Finite Group Databasebeta

← C4×C7×ΓL(1,𝔽8)×C11⋊C5 #44568457

Subgroups — C4×C7×ΓL(1,𝔽8)×C11⋊C5 #44568457

Order 32340.

120 conjugacy classes of subgroups; only the 54 normal subgroups are shown.

normal subgroups only

This group has 120 conjugacy classes of subgroups — too many to draw. Only its 54 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×C7×ΓL(1,𝔽8)×C11⋊C5C211yesmaximal, characteristic
2C4×C72×C11⋊C5C311yesmaximal, characteristic, complemented, Hall
3C7×ΓL(1,𝔽8)×C11⋊C5C411yescharacteristic, direct product factor, Hall
4C4×C7×C11×ΓL(1,𝔽8)C511yesmaximal, characteristic, complemented, Hall
5C2×C72×C11⋊C5C2×C311yescharacteristic
6C4×ΓL(1,𝔽8)×C11⋊C5C711yesmaximal, characteristic, direct product factor
7C3×C4×C7×C11⋊C5—71nomaximal
8C2×C7×C11×ΓL(1,𝔽8)C2×C511yescharacteristic
9C4×C5×C7×ΓL(1,𝔽8)—111nomaximal, Hall
10C72×C11⋊C5C3×C411yescharacteristic, complemented, Hall
11C2×ΓL(1,𝔽8)×C11⋊C5C2×C711yescharacteristic
12C2×C3×C7×C11⋊C5—71no—
13C4×C72×C11C3×C511yescharacteristic, complemented, Hall
14C7×C11×ΓL(1,𝔽8)C4×C511yescharacteristic, complemented, Hall
15C4×C7×C11⋊C5—32no—
16C4×C7×C11⋊C5ΓL(1,𝔽8)11yescharacteristic, direct product factor
17C4×C7×C11⋊C5C3×C711yescharacteristic, complemented
18C2×C5×C7×ΓL(1,𝔽8)—111no—
19C3×C7×C11⋊C5—71no—
20ΓL(1,𝔽8)×C11⋊C5C4×C711yescharacteristic, direct product factor
21C2×C72×C11C2×C3×C511yescharacteristic
22C4×C5×C72—111noHall
23C3×C4×C7×C11—71no—
24C4×C11×ΓL(1,𝔽8)C5×C711yescharacteristic, complemented
25C2×C7×C11⋊C5—32no—
26C2×C7×C11⋊C5C2×ΓL(1,𝔽8)11yescharacteristic
27C2×C7×C11⋊C5C2×C3×C711yescharacteristic
28C5×C7×ΓL(1,𝔽8)—111noHall
29C3×C4×C11⋊C5—71noHall
30C4×C7×ΓL(1,𝔽8)C11⋊C511yescharacteristic, direct product factor, Hall
31C72×C11C3×C4×C511yescharacteristic, complemented, Hall
32C2×C5×C72—111no—
33C2×C3×C7×C11—71no—
34C2×C11×ΓL(1,𝔽8)C2×C5×C711yescharacteristic
35C3×C4×C5×C7—771no—
36C4×C5×ΓL(1,𝔽8)—111no—
37C7×C11⋊C5—32no—
38C7×C11⋊C5C4×ΓL(1,𝔽8)11yescharacteristic, direct product factor
39C7×C11⋊C5C3×C4×C711yescharacteristic, complemented
40C2×C3×C11⋊C5—71no—
41C4×C7×C11—32no—
42C4×C7×C11C5×ΓL(1,𝔽8)11yescharacteristic, complemented
43C4×C7×C11C3×C5×C711yescharacteristic, complemented
44C2×C7×ΓL(1,𝔽8)C2×C11⋊C511yescharacteristic
45C5×C72—111noHall
46C3×C7×C11—71no—
47C11×ΓL(1,𝔽8)C4×C5×C711yescharacteristic, complemented
48C4×C11⋊C5C7×ΓL(1,𝔽8)11yescharacteristic, direct product factor, Hall
49C2×C3×C5×C7—771no—
50C2×C5×ΓL(1,𝔽8)—111no—
51C4×C72C3×C11⋊C511yescharacteristic, complemented, Hall
52C3×C11⋊C5—71noHall
53C2×C7×C11—32no—
54C2×C7×C11C2×C5×ΓL(1,𝔽8)11yescharacteristic
55C2×C7×C11C2×C3×C5×C711yescharacteristic
56C7×ΓL(1,𝔽8)C4×C11⋊C511yescharacteristic, direct product factor, Hall
57C4×C5×C7—111no—
58C4×C5×C7—111no—
59C4×C5×C7—332no—
60C3×C4×C11—71noHall
61C2×C11⋊C5C2×C7×ΓL(1,𝔽8)11yescharacteristic
62C3×C5×C7—771no—
63C5×ΓL(1,𝔽8)—111no—
64C2×C72C2×C3×C11⋊C511yescharacteristic
65C3×C4×C7—71no—
66C4×ΓL(1,𝔽8)C7×C11⋊C511yescharacteristic, direct product factor
67C7×C11—32no—
68C7×C11C4×C5×ΓL(1,𝔽8)11yescharacteristic, complemented
69C7×C11C3×C4×C5×C711yescharacteristic, complemented
70C2×C5×C7—111no—
71C2×C5×C7—111no—
72C2×C5×C7—332no—
73C2×C3×C11—71no—
74C3×C4×C5—771noHall
75C11⋊C5C4×C7×ΓL(1,𝔽8)11yescharacteristic, direct product factor, Hall
76C72C3×C4×C11⋊C511yescharacteristic, complemented, Sylow
77C4×C11C5×C7×ΓL(1,𝔽8)11yescharacteristic, complemented, Hall
78C2×C3×C7—71no—
79C2×ΓL(1,𝔽8)C2×C7×C11⋊C511yescharacteristic
80C5×C7—111no—
81C5×C7—111no—
82C5×C7—332no—
83C3×C11—71noHall
84C2×C3×C5—771no—
85C4×C7—32no—
86C4×C7ΓL(1,𝔽8)×C11⋊C511yescharacteristic, direct product factor
87C4×C7C3×C7×C11⋊C511yescharacteristic, complemented
88C2×C11C2×C5×C7×ΓL(1,𝔽8)11yescharacteristic
89C3×C7—71no—
90ΓL(1,𝔽8)C4×C7×C11⋊C511yescharacteristic, direct product factor
91C4×C5—111noHall
92C3×C5—771noHall
93C2×C7—32no—
94C2×C7C2×C3×C7×C11⋊C511yescharacteristic
95C2×C7C2×ΓL(1,𝔽8)×C11⋊C511yescharacteristic
96C3×C4—71noHall
97C11C4×C5×C7×ΓL(1,𝔽8)11yescharacteristic, complemented, Sylow
98C2×C5—111no—
99C7—32no—
100C7C3×C4×C7×C11⋊C511yescharacteristic, complemented
101C7C4×ΓL(1,𝔽8)×C11⋊C511yescharacteristic, direct product factor
102C2×C3—71no—
103C5—111noSylow
104C4C7×ΓL(1,𝔽8)×C11⋊C511yescharacteristic, direct product factor, Sylow
105C3—71noSylow
106C2C2×C7×ΓL(1,𝔽8)×C11⋊C511yescharacteristic
subgroupG/H
center, hypercenterC4×C7ΓL(1,𝔽8)×C11⋊C5
commutator, hypocenterC7×C11C3×C4×C5×C7
FrattiniC2C2×C7×ΓL(1,𝔽8)×C11⋊C5
FittingC4×C72×C11C3×C5
socleC2×C72×C11C2×C3×C5
prime radicalC2×C7×ΓL(1,𝔽8)×C11⋊C5C2
cosocleC2×C7×C11C2×C3×C5×C7
LCSG ▷ C7×C11
UCSC1 ◁ C4×C7

Complements

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

NH ≅ G/Ntype
2. C4×C72×C11⋊C5C3semidirect
3. C7×ΓL(1,𝔽8)×C11⋊C5C4direct (N × H)
4. C4×C7×C11×ΓL(1,𝔽8)C5semidirect
6. C4×ΓL(1,𝔽8)×C11⋊C5C7direct (N × H)
10. C72×C11⋊C5C3×C4semidirect
13. C4×C72×C11C3×C5semidirect
14. C7×C11×ΓL(1,𝔽8)C4×C5semidirect
16. C4×C7×C11⋊C5ΓL(1,𝔽8)direct (N × H)
17. C4×C7×C11⋊C5C3×C7semidirect
20. ΓL(1,𝔽8)×C11⋊C5C4×C7direct (N × H)
24. C4×C11×ΓL(1,𝔽8)C5×C7semidirect
30. C4×C7×ΓL(1,𝔽8)C11⋊C5direct (N × H)
31. C72×C11C3×C4×C5semidirect
38. C7×C11⋊C5C4×ΓL(1,𝔽8)direct (N × H)
39. C7×C11⋊C5C3×C4×C7semidirect
42. C4×C7×C11C5×ΓL(1,𝔽8)semidirect
43. C4×C7×C11C3×C5×C7semidirect
47. C11×ΓL(1,𝔽8)C4×C5×C7semidirect
48. C4×C11⋊C5C7×ΓL(1,𝔽8)direct (N × H)
51. C4×C72C3×C11⋊C5semidirect
56. C7×ΓL(1,𝔽8)C4×C11⋊C5direct (N × H)
66. C4×ΓL(1,𝔽8)C7×C11⋊C5direct (N × H)
68. C7×C11C4×C5×ΓL(1,𝔽8)semidirect
69. C7×C11C3×C4×C5×C7semidirect
75. C11⋊C5C4×C7×ΓL(1,𝔽8)direct (N × H)
76. C72C3×C4×C11⋊C5semidirect
77. C4×C11C5×C7×ΓL(1,𝔽8)semidirect
86. C4×C7ΓL(1,𝔽8)×C11⋊C5direct (N × H)
87. C4×C7C3×C7×C11⋊C5semidirect
90. ΓL(1,𝔽8)C4×C7×C11⋊C5direct (N × H)
97. C11C4×C5×C7×ΓL(1,𝔽8)semidirect
100. C7C3×C4×C7×C11⋊C5semidirect
101. C7C4×ΓL(1,𝔽8)×C11⋊C5direct (N × H)
104. C4C7×ΓL(1,𝔽8)×C11⋊C5direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C7×ΓL(1,𝔽8)×C11⋊C52
C4×C72×C11⋊C53
C4×C7×C11×ΓL(1,𝔽8)5
C4×ΓL(1,𝔽8)×C11⋊C57
C3×C4×C7×C11⋊C57
C4×C5×C7×ΓL(1,𝔽8)11