Finite Group Databasebeta

← D21⋊(C5⋊AGL(1,𝔽11)) #37528467

Subgroups — D21⋊(C5⋊AGL(1,𝔽11)) #37528467

Order 23100.

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
1C7×C3⋊(C5⋊AGL(1,𝔽11))C211yesmaximal, characteristic, complemented
2C5×D21×C11⋊C5C211yesmaximal, characteristic, complemented
3C3×C5⋊(C7⋊AGL(1,𝔽11))C211yesmaximal, characteristic, complemented
4D7×C5⋊AGL(1,𝔽11)—31nomaximal, Hall
5C3×C5×C7×C11⋊C5C2211yescharacteristic, complemented, Hall
6D21⋊D55C511yesmaximal, characteristic, complemented
7D21⋊AGL(1,𝔽11)—51nomaximal
8C5⋊(C7⋊AGL(1,𝔽11))D311yescharacteristic, complemented
9C7×C5⋊AGL(1,𝔽11)—31no—
10C5×D7×C11⋊C5—31no—
11D3×C5⋊AGL(1,𝔽11)—71nomaximal, Hall
12D21×C11⋊C5—22no—
13D21×C11⋊C5D511yescharacteristic, complemented
14C7×C3⋊AGL(1,𝔽11)—51no—
15C3×C7⋊AGL(1,𝔽11)—51no—
16C7×D165C2×C511yescharacteristic, complemented
17C5×C11×D21C2×C511yescharacteristic, complemented
18C3×D385C2×C511yescharacteristic, complemented
19C5×D15⋊D7—111nomaximal, Hall
20C5×C7×C11⋊C5C2×D311yescharacteristic, complemented, Hall
21C3⋊(C5⋊AGL(1,𝔽11))D711yescharacteristic, complemented
22C5×D3×C11⋊C5—71no—
23C3×C5⋊AGL(1,𝔽11)—71no—
24D7×D55—31no—
25D7×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×C7×D15—111no—
31C52×D21—221no—
32C3×C5×D35—111no—
33D21⋊D11—51noHall
34C3×C5×C11⋊C5C2×D711yescharacteristic, complemented, Hall
35D385C5×D311yescharacteristic, complemented
36C7×D55—31no—
37C5×C11×D7—31no—
38C7⋊AGL(1,𝔽11)—51no—
39D7×C11⋊C5—31no—
40D7×C11⋊C5—62no—
41C7×AGL(1,𝔽11)—151no—
42C5×D5×D7—331noHall
43D3×D55—71no—
44D3×AGL(1,𝔽11)—351no—
45C2×C5×C11⋊C5—211no—
46C5⋊AGL(1,𝔽11)—31no—
47C5⋊AGL(1,𝔽11)—71no—
48C3×C52×C7—221noHall
49C11×D21C5×D511yescharacteristic, complemented
50C7×D33—51no—
51C3×D77—51no—
52D15⋊D7—111no—
53C5×D3×D7—551no—
54C5×C7×C11C2×C5×D311yescharacteristic, complemented
55C7×C11⋊C5—22no—
56C7×C11⋊C5D3×D511yescharacteristic, complemented
57C5×D35—111no—
58C5×C7×D5—331no—
59C52×D7—661no—
60D165C5×D711yescharacteristic, complemented
61C5×D3×C11—71no—
62C3×D55—71no—
63C3⋊AGL(1,𝔽11)—51no—
64D3×C11⋊C5—71no—
65D3×C11⋊C5—142no—
66C3×AGL(1,𝔽11)—351no—
67D7×D11—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—
73C7×D15—111no—
74C5×D21—222no—
75C5×D21—221no—
76C5×D21AGL(1,𝔽11)11yescharacteristic, complemented
77C5×D3×C7—551no—
78C3×D35—111no—
79C3×C5×D7—551no—
80C52×C7—221noHall
81C3×C5×C11C2×C5×D711yescharacteristic, complemented
82C3×C11⋊C5—22no—
83C3×C11⋊C5D5×D711yescharacteristic, complemented
84D77—51no—
85C7×D11—151no—
86C11×D7—31no—
87C5×D15—111no—
88C52×D3—1541no—
89C3×C5×D5—771no—
90C2×C5×D7—1651no—
91D5×D7—331no—
92D3×D11—351noHall
93C2×C5×C11—211no—
94D55—31no—
95D55—71no—
96C2×C11⋊C5—211no—
97C2×C11⋊C5—422no—
98AGL(1,𝔽11)—151no—
99AGL(1,𝔽11)—351no—
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—1651no—
108D35—111no—
109C5×D7—31no—
110C5×D7—551no—
111C5×D7—661no—
112C5×D7—662no—
113C7×D5—331no—
114D33—51no—
115C3×D11—351no—
116D3×C11—71no—
117C2×C5×D3—3851no—
118D3×D5—771no—
119C5×C11C5×D3×D711yescharacteristic, complemented
120C11⋊C5—22no—
121C11⋊C5D15⋊D711yescharacteristic, complemented
122C2×C52—4621no—
123C5×D5—331no—
124C5×D5—771no—
125C2×D11—1051noHall
126D21C5⋊AGL(1,𝔽11)11yescharacteristic, complemented
127C3×D7—551no—
128D3×C7—551no—
129C5×C7—222no—
130C5×C7—221no—
131C5×C7D3×AGL(1,𝔽11)11yescharacteristic, complemented
132C3×C11C5×D5×D711yescharacteristic, complemented, Hall
133C2×C3×C5—3851no—
134D15—111no—
135C3×D5—771no—
136C5×D3—71no—
137C5×D3—551no—
138C5×D3—1541no—
139C5×D3—1542no—
140C2×D7—1651noHall
141C52—221noSylow
142C2×C11—211no—
143D11—151no—
144D11—351no—
145C3×C7C2×C5⋊AGL(1,𝔽11)11yescharacteristic, complemented, Hall
146C22×C5—11551no—
147C2×D5—2311no—
148C3×C5—221no—
149C3×C5—222no—
150C3×C5D7×AGL(1,𝔽11)11yescharacteristic, complemented
151C2×C7—1651no—
152D7—31no—
153D7—551no—
154C2×D3—3851noHall
155C11C5×D15⋊D711yescharacteristic, complemented, Sylow
156C2×C5—211no—
157C2×C5—3851no—
158C2×C5—1651no—
159C2×C5—4621no—
160C2×C5—4622no—
161D5—331no—
162D5—771no—
163C7D3×C5⋊AGL(1,𝔽11)11yescharacteristic, complemented, Sylow
164C2×C3—3851no—
165D3—71no—
166D3—551no—
167C5—221no—
168C5—222no—
169C5D21⋊AGL(1,𝔽11)11yescharacteristic, complemented
170C22—11551noSylow
171C3D7×C5⋊AGL(1,𝔽11)11yescharacteristic, complemented, Sylow
172C2—211no—
173C2—3851no—
174C2—1651no—
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. C7×C3⋊(C5⋊AGL(1,𝔽11))C2semidirect
2. C5×D21×C11⋊C5C2semidirect
3. C3×C5⋊(C7⋊AGL(1,𝔽11))C2semidirect
5. C3×C5×C7×C11⋊C5C22semidirect
6. D21⋊D55C5semidirect
8. C5⋊(C7⋊AGL(1,𝔽11))D3semidirect
13. D21×C11⋊C5D5semidirect
16. C7×D165C2×C5semidirect
17. C5×C11×D21C2×C5semidirect
18. C3×D385C2×C5semidirect
20. C5×C7×C11⋊C5C2×D3semidirect
21. C3⋊(C5⋊AGL(1,𝔽11))D7semidirect
26. C3×C5×C7×C11C22×C5semidirect
28. C3×C7×C11⋊C5C2×D5semidirect
34. C3×C5×C11⋊C5C2×D7semidirect
35. D385C5×D3semidirect
49. C11×D21C5×D5semidirect
54. C5×C7×C11C2×C5×D3semidirect
56. C7×C11⋊C5D3×D5semidirect
60. D165C5×D7semidirect
69. C5×C11⋊C5D3×D7semidirect
70. C3×C7×C11C2×C5×D5semidirect
76. C5×D21AGL(1,𝔽11)semidirect
81. C3×C5×C11C2×C5×D7semidirect
83. C3×C11⋊C5D5×D7semidirect
102. C3×C5×C7C2×AGL(1,𝔽11)semidirect
105. C7×C11C5×D3×D5semidirect
119. C5×C11C5×D3×D7semidirect
121. C11⋊C5D15⋊D7semidirect
126. D21C5⋊AGL(1,𝔽11)semidirect
131. C5×C7D3×AGL(1,𝔽11)semidirect
132. C3×C11C5×D5×D7semidirect
145. C3×C7C2×C5⋊AGL(1,𝔽11)semidirect
150. C3×C5D7×AGL(1,𝔽11)semidirect
155. C11C5×D15⋊D7semidirect
163. C7D3×C5⋊AGL(1,𝔽11)semidirect
169. C5D21⋊AGL(1,𝔽11)semidirect
171. C3D7×C5⋊AGL(1,𝔽11)semidirect

Maximal subgroups

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

subgroupindex
C7×C3⋊(C5⋊AGL(1,𝔽11))2
C5×D21×C11⋊C52
C3×C5⋊(C7⋊AGL(1,𝔽11))2
D7×C5⋊AGL(1,𝔽11)3
D21⋊D555
D21⋊AGL(1,𝔽11)5
D3×C5⋊AGL(1,𝔽11)7
C5×D15⋊D711