Finite Group Databasebeta

← #34115010

Subgroups — #34115010

Order 20096.

276 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 276 conjugacy classes of subgroups — too many to draw. Only its 60 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
1D157⋊(C22⋊C8)C211yesmaximal, characteristic
2#23758215C211yesmaximal, characteristic
3#95×D157C211yesmaximal, characteristic
4C2×D157⋊C8—21no—
5C2×C4⋊#10597845C412yescomplemented
6C2×C22⋊#10597845—21no—
7#19097828C412yescomplemented
8C22⋊#11929441—21no—
9(C2×#10597845)⋊C4—21no—
10C22×C4×D157—21no—
11C22×C4×D157C2211yescharacteristic
12#19097678—21no—
13#19097678C411yescharacteristic, complemented
14#95×C157C411yescharacteristic, complemented
15C22×#10597845—22no—
16D157⋊C8—42no—
17C2×#11929441—22no—
18C4⋊#10597845—42no—
19C22⋊#10597845—41no—
20C22⋊#10597845—41no—
21C23×D157D411yescharacteristic
22C22×Dic157—21no—
23C22×Dic157D411yescharacteristic
24C2×C4×D157—24no—
25C2×C4×D157—42no—
26C2×C4×D157—42no—
27C2×C4×D157—41no—
28C2×C4×D157—41no—
29C2×C4×D157C2×C411yescharacteristic
30C2×C4×D157C2×C411yescharacteristic
31C2×C4×D157D411yescharacteristic
32C2×C4×D157Q811yescharacteristic
33C22×C4×C157—21no—
34C22×C4×C157C2×C411yescharacteristic
35C2×#10597845—42no—
36C2×#10597845—42no—
37C2×#10597845—42no—
38#11929441—42no—
39C22×D157—22no—
40C22×D157—22no—
41C22×D157C22⋊C411yescharacteristic
42C22×D157C4⋊C411yescharacteristic
43C22×D157D811yescharacteristic
44C22×D157SD1611yescharacteristic
45C22×D157SD1611yescharacteristic
46C22×D157Q1611yescharacteristic
47C2×Dic157—22no—
48C2×Dic157—41no—
49C2×Dic157—41no—
50C2×Dic157—41no—
51C2×Dic157C22⋊C411yescharacteristic
52C2×Dic157C4⋊C411yescharacteristic
53C4×D157—22no—
54C4×D157—22no—
55C4×D157—41no—
56C4×D157—41no—
57C4×D157—44no—
58C4×D157—44no—
59C23×C157C22⋊C411yescharacteristic
60C2×C4×C157—22no—
61C2×C4×C157—41no—
62C2×C4×C157—41no—
63C2×C4×C157—41no—
64C2×C4×C157C4211yescharacteristic
65C2×C4×C157C4⋊C411yescharacteristic
66C22×C157—21no—
67C22×C157—21no—
68C22×C157#9511yescharacteristic
69C22×C157#10211yescharacteristic
70C22×C157#10311yescharacteristic
71C2×D157—21no—
72C2×D157—21no—
73C2×D157—22no—
74C2×D157—22no—
75C2×D157—22no—
76C2×D157—22no—
77C2×D157#9912yes—
78C2×D157#10211yescharacteristic
79C2×D157#10311yescharacteristic
80C2×D157#10412yes—
81C2×D157#10611yescharacteristic
82C2×D157#10711yescharacteristic
83#10597845—82no—
84C4×C157—21no—
85C4×C157—21no—
86C4×C157—42no—
87Dic157—21no—
88Dic157—21no—
89Dic157—42no—
90C2×C157—21no—
91C2×C157—21no—
92C2×C157#33911yescharacteristic
93C2×C157#34011yescharacteristic
94C2×C157#34211yescharacteristic
95D157—21no—
96D157—21no—
97D157#32712yes—
98D157#32812yes—
99C157#129411yescharacteristic, complemented, Sylow
100#1294—1571nomaximal, Sylow
101C2×C22⋊C8—1571no—
102#380—1571no—
103C2×#95—1571no—
104C23×C4—3141no—
105C23×C4—1571no—
106C22×C8—3141no—
107C2×C4⋊C4—1572no—
108C2×C22⋊C4—3141no—
109C22⋊C8—3141no—
110C22⋊C8—1572no—
111#95—3141no—
112#95—3141no—
113#95—1571no—
114#95#1059784511yescharacteristic, complemented
115C24—1571no—
116C22×C4—21no—
117C22×C4—3144no—
118C22×C4—3141no—
119C22×C4—3142no—
120C22×C4—6282no—
121C22×C4—6282no—
122C22×C4—6281no—
123C22×C4—6281no—
124C22×C4—1571no—
125C22×C4—1571no—
126C22×C4—1571no—
127C22×C4—1571no—
128C22×C4—1571no—
129C22×C4C2×#1059784511yescharacteristic
130C2×C8—3142no—
131C2×C8—6282no—
132C4⋊C4—6282no—
133C22⋊C4—6281no—
134C22⋊C4—6281no—
135C23—3142no—
136C23—3142no—
137C23—1571no—
138C23—1571no—
139C23—1571no—
140C23—1571no—
141C23—1571no—
142C23—1571no—
143C23C22⋊#1059784511yescharacteristic
144C2×C4—22no—
145C2×C4—41no—
146C2×C4—41no—
147C2×C4—41no—
148C2×C4—3142no—
149C2×C4—3142no—
150C2×C4—3142no—
151C2×C4—6281no—
152C2×C4—6281no—
153C2×C4—6284no—
154C2×C4—6284no—
155C2×C4—6281no—
156C2×C4—6281no—
157C2×C4—6281no—
158C2×C4—6282no—
159C2×C4—6282no—
160C2×C4—6282no—
161C2×C4—1571no—
162C2×C4—1571no—
163C2×C4C4×#1059784511yescharacteristic
164C2×C4C4⋊#1059784511yescharacteristic
165C8—6282no—
166C22—21no—
167C22—21no—
168C22—3142no—
169C22—3142no—
170C22—3142no—
171C22—3142no—
172C22—3141no—
173C22—3141no—
174C22—1571no—
175C22—1571no—
176C22—1572no—
177C22—1571no—
178C22—1571no—
179C22—1572no—
180C22(C2×#10597845)⋊C411yescharacteristic
181C22#1909783311yescharacteristic
182C22#1909783411yescharacteristic
183C4—21no—
184C4—21no—
185C4—42no—
186C4—3141no—
187C4—3141no—
188C4—6282no—
189C4—12562no—
190C2—21no—
191C2—21no—
192C2—3141no—
193C2—3141no—
194C2—1572no—
195C2—1572no—
196C2#2375814411yescharacteristic
197C2#2375814611yescharacteristic
198C2#2375815011yescharacteristic
subgroupG/H
centerC22(C2×#10597845)⋊C4
commutatorC2×C4×C157C42
FrattiniC22×C4C2×#10597845
Fitting#95×C157C4
socleC22×C157#95
prime radicalC23×D157D4
cosocleC22×C4×D157C22
hypercenter#95#10597845
hypocenterC157#1294
LCSG ▷ C2×C4×C157 ▷ C22×C157 ▷ C157
UCSC1 ◁ C22 ◁ C22×C4 ◁ #95

Complements

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

NH ≅ G/Ntype
5. C2×C4⋊#10597845C4semidirect
7. #19097828C4semidirect
13. #19097678C4semidirect
14. #95×C157C4semidirect
99. C157#1294semidirect
114. #95#10597845semidirect

Maximal subgroups

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

subgroupindex
D157⋊(C22⋊C8)2
#237582152
#95×D1572
#1294157