Subgroups — #14515641

Order 1944.

74 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#6872	C₂	1	1	yes	maximal, characteristic
2	#10619725	C₃	1	1	yes	maximal, characteristic
3	C₃⋊C₈×C₂₇	—	3	1	no	maximal
4	C₂×#6872	C₄	1	1	yes	characteristic
5	C₄×#737	C₂×C₃	1	1	yes	characteristic
6	C₄×C₂₇⋊C₃	—	2	1	no	—
7	C₃×C₄×C₂₇	D₃	1	1	yes	characteristic
8	#6872	C₈	1	1	yes	characteristic, complemented, Sylow
9	#6180	C₉	1	1	yes	characteristic
10	C₉×C₃⋊C₈	—	3	1	no	—
11	C₉×C₃⋊C₈	—	9	1	no	—
12	C₈×C₂₇	—	9	1	no	—
13	C₂×#737	C₃×C₄	1	1	yes	characteristic
14	C₂×C₂₇⋊C₃	—	2	1	no	—
15	C₂×C₃×C₂₇	Dic₃	1	1	yes	characteristic
16	C₄×3₋¹⁺²	—	2	1	no	—
17	C₄×3₋¹⁺²	—	6	1	no	—
18	C₄×H(3,𝔽₃)	C₂×C₉	1	1	yes	characteristic
19	C₃×C₄×C₉	—	3	1	no	—
20	C₃×C₄×C₉	C₃×D₃	1	1	yes	characteristic
21	C₄×C₂₇	—	3	1	no	—
22	C₄×C₂₇	—	6	1	no	—
23	#737	C₃×C₈	1	1	yes	characteristic
24	C₂₇⋊C₃	—	2	1	no	—
25	C₃×C₂₇	C₃⋊C₈	1	1	yes	characteristic, complemented
26	C₃×C₃⋊C₈	—	3	1	no	—
27	C₃×C₃⋊C₈	—	9	1	no	—
28	C₈×C₉	—	9	1	no	—
29	C₂×3₋¹⁺²	—	2	1	no	—
30	C₂×3₋¹⁺²	—	6	1	no	—
31	C₂×H(3,𝔽₃)	C₄×C₉	1	1	yes	characteristic
32	C₂×C₃×C₉	—	3	1	no	—
33	C₂×C₃×C₉	C₃×Dic₃	1	1	yes	characteristic
34	C₂×C₂₇	—	3	1	no	—
35	C₂×C₂₇	—	6	1	no	—
36	C₃²×C₄	—	3	1	no	—
37	C₃²×C₄	D₃×C₉	1	1	yes	characteristic
38	C₄×C₉	—	2	1	no	—
39	C₄×C₉	—	6	1	no	—
40	C₄×C₉	(C₃⋊D₃)⋊C₃	1	1	yes	characteristic
41	3₋¹⁺²	—	2	1	no	—
42	3₋¹⁺²	—	6	1	no	—
43	H(3,𝔽₃)	C₈×C₉	1	1	yes	characteristic
44	C₃×C₉	—	3	1	no	—
45	C₃×C₉	C₃×C₃⋊C₈	1	1	yes	characteristic
46	C₂₇	—	3	1	no	—
47	C₂₇	—	6	1	no	—
48	C₃×C₈	—	9	1	no	—
49	C₃⋊C₈	—	3	1	no	—
50	C₃⋊C₈	—	9	1	no	—
51	C₂×C₃²	—	3	1	no	—
52	C₂×C₃²	C₉×Dic₃	1	1	yes	characteristic
53	C₂×C₉	—	2	1	no	—
54	C₂×C₉	—	6	1	no	—
55	C₂×C₉	(C₃⋊Dic₃)⋊C₃	1	1	yes	characteristic
56	C₃×C₄	—	3	1	no	—
57	C₃×C₄	—	9	1	no	—
58	C₃×C₄	(C₃⋊D₃)⋊C₉	1	1	yes	characteristic
59	C₃²	—	3	1	no	—
60	C₃²	C₉×C₃⋊C₈	1	1	yes	characteristic
61	C₉	—	2	1	no	—
62	C₉	—	6	1	no	—
63	C₉	(C₃⋊(C₃⋊C₈))⋊C₃	1	1	yes	characteristic
64	C₈	—	9	1	no	Sylow
65	C₂×C₃	—	3	1	no	—
66	C₂×C₃	—	9	1	no	—
67	C₂×C₃	(C₃⋊Dic₃)⋊C₉	1	1	yes	characteristic
68	C₄	#92181	1	1	yes	characteristic
69	C₃	—	3	1	no	—
70	C₃	—	9	1	no	—
71	C₃	(C₃⋊(C₃⋊C₈))⋊C₉	1	1	yes	characteristic
72	C₂	#11757304	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₄×C₉	(C₃⋊D₃)⋊C₃
commutator, hypocenter	H(3,𝔽₃)	C₈×C₉
Frattini	C₃×C₄×C₉	C₃×D₃
Fitting	C₄×#6872	C₂
socle	C₂×C₃	(C₃⋊Dic₃)⋊C₉
prime radical	C₂×H(3,𝔽₃)	C₄×C₉
cosocle	C₄×#737	C₂×C₃
LCS	G ▷ H(3,𝔽₃)
UCS	C₁ ◁ C₄×C₉

Complements

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

N	H ≅ G/N	type
8. #6872	C₈	semidirect
25. 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×#6872	2
#10619725	3
C₃⋊C₈×C₂₇	3