Subgroups — C₂×C₁₁×#2155 #14610596

Order 2816.

658 conjugacy classes of subgroups.

The subgroup lattice has 304 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₁×M₃₂	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₁₁×#108	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₁×#427	C₂	1	1	yes	maximal, characteristic
4	C₁₁×#2155	C₂	1	8	yes	maximal, direct product factor
5	C₂×C₁₁×#365	C₂	1	4	yes	maximal, complemented
6	C₂²×C₁₁×M₁₆	—	2	1	no	—
7	C₂³×C₈×C₁₁	C₂²	1	1	yes	characteristic
8	C₂×C₁₁×#117	—	2	1	no	—
9	C₂×C₁₁×M₃₂	C₄	1	2	yes	complemented
10	C₂×C₁₁×M₃₂	C₄	1	4	yes	complemented
11	C₂×C₁₁×M₃₂	C₂²	1	2	yes	—
12	C₂×C₁₁×M₃₂	C₂²	1	4	yes	—
13	C₂²×C₁₁×C₁₆	C₄	1	2	yes	complemented
14	C₂×C₁₁×#108	—	2	1	no	—
15	C₂×C₁₁×#108	—	2	2	no	—
16	C₂×C₁₁×#108	C₂²	1	2	yes	—
17	C₂×C₁₁×#108	C₂²	1	4	yes	—
18	C₁₁×#427	—	2	2	no	—
19	C₁₁×#427	C₂²	1	4	yes	—
20	C₂×C₁₁×#107	—	2	1	no	—
21	C₂×C₁₁×#106	C₂²	1	2	yes	—
22	C₁₁×#365	C₂²	1	16	yes	complemented
23	C₂³×C₄×C₁₁	D₄	1	1	yes	characteristic
24	C₂×C₁₁×M₁₆	—	2	2	no	—
25	C₂×C₁₁×M₁₆	—	2	4	no	—
26	C₂×C₁₁×M₁₆	—	4	1	no	—
27	C₂×C₁₁×M₁₆	—	4	2	no	—
28	C₂²×C₈×C₁₁	—	4	1	no	—
29	C₂²×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
30	C₂²×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
31	C₂²×C₈×C₁₁	C₂×C₄	1	2	yes	—
32	C₂²×C₈×C₁₁	D₄	1	1	yes	characteristic
33	C₂²×C₈×C₁₁	D₄	1	2	yes	—
34	C₂²×C₈×C₁₁	Q₈	1	1	yes	characteristic
35	C₂²×C₈×C₁₁	Q₈	1	2	yes	—
36	C₂²×C₈×C₁₁	Q₈	1	1	yes	characteristic
37	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
38	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
39	C₁₁×#117	—	2	4	no	—
40	C₁₁×#117	—	4	2	no	—
41	C₂×C₁₁×C₄⋊C₄	—	2	2	no	—
42	C₂×C₁₁×C₂²⋊C₄	—	4	1	no	—
43	C₂×C₄²×C₁₁	—	4	1	no	—
44	C₁₁×M₃₂	C₂×C₄	1	4	yes	—
45	C₁₁×M₃₂	C₂×C₄	1	8	yes	complemented
46	C₁₁×M₃₂	C₂³	1	4	yes	—
47	C₂×C₁₁×C₁₆	C₂×C₄	1	4	yes	—
48	C₂×C₁₁×C₁₆	C₂×C₄	1	8	yes	complemented
49	C₁₁×#108	—	2	2	no	—
50	C₁₁×#108	—	2	4	no	—
51	C₁₁×#108	C₂³	1	4	yes	—
52	C₁₁×#107	—	2	4	no	—
53	C₁₁×#106	—	2	2	no	—
54	C₁₁×#106	C₂³	1	4	yes	—
55	C₂×#2155	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
56	C₂⁴×C₁₁	SD₁₆	1	1	yes	characteristic
57	C₂²×C₄×C₁₁	—	4	2	no	—
58	C₂²×C₄×C₁₁	C₄⋊C₄	1	1	yes	characteristic
59	C₂²×C₄×C₁₁	C₄⋊C₄	1	2	yes	—
60	C₂²×C₄×C₁₁	C₄⋊C₄	1	1	yes	characteristic
61	C₂²×C₄×C₁₁	SD₁₆	1	2	yes	—
62	C₂²×C₄×C₁₁	SD₁₆	1	1	yes	characteristic
63	C₂²×C₄×C₁₁	SD₁₆	1	1	yes	characteristic
64	C₂²×C₄×C₁₁	SD₁₆	1	2	yes	—
65	C₂²×C₄×C₁₁	SD₁₆	1	1	yes	characteristic
66	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
67	C₂²×C₄×C₁₁	C₂×D₄	1	2	yes	—
68	C₁₁×M₁₆	—	2	4	no	—
69	C₁₁×M₁₆	—	4	2	no	—
70	C₁₁×M₁₆	—	4	4	no	—
71	C₂×C₈×C₁₁	—	4	2	no	—
72	C₂×C₈×C₁₁	—	4	4	no	—
73	C₂×C₈×C₁₁	C₄⋊C₄	1	1	yes	characteristic
74	C₂×C₈×C₁₁	C₄⋊C₄	1	2	yes	—
75	C₂×C₈×C₁₁	C₄⋊C₄	1	2	yes	—
76	C₂×C₈×C₁₁	C₄⋊C₄	1	1	yes	characteristic
77	C₂×C₈×C₁₁	C₄⋊C₄	1	2	yes	—
78	C₂×C₈×C₁₁	C₄⋊C₄	1	2	yes	—
79	C₂×C₈×C₁₁	C₄⋊C₄	1	2	yes	—
80	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
81	C₂×C₈×C₁₁	C₂²×C₄	1	2	yes	—
82	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
83	C₂×C₈×C₁₁	C₂²×C₄	1	2	yes	—
84	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
85	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
86	C₂×C₈×C₁₁	C₂×Q₈	1	1	yes	characteristic
87	C₂×C₈×C₁₁	C₂×Q₈	1	1	yes	characteristic
88	C₂×C₈×C₁₁	C₂×Q₈	1	2	yes	—
89	C₂×C₈×C₁₁	C₂×Q₈	1	2	yes	—
90	C₂×C₈×C₁₁	C₂⁴	1	1	yes	characteristic
91	C₁₁×C₄⋊C₄	—	2	4	no	—
92	C₁₁×C₄⋊C₄	—	4	2	no	—
93	C₁₁×C₂²⋊C₄	—	4	4	no	—
94	C₄²×C₁₁	—	4	4	no	—
95	C₁₁×C₁₆	C₂²×C₄	1	8	yes	—
96	C₂²×M₃₂	C₂×C₁₁	1	1	yes	characteristic
97	C₂²×#108	C₂×C₁₁	1	1	yes	characteristic
98	C₂×#427	C₂×C₁₁	1	1	yes	characteristic
99	#2155	C₂×C₁₁	1	8	yes	direct product factor
100	C₂×#365	C₂×C₁₁	1	4	yes	complemented
101	C₂³×C₁₁	—	4	2	no	—
102	C₂³×C₁₁	#106	1	1	yes	characteristic
103	C₂³×C₁₁	#106	1	1	yes	characteristic
104	C₂³×C₁₁	#106	1	2	yes	—
105	C₂³×C₁₁	C₂×SD₁₆	1	1	yes	characteristic
106	C₂³×C₁₁	C₂×SD₁₆	1	2	yes	—
107	C₂×C₄×C₁₁	—	4	4	no	—
108	C₂×C₄×C₁₁	—	8	4	no	—
109	C₂×C₄×C₁₁	#106	1	2	yes	—
110	C₂×C₄×C₁₁	#106	1	2	yes	—
111	C₂×C₄×C₁₁	#106	1	1	yes	characteristic
112	C₂×C₄×C₁₁	#106	1	2	yes	—
113	C₂×C₄×C₁₁	#106	1	2	yes	—
114	C₂×C₄×C₁₁	#106	1	2	yes	—
115	C₂×C₄×C₁₁	#106	1	1	yes	characteristic
116	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
117	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	2	yes	—
118	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
119	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	2	yes	—
120	C₂×C₄×C₁₁	C₂×SD₁₆	1	1	yes	characteristic
121	C₂×C₄×C₁₁	C₂×SD₁₆	1	2	yes	—
122	C₂×C₄×C₁₁	C₂×SD₁₆	1	1	yes	characteristic
123	C₂×C₄×C₁₁	C₂×SD₁₆	1	2	yes	—
124	C₂×C₄×C₁₁	C₂×SD₁₆	1	2	yes	—
125	C₂×C₄×C₁₁	C₂×SD₁₆	1	1	yes	characteristic
126	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
127	C₈×C₁₁	—	4	4	no	—
128	C₈×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
129	C₈×C₁₁	C₂×C₄⋊C₄	1	2	yes	—
130	C₈×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
131	C₈×C₁₁	C₂×C₄⋊C₄	1	2	yes	—
132	C₈×C₁₁	C₂³×C₄	1	1	yes	characteristic
133	C₈×C₁₁	C₂²×Q₈	1	1	yes	characteristic
134	C₂²×M₁₆	—	2	1	no	—
135	C₂³×C₈	C₂²×C₁₁	1	1	yes	characteristic
136	C₂×#117	—	2	1	no	—
137	C₂×M₃₂	C₄×C₁₁	1	2	yes	complemented
138	C₂×M₃₂	C₄×C₁₁	1	4	yes	complemented
139	C₂×M₃₂	C₂²×C₁₁	1	2	yes	—
140	C₂×M₃₂	C₂²×C₁₁	1	4	yes	—
141	C₂²×C₁₆	C₄×C₁₁	1	2	yes	complemented
142	C₂×#108	—	2	1	no	—
143	C₂×#108	—	2	2	no	—
144	C₂×#108	C₂²×C₁₁	1	2	yes	—
145	C₂×#108	C₂²×C₁₁	1	4	yes	—
146	#427	—	2	2	no	—
147	#427	C₂²×C₁₁	1	4	yes	—
148	C₂×#107	—	2	1	no	—
149	C₂×#106	C₂²×C₁₁	1	2	yes	—
150	#365	C₂²×C₁₁	1	16	yes	complemented
151	C₂²×C₁₁	—	2	2	no	—
152	C₂²×C₁₁	—	2	2	no	—
153	C₂²×C₁₁	—	2	2	no	—
154	C₂²×C₁₁	—	4	2	no	—
155	C₂²×C₁₁	—	4	2	no	—
156	C₂²×C₁₁	C₂×#106	1	2	yes	—
157	C₂²×C₁₁	C₂×#106	1	2	yes	—
158	C₂²×C₁₁	C₂×#106	1	1	yes	characteristic
159	C₂²×C₁₁	C₂×#106	1	1	yes	characteristic
160	C₂²×C₁₁	C₂²×SD₁₆	1	1	yes	characteristic
161	C₄×C₁₁	—	8	4	no	—
162	C₄×C₁₁	C₂×#106	1	1	yes	characteristic
163	C₄×C₁₁	C₂×#106	1	2	yes	—
164	C₄×C₁₁	C₂×#106	1	1	yes	characteristic
165	C₄×C₁₁	C₂×#106	1	2	yes	—
166	C₄×C₁₁	C₂²×C₄⋊C₄	1	1	yes	characteristic
167	C₄×C₁₁	C₂²×SD₁₆	1	1	yes	characteristic
168	C₂³×C₄	D₄×C₁₁	1	1	yes	characteristic
169	C₂×M₁₆	—	2	2	no	—
170	C₂×M₁₆	—	2	4	no	—
171	C₂×M₁₆	—	4	1	no	—
172	C₂×M₁₆	—	4	2	no	—
173	C₂²×C₈	—	4	1	no	—
174	C₂²×C₈	C₂×C₄×C₁₁	1	1	yes	characteristic
175	C₂²×C₈	C₂×C₄×C₁₁	1	1	yes	characteristic
176	C₂²×C₈	C₂×C₄×C₁₁	1	2	yes	—
177	C₂²×C₈	D₄×C₁₁	1	1	yes	characteristic
178	C₂²×C₈	D₄×C₁₁	1	2	yes	—
179	C₂²×C₈	Q₈×C₁₁	1	1	yes	characteristic
180	C₂²×C₈	Q₈×C₁₁	1	2	yes	—
181	C₂²×C₈	Q₈×C₁₁	1	1	yes	characteristic
182	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
183	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
184	#117	—	2	4	no	—
185	#117	—	4	2	no	—
186	C₂×C₄⋊C₄	—	2	2	no	—
187	C₂×C₂²⋊C₄	—	4	1	no	—
188	C₂×C₄²	—	4	1	no	—
189	M₃₂	C₂×C₄×C₁₁	1	4	yes	—
190	M₃₂	C₂×C₄×C₁₁	1	8	yes	complemented
191	M₃₂	C₂³×C₁₁	1	4	yes	—
192	C₂×C₁₆	C₂×C₄×C₁₁	1	4	yes	—
193	C₂×C₁₆	C₂×C₄×C₁₁	1	8	yes	complemented
194	#108	—	2	2	no	—
195	#108	—	2	4	no	—
196	#108	C₂³×C₁₁	1	4	yes	—
197	#107	—	2	4	no	—
198	#106	—	2	2	no	—
199	#106	C₂³×C₁₁	1	4	yes	—
200	C₂×C₁₁	—	2	1	no	—
201	C₂×C₁₁	—	2	1	no	—
202	C₂×C₁₁	—	2	2	no	—
203	C₂×C₁₁	—	2	2	no	—
204	C₂×C₁₁	#2155	1	2	yes	direct product factor
205	C₂×C₁₁	C₂²×#106	1	1	yes	characteristic
206	C₂⁴	C₁₁×SD₁₆	1	1	yes	characteristic
207	C₂²×C₄	—	4	2	no	—
208	C₂²×C₄	C₁₁×C₄⋊C₄	1	1	yes	characteristic
209	C₂²×C₄	C₁₁×C₄⋊C₄	1	2	yes	—
210	C₂²×C₄	C₁₁×C₄⋊C₄	1	1	yes	characteristic
211	C₂²×C₄	C₁₁×SD₁₆	1	1	yes	characteristic
212	C₂²×C₄	C₁₁×SD₁₆	1	2	yes	—
213	C₂²×C₄	C₁₁×SD₁₆	1	1	yes	characteristic
214	C₂²×C₄	C₁₁×SD₁₆	1	1	yes	characteristic
215	C₂²×C₄	C₁₁×SD₁₆	1	2	yes	—
216	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
217	C₂²×C₄	C₂×D₄×C₁₁	1	2	yes	—
218	M₁₆	—	2	4	no	—
219	M₁₆	—	4	2	no	—
220	M₁₆	—	4	4	no	—
221	C₂×C₈	—	4	4	no	—
222	C₂×C₈	—	4	2	no	—
223	C₂×C₈	C₁₁×C₄⋊C₄	1	1	yes	characteristic
224	C₂×C₈	C₁₁×C₄⋊C₄	1	2	yes	—
225	C₂×C₈	C₁₁×C₄⋊C₄	1	2	yes	—
226	C₂×C₈	C₁₁×C₄⋊C₄	1	1	yes	characteristic
227	C₂×C₈	C₁₁×C₄⋊C₄	1	2	yes	—
228	C₂×C₈	C₁₁×C₄⋊C₄	1	2	yes	—
229	C₂×C₈	C₁₁×C₄⋊C₄	1	2	yes	—
230	C₂×C₈	C₂²×C₄×C₁₁	1	1	yes	characteristic
231	C₂×C₈	C₂²×C₄×C₁₁	1	2	yes	—
232	C₂×C₈	C₂²×C₄×C₁₁	1	1	yes	characteristic
233	C₂×C₈	C₂²×C₄×C₁₁	1	2	yes	—
234	C₂×C₈	C₂×D₄×C₁₁	1	1	yes	characteristic
235	C₂×C₈	C₂×D₄×C₁₁	1	2	yes	—
236	C₂×C₈	C₂×Q₈×C₁₁	1	1	yes	characteristic
237	C₂×C₈	C₂×Q₈×C₁₁	1	1	yes	characteristic
238	C₂×C₈	C₂×Q₈×C₁₁	1	2	yes	—
239	C₂×C₈	C₂×Q₈×C₁₁	1	2	yes	—
240	C₂×C₈	C₂⁴×C₁₁	1	1	yes	characteristic
241	C₄⋊C₄	—	2	4	no	—
242	C₄⋊C₄	—	4	2	no	—
243	C₂²⋊C₄	—	4	4	no	—
244	C₄²	—	4	4	no	—
245	C₁₆	C₂²×C₄×C₁₁	1	8	yes	—
246	C₁₁	C₂×#2155	1	1	yes	characteristic, direct product factor, Sylow
247	C₂³	—	4	2	no	—
248	C₂³	C₁₁×#106	1	1	yes	characteristic
249	C₂³	C₁₁×#106	1	1	yes	characteristic
250	C₂³	C₁₁×#106	1	2	yes	—
251	C₂³	C₂×C₁₁×SD₁₆	1	1	yes	characteristic
252	C₂³	C₂×C₁₁×SD₁₆	1	2	yes	—
253	C₂×C₄	—	4	4	no	—
254	C₂×C₄	—	8	4	no	—
255	C₂×C₄	C₁₁×#106	1	2	yes	—
256	C₂×C₄	C₁₁×#106	1	2	yes	—
257	C₂×C₄	C₁₁×#106	1	2	yes	—
258	C₂×C₄	C₁₁×#106	1	2	yes	—
259	C₂×C₄	C₁₁×#106	1	2	yes	—
260	C₂×C₄	C₁₁×#106	1	1	yes	characteristic
261	C₂×C₄	C₁₁×#106	1	1	yes	characteristic
262	C₂×C₄	C₂×C₁₁×C₄⋊C₄	1	2	yes	—
263	C₂×C₄	C₂×C₁₁×C₄⋊C₄	1	1	yes	characteristic
264	C₂×C₄	C₂×C₁₁×C₄⋊C₄	1	2	yes	—
265	C₂×C₄	C₂×C₁₁×C₄⋊C₄	1	1	yes	characteristic
266	C₂×C₄	C₂×C₁₁×SD₁₆	1	2	yes	—
267	C₂×C₄	C₂×C₁₁×SD₁₆	1	1	yes	characteristic
268	C₂×C₄	C₂×C₁₁×SD₁₆	1	2	yes	—
269	C₂×C₄	C₂×C₁₁×SD₁₆	1	1	yes	characteristic
270	C₂×C₄	C₂×C₁₁×SD₁₆	1	1	yes	characteristic
271	C₂×C₄	C₂×C₁₁×SD₁₆	1	2	yes	—
272	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
273	C₈	—	4	4	no	—
274	C₈	C₂×C₁₁×C₄⋊C₄	1	1	yes	characteristic
275	C₈	C₂×C₁₁×C₄⋊C₄	1	2	yes	—
276	C₈	C₂×C₁₁×C₄⋊C₄	1	1	yes	characteristic
277	C₈	C₂×C₁₁×C₄⋊C₄	1	2	yes	—
278	C₈	C₂³×C₄×C₁₁	1	1	yes	characteristic
279	C₈	C₂²×Q₈×C₁₁	1	1	yes	characteristic
280	C₂²	—	2	2	no	—
281	C₂²	—	2	2	no	—
282	C₂²	—	2	2	no	—
283	C₂²	—	4	2	no	—
284	C₂²	—	4	2	no	—
285	C₂²	C₂×C₁₁×#106	1	2	yes	—
286	C₂²	C₂×C₁₁×#106	1	2	yes	—
287	C₂²	C₂×C₁₁×#106	1	1	yes	characteristic
288	C₂²	C₂×C₁₁×#106	1	1	yes	characteristic
289	C₂²	C₂²×C₁₁×SD₁₆	1	1	yes	characteristic
290	C₄	—	8	4	no	—
291	C₄	C₂×C₁₁×#106	1	2	yes	—
292	C₄	C₂×C₁₁×#106	1	1	yes	characteristic
293	C₄	C₂×C₁₁×#106	1	1	yes	characteristic
294	C₄	C₂×C₁₁×#106	1	2	yes	—
295	C₄	C₂²×C₁₁×C₄⋊C₄	1	1	yes	characteristic
296	C₄	C₂²×C₁₁×SD₁₆	1	1	yes	characteristic
297	C₂	—	2	1	no	—
298	C₂	—	2	1	no	—
299	C₂	—	2	2	no	—
300	C₂	—	2	2	no	—
301	C₂	C₁₁×#2155	1	2	yes	direct product factor
302	C₂	C₂²×C₁₁×#106	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₁	#106
commutator	C₈	C₂³×C₄×C₁₁
Frattini, cosocle	C₂×C₈	C₂⁴×C₁₁
socle	C₂²×C₁₁	C₂×#106
prime radical	C₂⁴×C₁₁	SD₁₆
LCS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₁ ◁ C₂³×C₄×C₁₁ ◁ C₂³×C₈×C₁₁ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₁₁×#2155	C₂	direct (N × H)
5. C₂×C₁₁×#365	C₂	semidirect
9. C₂×C₁₁×M₃₂	C₄	semidirect
10. C₂×C₁₁×M₃₂	C₄	semidirect
13. C₂²×C₁₁×C₁₆	C₄	semidirect
22. C₁₁×#365	C₂²	semidirect
45. C₁₁×M₃₂	C₂×C₄	semidirect
48. C₂×C₁₁×C₁₆	C₂×C₄	semidirect
55. C₂×#2155	C₁₁	direct (N × H)
99. #2155	C₂×C₁₁	direct (N × H)
100. C₂×#365	C₂×C₁₁	semidirect
137. C₂×M₃₂	C₄×C₁₁	semidirect
138. C₂×M₃₂	C₄×C₁₁	semidirect
141. C₂²×C₁₆	C₄×C₁₁	semidirect
150. #365	C₂²×C₁₁	semidirect
190. M₃₂	C₂×C₄×C₁₁	semidirect
193. C₂×C₁₆	C₂×C₄×C₁₁	semidirect
204. C₂×C₁₁	#2155	direct (N × H)
246. C₁₁	C₂×#2155	direct (N × H)
301. C₂	C₁₁×#2155	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×M₃₂	2
C₂²×C₁₁×#108	2
C₂×C₁₁×#427	2
C₁₁×#2155	2
C₂×C₁₁×#365	2
C₂×#2155	11

Subgroups — C2×C11×#2155 #14610596

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₁×#2155 #14610596