Subgroups — #14582649

Order 2752.

54 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄⋊(C₄₃⋊C₈)	C₂	1	1	yes	maximal, characteristic
2	C₄×C₄₃⋊C₈	C₂	1	1	yes	maximal, characteristic
3	C₄⋊C₈×C₄₃	C₂	1	1	yes	maximal, characteristic
4	C₂×C₈×C₄₃	—	2	1	no	—
5	C₄²×C₄₃	C₂²	1	1	yes	characteristic
6	C₂×C₄₃⋊C₈	—	2	1	no	—
7	C₂×C₄₃⋊C₈	C₄	1	1	yes	characteristic
8	C₂×C₄₃⋊C₈	C₄	1	1	yes	characteristic
9	C₂×C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
10	C₂×C₄×C₄₃	D₄	1	1	yes	characteristic
11	C₂×C₄×C₄₃	Q₈	1	1	yes	characteristic
12	C₈×C₄₃	—	4	1	no	—
13	C₄₃⋊C₈	—	2	1	no	—
14	C₄₃⋊C₈	—	4	1	no	—
15	C₄₃⋊C₈	C₈	1	2	yes	complemented
16	C₂²×C₄₃	C₄⋊C₄	1	1	yes	characteristic
17	C₄×C₄₃	—	2	1	no	—
18	C₄×C₄₃	C₂×C₈	1	1	yes	characteristic
19	C₄×C₄₃	M₁₆	1	1	yes	characteristic
20	C₄×C₄₃	SD₁₆	1	1	yes	characteristic
21	C₄×C₄₃	SD₁₆	1	1	yes	characteristic
22	C₂×C₄₃	C₄⋊C₈	1	1	yes	characteristic
23	C₂×C₄₃	#106	1	1	yes	characteristic
24	C₂×C₄₃	#108	1	1	yes	characteristic
25	#334	—	43	1	no	maximal, Sylow
26	C₄₃	#334	1	1	yes	characteristic, complemented, Sylow
27	C₄⋊C₈	—	43	1	no	—
28	C₄⋊C₈	D₄₃	1	1	yes	characteristic
29	C₄×C₈	—	43	1	no	—
30	C₂×C₈	—	2	1	no	—
31	C₂×C₈	—	43	1	no	—
32	C₂×C₈	—	43	1	no	—
33	C₂×C₈	—	86	1	no	—
34	C₄²	C₂×D₄₃	1	1	yes	characteristic
35	C₂×C₄	Dic₈₆	1	1	yes	characteristic
36	C₂×C₄	C₄×D₄₃	1	1	yes	characteristic
37	C₂×C₄	C₂²⋊D₄₃	1	1	yes	characteristic
38	C₈	—	4	1	no	—
39	C₈	—	43	2	no	—
40	C₈	—	86	1	no	—
41	C₈	—	172	1	no	—
42	C₂²	Dic₄₃⋊C₄	1	1	yes	characteristic
43	C₄	—	2	1	no	—
44	C₄	C₈×D₄₃	1	1	yes	characteristic
45	C₄	#10621872	1	1	yes	characteristic
46	C₄	#10621883	1	1	yes	characteristic
47	C₄	#10621884	1	1	yes	characteristic
48	C₂	Dic₄₃⋊C₈	1	1	yes	characteristic
49	C₂	#13063256	1	1	yes	characteristic
50	C₂	#13063260	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²⋊D₄₃
commutator	C₄×C₄₃	C₂×C₈
Frattini	C₄²	C₂×D₄₃
Fitting	C₄⋊C₈×C₄₃	C₂
socle, prime radical	C₂²×C₄₃	C₄⋊C₄
cosocle	C₄²×C₄₃	C₂²
hypercenter	C₄⋊C₈	D₄₃
hypocenter	C₄₃	#334
LCS	G ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄ ◁ C₄² ◁ C₄⋊C₈

Complements

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

N	H ≅ G/N	type
15. C₄₃⋊C₈	C₈	semidirect
26. C₄₃	#334	semidirect

Maximal subgroups

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

subgroup	index
C₄⋊(C₄₃⋊C₈)	2
C₄×C₄₃⋊C₈	2
C₄⋊C₈×C₄₃	2
#334	43