Subgroups — #4183⋊C₄ #10619547

Order 648.

138 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#4183	C₂	1	1	yes	maximal, characteristic
2	#66322	C₂	1	1	yes	maximal, characteristic, complemented
3	#66321	C₂	1	1	yes	maximal, characteristic, complemented
4	Dic₃×C₃⋊D₃	—	3	1	no	maximal
5	((C₃⋊D₃)⋊C₃)⋊C₄	—	3	1	no	maximal
6	C₂×AΣL(1,𝔽₂₇)	C₂²	1	1	yes	characteristic
7	#4183	C₄	1	2	yes	complemented
8	C₂×C₃×C₃⋊D₃	—	3	1	no	—
9	C₃⋊(C₃⋊Dic₃)	D₃	1	1	yes	characteristic, complemented
10	C₃²×Dic₃	—	3	1	no	—
11	C₂×AGL(1,ℤ/9)	—	6	1	no	—
12	C₂×(C₃⋊D₃)⋊C₃	—	3	1	no	—
13	#1084	D₃	1	1	yes	characteristic, complemented
14	(C₃⋊Dic₃)⋊C₃	—	3	1	no	—
15	AΣL(1,𝔽₂₇)	C₂×C₄	1	1	yes	characteristic, complemented, Sylow
16	C₄×C₃⋊D₃	—	9	1	no	—
17	#624	—	9	1	no	—
18	D₃×Dic₃	—	9	1	no	—
19	D₃×Dic₃	—	9	3	no	—
20	C₂×C₃³	C₂×D₃	1	1	yes	characteristic
21	C₃×C₃⋊D₃	—	3	2	no	—
22	C₂×3₋¹⁺²	—	2	1	no	—
23	C₂×H(3,𝔽₃)	C₂×D₃	1	1	yes	characteristic
24	AGL(1,ℤ/9)	—	6	2	no	—
25	(C₃⋊D₃)⋊C₃	—	3	2	no	—
26	C₂×C₃⋊D₃	—	3	1	no	—
27	C₂×C₃⋊D₃	—	3	1	no	—
28	C₂×C₃×D₃	—	9	3	no	—
29	C₂×C₃×D₃	—	9	1	no	—
30	C₃²×C₄	—	9	1	no	—
31	C₃⋊Dic₃	—	3	1	no	—
32	C₃⋊Dic₃	—	18	1	no	—
33	C₃⋊Dic₃	—	18	3	no	—
34	C₃×Dic₃	—	3	3	no	—
35	C₃×Dic₃	—	3	1	no	—
36	C₃×Dic₃	—	9	1	no	—
37	C₃×Dic₃	—	9	1	no	—
38	C₂×D₉	—	6	1	no	—
39	C₃³	C₄×D₃	1	1	yes	characteristic, complemented
40	3₋¹⁺²	—	2	1	no	—
41	H(3,𝔽₃)	C₄×D₃	1	1	yes	characteristic, complemented
42	C₂×Dic₃	—	27	1	no	—
43	C₄×D₃	—	27	1	no	—
44	C₄×D₃	—	27	1	no	—
45	C₄×D₃	—	27	3	no	—
46	C₂×C₃²	—	3	1	no	—
47	C₂×C₃²	—	6	1	no	—
48	C₂×C₃²	—	6	3	no	—
49	C₂×C₃²	D₃²	1	1	yes	characteristic
50	C₃⋊D₃	—	3	2	no	—
51	C₃⋊D₃	—	3	2	no	—
52	C₃×D₃	—	9	6	no	—
53	C₃×D₃	—	9	2	no	—
54	C₂×C₉	—	6	1	no	—
55	D₉	—	6	2	no	—
56	C₂²×C₃	—	27	1	no	—
57	C₂×D₃	—	9	3	no	—
58	C₂×D₃	—	9	1	no	—
59	C₂×D₃	—	54	1	no	—
60	C₃×C₄	—	9	3	no	—
61	C₃×C₄	—	9	1	no	—
62	C₃×C₄	—	27	1	no	—
63	Dic₃	—	3	1	no	—
64	Dic₃	—	9	1	no	—
65	Dic₃	—	18	1	no	—
66	Dic₃	—	54	3	no	—
67	Dic₃	—	54	1	no	—
68	C₃²	—	3	1	no	—
69	C₃²	—	6	3	no	—
70	C₃²	—	6	1	no	—
71	C₃²	#624	1	1	yes	characteristic
72	C₉	—	6	1	no	—
73	C₂×C₄	—	81	1	no	Sylow
74	C₂×C₃	—	6	1	no	—
75	C₂×C₃	—	6	3	no	—
76	C₂×C₃	—	27	2	no	—
77	C₂×C₃	—	36	1	no	—
78	C₂×C₃	((C₃⋊D₃)⋊C₃)⋊C₂	1	1	yes	characteristic
79	D₃	—	9	6	no	—
80	D₃	—	9	2	no	—
81	D₃	—	54	2	no	—
82	C₂²	—	27	1	no	—
83	C₄	—	9	1	no	—
84	C₄	—	27	1	no	—
85	C₃	—	6	3	no	—
86	C₃	—	6	1	no	—
87	C₃	—	36	1	no	—
88	C₃	#6199	1	1	yes	characteristic
89	C₂	—	27	2	no	—
90	C₂	#4174⋊C₂	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂	#4174⋊C₂
commutator, hypocenter	AΣL(1,𝔽₂₇)	C₂×C₄
Frattini	C₂×C₃²	D₃²
Fitting, cosocle	C₂×AΣL(1,𝔽₂₇)	C₂²
socle	C₂×C₃	((C₃⋊D₃)⋊C₃)⋊C₂
prime radical	C₂×#4183	C₂
LCS	G ▷ AΣL(1,𝔽₂₇)
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
2. #66322	C₂	semidirect
3. #66321	C₂	semidirect
7. #4183	C₄	semidirect
9. C₃⋊(C₃⋊Dic₃)	D₃	semidirect
13. #1084	D₃	semidirect
15. AΣL(1,𝔽₂₇)	C₂×C₄	semidirect
39. C₃³	C₄×D₃	semidirect
41. H(3,𝔽₃)	C₄×D₃	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×#4183	2
#66322	2
#66321	2
Dic₃×C₃⋊D₃	3
((C₃⋊D₃)⋊C₃)⋊C₄	3

Subgroups — #4183⋊C4 #10619547

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #4183⋊C₄ #10619547