Subgroups — #14583716

Order 2752.

248 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13063372	C₂	1	2	yes	maximal, complemented
2	#13063358	C₂	1	6	yes	maximal, complemented
3	#13063347	C₂	1	3	yes	maximal, complemented
4	C₂×Dic₁₇₂	C₂	1	3	yes	maximal, complemented
5	#131×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
6	#41×C₄₃	C₂²	1	1	yes	characteristic
7	Q₈×D₄₃	—	2	2	no	—
8	#10621900	—	2	6	no	—
9	#10621898	C₂²	1	6	yes	—
10	C₂×Dic₈₆	C₂²	1	6	yes	—
11	M₁₆×C₄₃	C₂²	1	3	yes	—
12	C₂×C₈×C₄₃	C₂²	1	3	yes	—
13	Dic₁₇₂	C₂²	1	3	yes	—
14	Dic₁₇₂	C₂²	1	6	yes	—
15	D₃₄₄	C₂²	1	1	yes	characteristic
16	#10621873	C₂²	1	6	yes	—
17	Q₈×C₄₃	D₄	1	1	yes	characteristic
18	D₄×C₄₃	D₄	1	3	yes	—
19	C₂×C₄×C₄₃	C₂³	1	3	yes	—
20	C₂²⋊D₄₃	—	2	6	no	—
21	C₂×Dic₄₃	—	2	6	no	—
22	D₁₇₂	C₂³	1	2	yes	—
23	C₄×D₄₃	—	2	6	no	—
24	Dic₈₆	—	2	6	no	—
25	Dic₈₆	C₂³	1	6	yes	—
26	C₈×C₄₃	C₂³	1	3	yes	—
27	C₈×C₄₃	C₂³	1	1	yes	characteristic
28	C₂²×C₄₃	C₂×D₄	1	3	yes	—
29	C₂×D₄₃	—	2	2	no	—
30	C₄×C₄₃	C₂×D₄	1	3	yes	—
31	C₄×C₄₃	C₂⁴	1	1	yes	characteristic
32	Dic₄₃	—	2	6	no	—
33	C₂×C₄₃	—	2	3	no	—
34	C₂×C₄₃	C₂²×D₄	1	1	yes	characteristic
35	D₄₃	—	4	2	no	—
36	#578	—	43	1	no	maximal, Sylow
37	C₄₃	#578	1	1	yes	characteristic, complemented, Sylow
38	2₋¹⁺⁴	—	43	2	no	—
39	#137	—	43	6	no	—
40	#135	—	43	3	no	—
41	C₂×Q₁₆	—	43	3	no	—
42	#131	D₄₃	1	1	yes	characteristic, complemented
43	#41	—	43	6	no	—
44	#41	—	86	6	no	—
45	#41	C₂×D₄₃	1	1	yes	characteristic
46	C₂×Q₈	—	43	6	no	—
47	C₂×Q₈	—	86	2	no	—
48	Q₁₆	—	43	3	no	—
49	Q₁₆	—	43	6	no	—
50	SD₁₆	—	43	6	no	—
51	D₈	—	43	1	no	—
52	M₁₆	C₂×D₄₃	1	3	yes	—
53	C₂×C₈	C₂×D₄₃	1	3	yes	—
54	Q₈	—	43	6	no	—
55	Q₈	—	86	6	no	—
56	Q₈	D₁₇₂	1	1	yes	characteristic
57	D₄	—	43	2	no	—
58	D₄	—	86	6	no	—
59	D₄	D₁₇₂	1	3	yes	—
60	C₂×C₄	—	86	6	no	—
61	C₂×C₄	—	86	6	no	—
62	C₂×C₄	C₂²×D₄₃	1	3	yes	—
63	C₈	C₂²×D₄₃	1	1	yes	characteristic
64	C₈	C₂²×D₄₃	1	3	yes	—
65	C₂²	—	86	2	no	—
66	C₂²	C₂×D₁₇₂	1	3	yes	—
67	C₄	—	86	6	no	—
68	C₄	C₂×D₁₇₂	1	3	yes	—
69	C₄	C₂³×D₄₃	1	1	yes	characteristic
70	C₂	—	2	3	no	—
71	C₂	—	172	2	no	—
72	C₂	C₂²×D₁₇₂	1	1	yes	characteristic

	subgroup	G/H
center	C₂	C₂²×D₁₇₂
commutator, cosocle	C₄×C₄₃	C₂⁴
Frattini	C₄	C₂³×D₄₃
Fitting	#131×C₄₃	C₂
socle	C₂×C₄₃	C₂²×D₄
hypercenter	#131	D₄₃
hypocenter	C₄₃	#578
LCS	G ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂ ◁ #41 ◁ #131

Complements

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

N	H ≅ G/N	type
1. #13063372	C₂	semidirect
2. #13063358	C₂	semidirect
3. #13063347	C₂	semidirect
4. C₂×Dic₁₇₂	C₂	semidirect
5. #131×C₄₃	C₂	semidirect
37. C₄₃	#578	semidirect
42. #131	D₄₃	semidirect

Maximal subgroups

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

subgroup	index
#13063372	2
#13063358	2
#13063347	2
C₂×Dic₁₇₂	2
#131×C₄₃	2
#578	43