Subgroups — C₁₁×#22395 #14599588

Order 2816.

774 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₁₁×#124	C₂	1	1	yes	maximal, characteristic
2	C₁₁×#1985	C₂	1	2	yes	maximal, complemented
3	C₁₁×#1924	C₂	1	2	yes	maximal, complemented
4	C₁₁×#1924	C₂	1	2	yes	maximal, complemented
5	C₁₁×#1869	C₂	1	2	yes	maximal
6	C₁₁×#1850	C₂	1	2	yes	maximal, complemented
7	C₁₁×#1839	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₁×#1767	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₁×#1752	C₂	1	2	yes	maximal, complemented
10	C₂³×C₈×C₁₁	C₂²	1	2	yes	—
11	C₂×C₁₁×#124	C₄	1	1	yes	characteristic
12	C₂×C₄×Q₈×C₁₁	C₂²	1	1	yes	characteristic
13	C₂×C₄×D₄×C₁₁	C₂²	1	1	yes	characteristic
14	C₂×C₁₁×C₄⋊C₈	C₂²	1	2	yes	—
15	C₂×C₁₁×C₄⋊C₈	C₂²	1	2	yes	—
16	C₂×C₁₁×C₂²⋊C₈	C₂²	1	2	yes	—
17	C₂×C₁₁×C₂²⋊C₈	C₂²	1	2	yes	—
18	C₂×C₁₁×C₂²⋊C₈	C₂²	1	2	yes	—
19	C₂×C₁₁×#97	C₂²	1	1	yes	characteristic
20	C₂×C₁₁×#97	C₂²	1	2	yes	—
21	C₂×C₁₁×#97	C₂²	1	1	yes	characteristic
22	C₁₁×#391	C₄	1	1	yes	characteristic
23	C₁₁×#390	C₄	1	1	yes	characteristic
24	C₁₁×#388	C₄	1	2	yes	—
25	C₁₁×#388	C₄	1	2	yes	—
26	C₁₁×#382	C₄	1	1	yes	characteristic
27	C₄×C₁₁×C₂²⋊C₄	C₂²	1	2	yes	—
28	C₄×C₁₁×C₂²⋊C₄	C₂²	1	2	yes	—
29	C₄³×C₁₁	C₂²	1	1	yes	characteristic
30	C₁₁×#336	C₂²	1	2	yes	—
31	C₁₁×#336	C₂²	1	2	yes	—
32	C₁₁×#336	C₂²	1	2	yes	—
33	C₁₁×#336	C₂²	1	1	yes	characteristic
34	C₁₁×#336	C₂²	1	2	yes	—
35	C₁₁×#336	C₂²	1	2	yes	—
36	C₁₁×#336	C₂²	1	1	yes	characteristic
37	C₂²×Q₈×C₁₁	C₂×C₄	1	1	yes	characteristic
38	C₂²×D₄×C₁₁	C₂×C₄	1	1	yes	characteristic
39	C₂³×C₄×C₁₁	C₂³	1	2	yes	—
40	C₂²×C₈×C₁₁	—	2	4	no	—
41	C₂²×C₈×C₁₁	—	4	2	no	—
42	C₂²×C₈×C₁₁	—	4	2	no	—
43	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
44	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
45	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
46	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
47	C₁₁×#124	—	2	4	no	—
48	C₄×Q₈×C₁₁	—	4	2	no	—
49	C₄×D₄×C₁₁	—	4	2	no	—
50	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
51	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
52	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	2	yes	—
53	C₂×C₁₁×C₂²⋊C₄	C₂×C₄	1	2	yes	—
54	C₂×C₁₁×C₂²⋊C₄	C₂×C₄	1	2	yes	—
55	C₂×C₁₁×C₂²⋊C₄	C₂×C₄	1	2	yes	—
56	C₂×C₁₁×C₂²⋊C₄	C₂×C₄	1	2	yes	—
57	C₂×C₁₁×C₂²⋊C₄	C₂×C₄	1	2	yes	—
58	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
59	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
60	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
61	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
62	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
63	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
64	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
65	C₂×C₄²×C₁₁	C₂³	1	2	yes	—
66	C₁₁×C₄⋊C₈	—	2	4	no	—
67	C₁₁×C₄⋊C₈	—	4	2	no	—
68	C₁₁×C₂²⋊C₈	—	2	4	no	—
69	C₁₁×C₂²⋊C₈	—	4	2	no	—
70	C₁₁×C₂²⋊C₈	—	4	2	no	—
71	C₁₁×#97	—	4	1	no	—
72	C₁₁×#97	—	4	1	no	—
73	C₁₁×#97	—	4	2	no	—
74	C₁₁×#95	C₂×C₄	1	2	yes	—
75	C₁₁×#95	C₂×C₄	1	2	yes	—
76	C₁₁×#95	C₂×C₄	1	2	yes	—
77	C₁₁×#95	C₂×C₄	1	2	yes	—
78	#22395	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
79	C₂⁴×C₁₁	C₂²×C₄	1	2	yes	—
80	C₂×Q₈×C₁₁	—	2	2	no	—
81	C₂×Q₈×C₁₁	—	4	1	no	—
82	C₂×Q₈×C₁₁	—	4	1	no	—
83	C₂×D₄×C₁₁	—	4	1	no	—
84	C₂×D₄×C₁₁	—	4	1	no	—
85	C₂×D₄×C₁₁	M₁₆	1	4	yes	—
86	C₂²×C₄×C₁₁	—	2	2	no	—
87	C₂²×C₄×C₁₁	—	2	2	no	—
88	C₂²×C₄×C₁₁	—	2	2	no	—
89	C₂²×C₄×C₁₁	—	2	2	no	—
90	C₂²×C₄×C₁₁	—	2	2	no	—
91	C₂²×C₄×C₁₁	—	2	2	no	—
92	C₂²×C₄×C₁₁	C₂²×C₄	1	2	yes	—
93	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
94	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
95	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
96	C₂²×C₄×C₁₁	C₂²×C₄	1	2	yes	—
97	C₂²×C₄×C₁₁	C₂²×C₄	1	2	yes	—
98	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
99	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
100	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
101	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
102	C₂×C₈×C₁₁	—	2	2	no	—
103	C₂×C₈×C₁₁	—	2	2	no	—
104	C₂×C₈×C₁₁	—	2	2	no	—
105	C₂×C₈×C₁₁	—	2	2	no	—
106	C₂×C₈×C₁₁	—	2	2	no	—
107	C₂×C₈×C₁₁	—	2	2	no	—
108	C₂×C₈×C₁₁	—	2	2	no	—
109	C₂×C₈×C₁₁	—	2	2	no	—
110	C₂×C₈×C₁₁	—	2	2	no	—
111	C₂×C₈×C₁₁	—	2	2	no	—
112	C₂×C₈×C₁₁	—	2	2	no	—
113	C₂×C₈×C₁₁	—	4	8	no	—
114	C₂×C₈×C₁₁	#41	1	4	yes	—
115	C₁₁×C₄⋊C₄	—	4	1	no	—
116	C₁₁×C₄⋊C₄	—	4	1	no	—
117	C₁₁×C₄⋊C₄	—	4	2	no	—
118	C₁₁×C₂²⋊C₄	—	2	4	no	—
119	C₁₁×C₂²⋊C₄	—	2	4	no	—
120	C₁₁×C₂²⋊C₄	—	2	4	no	—
121	C₁₁×C₂²⋊C₄	—	4	2	no	—
122	C₁₁×C₂²⋊C₄	—	4	2	no	—
123	C₄²×C₁₁	—	2	2	no	—
124	C₄²×C₁₁	—	2	2	no	—
125	C₄²×C₁₁	—	2	2	no	—
126	C₄²×C₁₁	—	2	1	no	—
127	C₄²×C₁₁	—	2	2	no	—
128	C₄²×C₁₁	—	2	2	no	—
129	C₄²×C₁₁	—	2	2	no	—
130	C₄²×C₁₁	—	2	1	no	—
131	C₄²×C₁₁	—	4	1	no	—
132	C₄²×C₁₁	—	4	1	no	—
133	C₄×#124	C₂×C₁₁	1	1	yes	characteristic
134	#1985	C₂×C₁₁	1	2	yes	complemented
135	#1924	C₂×C₁₁	1	2	yes	complemented
136	#1924	C₂×C₁₁	1	2	yes	complemented
137	#1869	C₂×C₁₁	1	2	yes	—
138	#1850	C₂×C₁₁	1	2	yes	complemented
139	#1839	C₂×C₁₁	1	1	yes	characteristic, complemented
140	#1767	C₂×C₁₁	1	1	yes	characteristic, complemented
141	#1752	C₂×C₁₁	1	2	yes	complemented
142	C₂³×C₁₁	—	2	2	no	—
143	C₂³×C₁₁	—	2	2	no	—
144	C₂³×C₁₁	—	2	2	no	—
145	C₂³×C₁₁	—	2	2	no	—
146	C₂³×C₁₁	—	2	2	no	—
147	C₂³×C₁₁	—	2	2	no	—
148	C₂³×C₁₁	C₂×M₁₆	1	4	yes	—
149	C₂³×C₁₁	C₂³×C₄	1	1	yes	characteristic
150	Q₈×C₁₁	—	4	4	no	—
151	D₄×C₁₁	—	4	4	no	—
152	C₂×C₄×C₁₁	—	2	1	no	—
153	C₂×C₄×C₁₁	—	2	1	no	—
154	C₂×C₄×C₁₁	—	2	1	no	—
155	C₂×C₄×C₁₁	—	2	1	no	—
156	C₂×C₄×C₁₁	—	2	1	no	—
157	C₂×C₄×C₁₁	—	2	2	no	—
158	C₂×C₄×C₁₁	—	2	1	no	—
159	C₂×C₄×C₁₁	—	2	2	no	—
160	C₂×C₄×C₁₁	—	2	2	no	—
161	C₂×C₄×C₁₁	—	2	2	no	—
162	C₂×C₄×C₁₁	—	2	1	no	—
163	C₂×C₄×C₁₁	—	2	1	no	—
164	C₂×C₄×C₁₁	—	2	2	no	—
165	C₂×C₄×C₁₁	—	2	1	no	—
166	C₂×C₄×C₁₁	—	2	1	no	—
167	C₂×C₄×C₁₁	—	2	2	no	—
168	C₂×C₄×C₁₁	—	2	1	no	—
169	C₂×C₄×C₁₁	—	2	1	no	—
170	C₂×C₄×C₁₁	—	2	2	no	—
171	C₂×C₄×C₁₁	—	2	1	no	—
172	C₂×C₄×C₁₁	—	2	1	no	—
173	C₂×C₄×C₁₁	—	2	1	no	—
174	C₂×C₄×C₁₁	—	2	1	no	—
175	C₂×C₄×C₁₁	—	2	2	no	—
176	C₂×C₄×C₁₁	—	2	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	C₂×M₁₆	1	2	yes	—
182	C₂×C₄×C₁₁	#131	1	2	yes	—
183	C₂×C₄×C₁₁	C₂×#41	1	2	yes	—
184	C₂×C₄×C₁₁	H(5,𝔽₂)	1	1	yes	characteristic
185	C₂×C₄×C₁₁	H(5,𝔽₂)	1	2	yes	—
186	C₂×C₄×C₁₁	2₋¹⁺⁴	1	1	yes	characteristic
187	C₈×C₁₁	—	2	4	no	—
188	C₈×C₁₁	—	4	2	no	—
189	C₈×C₁₁	—	4	2	no	—
190	C₈×C₁₁	—	4	2	no	—
191	C₂³×C₈	C₂²×C₁₁	1	2	yes	—
192	C₂×#124	C₄×C₁₁	1	1	yes	characteristic
193	C₂×C₄×Q₈	C₂²×C₁₁	1	1	yes	characteristic
194	C₂×C₄×D₄	C₂²×C₁₁	1	1	yes	characteristic
195	C₂×C₄⋊C₈	C₂²×C₁₁	1	2	yes	—
196	C₂×C₄⋊C₈	C₂²×C₁₁	1	2	yes	—
197	C₂×C₂²⋊C₈	C₂²×C₁₁	1	2	yes	—
198	C₂×C₂²⋊C₈	C₂²×C₁₁	1	2	yes	—
199	C₂×C₂²⋊C₈	C₂²×C₁₁	1	2	yes	—
200	C₂×#97	C₂²×C₁₁	1	1	yes	characteristic
201	C₂×#97	C₂²×C₁₁	1	2	yes	—
202	C₂×#97	C₂²×C₁₁	1	1	yes	characteristic
203	#391	C₄×C₁₁	1	1	yes	characteristic
204	#390	C₄×C₁₁	1	1	yes	characteristic
205	#388	C₄×C₁₁	1	2	yes	—
206	#388	C₄×C₁₁	1	2	yes	—
207	#382	C₄×C₁₁	1	1	yes	characteristic
208	C₄×C₂²⋊C₄	C₂²×C₁₁	1	2	yes	—
209	C₄×C₂²⋊C₄	C₂²×C₁₁	1	2	yes	—
210	C₄³	C₂²×C₁₁	1	1	yes	characteristic
211	#336	C₂²×C₁₁	1	1	yes	characteristic
212	#336	C₂²×C₁₁	1	2	yes	—
213	#336	C₂²×C₁₁	1	1	yes	characteristic
214	#336	C₂²×C₁₁	1	2	yes	—
215	#336	C₂²×C₁₁	1	2	yes	—
216	#336	C₂²×C₁₁	1	2	yes	—
217	#336	C₂²×C₁₁	1	2	yes	—
218	C₂²×C₁₁	—	2	4	no	—
219	C₂²×C₁₁	—	2	4	no	—
220	C₂²×C₁₁	—	2	4	no	—
221	C₂²×C₁₁	—	4	2	no	—
222	C₂²×C₁₁	—	4	2	no	—
223	C₂²×C₁₁	—	4	2	no	—
224	C₂²×C₁₁	—	4	2	no	—
225	C₂²×C₁₁	C₄×#41	1	1	yes	characteristic
226	C₂²×C₁₁	#518	1	1	yes	characteristic
227	C₂²×C₁₁	#520	1	1	yes	characteristic
228	C₂²×C₁₁	C₂²×M₁₆	1	1	yes	characteristic
229	C₂²×C₁₁	C₂×#131	1	1	yes	characteristic
230	C₂²×C₁₁	#568	1	1	yes	characteristic
231	C₂²×C₁₁	#568	1	1	yes	characteristic
232	C₄×C₁₁	—	2	2	no	—
233	C₄×C₁₁	—	2	2	no	—
234	C₄×C₁₁	—	4	2	no	—
235	C₄×C₁₁	—	4	1	no	—
236	C₄×C₁₁	—	4	2	no	—
237	C₄×C₁₁	—	4	1	no	—
238	C₄×C₁₁	—	4	2	no	—
239	C₄×C₁₁	—	4	1	no	—
240	C₄×C₁₁	—	4	1	no	—
241	C₄×C₁₁	#538	1	2	yes	—
242	C₄×C₁₁	#542	1	2	yes	—
243	C₂²×Q₈	C₂×C₄×C₁₁	1	1	yes	characteristic
244	C₂²×D₄	C₂×C₄×C₁₁	1	1	yes	characteristic
245	C₂³×C₄	C₂³×C₁₁	1	2	yes	—
246	C₂²×C₈	—	2	4	no	—
247	C₂²×C₈	—	4	2	no	—
248	C₂²×C₈	—	4	2	no	—
249	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
250	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
251	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
252	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
253	#124	—	2	4	no	—
254	C₄×Q₈	—	4	2	no	—
255	C₄×D₄	—	4	2	no	—
256	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
257	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
258	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	2	yes	—
259	C₂×C₂²⋊C₄	C₂×C₄×C₁₁	1	2	yes	—
260	C₂×C₂²⋊C₄	C₂×C₄×C₁₁	1	2	yes	—
261	C₂×C₂²⋊C₄	C₂×C₄×C₁₁	1	2	yes	—
262	C₂×C₂²⋊C₄	C₂×C₄×C₁₁	1	2	yes	—
263	C₂×C₂²⋊C₄	C₂×C₄×C₁₁	1	2	yes	—
264	C₂×C₄²	C₂×C₄×C₁₁	1	1	yes	characteristic
265	C₂×C₄²	C₂×C₄×C₁₁	1	1	yes	characteristic
266	C₂×C₄²	C₂×C₄×C₁₁	1	1	yes	characteristic
267	C₂×C₄²	C₂×C₄×C₁₁	1	1	yes	characteristic
268	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
269	C₂×C₄²	C₂³×C₁₁	1	2	yes	—
270	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
271	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
272	C₄⋊C₈	—	2	4	no	—
273	C₄⋊C₈	—	4	2	no	—
274	C₂²⋊C₈	—	2	4	no	—
275	C₂²⋊C₈	—	4	2	no	—
276	C₂²⋊C₈	—	4	2	no	—
277	#97	—	4	1	no	—
278	#97	—	4	1	no	—
279	#97	—	4	2	no	—
280	#95	C₂×C₄×C₁₁	1	2	yes	—
281	#95	C₂×C₄×C₁₁	1	2	yes	—
282	#95	C₂×C₄×C₁₁	1	2	yes	—
283	#95	C₂×C₄×C₁₁	1	2	yes	—
284	C₂×C₁₁	—	4	4	no	—
285	C₂×C₁₁	#2337	1	1	yes	characteristic
286	C₂×C₁₁	#2968	1	1	yes	characteristic
287	C₂×C₁₁	#2970	1	1	yes	characteristic
288	C₂×C₁₁	#2973	1	1	yes	characteristic
289	C₂×C₁₁	#2981	1	1	yes	characteristic
290	C₂×C₁₁	#2990	1	1	yes	characteristic
291	C₂×C₁₁	#2995	1	1	yes	characteristic
292	C₂⁴	C₂²×C₄×C₁₁	1	2	yes	—
293	C₂×Q₈	—	2	2	no	—
294	C₂×Q₈	—	4	1	no	—
295	C₂×Q₈	—	4	1	no	—
296	C₂×D₄	—	4	1	no	—
297	C₂×D₄	—	4	1	no	—
298	C₂×D₄	C₁₁×M₁₆	1	4	yes	—
299	C₂²×C₄	—	2	2	no	—
300	C₂²×C₄	—	2	2	no	—
301	C₂²×C₄	—	2	2	no	—
302	C₂²×C₄	—	2	2	no	—
303	C₂²×C₄	—	2	2	no	—
304	C₂²×C₄	—	2	2	no	—
305	C₂²×C₄	C₂²×C₄×C₁₁	1	2	yes	—
306	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
307	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
308	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
309	C₂²×C₄	C₂²×C₄×C₁₁	1	2	yes	—
310	C₂²×C₄	C₂²×C₄×C₁₁	1	2	yes	—
311	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
312	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
313	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
314	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
315	C₂×C₈	—	2	2	no	—
316	C₂×C₈	—	2	2	no	—
317	C₂×C₈	—	2	2	no	—
318	C₂×C₈	—	2	2	no	—
319	C₂×C₈	—	2	2	no	—
320	C₂×C₈	—	2	2	no	—
321	C₂×C₈	—	2	2	no	—
322	C₂×C₈	—	2	2	no	—
323	C₂×C₈	—	2	2	no	—
324	C₂×C₈	—	2	2	no	—
325	C₂×C₈	—	2	2	no	—
326	C₂×C₈	—	4	8	no	—
327	C₂×C₈	C₁₁×#41	1	4	yes	—
328	C₄⋊C₄	—	4	1	no	—
329	C₄⋊C₄	—	4	1	no	—
330	C₄⋊C₄	—	4	2	no	—
331	C₂²⋊C₄	—	2	4	no	—
332	C₂²⋊C₄	—	2	4	no	—
333	C₂²⋊C₄	—	2	4	no	—
334	C₂²⋊C₄	—	4	2	no	—
335	C₂²⋊C₄	—	4	2	no	—
336	C₄²	—	2	2	no	—
337	C₄²	—	2	2	no	—
338	C₄²	—	2	2	no	—
339	C₄²	—	2	1	no	—
340	C₄²	—	2	2	no	—
341	C₄²	—	2	2	no	—
342	C₄²	—	2	2	no	—
343	C₄²	—	2	1	no	—
344	C₄²	—	4	1	no	—
345	C₄²	—	4	1	no	—
346	C₁₁	#22395	1	1	yes	characteristic, direct product factor, Sylow
347	C₂³	—	2	2	no	—
348	C₂³	—	2	2	no	—
349	C₂³	—	2	2	no	—
350	C₂³	—	2	2	no	—
351	C₂³	—	2	2	no	—
352	C₂³	—	2	2	no	—
353	C₂³	C₂×C₁₁×M₁₆	1	4	yes	—
354	C₂³	C₂³×C₄×C₁₁	1	1	yes	characteristic
355	Q₈	—	4	4	no	—
356	D₄	—	4	4	no	—
357	C₂×C₄	—	2	1	no	—
358	C₂×C₄	—	2	1	no	—
359	C₂×C₄	—	2	1	no	—
360	C₂×C₄	—	2	1	no	—
361	C₂×C₄	—	2	1	no	—
362	C₂×C₄	—	2	2	no	—
363	C₂×C₄	—	2	1	no	—
364	C₂×C₄	—	2	2	no	—
365	C₂×C₄	—	2	2	no	—
366	C₂×C₄	—	2	2	no	—
367	C₂×C₄	—	2	1	no	—
368	C₂×C₄	—	2	1	no	—
369	C₂×C₄	—	2	2	no	—
370	C₂×C₄	—	2	1	no	—
371	C₂×C₄	—	2	1	no	—
372	C₂×C₄	—	2	2	no	—
373	C₂×C₄	—	2	1	no	—
374	C₂×C₄	—	2	1	no	—
375	C₂×C₄	—	2	2	no	—
376	C₂×C₄	—	2	1	no	—
377	C₂×C₄	—	2	1	no	—
378	C₂×C₄	—	2	1	no	—
379	C₂×C₄	—	2	1	no	—
380	C₂×C₄	—	2	2	no	—
381	C₂×C₄	—	2	2	no	—
382	C₂×C₄	—	4	2	no	—
383	C₂×C₄	—	4	2	no	—
384	C₂×C₄	—	4	2	no	—
385	C₂×C₄	—	4	2	no	—
386	C₂×C₄	C₂×C₁₁×M₁₆	1	2	yes	—
387	C₂×C₄	C₁₁×#131	1	2	yes	—
388	C₂×C₄	C₂×C₁₁×#41	1	2	yes	—
389	C₂×C₄	C₁₁×H(5,𝔽₂)	1	1	yes	characteristic
390	C₂×C₄	C₁₁×H(5,𝔽₂)	1	2	yes	—
391	C₂×C₄	C₁₁×2₋¹⁺⁴	1	1	yes	characteristic
392	C₈	—	2	4	no	—
393	C₈	—	4	2	no	—
394	C₈	—	4	2	no	—
395	C₈	—	4	2	no	—
396	C₂²	—	2	4	no	—
397	C₂²	—	2	4	no	—
398	C₂²	—	2	4	no	—
399	C₂²	—	4	2	no	—
400	C₂²	—	4	2	no	—
401	C₂²	—	4	2	no	—
402	C₂²	—	4	2	no	—
403	C₂²	C₄×C₁₁×#41	1	1	yes	characteristic
404	C₂²	C₁₁×#518	1	1	yes	characteristic
405	C₂²	C₁₁×#520	1	1	yes	characteristic
406	C₂²	C₂²×C₁₁×M₁₆	1	1	yes	characteristic
407	C₂²	C₂×C₁₁×#131	1	1	yes	characteristic
408	C₂²	C₁₁×#568	1	1	yes	characteristic
409	C₂²	C₁₁×#568	1	1	yes	characteristic
410	C₄	—	2	2	no	—
411	C₄	—	2	2	no	—
412	C₄	—	4	1	no	—
413	C₄	—	4	2	no	—
414	C₄	—	4	1	no	—
415	C₄	—	4	2	no	—
416	C₄	—	4	1	no	—
417	C₄	—	4	1	no	—
418	C₄	—	4	2	no	—
419	C₄	C₁₁×#538	1	2	yes	—
420	C₄	C₁₁×#542	1	2	yes	—
421	C₂	—	4	4	no	—
422	C₂	C₁₁×#2337	1	1	yes	characteristic
423	C₂	C₁₁×#2968	1	1	yes	characteristic
424	C₂	C₁₁×#2970	1	1	yes	characteristic
425	C₂	C₁₁×#2973	1	1	yes	characteristic
426	C₂	C₁₁×#2981	1	1	yes	characteristic
427	C₂	C₁₁×#2990	1	1	yes	characteristic
428	C₂	C₁₁×#2995	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
2. C₁₁×#1985	C₂	semidirect
3. C₁₁×#1924	C₂	semidirect
4. C₁₁×#1924	C₂	semidirect
6. C₁₁×#1850	C₂	semidirect
7. C₁₁×#1839	C₂	semidirect
8. C₁₁×#1767	C₂	semidirect
9. C₁₁×#1752	C₂	semidirect
78. #22395	C₁₁	direct (N × H)
134. #1985	C₂×C₁₁	semidirect
135. #1924	C₂×C₁₁	semidirect
136. #1924	C₂×C₁₁	semidirect
138. #1850	C₂×C₁₁	semidirect
139. #1839	C₂×C₁₁	semidirect
140. #1767	C₂×C₁₁	semidirect
141. #1752	C₂×C₁₁	semidirect
346. C₁₁	#22395	direct (N × H)

Maximal subgroups

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

subgroup	index
C₄×C₁₁×#124	2
C₁₁×#1985	2
C₁₁×#1924	2
C₁₁×#1869	2
C₁₁×#1850	2
C₁₁×#1839	2
C₁₁×#1767	2
C₁₁×#1752	2
#22395	11

Subgroups — C11×#22395 #14599588

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#22395 #14599588