Subgroups — C₁₁×#2241 #13065079

Order 1408.

140 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×#500	C₂	1	1	yes	maximal, characteristic
2	C₁₁×#494	C₂	1	1	yes	maximal, characteristic
3	C₁₁×#358	C₂	1	4	yes	maximal
4	C₄×C₁₁×C₁₆	C₂	1	1	yes	maximal, characteristic
5	C₂×C₁₁×Q₁₆	—	2	1	no	—
6	C₂×C₁₁×Q₁₆	C₂²	1	2	yes	—
7	C₁₁×C₄⋊Q₈	—	2	1	no	—
8	C₁₁×C₄⋊Q₈	—	2	1	no	—
9	C₂×C₁₁×C₁₆	C₂²	1	2	yes	—
10	C₁₁×#107	—	2	1	no	—
11	C₁₁×#107	C₂²	1	2	yes	—
12	C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
13	C₂×Q₈×C₁₁	—	2	2	no	—
14	C₂×Q₈×C₁₁	—	4	1	no	—
15	C₁₁×Q₁₆	—	2	4	no	—
16	C₁₁×Q₁₆	—	4	2	no	—
17	C₂×C₈×C₁₁	D₄	1	1	yes	characteristic
18	C₂×C₈×C₁₁	C₂³	1	1	yes	characteristic
19	C₁₁×C₄⋊C₄	—	2	2	no	—
20	C₁₁×C₄⋊C₄	—	4	1	no	—
21	C₁₁×C₄⋊C₄	—	4	1	no	—
22	C₁₁×C₄⋊C₄	—	4	1	no	—
23	C₄²×C₁₁	D₄	1	1	yes	characteristic
24	C₁₁×C₁₆	—	2	2	no	—
25	#2241	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
26	Q₈×C₁₁	—	4	2	no	—
27	Q₈×C₁₁	—	4	2	no	—
28	Q₈×C₁₁	—	8	2	no	—
29	C₂×C₄×C₁₁	—	4	2	no	—
30	C₂×C₄×C₁₁	—	4	2	no	—
31	C₂×C₄×C₁₁	D₈	1	1	yes	characteristic
32	C₂×C₄×C₁₁	D₈	1	1	yes	characteristic
33	C₂×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
34	C₈×C₁₁	SD₁₆	1	2	yes	—
35	C₈×C₁₁	#41	1	2	yes	—
36	#500	C₂×C₁₁	1	1	yes	characteristic
37	#494	C₂×C₁₁	1	1	yes	characteristic
38	#358	C₂×C₁₁	1	4	yes	—
39	C₄×C₁₆	C₂×C₁₁	1	1	yes	characteristic
40	C₂²×C₁₁	C₂×D₈	1	1	yes	characteristic
41	C₄×C₁₁	—	8	2	no	—
42	C₄×C₁₁	—	8	2	no	—
43	C₄×C₁₁	SD₃₂	1	2	yes	—
44	C₄×C₁₁	Q₃₂	1	2	yes	—
45	C₄×C₁₁	#124	1	1	yes	characteristic
46	C₄×C₁₁	C₂×SD₁₆	1	1	yes	characteristic
47	C₂×Q₁₆	—	2	1	no	—
48	C₂×Q₁₆	C₂²×C₁₁	1	2	yes	—
49	C₄⋊Q₈	—	2	1	no	—
50	C₄⋊Q₈	—	2	1	no	—
51	C₂×C₁₆	C₂²×C₁₁	1	2	yes	—
52	#107	—	2	1	no	—
53	#107	C₂²×C₁₁	1	2	yes	—
54	C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
55	C₂×C₁₁	#486	1	1	yes	characteristic
56	C₂×C₁₁	C₂×SD₃₂	1	1	yes	characteristic
57	C₂×C₁₁	C₂×Q₃₂	1	1	yes	characteristic
58	C₂×Q₈	—	2	2	no	—
59	C₂×Q₈	—	4	1	no	—
60	Q₁₆	—	2	4	no	—
61	Q₁₆	—	4	2	no	—
62	C₂×C₈	D₄×C₁₁	1	1	yes	characteristic
63	C₂×C₈	C₂³×C₁₁	1	1	yes	characteristic
64	C₄⋊C₄	—	2	2	no	—
65	C₄⋊C₄	—	4	1	no	—
66	C₄⋊C₄	—	4	1	no	—
67	C₄⋊C₄	—	4	1	no	—
68	C₄²	D₄×C₁₁	1	1	yes	characteristic
69	C₁₆	—	2	2	no	—
70	C₁₁	#2241	1	1	yes	characteristic, direct product factor, Sylow
71	Q₈	—	4	2	no	—
72	Q₈	—	4	2	no	—
73	Q₈	—	8	2	no	—
74	C₂×C₄	—	4	2	no	—
75	C₂×C₄	—	4	2	no	—
76	C₂×C₄	C₁₁×D₈	1	1	yes	characteristic
77	C₂×C₄	C₁₁×D₈	1	1	yes	characteristic
78	C₂×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
79	C₈	C₁₁×SD₁₆	1	2	yes	—
80	C₈	C₁₁×#41	1	2	yes	—
81	C₂²	C₂×C₁₁×D₈	1	1	yes	characteristic
82	C₄	—	8	2	no	—
83	C₄	—	8	2	no	—
84	C₄	C₁₁×SD₃₂	1	2	yes	—
85	C₄	C₁₁×Q₃₂	1	2	yes	—
86	C₄	C₁₁×#124	1	1	yes	characteristic
87	C₄	C₂×C₁₁×SD₁₆	1	1	yes	characteristic
88	C₂	C₁₁×#486	1	1	yes	characteristic
89	C₂	C₂×C₁₁×SD₃₂	1	1	yes	characteristic
90	C₂	C₂×C₁₁×Q₃₂	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂²×C₁₁	C₂×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂³×C₁₁
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₁ ◁ C₄²×C₁₁ ◁ C₄×C₈×C₁₁ ◁ G

Complements

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

N	H ≅ G/N	type
25. #2241	C₁₁	direct (N × H)
70. C₁₁	#2241	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×#500	2
C₁₁×#494	2
C₁₁×#358	2
C₄×C₁₁×C₁₆	2
#2241	11

Subgroups — C11×#2241 #13065079

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#2241 #13065079