Finite Group Databasebeta

← #34115262

Subgroups — #34115262

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#23757458C211yesmaximal, characteristic
4#19097838—21no—
5#19097832—21no—
6#19097819C411yescharacteristic
7#19097804—21no—
8#19097769C2211yescharacteristic
9#19097697—21no—
10#101×C157C411yescharacteristic
11#14578963—41no—
12C2×#11929441—41no—
13#14578955—41no—
14#14578954—21no—
15#14578954—41no—
16C2×Dic314D411yescharacteristic
17Q8×D157—41no—
18Dic628—41no—
19#14578943—41no—
20#14578933—41no—
21C4×Dic157D411yescharacteristic
22C2×Q8×C157C2×C411yescharacteristic
23M16×C157—21no—
24#11929441—81no—
25#11929441—81no—
26Dic314—21no—
27Dic314—41no—
28Dic314—41no—
29D628—21no—
30D628—41no—
31C22⋊D157—41no—
32C2×Dic157—21no—
33C2×Dic157—21no—
34C4×D157—41no—
35C4×D157—42no—
36Q8×C157—41no—
37C2×C4×C157—21no—
38C2×C4×C157C22⋊C411yescharacteristic
39C8×C157—41no—
40C22×C157#9911yescharacteristic
41C2×D157—41no—
42C4×C157—21no—
43C4×C157—41no—
44Dic157—21no—
45Dic157—21no—
46Dic157—41no—
47Dic157—41no—
48C2×C157—21no—
49C2×C157AΣL(1,𝔽16)11yescharacteristic
50D157—81no—
51C157#140511yescharacteristic, complemented, Sylow
52#1405—1571nomaximal, Sylow
53#456—1571no—
54#356—1571no—
55#333—1571no—
562−1+4—1571no—
57#137—3141no—
58C4⋊Q8—1571no—
59C4⋊C8—3141no—
60#104—3141no—
61#101—3141no—
62#101#1059784511yescharacteristic
63#41—3141no—
64#41—6281no—
65#41—6281no—
66C2×Q8—6281no—
67C2×Q8—1571no—
68C2×Q8C2×#1059784511yescharacteristic
69Q16—6281no—
70SD16—6281no—
71M16—21no—
72M16—6281no—
73C2×C8—6281no—
74C4⋊C4—6281no—
75C42—1571no—
76Q8—41no—
77Q8—3141no—
78Q8—6281no—
79Q8—6281no—
80D4—3141no—
81D4—6281no—
82D4—6281no—
83C2×C4—21no—
84C2×C4—3141no—
85C2×C4—3141no—
86C2×C4—6281no—
87C2×C4—6282no—
88C2×C4C22⋊#1059784511yescharacteristic
89C8—41no—
90C8—12561no—
91C8—12561no—
92C22—6281no—
93C22#1909783011yescharacteristic
94C4—21no—
95C4—41no—
96C4—3141no—
97C4—3141no—
98C4—6281no—
99C4—6281no—
100C2—21no—
101C2—12561no—
102C2#2375817411yescharacteristic
subgroupG/H
centerC2#23758174
commutatorC2×Q8×C157C2×C4
FrattiniC2×Q8C2×#10597845
Fitting#101×C157C4
socleC2×C157AΣL(1,𝔽16)
prime radical#19097819C4
cosocle#19097769C22
hypercenter#101#10597845
hypocenterC157#1405
LCSG ▷ C2×Q8×C157 ▷ C2×C4×C157 ▷ C22×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ C2×Q8 ◁ #101

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
#237574582
#1405157