Subgroups — C₂×#3750 #64132

Order 288.

276 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃²×C₄	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₃⋊Dic₃	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₃⋊Dic₃	C₂	1	1	yes	maximal, characteristic
4	#3750	C₂	1	4	yes	maximal, direct product factor
5	C₂×Dic₃⋊C₄	—	3	4	no	maximal
6	C₂³×C₃²	C₂²	1	1	yes	characteristic
7	C₂×C₃²×C₄	—	2	2	no	—
8	C₂×C₃²×C₄	C₂²	1	2	yes	—
9	C₂×C₃⋊Dic₃	—	2	2	no	—
10	C₂×C₃⋊Dic₃	C₄	1	4	yes	complemented
11	C₂×C₃⋊Dic₃	C₂²	1	2	yes	—
12	C₂×C₃⋊Dic₃	C₂²	1	2	yes	—
13	C₂²×C₃×C₄	D₃	1	4	yes	—
14	C₂²×Dic₃	—	3	4	no	—
15	C₂²×Dic₃	—	3	4	no	—
16	Dic₃⋊C₄	—	3	16	no	—
17	C₂²×C₃²	C₂×C₄	1	2	yes	—
18	C₂²×C₃²	D₄	1	2	yes	—
19	C₂²×C₃²	Q₈	1	2	yes	—
20	C₂²×C₃²	C₂³	1	1	yes	characteristic
21	C₃²×C₄	—	2	2	no	—
22	C₃⋊Dic₃	—	2	2	no	—
23	C₃⋊Dic₃	C₂×C₄	1	4	yes	complemented
24	C₂×C₄⋊C₄	—	9	1	no	Sylow
25	C₂³×C₃	C₂×D₃	1	4	yes	—
26	C₂×C₃×C₄	—	2	8	no	—
27	C₂×C₃×C₄	C₂×D₃	1	8	yes	—
28	C₂×Dic₃	—	3	16	no	—
29	C₂×Dic₃	—	3	8	no	—
30	C₂×Dic₃	—	3	8	no	—
31	C₂×Dic₃	—	6	8	no	—
32	C₂×C₃²	C₄⋊C₄	1	4	yes	complemented
33	C₂×C₃²	C₂²×C₄	1	1	yes	characteristic
34	C₂×C₃²	C₂×D₄	1	1	yes	characteristic
35	C₂×C₃²	C₂×Q₈	1	1	yes	characteristic
36	C₂²×C₄	—	9	1	no	—
37	C₂²×C₄	—	9	1	no	—
38	C₂²×C₄	C₃⋊D₃	1	1	yes	characteristic
39	C₄⋊C₄	—	9	4	no	—
40	C₂²×C₃	Dic₆	1	8	yes	—
41	C₂²×C₃	C₄×D₃	1	8	yes	—
42	C₂²×C₃	#67	1	8	yes	—
43	C₂²×C₃	C₂²×D₃	1	4	yes	—
44	C₃×C₄	—	2	8	no	—
45	Dic₃	—	3	16	no	—
46	Dic₃	—	6	8	no	—
47	C₃²	C₂×C₄⋊C₄	1	1	yes	characteristic, complemented, Sylow
48	C₂³	C₂×C₃⋊D₃	1	1	yes	characteristic
49	C₂×C₄	—	2	2	no	—
50	C₂×C₄	—	9	4	no	—
51	C₂×C₄	—	9	2	no	—
52	C₂×C₄	—	9	2	no	—
53	C₂×C₄	—	18	2	no	—
54	C₂×C₄	C₂×C₃⋊D₃	1	2	yes	—
55	C₂×C₃	Dic₃⋊C₄	1	16	yes	complemented
56	C₂×C₃	C₂×Dic₆	1	4	yes	—
57	C₂×C₃	C₂×C₄×D₃	1	4	yes	—
58	C₂×C₃	C₂×#67	1	4	yes	—
59	C₂²	#634	1	2	yes	—
60	C₂²	C₄×C₃⋊D₃	1	2	yes	—
61	C₂²	#638	1	2	yes	—
62	C₂²	C₂²×C₃⋊D₃	1	1	yes	characteristic
63	C₄	—	2	2	no	—
64	C₄	—	9	4	no	—
65	C₄	—	18	2	no	—
66	C₃	C₂×Dic₃⋊C₄	1	4	yes	complemented
67	C₂	#3750	1	4	yes	direct product factor
68	C₂	C₂×#634	1	1	yes	characteristic
69	C₂	C₂×C₄×C₃⋊D₃	1	1	yes	characteristic
70	C₂	C₂×#638	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂×C₃⋊D₃
commutator	C₂×C₃²	C₂²×C₄
Frattini	C₂²	C₂²×C₃⋊D₃
Fitting	C₂²×C₃²×C₄	C₂
socle, prime radical	C₂³×C₃²	C₂²
cosocle	C₂²×C₃²	C₂³
hypercenter	C₂²×C₄	C₃⋊D₃
hypocenter	C₃²	C₂×C₄⋊C₄
LCS	G ▷ C₂×C₃² ▷ C₃²
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄

Complements

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

N	H ≅ G/N	type
4. #3750	C₂	direct (N × H)
10. C₂×C₃⋊Dic₃	C₄	semidirect
23. C₃⋊Dic₃	C₂×C₄	semidirect
32. C₂×C₃²	C₄⋊C₄	semidirect
47. C₃²	C₂×C₄⋊C₄	semidirect
55. C₂×C₃	Dic₃⋊C₄	semidirect
66. C₃	C₂×Dic₃⋊C₄	semidirect
67. C₂	#3750	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂²×C₃²×C₄	2
C₂²×C₃⋊Dic₃	2
#3750	2
C₂×Dic₃⋊C₄	3

Subgroups — C2×#3750 #64132

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#3750 #64132