Subgroups — C₃×#10587479 #13108751

Order 1632.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₄⋊C₄×C₁₇	C₂	1	1	yes	maximal, characteristic
2	C₃×C₄⋊Dic₁₇	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃×#3622	C₂	1	1	yes	maximal, characteristic
4	#10587479	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂×C₃×C₄×C₁₇	—	2	1	no	—
6	C₂×C₃×C₄×C₁₇	C₂²	1	1	yes	characteristic
7	C₂×C₃×Dic₁₇	—	2	1	no	—
8	C₃×#3622	C₄	1	2	yes	complemented
9	C₄⋊C₄×C₁₇	C₂×C₃	1	1	yes	characteristic
10	C₄⋊Dic₁₇	C₂×C₃	1	1	yes	characteristic
11	C₂×#3622	C₂×C₃	1	1	yes	characteristic
12	C₂²×C₃×C₁₇	D₄	1	1	yes	characteristic
13	C₃×C₄×C₁₇	—	4	1	no	—
14	C₃×C₄×C₁₇	C₂×C₄	1	1	yes	characteristic
15	C₃×C₄×C₁₇	Q₈	1	1	yes	characteristic
16	C₃×Dic₁₇	—	4	1	no	—
17	C₂×C₄×C₁₇	—	2	1	no	—
18	C₂×C₄×C₁₇	C₂²×C₃	1	1	yes	characteristic
19	C₂×Dic₁₇	—	2	1	no	—
20	#3622	C₃×C₄	1	2	yes	complemented
21	C₂×C₃×C₁₇	C₄⋊C₄	1	1	yes	characteristic
22	C₂×C₃×C₁₇	SD₁₆	1	1	yes	characteristic
23	C₂×C₃×C₁₇	SD₁₆	1	1	yes	characteristic
24	C₃×#106	—	17	1	no	maximal, Hall
25	C₂²×C₁₇	C₃×D₄	1	1	yes	characteristic
26	C₄×C₁₇	—	4	1	no	—
27	C₄×C₁₇	C₂×C₃×C₄	1	1	yes	characteristic
28	C₄×C₁₇	C₃×Q₈	1	1	yes	characteristic
29	Dic₁₇	—	4	1	no	—
30	C₃×C₁₇	#106	1	1	yes	characteristic, complemented, Hall
31	C₂×C₃×C₈	—	17	1	no	—
32	C₃×C₄⋊C₄	—	17	1	no	—
33	C₃×C₄⋊C₄	D₁₇	1	1	yes	characteristic
34	C₂×C₁₇	C₃×C₄⋊C₄	1	1	yes	characteristic
35	C₂×C₁₇	C₃×SD₁₆	1	1	yes	characteristic
36	C₂×C₁₇	C₃×SD₁₆	1	1	yes	characteristic
37	#106	—	17	1	no	Sylow
38	C₂×C₃×C₄	—	2	1	no	—
39	C₂×C₃×C₄	—	34	1	no	—
40	C₂×C₃×C₄	C₂×D₁₇	1	1	yes	characteristic
41	C₃×C₈	—	17	2	no	—
42	C₁₇	C₃×#106	1	1	yes	characteristic, complemented, Sylow
43	C₂×C₈	—	17	1	no	—
44	C₄⋊C₄	—	17	1	no	—
45	C₄⋊C₄	C₃×D₁₇	1	1	yes	characteristic
46	C₂²×C₃	C₂²⋊D₁₇	1	1	yes	characteristic
47	C₃×C₄	—	4	1	no	—
48	C₃×C₄	—	68	1	no	—
49	C₃×C₄	Dic₃₄	1	1	yes	characteristic
50	C₃×C₄	C₄×D₁₇	1	1	yes	characteristic
51	C₂×C₄	—	2	1	no	—
52	C₂×C₄	—	34	1	no	—
53	C₂×C₄	C₂×C₃×D₁₇	1	1	yes	characteristic
54	C₈	—	17	2	no	—
55	C₂×C₃	#63225	1	1	yes	characteristic
56	C₂×C₃	#63229	1	1	yes	characteristic
57	C₂×C₃	#63230	1	1	yes	characteristic
58	C₂²	C₃×C₂²⋊D₁₇	1	1	yes	characteristic
59	C₄	—	4	1	no	—
60	C₄	—	68	1	no	—
61	C₄	C₃×Dic₃₄	1	1	yes	characteristic
62	C₄	C₃×C₄×D₁₇	1	1	yes	characteristic
63	C₃	#10587479	1	1	yes	characteristic, direct product factor, Sylow
64	C₂	C₃×#63225	1	1	yes	characteristic
65	C₂	C₃×#63229	1	1	yes	characteristic
66	C₂	C₃×#63230	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	C₂²⋊D₁₇
commutator	C₄×C₁₇	C₂×C₃×C₄
Frattini	C₂×C₄	C₂×C₃×D₁₇
Fitting	C₃×C₄⋊C₄×C₁₇	C₂
socle, prime radical	C₂²×C₃×C₁₇	D₄
cosocle	C₂×C₄×C₁₇	C₂²×C₃
hypercenter	C₃×C₄⋊C₄	D₁₇
hypocenter	C₁₇	C₃×#106
LCS	G ▷ C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂²×C₃ ◁ C₂×C₃×C₄ ◁ C₃×C₄⋊C₄

Complements

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

N	H ≅ G/N	type
4. #10587479	C₃	direct (N × H)
8. C₃×#3622	C₄	semidirect
20. #3622	C₃×C₄	semidirect
30. C₃×C₁₇	#106	semidirect
42. C₁₇	C₃×#106	semidirect
63. C₃	#10587479	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×C₄⋊C₄×C₁₇	2
C₃×C₄⋊Dic₁₇	2
C₂×C₃×#3622	2
#10587479	3
C₃×#106	17

Subgroups — C3×#10587479 #13108751

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10587479 #13108751