Finite Group Databasebeta

← #34098085

Subgroups — #34098085

Order 20096.

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

normal subgroups only

This group has 158 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#23757145C211yesmaximal, characteristic
2#23756997C211yesmaximal, characteristic
3#323×C157C211yesmaximal, characteristic
4C23×Dic157C411yescharacteristic
5C2×#14578933—21no—
6C2×C22⋊Dic157C411yescharacteristic
7C22⋊#11929434—21no—
8#19097678—21no—
9C2×C22⋊C4×C157C2211yescharacteristic
10C22⋊C8×C157—21no—
11C22×Dic157—21no—
12C22×Dic157—21no—
13C22×Dic157—41no—
14C22×Dic157—42no—
15C2×#11929434—41no—
16#14578933—42no—
17C22⋊Dic157—21no—
18C22⋊Dic157C812yescomplemented
19C24×C157C2×C411yescharacteristic
20C22×C4×C157D411yescharacteristic
21C22×C4×C157D411yescharacteristic
22C2×C8×C157—41no—
23C22⋊C4×C157—41no—
24C2×Dic157—22no—
25C2×Dic157—22no—
26C2×Dic157—41no—
27C2×Dic157—41no—
28C2×Dic157—41no—
29C2×Dic157—42no—
30C2×Dic157—41no—
31C2×Dic157—42no—
32#11929434—81no—
33C23×C157—21no—
34C23×C157—21no—
35C23×C157—41no—
36C23×C157—41no—
37C23×C157C22⋊C411yescharacteristic
38C23×C157C2×C811yescharacteristic
39C23×C157M1611yescharacteristic
40C2×C4×C157—21no—
41C2×C4×C157—21no—
42C2×C4×C157—41no—
43C2×C4×C157—41no—
44C8×C157—81no—
45C22×C157—21no—
46C22×C157—21no—
47C22×C157—21no—
48C22×C157—21no—
49C22×C157—41no—
50C22×C157—41no—
51C22×C157—42no—
52C22×C157—41no—
53C22×C157—41no—
54C22×C157C22⋊C811yescharacteristic
55C22×C157#9911yescharacteristic
56C22×C157#10111yescharacteristic
57C4×C157—41no—
58C4×C157—41no—
59Dic157—42no—
60Dic157—42no—
61C2×C157—21no—
62C2×C157—21no—
63C2×C157—41no—
64C2×C157—41no—
65C2×C157#32411yescharacteristic
66C2×C157AΣL(1,𝔽16)11yescharacteristic
67C2×C157#35211yescharacteristic
68C157#132611yescharacteristic, complemented, Sylow
69#1326—1571nomaximal, Sylow
70#385—1571no—
71#323—1571no—
72#323D15711yescharacteristic
73C23×C4—1571no—
74C2×C4⋊C4—3141no—
75C2×C22⋊C4—1571no—
76C2×C22⋊C4C2×D15711yescharacteristic
77C22⋊C8—21no—
78C22⋊C8—3141no—
79#95—3141no—
80C24C4×D15711yescharacteristic
81C22×C4—3141no—
82C22×C4—3141no—
83C22×C4—6282no—
84C22×C4—6281no—
85C22×C4C22⋊D15711yescharacteristic
86C22×C4D62811yescharacteristic
87C2×C8—41no—
88C2×C8—6281no—
89C4⋊C4—6282no—
90C22⋊C4—41no—
91C22⋊C4—3141no—
92C22⋊C4—1572no—
93C23—21no—
94C23—21no—
95C23—41no—
96C23—41no—
97C23#1457893111yescharacteristic
98C23C8×D15711yescharacteristic
99C23#1457893711yescharacteristic
100C2×C4—21no—
101C2×C4—21no—
102C2×C4—41no—
103C2×C4—41no—
104C2×C4—3142no—
105C2×C4—3142no—
106C2×C4—6281no—
107C2×C4—6281no—
108C2×C4—6281no—
109C2×C4—6282no—
110C2×C4—6281no—
111C2×C4—6282no—
112C8—81no—
113C8—12561no—
114C22—21no—
115C22—21no—
116C22—21no—
117C22—21no—
118C22—41no—
119C22—41no—
120C22—42no—
121C22—41no—
122C22—41no—
123C22#1909768311yescharacteristic
124C22#1909768511yescharacteristic
125C22#1909768911yescharacteristic
126C4—41no—
127C4—41no—
128C4—6282no—
129C4—6282no—
130C2—21no—
131C2—21no—
132C2—41no—
133C2—41no—
134C2#2375699811yescharacteristic
135C2#2375706111yescharacteristic
136C2#2375706211yescharacteristic
subgroupG/H
centerC22#19097685
commutatorC23×C157C2×C8
FrattiniC2×C22⋊C4C2×D157
Fitting#323×C157C2
socleC22×C157#99
prime radicalC24×C157C2×C4
cosocleC2×C22⋊C4×C157C22
hypercenter#323D157
hypocenterC157#1326
LCSG ▷ C23×C157 ▷ C22×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #323

Complements

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

NH ≅ G/Ntype
18. C22⋊Dic157C8semidirect
68. C157#1326semidirect

Maximal subgroups

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

subgroupindex
#237571452
#237569972
#323×C1572
#1326157