Finite Group Databasebeta

← #35565401

Subgroups — #35565401

Order 21248.

2426 conjugacy classes of subgroups.

The subgroup lattice has 736 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19128182C211yesmaximal, characteristic
2#24910405C214yesmaximal, complemented
3#24910394C214yesmaximal, complemented
4#24910355C212yesmaximal, complemented
5#24910347C212yesmaximal, complemented
6#24910339C212yesmaximal, complemented
7#24910331C212yesmaximal, complemented
8#24910110C212yesmaximal, complemented
9#24910102C212yesmaximal, complemented
10#24910051C211yesmaximal, characteristic
11#24909951C211yesmaximal, characteristic
12#24909934C212yesmaximal, complemented
13#24909921C212yesmaximal, complemented
14C2×#19127600C211yesmaximal, characteristic, complemented
15#24909819C211yesmaximal, characteristic, complemented
16#117×Dic83C211yesmaximal, characteristic, complemented
17C83×#2316C211yesmaximal, characteristic, complemented
18C22×#13050590C2211yescharacteristic
19#19128182C4116yescomplemented
20C2×#14581757C2212yes—
21C2×#14581754C2212yes—
22C2×C4×C22⋊D83C2214yes—
23C2×#14581751C2211yescharacteristic
24C2×#14581750C2214yes—
25C2×#14581750C2212yes—
26C22×C4⋊Dic83C2211yescharacteristic
27C22×C4⋊Dic83C2212yes—
28C2×C4⋊C4×D83C2212yes—
29C22×C4×Dic83C2211yescharacteristic
30#19127607C2212yes—
31#19127606C2211yescharacteristic
32#19127606C2211yescharacteristic
33#19127603C2212yes—
34#19127602C2211yescharacteristic
35#19127602C2211yescharacteristic
36#19127600C2212yes—
37#19127600C2212yes—
38#19127600C2212yes—
39#19127600C2212yes—
40#19127593C2214yes—
41#19127593C2214yes—
42#19127591C2214yes—
43#19127591C2214yes—
44#19127588C2214yes—
45#19127588C2214yes—
46#19127582C2214yes—
47#19127582C2214yes—
48#19127578C2212yes—
49#19127578C2214yes—
50#19127578C2212yes—
51#19127568C2214yes—
52#19127566C2214yes—
53#19127563C2214yes—
54#19127558C2212yes—
55#19127558C2214yes—
56#19127558C2212yes—
57C4⋊C4×Dic83C2211yescharacteristic
58C4⋊C4×Dic83C2211yescharacteristic
59C4⋊C4×Dic83C2211yescharacteristic
60C4⋊C4×Dic83C2214yes—
61C4⋊C4×Dic83C2212yes—
62C4⋊C4×Dic83C2212yes—
63C4⋊C4×Dic83C2211yescharacteristic
64C4×C4⋊Dic83C2212yes—
65C4×C4⋊Dic83C2212yes—
66C22⋊C4×Dic83C2212yes—
67C22⋊C4×Dic83C2214yes—
68C22⋊C4×Dic83C2212yes—
69C4×(C2×D83)⋊C4C2212yes—
70C4×(C2×D83)⋊C4C2212yes—
71#19127548C2214yes—
72#19127547C2212yes—
73#19127546C2214yes—
74C2×C83⋊#95C2212yes—
75C42×Dic83C2212yes—
76C2×#117×C83C2211yescharacteristic
77C2×#117×C83C2211yescharacteristic
78C22×C4⋊C4×C83C2211yescharacteristic
79#389×C83C2212yes—
80#389×C83C2212yes—
81#389×C83C2212yes—
82#389×C83C2212yes—
83#380×C83C2214yes—
84C2×#13050590—24no—
85C2×#13050590—24no—
86C2×#13050590C2×C418yes—
87C22×Dic166C2311yescharacteristic
88C22×D332C2311yescharacteristic
89C22×C22⋊D83C2312yes—
90C23×Dic83C2311yescharacteristic
91C23×Dic83C2311yescharacteristic
92C23×Dic83C2312yes—
93C22×C4×D83C2312yes—
94C22×C4×D83C2314yes—
95#14581757C2×C4116yescomplemented
96#14581754C2×C4116yescomplemented
97C4×C22⋊D83C2×C4132yes—
98#14581751C2×C418yes—
99#14581750—48no—
100#14581750C2×C4116yescomplemented
101C2×C4⋊Dic83—24no—
102C2×C4⋊Dic83—44no—
103C2×C4⋊Dic83C2312yes—
104C2×C4⋊Dic83C2312yes—
105C2×C4⋊Dic83C2314yes—
106C2×C4⋊Dic83C2314yes—
107C2×C4⋊Dic83C2311yescharacteristic
108C2×C4⋊Dic83C2311yescharacteristic
109C2×Dic83⋊C4C2314yes—
110C4⋊C4×D83C2×C4116yescomplemented
111C2×C22⋊Dic83C2312yes—
112C2×(C2×D83)⋊C4C2312yes—
113C2×(C2×D83)⋊C4C2312yes—
114C2×(C2×D83)⋊C4C2314yes—
115C2×(C2×D83)⋊C4C2312yes—
116C2×(C2×D83)⋊C4C2314yes—
117C2×(C2×D83)⋊C4C2312yes—
118C2×(C2×D83)⋊C4C2314yes—
119C2×C4×Dic83—24no—
120C2×C4×Dic83C2311yescharacteristic
121C2×C4×Dic83C2311yescharacteristic
122C2×C4×Dic83C2312yes—
123C2×C4×Dic83C2312yes—
124C2×C4×Dic83C2311yescharacteristic
125C2×C4×Dic83C2311yescharacteristic
126C2×C4×Dic83C2314yes—
127C2×C4×Dic83C2314yes—
128C2×C4×Dic83C2312yes—
129C2×C4×Dic83C2312yes—
130C2×C4×Dic83C2312yes—
131C2×C4×Dic83C2314yes—
132C83⋊#95C2314yes—
133C83⋊#95C2314yes—
134C83⋊#95C2312yes—
135C83⋊#95C2312yes—
136C83⋊#95C2314yes—
137C83⋊#95C2312yes—
138C83⋊#95C2312yes—
139C83⋊#95C2312yes—
140C83⋊#95C2314yes—
141C83⋊#95C2314yes—
142C83⋊#95C2312yes—
143C83⋊#95C2312yes—
144C83⋊#95C2312yes—
145C83⋊#95C2314yes—
146C23×C4×C83C2312yes—
147C23×C4×C83C2311yescharacteristic
148#117×C83—24no—
149#117×C83—24no—
150C2×C4⋊C4×C83C2×C418yes—
151C2×C4⋊C4×C83C2311yescharacteristic
152C2×C4⋊C4×C83C2311yescharacteristic
153C2×C4⋊C4×C83C2311yescharacteristic
154C2×C4⋊C4×C83C2311yescharacteristic
155C2×C4⋊C4×C83C2314yes—
156C2×C4⋊C4×C83C2314yes—
157C2×C4⋊C4×C83C2312yes—
158C2×C4⋊C4×C83C2312yes—
159C2×C22⋊C4×C83C2312yes—
160C2×C22⋊C4×C83C2312yes—
161C2×C42×C83C2312yes—
162C2×C42×C83C2312yes—
163#95×C83C2314yes—
164#95×C83C2314yes—
165C23×D83C2412yes—
166#13050590—232no—
167C2×Dic166—22no—
168C2×Dic166—22no—
169C2×Dic166C22×C414yes—
170C2×D332—22no—
171C2×D332—22no—
172C2×D332C22×C414yes—
173C2×C22⋊D83—24no—
174C2×C22⋊D83—24no—
175C2×C22⋊D83C22×C418yes—
176C22×Dic83—22no—
177C22×Dic83—22no—
178C22×Dic83—24no—
179C22×Dic83—22no—
180C22×Dic83—22no—
181C22×Dic83—41no—
182C22×Dic83—41no—
183C22×Dic83—42no—
184C22×Dic83—42no—
185C22×Dic83C2411yescharacteristic
186C22×Dic83C2411yescharacteristic
187C22×Dic83C2414yes—
188C22×Dic83C2412yes—
189C22×Dic83C2412yes—
190C22×Dic83C2412yes—
191C22×Dic83C2411yescharacteristic
192C22×Dic83C2411yescharacteristic
193C2×C4×D83—24no—
194C2×C4×D83—24no—
195C2×C4×D83—44no—
196C2×C4×D83—44no—
197C2×C4×D83C22×C418yes—
198C2×C4×D83C22×C4116yes—
199C4⋊Dic83—24no—
200C4⋊Dic83—24no—
201C4⋊Dic83—28no—
202C4⋊Dic83—44no—
203C4⋊Dic83C22×C414yes—
204C4⋊Dic83C22×C414yes—
205Dic83⋊C4C22×C4116yes—
206C22⋊Dic83C22×C418yes—
207(C2×D83)⋊C4—24no—
208(C2×D83)⋊C4—24no—
209(C2×D83)⋊C4—44no—
210(C2×D83)⋊C4—42no—
211(C2×D83)⋊C4—42no—
212(C2×D83)⋊C4—44no—
213(C2×D83)⋊C4C22×C4116yes—
214C4×Dic83—22no—
215C4×Dic83—22no—
216C4×Dic83—22no—
217C4×Dic83—22no—
218C4×Dic83—24no—
219C4×Dic83—24no—
220C4×Dic83—42no—
221C4×Dic83—44no—
222C4×Dic83—42no—
223C4×Dic83—44no—
224C4×Dic83C22×C4116yes—
225C4×Dic83C22×C418yes—
226C24×C83C2411yescharacteristic
227C22×C4×C83—42no—
228C22×C4×C83—42no—
229C22×C4×C83C22×C418yes—
230C22×C4×C83C22×C414yes—
231C22×C4×C83#4114yes—
232C22×C4×C83#4114yes—
233C22×C4×C83C2412yes—
234C22×C4×C83C2412yes—
235C22×C4×C83C2412yes—
236C22×C4×C83C2412yes—
237C22×C4×C83C2414yes—
238C22×C4×C83C2411yescharacteristic
239C22×C4×C83C2411yescharacteristic
240C4⋊C4×C83—22no—
241C4⋊C4×C83—22no—
242C4⋊C4×C83—22no—
243C4⋊C4×C83—22no—
244C4⋊C4×C83—44no—
245C4⋊C4×C83—44no—
246C4⋊C4×C83C22×C418yes—
247C4⋊C4×C83C22×C418yes—
248C22⋊C4×C83—24no—
249C22⋊C4×C83—24no—
250C42×C83—24no—
251C42×C83—24no—
252C23×C83—21no—
253C23×C83—21no—
254C23×C83—21no—
255C23×C83—21no—
256C23×C83C23×C412yes—
257C23×C83C2×#4112yes—
258C23×C83C2×#4112yes—
259C23×C83C2511yescharacteristic
260C22×D83—22no—
261C22×D83—22no—
262C22×D83—22no—
263C22×D83—22no—
264C22×D83—22no—
265C22×D83—22no—
266C22×D83C23×C414yes—
267C2×C4×C83—24no—
268C2×C4×C83—24no—
269C2×C4×C83—22no—
270C2×C4×C83—22no—
271C2×C4×C83—22no—
272C2×C4×C83—22no—
273C2×C4×C83—22no—
274C2×C4×C83—22no—
275C2×C4×C83—22no—
276C2×C4×C83—22no—
277C2×C4×C83—22no—
278C2×C4×C83—22no—
279C2×C4×C83—22no—
280C2×C4×C83—22no—
281C2×C4×C83—48no—
282C2×C4×C83#117116yescomplemented
283C2×C4×C83C23×C418yes—
284C2×C4×C83C23×C412yes—
285C2×C4×C83C23×C412yes—
286C2×C4×C83C2×#4112yes—
287C2×C4×C83C2×#4112yes—
288C2×C4×C83C2×#4112yes—
289C2×C4×C83C2×#4112yes—
290C22⋊D83—216no—
291C2×Dic83—21no—
292C2×Dic83—21no—
293C2×Dic83—22no—
294C2×Dic83—22no—
295C2×Dic83—22no—
296C2×Dic83—22no—
297C2×Dic83—22no—
298C2×Dic83—21no—
299C2×Dic83—21no—
300C2×Dic83—22no—
301C2×Dic83—21no—
302C2×Dic83—21no—
303C2×Dic83—24no—
304C2×Dic83—24no—
305C2×Dic83—21no—
306C2×Dic83—21no—
307C2×Dic83—24no—
308C2×Dic83—21no—
309C2×Dic83—21no—
310C2×Dic83—44no—
311C2×Dic83—44no—
312C2×Dic83—84no—
313C2×Dic83C23×C414yes—
314C2×Dic83C23×C414yes—
315C2×Dic83C23×C414yes—
316C2×Dic83H(5,𝔽2)12yes—
317C2×Dic832−1+412yes—
318D332—28no—
319C4×D83—216no—
320C4×D83—416no—
321Dic166—28no—
322C22×C83—22no—
323C22×C83—22no—
324C22×C83—22no—
325C22×C83—22no—
326C22×C83—22no—
327C22×C83—22no—
328C22×C83C2×#11714yes—
329C22×C83C24×C411yescharacteristic
330C22×C83C22×#4111yescharacteristic
331C22×C83C22×#4111yescharacteristic
332C22×C83C2×H(5,𝔽2)11yescharacteristic
333C22×C83C2×2−1+411yescharacteristic
334C22×C83#58511yescharacteristic
335C22×C83#58511yescharacteristic
336C2×D83—24no—
337C2×D83—24no—
338C2×D83—24no—
339C2×D83—42no—
340C2×D83—42no—
341C2×D83—42no—
342C2×D83—42no—
343C4×C83—28no—
344C4×C83—42no—
345C4×C83—42no—
346C4×C83—42no—
347C4×C83—42no—
348C4×C83C2×#11714yes—
349C4×C83C2×#11714yes—
350Dic83—24no—
351Dic83—24no—
352Dic83—24no—
353Dic83—22no—
354Dic83—22no—
355Dic83—41no—
356Dic83—44no—
357Dic83—41no—
358#34253—831nomaximal, Sylow
359C2×C83—24no—
360C2×C83C22×#11711yescharacteristic
361C2×C83C4×H(5,𝔽2)11yescharacteristic
362C2×C83C4×2−1+411yescharacteristic
363C2×C83#349411yescharacteristic
364C2×C83#349511yescharacteristic
365C2×C83#351111yescharacteristic
366C2×C83#351211yescharacteristic
367D83—44no—
368C2×#520—831no—
369#2353—834no—
370#2352—834no—
371#2347—832no—
372#2346—832no—
373#2345—832no—
374#2344—832no—
375#2320—832no—
376#2319—832no—
377#2316D8311yescharacteristic, complemented
378#2311—831no—
379#2297—831no—
380#2295—832no—
381#2293—832no—
382C2×#389—831no—
383#2274—831no—
384C4×#117—831no—
385C83#3425311yescharacteristic, complemented, Sylow
386C22×#41—831no—
387#520—8316no—
388C2×C4×Q8—832no—
389C2×C4×D4—834no—
390C2×C4×D4—832no—
391C2×#117—831no—
392C2×#117—834no—
393C2×#117—832no—
394C2×#117C2×D8311yescharacteristic
395C2×#117C2×D8311yescharacteristic
396C22×C4⋊C4—832no—
397C22×C4⋊C4—832no—
398C22×C4⋊C4—831no—
399C22×C4⋊C4C2×D8311yescharacteristic
400C22×C42—831no—
401#391—831no—
402#391—831no—
403#391—832no—
404#390—831no—
405#390—831no—
406#390—832no—
407#389—832no—
408#389—832no—
409#389—832no—
410#389—832no—
411#389C2×D8312yes—
412#389C2×D8312yes—
413#389C2×D8312yes—
414#389C2×D8312yes—
415#388—834no—
416#388—834no—
417#388—834no—
418#388—834no—
419#387—834no—
420#387—834no—
421#387—834no—
422#387—834no—
423#386—834no—
424#386—832no—
425#386—832no—
426#383—834no—
427#382—834no—
428#381—834no—
429#380—832no—
430#380—832no—
431#380—834no—
432#380C2×D8314yes—
433C4×C4⋊C4—832no—
434C4×C4⋊C4—832no—
435C4×C4⋊C4—831no—
436C4×C4⋊C4—831no—
437C4×C4⋊C4—831no—
438C4×C4⋊C4—831no—
439C4×C4⋊C4—834no—
440C4×C4⋊C4—832no—
441C4×C4⋊C4—832no—
442C4×C22⋊C4—832no—
443C4×C22⋊C4—834no—
444C4×C22⋊C4—832no—
445C4×C22⋊C4—832no—
446C4×C22⋊C4—832no—
447C4×C22⋊C4—834no—
448#376—832no—
449#376—834no—
450C2×#95—832no—
451C43—832no—
452C2×#41—838no—
453C2×#41—1664no—
454C2×#41—1664no—
455C22×Q8—831no—
456C22×D4—832no—
457C22×D4—831no—
458C23×C4—834no—
459C23×C4—832no—
460C23×C4—831no—
461C23×C4—831no—
462C23×C4—832no—
463C23×C4C22×D8312yes—
464C23×C4C22×D8311yescharacteristic
465C4×Q8—8316no—
466C4×D4—8332no—
467C4×D4—8316no—
468#117—24no—
469#117—24no—
470#117—3328no—
471#117—838no—
472#117—8316no—
473C2×C4⋊C4—3324no—
474C2×C4⋊C4—834no—
475C2×C4⋊C4—831no—
476C2×C4⋊C4—834no—
477C2×C4⋊C4—831no—
478C2×C4⋊C4—8316no—
479C2×C4⋊C4—834no—
480C2×C4⋊C4—832no—
481C2×C4⋊C4—832no—
482C2×C4⋊C4—1664no—
483C2×C4⋊C4C4×D8318yes—
484C2×C4⋊C4C22×D8311yescharacteristic
485C2×C4⋊C4C22×D8311yescharacteristic
486C2×C4⋊C4C22×D8311yescharacteristic
487C2×C4⋊C4C22×D8311yescharacteristic
488C2×C4⋊C4C22×D8314yes—
489C2×C4⋊C4C22×D8314yes—
490C2×C4⋊C4C22×D8312yes—
491C2×C4⋊C4C22×D8312yes—
492C2×C22⋊C4—834no—
493C2×C22⋊C4—832no—
494C2×C22⋊C4—834no—
495C2×C22⋊C4—832no—
496C2×C22⋊C4—832no—
497C2×C22⋊C4—834no—
498C2×C22⋊C4—832no—
499C2×C22⋊C4—832no—
500C2×C22⋊C4C22×D8312yes—
501C2×C22⋊C4C22×D8312yes—
502C2×C42—834no—
503C2×C42—832no—
504C2×C42—832no—
505C2×C42—834no—
506C2×C42—832no—
507C2×C42—834no—
508C2×C42—832no—
509C2×C42—831no—
510C2×C42—832no—
511C2×C42—831no—
512C2×C42—831no—
513C2×C42—831no—
514C2×C42—1664no—
515C2×C42C22×D8312yes—
516C2×C42C22×D8312yes—
517#95—834no—
518#95—834no—
519#95—832no—
520#95—832no—
521#95—832no—
522#95—832no—
523#95—832no—
524#95—834no—
525#95—834no—
526#95—834no—
527#95—832no—
528#95—832no—
529#95—832no—
530#95—834no—
531#95C22×D8314yes—
532#95C22×D8314yes—
533C24—832no—
534C24C23×D8311yescharacteristic
535#41—16632no—
536C2×Q8—834no—
537C2×Q8—1662no—
538C2×Q8—1662no—
539C2×D4—838no—
540C2×D4—834no—
541C2×D4—1664no—
542C2×D4—1664no—
543C2×D4—1662no—
544C2×D4—1662no—
545C22×C4—42no—
546C22×C4—42no—
547C22×C4—3324no—
548C22×C4—3324no—
549C22×C4—3321no—
550C22×C4—3321no—
551C22×C4—3322no—
552C22×C4—3322no—
553C22×C4—8316no—
554C22×C4—832no—
555C22×C4—831no—
556C22×C4—832no—
557C22×C4—832no—
558C22×C4—831no—
559C22×C4—838no—
560C22×C4—831no—
561C22×C4—831no—
562C22×C4—834no—
563C22×C4—1662no—
564C22×C4—1662no—
565C22×C4—1662no—
566C22×C4—1662no—
567C22×C4—1664no—
568C22×C4—1664no—
569C22×C4—1664no—
570C22×C4C2×C4×D8318yes—
571C22×C4C2×C4×D8314yes—
572C22×C4#1305058914yes—
573C22×C4#1305059114yes—
574C22×C4C23×D8312yes—
575C22×C4C23×D8312yes—
576C22×C4C23×D8312yes—
577C22×C4C23×D8312yes—
578C22×C4C23×D8314yes—
579C22×C4C23×D8311yescharacteristic
580C22×C4C23×D8311yescharacteristic
581C4⋊C4—22no—
582C4⋊C4—22no—
583C4⋊C4—22no—
584C4⋊C4—22no—
585C4⋊C4—44no—
586C4⋊C4—44no—
587C4⋊C4—3324no—
588C4⋊C4—834no—
589C4⋊C4—8316no—
590C4⋊C4—834no—
591C4⋊C4—1668no—
592C4⋊C4—1664no—
593C4⋊C4—1664no—
594C4⋊C4C2×C4×D8318yes—
595C4⋊C4C2×C4×D8318yes—
596C22⋊C4—24no—
597C22⋊C4—24no—
598C22⋊C4—3324no—
599C22⋊C4—3322no—
600C22⋊C4—3322no—
601C22⋊C4—3324no—
602C22⋊C4—838no—
603C22⋊C4—8316no—
604C22⋊C4—1664no—
605C22⋊C4—1664no—
606C42—24no—
607C42—24no—
608C42—3324no—
609C42—3322no—
610C42—3324no—
611C42—3322no—
612C42—8316no—
613C42—838no—
614C42—1664no—
615C42—1664no—
616C42—1662no—
617C42—1662no—
618C42—1662no—
619C42—1662no—
620C23—21no—
621C23—21no—
622C23—21no—
623C23—21no—
624C23—834no—
625C23—1662no—
626C23—1662no—
627C23—1662no—
628C23—1662no—
629C23—1662no—
630C23—1662no—
631C23C22×C4×D8312yes—
632C23C2×#1305058912yes—
633C23C2×#1305059112yes—
634C23C24×D8311yescharacteristic
635Q8—1668no—
636D4—16616no—
637D4—1668no—
638C2×C4—24no—
639C2×C4—24no—
640C2×C4—22no—
641C2×C4—22no—
642C2×C4—22no—
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—48no—
653C2×C4—33216no—
654C2×C4—3324no—
655C2×C4—3324no—
656C2×C4—834no—
657C2×C4—834no—
658C2×C4—834no—
659C2×C4—832no—
660C2×C4—832no—
661C2×C4—6644no—
662C2×C4—1661no—
663C2×C4—1661no—
664C2×C4—1664no—
665C2×C4—1664no—
666C2×C4—1661no—
667C2×C4—1661no—
668C2×C4—1661no—
669C2×C4—1664no—
670C2×C4—1661no—
671C2×C4—1662no—
672C2×C4—1661no—
673C2×C4—1661no—
674C2×C4—1662no—
675C2×C4—1662no—
676C2×C4—1662no—
677C2×C4—1661no—
678C2×C4—1662no—
679C2×C4—1662no—
680C2×C4—1661no—
681C2×C4—16616no—
682C2×C4#14581750116yescomplemented
683C2×C4C22×C4×D8318yes—
684C2×C4C22×C4×D8312yes—
685C2×C4C22×C4×D8312yes—
686C2×C4C2×#1305058912yes—
687C2×C4C2×#1305058912yes—
688C2×C4C2×#1305059112yes—
689C2×C4C2×#1305059112yes—
690C22—22no—
691C22—22no—
692C22—22no—
693C22—22no—
694C22—22no—
695C22—22no—
696C22—3322no—
697C22—3322no—
698C22—3322no—
699C22—3322no—
700C22—1664no—
701C22—1664no—
702C22—1664no—
703C22C2×#1458175014yes—
704C22C23×C4×D8311yescharacteristic
705C22C22×#1305058911yescharacteristic
706C22C22×#1305059111yescharacteristic
707C22H(5,𝔽2)×D8311yescharacteristic
708C222−1+4×D8311yescharacteristic
709C22#1912853611yescharacteristic
710C22#1912853811yescharacteristic
711C4—28no—
712C4—42no—
713C4—42no—
714C4—42no—
715C4—42no—
716C4—3321no—
717C4—3324no—
718C4—3321no—
719C4—1664no—
720C4—1664no—
721C4—1664no—
722C4—1662no—
723C4—1662no—
724C4C2×#1458175014yes—
725C4C2×#1458175014yes—
726C2—24no—
727C2—3324no—
728C2C22×#1458175011yescharacteristic
729C2#2492066711yescharacteristic
730C2#2492067211yescharacteristic
731C2#2492120111yescharacteristic
732C2#2492121811yescharacteristic
733C2#2492137211yescharacteristic
734C2#2492138411yescharacteristic
subgroupG/H
center, FrattiniC23C24×D83
commutatorC22×C83C24×C4
FittingC83×#2316C2
socle, cosocleC23×C83C25
prime radicalC22×#13050590C22
hypercenter#2316D83
hypocenterC83#34253
LCSG ▷ C22×C83 ▷ C83
UCSC1 ◁ C23 ◁ #2316

Complements

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

NH ≅ G/Ntype
2. #24910405C2semidirect
3. #24910394C2semidirect
4. #24910355C2semidirect
5. #24910347C2semidirect
6. #24910339C2semidirect
7. #24910331C2semidirect
8. #24910110C2semidirect
9. #24910102C2semidirect
12. #24909934C2semidirect
13. #24909921C2semidirect
14. C2×#19127600C2semidirect
15. #24909819C2semidirect
16. #117×Dic83C2semidirect
17. C83×#2316C2semidirect
19. #19128182C4semidirect
95. #14581757C2×C4semidirect
96. #14581754C2×C4semidirect
100. #14581750C2×C4semidirect
110. C4⋊C4×D83C2×C4semidirect
282. C2×C4×C83#117semidirect
377. #2316D83semidirect
385. C83#34253semidirect
682. C2×C4#14581750semidirect

Maximal subgroups

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

subgroupindex
C2×#191281822
#249104052
#249103942
#249103552
#249103472
#249103392
#249103312
#249101102
#249101022
#249100512
#249099512
#249099342
#249099212
C2×#191276002
#249098192
#117×Dic832
C83×#23162
#3425383