Subgroups — C₂×(C₄₃⋊C₃)⋊D₃₇ #34061876

Order 19092.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	(C₄₃⋊C₃)⋊D₃₇	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃₇×C₄₃⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×D₁₅₉₁	C₃	1	1	yes	maximal, characteristic, complemented, Hall
4	C₃₇×C₄₃⋊C₃	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₃₇×C₄₃	C₂×C₃	1	1	yes	characteristic, complemented
6	D₁₅₉₁	C₂×C₃	1	2	yes	complemented
7	C₃₇×C₄₃	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
8	C₂×D₄₃⋊C₃	—	37	1	no	maximal, Hall
9	C₂×C₃×D₃₇	—	43	1	no	maximal, Hall
10	C₂×C₄₃⋊C₃	D₃₇	1	1	yes	characteristic, complemented
11	D₄₃⋊C₃	—	37	2	no	—
12	C₂×C₃×C₃₇	—	86	1	no	—
13	C₃×D₃₇	—	43	2	no	—
14	C₂×D₄₃	—	37	1	no	Hall
15	C₂×D₃₇	—	43	1	no	Hall
16	C₄₃⋊C₃	C₂×D₃₇	1	1	yes	characteristic, complemented, Hall
17	C₃×C₃₇	—	86	1	no	Hall
18	C₂×C₄₃	C₃×D₃₇	1	1	yes	characteristic, complemented
19	D₄₃	—	37	2	no	—
20	C₂×C₃₇	D₄₃⋊C₃	1	1	yes	characteristic, complemented
21	D₃₇	—	43	2	no	—
22	C₄₃	C₂×C₃×D₃₇	1	1	yes	characteristic, complemented, Sylow
23	C₃₇	C₂×D₄₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
24	C₂²×C₃	—	1591	1	no	Hall
25	C₂×C₃	—	1591	2	no	—
26	C₂×C₃	—	86	1	no	—
27	C₂²	—	1591	1	no	Sylow
28	C₃	—	86	1	no	Sylow
29	C₂	—	1591	2	no	—
30	C₂	(C₄₃⋊C₃)⋊D₃₇	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	(C₄₃⋊C₃)⋊D₃₇
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.