Subgroups — C₂×C₁₁×#1673 #14596296

Order 2816.

790 conjugacy classes of subgroups.

The subgroup lattice has 314 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₁×#500	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₁×#461	C₂	1	2	yes	maximal
3	C₂×C₈×D₄×C₁₁	C₂	1	1	yes	maximal, characteristic
4	C₁₁×#1673	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×SD₁₆	—	2	2	no	—
8	C₂³×C₈×C₁₁	—	2	1	no	—
9	C₂×C₁₁×C₄⋊Q₈	C₂²	1	2	yes	—
10	C₂×C₄×D₄×C₁₁	C₂²	1	1	yes	characteristic
11	C₁₁×#500	—	2	2	no	—
12	C₁₁×#500	C₂²	1	4	yes	complemented
13	C₁₁×#461	—	2	4	no	—
14	C₁₁×#461	C₂²	1	8	yes	—
15	C₈×D₄×C₁₁	—	2	2	no	—
16	C₈×D₄×C₁₁	C₂²	1	4	yes	—
17	C₂×C₁₁×#107	—	2	1	no	—
18	C₂×C₁₁×#107	—	2	1	no	—
19	C₂×C₁₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
20	C₂×C₁₁×C₄⋊C₈	C₂²	1	2	yes	—
21	C₂×C₁₁×#103	—	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×SD₁₆	—	2	8	no	—
30	C₂×C₁₁×SD₁₆	—	4	8	no	—
31	C₂²×C₈×C₁₁	—	2	1	no	—
32	C₂²×C₈×C₁₁	—	2	2	no	—
33	C₂²×C₈×C₁₁	—	2	4	no	—
34	C₂²×C₈×C₁₁	—	4	4	no	—
35	C₂²×C₈×C₁₁	D₄	1	1	yes	characteristic
36	C₂²×C₈×C₁₁	D₄	1	1	yes	characteristic
37	C₁₁×C₄⋊Q₈	—	2	2	no	—
38	C₁₁×C₄⋊Q₈	—	2	2	no	—
39	C₁₁×C₄⋊Q₈	—	2	2	no	—
40	C₁₁×C₄⋊Q₈	C₂³	1	4	yes	—
41	C₄×D₄×C₁₁	—	2	1	no	—
42	C₄×D₄×C₁₁	—	2	1	no	—
43	C₄×D₄×C₁₁	D₄	1	2	yes	—
44	C₄×D₄×C₁₁	C₂³	1	2	yes	—
45	C₂×C₁₁×C₄⋊C₄	—	2	2	no	—
46	C₂×C₁₁×C₄⋊C₄	—	2	2	no	—
47	C₂×C₁₁×C₄⋊C₄	D₄	1	1	yes	characteristic
48	C₂×C₁₁×C₂²⋊C₄	—	2	1	no	—
49	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
50	C₁₁×#107	—	2	4	no	—
51	C₁₁×#107	—	2	4	no	—
52	C₁₁×C₄⋊C₈	—	2	1	no	—
53	C₁₁×C₄⋊C₈	—	2	2	no	—
54	C₁₁×C₄⋊C₈	C₂³	1	2	yes	—
55	C₁₁×C₄⋊C₈	C₂³	1	4	yes	—
56	C₁₁×#103	—	2	8	no	—
57	C₁₁×C₂²⋊C₈	—	2	4	no	—
58	C₄×C₈×C₁₁	D₄	1	2	yes	—
59	C₄×C₈×C₁₁	C₂³	1	2	yes	—
60	C₂×#1673	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
61	C₂⁴×C₁₁	—	2	1	no	—
62	C₂×Q₈×C₁₁	—	2	4	no	—
63	C₂×Q₈×C₁₁	—	4	2	no	—
64	C₂×Q₈×C₁₁	—	4	4	no	—
65	C₂×Q₈×C₁₁	—	4	4	no	—
66	C₂×D₄×C₁₁	—	2	1	no	—
67	C₂×D₄×C₁₁	—	2	2	no	—
68	C₂×D₄×C₁₁	D₈	1	4	yes	—
69	C₂×D₄×C₁₁	C₂×D₄	1	2	yes	—
70	C₂²×C₄×C₁₁	—	2	1	no	—
71	C₂²×C₄×C₁₁	—	2	2	no	—
72	C₂²×C₄×C₁₁	—	2	2	no	—
73	C₂²×C₄×C₁₁	—	4	2	no	—
74	C₂²×C₄×C₁₁	—	4	2	no	—
75	C₂²×C₄×C₁₁	—	4	2	no	—
76	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
77	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
78	C₂²×C₄×C₁₁	#41	1	1	yes	characteristic
79	C₁₁×SD₁₆	—	4	16	no	—
80	C₂×C₈×C₁₁	—	2	2	no	—
81	C₂×C₈×C₁₁	—	2	2	no	—
82	C₂×C₈×C₁₁	—	2	4	no	—
83	C₂×C₈×C₁₁	—	4	8	no	—
84	C₂×C₈×C₁₁	—	4	4	no	—
85	C₂×C₈×C₁₁	—	4	2	no	—
86	C₂×C₈×C₁₁	SD₁₆	1	4	yes	complemented
87	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
88	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
89	C₁₁×C₄⋊C₄	—	2	1	no	—
90	C₁₁×C₄⋊C₄	—	2	4	no	—
91	C₁₁×C₄⋊C₄	—	2	4	no	—
92	C₁₁×C₄⋊C₄	—	4	2	no	—
93	C₁₁×C₄⋊C₄	—	4	2	no	—
94	C₁₁×C₄⋊C₄	C₂×D₄	1	2	yes	—
95	C₁₁×C₂²⋊C₄	—	2	2	no	—
96	C₁₁×C₂²⋊C₄	—	2	2	no	—
97	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
98	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
99	C₄²×C₁₁	#41	1	1	yes	characteristic
100	C₄²×C₁₁	C₂⁴	1	1	yes	characteristic
101	C₂×#500	C₂×C₁₁	1	1	yes	characteristic, complemented
102	C₂×#461	C₂×C₁₁	1	2	yes	—
103	C₂×C₈×D₄	C₂×C₁₁	1	1	yes	characteristic
104	#1673	C₂×C₁₁	1	8	yes	direct product factor
105	C₂×#335	C₂×C₁₁	1	1	yes	characteristic, complemented
106	C₂×#332	C₂×C₁₁	1	2	yes	complemented
107	C₂³×C₁₁	—	2	2	no	—
108	C₂³×C₁₁	—	2	4	no	—
109	C₂³×C₁₁	—	4	2	no	—
110	C₂³×C₁₁	—	4	2	no	—
111	C₂³×C₁₁	#121	1	1	yes	characteristic
112	Q₈×C₁₁	—	4	4	no	—
113	Q₈×C₁₁	—	4	4	no	—
114	Q₈×C₁₁	—	8	4	no	—
115	D₄×C₁₁	—	2	2	no	—
116	D₄×C₁₁	—	2	4	no	—
117	D₄×C₁₁	C₂×D₈	1	4	yes	—
118	C₂×C₄×C₁₁	—	2	2	no	—
119	C₂×C₄×C₁₁	—	2	2	no	—
120	C₂×C₄×C₁₁	—	4	2	no	—
121	C₂×C₄×C₁₁	—	4	2	no	—
122	C₂×C₄×C₁₁	—	4	2	no	—
123	C₂×C₄×C₁₁	—	4	4	no	—
124	C₂×C₄×C₁₁	—	4	4	no	—
125	C₂×C₄×C₁₁	—	8	4	no	—
126	C₂×C₄×C₁₁	#121	1	1	yes	characteristic
127	C₂×C₄×C₁₁	#121	1	1	yes	characteristic
128	C₂×C₄×C₁₁	#121	1	1	yes	characteristic
129	C₂×C₄×C₁₁	C₂×D₈	1	2	yes	—
130	C₂×C₄×C₁₁	C₂×SD₁₆	1	2	yes	—
131	C₂×C₄×C₁₁	#135	1	2	yes	—
132	C₂×C₄×C₁₁	#137	1	2	yes	—
133	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
134	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
135	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
136	C₈×C₁₁	—	2	2	no	—
137	C₈×C₁₁	—	4	4	no	—
138	C₈×C₁₁	—	4	2	no	—
139	C₈×C₁₁	C₂×SD₁₆	1	4	yes	complemented
140	C₂²×SD₁₆	—	2	2	no	—
141	C₂³×C₈	—	2	1	no	—
142	C₂×C₄⋊Q₈	C₂²×C₁₁	1	2	yes	—
143	C₂×C₄×D₄	C₂²×C₁₁	1	1	yes	characteristic
144	#500	—	2	2	no	—
145	#500	C₂²×C₁₁	1	4	yes	complemented
146	#461	—	2	4	no	—
147	#461	C₂²×C₁₁	1	8	yes	—
148	C₈×D₄	—	2	2	no	—
149	C₈×D₄	C₂²×C₁₁	1	4	yes	—
150	C₂×#107	—	2	1	no	—
151	C₂×#107	—	2	1	no	—
152	C₂×C₄⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
153	C₂×C₄⋊C₈	C₂²×C₁₁	1	2	yes	—
154	C₂×#103	—	2	2	no	—
155	C₂×C₂²⋊C₈	—	2	1	no	—
156	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
157	#335	C₂²×C₁₁	1	4	yes	complemented
158	#332	C₂²×C₁₁	1	8	yes	complemented
159	C₂²×C₁₁	—	2	4	no	—
160	C₂²×C₁₁	—	4	8	no	—
161	C₂²×C₁₁	—	4	2	no	—
162	C₂²×C₁₁	—	4	2	no	—
163	C₂²×C₁₁	#461	1	2	yes	—
164	C₂²×C₁₁	#466	1	2	yes	—
165	C₂²×C₁₁	#473	1	2	yes	—
166	C₂²×C₁₁	C₂×#121	1	1	yes	characteristic
167	C₄×C₁₁	—	2	1	no	—
168	C₄×C₁₁	—	2	1	no	—
169	C₄×C₁₁	—	4	2	no	—
170	C₄×C₁₁	—	8	4	no	—
171	C₄×C₁₁	#461	1	2	yes	—
172	C₄×C₁₁	#466	1	2	yes	—
173	C₄×C₁₁	C₂²×D₈	1	1	yes	characteristic
174	C₄×C₁₁	C₂²×SD₁₆	1	1	yes	characteristic
175	C₄×C₁₁	C₂×#135	1	1	yes	characteristic
176	C₄×C₁₁	C₂×#137	1	1	yes	characteristic
177	C₂²×Q₈	—	2	2	no	—
178	C₂²×D₄	D₄×C₁₁	1	1	yes	characteristic
179	C₂³×C₄	—	2	1	no	—
180	C₂×SD₁₆	—	2	8	no	—
181	C₂×SD₁₆	—	4	8	no	—
182	C₂²×C₈	—	2	1	no	—
183	C₂²×C₈	—	2	2	no	—
184	C₂²×C₈	—	2	4	no	—
185	C₂²×C₈	—	4	4	no	—
186	C₂²×C₈	D₄×C₁₁	1	1	yes	characteristic
187	C₂²×C₈	D₄×C₁₁	1	1	yes	characteristic
188	C₄⋊Q₈	—	2	2	no	—
189	C₄⋊Q₈	—	2	2	no	—
190	C₄⋊Q₈	—	2	2	no	—
191	C₄⋊Q₈	C₂³×C₁₁	1	4	yes	—
192	C₄×D₄	—	2	1	no	—
193	C₄×D₄	—	2	1	no	—
194	C₄×D₄	D₄×C₁₁	1	2	yes	—
195	C₄×D₄	C₂³×C₁₁	1	2	yes	—
196	C₂×C₄⋊C₄	—	2	2	no	—
197	C₂×C₄⋊C₄	—	2	2	no	—
198	C₂×C₄⋊C₄	D₄×C₁₁	1	1	yes	characteristic
199	C₂×C₂²⋊C₄	—	2	1	no	—
200	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
201	#107	—	2	4	no	—
202	#107	—	2	4	no	—
203	C₄⋊C₈	—	2	1	no	—
204	C₄⋊C₈	—	2	2	no	—
205	C₄⋊C₈	C₂³×C₁₁	1	2	yes	—
206	C₄⋊C₈	C₂³×C₁₁	1	4	yes	—
207	#103	—	2	8	no	—
208	C₂²⋊C₈	—	2	4	no	—
209	C₄×C₈	D₄×C₁₁	1	2	yes	—
210	C₄×C₈	C₂³×C₁₁	1	2	yes	—
211	C₂×C₁₁	—	4	4	no	—
212	C₂×C₁₁	#1673	1	4	yes	direct product factor
213	C₂×C₁₁	C₂×#461	1	1	yes	characteristic
214	C₂×C₁₁	C₂×#466	1	1	yes	characteristic
215	C₂×C₁₁	C₂×#473	1	1	yes	characteristic
216	C₂⁴	—	2	1	no	—
217	C₂×Q₈	—	2	4	no	—
218	C₂×Q₈	—	4	2	no	—
219	C₂×Q₈	—	4	4	no	—
220	C₂×Q₈	—	4	4	no	—
221	C₂×D₄	—	2	1	no	—
222	C₂×D₄	—	2	2	no	—
223	C₂×D₄	C₁₁×D₈	1	4	yes	—
224	C₂×D₄	C₂×D₄×C₁₁	1	2	yes	—
225	C₂²×C₄	—	2	1	no	—
226	C₂²×C₄	—	2	2	no	—
227	C₂²×C₄	—	2	2	no	—
228	C₂²×C₄	—	4	2	no	—
229	C₂²×C₄	—	4	2	no	—
230	C₂²×C₄	—	4	2	no	—
231	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
232	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
233	C₂²×C₄	C₁₁×#41	1	1	yes	characteristic
234	SD₁₆	—	4	16	no	—
235	C₂×C₈	—	2	2	no	—
236	C₂×C₈	—	2	2	no	—
237	C₂×C₈	—	2	4	no	—
238	C₂×C₈	—	4	4	no	—
239	C₂×C₈	—	4	2	no	—
240	C₂×C₈	—	4	8	no	—
241	C₂×C₈	C₁₁×SD₁₆	1	4	yes	complemented
242	C₂×C₈	C₂×D₄×C₁₁	1	2	yes	—
243	C₂×C₈	C₂×D₄×C₁₁	1	2	yes	—
244	C₄⋊C₄	—	2	1	no	—
245	C₄⋊C₄	—	2	4	no	—
246	C₄⋊C₄	—	2	4	no	—
247	C₄⋊C₄	—	4	2	no	—
248	C₄⋊C₄	—	4	2	no	—
249	C₄⋊C₄	C₂×D₄×C₁₁	1	2	yes	—
250	C₂²⋊C₄	—	2	2	no	—
251	C₂²⋊C₄	—	2	2	no	—
252	C₄²	C₂×D₄×C₁₁	1	1	yes	characteristic
253	C₄²	C₂×D₄×C₁₁	1	1	yes	characteristic
254	C₄²	C₁₁×#41	1	1	yes	characteristic
255	C₄²	C₂⁴×C₁₁	1	1	yes	characteristic
256	C₁₁	C₂×#1673	1	1	yes	characteristic, direct product factor, Sylow
257	C₂³	—	2	2	no	—
258	C₂³	—	2	4	no	—
259	C₂³	—	4	2	no	—
260	C₂³	—	4	2	no	—
261	C₂³	C₁₁×#121	1	1	yes	characteristic
262	Q₈	—	4	4	no	—
263	Q₈	—	4	4	no	—
264	Q₈	—	8	4	no	—
265	D₄	—	2	2	no	—
266	D₄	—	2	4	no	—
267	D₄	C₂×C₁₁×D₈	1	4	yes	—
268	C₂×C₄	—	2	2	no	—
269	C₂×C₄	—	2	2	no	—
270	C₂×C₄	—	4	2	no	—
271	C₂×C₄	—	4	2	no	—
272	C₂×C₄	—	4	2	no	—
273	C₂×C₄	—	4	4	no	—
274	C₂×C₄	—	4	4	no	—
275	C₂×C₄	—	8	4	no	—
276	C₂×C₄	C₁₁×#121	1	1	yes	characteristic
277	C₂×C₄	C₁₁×#121	1	1	yes	characteristic
278	C₂×C₄	C₁₁×#121	1	1	yes	characteristic
279	C₂×C₄	C₂×C₁₁×D₈	1	2	yes	—
280	C₂×C₄	C₂×C₁₁×SD₁₆	1	2	yes	—
281	C₂×C₄	C₁₁×#135	1	2	yes	—
282	C₂×C₄	C₁₁×#137	1	2	yes	—
283	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
284	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
285	C₂×C₄	C₂×C₁₁×#41	1	1	yes	characteristic
286	C₈	—	2	2	no	—
287	C₈	—	4	4	no	—
288	C₈	—	4	2	no	—
289	C₈	C₂×C₁₁×SD₁₆	1	4	yes	complemented
290	C₂²	—	2	4	no	—
291	C₂²	—	4	8	no	—
292	C₂²	—	4	2	no	—
293	C₂²	—	4	2	no	—
294	C₂²	C₁₁×#461	1	2	yes	—
295	C₂²	C₁₁×#466	1	2	yes	—
296	C₂²	C₁₁×#473	1	2	yes	—
297	C₂²	C₂×C₁₁×#121	1	1	yes	characteristic
298	C₄	—	2	1	no	—
299	C₄	—	2	1	no	—
300	C₄	—	4	2	no	—
301	C₄	—	8	4	no	—
302	C₄	C₁₁×#461	1	2	yes	—
303	C₄	C₁₁×#466	1	2	yes	—
304	C₄	C₂²×C₁₁×D₈	1	1	yes	characteristic
305	C₄	C₂²×C₁₁×SD₁₆	1	1	yes	characteristic
306	C₄	C₂×C₁₁×#135	1	1	yes	characteristic
307	C₄	C₂×C₁₁×#137	1	1	yes	characteristic
308	C₂	—	4	4	no	—
309	C₂	C₁₁×#1673	1	4	yes	direct product factor
310	C₂	C₂×C₁₁×#461	1	1	yes	characteristic
311	C₂	C₂×C₁₁×#466	1	1	yes	characteristic
312	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×#500	C₂	semidirect
4. C₁₁×#1673	C₂	direct (N × H)
5. C₂×C₁₁×#335	C₂	semidirect
6. C₂×C₁₁×#332	C₂	semidirect
12. C₁₁×#500	C₂²	semidirect
24. C₁₁×#335	C₂²	semidirect
25. C₁₁×#332	C₂²	semidirect
60. C₂×#1673	C₁₁	direct (N × H)
86. C₂×C₈×C₁₁	SD₁₆	semidirect
101. C₂×#500	C₂×C₁₁	semidirect
104. #1673	C₂×C₁₁	direct (N × H)
105. C₂×#335	C₂×C₁₁	semidirect
106. C₂×#332	C₂×C₁₁	semidirect
139. C₈×C₁₁	C₂×SD₁₆	semidirect
145. #500	C₂²×C₁₁	semidirect
157. #335	C₂²×C₁₁	semidirect
158. #332	C₂²×C₁₁	semidirect
212. C₂×C₁₁	#1673	direct (N × H)
241. C₂×C₈	C₁₁×SD₁₆	semidirect
256. C₁₁	C₂×#1673	direct (N × H)
289. C₈	C₂×C₁₁×SD₁₆	semidirect
309. C₂	C₁₁×#1673	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×#500	2
C₂×C₁₁×#461	2
C₂×C₈×D₄×C₁₁	2
C₁₁×#1673	2
C₂×C₁₁×#335	2
C₂×C₁₁×#332	2
C₂×#1673	11

Subgroups — C2×C11×#1673 #14596296

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₁×#1673 #14596296