Subgroups — #1426

Order 128.

26 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	M₆₄	C₂	1	1	yes	maximal, characteristic
2	#368	C₂	1	1	yes	maximal, characteristic
3	#367	C₂	1	1	yes	maximal, characteristic
4	C₂×C₁₆	C₂²	1	1	yes	characteristic
5	#108	—	2	1	no	—
6	#107	—	2	1	no	—
7	C₃₂	C₄	1	2	yes	complemented
8	M₁₆	—	4	1	no	—
9	C₂×C₈	D₄	1	1	yes	characteristic
10	C₄⋊C₄	—	4	1	no	—
11	C₁₆	C₂×C₄	1	1	yes	characteristic
12	C₁₆	Q₈	1	1	yes	characteristic
13	C₂×C₄	—	8	1	no	—
14	C₂×C₄	D₈	1	1	yes	characteristic
15	C₈	—	8	1	no	—
16	C₈	C₄⋊C₄	1	1	yes	characteristic
17	C₈	Q₁₆	1	1	yes	characteristic
18	C₂²	SD₃₂	1	1	yes	characteristic
19	C₄	—	16	1	no	—
20	C₄	#107	1	1	yes	characteristic
21	C₄	SD₃₂	1	1	yes	characteristic
22	C₂	—	2	1	no	—
23	C₂	#367	1	1	yes	characteristic

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

N	H ≅ G/N	type
7. C₃₂	C₄	semidirect

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