Subgroups — #14583305

Order 2752.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13063317	C₂	1	1	yes	maximal, characteristic
2	#13063258	C₂	1	2	yes	maximal
3	#13063256	C₂	1	2	yes	maximal
4	#13063236	C₂	1	1	yes	maximal, characteristic
5	C₄⋊Q₈×C₄₃	C₂	1	1	yes	maximal, characteristic
6	C₂×Q₈×C₄₃	—	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	C₂²	1	1	yes	characteristic
11	C₄⋊Dic₄₃	C₂²	1	1	yes	characteristic
12	Dic₄₃⋊C₄	—	2	1	no	—
13	Dic₄₃⋊C₄	—	2	1	no	—
14	C₂×C₄₃⋊C₈	C₂²	1	2	yes	—
15	Q₈×C₄₃	—	4	2	no	—
16	C₂×C₄×C₄₃	—	2	2	no	—
17	C₂×C₄×C₄₃	D₄	1	1	yes	characteristic
18	C₂×C₄×C₄₃	D₄	1	1	yes	characteristic
19	C₂×C₄×C₄₃	C₂³	1	1	yes	characteristic
20	C₂×Dic₄₃	—	2	1	no	—
21	C₂×Dic₄₃	—	2	1	no	—
22	C₄₃⋊C₈	Q₈	1	4	yes	complemented
23	C₂²×C₄₃	C₂×D₄	1	1	yes	characteristic
24	C₄×C₄₃	—	2	1	no	—
25	C₄×C₄₃	—	2	1	no	—
26	C₄×C₄₃	—	4	2	no	—
27	C₄×C₄₃	C₂×Q₈	1	2	yes	—
28	Dic₄₃	—	4	1	no	—
29	Dic₄₃	—	4	1	no	—
30	C₂×C₄₃	C₄⋊Q₈	1	1	yes	characteristic
31	C₂×C₄₃	AGL(1,ℤ/8)	1	1	yes	characteristic
32	C₂×C₄₃	#137	1	1	yes	characteristic
33	#501	—	43	1	no	maximal, Sylow
34	C₄₃	#501	1	1	yes	characteristic, complemented, Sylow
35	C₄⋊Q₈	D₄₃	1	1	yes	characteristic
36	#125	—	43	1	no	—
37	#107	—	43	2	no	—
38	#106	—	43	2	no	—
39	#97	—	43	1	no	—
40	C₂×Q₈	—	2	1	no	—
41	C₂×C₈	—	43	2	no	—
42	C₄⋊C₄	—	2	1	no	—
43	C₄⋊C₄	—	43	1	no	—
44	C₄⋊C₄	—	43	1	no	—
45	C₄⋊C₄	—	86	1	no	—
46	C₄⋊C₄	—	86	1	no	—
47	C₄⋊C₄	C₂×D₄₃	1	2	yes	—
48	C₄²	C₂×D₄₃	1	1	yes	characteristic
49	Q₈	—	4	2	no	—
50	C₂×C₄	—	2	2	no	—
51	C₂×C₄	—	86	1	no	—
52	C₂×C₄	—	86	1	no	—
53	C₂×C₄	C₂²⋊D₄₃	1	1	yes	characteristic
54	C₂×C₄	C₂²⋊D₄₃	1	1	yes	characteristic
55	C₂×C₄	C₂²×D₄₃	1	1	yes	characteristic
56	C₈	—	43	4	no	—
57	C₂²	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
58	C₄	—	2	1	no	—
59	C₄	—	2	1	no	—
60	C₄	—	4	2	no	—
61	C₄	—	172	1	no	—
62	C₄	—	172	1	no	—
63	C₄	Q₈×D₄₃	1	2	yes	—
64	C₂	#13063323	1	1	yes	characteristic
65	C₂	#13063351	1	1	yes	characteristic
66	C₂	#13063356	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	#501
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
22. C₄₃⋊C₈	Q₈	semidirect
34. C₄₃	#501	semidirect

Maximal subgroups

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

subgroup	index
#13063317	2
#13063258	2
#13063256	2
#13063236	2
C₄⋊Q₈×C₄₃	2
#501	43