Finite Group Databasebeta

← #34098469

Subgroups — #34098469

Order 20096.

252 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 252 conjugacy classes of subgroups — too many to draw. Only its 67 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×#19097729C211yesmaximal, characteristic
2#23757327C212yesmaximal, complemented
3#23756999C211yesmaximal, characteristic, complemented
4#23756996C212yesmaximal
5#324×C157C211yesmaximal, characteristic, complemented
6C22×C4×D157C411yescharacteristic
7#19097729—22no—
8#19097729—22no—
9C2×C4⋊Dic157C411yescharacteristic
10C2×#14578931C411yescharacteristic
11C2×#14578931C2211yescharacteristic
12C2×C4×Dic157C411yescharacteristic
13C2×C4×Dic157C2211yescharacteristic
14#19097700—22no—
15C22⋊#11929434C2212yes—
16#19097681—22no—
17C2×C4⋊C4×C157C2211yescharacteristic
18C22⋊C8×C157C2212yes—
19C23×D157C2×C411yescharacteristic
20C22×Dic157C2×C411yescharacteristic
21C22×Dic157C2×C411yescharacteristic
22C22×Dic157C2×C411yescharacteristic
23C2×C4×D157—22no—
24C2×C4×D157—21no—
25C2×C4×D157—21no—
26C2×C4×D157—22no—
27C2×#11929434—22no—
28C4⋊Dic157—22no—
29#14578931—22no—
30#14578931—22no—
31C4×Dic157—21no—
32C4×Dic157—21no—
33C4×Dic157D412yes—
34C4×Dic157D412yes—
35C22×C4×C157C2×C411yescharacteristic
36C22×C4×C157C2×C411yescharacteristic
37C22×C4×C157C2311yescharacteristic
38C2×C8×C157—22no—
39C4⋊C4×C157—22no—
40C22×D157—21no—
41C22×D157—21no—
42C22×D157—41no—
43C22×D157—41no—
44C22×D157M1612yes—
45C2×Dic157—21no—
46C2×Dic157—21no—
47C2×Dic157—21no—
48C2×Dic157—41no—
49C2×Dic157—41no—
50C2×Dic157C22⋊C411yescharacteristic
51C2×Dic157C22⋊C411yescharacteristic
52C2×Dic157C22⋊C412yes—
53C4×D157—24no—
54C4×D157—24no—
55#11929434—42no—
56C23×C157C22×C411yescharacteristic
57C2×C4×C157—21no—
58C2×C4×C157—21no—
59C2×C4×C157—21no—
60C2×C4×C157—41no—
61C2×C4×C157—41no—
62C2×C4×C157M1612yes—
63C2×C4×C157C2×D412yes—
64C8×C157—42no—
65C22×C157—21no—
66C22×C157—21no—
67C22×C157C2×C22⋊C411yescharacteristic
68C22×C157C2×M1611yescharacteristic
69C22×C157C2×M1611yescharacteristic
70C2×D157—22no—
71C2×D157—42no—
72C2×D157—41no—
73C2×D157—41no—
74C2×D157—42no—
75C4×C157—22no—
76C4×C157—22no—
77C4×C157—41no—
78Dic157—21no—
79Dic157—21no—
80Dic157—22no—
81Dic157—41no—
82C2×C157—21no—
83C2×C157—21no—
84C2×C157#40711yescharacteristic
85C2×C157#41011yescharacteristic
86C2×C157#41311yescharacteristic
87D157—42no—
88C157#146411yescharacteristic, complemented, Sylow
89#1464—1571nomaximal, Sylow
90C2×#117—1571no—
91#432—1572no—
92#324—1571no—
93#324D15711yescharacteristic, complemented
94#323—1572no—
95C23×C4—1571no—
96#117—3142no—
97#117—3142no—
98C2×C4⋊C4—1571no—
99C2×C4⋊C4C2×D15711yescharacteristic
100C2×C22⋊C4—1571no—
101C2×C22⋊C4—1571no—
102C2×C42—1571no—
103C2×C42—1571no—
104C4⋊C8—3142no—
105C22⋊C8—1572no—
106C22⋊C8C2×D15712yes—
107#97—3142no—
108C24—1571no—
109C22×C4—3142no—
110C22×C4—3141no—
111C22×C4—3141no—
112C22×C4—3142no—
113C22×C4—1571no—
114C22×C4—1571no—
115C22×C4—1571no—
116C22×C4C4×D15711yescharacteristic
117C22×C4C4×D15711yescharacteristic
118C22×C4C22×D15711yescharacteristic
119C2×C8—22no—
120C2×C8—3142no—
121C4⋊C4—22no—
122C4⋊C4—3142no—
123C22⋊C4—3142no—
124C22⋊C4—3142no—
125C42—3141no—
126C42—3141no—
127C42—1572no—
128C42—1572no—
129C23—3141no—
130C23—3141no—
131C23—6281no—
132C23—6281no—
133C23—1572no—
134C23C2×C4×D15711yescharacteristic
135C2×C4—21no—
136C2×C4—21no—
137C2×C4—21no—
138C2×C4—41no—
139C2×C4—41no—
140C2×C4—3144no—
141C2×C4—3144no—
142C2×C4—3141no—
143C2×C4—3141no—
144C2×C4—3141no—
145C2×C4—6281no—
146C2×C4—6281no—
147C2×C4—1571no—
148C2×C4—1571no—
149C2×C4—1572no—
150C2×C4#1457893712yes—
151C2×C4D4×D15712yes—
152C8—42no—
153C8—6282no—
154C22—21no—
155C22—21no—
156C22—3142no—
157C22—6282no—
158C22—6282no—
159C22—6281no—
160C22—6281no—
161C22C22⋊C4×D15711yescharacteristic
162C22M16×D15711yescharacteristic
163C22C2×#1457893711yescharacteristic
164C4—22no—
165C4—22no—
166C4—41no—
167C4—3141no—
168C4—3141no—
169C4—3142no—
170C4—6281no—
171C2—21no—
172C2—21no—
173C2—6282no—
174C2#2375723511yescharacteristic
175C2#2375724511yescharacteristic
176C2#2375725611yescharacteristic
subgroupG/H
centerC22C22⋊C4×D157
commutatorC23×C157C22×C4
FrattiniC22×C4C22×D157
Fitting#324×C157C2
socleC22×C157C2×C22⋊C4
prime radicalC23×D157C2×C4
cosocleC22×C4×C157C23
hypercenter#324D157
hypocenterC157#1464
LCSG ▷ C23×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C22 ◁ C22×C4 ◁ #324

Complements

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

NH ≅ G/Ntype
2. #23757327C2semidirect
3. #23756999C2semidirect
5. #324×C157C2semidirect
88. C157#1464semidirect
93. #324D157semidirect

Maximal subgroups

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

subgroupindex
C2×#190977292
#237573272
#237569992
#237569962
#324×C1572
#1464157