Subgroups — C₂²×C₉×D₂₇ #14516644

Order 1944.

252 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₉×C₂₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₉×D₂₇	C₂	1	6	yes	maximal, direct product factor
3	C₂²×C₃×D₂₇	C₃	1	1	yes	maximal, characteristic
4	C₂²×C₉×D₉	—	3	1	no	maximal
5	C₂×C₉×C₂₇	C₂²	1	3	yes	complemented
6	C₉×D₂₇	C₂²	1	4	yes	direct product factor
7	C₂²×C₃×C₂₇	—	2	1	no	—
8	C₂²×C₃×C₂₇	C₂×C₃	1	1	yes	characteristic
9	C₂²×C₉²	D₃	1	1	yes	characteristic
10	C₂×C₃×D₂₇	C₂×C₃	1	6	yes	—
11	C₂×C₉×D₉	—	3	6	no	—
12	C₉×C₂₇	C₂³	1	1	yes	characteristic, complemented, Sylow
13	C₂²×D₃×C₉	—	9	1	no	—
14	C₂²×C₃×D₉	—	3	1	no	—
15	C₂²×D₂₇	C₉	1	1	yes	characteristic, direct product factor
16	C₂×C₃×C₂₇	—	2	3	no	—
17	C₂×C₃×C₂₇	C₂²×C₃	1	3	yes	—
18	C₂×C₉²	C₂×D₃	1	3	yes	—
19	C₃×D₂₇	C₂²×C₃	1	4	yes	—
20	C₉×D₉	—	3	4	no	—
21	C₂²×C₃×C₉	—	2	1	no	—
22	C₂²×C₃×C₉	D₉	1	1	yes	characteristic
23	C₂²×C₃×C₉	C₃×D₃	1	1	yes	characteristic
24	C₂×D₃×C₉	—	9	6	no	—
25	C₂×C₃×D₉	—	3	6	no	—
26	C₂²×C₂₇	—	2	3	no	—
27	C₂²×C₂₇	—	2	1	no	—
28	C₂²×C₂₇	C₂×C₉	1	1	yes	characteristic, complemented
29	C₂×D₂₇	C₂×C₉	1	6	yes	direct product factor
30	C₃×C₂₇	—	2	1	no	—
31	C₃×C₂₇	C₂³×C₃	1	1	yes	characteristic
32	C₉²	C₂²×D₃	1	1	yes	characteristic
33	C₂²×C₃×D₃	—	9	1	no	—
34	C₂³×C₉	—	27	1	no	—
35	C₂²×D₉	—	3	1	no	—
36	C₂×C₃×C₉	—	2	3	no	—
37	C₂×C₃×C₉	C₂×D₉	1	3	yes	—
38	C₂×C₃×C₉	C₂×C₃×D₃	1	3	yes	—
39	D₃×C₉	—	9	4	no	—
40	C₃×D₉	—	3	4	no	—
41	C₂×C₂₇	—	2	9	no	—
42	C₂×C₂₇	—	2	3	no	—
43	C₂×C₂₇	C₂²×C₉	1	3	yes	complemented
44	D₂₇	C₂²×C₉	1	4	yes	direct product factor
45	C₂²×C₃²	C₃×D₉	1	1	yes	characteristic
46	C₂×C₃×D₃	—	9	6	no	—
47	C₂²×C₉	—	2	3	no	—
48	C₂²×C₉	—	2	1	no	—
49	C₂²×C₉	—	2	1	no	—
50	C₂²×C₉	—	27	6	no	—
51	C₂²×C₉	D₂₇	1	1	yes	characteristic, direct product factor
52	C₂²×C₉	D₃×C₉	1	1	yes	characteristic
53	C₂×D₉	—	3	6	no	—
54	C₃×C₉	—	2	1	no	—
55	C₃×C₉	C₂²×D₉	1	1	yes	characteristic
56	C₃×C₉	C₂²×C₃×D₃	1	1	yes	characteristic
57	C₂₇	—	2	3	no	—
58	C₂₇	—	2	1	no	—
59	C₂₇	C₂³×C₉	1	1	yes	characteristic, complemented
60	C₂³×C₃	—	27	1	no	—
61	C₂²×D₃	—	9	1	no	—
62	C₂×C₃²	C₂×C₃×D₉	1	3	yes	—
63	C₃×D₃	—	9	4	no	—
64	C₂×C₉	—	2	9	no	—
65	C₂×C₉	—	2	3	no	—
66	C₂×C₉	—	2	3	no	—
67	C₂×C₉	—	27	4	no	—
68	C₂×C₉	C₂×D₂₇	1	3	yes	direct product factor
69	C₂×C₉	C₂×D₃×C₉	1	3	yes	—
70	D₉	—	3	4	no	—
71	C₂²×C₃	—	2	1	no	—
72	C₂²×C₃	—	27	6	no	—
73	C₂²×C₃	C₉×D₉	1	1	yes	characteristic
74	C₂²×C₃	C₃×D₂₇	1	1	yes	characteristic
75	C₂×D₃	—	9	6	no	—
76	C₃²	C₂²×C₃×D₉	1	1	yes	characteristic
77	C₉	—	2	3	no	—
78	C₉	—	2	1	no	—
79	C₉	—	2	1	no	—
80	C₉	C₂²×D₂₇	1	1	yes	characteristic, direct product factor
81	C₉	C₂²×D₃×C₉	1	1	yes	characteristic
82	C₂³	—	27	1	no	Sylow
83	C₂×C₃	—	2	3	no	—
84	C₂×C₃	—	27	4	no	—
85	C₂×C₃	C₂×C₉×D₉	1	3	yes	—
86	C₂×C₃	C₂×C₃×D₂₇	1	3	yes	—
87	D₃	—	9	4	no	—
88	C₂²	—	27	6	no	—
89	C₂²	C₉×D₂₇	1	1	yes	characteristic, direct product factor
90	C₃	—	2	1	no	—
91	C₃	C₂²×C₉×D₉	1	1	yes	characteristic
92	C₃	C₂²×C₃×D₂₇	1	1	yes	characteristic
93	C₂	—	27	4	no	—
94	C₂	C₂×C₉×D₂₇	1	3	yes	direct product factor

	subgroup	G/H
center, hypercenter	C₂²×C₉	D₂₇
commutator, hypocenter	C₂₇	C₂³×C₉
Frattini	C₃×C₉	C₂²×C₃×D₃
Fitting	C₂²×C₉×C₂₇	C₂
socle	C₂²×C₃²	C₃×D₉
prime radical	C₂²×C₃×D₂₇	C₃
cosocle	C₃×C₂₇	C₂³×C₃
LCS	G ▷ C₂₇
UCS	C₁ ◁ C₂²×C₉

Complements

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

N	H ≅ G/N	type
1. C₂²×C₉×C₂₇	C₂	semidirect
2. C₂×C₉×D₂₇	C₂	direct (N × H)
5. C₂×C₉×C₂₇	C₂²	semidirect
6. C₉×D₂₇	C₂²	direct (N × H)
12. C₉×C₂₇	C₂³	semidirect
15. C₂²×D₂₇	C₉	direct (N × H)
28. C₂²×C₂₇	C₂×C₉	semidirect
29. C₂×D₂₇	C₂×C₉	direct (N × H)
43. C₂×C₂₇	C₂²×C₉	semidirect
44. D₂₇	C₂²×C₉	direct (N × H)
51. C₂²×C₉	D₂₇	direct (N × H)
59. C₂₇	C₂³×C₉	semidirect
68. C₂×C₉	C₂×D₂₇	direct (N × H)
80. C₉	C₂²×D₂₇	direct (N × H)
89. C₂²	C₉×D₂₇	direct (N × H)
94. C₂	C₂×C₉×D₂₇	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×C₉×C₂₇	2
C₂×C₉×D₂₇	2
C₂²×C₃×D₂₇	3
C₂²×C₉×D₉	3

Subgroups — C22×C9×D27 #14516644

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₉×D₂₇ #14516644