Subgroups — #14516149

Order 1944.

135 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#6879	C₂	1	1	yes	maximal, characteristic
2	#11757339	C₂	1	2	yes	maximal
3	#10619619	—	3	3	no	maximal
4	C₉×Dic₁₈	—	3	1	no	maximal
5	C₂×#6879	C₂²	1	1	yes	characteristic
6	C₄×#732	D₃	1	3	yes	—
7	C₄×C₉²	D₃	1	1	yes	characteristic
8	#66325	—	3	6	no	—
9	C₉×Dic₉	—	3	2	no	—
10	#6879	Q₈	1	1	yes	characteristic, complemented, Sylow
11	#6229	—	3	3	no	—
12	C₉×Dic₆	—	9	1	no	—
13	C₃×Dic₁₈	—	3	1	no	—
14	C₂×#732	C₂×D₃	1	3	yes	—
15	C₂×C₉²	C₂×D₃	1	1	yes	characteristic
16	C₄×H(3,𝔽₃)	—	3	3	no	—
17	C₃×C₄×C₉	—	3	1	no	—
18	C₃×C₄×C₉	C₃⋊D₃	1	1	yes	characteristic
19	#1084	—	3	6	no	—
20	C₉×Dic₃	—	9	2	no	—
21	C₃×Dic₉	—	3	2	no	—
22	#732	Dic₆	1	3	yes	complemented
23	C₉²	Dic₆	1	1	yes	characteristic, complemented
24	C₃×Dic₆	—	9	1	no	—
25	C₃×Dic₆	—	27	3	no	—
26	Q₈×C₉	—	27	1	no	—
27	Dic₁₈	—	3	1	no	—
28	C₂×H(3,𝔽₃)	—	3	3	no	—
29	C₂×C₃×C₉	—	3	1	no	—
30	C₂×C₃×C₉	C₂×C₃⋊D₃	1	1	yes	characteristic
31	C₃²×C₄	—	9	3	no	—
32	C₃²×C₄	#272	1	1	yes	characteristic
33	C₃×Dic₃	—	9	2	no	—
34	C₃×Dic₃	—	27	6	no	—
35	C₄×C₉	—	3	1	no	—
36	C₄×C₉	—	3	1	no	—
37	C₄×C₉	—	6	1	no	—
38	C₄×C₉	—	27	2	no	—
39	Dic₉	—	3	2	no	—
40	H(3,𝔽₃)	—	3	3	no	—
41	C₃×C₉	—	3	1	no	—
42	C₃×C₉	#634	1	1	yes	characteristic
43	C₃×Q₈	—	27	1	no	—
44	Dic₆	—	9	1	no	—
45	Dic₆	—	27	3	no	—
46	C₂×C₃²	—	9	3	no	—
47	C₂×C₃²	C₂×#272	1	1	yes	characteristic
48	C₂×C₉	—	3	1	no	—
49	C₂×C₉	—	3	1	no	—
50	C₂×C₉	—	6	1	no	—
51	C₃×C₄	—	3	1	no	—
52	C₃×C₄	—	27	2	no	—
53	C₃×C₄	—	27	3	no	—
54	C₃×C₄	#4185	1	1	yes	characteristic
55	Dic₃	—	9	2	no	—
56	Dic₃	—	27	6	no	—
57	C₃²	—	9	3	no	—
58	C₃²	#6229	1	1	yes	characteristic
59	C₉	—	3	1	no	—
60	C₉	—	3	1	no	—
61	C₉	—	6	1	no	—
62	Q₈	—	27	1	no	Sylow
63	C₂×C₃	—	3	1	no	—
64	C₂×C₃	—	27	3	no	—
65	C₂×C₃	C₂×#4185	1	1	yes	characteristic
66	C₄	—	27	2	no	—
67	C₄	#92216	1	1	yes	characteristic
68	C₃	—	3	1	no	—
69	C₃	—	27	3	no	—
70	C₃	#10619666	1	1	yes	characteristic
71	C₂	C₂×#92216	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₃	C₂×#4185
commutator, prime radical, cosocle	C₂×#6879	C₂²
Frattini	C₂×C₃×C₉	C₂×C₃⋊D₃
Fitting	C₄×#6879	C₂
hypercenter	C₃×C₄	#4185
hypocenter	#6879	Q₈
LCS	G ▷ C₂×#6879 ▷ #6879
UCS	C₁ ◁ C₂×C₃ ◁ C₃×C₄

Complements

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

N	H ≅ G/N	type
10. #6879	Q₈	semidirect
22. #732	Dic₆	semidirect
23. C₉²	Dic₆	semidirect

Maximal subgroups

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

subgroup	index
C₄×#6879	2
#11757339	2
#10619619	3
C₉×Dic₁₈	3