Finite Group Databasebeta

← #7647342

Subgroups — #7647342

Order 512.

6910 conjugacy classes of subgroups.

The subgroup lattice has 1386 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3515C211yesmaximal, characteristic, complemented
2C2×#3483C211yesmaximal, characteristic, complemented
3#42970C214yesmaximal, complemented
4#42927C214yesmaximal, complemented
5#42177C218yesmaximal, complemented
6#39619C211yesmaximal, characteristic, complemented
7#39617C211yesmaximal, characteristic, complemented
8#39491C211yesmaximal, characteristic, complemented
9#39489C211yesmaximal, characteristic, complemented
10#39174C211yesmaximal, characteristic, complemented
11#39169C211yesmaximal, characteristic, complemented
12#38956C211yesmaximal, characteristic, complemented
13#38952C211yesmaximal, characteristic, complemented
14#38093C212yesmaximal, complemented
15#38089C212yesmaximal, complemented
16#37871C212yesmaximal, complemented
17#37869C212yesmaximal, complemented
18#37616C212yesmaximal, complemented
19#37539C212yesmaximal, complemented
20#37234C218yesmaximal, complemented
21#35600C214yesmaximal, complemented
22#35333C212yesmaximal, complemented
23#35298C211yesmaximal, characteristic, complemented
24#35238C211yesmaximal, characteristic, complemented
25#35211C212yesmaximal, complemented
26#35205C214yesmaximal, complemented
27#34947C211yesmaximal, characteristic, complemented
28#34910C211yesmaximal, characteristic, complemented
29#34060C211yesmaximal, characteristic, complemented
30#3515—216no—
31#3483—216no—
32C2×Q82C2211yescharacteristic
33C2×#557C2211yescharacteristic
34C2×#555C2211yescharacteristic
35C2×#555C2214yes—
36C2×#555C2212yes—
37C2×#555C2212yes—
38C2×#554C2211yescharacteristic
39C2×#554C2211yescharacteristic
40C2×#553C2212yes—
41C2×#552C2214yes—
42C2×#552C2212yes—
43C2×#552C2212yes—
44C2×#550C2211yescharacteristic
45C2×#550C2211yescharacteristic
46C2×#550C2212yes—
47C2×#550C2212yes—
48C2×#547C2211yescharacteristic
49C2×#547C2212yes—
50C2×#541C2212yes—
51C2×#539C2214yes—
52C2×#533C2211yescharacteristic
53C2×#532C2212yes—
54C2×#532C2214yes—
55C2×#532C2212yes—
56C2×#532C2211yescharacteristic
57C2×#529C2211yescharacteristic
58C2×#529C2212yes—
59C22×#125C2212yes—
60C2×#520C2212yes—
61C2×C4×#41C2212yes—
62C2×C4×#41C2211yescharacteristic
63C2×C4×#41C2212yes—
64C2×C4×#41C2211yescharacteristic
65#2868C2211yescharacteristic
66#2862C2211yescharacteristic
67#2858C2211yescharacteristic
68#2858C2211yescharacteristic
69#2856C2212yes—
70#2852C2218yes—
71#2851C2218yes—
72#2850C2212yes—
73#2820C2218yes—
74#2813C2218yes—
75#2715C2218yes—
76#2713C2218yes—
77#2711C2218yes—
78#2710C2218yes—
79#2709C2218yes—
80#2708C2218yes—
81#2703C2218yes—
82#2691C2218yes—
83#2677C2218yes—
84#2676C2218yes—
85#2674C2218yes—
86#2673C2218yes—
87#2672C2218yes—
88#2672C2218yes—
89#2671C2218yes—
90#2671C2218yes—
91#2662C2214yes—
92#2660C2212yes—
93#2660C2212yes—
94#2641C2212yes—
95#2641C2212yes—
96#2636C2218yes—
97#2633C2218yes—
98#2630C2218yes—
99#2629C2218yes—
100#2620C2212yes—
101#2620C2212yes—
102#2620C2214yes—
103#2620C2218yes—
104#2619C2212yes—
105#2619C2212yes—
106#2618C2218yes—
107#2609C2218yes—
108#2602C2214yes—
109#2601C2214yes—
110#2600C2218yes—
111#2579C2218yes—
112#2579C2218yes—
113#2568C2211yescharacteristic
114#2568C2212yes—
115#2567C2211yescharacteristic
116#2567C2211yescharacteristic
117#2566C2212yes—
118#2566C2212yes—
119#2566C2212yes—
120#2566C2212yes—
121#2566C2211yescharacteristic
122#2566C2212yes—
123#2566C2212yes—
124#2565C2211yescharacteristic
125#2565C2212yes—
126#2565C2212yes—
127#2565C2212yes—
128#2564C2214yes—
129#2563C2211yescharacteristic
130#2563C2211yescharacteristic
131#2548C2211yescharacteristic
132#2548C2212yes—
133#2545C2211yescharacteristic
134#2545C2214yes—
135#2544C2211yescharacteristic
136#2544C2212yes—
137#2542C2211yescharacteristic
138#2542C2212yes—
139#2541C2211yescharacteristic
140#2541C2212yes—
141#2504C2212yes—
142#2504C2212yes—
143#2501C2212yes—
144#2501C2212yes—
145#2500C2212yes—
146#2500C2211yescharacteristic
147#2500C2212yes—
148#2500C2212yes—
149#2499C2212yes—
150#2499C2211yescharacteristic
151#2479C2218yes—
152#2476C2218yes—
153#2475C2218yes—
154#2474C2218yes—
155#2467C2218yes—
156#2464C2218yes—
157#2461C2218yes—
158#2460C2218yes—
159#2454C2214yes—
160#2451C2214yes—
161#2446C2214yes—
162#2445C2214yes—
163#2441C2214yes—
164#2440C2214yes—
165#2432C2214yes—
166#2432C2212yes—
167#2432C2211yescharacteristic
168#2432C2214yes—
169#2431C2214yes—
170#2431C2212yes—
171#2431C2211yescharacteristic
172#2430C2214yes—
173#2427C2214yes—
174#2426C2214yes—
175#2423C2214yes—
176#2422C2214yes—
177#2417C2214yes—
178#2416C2214yes—
179#2416C2214yes—
180#2415C2214yes—
181#2407C2214yes—
182#2407C2214yes—
183#2407C2218yes—
184#2406C2218yes—
185#2396C2214yes—
186#2392C2214yes—
187#2328C2212yes—
188#2327C2212yes—
189#2326C2212yes—
190#2326C2214yes—
191#2326C2212yes—
192#2324C2214yes—
193#2320C2212yes—
194#2319C2212yes—
195#2318C2214yes—
196#2317C2212yes—
197#2317C2212yes—
198#2317C2212yes—
199#2314C2214yes—
200#2311C2212yes—
201#2311C2212yes—
202#2311C2212yes—
203C4×C4⋊Q8C2211yescharacteristic
204C4×#127C2211yescharacteristic
205C4×#124C2211yescharacteristic
206C4×#124C2211yescharacteristic
207C4×C22⋊Q8C2214yes—
208#2297C2212yes—
209#2295C2211yescharacteristic
210#2295C2211yescharacteristic
211#2293C2211yescharacteristic
212#2293C2211yescharacteristic
213#2290C2212yes—
214#2290C2212yes—
215#2290C2214yes—
216#2285C2212yes—
217#2285C2212yes—
218#2283C2212yes—
219C4×#117C2211yescharacteristic
220C2×C4×C4⋊C4C2211yescharacteristic
221C22×#41C2312yes—
222C22×#41C2311yescharacteristic
223C22×#41C2312yes—
224C22×#41C2312yes—
225C22×#41C2314yes—
226C22×#41C2312yes—
227C22×#41C2311yescharacteristic
228Q82—28no—
229#557—28no—
230#555—28no—
231#555—216no—
232#555—232no—
233#555—216no—
234#554—28no—
235#554—28no—
236#553—216no—
237#552—216no—
238#552—232no—
239#552—216no—
240#550—216no—
241#550—28no—
242#550—28no—
243#550—216no—
244#547—216no—
245#547—28no—
246#541—216no—
247#539—232no—
248#533—28no—
249#532—216no—
250#532—232no—
251#532—216no—
252#532—28no—
253C2×C4⋊Q8C2311yescharacteristic
254C2×C4⋊Q8C2311yescharacteristic
255C2×C4⋊Q8C2311yescharacteristic
256C2×C4⋊Q8C2311yescharacteristic
257C2×C4⋊Q8C2312yes—
258C2×C4⋊Q8C2314yes—
259C2×C4⋊Q8C2312yes—
260C2×C4⋊Q8C2312yes—
261C2×C4⋊Q8C2314yes—
262C2×#127C2311yescharacteristic
263C2×#127C2312yes—
264C2×#127C2314yes—
265C2×#127C2312yes—
266C2×#127C2311yescharacteristic
267C2×#127C2312yes—
268#529—216no—
269#529—28no—
270C2×#126C2314yes—
271C2×#126C2312yes—
272C2×#126C2314yes—
273C2×#126C2314yes—
274C2×#125—216no—
275C2×#125C2314yes—
276C2×#125C2311yescharacteristic
277C2×#125C2312yes—
278C2×#125C2312yes—
279C2×#125C2312yes—
280C2×#125C2314yes—
281C2×#125C2314yes—
282C2×#125C2312yes—
283C2×#125C2314yes—
284C2×#124C2314yes—
285C2×#124C2311yescharacteristic
286C2×#124C2312yes—
287C2×#124C2311yescharacteristic
288C2×#124C2314yes—
289C2×#124C2314yes—
290C2×#124C2314yes—
291C2×#124C2312yes—
292C2×#124C2314yes—
293C2×#124C2311yescharacteristic
294C2×#124C2314yes—
295C2×#123C2312yes—
296C2×#123C2314yes—
297C2×#123C2314yes—
298C2×#123C2314yes—
299C2×#123C2314yes—
300C2×#123C2318yes—
301C2×#123C2318yes—
302C2×C22⋊Q8C2312yes—
303C2×C22⋊Q8C2311yescharacteristic
304C2×C22⋊Q8C2312yes—
305C2×C22⋊Q8C2312yes—
306C2×C22⋊Q8C2312yes—
307C2×C22⋊Q8C2312yes—
308C2×C22⋊Q8C2314yes—
309C2×C22⋊Q8C2314yes—
310C2×C22⋊Q8C2314yes—
311C2×C22⋊Q8C2318yes—
312C2×#121C2312yes—
313C2×#121C2311yescharacteristic
314C2×#121C2314yes—
315C2×#121C2312yes—
316C2×#121C2312yes—
317C2×#121C2312yes—
318C2×#121C2312yes—
319C2×#121C2312yes—
320C2×#121C2314yes—
321C2×#121C2314yes—
322C2×#121C2314yes—
323C2×#121C2312yes—
324C2×#121C2314yes—
325C2×#121C2314yes—
326C2×#121C2314yes—
327C2×#121C2314yes—
328C2×#121C2318yes—
329C2×#121C2318yes—
330#520—216no—
331C4×#41—216no—
332C4×#41—216no—
333C4×#41—28no—
334C4×#41D4116yescomplemented
335C2×C4×Q8C2311yescharacteristic
336C2×C4×Q8C2311yescharacteristic
337C2×C4×Q8C2311yescharacteristic
338C2×C4×Q8C2312yes—
339C2×C4×Q8C2312yes—
340C2×C4×Q8C2312yes—
341C2×C4×Q8C2312yes—
342C2×C4×Q8C2312yes—
343C2×C4×Q8C2312yes—
344C2×C4×Q8C2311yescharacteristic
345C2×C4×Q8C2311yescharacteristic
346C2×C4×D4C2311yescharacteristic
347C2×C4×D4C2311yescharacteristic
348C2×C4×D4C2312yes—
349C2×C4×D4C2312yes—
350C2×C4×D4C2311yescharacteristic
351C2×C4×D4C2312yes—
352C2×C4×D4C2314yes—
353C2×C4×D4C2314yes—
354C2×C4×D4C2312yes—
355C2×C4×D4C2312yes—
356C2×C4×D4C2314yes—
357C2×C4×D4C2314yes—
358C2×C4×D4C2312yes—
359C2×C4×D4C2312yes—
360C2×C4×D4C2312yes—
361C2×C4×D4C2314yes—
362C2×C4×D4C2312yes—
363C2×C4×D4C2314yes—
364C2×C4×D4C2314yes—
365C2×C4×D4C2312yes—
366C2×C4×D4C2311yescharacteristic
367C2×C4×D4C2311yescharacteristic
368C2×C4×D4C2312yes—
369C2×#117C2312yes—
370C2×#117C2312yes—
371C2×#117C2312yes—
372C2×#117C2314yes—
373C2×#117C2314yes—
374C2×#117C2312yes—
375C2×#117C2314yes—
376C2×#117C2311yescharacteristic
377C2×#117C2314yes—
378C2×#117C2312yes—
379C2×#117C2312yes—
380C2×#117C2312yes—
381C2×#117C2312yes—
382C2×#117C2312yes—
383C2×#117C2311yescharacteristic
384C22×C4⋊C4C2312yes—
385C22×C4⋊C4C2312yes—
386C22×C4⋊C4C2314yes—
387C22×C4⋊C4C2314yes—
388C22×C4⋊C4C2312yes—
389C22×C4⋊C4C2312yes—
390C22×C42C2314yes—
391C22×C42C2312yes—
392C22×C42C2312yes—
393C22×C42C2312yes—
394C22×C42C2311yescharacteristic
395#400C2314yes—
396#400C2318yes—
397#399C2314yes—
398#399C2318yes—
399#399C2318yes—
400#399C2318yes—
401#398C2314yes—
402#398C2318yes—
403#398C2318yes—
404#398C2318yes—
405#398C2318yes—
406#398C2318yes—
407#397C2318yes—
408#397C2318yes—
409#397C2318yes—
410#397C2314yes—
411#396C2314yes—
412#396C2318yes—
413#396C2318yes—
414#396C2318yes—
415#396C2318yes—
416#396C2318yes—
417#396C2318yes—
418#396C2314yes—
419#396C2318yes—
420#396C2318yes—
421#395C2314yes—
422#395C2318yes—
423#395C2318yes—
424#395C2314yes—
425#394C2318yes—
426#394C2318yes—
427#394C2318yes—
428#394C2318yes—
429#394C2314yes—
430#394C2314yes—
431#394C2314yes—
432#394C2318yes—
433#394C2318yes—
434#394C2318yes—
435#394C2318yes—
436#394C2318yes—
437#394C2318yes—
438#394C2318yes—
439#394C2318yes—
440#394C2318yes—
441#394C2318yes—
442#394C2314yes—
443#393C2314yes—
444#393C2314yes—
445#392C2318yes—
446#392C2314yes—
447#392C2318yes—
448#392C2318yes—
449#392C2318yes—
450#392C2314yes—
451#391C2311yescharacteristic
452#391C2311yescharacteristic
453#391C2311yescharacteristic
454#391C2312yes—
455#391C2312yes—
456#391C2312yes—
457#391C2312yes—
458#391C2312yes—
459#391C2318yes—
460#391C2314yes—
461#391C2311yescharacteristic
462#391C2314yes—
463#391C2314yes—
464#390C2311yescharacteristic
465#390C2311yescharacteristic
466#390C2314yes—
467#390C2312yes—
468#390C2312yes—
469#390C2312yes—
470#390C2312yes—
471#390C2312yes—
472#390C2312yes—
473#390C2312yes—
474#390C2312yes—
475#390C2312yes—
476#390C2311yescharacteristic
477#390C2312yes—
478#390C2312yes—
479#390C2318yes—
480#390C2314yes—
481#390C2314yes—
482#390C2314yes—
483#390C2311yescharacteristic
484#390C2318yes—
485#389C2314yes—
486#389C2314yes—
487#389C2314yes—
488#389C2312yes—
489#389C2312yes—
490#389C2312yes—
491#389C2312yes—
492#389C2318yes—
493#389C2318yes—
494#388C2314yes—
495#388C2314yes—
496#388C2314yes—
497#388C2314yes—
498#388C2318yes—
499#388C2318yes—
500#388C2318yes—
501#388C2318yes—
502#388C2318yes—
503#388C2314yes—
504#388C2318yes—
505#388C2314yes—
506#388C2314yes—
507#388C2314yes—
508#387C2318yes—
509#387C2314yes—
510#387C2318yes—
511#387C2318yes—
512#387C2314yes—
513#387C2314yes—
514#387C2314yes—
515#387C2314yes—
516#387C2318yes—
517#387C2318yes—
518#387C2318yes—
519#387C2314yes—
520#386C2318yes—
521#386C2314yes—
522#386C2314yes—
523#386C2318yes—
524#386C2318yes—
525#386C2318yes—
526#386C2318yes—
527#386C2318yes—
528#386C2318yes—
529#386C2318yes—
530#386C2314yes—
531#386C2314yes—
532#386C2318yes—
533#386C2318yes—
534#385C2318yes—
535#385C2318yes—
536#385C2318yes—
537#385C2318yes—
538#385C2318yes—
539#385C2318yes—
540#385C2314yes—
541#385C2314yes—
542#385C2314yes—
543#385C2318yes—
544#385C2318yes—
545#385C2318yes—
546#385C2318yes—
547#385C2318yes—
548#385C2314yes—
549#384C2311yescharacteristic
550#384C2311yescharacteristic
551#384C2312yes—
552#384C2312yes—
553#384C2312yes—
554#384C2312yes—
555#384C2312yes—
556#384C2314yes—
557#384C2314yes—
558#383C2314yes—
559#382C2312yes—
560#382C2312yes—
561#382C2314yes—
562#382C2311yescharacteristic
563#382C2312yes—
564#382C2312yes—
565#382C2312yes—
566#382C2311yescharacteristic
567#382C2314yes—
568#381C2314yes—
569#380C2314yes—
570#380C2314yes—
571#380C2318yes—
572#380C2314yes—
573#380C2314yes—
574#380C2318yes—
575#380C2318yes—
576#380C2314yes—
577C4×C4⋊C4C2314yes—
578C4×C4⋊C4C2311yescharacteristic
579C4×C4⋊C4C2311yescharacteristic
580C4×C4⋊C4C2312yes—
581C4×C4⋊C4C2311yescharacteristic
582C4×C4⋊C4C2312yes—
583C4×C4⋊C4C2312yes—
584C4×C4⋊C4C2311yescharacteristic
585C4×C4⋊C4C2312yes—
586C4×C4⋊C4C2312yes—
587C4×C4⋊C4C2312yes—
588C4×C4⋊C4C2318yes—
589C4×C22⋊C4C2312yes—
590C4×C22⋊C4C2314yes—
591C4×C22⋊C4C2314yes—
592C4×C22⋊C4C2318yes—
593C4×C22⋊C4C2311yescharacteristic
594C4×C22⋊C4C2312yes—
595C4×C22⋊C4C2311yescharacteristic
596C4×C22⋊C4C2312yes—
597#376C2312yes—
598#376C2312yes—
599#376C2312yes—
600C2×#95C2312yes—
601C43C2311yescharacteristic
602C43C2311yescharacteristic
603C2×#41—28no—
604C2×#41—28no—
605C2×#41—24no—
606C2×#41—28no—
607C2×#41—28no—
608C2×#41—24no—
609C2×#41—216no—
610C2×#41—28no—
611C2×#41—42no—
612C2×#41—44no—
613C2×#41—44no—
614C2×#41—48no—
615C2×#41—48no—
616C2×#41—84no—
617C2×#41—88no—
618C2×#41C2×D418yes—
619C22×Q8C2411yescharacteristic
620C22×Q8C2412yes—
621C22×Q8C2411yescharacteristic
622C22×Q8C2411yescharacteristic
623C22×Q8C2412yes—
624C22×Q8C2414yes—
625C22×Q8C2412yes—
626C22×D4C2411yescharacteristic
627C22×D4C2412yes—
628C22×D4C2411yescharacteristic
629C22×D4C2412yes—
630C22×D4C2412yes—
631C22×D4C2414yes—
632C22×D4C2411yescharacteristic
633C22×D4C2414yes—
634C22×D4C2414yes—
635C22×D4C2412yes—
636C22×D4C2414yes—
637C22×D4C2414yes—
638C22×D4C2414yes—
639C22×D4C2414yes—
640C22×D4C2412yes—
641C22×D4C2414yes—
642C22×D4C2418yes—
643C22×D4C2412yes—
644C23×C4C2412yes—
645C23×C4C2412yes—
646C23×C4C2412yes—
647C23×C4C2414yes—
648C23×C4C2411yescharacteristic
649C23×C4C2412yes—
650C23×C4C2411yescharacteristic
651C23×C4C2414yes—
652C23×C4C2414yes—
653C23×C4C2414yes—
654C23×C4C2414yes—
655C23×C4C2412yes—
656C23×C4C2414yes—
657C23×C4C2414yes—
658C23×C4C2412yes—
659C23×C4C2412yes—
660C23×C4C2411yescharacteristic
661C4⋊Q8—28no—
662C4⋊Q8—24no—
663C4⋊Q8—28no—
664C4⋊Q8—216no—
665C4⋊Q8—28no—
666C4⋊Q8—24no—
667C4⋊Q8—24no—
668C4⋊Q8—24no—
669C4⋊Q8—84no—
670#127—28no—
671#127—216no—
672#127—28no—
673#127—24no—
674#127—44no—
675#127—42no—
676#126—216no—
677#126—216no—
678#126—216no—
679#126—28no—
680#125—216no—
681#125—216no—
682#125—28no—
683#125—24no—
684#125—28no—
685#125—216no—
686#125—216no—
687#125—28no—
688#125—28no—
689#124—24no—
690#124—216no—
691#124—216no—
692#124—216no—
693#124—24no—
694#124—216no—
695#124—28no—
696#124—44no—
697#124—42no—
698#124—48no—
699#124—84no—
700#123—216no—
701#123—28no—
702#123—216no—
703#123—216no—
704#123—216no—
705#123—88no—
706#123—88no—
707C22⋊Q8—28no—
708C22⋊Q8—24no—
709C22⋊Q8—28no—
710C22⋊Q8—28no—
711C22⋊Q8—28no—
712C22⋊Q8—216no—
713C22⋊Q8—28no—
714C22⋊Q8—216no—
715C22⋊Q8—48no—
716C22⋊Q8—88no—
717#121—28no—
718#121—216no—
719#121—216no—
720#121—28no—
721#121—24no—
722#121—28no—
723#121—28no—
724#121—28no—
725#121—28no—
726#121—216no—
727#121—28no—
728#121—216no—
729#121—216no—
730#121—216no—
731#121—216no—
732#121—48no—
733#121—88no—
734#121—88no—
735C4×Q8—28no—
736C4×Q8—28no—
737C4×Q8—24no—
738C4×Q8—28no—
739C4×Q8—24no—
740C4×Q8—28no—
741C4×Q8—28no—
742C4×Q8—24no—
743C4×Q8—28no—
744C4×Q8C2×D418yes—
745C4×Q8C2×D418yes—
746C4×D4—28no—
747C4×D4—216no—
748C4×D4—28no—
749C4×D4—28no—
750C4×D4—216no—
751C4×D4—216no—
752C4×D4—28no—
753C4×D4—28no—
754C4×D4—216no—
755C4×D4—216no—
756C4×D4—28no—
757C4×D4—216no—
758C4×D4—28no—
759C4×D4—24no—
760C4×D4—28no—
761C4×D4—24no—
762C4×D4—24no—
763C4×D4—28no—
764C4×D4—48no—
765C4×D4C2×D418yes—
766C4×D4C2×D4116yes—
767C4×D4C2×D418yes—
768C4×D4C2×D4116yes—
769#117—28no—
770#117—24no—
771#117—28no—
772#117—28no—
773#117—216no—
774#117—216no—
775#117—216no—
776#117—28no—
777#117—28no—
778#117—216no—
779#117—44no—
780#117—44no—
781#117—44no—
782#117C2×D418yes—
783#117C2×D4116yes—
784C2×C4⋊C4—216no—
785C2×C4⋊C4—28no—
786C2×C4⋊C4—216no—
787C2×C4⋊C4—28no—
788C2×C4⋊C4—28no—
789C2×C4⋊C4—44no—
790C2×C4⋊C4C2414yes—
791C2×C4⋊C4C2412yes—
792C2×C4⋊C4C2411yescharacteristic
793C2×C4⋊C4C2412yes—
794C2×C4⋊C4C2411yescharacteristic
795C2×C4⋊C4C2412yes—
796C2×C4⋊C4C2412yes—
797C2×C4⋊C4C2414yes—
798C2×C4⋊C4C2412yes—
799C2×C4⋊C4C2414yes—
800C2×C4⋊C4C2414yes—
801C2×C4⋊C4C2412yes—
802C2×C4⋊C4C2414yes—
803C2×C4⋊C4C2414yes—
804C2×C4⋊C4C2412yes—
805C2×C4⋊C4C2414yes—
806C2×C4⋊C4C2414yes—
807C2×C4⋊C4C2411yescharacteristic
808C2×C4⋊C4C2412yes—
809C2×C4⋊C4C2412yes—
810C2×C4⋊C4C2412yes—
811C2×C4⋊C4C2412yes—
812C2×C4⋊C4C2411yescharacteristic
813C2×C4⋊C4C2414yes—
814C2×C4⋊C4C2412yes—
815C2×C4⋊C4C2414yes—
816C2×C4⋊C4C2414yes—
817C2×C4⋊C4C2412yes—
818C2×C4⋊C4C2412yes—
819C2×C4⋊C4C2414yes—
820C2×C4⋊C4C2414yes—
821C2×C4⋊C4C2414yes—
822C2×C4⋊C4C2412yes—
823C2×C4⋊C4C2412yes—
824C2×C4⋊C4C2414yes—
825C2×C4⋊C4C2414yes—
826C2×C4⋊C4C2414yes—
827C2×C4⋊C4C2414yes—
828C2×C4⋊C4C2418yes—
829C2×C4⋊C4C2414yes—
830C2×C4⋊C4C2418yes—
831C2×C4⋊C4C2418yes—
832C2×C4⋊C4C2418yes—
833C2×C4⋊C4C2414yes—
834C2×C4⋊C4C2418yes—
835C2×C4⋊C4C2411yescharacteristic
836C2×C4⋊C4C2411yescharacteristic
837C2×C4⋊C4C2412yes—
838C2×C4⋊C4C2412yes—
839C2×C22⋊C4C2412yes—
840C2×C22⋊C4C2412yes—
841C2×C22⋊C4C2414yes—
842C2×C22⋊C4C2414yes—
843C2×C22⋊C4C2414yes—
844C2×C22⋊C4C2412yes—
845C2×C22⋊C4C2412yes—
846C2×C22⋊C4C2414yes—
847C2×C22⋊C4C2414yes—
848C2×C22⋊C4C2414yes—
849C2×C22⋊C4C2412yes—
850C2×C22⋊C4C2414yes—
851C2×C22⋊C4C2412yes—
852C2×C22⋊C4C2414yes—
853C2×C22⋊C4C2414yes—
854C2×C22⋊C4C2414yes—
855C2×C22⋊C4C2412yes—
856C2×C22⋊C4C2412yes—
857C2×C22⋊C4C2414yes—
858C2×C22⋊C4C2412yes—
859C2×C22⋊C4C2412yes—
860C2×C22⋊C4C2414yes—
861C2×C22⋊C4C2414yes—
862C2×C22⋊C4C2414yes—
863C2×C22⋊C4C2414yes—
864C2×C22⋊C4C2418yes—
865C2×C22⋊C4C2418yes—
866C2×C22⋊C4C2418yes—
867C2×C22⋊C4C2418yes—
868C2×C22⋊C4C2418yes—
869C2×C22⋊C4C2414yes—
870C2×C22⋊C4C2418yes—
871C2×C22⋊C4C2414yes—
872C2×C22⋊C4C2414yes—
873C2×C22⋊C4C2414yes—
874C2×C22⋊C4C2418yes—
875C2×C22⋊C4C2414yes—
876C2×C22⋊C4C2418yes—
877C2×C22⋊C4C2418yes—
878C2×C22⋊C4C2418yes—
879C2×C22⋊C4C2412yes—
880C2×C22⋊C4C2412yes—
881C2×C22⋊C4C2412yes—
882C2×C42—28no—
883C2×C42—216no—
884C2×C42—44no—
885C2×C42C2×D4116yes—
886C2×C42C2×D418yes—
887C2×C42C2412yes—
888C2×C42C2414yes—
889C2×C42C2414yes—
890C2×C42C2414yes—
891C2×C42C2411yescharacteristic
892C2×C42C2411yescharacteristic
893C2×C42C2412yes—
894C2×C42C2412yes—
895C2×C42C2412yes—
896C2×C42C2412yes—
897C2×C42C2412yes—
898C2×C42C2412yes—
899C2×C42C2412yes—
900C2×C42C2414yes—
901C2×C42C2411yescharacteristic
902C2×C42C2411yescharacteristic
903C2×C42C2412yes—
904C2×C42C2412yes—
905C2×C42C2414yes—
906C2×C42C2412yes—
907C2×C42C2411yescharacteristic
908C2×C42C2411yescharacteristic
909C2×C42C2412yes—
910C2×C42C2411yescharacteristic
911C2×C42C2411yescharacteristic
912C2×C42C2412yes—
913#95C2414yes—
914#95C2412yes—
915#95C2412yes—
916#95C2412yes—
917#95C2412yes—
918#95C2412yes—
919#95C2412yes—
920#95C2414yes—
921#95C2414yes—
922#95C2414yes—
923#95C2414yes—
924#95C2414yes—
925#95C2418yes—
926#95C2418yes—
927#95C2414yes—
928#95C2414yes—
929#95C2414yes—
930#95C2414yes—
931#95C2414yes—
932#95C2418yes—
933#95C2414yes—
934#95C2414yes—
935#95C2414yes—
936#95C2418yes—
937#95C2414yes—
938#95C2418yes—
939#95C2418yes—
940#95C2418yes—
941#95C2418yes—
942C24C2512yes—
943C24C2512yes—
944C24C2514yes—
945C24C2512yes—
946C24C2511yescharacteristic
947#41—416no—
948#41—416no—
949#41—432no—
950#41—432no—
951#41—432no—
952#41—832no—
953#41—816no—
954C2×Q8—22no—
955C2×Q8—22no—
956C2×Q8—24no—
957C2×Q8—24no—
958C2×Q8—28no—
959C2×Q8—24no—
960C2×Q8—22no—
961C2×Q8—24no—
962C2×Q8—22no—
963C2×Q8—28no—
964C2×Q8—22no—
965C2×Q8—48no—
966C2×Q8—44no—
967C2×Q8—44no—
968C2×Q8C22×D414yes—
969C2×Q82−1+414yes—
970C2×D4—28no—
971C2×D4—24no—
972C2×D4—28no—
973C2×D4—24no—
974C2×D4—28no—
975C2×D4—28no—
976C2×D4—28no—
977C2×D4—22no—
978C2×D4—28no—
979C2×D4—24no—
980C2×D4—24no—
981C2×D4—22no—
982C2×D4—28no—
983C2×D4—24no—
984C2×D4—22no—
985C2×D4—24no—
986C2×D4—28no—
987C2×D4—22no—
988C2×D4—24no—
989C2×D4—24no—
990C2×D4—28no—
991C2×D4—22no—
992C2×D4—24no—
993C2×D4—22no—
994C2×D4—44no—
995C2×D4—44no—
996C2×D4—42no—
997C2×D4—48no—
998C2×D4—48no—
999C2×D4—44no—
1000C2×D4—44no—
1001C2×D4—44no—
1002C2×D4—48no—
1003C2×D4—48no—
1004C2×D4—48no—
1005C2×D4—48no—
1006C2×D4—44no—
1007C2×D4—44no—
1008C2×D4—48no—
1009C2×D4—48no—
1010C2×D4—48no—
1011C2×D4C22×D414yes—
1012C2×D4C22×D418yes—
1013C22×C4—24no—
1014C22×C4—22no—
1015C22×C4—22no—
1016C22×C4—24no—
1017C22×C4—24no—
1018C22×C4—28no—
1019C22×C4—28no—
1020C22×C4—24no—
1021C22×C4—28no—
1022C22×C4—28no—
1023C22×C4—24no—
1024C22×C4—24no—
1025C22×C4—28no—
1026C22×C4—24no—
1027C22×C4—24no—
1028C22×C4—28no—
1029C22×C4—28no—
1030C22×C4—28no—
1031C22×C4—28no—
1032C22×C4—42no—
1033C22×C4—44no—
1034C22×C4—44no—
1035C22×C4—48no—
1036C22×C4—48no—
1037C22×C4—42no—
1038C22×C4—44no—
1039C22×C4—48no—
1040C22×C4—44no—
1041C22×C4—44no—
1042C22×C4—44no—
1043C22×C4—44no—
1044C22×C4—48no—
1045C22×C4—48no—
1046C22×C4C22×D418yes—
1047C22×C4C22×D414yes—
1048C22×C4C22×D414yes—
1049C22×C4C22×D418yes—
1050C22×C4C22×D418yes—
1051C22×C4C22×D414yes—
1052C22×C4C2514yes—
1053C22×C4C2512yes—
1054C22×C4C2512yes—
1055C22×C4C2512yes—
1056C22×C4C2514yes—
1057C22×C4C2512yes—
1058C22×C4C2512yes—
1059C22×C4C2512yes—
1060C22×C4C2514yes—
1061C22×C4C2512yes—
1062C22×C4C2514yes—
1063C22×C4C2512yes—
1064C22×C4C2514yes—
1065C22×C4C2512yes—
1066C22×C4C2511yescharacteristic
1067C22×C4C2512yes—
1068C22×C4C2511yescharacteristic
1069C22×C4C2511yescharacteristic
1070C22×C4C2512yes—
1071C22×C4C2512yes—
1072C22×C4C2511yescharacteristic
1073C22×C4C2512yes—
1074C22×C4C2511yescharacteristic
1075C22×C4C2511yescharacteristic
1076C4⋊C4—28no—
1077C4⋊C4—24no—
1078C4⋊C4—22no—
1079C4⋊C4—24no—
1080C4⋊C4—22no—
1081C4⋊C4—24no—
1082C4⋊C4—24no—
1083C4⋊C4—28no—
1084C4⋊C4—24no—
1085C4⋊C4—28no—
1086C4⋊C4—28no—
1087C4⋊C4—28no—
1088C4⋊C4—28no—
1089C4⋊C4—28no—
1090C4⋊C4—28no—
1091C4⋊C4—24no—
1092C4⋊C4—22no—
1093C4⋊C4—24no—
1094C4⋊C4—28no—
1095C4⋊C4—24no—
1096C4⋊C4—28no—
1097C4⋊C4—24no—
1098C4⋊C4—24no—
1099C4⋊C4—22no—
1100C4⋊C4—28no—
1101C4⋊C4—24no—
1102C4⋊C4—24no—
1103C4⋊C4—28no—
1104C4⋊C4—28no—
1105C4⋊C4—24no—
1106C4⋊C4—24no—
1107C4⋊C4—44no—
1108C4⋊C4—44no—
1109C4⋊C4—44no—
1110C4⋊C4—42no—
1111C4⋊C4—42no—
1112C4⋊C4—44no—
1113C4⋊C4—44no—
1114C4⋊C4—48no—
1115C4⋊C4—48no—
1116C4⋊C4—44no—
1117C4⋊C4—48no—
1118C4⋊C4—48no—
1119C4⋊C4—44no—
1120C4⋊C4—48no—
1121C4⋊C4C22×D414yes—
1122C4⋊C4C22×D414yes—
1123C4⋊C4C22×D418yes—
1124C4⋊C4C22×D418yes—
1125C22⋊C4—24no—
1126C22⋊C4—28no—
1127C22⋊C4—28no—
1128C22⋊C4—28no—
1129C22⋊C4—24no—
1130C22⋊C4—24no—
1131C22⋊C4—28no—
1132C22⋊C4—24no—
1133C22⋊C4—28no—
1134C22⋊C4—28no—
1135C22⋊C4—28no—
1136C22⋊C4—24no—
1137C22⋊C4—28no—
1138C22⋊C4—24no—
1139C22⋊C4—24no—
1140C22⋊C4—28no—
1141C22⋊C4—28no—
1142C22⋊C4—24no—
1143C22⋊C4—28no—
1144C22⋊C4—44no—
1145C22⋊C4—44no—
1146C22⋊C4—42no—
1147C22⋊C4—42no—
1148C22⋊C4—44no—
1149C22⋊C4—44no—
1150C22⋊C4—48no—
1151C22⋊C4—48no—
1152C22⋊C4—48no—
1153C22⋊C4—48no—
1154C22⋊C4—48no—
1155C22⋊C4—48no—
1156C22⋊C4—44no—
1157C22⋊C4—44no—
1158C22⋊C4—44no—
1159C22⋊C4—44no—
1160C22⋊C4—48no—
1161C22⋊C4—48no—
1162C22⋊C4—48no—
1163C22⋊C4—48no—
1164C22⋊C4—44no—
1165C22⋊C4C22×D418yes—
1166C22⋊C4C22×D418yes—
1167C22⋊C4C22×D418yes—
1168C42—24no—
1169C42—24no—
1170C42—28no—
1171C42—28no—
1172C42—24no—
1173C42—28no—
1174C42—28no—
1175C42—24no—
1176C42—22no—
1177C42—22no—
1178C42—24no—
1179C42—24no—
1180C42—22no—
1181C42—22no—
1182C42—24no—
1183C42—24no—
1184C42—44no—
1185C42—42no—
1186C42—42no—
1187C42C22×D414yes—
1188C42C22×D418yes—
1189C42C22×D414yes—
1190C42C22×D418yes—
1191C42C22×D414yes—
1192C42C22×D418yes—
1193C42C22×D414yes—
1194C23—22no—
1195C23—21no—
1196C23—22no—
1197C23—22no—
1198C23—21no—
1199C23—24no—
1200C23—24no—
1201C23—22no—
1202C23—22no—
1203C23—24no—
1204C23—22no—
1205C23—22no—
1206C23—22no—
1207C23—24no—
1208C23—24no—
1209C23—28no—
1210C23—22no—
1211C23—24no—
1212C23—24no—
1213C23—22no—
1214C23—24no—
1215C23—24no—
1216C23—28no—
1217C23C23×D412yes—
1218C23C23×D414yes—
1219C23C2611yescharacteristic
1220Q8—28no—
1221Q8—28no—
1222Q8—48no—
1223Q8—44no—
1224Q8—84no—
1225Q8—88no—
1226Q8—84no—
1227D4—28no—
1228D4—48no—
1229D4—416no—
1230D4—48no—
1231D4—416no—
1232D4—416no—
1233D4—48no—
1234D4—44no—
1235D4—44no—
1236D4—48no—
1237D4—88no—
1238D4—84no—
1239D4—84no—
1240D4—88no—
1241D4—88no—
1242D4—88no—
1243D4—88no—
1244D4—168no—
1245C2×C4—22no—
1246C2×C4—21no—
1247C2×C4—22no—
1248C2×C4—21no—
1249C2×C4—22no—
1250C2×C4—22no—
1251C2×C4—22no—
1252C2×C4—24no—
1253C2×C4—22no—
1254C2×C4—24no—
1255C2×C4—22no—
1256C2×C4—28no—
1257C2×C4—28no—
1258C2×C4—216no—
1259C2×C4—22no—
1260C2×C4—22no—
1261C2×C4—22no—
1262C2×C4—24no—
1263C2×C4—24no—
1264C2×C4—24no—
1265C2×C4—22no—
1266C2×C4—22no—
1267C2×C4—22no—
1268C2×C4—22no—
1269C2×C4—22no—
1270C2×C4—24no—
1271C2×C4—24no—
1272C2×C4—22no—
1273C2×C4—22no—
1274C2×C4—22no—
1275C2×C4—22no—
1276C2×C4—22no—
1277C2×C4—22no—
1278C2×C4—22no—
1279C2×C4—24no—
1280C2×C4—28no—
1281C2×C4—24no—
1282C2×C4—24no—
1283C2×C4—24no—
1284C2×C4—22no—
1285C2×C4—22no—
1286C2×C4—22no—
1287C2×C4—22no—
1288C2×C4—24no—
1289C2×C4—24no—
1290C2×C4—28no—
1291C2×C4—24no—
1292C2×C4—28no—
1293C2×C4—24no—
1294C2×C4—48no—
1295C2×C4—48no—
1296C2×C4—44no—
1297C2×C4—48no—
1298C2×C4—416no—
1299C2×C4—416no—
1300C2×C4—416no—
1301C2×C4—48no—
1302C2×C4—416no—
1303C2×C4—48no—
1304C2×C4—48no—
1305C2×C4—88no—
1306C2×C4—88no—
1307C2×C4—88no—
1308C2×C4C23×D412yes—
1309C2×C4C23×D412yes—
1310C2×C4C23×D414yes—
1311C2×C4C23×D414yes—
1312C2×C4C23×D414yes—
1313C2×C4C23×D412yes—
1314C2×C4C23×D412yes—
1315C2×C4C23×D412yes—
1316C2×C4C23×D412yes—
1317C2×C4C2×2−1+414yes—
1318C2×C4C2×2−1+412yes—
1319C2×C4#58514yes—
1320C2×C4#58512yes—
1321C22—24no—
1322C22—22no—
1323C22—24no—
1324C22—22no—
1325C22—22no—
1326C22—24no—
1327C22—42no—
1328C22—44no—
1329C22—42no—
1330C22—44no—
1331C22—42no—
1332C22—44no—
1333C22—42no—
1334C22—42no—
1335C22—44no—
1336C22—42no—
1337C22—44no—
1338C22—44no—
1339C22—48no—
1340C22—44no—
1341C22—42no—
1342C22—42no—
1343C22—44no—
1344C22—44no—
1345C22—48no—
1346C22C24×D411yescharacteristic
1347C22C22×2−1+411yescharacteristic
1348C22C2×#58511yescharacteristic
1349C22C2×#58512yes—
1350C22H(7,𝔽2)12yes—
1351C4—22no—
1352C4—24no—
1353C4—24no—
1354C4—22no—
1355C4—24no—
1356C4—22no—
1357C4—22no—
1358C4—24no—
1359C4—42no—
1360C4—44no—
1361C4—42no—
1362C4—42no—
1363C4—44no—
1364C4—42no—
1365C4—44no—
1366C4—44no—
1367C4—42no—
1368C4—42no—
1369C4—42no—
1370C4—44no—
1371C4—42no—
1372C4—42no—
1373C4#344914yes—
1374C4#348914yes—
1375C2—44no—
1376C2—42no—
1377C2—82no—
1378C2—84no—
1379C2—82no—
1380C2C2×#344911yescharacteristic
1381C2C2×#348911yescharacteristic
1382C2#6285211yescharacteristic
1383C2#6293712yes—
1384C2#6295212yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
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×#3515C2semidirect
2. C2×#3483C2semidirect
3. #42970C2semidirect
4. #42927C2semidirect
5. #42177C2semidirect
6. #39619C2semidirect
7. #39617C2semidirect
8. #39491C2semidirect
9. #39489C2semidirect
10. #39174C2semidirect
11. #39169C2semidirect
12. #38956C2semidirect
13. #38952C2semidirect
14. #38093C2semidirect
15. #38089C2semidirect
16. #37871C2semidirect
17. #37869C2semidirect
18. #37616C2semidirect
19. #37539C2semidirect
20. #37234C2semidirect
21. #35600C2semidirect
22. #35333C2semidirect
23. #35298C2semidirect
24. #35238C2semidirect
25. #35211C2semidirect
26. #35205C2semidirect
27. #34947C2semidirect
28. #34910C2semidirect
29. #34060C2semidirect
334. C4×#41D4semidirect

Maximal subgroups

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

subgroupindex
C2×#35152
C2×#34832
#429702
#429272
#421772
#396192
#396172
#394912
#394892
#391742
#391692
#389562
#389522
#380932
#380892
#378712
#378692
#376162
#375392
#372342
#356002
#353332
#352982
#352382
#352112
#352052
#349472
#349102
#340602