Finite Group Databasebeta

← #34115370

Subgroups — #34115370

Order 20096.

264 conjugacy classes of subgroups; only the 76 normal subgroups are shown.

normal subgroups only

This group has 264 conjugacy classes of subgroups — too many to draw. Only its 76 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#23758290C212yesmaximal, complemented
2#23758118C212yesmaximal, complemented
3#23758117C212yesmaximal
4C2×#19097729C211yesmaximal, characteristic
5#19097838—22no—
6C22⋊#11929441C2214yes—
7C4×#11929441—22no—
8C22×C4×D157C411yescharacteristic
9#19097729—22no—
10#19097729—22no—
11C2×C4⋊Dic157C2211yescharacteristic
12C2×#14578931C411yescharacteristic
13C2×#14578931C2211yescharacteristic
14C2×C4×Dic157C411yescharacteristic
15C2×C4×Dic157C2211yescharacteristic
16C2×C4⋊C4×C157C411yescharacteristic
17C2×#11929441—24no—
18C23×D157C2×C411yescharacteristic
19C22×Dic157C2×C411yescharacteristic
20C22×Dic157C2×C411yescharacteristic
21C22×Dic157C2311yescharacteristic
22C2×C4×D157—21no—
23C2×C4×D157—21no—
24C2×C4×D157—22no—
25C2×C4×D157C814yescomplemented
26C4⋊Dic157—22no—
27#14578931—22no—
28#14578931—22no—
29C4×Dic157—21no—
30C4×Dic157—21no—
31C4×Dic157D412yes—
32C4×Dic157D412yes—
33C22×C4×C157C2×C411yescharacteristic
34C22×C4×C157C2×C411yescharacteristic
35C22×C4×C157C2×C411yescharacteristic
36C4⋊C4×C157—22no—
37#11929441—44no—
38C22×D157—21no—
39C22×D157—21no—
40C22×D157—41no—
41C22×D157—41no—
42C22×D157C2×C812yes—
43C2×Dic157—21no—
44C2×Dic157—41no—
45C2×Dic157—41no—
46C2×Dic157C22⋊C411yescharacteristic
47C2×Dic157C22⋊C411yescharacteristic
48C2×Dic157C2×C812yes—
49C2×Dic157M1612yes—
50C2×Dic157C2×D412yes—
51C4×D157—24no—
52C4×D157—24no—
53C23×C157C22×C411yescharacteristic
54C2×C4×C157—21no—
55C2×C4×C157—21no—
56C2×C4×C157—21no—
57C2×C4×C157—41no—
58C2×C4×C157—41no—
59C2×C4×C157C22⋊C412yes—
60C2×C4×C157C2×C812yes—
61C22×C157—21no—
62C22×C157—21no—
63C22×C157C2×C22⋊C411yescharacteristic
64C22×C157C22×C811yescharacteristic
65C22×C157C2×M1611yescharacteristic
66C2×D157—22no—
67C2×D157—42no—
68C2×D157—41no—
69C2×D157—41no—
70C2×D157—42no—
71C4×C157—22no—
72C4×C157—22no—
73C4×C157—41no—
74Dic157—22no—
75Dic157—41no—
76Dic157C22⋊C812yes—
77Dic157C22⋊C812yes—
78C2×C157—21no—
79C2×C157—21no—
80C2×C157C2×C22⋊C811yescharacteristic
81C2×C157#41011yescharacteristic
82C2×C157#41311yescharacteristic
83D157—42no—
84C157#145811yescharacteristic, complemented, Sylow
85#1458—1571nomaximal, Sylow
86C2×#117—1571no—
87#431—1572no—
88#324—1572no—
89#323—1572no—
90C23×C4—1571no—
91#117—3142no—
92#117—3142no—
93C2×C4⋊C4—1571no—
94C2×C4⋊C4#1059784511yescharacteristic
95C2×C22⋊C4—1571no—
96C2×C22⋊C4—1571no—
97C2×C42—1571no—
98C2×C42—1571no—
99C4⋊C8—3142no—
100C22⋊C8—1574no—
101C4×C8—3142no—
102C24—1571no—
103C22×C4—3141no—
104C22×C4—3141no—
105C22×C4—3142no—
106C22×C4—1574no—
107C22×C4—1571no—
108C22×C4—1571no—
109C22×C4—1571no—
110C22×C4C2×#1059784511yescharacteristic
111C22×C4C2×#1059784511yescharacteristic
112C22×C4C2×#1059784511yescharacteristic
113C2×C8—3144no—
114C4⋊C4—22no—
115C4⋊C4—3142no—
116C22⋊C4—3142no—
117C22⋊C4—3142no—
118C42—3141no—
119C42—3141no—
120C42—1572no—
121C42—1572no—
122C23—3141no—
123C23—3141no—
124C23—6281no—
125C23—6281no—
126C23—1572no—
127C23C22×#1059784511yescharacteristic
128C2×C4—21no—
129C2×C4—21no—
130C2×C4—21no—
131C2×C4—41no—
132C2×C4—41no—
133C2×C4—3144no—
134C2×C4—3144no—
135C2×C4—3141no—
136C2×C4—6281no—
137C2×C4—6281no—
138C2×C4—1572no—
139C2×C4—1572no—
140C2×C4—1571no—
141C2×C4—1571no—
142C2×C4—1572no—
143C2×C4C22⋊#1059784512yes—
144C2×C4D157⋊C812yes—
145C8—6284no—
146C22—21no—
147C22—21no—
148C22—3142no—
149C22—6282no—
150C22—6282no—
151C22—6281no—
152C22—6281no—
153C22C2×C22⋊#1059784511yescharacteristic
154C22C2×D157⋊C811yescharacteristic
155C22D157⋊M1611yescharacteristic
156C4—22no—
157C4—22no—
158C4—41no—
159C4—3142no—
160C4—6281no—
161C4—1572no—
162C4—1572no—
163C2—21no—
164C2—21no—
165C2—6282no—
166C2D157⋊(C22⋊C8)11yescharacteristic
167C2#2375825411yescharacteristic
168C2#2375826011yescharacteristic
subgroupG/H
centerC22C2×C22⋊#10597845
commutatorC22×C157C22×C8
FrattiniC23C22×#10597845
FittingC2×C4⋊C4×C157C4
socleC22×C157C2×C22⋊C4
prime radicalC23×D157C2×C4
cosocleC22×Dic157C23
hypercenterC2×C4⋊C4#10597845
hypocenterC157#1458
LCSG ▷ C22×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. #23758290C2semidirect
2. #23758118C2semidirect
25. C2×C4×D157C8semidirect
84. C157#1458semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#237582902
#237581182
#237581172
C2×#190977292
#1458157