Subgroups — #14582646

Order 2752.

64 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13063325	C₂	1	1	yes	maximal, characteristic
2	C₄⋊(C₄₃⋊C₈)	C₂	1	1	yes	maximal, characteristic
3	C₄⋊C₈×C₄₃	C₂	1	1	yes	maximal, characteristic
4	C₂×Dic₈₆	—	2	1	no	—
5	C₂×C₈×C₄₃	—	2	1	no	—
6	C₄²×C₄₃	C₂²	1	1	yes	characteristic
7	C₄⋊Dic₄₃	—	2	1	no	—
8	C₄⋊Dic₄₃	C₄	1	2	yes	—
9	C₂×C₄₃⋊C₈	—	2	1	no	—
10	C₂×C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
11	C₂×C₄×C₄₃	D₄	1	1	yes	characteristic
12	C₂×C₄×C₄₃	D₄	1	1	yes	characteristic
13	C₂×Dic₄₃	—	2	2	no	—
14	Dic₈₆	—	4	1	no	—
15	Dic₈₆	—	4	1	no	—
16	C₈×C₄₃	—	4	1	no	—
17	C₄₃⋊C₈	—	4	1	no	—
18	C₂²×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
19	C₄×C₄₃	—	2	1	no	—
20	C₄×C₄₃	D₈	1	1	yes	characteristic
21	C₄×C₄₃	SD₁₆	1	1	yes	characteristic
22	C₄×C₄₃	SD₁₆	1	1	yes	characteristic
23	C₄×C₄₃	Q₁₆	1	1	yes	characteristic
24	Dic₄₃	—	4	2	no	—
25	C₂×C₄₃	#101	1	1	yes	characteristic
26	C₂×C₄₃	#102	1	1	yes	characteristic
27	C₂×C₄₃	#103	1	1	yes	characteristic
28	#332	—	43	1	no	maximal, Sylow
29	C₄₃	#332	1	1	yes	characteristic, complemented, Sylow
30	C₄⋊Q₈	—	43	1	no	—
31	C₄⋊C₈	—	43	1	no	—
32	C₄⋊C₈	D₄₃	1	1	yes	characteristic
33	C₂×Q₈	—	86	1	no	—
34	C₂×C₈	—	2	1	no	—
35	C₂×C₈	—	86	1	no	—
36	C₄⋊C₄	—	43	2	no	—
37	C₄⋊C₄	—	86	1	no	—
38	C₄²	C₂×D₄₃	1	1	yes	characteristic
39	Q₈	—	172	1	no	—
40	Q₈	—	172	1	no	—
41	C₂×C₄	—	86	2	no	—
42	C₂×C₄	C₄×D₄₃	1	1	yes	characteristic
43	C₂×C₄	D₁₇₂	1	1	yes	characteristic
44	C₂×C₄	C₂²⋊D₄₃	1	1	yes	characteristic
45	C₈	—	4	1	no	—
46	C₈	—	172	1	no	—
47	C₂²	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
48	C₄	—	2	1	no	—
49	C₄	—	172	2	no	—
50	C₄	#10621873	1	1	yes	characteristic
51	C₄	Dic₁₇₂	1	1	yes	characteristic
52	C₄	#10621882	1	1	yes	characteristic
53	C₄	#10621884	1	1	yes	characteristic
54	C₂	#13063243	1	1	yes	characteristic
55	C₂	#13063245	1	1	yes	characteristic
56	C₂	#13063250	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	(C₂×D₄₃)⋊C₄
commutator	C₂×C₄×C₄₃	C₂×C₄
Frattini	C₄²	C₂×D₄₃
Fitting	C₄⋊C₈×C₄₃	C₂
socle, prime radical	C₂²×C₄₃	C₂²⋊C₄
cosocle	C₄²×C₄₃	C₂²
hypercenter	C₄⋊C₈	D₄₃
hypocenter	C₄₃	#332
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄⋊C₈

Complements

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

N	H ≅ G/N	type
29. C₄₃	#332	semidirect

Maximal subgroups

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

subgroup	index
#13063325	2
C₄⋊(C₄₃⋊C₈)	2
C₄⋊C₈×C₄₃	2
#332	43