Subgroups — C₂₇⋊((C₂²⋊C₉)⋊C₂) #14516476

Order 1944.

186 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, complemented
2	C₉⋊((C₂²⋊C₉)⋊C₂)	—	3	1	no	maximal
3	C₃⋊((C₂²⋊C₂₇)⋊C₂)	—	3	2	no	maximal
4	#10619677	—	3	1	no	maximal
5	C₉⋊D₂₇	—	4	1	no	maximal
6	C₂²×C₃×C₂₇	D₃	1	1	yes	characteristic
7	C₂×C₃⋊D₂₇	—	3	1	no	—
8	C₉×C₂²⋊C₉	D₃	1	1	yes	characteristic
9	C₃×C₂²⋊C₂₇	D₃	1	2	yes	—
10	C₃⋊Dic₂₇	—	3	1	no	—
11	C₉×C₂₇	—	4	1	no	Sylow
12	C₃⋊((C₂²⋊C₉)⋊C₂)	—	9	3	no	—
13	#6233	—	9	1	no	—
14	(C₂²⋊C₂₇)⋊C₂	—	9	6	no	—
15	#6171	—	9	3	no	—
16	C₂×C₃×C₂₇	—	3	1	no	—
17	C₃⋊D₂₇	—	6	1	no	—
18	C₃⋊D₂₇	—	12	2	no	—
19	C₉⋊D₉	—	12	1	no	—
20	C₂²×C₃×C₉	C₃⋊D₃	1	1	yes	characteristic
21	C₂×C₃⋊D₉	—	9	1	no	—
22	C₃×C₂²⋊C₉	D₉	1	3	yes	—
23	C₃⋊Dic₉	—	9	1	no	—
24	C₂²×C₂₇	D₉	1	3	yes	complemented
25	C₂×D₂₇	—	9	3	no	—
26	C₂²⋊C₂₇	D₉	1	6	yes	complemented
27	Dic₂₇	—	9	3	no	—
28	C₃×C₂₇	—	4	2	no	—
29	C₃×C₂₇	S₄	1	1	yes	characteristic
30	C₉²	—	4	1	no	—
31	#638	—	27	1	no	—
32	(C₂²⋊C₉)⋊C₂	—	27	9	no	—
33	#611	—	27	1	no	—
34	#611	—	27	2	no	—
35	C₂×C₃×C₉	—	3	1	no	—
36	C₃⋊D₉	—	18	1	no	—
37	C₃⋊D₉	—	36	3	no	—
38	C₂×C₂₇	—	3	3	no	—
39	D₂₇	—	18	3	no	—
40	D₂₇	—	36	6	no	—
41	C₂²×C₃²	C₃⋊D₉	1	1	yes	characteristic
42	C₂×C₃⋊D₃	—	27	1	no	—
43	C₃⋊Dic₃	—	27	1	no	—
44	C₂²×C₉	C₃⋊D₉	1	2	yes	—
45	C₂²×C₉	C₃⋊D₉	1	1	yes	characteristic
46	C₂×D₉	—	27	1	no	—
47	C₂×D₉	—	27	2	no	—
48	C₂²⋊C₉	D₂₇	1	9	yes	complemented
49	Dic₉	—	27	1	no	—
50	Dic₉	—	27	2	no	—
51	C₃×C₉	—	4	3	no	—
52	C₃×C₉	C₃⋊S₄	1	1	yes	characteristic
53	C₂₇	—	4	6	no	—
54	C₂₇	(C₂²⋊C₉)⋊C₂	1	3	yes	complemented
55	#67	—	81	1	no	—
56	#67	—	81	3	no	—
57	C₂×C₃²	—	3	1	no	—
58	C₃⋊D₃	—	54	1	no	—
59	C₂×C₉	—	3	2	no	—
60	C₂×C₉	—	3	1	no	—
61	D₉	—	54	2	no	—
62	D₉	—	54	1	no	—
63	D₉	—	108	9	no	—
64	C₂²×C₃	C₉⋊D₉	1	1	yes	characteristic
65	C₂²×C₃	C₃⋊D₂₇	1	3	yes	—
66	C₂×D₃	—	81	1	no	—
67	C₂×D₃	—	81	3	no	—
68	Dic₃	—	81	1	no	—
69	Dic₃	—	81	3	no	—
70	C₃²	C₉⋊S₄	1	1	yes	characteristic
71	C₉	—	4	9	no	—
72	C₉	C₉⋊S₄	1	2	yes	—
73	C₉	C₃⋊((C₂²⋊C₉)⋊C₂)	1	1	yes	characteristic
74	D₄	—	243	1	no	Sylow
75	C₂×C₃	—	3	3	no	—
76	C₂×C₃	—	3	1	no	—
77	D₃	—	162	3	no	—
78	D₃	—	162	1	no	—
79	C₂²	—	243	1	no	—
80	C₂²	C₉⋊D₂₇	1	1	yes	characteristic, complemented
81	C₄	—	243	1	no	—
82	C₃	A₄⋊D₂₇	1	3	yes	—
83	C₃	C₉⋊((C₂²⋊C₉)⋊C₂)	1	1	yes	characteristic
84	C₂	—	3	1	no	—
85	C₂	—	486	1	no	—

	subgroup	G/H
center, hypercenter	C₁	G
commutator, cosocle, hypocenter	C₂₇×C₂²⋊C₉	C₂
Frattini	C₃×C₉	C₃⋊S₄
Fitting	C₂²×C₃×C₂₇	D₃
socle	C₂²×C₃²	C₃⋊D₉
LCS	G ▷ C₂₇×C₂²⋊C₉
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₂₇×C₂²⋊C₉	C₂	semidirect
24. C₂²×C₂₇	D₉	semidirect
26. C₂²⋊C₂₇	D₉	semidirect
48. C₂²⋊C₉	D₂₇	semidirect
54. C₂₇	(C₂²⋊C₉)⋊C₂	semidirect
80. C₂²	C₉⋊D₂₇	semidirect

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
C₉⋊((C₂²⋊C₉)⋊C₂)	3
C₃⋊((C₂²⋊C₂₇)⋊C₂)	3
#10619677	3
C₉⋊D₂₇	4

Subgroups — C27⋊((C22⋊C9)⋊C2) #14516476

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₇⋊((C₂²⋊C₉)⋊C₂) #14516476