Subgroups — #14580444

Order 2624.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₁₆₄	C₂	1	1	yes	maximal, characteristic
2	C₄×Dic₈₂	C₂	1	2	yes	maximal
3	#13050096	C₂	1	1	yes	maximal, characteristic
4	#13050089	C₂	1	2	yes	maximal
5	#97×C₄₁	C₂	1	1	yes	maximal, characteristic
6	C₂×Dic₈₂	C₂²	1	2	yes	—
7	C₂×C₈×C₄₁	C₂²	1	1	yes	characteristic
8	C₂×C₈×C₄₁	C₂²	1	1	yes	characteristic
9	C₄²×C₄₁	C₂²	1	1	yes	characteristic
10	C₄⋊Dic₄₁	C₂²	1	2	yes	—
11	#10620279	—	2	2	no	—
12	C₄×Dic₄₁	—	2	2	no	—
13	Dic₁₆₄	C₄	1	4	yes	complemented
14	C₂×C₄×C₄₁	D₄	1	2	yes	—
15	C₂×C₄×C₄₁	C₂³	1	1	yes	characteristic
16	C₂×Dic₄₁	—	2	2	no	—
17	C₂×Dic₄₁	—	2	2	no	—
18	Dic₈₂	—	2	2	no	—
19	Dic₈₂	C₂×C₄	1	4	yes	—
20	C₈×C₄₁	—	2	1	no	—
21	C₈×C₄₁	C₂×C₄	1	2	yes	—
22	C₂²×C₄₁	C₂×D₄	1	1	yes	characteristic
23	C₄×C₄₁	—	2	2	no	—
24	C₄×C₄₁	C₂²×C₄	1	1	yes	characteristic
25	C₄×C₄₁	#41	1	1	yes	characteristic
26	Dic₄₁	—	2	4	no	—
27	Dic₄₁	—	4	2	no	—
28	C₂×C₄₁	C₄×D₄	1	1	yes	characteristic
29	C₂×C₄₁	#137	1	2	yes	—
30	#441	—	41	1	no	maximal, Sylow
31	C₄₁	#441	1	1	yes	characteristic, complemented, Sylow
32	C₂×Q₁₆	—	41	1	no	—
33	C₄×Q₈	—	41	2	no	—
34	#106	—	41	1	no	—
35	#103	—	41	2	no	—
36	#97	D₄₁	1	1	yes	characteristic
37	C₂×Q₈	—	41	2	no	—
38	Q₁₆	—	41	4	no	—
39	C₂×C₈	C₂×D₄₁	1	1	yes	characteristic
40	C₂×C₈	C₂×D₄₁	1	1	yes	characteristic
41	C₄⋊C₄	—	41	2	no	—
42	C₄⋊C₄	—	82	2	no	—
43	C₄²	—	82	2	no	—
44	C₄²	C₂×D₄₁	1	1	yes	characteristic
45	Q₈	—	41	4	no	—
46	Q₈	—	82	2	no	—
47	C₂×C₄	—	82	2	no	—
48	C₂×C₄	—	82	2	no	—
49	C₂×C₄	D₁₆₄	1	2	yes	—
50	C₂×C₄	C₂²×D₄₁	1	1	yes	characteristic
51	C₈	—	2	1	no	—
52	C₈	C₄×D₄₁	1	2	yes	—
53	C₂²	C₂×D₁₆₄	1	1	yes	characteristic
54	C₄	—	2	2	no	—
55	C₄	—	82	4	no	—
56	C₄	—	164	2	no	—
57	C₄	C₂×C₄×D₄₁	1	1	yes	characteristic
58	C₄	#10620306	1	1	yes	characteristic
59	C₂	C₄×D₁₆₄	1	1	yes	characteristic
60	C₂	#13050197	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂×D₁₆₄
commutator	C₄×C₄₁	C₂²×C₄
Frattini	C₂×C₄	C₂²×D₄₁
Fitting	#97×C₄₁	C₂
socle, prime radical	C₂²×C₄₁	C₂×D₄
cosocle	C₂×C₄×C₄₁	C₂³
hypercenter	#97	D₄₁
hypocenter	C₄₁	#441
LCS	G ▷ C₄×C₄₁ ▷ C₂×C₄₁ ▷ C₄₁
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #97

Complements

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

N	H ≅ G/N	type
13. Dic₁₆₄	C₄	semidirect
31. C₄₁	#441	semidirect

Maximal subgroups

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

subgroup	index
C₂×Dic₁₆₄	2
C₄×Dic₈₂	2
#13050096	2
#13050089	2
#97×C₄₁	2
#441	41