Subgroups — #14641455

Order 2816.

84 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13066750	C₂	1	1	yes	maximal, characteristic
2	#13066690	C₂	1	1	yes	maximal, characteristic
3	C₁₁×#1372	C₂	1	1	yes	maximal, characteristic
4	C₄×C₁₁×C₁₆	C₂²	1	1	yes	characteristic
5	C₁₁×#335	—	2	1	no	—
6	C₂×C₁₁⋊C₃₂	C₄	1	1	yes	characteristic
7	C₂×C₁₁⋊C₃₂	C₄	1	1	yes	characteristic
8	#10622096	—	2	1	no	—
9	C₂×C₁₁×C₁₆	C₂×C₄	1	1	yes	characteristic
10	C₂×C₁₁×C₁₆	Q₈	1	1	yes	characteristic
11	C₁₁×C₄⋊C₈	—	4	1	no	—
12	C₄×C₈×C₁₁	D₄	1	1	yes	characteristic
13	C₄⋊(C₁₁⋊C₈)	—	4	1	no	—
14	C₁₁⋊C₃₂	—	2	1	no	—
15	C₁₁⋊C₃₂	C₈	1	2	yes	complemented
16	#7463	—	11	1	no	maximal, Sylow
17	C₂×C₈×C₁₁	—	8	1	no	—
18	C₂×C₈×C₁₁	C₄⋊C₄	1	1	yes	characteristic
19	C₂×C₈×C₁₁	Q₁₆	1	1	yes	characteristic
20	C₄²×C₁₁	D₈	1	1	yes	characteristic
21	C₂×C₁₁⋊C₈	—	8	1	no	—
22	C₁₁×C₁₆	—	2	1	no	—
23	C₁₁×C₁₆	C₂×C₈	1	1	yes	characteristic
24	C₁₁×C₁₆	M₁₆	1	1	yes	characteristic
25	#1397	—	11	1	no	—
26	#1372	—	11	1	no	—
27	#1372	D₁₁	1	1	yes	characteristic
28	C₂×C₄×C₁₁	#107	1	1	yes	characteristic
29	C₂×C₄×C₁₁	SD₃₂	1	1	yes	characteristic
30	C₂×C₄×C₁₁	SD₃₂	1	1	yes	characteristic
31	C₈×C₁₁	—	2	1	no	—
32	C₈×C₁₁	—	16	1	no	—
33	C₈×C₁₁	C₄⋊C₈	1	1	yes	characteristic
34	C₈×C₁₁	#108	1	1	yes	characteristic
35	C₁₁⋊C₈	—	16	1	no	—
36	C₂×C₃₂	—	11	1	no	—
37	C₂×C₃₂	—	11	1	no	—
38	C₄×C₁₆	C₂×D₁₁	1	1	yes	characteristic
39	#335	—	2	1	no	—
40	#335	—	22	1	no	—
41	C₂²×C₁₁	#367	1	1	yes	characteristic
42	C₄×C₁₁	—	2	1	no	—
43	C₄×C₁₁	—	2	1	no	—
44	C₄×C₁₁	#335	1	1	yes	characteristic
45	C₄×C₁₁	#368	1	1	yes	characteristic
46	C₂×C₁₆	Dic₂₂	1	1	yes	characteristic
47	C₂×C₁₆	C₄×D₁₁	1	1	yes	characteristic
48	C₄⋊C₈	—	4	1	no	—
49	C₄⋊C₈	—	44	1	no	—
50	C₄×C₈	C₂²⋊D₁₁	1	1	yes	characteristic
51	C₃₂	—	11	2	no	—
52	C₃₂	—	22	1	no	—
53	C₂×C₁₁	#1372	1	1	yes	characteristic
54	C₂×C₁₁	#1426	1	1	yes	characteristic
55	C₂×C₁₁	#1426	1	1	yes	characteristic
56	C₂×C₈	—	8	1	no	—
57	C₂×C₈	—	88	1	no	—
58	C₂×C₈	Dic₁₁⋊C₄	1	1	yes	characteristic
59	C₂×C₈	#4326	1	1	yes	characteristic
60	C₄²	#4323	1	1	yes	characteristic
61	C₁₆	—	2	1	no	—
62	C₁₆	C₈×D₁₁	1	1	yes	characteristic
63	C₁₆	#4313	1	1	yes	characteristic
64	C₁₁	#7463	1	1	yes	characteristic, complemented, Sylow
65	C₂×C₄	#66871	1	1	yes	characteristic
66	C₂×C₄	#66891	1	1	yes	characteristic
67	C₂×C₄	#66892	1	1	yes	characteristic
68	C₈	—	2	1	no	—
69	C₈	—	16	1	no	—
70	C₈	—	176	1	no	—
71	C₈	Dic₁₁⋊C₈	1	1	yes	characteristic
72	C₈	#66886	1	1	yes	characteristic
73	C₂²	#10622128	1	1	yes	characteristic
74	C₄	—	2	1	no	—
75	C₄	—	2	1	no	—
76	C₄	#10622117	1	1	yes	characteristic
77	C₄	#10622131	1	1	yes	characteristic
78	C₂	#13066689	1	1	yes	characteristic
79	C₂	#13066821	1	1	yes	characteristic
80	C₂	#13066823	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#10622128
commutator	C₁₁×C₁₆	C₂×C₈
Frattini	C₄×C₁₆	C₂×D₁₁
Fitting	C₁₁×#1372	C₂
socle, prime radical	C₂²×C₁₁	#367
cosocle	C₄×C₁₁×C₁₆	C₂²
hypercenter	#1372	D₁₁
hypocenter	C₁₁	#7463
LCS	G ▷ C₁₁×C₁₆ ▷ C₈×C₁₁ ▷ C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ C₄×C₁₆ ◁ #1372

Complements

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

N	H ≅ G/N	type
15. C₁₁⋊C₃₂	C₈	semidirect
64. C₁₁	#7463	semidirect

Maximal subgroups

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

subgroup	index
#13066750	2
#13066690	2
C₁₁×#1372	2
#7463	11