Subgroups — #1419

Order 128.

39 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₁₆	C₂	1	1	yes	maximal, characteristic
2	M₆₄	C₂	1	1	yes	maximal, characteristic, complemented
3	#368	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₈	—	2	1	no	—
5	D₁₆	—	2	1	no	—
6	D₁₆	C₄	1	2	yes	—
7	C₂×C₁₆	C₂²	1	1	yes	characteristic
8	#108	—	2	1	no	—
9	C₃₂	—	2	1	no	—
10	C₂×D₄	—	4	1	no	—
11	D₈	—	2	2	no	—
12	D₈	—	4	1	no	—
13	M₁₆	—	4	1	no	—
14	C₂×C₈	D₄	1	1	yes	characteristic
15	C₁₆	C₂×C₄	1	1	yes	characteristic
16	C₁₆	D₄	1	1	yes	characteristic
17	C₂³	—	8	1	no	—
18	D₄	—	4	2	no	—
19	D₄	—	8	1	no	—
20	C₂×C₄	D₈	1	1	yes	characteristic
21	C₈	—	8	1	no	—
22	C₈	C₂²⋊C₄	1	1	yes	characteristic
23	C₈	SD₁₆	1	1	yes	characteristic
24	C₂²	—	8	2	no	—
25	C₂²	—	16	2	no	—
26	C₂²	SD₃₂	1	1	yes	characteristic
27	C₄	#102	1	1	yes	characteristic
28	C₄	D₁₆	1	1	yes	characteristic
29	C₂	—	2	1	no	—
30	C₂	—	16	2	no	—
31	C₂	#357	1	1	yes	characteristic

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

N	H ≅ G/N	type
2. M₆₄	C₂	semidirect
3. #368	C₂	semidirect

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