Subgroups — D₄⋊C₈×C₅₄₁ #46829632

Order 34624.

82 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×D₄×C₅₄₁	C₂	1	1	yes	maximal, characteristic
2	C₄⋊C₈×C₅₄₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×C₈×C₅₄₁	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₄×C₅₄₁	C₄	1	1	yes	characteristic
5	C₂²×C₄×C₅₄₁	—	2	1	no	—
6	C₂×C₈×C₅₄₁	—	2	1	no	—
7	C₂×C₈×C₅₄₁	—	2	1	no	—
8	C₄⋊C₄×C₅₄₁	C₄	1	1	yes	characteristic
9	C₂²⋊C₄×C₅₄₁	—	2	1	no	—
10	C₄²×C₅₄₁	C₂²	1	1	yes	characteristic
11	C₂³×C₅₄₁	—	2	1	no	—
12	D₄×C₅₄₁	—	2	1	no	—
13	D₄×C₅₄₁	C₈	1	2	yes	complemented
14	C₂×C₄×C₅₄₁	—	2	1	no	—
15	C₂×C₄×C₅₄₁	—	4	1	no	—
16	C₂×C₄×C₅₄₁	—	4	1	no	—
17	C₂×C₄×C₅₄₁	C₂×C₄	1	1	yes	characteristic
18	C₂×C₄×C₅₄₁	D₄	1	1	yes	characteristic
19	C₂×C₄×C₅₄₁	D₄	1	1	yes	characteristic
20	C₈×C₅₄₁	—	2	2	no	—
21	C₈×C₅₄₁	—	4	1	no	—
22	C₂²×C₅₄₁	—	2	2	no	—
23	C₂²×C₅₄₁	—	4	1	no	—
24	C₂²×C₅₄₁	—	4	1	no	—
25	C₂²×C₅₄₁	C₂²⋊C₄	1	1	yes	characteristic
26	C₄×C₅₄₁	—	2	1	no	—
27	C₄×C₅₄₁	—	4	1	no	—
28	C₄×C₅₄₁	C₂×C₈	1	1	yes	characteristic
29	C₄×C₅₄₁	M₁₆	1	1	yes	characteristic
30	C₄×C₅₄₁	D₈	1	1	yes	characteristic
31	C₄×C₅₄₁	SD₁₆	1	1	yes	characteristic
32	C₂×C₅₄₁	—	4	2	no	—
33	C₂×C₅₄₁	C₂²⋊C₈	1	1	yes	characteristic
34	C₂×C₅₄₁	#102	1	1	yes	characteristic
35	C₂×C₅₄₁	#104	1	1	yes	characteristic
36	C₅₄₁	D₄⋊C₈	1	1	yes	characteristic, direct product factor, Sylow
37	D₄⋊C₈	C₅₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
38	C₄×D₄	C₂×C₅₄₁	1	1	yes	characteristic
39	C₄⋊C₈	C₂×C₅₄₁	1	1	yes	characteristic, complemented
40	C₄×C₈	C₂×C₅₄₁	1	1	yes	characteristic, complemented
41	C₂×D₄	C₄×C₅₄₁	1	1	yes	characteristic
42	C₂²×C₄	—	2	1	no	—
43	C₂×C₈	—	2	1	no	—
44	C₂×C₈	—	2	1	no	—
45	C₄⋊C₄	C₄×C₅₄₁	1	1	yes	characteristic
46	C₂²⋊C₄	—	2	1	no	—
47	C₄²	C₂²×C₅₄₁	1	1	yes	characteristic
48	C₂³	—	2	1	no	—
49	D₄	—	2	1	no	—
50	D₄	C₈×C₅₄₁	1	2	yes	complemented
51	C₂×C₄	—	2	1	no	—
52	C₂×C₄	—	4	1	no	—
53	C₂×C₄	—	4	1	no	—
54	C₂×C₄	C₂×C₄×C₅₄₁	1	1	yes	characteristic
55	C₂×C₄	D₄×C₅₄₁	1	1	yes	characteristic
56	C₂×C₄	D₄×C₅₄₁	1	1	yes	characteristic
57	C₈	—	2	2	no	—
58	C₈	—	4	1	no	—
59	C₂²	—	2	2	no	—
60	C₂²	—	4	1	no	—
61	C₂²	—	4	1	no	—
62	C₂²	C₂²⋊C₄×C₅₄₁	1	1	yes	characteristic
63	C₄	—	2	1	no	—
64	C₄	—	4	1	no	—
65	C₄	C₂×C₈×C₅₄₁	1	1	yes	characteristic
66	C₄	M₁₆×C₅₄₁	1	1	yes	characteristic
67	C₄	D₈×C₅₄₁	1	1	yes	characteristic
68	C₄	SD₁₆×C₅₄₁	1	1	yes	characteristic
69	C₂	—	4	2	no	—
70	C₂	C₂²⋊C₈×C₅₄₁	1	1	yes	characteristic
71	C₂	#102×C₅₄₁	1	1	yes	characteristic
72	C₂	#104×C₅₄₁	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₅₄₁	D₄
commutator	C₄	C₂×C₈×C₅₄₁
Frattini, cosocle	C₄²	C₂²×C₅₄₁
socle	C₂²×C₅₄₁	C₂²⋊C₄
prime radical	C₂×D₄×C₅₄₁	C₄
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₅₄₁ ◁ C₄²×C₅₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₄⋊C₈×C₅₄₁	C₂	semidirect
3. C₄×C₈×C₅₄₁	C₂	semidirect
13. D₄×C₅₄₁	C₈	semidirect
36. C₅₄₁	D₄⋊C₈	direct (N × H)
37. D₄⋊C₈	C₅₄₁	direct (N × H)
39. C₄⋊C₈	C₂×C₅₄₁	semidirect
40. C₄×C₈	C₂×C₅₄₁	semidirect
50. D₄	C₈×C₅₄₁	semidirect

Maximal subgroups

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

subgroup	index
C₄×D₄×C₅₄₁	2
C₄⋊C₈×C₅₄₁	2
C₄×C₈×C₅₄₁	2
D₄⋊C₈	541

Subgroups — D4⋊C8×C541 #46829632

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₄⋊C₈×C₅₄₁ #46829632