Finite Group Databasebeta

← #34115419

Subgroups — #34115419

Order 20096.

214 conjugacy classes of subgroups; only the 58 normal subgroups are shown.

normal subgroups only

This group has 214 conjugacy classes of subgroups — too many to draw. Only its 58 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#23758294C211yesmaximal, characteristic, complemented
2#23758290C211yesmaximal, characteristic, complemented
3#23758119C212yesmaximal, complemented
4#23758117C212yesmaximal
5C2×#19097766C211yesmaximal, characteristic
6#19097838—21no—
7C4⋊#11929441—21no—
8C22⋊#11929441C2212yes—
9C22⋊#11929441C2212yes—
10#19097826—21no—
11C4×#11929441—21no—
12#19097766—21no—
13#19097766—21no—
14#19097766—21no—
15#19097766—21no—
16C2×C4⋊Dic157C411yescharacteristic
17C2×#14578933C2211yescharacteristic
18C2×#14578931C411yescharacteristic
19C2×#14578931C411yescharacteristic
20C2×#14578931C2211yescharacteristic
21C2×C4×Dic157C2211yescharacteristic
22C2×C4⋊C4×C157C411yescharacteristic
23C2×#11929441—22no—
24C2×#11929441—22no—
25C23×D157C2×C411yescharacteristic
26C22×Dic157C2×C411yescharacteristic
27C22×Dic157C2×C411yescharacteristic
28C22×Dic157C2311yescharacteristic
29C4⋊Dic157—21no—
30C4⋊Dic157—21no—
31#14578933—21no—
32#14578933—21no—
33#14578931—21no—
34#14578931—21no—
35#14578931—21no—
36#14578931—21no—
37#14578931—21no—
38#14578931—21no—
39C4×Dic157D411yescharacteristic
40C4×Dic157D411yescharacteristic
41C4×Dic157D411yescharacteristic
42C4×Dic157D411yescharacteristic
43C22×C4×C157C2×C411yescharacteristic
44C22×C4×C157C2×C411yescharacteristic
45C22×C4×C157C2×C411yescharacteristic
46C4⋊C4×C157—21no—
47C4⋊C4×C157—21no—
48#11929441—42no—
49#11929441—42no—
50C22×D157—21no—
51C22×D157—22no—
52C22×D157—41no—
53C22×D157—41no—
54C2×Dic157—22no—
55C2×Dic157—21no—
56C2×Dic157—22no—
57C2×Dic157—41no—
58C2×Dic157C22⋊C411yescharacteristic
59C2×Dic157C22⋊C411yescharacteristic
60C2×Dic157C2×D411yescharacteristic
61C2×Dic157C2×D411yescharacteristic
62C23×C157C22×C411yescharacteristic
63C2×C4×C157—21no—
64C2×C4×C157—21no—
65C2×C4×C157—41no—
66C2×C4×C157—41no—
67C2×C4×C157—41no—
68C2×C4×C157C22⋊C411yescharacteristic
69C2×C4×C157C22⋊C411yescharacteristic
70C22×C157—21no—
71C22×C157—21no—
72C22×C157C2×C22⋊C411yescharacteristic
73C22×C157#13112yes—
74C2×D157—41no—
75C2×D157—41no—
76C2×D157—41no—
77C2×D157—82no—
78C4×C157—21no—
79C4×C157—21no—
80C4×C157—41no—
81C4×C157—41no—
82Dic157—21no—
83Dic157—21no—
84Dic157—21no—
85Dic157—21no—
86Dic157—41no—
87C2×C157—22no—
88C2×C157#40811yescharacteristic
89C2×C157#41011yescharacteristic
90C2×C157#41311yescharacteristic
91D157—81no—
92C157#147311yescharacteristic, complemented, Sylow
93#1473—1571nomaximal, Sylow
94C2×#126—1571no—
95#432—1571no—
96#431—1571no—
97#324—1572no—
98#323—1572no—
99#126—3141no—
100#126—3141no—
101#126—3141no—
102#126—3141no—
103C2×C4⋊C4—1571no—
104C2×C4⋊C4—1571no—
105C2×C4⋊C4#1059784511yescharacteristic
106C2×C22⋊C4—1571no—
107C2×C22⋊C4—1571no—
108C2×C22⋊C4—1571no—
109C2×C42—1571no—
110C4⋊C8—3141no—
111C4⋊C8—3141no—
112C22⋊C8—1572no—
113C22⋊C8—1572no—
114#97—3141no—
115C4×C8—3141no—
116C24—1571no—
117C22×C4—1571no—
118C22×C4—1571no—
119C22×C4—1571no—
120C22×C4C2×#1059784511yescharacteristic
121C22×C4C2×#1059784511yescharacteristic
122C22×C4C2×#1059784511yescharacteristic
123C2×C8—3142no—
124C2×C8—3142no—
125C4⋊C4—21no—
126C4⋊C4—21no—
127C4⋊C4—3141no—
128C4⋊C4—3141no—
129C4⋊C4—3141no—
130C4⋊C4—3141no—
131C22⋊C4—3141no—
132C22⋊C4—3141no—
133C22⋊C4—3141no—
134C22⋊C4—3141no—
135C22⋊C4—3141no—
136C22⋊C4—3141no—
137C42—1571no—
138C42—1571no—
139C42—1571no—
140C42—1571no—
141C23—3141no—
142C23—3142no—
143C23—6281no—
144C23—6281no—
145C23C22×#1059784511yescharacteristic
146C2×C4—21no—
147C2×C4—21no—
148C2×C4—41no—
149C2×C4—41no—
150C2×C4—41no—
151C2×C4—3142no—
152C2×C4—3142no—
153C2×C4—3141no—
154C2×C4—6281no—
155C2×C4—1571no—
156C2×C4—1571no—
157C2×C4—1571no—
158C2×C4—1571no—
159C2×C4C22⋊#1059784511yescharacteristic
160C2×C4C22⋊#1059784511yescharacteristic
161C8—6282no—
162C8—6282no—
163C22—21no—
164C22—21no—
165C22—6281no—
166C22—6281no—
167C22—6281no—
168C22—12562no—
169C22C2×C22⋊#1059784511yescharacteristic
170C22#1909785912yes—
171C4—21no—
172C4—21no—
173C4—41no—
174C4—41no—
175C4—3141no—
176C4—3141no—
177C4—3141no—
178C4—3141no—
179C4—6281no—
180C2—22no—
181C2—12561no—
182C2#2375824811yescharacteristic
183C2#2375825211yescharacteristic
184C2#2375826011yescharacteristic
subgroupG/H
centerC22C2×C22⋊#10597845
commutatorC23×C157C22×C4
FrattiniC23C22×#10597845
FittingC2×C4⋊C4×C157C4
socleC22×C157C2×C22⋊C4
prime radicalC23×D157C2×C4
cosocleC22×Dic157C23
hypercenterC2×C4⋊C4#10597845
hypocenterC157#1473
LCSG ▷ C23×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
1. #23758294C2semidirect
2. #23758290C2semidirect
3. #23758119C2semidirect
92. C157#1473semidirect

Maximal subgroups

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

subgroupindex
#237582942
#237582902
#237581192
#237581172
C2×#190977662
#1473157