Finite Group Databasebeta

← #34099780

Subgroups — #34099780

Order 20096.

164 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 164 conjugacy classes of subgroups — too many to draw. Only its 57 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#23757676C211yesmaximal, characteristic
2#23757625C211yesmaximal, characteristic
3#23757624C211yesmaximal, characteristic
4#23757623C211yesmaximal, characteristic
5#23757623C211yesmaximal, characteristic
6#23756995C211yesmaximal, characteristic
7#498×C157C211yesmaximal, characteristic
8#19097771C2211yescharacteristic
9#19097771C2211yescharacteristic
10#19097704—22no—
11#19097696—22no—
12#19097695—22no—
13#19097695—22no—
14#19097694—22no—
15C4×#11929434C2211yescharacteristic
16C4×#11929434C2211yescharacteristic
17C4⋊Q8×C157C2211yescharacteristic
18C4⋊Q8×C157C2211yescharacteristic
19#106×C157—22no—
20C4×C8×C157C2211yescharacteristic
21C2×Dic314—21no—
22C2×Dic314—21no—
23C2×#11929434D412yes—
24C2×#11929434D412yes—
25C4⋊Dic157—21no—
26C4⋊Dic157—21no—
27C4⋊Dic157—21no—
28C4⋊Dic157—21no—
29C2×Q8×C157—21no—
30C2×Q8×C157—21no—
31C2×C8×C157D412yes—
32C4⋊C4×C157—21no—
33C4⋊C4×C157—21no—
34C4⋊C4×C157—21no—
35C4⋊C4×C157—21no—
36C42×C157C2311yescharacteristic
37Dic314—42no—
38Dic314—42no—
39C2×Dic157—41no—
40C2×Dic157—41no—
41#11929434—22no—
42#11929434—22no—
43Q8×C157—42no—
44Q8×C157—42no—
45C2×C4×C157—41no—
46C2×C4×C157—41no—
47C2×C4×C157C2×D411yescharacteristic
48C2×C4×C157C2×D411yescharacteristic
49C2×C4×C157C2×D411yescharacteristic
50C8×C157—22no—
51C22×C157#12711yescharacteristic
52C4×C157—81no—
53C4×C157—81no—
54C4×C157#13512yes—
55C4×C157#13712yes—
56C4×C157#13712yes—
57Dic157—81no—
58Dic157—81no—
59C2×C157#49511yescharacteristic
60C2×C157#49711yescharacteristic
61C2×C157#49711yescharacteristic
62C157#171811yescharacteristic, complemented, Sylow
63#1718—1571nomaximal, Sylow
64#500—1571no—
65#498D15711yescharacteristic
66#487—1571no—
67#487—1571no—
68#487—1571no—
69#487—1571no—
70#322—1571no—
71C4⋊Q8—1571no—
72C4⋊Q8—1571no—
73C4⋊Q8C2×D15711yescharacteristic
74C4⋊Q8C2×D15711yescharacteristic
75#107—3142no—
76#106—22no—
77#103—3142no—
78#103—3142no—
79#103—3142no—
80#103—3142no—
81C4×C8—1571no—
82C4×C8—1571no—
83C4×C8C2×D15711yescharacteristic
84C2×Q8—21no—
85C2×Q8—21no—
86C2×Q8—3141no—
87C2×Q8—3141no—
88C2×C8—1572no—
89C2×C8—1572no—
90C2×C8C22⋊D15712yes—
91C4⋊C4—21no—
92C4⋊C4—21no—
93C4⋊C4—21no—
94C4⋊C4—21no—
95C4⋊C4—3141no—
96C4⋊C4—3141no—
97C4⋊C4—3141no—
98C4⋊C4—3141no—
99C42C22×D15711yescharacteristic
100Q8—42no—
101Q8—42no—
102Q8—6282no—
103Q8—6282no—
104C2×C4—41no—
105C2×C4—41no—
106C2×C4—6281no—
107C2×C4—6281no—
108C2×C4D4×D15711yescharacteristic
109C2×C4D4×D15711yescharacteristic
110C2×C4C2×C22⋊D15711yescharacteristic
111C8—22no—
112C8—3142no—
113C8—3142no—
114C22#1909776711yescharacteristic
115C4—81no—
116C4—81no—
117C4—12561no—
118C4—12561no—
119C4#1909779212yes—
120C4#1909780012yes—
121C4#1909780212yes—
122C2#2375765411yescharacteristic
123C2#2375766411yescharacteristic
124C2#2375766511yescharacteristic
subgroupG/H
centerC22#19097767
commutator, cosocleC42×C157C23
FrattiniC42C22×D157
Fitting#498×C157C2
socle, prime radicalC22×C157#127
hypercenter#498D157
hypocenterC157#1718
LCSG ▷ C42×C157 ▷ C22×C157 ▷ C157
UCSC1 ◁ C22 ◁ C42 ◁ #498

Complements

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

NH ≅ G/Ntype
62. C157#1718semidirect

Maximal subgroups

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

subgroupindex
#237576762
#237576252
#237576242
#237576232
#237569952
#498×C1572
#1718157