Subgroups — #20241581

Order 6016.

70 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	#15688953	C₂	1	1	yes	maximal, characteristic
3	C₂×Q₃₂×C₄₇	C₂	1	1	yes	maximal, characteristic
4	#13093960	—	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	—
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	#10625329	—	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	C₈×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
22	C₈×C₄₇	SD₁₆	1	1	yes	characteristic
23	C₄₇⋊C₈	—	8	1	no	—
24	C₂²×C₄₇	SD₃₂	1	1	yes	characteristic
25	C₄×C₄₇	—	8	2	no	—
26	C₄×C₄₇	#102	1	1	yes	characteristic
27	C₄×C₄₇	D₁₆	1	1	yes	characteristic
28	#1420	—	47	1	no	maximal, Sylow
29	C₂×C₄₇	—	2	1	no	—
30	C₂×C₄₇	#357	1	1	yes	characteristic
31	C₂×Q₃₂	D₄₇	1	1	yes	characteristic
32	M₆₄	—	47	1	no	—
33	#368	—	47	1	no	—
34	C₄₇	#1420	1	1	yes	characteristic, complemented, Sylow
35	C₂×Q₁₆	—	2	1	no	—
36	Q₃₂	—	2	1	no	—
37	Q₃₂	Dic₄₇	1	2	yes	—
38	C₂×C₁₆	C₂×D₄₇	1	1	yes	characteristic
39	#108	—	94	1	no	—
40	C₃₂	—	94	1	no	—
41	C₂×Q₈	—	4	1	no	—
42	Q₁₆	—	2	2	no	—
43	Q₁₆	—	4	1	no	—
44	M₁₆	—	188	1	no	—
45	C₂×C₈	C₂²⋊D₄₇	1	1	yes	characteristic
46	C₁₆	C₂×Dic₄₇	1	1	yes	characteristic
47	C₁₆	C₂²⋊D₄₇	1	1	yes	characteristic
48	Q₈	—	4	2	no	—
49	Q₈	—	8	1	no	—
50	C₂×C₄	—	8	1	no	—
51	C₂×C₄	#10625334	1	1	yes	characteristic
52	C₈	—	376	1	no	—
53	C₈	#10625335	1	1	yes	characteristic
54	C₈	C₂²⋊Dic₄₇	1	1	yes	characteristic
55	C₂²	#13093968	1	1	yes	characteristic
56	C₄	—	8	2	no	—
57	C₄	#13093945	1	1	yes	characteristic
58	C₄	#13093965	1	1	yes	characteristic
59	C₂	—	2	1	no	—
60	C₂	#15688924	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#15688924
commutator	C₁₆×C₄₇	C₂×C₄
Frattini	C₂×C₁₆	C₂×D₄₇
Fitting	C₂×Q₃₂×C₄₇	C₂
socle	C₂×C₄₇	#357
hypercenter	C₂×Q₃₂	D₄₇
hypocenter	C₄₇	#1420
LCS	G ▷ C₁₆×C₄₇ ▷ C₈×C₄₇ ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ C₂×Q₃₂

Complements

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

N	H ≅ G/N	type
34. C₄₇	#1420	semidirect