Subgroups — #14640513

Order 2816.

102 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13066686	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	C₄	1	1	yes	characteristic
5	C₈²×C₁₁	C₂²	1	1	yes	characteristic
6	C₄⋊(C₁₁⋊C₁₆)	—	2	2	no	—
7	C₂×C₁₁×C₁₆	—	2	1	no	—
8	C₂×C₁₁×C₁₆	C₈	1	1	yes	characteristic
9	C₂×C₁₁×C₁₆	C₈	1	1	yes	characteristic
10	C₄×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
11	C₄×C₈×C₁₁	D₄	1	1	yes	characteristic
12	C₄×C₈×C₁₁	Q₈	1	1	yes	characteristic
13	C₂×C₁₁⋊C₁₆	—	4	2	no	—
14	#7100	—	11	1	no	maximal, Sylow
15	C₂×C₈×C₁₁	—	2	1	no	—
16	C₂×C₈×C₁₁	C₂×C₈	1	1	yes	characteristic
17	C₂×C₈×C₁₁	M₁₆	1	1	yes	characteristic
18	C₂×C₈×C₁₁	D₈	1	1	yes	characteristic
19	C₂×C₈×C₁₁	Q₁₆	1	1	yes	characteristic
20	C₄²×C₁₁	C₄⋊C₄	1	1	yes	characteristic
21	C₁₁×C₁₆	—	2	2	no	—
22	C₁₁×C₁₆	—	2	1	no	—
23	C₁₁×C₁₆	C₁₆	1	2	yes	complemented
24	C₁₁⋊C₁₆	—	8	2	no	—
25	#1370	—	11	2	no	—
26	C₈×C₁₆	D₁₁	1	1	yes	characteristic
27	C₂×C₄×C₁₁	C₄⋊C₈	1	1	yes	characteristic
28	C₂×C₄×C₁₁	#107	1	1	yes	characteristic
29	C₂×C₄×C₁₁	#108	1	1	yes	characteristic
30	C₈×C₁₁	—	2	2	no	—
31	C₈×C₁₁	—	2	1	no	—
32	C₈×C₁₁	—	2	1	no	—
33	C₈×C₁₁	C₂×C₁₆	1	1	yes	characteristic
34	C₈×C₁₁	M₃₂	1	1	yes	characteristic
35	C₈×C₁₁	D₁₆	1	1	yes	characteristic
36	C₈×C₁₁	Q₃₂	1	1	yes	characteristic
37	C₄⋊C₁₆	—	22	2	no	—
38	C₄×C₁₆	Dic₁₁	1	1	yes	characteristic
39	C₄×C₁₆	Dic₁₁	1	1	yes	characteristic
40	C₈²	C₂×D₁₁	1	1	yes	characteristic
41	C₂²×C₁₁	#335	1	1	yes	characteristic
42	C₄×C₁₁	—	2	1	no	—
43	C₄×C₁₁	C₄⋊C₁₆	1	1	yes	characteristic
44	C₄×C₁₁	#364	1	1	yes	characteristic
45	C₄×C₁₁	#366	1	1	yes	characteristic
46	C₄×C₁₁	#368	1	1	yes	characteristic
47	C₂×C₁₆	—	2	1	no	—
48	C₂×C₁₆	—	44	2	no	—
49	C₂×C₁₆	C₁₁⋊C₈	1	1	yes	characteristic
50	C₂×C₁₆	C₁₁⋊C₈	1	1	yes	characteristic
51	C₄×C₈	Dic₂₂	1	1	yes	characteristic
52	C₄×C₈	D₄₄	1	1	yes	characteristic
53	C₄×C₈	C₂×Dic₁₁	1	1	yes	characteristic
54	C₂×C₁₁	#1370	1	1	yes	characteristic
55	C₂×C₁₁	#1371	1	1	yes	characteristic
56	C₂×C₁₁	#1373	1	1	yes	characteristic
57	C₂×C₈	—	2	1	no	—
58	C₂×C₈	D₈₈	1	1	yes	characteristic
59	C₂×C₈	Dic₄₄	1	1	yes	characteristic
60	C₂×C₈	C₂×C₁₁⋊C₈	1	1	yes	characteristic
61	C₂×C₈	#4318	1	1	yes	characteristic
62	C₄²	C₄⋊Dic₁₁	1	1	yes	characteristic
63	C₁₆	—	2	2	no	—
64	C₁₆	—	2	1	no	—
65	C₁₆	—	88	2	no	—
66	C₁₆	C₁₁⋊C₁₆	1	2	yes	complemented
67	C₁₁	#7100	1	1	yes	characteristic, complemented, Sylow
68	C₂×C₄	C₄⋊(C₁₁⋊C₈)	1	1	yes	characteristic
69	C₂×C₄	#66882	1	1	yes	characteristic
70	C₂×C₄	#66883	1	1	yes	characteristic
71	C₈	—	2	2	no	—
72	C₈	—	2	1	no	—
73	C₈	—	2	1	no	—
74	C₈	D₁₇₆	1	1	yes	characteristic
75	C₈	Dic₈₈	1	1	yes	characteristic
76	C₈	C₂×C₁₁⋊C₁₆	1	1	yes	characteristic
77	C₈	#66876	1	1	yes	characteristic
78	C₂²	#10622096	1	1	yes	characteristic
79	C₄	—	2	1	no	—
80	C₄	C₄⋊(C₁₁⋊C₁₆)	1	1	yes	characteristic
81	C₄	#10622101	1	1	yes	characteristic
82	C₄	#10622142	1	1	yes	characteristic
83	C₄	#10622144	1	1	yes	characteristic
84	C₂	#13066686	1	1	yes	characteristic
85	C₂	#13066688	1	1	yes	characteristic
86	C₂	#13066692	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈	D₈₈
commutator	C₈×C₁₁	C₂×C₁₆
Frattini	C₈²	C₂×D₁₁
Fitting	C₈×C₁₁×C₁₆	C₂
socle, prime radical	C₂²×C₁₁	#335
cosocle	C₈²×C₁₁	C₂²
hypercenter	C₈×C₁₆	D₁₁
hypocenter	C₁₁	#7100
LCS	G ▷ C₈×C₁₁ ▷ C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂×C₈ ◁ C₄×C₈ ◁ C₈² ◁ C₈×C₁₆

Complements

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

N	H ≅ G/N	type
23. C₁₁×C₁₆	C₁₆	semidirect
66. C₁₆	C₁₁⋊C₁₆	semidirect
67. C₁₁	#7100	semidirect

Maximal subgroups

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

subgroup	index
#13066686	2
C₈×C₁₁×C₁₆	2
#7100	11