Subgroups — C₃×#823 #63609

Order 288.

102 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×D₁₂	C₂	1	1	yes	maximal, characteristic
2	C₃²×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#208	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#100	—	3	1	no	maximal
5	#823	C₃	1	1	yes	maximal, characteristic, direct product factor
6	C₂²×C₃×D₃	C₄	1	2	yes	—
7	C₂×C₃²×C₄	C₂²	1	1	yes	characteristic
8	C₃×D₁₂	—	2	1	no	—
9	C₃×D₁₂	—	2	1	no	—
10	C₃²×C₈	—	2	1	no	—
11	C₃×C₃⋊C₈	—	2	1	no	—
12	C₂×C₃×D₄	—	3	1	no	—
13	C₂×D₁₂	C₂×C₃	1	1	yes	characteristic
14	C₃×M₁₆	—	2	1	no	—
15	C₃×M₁₆	—	3	1	no	—
16	C₃×M₁₆	D₃	1	1	yes	characteristic, complemented
17	C₃×M₁₆	C₂×C₃	1	1	yes	characteristic, complemented
18	#208	C₂×C₃	1	1	yes	characteristic, complemented
19	C₂²×C₃²	C₂×C₄	1	1	yes	characteristic
20	C₂×C₃×D₃	—	2	2	no	—
21	C₂×C₃×D₃	—	4	2	no	—
22	C₃²×C₄	D₄	1	1	yes	characteristic
23	C₃²×C₄	D₄	1	1	yes	characteristic
24	#100	—	3	1	no	Sylow
25	C₂³×C₃	—	3	2	no	—
26	C₂²×D₃	C₃×C₄	1	2	yes	—
27	C₃×D₄	—	6	1	no	—
28	C₃×D₄	—	6	1	no	—
29	C₂×C₃×C₄	—	2	1	no	—
30	C₂×C₃×C₄	C₂×D₃	1	1	yes	characteristic
31	C₂×C₃×C₄	C₂²×C₃	1	1	yes	characteristic
32	D₁₂	—	2	1	no	—
33	D₁₂	—	2	1	no	—
34	C₃×C₈	—	2	2	no	—
35	C₃×C₈	—	2	1	no	—
36	C₃×C₈	—	2	1	no	—
37	C₃×C₈	—	6	1	no	—
38	C₃⋊C₈	—	2	1	no	—
39	C₂×C₃²	—	2	1	no	—
40	C₂×C₃²	C₂²⋊C₄	1	1	yes	characteristic
41	C₃×D₃	—	4	2	no	—
42	C₂×D₄	—	3	1	no	—
43	M₁₆	—	3	1	no	—
44	M₁₆	C₃×D₃	1	1	yes	characteristic, complemented
45	C₂²×C₃	—	2	1	no	—
46	C₂²×C₃	—	6	2	no	—
47	C₂²×C₃	—	12	2	no	—
48	C₂²×C₃	C₄×D₃	1	1	yes	characteristic
49	C₂²×C₃	C₂×C₃×C₄	1	1	yes	characteristic
50	C₂×D₃	—	2	2	no	—
51	C₂×D₃	—	4	2	no	—
52	C₃×C₄	—	2	1	no	—
53	C₃×C₄	—	2	1	no	—
54	C₃×C₄	D₁₂	1	1	yes	characteristic
55	C₃×C₄	#67	1	1	yes	characteristic
56	C₃×C₄	C₃×D₄	1	1	yes	characteristic
57	C₃×C₄	C₃×D₄	1	1	yes	characteristic
58	C₃²	#100	1	1	yes	characteristic, complemented, Sylow
59	C₂³	—	3	2	no	—
60	D₄	—	6	1	no	—
61	D₄	—	6	1	no	—
62	C₂×C₄	C₂×C₃×D₃	1	1	yes	characteristic
63	C₈	—	2	1	no	—
64	C₈	—	6	1	no	—
65	C₂×C₃	—	2	1	no	—
66	C₂×C₃	—	2	1	no	—
67	C₂×C₃	—	2	1	no	—
68	C₂×C₃	—	4	1	no	—
69	C₂×C₃	—	12	2	no	—
70	C₂×C₃	(C₂×D₃)⋊C₄	1	1	yes	characteristic
71	C₂×C₃	C₃×C₂²⋊C₄	1	1	yes	characteristic
72	D₃	—	4	2	no	—
73	C₂²	—	6	2	no	—
74	C₂²	—	12	2	no	—
75	C₂²	C₃×C₄×D₃	1	1	yes	characteristic
76	C₄	C₃×D₁₂	1	1	yes	characteristic
77	C₄	C₃×#67	1	1	yes	characteristic
78	C₃	—	2	1	no	—
79	C₃	#823	1	1	yes	characteristic, direct product factor
80	C₃	C₃×#100	1	1	yes	characteristic, complemented
81	C₂	—	2	1	no	—
82	C₂	—	12	2	no	—
83	C₂	C₃×(C₂×D₃)⋊C₄	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃	(C₂×D₃)⋊C₄
commutator	C₂²×C₃	C₂×C₃×C₄
Frattini	C₂×C₄	C₂×C₃×D₃
Fitting	C₃²×M₁₆	C₂
socle	C₂×C₃²	C₂²⋊C₄
prime radical	C₂×C₃×D₁₂	C₂
cosocle	C₂×C₃×C₄	C₂²×C₃
hypercenter	C₃×M₁₆	D₃
hypocenter	C₃	C₃×#100
LCS	G ▷ C₂²×C₃ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₃ ◁ C₂×C₃×C₄ ◁ C₃×M₁₆

Complements

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

N	H ≅ G/N	type
2. C₃²×M₁₆	C₂	semidirect
3. C₃×#208	C₂	semidirect
5. #823	C₃	direct (N × H)
16. C₃×M₁₆	D₃	semidirect
17. C₃×M₁₆	C₂×C₃	semidirect
18. #208	C₂×C₃	semidirect
44. M₁₆	C₃×D₃	semidirect
58. C₃²	#100	semidirect
79. C₃	#823	direct (N × H)
80. C₃	C₃×#100	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃×D₁₂	2
C₃²×M₁₆	2
C₃×#208	2
C₃×#100	3
#823	3

Subgroups — C3×#823 #63609

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#823 #63609