Finite Group Databasebeta

← #34099437

Subgroups — #34099437

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#23757637C212yesmaximal
3#23757015C211yesmaximal, characteristic, complemented
4#23757014C212yesmaximal, complemented
5#490×C157C211yesmaximal, characteristic
6#19097763C2212yes—
7#19097762—22no—
8#19097761—22no—
9#19097761—22no—
10#19097692—22no—
11#19097692—22no—
12#19097682C2212yes—
13#127×C157C2211yescharacteristic
14#125×C157C2211yescharacteristic
15#102×C157—22no—
16#97×C157C2211yescharacteristic
17C2×#11929434—22no—
18C4⋊Dic157—22no—
19C4⋊Dic157D412yes—
20C4⋊Dic157D412yes—
21#14578933—22no—
22#14578933—22no—
23#14578933—22no—
24#14578933—22no—
25C4×Dic157—22no—
26C2×D4×C157—21no—
27C2×D4×C157—22no—
28C2×C8×C157—21no—
29C4⋊C4×C157—22no—
30C4⋊C4×C157D412yes—
31C42×C157C2311yescharacteristic
32C2×Dic157—22no—
33C2×Dic157—22no—
34#11929434—42no—
35C23×C157—41no—
36D4×C157—42no—
37D4×C157—44no—
38C2×C4×C157—22no—
39C2×C4×C157C2×D412yes—
40C2×C4×C157C2×D411yescharacteristic
41C8×C157—41no—
42C22×C157—82no—
43C22×C157—81no—
44C22×C157#12011yescharacteristic
45C4×C157—21no—
46C4×C157—22no—
47C4×C157—42no—
48Dic157—42no—
49Dic157—42no—
50C2×C157—161no—
51C2×C157#45412yes—
52C2×C157#45411yescharacteristic
53C157#165811yescharacteristic, complemented, Sylow
54#1658—1571nomaximal, Sylow
55#564—1571no—
56#490—1572no—
57#490D15711yescharacteristic
58#330—1571no—
59#330—1572no—
60#127C2×D15711yescharacteristic
61#125—3142no—
62#125—3142no—
63#125—3142no—
64#125—1572no—
65#125C2×D15711yescharacteristic
66#102—22no—
67#102—3142no—
68#102—3142no—
69#97—1572no—
70#97C2×D15711yescharacteristic
71C2×D4—22no—
72C2×D4—21no—
73C2×C8—21no—
74C2×C8—3142no—
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⋊C4C22⋊D15712yes—
84C42—3142no—
85C42C22×D15711yescharacteristic
86C23—41no—
87D4—44no—
88D4—42no—
89C2×C4—22no—
90C2×C4—3142no—
91C2×C4—3142no—
92C2×C4D4×D15712yes—
93C2×C4C2×C22⋊D15711yescharacteristic
94C8—41no—
95C8—6282no—
96C22—82no—
97C22—81no—
98C22#1909773911yescharacteristic
99C4—22no—
100C4—21no—
101C4—42no—
102C4—6282no—
103C4—6282no—
104C2—161no—
105C2#2375744412yes—
106C2#2375744511yescharacteristic
subgroupG/H
centerC22#19097739
commutator, cosocleC42×C157C23
FrattiniC42C22×D157
Fitting#490×C157C2
socleC22×C157#120
prime radical#127×C157C22
hypercenter#490D157
hypocenterC157#1658
LCSG ▷ C42×C157 ▷ C22×C157 ▷ C157
UCSC1 ◁ C22 ◁ C42 ◁ #490

Complements

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

NH ≅ G/Ntype
1. C157⋊#564C2semidirect
3. #23757015C2semidirect
4. #23757014C2semidirect
53. C157#1658semidirect

Maximal subgroups

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

subgroupindex
C157⋊#5642
#237576372
#237570152
#237570142
#490×C1572
#1658157