Finite Group Databasebeta

← #34101483

Subgroups — #34101483

Order 20096.

230 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 230 conjugacy classes of subgroups — too many to draw. Only its 75 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#23757316C212yesmaximal
2#23757138C211yesmaximal, characteristic
3#23757042C211yesmaximal, characteristic
4#23757032C212yesmaximal
5#544×C157C211yesmaximal, characteristic
6C2×#14578938C2212yes—
7C2×C4⋊Dic157C2211yescharacteristic
8C2×C4×Dic157C2211yescharacteristic
9#19097704—22no—
10#19097702—22no—
11#19097678—22no—
12C4⋊Q8×C157—22no—
13#125×C157—22no—
14C22⋊Q8×C157—22no—
15#117×C157C2212yes—
16C2×C4⋊C4×C157C2211yescharacteristic
17C22×Dic157—21no—
18C22×Dic157—21no—
19#14578938—22no—
20#14578938Q814yescomplemented
21C2×#11929434—22no—
22C4⋊Dic157—22no—
23C4×Dic157—21no—
24C4×Dic157Q812yescomplemented
25C2×Q8×C157—22no—
26C22×C4×C157D412yes—
27C22×C4×C157C2311yescharacteristic
28C4⋊C4×C157—22no—
29C4⋊C4×C157—24no—
30C4⋊C4×C157—22no—
31C4⋊C4×C157D412yes—
32C4⋊C4×C157D412yes—
33C22⋊C4×C157—22no—
34C42×C157—22no—
35C2×Dic157—22no—
36C2×Dic157—41no—
37C2×Dic157—41no—
38C2×Dic157—42no—
39C2×Dic157—41no—
40#11929434—24no—
41C23×C157C2×D411yescharacteristic
42Q8×C157—82no—
43C2×C4×C157—22no—
44C2×C4×C157—22no—
45C2×C4×C157—22no—
46C2×C4×C157—42no—
47C2×C4×C157C2×D412yes—
48C2×C4×C157C2×Q812yes—
49C2×C4×C157C2×Q811yescharacteristic
50C2×C4×C157#4111yescharacteristic
51C22×C157—21no—
52C22×C157—21no—
53C22×C157#12011yescharacteristic
54C22×C157C22⋊Q811yescharacteristic
55C22×C157C4⋊Q811yescharacteristic
56C4×C157—42no—
57C4×C157—42no—
58C4×C157—42no—
59C4×C157C22⋊Q812yes—
60C4×C157C4⋊Q812yes—
61Dic157—42no—
62Dic157—81no—
63C2×C157—21no—
64C2×C157—21no—
65C2×C157#39511yescharacteristic
66C2×C157#45411yescharacteristic
67C2×C157#45511yescharacteristic
68C157#206111yescharacteristic, complemented, Sylow
69#2061—1571nomaximal, Sylow
70#544D15711yescharacteristic
71#428—1572no—
72#382—1571no—
73#343—1571no—
74#339—1572no—
75C2×M16—1572no—
76C4⋊Q8—22no—
77#125—22no—
78C22⋊Q8—22no—
79#117C2×D15712yes—
80C2×C4⋊C4—1571no—
81C2×C4⋊C4C2×D15711yescharacteristic
82C2×C42—1571no—
83#107—3142no—
84#106—3142no—
85#95—3142no—
86C2×Q8—22no—
87C22×C4—3141no—
88C22×C4—3141no—
89C22×C4C22⋊D15712yes—
90C22×C4C22×D15711yescharacteristic
91M16—3142no—
92M16—1574no—
93C2×C8—3142no—
94C4⋊C4—22no—
95C4⋊C4—24no—
96C4⋊C4—22no—
97C4⋊C4—3142no—
98C4⋊C4C22⋊D15712yes—
99C4⋊C4C22⋊D15712yes—
100C22⋊C4—22no—
101C42—22no—
102C42—3141no—
103C42—1572no—
104C23C2×C22⋊D15711yescharacteristic
105Q8—82no—
106C2×C4—22no—
107C2×C4—22no—
108C2×C4—22no—
109C2×C4—42no—
110C2×C4—3142no—
111C2×C4—6281no—
112C2×C4—6281no—
113C2×C4—6282no—
114C2×C4—6281no—
115C2×C4C2×C22⋊D15712yes—
116C2×C4Q8×D15712yes—
117C2×C4Q8×D15711yescharacteristic
118C2×C4#1457895511yescharacteristic
119C8—3144no—
120C22—21no—
121C22—21no—
122C22#1909774011yescharacteristic
123C22#1909774711yescharacteristic
124C22#1909776911yescharacteristic
125C4—42no—
126C4—42no—
127C4—42no—
128C4—6282no—
129C4—12561no—
130C4#1909774712yes—
131C4#1909776912yes—
132C2—21no—
133C2—21no—
134C2#2375719211yescharacteristic
135C2#2375744611yescharacteristic
136C2#2375745111yescharacteristic
subgroupG/H
centerC22#19097740
commutator, cosocleC22×C4×C157C23
FrattiniC22×C4C22×D157
Fitting#544×C157C2
socleC22×C157#120
prime radicalC23×C157C2×D4
hypercenter#544D157
hypocenterC157#2061
LCSG ▷ C22×C4×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C22 ◁ C22×C4 ◁ #544

Complements

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

NH ≅ G/Ntype
20. #14578938Q8semidirect
24. C4×Dic157Q8semidirect
68. C157#2061semidirect

Maximal subgroups

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

subgroupindex
#237573162
#237571382
#237570422
#237570322
#544×C1572
#2061157