Subgroups — #20241307

Order 6016.

92 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₄₇⋊C₁₆	C₂	1	1	yes	maximal, characteristic
2	C₈×C₄₇⋊C₈	C₂	1	1	yes	maximal, characteristic
3	C₄×C₁₆×C₄₇	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄₇⋊C₁₆	C₄	1	2	yes	—
5	C₄×C₄₇⋊C₈	C₄	1	1	yes	characteristic
6	C₄×C₄₇⋊C₈	C₄	1	1	yes	characteristic
7	C₂×C₁₆×C₄₇	C₄	1	2	yes	—
8	C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
9	C₂×C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
10	C₂×C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
11	C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
12	C₂×C₄₇⋊C₈	C₈	1	2	yes	—
13	C₂×C₄₇⋊C₈	C₈	1	2	yes	—
14	C₁₆×C₄₇	—	2	2	no	—
15	C₄₇⋊C₁₆	—	2	2	no	—
16	C₂×C₄×C₄₇	C₄²	1	1	yes	characteristic
17	C₂×C₄×C₄₇	C₂×C₈	1	1	yes	characteristic
18	C₂×C₄×C₄₇	C₂×C₈	1	1	yes	characteristic
19	C₈×C₄₇	M₁₆	1	2	yes	—
20	C₈×C₄₇	M₁₆	1	2	yes	—
21	C₄₇⋊C₈	—	2	2	no	—
22	C₄₇⋊C₈	C₁₆	1	4	yes	complemented
23	C₂²×C₄₇	C₄×C₈	1	1	yes	characteristic
24	C₄×C₄₇	#97	1	1	yes	characteristic
25	C₄×C₄₇	#97	1	1	yes	characteristic
26	C₄×C₄₇	C₂×C₁₆	1	2	yes	—
27	C₄×C₄₇	M₃₂	1	2	yes	—
28	#1312	—	47	1	no	maximal, Sylow
29	C₂×C₄₇	#322	1	1	yes	characteristic
30	C₂×C₄₇	C₄×C₁₆	1	1	yes	characteristic
31	C₂×C₄₇	#346	1	1	yes	characteristic
32	C₄×C₁₆	—	47	1	no	—
33	C₄×C₁₆	D₄₇	1	1	yes	characteristic
34	C₈²	—	47	1	no	—
35	C₄₇	#1312	1	1	yes	characteristic, complemented, Sylow
36	C₂×C₁₆	—	47	2	no	—
37	C₂×C₁₆	Dic₄₇	1	2	yes	—
38	C₄×C₈	—	47	1	no	—
39	C₄×C₈	—	47	1	no	—
40	C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
41	C₂×C₈	—	47	2	no	—
42	C₂×C₈	—	47	2	no	—
43	C₂×C₈	C₄×D₄₇	1	1	yes	characteristic
44	C₂×C₈	C₂×Dic₄₇	1	1	yes	characteristic
45	C₄²	C₄×D₄₇	1	1	yes	characteristic
46	C₁₆	—	2	2	no	—
47	C₁₆	—	94	2	no	—
48	C₂×C₄	C₈×D₄₇	1	1	yes	characteristic
49	C₂×C₄	C₈×D₄₇	1	1	yes	characteristic
50	C₂×C₄	C₄×Dic₄₇	1	1	yes	characteristic
51	C₈	—	47	4	no	—
52	C₈	—	94	2	no	—
53	C₈	#10625324	1	2	yes	—
54	C₈	#10625329	1	2	yes	—
55	C₂²	C₈×Dic₄₇	1	1	yes	characteristic
56	C₄	#13093934	1	1	yes	characteristic
57	C₄	#13093935	1	1	yes	characteristic
58	C₄	C₁₆×D₄₇	1	2	yes	—
59	C₄	#13093963	1	2	yes	—
60	C₂	#15688845	1	1	yes	characteristic
61	C₂	C₁₆×Dic₄₇	1	1	yes	characteristic
62	C₂	#15688898	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₄×C₈	C₂×D₄₇
commutator	C₂×C₄₇	C₄×C₁₆
Fitting	C₄×C₁₆×C₄₇	C₂
socle	C₂²×C₄₇	C₄×C₈
hypercenter	C₄×C₁₆	D₄₇
hypocenter	C₄₇	#1312
LCS	G ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₄×C₈ ◁ C₄×C₁₆

Complements

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

N	H ≅ G/N	type
22. C₄₇⋊C₈	C₁₆	semidirect
35. C₄₇	#1312	semidirect