Finite Group Databasebeta

← #34098729

Subgroups — #34098729

Order 20096.

226 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 226 conjugacy classes of subgroups — too many to draw. Only its 63 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#23757829C211yesmaximal, characteristic
2#23757225C212yesmaximal
3#23757015C211yesmaximal, characteristic, complemented
4#23757014C212yesmaximal, complemented
5#330×C157C211yesmaximal, characteristic, complemented
6C2×#14578937—22no—
7#19097770C412yes—
8#19097763C2211yescharacteristic
9#19097749—22no—
10#19097736—22no—
11#19097729C412yes—
12C42×D157C2211yescharacteristic
13#19097682C2212yes—
14C8×Dic157—22no—
15#125×C157C2211yescharacteristic
16#97×C157C2212yes—
17C2×Dic314—22no—
18C2×C4×D157C2×C411yescharacteristic
19C2×C4×D157D412yes—
20#14578937—28no—
21C2×#11929434—22no—
22C4⋊Dic157C2×C412yes—
23#14578933—22no—
24#14578933—22no—
25#14578931—22no—
26C4×Dic157—22no—
27C4×Dic157C2×C411yescharacteristic
28C4×Dic157D412yes—
29C2×C8×C157—22no—
30C4⋊C4×C157—22no—
31C4⋊C4×C157C2×C412yes—
32C42×C157C2311yescharacteristic
33C22×D157C22⋊C411yescharacteristic
34Dic314—44no—
35C2×Dic157—22no—
36C2×Dic157C22⋊C411yescharacteristic
37C2×Dic157C22⋊C412yes—
38C4×D157—22no—
39C4×D157—24no—
40#11929434—24no—
41C2×C4×C157—22no—
42C2×C4×C157C22×C411yescharacteristic
43C2×C4×C157C2×D412yes—
44C8×C157—24no—
45C22×C157C2×C22⋊C411yescharacteristic
46C2×D157—21no—
47C2×D157—22no—
48C4×C157—21no—
49C4×C157—22no—
50C4×C157—42no—
51Dic157—42no—
52Dic157#10112yes—
53Dic157#10414yes—
54C2×C157C2×#10111yescharacteristic
55C2×C157C2×#10412yes—
56D157—41no—
57C157#152611yescharacteristic, complemented, Sylow
58#1526—1571nomaximal, Sylow
59#533—1571no—
60C4×M16—1572no—
61#330—1571no—
62#330—1572no—
63#330D15711yescharacteristic, complemented
64C2×M16—3142no—
65C4⋊Q8—1572no—
66#125—1571no—
67#125C2×D15711yescharacteristic
68C22⋊Q8—3142no—
69C4×Q8—3142no—
70#117—1572no—
71C2×C42—1571no—
72#97—1572no—
73#97C2×D15712yes—
74C4×C8—3142no—
75C2×Q8—3142no—
76C22×C4—1571no—
77C22×C4—1572no—
78M16—3148no—
79C2×C8—22no—
80C2×C8—3142no—
81C4⋊C4—22no—
82C4⋊C4—3142no—
83C4⋊C4—3142no—
84C4⋊C4—1572no—
85C4⋊C4C4×D15712yes—
86C22⋊C4—3142no—
87C42—3142no—
88C42—1571no—
89C42—1572no—
90C42C22×D15711yescharacteristic
91C23—1571no—
92Q8—6284no—
93C2×C4—22no—
94C2×C4—3144no—
95C2×C4—3142no—
96C2×C4—3142no—
97C2×C4—1571no—
98C2×C4—1572no—
99C2×C4C2×C4×D15711yescharacteristic
100C2×C4D4×D15712yes—
101C8—24no—
102C8—3144no—
103C22—3141no—
104C22—3142no—
105C22C22⋊C4×D15711yescharacteristic
106C4—21no—
107C4—22no—
108C4—42no—
109C4—6282no—
110C4—1572no—
111C4—1574no—
112C2—6281no—
113C2#101×D15711yescharacteristic
114C2#104×D15712yes—
subgroupG/H
centerC22C22⋊C4×D157
commutatorC2×C4×C157C22×C4
FrattiniC42C22×D157
Fitting#330×C157C2
socleC22×C157C2×C22⋊C4
prime radicalC22×D157C22⋊C4
cosocleC42×C157C23
hypercenter#330D157
hypocenterC157#1526
LCSG ▷ C2×C4×C157 ▷ C22×C157 ▷ C157
UCSC1 ◁ C22 ◁ C42 ◁ #330

Complements

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

NH ≅ G/Ntype
3. #23757015C2semidirect
4. #23757014C2semidirect
5. #330×C157C2semidirect
57. C157#1526semidirect
63. #330D157semidirect

Maximal subgroups

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

subgroupindex
#237578292
#237572252
#237570152
#237570142
#330×C1572
#1526157