Finite Group Databasebeta

← #34115374

Subgroups — #34115374

Order 20096.

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

normal subgroups only

This group has 332 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
1C2×C22⋊#11929441C212yesmaximal, complemented
2#23758119C212yesmaximal, complemented
3#23758117C212yesmaximal, complemented
4C2×#19097731C211yesmaximal, characteristic
5C22×#11929441—22no—
6C22⋊#11929441—22no—
7C22⋊#11929441C2214yes—
8C22×C22⋊D157C411yescharacteristic
9C23×Dic157C2211yescharacteristic
10C22×C4×D157C411yescharacteristic
11#19097731—22no—
12#19097731—22no—
13C2×#14578933C2211yescharacteristic
14C2×#14578931C2211yescharacteristic
15C2×C4×Dic157C411yescharacteristic
16C2×C22⋊C4×C157C411yescharacteristic
17C2×#11929441—24no—
18C2×#11929441—44no—
19C23×D157C2×C411yescharacteristic
20C2×C22⋊D157—22no—
21C2×C22⋊D157—22no—
22C2×C22⋊D157C814yescomplemented
23C22×Dic157—42no—
24C22×Dic157C2×C411yescharacteristic
25C22×Dic157C2×C411yescharacteristic
26C22×Dic157D412yes—
27C22×Dic157D412yes—
28C22×Dic157C2311yescharacteristic
29C2×C4×D157—21no—
30C2×C4×D157—21no—
31C2×C4×D157—42no—
32#14578933—22no—
33#14578931—22no—
34C4×Dic157—21no—
35C4×Dic157—21no—
36C24×C157C2×C411yescharacteristic
37C22×C4×C157C2×C411yescharacteristic
38C22×C4×C157C2×C411yescharacteristic
39C22⋊C4×C157—22no—
40#11929441—44no—
41C22×D157—21no—
42C22×D157—21no—
43C22×D157—41no—
44C22×D157—41no—
45C22×D157C2×C812yescomplemented
46C22⋊D157—28no—
47C2×Dic157—21no—
48C2×Dic157—21no—
49C2×Dic157—22no—
50C2×Dic157—24no—
51C2×Dic157—42no—
52C2×Dic157—41no—
53C2×Dic157C22⋊C411yescharacteristic
54C2×Dic157C22⋊C411yescharacteristic
55C2×Dic157C2×C812yescomplemented
56C2×Dic157C2×D412yes—
57C4×D157—42no—
58C4×D157—42no—
59C23×C157—41no—
60C23×C157—41no—
61C23×C157C22⋊C412yes—
62C23×C157C2×C812yes—
63C23×C157M1612yes—
64C23×C157C22×C411yescharacteristic
65C2×C4×C157—21no—
66C2×C4×C157—21no—
67C2×C4×C157—41no—
68C2×C4×C157—41no—
69C22×C157—21no—
70C22×C157—22no—
71C22×C157—21no—
72C22×C157—22no—
73C22×C157—42no—
74C22×C157—42no—
75C22×C157C22⋊C814yes—
76C22×C157C2×C22⋊C411yescharacteristic
77C22×C157C22×C811yescharacteristic
78C22×C157C2×M1611yescharacteristic
79C2×D157—22no—
80C2×D157—42no—
81C2×D157—41no—
82C2×D157—41no—
83C2×D157—42no—
84C4×C157—41no—
85C4×C157—41no—
86Dic157—22no—
87Dic157—21no—
88Dic157—22no—
89Dic157#9912yes—
90C2×C157—21no—
91C2×C157—21no—
92C2×C157—24no—
93C2×C157C2×C22⋊C811yescharacteristic
94C2×C157C2×#9911yescharacteristic
95C2×C157#41311yescharacteristic
96D157—42no—
97C157#145911yescharacteristic, complemented, Sylow
98#1459—1571nomaximal, Sylow
99C2×C4×D4—1571no—
100C2×C22⋊C8—1572no—
101#324—1572no—
102#323—1572no—
103C22×D4—1571no—
104C23×C4—1571no—
105C23×C4—1571no—
106C22×C8—3142no—
107C4×D4—3142no—
108C4×D4—3142no—
109C2×C4⋊C4—1571no—
110C2×C22⋊C4—1571no—
111C2×C22⋊C4#1059784511yescharacteristic
112C2×C42—1571no—
113C22⋊C8—3142no—
114C22⋊C8—1574no—
115C24—1571no—
116C24C2×#1059784511yescharacteristic
117C2×D4—3142no—
118C2×D4—3142no—
119C2×D4—1574no—
120C22×C4—3141no—
121C22×C4—3141no—
122C22×C4—6282no—
123C22×C4—6282no—
124C22×C4—1572no—
125C22×C4—1571no—
126C22×C4—1571no—
127C22×C4—1572no—
128C22×C4—1571no—
129C22×C4C2×#1059784511yescharacteristic
130C22×C4C2×#1059784511yescharacteristic
131C2×C8—3144no—
132C2×C8—6284no—
133C4⋊C4—3142no—
134C22⋊C4—22no—
135C22⋊C4—3142no—
136C42—3141no—
137C42—3141no—
138C23—41no—
139C23—41no—
140C23—3141no—
141C23—3141no—
142C23—6281no—
143C23—6281no—
144C23—1572no—
145C23C22⋊#1059784512yes—
146C23D157⋊C812yes—
147C23#1457896412yes—
148C23C22×#1059784511yescharacteristic
149D4—3148no—
150C2×C4—21no—
151C2×C4—21no—
152C2×C4—41no—
153C2×C4—41no—
154C2×C4—3141no—
155C2×C4—3141no—
156C2×C4—3144no—
157C2×C4—3142no—
158C2×C4—6282no—
159C2×C4—6282no—
160C2×C4—6281no—
161C2×C4—6282no—
162C2×C4—1571no—
163C2×C4—1572no—
164C2×C4—1572no—
165C2×C4—1571no—
166C8—6284no—
167C22—21no—
168C22—22no—
169C22—21no—
170C22—22no—
171C22—42no—
172C22—42no—
173C22—3142no—
174C22—6282no—
175C22—6282no—
176C22—6281no—
177C22—6281no—
178C22#1909782814yes—
179C22C2×C22⋊#1059784511yescharacteristic
180C22C2×D157⋊C811yescharacteristic
181C22C2×#1457896411yescharacteristic
182C4—41no—
183C4—41no—
184C4—3142no—
185C4—3142no—
186C4—3141no—
187C4—1572no—
188C2—21no—
189C2—21no—
190C2—24no—
191C2—6282no—
192C2C2×#1909782811yescharacteristic
193C2D157⋊#9911yescharacteristic
194C2#2375826011yescharacteristic
subgroupG/H
centerC22C2×C22⋊#10597845
commutatorC22×C157C22×C8
FrattiniC23C22×#10597845
FittingC2×C22⋊C4×C157C4
socleC22×C157C2×C22⋊C4
prime radicalC22×C22⋊D157C4
cosocleC22×Dic157C23
hypercenterC2×C22⋊C4#10597845
hypocenterC157#1459
LCSG ▷ C22×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. C2×C22⋊#11929441C2semidirect
2. #23758119C2semidirect
3. #23758117C2semidirect
22. C2×C22⋊D157C8semidirect
45. C22×D157C2×C8semidirect
55. C2×Dic157C2×C8semidirect
97. C157#1459semidirect

Maximal subgroups

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

subgroupindex
C2×C22⋊#119294412
#237581192
#237581172
C2×#190977312
#1459157