Subgroups — C₂×#3754 #64142

Order 288.

204 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃²×D₄	C₂	1	1	yes	maximal, characteristic
2	C₂×#634	C₂	1	1	yes	maximal, characteristic, complemented
3	#3754	C₂	1	4	yes	maximal, direct product factor
4	C₂×C₃⋊(C₃⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#214	—	3	4	no	maximal
6	C₂³×C₃²	—	2	1	no	—
7	C₃²×D₄	—	2	1	no	—
8	C₃²×D₄	C₂²	1	2	yes	—
9	C₂×C₃²×C₄	C₂²	1	1	yes	characteristic
10	C₂×C₃⋊Dic₃	—	2	1	no	—
11	#634	—	2	1	no	—
12	#634	C₂²	1	2	yes	complemented
13	C₃⋊(C₃⋊C₈)	C₂²	1	2	yes	complemented
14	C₂×C₃×D₄	D₃	1	4	yes	—
15	C₂×Dic₆	—	3	4	no	—
16	#214	—	3	16	no	—
17	C₂×C₃⋊C₈	—	3	4	no	—
18	C₂²×C₃²	—	2	2	no	—
19	C₂²×C₃²	—	4	2	no	—
20	C₂²×C₃²	D₄	1	1	yes	characteristic
21	C₃²×C₄	D₄	1	1	yes	characteristic
22	C₃²×C₄	C₂³	1	1	yes	characteristic
23	C₃⋊Dic₃	—	2	2	no	—
24	C₂×SD₁₆	—	9	1	no	Sylow
25	C₂³×C₃	—	2	4	no	—
26	C₃×D₄	—	2	4	no	—
27	C₃×D₄	C₂×D₃	1	8	yes	—
28	C₂×C₃×C₄	C₂×D₃	1	4	yes	—
29	C₂×Dic₃	—	6	4	no	—
30	Dic₆	—	3	8	no	—
31	Dic₆	—	6	4	no	—
32	C₃⋊C₈	—	3	8	no	—
33	C₂×C₃²	—	4	2	no	—
34	C₂×C₃²	SD₁₆	1	2	yes	complemented
35	C₂×C₃²	C₂×D₄	1	1	yes	characteristic
36	C₂×Q₈	—	9	1	no	—
37	C₂×D₄	C₃⋊D₃	1	1	yes	characteristic
38	SD₁₆	—	9	4	no	—
39	C₂×C₈	—	9	1	no	—
40	C₂²×C₃	—	2	8	no	—
41	C₂²×C₃	—	4	8	no	—
42	C₂²×C₃	#67	1	4	yes	—
43	C₃×C₄	#67	1	4	yes	—
44	C₃×C₄	C₂²×D₃	1	4	yes	—
45	Dic₃	—	6	8	no	—
46	C₃²	C₂×SD₁₆	1	1	yes	characteristic, complemented, Sylow
47	C₂³	—	2	1	no	—
48	Q₈	—	9	2	no	—
49	Q₈	—	18	1	no	—
50	D₄	—	2	1	no	—
51	D₄	C₂×C₃⋊D₃	1	2	yes	—
52	C₂×C₄	—	18	1	no	—
53	C₂×C₄	C₂×C₃⋊D₃	1	1	yes	characteristic
54	C₈	—	9	2	no	—
55	C₂×C₃	—	4	8	no	—
56	C₂×C₃	#214	1	8	yes	complemented
57	C₂×C₃	C₂×#67	1	4	yes	—
58	C₂²	—	2	2	no	—
59	C₂²	—	4	2	no	—
60	C₂²	#638	1	1	yes	characteristic
61	C₄	—	18	2	no	—
62	C₄	#638	1	1	yes	characteristic
63	C₄	C₂²×C₃⋊D₃	1	1	yes	characteristic
64	C₃	C₂×#214	1	4	yes	complemented
65	C₂	—	4	2	no	—
66	C₂	#3754	1	2	yes	direct product factor
67	C₂	C₂×#638	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#638
commutator, cosocle	C₃²×C₄	C₂³
Frattini	C₄	C₂²×C₃⋊D₃
Fitting, prime radical	C₂×C₃²×D₄	C₂
socle	C₂²×C₃²	D₄
hypercenter	C₂×D₄	C₃⋊D₃
hypocenter	C₃²	C₂×SD₁₆
LCS	G ▷ C₃²×C₄ ▷ C₂×C₃² ▷ C₃²
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×D₄

Complements

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

N	H ≅ G/N	type
2. C₂×#634	C₂	semidirect
3. #3754	C₂	direct (N × H)
4. C₂×C₃⋊(C₃⋊C₈)	C₂	semidirect
12. #634	C₂²	semidirect
13. C₃⋊(C₃⋊C₈)	C₂²	semidirect
34. C₂×C₃²	SD₁₆	semidirect
46. C₃²	C₂×SD₁₆	semidirect
56. C₂×C₃	#214	semidirect
64. C₃	C₂×#214	semidirect
66. C₂	#3754	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×D₄	2
C₂×#634	2
#3754	2
C₂×C₃⋊(C₃⋊C₈)	2
C₂×#214	3

Subgroups — C2×#3754 #64142

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#3754 #64142