Subgroups — C₃⋊(C₃⋊((C₂²⋊C₂₇)⋊C₂)) #14518107

Order 1944.

438 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₂²⋊C₂₇	C₂	1	1	yes	maximal, characteristic, complemented
2	#10619992	—	3	1	no	maximal
3	C₃⋊((C₂²⋊C₂₇)⋊C₂)	—	3	12	no	maximal
4	C₃⋊(C₃⋊D₂₇)	—	4	1	no	maximal
5	C₂²×C₃²×C₉	D₃	1	1	yes	characteristic
6	C₂×C₃⋊(C₃⋊D₉)	—	3	1	no	—
7	C₃⋊(C₃⋊Dic₉)	—	3	1	no	—
8	C₃×C₂²⋊C₂₇	D₃	1	12	yes	complemented
9	C₃²×C₂₇	—	4	1	no	Sylow
10	#6312	—	9	1	no	—
11	#6233	—	9	8	no	—
12	#6233	—	9	4	no	—
13	(C₂²⋊C₂₇)⋊C₂	—	9	9	no	—
14	C₂×C₃²×C₉	—	3	1	no	—
15	C₃⋊(C₃⋊D₉)	—	6	1	no	—
16	C₃⋊D₂₇	—	12	12	no	—
17	C₂²×C₃³	D₉	1	1	yes	characteristic
18	C₂×C₃⋊(C₃⋊D₃)	—	9	1	no	—
19	C₃⋊(C₃⋊Dic₃)	—	9	1	no	—
20	C₂²×C₃×C₉	D₉	1	8	yes	—
21	C₂²×C₃×C₉	C₃⋊D₃	1	4	yes	—
22	C₂×C₃⋊D₉	—	9	8	no	—
23	C₂×C₃⋊D₉	—	9	4	no	—
24	C₃⋊Dic₉	—	9	8	no	—
25	C₃⋊Dic₉	—	9	4	no	—
26	C₂²⋊C₂₇	C₃⋊D₃	1	9	yes	complemented
27	C₃²×C₉	S₄	1	1	yes	characteristic
28	C₃×C₂₇	—	4	12	no	—
29	#638	—	27	9	no	—
30	#638	—	27	4	no	—
31	#611	—	27	8	no	—
32	#611	—	27	1	no	—
33	C₂×C₃³	—	3	1	no	—
34	C₃⋊(C₃⋊D₃)	—	18	1	no	—
35	C₂×C₃×C₉	—	3	8	no	—
36	C₂×C₃×C₉	—	3	4	no	—
37	C₃⋊D₉	—	18	8	no	—
38	C₃⋊D₉	—	18	4	no	—
39	D₂₇	—	36	9	no	—
40	C₂²×C₃²	D₂₇	1	9	yes	complemented
41	C₂²×C₃²	C₃⋊D₉	1	4	yes	—
42	C₂×C₃⋊D₃	—	27	4	no	—
43	C₂×C₃⋊D₃	—	27	9	no	—
44	C₃⋊Dic₃	—	27	4	no	—
45	C₃⋊Dic₃	—	27	9	no	—
46	C₂²×C₉	C₃⋊D₉	1	8	yes	—
47	C₂²×C₉	C₃⋊(C₃⋊D₃)	1	1	yes	characteristic
48	C₂×D₉	—	27	8	no	—
49	C₂×D₉	—	27	1	no	—
50	Dic₉	—	27	8	no	—
51	Dic₉	—	27	1	no	—
52	C₃³	(C₂²⋊C₉)⋊C₂	1	1	yes	characteristic
53	C₃×C₉	(C₂²⋊C₉)⋊C₂	1	8	yes	—
54	C₃×C₉	C₃⋊S₄	1	4	yes	—
55	C₂₇	—	4	9	no	—
56	#67	—	81	12	no	—
57	#67	—	81	1	no	—
58	C₂×C₃²	—	3	9	no	—
59	C₂×C₃²	—	3	4	no	—
60	C₃⋊D₃	—	54	9	no	—
61	C₃⋊D₃	—	54	4	no	—
62	C₂×C₉	—	3	8	no	—
63	C₂×C₉	—	3	1	no	—
64	D₉	—	54	8	no	—
65	D₉	—	54	1	no	—
66	C₂²×C₃	C₃⋊D₂₇	1	12	yes	complemented
67	C₂²×C₃	C₃⋊(C₃⋊D₉)	1	1	yes	characteristic
68	C₂×D₃	—	81	1	no	—
69	C₂×D₃	—	81	12	no	—
70	Dic₃	—	81	1	no	—
71	Dic₃	—	81	12	no	—
72	C₃²	(C₂²⋊C₂₇)⋊C₂	1	9	yes	complemented
73	C₃²	C₃⋊((C₂²⋊C₉)⋊C₂)	1	4	yes	—
74	C₉	C₃⋊((C₂²⋊C₉)⋊C₂)	1	8	yes	—
75	C₉	C₃⋊(C₃⋊S₄)	1	1	yes	characteristic
76	D₄	—	243	1	no	Sylow
77	C₂×C₃	—	3	12	no	—
78	C₂×C₃	—	3	1	no	—
79	D₃	—	162	12	no	—
80	D₃	—	162	1	no	—
81	C₂²	—	243	1	no	—
82	C₂²	C₃⋊(C₃⋊D₂₇)	1	1	yes	characteristic, complemented
83	C₄	—	243	1	no	—
84	C₃	C₃⋊((C₂²⋊C₂₇)⋊C₂)	1	12	yes	complemented
85	C₃	C₃⋊(C₃⋊((C₂²⋊C₉)⋊C₂))	1	1	yes	characteristic
86	C₂	—	3	1	no	—
87	C₂	—	486	1	no	—

	subgroup	G/H
center, hypercenter	C₁	G
commutator, cosocle, hypocenter	C₃²×C₂²⋊C₂₇	C₂
Frattini	C₉	C₃⋊(C₃⋊S₄)
Fitting	C₂²×C₃²×C₉	D₃
socle	C₂²×C₃³	D₉
LCS	G ▷ C₃²×C₂²⋊C₂₇
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₃²×C₂²⋊C₂₇	C₂	semidirect
8. C₃×C₂²⋊C₂₇	D₃	semidirect
26. C₂²⋊C₂₇	C₃⋊D₃	semidirect
40. C₂²×C₃²	D₂₇	semidirect
66. C₂²×C₃	C₃⋊D₂₇	semidirect
72. C₃²	(C₂²⋊C₂₇)⋊C₂	semidirect
82. C₂²	C₃⋊(C₃⋊D₂₇)	semidirect
84. C₃	C₃⋊((C₂²⋊C₂₇)⋊C₂)	semidirect

Maximal subgroups

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

subgroup	index
C₃²×C₂²⋊C₂₇	2
#10619992	3
C₃⋊((C₂²⋊C₂₇)⋊C₂)	3
C₃⋊(C₃⋊D₂₇)	4

Subgroups — C3⋊(C3⋊((C22⋊C27)⋊C2)) #14518107

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃⋊(C₃⋊((C₂²⋊C₂₇)⋊C₂)) #14518107