Subgroups — C₂×#3676 #63514

Order 288.

198 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
2	C₂²×Dic₉	C₂	1	2	yes	maximal, complemented
3	#3676	C₂	1	4	yes	maximal, direct product factor
4	C₂×#217	—	3	1	no	maximal
5	C₂³×C₉	—	2	4	no	—
6	C₂³×C₉	C₄	1	4	yes	complemented
7	C₂³×C₉	C₂²	1	2	yes	—
8	C₂³×C₉	C₂²	1	1	yes	characteristic
9	C₂×Dic₉	—	2	4	no	—
10	C₂×Dic₉	C₂²	1	4	yes	complemented
11	C₂⁴×C₃	D₃	1	1	yes	characteristic
12	C₂²×Dic₃	—	3	2	no	—
13	#217	—	3	4	no	—
14	C₂²×C₉	—	2	8	no	—
15	C₂²×C₉	—	2	4	no	—
16	C₂²×C₉	C₂×C₄	1	2	yes	—
17	C₂²×C₉	C₂×C₄	1	4	yes	complemented
18	C₂²×C₉	D₄	1	4	yes	—
19	C₂²×C₉	C₂³	1	1	yes	characteristic
20	Dic₉	—	2	4	no	—
21	C₂×C₂²⋊C₄	—	9	1	no	Sylow
22	C₂³×C₃	—	2	4	no	—
23	C₂³×C₃	Dic₃	1	4	yes	—
24	C₂³×C₃	C₂×D₃	1	2	yes	—
25	C₂³×C₃	C₂×D₃	1	1	yes	characteristic
26	C₂×Dic₃	—	3	4	no	—
27	C₂×Dic₃	—	6	4	no	—
28	C₂×C₉	—	2	4	no	—
29	C₂×C₉	C₂²⋊C₄	1	4	yes	complemented
30	C₂×C₉	C₂²×C₄	1	1	yes	characteristic
31	C₂×C₉	C₂×D₄	1	2	yes	—
32	C₂⁴	D₉	1	1	yes	characteristic
33	C₂²×C₄	—	9	2	no	—
34	C₂²⋊C₄	—	9	4	no	—
35	C₂²×C₃	—	2	8	no	—
36	C₂²×C₃	—	2	4	no	—
37	C₂²×C₃	C₂×Dic₃	1	2	yes	—
38	C₂²×C₃	C₂×Dic₃	1	4	yes	—
39	C₂²×C₃	#67	1	4	yes	—
40	C₂²×C₃	C₂²×D₃	1	1	yes	characteristic
41	Dic₃	—	6	4	no	—
42	C₉	C₂×C₂²⋊C₄	1	1	yes	characteristic, complemented, Sylow
43	C₂³	—	2	4	no	—
44	C₂³	Dic₉	1	4	yes	complemented
45	C₂³	C₂×D₉	1	2	yes	—
46	C₂³	C₂×D₉	1	1	yes	characteristic
47	C₂×C₄	—	9	4	no	—
48	C₂×C₄	—	18	4	no	—
49	C₂×C₃	—	2	4	no	—
50	C₂×C₃	#217	1	4	yes	—
51	C₂×C₃	C₂²×Dic₃	1	1	yes	characteristic
52	C₂×C₃	C₂×#67	1	2	yes	—
53	C₂²	—	2	8	no	—
54	C₂²	—	2	4	no	—
55	C₂²	C₂×Dic₉	1	2	yes	—
56	C₂²	C₂×Dic₉	1	4	yes	complemented
57	C₂²	#611	1	4	yes	—
58	C₂²	C₂²×D₉	1	1	yes	characteristic
59	C₄	—	18	4	no	—
60	C₃	C₂×#217	1	1	yes	characteristic
61	C₂	—	2	4	no	—
62	C₂	#3676	1	4	yes	direct product factor
63	C₂	C₂²×Dic₉	1	1	yes	characteristic
64	C₂	C₂×#611	1	2	yes	—

	subgroup	G/H
center	C₂³	C₂×D₉
commutator	C₂×C₉	C₂²×C₄
Frattini	C₂²×C₃	C₂²×D₃
Fitting	C₂⁴×C₉	C₂
socle	C₂³×C₃	C₂×D₃
prime radical	C₂⁴×C₃	D₃
cosocle	C₂²×C₉	C₂³
hypercenter	C₂⁴	D₉
hypocenter	C₉	C₂×C₂²⋊C₄
LCS	G ▷ C₂×C₉ ▷ C₉
UCS	C₁ ◁ C₂³ ◁ C₂⁴

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
2. C₂²×Dic₉	C₂	semidirect
3. #3676	C₂	direct (N × H)
6. C₂³×C₉	C₄	semidirect
10. C₂×Dic₉	C₂²	semidirect
17. C₂²×C₉	C₂×C₄	semidirect
29. C₂×C₉	C₂²⋊C₄	semidirect
42. C₉	C₂×C₂²⋊C₄	semidirect
44. C₂³	Dic₉	semidirect
56. C₂²	C₂×Dic₉	semidirect
62. C₂	#3676	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂⁴×C₉	2
C₂²×Dic₉	2
#3676	2
C₂×#217	3

Subgroups — C2×#3676 #63514

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#3676 #63514