Subgroups — D₄×#6923 #14519857

Order 1952.

94 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#6923	C₂	1	2	yes	maximal, complemented
2	D₄×D₆₁	C₂	1	1	yes	maximal, characteristic
3	C₂²⋊#6923	C₂	1	2	yes	maximal, complemented
4	C₄⋊#6923	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄×#6923	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×D₆₁	C₂²	1	2	yes	—
7	C₂×#6923	—	2	4	no	—
8	C₂×#6923	C₂²	1	1	yes	characteristic
9	C₂×#6923	C₂²	1	2	yes	—
10	C₂×#6923	C₂²	1	1	yes	characteristic
11	D₄×C₆₁	C₄	1	1	yes	characteristic, complemented
12	C₂²⋊D₆₁	C₄	1	2	yes	complemented
13	D₂₄₄	C₄	1	1	yes	characteristic, complemented
14	C₄×D₆₁	C₂²	1	1	yes	characteristic
15	C₂²×C₆₁	C₂×C₄	1	2	yes	complemented
16	C₂×D₆₁	—	2	2	no	—
17	C₂×D₆₁	—	2	2	no	—
18	C₂×D₆₁	C₂×C₄	1	2	yes	complemented
19	C₂×D₆₁	C₂³	1	1	yes	characteristic
20	#6923	—	2	2	no	—
21	#6923	—	2	1	no	—
22	#6923	D₄	1	2	yes	direct product factor
23	C₄×C₆₁	C₂×C₄	1	1	yes	characteristic, complemented
24	Dic₆₁	C₂×C₄	1	1	yes	characteristic, complemented
25	C₂×C₆₁	—	2	2	no	—
26	C₂×C₆₁	C₂²×C₄	1	1	yes	characteristic
27	D₆₁	—	2	2	no	—
28	D₆₁	C₂×D₄	1	1	yes	characteristic
29	D₆₁	#41	1	1	yes	characteristic
30	C₆₁	C₄×D₄	1	1	yes	characteristic, complemented, Sylow
31	C₄×D₄	—	61	1	no	maximal, Sylow
32	C₂×D₄	—	61	1	no	—
33	C₂²×C₄	—	61	2	no	—
34	C₄⋊C₄	—	61	1	no	—
35	C₂²⋊C₄	—	61	2	no	—
36	C₄²	—	61	1	no	—
37	C₂³	—	61	2	no	—
38	D₄	—	61	2	no	—
39	D₄	—	61	1	no	—
40	D₄	#6923	1	1	yes	characteristic, direct product factor
41	C₂×C₄	—	61	1	no	—
42	C₂×C₄	—	61	1	no	—
43	C₂×C₄	—	61	1	no	—
44	C₂×C₄	—	61	2	no	—
45	C₂×C₄	—	122	4	no	—
46	C₂²	—	61	1	no	—
47	C₂²	—	61	2	no	—
48	C₂²	—	122	2	no	—
49	C₂²	—	122	2	no	—
50	C₂²	C₂×#6923	1	2	yes	complemented
51	C₄	—	61	2	no	—
52	C₄	—	61	1	no	—
53	C₄	—	122	2	no	—
54	C₄	—	122	1	no	—
55	C₄	C₂×#6923	1	1	yes	characteristic, complemented
56	C₂	—	2	2	no	—
57	C₂	—	61	1	no	—
58	C₂	—	61	1	no	—
59	C₂	—	122	2	no	—
60	C₂	C₂²×#6923	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂	C₂²×#6923
commutator, socle	C₂×C₆₁	C₂²×C₄
Fitting	D₄×C₆₁	C₄
prime radical	D₄×D₆₁	C₂
cosocle	C₂×D₆₁	C₂³
hypercenter	D₄	#6923
hypocenter	C₆₁	C₄×D₄
LCS	G ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂ ◁ D₄

Complements

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

N	H ≅ G/N	type
1. C₂²×#6923	C₂	semidirect
3. C₂²⋊#6923	C₂	semidirect
4. C₄⋊#6923	C₂	semidirect
5. C₄×#6923	C₂	semidirect
11. D₄×C₆₁	C₄	semidirect
12. C₂²⋊D₆₁	C₄	semidirect
13. D₂₄₄	C₄	semidirect
15. C₂²×C₆₁	C₂×C₄	semidirect
18. C₂×D₆₁	C₂×C₄	semidirect
22. #6923	D₄	direct (N × H)
23. C₄×C₆₁	C₂×C₄	semidirect
24. Dic₆₁	C₂×C₄	semidirect
30. C₆₁	C₄×D₄	semidirect
40. D₄	#6923	direct (N × H)
50. C₂²	C₂×#6923	semidirect
55. C₄	C₂×#6923	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#6923	2
D₄×D₆₁	2
C₂²⋊#6923	2
C₄⋊#6923	2
C₄×#6923	2
C₄×D₄	61

Subgroups — D4×#6923 #14519857

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₄×#6923 #14519857