Subgroups — C₁₇×#7540 #16865284

Order 4352.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₇×#2262	C₂	1	1	yes	maximal, characteristic
2	C₁₇×M₁₂₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₇×#1424	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₇×#508	—	2	1	no	—
5	C₁₇×Q₆₄	C₄	1	1	yes	characteristic, complemented
6	C₁₇×SD₆₄	—	2	1	no	—
7	C₁₇×D₃₂	C₄	1	1	yes	characteristic, complemented
8	C₂×C₁₇×C₃₂	C₂²	1	1	yes	characteristic
9	C₁₇×#366	—	2	1	no	—
10	C₁₇×C₆₄	—	2	1	no	—
11	C₁₇×#135	—	4	1	no	—
12	C₁₇×Q₃₂	—	2	1	no	—
13	C₁₇×SD₃₂	—	4	1	no	—
14	C₁₇×D₁₆	—	2	1	no	—
15	C₂×C₁₆×C₁₇	D₄	1	1	yes	characteristic
16	C₁₇×#107	—	4	1	no	—
17	C₁₇×C₃₂	C₂×C₄	1	1	yes	characteristic
18	C₁₇×C₃₂	D₄	1	1	yes	characteristic
19	#41×C₁₇	—	8	1	no	—
20	Q₁₆×C₁₇	—	4	1	no	—
21	SD₁₆×C₁₇	—	8	1	no	—
22	D₈×C₁₇	—	4	1	no	—
23	C₂×C₈×C₁₇	D₈	1	1	yes	characteristic
24	C₄⋊C₄×C₁₇	—	8	1	no	—
25	C₁₆×C₁₇	C₂²⋊C₄	1	1	yes	characteristic
26	C₁₆×C₁₇	SD₁₆	1	1	yes	characteristic
27	#7540	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
28	Q₈×C₁₇	—	8	1	no	—
29	D₄×C₁₇	—	8	1	no	—
30	D₄×C₁₇	—	16	1	no	—
31	C₂×C₄×C₁₇	—	16	1	no	—
32	C₂×C₄×C₁₇	—	16	1	no	—
33	C₂×C₄×C₁₇	D₁₆	1	1	yes	characteristic
34	C₈×C₁₇	#102	1	1	yes	characteristic
35	C₈×C₁₇	SD₃₂	1	1	yes	characteristic
36	#2262	C₂×C₁₇	1	1	yes	characteristic
37	M₁₂₈	C₂×C₁₇	1	1	yes	characteristic, complemented
38	#1424	C₂×C₁₇	1	1	yes	characteristic, complemented
39	C₂²×C₁₇	—	16	1	no	—
40	C₂²×C₁₇	D₃₂	1	1	yes	characteristic
41	C₄×C₁₇	—	16	1	no	—
42	C₄×C₁₇	—	32	1	no	—
43	C₄×C₁₇	#357	1	1	yes	characteristic
44	C₄×C₁₇	SD₆₄	1	1	yes	characteristic
45	#508	—	2	1	no	—
46	Q₆₄	C₄×C₁₇	1	1	yes	characteristic, complemented
47	SD₆₄	—	2	1	no	—
48	D₃₂	C₄×C₁₇	1	1	yes	characteristic, complemented
49	C₂×C₃₂	C₂²×C₁₇	1	1	yes	characteristic
50	#366	—	2	1	no	—
51	C₆₄	—	2	1	no	—
52	C₂×C₁₇	—	2	1	no	—
53	C₂×C₁₇	—	32	1	no	—
54	C₂×C₁₇	#1415	1	1	yes	characteristic
55	#135	—	4	1	no	—
56	Q₃₂	—	2	1	no	—
57	SD₃₂	—	4	1	no	—
58	D₁₆	—	2	1	no	—
59	C₂×C₁₆	D₄×C₁₇	1	1	yes	characteristic
60	#107	—	4	1	no	—
61	C₃₂	C₂×C₄×C₁₇	1	1	yes	characteristic
62	C₃₂	D₄×C₁₇	1	1	yes	characteristic
63	C₁₇	#7540	1	1	yes	characteristic, direct product factor, Sylow
64	#41	—	8	1	no	—
65	Q₁₆	—	4	1	no	—
66	SD₁₆	—	8	1	no	—
67	D₈	—	4	1	no	—
68	C₂×C₈	D₈×C₁₇	1	1	yes	characteristic
69	C₄⋊C₄	—	8	1	no	—
70	C₁₆	C₂²⋊C₄×C₁₇	1	1	yes	characteristic
71	C₁₆	SD₁₆×C₁₇	1	1	yes	characteristic
72	Q₈	—	8	1	no	—
73	D₄	—	8	1	no	—
74	D₄	—	16	1	no	—
75	C₂×C₄	—	16	1	no	—
76	C₂×C₄	—	16	1	no	—
77	C₂×C₄	C₁₇×D₁₆	1	1	yes	characteristic
78	C₈	C₁₇×#102	1	1	yes	characteristic
79	C₈	C₁₇×SD₃₂	1	1	yes	characteristic
80	C₂²	—	16	1	no	—
81	C₂²	C₁₇×D₃₂	1	1	yes	characteristic
82	C₄	—	16	1	no	—
83	C₄	—	32	1	no	—
84	C₄	C₁₇×#357	1	1	yes	characteristic
85	C₄	C₁₇×SD₆₄	1	1	yes	characteristic
86	C₂	—	2	1	no	—
87	C₂	—	32	1	no	—
88	C₂	C₁₇×#1415	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₁₇	#1415
commutator	C₃₂	C₂×C₄×C₁₇
Frattini, cosocle	C₂×C₃₂	C₂²×C₁₇
prime radical	C₁₇×#2262	C₂
LCS	G ▷ C₃₂ ▷ C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₇ ◁ C₂×C₄×C₁₇ ◁ C₂×C₈×C₁₇ ◁ C₂×C₁₆×C₁₇ ◁ C₂×C₁₇×C₃₂ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₇×M₁₂₈	C₂	semidirect
3. C₁₇×#1424	C₂	semidirect
5. C₁₇×Q₆₄	C₄	semidirect
7. C₁₇×D₃₂	C₄	semidirect
27. #7540	C₁₇	direct (N × H)
37. M₁₂₈	C₂×C₁₇	semidirect
38. #1424	C₂×C₁₇	semidirect
46. Q₆₄	C₄×C₁₇	semidirect
48. D₃₂	C₄×C₁₇	semidirect
63. C₁₇	#7540	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×#2262	2
C₁₇×M₁₂₈	2
C₁₇×#1424	2
#7540	17

Subgroups — C17×#7540 #16865284

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₇×#7540 #16865284