Finite Group Databasebeta

← D157⋊(D4⋊C8) #34115422

Subgroups — D157⋊(D4⋊C8) #34115422

Order 20096.

344 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 344 conjugacy classes of subgroups — too many to draw. Only its 94 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⋊(C4⋊C8)C211yesmaximal, characteristic, complemented
2C4×D157⋊C8C211yesmaximal, characteristic, complemented
3#23758121C212yesmaximal, complemented
4D4⋊#11929441C212yesmaximal, complemented
5C4×D4×D157C211yesmaximal, characteristic
6C2×D157⋊C8—21no—
7C2×D157⋊C8—21no—
8#19097838—21no—
9C4⋊#11929441C2212yescomplemented
10C4×#11929441—21no—
11C4×#11929441C2212yescomplemented
12C2×D4×D157C411yescharacteristic
13C22×C4×D157—21no—
14C4×D628C411yescharacteristic
15D4×Dic157C2211yescharacteristic
16#19097733C2211yescharacteristic
17C4×C22⋊D157—21no—
18#19097731—21no—
19C4⋊C4×D157C411yescharacteristic
20C22⋊C4×D157—21no—
21C42×D157C2211yescharacteristic
22C4×D4×C157C411yescharacteristic
23D157⋊C8—24no—
24D157⋊C8—42no—
25C2×#11929441—22no—
26C2×#11929441—22no—
27C23×D157—21no—
28C2×D628C2×C411yescharacteristic
29C2×C22⋊D157—21no—
30D4×D157—22no—
31D4×D157C814yescomplemented
32C22×Dic157—21no—
33C2×C4×D157—21no—
34C2×C4×D157—21no—
35C2×C4×D157—21no—
36C2×C4×D157—42no—
37C2×C4×D157—42no—
38C2×C4×D157C2×C411yescharacteristic
39C2×C4×D157D411yescharacteristic
40C2×C4×D157D411yescharacteristic
41C4⋊Dic157C2×C411yescharacteristic
42#14578933—21no—
43C22⋊Dic157—21no—
44#14578931—21no—
45#14578931—21no—
46C4×Dic157D411yescharacteristic
47C4×Dic157D411yescharacteristic
48C4×Dic157C2311yescharacteristic
49C2×D4×C157C2×C411yescharacteristic
50C22×C4×C157—21no—
51C4⋊C4×C157C2×C411yescharacteristic
52C22⋊C4×C157—21no—
53C42×C157C2×C411yescharacteristic
54#11929441—24no—
55#11929441—42no—
56C22×D157—21no—
57C22×D157—24no—
58C22×D157—42no—
59C22×D157—42no—
60C22×D157C22⋊C411yescharacteristic
61D628—21no—
62D628C2×C812yescomplemented
63C22⋊D157—24no—
64C2×Dic157—21no—
65C2×Dic157—41no—
66C2×Dic157—41no—
67C2×Dic157C22⋊C411yescharacteristic
68C2×Dic157C2×D411yescharacteristic
69C2×Dic157C2×D411yescharacteristic
70C4×D157—22no—
71C4×D157—42no—
72C4×D157—42no—
73C4×D157—41no—
74C4×D157—41no—
75C4×D157C2×C812yes—
76C4×D157M1612yes—
77C4×D157D812yes—
78C4×D157SD1612yes—
79C23×C157—21no—
80D4×C157—21no—
81D4×C157C2×C812yescomplemented
82C2×C4×C157—21no—
83C2×C4×C157—42no—
84C2×C4×C157C22⋊C411yescharacteristic
85C2×C4×C157C22⋊C411yescharacteristic
86C2×C4×C157C22×C411yescharacteristic
87C22×C157—22no—
88C22×C157—41no—
89C22×C157—41no—
90C22×C157C2×C22⋊C411yescharacteristic
91C2×D157—22no—
92C2×D157—41no—
93C2×D157—41no—
94C2×D157—48no—
95C2×D157C22⋊C812yes—
96C2×D157#10212yes—
97C2×D157#10412yes—
98C4×C157—21no—
99C4×C157—41no—
100C4×C157#10212yes—
101C4×C157C22×C811yescharacteristic
102C4×C157C2×M1611yescharacteristic
103Dic157—21no—
104Dic157—41no—
105Dic157C22⋊C812yes—
106Dic157C2×D811yescharacteristic
107Dic157C2×SD1611yescharacteristic
108C2×C157—42no—
109C2×C157C2×C22⋊C811yescharacteristic
110C2×C157C2×#10211yescharacteristic
111C2×C157C2×#10411yescharacteristic
112D157—42no—
113D157D4⋊C814yescomplemented
114C157C2×D4⋊C811yescharacteristic, complemented, Sylow
115C2×D4⋊C8—1571nomaximal, Sylow
116C2×C4×D4—1571no—
117C2×C4⋊C8—1571no—
118C2×C4×C8—1571no—
119D4⋊C8—1572no—
120D4⋊C8—1572no—
121C22×D4—1571no—
122C23×C4—3141no—
123C22×C8—3141no—
124C22×C8—3141no—
125C4×D4—3141no—
126C4×D4—3141no—
127C4×D4—1571no—
128C4×D4—1571no—
129C4×D4—1571no—
130C4×D4#1059784511yescharacteristic
131C2×C4⋊C4—1571no—
132C2×C22⋊C4—3141no—
133C2×C42—1571no—
134C4⋊C8—3141no—
135C4⋊C8—1572no—
136C4×C8—3141no—
137C4×C8—1572no—
138C24—3141no—
139C2×D4—3142no—
140C2×D4—3141no—
141C2×D4—1574no—
142C2×D4—1571no—
143C2×D4C2×#1059784511yescharacteristic
144C22×C4—21no—
145C22×C4—3141no—
146C22×C4—3141no—
147C22×C4—3141no—
148C22×C4—3141no—
149C22×C4—6282no—
150C22×C4—6282no—
151C22×C4—1571no—
152C22×C4—1571no—
153C22×C4—1571no—
154C2×C8—3144no—
155C2×C8—3142no—
156C2×C8—3142no—
157C2×C8—6282no—
158C4⋊C4—3141no—
159C4⋊C4—1571no—
160C4⋊C4C2×#1059784511yescharacteristic
161C22⋊C4—21no—
162C22⋊C4—3141no—
163C22⋊C4—3141no—
164C22⋊C4—3141no—
165C42—1571no—
166C42—1571no—
167C42—1571no—
168C42C2×#1059784511yescharacteristic
169C23—21no—
170C23—3144no—
171C23—3141no—
172C23—6282no—
173C23—6282no—
174C23—1571no—
175D4—21no—
176D4—3144no—
177D4—3141no—
178D4—1572no—
179D4D157⋊C812yescomplemented
180C2×C4—21no—
181C2×C4—42no—
182C2×C4—3142no—
183C2×C4—3141no—
184C2×C4—6282no—
185C2×C4—6281no—
186C2×C4—6281no—
187C2×C4—6281no—
188C2×C4—6281no—
189C2×C4—6282no—
190C2×C4—1571no—
191C2×C4—1571no—
192C2×C4—1571no—
193C2×C4—1572no—
194C2×C4—1572no—
195C2×C4—1572no—
196C2×C4—1572no—
197C2×C4C22⋊#1059784511yescharacteristic
198C2×C4C22⋊#1059784511yescharacteristic
199C2×C4C22×#1059784511yescharacteristic
200C8—3144no—
201C8—6282no—
202C22—22no—
203C22—41no—
204C22—41no—
205C22—3142no—
206C22—6288no—
207C22—6281no—
208C22—6281no—
209C22—1572no—
210C22—1572no—
211C22—1572no—
212C22C2×C22⋊#1059784511yescharacteristic
213C4—21no—
214C4—41no—
215C4—3141no—
216C4—6281no—
217C4—1572no—
218C4—1571no—
219C4—1571no—
220C4#1909783312yes—
221C4C2×D157⋊C811yescharacteristic
222C4D157⋊M1611yescharacteristic
223C2—42no—
224C2—6282no—
225C2—1574no—
226C2D157⋊(C22⋊C8)11yescharacteristic
227C2C2×#1909783311yescharacteristic
228C2D157⋊#10411yescharacteristic
subgroupG/H
centerC2×C4C22⋊#10597845
commutatorC4×C157C22×C8
FrattiniC2×C4C22×#10597845
FittingC4×D4×C157C4
socleC22×C157C2×C22⋊C4
prime radicalC2×D4×D157C4
cosocleC4×Dic157C23
hypercenterC4×D4#10597845
hypocenterC157C2×D4⋊C8
LCSG ▷ C4×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. D157⋊(C4⋊C8)C2semidirect
2. C4×D157⋊C8C2semidirect
3. #23758121C2semidirect
4. D4⋊#11929441C2semidirect
9. C4⋊#11929441C22semidirect
11. C4×#11929441C22semidirect
31. D4×D157C8semidirect
62. D628C2×C8semidirect
81. D4×C157C2×C8semidirect
113. D157D4⋊C8semidirect
114. C157C2×D4⋊C8semidirect
179. D4D157⋊C8semidirect

Maximal subgroups

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

subgroupindex
D157⋊(C4⋊C8)2
C4×D157⋊C82
#237581212
D4⋊#119294412
C4×D4×D1572
C2×D4⋊C8157