Subgroups — C₃×#2845 #84709

Order 384.

340 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#398	C₂	1	12	yes	maximal
2	C₃×#382	C₂	1	3	yes	maximal
3	#2845	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
4	C₂×C₃×C₄⋊C₄	C₂²	1	6	yes	—
5	C₂×C₃×C₄⋊C₄	C₂²	1	12	yes	—
6	C₂×C₃×C₄²	C₂²	1	1	yes	characteristic
7	C₃×#95	C₂²	1	12	yes	—
8	C₃×#95	C₂²	1	4	yes	—
9	#398	C₂×C₃	1	12	yes	—
10	#382	C₂×C₃	1	3	yes	—
11	C₂²×C₃×C₄	C₂³	1	12	yes	—
12	C₂²×C₃×C₄	C₂³	1	3	yes	—
13	C₃×C₄⋊C₄	—	4	6	no	—
14	C₃×C₄⋊C₄	—	4	12	no	—
15	C₃×C₄²	Q₈	1	4	yes	—
16	C₂×C₄⋊C₄	C₂²×C₃	1	6	yes	—
17	C₂×C₄⋊C₄	C₂²×C₃	1	12	yes	—
18	C₂×C₄²	C₂²×C₃	1	1	yes	characteristic
19	#95	C₂²×C₃	1	12	yes	—
20	#95	C₂²×C₃	1	4	yes	—
21	C₂³×C₃	C₂⁴	1	1	yes	characteristic
22	C₂×C₃×C₄	—	2	3	no	—
23	C₂×C₃×C₄	—	2	3	no	—
24	C₂×C₃×C₄	—	2	12	no	—
25	C₂×C₃×C₄	—	2	12	no	—
26	C₂×C₃×C₄	—	2	12	no	—
27	C₂×C₃×C₄	C₂×Q₈	1	6	yes	—
28	C₂²×C₄	C₂³×C₃	1	12	yes	—
29	C₂²×C₄	C₂³×C₃	1	3	yes	—
30	C₄⋊C₄	—	4	6	no	—
31	C₄⋊C₄	—	4	12	no	—
32	C₄²	C₃×Q₈	1	4	yes	—
33	C₂²×C₃	C₂²×Q₈	1	1	yes	characteristic
34	C₂²×C₃	H(5,𝔽₂)	1	3	yes	—
35	C₂²×C₃	2₋¹⁺⁴	1	3	yes	—
36	C₃×C₄	—	2	6	no	—
37	C₃×C₄	—	4	12	no	—
38	C₂³	C₂⁴×C₃	1	1	yes	characteristic
39	C₂×C₄	—	2	3	no	—
40	C₂×C₄	—	2	3	no	—
41	C₂×C₄	—	2	12	no	—
42	C₂×C₄	—	2	12	no	—
43	C₂×C₄	—	2	12	no	—
44	C₂×C₄	C₂×C₃×Q₈	1	6	yes	—
45	C₂×C₃	#544	1	3	yes	—
46	C₂×C₃	#562	1	3	yes	—
47	C₂×C₃	#564	1	1	yes	characteristic
48	C₂²	C₂²×C₃×Q₈	1	1	yes	characteristic
49	C₂²	C₃×H(5,𝔽₂)	1	3	yes	—
50	C₂²	C₃×2₋¹⁺⁴	1	3	yes	—
51	C₄	—	2	6	no	—
52	C₄	—	4	12	no	—
53	C₃	#2845	1	1	yes	characteristic, direct product factor, Sylow
54	C₂	C₃×#544	1	3	yes	—
55	C₂	C₃×#562	1	3	yes	—
56	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
3. #2845	C₃	direct (N × H)
53. C₃	#2845	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×#398	2
C₃×#382	2
#2845	3

Subgroups — C3×#2845 #84709

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#2845 #84709