Subgroups — C₂²×C₄×C₁₁×C₁₆ #14610513

Order 2816.

1022 conjugacy classes of subgroups.

The subgroup lattice has 132 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

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

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂×C₈	C₂⁴×C₁₁
socle, prime radical	C₂⁴×C₁₁	C₂×C₈
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₂×C₄×C₁₁×C₁₆	C₂	direct (N × H)
7. C₂²×C₁₁×C₁₆	C₄	direct (N × H)
11. C₄×C₁₁×C₁₆	C₂²	direct (N × H)
21. C₂×C₁₁×C₁₆	C₂×C₄	direct (N × H)
25. C₂²×C₄×C₁₆	C₁₁	direct (N × H)
27. C₂²×C₄×C₁₁	C₁₆	direct (N × H)
41. C₁₁×C₁₆	C₂²×C₄	direct (N × H)
44. C₂×C₄×C₁₆	C₂×C₁₁	direct (N × H)
49. C₂×C₄×C₁₁	C₂×C₁₆	direct (N × H)
61. C₂²×C₁₆	C₄×C₁₁	direct (N × H)
65. C₄×C₁₆	C₂²×C₁₁	direct (N × H)
66. C₂²×C₁₁	C₄×C₁₆	direct (N × H)
71. C₄×C₁₁	C₂²×C₁₆	direct (N × H)
83. C₂×C₁₆	C₂×C₄×C₁₁	direct (N × H)
87. C₂×C₁₁	C₂×C₄×C₁₆	direct (N × H)
91. C₂²×C₄	C₁₁×C₁₆	direct (N × H)
105. C₁₆	C₂²×C₄×C₁₁	direct (N × H)
106. C₁₁	C₂²×C₄×C₁₆	direct (N × H)
111. C₂×C₄	C₂×C₁₁×C₁₆	direct (N × H)
120. C₂²	C₄×C₁₁×C₁₆	direct (N × H)
125. C₄	C₂²×C₁₁×C₁₆	direct (N × H)
128. C₂	C₂×C₄×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
C₂³×C₁₁×C₁₆	2
C₂²×C₄×C₈×C₁₁	2
C₂×C₄×C₁₁×C₁₆	2
C₂²×C₄×C₁₆	11

Subgroups — C22×C4×C11×C16 #14610513

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₄×C₁₁×C₁₆ #14610513