Subgroups — C₃×#890 #64013

Order 288.

125 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
2	C₃×C₄⋊Dic₃	C₂	1	2	yes	maximal
3	C₃×C₄⋊Dic₃	C₂	1	1	yes	maximal, characteristic
4	C₃×Dic₃⋊C₄	C₂	1	2	yes	maximal
5	C₃×C₄×Dic₃	C₂	1	1	yes	maximal, characteristic
6	C₃×#125	—	3	1	no	maximal
7	#890	C₃	1	1	yes	maximal, characteristic, direct product factor
8	C₂×C₃²×C₄	C₂²	1	2	yes	—
9	C₂×C₃²×C₄	C₂²	1	1	yes	characteristic
10	C₂×C₃×Dic₃	C₂²	1	1	yes	characteristic
11	C₂×C₃×Dic₃	C₂²	1	1	yes	characteristic
12	C₂×C₃×Dic₃	C₂²	1	2	yes	—
13	C₃×C₄⋊C₄	—	2	1	no	—
14	C₃×C₄⋊C₄	—	3	2	no	—
15	C₃×C₄⋊C₄	—	3	2	no	—
16	C₃×C₄⋊C₄	—	3	1	no	—
17	C₃×C₄⋊C₄	D₃	1	1	yes	characteristic
18	C₃×C₄⋊C₄	C₂×C₃	1	1	yes	characteristic
19	C₃×C₄²	—	3	1	no	—
20	C₄⋊Dic₃	C₂×C₃	1	2	yes	—
21	C₄⋊Dic₃	C₂×C₃	1	1	yes	characteristic
22	Dic₃⋊C₄	C₂×C₃	1	2	yes	—
23	C₄×Dic₃	C₂×C₃	1	1	yes	characteristic
24	C₂²×C₃²	C₂³	1	1	yes	characteristic
25	C₃²×C₄	—	2	2	no	—
26	C₃²×C₄	Q₈	1	2	yes	—
27	C₃×Dic₃	—	2	1	no	—
28	C₃×Dic₃	—	2	1	no	—
29	C₃×Dic₃	—	2	2	no	—
30	#125	—	3	1	no	Sylow
31	C₂×C₃×C₄	—	2	1	no	—
32	C₂×C₃×C₄	—	2	2	no	—
33	C₂×C₃×C₄	—	3	1	no	—
34	C₂×C₃×C₄	—	3	1	no	—
35	C₂×C₃×C₄	—	3	2	no	—
36	C₂×C₃×C₄	C₂×D₃	1	2	yes	—
37	C₂×C₃×C₄	C₂×D₃	1	1	yes	characteristic
38	C₂×C₃×C₄	C₂²×C₃	1	2	yes	—
39	C₂×C₃×C₄	C₂²×C₃	1	1	yes	characteristic
40	C₂×Dic₃	C₂²×C₃	1	1	yes	characteristic
41	C₂×Dic₃	C₂²×C₃	1	1	yes	characteristic
42	C₂×Dic₃	C₂²×C₃	1	2	yes	—
43	C₂×C₃²	C₂×Q₈	1	1	yes	characteristic
44	C₂×C₃²	#41	1	1	yes	characteristic
45	C₂×C₃²	#41	1	1	yes	characteristic
46	C₄⋊C₄	—	3	2	no	—
47	C₄⋊C₄	—	3	2	no	—
48	C₄⋊C₄	—	3	1	no	—
49	C₄⋊C₄	C₃×D₃	1	1	yes	characteristic
50	C₄²	—	3	1	no	—
51	C₂²×C₃	—	2	1	no	—
52	C₂²×C₃	C₂²×D₃	1	1	yes	characteristic
53	C₂²×C₃	C₂³×C₃	1	1	yes	characteristic
54	C₃×C₄	—	2	2	no	—
55	C₃×C₄	—	2	2	no	—
56	C₃×C₄	—	2	2	no	—
57	C₃×C₄	—	4	2	no	—
58	C₃×C₄	—	6	1	no	—
59	C₃×C₄	—	6	1	no	—
60	C₃×C₄	—	6	2	no	—
61	C₃×C₄	Dic₆	1	2	yes	—
62	C₃×C₄	C₃×Q₈	1	2	yes	—
63	Dic₃	—	2	1	no	—
64	Dic₃	—	2	1	no	—
65	Dic₃	—	2	2	no	—
66	C₃²	#125	1	1	yes	characteristic, complemented, Sylow
67	C₂×C₄	—	3	1	no	—
68	C₂×C₄	—	3	1	no	—
69	C₂×C₄	—	3	2	no	—
70	C₂×C₄	C₂×C₃×D₃	1	2	yes	—
71	C₂×C₄	C₂×C₃×D₃	1	1	yes	characteristic
72	C₂×C₃	—	2	1	no	—
73	C₂×C₃	—	2	1	no	—
74	C₂×C₃	—	2	1	no	—
75	C₂×C₃	C₂×Dic₆	1	1	yes	characteristic
76	C₂×C₃	#237	1	1	yes	characteristic
77	C₂×C₃	#239	1	1	yes	characteristic
78	C₂×C₃	C₂×C₃×Q₈	1	1	yes	characteristic
79	C₂×C₃	C₃×#41	1	1	yes	characteristic
80	C₂×C₃	C₃×#41	1	1	yes	characteristic
81	C₂²	C₂²×C₃×D₃	1	1	yes	characteristic
82	C₄	—	2	2	no	—
83	C₄	—	6	1	no	—
84	C₄	—	6	1	no	—
85	C₄	—	6	2	no	—
86	C₄	C₃×Dic₆	1	2	yes	—
87	C₃	—	2	1	no	—
88	C₃	#890	1	1	yes	characteristic, direct product factor
89	C₃	C₃×#125	1	1	yes	characteristic, complemented
90	C₂	C₂×C₃×Dic₆	1	1	yes	characteristic
91	C₂	C₃×#237	1	1	yes	characteristic
92	C₂	C₃×#239	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	C₂²×D₃
commutator, cosocle	C₂²×C₃	C₂³×C₃
Frattini	C₂²	C₂²×C₃×D₃
Fitting	C₃²×C₄⋊C₄	C₂
socle, prime radical	C₂²×C₃²	C₂³
hypercenter	C₃×C₄⋊C₄	D₃
hypocenter	C₃	C₃×#125
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×C₄⋊C₄

Complements

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

N	H ≅ G/N	type
7. #890	C₃	direct (N × H)
66. C₃²	#125	semidirect
88. C₃	#890	direct (N × H)
89. C₃	C₃×#125	semidirect

Maximal subgroups

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

subgroup	index
C₃²×C₄⋊C₄	2
C₃×C₄⋊Dic₃	2
C₃×Dic₃⋊C₄	2
C₃×C₄×Dic₃	2
C₃×#125	3
#890	3

Subgroups — C3×#890 #64013

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#890 #64013