Subgroups — C₂²×#66881 #13077188

Order 1408.

600 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₈×C₁₁	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₄⋊Dic₁₁	C₂	1	2	yes	maximal
3	C₂×#66881	C₂	1	12	yes	maximal, direct product factor
4	C₂³×C₄×C₁₁	C₂²	1	1	yes	characteristic
5	C₂³×Dic₁₁	—	2	2	no	—
6	C₂²×C₈×C₁₁	C₄	1	8	yes	complemented
7	C₂²×C₈×C₁₁	C₂²	1	6	yes	—
8	C₂×C₄⋊Dic₁₁	—	2	6	no	—
9	C₂×C₄⋊Dic₁₁	C₂²	1	12	yes	—
10	#66881	C₂²	1	16	yes	direct product factor
11	C₂⁴×C₁₁	D₄	1	1	yes	characteristic
12	C₂²×C₄×C₁₁	C₂×C₄	1	4	yes	—
13	C₂²×C₄×C₁₁	D₄	1	3	yes	—
14	C₂²×C₄×C₁₁	Q₈	1	4	yes	—
15	C₂²×C₄×C₁₁	C₂³	1	3	yes	—
16	C₂²×Dic₁₁	—	2	12	no	—
17	C₂²×Dic₁₁	—	4	8	no	—
18	C₂×C₈×C₁₁	C₂×C₄	1	24	yes	complemented
19	C₂×C₈×C₁₁	C₂³	1	4	yes	—
20	C₄⋊Dic₁₁	—	2	12	no	—
21	C₄⋊Dic₁₁	C₂³	1	8	yes	—
22	C₂²×#106	—	11	1	no	maximal, Sylow
23	C₂³×C₁₁	C₄⋊C₄	1	4	yes	—
24	C₂³×C₁₁	SD₁₆	1	8	yes	—
25	C₂³×C₁₁	C₂×D₄	1	3	yes	—
26	C₂×C₄×C₁₁	C₄⋊C₄	1	12	yes	—
27	C₂×C₄×C₁₁	C₂²×C₄	1	6	yes	—
28	C₂×C₄×C₁₁	C₂×D₄	1	3	yes	—
29	C₂×C₄×C₁₁	C₂×Q₈	1	6	yes	—
30	C₂×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
31	C₂×Dic₁₁	—	2	8	no	—
32	C₂×Dic₁₁	—	4	24	no	—
33	C₈×C₁₁	C₂²×C₄	1	8	yes	complemented
34	C₂³×C₈	D₁₁	1	1	yes	characteristic
35	C₂²×C₄⋊C₄	—	11	2	no	—
36	C₂×#106	—	11	12	no	—
37	C₂²×C₁₁	#106	1	16	yes	complemented
38	C₂²×C₁₁	C₂×C₄⋊C₄	1	6	yes	—
39	C₂²×C₁₁	C₂×SD₁₆	1	12	yes	—
40	C₂²×C₁₁	C₂²×D₄	1	1	yes	characteristic
41	C₄×C₁₁	C₂×C₄⋊C₄	1	6	yes	—
42	C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
43	C₄×C₁₁	C₂²×Q₈	1	1	yes	characteristic
44	Dic₁₁	—	4	8	no	—
45	C₂³×C₄	—	22	2	no	—
46	C₂³×C₄	C₂×D₁₁	1	1	yes	characteristic
47	C₂²×C₈	Dic₁₁	1	8	yes	complemented
48	C₂²×C₈	C₂×D₁₁	1	6	yes	—
49	C₂×C₄⋊C₄	—	11	12	no	—
50	C₂×C₄⋊C₄	—	22	6	no	—
51	#106	—	11	16	no	—
52	C₂×C₁₁	C₂×#106	1	12	yes	complemented
53	C₂×C₁₁	C₂²×C₄⋊C₄	1	1	yes	characteristic
54	C₂×C₁₁	C₂²×SD₁₆	1	2	yes	—
55	C₂⁴	D₄₄	1	1	yes	characteristic
56	C₂²×C₄	—	22	12	no	—
57	C₂²×C₄	—	44	8	no	—
58	C₂²×C₄	Dic₂₂	1	4	yes	—
59	C₂²×C₄	D₄₄	1	3	yes	—
60	C₂²×C₄	C₂×Dic₁₁	1	4	yes	—
61	C₂²×C₄	C₂²×D₁₁	1	3	yes	—
62	C₂×C₈	C₂×Dic₁₁	1	24	yes	complemented
63	C₂×C₈	C₂²×D₁₁	1	4	yes	—
64	C₄⋊C₄	—	11	8	no	—
65	C₄⋊C₄	—	22	12	no	—
66	C₁₁	C₂²×#106	1	1	yes	characteristic, complemented, Sylow
67	C₂³	#4314	1	8	yes	—
68	C₂³	C₄⋊Dic₁₁	1	4	yes	—
69	C₂³	C₂×D₄₄	1	3	yes	—
70	C₂×C₄	—	22	8	no	—
71	C₂×C₄	—	44	24	no	—
72	C₂×C₄	C₄⋊Dic₁₁	1	12	yes	—
73	C₂×C₄	C₂×Dic₂₂	1	6	yes	—
74	C₂×C₄	C₂×D₄₄	1	3	yes	—
75	C₂×C₄	C₂²×Dic₁₁	1	6	yes	—
76	C₂×C₄	C₂³×D₁₁	1	1	yes	characteristic
77	C₈	C₂²×Dic₁₁	1	8	yes	complemented
78	C₂²	#66881	1	16	yes	direct product factor
79	C₂²	C₂×#4314	1	12	yes	—
80	C₂²	C₂×C₄⋊Dic₁₁	1	6	yes	—
81	C₂²	C₂²×D₄₄	1	1	yes	characteristic
82	C₄	—	44	8	no	—
83	C₄	C₂×C₄⋊Dic₁₁	1	6	yes	—
84	C₄	C₂²×Dic₂₂	1	1	yes	characteristic
85	C₄	C₂³×Dic₁₁	1	1	yes	characteristic
86	C₂	C₂×#66881	1	12	yes	direct product factor
87	C₂	C₂²×#4314	1	2	yes	—
88	C₂	C₂²×C₄⋊Dic₁₁	1	1	yes	characteristic

	subgroup	G/H
center	C₂⁴	D₄₄
commutator	C₄×C₁₁	C₂³×C₄
Frattini	C₂×C₄	C₂³×D₁₁
Fitting	C₂³×C₈×C₁₁	C₂
socle, prime radical	C₂⁴×C₁₁	D₄
cosocle	C₂×C₄×C₁₁	C₂⁴
hypercenter	C₂³×C₈	D₁₁
hypocenter	C₁₁	C₂²×#106
LCS	G ▷ C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂⁴ ◁ C₂³×C₄ ◁ C₂³×C₈

Complements

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

N	H ≅ G/N	type
3. C₂×#66881	C₂	direct (N × H)
6. C₂²×C₈×C₁₁	C₄	semidirect
10. #66881	C₂²	direct (N × H)
18. C₂×C₈×C₁₁	C₂×C₄	semidirect
33. C₈×C₁₁	C₂²×C₄	semidirect
37. C₂²×C₁₁	#106	semidirect
47. C₂²×C₈	Dic₁₁	semidirect
52. C₂×C₁₁	C₂×#106	semidirect
62. C₂×C₈	C₂×Dic₁₁	semidirect
66. C₁₁	C₂²×#106	semidirect
77. C₈	C₂²×Dic₁₁	semidirect
78. C₂²	#66881	direct (N × H)
86. C₂	C₂×#66881	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×C₈×C₁₁	2
C₂²×C₄⋊Dic₁₁	2
C₂×#66881	2
C₂²×#106	11

Subgroups — C22×#66881 #13077188

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×#66881 #13077188