Subgroups — C₄³×C₁₁×C₁₆ #72189772

Order 11264.

9354 conjugacy classes of subgroups.

The subgroup lattice has 136 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄³×C₈×C₁₁	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄²×C₁₁×C₁₆	C₂	1	14	yes	maximal
3	C₄³×C₁₆	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
4	C₂²×C₄×C₁₁×C₁₆	C₂²	1	28	yes	—
5	C₂×C₄²×C₈×C₁₁	C₄	1	7	yes	—
6	C₂×C₄²×C₈×C₁₁	C₂²	1	7	yes	—
7	C₄⁴×C₁₁	C₄	1	1	yes	characteristic
8	C₄²×C₁₁×C₁₆	C₄	1	112	yes	direct product factor
9	C₂³×C₁₁×C₁₆	C₂³	1	8	yes	—
10	C₂²×C₄×C₈×C₁₁	C₂×C₄	1	21	yes	—
11	C₂²×C₄×C₈×C₁₁	C₂³	1	7	yes	—
12	C₂×C₄³×C₁₁	C₈	1	8	yes	—
13	C₂×C₄³×C₁₁	C₂×C₄	1	7	yes	—
14	C₂×C₄×C₁₁×C₁₆	C₂×C₄	1	336	yes	—
15	C₄²×C₈×C₁₁	C₈	1	56	yes	—
16	C₄²×C₈×C₁₁	C₂×C₄	1	56	yes	—
17	C₂³×C₈×C₁₁	C₂²×C₄	1	7	yes	—
18	C₂³×C₈×C₁₁	C₂⁴	1	1	yes	characteristic
19	C₂²×C₄²×C₁₁	C₂×C₈	1	28	yes	—
20	C₂²×C₄²×C₁₁	C₂²×C₄	1	7	yes	—
21	C₂²×C₁₁×C₁₆	C₂²×C₄	1	112	yes	—
22	C₂×C₄×C₈×C₁₁	C₄²	1	84	yes	—
23	C₂×C₄×C₈×C₁₁	C₂×C₈	1	168	yes	—
24	C₂×C₄×C₈×C₁₁	C₂²×C₄	1	84	yes	—
25	C₄³×C₁₁	C₁₆	1	64	yes	direct product factor
26	C₄³×C₁₁	C₄²	1	28	yes	—
27	C₄³×C₁₁	C₂×C₈	1	28	yes	—
28	C₄×C₁₁×C₁₆	C₄²	1	448	yes	direct product factor
29	C₂×C₄²×C₁₆	C₂×C₁₁	1	14	yes	—
30	C₄³×C₈	C₂×C₁₁	1	1	yes	characteristic
31	C₂³×C₄×C₁₁	C₂²×C₈	1	14	yes	—
32	C₂³×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
33	C₂²×C₈×C₁₁	C₂×C₄²	1	42	yes	—
34	C₂²×C₈×C₁₁	C₂²×C₈	1	56	yes	—
35	C₂²×C₈×C₁₁	C₂³×C₄	1	14	yes	—
36	C₂×C₄²×C₁₁	C₄×C₈	1	112	yes	—
37	C₂×C₄²×C₁₁	C₂×C₁₆	1	224	yes	—
38	C₂×C₄²×C₁₁	C₂×C₄²	1	42	yes	—
39	C₂×C₄²×C₁₁	C₂²×C₈	1	42	yes	—
40	C₂×C₁₁×C₁₆	C₂×C₄²	1	224	yes	—
41	C₄×C₈×C₁₁	C₄×C₈	1	336	yes	—
42	C₄×C₈×C₁₁	C₂×C₄²	1	112	yes	—
43	C₂²×C₄×C₁₆	C₂²×C₁₁	1	28	yes	—
44	C₂×C₄²×C₈	C₄×C₁₁	1	7	yes	—
45	C₂×C₄²×C₈	C₂²×C₁₁	1	7	yes	—
46	C₄⁴	C₄×C₁₁	1	1	yes	characteristic
47	C₄²×C₁₆	C₄×C₁₁	1	112	yes	direct product factor
48	C₂⁴×C₁₁	C₂³×C₈	1	1	yes	characteristic
49	C₂²×C₄×C₁₁	C₂×C₄×C₈	1	84	yes	—
50	C₂²×C₄×C₁₁	C₂²×C₁₆	1	112	yes	—
51	C₂²×C₄×C₁₁	C₂²×C₄²	1	7	yes	—
52	C₂²×C₄×C₁₁	C₂³×C₈	1	7	yes	—
53	C₂×C₈×C₁₁	C₄³	1	28	yes	—
54	C₂×C₈×C₁₁	C₂×C₄×C₈	1	168	yes	—
55	C₂×C₈×C₁₁	C₂²×C₄²	1	28	yes	—
56	C₄²×C₁₁	C₄×C₁₆	1	448	yes	direct product factor
57	C₄²×C₁₁	C₄³	1	28	yes	—
58	C₄²×C₁₁	C₂×C₄×C₈	1	84	yes	—
59	C₁₁×C₁₆	C₄³	1	64	yes	direct product factor
60	C₂³×C₁₆	C₂³×C₁₁	1	8	yes	—
61	C₂²×C₄×C₈	C₂×C₄×C₁₁	1	21	yes	—
62	C₂²×C₄×C₈	C₂³×C₁₁	1	7	yes	—
63	C₂×C₄³	C₈×C₁₁	1	8	yes	—
64	C₂×C₄³	C₂×C₄×C₁₁	1	7	yes	—
65	C₂×C₄×C₁₆	C₂×C₄×C₁₁	1	336	yes	—
66	C₄²×C₈	C₈×C₁₁	1	56	yes	—
67	C₄²×C₈	C₂×C₄×C₁₁	1	56	yes	—
68	C₂³×C₁₁	C₂²×C₄×C₈	1	7	yes	—
69	C₂³×C₁₁	C₂³×C₁₆	1	8	yes	—
70	C₂×C₄×C₁₁	C₄²×C₈	1	56	yes	—
71	C₂×C₄×C₁₁	C₂×C₄×C₁₆	1	336	yes	—
72	C₂×C₄×C₁₁	C₂×C₄³	1	7	yes	—
73	C₂×C₄×C₁₁	C₂²×C₄×C₈	1	21	yes	—
74	C₈×C₁₁	C₄²×C₈	1	56	yes	—
75	C₈×C₁₁	C₂×C₄³	1	8	yes	—
76	C₂³×C₈	C₂²×C₄×C₁₁	1	7	yes	—
77	C₂³×C₈	C₂⁴×C₁₁	1	1	yes	characteristic
78	C₂²×C₄²	C₂×C₈×C₁₁	1	28	yes	—
79	C₂²×C₄²	C₂²×C₄×C₁₁	1	7	yes	—
80	C₂²×C₁₆	C₂²×C₄×C₁₁	1	112	yes	—
81	C₂×C₄×C₈	C₄²×C₁₁	1	84	yes	—
82	C₂×C₄×C₈	C₂×C₈×C₁₁	1	168	yes	—
83	C₂×C₄×C₈	C₂²×C₄×C₁₁	1	84	yes	—
84	C₄³	C₁₁×C₁₆	1	64	yes	direct product factor
85	C₄³	C₄²×C₁₁	1	28	yes	—
86	C₄³	C₂×C₈×C₁₁	1	28	yes	—
87	C₄×C₁₆	C₄²×C₁₁	1	448	yes	direct product factor
88	C₂²×C₁₁	C₂×C₄²×C₈	1	7	yes	—
89	C₂²×C₁₁	C₂²×C₄×C₁₆	1	28	yes	—
90	C₄×C₁₁	C₄²×C₁₆	1	112	yes	direct product factor
91	C₄×C₁₁	C₄⁴	1	1	yes	characteristic
92	C₄×C₁₁	C₂×C₄²×C₈	1	7	yes	—
93	C₂³×C₄	C₂²×C₈×C₁₁	1	14	yes	—
94	C₂³×C₄	C₂³×C₄×C₁₁	1	1	yes	characteristic
95	C₂²×C₈	C₂×C₄²×C₁₁	1	42	yes	—
96	C₂²×C₈	C₂²×C₈×C₁₁	1	56	yes	—
97	C₂²×C₈	C₂³×C₄×C₁₁	1	14	yes	—
98	C₂×C₄²	C₄×C₈×C₁₁	1	112	yes	—
99	C₂×C₄²	C₂×C₁₁×C₁₆	1	224	yes	—
100	C₂×C₄²	C₂×C₄²×C₁₁	1	42	yes	—
101	C₂×C₄²	C₂²×C₈×C₁₁	1	42	yes	—
102	C₂×C₁₆	C₂×C₄²×C₁₁	1	224	yes	—
103	C₄×C₈	C₄×C₈×C₁₁	1	336	yes	—
104	C₄×C₈	C₂×C₄²×C₁₁	1	112	yes	—
105	C₂×C₁₁	C₄³×C₈	1	1	yes	characteristic
106	C₂×C₁₁	C₂×C₄²×C₁₆	1	14	yes	—
107	C₂⁴	C₂³×C₈×C₁₁	1	1	yes	characteristic
108	C₂²×C₄	C₂×C₄×C₈×C₁₁	1	84	yes	—
109	C₂²×C₄	C₂²×C₁₁×C₁₆	1	112	yes	—
110	C₂²×C₄	C₂²×C₄²×C₁₁	1	7	yes	—
111	C₂²×C₄	C₂³×C₈×C₁₁	1	7	yes	—
112	C₂×C₈	C₄³×C₁₁	1	28	yes	—
113	C₂×C₈	C₂×C₄×C₈×C₁₁	1	168	yes	—
114	C₂×C₈	C₂²×C₄²×C₁₁	1	28	yes	—
115	C₄²	C₄×C₁₁×C₁₆	1	448	yes	direct product factor
116	C₄²	C₄³×C₁₁	1	28	yes	—
117	C₄²	C₂×C₄×C₈×C₁₁	1	84	yes	—
118	C₁₆	C₄³×C₁₁	1	64	yes	direct product factor
119	C₁₁	C₄³×C₁₆	1	1	yes	characteristic, direct product factor, Sylow
120	C₂³	C₂²×C₄×C₈×C₁₁	1	7	yes	—
121	C₂³	C₂³×C₁₁×C₁₆	1	8	yes	—
122	C₂×C₄	C₄²×C₈×C₁₁	1	56	yes	—
123	C₂×C₄	C₂×C₄×C₁₁×C₁₆	1	336	yes	—
124	C₂×C₄	C₂×C₄³×C₁₁	1	7	yes	—
125	C₂×C₄	C₂²×C₄×C₈×C₁₁	1	21	yes	—
126	C₈	C₄²×C₈×C₁₁	1	56	yes	—
127	C₈	C₂×C₄³×C₁₁	1	8	yes	—
128	C₂²	C₂×C₄²×C₈×C₁₁	1	7	yes	—
129	C₂²	C₂²×C₄×C₁₁×C₁₆	1	28	yes	—
130	C₄	C₄²×C₁₁×C₁₆	1	112	yes	direct product factor
131	C₄	C₄⁴×C₁₁	1	1	yes	characteristic
132	C₄	C₂×C₄²×C₈×C₁₁	1	7	yes	—
133	C₂	C₂×C₄²×C₁₁×C₁₆	1	14	yes	—
134	C₂	C₄³×C₈×C₁₁	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂³×C₈	C₂⁴×C₁₁
socle, prime radical	C₂⁴×C₁₁	C₂³×C₈
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₄³×C₁₆	C₁₁	direct (N × H)
8. C₄²×C₁₁×C₁₆	C₄	direct (N × H)
25. C₄³×C₁₁	C₁₆	direct (N × H)
28. C₄×C₁₁×C₁₆	C₄²	direct (N × H)
47. C₄²×C₁₆	C₄×C₁₁	direct (N × H)
56. C₄²×C₁₁	C₄×C₁₆	direct (N × H)
59. C₁₁×C₁₆	C₄³	direct (N × H)
84. C₄³	C₁₁×C₁₆	direct (N × H)
87. C₄×C₁₆	C₄²×C₁₁	direct (N × H)
90. C₄×C₁₁	C₄²×C₁₆	direct (N × H)
115. C₄²	C₄×C₁₁×C₁₆	direct (N × H)
118. C₁₆	C₄³×C₁₁	direct (N × H)
119. C₁₁	C₄³×C₁₆	direct (N × H)
130. C₄	C₄²×C₁₁×C₁₆	direct (N × H)

Maximal subgroups

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

subgroup	index
C₄³×C₈×C₁₁	2
C₂×C₄²×C₁₁×C₁₆	2
C₄³×C₁₆	11

Subgroups — C43×C11×C16 #72189772

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄³×C₁₁×C₁₆ #72189772