Subgroups — C₁₇×#1455 #14524461

Order 2176.

214 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×M₁₆×C₁₇	C₂	1	3	yes	maximal
2	C₁₇×#322	C₂	1	3	yes	maximal, complemented
3	C₈²×C₁₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×M₁₆×C₁₇	C₄	1	6	yes	—
5	C₂×C₄²×C₁₇	C₂²	1	1	yes	characteristic
6	C₁₇×#97	C₄	1	6	yes	—
7	C₄×C₈×C₁₇	C₂²	1	3	yes	—
8	C₄×C₈×C₁₇	C₂²	1	3	yes	—
9	C₂²×C₄×C₁₇	C₂×C₄	1	3	yes	—
10	M₁₆×C₁₇	—	2	12	no	—
11	C₂×C₈×C₁₇	C₂×C₄	1	6	yes	—
12	C₂×C₈×C₁₇	C₂×C₄	1	6	yes	—
13	C₄²×C₁₇	C₂×C₄	1	3	yes	—
14	C₄²×C₁₇	C₂³	1	1	yes	characteristic
15	C₂³×C₁₇	C₄²	1	1	yes	characteristic
16	C₂×C₄×C₁₇	—	2	6	no	—
17	C₂×C₄×C₁₇	C₄²	1	3	yes	—
18	C₂×C₄×C₁₇	C₂²×C₄	1	3	yes	—
19	C₈×C₁₇	—	2	6	no	—
20	C₈×C₁₇	M₁₆	1	12	yes	complemented
21	#1455	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
22	C₂²×C₁₇	—	2	3	no	—
23	C₂²×C₁₇	C₂×C₄²	1	1	yes	characteristic
24	C₄×C₁₇	—	2	3	no	—
25	C₄×C₁₇	C₂×M₁₆	1	6	yes	—
26	C₄×M₁₆	C₂×C₁₇	1	3	yes	—
27	#322	C₂×C₁₇	1	3	yes	complemented
28	C₈²	C₂×C₁₇	1	1	yes	characteristic, complemented
29	C₂×C₁₇	—	4	1	no	—
30	C₂×C₁₇	C₄×M₁₆	1	3	yes	—
31	C₂×M₁₆	C₄×C₁₇	1	6	yes	—
32	C₂×C₄²	C₂²×C₁₇	1	1	yes	characteristic
33	#97	C₄×C₁₇	1	6	yes	—
34	C₄×C₈	C₂²×C₁₇	1	3	yes	—
35	C₄×C₈	C₂²×C₁₇	1	3	yes	—
36	C₁₇	#1455	1	1	yes	characteristic, direct product factor, Sylow
37	C₂²×C₄	C₂×C₄×C₁₇	1	3	yes	—
38	M₁₆	—	2	12	no	—
39	C₂×C₈	C₂×C₄×C₁₇	1	6	yes	—
40	C₂×C₈	C₂×C₄×C₁₇	1	6	yes	—
41	C₄²	C₂×C₄×C₁₇	1	3	yes	—
42	C₄²	C₂³×C₁₇	1	1	yes	characteristic
43	C₂³	C₄²×C₁₇	1	1	yes	characteristic
44	C₂×C₄	—	2	6	no	—
45	C₂×C₄	C₄²×C₁₇	1	3	yes	—
46	C₂×C₄	C₂²×C₄×C₁₇	1	3	yes	—
47	C₈	—	2	6	no	—
48	C₈	M₁₆×C₁₇	1	12	yes	complemented
49	C₂²	—	2	3	no	—
50	C₂²	C₂×C₄²×C₁₇	1	1	yes	characteristic
51	C₄	—	2	3	no	—
52	C₄	C₂×M₁₆×C₁₇	1	6	yes	—
53	C₂	—	4	1	no	—
54	C₂	C₄×M₁₆×C₁₇	1	3	yes	—

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

Complements

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

N	H ≅ G/N	type
2. C₁₇×#322	C₂	semidirect
3. C₈²×C₁₇	C₂	semidirect
20. C₈×C₁₇	M₁₆	semidirect
21. #1455	C₁₇	direct (N × H)
27. #322	C₂×C₁₇	semidirect
28. C₈²	C₂×C₁₇	semidirect
36. C₁₇	#1455	direct (N × H)
48. C₈	M₁₆×C₁₇	semidirect

Maximal subgroups

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

subgroup	index
C₄×M₁₆×C₁₇	2
C₁₇×#322	2
C₈²×C₁₇	2
#1455	17

Subgroups — C17×#1455 #14524461

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₇×#1455 #14524461