Subgroups — #14545851

Order 2176.

70 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11763899	C₂	1	2	yes	maximal
2	C₁₆×#595	C₂	1	1	yes	maximal, characteristic
3	C₄⋊#3633	—	2	2	no	—
4	C₈×#595	C₂²	1	1	yes	characteristic
5	#10587529	C₄	1	1	yes	characteristic
6	C₁₆×D₁₇	C₄	1	1	yes	characteristic
7	C₂×#3633	—	4	2	no	—
8	C₄×#595	D₄	1	1	yes	characteristic
9	#63242	Q₈	1	1	yes	characteristic
10	C₈×D₁₇	C₂×C₄	1	1	yes	characteristic
11	#63216	—	2	1	no	—
12	C₁₆×C₁₇	C₈	1	1	yes	characteristic, complemented
13	#63214	C₈	1	1	yes	characteristic, complemented
14	C₂×#595	D₈	1	1	yes	characteristic
15	C₂×#595	Q₁₆	1	1	yes	characteristic
16	#3633	—	8	2	no	—
17	C₄×D₁₇	C₄⋊C₄	1	1	yes	characteristic
18	#3624	—	2	1	no	—
19	C₈×C₁₇	C₂×C₈	1	1	yes	characteristic
20	#3622	M₁₆	1	1	yes	characteristic
21	#1372	—	17	1	no	maximal, Sylow
22	C₂×D₁₇	#107	1	1	yes	characteristic
23	#595	—	2	1	no	—
24	#595	SD₃₂	1	2	yes	—
25	C₄×C₁₇	C₄⋊C₈	1	1	yes	characteristic
26	Dic₁₇	#108	1	1	yes	characteristic
27	C₄×C₁₆	—	17	1	no	—
28	#335	—	17	2	no	—
29	C₂×C₁₇	#335	1	1	yes	characteristic
30	D₁₇	#367	1	1	yes	characteristic
31	D₁₇	#368	1	1	yes	characteristic
32	C₂×C₁₆	—	17	1	no	—
33	C₂×C₁₆	—	17	1	no	—
34	C₄⋊C₈	—	34	2	no	—
35	C₄×C₈	—	17	1	no	—
36	C₁₇	#1372	1	1	yes	characteristic, complemented, Sylow
37	C₂×C₈	—	17	1	no	—
38	C₂×C₈	—	17	1	no	—
39	C₂×C₈	—	68	2	no	—
40	C₄²	—	17	1	no	—
41	C₁₆	—	17	1	no	—
42	C₁₆	—	34	1	no	—
43	C₁₆	#3633	1	1	yes	characteristic, complemented
44	C₂×C₄	—	17	1	no	—
45	C₂×C₄	—	17	1	no	—
46	C₂×C₄	—	17	1	no	—
47	C₈	—	17	1	no	—
48	C₈	—	34	1	no	—
49	C₈	—	136	2	no	—
50	C₈	C₂×#3633	1	1	yes	characteristic
51	C₂²	—	17	1	no	—
52	C₄	—	17	2	no	—
53	C₄	—	17	1	no	—
54	C₄	—	34	1	no	—
55	C₄	C₄⋊#3633	1	1	yes	characteristic
56	C₂	—	17	1	no	—
57	C₂	—	17	1	no	—
58	C₂	#11763899	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#11763899
commutator	C₈×C₁₇	C₂×C₈
Frattini	C₈	C₂×#3633
Fitting	C₁₆×C₁₇	C₈
socle	C₂×C₁₇	#335
prime radical	C₂×D₁₇	#107
cosocle	C₈×#595	C₂²
hypercenter	C₁₆	#3633
hypocenter	C₁₇	#1372
LCS	G ▷ C₈×C₁₇ ▷ C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ C₁₆

Complements

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

N	H ≅ G/N	type
12. C₁₆×C₁₇	C₈	semidirect
13. #63214	C₈	semidirect
36. C₁₇	#1372	semidirect
43. C₁₆	#3633	semidirect

Maximal subgroups

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

subgroup	index
#11763899	2
C₁₆×#595	2
#1372	17