Subgroups — #1744

Order 128.

148 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×C₈	C₂	1	2	yes	maximal
2	C₄³	C₂	1	1	yes	maximal, characteristic
3	#336	C₂	1	4	yes	maximal
4	C₂²×C₈	C₂²	1	4	yes	—
5	C₂×C₄²	C₄	1	2	yes	—
6	C₂×C₄²	C₄	1	2	yes	—
7	C₂×C₄²	C₂²	1	2	yes	—
8	C₂×C₄²	C₂²	1	1	yes	characteristic
9	C₄×C₈	C₄	1	8	yes	complemented
10	C₂²×C₄	C₂×C₄	1	4	yes	—
11	C₂²×C₄	C₂×C₄	1	1	yes	characteristic
12	C₂²×C₄	C₂×C₄	1	1	yes	characteristic
13	C₂²×C₄	C₂³	1	1	yes	characteristic
14	C₂×C₈	—	2	8	no	—
15	C₂×C₈	C₂×C₄	1	8	yes	—
16	C₄²	—	2	4	no	—
17	C₄²	—	2	4	no	—
18	C₄²	C₈	1	8	yes	complemented
19	C₄²	C₂×C₄	1	4	yes	—
20	C₂³	C₂²×C₄	1	1	yes	characteristic
21	C₂×C₄	—	2	4	no	—
22	C₂×C₄	—	2	4	no	—
23	C₂×C₄	C₄²	1	2	yes	—
24	C₂×C₄	C₄²	1	2	yes	—
25	C₂×C₄	C₂×C₈	1	8	yes	—
26	C₂×C₄	C₂×C₈	1	4	yes	—
27	C₂×C₄	M₁₆	1	4	yes	—
28	C₂×C₄	C₂²×C₄	1	2	yes	—
29	C₂×C₄	#41	1	4	yes	—
30	C₈	—	2	8	no	—
31	C₂²	C₂×C₄²	1	1	yes	characteristic
32	C₂²	#117	1	2	yes	—
33	C₂²	C₂²×C₈	1	2	yes	—
34	C₂²	C₂×M₁₆	1	2	yes	—
35	C₄	—	2	8	no	—
36	C₄	C₄×C₈	1	4	yes	—
37	C₄	#97	1	4	yes	—
38	C₄	#117	1	4	yes	—
39	C₂	#376	1	1	yes	characteristic
40	C₂	C₂×C₄×C₈	1	1	yes	characteristic
41	C₂	C₂×#97	1	1	yes	characteristic
42	C₂	#431	1	4	yes	—

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

N	H ≅ G/N	type
9. C₄×C₈	C₄	semidirect
18. C₄²	C₈	semidirect

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