Subgroups — #19132780

Order 5504.

72 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	#14582729	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃₂×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
4	#13063347	—	2	1	no	—
5	Dic₃₄₄	C₄	1	1	yes	characteristic
6	#13063270	—	2	1	no	—
7	D₆₈₈	C₄	1	1	yes	characteristic
8	#13063261	—	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	#10621877	—	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	D₁₇₂	—	4	1	no	—
22	C₄×D₄₃	—	8	1	no	—
23	Dic₈₆	—	4	1	no	—
24	C₈×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
25	C₈×C₄₃	SD₁₆	1	1	yes	characteristic
26	C₄₃⋊C₈	—	8	1	no	—
27	C₂²×C₄₃	SD₃₂	1	1	yes	characteristic
28	C₂×D₄₃	—	8	1	no	—
29	C₄×C₄₃	#102	1	1	yes	characteristic
30	C₄×C₄₃	D₁₆	1	1	yes	characteristic
31	Dic₄₃	—	8	1	no	—
32	#1417	—	43	1	no	maximal, Sylow
33	C₂×C₄₃	—	2	1	no	—
34	C₂×C₄₃	#357	1	1	yes	characteristic
35	D₄₃	—	16	1	no	—
36	#508	—	43	1	no	—
37	C₂×C₃₂	D₄₃	1	1	yes	characteristic, complemented
38	#368	—	43	1	no	—
39	C₄₃	#1417	1	1	yes	characteristic, complemented, Sylow
40	#135	—	86	1	no	—
41	Q₃₂	—	43	1	no	—
42	SD₃₂	—	86	1	no	—
43	D₁₆	—	43	1	no	—
44	C₂×C₁₆	C₂×D₄₃	1	1	yes	characteristic
45	#108	—	86	1	no	—
46	C₃₂	—	2	1	no	—
47	#41	—	172	1	no	—
48	Q₁₆	—	86	1	no	—
49	SD₁₆	—	172	1	no	—
50	D₈	—	86	1	no	—
51	M₁₆	—	172	1	no	—
52	C₂×C₈	D₁₇₂	1	1	yes	characteristic
53	C₁₆	C₄×D₄₃	1	1	yes	characteristic
54	C₁₆	C₂²⋊D₄₃	1	1	yes	characteristic
55	Q₈	—	172	1	no	—
56	D₄	—	344	1	no	—
57	D₄	—	172	1	no	—
58	C₂×C₄	—	344	1	no	—
59	C₂×C₄	D₃₄₄	1	1	yes	characteristic
60	C₈	—	344	1	no	—
61	C₈	#10621873	1	1	yes	characteristic
62	C₈	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
63	C₂²	—	344	1	no	—
64	C₂²	#13063270	1	1	yes	characteristic
65	C₄	—	344	1	no	—
66	C₄	#13063247	1	1	yes	characteristic
67	C₄	D₆₈₈	1	1	yes	characteristic
68	C₂	—	2	1	no	—
69	C₂	—	688	1	no	—
70	C₂	#14582701	1	1	yes	characteristic

	subgroup	G/H
center	C₄	D₆₈₈
commutator	C₁₆×C₄₃	C₂×C₄
Frattini	C₂×C₁₆	C₂×D₄₃
Fitting	C₂×C₃₂×C₄₃	C₂
socle	C₂×C₄₃	#357
hypercenter	C₂×C₃₂	D₄₃
hypocenter	C₄₃	#1417
LCS	G ▷ C₁₆×C₄₃ ▷ C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ C₂×C₃₂

Complements

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

N	H ≅ G/N	type
2. #14582729	C₂	semidirect
3. C₂×C₃₂×C₄₃	C₂	semidirect
37. C₂×C₃₂	D₄₃	semidirect
39. C₄₃	#1417	semidirect