Subgroups — C₁₇×#1290 #14524296

Order 2176.

136 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₇×#432	C₂	1	2	yes	maximal
2	C₂×C₁₇×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₈×C₁₇	C₄	1	2	yes	—
4	C₂×C₄²×C₁₇	C₂²	1	1	yes	characteristic
5	C₁₇×C₄⋊C₈	—	2	2	no	—
6	C₁₇×C₄⋊C₈	—	2	2	no	—
7	C₁₇×C₂²⋊C₈	—	2	2	no	—
8	C₁₇×#97	C₄	1	4	yes	—
9	C₂²×C₄×C₁₇	C₂×C₄	1	1	yes	characteristic
10	C₂²×C₄×C₁₇	D₄	1	1	yes	characteristic
11	C₂²×C₄×C₁₇	Q₈	1	1	yes	characteristic
12	C₂×C₈×C₁₇	—	2	2	no	—
13	C₂×C₈×C₁₇	—	2	4	no	—
14	C₂×C₈×C₁₇	—	4	2	no	—
15	C₄²×C₁₇	C₂×C₄	1	2	yes	—
16	C₄²×C₁₇	D₄	1	2	yes	—
17	C₂³×C₁₇	C₄⋊C₄	1	1	yes	characteristic
18	C₂×C₄×C₁₇	—	2	2	no	—
19	C₂×C₄×C₁₇	—	2	1	no	—
20	C₂×C₄×C₁₇	—	2	1	no	—
21	C₂×C₄×C₁₇	—	4	1	no	—
22	C₂×C₄×C₁₇	C₄²	1	1	yes	characteristic
23	C₂×C₄×C₁₇	C₂²⋊C₄	1	2	yes	—
24	C₂×C₄×C₁₇	C₂²⋊C₄	1	1	yes	characteristic
25	C₂×C₄×C₁₇	C₄⋊C₄	1	2	yes	—
26	C₈×C₁₇	—	4	4	no	—
27	C₈×C₁₇	—	4	2	no	—
28	#1290	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
29	C₂²×C₁₇	—	2	1	no	—
30	C₂²×C₁₇	—	2	1	no	—
31	C₂²×C₁₇	#95	1	1	yes	characteristic
32	C₂²×C₁₇	#108	1	2	yes	—
33	C₄×C₁₇	—	2	2	no	—
34	C₄×C₁₇	—	2	2	no	—
35	C₄×C₁₇	—	2	1	no	—
36	C₄×C₁₇	#100	1	1	yes	characteristic
37	C₄×C₁₇	#101	1	1	yes	characteristic
38	#432	C₂×C₁₇	1	2	yes	—
39	C₂×C₄⋊C₈	C₂×C₁₇	1	1	yes	characteristic
40	C₂×C₁₇	—	2	2	no	—
41	C₂×C₁₇	H(3,ℤ/4)	1	1	yes	characteristic
42	C₂×C₁₇	#341	1	1	yes	characteristic
43	C₂×C₁₇	#343	1	1	yes	characteristic
44	C₂²×C₈	C₄×C₁₇	1	2	yes	—
45	C₂×C₄²	C₂²×C₁₇	1	1	yes	characteristic
46	C₄⋊C₈	—	2	2	no	—
47	C₄⋊C₈	—	2	2	no	—
48	C₂²⋊C₈	—	2	2	no	—
49	#97	C₄×C₁₇	1	4	yes	—
50	C₁₇	#1290	1	1	yes	characteristic, direct product factor, Sylow
51	C₂²×C₄	C₂×C₄×C₁₇	1	1	yes	characteristic
52	C₂²×C₄	D₄×C₁₇	1	1	yes	characteristic
53	C₂²×C₄	Q₈×C₁₇	1	1	yes	characteristic
54	C₂×C₈	—	2	4	no	—
55	C₂×C₈	—	2	2	no	—
56	C₂×C₈	—	4	2	no	—
57	C₄²	C₂×C₄×C₁₇	1	2	yes	—
58	C₄²	D₄×C₁₇	1	2	yes	—
59	C₂³	C₄⋊C₄×C₁₇	1	1	yes	characteristic
60	C₂×C₄	—	2	2	no	—
61	C₂×C₄	—	2	1	no	—
62	C₂×C₄	—	2	1	no	—
63	C₂×C₄	—	4	1	no	—
64	C₂×C₄	C₄²×C₁₇	1	1	yes	characteristic
65	C₂×C₄	C₂²⋊C₄×C₁₇	1	2	yes	—
66	C₂×C₄	C₂²⋊C₄×C₁₇	1	1	yes	characteristic
67	C₂×C₄	C₄⋊C₄×C₁₇	1	2	yes	—
68	C₈	—	4	4	no	—
69	C₈	—	4	2	no	—
70	C₂²	—	2	1	no	—
71	C₂²	—	2	1	no	—
72	C₂²	C₁₇×#95	1	1	yes	characteristic
73	C₂²	C₁₇×#108	1	2	yes	—
74	C₄	—	2	2	no	—
75	C₄	—	2	2	no	—
76	C₄	—	2	1	no	—
77	C₄	C₁₇×#100	1	1	yes	characteristic
78	C₄	C₁₇×#101	1	1	yes	characteristic
79	C₂	—	2	2	no	—
80	C₂	C₁₇×H(3,ℤ/4)	1	1	yes	characteristic
81	C₂	C₁₇×#341	1	1	yes	characteristic
82	C₂	C₁₇×#343	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₇	#95
commutator	C₂×C₄	C₄²×C₁₇
Frattini, cosocle	C₂×C₄²	C₂²×C₁₇
prime radical	C₂³×C₁₇	C₄⋊C₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₂×C₄²×C₁₇ ◁ G

Complements

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

N	H ≅ G/N	type
28. #1290	C₁₇	direct (N × H)
50. C₁₇	#1290	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×#432	2
C₂×C₁₇×C₄⋊C₈	2
#1290	17

Subgroups — C17×#1290 #14524296

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₇×#1290 #14524296