Finite Group Databasebeta

← #34099428

Subgroups — #34099428

Order 20096.

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

normal subgroups only

This group has 230 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
1#23758021C211yesmaximal, characteristic, complemented
2#23757660C212yesmaximal, complemented
3#23757015C211yesmaximal, characteristic, complemented
4#23757012C212yesmaximal, complemented
5#490×C157C211yesmaximal, characteristic, complemented
6C2×#14578942—22no—
7C2×#14578939—22no—
8#19097759C2212yes—
9#19097756—22no—
10#19097749—22no—
11#19097746—22no—
12#19097682C2212yes—
13#127×C157C2211yescharacteristic
14#125×C157C2211yescharacteristic
15#102×C157—22no—
16#97×C157C2211yescharacteristic
17C2×Dic314D412yes—
18C2×D628—22no—
19C2×D628D412yes—
20C2×C4×D157—22no—
21#14578942—44no—
22#14578939—44no—
23C2×#11929434—22no—
24#14578933—22no—
25#14578931—22no—
26#14578931—22no—
27#14578931—22no—
28C2×D4×C157—21no—
29C2×D4×C157—22no—
30C2×C8×C157—21no—
31C4⋊C4×C157—22no—
32C4⋊C4×C157D412yes—
33C42×C157C2311yescharacteristic
34C22×D157—22no—
35Dic314—42no—
36D628—42no—
37D628—82no—
38C2×Dic157—22no—
39C4×D157—82no—
40#11929434—24no—
41C23×C157—41no—
42D4×C157—42no—
43D4×C157—42no—
44D4×C157—42no—
45C2×C4×C157—22no—
46C2×C4×C157C2×D412yes—
47C2×C4×C157C2×D411yescharacteristic
48C8×C157—41no—
49C22×C157—82no—
50C22×C157—81no—
51C22×C157#12011yescharacteristic
52C2×D157—42no—
53C2×D157—42no—
54C2×D157—42no—
55C4×C157—22no—
56C4×C157—21no—
57C4×C157—42no—
58Dic157—42no—
59C2×C157—161no—
60C2×C157#45312yes—
61C2×C157#45411yescharacteristic
62D157—82no—
63C157#165611yescharacteristic, complemented, Sylow
64#1656—1571nomaximal, Sylow
65#562—1571no—
66#496—1572no—
67#490D15711yescharacteristic, complemented
68#330—1571no—
69#329—1572no—
70C2×SD16—3142no—
71C2×D8—3142no—
72#127C2×D15711yescharacteristic
73#125C2×D15711yescharacteristic
74#124—1572no—
75#123—3142no—
76C22⋊Q8—3142no—
77#121—3142no—
78#102—22no—
79#97—1572no—
80#97C2×D15711yescharacteristic
81C2×Q8—1572no—
82C2×D4—22no—
83C2×D4—21no—
84C2×D4—3142no—
85C2×D4—1572no—
86C22×C4—3142no—
87SD16—6284no—
88D8—6284no—
89C2×C8—21no—
90C2×C8—3142no—
91C4⋊C4—22no—
92C4⋊C4—3142no—
93C4⋊C4C22⋊D15712yes—
94C22⋊C4—3142no—
95C22⋊C4—3142no—
96C22⋊C4—3142no—
97C42C22×D15711yescharacteristic
98C23—41no—
99C23—3142no—
100Q8—6282no—
101D4—42no—
102D4—42no—
103D4—42no—
104D4—6282no—
105D4—12562no—
106C2×C4—22no—
107C2×C4—3142no—
108C2×C4—12562no—
109C2×C4D4×D15712yes—
110C2×C4C2×C22⋊D15711yescharacteristic
111C8—41no—
112C8—3144no—
113C22—82no—
114C22—81no—
115C22—6282no—
116C22—6282no—
117C22—6282no—
118C22#1909773911yescharacteristic
119C4—22no—
120C4—21no—
121C4—42no—
122C4—6282no—
123C2—161no—
124C2—12562no—
125C2#2375743912yes—
126C2#2375744511yescharacteristic
subgroupG/H
centerC22#19097739
commutator, cosocleC42×C157C23
FrattiniC42C22×D157
Fitting#490×C157C2
socleC22×C157#120
hypercenter#490D157
hypocenterC157#1656
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. #23758021C2semidirect
2. #23757660C2semidirect
3. #23757015C2semidirect
4. #23757012C2semidirect
5. #490×C157C2semidirect
63. C157#1656semidirect
67. #490D157semidirect

Maximal subgroups

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

subgroupindex
#237580212
#237576602
#237570152
#237570122
#490×C1572
#1656157