Subgroups — #16949065

Order 4352.

238 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14531066	C₂	1	2	yes	maximal
2	#14531059	C₂	1	2	yes	maximal
3	#14528394	C₂	1	2	yes	maximal
4	C₈×C₁₆×C₁₇	C₂	1	1	yes	maximal, characteristic
5	#11763214	C₂²	1	4	yes	—
6	#11763160	—	2	4	no	—
7	#11762637	—	2	4	no	—
8	#11762635	—	2	4	no	—
9	C₄×C₁₆×C₁₇	C₂²	1	1	yes	characteristic
10	C₄×C₁₆×C₁₇	C₂²	1	1	yes	characteristic
11	C₈²×C₁₇	C₂²	1	1	yes	characteristic
12	#10587555	—	2	4	no	—
13	C₂×C₁₆×C₁₇	D₄	1	2	yes	—
14	C₂×C₁₆×C₁₇	D₄	1	2	yes	—
15	C₄×C₈×C₁₇	D₄	1	2	yes	—
16	C₄×C₈×C₁₇	C₂³	1	1	yes	characteristic
17	#10587489	—	2	4	no	—
18	#10587489	—	2	4	no	—
19	#10587487	—	4	8	no	—
20	C₂×Dic₃₄	—	4	4	no	—
21	C₂×C₈×C₁₇	D₈	1	4	yes	—
22	C₂×C₈×C₁₇	C₂×D₄	1	1	yes	characteristic
23	C₂×C₈×C₁₇	C₂×D₄	1	1	yes	characteristic
24	C₄²×C₁₇	C₂×D₄	1	1	yes	characteristic
25	C₄⋊Dic₁₇	—	4	4	no	—
26	C₄⋊Dic₁₇	—	4	4	no	—
27	C₁₆×C₁₇	Q₁₆	1	4	yes	—
28	C₁₆×C₁₇	Q₁₆	1	4	yes	—
29	#12522	—	17	1	no	maximal, Sylow
30	C₂×C₄×C₁₇	#127	1	1	yes	characteristic
31	C₂×C₄×C₁₇	C₂×D₈	1	2	yes	—
32	C₂×Dic₁₇	—	8	4	no	—
33	Dic₃₄	—	8	8	no	—
34	C₈×C₁₇	—	2	4	no	—
35	C₈×C₁₇	C₂×Q₁₆	1	2	yes	—
36	C₈×C₁₇	C₂×Q₁₆	1	2	yes	—
37	#2254	—	17	2	no	—
38	#2252	—	17	2	no	—
39	#1710	—	17	2	no	—
40	C₈×C₁₆	D₁₇	1	1	yes	characteristic
41	C₂²×C₁₇	#493	1	1	yes	characteristic
42	C₄×C₁₇	#494	1	1	yes	characteristic
43	C₄×C₁₇	#494	1	1	yes	characteristic
44	C₄×C₁₇	#508	1	4	yes	—
45	Dic₁₇	—	16	4	no	—
46	#500	—	17	4	no	—
47	#487	—	34	4	no	—
48	#367	—	34	4	no	—
49	#366	—	34	4	no	—
50	C₄×C₁₆	C₂×D₁₇	1	1	yes	characteristic
51	C₄×C₁₆	C₂×D₁₇	1	1	yes	characteristic
52	C₈²	C₂×D₁₇	1	1	yes	characteristic
53	C₂×C₁₇	#1713	1	1	yes	characteristic
54	C₂×C₁₇	#2249	1	2	yes	—
55	C₄⋊Q₈	—	34	4	no	—
56	C₂×C₁₆	D₆₈	1	2	yes	—
57	C₂×C₁₆	D₆₈	1	2	yes	—
58	#107	—	34	4	no	—
59	#107	—	34	4	no	—
60	#103	—	68	8	no	—
61	C₄×C₈	D₆₈	1	2	yes	—
62	C₄×C₈	C₂²×D₁₇	1	1	yes	characteristic
63	C₁₇	#12522	1	1	yes	characteristic, complemented, Sylow
64	C₂×Q₈	—	68	4	no	—
65	C₂×C₈	D₁₃₆	1	4	yes	—
66	C₂×C₈	C₂×D₆₈	1	1	yes	characteristic
67	C₂×C₈	C₂×D₆₈	1	1	yes	characteristic
68	C₄⋊C₄	—	68	4	no	—
69	C₄⋊C₄	—	68	4	no	—
70	C₄²	C₂×D₆₈	1	1	yes	characteristic
71	C₁₆	Dic₆₈	1	4	yes	—
72	C₁₆	Dic₆₈	1	4	yes	—
73	Q₈	—	136	8	no	—
74	C₂×C₄	—	136	4	no	—
75	C₂×C₄	#10587560	1	1	yes	characteristic
76	C₂×C₄	C₂×D₁₃₆	1	2	yes	—
77	C₈	—	2	4	no	—
78	C₈	C₂×Dic₆₈	1	2	yes	—
79	C₈	C₂×Dic₆₈	1	2	yes	—
80	C₂²	#11763186	1	1	yes	characteristic
81	C₄	—	272	4	no	—
82	C₄	#11763189	1	1	yes	characteristic
83	C₄	#11763189	1	1	yes	characteristic
84	C₄	#11763241	1	4	yes	—
85	C₂	#14528402	1	1	yes	characteristic
86	C₂	#14531045	1	2	yes	—

	subgroup	G/H
center	C₂²	#11763186
commutator, cosocle	C₄×C₈×C₁₇	C₂³
Frattini	C₄×C₈	C₂²×D₁₇
Fitting	C₈×C₁₆×C₁₇	C₂
socle, prime radical	C₂²×C₁₇	#493
hypercenter	C₈×C₁₆	D₁₇
hypocenter	C₁₇	#12522
LCS	G ▷ C₄×C₈×C₁₇ ▷ C₂×C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₈² ◁ C₈×C₁₆

Complements

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

N	H ≅ G/N	type
63. C₁₇	#12522	semidirect

Maximal subgroups

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

subgroup	index
#14531066	2
#14531059	2
#14528394	2
C₈×C₁₆×C₁₇	2
#12522	17