Subgroups — C₂×C₁₆×D₂₁₁ #27213557

Order 13504.

98 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₈×D₂₁₁	C₂	1	1	yes	maximal, characteristic
2	C₂×C₂₁₁⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₆×D₂₁₁	C₂	1	4	yes	maximal, direct product factor
4	C₂×C₁₆×C₂₁₁	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₄×D₂₁₁	C₄	1	1	yes	characteristic
6	C₂×C₂₁₁⋊C₈	C₄	1	1	yes	characteristic
7	C₈×D₂₁₁	C₄	1	2	yes	—
8	C₈×D₂₁₁	C₂²	1	2	yes	—
9	C₂₁₁⋊C₁₆	C₂²	1	2	yes	complemented
10	C₂×C₈×C₂₁₁	C₂²	1	1	yes	characteristic
11	C₁₆×C₂₁₁	C₂²	1	2	yes	complemented
12	C₂²×D₂₁₁	C₈	1	1	yes	characteristic
13	C₂×Dic₂₁₁	C₈	1	1	yes	characteristic
14	C₄×D₂₁₁	C₈	1	2	yes	—
15	C₄×D₂₁₁	C₂×C₄	1	2	yes	—
16	C₂₁₁⋊C₈	C₂×C₄	1	2	yes	—
17	C₂×C₄×C₂₁₁	C₂×C₄	1	1	yes	characteristic
18	C₈×C₂₁₁	C₂×C₄	1	1	yes	characteristic
19	C₈×C₂₁₁	C₂³	1	1	yes	characteristic
20	C₂²×C₂₁₁	C₂×C₈	1	1	yes	characteristic
21	C₂×D₂₁₁	C₁₆	1	4	yes	direct product factor
22	C₂×D₂₁₁	C₂×C₈	1	2	yes	—
23	C₄×C₂₁₁	C₂×C₈	1	1	yes	characteristic
24	C₄×C₂₁₁	C₂²×C₄	1	1	yes	characteristic
25	Dic₂₁₁	C₂×C₈	1	2	yes	—
26	C₂×C₂₁₁	C₂×C₁₆	1	2	yes	complemented
27	C₂×C₂₁₁	C₂²×C₈	1	1	yes	characteristic
28	D₂₁₁	C₂×C₁₆	1	4	yes	direct product factor
29	C₂₁₁	C₂²×C₁₆	1	1	yes	characteristic, complemented, Sylow
30	C₂²×C₁₆	—	211	1	no	maximal, Sylow
31	C₂²×C₈	—	211	1	no	—
32	C₂×C₁₆	—	211	1	no	—
33	C₂×C₁₆	—	211	4	no	—
34	C₂×C₁₆	D₂₁₁	1	1	yes	characteristic, direct product factor
35	C₂²×C₄	—	211	1	no	—
36	C₂×C₈	—	211	1	no	—
37	C₂×C₈	—	211	2	no	—
38	C₂×C₈	—	211	2	no	—
39	C₂×C₈	C₂×D₂₁₁	1	1	yes	characteristic
40	C₁₆	—	211	2	no	—
41	C₁₆	C₂×D₂₁₁	1	2	yes	direct product factor
42	C₂³	—	211	1	no	—
43	C₂×C₄	—	211	1	no	—
44	C₂×C₄	—	211	2	no	—
45	C₂×C₄	—	211	2	no	—
46	C₂×C₄	C₄×D₂₁₁	1	1	yes	characteristic
47	C₈	—	211	2	no	—
48	C₈	C₄×D₂₁₁	1	1	yes	characteristic
49	C₈	C₂²×D₂₁₁	1	1	yes	characteristic
50	C₂²	—	211	4	no	—
51	C₂²	—	211	2	no	—
52	C₂²	C₈×D₂₁₁	1	1	yes	characteristic
53	C₄	—	211	2	no	—
54	C₄	C₈×D₂₁₁	1	1	yes	characteristic
55	C₄	C₂×C₄×D₂₁₁	1	1	yes	characteristic
56	C₂	—	211	4	no	—
57	C₂	C₁₆×D₂₁₁	1	2	yes	direct product factor
58	C₂	C₂×C₈×D₂₁₁	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₁₆	D₂₁₁
commutator, hypocenter	C₂₁₁	C₂²×C₁₆
Frattini	C₈	C₂²×D₂₁₁
Fitting	C₂×C₁₆×C₂₁₁	C₂
socle	C₂²×C₂₁₁	C₂×C₈
prime radical	C₂²×D₂₁₁	C₈
cosocle	C₈×C₂₁₁	C₂³
LCS	G ▷ C₂₁₁
UCS	C₁ ◁ C₂×C₁₆

Complements

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

N	H ≅ G/N	type
2. C₂×C₂₁₁⋊C₁₆	C₂	semidirect
3. C₁₆×D₂₁₁	C₂	direct (N × H)
4. C₂×C₁₆×C₂₁₁	C₂	semidirect
9. C₂₁₁⋊C₁₆	C₂²	semidirect
11. C₁₆×C₂₁₁	C₂²	semidirect
21. C₂×D₂₁₁	C₁₆	direct (N × H)
26. C₂×C₂₁₁	C₂×C₁₆	semidirect
28. D₂₁₁	C₂×C₁₆	direct (N × H)
29. C₂₁₁	C₂²×C₁₆	semidirect
34. C₂×C₁₆	D₂₁₁	direct (N × H)
41. C₁₆	C₂×D₂₁₁	direct (N × H)
57. C₂	C₁₆×D₂₁₁	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×C₈×D₂₁₁	2
C₂×C₂₁₁⋊C₁₆	2
C₁₆×D₂₁₁	2
C₂×C₁₆×C₂₁₁	2
C₂²×C₁₆	211

Subgroups — C2×C16×D211 #27213557

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₆×D₂₁₁ #27213557