Subgroups — C₂×#3832 #64363

Order 288.

492 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	#3832	C₂	1	8	yes	maximal, direct product factor
3	C₂×C₄⋊(C₃⋊D₃)	C₂	1	3	yes	maximal, complemented
4	C₂×C₄×C₃⋊D₃	C₂	1	3	yes	maximal, complemented
5	C₂×#239	—	3	4	no	maximal
6	C₂²×C₃⋊D₃	C₂²	1	3	yes	—
7	C₃²×Q₈	C₂²	1	4	yes	complemented
8	C₂×C₃²×C₄	C₂²	1	3	yes	—
9	C₂×C₃⋊Dic₃	C₂²	1	1	yes	characteristic
10	C₄⋊(C₃⋊D₃)	C₂²	1	12	yes	complemented
11	C₄×C₃⋊D₃	C₂²	1	12	yes	complemented
12	C₂×C₃×Q₈	D₃	1	4	yes	complemented
13	#239	—	3	32	no	—
14	C₂×D₁₂	—	3	12	no	—
15	C₂×C₄×D₃	—	3	12	no	—
16	C₂²×C₃²	C₂³	1	1	yes	characteristic
17	C₂×C₃⋊D₃	—	2	6	no	—
18	C₂×C₃⋊D₃	C₂³	1	6	yes	—
19	C₃²×C₄	C₂³	1	6	yes	—
20	C₃⋊Dic₃	C₂³	1	2	yes	—
21	C₂×#41	—	9	1	no	Sylow
22	C₂²×D₃	—	3	12	no	—
23	C₃×Q₈	C₂×D₃	1	16	yes	complemented
24	C₂×C₃×C₄	C₂×D₃	1	12	yes	—
25	C₂×Dic₃	—	3	4	no	—
26	D₁₂	—	3	48	no	—
27	C₄×D₃	—	3	48	no	—
28	C₂×C₃²	#41	1	2	yes	complemented
29	C₂×C₃²	C₂⁴	1	1	yes	characteristic
30	C₃⋊D₃	—	2	6	no	—
31	#41	—	9	8	no	—
32	C₂×Q₈	C₃⋊D₃	1	1	yes	characteristic, complemented
33	C₂×D₄	—	9	3	no	—
34	C₂²×C₄	—	9	3	no	—
35	C₂²×C₃	C₂²×D₃	1	4	yes	—
36	C₂×D₃	—	3	24	no	—
37	C₂×D₃	—	6	24	no	—
38	C₃×C₄	C₂²×D₃	1	24	yes	—
39	Dic₃	—	3	8	no	—
40	C₃²	C₂×#41	1	1	yes	characteristic, complemented, Sylow
41	C₂³	—	9	3	no	—
42	Q₈	C₂×C₃⋊D₃	1	4	yes	complemented
43	D₄	—	9	12	no	—
44	C₂×C₄	—	9	1	no	—
45	C₂×C₄	—	9	12	no	—
46	C₂×C₄	C₂×C₃⋊D₃	1	3	yes	—
47	C₂×C₃	#239	1	8	yes	complemented
48	C₂×C₃	C₂³×D₃	1	4	yes	—
49	D₃	—	6	24	no	—
50	C₂²	—	9	6	no	—
51	C₂²	—	18	6	no	—
52	C₂²	C₂²×C₃⋊D₃	1	1	yes	characteristic
53	C₄	—	9	2	no	—
54	C₄	C₂²×C₃⋊D₃	1	6	yes	—
55	C₃	C₂×#239	1	4	yes	complemented
56	C₂	—	18	6	no	—
57	C₂	#3832	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
hypercenter	C₂×Q₈	C₃⋊D₃
hypocenter	C₃²	C₂×#41
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. #3832	C₂	direct (N × H)
3. C₂×C₄⋊(C₃⋊D₃)	C₂	semidirect
4. C₂×C₄×C₃⋊D₃	C₂	semidirect
7. C₃²×Q₈	C₂²	semidirect
10. C₄⋊(C₃⋊D₃)	C₂²	semidirect
11. C₄×C₃⋊D₃	C₂²	semidirect
12. C₂×C₃×Q₈	D₃	semidirect
23. C₃×Q₈	C₂×D₃	semidirect
28. C₂×C₃²	#41	semidirect
32. C₂×Q₈	C₃⋊D₃	semidirect
40. C₃²	C₂×#41	semidirect
42. Q₈	C₂×C₃⋊D₃	semidirect
47. C₂×C₃	#239	semidirect
55. C₃	C₂×#239	semidirect
57. C₂	#3832	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
#3832	2
C₂×C₄⋊(C₃⋊D₃)	2
C₂×C₄×C₃⋊D₃	2
C₂×#239	3

Subgroups — C2×#3832 #64363

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#3832 #64363