Subgroups — C₁₇×#13183676 #44472907

Order 29988.

136 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₇×C₃⋊(C₃⋊(C₇⋊D₇))	C₂	1	1	yes	maximal, characteristic
2	C₃²×C₇²×C₁₇	C₄	1	1	yes	characteristic, complemented, Hall
3	C₁₇×C₃⋊(C₇⋊D₇)	—	6	2	no	—
4	C₁₇×#5997	—	9	1	no	maximal, Hall
5	C₃×C₇²×C₁₇	—	2	2	no	—
6	C₁₇×C₃⋊D₂₁	—	14	4	no	—
7	#13183676	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₁₇×C₇⋊D₇	—	9	1	no	—
9	C₃²×C₇×C₁₇	—	2	4	no	—
10	C₃⋊(C₃⋊(C₇⋊D₇))	C₂×C₁₇	1	1	yes	characteristic
11	C₇²×C₁₇	#157	1	1	yes	characteristic, complemented, Hall
12	C₁₇×D₂₁	—	42	16	no	—
13	C₁₇×#157	—	49	1	no	maximal, Hall
14	C₃²×C₇²	C₄×C₁₇	1	1	yes	characteristic, complemented, Hall
15	C₃×C₇×C₁₇	—	2	16	no	—
16	C₁₇×C₃⋊D₃	—	49	1	no	—
17	C₃⋊(C₇⋊D₇)	—	6	2	no	—
18	D₇×C₁₇	—	126	4	no	—
19	#5997	—	9	1	no	Hall
20	C₃²×C₁₇	#5997	1	1	yes	characteristic, complemented, Hall
21	C₃×C₇²	—	2	2	no	—
22	C₃⋊D₂₁	—	14	4	no	—
23	C₇×C₁₇	—	2	4	no	—
24	D₃×C₁₇	—	294	2	no	—
25	C₇⋊D₇	—	9	1	no	—
26	C₄×C₁₇	—	441	1	no	Hall
27	C₃²×C₇	—	2	4	no	—
28	C₃×C₁₇	—	2	2	no	—
29	C₇²	C₁₇×#157	1	1	yes	characteristic, complemented, Sylow
30	D₂₁	—	42	16	no	—
31	#157	—	49	1	no	Hall
32	C₂×C₁₇	—	441	1	no	—
33	C₃×C₇	—	2	16	no	—
34	C₃⋊D₃	—	49	1	no	—
35	C₁₇	#13183676	1	1	yes	characteristic, direct product factor, Sylow
36	D₇	—	126	4	no	—
37	C₃²	C₁₇×#5997	1	1	yes	characteristic, complemented, Sylow
38	C₇	—	2	4	no	—
39	D₃	—	294	2	no	—
40	C₄	—	441	1	no	Sylow
41	C₃	—	2	2	no	—
42	C₂	—	441	1	no	—

	subgroup	G/H
center, hypercenter	C₁₇	#13183676
commutator, hypocenter	C₃²×C₇²	C₄×C₁₇
Frattini	C₁	G
Fitting, socle	C₃²×C₇²×C₁₇	C₄
prime radical	C₁₇×C₃⋊(C₃⋊(C₇⋊D₇))	C₂
cosocle	C₃⋊(C₃⋊(C₇⋊D₇))	C₂×C₁₇
LCS	G ▷ C₃²×C₇²
UCS	C₁ ◁ C₁₇

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
2. C₃²×C₇²×C₁₇	C₄	semidirect
7. #13183676	C₁₇	direct (N × H)
11. C₇²×C₁₇	#157	semidirect
14. C₃²×C₇²	C₄×C₁₇	semidirect
20. C₃²×C₁₇	#5997	semidirect
29. C₇²	C₁₇×#157	semidirect
35. C₁₇	#13183676	direct (N × H)
37. C₃²	C₁₇×#5997	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₁₇×C₃⋊(C₃⋊(C₇⋊D₇))	2
C₁₇×#5997	9
#13183676	17
C₁₇×#157	49

Subgroups — C17×#13183676 #44472907

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₇×#13183676 #44472907