Subgroups — C₄×Dic₁₉₆₄ #44536821

Order 31424.

110 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₁₉₆₄	C₂	1	1	yes	maximal, characteristic
2	C₄×Dic₉₈₂	C₂	1	2	yes	maximal
3	#30628271	C₂	1	1	yes	maximal, characteristic
4	#30628262	C₂	1	2	yes	maximal
5	C₄×C₈×C₄₉₁	C₂	1	1	yes	maximal, characteristic
6	C₂×Dic₉₈₂	C₂²	1	2	yes	—
7	Dic₁₉₆₄	C₄	1	4	yes	direct product factor
8	C₄⋊Dic₄₉₁	C₂²	1	2	yes	—
9	Dic₄₉₁⋊C₄	—	2	2	no	—
10	C₄×Dic₄₉₁	—	2	2	no	—
11	C₂×C₈×C₄₉₁	C₂²	1	1	yes	characteristic
12	C₂×C₈×C₄₉₁	C₂²	1	1	yes	characteristic
13	C₄²×C₄₉₁	C₂²	1	1	yes	characteristic
14	Dic₉₈₂	—	2	2	no	—
15	Dic₉₈₂	C₂×C₄	1	4	yes	—
16	C₂×Dic₄₉₁	—	2	2	no	—
17	C₂×Dic₄₉₁	—	2	2	no	—
18	C₂×C₄×C₄₉₁	D₄	1	1	yes	characteristic
19	C₂×C₄×C₄₉₁	D₄	1	1	yes	characteristic
20	C₂×C₄×C₄₉₁	C₂³	1	1	yes	characteristic
21	C₈×C₄₉₁	—	2	1	no	—
22	C₈×C₄₉₁	C₂×C₄	1	2	yes	—
23	C₂²×C₄₉₁	C₂×D₄	1	1	yes	characteristic
24	C₄×C₄₉₁	—	2	1	no	—
25	C₄×C₄₉₁	Q₁₆	1	2	yes	complemented
26	C₄×C₄₉₁	C₂²×C₄	1	1	yes	characteristic
27	C₄×C₄₉₁	#41	1	1	yes	characteristic
28	Dic₄₉₁	—	2	4	no	—
29	Dic₄₉₁	—	4	2	no	—
30	C₂×C₄₉₁	C₄×D₄	1	1	yes	characteristic
31	C₂×C₄₉₁	C₂×Q₁₆	1	1	yes	characteristic
32	C₂×C₄₉₁	#135	1	1	yes	characteristic
33	C₄₉₁	C₄×Q₁₆	1	1	yes	characteristic, complemented, Sylow
34	C₄×Q₁₆	—	491	1	no	maximal, Sylow
35	C₂×Q₁₆	—	491	1	no	—
36	C₄×Q₈	—	491	2	no	—
37	#107	—	491	1	no	—
38	#103	—	491	2	no	—
39	C₄×C₈	D₄₉₁	1	1	yes	characteristic
40	C₂×Q₈	—	491	2	no	—
41	Q₁₆	—	491	4	no	—
42	C₂×C₈	C₂×D₄₉₁	1	1	yes	characteristic
43	C₂×C₈	C₂×D₄₉₁	1	1	yes	characteristic
44	C₄⋊C₄	—	982	2	no	—
45	C₄⋊C₄	—	491	2	no	—
46	C₄²	—	982	2	no	—
47	C₄²	C₂×D₄₉₁	1	1	yes	characteristic
48	Q₈	—	982	2	no	—
49	Q₈	—	491	4	no	—
50	C₂×C₄	—	982	2	no	—
51	C₂×C₄	—	982	2	no	—
52	C₂×C₄	D₁₉₆₄	1	1	yes	characteristic
53	C₂×C₄	D₁₉₆₄	1	1	yes	characteristic
54	C₂×C₄	C₂²×D₄₉₁	1	1	yes	characteristic
55	C₈	—	2	1	no	—
56	C₈	C₄×D₄₉₁	1	2	yes	—
57	C₂²	C₂×D₁₉₆₄	1	1	yes	characteristic
58	C₄	—	2	1	no	—
59	C₄	—	1964	2	no	—
60	C₄	—	982	4	no	—
61	C₄	Dic₁₉₆₄	1	2	yes	direct product factor
62	C₄	C₂×C₄×D₄₉₁	1	1	yes	characteristic
63	C₄	#21463328	1	1	yes	characteristic
64	C₂	C₄×D₁₉₆₄	1	1	yes	characteristic
65	C₂	C₂×Dic₁₉₆₄	1	1	yes	characteristic
66	C₂	#30628359	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	D₁₉₆₄
commutator	C₄×C₄₉₁	C₂²×C₄
Frattini	C₂×C₄	C₂²×D₄₉₁
Fitting	C₄×C₈×C₄₉₁	C₂
socle, prime radical	C₂²×C₄₉₁	C₂×D₄
cosocle	C₂×C₄×C₄₉₁	C₂³
hypercenter	C₄×C₈	D₄₉₁
hypocenter	C₄₉₁	C₄×Q₁₆
LCS	G ▷ C₄×C₄₉₁ ▷ C₂×C₄₉₁ ▷ C₄₉₁
UCS	C₁ ◁ C₂×C₄ ◁ C₄² ◁ C₄×C₈

Complements

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

N	H ≅ G/N	type
7. Dic₁₉₆₄	C₄	direct (N × H)
25. C₄×C₄₉₁	Q₁₆	semidirect
33. C₄₉₁	C₄×Q₁₆	semidirect
61. C₄	Dic₁₉₆₄	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×Dic₁₉₆₄	2
C₄×Dic₉₈₂	2
#30628271	2
#30628262	2
C₄×C₈×C₄₉₁	2
C₄×Q₁₆	491

Subgroups — C4×Dic1964 #44536821

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×Dic₁₉₆₄ #44536821