Subgroups — #14580765

Order 2624.

84 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13050183	C₂	1	2	yes	maximal, complemented
2	Dic₃₂₈	C₂	1	1	yes	maximal, characteristic, complemented
3	#13050108	C₂	1	2	yes	maximal, complemented
4	C₁₆×D₄₁	C₂	1	1	yes	maximal, characteristic, complemented
5	D₁₆×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
6	#10620308	—	2	2	no	—
7	D₈×C₄₁	C₂²	1	2	yes	—
8	#10620283	—	2	2	no	—
9	Dic₁₆₄	C₂²	1	2	yes	—
10	C₈×D₄₁	C₂²	1	1	yes	characteristic
11	C₁₆×C₄₁	C₂²	1	1	yes	characteristic
12	#10620268	C₂²	1	1	yes	characteristic
13	D₄×C₄₁	—	2	2	no	—
14	C₂²⋊D₄₁	—	4	2	no	—
15	C₂×Dic₄₁	—	4	2	no	—
16	C₄×D₄₁	D₄	1	1	yes	characteristic
17	Dic₈₂	—	2	2	no	—
18	C₈×C₄₁	C₂³	1	1	yes	characteristic
19	#66491	D₄	1	1	yes	characteristic
20	C₂²×C₄₁	—	4	2	no	—
21	C₂×D₄₁	D₈	1	1	yes	characteristic
22	C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
23	Dic₄₁	—	4	2	no	—
24	Dic₄₁	D₈	1	1	yes	characteristic
25	C₂×C₄₁	—	8	2	no	—
26	C₂×C₄₁	C₂×D₈	1	1	yes	characteristic
27	D₄₁	—	2	1	no	—
28	#508	—	41	1	no	maximal, Sylow
29	C₄₁	#508	1	1	yes	characteristic, complemented, Sylow
30	#135	—	41	2	no	—
31	Q₃₂	—	41	1	no	—
32	SD₃₂	—	41	2	no	—
33	D₁₆	D₄₁	1	1	yes	characteristic, complemented
34	C₂×C₁₆	—	41	1	no	—
35	#41	—	82	2	no	—
36	Q₁₆	—	41	2	no	—
37	SD₁₆	—	82	2	no	—
38	D₈	C₂×D₄₁	1	2	yes	—
39	C₂×C₈	—	41	1	no	—
40	C₁₆	—	41	1	no	—
41	C₁₆	C₂×D₄₁	1	1	yes	characteristic
42	Q₈	—	82	2	no	—
43	D₄	—	2	2	no	—
44	D₄	—	164	2	no	—
45	C₂×C₄	—	41	1	no	—
46	C₂×C₄	—	164	2	no	—
47	C₈	—	41	1	no	—
48	C₈	C₂²×D₄₁	1	1	yes	characteristic
49	C₂²	—	4	2	no	—
50	C₂²	—	41	1	no	—
51	C₄	—	41	1	no	—
52	C₄	—	164	2	no	—
53	C₄	D₄×D₄₁	1	1	yes	characteristic
54	C₂	—	8	2	no	—
55	C₂	—	82	1	no	—
56	C₂	D₈×D₄₁	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₈×D₄₁
commutator, cosocle	C₈×C₄₁	C₂³
Frattini	C₈	C₂²×D₄₁
Fitting	D₁₆×C₄₁	C₂
socle	C₂×C₄₁	C₂×D₈
hypercenter	D₁₆	D₄₁
hypocenter	C₄₁	#508
LCS	G ▷ C₈×C₄₁ ▷ C₄×C₄₁ ▷ C₂×C₄₁ ▷ C₄₁
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ D₁₆

Complements

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

N	H ≅ G/N	type
1. #13050183	C₂	semidirect
2. Dic₃₂₈	C₂	semidirect
3. #13050108	C₂	semidirect
4. C₁₆×D₄₁	C₂	semidirect
5. D₁₆×C₄₁	C₂	semidirect
29. C₄₁	#508	semidirect
33. D₁₆	D₄₁	semidirect

Maximal subgroups

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

subgroup	index
#13050183	2
Dic₃₂₈	2
#13050108	2
C₁₆×D₄₁	2
D₁₆×C₄₁	2
#508	41