Subgroups — #20243144

Order 6016.

200 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#15689081	C₂	1	3	yes	maximal
2	#15688880	C₂	1	3	yes	maximal
3	C₄₇×#338	C₂	1	1	yes	maximal, characteristic
4	C₂²×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
5	#13093983	C₂²	1	3	yes	—
6	#13093934	C₄	1	6	yes	complemented
7	C₈×Dic₄₇	C₄	1	6	yes	complemented
8	C₂×M₁₆×C₄₇	C₂²	1	3	yes	—
9	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
10	M₁₆×C₄₇	—	2	6	no	—
11	C₂×C₈×C₄₇	C₂×C₄	1	6	yes	—
12	C₂²⋊Dic₄₇	—	2	3	no	—
13	C₄⋊Dic₄₇	—	2	3	no	—
14	C₄×Dic₄₇	C₂×C₄	1	6	yes	—
15	C₂×C₄₇⋊C₈	C₂×C₄	1	3	yes	—
16	C₂×C₄₇⋊C₈	C₂×C₄	1	3	yes	—
17	C₂³×C₄₇	#41	1	1	yes	characteristic
18	C₂×C₄×C₄₇	C₂²×C₄	1	3	yes	—
19	C₂×C₄×C₄₇	#41	1	3	yes	—
20	C₂×Dic₄₇	—	2	6	no	—
21	C₈×C₄₇	—	2	6	no	—
22	C₄₇⋊C₈	C₄²	1	1	yes	characteristic
23	C₄₇⋊C₈	C₄²	1	3	yes	—
24	C₂²×C₄₇	—	4	1	no	—
25	C₂²×C₄₇	#117	1	3	yes	—
26	C₄×C₄₇	C₂×C₄²	1	1	yes	characteristic
27	C₄×C₄₇	#117	1	3	yes	—
28	Dic₄₇	—	4	6	no	—
29	#1747	—	47	1	no	maximal, Sylow
30	C₂×C₄₇	—	2	3	no	—
31	C₂×C₄₇	#376	1	1	yes	characteristic
32	#405	—	47	3	no	—
33	#338	D₄₇	1	1	yes	characteristic
34	H(3,ℤ/4)	—	47	3	no	—
35	C₄₇	#1747	1	1	yes	characteristic, complemented, Sylow
36	C₂×M₁₆	C₂×D₄₇	1	3	yes	—
37	C₂²×C₈	—	47	1	no	—
38	#117	—	47	3	no	—
39	#97	—	47	6	no	—
40	C₄×C₈	—	47	6	no	—
41	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
42	M₁₆	—	2	6	no	—
43	C₂×C₈	—	47	3	no	—
44	C₂×C₈	—	47	3	no	—
45	C₂×C₈	C₄×D₄₇	1	6	yes	—
46	C₄⋊C₄	—	94	3	no	—
47	C₂²⋊C₄	—	94	3	no	—
48	C₄²	—	47	6	no	—
49	C₂³	#10625354	1	1	yes	characteristic
50	C₂×C₄	—	94	6	no	—
51	C₂×C₄	C₂×C₄×D₄₇	1	3	yes	—
52	C₂×C₄	#10625352	1	3	yes	—
53	C₈	—	2	6	no	—
54	C₈	—	47	1	no	—
55	C₈	—	47	3	no	—
56	C₂²	—	4	1	no	—
57	C₂²	#13093982	1	3	yes	—
58	C₄	—	188	6	no	—
59	C₄	C₄²×D₄₇	1	1	yes	characteristic
60	C₄	#13093980	1	3	yes	—
61	C₂	—	2	3	no	—
62	C₂	#15688968	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₄²×D₄₇
commutator	C₄×C₄₇	C₂×C₄²
Frattini	C₂²×C₄	C₂²×D₄₇
Fitting	C₄₇×#338	C₂
socle	C₂×C₄₇	#376
hypercenter	#338	D₄₇
hypocenter	C₄₇	#1747
LCS	G ▷ C₄×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₄ ◁ #338

Complements

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

N	H ≅ G/N	type
6. #13093934	C₄	semidirect
7. C₈×Dic₄₇	C₄	semidirect
35. C₄₇	#1747	semidirect