Subgroups — #14582710

Order 2752.

58 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13063347	C₂	1	1	yes	maximal, characteristic
2	#13063257	C₂	1	1	yes	maximal, characteristic, complemented
3	M₃₂×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
4	#10621898	—	2	1	no	—
5	C₂×C₈×C₄₃	C₂²	1	1	yes	characteristic
6	C₄⋊Dic₄₃	—	2	1	no	—
7	Dic₁₇₂	C₄	1	1	yes	characteristic, complemented
8	D₃₄₄	C₄	1	1	yes	characteristic, complemented
9	#10621873	—	2	1	no	—
10	C₁₆×C₄₃	—	2	1	no	—
11	C₂×C₄×C₄₃	D₄	1	1	yes	characteristic
12	C₂²⋊D₄₃	—	4	1	no	—
13	C₂×Dic₄₃	—	4	1	no	—
14	D₁₇₂	—	2	1	no	—
15	C₄×D₄₃	—	4	1	no	—
16	Dic₈₆	—	2	1	no	—
17	C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
18	C₈×C₄₃	D₄	1	1	yes	characteristic
19	C₂²×C₄₃	D₈	1	1	yes	characteristic
20	C₂×D₄₃	—	4	1	no	—
21	C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
22	C₄×C₄₃	SD₁₆	1	1	yes	characteristic
23	Dic₄₃	—	4	1	no	—
24	Dic₄₃	—	8	1	no	—
25	C₂×C₄₃	—	2	1	no	—
26	C₂×C₄₃	#102	1	1	yes	characteristic
27	D₄₃	—	8	1	no	—
28	#360	—	43	1	no	maximal, Sylow
29	C₄₃	#360	1	1	yes	characteristic, complemented, Sylow
30	#135	—	43	1	no	—
31	M₃₂	D₄₃	1	1	yes	characteristic, complemented
32	#106	—	43	1	no	—
33	#41	—	86	1	no	—
34	Q₁₆	—	43	1	no	—
35	SD₁₆	—	86	1	no	—
36	D₈	—	43	1	no	—
37	C₂×C₈	C₂×D₄₃	1	1	yes	characteristic
38	C₄⋊C₄	—	86	1	no	—
39	C₁₆	—	2	1	no	—
40	Q₈	—	86	1	no	—
41	D₄	—	86	1	no	—
42	D₄	—	172	1	no	—
43	C₂×C₄	—	172	1	no	—
44	C₂×C₄	—	172	1	no	—
45	C₂×C₄	D₁₇₂	1	1	yes	characteristic
46	C₈	C₄×D₄₃	1	1	yes	characteristic
47	C₈	C₂²⋊D₄₃	1	1	yes	characteristic
48	C₂²	—	172	1	no	—
49	C₂²	D₃₄₄	1	1	yes	characteristic
50	C₄	—	344	1	no	—
51	C₄	—	172	1	no	—
52	C₄	#10621873	1	1	yes	characteristic
53	C₄	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
54	C₂	—	2	1	no	—
55	C₂	—	344	1	no	—
56	C₂	#13063247	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#13063247
commutator	C₈×C₄₃	C₂×C₄
Frattini	C₂×C₈	C₂×D₄₃
Fitting	M₃₂×C₄₃	C₂
socle	C₂×C₄₃	#102
prime radical	#13063347	C₂
cosocle	C₂×C₈×C₄₃	C₂²
hypercenter	M₃₂	D₄₃
hypocenter	C₄₃	#360
LCS	G ▷ C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ M₃₂

Complements

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

N	H ≅ G/N	type
2. #13063257	C₂	semidirect
3. M₃₂×C₄₃	C₂	semidirect
7. Dic₁₇₂	C₄	semidirect
8. D₃₄₄	C₄	semidirect
29. C₄₃	#360	semidirect
31. M₃₂	D₄₃	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
#13063347	2
#13063257	2
M₃₂×C₄₃	2
#360	43