Subgroups — #93666

Order 512.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#7329	C₂	1	1	yes	maximal, characteristic
2	#7329	C₂	1	1	yes	maximal, characteristic
3	#7052	C₂	1	1	yes	maximal, characteristic
4	C₄×C₃₂	C₄	1	2	yes	—
5	C₄×C₃₂	C₄	1	2	yes	—
6	C₈×C₁₆	C₄	1	2	yes	—
7	C₈×C₁₆	C₂²	1	1	yes	characteristic
8	C₂×C₃₂	C₈	1	4	yes	—
9	C₂×C₃₂	C₈	1	4	yes	—
10	C₄×C₁₆	C₈	1	4	yes	—
11	C₄×C₁₆	C₂×C₄	1	1	yes	characteristic
12	C₄×C₁₆	C₂×C₄	1	1	yes	characteristic
13	C₈²	C₂×C₄	1	1	yes	characteristic
14	C₂×C₁₆	—	2	4	no	—
15	C₂×C₁₆	C₂×C₈	1	2	yes	—
16	C₂×C₁₆	C₂×C₈	1	2	yes	—
17	C₄×C₈	C₄²	1	1	yes	characteristic
18	C₄×C₈	C₂×C₈	1	2	yes	—
19	C₃₂	—	2	4	no	—
20	C₃₂	C₁₆	1	8	yes	complemented
21	C₂×C₈	C₄×C₈	1	1	yes	characteristic
22	C₂×C₈	C₄×C₈	1	1	yes	characteristic
23	C₂×C₈	M₃₂	1	4	yes	—
24	C₄²	C₄×C₈	1	1	yes	characteristic
25	C₁₆	—	4	4	no	—
26	C₁₆	C₂×C₁₆	1	4	yes	—
27	C₁₆	M₃₂	1	4	yes	—
28	C₂×C₄	C₈²	1	1	yes	characteristic
29	C₂×C₄	#346	1	2	yes	—
30	C₈	—	2	4	no	—
31	C₈	C₄×C₁₆	1	2	yes	—
32	C₈	#346	1	2	yes	—
33	C₂²	#1311	1	1	yes	characteristic
34	C₄	C₈×C₁₆	1	1	yes	characteristic
35	C₄	#1311	1	1	yes	characteristic
36	C₄	#1398	1	4	yes	—
37	C₂	#7052	1	1	yes	characteristic
38	C₂	#7330	1	2	yes	—

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

N	H ≅ G/N	type
20. C₃₂	C₁₆	semidirect

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

subgroup	index
#7329	2
#7052	2