Subgroups — #20241482

Order 6016.

128 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#13093960	C₂	1	2	yes	maximal
2	C₂²×C₁₆×C₄₇	C₂	1	1	yes	maximal, characteristic
3	C₂×#10625329	—	2	2	no	—
4	#13093960	—	2	2	no	—
5	#13093960	C₄	1	4	yes	—
6	C₂²×C₈×C₄₇	C₂²	1	1	yes	characteristic
7	C₂×C₁₆×C₄₇	—	2	2	no	—
8	C₂×C₁₆×C₄₇	C₄	1	2	yes	—
9	C₂²×C₄×C₄₇	D₄	1	1	yes	characteristic
10	C₂×C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
11	C₂×C₈×C₄₇	C₂×C₄	1	2	yes	—
12	C₂×C₈×C₄₇	D₄	1	2	yes	—
13	C₂×C₈×C₄₇	Q₈	1	1	yes	characteristic
14	#10625329	—	2	4	no	—
15	#10625329	—	4	2	no	—
16	C₂×C₄₇⋊C₈	—	4	2	no	—
17	C₁₆×C₄₇	—	2	2	no	—
18	C₂³×C₄₇	Q₁₆	1	1	yes	characteristic
19	C₂×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
20	C₂×C₄×C₄₇	C₄⋊C₄	1	1	yes	characteristic
21	C₂×C₄×C₄₇	D₈	1	1	yes	characteristic
22	C₂×C₄×C₄₇	SD₁₆	1	2	yes	—
23	C₈×C₄₇	C₄²	1	1	yes	characteristic
24	C₈×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
25	C₈×C₄₇	C₄⋊C₄	1	2	yes	—
26	C₄₇⋊C₈	—	4	4	no	—
27	C₂²×C₄₇	—	2	2	no	—
28	C₂²×C₄₇	#103	1	2	yes	—
29	C₂²×C₄₇	#107	1	1	yes	characteristic
30	C₄×C₄₇	#95	1	1	yes	characteristic
31	C₄×C₄₇	#102	1	2	yes	—
32	C₄×C₄₇	#106	1	1	yes	characteristic
33	#1381	—	47	1	no	maximal, Sylow
34	C₂×C₄₇	—	2	2	no	—
35	C₂×C₄₇	#340	1	1	yes	characteristic
36	C₂×C₄₇	#368	1	2	yes	—
37	C₂²×C₁₆	D₄₇	1	1	yes	characteristic
38	C₂×#108	—	47	2	no	—
39	C₄₇	#1381	1	1	yes	characteristic, complemented, Sylow
40	C₂×M₁₆	—	94	2	no	—
41	C₂²×C₈	C₂×D₄₇	1	1	yes	characteristic
42	C₂×C₁₆	—	2	2	no	—
43	C₂×C₁₆	Dic₄₇	1	2	yes	—
44	#108	—	47	4	no	—
45	#108	—	94	2	no	—
46	C₂²×C₄	D₁₈₈	1	1	yes	characteristic
47	M₁₆	—	94	4	no	—
48	M₁₆	—	188	2	no	—
49	C₂×C₈	—	188	2	no	—
50	C₂×C₈	Dic₉₄	1	1	yes	characteristic
51	C₂×C₈	C₄×D₄₇	1	2	yes	—
52	C₂×C₈	C₂×Dic₄₇	1	1	yes	characteristic
53	C₂×C₈	C₂²⋊D₄₇	1	2	yes	—
54	C₁₆	—	2	2	no	—
55	C₂³	Dic₁₈₈	1	1	yes	characteristic
56	C₂×C₄	#10625325	1	2	yes	—
57	C₂×C₄	D₃₇₆	1	1	yes	characteristic
58	C₂×C₄	C₄⋊Dic₄₇	1	1	yes	characteristic
59	C₂×C₄	(C₂×D₄₇)⋊C₄	1	2	yes	—
60	C₈	—	188	4	no	—
61	C₈	C₄×Dic₄₇	1	1	yes	characteristic
62	C₈	Dic₄₇⋊C₄	1	2	yes	—
63	C₈	C₂²⋊Dic₄₇	1	1	yes	characteristic
64	C₂²	—	2	2	no	—
65	C₂²	#13093949	1	2	yes	—
66	C₂²	#13093958	1	1	yes	characteristic
67	C₄	C₄₇⋊#95	1	1	yes	characteristic
68	C₄	#13093946	1	2	yes	—
69	C₄	#13093956	1	1	yes	characteristic
70	C₂	—	2	2	no	—
71	C₂	#15688886	1	1	yes	characteristic
72	C₂	#15688953	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	D₃₇₆
commutator	C₈×C₄₇	C₄²
Frattini	C₂²×C₈	C₂×D₄₇
Fitting	C₂²×C₁₆×C₄₇	C₂
socle	C₂²×C₄₇	#107
hypercenter	C₂²×C₁₆	D₄₇
hypocenter	C₄₇	#1381
LCS	G ▷ C₈×C₄₇ ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂²×C₁₆

Complements

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

N	H ≅ G/N	type
39. C₄₇	#1381	semidirect