Finite Group Databasebeta

← #35575419

Subgroups — #35575419

Order 21248.

1870 conjugacy classes of subgroups.

The subgroup lattice has 808 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#24912731C212yesmaximal, complemented
2#24912716C212yesmaximal, complemented
3#24912707C212yesmaximal, complemented
4#24912508C212yesmaximal, complemented
5#24912205C212yesmaximal, complemented
6#24912082C212yesmaximal, complemented
7#24911529C212yesmaximal, complemented
8#24911370C212yesmaximal
9#24910768C211yesmaximal, characteristic, complemented
10#24910749C211yesmaximal, characteristic, complemented
11#24910731C211yesmaximal, characteristic, complemented
12#24910699C211yesmaximal, characteristic
13C4×#14581786C212yesmaximal, complemented
14C4×#14581775C212yesmaximal, complemented
15#24909940C211yesmaximal, characteristic, complemented
16#24909900C212yesmaximal, complemented
17#24909855C212yesmaximal, complemented
18C42×D332C211yesmaximal, characteristic, complemented
19C4×#117×C83C211yesmaximal, characteristic, complemented
20C2×#14581786C2212yes—
21C2×#14581775C2212yes—
22C2×C4×Dic166C2211yescharacteristic
23C2×C4×D332C2212yes—
24C2×C4×D332C2211yescharacteristic
25C2×C4×C22⋊D83C2212yes—
26C2×C42×D83C2212yes—
27#19127643C2212yes—
28#19127643C2212yes—
29#19127641C2212yes—
30#19127640C2211yescharacteristic
31#19127637C2211yescharacteristic
32#19127635C2212yes—
33#19127635C2212yes—
34#19127634C2212yes—
35#19127631C2211yescharacteristic
36#19127628C2212yes—
37#19127626C2211yescharacteristic
38#19127624C2212yes—
39#19127623C2212yes—
40#19127621C2211yescharacteristic
41#19127619C2212yes—
42#19127618C2211yescharacteristic
43#19127617C2212yes—
44#19127614C2212yes—
45#19127613C2211yescharacteristic
46#19127610C2211yescharacteristic
47#19127607C2212yes—
48#19127599C2212yes—
49#19127592C2212yes—
50#19127592C2212yes—
51#19127592C2212yes—
52#19127592C2212yes—
53#19127592C2212yes—
54#19127589C2212yes—
55#19127589C2212yes—
56#19127585C2212yes—
57#19127585C2212yes—
58#19127585C2212yes—
59#19127585C2212yes—
60#19127585C2212yes—
61#19127585C2212yes—
62#19127585C2212yes—
63#19127582C2212yes—
64#19127582C2212yes—
65#19127580C2212yes—
66#19127577C2212yes—
67#19127577C2212yes—
68#19127574C2212yes—
69#19127572C2212yes—
70#19127572C2212yes—
71#19127569C2212yes—
72#19127568C2212yes—
73#19127568C2212yes—
74#19127565C2212yes—
75#19127565C2212yes—
76#19127564C2212yes—
77#19127563C2212yes—
78#19127563C2212yes—
79#19127560C2212yes—
80#19127560C2212yes—
81C4×Dic83⋊C4C2212yes—
82C4×Dic83⋊C4C2212yes—
83C4×Dic83⋊C4C2212yes—
84C4×Dic83⋊C4C2212yes—
85C4×C4⋊Dic83C2212yes—
86C4×C4⋊Dic83C2211yescharacteristic
87C4×C4⋊Dic83C2211yescharacteristic
88C4×(C2×D83)⋊C4C2212yes—
89C4×(C2×D83)⋊C4C2212yes—
90C4×(C2×D83)⋊C4C2212yes—
91C4×(C2×D83)⋊C4C2212yes—
92C4×(C2×D83)⋊C4C2212yes—
93C4×(C2×D83)⋊C4C2212yes—
94C4×C22⋊Dic83C2212yes—
95#19127547C2212yes—
96C2×#117×C83C2211yescharacteristic
97C2×#117×C83C2211yescharacteristic
98C22×C42×C83C2211yescharacteristic
99C4×C4⋊C4×C83C2212yes—
100C4×C4⋊C4×C83C2212yes—
101C4×C22⋊C4×C83C2212yes—
102C4×C22⋊C4×C83C2212yes—
103#376×C83C2211yescharacteristic
104#376×C83C2211yescharacteristic
105C43×C83C2211yescharacteristic
106C43×C83C2211yescharacteristic
107C22×Dic166C2311yescharacteristic
108C22×D332C2311yescharacteristic
109C22×C22⋊D83C2312yes—
110C22×C4×D83C2312yes—
111C22×C4×D83C2312yes—
112C22×C4×D83C2312yes—
113#14581786—28no—
114#14581775—28no—
115C4×Dic166—24no—
116C4×D332—28no—
117C4×D332—24no—
118C4×C22⋊D83—28no—
119C2×C4⋊Dic83C2312yes—
120C2×C4⋊Dic83C2311yescharacteristic
121C2×C4⋊Dic83C2311yescharacteristic
122C2×C4⋊Dic83C2312yes—
123C2×Dic83⋊C4C2312yes—
124C2×Dic83⋊C4C2312yes—
125C2×Dic83⋊C4C2312yes—
126C2×Dic83⋊C4C2312yes—
127C2×Dic83⋊C4C2312yes—
128C2×Dic83⋊C4C2312yes—
129C2×Dic83⋊C4C2312yes—
130C2×Dic83⋊C4C2312yes—
131C2×Dic83⋊C4C2312yes—
132C2×Dic83⋊C4C2312yes—
133C2×C22⋊Dic83C2312yes—
134C2×C22⋊Dic83C2312yes—
135C2×C22⋊Dic83C2312yes—
136C2×(C2×D83)⋊C4C2312yes—
137C2×(C2×D83)⋊C4C2312yes—
138C2×(C2×D83)⋊C4C2312yes—
139C2×(C2×D83)⋊C4C2312yes—
140C2×(C2×D83)⋊C4C2312yes—
141C2×(C2×D83)⋊C4C2312yes—
142C2×(C2×D83)⋊C4C2312yes—
143C2×(C2×D83)⋊C4C2312yes—
144C2×(C2×D83)⋊C4C2312yes—
145C2×(C2×D83)⋊C4C2312yes—
146C2×C4×Dic83C2312yes—
147C2×C4×Dic83C2312yes—
148C2×C4×Dic83C2312yes—
149C2×C4×Dic83C2312yes—
150C2×C4×Dic83C2312yes—
151C42×D83—28no—
152C83⋊#95C2312yes—
153C83⋊#95C2312yes—
154C83⋊#95C2311yescharacteristic
155C83⋊#95C2311yescharacteristic
156C83⋊#95C2311yescharacteristic
157C83⋊#95C2311yescharacteristic
158C83⋊#95C2312yes—
159C83⋊#95C2312yes—
160C83⋊#95C2312yes—
161C83⋊#95C2312yes—
162C83⋊#95C2312yes—
163C83⋊#95C2312yes—
164C83⋊#95C2312yes—
165C83⋊#95C2312yes—
166C83⋊#95C2312yes—
167C83⋊#95C2312yes—
168C83⋊#95C2312yes—
169C83⋊#95C2312yes—
170C83⋊#95C2312yes—
171C83⋊#95C2312yes—
172C83⋊#95C2312yes—
173C83⋊#95C2312yes—
174C83⋊#95C2312yes—
175C83⋊#95C2312yes—
176C83⋊#95C2312yes—
177C83⋊#95C2312yes—
178C23×C4×C83C2312yes—
179C23×C4×C83C2311yescharacteristic
180#117×C83—24no—
181#117×C83—24no—
182C2×C4⋊C4×C83C2312yes—
183C2×C4⋊C4×C83C2311yescharacteristic
184C2×C4⋊C4×C83C2311yescharacteristic
185C2×C22⋊C4×C83C2312yes—
186C2×C22⋊C4×C83C2311yescharacteristic
187C2×C22⋊C4×C83C2311yescharacteristic
188C2×C42×C83—24no—
189C2×C42×C83C2312yes—
190C2×C42×C83C2311yescharacteristic
191C2×C42×C83C2311yescharacteristic
192C2×C42×C83C2311yescharacteristic
193C2×C42×C83C2311yescharacteristic
194C2×C42×C83C2312yes—
195C2×C42×C83C2312yes—
196C2×C42×C83C2312yes—
197C2×C42×C83C2312yes—
198C2×C42×C83C2311yescharacteristic
199C2×C42×C83C2311yescharacteristic
200#95×C83C2312yes—
201#95×C83C2312yes—
202#95×C83C2312yes—
203#95×C83C2312yes—
204C23×D83C2412yes—
205C2×Dic166—22no—
206C2×Dic166—42no—
207C2×D332—24no—
208C2×D332—22no—
209C2×C22⋊D83—24no—
210C2×C22⋊D83—24no—
211C2×C22⋊D83—42no—
212C22×Dic83C2412yes—
213C22×Dic83C2412yes—
214C22×Dic83C2412yes—
215C22×Dic83C2412yes—
216C22×Dic83C2412yes—
217C22×Dic83C2412yes—
218C22×Dic83C2412yes—
219C2×C4×D83—24no—
220C2×C4×D83—24no—
221C2×C4×D83—24no—
222C2×C4×D83—24no—
223C2×C4×D83—24no—
224C2×C4×D83—24no—
225C2×C4×D83—24no—
226C2×C4×D83—42no—
227C2×C4×D83—42no—
228C4⋊Dic83—22no—
229C4⋊Dic83—22no—
230C4⋊Dic83—24no—
231C4⋊Dic83—42no—
232Dic83⋊C4—24no—
233Dic83⋊C4—24no—
234Dic83⋊C4—24no—
235Dic83⋊C4—24no—
236Dic83⋊C4—24no—
237Dic83⋊C4—24no—
238Dic83⋊C4—24no—
239Dic83⋊C4—42no—
240Dic83⋊C4—42no—
241Dic83⋊C4—42no—
242C22⋊Dic83—24no—
243C22⋊Dic83—24no—
244C22⋊Dic83—42no—
245(C2×D83)⋊C4—24no—
246(C2×D83)⋊C4—24no—
247(C2×D83)⋊C4—24no—
248(C2×D83)⋊C4—24no—
249(C2×D83)⋊C4—24no—
250(C2×D83)⋊C4—24no—
251(C2×D83)⋊C4—42no—
252(C2×D83)⋊C4—42no—
253(C2×D83)⋊C4—42no—
254(C2×D83)⋊C4#4118yes—
255C4×Dic83—24no—
256C4×Dic83—24no—
257C4×Dic83—24no—
258C4×Dic83—24no—
259C4×Dic83—24no—
260C24×C83C2411yescharacteristic
261C22×C4×C83—22no—
262C22×C4×C83—22no—
263C22×C4×C83—24no—
264C22×C4×C83—24no—
265C22×C4×C83—42no—
266C22×C4×C83#4114yes—
267C22×C4×C83C2412yes—
268C22×C4×C83C2411yescharacteristic
269C22×C4×C83C2412yes—
270C22×C4×C83C2411yescharacteristic
271C22×C4×C83C2412yes—
272C22×C4×C83C2411yescharacteristic
273C22×C4×C83C2411yescharacteristic
274C22×C4×C83C2412yes—
275C22×C4×C83C2411yescharacteristic
276C22×C4×C83C2411yescharacteristic
277C4⋊C4×C83—24no—
278C4⋊C4×C83—22no—
279C4⋊C4×C83—22no—
280C22⋊C4×C83—24no—
281C22⋊C4×C83—22no—
282C22⋊C4×C83—22no—
283C42×C83—24no—
284C42×C83—22no—
285C42×C83—24no—
286C42×C83—22no—
287C42×C83—22no—
288C42×C83—22no—
289C42×C83—24no—
290C42×C83—42no—
291C42×C83—42no—
292C42×C83#4114yes—
293C42×C83#4114yes—
294C23×C83—21no—
295C23×C83—21no—
296C23×C83—22no—
297C23×C83—22no—
298C23×C83C2×#4112yes—
299C23×C83C2511yescharacteristic
300C22×D83—22no—
301C22×D83—22no—
302C22×D83—22no—
303C22×D83—22no—
304C22×D83—22no—
305C22×D83—22no—
306C22×D83C2×#4114yes—
307C2×C4×C83—22no—
308C2×C4×C83—22no—
309C2×C4×C83—22no—
310C2×C4×C83—21no—
311C2×C4×C83—21no—
312C2×C4×C83—22no—
313C2×C4×C83—22no—
314C2×C4×C83—22no—
315C2×C4×C83—28no—
316C2×C4×C83—22no—
317C2×C4×C83—21no—
318C2×C4×C83—21no—
319C2×C4×C83—22no—
320C2×C4×C83—22no—
321C2×C4×C83—22no—
322C2×C4×C83—22no—
323C2×C4×C83—22no—
324C2×C4×C83—22no—
325C2×C4×C83—22no—
326C2×C4×C83—48no—
327C2×C4×C83C2×#4114yes—
328C2×C4×C83C2×#4112yes—
329C2×C4×C83C2×#4114yes—
330C2×C4×C83C2×#4112yes—
331C2×C4×C83C2×#4112yes—
332C2×C4×C83C2×#4112yes—
333C2×C4×C83C2×#4112yes—
334C2×C4×C83C2×#4112yes—
335C22⋊D83—48no—
336C2×Dic83—22no—
337C2×Dic83—22no—
338C2×Dic83—22no—
339C2×Dic83—22no—
340C2×Dic83—22no—
341C2×Dic83—22no—
342C2×Dic83—22no—
343C2×Dic83—22no—
344C2×Dic83—22no—
345C2×Dic83—22no—
346C2×Dic83—22no—
347C2×Dic83—22no—
348C2×Dic83—22no—
349C2×Dic83—22no—
350C2×Dic83—22no—
351C2×Dic83—22no—
352C2×Dic83—22no—
353C2×Dic83—22no—
354C2×Dic83—22no—
355C2×Dic83—22no—
356C2×Dic83C2×#4114yes—
357D332—28no—
358C4×D83—48no—
359C4×D83—48no—
360C4×D83—48no—
361Dic166—44no—
362C22×C83—22no—
363C22×C83—24no—
364C22×C83—41no—
365C22×C83—41no—
366C22×C83—42no—
367C22×C83C22×#4112yes—
368C22×C83C22×#4111yescharacteristic
369C22×C83C22×#4111yescharacteristic
370C22×C83C22×#4111yescharacteristic
371C22×C83#58512yes—
372C2×D83—24no—
373C2×D83—24no—
374C2×D83—24no—
375C2×D83—42no—
376C2×D83—42no—
377C2×D83—42no—
378C2×D83—42no—
379C4×C83—22no—
380C4×C83—22no—
381C4×C83—22no—
382C4×C83—24no—
383C4×C83—24no—
384C4×C83—41no—
385C4×C83—41no—
386C4×C83—42no—
387C4×C83—42no—
388C4×C83#52914yes—
389Dic83—24no—
390Dic83—42no—
391Dic83—42no—
392Dic83—42no—
393Dic83—42no—
394Dic83—42no—
395Dic83—42no—
396#34879—831nomaximal, Sylow
397C2×C83—42no—
398C2×C83C2×#52911yescharacteristic
399C2×C83#344411yescharacteristic
400C2×C83#345511yescharacteristic
401C2×C83#347512yes—
402C2×C83#347512yes—
403D83—44no—
404#2574—832no—
405#2573—832no—
406#2572—832no—
407#2553—832no—
408#2524—832no—
409#2515—832no—
410#2468—832no—
411#2457—832no—
412#2402—831no—
413#2398—831no—
414#2396—831no—
415#2392—831no—
416C4×#126—832no—
417C4×#123—832no—
418#2295—831no—
419#2290—832no—
420#2283—832no—
421C42×D4—831no—
422C4×#117D8311yescharacteristic, complemented
423C83#3487911yescharacteristic, complemented, Sylow
424C2×#126—832no—
425C2×#123—832no—
426C2×C4×Q8—831no—
427C2×C4×D4—832no—
428C2×C4×D4—831no—
429C2×C4×D4—832no—
430C2×#117C2×D8311yescharacteristic
431C2×#117C2×D8311yescharacteristic
432C22×C42—832no—
433C22×C42C2×D8311yescharacteristic
434#400—831no—
435#400—832no—
436#400—832no—
437#400—832no—
438#399—831no—
439#398—831no—
440#398—832no—
441#398—832no—
442#398—832no—
443#397—831no—
444#397—832no—
445#396—832no—
446#396—832no—
447#395—831no—
448#394—831no—
449#394—832no—
450#394—832no—
451#393—831no—
452#393—832no—
453#392—831no—
454#391—832no—
455#389—832no—
456#388—832no—
457#388—832no—
458#388—832no—
459#388—832no—
460#388—832no—
461#388—832no—
462#388—832no—
463#387—832no—
464#387—832no—
465#387—832no—
466#387—832no—
467#387—832no—
468#387—832no—
469#387—832no—
470#387—832no—
471#387—832no—
472#386—832no—
473#386—832no—
474#386—832no—
475#385—832no—
476#385—832no—
477#385—832no—
478#383—832no—
479#383—832no—
480#383—832no—
481#382—832no—
482#382—832no—
483#381—832no—
484#381—832no—
485#381—832no—
486#380—832no—
487#380—832no—
488C4×C4⋊C4—832no—
489C4×C4⋊C4—832no—
490C4×C4⋊C4—832no—
491C4×C4⋊C4—831no—
492C4×C4⋊C4—831no—
493C4×C4⋊C4—832no—
494C4×C4⋊C4—832no—
495C4×C4⋊C4C2×D8312yes—
496C4×C4⋊C4C2×D8312yes—
497C4×C22⋊C4—832no—
498C4×C22⋊C4—832no—
499C4×C22⋊C4—832no—
500C4×C22⋊C4—832no—
501C4×C22⋊C4—832no—
502C4×C22⋊C4—832no—
503C4×C22⋊C4—832no—
504C4×C22⋊C4C2×D8312yes—
505C4×C22⋊C4C2×D8312yes—
506#376—832no—
507#376C2×D8311yescharacteristic
508#376C2×D8311yescharacteristic
509C43C2×D8311yescharacteristic
510C43C2×D8311yescharacteristic
511C22×Q8—831no—
512C22×D4—832no—
513C22×D4—831no—
514C23×C4—832no—
515C23×C4—832no—
516C23×C4—832no—
517C23×C4C22×D8312yes—
518C23×C4C22×D8311yescharacteristic
519#126—1668no—
520#123—1668no—
521C4×Q8—1664no—
522C4×D4—1668no—
523C4×D4—1668no—
524C4×D4—1664no—
525#117—24no—
526#117—24no—
527C2×C4⋊C4—832no—
528C2×C4⋊C4—832no—
529C2×C4⋊C4—832no—
530C2×C4⋊C4—832no—
531C2×C4⋊C4—832no—
532C2×C4⋊C4—831no—
533C2×C4⋊C4—832no—
534C2×C4⋊C4—832no—
535C2×C4⋊C4—831no—
536C2×C4⋊C4—832no—
537C2×C4⋊C4—832no—
538C2×C4⋊C4—832no—
539C2×C4⋊C4—832no—
540C2×C4⋊C4—832no—
541C2×C4⋊C4C22×D8312yes—
542C2×C4⋊C4C22×D8311yescharacteristic
543C2×C4⋊C4C22×D8311yescharacteristic
544C2×C22⋊C4—832no—
545C2×C22⋊C4—832no—
546C2×C22⋊C4—832no—
547C2×C22⋊C4—832no—
548C2×C22⋊C4—832no—
549C2×C22⋊C4—832no—
550C2×C22⋊C4—832no—
551C2×C22⋊C4—832no—
552C2×C22⋊C4—832no—
553C2×C22⋊C4—832no—
554C2×C22⋊C4—832no—
555C2×C22⋊C4—832no—
556C2×C22⋊C4—832no—
557C2×C22⋊C4C22×D8312yes—
558C2×C22⋊C4C22×D8311yescharacteristic
559C2×C22⋊C4C22×D8311yescharacteristic
560C2×C42—24no—
561C2×C42—832no—
562C2×C42—832no—
563C2×C42—832no—
564C2×C42—832no—
565C2×C42—832no—
566C2×C42—1668no—
567C2×C42C22×D8312yes—
568C2×C42C22×D8312yes—
569C2×C42C22×D8312yes—
570C2×C42C22×D8311yescharacteristic
571C2×C42C22×D8311yescharacteristic
572C2×C42C22×D8311yescharacteristic
573C2×C42C22×D8311yescharacteristic
574C2×C42C22×D8312yes—
575C2×C42C22×D8312yes—
576C2×C42C22×D8311yescharacteristic
577C2×C42C22×D8311yescharacteristic
578#95—832no—
579#95—832no—
580#95—832no—
581#95—832no—
582#95—832no—
583#95—832no—
584#95—831no—
585#95—831no—
586#95—832no—
587#95—832no—
588#95—832no—
589#95—832no—
590#95—832no—
591#95—832no—
592#95—832no—
593#95—832no—
594#95—832no—
595#95—832no—
596#95—832no—
597#95—832no—
598#95—832no—
599#95—832no—
600#95—832no—
601#95—832no—
602#95—831no—
603#95—831no—
604#95C22×D8312yes—
605#95C22×D8312yes—
606#95C22×D8312yes—
607#95C22×D8312yes—
608C24—832no—
609C24C23×D8311yescharacteristic
610C2×Q8—3322no—
611C2×Q8—1662no—
612C2×D4—3322no—
613C2×D4—1664no—
614C2×D4—1664no—
615C2×D4—1664no—
616C2×D4—1662no—
617C22×C4—22no—
618C22×C4—22no—
619C22×C4—24no—
620C22×C4—24no—
621C22×C4—42no—
622C22×C4—3322no—
623C22×C4—3322no—
624C22×C4—832no—
625C22×C4—832no—
626C22×C4—832no—
627C22×C4—832no—
628C22×C4—832no—
629C22×C4—832no—
630C22×C4—832no—
631C22×C4—1664no—
632C22×C4—1664no—
633C22×C4—1664no—
634C22×C4—1664no—
635C22×C4—1664no—
636C22×C4—1664no—
637C22×C4—1664no—
638C22×C4#1305059014yes—
639C22×C4C23×D8312yes—
640C22×C4C23×D8311yescharacteristic
641C22×C4C23×D8312yes—
642C22×C4C23×D8311yescharacteristic
643C22×C4C23×D8312yes—
644C22×C4C23×D8312yes—
645C22×C4C23×D8311yescharacteristic
646C22×C4C23×D8311yescharacteristic
647C22×C4C23×D8311yescharacteristic
648C22×C4C23×D8311yescharacteristic
649C4⋊C4—24no—
650C4⋊C4—22no—
651C4⋊C4—22no—
652C4⋊C4—3322no—
653C4⋊C4—3322no—
654C4⋊C4—3322no—
655C4⋊C4—3322no—
656C4⋊C4—1664no—
657C4⋊C4—1664no—
658C4⋊C4—1664no—
659C4⋊C4—1664no—
660C4⋊C4—1664no—
661C4⋊C4—1664no—
662C4⋊C4—1664no—
663C4⋊C4—1662no—
664C4⋊C4—1664no—
665C4⋊C4—1662no—
666C22⋊C4—24no—
667C22⋊C4—22no—
668C22⋊C4—22no—
669C22⋊C4—3322no—
670C22⋊C4—3322no—
671C22⋊C4—3322no—
672C22⋊C4—3322no—
673C22⋊C4—838no—
674C22⋊C4—1664no—
675C22⋊C4—1664no—
676C22⋊C4—1664no—
677C22⋊C4—1664no—
678C22⋊C4—1664no—
679C22⋊C4—1664no—
680C22⋊C4—1664no—
681C22⋊C4—1664no—
682C42—24no—
683C42—24no—
684C42—22no—
685C42—24no—
686C42—22no—
687C42—22no—
688C42—22no—
689C42—42no—
690C42—42no—
691C42—1664no—
692C42—1664no—
693C42—1664no—
694C42—1664no—
695C42—1664no—
696C42#1305059014yes—
697C42#1305059014yes—
698C23—22no—
699C23—21no—
700C23—21no—
701C23—22no—
702C23—834no—
703C23—1662no—
704C23—1662no—
705C23—1662no—
706C23—1662no—
707C23—1662no—
708C23—1662no—
709C23C2×#1305059012yes—
710C23C24×D8311yescharacteristic
711Q8—3324no—
712D4—3328no—
713D4—1668no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—28no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—48no—
734C2×C4—3328no—
735C2×C4—3328no—
736C2×C4—3328no—
737C2×C4—834no—
738C2×C4—1662no—
739C2×C4—1662no—
740C2×C4—1662no—
741C2×C4—1662no—
742C2×C4—1662no—
743C2×C4—1662no—
744C2×C4—1662no—
745C2×C4—1662no—
746C2×C4—1662no—
747C2×C4—1662no—
748C2×C4—1662no—
749C2×C4—1662no—
750C2×C4—1662no—
751C2×C4—1662no—
752C2×C4—1662no—
753C2×C4—1662no—
754C2×C4—1662no—
755C2×C4—1662no—
756C2×C4—1662no—
757C2×C4—1662no—
758C2×C4#41×D8314yes—
759C2×C4C2×#1305059012yes—
760C2×C4C2×#1305059014yes—
761C2×C4C2×#1305059012yes—
762C2×C4C2×#1305059012yes—
763C2×C4C2×#1305059012yes—
764C2×C4C2×#1305059012yes—
765C2×C4C2×#1305059012yes—
766C22—22no—
767C22—24no—
768C22—41no—
769C22—41no—
770C22—42no—
771C22—3322no—
772C22—3322no—
773C22—3322no—
774C22—3322no—
775C22—1664no—
776C22—1664no—
777C22—1664no—
778C22C2×#41×D8312yes—
779C22C22×#1305059011yescharacteristic
780C22C22×#1305059011yescharacteristic
781C22C22×#1305059011yescharacteristic
782C22#1912853712yes—
783C4—22no—
784C4—22no—
785C4—22no—
786C4—24no—
787C4—24no—
788C4—41no—
789C4—41no—
790C4—42no—
791C4—42no—
792C4—3322no—
793C4—3322no—
794C4—3322no—
795C4—3322no—
796C4—3322no—
797C4—3322no—
798C4—1664no—
799C4#1912823514yes—
800C2—42no—
801C2—3324no—
802C2C2×#1912823511yescharacteristic
803C2#2492075611yescharacteristic
804C2#2492084811yescharacteristic
805C2#2492101712yes—
806C2#2492102712yes—
subgroupG/H
centerC22×C4C23×D83
commutator, socle, cosocleC23×C83C25
FrattiniC23C24×D83
FittingC4×#117×C83C2
prime radical#19127610C22
hypercenterC4×#117D83
hypocenterC83#34879
LCSG ▷ C23×C83 ▷ C83
UCSC1 ◁ C22×C4 ◁ C4×#117

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #24912731C2semidirect
2. #24912716C2semidirect
3. #24912707C2semidirect
4. #24912508C2semidirect
5. #24912205C2semidirect
6. #24912082C2semidirect
7. #24911529C2semidirect
9. #24910768C2semidirect
10. #24910749C2semidirect
11. #24910731C2semidirect
13. C4×#14581786C2semidirect
14. C4×#14581775C2semidirect
15. #24909940C2semidirect
16. #24909900C2semidirect
17. #24909855C2semidirect
18. C42×D332C2semidirect
19. C4×#117×C83C2semidirect
422. C4×#117D83semidirect
423. C83#34879semidirect

Maximal subgroups

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

subgroupindex
#249127312
#249127162
#249127072
#249125082
#249122052
#249120822
#249115292
#249113702
#249107682
#249107492
#249107312
#249106992
C4×#145817862
C4×#145817752
#249099402
#249099002
#249098552
C42×D3322
C4×#117×C832
#3487983