Subgroups — C₃×#10587480 #13108752

Order 1632.

100 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×D₆₈	C₂	1	1	yes	maximal, characteristic
2	C₃×C₄⋊C₄×C₁₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×#3622	C₂	1	1	yes	maximal, characteristic, complemented
4	#10587480	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂²×C₃×D₁₇	—	2	1	no	—
6	C₂×C₃×C₄×C₁₇	—	2	1	no	—
7	C₂×C₃×C₄×C₁₇	C₂²	1	1	yes	characteristic
8	C₃×D₆₈	—	2	1	no	—
9	C₃×D₆₈	C₄	1	2	yes	complemented
10	C₃×#3622	—	2	1	no	—
11	C₂×D₆₈	C₂×C₃	1	1	yes	characteristic
12	C₄⋊C₄×C₁₇	C₂×C₃	1	1	yes	characteristic, complemented
13	C₂×#3622	C₂×C₃	1	1	yes	characteristic, complemented
14	C₂²×C₃×C₁₇	D₄	1	1	yes	characteristic
15	C₂×C₃×D₁₇	—	2	2	no	—
16	C₂×C₃×D₁₇	—	4	1	no	—
17	C₂×C₃×D₁₇	—	4	1	no	—
18	C₃×C₄×C₁₇	—	4	1	no	—
19	C₃×C₄×C₁₇	C₂×C₄	1	1	yes	characteristic
20	C₃×C₄×C₁₇	D₄	1	1	yes	characteristic
21	C₂²×D₁₇	—	2	1	no	—
22	C₂×C₄×C₁₇	—	2	1	no	—
23	C₂×C₄×C₁₇	C₂²×C₃	1	1	yes	characteristic
24	D₆₈	—	2	1	no	—
25	D₆₈	C₃×C₄	1	2	yes	complemented
26	#3622	—	2	1	no	—
27	C₂×C₃×C₁₇	C₂²⋊C₄	1	1	yes	characteristic
28	C₂×C₃×C₁₇	D₈	1	1	yes	characteristic
29	C₂×C₃×C₁₇	SD₁₆	1	1	yes	characteristic
30	C₃×D₁₇	—	4	2	no	—
31	C₃×#102	—	17	1	no	maximal, Hall
32	C₂²×C₁₇	C₃×D₄	1	1	yes	characteristic
33	C₂×D₁₇	—	2	2	no	—
34	C₂×D₁₇	—	4	1	no	—
35	C₂×D₁₇	—	4	1	no	—
36	C₄×C₁₇	—	4	1	no	—
37	C₄×C₁₇	C₂×C₃×C₄	1	1	yes	characteristic
38	C₄×C₁₇	C₃×D₄	1	1	yes	characteristic
39	C₃×C₁₇	#102	1	1	yes	characteristic, complemented, Hall
40	C₂×C₃×D₄	—	17	1	no	—
41	C₂×C₃×C₈	—	17	1	no	—
42	C₃×C₄⋊C₄	D₁₇	1	1	yes	characteristic, complemented
43	C₂×C₁₇	C₃×C₂²⋊C₄	1	1	yes	characteristic
44	C₂×C₁₇	C₃×D₈	1	1	yes	characteristic
45	C₂×C₁₇	C₃×SD₁₆	1	1	yes	characteristic
46	D₁₇	—	4	2	no	—
47	#102	—	17	1	no	Sylow
48	C₂³×C₃	—	34	1	no	—
49	C₃×D₄	—	17	2	no	—
50	C₃×D₄	—	34	1	no	—
51	C₂×C₃×C₄	—	2	1	no	—
52	C₂×C₃×C₄	C₂×D₁₇	1	1	yes	characteristic
53	C₃×C₈	—	34	1	no	—
54	C₁₇	C₃×#102	1	1	yes	characteristic, complemented, Sylow
55	C₂×D₄	—	17	1	no	—
56	C₂×C₈	—	17	1	no	—
57	C₄⋊C₄	C₃×D₁₇	1	1	yes	characteristic, complemented
58	C₂²×C₃	—	34	2	no	—
59	C₂²×C₃	—	68	1	no	—
60	C₂²×C₃	—	68	1	no	—
61	C₂²×C₃	C₂²⋊D₁₇	1	1	yes	characteristic
62	C₃×C₄	—	4	1	no	—
63	C₃×C₄	C₄×D₁₇	1	1	yes	characteristic
64	C₃×C₄	D₆₈	1	1	yes	characteristic
65	C₂³	—	34	1	no	—
66	D₄	—	17	2	no	—
67	D₄	—	34	1	no	—
68	C₂×C₄	—	2	1	no	—
69	C₂×C₄	C₂×C₃×D₁₇	1	1	yes	characteristic
70	C₈	—	34	1	no	—
71	C₂×C₃	—	68	2	no	—
72	C₂×C₃	#63227	1	1	yes	characteristic
73	C₂×C₃	#63228	1	1	yes	characteristic
74	C₂×C₃	#63230	1	1	yes	characteristic
75	C₂²	—	34	2	no	—
76	C₂²	—	68	1	no	—
77	C₂²	—	68	1	no	—
78	C₂²	C₃×C₂²⋊D₁₇	1	1	yes	characteristic
79	C₄	—	4	1	no	—
80	C₄	C₃×C₄×D₁₇	1	1	yes	characteristic
81	C₄	C₃×D₆₈	1	1	yes	characteristic
82	C₃	#10587480	1	1	yes	characteristic, direct product factor, Sylow
83	C₂	—	68	2	no	—
84	C₂	C₃×#63227	1	1	yes	characteristic
85	C₂	C₃×#63228	1	1	yes	characteristic
86	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	C₂²×C₃×C₁₇	D₄
prime radical	C₂×C₃×D₆₈	C₂
cosocle	C₂×C₄×C₁₇	C₂²×C₃
hypercenter	C₃×C₄⋊C₄	D₁₇
hypocenter	C₁₇	C₃×#102
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
2. C₃×C₄⋊C₄×C₁₇	C₂	semidirect
3. C₂×C₃×#3622	C₂	semidirect
4. #10587480	C₃	direct (N × H)
9. C₃×D₆₈	C₄	semidirect
12. C₄⋊C₄×C₁₇	C₂×C₃	semidirect
13. C₂×#3622	C₂×C₃	semidirect
25. D₆₈	C₃×C₄	semidirect
39. C₃×C₁₇	#102	semidirect
42. C₃×C₄⋊C₄	D₁₇	semidirect
54. C₁₇	C₃×#102	semidirect
57. C₄⋊C₄	C₃×D₁₇	semidirect
82. C₃	#10587480	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃×D₆₈	2
C₃×C₄⋊C₄×C₁₇	2
C₂×C₃×#3622	2
#10587480	3
C₃×#102	17

Subgroups — C3×#10587480 #13108752

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10587480 #13108752