Subgroups — C₃×#2810 #84674

Order 384.

344 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#400	C₂	1	6	yes	maximal
2	C₃×#389	C₂	1	3	yes	maximal
3	C₃×#387	C₂	1	6	yes	maximal
4	#2810	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
5	C₂×C₃×C₄⋊C₄	C₂²	1	6	yes	—
6	C₂×C₃×C₄⋊C₄	C₂²	1	3	yes	—
7	C₂×C₃×C₄⋊C₄	C₂²	1	3	yes	—
8	C₂×C₃×C₄²	C₂²	1	2	yes	—
9	C₂×C₃×C₄²	C₂²	1	1	yes	characteristic
10	C₃×#95	C₂²	1	6	yes	—
11	C₃×#95	C₂²	1	6	yes	—
12	C₃×#95	C₂²	1	6	yes	—
13	C₃×#95	C₂²	1	2	yes	—
14	#400	C₂×C₃	1	6	yes	—
15	#389	C₂×C₃	1	3	yes	—
16	#387	C₂×C₃	1	6	yes	—
17	C₂²×C₃×C₄	C₂³	1	6	yes	—
18	C₂²×C₃×C₄	C₂³	1	6	yes	—
19	C₂²×C₃×C₄	C₂³	1	3	yes	—
20	C₃×C₄⋊C₄	—	2	12	no	—
21	C₃×C₄⋊C₄	—	2	6	no	—
22	C₃×C₄⋊C₄	—	4	3	no	—
23	C₃×C₄²	—	4	1	no	—
24	C₃×C₄²	—	4	2	no	—
25	C₂×C₄⋊C₄	C₂²×C₃	1	6	yes	—
26	C₂×C₄⋊C₄	C₂²×C₃	1	3	yes	—
27	C₂×C₄⋊C₄	C₂²×C₃	1	3	yes	—
28	C₂×C₄²	C₂²×C₃	1	2	yes	—
29	C₂×C₄²	C₂²×C₃	1	1	yes	characteristic
30	#95	C₂²×C₃	1	6	yes	—
31	#95	C₂²×C₃	1	6	yes	—
32	#95	C₂²×C₃	1	6	yes	—
33	#95	C₂²×C₃	1	2	yes	—
34	C₂³×C₃	C₂⁴	1	1	yes	characteristic
35	C₂×C₃×C₄	—	2	3	no	—
36	C₂×C₃×C₄	—	2	3	no	—
37	C₂×C₃×C₄	—	2	6	no	—
38	C₂×C₃×C₄	—	2	6	no	—
39	C₂×C₃×C₄	—	2	6	no	—
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	#41	1	6	yes	—
44	C₂²×C₄	C₂³×C₃	1	6	yes	—
45	C₂²×C₄	C₂³×C₃	1	6	yes	—
46	C₂²×C₄	C₂³×C₃	1	3	yes	—
47	C₄⋊C₄	—	2	12	no	—
48	C₄⋊C₄	—	2	6	no	—
49	C₄⋊C₄	—	4	3	no	—
50	C₄²	—	4	1	no	—
51	C₄²	—	4	2	no	—
52	C₂²×C₃	C₂×#41	1	3	yes	—
53	C₂²×C₃	H(5,𝔽₂)	1	1	yes	characteristic
54	C₂²×C₃	2₋¹⁺⁴	1	3	yes	—
55	C₃×C₄	—	2	6	no	—
56	C₃×C₄	—	4	6	no	—
57	C₃×C₄	—	4	6	no	—
58	C₂³	C₂⁴×C₃	1	1	yes	characteristic
59	C₂×C₄	—	2	3	no	—
60	C₂×C₄	—	2	3	no	—
61	C₂×C₄	—	2	6	no	—
62	C₂×C₄	—	2	6	no	—
63	C₂×C₄	—	2	6	no	—
64	C₂×C₄	—	2	6	no	—
65	C₂×C₄	—	2	6	no	—
66	C₂×C₄	—	2	6	no	—
67	C₂×C₄	C₃×#41	1	6	yes	—
68	C₂×C₃	#539	1	3	yes	—
69	C₂×C₃	#556	1	3	yes	—
70	C₂×C₃	#564	1	1	yes	characteristic
71	C₂²	C₂×C₃×#41	1	3	yes	—
72	C₂²	C₃×H(5,𝔽₂)	1	1	yes	characteristic
73	C₂²	C₃×2₋¹⁺⁴	1	3	yes	—
74	C₄	—	2	6	no	—
75	C₄	—	4	6	no	—
76	C₄	—	4	6	no	—
77	C₃	#2810	1	1	yes	characteristic, direct product factor, Sylow
78	C₂	C₃×#539	1	3	yes	—
79	C₂	C₃×#556	1	3	yes	—
80	C₂	C₃×#564	1	1	yes	characteristic

	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
4. #2810	C₃	direct (N × H)
77. C₃	#2810	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×#400	2
C₃×#389	2
C₃×#387	2
#2810	3

Subgroups — C3×#2810 #84674

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#2810 #84674