Subgroups — #16955379

Order 4352.

128 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14531094	C₂	1	2	yes	maximal, complemented
2	#14526998	C₂	1	2	yes	maximal, complemented
3	D₁₀₈₈	C₂	1	1	yes	maximal, characteristic, complemented
4	D₁₇×C₆₄	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₇×Q₁₂₈	C₂	1	1	yes	maximal, characteristic, complemented
6	#11763242	—	2	2	no	—
7	#11762646	—	2	2	no	—
8	D₅₄₄	C₂²	1	2	yes	—
9	C₃₂×D₁₇	C₂²	1	1	yes	characteristic
10	#11762528	C₂²	1	1	yes	characteristic
11	C₁₇×Q₆₄	C₂²	1	2	yes	—
12	C₁₇×C₆₄	C₂²	1	1	yes	characteristic
13	#10587605	—	4	2	no	—
14	C₁₇×Q₃₂	—	2	2	no	—
15	#10587499	—	4	2	no	—
16	D₂₇₂	—	2	2	no	—
17	C₁₆×D₁₇	D₄	1	1	yes	characteristic
18	C₁₇×C₃₂	C₂³	1	1	yes	characteristic
19	#10587465	D₄	1	1	yes	characteristic
20	#63256	—	8	2	no	—
21	Q₁₆×C₁₇	—	4	2	no	—
22	#63230	—	8	2	no	—
23	D₁₃₆	—	4	2	no	—
24	C₈×D₁₇	D₈	1	1	yes	characteristic
25	C₁₆×C₁₇	C₂×D₄	1	1	yes	characteristic
26	#63214	D₈	1	1	yes	characteristic
27	#13741	—	17	1	no	maximal, Sylow
28	Q₈×C₁₇	—	8	2	no	—
29	D₆₈	—	8	2	no	—
30	D₆₈	—	16	2	no	—
31	C₄×D₁₇	—	16	2	no	—
32	C₄×D₁₇	D₁₆	1	1	yes	characteristic
33	C₈×C₁₇	C₂×D₈	1	1	yes	characteristic
34	#3622	D₁₆	1	1	yes	characteristic
35	#2262	—	17	2	no	—
36	Q₁₂₈	D₁₇	1	1	yes	characteristic, complemented
37	SD₁₂₈	—	17	2	no	—
38	D₆₄	—	17	1	no	—
39	C₂×C₆₄	—	17	1	no	—
40	C₂×D₁₇	—	16	2	no	—
41	C₂×D₁₇	D₃₂	1	1	yes	characteristic
42	C₄×C₁₇	—	16	2	no	—
43	C₄×C₁₇	C₂×D₁₆	1	1	yes	characteristic
44	Dic₁₇	D₃₂	1	1	yes	characteristic
45	#508	—	34	2	no	—
46	Q₆₄	C₂×D₁₇	1	2	yes	—
47	SD₆₄	—	34	2	no	—
48	D₃₂	—	17	2	no	—
49	C₂×C₃₂	—	17	1	no	—
50	C₆₄	—	17	1	no	—
51	C₆₄	C₂×D₁₇	1	1	yes	characteristic
52	C₂×C₁₇	C₂×D₃₂	1	1	yes	characteristic
53	D₁₇	—	2	1	no	—
54	D₁₇	—	32	2	no	—
55	#135	—	68	2	no	—
56	Q₃₂	—	2	2	no	—
57	SD₃₂	—	68	2	no	—
58	D₁₆	—	34	2	no	—
59	C₂×C₁₆	—	17	1	no	—
60	C₃₂	—	17	1	no	—
61	C₃₂	C₂²×D₁₇	1	1	yes	characteristic
62	C₁₇	#13741	1	1	yes	characteristic, complemented, Sylow
63	#41	—	136	2	no	—
64	Q₁₆	—	4	2	no	—
65	SD₁₆	—	136	2	no	—
66	D₈	—	68	2	no	—
67	C₂×C₈	—	17	1	no	—
68	C₁₆	—	17	1	no	—
69	C₁₆	D₄×D₁₇	1	1	yes	characteristic
70	Q₈	—	8	2	no	—
71	D₄	—	272	2	no	—
72	D₄	—	136	2	no	—
73	C₂×C₄	—	272	2	no	—
74	C₂×C₄	—	17	1	no	—
75	C₈	—	17	1	no	—
76	C₈	D₈×D₁₇	1	1	yes	characteristic
77	C₂²	—	272	2	no	—
78	C₂²	—	17	1	no	—
79	C₄	—	16	2	no	—
80	C₄	—	17	1	no	—
81	C₄	D₁₆×D₁₇	1	1	yes	characteristic
82	C₂	—	544	2	no	—
83	C₂	—	34	1	no	—
84	C₂	D₁₇×D₃₂	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₁₇×D₃₂
commutator, cosocle	C₁₇×C₃₂	C₂³
Frattini	C₃₂	C₂²×D₁₇
Fitting	C₁₇×Q₁₂₈	C₂
socle	C₂×C₁₇	C₂×D₃₂
hypercenter	Q₁₂₈	D₁₇
hypocenter	C₁₇	#13741
LCS	G ▷ C₁₇×C₃₂ ▷ C₁₆×C₁₇ ▷ C₈×C₁₇ ▷ C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ C₁₆ ◁ C₃₂ ◁ Q₁₂₈

Complements

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

N	H ≅ G/N	type
1. #14531094	C₂	semidirect
2. #14526998	C₂	semidirect
3. D₁₀₈₈	C₂	semidirect
4. D₁₇×C₆₄	C₂	semidirect
5. C₁₇×Q₁₂₈	C₂	semidirect
36. Q₁₂₈	D₁₇	semidirect
62. C₁₇	#13741	semidirect

Maximal subgroups

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

subgroup	index
#14531094	2
#14526998	2
D₁₀₈₈	2
D₁₇×C₆₄	2
C₁₇×Q₁₂₈	2
#13741	17