Subgroups — C₂×#504 #3406

Order 128.

184 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#131	C₂	1	1	yes	maximal, characteristic
2	#504	C₂	1	8	yes	maximal, direct product factor
3	C₂×M₃₂	C₂	1	3	yes	maximal, complemented
4	C₂²×C₁₆	C₂	1	3	yes	maximal, complemented
5	C₂×#41	C₄	1	1	yes	characteristic
6	#131	C₄	1	4	yes	—
7	#131	C₂²	1	4	yes	—
8	C₂×M₁₆	C₄	1	3	yes	—
9	C₂²×C₈	C₂²	1	3	yes	—
10	M₃₂	C₂²	1	12	yes	complemented
11	C₂×C₁₆	C₂²	1	3	yes	—
12	C₂×C₁₆	C₂²	1	1	yes	characteristic
13	C₂×C₁₆	C₂²	1	12	yes	complemented
14	#41	C₈	1	4	yes	—
15	#41	C₂×C₄	1	4	yes	—
16	C₂×Q₈	C₈	1	1	yes	characteristic
17	C₂×D₄	C₈	1	3	yes	—
18	C₂²×C₄	C₂×C₄	1	3	yes	—
19	M₁₆	C₂×C₄	1	12	yes	—
20	C₂×C₈	C₂×C₄	1	3	yes	—
21	C₂×C₈	C₂×C₄	1	6	yes	—
22	C₂×C₈	C₂³	1	1	yes	characteristic
23	C₂×C₈	C₂³	1	6	yes	—
24	C₁₆	C₂³	1	6	yes	—
25	C₁₆	C₂³	1	2	yes	—
26	C₂³	C₂×C₈	1	3	yes	—
27	Q₈	C₂×C₈	1	4	yes	—
28	D₄	C₂×C₈	1	12	yes	—
29	C₂×C₄	C₂×C₈	1	3	yes	—
30	C₂×C₄	C₂×C₈	1	6	yes	—
31	C₂×C₄	C₂²×C₄	1	1	yes	characteristic
32	C₂×C₄	C₂²×C₄	1	6	yes	—
33	C₈	C₂²×C₄	1	1	yes	characteristic
34	C₈	C₂²×C₄	1	6	yes	—
35	C₈	C₂⁴	1	1	yes	characteristic
36	C₂²	—	2	6	no	—
37	C₂²	C₂²×C₈	1	6	yes	—
38	C₂²	C₂²×C₈	1	1	yes	characteristic
39	C₄	C₂²×C₈	1	1	yes	characteristic
40	C₄	C₂²×C₈	1	6	yes	—
41	C₄	C₂³×C₄	1	1	yes	characteristic
42	C₂	—	2	6	no	—
43	C₂	#504	1	2	yes	direct product factor
44	C₂	C₂³×C₈	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.