Subgroups — #1452

Order 128.

98 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#431	C₂	1	2	yes	maximal
2	C₂×C₄×C₈	C₂	1	1	yes	maximal, characteristic
3	#322	C₂	1	4	yes	maximal, complemented
4	C₂²×C₈	C₄	1	2	yes	—
5	C₂×C₄²	C₂²	1	1	yes	characteristic
6	C₄⋊C₈	C₄	1	4	yes	—
7	C₂²⋊C₈	C₄	1	4	yes	—
8	C₄×C₈	C₄	1	2	yes	—
9	C₄×C₈	C₂²	1	2	yes	—
10	C₄×C₈	C₂²	1	4	yes	—
11	C₂²×C₄	C₂×C₄	1	2	yes	—
12	C₂²×C₄	C₂×C₄	1	1	yes	characteristic
13	C₂×C₈	—	2	4	no	—
14	C₂×C₈	C₂×C₄	1	4	yes	—
15	C₂×C₈	C₂×C₄	1	8	yes	—
16	C₄²	C₂×C₄	1	1	yes	characteristic
17	C₄²	C₂×C₄	1	2	yes	—
18	C₄²	C₂³	1	1	yes	characteristic
19	C₂³	C₄²	1	1	yes	characteristic
20	C₂×C₄	—	2	4	no	—
21	C₂×C₄	C₄²	1	2	yes	—
22	C₂×C₄	C₄²	1	1	yes	characteristic
23	C₂×C₄	M₁₆	1	4	yes	—
24	C₂×C₄	C₂²×C₄	1	1	yes	characteristic
25	C₂×C₄	C₂²×C₄	1	2	yes	—
26	C₈	—	2	4	no	—
27	C₈	—	2	8	no	—
28	C₂²	—	2	2	no	—
29	C₂²	#97	1	2	yes	—
30	C₂²	C₂×C₄²	1	1	yes	characteristic
31	C₄	—	2	2	no	—
32	C₄	#97	1	2	yes	—
33	C₄	C₂×M₁₆	1	2	yes	—
34	C₄	#131	1	4	yes	—
35	C₂	—	2	2	no	—
36	C₂	C₂×#97	1	1	yes	characteristic
37	C₂	#405	1	2	yes	—

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

N	H ≅ G/N	type
3. #322	C₂	semidirect

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