Subgroups — C₂×C₄⋊#157 #64285

Order 288.

146 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	—	2	4	no	—
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	D₄	1	2	yes	—
15	C₂×C₃⋊D₃	Q₈	1	2	yes	—
16	C₂×C₃⋊D₃	C₂³	1	1	yes	characteristic
17	#157	—	2	4	no	—
18	C₃²×C₄	C₂×C₄	1	2	yes	complemented
19	C₃⋊Dic₃	C₂×C₄	1	2	yes	complemented
20	C₂×C₄⋊C₄	—	9	1	no	maximal, Sylow
21	C₂²×D₃	—	6	2	no	—
22	C₂×C₃×C₄	—	2	2	no	—
23	C₂×Dic₃	—	6	2	no	—
24	C₄×D₃	—	6	4	no	—
25	C₄×D₃	—	6	4	no	—
26	C₂×C₃²	C₄⋊C₄	1	2	yes	complemented
27	C₂×C₃²	C₂²×C₄	1	1	yes	characteristic
28	C₃⋊D₃	C₄⋊C₄	1	2	yes	complemented
29	C₃⋊D₃	C₂×D₄	1	1	yes	characteristic
30	C₃⋊D₃	C₂×Q₈	1	1	yes	characteristic
31	C₂²×C₄	—	9	1	no	—
32	C₂²×C₄	—	9	2	no	—
33	C₄⋊C₄	—	9	4	no	—
34	C₂²×C₃	—	2	2	no	—
35	C₂×D₃	—	6	2	no	—
36	C₂×D₃	—	6	2	no	—
37	C₂×D₃	—	6	4	no	—
38	C₂×D₃	—	6	4	no	—
39	C₃×C₄	—	2	4	no	—
40	Dic₃	—	6	4	no	—
41	C₃²	C₂×C₄⋊C₄	1	1	yes	characteristic, complemented, Sylow
42	C₂³	—	9	1	no	—
43	C₂×C₄	—	9	1	no	—
44	C₂×C₄	—	9	2	no	—
45	C₂×C₄	—	9	2	no	—
46	C₂×C₄	—	9	4	no	—
47	C₂×C₄	—	18	4	no	—
48	C₂×C₄	#157	1	1	yes	characteristic, complemented
49	C₂×C₃	—	2	2	no	—
50	C₂×C₃	—	2	4	no	—
51	D₃	—	6	4	no	—
52	D₃	—	6	2	no	—
53	D₃	—	6	2	no	—
54	C₂²	—	9	1	no	—
55	C₂²	—	9	1	no	—
56	C₂²	—	9	2	no	—
57	C₂²	—	9	2	no	—
58	C₂²	C₂×#157	1	1	yes	characteristic
59	C₄	—	9	2	no	—
60	C₄	—	18	4	no	—
61	C₄	C₂×#157	1	2	yes	complemented
62	C₃	—	2	2	no	—
63	C₂	—	9	1	no	—
64	C₂	—	9	1	no	—
65	C₂	—	9	2	no	—
66	C₂	C₄⋊#157	1	2	yes	direct product factor
67	C₂	C₂²×#157	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×#157
commutator	C₂×C₃²	C₂²×C₄
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
hypercenter	C₂×C₄	#157
hypocenter	C₃²	C₂×C₄⋊C₄
LCS	G ▷ C₂×C₃² ▷ C₃²
UCS	C₁ ◁ C₂² ◁ 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)
7. C₂×C₃²×C₄	C₄	semidirect
8. C₂×C₃⋊Dic₃	C₄	semidirect
9. C₄×C₃⋊D₃	C₄	semidirect
18. C₃²×C₄	C₂×C₄	semidirect
19. C₃⋊Dic₃	C₂×C₄	semidirect
26. C₂×C₃²	C₄⋊C₄	semidirect
28. C₃⋊D₃	C₄⋊C₄	semidirect
41. C₃²	C₂×C₄⋊C₄	semidirect
48. C₂×C₄	#157	semidirect
61. C₄	C₂×#157	semidirect
66. 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×C₄⋊C₄	9

Subgroups — C2×C4⋊#157 #64285

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄⋊#157 #64285