Subgroups — C₂³×#66927 #15660460

Order 2816.

24030 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁴×D₄₄	C₂	1	6	yes	maximal, complemented
2	C₂²×#66927	C₂	1	56	yes	maximal, direct product factor
3	C₂³×C₄²×C₁₁	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂⁵×D₁₁	C₂²	1	4	yes	—
5	C₂⁴×C₄×C₁₁	C₂²	1	3	yes	—
6	C₂³×D₄₄	—	2	96	no	—
7	C₂³×D₄₄	C₂²	1	168	yes	complemented
8	C₂²×C₄²×C₁₁	C₂²	1	28	yes	complemented
9	C₂×#66927	C₂²	1	448	yes	direct product factor
10	C₂⁵×C₁₁	C₂³	1	1	yes	characteristic
11	C₂⁴×D₁₁	—	2	96	no	—
12	C₂⁴×D₁₁	C₂³	1	56	yes	—
13	C₂³×C₄×C₁₁	D₄	1	48	yes	complemented
14	C₂³×C₄×C₁₁	C₂³	1	42	yes	—
15	C₂²×D₄₄	—	2	1344	no	—
16	C₂²×D₄₄	C₂³	1	672	yes	complemented
17	C₂×C₄²×C₁₁	C₂³	1	112	yes	complemented
18	#66927	C₂³	1	512	yes	direct product factor
19	C₂³×#127	—	11	1	no	maximal, Sylow
20	C₂⁴×C₁₁	C₂×D₄	1	24	yes	—
21	C₂⁴×C₁₁	C₂⁴	1	7	yes	—
22	C₂³×D₁₁	—	2	672	no	—
23	C₂³×D₁₁	—	4	256	no	—
24	C₂³×D₁₁	C₂⁴	1	112	yes	—
25	C₂²×C₄×C₁₁	C₂×D₄	1	336	yes	complemented
26	C₂²×C₄×C₁₁	C₂⁴	1	84	yes	—
27	C₂×D₄₄	—	2	2688	no	—
28	C₂×D₄₄	C₂⁴	1	384	yes	complemented
29	C₄²×C₁₁	C₂⁴	1	64	yes	complemented
30	C₂⁴×D₄	—	11	6	no	—
31	C₂²×#127	—	11	56	no	—
32	C₂³×C₄²	D₁₁	1	1	yes	characteristic, complemented
33	C₂³×C₁₁	#127	1	64	yes	complemented
34	C₂³×C₁₁	C₂²×D₄	1	84	yes	—
35	C₂³×C₁₁	C₂⁵	1	7	yes	—
36	C₂²×D₁₁	—	2	672	no	—
37	C₂²×D₁₁	—	4	896	no	—
38	C₂²×D₁₁	C₂⁵	1	32	yes	—
39	C₂×C₄×C₁₁	C₂²×D₄	1	336	yes	complemented
40	C₂×C₄×C₁₁	C₂⁵	1	24	yes	—
41	D₄₄	—	2	768	no	—
42	C₂⁶	—	11	4	no	—
43	C₂³×D₄	—	11	168	no	—
44	C₂³×D₄	—	22	96	no	—
45	C₂⁴×C₄	C₂×D₁₁	1	3	yes	—
46	C₂×#127	—	11	448	no	—
47	C₂²×C₄²	C₂×D₁₁	1	28	yes	complemented
48	C₂²×C₁₁	C₂×#127	1	112	yes	complemented
49	C₂²×C₁₁	C₂³×D₄	1	42	yes	—
50	C₂²×C₁₁	C₂⁶	1	1	yes	characteristic
51	C₂×D₁₁	—	2	96	no	—
52	C₂×D₁₁	—	4	448	no	—
53	C₄×C₁₁	C₂³×D₄	1	48	yes	complemented
54	C₂⁵	—	11	56	no	—
55	C₂⁵	—	22	96	no	—
56	C₂⁵	C₂²×D₁₁	1	1	yes	characteristic
57	C₂²×D₄	—	11	672	no	—
58	C₂²×D₄	—	22	1344	no	—
59	C₂³×C₄	D₄₄	1	48	yes	complemented
60	C₂³×C₄	C₂²×D₁₁	1	42	yes	—
61	#127	—	11	512	no	—
62	C₂×C₄²	C₂²×D₁₁	1	112	yes	complemented
63	C₂×C₁₁	C₂²×#127	1	28	yes	complemented
64	C₂×C₁₁	C₂⁴×D₄	1	3	yes	—
65	D₁₁	—	4	32	no	—
66	C₂⁴	—	11	112	no	—
67	C₂⁴	—	22	672	no	—
68	C₂⁴	—	44	256	no	—
69	C₂⁴	C₂×D₄₄	1	24	yes	—
70	C₂⁴	C₂³×D₁₁	1	7	yes	—
71	C₂×D₄	—	11	384	no	—
72	C₂×D₄	—	22	2688	no	—
73	C₂²×C₄	C₂×D₄₄	1	336	yes	complemented
74	C₂²×C₄	C₂³×D₁₁	1	84	yes	—
75	C₄²	C₂³×D₁₁	1	64	yes	complemented
76	C₁₁	C₂³×#127	1	1	yes	characteristic, complemented, Sylow
77	C₂³	—	11	32	no	—
78	C₂³	—	22	672	no	—
79	C₂³	—	44	896	no	—
80	C₂³	#66927	1	64	yes	direct product factor
81	C₂³	C₂²×D₄₄	1	84	yes	—
82	C₂³	C₂⁴×D₁₁	1	7	yes	—
83	D₄	—	22	768	no	—
84	C₂×C₄	C₂²×D₄₄	1	336	yes	complemented
85	C₂×C₄	C₂⁴×D₁₁	1	24	yes	—
86	C₂²	—	22	96	no	—
87	C₂²	—	44	448	no	—
88	C₂²	C₂×#66927	1	112	yes	direct product factor
89	C₂²	C₂³×D₄₄	1	42	yes	—
90	C₂²	C₂⁵×D₁₁	1	1	yes	characteristic
91	C₄	C₂³×D₄₄	1	48	yes	complemented
92	C₂	—	44	32	no	—
93	C₂	C₂²×#66927	1	28	yes	direct product factor
94	C₂	C₂⁴×D₄₄	1	3	yes	—

	subgroup	G/H
center	C₂⁵	C₂²×D₁₁
commutator, cosocle	C₂²×C₁₁	C₂⁶
Frattini	C₂²	C₂⁵×D₁₁
Fitting	C₂³×C₄²×C₁₁	C₂
socle	C₂⁵×C₁₁	C₂³
hypercenter	C₂³×C₄²	D₁₁
hypocenter	C₁₁	C₂³×#127
LCS	G ▷ C₂²×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂⁵ ◁ C₂³×C₄²

Complements

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

N	H ≅ G/N	type
1. C₂⁴×D₄₄	C₂	semidirect
2. C₂²×#66927	C₂	direct (N × H)
3. C₂³×C₄²×C₁₁	C₂	semidirect
7. C₂³×D₄₄	C₂²	semidirect
8. C₂²×C₄²×C₁₁	C₂²	semidirect
9. C₂×#66927	C₂²	direct (N × H)
13. C₂³×C₄×C₁₁	D₄	semidirect
16. C₂²×D₄₄	C₂³	semidirect
17. C₂×C₄²×C₁₁	C₂³	semidirect
18. #66927	C₂³	direct (N × H)
25. C₂²×C₄×C₁₁	C₂×D₄	semidirect
28. C₂×D₄₄	C₂⁴	semidirect
29. C₄²×C₁₁	C₂⁴	semidirect
32. C₂³×C₄²	D₁₁	semidirect
33. C₂³×C₁₁	#127	semidirect
39. C₂×C₄×C₁₁	C₂²×D₄	semidirect
47. C₂²×C₄²	C₂×D₁₁	semidirect
48. C₂²×C₁₁	C₂×#127	semidirect
53. C₄×C₁₁	C₂³×D₄	semidirect
59. C₂³×C₄	D₄₄	semidirect
62. C₂×C₄²	C₂²×D₁₁	semidirect
63. C₂×C₁₁	C₂²×#127	semidirect
73. C₂²×C₄	C₂×D₄₄	semidirect
75. C₄²	C₂³×D₁₁	semidirect
76. C₁₁	C₂³×#127	semidirect
80. C₂³	#66927	direct (N × H)
84. C₂×C₄	C₂²×D₄₄	semidirect
88. C₂²	C₂×#66927	direct (N × H)
91. C₄	C₂³×D₄₄	semidirect
93. C₂	C₂²×#66927	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×D₄₄	2
C₂²×#66927	2
C₂³×C₄²×C₁₁	2
C₂³×#127	11

Subgroups — C23×#66927 #15660460

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂³×#66927 #15660460