Subgroups — #20245663

Order 6016.

128 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#15689528	C₂	1	2	yes	maximal
2	#15688949	C₂	1	4	yes	maximal
3	C₄×C₁₆×C₄₇	C₂	1	1	yes	maximal, characteristic
4	#13094024	—	2	2	no	—
5	#13093958	—	2	2	no	—
6	#13093958	C₂²	1	4	yes	—
7	C₂×C₁₆×C₄₇	C₂²	1	2	yes	—
8	C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
9	C₂×Dic₉₄	—	4	2	no	—
10	C₂×C₈×C₄₇	D₄	1	1	yes	characteristic
11	C₂×C₈×C₄₇	C₂³	1	1	yes	characteristic
12	C₄²×C₄₇	D₄	1	1	yes	characteristic
13	C₄⋊Dic₄₇	—	2	4	no	—
14	C₄⋊Dic₄₇	—	4	2	no	—
15	C₁₆×C₄₇	Q₈	1	4	yes	complemented
16	C₂×C₄×C₄₇	D₈	1	1	yes	characteristic
17	C₂×C₄×C₄₇	D₈	1	1	yes	characteristic
18	C₂×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
19	C₂×Dic₄₇	—	4	4	no	—
20	Dic₉₄	—	8	4	no	—
21	C₈×C₄₇	Q₁₆	1	2	yes	—
22	C₈×C₄₇	C₂×Q₈	1	2	yes	—
23	C₂²×C₄₇	C₂×D₈	1	1	yes	characteristic
24	C₄×C₄₇	D₁₆	1	2	yes	—
25	C₄×C₄₇	Q₃₂	1	2	yes	—
26	C₄×C₄₇	C₄⋊Q₈	1	1	yes	characteristic
27	C₄×C₄₇	C₂×Q₁₆	1	1	yes	characteristic
28	Dic₄₇	—	8	4	no	—
29	#2252	—	47	1	no	maximal, Sylow
30	C₂×C₄₇	#500	1	1	yes	characteristic
31	C₂×C₄₇	C₂×D₁₆	1	1	yes	characteristic
32	C₂×C₄₇	C₂×Q₃₂	1	1	yes	characteristic
33	#500	—	47	2	no	—
34	#366	—	47	4	no	—
35	C₄×C₁₆	D₄₇	1	1	yes	characteristic
36	C₄₇	#2252	1	1	yes	characteristic, complemented, Sylow
37	C₄⋊Q₈	—	94	2	no	—
38	C₂×C₁₆	C₂×D₄₇	1	2	yes	—
39	#107	—	47	4	no	—
40	#107	—	94	2	no	—
41	C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
42	C₂×Q₈	—	188	2	no	—
43	C₂×C₈	D₁₈₈	1	1	yes	characteristic
44	C₂×C₈	C₂²×D₄₇	1	1	yes	characteristic
45	C₄⋊C₄	—	94	4	no	—
46	C₄⋊C₄	—	188	2	no	—
47	C₄²	D₁₈₈	1	1	yes	characteristic
48	C₁₆	Dic₉₄	1	4	yes	complemented
49	Q₈	—	376	4	no	—
50	C₂×C₄	—	188	4	no	—
51	C₂×C₄	D₃₇₆	1	1	yes	characteristic
52	C₂×C₄	D₃₇₆	1	1	yes	characteristic
53	C₂×C₄	C₂×D₁₈₈	1	1	yes	characteristic
54	C₈	Dic₁₈₈	1	2	yes	—
55	C₈	C₂×Dic₉₄	1	2	yes	—
56	C₂²	C₂×D₃₇₆	1	1	yes	characteristic
57	C₄	—	376	4	no	—
58	C₄	D₇₅₂	1	2	yes	—
59	C₄	Dic₃₇₆	1	2	yes	—
60	C₄	#13094024	1	1	yes	characteristic
61	C₄	C₂×Dic₁₈₈	1	1	yes	characteristic
62	C₂	#15689528	1	1	yes	characteristic
63	C₂	C₂×D₇₅₂	1	1	yes	characteristic
64	C₂	C₂×Dic₃₇₆	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₃₇₆
commutator	C₂×C₈×C₄₇	C₂³
Frattini	C₂×C₈	C₂²×D₄₇
Fitting	C₄×C₁₆×C₄₇	C₂
socle	C₂²×C₄₇	C₂×D₈
hypercenter	C₄×C₁₆	D₄₇
hypocenter	C₄₇	#2252
LCS	G ▷ C₂×C₈×C₄₇ ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ C₄×C₁₆

Complements

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

N	H ≅ G/N	type
15. C₁₆×C₄₇	Q₈	semidirect
36. C₄₇	#2252	semidirect
48. C₁₆	Dic₉₄	semidirect