Subgroups — #13063325

Order 1376.

68 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₈₆	C₂	1	2	yes	maximal
2	C₄²×C₄₃	C₂	1	1	yes	maximal, characteristic
3	C₄⋊Dic₄₃	C₂	1	4	yes	maximal
4	C₂×C₄×C₄₃	C₂²	1	1	yes	characteristic
5	C₂×C₄×C₄₃	C₂²	1	2	yes	—
6	C₂×Dic₄₃	C₂²	1	4	yes	—
7	Dic₈₆	—	2	4	no	—
8	C₂²×C₄₃	C₂³	1	1	yes	characteristic
9	C₄×C₄₃	D₄	1	2	yes	—
10	C₄×C₄₃	Q₈	1	4	yes	complemented
11	Dic₄₃	—	2	4	no	—
12	C₂×C₄₃	C₂×D₄	1	1	yes	characteristic
13	C₂×C₄₃	C₂×Q₈	1	2	yes	—
14	C₄₃	C₄⋊Q₈	1	1	yes	characteristic, complemented, Sylow
15	C₄⋊Q₈	—	43	1	no	maximal, Sylow
16	C₂×Q₈	—	43	2	no	—
17	C₄⋊C₄	—	43	4	no	—
18	C₄²	D₄₃	1	1	yes	characteristic
19	Q₈	—	86	4	no	—
20	C₂×C₄	—	43	4	no	—
21	C₂×C₄	C₂×D₄₃	1	2	yes	—
22	C₂×C₄	C₂×D₄₃	1	1	yes	characteristic
23	C₂²	C₂²×D₄₃	1	1	yes	characteristic
24	C₄	—	86	4	no	—
25	C₄	Dic₈₆	1	4	yes	complemented
26	C₄	D₁₇₂	1	2	yes	—
27	C₂	C₂×Dic₈₆	1	2	yes	—
28	C₂	C₂×D₁₇₂	1	1	yes	characteristic

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

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

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