Finite Group Databasebeta

← #34099431

Subgroups — #34099431

Order 20096.

230 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 230 conjugacy classes of subgroups — too many to draw. Only its 45 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#23758021C211yesmaximal, characteristic, complemented
2#23757662C212yesmaximal, complemented
3#23757639C211yesmaximal, characteristic, complemented
4#23757012C212yesmaximal, complemented
5#330×C157C211yesmaximal, characteristic, complemented
6C2×#14578943—22no—
7C2×D1256—22no—
8#19097768C2211yescharacteristic
9#19097759C2212yes—
10#19097756—22no—
11#19097749—22no—
12#19097746—22no—
13#19097691—22no—
14#19097682C2211yescharacteristic
15#125×C157C2211yescharacteristic
16#97×C157C2212yes—
17C2×Dic314D412yes—
18C2×D628—22no—
19C2×D628—21no—
20C2×D628—22no—
21C2×D628D412yes—
22C2×C4×D157—22no—
23#14578943—44no—
24D1256—44no—
25C2×#11929434—21no—
26#14578933—22no—
27#14578931—22no—
28#14578931—22no—
29#14578931—22no—
30C2×C8×C157—22no—
31C4⋊C4×C157—22no—
32C4⋊C4×C157D412yes—
33C42×C157C2311yescharacteristic
34C22×D157—22no—
35C22×D157—41no—
36Dic314—42no—
37D628—42no—
38D628—42no—
39D628—42no—
40D628—42no—
41D628—82no—
42C2×Dic157—22no—
43C4×D157—82no—
44#11929434—41no—
45C2×C4×C157—22no—
46C2×C4×C157C2×D412yes—
47C2×C4×C157C2×D411yescharacteristic
48C8×C157—24no—
49C22×C157#12011yescharacteristic
50C2×D157—42no—
51C2×D157—42no—
52C2×D157—42no—
53C2×D157—82no—
54C2×D157—81no—
55C4×C157—22no—
56C4×C157—21no—
57C4×C157—42no—
58Dic157—42no—
59C2×C157#45312yes—
60C2×C157#45411yescharacteristic
61D157—82no—
62D157—161no—
63C157#165611yescharacteristic, complemented, Sylow
64#1656—1571nomaximal, Sylow
65#562—1571no—
66#496—1572no—
67#490—1571no—
68#330D15711yescharacteristic, complemented
69#329—1572no—
70C2×SD16—3142no—
71C2×D8—3142no—
72#127—1571no—
73#125C2×D15711yescharacteristic
74#124—1572no—
75#123—3142no—
76C22⋊Q8—3142no—
77#121—3142no—
78#102—3142no—
79#97—1571no—
80#97C2×D15712yes—
81C2×Q8—1572no—
82C2×D4—3142no—
83C2×D4—3142no—
84C2×D4—3141no—
85C2×D4—1572no—
86C22×C4—3142no—
87SD16—6284no—
88D8—6284no—
89C2×C8—22no—
90C2×C8—3141no—
91C4⋊C4—22no—
92C4⋊C4—3142no—
93C4⋊C4D62812yes—
94C22⋊C4—3142no—
95C22⋊C4—3142no—
96C22⋊C4—3142no—
97C42C22×D15711yescharacteristic
98C23—3142no—
99C23—6281no—
100Q8—6282no—
101D4—6282no—
102D4—6282no—
103D4—6282no—
104D4—6282no—
105D4—12562no—
106C2×C4—22no—
107C2×C4—3142no—
108C2×C4—12562no—
109C2×C4D4×D15712yes—
110C2×C4C2×D62811yescharacteristic
111C8—24no—
112C8—6281no—
113C22—6282no—
114C22—6282no—
115C22—6282no—
116C22—12562no—
117C22—12561no—
118C22#1909774111yescharacteristic
119C4—22no—
120C4—21no—
121C4—42no—
122C4—6282no—
123C2—25121no—
124C2—12562no—
125C2#2375744212yes—
126C2#2375744811yescharacteristic
subgroupG/H
centerC22#19097741
commutator, cosocleC42×C157C23
FrattiniC42C22×D157
Fitting#330×C157C2
socleC22×C157#120
hypercenter#330D157
hypocenterC157#1656
LCSG ▷ C42×C157 ▷ C22×C157 ▷ C157
UCSC1 ◁ C22 ◁ C42 ◁ #330

Complements

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

NH ≅ G/Ntype
1. #23758021C2semidirect
2. #23757662C2semidirect
3. #23757639C2semidirect
4. #23757012C2semidirect
5. #330×C157C2semidirect
63. C157#1656semidirect
68. #330D157semidirect

Maximal subgroups

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

subgroupindex
#237580212
#237576622
#237576392
#237570122
#330×C1572
#1656157