Subgroups — C₄×#92404 #14519014

Order 1944.

2344 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#92404	C₂	1	1	yes	maximal, characteristic
2	C₄×H(5,𝔽₃)	C₂	1	1	yes	maximal, characteristic, complemented
3	#11758025	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄×C₃⋊#272	—	3	40	no	maximal
5	C₂×H(5,𝔽₃)	C₂²	1	1	yes	characteristic
6	#92404	C₄	1	2	yes	direct product factor
7	C₂×C₃⋊#272	—	3	40	no	—
8	C₃×C₄×H(3,𝔽₃)	D₃	1	40	yes	complemented
9	C₃⋊#1084	—	3	40	no	—
10	H(5,𝔽₃)	C₂×C₄	1	1	yes	characteristic, complemented, Sylow
11	C₃×C₄×C₃⋊D₃	—	9	40	no	—
12	C₄×#272	—	9	90	no	—
13	C₂×C₃×H(3,𝔽₃)	C₂×D₃	1	40	yes	—
14	C₃⋊#272	—	3	80	no	—
15	C₂×C₃×C₃⋊D₃	—	9	40	no	—
16	C₃³×C₄	C₃⋊D₃	1	40	yes	complemented
17	C₃×C₃⋊Dic₃	—	9	40	no	—
18	C₂×#272	—	9	90	no	—
19	C₄×H(3,𝔽₃)	C₃⋊D₃	1	90	yes	complemented
20	#1084	—	9	90	no	—
21	C₃×H(3,𝔽₃)	C₄×D₃	1	40	yes	complemented
22	C₄×C₃⋊D₃	—	9	40	no	—
23	C₃×C₄×D₃	—	27	40	no	—
24	C₂×C₃³	C₂×C₃⋊D₃	1	40	yes	—
25	C₃×C₃⋊D₃	—	9	80	no	—
26	C₂×H(3,𝔽₃)	C₂×C₃⋊D₃	1	90	yes	—
27	#272	—	9	180	no	—
28	C₂×C₃⋊D₃	—	9	40	no	—
29	C₂×C₃×D₃	—	27	40	no	—
30	C₃²×C₄	—	9	40	no	—
31	C₃²×C₄	C₃⋊(C₃⋊D₃)	1	40	yes	—
32	C₃⋊Dic₃	—	9	40	no	—
33	C₃×Dic₃	—	27	40	no	—
34	C₃³	C₄×C₃⋊D₃	1	40	yes	complemented
35	H(3,𝔽₃)	C₄×C₃⋊D₃	1	90	yes	complemented
36	C₂×C₃×C₄	—	81	1	no	—
37	C₄×D₃	—	27	40	no	—
38	C₂×C₃²	—	9	40	no	—
39	C₂×C₃²	C₂×C₃⋊(C₃⋊D₃)	1	40	yes	—
40	C₃⋊D₃	—	9	80	no	—
41	C₃×D₃	—	27	80	no	—
42	C₂²×C₃	—	81	1	no	—
43	C₂×D₃	—	27	40	no	—
44	C₃×C₄	—	3	40	no	—
45	C₃×C₄	—	81	1	no	—
46	C₃×C₄	C₃⋊(C₃⋊(C₃⋊D₃))	1	1	yes	characteristic
47	Dic₃	—	27	40	no	—
48	C₃²	—	9	40	no	—
49	C₃²	C₄×C₃⋊(C₃⋊D₃)	1	40	yes	—
50	C₂×C₄	—	81	1	no	Sylow
51	C₂×C₃	—	3	40	no	—
52	C₂×C₃	—	81	2	no	—
53	C₂×C₃	C₂×C₃⋊(C₃⋊(C₃⋊D₃))	1	1	yes	characteristic
54	D₃	—	27	80	no	—
55	C₂²	—	81	1	no	—
56	C₄	—	81	1	no	—
57	C₄	#92404	1	1	yes	characteristic, direct product factor
58	C₃	—	3	40	no	—
59	C₃	C₄×C₃⋊(C₃⋊(C₃⋊D₃))	1	1	yes	characteristic
60	C₂	—	81	2	no	—
61	C₂	C₂×#92404	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₃×C₄	C₃⋊(C₃⋊(C₃⋊D₃))
commutator, hypocenter	H(5,𝔽₃)	C₂×C₄
Frattini, socle	C₂×C₃	C₂×C₃⋊(C₃⋊(C₃⋊D₃))
Fitting	C₄×H(5,𝔽₃)	C₂
prime radical	C₂×#92404	C₂
cosocle	C₂×H(5,𝔽₃)	C₂²
LCS	G ▷ H(5,𝔽₃)
UCS	C₁ ◁ C₃×C₄

Complements

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

N	H ≅ G/N	type
2. C₄×H(5,𝔽₃)	C₂	semidirect
3. #11758025	C₂	semidirect
6. #92404	C₄	direct (N × H)
8. C₃×C₄×H(3,𝔽₃)	D₃	semidirect
10. H(5,𝔽₃)	C₂×C₄	semidirect
16. C₃³×C₄	C₃⋊D₃	semidirect
19. C₄×H(3,𝔽₃)	C₃⋊D₃	semidirect
21. C₃×H(3,𝔽₃)	C₄×D₃	semidirect
34. C₃³	C₄×C₃⋊D₃	semidirect
35. H(3,𝔽₃)	C₄×C₃⋊D₃	semidirect
57. C₄	#92404	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#92404	2
C₄×H(5,𝔽₃)	2
#11758025	2
C₄×C₃⋊#272	3

Subgroups — C4×#92404 #14519014

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#92404 #14519014