Finite Group Databasebeta

← #34115259

Subgroups — #34115259

Order 20096.

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

normal subgroups only

This group has 112 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#23758179C211yesmaximal, characteristic, complemented
2#23758129C211yesmaximal, characteristic, complemented
3#23757446C211yesmaximal, characteristic
4#19097830—21no—
5#19097826—21no—
6#19097796—21no—
7#19097760C2211yescharacteristic
8#19097698—21no—
9#19097690C411yescharacteristic, complemented
102−1+4×C157C411yescharacteristic, complemented
11C2×#11929441—41no—
12C22⋊#10597845—41no—
13C2×D628D411yescharacteristic
14#14578941—41no—
15#14578939—41no—
16#14578938—21no—
17#14578931—41no—
18C4×Dic157D411yescharacteristic
19#41×C157—21no—
20#41×C157—41no—
21#41×C157—41no—
22C2×Q8×C157—41no—
23C2×Q8×C157C2×C411yescharacteristic
24C2×#10597845—81no—
25#11929441—42no—
26C22×D157—21no—
27D628—41no—
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
42C2×D157—41no—
43C2×D157—81no—
44#10597845—161no—
45C4×C157—21no—
46C4×C157—41no—
47C4×C157—41no—
48Dic157—41no—
49C2×C157—21no—
50C2×C157—81no—
51C2×C157AΣL(1,𝔽16)11yescharacteristic
52D157—81no—
53C157#140411yescharacteristic, complemented, Sylow
54#1404—1571nomaximal, Sylow
55#454—1571no—
56#354—1571no—
57#329—1571no—
582−1+4#1059784511yescharacteristic, complemented
59AGL(1,ℤ/8)—3141no—
60#124—1571no—
61#104—3141no—
62#101—1571no—
63#99—3141no—
64#97—3141no—
65#41—21no—
66#41—41no—
67#41—41no—
68C2×Q8—41no—
69C2×Q8C2×#1059784511yescharacteristic
70C2×D4—1571no—
71SD16—6281no—
72D8—6281no—
73M16—3141no—
74C2×C8—6281no—
75C22⋊C4—6281no—
76C22⋊C4—6281no—
77C42—1571no—
78C23—3141no—
79Q8—21no—
80Q8—41no—
81Q8—41no—
82D4—21no—
83D4—41no—
84D4—41no—
85D4—6281no—
86C2×C4—21no—
87C2×C4—41no—
88C2×C4—42no—
89C2×C4—3141no—
90C2×C4—12561no—
91C2×C4C22⋊#1059784511yescharacteristic
92C8—6281no—
93C8—6282no—
94C22—41no—
95C22—6281no—
96C22—12561no—
97C22#1909782911yescharacteristic
98C4—21no—
99C4—41no—
100C4—41no—
101C4—6281no—
102C4—25121no—
103C2—21no—
104C2—81no—
105C2—12561no—
106C2#2375817311yescharacteristic
subgroupG/H
centerC2#23758173
commutatorC2×Q8×C157C2×C4
FrattiniC2×Q8C2×#10597845
Fitting2−1+4×C157C4
socleC2×C157AΣL(1,𝔽16)
prime radical#23757446C2
cosocle#19097760C22
hypercenter2−1+4#10597845
hypocenterC157#1404
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. #23758179C2semidirect
2. #23758129C2semidirect
9. #19097690C4semidirect
10. 2−1+4×C157C4semidirect
53. C157#1404semidirect
58. 2−1+4#10597845semidirect

Maximal subgroups

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

subgroupindex
#237581792
#237581292
#237574462
#1404157