Subgroups — C₄₇⋊#1309 #20241301

Order 6016.

146 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#15689147	C₂	1	2	yes	maximal
2	C₄₇×#423	C₂	1	1	yes	maximal, characteristic
3	C₂×#10625329	C₄	1	4	yes	—
4	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
5	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
6	C₂×M₁₆×C₄₇	C₄	1	2	yes	—
7	C₂×C₄²×C₄₇	C₂²	1	1	yes	characteristic
8	C₄⋊C₈×C₄₇	—	2	2	no	—
9	C₂²×C₄×C₄₇	C₂×C₄	1	2	yes	—
10	C₂²×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
11	M₁₆×C₄₇	—	4	2	no	—
12	C₂×C₈×C₄₇	—	2	2	no	—
13	C₄²×C₄₇	D₄	1	1	yes	characteristic
14	C₄²×C₄₇	D₄	1	2	yes	—
15	C₄²×C₄₇	Q₈	1	1	yes	characteristic
16	#10625329	—	4	4	no	—
17	C₂×C₄₇⋊C₈	—	2	4	no	—
18	C₂³×C₄₇	C₄²	1	1	yes	characteristic
19	C₂×C₄×C₄₇	—	2	2	no	—
20	C₂×C₄×C₄₇	—	2	1	no	—
21	C₂×C₄×C₄₇	—	2	2	no	—
22	C₂×C₄×C₄₇	—	2	1	no	—
23	C₂×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
24	C₂×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
25	C₂×C₄×C₄₇	C₄⋊C₄	1	2	yes	—
26	C₂×C₄×C₄₇	C₄⋊C₄	1	1	yes	characteristic
27	C₈×C₄₇	—	4	2	no	—
28	C₄₇⋊C₈	—	4	4	no	—
29	C₂²×C₄₇	—	2	2	no	—
30	C₂²×C₄₇	—	2	1	no	—
31	C₂²×C₄₇	#95	1	1	yes	characteristic
32	C₄×C₄₇	—	2	2	no	—
33	C₄×C₄₇	—	2	1	no	—
34	C₄×C₄₇	#100	1	2	yes	—
35	C₄×C₄₇	#100	1	1	yes	characteristic
36	C₄×C₄₇	#101	1	2	yes	—
37	C₄×C₄₇	#101	1	1	yes	characteristic
38	#1309	—	47	1	no	maximal, Sylow
39	C₂×C₄₇	—	4	1	no	—
40	C₂×C₄₇	#343	1	2	yes	—
41	C₂×C₄₇	#343	1	1	yes	characteristic
42	#423	—	47	2	no	—
43	#423	D₄₇	1	1	yes	characteristic
44	C₄₇	#1309	1	1	yes	characteristic, complemented, Sylow
45	C₂×M₁₆	—	47	4	no	—
46	C₂×M₁₆	Dic₄₇	1	2	yes	—
47	C₂×C₄²	C₂×D₄₇	1	1	yes	characteristic
48	C₄⋊C₈	—	2	2	no	—
49	C₄⋊C₈	—	94	2	no	—
50	C₄⋊C₈	—	94	2	no	—
51	C₂²×C₄	C₄×D₄₇	1	2	yes	—
52	C₂²×C₄	C₂×Dic₄₇	1	1	yes	characteristic
53	M₁₆	—	4	2	no	—
54	M₁₆	—	188	4	no	—
55	C₂×C₈	—	2	2	no	—
56	C₂×C₈	—	94	4	no	—
57	C₄²	Dic₉₄	1	1	yes	characteristic
58	C₄²	D₁₈₈	1	1	yes	characteristic
59	C₄²	C₂²⋊D₄₇	1	2	yes	—
60	C₂³	C₄×Dic₄₇	1	1	yes	characteristic
61	C₂×C₄	—	2	2	no	—
62	C₂×C₄	—	2	1	no	—
63	C₂×C₄	—	2	2	no	—
64	C₂×C₄	—	2	1	no	—
65	C₂×C₄	Dic₄₇⋊C₄	1	2	yes	—
66	C₂×C₄	C₄⋊Dic₄₇	1	1	yes	characteristic
67	C₂×C₄	(C₂×D₄₇)⋊C₄	1	2	yes	—
68	C₂×C₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
69	C₈	—	4	2	no	—
70	C₈	—	188	4	no	—
71	C₂²	—	2	2	no	—
72	C₂²	—	2	1	no	—
73	C₂²	C₄₇⋊#95	1	1	yes	characteristic
74	C₄	—	2	2	no	—
75	C₄	—	2	1	no	—
76	C₄	#13093940	1	2	yes	—
77	C₄	#13093941	1	1	yes	characteristic
78	C₄	#13093942	1	2	yes	—
79	C₄	#13093943	1	1	yes	characteristic
80	C₂	—	4	1	no	—
81	C₂	#15688891	1	2	yes	—
82	C₂	#15688892	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₄₇⋊#95
commutator	C₂³×C₄₇	C₄²
Frattini	C₂×C₄²	C₂×D₄₇
Fitting	C₄₇×#423	C₂
socle	C₂²×C₄₇	#95
hypercenter	#423	D₄₇
hypocenter	C₄₇	#1309
LCS	G ▷ C₂³×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #423

Complements

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

N	H ≅ G/N	type
44. C₄₇	#1309	semidirect

Subgroups — C47⋊#1309 #20241301

Conjugacy classes of subgroups

Complements

Subgroups — C₄₇⋊#1309 #20241301