Finite Group Databasebeta

← #34099448

Subgroups — #34099448

Order 20096.

196 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 196 conjugacy classes of subgroups — too many to draw. Only its 45 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#23758023C211yesmaximal, characteristic
2#23757682C212yesmaximal, complemented
3#23757668C211yesmaximal, characteristic
4#23757014C212yesmaximal, complemented
5#329×C157C211yesmaximal, characteristic
6C2×#14578944—21no—
7C2×#14578942—21no—
8#19097771C2211yescharacteristic
9#19097769—21no—
10#19097764—22no—
11#19097763C2212yes—
12#19097752—21no—
13#19097748—22no—
14#19097705—22no—
15#19097703—22no—
16#19097682C2211yescharacteristic
17#124×C157C2211yescharacteristic
18#97×C157C2212yes—
19C2×Dic314—21no—
20C2×Dic314—21no—
21C22×Dic157—21no—
22#14578944—42no—
23#14578942—42no—
24C2×#11929434—21no—
25C4⋊Dic157—22no—
26C4⋊Dic157D412yes—
27C4⋊Dic157D412yes—
28#14578933—22no—
29#14578933—22no—
30#14578933—22no—
31C22⋊Dic157—22no—
32C22⋊Dic157—21no—
33C4×Dic157—21no—
34C2×Q8×C157D411yescharacteristic
35C2×D4×C157D411yescharacteristic
36C2×C8×C157—22no—
37C22⋊C4×C157—22no—
38C42×C157C2311yescharacteristic
39Dic314—41no—
40Dic314—41no—
41Dic314—81no—
42C2×Dic157—22no—
43C2×Dic157—22no—
44C2×Dic157—41no—
45C2×Dic157—81no—
46#11929434—22no—
47C23×C157—21no—
48Q8×C157—41no—
49D4×C157—41no—
50C2×C4×C157—21no—
51C2×C4×C157C2×D412yes—
52C2×C4×C157C2×D411yescharacteristic
53C8×C157—24no—
54C22×C157—41no—
55C22×C157—42no—
56C22×C157#12011yescharacteristic
57C4×C157—21no—
58C4×C157—22no—
59C4×C157—41no—
60Dic157—42no—
61Dic157—42no—
62Dic157—81no—
63C2×C157—81no—
64C2×C157#45311yescharacteristic
65C2×C157#45612yes—
66C157#166011yescharacteristic, complemented, Sylow
67#1660—1571nomaximal, Sylow
68#563—1571no—
69#501—1572no—
70#497—1571no—
71#330—1572no—
72#329D15711yescharacteristic
73C2×Q16—3141no—
74C2×SD16—3141no—
75C4⋊Q8—3141no—
76C4⋊Q8—1571no—
77#126—3142no—
78#125—1572no—
79#124C2×D15711yescharacteristic
80#123—3141no—
81C22⋊Q8—3142no—
82#107—3142no—
83#106—3142no—
84#97—1571no—
85#97C2×D15712yes—
86C2×Q8—3141no—
87C2×Q8—3141no—
88C2×Q8D62811yescharacteristic
89C2×D4D62811yescharacteristic
90C22×C4—3141no—
91Q16—6282no—
92SD16—6282no—
93C2×C8—22no—
94C2×C8—3141no—
95C4⋊C4—3142no—
96C4⋊C4—3142no—
97C4⋊C4—3142no—
98C4⋊C4—3142no—
99C4⋊C4—1572no—
100C4⋊C4—1572no—
101C22⋊C4—22no—
102C22⋊C4—3142no—
103C22⋊C4—3141no—
104C42—3141no—
105C42C22×D15711yescharacteristic
106C23—21no—
107Q8—41no—
108Q8—6281no—
109Q8—6281no—
110Q8—12561no—
111D4—41no—
112C2×C4—21no—
113C2×C4—3142no—
114C2×C4—3142no—
115C2×C4—6281no—
116C2×C4—12561no—
117C2×C4D4×D15712yes—
118C2×C4C2×D62811yescharacteristic
119C8—24no—
120C8—3142no—
121C22—41no—
122C22—42no—
123C22#1909774111yescharacteristic
124C4—21no—
125C4—22no—
126C4—41no—
127C4—6282no—
128C4—6282no—
129C4—12561no—
130C2—81no—
131C2#2375744311yescharacteristic
132C2#2375745712yes—
subgroupG/H
centerC22#19097741
commutator, cosocleC42×C157C23
FrattiniC42C22×D157
Fitting#329×C157C2
socleC22×C157#120
prime radicalC2×D4×C157D4
hypercenter#329D157
hypocenterC157#1660
LCSG ▷ C42×C157 ▷ C22×C157 ▷ C157
UCSC1 ◁ C22 ◁ C42 ◁ #329

Complements

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

NH ≅ G/Ntype
2. #23757682C2semidirect
4. #23757014C2semidirect
66. C157#1660semidirect

Maximal subgroups

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

subgroupindex
#237580232
#237576822
#237576682
#237570142
#329×C1572
#1660157