Finite Group Databasebeta

← C3×D77⋊D33 #44479201

Subgroups — C3×D77⋊D33 #44479201

Order 30492.

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

normal subgroups only

This group has 266 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
1C32×C11×D77C211yesmaximal, characteristic, complemented
2C3×C7×C3⋊(C11⋊D11)C211yesmaximal, characteristic, complemented
3C3×C11×D231C211yesmaximal, characteristic, complemented
4D77⋊D33C311yesmaximal, characteristic, direct product factor
5C3×D77⋊D11—31nomaximal
6C32×C7×C112C2211yescharacteristic, complemented, Hall
7C11×D231C2×C311yescharacteristic, complemented
8C7×C3⋊(C11⋊D11)C2×C311yescharacteristic, complemented
9C3×C11×D77—21no—
10C3×C11×D77—31no—
11C3×C11×D77D311yescharacteristic, complemented
12C3×C11×D77C2×C311yescharacteristic, complemented
13C3×C7×C11⋊D11—31no—
14C3×D11×D33—71nomaximal, Hall
15D77⋊D11—31noHall
16C3×D21⋊D11—111nomaximal
17C3×D7×D33—111nomaximal
18C3×C7×C112—21no—
19C3×C7×C112C2×D311yescharacteristic, complemented
20C3×C7×C112C22×C311yescharacteristic, complemented
21C3×C3⋊(C11⋊D11)D711yescharacteristic, complemented
22C3×C11×D33—71no—
23C32×C11×D11—71no—
24C11×D77—31no—
25C11×D77C3×D311yescharacteristic, complemented
26C7×C11⋊D11—31no—
27D11×D33—71no—
28C3×D112—211no—
29C3×D231D1111yescharacteristic, complemented
30C3×C11×D21—111no—
31C3×C7×D33—111no—
32C3×C7×D33—111no—
33C3×C7×D33—225no—
34C32×D77D1111yescharacteristic, complemented
35C32×C11×D7—111no—
36C32×C112C2×D711yescharacteristic, complemented, Hall
37D21⋊D11—111no—
38D7×D33—111no—
39C3×D7×D11—331no—
40C3×D7×D11—331no—
41C7×C112C2×C3×D311yescharacteristic, complemented, Hall
42C3⋊(C11⋊D11)C3×D711yescharacteristic, complemented
43C11×D33—71no—
44C3×C11⋊D11—31no—
45C3×C11×D11—71no—
46C3×C11×D11—71no—
47C3×C11×D11—141no—
48C3×C11×D11—211no—
49C32×C7×C11—25no—
50C32×C7×C11C2×D1111yescharacteristic, complemented
51C32×C7×C11C2×D1111yescharacteristic, complemented
52D112—211noHall
53D231C3×D1111yescharacteristic, complemented
54C11×D21—111no—
55C7×D33—111no—
56C7×D33—111no—
57C7×D33—225no—
58C3×D77—21no—
59C3×D77—31no—
60C3×D77C3×D1111yescharacteristic, complemented
61C3×D77D3311yescharacteristic, complemented
62C3×C11×D7—111no—
63C3×C11×D7—111no—
64C3×C11×D7—221no—
65C3×C11×D7—331no—
66C3×C7×D11—331no—
67C3×C7×D11—331no—
68C3×C7×D11—665no—
69C2×C3×D33—771no—
70C3×D3×D11—771no—
71C3×C112—21no—
72C3×C112D3×D711yescharacteristic, complemented
73C3×C112C2×C3×D711yescharacteristic, complemented
74D7×D11—331no—
75D7×D11—331no—
76C3×D3×D7—1211noHall
77C11⋊D11—31no—
78C11×D11—71no—
79C11×D11—211no—
80C3×C7×C11—21no—
81C3×C7×C11—21no—
82C3×C7×C11—25no—
83C3×C7×C11—25no—
84C3×C7×C11—45no—
85C3×C7×C11D3×D1111yescharacteristic, complemented
86C3×C7×C11C2×C3×D1111yescharacteristic, complemented
87C3×C7×C11C2×C3×D1111yescharacteristic, complemented
88C3×C7×C11C2×D3311yescharacteristic, complemented
89C2×C32×C11—771no—
90C3×D33—71no—
91C3×D33—111no—
92C3×D33—111no—
93C3×D33—225no—
94C3×D3×C11—771no—
95C32×D11—71no—
96D77—31no—
97D77C3×D3311yescharacteristic, complemented
98C7×D11—331no—
99C7×D11—331no—
100C7×D11—665no—
101C11×D7—111no—
102C11×D7—331no—
103C2×D33—771no—
104C2×C3×D11—2311no—
105C2×C3×D11—2311no—
106D3×D11—771no—
107C3×D21—111no—
108C3×D3×C7—1211no—
109C32×D7—111no—
110C112C3×D3×D711yescharacteristic, complemented, Sylow
111C32×C11—25no—
112C32×C11D7×D1111yescharacteristic, complemented
113C32×C11D7×D1111yescharacteristic, complemented
114C2×C3×D7—3631no—
115D3×D7—1211no—
116C7×C11—25no—
117C7×C11C3×D3×D1111yescharacteristic, complemented
118C7×C11C2×C3×D3311yescharacteristic, complemented
119C2×C3×C11—771no—
120C2×C3×C11—771no—
121C2×C3×C11—1541no—
122C2×C3×C11—2311no—
123D33—71no—
124D33—111no—
125D33—111no—
126D33—225no—
127C3×D11—71no—
128C3×D11—71no—
129C3×D11—141no—
130C3×D11—211no—
131C3×D11—331no—
132C3×D11—331no—
133C3×D11—665no—
134D3×C11—771no—
135C32×C7D11211yescharacteristic, complemented, Hall
136C2×D11—2311no—
137C2×D11—2311no—
138C2×C3×C7—3631no—
139D21—111no—
140C3×D7—111no—
141C3×D7—111no—
142C3×D7—221no—
143C3×D7—331no—
144D3×C7—1211no—
145C2×C3×D3—8471noHall
146C3×C11—21no—
147C3×C11—21no—
148C3×C11—25no—
149C3×C11—25no—
150C3×C11—45no—
151C3×C11C3×D7×D1111yescharacteristic, complemented
152C3×C11C3×D7×D1111yescharacteristic, complemented
153C3×C11D7×D3311yescharacteristic, complemented
154C3×C11D21⋊D1111yescharacteristic, complemented
155C2×D7—3631noHall
156C2×C11—771no—
157C2×C11—2311no—
158D11—71no—
159D11—211no—
160D11—331no—
161D11—331no—
162D11—665no—
163C3×C7—21no—
164C3×C7C3×D11211yescharacteristic, complemented
165C3×C7D11×D3311yescharacteristic, complemented
166C2×C32—771no—
167C3×D3—771no—
168C3×D3—1211no—
169C2×C7—3631no—
170D7—111no—
171D7—331no—
172C22×C3—25411no—
173C2×D3—8471no—
174C11—25no—
175C11C3×D7×D3311yescharacteristic, complemented
176C11C3×D21⋊D1111yescharacteristic, complemented
177C32D77⋊D1111yescharacteristic, complemented, Sylow
178C7C3×D11×D3311yescharacteristic, complemented, Sylow
179C2×C3—771no—
180C2×C3—771no—
181C2×C3—3631no—
182C2×C3—1541no—
183C2×C3—2311no—
184D3—771no—
185D3—1211no—
186C22—25411noSylow
187C3—21no—
188C3C3×D77⋊D1111yescharacteristic, complemented
189C3D77⋊D3311yescharacteristic, direct product factor
190C2—771no—
191C2—3631no—
192C2—2311no—
subgroupG/H
center, hypercenterC3D77⋊D33
commutator, cosocle, hypocenterC3×C7×C112C22×C3
FrattiniC1G
Fitting, socleC32×C7×C112C22
LCSG ▷ C3×C7×C112
UCSC1 ◁ C3

Complements

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

NH ≅ G/Ntype
1. C32×C11×D77C2semidirect
2. C3×C7×C3⋊(C11⋊D11)C2semidirect
3. C3×C11×D231C2semidirect
4. D77⋊D33C3direct (N × H)
6. C32×C7×C112C22semidirect
7. C11×D231C2×C3semidirect
8. C7×C3⋊(C11⋊D11)C2×C3semidirect
11. C3×C11×D77D3semidirect
12. C3×C11×D77C2×C3semidirect
19. C3×C7×C112C2×D3semidirect
20. C3×C7×C112C22×C3semidirect
21. C3×C3⋊(C11⋊D11)D7semidirect
25. C11×D77C3×D3semidirect
29. C3×D231D11semidirect
34. C32×D77D11semidirect
36. C32×C112C2×D7semidirect
41. C7×C112C2×C3×D3semidirect
42. C3⋊(C11⋊D11)C3×D7semidirect
50. C32×C7×C11C2×D11semidirect
51. C32×C7×C11C2×D11semidirect
53. D231C3×D11semidirect
60. C3×D77C3×D11semidirect
61. C3×D77D33semidirect
72. C3×C112D3×D7semidirect
73. C3×C112C2×C3×D7semidirect
85. C3×C7×C11D3×D11semidirect
86. C3×C7×C11C2×C3×D11semidirect
87. C3×C7×C11C2×C3×D11semidirect
88. C3×C7×C11C2×D33semidirect
97. D77C3×D33semidirect
110. C112C3×D3×D7semidirect
112. C32×C11D7×D11semidirect
113. C32×C11D7×D11semidirect
117. C7×C11C3×D3×D11semidirect
118. C7×C11C2×C3×D33semidirect
135. C32×C7D112semidirect
151. C3×C11C3×D7×D11semidirect
152. C3×C11C3×D7×D11semidirect
153. C3×C11D7×D33semidirect
154. C3×C11D21⋊D11semidirect
164. C3×C7C3×D112semidirect
165. C3×C7D11×D33semidirect
175. C11C3×D7×D33semidirect
176. C11C3×D21⋊D11semidirect
177. C32D77⋊D11semidirect
178. C7C3×D11×D33semidirect
188. C3C3×D77⋊D11semidirect
189. C3D77⋊D33direct (N × H)

Maximal subgroups

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

subgroupindex
C32×C11×D772
C3×C7×C3⋊(C11⋊D11)2
C3×C11×D2312
D77⋊D333
C3×D77⋊D113
C3×D11×D337
C3×D21⋊D1111
C3×D7×D3311