Subgroups — C₂×D₁₁×#335 #14722740

Order 2816.

942 conjugacy classes of subgroups.

The subgroup lattice has 326 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₁₁×C₄⋊C₈	C₂	1	2	yes	maximal
2	C₂×C₄×C₈×D₁₁	C₂	1	1	yes	maximal, characteristic
3	C₂×#10622096	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#10622117	C₂	1	2	yes	maximal, complemented
5	D₁₁×#335	C₂	1	8	yes	maximal, direct product factor
6	C₂×C₁₁×#335	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂²×C₈×D₁₁	—	2	2	no	—
8	C₂²×C₈×D₁₁	C₄	1	1	yes	characteristic
9	C₂²×C₈×D₁₁	C₄	1	1	yes	characteristic
10	C₂×C₄²×D₁₁	C₂²	1	1	yes	characteristic
11	C₂×C₁₁×C₄⋊C₈	C₂²	1	2	yes	—
12	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
13	C₂×Dic₁₁⋊C₈	—	2	2	no	—
14	C₂×C₈×Dic₁₁	C₄	1	1	yes	characteristic
15	C₂×C₈×Dic₁₁	C₄	1	1	yes	characteristic
16	C₂×C₄⋊(C₁₁⋊C₈)	C₂²	1	2	yes	—
17	C₂×C₄×C₁₁⋊C₈	C₂²	1	1	yes	characteristic
18	D₁₁×C₄⋊C₈	—	2	4	no	—
19	D₁₁×C₄⋊C₈	C₂²	1	8	yes	—
20	C₄×C₈×D₁₁	C₄	1	4	yes	—
21	C₄×C₈×D₁₁	C₂²	1	4	yes	—
22	C₁₁×#335	C₂²	1	4	yes	complemented
23	#10622117	C₂²	1	8	yes	complemented
24	#10622096	C₂²	1	4	yes	complemented
25	C₂²×C₄×D₁₁	C₂×C₄	1	1	yes	characteristic
26	C₂²×C₄×D₁₁	D₄	1	1	yes	characteristic
27	C₂²×C₄×D₁₁	Q₈	1	1	yes	characteristic
28	C₂²×C₈×C₁₁	—	2	2	no	—
29	C₂²×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
30	C₂²×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
31	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
32	C₂×C₄×Dic₁₁	C₂×C₄	1	1	yes	characteristic
33	C₂×C₄×Dic₁₁	D₄	1	1	yes	characteristic
34	C₂×C₄×Dic₁₁	Q₈	1	1	yes	characteristic
35	C₂²×C₁₁⋊C₈	—	2	2	no	—
36	C₂²×C₁₁⋊C₈	C₂×C₄	1	1	yes	characteristic
37	C₂²×C₁₁⋊C₈	C₂×C₄	1	1	yes	characteristic
38	C₂×C₈×D₁₁	—	2	4	no	—
39	C₂×C₈×D₁₁	—	2	8	no	—
40	C₂×C₈×D₁₁	—	4	8	no	—
41	C₂×C₈×D₁₁	C₈	1	8	yes	complemented
42	C₂×C₈×D₁₁	C₂×C₄	1	4	yes	—
43	C₂×C₈×D₁₁	C₂×C₄	1	4	yes	—
44	C₄²×D₁₁	C₂×C₄	1	2	yes	—
45	C₄²×D₁₁	D₄	1	2	yes	—
46	C₄²×D₁₁	Q₈	1	2	yes	—
47	C₄²×D₁₁	C₂³	1	2	yes	—
48	C₁₁×C₄⋊C₈	—	2	2	no	—
49	C₁₁×C₄⋊C₈	C₂³	1	4	yes	—
50	C₄×C₈×C₁₁	C₂×C₄	1	2	yes	—
51	C₄×C₈×C₁₁	C₂³	1	2	yes	—
52	Dic₁₁⋊C₈	—	2	8	no	—
53	C₈×Dic₁₁	C₂×C₄	1	4	yes	—
54	C₈×Dic₁₁	C₂×C₄	1	4	yes	—
55	C₄⋊(C₁₁⋊C₈)	—	2	2	no	—
56	C₄⋊(C₁₁⋊C₈)	C₂³	1	4	yes	—
57	C₄×C₁₁⋊C₈	C₂×C₄	1	2	yes	—
58	C₄×C₁₁⋊C₈	C₂³	1	2	yes	—
59	C₂²×#335	—	11	1	no	maximal, Sylow
60	C₂³×D₁₁	C₄⋊C₄	1	1	yes	characteristic
61	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
62	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
63	C₂²×C₄×C₁₁	C₂×Q₈	1	1	yes	characteristic
64	C₂²×Dic₁₁	C₄⋊C₄	1	1	yes	characteristic
65	C₂²×Dic₁₁	C₄⋊C₄	1	1	yes	characteristic
66	C₂²×Dic₁₁	C₄⋊C₄	1	1	yes	characteristic
67	C₂×C₄×D₁₁	—	2	4	no	—
68	C₂×C₄×D₁₁	C₄⋊C₄	1	2	yes	—
69	C₂×C₄×D₁₁	C₄⋊C₄	1	2	yes	—
70	C₂×C₄×D₁₁	C₄⋊C₄	1	2	yes	—
71	C₂×C₄×D₁₁	C₂×C₈	1	4	yes	—
72	C₂×C₄×D₁₁	M₁₆	1	4	yes	—
73	C₂×C₄×D₁₁	D₈	1	4	yes	—
74	C₂×C₄×D₁₁	Q₁₆	1	4	yes	—
75	C₂×C₄×D₁₁	C₂²×C₄	1	2	yes	—
76	C₂×C₄×D₁₁	C₂×D₄	1	2	yes	—
77	C₂×C₄×D₁₁	C₂×Q₈	1	2	yes	—
78	C₂×C₈×C₁₁	—	2	2	no	—
79	C₂×C₈×C₁₁	—	2	4	no	—
80	C₂×C₈×C₁₁	—	4	4	no	—
81	C₂×C₈×C₁₁	C₂×C₈	1	4	yes	complemented
82	C₂×C₈×C₁₁	C₂²×C₄	1	2	yes	—
83	C₂×C₈×C₁₁	C₂²×C₄	1	2	yes	—
84	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
85	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
86	C₄²×C₁₁	C₂×Q₈	1	1	yes	characteristic
87	C₄²×C₁₁	C₂⁴	1	1	yes	characteristic
88	C₄×Dic₁₁	C₄⋊C₄	1	2	yes	—
89	C₄×Dic₁₁	C₄⋊C₄	1	2	yes	—
90	C₄×Dic₁₁	C₄⋊C₄	1	2	yes	—
91	C₄×Dic₁₁	C₂²×C₄	1	2	yes	—
92	C₄×Dic₁₁	C₂×D₄	1	2	yes	—
93	C₄×Dic₁₁	C₂×Q₈	1	2	yes	—
94	C₂×C₁₁⋊C₈	—	2	2	no	—
95	C₂×C₁₁⋊C₈	—	2	4	no	—
96	C₂×C₁₁⋊C₈	—	4	4	no	—
97	C₂×C₁₁⋊C₈	C₂×C₈	1	4	yes	complemented
98	C₂×C₁₁⋊C₈	C₂²×C₄	1	2	yes	—
99	C₂×C₁₁⋊C₈	C₂²×C₄	1	2	yes	—
100	C₈×D₁₁	—	2	8	no	—
101	C₈×D₁₁	—	4	16	no	—
102	C₈×D₁₁	C₂×C₈	1	16	yes	complemented
103	C₂²×C₄⋊C₈	—	11	2	no	—
104	C₂²×C₄×C₈	—	11	1	no	—
105	C₂×#335	—	11	2	no	—
106	C₂×#335	—	11	1	no	—
107	C₂×#335	—	11	8	no	—
108	C₂×#335	D₁₁	1	1	yes	characteristic, direct product factor
109	C₂³×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
110	C₂²×D₁₁	C₄⋊C₈	1	4	yes	—
111	C₂²×D₁₁	#107	1	4	yes	—
112	C₂²×D₁₁	#108	1	4	yes	—
113	C₂²×D₁₁	C₂×C₄⋊C₄	1	2	yes	—
114	C₂×C₄×C₁₁	—	2	2	no	—
115	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
116	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
117	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
118	C₂×C₄×C₁₁	C₂²×C₈	1	2	yes	—
119	C₂×C₄×C₁₁	C₂×M₁₆	1	2	yes	—
120	C₂×C₄×C₁₁	C₂×D₈	1	2	yes	—
121	C₂×C₄×C₁₁	C₂×Q₁₆	1	2	yes	—
122	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
123	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
124	C₂×C₄×C₁₁	C₂²×Q₈	1	1	yes	characteristic
125	C₂×Dic₁₁	—	2	2	no	—
126	C₂×Dic₁₁	C₄⋊C₈	1	4	yes	—
127	C₂×Dic₁₁	#107	1	4	yes	—
128	C₂×Dic₁₁	C₂×C₄⋊C₄	1	2	yes	—
129	C₂×Dic₁₁	C₂×C₄⋊C₄	1	2	yes	—
130	C₂×Dic₁₁	C₂×C₄⋊C₄	1	2	yes	—
131	C₄×D₁₁	—	2	4	no	—
132	C₄×D₁₁	—	2	4	no	—
133	C₄×D₁₁	C₄⋊C₈	1	8	yes	—
134	C₄×D₁₁	#107	1	8	yes	—
135	C₄×D₁₁	C₂²×C₈	1	4	yes	—
136	C₄×D₁₁	C₂×M₁₆	1	4	yes	—
137	C₄×D₁₁	C₂×D₈	1	4	yes	—
138	C₄×D₁₁	C₂×Q₁₆	1	4	yes	—
139	C₈×C₁₁	—	2	2	no	—
140	C₈×C₁₁	—	4	4	no	—
141	C₈×C₁₁	C₂²×C₈	1	4	yes	complemented
142	C₁₁⋊C₈	—	2	2	no	—
143	C₁₁⋊C₈	—	4	4	no	—
144	C₁₁⋊C₈	C₂²×C₈	1	4	yes	complemented
145	C₂³×C₈	—	11	1	no	—
146	C₂³×C₈	—	11	1	no	—
147	C₂³×C₈	—	22	2	no	—
148	C₂²×C₄²	—	11	1	no	—
149	C₂×C₄⋊C₈	—	11	2	no	—
150	C₂×C₄⋊C₈	—	11	8	no	—
151	C₂×C₄⋊C₈	—	22	4	no	—
152	C₂×C₄⋊C₈	—	22	2	no	—
153	C₂×C₄⋊C₈	C₂×D₁₁	1	2	yes	—
154	C₂×C₄×C₈	—	11	1	no	—
155	C₂×C₄×C₈	—	11	1	no	—
156	C₂×C₄×C₈	—	11	1	no	—
157	C₂×C₄×C₈	—	11	4	no	—
158	C₂×C₄×C₈	—	11	4	no	—
159	C₂×C₄×C₈	C₂×D₁₁	1	1	yes	characteristic
160	#335	—	11	8	no	—
161	#335	—	11	4	no	—
162	#335	C₂×D₁₁	1	4	yes	direct product factor
163	C₂²×C₁₁	C₂×C₄⋊C₈	1	2	yes	—
164	C₂²×C₁₁	C₂×#107	1	2	yes	—
165	C₂²×C₁₁	C₂×#108	1	2	yes	—
166	C₂²×C₁₁	C₂²×C₄⋊C₄	1	1	yes	characteristic
167	C₂×D₁₁	#335	1	16	yes	direct product factor
168	C₂×D₁₁	C₂×C₄⋊C₈	1	4	yes	—
169	C₂×D₁₁	C₂×#107	1	4	yes	—
170	C₂×D₁₁	C₂×#108	1	4	yes	—
171	C₄×C₁₁	—	2	1	no	—
172	C₄×C₁₁	—	2	1	no	—
173	C₄×C₁₁	C₂×C₄⋊C₈	1	2	yes	—
174	C₄×C₁₁	C₂×#107	1	2	yes	—
175	C₄×C₁₁	C₂³×C₈	1	1	yes	characteristic
176	C₄×C₁₁	C₂²×M₁₆	1	1	yes	characteristic
177	C₄×C₁₁	C₂²×D₈	1	1	yes	characteristic
178	C₄×C₁₁	C₂²×Q₁₆	1	1	yes	characteristic
179	Dic₁₁	—	2	2	no	—
180	Dic₁₁	C₂×C₄⋊C₈	1	4	yes	—
181	Dic₁₁	C₂×#107	1	4	yes	—
182	C₂³×C₄	—	11	1	no	—
183	C₂³×C₄	—	11	1	no	—
184	C₂³×C₄	—	11	1	no	—
185	C₂²×C₈	—	2	2	no	—
186	C₂²×C₈	—	11	1	no	—
187	C₂²×C₈	—	11	8	no	—
188	C₂²×C₈	—	11	4	no	—
189	C₂²×C₈	—	11	1	no	—
190	C₂²×C₈	—	11	4	no	—
191	C₂²×C₈	—	22	4	no	—
192	C₂²×C₈	—	22	8	no	—
193	C₂²×C₈	—	22	2	no	—
194	C₂²×C₈	—	44	8	no	—
195	C₂²×C₈	C₄×D₁₁	1	1	yes	characteristic
196	C₂²×C₈	C₄×D₁₁	1	1	yes	characteristic
197	C₂×C₄²	—	11	1	no	—
198	C₂×C₄²	—	11	1	no	—
199	C₂×C₄²	—	11	1	no	—
200	C₂×C₄²	—	11	2	no	—
201	C₂×C₄²	—	11	2	no	—
202	C₂×C₄²	—	11	2	no	—
203	C₂×C₄²	—	11	2	no	—
204	C₂×C₄²	C₂²×D₁₁	1	1	yes	characteristic
205	C₄⋊C₈	—	2	2	no	—
206	C₄⋊C₈	—	11	4	no	—
207	C₄⋊C₈	—	22	8	no	—
208	C₄⋊C₈	—	22	2	no	—
209	C₄⋊C₈	C₂²×D₁₁	1	4	yes	—
210	C₄×C₈	—	11	4	no	—
211	C₄×C₈	—	11	4	no	—
212	C₄×C₈	—	11	2	no	—
213	C₄×C₈	—	11	2	no	—
214	C₄×C₈	C₄×D₁₁	1	2	yes	—
215	C₄×C₈	C₂²×D₁₁	1	2	yes	—
216	C₂×C₁₁	C₂×#335	1	4	yes	complemented
217	C₂×C₁₁	C₂²×C₄⋊C₈	1	1	yes	characteristic
218	C₂×C₁₁	C₂²×#107	1	1	yes	characteristic
219	C₂×C₁₁	C₂²×#108	1	1	yes	characteristic
220	D₁₁	C₂×#335	1	8	yes	direct product factor
221	C₂⁴	—	11	1	no	—
222	C₂²×C₄	—	11	1	no	—
223	C₂²×C₄	—	11	1	no	—
224	C₂²×C₄	—	11	2	no	—
225	C₂²×C₄	—	11	2	no	—
226	C₂²×C₄	—	11	4	no	—
227	C₂²×C₄	—	11	4	no	—
228	C₂²×C₄	—	11	4	no	—
229	C₂²×C₄	—	11	4	no	—
230	C₂²×C₄	—	11	2	no	—
231	C₂²×C₄	—	11	2	no	—
232	C₂²×C₄	—	11	1	no	—
233	C₂²×C₄	—	11	2	no	—
234	C₂²×C₄	—	11	2	no	—
235	C₂²×C₄	—	22	4	no	—
236	C₂²×C₄	C₂×C₄×D₁₁	1	1	yes	characteristic
237	C₂²×C₄	D₄×D₁₁	1	1	yes	characteristic
238	C₂²×C₄	Q₈×D₁₁	1	1	yes	characteristic
239	C₂×C₈	—	2	2	no	—
240	C₂×C₈	—	2	4	no	—
241	C₂×C₈	—	4	4	no	—
242	C₂×C₈	—	11	4	no	—
243	C₂×C₈	—	11	2	no	—
244	C₂×C₈	—	11	16	no	—
245	C₂×C₈	—	11	2	no	—
246	C₂×C₈	—	22	8	no	—
247	C₂×C₈	—	22	2	no	—
248	C₂×C₈	—	22	4	no	—
249	C₂×C₈	—	44	16	no	—
250	C₂×C₈	—	44	4	no	—
251	C₂×C₈	C₈×D₁₁	1	4	yes	complemented
252	C₂×C₈	C₂×C₄×D₁₁	1	2	yes	—
253	C₂×C₈	C₂×C₄×D₁₁	1	2	yes	—
254	C₄²	—	11	2	no	—
255	C₄²	—	11	2	no	—
256	C₄²	—	11	2	no	—
257	C₄²	—	11	2	no	—
258	C₄²	—	11	2	no	—
259	C₄²	—	11	2	no	—
260	C₄²	C₂×C₄×D₁₁	1	1	yes	characteristic
261	C₄²	D₄×D₁₁	1	1	yes	characteristic
262	C₄²	Q₈×D₁₁	1	1	yes	characteristic
263	C₄²	C₂³×D₁₁	1	1	yes	characteristic
264	C₁₁	C₂²×#335	1	1	yes	characteristic, complemented, Sylow
265	C₂³	—	11	4	no	—
266	C₂³	—	11	4	no	—
267	C₂³	—	11	2	no	—
268	C₂³	—	11	4	no	—
269	C₂³	C₄⋊C₄×D₁₁	1	1	yes	characteristic
270	C₂×C₄	—	2	2	no	—
271	C₂×C₄	—	11	4	no	—
272	C₂×C₄	—	11	2	no	—
273	C₂×C₄	—	11	2	no	—
274	C₂×C₄	—	11	4	no	—
275	C₂×C₄	—	11	8	no	—
276	C₂×C₄	—	11	4	no	—
277	C₂×C₄	—	11	4	no	—
278	C₂×C₄	—	11	4	no	—
279	C₂×C₄	—	11	4	no	—
280	C₂×C₄	—	11	8	no	—
281	C₂×C₄	—	11	2	no	—
282	C₂×C₄	—	22	4	no	—
283	C₂×C₄	—	22	4	no	—
284	C₂×C₄	—	22	2	no	—
285	C₂×C₄	C₄⋊C₄×D₁₁	1	1	yes	characteristic
286	C₂×C₄	C₄⋊C₄×D₁₁	1	1	yes	characteristic
287	C₂×C₄	C₄⋊C₄×D₁₁	1	1	yes	characteristic
288	C₂×C₄	C₂×C₈×D₁₁	1	2	yes	—
289	C₂×C₄	M₁₆×D₁₁	1	2	yes	—
290	C₂×C₄	D₈×D₁₁	1	2	yes	—
291	C₂×C₄	Q₁₆×D₁₁	1	2	yes	—
292	C₂×C₄	C₂²×C₄×D₁₁	1	1	yes	characteristic
293	C₂×C₄	C₂×D₄×D₁₁	1	1	yes	characteristic
294	C₂×C₄	C₂×Q₈×D₁₁	1	1	yes	characteristic
295	C₈	—	2	2	no	—
296	C₈	—	4	4	no	—
297	C₈	—	11	4	no	—
298	C₈	—	22	2	no	—
299	C₈	—	44	4	no	—
300	C₈	C₂×C₈×D₁₁	1	4	yes	complemented
301	C₂²	—	11	16	no	—
302	C₂²	—	11	4	no	—
303	C₂²	—	11	4	no	—
304	C₂²	—	11	4	no	—
305	C₂²	D₁₁×C₄⋊C₈	1	2	yes	—
306	C₂²	D₁₁×#107	1	2	yes	—
307	C₂²	D₁₁×#108	1	2	yes	—
308	C₂²	C₂×C₄⋊C₄×D₁₁	1	1	yes	characteristic
309	C₄	—	2	1	no	—
310	C₄	—	2	1	no	—
311	C₄	—	11	4	no	—
312	C₄	—	11	4	no	—
313	C₄	—	22	2	no	—
314	C₄	D₁₁×C₄⋊C₈	1	2	yes	—
315	C₄	D₁₁×#107	1	2	yes	—
316	C₄	C₂²×C₈×D₁₁	1	1	yes	characteristic
317	C₄	C₂×M₁₆×D₁₁	1	1	yes	characteristic
318	C₄	C₂×D₈×D₁₁	1	1	yes	characteristic
319	C₄	C₂×Q₁₆×D₁₁	1	1	yes	characteristic
320	C₂	—	11	8	no	—
321	C₂	D₁₁×#335	1	4	yes	direct product factor
322	C₂	C₂×D₁₁×C₄⋊C₈	1	1	yes	characteristic
323	C₂	C₂×D₁₁×#107	1	1	yes	characteristic
324	C₂	C₂×D₁₁×#108	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	D₄×D₁₁
commutator	C₄×C₁₁	C₂³×C₈
Frattini	C₄²	C₂³×D₁₁
Fitting	C₂×C₁₁×#335	C₂
socle	C₂³×C₁₁	C₂×C₄⋊C₄
prime radical	C₂³×D₁₁	C₄⋊C₄
cosocle	C₄²×C₁₁	C₂⁴
hypercenter	C₂×#335	D₁₁
hypocenter	C₁₁	C₂²×#335
LCS	G ▷ C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄² ◁ C₂×#335

Complements

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

N	H ≅ G/N	type
3. C₂×#10622096	C₂	semidirect
4. C₂×#10622117	C₂	semidirect
5. D₁₁×#335	C₂	direct (N × H)
6. C₂×C₁₁×#335	C₂	semidirect
22. C₁₁×#335	C₂²	semidirect
23. #10622117	C₂²	semidirect
24. #10622096	C₂²	semidirect
41. C₂×C₈×D₁₁	C₈	semidirect
81. C₂×C₈×C₁₁	C₂×C₈	semidirect
97. C₂×C₁₁⋊C₈	C₂×C₈	semidirect
102. C₈×D₁₁	C₂×C₈	semidirect
108. C₂×#335	D₁₁	direct (N × H)
141. C₈×C₁₁	C₂²×C₈	semidirect
144. C₁₁⋊C₈	C₂²×C₈	semidirect
162. #335	C₂×D₁₁	direct (N × H)
167. C₂×D₁₁	#335	direct (N × H)
216. C₂×C₁₁	C₂×#335	semidirect
220. D₁₁	C₂×#335	direct (N × H)
251. C₂×C₈	C₈×D₁₁	semidirect
264. C₁₁	C₂²×#335	semidirect
300. C₈	C₂×C₈×D₁₁	semidirect
321. C₂	D₁₁×#335	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×D₁₁×C₄⋊C₈	2
C₂×C₄×C₈×D₁₁	2
C₂×#10622096	2
C₂×#10622117	2
D₁₁×#335	2
C₂×C₁₁×#335	2
C₂²×#335	11

Subgroups — C2×D11×#335 #14722740

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×D₁₁×#335 #14722740