Subgroups — C₁₁×#11493 #14588686

Order 2816.

342 conjugacy classes of subgroups.

The subgroup lattice has 182 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₈×Q₈×C₁₁	C₂	1	1	yes	maximal, characteristic
2	C₁₁×#2162	C₂	1	2	yes	maximal
3	C₁₁×#1322	C₂	1	4	yes	maximal
4	C₂×C₄×Q₈×C₁₁	C₄	1	1	yes	characteristic
5	C₈×Q₈×C₁₁	—	2	2	no	—
6	C₈×Q₈×C₁₁	—	2	2	no	—
7	C₂×C₁₁×C₄⋊C₈	C₄	1	1	yes	characteristic
8	C₂×C₁₁×C₄⋊C₈	C₂²	1	2	yes	—
9	C₂×C₄×C₈×C₁₁	C₄	1	2	yes	—
10	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
11	C₁₁×C₄⋊C₁₆	—	2	2	no	—
12	C₁₁×C₂²⋊C₁₆	C₂²	1	4	yes	—
13	C₄×C₁₁×C₁₆	—	2	2	no	—
14	C₂²×Q₈×C₁₁	C₈	1	1	yes	characteristic
15	C₂²×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
16	C₂²×C₈×C₁₁	C₂×C₄	1	2	yes	—
17	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
18	C₄×Q₈×C₁₁	—	2	2	no	—
19	C₄×Q₈×C₁₁	—	2	2	no	—
20	C₂×C₁₁×C₄⋊C₄	C₈	1	2	yes	—
21	C₂×C₁₁×C₄⋊C₄	C₈	1	1	yes	characteristic
22	C₂×C₄²×C₁₁	C₂×C₄	1	2	yes	—
23	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
24	C₂×C₁₁×C₁₆	—	2	4	no	—
25	C₁₁×C₄⋊C₈	—	2	4	no	—
26	C₁₁×C₄⋊C₈	—	2	2	no	—
27	C₄×C₈×C₁₁	—	2	2	no	—
28	C₄×C₈×C₁₁	—	2	2	no	—
29	C₄×C₈×C₁₁	D₄	1	2	yes	—
30	C₄×C₈×C₁₁	D₄	1	2	yes	—
31	#11493	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
32	C₂×Q₈×C₁₁	—	2	2	no	—
33	C₂×Q₈×C₁₁	—	2	2	no	—
34	C₂×Q₈×C₁₁	C₁₆	1	4	yes	complemented
35	C₂²×C₄×C₁₁	C₂×C₈	1	2	yes	—
36	C₂²×C₄×C₁₁	C₂×C₈	1	2	yes	—
37	C₂²×C₄×C₁₁	C₂×C₈	1	1	yes	characteristic
38	C₂²×C₄×C₁₁	C₂×C₈	1	1	yes	characteristic
39	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
40	C₂×C₈×C₁₁	—	2	2	no	—
41	C₂×C₈×C₁₁	—	2	2	no	—
42	C₂×C₈×C₁₁	—	4	1	no	—
43	C₂×C₈×C₁₁	—	4	2	no	—
44	C₂×C₈×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
45	C₂×C₈×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
46	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
47	C₁₁×C₄⋊C₄	—	2	4	no	—
48	C₁₁×C₄⋊C₄	—	2	2	no	—
49	C₄²×C₁₁	—	2	2	no	—
50	C₄²×C₁₁	—	2	2	no	—
51	C₄²×C₁₁	C₂²⋊C₄	1	2	yes	—
52	C₄²×C₁₁	M₁₆	1	2	yes	—
53	C₁₁×C₁₆	—	4	4	no	—
54	C₂×C₈×Q₈	C₂×C₁₁	1	1	yes	characteristic
55	#2162	C₂×C₁₁	1	2	yes	—
56	#1322	C₂×C₁₁	1	4	yes	—
57	C₂³×C₁₁	C₂²×C₈	1	1	yes	characteristic
58	Q₈×C₁₁	—	2	8	no	—
59	C₂×C₄×C₁₁	—	2	2	no	—
60	C₂×C₄×C₁₁	—	2	2	no	—
61	C₂×C₄×C₁₁	—	2	1	no	—
62	C₂×C₄×C₁₁	—	2	1	no	—
63	C₂×C₄×C₁₁	—	2	2	no	—
64	C₂×C₄×C₁₁	—	4	1	no	—
65	C₂×C₄×C₁₁	—	4	2	no	—
66	C₂×C₄×C₁₁	C₂²⋊C₈	1	2	yes	—
67	C₂×C₄×C₁₁	C₂²⋊C₈	1	2	yes	—
68	C₂×C₄×C₁₁	C₂×C₁₆	1	4	yes	—
69	C₂×C₄×C₁₁	C₂×C₁₆	1	2	yes	—
70	C₂×C₄×C₁₁	M₃₂	1	2	yes	—
71	C₂×C₄×C₁₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
72	C₂×C₄×C₁₁	C₂×M₁₆	1	1	yes	characteristic
73	C₈×C₁₁	—	2	2	no	—
74	C₈×C₁₁	—	2	1	no	—
75	C₈×C₁₁	—	4	2	no	—
76	C₈×C₁₁	#101	1	2	yes	—
77	C₂×C₄×Q₈	C₄×C₁₁	1	1	yes	characteristic
78	C₈×Q₈	—	2	2	no	—
79	C₈×Q₈	—	2	2	no	—
80	C₂×C₄⋊C₈	C₄×C₁₁	1	1	yes	characteristic
81	C₂×C₄⋊C₈	C₂²×C₁₁	1	2	yes	—
82	C₂×C₄×C₈	C₄×C₁₁	1	2	yes	—
83	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
84	C₄⋊C₁₆	—	2	2	no	—
85	C₂²⋊C₁₆	C₂²×C₁₁	1	4	yes	—
86	C₄×C₁₆	—	2	2	no	—
87	C₂²×C₁₁	—	2	1	no	—
88	C₂²×C₁₁	—	2	1	no	—
89	C₂²×C₁₁	C₂×C₂²⋊C₈	1	1	yes	characteristic
90	C₂²×C₁₁	C₂²×C₁₆	1	1	yes	characteristic
91	C₂²×C₁₁	C₂×M₃₂	1	1	yes	characteristic
92	C₄×C₁₁	—	2	4	no	—
93	C₄×C₁₁	—	2	2	no	—
94	C₄×C₁₁	—	2	1	no	—
95	C₄×C₁₁	—	4	2	no	—
96	C₄×C₁₁	C₂²⋊C₁₆	1	4	yes	—
97	C₄×C₁₁	#410	1	1	yes	characteristic
98	C₄×C₁₁	C₂×#101	1	1	yes	characteristic
99	C₂²×Q₈	C₈×C₁₁	1	1	yes	characteristic
100	C₂²×C₈	C₂×C₄×C₁₁	1	1	yes	characteristic
101	C₂²×C₈	C₂×C₄×C₁₁	1	2	yes	—
102	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
103	C₄×Q₈	—	2	2	no	—
104	C₄×Q₈	—	2	2	no	—
105	C₂×C₄⋊C₄	C₈×C₁₁	1	2	yes	—
106	C₂×C₄⋊C₄	C₈×C₁₁	1	1	yes	characteristic
107	C₂×C₄²	C₂×C₄×C₁₁	1	2	yes	—
108	C₂×C₄²	C₂×C₄×C₁₁	1	1	yes	characteristic
109	C₂×C₁₆	—	2	4	no	—
110	C₄⋊C₈	—	2	4	no	—
111	C₄⋊C₈	—	2	2	no	—
112	C₄×C₈	—	2	2	no	—
113	C₄×C₈	—	2	2	no	—
114	C₄×C₈	D₄×C₁₁	1	2	yes	—
115	C₄×C₈	D₄×C₁₁	1	2	yes	—
116	C₂×C₁₁	—	2	1	no	—
117	C₂×C₁₁	—	2	1	no	—
118	C₂×C₁₁	#1461	1	1	yes	characteristic
119	C₂×C₁₁	C₂×C₂²⋊C₁₆	1	1	yes	characteristic
120	C₂×C₁₁	#2115	1	1	yes	characteristic
121	C₂×Q₈	—	2	2	no	—
122	C₂×Q₈	—	2	2	no	—
123	C₂×Q₈	C₁₁×C₁₆	1	4	yes	complemented
124	C₂²×C₄	C₂×C₈×C₁₁	1	2	yes	—
125	C₂²×C₄	C₂×C₈×C₁₁	1	2	yes	—
126	C₂²×C₄	C₂×C₈×C₁₁	1	1	yes	characteristic
127	C₂²×C₄	C₂×C₈×C₁₁	1	1	yes	characteristic
128	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
129	C₂×C₈	—	2	2	no	—
130	C₂×C₈	—	2	2	no	—
131	C₂×C₈	—	4	1	no	—
132	C₂×C₈	—	4	2	no	—
133	C₂×C₈	C₁₁×C₂²⋊C₄	1	1	yes	characteristic
134	C₂×C₈	C₁₁×C₂²⋊C₄	1	1	yes	characteristic
135	C₂×C₈	C₂×D₄×C₁₁	1	2	yes	—
136	C₄⋊C₄	—	2	4	no	—
137	C₄⋊C₄	—	2	2	no	—
138	C₄²	—	2	2	no	—
139	C₄²	—	2	2	no	—
140	C₄²	C₁₁×C₂²⋊C₄	1	2	yes	—
141	C₄²	C₁₁×M₁₆	1	2	yes	—
142	C₁₆	—	4	4	no	—
143	C₁₁	#11493	1	1	yes	characteristic, direct product factor, Sylow
144	C₂³	C₂²×C₈×C₁₁	1	1	yes	characteristic
145	Q₈	—	2	8	no	—
146	C₂×C₄	—	2	2	no	—
147	C₂×C₄	—	2	2	no	—
148	C₂×C₄	—	2	1	no	—
149	C₂×C₄	—	2	1	no	—
150	C₂×C₄	—	2	2	no	—
151	C₂×C₄	—	4	1	no	—
152	C₂×C₄	—	4	2	no	—
153	C₂×C₄	C₁₁×C₂²⋊C₈	1	2	yes	—
154	C₂×C₄	C₁₁×C₂²⋊C₈	1	2	yes	—
155	C₂×C₄	C₂×C₁₁×C₁₆	1	4	yes	—
156	C₂×C₄	C₂×C₁₁×C₁₆	1	2	yes	—
157	C₂×C₄	C₁₁×M₃₂	1	2	yes	—
158	C₂×C₄	C₂×C₁₁×C₂²⋊C₄	1	1	yes	characteristic
159	C₂×C₄	C₂×C₁₁×M₁₆	1	1	yes	characteristic
160	C₈	—	2	2	no	—
161	C₈	—	2	1	no	—
162	C₈	—	4	2	no	—
163	C₈	C₁₁×#101	1	2	yes	—
164	C₂²	—	2	1	no	—
165	C₂²	—	2	1	no	—
166	C₂²	C₂×C₁₁×C₂²⋊C₈	1	1	yes	characteristic
167	C₂²	C₂²×C₁₁×C₁₆	1	1	yes	characteristic
168	C₂²	C₂×C₁₁×M₃₂	1	1	yes	characteristic
169	C₄	—	2	1	no	—
170	C₄	—	2	4	no	—
171	C₄	—	2	2	no	—
172	C₄	—	4	2	no	—
173	C₄	C₁₁×C₂²⋊C₁₆	1	4	yes	—
174	C₄	C₁₁×#410	1	1	yes	characteristic
175	C₄	C₂×C₁₁×#101	1	1	yes	characteristic
176	C₂	—	2	1	no	—
177	C₂	—	2	1	no	—
178	C₂	C₁₁×#1461	1	1	yes	characteristic
179	C₂	C₂×C₁₁×C₂²⋊C₁₆	1	1	yes	characteristic
180	C₂	C₁₁×#2115	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈×C₁₁	C₂²⋊C₄
commutator	C₂²	C₂²×C₁₁×C₁₆
Frattini, cosocle	C₂²×C₈	C₂³×C₁₁
socle	C₂²×C₁₁	C₂×C₂²⋊C₈
prime radical	C₂³×C₁₁	C₂²×C₈
LCS	G ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₈×C₁₁ ◁ C₂×C₄×C₈×C₁₁ ◁ G

Complements

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

N	H ≅ G/N	type
31. #11493	C₁₁	direct (N × H)
34. C₂×Q₈×C₁₁	C₁₆	semidirect
123. C₂×Q₈	C₁₁×C₁₆	semidirect
143. C₁₁	#11493	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₈×Q₈×C₁₁	2
C₁₁×#2162	2
C₁₁×#1322	2
#11493	11

Subgroups — C11×#11493 #14588686

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#11493 #14588686