Subgroups — C₂²×C₄×Dic₁₁ #10623313

Order 704.

498 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₄×C₁₁	C₂	1	1	yes	maximal, characteristic
2	C₂³×Dic₁₁	C₂	1	2	yes	maximal
3	C₂×C₄×Dic₁₁	C₂	1	12	yes	maximal, direct product factor
4	C₂⁴×C₁₁	C₂²	1	1	yes	characteristic
5	C₂²×C₄×C₁₁	C₄	1	8	yes	complemented
6	C₂²×C₄×C₁₁	C₂²	1	6	yes	—
7	C₂²×Dic₁₁	C₄	1	16	yes	direct product factor
8	C₂²×Dic₁₁	C₂²	1	12	yes	—
9	C₄×Dic₁₁	C₂²	1	16	yes	direct product factor
10	C₂³×C₁₁	C₂×C₄	1	8	yes	—
11	C₂³×C₁₁	C₂×C₄	1	4	yes	—
12	C₂³×C₁₁	C₂³	1	3	yes	—
13	C₂×C₄×C₁₁	C₂×C₄	1	24	yes	complemented
14	C₂×C₄×C₁₁	C₂³	1	4	yes	—
15	C₂×Dic₁₁	C₂×C₄	1	48	yes	direct product factor
16	C₂×Dic₁₁	C₂³	1	8	yes	—
17	C₂²×C₄²	—	11	1	no	maximal, Sylow
18	C₂²×C₁₁	C₄²	1	16	yes	complemented
19	C₂²×C₁₁	C₂²×C₄	1	12	yes	—
20	C₂²×C₁₁	C₂²×C₄	1	6	yes	—
21	C₂²×C₁₁	C₂⁴	1	1	yes	characteristic
22	C₄×C₁₁	C₂²×C₄	1	8	yes	complemented
23	Dic₁₁	C₂²×C₄	1	16	yes	direct product factor
24	C₂³×C₄	—	11	2	no	—
25	C₂³×C₄	D₁₁	1	1	yes	characteristic
26	C₂×C₄²	—	11	12	no	—
27	C₂×C₁₁	C₂×C₄²	1	12	yes	complemented
28	C₂×C₁₁	C₂³×C₄	1	2	yes	—
29	C₂×C₁₁	C₂³×C₄	1	1	yes	characteristic
30	C₂⁴	C₂×D₁₁	1	1	yes	characteristic
31	C₂²×C₄	—	11	12	no	—
32	C₂²×C₄	—	11	16	no	—
33	C₂²×C₄	Dic₁₁	1	8	yes	direct product factor
34	C₂²×C₄	C₂×D₁₁	1	6	yes	—
35	C₄²	—	11	16	no	—
36	C₁₁	C₂²×C₄²	1	1	yes	characteristic, complemented, Sylow
37	C₂³	C₄×D₁₁	1	8	yes	—
38	C₂³	C₂×Dic₁₁	1	4	yes	—
39	C₂³	C₂²×D₁₁	1	3	yes	—
40	C₂×C₄	—	11	48	no	—
41	C₂×C₄	—	11	8	no	—
42	C₂×C₄	C₂×Dic₁₁	1	24	yes	direct product factor
43	C₂×C₄	C₂²×D₁₁	1	4	yes	—
44	C₂²	C₄×Dic₁₁	1	16	yes	direct product factor
45	C₂²	C₂×C₄×D₁₁	1	12	yes	—
46	C₂²	C₂²×Dic₁₁	1	6	yes	—
47	C₂²	C₂³×D₁₁	1	1	yes	characteristic
48	C₄	—	11	16	no	—
49	C₄	C₂²×Dic₁₁	1	8	yes	direct product factor
50	C₂	C₂×C₄×Dic₁₁	1	12	yes	direct product factor
51	C₂	C₂²×C₄×D₁₁	1	2	yes	—
52	C₂	C₂³×Dic₁₁	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂³×C₄	D₁₁
commutator, hypocenter	C₁₁	C₂²×C₄²
Frattini	C₂²	C₂³×D₁₁
Fitting	C₂³×C₄×C₁₁	C₂
socle, prime radical	C₂⁴×C₁₁	C₂²
cosocle	C₂²×C₁₁	C₂⁴
LCS	G ▷ C₁₁
UCS	C₁ ◁ C₂³×C₄

Complements

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

N	H ≅ G/N	type
3. C₂×C₄×Dic₁₁	C₂	direct (N × H)
5. C₂²×C₄×C₁₁	C₄	semidirect
7. C₂²×Dic₁₁	C₄	direct (N × H)
9. C₄×Dic₁₁	C₂²	direct (N × H)
13. C₂×C₄×C₁₁	C₂×C₄	semidirect
15. C₂×Dic₁₁	C₂×C₄	direct (N × H)
18. C₂²×C₁₁	C₄²	semidirect
22. C₄×C₁₁	C₂²×C₄	semidirect
23. Dic₁₁	C₂²×C₄	direct (N × H)
27. C₂×C₁₁	C₂×C₄²	semidirect
33. C₂²×C₄	Dic₁₁	direct (N × H)
36. C₁₁	C₂²×C₄²	semidirect
42. C₂×C₄	C₂×Dic₁₁	direct (N × H)
44. C₂²	C₄×Dic₁₁	direct (N × H)
49. C₄	C₂²×Dic₁₁	direct (N × H)
50. C₂	C₂×C₄×Dic₁₁	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×C₄×C₁₁	2
C₂³×Dic₁₁	2
C₂×C₄×Dic₁₁	2
C₂²×C₄²	11

Subgroups — C22×C4×Dic11 #10623313

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₄×Dic₁₁ #10623313