Finite Group Databasebeta

← #34115133

Subgroups — #34115133

Order 20096.

154 conjugacy classes of subgroups; only the 30 normal subgroups are shown.

normal subgroups only

This group has 154 conjugacy classes of subgroups — too many to draw. Only its 30 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#23758151C211yesmaximal, characteristic
2#23758117C211yesmaximal, characteristic
3#23757208C211yesmaximal, characteristic
4C2×C22⋊#10597845—21no—
5C22⋊#11929441—21no—
6C2×#14578933—21no—
7C2×#14578931—21no—
8C2×#14578931C2211yescharacteristic
9#19097678C411yescharacteristic, complemented
10C2×C4⋊C4×C157C411yescharacteristic, complemented
11C22×#10597845—41no—
12C2×#11929441—41no—
13C22⋊#10597845—22no—
14C22⋊#10597845—41no—
15C23×D157D411yescharacteristic
16C22×Dic157—21no—
17C22×Dic157D411yescharacteristic
18#14578933—42no—
19#14578931—41no—
20#14578931—42no—
21C22×C4×C157—21no—
22C22×C4×C157C2×C411yescharacteristic
23C4⋊C4×C157—41no—
24C2×#10597845—42no—
25C2×#10597845—81no—
26C2×#10597845—81no—
27#11929441—81no—
28C22×D157—21no—
29C22×D157—21no—
30C22×D157—41no—
31C22×D157—41no—
32C22×D157SD1611yescharacteristic
33C22×D157Q1611yescharacteristic
34C2×Dic157—22no—
35C2×Dic157—21no—
36C2×Dic157—41no—
37C2×Dic157—41no—
38C2×Dic157—41no—
39C23×C157C22⋊C411yescharacteristic
40C2×C4×C157—21no—
41C2×C4×C157—41no—
42C2×C4×C157—41no—
43C2×C4×C157—41no—
44C2×C4×C157—41no—
45C22×C157—21no—
46C22×C157—21no—
47C22×C157#9911yescharacteristic
48C22×C157#10311yescharacteristic
49C22×C157#10411yescharacteristic
50C2×D157—21no—
51C2×D157—21no—
52C2×D157—41no—
53C2×D157—41no—
54C2×D157—41no—
55C2×D157—41no—
56C2×D157—81no—
57#10597845—82no—
58C4×C157—41no—
59C4×C157—81no—
60Dic157—42no—
61Dic157—41no—
62C2×C157—21no—
63C2×C157—21no—
64C2×C157#32811yescharacteristic
65C2×C157#35211yescharacteristic
66C2×C157#35311yescharacteristic
67D157—41no—
68D157—41no—
69C157#135211yescharacteristic, complemented, Sylow
70#1352—1571nomaximal, Sylow
71#399—1571no—
72#342—1571no—
73#323—1571no—
74C2×C4⋊C4—3141no—
75C2×C4⋊C4#1059784511yescharacteristic, complemented
76C2×C22⋊C4—3141no—
77C2×C22⋊C4—3141no—
78C2×C22⋊C4—1571no—
79C22⋊C8—3141no—
80#95—1571no—
81C24—1571no—
82C22×C4—21no—
83C22×C4—3141no—
84C22×C4—6281no—
85C22×C4—1571no—
86C22×C4C2×#1059784511yescharacteristic
87C2×C8—6281no—
88C4⋊C4—41no—
89C4⋊C4—6282no—
90C22⋊C4—3142no—
91C22⋊C4—6281no—
92C22⋊C4—6282no—
93C22⋊C4—6281no—
94C23—3141no—
95C23—3141no—
96C23—6281no—
97C23—6281no—
98C23—1571no—
99C23—1571no—
100C23C22⋊#1059784511yescharacteristic
101C2×C4—21no—
102C2×C4—41no—
103C2×C4—41no—
104C2×C4—41no—
105C2×C4—41no—
106C2×C4—3142no—
107C2×C4—3141no—
108C2×C4—6281no—
109C2×C4—6281no—
110C2×C4—6281no—
111C2×C4—6282no—
112C2×C4—12561no—
113C2×C4—12561no—
114C8—12561no—
115C22—21no—
116C22—21no—
117C22—3141no—
118C22—3141no—
119C22—6281no—
120C22—6281no—
121C22—6281no—
122C22—6281no—
123C22—12561no—
124C22#1909782911yescharacteristic
125C22#1909783411yescharacteristic
126C22#1909783611yescharacteristic
127C4—41no—
128C4—81no—
129C4—6282no—
130C4—6281no—
131C4—12562no—
132C2—21no—
133C2—21no—
134C2—6281no—
135C2—6281no—
136C2#2375812711yescharacteristic
137C2#2375817511yescharacteristic
138C2#2375817711yescharacteristic
subgroupG/H
centerC22#19097829
commutatorC22×C4×C157C2×C4
FrattiniC22×C4C2×#10597845
FittingC2×C4⋊C4×C157C4
socleC22×C157#99
prime radicalC23×D157D4
cosocleC2×#14578931C22
hypercenterC2×C4⋊C4#10597845
hypocenterC157#1352
LCSG ▷ C22×C4×C157 ▷ C23×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
9. #19097678C4semidirect
10. C2×C4⋊C4×C157C4semidirect
69. C157#1352semidirect
75. C2×C4⋊C4#10597845semidirect

Maximal subgroups

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

subgroupindex
#237581512
#237581172
#237572082
#1352157