Finite Group Databasebeta

← #7648460

Subgroups — #7648460

Order 512.

6610 conjugacy classes of subgroups.

The subgroup lattice has 1252 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3504C211yesmaximal, characteristic, complemented
2C2×#3480C211yesmaximal, characteristic
3#42886C212yesmaximal, complemented
4#42811C212yesmaximal, complemented
5#42676C212yesmaximal, complemented
6#42479C212yesmaximal, complemented
7#41406C214yesmaximal, complemented
8#40589C214yesmaximal, complemented
9#39951C214yesmaximal, complemented
10#39949C214yesmaximal, complemented
11#38421C218yesmaximal, complemented
12#37560C212yesmaximal, complemented
13#37549C212yesmaximal, complemented
14#37281C214yesmaximal, complemented
15#37279C214yesmaximal, complemented
16#35517C212yesmaximal, complemented
17#35517C212yesmaximal, complemented
18#35341C211yesmaximal, characteristic, complemented
19#35297C212yesmaximal, complemented
20#35257C212yesmaximal, complemented
21#35257C212yesmaximal, complemented
22#35180C211yesmaximal, characteristic, complemented
23#35138C212yesmaximal, complemented
24#34953C211yesmaximal, characteristic, complemented
25C2×#2584C211yesmaximal, characteristic, complemented
26#34060C211yesmaximal, characteristic, complemented
27#3504—216no—
28#3480—216no—
29C2×#559C2212yes—
30C2×#559C2211yescharacteristic
31C2×#557C2212yes—
32C2×#557C2211yescharacteristic
33C2×#557C2212yes—
34C2×#556C2212yes—
35C2×#556C2211yescharacteristic
36C2×#554C2212yes—
37C2×#554C2214yes—
38C2×#554C2214yes—
39C2×#554C2212yes—
40C2×#553C2214yes—
41C2×#553C2212yes—
42C2×#550C2211yescharacteristic
43C2×#548C2212yes—
44C2×#544C2212yes—
45C2×#544C2212yes—
46C2×#544C2211yescharacteristic
47C2×#544C2211yescharacteristic
48C2×#533C2211yescharacteristic
49C2×#533C2212yes—
50C2×#532C2211yescharacteristic
51C2×#532C2212yes—
52C2×#529C2214yes—
53C2×#529C2212yes—
54C22×#125C2211yescharacteristic
55C22×#125C2212yes—
56C2×#520C2211yescharacteristic
57C2×#520C2211yescharacteristic
58C2×C4×#41C2212yes—
59C2×C4×#41C2212yes—
60C2×C4×#41C2211yescharacteristic
61C22×C4×Q8C2211yescharacteristic
62#2861C2214yes—
63#2857C2214yes—
64#2857C2214yes—
65#2851C2214yes—
66#2851C2214yes—
67#2850C2214yes—
68#2822C2214yes—
69#2820C2214yes—
70#2817C2214yes—
71#2816C2214yes—
72#2721C2218yes—
73#2719C2218yes—
74#2716C2218yes—
75#2713C2218yes—
76#2700C2218yes—
77#2698C2218yes—
78#2694C2218yes—
79#2690C2218yes—
80#2689C2218yes—
81#2687C2218yes—
82#2681C2218yes—
83#2680C2218yes—
84#2677C2218yes—
85#2674C2218yes—
86#2674C2218yes—
87#2672C2218yes—
88#2664C2218yes—
89#2663C2218yes—
90#2642C2212yes—
91#2641C2212yes—
92#2639C2214yes—
93#2634C2214yes—
94#2634C2214yes—
95#2633C2214yes—
96#2632C2214yes—
97#2629C2214yes—
98#2629C2214yes—
99#2628C2214yes—
100#2628C2214yes—
101#2627C2214yes—
102#2625C2214yes—
103#2618C2214yes—
104#2616C2214yes—
105#2611C2218yes—
106#2604C2218yes—
107#2592C2214yes—
108#2591C2214yes—
109#2591C2214yes—
110#2584C2214yes—
111#2584C2212yes—
112#2584C2211yescharacteristic
113#2584C2212yes—
114#2584C2212yes—
115#2584C2214yes—
116#2584C2212yes—
117#2584C2211yescharacteristic
118#2584C2211yescharacteristic
119#2584C2211yescharacteristic
120#2583C2214yes—
121#2581C2214yes—
122#2568C2212yes—
123#2567C2212yes—
124#2563C2212yes—
125#2562C2212yes—
126#2562C2214yes—
127#2562C2212yes—
128#2562C2212yes—
129#2562C2212yes—
130#2548C2212yes—
131#2547C2212yes—
132#2546C2212yes—
133#2536C2214yes—
134#2502C2212yes—
135#2487C2214yes—
136#2487C2214yes—
137#2486C2214yes—
138#2486C2214yes—
139#2485C2214yes—
140#2485C2214yes—
141#2485C2214yes—
142#2485C2214yes—
143#2484C2214yes—
144#2454C2214yes—
145#2454C2214yes—
146#2453C2214yes—
147#2453C2214yes—
148#2452C2214yes—
149#2452C2214yes—
150#2451C2214yes—
151#2451C2214yes—
152#2450C2218yes—
153#2450C2218yes—
154#2449C2218yes—
155#2449C2218yes—
156#2448C2214yes—
157#2448C2214yes—
158#2447C2214yes—
159#2447C2214yes—
160#2446C2214yes—
161#2446C2214yes—
162#2445C2214yes—
163#2445C2214yes—
164#2444C2218yes—
165#2444C2218yes—
166#2443C2218yes—
167#2443C2218yes—
168#2434C2212yes—
169#2415C2218yes—
170#2413C2218yes—
171#2406C2214yes—
172#2399C2212yes—
173#2399C2212yes—
174C2×#398C2212yes—
175C2×#395C2212yes—
176#2323C2218yes—
177#2322C2218yes—
178#2320C2212yes—
179#2319C2212yes—
180#2318C2214yes—
181#2317C2212yes—
182#2314C2214yes—
183#2311C2212yes—
184#2311C2212yes—
185#2311C2212yes—
186#2311C2212yes—
187#2311C2212yes—
188C4×C4⋊Q8C2214yes—
189#2296C2212yes—
190#2296C2212yes—
191#2295C2212yes—
192#2293C2212yes—
193C2×#389C2214yes—
194C2×#389C2212yes—
195C2×#389C2212yes—
196#2290C2214yes—
197#2285C2212yes—
198#2283C2212yes—
199C4×#117C2211yescharacteristic
200C2×C4×C4⋊C4C2211yescharacteristic
201C22×#41C2312yes—
202C22×#41C2311yescharacteristic
203C22×#41C2312yes—
204C23×Q8C2311yescharacteristic
205#559—28no—
206#559—216no—
207#557—28no—
208#557—216no—
209#557—216no—
210#556—216no—
211#556—28no—
212#554—232no—
213#554—216no—
214#554—232no—
215#554—216no—
216#553—216no—
217#553—232no—
218#550—28no—
219#548—216no—
220#544—28no—
221#544—28no—
222#544—216no—
223#544—216no—
224#533—28no—
225#533—216no—
226#532—216no—
227#532—28no—
228C2×C4⋊Q8C2311yescharacteristic
229C2×C4⋊Q8C2311yescharacteristic
230C2×C4⋊Q8C2311yescharacteristic
231C2×C4⋊Q8C2312yes—
232C2×C4⋊Q8C2312yes—
233C2×C4⋊Q8C2314yes—
234C2×C4⋊Q8C2312yes—
235C2×C4⋊Q8C2314yes—
236C2×C4⋊Q8C2312yes—
237C2×C4⋊Q8C2312yes—
238C2×C4⋊Q8C2314yes—
239C2×#127C2311yescharacteristic
240C2×#127C2312yes—
241#529—232no—
242#529—216no—
243C2×#126C2314yes—
244C2×#126C2314yes—
245C2×#126C2314yes—
246C2×#125—28no—
247C2×#125—216no—
248C2×#125C2312yes—
249C2×#125C2311yescharacteristic
250C2×#125C2312yes—
251C2×#125C2311yescharacteristic
252C2×#125C2314yes—
253C2×#125C2312yes—
254C2×#125C2312yes—
255C2×#125C2312yes—
256C2×#125C2312yes—
257C2×#125C2312yes—
258C2×#125C2314yes—
259C2×#125C2314yes—
260C2×#125C2314yes—
261C2×#125C2314yes—
262C2×#125C2312yes—
263C2×#125C2312yes—
264C2×#124C2312yes—
265C2×#124C2312yes—
266C2×#124C2314yes—
267C2×#124C2312yes—
268C2×#124C2312yes—
269C2×#124C2314yes—
270C2×#123C2314yes—
271C2×#123C2314yes—
272C2×#123C2314yes—
273C2×#123C2318yes—
274C2×#123C2318yes—
275C2×C22⋊Q8C2314yes—
276C2×C22⋊Q8C2312yes—
277C2×C22⋊Q8C2312yes—
278C2×C22⋊Q8C2312yes—
279C2×C22⋊Q8C2314yes—
280C2×C22⋊Q8C2314yes—
281C2×C22⋊Q8C2314yes—
282C2×C22⋊Q8C2314yes—
283C2×C22⋊Q8C2314yes—
284C2×C22⋊Q8C2314yes—
285C2×C22⋊Q8C2314yes—
286C2×C22⋊Q8C2314yes—
287C2×C22⋊Q8C2318yes—
288C2×C22⋊Q8C2318yes—
289C2×#121C2312yes—
290C2×#121C2312yes—
291C2×#121C2312yes—
292C2×#121C2314yes—
293C2×#121C2314yes—
294C2×#121C2314yes—
295#520—28no—
296#520—28no—
297C4×#41—216no—
298C4×#41—216no—
299C4×#41D4116yes—
300C2×C4×Q8—28no—
301C2×C4×Q8C2312yes—
302C2×C4×Q8C2312yes—
303C2×C4×Q8C2312yes—
304C2×C4×Q8C2312yes—
305C2×C4×Q8C2314yes—
306C2×C4×Q8C2312yes—
307C2×C4×Q8C2314yes—
308C2×C4×Q8C2311yescharacteristic
309C2×C4×Q8C2311yescharacteristic
310C2×C4×Q8C2311yescharacteristic
311C2×C4×Q8C2311yescharacteristic
312C2×C4×Q8C2312yes—
313C2×C4×Q8C2312yes—
314C2×C4×Q8C2312yes—
315C2×C4×Q8C2312yes—
316C2×C4×Q8C2311yescharacteristic
317C2×C4×Q8C2311yescharacteristic
318C2×C4×D4C2312yes—
319C2×C4×D4C2312yes—
320C2×C4×D4C2314yes—
321C2×C4×D4C2312yes—
322C2×C4×D4C2314yes—
323C2×C4×D4C2314yes—
324C2×C4×D4C2312yes—
325C2×C4×D4C2314yes—
326C2×C4×D4C2312yes—
327C2×C4×D4C2314yes—
328C2×C4×D4C2314yes—
329C2×C4×D4C2312yes—
330C2×C4×D4C2312yes—
331C2×C4×D4C2314yes—
332C2×C4×D4C2312yes—
333C2×C4×D4C2311yescharacteristic
334C2×C4×D4C2312yes—
335C2×C4×D4C2311yescharacteristic
336C2×#117C2312yes—
337C2×#117C2311yescharacteristic
338C2×#117C2311yescharacteristic
339C2×#117C2314yes—
340C2×#117C2312yes—
341C2×#117C2314yes—
342C2×#117C2312yes—
343C2×#117C2312yes—
344C2×#117C2314yes—
345C2×#117C2312yes—
346C2×#117C2311yescharacteristic
347C22×C4⋊C4C2312yes—
348C22×C4⋊C4C2311yescharacteristic
349C22×C4⋊C4C2311yescharacteristic
350C22×C4⋊C4C2314yes—
351C22×C4⋊C4C2312yes—
352C22×C4⋊C4C2312yes—
353C22×C4⋊C4C2312yes—
354C22×C4⋊C4C2314yes—
355C22×C4⋊C4C2311yescharacteristic
356C22×C4⋊C4C2312yes—
357C22×C4⋊C4C2312yes—
358C22×C4⋊C4C2314yes—
359C22×C4⋊C4C2314yes—
360C22×C42C2314yes—
361C22×C42C2312yes—
362C22×C42C2312yes—
363C22×C42C2311yescharacteristic
364C22×C42C2312yes—
365#400C2314yes—
366#400C2314yes—
367#400C2318yes—
368#400C2314yes—
369#400C2314yes—
370#400C2318yes—
371#400C2318yes—
372#400C2318yes—
373#400C2318yes—
374#399C2318yes—
375#399C2318yes—
376#399C2318yes—
377#399C2318yes—
378#398C2312yes—
379#398C2314yes—
380#398C2312yes—
381#398C2318yes—
382#398C2318yes—
383#398C2318yes—
384#398C2314yes—
385#398C2314yes—
386#398C2314yes—
387#398C2318yes—
388#398C2312yes—
389#398C2312yes—
390#398C2318yes—
391#398C2318yes—
392#398C2318yes—
393#397C2318yes—
394#397C2318yes—
395#397C2318yes—
396#397C2318yes—
397#397C2318yes—
398#397C2318yes—
399#397C2318yes—
400#396C2318yes—
401#396C2318yes—
402#396C2318yes—
403#396C2318yes—
404#395C2312yes—
405#395C2314yes—
406#395C2318yes—
407#395C2312yes—
408#395C2314yes—
409#395C2314yes—
410#395C2312yes—
411#395C2314yes—
412#395C2318yes—
413#395C2312yes—
414#395C2318yes—
415#394C2314yes—
416#394C2314yes—
417#394C2318yes—
418#394C2318yes—
419#394C2314yes—
420#394C2314yes—
421#394C2318yes—
422#394C2318yes—
423#394C2318yes—
424#393C2318yes—
425#393C2318yes—
426#393C2318yes—
427#391C2314yes—
428#391C2314yes—
429#391C2314yes—
430#391C2314yes—
431#391C2314yes—
432#391C2314yes—
433#391C2314yes—
434#391C2314yes—
435#391C2318yes—
436#391C2318yes—
437#390C2314yes—
438#390C2314yes—
439#390C2314yes—
440#390C2314yes—
441#390C2314yes—
442#390C2314yes—
443#389C2314yes—
444#389C2314yes—
445#389C2314yes—
446#389C2314yes—
447#389C2312yes—
448#389C2312yes—
449#389C2312yes—
450#389C2312yes—
451#389C2314yes—
452#389C2314yes—
453#389C2318yes—
454#389C2318yes—
455#389C2318yes—
456#389C2314yes—
457#389C2314yes—
458#389C2318yes—
459#389C2314yes—
460#389C2314yes—
461#389C2318yes—
462#389C2318yes—
463#389C2314yes—
464#389C2314yes—
465#389C2314yes—
466#389C2314yes—
467#389C2312yes—
468#389C2312yes—
469#389C2312yes—
470#389C2312yes—
471#388C2318yes—
472#388C2318yes—
473#388C2318yes—
474#388C2318yes—
475#388C2318yes—
476#388C2318yes—
477#388C2318yes—
478#388C2318yes—
479#388C2318yes—
480#388C2318yes—
481#388C2318yes—
482#388C2318yes—
483#387C2318yes—
484#387C2318yes—
485#387C2318yes—
486#387C2318yes—
487#387C2318yes—
488#387C2318yes—
489#387C2318yes—
490#387C2318yes—
491#387C2318yes—
492#387C2318yes—
493#386C2318yes—
494#386C2318yes—
495#386C2318yes—
496#386C2318yes—
497#386C2318yes—
498#386C2318yes—
499#386C2318yes—
500#385C2318yes—
501#385C2318yes—
502#385C2318yes—
503#385C2318yes—
504#385C2314yes—
505#385C2314yes—
506#385C2314yes—
507#385C2314yes—
508#385C2318yes—
509#385C2318yes—
510#385C2318yes—
511#384C2314yes—
512#384C2314yes—
513#383C2314yes—
514#382C2314yes—
515#382C2314yes—
516#382C2314yes—
517#381C2314yes—
518#381C2318yes—
519#381C2318yes—
520#380C2314yes—
521#380C2314yes—
522#380C2314yes—
523#380C2314yes—
524#380C2314yes—
525#380C2314yes—
526#380C2314yes—
527#380C2314yes—
528#380C2314yes—
529#380C2314yes—
530#380C2314yes—
531#380C2318yes—
532#380C2318yes—
533C4×C4⋊C4C2312yes—
534C4×C4⋊C4C2312yes—
535C4×C4⋊C4C2311yescharacteristic
536C4×C4⋊C4C2311yescharacteristic
537C4×C4⋊C4C2314yes—
538C4×C4⋊C4C2314yes—
539C4×C4⋊C4C2314yes—
540C4×C4⋊C4C2314yes—
541C4×C4⋊C4C2312yes—
542C4×C4⋊C4C2312yes—
543C4×C4⋊C4C2314yes—
544C4×C4⋊C4C2312yes—
545C4×C22⋊C4C2312yes—
546C4×C22⋊C4C2314yes—
547C4×C22⋊C4C2312yes—
548#376C2312yes—
549#376C2314yes—
550C2×#95C2312yes—
551C2×#95C2314yes—
552C2×#95C2314yes—
553C43C2312yes—
554C2×#41—28no—
555C2×#41—28no—
556C2×#41—28no—
557C2×#41—28no—
558C2×#41—28no—
559C2×#41—48no—
560C2×#41C2×D418yes—
561C22×Q8—24no—
562C22×Q8—44no—
563C22×Q8C2411yescharacteristic
564C22×Q8C2412yes—
565C22×Q8C2412yes—
566C22×Q8C2411yescharacteristic
567C22×Q8C2411yescharacteristic
568C22×Q8C2414yes—
569C22×Q8C2414yes—
570C22×Q8C2412yes—
571C22×Q8C2412yes—
572C22×D4C2414yes—
573C22×D4C2412yes—
574C22×D4C2414yes—
575C22×D4C2412yes—
576C22×D4C2411yescharacteristic
577C22×D4C2412yes—
578C22×D4C2414yes—
579C22×D4C2412yes—
580C23×C4C2414yes—
581C23×C4C2412yes—
582C23×C4C2414yes—
583C23×C4C2412yes—
584C23×C4C2412yes—
585C23×C4C2412yes—
586C23×C4C2412yes—
587C23×C4C2414yes—
588C23×C4C2414yes—
589C23×C4C2414yes—
590C23×C4C2414yes—
591C23×C4C2411yescharacteristic
592C23×C4C2411yescharacteristic
593C23×C4C2412yes—
594C23×C4C2412yes—
595C23×C4C2411yescharacteristic
596C4⋊Q8—28no—
597C4⋊Q8—28no—
598C4⋊Q8—28no—
599C4⋊Q8—216no—
600C4⋊Q8—216no—
601C4⋊Q8—24no—
602C4⋊Q8—28no—
603C4⋊Q8—28no—
604C4⋊Q8—24no—
605C4⋊Q8—24no—
606C4⋊Q8—48no—
607#127—28no—
608#127—24no—
609#126—216no—
610#126—216no—
611#126—216no—
612#125—216no—
613#125—28no—
614#125—28no—
615#125—216no—
616#125—216no—
617#125—28no—
618#125—24no—
619#125—28no—
620#125—28no—
621#125—28no—
622#125—216no—
623#125—216no—
624#125—28no—
625#125—28no—
626#125—28no—
627#125—24no—
628#124—28no—
629#124—28no—
630#124—216no—
631#124—28no—
632#124—28no—
633#124—84no—
634#123—216no—
635#123—216no—
636#123—216no—
637#123—416no—
638#123—88no—
639C22⋊Q8—28no—
640C22⋊Q8—28no—
641C22⋊Q8—28no—
642C22⋊Q8—216no—
643C22⋊Q8—216no—
644C22⋊Q8—216no—
645C22⋊Q8—216no—
646C22⋊Q8—216no—
647C22⋊Q8—216no—
648C22⋊Q8—216no—
649C22⋊Q8—216no—
650C22⋊Q8—216no—
651C22⋊Q8—416no—
652C22⋊Q8—88no—
653#121—216no—
654#121—216no—
655#121—28no—
656#121—28no—
657#121—28no—
658#121—216no—
659C4×Q8—28no—
660C4×Q8—28no—
661C4×Q8—28no—
662C4×Q8—28no—
663C4×Q8—24no—
664C4×Q8—28no—
665C4×Q8—24no—
666C4×Q8—24no—
667C4×Q8—24no—
668C4×Q8—28no—
669C4×Q8—28no—
670C4×Q8—216no—
671C4×Q8—216no—
672C4×Q8—28no—
673C4×Q8—28no—
674C4×Q8C2×D418yes—
675C4×Q8C2×D418yes—
676C4×D4—216no—
677C4×D4—216no—
678C4×D4—28no—
679C4×D4—28no—
680C4×D4—216no—
681C4×D4—216no—
682C4×D4—216no—
683C4×D4—28no—
684C4×D4—28no—
685C4×D4—216no—
686C4×D4—216no—
687C4×D4—28no—
688C4×D4—28no—
689C4×D4—28no—
690C4×D4C2×D4116yes—
691C4×D4C2×D418yes—
692C4×D4C2×D4116yes—
693C4×D4C2×D418yes—
694#117—28no—
695#117—28no—
696#117—28no—
697#117—24no—
698#117—24no—
699#117—28no—
700#117—216no—
701#117—216no—
702#117—84no—
703#117C2×D418yes—
704#117C2×D4116yes—
705C2×C4⋊C4—28no—
706C2×C4⋊C4—24no—
707C2×C4⋊C4—28no—
708C2×C4⋊C4—28no—
709C2×C4⋊C4—24no—
710C2×C4⋊C4—24no—
711C2×C4⋊C4—28no—
712C2×C4⋊C4—28no—
713C2×C4⋊C4—216no—
714C2×C4⋊C4—216no—
715C2×C4⋊C4—28no—
716C2×C4⋊C4—48no—
717C2×C4⋊C4—84no—
718C2×C4⋊C4C2412yes—
719C2×C4⋊C4C2412yes—
720C2×C4⋊C4C2411yescharacteristic
721C2×C4⋊C4C2411yescharacteristic
722C2×C4⋊C4C2412yes—
723C2×C4⋊C4C2414yes—
724C2×C4⋊C4C2414yes—
725C2×C4⋊C4C2412yes—
726C2×C4⋊C4C2412yes—
727C2×C4⋊C4C2411yescharacteristic
728C2×C4⋊C4C2412yes—
729C2×C4⋊C4C2412yes—
730C2×C4⋊C4C2414yes—
731C2×C4⋊C4C2414yes—
732C2×C4⋊C4C2412yes—
733C2×C4⋊C4C2411yescharacteristic
734C2×C4⋊C4C2412yes—
735C2×C4⋊C4C2412yes—
736C2×C4⋊C4C2412yes—
737C2×C4⋊C4C2414yes—
738C2×C4⋊C4C2414yes—
739C2×C4⋊C4C2414yes—
740C2×C4⋊C4C2414yes—
741C2×C4⋊C4C2414yes—
742C2×C4⋊C4C2414yes—
743C2×C4⋊C4C2418yes—
744C2×C4⋊C4C2414yes—
745C2×C4⋊C4C2414yes—
746C2×C4⋊C4C2411yescharacteristic
747C2×C4⋊C4C2411yescharacteristic
748C2×C4⋊C4C2414yes—
749C2×C4⋊C4C2412yes—
750C2×C4⋊C4C2414yes—
751C2×C4⋊C4C2414yes—
752C2×C4⋊C4C2412yes—
753C2×C4⋊C4C2412yes—
754C2×C4⋊C4C2412yes—
755C2×C4⋊C4C2414yes—
756C2×C4⋊C4C2412yes—
757C2×C4⋊C4C2412yes—
758C2×C4⋊C4C2414yes—
759C2×C4⋊C4C2414yes—
760C2×C4⋊C4C2412yes—
761C2×C4⋊C4C2412yes—
762C2×C4⋊C4C2414yes—
763C2×C4⋊C4C2414yes—
764C2×C4⋊C4C2418yes—
765C2×C4⋊C4C2418yes—
766C2×C4⋊C4C2418yes—
767C2×C4⋊C4C2418yes—
768C2×C4⋊C4C2414yes—
769C2×C4⋊C4C2418yes—
770C2×C4⋊C4C2414yes—
771C2×C4⋊C4C2414yes—
772C2×C4⋊C4C2414yes—
773C2×C4⋊C4C2414yes—
774C2×C4⋊C4C2414yes—
775C2×C4⋊C4C2411yescharacteristic
776C2×C4⋊C4C2411yescharacteristic
777C2×C4⋊C4C2412yes—
778C2×C4⋊C4C2412yes—
779C2×C22⋊C4C2414yes—
780C2×C22⋊C4C2414yes—
781C2×C22⋊C4C2414yes—
782C2×C22⋊C4C2414yes—
783C2×C22⋊C4C2412yes—
784C2×C22⋊C4C2412yes—
785C2×C22⋊C4C2414yes—
786C2×C22⋊C4C2414yes—
787C2×C22⋊C4C2414yes—
788C2×C22⋊C4C2414yes—
789C2×C22⋊C4C2414yes—
790C2×C22⋊C4C2414yes—
791C2×C22⋊C4C2414yes—
792C2×C22⋊C4C2418yes—
793C2×C22⋊C4C2418yes—
794C2×C22⋊C4C2418yes—
795C2×C22⋊C4C2418yes—
796C2×C22⋊C4C2418yes—
797C2×C22⋊C4C2418yes—
798C2×C22⋊C4C2418yes—
799C2×C22⋊C4C2418yes—
800C2×C22⋊C4C2418yes—
801C2×C22⋊C4C2418yes—
802C2×C22⋊C4C2412yes—
803C2×C22⋊C4C2412yes—
804C2×C22⋊C4C2412yes—
805C2×C42—28no—
806C2×C42—216no—
807C2×C42—82no—
808C2×C42C2×D418yes—
809C2×C42C2×D4116yes—
810C2×C42C2412yes—
811C2×C42C2414yes—
812C2×C42C2412yes—
813C2×C42C2412yes—
814C2×C42C2414yes—
815C2×C42C2414yes—
816C2×C42C2414yes—
817C2×C42C2414yes—
818C2×C42C2412yes—
819C2×C42C2412yes—
820C2×C42C2412yes—
821C2×C42C2412yes—
822C2×C42C2414yes—
823C2×C42C2414yes—
824C2×C42C2414yes—
825C2×C42C2412yes—
826C2×C42C2412yes—
827C2×C42C2411yescharacteristic
828C2×C42C2412yes—
829C2×C42C2412yes—
830C2×C42C2411yescharacteristic
831C2×C42C2411yescharacteristic
832C2×C42C2411yescharacteristic
833#95C2414yes—
834#95C2414yes—
835#95C2418yes—
836#95C2418yes—
837#95C2418yes—
838#95C2418yes—
839#95C2412yes—
840#95C2412yes—
841#95C2414yes—
842#95C2418yes—
843#95C2418yes—
844#95C2418yes—
845#95C2414yes—
846#95C2414yes—
847#95C2418yes—
848#95C2414yes—
849#95C2414yes—
850#95C2414yes—
851#95C2414yes—
852#95C2414yes—
853#95C2414yes—
854#95C2418yes—
855#95C2418yes—
856#95C2418yes—
857#95C2418yes—
858#95C2418yes—
859#95C2418yes—
860#95C2418yes—
861#95C2418yes—
862C24C2514yes—
863C24C2512yes—
864C24C2511yescharacteristic
865#41—232no—
866#41—432no—
867#41—432no—
868C2×Q8—22no—
869C2×Q8—24no—
870C2×Q8—22no—
871C2×Q8—24no—
872C2×Q8—28no—
873C2×Q8—28no—
874C2×Q8—24no—
875C2×Q8—24no—
876C2×Q8—24no—
877C2×Q8—24no—
878C2×Q8—24no—
879C2×Q8—24no—
880C2×Q8—24no—
881C2×Q8—42no—
882C2×Q8—42no—
883C2×Q8—48no—
884C2×Q8—44no—
885C2×Q8—42no—
886C2×Q8—44no—
887C2×Q8—44no—
888C2×Q8—42no—
889C2×Q8—416no—
890C2×Q8C22×D414yes—
891C2×D4—28no—
892C2×D4—28no—
893C2×D4—28no—
894C2×D4—28no—
895C2×D4—28no—
896C2×D4—28no—
897C2×D4—24no—
898C2×D4—24no—
899C2×D4—24no—
900C2×D4—24no—
901C2×D4—24no—
902C2×D4—24no—
903C2×D4—28no—
904C2×D4—44no—
905C2×D4—44no—
906C2×D4—44no—
907C2×D4—42no—
908C2×D4—42no—
909C2×D4—44no—
910C2×D4C22×D418yes—
911C2×D4C22×D414yes—
912C22×C4—28no—
913C22×C4—24no—
914C22×C4—28no—
915C22×C4—24no—
916C22×C4—28no—
917C22×C4—28no—
918C22×C4—24no—
919C22×C4—24no—
920C22×C4—28no—
921C22×C4—28no—
922C22×C4—28no—
923C22×C4—28no—
924C22×C4—24no—
925C22×C4—28no—
926C22×C4—28no—
927C22×C4—41no—
928C22×C4—44no—
929C22×C4—44no—
930C22×C4—42no—
931C22×C4—42no—
932C22×C4—41no—
933C22×C4—42no—
934C22×C4—42no—
935C22×C4—44no—
936C22×C4—44no—
937C22×C4—44no—
938C22×C4—42no—
939C22×C4—42no—
940C22×C4—44no—
941C22×C4—48no—
942C22×C4—44no—
943C22×C4—44no—
944C22×C4—42no—
945C22×C4—44no—
946C22×C4—42no—
947C22×C4C22×D418yes—
948C22×C4C22×D414yes—
949C22×C4C22×D414yes—
950C22×C4C22×D418yes—
951C22×C4C22×D418yes—
952C22×C4C22×D414yes—
953C22×C42−1+418yes—
954C22×C4C2514yes—
955C22×C4C2514yes—
956C22×C4C2518yes—
957C22×C4C2514yes—
958C22×C4C2512yes—
959C22×C4C2512yes—
960C22×C4C2512yes—
961C22×C4C2512yes—
962C22×C4C2512yes—
963C22×C4C2514yes—
964C22×C4C2512yes—
965C22×C4C2512yes—
966C22×C4C2514yes—
967C22×C4C2512yes—
968C22×C4C2511yescharacteristic
969C22×C4C2511yescharacteristic
970C22×C4C2511yescharacteristic
971C22×C4C2512yes—
972C22×C4C2512yes—
973C22×C4C2511yescharacteristic
974C22×C4C2512yes—
975C22×C4C2511yescharacteristic
976C22×C4C2511yescharacteristic
977C4⋊C4—22no—
978C4⋊C4—24no—
979C4⋊C4—22no—
980C4⋊C4—24no—
981C4⋊C4—28no—
982C4⋊C4—24no—
983C4⋊C4—28no—
984C4⋊C4—24no—
985C4⋊C4—24no—
986C4⋊C4—22no—
987C4⋊C4—28no—
988C4⋊C4—28no—
989C4⋊C4—24no—
990C4⋊C4—24no—
991C4⋊C4—24no—
992C4⋊C4—22no—
993C4⋊C4—24no—
994C4⋊C4—24no—
995C4⋊C4—24no—
996C4⋊C4—28no—
997C4⋊C4—28no—
998C4⋊C4—28no—
999C4⋊C4—28no—
1000C4⋊C4—28no—
1001C4⋊C4—28no—
1002C4⋊C4—22no—
1003C4⋊C4—22no—
1004C4⋊C4—28no—
1005C4⋊C4—24no—
1006C4⋊C4—28no—
1007C4⋊C4—28no—
1008C4⋊C4—24no—
1009C4⋊C4—28no—
1010C4⋊C4—24no—
1011C4⋊C4—24no—
1012C4⋊C4—28no—
1013C4⋊C4—28no—
1014C4⋊C4—24no—
1015C4⋊C4—24no—
1016C4⋊C4—28no—
1017C4⋊C4—28no—
1018C4⋊C4—24no—
1019C4⋊C4—24no—
1020C4⋊C4—216no—
1021C4⋊C4—28no—
1022C4⋊C4—28no—
1023C4⋊C4—48no—
1024C4⋊C4—48no—
1025C4⋊C4—48no—
1026C4⋊C4—44no—
1027C4⋊C4—44no—
1028C4⋊C4—48no—
1029C4⋊C4—48no—
1030C4⋊C4—44no—
1031C4⋊C4—44no—
1032C4⋊C4—44no—
1033C4⋊C4—44no—
1034C4⋊C4C22×D414yes—
1035C4⋊C4C22×D414yes—
1036C4⋊C4C22×D418yes—
1037C4⋊C4C22×D418yes—
1038C22⋊C4—28no—
1039C22⋊C4—28no—
1040C22⋊C4—28no—
1041C22⋊C4—24no—
1042C22⋊C4—24no—
1043C22⋊C4—28no—
1044C22⋊C4—28no—
1045C22⋊C4—28no—
1046C22⋊C4—28no—
1047C22⋊C4—28no—
1048C22⋊C4—28no—
1049C22⋊C4—28no—
1050C22⋊C4—28no—
1051C22⋊C4—48no—
1052C22⋊C4—48no—
1053C22⋊C4—48no—
1054C22⋊C4—48no—
1055C22⋊C4—48no—
1056C22⋊C4—48no—
1057C22⋊C4—48no—
1058C22⋊C4—48no—
1059C22⋊C4—48no—
1060C22⋊C4—48no—
1061C22⋊C4C22×D418yes—
1062C22⋊C4C22×D418yes—
1063C22⋊C4C22×D418yes—
1064C42—24no—
1065C42—24no—
1066C42—28no—
1067C42—28no—
1068C42—24no—
1069C42—24no—
1070C42—28no—
1071C42—28no—
1072C42—24no—
1073C42—24no—
1074C42—28no—
1075C42—44no—
1076C42—44no—
1077C42—42no—
1078C42—42no—
1079C42—44no—
1080C42C22×D418yes—
1081C42C22×D414yes—
1082C42C22×D418yes—
1083C42C22×D414yes—
1084C42C22×D418yes—
1085C42C22×D414yes—
1086C42C22×D414yes—
1087C23—22no—
1088C23—21no—
1089C23—21no—
1090C23—24no—
1091C23—24no—
1092C23—22no—
1093C23—22no—
1094C23—24no—
1095C23—24no—
1096C23—24no—
1097C23—24no—
1098C23—24no—
1099C23—24no—
1100C23—24no—
1101C23C23×D414yes—
1102C23C23×D412yes—
1103C23C2×2−1+414yes—
1104C23C2611yescharacteristic
1105Q8—28no—
1106Q8—28no—
1107Q8—48no—
1108Q8—44no—
1109Q8—48no—
1110Q8—88no—
1111Q8—84no—
1112Q8—88no—
1113Q8—84no—
1114D4—216no—
1115D4—28no—
1116D4—416no—
1117D4—48no—
1118D4—416no—
1119D4—48no—
1120D4—84no—
1121D4—88no—
1122C2×C4—22no—
1123C2×C4—24no—
1124C2×C4—22no—
1125C2×C4—24no—
1126C2×C4—22no—
1127C2×C4—22no—
1128C2×C4—21no—
1129C2×C4—21no—
1130C2×C4—22no—
1131C2×C4—21no—
1132C2×C4—22no—
1133C2×C4—21no—
1134C2×C4—216no—
1135C2×C4—22no—
1136C2×C4—22no—
1137C2×C4—22no—
1138C2×C4—22no—
1139C2×C4—24no—
1140C2×C4—22no—
1141C2×C4—24no—
1142C2×C4—22no—
1143C2×C4—22no—
1144C2×C4—24no—
1145C2×C4—24no—
1146C2×C4—24no—
1147C2×C4—28no—
1148C2×C4—24no—
1149C2×C4—24no—
1150C2×C4—24no—
1151C2×C4—24no—
1152C2×C4—28no—
1153C2×C4—28no—
1154C2×C4—24no—
1155C2×C4—24no—
1156C2×C4—22no—
1157C2×C4—22no—
1158C2×C4—28no—
1159C2×C4—24no—
1160C2×C4—22no—
1161C2×C4—22no—
1162C2×C4—24no—
1163C2×C4—22no—
1164C2×C4—22no—
1165C2×C4—24no—
1166C2×C4—24no—
1167C2×C4—22no—
1168C2×C4—22no—
1169C2×C4—22no—
1170C2×C4—22no—
1171C2×C4—48no—
1172C2×C4—44no—
1173C2×C4—44no—
1174C2×C4—48no—
1175C2×C4—416no—
1176C2×C4—48no—
1177C2×C4—416no—
1178C2×C4—416no—
1179C2×C4—88no—
1180C2×C4—84no—
1181C2×C4—88no—
1182C2×C4—84no—
1183C2×C4—84no—
1184C2×C4—88no—
1185C2×C4#536116yes—
1186C2×C4C23×D414yes—
1187C2×C4C23×D414yes—
1188C2×C4C23×D414yes—
1189C2×C4C23×D412yes—
1190C2×C4C23×D412yes—
1191C2×C4C23×D412yes—
1192C2×C4C23×D412yes—
1193C2×C4C23×D412yes—
1194C2×C4C23×D412yes—
1195C2×C4C2×2−1+414yes—
1196C2×C4C2×2−1+414yes—
1197C2×C4#58514yes—
1198C22—22no—
1199C22—22no—
1200C22—24no—
1201C22—24no—
1202C22—24no—
1203C22—24no—
1204C22—24no—
1205C22—44no—
1206C22—44no—
1207C22—44no—
1208C22—44no—
1209C22—44no—
1210C22—44no—
1211C22—44no—
1212C22—44no—
1213C22—44no—
1214C22C2×#53614yes—
1215C22C24×D411yescharacteristic
1216C22C22×2−1+412yes—
1217C22C2×#58512yes—
1218C22H(7,𝔽2)11yescharacteristic
1219C222−1+611yescharacteristic
1220C4—22no—
1221C4—24no—
1222C4—24no—
1223C4—22no—
1224C4—22no—
1225C4—24no—
1226C4—22no—
1227C4—24no—
1228C4—42no—
1229C4—44no—
1230C4—42no—
1231C4—42no—
1232C4—42no—
1233C4—42no—
1234C4—44no—
1235C4—42no—
1236C4—42no—
1237C4—44no—
1238C4—48no—
1239C4—44no—
1240C4—44no—
1241C4C2×#53614yes—
1242C4C2×#53614yes—
1243C2—24no—
1244C2—44no—
1245C2—84no—
1246C2C22×#53611yescharacteristic
1247C2#6281111yescharacteristic
1248C2#6285311yescharacteristic
1249C2#6292612yes—
1250C2#6295612yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#3480C2
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. #42886C2semidirect
4. #42811C2semidirect
5. #42676C2semidirect
6. #42479C2semidirect
7. #41406C2semidirect
8. #40589C2semidirect
9. #39951C2semidirect
10. #39949C2semidirect
11. #38421C2semidirect
12. #37560C2semidirect
13. #37549C2semidirect
14. #37281C2semidirect
15. #37279C2semidirect
16. #35517C2semidirect
17. #35517C2semidirect
18. #35341C2semidirect
19. #35297C2semidirect
20. #35257C2semidirect
21. #35257C2semidirect
22. #35180C2semidirect
23. #35138C2semidirect
24. #34953C2semidirect
25. C2×#2584C2semidirect
26. #34060C2semidirect

Maximal subgroups

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

subgroupindex
C2×#35042
C2×#34802
#428862
#428112
#426762
#424792
#414062
#405892
#399512
#399492
#384212
#375602
#375492
#372812
#372792
#355172
#353412
#352972
#352572
#351802
#351382
#349532
C2×#25842
#340602