Subgroups — C₁₁×#22824 #14600017

Order 2816.

636 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×#2295	C₂	1	1	yes	maximal, characteristic
2	C₁₁×#1985	C₂	1	2	yes	maximal
3	C₁₁×#1917	C₂	1	2	yes	maximal
4	C₁₁×#1916	C₂	1	2	yes	maximal
5	C₁₁×#1842	C₂	1	1	yes	maximal, characteristic
6	C₁₁×#1832	C₂	1	2	yes	maximal
7	C₁₁×#1771	C₂	1	2	yes	maximal
8	C₁₁×#1768	C₂	1	2	yes	maximal
9	C₁₁×#1767	C₂	1	1	yes	maximal, characteristic
10	C₂×C₄×Q₈×C₁₁	C₂²	1	1	yes	characteristic
11	C₂×C₁₁×C₄⋊C₈	C₂²	1	2	yes	—
12	C₂×C₁₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
13	C₂×C₁₁×C₄⋊C₈	C₂²	1	2	yes	—
14	C₂×C₁₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
15	C₂×C₁₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
16	C₂×C₁₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
17	C₂×C₁₁×#97	C₂²	1	2	yes	—
18	C₂×C₁₁×#97	C₂²	1	2	yes	—
19	C₂×C₄×C₈×C₁₁	C₂²	1	2	yes	—
20	C₁₁×#391	C₄	1	1	yes	characteristic
21	C₁₁×#391	C₄	1	1	yes	characteristic
22	C₁₁×#389	C₄	1	1	yes	characteristic
23	C₁₁×#389	C₄	1	1	yes	characteristic
24	C₁₁×#387	C₄	1	2	yes	—
25	C₁₁×#387	C₄	1	2	yes	—
26	C₄×C₁₁×C₄⋊C₄	C₂²	1	2	yes	—
27	C₄×C₁₁×C₄⋊C₄	C₂²	1	1	yes	characteristic
28	C₁₁×#376	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	2	yes	—
34	C₁₁×#336	C₂²	1	2	yes	—
35	C₁₁×#336	C₂²	1	2	yes	—
36	C₁₁×#336	C₂²	1	2	yes	—
37	C₂²×Q₈×C₁₁	C₂×C₄	1	1	yes	characteristic
38	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
39	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
40	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
41	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
42	C₄×Q₈×C₁₁	—	2	2	no	—
43	C₄×Q₈×C₁₁	—	2	2	no	—
44	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	2	yes	—
45	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	2	yes	—
46	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
47	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	2	yes	—
48	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
49	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
50	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
51	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
52	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
53	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
54	C₂×C₄²×C₁₁	C₂³	1	2	yes	—
55	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
56	C₂×C₄²×C₁₁	C₂³	1	2	yes	—
57	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
58	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
59	C₁₁×C₄⋊C₈	—	2	4	no	—
60	C₁₁×C₄⋊C₈	—	2	2	no	—
61	C₁₁×C₄⋊C₈	—	2	4	no	—
62	C₁₁×C₄⋊C₈	—	4	1	no	—
63	C₁₁×C₄⋊C₈	—	4	1	no	—
64	C₁₁×C₄⋊C₈	Q₈	1	4	yes	complemented
65	C₁₁×#97	—	2	4	no	—
66	C₁₁×#97	—	4	2	no	—
67	C₄×C₈×C₁₁	—	4	2	no	—
68	C₁₁×#95	C₂×C₄	1	2	yes	—
69	C₁₁×#95	C₂×C₄	1	2	yes	—
70	C₁₁×#95	C₂×C₄	1	2	yes	—
71	C₁₁×#95	C₂×C₄	1	2	yes	—
72	C₁₁×#95	C₂×C₄	1	2	yes	—
73	C₁₁×#95	C₂×C₄	1	2	yes	—
74	C₁₁×#95	C₂×C₄	1	2	yes	—
75	#22824	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
76	C₂×Q₈×C₁₁	—	2	2	no	—
77	C₂×Q₈×C₁₁	—	4	1	no	—
78	C₂×Q₈×C₁₁	—	4	1	no	—
79	C₂²×C₄×C₁₁	C₂²×C₄	1	2	yes	—
80	C₂²×C₄×C₁₁	C₂²×C₄	1	2	yes	—
81	C₂²×C₄×C₁₁	C₂²×C₄	1	2	yes	—
82	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
83	C₂²×C₄×C₁₁	C₂²×C₄	1	2	yes	—
84	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
85	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
86	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
87	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
88	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
89	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
90	C₂×C₈×C₁₁	—	2	2	no	—
91	C₂×C₈×C₁₁	—	2	2	no	—
92	C₂×C₈×C₁₁	—	2	2	no	—
93	C₂×C₈×C₁₁	—	2	2	no	—
94	C₂×C₈×C₁₁	—	2	2	no	—
95	C₂×C₈×C₁₁	—	2	2	no	—
96	C₂×C₈×C₁₁	—	2	2	no	—
97	C₂×C₈×C₁₁	—	2	2	no	—
98	C₂×C₈×C₁₁	—	2	2	no	—
99	C₂×C₈×C₁₁	—	2	2	no	—
100	C₂×C₈×C₁₁	—	2	2	no	—
101	C₂×C₈×C₁₁	C₂×Q₈	1	4	yes	—
102	C₁₁×C₄⋊C₄	—	2	2	no	—
103	C₁₁×C₄⋊C₄	—	2	4	no	—
104	C₁₁×C₄⋊C₄	—	2	4	no	—
105	C₁₁×C₄⋊C₄	—	4	1	no	—
106	C₁₁×C₄⋊C₄	—	4	1	no	—
107	C₁₁×C₄⋊C₄	—	4	2	no	—
108	C₄²×C₁₁	—	2	2	no	—
109	C₄²×C₁₁	—	2	2	no	—
110	C₄²×C₁₁	—	2	2	no	—
111	C₄²×C₁₁	—	2	2	no	—
112	C₄²×C₁₁	—	2	1	no	—
113	C₄²×C₁₁	—	2	1	no	—
114	C₄²×C₁₁	—	2	2	no	—
115	C₄²×C₁₁	—	4	1	no	—
116	C₄²×C₁₁	—	4	1	no	—
117	C₄²×C₁₁	—	4	1	no	—
118	C₄²×C₁₁	C₂×Q₈	1	2	yes	—
119	C₄²×C₁₁	#41	1	2	yes	—
120	C₄²×C₁₁	#41	1	2	yes	—
121	C₄²×C₁₁	#41	1	2	yes	—
122	#2295	C₂×C₁₁	1	1	yes	characteristic
123	#1985	C₂×C₁₁	1	2	yes	—
124	#1917	C₂×C₁₁	1	2	yes	—
125	#1916	C₂×C₁₁	1	2	yes	—
126	#1842	C₂×C₁₁	1	1	yes	characteristic
127	#1832	C₂×C₁₁	1	2	yes	—
128	#1771	C₂×C₁₁	1	2	yes	—
129	#1768	C₂×C₁₁	1	2	yes	—
130	#1767	C₂×C₁₁	1	1	yes	characteristic
131	C₂³×C₁₁	C₂³×C₄	1	1	yes	characteristic
132	Q₈×C₁₁	—	4	4	no	—
133	C₂×C₄×C₁₁	—	2	1	no	—
134	C₂×C₄×C₁₁	—	2	1	no	—
135	C₂×C₄×C₁₁	—	2	1	no	—
136	C₂×C₄×C₁₁	—	2	1	no	—
137	C₂×C₄×C₁₁	—	2	1	no	—
138	C₂×C₄×C₁₁	—	2	1	no	—
139	C₂×C₄×C₁₁	—	2	1	no	—
140	C₂×C₄×C₁₁	—	2	1	no	—
141	C₂×C₄×C₁₁	—	2	1	no	—
142	C₂×C₄×C₁₁	—	2	1	no	—
143	C₂×C₄×C₁₁	—	2	2	no	—
144	C₂×C₄×C₁₁	—	2	2	no	—
145	C₂×C₄×C₁₁	—	2	2	no	—
146	C₂×C₄×C₁₁	—	2	2	no	—
147	C₂×C₄×C₁₁	—	2	1	no	—
148	C₂×C₄×C₁₁	—	2	2	no	—
149	C₂×C₄×C₁₁	—	2	2	no	—
150	C₂×C₄×C₁₁	—	2	1	no	—
151	C₂×C₄×C₁₁	—	2	1	no	—
152	C₂×C₄×C₁₁	—	2	2	no	—
153	C₂×C₄×C₁₁	—	2	2	no	—
154	C₂×C₄×C₁₁	—	2	2	no	—
155	C₂×C₄×C₁₁	—	2	2	no	—
156	C₂×C₄×C₁₁	—	2	2	no	—
157	C₂×C₄×C₁₁	—	2	2	no	—
158	C₂×C₄×C₁₁	#117	1	2	yes	—
159	C₂×C₄×C₁₁	#117	1	2	yes	—
160	C₂×C₄×C₁₁	C₄×Q₈	1	2	yes	—
161	C₂×C₄×C₁₁	C₄×Q₈	1	2	yes	—
162	C₂×C₄×C₁₁	#131	1	2	yes	—
163	C₂×C₄×C₁₁	C₂²×Q₈	1	1	yes	characteristic
164	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
165	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
166	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
167	C₂×C₄×C₁₁	H(5,𝔽₂)	1	1	yes	characteristic
168	C₂×C₄×C₁₁	2₋¹⁺⁴	1	1	yes	characteristic
169	C₈×C₁₁	—	2	4	no	—
170	C₈×C₁₁	—	4	2	no	—
171	C₈×C₁₁	—	4	2	no	—
172	C₈×C₁₁	—	4	2	no	—
173	C₂×C₄×Q₈	C₂²×C₁₁	1	1	yes	characteristic
174	C₂×C₄⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
175	C₂×C₄⋊C₈	C₂²×C₁₁	1	2	yes	—
176	C₂×C₄⋊C₈	C₂²×C₁₁	1	2	yes	—
177	C₂×C₄⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
178	C₂×C₄⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
179	C₂×C₄⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
180	C₂×#97	C₂²×C₁₁	1	2	yes	—
181	C₂×#97	C₂²×C₁₁	1	2	yes	—
182	C₂×C₄×C₈	C₂²×C₁₁	1	2	yes	—
183	#391	C₄×C₁₁	1	1	yes	characteristic
184	#391	C₄×C₁₁	1	1	yes	characteristic
185	#389	C₄×C₁₁	1	1	yes	characteristic
186	#389	C₄×C₁₁	1	1	yes	characteristic
187	#387	C₄×C₁₁	1	2	yes	—
188	#387	C₄×C₁₁	1	2	yes	—
189	C₄×C₄⋊C₄	C₂²×C₁₁	1	2	yes	—
190	C₄×C₄⋊C₄	C₂²×C₁₁	1	1	yes	characteristic
191	#376	C₂²×C₁₁	1	2	yes	—
192	C₄³	C₂²×C₁₁	1	1	yes	characteristic
193	#336	C₂²×C₁₁	1	2	yes	—
194	#336	C₂²×C₁₁	1	2	yes	—
195	#336	C₂²×C₁₁	1	2	yes	—
196	#336	C₂²×C₁₁	1	2	yes	—
197	#336	C₂²×C₁₁	1	2	yes	—
198	#336	C₂²×C₁₁	1	2	yes	—
199	#336	C₂²×C₁₁	1	2	yes	—
200	C₂²×C₁₁	C₂×#117	1	1	yes	characteristic
201	C₂²×C₁₁	C₂×C₄×Q₈	1	1	yes	characteristic
202	C₂²×C₁₁	#520	1	1	yes	characteristic
203	C₂²×C₁₁	C₂×#131	1	1	yes	characteristic
204	C₂²×C₁₁	#568	1	1	yes	characteristic
205	C₂²×C₁₁	#568	1	1	yes	characteristic
206	C₂²×C₁₁	#568	1	1	yes	characteristic
207	C₄×C₁₁	—	2	2	no	—
208	C₄×C₁₁	—	2	2	no	—
209	C₄×C₁₁	—	2	2	no	—
210	C₄×C₁₁	—	2	2	no	—
211	C₄×C₁₁	—	2	2	no	—
212	C₄×C₁₁	—	4	2	no	—
213	C₄×C₁₁	—	4	2	no	—
214	C₄×C₁₁	—	4	2	no	—
215	C₄×C₁₁	—	4	1	no	—
216	C₄×C₁₁	—	4	2	no	—
217	C₄×C₁₁	#554	1	1	yes	characteristic
218	C₄×C₁₁	#556	1	1	yes	characteristic
219	C₄×C₁₁	#557	1	1	yes	characteristic
220	C₄×C₁₁	#559	1	1	yes	characteristic
221	C₂²×Q₈	C₂×C₄×C₁₁	1	1	yes	characteristic
222	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
223	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
224	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
225	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
226	C₄×Q₈	—	2	2	no	—
227	C₄×Q₈	—	2	2	no	—
228	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	2	yes	—
229	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
230	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	2	yes	—
231	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	2	yes	—
232	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
233	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
234	C₂×C₄²	C₂×C₄×C₁₁	1	1	yes	characteristic
235	C₂×C₄²	C₂×C₄×C₁₁	1	1	yes	characteristic
236	C₂×C₄²	C₂×C₄×C₁₁	1	1	yes	characteristic
237	C₂×C₄²	C₂×C₄×C₁₁	1	1	yes	characteristic
238	C₂×C₄²	C₂³×C₁₁	1	2	yes	—
239	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
240	C₂×C₄²	C₂³×C₁₁	1	2	yes	—
241	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
242	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
243	C₄⋊C₈	—	2	4	no	—
244	C₄⋊C₈	—	2	2	no	—
245	C₄⋊C₈	—	2	4	no	—
246	C₄⋊C₈	—	4	1	no	—
247	C₄⋊C₈	—	4	1	no	—
248	C₄⋊C₈	Q₈×C₁₁	1	4	yes	complemented
249	#97	—	2	4	no	—
250	#97	—	4	2	no	—
251	C₄×C₈	—	4	2	no	—
252	#95	C₂×C₄×C₁₁	1	2	yes	—
253	#95	C₂×C₄×C₁₁	1	2	yes	—
254	#95	C₂×C₄×C₁₁	1	2	yes	—
255	#95	C₂×C₄×C₁₁	1	2	yes	—
256	#95	C₂×C₄×C₁₁	1	2	yes	—
257	#95	C₂×C₄×C₁₁	1	2	yes	—
258	#95	C₂×C₄×C₁₁	1	2	yes	—
259	C₂×C₁₁	#2355	1	1	yes	characteristic
260	C₂×C₁₁	#2921	1	1	yes	characteristic
261	C₂×C₁₁	#2925	1	1	yes	characteristic
262	C₂×C₁₁	#2961	1	1	yes	characteristic
263	C₂×C₁₁	#2962	1	1	yes	characteristic
264	C₂×C₁₁	#2992	1	1	yes	characteristic
265	C₂×C₁₁	#2995	1	1	yes	characteristic
266	C₂×Q₈	—	2	2	no	—
267	C₂×Q₈	—	4	1	no	—
268	C₂×Q₈	—	4	1	no	—
269	C₂²×C₄	C₂²×C₄×C₁₁	1	2	yes	—
270	C₂²×C₄	C₂²×C₄×C₁₁	1	2	yes	—
271	C₂²×C₄	C₂²×C₄×C₁₁	1	2	yes	—
272	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
273	C₂²×C₄	C₂²×C₄×C₁₁	1	2	yes	—
274	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
275	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
276	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
277	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
278	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
279	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
280	C₂×C₈	—	2	2	no	—
281	C₂×C₈	—	2	2	no	—
282	C₂×C₈	—	2	2	no	—
283	C₂×C₈	—	2	2	no	—
284	C₂×C₈	—	2	2	no	—
285	C₂×C₈	—	2	2	no	—
286	C₂×C₈	—	2	2	no	—
287	C₂×C₈	—	2	2	no	—
288	C₂×C₈	—	2	2	no	—
289	C₂×C₈	—	2	2	no	—
290	C₂×C₈	—	2	2	no	—
291	C₂×C₈	C₂×Q₈×C₁₁	1	4	yes	—
292	C₄⋊C₄	—	2	2	no	—
293	C₄⋊C₄	—	2	4	no	—
294	C₄⋊C₄	—	2	4	no	—
295	C₄⋊C₄	—	4	1	no	—
296	C₄⋊C₄	—	4	1	no	—
297	C₄⋊C₄	—	4	2	no	—
298	C₄²	—	2	2	no	—
299	C₄²	—	2	2	no	—
300	C₄²	—	2	2	no	—
301	C₄²	—	2	2	no	—
302	C₄²	—	2	1	no	—
303	C₄²	—	2	1	no	—
304	C₄²	—	2	2	no	—
305	C₄²	—	4	1	no	—
306	C₄²	—	4	1	no	—
307	C₄²	—	4	1	no	—
308	C₄²	C₂×Q₈×C₁₁	1	2	yes	—
309	C₄²	C₁₁×#41	1	2	yes	—
310	C₄²	C₁₁×#41	1	2	yes	—
311	C₄²	C₁₁×#41	1	2	yes	—
312	C₁₁	#22824	1	1	yes	characteristic, direct product factor, Sylow
313	C₂³	C₂³×C₄×C₁₁	1	1	yes	characteristic
314	Q₈	—	4	4	no	—
315	C₂×C₄	—	2	1	no	—
316	C₂×C₄	—	2	1	no	—
317	C₂×C₄	—	2	1	no	—
318	C₂×C₄	—	2	1	no	—
319	C₂×C₄	—	2	1	no	—
320	C₂×C₄	—	2	1	no	—
321	C₂×C₄	—	2	1	no	—
322	C₂×C₄	—	2	1	no	—
323	C₂×C₄	—	2	1	no	—
324	C₂×C₄	—	2	1	no	—
325	C₂×C₄	—	2	2	no	—
326	C₂×C₄	—	2	2	no	—
327	C₂×C₄	—	2	2	no	—
328	C₂×C₄	—	2	2	no	—
329	C₂×C₄	—	2	1	no	—
330	C₂×C₄	—	2	2	no	—
331	C₂×C₄	—	2	2	no	—
332	C₂×C₄	—	2	1	no	—
333	C₂×C₄	—	2	1	no	—
334	C₂×C₄	—	2	2	no	—
335	C₂×C₄	—	2	2	no	—
336	C₂×C₄	—	2	2	no	—
337	C₂×C₄	—	2	2	no	—
338	C₂×C₄	—	2	2	no	—
339	C₂×C₄	—	2	2	no	—
340	C₂×C₄	C₁₁×#117	1	2	yes	—
341	C₂×C₄	C₁₁×#117	1	2	yes	—
342	C₂×C₄	C₄×Q₈×C₁₁	1	2	yes	—
343	C₂×C₄	C₄×Q₈×C₁₁	1	2	yes	—
344	C₂×C₄	C₁₁×#131	1	2	yes	—
345	C₂×C₄	C₂²×Q₈×C₁₁	1	1	yes	characteristic
346	C₂×C₄	C₂×C₁₁×#41	1	1	yes	characteristic
347	C₂×C₄	C₂×C₁₁×#41	1	1	yes	characteristic
348	C₂×C₄	C₂×C₁₁×#41	1	1	yes	characteristic
349	C₂×C₄	C₁₁×H(5,𝔽₂)	1	1	yes	characteristic
350	C₂×C₄	C₁₁×2₋¹⁺⁴	1	1	yes	characteristic
351	C₈	—	2	4	no	—
352	C₈	—	4	2	no	—
353	C₈	—	4	2	no	—
354	C₈	—	4	2	no	—
355	C₂²	C₂×C₁₁×#117	1	1	yes	characteristic
356	C₂²	C₂×C₄×Q₈×C₁₁	1	1	yes	characteristic
357	C₂²	C₁₁×#520	1	1	yes	characteristic
358	C₂²	C₂×C₁₁×#131	1	1	yes	characteristic
359	C₂²	C₁₁×#568	1	1	yes	characteristic
360	C₂²	C₁₁×#568	1	1	yes	characteristic
361	C₂²	C₁₁×#568	1	1	yes	characteristic
362	C₄	—	2	2	no	—
363	C₄	—	2	2	no	—
364	C₄	—	2	2	no	—
365	C₄	—	2	2	no	—
366	C₄	—	2	2	no	—
367	C₄	—	4	2	no	—
368	C₄	—	4	2	no	—
369	C₄	—	4	2	no	—
370	C₄	—	4	1	no	—
371	C₄	—	4	2	no	—
372	C₄	C₁₁×#554	1	1	yes	characteristic
373	C₄	C₁₁×#556	1	1	yes	characteristic
374	C₄	C₁₁×#557	1	1	yes	characteristic
375	C₄	C₁₁×#559	1	1	yes	characteristic
376	C₂	C₁₁×#2355	1	1	yes	characteristic
377	C₂	C₁₁×#2921	1	1	yes	characteristic
378	C₂	C₁₁×#2925	1	1	yes	characteristic
379	C₂	C₁₁×#2961	1	1	yes	characteristic
380	C₂	C₁₁×#2962	1	1	yes	characteristic
381	C₂	C₁₁×#2992	1	1	yes	characteristic
382	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, prime radical	C₂³×C₁₁	C₂³×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
64. C₁₁×C₄⋊C₈	Q₈	semidirect
75. #22824	C₁₁	direct (N × H)
248. C₄⋊C₈	Q₈×C₁₁	semidirect
312. C₁₁	#22824	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×#2295	2
C₁₁×#1985	2
C₁₁×#1917	2
C₁₁×#1916	2
C₁₁×#1842	2
C₁₁×#1832	2
C₁₁×#1771	2
C₁₁×#1768	2
C₁₁×#1767	2
#22824	11

Subgroups — C11×#22824 #14600017

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#22824 #14600017