Subgroups — #14583295

Order 2752.

98 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	#13063256	C₂	1	4	yes	maximal
3	C₄×C₄₃⋊C₈	C₂	1	1	yes	maximal, characteristic
4	C₄⋊Q₈×C₄₃	C₂	1	1	yes	maximal, characteristic
5	C₂×Q₈×C₄₃	—	2	1	no	—
6	C₂×Dic₈₆	—	2	1	no	—
7	C₄⋊C₄×C₄₃	—	2	1	no	—
8	C₄⋊C₄×C₄₃	C₂²	1	2	yes	—
9	C₄²×C₄₃	C₂²	1	1	yes	characteristic
10	C₄⋊Dic₄₃	—	2	1	no	—
11	C₄⋊Dic₄₃	C₂²	1	2	yes	—
12	C₂×C₄₃⋊C₈	C₂²	1	2	yes	—
13	Q₈×C₄₃	—	4	2	no	—
14	C₂×C₄×C₄₃	—	2	2	no	—
15	C₂×C₄×C₄₃	D₄	1	1	yes	characteristic
16	C₂×C₄×C₄₃	D₄	1	1	yes	characteristic
17	C₂×C₄×C₄₃	C₂³	1	1	yes	characteristic
18	C₂×Dic₄₃	—	2	2	no	—
19	Dic₈₆	—	4	2	no	—
20	C₄₃⋊C₈	Q₈	1	4	yes	complemented
21	C₂²×C₄₃	C₂×D₄	1	1	yes	characteristic
22	C₄×C₄₃	—	4	2	no	—
23	C₄×C₄₃	SD₁₆	1	2	yes	—
24	C₄×C₄₃	SD₁₆	1	2	yes	—
25	C₄×C₄₃	C₂×Q₈	1	2	yes	—
26	Dic₄₃	—	4	2	no	—
27	C₂×C₄₃	C₄⋊Q₈	1	1	yes	characteristic
28	C₂×C₄₃	C₂×SD₁₆	1	1	yes	characteristic
29	C₂×C₄₃	C₂×SD₁₆	1	1	yes	characteristic
30	#498	—	43	1	no	maximal, Sylow
31	C₄₃	#498	1	1	yes	characteristic, complemented, Sylow
32	C₄⋊Q₈	—	43	1	no	—
33	C₄⋊Q₈	D₄₃	1	1	yes	characteristic
34	#106	—	43	4	no	—
35	C₄×C₈	—	43	1	no	—
36	C₂×Q₈	—	2	1	no	—
37	C₂×Q₈	—	86	1	no	—
38	C₂×C₈	—	43	2	no	—
39	C₄⋊C₄	—	2	1	no	—
40	C₄⋊C₄	—	43	2	no	—
41	C₄⋊C₄	—	86	1	no	—
42	C₄⋊C₄	C₂×D₄₃	1	2	yes	—
43	C₄²	C₂×D₄₃	1	1	yes	characteristic
44	Q₈	—	4	2	no	—
45	Q₈	—	172	2	no	—
46	C₂×C₄	—	2	2	no	—
47	C₂×C₄	—	86	2	no	—
48	C₂×C₄	C₂²⋊D₄₃	1	1	yes	characteristic
49	C₂×C₄	C₂²⋊D₄₃	1	1	yes	characteristic
50	C₂×C₄	C₂²×D₄₃	1	1	yes	characteristic
51	C₈	—	43	4	no	—
52	C₂²	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
53	C₄	—	4	2	no	—
54	C₄	—	172	2	no	—
55	C₄	#10621883	1	2	yes	—
56	C₄	#10621884	1	2	yes	—
57	C₄	Q₈×D₄₃	1	2	yes	—
58	C₂	#13063323	1	1	yes	characteristic
59	C₂	C₂×#10621884	1	1	yes	characteristic
60	C₂	C₂×#10621883	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×C₂²⋊D₄₃
commutator, cosocle	C₂×C₄×C₄₃	C₂³
Frattini	C₂×C₄	C₂²×D₄₃
Fitting	C₄⋊Q₈×C₄₃	C₂
socle, prime radical	C₂²×C₄₃	C₂×D₄
hypercenter	C₄⋊Q₈	D₄₃
hypocenter	C₄₃	#498
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄⋊Q₈

Complements

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

N	H ≅ G/N	type
20. C₄₃⋊C₈	Q₈	semidirect
31. C₄₃	#498	semidirect

Maximal subgroups

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

subgroup	index
#13063325	2
#13063256	2
C₄×C₄₃⋊C₈	2
C₄⋊Q₈×C₄₃	2
#498	43