Finite Group Databasebeta

← #34115437

Subgroups — #34115437

Order 20096.

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

normal subgroups only

This group has 312 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
1#23758289C211yesmaximal, characteristic, complemented
2#23758289C211yesmaximal, characteristic, complemented
3#23758121C214yesmaximal, complemented
4C2×#19097733C211yesmaximal, characteristic
5C4⋊#11929441—21no—
6C4⋊#11929441C2212yescomplemented
7C22⋊#11929441—21no—
8C22⋊#11929441—21no—
9C4×#11929441—21no—
10C4×#11929441C2212yescomplemented
11C22×D628C411yescharacteristic
12C22×C4×D157—21no—
13#19097733—21no—
14#19097733—21no—
15#19097733C412yes—
16#19097733C2212yes—
17C2×#14578931—21no—
18C2×C4×Dic157C2211yescharacteristic
19C2×C4⋊C4×C157C411yescharacteristic
20C2×#11929441—22no—
21C2×#11929441—22no—
22C23×D157—21no—
23C2×D628—21no—
24C2×D628—22no—
25C2×D628C814yescomplemented
26C2×D628C2×C412yes—
27C22×Dic157D411yescharacteristic
28C22×Dic157D411yescharacteristic
29C2×C4×D157—22no—
30C2×C4×D157—22no—
31C2×C4×D157—44no—
32#14578931—22no—
33#14578931—22no—
34C4×Dic157C2×C411yescharacteristic
35C4×Dic157D411yescharacteristic
36C4×Dic157D411yescharacteristic
37C4×Dic157C2311yescharacteristic
38C22×C4×C157—21no—
39C22×C4×C157C2×C411yescharacteristic
40C4⋊C4×C157—21no—
41C4⋊C4×C157C2×C412yes—
42#11929441—42no—
43#11929441—42no—
44C22×D157—24no—
45C22×D157—22no—
46C22×D157—42no—
47C22×D157—42no—
48D628—24no—
49D628—22no—
50D628C2×C814yes—
51C2×Dic157—22no—
52C2×Dic157—41no—
53C2×Dic157C22⋊C411yescharacteristic
54C2×Dic157C22⋊C411yescharacteristic
55C2×Dic157C2×D411yescharacteristic
56C2×Dic157C2×D411yescharacteristic
57C4×D157—44no—
58C4×D157—44no—
59C23×C157C22⋊C411yescharacteristic
60C2×C4×C157—22no—
61C2×C4×C157—42no—
62C2×C4×C157C22⋊C411yescharacteristic
63C2×C4×C157C2×C812yes—
64C2×C4×C157M1612yes—
65C2×C4×C157C22×C411yescharacteristic
66C22×C157—21no—
67C22×C157—21no—
68C22×C157C22⋊C812yes—
69C22×C157C2×C22⋊C411yescharacteristic
70C2×D157—24no—
71C2×D157—48no—
72C2×D157—42no—
73C2×D157—42no—
74C4×C157—42no—
75C4×C157C22⋊C812yes—
76C4×C157C22×C811yescharacteristic
77C4×C157C2×M1611yescharacteristic
78Dic157—21no—
79Dic157—21no—
80Dic157—21no—
81Dic157AGL(1,ℤ/8)12yes—
82C2×C157—22no—
83C2×C157C2×C22⋊C811yescharacteristic
84C2×C157#41811yescharacteristic
85C2×C157#42111yescharacteristic
86D157—44no—
87C157#147811yescharacteristic, complemented, Sylow
88#1478—1571nomaximal, Sylow
89C2×C4×D4—1571no—
90#431—1571no—
91#431—1571no—
92D4⋊C8—1574no—
93C22×D4—1571no—
94C23×C4—3141no—
95C4×D4—3141no—
96C4×D4—3141no—
97C4×D4—1572no—
98C4×D4—1572no—
99C2×C4⋊C4#1059784511yescharacteristic
100C2×C22⋊C4—3141no—
101C2×C42—1571no—
102C4⋊C8—3141no—
103C4⋊C8—1572no—
104C22⋊C8—3141no—
105C22⋊C8—3141no—
106C4×C8—3141no—
107C4×C8—1572no—
108C24—3141no—
109C2×D4—3141no—
110C2×D4—3142no—
111C2×D4—1574no—
112C2×D4—1572no—
113C22×C4—21no—
114C22×C4—3142no—
115C22×C4—3142no—
116C22×C4—6284no—
117C22×C4—1571no—
118C22×C4—1571no—
119C22×C4C2×#1059784511yescharacteristic
120C2×C8—3142no—
121C2×C8—3142no—
122C4⋊C4—21no—
123C4⋊C4C2×#1059784512yes—
124C22⋊C4—3142no—
125C22⋊C4—3142no—
126C42—1571no—
127C42—1571no—
128C42—1571no—
129C42—1571no—
130C23—3144no—
131C23—3142no—
132C23—6282no—
133C23—6282no—
134C23C22⋊#1059784511yescharacteristic
135D4—3142no—
136D4—3144no—
137D4—1574no—
138C2×C4—22no—
139C2×C4—42no—
140C2×C4—3142no—
141C2×C4—6284no—
142C2×C4—6284no—
143C2×C4—6281no—
144C2×C4—1571no—
145C2×C4—1571no—
146C2×C4—1571no—
147C2×C4—1571no—
148C2×C4C22⋊#1059784511yescharacteristic
149C2×C4D157⋊C812yes—
150C2×C4#1457896412yes—
151C2×C4C22×#1059784511yescharacteristic
152C8—6282no—
153C8—6282no—
154C22—21no—
155C22—21no—
156C22—3144no—
157C22—6288no—
158C22—6282no—
159C22—6282no—
160C22#1909782812yes—
161C22C2×C22⋊#1059784511yescharacteristic
162C4—42no—
163C4—3141no—
164C4—3141no—
165C4—3141no—
166C4—1572no—
167C4#1909782812yes—
168C4C2×D157⋊C811yescharacteristic
169C4C2×#1457896411yescharacteristic
170C2—22no—
171C2—6284no—
172C2C2×#1909782811yescharacteristic
173C2#2375826511yescharacteristic
174C2#2375827211yescharacteristic
subgroupG/H
centerC22C2×C22⋊#10597845
commutatorC4×C157C22×C8
FrattiniC2×C4C22×#10597845
FittingC2×C4⋊C4×C157C4
socleC22×C157C2×C22⋊C4
prime radicalC22×D628C4
cosocleC4×Dic157C23
hypercenterC2×C4⋊C4#10597845
hypocenterC157#1478
LCSG ▷ C4×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. #23758289C2semidirect
2. #23758289C2semidirect
3. #23758121C2semidirect
6. C4⋊#11929441C22semidirect
10. C4×#11929441C22semidirect
25. C2×D628C8semidirect
87. C157#1478semidirect

Maximal subgroups

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

subgroupindex
#237582892
#237581212
C2×#190977332
#1478157