Subgroups — #19134182

Order 5504.

214 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14583297	C₂	1	3	yes	maximal, complemented
2	#14583272	C₂	1	3	yes	maximal
3	C₈²×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#10621873	—	2	6	no	—
5	#13063325	C₂²	1	3	yes	—
6	#13063322	C₂²	1	1	yes	characteristic
7	#13063257	—	2	6	no	—
8	C₄×C₈×C₄₃	C₂²	1	3	yes	—
9	C₂×D₁₇₂	—	2	3	no	—
10	C₂×Dic₈₆	—	2	3	no	—
11	C₂×C₈×C₄₃	D₄	1	6	yes	—
12	C₄²×C₄₃	C₂³	1	1	yes	characteristic
13	C₄⋊Dic₄₃	—	2	6	no	—
14	#10621873	—	4	12	no	—
15	C₂²×D₄₃	—	4	1	no	—
16	C₂×C₄×C₄₃	C₂×D₄	1	3	yes	—
17	C₂×Dic₄₃	—	4	3	no	—
18	D₁₇₂	—	4	6	no	—
19	Dic₈₆	—	4	6	no	—
20	C₈×C₄₃	SD₁₆	1	12	yes	complemented
21	C₂²×C₄₃	#127	1	1	yes	characteristic
22	C₂×D₄₃	—	8	3	no	—
23	C₄×C₄₃	C₂×SD₁₆	1	6	yes	—
24	Dic₄₃	—	8	3	no	—
25	#1705	—	43	1	no	maximal, Sylow
26	C₂×C₄₃	#492	1	3	yes	—
27	D₄₃	—	16	1	no	—
28	#498	—	43	3	no	—
29	#492	—	43	3	no	—
30	C₈²	D₄₃	1	1	yes	characteristic, complemented
31	C₄₃	#1705	1	1	yes	characteristic, complemented, Sylow
32	C₂×SD₁₆	—	86	6	no	—
33	C₄⋊Q₈	—	43	3	no	—
34	#127	—	43	1	no	—
35	#106	—	86	6	no	—
36	C₄×C₈	C₂×D₄₃	1	3	yes	—
37	C₂×Q₈	—	86	3	no	—
38	C₂×D₄	—	86	3	no	—
39	SD₁₆	—	172	12	no	—
40	C₂×C₈	D₁₇₂	1	6	yes	—
41	C₄⋊C₄	—	86	6	no	—
42	C₄²	C₂²×D₄₃	1	1	yes	characteristic
43	C₂³	—	172	1	no	—
44	Q₈	—	172	6	no	—
45	D₄	—	172	6	no	—
46	C₂×C₄	—	172	3	no	—
47	C₂×C₄	C₂×D₁₇₂	1	3	yes	—
48	C₈	#10621873	1	12	yes	complemented
49	C₂²	—	344	3	no	—
50	C₂²	#13063322	1	1	yes	characteristic
51	C₄	—	344	3	no	—
52	C₄	C₂×#10621873	1	6	yes	—
53	C₂	—	688	1	no	—
54	C₂	#14583272	1	3	yes	—

	subgroup	G/H
center	C₂²	#13063322
commutator	C₄²×C₄₃	C₂³
Frattini	C₄²	C₂²×D₄₃
Fitting	C₈²×C₄₃	C₂
socle	C₂²×C₄₃	#127
hypercenter	C₈²	D₄₃
hypocenter	C₄₃	#1705
LCS	G ▷ C₄²×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₈²

Complements

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

N	H ≅ G/N	type
1. #14583297	C₂	semidirect
3. C₈²×C₄₃	C₂	semidirect
20. C₈×C₄₃	SD₁₆	semidirect
30. C₈²	D₄₃	semidirect
31. C₄₃	#1705	semidirect
48. C₈	#10621873	semidirect