Finite Group Databasebeta

← D3×C13⋊C3×D77 #49114803

Subgroups — D3×C13⋊C3×D77 #49114803

Order 36036.

176 conjugacy classes of subgroups; only the 48 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 48 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
1C13⋊C3×D231C211yesmaximal, characteristic, complemented
2D3×C7×C11×C13⋊C3C211yesmaximal, characteristic, complemented
3C3×C13⋊C3×D77C211yesmaximal, characteristic, complemented
4D3×C13×D77C311yesmaximal, characteristic, complemented
5C2×C13⋊C3×D77—31nomaximal
6C3×C7×C11×C13⋊C3C2211yescharacteristic, complemented, Hall
7C13⋊C3×D77—21no—
8C13⋊C3×D77—31no—
9C13⋊C3×D77D311yescharacteristic, direct product factor
10C13×D231C2×C311yescharacteristic, complemented
11D3×C7×C11×C13C2×C311yescharacteristic, complemented
12C3×C13×D77C2×C311yescharacteristic, complemented
13C2×C7×C11×C13⋊C3—31no—
14D3×D11×C13⋊C3—71nomaximal, Hall
15C2×C13×D77—31noHall
16D3×D7×C13⋊C3—111nomaximal, Hall
17C7×C11×C13⋊C3—21no—
18C7×C11×C13⋊C3C2×D311yescharacteristic, complemented
19C3×C7×C11×C13C22×C311yescharacteristic, complemented
20C3×D3×D77—131nomaximal, Hall
21C13⋊C3×D33—71no—
22D3×C11×C13⋊C3D711yescharacteristic, complemented
23C3×D11×C13⋊C3—71no—
24C13×D77—31no—
25C13×D77C3×D311yescharacteristic, complemented
26C2×C7×C11×C13—31no—
27D3×C13×D11—71no—
28C2×D11×C13⋊C3—211no—
29C13⋊C3×D21—111no—
30D3×C7×C13⋊C3D1111yescharacteristic, complemented
31C3×D7×C13⋊C3—111no—
32C3×D231—131no—
33C3×D3×C7×C11—131no—
34C32×D77—131no—
35C3×C11×C13⋊C3C2×D711yescharacteristic, complemented, Hall
36D3×C13×D7—111no—
37C2×D7×C13⋊C3—331no—
38C7×C11×C13C2×C3×D311yescharacteristic, complemented, Hall
39C2×C3×D77—391no—
40D3×D77C13⋊C311yescharacteristic, direct product factor
41C13×D33—71no—
42D3×C11×C13C3×D711yescharacteristic, complemented
43C3×C13×D11—71no—
44C2×C11×C13⋊C3—31no—
45D11×C13⋊C3—71no—
46D11×C13⋊C3—141no—
47D11×C13⋊C3—211no—
48C3×C7×C13⋊C3C2×D1111yescharacteristic, complemented, Hall
49C32×C7×C11—131noHall
50C2×C13×D11—211noHall
51C13×D21—111no—
52D3×C7×C13C3×D1111yescharacteristic, complemented
53C3×C13×D7—111no—
54C2×C7×C13⋊C3—31no—
55D7×C13⋊C3—111no—
56D7×C13⋊C3—221no—
57D7×C13⋊C3—331no—
58C2×D3×C13⋊C3—771noHall
59C2×C3×C7×C11—391no—
60D231C2×C13⋊C311yescharacteristic, complemented
61D3×C7×C11C2×C13⋊C311yescharacteristic, complemented
62C3×D77—131no—
63C3×D77—261no—
64C3×D77—391no—
65C3×D77C2×C13⋊C311yescharacteristic, complemented
66C3×C11×C13C2×C3×D711yescharacteristic, complemented
67C11×C13⋊C3—21no—
68C11×C13⋊C3D3×D711yescharacteristic, complemented
69C3×D3×D11—911noHall
70C2×C13×D7—331noHall
71C2×D77—31noHall
72C2×C11×C13—31no—
73C13×D11—71no—
74C13×D11—211no—
75C3×C7×C13C2×C3×D1111yescharacteristic, complemented
76C7×C13⋊C3—21no—
77C7×C13⋊C3D3×D1111yescharacteristic, complemented
78C3×D3×D7—1431noHall
79C2×C3×C13⋊C3—771no—
80D3×C13⋊C3—771no—
81D3×C13⋊C3D7711yescharacteristic, direct product factor
82C3×C7×C11—131no—
83C3×C7×C11—261no—
84C3×C7×C11C22×C13⋊C311yescharacteristic, complemented
85C3×D33—911no—
86C3×D3×C11—131no—
87C32×D11—911no—
88C2×C7×C13—31no—
89C13×D7—111no—
90C13×D7—331no—
91C2×D3×C13—771no—
92C22×C13⋊C3—2311no—
93C2×C7×C11—31no—
94D77—31no—
95D77D3×C13⋊C311yescharacteristic, direct product factor
96C11×C13C3×D3×D711yescharacteristic, complemented, Hall
97C2×C3×D11—2731no—
98D3×D11—71no—
99C3×D21—1431no—
100C3×D3×C7—131no—
101C32×D7—1431no—
102C3×C13⋊C3C2×D7711yescharacteristic, complemented, Hall
103C32×C11—131noHall
104C7×C13C3×D3×D1111yescharacteristic, complemented, Hall
105C2×C3×D7—4291no—
106D3×D7—111no—
107C2×C3×C13—771no—
108D3×C13—771no—
109D3×C13C3×D7711yescharacteristic, complemented
110C2×C13⋊C3—31no—
111C2×C13⋊C3—771no—
112C2×C13⋊C3—1541no—
113C2×C13⋊C3—2311no—
114C7×C11C2×D3×C13⋊C311yescharacteristic, complemented, Hall
115C2×C3×C11—391no—
116D33—71no—
117C3×D11—71no—
118C3×D11—2731no—
119C3×D11—911no—
120C3×D11—1821no—
121D3×C11D7×C13⋊C311yescharacteristic, complemented
122C32×C7—131noHall
123C22×C13—2311noHall
124C2×D11—211noHall
125C2×C3×C7—391no—
126D21—111no—
127C3×D7—111no—
128C3×D7—2861no—
129C3×D7—1431no—
130C3×D7—4291no—
131D3×C7D11×C13⋊C311yescharacteristic, complemented
132C3×C13C2×C3×D7711yescharacteristic, complemented
133C13⋊C3—21no—
134C13⋊C3D3×D7711yescharacteristic, direct product factor
135C2×C3×D3—10011noHall
136C3×C11—131no—
137C3×C11—261no—
138C3×C11C2×D7×C13⋊C311yescharacteristic, complemented
139C2×D7—331noHall
140C2×C13—31no—
141C2×C13—771no—
142C2×C13—2311no—
143C2×C11—31no—
144D11—71no—
145D11—211no—
146C3×C7—131no—
147C3×C7—261no—
148C3×C7C2×D11×C13⋊C311yescharacteristic, complemented
149C2×C32—10011no—
150C3×D3—131no—
151C3×D3—10011no—
152C2×C7—31no—
153D7—111no—
154D7—331no—
155C13C3×D3×D7711yescharacteristic, complemented, Sylow
156C22×C3—30031no—
157C2×D3—771no—
158C11D3×D7×C13⋊C311yescharacteristic, complemented, Sylow
159C32—131noSylow
160C7D3×D11×C13⋊C311yescharacteristic, complemented, Sylow
161C2×C3—391no—
162C2×C3—771no—
163C2×C3—30031no—
164C2×C3—20021no—
165C2×C3—10011no—
166D3—771no—
167D3C13⋊C3×D7711yescharacteristic, direct product factor
168C22—2311noSylow
169C3—131no—
170C3—261no—
171C3C2×C13⋊C3×D7711yescharacteristic, complemented
172C2—31no—
173C2—771no—
174C2—2311no—
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. C13⋊C3×D231C2semidirect
2. D3×C7×C11×C13⋊C3C2semidirect
3. C3×C13⋊C3×D77C2semidirect
4. D3×C13×D77C3semidirect
6. C3×C7×C11×C13⋊C3C22semidirect
9. C13⋊C3×D77D3direct (N × H)
10. C13×D231C2×C3semidirect
11. D3×C7×C11×C13C2×C3semidirect
12. C3×C13×D77C2×C3semidirect
18. C7×C11×C13⋊C3C2×D3semidirect
19. C3×C7×C11×C13C22×C3semidirect
22. D3×C11×C13⋊C3D7semidirect
25. C13×D77C3×D3semidirect
30. D3×C7×C13⋊C3D11semidirect
35. C3×C11×C13⋊C3C2×D7semidirect
38. C7×C11×C13C2×C3×D3semidirect
40. D3×D77C13⋊C3direct (N × H)
42. D3×C11×C13C3×D7semidirect
48. C3×C7×C13⋊C3C2×D11semidirect
52. D3×C7×C13C3×D11semidirect
60. D231C2×C13⋊C3semidirect
61. D3×C7×C11C2×C13⋊C3semidirect
65. C3×D77C2×C13⋊C3semidirect
66. C3×C11×C13C2×C3×D7semidirect
68. C11×C13⋊C3D3×D7semidirect
75. C3×C7×C13C2×C3×D11semidirect
77. C7×C13⋊C3D3×D11semidirect
81. D3×C13⋊C3D77direct (N × H)
84. C3×C7×C11C22×C13⋊C3semidirect
95. D77D3×C13⋊C3direct (N × H)
96. C11×C13C3×D3×D7semidirect
102. C3×C13⋊C3C2×D77semidirect
104. C7×C13C3×D3×D11semidirect
109. D3×C13C3×D77semidirect
114. C7×C11C2×D3×C13⋊C3semidirect
121. D3×C11D7×C13⋊C3semidirect
131. D3×C7D11×C13⋊C3semidirect
132. C3×C13C2×C3×D77semidirect
134. C13⋊C3D3×D77direct (N × H)
138. C3×C11C2×D7×C13⋊C3semidirect
148. C3×C7C2×D11×C13⋊C3semidirect
155. C13C3×D3×D77semidirect
158. C11D3×D7×C13⋊C3semidirect
160. C7D3×D11×C13⋊C3semidirect
167. D3C13⋊C3×D77direct (N × H)
171. C3C2×C13⋊C3×D77semidirect

Maximal subgroups

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

subgroupindex
C13⋊C3×D2312
D3×C7×C11×C13⋊C32
C3×C13⋊C3×D772
D3×C13×D773
C2×C13⋊C3×D773
D3×D11×C13⋊C37
D3×D7×C13⋊C311
C3×D3×D7713