Subgroups — C₄×C₂₁₁⋊C₁₆ #27212920

Order 13504.

58 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₁₁⋊C₁₆	C₂	1	2	yes	maximal
2	C₄×C₈×C₂₁₁	C₂	1	1	yes	maximal, characteristic
3	C₂₁₁⋊C₁₆	C₄	1	4	yes	direct product factor
4	C₂×C₈×C₂₁₁	C₄	1	1	yes	characteristic
5	C₂×C₈×C₂₁₁	C₂²	1	1	yes	characteristic
6	C₄²×C₂₁₁	C₄	1	1	yes	characteristic
7	C₂×C₄×C₂₁₁	C₈	1	2	yes	—
8	C₂×C₄×C₂₁₁	C₂×C₄	1	1	yes	characteristic
9	C₈×C₂₁₁	C₈	1	2	yes	—
10	C₈×C₂₁₁	C₂×C₄	1	2	yes	—
11	C₂²×C₂₁₁	C₂×C₈	1	1	yes	characteristic
12	C₄×C₂₁₁	C₁₆	1	4	yes	complemented
13	C₄×C₂₁₁	C₄²	1	1	yes	characteristic
14	C₄×C₂₁₁	C₂×C₈	1	1	yes	characteristic
15	C₂×C₂₁₁	C₄×C₈	1	1	yes	characteristic
16	C₂×C₂₁₁	C₂×C₁₆	1	2	yes	—
17	C₂₁₁	C₄×C₁₆	1	1	yes	characteristic, complemented, Sylow
18	C₄×C₁₆	—	211	1	no	maximal, Sylow
19	C₂×C₁₆	—	211	2	no	—
20	C₄×C₈	D₂₁₁	1	1	yes	characteristic
21	C₂×C₈	Dic₂₁₁	1	1	yes	characteristic
22	C₂×C₈	C₂×D₂₁₁	1	1	yes	characteristic
23	C₄²	Dic₂₁₁	1	1	yes	characteristic
24	C₁₆	—	211	4	no	—
25	C₂×C₄	C₂₁₁⋊C₈	1	2	yes	—
26	C₂×C₄	C₂×Dic₂₁₁	1	1	yes	characteristic
27	C₈	C₂₁₁⋊C₈	1	2	yes	—
28	C₈	C₄×D₂₁₁	1	2	yes	—
29	C₂²	C₂×C₂₁₁⋊C₈	1	1	yes	characteristic
30	C₄	C₂₁₁⋊C₁₆	1	4	yes	direct product factor
31	C₄	C₄×Dic₂₁₁	1	1	yes	characteristic
32	C₄	C₂×C₂₁₁⋊C₈	1	1	yes	characteristic
33	C₂	C₄×C₂₁₁⋊C₈	1	1	yes	characteristic
34	C₂	C₂×C₂₁₁⋊C₁₆	1	2	yes	—

	subgroup	G/H
center, hypercenter	C₄×C₈	D₂₁₁
commutator, hypocenter	C₂₁₁	C₄×C₁₆
Frattini	C₂×C₈	C₂×D₂₁₁
Fitting	C₄×C₈×C₂₁₁	C₂
socle, prime radical	C₂²×C₂₁₁	C₂×C₈
cosocle	C₂×C₈×C₂₁₁	C₂²
LCS	G ▷ C₂₁₁
UCS	C₁ ◁ C₄×C₈

Complements

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

N	H ≅ G/N	type
3. C₂₁₁⋊C₁₆	C₄	direct (N × H)
12. C₄×C₂₁₁	C₁₆	semidirect
17. C₂₁₁	C₄×C₁₆	semidirect
30. C₄	C₂₁₁⋊C₁₆	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₂₁₁⋊C₁₆	2
C₄×C₈×C₂₁₁	2
C₄×C₁₆	211

Subgroups — C4×C211⋊C16 #27212920

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×C₂₁₁⋊C₁₆ #27212920