Subgroups — #17949374

Order 4352.

76 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14543811	C₂	1	1	yes	maximal, characteristic
2	#14543809	C₂	1	1	yes	maximal, characteristic
3	#14526919	C₂	1	1	yes	maximal, characteristic
4	#11763731	—	2	1	no	—
5	#11763670	—	2	1	no	—
6	#11762643	C₄	1	1	yes	characteristic
7	#11762584	C₂²	1	1	yes	characteristic
8	C₁₇×M₆₄	C₄	1	1	yes	characteristic
9	C₄⋊#3624	—	4	1	no	—
10	#10587538	—	4	1	no	—
11	C₂×C₁₆×C₁₇	C₂×C₄	1	1	yes	characteristic
12	C₈×Dic₁₇	D₄	1	1	yes	characteristic
13	C₂×#63214	Q₈	1	1	yes	characteristic
14	C₁₇×C₃₂	—	2	1	no	—
15	#10587465	C₈	1	2	yes	complemented
16	C₂×#3624	—	8	1	no	—
17	C₂×C₈×C₁₇	C₄⋊C₄	1	1	yes	characteristic
18	C₄×Dic₁₇	SD₁₆	1	1	yes	characteristic
19	C₂×#3622	SD₁₆	1	1	yes	characteristic
20	#63216	—	8	1	no	—
21	C₁₆×C₁₇	C₂×C₈	1	1	yes	characteristic
22	C₁₆×C₁₇	M₁₆	1	1	yes	characteristic
23	#63214	—	2	1	no	—
24	#7457	—	17	1	no	maximal, Sylow
25	C₂×C₄×C₁₇	#106	1	1	yes	characteristic
26	C₂×Dic₁₇	—	2	1	no	—
27	#3624	—	16	1	no	—
28	C₈×C₁₇	C₄⋊C₈	1	1	yes	characteristic
29	C₈×C₁₇	#108	1	1	yes	characteristic
30	#3622	—	2	1	no	—
31	#1398	—	17	1	no	—
32	#1369	—	17	1	no	—
33	#1368	—	17	1	no	—
34	C₂²×C₁₇	#365	1	1	yes	characteristic
35	C₄×C₁₇	#334	1	1	yes	characteristic
36	C₄×C₁₇	#365	1	1	yes	characteristic
37	Dic₁₇	—	4	1	no	—
38	M₆₄	—	17	1	no	—
39	M₆₄	#595	1	1	yes	characteristic
40	#364	—	34	1	no	—
41	#346	—	17	1	no	—
42	#334	—	34	1	no	—
43	C₂×C₁₇	—	2	1	no	—
44	C₂×C₁₇	#1368	1	1	yes	characteristic
45	M₃₂	—	68	1	no	—
46	C₂×C₁₆	—	17	1	no	—
47	C₂×C₁₆	C₂×#595	1	1	yes	characteristic
48	C₄⋊C₈	—	68	1	no	—
49	C₄×C₈	—	17	1	no	—
50	C₃₂	—	2	1	no	—
51	C₃₂	—	17	2	no	—
52	C₁₇	#7457	1	1	yes	characteristic, complemented, Sylow
53	C₂×C₈	—	17	1	no	—
54	C₂×C₈	—	136	1	no	—
55	C₂×C₈	C₄⋊#595	1	1	yes	characteristic
56	C₄²	—	17	1	no	—
57	C₁₆	—	34	1	no	—
58	C₁₆	—	136	1	no	—
59	C₁₆	#63242	1	1	yes	characteristic
60	C₁₆	#63247	1	1	yes	characteristic
61	C₂×C₄	—	34	1	no	—
62	C₂×C₄	#10587533	1	1	yes	characteristic
63	C₈	—	272	1	no	—
64	C₈	—	34	1	no	—
65	C₈	#10587536	1	1	yes	characteristic
66	C₈	#10587544	1	1	yes	characteristic
67	C₂²	#11763733	1	1	yes	characteristic
68	C₄	—	68	1	no	—
69	C₄	#11763671	1	1	yes	characteristic
70	C₄	#11763734	1	1	yes	characteristic
71	C₂	—	2	1	no	—
72	C₂	#14543810	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#14543810
commutator	C₁₆×C₁₇	C₂×C₈
Frattini	C₂×C₁₆	C₂×#595
Fitting	C₁₇×M₆₄	C₄
socle	C₂×C₁₇	#1368
prime radical	C₂²×C₁₇	#365
cosocle	#11762584	C₂²
hypercenter	M₆₄	#595
hypocenter	C₁₇	#7457
LCS	G ▷ C₁₆×C₁₇ ▷ C₈×C₁₇ ▷ C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ M₆₄

Complements

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

N	H ≅ G/N	type
15. #10587465	C₈	semidirect
52. C₁₇	#7457	semidirect

Maximal subgroups

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

subgroup	index
#14543811	2
#14543809	2
#14526919	2
#7457	17