Subgroups — #17949552

Order 4352.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14543953	C₂	1	2	yes	maximal, complemented
2	C₂×#11762643	C₂	1	1	yes	maximal, characteristic
3	#11763648	—	2	2	no	—
4	#11762643	—	2	2	no	—
5	C₂×#10587465	C₄	1	1	yes	characteristic
6	C₂×#10587465	C₂²	1	1	yes	characteristic
7	C₂²×C₁₆×C₁₇	C₄	1	1	yes	characteristic
8	C₂²×C₈×C₁₇	C₈	1	1	yes	characteristic
9	C₂×C₁₆×C₁₇	—	2	1	no	—
10	C₂×C₁₆×C₁₇	—	2	1	no	—
11	C₂×C₁₆×C₁₇	C₈	1	1	yes	characteristic
12	C₂×C₁₆×C₁₇	C₂×C₄	1	1	yes	characteristic
13	#10587465	—	2	1	no	—
14	#10587465	D₄	1	2	yes	—
15	C₂²×C₄×C₁₇	C₁₆	1	1	yes	characteristic
16	C₂×C₈×C₁₇	—	2	1	no	—
17	C₂×C₈×C₁₇	—	2	1	no	—
18	C₂×C₈×C₁₇	C₁₆	1	1	yes	characteristic
19	C₂×C₈×C₁₇	C₂×C₈	1	1	yes	characteristic
20	C₁₆×C₁₇	—	2	1	no	—
21	C₁₆×C₁₇	C₂²⋊C₄	1	1	yes	characteristic
22	C₁₆×C₁₇	M₁₆	1	1	yes	characteristic
23	#7513	—	17	1	no	maximal, Sylow
24	C₂³×C₁₇	C₃₂	1	1	yes	characteristic
25	C₂×C₄×C₁₇	—	2	1	no	—
26	C₂×C₄×C₁₇	—	2	1	no	—
27	C₂×C₄×C₁₇	C₃₂	1	1	yes	characteristic
28	C₂×C₄×C₁₇	C₂×C₁₆	1	1	yes	characteristic
29	C₈×C₁₇	—	2	1	no	—
30	C₈×C₁₇	C₂²⋊C₈	1	1	yes	characteristic
31	C₈×C₁₇	M₃₂	1	1	yes	characteristic
32	C₂×M₆₄	—	17	1	no	—
33	M₁₂₈	—	17	2	no	—
34	C₂²×C₁₇	—	2	1	no	—
35	C₂²×C₁₇	—	4	1	no	—
36	C₂²×C₁₇	C₂×C₃₂	1	1	yes	characteristic
37	C₄×C₁₇	—	2	1	no	—
38	C₄×C₁₇	C₂²⋊C₁₆	1	1	yes	characteristic
39	C₄×C₁₇	M₆₄	1	1	yes	characteristic
40	C₂²×C₁₆	#595	1	1	yes	characteristic
41	M₆₄	—	34	2	no	—
42	C₂×C₃₂	—	17	1	no	—
43	C₂×C₃₂	—	17	1	no	—
44	C₆₄	—	34	2	no	—
45	C₂×C₁₇	—	2	1	no	—
46	C₂×C₁₇	—	4	1	no	—
47	C₂×C₁₇	C₂²⋊C₃₂	1	1	yes	characteristic
48	C₂²×C₈	#3624	1	1	yes	characteristic
49	C₂×C₁₆	—	2	1	no	—
50	C₂×C₁₆	—	2	1	no	—
51	C₂×C₁₆	#3624	1	1	yes	characteristic
52	C₂×C₁₆	C₂×#595	1	1	yes	characteristic
53	C₃₂	—	17	2	no	—
54	C₃₂	—	34	1	no	—
55	C₁₇	#7513	1	1	yes	characteristic, complemented, Sylow
56	C₂²×C₄	#63216	1	1	yes	characteristic
57	C₂×C₈	—	2	1	no	—
58	C₂×C₈	—	2	1	no	—
59	C₂×C₈	#63216	1	1	yes	characteristic
60	C₂×C₈	C₂×#3624	1	1	yes	characteristic
61	C₁₆	—	2	1	no	—
62	C₁₆	#63247	1	1	yes	characteristic
63	C₁₆	C₂²⋊#595	1	1	yes	characteristic
64	C₂³	#10587467	1	1	yes	characteristic
65	C₂×C₄	—	2	1	no	—
66	C₂×C₄	—	2	1	no	—
67	C₂×C₄	#10587467	1	1	yes	characteristic
68	C₂×C₄	C₂×#63216	1	1	yes	characteristic
69	C₈	—	2	1	no	—
70	C₈	#10587538	1	1	yes	characteristic
71	C₈	C₂²⋊#3624	1	1	yes	characteristic
72	C₂²	—	2	1	no	—
73	C₂²	—	4	1	no	—
74	C₂²	C₂×#10587467	1	1	yes	characteristic
75	C₄	—	2	1	no	—
76	C₄	C₂²⋊#63216	1	1	yes	characteristic
77	C₄	#11763741	1	1	yes	characteristic
78	C₂	—	2	1	no	—
79	C₂	—	4	1	no	—
80	C₂	C₂²⋊#10587467	1	1	yes	characteristic

	subgroup	G/H
center	C₁₆	C₂²⋊#595
commutator	C₂²×C₁₇	C₂×C₃₂
Frattini	C₂×C₁₆	C₂×#595
Fitting	C₂²×C₁₆×C₁₇	C₄
socle	C₂×C₁₇	C₂²⋊C₃₂
prime radical	C₂³×C₁₇	C₃₂
cosocle	C₂×#10587465	C₂²
hypercenter	C₂²×C₁₆	#595
hypocenter	C₁₇	#7513
LCS	G ▷ C₂²×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₁₆ ◁ C₂×C₁₆ ◁ C₂²×C₁₆

Complements

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

N	H ≅ G/N	type
1. #14543953	C₂	semidirect
55. C₁₇	#7513	semidirect

Maximal subgroups

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

subgroup	index
#14543953	2
C₂×#11762643	2
#7513	17