Subgroups — #20242975

Order 6016.

214 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#15689521	C₂	1	3	yes	maximal, complemented
2	#15689496	C₂	1	3	yes	maximal
3	C₈²×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#10625325	—	2	6	no	—
5	#13094024	C₂²	1	3	yes	—
6	#13094021	C₂²	1	1	yes	characteristic
7	#13093956	—	2	6	no	—
8	C₄×C₈×C₄₇	C₂²	1	3	yes	—
9	C₂×D₁₈₈	—	2	3	no	—
10	C₂×Dic₉₄	—	2	3	no	—
11	C₂×C₈×C₄₇	D₄	1	6	yes	—
12	C₄²×C₄₇	C₂³	1	1	yes	characteristic
13	C₄⋊Dic₄₇	—	2	6	no	—
14	#10625325	—	4	12	no	—
15	C₂²×D₄₇	—	4	1	no	—
16	C₂×C₄×C₄₇	C₂×D₄	1	3	yes	—
17	C₂×Dic₄₇	—	4	3	no	—
18	D₁₈₈	—	4	6	no	—
19	Dic₉₄	—	4	6	no	—
20	C₈×C₄₇	SD₁₆	1	12	yes	complemented
21	C₂²×C₄₇	#127	1	1	yes	characteristic
22	C₂×D₄₇	—	8	3	no	—
23	C₄×C₄₇	C₂×SD₁₆	1	6	yes	—
24	Dic₄₇	—	8	3	no	—
25	#1705	—	47	1	no	maximal, Sylow
26	C₂×C₄₇	#492	1	3	yes	—
27	D₄₇	—	16	1	no	—
28	#498	—	47	3	no	—
29	#492	—	47	3	no	—
30	C₈²	D₄₇	1	1	yes	characteristic, complemented
31	C₄₇	#1705	1	1	yes	characteristic, complemented, Sylow
32	C₂×SD₁₆	—	94	6	no	—
33	C₄⋊Q₈	—	47	3	no	—
34	#127	—	47	1	no	—
35	#106	—	94	6	no	—
36	C₄×C₈	C₂×D₄₇	1	3	yes	—
37	C₂×Q₈	—	94	3	no	—
38	C₂×D₄	—	94	3	no	—
39	SD₁₆	—	188	12	no	—
40	C₂×C₈	D₁₈₈	1	6	yes	—
41	C₄⋊C₄	—	94	6	no	—
42	C₄²	C₂²×D₄₇	1	1	yes	characteristic
43	C₂³	—	188	1	no	—
44	Q₈	—	188	6	no	—
45	D₄	—	188	6	no	—
46	C₂×C₄	—	188	3	no	—
47	C₂×C₄	C₂×D₁₈₈	1	3	yes	—
48	C₈	#10625325	1	12	yes	complemented
49	C₂²	—	376	3	no	—
50	C₂²	#13094021	1	1	yes	characteristic
51	C₄	—	376	3	no	—
52	C₄	C₂×#10625325	1	6	yes	—
53	C₂	—	752	1	no	—
54	C₂	#15689496	1	3	yes	—

	subgroup	G/H
center	C₂²	#13094021
commutator	C₄²×C₄₇	C₂³
Frattini	C₄²	C₂²×D₄₇
Fitting	C₈²×C₄₇	C₂
socle	C₂²×C₄₇	#127
hypercenter	C₈²	D₄₇
hypocenter	C₄₇	#1705
LCS	G ▷ C₄²×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₈²

Complements

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

N	H ≅ G/N	type
1. #15689521	C₂	semidirect
3. C₈²×C₄₇	C₂	semidirect
20. C₈×C₄₇	SD₁₆	semidirect
30. C₈²	D₄₇	semidirect
31. C₄₇	#1705	semidirect
48. C₈	#10625325	semidirect