Finite Group Databasebeta

← #34098447

Subgroups — #34098447

Order 20096.

264 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 264 conjugacy classes of subgroups — too many to draw. Only its 79 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×#19097727C211yesmaximal, characteristic
2#23757323C212yesmaximal, complemented
3#23756998C212yesmaximal, complemented
4#23756997C211yesmaximal, characteristic
5#323×C157C211yesmaximal, characteristic
6C23×Dic157C411yescharacteristic
7#19097727—22no—
8#19097727—22no—
9C2×#14578933C411yescharacteristic
10C2×#14578933C2211yescharacteristic
11C2×C22⋊Dic157C411yescharacteristic
12C2×C4×Dic157C411yescharacteristic
13C2×C4×Dic157C2211yescharacteristic
14#19097700—22no—
15C22⋊#11929434C2212yes—
16C8×Dic157—22no—
17C2×C22⋊C4×C157C2211yescharacteristic
18C22⋊C8×C157C2212yes—
19C22×Dic157—21no—
20C22×Dic157—21no—
21C22×Dic157—22no—
22C22×Dic157C814yescomplemented
23C22×Dic157C2×C411yescharacteristic
24C22×Dic157C2×C411yescharacteristic
25C22×Dic157C2×C411yescharacteristic
26C22×Dic157C2×C411yescharacteristic
27C2×#11929434—22no—
28#14578933—22no—
29#14578933—22no—
30C22⋊Dic157—22no—
31C4×Dic157—21no—
32C4×Dic157—21no—
33C4×Dic157D412yes—
34C4×Dic157D412yes—
35C24×C157C2×C411yescharacteristic
36C22×C4×C157C2×C411yescharacteristic
37C22×C4×C157C2311yescharacteristic
38C2×C8×C157—22no—
39C22⋊C4×C157—22no—
40C2×Dic157—21no—
41C2×Dic157—21no—
42C2×Dic157—24no—
43C2×Dic157—24no—
44C2×Dic157—21no—
45C2×Dic157—41no—
46C2×Dic157—41no—
47C2×Dic157C22⋊C412yes—
48C2×Dic157C22⋊C411yescharacteristic
49C2×Dic157C22⋊C411yescharacteristic
50C2×Dic157C2×C812yes—
51C2×Dic157C2×C812yes—
52C2×Dic157M1612yes—
53#11929434—42no—
54C23×C157—21no—
55C23×C157—21no—
56C23×C157—41no—
57C23×C157—41no—
58C23×C157C2×C812yes—
59C23×C157C22×C411yescharacteristic
60C2×C4×C157—21no—
61C2×C4×C157—41no—
62C2×C4×C157—41no—
63C2×C4×C157C2×D412yes—
64C8×C157—42no—
65C22×C157—21no—
66C22×C157—21no—
67C22×C157—22no—
68C22×C157—42no—
69C22×C157—42no—
70C22×C157—41no—
71C22×C157—41no—
72C22×C157C2×C22⋊C411yescharacteristic
73C22×C157C22×C811yescharacteristic
74C22×C157C2×M1611yescharacteristic
75C4×C157—22no—
76C4×C157—41no—
77Dic157—22no—
78Dic157—22no—
79Dic157—41no—
80Dic157C22⋊C812yes—
81Dic157C22⋊C812yes—
82C2×C157—21no—
83C2×C157—21no—
84C2×C157—42no—
85C2×C157C2×C22⋊C811yescharacteristic
86C2×C157#41011yescharacteristic
87C2×C157#41311yescharacteristic
88C157#145811yescharacteristic, complemented, Sylow
89#1458—1571nomaximal, Sylow
90C2×#117—1571no—
91#431—1572no—
92#324—1572no—
93#323—1571no—
94#323D15711yescharacteristic
95C23×C4—1571no—
96#117—3142no—
97#117—3142no—
98C2×C4⋊C4—1571no—
99C2×C4⋊C4—1571no—
100C2×C22⋊C4—1571no—
101C2×C22⋊C4C2×D15711yescharacteristic
102C2×C42—1571no—
103C2×C42—1571no—
104C4⋊C8—3142no—
105C22⋊C8—1572no—
106C22⋊C8C2×D15712yes—
107C4×C8—3142no—
108C24C4×D15711yescharacteristic
109C22×C4—3141no—
110C22×C4—3141no—
111C22×C4—3142no—
112C22×C4—1571no—
113C22×C4—1574no—
114C22×C4—1571no—
115C22×C4—1571no—
116C22×C4—1571no—
117C22×C4C4×D15711yescharacteristic
118C22×C4C22×D15711yescharacteristic
119C2×C8—22no—
120C2×C8—3142no—
121C4⋊C4—3142no—
122C4⋊C4—3142no—
123C22⋊C4—22no—
124C22⋊C4—3142no—
125C42—3141no—
126C42—3141no—
127C42—1572no—
128C42—1572no—
129C23—21no—
130C23—21no—
131C23—41no—
132C23—41no—
133C23C8×D15712yes—
134C23C2×C4×D15711yescharacteristic
135C2×C4—21no—
136C2×C4—41no—
137C2×C4—41no—
138C2×C4—3141no—
139C2×C4—3141no—
140C2×C4—3144no—
141C2×C4—3144no—
142C2×C4—3141no—
143C2×C4—6281no—
144C2×C4—6281no—
145C2×C4—1572no—
146C2×C4—1572no—
147C2×C4—1571no—
148C2×C4—1571no—
149C2×C4—1572no—
150C2×C4—1572no—
151C2×C4D4×D15712yes—
152C8—42no—
153C8—6282no—
154C22—21no—
155C22—21no—
156C22—22no—
157C22—42no—
158C22—42no—
159C22—41no—
160C22—41no—
161C22C22⋊C4×D15711yescharacteristic
162C22C2×C8×D15711yescharacteristic
163C22M16×D15711yescharacteristic
164C4—22no—
165C4—41no—
166C4—3142no—
167C4—3142no—
168C4—6281no—
169C4—1572no—
170C4—1572no—
171C2—21no—
172C2—21no—
173C2—42no—
174C2C22⋊C8×D15711yescharacteristic
175C2#2375724511yescharacteristic
176C2#2375725411yescharacteristic
subgroupG/H
centerC22C22⋊C4×D157
commutatorC22×C157C22×C8
FrattiniC22×C4C22×D157
Fitting#323×C157C2
socleC22×C157C2×C22⋊C4
prime radicalC24×C157C2×C4
cosocleC22×C4×C157C23
hypercenter#323D157
hypocenterC157#1458
LCSG ▷ C22×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C22 ◁ C22×C4 ◁ #323

Complements

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

NH ≅ G/Ntype
2. #23757323C2semidirect
3. #23756998C2semidirect
22. C22×Dic157C8semidirect
88. C157#1458semidirect

Maximal subgroups

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

subgroupindex
C2×#190977272
#237573232
#237569982
#237569972
#323×C1572
#1458157