Subgroups — C₂²×C₇²×#4294 #45691706

Order 33516.

300 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇²×#4294	C₂	1	3	yes	maximal, direct product factor
2	C₂²×C₃×C₇²×C₁₉	C₃	1	1	yes	maximal, characteristic
3	C₇²×#4294	C₂²	1	1	yes	characteristic, direct product factor, Hall
4	C₂×C₃×C₇²×C₁₉	C₂×C₃	1	3	yes	—
5	C₂²×C₇×#4294	C₇	1	8	yes	maximal, direct product factor
6	C₂²×C₇²×C₁₉	C₉	1	1	yes	characteristic, complemented, Hall
7	C₃×C₇²×C₁₉	C₂²×C₃	1	1	yes	characteristic
8	C₂×C₇×#4294	C₂×C₇	1	24	yes	direct product factor
9	C₂×C₇²×C₁₉	C₂×C₉	1	3	yes	complemented
10	C₂²×C₇²×C₉	—	19	1	no	maximal, Hall
11	C₂²×C₃×C₇×C₁₉	C₃×C₇	1	8	yes	—
12	C₇×#4294	C₂²×C₇	1	8	yes	direct product factor
13	C₇²×C₁₉	C₂²×C₉	1	1	yes	characteristic, complemented, Hall
14	C₂×C₇²×C₉	—	19	3	no	—
15	C₂×C₃×C₇×C₁₉	C₂×C₃×C₇	1	24	yes	—
16	C₂²×#4294	C₇²	1	1	yes	characteristic, direct product factor, Hall
17	C₂²×C₃×C₇²	C₁₉⋊C₃	1	1	yes	characteristic
18	C₂²×C₇×C₁₉	C₇×C₉	1	8	yes	complemented
19	C₇²×C₉	—	19	1	no	Hall
20	C₃×C₇×C₁₉	C₂²×C₃×C₇	1	8	yes	—
21	C₂×#4294	C₂×C₇²	1	3	yes	direct product factor
22	C₂×C₃×C₇²	C₂×C₁₉⋊C₃	1	3	yes	—
23	C₂×C₇×C₁₉	C₂×C₇×C₉	1	24	yes	complemented
24	C₂²×C₇×C₉	—	19	8	no	—
25	C₂²×C₃×C₁₉	C₃×C₇²	1	1	yes	characteristic
26	C₂²×C₇²	#4294	1	1	yes	characteristic, direct product factor, Hall
27	#4294	C₂²×C₇²	1	1	yes	characteristic, direct product factor, Hall
28	C₃×C₇²	C₂²×C₁₉⋊C₃	1	1	yes	characteristic
29	C₇×C₁₉	C₂²×C₇×C₉	1	8	yes	complemented
30	C₂×C₇×C₉	—	19	24	no	—
31	C₂×C₃×C₁₉	C₂×C₃×C₇²	1	3	yes	—
32	C₂×C₇²	C₂×#4294	1	3	yes	direct product factor
33	C₂²×C₃×C₇	C₇×C₁₉⋊C₃	1	8	yes	—
34	C₂²×C₁₉	C₇²×C₉	1	1	yes	characteristic, complemented, Hall
35	C₇×C₉	—	19	8	no	—
36	C₃×C₁₉	C₂²×C₃×C₇²	1	1	yes	characteristic
37	C₇²	C₂²×#4294	1	1	yes	characteristic, direct product factor, Sylow
38	C₂×C₃×C₇	C₂×C₇×C₁₉⋊C₃	1	24	yes	—
39	C₂×C₁₉	C₂×C₇²×C₉	1	3	yes	complemented
40	C₂²×C₉	—	19	1	no	Hall
41	C₂²×C₇	C₇×#4294	1	8	yes	direct product factor
42	C₃×C₇	C₂²×C₇×C₁₉⋊C₃	1	8	yes	—
43	C₁₉	C₂²×C₇²×C₉	1	1	yes	characteristic, complemented, Sylow
44	C₂×C₉	—	19	3	no	—
45	C₂×C₇	C₂×C₇×#4294	1	24	yes	direct product factor
46	C₂²×C₃	C₇²×C₁₉⋊C₃	1	1	yes	characteristic
47	C₉	—	19	1	no	Sylow
48	C₇	C₂²×C₇×#4294	1	8	yes	direct product factor
49	C₂×C₃	C₂×C₇²×C₁₉⋊C₃	1	3	yes	—
50	C₂²	C₇²×#4294	1	1	yes	characteristic, direct product factor, Sylow
51	C₃	C₂²×C₇²×C₁₉⋊C₃	1	1	yes	characteristic
52	C₂	C₂×C₇²×#4294	1	3	yes	direct product factor

	subgroup	G/H
center, hypercenter	C₂²×C₃×C₇²	C₁₉⋊C₃
commutator, hypocenter	C₁₉	C₂²×C₇²×C₉
Frattini	C₃	C₂²×C₇²×C₁₉⋊C₃
Fitting, socle, prime radical	C₂²×C₃×C₇²×C₁₉	C₃
cosocle	C₃×C₁₉	C₂²×C₃×C₇²
LCS	G ▷ C₁₉
UCS	C₁ ◁ C₂²×C₃×C₇²

Complements

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

N	H ≅ G/N	type
1. C₂×C₇²×#4294	C₂	direct (N × H)
3. C₇²×#4294	C₂²	direct (N × H)
5. C₂²×C₇×#4294	C₇	direct (N × H)
6. C₂²×C₇²×C₁₉	C₉	semidirect
8. C₂×C₇×#4294	C₂×C₇	direct (N × H)
9. C₂×C₇²×C₁₉	C₂×C₉	semidirect
12. C₇×#4294	C₂²×C₇	direct (N × H)
13. C₇²×C₁₉	C₂²×C₉	semidirect
16. C₂²×#4294	C₇²	direct (N × H)
18. C₂²×C₇×C₁₉	C₇×C₉	semidirect
21. C₂×#4294	C₂×C₇²	direct (N × H)
23. C₂×C₇×C₁₉	C₂×C₇×C₉	semidirect
26. C₂²×C₇²	#4294	direct (N × H)
27. #4294	C₂²×C₇²	direct (N × H)
29. C₇×C₁₉	C₂²×C₇×C₉	semidirect
32. C₂×C₇²	C₂×#4294	direct (N × H)
34. C₂²×C₁₉	C₇²×C₉	semidirect
37. C₇²	C₂²×#4294	direct (N × H)
39. C₂×C₁₉	C₂×C₇²×C₉	semidirect
41. C₂²×C₇	C₇×#4294	direct (N × H)
43. C₁₉	C₂²×C₇²×C₉	semidirect
45. C₂×C₇	C₂×C₇×#4294	direct (N × H)
48. C₇	C₂²×C₇×#4294	direct (N × H)
50. C₂²	C₇²×#4294	direct (N × H)
52. C₂	C₂×C₇²×#4294	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×C₇²×#4294	2
C₂²×C₃×C₇²×C₁₉	3
C₂²×C₇×#4294	7
C₂²×C₇²×C₉	19

Subgroups — C22×C72×#4294 #45691706

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₇²×#4294 #45691706