Subgroups — C₂×#11757320 #14516152

Order 1944.

420 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#6855	C₂	1	1	yes	maximal, characteristic
2	#11757320	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₃×C₃⋊Dic₉	—	3	4	no	maximal
4	C₂×#6855	C₄	1	2	yes	complemented
5	C₂×#6855	C₂²	1	1	yes	characteristic
6	C₂²×C₃²×C₉	D₃	1	4	yes	—
7	C₃×C₃⋊Dic₉	—	3	8	no	—
8	#6855	C₂×C₄	1	1	yes	characteristic, complemented, Sylow
9	C₂×C₃×C₃⋊Dic₃	—	9	1	no	—
10	C₂×C₃⋊Dic₉	—	3	4	no	—
11	C₂×C₃×Dic₉	—	9	12	no	—
12	C₂×C₃²×C₉	Dic₃	1	8	yes	—
13	C₂×C₃²×C₉	C₂×D₃	1	4	yes	—
14	C₂²×C₃³	C₃⋊D₃	1	1	yes	characteristic
15	C₃×C₃⋊Dic₃	—	9	2	no	—
16	C₂²×C₃×C₉	—	3	4	no	—
17	C₂²×C₃×C₉	—	6	4	no	—
18	C₂²×C₃×C₉	D₉	1	12	yes	—
19	C₃⋊Dic₉	—	3	8	no	—
20	C₃×Dic₉	—	9	24	no	—
21	C₃²×C₉	C₂×Dic₃	1	4	yes	—
22	C₂×C₃⋊Dic₃	—	9	1	no	—
23	C₂×C₃×Dic₃	—	27	4	no	—
24	C₂×Dic₉	—	9	12	no	—
25	C₂×C₃³	C₃⋊Dic₃	1	2	yes	—
26	C₂×C₃³	C₂×C₃⋊D₃	1	1	yes	characteristic
27	C₂×C₃×C₉	—	3	8	no	—
28	C₂×C₃×C₉	—	3	4	no	—
29	C₂×C₃×C₉	—	6	8	no	—
30	C₂×C₃×C₉	—	6	4	no	—
31	C₂×C₃×C₉	Dic₉	1	24	yes	complemented
32	C₂×C₃×C₉	C₂×D₉	1	12	yes	—
33	C₂²×C₃²	—	2	4	no	—
34	C₂²×C₃²	C₃⋊D₉	1	4	yes	—
35	C₂²×C₃²	#272	1	1	yes	characteristic
36	C₃⋊Dic₃	—	9	2	no	—
37	C₃×Dic₃	—	27	8	no	—
38	C₂²×C₉	—	3	12	no	—
39	Dic₉	—	9	24	no	—
40	C₃³	C₂×C₃⋊Dic₃	1	1	yes	characteristic
41	C₃×C₉	—	3	4	no	—
42	C₃×C₉	—	6	4	no	—
43	C₃×C₉	C₂×Dic₉	1	12	yes	complemented
44	C₂×C₃×C₄	—	81	1	no	—
45	C₂×Dic₃	—	27	4	no	—
46	C₂×C₃²	—	2	8	no	—
47	C₂×C₃²	—	2	4	no	—
48	C₂×C₃²	C₃⋊Dic₉	1	8	yes	—
49	C₂×C₃²	#1084	1	2	yes	—
50	C₂×C₃²	C₂×C₃⋊D₉	1	4	yes	—
51	C₂×C₃²	C₂×#272	1	1	yes	characteristic
52	C₂×C₉	—	3	24	no	—
53	C₂×C₉	—	3	12	no	—
54	C₂²×C₃	—	2	4	no	—
55	C₂²×C₃	C₉⋊D₉	1	1	yes	characteristic
56	C₂²×C₃	#4181	1	4	yes	—
57	C₃×C₄	—	81	2	no	—
58	Dic₃	—	27	8	no	—
59	C₃²	—	2	4	no	—
60	C₃²	C₂×C₃⋊Dic₉	1	4	yes	—
61	C₃²	C₂×#1084	1	1	yes	characteristic
62	C₉	—	3	12	no	—
63	C₂×C₄	—	81	1	no	Sylow
64	C₂×C₃	—	2	8	no	—
65	C₂×C₃	—	2	4	no	—
66	C₂×C₃	C₉⋊Dic₉	1	2	yes	—
67	C₂×C₃	#66328	1	8	yes	—
68	C₂×C₃	C₂×C₉⋊D₉	1	1	yes	characteristic
69	C₂×C₃	C₂×#4181	1	4	yes	—
70	C₂²	#92197	1	1	yes	characteristic
71	C₄	—	81	2	no	—
72	C₃	—	2	4	no	—
73	C₃	C₂×C₉⋊Dic₉	1	1	yes	characteristic
74	C₃	C₂×#66328	1	4	yes	—
75	C₂	#11757320	1	2	yes	direct product factor
76	C₂	C₂×#92197	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂²×C₃	C₉⋊D₉
commutator, hypocenter	#6855	C₂×C₄
Frattini	C₂×C₃³	C₂×C₃⋊D₃
Fitting	C₂²×#6855	C₂
socle, prime radical	C₂²×C₃³	C₃⋊D₃
cosocle	C₂×#6855	C₂²
LCS	G ▷ #6855
UCS	C₁ ◁ C₂²×C₃

Complements

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

N	H ≅ G/N	type
2. #11757320	C₂	direct (N × H)
4. C₂×#6855	C₄	semidirect
8. #6855	C₂×C₄	semidirect
31. C₂×C₃×C₉	Dic₉	semidirect
43. C₃×C₉	C₂×Dic₉	semidirect
75. C₂	#11757320	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×#6855	2
#11757320	2
C₂×C₃×C₃⋊Dic₉	3

Subgroups — C2×#11757320 #14516152

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#11757320 #14516152