Subgroups — #7514

Order 256.

44 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#2258	C₂	1	1	yes	maximal, characteristic
2	M₁₂₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₆₄	C₂	1	1	yes	maximal, characteristic, complemented
4	#504	C₄	1	1	yes	characteristic
5	M₆₄	—	2	1	no	—
6	M₆₄	C₄	1	1	yes	characteristic
7	C₂×C₃₂	—	2	1	no	—
8	C₂×C₃₂	C₂²	1	1	yes	characteristic
9	C₆₄	—	2	1	no	—
10	C₆₄	—	2	1	no	—
11	#131	C₈	1	1	yes	characteristic
12	M₃₂	—	2	1	no	—
13	M₃₂	C₈	1	1	yes	characteristic
14	C₂×C₁₆	—	2	1	no	—
15	C₂×C₁₆	C₂×C₄	1	1	yes	characteristic
16	C₃₂	—	2	1	no	—
17	C₃₂	D₄	1	1	yes	characteristic
18	C₃₂	D₄	1	1	yes	characteristic
19	#41	C₁₆	1	1	yes	characteristic
20	M₁₆	—	2	1	no	—
21	M₁₆	C₁₆	1	1	yes	characteristic
22	C₂×C₈	—	2	1	no	—
23	C₂×C₈	C₂×C₈	1	1	yes	characteristic
24	C₁₆	—	2	1	no	—
25	C₁₆	C₂²⋊C₄	1	1	yes	characteristic
26	C₁₆	M₁₆	1	1	yes	characteristic
27	Q₈	C₃₂	1	1	yes	characteristic
28	D₄	—	2	1	no	—
29	D₄	C₃₂	1	1	yes	characteristic
30	C₂×C₄	—	2	1	no	—
31	C₂×C₄	C₂×C₁₆	1	1	yes	characteristic
32	C₈	—	2	1	no	—
33	C₈	C₂²⋊C₈	1	1	yes	characteristic
34	C₈	M₃₂	1	1	yes	characteristic
35	C₂²	—	2	1	no	—
36	C₂²	M₆₄	1	1	yes	characteristic
37	C₄	—	2	1	no	—
38	C₄	C₂²⋊C₁₆	1	1	yes	characteristic
39	C₄	C₂×C₃₂	1	1	yes	characteristic
40	C₂	—	2	1	no	—
41	C₂	—	4	1	no	—
42	C₂	C₂²⋊C₃₂	1	1	yes	characteristic

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

N	H ≅ G/N	type
2. M₁₂₈	C₂	semidirect
3. C₂×C₆₄	C₂	semidirect

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