Subgroups — C₂×#19150312 #26013988

Order 11172.

200 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14584116	C₂	1	1	yes	maximal, characteristic, complemented
2	#19150312	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₇²×D₁₉	C₃	1	1	yes	maximal, characteristic, complemented, Hall
4	#14584116	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₇²×C₁₉	C₂×C₃	1	1	yes	characteristic, complemented
6	C₇²×D₁₉	C₂×C₃	1	2	yes	complemented
7	C₂×#11716322	—	7	8	no	maximal
8	C₇²×C₁₉	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
9	C₂×#87705	—	7	8	no	—
10	#11716322	—	7	16	no	—
11	C₂²×#3861	—	19	1	no	maximal, Hall
12	C₂×C₇×D₁₉	ΓL(1,𝔽₈)	1	8	yes	complemented
13	#87705	—	7	8	no	—
14	C₂×#3861	—	19	2	no	—
15	C₂×#3861	—	19	1	no	—
16	C₂×C₇×C₁₉	C₂×ΓL(1,𝔽₈)	1	8	yes	complemented
17	C₇×D₁₉	C₂×ΓL(1,𝔽₈)	1	16	yes	complemented
18	C₂×D₁₉⋊C₃	—	49	1	no	Hall
19	C₂²×C₇²	—	19	1	no	Hall
20	#3861	—	19	1	no	Hall
21	C₇×C₁₉	C₂²×ΓL(1,𝔽₈)	1	8	yes	complemented
22	C₂×C₁₉⋊C₃	—	49	1	no	—
23	D₁₉⋊C₃	—	49	2	no	—
24	C₂×C₇²	—	19	2	no	—
25	C₂×C₇²	D₁₉⋊C₃	1	1	yes	characteristic, complemented
26	C₂²×ΓL(1,𝔽₈)	—	133	8	no	—
27	C₂×D₁₉	#3861	1	1	yes	characteristic, complemented, Hall
28	C₁₉⋊C₃	—	49	1	no	Hall
29	C₇²	C₂×D₁₉⋊C₃	1	1	yes	characteristic, complemented, Sylow
30	C₂×ΓL(1,𝔽₈)	—	133	16	no	—
31	C₂×ΓL(1,𝔽₈)	—	133	8	no	—
32	C₂×C₁₉	C₂×#3861	1	1	yes	characteristic, complemented
33	D₁₉	C₂×#3861	1	2	yes	complemented
34	C₂²×C₇	—	19	8	no	—
35	ΓL(1,𝔽₈)	—	133	8	no	—
36	C₁₉	C₂²×#3861	1	1	yes	characteristic, complemented, Sylow
37	C₂×C₇	—	19	16	no	—
38	C₂×C₇	#11716322	1	8	yes	complemented
39	C₂²×C₃	—	931	1	no	Hall
40	C₇	C₂×#11716322	1	8	yes	complemented
41	C₂×C₃	—	931	2	no	—
42	C₂×C₃	—	931	1	no	—
43	C₂²	—	19	1	no	Sylow
44	C₃	—	931	1	no	Sylow
45	C₂	—	19	2	no	—
46	C₂	#19150312	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	#19150312
commutator, cosocle, hypocenter	C₇²×C₁₉	C₂²×C₃
Frattini	C₁	G
Fitting, socle	C₂×C₇²×C₁₉	C₂×C₃
LCS	G ▷ C₇²×C₁₉
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
1. C₂×#14584116	C₂	semidirect
2. #19150312	C₂	direct (N × H)
3. C₂×C₇²×D₁₉	C₃	semidirect
4. #14584116	C₂²	semidirect
5. C₂×C₇²×C₁₉	C₂×C₃	semidirect
6. C₇²×D₁₉	C₂×C₃	semidirect
8. C₇²×C₁₉	C₂²×C₃	semidirect
12. C₂×C₇×D₁₉	ΓL(1,𝔽₈)	semidirect
16. C₂×C₇×C₁₉	C₂×ΓL(1,𝔽₈)	semidirect
17. C₇×D₁₉	C₂×ΓL(1,𝔽₈)	semidirect
21. C₇×C₁₉	C₂²×ΓL(1,𝔽₈)	semidirect
25. C₂×C₇²	D₁₉⋊C₃	semidirect
27. C₂×D₁₉	#3861	semidirect
29. C₇²	C₂×D₁₉⋊C₃	semidirect
32. C₂×C₁₉	C₂×#3861	semidirect
33. D₁₉	C₂×#3861	semidirect
36. C₁₉	C₂²×#3861	semidirect
38. C₂×C₇	#11716322	semidirect
40. C₇	C₂×#11716322	semidirect
46. C₂	#19150312	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×#14584116	2
#19150312	2
C₂×C₇²×D₁₉	3
C₂×#11716322	7
C₂²×#3861	19

Subgroups — C2×#19150312 #26013988

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#19150312 #26013988