Subgroups — C₈×C₁₁×C₁₂₈ #72189751

Order 11264.

194 conjugacy classes of subgroups.

The subgroup lattice has 100 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈×C₁₁×C₆₄	C₂	1	1	yes	maximal, characteristic
2	C₄×C₁₁×C₁₂₈	C₂	1	2	yes	maximal
3	C₈×C₁₂₈	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
4	C₂×C₁₁×C₁₂₈	C₄	1	4	yes	—
5	C₄×C₁₁×C₆₄	C₄	1	1	yes	characteristic
6	C₄×C₁₁×C₆₄	C₂²	1	1	yes	characteristic
7	C₈×C₁₁×C₃₂	C₄	1	1	yes	characteristic
8	C₂×C₁₁×C₆₄	C₈	1	2	yes	—
9	C₂×C₁₁×C₆₄	C₂×C₄	1	2	yes	—
10	C₄×C₁₁×C₃₂	C₈	1	1	yes	characteristic
11	C₄×C₁₁×C₃₂	C₂×C₄	1	1	yes	characteristic
12	C₈×C₁₁×C₁₆	C₈	1	1	yes	characteristic
13	C₁₁×C₁₂₈	C₈	1	8	yes	direct product factor
14	C₂×C₁₁×C₃₂	C₁₆	1	2	yes	—
15	C₂×C₁₁×C₃₂	C₄²	1	1	yes	characteristic
16	C₂×C₁₁×C₃₂	C₂×C₈	1	1	yes	characteristic
17	C₄×C₁₁×C₁₆	C₁₆	1	1	yes	characteristic
18	C₄×C₁₁×C₁₆	C₂×C₈	1	1	yes	characteristic
19	C₈²×C₁₁	C₁₆	1	1	yes	characteristic
20	C₁₁×C₆₄	C₁₆	1	4	yes	—
21	C₁₁×C₆₄	C₂×C₈	1	4	yes	—
22	C₄×C₁₂₈	C₂×C₁₁	1	2	yes	—
23	C₈×C₆₄	C₂×C₁₁	1	1	yes	characteristic
24	C₂×C₁₁×C₁₆	C₃₂	1	2	yes	—
25	C₂×C₁₁×C₁₆	C₄×C₈	1	1	yes	characteristic
26	C₂×C₁₁×C₁₆	C₂×C₁₆	1	1	yes	characteristic
27	C₄×C₈×C₁₁	C₃₂	1	2	yes	—
28	C₄×C₈×C₁₁	C₂×C₁₆	1	1	yes	characteristic
29	C₁₁×C₃₂	C₃₂	1	4	yes	—
30	C₁₁×C₃₂	C₄×C₈	1	2	yes	—
31	C₁₁×C₃₂	C₂×C₁₆	1	2	yes	—
32	C₂×C₁₂₈	C₄×C₁₁	1	4	yes	—
33	C₄×C₆₄	C₄×C₁₁	1	1	yes	characteristic
34	C₄×C₆₄	C₂²×C₁₁	1	1	yes	characteristic
35	C₈×C₃₂	C₄×C₁₁	1	1	yes	characteristic
36	C₂×C₈×C₁₁	C₆₄	1	4	yes	—
37	C₂×C₈×C₁₁	C₄×C₁₆	1	1	yes	characteristic
38	C₂×C₈×C₁₁	C₂×C₃₂	1	1	yes	characteristic
39	C₄²×C₁₁	C₂×C₃₂	1	1	yes	characteristic
40	C₁₁×C₁₆	C₆₄	1	4	yes	—
41	C₁₁×C₁₆	C₈²	1	1	yes	characteristic
42	C₁₁×C₁₆	C₄×C₁₆	1	1	yes	characteristic
43	C₁₁×C₁₆	C₂×C₃₂	1	2	yes	—
44	C₂×C₆₄	C₈×C₁₁	1	2	yes	—
45	C₂×C₆₄	C₂×C₄×C₁₁	1	2	yes	—
46	C₄×C₃₂	C₈×C₁₁	1	1	yes	characteristic
47	C₄×C₃₂	C₂×C₄×C₁₁	1	1	yes	characteristic
48	C₈×C₁₆	C₈×C₁₁	1	1	yes	characteristic
49	C₁₂₈	C₈×C₁₁	1	8	yes	direct product factor
50	C₂×C₄×C₁₁	C₄×C₃₂	1	1	yes	characteristic
51	C₂×C₄×C₁₁	C₂×C₆₄	1	2	yes	—
52	C₈×C₁₁	C₁₂₈	1	8	yes	direct product factor
53	C₈×C₁₁	C₈×C₁₆	1	1	yes	characteristic
54	C₈×C₁₁	C₄×C₃₂	1	1	yes	characteristic
55	C₈×C₁₁	C₂×C₆₄	1	2	yes	—
56	C₂×C₃₂	C₁₁×C₁₆	1	2	yes	—
57	C₂×C₃₂	C₄²×C₁₁	1	1	yes	characteristic
58	C₂×C₃₂	C₂×C₈×C₁₁	1	1	yes	characteristic
59	C₄×C₁₆	C₁₁×C₁₆	1	1	yes	characteristic
60	C₄×C₁₆	C₂×C₈×C₁₁	1	1	yes	characteristic
61	C₈²	C₁₁×C₁₆	1	1	yes	characteristic
62	C₆₄	C₁₁×C₁₆	1	4	yes	—
63	C₆₄	C₂×C₈×C₁₁	1	4	yes	—
64	C₂²×C₁₁	C₄×C₆₄	1	1	yes	characteristic
65	C₄×C₁₁	C₈×C₃₂	1	1	yes	characteristic
66	C₄×C₁₁	C₄×C₆₄	1	1	yes	characteristic
67	C₄×C₁₁	C₂×C₁₂₈	1	4	yes	—
68	C₂×C₁₆	C₁₁×C₃₂	1	2	yes	—
69	C₂×C₁₆	C₄×C₈×C₁₁	1	1	yes	characteristic
70	C₂×C₁₆	C₂×C₁₁×C₁₆	1	1	yes	characteristic
71	C₄×C₈	C₁₁×C₃₂	1	2	yes	—
72	C₄×C₈	C₂×C₁₁×C₁₆	1	1	yes	characteristic
73	C₃₂	C₁₁×C₃₂	1	4	yes	—
74	C₃₂	C₄×C₈×C₁₁	1	2	yes	—
75	C₃₂	C₂×C₁₁×C₁₆	1	2	yes	—
76	C₂×C₁₁	C₈×C₆₄	1	1	yes	characteristic
77	C₂×C₁₁	C₄×C₁₂₈	1	2	yes	—
78	C₂×C₈	C₁₁×C₆₄	1	4	yes	—
79	C₂×C₈	C₄×C₁₁×C₁₆	1	1	yes	characteristic
80	C₂×C₈	C₂×C₁₁×C₃₂	1	1	yes	characteristic
81	C₄²	C₂×C₁₁×C₃₂	1	1	yes	characteristic
82	C₁₆	C₁₁×C₆₄	1	4	yes	—
83	C₁₆	C₈²×C₁₁	1	1	yes	characteristic
84	C₁₆	C₄×C₁₁×C₁₆	1	1	yes	characteristic
85	C₁₆	C₂×C₁₁×C₃₂	1	2	yes	—
86	C₁₁	C₈×C₁₂₈	1	1	yes	characteristic, direct product factor, Sylow
87	C₂×C₄	C₄×C₁₁×C₃₂	1	1	yes	characteristic
88	C₂×C₄	C₂×C₁₁×C₆₄	1	2	yes	—
89	C₈	C₁₁×C₁₂₈	1	8	yes	direct product factor
90	C₈	C₈×C₁₁×C₁₆	1	1	yes	characteristic
91	C₈	C₄×C₁₁×C₃₂	1	1	yes	characteristic
92	C₈	C₂×C₁₁×C₆₄	1	2	yes	—
93	C₂²	C₄×C₁₁×C₆₄	1	1	yes	characteristic
94	C₄	C₈×C₁₁×C₃₂	1	1	yes	characteristic
95	C₄	C₄×C₁₁×C₆₄	1	1	yes	characteristic
96	C₄	C₂×C₁₁×C₁₂₈	1	4	yes	—
97	C₂	C₄×C₁₁×C₁₂₈	1	2	yes	—
98	C₂	C₈×C₁₁×C₆₄	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₄×C₆₄	C₂²×C₁₁
socle, prime radical	C₂²×C₁₁	C₄×C₆₄
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₈×C₁₂₈	C₁₁	direct (N × H)
13. C₁₁×C₁₂₈	C₈	direct (N × H)
49. C₁₂₈	C₈×C₁₁	direct (N × H)
52. C₈×C₁₁	C₁₂₈	direct (N × H)
86. C₁₁	C₈×C₁₂₈	direct (N × H)
89. C₈	C₁₁×C₁₂₈	direct (N × H)

Maximal subgroups

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

subgroup	index
C₈×C₁₁×C₆₄	2
C₄×C₁₁×C₁₂₈	2
C₈×C₁₂₈	11

Subgroups — C8×C11×C128 #72189751

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈×C₁₁×C₁₂₈ #72189751