Subgroups — #14516439

Order 1944.

95 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11757427	C₂	1	1	yes	maximal, characteristic, complemented
2	#10620044	C₃	1	1	yes	maximal, characteristic
3	#67×C₂₇	—	3	1	no	maximal
4	#92183	—	4	1	no	maximal
5	#66436	C₂×C₃	1	1	yes	characteristic
6	C₂²×C₃×C₂₇	D₃	1	1	yes	characteristic, complemented
7	C₂×D₃×C₂₇	—	3	1	no	—
8	#66353	—	2	1	no	—
9	Dic₃×C₂₇	—	3	1	no	—
10	#6873	—	4	1	no	Sylow
11	#6258	C₉	1	1	yes	characteristic
12	C₉×S₄	—	9	1	no	—
13	C₉×#67	—	3	1	no	—
14	D₄×C₂₇	—	9	1	no	—
15	#4208	—	4	1	no	—
16	C₂×C₃×C₂₇	—	3	1	no	—
17	D₃×C₂₇	—	6	1	no	—
18	C₂²×C₃×C₉	C₃×D₃	1	1	yes	characteristic
19	C₂×D₃×C₉	—	3	1	no	—
20	C₂²⋊H(3,𝔽₃)	C₂×C₉	1	1	yes	characteristic
21	#1094	—	2	1	no	—
22	C₉⋊A₄	—	6	1	no	—
23	C₉×A₄	—	3	1	no	—
24	C₉×Dic₃	—	3	1	no	—
25	C₂²×C₂₇	—	3	1	no	—
26	C₂²×C₂₇	—	9	1	no	—
27	C₂²⋊C₂₇	—	6	1	no	—
28	C₄×C₂₇	—	9	1	no	—
29	#737	—	4	1	no	—
30	C₂₇⋊C₃	—	8	1	no	—
31	C₃×C₂₇	S₄	1	1	yes	characteristic, complemented
32	C₃×S₄	—	9	1	no	—
33	C₃×#67	—	3	1	no	—
34	D₄×C₉	—	9	1	no	—
35	C₂×C₃×C₉	—	3	1	no	—
36	#272	—	4	1	no	—
37	D₃×C₉	—	6	1	no	—
38	D₃×C₉	—	36	1	no	—
39	C₂×C₂₇	—	3	1	no	—
40	C₂×C₂₇	—	6	1	no	—
41	C₂×C₂₇	—	18	1	no	—
42	C₂²×C₃²	D₃×C₉	1	1	yes	characteristic
43	C₂×C₃×D₃	—	3	1	no	—
44	C₃×A₄	—	3	1	no	—
45	C₃×Dic₃	—	3	1	no	—
46	C₂²×C₉	—	2	1	no	—
47	C₂²×C₉	—	9	1	no	—
48	C₂²×C₉	(C₃⋊D₃)⋊C₃	1	1	yes	characteristic
49	C₂²⋊C₉	—	6	1	no	—
50	C₄×C₉	—	9	1	no	—
51	3₋¹⁺²	—	8	1	no	—
52	3₋¹⁺²	—	24	1	no	—
53	H(3,𝔽₃)	—	4	1	no	—
54	C₃×C₉	—	12	1	no	—
55	C₃×C₉	C₃×S₄	1	1	yes	characteristic
56	C₂₇	—	3	1	no	—
57	C₂₇	—	24	1	no	—
58	S₄	—	9	1	no	—
59	C₃×D₄	—	9	1	no	—
60	#67	—	3	1	no	—
61	C₂×C₃²	—	3	1	no	—
62	C₃×D₃	—	6	1	no	—
63	C₃×D₃	—	36	1	no	—
64	C₂×C₉	—	3	1	no	—
65	C₂×C₉	—	6	1	no	—
66	C₂×C₉	—	18	1	no	—
67	C₂²×C₃	—	3	1	no	—
68	C₂²×C₃	—	9	1	no	—
69	C₂²×C₃	(C₃⋊D₃)⋊C₉	1	1	yes	characteristic
70	C₂×D₃	—	3	1	no	—
71	A₄	—	9	1	no	—
72	C₃×C₄	—	9	1	no	—
73	Dic₃	—	3	1	no	—
74	C₃²	—	12	1	no	—
75	C₃²	C₉×S₄	1	1	yes	characteristic
76	C₉	—	2	1	no	—
77	C₉	—	24	1	no	—
78	C₉	(C₃⋊S₄)⋊C₃	1	1	yes	characteristic
79	D₄	—	9	1	no	Sylow
80	C₂×C₃	—	3	1	no	—
81	C₂×C₃	—	3	1	no	—
82	C₂×C₃	—	6	1	no	—
83	C₂×C₃	—	18	1	no	—
84	D₃	—	6	1	no	—
85	D₃	—	36	1	no	—
86	C₂²	—	9	1	no	—
87	C₂²	#92183	1	1	yes	characteristic, complemented
88	C₄	—	9	1	no	—
89	C₃	—	3	1	no	—
90	C₃	—	36	1	no	—
91	C₃	(C₃⋊S₄)⋊C₉	1	1	yes	characteristic
92	C₂	—	3	1	no	—
93	C₂	—	18	1	no	—

	subgroup	G/H
center, hypercenter	C₉	(C₃⋊S₄)⋊C₃
commutator, hypocenter	C₂²⋊H(3,𝔽₃)	C₂×C₉
Frattini	C₃×C₉	C₃×S₄
Fitting	C₂²×C₃×C₂₇	D₃
socle	C₂²×C₃	(C₃⋊D₃)⋊C₉
prime radical	#6258	C₉
cosocle	#66436	C₂×C₃
LCS	G ▷ C₂²⋊H(3,𝔽₃)
UCS	C₁ ◁ C₉

Complements

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

N	H ≅ G/N	type
1. #11757427	C₂	semidirect
6. C₂²×C₃×C₂₇	D₃	semidirect
31. C₃×C₂₇	S₄	semidirect
87. C₂²	#92183	semidirect

Maximal subgroups

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

subgroup	index
#11757427	2
#10620044	3
#67×C₂₇	3
#92183	4