Subgroups — C₁₁×#22230 #14599423

Order 2816.

846 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₁×#486	C₂	1	1	yes	maximal, characteristic
2	C₁₁×#2331	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₁×#2328	C₂	1	1	yes	maximal, characteristic
4	C₁₁×#1993	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₁×#1961	C₂	1	1	yes	maximal, characteristic
6	C₁₁×#1926	C₂	1	2	yes	maximal, complemented
7	C₁₁×#1925	C₂	1	2	yes	maximal, complemented
8	C₁₁×#1864	C₂	1	2	yes	maximal, complemented
9	C₁₁×#1862	C₂	1	2	yes	maximal, complemented
10	C₁₁×#1846	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₁×#1746	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic
13	C₂×C₁₁×#127	C₂²	1	1	yes	characteristic
14	C₂×C₄×D₄×C₁₁	C₂²	1	2	yes	—
15	C₁₁×#486	C₄	1	8	yes	complemented
16	C₂×C₁₁×#107	C₂²	1	2	yes	—
17	C₂×C₁₁×#106	C₂²	1	2	yes	—
18	C₂×C₁₁×#102	C₂²	1	2	yes	—
19	C₂×C₁₁×#102	C₂²	1	2	yes	—
20	C₂×C₁₁×#102	C₂²	1	2	yes	—
21	C₂×C₁₁×#102	C₂²	1	2	yes	—
22	C₂×C₁₁×#97	C₂²	1	1	yes	characteristic
23	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
24	C₁₁×#391	—	2	2	no	—
25	C₁₁×#390	C₂²	1	2	yes	—
26	C₁₁×#389	C₂²	1	2	yes	—
27	C₁₁×#387	—	2	2	no	—
28	C₁₁×#386	—	2	2	no	—
29	C₁₁×#386	—	2	2	no	—
30	C₁₁×#382	C₂²	1	1	yes	characteristic
31	C₁₁×#382	C₂²	1	1	yes	characteristic
32	C₄×C₁₁×C₄⋊C₄	C₂²	1	2	yes	—
33	C₁₁×#376	C₂²	1	1	yes	characteristic
34	C₁₁×#340	C₂²	1	2	yes	—
35	C₁₁×#340	C₂²	1	2	yes	—
36	C₁₁×#336	C₂²	1	1	yes	characteristic
37	C₁₁×#336	C₂²	1	1	yes	characteristic
38	C₁₁×#336	C₂²	1	1	yes	characteristic
39	C₁₁×#336	C₂²	1	1	yes	characteristic
40	C₂²×Q₈×C₁₁	—	2	1	no	—
41	C₂²×D₄×C₁₁	—	2	1	no	—
42	C₂²×D₄×C₁₁	—	2	1	no	—
43	C₂²×D₄×C₁₁	C₂³	1	2	yes	—
44	C₂³×C₄×C₁₁	—	2	2	no	—
45	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
46	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
47	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
48	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
49	C₁₁×C₄⋊Q₈	—	2	2	no	—
50	C₁₁×C₄⋊Q₈	C₂×C₄	1	4	yes	complemented
51	C₁₁×#127	—	2	2	no	—
52	C₁₁×#127	C₂×C₄	1	4	yes	—
53	C₄×D₄×C₁₁	—	4	2	no	—
54	C₄×D₄×C₁₁	—	4	2	no	—
55	C₂×C₁₁×C₄⋊C₄	—	2	1	no	—
56	C₂×C₁₁×C₄⋊C₄	—	2	2	no	—
57	C₂×C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
58	C₂×C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
59	C₂×C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
60	C₂×C₁₁×C₂²⋊C₄	—	2	2	no	—
61	C₂×C₁₁×C₂²⋊C₄	—	2	2	no	—
62	C₂×C₁₁×C₂²⋊C₄	—	2	2	no	—
63	C₂×C₄²×C₁₁	—	2	2	no	—
64	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
65	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
66	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
67	C₁₁×#107	—	4	2	no	—
68	C₁₁×#106	—	4	2	no	—
69	C₁₁×#102	—	4	2	no	—
70	C₁₁×#102	—	4	2	no	—
71	C₁₁×#102	C₂×C₄	1	8	yes	complemented
72	C₁₁×#102	C₂×C₄	1	8	yes	complemented
73	C₁₁×#97	—	2	2	no	—
74	C₄×C₈×C₁₁	C₂×C₄	1	4	yes	complemented
75	C₁₁×#95	—	2	2	no	—
76	C₁₁×#95	—	2	1	no	—
77	C₁₁×#95	—	2	1	no	—
78	C₁₁×#95	—	2	1	no	—
79	C₁₁×#95	—	2	1	no	—
80	C₁₁×#95	—	2	2	no	—
81	C₁₁×#95	D₄	1	2	yes	—
82	C₁₁×#95	D₄	1	2	yes	—
83	#22230	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
84	C₂⁴×C₁₁	—	2	2	no	—
85	C₂×Q₈×C₁₁	—	2	4	no	—
86	C₂×Q₈×C₁₁	—	8	2	no	—
87	C₂×D₄×C₁₁	—	2	4	no	—
88	C₂×D₄×C₁₁	—	2	4	no	—
89	C₂×D₄×C₁₁	—	2	2	no	—
90	C₂×D₄×C₁₁	—	2	2	no	—
91	C₂×D₄×C₁₁	—	2	2	no	—
92	C₂×D₄×C₁₁	—	2	2	no	—
93	C₂×D₄×C₁₁	—	2	2	no	—
94	C₂×D₄×C₁₁	—	8	2	no	—
95	C₂×D₄×C₁₁	—	8	2	no	—
96	C₂×D₄×C₁₁	C₂²×C₄	1	4	yes	—
97	C₂²×C₄×C₁₁	—	2	2	no	—
98	C₂²×C₄×C₁₁	—	2	2	no	—
99	C₂²×C₄×C₁₁	—	2	2	no	—
100	C₂²×C₄×C₁₁	—	4	4	no	—
101	C₂²×C₄×C₁₁	—	8	2	no	—
102	C₂²×C₄×C₁₁	—	8	2	no	—
103	C₂²×C₄×C₁₁	C₂×D₄	1	2	yes	—
104	C₂²×C₄×C₁₁	C₂×D₄	1	2	yes	—
105	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
106	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
107	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
108	C₂×C₈×C₁₁	—	2	1	no	—
109	C₂×C₈×C₁₁	—	2	1	no	—
110	C₂×C₈×C₁₁	—	2	1	no	—
111	C₂×C₈×C₁₁	—	2	1	no	—
112	C₂×C₈×C₁₁	—	2	1	no	—
113	C₂×C₈×C₁₁	—	2	1	no	—
114	C₂×C₈×C₁₁	—	2	1	no	—
115	C₂×C₈×C₁₁	—	2	1	no	—
116	C₂×C₈×C₁₁	—	2	1	no	—
117	C₂×C₈×C₁₁	—	2	1	no	—
118	C₂×C₈×C₁₁	C₂²×C₄	1	2	yes	—
119	C₂×C₈×C₁₁	C₂²×C₄	1	2	yes	—
120	C₁₁×C₄⋊C₄	—	2	4	no	—
121	C₁₁×C₄⋊C₄	—	2	2	no	—
122	C₁₁×C₄⋊C₄	—	2	2	no	—
123	C₁₁×C₄⋊C₄	—	2	2	no	—
124	C₁₁×C₄⋊C₄	—	2	2	no	—
125	C₁₁×C₄⋊C₄	—	2	2	no	—
126	C₁₁×C₄⋊C₄	—	8	2	no	—
127	C₁₁×C₄⋊C₄	C₂²×C₄	1	4	yes	—
128	C₁₁×C₂²⋊C₄	—	4	4	no	—
129	C₁₁×C₂²⋊C₄	—	8	2	no	—
130	C₁₁×C₂²⋊C₄	—	8	2	no	—
131	C₄²×C₁₁	—	2	1	no	—
132	C₄²×C₁₁	—	2	1	no	—
133	C₄²×C₁₁	—	2	1	no	—
134	C₄²×C₁₁	—	2	1	no	—
135	C₄²×C₁₁	—	8	2	no	—
136	C₄²×C₁₁	C₂²×C₄	1	2	yes	—
137	C₄²×C₁₁	#41	1	2	yes	—
138	C₂×#486	C₂×C₁₁	1	1	yes	characteristic
139	#2331	C₂×C₁₁	1	1	yes	characteristic, complemented
140	#2328	C₂×C₁₁	1	1	yes	characteristic
141	#1993	C₂×C₁₁	1	1	yes	characteristic, complemented
142	#1961	C₂×C₁₁	1	1	yes	characteristic
143	#1926	C₂×C₁₁	1	2	yes	complemented
144	#1925	C₂×C₁₁	1	2	yes	complemented
145	#1864	C₂×C₁₁	1	2	yes	complemented
146	#1862	C₂×C₁₁	1	2	yes	complemented
147	#1846	C₂×C₁₁	1	1	yes	characteristic, complemented
148	#1746	C₂×C₁₁	1	1	yes	characteristic, complemented
149	C₂³×C₁₁	—	2	4	no	—
150	C₂³×C₁₁	—	4	2	no	—
151	C₂³×C₁₁	—	4	2	no	—
152	C₂³×C₁₁	—	4	2	no	—
153	C₂³×C₁₁	—	4	2	no	—
154	C₂³×C₁₁	—	4	2	no	—
155	C₂³×C₁₁	—	4	2	no	—
156	C₂³×C₁₁	C₂²×D₄	1	1	yes	characteristic
157	Q₈×C₁₁	—	8	4	no	—
158	D₄×C₁₁	—	2	4	no	—
159	D₄×C₁₁	—	2	4	no	—
160	D₄×C₁₁	—	4	2	no	—
161	D₄×C₁₁	—	4	2	no	—
162	D₄×C₁₁	—	8	4	no	—
163	D₄×C₁₁	—	8	4	no	—
164	C₂×C₄×C₁₁	—	2	2	no	—
165	C₂×C₄×C₁₁	—	2	2	no	—
166	C₂×C₄×C₁₁	—	2	4	no	—
167	C₂×C₄×C₁₁	—	2	2	no	—
168	C₂×C₄×C₁₁	—	2	2	no	—
169	C₂×C₄×C₁₁	—	2	2	no	—
170	C₂×C₄×C₁₁	—	2	2	no	—
171	C₂×C₄×C₁₁	—	2	2	no	—
172	C₂×C₄×C₁₁	—	2	2	no	—
173	C₂×C₄×C₁₁	—	4	2	no	—
174	C₂×C₄×C₁₁	—	4	2	no	—
175	C₂×C₄×C₁₁	—	4	2	no	—
176	C₂×C₄×C₁₁	—	4	2	no	—
177	C₂×C₄×C₁₁	—	4	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	—	8	8	no	—
182	C₂×C₄×C₁₁	C₄×D₄	1	2	yes	—
183	C₂×C₄×C₁₁	C₄×D₄	1	2	yes	—
184	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
185	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
186	C₂×C₄×C₁₁	H(5,𝔽₂)	1	1	yes	characteristic
187	C₂×C₄×C₁₁	H(5,𝔽₂)	1	1	yes	characteristic
188	C₂×C₄×C₁₁	2₋¹⁺⁴	1	1	yes	characteristic
189	C₂×C₄×C₁₁	2₋¹⁺⁴	1	1	yes	characteristic
190	C₈×C₁₁	—	2	2	no	—
191	C₈×C₁₁	—	2	2	no	—
192	C₈×C₁₁	—	4	1	no	—
193	C₈×C₁₁	—	4	1	no	—
194	C₂×C₄⋊Q₈	C₂²×C₁₁	1	1	yes	characteristic
195	C₂×#127	C₂²×C₁₁	1	1	yes	characteristic
196	C₂×C₄×D₄	C₂²×C₁₁	1	2	yes	—
197	#486	C₄×C₁₁	1	8	yes	complemented
198	C₂×#107	C₂²×C₁₁	1	2	yes	—
199	C₂×#106	C₂²×C₁₁	1	2	yes	—
200	C₂×#102	C₂²×C₁₁	1	2	yes	—
201	C₂×#102	C₂²×C₁₁	1	2	yes	—
202	C₂×#102	C₂²×C₁₁	1	2	yes	—
203	C₂×#102	C₂²×C₁₁	1	2	yes	—
204	C₂×#97	C₂²×C₁₁	1	1	yes	characteristic
205	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
206	#391	—	2	2	no	—
207	#390	C₂²×C₁₁	1	2	yes	—
208	#389	C₂²×C₁₁	1	2	yes	—
209	#387	—	2	2	no	—
210	#386	—	2	2	no	—
211	#386	—	2	2	no	—
212	#382	C₂²×C₁₁	1	1	yes	characteristic
213	#382	C₂²×C₁₁	1	1	yes	characteristic
214	C₄×C₄⋊C₄	C₂²×C₁₁	1	2	yes	—
215	#376	C₂²×C₁₁	1	1	yes	characteristic
216	#340	C₂²×C₁₁	1	2	yes	—
217	#340	C₂²×C₁₁	1	2	yes	—
218	#336	C₂²×C₁₁	1	1	yes	characteristic
219	#336	C₂²×C₁₁	1	1	yes	characteristic
220	#336	C₂²×C₁₁	1	1	yes	characteristic
221	#336	C₂²×C₁₁	1	1	yes	characteristic
222	C₂²×C₁₁	—	4	4	no	—
223	C₂²×C₁₁	—	4	4	no	—
224	C₂²×C₁₁	—	4	4	no	—
225	C₂²×C₁₁	—	8	2	no	—
226	C₂²×C₁₁	—	8	2	no	—
227	C₂²×C₁₁	—	8	2	no	—
228	C₂²×C₁₁	—	8	2	no	—
229	C₂²×C₁₁	C₂×C₄×D₄	1	1	yes	characteristic
230	C₂²×C₁₁	#535	1	1	yes	characteristic
231	C₂²×C₁₁	#536	1	1	yes	characteristic
232	C₂²×C₁₁	#576	1	2	yes	—
233	C₂²×C₁₁	#577	1	2	yes	—
234	C₄×C₁₁	—	2	2	no	—
235	C₄×C₁₁	—	2	2	no	—
236	C₄×C₁₁	—	4	4	no	—
237	C₄×C₁₁	—	4	2	no	—
238	C₄×C₁₁	—	4	2	no	—
239	C₄×C₁₁	—	8	2	no	—
240	C₄×C₁₁	—	8	2	no	—
241	C₄×C₁₁	#520	1	1	yes	characteristic
242	C₄×C₁₁	#520	1	1	yes	characteristic
243	C₄×C₁₁	#542	1	1	yes	characteristic
244	C₄×C₁₁	#542	1	1	yes	characteristic
245	C₂²×Q₈	—	2	1	no	—
246	C₂²×D₄	—	2	1	no	—
247	C₂²×D₄	—	2	1	no	—
248	C₂²×D₄	C₂³×C₁₁	1	2	yes	—
249	C₂³×C₄	—	2	2	no	—
250	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
251	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
252	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
253	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
254	C₄⋊Q₈	—	2	2	no	—
255	C₄⋊Q₈	C₂×C₄×C₁₁	1	4	yes	complemented
256	#127	—	2	2	no	—
257	#127	C₂×C₄×C₁₁	1	4	yes	—
258	C₄×D₄	—	4	2	no	—
259	C₄×D₄	—	4	2	no	—
260	C₂×C₄⋊C₄	—	2	1	no	—
261	C₂×C₄⋊C₄	—	2	2	no	—
262	C₂×C₄⋊C₄	C₂³×C₁₁	1	2	yes	—
263	C₂×C₄⋊C₄	C₂³×C₁₁	1	2	yes	—
264	C₂×C₄⋊C₄	C₂³×C₁₁	1	2	yes	—
265	C₂×C₂²⋊C₄	—	2	2	no	—
266	C₂×C₂²⋊C₄	—	2	2	no	—
267	C₂×C₂²⋊C₄	—	2	2	no	—
268	C₂×C₄²	—	2	2	no	—
269	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
270	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
271	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
272	#107	—	4	2	no	—
273	#106	—	4	2	no	—
274	#102	—	4	2	no	—
275	#102	—	4	2	no	—
276	#102	C₂×C₄×C₁₁	1	8	yes	complemented
277	#102	C₂×C₄×C₁₁	1	8	yes	complemented
278	#97	—	2	2	no	—
279	C₄×C₈	C₂×C₄×C₁₁	1	4	yes	complemented
280	#95	—	2	2	no	—
281	#95	—	2	1	no	—
282	#95	—	2	1	no	—
283	#95	—	2	1	no	—
284	#95	—	2	1	no	—
285	#95	—	2	2	no	—
286	#95	D₄×C₁₁	1	2	yes	—
287	#95	D₄×C₁₁	1	2	yes	—
288	C₂×C₁₁	—	8	4	no	—
289	C₂×C₁₁	#2326	1	1	yes	characteristic
290	C₂×C₁₁	#2948	1	1	yes	characteristic
291	C₂×C₁₁	#2949	1	1	yes	characteristic
292	C₂×C₁₁	#3224	1	2	yes	—
293	C₂×C₁₁	#3241	1	2	yes	—
294	C₂⁴	—	2	2	no	—
295	C₂×Q₈	—	2	4	no	—
296	C₂×Q₈	—	8	2	no	—
297	C₂×D₄	—	2	4	no	—
298	C₂×D₄	—	2	4	no	—
299	C₂×D₄	—	2	2	no	—
300	C₂×D₄	—	2	2	no	—
301	C₂×D₄	—	2	2	no	—
302	C₂×D₄	—	2	2	no	—
303	C₂×D₄	—	2	2	no	—
304	C₂×D₄	—	8	2	no	—
305	C₂×D₄	—	8	2	no	—
306	C₂×D₄	C₂²×C₄×C₁₁	1	4	yes	—
307	C₂²×C₄	—	2	2	no	—
308	C₂²×C₄	—	2	2	no	—
309	C₂²×C₄	—	2	2	no	—
310	C₂²×C₄	—	4	4	no	—
311	C₂²×C₄	—	8	2	no	—
312	C₂²×C₄	—	8	2	no	—
313	C₂²×C₄	C₂×D₄×C₁₁	1	2	yes	—
314	C₂²×C₄	C₂×D₄×C₁₁	1	2	yes	—
315	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
316	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
317	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
318	C₂×C₈	—	2	1	no	—
319	C₂×C₈	—	2	1	no	—
320	C₂×C₈	—	2	1	no	—
321	C₂×C₈	—	2	1	no	—
322	C₂×C₈	—	2	1	no	—
323	C₂×C₈	—	2	1	no	—
324	C₂×C₈	—	2	1	no	—
325	C₂×C₈	—	2	1	no	—
326	C₂×C₈	—	2	1	no	—
327	C₂×C₈	—	2	1	no	—
328	C₂×C₈	C₂²×C₄×C₁₁	1	2	yes	—
329	C₂×C₈	C₂²×C₄×C₁₁	1	2	yes	—
330	C₄⋊C₄	—	2	4	no	—
331	C₄⋊C₄	—	2	2	no	—
332	C₄⋊C₄	—	2	2	no	—
333	C₄⋊C₄	—	2	2	no	—
334	C₄⋊C₄	—	2	2	no	—
335	C₄⋊C₄	—	2	2	no	—
336	C₄⋊C₄	—	8	2	no	—
337	C₄⋊C₄	C₂²×C₄×C₁₁	1	4	yes	—
338	C₂²⋊C₄	—	4	4	no	—
339	C₂²⋊C₄	—	8	2	no	—
340	C₂²⋊C₄	—	8	2	no	—
341	C₄²	—	2	1	no	—
342	C₄²	—	2	1	no	—
343	C₄²	—	2	1	no	—
344	C₄²	—	2	1	no	—
345	C₄²	—	8	2	no	—
346	C₄²	C₂²×C₄×C₁₁	1	2	yes	—
347	C₄²	C₁₁×#41	1	2	yes	—
348	C₁₁	#22230	1	1	yes	characteristic, direct product factor, Sylow
349	C₂³	—	2	4	no	—
350	C₂³	—	4	2	no	—
351	C₂³	—	4	2	no	—
352	C₂³	—	4	2	no	—
353	C₂³	—	4	2	no	—
354	C₂³	—	4	2	no	—
355	C₂³	—	4	2	no	—
356	C₂³	C₂²×D₄×C₁₁	1	1	yes	characteristic
357	Q₈	—	8	4	no	—
358	D₄	—	2	4	no	—
359	D₄	—	2	4	no	—
360	D₄	—	4	2	no	—
361	D₄	—	4	2	no	—
362	D₄	—	8	4	no	—
363	D₄	—	8	4	no	—
364	C₂×C₄	—	2	2	no	—
365	C₂×C₄	—	2	2	no	—
366	C₂×C₄	—	2	4	no	—
367	C₂×C₄	—	2	2	no	—
368	C₂×C₄	—	2	2	no	—
369	C₂×C₄	—	2	2	no	—
370	C₂×C₄	—	2	2	no	—
371	C₂×C₄	—	2	2	no	—
372	C₂×C₄	—	2	2	no	—
373	C₂×C₄	—	4	2	no	—
374	C₂×C₄	—	4	2	no	—
375	C₂×C₄	—	4	2	no	—
376	C₂×C₄	—	4	2	no	—
377	C₂×C₄	—	4	2	no	—
378	C₂×C₄	—	4	2	no	—
379	C₂×C₄	—	4	2	no	—
380	C₂×C₄	—	4	2	no	—
381	C₂×C₄	—	8	8	no	—
382	C₂×C₄	C₄×D₄×C₁₁	1	2	yes	—
383	C₂×C₄	C₄×D₄×C₁₁	1	2	yes	—
384	C₂×C₄	C₂³×C₄×C₁₁	1	1	yes	characteristic
385	C₂×C₄	C₂×C₁₁×#41	1	1	yes	characteristic
386	C₂×C₄	C₁₁×H(5,𝔽₂)	1	1	yes	characteristic
387	C₂×C₄	C₁₁×H(5,𝔽₂)	1	1	yes	characteristic
388	C₂×C₄	C₁₁×2₋¹⁺⁴	1	1	yes	characteristic
389	C₂×C₄	C₁₁×2₋¹⁺⁴	1	1	yes	characteristic
390	C₈	—	2	2	no	—
391	C₈	—	2	2	no	—
392	C₈	—	4	1	no	—
393	C₈	—	4	1	no	—
394	C₂²	—	4	4	no	—
395	C₂²	—	4	4	no	—
396	C₂²	—	4	4	no	—
397	C₂²	—	8	2	no	—
398	C₂²	—	8	2	no	—
399	C₂²	—	8	2	no	—
400	C₂²	—	8	2	no	—
401	C₂²	C₂×C₄×D₄×C₁₁	1	1	yes	characteristic
402	C₂²	C₁₁×#535	1	1	yes	characteristic
403	C₂²	C₁₁×#536	1	1	yes	characteristic
404	C₂²	C₁₁×#576	1	2	yes	—
405	C₂²	C₁₁×#577	1	2	yes	—
406	C₄	—	2	2	no	—
407	C₄	—	2	2	no	—
408	C₄	—	4	4	no	—
409	C₄	—	4	2	no	—
410	C₄	—	4	2	no	—
411	C₄	—	8	2	no	—
412	C₄	—	8	2	no	—
413	C₄	C₁₁×#520	1	1	yes	characteristic
414	C₄	C₁₁×#520	1	1	yes	characteristic
415	C₄	C₁₁×#542	1	1	yes	characteristic
416	C₄	C₁₁×#542	1	1	yes	characteristic
417	C₂	—	8	4	no	—
418	C₂	C₁₁×#2326	1	1	yes	characteristic
419	C₂	C₁₁×#2948	1	1	yes	characteristic
420	C₂	C₁₁×#2949	1	1	yes	characteristic
421	C₂	C₁₁×#3224	1	2	yes	—
422	C₂	C₁₁×#3241	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₁	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₁
prime radical	C₂×C₁₁×#127	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₁ ◁ C₁₁×#376 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₁×#2331	C₂	semidirect
4. C₁₁×#1993	C₂	semidirect
6. C₁₁×#1926	C₂	semidirect
7. C₁₁×#1925	C₂	semidirect
8. C₁₁×#1864	C₂	semidirect
9. C₁₁×#1862	C₂	semidirect
10. C₁₁×#1846	C₂	semidirect
11. C₁₁×#1746	C₂	semidirect
15. C₁₁×#486	C₄	semidirect
50. C₁₁×C₄⋊Q₈	C₂×C₄	semidirect
71. C₁₁×#102	C₂×C₄	semidirect
72. C₁₁×#102	C₂×C₄	semidirect
74. C₄×C₈×C₁₁	C₂×C₄	semidirect
83. #22230	C₁₁	direct (N × H)
139. #2331	C₂×C₁₁	semidirect
141. #1993	C₂×C₁₁	semidirect
143. #1926	C₂×C₁₁	semidirect
144. #1925	C₂×C₁₁	semidirect
145. #1864	C₂×C₁₁	semidirect
146. #1862	C₂×C₁₁	semidirect
147. #1846	C₂×C₁₁	semidirect
148. #1746	C₂×C₁₁	semidirect
197. #486	C₄×C₁₁	semidirect
255. C₄⋊Q₈	C₂×C₄×C₁₁	semidirect
276. #102	C₂×C₄×C₁₁	semidirect
277. #102	C₂×C₄×C₁₁	semidirect
279. C₄×C₈	C₂×C₄×C₁₁	semidirect
348. C₁₁	#22230	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×#486	2
C₁₁×#2331	2
C₁₁×#2328	2
C₁₁×#1993	2
C₁₁×#1961	2
C₁₁×#1926	2
C₁₁×#1925	2
C₁₁×#1864	2
C₁₁×#1862	2
C₁₁×#1846	2
C₁₁×#1746	2
#22230	11

Subgroups — C11×#22230 #14599423

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#22230 #14599423