Subgroups — C₁₁×#22207 #14599400

Order 2816.

806 conjugacy classes of subgroups.

The subgroup lattice has 498 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×#3054	C₂	1	1	yes	maximal, characteristic
2	C₁₁×#2930	C₂	1	2	yes	maximal, complemented
3	C₁₁×#1929	C₂	1	2	yes	maximal, complemented
4	C₁₁×#1922	C₂	1	2	yes	maximal, complemented
5	C₁₁×#1896	C₂	1	2	yes	maximal, complemented
6	C₁₁×#1876	C₂	1	2	yes	maximal, complemented
7	C₁₁×#1866	C₂	1	2	yes	maximal, complemented
8	C₁₁×#1811	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₁×#1728	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₁₁×#135	C₂²	1	1	yes	characteristic
11	C₂×C₁₁×#131	C₂²	1	2	yes	—
12	C₂²×C₁₁×M₁₆	C₂²	1	1	yes	characteristic
13	C₂²×C₁₁×M₁₆	C₂²	1	1	yes	characteristic
14	C₁₁×#525	C₂²	1	2	yes	—
15	C₂²×C₄²×C₁₁	C₂²	1	1	yes	characteristic
16	C₁₁×#470	C₄	1	1	yes	characteristic, complemented
17	C₁₁×#470	C₄	1	1	yes	characteristic, complemented
18	C₁₁×#469	C₄	1	1	yes	characteristic, complemented
19	C₁₁×#469	C₄	1	1	yes	characteristic, complemented
20	C₁₁×#468	C₄	1	2	yes	complemented
21	C₁₁×#468	C₄	1	2	yes	complemented
22	C₁₁×#436	—	2	2	no	—
23	C₁₁×#436	—	2	2	no	—
24	C₁₁×#435	—	2	2	no	—
25	C₁₁×#435	—	2	2	no	—
26	C₂×C₁₁×#108	C₂²	1	1	yes	characteristic
27	C₂×C₁₁×#108	C₂²	1	1	yes	characteristic
28	C₁₁×#427	C₂²	1	1	yes	characteristic
29	C₁₁×#424	C₂²	1	2	yes	—
30	C₂×C₁₁×#104	C₂²	1	2	yes	—
31	C₂×C₁₁×#104	C₂²	1	2	yes	—
32	C₁₁×#416	C₂²	1	2	yes	—
33	C₁₁×#408	C₂²	1	2	yes	—
34	C₁₁×#407	C₂²	1	2	yes	—
35	C₁₁×#405	C₂²	1	2	yes	—
36	C₁₁×#341	C₂²	1	2	yes	—
37	C₁₁×#339	C₂²	1	2	yes	—
38	C₁₁×#339	C₂²	1	2	yes	—
39	C₁₁×#336	C₂²	1	2	yes	—
40	C₁₁×#336	C₂²	1	2	yes	—
41	C₂×C₁₁×#41	C₂³	1	2	yes	—
42	C₂³×C₄×C₁₁	—	2	1	no	—
43	C₂³×C₄×C₁₁	C₂³	1	1	yes	characteristic
44	C₁₁×#135	—	4	1	no	—
45	C₁₁×#135	—	4	1	no	—
46	C₂×C₁₁×Q₁₆	C₂×C₄	1	1	yes	characteristic, complemented
47	C₂×C₁₁×SD₁₆	C₂×C₄	1	2	yes	complemented
48	C₂×C₁₁×D₈	C₂×C₄	1	1	yes	characteristic, complemented
49	C₁₁×#131	—	4	2	no	—
50	C₁₁×#131	—	4	2	no	—
51	C₂×C₁₁×M₁₆	—	2	2	no	—
52	C₂×C₁₁×M₁₆	—	4	1	no	—
53	C₂×C₁₁×M₁₆	—	4	1	no	—
54	C₂×C₁₁×M₁₆	—	4	1	no	—
55	C₂×C₁₁×M₁₆	—	4	1	no	—
56	C₂×C₁₁×M₁₆	C₂×C₄	1	1	yes	characteristic
57	C₂×C₁₁×M₁₆	C₂×C₄	1	1	yes	characteristic
58	C₂×C₁₁×M₁₆	C₂×C₄	1	1	yes	characteristic
59	C₂×C₁₁×M₁₆	C₂×C₄	1	1	yes	characteristic
60	C₂×C₁₁×M₁₆	D₄	1	1	yes	characteristic
61	C₂×C₁₁×M₁₆	D₄	1	2	yes	—
62	C₂×C₁₁×M₁₆	D₄	1	1	yes	characteristic
63	C₂×C₁₁×M₁₆	C₂³	1	2	yes	—
64	C₂×C₁₁×M₁₆	C₂³	1	2	yes	—
65	C₂²×C₈×C₁₁	—	2	2	no	—
66	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
67	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
68	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
69	C₁₁×#123	—	2	2	no	—
70	C₁₁×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
71	C₁₁×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
72	C₁₁×#121	C₂×C₄	1	2	yes	—
73	C₁₁×#121	C₂×C₄	1	2	yes	—
74	C₁₁×#120	—	2	2	no	—
75	C₄×D₄×C₁₁	—	2	2	no	—
76	C₄×D₄×C₁₁	—	2	2	no	—
77	C₁₁×#117	C₂³	1	2	yes	—
78	C₂×C₄²×C₁₁	—	2	1	no	—
79	C₂×C₄²×C₁₁	—	4	1	no	—
80	C₂×C₄²×C₁₁	—	4	1	no	—
81	C₂×C₄²×C₁₁	C₂³	1	2	yes	—
82	C₁₁×#108	—	4	1	no	—
83	C₁₁×#108	—	4	1	no	—
84	C₁₁×#107	C₂×C₄	1	2	yes	complemented
85	C₁₁×#106	C₂×C₄	1	1	yes	characteristic, complemented
86	C₁₁×#106	C₂×C₄	1	1	yes	characteristic, complemented
87	C₁₁×C₄⋊C₈	—	2	2	no	—
88	C₁₁×C₄⋊C₈	—	2	2	no	—
89	C₁₁×#104	—	4	2	no	—
90	C₁₁×#104	—	4	2	no	—
91	C₁₁×#103	C₂×C₄	1	2	yes	complemented
92	C₁₁×#103	C₂×C₄	1	2	yes	complemented
93	C₁₁×#102	C₂×C₄	1	2	yes	complemented
94	C₁₁×#102	C₂×C₄	1	2	yes	complemented
95	C₁₁×C₂²⋊C₈	—	2	2	no	—
96	C₁₁×C₂²⋊C₈	—	2	2	no	—
97	C₁₁×C₂²⋊C₈	—	2	2	no	—
98	C₁₁×C₂²⋊C₈	—	2	2	no	—
99	C₁₁×#97	—	2	2	no	—
100	C₄×C₈×C₁₁	—	2	2	no	—
101	#22207	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
102	C₂⁴×C₁₁	#41	1	1	yes	characteristic
103	C₁₁×#41	—	2	2	no	—
104	C₁₁×#41	—	2	2	no	—
105	C₁₁×#41	—	2	2	no	—
106	C₁₁×#41	—	2	2	no	—
107	C₂×Q₈×C₁₁	C₂²×C₄	1	2	yes	—
108	C₂×D₄×C₁₁	—	2	2	no	—
109	C₂×D₄×C₁₁	—	2	2	no	—
110	C₂×D₄×C₁₁	—	2	2	no	—
111	C₂×D₄×C₁₁	C₂²×C₄	1	2	yes	—
112	C₂²×C₄×C₁₁	—	2	1	no	—
113	C₂²×C₄×C₁₁	—	2	1	no	—
114	C₂²×C₄×C₁₁	—	2	1	no	—
115	C₂²×C₄×C₁₁	—	2	1	no	—
116	C₂²×C₄×C₁₁	—	2	2	no	—
117	C₂²×C₄×C₁₁	—	2	2	no	—
118	C₂²×C₄×C₁₁	—	4	4	no	—
119	C₂²×C₄×C₁₁	—	4	2	no	—
120	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
121	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
122	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
123	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
124	C₂²×C₄×C₁₁	#41	1	1	yes	characteristic
125	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
126	C₁₁×Q₁₆	—	4	1	no	—
127	C₁₁×SD₁₆	—	4	2	no	—
128	C₁₁×D₈	—	4	1	no	—
129	C₁₁×M₁₆	—	2	2	no	—
130	C₁₁×M₁₆	—	2	2	no	—
131	C₁₁×M₁₆	—	2	2	no	—
132	C₁₁×M₁₆	—	2	2	no	—
133	C₁₁×M₁₆	—	4	1	no	—
134	C₁₁×M₁₆	—	4	1	no	—
135	C₁₁×M₁₆	—	4	1	no	—
136	C₁₁×M₁₆	—	4	1	no	—
137	C₁₁×M₁₆	—	4	1	no	—
138	C₁₁×M₁₆	—	4	2	no	—
139	C₁₁×M₁₆	—	4	1	no	—
140	C₁₁×M₁₆	—	4	4	no	—
141	C₂×C₈×C₁₁	—	2	2	no	—
142	C₂×C₈×C₁₁	—	2	2	no	—
143	C₂×C₈×C₁₁	—	2	1	no	—
144	C₂×C₈×C₁₁	—	2	1	no	—
145	C₂×C₈×C₁₁	—	2	2	no	—
146	C₂×C₈×C₁₁	—	2	2	no	—
147	C₂×C₈×C₁₁	—	2	1	no	—
148	C₂×C₈×C₁₁	—	2	1	no	—
149	C₂×C₈×C₁₁	—	4	4	no	—
150	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
151	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
152	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
153	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
154	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
155	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
156	C₁₁×C₄⋊C₄	—	2	2	no	—
157	C₁₁×C₄⋊C₄	—	2	2	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	C₁₁×C₂²⋊C₄	—	2	2	no	—
164	C₁₁×C₂²⋊C₄	—	2	2	no	—
165	C₄²×C₁₁	—	2	2	no	—
166	C₄²×C₁₁	—	2	2	no	—
167	C₄²×C₁₁	—	2	2	no	—
168	C₄²×C₁₁	—	4	2	no	—
169	#3054	C₂×C₁₁	1	1	yes	characteristic
170	#2930	C₂×C₁₁	1	2	yes	complemented
171	#1929	C₂×C₁₁	1	2	yes	complemented
172	#1922	C₂×C₁₁	1	2	yes	complemented
173	#1896	C₂×C₁₁	1	2	yes	complemented
174	#1876	C₂×C₁₁	1	2	yes	complemented
175	#1866	C₂×C₁₁	1	2	yes	complemented
176	#1811	C₂×C₁₁	1	1	yes	characteristic, complemented
177	#1728	C₂×C₁₁	1	1	yes	characteristic, complemented
178	C₂³×C₁₁	—	2	1	no	—
179	C₂³×C₁₁	—	2	1	no	—
180	C₂³×C₁₁	—	2	2	no	—
181	C₂³×C₁₁	—	4	2	no	—
182	C₂³×C₁₁	C₄×D₄	1	1	yes	characteristic
183	C₂³×C₁₁	C₄×D₄	1	1	yes	characteristic
184	C₂³×C₁₁	C₂×#41	1	1	yes	characteristic
185	Q₈×C₁₁	—	2	2	no	—
186	Q₈×C₁₁	—	2	2	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	—	8	2	no	—
192	D₄×C₁₁	—	8	2	no	—
193	C₂×C₄×C₁₁	—	2	1	no	—
194	C₂×C₄×C₁₁	—	2	1	no	—
195	C₂×C₄×C₁₁	—	2	1	no	—
196	C₂×C₄×C₁₁	—	2	1	no	—
197	C₂×C₄×C₁₁	—	2	1	no	—
198	C₂×C₄×C₁₁	—	2	1	no	—
199	C₂×C₄×C₁₁	—	2	1	no	—
200	C₂×C₄×C₁₁	—	2	1	no	—
201	C₂×C₄×C₁₁	—	2	1	no	—
202	C₂×C₄×C₁₁	—	2	1	no	—
203	C₂×C₄×C₁₁	—	2	4	no	—
204	C₂×C₄×C₁₁	—	2	2	no	—
205	C₂×C₄×C₁₁	—	2	2	no	—
206	C₂×C₄×C₁₁	—	2	2	no	—
207	C₂×C₄×C₁₁	—	4	2	no	—
208	C₂×C₄×C₁₁	—	4	8	no	—
209	C₂×C₄×C₁₁	—	4	2	no	—
210	C₂×C₄×C₁₁	—	4	2	no	—
211	C₂×C₄×C₁₁	—	4	2	no	—
212	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
213	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
214	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
215	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
216	C₂×C₄×C₁₁	H(5,𝔽₂)	1	1	yes	characteristic
217	C₂×C₄×C₁₁	H(5,𝔽₂)	1	1	yes	characteristic
218	C₂×C₄×C₁₁	H(5,𝔽₂)	1	1	yes	characteristic
219	C₂×C₄×C₁₁	2₋¹⁺⁴	1	1	yes	characteristic
220	C₈×C₁₁	—	2	1	no	—
221	C₈×C₁₁	—	2	1	no	—
222	C₈×C₁₁	—	2	1	no	—
223	C₈×C₁₁	—	2	1	no	—
224	C₈×C₁₁	—	2	2	no	—
225	C₈×C₁₁	—	2	2	no	—
226	C₈×C₁₁	—	4	2	no	—
227	C₈×C₁₁	—	4	2	no	—
228	C₂×#135	C₂²×C₁₁	1	1	yes	characteristic
229	C₂×#131	C₂²×C₁₁	1	2	yes	—
230	C₂²×M₁₆	C₂²×C₁₁	1	1	yes	characteristic
231	C₂²×M₁₆	C₂²×C₁₁	1	1	yes	characteristic
232	#525	C₂²×C₁₁	1	2	yes	—
233	C₂²×C₄²	C₂²×C₁₁	1	1	yes	characteristic
234	#470	C₄×C₁₁	1	1	yes	characteristic, complemented
235	#470	C₄×C₁₁	1	1	yes	characteristic, complemented
236	#469	C₄×C₁₁	1	1	yes	characteristic, complemented
237	#469	C₄×C₁₁	1	1	yes	characteristic, complemented
238	#468	C₄×C₁₁	1	2	yes	complemented
239	#468	C₄×C₁₁	1	2	yes	complemented
240	#436	—	2	2	no	—
241	#436	—	2	2	no	—
242	#435	—	2	2	no	—
243	#435	—	2	2	no	—
244	C₂×#108	C₂²×C₁₁	1	1	yes	characteristic
245	C₂×#108	C₂²×C₁₁	1	1	yes	characteristic
246	#427	C₂²×C₁₁	1	1	yes	characteristic
247	#424	C₂²×C₁₁	1	2	yes	—
248	C₂×#104	C₂²×C₁₁	1	2	yes	—
249	C₂×#104	C₂²×C₁₁	1	2	yes	—
250	#416	C₂²×C₁₁	1	2	yes	—
251	#408	C₂²×C₁₁	1	2	yes	—
252	#407	C₂²×C₁₁	1	2	yes	—
253	#405	C₂²×C₁₁	1	2	yes	—
254	#341	C₂²×C₁₁	1	2	yes	—
255	#339	C₂²×C₁₁	1	2	yes	—
256	#339	C₂²×C₁₁	1	2	yes	—
257	#336	C₂²×C₁₁	1	2	yes	—
258	#336	C₂²×C₁₁	1	2	yes	—
259	C₂²×C₁₁	—	2	2	no	—
260	C₂²×C₁₁	—	2	1	no	—
261	C₂²×C₁₁	—	2	1	no	—
262	C₂²×C₁₁	—	2	2	no	—
263	C₂²×C₁₁	—	2	2	no	—
264	C₂²×C₁₁	—	4	2	no	—
265	C₂²×C₁₁	—	4	2	no	—
266	C₂²×C₁₁	—	4	2	no	—
267	C₂²×C₁₁	—	4	2	no	—
268	C₂²×C₁₁	—	4	2	no	—
269	C₂²×C₁₁	C₂×C₄×D₄	1	1	yes	characteristic
270	C₂²×C₁₁	#538	1	1	yes	characteristic
271	C₂²×C₁₁	#539	1	1	yes	characteristic
272	C₄×C₁₁	—	2	1	no	—
273	C₄×C₁₁	—	2	1	no	—
274	C₄×C₁₁	—	4	4	no	—
275	C₄×C₁₁	—	4	2	no	—
276	C₄×C₁₁	—	4	2	no	—
277	C₄×C₁₁	—	4	2	no	—
278	C₄×C₁₁	#518	1	1	yes	characteristic
279	C₄×C₁₁	#520	1	1	yes	characteristic
280	C₄×C₁₁	#534	1	1	yes	characteristic
281	C₄×C₁₁	#537	1	1	yes	characteristic
282	C₂×#41	C₂³×C₁₁	1	2	yes	—
283	C₂³×C₄	—	2	1	no	—
284	C₂³×C₄	C₂³×C₁₁	1	1	yes	characteristic
285	#135	—	4	1	no	—
286	#135	—	4	1	no	—
287	C₂×Q₁₆	C₂×C₄×C₁₁	1	1	yes	characteristic, complemented
288	C₂×SD₁₆	C₂×C₄×C₁₁	1	2	yes	complemented
289	C₂×D₈	C₂×C₄×C₁₁	1	1	yes	characteristic, complemented
290	#131	—	4	2	no	—
291	#131	—	4	2	no	—
292	C₂×M₁₆	—	2	2	no	—
293	C₂×M₁₆	—	4	1	no	—
294	C₂×M₁₆	—	4	1	no	—
295	C₂×M₁₆	—	4	1	no	—
296	C₂×M₁₆	—	4	1	no	—
297	C₂×M₁₆	C₂×C₄×C₁₁	1	1	yes	characteristic
298	C₂×M₁₆	C₂×C₄×C₁₁	1	1	yes	characteristic
299	C₂×M₁₆	C₂×C₄×C₁₁	1	1	yes	characteristic
300	C₂×M₁₆	C₂×C₄×C₁₁	1	1	yes	characteristic
301	C₂×M₁₆	D₄×C₁₁	1	1	yes	characteristic
302	C₂×M₁₆	D₄×C₁₁	1	2	yes	—
303	C₂×M₁₆	D₄×C₁₁	1	1	yes	characteristic
304	C₂×M₁₆	C₂³×C₁₁	1	2	yes	—
305	C₂×M₁₆	C₂³×C₁₁	1	2	yes	—
306	C₂²×C₈	—	2	2	no	—
307	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
308	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
309	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
310	#123	—	2	2	no	—
311	C₂²⋊Q₈	C₂×C₄×C₁₁	1	2	yes	—
312	C₂²⋊Q₈	C₂×C₄×C₁₁	1	2	yes	—
313	#121	C₂×C₄×C₁₁	1	2	yes	—
314	#121	C₂×C₄×C₁₁	1	2	yes	—
315	#120	—	2	2	no	—
316	C₄×D₄	—	2	2	no	—
317	C₄×D₄	—	2	2	no	—
318	#117	C₂³×C₁₁	1	2	yes	—
319	C₂×C₄²	—	2	1	no	—
320	C₂×C₄²	—	4	1	no	—
321	C₂×C₄²	—	4	1	no	—
322	C₂×C₄²	C₂³×C₁₁	1	2	yes	—
323	#108	—	4	1	no	—
324	#108	—	4	1	no	—
325	#107	C₂×C₄×C₁₁	1	2	yes	complemented
326	#106	C₂×C₄×C₁₁	1	1	yes	characteristic, complemented
327	#106	C₂×C₄×C₁₁	1	1	yes	characteristic, complemented
328	C₄⋊C₈	—	2	2	no	—
329	C₄⋊C₈	—	2	2	no	—
330	#104	—	4	2	no	—
331	#104	—	4	2	no	—
332	#103	C₂×C₄×C₁₁	1	2	yes	complemented
333	#103	C₂×C₄×C₁₁	1	2	yes	complemented
334	#102	C₂×C₄×C₁₁	1	2	yes	complemented
335	#102	C₂×C₄×C₁₁	1	2	yes	complemented
336	C₂²⋊C₈	—	2	2	no	—
337	C₂²⋊C₈	—	2	2	no	—
338	C₂²⋊C₈	—	2	2	no	—
339	C₂²⋊C₈	—	2	2	no	—
340	#97	—	2	2	no	—
341	C₄×C₈	—	2	2	no	—
342	C₂×C₁₁	—	2	1	no	—
343	C₂×C₁₁	—	2	1	no	—
344	C₂×C₁₁	—	4	1	no	—
345	C₂×C₁₁	—	4	1	no	—
346	C₂×C₁₁	—	8	2	no	—
347	C₂×C₁₁	#2325	1	1	yes	characteristic
348	C₂×C₁₁	#2956	1	2	yes	—
349	C₂⁴	C₁₁×#41	1	1	yes	characteristic
350	#41	—	2	2	no	—
351	#41	—	2	2	no	—
352	#41	—	2	2	no	—
353	#41	—	2	2	no	—
354	C₂×Q₈	C₂²×C₄×C₁₁	1	2	yes	—
355	C₂×D₄	—	2	2	no	—
356	C₂×D₄	—	2	2	no	—
357	C₂×D₄	—	2	2	no	—
358	C₂×D₄	C₂²×C₄×C₁₁	1	2	yes	—
359	C₂²×C₄	—	2	1	no	—
360	C₂²×C₄	—	2	1	no	—
361	C₂²×C₄	—	2	1	no	—
362	C₂²×C₄	—	2	1	no	—
363	C₂²×C₄	—	2	2	no	—
364	C₂²×C₄	—	2	2	no	—
365	C₂²×C₄	—	4	4	no	—
366	C₂²×C₄	—	4	2	no	—
367	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
368	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
369	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
370	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
371	C₂²×C₄	C₁₁×#41	1	1	yes	characteristic
372	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
373	Q₁₆	—	4	1	no	—
374	SD₁₆	—	4	2	no	—
375	D₈	—	4	1	no	—
376	M₁₆	—	2	2	no	—
377	M₁₆	—	2	2	no	—
378	M₁₆	—	2	2	no	—
379	M₁₆	—	2	2	no	—
380	M₁₆	—	4	1	no	—
381	M₁₆	—	4	1	no	—
382	M₁₆	—	4	1	no	—
383	M₁₆	—	4	1	no	—
384	M₁₆	—	4	1	no	—
385	M₁₆	—	4	2	no	—
386	M₁₆	—	4	1	no	—
387	M₁₆	—	4	4	no	—
388	C₂×C₈	—	2	1	no	—
389	C₂×C₈	—	2	1	no	—
390	C₂×C₈	—	2	2	no	—
391	C₂×C₈	—	2	2	no	—
392	C₂×C₈	—	2	1	no	—
393	C₂×C₈	—	2	1	no	—
394	C₂×C₈	—	2	2	no	—
395	C₂×C₈	—	2	2	no	—
396	C₂×C₈	—	4	4	no	—
397	C₂×C₈	C₂²×C₄×C₁₁	1	1	yes	characteristic
398	C₂×C₈	C₂²×C₄×C₁₁	1	1	yes	characteristic
399	C₂×C₈	C₂²×C₄×C₁₁	1	1	yes	characteristic
400	C₂×C₈	C₂²×C₄×C₁₁	1	1	yes	characteristic
401	C₂×C₈	C₂×D₄×C₁₁	1	2	yes	—
402	C₂×C₈	C₂×D₄×C₁₁	1	2	yes	—
403	C₄⋊C₄	—	2	2	no	—
404	C₄⋊C₄	—	2	2	no	—
405	C₄⋊C₄	C₂²×C₄×C₁₁	1	2	yes	—
406	C₄⋊C₄	C₂²×C₄×C₁₁	1	2	yes	—
407	C₂²⋊C₄	—	2	2	no	—
408	C₂²⋊C₄	—	2	2	no	—
409	C₂²⋊C₄	—	2	2	no	—
410	C₂²⋊C₄	—	2	2	no	—
411	C₂²⋊C₄	—	2	2	no	—
412	C₄²	—	2	2	no	—
413	C₄²	—	2	2	no	—
414	C₄²	—	2	2	no	—
415	C₄²	—	4	2	no	—
416	C₁₁	#22207	1	1	yes	characteristic, direct product factor, Sylow
417	C₂³	—	2	1	no	—
418	C₂³	—	2	1	no	—
419	C₂³	—	2	2	no	—
420	C₂³	—	4	2	no	—
421	C₂³	C₄×D₄×C₁₁	1	1	yes	characteristic
422	C₂³	C₄×D₄×C₁₁	1	1	yes	characteristic
423	C₂³	C₂×C₁₁×#41	1	1	yes	characteristic
424	Q₈	—	2	2	no	—
425	Q₈	—	2	2	no	—
426	D₄	—	2	2	no	—
427	D₄	—	2	2	no	—
428	D₄	—	4	2	no	—
429	D₄	—	4	2	no	—
430	D₄	—	8	2	no	—
431	D₄	—	8	2	no	—
432	C₂×C₄	—	2	1	no	—
433	C₂×C₄	—	2	1	no	—
434	C₂×C₄	—	2	1	no	—
435	C₂×C₄	—	2	1	no	—
436	C₂×C₄	—	2	1	no	—
437	C₂×C₄	—	2	1	no	—
438	C₂×C₄	—	2	1	no	—
439	C₂×C₄	—	2	1	no	—
440	C₂×C₄	—	2	1	no	—
441	C₂×C₄	—	2	1	no	—
442	C₂×C₄	—	2	4	no	—
443	C₂×C₄	—	2	2	no	—
444	C₂×C₄	—	2	2	no	—
445	C₂×C₄	—	2	2	no	—
446	C₂×C₄	—	4	2	no	—
447	C₂×C₄	—	4	8	no	—
448	C₂×C₄	—	4	2	no	—
449	C₂×C₄	—	4	2	no	—
450	C₂×C₄	—	4	2	no	—
451	C₂×C₄	C₄×D₄×C₁₁	1	1	yes	characteristic
452	C₂×C₄	C₄×D₄×C₁₁	1	1	yes	characteristic
453	C₂×C₄	C₂³×C₄×C₁₁	1	1	yes	characteristic
454	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
455	C₂×C₄	C₁₁×H(5,𝔽₂)	1	1	yes	characteristic
456	C₂×C₄	C₁₁×H(5,𝔽₂)	1	1	yes	characteristic
457	C₂×C₄	C₁₁×H(5,𝔽₂)	1	1	yes	characteristic
458	C₂×C₄	C₁₁×2₋¹⁺⁴	1	1	yes	characteristic
459	C₈	—	2	1	no	—
460	C₈	—	2	1	no	—
461	C₈	—	2	1	no	—
462	C₈	—	2	1	no	—
463	C₈	—	2	2	no	—
464	C₈	—	2	2	no	—
465	C₈	—	4	2	no	—
466	C₈	—	4	2	no	—
467	C₂²	—	2	2	no	—
468	C₂²	—	2	2	no	—
469	C₂²	—	2	2	no	—
470	C₂²	—	2	1	no	—
471	C₂²	—	2	1	no	—
472	C₂²	—	4	2	no	—
473	C₂²	—	4	2	no	—
474	C₂²	—	4	2	no	—
475	C₂²	—	4	2	no	—
476	C₂²	—	4	2	no	—
477	C₂²	C₂×C₄×D₄×C₁₁	1	1	yes	characteristic
478	C₂²	C₁₁×#538	1	1	yes	characteristic
479	C₂²	C₁₁×#539	1	1	yes	characteristic
480	C₄	—	2	1	no	—
481	C₄	—	2	1	no	—
482	C₄	—	4	4	no	—
483	C₄	—	4	2	no	—
484	C₄	—	4	2	no	—
485	C₄	—	4	2	no	—
486	C₄	C₁₁×#518	1	1	yes	characteristic
487	C₄	C₁₁×#520	1	1	yes	characteristic
488	C₄	C₁₁×#534	1	1	yes	characteristic
489	C₄	C₁₁×#537	1	1	yes	characteristic
490	C₂	—	2	1	no	—
491	C₂	—	2	1	no	—
492	C₂	—	4	1	no	—
493	C₂	—	4	1	no	—
494	C₂	—	8	2	no	—
495	C₂	C₁₁×#2325	1	1	yes	characteristic
496	C₂	C₁₁×#2956	1	2	yes	—

	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×#3054	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₁ ◁ C₂²×C₁₁×M₁₆ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₁×#2930	C₂	semidirect
3. C₁₁×#1929	C₂	semidirect
4. C₁₁×#1922	C₂	semidirect
5. C₁₁×#1896	C₂	semidirect
6. C₁₁×#1876	C₂	semidirect
7. C₁₁×#1866	C₂	semidirect
8. C₁₁×#1811	C₂	semidirect
9. C₁₁×#1728	C₂	semidirect
16. C₁₁×#470	C₄	semidirect
17. C₁₁×#470	C₄	semidirect
18. C₁₁×#469	C₄	semidirect
19. C₁₁×#469	C₄	semidirect
20. C₁₁×#468	C₄	semidirect
21. C₁₁×#468	C₄	semidirect
46. C₂×C₁₁×Q₁₆	C₂×C₄	semidirect
47. C₂×C₁₁×SD₁₆	C₂×C₄	semidirect
48. C₂×C₁₁×D₈	C₂×C₄	semidirect
84. C₁₁×#107	C₂×C₄	semidirect
85. C₁₁×#106	C₂×C₄	semidirect
86. C₁₁×#106	C₂×C₄	semidirect
91. C₁₁×#103	C₂×C₄	semidirect
92. C₁₁×#103	C₂×C₄	semidirect
93. C₁₁×#102	C₂×C₄	semidirect
94. C₁₁×#102	C₂×C₄	semidirect
101. #22207	C₁₁	direct (N × H)
170. #2930	C₂×C₁₁	semidirect
171. #1929	C₂×C₁₁	semidirect
172. #1922	C₂×C₁₁	semidirect
173. #1896	C₂×C₁₁	semidirect
174. #1876	C₂×C₁₁	semidirect
175. #1866	C₂×C₁₁	semidirect
176. #1811	C₂×C₁₁	semidirect
177. #1728	C₂×C₁₁	semidirect
234. #470	C₄×C₁₁	semidirect
235. #470	C₄×C₁₁	semidirect
236. #469	C₄×C₁₁	semidirect
237. #469	C₄×C₁₁	semidirect
238. #468	C₄×C₁₁	semidirect
239. #468	C₄×C₁₁	semidirect
287. C₂×Q₁₆	C₂×C₄×C₁₁	semidirect
288. C₂×SD₁₆	C₂×C₄×C₁₁	semidirect
289. C₂×D₈	C₂×C₄×C₁₁	semidirect
325. #107	C₂×C₄×C₁₁	semidirect
326. #106	C₂×C₄×C₁₁	semidirect
327. #106	C₂×C₄×C₁₁	semidirect
332. #103	C₂×C₄×C₁₁	semidirect
333. #103	C₂×C₄×C₁₁	semidirect
334. #102	C₂×C₄×C₁₁	semidirect
335. #102	C₂×C₄×C₁₁	semidirect
416. C₁₁	#22207	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×#3054	2
C₁₁×#2930	2
C₁₁×#1929	2
C₁₁×#1922	2
C₁₁×#1896	2
C₁₁×#1876	2
C₁₁×#1866	2
C₁₁×#1811	2
C₁₁×#1728	2
#22207	11

Subgroups — C11×#22207 #14599400

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#22207 #14599400