Subgroups — #14580714

Order 2624.

122 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	C₂×#10620285	C₂	1	2	yes	maximal
3	#13050162	C₂	1	2	yes	maximal
4	C₈×Dic₄₁	C₂	1	1	yes	maximal, characteristic
5	C₂×Q₁₆×C₄₁	C₂	1	1	yes	maximal, characteristic
6	C₂×Q₈×C₄₁	C₂²	1	2	yes	—
7	C₂×Dic₈₂	C₂²	1	2	yes	—
8	Q₁₆×C₄₁	—	2	2	no	—
9	C₂×C₈×C₄₁	C₂²	1	1	yes	characteristic
10	#10620285	—	2	4	no	—
11	#10620279	—	2	4	no	—
12	C₄×Dic₄₁	C₂²	1	1	yes	characteristic
13	C₂×#66491	C₂²	1	1	yes	characteristic
14	Dic₁₆₄	—	2	2	no	—
15	Q₈×C₄₁	—	2	2	no	—
16	Q₈×C₄₁	—	2	2	no	—
17	C₂×C₄×C₄₁	—	2	2	no	—
18	C₂×C₄×C₄₁	C₂³	1	1	yes	characteristic
19	C₂×Dic₄₁	—	2	2	no	—
20	C₂×Dic₄₁	D₄	1	2	yes	—
21	Dic₈₂	—	2	2	no	—
22	Dic₈₂	—	2	2	no	—
23	C₈×C₄₁	D₄	1	2	yes	—
24	#66491	D₄	1	2	yes	—
25	C₂²×C₄₁	C₂×D₄	1	1	yes	characteristic
26	C₄×C₄₁	—	4	2	no	—
27	C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
28	C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
29	Dic₄₁	—	4	2	no	—
30	Dic₄₁	Q₁₆	1	4	yes	complemented
31	C₂×C₄₁	#127	1	1	yes	characteristic
32	C₂×C₄₁	C₂×Q₁₆	1	2	yes	—
33	#494	—	41	1	no	maximal, Sylow
34	C₄₁	#494	1	1	yes	characteristic, complemented, Sylow
35	C₂×Q₁₆	—	41	2	no	—
36	C₂×Q₁₆	—	41	1	no	—
37	C₂×Q₁₆	D₄₁	1	1	yes	characteristic
38	C₄⋊Q₈	—	41	2	no	—
39	C₄×C₈	—	41	1	no	—
40	C₂×Q₈	—	41	2	no	—
41	C₂×Q₈	C₂×D₄₁	1	2	yes	—
42	Q₁₆	—	2	2	no	—
43	Q₁₆	—	82	4	no	—
44	Q₁₆	—	82	2	no	—
45	C₂×C₈	—	41	1	no	—
46	C₂×C₈	C₂×D₄₁	1	1	yes	characteristic
47	C₄⋊C₄	—	82	4	no	—
48	C₄²	—	41	1	no	—
49	Q₈	—	2	2	no	—
50	Q₈	—	2	2	no	—
51	Q₈	—	82	2	no	—
52	Q₈	—	82	2	no	—
53	C₂×C₄	—	2	2	no	—
54	C₂×C₄	—	41	2	no	—
55	C₂×C₄	—	82	2	no	—
56	C₂×C₄	C₂²×D₄₁	1	1	yes	characteristic
57	C₈	—	41	2	no	—
58	C₈	C₂²⋊D₄₁	1	2	yes	—
59	C₂²	D₄×D₄₁	1	1	yes	characteristic
60	C₄	—	4	2	no	—
61	C₄	—	41	4	no	—
62	C₄	—	164	2	no	—
63	C₄	D₄×D₄₁	1	1	yes	characteristic
64	C₄	C₂×C₂²⋊D₄₁	1	1	yes	characteristic
65	C₂	#13050160	1	1	yes	characteristic
66	C₂	Q₁₆×D₄₁	1	2	yes	—

	subgroup	G/H
center	C₂²	D₄×D₄₁
commutator, cosocle	C₂×C₄×C₄₁	C₂³
Frattini	C₂×C₄	C₂²×D₄₁
Fitting	C₂×Q₁₆×C₄₁	C₂
socle, prime radical	C₂²×C₄₁	C₂×D₄
hypercenter	C₂×Q₁₆	D₄₁
hypocenter	C₄₁	#494
LCS	G ▷ C₂×C₄×C₄₁ ▷ C₂×C₄₁ ▷ C₄₁
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×Q₁₆

Complements

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

N	H ≅ G/N	type
30. Dic₄₁	Q₁₆	semidirect
34. C₄₁	#494	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
C₂×#10620285	2
#13050162	2
C₈×Dic₄₁	2
C₂×Q₁₆×C₄₁	2
#494	41