Subgroups — C₂×C₂₇×C₂²⋊C₉ #14516595

Order 1944.

200 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₇×C₂²⋊C₉	C₂	1	1	yes	maximal, characteristic, direct product factor
2	C₂³×C₃×C₂₇	C₃	1	1	yes	maximal, characteristic
3	C₂×C₉×C₂²⋊C₉	C₃	1	1	yes	maximal, characteristic
4	C₂×C₃×C₂²⋊C₂₇	C₃	1	2	yes	maximal
5	C₂×C₉×C₂₇	—	4	1	no	maximal
6	C₂²×C₃×C₂₇	—	3	1	no	—
7	C₂²×C₃×C₂₇	—	3	1	no	—
8	C₂²×C₃×C₂₇	C₂×C₃	1	1	yes	characteristic
9	C₉×C₂²⋊C₉	C₂×C₃	1	1	yes	characteristic
10	C₃×C₂²⋊C₂₇	C₂×C₃	1	2	yes	—
11	C₉×C₂₇	—	4	1	no	Sylow
12	C₂³×C₃×C₉	C₃²	1	1	yes	characteristic
13	C₂×C₃×C₂²⋊C₉	C₉	1	3	yes	—
14	C₂³×C₂₇	C₉	1	3	yes	complemented
15	C₂×C₂²⋊C₂₇	C₉	1	6	yes	complemented
16	C₂×C₃×C₂₇	—	3	1	no	—
17	C₂×C₃×C₂₇	—	3	1	no	—
18	C₂×C₃×C₂₇	—	4	2	no	—
19	C₂×C₃×C₂₇	A₄	1	1	yes	characteristic
20	C₂×C₉²	—	4	1	no	—
21	C₂²×C₃×C₉	—	3	1	no	—
22	C₂²×C₃×C₉	—	3	1	no	—
23	C₂²×C₃×C₉	C₂×C₃²	1	1	yes	characteristic
24	C₃×C₂²⋊C₉	C₂×C₉	1	3	yes	—
25	C₂²×C₂₇	—	3	3	no	—
26	C₂²×C₂₇	—	3	3	no	—
27	C₂²×C₂₇	C₂×C₉	1	3	yes	complemented
28	C₂²⋊C₂₇	C₂×C₉	1	6	yes	complemented
29	C₃×C₂₇	—	4	2	no	—
30	C₃×C₂₇	C₂×A₄	1	1	yes	characteristic
31	C₉²	—	4	1	no	—
32	C₂³×C₃²	C₃×C₉	1	1	yes	characteristic
33	C₂³×C₉	C₃×C₉	1	2	yes	—
34	C₂³×C₉	C₃×C₉	1	1	yes	characteristic
35	C₂×C₂²⋊C₉	C₂₇	1	9	yes	direct product factor
36	C₂×C₃×C₉	—	3	1	no	—
37	C₂×C₃×C₉	—	3	1	no	—
38	C₂×C₃×C₉	—	4	3	no	—
39	C₂×C₃×C₉	C₃×A₄	1	1	yes	characteristic
40	C₂×C₂₇	—	3	3	no	—
41	C₂×C₂₇	—	3	3	no	—
42	C₂×C₂₇	—	4	6	no	—
43	C₂×C₂₇	C₂²⋊C₉	1	3	yes	direct product factor
44	C₂²×C₃²	—	3	1	no	—
45	C₂²×C₃²	—	3	1	no	—
46	C₂²×C₃²	C₂×C₃×C₉	1	1	yes	characteristic
47	C₂²×C₉	—	3	1	no	—
48	C₂²×C₉	—	3	2	no	—
49	C₂²×C₉	—	3	2	no	—
50	C₂²×C₉	—	3	1	no	—
51	C₂²×C₉	C₂×C₃×C₉	1	2	yes	—
52	C₂²×C₉	C₂×C₃×C₉	1	1	yes	characteristic
53	C₂²⋊C₉	C₂×C₂₇	1	9	yes	direct product factor
54	C₃×C₉	—	4	3	no	—
55	C₃×C₉	C₂×C₃×A₄	1	1	yes	characteristic
56	C₂₇	—	4	6	no	—
57	C₂₇	C₂×C₂²⋊C₉	1	3	yes	direct product factor
58	C₂³×C₃	C₉²	1	1	yes	characteristic
59	C₂³×C₃	C₃×C₂₇	1	3	yes	—
60	C₂×C₃²	—	3	1	no	—
61	C₂×C₃²	—	3	1	no	—
62	C₂×C₃²	C₉×A₄	1	1	yes	characteristic
63	C₂×C₉	—	3	2	no	—
64	C₂×C₉	—	3	2	no	—
65	C₂×C₉	—	3	1	no	—
66	C₂×C₉	—	3	1	no	—
67	C₂×C₉	—	4	9	no	—
68	C₂×C₉	C₉×A₄	1	2	yes	—
69	C₂×C₉	C₃×C₂²⋊C₉	1	1	yes	characteristic
70	C₂²×C₃	—	3	1	no	—
71	C₂²×C₃	—	3	3	no	—
72	C₂²×C₃	—	3	3	no	—
73	C₂²×C₃	—	3	1	no	—
74	C₂²×C₃	C₂×C₉²	1	1	yes	characteristic
75	C₂²×C₃	C₂×C₃×C₂₇	1	3	yes	—
76	C₃²	C₂×C₉×A₄	1	1	yes	characteristic
77	C₉	—	4	9	no	—
78	C₉	C₂×C₉×A₄	1	2	yes	—
79	C₉	C₂×C₃×C₂²⋊C₉	1	1	yes	characteristic
80	C₂³	C₉×C₂₇	1	1	yes	characteristic, complemented, Sylow
81	C₂×C₃	—	3	3	no	—
82	C₂×C₃	—	3	3	no	—
83	C₂×C₃	—	3	1	no	—
84	C₂×C₃	—	3	1	no	—
85	C₂×C₃	A₄×C₂₇	1	3	yes	—
86	C₂×C₃	C₉×C₂²⋊C₉	1	1	yes	characteristic
87	C₂²	—	3	1	no	—
88	C₂²	—	3	1	no	—
89	C₂²	C₂×C₉×C₂₇	1	1	yes	characteristic, complemented
90	C₃	C₂×A₄×C₂₇	1	3	yes	—
91	C₃	C₂×C₉×C₂²⋊C₉	1	1	yes	characteristic
92	C₂	—	3	1	no	—
93	C₂	—	3	1	no	—
94	C₂	C₂₇×C₂²⋊C₉	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₃×C₂₇	A₄
commutator, hypocenter	C₂²	C₂×C₉×C₂₇
Frattini	C₃×C₉	C₂×C₃×A₄
Fitting	C₂³×C₃×C₂₇	C₃
socle, prime radical	C₂³×C₃²	C₃×C₉
cosocle	C₂²×C₃×C₉	C₂×C₃²
LCS	G ▷ C₂²
UCS	C₁ ◁ C₂×C₃×C₂₇

Complements

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

N	H ≅ G/N	type
1. C₂₇×C₂²⋊C₉	C₂	direct (N × H)
14. C₂³×C₂₇	C₉	semidirect
15. C₂×C₂²⋊C₂₇	C₉	semidirect
27. C₂²×C₂₇	C₂×C₉	semidirect
28. C₂²⋊C₂₇	C₂×C₉	semidirect
35. C₂×C₂²⋊C₉	C₂₇	direct (N × H)
43. C₂×C₂₇	C₂²⋊C₉	direct (N × H)
53. C₂²⋊C₉	C₂×C₂₇	direct (N × H)
57. C₂₇	C₂×C₂²⋊C₉	direct (N × H)
80. C₂³	C₉×C₂₇	semidirect
89. C₂²	C₂×C₉×C₂₇	semidirect
94. C₂	C₂₇×C₂²⋊C₉	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂₇×C₂²⋊C₉	2
C₂³×C₃×C₂₇	3
C₂×C₉×C₂²⋊C₉	3
C₂×C₃×C₂²⋊C₂₇	3
C₂×C₉×C₂₇	4

Subgroups — C2×C27×C22⋊C9 #14516595

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₂₇×C₂²⋊C₉ #14516595