Subgroups — #14674799

Order 2816.

158 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13070890	C₂	1	2	yes	maximal
2	#13066818	C₂	1	1	yes	maximal, characteristic
3	#13066817	C₂	1	2	yes	maximal
4	C₃₂×Dic₁₁	C₂	1	1	yes	maximal, characteristic
5	C₁₁×#1424	C₂	1	1	yes	maximal, characteristic
6	#10622487	—	2	2	no	—
7	C₂×C₁₁×C₃₂	C₂²	1	1	yes	characteristic
8	C₁₁×#366	C₂²	1	2	yes	—
9	#10622142	C₂²	1	2	yes	—
10	C₁₆×Dic₁₁	C₂²	1	1	yes	characteristic
11	C₂×C₁₁⋊C₃₂	C₂²	1	1	yes	characteristic
12	#10622127	—	2	2	no	—
13	#66941	—	4	2	no	—
14	C₂×C₁₁×C₁₆	C₂³	1	1	yes	characteristic
15	C₁₁×#107	—	2	2	no	—
16	#66882	—	2	2	no	—
17	C₈×Dic₁₁	D₄	1	1	yes	characteristic
18	C₂×C₁₁⋊C₁₆	D₄	1	1	yes	characteristic
19	#66871	—	4	2	no	—
20	C₁₁×C₃₂	Q₈	1	2	yes	complemented
21	C₁₁⋊C₃₂	Q₈	1	2	yes	complemented
22	#13733	—	11	1	no	maximal, Sylow
23	C₂×Dic₂₂	—	8	2	no	—
24	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
25	C₁₁×C₄⋊C₄	—	4	2	no	—
26	C₄⋊Dic₁₁	—	4	2	no	—
27	Dic₁₁⋊C₄	—	8	2	no	—
28	C₄×Dic₁₁	D₈	1	1	yes	characteristic
29	C₂×C₁₁⋊C₈	D₈	1	1	yes	characteristic
30	C₁₁×C₁₆	C₂×Q₈	1	1	yes	characteristic
31	C₁₁×C₁₆	C₂×Q₈	1	1	yes	characteristic
32	C₁₁⋊C₁₆	Q₁₆	1	2	yes	—
33	#2252	—	11	2	no	—
34	#1424	—	11	1	no	—
35	#1424	—	11	2	no	—
36	#1424	D₁₁	1	1	yes	characteristic
37	C₄×C₃₂	—	11	1	no	—
38	C₂×C₄×C₁₁	—	8	2	no	—
39	C₂×C₄×C₁₁	C₂×D₈	1	1	yes	characteristic
40	C₂×Dic₁₁	—	8	2	no	—
41	C₂×Dic₁₁	D₁₆	1	2	yes	—
42	Dic₂₂	—	16	4	no	—
43	C₈×C₁₁	C₄⋊Q₈	1	1	yes	characteristic
44	C₈×C₁₁	C₂×Q₁₆	1	1	yes	characteristic
45	C₁₁⋊C₈	Q₃₂	1	2	yes	—
46	#500	—	22	2	no	—
47	C₂×C₃₂	—	11	1	no	—
48	C₂×C₃₂	C₂×D₁₁	1	1	yes	characteristic
49	#366	—	11	2	no	—
50	#366	—	22	2	no	—
51	#366	C₂×D₁₁	1	2	yes	—
52	C₄×C₁₆	—	11	1	no	—
53	C₂²×C₁₁	C₂×D₁₆	1	1	yes	characteristic
54	C₄×C₁₁	—	16	2	no	—
55	C₄×C₁₁	#500	1	1	yes	characteristic
56	C₄×C₁₁	C₂×Q₃₂	1	1	yes	characteristic
57	Dic₁₁	—	16	2	no	—
58	Dic₁₁	SD₆₄	1	4	yes	—
59	C₄⋊Q₈	—	44	2	no	—
60	C₂×C₁₆	—	11	1	no	—
61	C₂×C₁₆	C₂²×D₁₁	1	1	yes	characteristic
62	#107	—	2	2	no	—
63	#107	—	22	2	no	—
64	#107	—	44	2	no	—
65	C₄×C₈	—	11	1	no	—
66	C₃₂	—	11	2	no	—
67	C₃₂	Dic₂₂	1	2	yes	complemented
68	C₂×C₁₁	#2252	1	1	yes	characteristic
69	C₂×C₁₁	C₂×SD₆₄	1	2	yes	—
70	C₂×Q₈	—	88	2	no	—
71	C₂×C₈	—	11	1	no	—
72	C₂×C₈	D₄×D₁₁	1	1	yes	characteristic
73	C₄⋊C₄	—	4	2	no	—
74	C₄⋊C₄	—	44	2	no	—
75	C₄⋊C₄	—	88	2	no	—
76	C₄²	—	11	1	no	—
77	C₁₆	—	11	2	no	—
78	C₁₆	C₂×Dic₂₂	1	1	yes	characteristic
79	C₁₆	Q₈×D₁₁	1	1	yes	characteristic
80	C₁₁	#13733	1	1	yes	characteristic, complemented, Sylow
81	Q₈	—	176	4	no	—
82	C₂×C₄	—	8	2	no	—
83	C₂×C₄	—	11	2	no	—
84	C₂×C₄	—	88	2	no	—
85	C₂×C₄	D₈×D₁₁	1	1	yes	characteristic
86	C₈	—	11	2	no	—
87	C₈	#66941	1	1	yes	characteristic
88	C₈	Q₁₆×D₁₁	1	1	yes	characteristic
89	C₂²	D₁₁×D₁₆	1	1	yes	characteristic
90	C₄	—	11	4	no	—
91	C₄	—	16	2	no	—
92	C₄	—	176	2	no	—
93	C₄	#10622487	1	1	yes	characteristic
94	C₄	D₁₁×Q₃₂	1	1	yes	characteristic
95	C₂	#13070890	1	1	yes	characteristic
96	C₂	D₁₁×SD₆₄	1	2	yes	—

	subgroup	G/H
center	C₂²	D₁₁×D₁₆
commutator, cosocle	C₂×C₁₁×C₁₆	C₂³
Frattini	C₂×C₁₆	C₂²×D₁₁
Fitting	C₁₁×#1424	C₂
socle, prime radical	C₂²×C₁₁	C₂×D₁₆
hypercenter	#1424	D₁₁
hypocenter	C₁₁	#13733
LCS	G ▷ C₂×C₁₁×C₁₆ ▷ C₈×C₁₁ ▷ C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ #1424

Complements

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

N	H ≅ G/N	type
20. C₁₁×C₃₂	Q₈	semidirect
21. C₁₁⋊C₃₂	Q₈	semidirect
67. C₃₂	Dic₂₂	semidirect
80. C₁₁	#13733	semidirect

Maximal subgroups

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

subgroup	index
#13070890	2
#13066818	2
#13066817	2
C₃₂×Dic₁₁	2
C₁₁×#1424	2
#13733	11