Subgroups — C₂×C₁₁×M₁₂₈ #14590929

Order 2816.

134 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₁×C₃₂	C₂	1	1	yes	maximal, characteristic
2	C₁₁×M₁₂₈	C₂	1	4	yes	maximal, direct product factor
3	C₂×C₁₁×C₆₄	C₂	1	2	yes	maximal, complemented
4	C₂²×C₁₁×C₁₆	C₄	1	1	yes	characteristic
5	C₂×C₁₁×C₃₂	C₄	1	1	yes	characteristic
6	C₂×C₁₁×C₃₂	C₄	1	2	yes	—
7	C₂×C₁₁×C₃₂	C₂²	1	2	yes	—
8	C₂×C₁₁×C₃₂	C₂²	1	1	yes	characteristic
9	C₁₁×C₆₄	C₂²	1	4	yes	complemented
10	C₂²×C₈×C₁₁	C₈	1	1	yes	characteristic
11	C₂×C₁₁×C₁₆	C₈	1	1	yes	characteristic
12	C₂×C₁₁×C₁₆	C₈	1	2	yes	—
13	C₂×C₁₁×C₁₆	C₂×C₄	1	2	yes	—
14	C₂×C₁₁×C₁₆	C₂×C₄	1	1	yes	characteristic
15	C₁₁×C₃₂	C₂×C₄	1	2	yes	—
16	C₁₁×C₃₂	C₂×C₄	1	1	yes	characteristic
17	C₁₁×C₃₂	C₂³	1	1	yes	characteristic
18	C₂×M₁₂₈	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
19	C₂²×C₄×C₁₁	C₁₆	1	1	yes	characteristic
20	C₂×C₈×C₁₁	C₁₆	1	2	yes	—
21	C₂×C₈×C₁₁	C₁₆	1	1	yes	characteristic
22	C₂×C₈×C₁₁	C₂×C₈	1	2	yes	—
23	C₂×C₈×C₁₁	C₂×C₈	1	1	yes	characteristic
24	C₁₁×C₁₆	C₂×C₈	1	2	yes	—
25	C₁₁×C₁₆	C₂×C₈	1	1	yes	characteristic
26	C₁₁×C₁₆	C₂²×C₄	1	1	yes	characteristic
27	C₂²×C₃₂	C₂×C₁₁	1	1	yes	characteristic
28	M₁₂₈	C₂×C₁₁	1	4	yes	direct product factor
29	C₂×C₆₄	C₂×C₁₁	1	2	yes	complemented
30	C₂³×C₁₁	C₃₂	1	1	yes	characteristic
31	C₂×C₄×C₁₁	C₃₂	1	2	yes	—
32	C₂×C₄×C₁₁	C₃₂	1	1	yes	characteristic
33	C₂×C₄×C₁₁	C₂×C₁₆	1	2	yes	—
34	C₂×C₄×C₁₁	C₂×C₁₆	1	1	yes	characteristic
35	C₈×C₁₁	C₂×C₁₆	1	2	yes	—
36	C₈×C₁₁	C₂×C₁₆	1	1	yes	characteristic
37	C₈×C₁₁	C₂²×C₈	1	1	yes	characteristic
38	C₂²×C₁₆	C₄×C₁₁	1	1	yes	characteristic
39	C₂×C₃₂	C₄×C₁₁	1	1	yes	characteristic
40	C₂×C₃₂	C₄×C₁₁	1	2	yes	—
41	C₂×C₃₂	C₂²×C₁₁	1	2	yes	—
42	C₂×C₃₂	C₂²×C₁₁	1	1	yes	characteristic
43	C₆₄	C₂²×C₁₁	1	4	yes	complemented
44	C₂²×C₁₁	—	2	2	no	—
45	C₂²×C₁₁	C₂×C₃₂	1	2	yes	—
46	C₂²×C₁₁	C₂×C₃₂	1	1	yes	characteristic
47	C₄×C₁₁	C₂×C₃₂	1	1	yes	characteristic
48	C₄×C₁₁	C₂×C₃₂	1	2	yes	—
49	C₄×C₁₁	C₂²×C₁₆	1	1	yes	characteristic
50	C₂²×C₈	C₈×C₁₁	1	1	yes	characteristic
51	C₂×C₁₆	C₈×C₁₁	1	1	yes	characteristic
52	C₂×C₁₆	C₈×C₁₁	1	2	yes	—
53	C₂×C₁₆	C₂×C₄×C₁₁	1	2	yes	—
54	C₂×C₁₆	C₂×C₄×C₁₁	1	1	yes	characteristic
55	C₃₂	C₂×C₄×C₁₁	1	2	yes	—
56	C₃₂	C₂×C₄×C₁₁	1	1	yes	characteristic
57	C₃₂	C₂³×C₁₁	1	1	yes	characteristic
58	C₂×C₁₁	—	2	2	no	—
59	C₂×C₁₁	M₁₂₈	1	2	yes	direct product factor
60	C₂×C₁₁	C₂²×C₃₂	1	1	yes	characteristic
61	C₂²×C₄	C₁₁×C₁₆	1	1	yes	characteristic
62	C₂×C₈	C₁₁×C₁₆	1	2	yes	—
63	C₂×C₈	C₁₁×C₁₆	1	1	yes	characteristic
64	C₂×C₈	C₂×C₈×C₁₁	1	2	yes	—
65	C₂×C₈	C₂×C₈×C₁₁	1	1	yes	characteristic
66	C₁₆	C₂×C₈×C₁₁	1	2	yes	—
67	C₁₆	C₂×C₈×C₁₁	1	1	yes	characteristic
68	C₁₆	C₂²×C₄×C₁₁	1	1	yes	characteristic
69	C₁₁	C₂×M₁₂₈	1	1	yes	characteristic, direct product factor, Sylow
70	C₂³	C₁₁×C₃₂	1	1	yes	characteristic
71	C₂×C₄	C₁₁×C₃₂	1	2	yes	—
72	C₂×C₄	C₁₁×C₃₂	1	1	yes	characteristic
73	C₂×C₄	C₂×C₁₁×C₁₆	1	2	yes	—
74	C₂×C₄	C₂×C₁₁×C₁₆	1	1	yes	characteristic
75	C₈	C₂×C₁₁×C₁₆	1	1	yes	characteristic
76	C₈	C₂×C₁₁×C₁₆	1	2	yes	—
77	C₈	C₂²×C₈×C₁₁	1	1	yes	characteristic
78	C₂²	—	2	2	no	—
79	C₂²	C₂×C₁₁×C₃₂	1	2	yes	—
80	C₂²	C₂×C₁₁×C₃₂	1	1	yes	characteristic
81	C₄	C₂×C₁₁×C₃₂	1	1	yes	characteristic
82	C₄	C₂×C₁₁×C₃₂	1	2	yes	—
83	C₄	C₂²×C₁₁×C₁₆	1	1	yes	characteristic
84	C₂	—	2	2	no	—
85	C₂	C₁₁×M₁₂₈	1	2	yes	direct product factor
86	C₂	C₂²×C₁₁×C₃₂	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₁₁×C₃₂	C₂²
commutator	C₂	C₂²×C₁₁×C₃₂
Frattini, cosocle	C₃₂	C₂³×C₁₁
socle	C₂²×C₁₁	C₂×C₃₂
prime radical	C₂³×C₁₁	C₃₂
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₁×C₃₂ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₁×M₁₂₈	C₂	direct (N × H)
3. C₂×C₁₁×C₆₄	C₂	semidirect
9. C₁₁×C₆₄	C₂²	semidirect
18. C₂×M₁₂₈	C₁₁	direct (N × H)
28. M₁₂₈	C₂×C₁₁	direct (N × H)
29. C₂×C₆₄	C₂×C₁₁	semidirect
43. C₆₄	C₂²×C₁₁	semidirect
59. C₂×C₁₁	M₁₂₈	direct (N × H)
69. C₁₁	C₂×M₁₂₈	direct (N × H)
85. C₂	C₁₁×M₁₂₈	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×C₃₂	2
C₁₁×M₁₂₈	2
C₂×C₁₁×C₆₄	2
C₂×M₁₂₈	11

Subgroups — C2×C11×M128 #14590929

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₁×M₁₂₈ #14590929