Subgroups — #17949104

Order 4352.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14543895	C₂	1	1	yes	maximal, characteristic
2	#14543895	C₂	1	1	yes	maximal, characteristic
3	#14526706	C₂	1	1	yes	maximal, characteristic
4	#11763741	C₄	1	2	yes	—
5	#11763741	C₄	1	2	yes	—
6	#11762585	C₂²	1	1	yes	characteristic
7	#11762530	C₄	1	1	yes	characteristic
8	C₁₇×#346	C₄	1	1	yes	characteristic
9	C₂×C₁₆×C₁₇	—	2	1	no	—
10	C₄×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
11	C₂×#63214	C₂×C₄	1	1	yes	characteristic
12	C₂×#63214	C₂×C₄	1	1	yes	characteristic
13	C₄×#3622	—	2	1	no	—
14	#10587467	—	2	2	no	—
15	#10587467	C₈	1	4	yes	complemented
16	C₂×C₈×C₁₇	C₄²	1	1	yes	characteristic
17	C₂×C₈×C₁₇	M₁₆	1	1	yes	characteristic
18	C₄²×C₁₇	M₁₆	1	1	yes	characteristic
19	C₂×#3622	—	4	1	no	—
20	C₁₆×C₁₇	—	4	1	no	—
21	#63214	C₂×C₈	1	2	yes	—
22	#63214	M₁₆	1	2	yes	—
23	#7333	—	17	1	no	maximal, Sylow
24	C₂×C₄×C₁₇	—	2	1	no	—
25	C₂×C₄×C₁₇	#97	1	1	yes	characteristic
26	C₈×C₁₇	—	2	1	no	—
27	C₈×C₁₇	C₄×C₈	1	1	yes	characteristic
28	C₈×C₁₇	#97	1	1	yes	characteristic
29	#3622	—	8	1	no	—
30	#1398	—	17	1	no	—
31	#1398	—	17	1	no	—
32	#1313	—	17	1	no	—
33	C₂²×C₁₇	#347	1	1	yes	characteristic
34	C₄×C₁₇	—	4	1	no	—
35	C₄×C₁₇	#322	1	1	yes	characteristic
36	C₄×C₁₇	#347	1	1	yes	characteristic
37	M₆₄	—	17	2	no	—
38	M₆₄	—	17	2	no	—
39	#346	—	17	1	no	—
40	#346	#595	1	1	yes	characteristic
41	#322	—	17	1	no	—
42	C₂×C₁₇	—	2	1	no	—
43	C₂×C₁₇	#1313	1	1	yes	characteristic
44	C₂×C₁₆	—	2	1	no	—
45	C₂×C₁₆	—	17	1	no	—
46	C₂×C₁₆	—	17	1	no	—
47	C₄×C₈	—	34	1	no	—
48	C₄×C₈	C₂×#595	1	1	yes	characteristic
49	C₃₂	—	17	4	no	—
50	C₃₂	—	34	2	no	—
51	C₁₇	#7333	1	1	yes	characteristic, complemented, Sylow
52	C₂×C₈	—	68	1	no	—
53	C₂×C₈	C₄×#595	1	1	yes	characteristic
54	C₂×C₈	#63247	1	1	yes	characteristic
55	C₄²	#63243	1	1	yes	characteristic
56	C₁₆	—	4	1	no	—
57	C₁₆	—	17	2	no	—
58	C₁₆	—	17	2	no	—
59	C₂×C₄	—	2	1	no	—
60	C₂×C₄	#10587542	1	1	yes	characteristic
61	C₈	—	2	1	no	—
62	C₈	—	136	1	no	—
63	C₈	C₈×#595	1	1	yes	characteristic
64	C₈	#10587532	1	1	yes	characteristic
65	C₂²	#11763702	1	1	yes	characteristic
66	C₄	—	4	1	no	—
67	C₄	#11763651	1	1	yes	characteristic
68	C₄	#11763701	1	1	yes	characteristic
69	C₂	—	2	1	no	—
70	C₂	#14543702	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#11763651
commutator	C₈×C₁₇	C₄×C₈
Frattini	C₄×C₈	C₂×#595
Fitting	C₁₇×#346	C₄
socle	C₂×C₁₇	#1313
prime radical	C₂²×C₁₇	#347
cosocle	#11762585	C₂²
hypercenter	#346	#595
hypocenter	C₁₇	#7333
LCS	G ▷ C₈×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₄ ◁ C₄×C₈ ◁ #346

Complements

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

N	H ≅ G/N	type
15. #10587467	C₈	semidirect
51. C₁₇	#7333	semidirect

Maximal subgroups

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

subgroup	index
#14543895	2
#14526706	2
#7333	17