Subgroups — C₁₇×#1419 #14524425

Order 2176.

78 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	C₁₇×M₆₄	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₇×#368	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	—
7	C₂×C₁₆×C₁₇	C₂²	1	1	yes	characteristic
8	C₁₇×#108	—	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	M₁₆×C₁₇	—	4	1	no	—
14	C₂×C₈×C₁₇	D₄	1	1	yes	characteristic
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	D₈	1	1	yes	characteristic
21	C₈×C₁₇	—	8	1	no	—
22	C₈×C₁₇	C₂²⋊C₄	1	1	yes	characteristic
23	C₈×C₁₇	SD₁₆	1	1	yes	characteristic
24	#1419	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
25	C₂²×C₁₇	—	8	2	no	—
26	C₂²×C₁₇	—	16	2	no	—
27	C₂²×C₁₇	SD₃₂	1	1	yes	characteristic
28	C₄×C₁₇	#102	1	1	yes	characteristic
29	C₄×C₁₇	D₁₆	1	1	yes	characteristic
30	C₂×D₁₆	C₂×C₁₇	1	1	yes	characteristic
31	M₆₄	C₂×C₁₇	1	1	yes	characteristic, complemented
32	#368	C₂×C₁₇	1	1	yes	characteristic, complemented
33	C₂×C₁₇	—	2	1	no	—
34	C₂×C₁₇	—	16	2	no	—
35	C₂×C₁₇	#357	1	1	yes	characteristic
36	C₂×D₈	—	2	1	no	—
37	D₁₆	—	2	1	no	—
38	D₁₆	C₄×C₁₇	1	2	yes	—
39	C₂×C₁₆	C₂²×C₁₇	1	1	yes	characteristic
40	#108	—	2	1	no	—
41	C₃₂	—	2	1	no	—
42	C₁₇	#1419	1	1	yes	characteristic, direct product factor, Sylow
43	C₂×D₄	—	4	1	no	—
44	D₈	—	2	2	no	—
45	D₈	—	4	1	no	—
46	M₁₆	—	4	1	no	—
47	C₂×C₈	D₄×C₁₇	1	1	yes	characteristic
48	C₁₆	C₂×C₄×C₁₇	1	1	yes	characteristic
49	C₁₆	D₄×C₁₇	1	1	yes	characteristic
50	C₂³	—	8	1	no	—
51	D₄	—	4	2	no	—
52	D₄	—	8	1	no	—
53	C₂×C₄	D₈×C₁₇	1	1	yes	characteristic
54	C₈	—	8	1	no	—
55	C₈	C₂²⋊C₄×C₁₇	1	1	yes	characteristic
56	C₈	SD₁₆×C₁₇	1	1	yes	characteristic
57	C₂²	—	8	2	no	—
58	C₂²	—	16	2	no	—
59	C₂²	C₁₇×SD₃₂	1	1	yes	characteristic
60	C₄	C₁₇×#102	1	1	yes	characteristic
61	C₄	C₁₇×D₁₆	1	1	yes	characteristic
62	C₂	—	2	1	no	—
63	C₂	—	16	2	no	—
64	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	C₂×C₁₇×D₁₆	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×#368	C₂	semidirect
24. #1419	C₁₇	direct (N × H)
31. M₆₄	C₂×C₁₇	semidirect
32. #368	C₂×C₁₇	semidirect
42. C₁₇	#1419	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
C₁₇×M₆₄	2
C₁₇×#368	2
#1419	17

Subgroups — C17×#1419 #14524425

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₇×#1419 #14524425