Subgroups — #14531094

Order 2176.

106 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

	subgroup	G/H
center	C₂	D₁₆×D₁₇
commutator, cosocle	C₁₆×C₁₇	C₂³
Frattini	C₁₆	C₂²×D₁₇
Fitting	C₁₇×Q₆₄	C₂
socle	C₂×C₁₇	C₂×D₁₆
hypercenter	Q₆₄	D₁₇
hypocenter	C₁₇	#2262
LCS	G ▷ C₁₆×C₁₇ ▷ C₈×C₁₇ ▷ C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ C₁₆ ◁ Q₆₄

Complements

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

N	H ≅ G/N	type
1. #11763242	C₂	semidirect
2. #11762646	C₂	semidirect
3. D₅₄₄	C₂	semidirect
4. C₃₂×D₁₇	C₂	semidirect
5. C₁₇×Q₆₄	C₂	semidirect
34. Q₆₄	D₁₇	semidirect
48. C₁₇	#2262	semidirect

Maximal subgroups

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

subgroup	index
#11763242	2
#11762646	2
D₅₄₄	2
C₃₂×D₁₇	2
C₁₇×Q₆₄	2
#2262	17