Subgroups — C₁₇×#1415 #14524421

Order 2176.

82 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₇×D₁₆	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₇×C₃₂	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₇×#366	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₈×C₁₇	—	2	1	no	—
5	C₁₇×D₁₆	—	2	1	no	—
6	C₁₇×D₁₆	C₄	1	2	yes	complemented
7	C₂×C₁₆×C₁₇	C₂²	1	1	yes	characteristic
8	C₁₇×#107	—	2	1	no	—
9	C₁₇×C₃₂	—	2	1	no	—
10	C₂×D₄×C₁₇	—	4	1	no	—
11	D₈×C₁₇	—	2	2	no	—
12	D₈×C₁₇	—	4	1	no	—
13	C₂×C₈×C₁₇	D₄	1	1	yes	characteristic
14	C₄⋊C₄×C₁₇	—	4	1	no	—
15	C₁₆×C₁₇	C₂×C₄	1	1	yes	characteristic
16	C₁₆×C₁₇	D₄	1	1	yes	characteristic
17	C₂³×C₁₇	—	8	1	no	—
18	D₄×C₁₇	—	4	2	no	—
19	D₄×C₁₇	—	8	1	no	—
20	C₂×C₄×C₁₇	—	8	1	no	—
21	C₂×C₄×C₁₇	D₈	1	1	yes	characteristic
22	C₈×C₁₇	C₂²⋊C₄	1	1	yes	characteristic
23	C₈×C₁₇	SD₁₆	1	1	yes	characteristic
24	#1415	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
25	C₂²×C₁₇	—	8	2	no	—
26	C₂²×C₁₇	—	16	1	no	—
27	C₂²×C₁₇	—	16	1	no	—
28	C₂²×C₁₇	D₁₆	1	1	yes	characteristic
29	C₄×C₁₇	—	16	1	no	—
30	C₄×C₁₇	#102	1	1	yes	characteristic
31	C₄×C₁₇	SD₃₂	1	1	yes	characteristic
32	C₂×D₁₆	C₂×C₁₇	1	1	yes	characteristic
33	C₂×C₃₂	C₂×C₁₇	1	1	yes	characteristic, complemented
34	#366	C₂×C₁₇	1	1	yes	characteristic, complemented
35	C₂×C₁₇	—	16	2	no	—
36	C₂×C₁₇	#357	1	1	yes	characteristic
37	C₂×C₁₇	D₃₂	1	1	yes	characteristic
38	C₂×C₁₇	SD₆₄	1	1	yes	characteristic
39	C₂×D₈	—	2	1	no	—
40	D₁₆	—	2	1	no	—
41	D₁₆	C₄×C₁₇	1	2	yes	complemented
42	C₂×C₁₆	C₂²×C₁₇	1	1	yes	characteristic
43	#107	—	2	1	no	—
44	C₃₂	—	2	1	no	—
45	C₁₇	#1415	1	1	yes	characteristic, direct product factor, Sylow
46	C₂×D₄	—	4	1	no	—
47	D₈	—	2	2	no	—
48	D₈	—	4	1	no	—
49	C₂×C₈	D₄×C₁₇	1	1	yes	characteristic
50	C₄⋊C₄	—	4	1	no	—
51	C₁₆	C₂×C₄×C₁₇	1	1	yes	characteristic
52	C₁₆	D₄×C₁₇	1	1	yes	characteristic
53	C₂³	—	8	1	no	—
54	D₄	—	4	2	no	—
55	D₄	—	8	1	no	—
56	C₂×C₄	—	8	1	no	—
57	C₂×C₄	D₈×C₁₇	1	1	yes	characteristic
58	C₈	C₂²⋊C₄×C₁₇	1	1	yes	characteristic
59	C₈	SD₁₆×C₁₇	1	1	yes	characteristic
60	C₂²	—	8	2	no	—
61	C₂²	—	16	1	no	—
62	C₂²	—	16	1	no	—
63	C₂²	C₁₇×D₁₆	1	1	yes	characteristic
64	C₄	—	16	1	no	—
65	C₄	C₁₇×#102	1	1	yes	characteristic
66	C₄	C₁₇×SD₃₂	1	1	yes	characteristic
67	C₂	—	16	2	no	—
68	C₂	C₁₇×#357	1	1	yes	characteristic
69	C₂	C₁₇×D₃₂	1	1	yes	characteristic
70	C₂	C₁₇×SD₆₄	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₇	D₁₆
commutator	C₁₆	C₂×C₄×C₁₇
Frattini, cosocle	C₂×C₁₆	C₂²×C₁₇
prime radical	C₂×C₁₇×D₁₆	C₂
LCS	G ▷ C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×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. C₂×C₁₇×C₃₂	C₂	semidirect
3. C₁₇×#366	C₂	semidirect
6. C₁₇×D₁₆	C₄	semidirect
24. #1415	C₁₇	direct (N × H)
33. C₂×C₃₂	C₂×C₁₇	semidirect
34. #366	C₂×C₁₇	semidirect
41. D₁₆	C₄×C₁₇	semidirect
45. C₁₇	#1415	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₁₇×D₁₆	2
C₂×C₁₇×C₃₂	2
C₁₇×#366	2
#1415	17

Subgroups — C17×#1415 #14524421

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₇×#1415 #14524421