Subgroups — Q₆₄×D₁₅₁ #34071413

Order 19328.

104 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Q₃₂×D₁₅₁	C₂	1	2	yes	maximal
2	Dic₂₄₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	#23752052	C₂	1	2	yes	maximal, complemented
4	C₃₂×D₁₅₁	C₂	1	1	yes	maximal, characteristic
5	Q₆₄×C₁₅₁	C₂	1	1	yes	maximal, characteristic, complemented
6	Q₁₆×D₁₅₁	—	2	2	no	—
7	Dic₁₂₀₈	C₂²	1	2	yes	—
8	#18012685	—	2	2	no	—
9	C₁₆×D₁₅₁	C₂²	1	1	yes	characteristic
10	C₁₅₁⋊C₃₂	C₂²	1	1	yes	characteristic
11	Q₃₂×C₁₅₁	C₂²	1	2	yes	—
12	C₃₂×C₁₅₁	C₂²	1	1	yes	characteristic
13	Q₈×D₁₅₁	—	4	2	no	—
14	Dic₆₀₄	—	2	2	no	—
15	#14558994	—	4	2	no	—
16	C₈×D₁₅₁	D₄	1	1	yes	characteristic
17	C₁₅₁⋊C₁₆	D₄	1	1	yes	characteristic
18	Q₁₆×C₁₅₁	—	2	2	no	—
19	C₁₆×C₁₅₁	C₂³	1	1	yes	characteristic
20	Dic₃₀₂	—	4	2	no	—
21	Dic₃₀₂	—	8	2	no	—
22	C₄×D₁₅₁	—	8	2	no	—
23	C₄×D₁₅₁	D₈	1	1	yes	characteristic
24	C₁₅₁⋊C₈	D₈	1	1	yes	characteristic
25	Q₈×C₁₅₁	—	4	2	no	—
26	C₈×C₁₅₁	C₂×D₄	1	1	yes	characteristic
27	C₂×D₁₅₁	D₁₆	1	1	yes	characteristic
28	C₄×C₁₅₁	—	8	2	no	—
29	C₄×C₁₅₁	C₂×D₈	1	1	yes	characteristic
30	Dic₁₅₁	—	8	2	no	—
31	Dic₁₅₁	D₁₆	1	1	yes	characteristic
32	C₂×C₁₅₁	C₂×D₁₆	1	1	yes	characteristic
33	D₁₅₁	Q₆₄	1	2	yes	direct product factor
34	C₁₅₁	C₂×Q₆₄	1	1	yes	characteristic, complemented, Sylow
35	C₂×Q₆₄	—	151	1	no	maximal, Sylow
36	C₂×Q₃₂	—	151	2	no	—
37	Q₆₄	—	151	2	no	—
38	Q₆₄	—	151	1	no	—
39	Q₆₄	D₁₅₁	1	1	yes	characteristic, direct product factor
40	C₂×C₃₂	—	151	1	no	—
41	C₂×Q₁₆	—	302	2	no	—
42	Q₃₂	—	302	2	no	—
43	Q₃₂	—	151	2	no	—
44	Q₃₂	C₂×D₁₅₁	1	2	yes	—
45	C₂×C₁₆	—	151	1	no	—
46	C₃₂	—	151	1	no	—
47	C₃₂	C₂×D₁₅₁	1	1	yes	characteristic
48	C₂×Q₈	—	604	2	no	—
49	Q₁₆	—	2	2	no	—
50	Q₁₆	—	302	2	no	—
51	Q₁₆	—	604	2	no	—
52	C₂×C₈	—	151	1	no	—
53	C₁₆	—	151	1	no	—
54	C₁₆	C₂²×D₁₅₁	1	1	yes	characteristic
55	Q₈	—	4	2	no	—
56	Q₈	—	604	2	no	—
57	Q₈	—	1208	2	no	—
58	C₂×C₄	—	151	1	no	—
59	C₂×C₄	—	1208	2	no	—
60	C₈	—	151	1	no	—
61	C₈	D₄×D₁₅₁	1	1	yes	characteristic
62	C₂²	—	151	1	no	—
63	C₄	—	8	2	no	—
64	C₄	—	151	1	no	—
65	C₄	—	1208	2	no	—
66	C₄	D₈×D₁₅₁	1	1	yes	characteristic
67	C₂	—	151	2	no	—
68	C₂	D₁₆×D₁₅₁	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₁₆×D₁₅₁
commutator, cosocle	C₁₆×C₁₅₁	C₂³
Frattini	C₁₆	C₂²×D₁₅₁
Fitting	Q₆₄×C₁₅₁	C₂
socle	C₂×C₁₅₁	C₂×D₁₆
prime radical	C₂×D₁₅₁	D₁₆
hypercenter	Q₆₄	D₁₅₁
hypocenter	C₁₅₁	C₂×Q₆₄
LCS	G ▷ C₁₆×C₁₅₁ ▷ C₈×C₁₅₁ ▷ C₄×C₁₅₁ ▷ C₂×C₁₅₁ ▷ C₁₅₁
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ C₁₆ ◁ Q₆₄

Complements

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

N	H ≅ G/N	type
2. Dic₂₄₁₆	C₂	semidirect
3. #23752052	C₂	semidirect
5. Q₆₄×C₁₅₁	C₂	semidirect
33. D₁₅₁	Q₆₄	direct (N × H)
34. C₁₅₁	C₂×Q₆₄	semidirect
39. Q₆₄	D₁₅₁	direct (N × H)

Maximal subgroups

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

subgroup	index
Q₃₂×D₁₅₁	2
Dic₂₄₁₆	2
#23752052	2
C₃₂×D₁₅₁	2
Q₆₄×C₁₅₁	2
C₂×Q₆₄	151

Subgroups — Q64×D151 #34071413

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — Q₆₄×D₁₅₁ #34071413