Subgroups — #26013900

Order 11172.

84 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19150303	C₂	1	1	yes	maximal, characteristic, complemented
2	#19150300	C₂	1	1	yes	maximal, characteristic, complemented
3	#19150290	C₂	1	1	yes	maximal, characteristic, complemented
4	D₇×D₁₃₃	C₃	1	1	yes	maximal, characteristic, complemented, Hall
5	C₁₉⋊#3862	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₇⋊D₁₃₃	C₂×C₃	1	1	yes	characteristic, complemented
7	C₇×D₁₃₃	C₂×C₃	1	1	yes	characteristic, complemented
8	C₇×D₇×C₁₉	C₂×C₃	1	1	yes	characteristic, complemented
9	C₂×#11716327	—	7	1	no	maximal
10	#11716322⋊C₂	—	7	1	no	maximal
11	C₇²×C₁₉	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
12	C₂×#87704	—	7	1	no	—
13	#11716328	—	7	1	no	—
14	#11716327	—	7	1	no	—
15	#11716327	—	7	1	no	—
16	#11716326	—	7	1	no	—
17	#11716322	—	7	1	no	—
18	#64422⋊C₂	—	19	1	no	maximal, Hall
19	C₂×D₁₃₃	—	7	1	no	—
20	D₇×D₁₉	—	7	1	no	—
21	#87705	—	7	1	no	—
22	#87704	—	7	1	no	—
23	#64425	—	19	1	no	—
24	#64422	—	19	1	no	—
25	#64422	—	19	1	no	—
26	C₂×C₇×C₁₉	—	7	1	no	—
27	D₁₃₃	—	7	1	no	—
28	D₁₃₃	—	7	1	no	—
29	D₁₃₃	—	42	1	no	—
30	D₁₃₃	AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
31	C₇×D₁₉	—	7	1	no	—
32	D₇×C₁₉	AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
33	C₂×D₁₉⋊C₃	—	49	1	no	Hall
34	D₇²	—	19	1	no	Hall
35	#3862	—	19	1	no	Hall
36	C₇×C₁₉	—	6	1	no	—
37	C₇×C₁₉	C₂×AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
38	C₇×C₁₉	C₂×AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
39	C₂×C₁₉⋊C₃	—	49	1	no	—
40	D₁₉⋊C₃	—	49	1	no	—
41	D₁₉⋊C₃	—	49	1	no	—
42	C₇⋊D₇	—	19	1	no	—
43	C₇×D₇	—	19	1	no	—
44	C₇×D₇	D₁₉⋊C₃	1	1	yes	characteristic, complemented
45	C₂×AGL(1,𝔽₇)	—	133	1	no	—
46	C₂×AGL(1,𝔽₇)	—	133	1	no	—
47	C₂×D₁₉	—	49	1	no	Hall
48	C₁₉⋊C₃	—	49	1	no	Hall
49	C₇²	C₂×D₁₉⋊C₃	1	1	yes	characteristic, complemented, Sylow
50	C₂×ΓL(1,𝔽₈)	—	133	1	no	—
51	C₂×ΓL(1,𝔽₈)	—	133	1	no	—
52	AGL(1,𝔽₇)	—	133	1	no	—
53	AGL(1,𝔽₇)	—	133	1	no	—
54	AGL(1,𝔽₇)	—	133	1	no	—
55	AGL(1,𝔽₇)	—	133	1	no	—
56	C₂×C₁₉	—	7	1	no	—
57	D₁₉	—	7	1	no	—
58	D₁₉	—	49	1	no	—
59	C₂×D₇	—	133	1	no	—
60	C₂×D₇	—	133	1	no	—
61	ΓL(1,𝔽₈)	—	133	1	no	—
62	ΓL(1,𝔽₈)	—	133	1	no	—
63	C₁₉	#64422⋊C₂	1	1	yes	characteristic, complemented, Sylow
64	C₂×C₇	—	7	1	no	—
65	C₂×C₇	—	133	1	no	—
66	D₇	—	19	1	no	—
67	D₇	—	798	1	no	—
68	D₇	—	133	1	no	—
69	D₇	—	133	1	no	—
70	D₇	#11716327	1	1	yes	characteristic, complemented
71	C₂²×C₃	—	931	1	no	Hall
72	C₇	—	6	1	no	—
73	C₇	#11716322⋊C₂	1	1	yes	characteristic, complemented
74	C₇	C₂×#11716327	1	1	yes	characteristic, complemented
75	C₂×C₃	—	931	1	no	—
76	C₂×C₃	—	931	1	no	—
77	C₂×C₃	—	931	1	no	—
78	C₂²	—	931	1	no	Sylow
79	C₃	—	931	1	no	Sylow
80	C₂	—	7	1	no	—
81	C₂	—	133	1	no	—
82	C₂	—	931	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. #19150303	C₂	semidirect
2. #19150300	C₂	semidirect
3. #19150290	C₂	semidirect
4. D₇×D₁₃₃	C₃	semidirect
5. C₁₉⋊#3862	C₂²	semidirect
6. C₇⋊D₁₃₃	C₂×C₃	semidirect
7. C₇×D₁₃₃	C₂×C₃	semidirect
8. C₇×D₇×C₁₉	C₂×C₃	semidirect
11. C₇²×C₁₉	C₂²×C₃	semidirect
30. D₁₃₃	AGL(1,𝔽₇)	semidirect
32. D₇×C₁₉	AGL(1,𝔽₇)	semidirect
37. C₇×C₁₉	C₂×AGL(1,𝔽₇)	semidirect
38. C₇×C₁₉	C₂×AGL(1,𝔽₇)	semidirect
44. C₇×D₇	D₁₉⋊C₃	semidirect
49. C₇²	C₂×D₁₉⋊C₃	semidirect
63. C₁₉	#64422⋊C₂	semidirect
70. D₇	#11716327	semidirect
73. C₇	#11716322⋊C₂	semidirect
74. C₇	C₂×#11716327	semidirect

Maximal subgroups

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

subgroup	index
#19150303	2
#19150300	2
#19150290	2
D₇×D₁₃₃	3
C₂×#11716327	7
#11716322⋊C₂	7
#64422⋊C₂	19