Finite Group Databasebeta

← #34099460

Subgroups — #34099460

Order 20096.

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

normal subgroups only

This group has 196 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
2#23757643C211yesmaximal, characteristic, complemented
3#23757633C212yesmaximal, complemented
4#23757012C212yesmaximal, complemented
5#330×C157C211yesmaximal, characteristic, complemented
6#19097771C2211yescharacteristic
7#19097759C2212yes—
8#19097756—22no—
9#19097749—22no—
10#19097746—22no—
11#19097696—22no—
12#19097694—22no—
13#19097693—22no—
14#19097682C2211yescharacteristic
15#125×C157C2211yescharacteristic
16#97×C157C2212yes—
17C2×Dic314—21no—
18C2×Dic314D412yes—
19C2×D628—22no—
20C2×D628D412yes—
21C2×C4×D157—22no—
22C2×#11929434—21no—
23C4⋊Dic157—22no—
24#14578933—22no—
25#14578931—22no—
26#14578931—22no—
27#14578931—22no—
28C2×C8×C157—22no—
29C4⋊C4×C157—22no—
30C4⋊C4×C157D412yes—
31C42×C157C2311yescharacteristic
32C22×D157—22no—
33Dic314—42no—
34Dic314—42no—
35D628—42no—
36D628—82no—
37C2×Dic157—22no—
38C2×Dic157—41no—
39C4×D157—82no—
40#11929434—41no—
41C2×C4×C157—22no—
42C2×C4×C157C2×D412yes—
43C2×C4×C157C2×D411yescharacteristic
44C8×C157—42no—
45C22×C157#12011yescharacteristic
46C2×D157—42no—
47C2×D157—42no—
48C2×D157—42no—
49C4×C157—21no—
50C4×C157—22no—
51C4×C157—42no—
52Dic157—42no—
53Dic157—81no—
54C2×C157#45411yescharacteristic
55C2×C157#45512yes—
56D157—82no—
57C157#166211yescharacteristic, complemented, Sylow
58#1662—1571nomaximal, Sylow
59#562—1571no—
60#491—1571no—
61#489—1572no—
62#330D15711yescharacteristic, complemented
63#329—1572no—
64C4⋊Q8—1571no—
65#125C2×D15711yescharacteristic
66#124—1572no—
67#123—3142no—
68C22⋊Q8—3142no—
69#121—3142no—
70#103—3142no—
71#103—3142no—
72#102—3142no—
73#97—1571no—
74#97C2×D15712yes—
75C2×Q8—3141no—
76C2×Q8—1572no—
77C2×D4—3142no—
78C2×D4—1572no—
79C22×C4—3142no—
80C2×C8—22no—
81C2×C8—3141no—
82C4⋊C4—22no—
83C4⋊C4—3142no—
84C4⋊C4—3142no—
85C4⋊C4D62812yes—
86C22⋊C4—3142no—
87C22⋊C4—3142no—
88C22⋊C4—3142no—
89C42C22×D15711yescharacteristic
90C23—3142no—
91Q8—6282no—
92Q8—6282no—
93D4—6282no—
94D4—12562no—
95C2×C4—22no—
96C2×C4—3142no—
97C2×C4—6281no—
98C2×C4—12562no—
99C2×C4D4×D15712yes—
100C2×C4C2×D62811yescharacteristic
101C8—42no—
102C8—6281no—
103C22—6282no—
104C22—6282no—
105C22—6282no—
106C22#1909774111yescharacteristic
107C4—21no—
108C4—22no—
109C4—42no—
110C4—6282no—
111C4—12561no—
112C2—12562no—
113C2#2375744811yescharacteristic
114C2#2375745212yes—
subgroupG/H
centerC22#19097741
commutator, cosocleC42×C157C23
FrattiniC42C22×D157
Fitting#330×C157C2
socleC22×C157#120
prime radical#23758021C2
hypercenter#330D157
hypocenterC157#1662
LCSG ▷ C42×C157 ▷ C22×C157 ▷ C157
UCSC1 ◁ C22 ◁ C42 ◁ #330

Complements

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

NH ≅ G/Ntype
2. #23757643C2semidirect
3. #23757633C2semidirect
4. #23757012C2semidirect
5. #330×C157C2semidirect
57. C157#1662semidirect
62. #330D157semidirect

Maximal subgroups

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

subgroupindex
#237580212
#237576432
#237576332
#237570122
#330×C1572
#1662157