Finite Group Databasebeta

← #34098166

Subgroups — #34098166

Order 20096.

140 conjugacy classes of subgroups; only the 37 normal subgroups are shown.

normal subgroups only

This group has 140 conjugacy classes of subgroups — too many to draw. Only its 37 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#23757042C211yesmaximal, characteristic
2#23756999C211yesmaximal, characteristic
3#395×C157C211yesmaximal, characteristic
4C2×#14578938—21no—
5C22⋊#11929434—21no—
6C22×Q8×C157C411yescharacteristic
7C2×C4⋊C4×C157—21no—
8C2×C4⋊C4×C157C2211yescharacteristic
9#95×C157—21no—
10#95×C157C411yescharacteristic
11#14578938—22no—
12#14578938—41no—
13C2×#11929434—41no—
14C2×#11929434—41no—
15C2×Q8×C157—42no—
16C2×Q8×C157—41no—
17C22×C4×C157—21no—
18C22×C4×C157—21no—
19C22×C4×C157C2×C411yescharacteristic
20C22×C4×C157D411yescharacteristic
21C22×C4×C157D411yescharacteristic
22C4⋊C4×C157—41no—
23C4⋊C4×C157—42no—
24#11929434—42no—
25#11929434—81no—
26C23×C157C22⋊C411yescharacteristic
27Q8×C157—42no—
28Q8×C157—42no—
29C2×C4×C157—21no—
30C2×C4×C157—21no—
31C2×C4×C157—22no—
32C2×C4×C157—22no—
33C2×C4×C157—21no—
34C2×C4×C157—21no—
35C2×C4×C157—41no—
36C2×C4×C157—41no—
37C2×C4×C157—41no—
38C2×C4×C157—41no—
39C2×C4×C157—41no—
40C2×C4×C157—41no—
41C2×C4×C157SD1611yescharacteristic
42C2×C4×C157Q1611yescharacteristic
43C22×C157—21no—
44C22×C157—21no—
45C22×C157#9911yescharacteristic
46C22×C157#10311yescharacteristic
47C22×C157#10411yescharacteristic
48C4×C157—21no—
49C4×C157—21no—
50C4×C157—42no—
51C4×C157—42no—
52C4×C157—41no—
53C4×C157—41no—
54C2×C157—21no—
55C2×C157—21no—
56C2×C157#32811yescharacteristic
57C2×C157AΣL(1,𝔽16)11yescharacteristic
58C2×C157#35611yescharacteristic
59C157#135411yescharacteristic, complemented, Sylow
60#1354—1571nomaximal, Sylow
61#395D15711yescharacteristic
62#343—1571no—
63#324—1571no—
64C22×Q8Dic15711yescharacteristic
65C2×M16—3141no—
66C2×C4⋊C4—21no—
67C2×C4⋊C4C2×D15711yescharacteristic
68C22⋊C8—3141no—
69#95—21no—
70#95Dic15711yescharacteristic
71C2×Q8—42no—
72C2×Q8—41no—
73C22×C4—21no—
74C22×C4—21no—
75C22×C4C2×Dic15711yescharacteristic
76C22×C4C22⋊D15711yescharacteristic
77C22×C4C22⋊D15711yescharacteristic
78M16—3142no—
79M16—6281no—
80C2×C8—6281no—
81C2×C8—6281no—
82C4⋊C4—41no—
83C4⋊C4—42no—
84C23C22⋊Dic15711yescharacteristic
85Q8—42no—
86Q8—42no—
87C2×C4—21no—
88C2×C4—21no—
89C2×C4—22no—
90C2×C4—22no—
91C2×C4—21no—
92C2×C4—21no—
93C2×C4—41no—
94C2×C4—41no—
95C2×C4—41no—
96C2×C4—41no—
97C2×C4—41no—
98C2×C4—41no—
99C2×C4#1457894111yescharacteristic
100C2×C4#1457894411yescharacteristic
101C8—6282no—
102C8—12561no—
103C22—21no—
104C22—21no—
105C22#1909768611yescharacteristic
106C22#1909769511yescharacteristic
107C22#1909769811yescharacteristic
108C4—21no—
109C4—21no—
110C4—42no—
111C4—41no—
112C4—42no—
113C4—41no—
114C2—21no—
115C2—21no—
116C2#2375701011yescharacteristic
117C2#2375706011yescharacteristic
118C2#2375707211yescharacteristic
subgroupG/H
centerC22#19097686
commutatorC22×C4×C157C2×C4
FrattiniC2×C4⋊C4C2×D157
Fitting#395×C157C2
socleC22×C157#99
prime radicalC23×C157C22⋊C4
cosocleC2×C4⋊C4×C157C22
hypercenter#395D157
hypocenterC157#1354
LCSG ▷ C22×C4×C157 ▷ C23×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #395

Complements

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

NH ≅ G/Ntype
59. C157#1354semidirect

Maximal subgroups

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

subgroupindex
#237570422
#237569992
#395×C1572
#1354157