Finite Group Databasebeta

← #23757862

Subgroups — #23757862

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#19097759C211yesmaximal, characteristic, complemented
3#19097757C211yesmaximal, characteristic, complemented
4#19097756C211yesmaximal, characteristic, complemented
5#19097753C211yesmaximal, characteristic, complemented
6#19097749C211yesmaximal, characteristic, complemented
7#19097746C211yesmaximal, characteristic, complemented
8#19097746C211yesmaximal, characteristic, complemented
9#19097744C211yesmaximal, characteristic, complemented
10#19097741C211yesmaximal, characteristic, complemented
11#19097741C211yesmaximal, characteristic, complemented
12C4×D628C211yesmaximal, characteristic, complemented
13#19097733C211yesmaximal, characteristic, complemented
14C22⋊C4×D157C211yesmaximal, characteristic, complemented
15#126×C157C211yesmaximal, characteristic, complemented
16C23×D157C2211yescharacteristic
17C2×Dic314C2211yescharacteristic, complemented
18C2×D628C2211yescharacteristic
19C2×D628C2211yescharacteristic
20C2×D628C2211yescharacteristic
21C2×D628C2211yescharacteristic
22C2×D628C2211yescharacteristic, complemented
23C2×C22⋊D157C2211yescharacteristic
24C2×C22⋊D157C2211yescharacteristic
25C2×C4×D157C2211yescharacteristic
26C2×C4×D157C2211yescharacteristic
27C2×C4×D157C2211yescharacteristic, complemented
28C2×C4×D157C2211yescharacteristic, complemented
29C4⋊Dic157C2211yescharacteristic, complemented
30#14578933C2211yescharacteristic, complemented
31#14578933C2211yescharacteristic, complemented
32C22⋊Dic157C2211yescharacteristic
33#14578931C2211yescharacteristic
34#14578931C2211yescharacteristic
35#14578931C2211yescharacteristic
36#14578931C2211yescharacteristic
37#14578931C2211yescharacteristic
38#14578931C2211yescharacteristic
39#14578931C2211yescharacteristic, complemented
40#14578931C2211yescharacteristic, complemented
41#14578931C2211yescharacteristic, complemented
42#14578931C2211yescharacteristic, complemented
43C4×Dic157C2211yescharacteristic, complemented
44C4⋊C4×C157C2211yescharacteristic, complemented
45C4⋊C4×C157C2211yescharacteristic, complemented
46C4⋊C4×C157C2211yescharacteristic, complemented
47C22⋊C4×C157C2211yescharacteristic
48C22⋊C4×C157C2211yescharacteristic
49C22⋊C4×C157C2211yescharacteristic
50C42×C157C2211yescharacteristic, complemented
51C22×D157—22no—
52C22×D157—41no—
53C22×D157—41no—
54C22×D157C2311yescharacteristic
55C22×D157C2311yescharacteristic
56C22×D157C2311yescharacteristic
57C22×D157C2311yescharacteristic
58Dic314—41no—
59D628—22no—
60D628—22no—
61D628—41no—
62D628—41no—
63D628—41no—
64C22⋊D157—41no—
65C22⋊D157—41no—
66C2×Dic157C2311yescharacteristic
67C2×Dic157C2311yescharacteristic
68C2×Dic157C2311yescharacteristic
69C2×Dic157C2311yescharacteristic
70C4×D157—41no—
71C4×D157—41no—
72C4×D157—41no—
73C4×D157—41no—
74C23×C157C2311yescharacteristic
75C2×C4×C157C2311yescharacteristic
76C2×C4×C157C2311yescharacteristic
77C2×C4×C157C2311yescharacteristic
78C2×C4×C157C2311yescharacteristic
79C2×C4×C157C2311yescharacteristic
80C2×C4×C157C2311yescharacteristic
81C22×C157—21no—
82C22×C157—21no—
83C22×C157—21no—
84C22×C157C2411yescharacteristic
85C2×D157—21no—
86C2×D157—21no—
87C2×D157—21no—
88C2×D157—21no—
89C2×D157—21no—
90C2×D157—21no—
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—
102C4×C157—21no—
103C4×C157—21no—
104Dic157—21no—
105Dic157—21no—
106Dic157—21no—
107Dic157—21no—
108C2×C157—41no—
109C2×C157C2×#4111yescharacteristic
110C2×C157H(5,𝔽2)11yescharacteristic
111C2×C157H(5,𝔽2)11yescharacteristic
112D157—22no—
113D157—41no—
114D157—41no—
115D157—41no—
116C157#53811yescharacteristic, complemented, Sylow
117#538—1571nomaximal, Sylow
118#126—1571no—
119#126D15711yescharacteristic, complemented
120#124—1571no—
121#124—1571no—
122#123—1571no—
123#123—1571no—
124C22⋊Q8—1571no—
125#121—1571no—
126#121—1571no—
127#121—1571no—
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×D4—1571no—
140C2×D4—1571no—
141C2×D4—1571no—
142C22×C4—1571no—
143C22×C4—1571no—
144C22×C4—1571no—
145C22×C4—1571no—
146C4⋊C4—1571no—
147C4⋊C4—1571no—
148C4⋊C4—1571no—
149C4⋊C4C2×D15711yescharacteristic, complemented
150C4⋊C4C2×D15711yescharacteristic, complemented
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⋊C4C2×D15711yescharacteristic
164C22⋊C4C2×D15711yescharacteristic
165C22⋊C4C2×D15711yescharacteristic
166C42—1571no—
167C42C2×D15711yescharacteristic, complemented
168C23—3142no—
169C23—6281no—
170C23—6281no—
171C23—1571no—
172C23—1571no—
173C23—1571no—
174C23—1571no—
175C23C22×D15711yescharacteristic
176Q8—6281no—
177D4—3142no—
178D4—3142no—
179D4—6281no—
180D4—6281no—
181D4—6281no—
182D4—6281no—
183D4—6281no—
184C2×C4—6281no—
185C2×C4—6281no—
186C2×C4—6281no—
187C2×C4—6281no—
188C2×C4—1571no—
189C2×C4—1571no—
190C2×C4—1571no—
191C2×C4—1571no—
192C2×C4C22×D15711yescharacteristic
193C2×C4C22×D15711yescharacteristic
194C2×C4C22×D15711yescharacteristic
195C2×C4C22×D15711yescharacteristic
196C2×C4C22×D15711yescharacteristic
197C2×C4C22×D15711yescharacteristic
198C22—21no—
199C22—21no—
200C22—21no—
201C22—3141no—
202C22—3141no—
203C22—3141no—
204C22—3141no—
205C22—3141no—
206C22—3141no—
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—21no—
220C4—21no—
221C4—3141no—
222C4—3141no—
223C4—3141no—
224C4—3141no—
225C2—41no—
226C2—3142no—
227C2—6281no—
228C2—6281no—
229C2—6281no—
230C2#41×D15711yescharacteristic
231C2#1909781711yescharacteristic
232C2#1909781711yescharacteristic
subgroupG/H
center, FrattiniC22C23×D157
commutator, socle, cosocleC22×C157C24
Fitting#126×C157C2
hypercenter#126D157
hypocenterC157#538
LCSG ▷ C22×C157 ▷ C157
UCSC1 ◁ C22 ◁ #126

Complements

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

NH ≅ G/Ntype
1. #19097766C2semidirect
2. #19097759C2semidirect
3. #19097757C2semidirect
4. #19097756C2semidirect
5. #19097753C2semidirect
6. #19097749C2semidirect
7. #19097746C2semidirect
8. #19097746C2semidirect
9. #19097744C2semidirect
10. #19097741C2semidirect
11. #19097741C2semidirect
12. C4×D628C2semidirect
13. #19097733C2semidirect
14. C22⋊C4×D157C2semidirect
15. #126×C157C2semidirect
17. C2×Dic314C22semidirect
22. C2×D628C22semidirect
27. C2×C4×D157C22semidirect
28. C2×C4×D157C22semidirect
29. C4⋊Dic157C22semidirect
30. #14578933C22semidirect
31. #14578933C22semidirect
39. #14578931C22semidirect
40. #14578931C22semidirect
41. #14578931C22semidirect
42. #14578931C22semidirect
43. C4×Dic157C22semidirect
44. C4⋊C4×C157C22semidirect
45. C4⋊C4×C157C22semidirect
46. C4⋊C4×C157C22semidirect
50. C42×C157C22semidirect
116. C157#538semidirect
119. #126D157semidirect
149. C4⋊C4C2×D157semidirect
150. C4⋊C4C2×D157semidirect
151. C4⋊C4C2×D157semidirect
167. C42C2×D157semidirect