Subgroups — #94740

Order 512.

65 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13731	C₂	1	1	yes	maximal, characteristic
2	C₄⋊C₆₄	C₂	1	1	yes	maximal, characteristic
3	#7460	C₂	1	1	yes	maximal, characteristic
4	#2252	—	2	1	no	—
5	C₂×C₆₄	—	2	1	no	—
6	#1423	—	2	1	no	—
7	#1423	C₄	1	2	yes	—
8	C₄×C₃₂	C₂²	1	1	yes	characteristic
9	#1371	—	2	1	no	—
10	#500	—	4	1	no	—
11	C₂×C₃₂	C₂×C₄	1	1	yes	characteristic
12	C₂×C₃₂	D₄	1	1	yes	characteristic
13	#366	—	2	2	no	—
14	#366	—	4	1	no	—
15	C₄×C₁₆	D₄	1	1	yes	characteristic
16	#335	—	4	1	no	—
17	C₆₄	—	4	1	no	—
18	C₄⋊Q₈	—	8	1	no	—
19	C₂×C₁₆	C₂²⋊C₄	1	1	yes	characteristic
20	C₂×C₁₆	SD₁₆	1	1	yes	characteristic
21	#107	—	4	2	no	—
22	#107	—	8	1	no	—
23	C₄⋊C₈	—	8	1	no	—
24	C₄×C₈	D₈	1	1	yes	characteristic
25	C₃₂	—	2	1	no	—
26	C₃₂	SD₁₆	1	1	yes	characteristic
27	C₃₂	Q₁₆	1	1	yes	characteristic
28	C₂×Q₈	—	16	1	no	—
29	C₂×C₈	—	16	1	no	—
30	C₂×C₈	#102	1	1	yes	characteristic
31	C₂×C₈	SD₃₂	1	1	yes	characteristic
32	C₄⋊C₄	—	8	2	no	—
33	C₄⋊C₄	—	16	1	no	—
34	C₄²	D₁₆	1	1	yes	characteristic
35	C₁₆	—	2	1	no	—
36	C₁₆	#101	1	1	yes	characteristic
37	C₁₆	#103	1	1	yes	characteristic
38	Q₈	—	32	1	no	—
39	Q₈	—	32	1	no	—
40	C₂×C₄	—	16	2	no	—
41	C₂×C₄	#357	1	1	yes	characteristic
42	C₂×C₄	D₃₂	1	1	yes	characteristic
43	C₂×C₄	SD₆₄	1	1	yes	characteristic
44	C₈	—	2	1	no	—
45	C₈	—	32	1	no	—
46	C₈	#332	1	1	yes	characteristic
47	C₈	#362	1	1	yes	characteristic
48	C₂²	#1415	1	1	yes	characteristic
49	C₄	—	2	1	no	—
50	C₄	—	32	2	no	—
51	C₄	#1364	1	1	yes	characteristic
52	C₄	#1420	1	1	yes	characteristic
53	C₄	D₆₄	1	1	yes	characteristic
54	C₄	SD₁₂₈	1	1	yes	characteristic
55	C₂	#7450	1	1	yes	characteristic
56	C₂	#7537	1	1	yes	characteristic
57	C₂	#7542	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂²	#1415
commutator	C₂×C₃₂	C₂×C₄
Frattini, cosocle	C₄×C₃₂	C₂²
LCS	G ▷ C₂×C₃₂ ▷ C₂×C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ C₄×C₁₆ ◁ C₄×C₃₂ ◁ G
LECS	G ▷ C₄×C₃₂ ▷ C₂×C₁₆ ▷ 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
#13731	2
C₄⋊C₆₄	2
#7460	2