Finite Group Databasebeta

← C3×#72223869 #72223871

Subgroups — C3×#72223869 #72223871

Order 7920.

116 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#72223869C311yesmaximal, characteristic, direct product factor
2C3×SL(2,𝔽11)C211yesmaximal, characteristic, complemented
3SL(2,𝔽11)C2×C311yescharacteristic, complemented
4C3×#6732—112nomaximal, Hall
5C3×C4×C11⋊C5—121nomaximal
6C3×SL(2,𝔽5)—112no—
7C2×C3×C11⋊C5—121no—
8#6732—112no—
9C4×C11⋊C5—121no—
10C3×C11⋊C5—121no—
11C3×#235—551nomaximal, Hall
12C3×#41⋊C3—551noHall
13C3×C4×C11—121no—
14C3×C4×D5—661no—
15SL(2,𝔽5)—112no—
16C2×C11⋊C5—121no—
17C2×C32×C4—551no—
18C3×#67—552no—
19C3×D12—551no—
20C3×C4×D3—552no—
21C3×Dic6—551no—
22C3×SL(2,𝔽3)—551no—
23C2×C3×C11—121no—
24C2×C3×D5—661no—
25C3×C4×C5—661no—
26C3×Dic5—661no—
27C11⋊C5—121noHall
28C3×#41—551no—
29#235—551no—
30#41⋊C3—551no—
31#41⋊C3—552no—
32C4×C11—121no—
33C4×D5—661no—
34C22×C32—551no—
35C2×C3×D3—552no—
36C32×C4—551no—
37C32×C4—551no—
38C3×Dic3—552no—
39C3×C11—121no—
40C2×C3×C5—661no—
41C3×D5—662no—
42C3×Q8—551no—
43C3×D4—1651no—
44C2×C3×C4—551no—
45C2×C3×C4—551no—
46C2×C3×C4—1101no—
47#67—552no—
48D12—551no—
49C4×D3—552no—
50Dic6—551no—
51SL(2,𝔽3)—551no—
52SL(2,𝔽3)—552no—
53C2×C11—121no—
54C2×D5—661no—
55C4×C5—661no—
56Dic5—661no—
57C2×C32—551no—
58C2×C32—1101no—
59C3×D3—1102no—
60#41—551noSylow
61C3×C5—661no—
62C22×C3—551no—
63C22×C3—551no—
64C22×C3—1101no—
65C2×D3—552no—
66C3×C4—551no—
67C3×C4—551no—
68C3×C4—551no—
69C3×C4—1101no—
70C3×C4—1101no—
71C3×C4PSL(2,𝔽11)11yesmaximal normal, characteristic
72Dic3—552no—
73C11—121noSylow
74C2×C5—661no—
75D5—662no—
76C32—551noSylow
77Q8—551no—
78D4—1651no—
79C2×C4—551no—
80C2×C3—551no—
81C2×C3—1101no—
82C2×C3—1102no—
83C2×C3—1101no—
84C2×C3—1101no—
85C2×C3C2×PSL(2,𝔽11)11yescharacteristic
86D3—1102no—
87C5—661noSylow
88C22—551no—
89C4—551no—
90C4C3×PSL(2,𝔽11)11yescharacteristic
91C3—551no—
92C3—1101no—
93C3#7222386911yescharacteristic, direct product factor
94C2—1101no—
95C2C2×C3×PSL(2,𝔽11)11yescharacteristic
subgroupG/H
center, Fitting, hypercenterC3×C4PSL(2,𝔽11)
commutator, hypocenterSL(2,𝔽11)C2×C3
Frattini, cosocleC2C2×C3×PSL(2,𝔽11)
socleC2×C3C2×PSL(2,𝔽11)
LCSG ▷ SL(2,𝔽11)
UCSC1 ◁ C3×C4

Complements

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

NH ≅ G/Ntype
1. #72223869C3direct (N × H)
2. C3×SL(2,𝔽11)C2semidirect
3. SL(2,𝔽11)C2×C3semidirect
93. C3#72223869direct (N × H)

Maximal subgroups

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

subgroupindex
#722238693
C3×SL(2,𝔽11)2
C3×#673211
C3×C4×C11⋊C512
C3×#23555