Subgroups — C₂×#346 #2106

Order 128.

100 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₆	C₂	1	2	yes	maximal
2	C₂×C₄×C₈	C₂	1	1	yes	maximal, characteristic
3	#346	C₂	1	4	yes	maximal, direct product factor
4	C₂²×C₈	C₄	1	1	yes	characteristic
5	C₂²×C₈	C₂²	1	1	yes	characteristic
6	C₂×C₄²	C₄	1	1	yes	characteristic
7	C₂×C₁₆	C₄	1	8	yes	complemented
8	C₂×C₁₆	C₂²	1	4	yes	—
9	C₄×C₈	C₄	1	2	yes	—
10	C₄×C₈	C₂²	1	2	yes	—
11	C₂²×C₄	C₈	1	2	yes	—
12	C₂²×C₄	C₂×C₄	1	1	yes	characteristic
13	C₂×C₈	C₈	1	4	yes	—
14	C₂×C₈	C₂×C₄	1	1	yes	characteristic
15	C₂×C₈	C₂×C₄	1	4	yes	—
16	C₂×C₈	C₂×C₄	1	2	yes	—
17	C₂×C₈	C₂³	1	1	yes	characteristic
18	C₄²	C₈	1	2	yes	—
19	C₄²	C₂×C₄	1	2	yes	—
20	C₁₆	C₂×C₄	1	8	yes	complemented
21	C₂³	C₂×C₈	1	1	yes	characteristic
22	C₂×C₄	—	2	4	no	—
23	C₂×C₄	C₄²	1	2	yes	—
24	C₂×C₄	C₂×C₈	1	4	yes	—
25	C₂×C₄	C₂×C₈	1	1	yes	characteristic
26	C₂×C₄	C₂×C₈	1	2	yes	—
27	C₂×C₄	C₂²×C₄	1	1	yes	characteristic
28	C₈	C₄²	1	2	yes	—
29	C₈	C₂×C₈	1	4	yes	—
30	C₈	C₂²×C₄	1	2	yes	—
31	C₂²	C₄×C₈	1	2	yes	—
32	C₂²	M₃₂	1	4	yes	—
33	C₂²	C₂²×C₈	1	1	yes	characteristic
34	C₄	—	2	4	no	—
35	C₄	C₄×C₈	1	2	yes	—
36	C₄	C₂×C₄²	1	1	yes	characteristic
37	C₄	C₂²×C₈	1	1	yes	characteristic
38	C₂	#346	1	4	yes	direct product factor
39	C₂	C₂×C₄×C₈	1	1	yes	characteristic
40	C₂	C₂×M₃₂	1	2	yes	—

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.