Subgroups — #1274

Order 128.

84 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#431	C₂	1	2	yes	maximal
2	#376	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄²	C₄	1	2	yes	—
4	C₂×C₄²	C₂²	1	1	yes	characteristic
5	C₄⋊C₈	—	2	2	no	—
6	C₂²⋊C₈	—	2	2	no	—
7	C₄×C₈	C₄	1	4	yes	complemented
8	#95	—	2	2	no	—
9	C₂²×C₄	—	2	2	no	—
10	C₂²×C₄	C₂×C₄	1	1	yes	characteristic
11	C₂²×C₄	D₄	1	2	yes	—
12	C₂×C₈	—	2	4	no	—
13	C₄²	—	2	2	no	—
14	C₄²	C₈	1	4	yes	complemented
15	C₄²	C₂×C₄	1	2	yes	—
16	C₄²	D₄	1	1	yes	characteristic
17	C₄²	Q₈	1	1	yes	characteristic
18	C₂³	C₂²⋊C₄	1	1	yes	characteristic
19	C₂×C₄	—	2	4	no	—
20	C₂×C₄	—	4	2	no	—
21	C₂×C₄	—	4	4	no	—
22	C₂×C₄	C₄²	1	1	yes	characteristic
23	C₂×C₄	C₂²⋊C₄	1	2	yes	—
24	C₂×C₄	C₄⋊C₄	1	2	yes	—
25	C₂×C₄	C₄⋊C₄	1	1	yes	characteristic
26	C₂×C₄	C₂×C₈	1	2	yes	—
27	C₂×C₄	M₁₆	1	2	yes	—
28	C₈	—	4	4	no	—
29	C₂²	—	2	2	no	—
30	C₂²	#95	1	1	yes	characteristic
31	C₂²	C₂²⋊C₈	1	2	yes	—
32	C₄	—	2	2	no	—
33	C₄	—	2	2	no	—
34	C₄	—	4	4	no	—
35	C₄	C₄×C₈	1	1	yes	characteristic
36	C₄	#97	1	1	yes	characteristic
37	C₄	C₄⋊C₈	1	2	yes	—
38	C₂	—	2	2	no	—
39	C₂	#336	1	1	yes	characteristic
40	C₂	H(3,ℤ/4)	1	2	yes	—

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

N	H ≅ G/N	type
7. C₄×C₈	C₄	semidirect
14. C₄²	C₈	semidirect

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

subgroup	index
#431	2
#376	2