Finite Group Databasebeta

← #7715670

Subgroups — #7715670

Order 512.

6728 conjugacy classes of subgroups.

The subgroup lattice has 1162 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3539C211yesmaximal, characteristic
2C2×#3538C211yesmaximal, characteristic, complemented
3#50885C218yesmaximal, complemented
4#48810C218yesmaximal, complemented
5#46383C218yesmaximal, complemented
6#46374C218yesmaximal, complemented
7#39485C212yesmaximal, complemented
8#39484C212yesmaximal, complemented
9#39363C212yesmaximal, complemented
10#39360C212yesmaximal, complemented
11#38093C212yesmaximal, complemented
12#38088C212yesmaximal, complemented
13#38085C212yesmaximal, complemented
14#38081C212yesmaximal, complemented
15#37449C212yesmaximal, complemented
16#37420C211yesmaximal, characteristic, complemented
17#37388C212yesmaximal, complemented
18#37387C211yesmaximal, characteristic, complemented
19#35332C211yesmaximal, characteristic, complemented
20#35319C211yesmaximal, characteristic, complemented
21#35308C212yesmaximal, complemented
22#35306C212yesmaximal, complemented
23#34065C211yesmaximal, characteristic, complemented
24#3539—216no—
25#3538—216no—
26C2×#563C2214yes—
27C2×#560C2214yes—
28C2×#553C2212yes—
29C2×#553C2214yes—
30C2×#552C2212yes—
31C2×#552C2212yes—
32C2×#552C2212yes—
33C2×#551C2214yes—
34C2×#550C2212yes—
35C2×D4×Q8C2212yes—
36C2×D4×Q8C2212yes—
37C2×#547C2212yes—
38C2×#544C2214yes—
39C2×#541C2211yescharacteristic
40C2×#541C2211yescharacteristic
41C2×#541C2211yescharacteristic
42C2×#540C2211yescharacteristic
43C2×#540C2214yes—
44C2×#539C2214yes—
45C2×#539C2214yes—
46C2×#537C2212yes—
47C2×#536C2212yes—
48C2×#536C2212yes—
49C2×#536C2212yescomplemented
50C2×#525C2212yes—
51C2×#525C2211yescharacteristic
52C22×C22⋊Q8C2212yes—
53C2×C4×#41C2211yescharacteristic
54C22×#117C2211yescharacteristic
55#2868C2211yescharacteristic, complemented
56#2859C2211yescharacteristic, complemented
57#2859C2211yescharacteristic, complemented
58#2858C2211yescharacteristic, complemented
59#2857C2212yes—
60#2857C2212yes—
61#2857C2212yescomplemented
62#2850C2212yes—
63#2850C2212yes—
64#2850C2212yescomplemented
65#2814C2218yes—
66#2729C2218yescomplemented
67#2726C2218yescomplemented
68#2726C2218yescomplemented
69#2725C2218yescomplemented
70#2724C2218yes—
71#2722C2218yes—
72#2716C2218yescomplemented
73#2713C2218yescomplemented
74#2709C2218yes—
75#2708C2218yes—
76#2708C2218yes—
77#2707C2218yescomplemented
78#2701C2218yes—
79#2701C2218yescomplemented
80#2695C2218yescomplemented
81#2691C2218yes—
82#2691C2218yescomplemented
83#2689C2218yes—
84#2687C2218yes—
85#2686C2218yes—
86#2681C2218yes—
87#2681C2218yescomplemented
88#2680C2218yes—
89#2680C2218yescomplemented
90#2642C2211yescharacteristic, complemented
91#2642C2211yescharacteristic, complemented
92#2642C2211yescharacteristic, complemented
93#2641C2211yescharacteristic, complemented
94#2638C2218yes—
95#2622C2218yes—
96#2621C2212yes—
97#2621C2212yes—
98#2621C2212yes—
99#2621C2212yes—
100#2621C2212yescomplemented
101#2620C2212yes—
102#2620C2212yes—
103#2620C2212yes—
104#2620C2212yes—
105#2620C2212yescomplemented
106#2579C2218yes—
107#2566C2212yescomplemented
108#2565C2212yescomplemented
109#2565C2212yescomplemented
110#2565C2212yescomplemented
111#2559C2218yes—
112#2558C2218yescomplemented
113#2548C2212yescomplemented
114#2547C2212yescomplemented
115#2546C2212yescomplemented
116#2546C2212yescomplemented
117#2506C2218yescomplemented
118#2504C2212yes—
119#2503C2212yescomplemented
120#2502C2212yes—
121#2502C2212yescomplemented
122#2500C2212yescomplemented
123#2499C2212yes—
124#2499C2212yes—
125#2499C2212yescomplemented
126#2496C2218yes—
127#2478C2218yes—
128#2478C2218yescomplemented
129#2476C2218yes—
130#2473C2218yescomplemented
131#2470C2218yes—
132#2470C2218yes—
133#2466C2218yescomplemented
134#2460C2218yescomplemented
135#2452C2218yescomplemented
136#2450C2218yescomplemented
137#2445C2218yes—
138#2444C2218yes—
139#2440C2218yescomplemented
140#2438C2218yescomplemented
141#2436C2212yes—
142#2436C2212yescomplemented
143#2434C2212yes—
144#2434C2212yescomplemented
145#2432C2212yes—
146#2432C2212yes—
147#2432C2212yescomplemented
148#2432C2212yescomplemented
149#2429C2218yescomplemented
150#2427C2218yes—
151#2425C2218yes—
152#2425C2218yescomplemented
153#2422C2218yes—
154#2419C2218yes—
155#2417C2218yes—
156#2415C2218yes—
157#2413C2218yes—
158#2412C2218yes—
159#2327C2212yescomplemented
160#2326C2212yescomplemented
161#2324C2214yes—
162#2323C2214yes—
163#2322C2214yes—
164#2321C2214yes—
165#2317C2212yes—
166#2317C2212yescomplemented
167#2311C2212yes—
168#2310C2212yes—
169C4×C4⋊Q8C2212yescomplemented
170C4×#124C2212yescomplemented
171#2297C2211yescharacteristic
172#2297C2212yescomplemented
173#2296C2211yescharacteristic
174C2×#391C2212yescomplemented
175#2293C2212yes—
176#2293C2212yes—
177#2290C2212yes—
178#2290C2212yes—
179#2280C2211yescharacteristic
180C4×#117C2211yescharacteristic
181C22×#41C2312yes—
182C22×#41C2312yes—
183C22×#41C2311yescharacteristic
184C23×Q8C2312yes—
185C23×Q8C2312yes—
186C24×C4C2311yescharacteristic
187#563—232no—
188#560—232no—
189#553—232no—
190#553—216no—
191#552—216no—
192#552—216no—
193#552—216no—
194#551—232no—
195#550—216no—
196D4×Q8—216no—
197D4×Q8—216no—
198#547—216no—
199#544—232no—
200#541—28no—
201#541—28no—
202#541—28no—
203#540—232no—
204#540—28no—
205#539—232no—
206#539—232no—
207#537—216no—
208#536—216no—
209#536—48no—
210#536—48no—
211C2×C4⋊Q8C2312yes—
212C2×C4⋊Q8C2311yescharacteristic
213C2×C4⋊Q8C2311yescharacteristic
214C2×C4⋊Q8C2311yescharacteristic
215C2×C4⋊Q8C2314yes—
216C2×C4⋊Q8C2314yes—
217C2×C4⋊Q8C2314yes—
218C2×C4⋊Q8C2312yes—
219C2×C4⋊Q8C2312yes—
220C2×C4⋊Q8C2312yes—
221C2×#127C2311yescharacteristic
222C2×#127C2314yes—
223C2×#126C2314yes—
224C2×#126C2314yes—
225C2×#126C2314yes—
226C2×#126C2314yes—
227C2×#126C2314yes—
228C2×#126C2314yes—
229C2×#126C2314yes—
230C2×#125C2311yescharacteristic
231C2×#125C2311yescharacteristic
232C2×#125C2311yescharacteristic
233C2×#125C2311yescharacteristic
234C2×#125C2314yes—
235C2×#125C2314yes—
236C2×#125C2314yes—
237C2×#125C2314yes—
238C2×#125C2314yes—
239C2×#125C2314yes—
240C2×#124C2312yes—
241C2×#124C2314yes—
242C2×#124C2312yes—
243C2×#124C2312yes—
244C2×#124C2312yes—
245#525—216no—
246#525D4116yes—
247C2×#123C2314yes—
248C2×#123C2314yes—
249C2×#123C2314yes—
250C2×#123C2314yes—
251C2×#123C2314yes—
252C2×#123C2314yes—
253C2×#123C2314yes—
254C2×#123C2314yes—
255C2×#123C2314yes—
256C2×#123C2314yes—
257C2×#123C2318yes—
258C2×#123C2318yes—
259C2×#123C2312yes—
260C2×C22⋊Q8—216no—
261C2×C22⋊Q8C2312yes—
262C2×C22⋊Q8C2312yes—
263C2×C22⋊Q8C2312yes—
264C2×C22⋊Q8C2312yes—
265C2×C22⋊Q8C2312yes—
266C2×C22⋊Q8C2312yes—
267C2×C22⋊Q8C2312yes—
268C2×C22⋊Q8C2312yes—
269C2×C22⋊Q8C2312yes—
270C2×C22⋊Q8C2314yes—
271C2×C22⋊Q8C2314yes—
272C2×C22⋊Q8C2314yes—
273C2×C22⋊Q8C2314yes—
274C2×C22⋊Q8C2314yes—
275C2×C22⋊Q8C2314yes—
276C2×C22⋊Q8C2314yes—
277C2×C22⋊Q8C2318yes—
278C2×C22⋊Q8C2318yes—
279C2×C22⋊Q8C2312yes—
280C2×#121C2312yes—
281C2×#121C2312yes—
282C2×#121C2312yes—
283C2×#121C2314yes—
284C2×#121C2314yes—
285C2×#121C2314yes—
286C2×#121C2314yes—
287C2×#121C2314yes—
288C2×#121C2314yes—
289C2×#121C2314yes—
290C2×#121C2314yes—
291C2×#121C2312yes—
292C2×#120C2314yes—
293C2×#120C2312yes—
294C4×#41—44no—
295C2×C4×Q8C2312yes—
296C2×C4×Q8C2312yes—
297C2×C4×Q8C2312yes—
298C2×C4×Q8C2312yes—
299C2×C4×D4C2312yes—
300C2×C4×D4C2314yes—
301C2×C4×D4C2314yes—
302C2×C4×D4C2314yes—
303C2×C4×D4C2314yes—
304C2×C4×D4C2314yes—
305C2×C4×D4C2314yes—
306C2×C4×D4C2314yes—
307C2×C4×D4C2312yes—
308C2×C4×D4C2312yes—
309C2×C4×D4C2312yes—
310C2×#117—44no—
311C2×#117C2312yes—
312C2×#117C2312yes—
313C2×#117C2312yes—
314C2×#117C2312yes—
315C2×#117C2314yes—
316C2×#117C2314yes—
317C2×#117C2314yes—
318C2×#117C2312yes—
319C2×#117C2314yes—
320C2×#117C2311yescharacteristic
321C2×#117C2311yescharacteristic
322C2×#117C2311yescharacteristic
323C22×C4⋊C4C2312yes—
324C22×C4⋊C4C2312yes—
325C22×C4⋊C4C2314yes—
326C22×C4⋊C4C2314yes—
327C22×C4⋊C4C2312yes—
328C22×C22⋊C4C2314yes—
329C22×C22⋊C4C2312yes—
330C22×C42C2311yescharacteristic
331C22×C42C2311yescharacteristic
332C22×C42C2312yes—
333#400C2318yes—
334#400C2318yes—
335#400C2318yes—
336#400C2318yes—
337#398C2318yes—
338#398C2318yes—
339#398C2318yes—
340#398C2318yes—
341#398C2318yes—
342#398C2318yes—
343#398C2318yes—
344#398C2318yes—
345#398C2318yes—
346#398C2318yes—
347#398C2318yes—
348#398C2318yes—
349#397C2318yes—
350#397C2318yes—
351#397C2318yes—
352#397C2318yes—
353#397C2318yes—
354#397C2318yes—
355#397C2318yes—
356#397C2318yes—
357#397C2318yes—
358#397C2318yes—
359#396C2318yes—
360#396C2318yes—
361#396C2318yes—
362#396C2318yes—
363#396C2318yes—
364#396C2318yes—
365#395C2318yes—
366#395C2318yes—
367#394C2318yes—
368#394C2318yes—
369#394C2318yes—
370#394C2318yes—
371#394C2318yes—
372#394C2318yes—
373#394C2318yes—
374#394C2318yes—
375#394C2318yes—
376#394C2318yes—
377#394C2318yes—
378#394C2318yes—
379#393C2318yes—
380#393C2318yes—
381#391C2312yes—
382#391C2312yes—
383#391C2312yes—
384#391C2312yes—
385#391C2312yes—
386#391C2312yes—
387#391C2312yes—
388#391C2312yes—
389#391C2312yes—
390#391C2312yes—
391#391C2318yes—
392#391C2312yes—
393#391C2312yes—
394#391C2312yes—
395#391C2318yes—
396#390C2312yes—
397#390C2312yes—
398#390C2312yes—
399#390C2314yes—
400#390C2314yes—
401#390C2312yes—
402#390C2318yes—
403#390C2312yes—
404#390C2318yes—
405#389C2318yes—
406#389C2318yes—
407#389C2318yes—
408#389C2314yes—
409#389C2314yes—
410#389C2314yes—
411#389C2318yes—
412#389C2318yes—
413#389C2318yes—
414#389C2318yes—
415#389C2318yes—
416#389C2318yes—
417#389C2318yes—
418#388C2314yes—
419#388C2314yes—
420#388C2314yes—
421#388C2314yes—
422#388C2314yes—
423#388C2314yes—
424#388C2318yes—
425#388C2318yes—
426#388C2318yes—
427#388C2318yes—
428#388C2318yes—
429#388C2318yes—
430#387C2318yes—
431#387C2318yes—
432#387C2318yes—
433#387C2314yes—
434#387C2314yes—
435#387C2318yes—
436#387C2318yes—
437#387C2318yes—
438#387C2318yes—
439#387C2318yes—
440#386C2318yes—
441#386C2314yes—
442#386C2314yes—
443#386C2314yes—
444#386C2318yes—
445#386C2318yes—
446#386C2318yes—
447#386C2318yes—
448#386C2318yes—
449#386C2318yes—
450#386C2318yes—
451#385C2318yes—
452#385C2318yes—
453#385C2318yes—
454#385C2314yes—
455#385C2314yes—
456#385C2314yes—
457#385C2318yes—
458#385C2318yes—
459#385C2318yes—
460#385C2318yes—
461#385C2318yes—
462#385C2318yes—
463#385C2318yes—
464#385C2318yes—
465#385C2318yes—
466#384C2312yes—
467#384C2312yes—
468#384C2312yes—
469#384C2312yes—
470#384C2318yes—
471#382C2312yes—
472#382C2312yes—
473#382C2312yes—
474#382C2312yes—
475#381C2318yes—
476#381C2312yes—
477#381C2318yes—
478#380C2318yes—
479#380C2314yes—
480#380C2318yes—
481#380C2318yes—
482#380C2318yes—
483#380C2318yes—
484#379C2312yes—
485C4×C4⋊C4C2318yes—
486C4×C4⋊C4C2312yes—
487C4×C4⋊C4C2312yes—
488C4×C4⋊C4C2314yes—
489C4×C22⋊C4C2314yes—
490C4×C22⋊C4C2318yes—
491C4×C22⋊C4C2318yes—
492C4×C22⋊C4C2312yes—
493C4×C22⋊C4C2312yes—
494C4×C22⋊C4C2312yes—
495C4×C22⋊C4C2312yes—
496#376C2311yescharacteristic
497#376C2311yescharacteristic
498C2×#95C2318yes—
499C43C2311yescharacteristic
500C43C2311yescharacteristic
501C25C2411yescharacteristic
502C2×#41—28no—
503C2×#41—28no—
504C2×#41—42no—
505C2×#41—42no—
506C2×#41—44no—
507C2×#41—44no—
508C2×#41—44no—
509C2×#41—44no—
510C2×#41C2×D418yes—
511C22×Q8—28no—
512C22×Q8—28no—
513C22×Q8—44no—
514C22×Q8—44no—
515C22×Q8—44no—
516C22×Q8—44no—
517C22×Q8C2412yes—
518C22×Q8C2412yes—
519C22×Q8C2412yes—
520C22×Q8C2414yes—
521C22×Q8C2414yes—
522C22×Q8C2411yescharacteristic
523C22×D4C2412yes—
524C22×D4C2414yes—
525C22×D4C2414yes—
526C22×D4C2414yes—
527C22×D4C2414yes—
528C22×D4C2414yes—
529C22×D4C2414yes—
530C22×D4C2412yes—
531C22×D4C2412yes—
532C22×D4C2412yes—
533C22×D4C2411yescharacteristic
534C23×C4—42no—
535C23×C4—42no—
536C23×C4C2×D418yes—
537C23×C4C2412yes—
538C23×C4C2412yes—
539C23×C4C2411yescharacteristic
540C23×C4C2414yes—
541C23×C4C2414yes—
542C23×C4C2412yes—
543C23×C4C2414yes—
544C23×C4C2414yes—
545C23×C4C2414yes—
546C23×C4C2414yes—
547C23×C4C2414yes—
548C23×C4C2412yes—
549C23×C4C2414yes—
550C23×C4C2412yes—
551C23×C4C2411yescharacteristic
552C4⋊Q8—216no—
553C4⋊Q8—216no—
554C4⋊Q8—216no—
555C4⋊Q8—24no—
556C4⋊Q8—24no—
557C4⋊Q8—24no—
558C4⋊Q8—28no—
559C4⋊Q8—44no—
560C4⋊Q8—44no—
561C4⋊Q8—44no—
562#127—216no—
563#127—24no—
564#126—216no—
565#126—216no—
566#126—216no—
567#126—216no—
568#126—216no—
569#126—216no—
570#126—216no—
571#125—216no—
572#125—216no—
573#125—216no—
574#125—216no—
575#125—216no—
576#125—216no—
577#125—24no—
578#125—24no—
579#125—24no—
580#125—24no—
581#124—216no—
582#124—28no—
583#124—44no—
584#124—44no—
585#124—44no—
586#123—216no—
587#123—216no—
588#123—216no—
589#123—216no—
590#123—216no—
591#123—216no—
592#123—216no—
593#123—216no—
594#123—216no—
595#123—216no—
596#123—416no—
597#123—416no—
598#123C2×D4116yes—
599C22⋊Q8—216no—
600C22⋊Q8—28no—
601C22⋊Q8—28no—
602C22⋊Q8—216no—
603C22⋊Q8—28no—
604C22⋊Q8—28no—
605C22⋊Q8—216no—
606C22⋊Q8—28no—
607C22⋊Q8—28no—
608C22⋊Q8—28no—
609C22⋊Q8—28no—
610C22⋊Q8—28no—
611C22⋊Q8—216no—
612C22⋊Q8—216no—
613C22⋊Q8—216no—
614C22⋊Q8—216no—
615C22⋊Q8—416no—
616C22⋊Q8—416no—
617C22⋊Q8C2×D4116yes—
618#121—216no—
619#121—216no—
620#121—216no—
621#121—216no—
622#121—216no—
623#121—28no—
624#121—28no—
625#121—28no—
626#121—216no—
627#121—216no—
628#121—216no—
629#121C2×D4116yes—
630#120—216no—
631#120C2×D4116yes—
632C4×Q8—28no—
633C4×Q8—28no—
634C4×Q8—28no—
635C4×Q8—44no—
636C4×D4—216no—
637C4×D4—216no—
638C4×D4—216no—
639C4×D4—216no—
640C4×D4—216no—
641C4×D4—216no—
642C4×D4—28no—
643C4×D4—44no—
644C4×D4—48no—
645C4×D4C2×D4116yes—
646C4×D4C2×D4116yes—
647#117—28no—
648#117—28no—
649#117—216no—
650#117—216no—
651#117—216no—
652#117—28no—
653#117—28no—
654#117—44no—
655#117—42no—
656#117—42no—
657#117—48no—
658#117C2×D418yes—
659C2×C4⋊C4—216no—
660C2×C4⋊C4—28no—
661C2×C4⋊C4—28no—
662C2×C4⋊C4—216no—
663C2×C4⋊C4—44no—
664C2×C4⋊C4C2414yes—
665C2×C4⋊C4C2412yes—
666C2×C4⋊C4C2414yes—
667C2×C4⋊C4C2412yes—
668C2×C4⋊C4C2412yes—
669C2×C4⋊C4C2412yes—
670C2×C4⋊C4C2414yes—
671C2×C4⋊C4C2414yes—
672C2×C4⋊C4C2414yes—
673C2×C4⋊C4C2414yes—
674C2×C4⋊C4C2414yes—
675C2×C4⋊C4C2414yes—
676C2×C4⋊C4C2414yes—
677C2×C4⋊C4C2414yes—
678C2×C4⋊C4C2414yes—
679C2×C4⋊C4C2414yes—
680C2×C4⋊C4C2414yes—
681C2×C4⋊C4C2414yes—
682C2×C4⋊C4C2414yes—
683C2×C4⋊C4C2414yes—
684C2×C4⋊C4C2414yes—
685C2×C4⋊C4C2414yes—
686C2×C4⋊C4C2414yes—
687C2×C4⋊C4C2414yes—
688C2×C4⋊C4C2414yes—
689C2×C4⋊C4C2414yes—
690C2×C4⋊C4C2414yes—
691C2×C4⋊C4C2418yes—
692C2×C4⋊C4C2414yes—
693C2×C4⋊C4C2412yes—
694C2×C4⋊C4C2412yes—
695C2×C4⋊C4C2418yes—
696C2×C4⋊C4C2418yes—
697C2×C4⋊C4C2418yes—
698C2×C4⋊C4C2414yes—
699C2×C4⋊C4C2418yes—
700C2×C4⋊C4C2414yes—
701C2×C4⋊C4C2418yes—
702C2×C4⋊C4C2418yes—
703C2×C4⋊C4C2418yes—
704C2×C4⋊C4C2412yes—
705C2×C4⋊C4C2412yes—
706C2×C4⋊C4C2412yes—
707C2×C22⋊C4—216no—
708C2×C22⋊C4—44no—
709C2×C22⋊C4C2414yes—
710C2×C22⋊C4C2414yes—
711C2×C22⋊C4C2414yes—
712C2×C22⋊C4C2414yes—
713C2×C22⋊C4C2414yes—
714C2×C22⋊C4C2414yes—
715C2×C22⋊C4C2414yes—
716C2×C22⋊C4C2414yes—
717C2×C22⋊C4C2414yes—
718C2×C22⋊C4C2414yes—
719C2×C22⋊C4C2414yes—
720C2×C22⋊C4C2414yes—
721C2×C22⋊C4C2414yes—
722C2×C22⋊C4C2414yes—
723C2×C22⋊C4C2414yes—
724C2×C22⋊C4C2414yes—
725C2×C22⋊C4C2414yes—
726C2×C22⋊C4C2418yes—
727C2×C22⋊C4C2414yes—
728C2×C22⋊C4C2412yes—
729C2×C22⋊C4C2412yes—
730C2×C22⋊C4C2418yes—
731C2×C22⋊C4C2418yes—
732C2×C22⋊C4C2418yes—
733C2×C22⋊C4C2414yes—
734C2×C22⋊C4C2414yes—
735C2×C22⋊C4C2418yes—
736C2×C22⋊C4C2414yes—
737C2×C22⋊C4C2414yes—
738C2×C22⋊C4C2418yes—
739C2×C22⋊C4C2418yes—
740C2×C22⋊C4C2418yes—
741C2×C22⋊C4C2412yes—
742C2×C22⋊C4C2412yes—
743C2×C22⋊C4C2412yes—
744C2×C22⋊C4C2412yes—
745C2×C22⋊C4C2412yes—
746C2×C42—24no—
747C2×C42—42no—
748C2×C42—44no—
749C2×C42C2414yes—
750C2×C42C2414yes—
751C2×C42C2412yes—
752C2×C42C2412yes—
753C2×C42C2412yes—
754C2×C42C2411yescharacteristic
755C2×C42C2414yes—
756C2×C42C2414yes—
757C2×C42C2414yes—
758C2×C42C2411yescharacteristic
759C2×C42C2411yescharacteristic
760C2×C42C2412yes—
761C2×C42C2414yes—
762C2×C42C2414yes—
763C2×C42C2414yes—
764C2×C42C2411yescharacteristic
765C2×C42C2411yescharacteristic
766C2×C42C2411yescharacteristic
767#95C2418yes—
768#95C2418yes—
769#95C2418yes—
770#95C2418yes—
771#95C2414yes—
772#95C2414yes—
773#95C2418yes—
774#95C2414yes—
775#95C2414yes—
776#95C2418yes—
777#95C2418yes—
778#95C2414yes—
779#95C2414yes—
780#95C2418yes—
781#95C2414yes—
782#95C2418yes—
783#95C2418yes—
784#95C2414yes—
785#95C2418yes—
786#95C2418yes—
787#95C2418yes—
788#95C2418yes—
789#95C2418yes—
790#95C2418yes—
791C24—41no—
792C24—41no—
793C24—44no—
794C24C22×D414yes—
795C24C2514yes—
796C24C2512yes—
797C24C2511yescharacteristic
798C24C2512yes—
799#41—416no—
800#41—816no—
801#41—816no—
802C2×Q8—24no—
803C2×Q8—24no—
804C2×Q8—24no—
805C2×Q8—28no—
806C2×Q8—28no—
807C2×Q8—24no—
808C2×Q8—24no—
809C2×Q8—24no—
810C2×Q8—24no—
811C2×Q8—24no—
812C2×Q8—24no—
813C2×Q8—41no—
814C2×Q8—41no—
815C2×Q8—44no—
816C2×Q8—44no—
817C2×Q8—44no—
818C2×Q8—44no—
819C2×Q8—816no—
820C2×Q8—816no—
821C2×Q8C22×D414yes—
822C2×D4—28no—
823C2×D4—28no—
824C2×D4—28no—
825C2×D4—28no—
826C2×D4—28no—
827C2×D4—24no—
828C2×D4—28no—
829C2×D4—24no—
830C2×D4—24no—
831C2×D4—41no—
832C2×D4—42no—
833C2×D4—44no—
834C2×D4—44no—
835C2×D4—41no—
836C2×D4—42no—
837C2×D4—44no—
838C2×D4—44no—
839C2×D4—48no—
840C2×D4—48no—
841C2×D4—48no—
842C2×D4—48no—
843C2×D4—44no—
844C2×D4—44no—
845C2×D4C22×D418yes—
846C2×D4C22×D418yes—
847C2×D4C22×D418yes—
848C2×D4C22×D414yes—
849C22×C4—22no—
850C22×C4—24no—
851C22×C4—24no—
852C22×C4—22no—
853C22×C4—24no—
854C22×C4—24no—
855C22×C4—28no—
856C22×C4—28no—
857C22×C4—28no—
858C22×C4—28no—
859C22×C4—28no—
860C22×C4—28no—
861C22×C4—28no—
862C22×C4—24no—
863C22×C4—416no—
864C22×C4—41no—
865C22×C4—42no—
866C22×C4—42no—
867C22×C4—41no—
868C22×C4—48no—
869C22×C4—42no—
870C22×C4—44no—
871C22×C4—44no—
872C22×C4—44no—
873C22×C4—44no—
874C22×C4—44no—
875C22×C4—44no—
876C22×C4—48no—
877C22×C4—44no—
878C22×C4—44no—
879C22×C4—44no—
880C22×C4—48no—
881C22×C4—44no—
882C22×C4—44no—
883C22×C4—44no—
884C22×C4—44no—
885C22×C4C22×D418yes—
886C22×C4C22×D418yes—
887C22×C4C22×D414yes—
888C22×C4C22×D418yes—
889C22×C4C22×D414yes—
890C22×C4C2512yes—
891C22×C4C2512yes—
892C22×C4C2512yes—
893C22×C4C2514yes—
894C22×C4C2514yes—
895C22×C4C2514yes—
896C22×C4C2514yes—
897C22×C4C2514yes—
898C22×C4C2514yes—
899C22×C4C2514yes—
900C22×C4C2514yes—
901C22×C4C2514yes—
902C22×C4C2512yes—
903C22×C4C2512yes—
904C22×C4C2512yes—
905C22×C4C2512yes—
906C22×C4C2511yescharacteristic
907C22×C4C2512yes—
908C22×C4C2511yescharacteristic
909C4⋊C4—24no—
910C4⋊C4—28no—
911C4⋊C4—24no—
912C4⋊C4—24no—
913C4⋊C4—24no—
914C4⋊C4—28no—
915C4⋊C4—28no—
916C4⋊C4—28no—
917C4⋊C4—28no—
918C4⋊C4—28no—
919C4⋊C4—28no—
920C4⋊C4—28no—
921C4⋊C4—28no—
922C4⋊C4—28no—
923C4⋊C4—28no—
924C4⋊C4—28no—
925C4⋊C4—28no—
926C4⋊C4—28no—
927C4⋊C4—28no—
928C4⋊C4—28no—
929C4⋊C4—28no—
930C4⋊C4—28no—
931C4⋊C4—28no—
932C4⋊C4—28no—
933C4⋊C4—28no—
934C4⋊C4—28no—
935C4⋊C4—28no—
936C4⋊C4—216no—
937C4⋊C4—44no—
938C4⋊C4—48no—
939C4⋊C4—44no—
940C4⋊C4—44no—
941C4⋊C4—48no—
942C4⋊C4—48no—
943C4⋊C4—48no—
944C4⋊C4—42no—
945C4⋊C4—42no—
946C4⋊C4—48no—
947C4⋊C4—48no—
948C4⋊C4—48no—
949C4⋊C4C22×D418yes—
950C4⋊C4C22×D418yes—
951C4⋊C4C22×D418yes—
952C22⋊C4—28no—
953C22⋊C4—28no—
954C22⋊C4—28no—
955C22⋊C4—28no—
956C22⋊C4—28no—
957C22⋊C4—28no—
958C22⋊C4—28no—
959C22⋊C4—28no—
960C22⋊C4—28no—
961C22⋊C4—28no—
962C22⋊C4—28no—
963C22⋊C4—28no—
964C22⋊C4—28no—
965C22⋊C4—28no—
966C22⋊C4—28no—
967C22⋊C4—28no—
968C22⋊C4—28no—
969C22⋊C4—216no—
970C22⋊C4—44no—
971C22⋊C4—44no—
972C22⋊C4—48no—
973C22⋊C4—44no—
974C22⋊C4—44no—
975C22⋊C4—44no—
976C22⋊C4—48no—
977C22⋊C4—48no—
978C22⋊C4—48no—
979C22⋊C4—42no—
980C22⋊C4—42no—
981C22⋊C4—48no—
982C22⋊C4—48no—
983C22⋊C4—48no—
984C22⋊C4C22×D418yes—
985C22⋊C4C22×D418yes—
986C22⋊C4C22×D418yes—
987C22⋊C4C22×D418yes—
988C22⋊C4C22×D418yes—
989C42—28no—
990C42—28no—
991C42—28no—
992C42—28no—
993C42—28no—
994C42—22no—
995C42—24no—
996C42—24no—
997C42—24no—
998C42—22no—
999C42—22no—
1000C42—42no—
1001C42—44no—
1002C42—44no—
1003C42—44no—
1004C42C22×D414yes—
1005C42C22×D414yes—
1006C42H(5,𝔽2)14yes—
1007C23—22no—
1008C23—22no—
1009C23—21no—
1010C23—21no—
1011C23—22no—
1012C23—22no—
1013C23—24no—
1014C23—24no—
1015C23—24no—
1016C23—24no—
1017C23—24no—
1018C23—24no—
1019C23—24no—
1020C23—24no—
1021C23—28no—
1022C23—28no—
1023C23—44no—
1024C23—48no—
1025C23—84no—
1026C23—84no—
1027C23C23×D412yes—
1028C23C23×D414yes—
1029C23C23×D414yes—
1030C23C2611yescharacteristic
1031Q8—44no—
1032Q8—48no—
1033Q8—48no—
1034Q8—48no—
1035Q8—88no—
1036Q8—88no—
1037D4—48no—
1038D4—48no—
1039D4—44no—
1040D4—48no—
1041D4—48no—
1042D4—88no—
1043D4—88no—
1044D4—88no—
1045D4—88no—
1046D4—88no—
1047D4—88no—
1048C2×C4—21no—
1049C2×C4—22no—
1050C2×C4—22no—
1051C2×C4—21no—
1052C2×C4—22no—
1053C2×C4—22no—
1054C2×C4—24no—
1055C2×C4—24no—
1056C2×C4—24no—
1057C2×C4—216no—
1058C2×C4—28no—
1059C2×C4—216no—
1060C2×C4—24no—
1061C2×C4—24no—
1062C2×C4—24no—
1063C2×C4—24no—
1064C2×C4—24no—
1065C2×C4—24no—
1066C2×C4—24no—
1067C2×C4—22no—
1068C2×C4—24no—
1069C2×C4—24no—
1070C2×C4—24no—
1071C2×C4—24no—
1072C2×C4—24no—
1073C2×C4—22no—
1074C2×C4—22no—
1075C2×C4—24no—
1076C2×C4—24no—
1077C2×C4—24no—
1078C2×C4—24no—
1079C2×C4—24no—
1080C2×C4—24no—
1081C2×C4—24no—
1082C2×C4—28no—
1083C2×C4—28no—
1084C2×C4—24no—
1085C2×C4—24no—
1086C2×C4—24no—
1087C2×C4—28no—
1088C2×C4—28no—
1089C2×C4—44no—
1090C2×C4—48no—
1091C2×C4—416no—
1092C2×C4—88no—
1093C2×C4—84no—
1094C2×C4—88no—
1095C2×C4—88no—
1096C2×C4—88no—
1097C2×C4—88no—
1098C2×C4—88no—
1099C2×C4—84no—
1100C2×C4—88no—
1101C2×C4C23×D414yes—
1102C2×C4C23×D414yes—
1103C2×C4C23×D414yes—
1104C2×C4C23×D414yes—
1105C2×C4C23×D412yes—
1106C2×C4C23×D412yes—
1107C2×C4C2×H(5,𝔽2)14yes—
1108C2×C4C2×H(5,𝔽2)12yes—
1109C2×C4#58512yes—
1110C22—24no—
1111C22—22no—
1112C22—24no—
1113C22—24no—
1114C22—24no—
1115C22—24no—
1116C22—24no—
1117C22—24no—
1118C22—42no—
1119C22—44no—
1120C22—44no—
1121C22—44no—
1122C22—42no—
1123C22—44no—
1124C22—44no—
1125C22—44no—
1126C22—44no—
1127C22—48no—
1128C22—48no—
1129C22—88no—
1130C22C24×D411yescharacteristic
1131C22C22×H(5,𝔽2)11yescharacteristic
1132C22C2×#58511yescharacteristic
1133C222−1+614yes—
1134C4—24no—
1135C4—22no—
1136C4—24no—
1137C4—24no—
1138C4—24no—
1139C4—24no—
1140C4—44no—
1141C4—44no—
1142C4—44no—
1143C4—44no—
1144C4—44no—
1145C4—44no—
1146C4—44no—
1147C4—44no—
1148C4—44no—
1149C4—42no—
1150C4—42no—
1151C4—42no—
1152C4#349614yes—
1153C2—44no—
1154C2—44no—
1155C2—42no—
1156C2—84no—
1157C2C2×#349611yescharacteristic
1158C2#6285912yes—
1159C2#6288812yes—
1160C2#6289012yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#3539C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C2×#3538C2semidirect
3. #50885C2semidirect
4. #48810C2semidirect
5. #46383C2semidirect
6. #46374C2semidirect
7. #39485C2semidirect
8. #39484C2semidirect
9. #39363C2semidirect
10. #39360C2semidirect
11. #38093C2semidirect
12. #38088C2semidirect
13. #38085C2semidirect
14. #38081C2semidirect
15. #37449C2semidirect
16. #37420C2semidirect
17. #37388C2semidirect
18. #37387C2semidirect
19. #35332C2semidirect
20. #35319C2semidirect
21. #35308C2semidirect
22. #35306C2semidirect
23. #34065C2semidirect
49. C2×#536C22semidirect
55. #2868C22semidirect
56. #2859C22semidirect
57. #2859C22semidirect
58. #2858C22semidirect
61. #2857C22semidirect
64. #2850C22semidirect
66. #2729C22semidirect
67. #2726C22semidirect
68. #2726C22semidirect
69. #2725C22semidirect
72. #2716C22semidirect
73. #2713C22semidirect
77. #2707C22semidirect
79. #2701C22semidirect
80. #2695C22semidirect
82. #2691C22semidirect
87. #2681C22semidirect
89. #2680C22semidirect
90. #2642C22semidirect
91. #2642C22semidirect
92. #2642C22semidirect
93. #2641C22semidirect
100. #2621C22semidirect
105. #2620C22semidirect
107. #2566C22semidirect
108. #2565C22semidirect
109. #2565C22semidirect
110. #2565C22semidirect
112. #2558C22semidirect
113. #2548C22semidirect
114. #2547C22semidirect
115. #2546C22semidirect
116. #2546C22semidirect
117. #2506C22semidirect
119. #2503C22semidirect
121. #2502C22semidirect
122. #2500C22semidirect
125. #2499C22semidirect
128. #2478C22semidirect
130. #2473C22semidirect
133. #2466C22semidirect
134. #2460C22semidirect
135. #2452C22semidirect
136. #2450C22semidirect
139. #2440C22semidirect
140. #2438C22semidirect
142. #2436C22semidirect
144. #2434C22semidirect
147. #2432C22semidirect
148. #2432C22semidirect
149. #2429C22semidirect
152. #2425C22semidirect
159. #2327C22semidirect
160. #2326C22semidirect
166. #2317C22semidirect
169. C4×C4⋊Q8C22semidirect
170. C4×#124C22semidirect
172. #2297C22semidirect
174. C2×#391C22semidirect

Maximal subgroups

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

subgroupindex
C2×#35392
C2×#35382
#508852
#488102
#463832
#463742
#394852
#394842
#393632
#393602
#380932
#380882
#380852
#380812
#374492
#374202
#373882
#373872
#353322
#353192
#353082
#353062
#340652