Subgroups — C₁₇×#1418 #14524424

Order 2176.

74 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₇×#508	C₂	1	1	yes	maximal, characteristic
2	C₁₇×M₆₄	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₇×#367	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₇×#135	—	2	1	no	—
5	C₁₇×Q₃₂	C₄	1	1	yes	characteristic, complemented
6	C₁₇×SD₃₂	—	2	1	no	—
7	C₁₇×D₁₆	C₄	1	1	yes	characteristic, complemented
8	C₂×C₁₆×C₁₇	C₂²	1	1	yes	characteristic
9	C₁₇×#107	—	2	1	no	—
10	C₁₇×C₃₂	—	2	1	no	—
11	#41×C₁₇	—	4	1	no	—
12	Q₁₆×C₁₇	—	2	1	no	—
13	SD₁₆×C₁₇	—	4	1	no	—
14	D₈×C₁₇	—	2	1	no	—
15	C₂×C₈×C₁₇	D₄	1	1	yes	characteristic
16	C₄⋊C₄×C₁₇	—	4	1	no	—
17	C₁₆×C₁₇	C₂×C₄	1	1	yes	characteristic
18	C₁₆×C₁₇	D₄	1	1	yes	characteristic
19	Q₈×C₁₇	—	4	1	no	—
20	D₄×C₁₇	—	4	1	no	—
21	D₄×C₁₇	—	8	1	no	—
22	C₂×C₄×C₁₇	—	8	1	no	—
23	C₂×C₄×C₁₇	—	8	1	no	—
24	C₂×C₄×C₁₇	D₈	1	1	yes	characteristic
25	C₈×C₁₇	C₂²⋊C₄	1	1	yes	characteristic
26	C₈×C₁₇	SD₁₆	1	1	yes	characteristic
27	#1418	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
28	C₂²×C₁₇	—	8	1	no	—
29	C₂²×C₁₇	D₁₆	1	1	yes	characteristic
30	C₄×C₁₇	—	8	1	no	—
31	C₄×C₁₇	—	16	1	no	—
32	C₄×C₁₇	#102	1	1	yes	characteristic
33	C₄×C₁₇	SD₃₂	1	1	yes	characteristic
34	#508	C₂×C₁₇	1	1	yes	characteristic
35	M₆₄	C₂×C₁₇	1	1	yes	characteristic, complemented
36	#367	C₂×C₁₇	1	1	yes	characteristic, complemented
37	C₂×C₁₇	—	2	1	no	—
38	C₂×C₁₇	—	16	1	no	—
39	C₂×C₁₇	#357	1	1	yes	characteristic
40	#135	—	2	1	no	—
41	Q₃₂	C₄×C₁₇	1	1	yes	characteristic, complemented
42	SD₃₂	—	2	1	no	—
43	D₁₆	C₄×C₁₇	1	1	yes	characteristic, complemented
44	C₂×C₁₆	C₂²×C₁₇	1	1	yes	characteristic
45	#107	—	2	1	no	—
46	C₃₂	—	2	1	no	—
47	C₁₇	#1418	1	1	yes	characteristic, direct product factor, Sylow
48	#41	—	4	1	no	—
49	Q₁₆	—	2	1	no	—
50	SD₁₆	—	4	1	no	—
51	D₈	—	2	1	no	—
52	C₂×C₈	D₄×C₁₇	1	1	yes	characteristic
53	C₄⋊C₄	—	4	1	no	—
54	C₁₆	C₂×C₄×C₁₇	1	1	yes	characteristic
55	C₁₆	D₄×C₁₇	1	1	yes	characteristic
56	Q₈	—	4	1	no	—
57	D₄	—	4	1	no	—
58	D₄	—	8	1	no	—
59	C₂×C₄	—	8	1	no	—
60	C₂×C₄	—	8	1	no	—
61	C₂×C₄	D₈×C₁₇	1	1	yes	characteristic
62	C₈	C₂²⋊C₄×C₁₇	1	1	yes	characteristic
63	C₈	SD₁₆×C₁₇	1	1	yes	characteristic
64	C₂²	—	8	1	no	—
65	C₂²	C₁₇×D₁₆	1	1	yes	characteristic
66	C₄	—	8	1	no	—
67	C₄	—	16	1	no	—
68	C₄	C₁₇×#102	1	1	yes	characteristic
69	C₄	C₁₇×SD₃₂	1	1	yes	characteristic
70	C₂	—	2	1	no	—
71	C₂	—	16	1	no	—
72	C₂	C₁₇×#357	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₁₇	#357
commutator	C₁₆	C₂×C₄×C₁₇
Frattini, cosocle	C₂×C₁₆	C₂²×C₁₇
prime radical	C₁₇×#508	C₂
LCS	G ▷ C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₇ ◁ C₂×C₄×C₁₇ ◁ C₂×C₈×C₁₇ ◁ C₂×C₁₆×C₁₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₇×M₆₄	C₂	semidirect
3. C₁₇×#367	C₂	semidirect
5. C₁₇×Q₃₂	C₄	semidirect
7. C₁₇×D₁₆	C₄	semidirect
27. #1418	C₁₇	direct (N × H)
35. M₆₄	C₂×C₁₇	semidirect
36. #367	C₂×C₁₇	semidirect
41. Q₃₂	C₄×C₁₇	semidirect
43. D₁₆	C₄×C₁₇	semidirect
47. C₁₇	#1418	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×#508	2
C₁₇×M₆₄	2
C₁₇×#367	2
#1418	17

Subgroups — C17×#1418 #14524424

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₇×#1418 #14524424