Finite Group Databasebeta

← #34099457

Subgroups — #34099457

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#23757635C212yesmaximal, complemented
3#23757015C211yesmaximal, characteristic, complemented
4#23757012C212yesmaximal, complemented
5#491×C157C211yesmaximal, characteristic, complemented
6#19097759C2212yes—
7#19097756—22no—
8#19097749—22no—
9#19097746—22no—
10#19097694—22no—
11#19097691—22no—
12#19097682C2212yes—
13C4⋊Q8×C157C2211yescharacteristic
14#125×C157C2211yescharacteristic
15#103×C157—22no—
16#97×C157C2211yescharacteristic
17C2×Dic314D412yes—
18C2×D628—22no—
19C2×D628D412yes—
20C2×C4×D157—22no—
21C2×#11929434—22no—
22#14578933—22no—
23#14578931—22no—
24#14578931—22no—
25#14578931—22no—
26C2×Q8×C157—21no—
27C2×C8×C157—21no—
28C4⋊C4×C157—22no—
29C4⋊C4×C157—22no—
30C4⋊C4×C157D412yes—
31C42×C157C2311yescharacteristic
32C22×D157—22no—
33Dic314—42no—
34D628—42no—
35D628—82no—
36C2×Dic157—22no—
37C4×D157—82no—
38#11929434—42no—
39Q8×C157—42no—
40C2×C4×C157—22no—
41C2×C4×C157—41no—
42C2×C4×C157C2×D412yes—
43C2×C4×C157C2×D411yescharacteristic
44C8×C157—41no—
45C22×C157#12011yescharacteristic
46C2×D157—42no—
47C2×D157—42no—
48C2×D157—42no—
49C4×C157—21no—
50C4×C157—22no—
51C4×C157—42no—
52C4×C157—81no—
53Dic157—42no—
54C2×C157#45411yescharacteristic
55C2×C157#45512yes—
56D157—82no—
57C157#166211yescharacteristic, complemented, Sylow
58#1662—1571nomaximal, Sylow
59#562—1571no—
60#491D15711yescharacteristic, complemented
61#489—1572no—
62#330—1571no—
63#329—1572no—
64C4⋊Q8C2×D15711yescharacteristic
65#125C2×D15711yescharacteristic
66#124—1572no—
67#123—3142no—
68C22⋊Q8—3142no—
69#121—3142no—
70#103—22no—
71#103—3142no—
72#102—3142no—
73#97—1572no—
74#97C2×D15711yescharacteristic
75C2×Q8—21no—
76C2×Q8—1572no—
77C2×D4—3142no—
78C2×D4—1572no—
79C22×C4—3142no—
80C2×C8—21no—
81C2×C8—3142no—
82C4⋊C4—22no—
83C4⋊C4—22no—
84C4⋊C4—3142no—
85C4⋊C4C22⋊D15712yes—
86C22⋊C4—3142no—
87C22⋊C4—3142no—
88C22⋊C4—3142no—
89C42C22×D15711yescharacteristic
90C23—3142no—
91Q8—42no—
92Q8—6282no—
93D4—6282no—
94D4—12562no—
95C2×C4—22no—
96C2×C4—41no—
97C2×C4—3142no—
98C2×C4—12562no—
99C2×C4D4×D15712yes—
100C2×C4C2×C22⋊D15711yescharacteristic
101C8—41no—
102C8—6282no—
103C22—6282no—
104C22—6282no—
105C22—6282no—
106C22#1909773911yescharacteristic
107C4—21no—
108C4—22no—
109C4—42no—
110C4—81no—
111C4—6282no—
112C2—12562no—
113C2#2375744511yescharacteristic
114C2#2375744912yes—
subgroupG/H
centerC22#19097739
commutator, cosocleC42×C157C23
FrattiniC42C22×D157
Fitting#491×C157C2
socleC22×C157#120
prime radical#23758021C2
hypercenter#491D157
hypocenterC157#1662
LCSG ▷ C42×C157 ▷ C22×C157 ▷ C157
UCSC1 ◁ C22 ◁ C42 ◁ #491

Complements

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

NH ≅ G/Ntype
2. #23757635C2semidirect
3. #23757015C2semidirect
4. #23757012C2semidirect
5. #491×C157C2semidirect
57. C157#1662semidirect
60. #491D157semidirect

Maximal subgroups

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

subgroupindex
#237580212
#237576352
#237570152
#237570122
#491×C1572
#1662157