Subgroups — C₁₁×#23234 #14600427

Order 2816.

722 conjugacy classes of subgroups.

The subgroup lattice has 476 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×#3131	C₂	1	1	yes	maximal, characteristic
2	C₁₁×#2962	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₁×#2935	C₂	1	1	yes	maximal, characteristic
4	C₁₁×#1986	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₁×#1980	C₂	1	1	yes	maximal, characteristic
6	C₁₁×#1937	C₂	1	2	yes	maximal, complemented
7	C₁₁×#1929	C₂	1	2	yes	maximal, complemented
8	C₁₁×#1866	C₂	1	2	yes	maximal, complemented
9	C₄×C₁₁×#108	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈×C₁₁×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₁×#1764	C₂	1	2	yes	maximal, complemented
12	C₂×C₁₁×#131	C₂²	1	2	yes	—
13	C₁₁×#533	C₂²	1	1	yes	characteristic
14	C₁₁×#532	C₂²	1	1	yes	characteristic
15	C₁₁×#488	C₄	1	2	yes	complemented
16	C₁₁×#488	C₄	1	2	yes	complemented
17	C₁₁×#487	C₄	1	1	yes	characteristic, complemented
18	C₁₁×#487	C₄	1	1	yes	characteristic, complemented
19	C₁₁×#486	C₄	1	1	yes	characteristic, complemented
20	C₁₁×#486	C₄	1	1	yes	characteristic, complemented
21	C₁₁×#446	—	2	2	no	—
22	C₁₁×#446	—	2	1	no	—
23	C₈×Q₈×C₁₁	—	2	1	no	—
24	C₁₁×#436	—	2	1	no	—
25	C₁₁×#435	—	2	2	no	—
26	C₈×D₄×C₁₁	—	2	1	no	—
27	C₂×C₁₁×#108	C₂²	1	1	yes	characteristic
28	C₂×C₁₁×#108	C₂²	1	1	yes	characteristic
29	C₁₁×#424	C₂²	1	2	yes	—
30	C₂×C₁₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
31	C₂×C₁₁×#104	C₂²	1	2	yes	—
32	C₂×C₁₁×#104	C₂²	1	2	yes	—
33	C₁₁×#416	C₂²	1	2	yes	—
34	C₁₁×#416	C₂²	1	2	yes	—
35	C₁₁×#408	C₂²	1	2	yes	—
36	C₁₁×#405	C₂²	1	2	yes	—
37	C₄×C₁₁×M₁₆	C₂²	1	1	yes	characteristic
38	C₄×C₁₁×M₁₆	C₂²	1	1	yes	characteristic
39	C₂×C₄×C₈×C₁₁	C₂²	1	2	yes	—
40	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
41	C₄×C₁₁×C₄⋊C₄	C₂²	1	1	yes	characteristic
42	C₁₁×#341	C₂²	1	1	yes	characteristic
43	C₁₁×#341	C₂²	1	1	yes	characteristic
44	C₁₁×#339	C₂²	1	2	yes	—
45	C₁₁×#339	C₂²	1	2	yes	—
46	C₁₁×#336	C₂²	1	2	yes	—
47	C₂×C₁₁×#41	C₂³	1	2	yes	—
48	C₁₁×#131	—	2	4	no	—
49	C₁₁×#131	—	4	2	no	—
50	C₂×C₁₁×M₁₆	—	2	2	no	—
51	C₂×C₁₁×M₁₆	C₂³	1	1	yes	characteristic
52	C₂×C₁₁×M₁₆	C₂³	1	1	yes	characteristic
53	C₂×C₁₁×M₁₆	C₂³	1	1	yes	characteristic
54	C₂×C₁₁×M₁₆	C₂³	1	1	yes	characteristic
55	C₂²×C₈×C₁₁	—	2	2	no	—
56	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
57	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
58	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
59	C₁₁×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
60	C₁₁×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
61	C₁₁×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
62	C₁₁×#127	C₂×C₄	1	1	yes	characteristic
63	C₁₁×#125	C₂×C₄	1	2	yes	—
64	C₁₁×#124	C₂×C₄	1	2	yes	—
65	C₁₁×C₂²⋊Q₈	—	2	1	no	—
66	C₁₁×C₂²⋊Q₈	—	2	1	no	—
67	C₁₁×#121	—	2	1	no	—
68	C₁₁×#121	—	2	1	no	—
69	C₄×Q₈×C₁₁	—	2	1	no	—
70	C₄×Q₈×C₁₁	—	2	1	no	—
71	C₄×D₄×C₁₁	—	2	1	no	—
72	C₄×D₄×C₁₁	—	2	1	no	—
73	C₁₁×#117	C₂³	1	2	yes	—
74	C₂×C₁₁×C₄⋊C₄	—	2	1	no	—
75	C₂×C₄²×C₁₁	C₂³	1	2	yes	—
76	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
77	C₁₁×#108	—	2	2	no	—
78	C₁₁×#108	—	2	2	no	—
79	C₁₁×C₄⋊C₈	—	2	2	no	—
80	C₁₁×C₄⋊C₈	—	2	2	no	—
81	C₁₁×C₄⋊C₈	D₄	1	1	yes	characteristic
82	C₁₁×C₄⋊C₈	D₄	1	2	yes	—
83	C₁₁×C₄⋊C₈	D₄	1	1	yes	characteristic
84	C₁₁×#104	—	2	4	no	—
85	C₁₁×#104	—	4	2	no	—
86	C₁₁×#103	C₂×C₄	1	2	yes	—
87	C₁₁×#103	C₂×C₄	1	2	yes	—
88	C₁₁×#103	C₂×C₄	1	2	yes	—
89	C₁₁×#103	C₂×C₄	1	2	yes	—
90	C₁₁×#102	C₂×C₄	1	2	yes	—
91	C₁₁×#102	C₂×C₄	1	2	yes	—
92	C₁₁×#102	C₂×C₄	1	2	yes	—
93	C₁₁×#102	C₂×C₄	1	2	yes	—
94	C₁₁×C₂²⋊C₈	—	2	2	no	—
95	C₁₁×C₂²⋊C₈	—	2	2	no	—
96	C₁₁×#97	—	2	2	no	—
97	C₁₁×#97	—	2	1	no	—
98	C₁₁×#97	—	2	1	no	—
99	C₄×C₈×C₁₁	—	2	2	no	—
100	C₄×C₈×C₁₁	—	2	1	no	—
101	C₄×C₈×C₁₁	—	2	1	no	—
102	C₄×C₈×C₁₁	—	4	2	no	—
103	C₄×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
104	C₄×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
105	C₄×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
106	C₄×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
107	C₁₁×#95	—	2	1	no	—
108	#23234	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
109	C₁₁×#41	—	2	2	no	—
110	C₁₁×#41	—	2	2	no	—
111	C₁₁×#41	—	2	2	no	—
112	C₁₁×#41	—	2	2	no	—
113	C₂×Q₈×C₁₁	—	2	1	no	—
114	C₂×Q₈×C₁₁	—	2	1	no	—
115	C₂×Q₈×C₁₁	C₂²×C₄	1	2	yes	—
116	C₂×D₄×C₁₁	—	2	2	no	—
117	C₂×D₄×C₁₁	—	2	1	no	—
118	C₂×D₄×C₁₁	—	2	1	no	—
119	C₂×D₄×C₁₁	C₂²×C₄	1	2	yes	—
120	C₂²×C₄×C₁₁	—	2	2	no	—
121	C₂²×C₄×C₁₁	—	2	2	no	—
122	C₂²×C₄×C₁₁	#41	1	1	yes	characteristic
123	C₂²×C₄×C₁₁	#41	1	1	yes	characteristic
124	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
125	C₁₁×M₁₆	—	2	1	no	—
126	C₁₁×M₁₆	—	2	1	no	—
127	C₁₁×M₁₆	—	2	1	no	—
128	C₁₁×M₁₆	—	2	1	no	—
129	C₁₁×M₁₆	—	2	1	no	—
130	C₁₁×M₁₆	—	2	1	no	—
131	C₁₁×M₁₆	—	4	4	no	—
132	C₁₁×M₁₆	#41	1	2	yes	—
133	C₁₁×M₁₆	#41	1	2	yes	—
134	C₂×C₈×C₁₁	—	2	1	no	—
135	C₂×C₈×C₁₁	—	2	1	no	—
136	C₂×C₈×C₁₁	—	2	1	no	—
137	C₂×C₈×C₁₁	—	2	1	no	—
138	C₂×C₈×C₁₁	—	2	1	no	—
139	C₂×C₈×C₁₁	—	2	1	no	—
140	C₂×C₈×C₁₁	—	2	2	no	—
141	C₂×C₈×C₁₁	—	2	1	no	—
142	C₂×C₈×C₁₁	—	2	2	no	—
143	C₂×C₈×C₁₁	—	2	1	no	—
144	C₂×C₈×C₁₁	—	4	4	no	—
145	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
146	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
147	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
148	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
149	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
150	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
151	C₁₁×C₄⋊C₄	—	2	4	no	—
152	C₁₁×C₄⋊C₄	—	2	1	no	—
153	C₁₁×C₄⋊C₄	—	2	1	no	—
154	C₁₁×C₄⋊C₄	—	2	2	no	—
155	C₁₁×C₄⋊C₄	—	2	2	no	—
156	C₁₁×C₄⋊C₄	—	2	1	no	—
157	C₁₁×C₄⋊C₄	—	2	1	no	—
158	C₁₁×C₄⋊C₄	C₂²×C₄	1	2	yes	—
159	C₁₁×C₄⋊C₄	C₂²×C₄	1	2	yes	—
160	C₁₁×C₂²⋊C₄	—	2	2	no	—
161	C₁₁×C₂²⋊C₄	—	2	2	no	—
162	C₁₁×C₂²⋊C₄	—	2	2	no	—
163	C₄²×C₁₁	—	2	2	no	—
164	C₄²×C₁₁	—	2	2	no	—
165	C₄²×C₁₁	—	2	2	no	—
166	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
167	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
168	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
169	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
170	#3131	C₂×C₁₁	1	1	yes	characteristic
171	#2962	C₂×C₁₁	1	1	yes	characteristic, complemented
172	#2935	C₂×C₁₁	1	1	yes	characteristic
173	#1986	C₂×C₁₁	1	1	yes	characteristic, complemented
174	#1980	C₂×C₁₁	1	1	yes	characteristic
175	#1937	C₂×C₁₁	1	2	yes	complemented
176	#1929	C₂×C₁₁	1	2	yes	complemented
177	#1866	C₂×C₁₁	1	2	yes	complemented
178	C₄×#108	C₂×C₁₁	1	1	yes	characteristic, complemented
179	C₈×C₄⋊C₄	C₂×C₁₁	1	1	yes	characteristic, complemented
180	#1764	C₂×C₁₁	1	2	yes	complemented
181	C₂³×C₁₁	—	2	2	no	—
182	C₂³×C₁₁	C₂×#41	1	1	yes	characteristic
183	Q₈×C₁₁	—	2	2	no	—
184	Q₈×C₁₁	—	2	2	no	—
185	Q₈×C₁₁	—	4	2	no	—
186	Q₈×C₁₁	—	8	1	no	—
187	D₄×C₁₁	—	2	2	no	—
188	D₄×C₁₁	—	2	2	no	—
189	D₄×C₁₁	—	4	2	no	—
190	D₄×C₁₁	—	4	2	no	—
191	D₄×C₁₁	—	4	2	no	—
192	D₄×C₁₁	—	8	1	no	—
193	C₂×C₄×C₁₁	—	2	2	no	—
194	C₂×C₄×C₁₁	—	2	4	no	—
195	C₂×C₄×C₁₁	—	2	2	no	—
196	C₂×C₄×C₁₁	—	2	2	no	—
197	C₂×C₄×C₁₁	—	2	2	no	—
198	C₂×C₄×C₁₁	—	4	1	no	—
199	C₂×C₄×C₁₁	—	4	2	no	—
200	C₂×C₄×C₁₁	—	4	2	no	—
201	C₂×C₄×C₁₁	—	4	2	no	—
202	C₂×C₄×C₁₁	—	4	2	no	—
203	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
204	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
205	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
206	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
207	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
208	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
209	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
210	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
211	C₂×C₄×C₁₁	H(5,𝔽₂)	1	1	yes	characteristic
212	C₂×C₄×C₁₁	2₋¹⁺⁴	1	1	yes	characteristic
213	C₈×C₁₁	—	2	1	no	—
214	C₈×C₁₁	—	2	1	no	—
215	C₈×C₁₁	—	2	1	no	—
216	C₈×C₁₁	—	2	1	no	—
217	C₈×C₁₁	—	2	2	no	—
218	C₈×C₁₁	—	2	2	no	—
219	C₈×C₁₁	—	2	2	no	—
220	C₈×C₁₁	—	2	2	no	—
221	C₈×C₁₁	—	4	1	no	—
222	C₈×C₁₁	—	4	1	no	—
223	C₂×#131	C₂²×C₁₁	1	2	yes	—
224	#533	C₂²×C₁₁	1	1	yes	characteristic
225	#532	C₂²×C₁₁	1	1	yes	characteristic
226	#488	C₄×C₁₁	1	2	yes	complemented
227	#488	C₄×C₁₁	1	2	yes	complemented
228	#487	C₄×C₁₁	1	1	yes	characteristic, complemented
229	#487	C₄×C₁₁	1	1	yes	characteristic, complemented
230	#486	C₄×C₁₁	1	1	yes	characteristic, complemented
231	#486	C₄×C₁₁	1	1	yes	characteristic, complemented
232	#446	—	2	2	no	—
233	#446	—	2	1	no	—
234	C₈×Q₈	—	2	1	no	—
235	#436	—	2	1	no	—
236	#435	—	2	2	no	—
237	C₈×D₄	—	2	1	no	—
238	C₂×#108	C₂²×C₁₁	1	1	yes	characteristic
239	C₂×#108	C₂²×C₁₁	1	1	yes	characteristic
240	#424	C₂²×C₁₁	1	2	yes	—
241	C₂×C₄⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
242	C₂×#104	C₂²×C₁₁	1	2	yes	—
243	C₂×#104	C₂²×C₁₁	1	2	yes	—
244	#416	C₂²×C₁₁	1	2	yes	—
245	#416	C₂²×C₁₁	1	2	yes	—
246	#408	C₂²×C₁₁	1	2	yes	—
247	#405	C₂²×C₁₁	1	2	yes	—
248	C₄×M₁₆	C₂²×C₁₁	1	1	yes	characteristic
249	C₄×M₁₆	C₂²×C₁₁	1	1	yes	characteristic
250	C₂×C₄×C₈	C₂²×C₁₁	1	2	yes	—
251	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
252	C₄×C₄⋊C₄	C₂²×C₁₁	1	1	yes	characteristic
253	#341	C₂²×C₁₁	1	1	yes	characteristic
254	#341	C₂²×C₁₁	1	1	yes	characteristic
255	#339	C₂²×C₁₁	1	2	yes	—
256	#339	C₂²×C₁₁	1	2	yes	—
257	#336	C₂²×C₁₁	1	2	yes	—
258	C₂²×C₁₁	—	2	1	no	—
259	C₂²×C₁₁	—	2	1	no	—
260	C₂²×C₁₁	—	4	2	no	—
261	C₂²×C₁₁	—	4	2	no	—
262	C₂²×C₁₁	—	4	2	no	—
263	C₂²×C₁₁	C₂×C₄×D₄	1	1	yes	characteristic
264	C₂²×C₁₁	#556	1	1	yes	characteristic
265	C₂²×C₁₁	#559	1	1	yes	characteristic
266	C₄×C₁₁	—	2	1	no	—
267	C₄×C₁₁	—	2	1	no	—
268	C₄×C₁₁	—	2	1	no	—
269	C₄×C₁₁	—	4	4	no	—
270	C₄×C₁₁	—	4	2	no	—
271	C₄×C₁₁	—	4	2	no	—
272	C₄×C₁₁	—	4	2	no	—
273	C₄×C₁₁	#443	1	2	yes	—
274	C₄×C₁₁	C₄×#41	1	1	yes	characteristic
275	C₄×C₁₁	#520	1	1	yes	characteristic
276	C₄×C₁₁	#546	1	1	yes	characteristic
277	C₄×C₁₁	#548	1	1	yes	characteristic
278	C₂×#41	C₂³×C₁₁	1	2	yes	—
279	#131	—	2	4	no	—
280	#131	—	4	2	no	—
281	C₂×M₁₆	—	2	2	no	—
282	C₂×M₁₆	C₂³×C₁₁	1	1	yes	characteristic
283	C₂×M₁₆	C₂³×C₁₁	1	1	yes	characteristic
284	C₂×M₁₆	C₂³×C₁₁	1	1	yes	characteristic
285	C₂×M₁₆	C₂³×C₁₁	1	1	yes	characteristic
286	C₂²×C₈	—	2	2	no	—
287	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
288	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
289	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
290	C₄⋊Q₈	C₂×C₄×C₁₁	1	1	yes	characteristic
291	C₄⋊Q₈	C₂×C₄×C₁₁	1	1	yes	characteristic
292	C₄⋊Q₈	C₂×C₄×C₁₁	1	1	yes	characteristic
293	#127	C₂×C₄×C₁₁	1	1	yes	characteristic
294	#125	C₂×C₄×C₁₁	1	2	yes	—
295	#124	C₂×C₄×C₁₁	1	2	yes	—
296	C₂²⋊Q₈	—	2	1	no	—
297	C₂²⋊Q₈	—	2	1	no	—
298	#121	—	2	1	no	—
299	#121	—	2	1	no	—
300	C₄×Q₈	—	2	1	no	—
301	C₄×Q₈	—	2	1	no	—
302	C₄×D₄	—	2	1	no	—
303	C₄×D₄	—	2	1	no	—
304	#117	C₂³×C₁₁	1	2	yes	—
305	C₂×C₄⋊C₄	—	2	1	no	—
306	C₂×C₄²	C₂³×C₁₁	1	2	yes	—
307	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
308	#108	—	2	2	no	—
309	#108	—	2	2	no	—
310	C₄⋊C₈	—	2	2	no	—
311	C₄⋊C₈	—	2	2	no	—
312	C₄⋊C₈	D₄×C₁₁	1	1	yes	characteristic
313	C₄⋊C₈	D₄×C₁₁	1	2	yes	—
314	C₄⋊C₈	D₄×C₁₁	1	1	yes	characteristic
315	#104	—	2	4	no	—
316	#104	—	4	2	no	—
317	#103	C₂×C₄×C₁₁	1	2	yes	—
318	#103	C₂×C₄×C₁₁	1	2	yes	—
319	#103	C₂×C₄×C₁₁	1	2	yes	—
320	#103	C₂×C₄×C₁₁	1	2	yes	—
321	#102	C₂×C₄×C₁₁	1	2	yes	—
322	#102	C₂×C₄×C₁₁	1	2	yes	—
323	#102	C₂×C₄×C₁₁	1	2	yes	—
324	#102	C₂×C₄×C₁₁	1	2	yes	—
325	C₂²⋊C₈	—	2	2	no	—
326	C₂²⋊C₈	—	2	2	no	—
327	#97	—	2	2	no	—
328	#97	—	2	1	no	—
329	#97	—	2	1	no	—
330	C₄×C₈	—	2	2	no	—
331	C₄×C₈	—	2	1	no	—
332	C₄×C₈	—	2	1	no	—
333	C₄×C₈	—	4	2	no	—
334	C₄×C₈	C₂×C₄×C₁₁	1	1	yes	characteristic
335	C₄×C₈	C₂×C₄×C₁₁	1	1	yes	characteristic
336	C₄×C₈	C₂×C₄×C₁₁	1	1	yes	characteristic
337	C₄×C₈	C₂×C₄×C₁₁	1	1	yes	characteristic
338	#95	—	2	1	no	—
339	C₂×C₁₁	—	2	1	no	—
340	C₂×C₁₁	—	2	1	no	—
341	C₂×C₁₁	—	8	2	no	—
342	C₂×C₁₁	#2367	1	1	yes	characteristic
343	C₂×C₁₁	C₂×#443	1	1	yes	characteristic
344	C₂×C₁₁	#2957	1	1	yes	characteristic
345	#41	—	2	2	no	—
346	#41	—	2	2	no	—
347	#41	—	2	2	no	—
348	#41	—	2	2	no	—
349	C₂×Q₈	—	2	1	no	—
350	C₂×Q₈	—	2	1	no	—
351	C₂×Q₈	C₂²×C₄×C₁₁	1	2	yes	—
352	C₂×D₄	—	2	2	no	—
353	C₂×D₄	—	2	1	no	—
354	C₂×D₄	—	2	1	no	—
355	C₂×D₄	C₂²×C₄×C₁₁	1	2	yes	—
356	C₂²×C₄	—	2	2	no	—
357	C₂²×C₄	—	2	2	no	—
358	C₂²×C₄	C₁₁×#41	1	1	yes	characteristic
359	C₂²×C₄	C₁₁×#41	1	1	yes	characteristic
360	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
361	M₁₆	—	2	1	no	—
362	M₁₆	—	2	1	no	—
363	M₁₆	—	2	1	no	—
364	M₁₆	—	2	1	no	—
365	M₁₆	—	2	1	no	—
366	M₁₆	—	2	1	no	—
367	M₁₆	—	4	4	no	—
368	M₁₆	C₁₁×#41	1	2	yes	—
369	M₁₆	C₁₁×#41	1	2	yes	—
370	C₂×C₈	—	2	1	no	—
371	C₂×C₈	—	2	1	no	—
372	C₂×C₈	—	2	1	no	—
373	C₂×C₈	—	2	1	no	—
374	C₂×C₈	—	2	2	no	—
375	C₂×C₈	—	2	1	no	—
376	C₂×C₈	—	2	2	no	—
377	C₂×C₈	—	2	1	no	—
378	C₂×C₈	—	2	1	no	—
379	C₂×C₈	—	2	1	no	—
380	C₂×C₈	—	4	4	no	—
381	C₂×C₈	C₂²×C₄×C₁₁	1	1	yes	characteristic
382	C₂×C₈	C₂²×C₄×C₁₁	1	1	yes	characteristic
383	C₂×C₈	C₂²×C₄×C₁₁	1	1	yes	characteristic
384	C₂×C₈	C₂²×C₄×C₁₁	1	1	yes	characteristic
385	C₂×C₈	C₂×D₄×C₁₁	1	2	yes	—
386	C₂×C₈	C₂×D₄×C₁₁	1	2	yes	—
387	C₄⋊C₄	—	2	4	no	—
388	C₄⋊C₄	—	2	1	no	—
389	C₄⋊C₄	—	2	1	no	—
390	C₄⋊C₄	—	2	2	no	—
391	C₄⋊C₄	—	2	2	no	—
392	C₄⋊C₄	—	2	1	no	—
393	C₄⋊C₄	—	2	1	no	—
394	C₄⋊C₄	C₂²×C₄×C₁₁	1	2	yes	—
395	C₄⋊C₄	C₂²×C₄×C₁₁	1	2	yes	—
396	C₂²⋊C₄	—	2	2	no	—
397	C₂²⋊C₄	—	2	2	no	—
398	C₂²⋊C₄	—	2	2	no	—
399	C₄²	—	2	2	no	—
400	C₄²	—	2	2	no	—
401	C₄²	—	2	2	no	—
402	C₄²	C₂²×C₄×C₁₁	1	1	yes	characteristic
403	C₄²	C₂²×C₄×C₁₁	1	1	yes	characteristic
404	C₄²	C₂×D₄×C₁₁	1	1	yes	characteristic
405	C₄²	C₂×D₄×C₁₁	1	1	yes	characteristic
406	C₁₁	#23234	1	1	yes	characteristic, direct product factor, Sylow
407	C₂³	—	2	2	no	—
408	C₂³	C₂×C₁₁×#41	1	1	yes	characteristic
409	Q₈	—	2	2	no	—
410	Q₈	—	2	2	no	—
411	Q₈	—	4	2	no	—
412	Q₈	—	8	1	no	—
413	D₄	—	2	2	no	—
414	D₄	—	2	2	no	—
415	D₄	—	4	2	no	—
416	D₄	—	4	2	no	—
417	D₄	—	4	2	no	—
418	D₄	—	8	1	no	—
419	C₂×C₄	—	2	2	no	—
420	C₂×C₄	—	2	4	no	—
421	C₂×C₄	—	2	2	no	—
422	C₂×C₄	—	2	2	no	—
423	C₂×C₄	—	2	2	no	—
424	C₂×C₄	—	4	1	no	—
425	C₂×C₄	—	4	2	no	—
426	C₂×C₄	—	4	2	no	—
427	C₂×C₄	—	4	2	no	—
428	C₂×C₄	—	4	2	no	—
429	C₂×C₄	C₄×D₄×C₁₁	1	1	yes	characteristic
430	C₂×C₄	C₄×D₄×C₁₁	1	1	yes	characteristic
431	C₂×C₄	C₄×D₄×C₁₁	1	1	yes	characteristic
432	C₂×C₄	C₄×D₄×C₁₁	1	1	yes	characteristic
433	C₂×C₄	C₂³×C₄×C₁₁	1	1	yes	characteristic
434	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
435	C₂×C₄	C₂×C₁₁×#41	1	1	yes	characteristic
436	C₂×C₄	C₂×C₁₁×#41	1	1	yes	characteristic
437	C₂×C₄	C₁₁×H(5,𝔽₂)	1	1	yes	characteristic
438	C₂×C₄	C₁₁×2₋¹⁺⁴	1	1	yes	characteristic
439	C₈	—	2	1	no	—
440	C₈	—	2	1	no	—
441	C₈	—	2	1	no	—
442	C₈	—	2	1	no	—
443	C₈	—	2	2	no	—
444	C₈	—	2	2	no	—
445	C₈	—	2	2	no	—
446	C₈	—	2	2	no	—
447	C₈	—	4	1	no	—
448	C₈	—	4	1	no	—
449	C₂²	—	2	1	no	—
450	C₂²	—	2	1	no	—
451	C₂²	—	4	2	no	—
452	C₂²	—	4	2	no	—
453	C₂²	—	4	2	no	—
454	C₂²	C₂×C₄×D₄×C₁₁	1	1	yes	characteristic
455	C₂²	C₁₁×#556	1	1	yes	characteristic
456	C₂²	C₁₁×#559	1	1	yes	characteristic
457	C₄	—	2	1	no	—
458	C₄	—	2	1	no	—
459	C₄	—	2	1	no	—
460	C₄	—	4	4	no	—
461	C₄	—	4	2	no	—
462	C₄	—	4	2	no	—
463	C₄	—	4	2	no	—
464	C₄	C₁₁×#443	1	2	yes	—
465	C₄	C₄×C₁₁×#41	1	1	yes	characteristic
466	C₄	C₁₁×#520	1	1	yes	characteristic
467	C₄	C₁₁×#546	1	1	yes	characteristic
468	C₄	C₁₁×#548	1	1	yes	characteristic
469	C₂	—	2	1	no	—
470	C₂	—	2	1	no	—
471	C₂	—	8	2	no	—
472	C₂	C₁₁×#2367	1	1	yes	characteristic
473	C₂	C₂×C₁₁×#443	1	1	yes	characteristic
474	C₂	C₁₁×#2957	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×#532	C₂²
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×#2962	C₂	semidirect
4. C₁₁×#1986	C₂	semidirect
6. C₁₁×#1937	C₂	semidirect
7. C₁₁×#1929	C₂	semidirect
8. C₁₁×#1866	C₂	semidirect
9. C₄×C₁₁×#108	C₂	semidirect
10. C₈×C₁₁×C₄⋊C₄	C₂	semidirect
11. C₁₁×#1764	C₂	semidirect
15. C₁₁×#488	C₄	semidirect
16. C₁₁×#488	C₄	semidirect
17. C₁₁×#487	C₄	semidirect
18. C₁₁×#487	C₄	semidirect
19. C₁₁×#486	C₄	semidirect
20. C₁₁×#486	C₄	semidirect
108. #23234	C₁₁	direct (N × H)
171. #2962	C₂×C₁₁	semidirect
173. #1986	C₂×C₁₁	semidirect
175. #1937	C₂×C₁₁	semidirect
176. #1929	C₂×C₁₁	semidirect
177. #1866	C₂×C₁₁	semidirect
178. C₄×#108	C₂×C₁₁	semidirect
179. C₈×C₄⋊C₄	C₂×C₁₁	semidirect
180. #1764	C₂×C₁₁	semidirect
226. #488	C₄×C₁₁	semidirect
227. #488	C₄×C₁₁	semidirect
228. #487	C₄×C₁₁	semidirect
229. #487	C₄×C₁₁	semidirect
230. #486	C₄×C₁₁	semidirect
231. #486	C₄×C₁₁	semidirect
406. C₁₁	#23234	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×#3131	2
C₁₁×#2962	2
C₁₁×#2935	2
C₁₁×#1986	2
C₁₁×#1980	2
C₁₁×#1937	2
C₁₁×#1929	2
C₁₁×#1866	2
C₄×C₁₁×#108	2
C₈×C₁₁×C₄⋊C₄	2
C₁₁×#1764	2
#23234	11

Subgroups — C11×#23234 #14600427

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#23234 #14600427