Subgroups — #20241687

Order 6016.

178 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#15689174	C₂	1	3	yes	maximal
2	#15688845	C₂	1	3	yes	maximal, complemented
3	C₈²×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄²×D₄₇	C₂²	1	1	yes	characteristic
5	Dic₄₇⋊C₈	C₄	1	6	yes	—
6	(C₂×D₄₇)⋊C₈	C₄	1	6	yes	—
7	C₄×C₄₇⋊C₈	C₂²	1	3	yes	—
8	C₄×C₈×C₄₇	C₂²	1	3	yes	—
9	C₂×C₄×D₄₇	C₂×C₄	1	3	yes	—
10	C₂×C₈×C₄₇	C₂×C₄	1	6	yes	—
11	C₄²×C₄₇	C₂³	1	1	yes	characteristic
12	C₄×Dic₄₇	C₂×C₄	1	3	yes	—
13	C₂×C₄₇⋊C₈	C₂×C₄	1	6	yes	—
14	C₂²×D₄₇	C₄²	1	1	yes	characteristic
15	C₂×C₄×C₄₇	C₂²×C₄	1	3	yes	—
16	C₂×Dic₄₇	C₄²	1	3	yes	—
17	C₄×D₄₇	—	2	6	no	—
18	C₈×C₄₇	—	2	6	no	—
19	C₄₇⋊C₈	—	2	6	no	—
20	C₂²×C₄₇	C₂×C₄²	1	1	yes	characteristic
21	C₂×D₄₇	—	2	3	no	—
22	C₄×C₄₇	#131	1	6	yes	—
23	Dic₄₇	—	2	3	no	—
24	#1454	—	47	1	no	maximal, Sylow
25	C₂×C₄₇	#405	1	3	yes	—
26	D₄₇	—	4	1	no	—
27	#431	—	47	3	no	—
28	#322	—	47	3	no	—
29	C₈²	D₄₇	1	1	yes	characteristic, complemented
30	C₄₇	#1454	1	1	yes	characteristic, complemented, Sylow
31	C₂×C₄²	—	47	1	no	—
32	C₄⋊C₈	—	47	6	no	—
33	C₂²⋊C₈	—	47	6	no	—
34	C₄×C₈	—	47	3	no	—
35	C₄×C₈	C₂×D₄₇	1	3	yes	—
36	C₂²×C₄	—	47	3	no	—
37	C₂×C₈	—	47	6	no	—
38	C₂×C₈	C₄×D₄₇	1	6	yes	—
39	C₄²	—	47	3	no	—
40	C₄²	C₂²×D₄₇	1	1	yes	characteristic
41	C₂³	—	47	1	no	—
42	C₂×C₄	—	47	3	no	—
43	C₂×C₄	—	94	6	no	—
44	C₂×C₄	C₂×C₄×D₄₇	1	3	yes	—
45	C₈	—	2	6	no	—
46	C₈	—	94	6	no	—
47	C₂²	—	94	3	no	—
48	C₂²	C₄²×D₄₇	1	1	yes	characteristic
49	C₄	—	94	3	no	—
50	C₄	#13094030	1	6	yes	—
51	C₂	—	188	1	no	—
52	C₂	#15689077	1	3	yes	—

	subgroup	G/H
center, Frattini	C₄²	C₂²×D₄₇
commutator, socle	C₂²×C₄₇	C₂×C₄²
Fitting	C₈²×C₄₇	C₂
hypercenter	C₈²	D₄₇
hypocenter	C₄₇	#1454
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₄² ◁ C₈²

Complements

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

N	H ≅ G/N	type
2. #15688845	C₂	semidirect
3. C₈²×C₄₇	C₂	semidirect
29. C₈²	D₄₇	semidirect
30. C₄₇	#1454	semidirect