Finite Group Databasebeta

← #7658960

Subgroups — #7658960

Order 512.

6332 conjugacy classes of subgroups.

The subgroup lattice has 1210 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3504C211yesmaximal, characteristic, complemented
2C2×#3515C211yesmaximal, characteristic
3#42978C212yesmaximal, complemented
4#42964C212yesmaximal, complemented
5#42814C212yesmaximal, complemented
6#42811C212yesmaximal, complemented
7#42801C214yesmaximal, complemented
8#42150C214yesmaximal, complemented
9#41939C214yesmaximal, complemented
10#41411C214yesmaximal, complemented
11#41406C214yesmaximal, complemented
12#40516C218yesmaximal, complemented
13#37641C211yesmaximal, characteristic, complemented
14#37607C212yesmaximal, complemented
15#37555C212yesmaximal, complemented
16#37549C211yesmaximal, characteristic, complemented
17#37540C212yesmaximal, complemented
18#37540C211yesmaximal, characteristic, complemented
19#36699C211yesmaximal, characteristic, complemented
20C2×#2822C212yesmaximal, complemented
21#36067C212yesmaximal, complemented
22#36042C212yesmaximal, complemented
23#35998C212yesmaximal, complemented
24#35950C212yesmaximal, complemented
25#35806C214yesmaximal, complemented
26#34191C211yesmaximal, characteristic, complemented
27#3515—216no—
28#3504—216no—
29C2×#557C2212yes—
30C2×#557C2211yescharacteristic
31C2×#557C2212yes—
32C2×#554C2211yescharacteristic
33C2×#554C2211yescharacteristic
34C2×#554C2214yes—
35C2×#554C2212yes—
36C2×#554C2214yes—
37C2×#554C2212yes—
38C2×#553C2212yes—
39C2×#552C2214yes—
40C2×#552C2212yes—
41C2×#552C2212yes—
42C2×#547C2212yes—
43C2×#547C2211yescharacteristic
44C2×#544C2212yes—
45C2×#544C2212yes—
46C2×#544C2211yescharacteristic
47C2×#544C2211yescharacteristic
48C2×#541C2212yes—
49C2×#539C2214yes—
50C2×#533C2211yescharacteristic
51C2×#533C2211yescharacteristic
52C2×#533C2212yes—
53C2×#529C2211yescharacteristic
54C2×#529C2212yes—
55C22×#125C2212yes—
56C22×#125C2212yes—
57C22×#125C2211yescharacteristic
58C2×#520C2212yes—
59C2×#520C2211yescharacteristic
60C2×#520C2211yescharacteristic
61C2×C4×#41C2211yescharacteristic
62#2822C2212yes—
63#2822C2212yes—
64#2822C2218yes—
65#2822C2214yes—
66#2822C2214yes—
67#2822C2211yescharacteristic
68#2822C2212yes—
69#2822C2212yes—
70#2822C2214yes—
71#2822C2214yes—
72#2822C2211yescharacteristic
73#2822C2212yes—
74#2821C2212yes—
75#2821C2212yes—
76#2820C2211yescharacteristic
77#2820C2211yescharacteristic
78#2820C2212yes—
79#2817C2212yes—
80#2816C2212yes—
81#2814C2214yes—
82#2721C2218yes—
83#2719C2218yes—
84#2719C2218yes—
85#2716C2218yes—
86#2713C2218yes—
87#2713C2218yes—
88#2698C2218yes—
89#2690C2218yes—
90#2689C2218yes—
91#2687C2218yes—
92#2680C2218yes—
93#2677C2218yes—
94#2664C2218yes—
95#2664C2214yes—
96#2660C2212yes—
97#2660C2214yes—
98#2659C2214yes—
99#2642C2212yes—
100#2642C2214yes—
101#2639C2214yes—
102#2637C2218yes—
103#2634C2214yes—
104#2634C2214yes—
105#2634C2214yes—
106#2634C2214yes—
107#2633C2214yes—
108#2629C2214yes—
109#2628C2214yes—
110#2627C2214yes—
111#2627C2218yes—
112#2627C2212yes—
113#2625C2212yes—
114#2625C2214yes—
115#2625C2212yes—
116#2623C2214yes—
117#2623C2214yes—
118#2621C2214yes—
119#2621C2214yes—
120#2618C2212yes—
121#2611C2214yes—
122#2611C2214yes—
123#2591C2214yes—
124#2584C2212yes—
125#2583C2214yes—
126#2582C2214yes—
127#2581C2214yes—
128#2579C2218yes—
129#2568C2212yes—
130#2568C2212yes—
131#2565C2218yes—
132#2565C2214yes—
133#2562C2212yes—
134#2552C2214yes—
135#2550C2214yes—
136#2549C2218yes—
137#2546C2212yes—
138#2546C2212yes—
139#2536C2214yes—
140#2503C2214yes—
141#2503C2212yes—
142#2502C2214yes—
143#2502C2212yes—
144#2498C2214yes—
145#2498C2214yes—
146#2492C2214yes—
147#2489C2214yes—
148#2488C2218yes—
149#2488C2218yes—
150#2487C2212yes—
151#2486C2212yes—
152#2484C2214yes—
153#2484C2214yes—
154#2484C2214yes—
155#2453C2214yes—
156#2451C2214yes—
157#2450C2218yes—
158#2449C2218yes—
159#2446C2214yes—
160#2446C2214yes—
161#2444C2218yes—
162#2443C2218yes—
163#2442C2214yes—
164#2440C2214yes—
165#2440C2218yes—
166#2438C2218yes—
167#2438C2218yes—
168#2423C2214yes—
169#2421C2214yes—
170#2419C2218yes—
171#2419C2218yes—
172#2417C2218yes—
173#2413C2214yes—
174#2399C2212yes—
175#2398C2212yes—
176#2396C2214yes—
177#2395C2212yes—
178#2395C2212yes—
179C2×#400C2214yes—
180C2×#400C2214yes—
181C2×#398C2218yes—
182C2×#398C2214yes—
183C2×#398C2214yes—
184#2355C2212yes—
185#2352C2214yes—
186#2349C2214yes—
187D4×C4⋊C4C2214yes—
188D4×C4⋊C4C2212yes—
189#2346C2212yes—
190#2343C2214yes—
191#2339C2212yes—
192#2339C2214yes—
193#2339C2214yes—
194#2320C2212yes—
195#2318C2214yes—
196#2285C2211yescharacteristic
197#2283C2211yescharacteristic
198#2283C2212yes—
199C2×#382C2212yes—
200#2275C2212yes—
201C22×#41C2312yes—
202C22×#41C2311yescharacteristic
203#557—216no—
204#557—216no—
205#557—28no—
206#554—28no—
207#554—216no—
208#554—232no—
209#554—216no—
210#554—232no—
211#554—28no—
212#553—216no—
213#552—216no—
214#552—232no—
215#552—216no—
216#547—216no—
217#547—28no—
218#544—216no—
219#544—216no—
220#544—28no—
221#544—28no—
222#541—216no—
223#539—232no—
224#533—216no—
225#533—28no—
226#533—28no—
227C2×C4⋊Q8C2311yescharacteristic
228C2×C4⋊Q8C2311yescharacteristic
229C2×C4⋊Q8C2311yescharacteristic
230C2×C4⋊Q8C2312yes—
231C2×C4⋊Q8C2312yes—
232C2×C4⋊Q8C2311yescharacteristic
233C2×C4⋊Q8C2314yes—
234C2×C4⋊Q8C2312yes—
235C2×C4⋊Q8C2312yes—
236C2×C4⋊Q8C2314yes—
237C2×C4⋊Q8C2312yes—
238C2×C4⋊Q8C2314yes—
239#529—216no—
240#529—28no—
241C2×#126C2312yes—
242C2×#126C2314yes—
243C2×#126C2314yes—
244C2×#126C2314yes—
245C2×#125—216no—
246C2×#125—28no—
247C2×#125—216no—
248C2×#125C2312yes—
249C2×#125C2311yescharacteristic
250C2×#125C2312yes—
251C2×#125C2311yescharacteristic
252C2×#125C2314yes—
253C2×#125C2312yes—
254C2×#125C2311yescharacteristic
255C2×#125C2312yes—
256C2×#125C2312yes—
257C2×#125C2312yes—
258C2×#125C2314yes—
259C2×#125C2312yes—
260C2×#125C2312yes—
261C2×#125C2314yes—
262C2×#125C2314yes—
263C2×#125C2312yes—
264C2×#125C2314yes—
265C2×#125C2314yes—
266C2×#125C2312yes—
267C2×#125C2314yes—
268C2×#125C2312yes—
269C2×#125C2314yes—
270C2×#125C2312yes—
271C2×#124C2311yescharacteristic
272C2×#123C2314yes—
273C2×#123C2312yes—
274C2×#123C2314yes—
275C2×#123C2314yes—
276C2×#123C2314yes—
277C2×#123C2314yes—
278C2×C22⋊Q8C2312yes—
279C2×C22⋊Q8C2311yescharacteristic
280C2×C22⋊Q8C2312yes—
281C2×C22⋊Q8C2312yes—
282C2×C22⋊Q8C2312yes—
283C2×C22⋊Q8C2312yes—
284C2×C22⋊Q8C2314yes—
285C2×C22⋊Q8C2314yes—
286C2×C22⋊Q8C2312yes—
287C2×C22⋊Q8C2314yes—
288C2×C22⋊Q8C2314yes—
289C2×C22⋊Q8C2314yes—
290C2×C22⋊Q8C2312yes—
291C2×C22⋊Q8C2314yes—
292C2×C22⋊Q8C2314yes—
293C2×C22⋊Q8C2314yes—
294C2×C22⋊Q8C2314yes—
295C2×C22⋊Q8C2314yes—
296C2×C22⋊Q8C2318yes—
297C2×#121C2311yescharacteristic
298C2×#121C2312yes—
299C2×#121C2314yes—
300#520—28no—
301#520—28no—
302#520—216no—
303C4×#41D4116yes—
304C2×C4×Q8C2312yes—
305C2×C4×Q8C2314yes—
306C2×C4×Q8C2312yes—
307C2×C4×Q8C2312yes—
308C2×C4×Q8C2312yes—
309C2×C4×Q8C2314yes—
310C2×C4×Q8C2312yes—
311C2×C4×Q8C2311yescharacteristic
312C2×C4×Q8C2312yes—
313C2×C4×Q8C2312yes—
314C2×C4×Q8C2312yes—
315C2×C4×Q8C2311yescharacteristic
316C2×C4×Q8C2311yescharacteristic
317C2×C4×D4C2311yescharacteristic
318C2×C4×D4C2314yes—
319C2×C4×D4C2314yes—
320C2×C4×D4C2312yes—
321C2×C4×D4C2312yes—
322C2×C4×D4C2312yes—
323C2×C4×D4C2312yes—
324C2×C4×D4C2312yes—
325C2×C4×D4C2314yes—
326C2×C4×D4C2314yes—
327C2×C4×D4C2314yes—
328C2×C4×D4C2312yes—
329C2×C4×D4C2311yescharacteristic
330C2×C4×D4C2312yes—
331C2×C4×D4C2311yescharacteristic
332C2×#117C2314yes—
333C2×#117C2311yescharacteristic
334C2×#117C2311yescharacteristic
335C2×#117C2312yes—
336C2×#117C2312yes—
337C2×#117C2312yes—
338C2×#117C2312yes—
339C2×#117C2314yes—
340C2×#117C2312yes—
341C2×#117C2312yes—
342C2×#117C2311yescharacteristic
343C22×C4⋊C4C2314yes—
344C22×C4⋊C4C2314yes—
345C22×C4⋊C4C2312yes—
346C22×C4⋊C4C2312yes—
347C22×C4⋊C4C2312yes—
348C22×C4⋊C4C2314yes—
349C22×C4⋊C4C2312yes—
350C22×C4⋊C4C2312yes—
351C22×C4⋊C4C2314yes—
352C22×C4⋊C4C2312yes—
353C22×C4⋊C4C2311yescharacteristic
354C22×C4⋊C4C2311yescharacteristic
355C22×C4⋊C4C2312yes—
356C22×C4⋊C4C2314yes—
357C22×C4⋊C4C2318yes—
358C22×C42C2312yes—
359C22×C42C2311yescharacteristic
360#400C2314yes—
361#400C2312yes—
362#400C2312yes—
363#400C2314yes—
364#400C2312yes—
365#400C2312yes—
366#400C2314yes—
367#400C2314yes—
368#400C2314yes—
369#400C2314yes—
370#400C2314yes—
371#400C2318yes—
372#400C2318yes—
373#400C2318yes—
374#400C2318yes—
375#400C2314yes—
376#400C2314yes—
377#400C2314yes—
378#400C2314yes—
379#400C2318yes—
380#400C2318yes—
381#400C2318yes—
382#400C2318yes—
383#399C2314yes—
384#399C2312yes—
385#399C2312yes—
386#399C2314yes—
387#399C2318yes—
388#398C2312yes—
389#398C2312yes—
390#398C2318yes—
391#398C2314yes—
392#398C2318yes—
393#398C2318yes—
394#398C2318yes—
395#398C2312yes—
396#398C2312yes—
397#398C2314yes—
398#398C2314yes—
399#398C2318yes—
400#398C2314yes—
401#398C2314yes—
402#398C2314yes—
403#398C2314yes—
404#398C2314yes—
405#398C2314yes—
406#398C2318yes—
407#398C2318yes—
408#398C2318yes—
409#398C2318yes—
410#398C2318yes—
411#398C2318yes—
412#398C2318yes—
413#398C2318yes—
414#398C2314yes—
415#398C2314yes—
416#398C2314yes—
417#398C2314yes—
418#398C2318yes—
419#398C2318yes—
420#398C2318yes—
421#397C2314yes—
422#397C2314yes—
423#397C2312yes—
424#397C2312yes—
425#397C2314yes—
426#397C2314yes—
427#397C2318yes—
428#397C2318yes—
429#397C2318yes—
430#397C2318yes—
431#396C2314yes—
432#396C2318yes—
433#396C2314yes—
434#396C2318yes—
435#395C2312yes—
436#395C2312yes—
437#395C2314yes—
438#395C2314yes—
439#395C2314yes—
440#395C2318yes—
441#395C2318yes—
442#395C2318yes—
443#395C2318yes—
444#394C2312yes—
445#394C2312yes—
446#394C2314yes—
447#394C2314yes—
448#394C2314yes—
449#393C2314yes—
450#393C2314yes—
451#393C2318yes—
452#391C2314yes—
453#391C2314yes—
454#391C2318yes—
455#391C2318yes—
456#391C2314yes—
457#391C2314yes—
458#391C2318yes—
459#391C2314yes—
460#391C2314yes—
461#391C2314yes—
462#391C2318yes—
463#389C2314yes—
464#389C2318yes—
465#389C2314yes—
466#389C2314yes—
467#389C2318yes—
468#389C2318yes—
469#389C2318yes—
470#389C2314yes—
471#389C2314yes—
472#389C2318yes—
473#388C2318yes—
474#388C2318yes—
475#388C2318yes—
476#388C2318yes—
477#388C2318yes—
478#388C2318yes—
479#387C2318yes—
480#387C2318yes—
481#387C2318yes—
482#387C2318yes—
483#387C2318yes—
484#387C2318yes—
485#387C2318yes—
486#387C2318yes—
487#387C2318yes—
488#387C2318yes—
489#387C2318yes—
490#387C2318yes—
491#386C2318yes—
492#386C2318yes—
493#386C2318yes—
494#386C2318yes—
495#386C2318yes—
496#386C2314yes—
497#385C2318yes—
498#385C2318yes—
499#385C2318yes—
500#385C2318yes—
501#385C2318yes—
502#385C2318yes—
503#385C2318yes—
504#385C2314yes—
505#385C2318yes—
506#384C2314yes—
507#384C2318yes—
508#384C2312yes—
509#383C2312yes—
510#383C2314yes—
511#382C2311yescharacteristic
512#382C2312yes—
513#382C2311yescharacteristic
514#382C2314yes—
515#382C2318yes—
516#382C2314yes—
517#382C2314yes—
518#382C2314yes—
519#382C2314yes—
520#381C2312yes—
521#381C2314yes—
522#381C2318yes—
523#381C2318yes—
524#381C2314yes—
525#381C2318yes—
526#380C2314yes—
527#380C2314yes—
528#380C2312yes—
529#380C2314yes—
530#380C2312yes—
531#380C2318yes—
532#380C2318yes—
533#380C2312yes—
534#380C2318yes—
535C4×C4⋊C4C2312yes—
536C4×C4⋊C4C2312yes—
537C4×C4⋊C4C2314yes—
538C4×C4⋊C4C2312yes—
539C4×C4⋊C4C2314yes—
540C4×C4⋊C4C2314yes—
541C4×C4⋊C4C2314yes—
542C4×C22⋊C4C2314yes—
543C4×C22⋊C4C2312yes—
544C4×C22⋊C4C2314yes—
545C4×C22⋊C4C2314yes—
546C4×C22⋊C4C2318yes—
547#376C2312yes—
548#376C2314yes—
549C2×#95C2314yes—
550C2×#95C2314yes—
551C2×#95C2318yes—
552C2×#95C2318yes—
553C2×#95C2318yes—
554C2×#41—28no—
555C2×#41—28no—
556C2×#41—216no—
557C2×#41C2×D418yes—
558C22×Q8C2412yes—
559C22×Q8C2411yescharacteristic
560C22×Q8C2411yescharacteristic
561C22×Q8C2414yes—
562C22×Q8C2412yes—
563C22×Q8C2412yes—
564C22×Q8C2414yes—
565C22×Q8C2412yes—
566C22×D4C2414yes—
567C22×D4C2412yes—
568C22×D4C2411yescharacteristic
569C22×D4C2412yes—
570C22×D4C2411yescharacteristic
571C23×C4C2414yes—
572C23×C4C2412yes—
573C23×C4C2412yes—
574C23×C4C2411yescharacteristic
575C23×C4C2414yes—
576C23×C4C2414yes—
577C23×C4C2412yes—
578C23×C4C2414yes—
579C23×C4C2412yes—
580C23×C4C2418yes—
581C23×C4C2414yes—
582C23×C4C2412yes—
583C23×C4C2412yes—
584C23×C4C2411yescharacteristic
585C23×C4C2411yescharacteristic
586C4⋊Q8—28no—
587C4⋊Q8—28no—
588C4⋊Q8—216no—
589C4⋊Q8—28no—
590C4⋊Q8—216no—
591C4⋊Q8—28no—
592C4⋊Q8—28no—
593C4⋊Q8—24no—
594C4⋊Q8—24no—
595C4⋊Q8—24no—
596C4⋊Q8—24no—
597C4⋊Q8—84no—
598#126—216no—
599#126—216no—
600#126—216no—
601#126—28no—
602#125—216no—
603#125—216no—
604#125—28no—
605#125—28no—
606#125—216no—
607#125—28no—
608#125—216no—
609#125—24no—
610#125—24no—
611#125—28no—
612#125—28no—
613#125—216no—
614#125—28no—
615#125—28no—
616#125—28no—
617#125—216no—
618#125—28no—
619#125—28no—
620#125—28no—
621#125—216no—
622#125—28no—
623#125—216no—
624#125—24no—
625#124—24no—
626#123—216no—
627#123—28no—
628#123—216no—
629#123—216no—
630#123—216no—
631#123—84no—
632C22⋊Q8—28no—
633C22⋊Q8—24no—
634C22⋊Q8—28no—
635C22⋊Q8—28no—
636C22⋊Q8—28no—
637C22⋊Q8—216no—
638C22⋊Q8—216no—
639C22⋊Q8—28no—
640C22⋊Q8—28no—
641C22⋊Q8—216no—
642C22⋊Q8—28no—
643C22⋊Q8—216no—
644C22⋊Q8—216no—
645C22⋊Q8—216no—
646C22⋊Q8—216no—
647C22⋊Q8—216no—
648C22⋊Q8—216no—
649C22⋊Q8—216no—
650C22⋊Q8—88no—
651#121—216no—
652#121—28no—
653#121—24no—
654C4×Q8—28no—
655C4×Q8—28no—
656C4×Q8—28no—
657C4×Q8—28no—
658C4×Q8—28no—
659C4×Q8—24no—
660C4×Q8—28no—
661C4×Q8—28no—
662C4×Q8—216no—
663C4×Q8—28no—
664C4×Q8—216no—
665C4×Q8C2×D418yes—
666C4×Q8C2×D418yes—
667C4×D4—28no—
668C4×D4—216no—
669C4×D4—216no—
670C4×D4—28no—
671C4×D4—28no—
672C4×D4—216no—
673C4×D4—216no—
674C4×D4—28no—
675C4×D4—216no—
676C4×D4—24no—
677C4×D4—28no—
678C4×D4C2×D418yes—
679C4×D4C2×D4116yes—
680C4×D4C2×D418yes—
681C4×D4C2×D4116yes—
682#117—28no—
683#117—28no—
684#117—24no—
685#117—24no—
686#117—28no—
687#117—216no—
688#117—28no—
689#117—216no—
690#117—82no—
691#117C2×D418yes—
692#117C2×D4116yes—
693C2×C4⋊C4—216no—
694C2×C4⋊C4—28no—
695C2×C4⋊C4—28no—
696C2×C4⋊C4—24no—
697C2×C4⋊C4—24no—
698C2×C4⋊C4—28no—
699C2×C4⋊C4—216no—
700C2×C4⋊C4—28no—
701C2×C4⋊C4—216no—
702C2×C4⋊C4—216no—
703C2×C4⋊C4—28no—
704C2×C4⋊C4—28no—
705C2×C4⋊C4—28no—
706C2×C4⋊C4—84no—
707C2×C4⋊C4—88no—
708C2×C4⋊C4C2414yes—
709C2×C4⋊C4C2412yes—
710C2×C4⋊C4C2411yescharacteristic
711C2×C4⋊C4C2412yes—
712C2×C4⋊C4C2411yescharacteristic
713C2×C4⋊C4C2412yes—
714C2×C4⋊C4C2411yescharacteristic
715C2×C4⋊C4C2412yes—
716C2×C4⋊C4C2411yescharacteristic
717C2×C4⋊C4C2412yes—
718C2×C4⋊C4C2414yes—
719C2×C4⋊C4C2412yes—
720C2×C4⋊C4C2414yes—
721C2×C4⋊C4C2412yes—
722C2×C4⋊C4C2412yes—
723C2×C4⋊C4C2414yes—
724C2×C4⋊C4C2412yes—
725C2×C4⋊C4C2414yes—
726C2×C4⋊C4C2414yes—
727C2×C4⋊C4C2412yes—
728C2×C4⋊C4C2412yes—
729C2×C4⋊C4C2414yes—
730C2×C4⋊C4C2414yes—
731C2×C4⋊C4C2414yes—
732C2×C4⋊C4C2414yes—
733C2×C4⋊C4C2414yes—
734C2×C4⋊C4C2414yes—
735C2×C4⋊C4C2414yes—
736C2×C4⋊C4C2414yes—
737C2×C4⋊C4C2414yes—
738C2×C4⋊C4C2414yes—
739C2×C4⋊C4C2414yes—
740C2×C4⋊C4C2414yes—
741C2×C4⋊C4C2412yes—
742C2×C4⋊C4C2411yescharacteristic
743C2×C4⋊C4C2411yescharacteristic
744C2×C4⋊C4C2414yes—
745C2×C4⋊C4C2414yes—
746C2×C4⋊C4C2412yes—
747C2×C4⋊C4C2412yes—
748C2×C4⋊C4C2414yes—
749C2×C4⋊C4C2414yes—
750C2×C4⋊C4C2412yes—
751C2×C4⋊C4C2412yes—
752C2×C4⋊C4C2412yes—
753C2×C4⋊C4C2412yes—
754C2×C4⋊C4C2414yes—
755C2×C4⋊C4C2412yes—
756C2×C4⋊C4C2414yes—
757C2×C4⋊C4C2414yes—
758C2×C4⋊C4C2418yes—
759C2×C4⋊C4C2418yes—
760C2×C4⋊C4C2418yes—
761C2×C4⋊C4C2418yes—
762C2×C4⋊C4C2418yes—
763C2×C4⋊C4C2412yes—
764C2×C4⋊C4C2414yes—
765C2×C4⋊C4C2414yes—
766C2×C4⋊C4C2414yes—
767C2×C4⋊C4C2414yes—
768C2×C4⋊C4C2418yes—
769C2×C4⋊C4C2418yes—
770C2×C4⋊C4C2411yescharacteristic
771C2×C4⋊C4C2411yescharacteristic
772C2×C4⋊C4C2412yes—
773C2×C4⋊C4C2412yes—
774C2×C22⋊C4C2412yes—
775C2×C22⋊C4C2412yes—
776C2×C22⋊C4C2414yes—
777C2×C22⋊C4C2414yes—
778C2×C22⋊C4C2412yes—
779C2×C22⋊C4C2412yes—
780C2×C22⋊C4C2414yes—
781C2×C22⋊C4C2412yes—
782C2×C22⋊C4C2414yes—
783C2×C22⋊C4C2414yes—
784C2×C22⋊C4C2414yes—
785C2×C22⋊C4C2412yes—
786C2×C22⋊C4C2412yes—
787C2×C22⋊C4C2418yes—
788C2×C22⋊C4C2414yes—
789C2×C22⋊C4C2414yes—
790C2×C22⋊C4C2418yes—
791C2×C22⋊C4C2414yes—
792C2×C22⋊C4C2414yes—
793C2×C22⋊C4C2414yes—
794C2×C22⋊C4C2414yes—
795C2×C22⋊C4C2418yes—
796C2×C22⋊C4C2412yes—
797C2×C22⋊C4C2412yes—
798C2×C22⋊C4C2412yes—
799C2×C42C2×D4116yes—
800C2×C42C2×D418yes—
801C2×C42C2414yes—
802C2×C42C2414yes—
803C2×C42C2412yes—
804C2×C42C2412yes—
805C2×C42C2412yes—
806C2×C42C2414yes—
807C2×C42C2414yes—
808C2×C42C2414yes—
809C2×C42C2414yes—
810C2×C42C2418yes—
811C2×C42C2412yes—
812C2×C42C2411yescharacteristic
813C2×C42C2411yescharacteristic
814C2×C42C2412yes—
815C2×C42C2411yescharacteristic
816C2×C42C2412yes—
817C2×C42C2411yescharacteristic
818#95C2412yes—
819#95C2412yes—
820#95C2414yes—
821#95C2414yes—
822#95C2414yes—
823#95C2414yes—
824#95C2414yes—
825#95C2418yes—
826#95C2418yes—
827#95C2418yes—
828#95C2418yes—
829#95C2418yes—
830#95C2418yes—
831#95C2418yes—
832#95C2418yes—
833#95C2418yes—
834#95C2418yes—
835#95C2418yes—
836#95C2412yes—
837#95C2414yes—
838#95C2412yes—
839#95C2418yes—
840#95C2414yes—
841#95C2414yes—
842#95C2414yes—
843#95C2414yes—
844#95C2418yes—
845#95C2414yes—
846#95C2414yes—
847#95C2418yes—
848#95C2418yes—
849#95C2418yes—
850#95C2418yes—
851#95C2418yes—
852#95C2418yes—
853#95C2418yes—
854C24C2512yes—
855C24C2511yescharacteristic
856C24C2512yes—
857#41—232no—
858#41—432no—
859C2×Q8—22no—
860C2×Q8—24no—
861C2×Q8—24no—
862C2×Q8—24no—
863C2×Q8—28no—
864C2×Q8—28no—
865C2×Q8—24no—
866C2×Q8—24no—
867C2×Q8—28no—
868C2×Q8—42no—
869C2×Q8—44no—
870C2×Q8—42no—
871C2×Q8—42no—
872C2×Q8—48no—
873C2×Q8—44no—
874C2×Q8—44no—
875C2×Q8—42no—
876C2×Q8—42no—
877C2×Q8C22×D414yes—
878C2×D4—28no—
879C2×D4—28no—
880C2×D4—216no—
881C2×D4—24no—
882C2×D4—22no—
883C2×D4—42no—
884C2×D4—42no—
885C2×D4—42no—
886C2×D4C22×D418yes—
887C2×D4C22×D414yes—
888C2×D42−1+418yes—
889C22×C4—28no—
890C22×C4—24no—
891C22×C4—28no—
892C22×C4—216no—
893C22×C4—28no—
894C22×C4—24no—
895C22×C4—24no—
896C22×C4—28no—
897C22×C4—28no—
898C22×C4—216no—
899C22×C4—24no—
900C22×C4—28no—
901C22×C4—28no—
902C22×C4—42no—
903C22×C4—41no—
904C22×C4—44no—
905C22×C4—42no—
906C22×C4—41no—
907C22×C4—42no—
908C22×C4—48no—
909C22×C4—44no—
910C22×C4—44no—
911C22×C4—44no—
912C22×C4—42no—
913C22×C4—44no—
914C22×C4—48no—
915C22×C4—44no—
916C22×C4—48no—
917C22×C4—44no—
918C22×C4—44no—
919C22×C4—42no—
920C22×C4C22×D418yes—
921C22×C4C22×D414yes—
922C22×C4C22×D418yes—
923C22×C4C22×D418yes—
924C22×C4C22×D414yes—
925C22×C4C22×D414yes—
926C22×C4C2514yes—
927C22×C4C2514yes—
928C22×C4C2518yes—
929C22×C4C2514yes—
930C22×C4C2512yes—
931C22×C4C2512yes—
932C22×C4C2512yes—
933C22×C4C2514yes—
934C22×C4C2512yes—
935C22×C4C2512yes—
936C22×C4C2514yes—
937C22×C4C2514yes—
938C22×C4C2512yes—
939C22×C4C2512yes—
940C22×C4C2512yes—
941C22×C4C2511yescharacteristic
942C22×C4C2511yescharacteristic
943C22×C4C2512yes—
944C22×C4C2511yescharacteristic
945C22×C4C2511yescharacteristic
946C22×C4C2512yes—
947C22×C4C2511yescharacteristic
948C22×C4C2511yescharacteristic
949C4⋊C4—28no—
950C4⋊C4—24no—
951C4⋊C4—22no—
952C4⋊C4—24no—
953C4⋊C4—22no—
954C4⋊C4—24no—
955C4⋊C4—22no—
956C4⋊C4—24no—
957C4⋊C4—22no—
958C4⋊C4—24no—
959C4⋊C4—28no—
960C4⋊C4—24no—
961C4⋊C4—28no—
962C4⋊C4—24no—
963C4⋊C4—24no—
964C4⋊C4—28no—
965C4⋊C4—24no—
966C4⋊C4—28no—
967C4⋊C4—28no—
968C4⋊C4—28no—
969C4⋊C4—28no—
970C4⋊C4—24no—
971C4⋊C4—24no—
972C4⋊C4—28no—
973C4⋊C4—28no—
974C4⋊C4—28no—
975C4⋊C4—28no—
976C4⋊C4—28no—
977C4⋊C4—28no—
978C4⋊C4—28no—
979C4⋊C4—28no—
980C4⋊C4—28no—
981C4⋊C4—28no—
982C4⋊C4—24no—
983C4⋊C4—22no—
984C4⋊C4—22no—
985C4⋊C4—28no—
986C4⋊C4—24no—
987C4⋊C4—24no—
988C4⋊C4—24no—
989C4⋊C4—28no—
990C4⋊C4—28no—
991C4⋊C4—24no—
992C4⋊C4—24no—
993C4⋊C4—24no—
994C4⋊C4—28no—
995C4⋊C4—28no—
996C4⋊C4—42no—
997C4⋊C4—44no—
998C4⋊C4—44no—
999C4⋊C4—48no—
1000C4⋊C4—48no—
1001C4⋊C4—48no—
1002C4⋊C4—48no—
1003C4⋊C4—42no—
1004C4⋊C4—44no—
1005C4⋊C4—44no—
1006C4⋊C4—48no—
1007C4⋊C4—44no—
1008C4⋊C4—44no—
1009C4⋊C4—48no—
1010C4⋊C4—48no—
1011C4⋊C4C22×D414yes—
1012C4⋊C4C22×D418yes—
1013C4⋊C4C22×D414yes—
1014C4⋊C4C22×D418yes—
1015C22⋊C4—24no—
1016C22⋊C4—24no—
1017C22⋊C4—28no—
1018C22⋊C4—28no—
1019C22⋊C4—28no—
1020C22⋊C4—28no—
1021C22⋊C4—24no—
1022C22⋊C4—216no—
1023C22⋊C4—24no—
1024C22⋊C4—24no—
1025C22⋊C4—24no—
1026C22⋊C4—28no—
1027C22⋊C4—28no—
1028C22⋊C4—24no—
1029C22⋊C4—44no—
1030C22⋊C4—44no—
1031C22⋊C4—48no—
1032C22⋊C4—44no—
1033C22⋊C4—44no—
1034C22⋊C4—44no—
1035C22⋊C4—44no—
1036C22⋊C4—48no—
1037C22⋊C4C22×D418yes—
1038C22⋊C4C22×D418yes—
1039C22⋊C4C22×D418yes—
1040C42—28no—
1041C42—28no—
1042C42—24no—
1043C42—28no—
1044C42—28no—
1045C42—24no—
1046C42—24no—
1047C42—28no—
1048C42—48no—
1049C42—44no—
1050C42C22×D414yes—
1051C42C22×D418yes—
1052C42C22×D414yes—
1053C42C22×D414yes—
1054C42C22×D418yes—
1055C42C22×D414yes—
1056C42C22×D418yes—
1057C23—22no—
1058C23—24no—
1059C23—22no—
1060C23—22no—
1061C23—21no—
1062C23—22no—
1063C23—21no—
1064C23—22no—
1065C23—24no—
1066C23—22no—
1067C23—24no—
1068C23—22no—
1069C23C23×D412yes—
1070C23C23×D414yes—
1071C23C2×2−1+418yes—
1072C23C2611yescharacteristic
1073Q8—28no—
1074Q8—44no—
1075Q8—48no—
1076Q8—88no—
1077Q8—84no—
1078Q8—84no—
1079Q8—88no—
1080Q8—84no—
1081D4—216no—
1082D4—44no—
1083D4—416no—
1084D4—84no—
1085D4#536116yes—
1086C2×C4—22no—
1087C2×C4—24no—
1088C2×C4—21no—
1089C2×C4—21no—
1090C2×C4—22no—
1091C2×C4—24no—
1092C2×C4—21no—
1093C2×C4—22no—
1094C2×C4—22no—
1095C2×C4—22no—
1096C2×C4—21no—
1097C2×C4—216no—
1098C2×C4—28no—
1099C2×C4—22no—
1100C2×C4—22no—
1101C2×C4—22no—
1102C2×C4—24no—
1103C2×C4—24no—
1104C2×C4—22no—
1105C2×C4—24no—
1106C2×C4—22no—
1107C2×C4—24no—
1108C2×C4—22no—
1109C2×C4—22no—
1110C2×C4—24no—
1111C2×C4—24no—
1112C2×C4—28no—
1113C2×C4—24no—
1114C2×C4—28no—
1115C2×C4—28no—
1116C2×C4—24no—
1117C2×C4—22no—
1118C2×C4—24no—
1119C2×C4—22no—
1120C2×C4—22no—
1121C2×C4—24no—
1122C2×C4—24no—
1123C2×C4—28no—
1124C2×C4—24no—
1125C2×C4—22no—
1126C2×C4—24no—
1127C2×C4—24no—
1128C2×C4—28no—
1129C2×C4—24no—
1130C2×C4—24no—
1131C2×C4—22no—
1132C2×C4—24no—
1133C2×C4—24no—
1134C2×C4—22no—
1135C2×C4—48no—
1136C2×C4—44no—
1137C2×C4—48no—
1138C2×C4—44no—
1139C2×C4—416no—
1140C2×C4—48no—
1141C2×C4—88no—
1142C2×C4—816no—
1143C2×C4—88no—
1144C2×C4—88no—
1145C2×C4—84no—
1146C2×C4—88no—
1147C2×C4—84no—
1148C2×C4C23×D412yes—
1149C2×C4C23×D414yes—
1150C2×C4C23×D414yes—
1151C2×C4C23×D412yes—
1152C2×C4C23×D412yes—
1153C2×C4C23×D412yes—
1154C2×C4C23×D414yes—
1155C2×C4C23×D412yes—
1156C2×C4C23×D412yes—
1157C2×C4C2×2−1+414yes—
1158C22—28no—
1159C22—28no—
1160C22—24no—
1161C22—24no—
1162C22—22no—
1163C22—22no—
1164C22—22no—
1165C22—42no—
1166C22—42no—
1167C22—44no—
1168C22—44no—
1169C22—42no—
1170C22—42no—
1171C22—42no—
1172C22C2×#53618yes—
1173C22C24×D411yescharacteristic
1174C22C22×2−1+412yes—
1175C22H(7,𝔽2)11yescharacteristic
1176C222−1+612yes—
1177C222−1+611yescharacteristic
1178C4—22no—
1179C4—24no—
1180C4—22no—
1181C4—22no—
1182C4—24no—
1183C4—22no—
1184C4—22no—
1185C4—24no—
1186C4—48no—
1187C4—44no—
1188C4—44no—
1189C4—42no—
1190C4—44no—
1191C4—44no—
1192C4—42no—
1193C4—42no—
1194C4—42no—
1195C4—44no—
1196C4—42no—
1197C4—42no—
1198C4—42no—
1199C4—44no—
1200C4C2×#53614yes—
1201C2—28no—
1202C2—42no—
1203C2—82no—
1204C2C22×#53611yescharacteristic
1205C2#6285311yescharacteristic
1206C2#6285911yescharacteristic
1207C2#6305812yes—
1208C2#6306712yes—
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×#3504C2semidirect
3. #42978C2semidirect
4. #42964C2semidirect
5. #42814C2semidirect
6. #42811C2semidirect
7. #42801C2semidirect
8. #42150C2semidirect
9. #41939C2semidirect
10. #41411C2semidirect
11. #41406C2semidirect
12. #40516C2semidirect
13. #37641C2semidirect
14. #37607C2semidirect
15. #37555C2semidirect
16. #37549C2semidirect
17. #37540C2semidirect
18. #37540C2semidirect
19. #36699C2semidirect
20. C2×#2822C2semidirect
21. #36067C2semidirect
22. #36042C2semidirect
23. #35998C2semidirect
24. #35950C2semidirect
25. #35806C2semidirect
26. #34191C2semidirect

Maximal subgroups

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

subgroupindex
C2×#35042
C2×#35152
#429782
#429642
#428142
#428112
#428012
#421502
#419392
#414112
#414062
#405162
#376412
#376072
#375552
#375492
#375402
#366992
C2×#28222
#360672
#360422
#359982
#359502
#358062
#341912