Subgroups — #4169⋊C₄ #10619534

Order 648.

110 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#4169	C₂	1	1	yes	maximal, characteristic
2	#66328	C₂	1	1	yes	maximal, characteristic, complemented
3	(C₃⋊Dic₃)⋊C₉	C₂	1	1	yes	maximal, characteristic, complemented
4	#6294	—	3	1	no	maximal
5	(C₃⋊D₉)⋊C₄	—	3	1	no	maximal
6	C₂×C₃²⋊C₉	C₂²	1	1	yes	characteristic
7	#4169	C₄	1	2	yes	complemented
8	C₂×C₃×C₃⋊D₃	—	3	1	no	—
9	C₃×C₃⋊Dic₃	—	3	1	no	—
10	C₃×C₃⋊Dic₃	D₃	1	1	yes	characteristic
11	C₂×C₃⋊D₉	D₃	1	1	yes	characteristic
12	C₉×Dic₃	—	3	1	no	—
13	C₃×Dic₉	—	3	1	no	—
14	C₃×Dic₉	—	6	1	no	—
15	C₃²⋊C₉	C₂×C₄	1	1	yes	characteristic, complemented, Sylow
16	#624	—	9	1	no	—
17	D₃×Dic₃	—	9	1	no	—
18	D₃×Dic₃	—	9	1	no	—
19	C₄×D₉	—	9	1	no	—
20	C₂×C₃³	C₂×D₃	1	1	yes	characteristic
21	C₃×C₃⋊D₃	—	3	2	no	—
22	C₂×C₃×C₉	—	2	1	no	—
23	C₂×C₃×C₉	C₂×D₃	1	1	yes	characteristic
24	C₃⋊D₉	Dic₃	1	2	yes	complemented
25	C₂×C₃⋊D₃	—	3	1	no	—
26	C₂×C₃×D₃	—	9	1	no	—
27	C₂×C₃×D₃	—	9	1	no	—
28	C₂×C₃×D₃	—	18	1	no	—
29	C₃⋊Dic₃	—	3	1	no	—
30	C₃⋊Dic₃	D₉	1	1	yes	characteristic, complemented
31	C₃×Dic₃	—	3	1	no	—
32	C₃×Dic₃	—	9	1	no	—
33	C₃×Dic₃	—	9	1	no	—
34	C₃×Dic₃	—	18	1	no	—
35	C₃×Dic₃	—	18	1	no	—
36	C₂×D₉	—	18	1	no	—
37	C₄×C₉	—	9	1	no	—
38	Dic₉	—	3	1	no	—
39	Dic₉	—	6	1	no	—
40	C₃³	C₄×D₃	1	1	yes	characteristic
41	C₃×C₉	—	2	1	no	—
42	C₃×C₉	C₂×Dic₃	1	1	yes	characteristic, complemented
43	C₂×Dic₃	—	27	1	no	—
44	C₄×D₃	—	27	1	no	—
45	C₄×D₃	—	27	1	no	—
46	C₂×C₃²	—	2	1	no	—
47	C₂×C₃²	—	6	1	no	—
48	C₂×C₃²	—	12	1	no	—
49	C₂×C₃²	C₂×D₉	1	1	yes	characteristic
50	C₂×C₃²	D₃²	1	1	yes	characteristic
51	C₃⋊D₃	—	3	2	no	—
52	C₃×D₃	—	9	2	no	—
53	C₃×D₃	—	9	2	no	—
54	C₃×D₃	—	18	2	no	—
55	C₂×C₉	—	6	1	no	—
56	C₂×C₉	—	12	1	no	—
57	D₉	—	18	2	no	—
58	C₂²×C₃	—	27	1	no	—
59	C₂×D₃	—	9	1	no	—
60	C₂×D₃	—	9	1	no	—
61	C₂×D₃	—	18	1	no	—
62	C₃×C₄	—	9	1	no	—
63	C₃×C₄	—	27	1	no	—
64	Dic₃	—	3	1	no	—
65	Dic₃	—	9	1	no	—
66	Dic₃	—	9	1	no	—
67	Dic₃	—	18	1	no	—
68	Dic₃	—	18	1	no	—
69	C₃²	—	2	1	no	—
70	C₃²	—	6	1	no	—
71	C₃²	—	12	1	no	—
72	C₃²	C₄×D₉	1	1	yes	characteristic, complemented
73	C₃²	D₃×Dic₃	1	1	yes	characteristic
74	C₉	—	6	1	no	—
75	C₉	—	12	1	no	—
76	C₂×C₄	—	81	1	no	Sylow
77	C₂×C₃	—	2	1	no	—
78	C₂×C₃	—	6	1	no	—
79	C₂×C₃	—	6	1	no	—
80	C₂×C₃	—	27	2	no	—
81	C₂×C₃	D₃×D₉	1	1	yes	characteristic
82	C₂×C₃	((C₃⋊D₃)⋊C₃)⋊C₂	1	1	yes	characteristic
83	D₃	—	9	2	no	—
84	D₃	—	9	2	no	—
85	D₃	—	18	2	no	—
86	C₂²	—	27	1	no	—
87	C₄	—	9	1	no	—
88	C₄	—	27	1	no	—
89	C₃	—	2	1	no	—
90	C₃	—	6	1	no	—
91	C₃	—	6	1	no	—
92	C₃	Dic₃×D₉	1	1	yes	characteristic
93	C₃	((C₃⋊D₃)⋊C₃)⋊C₄	1	1	yes	characteristic
94	C₂	—	27	2	no	—
95	C₂	((C₃⋊D₃)⋊C₉)⋊C₂	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂	((C₃⋊D₃)⋊C₉)⋊C₂
commutator, hypocenter	C₃²⋊C₉	C₂×C₄
Frattini, socle	C₂×C₃²	D₃²
Fitting, cosocle	C₂×C₃²⋊C₉	C₂²
prime radical	C₂×#4169	C₂
LCS	G ▷ C₃²⋊C₉
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
2. #66328	C₂	semidirect
3. (C₃⋊Dic₃)⋊C₉	C₂	semidirect
7. #4169	C₄	semidirect
15. C₃²⋊C₉	C₂×C₄	semidirect
24. C₃⋊D₉	Dic₃	semidirect
30. C₃⋊Dic₃	D₉	semidirect
42. C₃×C₉	C₂×Dic₃	semidirect
72. C₃²	C₄×D₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#4169	2
#66328	2
(C₃⋊Dic₃)⋊C₉	2
#6294	3
(C₃⋊D₉)⋊C₄	3

Subgroups — #4169⋊C4 #10619534

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #4169⋊C₄ #10619534