Subgroups — C₂²×#6897⋊C₂ #14518517

Order 1944.

476 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#6897	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#6897⋊C₂	C₂	1	6	yes	maximal, direct product factor
3	C₂²×C₉⋊D₉	C₃	1	1	yes	maximal, characteristic, complemented
4	C₂²×#4169	—	3	4	no	maximal
5	C₂×#6897	C₂²	1	3	yes	complemented
6	#6897⋊C₂	C₂²	1	4	yes	direct product factor
7	C₂²×C₉⋊C₉	—	2	4	no	—
8	C₂²×C₃²⋊C₉	D₃	1	4	yes	—
9	C₂²×C₉²	C₂×C₃	1	1	yes	characteristic, complemented
10	C₂×C₉⋊D₉	C₂×C₃	1	6	yes	complemented
11	C₂×#4169	—	3	24	no	—
12	#6897	C₂³	1	1	yes	characteristic, complemented, Sylow
13	C₂²×C₃×C₃⋊D₃	—	9	1	no	—
14	C₂²×C₃⋊D₉	—	3	4	no	—
15	C₂×C₉⋊C₉	—	2	12	no	—
16	C₂×C₃²⋊C₉	C₂×D₃	1	12	yes	—
17	C₂×C₉²	C₂²×C₃	1	3	yes	complemented
18	C₉⋊D₉	C₂²×C₃	1	4	yes	complemented
19	#4169	—	3	16	no	—
20	C₂²×C₃³	C₃⋊D₃	1	1	yes	characteristic
21	C₂×C₃×C₃⋊D₃	—	9	6	no	—
22	C₂²×C₃×C₉	—	2	4	no	—
23	C₂²×C₃×C₉	C₃×D₃	1	4	yes	—
24	C₂×C₃⋊D₉	—	3	24	no	—
25	C₉⋊C₉	—	2	4	no	—
26	C₃²⋊C₉	C₂²×D₃	1	4	yes	—
27	C₉²	C₂³×C₃	1	1	yes	characteristic, complemented
28	C₂²×C₃⋊D₃	—	9	1	no	—
29	C₂²×C₃×D₃	—	27	4	no	—
30	C₂²×D₉	—	27	4	no	—
31	C₂×C₃³	C₂×C₃⋊D₃	1	3	yes	—
32	C₃×C₃⋊D₃	—	9	4	no	—
33	C₂×C₃×C₉	—	2	12	no	—
34	C₂×C₃×C₉	C₂×C₃×D₃	1	12	yes	—
35	C₃⋊D₉	—	3	16	no	—
36	C₂²×C₃²	—	3	4	no	—
37	C₂²×C₃²	C₃×C₃⋊D₃	1	1	yes	characteristic
38	C₂×C₃⋊D₃	—	9	6	no	—
39	C₂×C₃×D₃	—	27	24	no	—
40	C₂²×C₉	—	3	4	no	—
41	C₂²×C₉	—	6	4	no	—
42	C₂×D₉	—	27	24	no	—
43	C₃³	C₂²×C₃⋊D₃	1	1	yes	characteristic
44	C₃×C₉	—	2	4	no	—
45	C₃×C₉	C₂²×C₃×D₃	1	4	yes	—
46	C₂³×C₃	—	81	1	no	—
47	C₂²×D₃	—	27	4	no	—
48	C₂×C₃²	—	3	12	no	—
49	C₂×C₃²	C₂×C₃×C₃⋊D₃	1	3	yes	—
50	C₃⋊D₃	—	9	4	no	—
51	C₃×D₃	—	27	16	no	—
52	C₂×C₉	—	3	12	no	—
53	C₂×C₉	—	6	12	no	—
54	D₉	—	27	16	no	—
55	C₂²×C₃	—	9	1	no	—
56	C₂²×C₃	—	81	6	no	—
57	C₂²×C₃	#4207	1	4	yes	—
58	C₂×D₃	—	27	24	no	—
59	C₃²	—	3	4	no	—
60	C₃²	C₂²×C₃×C₃⋊D₃	1	1	yes	characteristic
61	C₉	—	3	4	no	—
62	C₉	—	6	4	no	—
63	C₂³	—	81	1	no	Sylow
64	C₂×C₃	—	9	3	no	—
65	C₂×C₃	—	81	4	no	—
66	C₂×C₃	C₂×#4207	1	12	yes	—
67	D₃	—	27	16	no	—
68	C₂²	—	81	6	no	—
69	C₂²	#6897⋊C₂	1	1	yes	characteristic, direct product factor
70	C₃	—	9	1	no	—
71	C₃	C₂²×#4207	1	4	yes	—
72	C₂	—	81	4	no	—
73	C₂	C₂×#6897⋊C₂	1	3	yes	direct product factor

	subgroup	G/H
center, hypercenter	C₂²	#6897⋊C₂
commutator, cosocle, hypocenter	C₉²	C₂³×C₃
Frattini	C₃²	C₂²×C₃×C₃⋊D₃
Fitting	C₂²×#6897	C₂
socle	C₂²×C₃²	C₃×C₃⋊D₃
LCS	G ▷ C₉²
UCS	C₁ ◁ C₂²

Complements

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

N	H ≅ G/N	type
1. C₂²×#6897	C₂	semidirect
2. C₂×#6897⋊C₂	C₂	direct (N × H)
3. C₂²×C₉⋊D₉	C₃	semidirect
5. C₂×#6897	C₂²	semidirect
6. #6897⋊C₂	C₂²	direct (N × H)
9. C₂²×C₉²	C₂×C₃	semidirect
10. C₂×C₉⋊D₉	C₂×C₃	semidirect
12. #6897	C₂³	semidirect
17. C₂×C₉²	C₂²×C₃	semidirect
18. C₉⋊D₉	C₂²×C₃	semidirect
27. C₉²	C₂³×C₃	semidirect
69. C₂²	#6897⋊C₂	direct (N × H)
73. C₂	C₂×#6897⋊C₂	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×#6897	2
C₂×#6897⋊C₂	2
C₂²×C₉⋊D₉	3
C₂²×#4169	3

Subgroups — C22×#6897⋊C2 #14518517

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×#6897⋊C₂ #14518517