Finite Group Databasebeta

← #34099459

Subgroups — #34099459

Order 20096.

196 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 196 conjugacy classes of subgroups — too many to draw. Only its 49 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#23757643C211yesmaximal, characteristic, complemented
2#23757632C212yesmaximal, complemented
3#23757015C211yesmaximal, characteristic, complemented
4#23757013C212yesmaximal, complemented
5#562×C157C211yesmaximal, characteristic
6#19097771C2211yescharacteristic
7#19097695—22no—
8#19097694—22no—
9#19097692—22no—
10#19097682C2212yes—
11#19097682C2211yescharacteristic
12#125×C157C2211yescharacteristic
13#124×C157C2212yes—
14#123×C157—22no—
15C22⋊Q8×C157—22no—
16#121×C157—22no—
17C2×Dic314—21no—
18C2×#11929434—22no—
19C2×#11929434—21no—
20C4⋊Dic157—22no—
21C2×Q8×C157D412yes—
22C2×D4×C157—22no—
23C2×D4×C157D412yes—
24C22×C4×C157—22no—
25C4⋊C4×C157—22no—
26C4⋊C4×C157—22no—
27C4⋊C4×C157D412yes—
28C22⋊C4×C157—22no—
29C22⋊C4×C157—22no—
30C22⋊C4×C157—22no—
31C42×C157C2311yescharacteristic
32Dic314—42no—
33C2×Dic157—41no—
34#11929434—41no—
35#11929434—42no—
36C23×C157—22no—
37Q8×C157—42no—
38D4×C157—42no—
39D4×C157—82no—
40C2×C4×C157—22no—
41C2×C4×C157—22no—
42C2×C4×C157—82no—
43C2×C4×C157C2×D411yescharacteristic
44C2×C4×C157C2×D412yes—
45C22×C157—42no—
46C22×C157—42no—
47C22×C157—42no—
48C22×C157#12011yescharacteristic
49C4×C157—21no—
50C4×C157—22no—
51C4×C157—42no—
52C4×C157—42no—
53Dic157—81no—
54C2×C157—82no—
55C2×C157#45411yescharacteristic
56C2×C157#45512yes—
57C157#166211yescharacteristic, complemented, Sylow
58#1662—1571nomaximal, Sylow
59#562D15711yescharacteristic
60#491—1571no—
61#489—1572no—
62#330—1571no—
63#329—1572no—
64C4⋊Q8—1571no—
65#125C2×D15711yescharacteristic
66#124C2×D15712yes—
67#123—22no—
68C22⋊Q8—22no—
69#121—22no—
70#103—3142no—
71#103—3142no—
72#102—3142no—
73#97—1571no—
74#97—1572no—
75C2×Q8—3141no—
76C2×Q8C22⋊D15712yes—
77C2×D4—22no—
78C2×D4C22⋊D15712yes—
79C22×C4—22no—
80C2×C8—3142no—
81C2×C8—3141no—
82C4⋊C4—22no—
83C4⋊C4—22no—
84C4⋊C4—3142no—
85C4⋊C4C22⋊D15712yes—
86C22⋊C4—22no—
87C22⋊C4—22no—
88C22⋊C4—22no—
89C42C22×D15711yescharacteristic
90C23—22no—
91Q8—42no—
92Q8—6282no—
93D4—42no—
94D4—82no—
95C2×C4—22no—
96C2×C4—22no—
97C2×C4—82no—
98C2×C4—6281no—
99C2×C4C2×C22⋊D15711yescharacteristic
100C2×C4C2×C22⋊D15712yes—
101C8—6281no—
102C8—6282no—
103C22—42no—
104C22—42no—
105C22—42no—
106C22#1909774011yescharacteristic
107C4—21no—
108C4—22no—
109C4—42no—
110C4—42no—
111C4—12561no—
112C2—82no—
113C2#2375744611yescharacteristic
114C2#2375745112yes—
subgroupG/H
centerC22#19097740
commutator, cosocleC42×C157C23
FrattiniC42C22×D157
Fitting, prime radical#562×C157C2
socleC22×C157#120
hypercenter#562D157
hypocenterC157#1662
LCSG ▷ C42×C157 ▷ C22×C157 ▷ C157
UCSC1 ◁ C22 ◁ C42 ◁ #562

Complements

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

NH ≅ G/Ntype
1. #23757643C2semidirect
2. #23757632C2semidirect
3. #23757015C2semidirect
4. #23757013C2semidirect
57. C157#1662semidirect

Maximal subgroups

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

subgroupindex
#237576432
#237576322
#237570152
#237570132
#562×C1572
#1662157