Subgroups — C₂×C₃³×C₅×C₈×C₁₁ #72201079

Order 23760.

1232 conjugacy classes of subgroups.

The subgroup lattice has 144 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃³×C₄×C₅×C₁₁	C₂	1	1	yes	maximal, characteristic
2	C₃³×C₅×C₈×C₁₁	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₃²×C₅×C₈×C₁₁	C₃	1	13	yes	maximal, direct product factor
4	C₂²×C₃³×C₅×C₁₁	C₄	1	1	yes	characteristic
5	C₃³×C₄×C₅×C₁₁	C₄	1	1	yes	characteristic
6	C₃³×C₄×C₅×C₁₁	C₂²	1	1	yes	characteristic
7	C₂×C₃³×C₈×C₁₁	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₂×C₃²×C₄×C₅×C₁₁	C₂×C₃	1	13	yes	—
9	C₃²×C₅×C₈×C₁₁	C₂×C₃	1	26	yes	direct product factor
10	C₂×C₃³×C₅×C₁₁	C₈	1	2	yes	direct product factor
11	C₂×C₃³×C₅×C₁₁	C₂×C₄	1	1	yes	characteristic
12	C₂×C₃×C₅×C₈×C₁₁	C₃²	1	13	yes	direct product factor
13	C₂×C₃³×C₄×C₁₁	C₂×C₅	1	1	yes	characteristic
14	C₃³×C₈×C₁₁	C₂×C₅	1	2	yes	direct product factor
15	C₂×C₃³×C₅×C₈	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
16	C₂²×C₃²×C₅×C₁₁	C₃×C₄	1	13	yes	—
17	C₃²×C₄×C₅×C₁₁	C₃×C₄	1	13	yes	—
18	C₃²×C₄×C₅×C₁₁	C₂²×C₃	1	13	yes	—
19	C₂×C₃²×C₈×C₁₁	C₃×C₅	1	13	yes	direct product factor
20	C₃³×C₅×C₁₁	C₂×C₈	1	1	yes	characteristic, direct product factor, Hall
21	C₂×C₃×C₄×C₅×C₁₁	C₂×C₃²	1	13	yes	—
22	C₃×C₅×C₈×C₁₁	C₂×C₃²	1	26	yes	direct product factor
23	C₂²×C₃³×C₁₁	C₄×C₅	1	1	yes	characteristic
24	C₃³×C₄×C₁₁	C₄×C₅	1	1	yes	characteristic
25	C₃³×C₄×C₁₁	C₂²×C₅	1	1	yes	characteristic
26	C₂×C₃³×C₄×C₅	C₂×C₁₁	1	1	yes	characteristic
27	C₃³×C₅×C₈	C₂×C₁₁	1	2	yes	direct product factor
28	C₂×C₃²×C₅×C₁₁	C₃×C₈	1	26	yes	direct product factor
29	C₂×C₃²×C₅×C₁₁	C₂×C₃×C₄	1	13	yes	—
30	C₂×C₅×C₈×C₁₁	C₃³	1	1	yes	characteristic, direct product factor, Hall
31	C₂×C₃²×C₄×C₁₁	C₂×C₃×C₅	1	13	yes	—
32	C₃²×C₈×C₁₁	C₂×C₃×C₅	1	26	yes	direct product factor
33	C₂×C₃²×C₅×C₈	C₃×C₁₁	1	13	yes	direct product factor
34	C₂²×C₃×C₅×C₁₁	C₃²×C₄	1	13	yes	—
35	C₃×C₄×C₅×C₁₁	C₃²×C₄	1	13	yes	—
36	C₃×C₄×C₅×C₁₁	C₂²×C₃²	1	13	yes	—
37	C₂×C₃³×C₁₁	C₅×C₈	1	2	yes	direct product factor
38	C₂×C₃³×C₁₁	C₂×C₄×C₅	1	1	yes	characteristic
39	C₂²×C₃³×C₅	C₄×C₁₁	1	1	yes	characteristic
40	C₃³×C₄×C₅	C₄×C₁₁	1	1	yes	characteristic
41	C₃³×C₄×C₅	C₂²×C₁₁	1	1	yes	characteristic
42	C₂×C₃×C₈×C₁₁	C₃²×C₅	1	13	yes	direct product factor
43	C₃²×C₅×C₁₁	C₂×C₃×C₈	1	13	yes	direct product factor
44	C₂×C₄×C₅×C₁₁	C₂×C₃³	1	1	yes	characteristic
45	C₅×C₈×C₁₁	C₂×C₃³	1	2	yes	direct product factor
46	C₂×C₃³×C₈	C₅×C₁₁	1	1	yes	characteristic, direct product factor, Hall
47	C₂²×C₃²×C₁₁	C₃×C₄×C₅	1	13	yes	—
48	C₃²×C₄×C₁₁	C₃×C₄×C₅	1	13	yes	—
49	C₃²×C₄×C₁₁	C₂²×C₃×C₅	1	13	yes	—
50	C₂×C₃²×C₄×C₅	C₂×C₃×C₁₁	1	13	yes	—
51	C₃²×C₅×C₈	C₂×C₃×C₁₁	1	26	yes	direct product factor
52	C₂×C₃×C₅×C₁₁	C₃²×C₈	1	26	yes	direct product factor
53	C₂×C₃×C₅×C₁₁	C₂×C₃²×C₄	1	13	yes	—
54	C₃³×C₁₁	C₂×C₅×C₈	1	1	yes	characteristic, direct product factor, Hall
55	C₂×C₃³×C₅	C₈×C₁₁	1	2	yes	direct product factor
56	C₂×C₃³×C₅	C₂×C₄×C₁₁	1	1	yes	characteristic
57	C₂×C₃×C₄×C₁₁	C₂×C₃²×C₅	1	13	yes	—
58	C₃×C₈×C₁₁	C₂×C₃²×C₅	1	26	yes	direct product factor
59	C₂×C₃×C₅×C₈	C₃²×C₁₁	1	13	yes	direct product factor
60	C₂²×C₅×C₁₁	C₃³×C₄	1	1	yes	characteristic
61	C₄×C₅×C₁₁	C₃³×C₄	1	1	yes	characteristic
62	C₄×C₅×C₁₁	C₂²×C₃³	1	1	yes	characteristic
63	C₂×C₃³×C₄	C₂×C₅×C₁₁	1	1	yes	characteristic
64	C₃³×C₈	C₂×C₅×C₁₁	1	2	yes	direct product factor
65	C₂×C₃²×C₁₁	C₃×C₅×C₈	1	26	yes	direct product factor
66	C₂×C₃²×C₁₁	C₂×C₃×C₄×C₅	1	13	yes	—
67	C₂²×C₃²×C₅	C₃×C₄×C₁₁	1	13	yes	—
68	C₃²×C₄×C₅	C₃×C₄×C₁₁	1	13	yes	—
69	C₃²×C₄×C₅	C₂²×C₃×C₁₁	1	13	yes	—
70	C₂×C₈×C₁₁	C₃³×C₅	1	1	yes	characteristic, direct product factor, Hall
71	C₃×C₅×C₁₁	C₂×C₃²×C₈	1	13	yes	direct product factor
72	C₂×C₃²×C₈	C₃×C₅×C₁₁	1	13	yes	direct product factor
73	C₃³×C₅	C₂×C₈×C₁₁	1	1	yes	characteristic, direct product factor, Hall
74	C₂²×C₃×C₁₁	C₃²×C₄×C₅	1	13	yes	—
75	C₃×C₄×C₁₁	C₃²×C₄×C₅	1	13	yes	—
76	C₃×C₄×C₁₁	C₂²×C₃²×C₅	1	13	yes	—
77	C₂×C₃×C₄×C₅	C₂×C₃²×C₁₁	1	13	yes	—
78	C₃×C₅×C₈	C₂×C₃²×C₁₁	1	26	yes	direct product factor
79	C₂×C₅×C₁₁	C₃³×C₈	1	2	yes	direct product factor
80	C₂×C₅×C₁₁	C₂×C₃³×C₄	1	1	yes	characteristic
81	C₂²×C₃³	C₄×C₅×C₁₁	1	1	yes	characteristic
82	C₃³×C₄	C₄×C₅×C₁₁	1	1	yes	characteristic
83	C₃³×C₄	C₂²×C₅×C₁₁	1	1	yes	characteristic
84	C₃²×C₁₁	C₂×C₃×C₅×C₈	1	13	yes	direct product factor
85	C₂×C₃²×C₅	C₃×C₈×C₁₁	1	26	yes	direct product factor
86	C₂×C₃²×C₅	C₂×C₃×C₄×C₁₁	1	13	yes	—
87	C₂×C₄×C₁₁	C₂×C₃³×C₅	1	1	yes	characteristic
88	C₈×C₁₁	C₂×C₃³×C₅	1	2	yes	direct product factor
89	C₂×C₅×C₈	C₃³×C₁₁	1	1	yes	characteristic, direct product factor, Hall
90	C₂×C₃²×C₄	C₂×C₃×C₅×C₁₁	1	13	yes	—
91	C₃²×C₈	C₂×C₃×C₅×C₁₁	1	26	yes	direct product factor
92	C₂×C₃×C₁₁	C₃²×C₅×C₈	1	26	yes	direct product factor
93	C₂×C₃×C₁₁	C₂×C₃²×C₄×C₅	1	13	yes	—
94	C₂²×C₃×C₅	C₃²×C₄×C₁₁	1	13	yes	—
95	C₃×C₄×C₅	C₃²×C₄×C₁₁	1	13	yes	—
96	C₃×C₄×C₅	C₂²×C₃²×C₁₁	1	13	yes	—
97	C₅×C₁₁	C₂×C₃³×C₈	1	1	yes	characteristic, direct product factor, Hall
98	C₂×C₃³	C₅×C₈×C₁₁	1	2	yes	direct product factor
99	C₂×C₃³	C₂×C₄×C₅×C₁₁	1	1	yes	characteristic
100	C₂×C₃×C₈	C₃²×C₅×C₁₁	1	13	yes	direct product factor
101	C₃²×C₅	C₂×C₃×C₈×C₁₁	1	13	yes	direct product factor
102	C₂²×C₁₁	C₃³×C₄×C₅	1	1	yes	characteristic
103	C₄×C₁₁	C₃³×C₄×C₅	1	1	yes	characteristic
104	C₄×C₁₁	C₂²×C₃³×C₅	1	1	yes	characteristic
105	C₂×C₄×C₅	C₂×C₃³×C₁₁	1	1	yes	characteristic
106	C₅×C₈	C₂×C₃³×C₁₁	1	2	yes	direct product factor
107	C₂²×C₃²	C₃×C₄×C₅×C₁₁	1	13	yes	—
108	C₃²×C₄	C₃×C₄×C₅×C₁₁	1	13	yes	—
109	C₃²×C₄	C₂²×C₃×C₅×C₁₁	1	13	yes	—
110	C₃×C₁₁	C₂×C₃²×C₅×C₈	1	13	yes	direct product factor
111	C₂×C₃×C₅	C₃²×C₈×C₁₁	1	26	yes	direct product factor
112	C₂×C₃×C₅	C₂×C₃²×C₄×C₁₁	1	13	yes	—
113	C₃³	C₂×C₅×C₈×C₁₁	1	1	yes	characteristic, direct product factor, Sylow
114	C₂×C₃×C₄	C₂×C₃²×C₅×C₁₁	1	13	yes	—
115	C₃×C₈	C₂×C₃²×C₅×C₁₁	1	26	yes	direct product factor
116	C₂×C₁₁	C₃³×C₅×C₈	1	2	yes	direct product factor
117	C₂×C₁₁	C₂×C₃³×C₄×C₅	1	1	yes	characteristic
118	C₂²×C₅	C₃³×C₄×C₁₁	1	1	yes	characteristic
119	C₄×C₅	C₃³×C₄×C₁₁	1	1	yes	characteristic
120	C₄×C₅	C₂²×C₃³×C₁₁	1	1	yes	characteristic
121	C₂×C₃²	C₃×C₅×C₈×C₁₁	1	26	yes	direct product factor
122	C₂×C₃²	C₂×C₃×C₄×C₅×C₁₁	1	13	yes	—
123	C₂×C₈	C₃³×C₅×C₁₁	1	1	yes	characteristic, direct product factor, Sylow
124	C₃×C₅	C₂×C₃²×C₈×C₁₁	1	13	yes	direct product factor
125	C₂²×C₃	C₃²×C₄×C₅×C₁₁	1	13	yes	—
126	C₃×C₄	C₃²×C₄×C₅×C₁₁	1	13	yes	—
127	C₃×C₄	C₂²×C₃²×C₅×C₁₁	1	13	yes	—
128	C₁₁	C₂×C₃³×C₅×C₈	1	1	yes	characteristic, direct product factor, Sylow
129	C₂×C₅	C₃³×C₈×C₁₁	1	2	yes	direct product factor
130	C₂×C₅	C₂×C₃³×C₄×C₁₁	1	1	yes	characteristic
131	C₃²	C₂×C₃×C₅×C₈×C₁₁	1	13	yes	direct product factor
132	C₂×C₄	C₂×C₃³×C₅×C₁₁	1	1	yes	characteristic
133	C₈	C₂×C₃³×C₅×C₁₁	1	2	yes	direct product factor
134	C₂×C₃	C₃²×C₅×C₈×C₁₁	1	26	yes	direct product factor
135	C₂×C₃	C₂×C₃²×C₄×C₅×C₁₁	1	13	yes	—
136	C₅	C₂×C₃³×C₈×C₁₁	1	1	yes	characteristic, direct product factor, Sylow
137	C₂²	C₃³×C₄×C₅×C₁₁	1	1	yes	characteristic
138	C₄	C₃³×C₄×C₅×C₁₁	1	1	yes	characteristic
139	C₄	C₂²×C₃³×C₅×C₁₁	1	1	yes	characteristic
140	C₃	C₂×C₃²×C₅×C₈×C₁₁	1	13	yes	direct product factor
141	C₂	C₃³×C₅×C₈×C₁₁	1	2	yes	direct product factor
142	C₂	C₂×C₃³×C₄×C₅×C₁₁	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₄	C₂²×C₃³×C₅×C₁₁
socle, prime radical	C₂²×C₃³×C₅×C₁₁	C₄
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₃³×C₅×C₈×C₁₁	C₂	direct (N × H)
3. C₂×C₃²×C₅×C₈×C₁₁	C₃	direct (N × H)
7. C₂×C₃³×C₈×C₁₁	C₅	direct (N × H)
9. C₃²×C₅×C₈×C₁₁	C₂×C₃	direct (N × H)
10. C₂×C₃³×C₅×C₁₁	C₈	direct (N × H)
12. C₂×C₃×C₅×C₈×C₁₁	C₃²	direct (N × H)
14. C₃³×C₈×C₁₁	C₂×C₅	direct (N × H)
15. C₂×C₃³×C₅×C₈	C₁₁	direct (N × H)
19. C₂×C₃²×C₈×C₁₁	C₃×C₅	direct (N × H)
20. C₃³×C₅×C₁₁	C₂×C₈	direct (N × H)
22. C₃×C₅×C₈×C₁₁	C₂×C₃²	direct (N × H)
27. C₃³×C₅×C₈	C₂×C₁₁	direct (N × H)
28. C₂×C₃²×C₅×C₁₁	C₃×C₈	direct (N × H)
30. C₂×C₅×C₈×C₁₁	C₃³	direct (N × H)
32. C₃²×C₈×C₁₁	C₂×C₃×C₅	direct (N × H)
33. C₂×C₃²×C₅×C₈	C₃×C₁₁	direct (N × H)
37. C₂×C₃³×C₁₁	C₅×C₈	direct (N × H)
42. C₂×C₃×C₈×C₁₁	C₃²×C₅	direct (N × H)
43. C₃²×C₅×C₁₁	C₂×C₃×C₈	direct (N × H)
45. C₅×C₈×C₁₁	C₂×C₃³	direct (N × H)
46. C₂×C₃³×C₈	C₅×C₁₁	direct (N × H)
51. C₃²×C₅×C₈	C₂×C₃×C₁₁	direct (N × H)
52. C₂×C₃×C₅×C₁₁	C₃²×C₈	direct (N × H)
54. C₃³×C₁₁	C₂×C₅×C₈	direct (N × H)
55. C₂×C₃³×C₅	C₈×C₁₁	direct (N × H)
58. C₃×C₈×C₁₁	C₂×C₃²×C₅	direct (N × H)
59. C₂×C₃×C₅×C₈	C₃²×C₁₁	direct (N × H)
64. C₃³×C₈	C₂×C₅×C₁₁	direct (N × H)
65. C₂×C₃²×C₁₁	C₃×C₅×C₈	direct (N × H)
70. C₂×C₈×C₁₁	C₃³×C₅	direct (N × H)
71. C₃×C₅×C₁₁	C₂×C₃²×C₈	direct (N × H)
72. C₂×C₃²×C₈	C₃×C₅×C₁₁	direct (N × H)
73. C₃³×C₅	C₂×C₈×C₁₁	direct (N × H)
78. C₃×C₅×C₈	C₂×C₃²×C₁₁	direct (N × H)
79. C₂×C₅×C₁₁	C₃³×C₈	direct (N × H)
84. C₃²×C₁₁	C₂×C₃×C₅×C₈	direct (N × H)
85. C₂×C₃²×C₅	C₃×C₈×C₁₁	direct (N × H)
88. C₈×C₁₁	C₂×C₃³×C₅	direct (N × H)
89. C₂×C₅×C₈	C₃³×C₁₁	direct (N × H)
91. C₃²×C₈	C₂×C₃×C₅×C₁₁	direct (N × H)
92. C₂×C₃×C₁₁	C₃²×C₅×C₈	direct (N × H)
97. C₅×C₁₁	C₂×C₃³×C₈	direct (N × H)
98. C₂×C₃³	C₅×C₈×C₁₁	direct (N × H)
100. C₂×C₃×C₈	C₃²×C₅×C₁₁	direct (N × H)
101. C₃²×C₅	C₂×C₃×C₈×C₁₁	direct (N × H)
106. C₅×C₈	C₂×C₃³×C₁₁	direct (N × H)
110. C₃×C₁₁	C₂×C₃²×C₅×C₈	direct (N × H)
111. C₂×C₃×C₅	C₃²×C₈×C₁₁	direct (N × H)
113. C₃³	C₂×C₅×C₈×C₁₁	direct (N × H)
115. C₃×C₈	C₂×C₃²×C₅×C₁₁	direct (N × H)
116. C₂×C₁₁	C₃³×C₅×C₈	direct (N × H)
121. C₂×C₃²	C₃×C₅×C₈×C₁₁	direct (N × H)
123. C₂×C₈	C₃³×C₅×C₁₁	direct (N × H)
124. C₃×C₅	C₂×C₃²×C₈×C₁₁	direct (N × H)
128. C₁₁	C₂×C₃³×C₅×C₈	direct (N × H)
129. C₂×C₅	C₃³×C₈×C₁₁	direct (N × H)
131. C₃²	C₂×C₃×C₅×C₈×C₁₁	direct (N × H)
133. C₈	C₂×C₃³×C₅×C₁₁	direct (N × H)
134. C₂×C₃	C₃²×C₅×C₈×C₁₁	direct (N × H)
136. C₅	C₂×C₃³×C₈×C₁₁	direct (N × H)
140. C₃	C₂×C₃²×C₅×C₈×C₁₁	direct (N × H)
141. C₂	C₃³×C₅×C₈×C₁₁	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃³×C₄×C₅×C₁₁	2
C₃³×C₅×C₈×C₁₁	2
C₂×C₃²×C₅×C₈×C₁₁	3
C₂×C₃³×C₈×C₁₁	5
C₂×C₃³×C₅×C₈	11

Subgroups — C2×C33×C5×C8×C11 #72201079

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃³×C₅×C₈×C₁₁ #72201079