Subgroups — #17949377

Order 4352.

92 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14543943	C₂	1	2	yes	maximal
2	C₁₆×#3622	C₂	1	1	yes	maximal, characteristic
3	#11763741	—	2	2	no	—
4	C₄×#63214	C₂²	1	1	yes	characteristic
5	C₈×#3622	C₄	1	1	yes	characteristic
6	C₄×C₁₆×C₁₇	C₄	1	1	yes	characteristic
7	C₂×C₁₆×C₁₇	C₈	1	1	yes	characteristic
8	C₂×C₁₆×C₁₇	C₈	1	1	yes	characteristic
9	C₄×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
10	C₂×#63214	D₄	1	1	yes	characteristic
11	C₂×#63214	Q₈	1	1	yes	characteristic
12	C₄×#3622	—	2	1	no	—
13	#10587467	—	4	2	no	—
14	C₂×C₈×C₁₇	C₄⋊C₄	1	1	yes	characteristic
15	C₂×C₈×C₁₇	C₂×C₈	1	1	yes	characteristic
16	C₄²×C₁₇	M₁₆	1	1	yes	characteristic
17	C₂×#3622	—	2	2	no	—
18	C₁₆×C₁₇	—	2	1	no	—
19	C₁₆×C₁₇	C₁₆	1	2	yes	—
20	#63214	—	2	1	no	—
21	#63214	D₈	1	1	yes	characteristic
22	#63214	Q₁₆	1	1	yes	characteristic
23	#7459	—	17	1	no	maximal, Sylow
24	C₂×C₄×C₁₇	—	2	1	no	—
25	C₂×C₄×C₁₇	C₄⋊C₈	1	1	yes	characteristic
26	C₈×C₁₇	#107	1	1	yes	characteristic
27	C₈×C₁₇	#108	1	1	yes	characteristic
28	C₈×C₁₇	C₂×C₁₆	1	1	yes	characteristic
29	C₈×C₁₇	M₃₂	1	1	yes	characteristic
30	#3622	—	2	4	no	—
31	#1422	—	17	2	no	—
32	C₈×C₁₆	—	17	1	no	—
33	C₂²×C₁₇	#364	1	1	yes	characteristic
34	C₄×C₁₇	—	2	2	no	—
35	C₄×C₁₇	#335	1	1	yes	characteristic
36	C₄×C₁₇	C₄⋊C₁₆	1	1	yes	characteristic
37	M₆₄	—	34	2	no	—
38	C₄×C₁₆	—	17	1	no	—
39	C₄×C₁₆	#595	1	1	yes	characteristic
40	C₈²	—	17	1	no	—
41	C₂×C₁₇	—	2	1	no	—
42	C₂×C₁₇	#1370	1	1	yes	characteristic
43	C₂×C₁₆	—	17	1	no	—
44	C₂×C₁₆	—	17	1	no	—
45	C₂×C₁₆	#3624	1	1	yes	characteristic
46	C₂×C₁₆	#3624	1	1	yes	characteristic
47	C₄×C₈	—	34	1	no	—
48	C₄×C₈	C₂×#595	1	1	yes	characteristic
49	C₃₂	—	68	2	no	—
50	C₁₇	#7459	1	1	yes	characteristic, complemented, Sylow
51	C₂×C₈	—	34	2	no	—
52	C₂×C₈	C₄⋊#595	1	1	yes	characteristic
53	C₂×C₈	C₂×#3624	1	1	yes	characteristic
54	C₄²	#63243	1	1	yes	characteristic
55	C₁₆	—	2	1	no	—
56	C₁₆	—	17	1	no	—
57	C₁₆	—	17	1	no	—
58	C₁₆	—	34	1	no	—
59	C₁₆	#63216	1	2	yes	—
60	C₂×C₄	—	2	1	no	—
61	C₂×C₄	C₄⋊#3624	1	1	yes	characteristic
62	C₈	—	34	4	no	—
63	C₈	#10587534	1	1	yes	characteristic
64	C₈	#10587536	1	1	yes	characteristic
65	C₈	C₂×#63216	1	1	yes	characteristic
66	C₈	#10587538	1	1	yes	characteristic
67	C₂²	#11763731	1	1	yes	characteristic
68	C₄	—	2	2	no	—
69	C₄	#11763672	1	1	yes	characteristic
70	C₄	C₄⋊#63216	1	1	yes	characteristic
71	C₂	—	2	1	no	—
72	C₂	#14543813	1	1	yes	characteristic

	subgroup	G/H
center	C₈	#10587534
commutator	C₈×C₁₇	C₂×C₁₆
Frattini	C₄×C₈	C₂×#595
Fitting	C₄×C₁₆×C₁₇	C₄
socle	C₂×C₁₇	#1370
prime radical	C₂²×C₁₇	#364
cosocle	C₄×#63214	C₂²
hypercenter	C₄×C₁₆	#595
hypocenter	C₁₇	#7459
LCS	G ▷ C₈×C₁₇ ▷ C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₈ ◁ C₂×C₈ ◁ C₄×C₈ ◁ C₄×C₁₆

Complements

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

N	H ≅ G/N	type
50. C₁₇	#7459	semidirect

Maximal subgroups

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

subgroup	index
#14543943	2
C₁₆×#3622	2
#7459	17