Finite Group Databasebeta

← #23757947

Subgroups — #23757947

Order 10048.

248 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 248 conjugacy classes of subgroups — too many to draw. Only its 97 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#19097765C211yesmaximal, characteristic, complemented
3#19097759C211yesmaximal, characteristic, complemented
4#19097756C211yesmaximal, characteristic, complemented
5#19097756C211yesmaximal, characteristic, complemented
6#19097754C211yesmaximal, characteristic, complemented
7#19097749C211yesmaximal, characteristic, complemented
8#19097748C211yesmaximal, characteristic, complemented
9#19097741C211yesmaximal, characteristic
10C4×D628C211yesmaximal, characteristic, complemented
11#19097731C211yesmaximal, characteristic, complemented
12#19097728C211yesmaximal, characteristic, complemented
13C2×#14578931C211yesmaximal, characteristic, complemented
14C22⋊C4×D157C211yesmaximal, characteristic, complemented
15#117×C157C211yesmaximal, characteristic, complemented
16C23×D157C2211yescharacteristic
17C2×Dic314C2211yescharacteristic, complemented
18C2×D628C2211yescharacteristic
19C2×D628C2211yescharacteristic
20C2×C22⋊D157C2211yescharacteristic
21C22×Dic157C2211yescharacteristic
22C2×C4×D157C2211yescharacteristic
23C2×C4×D157C2211yescharacteristic
24C2×C4×D157C2211yescharacteristic, complemented
25C4⋊Dic157C2211yescharacteristic, complemented
26#14578933C2211yescharacteristic, complemented
27#14578933C2211yescharacteristic, complemented
28#14578933C2211yescharacteristic, complemented
29#14578933C2211yescharacteristic, complemented
30#14578933C2211yescharacteristic, complemented
31C22⋊Dic157C2211yescharacteristic
32#14578931C2211yescharacteristic
33#14578931C2211yescharacteristic
34#14578931C2211yescharacteristic
35#14578931C2211yescharacteristic
36#14578931C2211yescharacteristic
37#14578931C2211yescharacteristic
38#14578931C2211yescharacteristic
39#14578931C2211yescharacteristic
40#14578931C2211yescharacteristic, complemented
41#14578931C2211yescharacteristic, complemented
42#14578931C2211yescharacteristic, complemented
43C4×Dic157C2211yescharacteristic, complemented
44C22×C4×C157C2211yescharacteristic
45C4⋊C4×C157C2211yescharacteristic, complemented
46C4⋊C4×C157C2211yescharacteristic, complemented
47C22⋊C4×C157C2211yescharacteristic
48C22⋊C4×C157C2211yescharacteristic
49C42×C157C2211yescharacteristic, complemented
50C42×C157C2211yescharacteristic, complemented
51C22×D157—22no—
52C22×D157—22no—
53C22×D157—41no—
54C22×D157C2311yescharacteristic
55C22×D157C2311yescharacteristic
56C22×D157C2311yescharacteristic
57Dic314—41no—
58D628—22no—
59D628—41no—
60C22⋊D157—22no—
61C2×Dic157—41no—
62C2×Dic157C2311yescharacteristic
63C2×Dic157C2311yescharacteristic
64C2×Dic157C2311yescharacteristic
65C2×Dic157C2311yescharacteristic
66C2×Dic157C2311yescharacteristic
67C4×D157—22no—
68C4×D157—41no—
69C4×D157—41no—
70C23×C157C2311yescharacteristic
71C2×C4×C157—22no—
72C2×C4×C157C2311yescharacteristic
73C2×C4×C157C2311yescharacteristic
74C2×C4×C157C2311yescharacteristic
75C2×C4×C157C2311yescharacteristic
76C2×C4×C157C2311yescharacteristic
77C2×C4×C157C2311yescharacteristic
78C22×C157—21no—
79C22×C157—21no—
80C22×C157#4112yes—
81C22×C157C2411yescharacteristic
82C2×D157—21no—
83C2×D157—21no—
84C2×D157—21no—
85C2×D157—21no—
86C2×D157—21no—
87C2×D157—21no—
88C2×D157—21no—
89C2×D157—21no—
90C2×D157—44no—
91C2×D157#4112yes—
92C4×C157—21no—
93C4×C157—21no—
94C4×C157—21no—
95C4×C157—21no—
96C4×C157—21no—
97C4×C157—21no—
98Dic157—21no—
99Dic157—21no—
100Dic157—21no—
101Dic157—21no—
102Dic157—21no—
103C2×C157—22no—
104C2×C157C2×#4111yescharacteristic
105C2×C157C2×#4111yescharacteristic
106C2×C157H(5,𝔽2)11yescharacteristic
107D157—22no—
108D157—41no—
109D157—41no—
110C157#55111yescharacteristic, complemented, Sylow
111#551—1571nomaximal, Sylow
112#126—1571no—
113#126—1571no—
114#124—1571no—
115#123—1571no—
116#123—1571no—
117#123—1571no—
118C22⋊Q8—1571no—
119C22⋊Q8—1571no—
120#120—1571no—
121C4×D4—1571no—
122C4×D4—1571no—
123#117—1571no—
124#117D15711yescharacteristic, complemented
125C2×C22⋊C4—1571no—
126C2×C22⋊C4—1571no—
127C24—1571no—
128C2×Q8—1571no—
129C2×D4—1571no—
130C2×D4—1571no—
131C2×D4—1571no—
132C22×C4—1571no—
133C22×C4—1571no—
134C22×C4—1571no—
135C22×C4—1571no—
136C22×C4C2×D15711yescharacteristic
137C4⋊C4—1571no—
138C4⋊C4—1571no—
139C4⋊C4—1571no—
140C4⋊C4—1571no—
141C4⋊C4—1571no—
142C4⋊C4—1571no—
143C4⋊C4C2×D15711yescharacteristic, complemented
144C4⋊C4C2×D15711yescharacteristic, complemented
145C22⋊C4—1571no—
146C22⋊C4—1571no—
147C22⋊C4—1571no—
148C22⋊C4—1571no—
149C22⋊C4—1571no—
150C22⋊C4—1571no—
151C22⋊C4—1571no—
152C22⋊C4—1571no—
153C22⋊C4—1571no—
154C22⋊C4—1571no—
155C22⋊C4—1571no—
156C22⋊C4—1571no—
157C22⋊C4C2×D15711yescharacteristic
158C22⋊C4C2×D15711yescharacteristic
159C42—1571no—
160C42C2×D15711yescharacteristic, complemented
161C42C2×D15711yescharacteristic, complemented
162C23—3142no—
163C23—3142no—
164C23—6281no—
165C23—1571no—
166C23—1571no—
167C23—1571no—
168C23C22×D15711yescharacteristic
169Q8—6281no—
170D4—3142no—
171D4—3142no—
172D4—6281no—
173C2×C4—22no—
174C2×C4—3142no—
175C2×C4—6281no—
176C2×C4—6281no—
177C2×C4—6281no—
178C2×C4—1571no—
179C2×C4—1571no—
180C2×C4—1571no—
181C2×C4—1571no—
182C2×C4—1571no—
183C2×C4C22×D15711yescharacteristic
184C2×C4C22×D15711yescharacteristic
185C2×C4C22×D15711yescharacteristic
186C2×C4C22×D15711yescharacteristic
187C2×C4C22×D15711yescharacteristic
188C2×C4C22×D15711yescharacteristic
189C22—21no—
190C22—21no—
191C22—3141no—
192C22—3141no—
193C22—3141no—
194C22—3141no—
195C22—3141no—
196C22—3141no—
197C22—3141no—
198C22—3141no—
199C22—6284no—
200C22—1572no—
201C22#1457895412yes—
202C22C23×D15711yescharacteristic
203C4—21no—
204C4—21no—
205C4—21no—
206C4—21no—
207C4—21no—
208C4—21no—
209C4—3141no—
210C4—3141no—
211C4—3141no—
212C4—3141no—
213C4—3141no—
214C2—22no—
215C2—3142no—
216C2—6281no—
217C2—6281no—
218C2#41×D15711yescharacteristic
219C2C2×#1457895411yescharacteristic
220C2#1909781711yescharacteristic
subgroupG/H
center, FrattiniC22C23×D157
commutator, socle, cosocleC22×C157C24
Fitting#117×C157C2
prime radical#19097741C2
hypercenter#117D157
hypocenterC157#551
LCSG ▷ C22×C157 ▷ C157
UCSC1 ◁ C22 ◁ #117

Complements

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

NH ≅ G/Ntype
1. #19097766C2semidirect
2. #19097765C2semidirect
3. #19097759C2semidirect
4. #19097756C2semidirect
5. #19097756C2semidirect
6. #19097754C2semidirect
7. #19097749C2semidirect
8. #19097748C2semidirect
10. C4×D628C2semidirect
11. #19097731C2semidirect
12. #19097728C2semidirect
13. C2×#14578931C2semidirect
14. C22⋊C4×D157C2semidirect
15. #117×C157C2semidirect
17. C2×Dic314C22semidirect
24. C2×C4×D157C22semidirect
25. C4⋊Dic157C22semidirect
26. #14578933C22semidirect
27. #14578933C22semidirect
28. #14578933C22semidirect
29. #14578933C22semidirect
30. #14578933C22semidirect
40. #14578931C22semidirect
41. #14578931C22semidirect
42. #14578931C22semidirect
43. C4×Dic157C22semidirect
45. C4⋊C4×C157C22semidirect
46. C4⋊C4×C157C22semidirect
49. C42×C157C22semidirect
50. C42×C157C22semidirect
110. C157#551semidirect
124. #117D157semidirect
143. C4⋊C4C2×D157semidirect
144. C4⋊C4C2×D157semidirect
160. C42C2×D157semidirect
161. C42C2×D157semidirect