Finite Group Databasebeta

← #34115410

Subgroups — #34115410

Order 20096.

204 conjugacy classes of subgroups; only the 62 normal subgroups are shown.

normal subgroups only

This group has 204 conjugacy classes of subgroups — too many to draw. Only its 62 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#23758294C211yesmaximal, characteristic
2#23758290C211yesmaximal, characteristic
3#23758119C214yesmaximal
4C2×#19097762C211yesmaximal, characteristic
5#19097838—21no—
6C4⋊#11929441—21no—
7C22⋊#11929441C2212yes—
8C22⋊#11929441C2212yes—
9#19097826—21no—
10C4×#11929441—21no—
11#19097762—21no—
12#19097762—21no—
13#19097762—21no—
14#19097762—21no—
15C2×C4⋊Dic157C411yescharacteristic
16C2×C4⋊Dic157C412yes—
17C2×#14578933C2212yes—
18C2×C4×Dic157C2211yescharacteristic
19C2×C4⋊C4×C157C411yescharacteristic
20C2×#11929441—22no—
21C2×#11929441—22no—
22C22×Dic157C2×C412yes—
23C22×Dic157C2×C411yescharacteristic
24C22×Dic157C2311yescharacteristic
25C4⋊Dic157—22no—
26C4⋊Dic157—22no—
27C4⋊Dic157—21no—
28C4⋊Dic157—21no—
29#14578933—22no—
30#14578933—22no—
31C4×Dic157D411yescharacteristic
32C4×Dic157D411yescharacteristic
33C4×Dic157D411yescharacteristic
34C4×Dic157D411yescharacteristic
35C22×C4×C157C2×C412yes—
36C22×C4×C157C2×C411yescharacteristic
37C4⋊C4×C157—21no—
38C4⋊C4×C157—21no—
39#11929441—42no—
40#11929441—42no—
41C2×Dic157—22no—
42C2×Dic157—22no—
43C2×Dic157—24no—
44C2×Dic157—41no—
45C2×Dic157C22⋊C411yescharacteristic
46C2×Dic157C22⋊C411yescharacteristic
47C2×Dic157C2×D411yescharacteristic
48C2×Dic157C2×D411yescharacteristic
49C23×C157C22×C411yescharacteristic
50C2×C4×C157—22no—
51C2×C4×C157—22no—
52C2×C4×C157—42no—
53C2×C4×C157C22⋊C411yescharacteristic
54C2×C4×C157C22⋊C411yescharacteristic
55C22×C157—21no—
56C22×C157—21no—
57C22×C157C2×C22⋊C411yescharacteristic
58C22×C157#13112yes—
59C4×C157—21no—
60C4×C157—42no—
61C4×C157#10112yes—
62Dic157—21no—
63Dic157—21no—
64Dic157—21no—
65Dic157—21no—
66Dic157—42no—
67C2×C157—22no—
68C2×C157#40811yescharacteristic
69C2×C157#41011yescharacteristic
70C2×C157C2×#10111yescharacteristic
71C157#147011yescharacteristic, complemented, Sylow
72#1470—1571nomaximal, Sylow
73C2×#125—1571no—
74#432—1571no—
75#431—1571no—
76#324—1574no—
77#125—3141no—
78#125—3141no—
79#125—3141no—
80#125—3141no—
81C2×C4⋊C4—1572no—
82C2×C4⋊C4—1572no—
83C2×C4⋊C4—1571no—
84C2×C4⋊C4#1059784511yescharacteristic
85C2×C42—1571no—
86C4⋊C8—3141no—
87C4⋊C8—3141no—
88C22⋊C8—1572no—
89C22⋊C8—1572no—
90#97—3141no—
91C4×C8—3141no—
92C22×C4—1572no—
93C22×C4—1571no—
94C22×C4—1571no—
95C22×C4C2×#1059784512yes—
96C22×C4C2×#1059784511yescharacteristic
97C2×C8—3142no—
98C2×C8—3142no—
99C4⋊C4—21no—
100C4⋊C4—21no—
101C4⋊C4—3142no—
102C4⋊C4—3142no—
103C4⋊C4—3142no—
104C4⋊C4—3142no—
105C4⋊C4—3141no—
106C4⋊C4—3141no—
107C42—1571no—
108C42—1571no—
109C42—1571no—
110C42—1571no—
111C23C22×#1059784511yescharacteristic
112C2×C4—22no—
113C2×C4—22no—
114C2×C4—42no—
115C2×C4—3142no—
116C2×C4—3144no—
117C2×C4—3142no—
118C2×C4—6281no—
119C2×C4—1571no—
120C2×C4—1571no—
121C2×C4—1571no—
122C2×C4—1571no—
123C2×C4C22⋊#1059784511yescharacteristic
124C2×C4C22⋊#1059784511yescharacteristic
125C8—6282no—
126C8—6282no—
127C22—21no—
128C22—21no—
129C22C2×C22⋊#1059784511yescharacteristic
130C22#1909785912yes—
131C4—21no—
132C4—42no—
133C4—3141no—
134C4—3141no—
135C4—3141no—
136C4—3141no—
137C4—6282no—
138C4#1909783212yes—
139C2—22no—
140C2#2375824811yescharacteristic
141C2#2375825311yescharacteristic
142C2C2×#1909783211yescharacteristic
subgroupG/H
centerC22C2×C22⋊#10597845
commutator, prime radicalC23×C157C22×C4
FrattiniC23C22×#10597845
FittingC2×C4⋊C4×C157C4
socleC22×C157C2×C22⋊C4
cosocleC22×Dic157C23
hypercenterC2×C4⋊C4#10597845
hypocenterC157#1470
LCSG ▷ C23×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
71. C157#1470semidirect

Maximal subgroups

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

subgroupindex
#237582942
#237582902
#237581192
C2×#190977622
#1470157