Subgroups — #151731

Order 512.

154 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13733	C₂	1	2	yes	maximal
2	#13731	C₂	1	2	yes	maximal
3	#12522	C₂	1	2	yes	maximal
4	C₈×C₃₂	C₂	1	1	yes	maximal, characteristic
5	#2254	—	2	2	no	—
6	#2252	C₂²	1	4	yes	—
7	#1710	—	2	2	no	—
8	#1424	—	2	4	no	—
9	#1423	—	2	4	no	—
10	C₄×C₃₂	C₂²	1	1	yes	characteristic
11	C₄×C₃₂	C₂²	1	1	yes	characteristic
12	C₈×C₁₆	C₂²	1	1	yes	characteristic
13	#500	—	2	4	no	—
14	#487	—	4	4	no	—
15	C₂×C₃₂	D₄	1	2	yes	—
16	C₂×C₃₂	D₄	1	2	yes	—
17	#367	—	4	4	no	—
18	#366	—	2	4	no	—
19	#366	—	2	4	no	—
20	C₄×C₁₆	D₄	1	1	yes	characteristic
21	C₄×C₁₆	C₂³	1	1	yes	characteristic
22	C₈²	D₄	1	1	yes	characteristic
23	C₄⋊Q₈	—	4	4	no	—
24	C₂×C₁₆	D₈	1	2	yes	—
25	C₂×C₁₆	C₂×D₄	1	1	yes	characteristic
26	C₂×C₁₆	C₂×D₄	1	1	yes	characteristic
27	#107	—	4	4	no	—
28	#107	—	4	4	no	—
29	#103	—	8	8	no	—
30	C₄×C₈	D₈	1	2	yes	—
31	C₄×C₈	C₂×D₄	1	1	yes	characteristic
32	C₃₂	Q₁₆	1	4	yes	—
33	C₃₂	Q₁₆	1	4	yes	—
34	C₂×Q₈	—	8	4	no	—
35	C₂×C₈	D₁₆	1	4	yes	—
36	C₂×C₈	#127	1	1	yes	characteristic
37	C₂×C₈	C₂×D₈	1	1	yes	characteristic
38	C₄⋊C₄	—	8	4	no	—
39	C₄⋊C₄	—	8	4	no	—
40	C₄²	C₂×D₈	1	1	yes	characteristic
41	C₁₆	Q₃₂	1	4	yes	—
42	C₁₆	C₂×Q₁₆	1	2	yes	—
43	C₁₆	C₂×Q₁₆	1	2	yes	—
44	Q₈	—	16	8	no	—
45	C₂×C₄	—	16	4	no	—
46	C₂×C₄	#493	1	1	yes	characteristic
47	C₂×C₄	C₂×D₁₆	1	2	yes	—
48	C₈	—	2	4	no	—
49	C₈	#494	1	1	yes	characteristic
50	C₈	#494	1	1	yes	characteristic
51	C₈	C₂×Q₃₂	1	2	yes	—
52	C₂²	#2246	1	1	yes	characteristic
53	C₄	—	32	4	no	—
54	C₄	#1713	1	1	yes	characteristic
55	C₄	#2247	1	1	yes	characteristic
56	C₄	#2262	1	4	yes	—
57	C₂	#12521	1	1	yes	characteristic
58	C₂	#13728	1	2	yes	—

	subgroup	G/H
center, socle, prime radical	C₂²	#2246
commutator, Frattini, cosocle	C₄×C₁₆	C₂³
LCS	G ▷ C₄×C₁₆ ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₈² ◁ C₈×C₁₆ ◁ G
LECS	G ▷ C₄×C₁₆ ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁

Maximal subgroups

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

subgroup	index
#13733	2
#13731	2
#12522	2
C₈×C₃₂	2