Subgroups — C₂×C₃×#208 #64044

Order 288.

163 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃²×C₄	C₂	1	1	yes	maximal, characteristic
2	C₃×#208	C₂	1	4	yes	maximal, direct product factor
3	C₂×C₃×C₃⋊C₈	C₂	1	2	yes	maximal, complemented
4	C₂×C₃×M₁₆	—	3	1	no	maximal
5	C₂×#208	C₃	1	1	yes	maximal, characteristic, direct product factor
6	C₂³×C₃²	C₄	1	1	yes	characteristic
7	C₂×C₃²×C₄	C₄	1	2	yes	—
8	C₂×C₃²×C₄	C₄	1	1	yes	characteristic
9	C₂×C₃²×C₄	C₂²	1	2	yes	—
10	C₂×C₃²×C₄	C₂²	1	1	yes	characteristic
11	C₃×C₃⋊C₈	C₂²	1	4	yes	complemented
12	C₂²×C₃×C₄	—	2	1	no	—
13	C₂²×C₃×C₄	D₃	1	1	yes	characteristic
14	C₂²×C₃×C₄	C₂×C₃	1	1	yes	characteristic
15	C₃×M₁₆	—	3	4	no	—
16	C₂×C₃×C₈	—	3	2	no	—
17	#208	C₂×C₃	1	4	yes	direct product factor
18	C₂×C₃⋊C₈	C₂×C₃	1	2	yes	complemented
19	C₂²×C₃²	—	2	2	no	—
20	C₂²×C₃²	C₂×C₄	1	2	yes	—
21	C₂²×C₃²	C₂×C₄	1	1	yes	characteristic
22	C₃²×C₄	C₂×C₄	1	2	yes	—
23	C₃²×C₄	C₂×C₄	1	1	yes	characteristic
24	C₃²×C₄	C₂³	1	1	yes	characteristic
25	C₂×M₁₆	—	3	1	no	Sylow
26	C₂³×C₃	—	2	1	no	—
27	C₂³×C₃	Dic₃	1	1	yes	characteristic
28	C₂³×C₃	C₃×C₄	1	1	yes	characteristic
29	C₂×C₃×C₄	—	2	2	no	—
30	C₂×C₃×C₄	—	2	1	no	—
31	C₂×C₃×C₄	—	2	1	no	—
32	C₂×C₃×C₄	—	2	2	no	—
33	C₂×C₃×C₄	Dic₃	1	1	yes	characteristic
34	C₂×C₃×C₄	Dic₃	1	2	yes	—
35	C₂×C₃×C₄	C₃×C₄	1	2	yes	—
36	C₂×C₃×C₄	C₃×C₄	1	1	yes	characteristic
37	C₂×C₃×C₄	C₂×D₃	1	2	yes	—
38	C₂×C₃×C₄	C₂×D₃	1	1	yes	characteristic
39	C₂×C₃×C₄	C₂²×C₃	1	1	yes	characteristic
40	C₂×C₃×C₄	C₂²×C₃	1	2	yes	—
41	C₃×C₈	—	3	4	no	—
42	C₃⋊C₈	C₂²×C₃	1	4	yes	complemented
43	C₂×C₃²	—	2	2	no	—
44	C₂×C₃²	M₁₆	1	2	yes	complemented
45	C₂×C₃²	C₂²×C₄	1	1	yes	characteristic
46	C₂²×C₄	C₃×D₃	1	1	yes	characteristic
47	M₁₆	—	3	4	no	—
48	C₂×C₈	—	3	2	no	—
49	C₂²×C₃	—	2	4	no	—
50	C₂²×C₃	—	2	2	no	—
51	C₂²×C₃	—	2	2	no	—
52	C₂²×C₃	—	2	2	no	—
53	C₂²×C₃	—	2	1	no	—
54	C₂²×C₃	C₂×Dic₃	1	2	yes	—
55	C₂²×C₃	C₂×Dic₃	1	1	yes	characteristic
56	C₂²×C₃	C₂×C₃×C₄	1	2	yes	—
57	C₂²×C₃	C₂×C₃×C₄	1	1	yes	characteristic
58	C₃×C₄	—	2	1	no	—
59	C₃×C₄	—	2	2	no	—
60	C₃×C₄	—	2	1	no	—
61	C₃×C₄	C₂×Dic₃	1	2	yes	—
62	C₃×C₄	C₂×Dic₃	1	1	yes	characteristic
63	C₃×C₄	C₂×C₃×C₄	1	1	yes	characteristic
64	C₃×C₄	C₂×C₃×C₄	1	2	yes	—
65	C₃×C₄	C₂²×D₃	1	1	yes	characteristic
66	C₃×C₄	C₂³×C₃	1	1	yes	characteristic
67	C₃²	C₂×M₁₆	1	1	yes	characteristic, complemented, Sylow
68	C₂³	C₃×Dic₃	1	1	yes	characteristic
69	C₂×C₄	C₃×Dic₃	1	2	yes	—
70	C₂×C₄	C₃×Dic₃	1	1	yes	characteristic
71	C₂×C₄	C₂×C₃×D₃	1	1	yes	characteristic
72	C₂×C₄	C₂×C₃×D₃	1	2	yes	—
73	C₈	—	3	4	no	—
74	C₂×C₃	—	2	4	no	—
75	C₂×C₃	—	2	2	no	—
76	C₂×C₃	—	2	2	no	—
77	C₂×C₃	—	2	2	no	—
78	C₂×C₃	—	2	1	no	—
79	C₂×C₃	#208	1	2	yes	direct product factor
80	C₂×C₃	C₃×M₁₆	1	2	yes	complemented
81	C₂×C₃	C₂²×Dic₃	1	1	yes	characteristic
82	C₂×C₃	C₂²×C₃×C₄	1	1	yes	characteristic
83	C₂²	—	2	2	no	—
84	C₂²	C₂×C₃×Dic₃	1	2	yes	—
85	C₂²	C₂×C₃×Dic₃	1	1	yes	characteristic
86	C₄	C₂×C₃×Dic₃	1	1	yes	characteristic
87	C₄	C₂×C₃×Dic₃	1	2	yes	—
88	C₄	C₂²×C₃×D₃	1	1	yes	characteristic
89	C₃	—	2	1	no	—
90	C₃	C₂×#208	1	1	yes	characteristic, direct product factor
91	C₃	C₂×C₃×M₁₆	1	1	yes	characteristic, complemented
92	C₂	—	2	2	no	—
93	C₂	C₃×#208	1	2	yes	direct product factor
94	C₂	C₂²×C₃×Dic₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃×C₄	C₂×D₃
commutator	C₂×C₃	C₂²×C₃×C₄
Frattini	C₄	C₂²×C₃×D₃
Fitting	C₂²×C₃²×C₄	C₂
socle	C₂²×C₃²	C₂×C₄
prime radical	C₂³×C₃²	C₄
cosocle	C₃×C₄	C₂³×C₃
hypercenter	C₂²×C₃×C₄	D₃
hypocenter	C₃	C₂×C₃×M₁₆
LCS	G ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₃×C₄ ◁ C₂²×C₃×C₄

Complements

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

N	H ≅ G/N	type
2. C₃×#208	C₂	direct (N × H)
3. C₂×C₃×C₃⋊C₈	C₂	semidirect
5. C₂×#208	C₃	direct (N × H)
11. C₃×C₃⋊C₈	C₂²	semidirect
17. #208	C₂×C₃	direct (N × H)
18. C₂×C₃⋊C₈	C₂×C₃	semidirect
42. C₃⋊C₈	C₂²×C₃	semidirect
44. C₂×C₃²	M₁₆	semidirect
67. C₃²	C₂×M₁₆	semidirect
79. C₂×C₃	#208	direct (N × H)
80. C₂×C₃	C₃×M₁₆	semidirect
90. C₃	C₂×#208	direct (N × H)
91. C₃	C₂×C₃×M₁₆	semidirect
93. C₂	C₃×#208	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₃²×C₄	2
C₃×#208	2
C₂×C₃×C₃⋊C₈	2
C₂×C₃×M₁₆	3
C₂×#208	3

Subgroups — C2×C3×#208 #64044

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#208 #64044