Subgroups — C₂×(C₂×D₁₁)⋊C₄ #66980

Order 352.

132 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×D₁₁	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₄×C₁₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×Dic₁₁	C₂	1	1	yes	maximal, characteristic, complemented
4	(C₂×D₁₁)⋊C₄	C₂	1	4	yes	maximal, direct product factor
5	C₂³×C₁₁	C₂²	1	1	yes	characteristic
6	C₂²×D₁₁	—	2	2	no	—
7	C₂²×D₁₁	—	2	2	no	—
8	C₂²×D₁₁	C₄	1	4	yes	complemented
9	C₂²×D₁₁	C₂²	1	2	yes	—
10	C₂×C₄×C₁₁	—	2	2	no	—
11	C₂×C₄×C₁₁	C₂²	1	2	yes	complemented
12	C₂×Dic₁₁	—	2	2	no	—
13	C₂×Dic₁₁	C₂²	1	2	yes	complemented
14	C₂²×C₁₁	C₂×C₄	1	2	yes	—
15	C₂²×C₁₁	D₄	1	2	yes	—
16	C₂²×C₁₁	D₄	1	2	yes	—
17	C₂²×C₁₁	C₂³	1	1	yes	characteristic
18	C₂×D₁₁	—	2	8	no	—
19	C₂×D₁₁	—	2	2	no	—
20	C₂×D₁₁	—	2	2	no	—
21	C₂×D₁₁	C₂×C₄	1	4	yes	complemented
22	C₄×C₁₁	—	2	2	no	—
23	Dic₁₁	—	2	2	no	—
24	C₂×C₂²⋊C₄	—	11	1	no	maximal, Sylow
25	C₂×C₁₁	C₂²⋊C₄	1	4	yes	complemented
26	C₂×C₁₁	C₂²×C₄	1	1	yes	characteristic
27	C₂×C₁₁	C₂×D₄	1	1	yes	characteristic
28	C₂×C₁₁	C₂×D₄	1	1	yes	characteristic
29	D₁₁	—	2	4	no	—
30	C₂⁴	—	11	1	no	—
31	C₂²×C₄	—	11	1	no	—
32	C₂²×C₄	D₁₁	1	1	yes	characteristic, complemented
33	C₂²⋊C₄	—	11	4	no	—
34	C₁₁	C₂×C₂²⋊C₄	1	1	yes	characteristic, complemented, Sylow
35	C₂³	—	11	2	no	—
36	C₂³	—	11	4	no	—
37	C₂³	—	22	2	no	—
38	C₂³	—	22	2	no	—
39	C₂³	C₂×D₁₁	1	1	yes	characteristic
40	C₂×C₄	—	2	2	no	—
41	C₂×C₄	—	11	2	no	—
42	C₂×C₄	—	22	2	no	—
43	C₂×C₄	C₂×D₁₁	1	2	yes	complemented
44	C₂²	—	11	4	no	—
45	C₂²	—	22	8	no	—
46	C₂²	—	22	2	no	—
47	C₂²	—	22	2	no	—
48	C₂²	C₄×D₁₁	1	2	yes	—
49	C₂²	D₄₄	1	2	yes	—
50	C₂²	C₂²⋊D₁₁	1	2	yes	—
51	C₂²	C₂²×D₁₁	1	1	yes	characteristic
52	C₄	—	2	2	no	—
53	C₄	—	22	2	no	—
54	C₂	—	22	4	no	—
55	C₂	(C₂×D₁₁)⋊C₄	1	4	yes	direct product factor
56	C₂	C₂×C₄×D₁₁	1	1	yes	characteristic
57	C₂	C₂×D₄₄	1	1	yes	characteristic
58	C₂	C₂×C₂²⋊D₁₁	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
2. C₂²×C₄×C₁₁	C₂	semidirect
3. C₂²×Dic₁₁	C₂	semidirect
4. (C₂×D₁₁)⋊C₄	C₂	direct (N × H)
8. C₂²×D₁₁	C₄	semidirect
11. C₂×C₄×C₁₁	C₂²	semidirect
13. C₂×Dic₁₁	C₂²	semidirect
21. C₂×D₁₁	C₂×C₄	semidirect
25. C₂×C₁₁	C₂²⋊C₄	semidirect
32. C₂²×C₄	D₁₁	semidirect
34. C₁₁	C₂×C₂²⋊C₄	semidirect
43. C₂×C₄	C₂×D₁₁	semidirect
55. C₂	(C₂×D₁₁)⋊C₄	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×D₁₁	2
C₂²×C₄×C₁₁	2
C₂²×Dic₁₁	2
(C₂×D₁₁)⋊C₄	2
C₂×C₂²⋊C₄	11

Subgroups — C2×(C2×D11)⋊C4 #66980

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×(C₂×D₁₁)⋊C₄ #66980