Subgroups — C₂×C₃×C₈² #72162

Order 384.

280 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₄×C₈	C₂	1	3	yes	maximal
2	C₃×C₈²	C₂	1	4	yes	maximal, direct product factor
3	C₂×C₈²	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
4	C₂²×C₃×C₈	C₄	1	6	yes	—
5	C₂×C₃×C₄²	C₂²	1	1	yes	characteristic
6	C₃×C₄×C₈	C₄	1	6	yes	—
7	C₃×C₄×C₈	C₂²	1	6	yes	—
8	C₂×C₄×C₈	C₂×C₃	1	3	yes	—
9	C₈²	C₂×C₃	1	4	yes	direct product factor
10	C₂²×C₃×C₄	C₂×C₄	1	3	yes	—
11	C₂×C₃×C₈	C₈	1	24	yes	direct product factor
12	C₂×C₃×C₈	C₂×C₄	1	12	yes	—
13	C₃×C₄²	C₂×C₄	1	3	yes	—
14	C₃×C₄²	C₂³	1	1	yes	characteristic
15	C₂²×C₈	C₃×C₄	1	6	yes	—
16	C₂×C₄²	C₂²×C₃	1	1	yes	characteristic
17	C₄×C₈	C₃×C₄	1	6	yes	—
18	C₄×C₈	C₂²×C₃	1	6	yes	—
19	C₂³×C₃	C₄²	1	1	yes	characteristic
20	C₂×C₃×C₄	C₄²	1	3	yes	—
21	C₂×C₃×C₄	C₂×C₈	1	12	yes	—
22	C₂×C₃×C₄	C₂²×C₄	1	3	yes	—
23	C₃×C₈	C₂×C₈	1	24	yes	direct product factor
24	C₂²×C₄	C₂×C₃×C₄	1	3	yes	—
25	C₂×C₈	C₃×C₈	1	24	yes	direct product factor
26	C₂×C₈	C₂×C₃×C₄	1	12	yes	—
27	C₄²	C₂×C₃×C₄	1	3	yes	—
28	C₄²	C₂³×C₃	1	1	yes	characteristic
29	C₂²×C₃	C₄×C₈	1	6	yes	—
30	C₂²×C₃	C₂×C₄²	1	1	yes	characteristic
31	C₃×C₄	C₄×C₈	1	6	yes	—
32	C₃×C₄	C₂²×C₈	1	6	yes	—
33	C₂³	C₃×C₄²	1	1	yes	characteristic
34	C₂×C₄	C₃×C₄²	1	3	yes	—
35	C₂×C₄	C₂×C₃×C₈	1	12	yes	—
36	C₂×C₄	C₂²×C₃×C₄	1	3	yes	—
37	C₈	C₂×C₃×C₈	1	24	yes	direct product factor
38	C₂×C₃	C₈²	1	4	yes	direct product factor
39	C₂×C₃	C₂×C₄×C₈	1	3	yes	—
40	C₂²	C₃×C₄×C₈	1	6	yes	—
41	C₂²	C₂×C₃×C₄²	1	1	yes	characteristic
42	C₄	C₃×C₄×C₈	1	6	yes	—
43	C₄	C₂²×C₃×C₈	1	6	yes	—
44	C₃	C₂×C₈²	1	1	yes	characteristic, direct product factor, Sylow
45	C₂	C₃×C₈²	1	4	yes	direct product factor
46	C₂	C₂×C₃×C₄×C₈	1	3	yes	—

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

Complements

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

N	H ≅ G/N	type
2. C₃×C₈²	C₂	direct (N × H)
3. C₂×C₈²	C₃	direct (N × H)
9. C₈²	C₂×C₃	direct (N × H)
11. C₂×C₃×C₈	C₈	direct (N × H)
23. C₃×C₈	C₂×C₈	direct (N × H)
25. C₂×C₈	C₃×C₈	direct (N × H)
37. C₈	C₂×C₃×C₈	direct (N × H)
38. C₂×C₃	C₈²	direct (N × H)
44. C₃	C₂×C₈²	direct (N × H)
45. C₂	C₃×C₈²	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×C₄×C₈	2
C₃×C₈²	2
C₂×C₈²	3

Subgroups — C2×C3×C82 #72162

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×C₈² #72162