Subgroups — C₄₇×#1709 #20239319

Order 6016.

212 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₇×#494	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄₇×#493	C₂	1	1	yes	maximal, characteristic
3	C₄₇×#486	C₂	1	4	yes	maximal, complemented
4	C₈²×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×Q₁₆×C₄₇	—	2	2	no	—
6	C₂×D₈×C₄₇	—	2	2	no	—
7	C₄⋊Q₈×C₄₇	C₂²	1	2	yes	—
8	#127×C₄₇	C₂²	1	2	yes	—
9	#102×C₄₇	—	2	8	no	—
10	C₄×C₈×C₄₇	C₂²	1	2	yes	—
11	C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
12	C₂×Q₈×C₄₇	—	2	2	no	—
13	C₂×D₄×C₄₇	—	2	2	no	—
14	C₂×D₄×C₄₇	—	2	4	no	—
15	Q₁₆×C₄₇	—	4	4	no	—
16	D₈×C₄₇	—	4	4	no	—
17	C₂×C₈×C₄₇	D₄	1	4	yes	—
18	C₂×C₈×C₄₇	D₄	1	2	yes	—
19	C₄⋊C₄×C₄₇	—	2	4	no	—
20	C₄²×C₄₇	C₂³	1	1	yes	characteristic
21	C₂³×C₄₇	—	4	2	no	—
22	Q₈×C₄₇	—	4	4	no	—
23	D₄×C₄₇	—	4	4	no	—
24	D₄×C₄₇	—	4	8	no	—
25	C₂×C₄×C₄₇	—	4	2	no	—
26	C₂×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
27	C₂×C₄×C₄₇	C₂×D₄	1	2	yes	—
28	C₈×C₄₇	—	2	4	no	—
29	C₈×C₄₇	D₈	1	4	yes	—
30	C₂²×C₄₇	—	8	2	no	—
31	C₂²×C₄₇	—	8	4	no	—
32	C₂²×C₄₇	#127	1	1	yes	characteristic
33	C₄×C₄₇	—	8	2	no	—
34	C₄×C₄₇	C₂×D₈	1	2	yes	—
35	C₄×C₄₇	#135	1	4	yes	—
36	#1709	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
37	C₂×C₄₇	—	16	2	no	—
38	C₂×C₄₇	#493	1	1	yes	characteristic
39	C₂×C₄₇	#495	1	2	yes	—
40	#494	C₂×C₄₇	1	1	yes	characteristic, complemented
41	#493	C₂×C₄₇	1	1	yes	characteristic
42	#486	C₂×C₄₇	1	4	yes	complemented
43	C₈²	C₂×C₄₇	1	1	yes	characteristic, complemented
44	C₄₇	#1709	1	1	yes	characteristic, direct product factor, Sylow
45	C₂×Q₁₆	—	2	2	no	—
46	C₂×D₈	—	2	2	no	—
47	C₄⋊Q₈	C₂²×C₄₇	1	2	yes	—
48	#127	C₂²×C₄₇	1	2	yes	—
49	#102	—	2	8	no	—
50	C₄×C₈	C₂²×C₄₇	1	2	yes	—
51	C₄×C₈	C₂²×C₄₇	1	1	yes	characteristic
52	C₂×Q₈	—	2	2	no	—
53	C₂×D₄	—	2	4	no	—
54	C₂×D₄	—	2	2	no	—
55	Q₁₆	—	4	4	no	—
56	D₈	—	4	4	no	—
57	C₂×C₈	D₄×C₄₇	1	4	yes	—
58	C₂×C₈	D₄×C₄₇	1	2	yes	—
59	C₄⋊C₄	—	2	4	no	—
60	C₄²	C₂³×C₄₇	1	1	yes	characteristic
61	C₂³	—	4	2	no	—
62	Q₈	—	4	4	no	—
63	D₄	—	4	4	no	—
64	D₄	—	4	8	no	—
65	C₂×C₄	—	4	2	no	—
66	C₂×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
67	C₂×C₄	C₂×D₄×C₄₇	1	2	yes	—
68	C₈	—	2	4	no	—
69	C₈	D₈×C₄₇	1	4	yes	—
70	C₂²	—	8	2	no	—
71	C₂²	—	8	4	no	—
72	C₂²	#127×C₄₇	1	1	yes	characteristic
73	C₄	—	8	2	no	—
74	C₄	C₂×D₈×C₄₇	1	2	yes	—
75	C₄	#135×C₄₇	1	4	yes	—
76	C₂	—	16	2	no	—
77	C₂	C₄₇×#493	1	1	yes	characteristic
78	C₂	C₄₇×#495	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₄₇	#127
commutator, Frattini, cosocle	C₄²	C₂³×C₄₇
prime radical	C₄₇×#493	C₂
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
1. C₄₇×#494	C₂	semidirect
3. C₄₇×#486	C₂	semidirect
4. C₈²×C₄₇	C₂	semidirect
36. #1709	C₄₇	direct (N × H)
40. #494	C₂×C₄₇	semidirect
42. #486	C₂×C₄₇	semidirect
43. C₈²	C₂×C₄₇	semidirect
44. C₄₇	#1709	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×#494	2
C₄₇×#493	2
C₄₇×#486	2
C₈²×C₄₇	2
#1709	47

Subgroups — C47×#1709 #20239319

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₇×#1709 #20239319