Subgroups — C₃×#63656 #11722158

Order 864.

216 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃³×Q₁₆	C₂	1	1	yes	maximal, characteristic
2	C₃×#3746	C₂	1	1	yes	maximal, characteristic
3	C₃×C₃⋊(C₃⋊C₁₆)	C₂	1	1	yes	maximal, characteristic
4	#63656	C₃	1	1	yes	maximal, characteristic, direct product factor
5	C₃×#829	—	3	4	no	maximal
6	C₃³×Q₈	—	2	1	no	—
7	C₃×#634	—	2	1	no	—
8	C₃³×C₈	C₂²	1	1	yes	characteristic
9	C₃²×Q₁₆	—	2	4	no	—
10	C₃²×Q₁₆	D₃	1	4	yes	—
11	C₃²×Q₁₆	C₂×C₃	1	1	yes	characteristic
12	#3746	C₂×C₃	1	1	yes	characteristic
13	C₃×Dic₁₂	—	3	4	no	—
14	C₃⋊(C₃⋊C₁₆)	C₂×C₃	1	1	yes	characteristic
15	C₃×C₃⋊C₁₆	—	3	4	no	—
16	C₃³×C₄	—	4	1	no	—
17	C₃³×C₄	D₄	1	1	yes	characteristic
18	C₃×C₃⋊Dic₃	—	4	1	no	—
19	C₃×Q₃₂	—	9	1	no	—
20	#829	—	3	4	no	—
21	C₃²×Q₈	—	2	8	no	—
22	C₃²×Q₈	—	2	4	no	—
23	C₃²×Q₈	—	2	1	no	—
24	#634	—	2	1	no	—
25	C₃×Dic₆	—	6	4	no	—
26	C₃²×C₈	—	2	4	no	—
27	C₃²×C₈	C₂×D₃	1	4	yes	—
28	C₃²×C₈	C₂²×C₃	1	1	yes	characteristic
29	C₂×C₃³	D₈	1	1	yes	characteristic
30	C₃×Q₁₆	—	2	4	no	—
31	C₃×Q₁₆	—	9	1	no	—
32	C₃×Q₁₆	C₃×D₃	1	4	yes	—
33	C₃×Q₁₆	C₃⋊D₃	1	1	yes	characteristic
34	Dic₁₂	—	3	4	no	—
35	C₃×C₁₆	—	9	1	no	—
36	C₃⋊C₁₆	—	3	4	no	—
37	C₃²×C₄	—	2	4	no	—
38	C₃²×C₄	—	4	8	no	—
39	C₃²×C₄	—	4	4	no	—
40	C₃²×C₄	—	4	1	no	—
41	C₃²×C₄	#67	1	4	yes	—
42	C₃²×C₄	C₃×D₄	1	1	yes	characteristic
43	C₃⋊Dic₃	—	4	1	no	—
44	C₃×Dic₃	—	12	4	no	—
45	Q₃₂	—	9	1	no	Sylow
46	C₃³	Q₃₂	1	1	yes	characteristic, complemented, Sylow
47	C₃×Q₈	—	2	8	no	—
48	C₃×Q₈	—	2	4	no	—
49	C₃×Q₈	—	2	1	no	—
50	C₃×Q₈	—	18	1	no	—
51	Dic₆	—	6	4	no	—
52	C₃×C₈	—	2	4	no	—
53	C₃×C₈	C₂×C₃×D₃	1	4	yes	—
54	C₃×C₈	C₂×C₃⋊D₃	1	1	yes	characteristic
55	C₂×C₃²	—	2	4	no	—
56	C₂×C₃²	#213	1	4	yes	—
57	C₂×C₃²	C₃×D₈	1	1	yes	characteristic
58	Q₁₆	—	9	1	no	—
59	Q₁₆	C₃×C₃⋊D₃	1	1	yes	characteristic
60	C₁₆	—	9	1	no	—
61	C₃×C₄	—	2	4	no	—
62	C₃×C₄	—	4	8	no	—
63	C₃×C₄	—	4	4	no	—
64	C₃×C₄	—	4	1	no	—
65	C₃×C₄	—	36	1	no	—
66	C₃×C₄	C₃×#67	1	4	yes	—
67	C₃×C₄	#638	1	1	yes	characteristic
68	Dic₃	—	12	4	no	—
69	C₃²	—	2	4	no	—
70	C₃²	#829	1	4	yes	complemented
71	C₃²	C₃×Q₃₂	1	1	yes	characteristic, complemented
72	Q₈	—	2	1	no	—
73	Q₈	—	18	1	no	—
74	C₈	C₂×C₃×C₃⋊D₃	1	1	yes	characteristic
75	C₂×C₃	—	2	4	no	—
76	C₂×C₃	C₃×#213	1	4	yes	—
77	C₂×C₃	#3753	1	1	yes	characteristic
78	C₄	—	4	1	no	—
79	C₄	—	36	1	no	—
80	C₄	C₃×#638	1	1	yes	characteristic
81	C₃	—	2	4	no	—
82	C₃	C₃×#829	1	4	yes	complemented
83	C₃	#63656	1	1	yes	characteristic, direct product factor
84	C₂	C₃×#3753	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃	#3753
commutator, cosocle	C₃²×C₈	C₂²×C₃
Frattini	C₈	C₂×C₃×C₃⋊D₃
Fitting	C₃³×Q₁₆	C₂
socle, prime radical	C₂×C₃³	D₈
hypercenter	C₃×Q₁₆	C₃⋊D₃
hypocenter	C₃²	C₃×Q₃₂
LCS	G ▷ C₃²×C₈ ▷ C₃²×C₄ ▷ C₂×C₃² ▷ C₃²
UCS	C₁ ◁ C₂×C₃ ◁ C₃×C₄ ◁ C₃×C₈ ◁ C₃×Q₁₆

Complements

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

N	H ≅ G/N	type
4. #63656	C₃	direct (N × H)
46. C₃³	Q₃₂	semidirect
70. C₃²	#829	semidirect
71. C₃²	C₃×Q₃₂	semidirect
82. C₃	C₃×#829	semidirect
83. C₃	#63656	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃³×Q₁₆	2
C₃×#3746	2
C₃×C₃⋊(C₃⋊C₁₆)	2
#63656	3
C₃×#829	3

Subgroups — C3×#63656 #11722158

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#63656 #11722158