Finite Group Databasebeta

← #34098280

Subgroups — #34098280

Order 20096.

122 conjugacy classes of subgroups; only the 23 normal subgroups are shown.

normal subgroups only

This group has 122 conjugacy classes of subgroups — too many to draw. Only its 23 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#23757440C211yesmaximal, characteristic
2#23757017C211yesmaximal, characteristic, complemented
3#353×C157C211yesmaximal, characteristic, complemented
4#19097816C411yescharacteristic, complemented
5#19097797—21no—
6C4⋊#11929434—21no—
7#19097699—21no—
8#19097688C411yescharacteristic, complemented
9#127×C157C2211yescharacteristic
10#99×C157—21no—
11#14578954—21no—
12#14578953—41no—
13C2×C22⋊D157—41no—
14D4×D157—41no—
15#14578942—41no—
16#14578939—41no—
17#14578938—21no—
18C2×#11929434—41no—
19C2×D4×C157—41no—
20C2×D4×C157C2×C411yescharacteristic
21C2×D4×C157D411yescharacteristic
22C22⋊C4×C157—41no—
23C42×C157D411yescharacteristic
24C22×D157—41no—
25Dic314—21no—
26D628—21no—
27C22⋊D157—42no—
28C22⋊D157—41no—
29C2×Dic157—41no—
30C4×D157—41no—
31#11929434—41no—
32#11929434—81no—
33C23×C157—21no—
34C23×C157—21no—
35D4×C157—41no—
36D4×C157—41no—
37D4×C157—81no—
38D4×C157—81no—
39C2×C4×C157—21no—
40C2×C4×C157—81no—
41C2×C4×C157C22⋊C411yescharacteristic
42C22×C157—41no—
43C22×C157—41no—
44C22×C157—81no—
45C22×C157—81no—
46C22×C157#9911yescharacteristic
47C2×D157—41no—
48C2×D157—161no—
49C4×C157—21no—
50C4×C157—21no—
51C4×C157—21no—
52C4×C157—161no—
53Dic157—41no—
54C2×C157—21no—
55C2×C157—81no—
56C2×C157—81no—
57C2×C157AΣL(1,𝔽16)11yescharacteristic
58D157—81no—
59C157#140211yescharacteristic, complemented, Sylow
60#1402—1571nomaximal, Sylow
61#453—1571no—
62#353D15711yescharacteristic, complemented
63#331—1571no—
64H(5,𝔽2)—1571no—
65AGL(1,ℤ/8)—3141no—
66#127C2×D15711yescharacteristic
67C4⋊C8—3141no—
68#104—3141no—
69#100—1571no—
70#99—21no—
71#41—3141no—
72#41—6281no—
73C2×D4—41no—
74C2×D4—6281no—
75C2×D4—6281no—
76C2×D4C4×D15711yescharacteristic
77C2×D4C22⋊D15711yescharacteristic
78SD16—6281no—
79D8—6281no—
80M16—3141no—
81C2×C8—6281no—
82C22⋊C4—41no—
83C42D62811yescharacteristic
84C23—21no—
85C23—21no—
86C23—6281no—
87Q8—3141no—
88D4—41no—
89D4—41no—
90D4—81no—
91D4—81no—
92D4—3141no—
93D4—6282no—
94D4—6281no—
95C2×C4—21no—
96C2×C4—81no—
97C2×C4—6281no—
98C2×C4—6281no—
99C2×C4#1457893111yescharacteristic
100C8—6281no—
101C8—12561no—
102C22—41no—
103C22—41no—
104C22—81no—
105C22—81no—
106C22—6281no—
107C22—25121no—
108C22#1909768511yescharacteristic
109C4—21no—
110C4—21no—
111C4—21no—
112C4—161no—
113C4—6281no—
114C2—21no—
115C2—81no—
116C2—81no—
117C2—12561no—
118C2#2375705911yescharacteristic
subgroupG/H
centerC2#23757059
commutatorC2×D4×C157C2×C4
Frattini#127C2×D157
Fitting#353×C157C2
socleC2×C157AΣL(1,𝔽16)
prime radical#23757440C2
cosocle#127×C157C22
hypercenter#353D157
hypocenterC157#1402
LCSG ▷ C2×D4×C157 ▷ C2×C4×C157 ▷ C22×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ #127 ◁ #353

Complements

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

NH ≅ G/Ntype
2. #23757017C2semidirect
3. #353×C157C2semidirect
4. #19097816C4semidirect
8. #19097688C4semidirect
59. C157#1402semidirect
62. #353D157semidirect

Maximal subgroups

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

subgroupindex
#237574402
#237570172
#353×C1572
#1402157