Subgroups — #34071420

Order 19328.

106 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23752645	C₂	1	2	yes	maximal, complemented
2	#23752049	C₂	1	2	yes	maximal, complemented
3	D₄₈₃₂	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₂×D₁₅₁	C₂	1	1	yes	maximal, characteristic, complemented
5	Q₆₄×C₁₅₁	C₂	1	1	yes	maximal, characteristic, complemented
6	#18012762	—	2	2	no	—
7	#18012682	—	2	2	no	—
8	D₂₄₁₆	C₂²	1	2	yes	—
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	#14559005	—	4	2	no	—
14	#14558991	—	4	2	no	—
15	D₁₂₀₈	—	2	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	D₆₀₄	—	4	2	no	—
21	D₆₀₄	—	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	—	8	2	no	—
28	C₂×D₁₅₁	D₁₆	1	1	yes	characteristic
29	C₄×C₁₅₁	—	8	2	no	—
30	C₄×C₁₅₁	C₂×D₈	1	1	yes	characteristic
31	Dic₁₅₁	D₁₆	1	1	yes	characteristic
32	C₂×C₁₅₁	C₂×D₁₆	1	1	yes	characteristic
33	D₁₅₁	—	2	1	no	—
34	D₁₅₁	—	16	2	no	—
35	C₁₅₁	#2262	1	1	yes	characteristic, complemented, Sylow
36	#2262	—	151	1	no	maximal, Sylow
37	#508	—	151	2	no	—
38	Q₆₄	D₁₅₁	1	1	yes	characteristic, complemented
39	SD₆₄	—	151	2	no	—
40	D₃₂	—	151	1	no	—
41	C₂×C₃₂	—	151	1	no	—
42	#135	—	302	2	no	—
43	Q₃₂	C₂×D₁₅₁	1	2	yes	—
44	SD₃₂	—	302	2	no	—
45	D₁₆	—	151	2	no	—
46	C₂×C₁₆	—	151	1	no	—
47	C₃₂	—	151	1	no	—
48	C₃₂	C₂×D₁₅₁	1	1	yes	characteristic
49	#41	—	604	2	no	—
50	Q₁₆	—	2	2	no	—
51	SD₁₆	—	604	2	no	—
52	D₈	—	302	2	no	—
53	C₂×C₈	—	151	1	no	—
54	C₁₆	—	151	1	no	—
55	C₁₆	C₂²×D₁₅₁	1	1	yes	characteristic
56	Q₈	—	4	2	no	—
57	D₄	—	604	2	no	—
58	D₄	—	1208	2	no	—
59	C₂×C₄	—	151	1	no	—
60	C₂×C₄	—	1208	2	no	—
61	C₈	—	151	1	no	—
62	C₈	D₄×D₁₅₁	1	1	yes	characteristic
63	C₂²	—	151	1	no	—
64	C₂²	—	1208	2	no	—
65	C₄	—	8	2	no	—
66	C₄	—	151	1	no	—
67	C₄	D₈×D₁₅₁	1	1	yes	characteristic
68	C₂	—	302	1	no	—
69	C₂	—	2416	2	no	—
70	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
hypercenter	Q₆₄	D₁₅₁
hypocenter	C₁₅₁	#2262
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
1. #23752645	C₂	semidirect
2. #23752049	C₂	semidirect
3. D₄₈₃₂	C₂	semidirect
4. C₃₂×D₁₅₁	C₂	semidirect
5. Q₆₄×C₁₅₁	C₂	semidirect
35. C₁₅₁	#2262	semidirect
38. Q₆₄	D₁₅₁	semidirect

Maximal subgroups

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

subgroup	index
#23752645	2
#23752049	2
D₄₈₃₂	2
C₃₂×D₁₅₁	2
Q₆₄×C₁₅₁	2
#2262	151