Subgroups — #17981452

Order 4352.

76 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14545846	C₂	1	1	yes	maximal, characteristic
2	#14545844	C₂	1	1	yes	maximal, characteristic
3	#14543894	C₂	1	1	yes	maximal, characteristic
4	#11763913	—	2	1	no	—
5	#11763898	—	2	1	no	—
6	#11763742	C₄	1	1	yes	characteristic
7	#11763696	C₂²	1	1	yes	characteristic
8	#11762642	C₄	1	1	yes	characteristic
9	C₄⋊#3633	—	4	1	no	—
10	#10587666	—	4	1	no	—
11	C₈×#595	D₄	1	1	yes	characteristic
12	#10587529	Q₈	1	1	yes	characteristic
13	C₁₆×D₁₇	C₂×C₄	1	1	yes	characteristic
14	#10587467	—	2	1	no	—
15	C₁₇×C₃₂	C₈	1	1	yes	characteristic, complemented
16	#10587465	C₈	1	1	yes	characteristic, complemented
17	C₂×#3633	—	8	1	no	—
18	C₄×#595	SD₁₆	1	1	yes	characteristic
19	#63242	SD₁₆	1	1	yes	characteristic
20	#63241	—	8	1	no	—
21	C₈×D₁₇	C₄⋊C₄	1	1	yes	characteristic
22	#63216	—	2	1	no	—
23	C₁₆×C₁₇	C₂×C₈	1	1	yes	characteristic
24	#63214	M₁₆	1	1	yes	characteristic
25	#7457	—	17	1	no	maximal, Sylow
26	C₂×#595	—	2	1	no	—
27	#3633	—	16	1	no	—
28	C₄×D₁₇	#106	1	1	yes	characteristic
29	#3624	—	2	1	no	—
30	C₈×C₁₇	C₄⋊C₈	1	1	yes	characteristic
31	#3622	#108	1	1	yes	characteristic
32	#1398	—	17	1	no	—
33	#1369	—	17	1	no	—
34	#1368	—	17	1	no	—
35	C₂×D₁₇	#365	1	1	yes	characteristic
36	#595	—	4	1	no	—
37	C₄×C₁₇	#334	1	1	yes	characteristic
38	Dic₁₇	#365	1	1	yes	characteristic
39	M₆₄	—	17	1	no	—
40	M₆₄	—	17	1	no	—
41	#364	—	34	1	no	—
42	#346	—	17	1	no	—
43	#334	—	34	1	no	—
44	C₂×C₁₇	#1368	1	1	yes	characteristic
45	D₁₇	—	2	1	no	—
46	M₃₂	—	68	1	no	—
47	C₂×C₁₆	—	17	1	no	—
48	C₂×C₁₆	—	17	1	no	—
49	C₄⋊C₈	—	68	1	no	—
50	C₄×C₈	—	17	1	no	—
51	C₃₂	—	17	1	no	—
52	C₃₂	—	34	1	no	—
53	C₃₂	#3633	1	1	yes	characteristic, complemented
54	C₁₇	#7457	1	1	yes	characteristic, complemented, Sylow
55	C₂×C₈	—	17	1	no	—
56	C₂×C₈	—	17	1	no	—
57	C₂×C₈	—	136	1	no	—
58	C₄²	—	17	1	no	—
59	C₁₆	—	17	1	no	—
60	C₁₆	—	34	1	no	—
61	C₁₆	—	136	1	no	—
62	C₁₆	C₂×#3633	1	1	yes	characteristic
63	C₂×C₄	—	17	1	no	—
64	C₂×C₄	—	34	1	no	—
65	C₈	—	272	1	no	—
66	C₈	—	17	1	no	—
67	C₈	—	34	1	no	—
68	C₈	C₄⋊#3633	1	1	yes	characteristic
69	C₂²	—	17	1	no	—
70	C₄	—	17	1	no	—
71	C₄	—	68	1	no	—
72	C₄	#11763898	1	1	yes	characteristic
73	C₂	—	34	1	no	—
74	C₂	#14545844	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#14545844
commutator	C₁₆×C₁₇	C₂×C₈
Frattini	C₁₆	C₂×#3633
Fitting	C₁₇×C₃₂	C₈
socle	C₂×C₁₇	#1368
prime radical	C₂×D₁₇	#365
cosocle	#11763696	C₂²
hypercenter	C₃₂	#3633
hypocenter	C₁₇	#7457
LCS	G ▷ C₁₆×C₁₇ ▷ C₈×C₁₇ ▷ C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ C₁₆ ◁ C₃₂

Complements

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

N	H ≅ G/N	type
15. C₁₇×C₃₂	C₈	semidirect
16. #10587465	C₈	semidirect
53. C₃₂	#3633	semidirect
54. C₁₇	#7457	semidirect

Maximal subgroups

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

subgroup	index
#14545846	2
#14545844	2
#14543894	2
#7457	17