Subgroups — C₁₁×#17942 #14595135

Order 2816.

680 conjugacy classes of subgroups.

The subgroup lattice has 472 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×#3105	C₂	1	1	yes	maximal, characteristic
2	C₁₁×#2966	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₁×#436	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₁×#1590	C₂	1	2	yes	maximal, complemented
5	C₁₁×#1589	C₂	1	2	yes	maximal, complemented
6	C₁₁×#1588	C₂	1	2	yes	maximal, complemented
7	C₁₁×#1586	C₂	1	2	yes	maximal, complemented
8	C₁₁×#1573	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₁×#1490	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₁×#1483	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈×C₁₁×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₁₁×M₁₆	—	2	1	no	—
13	C₁₁×#529	C₂²	1	1	yes	characteristic
14	C₂×C₄×D₄×C₁₁	C₂²	1	1	yes	characteristic
15	C₁₁×#484	C₄	1	1	yes	characteristic
16	C₁₁×#481	C₄	1	1	yes	characteristic
17	C₁₁×#478	C₄	1	2	yes	—
18	C₁₁×#463	C₄	1	2	yes	—
19	C₁₁×#450	C₄	1	1	yes	characteristic
20	C₁₁×#447	C₄	1	1	yes	characteristic
21	C₁₁×#446	C₂²	1	1	yes	characteristic, complemented
22	C₈×Q₈×C₁₁	C₂²	1	1	yes	characteristic, complemented
23	C₄×C₁₁×SD₁₆	C₂²	1	2	yes	—
24	C₄×C₁₁×D₈	C₂²	1	2	yes	—
25	C₁₁×#436	—	2	1	no	—
26	C₁₁×#436	—	2	1	no	—
27	C₁₁×#436	C₂²	1	2	yes	—
28	C₁₁×#436	C₂²	1	2	yes	—
29	C₁₁×#436	C₂²	1	1	yes	characteristic, complemented
30	C₁₁×#435	—	2	1	no	—
31	C₈×D₄×C₁₁	—	2	1	no	—
32	C₈×D₄×C₁₁	C₂²	1	1	yes	characteristic, complemented
33	C₁₁×#433	—	2	1	no	—
34	C₁₁×#432	C₂²	1	1	yes	characteristic
35	C₁₁×#431	C₂²	1	1	yes	characteristic
36	C₂×C₁₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
37	C₂×C₁₁×C₂²⋊C₈	—	2	1	no	—
38	C₁₁×#405	—	2	1	no	—
39	C₄×C₁₁×M₁₆	C₂²	1	1	yes	characteristic
40	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
41	C₁₁×#335	C₂²	1	2	yes	complemented
42	C₁₁×#334	C₂²	1	2	yes	complemented
43	C₁₁×Q₈⋊C₈	C₂²	1	2	yes	complemented
44	C₁₁×D₄⋊C₈	C₂²	1	2	yes	—
45	C₁₁×D₄⋊C₈	C₂²	1	2	yes	—
46	C₁₁×D₄⋊C₈	C₂²	1	2	yes	complemented
47	C₁₁×#322	C₂²	1	2	yes	complemented
48	C₈²×C₁₁	C₂²	1	2	yes	complemented
49	C₂²×D₄×C₁₁	C₂×C₄	1	1	yes	characteristic
50	C₂³×C₄×C₁₁	—	2	1	no	—
51	C₂×C₁₁×SD₁₆	C₂×C₄	1	2	yes	—
52	C₂×C₁₁×D₈	C₂×C₄	1	2	yes	—
53	C₂×C₁₁×M₁₆	—	2	1	no	—
54	C₂×C₁₁×M₁₆	—	2	1	no	—
55	C₂×C₁₁×M₁₆	—	2	2	no	—
56	C₂×C₁₁×M₁₆	—	2	2	no	—
57	C₂×C₁₁×M₁₆	—	4	4	no	—
58	C₂²×C₈×C₁₁	—	2	1	no	—
59	C₂²×C₈×C₁₁	—	2	1	no	—
60	C₂²×C₈×C₁₁	D₄	1	1	yes	characteristic
61	C₂²×C₈×C₁₁	D₄	1	1	yes	characteristic
62	C₁₁×#126	—	2	1	no	—
63	C₁₁×#125	C₂×C₄	1	1	yes	characteristic
64	C₁₁×#124	C₂×C₄	1	1	yes	characteristic
65	C₁₁×#123	—	2	1	no	—
66	C₁₁×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
67	C₁₁×#121	C₂×C₄	1	1	yes	characteristic
68	C₄×Q₈×C₁₁	C₂³	1	1	yes	characteristic
69	C₄×D₄×C₁₁	—	2	1	no	—
70	C₄×D₄×C₁₁	—	2	1	no	—
71	C₄×D₄×C₁₁	—	2	1	no	—
72	C₄×D₄×C₁₁	C₂×C₄	1	2	yes	—
73	C₄×D₄×C₁₁	C₂³	1	2	yes	—
74	C₄×D₄×C₁₁	C₂³	1	1	yes	characteristic
75	C₁₁×#117	—	2	1	no	—
76	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
77	C₂×C₁₁×C₂²⋊C₄	—	2	1	no	—
78	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
79	C₁₁×#107	C₂×C₄	1	2	yes	—
80	C₁₁×#106	C₂×C₄	1	2	yes	—
81	C₁₁×C₄⋊C₈	—	2	1	no	—
82	C₁₁×C₄⋊C₈	—	2	1	no	—
83	C₁₁×C₄⋊C₈	—	2	1	no	—
84	C₁₁×C₄⋊C₈	C₂×C₄	1	2	yes	—
85	C₁₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
86	C₁₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
87	C₁₁×C₄⋊C₈	C₂³	1	2	yes	—
88	C₁₁×#103	C₂×C₄	1	2	yes	—
89	C₁₁×#102	C₂×C₄	1	2	yes	—
90	C₁₁×#102	C₂×C₄	1	2	yes	—
91	C₁₁×#102	C₂×C₄	1	2	yes	—
92	C₁₁×C₂²⋊C₈	—	2	1	no	—
93	C₁₁×C₂²⋊C₈	—	2	2	no	—
94	C₁₁×C₂²⋊C₈	—	2	2	no	—
95	C₁₁×C₂²⋊C₈	—	2	1	no	—
96	C₁₁×C₂²⋊C₈	—	2	1	no	—
97	C₁₁×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
98	C₁₁×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
99	C₁₁×#97	—	2	1	no	—
100	C₁₁×#97	—	2	1	no	—
101	C₁₁×#97	—	2	1	no	—
102	C₄×C₈×C₁₁	—	2	1	no	—
103	C₄×C₈×C₁₁	D₄	1	1	yes	characteristic
104	C₄×C₈×C₁₁	D₄	1	1	yes	characteristic
105	C₄×C₈×C₁₁	C₂³	1	2	yes	—
106	C₄×C₈×C₁₁	C₂³	1	2	yes	—
107	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
108	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
109	#17942	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
110	C₂⁴×C₁₁	—	2	1	no	—
111	C₂×Q₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
112	C₂×D₄×C₁₁	—	2	1	no	—
113	C₂×D₄×C₁₁	—	2	1	no	—
114	C₂×D₄×C₁₁	—	4	2	no	—
115	C₂×D₄×C₁₁	C₂²×C₄	1	2	yes	—
116	C₂×D₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
117	C₂²×C₄×C₁₁	—	2	1	no	—
118	C₂²×C₄×C₁₁	—	2	2	no	—
119	C₂²×C₄×C₁₁	—	2	1	no	—
120	C₂²×C₄×C₁₁	—	2	2	no	—
121	C₂²×C₄×C₁₁	—	4	2	no	—
122	C₂²×C₄×C₁₁	—	4	2	no	—
123	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
124	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
125	C₂²×C₄×C₁₁	#41	1	1	yes	characteristic
126	C₁₁×SD₁₆	—	4	2	no	—
127	C₁₁×D₈	—	4	2	no	—
128	C₁₁×M₁₆	—	2	4	no	—
129	C₁₁×M₁₆	—	4	4	no	—
130	C₁₁×M₁₆	—	4	2	no	—
131	C₁₁×M₁₆	—	4	4	no	—
132	C₂×C₈×C₁₁	—	2	2	no	—
133	C₂×C₈×C₁₁	—	2	1	no	—
134	C₂×C₈×C₁₁	—	2	1	no	—
135	C₂×C₈×C₁₁	—	2	2	no	—
136	C₂×C₈×C₁₁	—	2	2	no	—
137	C₂×C₈×C₁₁	—	4	1	no	—
138	C₂×C₈×C₁₁	—	4	2	no	—
139	C₂×C₈×C₁₁	—	4	2	no	—
140	C₂×C₈×C₁₁	C₂²×C₄	1	2	yes	—
141	C₂×C₈×C₁₁	C₂²×C₄	1	2	yes	—
142	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
143	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
144	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
145	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
146	C₁₁×C₄⋊C₄	—	2	1	no	—
147	C₁₁×C₄⋊C₄	—	2	1	no	—
148	C₁₁×C₄⋊C₄	—	2	1	no	—
149	C₁₁×C₄⋊C₄	—	2	1	no	—
150	C₁₁×C₄⋊C₄	—	2	1	no	—
151	C₁₁×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
152	C₁₁×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
153	C₁₁×C₄⋊C₄	C₂²×C₄	1	2	yes	—
154	C₁₁×C₂²⋊C₄	—	2	1	no	—
155	C₁₁×C₂²⋊C₄	—	2	2	no	—
156	C₁₁×C₂²⋊C₄	—	2	1	no	—
157	C₁₁×C₂²⋊C₄	—	2	1	no	—
158	C₁₁×C₂²⋊C₄	—	2	1	no	—
159	C₁₁×C₂²⋊C₄	—	2	2	no	—
160	C₁₁×C₂²⋊C₄	—	2	1	no	—
161	C₄²×C₁₁	—	2	1	no	—
162	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
163	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
164	C₄²×C₁₁	#41	1	1	yes	characteristic
165	C₄²×C₁₁	C₂⁴	1	1	yes	characteristic
166	#3105	C₂×C₁₁	1	1	yes	characteristic
167	#2966	C₂×C₁₁	1	1	yes	characteristic, complemented
168	C₂×#436	C₂×C₁₁	1	1	yes	characteristic, complemented
169	#1590	C₂×C₁₁	1	2	yes	complemented
170	#1589	C₂×C₁₁	1	2	yes	complemented
171	#1588	C₂×C₁₁	1	2	yes	complemented
172	#1586	C₂×C₁₁	1	2	yes	complemented
173	#1573	C₂×C₁₁	1	1	yes	characteristic, complemented
174	#1490	C₂×C₁₁	1	1	yes	characteristic, complemented
175	#1483	C₂×C₁₁	1	1	yes	characteristic, complemented
176	C₈×M₁₆	C₂×C₁₁	1	1	yes	characteristic, complemented
177	C₂³×C₁₁	—	2	1	no	—
178	C₂³×C₁₁	—	2	2	no	—
179	C₂³×C₁₁	—	4	2	no	—
180	C₂³×C₁₁	—	4	2	no	—
181	C₂³×C₁₁	—	4	2	no	—
182	C₂³×C₁₁	C₄×D₄	1	1	yes	characteristic
183	Q₈×C₁₁	—	2	2	no	—
184	D₄×C₁₁	—	2	2	no	—
185	D₄×C₁₁	—	2	2	no	—
186	D₄×C₁₁	—	2	2	no	—
187	D₄×C₁₁	—	4	2	no	—
188	D₄×C₁₁	—	4	2	no	—
189	C₂×C₄×C₁₁	—	2	2	no	—
190	C₂×C₄×C₁₁	—	2	2	no	—
191	C₂×C₄×C₁₁	—	2	1	no	—
192	C₂×C₄×C₁₁	—	2	1	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	2	no	—
197	C₂×C₄×C₁₁	—	4	4	no	—
198	C₂×C₄×C₁₁	—	4	2	no	—
199	C₂×C₄×C₁₁	—	4	2	no	—
200	C₂×C₄×C₁₁	—	4	1	no	—
201	C₂×C₄×C₁₁	—	4	1	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	C₂³×C₄	1	1	yes	characteristic
207	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
208	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
209	C₈×C₁₁	—	2	4	no	—
210	C₈×C₁₁	—	2	2	no	—
211	C₈×C₁₁	—	2	2	no	—
212	C₈×C₁₁	—	2	1	no	—
213	C₈×C₁₁	—	2	1	no	—
214	C₈×C₁₁	—	2	1	no	—
215	C₈×C₁₁	—	4	2	no	—
216	C₈×C₁₁	—	4	1	no	—
217	C₈×C₁₁	—	4	1	no	—
218	C₈×C₁₁	AGL(1,ℤ/8)	1	2	yes	—
219	C₂²×M₁₆	—	2	1	no	—
220	#529	C₂²×C₁₁	1	1	yes	characteristic
221	C₂×C₄×D₄	C₂²×C₁₁	1	1	yes	characteristic
222	#484	C₄×C₁₁	1	1	yes	characteristic
223	#481	C₄×C₁₁	1	1	yes	characteristic
224	#478	C₄×C₁₁	1	2	yes	—
225	#463	C₄×C₁₁	1	2	yes	—
226	#450	C₄×C₁₁	1	1	yes	characteristic
227	#447	C₄×C₁₁	1	1	yes	characteristic
228	#446	C₂²×C₁₁	1	1	yes	characteristic, complemented
229	C₈×Q₈	C₂²×C₁₁	1	1	yes	characteristic, complemented
230	C₄×SD₁₆	C₂²×C₁₁	1	2	yes	—
231	C₄×D₈	C₂²×C₁₁	1	2	yes	—
232	#436	—	2	1	no	—
233	#436	—	2	1	no	—
234	#436	C₂²×C₁₁	1	2	yes	—
235	#436	C₂²×C₁₁	1	2	yes	—
236	#436	C₂²×C₁₁	1	1	yes	characteristic, complemented
237	#435	—	2	1	no	—
238	C₈×D₄	—	2	1	no	—
239	C₈×D₄	C₂²×C₁₁	1	1	yes	characteristic, complemented
240	#433	—	2	1	no	—
241	#432	C₂²×C₁₁	1	1	yes	characteristic
242	#431	C₂²×C₁₁	1	1	yes	characteristic
243	C₂×C₄⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
244	C₂×C₂²⋊C₈	—	2	1	no	—
245	#405	—	2	1	no	—
246	C₄×M₁₆	C₂²×C₁₁	1	1	yes	characteristic
247	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
248	#335	C₂²×C₁₁	1	2	yes	complemented
249	#334	C₂²×C₁₁	1	2	yes	complemented
250	Q₈⋊C₈	C₂²×C₁₁	1	2	yes	complemented
251	D₄⋊C₈	C₂²×C₁₁	1	2	yes	—
252	D₄⋊C₈	C₂²×C₁₁	1	2	yes	—
253	D₄⋊C₈	C₂²×C₁₁	1	2	yes	complemented
254	#322	C₂²×C₁₁	1	2	yes	complemented
255	C₈²	C₂²×C₁₁	1	2	yes	complemented
256	C₂²×C₁₁	—	2	1	no	—
257	C₂²×C₁₁	—	2	1	no	—
258	C₂²×C₁₁	—	4	2	no	—
259	C₂²×C₁₁	—	4	1	no	—
260	C₂²×C₁₁	—	4	2	no	—
261	C₂²×C₁₁	—	4	1	no	—
262	C₂²×C₁₁	—	4	1	no	—
263	C₂²×C₁₁	—	4	2	no	—
264	C₂²×C₁₁	—	8	4	no	—
265	C₂²×C₁₁	#443	1	2	yes	—
266	C₂²×C₁₁	C₂×C₄×D₄	1	1	yes	characteristic
267	C₄×C₁₁	—	2	1	no	—
268	C₄×C₁₁	—	2	1	no	—
269	C₄×C₁₁	—	2	1	no	—
270	C₄×C₁₁	—	2	1	no	—
271	C₄×C₁₁	—	4	1	no	—
272	C₄×C₁₁	—	4	1	no	—
273	C₄×C₁₁	—	4	2	no	—
274	C₄×C₁₁	—	4	1	no	—
275	C₄×C₁₁	#568	1	2	yes	—
276	C₄×C₁₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
277	C₄×C₁₁	#575	1	1	yes	characteristic
278	C₂²×D₄	C₂×C₄×C₁₁	1	1	yes	characteristic
279	C₂³×C₄	—	2	1	no	—
280	C₂×SD₁₆	C₂×C₄×C₁₁	1	2	yes	—
281	C₂×D₈	C₂×C₄×C₁₁	1	2	yes	—
282	C₂×M₁₆	—	2	1	no	—
283	C₂×M₁₆	—	2	2	no	—
284	C₂×M₁₆	—	2	2	no	—
285	C₂×M₁₆	—	2	1	no	—
286	C₂×M₁₆	—	4	4	no	—
287	C₂²×C₈	—	2	1	no	—
288	C₂²×C₈	—	2	1	no	—
289	C₂²×C₈	D₄×C₁₁	1	1	yes	characteristic
290	C₂²×C₈	D₄×C₁₁	1	1	yes	characteristic
291	#126	—	2	1	no	—
292	#125	C₂×C₄×C₁₁	1	1	yes	characteristic
293	#124	C₂×C₄×C₁₁	1	1	yes	characteristic
294	#123	—	2	1	no	—
295	C₂²⋊Q₈	C₂×C₄×C₁₁	1	1	yes	characteristic
296	#121	C₂×C₄×C₁₁	1	1	yes	characteristic
297	C₄×Q₈	C₂³×C₁₁	1	1	yes	characteristic
298	C₄×D₄	—	2	1	no	—
299	C₄×D₄	—	2	1	no	—
300	C₄×D₄	—	2	1	no	—
301	C₄×D₄	C₂×C₄×C₁₁	1	2	yes	—
302	C₄×D₄	C₂³×C₁₁	1	2	yes	—
303	C₄×D₄	C₂³×C₁₁	1	1	yes	characteristic
304	#117	—	2	1	no	—
305	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
306	C₂×C₂²⋊C₄	—	2	1	no	—
307	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
308	#107	C₂×C₄×C₁₁	1	2	yes	—
309	#106	C₂×C₄×C₁₁	1	2	yes	—
310	C₄⋊C₈	—	2	1	no	—
311	C₄⋊C₈	—	2	1	no	—
312	C₄⋊C₈	—	2	1	no	—
313	C₄⋊C₈	C₂×C₄×C₁₁	1	2	yes	—
314	C₄⋊C₈	C₂³×C₁₁	1	1	yes	characteristic
315	C₄⋊C₈	C₂³×C₁₁	1	1	yes	characteristic
316	C₄⋊C₈	C₂³×C₁₁	1	2	yes	—
317	#103	C₂×C₄×C₁₁	1	2	yes	—
318	#102	C₂×C₄×C₁₁	1	2	yes	—
319	#102	C₂×C₄×C₁₁	1	2	yes	—
320	#102	C₂×C₄×C₁₁	1	2	yes	—
321	C₂²⋊C₈	—	2	1	no	—
322	C₂²⋊C₈	—	2	2	no	—
323	C₂²⋊C₈	—	2	2	no	—
324	C₂²⋊C₈	—	2	1	no	—
325	C₂²⋊C₈	—	2	1	no	—
326	C₂²⋊C₈	C₂×C₄×C₁₁	1	1	yes	characteristic
327	C₂²⋊C₈	C₂×C₄×C₁₁	1	1	yes	characteristic
328	#97	—	2	1	no	—
329	#97	—	2	1	no	—
330	#97	—	2	1	no	—
331	C₄×C₈	—	2	1	no	—
332	C₄×C₈	D₄×C₁₁	1	1	yes	characteristic
333	C₄×C₈	D₄×C₁₁	1	1	yes	characteristic
334	C₄×C₈	C₂³×C₁₁	1	2	yes	—
335	C₄×C₈	C₂³×C₁₁	1	2	yes	—
336	C₄×C₈	C₂³×C₁₁	1	1	yes	characteristic
337	C₄×C₈	C₂³×C₁₁	1	1	yes	characteristic
338	C₂×C₁₁	—	2	2	no	—
339	C₂×C₁₁	—	8	1	no	—
340	C₂×C₁₁	—	8	2	no	—
341	C₂×C₁₁	#2930	1	1	yes	characteristic
342	C₂×C₁₁	C₄×AGL(1,ℤ/8)	1	1	yes	characteristic
343	C₂×C₁₁	C₂×#443	1	1	yes	characteristic
344	C₂⁴	—	2	1	no	—
345	C₂×Q₈	C₂²×C₄×C₁₁	1	1	yes	characteristic
346	C₂×D₄	—	2	1	no	—
347	C₂×D₄	—	2	1	no	—
348	C₂×D₄	—	4	2	no	—
349	C₂×D₄	C₂²×C₄×C₁₁	1	2	yes	—
350	C₂×D₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
351	C₂²×C₄	—	2	1	no	—
352	C₂²×C₄	—	2	2	no	—
353	C₂²×C₄	—	2	1	no	—
354	C₂²×C₄	—	2	2	no	—
355	C₂²×C₄	—	4	2	no	—
356	C₂²×C₄	—	4	2	no	—
357	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
358	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
359	C₂²×C₄	C₁₁×#41	1	1	yes	characteristic
360	SD₁₆	—	4	2	no	—
361	D₈	—	4	2	no	—
362	M₁₆	—	2	4	no	—
363	M₁₆	—	4	4	no	—
364	M₁₆	—	4	4	no	—
365	M₁₆	—	4	2	no	—
366	C₂×C₈	—	2	2	no	—
367	C₂×C₈	—	2	2	no	—
368	C₂×C₈	—	2	1	no	—
369	C₂×C₈	—	2	1	no	—
370	C₂×C₈	—	2	2	no	—
371	C₂×C₈	—	4	1	no	—
372	C₂×C₈	—	4	2	no	—
373	C₂×C₈	—	4	2	no	—
374	C₂×C₈	C₂²×C₄×C₁₁	1	2	yes	—
375	C₂×C₈	C₂²×C₄×C₁₁	1	2	yes	—
376	C₂×C₈	C₂×D₄×C₁₁	1	1	yes	characteristic
377	C₂×C₈	C₂×D₄×C₁₁	1	1	yes	characteristic
378	C₂×C₈	C₂×D₄×C₁₁	1	1	yes	characteristic
379	C₂×C₈	C₂×D₄×C₁₁	1	1	yes	characteristic
380	C₄⋊C₄	—	2	1	no	—
381	C₄⋊C₄	—	2	1	no	—
382	C₄⋊C₄	—	2	1	no	—
383	C₄⋊C₄	—	2	1	no	—
384	C₄⋊C₄	—	2	1	no	—
385	C₄⋊C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
386	C₄⋊C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
387	C₄⋊C₄	C₂²×C₄×C₁₁	1	2	yes	—
388	C₂²⋊C₄	—	2	1	no	—
389	C₂²⋊C₄	—	2	2	no	—
390	C₂²⋊C₄	—	2	1	no	—
391	C₂²⋊C₄	—	2	1	no	—
392	C₂²⋊C₄	—	2	1	no	—
393	C₂²⋊C₄	—	2	2	no	—
394	C₂²⋊C₄	—	2	1	no	—
395	C₄²	—	2	1	no	—
396	C₄²	C₂²×C₄×C₁₁	1	1	yes	characteristic
397	C₄²	C₂×D₄×C₁₁	1	1	yes	characteristic
398	C₄²	C₁₁×#41	1	1	yes	characteristic
399	C₄²	C₂⁴×C₁₁	1	1	yes	characteristic
400	C₁₁	#17942	1	1	yes	characteristic, direct product factor, Sylow
401	C₂³	—	2	1	no	—
402	C₂³	—	2	2	no	—
403	C₂³	—	4	2	no	—
404	C₂³	—	4	2	no	—
405	C₂³	—	4	2	no	—
406	C₂³	C₄×D₄×C₁₁	1	1	yes	characteristic
407	Q₈	—	2	2	no	—
408	D₄	—	2	2	no	—
409	D₄	—	2	2	no	—
410	D₄	—	2	2	no	—
411	D₄	—	4	2	no	—
412	D₄	—	4	2	no	—
413	C₂×C₄	—	2	2	no	—
414	C₂×C₄	—	2	2	no	—
415	C₂×C₄	—	2	1	no	—
416	C₂×C₄	—	2	1	no	—
417	C₂×C₄	—	2	1	no	—
418	C₂×C₄	—	2	1	no	—
419	C₂×C₄	—	2	1	no	—
420	C₂×C₄	—	2	2	no	—
421	C₂×C₄	—	4	4	no	—
422	C₂×C₄	—	4	2	no	—
423	C₂×C₄	—	4	2	no	—
424	C₂×C₄	—	4	1	no	—
425	C₂×C₄	—	4	1	no	—
426	C₂×C₄	—	4	2	no	—
427	C₂×C₄	C₄×D₄×C₁₁	1	1	yes	characteristic
428	C₂×C₄	C₄×D₄×C₁₁	1	1	yes	characteristic
429	C₂×C₄	C₄×D₄×C₁₁	1	1	yes	characteristic
430	C₂×C₄	C₂³×C₄×C₁₁	1	1	yes	characteristic
431	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
432	C₂×C₄	C₂×C₁₁×#41	1	1	yes	characteristic
433	C₈	—	2	4	no	—
434	C₈	—	2	2	no	—
435	C₈	—	2	2	no	—
436	C₈	—	2	1	no	—
437	C₈	—	2	1	no	—
438	C₈	—	2	1	no	—
439	C₈	—	4	2	no	—
440	C₈	—	4	1	no	—
441	C₈	—	4	1	no	—
442	C₈	C₁₁×AGL(1,ℤ/8)	1	2	yes	—
443	C₂²	—	2	1	no	—
444	C₂²	—	2	1	no	—
445	C₂²	—	4	2	no	—
446	C₂²	—	4	1	no	—
447	C₂²	—	4	2	no	—
448	C₂²	—	4	1	no	—
449	C₂²	—	4	1	no	—
450	C₂²	—	4	2	no	—
451	C₂²	—	8	4	no	—
452	C₂²	C₁₁×#443	1	2	yes	—
453	C₂²	C₂×C₄×D₄×C₁₁	1	1	yes	characteristic
454	C₄	—	2	1	no	—
455	C₄	—	2	1	no	—
456	C₄	—	2	1	no	—
457	C₄	—	2	1	no	—
458	C₄	—	4	1	no	—
459	C₄	—	4	2	no	—
460	C₄	—	4	1	no	—
461	C₄	—	4	1	no	—
462	C₄	C₁₁×#568	1	2	yes	—
463	C₄	C₂×C₁₁×AGL(1,ℤ/8)	1	1	yes	characteristic
464	C₄	C₁₁×#575	1	1	yes	characteristic
465	C₂	—	2	2	no	—
466	C₂	—	8	2	no	—
467	C₂	—	8	1	no	—
468	C₂	C₁₁×#2930	1	1	yes	characteristic
469	C₂	C₄×C₁₁×AGL(1,ℤ/8)	1	1	yes	characteristic
470	C₂	C₂×C₁₁×#443	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₁	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₁
Frattini, cosocle	C₄²	C₂⁴×C₁₁
socle	C₂²×C₁₁	C₂×C₄×D₄
prime radical	C₁₁×#447	C₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₁ ◁ C₂×C₄×C₈×C₁₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₁×#2966	C₂	semidirect
3. C₂×C₁₁×#436	C₂	semidirect
4. C₁₁×#1590	C₂	semidirect
5. C₁₁×#1589	C₂	semidirect
6. C₁₁×#1588	C₂	semidirect
7. C₁₁×#1586	C₂	semidirect
8. C₁₁×#1573	C₂	semidirect
9. C₁₁×#1490	C₂	semidirect
10. C₁₁×#1483	C₂	semidirect
11. C₈×C₁₁×M₁₆	C₂	semidirect
21. C₁₁×#446	C₂²	semidirect
22. C₈×Q₈×C₁₁	C₂²	semidirect
29. C₁₁×#436	C₂²	semidirect
32. C₈×D₄×C₁₁	C₂²	semidirect
41. C₁₁×#335	C₂²	semidirect
42. C₁₁×#334	C₂²	semidirect
43. C₁₁×Q₈⋊C₈	C₂²	semidirect
46. C₁₁×D₄⋊C₈	C₂²	semidirect
47. C₁₁×#322	C₂²	semidirect
48. C₈²×C₁₁	C₂²	semidirect
109. #17942	C₁₁	direct (N × H)
167. #2966	C₂×C₁₁	semidirect
168. C₂×#436	C₂×C₁₁	semidirect
169. #1590	C₂×C₁₁	semidirect
170. #1589	C₂×C₁₁	semidirect
171. #1588	C₂×C₁₁	semidirect
172. #1586	C₂×C₁₁	semidirect
173. #1573	C₂×C₁₁	semidirect
174. #1490	C₂×C₁₁	semidirect
175. #1483	C₂×C₁₁	semidirect
176. C₈×M₁₆	C₂×C₁₁	semidirect
228. #446	C₂²×C₁₁	semidirect
229. C₈×Q₈	C₂²×C₁₁	semidirect
236. #436	C₂²×C₁₁	semidirect
239. C₈×D₄	C₂²×C₁₁	semidirect
248. #335	C₂²×C₁₁	semidirect
249. #334	C₂²×C₁₁	semidirect
250. Q₈⋊C₈	C₂²×C₁₁	semidirect
253. D₄⋊C₈	C₂²×C₁₁	semidirect
254. #322	C₂²×C₁₁	semidirect
255. C₈²	C₂²×C₁₁	semidirect
400. C₁₁	#17942	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×#3105	2
C₁₁×#2966	2
C₂×C₁₁×#436	2
C₁₁×#1590	2
C₁₁×#1589	2
C₁₁×#1588	2
C₁₁×#1586	2
C₁₁×#1573	2
C₁₁×#1490	2
C₁₁×#1483	2
C₈×C₁₁×M₁₆	2
#17942	11

Subgroups — C11×#17942 #14595135

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#17942 #14595135