Finite Group Databasebeta

← #7673827

Subgroups — #7673827

Order 512.

7430 conjugacy classes of subgroups.

The subgroup lattice has 945 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3506C211yesmaximal, characteristic, complemented
2C2×#3501C211yesmaximal, characteristic, complemented
3#45271C214yesmaximal, complemented
4#45042C218yesmaximal, complemented
5#44938C214yesmaximal, complemented
6#39171C214yesmaximal, complemented
7#39169C214yesmaximal, complemented
8#39163C214yesmaximal, complemented
9#39161C214yesmaximal, complemented
10#37752C218yesmaximal, complemented
11#37703C218yesmaximal, complemented
12#35620C212yesmaximal, complemented
13#35528C212yesmaximal, complemented
14#35264C212yesmaximal, complemented
15#35172C211yesmaximal, characteristic, complemented
16#35165C211yesmaximal, characteristic, complemented
17#34637C211yesmaximal, characteristic, complemented
18#34275C212yesmaximal, complemented
19#34074C211yesmaximal, characteristic, complemented
20C2×#2328C211yesmaximal, characteristic, complemented
21#3506—216no—
22#3501—216no—
23C2×#559C2214yescomplemented
24C2×#556C2212yescomplemented
25C2×#555C2212yescomplemented
26C2×#554C2214yescomplemented
27C2×#554C2212yescomplemented
28C2×#554C2214yescomplemented
29C2×#554C2212yescomplemented
30C2×#553C2214yescomplemented
31C2×#550C2212yescomplemented
32C2×D4×Q8C2212yescomplemented
33C2×D4×Q8C2212yescomplemented
34C2×#547C2212yescomplemented
35C2×#544C2212yes—
36C2×#543C2214yes—
37C2×#538C2214yes—
38C2×#535C2212yes—
39C2×#535C2212yes—
40C2×#533C2211yescharacteristic
41C2×#533C2211yescharacteristic
42C2×#532C2211yescharacteristic
43C22×#127C2211yescharacteristic
44C2×#525C2214yes—
45C22×C22⋊Q8C2214yes—
46C2×#520C2212yes—
47C2×#518C2212yes—
48C22×C4×D4C2211yescharacteristic
49C22×C4×D4C2211yescharacteristic
50#2861C2214yescomplemented
51#2858C2214yescomplemented
52#2848C2214yes—
53#2847C2214yes—
54#2730C22116yescomplemented
55#2728C22116yescomplemented
56#2702C22116yescomplemented
57#2696C22116yescomplemented
58#2696C22116yescomplemented
59#2681C22116yescomplemented
60#2676C22116yescomplemented
61#2676C22116yescomplemented
62#2642C2212yescomplemented
63#2641C2212yescomplemented
64#2641C2214yescomplemented
65#2640C2212yescomplemented
66#2640C2214yescomplemented
67#2640C2212yescomplemented
68#2639C2214yes—
69#2639C2214yes—
70#2626C2214yes—
71#2617C2214yes—
72#2580C2214yescomplemented
73#2568C2214yescomplemented
74#2566C2214yescomplemented
75#2566C2214yescomplemented
76#2565C2214yescomplemented
77#2563C2214yescomplemented
78#2563C2212yescomplemented
79#2547C2212yescomplemented
80#2544C2214yes—
81#2544C2214yes—
82#2544C2214yescomplemented
83#2542C2212yescomplemented
84#2541C2214yes—
85#2541C2214yes—
86#2541C2212yescomplemented
87#2538C2214yescomplemented
88#2537C2214yescomplemented
89#2535C2214yescomplemented
90#2491C2218yescomplemented
91#2490C2218yescomplemented
92#2481C22116yescomplemented
93#2477C22116yescomplemented
94#2472C22116yes—
95#2463C22116yescomplemented
96#2450C22116yes—
97#2443C22116yescomplemented
98#2442C2218yescomplemented
99#2439C2218yescomplemented
100#2436C22116yescomplemented
101#2428C2218yes—
102#2428C2218yes—
103#2427C22116yescomplemented
104#2416C22116yescomplemented
105#2410C22116yes—
106#2407C22116yescomplemented
107#2398C2214yescomplemented
108#2398C2214yescomplemented
109#2363C2218yescomplemented
110#2361C2218yescomplemented
111#2358C22116yes—
112#2331C2212yescomplemented
113#2331C2212yescomplemented
114#2330C2214yescomplemented
115#2329C2214yes—
116#2329C2214yes—
117#2328C2214yes—
118#2328C2214yes—
119#2328C2214yes—
120#2328C2214yes—
121#2328C2214yescomplemented
122#2326C2214yescomplemented
123#2317C2212yes—
124#2311C2212yes—
125#2309C2212yes—
126C4×#127C2214yescomplemented
127C4×#124C2214yescomplemented
128#2297C2212yes—
129#2297C2212yes—
130#2296C2212yes—
131#2295C2214yescomplemented
132#2295C2214yescomplemented
133C2×#390C2211yescharacteristic
134C2×#390C2211yescharacteristic
135C2×#386C2214yes—
136C2×#386C2214yes—
137#2285C2211yescharacteristic
138C2×#382C2211yescharacteristic
139C4×#117C2212yes—
140C2×#376C2211yescharacteristic
141C22×#41C2312yes—
142C22×#41C2314yes—
143C23×Q8C2314yes—
144C23×D4C2311yescharacteristic
145C23×D4C2311yescharacteristic
146C23×D4C2314yes—
147C24×C4C2312yes—
148C24×C4C2312yes—
149#559—232no—
150#556—216no—
151#555—216no—
152#554—216no—
153#554—232no—
154#554—216no—
155#554—232no—
156#553—232no—
157#550—216no—
158D4×Q8—216no—
159D4×Q8—216no—
160#547—216no—
161#544—216no—
162#543—232no—
163#538—232no—
164#535—216no—
165#535—216no—
166#533—28no—
167#533D4116yescomplemented
168#532—28no—
169C2×C4⋊Q8C2311yescharacteristic
170C2×C4⋊Q8C2314yes—
171C2×C4⋊Q8C2311yescharacteristic
172C2×C4⋊Q8C2311yescharacteristic
173C2×C4⋊Q8C2314yes—
174C2×C4⋊Q8C2311yescharacteristic
175C2×C4⋊Q8C2311yescharacteristic
176C2×#127—28no—
177C2×#127C2314yes—
178C2×#127C2314yes—
179C2×#127C2314yes—
180C2×#127C2314yes—
181C2×#127C2311yescharacteristic
182C2×#126C2318yes—
183C2×#125C2314yes—
184C2×#125C2312yes—
185C2×#125C2314yes—
186C2×#125C2312yes—
187C2×#124C2314yes—
188C2×#124C2314yes—
189C2×#124C2312yes—
190C2×#124C2318yes—
191C2×#124C23116yes—
192#525—232no—
193C2×#123C2318yes—
194C2×#123C2318yes—
195C2×C22⋊Q8—232no—
196C2×C22⋊Q8C2312yes—
197C2×C22⋊Q8C2312yes—
198C2×C22⋊Q8C2318yes—
199C2×C22⋊Q8C2318yes—
200C2×C22⋊Q8C2318yes—
201C2×C22⋊Q8C2314yes—
202C2×C22⋊Q8C2314yes—
203C2×C22⋊Q8C2314yes—
204C2×C22⋊Q8C2318yes—
205C2×C22⋊Q8C2318yes—
206C2×C22⋊Q8C2318yes—
207C2×C22⋊Q8C2318yes—
208C2×C22⋊Q8C2312yes—
209C2×C22⋊Q8C2312yes—
210C2×#121C2312yes—
211C2×#121C2318yes—
212C2×#121C2312yes—
213C2×#121C2314yes—
214C2×#121C2318yes—
215C2×#121C2314yes—
216C2×#121C2314yes—
217C2×#121C2318yes—
218C2×#121C23116yes—
219C2×#121C23116yes—
220C2×#120C2318yes—
221C2×#120C2318yes—
222#520—216no—
223#518—216no—
224C2×C4×Q8C2314yes—
225C2×C4×Q8C2312yes—
226C2×C4×Q8C2312yes—
227C2×C4×Q8C2312yes—
228C2×C4×Q8C2312yes—
229C2×C4×D4—28no—
230C2×C4×D4—28no—
231C2×C4×D4C2314yes—
232C2×C4×D4C2314yes—
233C2×C4×D4C2312yes—
234C2×C4×D4C2312yes—
235C2×C4×D4C2312yes—
236C2×C4×D4C2312yes—
237C2×C4×D4C2312yes—
238C2×C4×D4C2312yes—
239C2×C4×D4C2312yes—
240C2×C4×D4C2312yes—
241C2×C4×D4C2314yes—
242C2×C4×D4C2318yes—
243C2×C4×D4C2314yes—
244C2×C4×D4C2314yes—
245C2×C4×D4C2312yes—
246C2×C4×D4C2312yes—
247C2×C4×D4C2318yes—
248C2×C4×D4C23116yes—
249C2×#117C2312yes—
250C2×#117C2312yes—
251C2×#117C2314yes—
252C2×#117C2314yes—
253C2×#117C2312yes—
254C22×C4⋊C4C2311yescharacteristic
255C22×C4⋊C4C2311yescharacteristic
256C22×C4⋊C4C2314yes—
257C22×C4⋊C4C2318yes—
258C22×C4⋊C4C2314yes—
259C22×C22⋊C4C2318yes—
260C22×C22⋊C4C2312yes—
261C22×C22⋊C4C2312yes—
262C22×C22⋊C4C2314yes—
263C22×C22⋊C4C2314yes—
264C22×C42C2311yescharacteristic
265C22×C42C2311yescharacteristic
266C22×C42C2311yescharacteristic
267#400C23116yes—
268#400C2318yes—
269#400C2318yes—
270#399C2318yes—
271#398C23116yes—
272#397C2318yes—
273#397C2318yes—
274#397C2318yes—
275#397C23116yes—
276#396C23116yes—
277#396C23116yes—
278#394C23116yes—
279#394C2318yes—
280#394C2318yes—
281#394C23116yes—
282#394C23116yes—
283#394C23116yes—
284#394C23116yes—
285#393C2318yes—
286#393C23116yes—
287#393C2318yes—
288#393C2318yes—
289#393C23116yes—
290#392C2318yes—
291#392C23116yes—
292#392C23116yes—
293#391C2312yes—
294#391C2314yes—
295#391C2312yes—
296#391C23116yes—
297#391C2312yes—
298#391C2318yes—
299#391C2318yes—
300#391C2312yes—
301#390C2312yes—
302#390C2314yes—
303#390C23116yes—
304#390C2312yes—
305#390C2314yes—
306#390C2314yes—
307#390C2314yes—
308#390C2318yes—
309#390C2312yes—
310#390C2314yes—
311#390C2314yes—
312#390C2314yes—
313#390C2312yes—
314#390C23116yes—
315#389C2318yes—
316#389C2318yes—
317#389C2318yes—
318#389C2314yes—
319#389C2314yes—
320#388C23116yes—
321#388C23116yes—
322#388C23116yes—
323#388C23116yes—
324#387C23116yes—
325#387C2318yes—
326#387C2318yes—
327#387C2318yes—
328#387C2318yes—
329#386C2318yes—
330#386C23116yes—
331#386C23116yes—
332#386C23116yes—
333#386C23116yes—
334#386C23116yes—
335#386C23116yes—
336#386C23116yes—
337#386C2318yes—
338#386C2318yes—
339#386C23116yes—
340#386C23116yes—
341#385C23116yes—
342#385C23116yes—
343#385C2318yes—
344#385C23116yes—
345#385C2318yes—
346#384C2314yes—
347#384C2312yes—
348#382C2314yes—
349#382C2314yes—
350#382C2312yes—
351#382C2314yes—
352#380C2318yes—
353#380C23116yes—
354#380C2318yes—
355#380C2312yes—
356#380C2312yes—
357#380C2318yes—
358#379C2318yes—
359C4×C4⋊C4C2314yes—
360C4×C4⋊C4C2312yes—
361C4×C4⋊C4C2312yes—
362C4×C4⋊C4C2314yes—
363C4×C4⋊C4C2314yes—
364C4×C4⋊C4C2314yes—
365C4×C22⋊C4C2318yes—
366C4×C22⋊C4C23116yes—
367C4×C22⋊C4C2318yes—
368C4×C22⋊C4C2318yes—
369#376C2314yes—
370#376C2312yes—
371#376C2312yes—
372#376C2312yes—
373#376C2312yes—
374C2×#95C2312yes—
375C2×#95C2312yes—
376C2×#95C2314yes—
377C43C2314yes—
378C25C2412yes—
379C25C2412yes—
380C2×#41—216no—
381C2×#41—28no—
382C2×#41—28no—
383C2×#41—28no—
384C2×#41—88no—
385C22×Q8—216no—
386C22×Q8—88no—
387C22×Q8C2412yes—
388C22×Q8C2412yes—
389C22×Q8C2412yes—
390C22×Q8C2418yes—
391C22×Q8C2412yes—
392C22×Q8C2412yes—
393C22×D4—216no—
394C22×D4—24no—
395C22×D4—24no—
396C22×D4—24no—
397C22×D4—24no—
398C22×D4—24no—
399C22×D4—84no—
400C22×D4—84no—
401C22×D4#4118yescomplemented
402C22×D4C2414yes—
403C22×D4C2412yes—
404C22×D4C2412yes—
405C22×D4C2412yes—
406C22×D4C2412yes—
407C22×D4C2412yes—
408C22×D4C2418yes—
409C22×D4C24116yes—
410C22×D4C2412yes—
411C22×D4C2412yes—
412C22×D4C2418yes—
413C22×D4C24116yes—
414C23×C4—28no—
415C23×C4—28no—
416C23×C4—84no—
417C23×C4—84no—
418C23×C4C2414yes—
419C23×C4C2412yes—
420C23×C4C2412yes—
421C23×C4C2412yes—
422C23×C4C2418yes—
423C23×C4C2418yes—
424C23×C4C2414yes—
425C23×C4C2418yes—
426C23×C4C2414yes—
427C23×C4C2414yes—
428C23×C4C2414yes—
429C23×C4C2412yes—
430C23×C4C2411yescharacteristic
431C23×C4C2411yescharacteristic
432C23×C4C2411yescharacteristic
433C4⋊Q8—216no—
434C4⋊Q8—24no—
435C4⋊Q8—24no—
436C4⋊Q8—24no—
437C4⋊Q8—216no—
438C4⋊Q8C2×D418yescomplemented
439C4⋊Q8C2×D418yescomplemented
440#127—216no—
441#127—216no—
442#127—216no—
443#127—24no—
444#127—216no—
445#126—232no—
446#125—216no—
447#125—28no—
448#125—216no—
449#125C2×D4116yescomplemented
450#124—232no—
451#124—216no—
452#124—28no—
453#124—216no—
454#124—816no—
455#123—232no—
456#123—232no—
457C22⋊Q8—216no—
458C22⋊Q8—216no—
459C22⋊Q8—232no—
460C22⋊Q8—28no—
461C22⋊Q8—28no—
462C22⋊Q8—216no—
463C22⋊Q8—232no—
464C22⋊Q8—232no—
465C22⋊Q8—232no—
466C22⋊Q8—232no—
467C22⋊Q8—232no—
468C22⋊Q8—88no—
469C22⋊Q8C2×D4116yes—
470C22⋊Q8C2×D4116yes—
471#121—232no—
472#121—28no—
473#121—28no—
474#121—216no—
475#121—216no—
476#121—216no—
477#121—232no—
478#121—816no—
479#121—816no—
480#121—88no—
481#120—232no—
482#120—232no—
483C4×Q8—216no—
484C4×Q8—28no—
485C4×Q8—28no—
486C4×Q8C2×D4116yescomplemented
487C4×Q8C2×D4116yescomplemented
488C4×D4—216no—
489C4×D4—216no—
490C4×D4—232no—
491C4×D4—232no—
492C4×D4—28no—
493C4×D4—28no—
494C4×D4—28no—
495C4×D4—28no—
496C4×D4—28no—
497C4×D4—28no—
498C4×D4—28no—
499C4×D4—28no—
500C4×D4—216no—
501C4×D4—216no—
502C4×D4—216no—
503C4×D4—28no—
504C4×D4—28no—
505C4×D4—816no—
506#117—28no—
507#117—28no—
508#117—216no—
509#117—216no—
510#117C2×D4116yes—
511C2×C4⋊C4—24no—
512C2×C4⋊C4—24no—
513C2×C4⋊C4—216no—
514C2×C4⋊C4—232no—
515C2×C4⋊C4—216no—
516C2×C4⋊C4C2412yes—
517C2×C4⋊C4C2414yes—
518C2×C4⋊C4C2412yes—
519C2×C4⋊C4C2412yes—
520C2×C4⋊C4C2412yes—
521C2×C4⋊C4C2412yes—
522C2×C4⋊C4C2418yes—
523C2×C4⋊C4C2418yes—
524C2×C4⋊C4C2418yes—
525C2×C4⋊C4C2418yes—
526C2×C4⋊C4C2412yes—
527C2×C4⋊C4C2412yes—
528C2×C4⋊C4C2412yes—
529C2×C4⋊C4C2414yes—
530C2×C4⋊C4C2412yes—
531C2×C4⋊C4C2414yes—
532C2×C4⋊C4C2412yes—
533C2×C4⋊C4C24116yes—
534C2×C4⋊C4C2414yes—
535C2×C4⋊C4C2418yes—
536C2×C4⋊C4C2418yes—
537C2×C4⋊C4C2414yes—
538C2×C4⋊C4C2412yes—
539C2×C4⋊C4C2414yes—
540C2×C4⋊C4C2412yes—
541C2×C4⋊C4C2412yes—
542C2×C4⋊C4C2412yes—
543C2×C4⋊C4C2414yes—
544C2×C22⋊C4—28no—
545C2×C22⋊C4—28no—
546C2×C22⋊C4—232no—
547C2×C22⋊C4—84no—
548C2×C22⋊C4—84no—
549C2×C22⋊C4C2414yes—
550C2×C22⋊C4C2414yes—
551C2×C22⋊C4C2414yes—
552C2×C22⋊C4C2414yes—
553C2×C22⋊C4C2418yes—
554C2×C22⋊C4C2418yes—
555C2×C22⋊C4C2414yes—
556C2×C22⋊C4C2418yes—
557C2×C22⋊C4C2414yes—
558C2×C22⋊C4C2418yes—
559C2×C22⋊C4C2414yes—
560C2×C22⋊C4C2418yes—
561C2×C22⋊C4C2414yes—
562C2×C22⋊C4C24116yes—
563C2×C22⋊C4C24116yes—
564C2×C22⋊C4C24116yes—
565C2×C22⋊C4C2418yes—
566C2×C22⋊C4C2418yes—
567C2×C22⋊C4C2418yes—
568C2×C22⋊C4C24116yes—
569C2×C22⋊C4C24116yes—
570C2×C22⋊C4C24116yes—
571C2×C22⋊C4C2418yes—
572C2×C22⋊C4C2414yes—
573C2×C42—24no—
574C2×C42—24no—
575C2×C42C2×D418yes—
576C2×C42C2418yes—
577C2×C42C2414yes—
578C2×C42C2414yes—
579C2×C42C2412yes—
580C2×C42C2412yes—
581C2×C42C2412yes—
582C2×C42C2412yes—
583C2×C42C2418yes—
584C2×C42C2418yes—
585C2×C42C2414yes—
586C2×C42C2411yescharacteristic
587C2×C42C2411yescharacteristic
588C2×C42C2411yescharacteristic
589C2×C42C2411yescharacteristic
590#95C2414yes—
591#95C2414yes—
592#95C2414yes—
593#95C2414yes—
594#95C24116yes—
595#95C2418yes—
596#95C2418yes—
597#95C2418yes—
598#95C24116yes—
599#95C2418yes—
600#95C2418yes—
601#95C2418yes—
602#95C2414yes—
603#95C2414yes—
604#95C2418yes—
605#95C2418yes—
606#95C24116yes—
607C24—24no—
608C24—24no—
609C24—24no—
610C24—24no—
611C24—24no—
612C24—44no—
613C24—44no—
614C24—44no—
615C24—44no—
616C24C2×#4118yes—
617C24C2514yes—
618C24C2514yes—
619C24C2514yes—
620C24C2511yescharacteristic
621#41—432no—
622#41—832no—
623C2×Q8—24no—
624C2×Q8—24no—
625C2×Q8—24no—
626C2×Q8—216no—
627C2×Q8—24no—
628C2×Q8—24no—
629C2×Q8—44no—
630C2×Q8—44no—
631C2×Q8—44no—
632C2×Q8—44no—
633C2×Q8—416no—
634C2×Q8—832no—
635C2×Q8C22×D418yes—
636C2×Q8C22×D418yes—
637C2×D4—28no—
638C2×D4—28no—
639C2×D4—28no—
640C2×D4—232no—
641C2×D4—232no—
642C2×D4—232no—
643C2×D4—24no—
644C2×D4—24no—
645C2×D4—24no—
646C2×D4—24no—
647C2×D4—24no—
648C2×D4—24no—
649C2×D4—216no—
650C2×D4—24no—
651C2×D4—216no—
652C2×D4—24no—
653C2×D4—24no—
654C2×D4—24no—
655C2×D4—24no—
656C2×D4—24no—
657C2×D4—24no—
658C2×D4—24no—
659C2×D4—24no—
660C2×D4—44no—
661C2×D4—416no—
662C2×D4—44no—
663C2×D4—416no—
664C2×D4—416no—
665C2×D4—416no—
666C2×D4—416no—
667C2×D4—416no—
668C2×D4—416no—
669C2×D4—832no—
670C2×D4C2×#4118yes—
671C2×D4C2×#4118yes—
672C22×C4—24no—
673C22×C4—24no—
674C22×C4—24no—
675C22×C4—24no—
676C22×C4—28no—
677C22×C4—28no—
678C22×C4—28no—
679C22×C4—28no—
680C22×C4—28no—
681C22×C4—216no—
682C22×C4—216no—
683C22×C4—28no—
684C22×C4—216no—
685C22×C4—28no—
686C22×C4—42no—
687C22×C4—42no—
688C22×C4—48no—
689C22×C4—48no—
690C22×C4—42no—
691C22×C4—42no—
692C22×C4—42no—
693C22×C4—42no—
694C22×C4—44no—
695C22×C4—44no—
696C22×C4—416no—
697C22×C4—416no—
698C22×C4—48no—
699C22×C4—416no—
700C22×C4—48no—
701C22×C4—816no—
702C22×C4—816no—
703C22×C4C22×D414yes—
704C22×C4C22×D414yes—
705C22×C4C22×D414yes—
706C22×C4C2×#4114yes—
707C22×C42−1+414yes—
708C22×C4C2514yes—
709C22×C4C2514yes—
710C22×C4C2514yes—
711C22×C4C2518yes—
712C22×C4C2514yes—
713C22×C4C2514yes—
714C22×C4C2514yes—
715C22×C4C2514yes—
716C22×C4C2511yescharacteristic
717C22×C4C2511yescharacteristic
718C22×C4C2514yes—
719C22×C4C2514yes—
720C22×C4C2511yescharacteristic
721C22×C4C2511yescharacteristic
722C22×C4C2511yescharacteristic
723C22×C4C2511yescharacteristic
724C4⋊C4—24no—
725C4⋊C4—28no—
726C4⋊C4—24no—
727C4⋊C4—24no—
728C4⋊C4—24no—
729C4⋊C4—24no—
730C4⋊C4—216no—
731C4⋊C4—216no—
732C4⋊C4—216no—
733C4⋊C4—216no—
734C4⋊C4—24no—
735C4⋊C4—24no—
736C4⋊C4—24no—
737C4⋊C4—24no—
738C4⋊C4—28no—
739C4⋊C4—24no—
740C4⋊C4—28no—
741C4⋊C4—416no—
742C4⋊C4—48no—
743C4⋊C4—48no—
744C4⋊C4—44no—
745C4⋊C4—44no—
746C4⋊C4C22×D418yes—
747C4⋊C4C22×D4116yes—
748C4⋊C4C22×D418yes—
749C4⋊C4C22×D418yes—
750C4⋊C4C22×D418yes—
751C4⋊C4C22×D4116yes—
752C22⋊C4—28no—
753C22⋊C4—28no—
754C22⋊C4—232no—
755C22⋊C4—28no—
756C22⋊C4—216no—
757C22⋊C4—216no—
758C22⋊C4—28no—
759C22⋊C4—28no—
760C22⋊C4—28no—
761C22⋊C4—216no—
762C22⋊C4—216no—
763C22⋊C4—28no—
764C22⋊C4—216no—
765C22⋊C4—28no—
766C22⋊C4—416no—
767C22⋊C4—416no—
768C22⋊C4—48no—
769C22⋊C4—48no—
770C22⋊C4—48no—
771C22⋊C4—416no—
772C22⋊C4—416no—
773C22⋊C4—416no—
774C22⋊C4—48no—
775C22⋊C4C22×D4116yes—
776C42—216no—
777C42—28no—
778C42—24no—
779C42—24no—
780C42—28no—
781C42—24no—
782C42—24no—
783C42—48no—
784C42—48no—
785C42C22×D414yes—
786C42C22×D414yes—
787C42C22×D414yes—
788C42C22×D414yes—
789C42C22×D4116yes—
790C23—22no—
791C23—22no—
792C23—24no—
793C23—24no—
794C23—28no—
795C23—28no—
796C23—216no—
797C23—24no—
798C23—24no—
799C23—24no—
800C23—24no—
801C23—24no—
802C23—24no—
803C23—28no—
804C23—28no—
805C23—28no—
806C23—28no—
807C23—416no—
808C23—416no—
809C23—48no—
810C23—84no—
811C23—84no—
812C23—84no—
813C23—84no—
814C23—88no—
815C23—88no—
816C23C23×D412yes—
817C23C22×#4118yes—
818C23C22×#4112yes—
819C23C2×2−1+412yes—
820C23C2611yescharacteristic
821Q8—48no—
822Q8—48no—
823Q8—48no—
824Q8—48no—
825Q8—84no—
826Q8—816no—
827D4—216no—
828D4—216no—
829D4—48no—
830D4—416no—
831D4—48no—
832D4—48no—
833D4—48no—
834D4—84no—
835D4—816no—
836D4—816no—
837D4—832no—
838D4—832no—
839C2×C4—28no—
840C2×C4—28no—
841C2×C4—22no—
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—24no—
846C2×C4—24no—
847C2×C4—24no—
848C2×C4—24no—
849C2×C4—24no—
850C2×C4—24no—
851C2×C4—28no—
852C2×C4—24no—
853C2×C4—24no—
854C2×C4—24no—
855C2×C4—24no—
856C2×C4—24no—
857C2×C4—28no—
858C2×C4—28no—
859C2×C4—28no—
860C2×C4—28no—
861C2×C4—28no—
862C2×C4—28no—
863C2×C4—24no—
864C2×C4—24no—
865C2×C4—44no—
866C2×C4—44no—
867C2×C4—416no—
868C2×C4—416no—
869C2×C4—48no—
870C2×C4—416no—
871C2×C4—816no—
872C2×C4—88no—
873C2×C4—88no—
874C2×C4—816no—
875C2×C4—816no—
876C2×C4—84no—
877C2×C4—84no—
878C2×C4—84no—
879C2×C4#548116yes—
880C2×C4C23×D418yes—
881C2×C4C23×D412yes—
882C2×C4C23×D412yes—
883C2×C4C23×D412yes—
884C2×C4C23×D412yes—
885C2×C4C23×D418yes—
886C2×C4C23×D412yes—
887C2×C4C23×D412yes—
888C2×C4C22×#4112yes—
889C2×C4C22×#4112yes—
890C2×C4C2×2−1+412yes—
891C2×C4C2×2−1+412yes—
892C22—24no—
893C22—22no—
894C22—22no—
895C22—24no—
896C22—216no—
897C22—28no—
898C22—44no—
899C22—44no—
900C22—48no—
901C22—48no—
902C22—48no—
903C22—44no—
904C22—44no—
905C22—44no—
906C22—44no—
907C22—48no—
908C22—48no—
909C22—44no—
910C22—44no—
911C22—816no—
912C22—816no—
913C22C2×#54814yes—
914C22C24×D411yescharacteristic
915C22C23×#4111yescharacteristic
916C22C22×2−1+411yescharacteristic
917C22H(7,𝔽2)12yes—
918C22H(7,𝔽2)12yes—
919C4—22no—
920C4—22no—
921C4—22no—
922C4—22no—
923C4—28no—
924C4—28no—
925C4—44no—
926C4—48no—
927C4—44no—
928C4—44no—
929C4—44no—
930C4—44no—
931C4—44no—
932C4—44no—
933C4C2×#54814yes—
934C4C2×#54814yes—
935C2—24no—
936C2—48no—
937C2—84no—
938C2—84no—
939C2C22×#54811yescharacteristic
940C2#6284612yes—
941C2#6285211yescharacteristic
942C2#6285211yescharacteristic
943C2#6288112yes—
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×#3506C2semidirect
2. C2×#3501C2semidirect
3. #45271C2semidirect
4. #45042C2semidirect
5. #44938C2semidirect
6. #39171C2semidirect
7. #39169C2semidirect
8. #39163C2semidirect
9. #39161C2semidirect
10. #37752C2semidirect
11. #37703C2semidirect
12. #35620C2semidirect
13. #35528C2semidirect
14. #35264C2semidirect
15. #35172C2semidirect
16. #35165C2semidirect
17. #34637C2semidirect
18. #34275C2semidirect
19. #34074C2semidirect
20. C2×#2328C2semidirect
23. C2×#559C22semidirect
24. C2×#556C22semidirect
25. C2×#555C22semidirect
26. C2×#554C22semidirect
27. C2×#554C22semidirect
28. C2×#554C22semidirect
29. C2×#554C22semidirect
30. C2×#553C22semidirect
31. C2×#550C22semidirect
32. C2×D4×Q8C22semidirect
33. C2×D4×Q8C22semidirect
34. C2×#547C22semidirect
50. #2861C22semidirect
51. #2858C22semidirect
54. #2730C22semidirect
55. #2728C22semidirect
56. #2702C22semidirect
57. #2696C22semidirect
58. #2696C22semidirect
59. #2681C22semidirect
60. #2676C22semidirect
61. #2676C22semidirect
62. #2642C22semidirect
63. #2641C22semidirect
64. #2641C22semidirect
65. #2640C22semidirect
66. #2640C22semidirect
67. #2640C22semidirect
72. #2580C22semidirect
73. #2568C22semidirect
74. #2566C22semidirect
75. #2566C22semidirect
76. #2565C22semidirect
77. #2563C22semidirect
78. #2563C22semidirect
79. #2547C22semidirect
82. #2544C22semidirect
83. #2542C22semidirect
86. #2541C22semidirect
87. #2538C22semidirect
88. #2537C22semidirect
89. #2535C22semidirect
90. #2491C22semidirect
91. #2490C22semidirect
92. #2481C22semidirect
93. #2477C22semidirect
95. #2463C22semidirect
97. #2443C22semidirect
98. #2442C22semidirect
99. #2439C22semidirect
100. #2436C22semidirect
103. #2427C22semidirect
104. #2416C22semidirect
106. #2407C22semidirect
107. #2398C22semidirect
108. #2398C22semidirect
109. #2363C22semidirect
110. #2361C22semidirect
112. #2331C22semidirect
113. #2331C22semidirect
114. #2330C22semidirect
121. #2328C22semidirect
122. #2326C22semidirect
126. C4×#127C22semidirect
127. C4×#124C22semidirect
131. #2295C22semidirect
132. #2295C22semidirect
167. #533D4semidirect
401. C22×D4#41semidirect
438. C4⋊Q8C2×D4semidirect
439. C4⋊Q8C2×D4semidirect
449. #125C2×D4semidirect
486. C4×Q8C2×D4semidirect
487. C4×Q8C2×D4semidirect

Maximal subgroups

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

subgroupindex
C2×#35062
C2×#35012
#452712
#450422
#449382
#391712
#391692
#391632
#391612
#377522
#377032
#356202
#355282
#352642
#351722
#351652
#346372
#342752
#340742
C2×#23282