Subgroups — C₁₁×#11246 #14588439

Order 2816.

624 conjugacy classes of subgroups.

The subgroup lattice has 302 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₁×#430	C₂	1	1	yes	maximal, characteristic
2	C₁₁×#2905	C₂	1	1	yes	maximal, characteristic
3	C₁₁×#1742	C₂	1	2	yes	maximal
4	C₂×C₁₁×H(3,ℤ/4)	C₂	1	1	yes	maximal, characteristic
5	C₂×C₁₁×H(3,ℤ/4)	C₂	1	2	yes	maximal
6	C₂²×C₁₁×M₁₆	C₂²	1	1	yes	characteristic
7	C₂²×C₁₁×M₁₆	C₂²	1	2	yes	—
8	C₂²×C₁₁×M₁₆	C₂²	1	1	yes	characteristic
9	C₂×C₁₁×#117	C₂²	1	1	yes	characteristic
10	C₂×C₁₁×#117	C₂²	1	2	yes	—
11	C₁₁×#430	—	2	4	no	—
12	C₂×C₁₁×#108	—	2	2	no	—
13	C₁₁×#424	—	2	2	no	—
14	C₁₁×#424	—	2	2	no	—
15	C₁₁×#423	C₄	1	4	yes	complemented
16	C₁₁×#343	—	2	4	no	—
17	C₁₁×H(3,ℤ/4)	—	2	2	no	—
18	C₁₁×H(3,ℤ/4)	—	2	4	no	—
19	C₂³×C₄×C₁₁	C₂³	1	1	yes	characteristic
20	C₂×C₁₁×M₁₆	—	2	2	no	—
21	C₂×C₁₁×M₁₆	—	2	2	no	—
22	C₂×C₁₁×M₁₆	—	2	2	no	—
23	C₂×C₁₁×M₁₆	—	2	1	no	—
24	C₂×C₁₁×M₁₆	—	2	2	no	—
25	C₂×C₁₁×M₁₆	—	2	2	no	—
26	C₂×C₁₁×M₁₆	—	2	2	no	—
27	C₂×C₁₁×M₁₆	—	2	2	no	—
28	C₂×C₁₁×M₁₆	—	2	2	no	—
29	C₂×C₁₁×M₁₆	—	2	2	no	—
30	C₂×C₁₁×M₁₆	C₂×C₄	1	2	yes	—
31	C₂×C₁₁×M₁₆	C₂×C₄	1	2	yes	—
32	C₂×C₁₁×M₁₆	D₄	1	4	yes	—
33	C₂×C₁₁×M₁₆	D₄	1	2	yes	—
34	C₂²×C₈×C₁₁	—	2	1	no	—
35	C₂²×C₈×C₁₁	—	2	2	no	—
36	C₂²×C₈×C₁₁	D₄	1	2	yes	—
37	C₁₁×#117	—	2	1	no	—
38	C₁₁×#117	—	2	1	no	—
39	C₁₁×#117	—	2	2	no	—
40	C₁₁×#117	—	2	2	no	—
41	C₁₁×#117	—	2	2	no	—
42	C₁₁×#117	—	2	2	no	—
43	C₁₁×#117	D₄	1	2	yes	—
44	C₁₁×#117	Q₈	1	2	yes	—
45	C₂×C₁₁×C₄⋊C₄	—	2	1	no	—
46	C₂×C₁₁×C₄⋊C₄	—	2	2	no	—
47	C₂×C₁₁×C₂²⋊C₄	—	2	1	no	—
48	C₂×C₁₁×C₂²⋊C₄	—	2	2	no	—
49	C₂×C₄²×C₁₁	C₂×C₄	1	2	yes	—
50	C₂×C₄²×C₁₁	Q₈	1	4	yes	—
51	C₁₁×#108	—	2	8	no	—
52	C₁₁×C₄⋊C₈	—	2	8	no	—
53	#11246	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
54	C₂⁴×C₁₁	#41	1	1	yes	characteristic
55	C₂²×C₄×C₁₁	—	2	2	no	—
56	C₂²×C₄×C₁₁	—	2	4	no	—
57	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
58	C₂²×C₄×C₁₁	C₂×D₄	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×D₄	1	2	yes	—
62	C₂²×C₄×C₁₁	C₂×Q₈	1	1	yes	characteristic
63	C₂²×C₄×C₁₁	C₂×Q₈	1	2	yes	—
64	C₂²×C₄×C₁₁	#41	1	2	yes	—
65	C₂²×C₄×C₁₁	#41	1	2	yes	—
66	C₂²×C₄×C₁₁	#41	1	1	yes	characteristic
67	C₁₁×M₁₆	—	2	4	no	—
68	C₁₁×M₁₆	—	2	4	no	—
69	C₁₁×M₁₆	—	2	4	no	—
70	C₁₁×M₁₆	—	2	4	no	—
71	C₁₁×M₁₆	—	2	4	no	—
72	C₁₁×M₁₆	—	4	1	no	—
73	C₁₁×M₁₆	—	4	2	no	—
74	C₁₁×M₁₆	—	4	2	no	—
75	C₁₁×M₁₆	—	4	1	no	—
76	C₂×C₈×C₁₁	—	2	2	no	—
77	C₂×C₈×C₁₁	—	2	2	no	—
78	C₂×C₈×C₁₁	—	2	4	no	—
79	C₂×C₈×C₁₁	—	2	2	no	—
80	C₂×C₈×C₁₁	—	4	2	no	—
81	C₂×C₈×C₁₁	—	4	2	no	—
82	C₂×C₈×C₁₁	—	4	2	no	—
83	C₂×C₈×C₁₁	C₂²⋊C₄	1	4	yes	—
84	C₁₁×C₄⋊C₄	—	2	2	no	—
85	C₁₁×C₄⋊C₄	—	2	2	no	—
86	C₁₁×C₄⋊C₄	—	4	2	no	—
87	C₁₁×C₄⋊C₄	—	4	2	no	—
88	C₁₁×C₂²⋊C₄	—	2	2	no	—
89	C₁₁×C₂²⋊C₄	—	2	2	no	—
90	C₁₁×C₂²⋊C₄	—	4	2	no	—
91	C₁₁×C₂²⋊C₄	—	4	2	no	—
92	C₄²×C₁₁	—	2	2	no	—
93	C₄²×C₁₁	—	2	4	no	—
94	C₄²×C₁₁	—	2	4	no	—
95	C₄²×C₁₁	C₄⋊C₄	1	4	yes	—
96	C₂×#430	C₂×C₁₁	1	1	yes	characteristic
97	#2905	C₂×C₁₁	1	1	yes	characteristic
98	#1742	C₂×C₁₁	1	2	yes	—
99	C₂×H(3,ℤ/4)	C₂×C₁₁	1	2	yes	—
100	C₂×H(3,ℤ/4)	C₂×C₁₁	1	1	yes	characteristic
101	C₂³×C₁₁	—	8	1	no	—
102	C₂³×C₁₁	#117	1	1	yes	characteristic
103	C₂³×C₁₁	#121	1	1	yes	characteristic
104	C₂³×C₁₁	C₂²⋊Q₈	1	1	yes	characteristic
105	C₂³×C₁₁	C₂²⋊Q₈	1	2	yes	—
106	C₂³×C₁₁	#126	1	2	yes	—
107	C₂×C₄×C₁₁	—	2	4	no	—
108	C₂×C₄×C₁₁	—	4	4	no	—
109	C₂×C₄×C₁₁	—	8	2	no	—
110	C₂×C₄×C₁₁	—	8	4	no	—
111	C₂×C₄×C₁₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
112	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
113	C₂×C₄×C₁₁	C₄×D₄	1	2	yes	—
114	C₂×C₄×C₁₁	C₄×Q₈	1	2	yes	—
115	C₂×C₄×C₁₁	#120	1	1	yes	characteristic
116	C₂×C₄×C₁₁	#121	1	2	yes	—
117	C₂×C₄×C₁₁	#121	1	2	yes	—
118	C₂×C₄×C₁₁	#121	1	1	yes	characteristic
119	C₂×C₄×C₁₁	C₂²⋊Q₈	1	2	yes	—
120	C₂×C₄×C₁₁	C₂²⋊Q₈	1	2	yes	—
121	C₂×C₄×C₁₁	C₂²⋊Q₈	1	1	yes	characteristic
122	C₂×C₄×C₁₁	#123	1	1	yes	characteristic
123	C₂×C₄×C₁₁	#123	1	2	yes	—
124	C₂×C₄×C₁₁	#124	1	1	yes	characteristic
125	C₂×C₄×C₁₁	#125	1	2	yes	—
126	C₂×C₄×C₁₁	#125	1	2	yes	—
127	C₂×C₄×C₁₁	C₄⋊Q₈	1	2	yes	—
128	C₂×C₄×C₁₁	C₄⋊Q₈	1	1	yes	characteristic
129	C₈×C₁₁	—	2	4	no	—
130	C₈×C₁₁	—	4	2	no	—
131	C₈×C₁₁	—	4	4	no	—
132	C₂²×M₁₆	C₂²×C₁₁	1	1	yes	characteristic
133	C₂²×M₁₆	C₂²×C₁₁	1	2	yes	—
134	C₂²×M₁₆	C₂²×C₁₁	1	1	yes	characteristic
135	C₂×#117	C₂²×C₁₁	1	1	yes	characteristic
136	C₂×#117	C₂²×C₁₁	1	2	yes	—
137	#430	—	2	4	no	—
138	C₂×#108	—	2	2	no	—
139	#424	—	2	2	no	—
140	#424	—	2	2	no	—
141	#423	C₄×C₁₁	1	4	yes	complemented
142	#343	—	2	4	no	—
143	H(3,ℤ/4)	—	2	2	no	—
144	H(3,ℤ/4)	—	2	4	no	—
145	C₂²×C₁₁	—	4	1	no	—
146	C₂²×C₁₁	—	4	2	no	—
147	C₂²×C₁₁	—	4	1	no	—
148	C₂²×C₁₁	—	4	1	no	—
149	C₂²×C₁₁	—	4	2	no	—
150	C₂²×C₁₁	#380	1	1	yes	characteristic
151	C₂²×C₁₁	#387	1	2	yes	—
152	C₂²×C₁₁	#395	1	1	yes	characteristic
153	C₂²×C₁₁	#396	1	2	yes	—
154	C₂²×C₁₁	#400	1	1	yes	characteristic
155	C₄×C₁₁	—	4	4	no	—
156	C₄×C₁₁	—	8	4	no	—
157	C₄×C₁₁	#386	1	1	yes	characteristic
158	C₄×C₁₁	#389	1	2	yes	—
159	C₄×C₁₁	#391	1	1	yes	characteristic
160	C₄×C₁₁	#394	1	1	yes	characteristic
161	C₄×C₁₁	#398	1	2	yes	—
162	C₄×C₁₁	#398	1	1	yes	characteristic
163	C₂³×C₄	C₂³×C₁₁	1	1	yes	characteristic
164	C₂×M₁₆	—	2	2	no	—
165	C₂×M₁₆	—	2	2	no	—
166	C₂×M₁₆	—	2	2	no	—
167	C₂×M₁₆	—	2	1	no	—
168	C₂×M₁₆	—	2	2	no	—
169	C₂×M₁₆	—	2	2	no	—
170	C₂×M₁₆	—	2	2	no	—
171	C₂×M₁₆	—	2	2	no	—
172	C₂×M₁₆	—	2	2	no	—
173	C₂×M₁₆	—	2	2	no	—
174	C₂×M₁₆	C₂×C₄×C₁₁	1	2	yes	—
175	C₂×M₁₆	C₂×C₄×C₁₁	1	2	yes	—
176	C₂×M₁₆	D₄×C₁₁	1	4	yes	—
177	C₂×M₁₆	D₄×C₁₁	1	2	yes	—
178	C₂²×C₈	—	2	1	no	—
179	C₂²×C₈	—	2	2	no	—
180	C₂²×C₈	D₄×C₁₁	1	2	yes	—
181	#117	—	2	1	no	—
182	#117	—	2	1	no	—
183	#117	—	2	2	no	—
184	#117	—	2	2	no	—
185	#117	—	2	2	no	—
186	#117	—	2	2	no	—
187	#117	D₄×C₁₁	1	2	yes	—
188	#117	Q₈×C₁₁	1	2	yes	—
189	C₂×C₄⋊C₄	—	2	1	no	—
190	C₂×C₄⋊C₄	—	2	2	no	—
191	C₂×C₂²⋊C₄	—	2	1	no	—
192	C₂×C₂²⋊C₄	—	2	2	no	—
193	C₂×C₄²	C₂×C₄×C₁₁	1	2	yes	—
194	C₂×C₄²	Q₈×C₁₁	1	4	yes	—
195	#108	—	2	8	no	—
196	C₄⋊C₈	—	2	8	no	—
197	C₂×C₁₁	—	2	1	no	—
198	C₂×C₁₁	—	2	2	no	—
199	C₂×C₁₁	—	2	2	no	—
200	C₂×C₁₁	—	2	1	no	—
201	C₂×C₁₁	—	2	1	no	—
202	C₂×C₁₁	#1441	1	1	yes	characteristic
203	C₂⁴	C₁₁×#41	1	1	yes	characteristic
204	C₂²×C₄	—	2	2	no	—
205	C₂²×C₄	—	2	4	no	—
206	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
207	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
208	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
209	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
210	C₂²×C₄	C₂×D₄×C₁₁	1	2	yes	—
211	C₂²×C₄	C₂×Q₈×C₁₁	1	1	yes	characteristic
212	C₂²×C₄	C₂×Q₈×C₁₁	1	2	yes	—
213	C₂²×C₄	C₁₁×#41	1	2	yes	—
214	C₂²×C₄	C₁₁×#41	1	2	yes	—
215	C₂²×C₄	C₁₁×#41	1	1	yes	characteristic
216	M₁₆	—	2	4	no	—
217	M₁₆	—	2	4	no	—
218	M₁₆	—	2	4	no	—
219	M₁₆	—	2	4	no	—
220	M₁₆	—	2	4	no	—
221	M₁₆	—	4	1	no	—
222	M₁₆	—	4	2	no	—
223	M₁₆	—	4	2	no	—
224	M₁₆	—	4	1	no	—
225	C₂×C₈	—	2	2	no	—
226	C₂×C₈	—	2	2	no	—
227	C₂×C₈	—	2	2	no	—
228	C₂×C₈	—	2	4	no	—
229	C₂×C₈	—	4	2	no	—
230	C₂×C₈	—	4	2	no	—
231	C₂×C₈	—	4	2	no	—
232	C₂×C₈	C₁₁×C₂²⋊C₄	1	4	yes	—
233	C₄⋊C₄	—	2	2	no	—
234	C₄⋊C₄	—	2	2	no	—
235	C₄⋊C₄	—	4	2	no	—
236	C₄⋊C₄	—	4	2	no	—
237	C₂²⋊C₄	—	2	2	no	—
238	C₂²⋊C₄	—	2	2	no	—
239	C₂²⋊C₄	—	4	2	no	—
240	C₂²⋊C₄	—	4	2	no	—
241	C₄²	—	2	2	no	—
242	C₄²	—	2	4	no	—
243	C₄²	—	2	4	no	—
244	C₄²	C₁₁×C₄⋊C₄	1	4	yes	—
245	C₁₁	#11246	1	1	yes	characteristic, direct product factor, Sylow
246	C₂³	—	8	1	no	—
247	C₂³	C₁₁×#117	1	1	yes	characteristic
248	C₂³	C₁₁×#121	1	1	yes	characteristic
249	C₂³	C₁₁×C₂²⋊Q₈	1	1	yes	characteristic
250	C₂³	C₁₁×C₂²⋊Q₈	1	2	yes	—
251	C₂³	C₁₁×#126	1	2	yes	—
252	C₂×C₄	—	2	4	no	—
253	C₂×C₄	—	4	4	no	—
254	C₂×C₄	—	8	2	no	—
255	C₂×C₄	—	8	4	no	—
256	C₂×C₄	C₂×C₁₁×C₂²⋊C₄	1	1	yes	characteristic
257	C₂×C₄	C₂×C₁₁×C₄⋊C₄	1	1	yes	characteristic
258	C₂×C₄	C₄×D₄×C₁₁	1	2	yes	—
259	C₂×C₄	C₄×Q₈×C₁₁	1	2	yes	—
260	C₂×C₄	C₁₁×#120	1	1	yes	characteristic
261	C₂×C₄	C₁₁×#121	1	2	yes	—
262	C₂×C₄	C₁₁×#121	1	2	yes	—
263	C₂×C₄	C₁₁×#121	1	1	yes	characteristic
264	C₂×C₄	C₁₁×C₂²⋊Q₈	1	2	yes	—
265	C₂×C₄	C₁₁×C₂²⋊Q₈	1	2	yes	—
266	C₂×C₄	C₁₁×C₂²⋊Q₈	1	1	yes	characteristic
267	C₂×C₄	C₁₁×#123	1	1	yes	characteristic
268	C₂×C₄	C₁₁×#123	1	2	yes	—
269	C₂×C₄	C₁₁×#124	1	1	yes	characteristic
270	C₂×C₄	C₁₁×#125	1	2	yes	—
271	C₂×C₄	C₁₁×#125	1	2	yes	—
272	C₂×C₄	C₁₁×C₄⋊Q₈	1	2	yes	—
273	C₂×C₄	C₁₁×C₄⋊Q₈	1	1	yes	characteristic
274	C₈	—	2	4	no	—
275	C₈	—	4	2	no	—
276	C₈	—	4	4	no	—
277	C₂²	—	4	1	no	—
278	C₂²	—	4	2	no	—
279	C₂²	—	4	1	no	—
280	C₂²	—	4	1	no	—
281	C₂²	—	4	2	no	—
282	C₂²	C₁₁×#380	1	1	yes	characteristic
283	C₂²	C₁₁×#387	1	2	yes	—
284	C₂²	C₁₁×#395	1	1	yes	characteristic
285	C₂²	C₁₁×#396	1	2	yes	—
286	C₂²	C₁₁×#400	1	1	yes	characteristic
287	C₄	—	4	4	no	—
288	C₄	—	8	4	no	—
289	C₄	C₁₁×#386	1	1	yes	characteristic
290	C₄	C₁₁×#389	1	2	yes	—
291	C₄	C₁₁×#391	1	1	yes	characteristic
292	C₄	C₁₁×#394	1	1	yes	characteristic
293	C₄	C₁₁×#398	1	2	yes	—
294	C₄	C₁₁×#398	1	1	yes	characteristic
295	C₂	—	2	1	no	—
296	C₂	—	2	2	no	—
297	C₂	—	2	2	no	—
298	C₂	—	2	1	no	—
299	C₂	—	2	1	no	—
300	C₂	C₁₁×#1441	1	1	yes	characteristic

	subgroup	G/H
center	C₄×C₁₁	#391
commutator	C₂²×C₄	C₂²×C₄×C₁₁
Frattini, cosocle	C₂³×C₄	C₂³×C₁₁
socle	C₂×C₁₁	#1441
prime radical	C₂⁴×C₁₁	#41
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₁₁ ◁ C₂³×C₄×C₁₁ ◁ G

Complements

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

N	H ≅ G/N	type
15. C₁₁×#423	C₄	semidirect
53. #11246	C₁₁	direct (N × H)
141. #423	C₄×C₁₁	semidirect
245. C₁₁	#11246	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×C₁₁×#430	2
C₁₁×#2905	2
C₁₁×#1742	2
C₂×C₁₁×H(3,ℤ/4)	2
#11246	11

Subgroups — C11×#11246 #14588439

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#11246 #14588439