Subgroups — C₃×#4699 #10591796

Order 576.

266 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×Dic₁₂	C₂	1	4	yes	maximal
2	C₃×#869	C₂	1	2	yes	maximal
3	C₃²×C₄×C₈	C₂	1	1	yes	maximal, characteristic
4	C₃×#494	—	3	1	no	maximal
5	#4699	C₃	1	1	yes	maximal, characteristic, direct product factor
6	C₂×C₃×Dic₆	C₂²	1	4	yes	—
7	C₂×C₃²×C₈	C₂²	1	2	yes	—
8	C₃²×C₄²	C₂²	1	1	yes	characteristic
9	C₃×C₄⋊Dic₃	—	2	4	no	—
10	C₃×Dic₁₂	—	2	8	no	—
11	C₂×C₃×Q₁₆	—	3	4	no	—
12	C₃×C₄⋊Q₈	—	3	2	no	—
13	C₂×Dic₁₂	C₂×C₃	1	4	yes	—
14	#869	C₂×C₃	1	2	yes	—
15	C₃×C₄×C₈	—	2	1	no	—
16	C₃×C₄×C₈	D₃	1	1	yes	characteristic
17	C₃×C₄×C₈	C₂×C₃	1	1	yes	characteristic
18	C₂×C₃²×C₄	D₄	1	2	yes	—
19	C₂×C₃²×C₄	C₂³	1	1	yes	characteristic
20	C₂×C₃×Dic₃	—	2	4	no	—
21	C₃×Dic₆	—	2	8	no	—
22	C₃²×C₈	D₄	1	4	yes	—
23	#494	—	3	1	no	Sylow
24	C₂×C₃×Q₈	—	3	4	no	—
25	C₂×Dic₆	C₂²×C₃	1	4	yes	—
26	C₃×Q₁₆	—	6	8	no	—
27	C₂×C₃×C₈	—	2	2	no	—
28	C₂×C₃×C₈	C₂×D₃	1	2	yes	—
29	C₂×C₃×C₈	C₂²×C₃	1	2	yes	—
30	C₃×C₄⋊C₄	—	6	4	no	—
31	C₃×C₄²	—	2	1	no	—
32	C₃×C₄²	C₂×D₃	1	1	yes	characteristic
33	C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
34	C₄⋊Dic₃	—	2	4	no	—
35	Dic₁₂	—	2	8	no	—
36	C₂²×C₃²	C₂×D₄	1	1	yes	characteristic
37	C₃²×C₄	Q₁₆	1	4	yes	complemented
38	C₃²×C₄	C₂×D₄	1	2	yes	—
39	C₃×Dic₃	—	4	4	no	—
40	C₂×Q₁₆	—	3	4	no	—
41	C₄⋊Q₈	—	3	2	no	—
42	C₄×C₈	C₃×D₃	1	1	yes	characteristic
43	C₃×Q₈	—	6	8	no	—
44	C₂×C₃×C₄	—	2	2	no	—
45	C₂×C₃×C₄	—	2	1	no	—
46	C₂×C₃×C₄	—	6	4	no	—
47	C₂×C₃×C₄	D₁₂	1	2	yes	—
48	C₂×C₃×C₄	C₃×D₄	1	2	yes	—
49	C₂×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
50	C₂×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
51	C₂×Dic₃	—	2	4	no	—
52	Dic₆	—	2	8	no	—
53	C₃×C₈	—	2	4	no	—
54	C₃×C₈	D₁₂	1	4	yes	—
55	C₃×C₈	C₃×D₄	1	4	yes	—
56	C₂×C₃²	#127	1	1	yes	characteristic
57	C₂×C₃²	C₂×Q₁₆	1	2	yes	—
58	C₂×Q₈	—	3	4	no	—
59	Q₁₆	—	6	8	no	—
60	C₂×C₈	C₂×C₃×D₃	1	2	yes	—
61	C₄⋊C₄	—	6	4	no	—
62	C₄²	C₂×C₃×D₃	1	1	yes	characteristic
63	C₂²×C₃	—	2	1	no	—
64	C₂²×C₃	C₂×D₁₂	1	1	yes	characteristic
65	C₂²×C₃	C₂×C₃×D₄	1	1	yes	characteristic
66	C₃×C₄	—	2	4	no	—
67	C₃×C₄	—	2	2	no	—
68	C₃×C₄	—	12	4	no	—
69	C₃×C₄	Dic₁₂	1	4	yes	complemented
70	C₃×C₄	C₃×Q₁₆	1	4	yes	complemented
71	C₃×C₄	C₂×D₁₂	1	2	yes	—
72	C₃×C₄	C₂×C₃×D₄	1	2	yes	—
73	Dic₃	—	4	4	no	—
74	C₃²	#494	1	1	yes	characteristic, complemented, Sylow
75	Q₈	—	6	8	no	—
76	C₂×C₄	—	6	4	no	—
77	C₂×C₄	C₃×D₁₂	1	2	yes	—
78	C₂×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
79	C₈	C₃×D₁₂	1	4	yes	—
80	C₂×C₃	—	2	2	no	—
81	C₂×C₃	—	2	1	no	—
82	C₂×C₃	#874	1	1	yes	characteristic
83	C₂×C₃	C₂×Dic₁₂	1	2	yes	—
84	C₂×C₃	C₃×#127	1	1	yes	characteristic
85	C₂×C₃	C₂×C₃×Q₁₆	1	2	yes	—
86	C₂²	C₂×C₃×D₁₂	1	1	yes	characteristic
87	C₄	—	12	4	no	—
88	C₄	C₃×Dic₁₂	1	4	yes	complemented
89	C₄	C₂×C₃×D₁₂	1	2	yes	—
90	C₃	—	2	1	no	—
91	C₃	#4699	1	1	yes	characteristic, direct product factor
92	C₃	C₃×#494	1	1	yes	characteristic, complemented
93	C₂	C₃×#874	1	1	yes	characteristic
94	C₂	C₂×C₃×Dic₁₂	1	2	yes	—

	subgroup	G/H
center	C₂²×C₃	C₂×D₁₂
commutator, cosocle	C₂×C₃×C₄	C₂³×C₃
Frattini	C₂×C₄	C₂²×C₃×D₃
Fitting	C₃²×C₄×C₈	C₂
socle, prime radical	C₂²×C₃²	C₂×D₄
hypercenter	C₃×C₄×C₈	D₃
hypocenter	C₃	C₃×#494
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×C₄² ◁ C₃×C₄×C₈

Complements

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

N	H ≅ G/N	type
5. #4699	C₃	direct (N × H)
37. C₃²×C₄	Q₁₆	semidirect
69. C₃×C₄	Dic₁₂	semidirect
70. C₃×C₄	C₃×Q₁₆	semidirect
74. C₃²	#494	semidirect
88. C₄	C₃×Dic₁₂	semidirect
91. C₃	#4699	direct (N × H)
92. C₃	C₃×#494	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃×Dic₁₂	2
C₃×#869	2
C₃²×C₄×C₈	2
C₃×#494	3
#4699	3

Subgroups — C3×#4699 #10591796

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#4699 #10591796