Subgroups — C₂³×C₄×C₈×C₁₁ #14637243

Order 2816.

4638 conjugacy classes of subgroups.

The subgroup lattice has 114 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁴×C₈×C₁₁	C₂	1	2	yes	maximal
2	C₂³×C₄²×C₁₁	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₄×C₈×C₁₁	C₂	1	28	yes	maximal, direct product factor
4	C₂⁴×C₄×C₁₁	C₄	1	2	yes	—
5	C₂⁴×C₄×C₁₁	C₂²	1	1	yes	characteristic
6	C₂³×C₈×C₁₁	C₄	1	32	yes	direct product factor
7	C₂³×C₈×C₁₁	C₂²	1	28	yes	—
8	C₂²×C₄²×C₁₁	C₄	1	14	yes	—
9	C₂²×C₄²×C₁₁	C₂²	1	14	yes	—
10	C₂×C₄×C₈×C₁₁	C₂²	1	112	yes	direct product factor
11	C₂⁵×C₁₁	C₂×C₄	1	1	yes	characteristic
12	C₂³×C₄×C₁₁	C₈	1	32	yes	direct product factor
13	C₂³×C₄×C₁₁	C₂×C₄	1	7	yes	—
14	C₂³×C₄×C₁₁	C₂×C₄	1	16	yes	—
15	C₂³×C₄×C₁₁	C₂×C₄	1	28	yes	—
16	C₂³×C₄×C₁₁	C₂³	1	7	yes	—
17	C₂²×C₈×C₁₁	C₂×C₄	1	224	yes	direct product factor
18	C₂²×C₈×C₁₁	C₂³	1	56	yes	—
19	C₂×C₄²×C₁₁	C₂×C₄	1	84	yes	—
20	C₂×C₄²×C₁₁	C₂³	1	28	yes	—
21	C₄×C₈×C₁₁	C₂³	1	64	yes	direct product factor
22	C₂³×C₄×C₈	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
23	C₂⁴×C₁₁	C₄²	1	8	yes	—
24	C₂⁴×C₁₁	C₂×C₈	1	16	yes	—
25	C₂⁴×C₁₁	C₂²×C₄	1	7	yes	—
26	C₂²×C₄×C₁₁	C₄²	1	56	yes	—
27	C₂²×C₄×C₁₁	C₂×C₈	1	224	yes	direct product factor
28	C₂²×C₄×C₁₁	C₂²×C₄	1	21	yes	—
29	C₂²×C₄×C₁₁	C₂²×C₄	1	56	yes	—
30	C₂²×C₄×C₁₁	C₂²×C₄	1	56	yes	—
31	C₂²×C₄×C₁₁	C₂⁴	1	7	yes	—
32	C₂×C₈×C₁₁	C₂²×C₄	1	224	yes	direct product factor
33	C₂×C₈×C₁₁	C₂⁴	1	16	yes	—
34	C₄²×C₁₁	C₂²×C₄	1	56	yes	—
35	C₄²×C₁₁	C₂⁴	1	8	yes	—
36	C₂⁴×C₈	C₂×C₁₁	1	2	yes	—
37	C₂³×C₄²	C₂×C₁₁	1	1	yes	characteristic
38	C₂²×C₄×C₈	C₂×C₁₁	1	28	yes	direct product factor
39	C₂³×C₁₁	C₄×C₈	1	64	yes	direct product factor
40	C₂³×C₁₁	C₂×C₄²	1	28	yes	—
41	C₂³×C₁₁	C₂²×C₈	1	56	yes	—
42	C₂³×C₁₁	C₂³×C₄	1	7	yes	—
43	C₂×C₄×C₁₁	C₂×C₄²	1	84	yes	—
44	C₂×C₄×C₁₁	C₂²×C₈	1	224	yes	direct product factor
45	C₂×C₄×C₁₁	C₂³×C₄	1	7	yes	—
46	C₂×C₄×C₁₁	C₂³×C₄	1	16	yes	—
47	C₂×C₄×C₁₁	C₂³×C₄	1	28	yes	—
48	C₂×C₄×C₁₁	C₂⁵	1	1	yes	characteristic
49	C₈×C₁₁	C₂³×C₄	1	32	yes	direct product factor
50	C₂⁴×C₄	C₄×C₁₁	1	2	yes	—
51	C₂⁴×C₄	C₂²×C₁₁	1	1	yes	characteristic
52	C₂³×C₈	C₄×C₁₁	1	32	yes	direct product factor
53	C₂³×C₈	C₂²×C₁₁	1	28	yes	—
54	C₂²×C₄²	C₄×C₁₁	1	14	yes	—
55	C₂²×C₄²	C₂²×C₁₁	1	14	yes	—
56	C₂×C₄×C₈	C₂²×C₁₁	1	112	yes	direct product factor
57	C₂²×C₁₁	C₂×C₄×C₈	1	112	yes	direct product factor
58	C₂²×C₁₁	C₂²×C₄²	1	14	yes	—
59	C₂²×C₁₁	C₂³×C₈	1	28	yes	—
60	C₂²×C₁₁	C₂⁴×C₄	1	1	yes	characteristic
61	C₄×C₁₁	C₂²×C₄²	1	14	yes	—
62	C₄×C₁₁	C₂³×C₈	1	32	yes	direct product factor
63	C₄×C₁₁	C₂⁴×C₄	1	2	yes	—
64	C₂⁵	C₂×C₄×C₁₁	1	1	yes	characteristic
65	C₂³×C₄	C₈×C₁₁	1	32	yes	direct product factor
66	C₂³×C₄	C₂×C₄×C₁₁	1	7	yes	—
67	C₂³×C₄	C₂×C₄×C₁₁	1	16	yes	—
68	C₂³×C₄	C₂×C₄×C₁₁	1	28	yes	—
69	C₂³×C₄	C₂³×C₁₁	1	7	yes	—
70	C₂²×C₈	C₂×C₄×C₁₁	1	224	yes	direct product factor
71	C₂²×C₈	C₂³×C₁₁	1	56	yes	—
72	C₂×C₄²	C₂×C₄×C₁₁	1	84	yes	—
73	C₂×C₄²	C₂³×C₁₁	1	28	yes	—
74	C₄×C₈	C₂³×C₁₁	1	64	yes	direct product factor
75	C₂×C₁₁	C₂²×C₄×C₈	1	28	yes	direct product factor
76	C₂×C₁₁	C₂³×C₄²	1	1	yes	characteristic
77	C₂×C₁₁	C₂⁴×C₈	1	2	yes	—
78	C₂⁴	C₄²×C₁₁	1	8	yes	—
79	C₂⁴	C₂×C₈×C₁₁	1	16	yes	—
80	C₂⁴	C₂²×C₄×C₁₁	1	7	yes	—
81	C₂²×C₄	C₄²×C₁₁	1	56	yes	—
82	C₂²×C₄	C₂×C₈×C₁₁	1	224	yes	direct product factor
83	C₂²×C₄	C₂²×C₄×C₁₁	1	21	yes	—
84	C₂²×C₄	C₂²×C₄×C₁₁	1	56	yes	—
85	C₂²×C₄	C₂²×C₄×C₁₁	1	56	yes	—
86	C₂²×C₄	C₂⁴×C₁₁	1	7	yes	—
87	C₂×C₈	C₂²×C₄×C₁₁	1	224	yes	direct product factor
88	C₂×C₈	C₂⁴×C₁₁	1	16	yes	—
89	C₄²	C₂²×C₄×C₁₁	1	56	yes	—
90	C₄²	C₂⁴×C₁₁	1	8	yes	—
91	C₁₁	C₂³×C₄×C₈	1	1	yes	characteristic, direct product factor, Sylow
92	C₂³	C₄×C₈×C₁₁	1	64	yes	direct product factor
93	C₂³	C₂×C₄²×C₁₁	1	28	yes	—
94	C₂³	C₂²×C₈×C₁₁	1	56	yes	—
95	C₂³	C₂³×C₄×C₁₁	1	7	yes	—
96	C₂×C₄	C₂×C₄²×C₁₁	1	84	yes	—
97	C₂×C₄	C₂²×C₈×C₁₁	1	224	yes	direct product factor
98	C₂×C₄	C₂³×C₄×C₁₁	1	7	yes	—
99	C₂×C₄	C₂³×C₄×C₁₁	1	16	yes	—
100	C₂×C₄	C₂³×C₄×C₁₁	1	28	yes	—
101	C₂×C₄	C₂⁵×C₁₁	1	1	yes	characteristic
102	C₈	C₂³×C₄×C₁₁	1	32	yes	direct product factor
103	C₂²	C₂×C₄×C₈×C₁₁	1	112	yes	direct product factor
104	C₂²	C₂²×C₄²×C₁₁	1	14	yes	—
105	C₂²	C₂³×C₈×C₁₁	1	28	yes	—
106	C₂²	C₂⁴×C₄×C₁₁	1	1	yes	characteristic
107	C₄	C₂²×C₄²×C₁₁	1	14	yes	—
108	C₄	C₂³×C₈×C₁₁	1	32	yes	direct product factor
109	C₄	C₂⁴×C₄×C₁₁	1	2	yes	—
110	C₂	C₂²×C₄×C₈×C₁₁	1	28	yes	direct product factor
111	C₂	C₂³×C₄²×C₁₁	1	1	yes	characteristic
112	C₂	C₂⁴×C₈×C₁₁	1	2	yes	—

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂×C₄	C₂⁵×C₁₁
socle, prime radical	C₂⁵×C₁₁	C₂×C₄
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₂²×C₄×C₈×C₁₁	C₂	direct (N × H)
6. C₂³×C₈×C₁₁	C₄	direct (N × H)
10. C₂×C₄×C₈×C₁₁	C₂²	direct (N × H)
12. C₂³×C₄×C₁₁	C₈	direct (N × H)
17. C₂²×C₈×C₁₁	C₂×C₄	direct (N × H)
21. C₄×C₈×C₁₁	C₂³	direct (N × H)
22. C₂³×C₄×C₈	C₁₁	direct (N × H)
27. C₂²×C₄×C₁₁	C₂×C₈	direct (N × H)
32. C₂×C₈×C₁₁	C₂²×C₄	direct (N × H)
38. C₂²×C₄×C₈	C₂×C₁₁	direct (N × H)
39. C₂³×C₁₁	C₄×C₈	direct (N × H)
44. C₂×C₄×C₁₁	C₂²×C₈	direct (N × H)
49. C₈×C₁₁	C₂³×C₄	direct (N × H)
52. C₂³×C₈	C₄×C₁₁	direct (N × H)
56. C₂×C₄×C₈	C₂²×C₁₁	direct (N × H)
57. C₂²×C₁₁	C₂×C₄×C₈	direct (N × H)
62. C₄×C₁₁	C₂³×C₈	direct (N × H)
65. C₂³×C₄	C₈×C₁₁	direct (N × H)
70. C₂²×C₈	C₂×C₄×C₁₁	direct (N × H)
74. C₄×C₈	C₂³×C₁₁	direct (N × H)
75. C₂×C₁₁	C₂²×C₄×C₈	direct (N × H)
82. C₂²×C₄	C₂×C₈×C₁₁	direct (N × H)
87. C₂×C₈	C₂²×C₄×C₁₁	direct (N × H)
91. C₁₁	C₂³×C₄×C₈	direct (N × H)
92. C₂³	C₄×C₈×C₁₁	direct (N × H)
97. C₂×C₄	C₂²×C₈×C₁₁	direct (N × H)
102. C₈	C₂³×C₄×C₁₁	direct (N × H)
103. C₂²	C₂×C₄×C₈×C₁₁	direct (N × H)
108. C₄	C₂³×C₈×C₁₁	direct (N × H)
110. C₂	C₂²×C₄×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
C₂⁴×C₈×C₁₁	2
C₂³×C₄²×C₁₁	2
C₂²×C₄×C₈×C₁₁	2
C₂³×C₄×C₈	11

Subgroups — C23×C4×C8×C11 #14637243

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂³×C₄×C₈×C₁₁ #14637243