Subgroups — #14641448

Order 2816.

92 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13066814	C₂	1	2	yes	maximal
2	C₈×C₁₁×C₁₆	C₂	1	1	yes	maximal, characteristic
3	C₄×C₁₁×C₁₆	C₄	1	1	yes	characteristic
4	C₄×C₁₁×C₁₆	C₂²	1	1	yes	characteristic
5	C₈²×C₁₁	C₄	1	1	yes	characteristic
6	#10622137	—	2	2	no	—
7	C₂×C₁₁×C₁₆	C₈	1	1	yes	characteristic
8	C₂×C₁₁×C₁₆	C₈	1	1	yes	characteristic
9	C₂×C₁₁×C₁₆	D₄	1	1	yes	characteristic
10	C₂×C₁₁×C₁₆	Q₈	1	1	yes	characteristic
11	C₄×C₈×C₁₁	—	2	1	no	—
12	C₄×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
13	C₁₁⋊C₃₂	—	4	2	no	—
14	#7459	—	11	1	no	maximal, Sylow
15	C₂×C₈×C₁₁	—	2	2	no	—
16	C₂×C₈×C₁₁	C₄⋊C₄	1	1	yes	characteristic
17	C₂×C₈×C₁₁	C₂×C₈	1	1	yes	characteristic
18	C₄²×C₁₁	M₁₆	1	1	yes	characteristic
19	C₁₁×C₁₆	—	2	1	no	—
20	C₁₁×C₁₆	—	2	1	no	—
21	C₁₁×C₁₆	C₁₆	1	2	yes	—
22	C₁₁×C₁₆	D₈	1	1	yes	characteristic
23	C₁₁×C₁₆	Q₁₆	1	1	yes	characteristic
24	#1422	—	11	2	no	—
25	C₈×C₁₆	D₁₁	1	1	yes	characteristic
26	C₂×C₄×C₁₁	—	2	1	no	—
27	C₂×C₄×C₁₁	C₄⋊C₈	1	1	yes	characteristic
28	C₈×C₁₁	—	2	4	no	—
29	C₈×C₁₁	#107	1	1	yes	characteristic
30	C₈×C₁₁	#108	1	1	yes	characteristic
31	C₈×C₁₁	C₂×C₁₆	1	1	yes	characteristic
32	C₈×C₁₁	M₃₂	1	1	yes	characteristic
33	M₆₄	—	22	2	no	—
34	C₄×C₁₆	Dic₁₁	1	1	yes	characteristic
35	C₄×C₁₆	C₂×D₁₁	1	1	yes	characteristic
36	C₈²	Dic₁₁	1	1	yes	characteristic
37	C₂²×C₁₁	#364	1	1	yes	characteristic
38	C₄×C₁₁	—	2	2	no	—
39	C₄×C₁₁	#335	1	1	yes	characteristic
40	C₄×C₁₁	C₄⋊C₁₆	1	1	yes	characteristic
41	C₂×C₁₆	C₁₁⋊C₈	1	1	yes	characteristic
42	C₂×C₁₆	C₁₁⋊C₈	1	1	yes	characteristic
43	C₂×C₁₆	Dic₂₂	1	1	yes	characteristic
44	C₂×C₁₆	D₄₄	1	1	yes	characteristic
45	C₄×C₈	—	2	1	no	—
46	C₄×C₈	C₂×Dic₁₁	1	1	yes	characteristic
47	C₃₂	—	44	2	no	—
48	C₂×C₁₁	—	2	1	no	—
49	C₂×C₁₁	#1370	1	1	yes	characteristic
50	C₂×C₈	—	2	2	no	—
51	C₂×C₈	C₂×C₁₁⋊C₈	1	1	yes	characteristic
52	C₂×C₈	C₄⋊Dic₁₁	1	1	yes	characteristic
53	C₄²	#4318	1	1	yes	characteristic
54	C₁₆	—	2	1	no	—
55	C₁₆	—	2	1	no	—
56	C₁₆	C₁₁⋊C₁₆	1	2	yes	—
57	C₁₆	D₈₈	1	1	yes	characteristic
58	C₁₆	Dic₄₄	1	1	yes	characteristic
59	C₁₁	#7459	1	1	yes	characteristic, complemented, Sylow
60	C₂×C₄	—	2	1	no	—
61	C₂×C₄	C₄⋊(C₁₁⋊C₈)	1	1	yes	characteristic
62	C₈	—	2	4	no	—
63	C₈	C₂×C₁₁⋊C₁₆	1	1	yes	characteristic
64	C₈	#66876	1	1	yes	characteristic
65	C₈	#66882	1	1	yes	characteristic
66	C₈	#66883	1	1	yes	characteristic
67	C₂²	#10622101	1	1	yes	characteristic
68	C₄	—	2	2	no	—
69	C₄	#10622096	1	1	yes	characteristic
70	C₄	C₄⋊(C₁₁⋊C₁₆)	1	1	yes	characteristic
71	C₂	—	2	1	no	—
72	C₂	#13066686	1	1	yes	characteristic

	subgroup	G/H
center	C₁₆	D₈₈
commutator	C₈×C₁₁	C₂×C₁₆
Frattini	C₄×C₁₆	C₂×D₁₁
Fitting	C₈×C₁₁×C₁₆	C₂
socle	C₂×C₁₁	#1370
prime radical	C₂²×C₁₁	#364
cosocle	C₄×C₁₁×C₁₆	C₂²
hypercenter	C₈×C₁₆	D₁₁
hypocenter	C₁₁	#7459
LCS	G ▷ C₈×C₁₁ ▷ C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₁₆ ◁ C₂×C₁₆ ◁ C₄×C₁₆ ◁ C₈×C₁₆

Complements

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

N	H ≅ G/N	type
59. C₁₁	#7459	semidirect

Maximal subgroups

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

subgroup	index
#13066814	2
C₈×C₁₁×C₁₆	2
#7459	11