Subgroups — C₁₁×#22204 #14599397

Order 2816.

838 conjugacy classes of subgroups.

The subgroup lattice has 510 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×#3050	C₂	1	1	yes	maximal, characteristic
2	C₁₁×#2929	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×#1810	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₁₁×#336	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	C₂³×C₈×C₁₁	C₂²	1	1	yes	characteristic
13	C₂³×C₈×C₁₁	C₂²	1	1	yes	characteristic
14	C₁₁×#525	C₂²	1	2	yes	—
15	C₂²×C₄²×C₁₁	C₂²	1	1	yes	characteristic
16	C₁₁×#467	C₄	1	1	yes	characteristic, complemented
17	C₁₁×#467	C₄	1	1	yes	characteristic, complemented
18	C₁₁×#466	C₄	1	1	yes	characteristic, complemented
19	C₁₁×#466	C₄	1	1	yes	characteristic, complemented
20	C₁₁×#465	C₄	1	2	yes	complemented
21	C₁₁×#465	C₄	1	2	yes	complemented
22	C₁₁×#435	—	2	2	no	—
23	C₁₁×#435	—	2	2	no	—
24	C₈×D₄×C₁₁	—	2	2	no	—
25	C₈×D₄×C₁₁	—	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	C₂³	1	2	yes	—
53	C₂×C₁₁×M₁₆	C₂³	1	2	yes	—
54	C₂²×C₈×C₁₁	—	2	2	no	—
55	C₂²×C₈×C₁₁	—	4	1	no	—
56	C₂²×C₈×C₁₁	—	4	1	no	—
57	C₂²×C₈×C₁₁	—	4	1	no	—
58	C₂²×C₈×C₁₁	—	4	1	no	—
59	C₂²×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
60	C₂²×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
61	C₂²×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
62	C₂²×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
63	C₂²×C₈×C₁₁	D₄	1	1	yes	characteristic
64	C₂²×C₈×C₁₁	D₄	1	2	yes	—
65	C₂²×C₈×C₁₁	D₄	1	1	yes	characteristic
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	1	yes	characteristic, complemented
85	C₁₁×#107	C₂×C₄	1	1	yes	characteristic, complemented
86	C₁₁×#106	C₂×C₄	1	2	yes	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	#22204	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	4	no	—
117	C₂²×C₄×C₁₁	—	2	2	no	—
118	C₂²×C₄×C₁₁	—	2	2	no	—
119	C₂²×C₄×C₁₁	—	4	2	no	—
120	C₂²×C₄×C₁₁	—	4	2	no	—
121	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
122	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
123	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
124	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
125	C₂²×C₄×C₁₁	#41	1	1	yes	characteristic
126	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
127	C₁₁×Q₁₆	—	4	1	no	—
128	C₁₁×SD₁₆	—	4	2	no	—
129	C₁₁×D₈	—	4	1	no	—
130	C₁₁×M₁₆	—	2	2	no	—
131	C₁₁×M₁₆	—	2	2	no	—
132	C₁₁×M₁₆	—	2	2	no	—
133	C₁₁×M₁₆	—	2	2	no	—
134	C₁₁×M₁₆	—	4	4	no	—
135	C₂×C₈×C₁₁	—	2	2	no	—
136	C₂×C₈×C₁₁	—	2	2	no	—
137	C₂×C₈×C₁₁	—	2	1	no	—
138	C₂×C₈×C₁₁	—	2	1	no	—
139	C₂×C₈×C₁₁	—	2	2	no	—
140	C₂×C₈×C₁₁	—	2	2	no	—
141	C₂×C₈×C₁₁	—	2	1	no	—
142	C₂×C₈×C₁₁	—	2	1	no	—
143	C₂×C₈×C₁₁	—	4	1	no	—
144	C₂×C₈×C₁₁	—	4	1	no	—
145	C₂×C₈×C₁₁	—	4	1	no	—
146	C₂×C₈×C₁₁	—	4	1	no	—
147	C₂×C₈×C₁₁	—	4	1	no	—
148	C₂×C₈×C₁₁	—	4	2	no	—
149	C₂×C₈×C₁₁	—	4	1	no	—
150	C₂×C₈×C₁₁	—	4	4	no	—
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	C₂²×C₄	1	1	yes	characteristic
155	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
156	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
157	C₁₁×C₄⋊C₄	—	2	2	no	—
158	C₁₁×C₄⋊C₄	—	2	2	no	—
159	C₁₁×C₄⋊C₄	C₂²×C₄	1	2	yes	—
160	C₁₁×C₄⋊C₄	C₂²×C₄	1	2	yes	—
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	C₁₁×C₂²⋊C₄	—	2	2	no	—
166	C₄²×C₁₁	—	2	2	no	—
167	C₄²×C₁₁	—	2	2	no	—
168	C₄²×C₁₁	—	2	2	no	—
169	C₄²×C₁₁	—	4	2	no	—
170	#3050	C₂×C₁₁	1	1	yes	characteristic
171	#2929	C₂×C₁₁	1	2	yes	complemented
172	#1929	C₂×C₁₁	1	2	yes	complemented
173	#1922	C₂×C₁₁	1	2	yes	complemented
174	#1896	C₂×C₁₁	1	2	yes	complemented
175	#1876	C₂×C₁₁	1	2	yes	complemented
176	#1866	C₂×C₁₁	1	2	yes	complemented
177	#1810	C₂×C₁₁	1	1	yes	characteristic, complemented
178	C₂×#336	C₂×C₁₁	1	1	yes	characteristic, complemented
179	C₂³×C₁₁	—	2	1	no	—
180	C₂³×C₁₁	—	2	1	no	—
181	C₂³×C₁₁	—	2	2	no	—
182	C₂³×C₁₁	—	2	2	no	—
183	C₂³×C₁₁	—	2	2	no	—
184	C₂³×C₁₁	C₄×D₄	1	1	yes	characteristic
185	C₂³×C₁₁	C₄×D₄	1	1	yes	characteristic
186	C₂³×C₁₁	C₂×#41	1	1	yes	characteristic
187	Q₈×C₁₁	—	2	2	no	—
188	Q₈×C₁₁	—	2	2	no	—
189	D₄×C₁₁	—	2	2	no	—
190	D₄×C₁₁	—	2	2	no	—
191	D₄×C₁₁	—	4	2	no	—
192	D₄×C₁₁	—	4	2	no	—
193	D₄×C₁₁	—	4	4	no	—
194	D₄×C₁₁	—	4	4	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	1	no	—
204	C₂×C₄×C₁₁	—	2	1	no	—
205	C₂×C₄×C₁₁	—	2	4	no	—
206	C₂×C₄×C₁₁	—	2	2	no	—
207	C₂×C₄×C₁₁	—	2	2	no	—
208	C₂×C₄×C₁₁	—	2	2	no	—
209	C₂×C₄×C₁₁	—	4	8	no	—
210	C₂×C₄×C₁₁	—	4	2	no	—
211	C₂×C₄×C₁₁	—	4	2	no	—
212	C₂×C₄×C₁₁	—	4	2	no	—
213	C₂×C₄×C₁₁	—	4	2	no	—
214	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
215	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
216	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
217	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
218	C₂×C₄×C₁₁	H(5,𝔽₂)	1	1	yes	characteristic
219	C₂×C₄×C₁₁	H(5,𝔽₂)	1	1	yes	characteristic
220	C₂×C₄×C₁₁	H(5,𝔽₂)	1	1	yes	characteristic
221	C₂×C₄×C₁₁	2₋¹⁺⁴	1	1	yes	characteristic
222	C₈×C₁₁	—	2	1	no	—
223	C₈×C₁₁	—	2	1	no	—
224	C₈×C₁₁	—	2	1	no	—
225	C₈×C₁₁	—	2	1	no	—
226	C₈×C₁₁	—	2	2	no	—
227	C₈×C₁₁	—	2	2	no	—
228	C₈×C₁₁	—	4	2	no	—
229	C₈×C₁₁	—	4	2	no	—
230	C₂×#135	C₂²×C₁₁	1	1	yes	characteristic
231	C₂×#131	C₂²×C₁₁	1	2	yes	—
232	C₂³×C₈	C₂²×C₁₁	1	1	yes	characteristic
233	C₂³×C₈	C₂²×C₁₁	1	1	yes	characteristic
234	#525	C₂²×C₁₁	1	2	yes	—
235	C₂²×C₄²	C₂²×C₁₁	1	1	yes	characteristic
236	#467	C₄×C₁₁	1	1	yes	characteristic, complemented
237	#467	C₄×C₁₁	1	1	yes	characteristic, complemented
238	#466	C₄×C₁₁	1	1	yes	characteristic, complemented
239	#466	C₄×C₁₁	1	1	yes	characteristic, complemented
240	#465	C₄×C₁₁	1	2	yes	complemented
241	#465	C₄×C₁₁	1	2	yes	complemented
242	#435	—	2	2	no	—
243	#435	—	2	2	no	—
244	C₈×D₄	—	2	2	no	—
245	C₈×D₄	—	2	2	no	—
246	C₂×#108	C₂²×C₁₁	1	1	yes	characteristic
247	C₂×#108	C₂²×C₁₁	1	1	yes	characteristic
248	#427	C₂²×C₁₁	1	1	yes	characteristic
249	#424	C₂²×C₁₁	1	2	yes	—
250	C₂×#104	C₂²×C₁₁	1	2	yes	—
251	C₂×#104	C₂²×C₁₁	1	2	yes	—
252	#416	C₂²×C₁₁	1	2	yes	—
253	#408	C₂²×C₁₁	1	2	yes	—
254	#407	C₂²×C₁₁	1	2	yes	—
255	#405	C₂²×C₁₁	1	2	yes	—
256	#341	C₂²×C₁₁	1	2	yes	—
257	#339	C₂²×C₁₁	1	2	yes	—
258	#339	C₂²×C₁₁	1	2	yes	—
259	#336	C₂²×C₁₁	1	2	yes	—
260	#336	C₂²×C₁₁	1	2	yes	—
261	C₂²×C₁₁	—	2	4	no	—
262	C₂²×C₁₁	—	2	4	no	—
263	C₂²×C₁₁	—	2	1	no	—
264	C₂²×C₁₁	—	2	1	no	—
265	C₂²×C₁₁	—	2	1	no	—
266	C₂²×C₁₁	—	2	1	no	—
267	C₂²×C₁₁	—	2	1	no	—
268	C₂²×C₁₁	—	2	1	no	—
269	C₂²×C₁₁	—	4	2	no	—
270	C₂²×C₁₁	—	4	2	no	—
271	C₂²×C₁₁	—	4	2	no	—
272	C₂²×C₁₁	#443	1	2	yes	—
273	C₂²×C₁₁	#444	1	2	yes	—
274	C₂²×C₁₁	C₂×C₄×D₄	1	1	yes	characteristic
275	C₂²×C₁₁	#538	1	1	yes	characteristic
276	C₂²×C₁₁	#539	1	1	yes	characteristic
277	C₄×C₁₁	—	2	1	no	—
278	C₄×C₁₁	—	2	1	no	—
279	C₄×C₁₁	—	4	4	no	—
280	C₄×C₁₁	—	4	2	no	—
281	C₄×C₁₁	—	4	2	no	—
282	C₄×C₁₁	—	4	2	no	—
283	C₄×C₁₁	#518	1	1	yes	characteristic
284	C₄×C₁₁	#520	1	1	yes	characteristic
285	C₄×C₁₁	#534	1	1	yes	characteristic
286	C₄×C₁₁	#537	1	1	yes	characteristic
287	C₂×#41	C₂³×C₁₁	1	2	yes	—
288	C₂³×C₄	—	2	1	no	—
289	C₂³×C₄	C₂³×C₁₁	1	1	yes	characteristic
290	#135	—	4	1	no	—
291	#135	—	4	1	no	—
292	C₂×Q₁₆	C₂×C₄×C₁₁	1	1	yes	characteristic, complemented
293	C₂×SD₁₆	C₂×C₄×C₁₁	1	2	yes	complemented
294	C₂×D₈	C₂×C₄×C₁₁	1	1	yes	characteristic, complemented
295	#131	—	4	2	no	—
296	#131	—	4	2	no	—
297	C₂×M₁₆	—	2	2	no	—
298	C₂×M₁₆	C₂³×C₁₁	1	2	yes	—
299	C₂×M₁₆	C₂³×C₁₁	1	2	yes	—
300	C₂²×C₈	—	2	2	no	—
301	C₂²×C₈	—	4	1	no	—
302	C₂²×C₈	—	4	1	no	—
303	C₂²×C₈	—	4	1	no	—
304	C₂²×C₈	—	4	1	no	—
305	C₂²×C₈	C₂×C₄×C₁₁	1	1	yes	characteristic
306	C₂²×C₈	C₂×C₄×C₁₁	1	1	yes	characteristic
307	C₂²×C₈	C₂×C₄×C₁₁	1	1	yes	characteristic
308	C₂²×C₈	C₂×C₄×C₁₁	1	1	yes	characteristic
309	C₂²×C₈	D₄×C₁₁	1	1	yes	characteristic
310	C₂²×C₈	D₄×C₁₁	1	2	yes	—
311	C₂²×C₈	D₄×C₁₁	1	1	yes	characteristic
312	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
313	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
314	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
315	#123	—	2	2	no	—
316	C₂²⋊Q₈	C₂×C₄×C₁₁	1	2	yes	—
317	C₂²⋊Q₈	C₂×C₄×C₁₁	1	2	yes	—
318	#121	C₂×C₄×C₁₁	1	2	yes	—
319	#121	C₂×C₄×C₁₁	1	2	yes	—
320	#120	—	2	2	no	—
321	C₄×D₄	—	2	2	no	—
322	C₄×D₄	—	2	2	no	—
323	#117	C₂³×C₁₁	1	2	yes	—
324	C₂×C₄²	—	2	1	no	—
325	C₂×C₄²	—	4	1	no	—
326	C₂×C₄²	—	4	1	no	—
327	C₂×C₄²	C₂³×C₁₁	1	2	yes	—
328	#108	—	4	1	no	—
329	#108	—	4	1	no	—
330	#107	C₂×C₄×C₁₁	1	1	yes	characteristic, complemented
331	#107	C₂×C₄×C₁₁	1	1	yes	characteristic, complemented
332	#106	C₂×C₄×C₁₁	1	2	yes	complemented
333	C₄⋊C₈	—	2	2	no	—
334	C₄⋊C₈	—	2	2	no	—
335	#104	—	4	2	no	—
336	#104	—	4	2	no	—
337	#103	C₂×C₄×C₁₁	1	2	yes	complemented
338	#103	C₂×C₄×C₁₁	1	2	yes	complemented
339	#102	C₂×C₄×C₁₁	1	2	yes	complemented
340	#102	C₂×C₄×C₁₁	1	2	yes	complemented
341	C₂²⋊C₈	—	2	2	no	—
342	C₂²⋊C₈	—	2	2	no	—
343	C₂²⋊C₈	—	2	2	no	—
344	C₂²⋊C₈	—	2	2	no	—
345	#97	—	2	2	no	—
346	C₄×C₈	—	2	2	no	—
347	C₂×C₁₁	—	2	1	no	—
348	C₂×C₁₁	—	2	1	no	—
349	C₂×C₁₁	—	2	2	no	—
350	C₂×C₁₁	—	2	2	no	—
351	C₂×C₁₁	—	8	2	no	—
352	C₂×C₁₁	#2325	1	1	yes	characteristic
353	C₂×C₁₁	C₂×#443	1	1	yes	characteristic
354	C₂×C₁₁	C₂×#444	1	1	yes	characteristic
355	C₂⁴	C₁₁×#41	1	1	yes	characteristic
356	#41	—	2	2	no	—
357	#41	—	2	2	no	—
358	#41	—	2	2	no	—
359	#41	—	2	2	no	—
360	C₂×Q₈	C₂²×C₄×C₁₁	1	2	yes	—
361	C₂×D₄	—	2	2	no	—
362	C₂×D₄	—	2	2	no	—
363	C₂×D₄	—	2	2	no	—
364	C₂×D₄	C₂²×C₄×C₁₁	1	2	yes	—
365	C₂²×C₄	—	2	1	no	—
366	C₂²×C₄	—	2	1	no	—
367	C₂²×C₄	—	2	1	no	—
368	C₂²×C₄	—	2	1	no	—
369	C₂²×C₄	—	2	4	no	—
370	C₂²×C₄	—	2	2	no	—
371	C₂²×C₄	—	2	2	no	—
372	C₂²×C₄	—	4	2	no	—
373	C₂²×C₄	—	4	2	no	—
374	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
375	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
376	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
377	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
378	C₂²×C₄	C₁₁×#41	1	1	yes	characteristic
379	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
380	Q₁₆	—	4	1	no	—
381	SD₁₆	—	4	2	no	—
382	D₈	—	4	1	no	—
383	M₁₆	—	2	2	no	—
384	M₁₆	—	2	2	no	—
385	M₁₆	—	2	2	no	—
386	M₁₆	—	2	2	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	1	no	—
397	C₂×C₈	—	4	1	no	—
398	C₂×C₈	—	4	1	no	—
399	C₂×C₈	—	4	1	no	—
400	C₂×C₈	—	4	1	no	—
401	C₂×C₈	—	4	2	no	—
402	C₂×C₈	—	4	1	no	—
403	C₂×C₈	—	4	4	no	—
404	C₂×C₈	C₂²×C₄×C₁₁	1	1	yes	characteristic
405	C₂×C₈	C₂²×C₄×C₁₁	1	1	yes	characteristic
406	C₂×C₈	C₂²×C₄×C₁₁	1	1	yes	characteristic
407	C₂×C₈	C₂²×C₄×C₁₁	1	1	yes	characteristic
408	C₂×C₈	C₂×D₄×C₁₁	1	2	yes	—
409	C₂×C₈	C₂×D₄×C₁₁	1	2	yes	—
410	C₄⋊C₄	—	2	2	no	—
411	C₄⋊C₄	—	2	2	no	—
412	C₄⋊C₄	C₂²×C₄×C₁₁	1	2	yes	—
413	C₄⋊C₄	C₂²×C₄×C₁₁	1	2	yes	—
414	C₂²⋊C₄	—	2	2	no	—
415	C₂²⋊C₄	—	2	2	no	—
416	C₂²⋊C₄	—	2	2	no	—
417	C₂²⋊C₄	—	2	2	no	—
418	C₂²⋊C₄	—	2	2	no	—
419	C₄²	—	2	2	no	—
420	C₄²	—	2	2	no	—
421	C₄²	—	2	2	no	—
422	C₄²	—	4	2	no	—
423	C₁₁	#22204	1	1	yes	characteristic, direct product factor, Sylow
424	C₂³	—	2	1	no	—
425	C₂³	—	2	1	no	—
426	C₂³	—	2	2	no	—
427	C₂³	—	2	2	no	—
428	C₂³	—	2	2	no	—
429	C₂³	C₄×D₄×C₁₁	1	1	yes	characteristic
430	C₂³	C₄×D₄×C₁₁	1	1	yes	characteristic
431	C₂³	C₂×C₁₁×#41	1	1	yes	characteristic
432	Q₈	—	2	2	no	—
433	Q₈	—	2	2	no	—
434	D₄	—	2	2	no	—
435	D₄	—	2	2	no	—
436	D₄	—	4	2	no	—
437	D₄	—	4	2	no	—
438	D₄	—	4	4	no	—
439	D₄	—	4	4	no	—
440	C₂×C₄	—	2	1	no	—
441	C₂×C₄	—	2	1	no	—
442	C₂×C₄	—	2	1	no	—
443	C₂×C₄	—	2	1	no	—
444	C₂×C₄	—	2	1	no	—
445	C₂×C₄	—	2	1	no	—
446	C₂×C₄	—	2	1	no	—
447	C₂×C₄	—	2	1	no	—
448	C₂×C₄	—	2	1	no	—
449	C₂×C₄	—	2	1	no	—
450	C₂×C₄	—	2	4	no	—
451	C₂×C₄	—	2	2	no	—
452	C₂×C₄	—	2	2	no	—
453	C₂×C₄	—	2	2	no	—
454	C₂×C₄	—	4	8	no	—
455	C₂×C₄	—	4	2	no	—
456	C₂×C₄	—	4	2	no	—
457	C₂×C₄	—	4	2	no	—
458	C₂×C₄	—	4	2	no	—
459	C₂×C₄	C₄×D₄×C₁₁	1	1	yes	characteristic
460	C₂×C₄	C₄×D₄×C₁₁	1	1	yes	characteristic
461	C₂×C₄	C₂³×C₄×C₁₁	1	1	yes	characteristic
462	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
463	C₂×C₄	C₁₁×H(5,𝔽₂)	1	1	yes	characteristic
464	C₂×C₄	C₁₁×H(5,𝔽₂)	1	1	yes	characteristic
465	C₂×C₄	C₁₁×H(5,𝔽₂)	1	1	yes	characteristic
466	C₂×C₄	C₁₁×2₋¹⁺⁴	1	1	yes	characteristic
467	C₈	—	2	1	no	—
468	C₈	—	2	1	no	—
469	C₈	—	2	1	no	—
470	C₈	—	2	1	no	—
471	C₈	—	2	2	no	—
472	C₈	—	2	2	no	—
473	C₈	—	4	2	no	—
474	C₈	—	4	2	no	—
475	C₂²	—	2	4	no	—
476	C₂²	—	2	4	no	—
477	C₂²	—	2	1	no	—
478	C₂²	—	2	1	no	—
479	C₂²	—	2	1	no	—
480	C₂²	—	2	1	no	—
481	C₂²	—	2	1	no	—
482	C₂²	—	2	1	no	—
483	C₂²	—	4	2	no	—
484	C₂²	—	4	2	no	—
485	C₂²	—	4	2	no	—
486	C₂²	C₁₁×#443	1	2	yes	—
487	C₂²	C₁₁×#444	1	2	yes	—
488	C₂²	C₂×C₄×D₄×C₁₁	1	1	yes	characteristic
489	C₂²	C₁₁×#538	1	1	yes	characteristic
490	C₂²	C₁₁×#539	1	1	yes	characteristic
491	C₄	—	2	1	no	—
492	C₄	—	2	1	no	—
493	C₄	—	4	4	no	—
494	C₄	—	4	2	no	—
495	C₄	—	4	2	no	—
496	C₄	—	4	2	no	—
497	C₄	C₁₁×#518	1	1	yes	characteristic
498	C₄	C₁₁×#520	1	1	yes	characteristic
499	C₄	C₁₁×#534	1	1	yes	characteristic
500	C₄	C₁₁×#537	1	1	yes	characteristic
501	C₂	—	2	1	no	—
502	C₂	—	2	1	no	—
503	C₂	—	2	2	no	—
504	C₂	—	2	2	no	—
505	C₂	—	8	2	no	—
506	C₂	C₁₁×#2325	1	1	yes	characteristic
507	C₂	C₂×C₁₁×#443	1	1	yes	characteristic
508	C₂	C₂×C₁₁×#444	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×#3050	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₁ ◁ C₂³×C₈×C₁₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₁×#2929	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×#1810	C₂	semidirect
9. C₂×C₁₁×#336	C₂	semidirect
16. C₁₁×#467	C₄	semidirect
17. C₁₁×#467	C₄	semidirect
18. C₁₁×#466	C₄	semidirect
19. C₁₁×#466	C₄	semidirect
20. C₁₁×#465	C₄	semidirect
21. C₁₁×#465	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×#107	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. #22204	C₁₁	direct (N × H)
171. #2929	C₂×C₁₁	semidirect
172. #1929	C₂×C₁₁	semidirect
173. #1922	C₂×C₁₁	semidirect
174. #1896	C₂×C₁₁	semidirect
175. #1876	C₂×C₁₁	semidirect
176. #1866	C₂×C₁₁	semidirect
177. #1810	C₂×C₁₁	semidirect
178. C₂×#336	C₂×C₁₁	semidirect
236. #467	C₄×C₁₁	semidirect
237. #467	C₄×C₁₁	semidirect
238. #466	C₄×C₁₁	semidirect
239. #466	C₄×C₁₁	semidirect
240. #465	C₄×C₁₁	semidirect
241. #465	C₄×C₁₁	semidirect
292. C₂×Q₁₆	C₂×C₄×C₁₁	semidirect
293. C₂×SD₁₆	C₂×C₄×C₁₁	semidirect
294. C₂×D₈	C₂×C₄×C₁₁	semidirect
330. #107	C₂×C₄×C₁₁	semidirect
331. #107	C₂×C₄×C₁₁	semidirect
332. #106	C₂×C₄×C₁₁	semidirect
337. #103	C₂×C₄×C₁₁	semidirect
338. #103	C₂×C₄×C₁₁	semidirect
339. #102	C₂×C₄×C₁₁	semidirect
340. #102	C₂×C₄×C₁₁	semidirect
423. C₁₁	#22204	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×#3050	2
C₁₁×#2929	2
C₁₁×#1929	2
C₁₁×#1922	2
C₁₁×#1896	2
C₁₁×#1876	2
C₁₁×#1866	2
C₁₁×#1810	2
C₂×C₁₁×#336	2
#22204	11

Subgroups — C11×#22204 #14599397

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#22204 #14599397