Subgroups — #1401

Order 128.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

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

N	H ≅ G/N	type
2. M₆₄	C₂	semidirect
3. C₂×C₃₂	C₂	semidirect

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