Subgroups — #13068773

Order 1408.

280 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

	subgroup	G/H
center	C₂³	C₂×D₄₄
commutator	C₂×C₄×C₁₁	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₁₁
Fitting	C₂×C₄×C₈×C₁₁	C₂
socle, prime radical	C₂³×C₁₁	C₂×D₄
cosocle	C₂²×C₄×C₁₁	C₂³
hypercenter	C₂×C₄×C₈	D₁₁
hypocenter	C₁₁	#1844
LCS	G ▷ C₂×C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₄×C₈

Complements

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

N	H ≅ G/N	type
8. C₄×C₈×C₁₁	C₄	semidirect
30. C₈×C₁₁	C₄⋊C₄	semidirect
38. C₄×C₁₁	#106	semidirect
47. C₄×C₈	Dic₁₁	semidirect
62. C₁₁	#1844	semidirect
72. C₈	C₄⋊Dic₁₁	semidirect
78. C₄	#66881	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄×C₈×C₁₁	2
C₂×#66881	2
#10622548	2
#1844	11