Subgroups — #14580754

Order 2624.

84 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13050170	C₂	1	1	yes	maximal, characteristic
2	#13050103	C₂	1	2	yes	maximal, complemented
3	C₂×#10620268	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₆×D₄₁	C₂	1	2	yes	maximal, complemented
5	M₃₂×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
6	#10620306	C₄	1	1	yes	characteristic
7	C₂×C₈×C₄₁	C₂²	1	1	yes	characteristic
8	#10620277	C₄	1	1	yes	characteristic
9	#10620272	C₄	1	2	yes	—
10	C₈×D₄₁	C₂²	1	2	yes	—
11	C₁₆×C₄₁	C₂²	1	2	yes	—
12	#10620268	C₂²	1	1	yes	characteristic
13	#10620268	C₂²	1	1	yes	characteristic
14	C₂×C₄×C₄₁	C₂×C₄	1	1	yes	characteristic
15	C₂²⋊D₄₁	C₈	1	2	yes	—
16	D₁₆₄	C₈	1	1	yes	characteristic
17	C₄×D₄₁	C₂×C₄	1	2	yes	—
18	Dic₈₂	C₈	1	1	yes	characteristic
19	C₈×C₄₁	C₂×C₄	1	1	yes	characteristic
20	C₈×C₄₁	C₂³	1	1	yes	characteristic
21	#66491	C₂×C₄	1	2	yes	—
22	C₂²×C₄₁	C₂×C₈	1	1	yes	characteristic
23	C₂×D₄₁	C₂×C₈	1	2	yes	—
24	C₄×C₄₁	C₂×C₈	1	1	yes	characteristic
25	C₄×C₄₁	C₂²×C₄	1	1	yes	characteristic
26	Dic₄₁	C₂×C₈	1	2	yes	—
27	C₂×C₄₁	—	2	1	no	—
28	C₂×C₄₁	C₂²×C₈	1	1	yes	characteristic
29	D₄₁	—	2	2	no	—
30	#504	—	41	1	no	maximal, Sylow
31	C₄₁	#504	1	1	yes	characteristic, complemented, Sylow
32	#131	—	41	1	no	—
33	M₃₂	—	41	2	no	—
34	M₃₂	D₄₁	1	1	yes	characteristic, complemented
35	C₂×C₁₆	—	41	1	no	—
36	C₂×C₁₆	—	41	2	no	—
37	#41	—	41	1	no	—
38	M₁₆	—	41	1	no	—
39	M₁₆	—	41	2	no	—
40	C₂×C₈	—	41	2	no	—
41	C₂×C₈	C₂×D₄₁	1	1	yes	characteristic
42	C₁₆	—	41	1	no	—
43	C₁₆	—	41	1	no	—
44	C₁₆	C₂×D₄₁	1	2	yes	—
45	Q₈	—	41	1	no	—
46	D₄	—	41	2	no	—
47	D₄	—	41	1	no	—
48	C₂×C₄	—	41	2	no	—
49	C₂×C₄	C₄×D₄₁	1	1	yes	characteristic
50	C₈	—	41	2	no	—
51	C₈	C₄×D₄₁	1	1	yes	characteristic
52	C₈	C₂²×D₄₁	1	1	yes	characteristic
53	C₂²	—	41	2	no	—
54	C₂²	C₈×D₄₁	1	1	yes	characteristic
55	C₄	—	41	2	no	—
56	C₄	C₈×D₄₁	1	1	yes	characteristic
57	C₄	C₂×C₄×D₄₁	1	1	yes	characteristic
58	C₂	—	2	1	no	—
59	C₂	—	82	2	no	—
60	C₂	C₂×C₈×D₄₁	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₈	C₂²×D₄₁
commutator, socle	C₂×C₄₁	C₂²×C₈
Fitting	M₃₂×C₄₁	C₂
prime radical	#10620306	C₄
cosocle	C₈×C₄₁	C₂³
hypercenter	M₃₂	D₄₁
hypocenter	C₄₁	#504
LCS	G ▷ C₂×C₄₁ ▷ C₄₁
UCS	C₁ ◁ C₈ ◁ M₃₂

Complements

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

N	H ≅ G/N	type
2. #13050103	C₂	semidirect
3. C₂×#10620268	C₂	semidirect
4. C₁₆×D₄₁	C₂	semidirect
5. M₃₂×C₄₁	C₂	semidirect
31. C₄₁	#504	semidirect
34. M₃₂	D₄₁	semidirect

Maximal subgroups

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

subgroup	index
#13050170	2
#13050103	2
C₂×#10620268	2
C₁₆×D₄₁	2
M₃₂×C₄₁	2
#504	41