Subgroups — #1362

Order 128.

49 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#494	C₂	1	1	yes	maximal, characteristic
2	C₄⋊C₁₆	C₂	1	1	yes	maximal, characteristic
3	#335	C₂	1	1	yes	maximal, characteristic
4	C₂×Q₁₆	—	2	1	no	—
5	C₂×Q₁₆	C₄	1	2	yes	—
6	C₄⋊Q₈	—	2	1	no	—
7	C₂×C₁₆	—	2	1	no	—
8	C₄⋊C₈	—	2	1	no	—
9	C₄×C₈	C₂²	1	1	yes	characteristic
10	C₂×Q₈	—	2	2	no	—
11	Q₁₆	—	4	2	no	—
12	Q₁₆	—	4	1	no	—
13	Q₁₆	—	4	1	no	—
14	C₂×C₈	—	4	1	no	—
15	C₂×C₈	C₂×C₄	1	1	yes	characteristic
16	C₂×C₈	D₄	1	1	yes	characteristic
17	C₄⋊C₄	—	4	1	no	—
18	C₄⋊C₄	—	4	1	no	—
19	C₄²	D₄	1	1	yes	characteristic
20	C₁₆	—	4	1	no	—
21	Q₈	—	4	2	no	—
22	Q₈	—	4	2	no	—
23	C₂×C₄	—	4	2	no	—
24	C₂×C₄	C₂²⋊C₄	1	1	yes	characteristic
25	C₂×C₄	D₈	1	1	yes	characteristic
26	C₂×C₄	SD₁₆	1	1	yes	characteristic
27	C₈	—	2	1	no	—
28	C₈	—	8	1	no	—
29	C₈	D₈	1	1	yes	characteristic
30	C₈	SD₁₆	1	1	yes	characteristic
31	C₂²	#102	1	1	yes	characteristic
32	C₄	—	2	1	no	—
33	C₄	—	8	2	no	—
34	C₄	#100	1	1	yes	characteristic
35	C₄	#102	1	1	yes	characteristic
36	C₄	SD₃₂	1	1	yes	characteristic
37	C₄	Q₃₂	1	1	yes	characteristic
38	C₂	#331	1	1	yes	characteristic
39	C₂	#358	1	1	yes	characteristic
40	C₂	#362	1	1	yes	characteristic

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