Subgroups — C₃×C₄×#14579731 #44535674

Order 31356.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#14579731	C₂	1	1	yes	maximal, characteristic
2	C₄×#14579731	C₃	1	3	yes	maximal, direct product factor
3	C₃×C₄×C₁₃×C₆₇	C₃	1	1	yes	maximal, characteristic, complemented
4	C₃×#14579731	C₄	1	1	yes	characteristic, direct product factor, Hall
5	C₂×#14579731	C₂×C₃	1	3	yes	—
6	C₂×C₃×C₁₃×C₆₇	C₂×C₃	1	1	yes	characteristic
7	C₄×C₁₃×C₆₇	C₃²	1	1	yes	characteristic, complemented, Hall
8	C₃×C₁₃×C₆₇	C₃×C₄	1	1	yes	characteristic, complemented
9	#14579731	C₃×C₄	1	3	yes	direct product factor
10	C₃×C₄×C₆₇⋊C₃	—	13	1	no	maximal, Hall
11	C₂×C₁₃×C₆₇	C₂×C₃²	1	1	yes	characteristic
12	C₂×C₃×C₆₇⋊C₃	—	13	1	no	—
13	C₁₃×C₆₇	C₃²×C₄	1	1	yes	characteristic, complemented, Hall
14	C₃×C₄×C₆₇	C₁₃⋊C₃	1	1	yes	characteristic, complemented
15	C₄×C₆₇⋊C₃	—	13	3	no	—
16	C₃×C₆₇⋊C₃	—	13	1	no	Hall
17	C₃×C₄×C₁₃⋊C₃	—	67	1	no	maximal, Hall
18	C₂×C₃×C₆₇	C₂×C₁₃⋊C₃	1	1	yes	characteristic
19	C₂×C₆₇⋊C₃	—	13	3	no	—
20	C₄×C₆₇	C₃×C₁₃⋊C₃	1	1	yes	characteristic, complemented, Hall
21	C₂×C₃×C₁₃⋊C₃	—	67	1	no	—
22	C₃×C₆₇	C₄×C₁₃⋊C₃	1	1	yes	characteristic, complemented
23	C₆₇⋊C₃	—	13	3	no	—
24	C₃×C₄×C₁₃	C₆₇⋊C₃	1	1	yes	characteristic, complemented
25	C₄×C₁₃⋊C₃	—	67	3	no	—
26	C₂×C₆₇	C₂×C₃×C₁₃⋊C₃	1	1	yes	characteristic
27	C₃×C₁₃⋊C₃	—	67	1	no	Hall
28	C₂×C₃×C₁₃	C₂×C₆₇⋊C₃	1	1	yes	characteristic
29	C₂×C₁₃⋊C₃	—	67	3	no	—
30	C₆₇	C₃×C₄×C₁₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
31	C₄×C₁₃	C₃×C₆₇⋊C₃	1	1	yes	characteristic, complemented, Hall
32	C₃×C₁₃	C₄×C₆₇⋊C₃	1	1	yes	characteristic, complemented
33	C₁₃⋊C₃	—	67	3	no	—
34	C₃²×C₄	—	871	1	no	Hall
35	C₂×C₁₃	C₂×C₃×C₆₇⋊C₃	1	1	yes	characteristic
36	C₂×C₃²	—	871	1	no	—
37	C₁₃	C₃×C₄×C₆₇⋊C₃	1	1	yes	characteristic, complemented, Sylow
38	C₃×C₄	—	871	3	no	—
39	C₃×C₄	#14579731	1	1	yes	characteristic, direct product factor
40	C₃²	—	871	1	no	Sylow
41	C₂×C₃	—	871	3	no	—
42	C₂×C₃	C₂×#14579731	1	1	yes	characteristic
43	C₄	C₃×#14579731	1	1	yes	characteristic, direct product factor, Sylow
44	C₃	—	871	3	no	—
45	C₃	C₄×#14579731	1	1	yes	characteristic, direct product factor
46	C₂	C₂×C₃×#14579731	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₃×C₄	#14579731
commutator, hypocenter	C₁₃×C₆₇	C₃²×C₄
Frattini	C₂	C₂×C₃×#14579731
Fitting	C₃×C₄×C₁₃×C₆₇	C₃
socle	C₂×C₃×C₁₃×C₆₇	C₂×C₃
prime radical	C₂×C₃×#14579731	C₂
cosocle	C₂×C₁₃×C₆₇	C₂×C₃²
LCS	G ▷ C₁₃×C₆₇
UCS	C₁ ◁ C₃×C₄

Complements

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

N	H ≅ G/N	type
2. C₄×#14579731	C₃	direct (N × H)
3. C₃×C₄×C₁₃×C₆₇	C₃	semidirect
4. C₃×#14579731	C₄	direct (N × H)
7. C₄×C₁₃×C₆₇	C₃²	semidirect
8. C₃×C₁₃×C₆₇	C₃×C₄	semidirect
9. #14579731	C₃×C₄	direct (N × H)
13. C₁₃×C₆₇	C₃²×C₄	semidirect
14. C₃×C₄×C₆₇	C₁₃⋊C₃	semidirect
20. C₄×C₆₇	C₃×C₁₃⋊C₃	semidirect
22. C₃×C₆₇	C₄×C₁₃⋊C₃	semidirect
24. C₃×C₄×C₁₃	C₆₇⋊C₃	semidirect
30. C₆₇	C₃×C₄×C₁₃⋊C₃	semidirect
31. C₄×C₁₃	C₃×C₆₇⋊C₃	semidirect
32. C₃×C₁₃	C₄×C₆₇⋊C₃	semidirect
37. C₁₃	C₃×C₄×C₆₇⋊C₃	semidirect
39. C₃×C₄	#14579731	direct (N × H)
43. C₄	C₃×#14579731	direct (N × H)
45. C₃	C₄×#14579731	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×#14579731	2
C₄×#14579731	3
C₃×C₄×C₁₃×C₆₇	3
C₃×C₄×C₆₇⋊C₃	13
C₃×C₄×C₁₃⋊C₃	67

Subgroups — C3×C4×#14579731 #44535674

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₄×#14579731 #44535674