Subgroups — #564×Dic₁₇ #17197046

Order 4352.

1800 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14531970	C₂	1	15	yes	maximal
2	#125×Dic₁₇	C₂	1	15	yes	maximal
3	C₂×C₁₇×#564	C₂	1	1	yes	maximal, characteristic
4	#11762708	C₂²	1	30	yes	—
5	#11762695	C₂²	1	60	yes	—
6	#11762675	C₂²	1	15	yes	—
7	C₄⋊C₄×Dic₁₇	C₂²	1	30	yes	—
8	C₄²×Dic₁₇	C₂²	1	5	yes	—
9	C₁₇×#564	C₄	1	16	yes	complemented
10	C₂×C₁₇×#125	C₂²	1	15	yes	—
11	C₁₇×#125	C₂×C₄	1	120	yes	—
12	C₂×C₄⋊C₄×C₁₇	C₂³	1	30	yes	—
13	C₂×C₄²×C₁₇	C₂³	1	5	yes	—
14	C₂×C₄⋊Dic₁₇	C₂³	1	30	yes	—
15	C₂×C₄×Dic₁₇	C₂³	1	15	yes	—
16	C₂×C₄×Dic₁₇	C₂³	1	15	yes	—
17	#10587502	C₂³	1	60	yes	—
18	C₂²×C₄×C₁₇	C₂⁴	1	15	yes	—
19	C₂²×Dic₁₇	C₂⁴	1	15	yes	—
20	C₂²×Dic₁₇	C₂⁴	1	1	yes	characteristic
21	C₄⋊C₄×C₁₇	C₂²×C₄	1	120	yes	—
22	C₄²×C₁₇	C₂²×C₄	1	20	yes	—
23	C₄⋊Dic₁₇	—	4	30	no	—
24	C₄×Dic₁₇	—	2	30	no	—
25	C₄×Dic₁₇	—	4	15	no	—
26	C₄×#564	—	17	1	no	maximal, Sylow
27	C₂³×C₁₇	C₂⁵	1	1	yes	characteristic
28	C₂×C₄×C₁₇	—	2	15	no	—
29	C₂×C₄×C₁₇	—	2	15	no	—
30	C₂×C₄×C₁₇	C₂³×C₄	1	30	yes	—
31	C₂×Dic₁₇	—	2	15	no	—
32	C₂×Dic₁₇	—	2	30	no	—
33	C₂×Dic₁₇	2₋¹⁺⁴	1	6	yes	—
34	C₂×#564	D₁₇	1	1	yes	characteristic
35	#2382	—	17	15	no	—
36	C₄×#125	—	17	15	no	—
37	C₂²×C₁₇	C₂⁴×C₄	1	1	yes	characteristic
38	C₂²×C₁₇	C₂×2₋¹⁺⁴	1	3	yes	—
39	C₂²×C₁₇	#585	1	3	yes	—
40	C₄×C₁₇	—	2	30	no	—
41	Dic₁₇	—	4	15	no	—
42	Dic₁₇	#564	1	4	yes	direct product factor
43	#564	Dic₁₇	1	16	yes	direct product factor
44	C₂×#125	C₂×D₁₇	1	15	yes	—
45	#389	—	17	30	no	—
46	#387	—	17	60	no	—
47	#382	—	17	15	no	—
48	C₄×C₄⋊C₄	—	17	30	no	—
49	C₄³	—	17	5	no	—
50	C₂×C₁₇	C₄×2₋¹⁺⁴	1	3	yes	—
51	C₂×C₁₇	C₂×#564	1	1	yes	characteristic
52	C₂×C₁₇	#3531	1	3	yes	—
53	#125	C₂×Dic₁₇	1	120	yes	—
54	C₂×C₄⋊C₄	—	17	30	no	—
55	C₂×C₄⋊C₄	C₂²×D₁₇	1	30	yes	—
56	C₂×C₄²	—	17	15	no	—
57	C₂×C₄²	—	17	15	no	—
58	C₂×C₄²	C₂²×D₁₇	1	5	yes	—
59	#95	—	17	60	no	—
60	C₁₇	C₄×#564	1	1	yes	characteristic, complemented, Sylow
61	C₂²×C₄	—	17	1	no	—
62	C₂²×C₄	—	17	15	no	—
63	C₂²×C₄	C₂³×D₁₇	1	15	yes	—
64	C₄⋊C₄	—	68	30	no	—
65	C₄⋊C₄	C₂²×Dic₁₇	1	120	yes	—
66	C₄²	—	34	30	no	—
67	C₄²	—	68	15	no	—
68	C₄²	C₂²×Dic₁₇	1	20	yes	—
69	C₂³	C₂⁴×D₁₇	1	1	yes	characteristic
70	C₂×C₄	—	2	15	no	—
71	C₂×C₄	—	2	15	no	—
72	C₂×C₄	—	17	6	no	—
73	C₂×C₄	—	34	15	no	—
74	C₂×C₄	—	34	30	no	—
75	C₂×C₄	C₂³×Dic₁₇	1	30	yes	—
76	C₂²	C₂⁴×Dic₁₇	1	1	yes	characteristic
77	C₂²	2₋¹⁺⁴×D₁₇	1	3	yes	—
78	C₂²	#11763646	1	3	yes	—
79	C₄	—	2	30	no	—
80	C₄	—	17	4	no	—
81	C₄	—	68	15	no	—
82	C₂	2₋¹⁺⁴×Dic₁₇	1	3	yes	—
83	C₂	D₁₇×#564	1	1	yes	characteristic
84	C₂	#14542932	1	3	yes	—

	subgroup	G/H
center, Frattini	C₂³	C₂⁴×D₁₇
commutator	C₂²×C₁₇	C₂⁴×C₄
Fitting	C₂×C₁₇×#564	C₂
socle, prime radical, cosocle	C₂³×C₁₇	C₂⁵
hypercenter	C₂×#564	D₁₇
hypocenter	C₁₇	C₄×#564
LCS	G ▷ C₂²×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂³ ◁ C₂×#564

Complements

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

N	H ≅ G/N	type
9. C₁₇×#564	C₄	semidirect
42. Dic₁₇	#564	direct (N × H)
43. #564	Dic₁₇	direct (N × H)
60. C₁₇	C₄×#564	semidirect

Maximal subgroups

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

subgroup	index
#14531970	2
#125×Dic₁₇	2
C₂×C₁₇×#564	2
C₄×#564	17

Subgroups — #564×Dic17 #17197046

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #564×Dic₁₇ #17197046