Subgroups — #94833

Order 512.

53 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Q₁₂₈	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₂₈	C₂	1	1	yes	maximal, characteristic
3	#7545	C₂	1	1	yes	maximal, characteristic
4	C₂×Q₆₄	—	2	1	no	—
5	Q₁₂₈	—	2	1	no	—
6	Q₁₂₈	C₄	1	2	yes	complemented
7	C₂×C₆₄	C₂²	1	1	yes	characteristic
8	#1423	—	2	1	no	—
9	C₁₂₈	—	2	1	no	—
10	C₂×Q₃₂	—	4	1	no	—
11	Q₆₄	—	2	2	no	—
12	Q₆₄	—	4	1	no	—
13	C₂×C₃₂	D₄	1	1	yes	characteristic
14	#366	—	4	1	no	—
15	C₆₄	C₂×C₄	1	1	yes	characteristic
16	C₆₄	D₄	1	1	yes	characteristic
17	C₂×Q₁₆	—	8	1	no	—
18	Q₃₂	—	4	2	no	—
19	Q₃₂	—	8	1	no	—
20	C₂×C₁₆	D₈	1	1	yes	characteristic
21	#107	—	8	1	no	—
22	C₃₂	C₂²⋊C₄	1	1	yes	characteristic
23	C₃₂	SD₁₆	1	1	yes	characteristic
24	C₂×Q₈	—	16	1	no	—
25	Q₁₆	—	8	2	no	—
26	Q₁₆	—	16	1	no	—
27	C₂×C₈	D₁₆	1	1	yes	characteristic
28	C₄⋊C₄	—	16	1	no	—
29	C₁₆	#102	1	1	yes	characteristic
30	C₁₆	SD₃₂	1	1	yes	characteristic
31	Q₈	—	16	2	no	—
32	Q₈	—	32	1	no	—
33	C₂×C₄	—	32	1	no	—
34	C₂×C₄	—	32	1	no	—
35	C₂×C₄	D₃₂	1	1	yes	characteristic
36	C₈	#357	1	1	yes	characteristic
37	C₈	SD₆₄	1	1	yes	characteristic
38	C₂²	D₆₄	1	1	yes	characteristic
39	C₄	—	32	2	no	—
40	C₄	—	64	1	no	—
41	C₄	#1415	1	1	yes	characteristic
42	C₄	SD₁₂₈	1	1	yes	characteristic
43	C₂	#7537	1	1	yes	characteristic
44	C₂	SD₂₅₆	1	1	yes	characteristic
45	C₂	Q₂₅₆	1	1	yes	characteristic

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

N	H ≅ G/N	type
6. Q₁₂₈	C₄	semidirect

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