Subgroups — C₂×C₁₁×M₆₄ #13065095

Order 1408.

112 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₁×C₁₆	C₂	1	1	yes	maximal, characteristic
2	C₁₁×M₆₄	C₂	1	4	yes	maximal, direct product factor
3	C₂×C₁₁×C₃₂	C₂	1	2	yes	maximal, complemented
4	C₂²×C₈×C₁₁	C₄	1	1	yes	characteristic
5	C₂×C₁₁×C₁₆	C₄	1	1	yes	characteristic
6	C₂×C₁₁×C₁₆	C₄	1	2	yes	—
7	C₂×C₁₁×C₁₆	C₂²	1	2	yes	—
8	C₂×C₁₁×C₁₆	C₂²	1	1	yes	characteristic
9	C₁₁×C₃₂	C₂²	1	4	yes	complemented
10	C₂²×C₄×C₁₁	C₈	1	1	yes	characteristic
11	C₂×C₈×C₁₁	C₈	1	2	yes	—
12	C₂×C₈×C₁₁	C₈	1	1	yes	characteristic
13	C₂×C₈×C₁₁	C₂×C₄	1	2	yes	—
14	C₂×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
15	C₁₁×C₁₆	C₂×C₄	1	2	yes	—
16	C₁₁×C₁₆	C₂×C₄	1	1	yes	characteristic
17	C₁₁×C₁₆	C₂³	1	1	yes	characteristic
18	C₂×M₆₄	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
19	C₂³×C₁₁	C₁₆	1	1	yes	characteristic
20	C₂×C₄×C₁₁	C₁₆	1	2	yes	—
21	C₂×C₄×C₁₁	C₁₆	1	1	yes	characteristic
22	C₂×C₄×C₁₁	C₂×C₈	1	2	yes	—
23	C₂×C₄×C₁₁	C₂×C₈	1	1	yes	characteristic
24	C₈×C₁₁	C₂×C₈	1	2	yes	—
25	C₈×C₁₁	C₂×C₈	1	1	yes	characteristic
26	C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
27	C₂²×C₁₆	C₂×C₁₁	1	1	yes	characteristic
28	M₆₄	C₂×C₁₁	1	4	yes	direct product factor
29	C₂×C₃₂	C₂×C₁₁	1	2	yes	complemented
30	C₂²×C₁₁	—	2	2	no	—
31	C₂²×C₁₁	C₂×C₁₆	1	2	yes	—
32	C₂²×C₁₁	C₂×C₁₆	1	1	yes	characteristic
33	C₄×C₁₁	C₂×C₁₆	1	1	yes	characteristic
34	C₄×C₁₁	C₂×C₁₆	1	2	yes	—
35	C₄×C₁₁	C₂²×C₈	1	1	yes	characteristic
36	C₂²×C₈	C₄×C₁₁	1	1	yes	characteristic
37	C₂×C₁₆	C₄×C₁₁	1	1	yes	characteristic
38	C₂×C₁₆	C₄×C₁₁	1	2	yes	—
39	C₂×C₁₆	C₂²×C₁₁	1	2	yes	—
40	C₂×C₁₆	C₂²×C₁₁	1	1	yes	characteristic
41	C₃₂	C₂²×C₁₁	1	4	yes	complemented
42	C₂×C₁₁	—	2	2	no	—
43	C₂×C₁₁	M₆₄	1	2	yes	direct product factor
44	C₂×C₁₁	C₂²×C₁₆	1	1	yes	characteristic
45	C₂²×C₄	C₈×C₁₁	1	1	yes	characteristic
46	C₂×C₈	C₈×C₁₁	1	2	yes	—
47	C₂×C₈	C₈×C₁₁	1	1	yes	characteristic
48	C₂×C₈	C₂×C₄×C₁₁	1	2	yes	—
49	C₂×C₈	C₂×C₄×C₁₁	1	1	yes	characteristic
50	C₁₆	C₂×C₄×C₁₁	1	2	yes	—
51	C₁₆	C₂×C₄×C₁₁	1	1	yes	characteristic
52	C₁₆	C₂³×C₁₁	1	1	yes	characteristic
53	C₁₁	C₂×M₆₄	1	1	yes	characteristic, direct product factor, Sylow
54	C₂³	C₁₁×C₁₆	1	1	yes	characteristic
55	C₂×C₄	C₁₁×C₁₆	1	2	yes	—
56	C₂×C₄	C₁₁×C₁₆	1	1	yes	characteristic
57	C₂×C₄	C₂×C₈×C₁₁	1	2	yes	—
58	C₂×C₄	C₂×C₈×C₁₁	1	1	yes	characteristic
59	C₈	C₂×C₈×C₁₁	1	2	yes	—
60	C₈	C₂×C₈×C₁₁	1	1	yes	characteristic
61	C₈	C₂²×C₄×C₁₁	1	1	yes	characteristic
62	C₂²	—	2	2	no	—
63	C₂²	C₂×C₁₁×C₁₆	1	2	yes	—
64	C₂²	C₂×C₁₁×C₁₆	1	1	yes	characteristic
65	C₄	C₂×C₁₁×C₁₆	1	1	yes	characteristic
66	C₄	C₂×C₁₁×C₁₆	1	2	yes	—
67	C₄	C₂²×C₈×C₁₁	1	1	yes	characteristic
68	C₂	—	2	2	no	—
69	C₂	C₁₁×M₆₄	1	2	yes	direct product factor
70	C₂	C₂²×C₁₁×C₁₆	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₁₁×C₁₆	C₂²
commutator	C₂	C₂²×C₁₁×C₁₆
Frattini, cosocle	C₁₆	C₂³×C₁₁
socle	C₂²×C₁₁	C₂×C₁₆
prime radical	C₂³×C₁₁	C₁₆
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₁×C₁₆ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₁×M₆₄	C₂	direct (N × H)
3. C₂×C₁₁×C₃₂	C₂	semidirect
9. C₁₁×C₃₂	C₂²	semidirect
18. C₂×M₆₄	C₁₁	direct (N × H)
28. M₆₄	C₂×C₁₁	direct (N × H)
29. C₂×C₃₂	C₂×C₁₁	semidirect
41. C₃₂	C₂²×C₁₁	semidirect
43. C₂×C₁₁	M₆₄	direct (N × H)
53. C₁₁	C₂×M₆₄	direct (N × H)
69. C₂	C₁₁×M₆₄	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₁₁×C₁₆	2
C₁₁×M₆₄	2
C₂×C₁₁×C₃₂	2
C₂×M₆₄	11

Subgroups — C2×C11×M64 #13065095

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₁×M₆₄ #13065095