Subgroups — C₂×C₈×C₁₁×C₁₆ #14588589

Order 2816.

398 conjugacy classes of subgroups.

The subgroup lattice has 106 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×C₁₁×C₁₆	C₂	1	2	yes	maximal
2	C₂×C₈²×C₁₁	C₂	1	1	yes	maximal, characteristic
3	C₈×C₁₁×C₁₆	C₂	1	4	yes	maximal, direct product factor
4	C₂²×C₁₁×C₁₆	C₄	1	4	yes	—
5	C₂×C₄×C₈×C₁₁	C₄	1	2	yes	—
6	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
7	C₄×C₁₁×C₁₆	C₄	1	4	yes	—
8	C₄×C₁₁×C₁₆	C₂²	1	4	yes	—
9	C₈²×C₁₁	C₄	1	2	yes	—
10	C₈²×C₁₁	C₂²	1	2	yes	—
11	C₂²×C₈×C₁₁	C₈	1	4	yes	—
12	C₂²×C₈×C₁₁	C₂×C₄	1	2	yes	—
13	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
14	C₂×C₁₁×C₁₆	C₈	1	16	yes	direct product factor
15	C₂×C₁₁×C₁₆	C₂×C₄	1	8	yes	—
16	C₄×C₈×C₁₁	C₈	1	4	yes	—
17	C₄×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
18	C₄×C₈×C₁₁	C₂×C₄	1	2	yes	—
19	C₄×C₈×C₁₁	C₂×C₄	1	4	yes	—
20	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
21	C₂×C₈×C₁₆	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
22	C₂²×C₄×C₁₁	C₄²	1	1	yes	characteristic
23	C₂²×C₄×C₁₁	C₂×C₈	1	2	yes	—
24	C₂×C₈×C₁₁	C₁₆	1	16	yes	direct product factor
25	C₂×C₈×C₁₁	C₄²	1	2	yes	—
26	C₂×C₈×C₁₁	C₂×C₈	1	8	yes	—
27	C₂×C₈×C₁₁	C₂×C₈	1	8	yes	—
28	C₂×C₈×C₁₁	C₂²×C₄	1	2	yes	—
29	C₄²×C₁₁	C₄²	1	1	yes	characteristic
30	C₄²×C₁₁	C₂×C₈	1	2	yes	—
31	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
32	C₁₁×C₁₆	C₂×C₈	1	16	yes	direct product factor
33	C₂×C₄×C₁₆	C₂×C₁₁	1	2	yes	—
34	C₂×C₈²	C₂×C₁₁	1	1	yes	characteristic
35	C₈×C₁₆	C₂×C₁₁	1	4	yes	direct product factor
36	C₂³×C₁₁	C₄×C₈	1	1	yes	characteristic
37	C₂×C₄×C₁₁	C₄×C₈	1	1	yes	characteristic
38	C₂×C₄×C₁₁	C₄×C₈	1	2	yes	—
39	C₂×C₄×C₁₁	C₄×C₈	1	4	yes	—
40	C₂×C₄×C₁₁	C₂×C₁₆	1	8	yes	—
41	C₂×C₄×C₁₁	C₂×C₄²	1	1	yes	characteristic
42	C₂×C₄×C₁₁	C₂²×C₈	1	2	yes	—
43	C₈×C₁₁	C₄×C₈	1	4	yes	—
44	C₈×C₁₁	C₂×C₁₆	1	16	yes	direct product factor
45	C₈×C₁₁	C₂²×C₈	1	4	yes	—
46	C₂²×C₁₆	C₄×C₁₁	1	4	yes	—
47	C₂×C₄×C₈	C₄×C₁₁	1	2	yes	—
48	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
49	C₄×C₁₆	C₄×C₁₁	1	4	yes	—
50	C₄×C₁₆	C₂²×C₁₁	1	4	yes	—
51	C₈²	C₄×C₁₁	1	2	yes	—
52	C₈²	C₂²×C₁₁	1	2	yes	—
53	C₂²×C₁₁	C₈²	1	2	yes	—
54	C₂²×C₁₁	C₄×C₁₆	1	4	yes	—
55	C₂²×C₁₁	C₂×C₄×C₈	1	1	yes	characteristic
56	C₄×C₁₁	C₈²	1	2	yes	—
57	C₄×C₁₁	C₄×C₁₆	1	4	yes	—
58	C₄×C₁₁	C₂×C₄×C₈	1	2	yes	—
59	C₄×C₁₁	C₂²×C₁₆	1	4	yes	—
60	C₂²×C₈	C₈×C₁₁	1	4	yes	—
61	C₂²×C₈	C₂×C₄×C₁₁	1	2	yes	—
62	C₂×C₄²	C₂×C₄×C₁₁	1	1	yes	characteristic
63	C₂×C₁₆	C₈×C₁₁	1	16	yes	direct product factor
64	C₂×C₁₆	C₂×C₄×C₁₁	1	8	yes	—
65	C₄×C₈	C₈×C₁₁	1	4	yes	—
66	C₄×C₈	C₂×C₄×C₁₁	1	1	yes	characteristic
67	C₄×C₈	C₂×C₄×C₁₁	1	2	yes	—
68	C₄×C₈	C₂×C₄×C₁₁	1	4	yes	—
69	C₄×C₈	C₂³×C₁₁	1	1	yes	characteristic
70	C₂×C₁₁	C₈×C₁₆	1	4	yes	direct product factor
71	C₂×C₁₁	C₂×C₈²	1	1	yes	characteristic
72	C₂×C₁₁	C₂×C₄×C₁₆	1	2	yes	—
73	C₂²×C₄	C₄²×C₁₁	1	1	yes	characteristic
74	C₂²×C₄	C₂×C₈×C₁₁	1	2	yes	—
75	C₂×C₈	C₁₁×C₁₆	1	16	yes	direct product factor
76	C₂×C₈	C₄²×C₁₁	1	2	yes	—
77	C₂×C₈	C₂×C₈×C₁₁	1	8	yes	—
78	C₂×C₈	C₂×C₈×C₁₁	1	8	yes	—
79	C₂×C₈	C₂²×C₄×C₁₁	1	2	yes	—
80	C₄²	C₄²×C₁₁	1	1	yes	characteristic
81	C₄²	C₂×C₈×C₁₁	1	2	yes	—
82	C₄²	C₂²×C₄×C₁₁	1	1	yes	characteristic
83	C₁₆	C₂×C₈×C₁₁	1	16	yes	direct product factor
84	C₁₁	C₂×C₈×C₁₆	1	1	yes	characteristic, direct product factor, Sylow
85	C₂³	C₄×C₈×C₁₁	1	1	yes	characteristic
86	C₂×C₄	C₄×C₈×C₁₁	1	1	yes	characteristic
87	C₂×C₄	C₄×C₈×C₁₁	1	2	yes	—
88	C₂×C₄	C₄×C₈×C₁₁	1	4	yes	—
89	C₂×C₄	C₂×C₁₁×C₁₆	1	8	yes	—
90	C₂×C₄	C₂×C₄²×C₁₁	1	1	yes	characteristic
91	C₂×C₄	C₂²×C₈×C₁₁	1	2	yes	—
92	C₈	C₄×C₈×C₁₁	1	4	yes	—
93	C₈	C₂×C₁₁×C₁₆	1	16	yes	direct product factor
94	C₈	C₂²×C₈×C₁₁	1	4	yes	—
95	C₂²	C₈²×C₁₁	1	2	yes	—
96	C₂²	C₄×C₁₁×C₁₆	1	4	yes	—
97	C₂²	C₂×C₄×C₈×C₁₁	1	1	yes	characteristic
98	C₄	C₈²×C₁₁	1	2	yes	—
99	C₄	C₄×C₁₁×C₁₆	1	4	yes	—
100	C₄	C₂×C₄×C₈×C₁₁	1	2	yes	—
101	C₄	C₂²×C₁₁×C₁₆	1	4	yes	—
102	C₂	C₈×C₁₁×C₁₆	1	4	yes	direct product factor
103	C₂	C₂×C₈²×C₁₁	1	1	yes	characteristic
104	C₂	C₂×C₄×C₁₁×C₁₆	1	2	yes	—

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₄×C₈	C₂³×C₁₁
socle, prime radical	C₂³×C₁₁	C₄×C₈
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₈×C₁₁×C₁₆	C₂	direct (N × H)
14. C₂×C₁₁×C₁₆	C₈	direct (N × H)
21. C₂×C₈×C₁₆	C₁₁	direct (N × H)
24. C₂×C₈×C₁₁	C₁₆	direct (N × H)
32. C₁₁×C₁₆	C₂×C₈	direct (N × H)
35. C₈×C₁₆	C₂×C₁₁	direct (N × H)
44. C₈×C₁₁	C₂×C₁₆	direct (N × H)
63. C₂×C₁₆	C₈×C₁₁	direct (N × H)
70. C₂×C₁₁	C₈×C₁₆	direct (N × H)
75. C₂×C₈	C₁₁×C₁₆	direct (N × H)
83. C₁₆	C₂×C₈×C₁₁	direct (N × H)
84. C₁₁	C₂×C₈×C₁₆	direct (N × H)
93. C₈	C₂×C₁₁×C₁₆	direct (N × H)
102. C₂	C₈×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
C₂×C₄×C₁₁×C₁₆	2
C₂×C₈²×C₁₁	2
C₈×C₁₁×C₁₆	2
C₂×C₈×C₁₆	11

Subgroups — C2×C8×C11×C16 #14588589

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₈×C₁₁×C₁₆ #14588589