Finite Group Databasebeta

← #34099447

Subgroups — #34099447

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#23757683C212yesmaximal, complemented
2#23757668C211yesmaximal, characteristic
3#23757015C212yesmaximal, complemented
4#23757013C211yesmaximal, characteristic
5#563×C157C211yesmaximal, characteristic
6C2×#14578944—21no—
7C2×#14578942—21no—
8#19097771C2211yescharacteristic
9#19097704—22no—
10#19097702—22no—
11#19097682C2211yescharacteristic
12#19097682C2212yes—
13C4⋊Q8×C157—21no—
14#126×C157—22no—
15#125×C157C2212yes—
16#124×C157C2211yescharacteristic
17#123×C157—21no—
18C22⋊Q8×C157—22no—
19C2×Dic314—21no—
20#14578944—42no—
21#14578942—42no—
22C2×#11929434—22no—
23C2×#11929434—21no—
24C4⋊Dic157—22no—
25C2×Q8×C157—21no—
26C2×Q8×C157D411yescharacteristic
27C2×D4×C157D411yescharacteristic
28C22×C4×C157—21no—
29C4⋊C4×C157—22no—
30C4⋊C4×C157—22no—
31C4⋊C4×C157—22no—
32C4⋊C4×C157D412yes—
33C4⋊C4×C157D412yes—
34C22⋊C4×C157—22no—
35C22⋊C4×C157—21no—
36C22⋊C4×C157—22no—
37C42×C157—21no—
38C42×C157C2311yescharacteristic
39Dic314—41no—
40Dic314—41no—
41C2×Dic157—41no—
42#11929434—22no—
43#11929434—24no—
44C23×C157—21no—
45Q8×C157—41no—
46Q8×C157—81no—
47D4×C157—41no—
48C2×C4×C157—22no—
49C2×C4×C157—21no—
50C2×C4×C157—22no—
51C2×C4×C157—81no—
52C2×C4×C157C2×D411yescharacteristic
53C2×C4×C157C2×D412yes—
54C22×C157—41no—
55C22×C157—42no—
56C22×C157#12011yescharacteristic
57C4×C157—21no—
58C4×C157—22no—
59C4×C157—42no—
60C4×C157—41no—
61C4×C157—42no—
62Dic157—81no—
63C2×C157—81no—
64C2×C157#45311yescharacteristic
65C2×C157#45612yes—
66C157#166011yescharacteristic, complemented, Sylow
67#1660—1571nomaximal, Sylow
68#563D15711yescharacteristic
69#501—1572no—
70#497—1571no—
71#330—1572no—
72#329—1571no—
73C2×Q16—3141no—
74C2×SD16—3141no—
75C4⋊Q8—21no—
76C4⋊Q8—1571no—
77#126—22no—
78#125C2×D15712yes—
79#124C2×D15711yescharacteristic
80#123—21no—
81C22⋊Q8—22no—
82#107—3142no—
83#106—3142no—
84#97—1572no—
85#97—1571no—
86C2×Q8—21no—
87C2×Q8—3141no—
88C2×Q8C22⋊D15711yescharacteristic
89C2×D4C22⋊D15711yescharacteristic
90C22×C4—21no—
91Q16—6282no—
92SD16—6282no—
93C2×C8—3142no—
94C2×C8—3141no—
95C4⋊C4—22no—
96C4⋊C4—22no—
97C4⋊C4—22no—
98C4⋊C4—3142no—
99C4⋊C4C22⋊D15712yes—
100C4⋊C4C22⋊D15712yes—
101C22⋊C4—22no—
102C22⋊C4—21no—
103C22⋊C4—22no—
104C42—21no—
105C42C22×D15711yescharacteristic
106C23—21no—
107Q8—41no—
108Q8—81no—
109Q8—6281no—
110Q8—6281no—
111D4—41no—
112C2×C4—22no—
113C2×C4—21no—
114C2×C4—22no—
115C2×C4—81no—
116C2×C4—6281no—
117C2×C4C2×C22⋊D15712yes—
118C2×C4C2×C22⋊D15711yescharacteristic
119C8—3142no—
120C8—3144no—
121C22—41no—
122C22—42no—
123C22#1909774011yescharacteristic
124C4—21no—
125C4—22no—
126C4—42no—
127C4—41no—
128C4—42no—
129C4—12561no—
130C2—81no—
131C2#2375744111yescharacteristic
132C2#2375745612yes—
subgroupG/H
centerC22#19097740
commutator, cosocleC42×C157C23
FrattiniC42C22×D157
Fitting#563×C157C2
socleC22×C157#120
prime radicalC2×D4×C157D4
hypercenter#563D157
hypocenterC157#1660
LCSG ▷ C42×C157 ▷ C22×C157 ▷ C157
UCSC1 ◁ C22 ◁ C42 ◁ #563

Complements

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

NH ≅ G/Ntype
1. #23757683C2semidirect
3. #23757015C2semidirect
66. C157#1660semidirect

Maximal subgroups

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

subgroupindex
#237576832
#237576682
#237570152
#237570132
#563×C1572
#1660157