Finite Group Databasebeta

← #34099464

Subgroups — #34099464

Order 20096.

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

normal subgroups only

This group has 172 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#23757683C212yesmaximal
2#23757643C211yesmaximal, characteristic
3#23757015C211yesmaximal, characteristic
4#23757015C212yesmaximal
5#564×C157C211yesmaximal, characteristic
6#19097771C2211yescharacteristic
7#19097704—22no—
8#19097702—22no—
9#19097694—22no—
10#19097682C2211yescharacteristic
11#19097682C2212yes—
12#125×C157—22no—
13#125×C157—22no—
14#125×C157—22no—
15#125×C157C2211yescharacteristic
16#125×C157C2212yes—
17C2×Dic314—21no—
18C2×#11929434—22no—
19C2×#11929434—21no—
20C4⋊Dic157—22no—
21C4⋊C4×C157—22no—
22C4⋊C4×C157—22no—
23C4⋊C4×C157—22no—
24C4⋊C4×C157—22no—
25C4⋊C4×C157—22no—
26C4⋊C4×C157—22no—
27C4⋊C4×C157D412yes—
28C4⋊C4×C157D412yes—
29C4⋊C4×C157D412yes—
30C42×C157—22no—
31C42×C157C2311yescharacteristic
32Dic314—42no—
33C2×Dic157—41no—
34#11929434—24no—
35#11929434—41no—
36C2×C4×C157—22no—
37C2×C4×C157—22no—
38C2×C4×C157—22no—
39C2×C4×C157C2×D411yescharacteristic
40C2×C4×C157C2×D412yes—
41C22×C157#12011yescharacteristic
42C4×C157—21no—
43C4×C157—22no—
44C4×C157—42no—
45C4×C157—42no—
46C4×C157—42no—
47Dic157—81no—
48C2×C157#45411yescharacteristic
49C2×C157#45612yes—
50C157#166311yescharacteristic, complemented, Sylow
51#1663—1571nomaximal, Sylow
52#564D15711yescharacteristic
53#501—1572no—
54#491—1571no—
55#330—1572no—
56#330—1571no—
57C4⋊Q8—1571no—
58#125—22no—
59#125—22no—
60#125—22no—
61#125C2×D15711yescharacteristic
62#125C2×D15712yes—
63#107—3142no—
64#106—3142no—
65#103—3142no—
66#97—1571no—
67#97—1572no—
68C2×Q8—3141no—
69C2×C8—3142no—
70C2×C8—3141no—
71C4⋊C4—22no—
72C4⋊C4—22no—
73C4⋊C4—22no—
74C4⋊C4—22no—
75C4⋊C4—22no—
76C4⋊C4—22no—
77C4⋊C4—3142no—
78C4⋊C4C22⋊D15712yes—
79C4⋊C4C22⋊D15712yes—
80C4⋊C4C22⋊D15712yes—
81C42—22no—
82C42C22×D15711yescharacteristic
83Q8—6282no—
84C2×C4—22no—
85C2×C4—22no—
86C2×C4—22no—
87C2×C4—6281no—
88C2×C4C2×C22⋊D15712yes—
89C2×C4C2×C22⋊D15711yescharacteristic
90C8—3144no—
91C8—6281no—
92C22#1909774011yescharacteristic
93C4—21no—
94C4—22no—
95C4—42no—
96C4—42no—
97C4—42no—
98C4—12561no—
99C2#2375744611yescharacteristic
100C2#2375745612yes—
subgroupG/H
centerC22#19097740
commutator, cosocleC42×C157C23
FrattiniC42C22×D157
Fitting#564×C157C2
socle, prime radicalC22×C157#120
hypercenter#564D157
hypocenterC157#1663
LCSG ▷ C42×C157 ▷ C22×C157 ▷ C157
UCSC1 ◁ C22 ◁ C42 ◁ #564

Complements

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

NH ≅ G/Ntype
50. C157#1663semidirect

Maximal subgroups

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

subgroupindex
#237576832
#237576432
#237570152
#564×C1572
#1663157