Subgroups — C₂×#23750871 #34061871

Order 19092.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23750871	C₂	1	2	yes	maximal, direct product factor
2	C₂×#18012031	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄₃×D₃₇	C₃	1	1	yes	maximal, characteristic, complemented, Hall
4	#18012031	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₃₇×C₄₃	C₂×C₃	1	1	yes	characteristic, complemented
6	C₄₃×D₃₇	C₂×C₃	1	2	yes	complemented
7	C₃₇×C₄₃	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
8	C₂²×C₄₃⋊C₃	—	37	1	no	maximal, Hall
9	C₂×D₃₇⋊C₃	—	43	1	no	maximal, Hall
10	C₂×C₄₃⋊C₃	—	37	2	no	—
11	C₂×C₄₃⋊C₃	—	74	1	no	—
12	C₂×C₃₇⋊C₃	—	43	1	no	—
13	D₃₇⋊C₃	—	43	2	no	—
14	C₂²×C₄₃	—	37	1	no	Hall
15	C₂×D₃₇	C₄₃⋊C₃	1	1	yes	characteristic, complemented, Hall
16	C₄₃⋊C₃	—	74	1	no	Hall
17	C₃₇⋊C₃	—	43	1	no	Hall
18	C₂×C₄₃	—	37	2	no	—
19	C₂×C₄₃	D₃₇⋊C₃	1	1	yes	characteristic, complemented
20	C₂×C₃₇	C₂×C₄₃⋊C₃	1	1	yes	characteristic, complemented
21	D₃₇	C₂×C₄₃⋊C₃	1	2	yes	complemented
22	C₄₃	C₂×D₃₇⋊C₃	1	1	yes	characteristic, complemented, Sylow
23	C₃₇	C₂²×C₄₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
24	C₂²×C₃	—	1591	1	no	Hall
25	C₂×C₃	—	1591	2	no	—
26	C₂×C₃	—	3182	1	no	—
27	C₂²	—	37	1	no	Sylow
28	C₃	—	3182	1	no	Sylow
29	C₂	—	37	2	no	—
30	C₂	#23750871	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	#23750871
commutator, cosocle, hypocenter	C₃₇×C₄₃	C₂²×C₃
Frattini	C₁	G
Fitting, socle	C₂×C₃₇×C₄₃	C₂×C₃
LCS	G ▷ C₃₇×C₄₃
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.