Finite Group Databasebeta

← #34115256

Subgroups — #34115256

Order 20096.

122 conjugacy classes of subgroups; only the 20 normal subgroups are shown.

normal subgroups only

This group has 122 conjugacy classes of subgroups — too many to draw. Only its 20 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#23758177C211yesmaximal, characteristic, complemented
2#23758131C211yesmaximal, characteristic, complemented
3#23757443C211yesmaximal, characteristic
4#19097838—21no—
5#19097830—21no—
6#19097816C411yescharacteristic, complemented
7#19097799—21no—
8#19097767C2211yescharacteristic
9#19097697—21no—
10#100×C157C411yescharacteristic, complemented
11C2×#11929441—41no—
12C22⋊#10597845—41no—
13#14578954—21no—
14#14578953—41no—
15C2×D628D411yescharacteristic
16C2×C22⋊D157—41no—
17C2×C22⋊D157—41no—
18D4×D157—41no—
19#14578943—41no—
20D1256—41no—
21C4×Dic157D411yescharacteristic
22C2×D4×C157C2×C411yescharacteristic
23M16×C157—21no—
24C2×#10597845—81no—
25#11929441—81no—
26C22×D157—21no—
27C22×D157—41no—
28Dic314—21no—
29D628—21no—
30D628—41no—
31C22⋊D157—42no—
32C22⋊D157—41no—
33C22⋊D157—81no—
34C22⋊D157—81no—
35C2×Dic157—21no—
36C2×Dic157—41no—
37C4×D157—41no—
38C23×C157—21no—
39D4×C157—41no—
40C2×C4×C157C22⋊C411yescharacteristic
41C8×C157—41no—
42C22×C157—41no—
43C22×C157—81no—
44C22×C157#9911yescharacteristic
45C2×D157—41no—
46C2×D157—41no—
47C2×D157—81no—
48C2×D157—161no—
49#10597845—161no—
50C4×C157—21no—
51Dic157—21no—
52Dic157—21no—
53Dic157—41no—
54C2×C157—21no—
55C2×C157—81no—
56C2×C157AΣL(1,𝔽16)11yescharacteristic
57D157—81no—
58D157—81no—
59C157#140211yescharacteristic, complemented, Sylow
60#1402—1571nomaximal, Sylow
61#453—1571no—
62#353—1571no—
63#331—1571no—
64H(5,𝔽2)—1571no—
65AGL(1,ℤ/8)—3141no—
66#127—1571no—
67C4⋊C8—3141no—
68#104—3141no—
69#100#1059784511yescharacteristic, complemented
70#99—3141no—
71#41—3141no—
72#41—6281no—
73C2×D4—6281no—
74C2×D4—6281no—
75C2×D4—6281no—
76C2×D4—1571no—
77C2×D4C2×#1059784511yescharacteristic
78SD16—6281no—
79D8—6281no—
80M16—21no—
81C2×C8—6281no—
82C22⋊C4—6281no—
83C42—1571no—
84C23—21no—
85C23—3141no—
86C23—6281no—
87Q8—3141no—
88D4—41no—
89D4—3141no—
90D4—6281no—
91D4—6282no—
92D4—6281no—
93D4—12561no—
94D4—12561no—
95C2×C4—3141no—
96C2×C4—6281no—
97C2×C4—6281no—
98C2×C4—12561no—
99C2×C4C22⋊#1059784511yescharacteristic
100C8—41no—
101C8—12561no—
102C22—41no—
103C22—81no—
104C22—6281no—
105C22—6281no—
106C22—25121no—
107C22—12561no—
108C22#1909783011yescharacteristic
109C4—21no—
110C4—3141no—
111C4—3141no—
112C4—6281no—
113C4—25121no—
114C2—21no—
115C2—81no—
116C2—12561no—
117C2—12561no—
118C2#2375817411yescharacteristic
subgroupG/H
centerC2#23758174
commutatorC2×D4×C157C2×C4
FrattiniC2×D4C2×#10597845
Fitting#100×C157C4
socleC2×C157AΣL(1,𝔽16)
prime radical#23757443C2
cosocle#19097767C22
hypercenter#100#10597845
hypocenterC157#1402
LCSG ▷ C2×D4×C157 ▷ C2×C4×C157 ▷ C22×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ C2×D4 ◁ #100

Complements

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

NH ≅ G/Ntype
1. #23758177C2semidirect
2. #23758131C2semidirect
6. #19097816C4semidirect
10. #100×C157C4semidirect
59. C157#1402semidirect
69. #100#10597845semidirect

Maximal subgroups

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

subgroupindex
#237581772
#237581312
#237574432
#1402157