Subgroups — C₁₇×#7457 #16865201

Order 4352.

76 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₇×#1398	C₂	1	1	yes	maximal, characteristic
2	C₁₇×#1369	C₂	1	1	yes	maximal, characteristic
3	C₁₇×#1368	C₂	1	1	yes	maximal, characteristic
4	C₁₇×M₆₄	C₄	1	1	yes	characteristic
5	C₁₇×M₆₄	C₄	1	1	yes	characteristic
6	C₁₇×#364	—	2	1	no	—
7	C₁₇×#346	C₂²	1	1	yes	characteristic
8	C₁₇×#334	—	2	1	no	—
9	C₁₇×M₃₂	—	4	1	no	—
10	C₂×C₁₆×C₁₇	C₂×C₄	1	1	yes	characteristic
11	C₂×C₁₆×C₁₇	Q₈	1	1	yes	characteristic
12	C₁₇×C₄⋊C₈	—	4	1	no	—
13	C₄×C₈×C₁₇	D₄	1	1	yes	characteristic
14	C₁₇×C₃₂	—	2	1	no	—
15	C₁₇×C₃₂	C₈	1	2	yes	complemented
16	C₂×C₈×C₁₇	—	8	1	no	—
17	C₂×C₈×C₁₇	C₄⋊C₄	1	1	yes	characteristic
18	C₂×C₈×C₁₇	SD₁₆	1	1	yes	characteristic
19	C₄²×C₁₇	SD₁₆	1	1	yes	characteristic
20	C₁₆×C₁₇	—	2	1	no	—
21	C₁₆×C₁₇	—	8	1	no	—
22	C₁₆×C₁₇	C₂×C₈	1	1	yes	characteristic
23	C₁₆×C₁₇	M₁₆	1	1	yes	characteristic
24	#7457	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
25	C₂×C₄×C₁₇	—	2	1	no	—
26	C₂×C₄×C₁₇	#106	1	1	yes	characteristic
27	C₈×C₁₇	—	2	1	no	—
28	C₈×C₁₇	—	16	1	no	—
29	C₈×C₁₇	C₄⋊C₈	1	1	yes	characteristic
30	C₈×C₁₇	#108	1	1	yes	characteristic
31	#1398	C₂×C₁₇	1	1	yes	characteristic
32	#1369	C₂×C₁₇	1	1	yes	characteristic
33	#1368	C₂×C₁₇	1	1	yes	characteristic
34	C₂²×C₁₇	#365	1	1	yes	characteristic
35	C₄×C₁₇	—	4	1	no	—
36	C₄×C₁₇	#334	1	1	yes	characteristic
37	C₄×C₁₇	#365	1	1	yes	characteristic
38	M₆₄	C₄×C₁₇	1	1	yes	characteristic
39	M₆₄	C₄×C₁₇	1	1	yes	characteristic
40	#364	—	2	1	no	—
41	#346	C₂²×C₁₇	1	1	yes	characteristic
42	#334	—	2	1	no	—
43	C₂×C₁₇	—	2	1	no	—
44	C₂×C₁₇	#1368	1	1	yes	characteristic
45	M₃₂	—	4	1	no	—
46	C₂×C₁₆	C₂×C₄×C₁₇	1	1	yes	characteristic
47	C₂×C₁₆	Q₈×C₁₇	1	1	yes	characteristic
48	C₄⋊C₈	—	4	1	no	—
49	C₄×C₈	D₄×C₁₇	1	1	yes	characteristic
50	C₃₂	—	2	1	no	—
51	C₃₂	C₈×C₁₇	1	2	yes	complemented
52	C₁₇	#7457	1	1	yes	characteristic, direct product factor, Sylow
53	C₂×C₈	—	8	1	no	—
54	C₂×C₈	C₄⋊C₄×C₁₇	1	1	yes	characteristic
55	C₂×C₈	SD₁₆×C₁₇	1	1	yes	characteristic
56	C₄²	SD₁₆×C₁₇	1	1	yes	characteristic
57	C₁₆	—	2	1	no	—
58	C₁₆	—	8	1	no	—
59	C₁₆	C₂×C₈×C₁₇	1	1	yes	characteristic
60	C₁₆	M₁₆×C₁₇	1	1	yes	characteristic
61	C₂×C₄	—	2	1	no	—
62	C₂×C₄	C₁₇×#106	1	1	yes	characteristic
63	C₈	—	2	1	no	—
64	C₈	—	16	1	no	—
65	C₈	C₁₇×C₄⋊C₈	1	1	yes	characteristic
66	C₈	C₁₇×#108	1	1	yes	characteristic
67	C₂²	C₁₇×#365	1	1	yes	characteristic
68	C₄	—	4	1	no	—
69	C₄	C₁₇×#334	1	1	yes	characteristic
70	C₄	C₁₇×#365	1	1	yes	characteristic
71	C₂	—	2	1	no	—
72	C₂	C₁₇×#1368	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₁₇	#1368
commutator	C₁₆	C₂×C₈×C₁₇
Frattini, cosocle	#346	C₂²×C₁₇
prime radical	C₂²×C₁₇	#365
LCS	G ▷ C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₇ ◁ C₂×C₄×C₁₇ ◁ C₄×C₈×C₁₇ ◁ C₁₇×#346 ◁ G

Complements

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

N	H ≅ G/N	type
15. C₁₇×C₃₂	C₈	semidirect
24. #7457	C₁₇	direct (N × H)
51. C₃₂	C₈×C₁₇	semidirect
52. C₁₇	#7457	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₇×#1398	2
C₁₇×#1369	2
C₁₇×#1368	2
#7457	17

Subgroups — C17×#7457 #16865201

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₇×#7457 #16865201