Subgroups — (C₃⋊D₂₇)⋊C₄ #10619541

Order 648.

79 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃⋊D₂₇	C₂	1	1	yes	maximal, characteristic
2	Dic₃×C₂₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×Dic₂₇	C₂	1	1	yes	maximal, characteristic, complemented
4	(C₃⋊D₉)⋊C₄	—	3	1	no	maximal
5	C₄×D₂₇	—	3	1	no	maximal
6	C₂×C₃×C₂₇	C₂²	1	1	yes	characteristic
7	C₃⋊D₂₇	C₄	1	2	yes	complemented
8	C₂×C₃⋊D₉	—	3	1	no	—
9	C₉×Dic₃	D₃	1	1	yes	characteristic
10	C₃×Dic₉	—	3	1	no	—
11	C₂×D₂₇	—	3	1	no	—
12	C₂×D₂₇	—	6	1	no	—
13	C₄×C₂₇	—	3	1	no	—
14	Dic₂₇	D₃	1	1	yes	characteristic, complemented
15	C₃×C₂₇	C₂×C₄	1	1	yes	characteristic, complemented, Sylow
16	#624	—	9	1	no	—
17	C₄×D₉	—	9	1	no	—
18	C₂×C₃×C₉	C₂×D₃	1	1	yes	characteristic
19	C₃⋊D₉	—	3	2	no	—
20	C₂×C₂₇	—	2	1	no	—
21	C₂×C₂₇	C₂×D₃	1	1	yes	characteristic
22	D₂₇	—	3	2	no	—
23	D₂₇	—	6	2	no	—
24	C₂×C₃⋊D₃	—	9	1	no	—
25	C₃×Dic₃	—	9	1	no	—
26	C₃×Dic₃	D₉	1	1	yes	characteristic
27	C₂×D₉	—	9	1	no	—
28	C₂×D₉	—	18	1	no	—
29	C₄×C₉	—	3	1	no	—
30	Dic₉	—	3	1	no	—
31	C₃×C₉	C₄×D₃	1	1	yes	characteristic
32	C₂₇	—	2	1	no	—
33	C₂₇	C₄×D₃	1	1	yes	characteristic, complemented
34	C₄×D₃	—	27	1	no	—
35	C₄×D₃	—	27	1	no	—
36	C₂×C₃²	C₂×D₉	1	1	yes	characteristic
37	C₃⋊D₃	—	9	2	no	—
38	C₂×C₉	—	2	1	no	—
39	C₂×C₉	D₃²	1	1	yes	characteristic
40	D₉	—	9	2	no	—
41	D₉	—	18	2	no	—
42	C₂×D₃	—	27	1	no	—
43	C₂×D₃	—	27	1	no	—
44	C₂×D₃	—	54	1	no	—
45	C₃×C₄	—	3	1	no	—
46	C₃×C₄	—	27	1	no	—
47	Dic₃	—	9	1	no	—
48	Dic₃	D₂₇	1	1	yes	characteristic, complemented
49	C₃²	C₄×D₉	1	1	yes	characteristic
50	C₉	—	2	1	no	—
51	C₉	#624	1	1	yes	characteristic
52	C₂×C₄	—	81	1	no	Sylow
53	C₂×C₃	—	2	1	no	—
54	C₂×C₃	C₂×D₂₇	1	1	yes	characteristic
55	C₂×C₃	D₃×D₉	1	1	yes	characteristic
56	D₃	—	27	2	no	—
57	D₃	—	27	2	no	—
58	D₃	—	54	2	no	—
59	C₂²	—	81	1	no	—
60	C₄	—	3	1	no	—
61	C₄	—	27	1	no	—
62	C₃	—	2	1	no	—
63	C₃	C₄×D₂₇	1	1	yes	characteristic, complemented
64	C₃	(C₃⋊D₉)⋊C₄	1	1	yes	characteristic
65	C₂	—	81	2	no	—
66	C₂	D₃×D₂₇	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂	D₃×D₂₇
commutator, hypocenter	C₃×C₂₇	C₂×C₄
Frattini	C₂×C₉	D₃²
Fitting, cosocle	C₂×C₃×C₂₇	C₂²
socle	C₂×C₃²	C₂×D₉
prime radical	C₂×C₃⋊D₂₇	C₂
LCS	G ▷ C₃×C₂₇
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
2. Dic₃×C₂₇	C₂	semidirect
3. C₃×Dic₂₇	C₂	semidirect
7. C₃⋊D₂₇	C₄	semidirect
14. Dic₂₇	D₃	semidirect
15. C₃×C₂₇	C₂×C₄	semidirect
33. C₂₇	C₄×D₃	semidirect
48. Dic₃	D₂₇	semidirect
63. C₃	C₄×D₂₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃⋊D₂₇	2
Dic₃×C₂₇	2
C₃×Dic₂₇	2
(C₃⋊D₉)⋊C₄	3
C₄×D₂₇	3

Subgroups — (C3⋊D27)⋊C4 #10619541

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — (C₃⋊D₂₇)⋊C₄ #10619541