Subgroups — #4181⋊C₄ #10619533

Order 648.

114 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#4181	C₂	1	1	yes	maximal, characteristic
2	#66316	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	Dic₃×D₉	—	3	1	no	maximal
6	C₂×C₃²⋊C₉	C₂²	1	1	yes	characteristic
7	#4181	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	—	3	1	no	—
12	C₂×C₃×D₉	—	6	1	no	—
13	C₃⋊Dic₉	D₃	1	1	yes	characteristic, complemented
14	C₉×Dic₃	—	3	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	—	3	2	no	—
25	C₃×D₉	—	6	2	no	—
26	C₂×C₃⋊D₃	—	3	1	no	—
27	C₂×C₃×D₃	—	9	1	no	—
28	C₂×C₃×D₃	—	9	1	no	—
29	C₂×C₃×D₃	—	18	1	no	—
30	C₃⋊Dic₃	—	3	1	no	—
31	C₃⋊Dic₃	D₉	1	1	yes	characteristic, complemented
32	C₃×Dic₃	—	3	1	no	—
33	C₃×Dic₃	—	9	1	no	—
34	C₃×Dic₃	—	9	1	no	—
35	C₃×Dic₃	—	18	1	no	—
36	C₃×Dic₃	—	18	1	no	—
37	C₂×D₉	—	3	1	no	—
38	C₂×D₉	—	6	1	no	—
39	C₄×C₉	—	9	1	no	—
40	Dic₉	—	18	1	no	—
41	C₃³	C₄×D₃	1	1	yes	characteristic
42	C₃×C₉	—	2	1	no	—
43	C₃×C₉	C₄×D₃	1	1	yes	characteristic, complemented
44	C₂×Dic₃	—	27	1	no	—
45	C₄×D₃	—	27	1	no	—
46	C₄×D₃	—	27	1	no	—
47	C₂×C₃²	—	2	1	no	—
48	C₂×C₃²	—	6	1	no	—
49	C₂×C₃²	—	12	1	no	—
50	C₂×C₃²	C₂×D₉	1	1	yes	characteristic
51	C₂×C₃²	D₃²	1	1	yes	characteristic
52	C₃⋊D₃	—	3	2	no	—
53	C₃×D₃	—	9	2	no	—
54	C₃×D₃	—	9	2	no	—
55	C₃×D₃	—	18	2	no	—
56	C₂×C₉	—	6	1	no	—
57	C₂×C₉	—	6	1	no	—
58	D₉	—	3	2	no	—
59	D₉	—	6	2	no	—
60	C₂²×C₃	—	27	1	no	—
61	C₂×D₃	—	9	1	no	—
62	C₂×D₃	—	9	1	no	—
63	C₂×D₃	—	18	1	no	—
64	C₃×C₄	—	9	1	no	—
65	C₃×C₄	—	27	1	no	—
66	Dic₃	—	3	1	no	—
67	Dic₃	—	9	1	no	—
68	Dic₃	—	9	1	no	—
69	Dic₃	—	18	1	no	—
70	Dic₃	—	18	1	no	—
71	C₃²	—	2	1	no	—
72	C₃²	—	6	1	no	—
73	C₃²	—	12	1	no	—
74	C₃²	C₄×D₉	1	1	yes	characteristic, complemented
75	C₃²	#624	1	1	yes	characteristic
76	C₉	—	6	1	no	—
77	C₉	—	6	1	no	—
78	C₂×C₄	—	81	1	no	Sylow
79	C₂×C₃	—	2	1	no	—
80	C₂×C₃	—	6	1	no	—
81	C₂×C₃	—	6	1	no	—
82	C₂×C₃	—	27	2	no	—
83	C₂×C₃	D₃×D₉	1	1	yes	characteristic
84	C₂×C₃	((C₃⋊D₃)⋊C₃)⋊C₂	1	1	yes	characteristic
85	D₃	—	9	2	no	—
86	D₃	—	9	2	no	—
87	D₃	—	18	2	no	—
88	C₂²	—	27	1	no	—
89	C₄	—	9	1	no	—
90	C₄	—	27	1	no	—
91	C₃	—	2	1	no	—
92	C₃	—	6	1	no	—
93	C₃	—	6	1	no	—
94	C₃	(C₃⋊D₉)⋊C₄	1	1	yes	characteristic
95	C₃	#6199	1	1	yes	characteristic
96	C₂	—	27	2	no	—
97	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×#4181	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. #66316	C₂	semidirect
3. (C₃⋊Dic₃)⋊C₉	C₂	semidirect
7. #4181	C₄	semidirect
13. C₃⋊Dic₉	D₃	semidirect
15. C₃²⋊C₉	C₂×C₄	semidirect
31. C₃⋊Dic₃	D₉	semidirect
43. C₃×C₉	C₄×D₃	semidirect
74. 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×#4181	2
#66316	2
(C₃⋊Dic₃)⋊C₉	2
#6294	3
Dic₃×D₉	3

Subgroups — #4181⋊C4 #10619533

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #4181⋊C₄ #10619533