Finite Group Databasebeta

← #21435912

Subgroups — #21435912

Order 7552.

494 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 494 conjugacy classes of subgroups — too many to draw. Only its 123 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16838057C211yesmaximal, characteristic, complemented
2#16838037C211yesmaximal, characteristic, complemented
3#16837748C211yesmaximal, characteristic, complemented
4#16837714C212yesmaximal, complemented
5#16837683C211yesmaximal, characteristic, complemented
6#16837635C212yesmaximal, complemented
7#16837534C212yesmaximal, complemented
8C4×#11745669C211yesmaximal, characteristic, complemented
9#16837467C211yesmaximal, characteristic, complemented
10#102×D59C212yesmaximal, complemented
11C59×#459C211yesmaximal, characteristic, complemented
12C2×#11745685—21no—
13C2×D4×D59—21no—
14C2×D4×D59C2212yes—
15C2×#11745669C2211yescharacteristic
16C2×C8×D59C2212yescomplemented
17#14273727C2211yescharacteristic, complemented
18#14273709—22no—
19#14273706—21no—
20#14273698—21no—
21#14273698C2212yes—
22#14273698C2212yescomplemented
23#14273695—22no—
24C4×D236C2211yescharacteristic
25C4×D236C2211yescharacteristic
26C4⋊C4×D59C2212yescomplemented
27#14273661C2212yescomplemented
28#14273660C2211yescharacteristic, complemented
29#14273649C2212yes—
30#14273648C2211yescharacteristic, complemented
31#14273648C2212yescomplemented
32#14273648C2212yescomplemented
33#14273647C2211yescharacteristic
34(C2×D59)⋊C8C2212yescomplemented
35C4×C59⋊C8C2211yescharacteristic, complemented
36C2×D8×C59C2212yescomplemented
37#127×C59C2211yescharacteristic
38C4×D4×C59C2211yescharacteristic, complemented
39C4⋊C8×C59C2211yescharacteristic, complemented
40#102×C59C2212yescomplemented
41C23×D59—22no—
42C2×D4×C59—21no—
43C2×D4×C59—21no—
44C2×D4×C59C2312yes—
45C2×D4×C59C2311yescharacteristic
46C22×C4×C59—21no—
47C2×C22⋊D59—22no—
48C2×C22⋊D59—22no—
49C2×C22⋊D59—22no—
50D4×D59—24no—
51D4×D59—42no—
52D4×D59—44no—
53#11745685—44no—
54C2×D236D411yescharacteristic
55C2×D236C2311yescharacteristic
56C2×C4×D59—22no—
57C2×C4×D59—21no—
58C2×C4×D59C2312yes—
59C2×Dic118—21no—
60D8×C59—42no—
61C2×C8×C59C2312yes—
62C4⋊C4×C59C2311yescharacteristic
63C22⋊C4×C59—21no—
64C42×C59C2311yescharacteristic
65C22⋊Dic59—22no—
66C22⋊Dic59—22no—
67#11745669—22no—
68(C2×D59)⋊C4—21no—
69(C2×D59)⋊C4D412yes—
70C4⋊Dic59—21no—
71C4⋊Dic59D411yescharacteristic
72C4⋊Dic59C2312yes—
73C4⋊Dic59C2311yescharacteristic
74Dic59⋊C4—22no—
75C2×C59⋊C8C2311yescharacteristic
76C2×C59⋊C8C2311yescharacteristic
77C8×D59—42no—
78C23×C59—21no—
79C23×C59—22no—
80C22×D59—21no—
81C22×D59—44no—
82C22×D59—44no—
83C22×D59—82no—
84C22×D59C2×D412yes—
85D4×C59—21no—
86D4×C59—22no—
87D4×C59—21no—
88D4×C59—22no—
89D4×C59—42no—
90D4×C59—81no—
91C2×C4×C59—21no—
92C2×C4×C59—42no—
93C2×C4×C59C2×D411yescharacteristic
94C2×C4×C59C2×D411yescharacteristic
95C2×C4×C59C2411yescharacteristic
96C22⋊D59—44no—
97C22⋊D59—44no—
98C22⋊D59—44no—
99C2×Dic59—22no—
100C2×Dic59—21no—
101C2×Dic59C2×D412yes—
102D236—21no—
103D236D814yescomplemented
104D236#4112yescomplemented
105C4×D59—22no—
106C4×D59—22no—
107C4×D59—44no—
108C4×D59—42no—
109Dic118—42no—
110C8×C59—22no—
111C59⋊C8—21no—
112C59⋊C8—21no—
113C22×C59—42no—
114C22×C59—41no—
115C22×C59—41no—
116C22×C59—42no—
117C22×C59—42no—
118C22×C59—41no—
119C22×C59C22×D411yescharacteristic
120C2×D59—22no—
121C2×D59—22no—
122C2×D59—22no—
123C2×D59—41no—
124C2×D59—41no—
125C2×D59—88no—
126C2×D59C2×D814yes—
127C4×C59—21no—
128C4×C59—41no—
129C4×C59C2×D812yes—
130C4×C59C2×#4111yescharacteristic
131C4×C59H(5,𝔽2)11yescharacteristic
132Dic59—22no—
133Dic59—42no—
134Dic59—41no—
135#3294—591nomaximal, Sylow
136C2×C59—82no—
137C2×C59—81no—
138C2×C59#54611yescharacteristic
139C2×C59C22×D811yescharacteristic
140C2×C59#57711yescharacteristic
141D59—24no—
142D59—42no—
143#547—591no—
144D42—591no—
145#486—591no—
146#480—592no—
147#474—591no—
148#466—592no—
149#459D5911yescharacteristic, complemented
150#447—592no—
151C4×D8—591no—
152C8×D4—591no—
153C2×#102—592no—
154C59#329411yescharacteristic, complemented, Sylow
155C2×#41—1181no—
156C22×D4—592no—
157C22×D4—1181no—
158C2×D8—591no—
159C2×D8C2×D5912yescomplemented
160C22×C8—592no—
161C4⋊Q8—591no—
162#127C2×D5911yescharacteristic
163#123—1182no—
164C22⋊Q8—1181no—
165#121—592no—
166#121—592no—
167#121—1181no—
168#120—1182no—
169C4×D4—591no—
170C4×D4—591no—
171C4×D4C2×D5911yescharacteristic, complemented
172C2×C4⋊C4—592no—
173#107—592no—
174#107—591no—
175C4⋊C8C2×D5911yescharacteristic, complemented
176#102—592no—
177#102—591no—
178#102—592no—
179#102—592no—
180#102—591no—
181#102C2×D5912yescomplemented
182C22⋊C8—592no—
183C4×C8—591no—
184C24—1182no—
185#41—2364no—
186C2×Q8—1181no—
187C2×D4—21no—
188C2×D4—21no—
189C2×D4—591no—
190C2×D4—591no—
191C2×D4—1182no—
192C2×D4—1184no—
193C2×D4—1182no—
194C2×D4—1182no—
195C2×D4—2362no—
196C2×D4—2364no—
197C2×D4C22×D5912yes—
198C2×D4C22×D5911yescharacteristic
199C22×C4—21no—
200C22×C4—592no—
201C22×C4—1182no—
202C22×C4—1181no—
203D8—42no—
204D8—1182no—
205C2×C8—591no—
206C2×C8—591no—
207C2×C8—2362no—
208C2×C8C22×D5912yes—
209C4⋊C4—591no—
210C4⋊C4—592no—
211C4⋊C4—591no—
212C4⋊C4—1182no—
213C4⋊C4—1181no—
214C4⋊C4C22×D5911yescharacteristic
215C22⋊C4—21no—
216C22⋊C4—592no—
217C22⋊C4—1182no—
218C22⋊C4—1182no—
219C22⋊C4—1181no—
220C42C22×D5911yescharacteristic
221C23—21no—
222C23—22no—
223C23—592no—
224C23—1181no—
225C23—4722no—
226C23—2364no—
227C23—2364no—
228Q8—2362no—
229D4—21no—
230D4—22no—
231D4—21no—
232D4—22no—
233D4—42no—
234D4—81no—
235D4—594no—
236D4—592no—
237D4—1181no—
238D4—2364no—
239D4—2364no—
240D4—2364no—
241C2×C4—21no—
242C2×C4—42no—
243C2×C4—592no—
244C2×C4—1182no—
245C2×C4—1182no—
246C2×C4—1181no—
247C2×C4—1182no—
248C2×C4—2364no—
249C2×C4—2362no—
250C2×C4D4×D5911yescharacteristic
251C2×C4D4×D5911yescharacteristic
252C2×C4C23×D5911yescharacteristic
253C8—22no—
254C8—1181no—
255C8—1181no—
256C22—41no—
257C22—42no—
258C22—42no—
259C22—41no—
260C22—42no—
261C22—41no—
262C22—594no—
263C22—1182no—
264C22—1182no—
265C22—1182no—
266C22—4728no—
267C22—2361no—
268C22—2361no—
269C22C2×D4×D5911yescharacteristic
270C4—21no—
271C4—41no—
272C4—1182no—
273C4—2361no—
274C4—2362no—
275C4D8×D5912yes—
276C4#41×D5911yescharacteristic
277C4#1427377211yescharacteristic
278C2—82no—
279C2—81no—
280C2—1184no—
281C2—2362no—
282C2#1683804911yescharacteristic
283C2C2×D8×D5911yescharacteristic
284C2#1683821211yescharacteristic
subgroupG/H
centerC22C2×D4×D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#459C2
socleC22×C59C22×D4
hypercenter#459D59
hypocenterC59#3294
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C42 ◁ #459

Complements

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

NH ≅ G/Ntype
1. #16838057C2semidirect
2. #16838037C2semidirect
3. #16837748C2semidirect
4. #16837714C2semidirect
5. #16837683C2semidirect
6. #16837635C2semidirect
7. #16837534C2semidirect
8. C4×#11745669C2semidirect
9. #16837467C2semidirect
10. #102×D59C2semidirect
11. C59×#459C2semidirect
16. C2×C8×D59C22semidirect
17. #14273727C22semidirect
22. #14273698C22semidirect
26. C4⋊C4×D59C22semidirect
27. #14273661C22semidirect
28. #14273660C22semidirect
30. #14273648C22semidirect
31. #14273648C22semidirect
32. #14273648C22semidirect
34. (C2×D59)⋊C8C22semidirect
35. C4×C59⋊C8C22semidirect
36. C2×D8×C59C22semidirect
38. C4×D4×C59C22semidirect
39. C4⋊C8×C59C22semidirect
40. #102×C59C22semidirect
103. D236D8semidirect
104. D236#41semidirect
149. #459D59semidirect
154. C59#3294semidirect
159. C2×D8C2×D59semidirect
171. C4×D4C2×D59semidirect
175. C4⋊C8C2×D59semidirect
181. #102C2×D59semidirect