Subgroups — C₂×#15688899 #20244978

Order 6016.

200 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄₇⋊C₁₆	C₂	1	2	yes	maximal
2	#15688899	C₂	1	4	yes	maximal, direct product factor
3	C₂×C₄×C₈×C₄₇	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄₇⋊C₁₆	C₄	1	8	yes	complemented
5	C₂×C₄₇⋊C₁₆	C₂²	1	4	yes	—
6	C₂²×C₈×C₄₇	C₄	1	1	yes	characteristic
7	C₂²×C₈×C₄₇	C₂²	1	1	yes	characteristic
8	C₂×C₄²×C₄₇	C₄	1	1	yes	characteristic
9	C₄×C₈×C₄₇	C₄	1	2	yes	—
10	C₄×C₈×C₄₇	C₂²	1	2	yes	—
11	C₂²×C₄×C₄₇	C₈	1	2	yes	—
12	C₂²×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
13	C₂×C₈×C₄₇	C₈	1	4	yes	—
14	C₂×C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
15	C₂×C₈×C₄₇	C₂×C₄	1	4	yes	—
16	C₂×C₈×C₄₇	C₂×C₄	1	2	yes	—
17	C₂×C₈×C₄₇	C₂³	1	1	yes	characteristic
18	C₄²×C₄₇	C₈	1	2	yes	—
19	C₄²×C₄₇	C₂×C₄	1	2	yes	—
20	C₄₇⋊C₁₆	C₂×C₄	1	8	yes	complemented
21	C₂³×C₄₇	C₂×C₈	1	1	yes	characteristic
22	C₂×C₄×C₄₇	—	2	4	no	—
23	C₂×C₄×C₄₇	C₄²	1	2	yes	—
24	C₂×C₄×C₄₇	C₂×C₈	1	4	yes	—
25	C₂×C₄×C₄₇	C₂×C₈	1	1	yes	characteristic
26	C₂×C₄×C₄₇	C₂×C₈	1	2	yes	—
27	C₂×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
28	C₈×C₄₇	C₄²	1	2	yes	—
29	C₈×C₄₇	C₂×C₈	1	4	yes	—
30	C₈×C₄₇	C₂²×C₄	1	2	yes	—
31	C₂²×C₄₇	C₄×C₈	1	2	yes	—
32	C₂²×C₄₇	M₃₂	1	4	yes	—
33	C₂²×C₄₇	C₂²×C₈	1	1	yes	characteristic
34	C₄×C₄₇	—	2	4	no	—
35	C₄×C₄₇	C₄×C₈	1	2	yes	—
36	C₄×C₄₇	C₂×C₄²	1	1	yes	characteristic
37	C₄×C₄₇	C₂²×C₈	1	1	yes	characteristic
38	C₂×#346	—	47	1	no	maximal, Sylow
39	C₂×C₄₇	#346	1	4	yes	complemented
40	C₂×C₄₇	C₂×C₄×C₈	1	1	yes	characteristic
41	C₂×C₄₇	C₂×M₃₂	1	2	yes	—
42	C₂²×C₁₆	—	47	2	no	—
43	C₂×C₄×C₈	D₄₇	1	1	yes	characteristic
44	#346	—	47	4	no	—
45	C₄₇	C₂×#346	1	1	yes	characteristic, complemented, Sylow
46	C₂²×C₈	Dic₄₇	1	1	yes	characteristic
47	C₂²×C₈	C₂×D₄₇	1	1	yes	characteristic
48	C₂×C₄²	Dic₄₇	1	1	yes	characteristic
49	C₂×C₁₆	—	47	8	no	—
50	C₂×C₁₆	—	47	4	no	—
51	C₄×C₈	Dic₄₇	1	2	yes	—
52	C₄×C₈	C₂×D₄₇	1	2	yes	—
53	C₂²×C₄	C₄₇⋊C₈	1	2	yes	—
54	C₂²×C₄	C₂×Dic₄₇	1	1	yes	characteristic
55	C₂×C₈	C₄₇⋊C₈	1	4	yes	—
56	C₂×C₈	C₄×D₄₇	1	4	yes	—
57	C₂×C₈	C₂×Dic₄₇	1	2	yes	—
58	C₂×C₈	C₂×Dic₄₇	1	1	yes	characteristic
59	C₂×C₈	C₂²×D₄₇	1	1	yes	characteristic
60	C₄²	C₄₇⋊C₈	1	2	yes	—
61	C₄²	C₂×Dic₄₇	1	2	yes	—
62	C₁₆	—	47	8	no	—
63	C₂³	C₂×C₄₇⋊C₈	1	1	yes	characteristic
64	C₂×C₄	—	2	4	no	—
65	C₂×C₄	C₂×C₄₇⋊C₈	1	4	yes	—
66	C₂×C₄	C₂×C₄₇⋊C₈	1	1	yes	characteristic
67	C₂×C₄	C₂×C₄₇⋊C₈	1	2	yes	—
68	C₂×C₄	C₄×Dic₄₇	1	2	yes	—
69	C₂×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
70	C₈	C₂×C₄₇⋊C₈	1	4	yes	—
71	C₈	C₄×Dic₄₇	1	2	yes	—
72	C₈	C₂×C₄×D₄₇	1	2	yes	—
73	C₂²	C₄×C₄₇⋊C₈	1	2	yes	—
74	C₂²	#13093964	1	4	yes	—
75	C₂²	C₂²×C₄₇⋊C₈	1	1	yes	characteristic
76	C₄	—	2	4	no	—
77	C₄	C₄×C₄₇⋊C₈	1	2	yes	—
78	C₄	C₂×C₄×Dic₄₇	1	1	yes	characteristic
79	C₄	C₂²×C₄₇⋊C₈	1	1	yes	characteristic
80	C₂	#15688899	1	4	yes	direct product factor
81	C₂	C₂×C₄×C₄₇⋊C₈	1	1	yes	characteristic
82	C₂	C₂×#13093964	1	2	yes	—

	subgroup	G/H
center	C₂²×C₈	C₂×D₄₇
commutator	C₂×C₄₇	C₂×C₄×C₈
Frattini	C₂×C₈	C₂²×D₄₇
Fitting	C₂×C₄×C₈×C₄₇	C₂
socle	C₂³×C₄₇	C₂×C₈
hypercenter	C₂×C₄×C₈	D₄₇
hypocenter	C₄₇	C₂×#346
LCS	G ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₈ ◁ C₂×C₄×C₈

Complements

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

N	H ≅ G/N	type
2. #15688899	C₂	direct (N × H)
4. C₂×C₄₇⋊C₁₆	C₄	semidirect
20. C₄₇⋊C₁₆	C₂×C₄	semidirect
39. C₂×C₄₇	#346	semidirect
45. C₄₇	C₂×#346	semidirect
80. C₂	#15688899	direct (N × H)

Subgroups — C2×#15688899 #20244978

Conjugacy classes of subgroups

Complements

Subgroups — C₂×#15688899 #20244978