Finite Group Databasebeta

← #34115261

Subgroups — #34115261

Order 20096.

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

normal subgroups only

This group has 106 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#23758183C211yesmaximal, characteristic, complemented
2#23758133C211yesmaximal, characteristic, complemented
3#23757456C211yesmaximal, characteristic
4#19097838—21no—
5#19097832—21no—
6#19097801—21no—
7#19097769C2211yescharacteristic
8#19097698—21no—
9#19097690C411yescharacteristic
102−1+4×C157C411yescharacteristic
11#14578963—41no—
12C2×#11929441—41no—
13C2×Dic314D411yescharacteristic
14#14578944—41no—
15#14578942—41no—
16#14578938—21no—
17#14578933—41no—
18C4×Dic157D411yescharacteristic
19#41×C157—21no—
20#41×C157—41no—
21#41×C157—41no—
22C2×Q8×C157—41no—
23C2×Q8×C157C2×C411yescharacteristic
24#11929441—81no—
25#11929441—81no—
26Dic314—41no—
27C2×Dic157—21no—
28C2×Dic157—21no—
29#11929434—41no—
30Q8×C157—21no—
31Q8×C157—41no—
32Q8×C157—41no—
33D4×C157—21no—
34D4×C157—41no—
35D4×C157—41no—
36C2×C4×C157—21no—
37C2×C4×C157—41no—
38C2×C4×C157—42no—
39C2×C4×C157C22⋊C411yescharacteristic
40C22×C157—41no—
41C22×C157#9911yescharacteristic
42C4×C157—21no—
43C4×C157—41no—
44C4×C157—41no—
45Dic157—21no—
46Dic157—21no—
47Dic157—41no—
48C2×C157—21no—
49C2×C157—81no—
50C2×C157AΣL(1,𝔽16)11yescharacteristic
51C157#140511yescharacteristic, complemented, Sylow
52#1405—1571nomaximal, Sylow
53#456—1571no—
54#356—1571no—
55#333—1571no—
562−1+4#1059784511yescharacteristic
57#137—3141no—
58C4⋊Q8—1571no—
59C4⋊C8—3141no—
60#104—3141no—
61#101—3141no—
62#101—1571no—
63#41—21no—
64#41—41no—
65#41—41no—
66C2×Q8—41no—
67C2×Q8—1571no—
68C2×Q8C2×#1059784511yescharacteristic
69Q16—6281no—
70SD16—6281no—
71M16—3141no—
72M16—6281no—
73C2×C8—6281no—
74C4⋊C4—6281no—
75C42—1571no—
76Q8—21no—
77Q8—41no—
78Q8—41no—
79Q8—6281no—
80D4—21no—
81D4—41no—
82D4—41no—
83C2×C4—21no—
84C2×C4—41no—
85C2×C4—42no—
86C2×C4—3141no—
87C2×C4—3141no—
88C2×C4C22⋊#1059784511yescharacteristic
89C8—6281no—
90C8—12561no—
91C8—12561no—
92C22—41no—
93C22#1909782911yescharacteristic
94C4—21no—
95C4—41no—
96C4—41no—
97C4—3141no—
98C4—3141no—
99C4—6281no—
100C2—21no—
101C2—81no—
102C2#2375817311yescharacteristic
subgroupG/H
centerC2#23758173
commutatorC2×Q8×C157C2×C4
FrattiniC2×Q8C2×#10597845
Fitting, prime radical2−1+4×C157C4
socleC2×C157AΣL(1,𝔽16)
cosocle#19097769C22
hypercenter2−1+4#10597845
hypocenterC157#1405
LCSG ▷ C2×Q8×C157 ▷ C2×C4×C157 ▷ C22×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ C2×Q8 ◁ 2−1+4

Complements

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

NH ≅ G/Ntype
1. #23758183C2semidirect
2. #23758133C2semidirect
51. C157#1405semidirect

Maximal subgroups

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

subgroupindex
#237581832
#237581332
#237574562
#1405157