Subgroups — Dic₁₃⋊C₃×C₆₇⋊C₃ #44535643

Order 31356.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃⋊C₃×C₆₇⋊C₃	C₂	1	1	yes	maximal, characteristic
2	#23782978	C₃	1	1	yes	maximal, characteristic, complemented
3	#23782977	C₃	1	1	yes	maximal, characteristic, complemented
4	C₆₇×Dic₁₃⋊C₃	C₃	1	1	yes	maximal, characteristic, complemented
5	Dic₁₃×C₆₇⋊C₃	C₃	1	1	yes	maximal, characteristic, complemented
6	C₁₃⋊C₃×C₆₇⋊C₃	C₄	1	1	yes	characteristic, complemented, Hall
7	C₂×#14579731	C₂×C₃	1	1	yes	characteristic
8	C₂×#14579732	C₂×C₃	1	1	yes	characteristic
9	C₂×C₁₃⋊C₃×C₆₇	C₂×C₃	1	1	yes	characteristic
10	C₂×C₁₃×C₆₇⋊C₃	C₂×C₃	1	1	yes	characteristic
11	Dic₁₃×C₆₇	C₃²	1	1	yes	characteristic, complemented, Hall
12	#14579732	C₃×C₄	1	1	yes	characteristic, complemented
13	#14579731	C₃×C₄	1	1	yes	characteristic, complemented
14	C₁₃×C₆₇⋊C₃	C₃×C₄	1	1	yes	characteristic, complemented
15	C₁₃⋊C₃×C₆₇	C₃×C₄	1	1	yes	characteristic, complemented
16	C₃×C₄×C₆₇⋊C₃	—	13	1	no	maximal, Hall
17	C₂×C₁₃×C₆₇	C₂×C₃²	1	1	yes	characteristic
18	C₂×C₃×C₆₇⋊C₃	—	13	1	no	—
19	C₁₃×C₆₇	C₃²×C₄	1	1	yes	characteristic, complemented, Hall
20	C₃×C₄×C₆₇	—	13	1	no	—
21	C₄×C₆₇⋊C₃	—	13	1	no	—
22	C₄×C₆₇⋊C₃	—	13	1	no	—
23	C₄×C₆₇⋊C₃	—	13	1	no	—
24	C₃×C₆₇⋊C₃	—	13	1	no	Hall
25	C₃×Dic₁₃⋊C₃	—	67	1	no	maximal, Hall
26	C₂×C₃×C₆₇	—	13	1	no	—
27	C₂×C₆₇⋊C₃	—	13	1	no	—
28	C₂×C₆₇⋊C₃	—	13	1	no	—
29	C₂×C₆₇⋊C₃	D₁₃⋊C₃	1	1	yes	characteristic
30	C₄×C₆₇	—	13	1	no	Hall
31	C₂×C₃×C₁₃⋊C₃	—	67	1	no	—
32	C₃×C₆₇	—	13	1	no	—
33	C₆₇⋊C₃	—	13	1	no	—
34	C₆₇⋊C₃	—	13	1	no	—
35	C₆₇⋊C₃	Dic₁₃⋊C₃	1	1	yes	characteristic, direct product factor
36	C₃×Dic₁₃	—	67	1	no	—
37	Dic₁₃⋊C₃	—	67	1	no	—
38	Dic₁₃⋊C₃	—	67	1	no	—
39	Dic₁₃⋊C₃	C₆₇⋊C₃	1	1	yes	characteristic, direct product factor
40	C₂×C₆₇	C₃×D₁₃⋊C₃	1	1	yes	characteristic
41	C₃×C₁₃⋊C₃	—	67	1	no	Hall
42	C₂×C₃×C₁₃	—	67	1	no	—
43	C₂×C₁₃⋊C₃	—	67	1	no	—
44	C₂×C₁₃⋊C₃	—	67	1	no	—
45	C₂×C₁₃⋊C₃	C₂×C₆₇⋊C₃	1	1	yes	characteristic
46	C₆₇	C₃×Dic₁₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
47	Dic₁₃	C₃×C₆₇⋊C₃	1	1	yes	characteristic, complemented, Hall
48	C₃×C₁₃	—	67	1	no	—
49	C₁₃⋊C₃	—	67	1	no	—
50	C₁₃⋊C₃	—	67	1	no	—
51	C₁₃⋊C₃	C₄×C₆₇⋊C₃	1	1	yes	characteristic, complemented
52	C₃²×C₄	—	871	1	no	Hall
53	C₂×C₁₃	C₂×C₃×C₆₇⋊C₃	1	1	yes	characteristic
54	C₂×C₃²	—	871	1	no	—
55	C₁₃	C₃×C₄×C₆₇⋊C₃	1	1	yes	characteristic, complemented, Sylow
56	C₃×C₄	—	13	1	no	—
57	C₃×C₄	—	871	1	no	—
58	C₃×C₄	—	871	1	no	—
59	C₃×C₄	—	871	1	no	—
60	C₃²	—	871	1	no	Sylow
61	C₂×C₃	—	13	1	no	—
62	C₂×C₃	—	67	1	no	—
63	C₂×C₃	—	871	1	no	—
64	C₂×C₃	—	871	1	no	—
65	C₄	—	13	1	no	Sylow
66	C₃	—	13	1	no	—
67	C₃	—	67	1	no	—
68	C₃	—	871	1	no	—
69	C₃	—	871	1	no	—
70	C₂	D₁₃⋊C₃×C₆₇⋊C₃	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	D₁₃⋊C₃×C₆₇⋊C₃
commutator, hypocenter	C₁₃×C₆₇	C₃²×C₄
Fitting, socle, cosocle	C₂×C₁₃×C₆₇	C₂×C₃²
prime radical	C₂×C₁₃⋊C₃×C₆₇⋊C₃	C₂
LCS	G ▷ C₁₃×C₆₇
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
2. #23782978	C₃	semidirect
3. #23782977	C₃	semidirect
4. C₆₇×Dic₁₃⋊C₃	C₃	semidirect
5. Dic₁₃×C₆₇⋊C₃	C₃	semidirect
6. C₁₃⋊C₃×C₆₇⋊C₃	C₄	semidirect
11. Dic₁₃×C₆₇	C₃²	semidirect
12. #14579732	C₃×C₄	semidirect
13. #14579731	C₃×C₄	semidirect
14. C₁₃×C₆₇⋊C₃	C₃×C₄	semidirect
15. C₁₃⋊C₃×C₆₇	C₃×C₄	semidirect
19. C₁₃×C₆₇	C₃²×C₄	semidirect
35. C₆₇⋊C₃	Dic₁₃⋊C₃	direct (N × H)
39. Dic₁₃⋊C₃	C₆₇⋊C₃	direct (N × H)
46. C₆₇	C₃×Dic₁₃⋊C₃	semidirect
47. Dic₁₃	C₃×C₆₇⋊C₃	semidirect
51. C₁₃⋊C₃	C₄×C₆₇⋊C₃	semidirect
55. C₁₃	C₃×C₄×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×C₁₃⋊C₃×C₆₇⋊C₃	2
#23782978	3
#23782977	3
C₆₇×Dic₁₃⋊C₃	3
Dic₁₃×C₆₇⋊C₃	3
C₃×C₄×C₆₇⋊C₃	13
C₃×Dic₁₃⋊C₃	67

Subgroups — Dic13⋊C3×C67⋊C3 #44535643

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — Dic₁₃⋊C₃×C₆₇⋊C₃ #44535643