Finite Group Databasebeta

← #34115413

Subgroups — #34115413

Order 20096.

322 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 322 conjugacy classes of subgroups — too many to draw. Only its 64 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#23758244C211yesmaximal, characteristic, complemented
2D157⋊(C22⋊C8)C211yesmaximal, characteristic, complemented
3#23758117C214yesmaximal, complemented
4C2×#19097746C211yesmaximal, characteristic
5C2×#14578964—21no—
6C2×D157⋊C8—21no—
7#19097828—21no—
8#19097828—21no—
9C22⋊#11929441C2212yes—
10C22⋊#11929441C2212yes—
11C22×D628C412yes—
12C22×D628C411yescharacteristic
13C22×C4×D157C2211yescharacteristic
14#19097746—21no—
15#19097746—21no—
16#19097746—21no—
17#19097746—21no—
18C2×#14578931C2212yes—
19C2×C4⋊C4×C157C411yescharacteristic
20#14578964—42no—
21D157⋊C8—42no—
22C2×#11929441—22no—
23C2×#11929441—22no—
24C23×D157C2×C411yescharacteristic
25C23×D157C2×C412yes—
26C2×D628—22no—
27C2×D628—22no—
28C2×D628—21no—
29C2×D628—21no—
30C2×D628—42no—
31C2×D628—44no—
32C22×Dic157C2311yescharacteristic
33C2×C4×D157—42no—
34C2×C4×D157D411yescharacteristic
35C2×C4×D157D411yescharacteristic
36C2×C4×D157D411yescharacteristic
37C2×C4×D157D411yescharacteristic
38#14578931—22no—
39#14578931—22no—
40C22×C4×C157C2×C412yes—
41C22×C4×C157C2×C411yescharacteristic
42C4⋊C4×C157—21no—
43C4⋊C4×C157—21no—
44#11929441—42no—
45#11929441—42no—
46C22×D157—22no—
47C22×D157—22no—
48C22×D157—22no—
49C22×D157—24no—
50C22×D157—41no—
51C22×D157—42no—
52C22×D157—42no—
53C22×D157C22⋊C411yescharacteristic
54C22×D157C22⋊C411yescharacteristic
55D628—42no—
56D628—44no—
57D628—44no—
58D628—42no—
59C2×Dic157—41no—
60C2×Dic157C2×D411yescharacteristic
61C2×Dic157C2×D411yescharacteristic
62C4×D157—22no—
63C4×D157—22no—
64C4×D157—41no—
65C4×D157—41no—
66C23×C157C22×C411yescharacteristic
67C2×C4×C157—22no—
68C2×C4×C157—22no—
69C2×C4×C157—42no—
70C2×C4×C157C22⋊C411yescharacteristic
71C2×C4×C157C22⋊C411yescharacteristic
72C22×C157—21no—
73C22×C157—21no—
74C22×C157C2×C22⋊C411yescharacteristic
75C22×C157#13112yes—
76C2×D157—21no—
77C2×D157—21no—
78C2×D157—21no—
79C2×D157—21no—
80C2×D157—21no—
81C2×D157—44no—
82C2×D157—42no—
83C2×D157—42no—
84C2×D157—42no—
85C2×D157—84no—
86C2×D157#10012yes—
87C4×C157—21no—
88C4×C157—42no—
89C4×C157#9912yes—
90Dic157—21no—
91Dic157—21no—
92C2×C157—22no—
93C2×C157#40811yescharacteristic
94C2×C157C2×#9911yescharacteristic
95C2×C157C2×#10011yescharacteristic
96D157—22no—
97D157—41no—
98D157—82no—
99C157#147111yescharacteristic, complemented, Sylow
100#1471—1571nomaximal, Sylow
101C2×#121—1571no—
102#407—1571no—
103C2×C22⋊C8—1571no—
104#323—1574no—
105C22×D4—1572no—
106C22×D4—1571no—
107C23×C4—1571no—
108C2×M16—3141no—
109C22×C8—3141no—
110#121—3141no—
111#121—3141no—
112#121—3141no—
113#121—3141no—
114C2×C4⋊C4#1059784511yescharacteristic
115C2×C22⋊C4—1572no—
116C22⋊C8—3141no—
117C22⋊C8—3141no—
118C22⋊C8—1572no—
119C22⋊C8—1572no—
120C24—1571no—
121C24—1572no—
122C2×D4—3142no—
123C2×D4—3142no—
124C2×D4—3141no—
125C2×D4—3141no—
126C2×D4—6282no—
127C2×D4—6284no—
128C22×C4—6282no—
129C22×C4—1571no—
130C22×C4—1571no—
131C22×C4—1571no—
132C22×C4—1571no—
133C22×C4—1571no—
134C22×C4C2×#1059784512yes—
135C22×C4C2×#1059784511yescharacteristic
136M16—6282no—
137C2×C8—3142no—
138C2×C8—3142no—
139C2×C8—6282no—
140C4⋊C4—21no—
141C4⋊C4—21no—
142C22⋊C4—3142no—
143C22⋊C4—3142no—
144C23—3142no—
145C23—3142no—
146C23—3142no—
147C23—3144no—
148C23—6281no—
149C23—6282no—
150C23—6282no—
151C23—1571no—
152C23—1571no—
153C23C22×#1059784511yescharacteristic
154D4—6282no—
155D4—6284no—
156D4—6284no—
157D4—6282no—
158C2×C4—22no—
159C2×C4—22no—
160C2×C4—42no—
161C2×C4—3142no—
162C2×C4—3142no—
163C2×C4—6281no—
164C2×C4—6281no—
165C2×C4—6281no—
166C2×C4—1571no—
167C2×C4—1571no—
168C2×C4C22⋊#1059784511yescharacteristic
169C2×C4C22⋊#1059784511yescharacteristic
170C8—6282no—
171C8—6282no—
172C22—21no—
173C22—21no—
174C22—3141no—
175C22—3141no—
176C22—3141no—
177C22—3141no—
178C22—3141no—
179C22—6284no—
180C22—6282no—
181C22—6282no—
182C22—6282no—
183C22—1572no—
184C22—12564no—
185C22C2×C22⋊#1059784511yescharacteristic
186C22#1909785912yes—
187C4—21no—
188C4—42no—
189C4—3141no—
190C4—3141no—
191C4#1909783012yes—
192C2—22no—
193C2—3142no—
194C2—6281no—
195C2—12562no—
196C2#2375824811yescharacteristic
197C2C2×#1909783011yescharacteristic
198C2D157⋊#10011yescharacteristic
subgroupG/H
centerC22C2×C22⋊#10597845
commutatorC23×C157C22×C4
FrattiniC23C22×#10597845
FittingC2×C4⋊C4×C157C4
socleC22×C157C2×C22⋊C4
prime radicalC2×#19097746C2
cosocleC22×Dic157C23
hypercenterC2×C4⋊C4#10597845
hypocenterC157#1471
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
1. #23758244C2semidirect
2. D157⋊(C22⋊C8)C2semidirect
3. #23758117C2semidirect
99. C157#1471semidirect

Maximal subgroups

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

subgroupindex
#237582442
D157⋊(C22⋊C8)2
#237581172
C2×#190977462
#1471157