Finite Group Databasebeta

← #2552×D83 #35576220

Subgroups — #2552×D83 #35576220

Order 21248.

2446 conjugacy classes of subgroups.

The subgroup lattice has 714 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#125×D83C212yesmaximal
2#24912500C212yesmaximal, complemented
3#24912499C211yesmaximal, characteristic, complemented
4#24912498C211yesmaximal, characteristic, complemented
5#24912497C212yesmaximal, complemented
6#24912496C212yesmaximal, complemented
7#24912495C212yesmaximal, complemented
8#24912494C211yesmaximal, characteristic, complemented
9#24912493C214yesmaximal, complemented
10#398×D83C214yesmaximal
11#389×D83C212yesmaximal
12#389×D83C212yesmaximal
13#384×D83C211yesmaximal, characteristic
14#384×D83C212yesmaximal
15C4×C4⋊C4×D83C211yesmaximal, characteristic
16C4×C4⋊C4×D83C211yesmaximal, characteristic
17C83×#2552C211yesmaximal, characteristic, complemented
18C2×#14581784C2212yes—
19C2×#14581783C2212yes—
20C2×#14581783C2212yes—
21C2×#14581782C2214yes—
22C2×#14581782C2214yes—
23#125×D83—216no—
24C2×C4⋊C4×D83C2212yes—
25C2×C4⋊C4×D83C2211yescharacteristic
26C2×C4⋊C4×D83C2212yes—
27C2×C4⋊C4×D83C2214yes—
28C2×C4⋊C4×D83C2211yescharacteristic
29C2×C4⋊C4×D83C2214yes—
30C2×C4⋊C4×D83C2214yes—
31C2×C4⋊C4×D83C2212yes—
32C2×C4⋊C4×D83C2211yescharacteristic
33C2×C4⋊C4×D83C2211yescharacteristic
34C2×C42×D83C2212yes—
35C2×C42×D83C2212yes—
36C2×C42×D83C2211yescharacteristic
37#19127635C2214yes—
38#19127635C2214yes—
39#19127634C2214yes—
40#19127634C2214yes—
41#19127633C2214yes—
42#19127632C2214yes—
43#19127631C2214yes—
44#19127600C2212yes—
45#19127600C2212yes—
46#19127599C2212yes—
47#19127599C2212yes—
48#19127598C2214yes—
49#19127598C2214yes—
50#19127597C2212yes—
51#19127597C2212yes—
52#19127596C2214yes—
53#19127596C2214yes—
54#19127571C2212yes—
55#19127571C2211yescharacteristic
56#19127570C2212yes—
57#19127570C2214yes—
58#19127570C2214yes—
59#19127570C2212yes—
60#19127570C2212yes—
61#19127570C2212yes—
62#19127570C2212yes—
63C4⋊C4×Dic83C2211yescharacteristic
64C4⋊C4×Dic83C2211yescharacteristic
65C4⋊C4×Dic83C2211yescharacteristic
66C4⋊C4×Dic83C2211yescharacteristic
67C4×Dic83⋊C4C2212yes—
68C4×Dic83⋊C4C2212yes—
69C4×C4⋊Dic83C2211yescharacteristic
70C4×C4⋊Dic83C2211yescharacteristic
71#19127552C2212yes—
72#19127552C2212yes—
73#95×D83C2214yes—
74#95×D83C2212yes—
75#95×D83C2212yes—
76C2×#125×C83C2212yes—
77#398×C83C2214yes—
78#389×C83C2212yes—
79#389×C83C2212yes—
80#384×C83C2212yes—
81#384×C83C2211yescharacteristic
82C4×C4⋊C4×C83C2211yescharacteristic
83C4×C4⋊C4×C83C2211yescharacteristic
84C22×C4×D83C2312yes—
85C22×C4×D83C2312yes—
86C22×C4×D83C2314yes—
87C22×C4×D83C2312yes—
88C22×C4×D83C2312yes—
89C22×C4×D83C2311yescharacteristic
90C22×C4×D83C2311yescharacteristic
91C22×C4×D83C2311yescharacteristic
92#14581784—28no—
93#14581783—28no—
94#14581783—28no—
95#14581782—216no—
96#14581782—216no—
97C2×C4⋊Dic83C2311yescharacteristic
98C2×C4⋊Dic83C2311yescharacteristic
99C2×C4⋊Dic83C2312yes—
100C2×C4⋊Dic83C2312yes—
101C2×C4⋊Dic83C2314yes—
102C2×C4⋊Dic83C2314yes—
103C2×C4⋊Dic83C2314yes—
104C2×C4⋊Dic83C2312yes—
105C2×C4⋊Dic83C2311yescharacteristic
106C2×C4⋊Dic83C2311yescharacteristic
107C2×Dic83⋊C4C2312yes—
108C2×Dic83⋊C4C2312yes—
109C2×Dic83⋊C4C2314yes—
110C2×Dic83⋊C4C2314yes—
111C2×Dic83⋊C4C2314yes—
112C2×Dic83⋊C4C2314yes—
113C2×Dic83⋊C4C2314yes—
114C2×Dic83⋊C4C2314yes—
115C2×Dic83⋊C4C2314yes—
116C2×Dic83⋊C4C2314yes—
117C2×Dic83⋊C4C2314yes—
118C2×Dic83⋊C4C2312yes—
119C2×Dic83⋊C4C2312yes—
120C4⋊C4×D83—216no—
121C4⋊C4×D83—216no—
122C4⋊C4×D83—28no—
123C4⋊C4×D83—24no—
124C4⋊C4×D83—28no—
125C4⋊C4×D83—24no—
126C4⋊C4×D83—48no—
127C4⋊C4×D83—44no—
128C4⋊C4×D83D418yes—
129C4⋊C4×D83Q818yes—
130C2×C4×Dic83C2312yes—
131C2×C4×Dic83C2312yes—
132C2×C4×Dic83C2312yes—
133C2×C4×Dic83C2312yes—
134C2×C4×Dic83C2312yes—
135C2×C4×Dic83C2312yes—
136C2×C4×Dic83C2311yescharacteristic
137C2×C4×Dic83C2311yescharacteristic
138C2×C4×Dic83C2311yescharacteristic
139C42×D83—28no—
140C42×D83—28no—
141C42×D83Q818yes—
142C83⋊#95C2312yes—
143C83⋊#95C2312yes—
144C83⋊#95C2312yes—
145C83⋊#95C2312yes—
146C83⋊#95C2312yes—
147C83⋊#95C2312yes—
148C83⋊#95C2314yes—
149C83⋊#95C2314yes—
150C83⋊#95C2314yes—
151#125×C83—28no—
152C2×C4⋊C4×C83C2311yescharacteristic
153C2×C4⋊C4×C83C2311yescharacteristic
154C2×C4⋊C4×C83C2312yes—
155C2×C4⋊C4×C83C2312yes—
156C2×C4⋊C4×C83C2314yes—
157C2×C4⋊C4×C83C2314yes—
158C2×C4⋊C4×C83C2314yes—
159C2×C4⋊C4×C83C2312yes—
160C2×C4⋊C4×C83C2311yescharacteristic
161C2×C4⋊C4×C83C2311yescharacteristic
162C2×C42×C83C2312yes—
163C2×C42×C83C2312yes—
164C2×C42×C83C2311yescharacteristic
165#95×C83C2312yes—
166#95×C83C2312yes—
167#95×C83C2314yes—
168C23×D83C2411yescharacteristic
169C22×Dic83C2412yes—
170C22×Dic83C2412yes—
171C22×Dic83C2414yes—
172C22×Dic83C2412yes—
173C22×Dic83C2411yescharacteristic
174C22×Dic83C2412yes—
175C22×Dic83C2411yescharacteristic
176C22×Dic83C2411yescharacteristic
177C2×C4×D83—24no—
178C2×C4×D83—24no—
179C2×C4×D83—22no—
180C2×C4×D83—24no—
181C2×C4×D83—22no—
182C2×C4×D83—24no—
183C2×C4×D83—24no—
184C2×C4×D83—24no—
185C2×C4×D83—28no—
186C2×C4×D83—24no—
187C2×C4×D83—24no—
188C2×C4×D83—28no—
189C2×C4×D83—24no—
190C2×C4×D83—28no—
191C2×C4×D83—24no—
192C2×C4×D83C2×D418yes—
193C2×C4×D83C2×D414yes—
194C2×C4×D83C2×Q814yes—
195C2×C4×D83C2×Q818yes—
196C2×C4×D83C2×Q814yes—
197C2×C4×D83C2×Q814yes—
198C2×C4×D83C2×Q814yes—
199C2×C4×D83#4114yes—
200C2×C4×D83#4114yes—
201C4⋊Dic83—28no—
202C4⋊Dic83—24no—
203C4⋊Dic83—22no—
204C4⋊Dic83—22no—
205C4⋊Dic83—24no—
206C4⋊Dic83—28no—
207C4⋊Dic83—44no—
208C4⋊Dic83—42no—
209C4⋊Dic83C2×D414yes—
210C4⋊Dic83C2×Q814yes—
211Dic83⋊C4—28no—
212Dic83⋊C4—28no—
213Dic83⋊C4—28no—
214Dic83⋊C4—28no—
215Dic83⋊C4—28no—
216Dic83⋊C4—24no—
217Dic83⋊C4—24no—
218Dic83⋊C4—28no—
219Dic83⋊C4—44no—
220Dic83⋊C4—44no—
221Dic83⋊C4—44no—
222Dic83⋊C4C2×D418yes—
223Dic83⋊C4C2×Q818yes—
224C4×Dic83—24no—
225C4×Dic83—24no—
226C4×Dic83—24no—
227C4×Dic83—24no—
228C4×Dic83—24no—
229C4×Dic83—24no—
230C4×Dic83C2×Q814yes—
231C4×Dic83C2×Q814yes—
232C4×Dic83C2×Q814yes—
233C22×C4×C83C2412yes—
234C22×C4×C83C2412yes—
235C22×C4×C83C2414yes—
236C22×C4×C83C2412yes—
237C22×C4×C83C2411yescharacteristic
238C22×C4×C83C2412yes—
239C22×C4×C83C2411yescharacteristic
240C22×C4×C83C2411yescharacteristic
241C4⋊C4×C83—28no—
242C4⋊C4×C83—28no—
243C4⋊C4×C83—24no—
244C4⋊C4×C83—22no—
245C4⋊C4×C83—22no—
246C4⋊C4×C83—24no—
247C4⋊C4×C83—44no—
248C4⋊C4×C83—42no—
249C4⋊C4×C83C2×D414yes—
250C4⋊C4×C83C2×Q814yes—
251C42×C83—24no—
252C42×C83—24no—
253C42×C83C2×Q814yes—
254C23×C83C2511yescharacteristic
255C22×D83C22×D412yes—
256C22×D83C22×Q812yes—
257C22×D83C22×Q812yes—
258C22×D83C2×#4112yes—
259C22×D83C2×#4112yes—
260C22×D83H(5,𝔽2)12yes—
261C22×D832−1+412yes—
262C2×C4×C83—22no—
263C2×C4×C83—22no—
264C2×C4×C83—21no—
265C2×C4×C83—22no—
266C2×C4×C83—21no—
267C2×C4×C83—22no—
268C2×C4×C83—22no—
269C2×C4×C83—22no—
270C2×C4×C83—24no—
271C2×C4×C83—22no—
272C2×C4×C83—22no—
273C2×C4×C83—24no—
274C2×C4×C83—22no—
275C2×C4×C83—24no—
276C2×C4×C83—22no—
277C2×C4×C83C22×D414yes—
278C2×C4×C83C22×D412yes—
279C2×C4×C83C22×Q812yes—
280C2×C4×C83C22×Q814yes—
281C2×C4×C83C22×Q812yes—
282C2×C4×C83C22×Q812yes—
283C2×C4×C83C22×Q812yes—
284C2×C4×C83C2×#4112yes—
285C2×C4×C83C2×#4112yes—
286C2×Dic83—22no—
287C2×Dic83—22no—
288C2×Dic83—21no—
289C2×Dic83—22no—
290C2×Dic83—21no—
291C2×Dic83—22no—
292C2×Dic83—22no—
293C2×Dic83—22no—
294C2×Dic83—24no—
295C2×Dic83—22no—
296C2×Dic83—22no—
297C2×Dic83—24no—
298C2×Dic83—22no—
299C2×Dic83—24no—
300C2×Dic83—22no—
301C2×Dic83C22×D414yes—
302C2×Dic83C22×D412yes—
303C2×Dic83C22×Q812yes—
304C2×Dic83C22×Q814yes—
305C2×Dic83C22×Q812yes—
306C2×Dic83C22×Q812yes—
307C2×Dic83C22×Q812yes—
308C2×Dic83C2×#4112yes—
309C2×Dic83C2×#4112yes—
310C4×D83—28no—
311C4×D83—216no—
312C4×D83—216no—
313C4×D83—48no—
314C4×D83—48no—
315C4×D83—416no—
316C4×D83#125116yescomplemented
317C4×D83C4⋊Q8116yes—
318C22×C83C23×D411yescharacteristic
319C22×C83C23×Q811yescharacteristic
320C22×C83C23×Q811yescharacteristic
321C22×C83C22×#4111yescharacteristic
322C22×C83C22×#4111yescharacteristic
323C22×C83C2×H(5,𝔽2)11yescharacteristic
324C22×C83C2×2−1+411yescharacteristic
325C2×D83C2×#12514yes—
326C2×D83C2×C4⋊Q814yes—
327C2×D83#54414yes—
328C2×D83#54714yes—
329C2×D83#55014yes—
330C2×D83#55414yes—
331C2×D83#55714yes—
332C4×C83—22no—
333C4×C83—24no—
334C4×C83—24no—
335C4×C83—42no—
336C4×C83—42no—
337C4×C83—44no—
338C4×C83C2×#12514yescomplemented
339C4×C83C2×C4⋊Q814yes—
340Dic83—22no—
341Dic83—24no—
342Dic83—24no—
343Dic83—42no—
344Dic83—42no—
345Dic83—44no—
346Dic83C2×#12514yescomplemented
347Dic83C2×C4⋊Q814yes—
348C2×#2552—831nomaximal, Sylow
349C2×C83C22×#12511yescharacteristic
350C2×C83C22×C4⋊Q811yescharacteristic
351C2×C83C2×#54411yescharacteristic
352C2×C83C2×#54711yescharacteristic
353C2×C83C2×#55011yescharacteristic
354C2×C83C2×#55411yescharacteristic
355C2×C83C2×#55711yescharacteristic
356D83#255218yesdirect product factor
357C22×#125—832no—
358#2552—834no—
359#2552—832no—
360#2552—832no—
361#2552—832no—
362#2552—831no—
363#2552—831no—
364#2552—831no—
365#2552—832no—
366#2552D8311yescharacteristic, direct product factor
367C2×#398—834no—
368C2×#389—832no—
369C2×#389—832no—
370C2×#384—831no—
371C2×#384—832no—
372C2×C4×C4⋊C4—831no—
373C2×C4×C4⋊C4—831no—
374C83C2×#255211yescharacteristic, complemented, Sylow
375C2×#125—834no—
376C2×#125—834no—
377C2×#125—832no—
378C2×#125—832no—
379C2×#125—832no—
380C2×#125—16616no—
381C2×#125C2×D8312yes—
382C22×C4⋊C4—832no—
383C22×C4⋊C4—834no—
384C22×C4⋊C4—831no—
385C22×C4⋊C4—831no—
386C22×C4⋊C4—834no—
387C22×C4⋊C4—834no—
388C22×C4⋊C4—832no—
389C22×C4⋊C4—831no—
390C22×C4⋊C4—831no—
391C22×C4⋊C4—832no—
392C22×C42—831no—
393C22×C42—832no—
394C22×C42—832no—
395#398—834no—
396#398—834no—
397#398—834no—
398#398—834no—
399#398—834no—
400#398—834no—
401#398—834no—
402#398C2×D8314yes—
403#389—834no—
404#389—834no—
405#389—832no—
406#389—832no—
407#389—832no—
408#389—832no—
409#389—832no—
410#389—832no—
411#389—834no—
412#389—834no—
413#389C2×D8312yes—
414#389C2×D8312yes—
415#384—832no—
416#384—832no—
417#384—832no—
418#384—832no—
419#384—832no—
420#384—834no—
421#384—834no—
422#384—832no—
423#384—831no—
424#384C2×D8312yes—
425#384C2×D8311yescharacteristic
426C4×C4⋊C4—831no—
427C4×C4⋊C4—831no—
428C4×C4⋊C4—831no—
429C4×C4⋊C4—831no—
430C4×C4⋊C4—831no—
431C4×C4⋊C4—831no—
432C4×C4⋊C4—832no—
433C4×C4⋊C4—832no—
434C4×C4⋊C4—832no—
435C4×C4⋊C4—832no—
436C4×C4⋊C4C2×D8311yescharacteristic
437C4×C4⋊C4C2×D8311yescharacteristic
438C2×#95—832no—
439C2×#95—832no—
440C2×#95—834no—
441C23×C4—831no—
442C23×C4—831no—
443C23×C4—832no—
444C23×C4—832no—
445C23×C4—831no—
446C23×C4—834no—
447C23×C4—832no—
448C23×C4—832no—
449#125—28no—
450#125—1668no—
451#125—16616no—
452#125—16616no—
453#125—1668no—
454#125—1668no—
455C2×C4⋊C4—3324no—
456C2×C4⋊C4—3328no—
457C2×C4⋊C4—834no—
458C2×C4⋊C4—834no—
459C2×C4⋊C4—834no—
460C2×C4⋊C4—834no—
461C2×C4⋊C4—832no—
462C2×C4⋊C4—832no—
463C2×C4⋊C4—831no—
464C2×C4⋊C4—832no—
465C2×C4⋊C4—831no—
466C2×C4⋊C4—838no—
467C2×C4⋊C4—838no—
468C2×C4⋊C4—834no—
469C2×C4⋊C4—832no—
470C2×C4⋊C4—834no—
471C2×C4⋊C4—834no—
472C2×C4⋊C4—834no—
473C2×C4⋊C4—834no—
474C2×C4⋊C4—834no—
475C2×C4⋊C4—834no—
476C2×C4⋊C4—832no—
477C2×C4⋊C4—831no—
478C2×C4⋊C4—832no—
479C2×C4⋊C4—831no—
480C2×C4⋊C4—834no—
481C2×C4⋊C4—832no—
482C2×C4⋊C4—1668no—
483C2×C4⋊C4—16616no—
484C2×C4⋊C4—16616no—
485C2×C4⋊C4—1664no—
486C2×C4⋊C4—1664no—
487C2×C4⋊C4—1668no—
488C2×C4⋊C4C22×D8312yes—
489C2×C4⋊C4C22×D8314yes—
490C2×C4⋊C4C22×D8314yes—
491C2×C4⋊C4C22×D8311yescharacteristic
492C2×C4⋊C4C22×D8311yescharacteristic
493C2×C4⋊C4C22×D8312yes—
494C2×C4⋊C4C22×D8314yes—
495C2×C4⋊C4C22×D8312yes—
496C2×C4⋊C4C22×D8311yescharacteristic
497C2×C4⋊C4C22×D8311yescharacteristic
498C2×C42—831no—
499C2×C42—831no—
500C2×C42—831no—
501C2×C42—838no—
502C2×C42—832no—
503C2×C42—832no—
504C2×C42—832no—
505C2×C42—832no—
506C2×C42—832no—
507C2×C42—832no—
508C2×C42—1668no—
509C2×C42—1668no—
510C2×C42C22×D8312yes—
511C2×C42C22×D8312yes—
512C2×C42C22×D8311yescharacteristic
513#95—832no—
514#95—832no—
515#95—832no—
516#95—832no—
517#95—832no—
518#95—832no—
519#95—834no—
520#95—834no—
521#95—834no—
522#95C22×D8312yes—
523#95C22×D8312yes—
524#95C22×D8314yes—
525C24—831no—
526C22×C4—831no—
527C22×C4—831no—
528C22×C4—834no—
529C22×C4—834no—
530C22×C4—834no—
531C22×C4—834no—
532C22×C4—834no—
533C22×C4—834no—
534C22×C4—831no—
535C22×C4—832no—
536C22×C4—832no—
537C22×C4—838no—
538C22×C4—834no—
539C22×C4—838no—
540C22×C4—832no—
541C22×C4—832no—
542C22×C4—834no—
543C22×C4—1664no—
544C22×C4—1664no—
545C22×C4—1668no—
546C22×C4—1664no—
547C22×C4—1668no—
548C22×C4—1668no—
549C22×C4—1664no—
550C22×C4—1664no—
551C22×C4—1664no—
552C22×C4—1664no—
553C22×C4—1664no—
554C22×C4—1664no—
555C22×C4—1662no—
556C22×C4—1664no—
557C22×C4—1662no—
558C22×C4C23×D8312yes—
559C22×C4C23×D8312yes—
560C22×C4C23×D8314yes—
561C22×C4C23×D8312yes—
562C22×C4C23×D8311yescharacteristic
563C22×C4C23×D8312yes—
564C22×C4C23×D8311yescharacteristic
565C22×C4C23×D8311yescharacteristic
566C4⋊C4—28no—
567C4⋊C4—28no—
568C4⋊C4—24no—
569C4⋊C4—22no—
570C4⋊C4—22no—
571C4⋊C4—24no—
572C4⋊C4—44no—
573C4⋊C4—42no—
574C4⋊C4—3324no—
575C4⋊C4—3324no—
576C4⋊C4—3324no—
577C4⋊C4—3324no—
578C4⋊C4—3322no—
579C4⋊C4—838no—
580C4⋊C4—834no—
581C4⋊C4—838no—
582C4⋊C4—834no—
583C4⋊C4—1668no—
584C4⋊C4—1668no—
585C4⋊C4—1668no—
586C4⋊C4—1668no—
587C4⋊C4—1668no—
588C4⋊C4—1664no—
589C4⋊C4—1664no—
590C4⋊C4—1668no—
591C4⋊C4—1668no—
592C4⋊C4—1668no—
593C4⋊C4—1664no—
594C4⋊C4—1662no—
595C4⋊C4—1662no—
596C4⋊C4—1664no—
597C4⋊C4D4×D8314yes—
598C4⋊C4Q8×D8314yes—
599C42—24no—
600C42—24no—
601C42—834no—
602C42—834no—
603C42—834no—
604C42—1664no—
605C42—1664no—
606C42—1664no—
607C42—1664no—
608C42—1664no—
609C42—1664no—
610C42Q8×D8314yes—
611C23—832no—
612C23—832no—
613C23—832no—
614C23—832no—
615C23—832no—
616C23—832no—
617C23—832no—
618C23C24×D8311yescharacteristic
619C2×C4—22no—
620C2×C4—22no—
621C2×C4—21no—
622C2×C4—22no—
623C2×C4—21no—
624C2×C4—22no—
625C2×C4—22no—
626C2×C4—22no—
627C2×C4—24no—
628C2×C4—22no—
629C2×C4—22no—
630C2×C4—24no—
631C2×C4—22no—
632C2×C4—24no—
633C2×C4—22no—
634C2×C4—3328no—
635C2×C4—3328no—
636C2×C4—33216no—
637C2×C4—832no—
638C2×C4—832no—
639C2×C4—832no—
640C2×C4—832no—
641C2×C4—832no—
642C2×C4—832no—
643C2×C4—8316no—
644C2×C4—8316no—
645C2×C4—834no—
646C2×C4—832no—
647C2×C4—834no—
648C2×C4—1668no—
649C2×C4—16616no—
650C2×C4—16616no—
651C2×C4—1662no—
652C2×C4—1662no—
653C2×C4—1664no—
654C2×C4—1662no—
655C2×C4—1662no—
656C2×C4—1664no—
657C2×C4—1662no—
658C2×C4—1664no—
659C2×C4—1662no—
660C2×C4—1662no—
661C2×C4—1662no—
662C2×C4—1661no—
663C2×C4—1662no—
664C2×C4—1661no—
665C2×C4—1662no—
666C2×C4C2×D4×D8314yes—
667C2×C4C2×D4×D8312yes—
668C2×C4C2×Q8×D8312yes—
669C2×C4C2×Q8×D8314yes—
670C2×C4C2×Q8×D8312yes—
671C2×C4C2×Q8×D8312yes—
672C2×C4C2×Q8×D8312yes—
673C2×C4#41×D8312yes—
674C2×C4#41×D8312yes—
675C22—834no—
676C22—834no—
677C22—834no—
678C22—834no—
679C22—834no—
680C22—834no—
681C22—834no—
682C22C22×D4×D8311yescharacteristic
683C22C22×Q8×D8311yescharacteristic
684C22C22×Q8×D8311yescharacteristic
685C22C2×#41×D8311yescharacteristic
686C22C2×#41×D8311yescharacteristic
687C22H(5,𝔽2)×D8311yescharacteristic
688C222−1+4×D8311yescharacteristic
689C4—22no—
690C4—24no—
691C4—24no—
692C4—42no—
693C4—42no—
694C4—44no—
695C4—3322no—
696C4—3322no—
697C4—3324no—
698C4—834no—
699C4—834no—
700C4—1662no—
701C4—1664no—
702C4—1664no—
703C4#125×D8314yescomplemented
704C4C4⋊Q8×D8314yes—
705C2—838no—
706C2C2×#125×D8311yescharacteristic
707C2C2×C4⋊Q8×D8311yescharacteristic
708C2#544×D8311yescharacteristic
709C2#547×D8311yescharacteristic
710C2#550×D8311yescharacteristic
711C2#554×D8311yescharacteristic
712C2#557×D8311yescharacteristic
subgroupG/H
center, FrattiniC23C24×D83
commutator, socle, cosocleC23×C83C25
FittingC83×#2552C2
prime radicalC23×D83C24
hypercenter#2552D83
hypocenterC83C2×#2552
LCSG ▷ C23×C83 ▷ C83
UCSC1 ◁ C23 ◁ #2552

Complements

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

NH ≅ G/Ntype
2. #24912500C2semidirect
3. #24912499C2semidirect
4. #24912498C2semidirect
5. #24912497C2semidirect
6. #24912496C2semidirect
7. #24912495C2semidirect
8. #24912494C2semidirect
9. #24912493C2semidirect
17. C83×#2552C2semidirect
316. C4×D83#125semidirect
338. C4×C83C2×#125semidirect
346. Dic83C2×#125semidirect
356. D83#2552direct (N × H)
366. #2552D83direct (N × H)
374. C83C2×#2552semidirect
703. C4#125×D83semidirect

Maximal subgroups

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

subgroupindex
C2×#125×D832
#249125002
#249124992
#249124982
#249124972
#249124962
#249124952
#249124942
#249124932
#398×D832
#389×D832
#384×D832
C4×C4⋊C4×D832
C83×#25522
C2×#255283