Subgroups — #14543949

Order 2176.

52 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11763738	C₂	1	1	yes	maximal, characteristic
2	#11763736	C₂	1	1	yes	maximal, characteristic
3	#11762642	C₂	1	1	yes	maximal, characteristic
4	#10587536	—	2	1	no	—
5	#10587534	—	2	1	no	—
6	C₁₆×D₁₇	C₂²	1	1	yes	characteristic
7	C₁₇×C₃₂	C₄	1	1	yes	characteristic, complemented
8	#10587465	C₄	1	1	yes	characteristic, complemented
9	C₄⋊#595	—	4	1	no	—
10	#63243	—	4	1	no	—
11	C₈×D₁₇	D₄	1	1	yes	characteristic
12	C₁₆×C₁₇	C₂×C₄	1	1	yes	characteristic
13	#63214	Q₈	1	1	yes	characteristic
14	C₂×#595	—	8	1	no	—
15	C₄×D₁₇	D₈	1	1	yes	characteristic
16	#3624	—	8	1	no	—
17	C₈×C₁₇	C₄⋊C₄	1	1	yes	characteristic
18	#3622	Q₁₆	1	1	yes	characteristic
19	#1426	—	17	1	no	maximal, Sylow
20	C₂×D₁₇	SD₃₂	1	1	yes	characteristic
21	#595	—	16	1	no	—
22	C₄×C₁₇	#107	1	1	yes	characteristic
23	Dic₁₇	SD₃₂	1	1	yes	characteristic
24	M₆₄	—	17	1	no	—
25	#368	—	17	1	no	—
26	#367	—	17	1	no	—
27	C₂×C₁₇	#367	1	1	yes	characteristic
28	D₁₇	—	2	1	no	—
29	C₂×C₁₆	—	17	1	no	—
30	#108	—	34	1	no	—
31	#107	—	34	1	no	—
32	C₃₂	—	17	1	no	—
33	C₃₂	#595	1	1	yes	characteristic, complemented
34	C₁₇	#1426	1	1	yes	characteristic, complemented, Sylow
35	M₁₆	—	68	1	no	—
36	C₂×C₈	—	17	1	no	—
37	C₄⋊C₄	—	68	1	no	—
38	C₁₆	—	17	1	no	—
39	C₁₆	C₂×#595	1	1	yes	characteristic
40	C₂×C₄	—	17	1	no	—
41	C₂×C₄	—	136	1	no	—
42	C₈	—	17	1	no	—
43	C₈	—	136	1	no	—
44	C₈	C₄⋊#595	1	1	yes	characteristic
45	C₂²	—	17	1	no	—
46	C₄	—	272	1	no	—
47	C₄	—	17	1	no	—
48	C₄	#10587534	1	1	yes	characteristic
49	C₂	—	34	1	no	—
50	C₂	#11763736	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#11763736
commutator	C₁₆×C₁₇	C₂×C₄
Frattini	C₁₆	C₂×#595
Fitting	C₁₇×C₃₂	C₄
socle	C₂×C₁₇	#367
prime radical	C₂×D₁₇	SD₃₂
cosocle	C₁₆×D₁₇	C₂²
hypercenter	C₃₂	#595
hypocenter	C₁₇	#1426
LCS	G ▷ C₁₆×C₁₇ ▷ C₈×C₁₇ ▷ C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ C₁₆ ◁ C₃₂

Complements

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

N	H ≅ G/N	type
7. C₁₇×C₃₂	C₄	semidirect
8. #10587465	C₄	semidirect
33. C₃₂	#595	semidirect
34. C₁₇	#1426	semidirect

Maximal subgroups

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

subgroup	index
#11763738	2
#11763736	2
#11762642	2
#1426	17