Finite Group Databasebeta

← C3⋊(C5⋊(ΓL(1,𝔽8)⋊AGL(1,𝔽11))) #46831546

Subgroups — C3⋊(C5⋊(ΓL(1,𝔽8)⋊AGL(1,𝔽11))) #46831546

Order 34650.

192 conjugacy classes of subgroups; only the 40 normal subgroups are shown.

normal subgroups only

This group has 192 conjugacy classes of subgroups — too many to draw. Only its 40 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
1C3×C5×ΓL(1,𝔽8)×C11⋊C5C211yesmaximal, characteristic, complemented, Hall
2C3⋊(C5⋊(C7⋊AGL(1,𝔽11)))C311yesmaximal, characteristic, complemented
3C5⋊(ΓL(1,𝔽8)⋊AGL(1,𝔽11))—31nomaximal
4C3⋊(C5⋊(C11⋊AGL(1,𝔽7)))C511yesmaximal, characteristic, complemented
5C3⋊(ΓL(1,𝔽8)⋊AGL(1,𝔽11))—51nomaximal
6C3×C5×C7×C11⋊C5C2×C311yescharacteristic, complemented
7C5×ΓL(1,𝔽8)×C11⋊C5—21no—
8C5×ΓL(1,𝔽8)×C11⋊C5D311yescharacteristic, complemented
9C3×C3⋊(C5⋊AGL(1,𝔽11))—71nomaximal, Hall
10C5⋊(C7⋊AGL(1,𝔽11))—31noHall
11C3×C5×C11×ΓL(1,𝔽8)C2×C511yescharacteristic, complemented
12C3×ΓL(1,𝔽8)×C11⋊C5—22no—
13C3×ΓL(1,𝔽8)×C11⋊C5D511yescharacteristic, complemented
14C5×C3⋊(C5⋊AGL(1,𝔽7))—111nomaximal, Hall
15C32×C5×C11⋊C5—71noHall
16ΓL(1,𝔽8)⋊AGL(1,𝔽11)—151no—
17C5⋊(C11⋊AGL(1,𝔽7))—31no—
18C3⋊(C7⋊AGL(1,𝔽11))—51no—
19D1155C3×C511yescharacteristic, complemented
20C5×C7×C11⋊C5C3×D311yescharacteristic, complemented, Hall
21C3⋊(C5⋊AGL(1,𝔽11))—71no—
22C3×C5⋊AGL(1,𝔽11)—211no—
23C3×C52×ΓL(1,𝔽8)—111noHall
24C3⋊(C11⋊AGL(1,𝔽7))—51noHall
25C3×C5×C7×C11C2×C3×C511yescharacteristic, complemented
26C5×C11×ΓL(1,𝔽8)—21no—
27C5×C11×ΓL(1,𝔽8)C5×D311yescharacteristic, complemented
28C3×C7×C11⋊C5—22no—
29C3×C7×C11⋊C5C3×D511yescharacteristic, complemented
30ΓL(1,𝔽8)×C11⋊C5—24no—
31ΓL(1,𝔽8)×C11⋊C5—22no—
32ΓL(1,𝔽8)×C11⋊C5—21no—
33ΓL(1,𝔽8)×C11⋊C5D1511yescharacteristic, complemented
34C5×D105—111no—
35C5×C5⋊AGL(1,𝔽7)—331no—
36C3×D165—71no—
37C3×C3⋊AGL(1,𝔽11)—351no—
38C3×C5×C11⋊C5—71no—
39C3×C5×C11⋊C5—141no—
40C3×C5×C11⋊C5AGL(1,𝔽7)11yescharacteristic, complemented
41D385—31no—
42C7⋊AGL(1,𝔽11)—151no—
43C3×C11×ΓL(1,𝔽8)C5×D511yescharacteristic, complemented, Hall
44C3⋊(C5⋊AGL(1,𝔽7))—111no—
45C5×C3⋊AGL(1,𝔽7)—551no—
46C5⋊AGL(1,𝔽11)—211noHall
47C3×C52×C7—111no—
48C52×ΓL(1,𝔽8)—111no—
49C52×ΓL(1,𝔽8)—221no—
50C32×C5×C11—71no—
51C32×C11⋊C5—71no—
52C32×C11⋊C5—142no—
53D231—51no—
54C11⋊AGL(1,𝔽7)—151no—
55C3×C5×D15—771noHall
56C5×C7×C11C3×C5×D311yescharacteristic, complemented
57C7×C11⋊C5—22no—
58C7×C11⋊C5C3×D1511yescharacteristic, complemented
59C5×D35—331noHall
60D165—71no—
61C3×D55—211no—
62C3⋊AGL(1,𝔽11)—351no—
63C3×AGL(1,𝔽11)—1051no—
64C3×C5×ΓL(1,𝔽8)—111no—
65C3×C5×ΓL(1,𝔽8)—222no—
66C3×C5×ΓL(1,𝔽8)AGL(1,𝔽11)11yescharacteristic, complemented
67C5×C11⋊C5C3⋊AGL(1,𝔽7)11yescharacteristic, complemented, Hall
68C3×C7×C11C3×C5×D511yescharacteristic, complemented
69C11×ΓL(1,𝔽8)—21no—
70C11×ΓL(1,𝔽8)C5×D1511yescharacteristic, complemented
71C32×C52—771noHall
72D105—111no—
73C5×D21—551no—
74C5⋊AGL(1,𝔽7)—331no—
75C5×AGL(1,𝔽7)—1651no—
76C3×D33—351noHall
77C52×C7—111noHall
78C3×C5×C11—71no—
79C3×C5×C11—141no—
80C3×C5×C11C5×AGL(1,𝔽7)11yescharacteristic, complemented
81C3×C11⋊C5—22no—
82C3×C11⋊C5—71no—
83C3×C11⋊C5—142no—
84C3×C11⋊C5—144no—
85C3×C11⋊C5—141no—
86C3×C11⋊C5C5⋊AGL(1,𝔽7)11yescharacteristic, complemented
87D77—151noHall
88C5×D15—771no—
89C3×C5×D5—2311no—
90C3⋊AGL(1,𝔽7)—551noHall
91D55—211no—
92AGL(1,𝔽11)—1051no—
93C3×C5×C7—111no—
94C3×C5×C7—222no—
95C3×C5×C7C3×AGL(1,𝔽11)11yescharacteristic, complemented
96C5×ΓL(1,𝔽8)—21no—
97C5×ΓL(1,𝔽8)—111no—
98C5×ΓL(1,𝔽8)—221no—
99C5×ΓL(1,𝔽8)—224no—
100C5×ΓL(1,𝔽8)—222no—
101C5×ΓL(1,𝔽8)C3⋊AGL(1,𝔽11)11yescharacteristic, complemented
102C32×C11—71noHall
103C3×D15—771no—
104C3×C5×D3—3851no—
105C7×C11C3×C5×D1511yescharacteristic, complemented, Hall
106C3×C52—111no—
107C3×C52—771no—
108C3×C52—1541no—
109D35—331no—
110C5×D7—1651no—
111D33—351no—
112C3×D11—1051no—
113C3×ΓL(1,𝔽8)C5⋊AGL(1,𝔽11)11yescharacteristic, complemented, Hall
114C5×C11C5×C3⋊AGL(1,𝔽7)11yescharacteristic, complemented
115C11⋊C5—22no—
116C11⋊C5C3⋊(C5⋊AGL(1,𝔽7))11yescharacteristic, complemented
117C5×D5—2311noHall
118C32×C5—71no—
119C32×C5—771no—
120C32×C5—1542no—
121D21—551no—
122AGL(1,𝔽7)—1651no—
123C5×C7—111no—
124C5×C7—222no—
125C5×C7C3×C3⋊AGL(1,𝔽11)11yescharacteristic, complemented
126C3×C11—71no—
127C3×C11—141no—
128C3×C11C5×C5⋊AGL(1,𝔽7)11yescharacteristic, complemented
129C2×C3×C5—11551no—
130D15—771no—
131C3×D5—2311no—
132C5×D3—3851no—
133C52—111noSylow
134D11—1051noHall
135C3×C7C3×C5⋊AGL(1,𝔽11)11yescharacteristic, complemented
136ΓL(1,𝔽8)—21no—
137ΓL(1,𝔽8)C3⋊(C5⋊AGL(1,𝔽11))11yescharacteristic, complemented
138C3×D3—3851noHall
139C3×C5—71no—
140C3×C5—111no—
141C3×C5—141no—
142C3×C5—222no—
143C3×C5—771no—
144C3×C5—1542no—
145C3×C5—1541no—
146C3×C5—1544no—
147C3×C5ΓL(1,𝔽8)⋊AGL(1,𝔽11)11yescharacteristic, complemented
148D7—1651noHall
149C11C5×C3⋊(C5⋊AGL(1,𝔽7))11yescharacteristic, complemented, Sylow
150C2×C5—11551no—
151D5—2311no—
152C32—71noSylow
153C7C3×C3⋊(C5⋊AGL(1,𝔽11))11yescharacteristic, complemented, Sylow
154C2×C3—11551no—
155D3—3851no—
156C5—111no—
157C5—222no—
158C5C3⋊(ΓL(1,𝔽8)⋊AGL(1,𝔽11))11yescharacteristic, complemented
159C3—71no—
160C3—141no—
161C3C5⋊(ΓL(1,𝔽8)⋊AGL(1,𝔽11))11yescharacteristic, complemented
162C2—11551noSylow
subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC3×C5×C7×C11C2×C3×C5
LCSG ▷ C3×C5×C7×C11
UCSC1

Complements

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

NH ≅ G/Ntype
1. C3×C5×ΓL(1,𝔽8)×C11⋊C5C2semidirect
2. C3⋊(C5⋊(C7⋊AGL(1,𝔽11)))C3semidirect
4. C3⋊(C5⋊(C11⋊AGL(1,𝔽7)))C5semidirect
6. C3×C5×C7×C11⋊C5C2×C3semidirect
8. C5×ΓL(1,𝔽8)×C11⋊C5D3semidirect
11. C3×C5×C11×ΓL(1,𝔽8)C2×C5semidirect
13. C3×ΓL(1,𝔽8)×C11⋊C5D5semidirect
19. D1155C3×C5semidirect
20. C5×C7×C11⋊C5C3×D3semidirect
25. C3×C5×C7×C11C2×C3×C5semidirect
27. C5×C11×ΓL(1,𝔽8)C5×D3semidirect
29. C3×C7×C11⋊C5C3×D5semidirect
33. ΓL(1,𝔽8)×C11⋊C5D15semidirect
40. C3×C5×C11⋊C5AGL(1,𝔽7)semidirect
43. C3×C11×ΓL(1,𝔽8)C5×D5semidirect
56. C5×C7×C11C3×C5×D3semidirect
58. C7×C11⋊C5C3×D15semidirect
66. C3×C5×ΓL(1,𝔽8)AGL(1,𝔽11)semidirect
67. C5×C11⋊C5C3⋊AGL(1,𝔽7)semidirect
68. C3×C7×C11C3×C5×D5semidirect
70. C11×ΓL(1,𝔽8)C5×D15semidirect
80. C3×C5×C11C5×AGL(1,𝔽7)semidirect
86. C3×C11⋊C5C5⋊AGL(1,𝔽7)semidirect
95. C3×C5×C7C3×AGL(1,𝔽11)semidirect
101. C5×ΓL(1,𝔽8)C3⋊AGL(1,𝔽11)semidirect
105. C7×C11C3×C5×D15semidirect
113. C3×ΓL(1,𝔽8)C5⋊AGL(1,𝔽11)semidirect
114. C5×C11C5×C3⋊AGL(1,𝔽7)semidirect
116. C11⋊C5C3⋊(C5⋊AGL(1,𝔽7))semidirect
125. C5×C7C3×C3⋊AGL(1,𝔽11)semidirect
128. C3×C11C5×C5⋊AGL(1,𝔽7)semidirect
135. C3×C7C3×C5⋊AGL(1,𝔽11)semidirect
137. ΓL(1,𝔽8)C3⋊(C5⋊AGL(1,𝔽11))semidirect
147. C3×C5ΓL(1,𝔽8)⋊AGL(1,𝔽11)semidirect
149. C11C5×C3⋊(C5⋊AGL(1,𝔽7))semidirect
153. C7C3×C3⋊(C5⋊AGL(1,𝔽11))semidirect
158. C5C3⋊(ΓL(1,𝔽8)⋊AGL(1,𝔽11))semidirect
161. C3C5⋊(ΓL(1,𝔽8)⋊AGL(1,𝔽11))semidirect

Maximal subgroups

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

subgroupindex
C3×C5×ΓL(1,𝔽8)×C11⋊C52
C3⋊(C5⋊(C7⋊AGL(1,𝔽11)))3
C5⋊(ΓL(1,𝔽8)⋊AGL(1,𝔽11))3
C3⋊(C5⋊(C11⋊AGL(1,𝔽7)))5
C3⋊(ΓL(1,𝔽8)⋊AGL(1,𝔽11))5
C3×C3⋊(C5⋊AGL(1,𝔽11))7
C5×C3⋊(C5⋊AGL(1,𝔽7))11