Subgroups — C₃×#2252 #72967

Order 384.

128 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#500	C₂	1	2	yes	maximal
2	C₃×#366	C₂	1	4	yes	maximal
3	C₃×C₄×C₁₆	C₂	1	1	yes	maximal, characteristic
4	#2252	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
5	C₃×C₄⋊Q₈	—	2	2	no	—
6	C₂×C₃×C₁₆	C₂²	1	2	yes	—
7	C₃×#107	—	2	2	no	—
8	C₃×#107	C₂²	1	4	yes	—
9	C₃×C₄×C₈	C₂²	1	1	yes	characteristic
10	#500	C₂×C₃	1	2	yes	—
11	#366	C₂×C₃	1	4	yes	—
12	C₄×C₁₆	C₂×C₃	1	1	yes	characteristic
13	C₂×C₃×Q₈	—	4	2	no	—
14	C₂×C₃×C₈	D₄	1	1	yes	characteristic
15	C₂×C₃×C₈	C₂³	1	1	yes	characteristic
16	C₃×C₄⋊C₄	—	2	4	no	—
17	C₃×C₄⋊C₄	—	4	2	no	—
18	C₃×C₄²	D₄	1	1	yes	characteristic
19	C₃×C₁₆	Q₈	1	4	yes	complemented
20	C₄⋊Q₈	—	2	2	no	—
21	C₂×C₁₆	C₂²×C₃	1	2	yes	—
22	#107	—	2	2	no	—
23	#107	C₂²×C₃	1	4	yes	—
24	C₄×C₈	C₂²×C₃	1	1	yes	characteristic
25	C₃×Q₈	—	8	4	no	—
26	C₂×C₃×C₄	—	4	4	no	—
27	C₂×C₃×C₄	D₈	1	1	yes	characteristic
28	C₂×C₃×C₄	D₈	1	1	yes	characteristic
29	C₂×C₃×C₄	C₂×D₄	1	1	yes	characteristic
30	C₃×C₈	Q₁₆	1	2	yes	—
31	C₃×C₈	C₂×Q₈	1	2	yes	—
32	C₂×Q₈	—	4	2	no	—
33	C₂×C₈	C₃×D₄	1	1	yes	characteristic
34	C₂×C₈	C₂³×C₃	1	1	yes	characteristic
35	C₄⋊C₄	—	2	4	no	—
36	C₄⋊C₄	—	4	2	no	—
37	C₄²	C₃×D₄	1	1	yes	characteristic
38	C₁₆	C₃×Q₈	1	4	yes	complemented
39	C₂²×C₃	C₂×D₈	1	1	yes	characteristic
40	C₃×C₄	—	8	4	no	—
41	C₃×C₄	D₁₆	1	2	yes	—
42	C₃×C₄	Q₃₂	1	2	yes	—
43	C₃×C₄	C₄⋊Q₈	1	1	yes	characteristic
44	C₃×C₄	C₂×Q₁₆	1	1	yes	characteristic
45	Q₈	—	8	4	no	—
46	C₂×C₄	—	4	4	no	—
47	C₂×C₄	C₃×D₈	1	1	yes	characteristic
48	C₂×C₄	C₃×D₈	1	1	yes	characteristic
49	C₂×C₄	C₂×C₃×D₄	1	1	yes	characteristic
50	C₈	C₃×Q₁₆	1	2	yes	—
51	C₈	C₂×C₃×Q₈	1	2	yes	—
52	C₂×C₃	#500	1	1	yes	characteristic
53	C₂×C₃	C₂×D₁₆	1	1	yes	characteristic
54	C₂×C₃	C₂×Q₃₂	1	1	yes	characteristic
55	C₂²	C₂×C₃×D₈	1	1	yes	characteristic
56	C₄	—	8	4	no	—
57	C₄	C₃×D₁₆	1	2	yes	—
58	C₄	C₃×Q₃₂	1	2	yes	—
59	C₄	C₃×C₄⋊Q₈	1	1	yes	characteristic
60	C₄	C₂×C₃×Q₁₆	1	1	yes	characteristic
61	C₃	#2252	1	1	yes	characteristic, direct product factor, Sylow
62	C₂	C₃×#500	1	1	yes	characteristic
63	C₂	C₂×C₃×D₁₆	1	1	yes	characteristic
64	C₂	C₂×C₃×Q₃₂	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂²×C₃	C₂×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂³×C₃
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×C₄² ◁ C₃×C₄×C₈ ◁ G

Complements

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

N	H ≅ G/N	type
4. #2252	C₃	direct (N × H)
19. C₃×C₁₆	Q₈	semidirect
38. C₁₆	C₃×Q₈	semidirect
61. C₃	#2252	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×#500	2
C₃×#366	2
C₃×C₄×C₁₆	2
#2252	3

Subgroups — C3×#2252 #72967

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#2252 #72967