Finite Group Databasebeta

← #34099771

Subgroups — #34099771

Order 20096.

176 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 61 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#23757671C211yesmaximal, characteristic
2#23757669C211yesmaximal, characteristic
3#23757669C211yesmaximal, characteristic
4#23757652C211yesmaximal, characteristic
5#23757625C211yesmaximal, characteristic
6#23756995C211yesmaximal, characteristic
7#487×C157C211yesmaximal, characteristic
8C2×#14578944—22no—
9#19097771C2211yescharacteristic
10#19097771C2211yescharacteristic
11#19097703—22no—
12#19097702—22no—
13#19097702—22no—
14#19097694—22no—
15C4×#11929434C2211yescharacteristic
16C4×#11929434C2211yescharacteristic
17C4⋊Q8×C157C2211yescharacteristic
18C4⋊Q8×C157C2211yescharacteristic
19#103×C157—22no—
20C4×C8×C157C2211yescharacteristic
21C2×Dic314—21no—
22C2×Dic314—21no—
23#14578944—44no—
24C2×#11929434D412yes—
25C2×#11929434D412yes—
26C4⋊Dic157—21no—
27C4⋊Dic157—21no—
28C4⋊Dic157—21no—
29C4⋊Dic157—21no—
30C2×Q8×C157—21no—
31C2×Q8×C157—21no—
32C2×C8×C157D412yes—
33C4⋊C4×C157—21no—
34C4⋊C4×C157—21no—
35C4⋊C4×C157—21no—
36C4⋊C4×C157—21no—
37C42×C157C2311yescharacteristic
38Dic314—42no—
39Dic314—42no—
40C2×Dic157—41no—
41C2×Dic157—41no—
42#11929434—22no—
43#11929434SD1614yes—
44Q8×C157—42no—
45Q8×C157—42no—
46C2×C4×C157—41no—
47C2×C4×C157—41no—
48C2×C4×C157C2×D411yescharacteristic
49C2×C4×C157C2×D411yescharacteristic
50C2×C4×C157C2×D411yescharacteristic
51C8×C157—22no—
52C22×C157#12711yescharacteristic
53C4×C157—81no—
54C4×C157—81no—
55C4×C157C2×SD1612yes—
56C4×C157#13712yes—
57C4×C157#13712yes—
58Dic157—81no—
59Dic157—81no—
60C2×C157#49211yescharacteristic
61C2×C157#49711yescharacteristic
62C2×C157#49711yescharacteristic
63C157#171611yescharacteristic, complemented, Sylow
64#1716—1571nomaximal, Sylow
65#498—1571no—
66#498—1571no—
67#498—1571no—
68#494—1571no—
69#487—1571no—
70#487D15711yescharacteristic
71#322—1571no—
72C2×Q16—3142no—
73C4⋊Q8—1571no—
74C4⋊Q8—1571no—
75C4⋊Q8C2×D15711yescharacteristic
76C4⋊Q8C2×D15711yescharacteristic
77#106—3142no—
78#106—3142no—
79#106—3142no—
80#103—22no—
81#103—3142no—
82C4×C8—1571no—
83C4×C8—1571no—
84C4×C8C2×D15711yescharacteristic
85C2×Q8—21no—
86C2×Q8—21no—
87C2×Q8—3141no—
88C2×Q8—3141no—
89Q16—6284no—
90C2×C8—1572no—
91C2×C8—1572no—
92C2×C8C22⋊D15712yes—
93C4⋊C4—21no—
94C4⋊C4—21no—
95C4⋊C4—21no—
96C4⋊C4—21no—
97C4⋊C4—3141no—
98C4⋊C4—3141no—
99C4⋊C4—3141no—
100C4⋊C4—3141no—
101C42C22×D15711yescharacteristic
102Q8—42no—
103Q8—42no—
104Q8—6282no—
105Q8—6282no—
106C2×C4—41no—
107C2×C4—41no—
108C2×C4—6281no—
109C2×C4—6281no—
110C2×C4D4×D15711yescharacteristic
111C2×C4D4×D15711yescharacteristic
112C2×C4C2×C22⋊D15711yescharacteristic
113C8—22no—
114C8—3142no—
115C8—1574no—
116C22#1909776711yescharacteristic
117C4—81no—
118C4—81no—
119C4—12561no—
120C4—12561no—
121C4SD16×D15712yes—
122C4#1909780112yes—
123C4#1909780312yes—
124C2#2375764411yescharacteristic
125C2#2375766611yescharacteristic
126C2#2375766811yescharacteristic
subgroupG/H
centerC22#19097767
commutator, cosocleC42×C157C23
FrattiniC42C22×D157
Fitting#487×C157C2
socle, prime radicalC22×C157#127
hypercenter#487D157
hypocenterC157#1716
LCSG ▷ C42×C157 ▷ C22×C157 ▷ C157
UCSC1 ◁ C22 ◁ C42 ◁ #487

Complements

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

NH ≅ G/Ntype
63. C157#1716semidirect

Maximal subgroups

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

subgroupindex
#237576712
#237576692
#237576522
#237576252
#237569952
#487×C1572
#1716157