Subgroups — C₃×C₂²⋊#14274263 #37525656

Order 22932.

280 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²⋊#14274263	C₃	1	3	yes	maximal, direct product factor
2	C₂²×C₃×C₇²×C₁₃	C₃	1	1	yes	maximal, characteristic, complemented
3	C₃×#14274263	—	4	1	no	maximal, Hall
4	C₂×C₃×C₇²×C₁₃	—	3	1	no	—
5	C₃×C₂²⋊#63270	—	7	8	no	maximal
6	C₂²×C₇²×C₁₃	C₃²	1	1	yes	characteristic, complemented, Hall
7	C₃×C₇²×C₁₃	A₄	1	1	yes	characteristic, complemented
8	#14274263	—	4	3	no	—
9	C₃×C₂²⋊#3861	—	13	1	no	maximal, Hall
10	C₂×C₇²×C₁₃	—	3	1	no	—
11	C₂²×C₃×C₇×C₁₃	ΓL(1,𝔽₈)	1	8	yes	complemented
12	C₂²⋊#63270	—	7	24	no	—
13	C₃×#63270	—	28	8	no	—
14	C₇²×C₁₃	C₃×A₄	1	1	yes	characteristic, complemented, Hall
15	C₂²×C₃×C₇²	C₁₃⋊C₃	1	1	yes	characteristic, complemented
16	C₂²⋊#3861	—	13	3	no	—
17	C₂×C₃×C₇×C₁₃	—	3	8	no	—
18	C₃×C₂²⋊(C₁₃⋊C₃)	—	49	1	no	Hall
19	C₃×#3861	—	52	1	no	Hall
20	C₂²×C₇×C₁₃	C₃×ΓL(1,𝔽₈)	1	8	yes	complemented
21	C₂×C₃×C₇²	—	3	1	no	—
22	C₃×C₇×C₁₃	C₂²⋊ΓL(1,𝔽₈)	1	8	yes	complemented
23	#63270	—	28	24	no	—
24	C₃×C₂²⋊ΓL(1,𝔽₈)	—	91	8	no	—
25	C₂²×C₇²	C₃×C₁₃⋊C₃	1	1	yes	characteristic, complemented, Hall
26	C₂×C₇×C₁₃	—	3	8	no	—
27	C₂²×C₃×C₁₃	#3861	1	1	yes	characteristic, complemented
28	C₂²⋊(C₁₃⋊C₃)	—	49	3	no	—
29	C₃×C₇²	C₂²⋊(C₁₃⋊C₃)	1	1	yes	characteristic, complemented
30	#3861	—	52	3	no	—
31	C₃×C₁₃⋊C₃	—	196	1	no	Hall
32	C₂×C₇²	—	3	1	no	—
33	C₇×C₁₃	C₃×C₂²⋊ΓL(1,𝔽₈)	1	8	yes	complemented
34	C₂²×C₃×C₇	#63270	1	8	yes	complemented
35	C₂²⋊ΓL(1,𝔽₈)	—	91	24	no	—
36	C₂×C₃×C₁₃	—	3	1	no	—
37	C₃×ΓL(1,𝔽₈)	—	364	8	no	—
38	C₂²×C₁₃	C₃×#3861	1	1	yes	characteristic, complemented, Hall
39	C₇²	C₃×C₂²⋊(C₁₃⋊C₃)	1	1	yes	characteristic, complemented, Sylow
40	C₂×C₃×C₇	—	3	8	no	—
41	C₃×C₁₃	C₂²⋊#3861	1	1	yes	characteristic, complemented
42	C₁₃⋊C₃	—	196	3	no	—
43	C₃×A₄	—	637	1	no	Hall
44	C₂²×C₇	C₃×#63270	1	8	yes	complemented
45	C₂×C₁₃	—	3	1	no	—
46	C₃×C₇	C₂²⋊#63270	1	8	yes	complemented
47	ΓL(1,𝔽₈)	—	364	24	no	—
48	C₂×C₇	—	3	8	no	—
49	C₁₃	C₃×C₂²⋊#3861	1	1	yes	characteristic, complemented, Sylow
50	C₂²×C₃	#14274263	1	1	yes	characteristic, complemented
51	A₄	—	637	3	no	—
52	C₃²	—	2548	1	no	Sylow
53	C₇	C₃×C₂²⋊#63270	1	8	yes	complemented
54	C₂×C₃	—	3	1	no	—
55	C₂²	C₃×#14274263	1	1	yes	characteristic, complemented, Sylow
56	C₃	—	2548	3	no	—
57	C₃	C₂²⋊#14274263	1	1	yes	characteristic, direct product factor
58	C₂	—	3	1	no	—

	subgroup	G/H
center, hypercenter	C₃	C₂²⋊#14274263
commutator, cosocle, hypocenter	C₂²×C₇²×C₁₃	C₃²
Frattini	C₁	G
Fitting, socle	C₂²×C₃×C₇²×C₁₃	C₃
LCS	G ▷ C₂²×C₇²×C₁₃
UCS	C₁ ◁ C₃

Complements

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

N	H ≅ G/N	type
1. C₂²⋊#14274263	C₃	direct (N × H)
2. C₂²×C₃×C₇²×C₁₃	C₃	semidirect
6. C₂²×C₇²×C₁₃	C₃²	semidirect
7. C₃×C₇²×C₁₃	A₄	semidirect
11. C₂²×C₃×C₇×C₁₃	ΓL(1,𝔽₈)	semidirect
14. C₇²×C₁₃	C₃×A₄	semidirect
15. C₂²×C₃×C₇²	C₁₃⋊C₃	semidirect
20. C₂²×C₇×C₁₃	C₃×ΓL(1,𝔽₈)	semidirect
22. C₃×C₇×C₁₃	C₂²⋊ΓL(1,𝔽₈)	semidirect
25. C₂²×C₇²	C₃×C₁₃⋊C₃	semidirect
27. C₂²×C₃×C₁₃	#3861	semidirect
29. C₃×C₇²	C₂²⋊(C₁₃⋊C₃)	semidirect
33. C₇×C₁₃	C₃×C₂²⋊ΓL(1,𝔽₈)	semidirect
34. C₂²×C₃×C₇	#63270	semidirect
38. C₂²×C₁₃	C₃×#3861	semidirect
39. C₇²	C₃×C₂²⋊(C₁₃⋊C₃)	semidirect
41. C₃×C₁₃	C₂²⋊#3861	semidirect
44. C₂²×C₇	C₃×#63270	semidirect
46. C₃×C₇	C₂²⋊#63270	semidirect
49. C₁₃	C₃×C₂²⋊#3861	semidirect
50. C₂²×C₃	#14274263	semidirect
53. C₇	C₃×C₂²⋊#63270	semidirect
55. C₂²	C₃×#14274263	semidirect
57. C₃	C₂²⋊#14274263	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²⋊#14274263	3
C₂²×C₃×C₇²×C₁₃	3
C₃×#14274263	4
C₃×C₂²⋊#63270	7
C₃×C₂²⋊#3861	13

Subgroups — C3×C22⋊#14274263 #37525656

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₂²⋊#14274263 #37525656