Subgroups — C₃×#953 #64076

Order 288.

327 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁴×C₃²	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×#67	C₂	1	3	yes	maximal, complemented
3	C₃×#217	C₂	1	3	yes	maximal, complemented
4	C₃×#120	—	3	1	no	maximal
5	#953	C₃	1	1	yes	maximal, characteristic, direct product factor
6	C₂³×C₃²	—	2	6	no	—
7	C₂³×C₃²	C₂²	1	3	yes	—
8	C₂²×C₃×D₃	C₂²	1	1	yes	characteristic, complemented
9	C₃×#67	—	2	6	no	—
10	C₂×C₃×Dic₃	C₂²	1	3	yes	complemented
11	C₂⁴×C₃	—	2	1	no	—
12	C₂⁴×C₃	D₃	1	1	yes	characteristic, complemented
13	C₂⁴×C₃	C₂×C₃	1	1	yes	characteristic, complemented
14	C₂×C₃×D₄	—	3	3	no	—
15	C₂×#67	C₂×C₃	1	3	yes	complemented
16	C₃×C₂²⋊C₄	—	3	3	no	—
17	#217	C₂×C₃	1	3	yes	complemented
18	C₂²×C₃²	—	2	8	no	—
19	C₂²×C₃²	—	2	6	no	—
20	C₂²×C₃²	D₄	1	6	yes	complemented
21	C₂²×C₃²	C₂³	1	1	yes	characteristic
22	C₂×C₃×D₃	—	2	3	no	—
23	C₃×Dic₃	—	2	3	no	—
24	#120	—	3	1	no	Sylow
25	C₂³×C₃	—	2	12	no	—
26	C₂³×C₃	—	2	6	no	—
27	C₂³×C₃	—	2	6	no	—
28	C₂³×C₃	—	2	3	no	—
29	C₂³×C₃	—	3	1	no	—
30	C₂³×C₃	C₂×D₃	1	3	yes	—
31	C₂³×C₃	C₂²×C₃	1	3	yes	—
32	C₂²×D₃	C₂²×C₃	1	1	yes	characteristic, complemented
33	C₃×D₄	—	6	6	no	—
34	C₂×C₃×C₄	—	3	3	no	—
35	#67	—	2	6	no	—
36	C₂×Dic₃	C₂²×C₃	1	3	yes	complemented
37	C₂×C₃²	—	2	6	no	—
38	C₂×C₃²	C₂×D₄	1	3	yes	—
39	C₃×D₃	—	4	1	no	—
40	C₂⁴	C₃×D₃	1	1	yes	characteristic, complemented
41	C₂×D₄	—	3	3	no	—
42	C₂²⋊C₄	—	3	3	no	—
43	C₂²×C₃	—	2	16	no	—
44	C₂²×C₃	—	2	8	no	—
45	C₂²×C₃	—	2	8	no	—
46	C₂²×C₃	—	2	12	no	—
47	C₂²×C₃	—	2	6	no	—
48	C₂²×C₃	—	2	6	no	—
49	C₂²×C₃	—	2	6	no	—
50	C₂²×C₃	—	2	1	no	—
51	C₂²×C₃	—	6	3	no	—
52	C₂²×C₃	#67	1	6	yes	complemented
53	C₂²×C₃	C₃×D₄	1	6	yes	complemented
54	C₂²×C₃	C₂²×D₃	1	1	yes	characteristic
55	C₂²×C₃	C₂³×C₃	1	1	yes	characteristic
56	C₂×D₃	—	2	3	no	—
57	C₃×C₄	—	6	3	no	—
58	Dic₃	—	2	3	no	—
59	C₃²	#120	1	1	yes	characteristic, complemented, Sylow
60	C₂³	—	2	6	no	—
61	C₂³	—	3	1	no	—
62	C₂³	C₂×C₃×D₃	1	3	yes	—
63	D₄	—	6	6	no	—
64	C₂×C₄	—	3	3	no	—
65	C₂×C₃	—	2	12	no	—
66	C₂×C₃	—	2	6	no	—
67	C₂×C₃	—	2	6	no	—
68	C₂×C₃	—	2	3	no	—
69	C₂×C₃	—	12	1	no	—
70	C₂×C₃	C₂×#67	1	3	yes	—
71	C₂×C₃	C₂×C₃×D₄	1	3	yes	—
72	D₃	—	4	1	no	—
73	C₂²	—	2	8	no	—
74	C₂²	—	2	6	no	—
75	C₂²	—	6	3	no	—
76	C₂²	C₃×#67	1	6	yes	complemented
77	C₂²	C₂²×C₃×D₃	1	1	yes	characteristic
78	C₄	—	6	3	no	—
79	C₃	—	2	1	no	—
80	C₃	#953	1	1	yes	characteristic, direct product factor
81	C₃	C₃×#120	1	1	yes	characteristic, complemented
82	C₂	—	2	6	no	—
83	C₂	—	12	1	no	—
84	C₂	C₂×C₃×#67	1	3	yes	—

	subgroup	G/H
center	C₂²×C₃	C₂²×D₃
commutator, cosocle	C₂²×C₃	C₂³×C₃
Frattini	C₂²	C₂²×C₃×D₃
Fitting	C₂⁴×C₃²	C₂
socle	C₂²×C₃²	C₂³
hypercenter	C₂⁴×C₃	D₃
hypocenter	C₃	C₃×#120
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₃ ◁ C₂⁴×C₃

Complements

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

N	H ≅ G/N	type
1. C₂⁴×C₃²	C₂	semidirect
2. C₂×C₃×#67	C₂	semidirect
3. C₃×#217	C₂	semidirect
5. #953	C₃	direct (N × H)
8. C₂²×C₃×D₃	C₂²	semidirect
10. C₂×C₃×Dic₃	C₂²	semidirect
12. C₂⁴×C₃	D₃	semidirect
13. C₂⁴×C₃	C₂×C₃	semidirect
15. C₂×#67	C₂×C₃	semidirect
17. #217	C₂×C₃	semidirect
20. C₂²×C₃²	D₄	semidirect
32. C₂²×D₃	C₂²×C₃	semidirect
36. C₂×Dic₃	C₂²×C₃	semidirect
40. C₂⁴	C₃×D₃	semidirect
52. C₂²×C₃	#67	semidirect
53. C₂²×C₃	C₃×D₄	semidirect
59. C₃²	#120	semidirect
76. C₂²	C₃×#67	semidirect
80. C₃	#953	direct (N × H)
81. C₃	C₃×#120	semidirect

Maximal subgroups

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

subgroup	index
C₂⁴×C₃²	2
C₂×C₃×#67	2
C₃×#217	2
C₃×#120	3
#953	3

Subgroups — C3×#953 #64076

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#953 #64076