Finite Group Databasebeta

← #34115637

Subgroups — #34115637

Order 20096.

212 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 212 conjugacy classes of subgroups — too many to draw. Only its 68 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#23758291C211yesmaximal, characteristic
2D157⋊(C4⋊C8)C211yesmaximal, characteristic
3#23758133C212yesmaximal, complemented
4#23758132C212yesmaximal, complemented
5#23757827C211yesmaximal, characteristic
6C2×D157⋊C8—21no—
7#19097838C2212yes—
8#19097838C2212yes—
9C4⋊#11929441—21no—
10#19097828—21no—
11C4×#11929441—21no—
12#19097770C2211yescharacteristic
13#19097769C2211yescharacteristic
14#19097761—21no—
15#19097751C411yescharacteristic
16#19097749—21no—
17#19097747C411yescharacteristic
18C4×Dic314—21no—
19C4×Dic314C411yescharacteristic
20#19097728—21no—
21C42×D157C2211yescharacteristic
22C4×Q8×C157C411yescharacteristic
23D157⋊C8—42no—
24C2×#11929441—22no—
25C2×#11929441—22no—
26C2×Dic314—21no—
27C2×Dic314C2×C411yescharacteristic
28C2×C4×D157C2×C411yescharacteristic
29C2×C4×D157D411yescharacteristic
30C2×C4×D157D411yescharacteristic
31C4⋊Dic157—21no—
32C4⋊Dic157C2×C411yescharacteristic
33#14578933—21no—
34#14578933—21no—
35#14578933—21no—
36#14578933—21no—
37#14578933—21no—
38#14578931—21no—
39#14578931—21no—
40C4×Dic157—21no—
41C4×Dic157D411yescharacteristic
42C4×Dic157D411yescharacteristic
43C4×Dic157C2311yescharacteristic
44C2×Q8×C157C2×C411yescharacteristic
45C4⋊C4×C157—21no—
46C4⋊C4×C157C2×C411yescharacteristic
47C42×C157—21no—
48C42×C157C2×C411yescharacteristic
49#11929441—42no—
50#11929441—42no—
51C22×D157C22⋊C411yescharacteristic
52Dic314—42no—
53Dic314—41no—
54C2×Dic157—21no—
55C2×Dic157—21no—
56C2×Dic157C22⋊C411yescharacteristic
57C2×Dic157C2×D411yescharacteristic
58C2×Dic157C2×D411yescharacteristic
59C4×D157—22no—
60C4×D157—41no—
61C4×D157SD1612yes—
62C4×D157Q1612yes—
63Q8×C157—41no—
64C2×C4×C157—21no—
65C2×C4×C157—21no—
66C2×C4×C157C22⋊C411yescharacteristic
67C2×C4×C157C22⋊C411yescharacteristic
68C2×C4×C157C22×C411yescharacteristic
69C22×C157C2×C22⋊C411yescharacteristic
70C2×D157—21no—
71C2×D157—21no—
72C2×D157#10312yes—
73C4×C157—21no—
74C4×C157—21no—
75C4×C157—41no—
76C4×C157—41no—
77C4×C157#10312yes—
78Dic157—21no—
79Dic157—41no—
80Dic157—41no—
81Dic157C2×SD1611yescharacteristic
82Dic157C2×Q1611yescharacteristic
83Dic157#13512yes—
84C2×C157#41311yescharacteristic
85C2×C157C2×#10311yescharacteristic
86C2×C157#41611yescharacteristic
87D157—22no—
88C157#154211yescharacteristic, complemented, Sylow
89#1542—1571nomaximal, Sylow
90#533—1571no—
91#431—1571no—
92C2×C4⋊C8—1571no—
93#333—1572no—
94#332—1572no—
95C22×C8—3141no—
96C4⋊Q8—1571no—
97C4⋊Q8—1571no—
98#125—3141no—
99C22⋊Q8—3141no—
100C22⋊Q8—1571no—
101C22⋊Q8—1571no—
102C4×Q8—3141no—
103C4×Q8—1571no—
104C4×Q8#1059784511yescharacteristic
105#117—3141no—
106C2×C42—1571no—
107C4⋊C8—3141no—
108C4⋊C8—1572no—
109C4⋊C8—1572no—
110C22⋊C8—3141no—
111C4×C8—3141no—
112C2×Q8—3141no—
113C2×Q8—1571no—
114C2×Q8C2×#1059784511yescharacteristic
115C22×C4—1571no—
116C22×C4—1571no—
117C22×C4—1571no—
118C2×C8—3142no—
119C2×C8—3142no—
120C2×C8—6282no—
121C4⋊C4—21no—
122C4⋊C4—3141no—
123C4⋊C4—3141no—
124C4⋊C4—3141no—
125C4⋊C4—3141no—
126C4⋊C4—3141no—
127C4⋊C4—3141no—
128C4⋊C4—1571no—
129C4⋊C4C2×#1059784511yescharacteristic
130C22⋊C4—3141no—
131C22⋊C4—3141no—
132C42—21no—
133C42—3141no—
134C42—1571no—
135C42—1571no—
136C42—1571no—
137C42C2×#1059784511yescharacteristic
138C23—1571no—
139Q8—41no—
140Q8—6281no—
141Q8—6282no—
142C2×C4—21no—
143C2×C4—21no—
144C2×C4—3142no—
145C2×C4—3141no—
146C2×C4—3141no—
147C2×C4—6281no—
148C2×C4—1571no—
149C2×C4—1571no—
150C2×C4—1571no—
151C2×C4—1572no—
152C2×C4—1572no—
153C2×C4C22⋊#1059784511yescharacteristic
154C2×C4C22⋊#1059784511yescharacteristic
155C2×C4C22×#1059784511yescharacteristic
156C8—6282no—
157C8—6282no—
158C22—3141no—
159C22—3141no—
160C22—1572no—
161C22C2×C22⋊#1059784511yescharacteristic
162C4—21no—
163C4—21no—
164C4—41no—
165C4—41no—
166C4—3141no—
167C4—6281no—
168C4—6281no—
169C4—1571no—
170C4—1571no—
171C4—1572no—
172C4#1909783412yes—
173C2—3142no—
174C2#2375825911yescharacteristic
175C2C2×#1909783411yescharacteristic
176C2#2375826311yescharacteristic
subgroupG/H
centerC2×C4C22⋊#10597845
commutatorC2×C4×C157C22×C4
FrattiniC2×C4C22×#10597845
FittingC4×Q8×C157C4
socleC22×C157C2×C22⋊C4
prime radicalC22×D157C22⋊C4
cosocleC4×Dic157C23
hypercenterC4×Q8#10597845
hypocenterC157#1542
LCSG ▷ C2×C4×C157 ▷ C22×C157 ▷ C157
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
3. #23758133C2semidirect
4. #23758132C2semidirect
88. C157#1542semidirect

Maximal subgroups

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

subgroupindex
#237582912
D157⋊(C4⋊C8)2
#237581332
#237581322
#237578272
#1542157