Subgroups — C₃²×(C₂²⋊C₂₇)⋊C₂ #14517962

Order 1944.

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

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

Complements

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

N	H ≅ G/N	type
1. C₃²×C₂²⋊C₂₇	C₂	semidirect
3. C₃×(C₂²⋊C₂₇)⋊C₂	C₃	direct (N × H)
9. C₃×C₂²⋊C₂₇	C₂×C₃	semidirect
13. (C₂²⋊C₂₇)⋊C₂	C₃²	direct (N × H)
25. C₂²⋊C₂₇	C₂×C₃²	semidirect
40. C₂²×C₃²	D₂₇	semidirect
66. C₂²×C₃	C₃×D₂₇	semidirect
72. C₃²	(C₂²⋊C₂₇)⋊C₂	direct (N × H)
83. C₂²	C₃²×D₂₇	semidirect
86. C₃	C₃×(C₂²⋊C₂₇)⋊C₂	direct (N × H)

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
C₃²×#611	3
C₃×(C₂²⋊C₂₇)⋊C₂	3
C₃²×D₂₇	4

Subgroups — C32×(C22⋊C27)⋊C2 #14517962

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃²×(C₂²⋊C₂₇)⋊C₂ #14517962