Subgroups — #94754

Order 512.

46 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#7511	C₂	1	1	yes	maximal, characteristic
2	#7464	C₂	1	1	yes	maximal, characteristic
3	#7463	C₂	1	1	yes	maximal, characteristic
4	M₁₂₈	C₄	1	1	yes	characteristic
5	M₁₂₈	C₄	1	1	yes	characteristic
6	#1397	C₂²	1	1	yes	characteristic
7	#1373	—	2	1	no	—
8	#1372	—	2	1	no	—
9	C₂×C₃₂	C₂×C₄	1	1	yes	characteristic
10	C₂×C₃₂	Q₈	1	1	yes	characteristic
11	#364	—	4	1	no	—
12	C₄×C₁₆	D₄	1	1	yes	characteristic
13	#335	—	4	1	no	—
14	C₆₄	—	2	1	no	—
15	C₆₄	C₈	1	2	yes	complemented
16	M₃₂	—	8	1	no	—
17	C₂×C₁₆	C₄⋊C₄	1	1	yes	characteristic
18	C₂×C₁₆	Q₁₆	1	1	yes	characteristic
19	C₄⋊C₈	—	8	1	no	—
20	C₄×C₈	D₈	1	1	yes	characteristic
21	C₃₂	—	2	1	no	—
22	C₃₂	C₂×C₈	1	1	yes	characteristic
23	C₃₂	M₁₆	1	1	yes	characteristic
24	C₂×C₈	—	16	1	no	—
25	C₂×C₈	#107	1	1	yes	characteristic
26	C₂×C₈	SD₃₂	1	1	yes	characteristic
27	C₄²	SD₃₂	1	1	yes	characteristic
28	C₁₆	—	2	1	no	—
29	C₁₆	—	16	1	no	—
30	C₁₆	C₄⋊C₈	1	1	yes	characteristic
31	C₁₆	#108	1	1	yes	characteristic
32	C₂×C₄	—	2	1	no	—
33	C₂×C₄	#367	1	1	yes	characteristic
34	C₈	—	2	1	no	—
35	C₈	—	32	1	no	—
36	C₈	#335	1	1	yes	characteristic
37	C₈	#368	1	1	yes	characteristic
38	C₂²	#1426	1	1	yes	characteristic
39	C₄	—	4	1	no	—
40	C₄	#1372	1	1	yes	characteristic
41	C₄	#1426	1	1	yes	characteristic
42	C₂	—	2	1	no	—
43	C₂	#7463	1	1	yes	characteristic

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

N	H ≅ G/N	type
15. C₆₄	C₈	semidirect

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