Finite Group Databasebeta

← C8×C22⋊D157 #23757337

Subgroups — C8×C22⋊D157 #23757337

Order 10048.

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

normal subgroups only

This group has 134 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
1C2×C8×D157C211yesmaximal, characteristic, complemented
2C4×C22⋊D157C211yesmaximal, characteristic
3#19097700C211yesmaximal, characteristic, complemented
4C22⋊#11929434C211yesmaximal, characteristic, complemented
5#19097683C211yesmaximal, characteristic, complemented
6C8×Dic157C211yesmaximal, characteristic, complemented
7C22×C8×C157C211yesmaximal, characteristic, complemented
8C2×C22⋊D157C411yescharacteristic
9C2×C4×D157C2211yescharacteristic
10C2×#11929434C2211yescharacteristic
11C2×#11929434C2211yescharacteristic
12C8×D157—22no—
13#14578933C411yescharacteristic
14C22⋊Dic157C411yescharacteristic
15#14578931C411yescharacteristic
16C4×Dic157C2211yescharacteristic
17C22×C4×C157C2211yescharacteristic
18C2×C8×C157—22no—
19C2×C8×C157C2211yescharacteristic
20C2×C8×C157C2211yescharacteristic
21C22×D157C2×C411yescharacteristic
22C22⋊D157C814yesdirect product factor
23C2×Dic157C2×C411yescharacteristic
24C2×Dic157C2×C411yescharacteristic
25C2×Dic157C2×C411yescharacteristic
26C4×D157—21no—
27C4×D157—21no—
28#11929434—21no—
29#11929434—21no—
30C23×C157C2×C411yescharacteristic
31C2×C4×C157—21no—
32C2×C4×C157—21no—
33C2×C4×C157C2×C411yescharacteristic
34C2×C4×C157C2311yescharacteristic
35C8×C157—21no—
36C8×C157D412yescomplemented
37C22×C157—21no—
38C22×C157—21no—
39C22×C157C2×C812yescomplemented
40C22×C157C22×C411yescharacteristic
41C2×D157—21no—
42C2×D157—21no—
43C2×D157C2×C812yescomplemented
44C4×C157—21no—
45C4×C157C2×D411yescharacteristic
46C4×C157#4111yescharacteristic
47Dic157—21no—
48Dic157—21no—
49Dic157C2×C812yescomplemented
50C2×C157—22no—
51C2×C157C4×D411yescharacteristic
52C2×C157C22×C811yescharacteristic
53C2×C157#13111yescharacteristic
54D157—22no—
55C157C8×D411yescharacteristic, complemented, Sylow
56C8×D4—1571nomaximal, Sylow
57C22×C8—1571no—
58C22×C8D15711yescharacteristic, complemented
59C4×D4—1571no—
60C4⋊C8—1571no—
61C22⋊C8—1571no—
62C22⋊C8—1571no—
63C4×C8—1571no—
64C2×D4—1571no—
65C22×C4—1571no—
66C22×C4C2×D15711yescharacteristic
67C2×C8—22no—
68C2×C8—3142no—
69C2×C8—1571no—
70C2×C8—1571no—
71C2×C8C2×D15711yescharacteristic
72C2×C8C2×D15711yescharacteristic
73C4⋊C4—1571no—
74C22⋊C4—1571no—
75C22⋊C4—1571no—
76C42—1571no—
77C23—1571no—
78C23C4×D15711yescharacteristic
79D4—1574no—
80C2×C4—21no—
81C2×C4—21no—
82C2×C4—3141no—
83C2×C4—3141no—
84C2×C4—1571no—
85C2×C4—1571no—
86C2×C4—1571no—
87C2×C4C4×D15711yescharacteristic
88C2×C4C22×D15711yescharacteristic
89C8—21no—
90C8—3141no—
91C8—3141no—
92C8C22⋊D15712yesdirect product factor
93C22—21no—
94C22—21no—
95C22—3141no—
96C22—3141no—
97C22—1572no—
98C22C8×D15712yescomplemented
99C22C2×C4×D15711yescharacteristic
100C4—21no—
101C4—3141no—
102C4—3141no—
103C4—1572no—
104C4C2×C22⋊D15711yescharacteristic
105C4#1457895411yescharacteristic
106C2—22no—
107C2—3142no—
108C2C4×C22⋊D15711yescharacteristic
109C2C2×C8×D15711yescharacteristic
110C2#1909777711yescharacteristic
subgroupG/H
centerC2×C8C2×D157
commutatorC2×C157C22×C8
FrattiniC2×C4C22×D157
FittingC22×C8×C157C2
socleC22×C157C22×C4
prime radicalC2×C22⋊D157C4
cosocleC2×C4×C157C23
hypercenterC22×C8D157
hypocenterC157C8×D4
LCSG ▷ C2×C157 ▷ C157
UCSC1 ◁ C2×C8 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
1. C2×C8×D157C2semidirect
3. #19097700C2semidirect
4. C22⋊#11929434C2semidirect
5. #19097683C2semidirect
6. C8×Dic157C2semidirect
7. C22×C8×C157C2semidirect
22. C22⋊D157C8direct (N × H)
36. C8×C157D4semidirect
39. C22×C157C2×C8semidirect
43. C2×D157C2×C8semidirect
49. Dic157C2×C8semidirect
55. C157C8×D4semidirect
58. C22×C8D157semidirect
92. C8C22⋊D157direct (N × H)
98. C22C8×D157semidirect