Finite Group Databasebeta

← #3862×C3⋊#261 #37525366

Subgroups — #3862×C3⋊#261 #37525366

Order 22932.

136 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×D13×#3862C211yesmaximal, characteristic
2C72×C3⋊#261C311yesmaximal, characteristic, complemented
3#261×#3862—31nomaximal
4C3×C13×#3862C411yescharacteristic, complemented, Hall
5C3×C72×D13C2×C311yescharacteristic
6D13×#3862—21no—
7D13×#3862D311yescharacteristic
8ΓL(1,𝔽8)×C3⋊#261—72nomaximal
9C72×#261—31noHall
10C3×C72×C13C3×C411yescharacteristic, complemented
11C13×#3862—21no—
12C13×#3862Dic311yescharacteristic, complemented
13Dic3×#3862—131nomaximal, Hall
14C3×ΓL(1,𝔽8)×D13—72no—
15C72×D13C3×D311yescharacteristic
16C7×C3⋊#261—32no—
17C7×C3⋊#261ΓL(1,𝔽8)12yescomplemented
18ΓL(1,𝔽8)×#261—212no—
19C2×C3×#3862—131no—
20C3×C13×ΓL(1,𝔽8)—72no—
21C72×C13C3×Dic311yescharacteristic, complemented, Hall
22C72×Dic3—131no—
23C4×#3862—391no—
24C3×C7×D13—32no—
25C3×C7×D13C2×ΓL(1,𝔽8)12yes—
26ΓL(1,𝔽8)×D13—72no—
27ΓL(1,𝔽8)×D13—142no—
28C3×C3⋊#261—491noHall
29C3×#3862#26111yescharacteristic, complemented, Hall
30C7×#261—32no—
31C7×#261—92no—
32C2×C3×C72—131no—
33C2×#3862—131no—
34C2×#3862—261no—
35C3×C7×C13—32no—
36C3×C7×C13C4×ΓL(1,𝔽8)12yescomplemented
37C13×ΓL(1,𝔽8)—72no—
38C13×ΓL(1,𝔽8)—142no—
39Dic3×ΓL(1,𝔽8)—912no—
40C32×D13—491no—
41C4×C72—391noHall
42C7×D13—32no—
43C7×D13D3×ΓL(1,𝔽8)12yes—
44C3⋊#261#386211yescharacteristic, direct product factor
45C3×#261—1471no—
46C3×C72C3×#26111yescharacteristic, complemented
47#3862—21no—
48#3862C3⋊#26111yescharacteristic, direct product factor
49C2×C3×ΓL(1,𝔽8)—912no—
50C32×C13—491noHall
51C2×C72—131no—
52C7×C13—32no—
53C7×C13Dic3×ΓL(1,𝔽8)12yescomplemented
54C7×Dic3—132no—
55C7×Dic3—392no—
56C4×ΓL(1,𝔽8)—2732no—
57C3×D13—491no—
58C3×D13—981no—
59C3×D13C2×#386211yescharacteristic
60C3×ΓL(1,𝔽8)—72no—
61#261—31noHall
62C72C3×C3⋊#26111yescharacteristic, complemented, Sylow
63C2×C3×C7—132no—
64C2×C3×C7—392no—
65C2×ΓL(1,𝔽8)—912no—
66C2×ΓL(1,𝔽8)—1822no—
67C3×C13—491no—
68C3×C13—981no—
69C3×C13C4×#386211yescharacteristic, complemented
70C3×Dic3—6371noHall
71C4×C7—392no—
72C4×C7—1172no—
73D13D3×#386211yescharacteristic
74C3×C7—32no—
75C3×C7ΓL(1,𝔽8)×#26112yescomplemented
76ΓL(1,𝔽8)—72no—
77ΓL(1,𝔽8)—142no—
78C2×C32—6371no—
79C2×C7—132no—
80C2×C7—392no—
81C13Dic3×#386211yescharacteristic, complemented, Sylow
82C3×C4—19111no—
83Dic3—131no—
84C32—491noSylow
85C7—32no—
86C7ΓL(1,𝔽8)×C3⋊#26112yescomplemented
87C2×C3—131no—
88C2×C3—6371no—
89C2×C3—12741no—
90C4—391noSylow
91C3—491no—
92C3—981no—
93C3#261×#386211yescharacteristic, complemented
94C2—131no—
subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, hypocenterC3×C72×C13C3×C4
prime radicalC3×D13×#3862C2
cosocleC3×C72×D13C2×C3
LCSG ▷ C3×C72×C13
UCSC1

Complements

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

NH ≅ G/Ntype
2. C72×C3⋊#261C3semidirect
4. C3×C13×#3862C4semidirect
10. C3×C72×C13C3×C4semidirect
12. C13×#3862Dic3semidirect
17. C7×C3⋊#261ΓL(1,𝔽8)semidirect
21. C72×C13C3×Dic3semidirect
29. C3×#3862#261semidirect
36. C3×C7×C13C4×ΓL(1,𝔽8)semidirect
44. C3⋊#261#3862direct (N × H)
46. C3×C72C3×#261semidirect
48. #3862C3⋊#261direct (N × H)
53. C7×C13Dic3×ΓL(1,𝔽8)semidirect
62. C72C3×C3⋊#261semidirect
69. C3×C13C4×#3862semidirect
75. C3×C7ΓL(1,𝔽8)×#261semidirect
81. C13Dic3×#3862semidirect
86. C7ΓL(1,𝔽8)×C3⋊#261semidirect
93. C3#261×#3862semidirect

Maximal subgroups

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

subgroupindex
C3×D13×#38622
C72×C3⋊#2613
#261×#38623
ΓL(1,𝔽8)×C3⋊#2617
Dic3×#386213