Subgroups — C₁₁×#23199 #14600392

Order 2816.

914 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₁×#495	C₂	1	1	yes	maximal, characteristic
2	C₁₁×#2950	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₁×#2949	C₂	1	2	yes	maximal, complemented
4	C₁₁×#2948	C₂	1	1	yes	maximal, characteristic
5	C₁₁×#1979	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₁×#1978	C₂	1	1	yes	maximal, characteristic
7	C₁₁×#1977	C₂	1	2	yes	maximal, complemented
8	C₁₁×#1888	C₂	1	2	yes	maximal, complemented
9	C₁₁×#1885	C₂	1	2	yes	maximal, complemented
10	C₁₁×#1772	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₁×#1772	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₁₁×Q₁₆	C₂²	1	1	yes	characteristic
13	C₂²×C₁₁×SD₁₆	C₂²	1	2	yes	—
14	C₂²×C₁₁×D₈	C₂²	1	1	yes	characteristic
15	C₂×C₁₁×#124	C₂²	1	2	yes	—
16	C₁₁×#519	C₂²	1	2	yes	—
17	C₁₁×#518	C₂²	1	2	yes	—
18	C₁₁×#495	C₄	1	8	yes	complemented
19	C₁₁×#442	—	2	2	no	—
20	C₁₁×#441	—	2	2	no	—
21	C₁₁×#440	—	2	4	no	—
22	C₄×C₁₁×Q₁₆	—	2	2	no	—
23	C₄×C₁₁×SD₁₆	—	2	4	no	—
24	C₄×C₁₁×D₈	—	2	2	no	—
25	C₂×C₁₁×#108	C₂²	1	1	yes	characteristic
26	C₂×C₁₁×#108	C₂²	1	1	yes	characteristic
27	C₁₁×#427	C₂²	1	1	yes	characteristic
28	C₁₁×#427	C₂²	1	1	yes	characteristic
29	C₁₁×#419	C₂²	1	2	yes	—
30	C₁₁×#419	C₂²	1	2	yes	—
31	C₁₁×#418	C₂²	1	2	yes	—
32	C₁₁×#418	C₂²	1	2	yes	—
33	C₂×C₁₁×#101	C₂²	1	2	yes	—
34	C₂×C₁₁×#100	C₂²	1	2	yes	—
35	C₁₁×#405	C₂²	1	1	yes	characteristic
36	C₁₁×#405	C₂²	1	2	yes	—
37	C₁₁×#405	C₂²	1	1	yes	characteristic
38	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
39	C₁₁×#339	C₂²	1	1	yes	characteristic
40	C₁₁×#339	C₂²	1	2	yes	—
41	C₁₁×#339	C₂²	1	1	yes	characteristic
42	C₂²×Q₈×C₁₁	C₂³	1	2	yes	—
43	C₂²×D₄×C₁₁	C₂³	1	2	yes	—
44	C₂×C₁₁×Q₁₆	—	2	1	no	—
45	C₂×C₁₁×Q₁₆	—	2	1	no	—
46	C₂×C₁₁×Q₁₆	—	2	2	no	—
47	C₂×C₁₁×Q₁₆	C₂×C₄	1	4	yes	complemented
48	C₂×C₁₁×SD₁₆	—	2	2	no	—
49	C₂×C₁₁×SD₁₆	—	2	2	no	—
50	C₂×C₁₁×SD₁₆	—	2	4	no	—
51	C₂×C₁₁×SD₁₆	C₂×C₄	1	8	yes	complemented
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	—
56	C₂×C₁₁×M₁₆	C₂³	1	1	yes	characteristic
57	C₂×C₁₁×M₁₆	C₂³	1	2	yes	—
58	C₂×C₁₁×M₁₆	C₂³	1	1	yes	characteristic
59	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
60	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
61	C₁₁×#124	—	4	2	no	—
62	C₁₁×#124	C₂×C₄	1	8	yes	complemented
63	C₄×Q₈×C₁₁	—	2	4	no	—
64	C₄×Q₈×C₁₁	—	2	4	no	—
65	C₄×D₄×C₁₁	—	2	4	no	—
66	C₄×D₄×C₁₁	—	2	4	no	—
67	C₁₁×#117	—	4	2	no	—
68	C₁₁×#117	C₂³	1	1	yes	characteristic
69	C₁₁×#117	C₂³	1	2	yes	—
70	C₁₁×#117	C₂³	1	1	yes	characteristic
71	C₂×C₁₁×C₂²⋊C₄	—	4	2	no	—
72	C₂×C₁₁×C₂²⋊C₄	—	4	2	no	—
73	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
74	C₁₁×#108	—	2	2	no	—
75	C₁₁×#108	—	2	2	no	—
76	C₁₁×#107	D₄	1	2	yes	—
77	C₁₁×#107	D₄	1	2	yes	—
78	C₁₁×#106	D₄	1	2	yes	—
79	C₁₁×#106	D₄	1	2	yes	—
80	C₁₁×#103	—	2	4	no	—
81	C₁₁×#103	—	2	4	no	—
82	C₁₁×#102	—	2	4	no	—
83	C₁₁×#102	—	2	4	no	—
84	C₁₁×#101	—	4	2	no	—
85	C₁₁×#100	—	4	2	no	—
86	C₁₁×#97	—	2	2	no	—
87	C₁₁×#97	—	2	1	no	—
88	C₁₁×#97	—	2	1	no	—
89	C₄×C₈×C₁₁	—	2	1	no	—
90	C₄×C₈×C₁₁	—	2	2	no	—
91	C₄×C₈×C₁₁	—	2	1	no	—
92	C₄×C₈×C₁₁	C₂×C₄	1	4	yes	complemented
93	#23199	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
94	C₂⁴×C₁₁	—	2	2	no	—
95	C₂×Q₈×C₁₁	—	2	2	no	—
96	C₂×Q₈×C₁₁	—	2	2	no	—
97	C₂×Q₈×C₁₁	—	2	2	no	—
98	C₂×Q₈×C₁₁	—	2	2	no	—
99	C₂×Q₈×C₁₁	—	2	2	no	—
100	C₂×Q₈×C₁₁	C₂²×C₄	1	4	yes	—
101	C₂×D₄×C₁₁	—	2	2	no	—
102	C₂×D₄×C₁₁	—	2	2	no	—
103	C₂×D₄×C₁₁	—	2	2	no	—
104	C₂×D₄×C₁₁	—	2	2	no	—
105	C₂×D₄×C₁₁	—	2	2	no	—
106	C₂×D₄×C₁₁	C₂²×C₄	1	4	yes	—
107	C₂²×C₄×C₁₁	—	2	1	no	—
108	C₂²×C₄×C₁₁	—	2	2	no	—
109	C₂²×C₄×C₁₁	—	4	4	no	—
110	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
111	C₁₁×Q₁₆	—	2	4	no	—
112	C₁₁×Q₁₆	—	2	4	no	—
113	C₁₁×SD₁₆	—	2	8	no	—
114	C₁₁×SD₁₆	—	2	8	no	—
115	C₁₁×D₈	—	2	4	no	—
116	C₁₁×D₈	—	2	4	no	—
117	C₁₁×M₁₆	—	2	1	no	—
118	C₁₁×M₁₆	—	2	2	no	—
119	C₁₁×M₁₆	—	2	1	no	—
120	C₁₁×M₁₆	—	2	1	no	—
121	C₁₁×M₁₆	—	2	2	no	—
122	C₁₁×M₁₆	—	2	1	no	—
123	C₂×C₈×C₁₁	—	2	1	no	—
124	C₂×C₈×C₁₁	—	2	2	no	—
125	C₂×C₈×C₁₁	—	2	1	no	—
126	C₂×C₈×C₁₁	C₂²×C₄	1	2	yes	—
127	C₂×C₈×C₁₁	C₂²×C₄	1	2	yes	—
128	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
129	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
130	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
131	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
132	C₂×C₈×C₁₁	#41	1	2	yes	—
133	C₂×C₈×C₁₁	#41	1	2	yes	—
134	C₁₁×C₄⋊C₄	—	4	4	no	—
135	C₁₁×C₄⋊C₄	C₂×D₄	1	2	yes	—
136	C₁₁×C₄⋊C₄	C₂×D₄	1	4	yes	—
137	C₁₁×C₄⋊C₄	C₂×D₄	1	2	yes	—
138	C₁₁×C₂²⋊C₄	—	2	1	no	—
139	C₁₁×C₂²⋊C₄	—	2	2	no	—
140	C₁₁×C₂²⋊C₄	—	2	1	no	—
141	C₁₁×C₂²⋊C₄	—	4	8	no	—
142	C₁₁×C₂²⋊C₄	—	4	4	no	—
143	C₄²×C₁₁	—	2	1	no	—
144	C₄²×C₁₁	—	2	2	no	—
145	C₄²×C₁₁	—	2	1	no	—
146	C₄²×C₁₁	—	2	1	no	—
147	C₄²×C₁₁	—	4	4	no	—
148	C₄²×C₁₁	C₂²×C₄	1	2	yes	—
149	C₂×#495	C₂×C₁₁	1	1	yes	characteristic
150	#2950	C₂×C₁₁	1	1	yes	characteristic, complemented
151	#2949	C₂×C₁₁	1	2	yes	complemented
152	#2948	C₂×C₁₁	1	1	yes	characteristic
153	#1979	C₂×C₁₁	1	1	yes	characteristic, complemented
154	#1978	C₂×C₁₁	1	1	yes	characteristic
155	#1977	C₂×C₁₁	1	2	yes	complemented
156	#1888	C₂×C₁₁	1	2	yes	complemented
157	#1885	C₂×C₁₁	1	2	yes	complemented
158	#1772	C₂×C₁₁	1	1	yes	characteristic, complemented
159	#1772	C₂×C₁₁	1	1	yes	characteristic, complemented
160	C₂³×C₁₁	—	2	4	no	—
161	C₂³×C₁₁	—	4	2	no	—
162	C₂³×C₁₁	—	4	2	no	—
163	C₂³×C₁₁	—	8	4	no	—
164	C₂³×C₁₁	H(5,𝔽₂)	1	1	yes	characteristic
165	Q₈×C₁₁	—	2	4	no	—
166	Q₈×C₁₁	—	2	4	no	—
167	Q₈×C₁₁	—	4	2	no	—
168	Q₈×C₁₁	—	4	2	no	—
169	D₄×C₁₁	—	2	4	no	—
170	D₄×C₁₁	—	2	4	no	—
171	D₄×C₁₁	—	4	2	no	—
172	D₄×C₁₁	—	4	2	no	—
173	C₂×C₄×C₁₁	—	2	2	no	—
174	C₂×C₄×C₁₁	—	2	4	no	—
175	C₂×C₄×C₁₁	—	2	2	no	—
176	C₂×C₄×C₁₁	—	2	4	no	—
177	C₂×C₄×C₁₁	—	2	2	no	—
178	C₂×C₄×C₁₁	—	4	2	no	—
179	C₂×C₄×C₁₁	—	4	2	no	—
180	C₂×C₄×C₁₁	—	4	2	no	—
181	C₂×C₄×C₁₁	—	16	4	no	—
182	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
183	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
184	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
185	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
186	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
187	C₂×C₄×C₁₁	H(5,𝔽₂)	1	1	yes	characteristic
188	C₈×C₁₁	—	4	1	no	—
189	C₈×C₁₁	—	4	2	no	—
190	C₈×C₁₁	—	4	1	no	—
191	C₈×C₁₁	C₄×D₄	1	2	yes	—
192	C₈×C₁₁	C₄×D₄	1	2	yes	—
193	C₈×C₁₁	C₄×D₄	1	2	yes	—
194	C₈×C₁₁	C₄×D₄	1	2	yes	—
195	C₂²×Q₁₆	C₂²×C₁₁	1	1	yes	characteristic
196	C₂²×SD₁₆	C₂²×C₁₁	1	2	yes	—
197	C₂²×D₈	C₂²×C₁₁	1	1	yes	characteristic
198	C₂×#124	C₂²×C₁₁	1	2	yes	—
199	#519	C₂²×C₁₁	1	2	yes	—
200	#518	C₂²×C₁₁	1	2	yes	—
201	#495	C₄×C₁₁	1	8	yes	complemented
202	#442	—	2	2	no	—
203	#441	—	2	2	no	—
204	#440	—	2	4	no	—
205	C₄×Q₁₆	—	2	2	no	—
206	C₄×SD₁₆	—	2	4	no	—
207	C₄×D₈	—	2	2	no	—
208	C₂×#108	C₂²×C₁₁	1	1	yes	characteristic
209	C₂×#108	C₂²×C₁₁	1	1	yes	characteristic
210	#427	C₂²×C₁₁	1	1	yes	characteristic
211	#427	C₂²×C₁₁	1	1	yes	characteristic
212	#419	C₂²×C₁₁	1	2	yes	—
213	#419	C₂²×C₁₁	1	2	yes	—
214	#418	C₂²×C₁₁	1	2	yes	—
215	#418	C₂²×C₁₁	1	2	yes	—
216	C₂×#101	C₂²×C₁₁	1	2	yes	—
217	C₂×#100	C₂²×C₁₁	1	2	yes	—
218	#405	C₂²×C₁₁	1	1	yes	characteristic
219	#405	C₂²×C₁₁	1	2	yes	—
220	#405	C₂²×C₁₁	1	1	yes	characteristic
221	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
222	#339	C₂²×C₁₁	1	1	yes	characteristic
223	#339	C₂²×C₁₁	1	2	yes	—
224	#339	C₂²×C₁₁	1	1	yes	characteristic
225	C₂²×C₁₁	—	2	2	no	—
226	C₂²×C₁₁	—	4	4	no	—
227	C₂²×C₁₁	—	8	4	no	—
228	C₂²×C₁₁	—	8	4	no	—
229	C₂²×C₁₁	—	16	2	no	—
230	C₂²×C₁₁	#518	1	1	yes	characteristic
231	C₂²×C₁₁	D₄²	1	1	yes	characteristic
232	C₂²×C₁₁	#559	1	1	yes	characteristic
233	C₄×C₁₁	—	4	2	no	—
234	C₄×C₁₁	—	4	4	no	—
235	C₄×C₁₁	—	4	2	no	—
236	C₄×C₁₁	—	4	4	no	—
237	C₄×C₁₁	—	4	2	no	—
238	C₄×C₁₁	C₂×C₄×D₄	1	1	yes	characteristic
239	C₄×C₁₁	C₂×C₄×D₄	1	1	yes	characteristic
240	C₄×C₁₁	#550	1	1	yes	characteristic
241	C₄×C₁₁	#550	1	1	yes	characteristic
242	C₂²×Q₈	C₂³×C₁₁	1	2	yes	—
243	C₂²×D₄	C₂³×C₁₁	1	2	yes	—
244	C₂×Q₁₆	—	2	1	no	—
245	C₂×Q₁₆	—	2	1	no	—
246	C₂×Q₁₆	—	2	2	no	—
247	C₂×Q₁₆	C₂×C₄×C₁₁	1	4	yes	complemented
248	C₂×SD₁₆	—	2	2	no	—
249	C₂×SD₁₆	—	2	2	no	—
250	C₂×SD₁₆	—	2	4	no	—
251	C₂×SD₁₆	C₂×C₄×C₁₁	1	8	yes	complemented
252	C₂×D₈	—	2	1	no	—
253	C₂×D₈	—	2	1	no	—
254	C₂×D₈	—	2	2	no	—
255	C₂×D₈	C₂×C₄×C₁₁	1	4	yes	—
256	C₂×M₁₆	C₂³×C₁₁	1	1	yes	characteristic
257	C₂×M₁₆	C₂³×C₁₁	1	2	yes	—
258	C₂×M₁₆	C₂³×C₁₁	1	1	yes	characteristic
259	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
260	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
261	#124	—	4	2	no	—
262	#124	C₂×C₄×C₁₁	1	8	yes	complemented
263	C₄×Q₈	—	2	4	no	—
264	C₄×Q₈	—	2	4	no	—
265	C₄×D₄	—	2	4	no	—
266	C₄×D₄	—	2	4	no	—
267	#117	—	4	2	no	—
268	#117	C₂³×C₁₁	1	1	yes	characteristic
269	#117	C₂³×C₁₁	1	2	yes	—
270	#117	C₂³×C₁₁	1	1	yes	characteristic
271	C₂×C₂²⋊C₄	—	4	2	no	—
272	C₂×C₂²⋊C₄	—	4	2	no	—
273	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
274	#108	—	2	2	no	—
275	#108	—	2	2	no	—
276	#107	D₄×C₁₁	1	2	yes	—
277	#107	D₄×C₁₁	1	2	yes	—
278	#106	D₄×C₁₁	1	2	yes	—
279	#106	D₄×C₁₁	1	2	yes	—
280	#103	—	2	4	no	—
281	#103	—	2	4	no	—
282	#102	—	2	4	no	—
283	#102	—	2	4	no	—
284	#101	—	4	2	no	—
285	#100	—	4	2	no	—
286	#97	—	2	2	no	—
287	#97	—	2	1	no	—
288	#97	—	2	1	no	—
289	C₄×C₈	—	2	1	no	—
290	C₄×C₈	—	2	2	no	—
291	C₄×C₈	—	2	1	no	—
292	C₄×C₈	C₂×C₄×C₁₁	1	4	yes	complemented
293	C₂×C₁₁	—	2	1	no	—
294	C₂×C₁₁	—	2	1	no	—
295	C₂×C₁₁	—	8	4	no	—
296	C₂×C₁₁	#2366	1	1	yes	characteristic
297	C₂×C₁₁	#3290	1	2	yes	—
298	C₂⁴	—	2	2	no	—
299	C₂×Q₈	—	2	2	no	—
300	C₂×Q₈	—	2	2	no	—
301	C₂×Q₈	—	2	2	no	—
302	C₂×Q₈	—	2	2	no	—
303	C₂×Q₈	—	2	2	no	—
304	C₂×Q₈	C₂²×C₄×C₁₁	1	4	yes	—
305	C₂×D₄	—	2	2	no	—
306	C₂×D₄	—	2	2	no	—
307	C₂×D₄	—	2	2	no	—
308	C₂×D₄	—	2	2	no	—
309	C₂×D₄	—	2	2	no	—
310	C₂×D₄	C₂²×C₄×C₁₁	1	4	yes	—
311	C₂²×C₄	—	2	1	no	—
312	C₂²×C₄	—	2	2	no	—
313	C₂²×C₄	—	4	4	no	—
314	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
315	Q₁₆	—	2	4	no	—
316	Q₁₆	—	2	4	no	—
317	SD₁₆	—	2	8	no	—
318	SD₁₆	—	2	8	no	—
319	D₈	—	2	4	no	—
320	D₈	—	2	4	no	—
321	M₁₆	—	2	1	no	—
322	M₁₆	—	2	2	no	—
323	M₁₆	—	2	1	no	—
324	M₁₆	—	2	1	no	—
325	M₁₆	—	2	2	no	—
326	M₁₆	—	2	1	no	—
327	C₂×C₈	—	2	1	no	—
328	C₂×C₈	—	2	2	no	—
329	C₂×C₈	—	2	1	no	—
330	C₂×C₈	C₂²×C₄×C₁₁	1	2	yes	—
331	C₂×C₈	C₂²×C₄×C₁₁	1	2	yes	—
332	C₂×C₈	C₂×D₄×C₁₁	1	1	yes	characteristic
333	C₂×C₈	C₂×D₄×C₁₁	1	1	yes	characteristic
334	C₂×C₈	C₂×D₄×C₁₁	1	1	yes	characteristic
335	C₂×C₈	C₂×D₄×C₁₁	1	1	yes	characteristic
336	C₂×C₈	C₁₁×#41	1	2	yes	—
337	C₂×C₈	C₁₁×#41	1	2	yes	—
338	C₄⋊C₄	—	4	4	no	—
339	C₄⋊C₄	C₂×D₄×C₁₁	1	2	yes	—
340	C₄⋊C₄	C₂×D₄×C₁₁	1	4	yes	—
341	C₄⋊C₄	C₂×D₄×C₁₁	1	2	yes	—
342	C₂²⋊C₄	—	2	1	no	—
343	C₂²⋊C₄	—	2	2	no	—
344	C₂²⋊C₄	—	2	1	no	—
345	C₂²⋊C₄	—	4	8	no	—
346	C₂²⋊C₄	—	4	4	no	—
347	C₄²	—	2	1	no	—
348	C₄²	—	2	2	no	—
349	C₄²	—	2	1	no	—
350	C₄²	—	2	1	no	—
351	C₄²	—	4	4	no	—
352	C₄²	C₂²×C₄×C₁₁	1	2	yes	—
353	C₁₁	#23199	1	1	yes	characteristic, direct product factor, Sylow
354	C₂³	—	2	4	no	—
355	C₂³	—	4	2	no	—
356	C₂³	—	4	2	no	—
357	C₂³	—	8	4	no	—
358	C₂³	C₁₁×H(5,𝔽₂)	1	1	yes	characteristic
359	Q₈	—	2	4	no	—
360	Q₈	—	2	4	no	—
361	Q₈	—	4	2	no	—
362	Q₈	—	4	2	no	—
363	D₄	—	2	4	no	—
364	D₄	—	2	4	no	—
365	D₄	—	4	2	no	—
366	D₄	—	4	2	no	—
367	C₂×C₄	—	2	2	no	—
368	C₂×C₄	—	2	4	no	—
369	C₂×C₄	—	2	2	no	—
370	C₂×C₄	—	2	4	no	—
371	C₂×C₄	—	2	2	no	—
372	C₂×C₄	—	4	2	no	—
373	C₂×C₄	—	4	2	no	—
374	C₂×C₄	—	4	2	no	—
375	C₂×C₄	—	16	4	no	—
376	C₂×C₄	C₂³×C₄×C₁₁	1	1	yes	characteristic
377	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
378	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
379	C₂×C₄	C₂×C₁₁×#41	1	1	yes	characteristic
380	C₂×C₄	C₂×C₁₁×#41	1	1	yes	characteristic
381	C₂×C₄	C₁₁×H(5,𝔽₂)	1	1	yes	characteristic
382	C₈	—	4	1	no	—
383	C₈	—	4	2	no	—
384	C₈	—	4	1	no	—
385	C₈	C₄×D₄×C₁₁	1	2	yes	—
386	C₈	C₄×D₄×C₁₁	1	2	yes	—
387	C₈	C₄×D₄×C₁₁	1	2	yes	—
388	C₈	C₄×D₄×C₁₁	1	2	yes	—
389	C₂²	—	2	2	no	—
390	C₂²	—	4	4	no	—
391	C₂²	—	8	4	no	—
392	C₂²	—	8	4	no	—
393	C₂²	—	16	2	no	—
394	C₂²	C₁₁×#518	1	1	yes	characteristic
395	C₂²	D₄²×C₁₁	1	1	yes	characteristic
396	C₂²	C₁₁×#559	1	1	yes	characteristic
397	C₄	—	4	2	no	—
398	C₄	—	4	2	no	—
399	C₄	—	4	4	no	—
400	C₄	—	4	2	no	—
401	C₄	—	4	4	no	—
402	C₄	C₂×C₄×D₄×C₁₁	1	1	yes	characteristic
403	C₄	C₂×C₄×D₄×C₁₁	1	1	yes	characteristic
404	C₄	C₁₁×#550	1	1	yes	characteristic
405	C₄	C₁₁×#550	1	1	yes	characteristic
406	C₂	—	2	1	no	—
407	C₂	—	2	1	no	—
408	C₂	—	8	4	no	—
409	C₂	C₁₁×#2366	1	1	yes	characteristic
410	C₂	C₁₁×#3290	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₁	D₄²
commutator	C₂×C₄	C₂³×C₄×C₁₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₁
prime radical	C₂²×C₁₁×D₈	C₂²
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×#2950	C₂	semidirect
3. C₁₁×#2949	C₂	semidirect
5. C₁₁×#1979	C₂	semidirect
7. C₁₁×#1977	C₂	semidirect
8. C₁₁×#1888	C₂	semidirect
9. C₁₁×#1885	C₂	semidirect
10. C₁₁×#1772	C₂	semidirect
11. C₁₁×#1772	C₂	semidirect
18. C₁₁×#495	C₄	semidirect
47. C₂×C₁₁×Q₁₆	C₂×C₄	semidirect
51. C₂×C₁₁×SD₁₆	C₂×C₄	semidirect
62. C₁₁×#124	C₂×C₄	semidirect
92. C₄×C₈×C₁₁	C₂×C₄	semidirect
93. #23199	C₁₁	direct (N × H)
150. #2950	C₂×C₁₁	semidirect
151. #2949	C₂×C₁₁	semidirect
153. #1979	C₂×C₁₁	semidirect
155. #1977	C₂×C₁₁	semidirect
156. #1888	C₂×C₁₁	semidirect
157. #1885	C₂×C₁₁	semidirect
158. #1772	C₂×C₁₁	semidirect
159. #1772	C₂×C₁₁	semidirect
201. #495	C₄×C₁₁	semidirect
247. C₂×Q₁₆	C₂×C₄×C₁₁	semidirect
251. C₂×SD₁₆	C₂×C₄×C₁₁	semidirect
262. #124	C₂×C₄×C₁₁	semidirect
292. C₄×C₈	C₂×C₄×C₁₁	semidirect
353. C₁₁	#23199	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×#495	2
C₁₁×#2950	2
C₁₁×#2949	2
C₁₁×#2948	2
C₁₁×#1979	2
C₁₁×#1978	2
C₁₁×#1977	2
C₁₁×#1888	2
C₁₁×#1885	2
C₁₁×#1772	2
#23199	11

Subgroups — C11×#23199 #14600392

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#23199 #14600392