Subgroups — C₂×C₃²×Dic₂₇ #14517440

Order 1944.

312 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

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

Complements

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

N	H ≅ G/N	type
2. C₃²×Dic₂₇	C₂	direct (N × H)
4. C₂×C₃×Dic₂₇	C₃	direct (N × H)
5. C₂×C₃²×C₂₇	C₄	semidirect
11. C₃×Dic₂₇	C₂×C₃	direct (N × H)
12. C₃²×C₂₇	C₂×C₄	semidirect
15. C₂×Dic₂₇	C₃²	direct (N × H)
20. C₂×C₃×C₂₇	C₃×C₄	semidirect
29. Dic₂₇	C₂×C₃²	direct (N × H)
32. C₃×C₂₇	C₂×C₃×C₄	semidirect
44. C₂×C₂₇	C₃²×C₄	semidirect
58. C₂₇	C₂×C₃²×C₄	semidirect
63. C₂×C₃²	Dic₂₇	direct (N × H)
77. C₃²	C₂×Dic₂₇	direct (N × H)
84. C₂×C₃	C₃×Dic₂₇	direct (N × H)
91. C₃	C₂×C₃×Dic₂₇	direct (N × H)
93. C₂	C₃²×Dic₂₇	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₃²×C₂₇	2
C₃²×Dic₂₇	2
C₂×C₃²×Dic₉	3
C₂×C₃×Dic₂₇	3

Subgroups — C2×C32×Dic27 #14517440

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃²×Dic₂₇ #14517440