Finite Group Databasebeta

← D3×C5⋊(C7⋊AGL(1,𝔽11)) #37528463

Subgroups — D3×C5⋊(C7⋊AGL(1,𝔽11)) #37528463

Order 23100.

192 conjugacy classes of subgroups; only the 44 normal subgroups are shown.

normal subgroups only

This group has 192 conjugacy classes of subgroups — too many to draw. Only its 44 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⋊(C7⋊AGL(1,𝔽11)))C211yesmaximal, characteristic, complemented
2C5×D3×C7×C11⋊C5C211yesmaximal, characteristic, complemented
3C3×C5⋊(C7⋊AGL(1,𝔽11))C211yesmaximal, characteristic, complemented
4C2×C5⋊(C7⋊AGL(1,𝔽11))—31nomaximal, Hall
5C3×C5×C7×C11⋊C5C2211yescharacteristic, complemented, Hall
6D3×D385C511yesmaximal, characteristic, complemented
7D3×C7⋊AGL(1,𝔽11)—51nomaximal
8C2×C5×C7×C11⋊C5—31no—
9C5⋊(C7⋊AGL(1,𝔽11))—31no—
10C5⋊(C7⋊AGL(1,𝔽11))D311yescharacteristic, direct product factor
11D3×C5⋊AGL(1,𝔽11)—71nomaximal, Hall
12C3⋊(C7⋊AGL(1,𝔽11))—51no—
13D3×C7×C11⋊C5—22no—
14D3×C7×C11⋊C5D511yescharacteristic, complemented
15C3×C7⋊AGL(1,𝔽11)—51no—
16D1155C2×C511yescharacteristic, complemented
17C5×D3×C7×C11C2×C511yescharacteristic, complemented
18C3×D385C2×C511yescharacteristic, complemented
19C5×D3×D35—111nomaximal, Hall
20C5×C7×C11⋊C5C2×D311yescharacteristic, complemented, Hall
21C3⋊(C5⋊AGL(1,𝔽11))—71no—
22C5×D3×C11⋊C5D711yescharacteristic, complemented
23C3×C5⋊AGL(1,𝔽11)—71no—
24C2×D385—31no—
25C2×C7⋊AGL(1,𝔽11)—151no—
26C3×C5×C7×C11C22×C511yescharacteristic, complemented
27C3×C7×C11⋊C5—22no—
28C3×C7×C11⋊C5C2×D511yescharacteristic, complemented
29C2×C5⋊AGL(1,𝔽11)—211noHall
30C5×D105—111no—
31C52×D3×C7—221no—
32C3×C5×D35—111no—
33D3×D77—51noHall
34C3×C5×C11⋊C5C2×D711yescharacteristic, complemented, Hall
35C2×C5×C7×C11—31no—
36D385—31no—
37D385C5×D311yescharacteristic, complemented
38C2×C7×C11⋊C5—31no—
39C2×C7×C11⋊C5—62no—
40C7⋊AGL(1,𝔽11)—51no—
41C7⋊AGL(1,𝔽11)—151no—
42C2×C5×D35—331noHall
43D3×D55—71no—
44D3×AGL(1,𝔽11)—351no—
45C2×C5×C11⋊C5—31no—
46C5⋊AGL(1,𝔽11)—71no—
47C5⋊AGL(1,𝔽11)—211no—
48C3×C52×C7—221noHall
49D231—51no—
50D3×C7×C11C5×D511yescharacteristic, complemented
51C3×D77—51no—
52D3×D35—111no—
53C5×D3×D7—551no—
54C5×C7×C11C2×C5×D311yescharacteristic, complemented
55C7×C11⋊C5—22no—
56C7×C11⋊C5D3×D511yescharacteristic, complemented
57C2×C52×C7—661no—
58C5×D35—111no—
59C5×D35—331no—
60D165—71no—
61C5×D3×C11C5×D711yescharacteristic, complemented
62C3×D55—71no—
63C3⋊AGL(1,𝔽11)—351no—
64D3×C11⋊C5—22no—
65D3×C11⋊C5D3511yescharacteristic, complemented
66C3×AGL(1,𝔽11)—351no—
67C2×D77—151noHall
68C5×D3×D5—771noHall
69C5×C11⋊C5D3×D711yescharacteristic, complemented, Hall
70C3×C7×C11C2×C5×D511yescharacteristic, complemented, Hall
71C2×D55—211no—
72C2×AGL(1,𝔽11)—1051no—
73D105—111no—
74C5×D21—551no—
75C5×D3×C7—221no—
76C5×D3×C7—222no—
77C5×D3×C7AGL(1,𝔽11)11yescharacteristic, complemented
78C3×D35—111no—
79C3×C5×D7—551no—
80C52×C7—221noHall
81C3×C5×C11C2×C5×D711yescharacteristic, complemented
82C3×C11⋊C5—22no—
83C3×C11⋊C5C2×D3511yescharacteristic, complemented
84C2×C7×C11—31no—
85D77—51no—
86D77—151no—
87C5×D15—771no—
88C52×D3—221no—
89C3×C5×D5—771no—
90C2×D35—331no—
91C2×C5×D7—1651no—
92D3×D11—351noHall
93C2×C5×C11—31no—
94D55—71no—
95D55—211no—
96C2×C11⋊C5—31no—
97C2×C11⋊C5—62no—
98AGL(1,𝔽11)—351no—
99AGL(1,𝔽11)—1051no—
100C3×C5×C7—221no—
101C3×C5×C7—222no—
102C3×C5×C7C2×AGL(1,𝔽11)11yescharacteristic, complemented
103C2×C5×D5—2311noHall
104D3×D7—551noHall
105C7×C11C5×D3×D511yescharacteristic, complemented, Hall
106C3×C52—221noHall
107C2×C5×C7—31no—
108C2×C5×C7—331no—
109C2×C5×C7—662no—
110D35—111no—
111D35—331no—
112C5×D7—551no—
113C5×D7—1651no—
114D33—351no—
115C3×D11—351no—
116D3×C11C5×D3511yescharacteristic, complemented
117C2×C5×D3—3851no—
118D3×D5—771no—
119C5×C11C5×D3×D711yescharacteristic, complemented
120C11⋊C5—22no—
121C11⋊C5D3×D3511yescharacteristic, complemented
122C2×C52—661no—
123C5×D5—771no—
124C5×D5—2311no—
125C2×D11—1051noHall
126D21—551no—
127C3×D7—551no—
128D3×C7C5⋊AGL(1,𝔽11)11yescharacteristic, complemented
129C5×C7—111no—
130C5×C7—222no—
131C5×C7D3×AGL(1,𝔽11)11yescharacteristic, complemented
132C3×C11C2×C5×D3511yescharacteristic, complemented, Hall
133C2×C3×C5—3851no—
134D15—771no—
135C3×D5—771no—
136C5×D3—221no—
137C5×D3—222no—
138C5×D3—3851no—
139C5×D3C7⋊AGL(1,𝔽11)11yescharacteristic, complemented
140C2×D7—1651noHall
141C52—221noSylow
142C2×C11—31no—
143D11—351no—
144D11—1051no—
145C3×C7C2×C5⋊AGL(1,𝔽11)11yescharacteristic, complemented, Hall
146C22×C5—11551no—
147C2×D5—2311no—
148C3×C5—221no—
149C3×C5—222no—
150C3×C5C2×C7⋊AGL(1,𝔽11)11yescharacteristic, complemented
151C2×C7—31no—
152D7—551no—
153D7—1651no—
154C2×D3—3851noHall
155C11C5×D3×D3511yescharacteristic, complemented, Sylow
156C2×C5—31no—
157C2×C5—661no—
158C2×C5—662no—
159C2×C5—3851no—
160C2×C5—11551no—
161D5—771no—
162D5—2311no—
163C7D3×C5⋊AGL(1,𝔽11)11yescharacteristic, complemented, Sylow
164C2×C3—3851no—
165D3—3851no—
166D3C5⋊(C7⋊AGL(1,𝔽11))11yescharacteristic, direct product factor
167C5—221no—
168C5—222no—
169C5D3×C7⋊AGL(1,𝔽11)11yescharacteristic, complemented
170C22—11551noSylow
171C3C2×C5⋊(C7⋊AGL(1,𝔽11))11yescharacteristic, complemented, Sylow
172C2—31no—
173C2—3851no—
174C2—11551no—
subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC3×C5×C7×C11C22×C5
LCSG ▷ C3×C5×C7×C11
UCSC1

Complements

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

NH ≅ G/Ntype
1. C3⋊(C5⋊(C7⋊AGL(1,𝔽11)))C2semidirect
2. C5×D3×C7×C11⋊C5C2semidirect
3. C3×C5⋊(C7⋊AGL(1,𝔽11))C2semidirect
5. C3×C5×C7×C11⋊C5C22semidirect
6. D3×D385C5semidirect
10. C5⋊(C7⋊AGL(1,𝔽11))D3direct (N × H)
14. D3×C7×C11⋊C5D5semidirect
16. D1155C2×C5semidirect
17. C5×D3×C7×C11C2×C5semidirect
18. C3×D385C2×C5semidirect
20. C5×C7×C11⋊C5C2×D3semidirect
22. C5×D3×C11⋊C5D7semidirect
26. C3×C5×C7×C11C22×C5semidirect
28. C3×C7×C11⋊C5C2×D5semidirect
34. C3×C5×C11⋊C5C2×D7semidirect
37. D385C5×D3semidirect
50. D3×C7×C11C5×D5semidirect
54. C5×C7×C11C2×C5×D3semidirect
56. C7×C11⋊C5D3×D5semidirect
61. C5×D3×C11C5×D7semidirect
65. D3×C11⋊C5D35semidirect
69. C5×C11⋊C5D3×D7semidirect
70. C3×C7×C11C2×C5×D5semidirect
77. C5×D3×C7AGL(1,𝔽11)semidirect
81. C3×C5×C11C2×C5×D7semidirect
83. C3×C11⋊C5C2×D35semidirect
102. C3×C5×C7C2×AGL(1,𝔽11)semidirect
105. C7×C11C5×D3×D5semidirect
116. D3×C11C5×D35semidirect
119. C5×C11C5×D3×D7semidirect
121. C11⋊C5D3×D35semidirect
128. D3×C7C5⋊AGL(1,𝔽11)semidirect
131. C5×C7D3×AGL(1,𝔽11)semidirect
132. C3×C11C2×C5×D35semidirect
139. C5×D3C7⋊AGL(1,𝔽11)semidirect
145. C3×C7C2×C5⋊AGL(1,𝔽11)semidirect
150. C3×C5C2×C7⋊AGL(1,𝔽11)semidirect
155. C11C5×D3×D35semidirect
163. C7D3×C5⋊AGL(1,𝔽11)semidirect
166. D3C5⋊(C7⋊AGL(1,𝔽11))direct (N × H)
169. C5D3×C7⋊AGL(1,𝔽11)semidirect
171. C3C2×C5⋊(C7⋊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⋊(C7⋊AGL(1,𝔽11)))2
C5×D3×C7×C11⋊C52
C3×C5⋊(C7⋊AGL(1,𝔽11))2
C2×C5⋊(C7⋊AGL(1,𝔽11))3
D3×D3855
D3×C7⋊AGL(1,𝔽11)5
D3×C5⋊AGL(1,𝔽11)7
C5×D3×D3511