Subgroups — #14641453

Order 2816.

78 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₁₁⋊C₃₂	C₂	1	1	yes	maximal, characteristic
2	#13066692	C₂	1	1	yes	maximal, characteristic
3	C₁₁×#1373	C₂	1	1	yes	maximal, characteristic
4	C₁₁×#364	—	2	1	no	—
5	C₄×C₁₁×C₁₆	C₂²	1	1	yes	characteristic
6	C₂×C₁₁⋊C₃₂	C₄	1	1	yes	characteristic
7	C₂×C₁₁⋊C₃₂	C₄	1	1	yes	characteristic
8	#10622101	—	2	1	no	—
9	C₁₁×M₃₂	—	4	1	no	—
10	C₂×C₁₁×C₁₆	C₂×C₄	1	1	yes	characteristic
11	C₂×C₁₁×C₁₆	Q₈	1	1	yes	characteristic
12	C₄×C₈×C₁₁	D₄	1	1	yes	characteristic
13	#66876	—	4	1	no	—
14	C₁₁⋊C₃₂	—	2	1	no	—
15	C₁₁⋊C₃₂	C₈	1	2	yes	—
16	#7462	—	11	1	no	maximal, Sylow
17	C₂×C₈×C₁₁	C₄⋊C₄	1	1	yes	characteristic
18	C₂×C₈×C₁₁	D₈	1	1	yes	characteristic
19	C₄²×C₁₁	Q₁₆	1	1	yes	characteristic
20	C₁₁×C₁₆	—	2	1	no	—
21	C₁₁×C₁₆	—	8	1	no	—
22	C₁₁×C₁₆	C₂×C₈	1	1	yes	characteristic
23	C₁₁×C₁₆	M₁₆	1	1	yes	characteristic
24	C₁₁⋊C₁₆	—	8	1	no	—
25	C₄×C₃₂	—	11	1	no	—
26	#1373	—	11	1	no	—
27	#1373	D₁₁	1	1	yes	characteristic
28	C₂×C₄×C₁₁	—	2	1	no	—
29	C₂×C₄×C₁₁	#107	1	1	yes	characteristic
30	C₈×C₁₁	C₄⋊C₈	1	1	yes	characteristic
31	C₈×C₁₁	#108	1	1	yes	characteristic
32	C₈×C₁₁	D₁₆	1	1	yes	characteristic
33	C₈×C₁₁	Q₃₂	1	1	yes	characteristic
34	C₂×C₃₂	—	11	1	no	—
35	C₂×C₃₂	—	11	1	no	—
36	#364	—	2	1	no	—
37	#364	—	22	1	no	—
38	C₄×C₁₆	C₂×D₁₁	1	1	yes	characteristic
39	C₂²×C₁₁	#368	1	1	yes	characteristic
40	C₄×C₁₁	—	2	2	no	—
41	C₄×C₁₁	#335	1	1	yes	characteristic
42	C₄×C₁₁	#366	1	1	yes	characteristic
43	M₃₂	—	4	1	no	—
44	M₃₂	—	44	1	no	—
45	C₂×C₁₆	Dic₂₂	1	1	yes	characteristic
46	C₂×C₁₆	C₄×D₁₁	1	1	yes	characteristic
47	C₄×C₈	C₂²⋊D₁₁	1	1	yes	characteristic
48	C₃₂	—	11	2	no	—
49	C₃₂	—	22	1	no	—
50	C₂×C₁₁	—	2	1	no	—
51	C₂×C₁₁	#1371	1	1	yes	characteristic
52	C₂×C₈	Dic₁₁⋊C₄	1	1	yes	characteristic
53	C₂×C₈	#4323	1	1	yes	characteristic
54	C₄²	#4326	1	1	yes	characteristic
55	C₁₆	—	2	1	no	—
56	C₁₆	—	8	1	no	—
57	C₁₆	—	88	1	no	—
58	C₁₆	C₈×D₁₁	1	1	yes	characteristic
59	C₁₆	#4313	1	1	yes	characteristic
60	C₁₁	#7462	1	1	yes	characteristic, complemented, Sylow
61	C₂×C₄	—	2	1	no	—
62	C₂×C₄	#66871	1	1	yes	characteristic
63	C₈	Dic₁₁⋊C₈	1	1	yes	characteristic
64	C₈	#66886	1	1	yes	characteristic
65	C₈	#66890	1	1	yes	characteristic
66	C₈	#66893	1	1	yes	characteristic
67	C₂²	#10622131	1	1	yes	characteristic
68	C₄	—	2	2	no	—
69	C₄	#10622117	1	1	yes	characteristic
70	C₄	#10622127	1	1	yes	characteristic
71	C₂	—	2	1	no	—
72	C₂	#13066687	1	1	yes	characteristic

	subgroup	G/H
center	C₈	#66890
commutator	C₁₁×C₁₆	C₂×C₈
Frattini	C₄×C₁₆	C₂×D₁₁
Fitting	C₁₁×#1373	C₂
socle	C₂×C₁₁	#1371
prime radical	C₂²×C₁₁	#368
cosocle	C₄×C₁₁×C₁₆	C₂²
hypercenter	#1373	D₁₁
hypocenter	C₁₁	#7462
LCS	G ▷ C₁₁×C₁₆ ▷ C₈×C₁₁ ▷ C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₈ ◁ C₂×C₈ ◁ C₄×C₈ ◁ C₄×C₁₆ ◁ #1373

Complements

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

N	H ≅ G/N	type
60. C₁₁	#7462	semidirect

Maximal subgroups

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

subgroup	index
C₄×C₁₁⋊C₃₂	2
#13066692	2
C₁₁×#1373	2
#7462	11