Subgroups — #14543820

Order 2176.

62 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11763731	C₂	1	2	yes	maximal
2	C₁₆×Dic₁₇	C₂	1	1	yes	maximal, characteristic
3	#10587538	—	2	2	no	—
4	C₂×C₁₆×C₁₇	C₄	1	1	yes	characteristic
5	C₈×Dic₁₇	C₂²	1	1	yes	characteristic
6	C₂×#63214	C₄	1	1	yes	characteristic
7	C₂×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
8	C₄×Dic₁₇	Q₈	1	1	yes	characteristic
9	C₂×#3622	D₄	1	1	yes	characteristic
10	#63216	—	4	2	no	—
11	C₁₆×C₁₇	—	2	1	no	—
12	#63214	C₈	1	2	yes	—
13	C₂×C₄×C₁₇	C₄⋊C₄	1	1	yes	characteristic
14	C₂×Dic₁₇	—	2	1	no	—
15	C₈×C₁₇	C₂×C₈	1	1	yes	characteristic
16	C₈×C₁₇	M₁₆	1	1	yes	characteristic
17	#3622	D₈	1	1	yes	characteristic
18	#3622	Q₁₆	1	1	yes	characteristic
19	#1373	—	17	1	no	maximal, Sylow
20	C₂²×C₁₇	#108	1	1	yes	characteristic
21	C₄×C₁₇	C₄⋊C₈	1	1	yes	characteristic
22	C₄×C₁₇	#107	1	1	yes	characteristic
23	Dic₁₇	—	2	2	no	—
24	#364	—	17	2	no	—
25	C₄×C₁₆	—	17	1	no	—
26	C₂×C₁₇	—	2	1	no	—
27	C₂×C₁₇	#335	1	1	yes	characteristic
28	M₃₂	—	34	2	no	—
29	C₂×C₁₆	—	17	1	no	—
30	C₂×C₁₆	#595	1	1	yes	characteristic
31	C₄×C₈	—	17	1	no	—
32	C₁₇	#1373	1	1	yes	characteristic, complemented, Sylow
33	C₂×C₈	—	17	1	no	—
34	C₂×C₈	C₂×#595	1	1	yes	characteristic
35	C₄²	—	17	1	no	—
36	C₁₆	—	2	1	no	—
37	C₁₆	—	17	2	no	—
38	C₁₆	—	68	2	no	—
39	C₂×C₄	—	34	1	no	—
40	C₂×C₄	C₄⋊#595	1	1	yes	characteristic
41	C₈	—	17	1	no	—
42	C₈	—	17	1	no	—
43	C₈	#63242	1	1	yes	characteristic
44	C₈	#63247	1	1	yes	characteristic
45	C₂²	#10587535	1	1	yes	characteristic
46	C₄	—	34	2	no	—
47	C₄	#10587534	1	1	yes	characteristic
48	C₄	#10587544	1	1	yes	characteristic
49	C₂	—	2	1	no	—
50	C₂	#11763673	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#10587534
commutator	C₈×C₁₇	C₂×C₈
Frattini	C₂×C₈	C₂×#595
Fitting	C₂×C₁₆×C₁₇	C₄
socle	C₂×C₁₇	#335
prime radical	C₂²×C₁₇	#108
cosocle	C₈×Dic₁₇	C₂²
hypercenter	C₂×C₁₆	#595
hypocenter	C₁₇	#1373
LCS	G ▷ C₈×C₁₇ ▷ C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆

Complements

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

N	H ≅ G/N	type
32. C₁₇	#1373	semidirect

Maximal subgroups

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

subgroup	index
#11763731	2
C₁₆×Dic₁₇	2
#1373	17