Subgroups — C₂×GO⁺(4,𝔽₂) #3843

Order 144.

86 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₃²	C₂	1	2	yes	maximal, complemented
2	C₂×#157	C₂	1	1	yes	maximal, characteristic, complemented
3	GO⁺(4,𝔽₂)	C₂	1	4	yes	maximal, direct product factor
4	C₂×C₃⋊D₃	C₂²	1	1	yes	characteristic
5	C₂×C₃×D₃	—	2	2	no	—
6	D₃²	—	2	2	no	—
7	D₃²	C₂²	1	4	yes	complemented
8	#157	C₂²	1	2	yes	complemented
9	C₂²×D₃	—	6	2	no	—
10	C₂×C₃²	D₄	1	1	yes	characteristic, complemented
11	C₃⋊D₃	D₄	1	1	yes	characteristic, complemented
12	C₃⋊D₃	C₂³	1	1	yes	characteristic
13	C₃×D₃	—	2	4	no	—
14	C₂×D₄	—	9	1	no	maximal, Sylow
15	C₂²×C₃	—	6	2	no	—
16	C₂×D₃	—	2	2	no	—
17	C₂×D₃	—	6	4	no	—
18	C₂×D₃	—	6	2	no	—
19	C₂×D₃	—	6	4	no	—
20	C₃²	C₂×D₄	1	1	yes	characteristic, complemented, Sylow
21	C₂³	—	9	2	no	—
22	D₄	—	9	4	no	—
23	C₂×C₄	—	9	1	no	—
24	C₂×C₃	—	2	2	no	—
25	C₂×C₃	—	6	4	no	—
26	D₃	—	2	4	no	—
27	D₃	—	6	2	no	—
28	D₃	—	6	2	no	—
29	C₂²	—	6	2	no	—
30	C₂²	—	9	4	no	—
31	C₂²	—	9	1	no	—
32	C₂²	—	18	2	no	—
33	C₄	—	9	2	no	—
34	C₃	—	2	2	no	—
35	C₂	—	6	4	no	—
36	C₂	—	9	1	no	—
37	C₂	—	9	1	no	—
38	C₂	GO⁺(4,𝔽₂)	1	1	yes	characteristic, direct product factor

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.