Subgroups — C₂×C₉×C₁₁×C₆₄ #72191007

Order 12672.

120 conjugacy classes of subgroups.

The subgroup lattice has 108 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₉×C₁₁×C₃₂	C₂	1	1	yes	maximal, characteristic
2	C₉×C₁₁×C₆₄	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₃×C₁₁×C₆₄	C₃	1	1	yes	maximal, characteristic
4	C₂×C₉×C₁₁×C₁₆	C₄	1	1	yes	characteristic
5	C₉×C₁₁×C₃₂	C₄	1	1	yes	characteristic
6	C₉×C₁₁×C₃₂	C₂²	1	1	yes	characteristic
7	C₂×C₃×C₁₁×C₃₂	C₂×C₃	1	1	yes	characteristic
8	C₃×C₁₁×C₆₄	C₂×C₃	1	2	yes	—
9	C₂×C₈×C₉×C₁₁	C₈	1	1	yes	characteristic
10	C₉×C₁₁×C₁₆	C₈	1	1	yes	characteristic
11	C₉×C₁₁×C₁₆	C₂×C₄	1	1	yes	characteristic
12	C₂×C₁₁×C₆₄	C₉	1	1	yes	characteristic, direct product factor, Hall
13	C₂×C₉×C₆₄	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
14	C₂×C₃×C₁₁×C₁₆	C₃×C₄	1	1	yes	characteristic
15	C₃×C₁₁×C₃₂	C₃×C₄	1	1	yes	characteristic
16	C₃×C₁₁×C₃₂	C₂²×C₃	1	1	yes	characteristic
17	C₂×C₄×C₉×C₁₁	C₁₆	1	1	yes	characteristic
18	C₈×C₉×C₁₁	C₁₆	1	1	yes	characteristic
19	C₈×C₉×C₁₁	C₂×C₈	1	1	yes	characteristic
20	C₂×C₁₁×C₃₂	C₂×C₉	1	1	yes	characteristic
21	C₁₁×C₆₄	C₂×C₉	1	2	yes	direct product factor
22	C₂×C₉×C₃₂	C₂×C₁₁	1	1	yes	characteristic
23	C₉×C₆₄	C₂×C₁₁	1	2	yes	direct product factor
24	C₂×C₃×C₈×C₁₁	C₃×C₈	1	1	yes	characteristic
25	C₃×C₁₁×C₁₆	C₃×C₈	1	1	yes	characteristic
26	C₃×C₁₁×C₁₆	C₂×C₃×C₄	1	1	yes	characteristic
27	C₂²×C₉×C₁₁	C₃₂	1	1	yes	characteristic
28	C₄×C₉×C₁₁	C₃₂	1	1	yes	characteristic
29	C₄×C₉×C₁₁	C₂×C₁₆	1	1	yes	characteristic
30	C₂×C₃×C₆₄	C₃×C₁₁	1	1	yes	characteristic
31	C₂×C₁₁×C₁₆	C₄×C₉	1	1	yes	characteristic
32	C₁₁×C₃₂	C₄×C₉	1	1	yes	characteristic
33	C₁₁×C₃₂	C₂²×C₉	1	1	yes	characteristic
34	C₂×C₉×C₁₆	C₄×C₁₁	1	1	yes	characteristic
35	C₉×C₃₂	C₄×C₁₁	1	1	yes	characteristic
36	C₉×C₃₂	C₂²×C₁₁	1	1	yes	characteristic
37	C₂×C₃×C₄×C₁₁	C₃×C₁₆	1	1	yes	characteristic
38	C₃×C₈×C₁₁	C₃×C₁₆	1	1	yes	characteristic
39	C₃×C₈×C₁₁	C₂×C₃×C₈	1	1	yes	characteristic
40	C₂×C₉×C₁₁	C₆₄	1	2	yes	direct product factor
41	C₂×C₉×C₁₁	C₂×C₃₂	1	1	yes	characteristic
42	C₂×C₃×C₃₂	C₂×C₃×C₁₁	1	1	yes	characteristic
43	C₃×C₆₄	C₂×C₃×C₁₁	1	2	yes	—
44	C₂×C₈×C₁₁	C₈×C₉	1	1	yes	characteristic
45	C₁₁×C₁₆	C₈×C₉	1	1	yes	characteristic
46	C₁₁×C₁₆	C₂×C₄×C₉	1	1	yes	characteristic
47	C₂×C₈×C₉	C₈×C₁₁	1	1	yes	characteristic
48	C₉×C₁₆	C₈×C₁₁	1	1	yes	characteristic
49	C₉×C₁₆	C₂×C₄×C₁₁	1	1	yes	characteristic
50	C₂²×C₃×C₁₁	C₃×C₃₂	1	1	yes	characteristic
51	C₃×C₄×C₁₁	C₃×C₃₂	1	1	yes	characteristic
52	C₃×C₄×C₁₁	C₂×C₃×C₁₆	1	1	yes	characteristic
53	C₂×C₆₄	C₉×C₁₁	1	1	yes	characteristic, direct product factor, Sylow
54	C₉×C₁₁	C₂×C₆₄	1	1	yes	characteristic, direct product factor, Hall
55	C₂×C₃×C₁₆	C₃×C₄×C₁₁	1	1	yes	characteristic
56	C₃×C₃₂	C₃×C₄×C₁₁	1	1	yes	characteristic
57	C₃×C₃₂	C₂²×C₃×C₁₁	1	1	yes	characteristic
58	C₂×C₄×C₁₁	C₉×C₁₆	1	1	yes	characteristic
59	C₈×C₁₁	C₉×C₁₆	1	1	yes	characteristic
60	C₈×C₁₁	C₂×C₈×C₉	1	1	yes	characteristic
61	C₂×C₄×C₉	C₁₁×C₁₆	1	1	yes	characteristic
62	C₈×C₉	C₁₁×C₁₆	1	1	yes	characteristic
63	C₈×C₉	C₂×C₈×C₁₁	1	1	yes	characteristic
64	C₂×C₃×C₁₁	C₃×C₆₄	1	2	yes	—
65	C₂×C₃×C₁₁	C₂×C₃×C₃₂	1	1	yes	characteristic
66	C₂×C₃₂	C₂×C₉×C₁₁	1	1	yes	characteristic
67	C₆₄	C₂×C₉×C₁₁	1	2	yes	direct product factor
68	C₂×C₃×C₈	C₃×C₈×C₁₁	1	1	yes	characteristic
69	C₃×C₁₆	C₃×C₈×C₁₁	1	1	yes	characteristic
70	C₃×C₁₆	C₂×C₃×C₄×C₁₁	1	1	yes	characteristic
71	C₂²×C₁₁	C₉×C₃₂	1	1	yes	characteristic
72	C₄×C₁₁	C₉×C₃₂	1	1	yes	characteristic
73	C₄×C₁₁	C₂×C₉×C₁₆	1	1	yes	characteristic
74	C₂²×C₉	C₁₁×C₃₂	1	1	yes	characteristic
75	C₄×C₉	C₁₁×C₃₂	1	1	yes	characteristic
76	C₄×C₉	C₂×C₁₁×C₁₆	1	1	yes	characteristic
77	C₃×C₁₁	C₂×C₃×C₆₄	1	1	yes	characteristic
78	C₂×C₁₆	C₄×C₉×C₁₁	1	1	yes	characteristic
79	C₃₂	C₄×C₉×C₁₁	1	1	yes	characteristic
80	C₃₂	C₂²×C₉×C₁₁	1	1	yes	characteristic
81	C₂×C₃×C₄	C₃×C₁₁×C₁₆	1	1	yes	characteristic
82	C₃×C₈	C₃×C₁₁×C₁₆	1	1	yes	characteristic
83	C₃×C₈	C₂×C₃×C₈×C₁₁	1	1	yes	characteristic
84	C₂×C₁₁	C₉×C₆₄	1	2	yes	direct product factor
85	C₂×C₁₁	C₂×C₉×C₃₂	1	1	yes	characteristic
86	C₂×C₉	C₁₁×C₆₄	1	2	yes	direct product factor
87	C₂×C₉	C₂×C₁₁×C₃₂	1	1	yes	characteristic
88	C₂×C₈	C₈×C₉×C₁₁	1	1	yes	characteristic
89	C₁₆	C₈×C₉×C₁₁	1	1	yes	characteristic
90	C₁₆	C₂×C₄×C₉×C₁₁	1	1	yes	characteristic
91	C₂²×C₃	C₃×C₁₁×C₃₂	1	1	yes	characteristic
92	C₃×C₄	C₃×C₁₁×C₃₂	1	1	yes	characteristic
93	C₃×C₄	C₂×C₃×C₁₁×C₁₆	1	1	yes	characteristic
94	C₁₁	C₂×C₉×C₆₄	1	1	yes	characteristic, direct product factor, Sylow
95	C₉	C₂×C₁₁×C₆₄	1	1	yes	characteristic, direct product factor, Sylow
96	C₂×C₄	C₉×C₁₁×C₁₆	1	1	yes	characteristic
97	C₈	C₉×C₁₁×C₁₆	1	1	yes	characteristic
98	C₈	C₂×C₈×C₉×C₁₁	1	1	yes	characteristic
99	C₂×C₃	C₃×C₁₁×C₆₄	1	2	yes	—
100	C₂×C₃	C₂×C₃×C₁₁×C₃₂	1	1	yes	characteristic
101	C₂²	C₉×C₁₁×C₃₂	1	1	yes	characteristic
102	C₄	C₉×C₁₁×C₃₂	1	1	yes	characteristic
103	C₄	C₂×C₉×C₁₁×C₁₆	1	1	yes	characteristic
104	C₃	C₂×C₃×C₁₁×C₆₄	1	1	yes	characteristic
105	C₂	C₉×C₁₁×C₆₄	1	2	yes	direct product factor
106	C₂	C₂×C₉×C₁₁×C₃₂	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₃×C₃₂	C₂²×C₃×C₁₁
socle, prime radical	C₂²×C₃×C₁₁	C₃×C₃₂
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₉×C₁₁×C₆₄	C₂	direct (N × H)
12. C₂×C₁₁×C₆₄	C₉	direct (N × H)
13. C₂×C₉×C₆₄	C₁₁	direct (N × H)
21. C₁₁×C₆₄	C₂×C₉	direct (N × H)
23. C₉×C₆₄	C₂×C₁₁	direct (N × H)
40. C₂×C₉×C₁₁	C₆₄	direct (N × H)
53. C₂×C₆₄	C₉×C₁₁	direct (N × H)
54. C₉×C₁₁	C₂×C₆₄	direct (N × H)
67. C₆₄	C₂×C₉×C₁₁	direct (N × H)
84. C₂×C₁₁	C₉×C₆₄	direct (N × H)
86. C₂×C₉	C₁₁×C₆₄	direct (N × H)
94. C₁₁	C₂×C₉×C₆₄	direct (N × H)
95. C₉	C₂×C₁₁×C₆₄	direct (N × H)
105. C₂	C₉×C₁₁×C₆₄	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×C₉×C₁₁×C₃₂	2
C₉×C₁₁×C₆₄	2
C₂×C₃×C₁₁×C₆₄	3
C₂×C₉×C₆₄	11

Subgroups — C2×C9×C11×C64 #72191007

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₉×C₁₁×C₆₄ #72191007