Finite Group Databasebeta

← #34115131

Subgroups — #34115131

Order 20096.

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

normal subgroups only

This group has 162 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#23757184C211yesmaximal, characteristic
4C2×C22⋊#10597845—21no—
5C22⋊#11929441—21no—
6C2×#14578931—21no—
7C2×#14578931C2211yescharacteristic
8#19097678—21no—
9#19097678C411yescharacteristic, complemented
10C22×Q8×C157C411yescharacteristic, complemented
11C22×#10597845—41no—
12C2×#11929441—41no—
13C22⋊#10597845—22no—
14C22⋊#10597845—41no—
15C23×D157D411yescharacteristic
16C22×Dic157—21no—
17C22×Dic157D411yescharacteristic
18#14578931—41no—
19#14578931—42no—
20C2×Q8×C157—42no—
21C2×Q8×C157—41no—
22C22×C4×C157—21no—
23C22×C4×C157C2×C411yescharacteristic
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—21no—
35C2×Dic157—41no—
36C2×Dic157—41no—
37C2×Dic157—41no—
38C2×Dic157—41no—
39C23×C157C22⋊C411yescharacteristic
40Q8×C157—42no—
41Q8×C157—42no—
42C2×C4×C157—22no—
43C2×C4×C157—21no—
44C2×C4×C157—41no—
45C2×C4×C157—41no—
46C2×C4×C157—41no—
47C22×C157—21no—
48C22×C157—21no—
49C22×C157#9911yescharacteristic
50C22×C157#10311yescharacteristic
51C22×C157#10411yescharacteristic
52C2×D157—21no—
53C2×D157—21no—
54C2×D157—41no—
55C2×D157—41no—
56C2×D157—41no—
57C2×D157—41no—
58C2×D157—81no—
59#10597845—82no—
60C4×C157—42no—
61C4×C157—41no—
62Dic157—41no—
63Dic157—81no—
64C2×C157—21no—
65C2×C157—21no—
66C2×C157#32811yescharacteristic
67C2×C157AΣL(1,𝔽16)11yescharacteristic
68C2×C157#35411yescharacteristic
69D157—41no—
70D157—41no—
71C157#135111yescharacteristic, complemented, Sylow
72#1351—1571nomaximal, Sylow
73#393—1571no—
74#342—1571no—
75#323—1571no—
76C22×Q8#1059784511yescharacteristic, complemented
77C2×C22⋊C4—3141no—
78C2×C22⋊C4—3141no—
79C2×C22⋊C4—1571no—
80C22⋊C8—3141no—
81#95—3141no—
82#95—1571no—
83C24—1571no—
84C2×Q8—42no—
85C2×Q8—41no—
86C22×C4—21no—
87C22×C4—3141no—
88C22×C4—6281no—
89C22×C4—1571no—
90C22×C4C2×#1059784511yescharacteristic
91C2×C8—6281no—
92C22⋊C4—3142no—
93C22⋊C4—6281no—
94C22⋊C4—6282no—
95C22⋊C4—6281no—
96C23—3141no—
97C23—3141no—
98C23—6281no—
99C23—6281no—
100C23—1571no—
101C23—1571no—
102C23C22⋊#1059784511yescharacteristic
103Q8—42no—
104Q8—42no—
105C2×C4—22no—
106C2×C4—21no—
107C2×C4—41no—
108C2×C4—41no—
109C2×C4—41no—
110C2×C4—3141no—
111C2×C4—6281no—
112C2×C4—6281no—
113C2×C4—6281no—
114C2×C4—6282no—
115C2×C4—6281no—
116C2×C4—12561no—
117C2×C4—12561no—
118C8—12561no—
119C22—21no—
120C22—21no—
121C22—3141no—
122C22—3141no—
123C22—6281no—
124C22—6281no—
125C22—6281no—
126C22—6281no—
127C22—12561no—
128C22#1909782911yescharacteristic
129C22#1909783411yescharacteristic
130C22#1909783611yescharacteristic
131C4—42no—
132C4—41no—
133C4—6281no—
134C4—12561no—
135C4—12562no—
136C2—21no—
137C2—21no—
138C2—6281no—
139C2—6281no—
140C2#2375812711yescharacteristic
141C2#2375817311yescharacteristic
142C2#2375817911yescharacteristic
subgroupG/H
centerC22#19097829
commutatorC22×C4×C157C2×C4
FrattiniC22×C4C2×#10597845
FittingC22×Q8×C157C4
socleC22×C157#99
prime radicalC23×D157D4
cosocleC2×#14578931C22
hypercenterC22×Q8#10597845
hypocenterC157#1351
LCSG ▷ C22×C4×C157 ▷ C23×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
9. #19097678C4semidirect
10. C22×Q8×C157C4semidirect
71. C157#1351semidirect
76. C22×Q8#10597845semidirect

Maximal subgroups

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

subgroupindex
#237581512
#237581172
#237571842
#1351157