Subgroups — C₄×#624 #63882

Order 288.

243 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×C₃⋊D₃	C₂	1	1	yes	maximal, characteristic
2	C₂×#624	C₂	1	2	yes	maximal
3	C₃×C₄×Dic₃	C₂	1	2	yes	maximal, complemented
4	Dic₃²	C₂	1	2	yes	maximal, complemented
5	C₄²×D₃	—	3	2	no	maximal
6	C₂²×C₃⋊D₃	C₂²	1	1	yes	characteristic
7	C₂×C₃²×C₄	C₂²	1	1	yes	characteristic
8	C₂×C₃⋊Dic₃	C₂²	1	1	yes	characteristic
9	C₄×C₃⋊D₃	C₄	1	4	yes	complemented
10	C₂×C₃×Dic₃	C₂²	1	4	yes	—
11	#624	C₄	1	8	yes	direct product factor
12	C₂×C₄×D₃	—	3	2	no	—
13	C₂×C₄×D₃	—	3	4	no	—
14	C₂×C₄×D₃	—	6	1	no	—
15	C₃×C₄²	—	3	2	no	—
16	C₄×Dic₃	—	3	4	no	—
17	C₄×Dic₃	D₃	1	2	yes	complemented
18	C₂²×C₃²	C₂³	1	1	yes	characteristic
19	C₂×C₃⋊D₃	C₂×C₄	1	4	yes	—
20	C₂×C₃⋊D₃	C₂×C₄	1	2	yes	—
21	C₃²×C₄	C₂×C₄	1	2	yes	complemented
22	C₃⋊Dic₃	C₂×C₄	1	2	yes	complemented
23	C₃×Dic₃	C₂×C₄	1	8	yes	complemented
24	C₂×C₄²	—	9	1	no	Sylow
25	C₂²×D₃	—	3	2	no	—
26	C₂²×D₃	—	6	1	no	—
27	C₂×C₃×C₄	—	2	1	no	—
28	C₂×C₃×C₄	—	3	4	no	—
29	C₂×C₃×C₄	C₂×D₃	1	2	yes	—
30	C₂×Dic₃	—	3	2	no	—
31	C₂×Dic₃	—	6	1	no	—
32	C₂×Dic₃	C₂×D₃	1	4	yes	—
33	C₄×D₃	—	3	8	no	—
34	C₄×D₃	—	3	16	no	—
35	C₄×D₃	—	6	4	no	—
36	C₂×C₃²	C₂²×C₄	1	2	yes	—
37	C₂×C₃²	C₂²×C₄	1	1	yes	characteristic
38	C₃⋊D₃	C₄²	1	4	yes	complemented
39	C₂²×C₄	—	9	2	no	—
40	C₂²×C₄	—	9	1	no	—
41	C₄²	—	3	2	no	—
42	C₄²	—	9	2	no	—
43	C₂²×C₃	—	2	1	no	—
44	C₂²×C₃	C₂²×D₃	1	2	yes	—
45	C₂×D₃	—	3	8	no	—
46	C₂×D₃	—	3	4	no	—
47	C₂×D₃	—	6	2	no	—
48	C₂×D₃	—	6	4	no	—
49	C₃×C₄	—	2	2	no	—
50	C₃×C₄	—	3	8	no	—
51	C₃×C₄	C₄×D₃	1	4	yes	complemented
52	Dic₃	—	3	4	no	—
53	Dic₃	—	6	2	no	—
54	Dic₃	C₄×D₃	1	8	yes	complemented
55	C₃²	C₂×C₄²	1	1	yes	characteristic, complemented, Sylow
56	C₂³	—	9	1	no	—
57	C₂×C₄	—	3	4	no	—
58	C₂×C₄	—	9	8	no	—
59	C₂×C₄	—	9	1	no	—
60	C₂×C₄	—	9	4	no	—
61	C₂×C₄	D₃²	1	1	yes	characteristic
62	C₂×C₃	—	2	2	no	—
63	C₂×C₃	—	2	1	no	—
64	C₂×C₃	C₂×C₄×D₃	1	4	yes	—
65	C₂×C₃	C₂×C₄×D₃	1	2	yes	—
66	D₃	—	3	8	no	—
67	D₃	—	6	4	no	—
68	C₂²	—	9	4	no	—
69	C₂²	—	9	2	no	—
70	C₂²	C₂×D₃²	1	1	yes	characteristic
71	C₄	—	3	8	no	—
72	C₄	—	9	2	no	—
73	C₄	#624	1	2	yes	direct product factor
74	C₃	—	2	1	no	—
75	C₃	C₄²×D₃	1	2	yes	complemented
76	C₂	—	9	4	no	—
77	C₂	C₄×D₃²	1	2	yes	—
78	C₂	C₂×#624	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₄	D₃²
commutator, hypocenter	C₃²	C₂×C₄²
Frattini	C₂²	C₂×D₃²
Fitting	C₂×C₃²×C₄	C₂²
socle, cosocle	C₂²×C₃²	C₂³
prime radical	C₂²×C₃⋊D₃	C₂²
LCS	G ▷ C₃²
UCS	C₁ ◁ C₂×C₄

Complements

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

N	H ≅ G/N	type
3. C₃×C₄×Dic₃	C₂	semidirect
4. Dic₃²	C₂	semidirect
9. C₄×C₃⋊D₃	C₄	semidirect
11. #624	C₄	direct (N × H)
17. C₄×Dic₃	D₃	semidirect
21. C₃²×C₄	C₂×C₄	semidirect
22. C₃⋊Dic₃	C₂×C₄	semidirect
23. C₃×Dic₃	C₂×C₄	semidirect
38. C₃⋊D₃	C₄²	semidirect
51. C₃×C₄	C₄×D₃	semidirect
54. Dic₃	C₄×D₃	semidirect
55. C₃²	C₂×C₄²	semidirect
73. C₄	#624	direct (N × H)
75. C₃	C₄²×D₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄×C₃⋊D₃	2
C₂×#624	2
C₃×C₄×Dic₃	2
Dic₃²	2
C₄²×D₃	3

Subgroups — C4×#624 #63882

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#624 #63882