Subgroups — C₃²×C₂²⋊C₄ #3759

Order 144.

102 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₃²	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃²×C₄	C₂	1	2	yes	maximal, complemented
3	C₃×C₂²⋊C₄	C₃	1	4	yes	maximal, direct product factor
4	C₂²×C₃²	—	2	2	no	—
5	C₂²×C₃²	C₄	1	2	yes	complemented
6	C₂²×C₃²	C₂²	1	1	yes	characteristic
7	C₃²×C₄	—	2	2	no	—
8	C₂³×C₃	C₂×C₃	1	4	yes	—
9	C₂×C₃×C₄	C₂×C₃	1	8	yes	complemented
10	C₂×C₃²	—	2	2	no	—
11	C₂×C₃²	C₂×C₄	1	1	yes	characteristic
12	C₂×C₃²	D₄	1	2	yes	—
13	C₂²⋊C₄	C₃²	1	1	yes	characteristic, direct product factor, Sylow
14	C₂²×C₃	—	2	8	no	—
15	C₂²×C₃	C₃×C₄	1	8	yes	complemented
16	C₂²×C₃	C₂²×C₃	1	4	yes	—
17	C₃×C₄	—	2	8	no	—
18	C₃²	C₂²⋊C₄	1	1	yes	characteristic, direct product factor, Sylow
19	C₂³	C₂×C₃²	1	1	yes	characteristic
20	C₂×C₄	C₂×C₃²	1	2	yes	complemented
21	C₂×C₃	—	2	8	no	—
22	C₂×C₃	C₂×C₃×C₄	1	4	yes	—
23	C₂×C₃	C₃×D₄	1	8	yes	—
24	C₂²	—	2	2	no	—
25	C₂²	C₃²×C₄	1	2	yes	complemented
26	C₂²	C₂²×C₃²	1	1	yes	characteristic
27	C₄	—	2	2	no	—
28	C₃	C₃×C₂²⋊C₄	1	4	yes	direct product factor
29	C₂	—	2	2	no	—
30	C₂	C₂×C₃²×C₄	1	1	yes	characteristic
31	C₂	C₃²×D₄	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.