Subgroups — C₂×#15688956 #20245679

Order 6016.

112 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₆×D₄₇	C₂	1	1	yes	maximal, characteristic
2	#15688956	C₂	1	4	yes	maximal, direct product factor
3	C₂×C₄₇⋊C₃₂	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃₂×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₈×D₄₇	C₄	1	1	yes	characteristic
6	C₂×C₄₇⋊C₁₆	C₄	1	1	yes	characteristic
7	C₁₆×D₄₇	C₄	1	2	yes	—
8	C₁₆×D₄₇	C₂²	1	2	yes	—
9	C₄₇⋊C₃₂	C₂²	1	2	yes	complemented
10	C₂×C₁₆×C₄₇	C₂²	1	1	yes	characteristic
11	C₃₂×C₄₇	C₂²	1	2	yes	complemented
12	C₂×C₄×D₄₇	C₈	1	1	yes	characteristic
13	C₂×C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
14	C₂×C₄₇⋊C₈	C₈	1	1	yes	characteristic
15	C₈×D₄₇	C₈	1	2	yes	—
16	C₈×D₄₇	C₂×C₄	1	2	yes	—
17	C₁₆×C₄₇	C₂×C₄	1	1	yes	characteristic
18	C₁₆×C₄₇	C₂³	1	1	yes	characteristic
19	C₄₇⋊C₁₆	C₂×C₄	1	2	yes	—
20	C₂²×D₄₇	C₁₆	1	1	yes	characteristic
21	C₂×C₄×C₄₇	C₂×C₈	1	1	yes	characteristic
22	C₂×Dic₄₇	C₁₆	1	1	yes	characteristic
23	C₄×D₄₇	C₁₆	1	2	yes	—
24	C₄×D₄₇	C₂×C₈	1	2	yes	—
25	C₈×C₄₇	C₂×C₈	1	1	yes	characteristic
26	C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
27	C₄₇⋊C₈	C₂×C₈	1	2	yes	—
28	C₂²×C₄₇	C₂×C₁₆	1	1	yes	characteristic
29	C₂×D₄₇	—	2	2	no	—
30	C₂×D₄₇	C₂×C₁₆	1	2	yes	—
31	C₄×C₄₇	C₂×C₁₆	1	1	yes	characteristic
32	C₄×C₄₇	C₂²×C₈	1	1	yes	characteristic
33	Dic₄₇	C₂×C₁₆	1	2	yes	—
34	C₂×M₆₄	—	47	1	no	maximal, Sylow
35	C₂×C₄₇	M₆₄	1	2	yes	complemented
36	C₂×C₄₇	C₂²×C₁₆	1	1	yes	characteristic
37	D₄₇	—	2	2	no	—
38	C₂²×C₁₆	—	47	1	no	—
39	M₆₄	—	47	4	no	—
40	C₂×C₃₂	—	47	1	no	—
41	C₂×C₃₂	D₄₇	1	1	yes	characteristic, complemented
42	C₄₇	C₂×M₆₄	1	1	yes	characteristic, complemented, Sylow
43	C₂²×C₈	—	47	1	no	—
44	C₂×C₁₆	—	47	1	no	—
45	C₂×C₁₆	—	47	2	no	—
46	C₂×C₁₆	—	47	2	no	—
47	C₂×C₁₆	C₂×D₄₇	1	1	yes	characteristic
48	C₃₂	—	47	2	no	—
49	C₃₂	C₂×D₄₇	1	2	yes	complemented
50	C₂²×C₄	—	47	1	no	—
51	C₂×C₈	—	47	1	no	—
52	C₂×C₈	—	47	2	no	—
53	C₂×C₈	—	47	2	no	—
54	C₂×C₈	C₄×D₄₇	1	1	yes	characteristic
55	C₁₆	—	47	2	no	—
56	C₁₆	C₄×D₄₇	1	1	yes	characteristic
57	C₁₆	C₂²×D₄₇	1	1	yes	characteristic
58	C₂³	—	47	1	no	—
59	C₂×C₄	—	47	1	no	—
60	C₂×C₄	—	47	2	no	—
61	C₂×C₄	—	47	2	no	—
62	C₂×C₄	C₈×D₄₇	1	1	yes	characteristic
63	C₈	—	47	2	no	—
64	C₈	C₈×D₄₇	1	1	yes	characteristic
65	C₈	C₂×C₄×D₄₇	1	1	yes	characteristic
66	C₂²	—	47	2	no	—
67	C₂²	—	94	2	no	—
68	C₂²	C₁₆×D₄₇	1	1	yes	characteristic
69	C₄	—	47	2	no	—
70	C₄	C₁₆×D₄₇	1	1	yes	characteristic
71	C₄	C₂×C₈×D₄₇	1	1	yes	characteristic
72	C₂	—	94	2	no	—
73	C₂	#15688956	1	2	yes	direct product factor
74	C₂	C₂×C₁₆×D₄₇	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₁₆	C₂×D₄₇
commutator	C₂×C₄₇	C₂²×C₁₆
Frattini	C₁₆	C₂²×D₄₇
Fitting	C₂×C₃₂×C₄₇	C₂
socle	C₂²×C₄₇	C₂×C₁₆
hypercenter	C₂×C₃₂	D₄₇
hypocenter	C₄₇	C₂×M₆₄
LCS	G ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₁₆ ◁ C₂×C₃₂

Complements

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

N	H ≅ G/N	type
2. #15688956	C₂	direct (N × H)
3. C₂×C₄₇⋊C₃₂	C₂	semidirect
4. C₂×C₃₂×C₄₇	C₂	semidirect
9. C₄₇⋊C₃₂	C₂²	semidirect
11. C₃₂×C₄₇	C₂²	semidirect
35. C₂×C₄₇	M₆₄	semidirect
41. C₂×C₃₂	D₄₇	semidirect
42. C₄₇	C₂×M₆₄	semidirect
49. C₃₂	C₂×D₄₇	semidirect
73. C₂	#15688956	direct (N × H)

Subgroups — C2×#15688956 #20245679

Conjugacy classes of subgroups

Complements

Subgroups — C₂×#15688956 #20245679