Subgroups — #14643145

Order 2816.

486 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13068361	C₂	1	3	yes	maximal
2	C₂×#10622092	C₂	1	3	yes	maximal
3	C₂×C₈²×C₁₁	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄×C₈×C₁₁	C₂²	1	3	yes	—
5	C₄²×Dic₁₁	C₂²	1	1	yes	characteristic
6	C₂×C₄×C₁₁⋊C₈	C₂²	1	3	yes	—
7	C₈²×C₁₁	C₄	1	4	yes	complemented
8	#10622188	C₄	1	12	yes	—
9	#10622092	C₄	1	12	yes	complemented
10	C₂²×C₈×C₁₁	C₂×C₄	1	6	yes	—
11	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
12	C₂×C₄×Dic₁₁	C₂×C₄	1	6	yes	—
13	C₂²×C₁₁⋊C₈	C₂×C₄	1	6	yes	—
14	C₄×C₈×C₁₁	C₂×C₄	1	6	yes	—
15	C₄×C₈×C₁₁	C₂×C₄	1	6	yes	—
16	C₄×C₁₁⋊C₈	C₂×C₄	1	12	yes	—
17	#7845	—	11	1	no	maximal, Sylow
18	C₂²×C₄×C₁₁	C₂²×C₄	1	3	yes	—
19	C₂²×Dic₁₁	C₄²	1	4	yes	—
20	C₂×C₈×C₁₁	—	2	12	no	—
21	C₂×C₈×C₁₁	C₄²	1	12	yes	—
22	C₄²×C₁₁	C₂²×C₄	1	3	yes	—
23	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
24	C₄×Dic₁₁	—	2	12	no	—
25	C₂×C₁₁⋊C₈	—	2	12	no	—
26	C₂×C₁₁⋊C₈	C₄²	1	12	yes	—
27	#1744	—	11	3	no	—
28	C₂×#322	—	11	3	no	—
29	C₂×C₈²	D₁₁	1	1	yes	characteristic
30	C₂³×C₁₁	C₂×C₄²	1	1	yes	characteristic
31	C₂×C₄×C₁₁	C₂×C₄²	1	3	yes	—
32	C₂×C₄×C₁₁	C₂×C₄²	1	3	yes	—
33	C₂×C₄×C₁₁	#131	1	12	yes	—
34	C₂×Dic₁₁	—	2	12	no	—
35	C₈×C₁₁	—	2	12	no	—
36	C₁₁⋊C₈	—	2	12	no	—
37	C₂×C₄×C₈	—	11	3	no	—
38	C₂×C₄×C₈	C₂×D₁₁	1	3	yes	—
39	C₄³	—	11	1	no	—
40	#336	—	11	12	no	—
41	#322	—	11	12	no	—
42	C₈²	Dic₁₁	1	4	yes	complemented
43	C₂²×C₁₁	C₄³	1	1	yes	characteristic
44	C₂²×C₁₁	#405	1	6	yes	—
45	C₄×C₁₁	#405	1	6	yes	—
46	C₄×C₁₁	#405	1	6	yes	—
47	Dic₁₁	—	4	4	no	—
48	C₂²×C₈	—	11	6	no	—
49	C₂²×C₈	C₄×D₁₁	1	6	yes	—
50	C₂×C₄²	—	11	6	no	—
51	C₂×C₄²	C₂²×D₁₁	1	1	yes	characteristic
52	C₄×C₈	—	11	12	no	—
53	C₄×C₈	C₄×D₁₁	1	6	yes	—
54	C₄×C₈	C₂×Dic₁₁	1	6	yes	—
55	C₂×C₁₁	#1454	1	4	yes	—
56	C₂×C₁₁	#1726	1	3	yes	—
57	C₂²×C₄	—	11	4	no	—
58	C₂²×C₄	C₂×C₄×D₁₁	1	3	yes	—
59	C₂×C₈	—	2	12	no	—
60	C₂×C₈	—	11	12	no	—
61	C₂×C₈	—	22	12	no	—
62	C₂×C₈	C₄×Dic₁₁	1	12	yes	—
63	C₄²	—	22	12	no	—
64	C₄²	C₂×C₄×D₁₁	1	3	yes	—
65	C₄²	C₂²×Dic₁₁	1	1	yes	characteristic
66	C₁₁	#7845	1	1	yes	characteristic, complemented, Sylow
67	C₂³	C₄²×D₁₁	1	1	yes	characteristic
68	C₂×C₄	—	22	12	no	—
69	C₂×C₄	C₄²×D₁₁	1	3	yes	—
70	C₂×C₄	#66954	1	12	yes	—
71	C₂×C₄	C₂×C₄×Dic₁₁	1	3	yes	—
72	C₈	—	2	12	no	—
73	C₈	—	22	12	no	—
74	C₂²	#10622302	1	6	yes	—
75	C₂²	C₄²×Dic₁₁	1	1	yes	characteristic
76	C₄	—	44	4	no	—
77	C₄	#10622302	1	6	yes	—
78	C₄	#10622714	1	6	yes	—
79	C₂	#13066915	1	4	yes	—
80	C₂	#13068302	1	3	yes	—

	subgroup	G/H
center, Frattini	C₂×C₄²	C₂²×D₁₁
commutator	C₂²×C₁₁	C₄³
Fitting	C₂×C₈²×C₁₁	C₂
socle, prime radical	C₂³×C₁₁	C₂×C₄²
cosocle	C₂×C₄²×C₁₁	C₂³
hypercenter	C₂×C₈²	D₁₁
hypocenter	C₁₁	#7845
LCS	G ▷ C₂²×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂×C₄² ◁ C₂×C₈²

Complements

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

N	H ≅ G/N	type
7. C₈²×C₁₁	C₄	semidirect
9. #10622092	C₄	semidirect
42. C₈²	Dic₁₁	semidirect
66. C₁₁	#7845	semidirect

Maximal subgroups

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

subgroup	index
#13068361	2
C₂×#10622092	2
C₂×C₈²×C₁₁	2
#7845	11