Subgroups — #20241569

Order 6016.

74 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₇⋊C₃₂	C₂	1	1	yes	maximal, characteristic
2	#15688949	C₂	1	1	yes	maximal, characteristic
3	C₂×Q₃₂×C₄₇	C₂	1	1	yes	maximal, characteristic
4	#13093958	—	2	1	no	—
5	C₄₇⋊C₃₂	—	2	1	no	—
6	C₂×Q₁₆×C₄₇	—	2	1	no	—
7	Q₃₂×C₄₇	—	2	1	no	—
8	Q₃₂×C₄₇	C₄	1	2	yes	complemented
9	C₂×C₁₆×C₄₇	C₂²	1	1	yes	characteristic
10	C₂×Q₈×C₄₇	—	4	1	no	—
11	Q₁₆×C₄₇	—	2	2	no	—
12	Q₁₆×C₄₇	—	4	1	no	—
13	C₂×C₈×C₄₇	D₄	1	1	yes	characteristic
14	C₄⋊Dic₄₇	—	4	1	no	—
15	C₁₆×C₄₇	C₂×C₄	1	1	yes	characteristic
16	C₁₆×C₄₇	D₄	1	1	yes	characteristic
17	Q₈×C₄₇	—	4	2	no	—
18	Q₈×C₄₇	—	8	1	no	—
19	C₂×C₄×C₄₇	—	8	1	no	—
20	C₂×C₄×C₄₇	D₈	1	1	yes	characteristic
21	C₂×Dic₄₇	—	8	1	no	—
22	C₈×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
23	C₈×C₄₇	SD₁₆	1	1	yes	characteristic
24	C₂²×C₄₇	D₁₆	1	1	yes	characteristic
25	C₄×C₄₇	—	8	2	no	—
26	C₄×C₄₇	#102	1	1	yes	characteristic
27	C₄×C₄₇	SD₃₂	1	1	yes	characteristic
28	Dic₄₇	—	16	1	no	—
29	#1416	—	47	1	no	maximal, Sylow
30	C₂×C₄₇	#357	1	1	yes	characteristic
31	C₂×C₄₇	SD₆₄	1	1	yes	characteristic
32	C₂×C₄₇	Q₆₄	1	1	yes	characteristic
33	C₂×Q₃₂	D₄₇	1	1	yes	characteristic
34	C₂×C₃₂	—	47	1	no	—
35	#366	—	47	1	no	—
36	C₄₇	#1416	1	1	yes	characteristic, complemented, Sylow
37	C₂×Q₁₆	—	2	1	no	—
38	Q₃₂	—	2	1	no	—
39	Q₃₂	Dic₄₇	1	2	yes	complemented
40	C₂×C₁₆	C₂×D₄₇	1	1	yes	characteristic
41	#107	—	94	1	no	—
42	C₃₂	—	94	1	no	—
43	C₂×Q₈	—	4	1	no	—
44	Q₁₆	—	2	2	no	—
45	Q₁₆	—	4	1	no	—
46	C₂×C₈	C₂²⋊D₄₇	1	1	yes	characteristic
47	C₄⋊C₄	—	188	1	no	—
48	C₁₆	C₂×Dic₄₇	1	1	yes	characteristic
49	C₁₆	C₂²⋊D₄₇	1	1	yes	characteristic
50	Q₈	—	4	2	no	—
51	Q₈	—	8	1	no	—
52	C₂×C₄	—	8	1	no	—
53	C₂×C₄	—	376	1	no	—
54	C₂×C₄	#10625334	1	1	yes	characteristic
55	C₈	#10625335	1	1	yes	characteristic
56	C₈	C₂²⋊Dic₄₇	1	1	yes	characteristic
57	C₂²	#13093965	1	1	yes	characteristic
58	C₄	—	8	2	no	—
59	C₄	—	752	1	no	—
60	C₄	#13093945	1	1	yes	characteristic
61	C₄	#13093968	1	1	yes	characteristic
62	C₂	#15688924	1	1	yes	characteristic
63	C₂	#15688960	1	1	yes	characteristic
64	C₂	#15688963	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#13093965
commutator	C₁₆×C₄₇	C₂×C₄
Frattini	C₂×C₁₆	C₂×D₄₇
Fitting	C₂×Q₃₂×C₄₇	C₂
socle	C₂²×C₄₇	D₁₆
hypercenter	C₂×Q₃₂	D₄₇
hypocenter	C₄₇	#1416
LCS	G ▷ C₁₆×C₄₇ ▷ C₈×C₄₇ ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ C₂×Q₃₂

Complements

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

N	H ≅ G/N	type
8. Q₃₂×C₄₇	C₄	semidirect
36. C₄₇	#1416	semidirect
39. Q₃₂	Dic₄₇	semidirect