Subgroups — C₄₇×#1710 #20239320

Order 6016.

168 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₇×#500	C₂	1	2	yes	maximal
2	C₄₇×#487	C₂	1	4	yes	maximal
3	C₈²×C₄₇	C₂	1	1	yes	maximal, characteristic
4	C₄⋊Q₈×C₄₇	C₂²	1	4	yes	—
5	#107×C₄₇	—	2	4	no	—
6	#103×C₄₇	—	2	8	no	—
7	C₄×C₈×C₄₇	C₂²	1	2	yes	—
8	C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
9	C₂×Q₈×C₄₇	—	2	4	no	—
10	C₂×C₈×C₄₇	D₄	1	4	yes	—
11	C₂×C₈×C₄₇	D₄	1	2	yes	—
12	C₄⋊C₄×C₄₇	—	2	4	no	—
13	C₄⋊C₄×C₄₇	—	2	4	no	—
14	C₄²×C₄₇	C₂³	1	1	yes	characteristic
15	Q₈×C₄₇	—	4	8	no	—
16	C₂×C₄×C₄₇	—	4	4	no	—
17	C₂×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
18	C₂×C₄×C₄₇	C₂×D₄	1	2	yes	—
19	C₈×C₄₇	—	2	4	no	—
20	C₈×C₄₇	Q₁₆	1	4	yes	—
21	C₂²×C₄₇	#127	1	1	yes	characteristic
22	C₄×C₄₇	—	8	4	no	—
23	C₄×C₄₇	C₂×Q₁₆	1	2	yes	—
24	C₄×C₄₇	#135	1	4	yes	—
25	#1710	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
26	C₂×C₄₇	#494	1	1	yes	characteristic
27	C₂×C₄₇	#495	1	2	yes	—
28	#500	C₂×C₄₇	1	2	yes	—
29	#487	C₂×C₄₇	1	4	yes	—
30	C₈²	C₂×C₄₇	1	1	yes	characteristic
31	C₄₇	#1710	1	1	yes	characteristic, direct product factor, Sylow
32	C₄⋊Q₈	C₂²×C₄₇	1	4	yes	—
33	#107	—	2	4	no	—
34	#103	—	2	8	no	—
35	C₄×C₈	C₂²×C₄₇	1	2	yes	—
36	C₄×C₈	C₂²×C₄₇	1	1	yes	characteristic
37	C₂×Q₈	—	2	4	no	—
38	C₂×C₈	D₄×C₄₇	1	4	yes	—
39	C₂×C₈	D₄×C₄₇	1	2	yes	—
40	C₄⋊C₄	—	2	4	no	—
41	C₄⋊C₄	—	2	4	no	—
42	C₄²	C₂³×C₄₇	1	1	yes	characteristic
43	Q₈	—	4	8	no	—
44	C₂×C₄	—	4	4	no	—
45	C₂×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
46	C₂×C₄	C₂×D₄×C₄₇	1	2	yes	—
47	C₈	—	2	4	no	—
48	C₈	Q₁₆×C₄₇	1	4	yes	—
49	C₂²	#127×C₄₇	1	1	yes	characteristic
50	C₄	—	8	4	no	—
51	C₄	C₂×Q₁₆×C₄₇	1	2	yes	—
52	C₄	#135×C₄₇	1	4	yes	—
53	C₂	C₄₇×#494	1	1	yes	characteristic
54	C₂	C₄₇×#495	1	2	yes	—

	subgroup	G/H
center, socle, prime radical	C₂²×C₄₇	#127
commutator, Frattini, cosocle	C₄²	C₂³×C₄₇
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₄₇ ◁ C₄²×C₄₇ ◁ G

Complements

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

N	H ≅ G/N	type
25. #1710	C₄₇	direct (N × H)
31. C₄₇	#1710	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×#500	2
C₄₇×#487	2
C₈²×C₄₇	2
#1710	47

Subgroups — C47×#1710 #20239320

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₇×#1710 #20239320