Subgroups — C₃×#1416 #67976

Order 384.

74 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×Q₃₂	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×C₃₂	C₂	1	1	yes	maximal, characteristic
3	C₃×#366	C₂	1	1	yes	maximal, characteristic
4	#1416	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
5	C₂×C₃×Q₁₆	—	2	1	no	—
6	C₃×Q₃₂	—	2	1	no	—
7	C₃×Q₃₂	C₄	1	2	yes	complemented
8	C₂×C₃×C₁₆	C₂²	1	1	yes	characteristic
9	C₃×#107	—	2	1	no	—
10	C₃×C₃₂	—	2	1	no	—
11	C₂×Q₃₂	C₂×C₃	1	1	yes	characteristic
12	C₂×C₃₂	C₂×C₃	1	1	yes	characteristic
13	#366	C₂×C₃	1	1	yes	characteristic
14	C₂×C₃×Q₈	—	4	1	no	—
15	C₃×Q₁₆	—	2	2	no	—
16	C₃×Q₁₆	—	4	1	no	—
17	C₂×C₃×C₈	D₄	1	1	yes	characteristic
18	C₃×C₄⋊C₄	—	4	1	no	—
19	C₃×C₁₆	C₂×C₄	1	1	yes	characteristic
20	C₃×C₁₆	D₄	1	1	yes	characteristic
21	C₂×Q₁₆	—	2	1	no	—
22	Q₃₂	—	2	1	no	—
23	Q₃₂	C₃×C₄	1	2	yes	complemented
24	C₂×C₁₆	C₂²×C₃	1	1	yes	characteristic
25	#107	—	2	1	no	—
26	C₃₂	—	2	1	no	—
27	C₃×Q₈	—	4	2	no	—
28	C₃×Q₈	—	8	1	no	—
29	C₂×C₃×C₄	—	8	1	no	—
30	C₂×C₃×C₄	—	8	1	no	—
31	C₂×C₃×C₄	D₈	1	1	yes	characteristic
32	C₃×C₈	C₂²⋊C₄	1	1	yes	characteristic
33	C₃×C₈	SD₁₆	1	1	yes	characteristic
34	C₂×Q₈	—	4	1	no	—
35	Q₁₆	—	2	2	no	—
36	Q₁₆	—	4	1	no	—
37	C₂×C₈	C₃×D₄	1	1	yes	characteristic
38	C₄⋊C₄	—	4	1	no	—
39	C₁₆	C₂×C₃×C₄	1	1	yes	characteristic
40	C₁₆	C₃×D₄	1	1	yes	characteristic
41	C₂²×C₃	D₁₆	1	1	yes	characteristic
42	C₃×C₄	—	8	2	no	—
43	C₃×C₄	—	16	1	no	—
44	C₃×C₄	#102	1	1	yes	characteristic
45	C₃×C₄	SD₃₂	1	1	yes	characteristic
46	Q₈	—	4	2	no	—
47	Q₈	—	8	1	no	—
48	C₂×C₄	—	8	1	no	—
49	C₂×C₄	—	8	1	no	—
50	C₂×C₄	C₃×D₈	1	1	yes	characteristic
51	C₈	C₃×C₂²⋊C₄	1	1	yes	characteristic
52	C₈	C₃×SD₁₆	1	1	yes	characteristic
53	C₂×C₃	#357	1	1	yes	characteristic
54	C₂×C₃	SD₆₄	1	1	yes	characteristic
55	C₂×C₃	Q₆₄	1	1	yes	characteristic
56	C₂²	C₃×D₁₆	1	1	yes	characteristic
57	C₄	—	8	2	no	—
58	C₄	—	16	1	no	—
59	C₄	C₃×#102	1	1	yes	characteristic
60	C₄	C₃×SD₃₂	1	1	yes	characteristic
61	C₃	#1416	1	1	yes	characteristic, direct product factor, Sylow
62	C₂	C₃×#357	1	1	yes	characteristic
63	C₂	C₃×SD₆₄	1	1	yes	characteristic
64	C₂	C₃×Q₆₄	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂²×C₃	D₁₆
commutator	C₁₆	C₂×C₃×C₄
Frattini, cosocle	C₂×C₁₆	C₂²×C₃
LCS	G ▷ C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃ ◁ C₂×C₃×C₄ ◁ C₂×C₃×C₈ ◁ C₂×C₃×C₁₆ ◁ G

Complements

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

N	H ≅ G/N	type
4. #1416	C₃	direct (N × H)
7. C₃×Q₃₂	C₄	semidirect
23. Q₃₂	C₃×C₄	semidirect
61. C₃	#1416	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₃×Q₃₂	2
C₂×C₃×C₃₂	2
C₃×#366	2
#1416	3

Subgroups — C3×#1416 #67976

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#1416 #67976