Subgroups — #14582744

Order 2752.

178 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×Dic₄₃	C₂	1	3	yes	maximal
2	C₄₃⋊#95	C₂	1	3	yes	maximal
3	#95×C₄₃	C₂	1	1	yes	maximal, characteristic
4	C₂²×C₄×C₄₃	C₂²	1	3	yes	—
5	C₂²×Dic₄₃	C₂²	1	3	yes	—
6	C₂²×Dic₄₃	C₂²	1	1	yes	characteristic
7	C₄×Dic₄₃	C₄	1	12	yes	complemented
8	C₂³×C₄₃	C₂³	1	1	yes	characteristic
9	C₂×C₄×C₄₃	—	2	6	no	—
10	C₂×C₄×C₄₃	C₂×C₄	1	6	yes	—
11	C₂×Dic₄₃	—	2	3	no	—
12	C₂×Dic₄₃	—	2	3	no	—
13	C₂×Dic₄₃	C₂×C₄	1	6	yes	—
14	C₂×Dic₄₃	C₂×C₄	1	6	yes	—
15	C₂²×C₄₃	C₂²×C₄	1	3	yes	—
16	C₂²×C₄₃	#41	1	3	yes	—
17	C₂²×C₄₃	#41	1	1	yes	characteristic
18	C₄×C₄₃	—	2	6	no	—
19	Dic₄₃	—	2	6	no	—
20	Dic₄₃	C₄²	1	4	yes	—
21	C₂×C₄₃	C₂×C₄²	1	1	yes	characteristic
22	C₂×C₄₃	#117	1	3	yes	—
23	C₂×C₄₃	#117	1	3	yes	—
24	#376	—	43	1	no	maximal, Sylow
25	C₄₃	#376	1	1	yes	characteristic, complemented, Sylow
26	C₂×C₄²	—	43	3	no	—
27	#95	—	43	3	no	—
28	#95	D₄₃	1	1	yes	characteristic
29	C₂²×C₄	—	43	1	no	—
30	C₂²×C₄	—	43	3	no	—
31	C₂²×C₄	C₂×D₄₃	1	3	yes	—
32	C₄²	—	43	12	no	—
33	C₂³	C₂²×D₄₃	1	1	yes	characteristic
34	C₂×C₄	—	2	6	no	—
35	C₂×C₄	—	43	6	no	—
36	C₂×C₄	—	43	6	no	—
37	C₂×C₄	—	86	3	no	—
38	C₂×C₄	—	86	3	no	—
39	C₂×C₄	C₄×D₄₃	1	6	yes	—
40	C₂²	C₂×C₄×D₄₃	1	3	yes	—
41	C₂²	#10621900	1	3	yes	—
42	C₂²	#10621902	1	1	yes	characteristic
43	C₄	—	2	6	no	—
44	C₄	—	43	4	no	—
45	C₄	—	86	6	no	—
46	C₂	C₄²×D₄₃	1	1	yes	characteristic
47	C₂	#13063281	1	3	yes	—
48	C₂	#13063283	1	3	yes	—

	subgroup	G/H
center, Frattini	C₂³	C₂²×D₄₃
commutator	C₂×C₄₃	C₂×C₄²
Fitting	#95×C₄₃	C₂
socle, prime radical, cosocle	C₂³×C₄₃	C₂³
hypercenter	#95	D₄₃
hypocenter	C₄₃	#376
LCS	G ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³ ◁ #95

Complements

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

N	H ≅ G/N	type
7. C₄×Dic₄₃	C₄	semidirect
25. C₄₃	#376	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄×Dic₄₃	2
C₄₃⋊#95	2
#95×C₄₃	2
#376	43