Subgroups — #14516143

Order 1944.

138 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	#11757337	C₂	1	2	yes	maximal
3	#10619965	—	3	1	no	maximal
4	(C₂₇⋊C₃)⋊Q₈	—	3	2	no	maximal
5	C₃×Dic₅₄	—	3	1	no	maximal
6	C₂×#6873	C₂²	1	1	yes	characteristic
7	C₄×#737	D₃	1	1	yes	characteristic
8	#66409	—	3	2	no	—
9	C₄×C₂₇⋊C₃	D₃	1	2	yes	—
10	C₃×C₄×C₂₇	D₃	1	1	yes	characteristic
11	(C₂₇⋊C₃)⋊C₄	—	3	4	no	—
12	C₃×Dic₂₇	—	3	2	no	—
13	#6873	Q₈	1	1	yes	characteristic, complemented, Sylow
14	#6226	—	3	1	no	—
15	3₋¹⁺²⋊Q₈	—	9	2	no	—
16	#634⋊C₃	—	9	1	no	—
17	C₃×Dic₁₈	—	9	1	no	—
18	Dic₅₄	—	3	1	no	—
19	Dic₅₄	—	3	2	no	—
20	C₂×#737	C₂×D₃	1	1	yes	characteristic
21	C₂×C₂₇⋊C₃	C₂×D₃	1	2	yes	—
22	C₂×C₃×C₂₇	C₂×D₃	1	1	yes	characteristic
23	C₄×3₋¹⁺²	—	6	1	no	—
24	C₄×3₋¹⁺²	D₉	1	2	yes	—
25	C₄×H(3,𝔽₃)	D₉	1	1	yes	characteristic
26	C₃×C₄×C₉	—	3	1	no	—
27	C₃×C₄×C₉	C₃⋊D₃	1	1	yes	characteristic
28	C₃⋊Dic₉	—	3	2	no	—
29	3₋¹⁺²⋊C₄	—	9	4	no	—
30	(C₃⋊Dic₃)⋊C₃	—	9	2	no	—
31	C₃×Dic₉	—	9	2	no	—
32	C₄×C₂₇	—	3	1	no	—
33	C₄×C₂₇	—	3	2	no	—
34	Dic₂₇	—	3	2	no	—
35	Dic₂₇	—	3	4	no	—
36	#737	Dic₆	1	1	yes	characteristic
37	C₂₇⋊C₃	Dic₆	1	2	yes	complemented
38	C₃×C₂₇	Dic₆	1	1	yes	characteristic, complemented
39	#634	—	9	1	no	—
40	C₃×Dic₆	—	27	1	no	—
41	Dic₁₈	—	9	2	no	—
42	Dic₁₈	—	9	1	no	—
43	C₂×3₋¹⁺²	—	6	1	no	—
44	C₂×3₋¹⁺²	C₂×D₉	1	2	yes	—
45	C₂×H(3,𝔽₃)	C₂×D₉	1	1	yes	characteristic
46	C₂×C₃×C₉	—	3	1	no	—
47	C₂×C₃×C₉	C₂×C₃⋊D₃	1	1	yes	characteristic
48	C₂×C₂₇	—	3	1	no	—
49	C₂×C₂₇	—	3	2	no	—
50	C₃²×C₄	—	3	1	no	—
51	C₃²×C₄	C₃⋊D₉	1	1	yes	characteristic
52	C₃⋊Dic₃	—	9	2	no	—
53	C₃×Dic₃	—	27	2	no	—
54	C₄×C₉	—	2	1	no	—
55	C₄×C₉	—	3	2	no	—
56	C₄×C₉	#272	1	1	yes	characteristic
57	Dic₉	—	9	4	no	—
58	Dic₉	—	9	2	no	—
59	3₋¹⁺²	—	6	1	no	—
60	3₋¹⁺²	Dic₁₈	1	2	yes	—
61	H(3,𝔽₃)	Dic₁₈	1	1	yes	characteristic
62	C₃×C₉	—	3	1	no	—
63	C₃×C₉	#634	1	1	yes	characteristic
64	C₂₇	—	3	1	no	—
65	C₂₇	—	3	2	no	—
66	C₃×Q₈	—	81	1	no	—
67	Dic₆	—	27	1	no	—
68	Dic₆	—	81	1	no	—
69	C₂×C₃²	—	3	1	no	—
70	C₂×C₃²	C₂×C₃⋊D₉	1	1	yes	characteristic
71	C₂×C₉	—	2	1	no	—
72	C₂×C₉	—	3	2	no	—
73	C₂×C₉	C₂×#272	1	1	yes	characteristic
74	C₃×C₄	—	3	1	no	—
75	C₃×C₄	—	9	1	no	—
76	C₃×C₄	—	81	2	no	—
77	C₃×C₄	#4181	1	1	yes	characteristic
78	Dic₃	—	27	2	no	—
79	Dic₃	—	81	2	no	—
80	C₃²	—	3	1	no	—
81	C₃²	#6226	1	1	yes	characteristic
82	C₉	—	2	1	no	—
83	C₉	—	3	2	no	—
84	C₉	#6229	1	1	yes	characteristic
85	Q₈	—	81	1	no	Sylow
86	C₂×C₃	—	3	1	no	—
87	C₂×C₃	—	9	1	no	—
88	C₂×C₃	C₂×#4181	1	1	yes	characteristic
89	C₄	—	81	2	no	—
90	C₄	#92214	1	1	yes	characteristic
91	C₃	—	3	1	no	—
92	C₃	—	9	1	no	—
93	C₃	#10619654	1	1	yes	characteristic
94	C₂	C₂×#92214	1	1	yes	characteristic

	subgroup	G/H
center	C₂	C₂×#92214
commutator, cosocle	C₂×#6873	C₂²
Frattini	C₂×C₃×C₉	C₂×C₃⋊D₃
Fitting	C₄×#6873	C₂
socle	C₂×C₃	C₂×#4181
prime radical	C₂×H(3,𝔽₃)	C₂×D₉
hypercenter	C₄	#92214
hypocenter	#6873	Q₈
LCS	G ▷ C₂×#6873 ▷ #6873
UCS	C₁ ◁ C₂ ◁ C₄

Complements

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

N	H ≅ G/N	type
13. #6873	Q₈	semidirect
37. C₂₇⋊C₃	Dic₆	semidirect
38. C₃×C₂₇	Dic₆	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
#11757337	2
#10619965	3
(C₂₇⋊C₃)⋊Q₈	3
C₃×Dic₅₄	3