Subgroups — #63515

Order 288.

195 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁴×C₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#611	C₂	1	3	yes	maximal, complemented
3	#3676	C₂	1	3	yes	maximal, complemented
4	#953	—	3	1	no	maximal
5	C₂³×C₉	—	2	6	no	—
6	C₂³×C₉	C₂²	1	3	yes	—
7	C₂²×D₉	C₂²	1	1	yes	characteristic, complemented
8	#611	—	2	6	no	—
9	C₂×Dic₉	C₂²	1	3	yes	complemented
10	C₂⁴×C₃	D₃	1	1	yes	characteristic
11	C₂×#67	—	3	3	no	—
12	#217	—	3	3	no	—
13	C₂²×C₉	—	2	8	no	—
14	C₂²×C₉	—	2	6	no	—
15	C₂²×C₉	D₄	1	6	yes	complemented
16	C₂²×C₉	C₂³	1	1	yes	characteristic
17	C₂×D₉	—	2	3	no	—
18	Dic₉	—	2	3	no	—
19	#120	—	9	1	no	Sylow
20	C₂³×C₃	—	2	6	no	—
21	C₂³×C₃	C₂×D₃	1	3	yes	—
22	C₂²×D₃	—	3	1	no	—
23	#67	—	6	6	no	—
24	C₂×Dic₃	—	3	3	no	—
25	C₂×C₉	—	2	6	no	—
26	C₂×C₉	C₂×D₄	1	3	yes	—
27	D₉	—	4	1	no	—
28	C₂⁴	D₉	1	1	yes	characteristic, complemented
29	C₂×D₄	—	9	3	no	—
30	C₂²⋊C₄	—	9	3	no	—
31	C₂²×C₃	—	2	8	no	—
32	C₂²×C₃	—	2	6	no	—
33	C₂²×C₃	#67	1	6	yes	—
34	C₂²×C₃	C₂²×D₃	1	1	yes	characteristic
35	C₂×D₃	—	6	3	no	—
36	Dic₃	—	6	3	no	—
37	C₉	#120	1	1	yes	characteristic, complemented, Sylow
38	C₂³	—	2	6	no	—
39	C₂³	—	9	1	no	—
40	C₂³	C₂×D₉	1	3	yes	—
41	D₄	—	18	6	no	—
42	C₂×C₄	—	9	3	no	—
43	C₂×C₃	—	2	6	no	—
44	C₂×C₃	C₂×#67	1	3	yes	—
45	D₃	—	12	1	no	—
46	C₂²	—	2	8	no	—
47	C₂²	—	2	6	no	—
48	C₂²	—	18	3	no	—
49	C₂²	#611	1	6	yes	complemented
50	C₂²	C₂²×D₉	1	1	yes	characteristic
51	C₄	—	18	3	no	—
52	C₃	#953	1	1	yes	characteristic
53	C₂	—	2	6	no	—
54	C₂	—	36	1	no	—
55	C₂	C₂×#611	1	3	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.