Finite Group Databasebeta

← #34098473

Subgroups — #34098473

Order 20096.

316 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 316 conjugacy classes of subgroups — too many to draw. Only its 69 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×#19097733C211yesmaximal, characteristic
2#23757235C212yesmaximal, complemented
3#23756999C211yesmaximal, characteristic, complemented
4#23756996C212yesmaximal, complemented
5#324×C157C211yesmaximal, characteristic, complemented
6C22×D628C411yescharacteristic
7C22×C4×D157C411yescharacteristic
8C22×C4×D157C2211yescharacteristic
9C2×#14578937—22no—
10#19097733—22no—
11#19097733—22no—
12C2×#14578931C411yescharacteristic
13C2×#14578931C2211yescharacteristic
14C2×C4×Dic157C411yescharacteristic
15C22⋊#11929434C2212yes—
16#19097683—22no—
17C2×C4⋊C4×C157C2211yescharacteristic
18C22⋊C8×C157C2212yes—
19C23×D157C2×C411yescharacteristic
20C23×D157C2×C411yescharacteristic
21C2×D628—22no—
22C2×D628—22no—
23C2×D628—22no—
24C22×Dic157C2×C411yescharacteristic
25C22×Dic157C2×C411yescharacteristic
26C2×C4×D157—21no—
27C2×C4×D157—21no—
28C2×C4×D157—42no—
29C2×C4×D157—42no—
30C2×C4×D157D412yes—
31C2×C4×D157D412yes—
32#14578937—44no—
33C2×#11929434—22no—
34#14578931—22no—
35#14578931—22no—
36C4×Dic157—21no—
37C4×Dic157—21no—
38C22×C4×C157C2×C411yescharacteristic
39C22×C4×C157C2×C411yescharacteristic
40C22×C4×C157C2311yescharacteristic
41C2×C8×C157—22no—
42C4⋊C4×C157—22no—
43C22×D157—21no—
44C22×D157—21no—
45C22×D157—21no—
46C22×D157—21no—
47C22×D157—41no—
48C22×D157—41no—
49C22×D157—41no—
50C22×D157—41no—
51C22×D157C22⋊C412yes—
52C22×D157M1612yescomplemented
53D628—28no—
54C2×Dic157—22no—
55C2×Dic157—21no—
56C2×Dic157—41no—
57C2×Dic157C22⋊C411yescharacteristic
58C2×Dic157C22⋊C411yescharacteristic
59C4×D157—24no—
60C4×D157—42no—
61C4×D157—42no—
62C4×D157—42no—
63#11929434—42no—
64C23×C157C22×C411yescharacteristic
65C2×C4×C157—21no—
66C2×C4×C157—21no—
67C2×C4×C157—21no—
68C2×C4×C157—41no—
69C2×C4×C157—41no—
70C2×C4×C157M1612yescomplemented
71C2×C4×C157C2×D412yes—
72C8×C157—42no—
73C22×C157—21no—
74C22×C157—21no—
75C22×C157C2×C22⋊C411yescharacteristic
76C22×C157C2×M1611yescharacteristic
77C22×C157C2×M1611yescharacteristic
78C2×D157—22no—
79C2×D157—22no—
80C2×D157—22no—
81C2×D157—22no—
82C2×D157—42no—
83C2×D157—42no—
84C2×D157—42no—
85C2×D157—41no—
86C2×D157—41no—
87C2×D157—42no—
88C4×C157—22no—
89C4×C157—22no—
90C4×C157—41no—
91Dic157—21no—
92Dic157—41no—
93Dic157#9912yes—
94C2×C157—21no—
95C2×C157—21no—
96C2×C157#40711yescharacteristic
97C2×C157C2×#9911yescharacteristic
98C2×C157#41311yescharacteristic
99D157—42no—
100D157—42no—
101C157#146511yescharacteristic, complemented, Sylow
102#1465—1571nomaximal, Sylow
103C2×C4×D4—1571no—
104#407—1572no—
105#324—1571no—
106#324D15711yescharacteristic, complemented
107#323—1572no—
108C22×D4—1571no—
109C23×C4—1571no—
110C23×C4—1571no—
111C2×M16—3142no—
112C4×D4—3142no—
113C4×D4—3142no—
114C2×C4⋊C4C2×D15711yescharacteristic
115C2×C22⋊C4—1571no—
116C2×C22⋊C4—1571no—
117C2×C42—1571no—
118C22⋊C8—3142no—
119C22⋊C8—1572no—
120C22⋊C8C2×D15712yes—
121C24—1571no—
122C24—1571no—
123C2×D4—3142no—
124C2×D4—3142no—
125C2×D4—3142no—
126C22×C4—3141no—
127C22×C4—3141no—
128C22×C4—6282no—
129C22×C4—6282no—
130C22×C4—1571no—
131C22×C4—1572no—
132C22×C4—1571no—
133C22×C4—1572no—
134C22×C4C4×D15711yescharacteristic
135C22×C4C4×D15711yescharacteristic
136C22×C4C22×D15711yescharacteristic
137M16—6284no—
138C2×C8—22no—
139C2×C8—3142no—
140C4⋊C4—22no—
141C22⋊C4—3142no—
142C22⋊C4—3142no—
143C42—3141no—
144C42—3141no—
145C23—3141no—
146C23—3141no—
147C23—3141no—
148C23—3141no—
149C23—6281no—
150C23—6281no—
151C23—6281no—
152C23—6281no—
153C23—1572no—
154C23—1572no—
155C23C2×C4×D15711yescharacteristic
156D4—3148no—
157C2×C4—21no—
158C2×C4—21no—
159C2×C4—21no—
160C2×C4—41no—
161C2×C4—41no—
162C2×C4—3144no—
163C2×C4—3142no—
164C2×C4—3141no—
165C2×C4—6282no—
166C2×C4—6282no—
167C2×C4—6282no—
168C2×C4—6281no—
169C2×C4—1571no—
170C2×C4—1571no—
171C2×C4#1457893712yescomplemented
172C2×C4D4×D15712yes—
173C8—42no—
174C8—6282no—
175C22—21no—
176C22—21no—
177C22—3142no—
178C22—3142no—
179C22—3142no—
180C22—3142no—
181C22—6282no—
182C22—6282no—
183C22—6282no—
184C22—6282no—
185C22—6281no—
186C22—6281no—
187C22C22⋊C4×D15711yescharacteristic
188C22M16×D15711yescharacteristic
189C22C2×#1457893711yescharacteristic
190C4—22no—
191C4—22no—
192C4—41no—
193C4—3141no—
194C4—6281no—
195C4—1572no—
196C2—21no—
197C2—21no—
198C2—6282no—
199C2—6282no—
200C2#2375723511yescharacteristic
201C2#99×D15711yescharacteristic
202C2#2375725611yescharacteristic
subgroupG/H
centerC22C22⋊C4×D157
commutatorC23×C157C22×C4
FrattiniC22×C4C22×D157
Fitting#324×C157C2
socleC22×C157C2×C22⋊C4
prime radicalC22×D628C4
cosocleC22×C4×C157C23
hypercenter#324D157
hypocenterC157#1465
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. #23757235C2semidirect
3. #23756999C2semidirect
4. #23756996C2semidirect
5. #324×C157C2semidirect
52. C22×D157M16semidirect
70. C2×C4×C157M16semidirect
101. C157#1465semidirect
106. #324D157semidirect
171. C2×C4#14578937semidirect

Maximal subgroups

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

subgroupindex
C2×#190977332
#237572352
#237569992
#237569962
#324×C1572
#1465157