Subgroups — #19136388

Order 5504.

140 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#13063264	C₂	1	1	yes	maximal, characteristic
2	#108×D₄₃	C₂	1	2	yes	maximal
3	#14582729	C₂	1	1	yes	maximal, characteristic, complemented
4	#14582728	C₂	1	2	yes	maximal, complemented
5	C₄₃×#368	C₂	1	1	yes	maximal, characteristic, complemented
6	M₁₆×D₄₃	—	2	2	no	—
7	C₂×C₈×D₄₃	C₂²	1	1	yes	characteristic
8	#13063264	C₄	1	4	yes	—
9	C₂×C₄₃⋊C₁₆	C₂²	1	1	yes	characteristic
10	#13063261	C₂²	1	2	yes	—
11	#13063260	—	2	2	no	—
12	C₂×C₁₆×C₄₃	C₂²	1	1	yes	characteristic
13	#108×C₄₃	C₂²	1	2	yes	—
14	C₂×C₄×D₄₃	D₄	1	1	yes	characteristic
15	M₁₆×C₄₃	—	2	2	no	—
16	C₂×C₈×C₄₃	C₂³	1	1	yes	characteristic
17	#10621877	—	2	2	no	—
18	C₂×C₄₃⋊C₈	D₄	1	1	yes	characteristic
19	#10621872	—	4	2	no	—
20	C₈×D₄₃	—	4	2	no	—
21	C₈×D₄₃	C₂×C₄	1	2	yes	—
22	C₈×D₄₃	Q₈	1	2	yes	—
23	C₁₆×C₄₃	C₂×C₄	1	2	yes	—
24	C₄₃⋊C₁₆	C₂×C₄	1	2	yes	—
25	C₂²×D₄₃	Q₁₆	1	1	yes	characteristic
26	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
27	C₂×Dic₄₃	Q₁₆	1	1	yes	characteristic
28	C₄×D₄₃	C₄⋊C₄	1	2	yes	—
29	C₄×D₄₃	D₈	1	2	yes	—
30	C₈×C₄₃	—	4	2	no	—
31	C₈×C₄₃	C₂²×C₄	1	1	yes	characteristic
32	C₈×C₄₃	C₂×Q₈	1	1	yes	characteristic
33	C₄₃⋊C₈	—	4	2	no	—
34	C₄₃⋊C₈	C₄⋊C₄	1	2	yes	—
35	C₂²×C₄₃	C₂×Q₁₆	1	1	yes	characteristic
36	C₂×D₄₃	—	4	1	no	—
37	C₂×D₄₃	#107	1	2	yes	—
38	C₄×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
39	C₄×C₄₃	C₂×D₈	1	1	yes	characteristic
40	Dic₄₃	#107	1	2	yes	—
41	#2161	—	43	1	no	maximal, Sylow
42	C₂×C₄₃	—	2	1	no	—
43	C₂×C₄₃	C₂×#107	1	1	yes	characteristic
44	D₄₃	—	2	2	no	—
45	C₂×M₃₂	—	43	1	no	—
46	C₂×#108	—	43	2	no	—
47	#368	—	43	1	no	—
48	#368	—	43	2	no	—
49	#368	D₄₃	1	1	yes	characteristic, complemented
50	C₄₃	#2161	1	1	yes	characteristic, complemented, Sylow
51	C₂×M₁₆	—	86	2	no	—
52	C₂²×C₈	—	43	1	no	—
53	M₃₂	—	43	4	no	—
54	C₂×C₁₆	—	43	1	no	—
55	C₂×C₁₆	C₂×D₄₃	1	1	yes	characteristic
56	#108	—	43	2	no	—
57	#108	—	86	2	no	—
58	#108	C₂×D₄₃	1	2	yes	—
59	C₂²×C₄	—	43	1	no	—
60	M₁₆	—	2	2	no	—
61	M₁₆	—	86	2	no	—
62	M₁₆	—	172	2	no	—
63	C₂×C₈	—	43	1	no	—
64	C₂×C₈	—	43	2	no	—
65	C₂×C₈	—	43	2	no	—
66	C₂×C₈	—	172	2	no	—
67	C₂×C₈	C₂²×D₄₃	1	1	yes	characteristic
68	C₁₆	—	43	2	no	—
69	C₁₆	C₄×D₄₃	1	2	yes	—
70	C₂³	—	43	1	no	—
71	C₂×C₄	—	43	1	no	—
72	C₂×C₄	—	43	2	no	—
73	C₂×C₄	—	43	2	no	—
74	C₂×C₄	D₄×D₄₃	1	1	yes	characteristic
75	C₈	—	4	2	no	—
76	C₈	—	43	2	no	—
77	C₈	—	172	2	no	—
78	C₈	C₂×C₄×D₄₃	1	1	yes	characteristic
79	C₈	Q₈×D₄₃	1	1	yes	characteristic
80	C₂²	—	43	2	no	—
81	C₂²	—	172	1	no	—
82	C₂²	Q₁₆×D₄₃	1	1	yes	characteristic
83	C₄	—	43	2	no	—
84	C₄	C₄⋊C₄×D₄₃	1	1	yes	characteristic
85	C₄	D₈×D₄₃	1	1	yes	characteristic
86	C₂	—	2	1	no	—
87	C₂	—	86	2	no	—
88	C₂	#107×D₄₃	1	1	yes	characteristic

	subgroup	G/H
center	C₄	D₈×D₄₃
commutator	C₈×C₄₃	C₂²×C₄
Frattini	C₂×C₈	C₂²×D₄₃
Fitting	C₄₃×#368	C₂
socle	C₂×C₄₃	C₂×#107
hypercenter	#368	D₄₃
hypocenter	C₄₃	#2161
LCS	G ▷ C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂×C₈ ◁ #368

Complements

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

N	H ≅ G/N	type
3. #14582729	C₂	semidirect
4. #14582728	C₂	semidirect
5. C₄₃×#368	C₂	semidirect
49. #368	D₄₃	semidirect
50. C₄₃	#2161	semidirect