Subgroups — C₂²×#3771 #10596489

Order 576.

125 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#622	C₂	1	1	yes	maximal, characteristic
2	C₂×#3771	C₂	1	6	yes	maximal, direct product factor
3	C₂²×C₃⋊Dic₃	C₄	1	1	yes	characteristic
4	C₂×#622	C₄	1	3	yes	—
5	C₂×#622	C₂²	1	3	yes	—
6	#3771	C₂²	1	4	yes	direct product factor
7	C₂³×C₃²	C₈	1	1	yes	characteristic
8	C₂×C₃⋊Dic₃	C₈	1	3	yes	—
9	C₂×C₃⋊Dic₃	C₂×C₄	1	3	yes	—
10	#622	C₂×C₄	1	3	yes	—
11	#622	C₂³	1	1	yes	characteristic
12	C₂²×C₁₆	—	9	1	no	maximal, Sylow
13	C₂²×Dic₃	—	12	1	no	—
14	C₂²×C₃²	C₁₆	1	4	yes	complemented
15	C₂²×C₃²	C₂×C₈	1	3	yes	—
16	C₃⋊Dic₃	C₂×C₈	1	3	yes	—
17	C₃⋊Dic₃	C₂²×C₄	1	1	yes	characteristic
18	C₂²×C₈	—	9	1	no	—
19	C₂×C₁₆	—	9	6	no	—
20	C₂³×C₃	—	4	1	no	—
21	C₂×Dic₃	—	12	3	no	—
22	C₂×Dic₃	—	12	3	no	—
23	C₂×C₃²	C₂×C₁₆	1	6	yes	complemented
24	C₂×C₃²	C₂²×C₈	1	1	yes	characteristic
25	C₂²×C₄	—	9	1	no	—
26	C₂×C₈	—	9	3	no	—
27	C₂×C₈	—	9	3	no	—
28	C₁₆	—	9	4	no	—
29	C₂²×C₃	—	4	3	no	—
30	C₂²×C₃	—	4	4	no	—
31	Dic₃	—	12	3	no	—
32	Dic₃	—	12	1	no	—
33	C₃²	C₂²×C₁₆	1	1	yes	characteristic, complemented, Sylow
34	C₂³	AGL(1,𝔽₉)	1	1	yes	characteristic
35	C₂×C₄	—	9	3	no	—
36	C₂×C₄	—	9	3	no	—
37	C₈	—	9	1	no	—
38	C₈	—	9	3	no	—
39	C₂×C₃	—	4	1	no	—
40	C₂×C₃	—	4	6	no	—
41	C₂²	#3771	1	4	yes	direct product factor
42	C₂²	C₂×AGL(1,𝔽₉)	1	3	yes	—
43	C₄	—	9	1	no	—
44	C₄	—	9	3	no	—
45	C₃	—	4	1	no	—
46	C₂	C₂×#3771	1	6	yes	direct product factor
47	C₂	C₂²×AGL(1,𝔽₉)	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.