Subgroups — #14583011

Order 2752.

132 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₄×Dic₄₃	C₂	1	2	yes	maximal, complemented
2	#13063257	C₂	1	1	yes	maximal, characteristic, complemented
3	#13063246	C₂	1	2	yes	maximal, complemented
4	#13063235	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×D₈×C₄₃	C₂	1	1	yes	maximal, characteristic
6	C₂×D₄×C₄₃	C₂²	1	2	yes	—
7	C₂²×Dic₄₃	—	2	2	no	—
8	D₈×C₄₃	C₄	1	4	yes	complemented
9	C₂×C₈×C₄₃	C₂²	1	1	yes	characteristic
10	C₂²⋊Dic₄₃	—	2	2	no	—
11	C₄⋊Dic₄₃	C₂²	1	2	yes	—
12	C₄×Dic₄₃	C₂²	1	1	yes	characteristic
13	C₂×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
14	C₂³×C₄₃	—	2	2	no	—
15	D₄×C₄₃	—	2	2	no	—
16	D₄×C₄₃	C₂×C₄	1	4	yes	complemented
17	C₂×C₄×C₄₃	C₂³	1	1	yes	characteristic
18	C₂×Dic₄₃	—	2	2	no	—
19	C₂×Dic₄₃	—	4	4	no	—
20	C₂×Dic₄₃	D₄	1	2	yes	—
21	C₈×C₄₃	C₂×C₄	1	2	yes	complemented
22	C₄₃⋊C₈	—	2	1	no	—
23	C₂²×C₄₃	—	2	4	no	—
24	C₂²×C₄₃	—	4	2	no	—
25	C₂²×C₄₃	—	4	2	no	—
26	C₂²×C₄₃	C₂×D₄	1	1	yes	characteristic
27	C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
28	C₄×C₄₃	#41	1	1	yes	characteristic
29	Dic₄₃	—	2	2	no	—
30	Dic₄₃	—	4	2	no	—
31	C₂×C₄₃	—	4	4	no	—
32	C₂×C₄₃	C₄×D₄	1	1	yes	characteristic
33	C₂×C₄₃	AGL(1,ℤ/8)	1	2	yes	—
34	#442	—	43	1	no	maximal, Sylow
35	C₄₃	#442	1	1	yes	characteristic, complemented, Sylow
36	C₂×D₈	D₄₃	1	1	yes	characteristic
37	C₄×D₄	—	43	2	no	—
38	#106	—	43	1	no	—
39	#102	—	43	2	no	—
40	#97	—	43	1	no	—
41	C₂×D₄	C₂×D₄₃	1	2	yes	—
42	C₂²×C₄	—	86	2	no	—
43	D₈	Dic₄₃	1	4	yes	complemented
44	C₂×C₈	—	43	1	no	—
45	C₂×C₈	C₂×D₄₃	1	1	yes	characteristic
46	C₄⋊C₄	—	43	2	no	—
47	C₂²⋊C₄	—	86	2	no	—
48	C₄²	—	43	1	no	—
49	C₂³	—	2	2	no	—
50	D₄	—	2	2	no	—
51	D₄	C₂×Dic₄₃	1	4	yes	complemented
52	C₂×C₄	—	43	2	no	—
53	C₂×C₄	—	86	2	no	—
54	C₂×C₄	—	172	4	no	—
55	C₂×C₄	C₂²×D₄₃	1	1	yes	characteristic
56	C₈	—	86	1	no	—
57	C₈	C₂×Dic₄₃	1	2	yes	complemented
58	C₂²	—	2	4	no	—
59	C₂²	—	4	2	no	—
60	C₂²	—	4	2	no	—
61	C₂²	D₄×D₄₃	1	1	yes	characteristic
62	C₄	—	86	2	no	—
63	C₄	—	172	2	no	—
64	C₄	#10621900	1	1	yes	characteristic
65	C₄	C₂²×Dic₄₃	1	1	yes	characteristic
66	C₂	—	4	4	no	—
67	C₂	D₄×Dic₄₃	1	1	yes	characteristic
68	C₂	#13063349	1	2	yes	—

	subgroup	G/H
center	C₂²	D₄×D₄₃
commutator	C₄×C₄₃	C₂²×C₄
Frattini	C₂×C₄	C₂²×D₄₃
Fitting, prime radical	C₂×D₈×C₄₃	C₂
socle	C₂²×C₄₃	C₂×D₄
cosocle	C₂×C₄×C₄₃	C₂³
hypercenter	C₂×D₈	D₄₃
hypocenter	C₄₃	#442
LCS	G ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×D₈

Complements

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

N	H ≅ G/N	type
1. D₄×Dic₄₃	C₂	semidirect
2. #13063257	C₂	semidirect
3. #13063246	C₂	semidirect
4. #13063235	C₂	semidirect
8. D₈×C₄₃	C₄	semidirect
16. D₄×C₄₃	C₂×C₄	semidirect
21. C₈×C₄₃	C₂×C₄	semidirect
35. C₄₃	#442	semidirect
43. D₈	Dic₄₃	semidirect
51. D₄	C₂×Dic₄₃	semidirect
57. C₈	C₂×Dic₄₃	semidirect

Maximal subgroups

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

subgroup	index
D₄×Dic₄₃	2
#13063257	2
#13063246	2
#13063235	2
C₂×D₈×C₄₃	2
#442	43