Subgroups — C₂×#103 #415

Order 64.

81 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×Q₈	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₈	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
4	#103	C₂	1	4	yes	maximal, direct product factor
5	C₂×Q₈	—	2	2	no	—
6	C₂×Q₈	—	2	1	no	—
7	C₂×Q₈	C₄	1	4	yes	complemented
8	C₂×Q₈	C₂²	1	2	yes	—
9	C₂²×C₄	—	2	1	no	—
10	C₂²×C₄	—	2	1	no	—
11	C₂²×C₄	C₂²	1	1	yes	characteristic
12	C₂×C₈	—	2	2	no	—
13	C₂×C₈	C₂²	1	2	yes	—
14	C₄⋊C₄	—	2	1	no	—
15	C₄⋊C₄	C₂²	1	2	yes	—
16	C₂³	D₄	1	1	yes	characteristic
17	Q₈	—	2	4	no	—
18	Q₈	—	2	2	no	—
19	Q₈	C₂×C₄	1	4	yes	complemented
20	C₂×C₄	—	2	4	no	—
21	C₂×C₄	—	2	2	no	—
22	C₂×C₄	—	2	2	no	—
23	C₂×C₄	—	4	2	no	—
24	C₂×C₄	C₂×C₄	1	2	yes	—
25	C₂×C₄	D₄	1	1	yes	characteristic
26	C₂×C₄	D₄	1	2	yes	—
27	C₂×C₄	C₂³	1	1	yes	characteristic
28	C₈	—	2	2	no	—
29	C₂²	C₂²⋊C₄	1	2	yes	—
30	C₂²	SD₁₆	1	2	yes	—
31	C₂²	Q₁₆	1	2	yes	—
32	C₂²	C₂×D₄	1	1	yes	characteristic
33	C₄	—	2	4	no	—
34	C₄	—	4	2	no	—
35	C₄	C₂²⋊C₄	1	2	yes	—
36	C₄	C₂²×C₄	1	1	yes	characteristic
37	C₄	C₂×D₄	1	1	yes	characteristic
38	C₂	#103	1	4	yes	direct product factor
39	C₂	C₂×C₂²⋊C₄	1	1	yes	characteristic
40	C₂	C₂×SD₁₆	1	1	yes	characteristic
41	C₂	C₂×Q₁₆	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.