Subgroups — #14515674

Order 1944.

94 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#6873	C₂	1	1	yes	maximal, characteristic
2	#10619724	—	3	1	no	maximal
3	(C₂₇⋊C₃)⋊C₈	—	3	2	no	maximal
4	C₃×C₂₇⋊C₈	—	3	1	no	maximal
5	C₂×#6873	C₄	1	1	yes	characteristic
6	C₄×#737	D₃	1	1	yes	characteristic
7	C₄×C₂₇⋊C₃	D₃	1	2	yes	—
8	C₃×C₄×C₂₇	D₃	1	1	yes	characteristic
9	#6873	C₈	1	1	yes	characteristic, complemented, Sylow
10	C₃⋊(C₉⋊C₈)	—	3	1	no	—
11	3₋¹⁺²⋊C₈	—	9	2	no	—
12	(C₃⋊(C₃⋊C₈))⋊C₃	—	9	1	no	—
13	C₃×C₉⋊C₈	—	9	1	no	—
14	C₂₇⋊C₈	—	3	1	no	—
15	C₂₇⋊C₈	—	3	2	no	—
16	C₂×#737	Dic₃	1	1	yes	characteristic
17	C₂×C₂₇⋊C₃	Dic₃	1	2	yes	—
18	C₂×C₃×C₂₇	Dic₃	1	1	yes	characteristic
19	C₄×3₋¹⁺²	—	6	1	no	—
20	C₄×3₋¹⁺²	D₉	1	2	yes	—
21	C₄×H(3,𝔽₃)	D₉	1	1	yes	characteristic
22	C₃×C₄×C₉	—	3	1	no	—
23	C₃×C₄×C₉	C₃⋊D₃	1	1	yes	characteristic
24	C₄×C₂₇	—	3	1	no	—
25	C₄×C₂₇	—	3	2	no	—
26	#737	C₃⋊C₈	1	1	yes	characteristic
27	C₂₇⋊C₃	C₃⋊C₈	1	2	yes	complemented
28	C₃×C₂₇	C₃⋊C₈	1	1	yes	characteristic, complemented
29	C₃⋊(C₃⋊C₈)	—	9	1	no	—
30	C₃×C₃⋊C₈	—	27	1	no	—
31	C₉⋊C₈	—	9	2	no	—
32	C₉⋊C₈	—	9	1	no	—
33	C₂×3₋¹⁺²	—	6	1	no	—
34	C₂×3₋¹⁺²	Dic₉	1	2	yes	—
35	C₂×H(3,𝔽₃)	Dic₉	1	1	yes	characteristic
36	C₂×C₃×C₉	—	3	1	no	—
37	C₂×C₃×C₉	C₃⋊Dic₃	1	1	yes	characteristic
38	C₂×C₂₇	—	3	1	no	—
39	C₂×C₂₇	—	3	2	no	—
40	C₃²×C₄	—	3	1	no	—
41	C₃²×C₄	C₃⋊D₉	1	1	yes	characteristic
42	C₄×C₉	—	2	1	no	—
43	C₄×C₉	—	3	2	no	—
44	C₄×C₉	#272	1	1	yes	characteristic
45	3₋¹⁺²	—	6	1	no	—
46	3₋¹⁺²	C₉⋊C₈	1	2	yes	—
47	H(3,𝔽₃)	C₉⋊C₈	1	1	yes	characteristic
48	C₃×C₉	—	3	1	no	—
49	C₃×C₉	C₃⋊(C₃⋊C₈)	1	1	yes	characteristic
50	C₂₇	—	3	1	no	—
51	C₂₇	—	3	2	no	—
52	C₃×C₈	—	81	1	no	—
53	C₃⋊C₈	—	27	1	no	—
54	C₃⋊C₈	—	81	1	no	—
55	C₂×C₃²	—	3	1	no	—
56	C₂×C₃²	C₃⋊Dic₉	1	1	yes	characteristic
57	C₂×C₉	—	2	1	no	—
58	C₂×C₉	—	3	2	no	—
59	C₂×C₉	#1084	1	1	yes	characteristic
60	C₃×C₄	—	3	1	no	—
61	C₃×C₄	—	9	1	no	—
62	C₃×C₄	#4181	1	1	yes	characteristic
63	C₃²	—	3	1	no	—
64	C₃²	C₃⋊(C₉⋊C₈)	1	1	yes	characteristic
65	C₉	—	2	1	no	—
66	C₉	—	3	2	no	—
67	C₉	#6180	1	1	yes	characteristic
68	C₈	—	81	1	no	Sylow
69	C₂×C₃	—	3	1	no	—
70	C₂×C₃	—	9	1	no	—
71	C₂×C₃	#66328	1	1	yes	characteristic
72	C₄	#92214	1	1	yes	characteristic
73	C₃	—	3	1	no	—
74	C₃	—	9	1	no	—
75	C₃	#10619507	1	1	yes	characteristic
76	C₂	#11757337	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₄	#92214
commutator, hypocenter	#6873	C₈
Frattini	C₃×C₄×C₉	C₃⋊D₃
Fitting, cosocle	C₄×#6873	C₂
socle	C₂×C₃	#66328
prime radical	C₂×H(3,𝔽₃)	Dic₉
LCS	G ▷ #6873
UCS	C₁ ◁ C₄

Complements

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

N	H ≅ G/N	type
9. #6873	C₈	semidirect
27. C₂₇⋊C₃	C₃⋊C₈	semidirect
28. C₃×C₂₇	C₃⋊C₈	semidirect

Maximal subgroups

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

subgroup	index
C₄×#6873	2
#10619724	3
(C₂₇⋊C₃)⋊C₈	3
C₃×C₂₇⋊C₈	3