Subgroups — #14583636

Order 2752.

252 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13063319	C₂	1	2	yes	maximal, complemented
2	#13063306	C₂	1	3	yes	maximal, complemented
3	#13063297	C₂	1	6	yes	maximal, complemented
4	#13063293	C₂	1	3	yes	maximal, complemented
5	#127×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂³×D₄₃	C₂²	1	1	yes	characteristic
7	C₂×D₄×C₄₃	C₂²	1	3	yes	—
8	C₂×D₄×C₄₃	C₂²	1	3	yes	complemented
9	C₂×C₂²⋊D₄₃	C₂²	1	6	yes	—
10	C₂²×Dic₄₃	C₂²	1	3	yes	complemented
11	C₄²×C₄₃	C₂²	1	1	yes	characteristic, complemented
12	C₂²⋊Dic₄₃	C₂²	1	3	yes	—
13	C₂²⋊Dic₄₃	C₂²	1	3	yes	complemented
14	(C₂×D₄₃)⋊C₄	C₂²	1	6	yes	—
15	Dic₄₃⋊C₄	C₂²	1	6	yes	complemented
16	C₂³×C₄₃	C₂³	1	1	yes	characteristic
17	C₂³×C₄₃	C₂³	1	3	yes	—
18	C₂²×D₄₃	—	4	3	no	—
19	C₂²×D₄₃	C₂³	1	2	yes	—
20	D₄×C₄₃	—	4	3	no	—
21	D₄×C₄₃	—	4	3	no	—
22	C₂×C₄×C₄₃	C₂³	1	3	yes	—
23	C₂²⋊D₄₃	—	4	6	no	—
24	C₂×Dic₄₃	—	4	3	no	—
25	C₂×Dic₄₃	C₂³	1	6	yes	—
26	C₂²×C₄₃	—	2	3	no	—
27	C₂²×C₄₃	—	2	3	no	—
28	C₂²×C₄₃	—	2	6	no	—
29	C₂²×C₄₃	C₂⁴	1	1	yes	characteristic
30	C₂×D₄₃	—	2	6	no	—
31	C₂×D₄₃	—	4	4	no	—
32	C₄×C₄₃	—	2	3	no	—
33	Dic₄₃	—	2	6	no	—
34	C₂×C₄₃	—	4	1	no	—
35	C₂×C₄₃	—	4	3	no	—
36	C₂×C₄₃	H(5,𝔽₂)	1	3	yes	—
37	D₄₃	—	4	2	no	—
38	#560	—	43	1	no	maximal, Sylow
39	C₄₃	#560	1	1	yes	characteristic, complemented, Sylow
40	#127	D₄₃	1	1	yes	characteristic, complemented
41	#126	—	43	2	no	—
42	#123	—	43	3	no	—
43	#121	—	43	6	no	—
44	#120	—	43	3	no	—
45	C₂⁴	—	43	1	no	—
46	C₂×D₄	—	43	6	no	—
47	C₂×D₄	C₂×D₄₃	1	3	yes	—
48	C₂×D₄	C₂×D₄₃	1	3	yes	complemented
49	C₂²×C₄	—	43	3	no	—
50	C₄⋊C₄	—	43	6	no	—
51	C₂²⋊C₄	—	43	3	no	—
52	C₂²⋊C₄	—	43	3	no	—
53	C₂²⋊C₄	—	43	6	no	—
54	C₄²	C₂×D₄₃	1	1	yes	characteristic, complemented
55	C₂³	—	43	2	no	—
56	C₂³	—	172	3	no	—
57	C₂³	C₂²×D₄₃	1	1	yes	characteristic
58	C₂³	C₂²×D₄₃	1	3	yes	—
59	D₄	—	4	3	no	—
60	D₄	—	4	3	no	—
61	D₄	—	172	6	no	—
62	C₂×C₄	—	43	6	no	—
63	C₂×C₄	—	172	3	no	—
64	C₂×C₄	C₂²×D₄₃	1	3	yes	—
65	C₂²	—	2	3	no	—
66	C₂²	—	2	6	no	—
67	C₂²	—	2	3	no	—
68	C₂²	—	86	6	no	—
69	C₂²	—	172	4	no	—
70	C₂²	C₂³×D₄₃	1	1	yes	characteristic
71	C₄	—	2	3	no	—
72	C₄	—	86	6	no	—
73	C₂	—	4	1	no	—
74	C₂	—	4	3	no	—
75	C₂	—	172	2	no	—
76	C₂	#13063370	1	3	yes	—

	subgroup	G/H
center, Frattini	C₂²	C₂³×D₄₃
commutator, socle, cosocle	C₂²×C₄₃	C₂⁴
Fitting	#127×C₄₃	C₂
hypercenter	#127	D₄₃
hypocenter	C₄₃	#560
LCS	G ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ #127

Complements

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

N	H ≅ G/N	type
1. #13063319	C₂	semidirect
2. #13063306	C₂	semidirect
3. #13063297	C₂	semidirect
4. #13063293	C₂	semidirect
5. #127×C₄₃	C₂	semidirect
8. C₂×D₄×C₄₃	C₂²	semidirect
10. C₂²×Dic₄₃	C₂²	semidirect
11. C₄²×C₄₃	C₂²	semidirect
13. C₂²⋊Dic₄₃	C₂²	semidirect
15. Dic₄₃⋊C₄	C₂²	semidirect
39. C₄₃	#560	semidirect
40. #127	D₄₃	semidirect
48. C₂×D₄	C₂×D₄₃	semidirect
54. C₄²	C₂×D₄₃	semidirect

Maximal subgroups

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

subgroup	index
#13063319	2
#13063306	2
#13063297	2
#13063293	2
#127×C₄₃	2
#560	43