Subgroups — #19132699

Order 5504.

124 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#13063261	C₂	1	2	yes	maximal
2	C₂×M₃₂×C₄₃	C₂	1	1	yes	maximal, characteristic
3	C₂×#10621877	—	2	2	no	—
4	#13063261	—	2	2	no	—
5	#13063261	C₄	1	4	yes	—
6	C₂²×C₈×C₄₃	C₂²	1	1	yes	characteristic
7	M₃₂×C₄₃	—	2	2	no	—
8	C₂×C₁₆×C₄₃	C₄	1	2	yes	—
9	C₂²×C₄×C₄₃	D₄	1	1	yes	characteristic
10	C₂×C₈×C₄₃	C₂×C₄	1	2	yes	—
11	C₂×C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
12	C₂×C₈×C₄₃	D₄	1	2	yes	—
13	C₂×C₈×C₄₃	Q₈	1	1	yes	characteristic
14	#10621877	—	2	4	no	—
15	#10621877	—	4	2	no	—
16	C₂×C₄₃⋊C₈	—	4	2	no	—
17	C₁₆×C₄₃	—	2	2	no	—
18	C₂³×C₄₃	Q₁₆	1	1	yes	characteristic
19	C₂×C₄×C₄₃	C₂²⋊C₄	1	2	yes	—
20	C₂×C₄×C₄₃	C₄⋊C₄	1	1	yes	characteristic
21	C₂×C₄×C₄₃	D₈	1	1	yes	characteristic
22	C₂×C₄×C₄₃	SD₁₆	1	2	yes	—
23	C₈×C₄₃	C₄²	1	1	yes	characteristic
24	C₈×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
25	C₈×C₄₃	C₄⋊C₄	1	2	yes	—
26	C₄₃⋊C₈	—	4	4	no	—
27	C₂²×C₄₃	—	4	1	no	—
28	C₂²×C₄₃	#103	1	2	yes	—
29	C₂²×C₄₃	#107	1	1	yes	characteristic
30	C₄×C₄₃	#95	1	1	yes	characteristic
31	C₄×C₄₃	#102	1	2	yes	—
32	C₄×C₄₃	#106	1	1	yes	characteristic
33	#1385	—	43	1	no	maximal, Sylow
34	C₂×C₄₃	—	2	2	no	—
35	C₂×C₄₃	—	2	1	no	—
36	C₂×C₄₃	#340	1	1	yes	characteristic
37	C₂×M₃₂	D₄₃	1	1	yes	characteristic
38	C₂×#108	—	43	2	no	—
39	C₄₃	#1385	1	1	yes	characteristic, complemented, Sylow
40	C₂×M₁₆	—	86	2	no	—
41	C₂²×C₈	C₂×D₄₃	1	1	yes	characteristic
42	M₃₂	—	2	2	no	—
43	C₂×C₁₆	Dic₄₃	1	2	yes	—
44	#108	—	43	4	no	—
45	#108	—	86	2	no	—
46	C₂²×C₄	D₁₇₂	1	1	yes	characteristic
47	M₁₆	—	86	4	no	—
48	M₁₆	—	172	2	no	—
49	C₂×C₈	—	172	2	no	—
50	C₂×C₈	Dic₈₆	1	1	yes	characteristic
51	C₂×C₈	C₄×D₄₃	1	2	yes	—
52	C₂×C₈	C₂×Dic₄₃	1	1	yes	characteristic
53	C₂×C₈	C₂²⋊D₄₃	1	2	yes	—
54	C₁₆	—	2	2	no	—
55	C₂³	Dic₁₇₂	1	1	yes	characteristic
56	C₂×C₄	#10621873	1	2	yes	—
57	C₂×C₄	D₃₄₄	1	1	yes	characteristic
58	C₂×C₄	C₄⋊Dic₄₃	1	1	yes	characteristic
59	C₂×C₄	(C₂×D₄₃)⋊C₄	1	2	yes	—
60	C₈	—	172	4	no	—
61	C₈	C₄×Dic₄₃	1	1	yes	characteristic
62	C₈	Dic₄₃⋊C₄	1	2	yes	—
63	C₈	C₂²⋊Dic₄₃	1	1	yes	characteristic
64	C₂²	—	4	1	no	—
65	C₂²	#13063250	1	2	yes	—
66	C₂²	#13063259	1	1	yes	characteristic
67	C₄	C₄₃⋊#95	1	1	yes	characteristic
68	C₄	#13063247	1	2	yes	—
69	C₄	#13063257	1	1	yes	characteristic
70	C₂	—	2	2	no	—
71	C₂	—	2	1	no	—
72	C₂	#14582662	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#13063257
commutator	C₈×C₄₃	C₄²
Frattini	C₂²×C₈	C₂×D₄₃
Fitting	C₂×M₃₂×C₄₃	C₂
socle	C₂×C₄₃	#340
hypercenter	C₂×M₃₂	D₄₃
hypocenter	C₄₃	#1385
LCS	G ▷ C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂×M₃₂

Complements

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

N	H ≅ G/N	type
39. C₄₃	#1385	semidirect