Subgroups — C₂×C₄³×C₉×C₁₁ #72191027

Order 12672.

3816 conjugacy classes of subgroups.

The subgroup lattice has 120 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄²×C₉×C₁₁	C₂	1	7	yes	maximal
2	C₄³×C₉×C₁₁	C₂	1	8	yes	maximal, direct product factor
3	C₂×C₃×C₄³×C₁₁	C₃	1	1	yes	maximal, characteristic
4	C₂³×C₄×C₉×C₁₁	C₂²	1	7	yes	—
5	C₂×C₄²×C₉×C₁₁	C₄	1	56	yes	direct product factor
6	C₂×C₄²×C₉×C₁₁	C₂²	1	28	yes	—
7	C₂²×C₃×C₄²×C₁₁	C₂×C₃	1	7	yes	—
8	C₃×C₄³×C₁₁	C₂×C₃	1	8	yes	—
9	C₂⁴×C₉×C₁₁	C₂³	1	1	yes	characteristic
10	C₂²×C₄×C₉×C₁₁	C₂×C₄	1	84	yes	—
11	C₂²×C₄×C₉×C₁₁	C₂³	1	14	yes	—
12	C₄²×C₉×C₁₁	C₂×C₄	1	112	yes	direct product factor
13	C₂×C₄³×C₁₁	C₉	1	1	yes	characteristic, direct product factor, Hall
14	C₂×C₄³×C₉	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
15	C₂³×C₃×C₄×C₁₁	C₂²×C₃	1	7	yes	—
16	C₂×C₃×C₄²×C₁₁	C₃×C₄	1	56	yes	—
17	C₂×C₃×C₄²×C₁₁	C₂²×C₃	1	28	yes	—
18	C₂³×C₉×C₁₁	C₂²×C₄	1	14	yes	—
19	C₂³×C₉×C₁₁	C₂⁴	1	1	yes	characteristic
20	C₂×C₄×C₉×C₁₁	C₄²	1	112	yes	direct product factor
21	C₂×C₄×C₉×C₁₁	C₂²×C₄	1	84	yes	—
22	C₂²×C₄²×C₁₁	C₂×C₉	1	7	yes	—
23	C₄³×C₁₁	C₂×C₉	1	8	yes	direct product factor
24	C₂²×C₄²×C₉	C₂×C₁₁	1	7	yes	—
25	C₄³×C₉	C₂×C₁₁	1	8	yes	direct product factor
26	C₂⁴×C₃×C₁₁	C₂³×C₃	1	1	yes	characteristic
27	C₂²×C₃×C₄×C₁₁	C₂×C₃×C₄	1	84	yes	—
28	C₂²×C₃×C₄×C₁₁	C₂³×C₃	1	14	yes	—
29	C₃×C₄²×C₁₁	C₂×C₃×C₄	1	112	yes	—
30	C₂²×C₉×C₁₁	C₂×C₄²	1	28	yes	—
31	C₂²×C₉×C₁₁	C₂³×C₄	1	7	yes	—
32	C₄×C₉×C₁₁	C₂×C₄²	1	56	yes	direct product factor
33	C₂×C₃×C₄³	C₃×C₁₁	1	1	yes	characteristic
34	C₂³×C₄×C₁₁	C₂²×C₉	1	7	yes	—
35	C₂×C₄²×C₁₁	C₄×C₉	1	56	yes	direct product factor
36	C₂×C₄²×C₁₁	C₂²×C₉	1	28	yes	—
37	C₂³×C₄×C₉	C₂²×C₁₁	1	7	yes	—
38	C₂×C₄²×C₉	C₄×C₁₁	1	56	yes	direct product factor
39	C₂×C₄²×C₉	C₂²×C₁₁	1	28	yes	—
40	C₂³×C₃×C₁₁	C₂²×C₃×C₄	1	14	yes	—
41	C₂³×C₃×C₁₁	C₂⁴×C₃	1	1	yes	characteristic
42	C₂×C₃×C₄×C₁₁	C₃×C₄²	1	112	yes	—
43	C₂×C₃×C₄×C₁₁	C₂²×C₃×C₄	1	84	yes	—
44	C₂×C₉×C₁₁	C₄³	1	8	yes	direct product factor
45	C₂×C₉×C₁₁	C₂²×C₄²	1	7	yes	—
46	C₂²×C₃×C₄²	C₂×C₃×C₁₁	1	7	yes	—
47	C₃×C₄³	C₂×C₃×C₁₁	1	8	yes	—
48	C₂⁴×C₁₁	C₂³×C₉	1	1	yes	characteristic
49	C₂²×C₄×C₁₁	C₂×C₄×C₉	1	84	yes	—
50	C₂²×C₄×C₁₁	C₂³×C₉	1	14	yes	—
51	C₄²×C₁₁	C₂×C₄×C₉	1	112	yes	direct product factor
52	C₂⁴×C₉	C₂³×C₁₁	1	1	yes	characteristic
53	C₂²×C₄×C₉	C₂×C₄×C₁₁	1	84	yes	—
54	C₂²×C₄×C₉	C₂³×C₁₁	1	14	yes	—
55	C₄²×C₉	C₂×C₄×C₁₁	1	112	yes	direct product factor
56	C₂²×C₃×C₁₁	C₂×C₃×C₄²	1	28	yes	—
57	C₂²×C₃×C₁₁	C₂³×C₃×C₄	1	7	yes	—
58	C₃×C₄×C₁₁	C₂×C₃×C₄²	1	56	yes	—
59	C₂×C₄³	C₉×C₁₁	1	1	yes	characteristic, direct product factor, Sylow
60	C₉×C₁₁	C₂×C₄³	1	1	yes	characteristic, direct product factor, Hall
61	C₂³×C₃×C₄	C₂²×C₃×C₁₁	1	7	yes	—
62	C₂×C₃×C₄²	C₃×C₄×C₁₁	1	56	yes	—
63	C₂×C₃×C₄²	C₂²×C₃×C₁₁	1	28	yes	—
64	C₂³×C₁₁	C₂²×C₄×C₉	1	14	yes	—
65	C₂³×C₁₁	C₂⁴×C₉	1	1	yes	characteristic
66	C₂×C₄×C₁₁	C₄²×C₉	1	112	yes	direct product factor
67	C₂×C₄×C₁₁	C₂²×C₄×C₉	1	84	yes	—
68	C₂³×C₉	C₂²×C₄×C₁₁	1	14	yes	—
69	C₂³×C₉	C₂⁴×C₁₁	1	1	yes	characteristic
70	C₂×C₄×C₉	C₄²×C₁₁	1	112	yes	direct product factor
71	C₂×C₄×C₉	C₂²×C₄×C₁₁	1	84	yes	—
72	C₂×C₃×C₁₁	C₃×C₄³	1	8	yes	—
73	C₂×C₃×C₁₁	C₂²×C₃×C₄²	1	7	yes	—
74	C₂²×C₄²	C₂×C₉×C₁₁	1	7	yes	—
75	C₄³	C₂×C₉×C₁₁	1	8	yes	direct product factor
76	C₂⁴×C₃	C₂³×C₃×C₁₁	1	1	yes	characteristic
77	C₂²×C₃×C₄	C₂×C₃×C₄×C₁₁	1	84	yes	—
78	C₂²×C₃×C₄	C₂³×C₃×C₁₁	1	14	yes	—
79	C₃×C₄²	C₂×C₃×C₄×C₁₁	1	112	yes	—
80	C₂²×C₁₁	C₂×C₄²×C₉	1	28	yes	—
81	C₂²×C₁₁	C₂³×C₄×C₉	1	7	yes	—
82	C₄×C₁₁	C₂×C₄²×C₉	1	56	yes	direct product factor
83	C₂²×C₉	C₂×C₄²×C₁₁	1	28	yes	—
84	C₂²×C₉	C₂³×C₄×C₁₁	1	7	yes	—
85	C₄×C₉	C₂×C₄²×C₁₁	1	56	yes	direct product factor
86	C₃×C₁₁	C₂×C₃×C₄³	1	1	yes	characteristic
87	C₂³×C₄	C₂²×C₉×C₁₁	1	7	yes	—
88	C₂×C₄²	C₄×C₉×C₁₁	1	56	yes	direct product factor
89	C₂×C₄²	C₂²×C₉×C₁₁	1	28	yes	—
90	C₂³×C₃	C₂²×C₃×C₄×C₁₁	1	14	yes	—
91	C₂³×C₃	C₂⁴×C₃×C₁₁	1	1	yes	characteristic
92	C₂×C₃×C₄	C₃×C₄²×C₁₁	1	112	yes	—
93	C₂×C₃×C₄	C₂²×C₃×C₄×C₁₁	1	84	yes	—
94	C₂×C₁₁	C₄³×C₉	1	8	yes	direct product factor
95	C₂×C₁₁	C₂²×C₄²×C₉	1	7	yes	—
96	C₂×C₉	C₄³×C₁₁	1	8	yes	direct product factor
97	C₂×C₉	C₂²×C₄²×C₁₁	1	7	yes	—
98	C₂⁴	C₂³×C₉×C₁₁	1	1	yes	characteristic
99	C₂²×C₄	C₂×C₄×C₉×C₁₁	1	84	yes	—
100	C₂²×C₄	C₂³×C₉×C₁₁	1	14	yes	—
101	C₄²	C₂×C₄×C₉×C₁₁	1	112	yes	direct product factor
102	C₂²×C₃	C₂×C₃×C₄²×C₁₁	1	28	yes	—
103	C₂²×C₃	C₂³×C₃×C₄×C₁₁	1	7	yes	—
104	C₃×C₄	C₂×C₃×C₄²×C₁₁	1	56	yes	—
105	C₁₁	C₂×C₄³×C₉	1	1	yes	characteristic, direct product factor, Sylow
106	C₉	C₂×C₄³×C₁₁	1	1	yes	characteristic, direct product factor, Sylow
107	C₂³	C₂²×C₄×C₉×C₁₁	1	14	yes	—
108	C₂³	C₂⁴×C₉×C₁₁	1	1	yes	characteristic
109	C₂×C₄	C₄²×C₉×C₁₁	1	112	yes	direct product factor
110	C₂×C₄	C₂²×C₄×C₉×C₁₁	1	84	yes	—
111	C₂×C₃	C₃×C₄³×C₁₁	1	8	yes	—
112	C₂×C₃	C₂²×C₃×C₄²×C₁₁	1	7	yes	—
113	C₂²	C₂×C₄²×C₉×C₁₁	1	28	yes	—
114	C₂²	C₂³×C₄×C₉×C₁₁	1	7	yes	—
115	C₄	C₂×C₄²×C₉×C₁₁	1	56	yes	direct product factor
116	C₃	C₂×C₃×C₄³×C₁₁	1	1	yes	characteristic
117	C₂	C₄³×C₉×C₁₁	1	8	yes	direct product factor
118	C₂	C₂²×C₄²×C₉×C₁₁	1	7	yes	—

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂³×C₃	C₂⁴×C₃×C₁₁
socle, prime radical	C₂⁴×C₃×C₁₁	C₂³×C₃
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₄³×C₉×C₁₁	C₂	direct (N × H)
5. C₂×C₄²×C₉×C₁₁	C₄	direct (N × H)
12. C₄²×C₉×C₁₁	C₂×C₄	direct (N × H)
13. C₂×C₄³×C₁₁	C₉	direct (N × H)
14. C₂×C₄³×C₉	C₁₁	direct (N × H)
20. C₂×C₄×C₉×C₁₁	C₄²	direct (N × H)
23. C₄³×C₁₁	C₂×C₉	direct (N × H)
25. C₄³×C₉	C₂×C₁₁	direct (N × H)
32. C₄×C₉×C₁₁	C₂×C₄²	direct (N × H)
35. C₂×C₄²×C₁₁	C₄×C₉	direct (N × H)
38. C₂×C₄²×C₉	C₄×C₁₁	direct (N × H)
44. C₂×C₉×C₁₁	C₄³	direct (N × H)
51. C₄²×C₁₁	C₂×C₄×C₉	direct (N × H)
55. C₄²×C₉	C₂×C₄×C₁₁	direct (N × H)
59. C₂×C₄³	C₉×C₁₁	direct (N × H)
60. C₉×C₁₁	C₂×C₄³	direct (N × H)
66. C₂×C₄×C₁₁	C₄²×C₉	direct (N × H)
70. C₂×C₄×C₉	C₄²×C₁₁	direct (N × H)
75. C₄³	C₂×C₉×C₁₁	direct (N × H)
82. C₄×C₁₁	C₂×C₄²×C₉	direct (N × H)
85. C₄×C₉	C₂×C₄²×C₁₁	direct (N × H)
88. C₂×C₄²	C₄×C₉×C₁₁	direct (N × H)
94. C₂×C₁₁	C₄³×C₉	direct (N × H)
96. C₂×C₉	C₄³×C₁₁	direct (N × H)
101. C₄²	C₂×C₄×C₉×C₁₁	direct (N × H)
105. C₁₁	C₂×C₄³×C₉	direct (N × H)
106. C₉	C₂×C₄³×C₁₁	direct (N × H)
109. C₂×C₄	C₄²×C₉×C₁₁	direct (N × H)
115. C₄	C₂×C₄²×C₉×C₁₁	direct (N × H)
117. C₂	C₄³×C₉×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
C₂²×C₄²×C₉×C₁₁	2
C₄³×C₉×C₁₁	2
C₂×C₃×C₄³×C₁₁	3
C₂×C₄³×C₉	11

Subgroups — C2×C43×C9×C11 #72191027

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄³×C₉×C₁₁ #72191027