Subgroups — #14583029

Order 2752.

94 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×Dic₈₆	C₂	1	1	yes	maximal, characteristic
2	C₄⋊(C₄₃⋊C₈)	C₂	1	1	yes	maximal, characteristic
3	Dic₄₃⋊C₈	C₂	1	2	yes	maximal
4	#13063235	C₂	1	2	yes	maximal
5	C₄×C₈×C₄₃	C₂	1	1	yes	maximal, characteristic
6	C₂×Dic₈₆	C₄	1	1	yes	characteristic
7	C₂×C₈×C₄₃	C₂²	1	1	yes	characteristic
8	C₂×C₈×C₄₃	C₂²	1	1	yes	characteristic
9	C₄²×C₄₃	C₂²	1	1	yes	characteristic
10	C₄⋊Dic₄₃	C₄	1	1	yes	characteristic
11	Dic₄₃⋊C₄	C₄	1	2	yes	—
12	C₄×Dic₄₃	C₂²	1	2	yes	—
13	C₂×C₄₃⋊C₈	C₂²	1	2	yes	—
14	C₂×C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
15	C₂×C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
16	C₂×C₄×C₄₃	C₂³	1	1	yes	characteristic
17	C₂×Dic₄₃	C₂×C₄	1	2	yes	—
18	C₂×Dic₄₃	C₂×C₄	1	2	yes	—
19	Dic₈₆	—	2	2	no	—
20	C₈×C₄₃	—	2	1	no	—
21	C₈×C₄₃	Q₈	1	2	yes	complemented
22	C₄₃⋊C₈	—	2	2	no	—
23	C₂²×C₄₃	C₂²×C₄	1	1	yes	characteristic
24	C₄×C₄₃	—	2	1	no	—
25	C₄×C₄₃	M₁₆	1	2	yes	—
26	C₄×C₄₃	C₂×Q₈	1	1	yes	characteristic
27	C₄×C₄₃	#41	1	1	yes	characteristic
28	Dic₄₃	—	2	2	no	—
29	Dic₄₃	—	2	2	no	—
30	C₂×C₄₃	C₄×Q₈	1	1	yes	characteristic
31	C₂×C₄₃	C₂×M₁₆	1	1	yes	characteristic
32	C₂×C₄₃	#131	1	1	yes	characteristic
33	#446	—	43	1	no	maximal, Sylow
34	C₄₃	#446	1	1	yes	characteristic, complemented, Sylow
35	C₄×Q₈	—	43	1	no	—
36	C₄⋊C₈	—	43	2	no	—
37	C₄⋊C₈	—	43	1	no	—
38	#97	—	43	2	no	—
39	C₄×C₈	D₄₃	1	1	yes	characteristic
40	C₂×Q₈	—	43	1	no	—
41	C₂×C₈	—	43	2	no	—
42	C₂×C₈	C₂×D₄₃	1	1	yes	characteristic
43	C₂×C₈	C₂×D₄₃	1	1	yes	characteristic
44	C₄⋊C₄	—	43	2	no	—
45	C₄⋊C₄	—	43	1	no	—
46	C₄²	—	43	2	no	—
47	C₄²	C₂×D₄₃	1	1	yes	characteristic
48	Q₈	—	86	2	no	—
49	C₂×C₄	—	43	2	no	—
50	C₂×C₄	—	43	2	no	—
51	C₂×C₄	C₄×D₄₃	1	1	yes	characteristic
52	C₂×C₄	C₄×D₄₃	1	1	yes	characteristic
53	C₂×C₄	C₂²×D₄₃	1	1	yes	characteristic
54	C₈	—	2	1	no	—
55	C₈	—	86	2	no	—
56	C₈	Dic₈₆	1	2	yes	complemented
57	C₂²	C₂×C₄×D₄₃	1	1	yes	characteristic
58	C₄	—	2	1	no	—
59	C₄	—	86	2	no	—
60	C₄	—	86	2	no	—
61	C₄	#10621872	1	2	yes	—
62	C₄	C₂×Dic₈₆	1	1	yes	characteristic
63	C₄	#10621898	1	1	yes	characteristic
64	C₂	C₄×Dic₈₆	1	1	yes	characteristic
65	C₂	C₂×#10621872	1	1	yes	characteristic
66	C₂	#13063331	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂²×D₄₃
commutator, socle, prime radical	C₂²×C₄₃	C₂²×C₄
Fitting	C₄×C₈×C₄₃	C₂
cosocle	C₂×C₄×C₄₃	C₂³
hypercenter	C₄×C₈	D₄₃
hypocenter	C₄₃	#446
LCS	G ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄ ◁ C₄×C₈

Complements

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

N	H ≅ G/N	type
21. C₈×C₄₃	Q₈	semidirect
34. C₄₃	#446	semidirect
56. C₈	Dic₈₆	semidirect

Maximal subgroups

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

subgroup	index
C₄×Dic₈₆	2
C₄⋊(C₄₃⋊C₈)	2
Dic₄₃⋊C₈	2
#13063235	2
C₄×C₈×C₄₃	2
#446	43