Subgroups — C₂×#30633764 #44569458

Order 32412.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#30633764	C₂	1	2	yes	maximal, direct product factor
2	C₂×#22549194	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃₇×D₇₃	C₃	1	1	yes	maximal, characteristic, complemented, Hall
4	#22549194	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₃₇×C₇₃	C₂×C₃	1	1	yes	characteristic, complemented
6	C₃₇×D₇₃	C₂×C₃	1	2	yes	complemented
7	C₃₇×C₇₃	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
8	C₂×D₇₃⋊C₃	—	37	1	no	maximal, Hall
9	C₂²×C₃₇⋊C₃	—	73	1	no	maximal, Hall
10	C₂×C₇₃⋊C₃	—	37	1	no	—
11	D₇₃⋊C₃	—	37	2	no	—
12	C₂×D₇₃	C₃₇⋊C₃	1	1	yes	characteristic, complemented, Hall
13	C₂×C₃₇⋊C₃	—	73	2	no	—
14	C₂×C₃₇⋊C₃	—	73	1	no	—
15	C₇₃⋊C₃	—	37	1	no	Hall
16	C₂²×C₃₇	—	73	1	no	Hall
17	C₂×C₇₃	C₂×C₃₇⋊C₃	1	1	yes	characteristic, complemented
18	D₇₃	C₂×C₃₇⋊C₃	1	2	yes	complemented
19	C₃₇⋊C₃	—	73	1	no	Hall
20	C₂×C₃₇	—	73	2	no	—
21	C₂×C₃₇	D₇₃⋊C₃	1	1	yes	characteristic, complemented
22	C₇₃	C₂²×C₃₇⋊C₃	1	1	yes	characteristic, complemented, Sylow
23	C₃₇	C₂×D₇₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
24	C₂²×C₃	—	2701	1	no	Hall
25	C₂×C₃	—	2701	2	no	—
26	C₂×C₃	—	2701	1	no	—
27	C₂²	—	73	1	no	Sylow
28	C₃	—	2701	1	no	Sylow
29	C₂	—	73	2	no	—
30	C₂	#30633764	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	#30633764
commutator, cosocle, hypocenter	C₃₇×C₇₃	C₂²×C₃
Frattini	C₁	G
Fitting, socle	C₂×C₃₇×C₇₃	C₂×C₃
LCS	G ▷ C₃₇×C₇₃
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.