Subgroups — C₃×#4935 #10592032

Order 576.

426 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃²×C₄²	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×C₄⋊Dic₃	C₂	1	6	yes	maximal
3	C₃×#384	—	3	1	no	maximal
4	#4935	C₃	1	1	yes	maximal, characteristic, direct product factor
5	C₂²×C₃²×C₄	C₂²	1	3	yes	—
6	C₂²×C₃×Dic₃	C₂²	1	4	yes	—
7	C₃²×C₄²	C₄	1	4	yes	complemented
8	C₃×C₄⋊Dic₃	—	2	12	no	—
9	C₂×C₃×C₄⋊C₄	—	3	6	no	—
10	C₂×C₃×C₄²	—	2	1	no	—
11	C₂×C₃×C₄²	D₃	1	1	yes	characteristic
12	C₂×C₃×C₄²	C₂×C₃	1	1	yes	characteristic
13	C₂×C₄⋊Dic₃	C₂×C₃	1	6	yes	—
14	C₂³×C₃²	C₂³	1	1	yes	characteristic
15	C₂×C₃²×C₄	C₂×C₄	1	6	yes	—
16	C₂×C₃²×C₄	D₄	1	6	yes	—
17	C₂×C₃²×C₄	Q₈	1	6	yes	—
18	C₂×C₃×Dic₃	—	2	12	no	—
19	#384	—	3	1	no	Sylow
20	C₂²×C₃×C₄	—	2	3	no	—
21	C₂²×C₃×C₄	—	3	4	no	—
22	C₂²×C₃×C₄	C₂×D₃	1	3	yes	—
23	C₂²×C₃×C₄	C₂²×C₃	1	3	yes	—
24	C₂²×Dic₃	C₂²×C₃	1	4	yes	—
25	C₃×C₄⋊C₄	—	6	12	no	—
26	C₃×C₄²	—	2	4	no	—
27	C₃×C₄²	Dic₃	1	4	yes	complemented
28	C₃×C₄²	C₃×C₄	1	4	yes	complemented
29	C₄⋊Dic₃	—	2	12	no	—
30	C₂²×C₃²	C₂²×C₄	1	1	yes	characteristic
31	C₂²×C₃²	C₂×D₄	1	3	yes	—
32	C₂²×C₃²	C₂×Q₈	1	3	yes	—
33	C₃²×C₄	C₄⋊C₄	1	12	yes	complemented
34	C₃×Dic₃	—	4	4	no	—
35	C₂×C₄⋊C₄	—	3	6	no	—
36	C₂×C₄²	C₃×D₃	1	1	yes	characteristic
37	C₂³×C₃	—	2	1	no	—
38	C₂³×C₃	C₂²×D₃	1	1	yes	characteristic
39	C₂³×C₃	C₂³×C₃	1	1	yes	characteristic
40	C₂×C₃×C₄	—	2	6	no	—
41	C₂×C₃×C₄	—	2	6	no	—
42	C₂×C₃×C₄	—	2	6	no	—
43	C₂×C₃×C₄	—	6	12	no	—
44	C₂×C₃×C₄	Dic₆	1	6	yes	—
45	C₂×C₃×C₄	D₁₂	1	6	yes	—
46	C₂×C₃×C₄	C₂×Dic₃	1	6	yes	—
47	C₂×C₃×C₄	C₂×C₃×C₄	1	6	yes	—
48	C₂×C₃×C₄	C₃×D₄	1	6	yes	—
49	C₂×C₃×C₄	C₃×Q₈	1	6	yes	—
50	C₂×Dic₃	—	2	12	no	—
51	C₂×C₃²	C₂×C₄⋊C₄	1	3	yes	—
52	C₂×C₃²	#127	1	1	yes	characteristic
53	C₂×C₃²	C₄⋊Q₈	1	3	yes	—
54	C₂²×C₄	—	3	4	no	—
55	C₂²×C₄	C₂×C₃×D₃	1	3	yes	—
56	C₄⋊C₄	—	6	12	no	—
57	C₄²	C₃×Dic₃	1	4	yes	complemented
58	C₂²×C₃	—	2	3	no	—
59	C₂²×C₃	—	2	3	no	—
60	C₂²×C₃	—	2	1	no	—
61	C₂²×C₃	C₂×Dic₆	1	3	yes	—
62	C₂²×C₃	C₂×D₁₂	1	3	yes	—
63	C₂²×C₃	C₂²×Dic₃	1	1	yes	characteristic
64	C₂²×C₃	C₂²×C₃×C₄	1	1	yes	characteristic
65	C₂²×C₃	C₂×C₃×D₄	1	3	yes	—
66	C₂²×C₃	C₂×C₃×Q₈	1	3	yes	—
67	C₃×C₄	—	2	12	no	—
68	C₃×C₄	—	12	4	no	—
69	C₃×C₄	C₄⋊Dic₃	1	12	yes	complemented
70	C₃×C₄	C₃×C₄⋊C₄	1	12	yes	complemented
71	Dic₃	—	4	4	no	—
72	C₃²	#384	1	1	yes	characteristic, complemented, Sylow
73	C₂³	C₂²×C₃×D₃	1	1	yes	characteristic
74	C₂×C₄	—	6	12	no	—
75	C₂×C₄	C₃×Dic₆	1	6	yes	—
76	C₂×C₄	C₃×D₁₂	1	6	yes	—
77	C₂×C₄	C₂×C₃×Dic₃	1	6	yes	—
78	C₂×C₃	—	2	3	no	—
79	C₂×C₃	—	2	3	no	—
80	C₂×C₃	—	2	1	no	—
81	C₂×C₃	#869	1	3	yes	—
82	C₂×C₃	#874	1	1	yes	characteristic
83	C₂×C₃	C₂×C₄⋊Dic₃	1	3	yes	—
84	C₂×C₃	C₂×C₃×C₄⋊C₄	1	3	yes	—
85	C₂×C₃	C₃×#127	1	1	yes	characteristic
86	C₂×C₃	C₃×C₄⋊Q₈	1	3	yes	—
87	C₂²	C₂×C₃×Dic₆	1	3	yes	—
88	C₂²	C₂×C₃×D₁₂	1	3	yes	—
89	C₂²	C₂²×C₃×Dic₃	1	1	yes	characteristic
90	C₄	—	12	4	no	—
91	C₄	C₃×C₄⋊Dic₃	1	12	yes	complemented
92	C₃	—	2	1	no	—
93	C₃	#4935	1	1	yes	characteristic, direct product factor
94	C₃	C₃×#384	1	1	yes	characteristic, complemented
95	C₂	C₃×#869	1	3	yes	—
96	C₂	C₃×#874	1	1	yes	characteristic
97	C₂	C₂×C₃×C₄⋊Dic₃	1	3	yes	—

	subgroup	G/H
center	C₂³×C₃	C₂²×D₃
commutator	C₂²×C₃	C₂²×C₃×C₄
Frattini	C₂³	C₂²×C₃×D₃
Fitting	C₂×C₃²×C₄²	C₂
socle, prime radical	C₂³×C₃²	C₂³
cosocle	C₂³×C₃	C₂³×C₃
hypercenter	C₂×C₃×C₄²	D₃
hypocenter	C₃	C₃×#384
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₃ ◁ C₂×C₃×C₄²

Complements

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

N	H ≅ G/N	type
4. #4935	C₃	direct (N × H)
7. C₃²×C₄²	C₄	semidirect
27. C₃×C₄²	Dic₃	semidirect
28. C₃×C₄²	C₃×C₄	semidirect
33. C₃²×C₄	C₄⋊C₄	semidirect
57. C₄²	C₃×Dic₃	semidirect
69. C₃×C₄	C₄⋊Dic₃	semidirect
70. C₃×C₄	C₃×C₄⋊C₄	semidirect
72. C₃²	#384	semidirect
91. C₄	C₃×C₄⋊Dic₃	semidirect
93. C₃	#4935	direct (N × H)
94. C₃	C₃×#384	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃²×C₄²	2
C₂×C₃×C₄⋊Dic₃	2
C₃×#384	3
#4935	3

Subgroups — C3×#4935 #10592032

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#4935 #10592032