Subgroups — C₃⋊Dic₁₄₉₁ #31822053

Order 17892.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃²×C₇×C₇₁	C₂	1	1	yes	maximal, characteristic
2	Dic₁₄₉₁	—	3	4	no	maximal
3	C₃²×C₇×C₇₁	C₄	1	1	yes	characteristic, complemented, Hall
4	C₂×C₃×C₇×C₇₁	D₃	1	4	yes	—
5	C₃⋊Dic₂₁₃	—	7	1	no	maximal, Hall
6	Dic₄₉₇	—	9	1	no	Hall
7	C₃×C₇×C₇₁	Dic₃	1	4	yes	complemented
8	C₂×C₃²×C₇₁	D₇	1	1	yes	characteristic
9	C₂×C₇×C₇₁	C₃⋊D₃	1	1	yes	characteristic
10	Dic₂₁₃	—	21	4	no	—
11	C₃²×C₇₁	Dic₇	1	1	yes	characteristic, complemented, Hall
12	C₇×C₇₁	C₃⋊Dic₃	1	1	yes	characteristic, complemented, Hall
13	C₂×C₃×C₇₁	D₂₁	1	4	yes	—
14	Dic₇₁	—	63	1	no	Hall
15	C₃⋊Dic₂₁	—	71	1	no	maximal, Hall
16	C₃×C₇₁	Dic₂₁	1	4	yes	complemented
17	C₂×C₇₁	C₃⋊D₂₁	1	1	yes	characteristic
18	C₂×C₃²×C₇	D₇₁	1	1	yes	characteristic
19	Dic₂₁	—	213	4	no	—
20	C₇₁	C₃⋊Dic₂₁	1	1	yes	characteristic, complemented, Sylow
21	C₃²×C₇	Dic₇₁	1	1	yes	characteristic, complemented, Hall
22	C₂×C₃×C₇	D₂₁₃	1	4	yes	—
23	C₃⋊Dic₃	—	497	1	no	Hall
24	Dic₇	—	639	1	no	Hall
25	C₃×C₇	Dic₂₁₃	1	4	yes	complemented
26	C₂×C₃²	D₄₉₇	1	1	yes	characteristic
27	C₂×C₇	C₃⋊D₂₁₃	1	1	yes	characteristic
28	Dic₃	—	1491	4	no	—
29	C₃²	Dic₄₉₇	1	1	yes	characteristic, complemented, Sylow
30	C₇	C₃⋊Dic₂₁₃	1	1	yes	characteristic, complemented, Sylow
31	C₂×C₃	D₁₄₉₁	1	4	yes	—
32	C₄	—	4473	1	no	Sylow
33	C₃	Dic₁₄₉₁	1	4	yes	complemented
34	C₂	C₃⋊D₁₄₉₁	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	C₃⋊D₁₄₉₁
commutator, hypocenter	C₃²×C₇×C₇₁	C₄
Fitting, socle, prime radical, cosocle	C₂×C₃²×C₇×C₇₁	C₂
LCS	G ▷ C₃²×C₇×C₇₁
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.