Subgroups — C₂×#30628407 #44537689

Order 31434.

128 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#30628407	C₂	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₂×C₁₃²×C₃₁	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₁₃²×C₃₁	C₂×C₃	1	1	yes	characteristic, complemented, Hall
4	C₂×#11925881	—	13	14	no	maximal
5	#11925881	—	13	14	no	—
6	C₂×#92788	—	31	1	no	maximal, Hall
7	C₂×C₁₃×C₃₁	C₁₃⋊C₃	1	14	yes	complemented
8	#92788	—	31	1	no	Hall
9	C₁₃×C₃₁	C₂×C₁₃⋊C₃	1	14	yes	complemented
10	C₂×C₁₃²	C₃₁⋊C₃	1	1	yes	characteristic, complemented, Hall
11	C₂×C₃₁⋊C₃	—	169	1	no	Hall
12	C₁₃²	C₂×C₃₁⋊C₃	1	1	yes	characteristic, complemented, Sylow
13	C₃₁⋊C₃	—	169	1	no	Hall
14	C₂×C₁₃⋊C₃	—	403	14	no	—
15	C₂×C₃₁	#92788	1	1	yes	characteristic, complemented, Hall
16	C₁₃⋊C₃	—	403	14	no	—
17	C₃₁	C₂×#92788	1	1	yes	characteristic, complemented, Sylow
18	C₂×C₁₃	#11925881	1	14	yes	complemented
19	C₁₃	C₂×#11925881	1	14	yes	complemented
20	C₂×C₃	—	5239	1	no	Hall
21	C₃	—	5239	1	no	Sylow
22	C₂	#30628407	1	1	yes	characteristic, direct product factor, Sylow

	subgroup	G/H
center, hypercenter	C₂	#30628407
commutator, cosocle, hypocenter	C₁₃²×C₃₁	C₂×C₃
Frattini	C₁	G
Fitting, socle	C₂×C₁₃²×C₃₁	C₃
LCS	G ▷ C₁₃²×C₃₁
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.