Subgroups — C₃×#2866 #84730

Order 384.

418 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#388	C₂	1	7	yes	maximal
2	C₃×#387	C₂	1	7	yes	maximal, complemented
3	C₃×C₄³	C₂	1	1	yes	maximal, characteristic, complemented
4	#2866	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
5	C₂×C₃×C₄⋊C₄	C₂²	1	7	yes	—
6	C₂×C₃×C₂²⋊C₄	C₂²	1	7	yes	—
7	C₂×C₃×C₄²	C₂²	1	7	yes	—
8	C₃×#95	C₂²	1	14	yes	—
9	#388	C₂×C₃	1	7	yes	—
10	#387	C₂×C₃	1	7	yes	complemented
11	C₄³	C₂×C₃	1	1	yes	characteristic, complemented
12	C₂⁴×C₃	C₂³	1	1	yes	characteristic
13	C₂²×C₃×C₄	C₂³	1	7	yes	—
14	C₂²×C₃×C₄	C₂³	1	7	yes	—
15	C₃×C₄⋊C₄	—	2	14	no	—
16	C₃×C₂²⋊C₄	—	2	14	no	—
17	C₃×C₄²	—	2	14	no	—
18	C₂×C₄⋊C₄	C₂²×C₃	1	7	yes	—
19	C₂×C₂²⋊C₄	C₂²×C₃	1	7	yes	—
20	C₂×C₄²	C₂²×C₃	1	7	yes	—
21	#95	C₂²×C₃	1	14	yes	—
22	C₂³×C₃	—	2	7	no	—
23	C₂³×C₃	C₂⁴	1	1	yes	characteristic
24	C₂×C₃×C₄	—	2	14	no	—
25	C₂×C₃×C₄	—	2	7	no	—
26	C₂×C₃×C₄	—	2	14	no	—
27	C₂×C₃×C₄	#41	1	14	yes	—
28	C₂⁴	C₂³×C₃	1	1	yes	characteristic
29	C₂²×C₄	C₂³×C₃	1	7	yes	—
30	C₂²×C₄	C₂³×C₃	1	7	yes	—
31	C₄⋊C₄	—	2	14	no	—
32	C₂²⋊C₄	—	2	14	no	—
33	C₄²	—	2	14	no	—
34	C₂²×C₃	—	4	7	no	—
35	C₂²×C₃	C₂×#41	1	7	yes	—
36	C₃×C₄	—	2	14	no	—
37	C₃×C₄	—	4	7	no	—
38	C₂³	—	2	7	no	—
39	C₂³	C₂⁴×C₃	1	1	yes	characteristic
40	C₂×C₄	—	2	14	no	—
41	C₂×C₄	—	2	7	no	—
42	C₂×C₄	—	2	14	no	—
43	C₂×C₄	C₃×#41	1	14	yes	—
44	C₂×C₃	—	8	1	no	—
45	C₂×C₃	#529	1	7	yes	—
46	C₂²	—	4	7	no	—
47	C₂²	C₂×C₃×#41	1	7	yes	—
48	C₄	—	2	14	no	—
49	C₄	—	4	7	no	—
50	C₃	#2866	1	1	yes	characteristic, direct product factor, Sylow
51	C₂	—	8	1	no	—
52	C₂	C₃×#529	1	7	yes	—

	subgroup	G/H
center, socle	C₂³×C₃	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁴×C₃
prime radical	C₂⁴×C₃	C₂³
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
2. C₃×#387	C₂	semidirect
3. C₃×C₄³	C₂	semidirect
4. #2866	C₃	direct (N × H)
10. #387	C₂×C₃	semidirect
11. C₄³	C₂×C₃	semidirect
50. C₃	#2866	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×#388	2
C₃×#387	2
C₃×C₄³	2
#2866	3

Subgroups — C3×#2866 #84730

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#2866 #84730