Subgroups — #16955348

Order 4352.

146 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14531063	C₂	1	2	yes	maximal
2	#14526986	C₂	1	2	yes	maximal
3	#14526984	C₂	1	2	yes	maximal
4	C₄×C₁₇×C₃₂	C₂	1	1	yes	maximal, characteristic
5	#11763211	—	2	2	no	—
6	#11762637	—	2	2	no	—
7	#11762635	C₂²	1	4	yes	—
8	C₂×C₁₇×C₃₂	C₂²	1	1	yes	characteristic
9	C₂×C₁₇×C₃₂	C₂²	1	1	yes	characteristic
10	C₄×C₁₆×C₁₇	C₂²	1	1	yes	characteristic
11	#10587556	—	4	2	no	—
12	C₂×C₁₆×C₁₇	D₄	1	1	yes	characteristic
13	C₂×C₁₆×C₁₇	C₂³	1	1	yes	characteristic
14	C₄×C₈×C₁₇	D₄	1	1	yes	characteristic
15	#10587489	—	2	4	no	—
16	#10587488	—	4	2	no	—
17	C₁₇×C₃₂	Q₈	1	2	yes	—
18	C₁₇×C₃₂	Q₈	1	2	yes	—
19	C₂×C₈×C₁₇	D₈	1	1	yes	characteristic
20	C₂×C₈×C₁₇	C₂×D₄	1	1	yes	characteristic
21	C₄²×C₁₇	D₈	1	1	yes	characteristic
22	C₄⋊Dic₁₇	—	4	4	no	—
23	#63225	—	8	4	no	—
24	C₁₆×C₁₇	Q₁₆	1	2	yes	—
25	C₁₆×C₁₇	C₂×Q₈	1	1	yes	characteristic
26	C₁₆×C₁₇	C₂×Q₈	1	1	yes	characteristic
27	#13732	—	17	1	no	maximal, Sylow
28	C₂×C₄×C₁₇	D₁₆	1	2	yes	—
29	C₂×C₄×C₁₇	C₂×D₈	1	1	yes	characteristic
30	C₂×Dic₁₇	—	8	4	no	—
31	C₈×C₁₇	Q₃₂	1	2	yes	—
32	C₈×C₁₇	C₄⋊Q₈	1	1	yes	characteristic
33	C₈×C₁₇	C₂×Q₁₆	1	1	yes	characteristic
34	#2253	—	17	2	no	—
35	#1424	—	17	2	no	—
36	#1423	—	17	2	no	—
37	C₄×C₃₂	D₁₇	1	1	yes	characteristic
38	C₂²×C₁₇	C₂×D₁₆	1	1	yes	characteristic
39	C₄×C₁₇	—	2	2	no	—
40	C₄×C₁₇	#500	1	1	yes	characteristic
41	C₄×C₁₇	C₂×Q₃₂	1	1	yes	characteristic
42	Dic₁₇	—	16	4	no	—
43	#499	—	34	2	no	—
44	C₂×C₃₂	C₂×D₁₇	1	1	yes	characteristic
45	C₂×C₃₂	C₂×D₁₇	1	1	yes	characteristic
46	#367	—	34	2	no	—
47	#366	—	17	4	no	—
48	C₄×C₁₆	C₂×D₁₇	1	1	yes	characteristic
49	C₂×C₁₇	#2252	1	1	yes	characteristic
50	C₂×C₁₇	#2262	1	2	yes	—
51	#125	—	68	2	no	—
52	C₂×C₁₆	D₆₈	1	1	yes	characteristic
53	C₂×C₁₆	C₂²×D₁₇	1	1	yes	characteristic
54	#107	—	34	4	no	—
55	#106	—	68	2	no	—
56	C₄×C₈	D₆₈	1	1	yes	characteristic
57	C₃₂	Dic₃₄	1	2	yes	—
58	C₃₂	Dic₃₄	1	2	yes	—
59	C₁₇	#13732	1	1	yes	characteristic, complemented, Sylow
60	C₂×C₈	D₁₃₆	1	1	yes	characteristic
61	C₂×C₈	C₂×D₆₈	1	1	yes	characteristic
62	C₄⋊C₄	—	68	4	no	—
63	C₄⋊C₄	—	136	4	no	—
64	C₄²	D₁₃₆	1	1	yes	characteristic
65	C₁₆	Dic₆₈	1	2	yes	—
66	C₁₆	C₂×Dic₃₄	1	1	yes	characteristic
67	C₁₆	C₂×Dic₃₄	1	1	yes	characteristic
68	C₂×C₄	—	136	4	no	—
69	C₂×C₄	D₂₇₂	1	2	yes	—
70	C₂×C₄	C₂×D₁₃₆	1	1	yes	characteristic
71	C₈	Dic₁₃₆	1	2	yes	—
72	C₈	#10587555	1	1	yes	characteristic
73	C₈	C₂×Dic₆₈	1	1	yes	characteristic
74	C₂²	C₂×D₂₇₂	1	1	yes	characteristic
75	C₄	—	2	2	no	—
76	C₄	—	272	4	no	—
77	C₄	#11763214	1	1	yes	characteristic
78	C₄	C₂×Dic₁₃₆	1	1	yes	characteristic
79	C₂	#14531059	1	1	yes	characteristic
80	C₂	#14531093	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂×D₂₇₂
commutator, cosocle	C₂×C₁₆×C₁₇	C₂³
Frattini	C₂×C₁₆	C₂²×D₁₇
Fitting	C₄×C₁₇×C₃₂	C₂
socle, prime radical	C₂²×C₁₇	C₂×D₁₆
hypercenter	C₄×C₃₂	D₁₇
hypocenter	C₁₇	#13732
LCS	G ▷ C₂×C₁₆×C₁₇ ▷ C₈×C₁₇ ▷ C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ C₄×C₁₆ ◁ C₄×C₃₂

Complements

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

N	H ≅ G/N	type
59. C₁₇	#13732	semidirect

Maximal subgroups

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

subgroup	index
#14531063	2
#14526986	2
#14526984	2
C₄×C₁₇×C₃₂	2
#13732	17