Subgroups — C₂×#117 #514

Order 64.

165 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₄	C₂	1	1	yes	maximal, characteristic
2	#117	C₂	1	8	yes	maximal, direct product factor
3	C₂×C₄⋊C₄	C₂	1	2	yes	maximal, complemented
4	C₂×C₂²⋊C₄	C₂	1	2	yes	maximal
5	C₂×C₄²	C₂	1	2	yes	maximal, complemented
6	C₂⁴	C₂²	1	1	yes	characteristic
7	C₂²×C₄	C₄	1	8	yes	complemented
8	C₂²×C₄	C₂²	1	4	yes	—
9	C₂²×C₄	C₂²	1	1	yes	characteristic
10	C₂²×C₄	C₂²	1	4	yes	—
11	C₂²×C₄	C₂²	1	1	yes	characteristic
12	C₄⋊C₄	C₂²	1	8	yes	complemented
13	C₂²⋊C₄	C₂²	1	8	yes	—
14	C₄²	C₂²	1	8	yes	complemented
15	C₂³	—	2	4	no	—
16	C₂³	C₂×C₄	1	4	yes	—
17	C₂³	C₂³	1	2	yes	—
18	C₂³	C₂³	1	1	yes	characteristic
19	C₂×C₄	—	2	8	no	—
20	C₂×C₄	C₂×C₄	1	4	yes	—
21	C₂×C₄	C₂×C₄	1	4	yes	—
22	C₂×C₄	C₂×C₄	1	16	yes	complemented
23	C₂×C₄	C₂³	1	8	yes	—
24	C₂×C₄	C₂³	1	2	yes	—
25	C₂×C₄	C₂³	1	2	yes	—
26	C₂²	—	2	8	no	—
27	C₂²	—	2	4	no	—
28	C₂²	C₂²×C₄	1	4	yes	—
29	C₂²	C₂²×C₄	1	2	yes	—
30	C₂²	#41	1	4	yes	—
31	C₂²	C₂⁴	1	1	yes	characteristic
32	C₄	—	2	8	no	—
33	C₄	C₂²×C₄	1	4	yes	—
34	C₄	C₂²×C₄	1	4	yes	—
35	C₂	—	2	4	no	—
36	C₂	#117	1	4	yes	direct product factor
37	C₂	C₂³×C₄	1	1	yes	characteristic
38	C₂	C₂×#41	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.