Subgroups — #14647540

Order 2816.

486 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13068773	C₂	1	6	yes	maximal
2	C₂×C₈²×C₁₁	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×C₈×C₁₁	C₂²	1	3	yes	—
4	C₂×#66881	—	2	12	no	—
5	#10622548	C₂²	1	4	yes	—
6	C₈²×C₁₁	C₄	1	4	yes	complemented
7	C₂²×C₈×C₁₁	D₄	1	6	yes	—
8	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
9	C₂×C₄⋊Dic₁₁	—	2	12	no	—
10	C₄×C₈×C₁₁	C₂×C₄	1	6	yes	—
11	C₄×C₈×C₁₁	Q₈	1	6	yes	—
12	#66881	—	4	24	no	—
13	#8813	—	11	1	no	maximal, Sylow
14	C₂²×C₄×C₁₁	C₂×D₄	1	3	yes	—
15	C₂²×Dic₁₁	—	4	4	no	—
16	C₂×C₈×C₁₁	C₄⋊C₄	1	12	yes	—
17	C₂×C₈×C₁₁	SD₁₆	1	24	yes	—
18	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
19	C₄²×C₁₁	C₂×Q₈	1	3	yes	—
20	C₄⋊Dic₁₁	—	4	24	no	—
21	#1844	—	11	6	no	—
22	C₂×C₈²	D₁₁	1	1	yes	characteristic
23	C₂³×C₁₁	#127	1	1	yes	characteristic
24	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	3	yes	—
25	C₂×C₄×C₁₁	C₄⋊Q₈	1	3	yes	—
26	C₂×C₄×C₁₁	C₂×SD₁₆	1	12	yes	—
27	C₂×Dic₁₁	—	8	12	no	—
28	C₈×C₁₁	#106	1	24	yes	complemented
29	C₂×#106	—	22	12	no	—
30	C₂×C₄×C₈	C₂×D₁₁	1	3	yes	—
31	#384	—	11	4	no	—
32	C₈²	Dic₁₁	1	4	yes	complemented
33	C₂²×C₁₁	#384	1	1	yes	characteristic
34	C₂²×C₁₁	#492	1	6	yes	—
35	C₄×C₁₁	C₂×#106	1	6	yes	—
36	C₄×C₁₁	#498	1	6	yes	—
37	Dic₁₁	—	16	4	no	—
38	C₂²×C₈	D₄₄	1	6	yes	—
39	C₂×C₄⋊C₄	—	22	12	no	—
40	C₂×C₄²	C₂²×D₁₁	1	1	yes	characteristic
41	#106	—	44	24	no	—
42	C₄×C₈	Dic₂₂	1	6	yes	—
43	C₄×C₈	C₂×Dic₁₁	1	6	yes	—
44	C₂×C₁₁	#1705	1	4	yes	—
45	C₂×C₁₁	#1844	1	3	yes	—
46	C₂²×C₄	—	44	4	no	—
47	C₂²×C₄	C₂×D₄₄	1	3	yes	—
48	C₂×C₈	#4314	1	24	yes	—
49	C₂×C₈	C₄⋊Dic₁₁	1	12	yes	—
50	C₄⋊C₄	—	44	24	no	—
51	C₄²	C₂×Dic₂₂	1	3	yes	—
52	C₄²	C₂²×Dic₁₁	1	1	yes	characteristic
53	C₁₁	#8813	1	1	yes	characteristic, complemented, Sylow
54	C₂³	#66927	1	1	yes	characteristic
55	C₂×C₄	—	88	12	no	—
56	C₂×C₄	#66922	1	3	yes	—
57	C₂×C₄	C₂×#4314	1	12	yes	—
58	C₂×C₄	C₂×C₄⋊Dic₁₁	1	3	yes	—
59	C₈	#66881	1	24	yes	complemented
60	C₂²	#10622306	1	6	yes	—
61	C₂²	#10622548	1	1	yes	characteristic
62	C₄	—	176	4	no	—
63	C₄	#10622293	1	6	yes	—
64	C₄	C₂×#66881	1	6	yes	—
65	C₂	#13068203	1	4	yes	—
66	C₂	#13068773	1	3	yes	—

	subgroup	G/H
center	C₂³	#66927
commutator	C₄²×C₁₁	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₁
Fitting	C₂×C₈²×C₁₁	C₂
socle, prime radical	C₂³×C₁₁	#127
cosocle	C₂×C₄²×C₁₁	C₂³
hypercenter	C₂×C₈²	D₁₁
hypocenter	C₁₁	#8813
LCS	G ▷ C₄²×C₁₁ ▷ C₂²×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₈²

Complements

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

N	H ≅ G/N	type
6. C₈²×C₁₁	C₄	semidirect
28. C₈×C₁₁	#106	semidirect
32. C₈²	Dic₁₁	semidirect
53. C₁₁	#8813	semidirect
59. C₈	#66881	semidirect

Maximal subgroups

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

subgroup	index
#13068773	2
C₂×C₈²×C₁₁	2
#8813	11