Finite Group Databasebeta

← #34098795

Subgroups — #34098795

Order 20096.

246 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 246 conjugacy classes of subgroups — too many to draw. Only its 67 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#23757821C211yesmaximal, characteristic
2#23757325C212yesmaximal, complemented
3#23757021C212yesmaximal, complemented
4#23757017C211yesmaximal, characteristic, complemented
5#331×C157C211yesmaximal, characteristic, complemented
6C2×#14578953C412yes—
7#19097771C2211yescharacteristic
8#19097758C412yes—
9#19097742—22no—
10D4×Dic157—22no—
11C42×D157C2211yescharacteristic
12C4⋊#11929434C2212yes—
13#19097683—22no—
14C8×Dic157—22no—
15#127×C157C2211yescharacteristic
16C4⋊C8×C157C2212yes—
17#14578953—44no—
18C2×Dic314C2×C412yes—
19C2×C22⋊D157—22no—
20C22×Dic157—22no—
21C2×C4×D157C2×C411yescharacteristic
22C2×C4×D157D412yes—
23C2×#11929434—22no—
24C4⋊Dic157—22no—
25C22⋊Dic157—24no—
26C4×Dic157C2×C411yescharacteristic
27C4×Dic157D412yes—
28C2×D4×C157—22no—
29C2×D4×C157C2×C412yes—
30C2×C8×C157—22no—
31C42×C157C2311yescharacteristic
32C22×D157C22⋊C411yescharacteristic
33Dic314—42no—
34C22⋊D157—44no—
35C2×Dic157—22no—
36C2×Dic157—44no—
37C2×Dic157C22⋊C412yes—
38C2×Dic157C22⋊C411yescharacteristic
39C4×D157—22no—
40C4×D157—22no—
41C4×D157—22no—
42#11929434—42no—
43C23×C157—22no—
44D4×C157—42no—
45D4×C157—42no—
46D4×C157—42no—
47C2×C4×C157C22×C411yescharacteristic
48C2×C4×C157C2×D412yes—
49C8×C157—42no—
50C22×C157—42no—
51C22×C157—44no—
52C22×C157C2×C22⋊C411yescharacteristic
53C2×D157—21no—
54C2×D157—22no—
55C4×C157—21no—
56C4×C157#13512yes—
57C4×C157#13512yes—
58Dic157—22no—
59Dic157—42no—
60Dic157#10012yes—
61C2×C157—82no—
62C2×C157C2×#10011yescharacteristic
63C2×C157#41612yes—
64D157—41no—
65C157#154311yescharacteristic, complemented, Sylow
66#1543—1571nomaximal, Sylow
67#532—1571no—
68#431—1572no—
69#333—1572no—
70#331—1571no—
71#331D15711yescharacteristic, complemented
72C2×#41—1572no—
73C4⋊Q8—1571no—
74#127C2×D15711yescharacteristic
75#124—1572no—
76#121—3142no—
77C4×D4—3142no—
78C2×C42—1571no—
79C4⋊C8—1572no—
80C4⋊C8C2×D15712yes—
81C22⋊C8—3142no—
82C4×C8—3142no—
83#41—6284no—
84C2×Q8—1572no—
85C2×D4—22no—
86C2×D4—3142no—
87C2×D4C4×D15712yes—
88C22×C4—3142no—
89C22×C4—1571no—
90C22×C4—1572no—
91C2×C8—22no—
92C2×C8—3142no—
93C4⋊C4—3142no—
94C22⋊C4—3144no—
95C42—1571no—
96C42—1572no—
97C42C22×D15711yescharacteristic
98C23—22no—
99C23—1571no—
100Q8—6282no—
101D4—42no—
102D4—42no—
103D4—42no—
104D4—6284no—
105C2×C4—3142no—
106C2×C4—3142no—
107C2×C4—3142no—
108C2×C4—3142no—
109C2×C4—6284no—
110C2×C4—1572no—
111C2×C4—1571no—
112C2×C4C2×C4×D15711yescharacteristic
113C2×C4D4×D15712yes—
114C8—42no—
115C8—6282no—
116C22—42no—
117C22—44no—
118C22—3141no—
119C22—3142no—
120C22C22⋊C4×D15711yescharacteristic
121C4—21no—
122C4—3142no—
123C4—6282no—
124C4—1572no—
125C4#1909779012yes—
126C4#1909779212yes—
127C2—82no—
128C2—6281no—
129C2#100×D15711yescharacteristic
130C2#2375726612yes—
subgroupG/H
centerC22C22⋊C4×D157
commutatorC2×C4×C157C22×C4
FrattiniC42C22×D157
Fitting#331×C157C2
socleC22×C157C2×C22⋊C4
prime radical#23757821C2
cosocleC42×C157C23
hypercenter#331D157
hypocenterC157#1543
LCSG ▷ C2×C4×C157 ▷ C22×C157 ▷ C157
UCSC1 ◁ C22 ◁ C42 ◁ #331

Complements

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

NH ≅ G/Ntype
2. #23757325C2semidirect
3. #23757021C2semidirect
4. #23757017C2semidirect
5. #331×C157C2semidirect
65. C157#1543semidirect
71. #331D157semidirect

Maximal subgroups

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

subgroupindex
#237578212
#237573252
#237570212
#237570172
#331×C1572
#1543157