Subgroups — C₂×C₂₃⋊(#4294⋊C₂) #30628554

Order 15732.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃⋊(#4294⋊C₂)	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₂₃×#4294	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×D₄₃₇	C₃	1	1	yes	maximal, characteristic
4	C₂₃×#4294	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₃×D₄₃₇	C₂×C₃	1	2	yes	—
6	C₂×C₃×C₁₉×C₂₃	C₂×C₃	1	1	yes	characteristic
7	C₂×D₄₃₇	C₉	1	1	yes	characteristic, complemented, Hall
8	C₃×C₁₉×C₂₃	C₂²×C₃	1	1	yes	characteristic
9	C₂×C₁₉×C₂₃	C₂×C₉	1	1	yes	characteristic, complemented
10	D₄₃₇	C₂×C₉	1	2	yes	complemented
11	C₂×C₉×D₂₃	—	19	1	no	maximal, Hall
12	C₂×#4294⋊C₂	—	23	1	no	maximal, Hall
13	C₁₉×C₂₃	C₂²×C₉	1	1	yes	characteristic, complemented, Hall
14	C₂×C₉×C₂₃	—	19	1	no	—
15	C₉×D₂₃	—	19	2	no	—
16	C₂×#4294	D₂₃	1	1	yes	characteristic, complemented
17	#4294⋊C₂	—	23	2	no	—
18	C₂×C₃×D₂₃	—	57	1	no	—
19	C₂×C₃×D₁₉	—	23	1	no	—
20	C₉×C₂₃	—	19	1	no	Hall
21	#4294	C₂×D₂₃	1	1	yes	characteristic, complemented, Hall
22	C₂×C₃×C₂₃	D₁₉⋊C₃	1	1	yes	characteristic
23	C₃×D₂₃	—	57	2	no	—
24	C₂×C₃×C₁₉	C₃×D₂₃	1	1	yes	characteristic
25	C₃×D₁₉	—	23	2	no	—
26	C₂×D₂₃	—	57	1	no	Hall
27	C₂×D₁₉	—	23	1	no	Hall
28	C₃×C₂₃	C₂×D₁₉⋊C₃	1	1	yes	characteristic
29	C₃×C₁₉	C₂×C₃×D₂₃	1	1	yes	characteristic
30	C₂×C₂₃	#4294⋊C₂	1	1	yes	characteristic, complemented
31	D₂₃	—	57	2	no	—
32	C₂×C₁₉	C₉×D₂₃	1	1	yes	characteristic, complemented
33	D₁₉	—	23	2	no	—
34	C₂²×C₉	—	437	1	no	Hall
35	C₂₃	C₂×#4294⋊C₂	1	1	yes	characteristic, complemented, Sylow
36	C₁₉	C₂×C₉×D₂₃	1	1	yes	characteristic, complemented, Sylow
37	C₂×C₉	—	19	1	no	—
38	C₂×C₉	—	437	2	no	—
39	C₂²×C₃	—	1311	1	no	—
40	C₉	—	19	1	no	Sylow
41	C₂×C₃	—	1311	2	no	—
42	C₂×C₃	C₂₃⋊(D₁₉⋊C₃)	1	1	yes	characteristic
43	C₂²	—	1311	1	no	Sylow
44	C₃	C₂×C₂₃⋊(D₁₉⋊C₃)	1	1	yes	characteristic
45	C₂	—	1311	2	no	—
46	C₂	C₂₃⋊(#4294⋊C₂)	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₃	C₂₃⋊(D₁₉⋊C₃)
commutator, hypocenter	C₁₉×C₂₃	C₂²×C₉
Frattini	C₃	C₂×C₂₃⋊(D₁₉⋊C₃)
Fitting, socle	C₂×C₃×C₁₉×C₂₃	C₂×C₃
prime radical	C₂×C₃×D₄₃₇	C₃
cosocle	C₃×C₁₉×C₂₃	C₂²×C₃
LCS	G ▷ C₁₉×C₂₃
UCS	C₁ ◁ C₂×C₃

Complements

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

N	H ≅ G/N	type
1. C₂₃⋊(#4294⋊C₂)	C₂	direct (N × H)
2. C₂×C₂₃×#4294	C₂	semidirect
4. C₂₃×#4294	C₂²	semidirect
7. C₂×D₄₃₇	C₉	semidirect
9. C₂×C₁₉×C₂₃	C₂×C₉	semidirect
10. D₄₃₇	C₂×C₉	semidirect
13. C₁₉×C₂₃	C₂²×C₉	semidirect
16. C₂×#4294	D₂₃	semidirect
21. #4294	C₂×D₂₃	semidirect
30. C₂×C₂₃	#4294⋊C₂	semidirect
32. C₂×C₁₉	C₉×D₂₃	semidirect
35. C₂₃	C₂×#4294⋊C₂	semidirect
36. C₁₉	C₂×C₉×D₂₃	semidirect
46. C₂	C₂₃⋊(#4294⋊C₂)	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂₃⋊(#4294⋊C₂)	2
C₂×C₂₃×#4294	2
C₂×C₃×D₄₃₇	3
C₂×C₉×D₂₃	19
C₂×#4294⋊C₂	23

Subgroups — C2×C23⋊(#4294⋊C2) #30628554

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₂₃⋊(#4294⋊C₂) #30628554