Subgroups — C₁₁×#23114 #14600307

Order 2816.

778 conjugacy classes of subgroups.

The subgroup lattice has 536 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×#3035	C₂	1	1	yes	maximal, characteristic
2	C₁₁×#2935	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₁×#2925	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₁×#1975	C₂	1	2	yes	maximal, complemented
5	C₁₁×#1962	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₁×#1950	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₁×#1929	C₂	1	2	yes	maximal, complemented
8	C₁₁×#1876	C₂	1	2	yes	maximal, complemented
9	C₁₁×#1767	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₁×#1765	C₂	1	2	yes	maximal, complemented
11	C₄×C₁₁×#104	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₁×#135	C₂²	1	2	yes	—
13	C₂×C₁₁×#131	C₂²	1	2	yes	—
14	C₁₁×#532	C₂²	1	1	yes	characteristic
15	C₄×C₁₁×#41	C₂²	1	1	yes	characteristic
16	C₁₁×#464	C₄	1	2	yes	complemented
17	C₁₁×#463	C₄	1	2	yes	complemented
18	C₁₁×#462	C₄	1	1	yes	characteristic, complemented
19	C₁₁×#461	C₄	1	1	yes	characteristic, complemented
20	C₁₁×#460	C₄	1	1	yes	characteristic, complemented
21	C₁₁×#459	C₄	1	1	yes	characteristic, complemented
22	C₁₁×#436	—	2	1	no	—
23	C₁₁×#435	—	2	2	no	—
24	C₈×D₄×C₁₁	—	2	1	no	—
25	C₁₁×#433	—	2	2	no	—
26	C₁₁×#432	—	2	1	no	—
27	C₁₁×#431	—	2	1	no	—
28	C₂×C₁₁×#108	C₂²	1	2	yes	—
29	C₁₁×#423	C₂²	1	1	yes	characteristic
30	C₂×C₁₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
31	C₂×C₁₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
32	C₂×C₁₁×#104	C₂²	1	1	yes	characteristic
33	C₂×C₁₁×#104	C₂²	1	2	yes	—
34	C₂×C₁₁×#104	C₂²	1	1	yes	characteristic
35	C₂×C₁₁×#104	C₂²	1	2	yes	—
36	C₁₁×#416	C₂²	1	2	yes	—
37	C₁₁×#408	C₂²	1	2	yes	—
38	C₁₁×#408	C₂²	1	2	yes	—
39	C₁₁×#405	C₂²	1	2	yes	—
40	C₄×C₁₁×M₁₆	C₂²	1	1	yes	characteristic
41	C₂×C₁₁×#97	C₂²	1	2	yes	—
42	C₄³×C₁₁	C₂²	1	1	yes	characteristic
43	C₁₁×#341	C₂²	1	2	yes	—
44	C₁₁×#339	C₂²	1	1	yes	characteristic
45	C₁₁×#339	C₂²	1	1	yes	characteristic
46	C₁₁×#336	C₂²	1	2	yes	—
47	C₂×C₁₁×#41	C₂³	1	1	yes	characteristic
48	C₂×C₁₁×#41	C₂³	1	2	yes	—
49	C₁₁×#135	—	4	2	no	—
50	C₁₁×#135	—	4	2	no	—
51	C₂×C₁₁×Q₁₆	C₂×C₄	1	2	yes	—
52	C₂×C₁₁×SD₁₆	C₂×C₄	1	2	yes	—
53	C₂×C₁₁×SD₁₆	C₂×C₄	1	2	yes	—
54	C₂×C₁₁×D₈	C₂×C₄	1	2	yes	—
55	C₁₁×#131	—	2	4	no	—
56	C₁₁×#131	—	4	2	no	—
57	C₂×C₁₁×M₁₆	—	2	2	no	—
58	C₂×C₁₁×M₁₆	C₂³	1	1	yes	characteristic
59	C₂×C₁₁×M₁₆	C₂³	1	2	yes	—
60	C₂×C₁₁×M₁₆	C₂³	1	1	yes	characteristic
61	C₂²×C₈×C₁₁	—	2	2	no	—
62	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
63	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
64	C₁₁×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
65	C₁₁×#127	C₂×C₄	1	1	yes	characteristic
66	C₁₁×#124	C₂×C₄	1	2	yes	—
67	C₁₁×#121	—	2	1	no	—
68	C₁₁×#121	—	2	1	no	—
69	C₄×Q₈×C₁₁	C₂×C₄	1	1	yes	characteristic
70	C₄×Q₈×C₁₁	C₂×C₄	1	1	yes	characteristic
71	C₄×D₄×C₁₁	—	2	1	no	—
72	C₄×D₄×C₁₁	—	2	1	no	—
73	C₄×D₄×C₁₁	—	2	1	no	—
74	C₄×D₄×C₁₁	—	2	1	no	—
75	C₄×D₄×C₁₁	C₂×C₄	1	1	yes	characteristic
76	C₄×D₄×C₁₁	C₂×C₄	1	1	yes	characteristic
77	C₁₁×#117	—	2	1	no	—
78	C₁₁×#117	C₂³	1	1	yes	characteristic
79	C₂×C₄²×C₁₁	—	2	1	no	—
80	C₂×C₄²×C₁₁	—	2	1	no	—
81	C₂×C₄²×C₁₁	—	2	1	no	—
82	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
83	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
84	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
85	C₁₁×#108	—	4	2	no	—
86	C₁₁×C₄⋊C₈	—	2	1	no	—
87	C₁₁×C₄⋊C₈	—	2	1	no	—
88	C₁₁×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
89	C₁₁×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
90	C₁₁×C₄⋊C₈	C₂×C₄	1	2	yes	—
91	C₁₁×C₄⋊C₈	D₄	1	1	yes	characteristic
92	C₁₁×C₄⋊C₈	D₄	1	1	yes	characteristic
93	C₁₁×C₄⋊C₈	D₄	1	2	yes	—
94	C₁₁×#104	—	2	2	no	—
95	C₁₁×#104	—	2	4	no	—
96	C₁₁×#104	—	2	2	no	—
97	C₁₁×#104	—	4	2	no	—
98	C₁₁×#103	C₂×C₄	1	2	yes	—
99	C₁₁×#103	C₂×C₄	1	2	yes	—
100	C₁₁×#102	C₂×C₄	1	2	yes	—
101	C₁₁×#102	C₂×C₄	1	2	yes	—
102	C₁₁×C₂²⋊C₈	—	2	2	no	—
103	C₁₁×C₂²⋊C₈	—	2	2	no	—
104	C₁₁×C₂²⋊C₈	—	2	2	no	—
105	C₁₁×C₂²⋊C₈	—	2	2	no	—
106	C₁₁×#97	—	2	2	no	—
107	C₁₁×#97	—	2	1	no	—
108	C₁₁×#97	—	4	2	no	—
109	C₄×C₈×C₁₁	—	2	2	no	—
110	C₄×C₈×C₁₁	—	2	1	no	—
111	#23114	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
112	C₁₁×#41	—	2	1	no	—
113	C₁₁×#41	—	2	1	no	—
114	C₁₁×#41	—	2	2	no	—
115	C₁₁×#41	—	2	2	no	—
116	C₁₁×#41	—	2	2	no	—
117	C₁₁×#41	—	2	2	no	—
118	C₁₁×#41	—	2	1	no	—
119	C₁₁×#41	—	2	1	no	—
120	C₂×Q₈×C₁₁	C₂²×C₄	1	2	yes	—
121	C₂×Q₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
122	C₂×D₄×C₁₁	—	2	1	no	—
123	C₂×D₄×C₁₁	—	2	2	no	—
124	C₂×D₄×C₁₁	—	2	1	no	—
125	C₂×D₄×C₁₁	—	2	1	no	—
126	C₂×D₄×C₁₁	C₂²×C₄	1	2	yes	—
127	C₂×D₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
128	C₂²×C₄×C₁₁	—	2	1	no	—
129	C₂²×C₄×C₁₁	—	2	1	no	—
130	C₂²×C₄×C₁₁	—	2	1	no	—
131	C₂²×C₄×C₁₁	—	2	1	no	—
132	C₂²×C₄×C₁₁	—	2	2	no	—
133	C₂²×C₄×C₁₁	—	2	1	no	—
134	C₂²×C₄×C₁₁	#41	1	1	yes	characteristic
135	C₂²×C₄×C₁₁	#41	1	1	yes	characteristic
136	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
137	C₁₁×Q₁₆	—	4	2	no	—
138	C₁₁×SD₁₆	—	4	2	no	—
139	C₁₁×SD₁₆	—	4	2	no	—
140	C₁₁×D₈	—	4	2	no	—
141	C₁₁×M₁₆	—	2	1	no	—
142	C₁₁×M₁₆	—	2	2	no	—
143	C₁₁×M₁₆	—	2	1	no	—
144	C₁₁×M₁₆	—	2	2	no	—
145	C₁₁×M₁₆	—	2	1	no	—
146	C₁₁×M₁₆	—	4	4	no	—
147	C₁₁×M₁₆	#41	1	2	yes	—
148	C₂×C₈×C₁₁	—	2	1	no	—
149	C₂×C₈×C₁₁	—	2	1	no	—
150	C₂×C₈×C₁₁	—	2	2	no	—
151	C₂×C₈×C₁₁	—	2	2	no	—
152	C₂×C₈×C₁₁	—	2	2	no	—
153	C₂×C₈×C₁₁	—	2	2	no	—
154	C₂×C₈×C₁₁	—	2	2	no	—
155	C₂×C₈×C₁₁	—	4	4	no	—
156	C₂×C₈×C₁₁	C₂²×C₄	1	2	yes	—
157	C₂×C₈×C₁₁	C₂²×C₄	1	2	yes	—
158	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
159	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
160	C₁₁×C₄⋊C₄	—	2	1	no	—
161	C₁₁×C₄⋊C₄	—	2	1	no	—
162	C₁₁×C₄⋊C₄	—	2	1	no	—
163	C₁₁×C₄⋊C₄	—	2	1	no	—
164	C₁₁×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
165	C₁₁×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
166	C₁₁×C₂²⋊C₄	—	2	1	no	—
167	C₁₁×C₂²⋊C₄	—	2	1	no	—
168	C₁₁×C₂²⋊C₄	—	2	1	no	—
169	C₁₁×C₂²⋊C₄	—	2	2	no	—
170	C₁₁×C₂²⋊C₄	—	2	2	no	—
171	C₄²×C₁₁	—	2	1	no	—
172	C₄²×C₁₁	—	2	1	no	—
173	C₄²×C₁₁	—	2	1	no	—
174	C₄²×C₁₁	—	2	1	no	—
175	C₄²×C₁₁	—	2	1	no	—
176	C₄²×C₁₁	—	2	1	no	—
177	C₄²×C₁₁	—	4	2	no	—
178	C₄²×C₁₁	—	4	2	no	—
179	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
180	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
181	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
182	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
183	C₄²×C₁₁	#41	1	2	yes	—
184	#3035	C₂×C₁₁	1	1	yes	characteristic
185	#2935	C₂×C₁₁	1	1	yes	characteristic, complemented
186	#2925	C₂×C₁₁	1	1	yes	characteristic, complemented
187	#1975	C₂×C₁₁	1	2	yes	complemented
188	#1962	C₂×C₁₁	1	1	yes	characteristic, complemented
189	#1950	C₂×C₁₁	1	1	yes	characteristic, complemented
190	#1929	C₂×C₁₁	1	2	yes	complemented
191	#1876	C₂×C₁₁	1	2	yes	complemented
192	#1767	C₂×C₁₁	1	1	yes	characteristic, complemented
193	#1765	C₂×C₁₁	1	2	yes	complemented
194	C₄×#104	C₂×C₁₁	1	1	yes	characteristic, complemented
195	C₂³×C₁₁	—	2	1	no	—
196	C₂³×C₁₁	—	2	2	no	—
197	C₂³×C₁₁	C₂×#41	1	1	yes	characteristic
198	Q₈×C₁₁	—	2	2	no	—
199	Q₈×C₁₁	—	2	1	no	—
200	Q₈×C₁₁	—	2	1	no	—
201	Q₈×C₁₁	—	2	2	no	—
202	D₄×C₁₁	—	2	2	no	—
203	D₄×C₁₁	—	2	1	no	—
204	D₄×C₁₁	—	2	1	no	—
205	D₄×C₁₁	—	2	2	no	—
206	D₄×C₁₁	—	4	1	no	—
207	D₄×C₁₁	—	4	2	no	—
208	D₄×C₁₁	—	4	1	no	—
209	D₄×C₁₁	—	4	2	no	—
210	D₄×C₁₁	—	4	2	no	—
211	D₄×C₁₁	—	8	1	no	—
212	C₂×C₄×C₁₁	—	2	2	no	—
213	C₂×C₄×C₁₁	—	2	2	no	—
214	C₂×C₄×C₁₁	—	2	1	no	—
215	C₂×C₄×C₁₁	—	2	1	no	—
216	C₂×C₄×C₁₁	—	2	1	no	—
217	C₂×C₄×C₁₁	—	2	2	no	—
218	C₂×C₄×C₁₁	—	2	2	no	—
219	C₂×C₄×C₁₁	—	4	1	no	—
220	C₂×C₄×C₁₁	—	4	1	no	—
221	C₂×C₄×C₁₁	—	4	1	no	—
222	C₂×C₄×C₁₁	—	4	1	no	—
223	C₂×C₄×C₁₁	—	4	1	no	—
224	C₂×C₄×C₁₁	—	4	2	no	—
225	C₂×C₄×C₁₁	—	4	1	no	—
226	C₂×C₄×C₁₁	—	4	1	no	—
227	C₂×C₄×C₁₁	—	4	2	no	—
228	C₂×C₄×C₁₁	—	4	2	no	—
229	C₂×C₄×C₁₁	—	8	1	no	—
230	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
231	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
232	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
233	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
234	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
235	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
236	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
237	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
238	C₂×C₄×C₁₁	H(5,𝔽₂)	1	1	yes	characteristic
239	C₂×C₄×C₁₁	H(5,𝔽₂)	1	1	yes	characteristic
240	C₈×C₁₁	—	2	2	no	—
241	C₈×C₁₁	—	2	2	no	—
242	C₈×C₁₁	—	2	2	no	—
243	C₈×C₁₁	—	2	2	no	—
244	C₈×C₁₁	—	2	2	no	—
245	C₈×C₁₁	—	4	1	no	—
246	C₈×C₁₁	—	4	2	no	—
247	C₂×#135	C₂²×C₁₁	1	2	yes	—
248	C₂×#131	C₂²×C₁₁	1	2	yes	—
249	#532	C₂²×C₁₁	1	1	yes	characteristic
250	C₄×#41	C₂²×C₁₁	1	1	yes	characteristic
251	#464	C₄×C₁₁	1	2	yes	complemented
252	#463	C₄×C₁₁	1	2	yes	complemented
253	#462	C₄×C₁₁	1	1	yes	characteristic, complemented
254	#461	C₄×C₁₁	1	1	yes	characteristic, complemented
255	#460	C₄×C₁₁	1	1	yes	characteristic, complemented
256	#459	C₄×C₁₁	1	1	yes	characteristic, complemented
257	#436	—	2	1	no	—
258	#435	—	2	2	no	—
259	C₈×D₄	—	2	1	no	—
260	#433	—	2	2	no	—
261	#432	—	2	1	no	—
262	#431	—	2	1	no	—
263	C₂×#108	C₂²×C₁₁	1	2	yes	—
264	#423	C₂²×C₁₁	1	1	yes	characteristic
265	C₂×C₄⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
266	C₂×C₄⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
267	C₂×#104	C₂²×C₁₁	1	1	yes	characteristic
268	C₂×#104	C₂²×C₁₁	1	2	yes	—
269	C₂×#104	C₂²×C₁₁	1	1	yes	characteristic
270	C₂×#104	C₂²×C₁₁	1	2	yes	—
271	#416	C₂²×C₁₁	1	2	yes	—
272	#408	C₂²×C₁₁	1	2	yes	—
273	#408	C₂²×C₁₁	1	2	yes	—
274	#405	C₂²×C₁₁	1	2	yes	—
275	C₄×M₁₆	C₂²×C₁₁	1	1	yes	characteristic
276	C₂×#97	C₂²×C₁₁	1	2	yes	—
277	C₄³	C₂²×C₁₁	1	1	yes	characteristic
278	#341	C₂²×C₁₁	1	2	yes	—
279	#339	C₂²×C₁₁	1	1	yes	characteristic
280	#339	C₂²×C₁₁	1	1	yes	characteristic
281	#336	C₂²×C₁₁	1	2	yes	—
282	C₂²×C₁₁	—	2	1	no	—
283	C₂²×C₁₁	—	2	1	no	—
284	C₂²×C₁₁	—	4	2	no	—
285	C₂²×C₁₁	—	4	1	no	—
286	C₂²×C₁₁	—	4	1	no	—
287	C₂²×C₁₁	—	4	2	no	—
288	C₂²×C₁₁	—	4	1	no	—
289	C₂²×C₁₁	—	4	2	no	—
290	C₂²×C₁₁	C₂×C₄×D₄	1	1	yes	characteristic
291	C₂²×C₁₁	#553	1	1	yes	characteristic
292	C₂²×C₁₁	#555	1	1	yes	characteristic
293	C₄×C₁₁	—	2	1	no	—
294	C₄×C₁₁	—	2	1	no	—
295	C₄×C₁₁	—	2	1	no	—
296	C₄×C₁₁	—	4	2	no	—
297	C₄×C₁₁	—	4	2	no	—
298	C₄×C₁₁	—	4	1	no	—
299	C₄×C₁₁	—	4	2	no	—
300	C₄×C₁₁	—	4	1	no	—
301	C₄×C₁₁	—	4	1	no	—
302	C₄×C₁₁	#444	1	2	yes	—
303	C₄×C₁₁	C₄×#41	1	1	yes	characteristic
304	C₄×C₁₁	#518	1	1	yes	characteristic
305	C₄×C₁₁	#546	1	1	yes	characteristic
306	C₄×C₁₁	#550	1	1	yes	characteristic
307	C₂×#41	C₂³×C₁₁	1	1	yes	characteristic
308	C₂×#41	C₂³×C₁₁	1	2	yes	—
309	#135	—	4	2	no	—
310	#135	—	4	2	no	—
311	C₂×Q₁₆	C₂×C₄×C₁₁	1	2	yes	—
312	C₂×SD₁₆	C₂×C₄×C₁₁	1	2	yes	—
313	C₂×SD₁₆	C₂×C₄×C₁₁	1	2	yes	—
314	C₂×D₈	C₂×C₄×C₁₁	1	2	yes	—
315	#131	—	2	4	no	—
316	#131	—	4	2	no	—
317	C₂×M₁₆	—	2	2	no	—
318	C₂×M₁₆	C₂³×C₁₁	1	1	yes	characteristic
319	C₂×M₁₆	C₂³×C₁₁	1	2	yes	—
320	C₂×M₁₆	C₂³×C₁₁	1	1	yes	characteristic
321	C₂²×C₈	—	2	2	no	—
322	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
323	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
324	C₄⋊Q₈	C₂×C₄×C₁₁	1	1	yes	characteristic
325	#127	C₂×C₄×C₁₁	1	1	yes	characteristic
326	#124	C₂×C₄×C₁₁	1	2	yes	—
327	#121	—	2	1	no	—
328	#121	—	2	1	no	—
329	C₄×Q₈	C₂×C₄×C₁₁	1	1	yes	characteristic
330	C₄×Q₈	C₂×C₄×C₁₁	1	1	yes	characteristic
331	C₄×D₄	—	2	1	no	—
332	C₄×D₄	—	2	1	no	—
333	C₄×D₄	—	2	1	no	—
334	C₄×D₄	—	2	1	no	—
335	C₄×D₄	C₂×C₄×C₁₁	1	1	yes	characteristic
336	C₄×D₄	C₂×C₄×C₁₁	1	1	yes	characteristic
337	#117	—	2	1	no	—
338	#117	C₂³×C₁₁	1	1	yes	characteristic
339	C₂×C₄²	—	2	1	no	—
340	C₂×C₄²	—	2	1	no	—
341	C₂×C₄²	—	2	1	no	—
342	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
343	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
344	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
345	#108	—	4	2	no	—
346	C₄⋊C₈	—	2	1	no	—
347	C₄⋊C₈	—	2	1	no	—
348	C₄⋊C₈	C₂×C₄×C₁₁	1	1	yes	characteristic
349	C₄⋊C₈	C₂×C₄×C₁₁	1	1	yes	characteristic
350	C₄⋊C₈	C₂×C₄×C₁₁	1	2	yes	—
351	C₄⋊C₈	D₄×C₁₁	1	1	yes	characteristic
352	C₄⋊C₈	D₄×C₁₁	1	1	yes	characteristic
353	C₄⋊C₈	D₄×C₁₁	1	2	yes	—
354	#104	—	2	2	no	—
355	#104	—	2	4	no	—
356	#104	—	2	2	no	—
357	#104	—	4	2	no	—
358	#103	C₂×C₄×C₁₁	1	2	yes	—
359	#103	C₂×C₄×C₁₁	1	2	yes	—
360	#102	C₂×C₄×C₁₁	1	2	yes	—
361	#102	C₂×C₄×C₁₁	1	2	yes	—
362	C₂²⋊C₈	—	2	2	no	—
363	C₂²⋊C₈	—	2	2	no	—
364	C₂²⋊C₈	—	2	2	no	—
365	C₂²⋊C₈	—	2	2	no	—
366	#97	—	2	2	no	—
367	#97	—	2	1	no	—
368	#97	—	4	2	no	—
369	C₄×C₈	—	2	2	no	—
370	C₄×C₈	—	2	1	no	—
371	C₂×C₁₁	—	2	1	no	—
372	C₂×C₁₁	—	2	1	no	—
373	C₂×C₁₁	—	8	1	no	—
374	C₂×C₁₁	—	8	2	no	—
375	C₂×C₁₁	#2363	1	1	yes	characteristic
376	C₂×C₁₁	C₂×#444	1	1	yes	characteristic
377	C₂×C₁₁	#2956	1	1	yes	characteristic
378	#41	—	2	1	no	—
379	#41	—	2	1	no	—
380	#41	—	2	2	no	—
381	#41	—	2	2	no	—
382	#41	—	2	2	no	—
383	#41	—	2	2	no	—
384	#41	—	2	1	no	—
385	#41	—	2	1	no	—
386	C₂×Q₈	C₂²×C₄×C₁₁	1	2	yes	—
387	C₂×Q₈	C₂²×C₄×C₁₁	1	1	yes	characteristic
388	C₂×D₄	—	2	1	no	—
389	C₂×D₄	—	2	2	no	—
390	C₂×D₄	—	2	1	no	—
391	C₂×D₄	—	2	1	no	—
392	C₂×D₄	C₂²×C₄×C₁₁	1	2	yes	—
393	C₂×D₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
394	C₂²×C₄	—	2	1	no	—
395	C₂²×C₄	—	2	1	no	—
396	C₂²×C₄	—	2	1	no	—
397	C₂²×C₄	—	2	1	no	—
398	C₂²×C₄	—	2	2	no	—
399	C₂²×C₄	—	2	1	no	—
400	C₂²×C₄	C₁₁×#41	1	1	yes	characteristic
401	C₂²×C₄	C₁₁×#41	1	1	yes	characteristic
402	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
403	Q₁₆	—	4	2	no	—
404	SD₁₆	—	4	2	no	—
405	SD₁₆	—	4	2	no	—
406	D₈	—	4	2	no	—
407	M₁₆	—	2	1	no	—
408	M₁₆	—	2	1	no	—
409	M₁₆	—	2	2	no	—
410	M₁₆	—	2	2	no	—
411	M₁₆	—	2	1	no	—
412	M₁₆	—	4	4	no	—
413	M₁₆	C₁₁×#41	1	2	yes	—
414	C₂×C₈	—	2	1	no	—
415	C₂×C₈	—	2	2	no	—
416	C₂×C₈	—	2	2	no	—
417	C₂×C₈	—	2	2	no	—
418	C₂×C₈	—	2	2	no	—
419	C₂×C₈	—	2	1	no	—
420	C₂×C₈	—	2	2	no	—
421	C₂×C₈	—	4	4	no	—
422	C₂×C₈	C₂²×C₄×C₁₁	1	2	yes	—
423	C₂×C₈	C₂²×C₄×C₁₁	1	2	yes	—
424	C₂×C₈	C₂×D₄×C₁₁	1	2	yes	—
425	C₂×C₈	C₂×D₄×C₁₁	1	2	yes	—
426	C₄⋊C₄	—	2	1	no	—
427	C₄⋊C₄	—	2	1	no	—
428	C₄⋊C₄	—	2	1	no	—
429	C₄⋊C₄	—	2	1	no	—
430	C₄⋊C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
431	C₄⋊C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
432	C₂²⋊C₄	—	2	1	no	—
433	C₂²⋊C₄	—	2	1	no	—
434	C₂²⋊C₄	—	2	1	no	—
435	C₂²⋊C₄	—	2	2	no	—
436	C₂²⋊C₄	—	2	2	no	—
437	C₄²	—	2	1	no	—
438	C₄²	—	2	1	no	—
439	C₄²	—	2	1	no	—
440	C₄²	—	2	1	no	—
441	C₄²	—	2	1	no	—
442	C₄²	—	2	1	no	—
443	C₄²	—	4	2	no	—
444	C₄²	—	4	2	no	—
445	C₄²	C₂²×C₄×C₁₁	1	1	yes	characteristic
446	C₄²	C₂²×C₄×C₁₁	1	1	yes	characteristic
447	C₄²	C₂×D₄×C₁₁	1	1	yes	characteristic
448	C₄²	C₂×D₄×C₁₁	1	1	yes	characteristic
449	C₄²	C₁₁×#41	1	2	yes	—
450	C₁₁	#23114	1	1	yes	characteristic, direct product factor, Sylow
451	C₂³	—	2	1	no	—
452	C₂³	—	2	2	no	—
453	C₂³	C₂×C₁₁×#41	1	1	yes	characteristic
454	Q₈	—	2	2	no	—
455	Q₈	—	2	1	no	—
456	Q₈	—	2	1	no	—
457	Q₈	—	2	2	no	—
458	D₄	—	2	2	no	—
459	D₄	—	2	1	no	—
460	D₄	—	2	1	no	—
461	D₄	—	2	2	no	—
462	D₄	—	4	1	no	—
463	D₄	—	4	2	no	—
464	D₄	—	4	1	no	—
465	D₄	—	4	2	no	—
466	D₄	—	4	2	no	—
467	D₄	—	8	1	no	—
468	C₂×C₄	—	2	2	no	—
469	C₂×C₄	—	2	2	no	—
470	C₂×C₄	—	2	1	no	—
471	C₂×C₄	—	2	1	no	—
472	C₂×C₄	—	2	1	no	—
473	C₂×C₄	—	2	2	no	—
474	C₂×C₄	—	2	2	no	—
475	C₂×C₄	—	4	1	no	—
476	C₂×C₄	—	4	1	no	—
477	C₂×C₄	—	4	1	no	—
478	C₂×C₄	—	4	1	no	—
479	C₂×C₄	—	4	1	no	—
480	C₂×C₄	—	4	2	no	—
481	C₂×C₄	—	4	1	no	—
482	C₂×C₄	—	4	1	no	—
483	C₂×C₄	—	4	2	no	—
484	C₂×C₄	—	4	2	no	—
485	C₂×C₄	—	8	1	no	—
486	C₂×C₄	C₄×D₄×C₁₁	1	1	yes	characteristic
487	C₂×C₄	C₄×D₄×C₁₁	1	1	yes	characteristic
488	C₂×C₄	C₄×D₄×C₁₁	1	1	yes	characteristic
489	C₂×C₄	C₄×D₄×C₁₁	1	1	yes	characteristic
490	C₂×C₄	C₂³×C₄×C₁₁	1	1	yes	characteristic
491	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
492	C₂×C₄	C₂×C₁₁×#41	1	1	yes	characteristic
493	C₂×C₄	C₂×C₁₁×#41	1	1	yes	characteristic
494	C₂×C₄	C₁₁×H(5,𝔽₂)	1	1	yes	characteristic
495	C₂×C₄	C₁₁×H(5,𝔽₂)	1	1	yes	characteristic
496	C₈	—	2	2	no	—
497	C₈	—	2	2	no	—
498	C₈	—	2	2	no	—
499	C₈	—	2	2	no	—
500	C₈	—	2	2	no	—
501	C₈	—	4	1	no	—
502	C₈	—	4	2	no	—
503	C₂²	—	2	1	no	—
504	C₂²	—	2	1	no	—
505	C₂²	—	4	1	no	—
506	C₂²	—	4	2	no	—
507	C₂²	—	4	1	no	—
508	C₂²	—	4	2	no	—
509	C₂²	—	4	2	no	—
510	C₂²	—	4	1	no	—
511	C₂²	C₂×C₄×D₄×C₁₁	1	1	yes	characteristic
512	C₂²	C₁₁×#553	1	1	yes	characteristic
513	C₂²	C₁₁×#555	1	1	yes	characteristic
514	C₄	—	2	1	no	—
515	C₄	—	2	1	no	—
516	C₄	—	2	1	no	—
517	C₄	—	4	2	no	—
518	C₄	—	4	2	no	—
519	C₄	—	4	1	no	—
520	C₄	—	4	1	no	—
521	C₄	—	4	1	no	—
522	C₄	—	4	2	no	—
523	C₄	C₁₁×#444	1	2	yes	—
524	C₄	C₄×C₁₁×#41	1	1	yes	characteristic
525	C₄	C₁₁×#518	1	1	yes	characteristic
526	C₄	C₁₁×#546	1	1	yes	characteristic
527	C₄	C₁₁×#550	1	1	yes	characteristic
528	C₂	—	2	1	no	—
529	C₂	—	2	1	no	—
530	C₂	—	8	1	no	—
531	C₂	—	8	2	no	—
532	C₂	C₁₁×#2363	1	1	yes	characteristic
533	C₂	C₂×C₁₁×#444	1	1	yes	characteristic
534	C₂	C₁₁×#2956	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₁	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₁
socle	C₂²×C₁₁	C₂×C₄×D₄
prime radical	C₁₁×#3035	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₁ ◁ C₂×C₁₁×C₄⋊C₈ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₁×#2935	C₂	semidirect
3. C₁₁×#2925	C₂	semidirect
4. C₁₁×#1975	C₂	semidirect
5. C₁₁×#1962	C₂	semidirect
6. C₁₁×#1950	C₂	semidirect
7. C₁₁×#1929	C₂	semidirect
8. C₁₁×#1876	C₂	semidirect
9. C₁₁×#1767	C₂	semidirect
10. C₁₁×#1765	C₂	semidirect
11. C₄×C₁₁×#104	C₂	semidirect
16. C₁₁×#464	C₄	semidirect
17. C₁₁×#463	C₄	semidirect
18. C₁₁×#462	C₄	semidirect
19. C₁₁×#461	C₄	semidirect
20. C₁₁×#460	C₄	semidirect
21. C₁₁×#459	C₄	semidirect
111. #23114	C₁₁	direct (N × H)
185. #2935	C₂×C₁₁	semidirect
186. #2925	C₂×C₁₁	semidirect
187. #1975	C₂×C₁₁	semidirect
188. #1962	C₂×C₁₁	semidirect
189. #1950	C₂×C₁₁	semidirect
190. #1929	C₂×C₁₁	semidirect
191. #1876	C₂×C₁₁	semidirect
192. #1767	C₂×C₁₁	semidirect
193. #1765	C₂×C₁₁	semidirect
194. C₄×#104	C₂×C₁₁	semidirect
251. #464	C₄×C₁₁	semidirect
252. #463	C₄×C₁₁	semidirect
253. #462	C₄×C₁₁	semidirect
254. #461	C₄×C₁₁	semidirect
255. #460	C₄×C₁₁	semidirect
256. #459	C₄×C₁₁	semidirect
450. C₁₁	#23114	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₁×#3035	2
C₁₁×#2935	2
C₁₁×#2925	2
C₁₁×#1975	2
C₁₁×#1962	2
C₁₁×#1950	2
C₁₁×#1929	2
C₁₁×#1876	2
C₁₁×#1767	2
C₁₁×#1765	2
C₄×C₁₁×#104	2
#23114	11

Subgroups — C11×#23114 #14600307

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#23114 #14600307