Subgroups — (C₂×D₉)⋊C₄ #3671

Order 144.

51 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×D₉	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×C₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×Dic₉	C₂	1	1	yes	maximal, characteristic, complemented
4	(C₂×D₃)⋊C₄	—	3	1	no	maximal
5	C₂²×C₉	C₂²	1	1	yes	characteristic
6	C₂×D₉	—	2	1	no	—
7	C₂×D₉	—	2	1	no	—
8	C₂×D₉	C₄	1	2	yes	complemented
9	C₄×C₉	—	2	1	no	—
10	Dic₉	—	2	1	no	—
11	C₂²×D₃	—	3	1	no	—
12	C₂×C₃×C₄	D₃	1	1	yes	characteristic
13	C₂×Dic₃	—	3	1	no	—
14	C₂×C₉	C₂×C₄	1	1	yes	characteristic
15	C₂×C₉	D₄	1	1	yes	characteristic
16	C₂×C₉	D₄	1	1	yes	characteristic
17	D₉	—	2	2	no	—
18	C₂²⋊C₄	—	9	1	no	Sylow
19	C₂²×C₃	C₂×D₃	1	1	yes	characteristic
20	C₂×D₃	—	3	2	no	—
21	C₂×D₃	—	6	1	no	—
22	C₂×D₃	—	6	1	no	—
23	C₃×C₄	—	2	1	no	—
24	Dic₃	—	6	1	no	—
25	C₉	C₂²⋊C₄	1	1	yes	characteristic, complemented, Sylow
26	C₂³	—	9	1	no	—
27	C₂×C₄	—	9	1	no	—
28	C₂×C₄	D₉	1	1	yes	characteristic, complemented
29	C₂×C₃	C₄×D₃	1	1	yes	characteristic
30	C₂×C₃	D₁₂	1	1	yes	characteristic
31	C₂×C₃	#67	1	1	yes	characteristic
32	D₃	—	6	2	no	—
33	C₂²	—	9	2	no	—
34	C₂²	—	18	1	no	—
35	C₂²	—	18	1	no	—
36	C₂²	C₂×D₉	1	1	yes	characteristic
37	C₄	—	2	1	no	—
38	C₄	—	18	1	no	—
39	C₃	(C₂×D₃)⋊C₄	1	1	yes	characteristic
40	C₂	—	18	2	no	—
41	C₂	C₄×D₉	1	1	yes	characteristic
42	C₂	D₃₆	1	1	yes	characteristic
43	C₂	#611	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.