Finite Group Databasebeta

← #7654921

Subgroups — #7654921

Order 512.

6850 conjugacy classes of subgroups.

The subgroup lattice has 1035 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3511C211yesmaximal, characteristic, complemented
2C2×#3482C211yesmaximal, characteristic, complemented
3#42992C214yesmaximal, complemented
4#42157C218yesmaximal, complemented
5#39727C214yesmaximal, complemented
6#39491C212yesmaximal, complemented
7#39485C214yesmaximal, complemented
8#38958C212yesmaximal, complemented
9#38948C214yesmaximal, complemented
10#38035C218yesmaximal, complemented
11#37640C211yesmaximal, characteristic, complemented
12#37616C212yesmaximal, complemented
13#36562C212yesmaximal, complemented
14#36534C212yesmaximal, complemented
15#36404C214yesmaximal, complemented
16#35759C214yesmaximal, complemented
17#35320C211yesmaximal, characteristic, complemented
18#35279C211yesmaximal, characteristic, complemented
19#35201C212yesmaximal, complemented
20#35179C212yesmaximal, complemented
21#34977C211yesmaximal, characteristic, complemented
22#34955C212yesmaximal, complemented
23#34129C211yesmaximal, characteristic, complemented
24#3511—216no—
25#3482—216no—
26C2×#557C2211yescharacteristic
27C2×#556C2212yes—
28C2×#556C2212yes—
29C2×#556C2211yescharacteristic
30C2×#555C2212yes—
31C2×#554C2212yes—
32C2×#553C2214yes—
33C2×#552C2212yes—
34C2×#552C2214yes—
35C2×D4×Q8C2211yescharacteristic
36C2×#548C2212yes—
37C2×#548C2214yes—
38C2×#547C2212yes—
39C2×#547C2211yescharacteristic
40C2×#547C2212yes—
41C2×#542C2214yes—
42C2×#537C2212yes—
43C2×#533C2211yescharacteristic
44C2×#533C2212yes—
45C2×#533C2212yes—
46C2×#532C2211yescharacteristic
47C2×#532C2212yes—
48C22×C4⋊Q8C2211yescharacteristic
49C2×#529C2212yes—
50C2×#529C2214yes—
51C2×#520C2212yes—
52C2×C4×#41C2212yes—
53C2×C4×#41C2211yescharacteristic
54C2×C4×#41C2211yescharacteristic
55C22×C4×Q8C2212yes—
56#2862C2212yes—
57#2862C2212yes—
58#2861C2214yes—
59#2859C2214yes—
60#2857C2214yes—
61#2855C2218yes—
62#2820C2214yes—
63#2813C2218yes—
64#2725C22116yes—
65#2710C22116yes—
66#2702C22116yes—
67#2701C22116yes—
68#2700C22116yes—
69#2699C22116yes—
70#2663C2218yes—
71#2642C2214yes—
72#2636C2218yes—
73#2628C2214yes—
74#2627C2218yes—
75#2624C2214yes—
76#2620C2214yes—
77#2620C2214yes—
78#2620C2218yes—
79#2619C2214yes—
80#2616C2214yes—
81#2610C2214yes—
82#2604C2218yes—
83#2592C2218yes—
84#2591C2218yes—
85#2582C2218yes—
86#2581C2218yes—
87#2568C2214yes—
88#2568C2212yes—
89#2568C2212yes—
90#2568C2212yes—
91#2567C2212yes—
92#2567C2212yes—
93#2567C2211yescharacteristic
94#2566C2214yes—
95#2565C2214yes—
96#2565C2214yes—
97#2563C2212yes—
98#2563C2211yescharacteristic
99#2560C22116yes—
100#2556C22116yes—
101#2548C2212yes—
102#2548C2211yescharacteristic
103#2547C2212yes—
104#2544C2214yes—
105#2542C2212yes—
106#2542C2212yes—
107#2541C2211yescharacteristic
108#2538C2214yes—
109#2536C2218yes—
110#2504C2214yes—
111#2503C2214yes—
112#2503C2214yes—
113#2500C2214yes—
114#2500C2212yes—
115#2499C2214yes—
116#2487C2214yes—
117#2470C22116yes—
118#2466C22116yes—
119#2459C22116yes—
120#2457C22116yes—
121#2439C2218yes—
122#2436C2214yes—
123#2431C2212yes—
124#2429C2218yes—
125#2420C2218yes—
126#2415C2218yes—
127#2415C2218yes—
128#2414C2214yes—
129#2409C2214yes—
130#2407C2218yes—
131#2407C2218yes—
132#2398C2218yes—
133#2388C2214yes—
134#2360C2218yes—
135#2354C2212yes—
136#2354C2214yes—
137#2352C2218yes—
138Q8×C4⋊C4C2212yes—
139#2346C2214yes—
140#2346C2212yes—
141#2341C2212yes—
142#2323C2218yes—
143#2317C2212yes—
144#2317C2214yes—
145#2311C2212yes—
146#2310C2214yes—
147#2310C2214yes—
148C4×#127C2212yes—
149C4×#124C2214yes—
150C4×#124C2212yes—
151C4×#124C2214yes—
152C4×#121C2214yes—
153#2297C2218yes—
154#2293C2214yes—
155#2293C2212yes—
156#2285C2211yescharacteristic
157#2285C2212yes—
158C42×Q8C2212yes—
159C4×#117C2212yes—
160C4×#117C2211yescharacteristic
161C22×#41C2311yescharacteristic
162C22×#41C2312yes—
163C22×#41C2312yes—
164C22×#41C2314yes—
165C22×#41C2311yescharacteristic
166C23×Q8C2312yes—
167C23×Q8C2312yes—
168#557—28no—
169#556—28no—
170#556—216no—
171#556—216no—
172#555—216no—
173#554—216no—
174#553—232no—
175#552—216no—
176#552—232no—
177D4×Q8—28no—
178#548—216no—
179#548—232no—
180#547—216no—
181#547—28no—
182#547—216no—
183#542—232no—
184#537—216no—
185#533—216no—
186#533—28no—
187#533—216no—
188#532—216no—
189#532—28no—
190C2×C4⋊Q8—28no—
191C2×C4⋊Q8C2311yescharacteristic
192C2×C4⋊Q8C2312yes—
193C2×C4⋊Q8C2312yes—
194C2×C4⋊Q8C2312yes—
195C2×C4⋊Q8C2311yescharacteristic
196C2×C4⋊Q8C2311yescharacteristic
197C2×C4⋊Q8C2312yes—
198C2×C4⋊Q8C2312yes—
199C2×C4⋊Q8C2312yes—
200C2×#127C2311yescharacteristic
201C2×#127C2312yes—
202#529—232no—
203#529—216no—
204C2×#126C2314yes—
205C2×#126C2314yes—
206C2×#126C2314yes—
207C2×#126C2318yes—
208C2×#125C2312yes—
209C2×#125C2314yes—
210C2×#125C2312yes—
211C2×#125C2314yes—
212C2×#125C2314yes—
213C2×#124C2312yes—
214C2×#124C2314yes—
215C2×#124C2312yes—
216C2×#124C2314yes—
217C2×#124C2318yes—
218C2×#124C2312yes—
219C2×#124C2314yes—
220C2×#123C2314yes—
221C2×#123C2314yes—
222C2×#123C2314yes—
223C2×#123C2318yes—
224C2×C22⋊Q8C2318yes—
225C2×C22⋊Q8C2314yes—
226C2×C22⋊Q8C2312yes—
227C2×C22⋊Q8C2312yes—
228C2×C22⋊Q8C2312yes—
229C2×C22⋊Q8C2314yes—
230C2×C22⋊Q8C2312yes—
231C2×C22⋊Q8C2314yes—
232C2×C22⋊Q8C2312yes—
233C2×C22⋊Q8C2314yes—
234C2×C22⋊Q8C2314yes—
235C2×C22⋊Q8C2318yes—
236C2×C22⋊Q8C2318yes—
237C2×#121C2314yes—
238C2×#121C2312yes—
239C2×#121C2314yes—
240C2×#121C2312yes—
241C2×#121C2312yes—
242C2×#121C2314yes—
243C2×#121C2314yes—
244C2×#121C2318yes—
245C2×#121C2314yes—
246#520—216no—
247C4×#41—216no—
248C4×#41—28no—
249C4×#41D4116yescomplemented
250C2×C4×Q8—216no—
251C2×C4×Q8C2312yes—
252C2×C4×Q8C2312yes—
253C2×C4×Q8C2311yescharacteristic
254C2×C4×Q8C2311yescharacteristic
255C2×C4×Q8C2312yes—
256C2×C4×Q8C2312yes—
257C2×C4×Q8C2314yes—
258C2×C4×Q8C2314yes—
259C2×C4×Q8C2314yes—
260C2×C4×Q8C2314yes—
261C2×C4×Q8C2312yes—
262C2×C4×Q8C2314yes—
263C2×C4×Q8C2311yescharacteristic
264C2×C4×Q8C2311yescharacteristic
265C2×C4×D4C2311yescharacteristic
266C2×C4×D4C2312yes—
267C2×C4×D4C2311yescharacteristic
268C2×C4×D4C2314yes—
269C2×C4×D4C2314yes—
270C2×C4×D4C2312yes—
271C2×C4×D4C2314yes—
272C2×C4×D4C2312yes—
273C2×C4×D4C2312yes—
274C2×C4×D4C2314yes—
275C2×C4×D4C2318yes—
276C2×C4×D4C2312yes—
277C2×C4×D4C2318yes—
278C2×C4×D4C2311yescharacteristic
279C2×C4×D4C2312yes—
280C2×C4×D4C2311yescharacteristic
281C2×C4×D4C2312yes—
282C2×#117C2312yes—
283C2×#117C2314yes—
284C2×#117C2311yescharacteristic
285C2×#117C2314yes—
286C2×#117C2312yes—
287C2×#117C2312yes—
288C2×#117C2314yes—
289C2×#117C2314yes—
290C2×#117C2312yes—
291C2×#117C2314yes—
292C2×#117C2312yes—
293C2×#117C2314yes—
294C2×#117C2311yescharacteristic
295C2×#117C2312yes—
296C22×C4⋊C4C2312yes—
297C22×C4⋊C4C2312yes—
298C22×C4⋊C4C2314yes—
299C22×C4⋊C4C2314yes—
300C22×C4⋊C4C2312yes—
301C22×C42C2314yes—
302C22×C42C2312yes—
303C22×C42C2312yes—
304C22×C42C2311yescharacteristic
305#400C2318yes—
306#400C2318yes—
307#400C2318yes—
308#400C23116yes—
309#399C2318yes—
310#399C2318yes—
311#398C23116yes—
312#398C23116yes—
313#397C2318yes—
314#397C23116yes—
315#397C23116yes—
316#396C23116yes—
317#396C23116yes—
318#396C23116yes—
319#395C2318yes—
320#395C2314yes—
321#395C2318yes—
322#394C23116yes—
323#394C2318yes—
324#394C2314yes—
325#394C23116yes—
326#394C23116yes—
327#394C23116yes—
328#394C2318yes—
329#394C23116yes—
330#393C2318yes—
331#393C2314yes—
332#393C23116yes—
333#392C2314yes—
334#392C23116yes—
335#392C2318yes—
336#391C2318yes—
337#391C2312yes—
338#391C2314yes—
339#391C2314yes—
340#391C2314yes—
341#391C2318yes—
342#391C2318yes—
343#391C23116yes—
344#391C2318yes—
345#391C2318yes—
346#391C2314yes—
347#391C2318yes—
348#390C2318yes—
349#390C2312yes—
350#390C2312yes—
351#390C2314yes—
352#390C2312yes—
353#390C2314yes—
354#390C2314yes—
355#390C2318yes—
356#390C2314yes—
357#390C2318yes—
358#389C2318yes—
359#389C2314yes—
360#389C2318yes—
361#389C23116yes—
362#389C2318yes—
363#389C23116yes—
364#389C2314yes—
365#389C2318yes—
366#389C23116yes—
367#388C23116yes—
368#388C23116yes—
369#388C23116yes—
370#388C23116yes—
371#388C23116yes—
372#388C2318yes—
373#388C2318yes—
374#388C2318yes—
375#388C2318yes—
376#388C2318yes—
377#387C23116yes—
378#387C23116yes—
379#387C23116yes—
380#386C23116yes—
381#386C2318yes—
382#386C23116yes—
383#386C23116yes—
384#386C2318yes—
385#385C23116yes—
386#385C23116yes—
387#385C2318yes—
388#384C2312yes—
389#384C2314yes—
390#384C2314yes—
391#384C2314yes—
392#384C2312yes—
393#382C2314yes—
394#382C2312yes—
395#382C2312yes—
396#382C2314yes—
397#382C2314yes—
398#382C2318yes—
399#382C2314yes—
400#381C23116yes—
401#381C23116yes—
402#380C2314yes—
403#380C2318yes—
404#380C2318yes—
405#380C2312yes—
406#380C2314yes—
407#380C2314yes—
408#380C2318yes—
409#380C2312yes—
410C4×C4⋊C4C2318yes—
411C4×C4⋊C4C2312yes—
412C4×C4⋊C4C2311yescharacteristic
413C4×C4⋊C4C2314yes—
414C4×C4⋊C4C2311yescharacteristic
415C4×C4⋊C4C2312yes—
416C4×C4⋊C4C2312yes—
417C4×C4⋊C4C2314yes—
418C4×C4⋊C4C2314yes—
419C4×C22⋊C4C23116yes—
420C4×C22⋊C4C2314yes—
421C4×C22⋊C4C2312yes—
422C4×C22⋊C4C2318yes—
423C4×C22⋊C4C23116yes—
424C4×C22⋊C4C2312yes—
425C4×C22⋊C4C2314yes—
426#376C2314yes—
427#376C2312yes—
428C43C2312yes—
429C43C2314yes—
430C2×#41—24no—
431C2×#41—28no—
432C2×#41—24no—
433C2×#41—28no—
434C2×#41—216no—
435C2×#41—48no—
436C2×#41—42no—
437C2×#41—44no—
438C2×#41—48no—
439C2×#41—416no—
440C2×#41C2×D418yes—
441C22×Q8—28no—
442C22×Q8—28no—
443C22×Q8—28no—
444C22×Q8—44no—
445C22×Q8—48no—
446C22×Q8C2412yes—
447C22×Q8C2412yes—
448C22×Q8C2414yes—
449C22×Q8C2414yes—
450C22×Q8C2411yescharacteristic
451C22×Q8C2411yescharacteristic
452C22×Q8C2412yes—
453C22×Q8C2414yes—
454C22×D4C2412yes—
455C22×D4C2411yescharacteristic
456C22×D4C2412yes—
457C22×D4C2412yes—
458C22×D4C2411yescharacteristic
459C22×D4C2414yes—
460C22×D4C2414yes—
461C22×D4C2412yes—
462C22×D4C2418yes—
463C22×D4C2418yes—
464C22×D4C2412yes—
465C23×C4C2414yes—
466C23×C4C2412yes—
467C23×C4C2412yes—
468C23×C4C2414yes—
469C23×C4C2412yes—
470C23×C4C2411yescharacteristic
471C23×C4C2411yescharacteristic
472C23×C4C2412yes—
473C23×C4C2411yescharacteristic
474C23×C4C2412yes—
475C23×C4C2414yes—
476C23×C4C2414yes—
477C23×C4C2418yes—
478C23×C4C2412yes—
479C4⋊Q8—28no—
480C4⋊Q8—28no—
481C4⋊Q8—28no—
482C4⋊Q8—28no—
483C4⋊Q8—28no—
484C4⋊Q8—28no—
485C4⋊Q8—24no—
486C4⋊Q8—24no—
487C4⋊Q8—24no—
488#127—24no—
489#127—44no—
490#126—216no—
491#126—232no—
492#126—216no—
493#126—216no—
494#125—216no—
495#125—216no—
496#125—28no—
497#125—28no—
498#125—216no—
499#124—28no—
500#124—216no—
501#124—232no—
502#124—28no—
503#124—28no—
504#124—216no—
505#124—48no—
506#123—216no—
507#123—216no—
508#123—216no—
509#123—232no—
510C22⋊Q8—28no—
511C22⋊Q8—216no—
512C22⋊Q8—28no—
513C22⋊Q8—216no—
514C22⋊Q8—216no—
515C22⋊Q8—28no—
516C22⋊Q8—28no—
517C22⋊Q8—28no—
518C22⋊Q8—216no—
519C22⋊Q8—232no—
520C22⋊Q8—216no—
521C22⋊Q8—416no—
522C22⋊Q8—416no—
523#121—216no—
524#121—216no—
525#121—232no—
526#121—28no—
527#121—216no—
528#121—28no—
529#121—28no—
530#121—216no—
531#121—48no—
532C4×Q8—28no—
533C4×Q8—24no—
534C4×Q8—216no—
535C4×Q8—28no—
536C4×Q8—28no—
537C4×Q8—28no—
538C4×Q8—216no—
539C4×Q8—28no—
540C4×Q8—24no—
541C4×Q8—216no—
542C4×Q8—216no—
543C4×Q8—48no—
544C4×Q8C2×D418yes—
545C4×Q8C2×D418yes—
546C4×D4—28no—
547C4×D4—28no—
548C4×D4—216no—
549C4×D4—28no—
550C4×D4—216no—
551C4×D4—232no—
552C4×D4—24no—
553C4×D4—24no—
554C4×D4—216no—
555C4×D4—28no—
556C4×D4—216no—
557C4×D4—28no—
558C4×D4—416no—
559C4×D4C2×D418yes—
560C4×D4C2×D4116yes—
561C4×D4C2×D418yes—
562C4×D4C2×D4116yes—
563#117—24no—
564#117—28no—
565#117—216no—
566#117—28no—
567#117—216no—
568#117—216no—
569#117—28no—
570#117—216no—
571#117—44no—
572#117—48no—
573#117—44no—
574#117—48no—
575#117C2×D418yes—
576#117C2×D4116yes—
577C2×C4⋊C4—28no—
578C2×C4⋊C4—216no—
579C2×C4⋊C4—28no—
580C2×C4⋊C4—28no—
581C2×C4⋊C4—216no—
582C2×C4⋊C4C2411yescharacteristic
583C2×C4⋊C4C2412yes—
584C2×C4⋊C4C2414yes—
585C2×C4⋊C4C2414yes—
586C2×C4⋊C4C2414yes—
587C2×C4⋊C4C2418yes—
588C2×C4⋊C4C2412yes—
589C2×C4⋊C4C2414yes—
590C2×C4⋊C4C2414yes—
591C2×C4⋊C4C2414yes—
592C2×C4⋊C4C2414yes—
593C2×C4⋊C4C2414yes—
594C2×C4⋊C4C2412yes—
595C2×C4⋊C4C2412yes—
596C2×C4⋊C4C2411yescharacteristic
597C2×C4⋊C4C2412yes—
598C2×C4⋊C4C2414yes—
599C2×C4⋊C4C2412yes—
600C2×C4⋊C4C2414yes—
601C2×C4⋊C4C2412yes—
602C2×C4⋊C4C2414yes—
603C2×C4⋊C4C2412yes—
604C2×C4⋊C4C2414yes—
605C2×C4⋊C4C2414yes—
606C2×C4⋊C4C2412yes—
607C2×C4⋊C4C2412yes—
608C2×C4⋊C4C2418yes—
609C2×C4⋊C4C2414yes—
610C2×C4⋊C4C2414yes—
611C2×C4⋊C4C2418yes—
612C2×C4⋊C4C2418yes—
613C2×C4⋊C4C2418yes—
614C2×C4⋊C4C24116yes—
615C2×C4⋊C4C24116yes—
616C2×C4⋊C4C2411yescharacteristic
617C2×C4⋊C4C2411yescharacteristic
618C2×C4⋊C4C2412yes—
619C2×C4⋊C4C2412yes—
620C2×C22⋊C4C2418yes—
621C2×C22⋊C4C2414yes—
622C2×C22⋊C4C2412yes—
623C2×C22⋊C4C2412yes—
624C2×C22⋊C4C2412yes—
625C2×C22⋊C4C2414yes—
626C2×C22⋊C4C2418yes—
627C2×C22⋊C4C2414yes—
628C2×C22⋊C4C2414yes—
629C2×C22⋊C4C2414yes—
630C2×C22⋊C4C2418yes—
631C2×C22⋊C4C2414yes—
632C2×C22⋊C4C2414yes—
633C2×C22⋊C4C2418yes—
634C2×C22⋊C4C2414yes—
635C2×C22⋊C4C2418yes—
636C2×C22⋊C4C2418yes—
637C2×C22⋊C4C2414yes—
638C2×C22⋊C4C2418yes—
639C2×C22⋊C4C2418yes—
640C2×C22⋊C4C2418yes—
641C2×C22⋊C4C24116yes—
642C2×C22⋊C4C24116yes—
643C2×C22⋊C4C24116yes—
644C2×C22⋊C4C2412yes—
645C2×C22⋊C4C2412yes—
646C2×C22⋊C4C2412yes—
647C2×C42—216no—
648C2×C42—28no—
649C2×C42C2×D4116yes—
650C2×C42C2×D418yes—
651C2×C42C2412yes—
652C2×C42C2414yes—
653C2×C42C2418yes—
654C2×C42C2414yes—
655C2×C42C2414yes—
656C2×C42C2412yes—
657C2×C42C2412yes—
658C2×C42C2414yes—
659C2×C42C2414yes—
660C2×C42C2412yes—
661C2×C42C2412yes—
662C2×C42C2418yes—
663C2×C42C2414yes—
664C2×C42C2418yes—
665C2×C42C2411yescharacteristic
666C2×C42C2412yes—
667C2×C42C2412yes—
668C2×C42C2411yescharacteristic
669C2×C42C2412yes—
670C2×C42C2411yescharacteristic
671C2×C42C2411yescharacteristic
672#95C2412yes—
673#95C2412yes—
674#95C2414yes—
675#95C2414yes—
676#95C2418yes—
677#95C24116yes—
678#95C24116yes—
679#95C2418yes—
680#95C2418yes—
681#95C24116yes—
682#95C24116yes—
683#95C2418yes—
684#95C2414yes—
685#95C24116yes—
686#95C24116yes—
687#95C24116yes—
688C24C2512yes—
689C24C2514yes—
690C24C2512yes—
691C24C2511yescharacteristic
692#41—416no—
693#41—416no—
694#41—432no—
695#41—432no—
696#41—832no—
697C2×Q8—22no—
698C2×Q8—28no—
699C2×Q8—24no—
700C2×Q8—24no—
701C2×Q8—24no—
702C2×Q8—28no—
703C2×Q8—28no—
704C2×Q8—28no—
705C2×Q8—24no—
706C2×Q8—24no—
707C2×Q8—22no—
708C2×Q8—28no—
709C2×Q8—216no—
710C2×Q8—24no—
711C2×Q8—44no—
712C2×Q8—44no—
713C2×Q8—48no—
714C2×Q8—432no—
715C2×Q8—816no—
716C2×Q8C22×D414yes—
717C2×Q82−1+414yes—
718C2×D4—28no—
719C2×D4—28no—
720C2×D4—24no—
721C2×D4—216no—
722C2×D4—24no—
723C2×D4—22no—
724C2×D4—24no—
725C2×D4—24no—
726C2×D4—24no—
727C2×D4—24no—
728C2×D4—22no—
729C2×D4—24no—
730C2×D4—28no—
731C2×D4—24no—
732C2×D4—22no—
733C2×D4—44no—
734C2×D4—44no—
735C2×D4—42no—
736C2×D4—48no—
737C2×D4—48no—
738C2×D4—48no—
739C2×D4—48no—
740C2×D4—48no—
741C2×D4—416no—
742C2×D4C22×D414yes—
743C2×D4C22×D418yes—
744C22×C4—24no—
745C22×C4—22no—
746C22×C4—24no—
747C22×C4—22no—
748C22×C4—24no—
749C22×C4—28no—
750C22×C4—24no—
751C22×C4—28no—
752C22×C4—28no—
753C22×C4—28no—
754C22×C4—24no—
755C22×C4—24no—
756C22×C4—24no—
757C22×C4—28no—
758C22×C4—28no—
759C22×C4—24no—
760C22×C4—28no—
761C22×C4—216no—
762C22×C4—28no—
763C22×C4—216no—
764C22×C4—44no—
765C22×C4—44no—
766C22×C4—42no—
767C22×C4—48no—
768C22×C4—48no—
769C22×C4—416no—
770C22×C4C22×D418yes—
771C22×C4C22×D414yes—
772C22×C4C22×D414yes—
773C22×C4C22×D418yes—
774C22×C4C22×D414yes—
775C22×C4C22×D418yes—
776C22×C4C2514yes—
777C22×C4C2514yes—
778C22×C4C2514yes—
779C22×C4C2518yes—
780C22×C4C2518yes—
781C22×C4C2512yes—
782C22×C4C2514yes—
783C22×C4C2514yes—
784C22×C4C2512yes—
785C22×C4C2511yescharacteristic
786C22×C4C2512yes—
787C22×C4C2512yes—
788C22×C4C2511yescharacteristic
789C22×C4C2511yescharacteristic
790C22×C4C2512yes—
791C22×C4C2512yes—
792C22×C4C2511yescharacteristic
793C22×C4C2511yescharacteristic
794C22×C4C2511yescharacteristic
795C4⋊C4—24no—
796C4⋊C4—22no—
797C4⋊C4—28no—
798C4⋊C4—28no—
799C4⋊C4—28no—
800C4⋊C4—216no—
801C4⋊C4—28no—
802C4⋊C4—24no—
803C4⋊C4—28no—
804C4⋊C4—28no—
805C4⋊C4—28no—
806C4⋊C4—28no—
807C4⋊C4—24no—
808C4⋊C4—24no—
809C4⋊C4—22no—
810C4⋊C4—28no—
811C4⋊C4—24no—
812C4⋊C4—28no—
813C4⋊C4—28no—
814C4⋊C4—24no—
815C4⋊C4—28no—
816C4⋊C4—24no—
817C4⋊C4—24no—
818C4⋊C4—216no—
819C4⋊C4—24no—
820C4⋊C4—24no—
821C4⋊C4—28no—
822C4⋊C4—28no—
823C4⋊C4—44no—
824C4⋊C4—48no—
825C4⋊C4—48no—
826C4⋊C4—48no—
827C4⋊C4—416no—
828C4⋊C4—416no—
829C4⋊C4C22×D414yes—
830C4⋊C4C22×D414yes—
831C4⋊C4C22×D418yes—
832C4⋊C4C22×D418yes—
833C22⋊C4—28no—
834C22⋊C4—24no—
835C22⋊C4—216no—
836C22⋊C4—28no—
837C22⋊C4—216no—
838C22⋊C4—24no—
839C22⋊C4—24no—
840C22⋊C4—28no—
841C22⋊C4—28no—
842C22⋊C4—28no—
843C22⋊C4—216no—
844C22⋊C4—28no—
845C22⋊C4—28no—
846C22⋊C4—216no—
847C22⋊C4—44no—
848C22⋊C4—48no—
849C22⋊C4—48no—
850C22⋊C4—44no—
851C22⋊C4—48no—
852C22⋊C4—48no—
853C22⋊C4—48no—
854C22⋊C4—416no—
855C22⋊C4—416no—
856C22⋊C4—416no—
857C22⋊C4C22×D418yes—
858C22⋊C4C22×D418yes—
859C22⋊C4C22×D418yes—
860C42—24no—
861C42—24no—
862C42—28no—
863C42—28no—
864C42—24no—
865C42—28no—
866C42—216no—
867C42—24no—
868C42—28no—
869C42—24no—
870C42—28no—
871C42—48no—
872C42—44no—
873C42—48no—
874C42C22×D414yes—
875C42C22×D414yes—
876C42C22×D414yes—
877C42C22×D418yes—
878C42C22×D418yes—
879C42C22×D414yes—
880C42C22×D418yes—
881C23—22no—
882C23—21no—
883C23—22no—
884C23—21no—
885C23—22no—
886C23—24no—
887C23—22no—
888C23—24no—
889C23—22no—
890C23—24no—
891C23—24no—
892C23—22no—
893C23—24no—
894C23—24no—
895C23—28no—
896C23—24no—
897C23—28no—
898C23—22no—
899C23C23×D414yes—
900C23C23×D412yes—
901C23C2611yescharacteristic
902Q8—28no—
903Q8—28no—
904Q8—416no—
905Q8—48no—
906Q8—48no—
907Q8—48no—
908Q8—416no—
909Q8—88no—
910D4—28no—
911D4—48no—
912D4—48no—
913D4—48no—
914D4—416no—
915D4—416no—
916D4—48no—
917D4—44no—
918D4—48no—
919D4—816no—
920D4—816no—
921C2×C4—22no—
922C2×C4—21no—
923C2×C4—22no—
924C2×C4—24no—
925C2×C4—24no—
926C2×C4—22no—
927C2×C4—21no—
928C2×C4—22no—
929C2×C4—22no—
930C2×C4—22no—
931C2×C4—28no—
932C2×C4—216no—
933C2×C4—28no—
934C2×C4—28no—
935C2×C4—216no—
936C2×C4—22no—
937C2×C4—22no—
938C2×C4—24no—
939C2×C4—24no—
940C2×C4—24no—
941C2×C4—28no—
942C2×C4—24no—
943C2×C4—24no—
944C2×C4—24no—
945C2×C4—28no—
946C2×C4—24no—
947C2×C4—24no—
948C2×C4—24no—
949C2×C4—28no—
950C2×C4—24no—
951C2×C4—28no—
952C2×C4—24no—
953C2×C4—24no—
954C2×C4—24no—
955C2×C4—28no—
956C2×C4—28no—
957C2×C4—216no—
958C2×C4—48no—
959C2×C4—48no—
960C2×C4—416no—
961C2×C4—416no—
962C2×C4—48no—
963C2×C4—416no—
964C2×C4—48no—
965C2×C4—816no—
966C2×C4—88no—
967C2×C4C23×D414yes—
968C2×C4C23×D414yes—
969C2×C4C23×D412yes—
970C2×C4C23×D412yes—
971C2×C4C23×D412yes—
972C2×C4C23×D414yes—
973C2×C4C23×D412yes—
974C2×C4C23×D412yes—
975C2×C4C23×D412yes—
976C2×C4C2×2−1+414yes—
977C2×C4C2×2−1+412yes—
978C2×C4#58514yes—
979C2×C4#58512yes—
980C2×C4#58514yes—
981C22—24no—
982C22—22no—
983C22—22no—
984C22—24no—
985C22—22no—
986C22—24no—
987C22—44no—
988C22—42no—
989C22—44no—
990C22—42no—
991C22—44no—
992C22—48no—
993C22—48no—
994C22—44no—
995C22—42no—
996C22—44no—
997C22—42no—
998C22—44no—
999C22—44no—
1000C22—42no—
1001C22C24×D411yescharacteristic
1002C22C22×2−1+411yescharacteristic
1003C22C2×#58511yescharacteristic
1004C22C2×#58512yes—
1005C22C2×#58512yes—
1006C4—22no—
1007C4—24no—
1008C4—24no—
1009C4—24no—
1010C4—22no—
1011C4—22no—
1012C4—24no—
1013C4—48no—
1014C4—44no—
1015C4—44no—
1016C4—44no—
1017C4—42no—
1018C4—48no—
1019C4—42no—
1020C4—44no—
1021C4—44no—
1022C4#344914yes—
1023C4#348914yes—
1024C4#350014yes—
1025C2—44no—
1026C2—42no—
1027C2—82no—
1028C2—84no—
1029C2C2×#344911yescharacteristic
1030C2C2×#348911yescharacteristic
1031C2C2×#350011yescharacteristic
1032C2#6303112yes—
1033C2#6303412yes—
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×#3511C2semidirect
2. C2×#3482C2semidirect
3. #42992C2semidirect
4. #42157C2semidirect
5. #39727C2semidirect
6. #39491C2semidirect
7. #39485C2semidirect
8. #38958C2semidirect
9. #38948C2semidirect
10. #38035C2semidirect
11. #37640C2semidirect
12. #37616C2semidirect
13. #36562C2semidirect
14. #36534C2semidirect
15. #36404C2semidirect
16. #35759C2semidirect
17. #35320C2semidirect
18. #35279C2semidirect
19. #35201C2semidirect
20. #35179C2semidirect
21. #34977C2semidirect
22. #34955C2semidirect
23. #34129C2semidirect
249. C4×#41D4semidirect

Maximal subgroups

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

subgroupindex
C2×#35112
C2×#34822
#429922
#421572
#397272
#394912
#394852
#389582
#389482
#380352
#376402
#376162
#365622
#365342
#364042
#357592
#353202
#352792
#352012
#351792
#349772
#349552
#341292