Subgroups — C₃×#2247 #72962

Order 384.

176 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×Q₃₂	C₂	1	4	yes	maximal
2	C₃×#494	C₂	1	2	yes	maximal
3	C₃×C₄×C₁₆	C₂	1	1	yes	maximal, characteristic
4	#2247	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
5	C₂×C₃×Q₁₆	—	2	2	no	—
6	C₂×C₃×Q₁₆	C₂²	1	4	yes	—
7	C₃×C₄⋊Q₈	—	2	2	no	—
8	C₃×Q₃₂	—	2	8	no	—
9	C₂×C₃×C₁₆	C₂²	1	2	yes	—
10	C₃×C₄×C₈	C₂²	1	1	yes	characteristic
11	C₂×Q₃₂	C₂×C₃	1	4	yes	—
12	#494	C₂×C₃	1	2	yes	—
13	C₄×C₁₆	C₂×C₃	1	1	yes	characteristic
14	C₂×C₃×Q₈	—	2	4	no	—
15	C₃×Q₁₆	—	2	8	no	—
16	C₃×Q₁₆	—	4	4	no	—
17	C₂×C₃×C₈	D₄	1	1	yes	characteristic
18	C₂×C₃×C₈	C₂³	1	1	yes	characteristic
19	C₃×C₄⋊C₄	—	4	4	no	—
20	C₃×C₄²	D₄	1	1	yes	characteristic
21	C₃×C₁₆	D₄	1	4	yes	—
22	C₂×Q₁₆	—	2	2	no	—
23	C₂×Q₁₆	C₂²×C₃	1	4	yes	—
24	C₄⋊Q₈	—	2	2	no	—
25	Q₃₂	—	2	8	no	—
26	C₂×C₁₆	C₂²×C₃	1	2	yes	—
27	C₄×C₈	C₂²×C₃	1	1	yes	characteristic
28	C₃×Q₈	—	4	4	no	—
29	C₃×Q₈	—	4	4	no	—
30	C₂×C₃×C₄	—	4	4	no	—
31	C₂×C₃×C₄	D₈	1	2	yes	—
32	C₂×C₃×C₄	C₂×D₄	1	1	yes	characteristic
33	C₃×C₈	D₈	1	2	yes	—
34	C₃×C₈	C₂×D₄	1	2	yes	—
35	C₂×Q₈	—	2	4	no	—
36	Q₁₆	—	2	8	no	—
37	Q₁₆	—	4	4	no	—
38	C₂×C₈	C₃×D₄	1	1	yes	characteristic
39	C₂×C₈	C₂³×C₃	1	1	yes	characteristic
40	C₄⋊C₄	—	4	4	no	—
41	C₄²	C₃×D₄	1	1	yes	characteristic
42	C₁₆	C₃×D₄	1	4	yes	—
43	C₂²×C₃	C₂×D₈	1	1	yes	characteristic
44	C₃×C₄	—	8	4	no	—
45	C₃×C₄	Q₃₂	1	4	yes	complemented
46	C₃×C₄	#127	1	1	yes	characteristic
47	C₃×C₄	C₂×D₈	1	1	yes	characteristic
48	Q₈	—	4	4	no	—
49	Q₈	—	4	4	no	—
50	C₂×C₄	—	4	4	no	—
51	C₂×C₄	C₃×D₈	1	2	yes	—
52	C₂×C₄	C₂×C₃×D₄	1	1	yes	characteristic
53	C₈	C₃×D₈	1	2	yes	—
54	C₈	C₂×C₃×D₄	1	2	yes	—
55	C₂×C₃	#493	1	1	yes	characteristic
56	C₂×C₃	C₂×Q₃₂	1	2	yes	—
57	C₂²	C₂×C₃×D₈	1	1	yes	characteristic
58	C₄	—	8	4	no	—
59	C₄	C₃×Q₃₂	1	4	yes	complemented
60	C₄	C₃×#127	1	1	yes	characteristic
61	C₄	C₂×C₃×D₈	1	1	yes	characteristic
62	C₃	#2247	1	1	yes	characteristic, direct product factor, Sylow
63	C₂	C₃×#493	1	1	yes	characteristic
64	C₂	C₂×C₃×Q₃₂	1	2	yes	—

	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. #2247	C₃	direct (N × H)
45. C₃×C₄	Q₃₂	semidirect
59. C₄	C₃×Q₃₂	semidirect
62. C₃	#2247	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
C₃×#494	2
C₃×C₄×C₁₆	2
#2247	3

Subgroups — C3×#2247 #72962

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#2247 #72962