Finite Group Databasebeta

← #34099439

Subgroups — #34099439

Order 20096.

182 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 182 conjugacy classes of subgroups — too many to draw. Only its 45 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
1C157⋊#564C211yesmaximal, characteristic, complemented
2#23757639C211yesmaximal, characteristic
3#23757638C212yesmaximal
4#23757014C212yesmaximal, complemented
5#330×C157C211yesmaximal, characteristic, complemented
6#19097768C2211yescharacteristic
7#19097763C2212yes—
8#19097762—22no—
9#19097761—22no—
10#19097761—22no—
11#19097693—22no—
12#19097693—22no—
13#19097691—22no—
14#19097682C2211yescharacteristic
15#125×C157C2211yescharacteristic
16#97×C157C2212yes—
17C2×D628—21no—
18C2×D628—22no—
19C2×#11929434—21no—
20C4⋊Dic157—22no—
21C4⋊Dic157D412yes—
22C4⋊Dic157D412yes—
23#14578933—22no—
24#14578933—22no—
25#14578933—22no—
26#14578933—22no—
27C4×Dic157—22no—
28C2×C8×C157—22no—
29C4⋊C4×C157—22no—
30C4⋊C4×C157D412yes—
31C42×C157C2311yescharacteristic
32C22×D157—41no—
33D628—44no—
34D628—42no—
35C2×Dic157—22no—
36C2×Dic157—22no—
37#11929434—41no—
38C2×C4×C157—22no—
39C2×C4×C157C2×D412yes—
40C2×C4×C157C2×D411yescharacteristic
41C8×C157—42no—
42C22×C157#12011yescharacteristic
43C2×D157—82no—
44C2×D157—81no—
45C4×C157—22no—
46C4×C157—21no—
47C4×C157—42no—
48Dic157—42no—
49Dic157—42no—
50C2×C157#45412yes—
51C2×C157#45411yescharacteristic
52D157—161no—
53C157#165811yescharacteristic, complemented, Sylow
54#1658—1571nomaximal, Sylow
55#564—1571no—
56#490—1571no—
57#490—1572no—
58#330—1572no—
59#330D15711yescharacteristic, complemented
60#127—1571no—
61#125—3142no—
62#125—3142no—
63#125—3142no—
64#125—1572no—
65#125C2×D15711yescharacteristic
66#102—3142no—
67#102—3142no—
68#102—3142no—
69#97—1571no—
70#97C2×D15712yes—
71C2×D4—3142no—
72C2×D4—3141no—
73C2×C8—22no—
74C2×C8—3141no—
75C4⋊C4—22no—
76C4⋊C4—3142no—
77C4⋊C4—3142no—
78C4⋊C4—3142no—
79C4⋊C4—3142no—
80C4⋊C4—3142no—
81C4⋊C4—1572no—
82C4⋊C4—1572no—
83C4⋊C4D62812yes—
84C42—3142no—
85C42C22×D15711yescharacteristic
86C23—6281no—
87D4—6284no—
88D4—6282no—
89C2×C4—22no—
90C2×C4—3142no—
91C2×C4—3142no—
92C2×C4D4×D15712yes—
93C2×C4C2×D62811yescharacteristic
94C8—42no—
95C8—6281no—
96C22—12562no—
97C22—12561no—
98C22#1909774111yescharacteristic
99C4—22no—
100C4—21no—
101C4—42no—
102C4—6282no—
103C4—6282no—
104C2—25121no—
105C2#2375744712yes—
106C2#2375744811yescharacteristic
subgroupG/H
centerC22#19097741
commutator, cosocleC42×C157C23
FrattiniC42C22×D157
Fitting#330×C157C2
socleC22×C157#120
prime radical#19097768C22
hypercenter#330D157
hypocenterC157#1658
LCSG ▷ C42×C157 ▷ C22×C157 ▷ C157
UCSC1 ◁ C22 ◁ C42 ◁ #330

Complements

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

NH ≅ G/Ntype
1. C157⋊#564C2semidirect
4. #23757014C2semidirect
5. #330×C157C2semidirect
53. C157#1658semidirect
59. #330D157semidirect

Maximal subgroups

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

subgroupindex
C157⋊#5642
#237576392
#237576382
#237570142
#330×C1572
#1658157