Finite Group Databasebeta

← #23757165

Subgroups — #23757165

Order 10048.

190 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 190 conjugacy classes of subgroups — too many to draw. Only its 69 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
1C2×C4⋊Dic157C211yesmaximal, characteristic, complemented
2C2×#14578931C211yesmaximal, characteristic
3C2×#14578931C211yesmaximal, characteristic
4C2×#14578931C211yesmaximal, characteristic
5C2×C4×Dic157C211yesmaximal, characteristic, complemented
6#19097678C211yesmaximal, characteristic, complemented
7#95×C157C211yesmaximal, characteristic, complemented
8C23×D157C2211yescharacteristic
9C22×Dic157C2211yescharacteristic
10C22×Dic157C2211yescharacteristic
11C22×Dic157C2211yescharacteristic
12C4⋊Dic157—22no—
13#14578931—22no—
14#14578931—22no—
15#14578931C414yescomplemented
16C4×Dic157—22no—
17C22×C4×C157C2211yescharacteristic
18C22×C4×C157C2211yescharacteristic
19C22×C4×C157C2211yescharacteristic
20C22×D157—21no—
21C22×D157—21no—
22C22×D157—21no—
23C22×D157—21no—
24C22×D157—21no—
25C22×D157—21no—
26C22×D157C2×C412yes—
27C2×Dic157—21no—
28C2×Dic157—21no—
29C2×Dic157—21no—
30C2×Dic157—21no—
31C2×Dic157—21no—
32C2×Dic157—21no—
33C2×Dic157—21no—
34C2×Dic157C2×C412yes—
35C2×Dic157D412yes—
36C23×C157C2311yescharacteristic
37C2×C4×C157—21no—
38C2×C4×C157—21no—
39C2×C4×C157—21no—
40C2×C4×C157—21no—
41C2×C4×C157—21no—
42C2×C4×C157—21no—
43C2×C4×C157—21no—
44C2×C4×C157C2×C412yes—
45C2×C4×C157D412yes—
46C22×C157C22×C411yescharacteristic
47C22×C157C2×D411yescharacteristic
48C22×C157C2×D411yescharacteristic
49C22×C157#4111yescharacteristic
50C22×C157#4111yescharacteristic
51C22×C157#4111yescharacteristic
52C22×C157#4111yescharacteristic
53C2×D157—22no—
54C2×D157—22no—
55C2×D157—22no—
56C2×D157—41no—
57C2×D157—41no—
58C2×D157—41no—
59C2×D157—41no—
60C4×C157—22no—
61C4×C157—22no—
62C4×C157—41no—
63Dic157—22no—
64Dic157—22no—
65Dic157—41no—
66C2×C157#11711yescharacteristic
67C2×C157C4×D411yescharacteristic
68C2×C157C4×D411yescharacteristic
69C2×C157#12111yescharacteristic
70C2×C157#12311yescharacteristic
71C2×C157#12411yescharacteristic
72C2×C157#12611yescharacteristic
73D157—42no—
74C157#38811yescharacteristic, complemented, Sylow
75#388—1571nomaximal, Sylow
76C2×C4⋊C4—1571no—
77C2×C22⋊C4—1571no—
78C2×C22⋊C4—1571no—
79C2×C22⋊C4—1571no—
80C2×C42—1571no—
81#95—1571no—
82#95D15711yescharacteristic, complemented
83C24—1571no—
84C22×C4—1571no—
85C22×C4—1571no—
86C22×C4—1571no—
87C22×C4C2×D15711yescharacteristic
88C22×C4C2×D15711yescharacteristic
89C22×C4C2×D15711yescharacteristic
90C4⋊C4—3142no—
91C22⋊C4—3142no—
92C22⋊C4—3142no—
93C22⋊C4—1574no—
94C42—3142no—
95C23—3141no—
96C23—3141no—
97C23—3141no—
98C23—3141no—
99C23—3141no—
100C23—3141no—
101C23—1572no—
102C23C22×D15711yescharacteristic
103C2×C4—21no—
104C2×C4—21no—
105C2×C4—21no—
106C2×C4—21no—
107C2×C4—21no—
108C2×C4—21no—
109C2×C4—21no—
110C2×C4—3141no—
111C2×C4—3141no—
112C2×C4—3141no—
113C2×C4—3141no—
114C2×C4—3141no—
115C2×C4—3141no—
116C2×C4—3141no—
117C2×C4—1572no—
118C2×C4—1572no—
119C2×C4C4×D15712yes—
120C2×C4D62812yes—
121C22—3142no—
122C22—3142no—
123C22—3142no—
124C22—6281no—
125C22—6281no—
126C22—6281no—
127C22—6281no—
128C22C2×C4×D15711yescharacteristic
129C22D4×D15711yescharacteristic
130C22C2×D62811yescharacteristic
131C22#1457895311yescharacteristic
132C22#1457895311yescharacteristic
133C22#1457895411yescharacteristic
134C22#1457895511yescharacteristic
135C4—22no—
136C4—22no—
137C4—41no—
138C4—3142no—
139C4—3142no—
140C4—6281no—
141C2—6282no—
142C2#1909772911yescharacteristic
143C2#1909773111yescharacteristic
144C2C4×D62811yescharacteristic
145C2#1909774611yescharacteristic
146C2#1909775511yescharacteristic
147C2#1909775711yescharacteristic
148C2#1909776611yescharacteristic
subgroupG/H
center, FrattiniC23C22×D157
commutatorC22×C157C22×C4
Fitting#95×C157C2
socle, cosocleC23×C157C23
prime radicalC23×D157C22
hypercenter#95D157
hypocenterC157#388
LCSG ▷ C22×C157 ▷ C157
UCSC1 ◁ C23 ◁ #95

Complements

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

NH ≅ G/Ntype
1. C2×C4⋊Dic157C2semidirect
5. C2×C4×Dic157C2semidirect
6. #19097678C2semidirect
7. #95×C157C2semidirect
15. #14578931C4semidirect
74. C157#388semidirect
82. #95D157semidirect