Subgroups — C₁₁×#21925 #14599118

Order 2816.

648 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×#2298	C₂	1	1	yes	maximal, characteristic
2	C₁₁×#1924	C₂	1	2	yes	maximal
3	C₁₁×#1923	C₂	1	2	yes	maximal
4	C₁₁×#1917	C₂	1	2	yes	maximal, complemented
5	C₁₁×#1916	C₂	1	2	yes	maximal, complemented
6	C₁₁×#1843	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₁×#1832	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₁×#1798	C₂	1	1	yes	maximal, characteristic
9	C₁₁×#1798	C₂	1	1	yes	maximal, characteristic
10	C₁₁×#1767	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×C₁₁×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₁×#117	C₂²	1	1	yes	characteristic
13	C₂×C₁₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
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×C₄⋊C₈	C₂²	1	2	yes	—
18	C₂×C₁₁×C₄⋊C₈	C₂²	1	2	yes	—
19	C₂×C₁₁×C₂²⋊C₈	C₂²	1	2	yes	—
20	C₂×C₁₁×C₂²⋊C₈	C₂²	1	2	yes	—
21	C₂×C₁₁×#97	C₂²	1	2	yes	—
22	C₂×C₄×C₈×C₁₁	C₂²	1	2	yes	—
23	C₁₁×#388	C₄	1	2	yes	—
24	C₁₁×#388	C₄	1	2	yes	—
25	C₁₁×#387	C₄	1	2	yes	—
26	C₁₁×#387	C₄	1	2	yes	—
27	C₄×C₁₁×C₄⋊C₄	C₂²	1	1	yes	characteristic
28	C₄×C₁₁×C₄⋊C₄	C₂²	1	1	yes	characteristic
29	C₄×C₁₁×C₂²⋊C₄	C₂²	1	1	yes	characteristic
30	C₄×C₁₁×C₂²⋊C₄	C₂²	1	1	yes	characteristic
31	C₁₁×#376	C₂²	1	1	yes	characteristic
32	C₄³×C₁₁	C₂²	1	1	yes	characteristic
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	C₁₁×#336	C₂²	1	2	yes	—
38	C₁₁×#336	C₂²	1	2	yes	—
39	C₂³×C₄×C₁₁	C₂³	1	1	yes	characteristic
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	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
44	C₁₁×#117	—	2	2	no	—
45	C₁₁×#117	—	2	2	no	—
46	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
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×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
51	C₂×C₁₁×C₂²⋊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×C₄²×C₁₁	C₂×C₄	1	2	yes	—
55	C₂×C₄²×C₁₁	C₂×C₄	1	2	yes	—
56	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
57	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
58	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
59	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
60	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
61	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
62	C₁₁×C₄⋊C₈	—	2	2	no	—
63	C₁₁×C₄⋊C₈	—	2	2	no	—
64	C₁₁×C₄⋊C₈	—	2	2	no	—
65	C₁₁×C₄⋊C₈	—	2	2	no	—
66	C₁₁×C₄⋊C₈	—	4	2	no	—
67	C₁₁×C₄⋊C₈	—	4	2	no	—
68	C₁₁×C₂²⋊C₈	—	4	2	no	—
69	C₁₁×C₂²⋊C₈	—	4	2	no	—
70	C₁₁×#97	—	4	2	no	—
71	C₄×C₈×C₁₁	—	4	2	no	—
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	C₁₁×#95	C₂×C₄	1	2	yes	—
76	C₁₁×#95	C₂×C₄	1	2	yes	—
77	C₁₁×#95	C₂×C₄	1	2	yes	—
78	#21925	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
79	C₂⁴×C₁₁	C₂²×C₄	1	1	yes	characteristic
80	C₂²×C₄×C₁₁	—	2	1	no	—
81	C₂²×C₄×C₁₁	—	2	1	no	—
82	C₂²×C₄×C₁₁	—	2	1	no	—
83	C₂²×C₄×C₁₁	—	2	1	no	—
84	C₂²×C₄×C₁₁	—	2	1	no	—
85	C₂²×C₄×C₁₁	—	2	1	no	—
86	C₂²×C₄×C₁₁	C₂²×C₄	1	2	yes	—
87	C₂²×C₄×C₁₁	C₂²×C₄	1	2	yes	—
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	1	yes	characteristic
91	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
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	2	yes	—
95	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
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	—	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	C₁₁×C₄⋊C₄	—	2	2	no	—
109	C₁₁×C₄⋊C₄	—	2	2	no	—
110	C₁₁×C₄⋊C₄	—	2	4	no	—
111	C₁₁×C₄⋊C₄	—	4	2	no	—
112	C₁₁×C₂²⋊C₄	—	2	2	no	—
113	C₁₁×C₂²⋊C₄	—	2	2	no	—
114	C₁₁×C₂²⋊C₄	—	2	4	no	—
115	C₁₁×C₂²⋊C₄	—	4	2	no	—
116	C₄²×C₁₁	—	2	4	no	—
117	C₄²×C₁₁	—	2	1	no	—
118	C₄²×C₁₁	—	2	1	no	—
119	C₄²×C₁₁	—	2	1	no	—
120	C₄²×C₁₁	—	2	1	no	—
121	C₄²×C₁₁	—	2	1	no	—
122	C₄²×C₁₁	—	2	1	no	—
123	C₄²×C₁₁	—	2	1	no	—
124	C₄²×C₁₁	—	2	1	no	—
125	C₄²×C₁₁	—	2	1	no	—
126	C₄²×C₁₁	—	2	1	no	—
127	C₄²×C₁₁	—	4	2	no	—
128	C₄²×C₁₁	#41	1	2	yes	—
129	C₄²×C₁₁	#41	1	2	yes	—
130	#2298	C₂×C₁₁	1	1	yes	characteristic
131	#1924	C₂×C₁₁	1	2	yes	—
132	#1923	C₂×C₁₁	1	2	yes	—
133	#1917	C₂×C₁₁	1	2	yes	complemented
134	#1916	C₂×C₁₁	1	2	yes	complemented
135	#1843	C₂×C₁₁	1	1	yes	characteristic, complemented
136	#1832	C₂×C₁₁	1	1	yes	characteristic, complemented
137	#1798	C₂×C₁₁	1	1	yes	characteristic
138	#1798	C₂×C₁₁	1	1	yes	characteristic
139	#1767	C₂×C₁₁	1	1	yes	characteristic, complemented
140	C₄×C₄⋊C₈	C₂×C₁₁	1	1	yes	characteristic, complemented
141	C₂³×C₁₁	—	2	1	no	—
142	C₂³×C₁₁	—	2	1	no	—
143	C₂³×C₁₁	—	2	1	no	—
144	C₂³×C₁₁	—	2	2	no	—
145	C₂³×C₁₁	—	2	2	no	—
146	C₂³×C₁₁	C₂³×C₄	1	1	yes	characteristic
147	C₂×C₄×C₁₁	—	2	2	no	—
148	C₂×C₄×C₁₁	—	2	2	no	—
149	C₂×C₄×C₁₁	—	2	2	no	—
150	C₂×C₄×C₁₁	—	2	2	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	2	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	2	no	—
163	C₂×C₄×C₁₁	—	2	2	no	—
164	C₂×C₄×C₁₁	—	2	2	no	—
165	C₂×C₄×C₁₁	—	2	2	no	—
166	C₂×C₄×C₁₁	—	2	2	no	—
167	C₂×C₄×C₁₁	—	4	1	no	—
168	C₂×C₄×C₁₁	—	4	1	no	—
169	C₂×C₄×C₁₁	—	4	1	no	—
170	C₂×C₄×C₁₁	—	4	1	no	—
171	C₂×C₄×C₁₁	#117	1	2	yes	—
172	C₂×C₄×C₁₁	#117	1	2	yes	—
173	C₂×C₄×C₁₁	#131	1	4	yes	—
174	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
175	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
176	C₂×C₄×C₁₁	H(5,𝔽₂)	1	1	yes	characteristic
177	C₂×C₄×C₁₁	H(5,𝔽₂)	1	1	yes	characteristic
178	C₂×C₄×C₁₁	2₋¹⁺⁴	1	1	yes	characteristic
179	C₂×C₄×C₁₁	2₋¹⁺⁴	1	1	yes	characteristic
180	C₈×C₁₁	—	4	2	no	—
181	C₈×C₁₁	—	4	2	no	—
182	C₈×C₁₁	—	4	2	no	—
183	C₈×C₁₁	—	4	2	no	—
184	C₂×#117	C₂²×C₁₁	1	1	yes	characteristic
185	C₂×C₄⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
186	C₂×C₄⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
187	C₂×C₄⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
188	C₂×C₄⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
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×#97	C₂²×C₁₁	1	2	yes	—
194	C₂×C₄×C₈	C₂²×C₁₁	1	2	yes	—
195	#388	C₄×C₁₁	1	2	yes	—
196	#388	C₄×C₁₁	1	2	yes	—
197	#387	C₄×C₁₁	1	2	yes	—
198	#387	C₄×C₁₁	1	2	yes	—
199	C₄×C₄⋊C₄	C₂²×C₁₁	1	1	yes	characteristic
200	C₄×C₄⋊C₄	C₂²×C₁₁	1	1	yes	characteristic
201	C₄×C₂²⋊C₄	C₂²×C₁₁	1	1	yes	characteristic
202	C₄×C₂²⋊C₄	C₂²×C₁₁	1	1	yes	characteristic
203	#376	C₂²×C₁₁	1	1	yes	characteristic
204	C₄³	C₂²×C₁₁	1	1	yes	characteristic
205	#336	C₂²×C₁₁	1	2	yes	—
206	#336	C₂²×C₁₁	1	2	yes	—
207	#336	C₂²×C₁₁	1	2	yes	—
208	#336	C₂²×C₁₁	1	2	yes	—
209	#336	C₂²×C₁₁	1	2	yes	—
210	#336	C₂²×C₁₁	1	2	yes	—
211	C₂²×C₁₁	—	4	1	no	—
212	C₂²×C₁₁	—	4	1	no	—
213	C₂²×C₁₁	—	4	1	no	—
214	C₂²×C₁₁	—	4	2	no	—
215	C₂²×C₁₁	—	4	2	no	—
216	C₂²×C₁₁	C₂×#117	1	1	yes	characteristic
217	C₂²×C₁₁	#520	1	1	yes	characteristic
218	C₂²×C₁₁	#520	1	1	yes	characteristic
219	C₂²×C₁₁	C₂×#131	1	2	yes	—
220	C₂²×C₁₁	#568	1	2	yes	—
221	C₄×C₁₁	—	2	2	no	—
222	C₄×C₁₁	—	2	2	no	—
223	C₄×C₁₁	—	2	4	no	—
224	C₄×C₁₁	—	4	1	no	—
225	C₄×C₁₁	—	4	1	no	—
226	C₄×C₁₁	—	4	1	no	—
227	C₄×C₁₁	—	4	2	no	—
228	C₄×C₁₁	—	4	2	no	—
229	C₄×C₁₁	—	4	2	no	—
230	C₄×C₁₁	#540	1	1	yes	characteristic
231	C₄×C₁₁	#541	1	1	yes	characteristic
232	C₄×C₁₁	#542	1	1	yes	characteristic
233	C₄×C₁₁	#542	1	1	yes	characteristic
234	C₂³×C₄	C₂³×C₁₁	1	1	yes	characteristic
235	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
236	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
237	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
238	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
239	#117	—	2	2	no	—
240	#117	—	2	2	no	—
241	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
242	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
243	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	2	yes	—
244	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	2	yes	—
245	C₂×C₂²⋊C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
246	C₂×C₂²⋊C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
247	C₂×C₂²⋊C₄	C₂×C₄×C₁₁	1	2	yes	—
248	C₂×C₂²⋊C₄	C₂×C₄×C₁₁	1	2	yes	—
249	C₂×C₄²	C₂×C₄×C₁₁	1	2	yes	—
250	C₂×C₄²	C₂×C₄×C₁₁	1	2	yes	—
251	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
252	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
253	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
254	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
255	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
256	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
257	C₄⋊C₈	—	2	2	no	—
258	C₄⋊C₈	—	2	2	no	—
259	C₄⋊C₈	—	2	2	no	—
260	C₄⋊C₈	—	2	2	no	—
261	C₄⋊C₈	—	4	2	no	—
262	C₄⋊C₈	—	4	2	no	—
263	C₂²⋊C₈	—	4	2	no	—
264	C₂²⋊C₈	—	4	2	no	—
265	#97	—	4	2	no	—
266	C₄×C₈	—	4	2	no	—
267	#95	C₂×C₄×C₁₁	1	2	yes	—
268	#95	C₂×C₄×C₁₁	1	2	yes	—
269	#95	C₂×C₄×C₁₁	1	2	yes	—
270	#95	C₂×C₄×C₁₁	1	2	yes	—
271	#95	C₂×C₄×C₁₁	1	2	yes	—
272	#95	C₂×C₄×C₁₁	1	2	yes	—
273	C₂×C₁₁	—	8	1	no	—
274	C₂×C₁₁	#2314	1	1	yes	characteristic
275	C₂×C₁₁	#2922	1	1	yes	characteristic
276	C₂×C₁₁	#2923	1	1	yes	characteristic
277	C₂×C₁₁	#2992	1	2	yes	—
278	C₂×C₁₁	#2993	1	2	yes	—
279	C₂⁴	C₂²×C₄×C₁₁	1	1	yes	characteristic
280	C₂²×C₄	—	2	1	no	—
281	C₂²×C₄	—	2	1	no	—
282	C₂²×C₄	—	2	1	no	—
283	C₂²×C₄	—	2	1	no	—
284	C₂²×C₄	—	2	1	no	—
285	C₂²×C₄	—	2	1	no	—
286	C₂²×C₄	C₂²×C₄×C₁₁	1	2	yes	—
287	C₂²×C₄	C₂²×C₄×C₁₁	1	2	yes	—
288	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
289	C₂²×C₄	C₂²×C₄×C₁₁	1	2	yes	—
290	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
291	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
292	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
293	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
294	C₂²×C₄	C₂²×C₄×C₁₁	1	2	yes	—
295	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
296	C₂×C₈	—	2	2	no	—
297	C₂×C₈	—	2	2	no	—
298	C₂×C₈	—	2	2	no	—
299	C₂×C₈	—	2	2	no	—
300	C₂×C₈	—	2	2	no	—
301	C₂×C₈	—	2	2	no	—
302	C₂×C₈	—	2	2	no	—
303	C₂×C₈	—	2	2	no	—
304	C₂×C₈	—	2	2	no	—
305	C₂×C₈	—	2	2	no	—
306	C₂×C₈	—	2	2	no	—
307	C₂×C₈	—	2	2	no	—
308	C₄⋊C₄	—	2	2	no	—
309	C₄⋊C₄	—	2	2	no	—
310	C₄⋊C₄	—	2	4	no	—
311	C₄⋊C₄	—	4	2	no	—
312	C₂²⋊C₄	—	2	2	no	—
313	C₂²⋊C₄	—	2	2	no	—
314	C₂²⋊C₄	—	2	4	no	—
315	C₂²⋊C₄	—	4	2	no	—
316	C₄²	—	2	4	no	—
317	C₄²	—	2	1	no	—
318	C₄²	—	2	1	no	—
319	C₄²	—	2	1	no	—
320	C₄²	—	2	1	no	—
321	C₄²	—	2	1	no	—
322	C₄²	—	2	1	no	—
323	C₄²	—	2	1	no	—
324	C₄²	—	2	1	no	—
325	C₄²	—	2	1	no	—
326	C₄²	—	2	1	no	—
327	C₄²	—	4	2	no	—
328	C₄²	C₁₁×#41	1	2	yes	—
329	C₄²	C₁₁×#41	1	2	yes	—
330	C₁₁	#21925	1	1	yes	characteristic, direct product factor, Sylow
331	C₂³	—	2	1	no	—
332	C₂³	—	2	1	no	—
333	C₂³	—	2	1	no	—
334	C₂³	—	2	2	no	—
335	C₂³	—	2	2	no	—
336	C₂³	C₂³×C₄×C₁₁	1	1	yes	characteristic
337	C₂×C₄	—	2	2	no	—
338	C₂×C₄	—	2	2	no	—
339	C₂×C₄	—	2	2	no	—
340	C₂×C₄	—	2	2	no	—
341	C₂×C₄	—	2	1	no	—
342	C₂×C₄	—	2	1	no	—
343	C₂×C₄	—	2	1	no	—
344	C₂×C₄	—	2	2	no	—
345	C₂×C₄	—	2	2	no	—
346	C₂×C₄	—	2	2	no	—
347	C₂×C₄	—	2	1	no	—
348	C₂×C₄	—	2	1	no	—
349	C₂×C₄	—	2	2	no	—
350	C₂×C₄	—	2	2	no	—
351	C₂×C₄	—	2	2	no	—
352	C₂×C₄	—	2	2	no	—
353	C₂×C₄	—	2	2	no	—
354	C₂×C₄	—	2	2	no	—
355	C₂×C₄	—	2	2	no	—
356	C₂×C₄	—	2	2	no	—
357	C₂×C₄	—	4	1	no	—
358	C₂×C₄	—	4	1	no	—
359	C₂×C₄	—	4	1	no	—
360	C₂×C₄	—	4	1	no	—
361	C₂×C₄	C₁₁×#117	1	2	yes	—
362	C₂×C₄	C₁₁×#117	1	2	yes	—
363	C₂×C₄	C₁₁×#131	1	4	yes	—
364	C₂×C₄	C₂×C₁₁×#41	1	1	yes	characteristic
365	C₂×C₄	C₂×C₁₁×#41	1	1	yes	characteristic
366	C₂×C₄	C₁₁×H(5,𝔽₂)	1	1	yes	characteristic
367	C₂×C₄	C₁₁×H(5,𝔽₂)	1	1	yes	characteristic
368	C₂×C₄	C₁₁×2₋¹⁺⁴	1	1	yes	characteristic
369	C₂×C₄	C₁₁×2₋¹⁺⁴	1	1	yes	characteristic
370	C₈	—	4	2	no	—
371	C₈	—	4	2	no	—
372	C₈	—	4	2	no	—
373	C₈	—	4	2	no	—
374	C₂²	—	4	1	no	—
375	C₂²	—	4	1	no	—
376	C₂²	—	4	2	no	—
377	C₂²	—	4	2	no	—
378	C₂²	—	4	1	no	—
379	C₂²	C₂×C₁₁×#117	1	1	yes	characteristic
380	C₂²	C₁₁×#520	1	1	yes	characteristic
381	C₂²	C₁₁×#520	1	1	yes	characteristic
382	C₂²	C₂×C₁₁×#131	1	2	yes	—
383	C₂²	C₁₁×#568	1	2	yes	—
384	C₄	—	2	2	no	—
385	C₄	—	2	2	no	—
386	C₄	—	2	4	no	—
387	C₄	—	4	1	no	—
388	C₄	—	4	1	no	—
389	C₄	—	4	2	no	—
390	C₄	—	4	2	no	—
391	C₄	—	4	2	no	—
392	C₄	—	4	1	no	—
393	C₄	C₁₁×#540	1	1	yes	characteristic
394	C₄	C₁₁×#541	1	1	yes	characteristic
395	C₄	C₁₁×#542	1	1	yes	characteristic
396	C₄	C₁₁×#542	1	1	yes	characteristic
397	C₂	—	8	1	no	—
398	C₂	C₁₁×#2314	1	1	yes	characteristic
399	C₂	C₁₁×#2922	1	1	yes	characteristic
400	C₂	C₁₁×#2923	1	1	yes	characteristic
401	C₂	C₁₁×#2992	1	2	yes	—
402	C₂	C₁₁×#2993	1	2	yes	—

	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	C₂⁴×C₁₁	C₂²×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
4. C₁₁×#1917	C₂	semidirect
5. C₁₁×#1916	C₂	semidirect
6. C₁₁×#1843	C₂	semidirect
7. C₁₁×#1832	C₂	semidirect
10. C₁₁×#1767	C₂	semidirect
11. C₄×C₁₁×C₄⋊C₈	C₂	semidirect
78. #21925	C₁₁	direct (N × H)
133. #1917	C₂×C₁₁	semidirect
134. #1916	C₂×C₁₁	semidirect
135. #1843	C₂×C₁₁	semidirect
136. #1832	C₂×C₁₁	semidirect
139. #1767	C₂×C₁₁	semidirect
140. C₄×C₄⋊C₈	C₂×C₁₁	semidirect
330. C₁₁	#21925	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×#2298	2
C₁₁×#1924	2
C₁₁×#1923	2
C₁₁×#1917	2
C₁₁×#1916	2
C₁₁×#1843	2
C₁₁×#1832	2
C₁₁×#1798	2
C₁₁×#1767	2
C₄×C₁₁×C₄⋊C₈	2
#21925	11

Subgroups — C11×#21925 #14599118

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#21925 #14599118