Finite Group Databasebeta

← #34098870

Subgroups — #34098870

Order 20096.

254 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 254 conjugacy classes of subgroups — too many to draw. Only its 67 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#23757824C211yesmaximal, characteristic
2#23757295C212yesmaximal, complemented
3#23757022C211yesmaximal, characteristic, complemented
4#23757016C212yesmaximal, complemented
5#333×C157C211yesmaximal, characteristic, complemented
6C2×#14578955C412yes—
7C2×#14578937—22no—
8#19097768C2211yescharacteristic
9#19097760C412yes—
10#19097746—22no—
11#19097733—22no—
12C42×D157C2211yescharacteristic
13C4⋊#11929434C2212yes—
14#19097700—22no—
15C4⋊Q8×C157C2211yescharacteristic
16C4⋊C8×C157C2212yes—
17#14578955—44no—
18C2×D628—22no—
19C2×D628—22no—
20C2×D628C2×C412yes—
21C2×C4×D157—22no—
22C2×C4×D157C2×C411yescharacteristic
23C2×C4×D157D412yes—
24#14578937—44no—
25C2×#11929434—22no—
26#14578931—24no—
27C4×Dic157C2×C411yescharacteristic
28C4×Dic157D412yes—
29C2×Q8×C157C2×C412yes—
30C2×C8×C157—22no—
31C4⋊C4×C157—22no—
32C42×C157C2311yescharacteristic
33C22×D157—22no—
34C22×D157C22⋊C411yescharacteristic
35D628—42no—
36D628—44no—
37D628—42no—
38D628—42no—
39C2×Dic157C22⋊C412yes—
40C2×Dic157C22⋊C411yescharacteristic
41C4×D157—22no—
42C4×D157—22no—
43C4×D157—22no—
44C4×D157—44no—
45#11929434—42no—
46Q8×C157—42no—
47C2×C4×C157—22no—
48C2×C4×C157C22×C411yescharacteristic
49C2×C4×C157C2×D412yes—
50C8×C157—42no—
51C22×C157C2×C22⋊C411yescharacteristic
52C2×D157—21no—
53C2×D157—22no—
54C2×D157—42no—
55C2×D157—44no—
56C4×C157—21no—
57C4×C157—42no—
58C4×C157AGL(1,ℤ/8)12yes—
59C4×C157#13712yes—
60Dic157—22no—
61Dic157#10012yes—
62C2×C157C2×#10011yescharacteristic
63C2×C157#41712yes—
64D157—41no—
65D157—82no—
66C157#156011yescharacteristic, complemented, Sylow
67#1560—1571nomaximal, Sylow
68#532—1571no—
69#423—1572no—
70#333—1571no—
71#333D15711yescharacteristic, complemented
72#331—1572no—
73C2×#41—1572no—
74C2×M16—3142no—
75C4⋊Q8C2×D15711yescharacteristic
76#127—1571no—
77#124—1572no—
78#121—3142no—
79C4×D4—3142no—
80C2×C42—1571no—
81C4⋊C8—3142no—
82C4⋊C8—1572no—
83C4⋊C8C2×D15712yes—
84#41—6284no—
85C2×Q8C4×D15712yes—
86C2×D4—3142no—
87C2×D4—3142no—
88C2×D4—1572no—
89C22×C4—3142no—
90C22×C4—1571no—
91C22×C4—1572no—
92M16—6284no—
93C2×C8—22no—
94C2×C8—3142no—
95C4⋊C4—22no—
96C22⋊C4—3144no—
97C42—1571no—
98C42—1572no—
99C42C22×D15711yescharacteristic
100C23—3142no—
101C23—1571no—
102Q8—42no—
103D4—6282no—
104D4—6284no—
105D4—6282no—
106D4—6282no—
107C2×C4—22no—
108C2×C4—3142no—
109C2×C4—3142no—
110C2×C4—3142no—
111C2×C4—6284no—
112C2×C4—1572no—
113C2×C4—1571no—
114C2×C4C2×C4×D15711yescharacteristic
115C2×C4D4×D15712yes—
116C8—42no—
117C8—6282no—
118C22—3141no—
119C22—3142no—
120C22—6282no—
121C22—6284no—
122C22C22⋊C4×D15711yescharacteristic
123C4—21no—
124C4—42no—
125C4—3142no—
126C4—1572no—
127C4#1909779812yes—
128C4#1909780312yes—
129C2—6281no—
130C2—12562no—
131C2#100×D15711yescharacteristic
132C2#2375727312yes—
subgroupG/H
centerC22C22⋊C4×D157
commutatorC2×C4×C157C22×C4
FrattiniC42C22×D157
Fitting#333×C157C2
socleC22×C157C2×C22⋊C4
prime radical#23757824C2
cosocleC42×C157C23
hypercenter#333D157
hypocenterC157#1560
LCSG ▷ C2×C4×C157 ▷ C22×C157 ▷ C157
UCSC1 ◁ C22 ◁ C42 ◁ #333

Complements

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

NH ≅ G/Ntype
2. #23757295C2semidirect
3. #23757022C2semidirect
4. #23757016C2semidirect
5. #333×C157C2semidirect
66. C157#1560semidirect
71. #333D157semidirect

Maximal subgroups

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

subgroupindex
#237578242
#237572952
#237570222
#237570162
#333×C1572
#1560157