Subgroups — C₂×C₃²×SD₁₆ #64182

Order 288.

204 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃²×Q₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃²×D₄	C₂	1	1	yes	maximal, characteristic
3	C₃²×SD₁₆	C₂	1	4	yes	maximal, direct product factor
4	C₂×C₃²×C₈	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₃×SD₁₆	C₃	1	4	yes	maximal, direct product factor
6	C₂³×C₃²	—	2	1	no	—
7	C₃²×Q₈	—	2	1	no	—
8	C₃²×Q₈	C₂²	1	2	yes	complemented
9	C₃²×D₄	—	2	1	no	—
10	C₃²×D₄	C₂²	1	2	yes	—
11	C₂×C₃²×C₄	—	2	1	no	—
12	C₂×C₃²×C₄	C₂²	1	1	yes	characteristic
13	C₃²×C₈	C₂²	1	2	yes	complemented
14	C₂×C₃×Q₈	C₂×C₃	1	4	yes	complemented
15	C₂×C₃×D₄	C₂×C₃	1	4	yes	—
16	C₃×SD₁₆	C₂×C₃	1	16	yes	direct product factor
17	C₂×C₃×C₈	C₂×C₃	1	4	yes	complemented
18	C₂²×C₃²	—	2	2	no	—
19	C₂²×C₃²	—	4	2	no	—
20	C₂²×C₃²	D₄	1	1	yes	characteristic
21	C₃²×C₄	—	2	2	no	—
22	C₃²×C₄	D₄	1	1	yes	characteristic
23	C₃²×C₄	C₂³	1	1	yes	characteristic
24	C₂×SD₁₆	C₃²	1	1	yes	characteristic, direct product factor, Sylow
25	C₂³×C₃	—	2	4	no	—
26	C₃×Q₈	—	2	4	no	—
27	C₃×Q₈	C₂²×C₃	1	8	yes	complemented
28	C₃×D₄	—	2	4	no	—
29	C₃×D₄	C₂²×C₃	1	8	yes	—
30	C₂×C₃×C₄	—	2	4	no	—
31	C₂×C₃×C₄	C₂²×C₃	1	4	yes	—
32	C₃×C₈	C₂²×C₃	1	8	yes	complemented
33	C₂×C₃²	—	4	2	no	—
34	C₂×C₃²	SD₁₆	1	2	yes	direct product factor
35	C₂×C₃²	C₂×D₄	1	1	yes	characteristic
36	C₂×Q₈	C₂×C₃²	1	1	yes	characteristic, complemented
37	C₂×D₄	C₂×C₃²	1	1	yes	characteristic
38	SD₁₆	C₂×C₃²	1	4	yes	direct product factor
39	C₂×C₈	C₂×C₃²	1	1	yes	characteristic, complemented
40	C₂²×C₃	—	2	8	no	—
41	C₂²×C₃	—	4	8	no	—
42	C₂²×C₃	C₃×D₄	1	4	yes	—
43	C₃×C₄	—	2	8	no	—
44	C₃×C₄	C₃×D₄	1	4	yes	—
45	C₃×C₄	C₂³×C₃	1	4	yes	—
46	C₃²	C₂×SD₁₆	1	1	yes	characteristic, direct product factor, Sylow
47	C₂³	—	2	1	no	—
48	Q₈	—	2	1	no	—
49	Q₈	C₂²×C₃²	1	2	yes	complemented
50	D₄	—	2	1	no	—
51	D₄	C₂²×C₃²	1	2	yes	—
52	C₂×C₄	—	2	1	no	—
53	C₂×C₄	C₂²×C₃²	1	1	yes	characteristic
54	C₈	C₂²×C₃²	1	2	yes	complemented
55	C₂×C₃	—	4	8	no	—
56	C₂×C₃	C₃×SD₁₆	1	8	yes	direct product factor
57	C₂×C₃	C₂×C₃×D₄	1	4	yes	—
58	C₂²	—	2	2	no	—
59	C₂²	—	4	2	no	—
60	C₂²	C₃²×D₄	1	1	yes	characteristic
61	C₄	—	2	2	no	—
62	C₄	C₃²×D₄	1	1	yes	characteristic
63	C₄	C₂³×C₃²	1	1	yes	characteristic
64	C₃	C₂×C₃×SD₁₆	1	4	yes	direct product factor
65	C₂	—	4	2	no	—
66	C₂	C₃²×SD₁₆	1	2	yes	direct product factor
67	C₂	C₂×C₃²×D₄	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃²	D₄
commutator, Frattini, cosocle	C₄	C₂³×C₃²
prime radical	C₂×C₃²×D₄	C₂
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃² ◁ C₂×C₃²×C₄ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₃²×Q₈	C₂	semidirect
3. C₃²×SD₁₆	C₂	direct (N × H)
4. C₂×C₃²×C₈	C₂	semidirect
5. C₂×C₃×SD₁₆	C₃	direct (N × H)
8. C₃²×Q₈	C₂²	semidirect
13. C₃²×C₈	C₂²	semidirect
14. C₂×C₃×Q₈	C₂×C₃	semidirect
16. C₃×SD₁₆	C₂×C₃	direct (N × H)
17. C₂×C₃×C₈	C₂×C₃	semidirect
24. C₂×SD₁₆	C₃²	direct (N × H)
27. C₃×Q₈	C₂²×C₃	semidirect
32. C₃×C₈	C₂²×C₃	semidirect
34. C₂×C₃²	SD₁₆	direct (N × H)
36. C₂×Q₈	C₂×C₃²	semidirect
38. SD₁₆	C₂×C₃²	direct (N × H)
39. C₂×C₈	C₂×C₃²	semidirect
46. C₃²	C₂×SD₁₆	direct (N × H)
49. Q₈	C₂²×C₃²	semidirect
54. C₈	C₂²×C₃²	semidirect
56. C₂×C₃	C₃×SD₁₆	direct (N × H)
64. C₃	C₂×C₃×SD₁₆	direct (N × H)
66. C₂	C₃²×SD₁₆	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×C₃²×Q₈	2
C₂×C₃²×D₄	2
C₃²×SD₁₆	2
C₂×C₃²×C₈	2
C₂×C₃×SD₁₆	3

Subgroups — C2×C32×SD16 #64182

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃²×SD₁₆ #64182