Subgroups — #20245681

Order 6016.

106 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#15689539	C₂	1	1	yes	maximal, characteristic
2	#15688957	C₂	1	1	yes	maximal, characteristic, complemented
3	#15688956	C₂	1	2	yes	maximal, complemented
4	C₃₂×D₄₇	C₂	1	2	yes	maximal, complemented
5	C₂×C₃₂×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
6	#13094030	C₄	1	1	yes	characteristic
7	#13093964	C₄	1	1	yes	characteristic
8	#13093963	C₄	1	2	yes	—
9	C₁₆×D₄₇	C₂²	1	2	yes	—
10	C₄₇⋊C₃₂	C₂²	1	2	yes	—
11	C₂×C₁₆×C₄₇	C₂²	1	1	yes	characteristic
12	C₃₂×C₄₇	C₂²	1	1	yes	characteristic
13	C₃₂×C₄₇	C₂²	1	1	yes	characteristic
14	#10625350	C₈	1	1	yes	characteristic
15	C₂×C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
16	#10625329	C₈	1	1	yes	characteristic
17	#10625324	C₈	1	2	yes	—
18	C₈×D₄₇	C₂×C₄	1	2	yes	—
19	C₁₆×C₄₇	C₂×C₄	1	1	yes	characteristic
20	C₁₆×C₄₇	C₂³	1	1	yes	characteristic
21	C₄₇⋊C₁₆	C₂×C₄	1	2	yes	—
22	C₂×C₄×C₄₇	C₂×C₈	1	1	yes	characteristic
23	C₂²⋊D₄₇	C₁₆	1	2	yes	—
24	D₁₈₈	C₁₆	1	1	yes	characteristic
25	C₄×D₄₇	C₂×C₈	1	2	yes	—
26	Dic₉₄	C₁₆	1	1	yes	characteristic
27	C₈×C₄₇	C₂×C₈	1	1	yes	characteristic
28	C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
29	C₄₇⋊C₈	C₂×C₈	1	2	yes	—
30	C₂²×C₄₇	C₂×C₁₆	1	1	yes	characteristic
31	C₂×D₄₇	C₂×C₁₆	1	2	yes	—
32	C₄×C₄₇	C₂×C₁₆	1	1	yes	characteristic
33	C₄×C₄₇	C₂²×C₈	1	1	yes	characteristic
34	Dic₄₇	C₂×C₁₆	1	2	yes	—
35	#2258	—	47	1	no	maximal, Sylow
36	C₂×C₄₇	—	2	1	no	—
37	C₂×C₄₇	C₂²×C₁₆	1	1	yes	characteristic
38	D₄₇	—	2	2	no	—
39	#504	—	47	1	no	—
40	M₆₄	—	47	1	no	—
41	M₆₄	—	47	2	no	—
42	C₂×C₃₂	—	47	2	no	—
43	C₂×C₃₂	D₄₇	1	1	yes	characteristic, complemented
44	C₄₇	#2258	1	1	yes	characteristic, complemented, Sylow
45	#131	—	47	1	no	—
46	M₃₂	—	47	1	no	—
47	M₃₂	—	47	2	no	—
48	C₂×C₁₆	—	47	2	no	—
49	C₂×C₁₆	C₂×D₄₇	1	1	yes	characteristic
50	C₃₂	—	47	2	no	—
51	C₃₂	C₂×D₄₇	1	1	yes	characteristic
52	C₃₂	C₂×D₄₇	1	1	yes	characteristic
53	#41	—	47	1	no	—
54	M₁₆	—	47	1	no	—
55	M₁₆	—	47	2	no	—
56	C₂×C₈	—	47	2	no	—
57	C₂×C₈	C₄×D₄₇	1	1	yes	characteristic
58	C₁₆	—	47	2	no	—
59	C₁₆	C₄×D₄₇	1	1	yes	characteristic
60	C₁₆	C₂²×D₄₇	1	1	yes	characteristic
61	Q₈	—	47	1	no	—
62	D₄	—	47	2	no	—
63	D₄	—	47	1	no	—
64	C₂×C₄	—	47	2	no	—
65	C₂×C₄	C₈×D₄₇	1	1	yes	characteristic
66	C₈	—	47	2	no	—
67	C₈	C₈×D₄₇	1	1	yes	characteristic
68	C₈	C₂×C₄×D₄₇	1	1	yes	characteristic
69	C₂²	—	47	2	no	—
70	C₂²	C₁₆×D₄₇	1	1	yes	characteristic
71	C₄	—	47	2	no	—
72	C₄	C₁₆×D₄₇	1	1	yes	characteristic
73	C₄	C₂×C₈×D₄₇	1	1	yes	characteristic
74	C₂	—	2	1	no	—
75	C₂	—	94	2	no	—
76	C₂	C₂×C₁₆×D₄₇	1	1	yes	characteristic

	subgroup	G/H
center	C₃₂	C₂×D₄₇
commutator, socle	C₂×C₄₇	C₂²×C₁₆
Frattini	C₁₆	C₂²×D₄₇
Fitting	C₂×C₃₂×C₄₇	C₂
hypercenter	C₂×C₃₂	D₄₇
hypocenter	C₄₇	#2258
LCS	G ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₃₂ ◁ C₂×C₃₂

Complements

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

N	H ≅ G/N	type
2. #15688957	C₂	semidirect
3. #15688956	C₂	semidirect
4. C₃₂×D₄₇	C₂	semidirect
5. C₂×C₃₂×C₄₇	C₂	semidirect
43. C₂×C₃₂	D₄₇	semidirect
44. C₄₇	#2258	semidirect