Subgroups — C₄×C₂²⋊A₄ #5946

Order 192.

262 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂²⋊A₄	C₂	1	1	yes	maximal, characteristic
2	C₂⁴×C₄	C₃	1	1	yes	maximal, characteristic, complemented, Sylow
3	C₂²⋊A₄	C₄	1	1	yes	characteristic, direct product factor
4	C₄×A₄	—	4	5	no	maximal
5	C₂⁵	C₂×C₃	1	1	yes	characteristic
6	C₂³×C₄	—	3	5	no	—
7	C₂³×C₄	—	3	5	no	—
8	C₂×A₄	—	4	5	no	—
9	C₂⁴	—	3	5	no	—
10	C₂⁴	—	3	5	no	—
11	C₂⁴	C₃×C₄	1	1	yes	characteristic, complemented
12	C₂²×C₄	—	3	30	no	—
13	C₂²×C₄	—	3	10	no	—
14	C₂²×C₄	—	3	5	no	—
15	C₂²×C₄	A₄	1	5	yes	complemented
16	A₄	—	4	5	no	—
17	C₃×C₄	—	16	1	no	—
18	C₂³	—	3	10	no	—
19	C₂³	—	3	30	no	—
20	C₂³	—	3	5	no	—
21	C₂³	—	3	5	no	—
22	C₂³	C₂×A₄	1	5	yes	—
23	C₂×C₄	—	3	30	no	—
24	C₂×C₄	—	3	5	no	—
25	C₂×C₄	—	3	5	no	—
26	C₂×C₃	—	16	1	no	—
27	C₂²	—	3	5	no	—
28	C₂²	—	3	30	no	—
29	C₂²	—	3	10	no	—
30	C₂²	—	3	5	no	—
31	C₂²	C₄×A₄	1	5	yes	complemented
32	C₄	—	3	5	no	—
33	C₄	C₂²⋊A₄	1	1	yes	characteristic, direct product factor
34	C₃	—	16	1	no	Sylow
35	C₂	—	3	5	no	—
36	C₂	—	3	5	no	—
37	C₂	C₂×C₂²⋊A₄	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.