Subgroups — #72277918

Order 1024.

85 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#94814	C₂	1	2	yes	maximal
2	#94504	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₂₈	C₄	1	4	yes	—
4	C₄×C₆₄	C₄	1	1	yes	characteristic
5	C₄×C₆₄	C₂²	1	1	yes	characteristic
6	C₈×C₃₂	C₄	1	1	yes	characteristic
7	C₂×C₆₄	C₈	1	2	yes	—
8	C₂×C₆₄	C₂×C₄	1	2	yes	—
9	C₄×C₃₂	C₈	1	1	yes	characteristic
10	C₄×C₃₂	C₂×C₄	1	1	yes	characteristic
11	C₈×C₁₆	C₈	1	1	yes	characteristic
12	C₁₂₈	C₈	1	8	yes	complemented
13	C₂×C₃₂	C₁₆	1	2	yes	—
14	C₂×C₃₂	C₄²	1	1	yes	characteristic
15	C₂×C₃₂	C₂×C₈	1	1	yes	characteristic
16	C₄×C₁₆	C₁₆	1	1	yes	characteristic
17	C₄×C₁₆	C₂×C₈	1	1	yes	characteristic
18	C₈²	C₁₆	1	1	yes	characteristic
19	C₆₄	C₁₆	1	4	yes	—
20	C₆₄	C₂×C₈	1	4	yes	—
21	C₂×C₁₆	C₃₂	1	2	yes	—
22	C₂×C₁₆	C₄×C₈	1	1	yes	characteristic
23	C₂×C₁₆	C₂×C₁₆	1	1	yes	characteristic
24	C₄×C₈	C₃₂	1	2	yes	—
25	C₄×C₈	C₂×C₁₆	1	1	yes	characteristic
26	C₃₂	C₃₂	1	4	yes	—
27	C₃₂	C₄×C₈	1	2	yes	—
28	C₃₂	C₂×C₁₆	1	2	yes	—
29	C₂×C₈	—	2	2	no	—
30	C₂×C₈	C₄×C₁₆	1	1	yes	characteristic
31	C₂×C₈	C₂×C₃₂	1	1	yes	characteristic
32	C₄²	C₂×C₃₂	1	1	yes	characteristic
33	C₁₆	—	2	2	no	—
34	C₁₆	C₈²	1	1	yes	characteristic
35	C₁₆	C₄×C₁₆	1	1	yes	characteristic
36	C₁₆	C₂×C₃₂	1	2	yes	—
37	C₂×C₄	C₄×C₃₂	1	1	yes	characteristic
38	C₂×C₄	M₁₂₈	1	2	yes	—
39	C₈	—	4	2	no	—
40	C₈	C₈×C₁₆	1	1	yes	characteristic
41	C₈	C₄×C₃₂	1	1	yes	characteristic
42	C₈	M₁₂₈	1	2	yes	—
43	C₂²	#7510	1	1	yes	characteristic
44	C₄	—	2	2	no	—
45	C₄	C₈×C₃₂	1	1	yes	characteristic
46	C₄	#7510	1	1	yes	characteristic
47	C₂	#94504	1	1	yes	characteristic
48	C₂	#94815	1	2	yes	—

	subgroup	G/H
center	C₂×C₃₂	C₄²
commutator	C₄	C₈×C₃₂
Frattini, cosocle	C₄×C₆₄	C₂²
socle, prime radical	C₂²	#7510
LCS	G ▷ C₄ ▷ C₁
UCS	C₁ ◁ C₂×C₃₂ ◁ G
LECS	G ▷ C₄×C₆₄ ▷ C₂×C₃₂ ▷ C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
12. C₁₂₈	C₈	semidirect

Maximal subgroups

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

subgroup	index
#94814	2
#94504	2