Subgroups — #2110

Order 128.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×M₃₂	C₂	1	2	yes	maximal
2	#405	C₂	1	1	yes	maximal, characteristic
3	#347	C₂	1	4	yes	maximal, complemented
4	C₂×M₁₆	C₄	1	1	yes	characteristic
5	C₂²×C₈	C₂²	1	1	yes	characteristic
6	#117	C₄	1	1	yes	characteristic
7	M₃₂	C₄	1	4	yes	complemented
8	M₃₂	C₂²	1	4	yes	—
9	C₂×C₁₆	C₄	1	4	yes	complemented
10	#97	C₂²	1	2	yes	—
11	C₄×C₈	C₄	1	2	yes	—
12	C₂²×C₄	C₂×C₄	1	1	yes	characteristic
13	M₁₆	—	2	2	no	—
14	C₂×C₈	C₂×C₄	1	2	yes	—
15	C₂×C₈	C₂×C₄	1	1	yes	characteristic
16	C₂×C₈	C₂×C₄	1	2	yes	—
17	C₂×C₈	C₂×C₄	1	2	yes	—
18	C₂×C₈	C₂³	1	1	yes	characteristic
19	C₄⋊C₄	—	2	1	no	—
20	C₂²⋊C₄	—	2	1	no	—
21	C₄²	C₂×C₄	1	2	yes	—
22	C₁₆	C₂×C₄	1	8	yes	—
23	C₂³	M₁₆	1	1	yes	characteristic
24	C₂×C₄	—	2	2	no	—
25	C₂×C₄	C₄²	1	2	yes	—
26	C₂×C₄	M₁₆	1	1	yes	characteristic
27	C₂×C₄	M₁₆	1	2	yes	—
28	C₂×C₄	C₂²×C₄	1	1	yes	characteristic
29	C₈	—	2	2	no	—
30	C₈	C₄²	1	1	yes	characteristic
31	C₈	C₄²	1	1	yes	characteristic
32	C₈	C₂²×C₄	1	2	yes	—
33	C₂²	—	4	1	no	—
34	C₂²	#97	1	2	yes	—
35	C₂²	C₂×M₁₆	1	1	yes	characteristic
36	C₄	—	4	2	no	—
37	C₄	#97	1	2	yes	—
38	C₄	C₂×C₄²	1	1	yes	characteristic
39	C₄	C₂×M₁₆	1	1	yes	characteristic
40	C₂	—	2	1	no	—
41	C₂	—	2	2	no	—
42	C₂	C₂×#97	1	1	yes	characteristic

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

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