Subgroups — C₁₁×#22838 #14600031

Order 2816.

732 conjugacy classes of subgroups.

The subgroup lattice has 422 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×#2293	C₂	1	1	yes	maximal, characteristic
2	C₁₁×#1955	C₂	1	2	yes	maximal
3	C₁₁×#1924	C₂	1	2	yes	maximal, complemented
4	C₁₁×#1923	C₂	1	2	yes	maximal, complemented
5	C₁₁×#1831	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₁×#1818	C₂	1	2	yes	maximal, complemented
7	C₁₁×#1771	C₂	1	2	yes	maximal, complemented
8	C₁₁×#1767	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₁×#1750	C₂	1	2	yes	maximal, complemented
10	C₂×C₄×D₄×C₁₁	C₂²	1	1	yes	characteristic
11	C₂×C₁₁×#117	C₂²	1	2	yes	—
12	C₂×C₁₁×C₄⋊C₈	C₂²	1	2	yes	—
13	C₂×C₁₁×C₄⋊C₈	C₂²	1	2	yes	—
14	C₂×C₁₁×C₂²⋊C₈	C₂²	1	2	yes	—
15	C₂×C₁₁×C₂²⋊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×#97	C₂²	1	2	yes	—
19	C₂×C₁₁×#97	C₂²	1	2	yes	—
20	C₂×C₄×C₈×C₁₁	C₂²	1	2	yes	—
21	C₁₁×#390	C₄	1	1	yes	characteristic
22	C₁₁×#390	C₄	1	1	yes	characteristic
23	C₁₁×#389	C₄	1	1	yes	characteristic
24	C₁₁×#389	C₄	1	1	yes	characteristic
25	C₁₁×#388	C₄	1	2	yes	—
26	C₁₁×#388	C₄	1	2	yes	—
27	C₄×C₁₁×C₄⋊C₄	C₂²	1	1	yes	characteristic
28	C₄×C₁₁×C₂²⋊C₄	C₂²	1	2	yes	—
29	C₄³×C₁₁	C₂²	1	1	yes	characteristic
30	C₁₁×#336	C₂²	1	1	yes	characteristic
31	C₁₁×#336	C₂²	1	2	yes	—
32	C₁₁×#336	C₂²	1	1	yes	characteristic
33	C₁₁×#336	C₂²	1	2	yes	—
34	C₁₁×#336	C₂²	1	1	yes	characteristic
35	C₁₁×#336	C₂²	1	2	yes	—
36	C₁₁×#336	C₂²	1	1	yes	characteristic
37	C₂²×D₄×C₁₁	C₂×C₄	1	1	yes	characteristic
38	C₂³×C₄×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	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
43	C₄×D₄×C₁₁	—	2	2	no	—
44	C₄×D₄×C₁₁	—	2	2	no	—
45	C₁₁×#117	—	4	2	no	—
46	C₁₁×#117	—	4	2	no	—
47	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
48	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	2	yes	—
49	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	2	yes	—
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×C₂²⋊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×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
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	C₂³	1	1	yes	characteristic
62	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
63	C₂×C₄²×C₁₁	C₂³	1	2	yes	—
64	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
65	C₁₁×C₄⋊C₈	—	2	4	no	—
66	C₁₁×C₄⋊C₈	—	2	4	no	—
67	C₁₁×C₂²⋊C₈	—	2	4	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	—	2	4	no	—
72	C₁₁×#97	—	4	2	no	—
73	C₄×C₈×C₁₁	—	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	#22838	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
78	C₂⁴×C₁₁	C₂²×C₄	1	2	yes	—
79	C₂×D₄×C₁₁	—	2	2	no	—
80	C₂×D₄×C₁₁	—	4	1	no	—
81	C₂×D₄×C₁₁	—	4	1	no	—
82	C₂²×C₄×C₁₁	—	2	2	no	—
83	C₂²×C₄×C₁₁	—	2	2	no	—
84	C₂²×C₄×C₁₁	—	2	2	no	—
85	C₂²×C₄×C₁₁	—	2	2	no	—
86	C₂²×C₄×C₁₁	—	2	2	no	—
87	C₂²×C₄×C₁₁	—	2	2	no	—
88	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
89	C₂²×C₄×C₁₁	C₂²×C₄	1	2	yes	—
90	C₂²×C₄×C₁₁	C₂²×C₄	1	2	yes	—
91	C₂²×C₄×C₁₁	C₂²×C₄	1	2	yes	—
92	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
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	1	yes	characteristic
97	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
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	—	2	2	no	—
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	#41	1	4	yes	—
110	C₁₁×C₄⋊C₄	—	2	2	no	—
111	C₁₁×C₄⋊C₄	—	4	1	no	—
112	C₁₁×C₄⋊C₄	—	4	1	no	—
113	C₁₁×C₄⋊C₄	—	4	2	no	—
114	C₁₁×C₄⋊C₄	—	4	2	no	—
115	C₁₁×C₂²⋊C₄	—	2	4	no	—
116	C₁₁×C₂²⋊C₄	—	2	4	no	—
117	C₁₁×C₂²⋊C₄	—	4	2	no	—
118	C₁₁×C₂²⋊C₄	—	4	2	no	—
119	C₁₁×C₂²⋊C₄	—	4	2	no	—
120	C₄²×C₁₁	—	2	2	no	—
121	C₄²×C₁₁	—	2	2	no	—
122	C₄²×C₁₁	—	2	2	no	—
123	C₄²×C₁₁	—	2	2	no	—
124	C₄²×C₁₁	—	2	2	no	—
125	C₄²×C₁₁	—	4	1	no	—
126	C₄²×C₁₁	—	4	1	no	—
127	C₄²×C₁₁	—	4	1	no	—
128	C₄²×C₁₁	#41	1	2	yes	—
129	C₄²×C₁₁	#41	1	2	yes	—
130	#2293	C₂×C₁₁	1	1	yes	characteristic
131	#1955	C₂×C₁₁	1	2	yes	—
132	#1924	C₂×C₁₁	1	2	yes	complemented
133	#1923	C₂×C₁₁	1	2	yes	complemented
134	#1831	C₂×C₁₁	1	1	yes	characteristic, complemented
135	#1818	C₂×C₁₁	1	2	yes	complemented
136	#1771	C₂×C₁₁	1	2	yes	complemented
137	#1767	C₂×C₁₁	1	1	yes	characteristic, complemented
138	#1750	C₂×C₁₁	1	2	yes	complemented
139	C₂³×C₁₁	—	2	2	no	—
140	C₂³×C₁₁	—	2	2	no	—
141	C₂³×C₁₁	—	2	2	no	—
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	C₂³×C₄	1	1	yes	characteristic
147	D₄×C₁₁	—	4	4	no	—
148	C₂×C₄×C₁₁	—	2	1	no	—
149	C₂×C₄×C₁₁	—	2	1	no	—
150	C₂×C₄×C₁₁	—	2	1	no	—
151	C₂×C₄×C₁₁	—	2	1	no	—
152	C₂×C₄×C₁₁	—	2	1	no	—
153	C₂×C₄×C₁₁	—	2	1	no	—
154	C₂×C₄×C₁₁	—	2	2	no	—
155	C₂×C₄×C₁₁	—	2	1	no	—
156	C₂×C₄×C₁₁	—	2	2	no	—
157	C₂×C₄×C₁₁	—	2	1	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	2	no	—
164	C₂×C₄×C₁₁	—	2	1	no	—
165	C₂×C₄×C₁₁	—	2	1	no	—
166	C₂×C₄×C₁₁	—	2	1	no	—
167	C₂×C₄×C₁₁	—	2	1	no	—
168	C₂×C₄×C₁₁	—	2	1	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	—	4	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	#117	1	2	yes	—
177	C₂×C₄×C₁₁	#117	1	2	yes	—
178	C₂×C₄×C₁₁	#131	1	2	yes	—
179	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
180	C₂×C₄×C₁₁	C₂×#41	1	2	yes	—
181	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
182	C₂×C₄×C₁₁	H(5,𝔽₂)	1	2	yes	—
183	C₈×C₁₁	—	2	4	no	—
184	C₈×C₁₁	—	4	2	no	—
185	C₈×C₁₁	—	4	2	no	—
186	C₈×C₁₁	—	4	2	no	—
187	C₂×C₄×D₄	C₂²×C₁₁	1	1	yes	characteristic
188	C₂×#117	C₂²×C₁₁	1	2	yes	—
189	C₂×C₄⋊C₈	C₂²×C₁₁	1	2	yes	—
190	C₂×C₄⋊C₈	C₂²×C₁₁	1	2	yes	—
191	C₂×C₂²⋊C₈	C₂²×C₁₁	1	2	yes	—
192	C₂×C₂²⋊C₈	C₂²×C₁₁	1	2	yes	—
193	C₂×C₂²⋊C₈	C₂²×C₁₁	1	2	yes	—
194	C₂×C₂²⋊C₈	C₂²×C₁₁	1	2	yes	—
195	C₂×#97	C₂²×C₁₁	1	2	yes	—
196	C₂×#97	C₂²×C₁₁	1	2	yes	—
197	C₂×C₄×C₈	C₂²×C₁₁	1	2	yes	—
198	#390	C₄×C₁₁	1	1	yes	characteristic
199	#390	C₄×C₁₁	1	1	yes	characteristic
200	#389	C₄×C₁₁	1	1	yes	characteristic
201	#389	C₄×C₁₁	1	1	yes	characteristic
202	#388	C₄×C₁₁	1	2	yes	—
203	#388	C₄×C₁₁	1	2	yes	—
204	C₄×C₄⋊C₄	C₂²×C₁₁	1	1	yes	characteristic
205	C₄×C₂²⋊C₄	C₂²×C₁₁	1	2	yes	—
206	C₄³	C₂²×C₁₁	1	1	yes	characteristic
207	#336	C₂²×C₁₁	1	1	yes	characteristic
208	#336	C₂²×C₁₁	1	2	yes	—
209	#336	C₂²×C₁₁	1	2	yes	—
210	#336	C₂²×C₁₁	1	2	yes	—
211	#336	C₂²×C₁₁	1	1	yes	characteristic
212	#336	C₂²×C₁₁	1	1	yes	characteristic
213	#336	C₂²×C₁₁	1	1	yes	characteristic
214	C₂²×C₁₁	—	4	2	no	—
215	C₂²×C₁₁	—	4	2	no	—
216	C₂²×C₁₁	—	4	2	no	—
217	C₂²×C₁₁	—	4	2	no	—
218	C₂²×C₁₁	—	4	2	no	—
219	C₂²×C₁₁	—	4	2	no	—
220	C₂²×C₁₁	—	4	2	no	—
221	C₂²×C₁₁	C₂×#117	1	1	yes	characteristic
222	C₂²×C₁₁	C₄×#41	1	1	yes	characteristic
223	C₂²×C₁₁	#518	1	1	yes	characteristic
224	C₂²×C₁₁	C₂×#131	1	1	yes	characteristic
225	C₂²×C₁₁	#568	1	1	yes	characteristic
226	C₂²×C₁₁	#568	1	1	yes	characteristic
227	C₂²×C₁₁	#568	1	1	yes	characteristic
228	C₄×C₁₁	—	2	2	no	—
229	C₄×C₁₁	—	2	2	no	—
230	C₄×C₁₁	—	2	2	no	—
231	C₄×C₁₁	—	4	2	no	—
232	C₄×C₁₁	—	4	1	no	—
233	C₄×C₁₁	—	4	1	no	—
234	C₄×C₁₁	—	4	2	no	—
235	C₄×C₁₁	—	4	1	no	—
236	C₄×C₁₁	—	4	2	no	—
237	C₄×C₁₁	#553	1	2	yes	—
238	C₄×C₁₁	#559	1	2	yes	—
239	C₂²×D₄	C₂×C₄×C₁₁	1	1	yes	characteristic
240	C₂³×C₄	C₂³×C₁₁	1	2	yes	—
241	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
242	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
243	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
244	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
245	C₄×D₄	—	2	2	no	—
246	C₄×D₄	—	2	2	no	—
247	#117	—	4	2	no	—
248	#117	—	4	2	no	—
249	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
250	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	2	yes	—
251	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	2	yes	—
252	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
253	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
254	C₂×C₂²⋊C₄	C₂×C₄×C₁₁	1	2	yes	—
255	C₂×C₂²⋊C₄	C₂×C₄×C₁₁	1	2	yes	—
256	C₂×C₂²⋊C₄	C₂×C₄×C₁₁	1	2	yes	—
257	C₂×C₂²⋊C₄	C₂×C₄×C₁₁	1	2	yes	—
258	C₂×C₂²⋊C₄	C₂×C₄×C₁₁	1	2	yes	—
259	C₂×C₄²	C₂×C₄×C₁₁	1	1	yes	characteristic
260	C₂×C₄²	C₂×C₄×C₁₁	1	1	yes	characteristic
261	C₂×C₄²	C₂×C₄×C₁₁	1	1	yes	characteristic
262	C₂×C₄²	C₂×C₄×C₁₁	1	1	yes	characteristic
263	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
264	C₂×C₄²	C₂³×C₁₁	1	2	yes	—
265	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
266	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
267	C₄⋊C₈	—	2	4	no	—
268	C₄⋊C₈	—	2	4	no	—
269	C₂²⋊C₈	—	2	4	no	—
270	C₂²⋊C₈	—	2	4	no	—
271	C₂²⋊C₈	—	4	2	no	—
272	C₂²⋊C₈	—	4	2	no	—
273	#97	—	2	4	no	—
274	#97	—	4	2	no	—
275	C₄×C₈	—	4	2	no	—
276	#95	C₂×C₄×C₁₁	1	2	yes	—
277	#95	C₂×C₄×C₁₁	1	2	yes	—
278	#95	C₂×C₄×C₁₁	1	2	yes	—
279	C₂×C₁₁	—	8	2	no	—
280	C₂×C₁₁	#2357	1	1	yes	characteristic
281	C₂×C₁₁	#2921	1	1	yes	characteristic
282	C₂×C₁₁	#2925	1	1	yes	characteristic
283	C₂×C₁₁	#2967	1	1	yes	characteristic
284	C₂×C₁₁	#2968	1	1	yes	characteristic
285	C₂×C₁₁	#2980	1	1	yes	characteristic
286	C₂×C₁₁	#2981	1	1	yes	characteristic
287	C₂⁴	C₂²×C₄×C₁₁	1	2	yes	—
288	C₂×D₄	—	2	2	no	—
289	C₂×D₄	—	4	1	no	—
290	C₂×D₄	—	4	1	no	—
291	C₂²×C₄	—	2	2	no	—
292	C₂²×C₄	—	2	2	no	—
293	C₂²×C₄	—	2	2	no	—
294	C₂²×C₄	—	2	2	no	—
295	C₂²×C₄	—	2	2	no	—
296	C₂²×C₄	—	2	2	no	—
297	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
298	C₂²×C₄	C₂²×C₄×C₁₁	1	2	yes	—
299	C₂²×C₄	C₂²×C₄×C₁₁	1	2	yes	—
300	C₂²×C₄	C₂²×C₄×C₁₁	1	2	yes	—
301	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
302	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
303	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
304	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
305	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
306	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
307	C₂×C₈	—	2	2	no	—
308	C₂×C₈	—	2	2	no	—
309	C₂×C₈	—	2	2	no	—
310	C₂×C₈	—	2	2	no	—
311	C₂×C₈	—	2	2	no	—
312	C₂×C₈	—	2	2	no	—
313	C₂×C₈	—	2	2	no	—
314	C₂×C₈	—	2	2	no	—
315	C₂×C₈	—	2	2	no	—
316	C₂×C₈	—	2	2	no	—
317	C₂×C₈	—	2	2	no	—
318	C₂×C₈	C₁₁×#41	1	4	yes	—
319	C₄⋊C₄	—	2	2	no	—
320	C₄⋊C₄	—	4	2	no	—
321	C₄⋊C₄	—	4	2	no	—
322	C₄⋊C₄	—	4	1	no	—
323	C₄⋊C₄	—	4	1	no	—
324	C₂²⋊C₄	—	2	4	no	—
325	C₂²⋊C₄	—	2	4	no	—
326	C₂²⋊C₄	—	4	2	no	—
327	C₂²⋊C₄	—	4	2	no	—
328	C₂²⋊C₄	—	4	2	no	—
329	C₄²	—	2	2	no	—
330	C₄²	—	2	2	no	—
331	C₄²	—	2	2	no	—
332	C₄²	—	2	2	no	—
333	C₄²	—	2	2	no	—
334	C₄²	—	4	1	no	—
335	C₄²	—	4	1	no	—
336	C₄²	—	4	1	no	—
337	C₄²	C₁₁×#41	1	2	yes	—
338	C₄²	C₁₁×#41	1	2	yes	—
339	C₁₁	#22838	1	1	yes	characteristic, direct product factor, Sylow
340	C₂³	—	2	2	no	—
341	C₂³	—	2	2	no	—
342	C₂³	—	2	2	no	—
343	C₂³	—	2	2	no	—
344	C₂³	—	2	2	no	—
345	C₂³	—	2	2	no	—
346	C₂³	—	2	2	no	—
347	C₂³	C₂³×C₄×C₁₁	1	1	yes	characteristic
348	D₄	—	4	4	no	—
349	C₂×C₄	—	2	1	no	—
350	C₂×C₄	—	2	1	no	—
351	C₂×C₄	—	2	1	no	—
352	C₂×C₄	—	2	1	no	—
353	C₂×C₄	—	2	1	no	—
354	C₂×C₄	—	2	1	no	—
355	C₂×C₄	—	2	2	no	—
356	C₂×C₄	—	2	1	no	—
357	C₂×C₄	—	2	2	no	—
358	C₂×C₄	—	2	1	no	—
359	C₂×C₄	—	2	1	no	—
360	C₂×C₄	—	2	2	no	—
361	C₂×C₄	—	2	2	no	—
362	C₂×C₄	—	2	2	no	—
363	C₂×C₄	—	2	1	no	—
364	C₂×C₄	—	2	2	no	—
365	C₂×C₄	—	2	1	no	—
366	C₂×C₄	—	2	1	no	—
367	C₂×C₄	—	2	1	no	—
368	C₂×C₄	—	2	1	no	—
369	C₂×C₄	—	2	1	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	C₁₁×#117	1	2	yes	—
378	C₂×C₄	C₁₁×#117	1	2	yes	—
379	C₂×C₄	C₁₁×#131	1	2	yes	—
380	C₂×C₄	C₂×C₁₁×#41	1	1	yes	characteristic
381	C₂×C₄	C₂×C₁₁×#41	1	2	yes	—
382	C₂×C₄	C₂×C₁₁×#41	1	1	yes	characteristic
383	C₂×C₄	C₁₁×H(5,𝔽₂)	1	2	yes	—
384	C₈	—	2	4	no	—
385	C₈	—	4	2	no	—
386	C₈	—	4	2	no	—
387	C₈	—	4	2	no	—
388	C₂²	—	4	2	no	—
389	C₂²	—	4	2	no	—
390	C₂²	—	4	2	no	—
391	C₂²	—	4	2	no	—
392	C₂²	—	4	2	no	—
393	C₂²	—	4	2	no	—
394	C₂²	—	4	2	no	—
395	C₂²	C₂×C₁₁×#117	1	1	yes	characteristic
396	C₂²	C₄×C₁₁×#41	1	1	yes	characteristic
397	C₂²	C₁₁×#518	1	1	yes	characteristic
398	C₂²	C₂×C₁₁×#131	1	1	yes	characteristic
399	C₂²	C₁₁×#568	1	1	yes	characteristic
400	C₂²	C₁₁×#568	1	1	yes	characteristic
401	C₂²	C₁₁×#568	1	1	yes	characteristic
402	C₄	—	2	2	no	—
403	C₄	—	2	2	no	—
404	C₄	—	2	2	no	—
405	C₄	—	4	1	no	—
406	C₄	—	4	1	no	—
407	C₄	—	4	2	no	—
408	C₄	—	4	1	no	—
409	C₄	—	4	2	no	—
410	C₄	—	4	2	no	—
411	C₄	C₁₁×#553	1	2	yes	—
412	C₄	C₁₁×#559	1	2	yes	—
413	C₂	—	8	2	no	—
414	C₂	C₁₁×#2357	1	1	yes	characteristic
415	C₂	C₁₁×#2921	1	1	yes	characteristic
416	C₂	C₁₁×#2925	1	1	yes	characteristic
417	C₂	C₁₁×#2967	1	1	yes	characteristic
418	C₂	C₁₁×#2968	1	1	yes	characteristic
419	C₂	C₁₁×#2980	1	1	yes	characteristic
420	C₂	C₁₁×#2981	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
3. C₁₁×#1924	C₂	semidirect
4. C₁₁×#1923	C₂	semidirect
5. C₁₁×#1831	C₂	semidirect
6. C₁₁×#1818	C₂	semidirect
7. C₁₁×#1771	C₂	semidirect
8. C₁₁×#1767	C₂	semidirect
9. C₁₁×#1750	C₂	semidirect
77. #22838	C₁₁	direct (N × H)
132. #1924	C₂×C₁₁	semidirect
133. #1923	C₂×C₁₁	semidirect
134. #1831	C₂×C₁₁	semidirect
135. #1818	C₂×C₁₁	semidirect
136. #1771	C₂×C₁₁	semidirect
137. #1767	C₂×C₁₁	semidirect
138. #1750	C₂×C₁₁	semidirect
339. C₁₁	#22838	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×#2293	2
C₁₁×#1955	2
C₁₁×#1924	2
C₁₁×#1923	2
C₁₁×#1831	2
C₁₁×#1818	2
C₁₁×#1771	2
C₁₁×#1767	2
C₁₁×#1750	2
#22838	11

Subgroups — C11×#22838 #14600031

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#22838 #14600031