Finite Group Databasebeta

← C11×#63270⋊A4 #49114814

Subgroups — C11×#63270⋊A4 #49114814

Order 36036.

112 conjugacy classes of subgroups; only the 32 normal subgroups are shown.

normal subgroups only

This group has 112 conjugacy classes of subgroups — too many to draw. Only its 32 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
1C22×C11×#63270C311yesmaximal, characteristic, complemented
2C7×C11×C22⋊(C13⋊C3)C311yesmaximal, characteristic, complemented
3C11×C13×C22⋊ΓL(1,𝔽8)C311yesmaximal, characteristic, complemented
4C11×C22⋊#63271C311yesmaximal, characteristic, complemented
5C11×ΓL(1,𝔽8)×C13⋊C3—41nomaximal, Hall
6C2×C11×#63270—31no—
7C11×A4×C13⋊C3—71nomaximal, Hall
8C22×C7×C11×C13C3211yescharacteristic, complemented, Hall
9#63270⋊A4C1111yesmaximal, characteristic, direct product factor, Hall
10C11×#63271—41no—
11C11×#63270A411yescharacteristic, complemented
12C11×C13×ΓL(1,𝔽8)—41no—
13C7×C11×C13⋊C3—41no—
14C11×A4×ΓL(1,𝔽8)—131nomaximal, Hall
15C2×C7×C11×C13—31no—
16C11×C22⋊(C13⋊C3)—71no—
17C11×C22⋊(C13⋊C3)ΓL(1,𝔽8)11yescharacteristic, complemented
18C11×A4×C13—71no—
19C22×C11×C13⋊C3—71no—
20C3×C11×C13⋊C3—281noHall
21C22⋊#63271C3×C1111yescharacteristic, complemented
22C13×C22⋊ΓL(1,𝔽8)C3×C1111yescharacteristic, complemented
23C7×C22⋊(C13⋊C3)C3×C1111yescharacteristic, complemented
24C22×#63270C3×C1111yescharacteristic, complemented
25C7×C11×C13C3×A411yescharacteristic, complemented, Hall
26C11×C22⋊ΓL(1,𝔽8)—131no—
27C11×C22⋊ΓL(1,𝔽8)C13⋊C311yescharacteristic, complemented
28C7×C11×A4—131no—
29C22×C11×ΓL(1,𝔽8)—131no—
30C2×C11×C13⋊C3—211no—
31ΓL(1,𝔽8)×C13⋊C3—41noHall
32C3×C11×ΓL(1,𝔽8)—521noHall
33C22×C11×C13C3×ΓL(1,𝔽8)11yescharacteristic, complemented, Hall
34C2×#63270—31no—
35A4×C13⋊C3—71noHall
36C2×C11×ΓL(1,𝔽8)—391no—
37C3×C11×C13—281no—
38C11×C13⋊C3—41no—
39C11×C13⋊C3—71no—
40C11×C13⋊C3—281no—
41C3×C11×A4—911noHall
42C22×C7×C13C32×C1111yescharacteristic, complemented, Hall
43C22×C7×C11C3×C13⋊C311yescharacteristic, complemented, Hall
44C2×C11×C13—31no—
45#63271—41no—
46#63270C11×A411yescharacteristic, complemented
47C7×C13⋊C3—41no—
48C13×ΓL(1,𝔽8)—41no—
49A4×ΓL(1,𝔽8)—131noHall
50C3×C7×C11—521no—
51C11×ΓL(1,𝔽8)—41no—
52C11×ΓL(1,𝔽8)—131no—
53C11×ΓL(1,𝔽8)—521no—
54C2×C7×C13—31no—
55C22⋊(C13⋊C3)—71no—
56C22⋊(C13⋊C3)C11×ΓL(1,𝔽8)11yescharacteristic, complemented
57A4×C13—71no—
58C22×C13⋊C3—71no—
59C2×C7×C11—31no—
60C11×C13A4×ΓL(1,𝔽8)11yescharacteristic, complemented, Hall
61C22×C3×C11—911no—
62C11×A4—71no—
63C11×A4—131no—
64C11×A4—911no—
65C3×C13⋊C3—281noHall
66C32×C11—3641noHall
67C7×C13C3×C11×A411yescharacteristic, complemented, Hall
68C22⋊ΓL(1,𝔽8)—131no—
69C22⋊ΓL(1,𝔽8)C11×C13⋊C311yescharacteristic, complemented
70C7×A4—131no—
71C22×ΓL(1,𝔽8)—131no—
72C2×C13⋊C3—211no—
73C7×C11A4×C13⋊C311yescharacteristic, complemented, Hall
74C2×C3×C11—2731no—
75C3×ΓL(1,𝔽8)—521noHall
76C22×C13C3×C11×ΓL(1,𝔽8)11yescharacteristic, complemented, Hall
77C22×C11ΓL(1,𝔽8)×C13⋊C311yescharacteristic, complemented, Hall
78C2×ΓL(1,𝔽8)—391no—
79C3×C13—281no—
80C13⋊C3—41no—
81C13⋊C3—71no—
82C13⋊C3—281no—
83C3×A4—911noHall
84C3×C11—281no—
85C3×C11—521no—
86C3×C11—911no—
87C3×C11—3641no—
88C22×C7C3×C11×C13⋊C311yescharacteristic, complemented, Hall
89C2×C13—31no—
90C2×C11—31no—
91C3×C7—521no—
92ΓL(1,𝔽8)—41no—
93ΓL(1,𝔽8)—131no—
94ΓL(1,𝔽8)—521no—
95C2×C7—31no—
96C13C11×A4×ΓL(1,𝔽8)11yescharacteristic, complemented, Sylow
97C22×C3—911no—
98A4—71no—
99A4—131no—
100A4—911no—
101C11#63270⋊A411yescharacteristic, direct product factor, Sylow
102C32—3641noSylow
103C7C11×A4×C13⋊C311yescharacteristic, complemented, Sylow
104C2×C3—2731no—
105C22C11×ΓL(1,𝔽8)×C13⋊C311yescharacteristic, complemented, Sylow
106C3—281no—
107C3—521no—
108C3—911no—
109C3—3641no—
110C2—31no—
subgroupG/H
center, hypercenterC11#63270⋊A4
commutator, cosocle, hypocenterC22×C7×C13C32×C11
FrattiniC1G
Fitting, socleC22×C7×C11×C13C32
LCSG ▷ C22×C7×C13
UCSC1 ◁ C11

Complements

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

NH ≅ G/Ntype
1. C22×C11×#63270C3semidirect
2. C7×C11×C22⋊(C13⋊C3)C3semidirect
3. C11×C13×C22⋊ΓL(1,𝔽8)C3semidirect
4. C11×C22⋊#63271C3semidirect
8. C22×C7×C11×C13C32semidirect
9. #63270⋊A4C11direct (N × H)
11. C11×#63270A4semidirect
17. C11×C22⋊(C13⋊C3)ΓL(1,𝔽8)semidirect
21. C22⋊#63271C3×C11semidirect
22. C13×C22⋊ΓL(1,𝔽8)C3×C11semidirect
23. C7×C22⋊(C13⋊C3)C3×C11semidirect
24. C22×#63270C3×C11semidirect
25. C7×C11×C13C3×A4semidirect
27. C11×C22⋊ΓL(1,𝔽8)C13⋊C3semidirect
33. C22×C11×C13C3×ΓL(1,𝔽8)semidirect
42. C22×C7×C13C32×C11semidirect
43. C22×C7×C11C3×C13⋊C3semidirect
46. #63270C11×A4semidirect
56. C22⋊(C13⋊C3)C11×ΓL(1,𝔽8)semidirect
60. C11×C13A4×ΓL(1,𝔽8)semidirect
67. C7×C13C3×C11×A4semidirect
69. C22⋊ΓL(1,𝔽8)C11×C13⋊C3semidirect
73. C7×C11A4×C13⋊C3semidirect
76. C22×C13C3×C11×ΓL(1,𝔽8)semidirect
77. C22×C11ΓL(1,𝔽8)×C13⋊C3semidirect
88. C22×C7C3×C11×C13⋊C3semidirect
96. C13C11×A4×ΓL(1,𝔽8)semidirect
101. C11#63270⋊A4direct (N × H)
103. C7C11×A4×C13⋊C3semidirect
105. C22C11×ΓL(1,𝔽8)×C13⋊C3semidirect

Maximal subgroups

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

subgroupindex
C22×C11×#632703
C7×C11×C22⋊(C13⋊C3)3
C11×C13×C22⋊ΓL(1,𝔽8)3
C11×C22⋊#632713
C11×ΓL(1,𝔽8)×C13⋊C34
C11×A4×C13⋊C37
#63270⋊A411
C11×A4×ΓL(1,𝔽8)13