Subgroups — C₂×Q₈×C₃⋊D₃ #64362

Order 288.

468 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	Q₈×C₃⋊D₃	C₂	1	8	yes	maximal, direct product factor
3	C₂×C₄×C₃⋊D₃	C₂	1	3	yes	maximal
4	C₂×#634	C₂	1	3	yes	maximal, complemented
5	C₂×D₃×Q₈	—	3	4	no	maximal
6	C₂²×C₃⋊D₃	C₂²	1	1	yes	characteristic
7	C₃²×Q₈	C₂²	1	4	yes	complemented
8	C₂×C₃²×C₄	C₂²	1	3	yes	—
9	C₂×C₃⋊Dic₃	C₂²	1	3	yes	—
10	C₄×C₃⋊D₃	C₂²	1	12	yes	—
11	#634	C₂²	1	12	yes	complemented
12	C₂×C₃×Q₈	D₃	1	4	yes	complemented
13	D₃×Q₈	—	3	32	no	—
14	C₂×C₄×D₃	—	3	12	no	—
15	C₂×Dic₆	—	3	12	no	—
16	C₂²×C₃²	C₂³	1	1	yes	characteristic
17	C₂×C₃⋊D₃	Q₈	1	4	yes	direct product factor
18	C₂×C₃⋊D₃	C₂³	1	2	yes	—
19	C₃²×C₄	C₂³	1	6	yes	—
20	C₃⋊Dic₃	C₂³	1	6	yes	—
21	C₂²×Q₈	—	9	1	no	Sylow
22	C₂²×D₃	—	3	4	no	—
23	C₃×Q₈	C₂×D₃	1	16	yes	complemented
24	C₂×C₃×C₄	C₂×D₃	1	12	yes	—
25	C₂×Dic₃	—	3	12	no	—
26	C₄×D₃	—	3	48	no	—
27	Dic₆	—	3	48	no	—
28	C₂×C₃²	C₂×Q₈	1	2	yes	complemented
29	C₂×C₃²	C₂⁴	1	1	yes	characteristic
30	C₃⋊D₃	C₂×Q₈	1	4	yes	direct product factor
31	C₂×Q₈	—	9	8	no	—
32	C₂×Q₈	—	9	3	no	—
33	C₂×Q₈	C₃⋊D₃	1	1	yes	characteristic, direct product factor
34	C₂²×C₄	—	9	3	no	—
35	C₂²×C₃	C₂²×D₃	1	4	yes	—
36	C₂×D₃	—	3	16	no	—
37	C₂×D₃	—	3	8	no	—
38	C₃×C₄	C₂²×D₃	1	24	yes	—
39	Dic₃	—	3	24	no	—
40	C₃²	C₂²×Q₈	1	1	yes	characteristic, complemented, Sylow
41	C₂³	—	9	1	no	—
42	Q₈	—	9	12	no	—
43	Q₈	C₂×C₃⋊D₃	1	4	yes	direct product factor
44	C₂×C₄	—	9	3	no	—
45	C₂×C₄	—	9	12	no	—
46	C₂×C₄	C₂×C₃⋊D₃	1	3	yes	—
47	C₂×C₃	D₃×Q₈	1	8	yes	complemented
48	C₂×C₃	C₂³×D₃	1	4	yes	—
49	D₃	—	3	16	no	—
50	C₂²	—	9	2	no	—
51	C₂²	—	9	4	no	—
52	C₂²	C₂²×C₃⋊D₃	1	1	yes	characteristic
53	C₄	—	9	6	no	—
54	C₄	C₂²×C₃⋊D₃	1	6	yes	—
55	C₃	C₂×D₃×Q₈	1	4	yes	complemented
56	C₂	—	9	4	no	—
57	C₂	Q₈×C₃⋊D₃	1	2	yes	direct product factor
58	C₂	C₂³×C₃⋊D₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²×C₃⋊D₃
commutator, cosocle	C₂×C₃²	C₂⁴
Frattini	C₂	C₂³×C₃⋊D₃
Fitting	C₂×C₃²×Q₈	C₂
socle	C₂²×C₃²	C₂³
prime radical	C₂²×C₃⋊D₃	C₂²
hypercenter	C₂×Q₈	C₃⋊D₃
hypocenter	C₃²	C₂²×Q₈
LCS	G ▷ C₂×C₃² ▷ C₃²
UCS	C₁ ◁ C₂² ◁ C₂×Q₈

Complements

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

N	H ≅ G/N	type
1. C₂×C₃²×Q₈	C₂	semidirect
2. Q₈×C₃⋊D₃	C₂	direct (N × H)
4. C₂×#634	C₂	semidirect
7. C₃²×Q₈	C₂²	semidirect
11. #634	C₂²	semidirect
12. C₂×C₃×Q₈	D₃	semidirect
17. C₂×C₃⋊D₃	Q₈	direct (N × H)
23. C₃×Q₈	C₂×D₃	semidirect
28. C₂×C₃²	C₂×Q₈	semidirect
30. C₃⋊D₃	C₂×Q₈	direct (N × H)
33. C₂×Q₈	C₃⋊D₃	direct (N × H)
40. C₃²	C₂²×Q₈	semidirect
43. Q₈	C₂×C₃⋊D₃	direct (N × H)
47. C₂×C₃	D₃×Q₈	semidirect
55. C₃	C₂×D₃×Q₈	semidirect
57. C₂	Q₈×C₃⋊D₃	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
Q₈×C₃⋊D₃	2
C₂×C₄×C₃⋊D₃	2
C₂×#634	2
C₂×D₃×Q₈	3

Subgroups — C2×Q8×C3⋊D3 #64362

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×Q₈×C₃⋊D₃ #64362