Subgroups — C₁₁×#8293 #14585486

Order 2816.

350 conjugacy classes of subgroups.

The subgroup lattice has 196 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₁₁×#108	C₂	1	1	yes	maximal, characteristic
2	C₁₁×#1564	C₂	1	1	yes	maximal, characteristic
3	C₁₁×#1451	C₂	1	2	yes	maximal
4	C₂×C₈²×C₁₁	C₂	1	1	yes	maximal, characteristic
5	C₁₁×#1278	C₂	1	2	yes	maximal
6	C₁₁×#431	C₂²	1	2	yes	—
7	C₂×C₁₁×#108	C₄	1	2	yes	—
8	C₄×C₁₁×M₁₆	C₂²	1	2	yes	—
9	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
10	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
11	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
12	C₁₁×#341	C₄	1	2	yes	—
13	C₁₁×#335	C₄	1	2	yes	—
14	C₁₁×#334	C₄	1	2	yes	—
15	C₁₁×#322	—	2	2	no	—
16	C₁₁×#322	—	2	2	no	—
17	C₈²×C₁₁	C₄	1	2	yes	—
18	C₈²×C₁₁	C₄	1	2	yes	—
19	C₂×C₁₁×M₁₆	C₂×C₄	1	4	yes	—
20	C₂²×C₈×C₁₁	—	2	1	no	—
21	C₂²×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
22	C₂²×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
23	C₂²×C₈×C₁₁	Q₈	1	2	yes	—
24	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
25	C₁₁×#108	—	2	4	no	—
26	C₁₁×C₄⋊C₈	C₂×C₄	1	4	yes	—
27	C₁₁×C₂²⋊C₈	—	2	2	no	—
28	C₁₁×#97	—	2	2	no	—
29	C₄×C₈×C₁₁	—	2	2	no	—
30	C₄×C₈×C₁₁	—	2	2	no	—
31	C₄×C₈×C₁₁	—	2	1	no	—
32	C₄×C₈×C₁₁	C₂×C₄	1	2	yes	—
33	C₄×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
34	C₄×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
35	C₄×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
36	C₄×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
37	C₄×C₈×C₁₁	C₂×C₄	1	2	yes	—
38	C₄×C₈×C₁₁	D₄	1	1	yes	characteristic
39	C₄×C₈×C₁₁	D₄	1	1	yes	characteristic
40	#8293	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
41	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
42	C₂²×C₄×C₁₁	C₂×Q₈	1	1	yes	characteristic
43	C₂²×C₄×C₁₁	#41	1	1	yes	characteristic
44	C₁₁×M₁₆	—	2	4	no	—
45	C₁₁×M₁₆	—	2	4	no	—
46	C₂×C₈×C₁₁	—	2	4	no	—
47	C₂×C₈×C₁₁	—	2	4	no	—
48	C₂×C₈×C₁₁	—	2	2	no	—
49	C₂×C₈×C₁₁	—	2	4	no	—
50	C₂×C₈×C₁₁	—	2	4	no	—
51	C₂×C₈×C₁₁	—	2	2	no	—
52	C₂×C₈×C₁₁	C₄²	1	1	yes	characteristic
53	C₂×C₈×C₁₁	C₄²	1	1	yes	characteristic
54	C₂×C₈×C₁₁	C₄²	1	1	yes	characteristic
55	C₂×C₈×C₁₁	C₄²	1	1	yes	characteristic
56	C₂×C₈×C₁₁	C₄⋊C₄	1	2	yes	—
57	C₂×C₈×C₁₁	C₄⋊C₄	1	2	yes	—
58	C₂×C₈×C₁₁	M₁₆	1	4	yes	—
59	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
60	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
61	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
62	C₄²×C₁₁	#41	1	1	yes	characteristic
63	C₄×#108	C₂×C₁₁	1	1	yes	characteristic
64	#1564	C₂×C₁₁	1	1	yes	characteristic
65	#1451	C₂×C₁₁	1	2	yes	—
66	C₂×C₈²	C₂×C₁₁	1	1	yes	characteristic
67	#1278	C₂×C₁₁	1	2	yes	—
68	C₂³×C₁₁	C₄×Q₈	1	1	yes	characteristic
69	C₂×C₄×C₁₁	—	2	2	no	—
70	C₂×C₄×C₁₁	—	2	2	no	—
71	C₂×C₄×C₁₁	C₂×C₄²	1	1	yes	characteristic
72	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
73	C₂×C₄×C₁₁	#117	1	1	yes	characteristic
74	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
75	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
76	C₂×C₄×C₁₁	C₄×Q₈	1	1	yes	characteristic
77	C₂×C₄×C₁₁	C₂×M₁₆	1	2	yes	—
78	C₂×C₄×C₁₁	#131	1	2	yes	—
79	C₈×C₁₁	—	2	4	no	—
80	C₈×C₁₁	—	2	1	no	—
81	C₈×C₁₁	—	2	1	no	—
82	C₈×C₁₁	—	2	2	no	—
83	C₈×C₁₁	—	4	4	no	—
84	C₈×C₁₁	—	4	4	no	—
85	C₈×C₁₁	#97	1	2	yes	—
86	C₈×C₁₁	#97	1	2	yes	—
87	C₈×C₁₁	#108	1	4	yes	complemented
88	#431	C₂²×C₁₁	1	2	yes	—
89	C₂×#108	C₄×C₁₁	1	2	yes	—
90	C₄×M₁₆	C₂²×C₁₁	1	2	yes	—
91	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
92	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
93	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
94	#341	C₄×C₁₁	1	2	yes	—
95	#335	C₄×C₁₁	1	2	yes	—
96	#334	C₄×C₁₁	1	2	yes	—
97	#322	—	2	2	no	—
98	#322	—	2	2	no	—
99	C₈²	C₄×C₁₁	1	2	yes	—
100	C₈²	C₄×C₁₁	1	2	yes	—
101	C₂²×C₁₁	—	2	1	no	—
102	C₂²×C₁₁	—	2	1	no	—
103	C₂²×C₁₁	C₄×C₄⋊C₄	1	1	yes	characteristic
104	C₂²×C₁₁	#446	1	2	yes	—
105	C₄×C₁₁	—	2	1	no	—
106	C₄×C₁₁	—	2	1	no	—
107	C₄×C₁₁	C₂×#97	1	1	yes	characteristic
108	C₄×C₁₁	#405	1	1	yes	characteristic
109	C₄×C₁₁	C₂×#108	1	2	yes	—
110	C₄×C₁₁	#436	1	2	yes	—
111	C₄×C₁₁	#443	1	2	yes	—
112	C₂×M₁₆	C₂×C₄×C₁₁	1	4	yes	—
113	C₂²×C₈	—	2	1	no	—
114	C₂²×C₈	C₂×C₄×C₁₁	1	1	yes	characteristic
115	C₂²×C₈	C₂×C₄×C₁₁	1	1	yes	characteristic
116	C₂²×C₈	Q₈×C₁₁	1	2	yes	—
117	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
118	#108	—	2	4	no	—
119	C₄⋊C₈	C₂×C₄×C₁₁	1	4	yes	—
120	C₂²⋊C₈	—	2	2	no	—
121	#97	—	2	2	no	—
122	C₄×C₈	—	2	2	no	—
123	C₄×C₈	—	2	2	no	—
124	C₄×C₈	—	2	1	no	—
125	C₄×C₈	C₂×C₄×C₁₁	1	2	yes	—
126	C₄×C₈	C₂×C₄×C₁₁	1	1	yes	characteristic
127	C₄×C₈	C₂×C₄×C₁₁	1	1	yes	characteristic
128	C₄×C₈	C₂×C₄×C₁₁	1	1	yes	characteristic
129	C₄×C₈	C₂×C₄×C₁₁	1	1	yes	characteristic
130	C₄×C₈	C₂×C₄×C₁₁	1	2	yes	—
131	C₄×C₈	D₄×C₁₁	1	1	yes	characteristic
132	C₄×C₈	D₄×C₁₁	1	1	yes	characteristic
133	C₂×C₁₁	—	2	2	no	—
134	C₂×C₁₁	#1770	1	1	yes	characteristic
135	C₂×C₁₁	#1772	1	1	yes	characteristic
136	C₂×C₁₁	C₄×#108	1	1	yes	characteristic
137	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
138	C₂²×C₄	C₂×Q₈×C₁₁	1	1	yes	characteristic
139	C₂²×C₄	C₁₁×#41	1	1	yes	characteristic
140	M₁₆	—	2	4	no	—
141	M₁₆	—	2	4	no	—
142	C₂×C₈	—	2	4	no	—
143	C₂×C₈	—	2	2	no	—
144	C₂×C₈	—	2	2	no	—
145	C₂×C₈	—	2	4	no	—
146	C₂×C₈	—	2	4	no	—
147	C₂×C₈	—	2	4	no	—
148	C₂×C₈	C₄²×C₁₁	1	1	yes	characteristic
149	C₂×C₈	C₄²×C₁₁	1	1	yes	characteristic
150	C₂×C₈	C₄²×C₁₁	1	1	yes	characteristic
151	C₂×C₈	C₄²×C₁₁	1	1	yes	characteristic
152	C₂×C₈	C₁₁×C₄⋊C₄	1	2	yes	—
153	C₂×C₈	C₁₁×C₄⋊C₄	1	2	yes	—
154	C₂×C₈	C₁₁×M₁₆	1	4	yes	—
155	C₄²	C₂²×C₄×C₁₁	1	1	yes	characteristic
156	C₄²	C₂²×C₄×C₁₁	1	1	yes	characteristic
157	C₄²	C₂×D₄×C₁₁	1	1	yes	characteristic
158	C₄²	C₁₁×#41	1	1	yes	characteristic
159	C₁₁	#8293	1	1	yes	characteristic, direct product factor, Sylow
160	C₂³	C₄×Q₈×C₁₁	1	1	yes	characteristic
161	C₂×C₄	—	2	2	no	—
162	C₂×C₄	—	2	2	no	—
163	C₂×C₄	C₂×C₄²×C₁₁	1	1	yes	characteristic
164	C₂×C₄	C₂×C₁₁×C₄⋊C₄	1	1	yes	characteristic
165	C₂×C₄	C₁₁×#117	1	1	yes	characteristic
166	C₂×C₄	C₄×D₄×C₁₁	1	1	yes	characteristic
167	C₂×C₄	C₄×D₄×C₁₁	1	1	yes	characteristic
168	C₂×C₄	C₄×Q₈×C₁₁	1	1	yes	characteristic
169	C₂×C₄	C₂×C₁₁×M₁₆	1	2	yes	—
170	C₂×C₄	C₁₁×#131	1	2	yes	—
171	C₈	—	2	4	no	—
172	C₈	—	2	1	no	—
173	C₈	—	2	1	no	—
174	C₈	—	2	2	no	—
175	C₈	—	4	4	no	—
176	C₈	—	4	4	no	—
177	C₈	C₁₁×#97	1	2	yes	—
178	C₈	C₁₁×#97	1	2	yes	—
179	C₈	C₁₁×#108	1	4	yes	complemented
180	C₂²	—	2	1	no	—
181	C₂²	—	2	1	no	—
182	C₂²	C₄×C₁₁×C₄⋊C₄	1	1	yes	characteristic
183	C₂²	C₁₁×#446	1	2	yes	—
184	C₄	—	2	1	no	—
185	C₄	—	2	1	no	—
186	C₄	C₂×C₁₁×#97	1	1	yes	characteristic
187	C₄	C₁₁×#405	1	1	yes	characteristic
188	C₄	C₂×C₁₁×#108	1	2	yes	—
189	C₄	C₁₁×#436	1	2	yes	—
190	C₄	C₁₁×#443	1	2	yes	—
191	C₂	—	2	2	no	—
192	C₂	C₁₁×#1770	1	1	yes	characteristic
193	C₂	C₁₁×#1772	1	1	yes	characteristic
194	C₂	C₄×C₁₁×#108	1	1	yes	characteristic

	subgroup	G/H
center	C₄²×C₁₁	C₂×D₄
commutator	C₂×C₄	C₂×C₄²×C₁₁
Frattini, cosocle	C₂×C₄²	C₂³×C₁₁
socle	C₂²×C₁₁	C₄×C₄⋊C₄
prime radical	C₂³×C₁₁	C₄×Q₈
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄²×C₁₁ ◁ C₂×C₄×C₈×C₁₁ ◁ G

Complements

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

N	H ≅ G/N	type
40. #8293	C₁₁	direct (N × H)
87. C₈×C₁₁	#108	semidirect
159. C₁₁	#8293	direct (N × H)
179. C₈	C₁₁×#108	semidirect

Maximal subgroups

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

subgroup	index
C₄×C₁₁×#108	2
C₁₁×#1564	2
C₁₁×#1451	2
C₂×C₈²×C₁₁	2
C₁₁×#1278	2
#8293	11

Subgroups — C11×#8293 #14585486

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#8293 #14585486