Subgroups — C₂×#366 #2156

Order 128.

84 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₆	C₂	1	1	yes	maximal, characteristic
2	C₂×#107	C₂	1	2	yes	maximal
3	#366	C₂	1	4	yes	maximal, direct product factor
4	C₂²×C₈	C₂²	1	1	yes	characteristic
5	C₂×C₄⋊C₄	—	2	2	no	—
6	C₂×C₁₆	C₄	1	4	yes	complemented
7	C₂×C₁₆	C₂²	1	2	yes	—
8	#107	—	2	2	no	—
9	#107	C₂²	1	4	yes	—
10	C₂²×C₄	—	4	2	no	—
11	C₂²×C₄	D₄	1	1	yes	characteristic
12	C₂×C₈	C₂×C₄	1	2	yes	—
13	C₂×C₈	D₄	1	1	yes	characteristic
14	C₂×C₈	Q₈	1	2	yes	—
15	C₂×C₈	C₂³	1	1	yes	characteristic
16	C₄⋊C₄	—	2	4	no	—
17	C₄⋊C₄	—	4	2	no	—
18	C₁₆	C₂×C₄	1	4	yes	complemented
19	C₂³	D₈	1	1	yes	characteristic
20	C₂×C₄	—	4	4	no	—
21	C₂×C₄	—	8	4	no	—
22	C₂×C₄	C₄⋊C₄	1	2	yes	—
23	C₂×C₄	D₈	1	1	yes	characteristic
24	C₂×C₄	Q₁₆	1	2	yes	—
25	C₂×C₄	C₂×D₄	1	1	yes	characteristic
26	C₈	C₄⋊C₄	1	2	yes	—
27	C₈	C₂²×C₄	1	1	yes	characteristic
28	C₈	C₂×Q₈	1	1	yes	characteristic
29	C₂²	#107	1	2	yes	—
30	C₂²	D₁₆	1	2	yes	—
31	C₂²	Q₃₂	1	2	yes	—
32	C₂²	C₂×D₈	1	1	yes	characteristic
33	C₄	—	8	4	no	—
34	C₄	#107	1	2	yes	—
35	C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
36	C₄	C₂×Q₁₆	1	1	yes	characteristic
37	C₂	#366	1	4	yes	direct product factor
38	C₂	C₂×#107	1	1	yes	characteristic
39	C₂	C₂×D₁₆	1	1	yes	characteristic
40	C₂	C₂×Q₃₂	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.