Subgroups — C₁₁×#12514 #14589707

Order 2816.

246 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×#2241	C₂	1	4	yes	maximal
2	C₁₁×#1713	C₂	1	1	yes	maximal, characteristic
3	C₁₁×#1710	C₂	1	1	yes	maximal, characteristic
4	C₁₁×#1311	C₂	1	1	yes	maximal, characteristic
5	C₁₁×#500	—	2	2	no	—
6	C₁₁×#500	C₂²	1	2	yes	—
7	C₁₁×#494	C₂²	1	2	yes	—
8	C₁₁×#487	—	2	2	no	—
9	C₁₁×#358	—	2	8	no	—
10	C₄×C₁₁×C₁₆	C₂²	1	2	yes	—
11	C₈²×C₁₁	C₂²	1	1	yes	characteristic
12	C₂×C₁₁×Q₁₆	—	2	4	no	—
13	C₁₁×C₄⋊Q₈	—	2	2	no	—
14	C₁₁×C₄⋊Q₈	—	2	2	no	—
15	C₂×C₁₁×C₁₆	D₄	1	4	yes	—
16	C₁₁×#107	—	2	4	no	—
17	C₁₁×#107	—	4	4	no	—
18	C₁₁×#103	—	4	4	no	—
19	C₄×C₈×C₁₁	D₄	1	2	yes	—
20	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
21	#12514	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
22	C₂×Q₈×C₁₁	—	4	2	no	—
23	C₂×Q₈×C₁₁	—	4	2	no	—
24	C₁₁×Q₁₆	—	4	8	no	—
25	C₂×C₈×C₁₁	D₈	1	4	yes	—
26	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
27	C₁₁×C₄⋊C₄	—	4	2	no	—
28	C₁₁×C₄⋊C₄	—	4	2	no	—
29	C₁₁×C₄⋊C₄	—	4	4	no	—
30	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
31	C₁₁×C₁₆	—	2	4	no	—
32	#2241	C₂×C₁₁	1	4	yes	—
33	#1713	C₂×C₁₁	1	1	yes	characteristic
34	#1710	C₂×C₁₁	1	1	yes	characteristic
35	#1311	C₂×C₁₁	1	1	yes	characteristic
36	Q₈×C₁₁	—	8	4	no	—
37	Q₈×C₁₁	—	8	4	no	—
38	C₂×C₄×C₁₁	—	8	2	no	—
39	C₂×C₄×C₁₁	—	8	2	no	—
40	C₂×C₄×C₁₁	#127	1	1	yes	characteristic
41	C₂×C₄×C₁₁	C₂×D₈	1	2	yes	—
42	C₈×C₁₁	—	2	4	no	—
43	C₈×C₁₁	#135	1	4	yes	—
44	#500	—	2	2	no	—
45	#500	C₂²×C₁₁	1	2	yes	—
46	#494	C₂²×C₁₁	1	2	yes	—
47	#487	—	2	2	no	—
48	#358	—	2	8	no	—
49	C₄×C₁₆	C₂²×C₁₁	1	2	yes	—
50	C₈²	C₂²×C₁₁	1	1	yes	characteristic
51	C₂²×C₁₁	#493	1	1	yes	characteristic
52	C₄×C₁₁	—	16	2	no	—
53	C₄×C₁₁	—	16	2	no	—
54	C₄×C₁₁	#495	1	2	yes	—
55	C₄×C₁₁	#510	1	4	yes	—
56	C₂×Q₁₆	—	2	4	no	—
57	C₄⋊Q₈	—	2	2	no	—
58	C₄⋊Q₈	—	2	2	no	—
59	C₂×C₁₆	D₄×C₁₁	1	4	yes	—
60	#107	—	2	4	no	—
61	#107	—	4	4	no	—
62	#103	—	4	4	no	—
63	C₄×C₈	D₄×C₁₁	1	2	yes	—
64	C₄×C₈	C₂³×C₁₁	1	1	yes	characteristic
65	C₂×C₁₁	#1709	1	1	yes	characteristic
66	C₂×C₁₁	#2251	1	2	yes	—
67	C₂×Q₈	—	4	2	no	—
68	C₂×Q₈	—	4	2	no	—
69	Q₁₆	—	4	8	no	—
70	C₂×C₈	C₁₁×D₈	1	4	yes	—
71	C₂×C₈	C₂×D₄×C₁₁	1	2	yes	—
72	C₄⋊C₄	—	4	2	no	—
73	C₄⋊C₄	—	4	2	no	—
74	C₄⋊C₄	—	4	4	no	—
75	C₄²	C₂×D₄×C₁₁	1	1	yes	characteristic
76	C₁₆	—	2	4	no	—
77	C₁₁	#12514	1	1	yes	characteristic, direct product factor, Sylow
78	Q₈	—	8	4	no	—
79	Q₈	—	8	4	no	—
80	C₂×C₄	—	8	2	no	—
81	C₂×C₄	—	8	2	no	—
82	C₂×C₄	C₁₁×#127	1	1	yes	characteristic
83	C₂×C₄	C₂×C₁₁×D₈	1	2	yes	—
84	C₈	—	2	4	no	—
85	C₈	C₁₁×#135	1	4	yes	—
86	C₂²	C₁₁×#493	1	1	yes	characteristic
87	C₄	—	16	2	no	—
88	C₄	—	16	2	no	—
89	C₄	C₁₁×#495	1	2	yes	—
90	C₄	C₁₁×#510	1	4	yes	—
91	C₂	C₁₁×#1709	1	1	yes	characteristic
92	C₂	C₁₁×#2251	1	2	yes	—

	subgroup	G/H
center, socle, prime radical	C₂²×C₁₁	#493
commutator, Frattini, cosocle	C₄×C₈	C₂³×C₁₁
LCS	G ▷ C₄×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₁ ◁ C₄²×C₁₁ ◁ C₈²×C₁₁ ◁ G

Complements

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

N	H ≅ G/N	type
21. #12514	C₁₁	direct (N × H)
77. C₁₁	#12514	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×#2241	2
C₁₁×#1713	2
C₁₁×#1710	2
C₁₁×#1311	2
#12514	11

Subgroups — C11×#12514 #14589707

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#12514 #14589707