Subgroups — #20241585

Order 6016.

58 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#15688957	C₂	1	1	yes	maximal, characteristic
2	C₁₆×Dic₄₇	C₂	1	1	yes	maximal, characteristic
3	C₄₇×M₆₄	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄₇⋊C₁₆	C₄	1	1	yes	characteristic
5	C₈×Dic₄₇	C₄	1	1	yes	characteristic
6	C₄₇⋊C₃₂	—	2	1	no	—
7	C₂×C₁₆×C₄₇	C₂²	1	1	yes	characteristic
8	C₃₂×C₄₇	—	2	1	no	—
9	C₂×C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
10	C₄×Dic₄₇	C₈	1	1	yes	characteristic
11	C₂×C₄₇⋊C₈	C₈	1	1	yes	characteristic
12	C₁₆×C₄₇	D₄	1	1	yes	characteristic
13	C₁₆×C₄₇	Q₈	1	1	yes	characteristic
14	C₄₇⋊C₁₆	—	2	1	no	—
15	C₂×C₄×C₄₇	C₂×C₈	1	1	yes	characteristic
16	C₂×Dic₄₇	—	2	1	no	—
17	C₈×C₄₇	C₄⋊C₄	1	1	yes	characteristic
18	C₈×C₄₇	M₁₆	1	1	yes	characteristic
19	C₄₇⋊C₈	C₁₆	1	2	yes	—
20	C₂²×C₄₇	M₃₂	1	1	yes	characteristic
21	C₄×C₄₇	C₄⋊C₈	1	1	yes	characteristic
22	C₄×C₄₇	C₂×C₁₆	1	1	yes	characteristic
23	Dic₄₇	—	2	2	no	—
24	#1422	—	47	1	no	maximal, Sylow
25	C₂×C₄₇	—	2	1	no	—
26	C₂×C₄₇	C₄⋊C₁₆	1	1	yes	characteristic
27	M₆₄	—	47	1	no	—
28	M₆₄	D₄₇	1	1	yes	characteristic
29	C₄×C₁₆	—	47	1	no	—
30	C₄₇	#1422	1	1	yes	characteristic, complemented, Sylow
31	C₂×C₁₆	—	47	1	no	—
32	C₂×C₁₆	C₂×D₄₇	1	1	yes	characteristic
33	C₄×C₈	—	47	1	no	—
34	C₃₂	—	2	1	no	—
35	C₃₂	—	94	1	no	—
36	C₂×C₈	—	47	1	no	—
37	C₂×C₈	C₄×D₄₇	1	1	yes	characteristic
38	C₄²	—	47	1	no	—
39	C₁₆	—	94	1	no	—
40	C₁₆	Dic₉₄	1	1	yes	characteristic
41	C₁₆	C₂²⋊D₄₇	1	1	yes	characteristic
42	C₂×C₄	—	94	1	no	—
43	C₂×C₄	C₈×D₄₇	1	1	yes	characteristic
44	C₈	—	47	2	no	—
45	C₈	#10625324	1	1	yes	characteristic
46	C₈	Dic₄₇⋊C₄	1	1	yes	characteristic
47	C₂²	#13093963	1	1	yes	characteristic
48	C₄	—	94	2	no	—
49	C₄	Dic₄₇⋊C₈	1	1	yes	characteristic
50	C₄	C₁₆×D₄₇	1	1	yes	characteristic
51	C₂	—	2	1	no	—
52	C₂	Dic₄₇⋊C₁₆	1	1	yes	characteristic

	subgroup	G/H
center	C₁₆	C₂²⋊D₄₇
commutator	C₄×C₄₇	C₂×C₁₆
Frattini	C₂×C₁₆	C₂×D₄₇
Fitting	C₄₇×M₆₄	C₂
socle	C₂×C₄₇	C₄⋊C₁₆
hypercenter	M₆₄	D₄₇
hypocenter	C₄₇	#1422
LCS	G ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₁₆ ◁ C₂×C₁₆ ◁ M₆₄

Complements

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

N	H ≅ G/N	type
30. C₄₇	#1422	semidirect