Subgroups — C₁₇×#2244 #14525250

Order 2176.

152 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₇×#499	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₇×#493	C₂	1	1	yes	maximal, characteristic
3	C₁₇×#357	C₂	1	4	yes	maximal, complemented
4	C₁₇×#346	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×D₈×C₁₇	—	2	1	no	—
6	C₂×D₈×C₁₇	C₂²	1	2	yes	—
7	C₁₇×#127	—	2	1	no	—
8	C₁₇×#125	—	2	1	no	—
9	C₂×C₁₆×C₁₇	C₂²	1	2	yes	—
10	C₁₇×#107	C₂²	1	2	yes	—
11	C₁₇×#106	—	2	1	no	—
12	C₄×C₈×C₁₇	C₂²	1	1	yes	characteristic
13	C₂×D₄×C₁₇	—	2	2	no	—
14	C₂×D₄×C₁₇	—	4	2	no	—
15	D₈×C₁₇	—	2	4	no	—
16	D₈×C₁₇	—	4	2	no	—
17	C₂×C₈×C₁₇	D₄	1	1	yes	characteristic
18	C₂×C₈×C₁₇	C₂³	1	1	yes	characteristic
19	C₄⋊C₄×C₁₇	—	2	2	no	—
20	C₄⋊C₄×C₁₇	—	4	2	no	—
21	C₄²×C₁₇	D₄	1	1	yes	characteristic
22	C₁₆×C₁₇	—	2	2	no	—
23	C₂³×C₁₇	—	4	2	no	—
24	D₄×C₁₇	—	4	2	no	—
25	D₄×C₁₇	—	4	2	no	—
26	D₄×C₁₇	—	8	4	no	—
27	C₂×C₄×C₁₇	—	4	2	no	—
28	C₂×C₄×C₁₇	D₈	1	2	yes	—
29	C₂×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
30	C₈×C₁₇	SD₁₆	1	2	yes	—
31	C₈×C₁₇	#41	1	2	yes	—
32	#2244	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
33	C₂²×C₁₇	—	8	2	no	—
34	C₂²×C₁₇	—	8	4	no	—
35	C₂²×C₁₇	C₂×D₈	1	1	yes	characteristic
36	C₄×C₁₇	—	2	2	no	—
37	C₄×C₁₇	—	8	2	no	—
38	C₄×C₁₇	#124	1	1	yes	characteristic
39	C₄×C₁₇	C₂×SD₁₆	1	1	yes	characteristic
40	#499	C₂×C₁₇	1	1	yes	characteristic, complemented
41	#493	C₂×C₁₇	1	1	yes	characteristic
42	#357	C₂×C₁₇	1	4	yes	complemented
43	#346	C₂×C₁₇	1	1	yes	characteristic, complemented
44	C₂×C₁₇	—	16	2	no	—
45	C₂×C₁₇	#486	1	1	yes	characteristic
46	C₂×C₁₇	#509	1	2	yes	—
47	C₂×D₈	—	2	1	no	—
48	C₂×D₈	C₂²×C₁₇	1	2	yes	—
49	#127	—	2	1	no	—
50	#125	—	2	1	no	—
51	C₂×C₁₆	C₂²×C₁₇	1	2	yes	—
52	#107	C₂²×C₁₇	1	2	yes	—
53	#106	—	2	1	no	—
54	C₄×C₈	C₂²×C₁₇	1	1	yes	characteristic
55	C₁₇	#2244	1	1	yes	characteristic, direct product factor, Sylow
56	C₂×D₄	—	2	2	no	—
57	C₂×D₄	—	4	2	no	—
58	D₈	—	2	4	no	—
59	D₈	—	4	2	no	—
60	C₂×C₈	D₄×C₁₇	1	1	yes	characteristic
61	C₂×C₈	C₂³×C₁₇	1	1	yes	characteristic
62	C₄⋊C₄	—	2	2	no	—
63	C₄⋊C₄	—	4	2	no	—
64	C₄²	D₄×C₁₇	1	1	yes	characteristic
65	C₁₆	—	2	2	no	—
66	C₂³	—	4	2	no	—
67	D₄	—	4	2	no	—
68	D₄	—	4	2	no	—
69	D₄	—	8	4	no	—
70	C₂×C₄	—	4	2	no	—
71	C₂×C₄	D₈×C₁₇	1	2	yes	—
72	C₂×C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
73	C₈	SD₁₆×C₁₇	1	2	yes	—
74	C₈	#41×C₁₇	1	2	yes	—
75	C₂²	—	8	4	no	—
76	C₂²	—	8	2	no	—
77	C₂²	C₂×D₈×C₁₇	1	1	yes	characteristic
78	C₄	—	2	2	no	—
79	C₄	—	8	2	no	—
80	C₄	C₁₇×#124	1	1	yes	characteristic
81	C₄	C₂×SD₁₆×C₁₇	1	1	yes	characteristic
82	C₂	—	16	2	no	—
83	C₂	C₁₇×#486	1	1	yes	characteristic
84	C₂	C₁₇×#509	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₇	C₂×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂³×C₁₇
prime radical	C₁₇×#493	C₂
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₄²×C₁₇ ◁ C₄×C₈×C₁₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₇×#499	C₂	semidirect
3. C₁₇×#357	C₂	semidirect
4. C₁₇×#346	C₂	semidirect
32. #2244	C₁₇	direct (N × H)
40. #499	C₂×C₁₇	semidirect
42. #357	C₂×C₁₇	semidirect
43. #346	C₂×C₁₇	semidirect
55. C₁₇	#2244	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×#499	2
C₁₇×#493	2
C₁₇×#357	2
C₁₇×#346	2
#2244	17

Subgroups — C17×#2244 #14525250

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₇×#2244 #14525250