Subgroups — #1365

Order 128.

43 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#500	C₂	1	1	yes	maximal, characteristic
2	C₄⋊C₁₆	C₂	1	1	yes	maximal, characteristic
3	#335	C₂	1	1	yes	maximal, characteristic
4	C₄⋊Q₈	—	2	1	no	—
5	C₂×C₁₆	—	2	1	no	—
6	#107	—	2	1	no	—
7	#107	C₄	1	2	yes	—
8	C₄⋊C₈	—	2	1	no	—
9	C₄×C₈	C₂²	1	1	yes	characteristic
10	C₂×Q₈	—	4	1	no	—
11	C₂×C₈	—	4	1	no	—
12	C₂×C₈	C₂×C₄	1	1	yes	characteristic
13	C₂×C₈	D₄	1	1	yes	characteristic
14	C₄⋊C₄	—	2	2	no	—
15	C₄⋊C₄	—	4	1	no	—
16	C₄²	D₄	1	1	yes	characteristic
17	C₁₆	—	4	1	no	—
18	Q₈	—	8	2	no	—
19	C₂×C₄	—	4	2	no	—
20	C₂×C₄	C₂²⋊C₄	1	1	yes	characteristic
21	C₂×C₄	D₈	1	1	yes	characteristic
22	C₂×C₄	SD₁₆	1	1	yes	characteristic
23	C₈	—	2	1	no	—
24	C₈	—	8	1	no	—
25	C₈	SD₁₆	1	1	yes	characteristic
26	C₈	Q₁₆	1	1	yes	characteristic
27	C₂²	#102	1	1	yes	characteristic
28	C₄	—	2	1	no	—
29	C₄	—	8	2	no	—
30	C₄	#101	1	1	yes	characteristic
31	C₄	#103	1	1	yes	characteristic
32	C₄	SD₃₂	1	1	yes	characteristic
33	C₄	Q₃₂	1	1	yes	characteristic
34	C₂	#332	1	1	yes	characteristic
35	C₂	#358	1	1	yes	characteristic
36	C₂	#361	1	1	yes	characteristic

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