Subgroups — #20241690

Order 6016.

214 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#10625324	C₂	1	3	yes	maximal
2	#15688844	C₂	1	3	yes	maximal, complemented
3	C₈²×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#10625324	C₄	1	6	yes	—
5	C₄²×D₄₇	C₂²	1	1	yes	characteristic
6	#13093934	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	#10625324	—	2	12	no	—
15	C₂²×D₄₇	C₄²	1	1	yes	characteristic
16	C₂×C₄×C₄₇	C₂²×C₄	1	3	yes	—
17	C₂×Dic₄₇	C₄²	1	3	yes	—
18	C₄×D₄₇	—	2	6	no	—
19	C₈×C₄₇	M₁₆	1	12	yes	complemented
20	C₄₇⋊C₈	—	2	6	no	—
21	C₂²×C₄₇	C₂×C₄²	1	1	yes	characteristic
22	C₂×D₄₇	—	2	3	no	—
23	C₄×C₄₇	C₂×M₁₆	1	6	yes	—
24	Dic₄₇	—	2	3	no	—
25	#1455	—	47	1	no	maximal, Sylow
26	C₂×C₄₇	C₄×M₁₆	1	3	yes	—
27	D₄₇	—	4	1	no	—
28	C₄×M₁₆	—	47	3	no	—
29	#322	—	47	3	no	—
30	C₈²	D₄₇	1	1	yes	characteristic, complemented
31	C₄₇	#1455	1	1	yes	characteristic, complemented, Sylow
32	C₂×M₁₆	—	47	6	no	—
33	C₂×C₄²	—	47	1	no	—
34	#97	—	47	6	no	—
35	C₄×C₈	—	47	3	no	—
36	C₄×C₈	C₂×D₄₇	1	3	yes	—
37	C₂²×C₄	—	47	3	no	—
38	M₁₆	—	94	12	no	—
39	C₂×C₈	—	47	6	no	—
40	C₂×C₈	C₄×D₄₇	1	6	yes	—
41	C₄²	—	47	3	no	—
42	C₄²	C₂²×D₄₇	1	1	yes	characteristic
43	C₂³	—	47	1	no	—
44	C₂×C₄	—	47	3	no	—
45	C₂×C₄	—	94	6	no	—
46	C₂×C₄	C₂×C₄×D₄₇	1	3	yes	—
47	C₈	—	94	6	no	—
48	C₈	#10625324	1	12	yes	complemented
49	C₂²	—	94	3	no	—
50	C₂²	C₄²×D₄₇	1	1	yes	characteristic
51	C₄	—	94	3	no	—
52	C₄	C₂×#10625324	1	6	yes	—
53	C₂	—	188	1	no	—
54	C₂	C₄×#10625324	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	#1455
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. #15688844	C₂	semidirect
3. C₈²×C₄₇	C₂	semidirect
19. C₈×C₄₇	M₁₆	semidirect
30. C₈²	D₄₇	semidirect
31. C₄₇	#1455	semidirect
48. C₈	#10625324	semidirect