Subgroups — #1332

Order 128.

49 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×Q₁₆	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	C₄	1	1	yes	characteristic
5	C₄×Q₈	—	2	1	no	—
6	C₂×C₁₆	—	2	1	no	—
7	#107	C₄	1	1	yes	characteristic
8	C₄⋊C₈	—	2	1	no	—
9	#103	—	2	1	no	—
10	C₄×C₈	C₂²	1	1	yes	characteristic
11	C₂×Q₈	—	2	1	no	—
12	Q₁₆	—	2	1	no	—
13	Q₁₆	C₈	1	2	yes	complemented
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	—	2	1	no	—
18	C₄⋊C₄	—	4	1	no	—
19	C₄²	—	4	1	no	—
20	C₄²	D₄	1	1	yes	characteristic
21	C₁₆	—	2	2	no	—
22	Q₈	—	2	2	no	—
23	Q₈	—	4	1	no	—
24	C₂×C₄	—	4	1	no	—
25	C₂×C₄	—	4	1	no	—
26	C₂×C₄	C₂²⋊C₄	1	1	yes	characteristic
27	C₂×C₄	D₈	1	1	yes	characteristic
28	C₂×C₄	SD₁₆	1	1	yes	characteristic
29	C₈	—	2	1	no	—
30	C₈	—	8	1	no	—
31	C₈	C₂×C₈	1	1	yes	characteristic
32	C₈	M₁₆	1	1	yes	characteristic
33	C₂²	#102	1	1	yes	characteristic
34	C₄	—	2	1	no	—
35	C₄	—	4	2	no	—
36	C₄	—	8	1	no	—
37	C₄	C₂²⋊C₈	1	1	yes	characteristic
38	C₄	#104	1	1	yes	characteristic
39	C₄	SD₃₂	1	1	yes	characteristic
40	C₄	Q₃₂	1	1	yes	characteristic
41	C₂	D₄⋊C₈	1	1	yes	characteristic
42	C₂	#358	1	1	yes	characteristic
43	C₂	#359	1	1	yes	characteristic

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

N	H ≅ G/N	type
13. Q₁₆	C₈	semidirect

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