Subgroups — C₄₇×#7545 #26047243

Order 12032.

66 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₇×C₆₄	C₂	1	1	yes	maximal, characteristic
2	C₄₇×#1423	C₂	1	2	yes	maximal
3	C₂×C₃₂×C₄₇	C₂²	1	1	yes	characteristic
4	C₄₇×#366	—	2	2	no	—
5	C₄₇×C₆₄	C₄	1	2	yes	complemented
6	C₂×C₁₆×C₄₇	D₄	1	1	yes	characteristic
7	#107×C₄₇	—	4	2	no	—
8	C₃₂×C₄₇	C₂×C₄	1	1	yes	characteristic
9	C₃₂×C₄₇	Q₈	1	1	yes	characteristic
10	C₂×C₈×C₄₇	D₈	1	1	yes	characteristic
11	C₄⋊C₄×C₄₇	—	8	2	no	—
12	C₁₆×C₄₇	C₄⋊C₄	1	1	yes	characteristic
13	C₁₆×C₄₇	Q₁₆	1	1	yes	characteristic
14	C₂×C₄×C₄₇	—	16	2	no	—
15	C₂×C₄×C₄₇	D₁₆	1	1	yes	characteristic
16	C₈×C₄₇	#107	1	1	yes	characteristic
17	C₈×C₄₇	Q₃₂	1	1	yes	characteristic
18	#7545	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
19	C₂²×C₄₇	D₃₂	1	1	yes	characteristic
20	C₄×C₄₇	—	32	2	no	—
21	C₄×C₄₇	#366	1	1	yes	characteristic
22	C₄×C₄₇	Q₆₄	1	1	yes	characteristic
23	C₂×C₆₄	C₂×C₄₇	1	1	yes	characteristic
24	#1423	C₂×C₄₇	1	2	yes	—
25	C₂×C₄₇	#1423	1	1	yes	characteristic
26	C₂×C₄₇	D₆₄	1	1	yes	characteristic
27	C₂×C₄₇	Q₁₂₈	1	1	yes	characteristic
28	C₂×C₃₂	C₂²×C₄₇	1	1	yes	characteristic
29	#366	—	2	2	no	—
30	C₆₄	C₄×C₄₇	1	2	yes	complemented
31	C₄₇	#7545	1	1	yes	characteristic, direct product factor, Sylow
32	C₂×C₁₆	D₄×C₄₇	1	1	yes	characteristic
33	#107	—	4	2	no	—
34	C₃₂	C₂×C₄×C₄₇	1	1	yes	characteristic
35	C₃₂	Q₈×C₄₇	1	1	yes	characteristic
36	C₂×C₈	D₈×C₄₇	1	1	yes	characteristic
37	C₄⋊C₄	—	8	2	no	—
38	C₁₆	C₄⋊C₄×C₄₇	1	1	yes	characteristic
39	C₁₆	Q₁₆×C₄₇	1	1	yes	characteristic
40	C₂×C₄	—	16	2	no	—
41	C₂×C₄	D₁₆×C₄₇	1	1	yes	characteristic
42	C₈	#107×C₄₇	1	1	yes	characteristic
43	C₈	Q₃₂×C₄₇	1	1	yes	characteristic
44	C₂²	C₄₇×D₃₂	1	1	yes	characteristic
45	C₄	—	32	2	no	—
46	C₄	C₄₇×#366	1	1	yes	characteristic
47	C₄	C₄₇×Q₆₄	1	1	yes	characteristic
48	C₂	C₄₇×#1423	1	1	yes	characteristic
49	C₂	C₄₇×D₆₄	1	1	yes	characteristic
50	C₂	C₄₇×Q₁₂₈	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂²×C₄₇	D₃₂
commutator	C₃₂	C₂×C₄×C₄₇
Frattini, cosocle	C₂×C₃₂	C₂²×C₄₇
LCS	G ▷ C₃₂ ▷ C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄₇ ◁ C₂×C₄×C₄₇ ◁ C₂×C₈×C₄₇ ◁ C₂×C₁₆×C₄₇ ◁ C₂×C₃₂×C₄₇ ◁ G

Complements

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

N	H ≅ G/N	type
5. C₄₇×C₆₄	C₄	semidirect
18. #7545	C₄₇	direct (N × H)
30. C₆₄	C₄×C₄₇	semidirect
31. C₄₇	#7545	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×C₄₇×C₆₄	2
C₄₇×#1423	2
#7545	47

Subgroups — C47×#7545 #26047243

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₇×#7545 #26047243