Subgroups — C₁₁×#1770 #13064608

Order 1408.

272 conjugacy classes of subgroups.

The subgroup lattice has 138 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₁×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₁×#97	C₂	1	2	yes	maximal
3	C₂×C₄×C₈×C₁₁	C₂	1	1	yes	maximal, characteristic
4	C₄×C₁₁×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
5	C₁₁×#336	C₂	1	2	yes	maximal
6	C₂²×C₈×C₁₁	C₂²	1	1	yes	characteristic
7	C₂²×C₈×C₁₁	C₂²	1	2	yes	—
8	C₂²×C₈×C₁₁	C₂²	1	1	yes	characteristic
9	C₂×C₁₁×C₄⋊C₄	C₄	1	2	yes	—
10	C₂×C₄²×C₁₁	C₂²	1	2	yes	—
11	C₂×C₄²×C₁₁	C₂²	1	1	yes	characteristic
12	C₁₁×C₄⋊C₈	C₄	1	4	yes	complemented
13	C₁₁×#97	—	2	4	no	—
14	C₄×C₈×C₁₁	C₄	1	4	yes	complemented
15	C₁₁×#95	C₄	1	2	yes	—
16	C₂²×C₄×C₁₁	C₂×C₄	1	4	yes	—
17	C₂²×C₄×C₁₁	C₂×C₄	1	1	yes	characteristic
18	C₂²×C₄×C₁₁	C₂×C₄	1	1	yes	characteristic
19	C₂²×C₄×C₁₁	C₂³	1	1	yes	characteristic
20	C₂×C₈×C₁₁	—	2	2	no	—
21	C₂×C₈×C₁₁	—	2	1	no	—
22	C₂×C₈×C₁₁	—	2	2	no	—
23	C₂×C₈×C₁₁	—	2	1	no	—
24	C₂×C₈×C₁₁	C₂×C₄	1	2	yes	—
25	C₂×C₈×C₁₁	C₂×C₄	1	4	yes	—
26	C₂×C₈×C₁₁	C₂×C₄	1	2	yes	—
27	C₂×C₈×C₁₁	D₄	1	2	yes	—
28	C₂×C₈×C₁₁	Q₈	1	2	yes	—
29	C₁₁×C₄⋊C₄	—	2	4	no	—
30	C₄²×C₁₁	—	2	2	no	—
31	C₄²×C₁₁	—	2	2	no	—
32	C₄²×C₁₁	C₂×C₄	1	2	yes	—
33	C₄²×C₁₁	C₂×C₄	1	2	yes	—
34	#1770	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
35	C₂³×C₁₁	C₂²×C₄	1	1	yes	characteristic
36	C₂×C₄×C₁₁	—	2	2	no	—
37	C₂×C₄×C₁₁	—	2	4	no	—
38	C₂×C₄×C₁₁	—	2	4	no	—
39	C₂×C₄×C₁₁	—	2	4	no	—
40	C₂×C₄×C₁₁	C₄²	1	2	yes	—
41	C₂×C₄×C₁₁	C₄²	1	2	yes	—
42	C₂×C₄×C₁₁	M₁₆	1	4	yes	—
43	C₂×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
44	C₂×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
45	C₂×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
46	C₂×C₄×C₁₁	C₂×Q₈	1	1	yes	characteristic
47	C₂×C₄×C₁₁	#41	1	1	yes	characteristic
48	C₂×C₄×C₁₁	#41	1	1	yes	characteristic
49	C₈×C₁₁	—	2	2	no	—
50	C₈×C₁₁	—	2	4	no	—
51	C₈×C₁₁	C₄⋊C₄	1	4	yes	complemented
52	C₂×C₄⋊C₈	C₂×C₁₁	1	1	yes	characteristic
53	C₂×#97	C₂×C₁₁	1	2	yes	—
54	C₂×C₄×C₈	C₂×C₁₁	1	1	yes	characteristic
55	C₄×C₄⋊C₄	C₂×C₁₁	1	1	yes	characteristic
56	#336	C₂×C₁₁	1	2	yes	—
57	C₂²×C₁₁	C₂×C₄²	1	1	yes	characteristic
58	C₂²×C₁₁	C₄×D₄	1	1	yes	characteristic
59	C₂²×C₁₁	C₄×Q₈	1	1	yes	characteristic
60	C₂²×C₁₁	C₂×M₁₆	1	2	yes	—
61	C₂²×C₁₁	#131	1	2	yes	—
62	C₄×C₁₁	—	2	2	no	—
63	C₄×C₁₁	—	4	4	no	—
64	C₄×C₁₁	#97	1	4	yes	complemented
65	C₄×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
66	C₄×C₁₁	#117	1	1	yes	characteristic
67	C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
68	C₄×C₁₁	C₄×Q₈	1	1	yes	characteristic
69	C₂²×C₈	C₂²×C₁₁	1	1	yes	characteristic
70	C₂²×C₈	C₂²×C₁₁	1	2	yes	—
71	C₂²×C₈	C₂²×C₁₁	1	1	yes	characteristic
72	C₂×C₄⋊C₄	C₄×C₁₁	1	2	yes	—
73	C₂×C₄²	C₂²×C₁₁	1	2	yes	—
74	C₂×C₄²	C₂²×C₁₁	1	1	yes	characteristic
75	C₄⋊C₈	C₄×C₁₁	1	4	yes	complemented
76	#97	—	2	4	no	—
77	C₄×C₈	C₄×C₁₁	1	4	yes	complemented
78	#95	C₄×C₁₁	1	2	yes	—
79	C₂×C₁₁	C₄×C₄⋊C₄	1	1	yes	characteristic
80	C₂×C₁₁	C₂×#97	1	1	yes	characteristic
81	C₂×C₁₁	#405	1	1	yes	characteristic
82	C₂×C₁₁	#436	1	2	yes	—
83	C₂×C₁₁	#446	1	2	yes	—
84	C₂²×C₄	C₂×C₄×C₁₁	1	4	yes	—
85	C₂²×C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
86	C₂²×C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
87	C₂²×C₄	C₂³×C₁₁	1	1	yes	characteristic
88	C₂×C₈	—	2	2	no	—
89	C₂×C₈	—	2	1	no	—
90	C₂×C₈	—	2	1	no	—
91	C₂×C₈	—	2	2	no	—
92	C₂×C₈	C₂×C₄×C₁₁	1	2	yes	—
93	C₂×C₈	C₂×C₄×C₁₁	1	4	yes	—
94	C₂×C₈	C₂×C₄×C₁₁	1	2	yes	—
95	C₂×C₈	D₄×C₁₁	1	2	yes	—
96	C₂×C₈	Q₈×C₁₁	1	2	yes	—
97	C₄⋊C₄	—	2	4	no	—
98	C₄²	—	2	2	no	—
99	C₄²	—	2	2	no	—
100	C₄²	C₂×C₄×C₁₁	1	2	yes	—
101	C₄²	C₂×C₄×C₁₁	1	2	yes	—
102	C₁₁	#1770	1	1	yes	characteristic, direct product factor, Sylow
103	C₂³	C₂²×C₄×C₁₁	1	1	yes	characteristic
104	C₂×C₄	—	2	2	no	—
105	C₂×C₄	—	2	4	no	—
106	C₂×C₄	—	2	4	no	—
107	C₂×C₄	—	2	4	no	—
108	C₂×C₄	C₄²×C₁₁	1	2	yes	—
109	C₂×C₄	C₄²×C₁₁	1	2	yes	—
110	C₂×C₄	C₁₁×M₁₆	1	4	yes	—
111	C₂×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
112	C₂×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
113	C₂×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
114	C₂×C₄	C₂×Q₈×C₁₁	1	1	yes	characteristic
115	C₂×C₄	C₁₁×#41	1	1	yes	characteristic
116	C₂×C₄	C₁₁×#41	1	1	yes	characteristic
117	C₈	—	2	2	no	—
118	C₈	—	2	4	no	—
119	C₈	C₁₁×C₄⋊C₄	1	4	yes	complemented
120	C₂²	C₂×C₄²×C₁₁	1	1	yes	characteristic
121	C₂²	C₄×D₄×C₁₁	1	1	yes	characteristic
122	C₂²	C₄×Q₈×C₁₁	1	1	yes	characteristic
123	C₂²	C₂×C₁₁×M₁₆	1	2	yes	—
124	C₂²	C₁₁×#131	1	2	yes	—
125	C₄	—	2	2	no	—
126	C₄	—	4	4	no	—
127	C₄	C₁₁×#97	1	4	yes	complemented
128	C₄	C₂×C₁₁×C₄⋊C₄	1	1	yes	characteristic
129	C₄	C₁₁×#117	1	1	yes	characteristic
130	C₄	C₄×D₄×C₁₁	1	1	yes	characteristic
131	C₄	C₄×Q₈×C₁₁	1	1	yes	characteristic
132	C₂	C₄×C₁₁×C₄⋊C₄	1	1	yes	characteristic
133	C₂	C₂×C₁₁×#97	1	1	yes	characteristic
134	C₂	C₁₁×#405	1	1	yes	characteristic
135	C₂	C₁₁×#436	1	2	yes	—
136	C₂	C₁₁×#446	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄×C₁₁	C₂³
commutator	C₂²	C₂×C₄²×C₁₁
Frattini, cosocle	C₂²×C₄	C₂³×C₁₁
socle, prime radical	C₂³×C₁₁	C₂²×C₄
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₁ ◁ G

Complements

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

N	H ≅ G/N	type
12. C₁₁×C₄⋊C₈	C₄	semidirect
14. C₄×C₈×C₁₁	C₄	semidirect
34. #1770	C₁₁	direct (N × H)
51. C₈×C₁₁	C₄⋊C₄	semidirect
64. C₄×C₁₁	#97	semidirect
75. C₄⋊C₈	C₄×C₁₁	semidirect
77. C₄×C₈	C₄×C₁₁	semidirect
102. C₁₁	#1770	direct (N × H)
119. C₈	C₁₁×C₄⋊C₄	semidirect
127. C₄	C₁₁×#97	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₁×C₄⋊C₈	2
C₂×C₁₁×#97	2
C₂×C₄×C₈×C₁₁	2
C₄×C₁₁×C₄⋊C₄	2
C₁₁×#336	2
#1770	11

Subgroups — C11×#1770 #13064608

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#1770 #13064608