Subgroups — #19134344

Order 5504.

272 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#13063236	C₂	1	2	yes	maximal
2	#14582654	C₂	1	4	yes	maximal
3	C₄³×C₄₃	C₂	1	1	yes	maximal, characteristic
4	C₂²×C₄₃⋊C₈	C₂²	1	4	yes	—
5	#13063236	C₄	1	8	yes	complemented
6	C₂×C₄²×C₄₃	C₄	1	4	yes	—
7	C₂×C₄²×C₄₃	C₂²	1	2	yes	—
8	C₂×C₄²×C₄₃	C₂²	1	1	yes	characteristic
9	C₂²×C₄×C₄₃	C₂×C₄	1	2	yes	—
10	C₂²×C₄×C₄₃	C₂×C₄	1	4	yes	—
11	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
12	C₄²×C₄₃	—	2	8	no	—
13	C₄²×C₄₃	—	2	4	no	—
14	C₄²×C₄₃	C₂×C₄	1	4	yes	—
15	C₂×C₄₃⋊C₈	—	2	8	no	—
16	C₂×C₄₃⋊C₈	C₂×C₄	1	8	yes	—
17	C₂³×C₄₃	C₂²×C₄	1	1	yes	characteristic
18	C₂×C₄×C₄₃	—	2	4	no	—
19	C₂×C₄×C₄₃	—	2	4	no	—
20	C₂×C₄×C₄₃	—	2	4	no	—
21	C₂×C₄×C₄₃	C₄²	1	4	yes	—
22	C₂×C₄×C₄₃	M₁₆	1	8	yes	—
23	C₂×C₄×C₄₃	C₂²×C₄	1	2	yes	—
24	C₂×C₄×C₄₃	#41	1	4	yes	—
25	C₄₃⋊C₈	—	2	8	no	—
26	C₂²×C₄₃	C₂×C₄²	1	1	yes	characteristic
27	C₂²×C₄₃	#117	1	2	yes	—
28	C₂²×C₄₃	C₂×M₁₆	1	4	yes	—
29	C₄×C₄₃	—	2	4	no	—
30	C₄×C₄₃	—	2	8	no	—
31	C₄×C₄₃	#117	1	4	yes	—
32	#1745	—	43	1	no	maximal, Sylow
33	C₂×C₄₃	#376	1	1	yes	characteristic
34	C₂×C₄₃	C₄×M₁₆	1	2	yes	—
35	C₂×C₄₃	#432	1	4	yes	—
36	C₂×#97	—	43	2	no	—
37	C₄³	D₄₃	1	1	yes	characteristic
38	#336	—	43	4	no	—
39	C₄₃	#1745	1	1	yes	characteristic, complemented, Sylow
40	C₂²×C₈	—	43	4	no	—
41	C₂×C₄²	Dic₄₃	1	4	yes	—
42	C₂×C₄²	C₂×D₄₃	1	2	yes	—
43	C₂×C₄²	C₂×D₄₃	1	1	yes	characteristic
44	#97	—	43	8	no	—
45	C₂²×C₄	C₂×Dic₄₃	1	4	yes	—
46	C₂²×C₄	C₂×Dic₄₃	1	2	yes	—
47	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
48	C₂×C₈	—	43	8	no	—
49	C₂×C₈	—	86	8	no	—
50	C₄²	—	2	8	no	—
51	C₄²	—	2	4	no	—
52	C₄²	C₄×D₄₃	1	4	yes	—
53	C₂³	C₂²×Dic₄₃	1	1	yes	characteristic
54	C₂×C₄	—	2	4	no	—
55	C₂×C₄	—	2	4	no	—
56	C₂×C₄	—	2	4	no	—
57	C₂×C₄	#10621877	1	8	yes	—
58	C₂×C₄	C₄×Dic₄₃	1	4	yes	—
59	C₂×C₄	C₂×C₄×D₄₃	1	2	yes	—
60	C₂×C₄	#10621898	1	4	yes	—
61	C₈	—	86	8	no	—
62	C₂²	C₂×C₄×Dic₄₃	1	1	yes	characteristic
63	C₂²	#13063284	1	2	yes	—
64	C₂²	C₂×#10621877	1	4	yes	—
65	C₄	—	2	4	no	—
66	C₄	—	2	8	no	—
67	C₄	#13063282	1	4	yes	—
68	C₂	#14582745	1	1	yes	characteristic
69	C₂	C₄×#10621877	1	2	yes	—
70	C₂	#14582956	1	4	yes	—

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂²×D₄₃
commutator	C₂²×C₄₃	C₂×C₄²
Fitting	C₄³×C₄₃	C₂
socle	C₂³×C₄₃	C₂²×C₄
hypercenter	C₄³	D₄₃
hypocenter	C₄₃	#1745
LCS	G ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₄³

Complements

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

N	H ≅ G/N	type
5. #13063236	C₄	semidirect
39. C₄₃	#1745	semidirect