Finite Group Databasebeta

← #7658111

Subgroups — #7658111

Order 512.

7844 conjugacy classes of subgroups.

The subgroup lattice has 1019 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3499C211yesmaximal, characteristic, complemented
2C2×#3515C211yesmaximal, characteristic, complemented
3#42994C214yesmaximal, complemented
4#42792C214yesmaximal, complemented
5#42297C218yesmaximal, complemented
6#41375C218yesmaximal, complemented
7#39618C212yesmaximal, complemented
8#39616C212yesmaximal, complemented
9#37864C214yesmaximal, complemented
10#37863C214yesmaximal, complemented
11#37634C211yesmaximal, characteristic, complemented
12#37632C212yesmaximal, complemented
13#37615C211yesmaximal, characteristic, complemented
14#37539C212yesmaximal, complemented
15#36179C212yesmaximal, complemented
16#36164C212yesmaximal, complemented
17#36085C214yesmaximal, complemented
18#36020C214yesmaximal, complemented
19#35303C212yesmaximal, complemented
20#35281C211yesmaximal, characteristic, complemented
21#34624C211yesmaximal, characteristic, complemented
22C2×#2660C212yesmaximal, complemented
23#34123C211yesmaximal, characteristic, complemented
24C22×2−1+4C2212yes—
25#3515—216no—
26#3499—216no—
27C2×#557C2211yescharacteristic
28C2×#554C2211yescharacteristic
29C2×#554C2211yescharacteristic
30C2×#553C2212yes—
31C2×#552C2214yes—
32C2×#552C2212yes—
33C2×#552C2212yes—
34C2×D4×Q8C2212yes—
35C2×D4×Q8C2212yes—
36C2×#547C2211yescharacteristic
37C2×#547C2212yes—
38C2×#547C2212yes—
39C2×#547C2214yes—
40C2×#547C2212yes—
41C2×#547C2214yes—
42C2×#547C2218yes—
43C2×#541C2212yes—
44C2×#539C2214yes—
45C2×#536C2214yes—
46C2×#536C2212yes—
47C2×#533C2211yescharacteristic
48C2×#532C2211yescharacteristic
49C2×#532C2212yes—
50C22×C4⋊Q8C2212yes—
51C22×C4⋊Q8C2211yescharacteristic
52C2×#529C2212yes—
53C2×#529C2211yescharacteristic
54C22×#125C2212yes—
55C2×#520C2212yes—
56C2×C4×#41C2211yescharacteristic
57#2868C2212yes—
58#2862C2212yes—
59#2856C2214yes—
60#2850C2214yes—
61#2821C2218yes—
62#2821C2214yes—
63#2820C2218yes—
64#2816C2214yes—
65#2723C22116yes—
66#2720C22116yes—
67#2720C22116yes—
68#2718C22116yes—
69#2706C22116yes—
70#2692C22116yes—
71#2662C2214yes—
72#2661C2214yes—
73#2660C2212yes—
74#2660C2212yes—
75#2660C2218yes—
76#2660C2218yes—
77#2660C2211yescharacteristic
78#2660C2212yes—
79#2660C2214yes—
80#2660C2214yes—
81#2660C2212yes—
82#2657C2211yescharacteristic
83#2641C2212yes—
84#2641C2211yescharacteristic
85#2640C2211yescharacteristic
86#2640C2212yes—
87#2633C2218yes—
88#2632C2214yes—
89#2628C2218yes—
90#2623C2214yes—
91#2621C2214yes—
92#2620C2212yes—
93#2619C2212yes—
94#2618C2218yes—
95#2616C2214yes—
96#2614C2218yes—
97#2610C2218yes—
98#2603C2218yes—
99#2568C2212yes—
100#2567C2214yes—
101#2567C2214yes—
102#2566C2214yes—
103#2566C2214yes—
104#2563C2214yes—
105#2563C2212yes—
106#2546C2214yes—
107#2543C2218yes—
108#2542C2212yes—
109#2542C2218yes—
110#2542C2212yes—
111#2536C2214yes—
112#2504C2214yes—
113#2504C2212yes—
114#2503C2214yes—
115#2502C2214yes—
116#2502C2212yes—
117#2501C2214yes—
118#2501C22116yes—
119#2501C2214yes—
120#2500C2214yes—
121#2489C2218yes—
122#2488C22116yes—
123#2486C2218yes—
124#2434C2218yes—
125#2434C2214yes—
126#2430C2218yes—
127#2430C22116yes—
128#2429C2218yes—
129#2425C22116yes—
130#2417C2218yes—
131#2413C22116yes—
132#2409C2218yes—
133#2409C2214yes—
134#2406C2218yes—
135#2406C22116yes—
136#2392C2214yes—
137C2×#398C2218yes—
138#2388C2214yes—
139C2×#395C2218yes—
140#2356C2212yes—
141#2353C2214yes—
142#2349C2212yes—
143#2346C2212yes—
144#2343C2214yes—
145#2339C2218yes—
146#2339C2212yes—
147#2328C2214yes—
148#2326C2214yes—
149#2317C2214yes—
150C4×#127C2212yes—
151C4×#124C2212yes—
152#2295C2212yes—
153#2290C2214yes—
154C2×#384C2214yes—
155#2283C2212yes—
156#2283C2211yescharacteristic
157C2×#382C2214yes—
158C42×D4C2212yes—
159C4×#117C2211yescharacteristic
160C2×#376C2212yes—
161C2×2−1+4—216no—
162C2×2−1+4—416no—
163C22×#41C2314yes—
164C22×#41C2312yes—
165C22×#41C2311yescharacteristic
166C22×#41C2312yes—
167C22×#41C2314yes—
168C22×#41C2318yes—
169C23×Q8C2314yes—
170C23×Q8C2312yes—
171C23×Q8C2314yes—
172#557—28no—
173#554—28no—
174#554—28no—
175#553—216no—
176#552—216no—
177#552—232no—
178#552—216no—
179D4×Q8—216no—
180D4×Q8—216no—
181#547—216no—
182#547—216no—
183#547—232no—
184#547—216no—
185#547—232no—
186#547—28no—
187#547—432no—
188#541—216no—
189#539—232no—
190#536—232no—
191#536—216no—
192#533—28no—
193#532—216no—
194#532—28no—
195C2×C4⋊Q8—216no—
196C2×C4⋊Q8—28no—
197C2×C4⋊Q8C2311yescharacteristic
198C2×C4⋊Q8C2314yes—
199C2×C4⋊Q8C2312yes—
200C2×C4⋊Q8C2314yes—
201C2×C4⋊Q8C2312yes—
202C2×C4⋊Q8C2311yescharacteristic
203C2×C4⋊Q8C2312yes—
204C2×C4⋊Q8C2314yes—
205C2×C4⋊Q8C2311yescharacteristic
206C2×C4⋊Q8C2312yes—
207C2×C4⋊Q8C2312yes—
208C2×C4⋊Q8C2318yes—
209C2×#127C2312yes—
210C2×#127C2311yescharacteristic
211#529—216no—
212#529—28no—
213C2×#126C2314yes—
214C2×#126C2312yes—
215C2×#126C2314yes—
216C2×#126C2314yes—
217C2×#125—216no—
218C2×#125C2314yes—
219C2×#125C2312yes—
220C2×#125C2312yes—
221C2×#125C2314yes—
222C2×#125C2311yescharacteristic
223C2×#125C2312yes—
224C2×#125C2314yes—
225C2×#125C2314yes—
226C2×#125C2312yes—
227C2×#124C2314yes—
228C2×#124C2312yes—
229C2×#124C2312yes—
230C2×#124C2311yescharacteristic
231C2×#123C2314yes—
232C2×#123C2312yes—
233C2×#123C2314yes—
234C2×#123C2318yes—
235C2×#123C2318yes—
236C2×#123C2318yes—
237C2×#123C2314yes—
238C2×#123C2314yes—
239C2×#123C23116yes—
240C2×#123C23116yes—
241C2×C22⋊Q8C2312yes—
242C2×C22⋊Q8C2312yes—
243C2×C22⋊Q8C2312yes—
244C2×C22⋊Q8C2311yescharacteristic
245C2×C22⋊Q8C2312yes—
246C2×C22⋊Q8C2314yes—
247C2×C22⋊Q8C2318yes—
248C2×C22⋊Q8C2318yes—
249C2×C22⋊Q8C2314yes—
250C2×C22⋊Q8C2314yes—
251C2×C22⋊Q8C2314yes—
252C2×C22⋊Q8C2312yes—
253C2×C22⋊Q8C2318yes—
254C2×C22⋊Q8C2318yes—
255C2×#121C2312yes—
256C2×#121C2314yes—
257C2×#121C2312yes—
258C2×#121C2314yes—
259C2×#121C2311yescharacteristic
260C2×#121C2312yes—
261C2×#121C2314yes—
262C2×#121C23116yes—
263#520—216no—
264C4×#41D4116yescomplemented
265C2×C4×Q8C2312yes—
266C2×C4×Q8C2312yes—
267C2×C4×Q8C2311yescharacteristic
268C2×C4×Q8C2312yes—
269C2×C4×Q8C2312yes—
270C2×C4×Q8C2311yescharacteristic
271C2×C4×Q8C2311yescharacteristic
272C2×C4×D4C2311yescharacteristic
273C2×C4×D4C2312yes—
274C2×C4×D4C2312yes—
275C2×C4×D4C2314yes—
276C2×C4×D4C2312yes—
277C2×C4×D4C2314yes—
278C2×C4×D4C2314yes—
279C2×C4×D4C2312yes—
280C2×C4×D4C2312yes—
281C2×C4×D4C2314yes—
282C2×C4×D4C2314yes—
283C2×C4×D4C2318yes—
284C2×C4×D4C2311yescharacteristic
285C2×C4×D4C2312yes—
286C2×C4×D4C2311yescharacteristic
287C2×C4×D4C2312yes—
288C2×#117C2312yes—
289C2×#117C2312yes—
290C2×#117C2314yes—
291C2×#117C2312yes—
292C2×#117C2314yes—
293C2×#117C2312yes—
294C2×#117C2311yescharacteristic
295C22×C4⋊C4C2312yes—
296C22×C4⋊C4C2314yes—
297C22×C4⋊C4C2312yes—
298C22×C4⋊C4C2314yes—
299C22×C4⋊C4C2314yes—
300C22×C4⋊C4C2312yes—
301C22×C4⋊C4C2312yes—
302C22×C4⋊C4C2312yes—
303C22×C4⋊C4C2314yes—
304C22×C4⋊C4C23116yes—
305C22×C42C2314yes—
306C22×C42C2312yes—
307C22×C42C2311yescharacteristic
308#400C2318yes—
309#400C23116yes—
310#399C2318yes—
311#399C23116yes—
312#399C2318yes—
313#399C23116yes—
314#398C2318yes—
315#398C2318yes—
316#398C2318yes—
317#398C2318yes—
318#398C2318yes—
319#398C2314yes—
320#398C23116yes—
321#398C23116yes—
322#397C23116yes—
323#397C2314yes—
324#397C2318yes—
325#397C2318yes—
326#396C23116yes—
327#396C23116yes—
328#396C2318yes—
329#395C2318yes—
330#395C2318yes—
331#395C23116yes—
332#395C2318yes—
333#395C2318yes—
334#395C2314yes—
335#395C23116yes—
336#395C23116yes—
337#394C2318yes—
338#394C23116yes—
339#394C2314yes—
340#394C2318yes—
341#394C2314yes—
342#394C2318yes—
343#394C2318yes—
344#393C2318yes—
345#393C23116yes—
346#393C2318yes—
347#393C2314yes—
348#392C2314yes—
349#392C2314yes—
350#392C2318yes—
351#391C2312yes—
352#391C2314yes—
353#391C2318yes—
354#391C2318yes—
355#391C2318yes—
356#391C2314yes—
357#390C2312yes—
358#390C2312yes—
359#390C2318yes—
360#390C2314yes—
361#390C2314yes—
362#390C2312yes—
363#390C2314yes—
364#390C23116yes—
365#389C23116yes—
366#389C23116yes—
367#389C2314yes—
368#388C23116yes—
369#388C23116yes—
370#388C2318yes—
371#388C23116yes—
372#388C2318yes—
373#387C2318yes—
374#387C2318yes—
375#386C23116yes—
376#386C23116yes—
377#386C23116yes—
378#386C2318yes—
379#386C23116yes—
380#386C2318yes—
381#385C23116yes—
382#385C23116yes—
383#385C23116yes—
384#385C23116yes—
385#385C2318yes—
386#385C2318yes—
387#384C2312yes—
388#384C2314yes—
389#384C2314yes—
390#384C2318yes—
391#384C2314yes—
392#384C2314yes—
393#384C23116yes—
394#383C2312yes—
395#383C2314yes—
396#382C2314yes—
397#382C2314yes—
398#382C2314yes—
399#382C2314yes—
400#382C2314yes—
401#382C2312yes—
402#382C2312yes—
403#382C23116yes—
404#381C2312yes—
405#381C2314yes—
406#381C23116yes—
407#380C2318yes—
408#380C23116yes—
409#380C2312yes—
410#380C2314yes—
411C4×C4⋊C4C2314yes—
412C4×C4⋊C4C2312yes—
413C4×C4⋊C4C2312yes—
414C4×C4⋊C4C2314yes—
415C4×C4⋊C4C2312yes—
416C4×C22⋊C4C2312yes—
417C4×C22⋊C4C2318yes—
418C4×C22⋊C4C2318yes—
419C4×C22⋊C4C2312yes—
420C4×C22⋊C4C2312yes—
421C4×C22⋊C4C2314yes—
422#376C2314yes—
423#376C2314yes—
424#376C2314yes—
425#376C2312yes—
426#376C2311yescharacteristic
427#376C2311yescharacteristic
428C2×#95C2314yes—
429C2×#95C23116yes—
430C2×#95C2314yes—
431C43C2312yes—
4322−1+4—4128no—
433C2×#41—28no—
434C2×#41—232no—
435C2×#41—216no—
436C2×#41—28no—
437C2×#41—216no—
438C2×#41—232no—
439C2×#41—216no—
440C2×#41—28no—
441C2×#41—48no—
442C2×#41—416no—
443C2×#41—432no—
444C2×#41C2×D418yes—
445C22×Q8—216no—
446C22×Q8—216no—
447C22×Q8—28no—
448C22×Q8—416no—
449C22×Q8—48no—
450C22×Q8—416no—
451C22×Q8C2411yescharacteristic
452C22×Q8C2412yes—
453C22×Q8C2414yes—
454C22×Q8C2411yescharacteristic
455C22×Q8C2412yes—
456C22×Q8C2418yes—
457C22×Q8C2414yes—
458C22×Q8C2412yes—
459C22×D4C2411yescharacteristic
460C22×D4C2412yes—
461C22×D4C2414yes—
462C22×D4C2418yes—
463C22×D4C2412yes—
464C22×D4C2412yes—
465C22×D4C2412yes—
466C22×D4C2418yes—
467C22×D4C2414yes—
468C22×D4C2412yes—
469C22×D4C2411yescharacteristic
470C23×C4C2414yes—
471C23×C4C2418yes—
472C23×C4C2412yes—
473C23×C4C2414yes—
474C23×C4C2418yes—
475C23×C4C2412yes—
476C23×C4C2411yescharacteristic
477C23×C4C2412yes—
478C23×C4C2411yescharacteristic
479C23×C4C2414yes—
480C23×C4C2414yes—
481C23×C4C2414yes—
482C23×C4C2418yes—
483C23×C4C2412yes—
484C23×C4C2411yescharacteristic
485C4⋊Q8—28no—
486C4⋊Q8—24no—
487C4⋊Q8—28no—
488C4⋊Q8—216no—
489C4⋊Q8—28no—
490C4⋊Q8—28no—
491C4⋊Q8—216no—
492C4⋊Q8—28no—
493C4⋊Q8—216no—
494C4⋊Q8—24no—
495C4⋊Q8—24no—
496C4⋊Q8—416no—
497#127—24no—
498#127—28no—
499#126—216no—
500#126—216no—
501#126—216no—
502#126—28no—
503#125—216no—
504#125—216no—
505#125—28no—
506#125—24no—
507#125—28no—
508#125—216no—
509#125—216no—
510#125—28no—
511#125—28no—
512#124—24no—
513#124—216no—
514#124—28no—
515#124—28no—
516#123—216no—
517#123—28no—
518#123—216no—
519#123—232no—
520#123—232no—
521#123—232no—
522#123—216no—
523#123—216no—
524#123—432no—
525#123—432no—
526C22⋊Q8—28no—
527C22⋊Q8—24no—
528C22⋊Q8—28no—
529C22⋊Q8—28no—
530C22⋊Q8—28no—
531C22⋊Q8—216no—
532C22⋊Q8—232no—
533C22⋊Q8—216no—
534C22⋊Q8—232no—
535C22⋊Q8—216no—
536C22⋊Q8—28no—
537C22⋊Q8—216no—
538C22⋊Q8—416no—
539C22⋊Q8—416no—
540#121—216no—
541#121—28no—
542#121—24no—
543#121—216no—
544#121—28no—
545#121—216no—
546#121—28no—
547#121—432no—
548C4×Q8—28no—
549C4×Q8—28no—
550C4×Q8—28no—
551C4×Q8—24no—
552C4×Q8—28no—
553C4×Q8C2×D418yes—
554C4×Q8C2×D418yes—
555C4×D4—28no—
556C4×D4—216no—
557C4×D4—216no—
558C4×D4—28no—
559C4×D4—216no—
560C4×D4—24no—
561C4×D4—28no—
562C4×D4—28no—
563C4×D4—216no—
564C4×D4—28no—
565C4×D4—216no—
566C4×D4—416no—
567C4×D4C2×D418yes—
568C4×D4C2×D4116yes—
569C4×D4C2×D418yes—
570C4×D4C2×D4116yes—
571#117—28no—
572#117—216no—
573#117—28no—
574#117—216no—
575#117—28no—
576#117C2×D418yes—
577#117C2×D4116yes—
578C2×C4⋊C4—216no—
579C2×C4⋊C4—28no—
580C2×C4⋊C4—216no—
581C2×C4⋊C4—28no—
582C2×C4⋊C4—216no—
583C2×C4⋊C4—28no—
584C2×C4⋊C4—216no—
585C2×C4⋊C4—28no—
586C2×C4⋊C4—28no—
587C2×C4⋊C4—432no—
588C2×C4⋊C4C2414yes—
589C2×C4⋊C4C2412yes—
590C2×C4⋊C4C2414yes—
591C2×C4⋊C4C2412yes—
592C2×C4⋊C4C2414yes—
593C2×C4⋊C4C2412yes—
594C2×C4⋊C4C2411yescharacteristic
595C2×C4⋊C4C2412yes—
596C2×C4⋊C4C2411yescharacteristic
597C2×C4⋊C4C2412yes—
598C2×C4⋊C4C2412yes—
599C2×C4⋊C4C2414yes—
600C2×C4⋊C4C2412yes—
601C2×C4⋊C4C2414yes—
602C2×C4⋊C4C2414yes—
603C2×C4⋊C4C2414yes—
604C2×C4⋊C4C2418yes—
605C2×C4⋊C4C2418yes—
606C2×C4⋊C4C2414yes—
607C2×C4⋊C4C2414yes—
608C2×C4⋊C4C2414yes—
609C2×C4⋊C4C2414yes—
610C2×C4⋊C4C2414yes—
611C2×C4⋊C4C2412yes—
612C2×C4⋊C4C2414yes—
613C2×C4⋊C4C2414yes—
614C2×C4⋊C4C2414yes—
615C2×C4⋊C4C2412yes—
616C2×C4⋊C4C2412yes—
617C2×C4⋊C4C2414yes—
618C2×C4⋊C4C2418yes—
619C2×C4⋊C4C24116yes—
620C2×C4⋊C4C24116yes—
621C2×C4⋊C4C24116yes—
622C2×C4⋊C4C24116yes—
623C2×C4⋊C4C2418yes—
624C2×C4⋊C4C2411yescharacteristic
625C2×C4⋊C4C2411yescharacteristic
626C2×C4⋊C4C2412yes—
627C2×C4⋊C4C2412yes—
628C2×C22⋊C4C2412yes—
629C2×C22⋊C4C2412yes—
630C2×C22⋊C4C2414yes—
631C2×C22⋊C4C2412yes—
632C2×C22⋊C4C2414yes—
633C2×C22⋊C4C2414yes—
634C2×C22⋊C4C2414yes—
635C2×C22⋊C4C2418yes—
636C2×C22⋊C4C2414yes—
637C2×C22⋊C4C2414yes—
638C2×C22⋊C4C2418yes—
639C2×C22⋊C4C2414yes—
640C2×C22⋊C4C2412yes—
641C2×C22⋊C4C2412yes—
642C2×C22⋊C4C2418yes—
643C2×C22⋊C4C2418yes—
644C2×C22⋊C4C2418yes—
645C2×C22⋊C4C2418yes—
646C2×C22⋊C4C24116yes—
647C2×C22⋊C4C24116yes—
648C2×C22⋊C4C2414yes—
649C2×C22⋊C4C2418yes—
650C2×C22⋊C4C24116yes—
651C2×C22⋊C4C2412yes—
652C2×C22⋊C4C2412yes—
653C2×C22⋊C4C2412yes—
654C2×C42—216no—
655C2×C42C2×D4116yes—
656C2×C42C2×D418yes—
657C2×C42C2414yes—
658C2×C42C2414yes—
659C2×C42C2412yes—
660C2×C42C2412yes—
661C2×C42C2414yes—
662C2×C42C2414yes—
663C2×C42C2418yes—
664C2×C42C2414yes—
665C2×C42C2412yes—
666C2×C42C2411yescharacteristic
667C2×C42C2411yescharacteristic
668C2×C42C2412yes—
669C2×C42C2411yescharacteristic
670C2×C42C2412yes—
671C2×C42C2411yescharacteristic
672C2×C42C2412yes—
673#95C2412yes—
674#95C2412yes—
675#95C2418yes—
676#95C2414yes—
677#95C2414yes—
678#95C2418yes—
679#95C2418yes—
680#95C24116yes—
681#95C24116yes—
682#95C24116yes—
683#95C2412yes—
684#95C2412yes—
685#95C2414yes—
686#95C2418yes—
687#95C2418yes—
688#95C2414yes—
689#95C2418yes—
690#95C24116yes—
691#95C24116yes—
692C24C2512yes—
693C24C2514yes—
694C24C2511yescharacteristic
695C24C2512yes—
696#41—232no—
697#41—464no—
698#41—432no—
699#41—4128no—
700#41—432no—
701#41—464no—
702C2×Q8—22no—
703C2×Q8—24no—
704C2×Q8—216no—
705C2×Q8—28no—
706C2×Q8—28no—
707C2×Q8—24no—
708C2×Q8—24no—
709C2×Q8—24no—
710C2×Q8—28no—
711C2×Q8—216no—
712C2×Q8—24no—
713C2×Q8—44no—
714C2×Q8—48no—
715C2×Q8—416no—
716C2×Q8—44no—
717C2×Q8—464no—
718C2×Q8—432no—
719C2×Q8—464no—
720C2×Q8C22×D414yes—
721C2×D4—28no—
722C2×D4—28no—
723C2×D4—28no—
724C2×D4—216no—
725C2×D4—216no—
726C2×D4—232no—
727C2×D4—24no—
728C2×D4—22no—
729C2×D4—24no—
730C2×D4—24no—
731C2×D4—24no—
732C2×D4—24no—
733C2×D4—24no—
734C2×D4—24no—
735C2×D4—216no—
736C2×D4—44no—
737C2×D4—44no—
738C2×D4—48no—
739C2×D4—48no—
740C2×D4—48no—
741C2×D4—44no—
742C2×D4C22×D418yes—
743C2×D4C22×D414yes—
744C2×D4H(5,𝔽2)18yes—
745C22×C4—28no—
746C22×C4—24no—
747C22×C4—28no—
748C22×C4—24no—
749C22×C4—28no—
750C22×C4—28no—
751C22×C4—216no—
752C22×C4—216no—
753C22×C4—216no—
754C22×C4—232no—
755C22×C4—28no—
756C22×C4—24no—
757C22×C4—216no—
758C22×C4—28no—
759C22×C4—28no—
760C22×C4—216no—
761C22×C4—216no—
762C22×C4—28no—
763C22×C4—42no—
764C22×C4—48no—
765C22×C4—44no—
766C22×C4—416no—
767C22×C4—48no—
768C22×C4—48no—
769C22×C4—48no—
770C22×C4C22×D418yes—
771C22×C4C22×D414yes—
772C22×C4C22×D418yes—
773C22×C4C22×D414yes—
774C22×C4C22×D418yes—
775C22×C4C22×D414yes—
776C22×C4C2518yes—
777C22×C4C2514yes—
778C22×C4C2512yes—
779C22×C4C2514yes—
780C22×C4C2512yes—
781C22×C4C2514yes—
782C22×C4C2518yes—
783C22×C4C2514yes—
784C22×C4C2512yes—
785C22×C4C2511yescharacteristic
786C22×C4C2511yescharacteristic
787C22×C4C2512yes—
788C22×C4C2512yes—
789C22×C4C2511yescharacteristic
790C22×C4C2511yescharacteristic
791C22×C4C2512yes—
792C22×C4C2514yes—
793C22×C4C2511yescharacteristic
794C22×C4C2511yescharacteristic
795C4⋊C4—28no—
796C4⋊C4—24no—
797C4⋊C4—24no—
798C4⋊C4—28no—
799C4⋊C4—24no—
800C4⋊C4—28no—
801C4⋊C4—22no—
802C4⋊C4—24no—
803C4⋊C4—22no—
804C4⋊C4—24no—
805C4⋊C4—24no—
806C4⋊C4—28no—
807C4⋊C4—24no—
808C4⋊C4—28no—
809C4⋊C4—28no—
810C4⋊C4—28no—
811C4⋊C4—28no—
812C4⋊C4—216no—
813C4⋊C4—216no—
814C4⋊C4—28no—
815C4⋊C4—28no—
816C4⋊C4—28no—
817C4⋊C4—28no—
818C4⋊C4—24no—
819C4⋊C4—28no—
820C4⋊C4—24no—
821C4⋊C4—24no—
822C4⋊C4—28no—
823C4⋊C4—28no—
824C4⋊C4—28no—
825C4⋊C4—48no—
826C4⋊C4—416no—
827C4⋊C4—416no—
828C4⋊C4—416no—
829C4⋊C4—48no—
830C4⋊C4—416no—
831C4⋊C4C22×D414yes—
832C4⋊C4C22×D418yes—
833C4⋊C4C22×D414yes—
834C4⋊C4C22×D418yes—
835C22⋊C4—28no—
836C22⋊C4—28no—
837C22⋊C4—24no—
838C22⋊C4—216no—
839C22⋊C4—24no—
840C22⋊C4—24no—
841C22⋊C4—24no—
842C22⋊C4—28no—
843C22⋊C4—28no—
844C22⋊C4—216no—
845C22⋊C4—216no—
846C22⋊C4—28no—
847C22⋊C4—28no—
848C22⋊C4—24no—
849C22⋊C4—28no—
850C22⋊C4—216no—
851C22⋊C4—48no—
852C22⋊C4—44no—
853C22⋊C4—416no—
854C22⋊C4—48no—
855C22⋊C4—48no—
856C22⋊C4—416no—
857C22⋊C4—416no—
858C22⋊C4C22×D418yes—
859C22⋊C4C22×D418yes—
860C22⋊C4C22×D418yes—
861C42—28no—
862C42—28no—
863C42—24no—
864C42—28no—
865C42—216no—
866C42—28no—
867C42—24no—
868C42—44no—
869C42C22×D414yes—
870C42C22×D418yes—
871C42C22×D414yes—
872C42C22×D414yes—
873C42C22×D418yes—
874C42C22×D414yes—
875C42C22×D418yes—
876C422−1+418yescomplemented
877C23—24no—
878C23—24no—
879C23—22no—
880C23—22no—
881C23—22no—
882C23—22no—
883C23—24no—
884C23—24no—
885C23—28no—
886C23—24no—
887C23—24no—
888C23—24no—
889C23—28no—
890C23—24no—
891C23C23×D412yes—
892C23C23×D414yes—
893C23C2×H(5,𝔽2)18yes—
894C23C2611yescharacteristic
895Q8—28no—
896Q8—48no—
897Q8—416no—
898Q8—432no—
899Q8—416no—
900Q8—48no—
901Q8—44no—
902Q8—84no—
903D4—216no—
904D4—48no—
905D4—48no—
906D4—416no—
907D4—416no—
908D4—432no—
909D4—44no—
910D4—48no—
911D4—816no—
912D4—84no—
913D4#535116yes—
914C2×C4—24no—
915C2×C4—22no—
916C2×C4—24no—
917C2×C4—24no—
918C2×C4—22no—
919C2×C4—22no—
920C2×C4—24no—
921C2×C4—24no—
922C2×C4—22no—
923C2×C4—216no—
924C2×C4—28no—
925C2×C4—216no—
926C2×C4—28no—
927C2×C4—22no—
928C2×C4—24no—
929C2×C4—24no—
930C2×C4—22no—
931C2×C4—22no—
932C2×C4—24no—
933C2×C4—28no—
934C2×C4—24no—
935C2×C4—28no—
936C2×C4—24no—
937C2×C4—28no—
938C2×C4—28no—
939C2×C4—216no—
940C2×C4—28no—
941C2×C4—24no—
942C2×C4—24no—
943C2×C4—24no—
944C2×C4—28no—
945C2×C4—24no—
946C2×C4—28no—
947C2×C4—48no—
948C2×C4—44no—
949C2×C4—432no—
950C2×C4—432no—
951C2×C4—416no—
952C2×C4—432no—
953C2×C4—416no—
954C2×C4—416no—
955C2×C4—48no—
956C2×C4—88no—
957C2×C4—88no—
958C2×C4C23×D412yes—
959C2×C4C23×D414yes—
960C2×C4C23×D412yes—
961C2×C4C23×D412yes—
962C2×C4C23×D414yes—
963C2×C4C23×D412yes—
964C2×C4C23×D414yes—
965C2×C4C23×D412yes—
966C2×C4C23×D412yes—
967C2×C4C2×H(5,𝔽2)14yes—
968C2×C4C2×2−1+418yes—
969C2×C4C2×2−1+414yes—
970C22—24no—
971C22—24no—
972C22—216no—
973C22—22no—
974C22—22no—
975C22—22no—
976C22—44no—
977C22—42no—
978C22—44no—
979C22—42no—
980C22—44no—
981C22—48no—
982C22—48no—
983C22—48no—
984C22—44no—
985C22—42no—
986C22C2×#53518yes—
987C22C24×D411yescharacteristic
988C22C22×H(5,𝔽2)12yes—
989C22C22×2−1+412yes—
990C222−1+612yes—
991C4—24no—
992C4—22no—
993C4—22no—
994C4—24no—
995C4—22no—
996C4—28no—
997C4—22no—
998C4—24no—
999C4—42no—
1000C4—42no—
1001C4—44no—
1002C4—44no—
1003C4—48no—
1004C4—42no—
1005C4—44no—
1006C4—48no—
1007C4—44no—
1008C4C2×#53514yes—
1009C4#349914yes—
1010C2—28no—
1011C2—42no—
1012C2—82no—
1013C2—84no—
1014C2C22×#53511yescharacteristic
1015C2C2×#349911yescharacteristic
1016C2#6285911yescharacteristic
1017C2#6291514yes—
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×#3499C2semidirect
2. C2×#3515C2semidirect
3. #42994C2semidirect
4. #42792C2semidirect
5. #42297C2semidirect
6. #41375C2semidirect
7. #39618C2semidirect
8. #39616C2semidirect
9. #37864C2semidirect
10. #37863C2semidirect
11. #37634C2semidirect
12. #37632C2semidirect
13. #37615C2semidirect
14. #37539C2semidirect
15. #36179C2semidirect
16. #36164C2semidirect
17. #36085C2semidirect
18. #36020C2semidirect
19. #35303C2semidirect
20. #35281C2semidirect
21. #34624C2semidirect
22. C2×#2660C2semidirect
23. #34123C2semidirect
264. C4×#41D4semidirect
876. C422−1+4semidirect

Maximal subgroups

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

subgroupindex
C2×#34992
C2×#35152
#429942
#427922
#422972
#413752
#396182
#396162
#378642
#378632
#376342
#376322
#376152
#375392
#361792
#361642
#360852
#360202
#353032
#352812
#346242
C2×#26602
#341232