Subgroups — C₂²×C₆₁×D₃₂ #29537408

Order 15616.

542 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×D₁₆×C₆₁	C₂	1	2	yes	maximal, complemented
2	C₂×C₆₁×D₃₂	C₂	1	12	yes	maximal, direct product factor
3	C₂²×C₃₂×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×D₈×C₆₁	—	2	2	no	—
5	C₂×D₁₆×C₆₁	—	2	6	no	—
6	C₂×D₁₆×C₆₁	C₂²	1	12	yes	complemented
7	C₂²×C₁₆×C₆₁	C₂²	1	1	yes	characteristic
8	C₆₁×D₃₂	C₂²	1	16	yes	direct product factor
9	C₂×C₃₂×C₆₁	C₂²	1	6	yes	complemented
10	C₂²×D₄×C₆₁	—	4	2	no	—
11	C₂×D₈×C₆₁	—	2	12	no	—
12	C₂×D₈×C₆₁	—	4	6	no	—
13	C₂²×C₈×C₆₁	D₄	1	1	yes	characteristic
14	D₁₆×C₆₁	—	2	12	no	—
15	D₁₆×C₆₁	C₂³	1	8	yes	complemented
16	C₂×C₁₆×C₆₁	D₄	1	3	yes	—
17	C₂×C₁₆×C₆₁	C₂³	1	3	yes	—
18	C₃₂×C₆₁	C₂³	1	4	yes	complemented
19	C₂⁴×C₆₁	—	8	2	no	—
20	C₂×D₄×C₆₁	—	4	12	no	—
21	C₂×D₄×C₆₁	—	8	6	no	—
22	C₂²×C₄×C₆₁	D₈	1	1	yes	characteristic
23	D₈×C₆₁	—	2	8	no	—
24	D₈×C₆₁	—	4	12	no	—
25	C₂×C₈×C₆₁	D₈	1	3	yes	—
26	C₂×C₈×C₆₁	C₂×D₄	1	3	yes	—
27	C₁₆×C₆₁	C₂×D₄	1	3	yes	—
28	C₁₆×C₆₁	C₂⁴	1	1	yes	characteristic
29	C₂³×C₆₁	—	8	12	no	—
30	C₂³×C₆₁	—	16	8	no	—
31	C₂³×C₆₁	D₁₆	1	1	yes	characteristic
32	D₄×C₆₁	—	4	8	no	—
33	D₄×C₆₁	—	8	12	no	—
34	C₂×C₄×C₆₁	D₁₆	1	3	yes	—
35	C₂×C₄×C₆₁	C₂×D₈	1	3	yes	—
36	C₈×C₆₁	C₂×D₈	1	3	yes	—
37	C₈×C₆₁	C₂²×D₄	1	1	yes	characteristic
38	C₂²×D₃₂	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
39	C₂²×C₆₁	—	8	8	no	—
40	C₂²×C₆₁	—	16	24	no	—
41	C₂²×C₆₁	D₃₂	1	4	yes	direct product factor
42	C₂²×C₆₁	C₂×D₁₆	1	3	yes	—
43	C₄×C₆₁	C₂×D₁₆	1	3	yes	—
44	C₄×C₆₁	C₂²×D₈	1	1	yes	characteristic
45	C₂²×D₁₆	C₂×C₆₁	1	2	yes	complemented
46	C₂×D₃₂	C₂×C₆₁	1	12	yes	direct product factor
47	C₂²×C₃₂	C₂×C₆₁	1	1	yes	characteristic, complemented
48	C₂×C₆₁	—	16	8	no	—
49	C₂×C₆₁	C₂×D₃₂	1	6	yes	direct product factor
50	C₂×C₆₁	C₂²×D₁₆	1	1	yes	characteristic
51	C₂²×D₈	—	2	2	no	—
52	C₂×D₁₆	—	2	6	no	—
53	C₂×D₁₆	C₂²×C₆₁	1	12	yes	complemented
54	C₂²×C₁₆	C₂²×C₆₁	1	1	yes	characteristic
55	D₃₂	C₂²×C₆₁	1	16	yes	direct product factor
56	C₂×C₃₂	C₂²×C₆₁	1	6	yes	complemented
57	C₆₁	C₂²×D₃₂	1	1	yes	characteristic, direct product factor, Sylow
58	C₂²×D₄	—	4	2	no	—
59	C₂×D₈	—	2	12	no	—
60	C₂×D₈	—	4	6	no	—
61	C₂²×C₈	D₄×C₆₁	1	1	yes	characteristic
62	D₁₆	—	2	12	no	—
63	D₁₆	C₂³×C₆₁	1	8	yes	complemented
64	C₂×C₁₆	D₄×C₆₁	1	3	yes	—
65	C₂×C₁₆	C₂³×C₆₁	1	3	yes	—
66	C₃₂	C₂³×C₆₁	1	4	yes	complemented
67	C₂⁴	—	8	2	no	—
68	C₂×D₄	—	4	12	no	—
69	C₂×D₄	—	8	6	no	—
70	C₂²×C₄	D₈×C₆₁	1	1	yes	characteristic
71	D₈	—	2	8	no	—
72	D₈	—	4	12	no	—
73	C₂×C₈	D₈×C₆₁	1	3	yes	—
74	C₂×C₈	C₂×D₄×C₆₁	1	3	yes	—
75	C₁₆	C₂×D₄×C₆₁	1	3	yes	—
76	C₁₆	C₂⁴×C₆₁	1	1	yes	characteristic
77	C₂³	—	8	12	no	—
78	C₂³	—	16	8	no	—
79	C₂³	D₁₆×C₆₁	1	1	yes	characteristic
80	D₄	—	4	8	no	—
81	D₄	—	8	12	no	—
82	C₂×C₄	D₁₆×C₆₁	1	3	yes	—
83	C₂×C₄	C₂×D₈×C₆₁	1	3	yes	—
84	C₈	C₂×D₈×C₆₁	1	3	yes	—
85	C₈	C₂²×D₄×C₆₁	1	1	yes	characteristic
86	C₂²	—	8	8	no	—
87	C₂²	—	16	24	no	—
88	C₂²	C₆₁×D₃₂	1	4	yes	direct product factor
89	C₂²	C₂×D₁₆×C₆₁	1	3	yes	—
90	C₄	C₂×D₁₆×C₆₁	1	3	yes	—
91	C₄	C₂²×D₈×C₆₁	1	1	yes	characteristic
92	C₂	—	16	8	no	—
93	C₂	C₂×C₆₁×D₃₂	1	6	yes	direct product factor
94	C₂	C₂²×D₁₆×C₆₁	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₆₁	D₁₆
commutator, Frattini, cosocle	C₁₆	C₂⁴×C₆₁
LCS	G ▷ C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₆₁ ◁ C₂²×C₄×C₆₁ ◁ C₂²×C₈×C₆₁ ◁ C₂²×C₁₆×C₆₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×D₁₆×C₆₁	C₂	semidirect
2. C₂×C₆₁×D₃₂	C₂	direct (N × H)
3. C₂²×C₃₂×C₆₁	C₂	semidirect
6. C₂×D₁₆×C₆₁	C₂²	semidirect
8. C₆₁×D₃₂	C₂²	direct (N × H)
9. C₂×C₃₂×C₆₁	C₂²	semidirect
15. D₁₆×C₆₁	C₂³	semidirect
18. C₃₂×C₆₁	C₂³	semidirect
38. C₂²×D₃₂	C₆₁	direct (N × H)
41. C₂²×C₆₁	D₃₂	direct (N × H)
45. C₂²×D₁₆	C₂×C₆₁	semidirect
46. C₂×D₃₂	C₂×C₆₁	direct (N × H)
47. C₂²×C₃₂	C₂×C₆₁	semidirect
49. C₂×C₆₁	C₂×D₃₂	direct (N × H)
53. C₂×D₁₆	C₂²×C₆₁	semidirect
55. D₃₂	C₂²×C₆₁	direct (N × H)
56. C₂×C₃₂	C₂²×C₆₁	semidirect
57. C₆₁	C₂²×D₃₂	direct (N × H)
63. D₁₆	C₂³×C₆₁	semidirect
66. C₃₂	C₂³×C₆₁	semidirect
88. C₂²	C₆₁×D₃₂	direct (N × H)
93. C₂	C₂×C₆₁×D₃₂	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×D₁₆×C₆₁	2
C₂×C₆₁×D₃₂	2
C₂²×C₃₂×C₆₁	2
C₂²×D₃₂	61

Subgroups — C22×C61×D32 #29537408

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₆₁×D₃₂ #29537408