Subgroups — C₁₇×#1746 #14524752

Order 2176.

240 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₇×#97	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×C₈×C₁₇	C₂	1	1	yes	maximal, characteristic
3	C₁₇×#376	C₂	1	1	yes	maximal, characteristic
4	C₁₇×#336	C₂	1	4	yes	maximal
5	C₂²×C₈×C₁₇	C₂²	1	2	yes	—
6	C₂²×C₈×C₁₇	C₂²	1	2	yes	—
7	C₂×C₄²×C₁₇	C₂²	1	2	yes	—
8	C₂×C₄²×C₁₇	C₂²	1	1	yes	characteristic
9	C₁₇×#97	C₄	1	4	yes	complemented
10	C₄×C₈×C₁₇	C₄	1	4	yes	complemented
11	C₁₇×#95	C₄	1	4	yes	—
12	C₂²×C₄×C₁₇	C₂×C₄	1	4	yes	—
13	C₂²×C₄×C₁₇	C₂×C₄	1	2	yes	—
14	C₂²×C₄×C₁₇	C₂³	1	1	yes	characteristic
15	C₂×C₈×C₁₇	—	2	4	no	—
16	C₂×C₈×C₁₇	—	2	4	no	—
17	C₂×C₈×C₁₇	C₂×C₄	1	4	yes	—
18	C₂×C₈×C₁₇	C₂×C₄	1	4	yes	—
19	C₄²×C₁₇	—	2	4	no	—
20	C₄²×C₁₇	C₂×C₄	1	2	yes	—
21	C₄²×C₁₇	C₂×C₄	1	2	yes	—
22	C₂³×C₁₇	C₂²×C₄	1	1	yes	characteristic
23	C₂×C₄×C₁₇	—	2	4	no	—
24	C₂×C₄×C₁₇	—	2	4	no	—
25	C₂×C₄×C₁₇	—	2	8	no	—
26	C₂×C₄×C₁₇	C₄²	1	4	yes	—
27	C₂×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
28	C₂×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
29	C₂×C₄×C₁₇	#41	1	4	yes	—
30	C₈×C₁₇	—	2	4	no	—
31	C₈×C₁₇	—	2	4	no	—
32	#1746	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
33	C₂²×C₁₇	C₂×C₄²	1	1	yes	characteristic
34	C₂²×C₁₇	#117	1	2	yes	—
35	C₂²×C₁₇	#131	1	4	yes	—
36	C₄×C₁₇	—	2	4	no	—
37	C₄×C₁₇	—	4	4	no	—
38	C₄×C₁₇	#117	1	2	yes	—
39	C₄×C₁₇	#117	1	2	yes	—
40	C₂×#97	C₂×C₁₇	1	1	yes	characteristic
41	C₂×C₄×C₈	C₂×C₁₇	1	1	yes	characteristic
42	#376	C₂×C₁₇	1	1	yes	characteristic
43	#336	C₂×C₁₇	1	4	yes	—
44	C₂×C₁₇	#376	1	1	yes	characteristic
45	C₂×C₁₇	#405	1	2	yes	—
46	C₂×C₁₇	#433	1	4	yes	—
47	C₂²×C₈	C₂²×C₁₇	1	2	yes	—
48	C₂²×C₈	C₂²×C₁₇	1	2	yes	—
49	C₂×C₄²	C₂²×C₁₇	1	2	yes	—
50	C₂×C₄²	C₂²×C₁₇	1	1	yes	characteristic
51	#97	C₄×C₁₇	1	4	yes	complemented
52	C₄×C₈	C₄×C₁₇	1	4	yes	complemented
53	#95	C₄×C₁₇	1	4	yes	—
54	C₁₇	#1746	1	1	yes	characteristic, direct product factor, Sylow
55	C₂²×C₄	C₂×C₄×C₁₇	1	4	yes	—
56	C₂²×C₄	C₂×C₄×C₁₇	1	2	yes	—
57	C₂²×C₄	C₂³×C₁₇	1	1	yes	characteristic
58	C₂×C₈	—	2	4	no	—
59	C₂×C₈	—	2	4	no	—
60	C₂×C₈	C₂×C₄×C₁₇	1	4	yes	—
61	C₂×C₈	C₂×C₄×C₁₇	1	4	yes	—
62	C₄²	—	2	4	no	—
63	C₄²	C₂×C₄×C₁₇	1	2	yes	—
64	C₄²	C₂×C₄×C₁₇	1	2	yes	—
65	C₂³	C₂²×C₄×C₁₇	1	1	yes	characteristic
66	C₂×C₄	—	2	4	no	—
67	C₂×C₄	—	2	8	no	—
68	C₂×C₄	—	2	4	no	—
69	C₂×C₄	C₄²×C₁₇	1	4	yes	—
70	C₂×C₄	C₂²×C₄×C₁₇	1	1	yes	characteristic
71	C₂×C₄	C₂²×C₄×C₁₇	1	1	yes	characteristic
72	C₂×C₄	#41×C₁₇	1	4	yes	—
73	C₈	—	2	4	no	—
74	C₈	—	2	4	no	—
75	C₂²	C₂×C₄²×C₁₇	1	1	yes	characteristic
76	C₂²	C₁₇×#117	1	2	yes	—
77	C₂²	C₁₇×#131	1	4	yes	—
78	C₄	—	2	4	no	—
79	C₄	—	4	4	no	—
80	C₄	C₁₇×#117	1	2	yes	—
81	C₄	C₁₇×#117	1	2	yes	—
82	C₂	C₁₇×#376	1	1	yes	characteristic
83	C₂	C₁₇×#405	1	2	yes	—
84	C₂	C₁₇×#433	1	4	yes	—

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

Complements

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

N	H ≅ G/N	type
9. C₁₇×#97	C₄	semidirect
10. C₄×C₈×C₁₇	C₄	semidirect
32. #1746	C₁₇	direct (N × H)
51. #97	C₄×C₁₇	semidirect
52. C₄×C₈	C₄×C₁₇	semidirect
54. C₁₇	#1746	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×#97	2
C₂×C₄×C₈×C₁₇	2
C₁₇×#376	2
C₁₇×#336	2
#1746	17

Subgroups — C17×#1746 #14524752

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₇×#1746 #14524752