Subgroups — D₁₆×D₄₂₁ #41003259

Order 26944.

98 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₈×D₄₂₁	C₂	1	2	yes	maximal, complemented
2	D₆₇₃₆	C₂	1	1	yes	maximal, characteristic, complemented
3	#27212307	C₂	1	2	yes	maximal, complemented
4	C₁₆×D₄₂₁	C₂	1	1	yes	maximal, characteristic, complemented
5	D₁₆×C₄₂₁	C₂	1	1	yes	maximal, characteristic, complemented
6	D₄×D₄₂₁	—	2	2	no	—
7	D₃₃₆₈	C₂²	1	2	yes	complemented
8	#20269756	—	2	2	no	—
9	C₈×D₄₂₁	C₂²	1	1	yes	characteristic
10	#20269746	C₂²	1	1	yes	characteristic, complemented
11	D₈×C₄₂₁	C₂²	1	2	yes	complemented
12	C₁₆×C₄₂₁	C₂²	1	1	yes	characteristic, complemented
13	C₂²×D₄₂₁	—	4	2	no	—
14	D₁₆₈₄	—	2	2	no	—
15	C₂²⋊D₄₂₁	—	4	2	no	—
16	C₄×D₄₂₁	D₄	1	1	yes	characteristic
17	#16809890	D₄	1	1	yes	characteristic
18	D₄×C₄₂₁	—	2	2	no	—
19	C₈×C₄₂₁	C₂³	1	1	yes	characteristic
20	C₂²×C₄₂₁	—	4	2	no	—
21	C₂×D₄₂₁	—	4	2	no	—
22	C₂×D₄₂₁	—	8	4	no	—
23	C₂×D₄₂₁	D₈	1	1	yes	characteristic
24	C₄×C₄₂₁	C₂×D₄	1	1	yes	characteristic
25	Dic₄₂₁	D₈	1	1	yes	characteristic
26	C₂×C₄₂₁	—	8	2	no	—
27	C₂×C₄₂₁	C₂×D₈	1	1	yes	characteristic
28	D₄₂₁	—	8	2	no	—
29	D₄₂₁	D₁₆	1	2	yes	direct product factor
30	C₄₂₁	C₂×D₁₆	1	1	yes	characteristic, complemented, Sylow
31	C₂×D₁₆	—	421	1	no	maximal, Sylow
32	C₂×D₈	—	421	2	no	—
33	D₁₆	—	421	2	no	—
34	D₁₆	—	421	1	no	—
35	D₁₆	D₄₂₁	1	1	yes	characteristic, direct product factor
36	C₂×C₁₆	—	421	1	no	—
37	C₂×D₄	—	842	2	no	—
38	D₈	—	842	2	no	—
39	D₈	—	421	2	no	—
40	D₈	C₂×D₄₂₁	1	2	yes	complemented
41	C₂×C₈	—	421	1	no	—
42	C₁₆	—	421	1	no	—
43	C₁₆	C₂×D₄₂₁	1	1	yes	characteristic, complemented
44	C₂³	—	1684	2	no	—
45	D₄	—	2	2	no	—
46	D₄	—	842	2	no	—
47	D₄	—	1684	2	no	—
48	C₂×C₄	—	421	1	no	—
49	C₈	—	421	1	no	—
50	C₈	C₂²×D₄₂₁	1	1	yes	characteristic
51	C₂²	—	4	2	no	—
52	C₂²	—	3368	4	no	—
53	C₂²	—	1684	2	no	—
54	C₂²	—	421	1	no	—
55	C₄	—	421	1	no	—
56	C₄	D₄×D₄₂₁	1	1	yes	characteristic
57	C₂	—	8	2	no	—
58	C₂	—	3368	2	no	—
59	C₂	—	421	2	no	—
60	C₂	D₈×D₄₂₁	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₈×D₄₂₁
commutator, cosocle	C₈×C₄₂₁	C₂³
Frattini	C₈	C₂²×D₄₂₁
Fitting	D₁₆×C₄₂₁	C₂
socle	C₂×C₄₂₁	C₂×D₈
hypercenter	D₁₆	D₄₂₁
hypocenter	C₄₂₁	C₂×D₁₆
LCS	G ▷ C₈×C₄₂₁ ▷ C₄×C₄₂₁ ▷ C₂×C₄₂₁ ▷ C₄₂₁
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ D₁₆

Complements

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

N	H ≅ G/N	type
1. D₈×D₄₂₁	C₂	semidirect
2. D₆₇₃₆	C₂	semidirect
3. #27212307	C₂	semidirect
4. C₁₆×D₄₂₁	C₂	semidirect
5. D₁₆×C₄₂₁	C₂	semidirect
7. D₃₃₆₈	C₂²	semidirect
10. #20269746	C₂²	semidirect
11. D₈×C₄₂₁	C₂²	semidirect
12. C₁₆×C₄₂₁	C₂²	semidirect
29. D₄₂₁	D₁₆	direct (N × H)
30. C₄₂₁	C₂×D₁₆	semidirect
35. D₁₆	D₄₂₁	direct (N × H)
40. D₈	C₂×D₄₂₁	semidirect
43. C₁₆	C₂×D₄₂₁	semidirect

Maximal subgroups

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

subgroup	index
D₈×D₄₂₁	2
D₆₇₃₆	2
#27212307	2
C₁₆×D₄₂₁	2
D₁₆×C₄₂₁	2
C₂×D₁₆	421

Subgroups — D16×D421 #41003259

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₁₆×D₄₂₁ #41003259