Subgroups — #19132897

Order 5504.

214 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#10621872	C₂	1	3	yes	maximal
2	#14582620	C₂	1	3	yes	maximal, complemented
3	C₈²×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#10621872	C₄	1	6	yes	—
5	C₄²×D₄₃	C₂²	1	1	yes	characteristic
6	#13063235	C₄	1	6	yes	—
7	C₄×C₄₃⋊C₈	C₂²	1	3	yes	—
8	C₄×C₈×C₄₃	C₂²	1	3	yes	—
9	C₂×C₄×D₄₃	C₂×C₄	1	3	yes	—
10	C₂×C₈×C₄₃	C₂×C₄	1	6	yes	—
11	C₄²×C₄₃	C₂³	1	1	yes	characteristic
12	C₄×Dic₄₃	C₂×C₄	1	3	yes	—
13	C₂×C₄₃⋊C₈	C₂×C₄	1	6	yes	—
14	#10621872	—	2	12	no	—
15	C₂²×D₄₃	C₄²	1	1	yes	characteristic
16	C₂×C₄×C₄₃	C₂²×C₄	1	3	yes	—
17	C₂×Dic₄₃	C₄²	1	3	yes	—
18	C₄×D₄₃	—	2	6	no	—
19	C₈×C₄₃	M₁₆	1	12	yes	complemented
20	C₄₃⋊C₈	—	2	6	no	—
21	C₂²×C₄₃	C₂×C₄²	1	1	yes	characteristic
22	C₂×D₄₃	—	2	3	no	—
23	C₄×C₄₃	C₂×M₁₆	1	6	yes	—
24	Dic₄₃	—	2	3	no	—
25	#1455	—	43	1	no	maximal, Sylow
26	C₂×C₄₃	C₄×M₁₆	1	3	yes	—
27	D₄₃	—	4	1	no	—
28	C₄×M₁₆	—	43	3	no	—
29	#322	—	43	3	no	—
30	C₈²	D₄₃	1	1	yes	characteristic, complemented
31	C₄₃	#1455	1	1	yes	characteristic, complemented, Sylow
32	C₂×M₁₆	—	43	6	no	—
33	C₂×C₄²	—	43	1	no	—
34	#97	—	43	6	no	—
35	C₄×C₈	—	43	3	no	—
36	C₄×C₈	C₂×D₄₃	1	3	yes	—
37	C₂²×C₄	—	43	3	no	—
38	M₁₆	—	86	12	no	—
39	C₂×C₈	—	43	6	no	—
40	C₂×C₈	C₄×D₄₃	1	6	yes	—
41	C₄²	—	43	3	no	—
42	C₄²	C₂²×D₄₃	1	1	yes	characteristic
43	C₂³	—	43	1	no	—
44	C₂×C₄	—	43	3	no	—
45	C₂×C₄	—	86	6	no	—
46	C₂×C₄	C₂×C₄×D₄₃	1	3	yes	—
47	C₈	—	86	6	no	—
48	C₈	#10621872	1	12	yes	complemented
49	C₂²	—	86	3	no	—
50	C₂²	C₄²×D₄₃	1	1	yes	characteristic
51	C₄	—	86	3	no	—
52	C₄	C₂×#10621872	1	6	yes	—
53	C₂	—	172	1	no	—
54	C₂	C₄×#10621872	1	3	yes	—

	subgroup	G/H
center, Frattini	C₄²	C₂²×D₄₃
commutator, socle	C₂²×C₄₃	C₂×C₄²
Fitting	C₈²×C₄₃	C₂
hypercenter	C₈²	D₄₃
hypocenter	C₄₃	#1455
LCS	G ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₄² ◁ C₈²

Complements

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

N	H ≅ G/N	type
2. #14582620	C₂	semidirect
3. C₈²×C₄₃	C₂	semidirect
19. C₈×C₄₃	M₁₆	semidirect
30. C₈²	D₄₃	semidirect
31. C₄₃	#1455	semidirect
48. C₈	#10621872	semidirect