Subgroups — C₂×#30628684 #44538366

Order 31476.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#30628684	C₂	1	2	yes	maximal, direct product factor
2	C₂×#21463501	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₆₁×D₄₃	C₃	1	1	yes	maximal, characteristic, complemented, Hall
4	#21463501	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₄₃×C₆₁	C₂×C₃	1	1	yes	characteristic, complemented
6	C₆₁×D₄₃	C₂×C₃	1	2	yes	complemented
7	C₄₃×C₆₁	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
8	C₂²×C₆₁⋊C₃	—	43	1	no	maximal, Hall
9	C₂×D₄₃⋊C₃	—	61	1	no	maximal, Hall
10	C₂×C₆₁⋊C₃	—	43	2	no	—
11	C₂×C₆₁⋊C₃	—	43	1	no	—
12	C₂×C₄₃⋊C₃	—	61	1	no	—
13	D₄₃⋊C₃	—	61	2	no	—
14	C₂²×C₆₁	—	43	1	no	Hall
15	C₆₁⋊C₃	—	43	1	no	Hall
16	C₂×D₄₃	C₆₁⋊C₃	1	1	yes	characteristic, complemented, Hall
17	C₄₃⋊C₃	—	61	1	no	Hall
18	C₂×C₆₁	—	43	2	no	—
19	C₂×C₆₁	D₄₃⋊C₃	1	1	yes	characteristic, complemented
20	C₂×C₄₃	C₂×C₆₁⋊C₃	1	1	yes	characteristic, complemented
21	D₄₃	C₂×C₆₁⋊C₃	1	2	yes	complemented
22	C₆₁	C₂×D₄₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
23	C₄₃	C₂²×C₆₁⋊C₃	1	1	yes	characteristic, complemented, Sylow
24	C₂²×C₃	—	2623	1	no	Hall
25	C₂×C₃	—	2623	2	no	—
26	C₂×C₃	—	2623	1	no	—
27	C₂²	—	43	1	no	Sylow
28	C₃	—	2623	1	no	Sylow
29	C₂	—	43	2	no	—
30	C₂	#30628684	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	#30628684
commutator, cosocle, hypocenter	C₄₃×C₆₁	C₂²×C₃
Frattini	C₁	G
Fitting, socle	C₂×C₄₃×C₆₁	C₂×C₃
LCS	G ▷ C₄₃×C₆₁
UCS	C₁ ◁ C₂

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.