Subgroups — C₁₁⋊C₅×#498 #72249019

Order 3520.

196 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄⋊Q₈×C₁₁⋊C₅	C₂	1	2	yes	maximal
2	#106×C₁₁⋊C₅	C₂	1	4	yes	maximal
3	C₄×C₈×C₁₁⋊C₅	C₂	1	1	yes	maximal, characteristic
4	C₂×Q₈×C₁₁⋊C₅	—	2	2	no	—
5	C₂×C₈×C₁₁⋊C₅	C₂²	1	2	yes	—
6	C₄⋊C₄×C₁₁⋊C₅	—	2	2	no	—
7	C₄⋊C₄×C₁₁⋊C₅	C₂²	1	4	yes	—
8	C₄²×C₁₁⋊C₅	C₂²	1	1	yes	characteristic
9	C₁₁×#498	C₅	1	1	yes	maximal, characteristic, complemented, Hall
10	Q₈×C₁₁⋊C₅	—	4	4	no	—
11	C₂×C₄×C₁₁⋊C₅	—	2	4	no	—
12	C₂×C₄×C₁₁⋊C₅	D₄	1	2	yes	—
13	C₂×C₄×C₁₁⋊C₅	C₂³	1	1	yes	characteristic
14	C₈×C₁₁⋊C₅	Q₈	1	4	yes	complemented
15	C₁₁×C₄⋊Q₈	C₂×C₅	1	2	yes	—
16	C₁₁×#106	C₂×C₅	1	4	yes	—
17	C₄×C₈×C₁₁	C₂×C₅	1	1	yes	characteristic
18	C₅×#498	—	11	1	no	maximal, Hall
19	C₂²×C₁₁⋊C₅	C₂×D₄	1	1	yes	characteristic
20	C₄×C₁₁⋊C₅	—	4	4	no	—
21	C₄×C₁₁⋊C₅	SD₁₆	1	4	yes	—
22	C₄×C₁₁⋊C₅	C₂×Q₈	1	2	yes	—
23	C₂×Q₈×C₁₁	—	2	2	no	—
24	C₂×C₈×C₁₁	C₂²×C₅	1	2	yes	—
25	C₁₁×C₄⋊C₄	—	2	2	no	—
26	C₁₁×C₄⋊C₄	C₂²×C₅	1	4	yes	—
27	C₄²×C₁₁	C₂²×C₅	1	1	yes	characteristic
28	C₅×C₄⋊Q₈	—	11	2	no	—
29	C₅×#106	—	11	4	no	—
30	C₄×C₅×C₈	—	11	1	no	—
31	C₂×C₁₁⋊C₅	C₄⋊Q₈	1	1	yes	characteristic
32	C₂×C₁₁⋊C₅	C₂×SD₁₆	1	2	yes	—
33	Q₈×C₁₁	—	4	4	no	—
34	C₂×C₄×C₁₁	—	2	4	no	—
35	C₂×C₄×C₁₁	C₅×D₄	1	2	yes	—
36	C₂×C₄×C₁₁	C₂³×C₅	1	1	yes	characteristic
37	C₈×C₁₁	C₅×Q₈	1	4	yes	complemented
38	C₂×C₅×Q₈	—	22	2	no	—
39	C₂×C₅×C₈	—	11	2	no	—
40	C₅×C₄⋊C₄	—	11	4	no	—
41	C₅×C₄⋊C₄	—	22	2	no	—
42	C₄²×C₅	—	11	1	no	—
43	#498	C₁₁⋊C₅	1	1	yes	characteristic, direct product factor, Sylow
44	C₁₁⋊C₅	#498	1	1	yes	characteristic, direct product factor, Hall
45	C₂²×C₁₁	C₂×C₅×D₄	1	1	yes	characteristic
46	C₄×C₁₁	—	4	4	no	—
47	C₄×C₁₁	C₅×SD₁₆	1	4	yes	—
48	C₄×C₁₁	C₂×C₅×Q₈	1	2	yes	—
49	C₅×Q₈	—	44	4	no	—
50	C₂×C₄×C₅	—	11	2	no	—
51	C₂×C₄×C₅	—	11	1	no	—
52	C₂×C₄×C₅	—	22	4	no	—
53	C₅×C₈	—	11	4	no	—
54	C₄⋊Q₈	C₂×C₁₁⋊C₅	1	2	yes	—
55	#106	C₂×C₁₁⋊C₅	1	4	yes	—
56	C₄×C₈	C₂×C₁₁⋊C₅	1	1	yes	characteristic
57	C₂×C₁₁	C₅×C₄⋊Q₈	1	1	yes	characteristic
58	C₂×C₁₁	C₂×C₅×SD₁₆	1	2	yes	—
59	C₂²×C₅	—	11	1	no	—
60	C₄×C₅	—	11	4	no	—
61	C₄×C₅	—	11	2	no	—
62	C₄×C₅	—	44	4	no	—
63	C₂×Q₈	—	2	2	no	—
64	C₂×C₈	C₂²×C₁₁⋊C₅	1	2	yes	—
65	C₄⋊C₄	—	2	2	no	—
66	C₄⋊C₄	C₂²×C₁₁⋊C₅	1	4	yes	—
67	C₄²	C₂²×C₁₁⋊C₅	1	1	yes	characteristic
68	C₁₁	C₅×#498	1	1	yes	characteristic, complemented, Sylow
69	C₂×C₅	—	11	1	no	—
70	C₂×C₅	—	11	2	no	—
71	Q₈	—	4	4	no	—
72	C₂×C₄	—	2	4	no	—
73	C₂×C₄	D₄×C₁₁⋊C₅	1	2	yes	—
74	C₂×C₄	C₂³×C₁₁⋊C₅	1	1	yes	characteristic
75	C₈	Q₈×C₁₁⋊C₅	1	4	yes	complemented
76	C₅	—	11	1	no	Sylow
77	C₂²	C₂×D₄×C₁₁⋊C₅	1	1	yes	characteristic
78	C₄	—	4	4	no	—
79	C₄	SD₁₆×C₁₁⋊C₅	1	4	yes	—
80	C₄	C₂×Q₈×C₁₁⋊C₅	1	2	yes	—
81	C₂	C₄⋊Q₈×C₁₁⋊C₅	1	1	yes	characteristic
82	C₂	C₂×SD₁₆×C₁₁⋊C₅	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂×D₄×C₁₁⋊C₅
commutator, cosocle	C₂×C₄×C₁₁	C₂³×C₅
Frattini	C₂×C₄	C₂³×C₁₁⋊C₅
Fitting	C₁₁×#498	C₅
socle	C₂²×C₁₁	C₂×C₅×D₄
prime radical	C₂²×C₁₁⋊C₅	C₂×D₄
hypercenter	#498	C₁₁⋊C₅
hypocenter	C₁₁	C₅×#498
LCS	G ▷ C₂×C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #498

Complements

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

N	H ≅ G/N	type
9. C₁₁×#498	C₅	semidirect
14. C₈×C₁₁⋊C₅	Q₈	semidirect
37. C₈×C₁₁	C₅×Q₈	semidirect
43. #498	C₁₁⋊C₅	direct (N × H)
44. C₁₁⋊C₅	#498	direct (N × H)
68. C₁₁	C₅×#498	semidirect
75. C₈	Q₈×C₁₁⋊C₅	semidirect

Maximal subgroups

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

subgroup	index
C₄⋊Q₈×C₁₁⋊C₅	2
#106×C₁₁⋊C₅	2
C₄×C₈×C₁₁⋊C₅	2
C₁₁×#498	5
C₅×#498	11

Subgroups — C11⋊C5×#498 #72249019

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁⋊C₅×#498 #72249019