Subgroups — C₂³×C₄×C₁₁⋊C₈ #15617153

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×C₁₁⋊C₈	C₂	1	2	yes	maximal
2	C₂²×C₄×C₁₁⋊C₈	C₂	1	28	yes	maximal, direct product factor
3	C₂³×C₄²×C₁₁	C₂	1	1	yes	maximal, characteristic
4	C₂⁴×C₄×C₁₁	C₄	1	2	yes	—
5	C₂⁴×C₄×C₁₁	C₂²	1	1	yes	characteristic
6	C₂²×C₄²×C₁₁	C₄	1	14	yes	—
7	C₂²×C₄²×C₁₁	C₂²	1	14	yes	—
8	C₂³×C₁₁⋊C₈	C₄	1	32	yes	direct product factor
9	C₂³×C₁₁⋊C₈	C₂²	1	28	yes	—
10	C₂×C₄×C₁₁⋊C₈	C₂²	1	112	yes	direct product factor
11	C₂⁵×C₁₁	C₂×C₄	1	1	yes	characteristic
12	C₂³×C₄×C₁₁	C₈	1	32	yes	complemented
13	C₂³×C₄×C₁₁	C₂×C₄	1	16	yes	—
14	C₂³×C₄×C₁₁	C₂×C₄	1	7	yes	—
15	C₂³×C₄×C₁₁	C₂×C₄	1	28	yes	—
16	C₂³×C₄×C₁₁	C₂³	1	7	yes	—
17	C₂×C₄²×C₁₁	C₂×C₄	1	84	yes	—
18	C₂×C₄²×C₁₁	C₂³	1	28	yes	—
19	C₂²×C₁₁⋊C₈	C₂×C₄	1	224	yes	direct product factor
20	C₂²×C₁₁⋊C₈	C₂³	1	56	yes	—
21	C₄×C₁₁⋊C₈	C₂³	1	64	yes	direct product factor
22	C₂³×C₄×C₈	—	11	1	no	maximal, 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	complemented
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	C₄²×C₁₁	C₂²×C₄	1	56	yes	—
33	C₄²×C₁₁	C₂⁴	1	8	yes	—
34	C₂×C₁₁⋊C₈	C₂²×C₄	1	224	yes	direct product factor
35	C₂×C₁₁⋊C₈	C₂⁴	1	16	yes	—
36	C₂⁴×C₈	—	11	2	no	—
37	C₂³×C₄²	D₁₁	1	1	yes	characteristic
38	C₂²×C₄×C₈	—	11	28	no	—
39	C₂³×C₁₁	C₄×C₈	1	64	yes	complemented
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	complemented
45	C₂×C₄×C₁₁	C₂³×C₄	1	28	yes	—
46	C₂×C₄×C₁₁	C₂³×C₄	1	16	yes	—
47	C₂×C₄×C₁₁	C₂³×C₄	1	7	yes	—
48	C₂×C₄×C₁₁	C₂⁵	1	1	yes	characteristic
49	C₁₁⋊C₈	C₂³×C₄	1	32	yes	direct product factor
50	C₂⁴×C₄	Dic₁₁	1	2	yes	—
51	C₂⁴×C₄	C₂×D₁₁	1	1	yes	characteristic
52	C₂³×C₈	—	11	28	no	—
53	C₂³×C₈	—	11	32	no	—
54	C₂²×C₄²	Dic₁₁	1	14	yes	—
55	C₂²×C₄²	C₂×D₁₁	1	14	yes	—
56	C₂×C₄×C₈	—	11	112	no	—
57	C₂²×C₁₁	C₂×C₄×C₈	1	112	yes	complemented
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	complemented
63	C₄×C₁₁	C₂⁴×C₄	1	2	yes	—
64	C₂⁵	C₂×Dic₁₁	1	1	yes	characteristic
65	C₂³×C₄	C₁₁⋊C₈	1	32	yes	direct product factor
66	C₂³×C₄	C₄×D₁₁	1	16	yes	—
67	C₂³×C₄	C₂×Dic₁₁	1	28	yes	—
68	C₂³×C₄	C₂×Dic₁₁	1	7	yes	—
69	C₂³×C₄	C₂²×D₁₁	1	7	yes	—
70	C₂²×C₈	—	11	224	no	—
71	C₂²×C₈	—	11	56	no	—
72	C₂×C₄²	C₂×Dic₁₁	1	84	yes	—
73	C₂×C₄²	C₂²×D₁₁	1	28	yes	—
74	C₄×C₈	—	11	64	no	—
75	C₂×C₁₁	C₂²×C₄×C₈	1	28	yes	complemented
76	C₂×C₁₁	C₂³×C₄²	1	1	yes	characteristic
77	C₂×C₁₁	C₂⁴×C₈	1	2	yes	—
78	C₂⁴	C₂×C₁₁⋊C₈	1	16	yes	—
79	C₂⁴	C₄×Dic₁₁	1	8	yes	—
80	C₂⁴	C₂²×Dic₁₁	1	7	yes	—
81	C₂²×C₄	C₂×C₁₁⋊C₈	1	224	yes	direct product factor
82	C₂²×C₄	C₄×Dic₁₁	1	56	yes	—
83	C₂²×C₄	C₂×C₄×D₁₁	1	56	yes	—
84	C₂²×C₄	C₂²×Dic₁₁	1	56	yes	—
85	C₂²×C₄	C₂²×Dic₁₁	1	21	yes	—
86	C₂²×C₄	C₂³×D₁₁	1	7	yes	—
87	C₂×C₈	—	11	224	no	—
88	C₂×C₈	—	11	16	no	—
89	C₄²	C₂²×Dic₁₁	1	56	yes	—
90	C₄²	C₂³×D₁₁	1	8	yes	—
91	C₁₁	C₂³×C₄×C₈	1	1	yes	characteristic, complemented, Sylow
92	C₂³	C₄×C₁₁⋊C₈	1	64	yes	direct product factor
93	C₂³	C₂²×C₁₁⋊C₈	1	56	yes	—
94	C₂³	C₂×C₄×Dic₁₁	1	28	yes	—
95	C₂³	C₂³×Dic₁₁	1	7	yes	—
96	C₂×C₄	C₂²×C₁₁⋊C₈	1	224	yes	direct product factor
97	C₂×C₄	C₂×C₄×Dic₁₁	1	84	yes	—
98	C₂×C₄	C₂²×C₄×D₁₁	1	28	yes	—
99	C₂×C₄	C₂³×Dic₁₁	1	16	yes	—
100	C₂×C₄	C₂³×Dic₁₁	1	7	yes	—
101	C₂×C₄	C₂⁴×D₁₁	1	1	yes	characteristic
102	C₈	—	11	32	no	—
103	C₂²	C₂×C₄×C₁₁⋊C₈	1	112	yes	direct product factor
104	C₂²	C₂³×C₁₁⋊C₈	1	28	yes	—
105	C₂²	C₂²×C₄×Dic₁₁	1	14	yes	—
106	C₂²	C₂⁴×Dic₁₁	1	1	yes	characteristic
107	C₄	C₂³×C₁₁⋊C₈	1	32	yes	direct product factor
108	C₄	C₂²×C₄×Dic₁₁	1	14	yes	—
109	C₄	C₂³×C₄×D₁₁	1	2	yes	—
110	C₂	C₂²×C₄×C₁₁⋊C₈	1	28	yes	direct product factor
111	C₂	C₂³×C₄×Dic₁₁	1	1	yes	characteristic
112	C₂	C₂⁴×C₁₁⋊C₈	1	2	yes	—

	subgroup	G/H
center, hypercenter	C₂³×C₄²	D₁₁
commutator, hypocenter	C₁₁	C₂³×C₄×C₈
Frattini	C₂×C₄	C₂⁴×D₁₁
Fitting	C₂³×C₄²×C₁₁	C₂
socle, prime radical	C₂⁵×C₁₁	C₂×C₄
cosocle	C₂×C₄×C₁₁	C₂⁵
LCS	G ▷ C₁₁
UCS	C₁ ◁ C₂³×C₄²

Complements

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

N	H ≅ G/N	type
2. C₂²×C₄×C₁₁⋊C₈	C₂	direct (N × H)
8. C₂³×C₁₁⋊C₈	C₄	direct (N × H)
10. C₂×C₄×C₁₁⋊C₈	C₂²	direct (N × H)
12. C₂³×C₄×C₁₁	C₈	semidirect
19. C₂²×C₁₁⋊C₈	C₂×C₄	direct (N × H)
21. C₄×C₁₁⋊C₈	C₂³	direct (N × H)
27. C₂²×C₄×C₁₁	C₂×C₈	semidirect
34. C₂×C₁₁⋊C₈	C₂²×C₄	direct (N × H)
39. C₂³×C₁₁	C₄×C₈	semidirect
44. C₂×C₄×C₁₁	C₂²×C₈	semidirect
49. C₁₁⋊C₈	C₂³×C₄	direct (N × H)
57. C₂²×C₁₁	C₂×C₄×C₈	semidirect
62. C₄×C₁₁	C₂³×C₈	semidirect
65. C₂³×C₄	C₁₁⋊C₈	direct (N × H)
75. C₂×C₁₁	C₂²×C₄×C₈	semidirect
81. C₂²×C₄	C₂×C₁₁⋊C₈	direct (N × H)
91. C₁₁	C₂³×C₄×C₈	semidirect
92. C₂³	C₄×C₁₁⋊C₈	direct (N × H)
96. C₂×C₄	C₂²×C₁₁⋊C₈	direct (N × H)
103. C₂²	C₂×C₄×C₁₁⋊C₈	direct (N × H)
107. C₄	C₂³×C₁₁⋊C₈	direct (N × H)
110. C₂	C₂²×C₄×C₁₁⋊C₈	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×C₁₁⋊C₈	2
C₂²×C₄×C₁₁⋊C₈	2
C₂³×C₄²×C₁₁	2
C₂³×C₄×C₈	11

Subgroups — C23×C4×C11⋊C8 #15617153

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂³×C₄×C₁₁⋊C₈ #15617153