Finite Group Databasebeta

← #34115257

Subgroups — #34115257

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#23758181C211yesmaximal, characteristic, complemented
2#23758128C211yesmaximal, characteristic, complemented
3#23757451C211yesmaximal, characteristic
4#19097832—21no—
5#19097826—21no—
6#19097801—21no—
7#19097758C2211yescharacteristic
8#19097698—21no—
9#19097688C411yescharacteristic
10H(5,𝔽2)×C157C411yescharacteristic
11#14578963—41no—
12C2×#11929441—41no—
13C2×Dic314D411yescharacteristic
14#14578944—41no—
15#14578942—41no—
16#14578938—21no—
17C22⋊Dic157—41no—
18C4×Dic157D411yescharacteristic
19#41×C157—21no—
20#41×C157—41no—
21C2×D4×C157—41no—
22C2×D4×C157—41no—
23C2×D4×C157C2×C411yescharacteristic
24#11929441—42no—
25#11929441—81no—
26Dic314—41no—
27C2×Dic157—21no—
28C2×Dic157—21no—
29#11929434—41no—
30C23×C157—21no—
31C23×C157—41no—
32Q8×C157—21no—
33D4×C157—21no—
34D4×C157—41no—
35D4×C157—42no—
36D4×C157—41no—
37C2×C4×C157—41no—
38C2×C4×C157—41no—
39C2×C4×C157C22⋊C411yescharacteristic
40C22×C157—41no—
41C22×C157—41no—
42C22×C157—81no—
43C22×C157—161no—
44C22×C157#9911yescharacteristic
45C4×C157—21no—
46C4×C157—41no—
47Dic157—41no—
48Dic157—41no—
49C2×C157—21no—
50C2×C157—81no—
51C2×C157—81no—
52C2×C157AΣL(1,𝔽16)11yescharacteristic
53C157#140311yescharacteristic, complemented, Sylow
54#1403—1571nomaximal, Sylow
55#455—1571no—
56#355—1571no—
57#329—1571no—
58H(5,𝔽2)#1059784511yescharacteristic
59#137—3141no—
60#124—1571no—
61#104—3141no—
62#101—3141no—
63#100—1571no—
64#97—3141no—
65#41—21no—
66#41—41no—
67C2×Q8—1571no—
68C2×D4—41no—
69C2×D4—41no—
70C2×D4C2×#1059784511yescharacteristic
71Q16—6281no—
72SD16—6281no—
73M16—3141no—
74M16—6281no—
75C2×C8—6281no—
76C22⋊C4—6281no—
77C42—1571no—
78C23—21no—
79C23—41no—
80Q8—21no—
81Q8—6281no—
82D4—21no—
83D4—41no—
84D4—42no—
85D4—41no—
86C2×C4—41no—
87C2×C4—41no—
88C2×C4—3141no—
89C2×C4—3141no—
90C2×C4C22⋊#1059784511yescharacteristic
91C8—6281no—
92C8—6282no—
93C8—12561no—
94C22—41no—
95C22—41no—
96C22—81no—
97C22—161no—
98C22#1909782911yescharacteristic
99C4—21no—
100C4—41no—
101C4—6281no—
102C4—6281no—
103C2—21no—
104C2—81no—
105C2—81no—
106C2#2375817311yescharacteristic
subgroupG/H
centerC2#23758173
commutatorC2×D4×C157C2×C4
FrattiniC2×D4C2×#10597845
Fitting, prime radicalH(5,𝔽2)×C157C4
socleC2×C157AΣL(1,𝔽16)
cosocle#19097758C22
hypercenterH(5,𝔽2)#10597845
hypocenterC157#1403
LCSG ▷ C2×D4×C157 ▷ C2×C4×C157 ▷ C22×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ C2×D4 ◁ H(5,𝔽2)

Complements

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

NH ≅ G/Ntype
1. #23758181C2semidirect
2. #23758128C2semidirect
53. C157#1403semidirect

Maximal subgroups

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

subgroupindex
#237581812
#237581282
#237574512
#1403157