Subgroups — #26013851

Order 11172.

52 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×#87705	C₂	1	1	yes	maximal, characteristic
2	C₇×Dic₁₃₃	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₇×#87705	C₄	1	1	yes	characteristic, complemented, Hall
4	C₂×C₇²×C₁₉	C₂×C₃	1	1	yes	characteristic
5	#13097583	—	7	1	no	maximal
6	(C₁₉⋊C₃)⋊Dic₇	—	7	1	no	maximal
7	C₇²×C₁₉	C₃×C₄	1	1	yes	characteristic, complemented, Hall
8	C₂×#87705	D₇	1	1	yes	characteristic
9	C₂×C₇×C₁₉⋊C₃	—	7	1	no	—
10	ΓL(1,𝔽₈)×Dic₇	—	19	1	no	maximal, Hall
11	Dic₁₃₃	ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
12	C₇×Dic₁₉	—	7	1	no	—
13	#87705	Dic₇	1	1	yes	characteristic, complemented
14	C₇×C₁₉⋊C₃	—	7	1	no	—
15	C₂×C₇×ΓL(1,𝔽₈)	—	19	1	no	—
16	C₂×C₇×C₁₉	—	6	1	no	—
17	C₂×C₇×C₁₉	C₂×ΓL(1,𝔽₈)	1	1	yes	characteristic
18	C₂×C₇×C₁₉	C₃×D₇	1	1	yes	characteristic
19	(C₁₉⋊C₃)⋊C₄	—	49	1	no	Hall
20	C₇×Dic₇	—	19	1	no	Hall
21	C₇×ΓL(1,𝔽₈)	—	19	1	no	Hall
22	C₇×C₁₉	—	6	1	no	—
23	C₇×C₁₉	C₄×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
24	C₇×C₁₉	C₃×Dic₇	1	1	yes	characteristic, complemented
25	C₂×C₁₉⋊C₃	—	7	1	no	—
26	C₂×C₇²	D₁₉⋊C₃	1	1	yes	characteristic
27	C₃×Dic₇	—	133	1	no	—
28	C₄×ΓL(1,𝔽₈)	—	133	1	no	—
29	Dic₁₉	—	7	1	no	Hall
30	C₁₉⋊C₃	—	7	1	no	Hall
31	C₇²	(C₁₉⋊C₃)⋊C₄	1	1	yes	characteristic, complemented, Sylow
32	C₂×C₃×C₇	—	133	1	no	—
33	C₂×ΓL(1,𝔽₈)	—	19	1	no	—
34	C₂×C₁₉	D₇×ΓL(1,𝔽₈)	1	1	yes	characteristic
35	C₄×C₇	—	133	1	no	—
36	Dic₇	—	19	1	no	—
37	C₃×C₇	—	133	1	no	—
38	ΓL(1,𝔽₈)	—	19	1	no	—
39	C₁₉	ΓL(1,𝔽₈)×Dic₇	1	1	yes	characteristic, complemented, Sylow
40	C₂×C₇	—	6	1	no	—
41	C₂×C₇	(C₁₉⋊C₃)⋊D₇	1	1	yes	characteristic
42	C₂×C₇	#11716322	1	1	yes	characteristic
43	C₃×C₄	—	931	1	no	Hall
44	C₇	—	6	1	no	—
45	C₇	(C₁₉⋊C₃)⋊Dic₇	1	1	yes	characteristic, complemented
46	C₇	#13097583	1	1	yes	characteristic, complemented
47	C₂×C₃	—	133	1	no	—
48	C₄	—	133	1	no	Sylow
49	C₃	—	133	1	no	Sylow
50	C₂	#19150318	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	#19150318
commutator, hypocenter	C₇²×C₁₉	C₃×C₄
Fitting, socle, cosocle	C₂×C₇²×C₁₉	C₂×C₃
prime radical	C₂×C₇×#87705	C₂
LCS	G ▷ C₇²×C₁₉
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
2. C₇×Dic₁₃₃	C₃	semidirect
3. C₇×#87705	C₄	semidirect
7. C₇²×C₁₉	C₃×C₄	semidirect
11. Dic₁₃₃	ΓL(1,𝔽₈)	semidirect
13. #87705	Dic₇	semidirect
23. C₇×C₁₉	C₄×ΓL(1,𝔽₈)	semidirect
24. C₇×C₁₉	C₃×Dic₇	semidirect
31. C₇²	(C₁₉⋊C₃)⋊C₄	semidirect
39. C₁₉	ΓL(1,𝔽₈)×Dic₇	semidirect
45. C₇	(C₁₉⋊C₃)⋊Dic₇	semidirect
46. C₇	#13097583	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₇×#87705	2
C₇×Dic₁₃₃	3
#13097583	7
(C₁₉⋊C₃)⋊Dic₇	7
ΓL(1,𝔽₈)×Dic₇	19