Finite Group Databasebeta

← #34098140

Subgroups — #34098140

Order 20096.

168 conjugacy classes of subgroups; only the 35 normal subgroups are shown.

normal subgroups only

This group has 168 conjugacy classes of subgroups — too many to draw. Only its 35 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#23757190C211yesmaximal, characteristic
2#23757042C211yesmaximal, characteristic, complemented
3#324×C157C211yesmaximal, characteristic, complemented
4C22×D628C411yescharacteristic
5C2×#14578938—21no—
6C2×#14578931—21no—
7C2×#14578931—21no—
8#19097678C411yescharacteristic
9C2×C4⋊C4×C157C2211yescharacteristic
10C22⋊C8×C157—21no—
11C23×D157—21no—
12C2×D628—41no—
13C2×D628—42no—
14C22×Dic157—21no—
15#14578938—22no—
16#14578938—41no—
17C2×#11929434—41no—
18#14578931—42no—
19#14578931—41no—
20#14578931—41no—
21C22×C4×C157C2×C411yescharacteristic
22C22×C4×C157D411yescharacteristic
23C22×C4×C157D411yescharacteristic
24C2×C8×C157—41no—
25C4⋊C4×C157—41no—
26C22×D157—22no—
27C22×D157—41no—
28C22×D157—41no—
29C22×D157—41no—
30C22×D157—41no—
31C22×D157—41no—
32C22×D157—41no—
33D628—42no—
34D628—42no—
35C2×Dic157—41no—
36C2×Dic157—41no—
37C2×Dic157—41no—
38#11929434—42no—
39C23×C157C22⋊C411yescharacteristic
40C2×C4×C157—21no—
41C2×C4×C157—21no—
42C2×C4×C157—21no—
43C2×C4×C157—21no—
44C2×C4×C157—41no—
45C2×C4×C157—41no—
46C2×C4×C157D811yescharacteristic
47C2×C4×C157SD1611yescharacteristic
48C8×C157—81no—
49C22×C157—21no—
50C22×C157—21no—
51C22×C157#9911yescharacteristic
52C22×C157#10211yescharacteristic
53C22×C157#10411yescharacteristic
54C2×D157—42no—
55C2×D157—42no—
56C2×D157—42no—
57C2×D157—81no—
58C2×D157—81no—
59C2×D157—81no—
60C2×D157—81no—
61C4×C157—21no—
62C4×C157—21no—
63C4×C157—41no—
64C4×C157—41no—
65Dic157—81no—
66C2×C157—21no—
67C2×C157—21no—
68C2×C157#32711yescharacteristic
69C2×C157AΣL(1,𝔽16)11yescharacteristic
70C2×C157#35511yescharacteristic
71D157—82no—
72C157#134511yescharacteristic, complemented, Sylow
73#1345—1571nomaximal, Sylow
74#394—1571no—
75#343—1571no—
76#324D15711yescharacteristic, complemented
77C22×D4—1571no—
78C2×M16—3141no—
79C2×C4⋊C4C2×D15711yescharacteristic
80C2×C22⋊C4—3141no—
81C2×C22⋊C4—3141no—
82C22⋊C8—21no—
83#95—1571no—
84C24—3141no—
85C2×D4—6281no—
86C2×D4—6282no—
87C22×C4—3141no—
88C22×C4C4×D15711yescharacteristic
89C22×C4C22⋊D15711yescharacteristic
90C22×C4D62811yescharacteristic
91M16—3142no—
92M16—6281no—
93C2×C8—41no—
94C2×C8—6281no—
95C4⋊C4—41no—
96C22⋊C4—6282no—
97C22⋊C4—6281no—
98C22⋊C4—6281no—
99C23—3142no—
100C23—6281no—
101C23—6281no—
102C23—6281no—
103C23—6281no—
104C23—6281no—
105C23—6281no—
106C23#1457893111yescharacteristic
107D4—6282no—
108D4—6282no—
109C2×C4—21no—
110C2×C4—21no—
111C2×C4—21no—
112C2×C4—21no—
113C2×C4—41no—
114C2×C4—41no—
115C2×C4—6281no—
116C2×C4—6281no—
117C2×C4—6281no—
118C2×C4D125611yescharacteristic
119C2×C4#1457894311yescharacteristic
120C8—81no—
121C8—6282no—
122C22—21no—
123C22—21no—
124C22—6282no—
125C22—6282no—
126C22—6282no—
127C22—12561no—
128C22—12561no—
129C22—12561no—
130C22—12561no—
131C22#1909768511yescharacteristic
132C22#1909769311yescharacteristic
133C22#1909769711yescharacteristic
134C4—21no—
135C4—21no—
136C4—41no—
137C4—41no—
138C4—12561no—
139C2—21no—
140C2—21no—
141C2—12562no—
142C2#2375700811yescharacteristic
143C2#2375705911yescharacteristic
144C2#2375706911yescharacteristic
subgroupG/H
centerC22#19097685
commutatorC22×C4×C157C2×C4
FrattiniC2×C4⋊C4C2×D157
Fitting#324×C157C2
socleC22×C157#99
prime radicalC22×D628C4
cosocleC2×C4⋊C4×C157C22
hypercenter#324D157
hypocenterC157#1345
LCSG ▷ C22×C4×C157 ▷ C23×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #324

Complements

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

NH ≅ G/Ntype
2. #23757042C2semidirect
3. #324×C157C2semidirect
72. C157#1345semidirect
76. #324D157semidirect

Maximal subgroups

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

subgroupindex
#237571902
#237570422
#324×C1572
#1345157