Subgroups — C₂²⋊C₄×C₃⋊D₃ #64089

Order 288.

396 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	C₂×C₄×C₃⋊D₃	C₂	1	2	yes	maximal, complemented
3	C₃²×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
4	#3757	C₂	1	1	yes	maximal, characteristic, complemented
5	#3752	C₂	1	2	yes	maximal, complemented
6	D₃×C₂²⋊C₄	—	3	4	no	maximal
7	C₂³×C₃²	C₂²	1	1	yes	characteristic
8	C₂²×C₃⋊D₃	—	2	4	no	—
9	C₂²×C₃⋊D₃	C₄	1	4	yes	complemented
10	C₂²×C₃⋊D₃	C₂²	1	1	yes	characteristic
11	C₂²×C₃⋊D₃	C₂²	1	1	yes	characteristic
12	C₂×C₃²×C₄	C₂²	1	2	yes	complemented
13	C₂×C₃⋊Dic₃	C₂²	1	2	yes	complemented
14	C₄×C₃⋊D₃	—	2	4	no	—
15	C₂³×D₃	—	3	4	no	—
16	C₂×C₄×D₃	—	3	8	no	—
17	C₃×C₂²⋊C₄	D₃	1	4	yes	complemented
18	#217	—	3	4	no	—
19	(C₂×D₃)⋊C₄	—	3	8	no	—
20	C₂²×C₃²	—	2	2	no	—
21	C₂²×C₃²	C₂×C₄	1	2	yes	complemented
22	C₂²×C₃²	C₂³	1	1	yes	characteristic
23	C₂×C₃⋊D₃	—	2	2	no	—
24	C₂×C₃⋊D₃	—	2	8	no	—
25	C₂×C₃⋊D₃	C₂×C₄	1	2	yes	—
26	C₂×C₃⋊D₃	C₂×C₄	1	2	yes	complemented
27	C₂×C₃⋊D₃	D₄	1	4	yes	—
28	C₃²×C₄	—	2	2	no	—
29	C₃⋊Dic₃	—	2	2	no	—
30	C₂×C₂²⋊C₄	—	9	1	no	Sylow
31	C₂³×C₃	C₂×D₃	1	4	yes	—
32	C₂²×D₃	—	3	4	no	—
33	C₂²×D₃	—	3	16	no	—
34	C₂²×D₃	—	3	4	no	—
35	C₂²×D₃	—	6	16	no	—
36	C₂×C₃×C₄	C₂×D₃	1	8	yes	complemented
37	C₂×Dic₃	—	3	8	no	—
38	C₄×D₃	—	6	16	no	—
39	C₂×C₃²	—	2	2	no	—
40	C₂×C₃²	C₂²×C₄	1	1	yes	characteristic
41	C₂×C₃²	C₂×D₄	1	2	yes	—
42	C₃⋊D₃	—	2	2	no	—
43	C₃⋊D₃	C₂²⋊C₄	1	4	yes	direct product factor
44	C₂⁴	—	9	1	no	—
45	C₂²×C₄	—	9	2	no	—
46	C₂²⋊C₄	—	9	1	no	—
47	C₂²⋊C₄	—	9	2	no	—
48	C₂²⋊C₄	C₃⋊D₃	1	1	yes	characteristic, direct product factor
49	C₂²×C₃	—	2	8	no	—
50	C₂²×C₃	C₄×D₃	1	8	yes	complemented
51	C₂²×C₃	C₂²×D₃	1	4	yes	—
52	C₂×D₃	—	3	8	no	—
53	C₂×D₃	—	3	16	no	—
54	C₂×D₃	—	3	8	no	—
55	C₂×D₃	—	6	32	no	—
56	C₂×D₃	—	6	8	no	—
57	C₃×C₄	—	2	8	no	—
58	Dic₃	—	6	8	no	—
59	C₃²	C₂×C₂²⋊C₄	1	1	yes	characteristic, complemented, Sylow
60	C₂³	—	9	1	no	—
61	C₂³	—	9	4	no	—
62	C₂³	—	9	1	no	—
63	C₂³	—	18	4	no	—
64	C₂³	C₂×C₃⋊D₃	1	1	yes	characteristic
65	C₂×C₄	—	9	2	no	—
66	C₂×C₄	—	18	4	no	—
67	C₂×C₄	C₂×C₃⋊D₃	1	2	yes	complemented
68	C₂×C₃	—	2	8	no	—
69	C₂×C₃	C₂×C₄×D₃	1	4	yes	—
70	C₂×C₃	D₃×D₄	1	8	yes	—
71	D₃	—	3	16	no	—
72	D₃	—	6	8	no	—
73	C₂²	—	2	2	no	—
74	C₂²	—	9	2	no	—
75	C₂²	—	9	4	no	—
76	C₂²	—	9	2	no	—
77	C₂²	—	18	8	no	—
78	C₂²	—	18	2	no	—
79	C₂²	C₄×C₃⋊D₃	1	2	yes	complemented
80	C₂²	C₂²×C₃⋊D₃	1	1	yes	characteristic
81	C₄	—	2	2	no	—
82	C₄	—	18	2	no	—
83	C₃	D₃×C₂²⋊C₄	1	4	yes	complemented
84	C₂	—	2	2	no	—
85	C₂	—	9	4	no	—
86	C₂	—	18	2	no	—
87	C₂	C₂×C₄×C₃⋊D₃	1	1	yes	characteristic
88	C₂	D₄×C₃⋊D₃	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
2. C₂×C₄×C₃⋊D₃	C₂	semidirect
3. C₃²×C₂²⋊C₄	C₂	semidirect
4. #3757	C₂	semidirect
5. #3752	C₂	semidirect
9. C₂²×C₃⋊D₃	C₄	semidirect
12. C₂×C₃²×C₄	C₂²	semidirect
13. C₂×C₃⋊Dic₃	C₂²	semidirect
17. C₃×C₂²⋊C₄	D₃	semidirect
21. C₂²×C₃²	C₂×C₄	semidirect
26. C₂×C₃⋊D₃	C₂×C₄	semidirect
36. C₂×C₃×C₄	C₂×D₃	semidirect
43. C₃⋊D₃	C₂²⋊C₄	direct (N × H)
48. C₂²⋊C₄	C₃⋊D₃	direct (N × H)
50. C₂²×C₃	C₄×D₃	semidirect
59. C₃²	C₂×C₂²⋊C₄	semidirect
67. C₂×C₄	C₂×C₃⋊D₃	semidirect
79. C₂²	C₄×C₃⋊D₃	semidirect
83. C₃	D₃×C₂²⋊C₄	semidirect

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
C₂×C₄×C₃⋊D₃	2
C₃²×C₂²⋊C₄	2
#3757	2
#3752	2
D₃×C₂²⋊C₄	3

Subgroups — C22⋊C4×C3⋊D3 #64089

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²⋊C₄×C₃⋊D₃ #64089