Subgroups — C₁₁×#11725071⋊C₂ #34084673

Order 19404.

112 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×#11725071	C₂	1	2	yes	maximal, complemented
2	C₁₁×#11725078	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₁×D₂₁⋊D₇	—	3	1	no	maximal
4	C₁₁×#89205	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₇×C₁₁×D₂₁	—	3	2	no	—
6	C₃×C₁₁×C₇⋊D₇	D₃	1	1	yes	characteristic
7	C₁₁×D₇²	—	9	1	no	Hall
8	#11725071⋊C₂	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₃×C₇²×C₁₁	C₂×D₃	1	1	yes	characteristic
10	C₁₁×D₇⋊C₉	—	14	1	no	—
11	C₁₁×C₇⋊D₇	D₉	1	1	yes	characteristic, complemented
12	C₇×C₁₁×D₇	—	9	2	no	—
13	D₃×C₁₁×D₇	—	21	2	no	—
14	#11725078	C₂×C₁₁	1	1	yes	characteristic, complemented
15	#11725071	C₂×C₁₁	1	2	yes	complemented
16	C₁₁×C₇⋊C₉	—	14	1	no	—
17	D₂₁⋊D₇	—	3	1	no	—
18	C₇²×C₁₁	C₂×D₉	1	1	yes	characteristic, complemented, Hall
19	C₁₁×D₂₁	—	3	2	no	—
20	D₃×C₇×C₁₁	—	21	2	no	—
21	C₃×C₁₁×D₇	—	14	1	no	—
22	C₃×C₁₁×D₇	—	21	2	no	—
23	#89205	C₂²×C₁₁	1	1	yes	characteristic, complemented, Hall
24	C₂×C₁₁×D₉	—	49	1	no	maximal, Hall
25	C₂×C₁₁×D₇	—	63	2	no	—
26	C₇×D₂₁	—	3	2	no	—
27	C₃×C₇⋊D₇	D₃×C₁₁	1	1	yes	characteristic
28	C₃×C₇×C₁₁	—	2	1	no	—
29	C₃×C₇×C₁₁	—	3	2	no	—
30	C₂×C₉×C₁₁	—	49	1	no	—
31	C₁₁×D₉	—	49	2	no	—
32	D₇²	—	9	1	no	Hall
33	C₂×C₇×C₁₁	—	63	2	no	—
34	C₁₁×D₇	—	9	2	no	—
35	C₁₁×D₇	—	14	1	no	—
36	C₁₁×D₇	—	21	2	no	—
37	C₃×C₇²	C₂×D₃×C₁₁	1	1	yes	characteristic
38	C₂×D₃×C₁₁	—	147	1	no	—
39	D₇⋊C₉	—	14	1	no	—
40	C₉×C₁₁	—	49	1	no	Hall
41	C₇⋊D₇	C₁₁×D₉	1	1	yes	characteristic, complemented
42	C₇×D₇	—	9	2	no	—
43	D₃×D₇	—	21	2	no	—
44	C₇×C₁₁	—	2	1	no	—
45	C₇×C₁₁	—	3	2	no	—
46	C₂×C₃×C₁₁	—	49	1	no	—
47	D₃×C₁₁	—	21	2	no	—
48	C₇⋊C₉	—	14	1	no	—
49	C₇²	C₂×C₁₁×D₉	1	1	yes	characteristic, complemented, Sylow
50	C₂²×C₁₁	—	441	1	no	Hall
51	D₂₁	—	3	2	no	—
52	C₃×D₇	—	14	1	no	—
53	C₃×D₇	—	21	2	no	—
54	D₃×C₇	—	21	2	no	—
55	C₂×D₉	—	49	1	no	Hall
56	C₃×C₁₁	#64418⋊C₂	1	1	yes	characteristic
57	C₂×D₇	—	63	2	no	—
58	C₂×C₁₁	—	49	1	no	—
59	C₂×C₁₁	—	63	2	no	—
60	C₃×C₇	—	2	1	no	—
61	C₃×C₇	—	3	2	no	—
62	C₂×C₉	—	49	1	no	—
63	D₉	—	49	2	no	—
64	C₂×C₇	—	63	2	no	—
65	D₇	—	9	2	no	—
66	D₇	—	14	1	no	—
67	D₇	—	21	2	no	—
68	C₂×D₃	—	147	1	no	—
69	C₁₁	#11725071⋊C₂	1	1	yes	characteristic, direct product factor, Sylow
70	C₉	—	49	1	no	Sylow
71	C₇	—	2	1	no	—
72	C₇	—	3	2	no	—
73	C₂×C₃	—	49	1	no	—
74	D₃	—	21	2	no	—
75	C₂²	—	441	1	no	Sylow
76	C₃	C₁₁×#64418⋊C₂	1	1	yes	characteristic
77	C₂	—	49	1	no	—
78	C₂	—	63	2	no	—

	subgroup	G/H
center, hypercenter	C₁₁	#11725071⋊C₂
commutator, cosocle, hypocenter	#89205	C₂²×C₁₁
Frattini	C₃	C₁₁×#64418⋊C₂
Fitting, socle	C₃×C₇²×C₁₁	C₂×D₃
LCS	G ▷ #89205
UCS	C₁ ◁ C₁₁

Complements

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

N	H ≅ G/N	type
1. C₁₁×#11725071	C₂	semidirect
2. C₁₁×#11725078	C₂	semidirect
4. C₁₁×#89205	C₂²	semidirect
8. #11725071⋊C₂	C₁₁	direct (N × H)
11. C₁₁×C₇⋊D₇	D₉	semidirect
14. #11725078	C₂×C₁₁	semidirect
15. #11725071	C₂×C₁₁	semidirect
18. C₇²×C₁₁	C₂×D₉	semidirect
23. #89205	C₂²×C₁₁	semidirect
41. C₇⋊D₇	C₁₁×D₉	semidirect
49. C₇²	C₂×C₁₁×D₉	semidirect
69. C₁₁	#11725071⋊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
C₁₁×#11725071	2
C₁₁×#11725078	2
C₁₁×D₂₁⋊D₇	3
#11725071⋊C₂	11
C₂×C₁₁×D₉	49

Subgroups — C11×#11725071⋊C2 #34084673

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#11725071⋊C₂ #34084673