Subgroups — C₁₇×#1312 #14524318

Order 2176.

92 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₁₆×C₁₇	C₂	1	2	yes	maximal
2	C₈²×C₁₇	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₆×C₁₇	C₄	1	4	yes	—
4	C₄×C₈×C₁₇	C₄	1	1	yes	characteristic
5	C₄×C₈×C₁₇	C₄	1	1	yes	characteristic
6	C₄×C₈×C₁₇	C₂²	1	1	yes	characteristic
7	C₂×C₈×C₁₇	C₈	1	2	yes	—
8	C₂×C₈×C₁₇	C₈	1	2	yes	—
9	C₂×C₈×C₁₇	C₂×C₄	1	2	yes	—
10	C₄²×C₁₇	C₂×C₄	1	1	yes	characteristic
11	C₁₆×C₁₇	—	2	4	no	—
12	C₂×C₄×C₁₇	C₄²	1	1	yes	characteristic
13	C₂×C₄×C₁₇	C₂×C₈	1	1	yes	characteristic
14	C₂×C₄×C₁₇	C₂×C₈	1	1	yes	characteristic
15	C₈×C₁₇	—	2	2	no	—
16	C₈×C₁₇	C₁₆	1	4	yes	complemented
17	C₈×C₁₇	M₁₆	1	4	yes	—
18	#1312	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
19	C₂²×C₁₇	C₄×C₈	1	1	yes	characteristic
20	C₄×C₁₇	#97	1	2	yes	—
21	C₄×C₁₇	C₂×C₁₆	1	2	yes	—
22	C₄×C₁₇	M₃₂	1	2	yes	—
23	C₄×C₁₆	C₂×C₁₇	1	2	yes	—
24	C₈²	C₂×C₁₇	1	1	yes	characteristic
25	C₂×C₁₇	#322	1	1	yes	characteristic
26	C₂×C₁₇	C₄×C₁₆	1	1	yes	characteristic
27	C₂×C₁₇	#346	1	1	yes	characteristic
28	C₂×C₁₆	C₄×C₁₇	1	4	yes	—
29	C₄×C₈	C₄×C₁₇	1	1	yes	characteristic
30	C₄×C₈	C₄×C₁₇	1	1	yes	characteristic
31	C₄×C₈	C₂²×C₁₇	1	1	yes	characteristic
32	C₁₇	#1312	1	1	yes	characteristic, direct product factor, Sylow
33	C₂×C₈	C₈×C₁₇	1	2	yes	—
34	C₂×C₈	C₈×C₁₇	1	2	yes	—
35	C₂×C₈	C₂×C₄×C₁₇	1	2	yes	—
36	C₄²	C₂×C₄×C₁₇	1	1	yes	characteristic
37	C₁₆	—	2	4	no	—
38	C₂×C₄	C₄²×C₁₇	1	1	yes	characteristic
39	C₂×C₄	C₂×C₈×C₁₇	1	1	yes	characteristic
40	C₂×C₄	C₂×C₈×C₁₇	1	1	yes	characteristic
41	C₈	—	2	2	no	—
42	C₈	C₁₆×C₁₇	1	4	yes	complemented
43	C₈	M₁₆×C₁₇	1	4	yes	—
44	C₂²	C₄×C₈×C₁₇	1	1	yes	characteristic
45	C₄	C₁₇×#97	1	2	yes	—
46	C₄	C₂×C₁₆×C₁₇	1	2	yes	—
47	C₄	C₁₇×M₃₂	1	2	yes	—
48	C₂	C₁₇×#322	1	1	yes	characteristic
49	C₂	C₄×C₁₆×C₁₇	1	1	yes	characteristic
50	C₂	C₁₇×#346	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
16. C₈×C₁₇	C₁₆	semidirect
18. #1312	C₁₇	direct (N × H)
32. C₁₇	#1312	direct (N × H)
42. C₈	C₁₆×C₁₇	semidirect

Maximal subgroups

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

subgroup	index
C₄×C₁₆×C₁₇	2
C₈²×C₁₇	2
#1312	17

Subgroups — C17×#1312 #14524318

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₇×#1312 #14524318