Subgroups — #17981459

Order 4352.

86 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14545850	C₂	1	2	yes	maximal
2	C₃₂×#595	C₂	1	1	yes	maximal, characteristic
3	#11763899	—	2	2	no	—
4	#11763740	C₄	1	1	yes	characteristic
5	C₁₆×#595	C₂²	1	1	yes	characteristic
6	C₃₂×D₁₇	C₄	1	1	yes	characteristic
7	C₄⋊#3633	—	4	2	no	—
8	C₈×#595	D₄	1	1	yes	characteristic
9	#10587529	Q₈	1	1	yes	characteristic
10	C₁₆×D₁₇	C₂×C₄	1	1	yes	characteristic
11	#10587467	—	2	1	no	—
12	C₁₇×C₃₂	C₈	1	1	yes	characteristic, complemented
13	#10587465	C₈	1	1	yes	characteristic, complemented
14	C₂×#3633	—	8	2	no	—
15	C₄×#595	D₈	1	1	yes	characteristic
16	#63242	Q₁₆	1	1	yes	characteristic
17	C₈×D₁₇	C₄⋊C₄	1	1	yes	characteristic
18	#63216	—	2	1	no	—
19	C₁₆×C₁₇	C₂×C₈	1	1	yes	characteristic
20	#63214	M₁₆	1	1	yes	characteristic
21	#7460	—	17	1	no	maximal, Sylow
22	C₂×#595	D₁₆	1	1	yes	characteristic
23	C₂×#595	Q₃₂	1	1	yes	characteristic
24	#3633	—	16	2	no	—
25	C₄×D₁₇	#107	1	1	yes	characteristic
26	#3624	—	2	1	no	—
27	C₈×C₁₇	C₄⋊C₈	1	1	yes	characteristic
28	#3622	#108	1	1	yes	characteristic
29	C₄×C₃₂	—	17	1	no	—
30	#1371	—	17	2	no	—
31	C₂×D₁₇	#366	1	1	yes	characteristic
32	#595	—	2	1	no	—
33	#595	D₃₂	1	1	yes	characteristic
34	#595	Q₆₄	1	1	yes	characteristic
35	C₄×C₁₇	#335	1	1	yes	characteristic
36	Dic₁₇	#368	1	1	yes	characteristic
37	C₂×C₃₂	—	17	1	no	—
38	C₂×C₃₂	—	17	1	no	—
39	C₄×C₁₆	—	17	1	no	—
40	#335	—	34	2	no	—
41	C₂×C₁₇	#1371	1	1	yes	characteristic
42	D₁₇	#1423	1	1	yes	characteristic
43	D₁₇	#1425	1	1	yes	characteristic
44	C₂×C₁₆	—	17	1	no	—
45	C₂×C₁₆	—	17	1	no	—
46	C₄⋊C₈	—	68	2	no	—
47	C₄×C₈	—	17	1	no	—
48	C₃₂	—	17	1	no	—
49	C₃₂	—	34	1	no	—
50	C₃₂	#3633	1	1	yes	characteristic, complemented
51	C₁₇	#7460	1	1	yes	characteristic, complemented, Sylow
52	C₂×C₈	—	17	1	no	—
53	C₂×C₈	—	17	1	no	—
54	C₂×C₈	—	136	2	no	—
55	C₄²	—	17	1	no	—
56	C₁₆	—	17	1	no	—
57	C₁₆	—	34	1	no	—
58	C₁₆	C₂×#3633	1	1	yes	characteristic
59	C₂×C₄	—	17	1	no	—
60	C₂×C₄	—	17	1	no	—
61	C₂×C₄	—	17	1	no	—
62	C₈	—	272	2	no	—
63	C₈	—	17	1	no	—
64	C₈	—	34	1	no	—
65	C₈	C₄⋊#3633	1	1	yes	characteristic
66	C₂²	—	17	1	no	—
67	C₄	—	17	1	no	—
68	C₄	—	17	1	no	—
69	C₄	—	17	1	no	—
70	C₄	—	34	1	no	—
71	C₄	#11763899	1	1	yes	characteristic
72	C₂	—	17	1	no	—
73	C₂	—	17	1	no	—
74	C₂	#14545850	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#14545850
commutator	C₁₆×C₁₇	C₂×C₈
Frattini	C₁₆	C₂×#3633
Fitting	C₁₇×C₃₂	C₈
socle	C₂×C₁₇	#1371
prime radical	C₂×D₁₇	#366
cosocle	C₁₆×#595	C₂²
hypercenter	C₃₂	#3633
hypocenter	C₁₇	#7460
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
12. C₁₇×C₃₂	C₈	semidirect
13. #10587465	C₈	semidirect
50. C₃₂	#3633	semidirect
51. C₁₇	#7460	semidirect

Maximal subgroups

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

subgroup	index
#14545850	2
C₃₂×#595	2
#7460	17