Subgroups — C₂×C₁₁×#1941 #14598342

Order 2816.

1182 conjugacy classes of subgroups.

The subgroup lattice has 300 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₁×#106	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₁₁×#106	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₄×C₈×C₁₁	C₂	1	1	yes	maximal, characteristic
4	C₂×C₁₁×#389	C₂	1	2	yes	maximal
5	C₁₁×#1941	C₂	1	8	yes	maximal, direct product factor
6	C₂×C₁₁×#340	C₂	1	2	yes	maximal
7	C₂³×C₈×C₁₁	C₂²	1	1	yes	characteristic
8	C₂³×C₈×C₁₁	C₂²	1	1	yes	characteristic
9	C₂²×C₁₁×C₄⋊C₄	—	2	2	no	—
10	C₂²×C₁₁×C₄⋊C₄	C₂²	1	2	yes	—
11	C₂²×C₁₁×C₄⋊C₄	C₂²	1	2	yes	—
12	C₂²×C₄²×C₁₁	C₂²	1	1	yes	characteristic
13	C₂×C₁₁×#106	—	2	4	no	—
14	C₂×C₁₁×#106	C₄	1	8	yes	complemented
15	C₂×C₁₁×#106	C₂²	1	4	yes	—
16	C₂×C₁₁×#106	C₂²	1	4	yes	—
17	C₂×C₄×C₈×C₁₁	—	2	4	no	—
18	C₂×C₄×C₈×C₁₁	C₂²	1	4	yes	—
19	C₁₁×#389	—	2	4	no	—
20	C₁₁×#389	C₂²	1	8	yes	—
21	C₂×C₁₁×#95	—	2	2	no	—
22	C₁₁×#340	C₂²	1	8	yes	—
23	C₂³×C₄×C₁₁	—	2	2	no	—
24	C₂³×C₄×C₁₁	—	2	2	no	—
25	C₂³×C₄×C₁₁	D₄	1	2	yes	—
26	C₂³×C₄×C₁₁	C₂³	1	1	yes	characteristic
27	C₂²×C₈×C₁₁	—	2	2	no	—
28	C₂²×C₈×C₁₁	—	2	2	no	—
29	C₂²×C₈×C₁₁	C₂×C₄	1	4	yes	—
30	C₂²×C₈×C₁₁	D₄	1	4	yes	—
31	C₂²×C₈×C₁₁	Q₈	1	4	yes	—
32	C₂²×C₈×C₁₁	Q₈	1	4	yes	—
33	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
34	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
35	C₂×C₁₁×C₄⋊C₄	—	2	2	no	—
36	C₂×C₁₁×C₄⋊C₄	—	2	4	no	—
37	C₂×C₁₁×C₄⋊C₄	—	2	4	no	—
38	C₂×C₁₁×C₄⋊C₄	—	2	4	no	—
39	C₂×C₁₁×C₄⋊C₄	—	2	8	no	—
40	C₂×C₁₁×C₄⋊C₄	—	2	2	no	—
41	C₂×C₁₁×C₄⋊C₄	—	4	8	no	—
42	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	8	yes	—
43	C₂×C₁₁×C₄⋊C₄	C₂³	1	4	yes	—
44	C₂×C₁₁×C₄⋊C₄	C₂³	1	4	yes	—
45	C₂×C₄²×C₁₁	—	2	2	no	—
46	C₂×C₄²×C₁₁	—	2	2	no	—
47	C₂×C₄²×C₁₁	D₄	1	2	yes	—
48	C₂×C₄²×C₁₁	C₂³	1	2	yes	—
49	C₁₁×#106	—	2	8	no	—
50	C₁₁×#106	C₂×C₄	1	16	yes	complemented
51	C₄×C₈×C₁₁	—	2	8	no	—
52	C₁₁×#95	—	2	8	no	—
53	C₂×#1941	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
54	C₂⁴×C₁₁	C₂×D₄	1	1	yes	characteristic
55	C₂²×C₄×C₁₁	—	2	4	no	—
56	C₂²×C₄×C₁₁	—	2	4	no	—
57	C₂²×C₄×C₁₁	—	2	8	no	—
58	C₂²×C₄×C₁₁	—	2	4	no	—
59	C₂²×C₄×C₁₁	—	2	4	no	—
60	C₂²×C₄×C₁₁	—	4	4	no	—
61	C₂²×C₄×C₁₁	—	4	4	no	—
62	C₂²×C₄×C₁₁	—	4	4	no	—
63	C₂²×C₄×C₁₁	—	4	4	no	—
64	C₂²×C₄×C₁₁	—	4	4	no	—
65	C₂²×C₄×C₁₁	SD₁₆	1	8	yes	—
66	C₂²×C₄×C₁₁	C₂²×C₄	1	2	yes	—
67	C₂²×C₄×C₁₁	C₂×D₄	1	4	yes	—
68	C₂²×C₄×C₁₁	C₂×D₄	1	2	yes	—
69	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
70	C₂²×C₄×C₁₁	C₂×Q₈	1	2	yes	—
71	C₂²×C₄×C₁₁	C₂×Q₈	1	2	yes	—
72	C₂²×C₄×C₁₁	#41	1	2	yes	—
73	C₂²×C₄×C₁₁	#41	1	2	yes	—
74	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
75	C₂×C₈×C₁₁	—	2	8	no	—
76	C₂×C₈×C₁₁	—	2	2	no	—
77	C₂×C₈×C₁₁	—	2	2	no	—
78	C₂×C₈×C₁₁	C₄⋊C₄	1	16	yes	complemented
79	C₂×C₈×C₁₁	C₂²×C₄	1	4	yes	—
80	C₂×C₈×C₁₁	C₂×D₄	1	4	yes	—
81	C₂×C₈×C₁₁	C₂×Q₈	1	4	yes	—
82	C₂×C₈×C₁₁	C₂×Q₈	1	4	yes	—
83	C₁₁×C₄⋊C₄	—	2	8	no	—
84	C₁₁×C₄⋊C₄	—	2	4	no	—
85	C₁₁×C₄⋊C₄	—	2	4	no	—
86	C₁₁×C₄⋊C₄	—	2	4	no	—
87	C₁₁×C₄⋊C₄	—	4	4	no	—
88	C₁₁×C₄⋊C₄	—	4	16	no	—
89	C₁₁×C₄⋊C₄	C₂²×C₄	1	8	yes	—
90	C₄²×C₁₁	—	2	4	no	—
91	C₄²×C₁₁	—	2	2	no	—
92	C₄²×C₁₁	—	2	2	no	—
93	C₂²×#106	C₂×C₁₁	1	1	yes	characteristic
94	C₂²×#106	C₂×C₁₁	1	1	yes	characteristic
95	C₂²×C₄×C₈	C₂×C₁₁	1	1	yes	characteristic
96	C₂×#389	C₂×C₁₁	1	2	yes	—
97	#1941	C₂×C₁₁	1	8	yes	direct product factor
98	C₂×#340	C₂×C₁₁	1	2	yes	—
99	C₂³×C₁₁	C₄×D₄	1	2	yes	—
100	C₂³×C₁₁	#121	1	2	yes	—
101	C₂³×C₁₁	C₄⋊Q₈	1	2	yes	—
102	C₂³×C₁₁	C₂×SD₁₆	1	4	yes	—
103	C₂³×C₁₁	#135	1	4	yes	—
104	C₂³×C₁₁	C₂²×D₄	1	1	yes	characteristic
105	C₂×C₄×C₁₁	—	2	4	no	—
106	C₂×C₄×C₁₁	—	2	4	no	—
107	C₂×C₄×C₁₁	—	2	16	no	—
108	C₂×C₄×C₁₁	—	2	8	no	—
109	C₂×C₄×C₁₁	—	4	4	no	—
110	C₂×C₄×C₁₁	—	4	4	no	—
111	C₂×C₄×C₁₁	—	4	16	no	—
112	C₂×C₄×C₁₁	—	4	4	no	—
113	C₂×C₄×C₁₁	—	4	4	no	—
114	C₂×C₄×C₁₁	—	4	4	no	—
115	C₂×C₄×C₁₁	—	8	8	no	—
116	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	4	yes	—
117	C₂×C₄×C₁₁	C₄×D₄	1	2	yes	—
118	C₂×C₄×C₁₁	C₄×Q₈	1	4	yes	—
119	C₂×C₄×C₁₁	#121	1	2	yes	—
120	C₂×C₄×C₁₁	C₂²⋊Q₈	1	4	yes	—
121	C₂×C₄×C₁₁	#125	1	4	yes	—
122	C₂×C₄×C₁₁	C₄⋊Q₈	1	2	yes	—
123	C₂×C₄×C₁₁	C₂×SD₁₆	1	8	yes	—
124	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
125	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
126	C₂×C₄×C₁₁	C₂²×Q₈	1	1	yes	characteristic
127	C₂×C₄×C₁₁	C₂²×Q₈	1	1	yes	characteristic
128	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
129	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
130	C₈×C₁₁	—	2	4	no	—
131	C₈×C₁₁	C₂×C₄⋊C₄	1	8	yes	complemented
132	C₂³×C₈	C₂²×C₁₁	1	1	yes	characteristic
133	C₂³×C₈	C₂²×C₁₁	1	1	yes	characteristic
134	C₂²×C₄⋊C₄	—	2	2	no	—
135	C₂²×C₄⋊C₄	C₂²×C₁₁	1	2	yes	—
136	C₂²×C₄⋊C₄	C₂²×C₁₁	1	2	yes	—
137	C₂²×C₄²	C₂²×C₁₁	1	1	yes	characteristic
138	C₂×#106	—	2	4	no	—
139	C₂×#106	C₄×C₁₁	1	8	yes	complemented
140	C₂×#106	C₂²×C₁₁	1	4	yes	—
141	C₂×#106	C₂²×C₁₁	1	4	yes	—
142	C₂×C₄×C₈	—	2	4	no	—
143	C₂×C₄×C₈	C₂²×C₁₁	1	4	yes	—
144	#389	—	2	4	no	—
145	#389	C₂²×C₁₁	1	8	yes	—
146	C₂×#95	—	2	2	no	—
147	#340	C₂²×C₁₁	1	8	yes	—
148	C₂²×C₁₁	#389	1	4	yes	—
149	C₂²×C₁₁	C₄×SD₁₆	1	8	yes	—
150	C₂²×C₁₁	#465	1	8	yes	—
151	C₂²×C₁₁	#498	1	4	yes	—
152	C₂²×C₁₁	#499	1	4	yes	—
153	C₂²×C₁₁	C₂×C₄×D₄	1	1	yes	characteristic
154	C₂²×C₁₁	C₂×#121	1	1	yes	characteristic
155	C₂²×C₁₁	C₂×C₄⋊Q₈	1	1	yes	characteristic
156	C₂²×C₁₁	C₂²×SD₁₆	1	2	yes	—
157	C₂²×C₁₁	C₂×#135	1	2	yes	—
158	C₄×C₁₁	—	2	8	no	—
159	C₄×C₁₁	—	4	8	no	—
160	C₄×C₁₁	—	8	4	no	—
161	C₄×C₁₁	#389	1	4	yes	—
162	C₄×C₁₁	C₂²×C₄⋊C₄	1	1	yes	characteristic
163	C₄×C₁₁	C₂×C₄×Q₈	1	1	yes	characteristic
164	C₄×C₁₁	C₂×C₂²⋊Q₈	1	1	yes	characteristic
165	C₄×C₁₁	C₂×#125	1	1	yes	characteristic
166	C₂³×C₄	—	2	2	no	—
167	C₂³×C₄	—	2	2	no	—
168	C₂³×C₄	D₄×C₁₁	1	2	yes	—
169	C₂³×C₄	C₂³×C₁₁	1	1	yes	characteristic
170	C₂²×C₈	—	2	2	no	—
171	C₂²×C₈	—	2	2	no	—
172	C₂²×C₈	C₂×C₄×C₁₁	1	4	yes	—
173	C₂²×C₈	D₄×C₁₁	1	4	yes	—
174	C₂²×C₈	Q₈×C₁₁	1	4	yes	—
175	C₂²×C₈	Q₈×C₁₁	1	4	yes	—
176	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
177	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
178	C₂×C₄⋊C₄	—	2	2	no	—
179	C₂×C₄⋊C₄	—	2	4	no	—
180	C₂×C₄⋊C₄	—	2	4	no	—
181	C₂×C₄⋊C₄	—	2	4	no	—
182	C₂×C₄⋊C₄	—	2	8	no	—
183	C₂×C₄⋊C₄	—	2	2	no	—
184	C₂×C₄⋊C₄	—	4	8	no	—
185	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	8	yes	—
186	C₂×C₄⋊C₄	C₂³×C₁₁	1	4	yes	—
187	C₂×C₄⋊C₄	C₂³×C₁₁	1	4	yes	—
188	C₂×C₄²	—	2	2	no	—
189	C₂×C₄²	—	2	2	no	—
190	C₂×C₄²	D₄×C₁₁	1	2	yes	—
191	C₂×C₄²	C₂³×C₁₁	1	2	yes	—
192	#106	—	2	8	no	—
193	#106	C₂×C₄×C₁₁	1	16	yes	complemented
194	C₄×C₈	—	2	8	no	—
195	#95	—	2	8	no	—
196	C₂×C₁₁	#1941	1	8	yes	direct product factor
197	C₂×C₁₁	C₂×#389	1	1	yes	characteristic
198	C₂×C₁₁	C₂×C₄×SD₁₆	1	2	yes	—
199	C₂×C₁₁	C₂×#465	1	2	yes	—
200	C₂×C₁₁	C₂×#498	1	1	yes	characteristic
201	C₂×C₁₁	C₂×#499	1	1	yes	characteristic
202	C₂⁴	C₂×D₄×C₁₁	1	1	yes	characteristic
203	C₂²×C₄	—	2	4	no	—
204	C₂²×C₄	—	2	4	no	—
205	C₂²×C₄	—	2	8	no	—
206	C₂²×C₄	—	2	4	no	—
207	C₂²×C₄	—	2	4	no	—
208	C₂²×C₄	—	4	4	no	—
209	C₂²×C₄	—	4	4	no	—
210	C₂²×C₄	—	4	4	no	—
211	C₂²×C₄	—	4	4	no	—
212	C₂²×C₄	—	4	4	no	—
213	C₂²×C₄	C₁₁×SD₁₆	1	8	yes	—
214	C₂²×C₄	C₂²×C₄×C₁₁	1	2	yes	—
215	C₂²×C₄	C₂×D₄×C₁₁	1	4	yes	—
216	C₂²×C₄	C₂×D₄×C₁₁	1	2	yes	—
217	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
218	C₂²×C₄	C₂×Q₈×C₁₁	1	2	yes	—
219	C₂²×C₄	C₂×Q₈×C₁₁	1	2	yes	—
220	C₂²×C₄	C₁₁×#41	1	2	yes	—
221	C₂²×C₄	C₁₁×#41	1	2	yes	—
222	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
223	C₂×C₈	—	2	8	no	—
224	C₂×C₈	—	2	2	no	—
225	C₂×C₈	—	2	2	no	—
226	C₂×C₈	C₁₁×C₄⋊C₄	1	16	yes	complemented
227	C₂×C₈	C₂²×C₄×C₁₁	1	4	yes	—
228	C₂×C₈	C₂×D₄×C₁₁	1	4	yes	—
229	C₂×C₈	C₂×Q₈×C₁₁	1	4	yes	—
230	C₂×C₈	C₂×Q₈×C₁₁	1	4	yes	—
231	C₄⋊C₄	—	2	8	no	—
232	C₄⋊C₄	—	2	4	no	—
233	C₄⋊C₄	—	2	4	no	—
234	C₄⋊C₄	—	2	4	no	—
235	C₄⋊C₄	—	4	4	no	—
236	C₄⋊C₄	—	4	16	no	—
237	C₄⋊C₄	C₂²×C₄×C₁₁	1	8	yes	—
238	C₄²	—	2	4	no	—
239	C₄²	—	2	2	no	—
240	C₄²	—	2	2	no	—
241	C₁₁	C₂×#1941	1	1	yes	characteristic, direct product factor, Sylow
242	C₂³	C₄×D₄×C₁₁	1	2	yes	—
243	C₂³	C₁₁×#121	1	2	yes	—
244	C₂³	C₁₁×C₄⋊Q₈	1	2	yes	—
245	C₂³	C₂×C₁₁×SD₁₆	1	4	yes	—
246	C₂³	C₁₁×#135	1	4	yes	—
247	C₂³	C₂²×D₄×C₁₁	1	1	yes	characteristic
248	C₂×C₄	—	2	4	no	—
249	C₂×C₄	—	2	4	no	—
250	C₂×C₄	—	2	16	no	—
251	C₂×C₄	—	2	8	no	—
252	C₂×C₄	—	4	4	no	—
253	C₂×C₄	—	4	4	no	—
254	C₂×C₄	—	4	16	no	—
255	C₂×C₄	—	4	4	no	—
256	C₂×C₄	—	4	4	no	—
257	C₂×C₄	—	4	4	no	—
258	C₂×C₄	—	8	8	no	—
259	C₂×C₄	C₂×C₁₁×C₄⋊C₄	1	4	yes	—
260	C₂×C₄	C₄×D₄×C₁₁	1	2	yes	—
261	C₂×C₄	C₄×Q₈×C₁₁	1	4	yes	—
262	C₂×C₄	C₁₁×#121	1	2	yes	—
263	C₂×C₄	C₁₁×C₂²⋊Q₈	1	4	yes	—
264	C₂×C₄	C₁₁×#125	1	4	yes	—
265	C₂×C₄	C₁₁×C₄⋊Q₈	1	2	yes	—
266	C₂×C₄	C₂×C₁₁×SD₁₆	1	8	yes	—
267	C₂×C₄	C₂³×C₄×C₁₁	1	1	yes	characteristic
268	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
269	C₂×C₄	C₂²×Q₈×C₁₁	1	1	yes	characteristic
270	C₂×C₄	C₂²×Q₈×C₁₁	1	1	yes	characteristic
271	C₂×C₄	C₂×C₁₁×#41	1	1	yes	characteristic
272	C₂×C₄	C₂×C₁₁×#41	1	1	yes	characteristic
273	C₈	—	2	4	no	—
274	C₈	C₂×C₁₁×C₄⋊C₄	1	8	yes	complemented
275	C₂²	C₁₁×#389	1	4	yes	—
276	C₂²	C₄×C₁₁×SD₁₆	1	8	yes	—
277	C₂²	C₁₁×#465	1	8	yes	—
278	C₂²	C₁₁×#498	1	4	yes	—
279	C₂²	C₁₁×#499	1	4	yes	—
280	C₂²	C₂×C₄×D₄×C₁₁	1	1	yes	characteristic
281	C₂²	C₂×C₁₁×#121	1	1	yes	characteristic
282	C₂²	C₂×C₁₁×C₄⋊Q₈	1	1	yes	characteristic
283	C₂²	C₂²×C₁₁×SD₁₆	1	2	yes	—
284	C₂²	C₂×C₁₁×#135	1	2	yes	—
285	C₄	—	2	8	no	—
286	C₄	—	4	8	no	—
287	C₄	—	8	4	no	—
288	C₄	C₁₁×#389	1	4	yes	—
289	C₄	C₂²×C₁₁×C₄⋊C₄	1	1	yes	characteristic
290	C₄	C₂×C₄×Q₈×C₁₁	1	1	yes	characteristic
291	C₄	C₂×C₁₁×C₂²⋊Q₈	1	1	yes	characteristic
292	C₄	C₂×C₁₁×#125	1	1	yes	characteristic
293	C₂	C₁₁×#1941	1	8	yes	direct product factor
294	C₂	C₂×C₁₁×#389	1	1	yes	characteristic
295	C₂	C₂×C₄×C₁₁×SD₁₆	1	2	yes	—
296	C₂	C₂×C₁₁×#465	1	2	yes	—
297	C₂	C₂×C₁₁×#498	1	1	yes	characteristic
298	C₂	C₂×C₁₁×#499	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
5. C₁₁×#1941	C₂	direct (N × H)
14. C₂×C₁₁×#106	C₄	semidirect
50. C₁₁×#106	C₂×C₄	semidirect
53. C₂×#1941	C₁₁	direct (N × H)
78. C₂×C₈×C₁₁	C₄⋊C₄	semidirect
97. #1941	C₂×C₁₁	direct (N × H)
131. C₈×C₁₁	C₂×C₄⋊C₄	semidirect
139. C₂×#106	C₄×C₁₁	semidirect
193. #106	C₂×C₄×C₁₁	semidirect
196. C₂×C₁₁	#1941	direct (N × H)
226. C₂×C₈	C₁₁×C₄⋊C₄	semidirect
241. C₁₁	C₂×#1941	direct (N × H)
274. C₈	C₂×C₁₁×C₄⋊C₄	semidirect
293. C₂	C₁₁×#1941	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₁₁×#106	2
C₂²×C₄×C₈×C₁₁	2
C₂×C₁₁×#389	2
C₁₁×#1941	2
C₂×C₁₁×#340	2
C₂×#1941	11

Subgroups — C2×C11×#1941 #14598342

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₁×#1941 #14598342