Subgroups — C₁₁×#7453 #14584646

Order 2816.

102 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×#2254	C₂	1	1	yes	maximal, characteristic
2	C₁₁×#1422	C₂	1	1	yes	maximal, characteristic
3	C₁₁×#1373	C₂	1	1	yes	maximal, characteristic
4	C₁₁×#500	—	2	1	no	—
5	C₁₁×M₆₄	—	2	1	no	—
6	C₁₁×#367	—	2	1	no	—
7	C₁₁×#367	C₄	1	2	yes	—
8	C₁₁×#364	—	2	1	no	—
9	C₄×C₁₁×C₁₆	C₂²	1	1	yes	characteristic
10	C₁₁×C₄⋊Q₈	—	4	1	no	—
11	C₁₁×M₃₂	—	4	1	no	—
12	C₂×C₁₁×C₁₆	C₂×C₄	1	1	yes	characteristic
13	C₂×C₁₁×C₁₆	D₄	1	1	yes	characteristic
14	C₁₁×#107	—	2	2	no	—
15	C₁₁×#107	—	4	1	no	—
16	C₄×C₈×C₁₁	D₄	1	1	yes	characteristic
17	C₁₁×C₃₂	—	4	1	no	—
18	#7453	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
19	C₂×Q₈×C₁₁	—	8	1	no	—
20	C₂×C₈×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
21	C₂×C₈×C₁₁	D₈	1	1	yes	characteristic
22	C₁₁×C₄⋊C₄	—	4	2	no	—
23	C₁₁×C₄⋊C₄	—	8	1	no	—
24	C₄²×C₁₁	SD₁₆	1	1	yes	characteristic
25	C₁₁×C₁₆	—	2	1	no	—
26	C₁₁×C₁₆	—	8	1	no	—
27	C₁₁×C₁₆	SD₁₆	1	1	yes	characteristic
28	C₁₁×C₁₆	Q₁₆	1	1	yes	characteristic
29	#2254	C₂×C₁₁	1	1	yes	characteristic
30	#1422	C₂×C₁₁	1	1	yes	characteristic
31	#1373	C₂×C₁₁	1	1	yes	characteristic
32	Q₈×C₁₁	—	16	2	no	—
33	C₂×C₄×C₁₁	—	2	1	no	—
34	C₂×C₄×C₁₁	—	8	2	no	—
35	C₂×C₄×C₁₁	#102	1	1	yes	characteristic
36	C₈×C₁₁	#101	1	1	yes	characteristic
37	C₈×C₁₁	#103	1	1	yes	characteristic
38	C₈×C₁₁	SD₃₂	1	1	yes	characteristic
39	C₈×C₁₁	Q₃₂	1	1	yes	characteristic
40	#500	—	2	1	no	—
41	M₆₄	—	2	1	no	—
42	#367	—	2	1	no	—
43	#367	C₄×C₁₁	1	2	yes	—
44	#364	—	2	1	no	—
45	C₄×C₁₆	C₂²×C₁₁	1	1	yes	characteristic
46	C₂²×C₁₁	#361	1	1	yes	characteristic
47	C₄×C₁₁	—	2	2	no	—
48	C₄×C₁₁	—	16	2	no	—
49	C₄×C₁₁	#332	1	1	yes	characteristic
50	C₄×C₁₁	#358	1	1	yes	characteristic
51	C₄⋊Q₈	—	4	1	no	—
52	M₃₂	—	4	1	no	—
53	C₂×C₁₆	C₂×C₄×C₁₁	1	1	yes	characteristic
54	C₂×C₁₆	D₄×C₁₁	1	1	yes	characteristic
55	#107	—	2	2	no	—
56	#107	—	4	1	no	—
57	C₄×C₈	D₄×C₁₁	1	1	yes	characteristic
58	C₃₂	—	4	1	no	—
59	C₂×C₁₁	—	2	1	no	—
60	C₂×C₁₁	#1365	1	1	yes	characteristic
61	C₂×Q₈	—	8	1	no	—
62	C₂×C₈	C₁₁×C₂²⋊C₄	1	1	yes	characteristic
63	C₂×C₈	C₁₁×D₈	1	1	yes	characteristic
64	C₄⋊C₄	—	4	2	no	—
65	C₄⋊C₄	—	8	1	no	—
66	C₄²	C₁₁×SD₁₆	1	1	yes	characteristic
67	C₁₆	—	2	1	no	—
68	C₁₆	—	8	1	no	—
69	C₁₆	C₁₁×SD₁₆	1	1	yes	characteristic
70	C₁₆	C₁₁×Q₁₆	1	1	yes	characteristic
71	C₁₁	#7453	1	1	yes	characteristic, direct product factor, Sylow
72	Q₈	—	16	2	no	—
73	C₂×C₄	—	2	1	no	—
74	C₂×C₄	—	8	2	no	—
75	C₂×C₄	C₁₁×#102	1	1	yes	characteristic
76	C₈	C₁₁×#101	1	1	yes	characteristic
77	C₈	C₁₁×#103	1	1	yes	characteristic
78	C₈	C₁₁×SD₃₂	1	1	yes	characteristic
79	C₈	C₁₁×Q₃₂	1	1	yes	characteristic
80	C₂²	C₁₁×#361	1	1	yes	characteristic
81	C₄	—	2	2	no	—
82	C₄	—	16	2	no	—
83	C₄	C₁₁×#332	1	1	yes	characteristic
84	C₄	C₁₁×#358	1	1	yes	characteristic
85	C₂	—	2	1	no	—
86	C₂	C₁₁×#1365	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₁₁	#1365
commutator	C₂×C₁₆	C₂×C₄×C₁₁
Frattini, cosocle	C₄×C₁₆	C₂²×C₁₁
prime radical	C₂²×C₁₁	#361
LCS	G ▷ C₂×C₁₆ ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₁ ◁ C₂×C₄×C₁₁ ◁ C₄×C₈×C₁₁ ◁ C₄×C₁₁×C₁₆ ◁ G

Complements

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

N	H ≅ G/N	type
18. #7453	C₁₁	direct (N × H)
71. C₁₁	#7453	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×#2254	2
C₁₁×#1422	2
C₁₁×#1373	2
#7453	11

Subgroups — C11×#7453 #14584646

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#7453 #14584646