Subgroups — C₁₁×#23016 #14600209

Order 2816.

880 conjugacy classes of subgroups.

The subgroup lattice has 546 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	C₂×C₁₁×#444	C₂	1	2	yes	maximal, complemented
3	C₁₁×#2935	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₁×#2906	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₁×#1962	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₁×#1950	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₁×#1938	C₂	1	2	yes	maximal, complemented
8	C₁₁×#1876	C₂	1	2	yes	maximal, complemented
9	C₁₁×#1866	C₂	1	2	yes	maximal, complemented
10	C₁₁×#1767	C₂	1	1	yes	maximal, characteristic, 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	C₂×C₁₁×#131	C₂²	1	2	yes	—
15	C₁₁×#532	C₂²	1	1	yes	characteristic
16	C₄×C₁₁×#41	C₂²	1	1	yes	characteristic
17	C₁₁×#464	C₄	1	2	yes	complemented
18	C₁₁×#463	C₄	1	2	yes	complemented
19	C₁₁×#462	C₄	1	1	yes	characteristic, complemented
20	C₁₁×#461	C₄	1	1	yes	characteristic, complemented
21	C₁₁×#460	C₄	1	1	yes	characteristic, complemented
22	C₁₁×#459	C₄	1	1	yes	characteristic, complemented
23	C₁₁×#444	—	2	8	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	2	yes	—
28	C₁₁×#424	—	2	2	no	—
29	C₁₁×#424	C₂²	1	2	yes	—
30	C₁₁×#423	—	2	1	no	—
31	C₁₁×#423	C₂²	1	1	yes	characteristic
32	C₂×C₁₁×C₄⋊C₈	—	2	1	no	—
33	C₂×C₁₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
34	C₂×C₁₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
35	C₂×C₁₁×#104	C₂²	1	1	yes	characteristic
36	C₂×C₁₁×#104	C₂²	1	2	yes	—
37	C₂×C₁₁×#104	C₂²	1	2	yes	—
38	C₂×C₁₁×#104	C₂²	1	1	yes	characteristic
39	C₁₁×#416	C₂²	1	2	yes	—
40	C₁₁×#408	C₂²	1	2	yes	—
41	C₄×C₁₁×M₁₆	C₂²	1	1	yes	characteristic
42	C₂×C₁₁×#97	C₂²	1	2	yes	—
43	C₄³×C₁₁	C₂²	1	1	yes	characteristic
44	C₁₁×#341	C₂²	1	2	yes	—
45	C₁₁×#339	C₂²	1	1	yes	characteristic
46	C₁₁×#339	C₂²	1	1	yes	characteristic
47	C₁₁×#336	C₂²	1	2	yes	—
48	C₂×C₁₁×#41	C₂³	1	2	yes	—
49	C₂×C₁₁×#41	C₂³	1	1	yes	characteristic
50	C₁₁×#135	—	2	4	no	—
51	C₁₁×#135	—	2	4	no	—
52	C₂×C₁₁×Q₁₆	C₂×C₄	1	2	yes	—
53	C₂×C₁₁×SD₁₆	C₂×C₄	1	2	yes	—
54	C₂×C₁₁×SD₁₆	C₂×C₄	1	2	yes	—
55	C₂×C₁₁×D₈	C₂×C₄	1	2	yes	—
56	C₁₁×#131	—	2	4	no	—
57	C₁₁×#131	—	2	4	no	—
58	C₁₁×#131	—	4	2	no	—
59	C₁₁×#131	—	4	2	no	—
60	C₂×C₁₁×M₁₆	—	2	2	no	—
61	C₂×C₁₁×M₁₆	—	2	2	no	—
62	C₂×C₁₁×M₁₆	C₂³	1	1	yes	characteristic
63	C₂×C₁₁×M₁₆	C₂³	1	2	yes	—
64	C₂×C₁₁×M₁₆	C₂³	1	1	yes	characteristic
65	C₂²×C₈×C₁₁	—	2	2	no	—
66	C₂²×C₈×C₁₁	—	2	2	no	—
67	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
68	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
69	C₁₁×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
70	C₁₁×#127	C₂×C₄	1	1	yes	characteristic
71	C₁₁×#124	C₂×C₄	1	2	yes	—
72	C₁₁×#121	—	2	1	no	—
73	C₁₁×#121	—	2	1	no	—
74	C₄×Q₈×C₁₁	C₂×C₄	1	1	yes	characteristic
75	C₄×Q₈×C₁₁	C₂×C₄	1	1	yes	characteristic
76	C₄×D₄×C₁₁	—	2	1	no	—
77	C₄×D₄×C₁₁	—	2	1	no	—
78	C₄×D₄×C₁₁	—	2	1	no	—
79	C₄×D₄×C₁₁	—	2	1	no	—
80	C₄×D₄×C₁₁	C₂×C₄	1	1	yes	characteristic
81	C₄×D₄×C₁₁	C₂×C₄	1	1	yes	characteristic
82	C₁₁×#117	—	2	1	no	—
83	C₁₁×#117	C₂³	1	1	yes	characteristic
84	C₂×C₄²×C₁₁	—	2	1	no	—
85	C₂×C₄²×C₁₁	—	2	1	no	—
86	C₂×C₄²×C₁₁	—	2	1	no	—
87	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
88	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
89	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
90	C₁₁×#108	—	2	4	no	—
91	C₁₁×C₄⋊C₈	—	2	2	no	—
92	C₁₁×C₄⋊C₈	—	2	2	no	—
93	C₁₁×C₄⋊C₈	—	2	1	no	—
94	C₁₁×C₄⋊C₈	—	2	1	no	—
95	C₁₁×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
96	C₁₁×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
97	C₁₁×C₄⋊C₈	C₂×C₄	1	2	yes	—
98	C₁₁×C₄⋊C₈	D₄	1	1	yes	characteristic
99	C₁₁×C₄⋊C₈	D₄	1	1	yes	characteristic
100	C₁₁×C₄⋊C₈	D₄	1	2	yes	—
101	C₁₁×#104	—	2	2	no	—
102	C₁₁×#104	—	2	4	no	—
103	C₁₁×#104	—	4	2	no	—
104	C₁₁×#104	D₄	1	4	yes	complemented
105	C₁₁×#103	C₂×C₄	1	2	yes	—
106	C₁₁×#103	C₂×C₄	1	2	yes	—
107	C₁₁×#102	C₂×C₄	1	2	yes	—
108	C₁₁×#102	C₂×C₄	1	2	yes	—
109	C₁₁×C₂²⋊C₈	—	2	2	no	—
110	C₁₁×C₂²⋊C₈	—	2	2	no	—
111	C₁₁×#97	—	2	4	no	—
112	C₁₁×#97	—	2	1	no	—
113	C₄×C₈×C₁₁	—	2	1	no	—
114	#23016	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
115	C₁₁×#41	—	2	1	no	—
116	C₁₁×#41	—	2	1	no	—
117	C₁₁×#41	—	2	2	no	—
118	C₁₁×#41	—	2	2	no	—
119	C₁₁×#41	—	2	2	no	—
120	C₁₁×#41	—	2	2	no	—
121	C₁₁×#41	C₂×D₄	1	2	yes	—
122	C₁₁×#41	#41	1	2	yes	—
123	C₂×Q₈×C₁₁	C₂²×C₄	1	2	yes	—
124	C₂×Q₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
125	C₂×D₄×C₁₁	—	2	1	no	—
126	C₂×D₄×C₁₁	—	2	2	no	—
127	C₂×D₄×C₁₁	—	2	1	no	—
128	C₂×D₄×C₁₁	—	2	1	no	—
129	C₂×D₄×C₁₁	C₂²×C₄	1	2	yes	—
130	C₂×D₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
131	C₂²×C₄×C₁₁	—	2	1	no	—
132	C₂²×C₄×C₁₁	—	2	1	no	—
133	C₂²×C₄×C₁₁	—	2	1	no	—
134	C₂²×C₄×C₁₁	—	2	1	no	—
135	C₂²×C₄×C₁₁	—	2	2	no	—
136	C₂²×C₄×C₁₁	—	2	1	no	—
137	C₂²×C₄×C₁₁	#41	1	1	yes	characteristic
138	C₂²×C₄×C₁₁	#41	1	1	yes	characteristic
139	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
140	C₁₁×Q₁₆	—	2	4	no	—
141	C₁₁×SD₁₆	—	2	4	no	—
142	C₁₁×SD₁₆	—	2	4	no	—
143	C₁₁×D₈	—	2	4	no	—
144	C₁₁×M₁₆	—	2	2	no	—
145	C₁₁×M₁₆	—	2	1	no	—
146	C₁₁×M₁₆	—	2	1	no	—
147	C₁₁×M₁₆	—	2	2	no	—
148	C₁₁×M₁₆	—	2	1	no	—
149	C₁₁×M₁₆	—	4	4	no	—
150	C₁₁×M₁₆	—	4	4	no	—
151	C₁₁×M₁₆	C₂×D₄	1	2	yes	—
152	C₂×C₈×C₁₁	—	2	2	no	—
153	C₂×C₈×C₁₁	—	2	2	no	—
154	C₂×C₈×C₁₁	—	2	1	no	—
155	C₂×C₈×C₁₁	—	2	1	no	—
156	C₂×C₈×C₁₁	—	2	2	no	—
157	C₂×C₈×C₁₁	—	2	2	no	—
158	C₂×C₈×C₁₁	—	2	2	no	—
159	C₂×C₈×C₁₁	—	4	4	no	—
160	C₂×C₈×C₁₁	—	4	4	no	—
161	C₂×C₈×C₁₁	C₂²×C₄	1	2	yes	—
162	C₂×C₈×C₁₁	C₂²×C₄	1	2	yes	—
163	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
164	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
165	C₁₁×C₄⋊C₄	—	2	1	no	—
166	C₁₁×C₄⋊C₄	—	2	1	no	—
167	C₁₁×C₄⋊C₄	—	2	1	no	—
168	C₁₁×C₄⋊C₄	—	2	1	no	—
169	C₁₁×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
170	C₁₁×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
171	C₁₁×C₂²⋊C₄	—	2	1	no	—
172	C₁₁×C₂²⋊C₄	—	2	1	no	—
173	C₁₁×C₂²⋊C₄	—	2	1	no	—
174	C₁₁×C₂²⋊C₄	—	2	2	no	—
175	C₁₁×C₂²⋊C₄	—	2	2	no	—
176	C₄²×C₁₁	—	2	1	no	—
177	C₄²×C₁₁	—	2	1	no	—
178	C₄²×C₁₁	—	2	1	no	—
179	C₄²×C₁₁	—	2	1	no	—
180	C₄²×C₁₁	—	2	1	no	—
181	C₄²×C₁₁	—	2	1	no	—
182	C₄²×C₁₁	—	4	2	no	—
183	C₄²×C₁₁	—	4	2	no	—
184	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
185	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
186	C₄²×C₁₁	C₂×D₄	1	2	yes	—
187	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
188	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
189	#3035	C₂×C₁₁	1	1	yes	characteristic
190	C₂×#444	C₂×C₁₁	1	2	yes	complemented
191	#2935	C₂×C₁₁	1	1	yes	characteristic, complemented
192	#2906	C₂×C₁₁	1	1	yes	characteristic, complemented
193	#1962	C₂×C₁₁	1	1	yes	characteristic, complemented
194	#1950	C₂×C₁₁	1	1	yes	characteristic, complemented
195	#1938	C₂×C₁₁	1	2	yes	complemented
196	#1876	C₂×C₁₁	1	2	yes	complemented
197	#1866	C₂×C₁₁	1	2	yes	complemented
198	#1767	C₂×C₁₁	1	1	yes	characteristic, complemented
199	C₄×#104	C₂×C₁₁	1	1	yes	characteristic, complemented
200	C₂³×C₁₁	—	2	1	no	—
201	C₂³×C₁₁	—	2	2	no	—
202	C₂³×C₁₁	C₂×#41	1	1	yes	characteristic
203	Q₈×C₁₁	—	2	1	no	—
204	Q₈×C₁₁	—	2	2	no	—
205	Q₈×C₁₁	—	2	2	no	—
206	Q₈×C₁₁	C₄×D₄	1	2	yes	—
207	D₄×C₁₁	—	2	2	no	—
208	D₄×C₁₁	—	2	2	no	—
209	D₄×C₁₁	—	2	2	no	—
210	D₄×C₁₁	—	2	1	no	—
211	D₄×C₁₁	—	2	2	no	—
212	D₄×C₁₁	—	4	2	no	—
213	D₄×C₁₁	—	4	2	no	—
214	D₄×C₁₁	—	4	2	no	—
215	D₄×C₁₁	—	8	1	no	—
216	D₄×C₁₁	C₄×D₄	1	2	yes	—
217	C₂×C₄×C₁₁	—	2	1	no	—
218	C₂×C₄×C₁₁	—	2	2	no	—
219	C₂×C₄×C₁₁	—	2	2	no	—
220	C₂×C₄×C₁₁	—	2	2	no	—
221	C₂×C₄×C₁₁	—	2	2	no	—
222	C₂×C₄×C₁₁	—	2	1	no	—
223	C₂×C₄×C₁₁	—	2	1	no	—
224	C₂×C₄×C₁₁	—	2	2	no	—
225	C₂×C₄×C₁₁	—	2	2	no	—
226	C₂×C₄×C₁₁	—	4	1	no	—
227	C₂×C₄×C₁₁	—	4	1	no	—
228	C₂×C₄×C₁₁	—	4	1	no	—
229	C₂×C₄×C₁₁	—	4	1	no	—
230	C₂×C₄×C₁₁	—	4	1	no	—
231	C₂×C₄×C₁₁	—	4	2	no	—
232	C₂×C₄×C₁₁	—	4	2	no	—
233	C₂×C₄×C₁₁	—	4	2	no	—
234	C₂×C₄×C₁₁	—	8	1	no	—
235	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
236	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
237	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
238	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
239	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
240	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
241	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
242	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
243	C₂×C₄×C₁₁	H(5,𝔽₂)	1	1	yes	characteristic
244	C₂×C₄×C₁₁	2₋¹⁺⁴	1	1	yes	characteristic
245	C₈×C₁₁	—	2	2	no	—
246	C₈×C₁₁	—	2	2	no	—
247	C₈×C₁₁	—	2	2	no	—
248	C₈×C₁₁	—	2	2	no	—
249	C₈×C₁₁	—	2	2	no	—
250	C₈×C₁₁	—	4	2	no	—
251	C₈×C₁₁	—	4	1	no	—
252	C₂×#135	C₂²×C₁₁	1	2	yes	—
253	C₂×#131	C₂²×C₁₁	1	2	yes	—
254	C₂×#131	C₂²×C₁₁	1	2	yes	—
255	#532	C₂²×C₁₁	1	1	yes	characteristic
256	C₄×#41	C₂²×C₁₁	1	1	yes	characteristic
257	#464	C₄×C₁₁	1	2	yes	complemented
258	#463	C₄×C₁₁	1	2	yes	complemented
259	#462	C₄×C₁₁	1	1	yes	characteristic, complemented
260	#461	C₄×C₁₁	1	1	yes	characteristic, complemented
261	#460	C₄×C₁₁	1	1	yes	characteristic, complemented
262	#459	C₄×C₁₁	1	1	yes	characteristic, complemented
263	#444	—	2	8	no	—
264	#436	—	2	1	no	—
265	#435	—	2	2	no	—
266	C₈×D₄	—	2	1	no	—
267	C₂×#108	C₂²×C₁₁	1	2	yes	—
268	#424	—	2	2	no	—
269	#424	C₂²×C₁₁	1	2	yes	—
270	#423	—	2	1	no	—
271	#423	C₂²×C₁₁	1	1	yes	characteristic
272	C₂×C₄⋊C₈	—	2	1	no	—
273	C₂×C₄⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
274	C₂×C₄⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
275	C₂×#104	C₂²×C₁₁	1	1	yes	characteristic
276	C₂×#104	C₂²×C₁₁	1	2	yes	—
277	C₂×#104	C₂²×C₁₁	1	2	yes	—
278	C₂×#104	C₂²×C₁₁	1	1	yes	characteristic
279	#416	C₂²×C₁₁	1	2	yes	—
280	#408	C₂²×C₁₁	1	2	yes	—
281	C₄×M₁₆	C₂²×C₁₁	1	1	yes	characteristic
282	C₂×#97	C₂²×C₁₁	1	2	yes	—
283	C₄³	C₂²×C₁₁	1	1	yes	characteristic
284	#341	C₂²×C₁₁	1	2	yes	—
285	#339	C₂²×C₁₁	1	1	yes	characteristic
286	#339	C₂²×C₁₁	1	1	yes	characteristic
287	#336	C₂²×C₁₁	1	2	yes	—
288	C₂²×C₁₁	—	2	1	no	—
289	C₂²×C₁₁	—	2	1	no	—
290	C₂²×C₁₁	—	2	2	no	—
291	C₂²×C₁₁	—	4	1	no	—
292	C₂²×C₁₁	—	4	1	no	—
293	C₂²×C₁₁	—	4	2	no	—
294	C₂²×C₁₁	—	4	2	no	—
295	C₂²×C₁₁	—	4	2	no	—
296	C₂²×C₁₁	C₂×C₄×D₄	1	1	yes	characteristic
297	C₂²×C₁₁	#547	1	1	yes	characteristic
298	C₂²×C₁₁	#553	1	1	yes	characteristic
299	C₄×C₁₁	—	2	2	no	—
300	C₄×C₁₁	—	2	1	no	—
301	C₄×C₁₁	—	2	1	no	—
302	C₄×C₁₁	—	2	1	no	—
303	C₄×C₁₁	—	4	2	no	—
304	C₄×C₁₁	—	4	2	no	—
305	C₄×C₁₁	—	4	2	no	—
306	C₄×C₁₁	—	4	1	no	—
307	C₄×C₁₁	—	4	1	no	—
308	C₄×C₁₁	#444	1	2	yes	complemented
309	C₄×C₁₁	C₂×C₄×D₄	1	1	yes	characteristic
310	C₄×C₁₁	#520	1	1	yes	characteristic
311	C₄×C₁₁	D₄²	1	1	yes	characteristic
312	C₄×C₁₁	#548	1	1	yes	characteristic
313	C₂×#41	C₂³×C₁₁	1	2	yes	—
314	C₂×#41	C₂³×C₁₁	1	1	yes	characteristic
315	#135	—	2	4	no	—
316	#135	—	2	4	no	—
317	C₂×Q₁₆	C₂×C₄×C₁₁	1	2	yes	—
318	C₂×SD₁₆	C₂×C₄×C₁₁	1	2	yes	—
319	C₂×SD₁₆	C₂×C₄×C₁₁	1	2	yes	—
320	C₂×D₈	C₂×C₄×C₁₁	1	2	yes	—
321	#131	—	2	4	no	—
322	#131	—	2	4	no	—
323	#131	—	4	2	no	—
324	#131	—	4	2	no	—
325	C₂×M₁₆	—	2	2	no	—
326	C₂×M₁₆	—	2	2	no	—
327	C₂×M₁₆	C₂³×C₁₁	1	2	yes	—
328	C₂×M₁₆	C₂³×C₁₁	1	1	yes	characteristic
329	C₂×M₁₆	C₂³×C₁₁	1	1	yes	characteristic
330	C₂²×C₈	—	2	2	no	—
331	C₂²×C₈	—	2	2	no	—
332	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
333	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
334	C₄⋊Q₈	C₂×C₄×C₁₁	1	1	yes	characteristic
335	#127	C₂×C₄×C₁₁	1	1	yes	characteristic
336	#124	C₂×C₄×C₁₁	1	2	yes	—
337	#121	—	2	1	no	—
338	#121	—	2	1	no	—
339	C₄×Q₈	C₂×C₄×C₁₁	1	1	yes	characteristic
340	C₄×Q₈	C₂×C₄×C₁₁	1	1	yes	characteristic
341	C₄×D₄	—	2	1	no	—
342	C₄×D₄	—	2	1	no	—
343	C₄×D₄	—	2	1	no	—
344	C₄×D₄	—	2	1	no	—
345	C₄×D₄	C₂×C₄×C₁₁	1	1	yes	characteristic
346	C₄×D₄	C₂×C₄×C₁₁	1	1	yes	characteristic
347	#117	—	2	1	no	—
348	#117	C₂³×C₁₁	1	1	yes	characteristic
349	C₂×C₄²	—	2	1	no	—
350	C₂×C₄²	—	2	1	no	—
351	C₂×C₄²	—	2	1	no	—
352	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
353	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
354	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
355	#108	—	2	4	no	—
356	C₄⋊C₈	—	2	2	no	—
357	C₄⋊C₈	—	2	2	no	—
358	C₄⋊C₈	—	2	1	no	—
359	C₄⋊C₈	—	2	1	no	—
360	C₄⋊C₈	C₂×C₄×C₁₁	1	1	yes	characteristic
361	C₄⋊C₈	C₂×C₄×C₁₁	1	1	yes	characteristic
362	C₄⋊C₈	C₂×C₄×C₁₁	1	2	yes	—
363	C₄⋊C₈	D₄×C₁₁	1	1	yes	characteristic
364	C₄⋊C₈	D₄×C₁₁	1	1	yes	characteristic
365	C₄⋊C₈	D₄×C₁₁	1	2	yes	—
366	#104	—	2	2	no	—
367	#104	—	2	4	no	—
368	#104	—	4	2	no	—
369	#104	D₄×C₁₁	1	4	yes	complemented
370	#103	C₂×C₄×C₁₁	1	2	yes	—
371	#103	C₂×C₄×C₁₁	1	2	yes	—
372	#102	C₂×C₄×C₁₁	1	2	yes	—
373	#102	C₂×C₄×C₁₁	1	2	yes	—
374	C₂²⋊C₈	—	2	2	no	—
375	C₂²⋊C₈	—	2	2	no	—
376	#97	—	2	4	no	—
377	#97	—	2	1	no	—
378	C₄×C₈	—	2	1	no	—
379	C₂×C₁₁	—	2	1	no	—
380	C₂×C₁₁	—	2	1	no	—
381	C₂×C₁₁	—	4	2	no	—
382	C₂×C₁₁	—	8	2	no	—
383	C₂×C₁₁	#2361	1	1	yes	characteristic
384	C₂×C₁₁	C₂×#444	1	1	yes	characteristic
385	C₂×C₁₁	#2956	1	1	yes	characteristic
386	#41	—	2	1	no	—
387	#41	—	2	1	no	—
388	#41	—	2	2	no	—
389	#41	—	2	2	no	—
390	#41	—	2	2	no	—
391	#41	—	2	2	no	—
392	#41	C₂×D₄×C₁₁	1	2	yes	—
393	#41	C₁₁×#41	1	2	yes	—
394	C₂×Q₈	C₂²×C₄×C₁₁	1	2	yes	—
395	C₂×Q₈	C₂²×C₄×C₁₁	1	1	yes	characteristic
396	C₂×D₄	—	2	1	no	—
397	C₂×D₄	—	2	2	no	—
398	C₂×D₄	—	2	1	no	—
399	C₂×D₄	—	2	1	no	—
400	C₂×D₄	C₂²×C₄×C₁₁	1	2	yes	—
401	C₂×D₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
402	C₂²×C₄	—	2	1	no	—
403	C₂²×C₄	—	2	1	no	—
404	C₂²×C₄	—	2	1	no	—
405	C₂²×C₄	—	2	1	no	—
406	C₂²×C₄	—	2	2	no	—
407	C₂²×C₄	—	2	1	no	—
408	C₂²×C₄	C₁₁×#41	1	1	yes	characteristic
409	C₂²×C₄	C₁₁×#41	1	1	yes	characteristic
410	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
411	Q₁₆	—	2	4	no	—
412	SD₁₆	—	2	4	no	—
413	SD₁₆	—	2	4	no	—
414	D₈	—	2	4	no	—
415	M₁₆	—	2	1	no	—
416	M₁₆	—	2	2	no	—
417	M₁₆	—	2	1	no	—
418	M₁₆	—	2	2	no	—
419	M₁₆	—	2	1	no	—
420	M₁₆	—	4	4	no	—
421	M₁₆	—	4	4	no	—
422	M₁₆	C₂×D₄×C₁₁	1	2	yes	—
423	C₂×C₈	—	2	1	no	—
424	C₂×C₈	—	2	2	no	—
425	C₂×C₈	—	2	2	no	—
426	C₂×C₈	—	2	2	no	—
427	C₂×C₈	—	2	2	no	—
428	C₂×C₈	—	2	1	no	—
429	C₂×C₈	—	2	2	no	—
430	C₂×C₈	—	4	4	no	—
431	C₂×C₈	—	4	4	no	—
432	C₂×C₈	C₂²×C₄×C₁₁	1	2	yes	—
433	C₂×C₈	C₂²×C₄×C₁₁	1	2	yes	—
434	C₂×C₈	C₂×D₄×C₁₁	1	2	yes	—
435	C₂×C₈	C₂×D₄×C₁₁	1	2	yes	—
436	C₄⋊C₄	—	2	1	no	—
437	C₄⋊C₄	—	2	1	no	—
438	C₄⋊C₄	—	2	1	no	—
439	C₄⋊C₄	—	2	1	no	—
440	C₄⋊C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
441	C₄⋊C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
442	C₂²⋊C₄	—	2	1	no	—
443	C₂²⋊C₄	—	2	1	no	—
444	C₂²⋊C₄	—	2	1	no	—
445	C₂²⋊C₄	—	2	2	no	—
446	C₂²⋊C₄	—	2	2	no	—
447	C₄²	—	2	1	no	—
448	C₄²	—	2	1	no	—
449	C₄²	—	2	1	no	—
450	C₄²	—	2	1	no	—
451	C₄²	—	2	1	no	—
452	C₄²	—	2	1	no	—
453	C₄²	—	4	2	no	—
454	C₄²	—	4	2	no	—
455	C₄²	C₂²×C₄×C₁₁	1	1	yes	characteristic
456	C₄²	C₂²×C₄×C₁₁	1	1	yes	characteristic
457	C₄²	C₂×D₄×C₁₁	1	2	yes	—
458	C₄²	C₂×D₄×C₁₁	1	1	yes	characteristic
459	C₄²	C₂×D₄×C₁₁	1	1	yes	characteristic
460	C₁₁	#23016	1	1	yes	characteristic, direct product factor, Sylow
461	C₂³	—	2	1	no	—
462	C₂³	—	2	2	no	—
463	C₂³	C₂×C₁₁×#41	1	1	yes	characteristic
464	Q₈	—	2	1	no	—
465	Q₈	—	2	2	no	—
466	Q₈	—	2	2	no	—
467	Q₈	C₄×D₄×C₁₁	1	2	yes	—
468	D₄	—	2	2	no	—
469	D₄	—	2	2	no	—
470	D₄	—	2	2	no	—
471	D₄	—	2	1	no	—
472	D₄	—	2	2	no	—
473	D₄	—	4	2	no	—
474	D₄	—	4	2	no	—
475	D₄	—	4	2	no	—
476	D₄	—	8	1	no	—
477	D₄	C₄×D₄×C₁₁	1	2	yes	—
478	C₂×C₄	—	2	1	no	—
479	C₂×C₄	—	2	2	no	—
480	C₂×C₄	—	2	2	no	—
481	C₂×C₄	—	2	2	no	—
482	C₂×C₄	—	2	2	no	—
483	C₂×C₄	—	2	1	no	—
484	C₂×C₄	—	2	1	no	—
485	C₂×C₄	—	2	2	no	—
486	C₂×C₄	—	2	2	no	—
487	C₂×C₄	—	4	1	no	—
488	C₂×C₄	—	4	1	no	—
489	C₂×C₄	—	4	1	no	—
490	C₂×C₄	—	4	1	no	—
491	C₂×C₄	—	4	1	no	—
492	C₂×C₄	—	4	2	no	—
493	C₂×C₄	—	4	2	no	—
494	C₂×C₄	—	4	2	no	—
495	C₂×C₄	—	8	1	no	—
496	C₂×C₄	C₄×D₄×C₁₁	1	1	yes	characteristic
497	C₂×C₄	C₄×D₄×C₁₁	1	1	yes	characteristic
498	C₂×C₄	C₄×D₄×C₁₁	1	1	yes	characteristic
499	C₂×C₄	C₄×D₄×C₁₁	1	1	yes	characteristic
500	C₂×C₄	C₂³×C₄×C₁₁	1	1	yes	characteristic
501	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
502	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
503	C₂×C₄	C₂×C₁₁×#41	1	1	yes	characteristic
504	C₂×C₄	C₁₁×H(5,𝔽₂)	1	1	yes	characteristic
505	C₂×C₄	C₁₁×2₋¹⁺⁴	1	1	yes	characteristic
506	C₈	—	2	2	no	—
507	C₈	—	2	2	no	—
508	C₈	—	2	2	no	—
509	C₈	—	2	2	no	—
510	C₈	—	2	2	no	—
511	C₈	—	4	2	no	—
512	C₈	—	4	1	no	—
513	C₂²	—	2	1	no	—
514	C₂²	—	2	1	no	—
515	C₂²	—	2	2	no	—
516	C₂²	—	4	1	no	—
517	C₂²	—	4	1	no	—
518	C₂²	—	4	2	no	—
519	C₂²	—	4	2	no	—
520	C₂²	—	4	2	no	—
521	C₂²	C₂×C₄×D₄×C₁₁	1	1	yes	characteristic
522	C₂²	C₁₁×#547	1	1	yes	characteristic
523	C₂²	C₁₁×#553	1	1	yes	characteristic
524	C₄	—	2	1	no	—
525	C₄	—	2	1	no	—
526	C₄	—	2	1	no	—
527	C₄	—	2	2	no	—
528	C₄	—	4	2	no	—
529	C₄	—	4	2	no	—
530	C₄	—	4	1	no	—
531	C₄	—	4	1	no	—
532	C₄	—	4	2	no	—
533	C₄	C₁₁×#444	1	2	yes	complemented
534	C₄	C₂×C₄×D₄×C₁₁	1	1	yes	characteristic
535	C₄	C₁₁×#520	1	1	yes	characteristic
536	C₄	D₄²×C₁₁	1	1	yes	characteristic
537	C₄	C₁₁×#548	1	1	yes	characteristic
538	C₂	—	2	1	no	—
539	C₂	—	2	1	no	—
540	C₂	—	4	2	no	—
541	C₂	—	8	2	no	—
542	C₂	C₁₁×#2361	1	1	yes	characteristic
543	C₂	C₂×C₁₁×#444	1	1	yes	characteristic
544	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. C₂×C₁₁×#444	C₂	semidirect
3. C₁₁×#2935	C₂	semidirect
4. C₁₁×#2906	C₂	semidirect
5. C₁₁×#1962	C₂	semidirect
6. C₁₁×#1950	C₂	semidirect
7. C₁₁×#1938	C₂	semidirect
8. C₁₁×#1876	C₂	semidirect
9. C₁₁×#1866	C₂	semidirect
10. C₁₁×#1767	C₂	semidirect
11. C₄×C₁₁×#104	C₂	semidirect
17. C₁₁×#464	C₄	semidirect
18. C₁₁×#463	C₄	semidirect
19. C₁₁×#462	C₄	semidirect
20. C₁₁×#461	C₄	semidirect
21. C₁₁×#460	C₄	semidirect
22. C₁₁×#459	C₄	semidirect
104. C₁₁×#104	D₄	semidirect
114. #23016	C₁₁	direct (N × H)
190. C₂×#444	C₂×C₁₁	semidirect
191. #2935	C₂×C₁₁	semidirect
192. #2906	C₂×C₁₁	semidirect
193. #1962	C₂×C₁₁	semidirect
194. #1950	C₂×C₁₁	semidirect
195. #1938	C₂×C₁₁	semidirect
196. #1876	C₂×C₁₁	semidirect
197. #1866	C₂×C₁₁	semidirect
198. #1767	C₂×C₁₁	semidirect
199. C₄×#104	C₂×C₁₁	semidirect
257. #464	C₄×C₁₁	semidirect
258. #463	C₄×C₁₁	semidirect
259. #462	C₄×C₁₁	semidirect
260. #461	C₄×C₁₁	semidirect
261. #460	C₄×C₁₁	semidirect
262. #459	C₄×C₁₁	semidirect
308. C₄×C₁₁	#444	semidirect
369. #104	D₄×C₁₁	semidirect
460. C₁₁	#23016	direct (N × H)
533. C₄	C₁₁×#444	semidirect

Maximal subgroups

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

subgroup	index
C₁₁×#3035	2
C₂×C₁₁×#444	2
C₁₁×#2935	2
C₁₁×#2906	2
C₁₁×#1962	2
C₁₁×#1950	2
C₁₁×#1938	2
C₁₁×#1876	2
C₁₁×#1866	2
C₁₁×#1767	2
C₄×C₁₁×#104	2
#23016	11

Subgroups — C11×#23016 #14600209

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#23016 #14600209