Subgroups — C₂²×#733⋊C₄ #13047481

Order 1296.

351 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×#733	C₂	1	1	yes	maximal, characteristic
2	C₂×#733⋊C₄	C₂	1	6	yes	maximal, direct product factor
3	C₂²×3₋¹⁺²⋊C₄	—	3	3	no	maximal
4	C₂²×C₃×Dic₉	—	3	1	no	maximal
5	C₂²×#733	C₄	1	4	yes	complemented
6	C₂²×#733	C₂²	1	3	yes	—
7	#733⋊C₄	C₂²	1	4	yes	direct product factor
8	C₂³×3₋¹⁺²	D₃	1	3	yes	—
9	C₂³×C₃×C₉	D₃	1	1	yes	characteristic
10	C₂×3₋¹⁺²⋊C₄	—	3	18	no	—
11	C₂×C₃×Dic₉	—	3	6	no	—
12	C₂×#733	C₂×C₄	1	6	yes	complemented
13	C₂×#733	C₂³	1	1	yes	characteristic
14	C₂²×C₃×Dic₃	—	9	1	no	—
15	C₂²×Dic₉	—	3	1	no	—
16	C₂²×Dic₉	—	3	3	no	—
17	C₂²×3₋¹⁺²	Dic₃	1	12	yes	—
18	C₂²×3₋¹⁺²	C₂×D₃	1	9	yes	—
19	C₂²×C₃×C₉	Dic₃	1	4	yes	—
20	C₂²×C₃×C₉	C₂×D₃	1	3	yes	—
21	3₋¹⁺²⋊C₄	—	3	12	no	—
22	C₃×Dic₉	—	3	4	no	—
23	#733	C₂²×C₄	1	1	yes	characteristic, complemented, Sylow
24	C₂³×C₃²	C₃⋊D₃	1	1	yes	characteristic
25	C₂×C₃×Dic₃	—	9	6	no	—
26	C₂³×C₉	—	3	1	no	—
27	C₂³×C₉	—	3	3	no	—
28	C₂×Dic₉	—	3	6	no	—
29	C₂×Dic₉	—	3	18	no	—
30	C₂×3₋¹⁺²	C₂×Dic₃	1	18	yes	—
31	C₂×3₋¹⁺²	C₂²×D₃	1	3	yes	—
32	C₂×C₃×C₉	C₂×Dic₃	1	6	yes	—
33	C₂×C₃×C₉	C₂²×D₃	1	1	yes	characteristic
34	C₂²×C₃×C₄	—	27	1	no	—
35	C₂²×Dic₃	—	9	1	no	—
36	C₂²×C₃²	C₃⋊Dic₃	1	4	yes	—
37	C₂²×C₃²	C₂×C₃⋊D₃	1	3	yes	—
38	C₃×Dic₃	—	9	4	no	—
39	C₂²×C₉	—	3	4	no	—
40	C₂²×C₉	—	3	12	no	—
41	C₂²×C₉	—	3	3	no	—
42	C₂²×C₉	—	3	9	no	—
43	Dic₉	—	3	4	no	—
44	Dic₉	—	3	12	no	—
45	3₋¹⁺²	C₂²×Dic₃	1	3	yes	—
46	C₃×C₉	C₂²×Dic₃	1	1	yes	characteristic
47	C₂³×C₃	—	3	1	no	—
48	C₂³×C₃	#272	1	1	yes	characteristic
49	C₂×C₃×C₄	—	27	6	no	—
50	C₂×Dic₃	—	9	6	no	—
51	C₂×C₃²	C₂×C₃⋊Dic₃	1	6	yes	—
52	C₂×C₃²	C₂²×C₃⋊D₃	1	1	yes	characteristic
53	C₂×C₉	—	3	6	no	—
54	C₂×C₉	—	3	18	no	—
55	C₂×C₉	—	3	1	no	—
56	C₂×C₉	—	3	3	no	—
57	C₂²×C₄	—	27	1	no	Sylow
58	C₂²×C₃	—	3	4	no	—
59	C₂²×C₃	—	3	3	no	—
60	C₂²×C₃	#1084	1	4	yes	—
61	C₂²×C₃	C₂×#272	1	3	yes	—
62	C₃×C₄	—	27	4	no	—
63	Dic₃	—	9	4	no	—
64	C₃²	C₂²×C₃⋊Dic₃	1	1	yes	characteristic
65	C₉	—	3	1	no	—
66	C₉	—	3	3	no	—
67	C₂³	#733⋊C₂	1	1	yes	characteristic
68	C₂×C₄	—	27	6	no	—
69	C₂×C₃	—	3	6	no	—
70	C₂×C₃	—	3	1	no	—
71	C₂×C₃	C₂×#1084	1	6	yes	—
72	C₂×C₃	C₂²×#272	1	1	yes	characteristic
73	C₂²	#733⋊C₄	1	4	yes	direct product factor
74	C₂²	C₂×#733⋊C₂	1	3	yes	—
75	C₄	—	27	4	no	—
76	C₃	—	3	1	no	—
77	C₃	C₂²×#1084	1	1	yes	characteristic
78	C₂	C₂×#733⋊C₄	1	6	yes	direct product factor
79	C₂	C₂²×#733⋊C₂	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂³	#733⋊C₂
commutator, hypocenter	#733	C₂²×C₄
Frattini	C₂×C₃²	C₂²×C₃⋊D₃
Fitting	C₂³×#733	C₂
socle	C₂³×C₃	#272
prime radical	C₂³×C₃²	C₃⋊D₃
cosocle	C₂×#733	C₂³
LCS	G ▷ #733
UCS	C₁ ◁ C₂³

Complements

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

N	H ≅ G/N	type
2. C₂×#733⋊C₄	C₂	direct (N × H)
5. C₂²×#733	C₄	semidirect
7. #733⋊C₄	C₂²	direct (N × H)
12. C₂×#733	C₂×C₄	semidirect
23. #733	C₂²×C₄	semidirect
73. C₂²	#733⋊C₄	direct (N × H)
78. C₂	C₂×#733⋊C₄	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×#733	2
C₂×#733⋊C₄	2
C₂²×3₋¹⁺²⋊C₄	3
C₂²×C₃×Dic₉	3

Subgroups — C22×#733⋊C4 #13047481

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×#733⋊C₄ #13047481