Finite Group Databasebeta

← #34115017

Subgroups — #34115017

Order 20096.

246 conjugacy classes of subgroups; only the 48 normal subgroups are shown.

normal subgroups only

This group has 246 conjugacy classes of subgroups — too many to draw. Only its 48 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#23758244C211yesmaximal, characteristic
2C4×C22⋊#10597845C211yesmaximal, characteristic
3#23757120C211yesmaximal, characteristic
4C2×#14578964C412yescomplemented
5C2×C22⋊#10597845—21no—
6C2×C4×#10597845—21no—
7#19097828—21no—
8C22⋊#11929441—21no—
9(C2×#10597845)⋊C4C412yescomplemented
10C22×C4×D157C2211yescharacteristic
11C2×#14578931—21no—
12C2×C4×Dic157—21no—
13#19097678C411yescharacteristic, complemented
14#95×C157C411yescharacteristic, complemented
15C22×#10597845—22no—
16#14578964—42no—
17C2×#11929441—22no—
18C22⋊#10597845—22no—
19C22⋊#10597845—22no—
20C4×#10597845—42no—
21C23×D157D411yescharacteristic
22C22×Dic157—21no—
23C22×Dic157D411yescharacteristic
24C2×C4×D157—42no—
25C2×C4×D157C2×C411yescharacteristic
26C2×C4×D157C2×C411yescharacteristic
27C2×C4×D157D411yescharacteristic
28C2×C4×D157Q811yescharacteristic
29#14578931—24no—
30C4×Dic157—42no—
31C22×C4×C157—21no—
32C22×C4×C157C2×C411yescharacteristic
33C2×#10597845—24no—
34C2×#10597845—42no—
35C2×#10597845—42no—
36#11929441—42no—
37C22×D157—21no—
38C22×D157—21no—
39C22×D157—22no—
40C22×D157—41no—
41C22×D157C22⋊C411yescharacteristic
42C22×D157C4⋊C411yescharacteristic
43C2×Dic157—22no—
44C2×Dic157—22no—
45C2×Dic157—41no—
46C2×Dic157—41no—
47C2×Dic157C22⋊C411yescharacteristic
48C2×Dic157C4⋊C411yescharacteristic
49C4×D157—22no—
50C4×D157—22no—
51C4×D157—41no—
52C4×D157—41no—
53C23×C157C22⋊C411yescharacteristic
54C2×C4×C157—22no—
55C2×C4×C157—41no—
56C2×C4×C157—41no—
57C2×C4×C157—41no—
58C2×C4×C157C4211yescharacteristic
59C2×C4×C157C4⋊C411yescharacteristic
60C22×C157—21no—
61C22×C157—21no—
62C22×C157#9511yescharacteristic
63C22×C157#10411yescharacteristic
64C22×C157#10411yescharacteristic
65C2×D157—21no—
66C2×D157—21no—
67C2×D157—21no—
68C2×D157—21no—
69C2×D157—21no—
70C2×D157—42no—
71C2×D157—42no—
72C2×D157#10412yes—
73#10597845—44no—
74C4×C157—21no—
75C4×C157—21no—
76C4×C157—42no—
77Dic157—21no—
78Dic157—42no—
79Dic157#9912yes—
80C2×C157—21no—
81C2×C157—21no—
82C2×C157#33911yescharacteristic
83C2×C157#33911yescharacteristic
84C2×C157#34211yescharacteristic
85D157—22no—
86D157—41no—
87C157#129711yescharacteristic, complemented, Sylow
88#1297—1571nomaximal, Sylow
89#407—1571no—
90C4×C22⋊C4—1571no—
91C4×C22⋊C4—1571no—
92C23×C4—1571no—
93C2×M16—1572no—
94C2×C22⋊C4—3141no—
95C2×C22⋊C4—3141no—
96C2×C42—3141no—
97C2×C42—3141no—
98C22⋊C8—3141no—
99C22⋊C8—3141no—
100#95—1572no—
101#95—1571no—
102#95#1059784511yescharacteristic, complemented
103C24—1571no—
104C22×C4—21no—
105C22×C4—3142no—
106C22×C4—3141no—
107C22×C4—6282no—
108C22×C4—1571no—
109C22×C4—1571no—
110C22×C4—1571no—
111C22×C4—1571no—
112C22×C4—1571no—
113C22×C4C2×#1059784511yescharacteristic
114M16—6282no—
115C2×C8—3142no—
116C22⋊C4—3144no—
117C22⋊C4—3142no—
118C22⋊C4—3142no—
119C42—6282no—
120C42—6282no—
121C23—3142no—
122C23—3141no—
123C23—3141no—
124C23—6281no—
125C23—1571no—
126C23—1571no—
127C23C22⋊#1059784511yescharacteristic
128C2×C4—22no—
129C2×C4—41no—
130C2×C4—41no—
131C2×C4—41no—
132C2×C4—3142no—
133C2×C4—3142no—
134C2×C4—3142no—
135C2×C4—3142no—
136C2×C4—3144no—
137C2×C4—6281no—
138C2×C4—6281no—
139C2×C4—6281no—
140C2×C4—6282no—
141C2×C4—6282no—
142C2×C4—6281no—
143C2×C4—1571no—
144C2×C4—1571no—
145C2×C4C4×#1059784511yescharacteristic
146C2×C4C4⋊#1059784511yescharacteristic
147C8—6282no—
148C22—21no—
149C22—21no—
150C22—3141no—
151C22—3141no—
152C22—3141no—
153C22—3141no—
154C22—3141no—
155C22—6282no—
156C22—6282no—
157C22—1572no—
158C22(C2×#10597845)⋊C411yescharacteristic
159C22#1909783511yescharacteristic
160C22#1909783611yescharacteristic
161C4—21no—
162C4—21no—
163C4—42no—
164C4—3141no—
165C4—6282no—
166C4—6284no—
167C4—1572no—
168C2—21no—
169C2—21no—
170C2—3142no—
171C2—6281no—
172C2#2375814311yescharacteristic
173C2#2375814411yescharacteristic
174C2#2375815011yescharacteristic
subgroupG/H
centerC22(C2×#10597845)⋊C4
commutatorC2×C4×C157C42
FrattiniC22×C4C2×#10597845
Fitting#95×C157C4
socleC22×C157#95
prime radicalC23×D157D4
cosocleC22×C4×D157C22
hypercenter#95#10597845
hypocenterC157#1297
LCSG ▷ C2×C4×C157 ▷ C22×C157 ▷ C157
UCSC1 ◁ C22 ◁ C22×C4 ◁ #95

Complements

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

NH ≅ G/Ntype
4. C2×#14578964C4semidirect
9. (C2×#10597845)⋊C4C4semidirect
13. #19097678C4semidirect
14. #95×C157C4semidirect
87. C157#1297semidirect
102. #95#10597845semidirect

Maximal subgroups

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

subgroupindex
#237582442
C4×C22⋊#105978452
#237571202
#1297157