Finite Group Databasebeta

← #34115403

Subgroups — #34115403

Order 20096.

280 conjugacy classes of subgroups; only the 62 normal subgroups are shown.

normal subgroups only

This group has 280 conjugacy classes of subgroups — too many to draw. Only its 62 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#23758243C211yesmaximal, characteristic, complemented
2C2×C22⋊#11929441C211yesmaximal, characteristic, complemented
3#23758118C212yesmaximal, complemented
4#23758117C212yesmaximal, complemented
5C2×#19097755C211yesmaximal, characteristic
6C2×#14578963—21no—
7C22×#11929441—21no—
8C22⋊#11929441—21no—
9C22⋊#11929441—21no—
10C22⋊#11929441C2212yes—
11C22⋊#11929441C2212yes—
12C22×C22⋊D157C411yescharacteristic
13C23×Dic157C2211yescharacteristic
14#19097755—21no—
15#19097755—21no—
16#19097755—21no—
17#19097755—21no—
18C2×C4⋊Dic157C411yescharacteristic
19C2×C4⋊Dic157C2211yescharacteristic
20C2×#14578931C411yescharacteristic
21C2×#14578931C2211yescharacteristic
22C2×C22⋊C4×C157C411yescharacteristic
23#14578963—42no—
24C2×#11929441—22no—
25C2×#11929441—22no—
26C2×#11929441—42no—
27C23×D157C2×C411yescharacteristic
28C2×C22⋊D157—21no—
29C2×C22⋊D157—21no—
30C2×C22⋊D157—42no—
31C22×Dic157—42no—
32C22×Dic157C2×C411yescharacteristic
33C22×Dic157C2×C411yescharacteristic
34C22×Dic157D411yescharacteristic
35C22×Dic157D411yescharacteristic
36C22×Dic157D411yescharacteristic
37C22×Dic157D411yescharacteristic
38C22×Dic157C2311yescharacteristic
39C4⋊Dic157—21no—
40C4⋊Dic157—21no—
41C4⋊Dic157—21no—
42C4⋊Dic157—21no—
43#14578931—21no—
44#14578931—21no—
45#14578931—21no—
46#14578931—21no—
47C24×C157C2×C411yescharacteristic
48C22×C4×C157C2×C411yescharacteristic
49C22×C4×C157C2×C411yescharacteristic
50C22⋊C4×C157—21no—
51C22⋊C4×C157—21no—
52#11929441—42no—
53#11929441—42no—
54C22×D157—21no—
55C22×D157—22no—
56C22×D157—41no—
57C22×D157—41no—
58C22⋊D157—42no—
59C22⋊D157—42no—
60C2×Dic157—22no—
61C2×Dic157—22no—
62C2×Dic157—21no—
63C2×Dic157—41no—
64C2×Dic157—41no—
65C2×Dic157—41no—
66C2×Dic157—41no—
67C2×Dic157—41no—
68C2×Dic157C22⋊C411yescharacteristic
69C2×Dic157C22⋊C411yescharacteristic
70C2×Dic157C2×D411yescharacteristic
71C2×Dic157C2×D411yescharacteristic
72C23×C157—22no—
73C23×C157—22no—
74C23×C157—41no—
75C23×C157C22⋊C411yescharacteristic
76C23×C157C22⋊C411yescharacteristic
77C23×C157C22×C411yescharacteristic
78C2×C4×C157—21no—
79C2×C4×C157—21no—
80C2×C4×C157—22no—
81C2×C4×C157—41no—
82C22×C157—21no—
83C22×C157—21no—
84C22×C157—21no—
85C22×C157—21no—
86C22×C157—21no—
87C22×C157—21no—
88C22×C157—21no—
89C22×C157—44no—
90C22×C157#9912yes—
91C22×C157C2×C22⋊C411yescharacteristic
92C22×C157#13112yes—
93C2×D157—41no—
94C2×D157—41no—
95C2×D157—41no—
96C2×D157—82no—
97C4×C157—41no—
98C4×C157—41no—
99Dic157—21no—
100Dic157—21no—
101Dic157—21no—
102Dic157—21no—
103Dic157—41no—
104C2×C157—22no—
105C2×C157—22no—
106C2×C157—41no—
107C2×C157#40811yescharacteristic
108C2×C157C2×#9911yescharacteristic
109C2×C157#41311yescharacteristic
110D157—81no—
111C157#146811yescharacteristic, complemented, Sylow
112#1468—1571nomaximal, Sylow
113C2×#123—1571no—
114#407—1571no—
115C2×C22⋊C8—1571no—
116#324—1572no—
117#323—1572no—
118C22×D4—1571no—
119C23×C4—1571no—
120C2×M16—3141no—
121C22×C8—3141no—
122#123—3141no—
123#123—3141no—
124#123—3141no—
125#123—3141no—
126C2×C4⋊C4—1571no—
127C2×C4⋊C4—1571no—
128C2×C22⋊C4—1571no—
129C2×C22⋊C4—1571no—
130C2×C22⋊C4#1059784511yescharacteristic
131C22⋊C8—3141no—
132C22⋊C8—3141no—
133C22⋊C8—1572no—
134C22⋊C8—1572no—
135C24—1571no—
136C24C2×#1059784511yescharacteristic
137C2×D4—3141no—
138C2×D4—3141no—
139C2×D4—6282no—
140C22×C4—6282no—
141C22×C4—1571no—
142C22×C4—1571no—
143C22×C4—1571no—
144C22×C4—1571no—
145C22×C4—1571no—
146C22×C4—1571no—
147C22×C4—1571no—
148C22×C4C2×#1059784511yescharacteristic
149C22×C4C2×#1059784511yescharacteristic
150M16—6282no—
151C2×C8—3142no—
152C2×C8—3142no—
153C2×C8—6282no—
154C4⋊C4—3141no—
155C4⋊C4—3141no—
156C4⋊C4—3141no—
157C4⋊C4—3141no—
158C22⋊C4—21no—
159C22⋊C4—21no—
160C22⋊C4—3141no—
161C22⋊C4—3141no—
162C22⋊C4—3141no—
163C22⋊C4—3141no—
164C23—22no—
165C23—22no—
166C23—41no—
167C23—3141no—
168C23—3142no—
169C23—6281no—
170C23—6281no—
171C23C22⋊#1059784511yescharacteristic
172C23C22⋊#1059784511yescharacteristic
173C23C22×#1059784511yescharacteristic
174D4—6282no—
175D4—6282no—
176C2×C4—22no—
177C2×C4—21no—
178C2×C4—21no—
179C2×C4—41no—
180C2×C4—3142no—
181C2×C4—3142no—
182C2×C4—3141no—
183C2×C4—6281no—
184C2×C4—6281no—
185C2×C4—6281no—
186C2×C4—6281no—
187C2×C4—6281no—
188C2×C4—1571no—
189C2×C4—1571no—
190C2×C4—1571no—
191C2×C4—1571no—
192C8—6282no—
193C8—6282no—
194C22—21no—
195C22—21no—
196C22—21no—
197C22—21no—
198C22—21no—
199C22—21no—
200C22—21no—
201C22—44no—
202C22—6281no—
203C22—6281no—
204C22—6281no—
205C22—12562no—
206C22#1909783012yes—
207C22C2×C22⋊#1059784511yescharacteristic
208C22#1909785812yes—
209C4—41no—
210C4—41no—
211C4—3141no—
212C4—3141no—
213C4—3141no—
214C4—3141no—
215C4—6281no—
216C2—22no—
217C2—22no—
218C2—41no—
219C2—12561no—
220C2#2375824611yescharacteristic
221C2C2×#1909783011yescharacteristic
222C2#2375826011yescharacteristic
subgroupG/H
centerC22C2×C22⋊#10597845
commutatorC23×C157C22×C4
FrattiniC23C22×#10597845
FittingC2×C22⋊C4×C157C4
socleC22×C157C2×C22⋊C4
prime radicalC22×C22⋊D157C4
cosocleC22×Dic157C23
hypercenterC2×C22⋊C4#10597845
hypocenterC157#1468
LCSG ▷ C23×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C22 ◁ C24 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. #23758243C2semidirect
2. C2×C22⋊#11929441C2semidirect
3. #23758118C2semidirect
4. #23758117C2semidirect
111. C157#1468semidirect

Maximal subgroups

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

subgroupindex
#237582432
C2×C22⋊#119294412
#237581182
#237581172
C2×#190977552
#1468157