Finite Group Databasebeta

← #34115429

Subgroups — #34115429

Order 20096.

276 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 276 conjugacy classes of subgroups — too many to draw. Only its 86 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#23758289C211yesmaximal, characteristic, complemented
2C2×C4×#11929441C211yesmaximal, characteristic, complemented
3#23758123C212yesmaximal, complemented
4#23758121C212yesmaximal, complemented
5#23757741C211yesmaximal, characteristic
6C22×#11929441—21no—
7C4⋊#11929441C2212yes—
8C22⋊#11929441—21no—
9C4×#11929441—21no—
10C4×#11929441—21no—
11C4×#11929441C2212yes—
12C2×#14578954C411yescharacteristic
13#19097736C411yescharacteristic
14#19097736C2211yescharacteristic
15#19097733C411yescharacteristic
16#19097733C2211yescharacteristic
17#19097731—21no—
18#19097731—21no—
19#19097728—21no—
20C2×C4×Dic157C2211yescharacteristic
21C42×D157—21no—
22#117×C157C411yescharacteristic
23C2×#11929441—24no—
24C2×#11929441—22no—
25C2×#11929441—22no—
26#14578954—22no—
27#14578954C814yescomplemented
28C2×Dic314C2×C411yescharacteristic
29C2×D628C2×C411yescharacteristic
30C2×C22⋊D157—21no—
31C22×Dic157D411yescharacteristic
32C22×Dic157D411yescharacteristic
33C2×C4×D157—21no—
34C2×C4×D157—21no—
35C2×C4×D157—21no—
36#14578933—21no—
37#14578933—21no—
38#14578931—21no—
39#14578931—21no—
40C4×Dic157—21no—
41C4×Dic157—21no—
42C4×Dic157C2×C411yescharacteristic
43C4×Dic157D411yescharacteristic
44C4×Dic157D411yescharacteristic
45C4×Dic157C2311yescharacteristic
46C22×C4×C157C2×C411yescharacteristic
47C4⋊C4×C157C2×C411yescharacteristic
48C4⋊C4×C157C2×C411yescharacteristic
49C22⋊C4×C157—21no—
50C42×C157—21no—
51#11929441—24no—
52#11929441—42no—
53C22×D157—21no—
54Dic314—21no—
55Dic314C2×C812yescomplemented
56D628—21no—
57D628C2×C812yescomplemented
58C22⋊D157—24no—
59C2×Dic157—21no—
60C2×Dic157—22no—
61C2×Dic157—22no—
62C2×Dic157C22⋊C411yescharacteristic
63C2×Dic157C22⋊C411yescharacteristic
64C2×Dic157C2×D411yescharacteristic
65C2×Dic157C2×D411yescharacteristic
66C4×D157—24no—
67C4×D157—42no—
68C4×D157—42no—
69C23×C157C22⋊C411yescharacteristic
70C2×C4×C157—21no—
71C2×C4×C157—21no—
72C2×C4×C157C22⋊C411yescharacteristic
73C2×C4×C157C2×C812yes—
74C2×C4×C157M1612yes—
75C2×C4×C157C22×C411yescharacteristic
76C22×C157—21no—
77C22×C157—21no—
78C22×C157C22⋊C812yes—
79C22×C157C2×C22⋊C411yescharacteristic
80C2×D157—22no—
81C2×D157—41no—
82C2×D157—41no—
83C4×C157—41no—
84C4×C157—41no—
85C4×C157C22⋊C812yes—
86C4×C157C22×C811yescharacteristic
87C4×C157C2×M1611yescharacteristic
88Dic157—22no—
89Dic157—21no—
90Dic157—21no—
91Dic157#10412yes—
92Dic157#13512yes—
93C2×C157—22no—
94C2×C157C2×C22⋊C811yescharacteristic
95C2×C157#41611yescharacteristic
96C2×C157C2×#10411yescharacteristic
97D157—42no—
98C157#147611yescharacteristic, complemented, Sylow
99#1476—1571nomaximal, Sylow
100C4×#41—1571no—
101#431—1571no—
102C2×C4×C8—1571no—
103Q8⋊C8—1572no—
104D4⋊C8—1572no—
105C2×#41—1571no—
106C22×C8—3141no—
107C4×Q8—1571no—
108C4×Q8—1571no—
109C4×D4—3141no—
110C4×D4—3141no—
111C4×D4—1571no—
112C4×D4—1571no—
113#117—3141no—
114#117#1059784511yescharacteristic
115C2×C42—3141no—
116C2×C42—1571no—
117C4⋊C8—1572no—
118C22⋊C8—3141no—
119C4×C8—3141no—
120C4×C8—3141no—
121C4×C8—1572no—
122#41—3142no—
123#41—1574no—
124C2×Q8—1571no—
125C2×D4—3141no—
126C2×D4—1571no—
127C22×C4—3141no—
128C22×C4—3141no—
129C22×C4—3141no—
130C22×C4—1571no—
131C22×C4—1571no—
132C22×C4C2×#1059784511yescharacteristic
133C2×C8—3144no—
134C2×C8—3142no—
135C2×C8—3142no—
136C4⋊C4—3141no—
137C4⋊C4—3141no—
138C4⋊C4C2×#1059784511yescharacteristic
139C4⋊C4C2×#1059784511yescharacteristic
140C22⋊C4—21no—
141C22⋊C4—3141no—
142C22⋊C4—3141no—
143C42—21no—
144C42—3141no—
145C42—3141no—
146C42—1571no—
147C42—1571no—
148C42—1571no—
149C42—1571no—
150C23—3141no—
151C23C22⋊#1059784511yescharacteristic
152Q8—3141no—
153Q8—1572no—
154D4—3144no—
155D4—3141no—
156D4—1572no—
157C2×C4—21no—
158C2×C4—21no—
159C2×C4—3141no—
160C2×C4—3142no—
161C2×C4—3142no—
162C2×C4—3144no—
163C2×C4—6282no—
164C2×C4—6282no—
165C2×C4—1571no—
166C2×C4—1571no—
167C2×C4—1571no—
168C2×C4—1571no—
169C2×C4C22⋊#1059784511yescharacteristic
170C2×C4D157⋊C812yes—
171C2×C4#1457896412yes—
172C2×C4C22×#1059784511yescharacteristic
173C8—3144no—
174C8—6282no—
175C22—21no—
176C22—21no—
177C22—3142no—
178C22—6281no—
179C22—6281no—
180C22#1909782812yes—
181C22C2×C22⋊#1059784511yescharacteristic
182C4—41no—
183C4—41no—
184C4—3142no—
185C4—3141no—
186C4—3141no—
187C4—1572no—
188C4—1572no—
189C4#1909782812yes—
190C4C2×D157⋊C811yescharacteristic
191C4C2×#1457896411yescharacteristic
192C2—22no—
193C2—6282no—
194C2C2×#1909782811yescharacteristic
195C2#2375826311yescharacteristic
196C2D157⋊#10411yescharacteristic
subgroupG/H
centerC2×C4C22⋊#10597845
commutatorC4×C157C22×C8
FrattiniC2×C4C22×#10597845
Fitting#117×C157C4
socleC22×C157C2×C22⋊C4
prime radicalC2×#14578954C4
cosocleC4×Dic157C23
hypercenter#117#10597845
hypocenterC157#1476
LCSG ▷ C4×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
1. #23758289C2semidirect
2. C2×C4×#11929441C2semidirect
3. #23758123C2semidirect
4. #23758121C2semidirect
27. #14578954C8semidirect
55. Dic314C2×C8semidirect
57. D628C2×C8semidirect
98. C157#1476semidirect

Maximal subgroups

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

subgroupindex
#237582892
C2×C4×#119294412
#237581232
#237581212
#237577412
#1476157