Subgroups — #1417

Order 128.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#508	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃₂	C₂	1	1	yes	maximal, characteristic, complemented
3	#368	C₂	1	1	yes	maximal, characteristic, complemented
4	#135	—	2	1	no	—
5	Q₃₂	C₄	1	1	yes	characteristic
6	SD₃₂	—	2	1	no	—
7	D₁₆	C₄	1	1	yes	characteristic
8	C₂×C₁₆	C₂²	1	1	yes	characteristic
9	#108	—	2	1	no	—
10	C₃₂	—	2	1	no	—
11	#41	—	4	1	no	—
12	Q₁₆	—	2	1	no	—
13	SD₁₆	—	4	1	no	—
14	D₈	—	2	1	no	—
15	M₁₆	—	4	1	no	—
16	C₂×C₈	D₄	1	1	yes	characteristic
17	C₁₆	C₂×C₄	1	1	yes	characteristic
18	C₁₆	D₄	1	1	yes	characteristic
19	Q₈	—	4	1	no	—
20	D₄	—	4	1	no	—
21	D₄	—	8	1	no	—
22	C₂×C₄	—	8	1	no	—
23	C₂×C₄	D₈	1	1	yes	characteristic
24	C₈	—	8	1	no	—
25	C₈	C₂²⋊C₄	1	1	yes	characteristic
26	C₈	SD₁₆	1	1	yes	characteristic
27	C₂²	—	8	1	no	—
28	C₂²	SD₃₂	1	1	yes	characteristic
29	C₄	—	8	1	no	—
30	C₄	#102	1	1	yes	characteristic
31	C₄	D₁₆	1	1	yes	characteristic
32	C₂	—	2	1	no	—
33	C₂	—	16	1	no	—
34	C₂	#357	1	1	yes	characteristic

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

N	H ≅ G/N	type
2. C₂×C₃₂	C₂	semidirect
3. #368	C₂	semidirect

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