Subgroups — C₄₇×#1454 #20239064

Order 6016.

178 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₇×#431	C₂	1	3	yes	maximal
2	C₄₇×#322	C₂	1	3	yes	maximal, complemented
3	C₈²×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₄²×C₄₇	C₂²	1	1	yes	characteristic
5	C₄⋊C₈×C₄₇	C₄	1	6	yes	—
6	C₂²⋊C₈×C₄₇	C₄	1	6	yes	—
7	C₄×C₈×C₄₇	C₂²	1	3	yes	—
8	C₄×C₈×C₄₇	C₂²	1	3	yes	—
9	C₂²×C₄×C₄₇	C₂×C₄	1	3	yes	—
10	C₂×C₈×C₄₇	C₂×C₄	1	6	yes	—
11	C₂×C₈×C₄₇	C₂×C₄	1	6	yes	—
12	C₄²×C₄₇	C₂×C₄	1	3	yes	—
13	C₄²×C₄₇	C₂³	1	1	yes	characteristic
14	C₂³×C₄₇	C₄²	1	1	yes	characteristic
15	C₂×C₄×C₄₇	—	2	6	no	—
16	C₂×C₄×C₄₇	C₄²	1	3	yes	—
17	C₂×C₄×C₄₇	C₂²×C₄	1	3	yes	—
18	C₈×C₄₇	—	2	6	no	—
19	C₈×C₄₇	—	2	6	no	—
20	C₂²×C₄₇	—	2	3	no	—
21	C₂²×C₄₇	C₂×C₄²	1	1	yes	characteristic
22	C₄×C₄₇	—	2	3	no	—
23	C₄×C₄₇	#131	1	6	yes	—
24	#1454	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
25	C₂×C₄₇	—	4	1	no	—
26	C₂×C₄₇	#405	1	3	yes	—
27	#431	C₂×C₄₇	1	3	yes	—
28	#322	C₂×C₄₇	1	3	yes	complemented
29	C₈²	C₂×C₄₇	1	1	yes	characteristic, complemented
30	C₄₇	#1454	1	1	yes	characteristic, direct product factor, Sylow
31	C₂×C₄²	C₂²×C₄₇	1	1	yes	characteristic
32	C₄⋊C₈	C₄×C₄₇	1	6	yes	—
33	C₂²⋊C₈	C₄×C₄₇	1	6	yes	—
34	C₄×C₈	C₂²×C₄₇	1	3	yes	—
35	C₄×C₈	C₂²×C₄₇	1	3	yes	—
36	C₂²×C₄	C₂×C₄×C₄₇	1	3	yes	—
37	C₂×C₈	C₂×C₄×C₄₇	1	6	yes	—
38	C₂×C₈	C₂×C₄×C₄₇	1	6	yes	—
39	C₄²	C₂×C₄×C₄₇	1	3	yes	—
40	C₄²	C₂³×C₄₇	1	1	yes	characteristic
41	C₂³	C₄²×C₄₇	1	1	yes	characteristic
42	C₂×C₄	—	2	6	no	—
43	C₂×C₄	C₄²×C₄₇	1	3	yes	—
44	C₂×C₄	C₂²×C₄×C₄₇	1	3	yes	—
45	C₈	—	2	6	no	—
46	C₈	—	2	6	no	—
47	C₂²	—	2	3	no	—
48	C₂²	C₂×C₄²×C₄₇	1	1	yes	characteristic
49	C₄	—	2	3	no	—
50	C₄	#131×C₄₇	1	6	yes	—
51	C₂	—	4	1	no	—
52	C₂	C₄₇×#405	1	3	yes	—

	subgroup	G/H
center	C₄²×C₄₇	C₂³
commutator	C₂²	C₂×C₄²×C₄₇
Frattini, cosocle	C₄²	C₂³×C₄₇
socle	C₂²×C₄₇	C₂×C₄²
prime radical	C₂³×C₄₇	C₄²
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₄²×C₄₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₄₇×#322	C₂	semidirect
3. C₈²×C₄₇	C₂	semidirect
24. #1454	C₄₇	direct (N × H)
28. #322	C₂×C₄₇	semidirect
29. C₈²	C₂×C₄₇	semidirect
30. C₄₇	#1454	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×#431	2
C₄₇×#322	2
C₈²×C₄₇	2
#1454	47

Subgroups — C47×#1454 #20239064

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₇×#1454 #20239064