Subgroups — C₂×C₂²⋊#157 #64293

Order 288.

266 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₃⋊D₃	C₂	1	1	yes	maximal, characteristic
2	C₂²×#157	C₂	1	2	yes	maximal, complemented
3	C₂²⋊#157	C₂	1	4	yes	maximal, direct product factor
4	C₂³×C₃²	C₄	1	1	yes	characteristic, complemented
5	C₂²×C₃⋊D₃	—	2	4	no	—
6	C₂²×C₃⋊D₃	C₄	1	2	yes	complemented
7	C₂²×C₃⋊D₃	C₄	1	1	yes	characteristic, complemented
8	C₂²×C₃⋊D₃	C₂²	1	2	yes	—
9	C₂²×C₃⋊D₃	C₂²	1	1	yes	characteristic
10	C₂×#157	—	2	4	no	—
11	C₂×#157	C₂²	1	4	yes	complemented
12	C₂³×D₃	—	6	2	no	—
13	C₂²×C₃²	—	2	2	no	—
14	C₂²×C₃²	C₂×C₄	1	1	yes	characteristic
15	C₂²×C₃²	C₂×C₄	1	2	yes	complemented
16	C₂×C₃⋊D₃	—	2	2	no	—
17	C₂×C₃⋊D₃	—	2	4	no	—
18	C₂×C₃⋊D₃	—	2	4	no	—
19	C₂×C₃⋊D₃	C₂×C₄	1	1	yes	characteristic
20	C₂×C₃⋊D₃	C₂×C₄	1	2	yes	complemented
21	C₂×C₃⋊D₃	D₄	1	4	yes	—
22	C₂×C₃⋊D₃	C₂³	1	1	yes	characteristic
23	#157	—	2	4	no	—
24	C₂×C₂²⋊C₄	—	9	1	no	maximal, Sylow
25	C₂³×C₃	—	2	2	no	—
26	C₂²×D₃	—	6	2	no	—
27	C₂²×D₃	—	6	4	no	—
28	C₂²×D₃	—	6	2	no	—
29	C₂²×D₃	—	6	4	no	—
30	C₂²×D₃	—	6	16	no	—
31	C₂×C₃²	—	2	2	no	—
32	C₂×C₃²	C₂²⋊C₄	1	2	yes	complemented
33	C₂×C₃²	C₂²×C₄	1	1	yes	characteristic
34	C₃⋊D₃	—	2	2	no	—
35	C₃⋊D₃	C₂²⋊C₄	1	2	yes	complemented
36	C₃⋊D₃	C₂×D₄	1	2	yes	—
37	C₂⁴	—	9	1	no	—
38	C₂²×C₄	—	9	2	no	—
39	C₂²⋊C₄	—	9	4	no	—
40	C₂²×C₃	—	2	8	no	—
41	C₂²×C₃	—	2	2	no	—
42	C₂²×C₃	—	2	4	no	—
43	C₂×D₃	—	6	2	no	—
44	C₂×D₃	—	6	4	no	—
45	C₂×D₃	—	6	8	no	—
46	C₂×D₃	—	6	2	no	—
47	C₂×D₃	—	6	16	no	—
48	C₂×D₃	—	6	16	no	—
49	C₂×D₃	—	6	8	no	—
50	C₃²	C₂×C₂²⋊C₄	1	1	yes	characteristic, complemented, Sylow
51	C₂³	—	9	1	no	—
52	C₂³	—	9	1	no	—
53	C₂³	—	9	2	no	—
54	C₂³	—	9	2	no	—
55	C₂³	—	18	4	no	—
56	C₂³	#157	1	1	yes	characteristic, complemented
57	C₂×C₄	—	9	4	no	—
58	C₂×C₄	—	18	4	no	—
59	C₂×C₃	—	2	8	no	—
60	C₂×C₃	—	2	2	no	—
61	C₂×C₃	—	2	4	no	—
62	D₃	—	6	4	no	—
63	D₃	—	6	4	no	—
64	D₃	—	6	8	no	—
65	C₂²	—	2	2	no	—
66	C₂²	—	9	1	no	—
67	C₂²	—	9	1	no	—
68	C₂²	—	9	4	no	—
69	C₂²	—	9	2	no	—
70	C₂²	—	18	4	no	—
71	C₂²	—	18	4	no	—
72	C₂²	—	18	2	no	—
73	C₂²	C₂×#157	1	1	yes	characteristic
74	C₂²	C₂×#157	1	2	yes	complemented
75	C₄	—	18	4	no	—
76	C₃	—	2	2	no	—
77	C₂	—	2	2	no	—
78	C₂	—	9	2	no	—
79	C₂	—	9	2	no	—
80	C₂	—	18	2	no	—
81	C₂	C₂²⋊#157	1	2	yes	direct product factor
82	C₂	C₂²×#157	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
2. C₂²×#157	C₂	semidirect
3. C₂²⋊#157	C₂	direct (N × H)
4. C₂³×C₃²	C₄	semidirect
6. C₂²×C₃⋊D₃	C₄	semidirect
7. C₂²×C₃⋊D₃	C₄	semidirect
11. C₂×#157	C₂²	semidirect
15. C₂²×C₃²	C₂×C₄	semidirect
20. C₂×C₃⋊D₃	C₂×C₄	semidirect
32. C₂×C₃²	C₂²⋊C₄	semidirect
35. C₃⋊D₃	C₂²⋊C₄	semidirect
50. C₃²	C₂×C₂²⋊C₄	semidirect
56. C₂³	#157	semidirect
74. C₂²	C₂×#157	semidirect
81. C₂	C₂²⋊#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
C₂³×C₃⋊D₃	2
C₂²×#157	2
C₂²⋊#157	2
C₂×C₂²⋊C₄	9

Subgroups — C2×C22⋊#157 #64293

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₂²⋊#157 #64293