Finite Group Databasebeta

← C2×D55×#3861 #44568790

Subgroups — C2×D55×#3861 #44568790

Order 32340.

400 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×C11×#3861C211yesmaximal, characteristic, complemented
2D55×#3861C212yesmaximal, direct product factor
3C2×C72×D55C311yesmaximal, characteristic, complemented, Hall
4C5×C11×#3861C2211yescharacteristic, complemented, Hall
5C2×D11×#3861—51nomaximal, Hall
6C72×D55C2×C312yescomplemented
7C2×C5×C72×C11C2×C311yescharacteristic, complemented
8C2×ΓL(1,𝔽8)×D55—78nomaximal
9C2×C11×#3861D511yescharacteristic, complemented
10D11×#3861—52no—
11C2×D5×#3861—111nomaximal, Hall
12C5×C72×C11C22×C311yescharacteristic, complemented, Hall
13ΓL(1,𝔽8)×D55—716no—
14C2×C5×C11×ΓL(1,𝔽8)—78no—
15C2×C72×D11—51noHall
16C11×#3861C2×D511yescharacteristic, complemented, Hall
17C2×C7×D55ΓL(1,𝔽8)18yescomplemented
18C2×C5×#3861D1111yescharacteristic, complemented
19D5×#3861—112no—
20C5×C11×ΓL(1,𝔽8)—78no—
21C2×C72×C11C3×D511yescharacteristic, complemented
22C72×D11—52no—
23C2×C72×D5—111noHall
24C2×ΓL(1,𝔽8)×D11—358no—
25C2×C5×C7×C11C2×ΓL(1,𝔽8)18yescomplemented
26C7×D55C2×ΓL(1,𝔽8)116yescomplemented
27C5×#3861C2×D1111yescharacteristic, complemented, Hall
28C2×C3×D55—491noHall
29C22×#3861—551noHall
30C72×C11C2×C3×D511yescharacteristic, complemented, Hall
31C2×C5×C72C3×D1111yescharacteristic, complemented
32C72×D5—112no—
33C2×C11×ΓL(1,𝔽8)—78no—
34ΓL(1,𝔽8)×D11—3516no—
35C2×D5×ΓL(1,𝔽8)—778no—
36C5×C7×C11C22×ΓL(1,𝔽8)18yescomplemented
37C2×C3×C5×C11—491no—
38C3×D55—492no—
39C2×C7×D11—58no—
40C2×#3861—552no—
41C2×#3861D5511yescharacteristic, direct product factor
42C5×C72C2×C3×D1111yescharacteristic, complemented, Hall
43C11×ΓL(1,𝔽8)—78no—
44C2×D55#386111yescharacteristic, direct product factor, Hall
45C2×C5×ΓL(1,𝔽8)—78no—
46D5×ΓL(1,𝔽8)—7716no—
47C22×C72—551noHall
48C3×C5×C11—491noHall
49C2×C7×C11D5×ΓL(1,𝔽8)18yescomplemented
50C7×D11—516no—
51#3861C2×D5511yescharacteristic, direct product factor, Hall
52C2×C7×D5—118no—
53C2×C3×D11—2451noHall
54C2×C5×C11C2×#386111yescharacteristic, complemented
55D55C2×#386112yesdirect product factor
56C5×ΓL(1,𝔽8)—78no—
57C2×C72—552no—
58C2×C72C3×D5511yescharacteristic, complemented
59C22×ΓL(1,𝔽8)—3858no—
60C7×C11C2×D5×ΓL(1,𝔽8)18yescomplemented
61C2×C5×C7ΓL(1,𝔽8)×D1118yescomplemented
62C7×D5—1116no—
63C2×C3×C11—491no—
64C3×D11—2452no—
65C2×C3×D5—5391noHall
66C5×C11C22×#386111yescharacteristic, complemented, Hall
67C72C2×C3×D5511yescharacteristic, complemented, Sylow
68C2×D11—51noHall
69C2×ΓL(1,𝔽8)—78no—
70C2×ΓL(1,𝔽8)—38516no—
71C5×C7C2×ΓL(1,𝔽8)×D1118yescomplemented
72C3×C11—491noHall
73C2×C3×C5—491no—
74C3×D5—5392no—
75C22×C7—558no—
76C2×C11D5×#386111yescharacteristic, complemented
77D11—52no—
78ΓL(1,𝔽8)—78no—
79C2×D5—111noHall
80C3×C5—491noHall
81C2×C7—5516no—
82C2×C7ΓL(1,𝔽8)×D5518yescomplemented
83C22×C3—26951noHall
84C11C2×D5×#386111yescharacteristic, complemented, Sylow
85C2×C5D11×#386111yescharacteristic, complemented
86D5—112no—
87C7C2×ΓL(1,𝔽8)×D5518yescomplemented
88C2×C3—491no—
89C2×C3—26952no—
90C5C2×D11×#386111yescharacteristic, complemented, Sylow
91C22—551noSylow
92C3—491noSylow
93C2—552no—
94C2D55×#386111yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2D55×#3861
commutator, cosocle, hypocenterC5×C72×C11C22×C3
FrattiniC1G
Fitting, socleC2×C5×C72×C11C2×C3
LCSG ▷ C5×C72×C11
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
1. C2×C5×C11×#3861C2semidirect
2. D55×#3861C2direct (N × H)
3. C2×C72×D55C3semidirect
4. C5×C11×#3861C22semidirect
6. C72×D55C2×C3semidirect
7. C2×C5×C72×C11C2×C3semidirect
9. C2×C11×#3861D5semidirect
12. C5×C72×C11C22×C3semidirect
16. C11×#3861C2×D5semidirect
17. C2×C7×D55ΓL(1,𝔽8)semidirect
18. C2×C5×#3861D11semidirect
21. C2×C72×C11C3×D5semidirect
25. C2×C5×C7×C11C2×ΓL(1,𝔽8)semidirect
26. C7×D55C2×ΓL(1,𝔽8)semidirect
27. C5×#3861C2×D11semidirect
30. C72×C11C2×C3×D5semidirect
31. C2×C5×C72C3×D11semidirect
36. C5×C7×C11C22×ΓL(1,𝔽8)semidirect
41. C2×#3861D55direct (N × H)
42. C5×C72C2×C3×D11semidirect
44. C2×D55#3861direct (N × H)
49. C2×C7×C11D5×ΓL(1,𝔽8)semidirect
51. #3861C2×D55direct (N × H)
54. C2×C5×C11C2×#3861semidirect
55. D55C2×#3861direct (N × H)
58. C2×C72C3×D55semidirect
60. C7×C11C2×D5×ΓL(1,𝔽8)semidirect
61. C2×C5×C7ΓL(1,𝔽8)×D11semidirect
66. C5×C11C22×#3861semidirect
67. C72C2×C3×D55semidirect
71. C5×C7C2×ΓL(1,𝔽8)×D11semidirect
76. C2×C11D5×#3861semidirect
82. C2×C7ΓL(1,𝔽8)×D55semidirect
84. C11C2×D5×#3861semidirect
85. C2×C5D11×#3861semidirect
87. C7C2×ΓL(1,𝔽8)×D55semidirect
90. C5C2×D11×#3861semidirect
94. C2D55×#3861direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×C11×#38612
D55×#38612
C2×C72×D553
C2×D11×#38615
C2×ΓL(1,𝔽8)×D557
C2×D5×#386111