214yes—
49C2×#533C2212yes—
50C2×#533C2212yes—
51C2×#533C2211yescharacteristic
52C2×#533C2211yescharacteristic
53C2×#533C2214yes—
54C2×#533C2212yes—
55C2×#529C2212yes—
56C2×#529C2211yescharacteristic
57C2×#519C2212yes—
58C2×C4×#41C2212yes—
59C2×C4×#41C2211yescharacteristic
60C22×C4×Q8C2212yes—
61C22×C4×Q8C2211yescharacteristic
62#2857C2212yes—
63#2857C2212yes—
64#2851C2214yes—
65#2850C2214yes—
66#2822C2214yes—
67#2821C2214yes—
68#2821C2214yes—
69#2817C2218yes—
70#2814C2214yes—
71#2734C2218yes—
72#2729C2218yes—
73#2729C2218yes—
74#2728C2218yes—
75#2723C2218yes—
76#2720C2218yes—
77#2720C2218yes—
78#2719C2218yes—
79#2716C2218yes—
80#2713C2218yes—
81#2692C2218yes—
82#2690C2218yes—
83#2664C2214yes—
84#2663C2218yes—
85#2660C2214yes—
86#2642C2214yes—
87#2638C2218yes—
88#2638C2218yes—
89#2637C2212yes—
90#2636C2212yes—
91#2634C2214yes—
92#2634C2214yes—
93#2634C2214yes—
94#2633C2214yes—
95#2630C2214yes—
96#2629C2212yes—
97#2628C2212yes—
98#2628C2214yes—
99#2625C2211yescharacteristic
100#2625C2212yes—
101#2625C2212yes—
102#2625C2212yes—
103#2625C2212yes—
104#2625C2214yes—
105#2624C2212yes—
106#2624C2211yescharacteristic
107#2621C2214yes—
108#2621C2214yes—
109#2621C2212yes—
110#2620C2212yes—
111#2616C2212yes—
112#2616C2211yescharacteristic
113#2615C2211yescharacteristic
114#2611C2214yes—
115#2611C2214yes—
116#2604C2214yes—
117#2603C2214yes—
118#2602C2218yes—
119#2600C2218yes—
120#2599C2214yes—
121#2598C2214yes—
122#2592C2212yes—
123#2592C2214yes—
124#2584C2212yes—
125#2584C2212yes—
126#2584C2214yes—
127#2582C2214yes—
128#2582C2212yes—
129#2581C2214yes—
130#2581C2214yes—
131#2581C2212yes—
132#2581C2214yes—
133#2580C2214yes—
134#2568C2214yes—
135#2568C2212yes—
136#2568C2212yes—
137#2567C2214yes—
138#2562C2212yes—
139#2560C2218yes—
140#2556C2218yes—
141#2550C2214yes—
142#2546C2212yes—
143#2546C2212yes—
144#2542C2214yes—
145#2538C2212yes—
146#2536C2212yes—
147#2519C2218yes—
148#2506C2218yes—
149#2499C2218yes—
150#2492C2214yes—
151#2489C2214yes—
152#2485C2214yes—
153#2481C2218yes—
154#2477C2218yes—
155#2475C2218yes—
156#2473C2218yes—
157#2469C2218yes—
158#2465C2218yes—
159#2462C2218yes—
160#2462C2218yes—
161#2446C2214yes—
162#2446C2214yes—
163#2434C2214yes—
164#2434C2214yes—
165#2421C2214yes—
166#2421C2214yes—
167#2415C2214yes—
168#2415C2214yes—
169#2409C2214yes—
170#2409C2214yes—
171#2399C2214yes—
172#2398C2214yes—
173#2396C2212yes—
174#2395C2218yes—
175#2392C2212yes—
176#2392C2214yes—
177#2365C2214yes—
178#2362C2214yes—
179#2360C2214yes—
180#2356C2212yes—
181#2356C2214yes—
182#2356C2212yes—
183#2355C2214yes—
184#2355C2212yes—
185#2355C2212yes—
186#2352C2214yes—
187#2324C2214yes—
188#2323C2214yes—
189#2323C2214yes—
190#2313C2214yes—
191#2310C2212yes—
192C4×C22⋊Q8C2214yes—
193C4×C22⋊Q8C2212yes—
194C4×C22⋊Q8C2214yes—
195C4×#121C2212yes—
196#2285C2211yescharacteristic
197#2285C2211yescharacteristic
198#2283C2212yes—
199#2283C2212yes—
200#2274C2212yes—
201C22×#41C2311yescharacteristic
202C23×Q8C2312yes—
203C23×Q8C2312yes—
204C23×Q8C2311yescharacteristic
205Q82—28no—
206#557—28no—
207#557—216no—
208#557—28no—
209#557—28no—
210#557—216no—
211#556—28no—
212#556—216no—
213#554—28no—
214#554—216no—
215#554—216no—
216#554—232no—
217#552—216no—
218#552—232no—
219D4×Q8—216no—
220D4×Q8—216no—
221D4×Q8—28no—
222D4×Q8—28no—
223#541—216no—
224#541—232no—
225#533—216no—
226#533—232no—
227#533—216no—
228#533—28no—
229#533—216no—
230#533—28no—
231C2×C4⋊Q8C2312yes—
232C2×C4⋊Q8C2312yes—
233C2×C4⋊Q8C2312yes—
234C2×C4⋊Q8C2311yescharacteristic
235C2×C4⋊Q8C2312yes—
236C2×C4⋊Q8C2311yescharacteristic
237C2×C4⋊Q8C2311yescharacteristic
238C2×C4⋊Q8C2311yescharacteristic
239C2×C4⋊Q8C2312yes—
240C2×C4⋊Q8C2314yes—
241C2×C4⋊Q8C2314yes—
242C2×C4⋊Q8C2312yes—
243C2×C4⋊Q8C2312yes—
244C2×C4⋊Q8C2314yes—
245C2×C4⋊Q8C2314yes—
246#529—216no—
247#529—28no—
248C2×#126C2314yes—
249C2×#126C2314yes—
250C2×#126C2312yes—
251C2×#126C2314yes—
252C2×#126C2314yes—
253C2×#125C2312yes—
254C2×#125C2312yes—
255C2×#125C2312yes—
256C2×#125C2311yescharacteristic
257C2×#125C2312yes—
258C2×#125C2312yes—
259C2×#125C2314yes—
260C2×#125C2314yes—
261C2×#125C2314yes—
262C2×#125C2314yes—
263C2×#125C2314yes—
264C2×#125C2314yes—
265C2×#125C2314yes—
266C2×#125C2312yes—
267C2×#125C2314yes—
268C2×#124C2312yes—
269C2×#124C2311yescharacteristic
270C2×#123C2314yes—
271C2×#123C2312yes—
272C2×C22⋊Q8C2314yes—
273C2×C22⋊Q8C2314yes—
274C2×C22⋊Q8C2314yes—
275C2×C22⋊Q8C2314yes—
276C2×C22⋊Q8C2312yes—
277C2×C22⋊Q8C2312yes—
278C2×C22⋊Q8C2311yescharacteristic
279C2×C22⋊Q8C2312yes—
280C2×C22⋊Q8C2312yes—
281C2×C22⋊Q8C2312yes—
282C2×C22⋊Q8C2314yes—
283C2×C22⋊Q8C2312yes—
284C2×C22⋊Q8C2312yes—
285C2×C22⋊Q8C2314yes—
286C2×C22⋊Q8C2314yes—
287C2×C22⋊Q8C2314yes—
288C2×C22⋊Q8C2312yes—
289C2×C22⋊Q8C2314yes—
290C2×C22⋊Q8C2314yes—
291C2×C22⋊Q8C2312yes—
292C2×C22⋊Q8C2314yes—
293C2×C22⋊Q8C2314yes—
294C2×C22⋊Q8C2314yes—
295C2×#121C2312yes—
296C2×#121C2311yescharacteristic
297#519—216no—
298C4×#41—216no—
299C4×#41—28no—
300C2×C4×Q8—216no—
301C2×C4×Q8D4116yescomplemented
302C2×C4×Q8C2314yes—
303C2×C4×Q8C2312yes—
304C2×C4×Q8C2312yes—
305C2×C4×Q8C2312yes—
306C2×C4×Q8C2312yes—
307C2×C4×Q8C2314yes—
308C2×C4×Q8C2311yescharacteristic
309C2×C4×Q8C2312yes—
310C2×C4×Q8C2312yes—
311C2×C4×Q8C2312yes—
312C2×C4×Q8C2311yescharacteristic
313C2×C4×Q8C2311yescharacteristic
314C2×C4×Q8C2312yes—
315C2×C4×Q8C2312yes—
316C2×C4×Q8C2312yes—
317C2×C4×Q8C2312yes—
318C2×C4×Q8C2314yes—
319C2×C4×Q8C2312yes—
320C2×C4×Q8C2314yes—
321C2×C4×Q8C2312yes—
322C2×C4×Q8C2314yes—
323C2×C4×Q8C2311yescharacteristic
324C2×C4×Q8C2311yescharacteristic
325C2×C4×Q8C2312yes—
326C2×C4×Q8C2311yescharacteristic
327C2×C4×Q8C2311yescharacteristic
328C2×C4×Q8C2312yes—
329C2×C4×D4C2311yescharacteristic
330C2×C4×D4C2312yes—
331C2×C4×D4C2312yes—
332C2×C4×D4C2314yes—
333C2×C4×D4C2314yes—
334C2×C4×D4C2314yes—
335C2×C4×D4C2312yes—
336C2×C4×D4C2312yes—
337C2×C4×D4C2312yes—
338C2×C4×D4C2311yescharacteristic
339C2×C4×D4C2312yes—
340C2×C4×D4C2311yescharacteristic
341C2×C4×D4C2314yes—
342C2×#117C2312yes—
343C2×#117C2314yes—
344C2×#117C2314yes—
345C2×#117C2312yes—
346C2×#117C2312yes—
347C2×#117C2312yes—
348C2×#117C2311yescharacteristic
349C2×#117C2312yes—
350C2×#117C2314yes—
351C2×#117C2314yes—
352C2×#117C2312yes—
353C2×#117C2312yes—
354C22×C4⋊C4C2312yes—
355C22×C4⋊C4C2314yes—
356C22×C4⋊C4C2312yes—
357C22×C4⋊C4C2311yescharacteristic
358C22×C42C2314yes—
359C22×C42C2312yes—
360C22×C42C2312yes—
361C22×C42C2311yescharacteristic
362#400C2318yes—
363#400C2318yes—
364#400C2318yes—
365#400C2318yes—
366#400C2314yes—
367#400C2314yes—
368#400C2318yes—
369#400C2314yes—
370#400C2318yes—
371#400C2314yes—
372#400C2312yes—
373#400C2318yes—
374#399C2312yes—
375#399C2318yes—
376#399C2314yes—
377#399C2318yes—
378#398C2318yes—
379#398C2314yes—
380#398C2314yes—
381#398C2318yes—
382#398C2318yes—
383#398C2314yes—
384#398C2318yes—
385#398C2318yes—
386#398C2314yes—
387#398C2314yes—
388#398C2318yes—
389#398C2318yes—
390#398C2312yes—
391#398C2314yes—
392#398C2314yes—
393#397C2318yes—
394#397C2314yes—
395#397C2318yes—
396#397C2318yes—
397#397C2318yes—
398#397C2312yes—
399#397C2318yes—
400#397C2314yes—
401#397C2314yes—
402#397C2318yes—
403#397C2318yes—
404#396C2314yes—
405#396C2314yes—
406#396C2314yes—
407#396C2314yes—
408#396C2318yes—
409#395C2318yes—
410#395C2318yes—
411#395C2318yes—
412#395C2318yes—
413#395C2318yes—
414#395C2318yes—
415#395C2314yes—
416#395C2314yes—
417#395C2312yes—
418#395C2318yes—
419#394C2314yes—
420#394C2314yes—
421#394C2318yes—
422#394C2318yes—
423#394C2314yes—
424#394C2312yes—
425#394C2314yes—
426#394C2314yes—
427#393C2318yes—
428#393C2318yes—
429#393C2314yes—
430#393C2312yes—
431#393C2318yes—
432#392C2312yes—
433#392C2314yes—
434#391C2318yes—
435#391C2314yes—
436#391C2314yes—
437#391C2318yes—
438#391C2318yes—
439#391C2314yes—
440#391C2312yes—
441#391C2314yes—
442#391C2314yes—
443#391C2314yes—
444#391C2318yes—
445#391C2314yes—
446#391C2314yes—
447#391C2314yes—
448#391C2314yes—
449#390C2318yes—
450#390C2314yes—
451#390C2312yes—
452#389C2312yes—
453#389C2314yes—
454#389C2314yes—
455#389C2314yes—
456#389C2314yes—
457#389C2318yes—
458#389C2318yes—
459#389C2314yes—
460#389C2312yes—
461#389C2314yes—
462#389C2314yes—
463#389C2318yes—
464#389C2314yes—
465#389C2314yes—
466#389C2318yes—
467#389C2318yes—
468#389C2318yes—
469#388C2318yes—
470#388C2318yes—
471#388C2318yes—
472#388C2318yes—
473#388C2318yes—
474#388C2318yes—
475#388C2318yes—
476#388C2318yes—
477#388C2318yes—
478#388C2318yes—
479#388C2314yes—
480#387C2318yes—
481#387C2318yes—
482#387C2318yes—
483#387C2318yes—
484#387C2318yes—
485#387C2318yes—
486#387C2318yes—
487#387C2318yes—
488#387C2318yes—
489#387C2318yes—
490#387C2318yes—
491#387C2318yes—
492#387C2318yes—
493#387C2318yes—
494#387C2314yes—
495#387C2318yes—
496#387C2318yes—
497#386C2318yes—
498#386C2318yes—
499#386C2318yes—
500#386C2314yes—
501#385C2318yes—
502#385C2318yes—
503#385C2318yes—
504#385C2318yes—
505#385C2318yes—
506#385C2314yes—
507#385C2318yes—
508#385C2318yes—
509#384C2318yes—
510#384C2312yes—
511#384C2312yes—
512#383C2314yes—
513#383C2314yes—
514#382C2312yes—
515#382C2314yes—
516#382C2318yes—
517#382C2314yes—
518#382C2314yes—
519#382C2312yes—
520#381C2314yes—
521#381C2314yes—
522#380C2314yes—
523#380C2314yes—
524#380C2312yes—
525#380C2312yes—
526#380C2312yes—
527#380C2314yes—
528#380C2314yes—
529#380C2314yes—
530#380C2311yescharacteristic
531#380C2312yes—
532#380C2311yescharacteristic
533#380C2312yes—
534C4×C4⋊C4C2318yes—
535C4×C4⋊C4C2312yes—
536C4×C4⋊C4C2314yes—
537C4×C4⋊C4C2312yes—
538C4×C4⋊C4C2312yes—
539C4×C4⋊C4C2312yes—
540C4×C4⋊C4C2314yes—
541C4×C4⋊C4C2314yes—
542C4×C4⋊C4C2314yes—
543C4×C4⋊C4C2318yes—
544C4×C4⋊C4C2314yes—
545C4×C4⋊C4C2318yes—
546C4×C22⋊C4C2318yes—
547C4×C22⋊C4C2314yes—
548C4×C22⋊C4C2314yes—
549C4×C22⋊C4C2318yes—
550C4×C22⋊C4C2314yes—
551C4×C22⋊C4C2314yes—
552#376C2314yes—
553#376C2314yes—
554C2×#41—24no—
555C2×#41—28no—
556C22×Q8—28no—
557C22×Q8—28no—
558C22×Q8—42no—
559C22×Q8—42no—
560C22×Q8—44no—
561C22×Q8—44no—
562C22×Q8—44no—
563C22×Q8—44no—
564C22×Q8C2×D418yes—
565C22×Q8C2411yescharacteristic
566C22×Q8C2412yes—
567C22×Q8C2411yescharacteristic
568C22×Q8C2412yes—
569C22×Q8C2412yes—
570C22×Q8C2411yescharacteristic
571C22×Q8C2411yescharacteristic
572C22×Q8C2414yes—
573C22×Q8C2414yes—
574C22×Q8C2414yes—
575C22×Q8C2412yes—
576C22×Q8C2412yes—
577C22×D4C2411yescharacteristic
578C22×D4C2412yes—
579C22×D4C2411yescharacteristic
580C22×D4C2412yes—
581C22×D4C2414yes—
582C23×C4C2412yes—
583C23×C4C2412yes—
584C23×C4C2411yescharacteristic
585C23×C4C2411yescharacteristic
586C23×C4C2412yes—
587C23×C4C2414yes—
588C23×C4C2412yes—
589C23×C4C2414yes—
590C23×C4C2414yes—
591C23×C4C2412yes—
592C23×C4C2411yescharacteristic
593C23×C4C2412yes—
594C4⋊Q8—28no—
595C4⋊Q8—216no—
596C4⋊Q8—28no—
597C4⋊Q8—216no—
598C4⋊Q8—28no—
599C4⋊Q8—216no—
600C4⋊Q8—24no—
601C4⋊Q8—24no—
602C4⋊Q8—28no—
603C4⋊Q8—28no—
604C4⋊Q8—24no—
605C4⋊Q8—28no—
606C4⋊Q8—24no—
607C4⋊Q8—28no—
608C4⋊Q8—48no—
609#126—216no—
610#126—216no—
611#126—216no—
612#126—28no—
613#126—216no—
614#125—216no—
615#125—216no—
616#125—216no—
617#125—216no—
618#125—216no—
619#125—216no—
620#125—216no—
621#125—28no—
622#125—28no—
623#125—24no—
624#125—28no—
625#125—216no—
626#125—28no—
627#125—28no—
628#125—28no—
629#124—28no—
630#124—24no—
631#123—216no—
632#123—28no—
633C22⋊Q8—28no—
634C22⋊Q8—216no—
635C22⋊Q8—28no—
636C22⋊Q8—216no—
637C22⋊Q8—28no—
638C22⋊Q8—24no—
639C22⋊Q8—28no—
640C22⋊Q8—216no—
641C22⋊Q8—28no—
642C22⋊Q8—216no—
643C22⋊Q8—28no—
644C22⋊Q8—216no—
645C22⋊Q8—216no—
646C22⋊Q8—28no—
647C22⋊Q8—28no—
648C22⋊Q8—216no—
649C22⋊Q8—216no—
650C22⋊Q8—216no—
651C22⋊Q8—216no—
652C22⋊Q8—216no—
653C22⋊Q8—28no—
654C22⋊Q8—48no—
655C22⋊Q8—48no—
656#121—24no—
657#121—28no—
658C4×Q8—28no—
659C4×Q8—28no—
660C4×Q8—28no—
661C4×Q8—216no—
662C4×Q8—28no—
663C4×Q8—216no—
664C4×Q8—28no—
665C4×Q8—216no—
666C4×Q8—28no—
667C4×Q8—24no—
668C4×Q8—24no—
669C4×Q8—28no—
670C4×Q8—216no—
671C4×Q8—28no—
672C4×Q8—24no—
673C4×Q8—28no—
674C4×Q8—216no—
675C4×Q8—28no—
676C4×Q8—28no—
677C4×Q8—28no—
678C4×Q8—28no—
679C4×Q8C2×D418yes—
680C4×Q8C2×D418yes—
681C4×Q8C2×D418yes—
682C4×Q8C2×D4116yes—
683C4×Q8C2×D418yes—
684C4×Q8C2×D4116yes—
685C4×D4—28no—
686C4×D4—216no—
687C4×D4—216no—
688C4×D4—28no—
689C4×D4—28no—
690C4×D4—216no—
691C4×D4—24no—
692C4×D4—28no—
693C4×D4—28no—
694C4×D4—24no—
695C4×D4—24no—
696C4×D4—28no—
697C4×D4—48no—
698#117—28no—
699#117—24no—
700#117—28no—
701#117—216no—
702#117—28no—
703#117—216no—
704#117—216no—
705#117—28no—
706#117—216no—
707#117—28no—
708#117—44no—
709#117—44no—
710C2×C4⋊C4—28no—
711C2×C4⋊C4—216no—
712C2×C4⋊C4C2×D418yes—
713C2×C4⋊C4C2×D4116yes—
714C2×C4⋊C4C2414yes—
715C2×C4⋊C4C2414yes—
716C2×C4⋊C4C2414yes—
717C2×C4⋊C4C2412yes—
718C2×C4⋊C4C2414yes—
719C2×C4⋊C4C2414yes—
720C2×C4⋊C4C2412yes—
721C2×C4⋊C4C2414yes—
722C2×C4⋊C4C2412yes—
723C2×C4⋊C4C2412yes—
724C2×C4⋊C4C2411yescharacteristic
725C2×C4⋊C4C2411yescharacteristic
726C2×C4⋊C4C2412yes—
727C2×C4⋊C4C2412yes—
728C2×C4⋊C4C2414yes—
729C2×C4⋊C4C2414yes—
730C2×C4⋊C4C2412yes—
731C2×C4⋊C4C2414yes—
732C2×C4⋊C4C2412yes—
733C2×C4⋊C4C2412yes—
734C2×C4⋊C4C2414yes—
735C2×C4⋊C4C2414yes—
736C2×C4⋊C4C2412yes—
737C2×C4⋊C4C2414yes—
738C2×C4⋊C4C2412yes—
739C2×C4⋊C4C2411yescharacteristic
740C2×C4⋊C4C2414yes—
741C2×C4⋊C4C2412yes—
742C2×C4⋊C4C2411yescharacteristic
743C2×C4⋊C4C2414yes—
744C2×C4⋊C4C2414yes—
745C2×C4⋊C4C2414yes—
746C2×C4⋊C4C2414yes—
747C2×C4⋊C4C2412yes—
748C2×C4⋊C4C2414yes—
749C2×C4⋊C4C2414yes—
750C2×C4⋊C4C2414yes—
751C2×C4⋊C4C2412yes—
752C2×C4⋊C4C2414yes—
753C2×C4⋊C4C2412yes—
754C2×C4⋊C4C2414yes—
755C2×C4⋊C4C2412yes—
756C2×C4⋊C4C2414yes—
757C2×C4⋊C4C2418yes—
758C2×C4⋊C4C2414yes—
759C2×C4⋊C4C2414yes—
760C2×C4⋊C4C2418yes—
761C2×C4⋊C4C2418yes—
762C2×C4⋊C4C2418yes—
763C2×C4⋊C4C2418yes—
764C2×C4⋊C4C2414yes—
765C2×C4⋊C4C2414yes—
766C2×C4⋊C4C2414yes—
767C2×C4⋊C4C2418yes—
768C2×C4⋊C4C2411yescharacteristic
769C2×C4⋊C4C2412yes—
770C2×C4⋊C4C2412yes—
771C2×C4⋊C4C2412yes—
772C2×C4⋊C4C2411yescharacteristic
773C2×C4⋊C4C2412yes—
774C2×C4⋊C4C2412yes—
775C2×C22⋊C4C2412yes—
776C2×C22⋊C4C2414yes—
777C2×C22⋊C4C2412yes—
778C2×C22⋊C4C2414yes—
779C2×C22⋊C4C2412yes—
780C2×C22⋊C4C2414yes—
781C2×C22⋊C4C2412yes—
782C2×C22⋊C4C2412yes—
783C2×C22⋊C4C2414yes—
784C2×C22⋊C4C2414yes—
785C2×C22⋊C4C2412yes—
786C2×C22⋊C4C2412yes—
787C2×C22⋊C4C2414yes—
788C2×C22⋊C4C2414yes—
789C2×C22⋊C4C2412yes—
790C2×C22⋊C4C2414yes—
791C2×C22⋊C4C2414yes—
792C2×C22⋊C4C2418yes—
793C2×C22⋊C4C2412yes—
794C2×C22⋊C4C2412yes—
795C2×C22⋊C4C2414yes—
796C2×C22⋊C4C2414yes—
797C2×C22⋊C4C2414yes—
798C2×C22⋊C4C2418yes—
799C2×C22⋊C4C2418yes—
800C2×C22⋊C4C2414yes—
801C2×C22⋊C4C2414yes—
802C2×C22⋊C4C2418yes—
803C2×C42—28no—
804C2×C42—216no—
805C2×C42C2×D418yes—
806C2×C42C2×D4116yes—
807C2×C42C2412yes—
808C2×C42C2414yes—
809C2×C42C2414yes—
810C2×C42C2414yes—
811C2×C42C2414yes—
812C2×C42C2412yes—
813C2×C42C2414yes—
814C2×C42C2414yes—
815C2×C42C2414yes—
816C2×C42C2412yes—
817C2×C42C2412yes—
818C2×C42C2414yes—
819C2×C42C2414yes—
820C2×C42C2418yes—
821C2×C42C2418yes—
822C2×C42C2412yes—
823C2×C42C2411yescharacteristic
824C2×C42C2412yes—
825C2×C42C2411yescharacteristic
826C2×C42C2411yescharacteristic
827C2×C42C2411yescharacteristic
828C2×C42C2412yes—
829C2×C42C2412yes—
830#95C2412yes—
831#95C2414yes—
832#95C2412yes—
833#95C2418yes—
834#95C2418yes—
835#95C2414yes—
836#95C2418yes—
837#95C2418yes—
838#95C2418yes—
839#95C2414yes—
840#95C2418yes—
841#95C2418yes—
842#95C2414yes—
843#95C2414yes—
844#95C2418yes—
845#95C2414yes—
846#95C2414yes—
847#95C2418yes—
848#95C2414yes—
849#95C2418yes—
850#95C2418yes—
851#95C2418yes—
852#95C2414yes—
853#95C2418yes—
854#95C2418yes—
855#95C2418yes—
856#95C2418yes—
857#95C2418yes—
858#95C2418yes—
859#95C2418yes—
860#95C2418yes—
861C24C2512yes—
862C24C2511yescharacteristic
863C24C2512yes—
864#41—232no—
865C2×Q8—22no—
866C2×Q8—22no—
867C2×Q8—24no—
868C2×Q8—28no—
869C2×Q8—28no—
870C2×Q8—24no—
871C2×Q8—24no—
872C2×Q8—24no—
873C2×Q8—28no—
874C2×Q8—24no—
875C2×Q8—28no—
876C2×Q8—24no—
877C2×Q8—22no—
878C2×Q8—22no—
879C2×Q8—22no—
880C2×Q8—22no—
881C2×Q8—24no—
882C2×Q8—24no—
883C2×Q8—24no—
884C2×Q8—24no—
885C2×Q8—42no—
886C2×Q8—42no—
887C2×Q8—44no—
888C2×Q8—44no—
889C2×Q8—44no—
890C2×Q8—44no—
891C2×Q8—44no—
892C2×Q8—44no—
893C2×Q8—44no—
894C2×Q8—416no—
895C2×Q8—432no—
896C2×Q8—432no—
897C2×Q8C22×D414yes—
898C2×Q8C22×D414yes—
899C2×Q8C22×D418yes—
900C2×D4—24no—
901C2×D4—24no—
902C2×D4—24no—
903C2×D4—24no—
904C2×D4—28no—
905C2×D4—22no—
906C2×D4—22no—
907C2×D4—24no—
908C2×D4—24no—
909C2×D4—44no—
910C2×D4—44no—
911C2×D4—44no—
912C22×C4—24no—
913C22×C4—24no—
914C22×C4—24no—
915C22×C4—22no—
916C22×C4—22no—
917C22×C4—28no—
918C22×C4—24no—
919C22×C4—28no—
920C22×C4—24no—
921C22×C4—24no—
922C22×C4—24no—
923C22×C4—24no—
924C22×C4—24no—
925C22×C4—28no—
926C22×C4—24no—
927C22×C4—44no—
928C22×C4—42no—
929C22×C4—42no—
930C22×C4—42no—
931C22×C4—44no—
932C22×C4—44no—
933C22×C4—44no—
934C22×C4—44no—
935C22×C4—44no—
936C22×C4—44no—
937C22×C4—42no—
938C22×C4—42no—
939C22×C4C22×D414yes—
940C22×C4C22×D414yes—
941C22×C4C22×D418yes—
942C22×C4C22×D414yes—
943C22×C4C22×D418yes—
944C22×C42−1+418yes—
945C22×C4C2514yes—
946C22×C4C2514yes—
947C22×C4C2518yes—
948C22×C4C2512yes—
949C22×C4C2514yes—
950C22×C4C2514yes—
951C22×C4C2512yes—
952C22×C4C2512yes—
953C22×C4C2512yes—
954C22×C4C2512yes—
955C22×C4C2514yes—
956C22×C4C2514yes—
957C22×C4C2511yescharacteristic
958C22×C4C2512yes—
959C22×C4C2512yes—
960C22×C4C2512yes—
961C22×C4C2512yes—
962C22×C4C2511yescharacteristic
963C22×C4C2511yescharacteristic
964C22×C4C2511yescharacteristic
965C22×C4C2512yes—
966C22×C4C2511yescharacteristic
967C22×C4C2511yescharacteristic
968C4⋊C4—28no—
969C4⋊C4—28no—
970C4⋊C4—28no—
971C4⋊C4—28no—
972C4⋊C4—24no—
973C4⋊C4—24no—
974C4⋊C4—28no—
975C4⋊C4—24no—
976C4⋊C4—28no—
977C4⋊C4—24no—
978C4⋊C4—22no—
979C4⋊C4—22no—
980C4⋊C4—24no—
981C4⋊C4—28no—
982C4⋊C4—24no—
983C4⋊C4—28no—
984C4⋊C4—24no—
985C4⋊C4—28no—
986C4⋊C4—24no—
987C4⋊C4—24no—
988C4⋊C4—28no—
989C4⋊C4—24no—
990C4⋊C4—28no—
991C4⋊C4—24no—
992C4⋊C4—22no—
993C4⋊C4—28no—
994C4⋊C4—24no—
995C4⋊C4—22no—
996C4⋊C4—24no—
997C4⋊C4—28no—
998C4⋊C4—28no—
999C4⋊C4—28no—
1000C4⋊C4—28no—
1001C4⋊C4—28no—
1002C4⋊C4—28no—
1003C4⋊C4—28no—
1004C4⋊C4—24no—
1005C4⋊C4—28no—
1006C4⋊C4—24no—
1007C4⋊C4—24no—
1008C4⋊C4—28no—
1009C4⋊C4—28no—
1010C4⋊C4—216no—
1011C4⋊C4—28no—
1012C4⋊C4—44no—
1013C4⋊C4—44no—
1014C4⋊C4—44no—
1015C4⋊C4—48no—
1016C4⋊C4—44no—
1017C4⋊C4—44no—
1018C4⋊C4—48no—
1019C4⋊C4—48no—
1020C4⋊C4—48no—
1021C4⋊C4—48no—
1022C4⋊C4C22×D414yes—
1023C4⋊C4C22×D418yes—
1024C4⋊C4C22×D418yes—
1025C4⋊C4C22×D418yes—
1026C4⋊C4C22×D414yes—
1027C4⋊C4C22×D418yes—
1028C4⋊C4C22×D418yes—
1029C22⋊C4—28no—
1030C22⋊C4—24no—
1031C22⋊C4—28no—
1032C22⋊C4—24no—
1033C22⋊C4—28no—
1034C22⋊C4—216no—
1035C22⋊C4—24no—
1036C22⋊C4—28no—
1037C22⋊C4—24no—
1038C22⋊C4—24no—
1039C22⋊C4—28no—
1040C22⋊C4—24no—
1041C22⋊C4—28no—
1042C22⋊C4—24no—
1043C22⋊C4—28no—
1044C22⋊C4—28no—
1045C22⋊C4—24no—
1046C22⋊C4—28no—
1047C22⋊C4—44no—
1048C22⋊C4—48no—
1049C22⋊C4—44no—
1050C22⋊C4—42no—
1051C22⋊C4—42no—
1052C22⋊C4—44no—
1053C22⋊C4—44no—
1054C22⋊C4—44no—
1055C22⋊C4—48no—
1056C22⋊C4—48no—
1057C42—24no—
1058C42—28no—
1059C42—28no—
1060C42—24no—
1061C42—28no—
1062C42—24no—
1063C42—28no—
1064C42—28no—
1065C42—28no—
1066C42—28no—
1067C42—24no—
1068C42—28no—
1069C42—48no—
1070C42—48no—
1071C42—44no—
1072C42C22×D414yes—
1073C42C22×D418yes—
1074C42C22×D418yes—
1075C42C22×D414yes—
1076C42C22×D418yes—
1077C42C22×D414yes—
1078C42C22×D414yes—
1079C42C22×D418yes—
1080C23—22no—
1081C23—22no—
1082C23—22no—
1083C23—21no—
1084C23—21no—
1085C23—22no—
1086C23—22no—
1087C23—22no—
1088C23—22no—
1089C23—22no—
1090C23—22no—
1091C23—24no—
1092C23—22no—
1093C23—22no—
1094C23—24no—
1095C23C23×D412yes—
1096C23C2×2−1+414yes—
1097C23C2611yescharacteristic
1098Q8—28no—
1099Q8—28no—
1100Q8—28no—
1101Q8—48no—
1102Q8—416no—
1103Q8—416no—
1104Q8—48no—
1105Q8—48no—
1106Q8—44no—
1107Q8—48no—
1108Q8—88no—
1109Q8—84no—
1110D4—28no—
1111D4—216no—
1112D4—48no—
1113D4—44no—
1114D4—88no—
1115C2×C4—22no—
1116C2×C4—22no—
1117C2×C4—22no—
1118C2×C4—21no—
1119C2×C4—21no—
1120C2×C4—22no—
1121C2×C4—22no—
1122C2×C4—22no—
1123C2×C4—22no—
1124C2×C4—24no—
1125C2×C4—24no—
1126C2×C4—22no—
1127C2×C4—22no—
1128C2×C4—28no—
1129C2×C4—28no—
1130C2×C4—216no—
1131C2×C4—22no—
1132C2×C4—24no—
1133C2×C4—22no—
1134C2×C4—24no—
1135C2×C4—22no—
1136C2×C4—22no—
1137C2×C4—24no—
1138C2×C4—22no—
1139C2×C4—24no—
1140C2×C4—24no—
1141C2×C4—28no—
1142C2×C4—24no—
1143C2×C4—24no—
1144C2×C4—28no—
1145C2×C4—24no—
1146C2×C4—24no—
1147C2×C4—28no—
1148C2×C4—22no—
1149C2×C4—22no—
1150C2×C4—24no—
1151C2×C4—24no—
1152C2×C4—22no—
1153C2×C4—22no—
1154C2×C4—24no—
1155C2×C4—24no—
1156C2×C4—24no—
1157C2×C4—28no—
1158C2×C4—24no—
1159C2×C4—22no—
1160C2×C4—24no—
1161C2×C4—24no—
1162C2×C4—22no—
1163C2×C4—24no—
1164C2×C4—48no—
1165C2×C4—44no—
1166C2×C4—48no—
1167C2×C4—416no—
1168C2×C4—416no—
1169C2×C4—48no—
1170C2×C4—48no—
1171C2×C4—88no—
1172C2×C4—84no—
1173C2×C4C23×D414yes—
1174C2×C4C23×D412yes—
1175C2×C4C23×D412yes—
1176C2×C4C23×D414yes—
1177C2×C4C23×D414yes—
1178C2×C4C23×D412yes—
1179C2×C4C23×D412yes—
1180C2×C4C23×D414yes—
1181C2×C4C23×D412yes—
1182C2×C4C23×D412yes—
1183C2×C4C2×2−1+414yes—
1184C2×C4C2×2−1+414yes—
1185C2×C4#58512yes—
1186C2×C4#58512yes—
1187C22—22no—
1188C22—24no—
1189C22—22no—
1190C22—24no—
1191C22—22no—
1192C22—24no—
1193C22—42no—
1194C22—42no—
1195C22—42no—
1196C22—42no—
1197C22—42no—
1198C22—42no—
1199C22—42no—
1200C22—42no—
1201C22—44no—
1202C22—42no—
1203C22—44no—
1204C22C24×D411yescharacteristic
1205C22C22×2−1+412yes—
1206C22C2×#58511yescharacteristic
1207C22C2×#58511yescharacteristic
1208C222−1+612yes—
1209C4—22no—
1210C4—24no—
1211C4—24no—
1212C4—22no—
1213C4—24no—
1214C4—22no—
1215C4—22no—
1216C4—24no—
1217C4—24no—
1218C4—42no—
1219C4—44no—
1220C4—44no—
1221C4—42no—
1222C4—42no—
1223C4—44no—
1224C4—44no—
1225C4—42no—
1226C4—42no—
1227C4—44no—
1228C4—44no—
1229C4—48no—
1230C4#344914yes—
1231C4#348614yes—
1232C2—42no—
1233C2—44no—
1234C2—82no—
1235C2C2×#344911yescharacteristic
1236C2C2×#348611yescharacteristic
1237C2#6285911yescharacteristic
1238C2#6293212yes—
1239C2#6295612yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#2615C22
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
2. C2×Q8×#41C2semidirect
3. #42807C2semidirect
4. #42793C2semidirect
5. #42792C2semidirect
6. #42389C2semidirect
7. #42313C2semidirect
8. #41417C2semidirect
9. #39724C2semidirect
10. #39719C2semidirect
11. #39596C2semidirect
12. #39591C2semidirect
13. #37641C2semidirect
14. #37635C2semidirect
15. #37622C2semidirect
16. #37551C2semidirect
17. #36579C2semidirect
18. #36545C2semidirect
19. #35773C2semidirect
20. #35749C2semidirect
21. #35738C2semidirect
23. #35297C2semidirect
24. #34627C2semidirect
26. #34187C2semidirect
301. C2×C4×Q8D4semidirect

Maximal subgroups

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

subgroupindex
C2×#35232
C2×Q8×#412
#428072
#427932
#427922
#423892
#423132
#414172
#397242
#397192
#395962
#395912
#376412
#376352
#376222
#375512
#365792
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