Finite Group Databasebeta

← #7712006

Subgroups — #7712006

Order 512.

7206 conjugacy classes of subgroups.

The subgroup lattice has 939 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3544C212yesmaximal, complemented
2#59313C214yesmaximal, complemented
3#59312C214yesmaximal, complemented
4#45993C218yesmaximal, complemented
5#39617C212yesmaximal, complemented
6#39489C212yesmaximal, complemented
7#39377C214yesmaximal, complemented
8#39369C214yesmaximal, complemented
9#39337C218yesmaximal, complemented
10#37863C214yesmaximal, complemented
11#37632C212yesmaximal, complemented
12#37303C214yesmaximal, complemented
13C2×#2868C211yesmaximal, characteristic, complemented
14#36631C211yesmaximal, characteristic, complemented
15#36559C211yesmaximal, characteristic, complemented
16Q8×C4⋊Q8C211yesmaximal, characteristic, complemented
17#36187C211yesmaximal, characteristic, complemented
18#36181C212yesmaximal, complemented
19#36180C211yesmaximal, characteristic, complemented
20#36179C212yesmaximal, complemented
21#35277C212yesmaximal, complemented
22#35275C212yesmaximal, complemented
23C4×#529C211yesmaximal, characteristic, complemented
24#3544—232no—
25C2×#563C2218yes—
26C2×Q82C2212yes—
27C2×#555C2212yes—
28C2×#554C2212yes—
29C2×#554C2212yes—
30C2×#552C2214yes—
31C2×#552C2214yes—
32C2×#547C2214yes—
33C2×#547C2214yes—
34C2×#547C2218yes—
35C2×#544C2214yes—
36C2×#544C2214yes—
37C2×#542C2214yes—
38C2×#542C2214yes—
39C2×#536C2218yes—
40C22×C4⋊Q8C2212yes—
41C22×C4⋊Q8C2214yes—
42C2×#529C2212yes—
43C2×#529C2211yescharacteristic
44#2868C2212yes—
45#2868C2211yescharacteristic
46#2868C2211yescharacteristic
47#2868C2214yes—
48#2868C2212yes—
49#2868C2214yes—
50#2868C2212yes—
51#2868C2212yes—
52#2861C2212yes—
53#2860C2214yes—
54#2859C2211yescharacteristic
55#2859C2212yes—
56#2858C2211yescharacteristic
57#2857C2211yescharacteristic
58#2857C2212yes—
59#2856C2211yescharacteristic
60#2856C2212yes—
61#2854C2214yes—
62#2850C2212yes—
63#2821C2218yes—
64#2721C22116yes—
65#2720C22116yes—
66#2718C22116yes—
67#2680C22116yes—
68#2677C22116yes—
69#2677C22116yes—
70#2674C22116yes—
71#2674C22116yes—
72#2660C2214yes—
73#2660C2214yes—
74#2640C2214yes—
75#2628C2218yes—
76#2620C2214yes—
77#2614C2218yes—
78#2567C2212yes—
79#2567C2212yes—
80#2567C2214yes—
81#2566C2214yes—
82#2565C2214yes—
83#2563C2212yes—
84#2563C2212yes—
85#2552C2214yes—
86#2552C2218yes—
87#2551C2218yes—
88#2551C2218yes—
89#2551C2214yes—
90#2542C2218yes—
91#2542C2214yes—
92#2538C2214yes—
93#2537C2214yes—
94#2512C2218yes—
95#2506C2218yes—
96#2503C2214yes—
97#2502C2214yes—
98#2501C2214yes—
99#2501C2214yes—
100#2501C2218yes—
101#2501C2218yes—
102#2500C2214yes—
103#2499C2214yes—
104#2496C2218yes—
105#2491C2218yes—
106#2491C2218yes—
107#2486C2218yes—
108#2486C2218yes—
109#2452C2218yes—
110#2452C2218yes—
111#2441C2218yes—
112#2440C2218yes—
113#2440C2218yes—
114#2440C2218yes—
115#2440C2218yes—
116#2423C2218yes—
117#2422C2218yes—
118#2422C2218yes—
119#2413C22116yes—
120#2406C22116yes—
121#2354C2214yes—
122Q8×C4⋊C4C2214yes—
123D4×C4⋊C4C2214yes—
124D4×C4⋊C4C2214yes—
125#2344C2218yes—
126#2326C2214yes—
127#2317C2214yes—
128C4×C4⋊Q8C2211yescharacteristic
129C4×C4⋊Q8C2212yes—
130C4×#127C2211yescharacteristic
131C4×#127C2212yes—
132C4×#125C2212yes—
133C4×#126C2214yes—
134C4×#124C2212yes—
135C4×#124C2212yes—
136C4×C22⋊Q8C2212yes—
137C4×#123C2214yes—
138C4×#121C2214yes—
139C4×#121C2212yes—
140#2298C2212yes—
141#2295C2211yescharacteristic
142#2293C2214yes—
143#2293C2211yescharacteristic
144#2290C2212yes—
145#2285C2212yes—
146C2×#384C2212yes—
147C2×#384C2214yes—
148C2×#384C2212yes—
149C2×#384C2212yes—
150#2283C2211yescharacteristic
151C42×Q8C2211yescharacteristic
152C42×D4C2212yes—
153C42×D4C2211yescharacteristic
154C4×#117C2212yes—
155C2×C43C2211yescharacteristic
156C22×#41C2318yes—
157C23×Q8C2314yes—
158#563—264no—
159Q82—216no—
160#555—216no—
161#554—216no—
162#554—216no—
163#552—232no—
164#552—232no—
165#547—232no—
166#547—232no—
167#547—432no—
168#544—232no—
169#544—232no—
170#542—232no—
171#542—232no—
172#536—264no—
173C2×C4⋊Q8—216no—
174C2×C4⋊Q8—416no—
175C2×C4⋊Q8C2311yescharacteristic
176C2×C4⋊Q8C2312yes—
177C2×C4⋊Q8C2312yes—
178C2×C4⋊Q8C2314yes—
179C2×C4⋊Q8C2314yes—
180C2×C4⋊Q8C2314yes—
181C2×C4⋊Q8C2314yes—
182C2×C4⋊Q8C2318yes—
183C2×C4⋊Q8C2318yes—
184C2×C4⋊Q8C2314yes—
185C2×C4⋊Q8C2318yes—
186C2×C4⋊Q8C2318yes—
187C2×C4⋊Q8C2314yes—
188C2×C4⋊Q8C2318yes—
189C2×C4⋊Q8C2314yes—
190C2×C4⋊Q8C2318yes—
191C2×#127C2311yescharacteristic
192#529—216no—
193#529D4116yescomplemented
194C2×#126C2314yes—
195C2×#126C2318yes—
196C2×#126C2318yes—
197C2×#126C2312yes—
198C2×#125C2314yes—
199C2×#125C2312yes—
200C2×#125C2314yes—
201C2×#125C2318yes—
202C2×#125C2318yes—
203C2×#125C2311yescharacteristic
204C2×#124C2312yes—
205C2×#124C2312yes—
206C2×#124C2318yes—
207C2×#124C2318yes—
208C2×#124C2311yescharacteristic
209C2×#123C2314yes—
210C2×#123C2318yes—
211C2×#123C2318yes—
212C2×#123C2318yes—
213C2×#123C2318yes—
214C2×#123C23116yes—
215C2×#123C23116yes—
216C2×#123C2312yes—
217C2×C22⋊Q8C2312yes—
218C2×C22⋊Q8C2314yes—
219C2×C22⋊Q8C2318yes—
220C2×C22⋊Q8C2318yes—
221C2×C22⋊Q8C2318yes—
222C2×C22⋊Q8C2318yes—
223C2×C22⋊Q8C2314yes—
224C2×C22⋊Q8C2318yes—
225C2×C22⋊Q8C2318yes—
226C2×C22⋊Q8C23116yes—
227C2×C22⋊Q8C2311yescharacteristic
228C2×#121C2312yes—
229C2×#121C2314yes—
230C2×#121C2314yes—
231C2×#121C2314yes—
232C2×#121C2318yes—
233C2×#121C2311yescharacteristic
234C2×C4×Q8C2314yes—
235C2×C4×Q8C2312yes—
236C2×C4×Q8C2314yes—
237C2×C4×Q8C2312yes—
238C2×C4×Q8C2311yescharacteristic
239C2×C4×D4C2312yes—
240C2×C4×D4C2314yes—
241C2×C4×D4C2314yes—
242C2×C4×D4C2314yes—
243C2×C4×D4C2312yes—
244C2×C4×D4C2314yes—
245C2×C4×D4C2314yes—
246C2×C4×D4C2318yes—
247C2×C4×D4C2312yes—
248C2×C4×D4C2311yescharacteristic
249C2×#117C2312yes—
250C2×#117C2314yes—
251C2×#117C2318yes—
252C2×#117C2314yes—
253C2×#117C2314yes—
254C2×#117C2312yes—
255C22×C4⋊C4C2314yes—
256C22×C4⋊C4C2318yes—
257C22×C4⋊C4C2314yes—
258C22×C4⋊C4C2314yes—
259C22×C4⋊C4C2314yes—
260C22×C4⋊C4C2318yes—
261C22×C4⋊C4C2318yes—
262C22×C42C2311yescharacteristic
263C22×C42C2312yes—
264C22×C42C2311yescharacteristic
265C22×C42C2312yes—
266C22×C42C2312yes—
267C22×C42C2311yescharacteristic
268#400C23116yes—
269#399C23116yes—
270#399C23116yes—
271#399C23116yes—
272#398C23116yes—
273#398C23116yes—
274#398C23116yes—
275#398C23116yes—
276#397C23116yes—
277#397C23116yes—
278#396C23116yes—
279#396C23116yes—
280#395C2318yes—
281#395C2318yes—
282#395C23116yes—
283#395C23116yes—
284#395C23116yes—
285#394C23116yes—
286#394C23116yes—
287#393C2318yes—
288#393C2318yes—
289#393C23116yes—
290#391C2312yes—
291#391C2314yes—
292#391C2312yes—
293#391C2314yes—
294#391C2312yes—
295#390C2314yes—
296#390C2312yes—
297#390C2314yes—
298#390C2318yes—
299#390C2314yes—
300#390C2314yes—
301#390C2314yes—
302#390C2312yes—
303#390C2318yes—
304#390C2314yes—
305#390C2312yes—
306#389C2312yes—
307#389C2312yes—
308#389C2314yes—
309#389C2318yes—
310#389C2318yes—
311#389C2318yes—
312#389C23116yes—
313#389C23116yes—
314#389C2314yes—
315#389C2318yes—
316#389C2318yes—
317#389C2314yes—
318#389C2318yes—
319#389C2314yes—
320#388C2314yes—
321#388C2314yes—
322#388C2314yes—
323#388C23116yes—
324#388C2318yes—
325#388C2318yes—
326#388C2318yes—
327#388C2318yes—
328#388C23116yes—
329#388C2314yes—
330#387C2314yes—
331#387C2314yes—
332#387C2314yes—
333#387C2314yes—
334#387C23116yes—
335#387C23116yes—
336#386C2318yes—
337#386C2314yes—
338#385C23116yes—
339#385C23116yes—
340#385C23116yes—
341#385C23116yes—
342#385C2314yes—
343#384C2311yescharacteristic
344#384C2312yes—
345#384C2311yescharacteristic
346#384C2312yes—
347#384C2314yes—
348#384C2312yes—
349#384C2314yes—
350#384C2312yes—
351#384C2314yes—
352#384C2314yes—
353#384C2314yes—
354#384C2314yes—
355#384C2318yes—
356#384C2318yes—
357#384C2318yes—
358#384C2318yes—
359#384C2318yes—
360#384C2318yes—
361#384C2318yes—
362#383C2312yes—
363#382C2312yes—
364#382C2314yes—
365#382C2314yes—
366#382C2312yes—
367#381C23116yes—
368#381C2312yes—
369#380C2318yes—
370#380C2318yes—
371#380C2314yes—
372#380C2318yes—
373#380C2318yes—
374#380C2312yes—
375C4×C4⋊C4C2314yes—
376C4×C4⋊C4C2314yes—
377C4×C4⋊C4C2314yes—
378C4×C4⋊C4C2312yes—
379C4×C4⋊C4C2312yes—
380C4×C4⋊C4C2314yes—
381C4×C4⋊C4C2318yes—
382C4×C4⋊C4C2314yes—
383C4×C4⋊C4C2311yescharacteristic
384C4×C4⋊C4C2311yescharacteristic
385C4×C4⋊C4C2312yes—
386C4×C4⋊C4C2312yes—
387C4×C4⋊C4C2318yes—
388C4×C22⋊C4C2314yes—
389C4×C22⋊C4C2314yes—
390C4×C22⋊C4C2314yes—
391C4×C22⋊C4C2314yes—
392C4×C22⋊C4C2318yes—
393C4×C22⋊C4C2314yes—
394C4×C22⋊C4C2312yes—
395C4×C22⋊C4C2312yes—
396C4×C22⋊C4C2312yes—
397#376C2312yes—
398#376C2312yes—
399C43C2312yes—
400C43C2312yes—
401C43C2312yes—
402C43C2311yescharacteristic
403C43C2311yescharacteristic
404C43C2311yescharacteristic
405C43C2311yescharacteristic
406C2×#41—232no—
407C2×#41—432no—
408C22×Q8—216no—
409C22×Q8—416no—
410C22×Q8C2412yes—
411C22×Q8C2411yescharacteristic
412C22×Q8C2414yes—
413C22×Q8C2418yes—
414C22×Q8C2418yes—
415C22×Q8C2414yes—
416C22×D4C2412yes—
417C22×D4C2414yes—
418C22×D4C2414yes—
419C22×D4C2411yescharacteristic
420C22×D4C2412yes—
421C22×D4C2418yes—
422C23×C4C2418yes—
423C23×C4C2412yes—
424C23×C4C2414yes—
425C23×C4C2414yes—
426C23×C4C2411yescharacteristic
427C23×C4C2411yescharacteristic
428C23×C4C2412yes—
429C23×C4C2411yescharacteristic
430C23×C4C2412yes—
431C23×C4C2418yes—
432C23×C4C2418yes—
433C4⋊Q8—232no—
434C4⋊Q8—232no—
435C4⋊Q8—216no—
436C4⋊Q8—216no—
437C4⋊Q8—216no—
438C4⋊Q8—28no—
439C4⋊Q8—28no—
440C4⋊Q8—216no—
441C4⋊Q8—216no—
442C4⋊Q8—24no—
443C4⋊Q8—48no—
444C4⋊Q8—416no—
445C4⋊Q8—48no—
446C4⋊Q8—416no—
447C4⋊Q8—416no—
448C4⋊Q8—416no—
449#127—24no—
450#126—232no—
451#126—232no—
452#126—216no—
453#126C2×D4116yes—
454#125—216no—
455#125—232no—
456#125—232no—
457#125—28no—
458#125—216no—
459#125C2×D418yes—
460#124—232no—
461#124—232no—
462#124—28no—
463#124—28no—
464#124C2×D418yes—
465#123—232no—
466#123—216no—
467#123—232no—
468#123—232no—
469#123—232no—
470#123—432no—
471#123—432no—
472#123C2×D4116yes—
473C22⋊Q8—216no—
474C22⋊Q8—28no—
475C22⋊Q8—216no—
476C22⋊Q8—232no—
477C22⋊Q8—232no—
478C22⋊Q8—232no—
479C22⋊Q8—232no—
480C22⋊Q8—232no—
481C22⋊Q8—232no—
482C22⋊Q8—432no—
483C22⋊Q8C2×D418yes—
484#121—216no—
485#121—28no—
486#121—216no—
487#121—216no—
488#121—416no—
489#121C2×D418yes—
490C4×Q8—216no—
491C4×Q8—28no—
492C4×Q8—216no—
493C4×Q8—28no—
494C4×Q8C2×D418yes—
495C4×D4—216no—
496C4×D4—216no—
497C4×D4—216no—
498C4×D4—28no—
499C4×D4—216no—
500C4×D4—28no—
501C4×D4—216no—
502C4×D4—416no—
503C4×D4C2×D4116yes—
504C4×D4C2×D418yes—
505#117—216no—
506#117—216no—
507#117—232no—
508#117—216no—
509#117—28no—
510#117C2×D4116yes—
511C2×C4⋊C4—216no—
512C2×C4⋊C4—216no—
513C2×C4⋊C4—216no—
514C2×C4⋊C4—232no—
515C2×C4⋊C4—216no—
516C2×C4⋊C4—416no—
517C2×C4⋊C4—416no—
518C2×C4⋊C4C2414yes—
519C2×C4⋊C4C2414yes—
520C2×C4⋊C4C2418yes—
521C2×C4⋊C4C2412yes—
522C2×C4⋊C4C2414yes—
523C2×C4⋊C4C2414yes—
524C2×C4⋊C4C2414yes—
525C2×C4⋊C4C2418yes—
526C2×C4⋊C4C2418yes—
527C2×C4⋊C4C2418yes—
528C2×C4⋊C4C2418yes—
529C2×C4⋊C4C2418yes—
530C2×C4⋊C4C24116yes—
531C2×C4⋊C4C2412yes—
532C2×C4⋊C4C2418yes—
533C2×C4⋊C4C2418yes—
534C2×C4⋊C4C2414yes—
535C2×C4⋊C4C2414yes—
536C2×C4⋊C4C2414yes—
537C2×C4⋊C4C2414yes—
538C2×C4⋊C4C2414yes—
539C2×C4⋊C4C2412yes—
540C2×C4⋊C4C2414yes—
541C2×C4⋊C4C2414yes—
542C2×C4⋊C4C2418yes—
543C2×C4⋊C4C2418yes—
544C2×C4⋊C4C2412yes—
545C2×C4⋊C4C2414yes—
546C2×C4⋊C4C2414yes—
547C2×C4⋊C4C24116yes—
548C2×C4⋊C4C2418yes—
549C2×C4⋊C4C24116yes—
550C2×C4⋊C4C2418yes—
551C2×C4⋊C4C24116yes—
552C2×C4⋊C4C2411yescharacteristic
553C2×C4⋊C4C2411yescharacteristic
554C2×C4⋊C4C2412yes—
555C2×C4⋊C4C2412yes—
556C2×C4⋊C4C2412yes—
557C2×C4⋊C4C2412yes—
558C2×C22⋊C4C2414yes—
559C2×C22⋊C4C2414yes—
560C2×C22⋊C4C2418yes—
561C2×C22⋊C4C2418yes—
562C2×C22⋊C4C2414yes—
563C2×C22⋊C4C2414yes—
564C2×C22⋊C4C2418yes—
565C2×C22⋊C4C2418yes—
566C2×C22⋊C4C2414yes—
567C2×C22⋊C4C2414yes—
568C2×C22⋊C4C2414yes—
569C2×C22⋊C4C2414yes—
570C2×C22⋊C4C2414yes—
571C2×C22⋊C4C2418yes—
572C2×C22⋊C4C2418yes—
573C2×C22⋊C4C2418yes—
574C2×C22⋊C4C24116yes—
575C2×C22⋊C4C24116yes—
576C2×C22⋊C4C2412yes—
577C2×C22⋊C4C2412yes—
578C2×C22⋊C4C2412yes—
579C2×C22⋊C4C2412yes—
580C2×C22⋊C4C2412yes—
581C2×C42—28no—
582C2×C42—24no—
583C2×C42—28no—
584C2×C42—24no—
585C2×C42—28no—
586C2×C42C2×D418yes—
587C2×C42C2418yes—
588C2×C42C2414yes—
589C2×C42C2418yes—
590C2×C42C2412yes—
591C2×C42C2414yes—
592C2×C42C2414yes—
593C2×C42C2412yes—
594C2×C42C2412yes—
595C2×C42C2412yes—
596C2×C42C2412yes—
597C2×C42C2412yes—
598C2×C42C2412yes—
599C2×C42C2412yes—
600C2×C42C2411yescharacteristic
601C2×C42C2411yescharacteristic
602C2×C42C2412yes—
603C2×C42C2412yes—
604C2×C42C2412yes—
605C2×C42C2414yes—
606C2×C42C2411yescharacteristic
607C2×C42C2411yescharacteristic
608C2×C42C2412yes—
609C2×C42C2411yescharacteristic
610C2×C42C2411yescharacteristic
611C2×C42C2411yescharacteristic
612C2×C42C2412yes—
613C2×C42C2411yescharacteristic
614#95C2414yes—
615#95C2414yes—
616#95C2414yes—
617#95C2414yes—
618#95C2412yes—
619#95C2414yes—
620#95C2414yes—
621#95C2414yes—
622#95C2414yes—
623#95C2418yes—
624#95C2418yes—
625#95C2412yes—
626#95C2414yes—
627#95C24116yes—
628#95C24116yes—
629#95C2418yes—
630#95C24116yes—
631#95C24116yes—
632C24C2514yes—
633C24C2512yes—
634C24C2511yescharacteristic
635#41—864no—
636C2×Q8—24no—
637C2×Q8—28no—
638C2×Q8—216no—
639C2×Q8—216no—
640C2×Q8—28no—
641C2×Q8—24no—
642C2×Q8—24no—
643C2×Q8—24no—
644C2×Q8—416no—
645C2×Q8—48no—
646C2×Q8—416no—
647C2×Q8—48no—
648C2×Q8—832no—
649C2×Q8C22×D414yes—
650C2×D4—28no—
651C2×D4—28no—
652C2×D4—216no—
653C2×D4—216no—
654C2×D4—24no—
655C2×D4—28no—
656C2×D4—24no—
657C2×D4—28no—
658C2×D4—24no—
659C2×D4—24no—
660C2×D4—28no—
661C2×D4—416no—
662C2×D4C22×D414yes—
663C2×D4C22×D418yes—
664C22×C4—24no—
665C22×C4—24no—
666C22×C4—24no—
667C22×C4—24no—
668C22×C4—22no—
669C22×C4—22no—
670C22×C4—24no—
671C22×C4—24no—
672C22×C4—24no—
673C22×C4—24no—
674C22×C4—24no—
675C22×C4—216no—
676C22×C4—232no—
677C22×C4—216no—
678C22×C4—28no—
679C22×C4—28no—
680C22×C4—28no—
681C22×C4—216no—
682C22×C4—28no—
683C22×C4—216no—
684C22×C4—416no—
685C22×C4—416no—
686C22×C4C22×D414yes—
687C22×C4C22×D414yes—
688C22×C4C22×D414yes—
689C22×C4C22×D418yes—
690C22×C4H(5,𝔽2)18yes—
691C22×C4C2514yes—
692C22×C4C2514yes—
693C22×C4C2514yes—
694C22×C4C2514yes—
695C22×C4C2518yes—
696C22×C4C2514yes—
697C22×C4C2518yes—
698C22×C4C2512yes—
699C22×C4C2511yescharacteristic
700C22×C4C2511yescharacteristic
701C22×C4C2512yes—
702C22×C4C2511yescharacteristic
703C22×C4C2511yescharacteristic
704C22×C4C2512yes—
705C22×C4C2512yes—
706C22×C4C2512yes—
707C22×C4C2512yes—
708C22×C4C2511yescharacteristic
709C22×C4C2511yescharacteristic
710C22×C4C2512yes—
711C4⋊C4—28no—
712C4⋊C4—28no—
713C4⋊C4—24no—
714C4⋊C4—28no—
715C4⋊C4—28no—
716C4⋊C4—216no—
717C4⋊C4—216no—
718C4⋊C4—216no—
719C4⋊C4—216no—
720C4⋊C4—24no—
721C4⋊C4—216no—
722C4⋊C4—216no—
723C4⋊C4—28no—
724C4⋊C4—28no—
725C4⋊C4—28no—
726C4⋊C4—28no—
727C4⋊C4—216no—
728C4⋊C4—216no—
729C4⋊C4—216no—
730C4⋊C4—216no—
731C4⋊C4—232no—
732C4⋊C4—28no—
733C4⋊C4—28no—
734C4⋊C4—28no—
735C4⋊C4—24no—
736C4⋊C4—28no—
737C4⋊C4—28no—
738C4⋊C4—24no—
739C4⋊C4—28no—
740C4⋊C4—416no—
741C4⋊C4—48no—
742C4⋊C4—416no—
743C4⋊C4—48no—
744C4⋊C4—416no—
745C4⋊C4C22×D414yes—
746C4⋊C4C22×D414yes—
747C4⋊C4C22×D418yes—
748C4⋊C4C22×D418yes—
749C4⋊C4C22×D418yes—
750C4⋊C4C22×D418yes—
751C22⋊C4—28no—
752C22⋊C4—216no—
753C22⋊C4—216no—
754C22⋊C4—28no—
755C22⋊C4—28no—
756C22⋊C4—216no—
757C22⋊C4—28no—
758C22⋊C4—216no—
759C22⋊C4—28no—
760C22⋊C4—28no—
761C22⋊C4—28no—
762C22⋊C4—216no—
763C22⋊C4—28no—
764C22⋊C4—28no—
765C22⋊C4—216no—
766C22⋊C4—216no—
767C22⋊C4—416no—
768C22⋊C4—416no—
769C22⋊C4C22×D418yes—
770C22⋊C4C22×D418yes—
771C22⋊C4C22×D418yes—
772C22⋊C4C22×D418yes—
773C22⋊C4C22×D418yes—
774C42—216no—
775C42—28no—
776C42—216no—
777C42—24no—
778C42—24no—
779C42—24no—
780C42—24no—
781C42—28no—
782C42—24no—
783C42—24no—
784C42—22no—
785C42—22no—
786C42—24no—
787C42—24no—
788C42—24no—
789C42—28no—
790C42—24no—
791C42—24no—
792C42—28no—
793C42C22×D414yes—
794C42C22×D414yes—
795C42C22×D414yes—
796C42C22×D414yes—
797C42C22×D418yes—
798C422−1+414yes—
799C422−1+414yes—
800C422−1+418yes—
801C23—21no—
802C23—22no—
803C23—21no—
804C23—24no—
805C23—22no—
806C23—24no—
807C23—22no—
808C23—24no—
809C23—28no—
810C23—24no—
811C23—28no—
812C23—24no—
813C23C23×D414yes—
814C23C23×D412yes—
815C23C2×H(5,𝔽2)14yes—
816C23C2611yescharacteristic
817Q8—28no—
818Q8—48no—
819Q8—88no—
820Q8—816no—
821Q8—88no—
822Q8—816no—
823D4—216no—
824D4—28no—
825D4—416no—
826D4—48no—
827D4—416no—
828D4—816no—
829C2×C4—216no—
830C2×C4—22no—
831C2×C4—22no—
832C2×C4—22no—
833C2×C4—22no—
834C2×C4—24no—
835C2×C4—22no—
836C2×C4—22no—
837C2×C4—21no—
838C2×C4—22no—
839C2×C4—22no—
840C2×C4—21no—
841C2×C4—22no—
842C2×C4—22no—
843C2×C4—24no—
844C2×C4—22no—
845C2×C4—28no—
846C2×C4—28no—
847C2×C4—216no—
848C2×C4—28no—
849C2×C4—216no—
850C2×C4—24no—
851C2×C4—24no—
852C2×C4—28no—
853C2×C4—24no—
854C2×C4—28no—
855C2×C4—24no—
856C2×C4—24no—
857C2×C4—28no—
858C2×C4—216no—
859C2×C4—216no—
860C2×C4—24no—
861C2×C4—24no—
862C2×C4—24no—
863C2×C4—24no—
864C2×C4—24no—
865C2×C4—28no—
866C2×C4—24no—
867C2×C4—432no—
868C2×C4—416no—
869C2×C4—416no—
870C2×C4—816no—
871C2×C4—816no—
872C2×C4C23×D414yes—
873C2×C4C23×D414yes—
874C2×C4C23×D412yes—
875C2×C4C23×D412yes—
876C2×C4C23×D412yes—
877C2×C4C23×D412yes—
878C2×C4C23×D414yes—
879C2×C4C23×D412yes—
880C2×C4C23×D412yes—
881C2×C4C2×H(5,𝔽2)14yes—
882C2×C4C2×H(5,𝔽2)14yes—
883C2×C4C2×2−1+414yes—
884C2×C4C2×2−1+414yes—
885C2×C4C2×2−1+412yes—
886C2×C4C2×2−1+412yes—
887C2×C4C2×2−1+414yes—
888C2×C4C2×2−1+414yes—
889C2×C4C2×2−1+414yes—
890C22—24no—
891C22—22no—
892C22—22no—
893C22—24no—
894C22—24no—
895C22—24no—
896C22—24no—
897C22—44no—
898C22—44no—
899C22—48no—
900C22—44no—
901C22—44no—
902C22—44no—
903C22—48no—
904C22#349814yes—
905C22C24×D411yescharacteristic
906C22C22×H(5,𝔽2)12yes—
907C22C22×2−1+411yescharacteristic
908C22C22×2−1+412yes—
909C22C22×2−1+411yescharacteristic
910C4—24no—
911C4—22no—
912C4—22no—
913C4—24no—
914C4—22no—
915C4—22no—
916C4—24no—
917C4—24no—
918C4—24no—
919C4—24no—
920C4—44no—
921C4—48no—
922C4—48no—
923C4—44no—
924C4—44no—
925C4—44no—
926C4—44no—
927C4#349914yes—
928C4#349914yes—
929C4#354418yescomplemented
930C2—24no—
931C2—44no—
932C2—84no—
933C2C2×#354412yes—
934C2C2×#349811yescharacteristic
935C2C2×#349911yescharacteristic
936C2C2×#349911yescharacteristic
937C2#6283312yes—
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×#3544C2semidirect
2. #59313C2semidirect
3. #59312C2semidirect
4. #45993C2semidirect
5. #39617C2semidirect
6. #39489C2semidirect
7. #39377C2semidirect
8. #39369C2semidirect
9. #39337C2semidirect
10. #37863C2semidirect
11. #37632C2semidirect
12. #37303C2semidirect
13. C2×#2868C2semidirect
14. #36631C2semidirect
15. #36559C2semidirect
16. Q8×C4⋊Q8C2semidirect
17. #36187C2semidirect
18. #36181C2semidirect
19. #36180C2semidirect
20. #36179C2semidirect
21. #35277C2semidirect
22. #35275C2semidirect
23. C4×#529C2semidirect
193. #529D4semidirect
929. C4#3544semidirect

Maximal subgroups

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

subgroupindex
C2×#35442
#593132
#593122
#459932
#396172
#394892
#393772
#393692
#393372
#378632
#376322
#373032
C2×#28682
#366312
#365592
Q8×C4⋊Q82
#361872
#361812
#361802
#361792
#352772
#352752
C4×#5292