Subgroups — #14582950

Order 2752.

118 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄²×D₄₃	C₂	1	1	yes	maximal, characteristic
2	Dic₄₃⋊C₈	C₂	1	2	yes	maximal, complemented
3	(C₂×D₄₃)⋊C₈	C₂	1	2	yes	maximal
4	C₄×C₄₃⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄×C₈×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₄×D₄₃	C₄	1	1	yes	characteristic
7	C₂×C₄×D₄₃	C₄	1	1	yes	characteristic
8	C₂×C₄×D₄₃	C₂²	1	1	yes	characteristic
9	C₂×C₈×C₄₃	C₂²	1	2	yes	—
10	C₄²×C₄₃	C₂²	1	1	yes	characteristic
11	C₄×Dic₄₃	C₄	1	1	yes	characteristic
12	C₄×Dic₄₃	C₄	1	1	yes	characteristic
13	C₄×Dic₄₃	C₂²	1	1	yes	characteristic
14	C₂×C₄₃⋊C₈	C₂²	1	2	yes	—
15	C₂²×D₄₃	C₂×C₄	1	1	yes	characteristic
16	C₂×C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
17	C₂×C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
18	C₂×C₄×C₄₃	C₂³	1	1	yes	characteristic
19	C₂×Dic₄₃	C₂×C₄	1	1	yes	characteristic
20	C₂×Dic₄₃	C₂×C₄	1	1	yes	characteristic
21	C₂×Dic₄₃	C₂×C₄	1	1	yes	characteristic
22	C₄×D₄₃	—	2	2	no	—
23	C₄×D₄₃	—	2	2	no	—
24	C₄×D₄₃	C₈	1	4	yes	complemented
25	C₈×C₄₃	—	2	2	no	—
26	C₄₃⋊C₈	—	2	2	no	—
27	C₂²×C₄₃	C₂²×C₄	1	1	yes	characteristic
28	C₂×D₄₃	—	2	1	no	—
29	C₂×D₄₃	—	2	1	no	—
30	C₂×D₄₃	C₂×C₈	1	2	yes	—
31	C₄×C₄₃	C₂×C₈	1	2	yes	—
32	C₄×C₄₃	M₁₆	1	2	yes	—
33	C₄×C₄₃	#41	1	2	yes	—
34	Dic₄₃	—	2	1	no	—
35	Dic₄₃	—	2	1	no	—
36	Dic₄₃	C₂×C₈	1	2	yes	—
37	C₂×C₄₃	#117	1	1	yes	characteristic
38	C₂×C₄₃	C₂²×C₈	1	1	yes	characteristic
39	C₂×C₄₃	C₂×M₁₆	1	1	yes	characteristic
40	D₄₃	—	2	2	no	—
41	#431	—	43	1	no	maximal, Sylow
42	C₄₃	#431	1	1	yes	characteristic, complemented, Sylow
43	C₂×C₄²	—	43	1	no	—
44	C₄⋊C₈	—	43	2	no	—
45	C₂²⋊C₈	—	43	2	no	—
46	C₄×C₈	—	43	1	no	—
47	C₄×C₈	D₄₃	1	1	yes	characteristic, complemented
48	C₂²×C₄	—	43	1	no	—
49	C₂²×C₄	—	43	1	no	—
50	C₂²×C₄	—	43	1	no	—
51	C₂×C₈	—	43	2	no	—
52	C₂×C₈	C₂×D₄₃	1	2	yes	—
53	C₄²	—	43	1	no	—
54	C₄²	—	43	1	no	—
55	C₄²	—	43	1	no	—
56	C₄²	C₂×D₄₃	1	1	yes	characteristic
57	C₂³	—	43	1	no	—
58	C₂×C₄	—	43	1	no	—
59	C₂×C₄	—	43	4	no	—
60	C₂×C₄	—	43	1	no	—
61	C₂×C₄	—	43	1	no	—
62	C₂×C₄	—	86	2	no	—
63	C₂×C₄	—	86	2	no	—
64	C₂×C₄	C₄×D₄₃	1	1	yes	characteristic
65	C₂×C₄	C₄×D₄₃	1	1	yes	characteristic
66	C₂×C₄	C₂²×D₄₃	1	1	yes	characteristic
67	C₈	—	2	2	no	—
68	C₈	—	86	2	no	—
69	C₂²	—	43	2	no	—
70	C₂²	—	86	1	no	—
71	C₂²	—	86	1	no	—
72	C₂²	C₂×C₄×D₄₃	1	1	yes	characteristic
73	C₄	—	43	2	no	—
74	C₄	—	86	1	no	—
75	C₄	—	86	1	no	—
76	C₄	C₈×D₄₃	1	2	yes	—
77	C₄	#10621872	1	2	yes	—
78	C₄	#10621898	1	2	yes	—
79	C₂	—	86	2	no	—
80	C₂	#13063282	1	1	yes	characteristic
81	C₂	C₂×C₈×D₄₃	1	1	yes	characteristic
82	C₂	C₂×#10621872	1	1	yes	characteristic

	subgroup	G/H
center	C₄²	C₂×D₄₃
commutator	C₂×C₄₃	C₂²×C₈
Frattini	C₂×C₄	C₂²×D₄₃
Fitting	C₄×C₈×C₄₃	C₂
socle	C₂²×C₄₃	C₂²×C₄
prime radical	C₂²×D₄₃	C₂×C₄
cosocle	C₂×C₄×C₄₃	C₂³
hypercenter	C₄×C₈	D₄₃
hypocenter	C₄₃	#431
LCS	G ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₄² ◁ C₄×C₈

Complements

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

N	H ≅ G/N	type
2. Dic₄₃⋊C₈	C₂	semidirect
4. C₄×C₄₃⋊C₈	C₂	semidirect
5. C₄×C₈×C₄₃	C₂	semidirect
24. C₄×D₄₃	C₈	semidirect
42. C₄₃	#431	semidirect
47. C₄×C₈	D₄₃	semidirect

Maximal subgroups

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

subgroup	index
C₄²×D₄₃	2
Dic₄₃⋊C₈	2
(C₂×D₄₃)⋊C₈	2
C₄×C₄₃⋊C₈	2
C₄×C₈×C₄₃	2
#431	43