Subgroups — #14583307

Order 2752.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13063324	C₂	1	1	yes	maximal, characteristic
2	#13063316	C₂	1	1	yes	maximal, characteristic
3	#13063258	C₂	1	1	yes	maximal, characteristic
4	#13063257	C₂	1	1	yes	maximal, characteristic
5	#13063256	C₂	1	1	yes	maximal, characteristic
6	#13063235	C₂	1	1	yes	maximal, characteristic
7	#107×C₄₃	C₂	1	1	yes	maximal, characteristic
8	C₂×Dic₈₆	—	2	1	no	—
9	C₂×C₈×C₄₃	C₂²	1	1	yes	characteristic
10	C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
11	C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
12	C₄⋊Dic₄₃	—	2	1	no	—
13	C₄⋊Dic₄₃	C₂²	1	1	yes	characteristic
14	C₄⋊Dic₄₃	C₂²	1	1	yes	characteristic
15	Dic₄₃⋊C₄	—	2	1	no	—
16	Dic₄₃⋊C₄	—	2	1	no	—
17	C₄×Dic₄₃	C₂²	1	1	yes	characteristic
18	C₂×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
19	C₂×C₄×C₄₃	—	2	1	no	—
20	C₂×C₄×C₄₃	—	2	1	no	—
21	C₂×C₄×C₄₃	C₂³	1	1	yes	characteristic
22	C₂×Dic₄₃	—	2	1	no	—
23	C₂×Dic₄₃	—	2	1	no	—
24	C₂×Dic₄₃	D₄	1	1	yes	characteristic
25	C₂×Dic₄₃	D₄	1	1	yes	characteristic
26	Dic₈₆	—	4	2	no	—
27	C₈×C₄₃	Q₈	1	2	yes	complemented
28	C₄₃⋊C₈	Q₈	1	2	yes	complemented
29	C₂²×C₄₃	C₂×D₄	1	1	yes	characteristic
30	C₄×C₄₃	—	4	1	no	—
31	C₄×C₄₃	—	4	1	no	—
32	C₄×C₄₃	C₂×Q₈	1	1	yes	characteristic
33	C₄×C₄₃	C₂×Q₈	1	1	yes	characteristic
34	Dic₄₃	—	2	1	no	—
35	Dic₄₃	—	2	1	no	—
36	Dic₄₃	—	4	1	no	—
37	Dic₄₃	—	4	1	no	—
38	C₂×C₄₃	C₄⋊Q₈	1	1	yes	characteristic
39	C₂×C₄₃	AGL(1,ℤ/8)	1	1	yes	characteristic
40	C₂×C₄₃	#137	1	1	yes	characteristic
41	#501	—	43	1	no	maximal, Sylow
42	C₄₃	#501	1	1	yes	characteristic, complemented, Sylow
43	C₄⋊Q₈	—	43	1	no	—
44	#125	—	43	1	no	—
45	#107	—	43	1	no	—
46	#107	D₄₃	1	1	yes	characteristic
47	#106	—	43	1	no	—
48	#106	—	43	1	no	—
49	#97	—	43	1	no	—
50	C₂×Q₈	—	86	1	no	—
51	C₂×C₈	—	43	1	no	—
52	C₂×C₈	C₂×D₄₃	1	1	yes	characteristic
53	C₄⋊C₄	—	43	1	no	—
54	C₄⋊C₄	—	43	1	no	—
55	C₄⋊C₄	—	86	1	no	—
56	C₄⋊C₄	—	86	1	no	—
57	C₄⋊C₄	—	86	1	no	—
58	C₄⋊C₄	C₂×D₄₃	1	1	yes	characteristic
59	C₄⋊C₄	C₂×D₄₃	1	1	yes	characteristic
60	C₄²	—	43	1	no	—
61	Q₈	—	172	2	no	—
62	C₂×C₄	—	2	1	no	—
63	C₂×C₄	—	2	1	no	—
64	C₂×C₄	—	43	1	no	—
65	C₂×C₄	—	43	1	no	—
66	C₂×C₄	—	86	1	no	—
67	C₂×C₄	—	86	1	no	—
68	C₂×C₄	C₂²×D₄₃	1	1	yes	characteristic
69	C₈	—	43	2	no	—
70	C₈	Dic₈₆	1	2	yes	complemented
71	C₂²	D₄×D₄₃	1	1	yes	characteristic
72	C₄	—	4	1	no	—
73	C₄	—	4	1	no	—
74	C₄	—	86	1	no	—
75	C₄	—	86	1	no	—
76	C₄	—	172	1	no	—
77	C₄	—	172	1	no	—
78	C₄	C₂×Dic₈₆	1	1	yes	characteristic
79	C₄	Q₈×D₄₃	1	1	yes	characteristic
80	C₂	#13063324	1	1	yes	characteristic
81	C₂	#13063349	1	1	yes	characteristic
82	C₂	#13063357	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₄×D₄₃
commutator, cosocle	C₂×C₄×C₄₃	C₂³
Frattini	C₂×C₄	C₂²×D₄₃
Fitting	#107×C₄₃	C₂
socle, prime radical	C₂²×C₄₃	C₂×D₄
hypercenter	#107	D₄₃
hypocenter	C₄₃	#501
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ #107

Complements

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

N	H ≅ G/N	type
27. C₈×C₄₃	Q₈	semidirect
28. C₄₃⋊C₈	Q₈	semidirect
42. C₄₃	#501	semidirect
70. C₈	Dic₈₆	semidirect

Maximal subgroups

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

subgroup	index
#13063324	2
#13063316	2
#13063258	2
#13063257	2
#13063256	2
#13063235	2
#107×C₄₃	2
#501	43