Subgroups — C₃⋊#23782973 #44535668

Order 31356.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#14579732	C₂	1	1	yes	maximal, characteristic
2	#23782973	—	3	1	no	maximal
3	C₁₃×Dic₂₀₁	C₃	1	1	yes	maximal, characteristic, complemented
4	C₃×#14579732	C₄	1	1	yes	characteristic, complemented, Hall
5	C₂×#14579732	—	2	1	no	—
6	C₂×#14579732	D₃	1	1	yes	characteristic
7	C₂×C₃×C₁₃×C₆₇	C₂×C₃	1	1	yes	characteristic
8	C₁₃×Dic₆₇	—	3	1	no	Hall
9	C₃×C₁₃×C₆₇	C₃×C₄	1	1	yes	characteristic, complemented
10	#14579732	—	2	1	no	—
11	#14579732	Dic₃	1	1	yes	characteristic, complemented
12	C₃⋊((C₆₇⋊C₃)⋊C₄)	—	13	1	no	maximal, Hall
13	C₂×C₁₃×C₆₇	C₃×D₃	1	1	yes	characteristic
14	C₂×C₃×C₆₇⋊C₃	—	13	1	no	—
15	C₁₃×C₆₇	C₃×Dic₃	1	1	yes	characteristic, complemented, Hall
16	Dic₂₀₁	C₁₃⋊C₃	1	1	yes	characteristic, complemented
17	(C₆₇⋊C₃)⋊C₄	—	39	1	no	—
18	C₃×C₆₇⋊C₃	—	13	1	no	Hall
19	Dic₃×C₁₃⋊C₃	—	67	1	no	maximal, Hall
20	C₂×C₃×C₆₇	C₂×C₁₃⋊C₃	1	1	yes	characteristic
21	C₂×C₆₇⋊C₃	—	13	1	no	—
22	C₂×C₆₇⋊C₃	—	26	1	no	—
23	Dic₆₇	—	3	1	no	Hall
24	C₂×C₃×C₁₃⋊C₃	—	67	1	no	—
25	C₃×C₆₇	C₄×C₁₃⋊C₃	1	1	yes	characteristic, complemented
26	C₆₇⋊C₃	—	13	1	no	—
27	C₆₇⋊C₃	—	26	1	no	—
28	Dic₃×C₁₃	—	67	1	no	—
29	C₄×C₁₃⋊C₃	—	201	1	no	—
30	C₂×C₆₇	D₃×C₁₃⋊C₃	1	1	yes	characteristic
31	C₃×C₁₃⋊C₃	—	67	1	no	Hall
32	C₂×C₃×C₁₃	D₆₇⋊C₃	1	1	yes	characteristic
33	C₂×C₁₃⋊C₃	—	67	1	no	—
34	C₂×C₁₃⋊C₃	—	134	1	no	—
35	C₆₇	Dic₃×C₁₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
36	C₄×C₁₃	—	201	1	no	Hall
37	C₃×C₁₃	(C₆₇⋊C₃)⋊C₄	1	1	yes	characteristic, complemented
38	C₁₃⋊C₃	—	67	1	no	—
39	C₁₃⋊C₃	—	134	1	no	—
40	C₃×Dic₃	—	871	1	no	Hall
41	C₂×C₁₃	C₃⋊(D₆₇⋊C₃)	1	1	yes	characteristic
42	C₂×C₃²	—	871	1	no	—
43	C₁₃	C₃⋊((C₆₇⋊C₃)⋊C₄)	1	1	yes	characteristic, complemented, Sylow
44	C₃×C₄	—	2613	1	no	—
45	Dic₃	—	67	1	no	—
46	C₃²	—	871	1	no	Sylow
47	C₂×C₃	—	871	1	no	—
48	C₂×C₃	—	1742	1	no	—
49	C₂×C₃	#19104943	1	1	yes	characteristic
50	C₄	—	201	1	no	Sylow
51	C₃	—	871	1	no	—
52	C₃	—	1742	1	no	—
53	C₃	#23782973	1	1	yes	characteristic, complemented
54	C₂	C₃⋊#19104943	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	C₃⋊#19104943
commutator, hypocenter	C₃×C₁₃×C₆₇	C₃×C₄
Fitting, socle, cosocle	C₂×C₃×C₁₃×C₆₇	C₂×C₃
prime radical	C₂×C₃×#14579732	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. C₁₃×Dic₂₀₁	C₃	semidirect
4. C₃×#14579732	C₄	semidirect
9. C₃×C₁₃×C₆₇	C₃×C₄	semidirect
11. #14579732	Dic₃	semidirect
15. C₁₃×C₆₇	C₃×Dic₃	semidirect
16. Dic₂₀₁	C₁₃⋊C₃	semidirect
25. C₃×C₆₇	C₄×C₁₃⋊C₃	semidirect
35. C₆₇	Dic₃×C₁₃⋊C₃	semidirect
37. C₃×C₁₃	(C₆₇⋊C₃)⋊C₄	semidirect
43. C₁₃	C₃⋊((C₆₇⋊C₃)⋊C₄)	semidirect
53. C₃	#23782973	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃×#14579732	2
#23782973	3
C₁₃×Dic₂₀₁	3
C₃⋊((C₆₇⋊C₃)⋊C₄)	13
Dic₃×C₁₃⋊C₃	67

Subgroups — C3⋊#23782973 #44535668

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃⋊#23782973 #44535668