Finite Group Databasebeta

← #34115119

Subgroups — #34115119

Order 20096.

168 conjugacy classes of subgroups; only the 30 normal subgroups are shown.

normal subgroups only

This group has 168 conjugacy classes of subgroups — too many to draw. Only its 30 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#23758153C211yesmaximal, characteristic, complemented
2#23758119C211yesmaximal, characteristic, complemented
3#23757191C211yesmaximal, characteristic
4C2×#14578963—21no—
5C22⋊#11929441—21no—
6C22×D628C411yescharacteristic
7C2×#14578933C2211yescharacteristic
8C2×#14578931—21no—
9C2×#14578931—21no—
10#95×C157C411yescharacteristic
11#14578963—22no—
12#14578963—41no—
13C2×#11929441—41no—
14C2×#11929441—41no—
15C23×D157—21no—
16C2×D628—41no—
17C2×D628—42no—
18C22×Dic157D411yescharacteristic
19C22×Dic157D411yescharacteristic
20#14578933—41no—
21#14578931—42no—
22#14578931—41no—
23#14578931—41no—
24C22×C4×C157—21no—
25C22×C4×C157C2×C411yescharacteristic
26#11929441—42no—
27#11929441—81no—
28C22×D157—22no—
29C22×D157—41no—
30C22×D157—41no—
31C22×D157—41no—
32C22×D157—41no—
33C22×D157—41no—
34C22×D157—41no—
35D628—42no—
36D628—42no—
37C2×Dic157—21no—
38C2×Dic157—21no—
39C2×Dic157—21no—
40C2×Dic157—41no—
41C2×Dic157D811yescharacteristic
42C2×Dic157SD1611yescharacteristic
43C23×C157C22⋊C411yescharacteristic
44C2×C4×C157—21no—
45C2×C4×C157—41no—
46C2×C4×C157—41no—
47C2×C4×C157—41no—
48C2×C4×C157—41no—
49C22×C157—21no—
50C22×C157—21no—
51C22×C157#9911yescharacteristic
52C22×C157#10211yescharacteristic
53C22×C157#10411yescharacteristic
54C2×D157—42no—
55C2×D157—42no—
56C2×D157—42no—
57C2×D157—81no—
58C2×D157—81no—
59C2×D157—81no—
60C2×D157—81no—
61C4×C157—41no—
62C4×C157—81no—
63Dic157—21no—
64Dic157—21no—
65Dic157—41no—
66C2×C157—21no—
67C2×C157—21no—
68C2×C157#32711yescharacteristic
69C2×C157AΣL(1,𝔽16)11yescharacteristic
70C2×C157#35511yescharacteristic
71D157—82no—
72C157#134511yescharacteristic, complemented, Sylow
73#1345—1571nomaximal, Sylow
74#394—1571no—
75#343—1571no—
76#324—1571no—
77C22×D4—1571no—
78C2×M16—3141no—
79C2×C4⋊C4—1571no—
80C2×C22⋊C4—3141no—
81C2×C22⋊C4—3141no—
82C22⋊C8—3141no—
83#95#1059784511yescharacteristic
84C24—3141no—
85C2×D4—6281no—
86C2×D4—6282no—
87C22×C4—21no—
88C22×C4—1571no—
89C22×C4—1571no—
90C22×C4C2×#1059784511yescharacteristic
91M16—3142no—
92M16—6281no—
93C2×C8—6281no—
94C2×C8—6281no—
95C4⋊C4—6281no—
96C22⋊C4—6282no—
97C22⋊C4—6281no—
98C22⋊C4—6281no—
99C23—3142no—
100C23—6281no—
101C23—6281no—
102C23—6281no—
103C23—6281no—
104C23—6281no—
105C23—6281no—
106C23C22⋊#1059784511yescharacteristic
107D4—6282no—
108D4—6282no—
109C2×C4—21no—
110C2×C4—41no—
111C2×C4—41no—
112C2×C4—41no—
113C2×C4—41no—
114C2×C4—3141no—
115C2×C4—3141no—
116C2×C4—3141no—
117C2×C4—6281no—
118C2×C4—1571no—
119C2×C4—1571no—
120C8—6282no—
121C8—12561no—
122C22—21no—
123C22—21no—
124C22—6282no—
125C22—6282no—
126C22—6282no—
127C22—12561no—
128C22—12561no—
129C22—12561no—
130C22—12561no—
131C22#1909783011yescharacteristic
132C22#1909783311yescharacteristic
133C22#1909783611yescharacteristic
134C4—41no—
135C4—81no—
136C4—3141no—
137C4—3141no—
138C4—6281no—
139C2—21no—
140C2—21no—
141C2—12562no—
142C2#2375812511yescharacteristic
143C2#2375817411yescharacteristic
144C2#2375818211yescharacteristic
subgroupG/H
centerC22#19097830
commutatorC22×C4×C157C2×C4
FrattiniC22×C4C2×#10597845
Fitting#95×C157C4
socleC22×C157#99
prime radicalC22×D628C4
cosocleC2×#14578933C22
hypercenter#95#10597845
hypocenterC157#1345
LCSG ▷ C22×C4×C157 ▷ C23×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4 ◁ #95

Complements

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

NH ≅ G/Ntype
1. #23758153C2semidirect
2. #23758119C2semidirect
72. C157#1345semidirect

Maximal subgroups

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

subgroupindex
#237581532
#237581192
#237571912
#1345157