Subgroups — #20241453

Order 6016.

68 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#15688899	C₂	1	1	yes	maximal, characteristic
2	#15688874	C₂	1	1	yes	maximal, characteristic
3	C₄₇×#334	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄₇⋊C₁₆	C₄	1	1	yes	characteristic
5	C₂×C₄₇⋊C₁₆	C₄	1	1	yes	characteristic
6	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
7	C₄⋊C₈×C₄₇	—	2	1	no	—
8	C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
9	C₂×C₈×C₄₇	—	4	1	no	—
10	C₂×C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
11	C₂×C₈×C₄₇	Q₈	1	1	yes	characteristic
12	C₄²×C₄₇	D₄	1	1	yes	characteristic
13	C₂×C₄₇⋊C₈	—	4	1	no	—
14	C₄₇⋊C₁₆	—	2	1	no	—
15	C₄₇⋊C₁₆	C₈	1	2	yes	complemented
16	C₂×C₄×C₄₇	C₄⋊C₄	1	1	yes	characteristic
17	C₂×C₄×C₄₇	SD₁₆	1	1	yes	characteristic
18	C₂×C₄×C₄₇	SD₁₆	1	1	yes	characteristic
19	C₈×C₄₇	—	2	1	no	—
20	C₈×C₄₇	—	8	1	no	—
21	C₈×C₄₇	C₂×C₈	1	1	yes	characteristic
22	C₈×C₄₇	M₁₆	1	1	yes	characteristic
23	C₄₇⋊C₈	—	8	1	no	—
24	C₂²×C₄₇	#106	1	1	yes	characteristic
25	C₄×C₄₇	—	2	1	no	—
26	C₄×C₄₇	—	2	1	no	—
27	C₄×C₄₇	C₄⋊C₈	1	1	yes	characteristic
28	C₄×C₄₇	#108	1	1	yes	characteristic
29	#1368	—	47	1	no	maximal, Sylow
30	C₂×C₄₇	#334	1	1	yes	characteristic
31	C₂×C₄₇	#365	1	1	yes	characteristic
32	C₂×C₄₇	#365	1	1	yes	characteristic
33	#346	—	47	1	no	—
34	#334	—	47	1	no	—
35	#334	D₄₇	1	1	yes	characteristic
36	C₄₇	#1368	1	1	yes	characteristic, complemented, Sylow
37	C₂×C₁₆	—	47	1	no	—
38	C₂×C₁₆	—	47	1	no	—
39	C₄⋊C₈	—	2	1	no	—
40	C₄⋊C₈	—	94	1	no	—
41	C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
42	C₂×C₈	—	4	1	no	—
43	C₂×C₈	—	188	1	no	—
44	C₂×C₈	Dic₉₄	1	1	yes	characteristic
45	C₂×C₈	C₄×D₄₇	1	1	yes	characteristic
46	C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
47	C₁₆	—	47	2	no	—
48	C₁₆	—	94	1	no	—
49	C₂×C₄	Dic₄₇⋊C₄	1	1	yes	characteristic
50	C₂×C₄	#10625335	1	1	yes	characteristic
51	C₂×C₄	#10625336	1	1	yes	characteristic
52	C₈	—	2	1	no	—
53	C₈	—	8	1	no	—
54	C₈	—	376	1	no	—
55	C₈	C₈×D₄₇	1	1	yes	characteristic
56	C₈	#10625324	1	1	yes	characteristic
57	C₂²	#13093955	1	1	yes	characteristic
58	C₄	—	2	1	no	—
59	C₄	—	2	1	no	—
60	C₄	Dic₄₇⋊C₈	1	1	yes	characteristic
61	C₄	#13093959	1	1	yes	characteristic
62	C₂	#15688873	1	1	yes	characteristic
63	C₂	#15688945	1	1	yes	characteristic
64	C₂	#15688947	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#13093955
commutator	C₈×C₄₇	C₂×C₈
Frattini	C₄×C₈	C₂×D₄₇
Fitting	C₄₇×#334	C₂
socle	C₂²×C₄₇	#106
hypercenter	#334	D₄₇
hypocenter	C₄₇	#1368
LCS	G ▷ C₈×C₄₇ ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #334

Complements

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

N	H ≅ G/N	type
15. C₄₇⋊C₁₆	C₈	semidirect
36. C₄₇	#1368	semidirect