Subgroups — C₂×C₄×#157 #64284

Order 288.

162 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#157	C₂	1	2	yes	maximal
2	C₂×C₄×C₃⋊D₃	C₂	1	1	yes	maximal, characteristic
3	C₄×#157	C₂	1	4	yes	maximal, direct product factor
4	C₂²×C₃⋊D₃	C₂²	1	1	yes	characteristic
5	C₂×#157	C₄	1	8	yes	direct product factor
6	C₂×#157	C₂²	1	4	yes	—
7	C₂×C₃²×C₄	C₄	1	1	yes	characteristic, complemented
8	C₂×C₃⋊Dic₃	C₄	1	1	yes	characteristic, complemented
9	C₄×C₃⋊D₃	C₄	1	2	yes	complemented
10	C₄×C₃⋊D₃	C₂²	1	2	yes	—
11	C₂×C₄×D₃	—	6	2	no	—
12	C₂²×C₃²	C₂×C₄	1	1	yes	characteristic
13	C₂×C₃⋊D₃	C₂×C₄	1	1	yes	characteristic
14	C₂×C₃⋊D₃	C₂×C₄	1	4	yes	—
15	C₂×C₃⋊D₃	C₂³	1	1	yes	characteristic
16	#157	C₂×C₄	1	8	yes	direct product factor
17	C₃²×C₄	C₂×C₄	1	2	yes	complemented
18	C₃⋊Dic₃	C₂×C₄	1	2	yes	complemented
19	C₂×C₄²	—	9	1	no	maximal, Sylow
20	C₂²×D₃	—	6	2	no	—
21	C₂×C₃×C₄	—	2	2	no	—
22	C₂×Dic₃	—	6	2	no	—
23	C₄×D₃	—	6	4	no	—
24	C₄×D₃	—	6	4	no	—
25	C₂×C₃²	C₄²	1	2	yes	complemented
26	C₂×C₃²	C₂²×C₄	1	1	yes	characteristic
27	C₃⋊D₃	C₄²	1	2	yes	complemented
28	C₃⋊D₃	C₂²×C₄	1	2	yes	—
29	C₂²×C₄	—	9	2	no	—
30	C₂²×C₄	—	9	1	no	—
31	C₄²	—	9	4	no	—
32	C₂²×C₃	—	2	2	no	—
33	C₂×D₃	—	6	2	no	—
34	C₂×D₃	—	6	2	no	—
35	C₂×D₃	—	6	8	no	—
36	C₃×C₄	—	2	4	no	—
37	Dic₃	—	6	4	no	—
38	C₃²	C₂×C₄²	1	1	yes	characteristic, complemented, Sylow
39	C₂³	—	9	1	no	—
40	C₂×C₄	—	9	4	no	—
41	C₂×C₄	—	9	8	no	—
42	C₂×C₄	—	9	1	no	—
43	C₂×C₄	—	9	2	no	—
44	C₂×C₄	—	9	2	no	—
45	C₂×C₄	#157	1	1	yes	characteristic, direct product factor
46	C₂×C₃	—	2	2	no	—
47	C₂×C₃	—	2	4	no	—
48	D₃	—	6	4	no	—
49	D₃	—	6	4	no	—
50	C₂²	—	9	1	no	—
51	C₂²	—	9	1	no	—
52	C₂²	—	9	4	no	—
53	C₂²	C₂×#157	1	1	yes	characteristic
54	C₄	—	9	8	no	—
55	C₄	—	9	2	no	—
56	C₄	C₂×#157	1	2	yes	direct product factor
57	C₃	—	2	2	no	—
58	C₂	—	9	2	no	—
59	C₂	—	9	2	no	—
60	C₂	C₄×#157	1	2	yes	direct product factor
61	C₂	C₂²×#157	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₄	#157
commutator, hypocenter	C₃²	C₂×C₄²
Frattini	C₂	C₂²×#157
Fitting	C₂×C₃²×C₄	C₄
socle	C₂²×C₃²	C₂×C₄
prime radical	C₂²×C₃⋊D₃	C₂²
cosocle	C₂×C₃⋊D₃	C₂³
LCS	G ▷ C₃²
UCS	C₁ ◁ C₂×C₄

Complements

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

N	H ≅ G/N	type
3. C₄×#157	C₂	direct (N × H)
5. C₂×#157	C₄	direct (N × H)
7. C₂×C₃²×C₄	C₄	semidirect
8. C₂×C₃⋊Dic₃	C₄	semidirect
9. C₄×C₃⋊D₃	C₄	semidirect
16. #157	C₂×C₄	direct (N × H)
17. C₃²×C₄	C₂×C₄	semidirect
18. C₃⋊Dic₃	C₂×C₄	semidirect
25. C₂×C₃²	C₄²	semidirect
27. C₃⋊D₃	C₄²	semidirect
38. C₃²	C₂×C₄²	semidirect
45. C₂×C₄	#157	direct (N × H)
56. C₄	C₂×#157	direct (N × H)
60. C₂	C₄×#157	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×#157	2
C₂×C₄×C₃⋊D₃	2
C₄×#157	2
C₂×C₄²	9

Subgroups — C2×C4×#157 #64284

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄×#157 #64284