Subgroups — Dic₃₉×C₆₇⋊C₃ #44535673

Order 31356.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₁₃×C₆₇⋊C₃	C₂	1	1	yes	maximal, characteristic
2	Dic₁₃×C₆₇⋊C₃	—	3	1	no	maximal
3	C₆₇×Dic₃₉	C₃	1	1	yes	maximal, characteristic, complemented
4	C₃×C₁₃×C₆₇⋊C₃	C₄	1	1	yes	characteristic, complemented, Hall
5	C₂×C₁₃×C₆₇⋊C₃	—	2	1	no	—
6	C₂×C₁₃×C₆₇⋊C₃	D₃	1	1	yes	characteristic
7	C₂×C₃×C₁₃×C₆₇	C₂×C₃	1	1	yes	characteristic
8	Dic₁₃×C₆₇	—	3	1	no	Hall
9	C₃×C₁₃×C₆₇	C₃×C₄	1	1	yes	characteristic, complemented
10	C₁₃×C₆₇⋊C₃	—	2	1	no	—
11	C₁₃×C₆₇⋊C₃	Dic₃	1	1	yes	characteristic, complemented
12	Dic₃×C₆₇⋊C₃	—	13	1	no	maximal, Hall
13	C₂×C₁₃×C₆₇	C₃×D₃	1	1	yes	characteristic
14	C₂×C₃×C₆₇⋊C₃	D₁₃	1	1	yes	characteristic
15	C₁₃×C₆₇	C₃×Dic₃	1	1	yes	characteristic, complemented, Hall
16	Dic₃×C₆₇	—	13	1	no	—
17	C₄×C₆₇⋊C₃	—	39	1	no	—
18	C₃×C₆₇⋊C₃	Dic₁₃	1	1	yes	characteristic, complemented, Hall
19	C₃×Dic₃₉	—	67	1	no	maximal, Hall
20	C₂×C₃×C₆₇	C₃×D₁₃	1	1	yes	characteristic
21	C₂×C₆₇⋊C₃	—	2	1	no	—
22	C₂×C₆₇⋊C₃	D₃₉	1	1	yes	characteristic
23	C₄×C₆₇	—	39	1	no	Hall
24	C₂×C₃²×C₁₃	—	67	1	no	—
25	C₃×C₆₇	C₃×Dic₁₃	1	1	yes	characteristic, complemented
26	C₆₇⋊C₃	—	2	1	no	—
27	C₆₇⋊C₃	Dic₃₉	1	1	yes	characteristic, direct product factor
28	Dic₃₉	C₆₇⋊C₃	1	1	yes	characteristic, direct product factor
29	C₃×Dic₁₃	—	201	1	no	—
30	C₂×C₆₇	C₃×D₃₉	1	1	yes	characteristic
31	C₃²×C₁₃	—	67	1	no	Hall
32	C₂×C₃×C₁₃	—	67	1	no	—
33	C₂×C₃×C₁₃	—	134	1	no	—
34	C₂×C₃×C₁₃	C₂×C₆₇⋊C₃	1	1	yes	characteristic
35	C₆₇	C₃×Dic₃₉	1	1	yes	characteristic, complemented, Sylow
36	Dic₁₃	—	3	1	no	Hall
37	C₃×C₁₃	—	67	1	no	—
38	C₃×C₁₃	—	134	1	no	—
39	C₃×C₁₃	C₄×C₆₇⋊C₃	1	1	yes	characteristic, complemented
40	C₃×Dic₃	—	871	1	no	Hall
41	C₂×C₁₃	D₃×C₆₇⋊C₃	1	1	yes	characteristic
42	C₂×C₃²	—	67	1	no	—
43	C₁₃	Dic₃×C₆₇⋊C₃	1	1	yes	characteristic, complemented, Sylow
44	C₃×C₄	—	2613	1	no	—
45	Dic₃	—	13	1	no	—
46	C₃²	—	67	1	no	Sylow
47	C₂×C₃	—	67	1	no	—
48	C₂×C₃	—	134	1	no	—
49	C₂×C₃	D₁₃×C₆₇⋊C₃	1	1	yes	characteristic
50	C₄	—	39	1	no	Sylow
51	C₃	—	67	1	no	—
52	C₃	—	134	1	no	—
53	C₃	Dic₁₃×C₆₇⋊C₃	1	1	yes	characteristic, complemented
54	C₂	D₃₉×C₆₇⋊C₃	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	D₃₉×C₆₇⋊C₃
commutator, hypocenter	C₃×C₁₃×C₆₇	C₃×C₄
Fitting, socle, cosocle	C₂×C₃×C₁₃×C₆₇	C₂×C₃
prime radical	C₂×C₃×C₁₃×C₆₇⋊C₃	C₂
LCS	G ▷ C₃×C₁₃×C₆₇
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
3. C₆₇×Dic₃₉	C₃	semidirect
4. C₃×C₁₃×C₆₇⋊C₃	C₄	semidirect
9. C₃×C₁₃×C₆₇	C₃×C₄	semidirect
11. C₁₃×C₆₇⋊C₃	Dic₃	semidirect
15. C₁₃×C₆₇	C₃×Dic₃	semidirect
18. C₃×C₆₇⋊C₃	Dic₁₃	semidirect
25. C₃×C₆₇	C₃×Dic₁₃	semidirect
27. C₆₇⋊C₃	Dic₃₉	direct (N × H)
28. Dic₃₉	C₆₇⋊C₃	direct (N × H)
35. C₆₇	C₃×Dic₃₉	semidirect
39. C₃×C₁₃	C₄×C₆₇⋊C₃	semidirect
43. C₁₃	Dic₃×C₆₇⋊C₃	semidirect
53. C₃	Dic₁₃×C₆₇⋊C₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃×C₁₃×C₆₇⋊C₃	2
Dic₁₃×C₆₇⋊C₃	3
C₆₇×Dic₃₉	3
Dic₃×C₆₇⋊C₃	13
C₃×Dic₃₉	67

Subgroups — Dic39×C67⋊C3 #44535673

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — Dic₃₉×C₆₇⋊C₃ #44535673