Subgroups — C₂×#11757616 #14517672

Order 1944.

268 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#6898	C₂	1	1	yes	maximal, characteristic
2	#11757616	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₉⋊Dic₉	C₃	1	1	yes	maximal, characteristic, complemented
4	C₂×#66316	—	3	4	no	maximal
5	C₂×#6898	C₄	1	2	yes	complemented
6	C₂×#6898	C₂²	1	1	yes	characteristic
7	C₂²×C₉⋊C₉	—	2	4	no	—
8	C₂²×C₃²⋊C₉	D₃	1	4	yes	—
9	C₂²×C₉²	C₂×C₃	1	1	yes	characteristic
10	C₉⋊Dic₉	C₂×C₃	1	2	yes	complemented
11	#66316	—	3	8	no	—
12	#6898	C₂×C₄	1	1	yes	characteristic, complemented, Sylow
13	C₂×C₃×C₃⋊Dic₃	—	9	1	no	—
14	C₂×C₃⋊Dic₉	—	3	4	no	—
15	C₂×C₉⋊C₉	—	2	8	no	—
16	C₂×C₉⋊C₉	—	2	4	no	—
17	C₂×C₃²⋊C₉	Dic₃	1	8	yes	—
18	C₂×C₃²⋊C₉	C₂×D₃	1	4	yes	—
19	C₂×C₉²	C₃×C₄	1	2	yes	complemented
20	C₂×C₉²	C₂²×C₃	1	1	yes	characteristic
21	C₂²×C₃³	C₃⋊D₃	1	1	yes	characteristic
22	C₃×C₃⋊Dic₃	—	9	2	no	—
23	C₂²×C₃×C₉	—	2	4	no	—
24	C₂²×C₃×C₉	C₃×D₃	1	4	yes	—
25	C₃⋊Dic₉	—	3	8	no	—
26	C₉⋊C₉	—	2	4	no	—
27	C₃²⋊C₉	C₂×Dic₃	1	4	yes	—
28	C₉²	C₂×C₃×C₄	1	1	yes	characteristic, complemented
29	C₂×C₃⋊Dic₃	—	9	1	no	—
30	C₂×C₃×Dic₃	—	27	4	no	—
31	C₂×Dic₉	—	27	4	no	—
32	C₂×C₃³	C₃⋊Dic₃	1	2	yes	—
33	C₂×C₃³	C₂×C₃⋊D₃	1	1	yes	characteristic
34	C₂×C₃×C₉	—	2	8	no	—
35	C₂×C₃×C₉	—	2	4	no	—
36	C₂×C₃×C₉	C₃×Dic₃	1	8	yes	—
37	C₂×C₃×C₉	C₂×C₃×D₃	1	4	yes	—
38	C₂²×C₃²	—	3	4	no	—
39	C₂²×C₃²	C₃×C₃⋊D₃	1	1	yes	characteristic
40	C₃⋊Dic₃	—	9	2	no	—
41	C₃×Dic₃	—	27	8	no	—
42	C₂²×C₉	—	3	4	no	—
43	C₂²×C₉	—	6	4	no	—
44	Dic₉	—	27	8	no	—
45	C₃³	C₂×C₃⋊Dic₃	1	1	yes	characteristic
46	C₃×C₉	—	2	4	no	—
47	C₃×C₉	C₂×C₃×Dic₃	1	4	yes	—
48	C₂×C₃×C₄	—	81	1	no	—
49	C₂×Dic₃	—	27	4	no	—
50	C₂×C₃²	—	3	8	no	—
51	C₂×C₃²	—	3	4	no	—
52	C₂×C₃²	C₃×C₃⋊Dic₃	1	2	yes	—
53	C₂×C₃²	C₂×C₃×C₃⋊D₃	1	1	yes	characteristic
54	C₂×C₉	—	3	8	no	—
55	C₂×C₉	—	3	4	no	—
56	C₂×C₉	—	6	8	no	—
57	C₂×C₉	—	6	4	no	—
58	C₂²×C₃	—	9	1	no	—
59	C₂²×C₃	#4207	1	4	yes	—
60	C₃×C₄	—	81	2	no	—
61	Dic₃	—	27	8	no	—
62	C₃²	—	3	4	no	—
63	C₃²	C₂×C₃×C₃⋊Dic₃	1	1	yes	characteristic
64	C₉	—	3	4	no	—
65	C₉	—	6	4	no	—
66	C₂×C₄	—	81	1	no	Sylow
67	C₂×C₃	—	9	2	no	—
68	C₂×C₃	—	9	1	no	—
69	C₂×C₃	#66409	1	8	yes	—
70	C₂×C₃	C₂×#4207	1	4	yes	—
71	C₂²	#92312	1	1	yes	characteristic
72	C₄	—	81	2	no	—
73	C₃	—	9	1	no	—
74	C₃	C₂×#66409	1	4	yes	—
75	C₂	#11757616	1	2	yes	direct product factor
76	C₂	C₂×#92312	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂²	#92312
commutator, hypocenter	C₉²	C₂×C₃×C₄
Frattini	C₂×C₃²	C₂×C₃×C₃⋊D₃
Fitting	C₂²×#6898	C₂
socle	C₂²×C₃²	C₃×C₃⋊D₃
prime radical	C₂²×C₃³	C₃⋊D₃
cosocle	C₂×C₉²	C₂²×C₃
LCS	G ▷ C₉²
UCS	C₁ ◁ C₂²

Complements

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

N	H ≅ G/N	type
2. #11757616	C₂	direct (N × H)
3. C₂×C₉⋊Dic₉	C₃	semidirect
5. C₂×#6898	C₄	semidirect
10. C₉⋊Dic₉	C₂×C₃	semidirect
12. #6898	C₂×C₄	semidirect
19. C₂×C₉²	C₃×C₄	semidirect
28. C₉²	C₂×C₃×C₄	semidirect
75. C₂	#11757616	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×#6898	2
#11757616	2
C₂×C₉⋊Dic₉	3
C₂×#66316	3

Subgroups — C2×#11757616 #14517672

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#11757616 #14517672