Subgroups — C₃×#1455 #72170

Order 384.

214 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₄×M₁₆	C₂	1	3	yes	maximal
2	C₃×#322	C₂	1	3	yes	maximal, complemented
3	C₃×C₈²	C₂	1	1	yes	maximal, characteristic, complemented
4	#1455	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
5	C₂×C₃×M₁₆	C₄	1	6	yes	—
6	C₂×C₃×C₄²	C₂²	1	1	yes	characteristic
7	C₃×#97	C₄	1	6	yes	—
8	C₃×C₄×C₈	C₂²	1	3	yes	—
9	C₃×C₄×C₈	C₂²	1	3	yes	—
10	C₄×M₁₆	C₂×C₃	1	3	yes	—
11	#322	C₂×C₃	1	3	yes	complemented
12	C₈²	C₂×C₃	1	1	yes	characteristic, complemented
13	C₂²×C₃×C₄	C₂×C₄	1	3	yes	—
14	C₃×M₁₆	—	2	12	no	—
15	C₂×C₃×C₈	C₂×C₄	1	6	yes	—
16	C₂×C₃×C₈	C₂×C₄	1	6	yes	—
17	C₃×C₄²	C₂×C₄	1	3	yes	—
18	C₃×C₄²	C₂³	1	1	yes	characteristic
19	C₂×M₁₆	C₃×C₄	1	6	yes	—
20	C₂×C₄²	C₂²×C₃	1	1	yes	characteristic
21	#97	C₃×C₄	1	6	yes	—
22	C₄×C₈	C₂²×C₃	1	3	yes	—
23	C₄×C₈	C₂²×C₃	1	3	yes	—
24	C₂³×C₃	C₄²	1	1	yes	characteristic
25	C₂×C₃×C₄	—	2	6	no	—
26	C₂×C₃×C₄	C₄²	1	3	yes	—
27	C₂×C₃×C₄	C₂²×C₄	1	3	yes	—
28	C₃×C₈	—	2	6	no	—
29	C₃×C₈	M₁₆	1	12	yes	complemented
30	C₂²×C₄	C₂×C₃×C₄	1	3	yes	—
31	M₁₆	—	2	12	no	—
32	C₂×C₈	C₂×C₃×C₄	1	6	yes	—
33	C₂×C₈	C₂×C₃×C₄	1	6	yes	—
34	C₄²	C₂×C₃×C₄	1	3	yes	—
35	C₄²	C₂³×C₃	1	1	yes	characteristic
36	C₂²×C₃	—	2	3	no	—
37	C₂²×C₃	C₂×C₄²	1	1	yes	characteristic
38	C₃×C₄	—	2	3	no	—
39	C₃×C₄	C₂×M₁₆	1	6	yes	—
40	C₂³	C₃×C₄²	1	1	yes	characteristic
41	C₂×C₄	—	2	6	no	—
42	C₂×C₄	C₃×C₄²	1	3	yes	—
43	C₂×C₄	C₂²×C₃×C₄	1	3	yes	—
44	C₈	—	2	6	no	—
45	C₈	C₃×M₁₆	1	12	yes	complemented
46	C₂×C₃	—	4	1	no	—
47	C₂×C₃	C₄×M₁₆	1	3	yes	—
48	C₂²	—	2	3	no	—
49	C₂²	C₂×C₃×C₄²	1	1	yes	characteristic
50	C₄	—	2	3	no	—
51	C₄	C₂×C₃×M₁₆	1	6	yes	—
52	C₃	#1455	1	1	yes	characteristic, direct product factor, Sylow
53	C₂	—	4	1	no	—
54	C₂	C₃×C₄×M₁₆	1	3	yes	—

	subgroup	G/H
center	C₃×C₄²	C₂³
commutator	C₂²	C₂×C₃×C₄²
Frattini, cosocle	C₄²	C₂³×C₃
socle	C₂²×C₃	C₂×C₄²
prime radical	C₂³×C₃	C₄²
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₃×C₄² ◁ G

Complements

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

N	H ≅ G/N	type
2. C₃×#322	C₂	semidirect
3. C₃×C₈²	C₂	semidirect
4. #1455	C₃	direct (N × H)
11. #322	C₂×C₃	semidirect
12. C₈²	C₂×C₃	semidirect
29. C₃×C₈	M₁₆	semidirect
45. C₈	C₃×M₁₆	semidirect
52. C₃	#1455	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×C₄×M₁₆	2
C₃×#322	2
C₃×C₈²	2
#1455	3

Subgroups — C3×#1455 #72170

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#1455 #72170