Subgroups — #14543934

Order 2176.

74 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11763740	C₂	1	1	yes	maximal, characteristic
2	#11763735	C₂	1	1	yes	maximal, characteristic
3	Q₃₂×D₁₇	C₂	1	1	yes	maximal, characteristic
4	Q₁₆×D₁₇	—	2	1	no	—
5	#10587534	—	2	1	no	—
6	C₁₇×Q₃₂	C₄	1	1	yes	characteristic, complemented
7	#10587500	—	2	1	no	—
8	Dic₁₃₆	C₄	1	1	yes	characteristic, complemented
9	C₁₆×D₁₇	C₂²	1	1	yes	characteristic
10	#10587467	—	2	1	no	—
11	Q₈×D₁₇	—	4	1	no	—
12	C₄⋊#595	—	4	1	no	—
13	Q₁₆×C₁₇	—	2	1	no	—
14	#63231	—	4	1	no	—
15	Dic₆₈	—	2	1	no	—
16	C₈×D₁₇	D₄	1	1	yes	characteristic
17	C₁₆×C₁₇	C₂×C₄	1	1	yes	characteristic
18	#63214	D₄	1	1	yes	characteristic
19	C₂×#595	—	8	1	no	—
20	Q₈×C₁₇	—	4	1	no	—
21	C₄×D₁₇	—	8	1	no	—
22	C₄×D₁₇	D₈	1	1	yes	characteristic
23	Dic₃₄	—	4	1	no	—
24	Dic₃₄	—	8	1	no	—
25	C₈×C₁₇	C₂²⋊C₄	1	1	yes	characteristic
26	#3622	SD₁₆	1	1	yes	characteristic
27	#1416	—	17	1	no	maximal, Sylow
28	C₂×D₁₇	D₁₆	1	1	yes	characteristic
29	#595	—	16	1	no	—
30	C₄×C₁₇	—	8	1	no	—
31	C₄×C₁₇	#102	1	1	yes	characteristic
32	Dic₁₇	—	8	1	no	—
33	Dic₁₇	SD₃₂	1	1	yes	characteristic
34	C₂×Q₃₂	—	17	1	no	—
35	C₂×C₃₂	—	17	1	no	—
36	#366	—	17	1	no	—
37	C₂×C₁₇	#357	1	1	yes	characteristic
38	D₁₇	SD₆₄	1	1	yes	characteristic
39	D₁₇	Q₆₄	1	1	yes	characteristic
40	C₂×Q₁₆	—	34	1	no	—
41	Q₃₂	—	17	1	no	—
42	Q₃₂	—	34	1	no	—
43	Q₃₂	#595	1	1	yes	characteristic, complemented
44	C₂×C₁₆	—	17	1	no	—
45	#107	—	34	1	no	—
46	C₃₂	—	34	1	no	—
47	C₁₇	#1416	1	1	yes	characteristic, complemented, Sylow
48	C₂×Q₈	—	68	1	no	—
49	Q₁₆	—	2	1	no	—
50	Q₁₆	—	34	1	no	—
51	Q₁₆	—	68	1	no	—
52	C₂×C₈	—	17	1	no	—
53	C₄⋊C₄	—	68	1	no	—
54	C₁₆	—	17	1	no	—
55	C₁₆	C₂×#595	1	1	yes	characteristic
56	Q₈	—	4	1	no	—
57	Q₈	—	68	1	no	—
58	Q₈	—	136	1	no	—
59	C₂×C₄	—	17	1	no	—
60	C₂×C₄	—	136	1	no	—
61	C₂×C₄	—	136	1	no	—
62	C₈	—	17	1	no	—
63	C₈	C₂²⋊#595	1	1	yes	characteristic
64	C₂²	—	17	1	no	—
65	C₄	—	8	1	no	—
66	C₄	—	272	1	no	—
67	C₄	—	17	1	no	—
68	C₄	—	136	1	no	—
69	C₄	#10587547	1	1	yes	characteristic
70	C₂	—	17	1	no	—
71	C₂	—	17	1	no	—
72	C₂	#11763721	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#11763721
commutator	C₁₆×C₁₇	C₂×C₄
Frattini	C₁₆	C₂×#595
Fitting	C₁₇×Q₃₂	C₄
socle	C₂×C₁₇	#357
prime radical	C₂×D₁₇	D₁₆
cosocle	C₁₆×D₁₇	C₂²
hypercenter	Q₃₂	#595
hypocenter	C₁₇	#1416
LCS	G ▷ C₁₆×C₁₇ ▷ C₈×C₁₇ ▷ C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ C₁₆ ◁ Q₃₂

Complements

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

N	H ≅ G/N	type
6. C₁₇×Q₃₂	C₄	semidirect
8. Dic₁₃₆	C₄	semidirect
43. Q₃₂	#595	semidirect
47. C₁₇	#1416	semidirect

Maximal subgroups

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

subgroup	index
#11763740	2
#11763735	2
Q₃₂×D₁₇	2
#1416	17