Subgroups — #17949554

Order 4352.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14543953	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#11763648	C₂	1	1	yes	maximal, characteristic, complemented
3	#14531078	C₂	1	1	yes	maximal, characteristic
4	#11763648	—	2	1	no	—
5	#11763648	—	2	1	no	—
6	#11762643	—	2	1	no	—
7	#11762643	C₄	1	1	yes	characteristic
8	C₂×#10587465	—	2	1	no	—
9	C₂×#10587465	C₂²	1	1	yes	characteristic
10	C₁₇×#504	C₄	1	1	yes	characteristic
11	C₁₇×#131	C₈	1	1	yes	characteristic
12	C₁₇×M₃₂	—	2	1	no	—
13	C₁₇×M₃₂	C₈	1	1	yes	characteristic
14	C₂×C₁₆×C₁₇	—	2	1	no	—
15	C₂×C₁₆×C₁₇	C₂×C₄	1	1	yes	characteristic
16	#10587465	—	2	1	no	—
17	#10587465	D₄	1	1	yes	characteristic
18	#10587465	D₄	1	1	yes	characteristic
19	#41×C₁₇	C₁₆	1	1	yes	characteristic
20	M₁₆×C₁₇	—	2	1	no	—
21	M₁₆×C₁₇	C₁₆	1	1	yes	characteristic
22	C₂×C₈×C₁₇	—	2	1	no	—
23	C₂×C₈×C₁₇	C₂×C₈	1	1	yes	characteristic
24	C₁₆×C₁₇	—	2	1	no	—
25	C₁₆×C₁₇	C₂²⋊C₄	1	1	yes	characteristic
26	C₁₆×C₁₇	M₁₆	1	1	yes	characteristic
27	#7514	—	17	1	no	maximal, Sylow
28	Q₈×C₁₇	C₃₂	1	1	yes	characteristic
29	D₄×C₁₇	—	2	1	no	—
30	D₄×C₁₇	C₃₂	1	1	yes	characteristic
31	C₂×C₄×C₁₇	—	2	1	no	—
32	C₂×C₄×C₁₇	C₂×C₁₆	1	1	yes	characteristic
33	C₈×C₁₇	—	2	1	no	—
34	C₈×C₁₇	C₂²⋊C₈	1	1	yes	characteristic
35	C₈×C₁₇	M₃₂	1	1	yes	characteristic
36	#2258	—	17	1	no	—
37	M₁₂₈	—	17	1	no	—
38	C₂×C₆₄	—	17	1	no	—
39	C₂²×C₁₇	—	2	1	no	—
40	C₂²×C₁₇	M₆₄	1	1	yes	characteristic
41	C₄×C₁₇	—	2	1	no	—
42	C₄×C₁₇	C₂²⋊C₁₆	1	1	yes	characteristic
43	C₄×C₁₇	C₂×C₃₂	1	1	yes	characteristic
44	#504	#595	1	1	yes	characteristic
45	M₆₄	—	17	1	no	—
46	M₆₄	—	34	1	no	—
47	C₂×C₃₂	—	17	1	no	—
48	C₂×C₃₂	—	34	1	no	—
49	C₆₄	—	34	1	no	—
50	C₆₄	—	34	1	no	—
51	C₂×C₁₇	—	2	1	no	—
52	C₂×C₁₇	—	4	1	no	—
53	C₂×C₁₇	C₂²⋊C₃₂	1	1	yes	characteristic
54	#131	#3624	1	1	yes	characteristic
55	M₃₂	—	2	1	no	—
56	M₃₂	#3624	1	1	yes	characteristic
57	C₂×C₁₆	—	2	1	no	—
58	C₂×C₁₆	C₂×#595	1	1	yes	characteristic
59	C₃₂	—	17	1	no	—
60	C₃₂	—	17	1	no	—
61	C₃₂	—	34	1	no	—
62	C₁₇	#7514	1	1	yes	characteristic, complemented, Sylow
63	#41	#63216	1	1	yes	characteristic
64	M₁₆	—	2	1	no	—
65	M₁₆	#63216	1	1	yes	characteristic
66	C₂×C₈	—	2	1	no	—
67	C₂×C₈	C₂×#3624	1	1	yes	characteristic
68	C₁₆	—	2	1	no	—
69	C₁₆	#63247	1	1	yes	characteristic
70	C₁₆	C₂²⋊#595	1	1	yes	characteristic
71	Q₈	#10587467	1	1	yes	characteristic
72	D₄	—	2	1	no	—
73	D₄	#10587467	1	1	yes	characteristic
74	C₂×C₄	—	2	1	no	—
75	C₂×C₄	C₂×#63216	1	1	yes	characteristic
76	C₈	—	2	1	no	—
77	C₈	#10587538	1	1	yes	characteristic
78	C₈	C₂²⋊#3624	1	1	yes	characteristic
79	C₂²	—	2	1	no	—
80	C₂²	#11763741	1	1	yes	characteristic
81	C₄	—	2	1	no	—
82	C₄	C₂²⋊#63216	1	1	yes	characteristic
83	C₄	C₂×#10587467	1	1	yes	characteristic
84	C₂	—	2	1	no	—
85	C₂	—	4	1	no	—
86	C₂	C₂²⋊#10587467	1	1	yes	characteristic

	subgroup	G/H
center	C₁₆	C₂²⋊#595
commutator	C₄×C₁₇	C₂×C₃₂
Frattini	C₂×C₁₆	C₂×#595
Fitting	C₁₇×#504	C₄
socle	C₂×C₁₇	C₂²⋊C₃₂
prime radical	#41×C₁₇	C₁₆
cosocle	C₂×#10587465	C₂²
hypercenter	#504	#595
hypocenter	C₁₇	#7514
LCS	G ▷ C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₁₆ ◁ C₂×C₁₆ ◁ #504

Complements

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

N	H ≅ G/N	type
1. #14543953	C₂	semidirect
2. C₂×#11763648	C₂	semidirect
62. C₁₇	#7514	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×#11763648	2
#14531078	2
#7514	17