Subgroups — #26013895

Order 11172.

104 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19150297	C₂	1	2	yes	maximal, complemented
2	#19150287	C₂	1	1	yes	maximal, characteristic, complemented
3	D₇²×C₁₉	C₃	1	1	yes	maximal, characteristic, complemented, Hall
4	#14584116	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₁₉×C₇⋊D₇	C₂×C₃	1	1	yes	characteristic, complemented
6	C₇×D₇×C₁₉	C₂×C₃	1	2	yes	complemented
7	C₂×#11716326	—	7	2	no	maximal
8	C₇²×C₁₉	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
9	C₂×#87705	—	7	2	no	—
10	#11716326	—	7	2	no	—
11	#11716326	—	7	2	no	—
12	#11716326	—	14	3	no	—
13	#64423⋊C₂	—	19	1	no	maximal, Hall
14	C₂×D₇×C₁₉	—	7	2	no	—
15	#87705	—	7	2	no	—
16	#87705	—	14	3	no	—
17	#64424	—	19	1	no	—
18	#64423	—	19	2	no	—
19	C₂×C₇×C₁₉	—	7	2	no	—
20	D₇×C₁₉	—	7	2	no	—
21	D₇×C₁₉	—	14	3	no	—
22	D₇×C₁₉	AGL(1,𝔽₇)	1	2	yes	complemented
23	C₂²×C₁₉⋊C₃	—	49	1	no	Hall
24	D₇²	C₁₉⋊C₃	1	1	yes	characteristic, complemented, Hall
25	#3861	—	19	1	no	Hall
26	C₇×C₁₉	—	2	3	no	—
27	C₇×C₁₉	C₂×AGL(1,𝔽₇)	1	2	yes	complemented
28	C₂×C₁₉⋊C₃	—	49	2	no	—
29	C₂×C₁₉⋊C₃	—	49	1	no	—
30	C₇⋊D₇	C₂×C₁₉⋊C₃	1	1	yes	characteristic, complemented
31	C₇×D₇	C₂×C₁₉⋊C₃	1	2	yes	complemented
32	C₂×AGL(1,𝔽₇)	—	133	2	no	—
33	C₂²×C₁₉	—	49	1	no	Hall
34	C₁₉⋊C₃	—	49	1	no	Hall
35	C₇²	C₂²×C₁₉⋊C₃	1	1	yes	characteristic, complemented, Sylow
36	C₂×ΓL(1,𝔽₈)	—	133	2	no	—
37	AGL(1,𝔽₇)	—	266	3	no	—
38	AGL(1,𝔽₇)	—	133	2	no	—
39	AGL(1,𝔽₇)	—	133	2	no	—
40	C₂×C₁₉	—	7	2	no	—
41	C₂×C₁₉	—	49	1	no	—
42	C₂×D₇	—	7	2	no	—
43	ΓL(1,𝔽₈)	—	266	3	no	—
44	ΓL(1,𝔽₈)	—	133	2	no	—
45	C₁₉	#64423⋊C₂	1	1	yes	characteristic, complemented, Sylow
46	C₂×C₇	—	7	2	no	—
47	D₇	—	7	2	no	—
48	D₇	—	14	3	no	—
49	D₇	#11716326	1	2	yes	complemented
50	C₂²×C₃	—	931	1	no	Hall
51	C₇	—	2	3	no	—
52	C₇	C₂×#11716326	1	2	yes	complemented
53	C₂×C₃	—	931	2	no	—
54	C₂×C₃	—	931	1	no	—
55	C₂²	—	49	1	no	Sylow
56	C₃	—	931	1	no	Sylow
57	C₂	—	7	2	no	—
58	C₂	—	49	1	no	—

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

Complements

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

N	H ≅ G/N	type
1. #19150297	C₂	semidirect
2. #19150287	C₂	semidirect
3. D₇²×C₁₉	C₃	semidirect
4. #14584116	C₂²	semidirect
5. C₁₉×C₇⋊D₇	C₂×C₃	semidirect
6. C₇×D₇×C₁₉	C₂×C₃	semidirect
8. C₇²×C₁₉	C₂²×C₃	semidirect
22. D₇×C₁₉	AGL(1,𝔽₇)	semidirect
24. D₇²	C₁₉⋊C₃	semidirect
27. C₇×C₁₉	C₂×AGL(1,𝔽₇)	semidirect
30. C₇⋊D₇	C₂×C₁₉⋊C₃	semidirect
31. C₇×D₇	C₂×C₁₉⋊C₃	semidirect
35. C₇²	C₂²×C₁₉⋊C₃	semidirect
45. C₁₉	#64423⋊C₂	semidirect
49. D₇	#11716326	semidirect
52. C₇	C₂×#11716326	semidirect

Maximal subgroups

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

subgroup	index
#19150297	2
#19150287	2
D₇²×C₁₉	3
C₂×#11716326	7
#64423⋊C₂	19