Subgroups — C₁₁⋊C₅×#10596868 #44568456

Order 32340.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₁⋊C₅×#3862	C₂	1	1	yes	maximal, characteristic
2	C₇×Dic₇×C₁₁⋊C₅	—	3	1	no	maximal, Hall
3	C₁₁⋊C₅×#3862	C₄	1	1	yes	characteristic, complemented, Hall
4	C₁₁×#10596868	C₅	1	1	yes	maximal, characteristic, complemented, Hall
5	C₂×C₇²×C₁₁⋊C₅	D₃	1	1	yes	characteristic
6	C₂×C₁₁×#3862	C₂×C₅	1	1	yes	characteristic
7	C₅×#10596868	—	11	1	no	maximal, Hall
8	C₇²×C₁₁⋊C₅	Dic₃	1	1	yes	characteristic, complemented, Hall
9	C₂×ΓL(1,𝔽₈)×C₁₁⋊C₅	—	14	1	no	—
10	C₇×C₁₁×Dic₇	—	3	1	no	Hall
11	C₁₁×#3862	C₄×C₅	1	1	yes	characteristic, complemented, Hall
12	C₄×C₇×C₁₁⋊C₅	—	21	1	no	—
13	Dic₇×C₁₁⋊C₅	—	3	1	no	—
14	C₂×C₅×#3862	—	11	1	no	—
15	ΓL(1,𝔽₈)×C₁₁⋊C₅	—	14	1	no	—
16	C₂×C₇²×C₁₁	C₅×D₃	1	1	yes	characteristic
17	C₅×C₇×Dic₇	—	33	1	no	Hall
18	C₂×C₇×C₁₁⋊C₅	—	2	1	no	—
19	C₂×C₇×C₁₁⋊C₅	—	3	1	no	—
20	C₂×C₇×C₁₁⋊C₅	—	3	1	no	—
21	C₅×#3862	—	11	1	no	Hall
22	Dic₃×C₁₁⋊C₅	—	49	1	no	maximal, Hall
23	#10596868	C₁₁⋊C₅	1	1	yes	characteristic, direct product factor, Hall
24	C₇²×C₁₁	C₅×Dic₃	1	1	yes	characteristic, complemented, Hall
25	C₂×C₅×C₇²	—	11	1	no	—
26	C₂×C₁₁×ΓL(1,𝔽₈)	—	14	1	no	—
27	C₇×C₁₁⋊C₅	—	2	1	no	—
28	C₇×C₁₁⋊C₅	—	3	1	no	—
29	C₇×C₁₁⋊C₅	—	3	1	no	—
30	C₂×C₃×C₁₁⋊C₅	—	49	1	no	—
31	C₄×C₇×C₁₁	—	21	1	no	—
32	C₁₁×Dic₇	—	3	1	no	—
33	C₂×#3862	C₂×C₁₁⋊C₅	1	1	yes	characteristic
34	C₅×C₇²	—	11	1	no	Hall
35	C₁₁×ΓL(1,𝔽₈)	—	14	1	no	—
36	C₄×C₁₁⋊C₅	—	21	1	no	Hall
37	C₂×C₅×ΓL(1,𝔽₈)	—	154	1	no	—
38	C₇×Dic₇	—	3	1	no	Hall
39	C₃×C₁₁⋊C₅	—	49	1	no	Hall
40	C₂×C₇×C₁₁	—	2	1	no	—
41	C₂×C₇×C₁₁	—	3	1	no	—
42	C₂×C₇×C₁₁	—	3	1	no	—
43	#3862	C₄×C₁₁⋊C₅	1	1	yes	characteristic, complemented, Hall
44	C₄×C₅×C₇	—	231	1	no	—
45	C₅×Dic₇	—	33	1	no	—
46	C₁₁×Dic₃	—	49	1	no	Hall
47	C₂×C₁₁⋊C₅	#64418	1	1	yes	characteristic
48	C₅×ΓL(1,𝔽₈)	—	154	1	no	—
49	C₂×C₇²	D₃×C₁₁⋊C₅	1	1	yes	characteristic
50	C₇×C₁₁	—	2	1	no	—
51	C₇×C₁₁	—	3	1	no	—
52	C₇×C₁₁	—	3	1	no	—
53	C₂×C₅×C₇	—	22	1	no	—
54	C₂×C₅×C₇	—	33	1	no	—
55	C₂×C₅×C₇	—	33	1	no	—
56	C₂×C₃×C₁₁	—	49	1	no	—
57	C₅×Dic₃	—	539	1	no	Hall
58	C₁₁⋊C₅	#10596868	1	1	yes	characteristic, direct product factor, Hall
59	C₇²	Dic₃×C₁₁⋊C₅	1	1	yes	characteristic, complemented, Sylow
60	C₄×C₁₁	—	21	1	no	Hall
61	C₂×ΓL(1,𝔽₈)	—	14	1	no	—
62	C₅×C₇	—	22	1	no	—
63	C₅×C₇	—	33	1	no	—
64	C₅×C₇	—	33	1	no	—
65	C₃×C₁₁	—	49	1	no	Hall
66	C₂×C₃×C₅	—	539	1	no	—
67	C₄×C₇	—	21	1	no	—
68	Dic₇	—	3	1	no	—
69	C₂×C₁₁	C₅×#64418	1	1	yes	characteristic
70	ΓL(1,𝔽₈)	—	14	1	no	—
71	C₄×C₅	—	231	1	no	Hall
72	C₃×C₅	—	539	1	no	Hall
73	C₂×C₇	—	2	1	no	—
74	C₂×C₇	—	3	1	no	—
75	C₂×C₇	—	3	1	no	—
76	Dic₃	—	49	1	no	Hall
77	C₁₁	C₅×#10596868	1	1	yes	characteristic, complemented, Sylow
78	C₂×C₅	—	11	1	no	—
79	C₇	—	2	1	no	—
80	C₇	—	3	1	no	—
81	C₇	—	3	1	no	—
82	C₂×C₃	—	49	1	no	—
83	C₅	—	11	1	no	Sylow
84	C₄	—	21	1	no	Sylow
85	C₃	—	49	1	no	Sylow
86	C₂	C₁₁⋊C₅×#64418	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	C₁₁⋊C₅×#64418
commutator, hypocenter	C₁₁×#3862	C₄×C₅
Fitting, socle	C₂×C₇²×C₁₁	C₅×D₃
prime radical	C₂×C₁₁⋊C₅×#3862	C₂
cosocle	C₂×C₁₁×#3862	C₂×C₅
LCS	G ▷ C₁₁×#3862
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
3. C₁₁⋊C₅×#3862	C₄	semidirect
4. C₁₁×#10596868	C₅	semidirect
8. C₇²×C₁₁⋊C₅	Dic₃	semidirect
11. C₁₁×#3862	C₄×C₅	semidirect
23. #10596868	C₁₁⋊C₅	direct (N × H)
24. C₇²×C₁₁	C₅×Dic₃	semidirect
43. #3862	C₄×C₁₁⋊C₅	semidirect
58. C₁₁⋊C₅	#10596868	direct (N × H)
59. C₇²	Dic₃×C₁₁⋊C₅	semidirect
77. C₁₁	C₅×#10596868	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₁⋊C₅×#3862	2
C₇×Dic₇×C₁₁⋊C₅	3
C₁₁×#10596868	5
C₅×#10596868	11
Dic₃×C₁₁⋊C₅	49

Subgroups — C11⋊C5×#10596868 #44568456

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁⋊C₅×#10596868 #44568456