Subgroups — #1416

Order 128.

37 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Q₃₂	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃₂	C₂	1	1	yes	maximal, characteristic
3	#366	C₂	1	1	yes	maximal, characteristic
4	C₂×Q₁₆	—	2	1	no	—
5	Q₃₂	—	2	1	no	—
6	Q₃₂	C₄	1	2	yes	complemented
7	C₂×C₁₆	C₂²	1	1	yes	characteristic
8	#107	—	2	1	no	—
9	C₃₂	—	2	1	no	—
10	C₂×Q₈	—	4	1	no	—
11	Q₁₆	—	2	2	no	—
12	Q₁₆	—	4	1	no	—
13	C₂×C₈	D₄	1	1	yes	characteristic
14	C₄⋊C₄	—	4	1	no	—
15	C₁₆	C₂×C₄	1	1	yes	characteristic
16	C₁₆	D₄	1	1	yes	characteristic
17	Q₈	—	4	2	no	—
18	Q₈	—	8	1	no	—
19	C₂×C₄	—	8	1	no	—
20	C₂×C₄	—	8	1	no	—
21	C₂×C₄	D₈	1	1	yes	characteristic
22	C₈	C₂²⋊C₄	1	1	yes	characteristic
23	C₈	SD₁₆	1	1	yes	characteristic
24	C₂²	D₁₆	1	1	yes	characteristic
25	C₄	—	8	2	no	—
26	C₄	—	16	1	no	—
27	C₄	#102	1	1	yes	characteristic
28	C₄	SD₃₂	1	1	yes	characteristic
29	C₂	#357	1	1	yes	characteristic
30	C₂	SD₆₄	1	1	yes	characteristic
31	C₂	Q₆₄	1	1	yes	characteristic

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

N	H ≅ G/N	type
6. Q₃₂	C₄	semidirect

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