Subgroups — #16921983

Order 4352.

102 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14531066	C₂	1	1	yes	maximal, characteristic
2	#14526860	C₂	1	1	yes	maximal, characteristic
3	C₁₇×#1422	C₂	1	1	yes	maximal, characteristic
4	#11763214	—	2	1	no	—
5	#11762637	—	2	1	no	—
6	#11762637	C₄	1	2	yes	—
7	#11762630	—	2	1	no	—
8	C₁₇×M₆₄	—	2	1	no	—
9	C₄×C₁₆×C₁₇	C₂²	1	1	yes	characteristic
10	#10587555	—	4	1	no	—
11	C₂×C₁₆×C₁₇	C₂×C₄	1	1	yes	characteristic
12	C₂×C₁₆×C₁₇	D₄	1	1	yes	characteristic
13	C₄×C₈×C₁₇	D₄	1	1	yes	characteristic
14	#10587489	—	2	2	no	—
15	#10587489	—	4	1	no	—
16	#10587483	—	4	1	no	—
17	C₁₇×C₃₂	—	4	1	no	—
18	C₂×Dic₃₄	—	8	1	no	—
19	C₂×C₈×C₁₇	C₂²⋊C₄	1	1	yes	characteristic
20	C₂×C₈×C₁₇	D₈	1	1	yes	characteristic
21	C₄²×C₁₇	SD₁₆	1	1	yes	characteristic
22	C₄⋊Dic₁₇	—	4	2	no	—
23	C₄⋊Dic₁₇	—	8	1	no	—
24	C₁₆×C₁₇	—	2	1	no	—
25	C₁₆×C₁₇	SD₁₆	1	1	yes	characteristic
26	C₁₆×C₁₇	Q₁₆	1	1	yes	characteristic
27	#63214	—	8	1	no	—
28	#7453	—	17	1	no	maximal, Sylow
29	C₂×C₄×C₁₇	—	2	1	no	—
30	C₂×C₄×C₁₇	#102	1	1	yes	characteristic
31	C₂×Dic₁₇	—	8	2	no	—
32	Dic₃₄	—	16	2	no	—
33	C₈×C₁₇	#101	1	1	yes	characteristic
34	C₈×C₁₇	#103	1	1	yes	characteristic
35	C₈×C₁₇	SD₃₂	1	1	yes	characteristic
36	C₈×C₁₇	Q₃₂	1	1	yes	characteristic
37	#2254	—	17	1	no	—
38	#1422	D₁₇	1	1	yes	characteristic
39	#1373	—	17	1	no	—
40	C₂²×C₁₇	#361	1	1	yes	characteristic
41	C₄×C₁₇	—	2	2	no	—
42	C₄×C₁₇	#332	1	1	yes	characteristic
43	C₄×C₁₇	#358	1	1	yes	characteristic
44	Dic₁₇	—	16	2	no	—
45	#500	—	34	1	no	—
46	M₆₄	—	2	1	no	—
47	#367	—	17	2	no	—
48	#367	—	34	1	no	—
49	#364	—	34	1	no	—
50	C₄×C₁₆	C₂×D₁₇	1	1	yes	characteristic
51	C₂×C₁₇	—	2	1	no	—
52	C₂×C₁₇	#1365	1	1	yes	characteristic
53	C₄⋊Q₈	—	68	1	no	—
54	M₃₂	—	68	1	no	—
55	C₂×C₁₆	C₄×D₁₇	1	1	yes	characteristic
56	C₂×C₁₆	C₂²⋊D₁₇	1	1	yes	characteristic
57	#107	—	34	2	no	—
58	#107	—	68	1	no	—
59	C₄×C₈	D₆₈	1	1	yes	characteristic
60	C₃₂	—	4	1	no	—
61	C₁₇	#7453	1	1	yes	characteristic, complemented, Sylow
62	C₂×Q₈	—	136	1	no	—
63	C₂×C₈	D₁₃₆	1	1	yes	characteristic
64	C₂×C₈	#63227	1	1	yes	characteristic
65	C₄⋊C₄	—	68	2	no	—
66	C₄⋊C₄	—	136	1	no	—
67	C₄²	#63219	1	1	yes	characteristic
68	C₁₆	—	2	1	no	—
69	C₁₆	—	136	1	no	—
70	C₁₆	#63229	1	1	yes	characteristic
71	C₁₆	#63231	1	1	yes	characteristic
72	Q₈	—	272	2	no	—
73	C₂×C₄	—	2	1	no	—
74	C₂×C₄	—	136	2	no	—
75	C₂×C₄	#10587492	1	1	yes	characteristic
76	C₈	#10587471	1	1	yes	characteristic
77	C₈	Dic₁₃₆	1	1	yes	characteristic
78	C₈	#10587481	1	1	yes	characteristic
79	C₈	#10587495	1	1	yes	characteristic
80	C₂²	#11762623	1	1	yes	characteristic
81	C₄	—	2	2	no	—
82	C₄	—	272	2	no	—
83	C₄	#11762554	1	1	yes	characteristic
84	C₄	#11762614	1	1	yes	characteristic
85	C₂	—	2	1	no	—
86	C₂	#14526841	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#14526841
commutator	C₂×C₁₆×C₁₇	C₂×C₄
Frattini	C₄×C₁₆	C₂×D₁₇
Fitting	C₁₇×#1422	C₂
socle	C₂×C₁₇	#1365
prime radical	C₂²×C₁₇	#361
cosocle	C₄×C₁₆×C₁₇	C₂²
hypercenter	#1422	D₁₇
hypocenter	C₁₇	#7453
LCS	G ▷ C₂×C₁₆×C₁₇ ▷ C₂×C₈×C₁₇ ▷ C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₄×C₈ ◁ C₄×C₁₆ ◁ #1422

Complements

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

N	H ≅ G/N	type
61. C₁₇	#7453	semidirect

Maximal subgroups

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

subgroup	index
#14531066	2
#14526860	2
C₁₇×#1422	2
#7453	17