Finite Group Databasebeta

← #34114998

Subgroups — #34114998

Order 20096.

228 conjugacy classes of subgroups; only the 54 normal subgroups are shown.

normal subgroups only

This group has 228 conjugacy classes of subgroups — too many to draw. Only its 54 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#23757132C211yesmaximal, characteristic
4C2×D157⋊C8C412yescomplemented
5C2×C4⋊#10597845—21no—
6C2×C22⋊#10597845—21no—
7#19097828—21no—
8C22⋊#11929441—21no—
9(C2×#10597845)⋊C4C412yescomplemented
10C22×C4×D157C2211yescharacteristic
11C2×#14578933—21no—
12C2×#14578931—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—42no—
25C2×C4×D157C2×C411yescharacteristic
26C2×C4×D157C2×C411yescharacteristic
27C2×C4×D157D411yescharacteristic
28C2×C4×D157Q811yescharacteristic
29#14578933—42no—
30#14578931—41no—
31#14578931—41no—
32C22×C4×C157—21no—
33C22×C4×C157C2×C411yescharacteristic
34C2×#10597845—42no—
35C2×#10597845—42no—
36C2×#10597845—42no—
37#11929441—42no—
38C22×D157—41no—
39C22×D157—41no—
40C22×D157C22⋊C411yescharacteristic
41C22×D157C4⋊C411yescharacteristic
42C22×D157D811yescharacteristic
43C22×D157SD1611yescharacteristic
44C22×D157SD1611yescharacteristic
45C22×D157Q1611yescharacteristic
46C2×Dic157—22no—
47C2×Dic157—41no—
48C2×Dic157—41no—
49C2×Dic157—41no—
50C2×Dic157C22⋊C411yescharacteristic
51C2×Dic157C4⋊C411yescharacteristic
52C4×D157—22no—
53C4×D157—22no—
54C4×D157—41no—
55C4×D157—41no—
56C23×C157C22⋊C411yescharacteristic
57C2×C4×C157—41no—
58C2×C4×C157—41no—
59C2×C4×C157—41no—
60C2×C4×C157—41no—
61C2×C4×C157C4211yescharacteristic
62C2×C4×C157C4⋊C411yescharacteristic
63C22×C157—21no—
64C22×C157—21no—
65C22×C157#9511yescharacteristic
66C22×C157#10211yescharacteristic
67C22×C157#10311yescharacteristic
68C2×D157—21no—
69C2×D157—21no—
70C2×D157—21no—
71C2×D157—21no—
72C2×D157—41no—
73C2×D157—41no—
74C2×D157—41no—
75C2×D157—41no—
76C2×D157#10211yescharacteristic
77C2×D157#10311yescharacteristic
78C2×D157#10611yescharacteristic
79C2×D157#10711yescharacteristic
80#10597845—82no—
81C4×C157—21no—
82C4×C157—21no—
83C4×C157—81no—
84Dic157—21no—
85Dic157—81no—
86Dic157#9912yes—
87C2×C157—21no—
88C2×C157—21no—
89C2×C157H(3,ℤ/4)11yescharacteristic
90C2×C157#34011yescharacteristic
91C2×C157#34211yescharacteristic
92D157—21no—
93D157—21no—
94D157—21no—
95D157—21no—
96C157#128911yescharacteristic, complemented, Sylow
97#1289—1571nomaximal, Sylow
98C2×C22⋊C8—1571no—
99#380—1571no—
100#380—1571no—
101C23×C4—1571no—
102C22×C8—1572no—
103C2×C4⋊C4—3141no—
104C2×C4⋊C4—3141no—
105C2×C22⋊C4—3141no—
106C2×C22⋊C4—3141no—
107C22⋊C8—3141no—
108C22⋊C8—3141no—
109#95—1572no—
110#95—1571no—
111#95#1059784511yescharacteristic, complemented
112C24—1571no—
113C22×C4—21no—
114C22×C4—3142no—
115C22×C4—3141no—
116C22×C4—6282no—
117C22×C4—1571no—
118C22×C4—1571no—
119C22×C4—1571no—
120C22×C4—1571no—
121C22×C4—1571no—
122C22×C4C2×#1059784511yescharacteristic
123C2×C8—3142no—
124C2×C8—6282no—
125C4⋊C4—6282no—
126C4⋊C4—6282no—
127C22⋊C4—6281no—
128C22⋊C4—6281no—
129C22⋊C4—6281no—
130C22⋊C4—6281no—
131C23—6281no—
132C23—6281no—
133C23—1571no—
134C23—1571no—
135C23—1571no—
136C23—1571no—
137C23—1571no—
138C23—1571no—
139C23C22⋊#1059784511yescharacteristic
140C2×C4—41no—
141C2×C4—41no—
142C2×C4—41no—
143C2×C4—41no—
144C2×C4—3142no—
145C2×C4—3142no—
146C2×C4—3142no—
147C2×C4—6281no—
148C2×C4—6281no—
149C2×C4—6281no—
150C2×C4—6281no—
151C2×C4—6282no—
152C2×C4—6282no—
153C2×C4—6282no—
154C2×C4—6281no—
155C2×C4—1571no—
156C2×C4—1571no—
157C2×C4C4×#1059784511yescharacteristic
158C2×C4C4⋊#1059784511yescharacteristic
159C8—6282no—
160C22—21no—
161C22—21no—
162C22—3141no—
163C22—3141no—
164C22—3141no—
165C22—3141no—
166C22—6281no—
167C22—6281no—
168C22—6281no—
169C22—6281no—
170C22—1571no—
171C22—1571no—
172C22—1571no—
173C22—1571no—
174C22(C2×#10597845)⋊C411yescharacteristic
175C22#1909783311yescharacteristic
176C22#1909783411yescharacteristic
177C4—21no—
178C4—21no—
179C4—81no—
180C4—3141no—
181C4—1572no—
182C4—12561no—
183C4—12562no—
184C2—21no—
185C2—21no—
186C2—3141no—
187C2—3141no—
188C2—3141no—
189C2—3141no—
190C2#2375814011yescharacteristic
191C2#2375814611yescharacteristic
192C2#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#1289
LCSG ▷ C2×C4×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C22 ◁ C22×C4 ◁ #95

Complements

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

NH ≅ G/Ntype
4. C2×D157⋊C8C4semidirect
9. (C2×#10597845)⋊C4C4semidirect
13. #19097678C4semidirect
14. #95×C157C4semidirect
96. C157#1289semidirect
111. #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
#237571322
#1289157