Subgroups — #20241527

Order 6016.

74 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#13093963	C₂	1	1	yes	maximal, characteristic
2	#15688957	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₇×M₆₄	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₈×D₄₇	C₄	1	1	yes	characteristic
5	#13093963	—	2	1	no	—
6	#13093963	—	2	1	no	—
7	C₂×C₄₇⋊C₁₆	C₄	1	1	yes	characteristic
8	C₄₇⋊C₃₂	—	2	1	no	—
9	C₂×C₁₆×C₄₇	C₂²	1	1	yes	characteristic
10	C₃₂×C₄₇	—	2	1	no	—
11	C₂×C₄×D₄₇	C₈	1	1	yes	characteristic
12	C₂×C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
13	C₂×C₄₇⋊C₈	C₈	1	1	yes	characteristic
14	C₈×D₄₇	—	2	1	no	—
15	C₈×D₄₇	—	2	1	no	—
16	C₁₆×C₄₇	D₄	1	1	yes	characteristic
17	C₁₆×C₄₇	D₄	1	1	yes	characteristic
18	C₄₇⋊C₁₆	—	2	1	no	—
19	C₂²×D₄₇	C₁₆	1	1	yes	characteristic
20	C₂×C₄×C₄₇	C₂×C₈	1	1	yes	characteristic
21	C₂×Dic₄₇	C₁₆	1	1	yes	characteristic
22	C₄×D₄₇	—	2	1	no	—
23	C₄×D₄₇	—	2	1	no	—
24	C₈×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
25	C₈×C₄₇	M₁₆	1	1	yes	characteristic
26	C₄₇⋊C₈	—	2	1	no	—
27	C₂²×C₄₇	C₂×C₁₆	1	1	yes	characteristic
28	C₂×D₄₇	—	2	1	no	—
29	C₂×D₄₇	—	4	1	no	—
30	C₄×C₄₇	C₂²⋊C₈	1	1	yes	characteristic
31	C₄×C₄₇	M₃₂	1	1	yes	characteristic
32	Dic₄₇	—	2	1	no	—
33	#1400	—	47	1	no	maximal, Sylow
34	C₂×C₄₇	—	2	1	no	—
35	C₂×C₄₇	C₂²⋊C₁₆	1	1	yes	characteristic
36	D₄₇	—	4	1	no	—
37	C₂×M₃₂	—	47	1	no	—
38	M₆₄	—	47	1	no	—
39	M₆₄	D₄₇	1	1	yes	characteristic, complemented
40	C₄₇	#1400	1	1	yes	characteristic, complemented, Sylow
41	C₂²×C₈	—	47	1	no	—
42	M₃₂	—	94	1	no	—
43	M₃₂	—	94	1	no	—
44	C₂×C₁₆	—	47	1	no	—
45	C₂×C₁₆	C₂×D₄₇	1	1	yes	characteristic
46	C₃₂	—	2	1	no	—
47	C₃₂	—	94	1	no	—
48	C₂²×C₄	—	47	1	no	—
49	C₂×C₈	—	47	1	no	—
50	C₂×C₈	—	94	1	no	—
51	C₂×C₈	—	94	1	no	—
52	C₂×C₈	C₄×D₄₇	1	1	yes	characteristic
53	C₁₆	—	94	1	no	—
54	C₁₆	D₁₈₈	1	1	yes	characteristic
55	C₁₆	C₂²⋊D₄₇	1	1	yes	characteristic
56	C₂³	—	47	1	no	—
57	C₂×C₄	—	47	1	no	—
58	C₂×C₄	—	94	1	no	—
59	C₂×C₄	—	94	1	no	—
60	C₂×C₄	C₈×D₄₇	1	1	yes	characteristic
61	C₈	—	94	1	no	—
62	C₈	#10625324	1	1	yes	characteristic
63	C₈	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
64	C₂²	—	94	1	no	—
65	C₂²	—	188	1	no	—
66	C₂²	C₁₆×D₄₇	1	1	yes	characteristic
67	C₄	—	94	1	no	—
68	C₄	(C₂×D₄₇)⋊C₈	1	1	yes	characteristic
69	C₄	#13093963	1	1	yes	characteristic
70	C₂	—	2	1	no	—
71	C₂	—	188	1	no	—
72	C₂	(C₂×D₄₇)⋊C₁₆	1	1	yes	characteristic

	subgroup	G/H
center	C₈	(C₂×D₄₇)⋊C₄
commutator	C₂²×C₄₇	C₂×C₁₆
Frattini	C₂×C₁₆	C₂×D₄₇
Fitting	C₄₇×M₆₄	C₂
socle	C₂×C₄₇	C₂²⋊C₁₆
hypercenter	M₆₄	D₄₇
hypocenter	C₄₇	#1400
LCS	G ▷ C₂²×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₈ ◁ C₂×C₁₆ ◁ M₆₄

Complements

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

N	H ≅ G/N	type
2. #15688957	C₂	semidirect
3. C₄₇×M₆₄	C₂	semidirect
39. M₆₄	D₄₇	semidirect
40. C₄₇	#1400	semidirect