Subgroups — C₂×C₁₁×#1669 #14596293

Order 2816.

790 conjugacy classes of subgroups.

The subgroup lattice has 318 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₁×#494	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₁×#474	C₂	1	2	yes	maximal
3	C₂×C₈×D₄×C₁₁	C₂	1	1	yes	maximal, characteristic
4	C₁₁×#1669	C₂	1	8	yes	maximal, direct product factor
5	C₂×C₁₁×#335	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₁₁×#332	C₂	1	2	yes	maximal, complemented
7	C₂²×C₁₁×Q₁₆	—	2	1	no	—
8	C₂²×C₁₁×Q₁₆	—	2	1	no	—
9	C₂³×C₈×C₁₁	—	2	1	no	—
10	C₂×C₁₁×C₄⋊Q₈	C₂²	1	2	yes	—
11	C₂×C₄×D₄×C₁₁	C₂²	1	1	yes	characteristic
12	C₁₁×#494	—	2	2	no	—
13	C₁₁×#494	C₂²	1	4	yes	complemented
14	C₁₁×#474	—	2	4	no	—
15	C₁₁×#474	C₂²	1	8	yes	—
16	C₈×D₄×C₁₁	—	2	2	no	—
17	C₈×D₄×C₁₁	C₂²	1	4	yes	—
18	C₂×C₁₁×#107	—	2	2	no	—
19	C₂×C₁₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
20	C₂×C₁₁×C₄⋊C₈	C₂²	1	2	yes	—
21	C₂×C₁₁×#102	—	2	2	no	—
22	C₂×C₁₁×C₂²⋊C₈	—	2	1	no	—
23	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
24	C₁₁×#335	C₂²	1	4	yes	complemented
25	C₁₁×#332	C₂²	1	8	yes	complemented
26	C₂²×Q₈×C₁₁	—	2	2	no	—
27	C₂²×D₄×C₁₁	D₄	1	1	yes	characteristic
28	C₂³×C₄×C₁₁	—	2	1	no	—
29	C₂×C₁₁×Q₁₆	—	2	4	no	—
30	C₂×C₁₁×Q₁₆	—	2	4	no	—
31	C₂×C₁₁×Q₁₆	—	4	4	no	—
32	C₂×C₁₁×Q₁₆	—	4	4	no	—
33	C₂²×C₈×C₁₁	—	2	1	no	—
34	C₂²×C₈×C₁₁	—	2	2	no	—
35	C₂²×C₈×C₁₁	—	2	4	no	—
36	C₂²×C₈×C₁₁	—	4	4	no	—
37	C₂²×C₈×C₁₁	D₄	1	1	yes	characteristic
38	C₂²×C₈×C₁₁	D₄	1	1	yes	characteristic
39	C₁₁×C₄⋊Q₈	—	2	2	no	—
40	C₁₁×C₄⋊Q₈	—	2	2	no	—
41	C₁₁×C₄⋊Q₈	—	2	2	no	—
42	C₁₁×C₄⋊Q₈	C₂³	1	4	yes	—
43	C₄×D₄×C₁₁	—	2	1	no	—
44	C₄×D₄×C₁₁	—	2	1	no	—
45	C₄×D₄×C₁₁	D₄	1	2	yes	—
46	C₄×D₄×C₁₁	C₂³	1	2	yes	—
47	C₂×C₁₁×C₄⋊C₄	—	2	2	no	—
48	C₂×C₁₁×C₄⋊C₄	—	2	2	no	—
49	C₂×C₁₁×C₄⋊C₄	D₄	1	1	yes	characteristic
50	C₂×C₁₁×C₂²⋊C₄	—	2	1	no	—
51	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
52	C₁₁×#107	—	2	8	no	—
53	C₁₁×C₄⋊C₈	—	2	1	no	—
54	C₁₁×C₄⋊C₈	—	2	2	no	—
55	C₁₁×C₄⋊C₈	C₂³	1	2	yes	—
56	C₁₁×C₄⋊C₈	C₂³	1	4	yes	—
57	C₁₁×#102	—	2	8	no	—
58	C₁₁×C₂²⋊C₈	—	2	4	no	—
59	C₄×C₈×C₁₁	D₄	1	2	yes	—
60	C₄×C₈×C₁₁	C₂³	1	2	yes	—
61	C₂×#1669	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
62	C₂⁴×C₁₁	—	2	1	no	—
63	C₂×Q₈×C₁₁	—	2	4	no	—
64	C₂×Q₈×C₁₁	—	4	2	no	—
65	C₂×Q₈×C₁₁	—	4	4	no	—
66	C₂×Q₈×C₁₁	—	4	4	no	—
67	C₂×D₄×C₁₁	—	2	1	no	—
68	C₂×D₄×C₁₁	—	2	2	no	—
69	C₂×D₄×C₁₁	Q₁₆	1	4	yes	complemented
70	C₂×D₄×C₁₁	C₂×D₄	1	2	yes	—
71	C₂²×C₄×C₁₁	—	2	1	no	—
72	C₂²×C₄×C₁₁	—	2	2	no	—
73	C₂²×C₄×C₁₁	—	2	2	no	—
74	C₂²×C₄×C₁₁	—	4	2	no	—
75	C₂²×C₄×C₁₁	—	4	2	no	—
76	C₂²×C₄×C₁₁	—	4	2	no	—
77	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
78	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
79	C₂²×C₄×C₁₁	#41	1	1	yes	characteristic
80	C₁₁×Q₁₆	—	4	8	no	—
81	C₁₁×Q₁₆	—	4	8	no	—
82	C₂×C₈×C₁₁	—	2	2	no	—
83	C₂×C₈×C₁₁	—	2	2	no	—
84	C₂×C₈×C₁₁	—	2	4	no	—
85	C₂×C₈×C₁₁	—	4	8	no	—
86	C₂×C₈×C₁₁	—	4	2	no	—
87	C₂×C₈×C₁₁	—	4	4	no	—
88	C₂×C₈×C₁₁	D₈	1	4	yes	—
89	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
90	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
91	C₁₁×C₄⋊C₄	—	2	1	no	—
92	C₁₁×C₄⋊C₄	—	2	4	no	—
93	C₁₁×C₄⋊C₄	—	2	4	no	—
94	C₁₁×C₄⋊C₄	—	4	2	no	—
95	C₁₁×C₄⋊C₄	—	4	2	no	—
96	C₁₁×C₄⋊C₄	C₂×D₄	1	2	yes	—
97	C₁₁×C₂²⋊C₄	—	2	2	no	—
98	C₁₁×C₂²⋊C₄	—	2	2	no	—
99	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
100	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
101	C₄²×C₁₁	#41	1	1	yes	characteristic
102	C₄²×C₁₁	C₂⁴	1	1	yes	characteristic
103	C₂×#494	C₂×C₁₁	1	1	yes	characteristic, complemented
104	C₂×#474	C₂×C₁₁	1	2	yes	—
105	C₂×C₈×D₄	C₂×C₁₁	1	1	yes	characteristic
106	#1669	C₂×C₁₁	1	8	yes	direct product factor
107	C₂×#335	C₂×C₁₁	1	1	yes	characteristic, complemented
108	C₂×#332	C₂×C₁₁	1	2	yes	complemented
109	C₂³×C₁₁	—	2	2	no	—
110	C₂³×C₁₁	—	2	4	no	—
111	C₂³×C₁₁	—	4	2	no	—
112	C₂³×C₁₁	—	4	2	no	—
113	C₂³×C₁₁	#121	1	1	yes	characteristic
114	Q₈×C₁₁	—	4	4	no	—
115	Q₈×C₁₁	—	4	4	no	—
116	Q₈×C₁₁	—	8	4	no	—
117	D₄×C₁₁	—	2	2	no	—
118	D₄×C₁₁	—	2	4	no	—
119	D₄×C₁₁	C₂×Q₁₆	1	4	yes	complemented
120	C₂×C₄×C₁₁	—	2	2	no	—
121	C₂×C₄×C₁₁	—	2	2	no	—
122	C₂×C₄×C₁₁	—	4	2	no	—
123	C₂×C₄×C₁₁	—	4	2	no	—
124	C₂×C₄×C₁₁	—	4	2	no	—
125	C₂×C₄×C₁₁	—	4	4	no	—
126	C₂×C₄×C₁₁	—	4	4	no	—
127	C₂×C₄×C₁₁	—	8	4	no	—
128	C₂×C₄×C₁₁	#121	1	1	yes	characteristic
129	C₂×C₄×C₁₁	#121	1	1	yes	characteristic
130	C₂×C₄×C₁₁	#121	1	1	yes	characteristic
131	C₂×C₄×C₁₁	C₂×D₈	1	2	yes	—
132	C₂×C₄×C₁₁	C₂×Q₁₆	1	2	yes	—
133	C₂×C₄×C₁₁	#135	1	2	yes	—
134	C₂×C₄×C₁₁	AGL(1,ℤ/8)	1	2	yes	—
135	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
136	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
137	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
138	C₈×C₁₁	—	2	2	no	—
139	C₈×C₁₁	—	4	2	no	—
140	C₈×C₁₁	—	4	4	no	—
141	C₈×C₁₁	C₂×D₈	1	4	yes	—
142	C₂²×Q₁₆	—	2	1	no	—
143	C₂²×Q₁₆	—	2	1	no	—
144	C₂³×C₈	—	2	1	no	—
145	C₂×C₄⋊Q₈	C₂²×C₁₁	1	2	yes	—
146	C₂×C₄×D₄	C₂²×C₁₁	1	1	yes	characteristic
147	#494	—	2	2	no	—
148	#494	C₂²×C₁₁	1	4	yes	complemented
149	#474	—	2	4	no	—
150	#474	C₂²×C₁₁	1	8	yes	—
151	C₈×D₄	—	2	2	no	—
152	C₈×D₄	C₂²×C₁₁	1	4	yes	—
153	C₂×#107	—	2	2	no	—
154	C₂×C₄⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
155	C₂×C₄⋊C₈	C₂²×C₁₁	1	2	yes	—
156	C₂×#102	—	2	2	no	—
157	C₂×C₂²⋊C₈	—	2	1	no	—
158	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
159	#335	C₂²×C₁₁	1	4	yes	complemented
160	#332	C₂²×C₁₁	1	8	yes	complemented
161	C₂²×C₁₁	—	2	4	no	—
162	C₂²×C₁₁	—	4	8	no	—
163	C₂²×C₁₁	—	4	2	no	—
164	C₂²×C₁₁	—	4	2	no	—
165	C₂²×C₁₁	#459	1	2	yes	—
166	C₂²×C₁₁	#467	1	2	yes	—
167	C₂²×C₁₁	#473	1	2	yes	—
168	C₂²×C₁₁	C₂×#121	1	1	yes	characteristic
169	C₄×C₁₁	—	2	1	no	—
170	C₄×C₁₁	—	2	1	no	—
171	C₄×C₁₁	—	4	2	no	—
172	C₄×C₁₁	—	8	4	no	—
173	C₄×C₁₁	#459	1	2	yes	—
174	C₄×C₁₁	#467	1	2	yes	—
175	C₄×C₁₁	C₂²×D₈	1	1	yes	characteristic
176	C₄×C₁₁	C₂²×Q₁₆	1	1	yes	characteristic
177	C₄×C₁₁	C₂×#135	1	1	yes	characteristic
178	C₄×C₁₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
179	C₂²×Q₈	—	2	2	no	—
180	C₂²×D₄	D₄×C₁₁	1	1	yes	characteristic
181	C₂³×C₄	—	2	1	no	—
182	C₂×Q₁₆	—	2	4	no	—
183	C₂×Q₁₆	—	2	4	no	—
184	C₂×Q₁₆	—	4	4	no	—
185	C₂×Q₁₆	—	4	4	no	—
186	C₂²×C₈	—	2	1	no	—
187	C₂²×C₈	—	2	2	no	—
188	C₂²×C₈	—	2	4	no	—
189	C₂²×C₈	—	4	4	no	—
190	C₂²×C₈	D₄×C₁₁	1	1	yes	characteristic
191	C₂²×C₈	D₄×C₁₁	1	1	yes	characteristic
192	C₄⋊Q₈	—	2	2	no	—
193	C₄⋊Q₈	—	2	2	no	—
194	C₄⋊Q₈	—	2	2	no	—
195	C₄⋊Q₈	C₂³×C₁₁	1	4	yes	—
196	C₄×D₄	—	2	1	no	—
197	C₄×D₄	—	2	1	no	—
198	C₄×D₄	D₄×C₁₁	1	2	yes	—
199	C₄×D₄	C₂³×C₁₁	1	2	yes	—
200	C₂×C₄⋊C₄	—	2	2	no	—
201	C₂×C₄⋊C₄	—	2	2	no	—
202	C₂×C₄⋊C₄	D₄×C₁₁	1	1	yes	characteristic
203	C₂×C₂²⋊C₄	—	2	1	no	—
204	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
205	#107	—	2	8	no	—
206	C₄⋊C₈	—	2	1	no	—
207	C₄⋊C₈	—	2	2	no	—
208	C₄⋊C₈	C₂³×C₁₁	1	2	yes	—
209	C₄⋊C₈	C₂³×C₁₁	1	4	yes	—
210	#102	—	2	8	no	—
211	C₂²⋊C₈	—	2	4	no	—
212	C₄×C₈	D₄×C₁₁	1	2	yes	—
213	C₄×C₈	C₂³×C₁₁	1	2	yes	—
214	C₂×C₁₁	—	4	4	no	—
215	C₂×C₁₁	#1669	1	4	yes	direct product factor
216	C₂×C₁₁	C₂×#459	1	1	yes	characteristic
217	C₂×C₁₁	C₂×#467	1	1	yes	characteristic
218	C₂×C₁₁	C₂×#473	1	1	yes	characteristic
219	C₂⁴	—	2	1	no	—
220	C₂×Q₈	—	2	4	no	—
221	C₂×Q₈	—	4	2	no	—
222	C₂×Q₈	—	4	4	no	—
223	C₂×Q₈	—	4	4	no	—
224	C₂×D₄	—	2	1	no	—
225	C₂×D₄	—	2	2	no	—
226	C₂×D₄	C₁₁×Q₁₆	1	4	yes	complemented
227	C₂×D₄	C₂×D₄×C₁₁	1	2	yes	—
228	C₂²×C₄	—	2	1	no	—
229	C₂²×C₄	—	2	2	no	—
230	C₂²×C₄	—	2	2	no	—
231	C₂²×C₄	—	4	2	no	—
232	C₂²×C₄	—	4	2	no	—
233	C₂²×C₄	—	4	2	no	—
234	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
235	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
236	C₂²×C₄	C₁₁×#41	1	1	yes	characteristic
237	Q₁₆	—	4	8	no	—
238	Q₁₆	—	4	8	no	—
239	C₂×C₈	—	2	2	no	—
240	C₂×C₈	—	2	2	no	—
241	C₂×C₈	—	2	4	no	—
242	C₂×C₈	—	4	2	no	—
243	C₂×C₈	—	4	4	no	—
244	C₂×C₈	—	4	8	no	—
245	C₂×C₈	C₁₁×D₈	1	4	yes	—
246	C₂×C₈	C₂×D₄×C₁₁	1	2	yes	—
247	C₂×C₈	C₂×D₄×C₁₁	1	2	yes	—
248	C₄⋊C₄	—	2	1	no	—
249	C₄⋊C₄	—	2	4	no	—
250	C₄⋊C₄	—	2	4	no	—
251	C₄⋊C₄	—	4	2	no	—
252	C₄⋊C₄	—	4	2	no	—
253	C₄⋊C₄	C₂×D₄×C₁₁	1	2	yes	—
254	C₂²⋊C₄	—	2	2	no	—
255	C₂²⋊C₄	—	2	2	no	—
256	C₄²	C₂×D₄×C₁₁	1	1	yes	characteristic
257	C₄²	C₂×D₄×C₁₁	1	1	yes	characteristic
258	C₄²	C₁₁×#41	1	1	yes	characteristic
259	C₄²	C₂⁴×C₁₁	1	1	yes	characteristic
260	C₁₁	C₂×#1669	1	1	yes	characteristic, direct product factor, Sylow
261	C₂³	—	2	2	no	—
262	C₂³	—	2	4	no	—
263	C₂³	—	4	2	no	—
264	C₂³	—	4	2	no	—
265	C₂³	C₁₁×#121	1	1	yes	characteristic
266	Q₈	—	4	4	no	—
267	Q₈	—	4	4	no	—
268	Q₈	—	8	4	no	—
269	D₄	—	2	2	no	—
270	D₄	—	2	4	no	—
271	D₄	C₂×C₁₁×Q₁₆	1	4	yes	complemented
272	C₂×C₄	—	2	2	no	—
273	C₂×C₄	—	2	2	no	—
274	C₂×C₄	—	4	2	no	—
275	C₂×C₄	—	4	2	no	—
276	C₂×C₄	—	4	2	no	—
277	C₂×C₄	—	4	4	no	—
278	C₂×C₄	—	4	4	no	—
279	C₂×C₄	—	8	4	no	—
280	C₂×C₄	C₁₁×#121	1	1	yes	characteristic
281	C₂×C₄	C₁₁×#121	1	1	yes	characteristic
282	C₂×C₄	C₁₁×#121	1	1	yes	characteristic
283	C₂×C₄	C₂×C₁₁×D₈	1	2	yes	—
284	C₂×C₄	C₂×C₁₁×Q₁₆	1	2	yes	—
285	C₂×C₄	C₁₁×#135	1	2	yes	—
286	C₂×C₄	C₁₁×AGL(1,ℤ/8)	1	2	yes	—
287	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
288	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
289	C₂×C₄	C₂×C₁₁×#41	1	1	yes	characteristic
290	C₈	—	2	2	no	—
291	C₈	—	4	2	no	—
292	C₈	—	4	4	no	—
293	C₈	C₂×C₁₁×D₈	1	4	yes	—
294	C₂²	—	2	4	no	—
295	C₂²	—	4	8	no	—
296	C₂²	—	4	2	no	—
297	C₂²	—	4	2	no	—
298	C₂²	C₁₁×#459	1	2	yes	—
299	C₂²	C₁₁×#467	1	2	yes	—
300	C₂²	C₁₁×#473	1	2	yes	—
301	C₂²	C₂×C₁₁×#121	1	1	yes	characteristic
302	C₄	—	2	1	no	—
303	C₄	—	2	1	no	—
304	C₄	—	4	2	no	—
305	C₄	—	8	4	no	—
306	C₄	C₁₁×#459	1	2	yes	—
307	C₄	C₁₁×#467	1	2	yes	—
308	C₄	C₂²×C₁₁×D₈	1	1	yes	characteristic
309	C₄	C₂²×C₁₁×Q₁₆	1	1	yes	characteristic
310	C₄	C₂×C₁₁×#135	1	1	yes	characteristic
311	C₄	C₂×C₁₁×AGL(1,ℤ/8)	1	1	yes	characteristic
312	C₂	—	4	4	no	—
313	C₂	C₁₁×#1669	1	4	yes	direct product factor
314	C₂	C₂×C₁₁×#459	1	1	yes	characteristic
315	C₂	C₂×C₁₁×#467	1	1	yes	characteristic
316	C₂	C₂×C₁₁×#473	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₁	#121
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₁
prime radical	C₂²×D₄×C₁₁	D₄
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₁ ◁ C₂×C₄²×C₁₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₁×#494	C₂	semidirect
4. C₁₁×#1669	C₂	direct (N × H)
5. C₂×C₁₁×#335	C₂	semidirect
6. C₂×C₁₁×#332	C₂	semidirect
13. C₁₁×#494	C₂²	semidirect
24. C₁₁×#335	C₂²	semidirect
25. C₁₁×#332	C₂²	semidirect
61. C₂×#1669	C₁₁	direct (N × H)
69. C₂×D₄×C₁₁	Q₁₆	semidirect
103. C₂×#494	C₂×C₁₁	semidirect
106. #1669	C₂×C₁₁	direct (N × H)
107. C₂×#335	C₂×C₁₁	semidirect
108. C₂×#332	C₂×C₁₁	semidirect
119. D₄×C₁₁	C₂×Q₁₆	semidirect
148. #494	C₂²×C₁₁	semidirect
159. #335	C₂²×C₁₁	semidirect
160. #332	C₂²×C₁₁	semidirect
215. C₂×C₁₁	#1669	direct (N × H)
226. C₂×D₄	C₁₁×Q₁₆	semidirect
260. C₁₁	C₂×#1669	direct (N × H)
271. D₄	C₂×C₁₁×Q₁₆	semidirect
313. C₂	C₁₁×#1669	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×#494	2
C₂×C₁₁×#474	2
C₂×C₈×D₄×C₁₁	2
C₁₁×#1669	2
C₂×C₁₁×#335	2
C₂×C₁₁×#332	2
C₂×#1669	11

Subgroups — C2×C11×#1669 #14596293

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₁×#1669 #14596293