Subgroups — #4178⋊C₄ #10619560

Order 648.

89 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#4178	C₂	1	1	yes	maximal, characteristic
2	#66332	C₂	1	1	yes	maximal, characteristic, complemented
3	#66326	C₂	1	1	yes	maximal, characteristic, complemented
4	#6199	—	3	1	no	maximal
5	D₃×Dic₉	—	3	1	no	maximal
6	C₂×#732	C₂²	1	1	yes	characteristic
7	#4178	C₄	1	2	yes	complemented
8	C₂×#272	D₃	1	1	yes	characteristic
9	C₂×D₃×C₉	—	3	1	no	—
10	C₃⋊Dic₉	D₃	1	1	yes	characteristic, complemented
11	(C₃⋊Dic₃)⋊C₃	—	3	1	no	—
12	(C₃⋊Dic₃)⋊C₃	—	3	1	no	—
13	(C₃⋊Dic₃)⋊C₃	—	6	1	no	—
14	C₃×Dic₉	—	3	1	no	—
15	#732	C₂×C₄	1	1	yes	characteristic, complemented, Sylow
16	D₃×Dic₃	—	9	1	no	—
17	D₃×Dic₃	—	9	1	no	—
18	C₂×Dic₉	—	9	1	no	—
19	C₂×H(3,𝔽₃)	—	2	1	no	—
20	C₂×H(3,𝔽₃)	C₂×D₃	1	1	yes	characteristic
21	C₂×C₃×C₉	C₂×D₃	1	1	yes	characteristic
22	#272	Dic₃	1	2	yes	complemented
23	D₃×C₉	—	3	2	no	—
24	C₂×C₃×D₃	—	3	1	no	—
25	C₂×C₃×D₃	—	18	1	no	—
26	C₃⋊Dic₃	—	3	1	no	—
27	C₃⋊Dic₃	—	3	1	no	—
28	C₃⋊Dic₃	—	6	1	no	—
29	C₃×Dic₃	—	9	1	no	—
30	C₃×Dic₃	—	9	1	no	—
31	C₂²×C₉	—	9	1	no	—
32	Dic₉	—	3	1	no	—
33	Dic₉	—	18	1	no	—
34	H(3,𝔽₃)	—	2	1	no	—
35	H(3,𝔽₃)	C₂×Dic₃	1	1	yes	characteristic
36	C₃×C₉	C₄×D₃	1	1	yes	characteristic, complemented
37	C₂×Dic₃	—	27	1	no	—
38	C₄×D₃	—	27	1	no	—
39	C₄×D₃	—	27	1	no	—
40	C₂×C₃²	—	6	1	no	—
41	C₂×C₃²	—	12	1	no	—
42	C₂×C₃²	D₃²	1	1	yes	characteristic
43	C₃×D₃	—	3	2	no	—
44	C₃×D₃	—	18	2	no	—
45	C₂×C₉	—	6	1	no	—
46	C₂×C₉	—	9	2	no	—
47	C₂²×C₃	—	9	1	no	—
48	C₂×D₃	—	3	1	no	—
49	C₂×D₃	—	18	1	no	—
50	C₃×C₄	—	27	1	no	—
51	C₃×C₄	—	27	1	no	—
52	Dic₃	—	9	1	no	—
53	Dic₃	—	9	1	no	—
54	Dic₃	—	27	1	no	—
55	Dic₃	—	54	1	no	—
56	Dic₃	—	54	1	no	—
57	C₃²	—	6	1	no	—
58	C₃²	—	12	1	no	—
59	C₃²	D₃×Dic₃	1	1	yes	characteristic
60	C₉	—	6	1	no	—
61	C₂×C₄	—	81	1	no	Sylow
62	C₂×C₃	—	6	1	no	—
63	C₂×C₃	—	9	2	no	—
64	C₂×C₃	—	18	1	no	—
65	C₂×C₃	—	36	1	no	—
66	C₂×C₃	((C₃⋊D₃)⋊C₃)⋊C₂	1	1	yes	characteristic
67	D₃	—	3	2	no	—
68	D₃	—	18	2	no	—
69	C₂²	—	9	1	no	—
70	C₄	—	27	1	no	—
71	C₄	—	27	1	no	—
72	C₃	—	6	1	no	—
73	C₃	—	18	1	no	—
74	C₃	—	36	1	no	—
75	C₃	((C₃⋊D₃)⋊C₃)⋊C₄	1	1	yes	characteristic
76	C₂	—	9	2	no	—
77	C₂	#4178⋊C₂	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂	#4178⋊C₂
commutator, hypocenter	#732	C₂×C₄
Frattini	C₂×C₃²	D₃²
Fitting, cosocle	C₂×#732	C₂²
socle	C₂×C₃	((C₃⋊D₃)⋊C₃)⋊C₂
prime radical	C₂×#4178	C₂
LCS	G ▷ #732
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
2. #66332	C₂	semidirect
3. #66326	C₂	semidirect
7. #4178	C₄	semidirect
10. C₃⋊Dic₉	D₃	semidirect
15. #732	C₂×C₄	semidirect
22. #272	Dic₃	semidirect
36. C₃×C₉	C₄×D₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×#4178	2
#66332	2
#66326	2
#6199	3
D₃×Dic₉	3

Subgroups — #4178⋊C4 #10619560

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #4178⋊C₄ #10619560