Finite Group Databasebeta

← D3×C3⋊#11925896 #36345140

Subgroups — D3×C3⋊#11925896 #36345140

Order 21780.

185 conjugacy classes of subgroups; only the 42 normal subgroups are shown.

normal subgroups only

This group has 185 conjugacy classes of subgroups — too many to draw. Only its 42 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⋊(C3⋊#11925896)C211yesmaximal, characteristic, complemented
2C3×D3×#10597245C211yesmaximal, characteristic, complemented
3C3×C3⋊#11925896C211yesmaximal, characteristic, complemented
4C2×C3⋊#11925896—31nomaximal
5D3×#11925896—31nomaximal
6C32×#10597245C2211yescharacteristic, complemented, Hall
7D3×C11×D33C511yesmaximal, characteristic, complemented, Hall
8C2×C3×#10597245—31no—
9D3×#10597245D311yescharacteristic, complemented
10C3⋊#11925896—31no—
11C3⋊#11925896—31no—
12C3⋊#11925896—61no—
13C3⋊#11925896D311yescharacteristic, direct product factor
14C3×#11925896—31no—
15C2×#11925896—91noHall
16C11×C3⋊D33C2×C511yescharacteristic, complemented
17C3×C11×D33C2×C511yescharacteristic, complemented
18C3×D3×C112C2×C511yescharacteristic, complemented
19D3×C3⋊AGL(1,𝔽11)—111nomaximal
20D32×C11⋊C5—111nomaximal
21C3×#10597245—21no—
22C3×#10597245C2×D311yescharacteristic, complemented
23C3×#10597245C2×D311yescharacteristic, complemented
24C2×C11×D33—31no—
25D3×C11×D11—31no—
26C2×#10597245—31no—
27#11925896—31no—
28#11925896—91no—
29C32×C112C22×C511yescharacteristic, complemented, Hall
30C3⋊(C3⋊AGL(1,𝔽11))—111no—
31C3⋊D3×C11⋊C5—111no—
32C3×C3⋊AGL(1,𝔽11)—111no—
33C3×D3×C11⋊C5—111no—
34C3×D3×C11⋊C5—111no—
35C3×D3×C11⋊C5—111no—
36C2×C3×C112—31no—
37C11×D33—31no—
38C11×D33—31no—
39C11×D33—61no—
40C11×D33C5×D311yescharacteristic, complemented
41D3×C112C5×D311yescharacteristic, complemented
42C3×C11×D11—31no—
43C2×C3⋊AGL(1,𝔽11)—331no—
44C2×D3×C11⋊C5—331no—
45C2×D3×C11⋊C5—331no—
46D3×AGL(1,𝔽11)—331no—
47#10597245D3211yescharacteristic, complemented, Hall
48C32×C11⋊C5—111no—
49C32×C11⋊C5—111no—
50C2×C11×D11—91noHall
51D3×D33C11⋊C511yescharacteristic, complemented
52D32×C11—111no—
53C3×C112—21no—
54C3×C112C2×C5×D311yescharacteristic, complemented
55C3×C112C2×C5×D311yescharacteristic, complemented
56C2×C3×C11⋊C5—331no—
57C2×C3×C11⋊C5—331no—
58C2×C3×C11⋊C5—331no—
59C3⋊AGL(1,𝔽11)—111no—
60C3⋊AGL(1,𝔽11)—331no—
61C3⋊AGL(1,𝔽11)—331no—
62C3⋊AGL(1,𝔽11)—661no—
63D3×C11⋊C5—111no—
64D3×C11⋊C5—111no—
65D3×C11⋊C5—111no—
66D3×C11⋊C5—331no—
67D3×C11⋊C5—331no—
68D3×C11⋊C5—661no—
69C3×AGL(1,𝔽11)—331no—
70C2×C112—31no—
71C11×D11—31no—
72C11×D11—91no—
73C22×C11⋊C5—991no—
74C2×AGL(1,𝔽11)—991no—
75C3⋊D33C2×C11⋊C511yescharacteristic, complemented
76C11×C3⋊D3—111no—
77C3×D33C2×C11⋊C511yescharacteristic, complemented
78C3×D3×C11—101no—
79C3×D3×C11—111no—
80C3×D3×C11AGL(1,𝔽11)11yescharacteristic, complemented
81C3×D3×C11C2×C11⋊C511yescharacteristic, complemented
82C5×D32—1211noHall
83C3×C11⋊C5—111no—
84C3×C11⋊C5—111no—
85C3×C11⋊C5—111no—
86C3×C11⋊C5—111no—
87C3×C11⋊C5—221no—
88C3×C11⋊C5—221no—
89C2×D33—31no—
90C2×D3×C11—331no—
91C2×D3×C11—331no—
92D3×D11—31no—
93C112C5×D3211yescharacteristic, complemented, Sylow
94C2×C11⋊C5—331no—
95C2×C11⋊C5—331no—
96C2×C11⋊C5—331no—
97C2×C11⋊C5—991no—
98AGL(1,𝔽11)—331no—
99AGL(1,𝔽11)—991no—
100C32×C11—101no—
101C32×C11C2×AGL(1,𝔽11)11yescharacteristic, complemented
102C32×C11C22×C11⋊C511yescharacteristic, complemented
103C5×C3⋊D3—1211no—
104C3×C5×D3—1211no—
105C3×C5×D3—1211no—
106C2×C3×C11—31no—
107C2×C3×C11—31no—
108C2×C3×C11—301no—
109C2×C3×C11—331no—
110D33—31no—
111D33—31no—
112D33—61no—
113D33D3×C11⋊C511yescharacteristic, complemented
114C3×D11—31no—
115D3×C11—101no—
116D3×C11—111no—
117D3×C11—331no—
118D3×C11—331no—
119D3×C11—661no—
120D3×C11D3×C11⋊C511yescharacteristic, complemented
121D3×C11C3⋊AGL(1,𝔽11)11yescharacteristic, complemented
122C2×C5×D3—3631no—
123C2×C5×D3—3631no—
124C11⋊C5—111no—
125C11⋊C5—111no—
126C32×C5—1211noHall
127C22×C11—991no—
128C2×D11—91no—
129D32—111noHall
130C3×C11—21no—
131C3×C11—21no—
132C3×C11—101no—
133C3×C11—101no—
134C3×C11—201no—
135C3×C11D3×AGL(1,𝔽11)11yescharacteristic, complemented
136C3×C11C2×D3×C11⋊C511yescharacteristic, complemented
137C3×C11C2×D3×C11⋊C511yescharacteristic, complemented
138C3×C11C2×C3⋊AGL(1,𝔽11)11yescharacteristic, complemented
139C2×C3×C5—3631no—
140C2×C3×C5—3631no—
141C5×D3—3631no—
142C5×D3—3631no—
143C5×D3—1211no—
144C5×D3—1211no—
145C5×D3—7261no—
146C2×C11—31no—
147C2×C11—31no—
148C2×C11—301no—
149C2×C11—331no—
150C2×C11—991no—
151D11—31no—
152D11—91no—
153C22×C5—10891noHall
154C3⋊D3—111no—
155C3×D3—111no—
156C3×D3#1192589611yescharacteristic, complemented
157C3×C5—1211no—
158C3×C5—1211no—
159C3×C5—2421no—
160C2×D3—331no—
161C2×D3—331no—
162C11—101no—
163C11D32×C11⋊C511yescharacteristic, complemented
164C11D3×C3⋊AGL(1,𝔽11)11yescharacteristic, complemented
165C2×C5—10891no—
166C2×C5—3631no—
167C2×C5—3631no—
168C32C2×#1192589611yescharacteristic, complemented, Sylow
169C2×C3—31no—
170C2×C3—331no—
171D3—111no—
172D3—331no—
173D3—331no—
174D3—661no—
175D3C3⋊#1192589611yescharacteristic, direct product factor
176C5—1211noSylow
177C22—991noSylow
178C3—21no—
179C3D3×#1192589611yescharacteristic, complemented
180C3C2×C3⋊#1192589611yescharacteristic, complemented
181C2—31no—
182C2—331no—
183C2—991no—
subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC32×C112C22×C5
LCSG ▷ C32×C112
UCSC1

Complements

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

NH ≅ G/Ntype
1. C3⋊(C3⋊#11925896)C2semidirect
2. C3×D3×#10597245C2semidirect
3. C3×C3⋊#11925896C2semidirect
6. C32×#10597245C22semidirect
7. D3×C11×D33C5semidirect
9. D3×#10597245D3semidirect
13. C3⋊#11925896D3direct (N × H)
16. C11×C3⋊D33C2×C5semidirect
17. C3×C11×D33C2×C5semidirect
18. C3×D3×C112C2×C5semidirect
22. C3×#10597245C2×D3semidirect
23. C3×#10597245C2×D3semidirect
29. C32×C112C22×C5semidirect
40. C11×D33C5×D3semidirect
41. D3×C112C5×D3semidirect
47. #10597245D32semidirect
51. D3×D33C11⋊C5semidirect
54. C3×C112C2×C5×D3semidirect
55. C3×C112C2×C5×D3semidirect
75. C3⋊D33C2×C11⋊C5semidirect
77. C3×D33C2×C11⋊C5semidirect
80. C3×D3×C11AGL(1,𝔽11)semidirect
81. C3×D3×C11C2×C11⋊C5semidirect
93. C112C5×D32semidirect
101. C32×C11C2×AGL(1,𝔽11)semidirect
102. C32×C11C22×C11⋊C5semidirect
113. D33D3×C11⋊C5semidirect
120. D3×C11D3×C11⋊C5semidirect
121. D3×C11C3⋊AGL(1,𝔽11)semidirect
135. C3×C11D3×AGL(1,𝔽11)semidirect
136. C3×C11C2×D3×C11⋊C5semidirect
137. C3×C11C2×D3×C11⋊C5semidirect
138. C3×C11C2×C3⋊AGL(1,𝔽11)semidirect
156. C3×D3#11925896semidirect
163. C11D32×C11⋊C5semidirect
164. C11D3×C3⋊AGL(1,𝔽11)semidirect
168. C32C2×#11925896semidirect
175. D3C3⋊#11925896direct (N × H)
179. C3D3×#11925896semidirect
180. C3C2×C3⋊#11925896semidirect

Maximal subgroups

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

subgroupindex
C3⋊(C3⋊#11925896)2
C3×D3×#105972452
C3×C3⋊#119258962
C2×C3⋊#119258963
D3×#119258963
D3×C11×D335
D3×C3⋊AGL(1,𝔽11)11
D32×C11⋊C511