Subgroups — C₂×D₃×D₁₇ #88004

Order 408.

64 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₅₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×D₃×C₁₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×D₁₇	C₂	1	1	yes	maximal, characteristic, complemented
4	D₃×D₁₇	C₂	1	4	yes	maximal, direct product factor
5	C₂²×D₁₇	—	3	1	no	maximal, Hall
6	C₂×C₃×C₁₇	C₂²	1	1	yes	characteristic, complemented
7	D₅₁	C₂²	1	2	yes	complemented
8	C₃×D₁₇	C₂²	1	2	yes	complemented
9	D₃×C₁₇	C₂²	1	2	yes	complemented
10	C₂²×C₁₇	—	3	1	no	—
11	C₂×D₁₇	—	3	1	no	—
12	C₂×D₁₇	—	3	4	no	—
13	C₂×D₁₇	D₃	1	1	yes	characteristic, direct product factor
14	C₃×C₁₇	C₂³	1	1	yes	characteristic, complemented, Hall
15	C₂×C₁₇	—	3	2	no	—
16	C₂×C₁₇	C₂×D₃	1	1	yes	characteristic, complemented
17	D₁₇	—	3	2	no	—
18	D₁₇	C₂×D₃	1	2	yes	direct product factor
19	C₂²×D₃	—	17	1	no	maximal, Hall
20	C₁₇	C₂²×D₃	1	1	yes	characteristic, complemented, Sylow
21	C₂²×C₃	—	17	1	no	—
22	C₂×D₃	—	17	1	no	—
23	C₂×D₃	—	17	4	no	—
24	C₂×D₃	D₁₇	1	1	yes	characteristic, direct product factor
25	C₂³	—	51	1	no	Sylow
26	C₂×C₃	—	17	2	no	—
27	C₂×C₃	C₂×D₁₇	1	1	yes	characteristic, complemented
28	D₃	—	17	2	no	—
29	D₃	C₂×D₁₇	1	2	yes	direct product factor
30	C₂²	—	3	1	no	—
31	C₂²	—	17	1	no	—
32	C₂²	—	51	4	no	—
33	C₂²	—	51	1	no	—
34	C₃	C₂²×D₁₇	1	1	yes	characteristic, complemented, Sylow
35	C₂	—	3	2	no	—
36	C₂	—	17	2	no	—
37	C₂	—	51	2	no	—
38	C₂	D₃×D₁₇	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	D₃×D₁₇
commutator, cosocle, hypocenter	C₃×C₁₇	C₂³
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₁₇	C₂²
LCS	G ▷ C₃×C₁₇
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.