Subgroups — #30595233

Order 15616.

82 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#16840601	C₂	1	2	yes	maximal
2	C₄×#14519683	C₂	1	1	yes	maximal, characteristic
3	#16840601	C₄	1	4	yes	complemented
4	C₂×#14519683	C₄	1	1	yes	characteristic
5	C₂×#14519683	C₂²	1	1	yes	characteristic
6	C₄×C₁₆×C₆₁	C₄	1	1	yes	characteristic
7	#14519683	C₈	1	2	yes	—
8	#14519683	C₂×C₄	1	2	yes	—
9	C₂×C₁₆×C₆₁	C₈	1	1	yes	characteristic
10	C₂×C₁₆×C₆₁	C₂×C₄	1	1	yes	characteristic
11	C₄×C₈×C₆₁	C₈	1	1	yes	characteristic
12	C₂×C₈×C₆₁	C₁₆	1	1	yes	characteristic
13	C₂×C₈×C₆₁	C₂×C₈	1	1	yes	characteristic
14	C₄²×C₆₁	C₁₆	1	1	yes	characteristic
15	C₁₆×C₆₁	C₁₆	1	2	yes	—
16	C₁₆×C₆₁	C₄²	1	1	yes	characteristic
17	C₁₆×C₆₁	C₂×C₈	1	1	yes	characteristic
18	C₂×C₄×C₆₁	C₃₂	1	2	yes	—
19	C₂×C₄×C₆₁	C₂×C₁₆	1	1	yes	characteristic
20	C₈×C₆₁	C₃₂	1	2	yes	—
21	C₈×C₆₁	C₄×C₈	1	1	yes	characteristic
22	C₈×C₆₁	C₂×C₁₆	1	1	yes	characteristic
23	#7510	—	61	1	no	maximal, Sylow
24	C₂²×C₆₁	C₂×C₃₂	1	1	yes	characteristic
25	C₄×C₆₁	—	2	2	no	—
26	C₄×C₆₁	C₄×C₁₆	1	1	yes	characteristic
27	C₄×C₆₁	C₂×C₃₂	1	1	yes	characteristic
28	C₂×C₆₄	—	61	2	no	—
29	C₄×C₃₂	—	61	1	no	—
30	C₂×C₆₁	C₄×C₃₂	1	1	yes	characteristic
31	C₂×C₆₁	M₁₂₈	1	2	yes	—
32	C₂×C₃₂	—	61	1	no	—
33	C₂×C₃₂	—	61	1	no	—
34	C₄×C₁₆	#6923	1	1	yes	characteristic
35	C₆₄	—	61	4	no	—
36	C₆₁	#7510	1	1	yes	characteristic, complemented, Sylow
37	C₂×C₁₆	#92420	1	1	yes	characteristic
38	C₂×C₁₆	C₂×#6923	1	1	yes	characteristic
39	C₄×C₈	#92420	1	1	yes	characteristic
40	C₃₂	—	61	2	no	—
41	C₃₂	—	61	2	no	—
42	C₂×C₈	#11758187	1	1	yes	characteristic
43	C₂×C₈	C₂×#92420	1	1	yes	characteristic
44	C₄²	#11758187	1	1	yes	characteristic
45	C₁₆	#11758187	1	2	yes	—
46	C₁₆	D₆₁⋊C₈	1	1	yes	characteristic
47	C₁₆	C₄×#6923	1	1	yes	characteristic
48	C₂×C₄	#14519827	1	2	yes	—
49	C₂×C₄	C₂×#11758187	1	1	yes	characteristic
50	C₈	#14519827	1	2	yes	—
51	C₈	C₄×#92420	1	1	yes	characteristic
52	C₈	C₂×#11758187	1	1	yes	characteristic
53	C₂²	C₂×#14519827	1	1	yes	characteristic
54	C₄	—	2	2	no	—
55	C₄	C₄×#11758187	1	1	yes	characteristic
56	C₄	C₂×#14519827	1	1	yes	characteristic
57	C₂	C₄×#14519827	1	1	yes	characteristic
58	C₂	#21460988	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂×C₁₆	C₂×#6923
commutator	C₂×C₆₁	C₄×C₃₂
Fitting	C₄×C₁₆×C₆₁	C₄
socle, prime radical	C₂²×C₆₁	C₂×C₃₂
cosocle	C₂×#14519683	C₂²
hypercenter	C₄×C₁₆	#6923
hypocenter	C₆₁	#7510
LCS	G ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂×C₁₆ ◁ C₄×C₁₆

Complements

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

N	H ≅ G/N	type
3. #16840601	C₄	semidirect
36. C₆₁	#7510	semidirect

Maximal subgroups

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

subgroup	index
C₂×#16840601	2
C₄×#14519683	2
#7510	61