Subgroups — #14583308

Order 2752.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13063325	C₂	1	1	yes	maximal, characteristic
2	#13063317	C₂	1	1	yes	maximal, characteristic
3	#13063259	C₂	1	2	yes	maximal
4	#13063257	C₂	1	2	yes	maximal
5	#97×C₄₃	C₂	1	1	yes	maximal, characteristic
6	C₂×Dic₈₆	—	2	1	no	—
7	C₂×C₈×C₄₃	C₂²	1	2	yes	—
8	C₄²×C₄₃	C₂²	1	1	yes	characteristic
9	C₄⋊Dic₄₃	—	2	1	no	—
10	C₄⋊Dic₄₃	C₂²	1	1	yes	characteristic
11	C₄⋊Dic₄₃	C₂²	1	2	yes	—
12	C₄⋊Dic₄₃	C₂²	1	1	yes	characteristic
13	Dic₄₃⋊C₄	—	2	1	no	—
14	Dic₄₃⋊C₄	—	2	1	no	—
15	C₂×C₄×C₄₃	D₄	1	1	yes	characteristic
16	C₂×C₄×C₄₃	D₄	1	1	yes	characteristic
17	C₂×C₄×C₄₃	C₂³	1	1	yes	characteristic
18	C₂×Dic₄₃	—	2	1	no	—
19	C₂×Dic₄₃	—	2	1	no	—
20	C₂×Dic₄₃	—	2	2	no	—
21	Dic₈₆	—	4	2	no	—
22	C₈×C₄₃	Q₈	1	4	yes	complemented
23	C₂²×C₄₃	C₂×D₄	1	1	yes	characteristic
24	C₄×C₄₃	—	2	1	no	—
25	C₄×C₄₃	—	2	1	no	—
26	C₄×C₄₃	C₂×Q₈	1	2	yes	—
27	Dic₄₃	—	4	2	no	—
28	Dic₄₃	—	4	1	no	—
29	Dic₄₃	—	4	1	no	—
30	C₂×C₄₃	C₄⋊Q₈	1	1	yes	characteristic
31	C₂×C₄₃	AGL(1,ℤ/8)	1	1	yes	characteristic
32	C₂×C₄₃	#137	1	1	yes	characteristic
33	#501	—	43	1	no	maximal, Sylow
34	C₄₃	#501	1	1	yes	characteristic, complemented, Sylow
35	C₄⋊Q₈	—	43	1	no	—
36	#125	—	43	1	no	—
37	#107	—	43	2	no	—
38	#106	—	43	2	no	—
39	#97	D₄₃	1	1	yes	characteristic
40	C₂×Q₈	—	86	1	no	—
41	C₂×C₈	C₂×D₄₃	1	2	yes	—
42	C₄⋊C₄	—	43	1	no	—
43	C₄⋊C₄	—	43	2	no	—
44	C₄⋊C₄	—	43	1	no	—
45	C₄⋊C₄	—	86	1	no	—
46	C₄⋊C₄	—	86	1	no	—
47	C₄⋊C₄	—	86	1	no	—
48	C₄²	C₂×D₄₃	1	1	yes	characteristic
49	Q₈	—	172	2	no	—
50	C₂×C₄	—	86	1	no	—
51	C₂×C₄	—	86	1	no	—
52	C₂×C₄	—	86	2	no	—
53	C₂×C₄	D₁₇₂	1	1	yes	characteristic
54	C₂×C₄	D₁₇₂	1	1	yes	characteristic
55	C₂×C₄	C₂²×D₄₃	1	1	yes	characteristic
56	C₈	Dic₈₆	1	4	yes	complemented
57	C₂²	C₂×D₁₇₂	1	1	yes	characteristic
58	C₄	—	2	1	no	—
59	C₄	—	2	1	no	—
60	C₄	—	172	2	no	—
61	C₄	—	172	1	no	—
62	C₄	—	172	1	no	—
63	C₄	C₂×Dic₈₆	1	2	yes	—
64	C₂	#13063325	1	1	yes	characteristic
65	C₂	#13063353	1	1	yes	characteristic
66	C₂	#13063358	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₁₇₂
commutator, cosocle	C₂×C₄×C₄₃	C₂³
Frattini	C₂×C₄	C₂²×D₄₃
Fitting	#97×C₄₃	C₂
socle, prime radical	C₂²×C₄₃	C₂×D₄
hypercenter	#97	D₄₃
hypocenter	C₄₃	#501
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #97

Complements

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

N	H ≅ G/N	type
22. C₈×C₄₃	Q₈	semidirect
34. C₄₃	#501	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
#13063325	2
#13063317	2
#13063259	2
#13063257	2
#97×C₄₃	2
#501	43