Finite Group Databasebeta

← #34098772

Subgroups — #34098772

Order 20096.

194 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 194 conjugacy classes of subgroups — too many to draw. Only its 59 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#23757328C212yesmaximal
3#23757015C211yesmaximal, characteristic, complemented
4#23757014C212yesmaximal, complemented
5#330×C157C211yesmaximal, characteristic, complemented
6#19097770C412yes—
7#19097763C2211yescharacteristic
8#19097749—22no—
9#19097736—22no—
10#19097729C412yes—
11C42×D157C2211yescharacteristic
12#19097700—22no—
13#19097683—22no—
14#19097682C2212yes—
15#125×C157C2211yescharacteristic
16#97×C157C2212yes—
17C2×Dic314—22no—
18C2×C4×D157C2×C411yescharacteristic
19C2×C4×D157D412yes—
20C2×#11929434—22no—
21C4⋊Dic157C2×C412yes—
22#14578933—22no—
23#14578933—22no—
24#14578931—22no—
25C4×Dic157—22no—
26C4×Dic157C2×C411yescharacteristic
27C4×Dic157D412yes—
28C2×C8×C157—22no—
29C4⋊C4×C157—22no—
30C4⋊C4×C157C2×C412yes—
31C42×C157C2311yescharacteristic
32C22×D157C22⋊C411yescharacteristic
33Dic314—44no—
34C2×Dic157—22no—
35C2×Dic157C22⋊C412yes—
36C2×Dic157C22⋊C411yescharacteristic
37C4×D157—22no—
38C4×D157—42no—
39#11929434—42no—
40C2×C4×C157—22no—
41C2×C4×C157C22×C411yescharacteristic
42C2×C4×C157C2×D412yes—
43C8×C157—42no—
44C22×C157C2×C22⋊C411yescharacteristic
45C2×D157—21no—
46C2×D157—22no—
47C4×C157—21no—
48C4×C157—22no—
49C4×C157—42no—
50Dic157—22no—
51Dic157—42no—
52Dic157#10112yes—
53C2×C157C2×#10111yescharacteristic
54C2×C157#42112yes—
55D157—41no—
56C157#153711yescharacteristic, complemented, Sylow
57#1537—1571nomaximal, Sylow
58#533—1571no—
59#432—1572no—
60#330—1571no—
61#330—1572no—
62#330D15711yescharacteristic, complemented
63C4⋊Q8—1572no—
64#125—1571no—
65#125C2×D15711yescharacteristic
66C22⋊Q8—3142no—
67C4×Q8—3142no—
68#117—1572no—
69C2×C42—1571no—
70C4⋊C8—3142no—
71C22⋊C8—3142no—
72#97—1572no—
73#97C2×D15712yes—
74C2×Q8—3142no—
75C22×C4—1571no—
76C22×C4—1572no—
77C2×C8—22no—
78C2×C8—3142no—
79C4⋊C4—22no—
80C4⋊C4—3142no—
81C4⋊C4—3142no—
82C4⋊C4—1572no—
83C4⋊C4C4×D15712yes—
84C22⋊C4—3142no—
85C42—3142no—
86C42—1571no—
87C42—1572no—
88C42C22×D15711yescharacteristic
89C23—1571no—
90Q8—6284no—
91C2×C4—22no—
92C2×C4—3142no—
93C2×C4—3142no—
94C2×C4—6282no—
95C2×C4—1572no—
96C2×C4—1571no—
97C2×C4C2×C4×D15711yescharacteristic
98C2×C4D4×D15712yes—
99C8—42no—
100C8—6282no—
101C22—3141no—
102C22—3142no—
103C22C22⋊C4×D15711yescharacteristic
104C4—21no—
105C4—22no—
106C4—42no—
107C4—3142no—
108C4—6282no—
109C4—1572no—
110C2—6281no—
111C2#101×D15711yescharacteristic
112C2#2375728812yes—
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#1537
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
56. C157#1537semidirect
62. #330D157semidirect

Maximal subgroups

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

subgroupindex
#237578292
#237573282
#237570152
#237570142
#330×C1572
#1537157