Subgroups — #30595238

Order 15616.

74 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#21460988	C₂	1	2	yes	maximal
2	#21443952	C₂	1	1	yes	maximal, characteristic
3	#16840601	C₄	1	4	yes	complemented
4	C₂×#14519683	C₂²	1	1	yes	characteristic
5	C₁₆×Dic₆₁	C₄	1	1	yes	characteristic
6	C₂×C₃₂×C₆₁	C₄	1	1	yes	characteristic
7	C₂×#11758185	C₈	1	1	yes	characteristic
8	C₈×Dic₆₁	C₈	1	1	yes	characteristic
9	#14519683	C₂×C₄	1	2	yes	—
10	C₂×C₁₆×C₆₁	C₂×C₄	1	1	yes	characteristic
11	C₃₂×C₆₁	C₈	1	2	yes	—
12	C₂×C₈×C₆₁	C₂×C₈	1	1	yes	characteristic
13	C₄×Dic₆₁	C₁₆	1	1	yes	characteristic
14	C₂×#92418	C₁₆	1	1	yes	characteristic
15	C₁₆×C₆₁	C₄²	1	1	yes	characteristic
16	C₁₆×C₆₁	C₂×C₈	1	1	yes	characteristic
17	#11758185	C₁₆	1	2	yes	—
18	C₂×C₄×C₆₁	C₂×C₁₆	1	1	yes	characteristic
19	C₂×Dic₆₁	—	2	1	no	—
20	C₈×C₆₁	C₄×C₈	1	1	yes	characteristic
21	C₈×C₆₁	C₂×C₁₆	1	1	yes	characteristic
22	#92418	—	2	1	no	—
23	#7511	—	61	1	no	maximal, Sylow
24	C₂²×C₆₁	M₆₄	1	1	yes	characteristic
25	C₄×C₆₁	C₄×C₁₆	1	1	yes	characteristic
26	C₄×C₆₁	M₆₄	1	1	yes	characteristic
27	Dic₆₁	—	4	1	no	—
28	M₁₂₈	—	61	2	no	—
29	#1397	—	61	1	no	—
30	C₂×C₆₁	—	2	1	no	—
31	C₂×C₆₁	#1397	1	1	yes	characteristic
32	C₂×C₃₂	—	61	1	no	—
33	C₂×C₃₂	#6923	1	1	yes	characteristic
34	C₄×C₁₆	—	61	1	no	—
35	C₆₄	—	61	4	no	—
36	C₆₁	#7511	1	1	yes	characteristic, complemented, Sylow
37	C₂×C₁₆	—	61	1	no	—
38	C₂×C₁₆	C₂×#6923	1	1	yes	characteristic
39	C₄×C₈	—	61	1	no	—
40	C₃₂	—	61	2	no	—
41	C₃₂	#92420	1	2	yes	—
42	C₂×C₈	—	61	1	no	—
43	C₂×C₈	D₆₁⋊C₈	1	1	yes	characteristic
44	C₄²	—	61	1	no	—
45	C₁₆	—	61	2	no	—
46	C₁₆	C₄×#6923	1	1	yes	characteristic
47	C₁₆	C₂×#92420	1	1	yes	characteristic
48	C₂×C₄	—	122	1	no	—
49	C₂×C₄	D₆₁⋊C₁₆	1	1	yes	characteristic
50	C₈	—	122	1	no	—
51	C₈	C₄×#92420	1	1	yes	characteristic
52	C₈	D₆₁⋊C₁₆	1	1	yes	characteristic
53	C₂²	#16840695	1	1	yes	characteristic
54	C₄	—	244	1	no	—
55	C₄	#16840648	1	1	yes	characteristic
56	C₄	#16840695	1	1	yes	characteristic
57	C₂	—	2	1	no	—
58	C₂	#21460927	1	1	yes	characteristic

	subgroup	G/H
center	C₁₆	C₄×#6923
commutator	C₄×C₆₁	C₄×C₁₆
Frattini	C₂×C₁₆	C₂×#6923
Fitting	C₂×C₃₂×C₆₁	C₄
socle	C₂×C₆₁	#1397
prime radical	C₂²×C₆₁	M₆₄
cosocle	C₂×#14519683	C₂²
hypercenter	C₂×C₃₂	#6923
hypocenter	C₆₁	#7511
LCS	G ▷ C₄×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₁₆ ◁ C₂×C₃₂

Complements

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

N	H ≅ G/N	type
3. #16840601	C₄	semidirect
36. C₆₁	#7511	semidirect

Maximal subgroups

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

subgroup	index
#21460988	2
#21443952	2
#7511	61