Subgroups — C₄×C₂²⋊C₄ #377

Order 64.

129 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	C₂×C₂²⋊C₄	C₂	1	2	yes	maximal
3	C₂×C₄²	C₂	1	2	yes	maximal, complemented
4	#95	C₂	1	2	yes	maximal, complemented
5	C₂⁴	C₂²	1	1	yes	characteristic
6	C₂²×C₄	—	2	4	no	—
7	C₂²×C₄	C₄	1	4	yes	complemented
8	C₂²×C₄	C₂²	1	1	yes	characteristic
9	C₂²×C₄	C₂²	1	4	yes	—
10	C₂²×C₄	C₂²	1	1	yes	characteristic
11	C₂²⋊C₄	C₄	1	8	yes	direct product factor
12	C₄²	—	2	4	no	—
13	C₂³	—	2	2	no	—
14	C₂³	—	2	2	no	—
15	C₂³	C₂×C₄	1	4	yes	—
16	C₂³	C₂×C₄	1	2	yes	—
17	C₂³	C₂³	1	1	yes	characteristic
18	C₂×C₄	—	2	4	no	—
19	C₂×C₄	—	2	2	no	—
20	C₂×C₄	—	2	4	no	—
21	C₂×C₄	—	2	8	no	—
22	C₂×C₄	C₂×C₄	1	2	yes	—
23	C₂×C₄	C₂×C₄	1	2	yes	—
24	C₂×C₄	C₂×C₄	1	8	yes	complemented
25	C₂×C₄	D₄	1	4	yes	—
26	C₂²	—	2	2	no	—
27	C₂²	—	2	2	no	—
28	C₂²	—	2	8	no	—
29	C₂²	C₄²	1	4	yes	complemented
30	C₂²	C₂²×C₄	1	1	yes	characteristic
31	C₂²	C₂²×C₄	1	2	yes	—
32	C₂²	C₂×D₄	1	2	yes	—
33	C₂²	#41	1	2	yes	—
34	C₄	—	2	2	no	—
35	C₄	—	2	8	no	—
36	C₄	C₂²⋊C₄	1	4	yes	direct product factor
37	C₂	—	2	4	no	—
38	C₂	C₂×C₄²	1	1	yes	characteristic
39	C₂	C₂×C₂²⋊C₄	1	1	yes	characteristic
40	C₂	#117	1	1	yes	characteristic
41	C₂	C₄×D₄	1	4	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.