Subgroups — C₄₇×#7464 #26047162

Order 12032.

76 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₇×#1397	C₂	1	1	yes	maximal, characteristic
2	C₄₇×#1373	C₂	1	2	yes	maximal
3	C₂×C₃₂×C₄₇	C₄	1	1	yes	characteristic
4	C₂×C₃₂×C₄₇	C₄	1	1	yes	characteristic
5	C₄₇×#364	—	2	2	no	—
6	C₄×C₁₆×C₄₇	C₂²	1	1	yes	characteristic
7	M₃₂×C₄₇	—	4	2	no	—
8	C₂×C₁₆×C₄₇	C₂×C₄	1	1	yes	characteristic
9	C₂×C₁₆×C₄₇	Q₈	1	1	yes	characteristic
10	C₄×C₈×C₄₇	D₄	1	1	yes	characteristic
11	C₃₂×C₄₇	—	2	1	no	—
12	C₃₂×C₄₇	C₈	1	2	yes	—
13	C₂×C₈×C₄₇	C₄⋊C₄	1	1	yes	characteristic
14	C₂×C₈×C₄₇	D₈	1	1	yes	characteristic
15	C₄²×C₄₇	Q₁₆	1	1	yes	characteristic
16	C₁₆×C₄₇	—	2	1	no	—
17	C₁₆×C₄₇	—	8	2	no	—
18	C₁₆×C₄₇	C₂×C₈	1	1	yes	characteristic
19	C₁₆×C₄₇	M₁₆	1	1	yes	characteristic
20	C₂×C₄×C₄₇	—	2	1	no	—
21	C₂×C₄×C₄₇	#107	1	1	yes	characteristic
22	C₈×C₄₇	C₄⋊C₈	1	1	yes	characteristic
23	C₈×C₄₇	#108	1	1	yes	characteristic
24	C₈×C₄₇	SD₃₂	1	2	yes	—
25	#7464	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
26	C₂²×C₄₇	#368	1	1	yes	characteristic
27	C₄×C₄₇	—	4	1	no	—
28	C₄×C₄₇	#335	1	1	yes	characteristic
29	C₄×C₄₇	#367	1	1	yes	characteristic
30	#1397	C₂×C₄₇	1	1	yes	characteristic
31	#1373	C₂×C₄₇	1	2	yes	—
32	C₂×C₄₇	—	2	1	no	—
33	C₂×C₄₇	#1372	1	1	yes	characteristic
34	C₂×C₃₂	C₄×C₄₇	1	1	yes	characteristic
35	C₂×C₃₂	C₄×C₄₇	1	1	yes	characteristic
36	#364	—	2	2	no	—
37	C₄×C₁₆	C₂²×C₄₇	1	1	yes	characteristic
38	C₄₇	#7464	1	1	yes	characteristic, direct product factor, Sylow
39	M₃₂	—	4	2	no	—
40	C₂×C₁₆	C₂×C₄×C₄₇	1	1	yes	characteristic
41	C₂×C₁₆	Q₈×C₄₇	1	1	yes	characteristic
42	C₄×C₈	D₄×C₄₇	1	1	yes	characteristic
43	C₃₂	—	2	1	no	—
44	C₃₂	C₈×C₄₇	1	2	yes	—
45	C₂×C₈	C₄⋊C₄×C₄₇	1	1	yes	characteristic
46	C₂×C₈	D₈×C₄₇	1	1	yes	characteristic
47	C₄²	Q₁₆×C₄₇	1	1	yes	characteristic
48	C₁₆	—	2	1	no	—
49	C₁₆	—	8	2	no	—
50	C₁₆	C₂×C₈×C₄₇	1	1	yes	characteristic
51	C₁₆	M₁₆×C₄₇	1	1	yes	characteristic
52	C₂×C₄	—	2	1	no	—
53	C₂×C₄	#107×C₄₇	1	1	yes	characteristic
54	C₈	C₄⋊C₈×C₄₇	1	1	yes	characteristic
55	C₈	#108×C₄₇	1	1	yes	characteristic
56	C₈	SD₃₂×C₄₇	1	2	yes	—
57	C₂²	C₄₇×#368	1	1	yes	characteristic
58	C₄	—	4	1	no	—
59	C₄	C₄₇×#335	1	1	yes	characteristic
60	C₄	C₄₇×#367	1	1	yes	characteristic
61	C₂	—	2	1	no	—
62	C₂	C₄₇×#1372	1	1	yes	characteristic

	subgroup	G/H
center	C₄×C₄₇	#367
commutator	C₁₆	C₂×C₈×C₄₇
Frattini, cosocle	C₄×C₁₆	C₂²×C₄₇
socle	C₂×C₄₇	#1372
prime radical	C₂²×C₄₇	#368
LCS	G ▷ C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₄₇ ◁ C₂×C₈×C₄₇ ◁ C₄×C₈×C₄₇ ◁ C₄×C₁₆×C₄₇ ◁ G

Complements

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

N	H ≅ G/N	type
25. #7464	C₄₇	direct (N × H)
38. C₄₇	#7464	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×#1397	2
C₄₇×#1373	2
#7464	47

Subgroups — C47×#7464 #26047162

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₇×#7464 #26047162