Finite Group Databasebeta

← #7630933

Subgroups — #7630933

Order 512.

6990 conjugacy classes of subgroups.

The subgroup lattice has 885 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3495C212yesmaximal, complemented
2#36024C218yesmaximal, complemented
3#36012C218yesmaximal, complemented
4#35834C218yesmaximal, complemented
5#35773C218yesmaximal, complemented
6#35343C212yesmaximal, complemented
7#35331C212yesmaximal, complemented
8#35330C211yesmaximal, characteristic, complemented
9#35322C212yesmaximal, complemented
10#35319C212yesmaximal, complemented
11#35318C214yesmaximal, complemented
12#35317C211yesmaximal, characteristic, complemented
13#35312C212yesmaximal, complemented
14#35306C212yesmaximal, complemented
15#34633C211yesmaximal, characteristic
16#34631C214yesmaximal, complemented
17C2×#2621C211yesmaximal, characteristic, complemented
18#34276C212yesmaximal, complemented
19#34209C211yesmaximal, characteristic, complemented
20#34208C211yesmaximal, characteristic, complemented
21#33996C211yesmaximal, characteristic, complemented
22#3495—232no—
23C2×#556C2214yes—
24C2×#554C2214yes—
25C2×#552C2218yes—
26C2×#552C2214yes—
27C2×#552C2214yes—
28C2×#551C2218yes—
29C2×#544C2212yes—
30C2×#542C2214yes—
31C2×#541C2214yes—
32C2×#536C2212yes—
33C2×#536C2212yes—
34C2×#533C2214yes—
35C2×#532C2211yescharacteristic
36C22×C4⋊Q8C2211yescharacteristic
37C2×#529C2214yes—
38C2×#525C2212yes—
39C22×C22⋊Q8C2212yes—
40C2×#520C2212yes—
41C2×#519C2212yes—
42C22×#117C2211yescharacteristic
43C22×#117C2211yescharacteristic
44C22×#117C2211yescharacteristic
45#2868C2212yescomplemented
46#2862C2212yescomplemented
47#2862C2214yescomplemented
48#2861C2214yescomplemented
49#2859C2212yescomplemented
50#2858C2212yescomplemented
51#2857C2214yes—
52#2850C2214yes—
53#2664C22116yescomplemented
54#2663C22116yes—
55#2660C2214yescomplemented
56#2658C2214yescomplemented
57#2642C2214yescomplemented
58#2640C2214yescomplemented
59#2621C2212yes—
60#2621C2212yes—
61#2621C2212yes—
62#2621C2214yes—
63#2621C2212yes—
64#2621C2214yes—
65#2621C2214yes—
66#2621C2211yescharacteristic
67#2621C2211yescharacteristic
68#2620C2214yes—
69#2620C2212yes—
70#2620C2212yes—
71#2619C2211yescharacteristic
72#2619C2211yescharacteristic
73#2618C2214yes—
74#2617C2214yes—
75#2602C22116yes—
76#2601C22116yescomplemented
77#2565C22116yescomplemented
78#2560C22116yescomplemented
79#2557C22116yes—
80#2556C22116yescomplemented
81#2553C22116yes—
82#2550C2218yescomplemented
83#2549C2218yes—
84#2542C2218yescomplemented
85#2521C22116yes—
86#2519C22116yescomplemented
87#2506C22116yescomplemented
88#2501C2218yes—
89#2499C22116yes—
90#2496C22116yes—
91#2492C2218yescomplemented
92#2489C2218yescomplemented
93#2488C22116yes—
94#2417C2218yes—
95#2415C2218yes—
96#2413C2218yes—
97#2412C2218yes—
98#2396C22116yescomplemented
99#2395C22116yes—
100#2392C2214yes—
101#2392C2214yes—
102C2×#398C2214yes—
103C2×#397C2214yes—
104#2365C2218yescomplemented
105#2364C2218yes—
106#2362C2218yescomplemented
107#2360C2218yescomplemented
108#2359C22116yes—
109#2352C2218yescomplemented
110#2344C2218yes—
111#2328C2212yescomplemented
112#2327C2212yescomplemented
113#2327C2212yescomplemented
114#2327C2212yescomplemented
115#2327C2214yescomplemented
116#2326C2214yescomplemented
117#2317C2212yes—
118#2311C2212yes—
119#2310C2212yes—
120C4×C4⋊Q8C2214yescomplemented
121C4×C4⋊Q8C2214yescomplemented
122C4×#124C2214yescomplemented
123C4×#124C2214yescomplemented
124#2297C2212yes—
125C2×#391C2212yes—
126#2285C2211yescharacteristic
127C2×#382C2211yescharacteristic
128#2274C2214yes—
129#2274C2214yes—
130#2274C2214yes—
131#2273C2214yes—
132C4×#117C2211yescharacteristic
133C4×#117C2212yes—
134C4×#117C2212yes—
135C4×#117C2212yes—
136C4×#117C2211yescharacteristic
137C4×#117C2211yescharacteristic
138C4×#117C2211yescharacteristic
139C4×#117C2212yes—
140C22×#41C2312yes—
141C23×Q8C2312yes—
142C24×C4C2311yescharacteristic
143#556—232no—
144#554—232no—
145#552—264no—
146#552—232no—
147#552—232no—
148#551—264no—
149#544—216no—
150#542—232no—
151#541—232no—
152#536—216no—
153#536—216no—
154#533—232no—
155#532—28no—
156C2×C4⋊Q8—28no—
157C2×C4⋊Q8C2312yes—
158C2×C4⋊Q8C2314yes—
159C2×C4⋊Q8C2312yes—
160C2×C4⋊Q8C2311yescharacteristic
161C2×C4⋊Q8C2314yes—
162C2×C4⋊Q8C2314yes—
163C2×C4⋊Q8C2314yes—
164C2×C4⋊Q8C2314yes—
165C2×#127C2311yescharacteristic
166#529—232no—
167C2×#126C2318yes—
168C2×#126C2318yes—
169C2×#126C2318yes—
170C2×#126C2318yes—
171C2×#125C2318yes—
172C2×#125C2314yes—
173C2×#125C2318yes—
174C2×#125C2318yes—
175C2×#125C2314yes—
176C2×#124C2314yes—
177C2×#124C2314yes—
178C2×#124C2312yes—
179C2×#124C2318yes—
180#525—216no—
181C2×#123C2318yes—
182C2×#123C2318yes—
183C2×#123C2314yes—
184C2×#123C2318yes—
185C2×#123C2318yes—
186C2×C22⋊Q8—216no—
187C2×C22⋊Q8C2318yes—
188C2×C22⋊Q8C2314yes—
189C2×C22⋊Q8C2312yes—
190C2×C22⋊Q8C2318yes—
191C2×C22⋊Q8C2314yes—
192C2×C22⋊Q8C2312yes—
193C2×C22⋊Q8C2314yes—
194C2×C22⋊Q8C2314yes—
195C2×C22⋊Q8C2318yes—
196C2×C22⋊Q8C2314yes—
197C2×C22⋊Q8C2314yes—
198C2×C22⋊Q8C2318yes—
199C2×#121C2312yes—
200C2×#121C2314yes—
201C2×#121C2312yes—
202C2×#120C2314yes—
203#520—216no—
204#519—216no—
205C2×C4×Q8C2314yes—
206C2×C4×Q8C2314yes—
207C2×C4×Q8C2314yes—
208C2×C4×Q8C2318yes—
209C2×C4×Q8C2314yes—
210C2×C4×Q8C2314yes—
211C2×C4×D4C2314yes—
212C2×C4×D4C2318yes—
213C2×C4×D4C2314yes—
214C2×C4×D4C2318yes—
215C2×C4×D4C2314yes—
216C2×C4×D4C2314yes—
217C2×#117—28no—
218C2×#117—28no—
219C2×#117D4116yescomplemented
220C2×#117C2311yescharacteristic
221C2×#117C2312yes—
222C2×#117C2318yes—
223C2×#117C2318yes—
224C2×#117C2314yes—
225C2×#117C2311yescharacteristic
226C2×#117C2311yescharacteristic
227C2×#117C2312yes—
228C2×#117C2311yescharacteristic
229C2×#117C2311yescharacteristic
230C2×#117C2312yes—
231C2×#117C2312yes—
232C2×#117C2318yes—
233C2×#117C2312yes—
234C2×#117C2312yes—
235C2×#117C2311yescharacteristic
236C2×#117C2311yescharacteristic
237C2×#117C2312yes—
238C2×#117C2312yes—
239C2×#117C2312yes—
240C2×#117C2311yescharacteristic
241C22×C4⋊C4C2312yes—
242C22×C4⋊C4C2314yes—
243C22×C4⋊C4C2314yes—
244C22×C4⋊C4C2312yes—
245C22×C4⋊C4C2314yes—
246C22×C4⋊C4C2312yes—
247C22×C4⋊C4C2312yes—
248C22×C22⋊C4C2312yes—
249C22×C22⋊C4C2314yes—
250C22×C22⋊C4C2312yes—
251C22×C22⋊C4C2312yes—
252C22×C42C2312yes—
253C22×C42C2311yescharacteristic
254C22×C42C2312yes—
255C22×C42C2311yescharacteristic
256#400C23116yes—
257#400C23116yes—
258#399C23116yes—
259#399C23116yes—
260#398C2318yes—
261#398C2314yes—
262#398C2318yes—
263#398C23116yes—
264#398C2314yes—
265#398C2318yes—
266#398C2318yes—
267#398C23116yes—
268#397C23116yes—
269#397C2318yes—
270#397C2314yes—
271#397C2314yes—
272#397C2318yes—
273#397C2318yes—
274#397C2318yes—
275#397C23116yes—
276#396C23116yes—
277#396C2318yes—
278#396C2318yes—
279#395C23116yes—
280#394C2314yes—
281#394C2314yes—
282#394C23116yes—
283#394C2318yes—
284#394C2318yes—
285#393C23116yes—
286#392C2314yes—
287#392C2314yes—
288#391C23116yes—
289#391C2312yes—
290#391C2314yes—
291#391C2314yes—
292#391C2314yes—
293#391C23116yes—
294#391C2318yes—
295#391C2314yes—
296#391C2314yes—
297#391C2312yes—
298#391C2318yes—
299#390C23116yes—
300#390C2314yes—
301#390C2312yes—
302#390C2312yes—
303#389C23116yes—
304#389C23116yes—
305#389C2318yes—
306#389C23116yes—
307#389C23116yes—
308#388C23116yes—
309#388C23116yes—
310#388C23116yes—
311#388C23116yes—
312#388C23116yes—
313#388C23116yes—
314#387C23116yes—
315#387C23116yes—
316#387C23116yes—
317#387C23116yes—
318#387C23116yes—
319#386C23116yes—
320#386C2318yes—
321#386C23116yes—
322#386C2318yes—
323#385C2318yes—
324#385C23116yes—
325#384C2312yes—
326#384C2314yes—
327#384C23116yes—
328#382C23116yes—
329#382C2314yes—
330#382C2311yescharacteristic
331#382C2311yescharacteristic
332#382C2312yes—
333#382C2314yes—
334#382C2312yes—
335#381C2318yes—
336#380C2318yes—
337#380C2314yes—
338#380C23116yes—
339C4×C4⋊C4C2318yes—
340C4×C4⋊C4C23116yes—
341C4×C4⋊C4C23116yes—
342C4×C4⋊C4C2318yes—
343C4×C4⋊C4C2314yes—
344C4×C4⋊C4C2314yes—
345C4×C4⋊C4C2314yes—
346C4×C4⋊C4C2318yes—
347C4×C4⋊C4C2314yes—
348C4×C4⋊C4C2318yes—
349C4×C4⋊C4C2314yes—
350C4×C22⋊C4C23116yes—
351C4×C22⋊C4C2314yes—
352C4×C22⋊C4C2318yes—
353C4×C22⋊C4C23116yes—
354C4×C22⋊C4C2314yes—
355C4×C22⋊C4C2318yes—
356C4×C22⋊C4C2318yes—
357C4×C22⋊C4C2314yes—
358C4×C22⋊C4C2318yes—
359C4×C22⋊C4C2314yes—
360C4×C22⋊C4C2318yes—
361#376C2312yes—
362#376C2312yes—
363#376C2312yes—
364#376C2312yes—
365C2×#95C2318yes—
366C2×#95C2314yes—
367C43C2312yes—
368C43C2312yes—
369C43C2312yes—
370C43C2312yes—
371C25C2411yescharacteristic
372C2×#41—28no—
373C2×#41—28no—
374C2×#41—28no—
375C22×Q8—28no—
376C22×Q8—28no—
377C22×Q8—28no—
378C22×Q8C2414yes—
379C22×Q8C2414yes—
380C22×Q8C2412yes—
381C22×Q8C2418yes—
382C22×D4C2414yes—
383C22×D4C2412yes—
384C22×D4C2414yes—
385C22×D4C2414yes—
386C22×D4C2414yes—
387C23×C4—24no—
388C23×C4—24no—
389C23×C4C2×D418yes—
390C23×C4C2414yes—
391C23×C4C2414yes—
392C23×C4C2411yescharacteristic
393C23×C4C2411yescharacteristic
394C23×C4C2411yescharacteristic
395C23×C4C2411yescharacteristic
396C23×C4C2411yescharacteristic
397C23×C4C2414yes—
398C23×C4C2412yes—
399C23×C4C2414yes—
400C23×C4C2418yes—
401C23×C4C2414yes—
402C23×C4C2412yes—
403C23×C4C2411yescharacteristic
404C4⋊Q8—216no—
405C4⋊Q8—216no—
406C4⋊Q8—216no—
407C4⋊Q8—216no—
408C4⋊Q8—28no—
409C4⋊Q8—28no—
410C4⋊Q8—24no—
411C4⋊Q8—216no—
412#127—24no—
413#126—232no—
414#126—232no—
415#126—232no—
416#126—232no—
417#125—232no—
418#125—232no—
419#125—216no—
420#125—216no—
421#125—232no—
422#124—232no—
423#124—216no—
424#124—28no—
425#124—216no—
426#123—216no—
427#123—232no—
428#123—232no—
429#123—232no—
430#123—232no—
431C22⋊Q8—216no—
432C22⋊Q8—216no—
433C22⋊Q8—216no—
434C22⋊Q8—216no—
435C22⋊Q8—28no—
436C22⋊Q8—28no—
437C22⋊Q8—232no—
438C22⋊Q8—216no—
439C22⋊Q8—216no—
440C22⋊Q8—232no—
441C22⋊Q8—232no—
442C22⋊Q8—232no—
443#121—28no—
444#121—28no—
445#121—216no—
446#120—216no—
447C4×Q8—216no—
448C4×Q8—216no—
449C4×Q8—216no—
450C4×Q8—216no—
451C4×Q8—216no—
452C4×Q8—232no—
453C4×D4—216no—
454C4×D4—216no—
455C4×D4—232no—
456C4×D4—232no—
457C4×D4—216no—
458C4×D4—216no—
459#117—28no—
460#117—232no—
461#117—24no—
462#117—216no—
463#117—28no—
464#117—232no—
465#117—28no—
466#117—232no—
467#117—28no—
468#117—28no—
469#117—28no—
470#117—24no—
471#117—24no—
472#117—24no—
473#117—24no—
474#117C2×D418yes—
475#117C2×D418yes—
476#117C2×D4116yes—
477#117C2×D4116yes—
478#117C2×D4116yes—
479#117#4118yes—
480C2×C4⋊C4—28no—
481C2×C4⋊C4—216no—
482C2×C4⋊C4—28no—
483C2×C4⋊C4—216no—
484C2×C4⋊C4—216no—
485C2×C4⋊C4—28no—
486C2×C4⋊C4C2×D4116yes—
487C2×C4⋊C4C2414yes—
488C2×C4⋊C4C2412yes—
489C2×C4⋊C4C2412yes—
490C2×C4⋊C4C2412yes—
491C2×C4⋊C4C2412yes—
492C2×C4⋊C4C2412yes—
493C2×C4⋊C4C2414yes—
494C2×C4⋊C4C2418yes—
495C2×C4⋊C4C2414yes—
496C2×C4⋊C4C2418yes—
497C2×C4⋊C4C2418yes—
498C2×C4⋊C4C2418yes—
499C2×C4⋊C4C2418yes—
500C2×C4⋊C4C2412yes—
501C2×C4⋊C4C2412yes—
502C2×C4⋊C4C2418yes—
503C2×C4⋊C4C2418yes—
504C2×C4⋊C4C2418yes—
505C2×C4⋊C4C2418yes—
506C2×C4⋊C4C2418yes—
507C2×C4⋊C4C2414yes—
508C2×C4⋊C4C2414yes—
509C2×C4⋊C4C2414yes—
510C2×C4⋊C4C2418yes—
511C2×C4⋊C4C2418yes—
512C2×C4⋊C4C24116yes—
513C2×C4⋊C4C2418yes—
514C2×C4⋊C4C24116yes—
515C2×C4⋊C4C2412yes—
516C2×C4⋊C4C2412yes—
517C2×C4⋊C4C2414yes—
518C2×C4⋊C4C2412yes—
519C2×C22⋊C4—216no—
520C2×C22⋊C4—28no—
521C2×C22⋊C4—28no—
522C2×C22⋊C4C2×D4116yes—
523C2×C22⋊C4C2412yes—
524C2×C22⋊C4C2412yes—
525C2×C22⋊C4C2412yes—
526C2×C22⋊C4C2412yes—
527C2×C22⋊C4C2412yes—
528C2×C22⋊C4C2414yes—
529C2×C22⋊C4C2418yes—
530C2×C22⋊C4C2418yes—
531C2×C22⋊C4C2414yes—
532C2×C22⋊C4C2414yes—
533C2×C22⋊C4C2414yes—
534C2×C22⋊C4C2418yes—
535C2×C22⋊C4C2418yes—
536C2×C22⋊C4C2414yes—
537C2×C22⋊C4C2414yes—
538C2×C22⋊C4C2418yes—
539C2×C22⋊C4C2418yes—
540C2×C22⋊C4C24116yes—
541C2×C22⋊C4C2418yes—
542C2×C22⋊C4C24116yes—
543C2×C22⋊C4C2418yes—
544C2×C22⋊C4C2412yes—
545C2×C22⋊C4C2412yes—
546C2×C22⋊C4C2414yes—
547C2×C22⋊C4C2412yes—
548C2×C42—24no—
549C2×C42—28no—
550C2×C42C2×D4116yes—
551C2×C42#4118yes—
552C2×C42C2418yes—
553C2×C42C2418yes—
554C2×C42C2418yes—
555C2×C42C2412yes—
556C2×C42C2411yescharacteristic
557C2×C42C2411yescharacteristic
558C2×C42C2412yes—
559C2×C42C2414yes—
560C2×C42C2414yes—
561C2×C42C2418yes—
562C2×C42C2418yes—
563C2×C42C2418yes—
564C2×C42C2418yes—
565C2×C42C2414yes—
566C2×C42C2412yes—
567C2×C42C2412yes—
568C2×C42C2412yes—
569C2×C42C2412yes—
570C2×C42C2411yescharacteristic
571C2×C42C2411yescharacteristic
572#95C2418yes—
573#95C24116yes—
574#95C2418yes—
575#95C24116yes—
576#95C2418yes—
577#95C2418yes—
578#95C2418yes—
579#95C2418yes—
580#95C2418yes—
581#95C24116yes—
582#95C2418yes—
583#95C24116yes—
584#95C24116yes—
585#95C2414yes—
586#95C2414yes—
587#95C24116yes—
588C24—22no—
589C24—22no—
590C24—44no—
591C24C22×D414yes—
592C24C2514yes—
593C24C2511yescharacteristic
594C24C2511yescharacteristic
595C24C2511yescharacteristic
596#41—432no—
597C2×Q8—28no—
598C2×Q8—28no—
599C2×Q8—24no—
600C2×Q8—216no—
601C2×Q8—28no—
602C2×Q8—28no—
603C2×Q8—24no—
604C2×Q8—28no—
605C2×Q8—28no—
606C2×Q8—24no—
607C2×Q8—416no—
608C2×Q8—432no—
609C2×D4—28no—
610C2×D4—28no—
611C2×D4—28no—
612C2×D4—28no—
613C2×D4—28no—
614C2×D4—24no—
615C2×D4—24no—
616C2×D4—24no—
617C2×D4—28no—
618C2×D4—48no—
619C2×D4—48no—
620C2×D4—48no—
621C22×C4—22no—
622C22×C4—22no—
623C22×C4—232no—
624C22×C4—22no—
625C22×C4—22no—
626C22×C4—22no—
627C22×C4—22no—
628C22×C4—22no—
629C22×C4—22no—
630C22×C4—22no—
631C22×C4—22no—
632C22×C4—28no—
633C22×C4—28no—
634C22×C4—28no—
635C22×C4—28no—
636C22×C4—24no—
637C22×C4—28no—
638C22×C4—28no—
639C22×C4—28no—
640C22×C4—216no—
641C22×C4—28no—
642C22×C4—44no—
643C22×C4—48no—
644C22×C4—48no—
645C22×C4—416no—
646C22×C4—44no—
647C22×C4—48no—
648C22×C4C22×D414yes—
649C22×C4C22×D414yes—
650C22×C4C22×D414yes—
651C22×C4C22×D414yes—
652C22×C4C22×D414yes—
653C22×C4C22×D4116yes—
654C22×C4C22×D414yes—
655C22×C4C2×#4118yes—
656C22×C4C2×#4114yes—
657C22×C4C2×#4114yes—
658C22×C4C2512yes—
659C22×C4C2512yes—
660C22×C4C2514yes—
661C22×C4C2514yes—
662C22×C4C2518yes—
663C22×C4C2514yes—
664C22×C4C2518yes—
665C22×C4C2514yes—
666C22×C4C2514yes—
667C22×C4C2514yes—
668C22×C4C2511yescharacteristic
669C22×C4C2511yescharacteristic
670C22×C4C2512yes—
671C22×C4C2514yes—
672C22×C4C2512yes—
673C22×C4C2511yescharacteristic
674C22×C4C2511yescharacteristic
675C4⋊C4—28no—
676C4⋊C4—216no—
677C4⋊C4—28no—
678C4⋊C4—216no—
679C4⋊C4—216no—
680C4⋊C4—24no—
681C4⋊C4—24no—
682C4⋊C4—216no—
683C4⋊C4—216no—
684C4⋊C4—216no—
685C4⋊C4—216no—
686C4⋊C4—216no—
687C4⋊C4—28no—
688C4⋊C4—28no—
689C4⋊C4—216no—
690C4⋊C4—216no—
691C4⋊C4—28no—
692C4⋊C4—24no—
693C4⋊C4—24no—
694C4⋊C4—24no—
695C4⋊C4—24no—
696C4⋊C4—24no—
697C4⋊C4—216no—
698C4⋊C4—216no—
699C4⋊C4—28no—
700C4⋊C4—232no—
701C4⋊C4—416no—
702C4⋊C4—48no—
703C4⋊C4C22×D418yes—
704C4⋊C4C22×D418yes—
705C4⋊C4C22×D4116yes—
706C4⋊C4C2×#4118yes—
707C22⋊C4—216no—
708C22⋊C4—216no—
709C22⋊C4—28no—
710C22⋊C4—28no—
711C22⋊C4—28no—
712C22⋊C4—24no—
713C22⋊C4—28no—
714C22⋊C4—216no—
715C22⋊C4—216no—
716C22⋊C4—28no—
717C22⋊C4—216no—
718C22⋊C4—28no—
719C22⋊C4—24no—
720C22⋊C4—24no—
721C22⋊C4—24no—
722C22⋊C4—24no—
723C22⋊C4—216no—
724C22⋊C4—232no—
725C22⋊C4—48no—
726C22⋊C4—416no—
727C22⋊C4—48no—
728C22⋊C4C22×D418yes—
729C22⋊C4C22×D418yes—
730C22⋊C4C22×D4116yes—
731C22⋊C4C2×#4118yes—
732C42—216no—
733C42—216no—
734C42—216no—
735C42—28no—
736C42—28no—
737C42—24no—
738C42—22no—
739C42—22no—
740C42—24no—
741C42—48no—
742C42—48no—
743C42—48no—
744C42—48no—
745C42C22×D4116yes—
746C42C22×D418yes—
747C42C22×D418yes—
748C42C2×#4118yes—
749C42C2×#4118yes—
750C42C2×#4114yes—
751C42C2×#4114yes—
752C23—24no—
753C23—21no—
754C23—21no—
755C23—21no—
756C23—21no—
757C23—24no—
758C23—24no—
759C23—28no—
760C23—24no—
761C23—24no—
762C23—24no—
763C23—28no—
764C23—28no—
765C23—48no—
766C23—84no—
767C23—84no—
768C23C23×D412yes—
769C23C23×D412yes—
770C23C23×D412yes—
771C23C22×#4112yes—
772C23C22×#4112yes—
773C23C2611yescharacteristic
774Q8—416no—
775Q8—416no—
776Q8—48no—
777Q8—816no—
778D4—416no—
779D4—416no—
780D4—48no—
781D4—88no—
782D4—88no—
783C2×C4—21no—
784C2×C4—21no—
785C2×C4—21no—
786C2×C4—21no—
787C2×C4—24no—
788C2×C4—28no—
789C2×C4—28no—
790C2×C4—24no—
791C2×C4—28no—
792C2×C4—28no—
793C2×C4—28no—
794C2×C4—28no—
795C2×C4—28no—
796C2×C4—28no—
797C2×C4—24no—
798C2×C4—24no—
799C2×C4—28no—
800C2×C4—24no—
801C2×C4—28no—
802C2×C4—22no—
803C2×C4—22no—
804C2×C4—24no—
805C2×C4—24no—
806C2×C4—28no—
807C2×C4—24no—
808C2×C4—28no—
809C2×C4—24no—
810C2×C4—24no—
811C2×C4—28no—
812C2×C4—28no—
813C2×C4—216no—
814C2×C4—28no—
815C2×C4—416no—
816C2×C4—48no—
817C2×C4—416no—
818C2×C4—416no—
819C2×C4—816no—
820C2×C4—88no—
821C2×C4—88no—
822C2×C4—84no—
823C2×C4#532116yes—
824C2×C4C23×D418yes—
825C2×C4C23×D412yes—
826C2×C4C23×D418yes—
827C2×C4C23×D412yes—
828C2×C4C23×D412yes—
829C2×C4C23×D412yes—
830C2×C4C22×#4118yes—
831C2×C4C22×#4114yes—
832C2×C4C22×#4114yes—
833C2×C4C22×#4112yes—
834C2×C4C22×#4112yes—
835C2×C4C22×#4112yes—
836C2×C4C22×#4112yes—
837C22—24no—
838C22—24no—
839C22—24no—
840C22—24no—
841C22—24no—
842C22—22no—
843C22—22no—
844C22—42no—
845C22—42no—
846C22—42no—
847C22—42no—
848C22—44no—
849C22—44no—
850C22—48no—
851C22—48no—
852C22—44no—
853C22—88no—
854C22C2×#53214yes—
855C22C24×D411yescharacteristic
856C22C23×#4111yescharacteristic
857C22C23×#4111yescharacteristic
858C222−1+614yes—
859C4—28no—
860C4—28no—
861C4—24no—
862C4—24no—
863C4—28no—
864C4—22no—
865C4—22no—
866C4—48no—
867C4—44no—
868C4—44no—
869C4—42no—
870C4—42no—
871C4—44no—
872C4—44no—
873C4—48no—
874C4C2×#53214yes—
875C4C2×#53214yes—
876C2—24no—
877C2—42no—
878C2—42no—
879C2—84no—
880C2C22×#53211yescharacteristic
881C2#6285912yes—
882C2#6286012yes—
883C2#6286112yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#34633C2
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×#3495C2semidirect
2. #36024C2semidirect
3. #36012C2semidirect
4. #35834C2semidirect
5. #35773C2semidirect
6. #35343C2semidirect
7. #35331C2semidirect
8. #35330C2semidirect
9. #35322C2semidirect
10. #35319C2semidirect
11. #35318C2semidirect
12. #35317C2semidirect
13. #35312C2semidirect
14. #35306C2semidirect
16. #34631C2semidirect
17. C2×#2621C2semidirect
18. #34276C2semidirect
19. #34209C2semidirect
20. #34208C2semidirect
21. #33996C2semidirect
45. #2868C22semidirect
46. #2862C22semidirect
47. #2862C22semidirect
48. #2861C22semidirect
49. #2859C22semidirect
50. #2858C22semidirect
53. #2664C22semidirect
55. #2660C22semidirect
56. #2658C22semidirect
57. #2642C22semidirect
58. #2640C22semidirect
76. #2601C22semidirect
77. #2565C22semidirect
78. #2560C22semidirect
80. #2556C22semidirect
82. #2550C22semidirect
84. #2542C22semidirect
86. #2519C22semidirect
87. #2506C22semidirect
91. #2492C22semidirect
92. #2489C22semidirect
98. #2396C22semidirect
104. #2365C22semidirect
106. #2362C22semidirect
107. #2360C22semidirect
109. #2352C22semidirect
111. #2328C22semidirect
112. #2327C22semidirect
113. #2327C22semidirect
114. #2327C22semidirect
115. #2327C22semidirect
116. #2326C22semidirect
120. C4×C4⋊Q8C22semidirect
121. C4×C4⋊Q8C22semidirect
122. C4×#124C22semidirect
123. C4×#124C22semidirect
219. C2×#117D4semidirect

Maximal subgroups

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

subgroupindex
C2×#34952
#360242
#360122
#358342
#357732
#353432
#353312
#353302
#353222
#353192
#353182
#353172
#353122
#353062
#346332
#346312
C2×#26212
#342762
#342092
#342082
#339962