Subgroups — C₄×C₃⋊(C₃⋊D₂₇) #14517732

Order 1944.

576 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃⋊(C₃⋊D₂₇)	C₂	1	1	yes	maximal, characteristic
2	C₃²×C₄×C₂₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃⋊(C₃⋊Dic₂₇)	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄×C₃⋊(C₃⋊D₉)	—	3	1	no	maximal
5	C₄×C₃⋊D₂₇	—	3	12	no	maximal
6	C₂×C₃²×C₂₇	C₂²	1	1	yes	characteristic
7	C₃⋊(C₃⋊D₂₇)	C₄	1	2	yes	direct product factor
8	C₂×C₃⋊(C₃⋊D₉)	—	3	1	no	—
9	C₃²×C₄×C₉	D₃	1	1	yes	characteristic
10	C₃⋊(C₃⋊Dic₉)	—	3	1	no	—
11	C₂×C₃⋊D₂₇	—	3	12	no	—
12	C₃×C₄×C₂₇	D₃	1	12	yes	complemented
13	C₃⋊Dic₂₇	—	3	12	no	—
14	C₃²×C₂₇	C₂×C₄	1	1	yes	characteristic, complemented, Sylow
15	C₄×C₃⋊(C₃⋊D₃)	—	9	1	no	—
16	C₄×C₃⋊D₉	—	9	8	no	—
17	C₄×C₃⋊D₉	—	9	4	no	—
18	C₄×D₂₇	—	9	9	no	—
19	C₂×C₃²×C₉	C₂×D₃	1	1	yes	characteristic
20	C₃⋊(C₃⋊D₉)	—	3	2	no	—
21	C₂×C₃×C₂₇	C₂×D₃	1	12	yes	—
22	C₃⋊D₂₇	—	3	24	no	—
23	C₂×C₃⋊(C₃⋊D₃)	—	9	1	no	—
24	C₃³×C₄	D₉	1	1	yes	characteristic
25	C₃⋊(C₃⋊Dic₃)	—	9	1	no	—
26	C₂×C₃⋊D₉	—	9	8	no	—
27	C₂×C₃⋊D₉	—	9	4	no	—
28	C₃×C₄×C₉	D₉	1	8	yes	—
29	C₃×C₄×C₉	C₃⋊D₃	1	4	yes	—
30	C₃⋊Dic₉	—	9	8	no	—
31	C₃⋊Dic₉	—	9	4	no	—
32	C₂×D₂₇	—	9	9	no	—
33	C₄×C₂₇	C₃⋊D₃	1	9	yes	complemented
34	Dic₂₇	—	9	9	no	—
35	C₃²×C₉	C₄×D₃	1	1	yes	characteristic
36	C₃×C₂₇	C₄×D₃	1	12	yes	complemented
37	C₄×C₃⋊D₃	—	27	9	no	—
38	C₄×C₃⋊D₃	—	27	4	no	—
39	C₄×D₉	—	27	8	no	—
40	C₄×D₉	—	27	1	no	—
41	C₂×C₃³	C₂×D₉	1	1	yes	characteristic
42	C₃⋊(C₃⋊D₃)	—	9	2	no	—
43	C₂×C₃×C₉	C₂×D₉	1	8	yes	—
44	C₂×C₃×C₉	C₂×C₃⋊D₃	1	4	yes	—
45	C₃⋊D₉	—	9	16	no	—
46	C₃⋊D₉	—	9	8	no	—
47	C₂×C₂₇	C₂×C₃⋊D₃	1	9	yes	—
48	D₂₇	—	9	18	no	—
49	C₂×C₃⋊D₃	—	27	9	no	—
50	C₂×C₃⋊D₃	—	27	4	no	—
51	C₃²×C₄	D₂₇	1	9	yes	complemented
52	C₃²×C₄	C₃⋊D₉	1	4	yes	—
53	C₃⋊Dic₃	—	27	9	no	—
54	C₃⋊Dic₃	—	27	4	no	—
55	C₂×D₉	—	27	8	no	—
56	C₂×D₉	—	27	1	no	—
57	C₄×C₉	C₃⋊D₉	1	8	yes	—
58	C₄×C₉	C₃⋊(C₃⋊D₃)	1	1	yes	characteristic
59	Dic₉	—	27	8	no	—
60	Dic₉	—	27	1	no	—
61	C₃³	C₄×D₉	1	1	yes	characteristic
62	C₃×C₉	C₄×D₉	1	8	yes	—
63	C₃×C₉	C₄×C₃⋊D₃	1	4	yes	—
64	C₂₇	C₄×C₃⋊D₃	1	9	yes	complemented
65	C₄×D₃	—	81	12	no	—
66	C₄×D₃	—	81	1	no	—
67	C₂×C₃²	C₂×D₂₇	1	9	yes	—
68	C₂×C₃²	C₂×C₃⋊D₉	1	4	yes	—
69	C₃⋊D₃	—	27	18	no	—
70	C₃⋊D₃	—	27	8	no	—
71	C₂×C₉	C₂×C₃⋊D₉	1	8	yes	—
72	C₂×C₉	C₂×C₃⋊(C₃⋊D₃)	1	1	yes	characteristic
73	D₉	—	27	16	no	—
74	D₉	—	27	2	no	—
75	C₂×D₃	—	81	12	no	—
76	C₂×D₃	—	81	1	no	—
77	C₃×C₄	C₃⋊D₂₇	1	12	yes	complemented
78	C₃×C₄	C₃⋊(C₃⋊D₉)	1	1	yes	characteristic
79	Dic₃	—	81	12	no	—
80	Dic₃	—	81	1	no	—
81	C₃²	C₄×D₂₇	1	9	yes	complemented
82	C₃²	C₄×C₃⋊D₉	1	4	yes	—
83	C₉	C₄×C₃⋊D₉	1	8	yes	—
84	C₉	C₄×C₃⋊(C₃⋊D₃)	1	1	yes	characteristic
85	C₂×C₄	—	243	1	no	Sylow
86	C₂×C₃	C₂×C₃⋊D₂₇	1	12	yes	—
87	C₂×C₃	C₂×C₃⋊(C₃⋊D₉)	1	1	yes	characteristic
88	D₃	—	81	24	no	—
89	D₃	—	81	2	no	—
90	C₂²	—	243	1	no	—
91	C₄	—	243	1	no	—
92	C₄	C₃⋊(C₃⋊D₂₇)	1	1	yes	characteristic, direct product factor
93	C₃	C₄×C₃⋊D₂₇	1	12	yes	complemented
94	C₃	C₄×C₃⋊(C₃⋊D₉)	1	1	yes	characteristic
95	C₂	—	243	2	no	—
96	C₂	C₂×C₃⋊(C₃⋊D₂₇)	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₄	C₃⋊(C₃⋊D₂₇)
commutator, hypocenter	C₃²×C₂₇	C₂×C₄
Frattini	C₂×C₉	C₂×C₃⋊(C₃⋊D₃)
Fitting	C₃²×C₄×C₂₇	C₂
socle	C₂×C₃³	C₂×D₉
prime radical	C₂×C₃⋊(C₃⋊D₂₇)	C₂
cosocle	C₂×C₃²×C₂₇	C₂²
LCS	G ▷ C₃²×C₂₇
UCS	C₁ ◁ C₄

Complements

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

N	H ≅ G/N	type
2. C₃²×C₄×C₂₇	C₂	semidirect
3. C₃⋊(C₃⋊Dic₂₇)	C₂	semidirect
7. C₃⋊(C₃⋊D₂₇)	C₄	direct (N × H)
12. C₃×C₄×C₂₇	D₃	semidirect
14. C₃²×C₂₇	C₂×C₄	semidirect
33. C₄×C₂₇	C₃⋊D₃	semidirect
36. C₃×C₂₇	C₄×D₃	semidirect
51. C₃²×C₄	D₂₇	semidirect
64. C₂₇	C₄×C₃⋊D₃	semidirect
77. C₃×C₄	C₃⋊D₂₇	semidirect
81. C₃²	C₄×D₂₇	semidirect
92. C₄	C₃⋊(C₃⋊D₂₇)	direct (N × H)
93. C₃	C₄×C₃⋊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⋊(C₃⋊D₂₇)	2
C₃²×C₄×C₂₇	2
C₃⋊(C₃⋊Dic₂₇)	2
C₄×C₃⋊(C₃⋊D₉)	3
C₄×C₃⋊D₂₇	3

Subgroups — C4×C3⋊(C3⋊D27) #14517732

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×C₃⋊(C₃⋊D₂₇) #14517732