Finite Group Databasebeta

← #23757855

Subgroups — #23757855

Order 10048.

250 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 250 conjugacy classes of subgroups — too many to draw. Only its 93 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#19097766C211yesmaximal, characteristic, complemented
2#19097764C211yesmaximal, characteristic, complemented
3#19097758C211yesmaximal, characteristic, complemented
4#19097757C211yesmaximal, characteristic, complemented
5#19097754C211yesmaximal, characteristic, complemented
6#19097752C211yesmaximal, characteristic, complemented
7#19097749C211yesmaximal, characteristic, complemented
8#19097743C211yesmaximal, characteristic, complemented
9#19097742C211yesmaximal, characteristic, complemented
10#19097739C211yesmaximal, characteristic, complemented
11#19097739C211yesmaximal, characteristic, complemented
12C4×C22⋊D157C211yesmaximal, characteristic, complemented
13#19097731C211yesmaximal, characteristic, complemented
14C22⋊C4×D157C211yesmaximal, characteristic, complemented
15#121×C157C211yesmaximal, characteristic, complemented
16C23×D157C2211yescharacteristic
17C2×Dic314C2211yescharacteristic, complemented
18C2×C22⋊D157C2211yescharacteristic
19C2×C22⋊D157C2211yescharacteristic
20C2×C22⋊D157C2211yescharacteristic
21C2×C22⋊D157C2211yescharacteristic
22C22×Dic157C2211yescharacteristic, complemented
23C2×C4×D157C2211yescharacteristic
24C2×C4×D157C2211yescharacteristic
25C4⋊Dic157C2211yescharacteristic, complemented
26#14578933C2211yescharacteristic, complemented
27#14578933C2211yescharacteristic, complemented
28#14578933C2211yescharacteristic, complemented
29#14578933C2211yescharacteristic, complemented
30C22⋊Dic157C2211yescharacteristic
31C22⋊Dic157C2211yescharacteristic
32C22⋊Dic157C2211yescharacteristic
33C22⋊Dic157C2211yescharacteristic, complemented
34C22⋊Dic157C2211yescharacteristic, complemented
35C22⋊Dic157C2211yescharacteristic, complemented
36#14578931C2211yescharacteristic
37#14578931C2211yescharacteristic
38#14578931C2211yescharacteristic
39#14578931C2211yescharacteristic
40#14578931C2211yescharacteristic
41#14578931C2211yescharacteristic
42C4×Dic157C2211yescharacteristic, complemented
43C4×Dic157C2211yescharacteristic, complemented
44C2×D4×C157C2211yescharacteristic
45C2×D4×C157C2211yescharacteristic
46C2×D4×C157C2211yescharacteristic, complemented
47C22×C4×C157C2211yescharacteristic, complemented
48C4⋊C4×C157C2211yescharacteristic, complemented
49C22⋊C4×C157C2211yescharacteristic
50C22⋊C4×C157C2211yescharacteristic, complemented
51C22×D157—22no—
52C22×D157—41no—
53C22×D157—41no—
54C22×D157C2311yescharacteristic
55C22×D157C2311yescharacteristic
56Dic314—41no—
57C22⋊D157—22no—
58C22⋊D157—22no—
59C22⋊D157—41no—
60C22⋊D157—41no—
61C2×Dic157—41no—
62C2×Dic157C2311yescharacteristic
63C2×Dic157C2311yescharacteristic
64C2×Dic157C2311yescharacteristic
65C2×Dic157C2311yescharacteristic
66C2×Dic157C2311yescharacteristic
67C2×Dic157C2311yescharacteristic
68C4×D157—41no—
69C4×D157—41no—
70C23×C157C2311yescharacteristic
71C23×C157C2311yescharacteristic
72C23×C157C2311yescharacteristic
73D4×C157—41no—
74D4×C157—41no—
75D4×C157—41no—
76C2×C4×C157—41no—
77C2×C4×C157C2311yescharacteristic
78C2×C4×C157C2311yescharacteristic
79C2×C4×C157C2311yescharacteristic
80C2×C4×C157C2311yescharacteristic
81C22×C157—21no—
82C22×C157—21no—
83C22×C157—21no—
84C22×C157—21no—
85C22×C157—21no—
86C22×C157—21no—
87C22×C157—21no—
88C22×C157—21no—
89C22×C157—21no—
90C22×C157C2411yescharacteristic
91C2×D157—21no—
92C2×D157—21no—
93C2×D157—21no—
94C2×D157—21no—
95C2×D157—21no—
96C2×D157—44no—
97C2×D157#4112yes—
98C4×C157—21no—
99C4×C157—21no—
100C4×C157—21no—
101C4×C157—21no—
102Dic157—21no—
103Dic157—21no—
104Dic157—21no—
105Dic157—21no—
106Dic157—21no—
107Dic157—21no—
108C2×C157—41no—
109C2×C157—41no—
110C2×C157—41no—
111C2×C157C2×#4111yescharacteristic
112C2×C157H(5,𝔽2)11yescharacteristic
113C2×C157H(5,𝔽2)11yescharacteristic
114D157—22no—
115D157—41no—
116C157#53811yescharacteristic, complemented, Sylow
117#538—1571nomaximal, Sylow
118#126—1571no—
119#126—1571no—
120#124—1571no—
121#124—1571no—
122#123—1571no—
123#123—1571no—
124C22⋊Q8—1571no—
125#121—1571no—
126#121—1571no—
127#121D15711yescharacteristic, complemented
128#120—1571no—
129#120—1571no—
130C4×D4—1571no—
131C4×D4—1571no—
132C2×C22⋊C4—1571no—
133C24—1571no—
134C2×Q8—1571no—
135C2×D4—1571no—
136C2×D4—1571no—
137C2×D4—1571no—
138C2×D4—1571no—
139C2×D4C2×D15711yescharacteristic
140C2×D4C2×D15711yescharacteristic
141C2×D4C2×D15711yescharacteristic, complemented
142C22×C4—1571no—
143C22×C4—1571no—
144C22×C4—1571no—
145C22×C4C2×D15711yescharacteristic, complemented
146C4⋊C4—1571no—
147C4⋊C4—1571no—
148C4⋊C4—1571no—
149C4⋊C4—1571no—
150C4⋊C4—1571no—
151C4⋊C4C2×D15711yescharacteristic, complemented
152C22⋊C4—1571no—
153C22⋊C4—1571no—
154C22⋊C4—1571no—
155C22⋊C4—1571no—
156C22⋊C4—1571no—
157C22⋊C4—1571no—
158C22⋊C4—1571no—
159C22⋊C4—1571no—
160C22⋊C4—1571no—
161C22⋊C4—1571no—
162C22⋊C4—1571no—
163C22⋊C4—1571no—
164C22⋊C4C2×D15711yescharacteristic
165C22⋊C4C2×D15711yescharacteristic, complemented
166C42—1571no—
167C42—1571no—
168C23—3142no—
169C23—6281no—
170C23—6281no—
171C23—1571no—
172C23—1571no—
173C23C22×D15711yescharacteristic
174C23C22×D15711yescharacteristic
175C23C22×D15711yescharacteristic
176Q8—6281no—
177D4—41no—
178D4—41no—
179D4—41no—
180D4—3142no—
181D4—3142no—
182D4—6281no—
183D4—6281no—
184C2×C4—41no—
185C2×C4—6281no—
186C2×C4—6281no—
187C2×C4—6281no—
188C2×C4—1571no—
189C2×C4—1571no—
190C2×C4—1571no—
191C2×C4—1571no—
192C2×C4—1571no—
193C2×C4—1571no—
194C2×C4C22×D15711yescharacteristic
195C2×C4C22×D15711yescharacteristic
196C2×C4C22×D15711yescharacteristic
197C2×C4C22×D15711yescharacteristic
198C22—21no—
199C22—21no—
200C22—21no—
201C22—21no—
202C22—21no—
203C22—21no—
204C22—21no—
205C22—21no—
206C22—21no—
207C22—3141no—
208C22—3141no—
209C22—3141no—
210C22—3141no—
211C22—3141no—
212C22—6284no—
213C22—1572no—
214C22C23×D15711yescharacteristic
215C4—21no—
216C4—21no—
217C4—21no—
218C4—21no—
219C4—3141no—
220C4—3141no—
221C4—3141no—
222C4—3141no—
223C4—3141no—
224C4—3141no—
225C2—41no—
226C2—41no—
227C2—41no—
228C2—3142no—
229C2—6281no—
230C2#41×D15711yescharacteristic
231C2#1909781611yescharacteristic
232C2#1909781611yescharacteristic
subgroupG/H
center, FrattiniC22C23×D157
commutator, socle, cosocleC22×C157C24
Fitting#121×C157C2
hypercenter#121D157
hypocenterC157#538
LCSG ▷ C22×C157 ▷ C157
UCSC1 ◁ C22 ◁ #121

Complements

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

NH ≅ G/Ntype
1. #19097766C2semidirect
2. #19097764C2semidirect
3. #19097758C2semidirect
4. #19097757C2semidirect
5. #19097754C2semidirect
6. #19097752C2semidirect
7. #19097749C2semidirect
8. #19097743C2semidirect
9. #19097742C2semidirect
10. #19097739C2semidirect
11. #19097739C2semidirect
12. C4×C22⋊D157C2semidirect
13. #19097731C2semidirect
14. C22⋊C4×D157C2semidirect
15. #121×C157C2semidirect
17. C2×Dic314C22semidirect
22. C22×Dic157C22semidirect
25. C4⋊Dic157C22semidirect
26. #14578933C22semidirect
27. #14578933C22semidirect
28. #14578933C22semidirect
29. #14578933C22semidirect
33. C22⋊Dic157C22semidirect
34. C22⋊Dic157C22semidirect
35. C22⋊Dic157C22semidirect
42. C4×Dic157C22semidirect
43. C4×Dic157C22semidirect
46. C2×D4×C157C22semidirect
47. C22×C4×C157C22semidirect
48. C4⋊C4×C157C22semidirect
50. C22⋊C4×C157C22semidirect
116. C157#538semidirect
127. #121D157semidirect
141. C2×D4C2×D157semidirect
145. C22×C4C2×D157semidirect
151. C4⋊C4C2×D157semidirect
165. C22⋊C4C2×D157semidirect