Subgroups — C₂×C₃⋊((C₇₃⋊C₃)⋊D₁₃) #46802953

Order 34164.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₁₃×C₇₃⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃⋊((C₇₃⋊C₃)⋊D₁₃)	C₂	1	2	yes	maximal, direct product factor
3	C₂×D₂₈₄₇	C₃	1	1	yes	maximal, characteristic, complemented
4	C₂×(C₇₃⋊C₃)⋊D₁₃	—	3	1	no	maximal
5	C₃×C₁₃×C₇₃⋊C₃	C₂²	1	1	yes	characteristic, complemented, Hall
6	(C₇₃⋊C₃)⋊D₁₃	—	3	2	no	—
7	D₂₈₄₇	C₂×C₃	1	2	yes	complemented
8	C₂×C₁₃×C₇₃⋊C₃	—	2	1	no	—
9	C₂×C₁₃×C₇₃⋊C₃	D₃	1	1	yes	characteristic, complemented
10	C₂×C₃×C₁₃×C₇₃	C₂×C₃	1	1	yes	characteristic, complemented
11	C₂×D₉₄₉	—	3	1	no	Hall
12	C₃×C₁₃×C₇₃	C₂²×C₃	1	1	yes	characteristic, complemented
13	C₁₃×C₇₃⋊C₃	—	2	1	no	—
14	C₁₃×C₇₃⋊C₃	C₂×D₃	1	1	yes	characteristic, complemented
15	C₂×C₃⋊(D₇₃⋊C₃)	—	13	1	no	maximal, Hall
16	C₂×C₁₃×C₇₃	C₃×D₃	1	1	yes	characteristic, complemented
17	D₉₄₉	—	3	2	no	—
18	C₂×C₃×C₇₃⋊C₃	D₁₃	1	1	yes	characteristic, complemented
19	C₃⋊(D₇₃⋊C₃)	—	13	2	no	—
20	C₁₃×C₇₃	C₂×C₃×D₃	1	1	yes	characteristic, complemented, Hall
21	C₂×D₂₁₉	—	13	1	no	—
22	C₂×D₇₃⋊C₃	—	39	1	no	—
23	C₃×C₇₃⋊C₃	C₂×D₁₃	1	1	yes	characteristic, complemented, Hall
24	C₂×C₃×D₃₉	—	73	1	no	maximal, Hall
25	C₂×C₃×C₇₃	C₃×D₁₃	1	1	yes	characteristic, complemented
26	D₂₁₉	—	13	2	no	—
27	C₂×C₇₃⋊C₃	—	2	1	no	—
28	C₂×C₇₃⋊C₃	D₃₉	1	1	yes	characteristic, complemented
29	D₇₃⋊C₃	—	39	2	no	—
30	C₂×D₇₃	—	39	1	no	Hall
31	C₂×C₃²×C₁₃	—	73	1	no	—
32	C₃×D₃₉	—	73	2	no	—
33	C₃×C₇₃	C₂×C₃×D₁₃	1	1	yes	characteristic, complemented
34	C₇₃⋊C₃	—	2	1	no	—
35	C₇₃⋊C₃	C₂×D₃₉	1	1	yes	characteristic, complemented
36	C₂×D₃₉	—	73	1	no	—
37	C₂×C₃×D₁₃	—	219	1	no	—
38	C₂×C₇₃	C₃×D₃₉	1	1	yes	characteristic, complemented
39	D₇₃	—	39	2	no	—
40	C₃²×C₁₃	—	73	1	no	Hall
41	C₂×C₃×C₁₃	—	73	1	no	—
42	C₂×C₃×C₁₃	—	146	1	no	—
43	C₂×C₃×C₁₃	D₇₃⋊C₃	1	1	yes	characteristic, complemented
44	D₃₉	—	73	2	no	—
45	C₃×D₁₃	—	219	2	no	—
46	C₇₃	C₂×C₃×D₃₉	1	1	yes	characteristic, complemented, Sylow
47	C₂×D₁₃	—	219	1	no	Hall
48	C₃×C₁₃	—	73	1	no	—
49	C₃×C₁₃	—	146	1	no	—
50	C₃×C₁₃	C₂×D₇₃⋊C₃	1	1	yes	characteristic, complemented
51	C₂×C₃×D₃	—	949	1	no	Hall
52	C₂×C₁₃	C₃⋊(D₇₃⋊C₃)	1	1	yes	characteristic, complemented
53	D₁₃	—	219	2	no	—
54	C₂×C₃²	—	73	1	no	—
55	C₃×D₃	—	949	2	no	—
56	C₁₃	C₂×C₃⋊(D₇₃⋊C₃)	1	1	yes	characteristic, complemented, Sylow
57	C₂²×C₃	—	2847	1	no	—
58	C₂×D₃	—	949	1	no	—
59	C₃²	—	73	1	no	Sylow
60	C₂×C₃	—	2847	2	no	—
61	C₂×C₃	—	73	1	no	—
62	C₂×C₃	—	146	1	no	—
63	C₂×C₃	(C₇₃⋊C₃)⋊D₁₃	1	1	yes	characteristic, complemented
64	D₃	—	949	2	no	—
65	C₂²	—	2847	1	no	Sylow
66	C₃	—	73	1	no	—
67	C₃	—	146	1	no	—
68	C₃	C₂×(C₇₃⋊C₃)⋊D₁₃	1	1	yes	characteristic, complemented
69	C₂	—	2847	2	no	—
70	C₂	C₃⋊((C₇₃⋊C₃)⋊D₁₃)	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	C₃⋊((C₇₃⋊C₃)⋊D₁₃)
commutator, cosocle, hypocenter	C₃×C₁₃×C₇₃	C₂²×C₃
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₁₃×C₇₃	C₂×C₃
LCS	G ▷ C₃×C₁₃×C₇₃
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×C₁₃×C₇₃⋊C₃	C₂	semidirect
2. C₃⋊((C₇₃⋊C₃)⋊D₁₃)	C₂	direct (N × H)
3. C₂×D₂₈₄₇	C₃	semidirect
5. C₃×C₁₃×C₇₃⋊C₃	C₂²	semidirect
7. D₂₈₄₇	C₂×C₃	semidirect
9. C₂×C₁₃×C₇₃⋊C₃	D₃	semidirect
10. C₂×C₃×C₁₃×C₇₃	C₂×C₃	semidirect
12. C₃×C₁₃×C₇₃	C₂²×C₃	semidirect
14. C₁₃×C₇₃⋊C₃	C₂×D₃	semidirect
16. C₂×C₁₃×C₇₃	C₃×D₃	semidirect
18. C₂×C₃×C₇₃⋊C₃	D₁₃	semidirect
20. C₁₃×C₇₃	C₂×C₃×D₃	semidirect
23. C₃×C₇₃⋊C₃	C₂×D₁₃	semidirect
25. C₂×C₃×C₇₃	C₃×D₁₃	semidirect
28. C₂×C₇₃⋊C₃	D₃₉	semidirect
33. C₃×C₇₃	C₂×C₃×D₁₃	semidirect
35. C₇₃⋊C₃	C₂×D₃₉	semidirect
38. C₂×C₇₃	C₃×D₃₉	semidirect
43. C₂×C₃×C₁₃	D₇₃⋊C₃	semidirect
46. C₇₃	C₂×C₃×D₃₉	semidirect
50. C₃×C₁₃	C₂×D₇₃⋊C₃	semidirect
52. C₂×C₁₃	C₃⋊(D₇₃⋊C₃)	semidirect
56. C₁₃	C₂×C₃⋊(D₇₃⋊C₃)	semidirect
63. C₂×C₃	(C₇₃⋊C₃)⋊D₁₃	semidirect
68. C₃	C₂×(C₇₃⋊C₃)⋊D₁₃	semidirect
70. C₂	C₃⋊((C₇₃⋊C₃)⋊D₁₃)	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×C₃×C₁₃×C₇₃⋊C₃	2
C₃⋊((C₇₃⋊C₃)⋊D₁₃)	2
C₂×D₂₈₄₇	3
C₂×(C₇₃⋊C₃)⋊D₁₃	3
C₂×C₃⋊(D₇₃⋊C₃)	13
C₂×C₃×D₃₉	73

Subgroups — C2×C3⋊((C73⋊C3)⋊D13) #46802953

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃⋊((C₇₃⋊C₃)⋊D₁₃) #46802953