Finite Group Databasebeta

← D157⋊#324 #34115365

Subgroups — D157⋊#324 #34115365

Order 20096.

328 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 328 conjugacy classes of subgroups — too many to draw. Only its 84 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)C212yesmaximal
2#23758119C212yesmaximal, complemented
3#23758118C212yesmaximal, complemented
4C2×C4⋊C4×D157C211yesmaximal, characteristic
5C2×D157⋊C8—22no—
6#19097828—22no—
7C22⋊#11929441C2214yes—
8C22×C4×D157C411yescharacteristic
9C22×C4×D157C411yescharacteristic
10C22×C4×D157C2211yescharacteristic
11C2×C4⋊Dic157C2211yescharacteristic
12C2×#14578933C411yescharacteristic
13C2×#14578933C2211yescharacteristic
14C4⋊C4×D157—22no—
15C4⋊C4×D157—22no—
16C2×C4⋊C4×C157C411yescharacteristic
17D157⋊C8—44no—
18C2×#11929441—24no—
19C23×D157C2×C411yescharacteristic
20C22×Dic157C2×C411yescharacteristic
21C22×Dic157C2×C411yescharacteristic
22C22×Dic157C2311yescharacteristic
23C2×C4×D157—21no—
24C2×C4×D157—21no—
25C2×C4×D157—22no—
26C2×C4×D157—21no—
27C2×C4×D157—21no—
28C2×C4×D157—42no—
29C2×C4×D157—42no—
30C2×C4×D157C814yescomplemented
31C2×C4×D157D412yes—
32C2×C4×D157D412yes—
33C4⋊Dic157—22no—
34#14578933—22no—
35#14578933—22no—
36C22×C4×C157C2×C411yescharacteristic
37C22×C4×C157C2×C411yescharacteristic
38C22×C4×C157C2×C411yescharacteristic
39C4⋊C4×C157—22no—
40#11929441—44no—
41C22×D157—22no—
42C22×D157—22no—
43C22×D157C22⋊C411yescharacteristic
44C22×D157C22⋊C411yescharacteristic
45C22×D157C2×C812yes—
46C22×D157M1612yes—
47C2×Dic157—21no—
48C2×Dic157—21no—
49C2×Dic157—21no—
50C2×Dic157—41no—
51C2×Dic157—41no—
52C2×Dic157C2×C812yescomplemented
53C2×Dic157C2×D412yes—
54C4×D157—24no—
55C4×D157—24no—
56C4×D157—24no—
57C4×D157—42no—
58C4×D157—42no—
59C4×D157—42no—
60C23×C157C22×C411yescharacteristic
61C2×C4×C157—21no—
62C2×C4×C157—21no—
63C2×C4×C157—21no—
64C2×C4×C157—41no—
65C2×C4×C157—41no—
66C2×C4×C157C22⋊C412yes—
67C2×C4×C157C2×C812yescomplemented
68C22×C157—21no—
69C22×C157—21no—
70C22×C157C2×C22⋊C411yescharacteristic
71C22×C157C22×C811yescharacteristic
72C22×C157C2×M1611yescharacteristic
73C2×D157—21no—
74C2×D157—21no—
75C2×D157—24no—
76C2×D157—24no—
77C2×D157C22⋊C812yes—
78C2×D157C22⋊C812yes—
79C2×D157#9912yes—
80C2×D157#10112yes—
81C4×C157—22no—
82C4×C157—22no—
83C4×C157—41no—
84Dic157—22no—
85Dic157—22no—
86Dic157—41no—
87C2×C157—21no—
88C2×C157—21no—
89C2×C157C2×C22⋊C811yescharacteristic
90C2×C157C2×#9911yescharacteristic
91C2×C157C2×#10111yescharacteristic
92D157—22no—
93D157#32414yescomplemented
94C157C2×#32411yescharacteristic, complemented, Sylow
95C2×#324—1571nomaximal, Sylow
96C22×C4⋊C4—1571no—
97C2×C22⋊C8—1572no—
98#324—1572no—
99#324—1572no—
100C23×C4—1571no—
101C23×C4—1571no—
102C23×C4—1571no—
103C22×C8—3142no—
104C2×C4⋊C4—3142no—
105C2×C4⋊C4—3142no—
106C2×C4⋊C4—1571no—
107C2×C4⋊C4—1571no—
108C2×C4⋊C4—1571no—
109C2×C4⋊C4#1059784511yescharacteristic
110C22⋊C8—3142no—
111C22⋊C8—1574no—
112C24—1571no—
113C22×C4—3141no—
114C22×C4—3141no—
115C22×C4—3142no—
116C22×C4—3141no—
117C22×C4—3141no—
118C22×C4—6282no—
119C22×C4—6282no—
120C22×C4—1571no—
121C22×C4—1572no—
122C22×C4—1574no—
123C22×C4—1571no—
124C22×C4—1571no—
125C22×C4—1572no—
126C22×C4C2×#1059784511yescharacteristic
127C22×C4C2×#1059784511yescharacteristic
128C22×C4C2×#1059784511yescharacteristic
129C2×C8—3144no—
130C2×C8—6284no—
131C4⋊C4—22no—
132C4⋊C4—3142no—
133C4⋊C4—3142no—
134C4⋊C4—3142no—
135C23—3142no—
136C23—3142no—
137C23—1572no—
138C23—1571no—
139C23—1572no—
140C23—1571no—
141C23C22×#1059784511yescharacteristic
142C2×C4—21no—
143C2×C4—21no—
144C2×C4—21no—
145C2×C4—41no—
146C2×C4—41no—
147C2×C4—3144no—
148C2×C4—3144no—
149C2×C4—3144no—
150C2×C4—3141no—
151C2×C4—3141no—
152C2×C4—3141no—
153C2×C4—6282no—
154C2×C4—6282no—
155C2×C4—6282no—
156C2×C4—6281no—
157C2×C4—6281no—
158C2×C4—1572no—
159C2×C4—1572no—
160C2×C4C22⋊#1059784512yes—
161C2×C4D157⋊C812yescomplemented
162C8—6284no—
163C22—21no—
164C22—21no—
165C22—3144no—
166C22—3144no—
167C22—3141no—
168C22—3141no—
169C22—1572no—
170C22—1572no—
171C22—1572no—
172C22—1572no—
173C22C2×C22⋊#1059784511yescharacteristic
174C22C2×D157⋊C811yescharacteristic
175C22D157⋊M1611yescharacteristic
176C4—22no—
177C4—22no—
178C4—41no—
179C4—3142no—
180C4—3142no—
181C4—6281no—
182C2—21no—
183C2—21no—
184C2—3142no—
185C2—1574no—
186C2D157⋊(C22⋊C8)11yescharacteristic
187C2D157⋊#9911yescharacteristic
188C2D157⋊#10111yescharacteristic
subgroupG/H
centerC22C2×C22⋊#10597845
commutatorC22×C157C22×C8
FrattiniC23C22×#10597845
FittingC2×C4⋊C4×C157C4
socleC22×C157C2×C22⋊C4
prime radicalC23×D157C2×C4
cosocleC22×Dic157C23
hypercenterC2×C4⋊C4#10597845
hypocenterC157C2×#324
LCSG ▷ C22×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
2. #23758119C2semidirect
3. #23758118C2semidirect
30. C2×C4×D157C8semidirect
52. C2×Dic157C2×C8semidirect
67. C2×C4×C157C2×C8semidirect
93. D157#324semidirect
94. C157C2×#324semidirect
161. C2×C4D157⋊C8semidirect

Maximal subgroups

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

subgroupindex
D157⋊(C22⋊C8)2
#237581192
#237581182
C2×C4⋊C4×D1572
C2×#324157