Subgroups — #14641454

Order 2816.

78 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13066692	C₂	1	2	yes	maximal
2	C₄×C₁₁×C₃₂	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₁×C₃₂	C₄	1	1	yes	characteristic
4	C₂×C₁₁×C₃₂	C₄	1	1	yes	characteristic
5	C₄×C₁₁×C₁₆	C₂²	1	1	yes	characteristic
6	#10622101	—	2	2	no	—
7	C₂×C₁₁×C₁₆	C₂×C₄	1	1	yes	characteristic
8	C₂×C₁₁×C₁₆	Q₈	1	1	yes	characteristic
9	C₄×C₈×C₁₁	D₄	1	1	yes	characteristic
10	#66876	—	4	2	no	—
11	C₁₁×C₃₂	—	2	1	no	—
12	C₁₁×C₃₂	C₈	1	2	yes	—
13	#7462	—	11	1	no	maximal, Sylow
14	C₂×C₈×C₁₁	C₄⋊C₄	1	1	yes	characteristic
15	C₂×C₈×C₁₁	D₈	1	1	yes	characteristic
16	C₄²×C₁₁	Q₁₆	1	1	yes	characteristic
17	C₁₁×C₁₆	—	2	1	no	—
18	C₁₁×C₁₆	C₂×C₈	1	1	yes	characteristic
19	C₁₁×C₁₆	M₁₆	1	1	yes	characteristic
20	C₁₁⋊C₁₆	—	8	2	no	—
21	C₄×C₃₂	D₁₁	1	1	yes	characteristic
22	#1373	—	11	2	no	—
23	C₂×C₄×C₁₁	—	2	1	no	—
24	C₂×C₄×C₁₁	#107	1	1	yes	characteristic
25	C₈×C₁₁	C₄⋊C₈	1	1	yes	characteristic
26	C₈×C₁₁	#108	1	1	yes	characteristic
27	C₈×C₁₁	D₁₆	1	1	yes	characteristic
28	C₈×C₁₁	Q₃₂	1	1	yes	characteristic
29	C₂×C₃₂	Dic₁₁	1	1	yes	characteristic
30	C₂×C₃₂	Dic₁₁	1	1	yes	characteristic
31	#364	—	22	2	no	—
32	C₄×C₁₆	C₂×D₁₁	1	1	yes	characteristic
33	C₂²×C₁₁	#368	1	1	yes	characteristic
34	C₄×C₁₁	—	2	2	no	—
35	C₄×C₁₁	#335	1	1	yes	characteristic
36	C₄×C₁₁	#366	1	1	yes	characteristic
37	M₃₂	—	44	2	no	—
38	C₂×C₁₆	Dic₂₂	1	1	yes	characteristic
39	C₂×C₁₆	C₂×Dic₁₁	1	1	yes	characteristic
40	C₄×C₈	D₄₄	1	1	yes	characteristic
41	C₃₂	—	2	1	no	—
42	C₃₂	C₁₁⋊C₈	1	2	yes	—
43	C₂×C₁₁	—	2	1	no	—
44	C₂×C₁₁	#1371	1	1	yes	characteristic
45	C₂×C₈	D₈₈	1	1	yes	characteristic
46	C₂×C₈	C₄⋊Dic₁₁	1	1	yes	characteristic
47	C₄²	Dic₄₄	1	1	yes	characteristic
48	C₁₆	—	2	1	no	—
49	C₁₆	—	88	2	no	—
50	C₁₆	C₂×C₁₁⋊C₈	1	1	yes	characteristic
51	C₁₆	#4318	1	1	yes	characteristic
52	C₁₁	#7462	1	1	yes	characteristic, complemented, Sylow
53	C₂×C₄	—	2	1	no	—
54	C₂×C₄	#66882	1	1	yes	characteristic
55	C₈	D₁₇₆	1	1	yes	characteristic
56	C₈	Dic₈₈	1	1	yes	characteristic
57	C₈	C₄⋊(C₁₁⋊C₈)	1	1	yes	characteristic
58	C₈	#66883	1	1	yes	characteristic
59	C₂²	#10622144	1	1	yes	characteristic
60	C₄	—	2	2	no	—
61	C₄	#10622096	1	1	yes	characteristic
62	C₄	#10622142	1	1	yes	characteristic
63	C₂	—	2	1	no	—
64	C₂	#13066688	1	1	yes	characteristic

	subgroup	G/H
center	C₈	D₁₇₆
commutator	C₁₁×C₁₆	C₂×C₈
Frattini	C₄×C₁₆	C₂×D₁₁
Fitting	C₄×C₁₁×C₃₂	C₂
socle	C₂×C₁₁	#1371
prime radical	C₂²×C₁₁	#368
cosocle	C₄×C₁₁×C₁₆	C₂²
hypercenter	C₄×C₃₂	D₁₁
hypocenter	C₁₁	#7462
LCS	G ▷ C₁₁×C₁₆ ▷ C₈×C₁₁ ▷ C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₈ ◁ C₂×C₈ ◁ C₄×C₈ ◁ C₄×C₁₆ ◁ C₄×C₃₂

Complements

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

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

Maximal subgroups

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

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