Subgroups — C₂×#3788 #64282

Order 288.

122 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×C₃⋊D₃	C₂	1	1	yes	maximal, characteristic
2	C₂×#622	C₂	1	2	yes	maximal, complemented
3	#3788	C₂	1	4	yes	maximal, direct product factor
4	C₂²×C₃⋊D₃	C₄	1	1	yes	characteristic
5	C₂×C₃²×C₄	C₄	1	1	yes	characteristic
6	C₂×C₃⋊Dic₃	C₂²	1	1	yes	characteristic
7	C₄×C₃⋊D₃	C₄	1	2	yes	—
8	C₄×C₃⋊D₃	C₂²	1	2	yes	—
9	#622	C₂²	1	4	yes	complemented
10	C₂×C₄×D₃	—	6	2	no	—
11	C₂²×C₃²	C₂×C₄	1	1	yes	characteristic
12	C₂×C₃⋊D₃	—	2	2	no	—
13	C₂×C₃⋊D₃	C₂×C₄	1	2	yes	—
14	C₃²×C₄	C₂×C₄	1	2	yes	—
15	C₃⋊Dic₃	C₂×C₄	1	1	yes	characteristic
16	C₃⋊Dic₃	C₂³	1	1	yes	characteristic
17	C₂×M₁₆	—	9	1	no	maximal, Sylow
18	C₂²×D₃	—	6	2	no	—
19	C₂×C₃×C₄	—	2	2	no	—
20	C₂×Dic₃	—	6	2	no	—
21	C₄×D₃	—	6	4	no	—
22	C₄×D₃	—	6	4	no	—
23	C₂×C₃²	M₁₆	1	2	yes	complemented
24	C₂×C₃²	C₂²×C₄	1	1	yes	characteristic
25	C₃⋊D₃	—	2	2	no	—
26	C₂²×C₄	—	9	1	no	—
27	M₁₆	—	9	4	no	—
28	C₂×C₈	—	9	2	no	—
29	C₂²×C₃	—	2	2	no	—
30	C₂×D₃	—	6	4	no	—
31	C₂×D₃	—	6	8	no	—
32	C₃×C₄	—	2	4	no	—
33	Dic₃	—	6	2	no	—
34	Dic₃	—	6	2	no	—
35	C₃²	C₂×M₁₆	1	1	yes	characteristic, complemented, Sylow
36	C₂³	—	9	1	no	—
37	C₂×C₄	—	9	1	no	—
38	C₂×C₄	—	9	2	no	—
39	C₂×C₄	—	9	2	no	—
40	C₂×C₄	#157	1	1	yes	characteristic
41	C₈	—	9	4	no	—
42	C₂×C₃	—	2	2	no	—
43	C₂×C₃	—	2	4	no	—
44	D₃	—	6	8	no	—
45	C₂²	—	9	2	no	—
46	C₂²	—	18	2	no	—
47	C₂²	C₂×#157	1	1	yes	characteristic
48	C₄	—	9	1	no	—
49	C₄	—	9	1	no	—
50	C₄	C₂×#157	1	2	yes	—
51	C₃	—	2	2	no	—
52	C₂	—	18	2	no	—
53	C₂	#3788	1	2	yes	direct product factor
54	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	C₄
cosocle	C₃⋊Dic₃	C₂³
hypercenter	C₂×C₄	#157
hypocenter	C₃²	C₂×M₁₆
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
2. C₂×#622	C₂	semidirect
3. #3788	C₂	direct (N × H)
9. #622	C₂²	semidirect
23. C₂×C₃²	M₁₆	semidirect
35. C₃²	C₂×M₁₆	semidirect
53. C₂	#3788	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×C₄×C₃⋊D₃	2
C₂×#622	2
#3788	2
C₂×M₁₆	9

Subgroups — C2×#3788 #64282

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#3788 #64282