Subgroups — C₁₁×#21969 #14599162

Order 2816.

734 conjugacy classes of subgroups.

The subgroup lattice has 278 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×#2920	C₂	1	2	yes	maximal
2	C₂²×C₁₁×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic
3	C₁₁×#1950	C₂	1	8	yes	maximal, complemented
4	C₁₁×#1810	C₂	1	4	yes	maximal
5	C₂³×C₈×C₁₁	C₂²	1	2	yes	—
6	C₂²×C₄²×C₁₁	C₂²	1	1	yes	characteristic
7	C₁₁×#432	—	2	2	no	—
8	C₁₁×#432	—	2	2	no	—
9	C₁₁×#431	—	2	2	no	—
10	C₁₁×#431	—	2	2	no	—
11	C₂×C₁₁×#108	C₂²	1	8	yes	—
12	C₁₁×#423	C₂²	1	4	yes	—
13	C₂×C₁₁×C₄⋊C₈	C₄	1	4	yes	—
14	C₂×C₁₁×C₄⋊C₈	C₄	1	2	yes	—
15	C₂×C₁₁×C₄⋊C₈	C₄	1	2	yes	—
16	C₂×C₁₁×C₄⋊C₈	C₂²	1	4	yes	—
17	C₁₁×#407	C₂²	1	4	yes	—
18	C₄×C₁₁×M₁₆	C₂²	1	4	yes	—
19	C₁₁×#341	C₂²	1	8	yes	—
20	C₂³×C₄×C₁₁	Q₈	1	1	yes	characteristic
21	C₂³×C₄×C₁₁	Q₈	1	1	yes	characteristic
22	C₂³×C₄×C₁₁	C₂³	1	1	yes	characteristic
23	C₂×C₁₁×M₁₆	C₂³	1	8	yes	—
24	C₂²×C₈×C₁₁	—	4	4	no	—
25	C₂²×C₈×C₁₁	C₂×C₄	1	4	yes	—
26	C₂²×C₈×C₁₁	C₂×C₄	1	4	yes	—
27	C₂²×C₈×C₁₁	C₂³	1	4	yes	—
28	C₂×C₄²×C₁₁	C₂×C₄	1	2	yes	—
29	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
30	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
31	C₂×C₄²×C₁₁	D₄	1	1	yes	characteristic
32	C₂×C₄²×C₁₁	D₄	1	2	yes	—
33	C₂×C₄²×C₁₁	D₄	1	1	yes	characteristic
34	C₂×C₄²×C₁₁	Q₈	1	2	yes	—
35	C₂×C₄²×C₁₁	C₂³	1	2	yes	—
36	C₁₁×#108	—	4	8	no	—
37	C₁₁×C₄⋊C₈	—	2	4	no	—
38	C₁₁×C₄⋊C₈	—	2	4	no	—
39	C₁₁×C₄⋊C₈	C₂×C₄	1	8	yes	—
40	C₁₁×C₄⋊C₈	C₂×C₄	1	8	yes	—
41	C₁₁×C₂²⋊C₈	—	2	4	no	—
42	C₁₁×C₂²⋊C₈	—	2	4	no	—
43	C₁₁×#97	—	2	4	no	—
44	C₄×C₈×C₁₁	—	2	4	no	—
45	#21969	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
46	C₂⁴×C₁₁	C₂×Q₈	1	1	yes	characteristic
47	C₂²×C₄×C₁₁	—	2	4	no	—
48	C₂²×C₄×C₁₁	—	2	2	no	—
49	C₂²×C₄×C₁₁	—	2	2	no	—
50	C₂²×C₄×C₁₁	—	4	2	no	—
51	C₂²×C₄×C₁₁	C₄⋊C₄	1	1	yes	characteristic
52	C₂²×C₄×C₁₁	C₄⋊C₄	1	2	yes	—
53	C₂²×C₄×C₁₁	C₄⋊C₄	1	2	yes	—
54	C₂²×C₄×C₁₁	C₄⋊C₄	1	1	yes	characteristic
55	C₂²×C₄×C₁₁	C₄⋊C₄	1	1	yes	characteristic
56	C₂²×C₄×C₁₁	C₄⋊C₄	1	1	yes	characteristic
57	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
58	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
59	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
60	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
61	C₂²×C₄×C₁₁	C₂×Q₈	1	1	yes	characteristic
62	C₂²×C₄×C₁₁	C₂×Q₈	1	2	yes	—
63	C₂²×C₄×C₁₁	C₂×Q₈	1	2	yes	—
64	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
65	C₁₁×M₁₆	—	2	8	no	—
66	C₁₁×M₁₆	—	2	8	no	—
67	C₂×C₈×C₁₁	—	2	8	no	—
68	C₂×C₈×C₁₁	—	2	8	no	—
69	C₂×C₈×C₁₁	—	4	4	no	—
70	C₂×C₈×C₁₁	—	4	4	no	—
71	C₂×C₈×C₁₁	C₂²×C₄	1	8	yes	—
72	C₄²×C₁₁	C₄⋊C₄	1	2	yes	—
73	C₄²×C₁₁	C₄⋊C₄	1	2	yes	—
74	C₄²×C₁₁	C₄⋊C₄	1	2	yes	—
75	C₄²×C₁₁	C₄⋊C₄	1	2	yes	—
76	C₄²×C₁₁	C₂²×C₄	1	2	yes	—
77	C₄²×C₁₁	C₂²×C₄	1	2	yes	—
78	C₄²×C₁₁	C₂×D₄	1	2	yes	—
79	C₄²×C₁₁	C₂×D₄	1	2	yes	—
80	#2920	C₂×C₁₁	1	2	yes	—
81	C₂²×C₄⋊C₈	C₂×C₁₁	1	1	yes	characteristic
82	#1950	C₂×C₁₁	1	8	yes	complemented
83	#1810	C₂×C₁₁	1	4	yes	—
84	C₂³×C₁₁	—	2	2	no	—
85	C₂³×C₁₁	—	2	2	no	—
86	C₂³×C₁₁	—	2	2	no	—
87	C₂³×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
88	C₂³×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
89	C₂³×C₁₁	C₂²×Q₈	1	1	yes	characteristic
90	C₂×C₄×C₁₁	—	2	2	no	—
91	C₂×C₄×C₁₁	—	2	2	no	—
92	C₂×C₄×C₁₁	—	2	4	no	—
93	C₂×C₄×C₁₁	—	2	1	no	—
94	C₂×C₄×C₁₁	—	2	1	no	—
95	C₂×C₄×C₁₁	—	2	1	no	—
96	C₂×C₄×C₁₁	—	2	1	no	—
97	C₂×C₄×C₁₁	—	2	2	no	—
98	C₂×C₄×C₁₁	—	2	2	no	—
99	C₂×C₄×C₁₁	—	2	4	no	—
100	C₂×C₄×C₁₁	—	2	4	no	—
101	C₂×C₄×C₁₁	—	4	1	no	—
102	C₂×C₄×C₁₁	—	4	1	no	—
103	C₂×C₄×C₁₁	—	4	2	no	—
104	C₂×C₄×C₁₁	#108	1	4	yes	complemented
105	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
106	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
107	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	2	yes	—
108	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	2	yes	—
109	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	2	yes	—
110	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	2	yes	—
111	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
112	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
113	C₂×C₄×C₁₁	H(5,𝔽₂)	1	2	yes	—
114	C₂×C₄×C₁₁	2₋¹⁺⁴	1	2	yes	—
115	C₈×C₁₁	—	2	8	no	—
116	C₈×C₁₁	—	4	8	no	—
117	C₂³×C₈	C₂²×C₁₁	1	2	yes	—
118	C₂²×C₄²	C₂²×C₁₁	1	1	yes	characteristic
119	#432	—	2	2	no	—
120	#432	—	2	2	no	—
121	#431	—	2	2	no	—
122	#431	—	2	2	no	—
123	C₂×#108	C₂²×C₁₁	1	8	yes	—
124	#423	C₂²×C₁₁	1	4	yes	—
125	C₂×C₄⋊C₈	C₄×C₁₁	1	4	yes	—
126	C₂×C₄⋊C₈	C₄×C₁₁	1	2	yes	—
127	C₂×C₄⋊C₈	C₄×C₁₁	1	2	yes	—
128	C₂×C₄⋊C₈	C₂²×C₁₁	1	4	yes	—
129	#407	C₂²×C₁₁	1	4	yes	—
130	C₄×M₁₆	C₂²×C₁₁	1	4	yes	—
131	#341	C₂²×C₁₁	1	8	yes	—
132	C₂²×C₁₁	—	2	8	no	—
133	C₂²×C₁₁	—	2	1	no	—
134	C₂²×C₁₁	—	2	1	no	—
135	C₂²×C₁₁	—	2	1	no	—
136	C₂²×C₁₁	—	2	1	no	—
137	C₂²×C₁₁	—	2	1	no	—
138	C₂²×C₁₁	—	2	1	no	—
139	C₂²×C₁₁	C₂×#108	1	2	yes	—
140	C₂²×C₁₁	#430	1	2	yes	—
141	C₂²×C₁₁	C₂²×C₄⋊C₄	1	1	yes	characteristic
142	C₂²×C₁₁	#544	1	2	yes	—
143	C₄×C₁₁	—	2	1	no	—
144	C₄×C₁₁	—	2	1	no	—
145	C₄×C₁₁	—	2	2	no	—
146	C₄×C₁₁	—	2	2	no	—
147	C₄×C₁₁	—	2	2	no	—
148	C₄×C₁₁	C₂×#108	1	4	yes	—
149	C₄×C₁₁	#518	1	1	yes	characteristic
150	C₄×C₁₁	#519	1	1	yes	characteristic
151	C₄×C₁₁	#537	1	2	yes	—
152	C₂³×C₄	Q₈×C₁₁	1	1	yes	characteristic
153	C₂³×C₄	Q₈×C₁₁	1	1	yes	characteristic
154	C₂³×C₄	C₂³×C₁₁	1	1	yes	characteristic
155	C₂×M₁₆	C₂³×C₁₁	1	8	yes	—
156	C₂²×C₈	—	4	4	no	—
157	C₂²×C₈	C₂×C₄×C₁₁	1	4	yes	—
158	C₂²×C₈	C₂×C₄×C₁₁	1	4	yes	—
159	C₂²×C₈	C₂³×C₁₁	1	4	yes	—
160	C₂×C₄²	C₂×C₄×C₁₁	1	2	yes	—
161	C₂×C₄²	C₂×C₄×C₁₁	1	1	yes	characteristic
162	C₂×C₄²	C₂×C₄×C₁₁	1	1	yes	characteristic
163	C₂×C₄²	D₄×C₁₁	1	1	yes	characteristic
164	C₂×C₄²	D₄×C₁₁	1	2	yes	—
165	C₂×C₄²	D₄×C₁₁	1	1	yes	characteristic
166	C₂×C₄²	Q₈×C₁₁	1	2	yes	—
167	C₂×C₄²	C₂³×C₁₁	1	2	yes	—
168	#108	—	4	8	no	—
169	C₄⋊C₈	—	2	4	no	—
170	C₄⋊C₈	—	2	4	no	—
171	C₄⋊C₈	C₂×C₄×C₁₁	1	8	yes	—
172	C₄⋊C₈	C₂×C₄×C₁₁	1	8	yes	—
173	C₂²⋊C₈	—	2	4	no	—
174	C₂²⋊C₈	—	2	4	no	—
175	#97	—	2	4	no	—
176	C₄×C₈	—	2	4	no	—
177	C₂×C₁₁	—	2	2	no	—
178	C₂×C₁₁	—	2	2	no	—
179	C₂×C₁₁	—	2	2	no	—
180	C₂×C₁₁	#2316	1	1	yes	characteristic
181	C₂×C₁₁	C₂²×#108	1	1	yes	characteristic
182	C₂×C₁₁	C₂×#430	1	1	yes	characteristic
183	C₂⁴	C₂×Q₈×C₁₁	1	1	yes	characteristic
184	C₂²×C₄	—	2	4	no	—
185	C₂²×C₄	—	2	2	no	—
186	C₂²×C₄	—	2	2	no	—
187	C₂²×C₄	—	4	2	no	—
188	C₂²×C₄	C₁₁×C₄⋊C₄	1	1	yes	characteristic
189	C₂²×C₄	C₁₁×C₄⋊C₄	1	2	yes	—
190	C₂²×C₄	C₁₁×C₄⋊C₄	1	2	yes	—
191	C₂²×C₄	C₁₁×C₄⋊C₄	1	1	yes	characteristic
192	C₂²×C₄	C₁₁×C₄⋊C₄	1	1	yes	characteristic
193	C₂²×C₄	C₁₁×C₄⋊C₄	1	1	yes	characteristic
194	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
195	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
196	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
197	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
198	C₂²×C₄	C₂×Q₈×C₁₁	1	1	yes	characteristic
199	C₂²×C₄	C₂×Q₈×C₁₁	1	2	yes	—
200	C₂²×C₄	C₂×Q₈×C₁₁	1	2	yes	—
201	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
202	M₁₆	—	2	8	no	—
203	M₁₆	—	2	8	no	—
204	C₂×C₈	—	2	8	no	—
205	C₂×C₈	—	2	8	no	—
206	C₂×C₈	—	4	4	no	—
207	C₂×C₈	—	4	4	no	—
208	C₂×C₈	C₂²×C₄×C₁₁	1	8	yes	—
209	C₄²	C₁₁×C₄⋊C₄	1	2	yes	—
210	C₄²	C₁₁×C₄⋊C₄	1	2	yes	—
211	C₄²	C₁₁×C₄⋊C₄	1	2	yes	—
212	C₄²	C₁₁×C₄⋊C₄	1	2	yes	—
213	C₄²	C₂²×C₄×C₁₁	1	2	yes	—
214	C₄²	C₂²×C₄×C₁₁	1	2	yes	—
215	C₄²	C₂×D₄×C₁₁	1	2	yes	—
216	C₄²	C₂×D₄×C₁₁	1	2	yes	—
217	C₁₁	#21969	1	1	yes	characteristic, direct product factor, Sylow
218	C₂³	—	2	2	no	—
219	C₂³	—	2	2	no	—
220	C₂³	—	2	2	no	—
221	C₂³	C₂×C₁₁×C₄⋊C₄	1	1	yes	characteristic
222	C₂³	C₂×C₁₁×C₄⋊C₄	1	1	yes	characteristic
223	C₂³	C₂²×Q₈×C₁₁	1	1	yes	characteristic
224	C₂×C₄	—	2	2	no	—
225	C₂×C₄	—	2	2	no	—
226	C₂×C₄	—	2	4	no	—
227	C₂×C₄	—	2	1	no	—
228	C₂×C₄	—	2	1	no	—
229	C₂×C₄	—	2	1	no	—
230	C₂×C₄	—	2	1	no	—
231	C₂×C₄	—	2	2	no	—
232	C₂×C₄	—	2	2	no	—
233	C₂×C₄	—	2	4	no	—
234	C₂×C₄	—	2	4	no	—
235	C₂×C₄	—	4	1	no	—
236	C₂×C₄	—	4	1	no	—
237	C₂×C₄	—	4	2	no	—
238	C₂×C₄	C₁₁×#108	1	4	yes	complemented
239	C₂×C₄	C₂×C₁₁×C₄⋊C₄	1	1	yes	characteristic
240	C₂×C₄	C₂×C₁₁×C₄⋊C₄	1	1	yes	characteristic
241	C₂×C₄	C₂×C₁₁×C₄⋊C₄	1	2	yes	—
242	C₂×C₄	C₂×C₁₁×C₄⋊C₄	1	2	yes	—
243	C₂×C₄	C₂×C₁₁×C₄⋊C₄	1	2	yes	—
244	C₂×C₄	C₂×C₁₁×C₄⋊C₄	1	2	yes	—
245	C₂×C₄	C₂³×C₄×C₁₁	1	1	yes	characteristic
246	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
247	C₂×C₄	C₁₁×H(5,𝔽₂)	1	2	yes	—
248	C₂×C₄	C₁₁×2₋¹⁺⁴	1	2	yes	—
249	C₈	—	2	8	no	—
250	C₈	—	4	8	no	—
251	C₂²	—	2	8	no	—
252	C₂²	—	2	1	no	—
253	C₂²	—	2	1	no	—
254	C₂²	—	2	1	no	—
255	C₂²	—	2	1	no	—
256	C₂²	—	2	1	no	—
257	C₂²	—	2	1	no	—
258	C₂²	C₂×C₁₁×#108	1	2	yes	—
259	C₂²	C₁₁×#430	1	2	yes	—
260	C₂²	C₂²×C₁₁×C₄⋊C₄	1	1	yes	characteristic
261	C₂²	C₁₁×#544	1	2	yes	—
262	C₄	—	2	2	no	—
263	C₄	—	2	2	no	—
264	C₄	—	2	2	no	—
265	C₄	—	2	1	no	—
266	C₄	—	2	1	no	—
267	C₄	C₂×C₁₁×#108	1	4	yes	—
268	C₄	C₁₁×#518	1	1	yes	characteristic
269	C₄	C₁₁×#519	1	1	yes	characteristic
270	C₄	C₁₁×#537	1	2	yes	—
271	C₂	—	2	2	no	—
272	C₂	—	2	2	no	—
273	C₂	—	2	2	no	—
274	C₂	C₁₁×#2316	1	1	yes	characteristic
275	C₂	C₂²×C₁₁×#108	1	1	yes	characteristic
276	C₂	C₂×C₁₁×#430	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₁	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₁
socle	C₂²×C₁₁	C₂²×C₄⋊C₄
prime radical	C₂⁴×C₁₁	C₂×Q₈
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₁ ◁ C₂²×C₄²×C₁₁ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₁₁×#1950	C₂	semidirect
45. #21969	C₁₁	direct (N × H)
82. #1950	C₂×C₁₁	semidirect
104. C₂×C₄×C₁₁	#108	semidirect
217. C₁₁	#21969	direct (N × H)
238. C₂×C₄	C₁₁×#108	semidirect

Maximal subgroups

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

subgroup	index
C₁₁×#2920	2
C₂²×C₁₁×C₄⋊C₈	2
C₁₁×#1950	2
C₁₁×#1810	2
#21969	11

Subgroups — C11×#21969 #14599162

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#21969 #14599162