Finite Group Databasebeta

← #34099429

Subgroups — #34099429

Order 20096.

230 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 230 conjugacy classes of subgroups — too many to draw. Only its 49 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#23757663C212yesmaximal, complemented
2#23757639C211yesmaximal, characteristic, complemented
3#23757015C211yesmaximal, characteristic, complemented
4#23757013C212yesmaximal, complemented
5#562×C157C211yesmaximal, characteristic, complemented
6C2×#14578941—22no—
7C2×#14578939—22no—
8#19097768C2211yescharacteristic
9#19097691—22no—
10#19097682C2211yescharacteristic
11#19097682C2212yes—
12#125×C157C2211yescharacteristic
13#124×C157C2212yes—
14#123×C157—22no—
15C22⋊Q8×C157—22no—
16#121×C157—22no—
17C2×D628—21no—
18C2×D628—22no—
19#14578941—44no—
20#14578939—44no—
21C2×#11929434—22no—
22C2×#11929434—21no—
23C2×Q8×C157D412yes—
24C2×D4×C157—22no—
25C2×D4×C157D412yes—
26C22×C4×C157—22no—
27C4⋊C4×C157—22no—
28C4⋊C4×C157—22no—
29C4⋊C4×C157D412yes—
30C22⋊C4×C157—22no—
31C22⋊C4×C157—22no—
32C22⋊C4×C157—22no—
33C42×C157C2311yescharacteristic
34C22×D157—41no—
35D628—42no—
36D628—42no—
37D628—42no—
38#11929434—24no—
39#11929434—41no—
40C23×C157—22no—
41Q8×C157—42no—
42D4×C157—42no—
43D4×C157—82no—
44C2×C4×C157—22no—
45C2×C4×C157—22no—
46C2×C4×C157—82no—
47C2×C4×C157C2×D411yescharacteristic
48C2×C4×C157C2×D412yes—
49C22×C157—42no—
50C22×C157—42no—
51C22×C157—42no—
52C22×C157#12011yescharacteristic
53C2×D157—82no—
54C2×D157—81no—
55C4×C157—22no—
56C4×C157—21no—
57C4×C157—42no—
58C4×C157—42no—
59C2×C157—82no—
60C2×C157#45312yes—
61C2×C157#45411yescharacteristic
62D157—161no—
63C157#165611yescharacteristic, complemented, Sylow
64#1656—1571nomaximal, Sylow
65#562D15711yescharacteristic, complemented
66#496—1572no—
67#490—1571no—
68#330—1571no—
69#329—1572no—
70C2×SD16—3142no—
71C2×D8—3142no—
72#127—1571no—
73#125C2×D15711yescharacteristic
74#124C2×D15712yes—
75#123—22no—
76C22⋊Q8—22no—
77#121—22no—
78#102—3142no—
79#97—1571no—
80#97—1572no—
81C2×Q8C22⋊D15712yes—
82C2×D4—22no—
83C2×D4—3141no—
84C2×D4—3142no—
85C2×D4C22⋊D15712yes—
86C22×C4—22no—
87SD16—6284no—
88D8—6284no—
89C2×C8—3142no—
90C2×C8—3141no—
91C4⋊C4—22no—
92C4⋊C4—22no—
93C4⋊C4C22⋊D15712yes—
94C22⋊C4—22no—
95C22⋊C4—22no—
96C22⋊C4—22no—
97C42C22×D15711yescharacteristic
98C23—22no—
99C23—6281no—
100Q8—42no—
101D4—42no—
102D4—82no—
103D4—6282no—
104D4—6282no—
105D4—6282no—
106C2×C4—22no—
107C2×C4—22no—
108C2×C4—82no—
109C2×C4C2×C22⋊D15711yescharacteristic
110C2×C4C2×C22⋊D15712yes—
111C8—3144no—
112C8—6281no—
113C22—42no—
114C22—42no—
115C22—42no—
116C22—12562no—
117C22—12561no—
118C22#1909774011yescharacteristic
119C4—22no—
120C4—21no—
121C4—42no—
122C4—42no—
123C2—82no—
124C2—25121no—
125C2#2375744112yes—
126C2#2375744611yescharacteristic
subgroupG/H
centerC22#19097740
commutator, cosocleC42×C157C23
FrattiniC42C22×D157
Fitting#562×C157C2
socleC22×C157#120
hypercenter#562D157
hypocenterC157#1656
LCSG ▷ C42×C157 ▷ C22×C157 ▷ C157
UCSC1 ◁ C22 ◁ C42 ◁ #562

Complements

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

NH ≅ G/Ntype
1. #23757663C2semidirect
2. #23757639C2semidirect
3. #23757015C2semidirect
4. #23757013C2semidirect
5. #562×C157C2semidirect
63. C157#1656semidirect
65. #562D157semidirect

Maximal subgroups

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

subgroupindex
#237576632
#237576392
#237570152
#237570132
#562×C1572
#1656157