Subgroups — C₃×#2645 #84509

Order 384.

352 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#401	C₂	1	2	yes	maximal
2	C₃×#400	C₂	1	6	yes	maximal
3	C₃×#391	C₂	1	3	yes	maximal
4	C₃×#389	C₂	1	3	yes	maximal
5	C₃×#376	C₂	1	1	yes	maximal, characteristic
6	#2645	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
7	C₂²×C₃×Q₈	C₂²	1	1	yes	characteristic
8	C₂×C₃×C₄⋊C₄	C₂²	1	3	yes	—
9	C₂×C₃×C₄⋊C₄	C₂²	1	6	yes	—
10	C₂×C₃×C₄²	C₂²	1	3	yes	—
11	C₃×#95	C₂²	1	3	yes	—
12	C₃×#95	C₂²	1	1	yes	characteristic
13	C₃×#95	C₂²	1	6	yes	—
14	C₃×#95	C₂²	1	6	yes	—
15	C₃×#95	C₂²	1	6	yes	—
16	#401	C₂×C₃	1	2	yes	—
17	#400	C₂×C₃	1	6	yes	—
18	#391	C₂×C₃	1	3	yes	—
19	#389	C₂×C₃	1	3	yes	—
20	#376	C₂×C₃	1	1	yes	characteristic
21	C₂×C₃×Q₈	—	2	6	no	—
22	C₂²×C₃×C₄	C₂³	1	3	yes	—
23	C₂²×C₃×C₄	C₂³	1	2	yes	—
24	C₂²×C₃×C₄	C₂³	1	3	yes	—
25	C₂²×C₃×C₄	C₂³	1	6	yes	—
26	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
27	C₃×C₄⋊C₄	—	2	6	no	—
28	C₃×C₄⋊C₄	—	4	6	no	—
29	C₃×C₄²	—	2	6	no	—
30	C₂²×Q₈	C₂²×C₃	1	1	yes	characteristic
31	C₂×C₄⋊C₄	C₂²×C₃	1	3	yes	—
32	C₂×C₄⋊C₄	C₂²×C₃	1	6	yes	—
33	C₂×C₄²	C₂²×C₃	1	3	yes	—
34	#95	C₂²×C₃	1	3	yes	—
35	#95	C₂²×C₃	1	1	yes	characteristic
36	#95	C₂²×C₃	1	6	yes	—
37	#95	C₂²×C₃	1	6	yes	—
38	#95	C₂²×C₃	1	6	yes	—
39	C₂³×C₃	C₂⁴	1	1	yes	characteristic
40	C₃×Q₈	—	4	4	no	—
41	C₂×C₃×C₄	—	2	3	no	—
42	C₂×C₃×C₄	—	2	3	no	—
43	C₂×C₃×C₄	—	2	6	no	—
44	C₂×C₃×C₄	—	2	6	no	—
45	C₂×C₃×C₄	—	2	3	no	—
46	C₂×C₃×C₄	—	2	6	no	—
47	C₂×C₃×C₄	—	2	6	no	—
48	C₂×C₃×C₄	—	2	3	no	—
49	C₂×C₃×C₄	—	2	6	no	—
50	C₂×C₃×C₄	#41	1	6	yes	—
51	C₂×Q₈	—	2	6	no	—
52	C₂²×C₄	C₂³×C₃	1	3	yes	—
53	C₂²×C₄	C₂³×C₃	1	2	yes	—
54	C₂²×C₄	C₂³×C₃	1	3	yes	—
55	C₂²×C₄	C₂³×C₃	1	6	yes	—
56	C₂²×C₄	C₂³×C₃	1	1	yes	characteristic
57	C₄⋊C₄	—	2	6	no	—
58	C₄⋊C₄	—	4	6	no	—
59	C₄²	—	2	6	no	—
60	C₂²×C₃	C₂×#41	1	3	yes	—
61	C₂²×C₃	H(5,𝔽₂)	1	1	yes	characteristic
62	C₂²×C₃	2₋¹⁺⁴	1	3	yes	—
63	C₃×C₄	—	4	2	no	—
64	C₃×C₄	—	4	3	no	—
65	C₃×C₄	—	4	3	no	—
66	C₃×C₄	—	4	6	no	—
67	C₃×C₄	#126	1	4	yes	—
68	C₂³	C₂⁴×C₃	1	1	yes	characteristic
69	Q₈	—	4	4	no	—
70	C₂×C₄	—	2	3	no	—
71	C₂×C₄	—	2	3	no	—
72	C₂×C₄	—	2	6	no	—
73	C₂×C₄	—	2	6	no	—
74	C₂×C₄	—	2	3	no	—
75	C₂×C₄	—	2	6	no	—
76	C₂×C₄	—	2	6	no	—
77	C₂×C₄	—	2	3	no	—
78	C₂×C₄	—	2	6	no	—
79	C₂×C₄	C₃×#41	1	6	yes	—
80	C₂×C₃	C₂×#126	1	1	yes	characteristic
81	C₂×C₃	#541	1	3	yes	—
82	C₂×C₃	#542	1	3	yes	—
83	C₂²	C₂×C₃×#41	1	3	yes	—
84	C₂²	C₃×H(5,𝔽₂)	1	1	yes	characteristic
85	C₂²	C₃×2₋¹⁺⁴	1	3	yes	—
86	C₄	—	4	2	no	—
87	C₄	—	4	3	no	—
88	C₄	—	4	3	no	—
89	C₄	—	4	6	no	—
90	C₄	C₃×#126	1	4	yes	—
91	C₃	#2645	1	1	yes	characteristic, direct product factor, Sylow
92	C₂	C₂×C₃×#126	1	1	yes	characteristic
93	C₂	C₃×#541	1	3	yes	—
94	C₂	C₃×#542	1	3	yes	—

	subgroup	G/H
center, socle, prime radical	C₂³×C₃	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁴×C₃
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₃ ◁ G

Complements

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

N	H ≅ G/N	type
6. #2645	C₃	direct (N × H)
91. C₃	#2645	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×#401	2
C₃×#400	2
C₃×#391	2
C₃×#389	2
C₃×#376	2
#2645	3

Subgroups — C3×#2645 #84509

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#2645 #84509