Subgroups — C₁₁×#23046 #14600239

Order 2816.

896 conjugacy classes of subgroups.

The subgroup lattice has 488 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₁×#472	C₂	1	1	yes	maximal, characteristic
2	C₁₁×#2948	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₁×#2946	C₂	1	2	yes	maximal, complemented
4	C₁₁×#2913	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₁×#1970	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₁×#1952	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₁×#1931	C₂	1	2	yes	maximal, complemented
8	C₁₁×#1883	C₂	1	2	yes	maximal, complemented
9	C₁₁×#1856	C₂	1	2	yes	maximal, complemented
10	C₁₁×#1772	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₁×#1764	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₁×AGL(1,ℤ/8)	C₂²	1	2	yes	—
13	C₂²×C₁₁×D₈	C₂²	1	1	yes	characteristic
14	C₂×C₁₁×#131	C₂²	1	1	yes	characteristic
15	C₁₁×#520	C₂²	1	2	yes	—
16	C₁₁×#518	C₂²	1	2	yes	—
17	C₁₁×#472	C₄	1	8	yes	complemented
18	C₁₁×#442	—	2	2	no	—
19	C₁₁×#442	—	2	2	no	—
20	C₁₁×#440	—	2	2	no	—
21	C₄×C₁₁×SD₁₆	—	2	2	no	—
22	C₄×C₁₁×D₈	—	2	1	no	—
23	C₄×C₁₁×D₈	—	2	1	no	—
24	C₄×C₁₁×D₈	—	2	2	no	—
25	C₂×C₁₁×#108	C₂²	1	1	yes	characteristic
26	C₁₁×#428	—	2	2	no	—
27	C₁₁×#428	C₂²	1	2	yes	—
28	C₁₁×#428	C₂²	1	2	yes	—
29	C₁₁×#427	—	2	1	no	—
30	C₁₁×#427	C₂²	1	1	yes	characteristic
31	C₂×C₁₁×#107	—	2	1	no	—
32	C₂×C₁₁×#107	C₂²	1	1	yes	characteristic
33	C₂×C₁₁×#104	C₂²	1	1	yes	characteristic
34	C₁₁×#418	C₂²	1	2	yes	—
35	C₁₁×#416	C₂²	1	1	yes	characteristic
36	C₂×C₁₁×#102	C₂²	1	2	yes	—
37	C₂×C₁₁×#100	C₂²	1	2	yes	—
38	C₁₁×#405	C₂²	1	2	yes	—
39	C₁₁×#405	C₂²	1	1	yes	characteristic
40	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
41	C₁₁×#390	C₂²	1	2	yes	—
42	C₁₁×#343	C₂²	1	2	yes	—
43	C₁₁×#341	C₂²	1	1	yes	characteristic
44	C₁₁×#339	C₂²	1	2	yes	—
45	C₁₁×#339	C₂²	1	1	yes	characteristic
46	C₂×C₁₁×#41	C₂³	1	1	yes	characteristic
47	C₂²×D₄×C₁₁	C₂³	1	2	yes	—
48	C₁₁×AGL(1,ℤ/8)	—	2	4	no	—
49	C₁₁×AGL(1,ℤ/8)	C₂×C₄	1	8	yes	complemented
50	C₂×C₁₁×SD₁₆	—	2	2	no	—
51	C₂×C₁₁×D₈	—	2	2	no	—
52	C₂×C₁₁×D₈	—	2	1	no	—
53	C₂×C₁₁×D₈	—	2	1	no	—
54	C₂×C₁₁×D₈	—	2	2	no	—
55	C₂×C₁₁×D₈	C₂×C₄	1	4	yes	complemented
56	C₁₁×#131	—	2	2	no	—
57	C₁₁×#131	C₂×C₄	1	4	yes	complemented
58	C₂×C₁₁×M₁₆	—	2	1	no	—
59	C₂×C₁₁×M₁₆	C₂³	1	1	yes	characteristic
60	C₂×C₁₁×M₁₆	C₂³	1	1	yes	characteristic
61	C₂×C₁₁×M₁₆	C₂³	1	2	yes	—
62	C₂²×C₈×C₁₁	—	2	1	no	—
63	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
64	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
65	C₄×Q₈×C₁₁	—	2	2	no	—
66	C₄×D₄×C₁₁	—	2	2	no	—
67	C₄×D₄×C₁₁	—	2	2	no	—
68	C₄×D₄×C₁₁	—	2	2	no	—
69	C₄×D₄×C₁₁	—	2	2	no	—
70	C₄×D₄×C₁₁	—	2	2	no	—
71	C₄×D₄×C₁₁	—	4	2	no	—
72	C₁₁×#117	—	2	2	no	—
73	C₁₁×#117	C₂³	1	1	yes	characteristic
74	C₁₁×#117	C₂³	1	2	yes	—
75	C₂×C₁₁×C₄⋊C₄	—	2	2	no	—
76	C₂×C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
77	C₂×C₁₁×C₂²⋊C₄	—	4	2	no	—
78	C₂×C₁₁×C₂²⋊C₄	—	4	2	no	—
79	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
80	C₁₁×#108	C₂×C₄	1	4	yes	complemented
81	C₁₁×#107	—	2	1	no	—
82	C₁₁×#107	—	2	1	no	—
83	C₁₁×#107	—	2	2	no	—
84	C₁₁×#107	—	2	2	no	—
85	C₁₁×#107	D₄	1	1	yes	characteristic
86	C₁₁×#107	D₄	1	1	yes	characteristic
87	C₁₁×#106	—	2	2	no	—
88	C₁₁×#106	—	2	2	no	—
89	C₁₁×#106	D₄	1	2	yes	—
90	C₁₁×#104	—	2	2	no	—
91	C₁₁×#103	D₄	1	1	yes	characteristic
92	C₁₁×#103	D₄	1	1	yes	characteristic
93	C₁₁×#102	—	2	2	no	—
94	C₁₁×#102	—	2	2	no	—
95	C₁₁×#102	—	2	2	no	—
96	C₁₁×#102	—	2	2	no	—
97	C₁₁×#102	D₄	1	1	yes	characteristic
98	C₁₁×#102	D₄	1	1	yes	characteristic
99	C₁₁×#100	C₂×C₄	1	8	yes	complemented
100	C₁₁×#97	—	2	2	no	—
101	C₁₁×#97	—	2	1	no	—
102	C₄×C₈×C₁₁	—	2	1	no	—
103	C₄×C₈×C₁₁	—	2	2	no	—
104	C₄×C₈×C₁₁	—	2	2	no	—
105	#23046	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
106	C₂⁴×C₁₁	—	2	2	no	—
107	C₁₁×#41	—	2	1	no	—
108	C₁₁×#41	—	2	1	no	—
109	C₁₁×#41	C₂²×C₄	1	2	yes	—
110	C₁₁×#41	#41	1	2	yes	—
111	C₂×Q₈×C₁₁	C₂×D₄	1	1	yes	characteristic
112	C₂×D₄×C₁₁	—	2	1	no	—
113	C₂×D₄×C₁₁	—	2	2	no	—
114	C₂×D₄×C₁₁	—	2	2	no	—
115	C₂×D₄×C₁₁	—	2	2	no	—
116	C₂×D₄×C₁₁	—	2	2	no	—
117	C₂×D₄×C₁₁	—	2	2	no	—
118	C₂×D₄×C₁₁	C₂²×C₄	1	4	yes	—
119	C₂×D₄×C₁₁	C₂×D₄	1	1	yes	characteristic
120	C₂²×C₄×C₁₁	—	2	1	no	—
121	C₂²×C₄×C₁₁	—	2	1	no	—
122	C₂²×C₄×C₁₁	—	2	2	no	—
123	C₂²×C₄×C₁₁	—	4	2	no	—
124	C₂²×C₄×C₁₁	—	4	2	no	—
125	C₂²×C₄×C₁₁	—	4	2	no	—
126	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
127	C₁₁×SD₁₆	—	2	8	no	—
128	C₁₁×D₈	—	2	4	no	—
129	C₁₁×D₈	—	2	4	no	—
130	C₁₁×D₈	—	2	8	no	—
131	C₁₁×M₁₆	—	2	4	no	—
132	C₁₁×M₁₆	—	2	1	no	—
133	C₁₁×M₁₆	—	2	2	no	—
134	C₁₁×M₁₆	—	2	1	no	—
135	C₁₁×M₁₆	—	2	1	no	—
136	C₁₁×M₁₆	C₂²×C₄	1	2	yes	—
137	C₁₁×M₁₆	C₂²×C₄	1	4	yes	—
138	C₂×C₈×C₁₁	—	2	4	no	—
139	C₂×C₈×C₁₁	—	2	2	no	—
140	C₂×C₈×C₁₁	—	2	1	no	—
141	C₂×C₈×C₁₁	—	2	1	no	—
142	C₂×C₈×C₁₁	—	2	1	no	—
143	C₂×C₈×C₁₁	—	2	1	no	—
144	C₂×C₈×C₁₁	C₂²×C₄	1	2	yes	—
145	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
146	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
147	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
148	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
149	C₂×C₈×C₁₁	#41	1	2	yes	—
150	C₁₁×C₄⋊C₄	—	2	2	no	—
151	C₁₁×C₄⋊C₄	—	2	2	no	—
152	C₁₁×C₄⋊C₄	—	4	2	no	—
153	C₁₁×C₄⋊C₄	C₂×D₄	1	2	yes	—
154	C₁₁×C₄⋊C₄	C₂×D₄	1	2	yes	—
155	C₁₁×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
156	C₁₁×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
157	C₁₁×C₂²⋊C₄	—	2	1	no	—
158	C₁₁×C₂²⋊C₄	—	2	2	no	—
159	C₁₁×C₂²⋊C₄	—	4	2	no	—
160	C₁₁×C₂²⋊C₄	—	4	2	no	—
161	C₁₁×C₂²⋊C₄	—	4	2	no	—
162	C₁₁×C₂²⋊C₄	—	8	4	no	—
163	C₄²×C₁₁	—	2	1	no	—
164	C₄²×C₁₁	—	2	2	no	—
165	C₄²×C₁₁	—	2	1	no	—
166	C₄²×C₁₁	—	2	1	no	—
167	C₄²×C₁₁	—	4	2	no	—
168	C₂×#472	C₂×C₁₁	1	1	yes	characteristic
169	#2948	C₂×C₁₁	1	1	yes	characteristic, complemented
170	#2946	C₂×C₁₁	1	2	yes	complemented
171	#2913	C₂×C₁₁	1	1	yes	characteristic, complemented
172	#1970	C₂×C₁₁	1	1	yes	characteristic, complemented
173	#1952	C₂×C₁₁	1	1	yes	characteristic, complemented
174	#1931	C₂×C₁₁	1	2	yes	complemented
175	#1883	C₂×C₁₁	1	2	yes	complemented
176	#1856	C₂×C₁₁	1	2	yes	complemented
177	#1772	C₂×C₁₁	1	1	yes	characteristic, complemented
178	#1764	C₂×C₁₁	1	1	yes	characteristic, complemented
179	C₂³×C₁₁	—	2	1	no	—
180	C₂³×C₁₁	—	2	4	no	—
181	C₂³×C₁₁	—	4	2	no	—
182	C₂³×C₁₁	—	4	2	no	—
183	C₂³×C₁₁	—	8	2	no	—
184	C₂³×C₁₁	—	8	2	no	—
185	C₂³×C₁₁	H(5,𝔽₂)	1	1	yes	characteristic
186	Q₈×C₁₁	—	2	1	no	—
187	Q₈×C₁₁	C₄×D₄	1	2	yes	—
188	D₄×C₁₁	—	2	2	no	—
189	D₄×C₁₁	—	2	2	no	—
190	D₄×C₁₁	—	2	4	no	—
191	D₄×C₁₁	—	2	4	no	—
192	D₄×C₁₁	—	2	1	no	—
193	D₄×C₁₁	—	4	2	no	—
194	D₄×C₁₁	—	4	2	no	—
195	D₄×C₁₁	C₄×D₄	1	2	yes	—
196	C₂×C₄×C₁₁	—	2	1	no	—
197	C₂×C₄×C₁₁	—	2	2	no	—
198	C₂×C₄×C₁₁	—	2	2	no	—
199	C₂×C₄×C₁₁	—	2	2	no	—
200	C₂×C₄×C₁₁	—	2	2	no	—
201	C₂×C₄×C₁₁	—	2	1	no	—
202	C₂×C₄×C₁₁	—	2	1	no	—
203	C₂×C₄×C₁₁	—	2	2	no	—
204	C₂×C₄×C₁₁	—	4	1	no	—
205	C₂×C₄×C₁₁	—	4	1	no	—
206	C₂×C₄×C₁₁	—	4	2	no	—
207	C₂×C₄×C₁₁	—	8	2	no	—
208	C₂×C₄×C₁₁	—	16	2	no	—
209	C₂×C₄×C₁₁	—	16	2	no	—
210	C₂×C₄×C₁₁	—	16	2	no	—
211	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
212	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
213	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
214	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
215	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
216	C₂×C₄×C₁₁	2₋¹⁺⁴	1	1	yes	characteristic
217	C₈×C₁₁	—	2	2	no	—
218	C₈×C₁₁	—	2	4	no	—
219	C₈×C₁₁	—	2	1	no	—
220	C₈×C₁₁	—	2	1	no	—
221	C₈×C₁₁	—	4	1	no	—
222	C₈×C₁₁	C₄×D₄	1	2	yes	—
223	C₈×C₁₁	C₄×D₄	1	2	yes	—
224	C₂×AGL(1,ℤ/8)	C₂²×C₁₁	1	2	yes	—
225	C₂²×D₈	C₂²×C₁₁	1	1	yes	characteristic
226	C₂×#131	C₂²×C₁₁	1	1	yes	characteristic
227	#520	C₂²×C₁₁	1	2	yes	—
228	#518	C₂²×C₁₁	1	2	yes	—
229	#472	C₄×C₁₁	1	8	yes	complemented
230	#442	—	2	2	no	—
231	#442	—	2	2	no	—
232	#440	—	2	2	no	—
233	C₄×SD₁₆	—	2	2	no	—
234	C₄×D₈	—	2	1	no	—
235	C₄×D₈	—	2	1	no	—
236	C₄×D₈	—	2	2	no	—
237	C₂×#108	C₂²×C₁₁	1	1	yes	characteristic
238	#428	—	2	2	no	—
239	#428	C₂²×C₁₁	1	2	yes	—
240	#428	C₂²×C₁₁	1	2	yes	—
241	#427	—	2	1	no	—
242	#427	C₂²×C₁₁	1	1	yes	characteristic
243	C₂×#107	—	2	1	no	—
244	C₂×#107	C₂²×C₁₁	1	1	yes	characteristic
245	C₂×#104	C₂²×C₁₁	1	1	yes	characteristic
246	#418	C₂²×C₁₁	1	2	yes	—
247	#416	C₂²×C₁₁	1	1	yes	characteristic
248	C₂×#102	C₂²×C₁₁	1	2	yes	—
249	C₂×#100	C₂²×C₁₁	1	2	yes	—
250	#405	C₂²×C₁₁	1	2	yes	—
251	#405	C₂²×C₁₁	1	1	yes	characteristic
252	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
253	#390	C₂²×C₁₁	1	2	yes	—
254	#343	C₂²×C₁₁	1	2	yes	—
255	#341	C₂²×C₁₁	1	1	yes	characteristic
256	#339	C₂²×C₁₁	1	1	yes	characteristic
257	#339	C₂²×C₁₁	1	2	yes	—
258	C₂²×C₁₁	—	2	1	no	—
259	C₂²×C₁₁	—	2	1	no	—
260	C₂²×C₁₁	—	2	2	no	—
261	C₂²×C₁₁	—	4	1	no	—
262	C₂²×C₁₁	—	4	1	no	—
263	C₂²×C₁₁	—	4	4	no	—
264	C₂²×C₁₁	—	8	4	no	—
265	C₂²×C₁₁	—	8	2	no	—
266	C₂²×C₁₁	—	8	2	no	—
267	C₂²×C₁₁	—	16	2	no	—
268	C₂²×C₁₁	#520	1	1	yes	characteristic
269	C₂²×C₁₁	D₄²	1	1	yes	characteristic
270	C₂²×C₁₁	#553	1	1	yes	characteristic
271	C₄×C₁₁	—	2	2	no	—
272	C₄×C₁₁	—	4	2	no	—
273	C₄×C₁₁	—	4	2	no	—
274	C₄×C₁₁	—	4	1	no	—
275	C₄×C₁₁	—	4	1	no	—
276	C₄×C₁₁	—	4	2	no	—
277	C₄×C₁₁	—	8	2	no	—
278	C₄×C₁₁	C₂×C₄×D₄	1	1	yes	characteristic
279	C₄×C₁₁	C₂×C₄×D₄	1	1	yes	characteristic
280	C₄×C₁₁	#547	1	1	yes	characteristic
281	C₄×C₁₁	#548	1	1	yes	characteristic
282	C₂×#41	C₂³×C₁₁	1	1	yes	characteristic
283	C₂²×D₄	C₂³×C₁₁	1	2	yes	—
284	AGL(1,ℤ/8)	—	2	4	no	—
285	AGL(1,ℤ/8)	C₂×C₄×C₁₁	1	8	yes	complemented
286	C₂×SD₁₆	—	2	2	no	—
287	C₂×D₈	—	2	2	no	—
288	C₂×D₈	—	2	1	no	—
289	C₂×D₈	—	2	1	no	—
290	C₂×D₈	—	2	2	no	—
291	C₂×D₈	C₂×C₄×C₁₁	1	4	yes	complemented
292	#131	—	2	2	no	—
293	#131	C₂×C₄×C₁₁	1	4	yes	complemented
294	C₂×M₁₆	—	2	1	no	—
295	C₂×M₁₆	C₂³×C₁₁	1	1	yes	characteristic
296	C₂×M₁₆	C₂³×C₁₁	1	1	yes	characteristic
297	C₂×M₁₆	C₂³×C₁₁	1	2	yes	—
298	C₂²×C₈	—	2	1	no	—
299	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
300	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
301	C₄×Q₈	—	2	2	no	—
302	C₄×D₄	—	2	2	no	—
303	C₄×D₄	—	2	2	no	—
304	C₄×D₄	—	2	2	no	—
305	C₄×D₄	—	2	2	no	—
306	C₄×D₄	—	2	2	no	—
307	C₄×D₄	—	4	2	no	—
308	#117	—	2	2	no	—
309	#117	C₂³×C₁₁	1	1	yes	characteristic
310	#117	C₂³×C₁₁	1	2	yes	—
311	C₂×C₄⋊C₄	—	2	2	no	—
312	C₂×C₄⋊C₄	C₂³×C₁₁	1	2	yes	—
313	C₂×C₂²⋊C₄	—	4	2	no	—
314	C₂×C₂²⋊C₄	—	4	2	no	—
315	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
316	#108	C₂×C₄×C₁₁	1	4	yes	complemented
317	#107	—	2	1	no	—
318	#107	—	2	1	no	—
319	#107	—	2	2	no	—
320	#107	—	2	2	no	—
321	#107	D₄×C₁₁	1	1	yes	characteristic
322	#107	D₄×C₁₁	1	1	yes	characteristic
323	#106	—	2	2	no	—
324	#106	—	2	2	no	—
325	#106	D₄×C₁₁	1	2	yes	—
326	#104	—	2	2	no	—
327	#103	D₄×C₁₁	1	1	yes	characteristic
328	#103	D₄×C₁₁	1	1	yes	characteristic
329	#102	—	2	2	no	—
330	#102	—	2	2	no	—
331	#102	—	2	2	no	—
332	#102	—	2	2	no	—
333	#102	D₄×C₁₁	1	1	yes	characteristic
334	#102	D₄×C₁₁	1	1	yes	characteristic
335	#100	C₂×C₄×C₁₁	1	8	yes	complemented
336	#97	—	2	2	no	—
337	#97	—	2	1	no	—
338	C₄×C₈	—	2	1	no	—
339	C₄×C₈	—	2	2	no	—
340	C₄×C₈	—	2	2	no	—
341	C₂×C₁₁	—	2	1	no	—
342	C₂×C₁₁	—	2	1	no	—
343	C₂×C₁₁	—	4	2	no	—
344	C₂×C₁₁	—	8	4	no	—
345	C₂×C₁₁	#2361	1	1	yes	characteristic
346	C₂×C₁₁	#3290	1	1	yes	characteristic
347	C₂×C₁₁	#3292	1	1	yes	characteristic
348	C₂⁴	—	2	2	no	—
349	#41	—	2	1	no	—
350	#41	—	2	1	no	—
351	#41	C₂²×C₄×C₁₁	1	2	yes	—
352	#41	C₁₁×#41	1	2	yes	—
353	C₂×Q₈	C₂×D₄×C₁₁	1	1	yes	characteristic
354	C₂×D₄	—	2	1	no	—
355	C₂×D₄	—	2	2	no	—
356	C₂×D₄	—	2	2	no	—
357	C₂×D₄	—	2	2	no	—
358	C₂×D₄	—	2	2	no	—
359	C₂×D₄	—	2	2	no	—
360	C₂×D₄	C₂²×C₄×C₁₁	1	4	yes	—
361	C₂×D₄	C₂×D₄×C₁₁	1	1	yes	characteristic
362	C₂²×C₄	—	2	1	no	—
363	C₂²×C₄	—	2	1	no	—
364	C₂²×C₄	—	2	2	no	—
365	C₂²×C₄	—	4	2	no	—
366	C₂²×C₄	—	4	2	no	—
367	C₂²×C₄	—	4	2	no	—
368	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
369	SD₁₆	—	2	8	no	—
370	D₈	—	2	8	no	—
371	D₈	—	2	4	no	—
372	D₈	—	2	4	no	—
373	M₁₆	—	2	1	no	—
374	M₁₆	—	2	2	no	—
375	M₁₆	—	2	4	no	—
376	M₁₆	—	2	1	no	—
377	M₁₆	—	2	1	no	—
378	M₁₆	C₂²×C₄×C₁₁	1	2	yes	—
379	M₁₆	C₂²×C₄×C₁₁	1	4	yes	—
380	C₂×C₈	—	2	2	no	—
381	C₂×C₈	—	2	1	no	—
382	C₂×C₈	—	2	1	no	—
383	C₂×C₈	—	2	1	no	—
384	C₂×C₈	—	2	4	no	—
385	C₂×C₈	—	2	1	no	—
386	C₂×C₈	C₂²×C₄×C₁₁	1	2	yes	—
387	C₂×C₈	C₂×D₄×C₁₁	1	1	yes	characteristic
388	C₂×C₈	C₂×D₄×C₁₁	1	1	yes	characteristic
389	C₂×C₈	C₂×D₄×C₁₁	1	1	yes	characteristic
390	C₂×C₈	C₂×D₄×C₁₁	1	1	yes	characteristic
391	C₂×C₈	C₁₁×#41	1	2	yes	—
392	C₄⋊C₄	—	2	2	no	—
393	C₄⋊C₄	—	2	2	no	—
394	C₄⋊C₄	—	4	2	no	—
395	C₄⋊C₄	C₂×D₄×C₁₁	1	2	yes	—
396	C₄⋊C₄	C₂×D₄×C₁₁	1	2	yes	—
397	C₄⋊C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
398	C₄⋊C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
399	C₂²⋊C₄	—	2	1	no	—
400	C₂²⋊C₄	—	2	2	no	—
401	C₂²⋊C₄	—	4	2	no	—
402	C₂²⋊C₄	—	4	2	no	—
403	C₂²⋊C₄	—	4	2	no	—
404	C₂²⋊C₄	—	8	4	no	—
405	C₄²	—	2	1	no	—
406	C₄²	—	2	2	no	—
407	C₄²	—	2	1	no	—
408	C₄²	—	2	1	no	—
409	C₄²	—	4	2	no	—
410	C₁₁	#23046	1	1	yes	characteristic, direct product factor, Sylow
411	C₂³	—	2	1	no	—
412	C₂³	—	2	4	no	—
413	C₂³	—	4	2	no	—
414	C₂³	—	4	2	no	—
415	C₂³	—	8	2	no	—
416	C₂³	—	8	2	no	—
417	C₂³	C₁₁×H(5,𝔽₂)	1	1	yes	characteristic
418	Q₈	—	2	1	no	—
419	Q₈	C₄×D₄×C₁₁	1	2	yes	—
420	D₄	—	2	2	no	—
421	D₄	—	2	2	no	—
422	D₄	—	2	4	no	—
423	D₄	—	2	4	no	—
424	D₄	—	2	1	no	—
425	D₄	—	4	2	no	—
426	D₄	—	4	2	no	—
427	D₄	C₄×D₄×C₁₁	1	2	yes	—
428	C₂×C₄	—	2	1	no	—
429	C₂×C₄	—	2	2	no	—
430	C₂×C₄	—	2	2	no	—
431	C₂×C₄	—	2	2	no	—
432	C₂×C₄	—	2	2	no	—
433	C₂×C₄	—	2	1	no	—
434	C₂×C₄	—	2	1	no	—
435	C₂×C₄	—	2	2	no	—
436	C₂×C₄	—	4	1	no	—
437	C₂×C₄	—	4	1	no	—
438	C₂×C₄	—	4	2	no	—
439	C₂×C₄	—	8	2	no	—
440	C₂×C₄	—	16	2	no	—
441	C₂×C₄	—	16	2	no	—
442	C₂×C₄	—	16	2	no	—
443	C₂×C₄	C₂³×C₄×C₁₁	1	1	yes	characteristic
444	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
445	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
446	C₂×C₄	C₂×C₁₁×#41	1	1	yes	characteristic
447	C₂×C₄	C₂×C₁₁×#41	1	1	yes	characteristic
448	C₂×C₄	C₁₁×2₋¹⁺⁴	1	1	yes	characteristic
449	C₈	—	2	2	no	—
450	C₈	—	2	4	no	—
451	C₈	—	2	1	no	—
452	C₈	—	2	1	no	—
453	C₈	—	4	1	no	—
454	C₈	C₄×D₄×C₁₁	1	2	yes	—
455	C₈	C₄×D₄×C₁₁	1	2	yes	—
456	C₂²	—	2	1	no	—
457	C₂²	—	2	1	no	—
458	C₂²	—	2	2	no	—
459	C₂²	—	4	1	no	—
460	C₂²	—	4	1	no	—
461	C₂²	—	4	4	no	—
462	C₂²	—	8	4	no	—
463	C₂²	—	8	2	no	—
464	C₂²	—	8	2	no	—
465	C₂²	—	16	2	no	—
466	C₂²	C₁₁×#520	1	1	yes	characteristic
467	C₂²	D₄²×C₁₁	1	1	yes	characteristic
468	C₂²	C₁₁×#553	1	1	yes	characteristic
469	C₄	—	2	2	no	—
470	C₄	—	4	2	no	—
471	C₄	—	4	1	no	—
472	C₄	—	4	2	no	—
473	C₄	—	4	1	no	—
474	C₄	—	4	2	no	—
475	C₄	—	8	2	no	—
476	C₄	C₂×C₄×D₄×C₁₁	1	1	yes	characteristic
477	C₄	C₂×C₄×D₄×C₁₁	1	1	yes	characteristic
478	C₄	C₁₁×#547	1	1	yes	characteristic
479	C₄	C₁₁×#548	1	1	yes	characteristic
480	C₂	—	2	1	no	—
481	C₂	—	2	1	no	—
482	C₂	—	4	2	no	—
483	C₂	—	8	4	no	—
484	C₂	C₁₁×#2361	1	1	yes	characteristic
485	C₂	C₁₁×#3290	1	1	yes	characteristic
486	C₂	C₁₁×#3292	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₁	D₄²
commutator	C₂×C₄	C₂³×C₄×C₁₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₁
prime radical	C₂×C₁₁×#472	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₁ ◁ C₂²×C₄×C₁₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₁×#2948	C₂	semidirect
3. C₁₁×#2946	C₂	semidirect
4. C₁₁×#2913	C₂	semidirect
5. C₁₁×#1970	C₂	semidirect
6. C₁₁×#1952	C₂	semidirect
7. C₁₁×#1931	C₂	semidirect
8. C₁₁×#1883	C₂	semidirect
9. C₁₁×#1856	C₂	semidirect
10. C₁₁×#1772	C₂	semidirect
11. C₁₁×#1764	C₂	semidirect
17. C₁₁×#472	C₄	semidirect
49. C₁₁×AGL(1,ℤ/8)	C₂×C₄	semidirect
55. C₂×C₁₁×D₈	C₂×C₄	semidirect
57. C₁₁×#131	C₂×C₄	semidirect
80. C₁₁×#108	C₂×C₄	semidirect
99. C₁₁×#100	C₂×C₄	semidirect
105. #23046	C₁₁	direct (N × H)
169. #2948	C₂×C₁₁	semidirect
170. #2946	C₂×C₁₁	semidirect
171. #2913	C₂×C₁₁	semidirect
172. #1970	C₂×C₁₁	semidirect
173. #1952	C₂×C₁₁	semidirect
174. #1931	C₂×C₁₁	semidirect
175. #1883	C₂×C₁₁	semidirect
176. #1856	C₂×C₁₁	semidirect
177. #1772	C₂×C₁₁	semidirect
178. #1764	C₂×C₁₁	semidirect
229. #472	C₄×C₁₁	semidirect
285. AGL(1,ℤ/8)	C₂×C₄×C₁₁	semidirect
291. C₂×D₈	C₂×C₄×C₁₁	semidirect
293. #131	C₂×C₄×C₁₁	semidirect
316. #108	C₂×C₄×C₁₁	semidirect
335. #100	C₂×C₄×C₁₁	semidirect
410. C₁₁	#23046	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×C₁₁×#472	2
C₁₁×#2948	2
C₁₁×#2946	2
C₁₁×#2913	2
C₁₁×#1970	2
C₁₁×#1952	2
C₁₁×#1931	2
C₁₁×#1883	2
C₁₁×#1856	2
C₁₁×#1772	2
C₁₁×#1764	2
#23046	11

Subgroups — C11×#23046 #14600239

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#23046 #14600239