Subgroups — C₄₇×#62624 #26102322

Order 12032.

2038 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₇×#3573	C₂	1	1	yes	maximal, characteristic
2	C₄₇×#3407	C₂	1	15	yes	maximal, complemented
3	C₂×C₄₇×#504	C₂	1	15	yes	maximal, complemented
4	C₄₇×#585	C₄	1	1	yes	characteristic
5	C₄₇×#568	C₄	1	15	yes	—
6	C₂×#131×C₄₇	C₂²	1	15	yes	—
7	C₄₇×#504	C₂²	1	20	yes	complemented
8	C₄₇×#504	C₂²	1	60	yes	complemented
9	C₂×M₃₂×C₄₇	C₂²	1	45	yes	complemented
10	C₂²×C₁₆×C₄₇	C₂²	1	15	yes	complemented
11	2₋¹⁺⁴×C₄₇	C₈	1	6	yes	—
12	H(5,𝔽₂)×C₄₇	C₈	1	10	yes	—
13	C₂×#41×C₄₇	C₂×C₄	1	15	yes	—
14	#131×C₄₇	C₂×C₄	1	60	yes	—
15	#131×C₄₇	C₂³	1	20	yes	—
16	C₂×M₁₆×C₄₇	C₂×C₄	1	45	yes	—
17	C₂²×C₈×C₄₇	C₂³	1	15	yes	—
18	M₃₂×C₄₇	C₂³	1	60	yes	—
19	C₂×C₁₆×C₄₇	C₂³	1	45	yes	—
20	C₂×C₁₆×C₄₇	C₂³	1	15	yes	—
21	#41×C₄₇	C₂×C₈	1	60	yes	—
22	#41×C₄₇	C₂²×C₄	1	20	yes	—
23	C₂×Q₈×C₄₇	C₂×C₈	1	15	yes	—
24	C₂×D₄×C₄₇	C₂×C₈	1	45	yes	—
25	C₂²×C₄×C₄₇	C₂²×C₄	1	15	yes	—
26	M₁₆×C₄₇	C₂²×C₄	1	60	yes	—
27	C₂×C₈×C₄₇	C₂²×C₄	1	45	yes	—
28	C₂×C₈×C₄₇	C₂⁴	1	15	yes	—
29	C₁₆×C₄₇	C₂⁴	1	15	yes	—
30	C₁₆×C₄₇	C₂⁴	1	1	yes	characteristic
31	C₂³×C₄₇	C₂²×C₈	1	15	yes	—
32	Q₈×C₄₇	C₂²×C₈	1	20	yes	—
33	D₄×C₄₇	C₂²×C₈	1	60	yes	—
34	C₂×C₄×C₄₇	C₂²×C₈	1	45	yes	—
35	C₂×C₄×C₄₇	C₂³×C₄	1	15	yes	—
36	C₈×C₄₇	C₂³×C₄	1	15	yes	—
37	C₈×C₄₇	C₂⁵	1	1	yes	characteristic
38	#62624	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
39	C₂²×C₄₇	—	4	15	no	—
40	C₂²×C₄₇	C₂³×C₈	1	15	yes	—
41	C₄×C₄₇	C₂³×C₈	1	15	yes	—
42	C₄×C₄₇	C₂⁴×C₄	1	1	yes	characteristic
43	#3573	C₂×C₄₇	1	1	yes	characteristic
44	#3407	C₂×C₄₇	1	15	yes	complemented
45	C₂×#504	C₂×C₄₇	1	15	yes	complemented
46	C₂×C₄₇	—	2	15	no	—
47	C₂×C₄₇	C₂⁴×C₈	1	1	yes	characteristic
48	#585	C₄×C₄₇	1	1	yes	characteristic
49	#568	C₄×C₄₇	1	15	yes	—
50	C₂×#131	C₂²×C₄₇	1	15	yes	—
51	#504	C₂²×C₄₇	1	20	yes	complemented
52	#504	C₂²×C₄₇	1	60	yes	complemented
53	C₂×M₃₂	C₂²×C₄₇	1	45	yes	complemented
54	C₂²×C₁₆	C₂²×C₄₇	1	15	yes	complemented
55	C₄₇	#62624	1	1	yes	characteristic, direct product factor, Sylow
56	2₋¹⁺⁴	C₈×C₄₇	1	6	yes	—
57	H(5,𝔽₂)	C₈×C₄₇	1	10	yes	—
58	C₂×#41	C₂×C₄×C₄₇	1	15	yes	—
59	#131	C₂×C₄×C₄₇	1	60	yes	—
60	#131	C₂³×C₄₇	1	20	yes	—
61	C₂×M₁₆	C₂×C₄×C₄₇	1	45	yes	—
62	C₂²×C₈	C₂³×C₄₇	1	15	yes	—
63	M₃₂	C₂³×C₄₇	1	60	yes	—
64	C₂×C₁₆	C₂³×C₄₇	1	15	yes	—
65	C₂×C₁₆	C₂³×C₄₇	1	45	yes	—
66	#41	C₂×C₈×C₄₇	1	60	yes	—
67	#41	C₂²×C₄×C₄₇	1	20	yes	—
68	C₂×Q₈	C₂×C₈×C₄₇	1	15	yes	—
69	C₂×D₄	C₂×C₈×C₄₇	1	45	yes	—
70	C₂²×C₄	C₂²×C₄×C₄₇	1	15	yes	—
71	M₁₆	C₂²×C₄×C₄₇	1	60	yes	—
72	C₂×C₈	C₂²×C₄×C₄₇	1	45	yes	—
73	C₂×C₈	C₂⁴×C₄₇	1	15	yes	—
74	C₁₆	C₂⁴×C₄₇	1	15	yes	—
75	C₁₆	C₂⁴×C₄₇	1	1	yes	characteristic
76	C₂³	C₂²×C₈×C₄₇	1	15	yes	—
77	Q₈	C₂²×C₈×C₄₇	1	20	yes	—
78	D₄	C₂²×C₈×C₄₇	1	60	yes	—
79	C₂×C₄	C₂²×C₈×C₄₇	1	45	yes	—
80	C₂×C₄	C₂³×C₄×C₄₇	1	15	yes	—
81	C₈	C₂³×C₄×C₄₇	1	15	yes	—
82	C₈	C₂⁵×C₄₇	1	1	yes	characteristic
83	C₂²	—	4	15	no	—
84	C₂²	C₂³×C₈×C₄₇	1	15	yes	—
85	C₄	C₂³×C₈×C₄₇	1	15	yes	—
86	C₄	C₂⁴×C₄×C₄₇	1	1	yes	characteristic
87	C₂	—	2	15	no	—
88	C₂	C₂⁴×C₈×C₄₇	1	1	yes	characteristic

	subgroup	G/H
center	C₁₆×C₄₇	C₂⁴
commutator	C₂	C₂⁴×C₈×C₄₇
Frattini, cosocle	C₈	C₂⁵×C₄₇
socle	C₂×C₄₇	C₂⁴×C₈
prime radical	C₄₇×#585	C₄
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₁₆×C₄₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₄₇×#3407	C₂	semidirect
3. C₂×C₄₇×#504	C₂	semidirect
7. C₄₇×#504	C₂²	semidirect
8. C₄₇×#504	C₂²	semidirect
9. C₂×M₃₂×C₄₇	C₂²	semidirect
10. C₂²×C₁₆×C₄₇	C₂²	semidirect
38. #62624	C₄₇	direct (N × H)
44. #3407	C₂×C₄₇	semidirect
45. C₂×#504	C₂×C₄₇	semidirect
51. #504	C₂²×C₄₇	semidirect
52. #504	C₂²×C₄₇	semidirect
53. C₂×M₃₂	C₂²×C₄₇	semidirect
54. C₂²×C₁₆	C₂²×C₄₇	semidirect
55. C₄₇	#62624	direct (N × H)

Maximal subgroups

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

subgroup	index
C₄₇×#3573	2
C₄₇×#3407	2
C₂×C₄₇×#504	2
#62624	47

Subgroups — C47×#62624 #26102322

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₇×#62624 #26102322