Subgroups — #19132783

Order 5504.

74 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14583331	C₂	1	1	yes	maximal, characteristic
2	#14582727	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₃×M₆₄	C₂	1	1	yes	maximal, characteristic, complemented
4	#13063347	—	2	1	no	—
5	Dic₃₄₄	C₄	1	1	yes	characteristic, complemented
6	#13063270	—	2	1	no	—
7	D₆₈₈	C₄	1	1	yes	characteristic, complemented
8	#13063259	—	2	1	no	—
9	C₂×C₁₆×C₄₃	C₂²	1	1	yes	characteristic
10	C₃₂×C₄₃	—	2	1	no	—
11	#10621898	—	4	1	no	—
12	C₂×C₈×C₄₃	D₄	1	1	yes	characteristic
13	C₄⋊Dic₄₃	—	4	1	no	—
14	Dic₁₇₂	—	2	1	no	—
15	D₃₄₄	—	2	1	no	—
16	#10621873	—	4	1	no	—
17	C₁₆×C₄₃	C₂×C₄	1	1	yes	characteristic
18	C₁₆×C₄₃	D₄	1	1	yes	characteristic
19	C₂×C₄×C₄₃	D₈	1	1	yes	characteristic
20	C₂²⋊D₄₃	—	8	1	no	—
21	C₂×Dic₄₃	—	8	1	no	—
22	D₁₇₂	—	4	1	no	—
23	C₄×D₄₃	—	8	1	no	—
24	Dic₈₆	—	4	1	no	—
25	C₈×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
26	C₈×C₄₃	SD₁₆	1	1	yes	characteristic
27	C₂²×C₄₃	D₁₆	1	1	yes	characteristic
28	C₂×D₄₃	—	8	1	no	—
29	C₄×C₄₃	#102	1	1	yes	characteristic
30	C₄×C₄₃	SD₃₂	1	1	yes	characteristic
31	Dic₄₃	—	8	1	no	—
32	Dic₄₃	—	16	1	no	—
33	#1418	—	43	1	no	maximal, Sylow
34	C₂×C₄₃	—	2	1	no	—
35	C₂×C₄₃	#357	1	1	yes	characteristic
36	D₄₃	—	16	1	no	—
37	#508	—	43	1	no	—
38	M₆₄	D₄₃	1	1	yes	characteristic, complemented
39	#367	—	43	1	no	—
40	C₄₃	#1418	1	1	yes	characteristic, complemented, Sylow
41	#135	—	86	1	no	—
42	Q₃₂	—	43	1	no	—
43	SD₃₂	—	86	1	no	—
44	D₁₆	—	43	1	no	—
45	C₂×C₁₆	C₂×D₄₃	1	1	yes	characteristic
46	#107	—	86	1	no	—
47	C₃₂	—	2	1	no	—
48	#41	—	172	1	no	—
49	Q₁₆	—	86	1	no	—
50	SD₁₆	—	172	1	no	—
51	D₈	—	86	1	no	—
52	C₂×C₈	D₁₇₂	1	1	yes	characteristic
53	C₄⋊C₄	—	172	1	no	—
54	C₁₆	C₄×D₄₃	1	1	yes	characteristic
55	C₁₆	C₂²⋊D₄₃	1	1	yes	characteristic
56	Q₈	—	172	1	no	—
57	D₄	—	344	1	no	—
58	D₄	—	172	1	no	—
59	C₂×C₄	—	344	1	no	—
60	C₂×C₄	—	344	1	no	—
61	C₂×C₄	D₃₄₄	1	1	yes	characteristic
62	C₈	#10621873	1	1	yes	characteristic
63	C₈	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
64	C₂²	—	344	1	no	—
65	C₂²	D₆₈₈	1	1	yes	characteristic
66	C₄	—	344	1	no	—
67	C₄	—	688	1	no	—
68	C₄	#13063247	1	1	yes	characteristic
69	C₄	#13063270	1	1	yes	characteristic
70	C₂	—	2	1	no	—
71	C₂	—	688	1	no	—
72	C₂	#14582701	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#14582701
commutator	C₁₆×C₄₃	C₂×C₄
Frattini	C₂×C₁₆	C₂×D₄₃
Fitting	C₄₃×M₆₄	C₂
socle	C₂×C₄₃	#357
hypercenter	M₆₄	D₄₃
hypocenter	C₄₃	#1418
LCS	G ▷ C₁₆×C₄₃ ▷ C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ M₆₄

Complements

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

N	H ≅ G/N	type
2. #14582727	C₂	semidirect
3. C₄₃×M₆₄	C₂	semidirect
5. Dic₃₄₄	C₄	semidirect
7. D₆₈₈	C₄	semidirect
38. M₆₄	D₄₃	semidirect
40. C₄₃	#1418	semidirect