Subgroups — #1418

Order 128.

37 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	M₆₄	C₂	1	1	yes	maximal, characteristic, complemented
3	#367	C₂	1	1	yes	maximal, characteristic, complemented
4	#135	—	2	1	no	—
5	Q₃₂	C₄	1	1	yes	characteristic, complemented
6	SD₃₂	—	2	1	no	—
7	D₁₆	C₄	1	1	yes	characteristic, complemented
8	C₂×C₁₆	C₂²	1	1	yes	characteristic
9	#107	—	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	C₂×C₈	D₄	1	1	yes	characteristic
16	C₄⋊C₄	—	4	1	no	—
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	—	8	1	no	—
24	C₂×C₄	D₈	1	1	yes	characteristic
25	C₈	C₂²⋊C₄	1	1	yes	characteristic
26	C₈	SD₁₆	1	1	yes	characteristic
27	C₂²	—	8	1	no	—
28	C₂²	D₁₆	1	1	yes	characteristic
29	C₄	—	8	1	no	—
30	C₄	—	16	1	no	—
31	C₄	#102	1	1	yes	characteristic
32	C₄	SD₃₂	1	1	yes	characteristic
33	C₂	—	2	1	no	—
34	C₂	—	16	1	no	—
35	C₂	#357	1	1	yes	characteristic

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

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