Finite Group Databasebeta

← D3×D11×#63271 #49114780

Subgroups — D3×D11×#63271 #49114780

Order 36036.

176 conjugacy classes of subgroups; only the 50 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 50 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
1D33×#63271C211yesmaximal, characteristic, complemented
2D3×C11×#63271C211yesmaximal, characteristic, complemented
3C3×D11×#63271C211yesmaximal, characteristic, complemented
4D3×C7×C13×D11C311yesmaximal, characteristic, complemented
5C2×D11×#63271—31nomaximal
6C3×C11×#63271C2211yescharacteristic, complemented, Hall
7D11×#63271—21no—
8D11×#63271—31no—
9D11×#63271D311yescharacteristic, direct product factor
10C7×C13×D33C2×C311yescharacteristic, complemented
11D3×C7×C11×C13C2×C311yescharacteristic, complemented
12C3×C7×C13×D11C2×C311yescharacteristic, complemented
13C2×C11×#63271—31no—
14D3×D11×C13⋊C3—71nomaximal, Hall
15C2×C7×C13×D11—31noHall
16C2×D3×#63271—111nomaximal, Hall
17C11×#63271—21no—
18C11×#63271C2×D311yescharacteristic, complemented
19C3×C7×C11×C13C22×C311yescharacteristic, complemented
20D3×ΓL(1,𝔽8)×D11—131nomaximal, Hall
21C13⋊C3×D33—71no—
22D3×C11×C13⋊C3—71no—
23C3×D11×C13⋊C3—71no—
24C7×C13×D11—31no—
25C7×C13×D11C3×D311yescharacteristic, complemented
26C2×C7×C11×C13—31no—
27D3×C13×D11ΓL(1,𝔽8)11yescharacteristic, complemented
28C2×D11×C13⋊C3—211no—
29C2×C3×#63271—111no—
30D3×#63271—111no—
31D3×#63271D1111yescharacteristic, direct product factor
32ΓL(1,𝔽8)×D33—131no—
33D3×C11×ΓL(1,𝔽8)—131no—
34C3×ΓL(1,𝔽8)×D11—131no—
35C3×C11×C13⋊C3—71noHall
36C2×D3×C7×C13—111no—
37C22×#63271—331no—
38C7×C11×C13C2×C3×D311yescharacteristic, complemented, Hall
39D3×C7×D11C13⋊C311yescharacteristic, complemented
40C2×ΓL(1,𝔽8)×D11—391no—
41C13×D33C2×ΓL(1,𝔽8)11yescharacteristic, complemented
42D3×C11×C13C2×ΓL(1,𝔽8)11yescharacteristic, complemented
43C3×C13×D11C2×ΓL(1,𝔽8)11yescharacteristic, complemented
44C2×C11×C13⋊C3—211no—
45D11×C13⋊C3—71no—
46D11×C13⋊C3—141no—
47D11×C13⋊C3—211no—
48C3×#63271C2×D1111yescharacteristic, complemented, Hall
49C3×C11×ΓL(1,𝔽8)—131noHall
50C2×C13×D11—31noHall
51C2×C3×C7×C13—111no—
52D3×C7×C13—111no—
53D3×C7×C13C3×D1111yescharacteristic, complemented
54C2×#63271—31no—
55C2×#63271—111no—
56C2×#63271—221no—
57C2×#63271—331no—
58C2×D3×C13⋊C3—771noHall
59C7×D33C2×C13⋊C311yescharacteristic, complemented
60D3×C7×C11C2×C13⋊C311yescharacteristic, complemented
61C3×C7×D11C2×C13⋊C311yescharacteristic, complemented
62C2×C11×ΓL(1,𝔽8)—391no—
63ΓL(1,𝔽8)×D11—131no—
64ΓL(1,𝔽8)×D11—261no—
65ΓL(1,𝔽8)×D11—391no—
66C3×C11×C13C22×ΓL(1,𝔽8)11yescharacteristic, complemented
67C11×C13⋊C3—71no—
68C11×C13⋊C3—141no—
69C3×D3×D11—911noHall
70C22×C7×C13—331noHall
71C2×C7×D11—31noHall
72C2×C11×C13—31no—
73C13×D11—31no—
74C13×D11D3×ΓL(1,𝔽8)11yescharacteristic, complemented
75C3×C7×C13C2×C3×D1111yescharacteristic, complemented
76#63271—21no—
77#63271D3×D1111yescharacteristic, direct product factor
78C2×D3×ΓL(1,𝔽8)—1431noHall
79C2×C3×C13⋊C3—771no—
80D3×C13⋊C3—71no—
81D3×C13⋊C3—771no—
82C3×C7×C11C22×C13⋊C311yescharacteristic, complemented
83C11×ΓL(1,𝔽8)—131no—
84C11×ΓL(1,𝔽8)—261no—
85C3×D33—911no—
86C3×D3×C11—911no—
87C32×D11—911no—
88C2×C7×C13—31no—
89C2×C7×C13—111no—
90C2×C7×C13—331no—
91C2×D3×C13—111no—
92C22×C13⋊C3—2311no—
93C2×C7×C11—31no—
94C7×D11—31no—
95C7×D11D3×C13⋊C311yescharacteristic, complemented
96C11×C13C2×D3×ΓL(1,𝔽8)11yescharacteristic, complemented, Hall
97C2×C3×D11—2731no—
98D3×D11#6327111yescharacteristic, direct product factor
99C2×C3×ΓL(1,𝔽8)—1431no—
100D3×ΓL(1,𝔽8)—131no—
101D3×ΓL(1,𝔽8)—1431no—
102C3×C13⋊C3—71noHall
103C32×C11—911noHall
104C7×C13C3×D3×D1111yescharacteristic, complemented, Hall
105C2×D3×C7—111no—
106C22×ΓL(1,𝔽8)—4291no—
107C2×C3×C13—111no—
108D3×C13—111no—
109D3×C13ΓL(1,𝔽8)×D1111yescharacteristic, complemented
110C2×C13⋊C3—211no—
111C2×C13⋊C3—771no—
112C2×C13⋊C3—1541no—
113C2×C13⋊C3—2311no—
114C7×C11C2×D3×C13⋊C311yescharacteristic, complemented, Hall
115C2×C3×C11—2731no—
116D33C2×#6327111yescharacteristic, complemented
117C3×D11—2731no—
118C3×D11—911no—
119C3×D11—1821no—
120C3×D11C2×#6327111yescharacteristic, complemented
121D3×C11C2×#6327111yescharacteristic, complemented
122C3×ΓL(1,𝔽8)—131noHall
123C22×C13—331noHall
124C2×D11—31noHall
125C2×C3×C7—111no—
126D3×C7—111no—
127D3×C7D11×C13⋊C311yescharacteristic, complemented
128C2×ΓL(1,𝔽8)—2861no—
129C2×ΓL(1,𝔽8)—391no—
130C2×ΓL(1,𝔽8)—1431no—
131C2×ΓL(1,𝔽8)—4291no—
132C3×C13C2×ΓL(1,𝔽8)×D1111yescharacteristic, complemented
133C13⋊C3—71no—
134C13⋊C3—141no—
135C2×C3×D3—10011noHall
136C3×C11—911no—
137C3×C11—1821no—
138C3×C11C22×#6327111yescharacteristic, complemented
139C22×C7—331noHall
140C2×C13—31no—
141C2×C13—111no—
142C2×C13—331no—
143C2×C11—31no—
144D11—31no—
145D11D3×#6327111yescharacteristic, direct product factor
146C3×C7C2×D11×C13⋊C311yescharacteristic, complemented
147ΓL(1,𝔽8)—131no—
148ΓL(1,𝔽8)—261no—
149C2×C32—10011no—
150C3×D3—911no—
151C3×D3—10011no—
152C2×C7—31no—
153C2×C7—111no—
154C2×C7—331no—
155C13D3×ΓL(1,𝔽8)×D1111yescharacteristic, complemented, Sylow
156C22×C3—30031no—
157C2×D3—111no—
158C11C2×D3×#6327111yescharacteristic, complemented, Sylow
159C32—911noSylow
160C7D3×D11×C13⋊C311yescharacteristic, complemented, Sylow
161C2×C3—111no—
162C2×C3—2731no—
163C2×C3—30031no—
164C2×C3—20021no—
165C2×C3—10011no—
166D3—111no—
167D3D11×#6327111yescharacteristic, direct product factor
168C22—331noSylow
169C3—911no—
170C3—1821no—
171C3C2×D11×#6327111yescharacteristic, complemented
172C2—31no—
173C2—111no—
174C2—331no—
subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC3×C7×C11×C13C22×C3
LCSG ▷ C3×C7×C11×C13
UCSC1

Complements

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

NH ≅ G/Ntype
1. D33×#63271C2semidirect
2. D3×C11×#63271C2semidirect
3. C3×D11×#63271C2semidirect
4. D3×C7×C13×D11C3semidirect
6. C3×C11×#63271C22semidirect
9. D11×#63271D3direct (N × H)
10. C7×C13×D33C2×C3semidirect
11. D3×C7×C11×C13C2×C3semidirect
12. C3×C7×C13×D11C2×C3semidirect
18. C11×#63271C2×D3semidirect
19. C3×C7×C11×C13C22×C3semidirect
25. C7×C13×D11C3×D3semidirect
27. D3×C13×D11ΓL(1,𝔽8)semidirect
31. D3×#63271D11direct (N × H)
38. C7×C11×C13C2×C3×D3semidirect
39. D3×C7×D11C13⋊C3semidirect
41. C13×D33C2×ΓL(1,𝔽8)semidirect
42. D3×C11×C13C2×ΓL(1,𝔽8)semidirect
43. C3×C13×D11C2×ΓL(1,𝔽8)semidirect
48. C3×#63271C2×D11semidirect
53. D3×C7×C13C3×D11semidirect
59. C7×D33C2×C13⋊C3semidirect
60. D3×C7×C11C2×C13⋊C3semidirect
61. C3×C7×D11C2×C13⋊C3semidirect
66. C3×C11×C13C22×ΓL(1,𝔽8)semidirect
74. C13×D11D3×ΓL(1,𝔽8)semidirect
75. C3×C7×C13C2×C3×D11semidirect
77. #63271D3×D11direct (N × H)
82. C3×C7×C11C22×C13⋊C3semidirect
95. C7×D11D3×C13⋊C3semidirect
96. C11×C13C2×D3×ΓL(1,𝔽8)semidirect
98. D3×D11#63271direct (N × H)
104. C7×C13C3×D3×D11semidirect
109. D3×C13ΓL(1,𝔽8)×D11semidirect
114. C7×C11C2×D3×C13⋊C3semidirect
116. D33C2×#63271semidirect
120. C3×D11C2×#63271semidirect
121. D3×C11C2×#63271semidirect
127. D3×C7D11×C13⋊C3semidirect
132. C3×C13C2×ΓL(1,𝔽8)×D11semidirect
138. C3×C11C22×#63271semidirect
145. D11D3×#63271direct (N × H)
146. C3×C7C2×D11×C13⋊C3semidirect
155. C13D3×ΓL(1,𝔽8)×D11semidirect
158. C11C2×D3×#63271semidirect
160. C7D3×D11×C13⋊C3semidirect
167. D3D11×#63271direct (N × H)
171. C3C2×D11×#63271semidirect

Maximal subgroups

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

subgroupindex
D33×#632712
D3×C11×#632712
C3×D11×#632712
D3×C7×C13×D113
C2×D11×#632713
D3×D11×C13⋊C37
C2×D3×#6327111
D3×ΓL(1,𝔽8)×D1113