Subgroups — #7541

Order 256.

47 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₃₂	C₂	1	1	yes	maximal, characteristic
2	M₁₂₈	C₂	1	1	yes	maximal, characteristic, complemented
3	#1425	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₁₆	—	2	1	no	—
5	D₃₂	—	2	1	no	—
6	D₃₂	C₄	1	2	yes	—
7	C₂×C₃₂	C₂²	1	1	yes	characteristic
8	#368	—	2	1	no	—
9	C₆₄	—	2	1	no	—
10	C₂×D₈	—	4	1	no	—
11	D₁₆	—	2	2	no	—
12	D₁₆	—	4	1	no	—
13	C₂×C₁₆	D₄	1	1	yes	characteristic
14	#108	—	4	1	no	—
15	C₃₂	C₂×C₄	1	1	yes	characteristic
16	C₃₂	D₄	1	1	yes	characteristic
17	C₂×D₄	—	8	1	no	—
18	D₈	—	4	2	no	—
19	D₈	—	8	1	no	—
20	M₁₆	—	8	1	no	—
21	C₂×C₈	D₈	1	1	yes	characteristic
22	C₁₆	C₂²⋊C₄	1	1	yes	characteristic
23	C₁₆	SD₁₆	1	1	yes	characteristic
24	C₂³	—	16	1	no	—
25	D₄	—	8	2	no	—
26	D₄	—	16	1	no	—
27	C₂×C₄	D₁₆	1	1	yes	characteristic
28	C₈	—	16	1	no	—
29	C₈	#102	1	1	yes	characteristic
30	C₈	SD₃₂	1	1	yes	characteristic
31	C₂²	—	16	2	no	—
32	C₂²	—	32	2	no	—
33	C₂²	SD₆₄	1	1	yes	characteristic
34	C₄	#357	1	1	yes	characteristic
35	C₄	D₃₂	1	1	yes	characteristic
36	C₂	—	2	1	no	—
37	C₂	—	32	2	no	—
38	C₂	#1415	1	1	yes	characteristic

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

N	H ≅ G/N	type
2. M₁₂₈	C₂	semidirect
3. #1425	C₂	semidirect

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