Subgroups — C₁₁×#22102 #14599295

Order 2816.

814 conjugacy classes of subgroups.

The subgroup lattice has 484 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₁×#446	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₁×#431	C₂	1	1	yes	maximal, characteristic
3	C₄×C₁₁×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic
4	C₁₁×#1984	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₁×#1939	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₁×#1939	C₂	1	2	yes	maximal, complemented
7	C₁₁×#1924	C₂	1	2	yes	maximal
8	C₁₁×#1923	C₂	1	2	yes	maximal
9	C₁₁×#1917	C₂	1	2	yes	maximal, complemented
10	C₁₁×#1797	C₂	1	1	yes	maximal, characteristic
11	C₈×C₁₁×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₁×C₂²⋊Q₈	C₄	1	1	yes	characteristic
13	C₂×C₄×Q₈×C₁₁	C₂²	1	1	yes	characteristic
14	C₂²×C₄²×C₁₁	C₂²	1	1	yes	characteristic
15	C₁₁×#446	—	2	4	no	—
16	C₁₁×#431	—	2	4	no	—
17	C₂×C₁₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
18	C₂×C₁₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
19	C₂×C₁₁×C₄⋊C₈	C₂²	1	2	yes	—
20	C₂×C₁₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
21	C₂×C₁₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
22	C₂×C₁₁×C₄⋊C₈	C₂²	1	2	yes	—
23	C₂×C₁₁×C₂²⋊C₈	C₂²	1	1	yes	characteristic
24	C₂×C₁₁×C₂²⋊C₈	C₂²	1	1	yes	characteristic
25	C₂×C₁₁×C₂²⋊C₈	C₂²	1	2	yes	—
26	C₂×C₁₁×#97	C₂²	1	2	yes	—
27	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
28	C₂×C₄×C₈×C₁₁	C₂²	1	2	yes	—
29	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
30	C₁₁×#391	C₄	1	1	yes	characteristic
31	C₁₁×#389	C₄	1	1	yes	characteristic
32	C₁₁×#387	C₄	1	2	yes	—
33	C₁₁×#385	C₄	1	2	yes	—
34	C₁₁×#380	C₄	1	1	yes	characteristic
35	C₄×C₁₁×C₄⋊C₄	C₂²	1	2	yes	—
36	C₄×C₁₁×C₄⋊C₄	C₂²	1	1	yes	characteristic
37	C₄×C₁₁×C₂²⋊C₄	C₂²	1	2	yes	—
38	C₁₁×#336	C₂²	1	2	yes	—
39	C₁₁×#336	C₂²	1	2	yes	—
40	C₁₁×#336	C₂²	1	2	yes	—
41	C₁₁×#336	C₂²	1	2	yes	—
42	C₁₁×#336	C₂²	1	2	yes	—
43	C₂²×Q₈×C₁₁	C₂×C₄	1	1	yes	characteristic
44	C₂³×C₄×C₁₁	C₂×C₄	1	1	yes	characteristic
45	C₂³×C₄×C₁₁	C₂×C₄	1	1	yes	characteristic
46	C₂³×C₄×C₁₁	C₂³	1	1	yes	characteristic
47	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
48	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
49	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
50	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
51	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
52	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
53	C₁₁×C₂²⋊Q₈	—	2	4	no	—
54	C₄×Q₈×C₁₁	—	2	2	no	—
55	C₄×Q₈×C₁₁	—	2	2	no	—
56	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
57	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	2	yes	—
58	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	2	yes	—
59	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
60	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	2	yes	—
61	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
62	C₂×C₁₁×C₂²⋊C₄	C₂×C₄	1	2	yes	—
63	C₂×C₁₁×C₂²⋊C₄	C₂×C₄	1	2	yes	—
64	C₂×C₄²×C₁₁	—	2	2	no	—
65	C₂×C₄²×C₁₁	—	2	2	no	—
66	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
67	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
68	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
69	C₂×C₄²×C₁₁	C₂³	1	2	yes	—
70	C₂×C₄²×C₁₁	C₂³	1	2	yes	—
71	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
72	C₁₁×C₄⋊C₈	—	2	2	no	—
73	C₁₁×C₄⋊C₈	—	2	2	no	—
74	C₁₁×C₄⋊C₈	—	2	4	no	—
75	C₁₁×C₄⋊C₈	—	2	2	no	—
76	C₁₁×C₄⋊C₈	—	2	2	no	—
77	C₁₁×C₄⋊C₈	—	4	2	no	—
78	C₁₁×C₂²⋊C₈	—	2	2	no	—
79	C₁₁×C₂²⋊C₈	—	2	2	no	—
80	C₁₁×C₂²⋊C₈	—	4	2	no	—
81	C₁₁×#97	—	2	4	no	—
82	C₄×C₈×C₁₁	—	2	2	no	—
83	C₄×C₈×C₁₁	—	4	2	no	—
84	C₄×C₈×C₁₁	D₄	1	4	yes	—
85	C₁₁×#95	C₂×C₄	1	2	yes	—
86	C₁₁×#95	C₂×C₄	1	2	yes	—
87	C₁₁×#95	C₂×C₄	1	2	yes	—
88	C₁₁×#95	C₂×C₄	1	2	yes	—
89	C₁₁×#95	C₂×C₄	1	2	yes	—
90	#22102	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
91	C₂⁴×C₁₁	C₂²×C₄	1	1	yes	characteristic
92	C₂×Q₈×C₁₁	—	2	2	no	—
93	C₂×Q₈×C₁₁	—	2	2	no	—
94	C₂×Q₈×C₁₁	—	2	2	no	—
95	C₂²×C₄×C₁₁	—	2	2	no	—
96	C₂²×C₄×C₁₁	—	2	2	no	—
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	—	2	2	no	—
101	C₂²×C₄×C₁₁	—	2	1	no	—
102	C₂²×C₄×C₁₁	—	2	1	no	—
103	C₂²×C₄×C₁₁	—	2	1	no	—
104	C₂²×C₄×C₁₁	—	2	1	no	—
105	C₂²×C₄×C₁₁	—	2	1	no	—
106	C₂²×C₄×C₁₁	—	2	1	no	—
107	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
108	C₂²×C₄×C₁₁	C₂²×C₄	1	2	yes	—
109	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
110	C₂²×C₄×C₁₁	C₂²×C₄	1	2	yes	—
111	C₂²×C₄×C₁₁	C₂²×C₄	1	2	yes	—
112	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
113	C₂²×C₄×C₁₁	C₂²×C₄	1	2	yes	—
114	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
115	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
116	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
117	C₂×C₈×C₁₁	—	2	1	no	—
118	C₂×C₈×C₁₁	—	2	1	no	—
119	C₂×C₈×C₁₁	—	2	2	no	—
120	C₂×C₈×C₁₁	—	2	2	no	—
121	C₂×C₈×C₁₁	—	2	1	no	—
122	C₂×C₈×C₁₁	—	2	2	no	—
123	C₂×C₈×C₁₁	—	2	2	no	—
124	C₂×C₈×C₁₁	—	2	1	no	—
125	C₂×C₈×C₁₁	—	2	1	no	—
126	C₂×C₈×C₁₁	—	2	1	no	—
127	C₂×C₈×C₁₁	—	2	1	no	—
128	C₂×C₈×C₁₁	—	2	1	no	—
129	C₂×C₈×C₁₁	—	2	1	no	—
130	C₂×C₈×C₁₁	—	2	2	no	—
131	C₂×C₈×C₁₁	—	2	1	no	—
132	C₂×C₈×C₁₁	—	2	2	no	—
133	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
134	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
135	C₁₁×C₄⋊C₄	—	2	2	no	—
136	C₁₁×C₄⋊C₄	—	2	4	no	—
137	C₁₁×C₄⋊C₄	—	2	4	no	—
138	C₁₁×C₄⋊C₄	—	2	4	no	—
139	C₁₁×C₄⋊C₄	—	2	2	no	—
140	C₁₁×C₄⋊C₄	M₁₆	1	4	yes	—
141	C₁₁×C₂²⋊C₄	—	2	4	no	—
142	C₁₁×C₂²⋊C₄	—	2	4	no	—
143	C₄²×C₁₁	—	2	2	no	—
144	C₄²×C₁₁	—	2	2	no	—
145	C₄²×C₁₁	—	2	2	no	—
146	C₄²×C₁₁	—	2	1	no	—
147	C₄²×C₁₁	—	2	1	no	—
148	C₄²×C₁₁	—	2	2	no	—
149	C₄²×C₁₁	—	2	2	no	—
150	C₄²×C₁₁	—	2	2	no	—
151	C₄²×C₁₁	C₂×D₄	1	2	yes	—
152	C₄²×C₁₁	#41	1	2	yes	—
153	C₂×#446	C₂×C₁₁	1	1	yes	characteristic, complemented
154	C₂×#431	C₂×C₁₁	1	1	yes	characteristic
155	C₄×C₂²⋊Q₈	C₂×C₁₁	1	1	yes	characteristic
156	#1984	C₂×C₁₁	1	1	yes	characteristic, complemented
157	#1939	C₂×C₁₁	1	2	yes	complemented
158	#1939	C₂×C₁₁	1	1	yes	characteristic, complemented
159	#1924	C₂×C₁₁	1	2	yes	—
160	#1923	C₂×C₁₁	1	2	yes	—
161	#1917	C₂×C₁₁	1	2	yes	complemented
162	#1797	C₂×C₁₁	1	1	yes	characteristic
163	C₈×C₄⋊C₄	C₂×C₁₁	1	1	yes	characteristic, complemented
164	C₂³×C₁₁	—	2	1	no	—
165	C₂³×C₁₁	—	2	1	no	—
166	C₂³×C₁₁	—	2	1	no	—
167	C₂³×C₁₁	—	2	1	no	—
168	C₂³×C₁₁	—	2	1	no	—
169	C₂³×C₁₁	—	2	1	no	—
170	C₂³×C₁₁	#131	1	2	yes	—
171	C₂³×C₁₁	C₂³×C₄	1	1	yes	characteristic
172	Q₈×C₁₁	—	4	4	no	—
173	C₂×C₄×C₁₁	—	2	8	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	—	2	1	no	—
178	C₂×C₄×C₁₁	—	2	1	no	—
179	C₂×C₄×C₁₁	—	2	1	no	—
180	C₂×C₄×C₁₁	—	2	1	no	—
181	C₂×C₄×C₁₁	—	2	1	no	—
182	C₂×C₄×C₁₁	—	2	2	no	—
183	C₂×C₄×C₁₁	—	2	2	no	—
184	C₂×C₄×C₁₁	—	2	1	no	—
185	C₂×C₄×C₁₁	—	2	2	no	—
186	C₂×C₄×C₁₁	—	2	1	no	—
187	C₂×C₄×C₁₁	—	2	2	no	—
188	C₂×C₄×C₁₁	—	2	1	no	—
189	C₂×C₄×C₁₁	—	2	2	no	—
190	C₂×C₄×C₁₁	—	2	2	no	—
191	C₂×C₄×C₁₁	—	2	2	no	—
192	C₂×C₄×C₁₁	—	2	2	no	—
193	C₂×C₄×C₁₁	—	2	1	no	—
194	C₂×C₄×C₁₁	—	2	2	no	—
195	C₂×C₄×C₁₁	—	4	1	no	—
196	C₂×C₄×C₁₁	—	4	1	no	—
197	C₂×C₄×C₁₁	—	4	1	no	—
198	C₂×C₄×C₁₁	—	4	1	no	—
199	C₂×C₄×C₁₁	—	4	4	no	—
200	C₂×C₄×C₁₁	C₄×D₄	1	2	yes	—
201	C₂×C₄×C₁₁	C₄×D₄	1	2	yes	—
202	C₂×C₄×C₁₁	C₂×M₁₆	1	4	yes	—
203	C₂×C₄×C₁₁	C₂×M₁₆	1	2	yes	—
204	C₂×C₄×C₁₁	#131	1	2	yes	—
205	C₂×C₄×C₁₁	#131	1	2	yes	—
206	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
207	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
208	C₂×C₄×C₁₁	H(5,𝔽₂)	1	1	yes	characteristic
209	C₂×C₄×C₁₁	2₋¹⁺⁴	1	1	yes	characteristic
210	C₂×C₄×C₁₁	2₋¹⁺⁴	1	1	yes	characteristic
211	C₂×C₄×C₁₁	2₋¹⁺⁴	1	1	yes	characteristic
212	C₈×C₁₁	—	2	2	no	—
213	C₈×C₁₁	—	2	2	no	—
214	C₈×C₁₁	—	4	1	no	—
215	C₈×C₁₁	—	4	1	no	—
216	C₈×C₁₁	—	4	2	no	—
217	C₈×C₁₁	—	4	2	no	—
218	C₂×C₂²⋊Q₈	C₄×C₁₁	1	1	yes	characteristic
219	C₂×C₄×Q₈	C₂²×C₁₁	1	1	yes	characteristic
220	C₂²×C₄²	C₂²×C₁₁	1	1	yes	characteristic
221	#446	—	2	4	no	—
222	#431	—	2	4	no	—
223	C₂×C₄⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
224	C₂×C₄⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
225	C₂×C₄⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
226	C₂×C₄⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
227	C₂×C₄⋊C₈	C₂²×C₁₁	1	2	yes	—
228	C₂×C₄⋊C₈	C₂²×C₁₁	1	2	yes	—
229	C₂×C₂²⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
230	C₂×C₂²⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
231	C₂×C₂²⋊C₈	C₂²×C₁₁	1	2	yes	—
232	C₂×#97	C₂²×C₁₁	1	2	yes	—
233	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
234	C₂×C₄×C₈	C₂²×C₁₁	1	2	yes	—
235	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
236	#391	C₄×C₁₁	1	1	yes	characteristic
237	#389	C₄×C₁₁	1	1	yes	characteristic
238	#387	C₄×C₁₁	1	2	yes	—
239	#385	C₄×C₁₁	1	2	yes	—
240	#380	C₄×C₁₁	1	1	yes	characteristic
241	C₄×C₄⋊C₄	C₂²×C₁₁	1	2	yes	—
242	C₄×C₄⋊C₄	C₂²×C₁₁	1	1	yes	characteristic
243	C₄×C₂²⋊C₄	C₂²×C₁₁	1	2	yes	—
244	#336	C₂²×C₁₁	1	2	yes	—
245	#336	C₂²×C₁₁	1	2	yes	—
246	#336	C₂²×C₁₁	1	2	yes	—
247	#336	C₂²×C₁₁	1	2	yes	—
248	#336	C₂²×C₁₁	1	2	yes	—
249	C₂²×C₁₁	—	2	2	no	—
250	C₂²×C₁₁	—	2	2	no	—
251	C₂²×C₁₁	—	2	2	no	—
252	C₂²×C₁₁	—	4	1	no	—
253	C₂²×C₁₁	—	4	1	no	—
254	C₂²×C₁₁	—	4	1	no	—
255	C₂²×C₁₁	—	4	1	no	—
256	C₂²×C₁₁	C₂×C₄×D₄	1	1	yes	characteristic
257	C₂²×C₁₁	#519	1	1	yes	characteristic
258	C₂²×C₁₁	#520	1	1	yes	characteristic
259	C₂²×C₁₁	C₂²×M₁₆	1	1	yes	characteristic
260	C₂²×C₁₁	C₂×#131	1	1	yes	characteristic
261	C₂²×C₁₁	C₂×#131	1	1	yes	characteristic
262	C₂²×C₁₁	C₂×#131	1	1	yes	characteristic
263	C₄×C₁₁	—	2	2	no	—
264	C₄×C₁₁	—	2	2	no	—
265	C₄×C₁₁	—	2	4	no	—
266	C₄×C₁₁	—	4	1	no	—
267	C₄×C₁₁	—	4	1	no	—
268	C₄×C₁₁	—	4	2	no	—
269	C₄×C₁₁	—	4	2	no	—
270	C₄×C₁₁	—	4	2	no	—
271	C₄×C₁₁	#436	1	4	yes	—
272	C₄×C₁₁	#536	1	1	yes	characteristic
273	C₄×C₁₁	#537	1	1	yes	characteristic
274	C₄×C₁₁	#541	1	1	yes	characteristic
275	C₄×C₁₁	#542	1	1	yes	characteristic
276	C₂²×Q₈	C₂×C₄×C₁₁	1	1	yes	characteristic
277	C₂³×C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
278	C₂³×C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
279	C₂³×C₄	C₂³×C₁₁	1	1	yes	characteristic
280	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
281	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
282	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
283	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
284	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
285	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
286	C₂²⋊Q₈	—	2	4	no	—
287	C₄×Q₈	—	2	2	no	—
288	C₄×Q₈	—	2	2	no	—
289	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
290	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	2	yes	—
291	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	2	yes	—
292	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
293	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	2	yes	—
294	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
295	C₂×C₂²⋊C₄	C₂×C₄×C₁₁	1	2	yes	—
296	C₂×C₂²⋊C₄	C₂×C₄×C₁₁	1	2	yes	—
297	C₂×C₄²	—	2	2	no	—
298	C₂×C₄²	—	2	2	no	—
299	C₂×C₄²	C₂×C₄×C₁₁	1	1	yes	characteristic
300	C₂×C₄²	C₂×C₄×C₁₁	1	1	yes	characteristic
301	C₂×C₄²	C₂³×C₁₁	1	2	yes	—
302	C₂×C₄²	C₂³×C₁₁	1	2	yes	—
303	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
304	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
305	C₄⋊C₈	—	2	2	no	—
306	C₄⋊C₈	—	2	2	no	—
307	C₄⋊C₈	—	2	4	no	—
308	C₄⋊C₈	—	2	2	no	—
309	C₄⋊C₈	—	2	2	no	—
310	C₄⋊C₈	—	4	2	no	—
311	C₂²⋊C₈	—	2	2	no	—
312	C₂²⋊C₈	—	2	2	no	—
313	C₂²⋊C₈	—	4	2	no	—
314	#97	—	2	4	no	—
315	C₄×C₈	—	2	2	no	—
316	C₄×C₈	—	4	2	no	—
317	C₄×C₈	D₄×C₁₁	1	4	yes	—
318	#95	C₂×C₄×C₁₁	1	2	yes	—
319	#95	C₂×C₄×C₁₁	1	2	yes	—
320	#95	C₂×C₄×C₁₁	1	2	yes	—
321	#95	C₂×C₄×C₁₁	1	2	yes	—
322	#95	C₂×C₄×C₁₁	1	2	yes	—
323	C₂×C₁₁	—	4	2	no	—
324	C₂×C₁₁	#2323	1	1	yes	characteristic
325	C₂×C₁₁	C₂×#436	1	1	yes	characteristic
326	C₂×C₁₁	#2929	1	1	yes	characteristic
327	C₂×C₁₁	#2984	1	1	yes	characteristic
328	C₂×C₁₁	#2986	1	1	yes	characteristic
329	C₂×C₁₁	#2990	1	1	yes	characteristic
330	C₂×C₁₁	#2994	1	1	yes	characteristic
331	C₂⁴	C₂²×C₄×C₁₁	1	1	yes	characteristic
332	C₂×Q₈	—	2	2	no	—
333	C₂×Q₈	—	2	2	no	—
334	C₂×Q₈	—	2	2	no	—
335	C₂²×C₄	—	2	2	no	—
336	C₂²×C₄	—	2	2	no	—
337	C₂²×C₄	—	2	2	no	—
338	C₂²×C₄	—	2	2	no	—
339	C₂²×C₄	—	2	2	no	—
340	C₂²×C₄	—	2	2	no	—
341	C₂²×C₄	—	2	1	no	—
342	C₂²×C₄	—	2	1	no	—
343	C₂²×C₄	—	2	1	no	—
344	C₂²×C₄	—	2	1	no	—
345	C₂²×C₄	—	2	1	no	—
346	C₂²×C₄	—	2	1	no	—
347	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
348	C₂²×C₄	C₂²×C₄×C₁₁	1	2	yes	—
349	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
350	C₂²×C₄	C₂²×C₄×C₁₁	1	2	yes	—
351	C₂²×C₄	C₂²×C₄×C₁₁	1	2	yes	—
352	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
353	C₂²×C₄	C₂²×C₄×C₁₁	1	2	yes	—
354	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
355	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
356	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
357	C₂×C₈	—	2	1	no	—
358	C₂×C₈	—	2	1	no	—
359	C₂×C₈	—	2	1	no	—
360	C₂×C₈	—	2	1	no	—
361	C₂×C₈	—	2	1	no	—
362	C₂×C₈	—	2	1	no	—
363	C₂×C₈	—	2	2	no	—
364	C₂×C₈	—	2	2	no	—
365	C₂×C₈	—	2	2	no	—
366	C₂×C₈	—	2	2	no	—
367	C₂×C₈	—	2	1	no	—
368	C₂×C₈	—	2	1	no	—
369	C₂×C₈	—	2	1	no	—
370	C₂×C₈	—	2	1	no	—
371	C₂×C₈	—	2	2	no	—
372	C₂×C₈	—	2	2	no	—
373	C₂×C₈	C₂×D₄×C₁₁	1	2	yes	—
374	C₂×C₈	C₂×D₄×C₁₁	1	2	yes	—
375	C₄⋊C₄	—	2	2	no	—
376	C₄⋊C₄	—	2	4	no	—
377	C₄⋊C₄	—	2	4	no	—
378	C₄⋊C₄	—	2	4	no	—
379	C₄⋊C₄	—	2	2	no	—
380	C₄⋊C₄	C₁₁×M₁₆	1	4	yes	—
381	C₂²⋊C₄	—	2	4	no	—
382	C₂²⋊C₄	—	2	4	no	—
383	C₄²	—	2	2	no	—
384	C₄²	—	2	2	no	—
385	C₄²	—	2	2	no	—
386	C₄²	—	2	1	no	—
387	C₄²	—	2	1	no	—
388	C₄²	—	2	2	no	—
389	C₄²	—	2	2	no	—
390	C₄²	—	2	2	no	—
391	C₄²	C₂×D₄×C₁₁	1	2	yes	—
392	C₄²	C₁₁×#41	1	2	yes	—
393	C₁₁	#22102	1	1	yes	characteristic, direct product factor, Sylow
394	C₂³	—	2	1	no	—
395	C₂³	—	2	1	no	—
396	C₂³	—	2	1	no	—
397	C₂³	—	2	1	no	—
398	C₂³	—	2	1	no	—
399	C₂³	—	2	1	no	—
400	C₂³	C₁₁×#131	1	2	yes	—
401	C₂³	C₂³×C₄×C₁₁	1	1	yes	characteristic
402	Q₈	—	4	4	no	—
403	C₂×C₄	—	2	8	no	—
404	C₂×C₄	—	2	1	no	—
405	C₂×C₄	—	2	2	no	—
406	C₂×C₄	—	2	2	no	—
407	C₂×C₄	—	2	1	no	—
408	C₂×C₄	—	2	1	no	—
409	C₂×C₄	—	2	1	no	—
410	C₂×C₄	—	2	1	no	—
411	C₂×C₄	—	2	1	no	—
412	C₂×C₄	—	2	2	no	—
413	C₂×C₄	—	2	2	no	—
414	C₂×C₄	—	2	1	no	—
415	C₂×C₄	—	2	2	no	—
416	C₂×C₄	—	2	1	no	—
417	C₂×C₄	—	2	2	no	—
418	C₂×C₄	—	2	1	no	—
419	C₂×C₄	—	2	2	no	—
420	C₂×C₄	—	2	2	no	—
421	C₂×C₄	—	2	2	no	—
422	C₂×C₄	—	2	2	no	—
423	C₂×C₄	—	2	1	no	—
424	C₂×C₄	—	2	2	no	—
425	C₂×C₄	—	4	1	no	—
426	C₂×C₄	—	4	1	no	—
427	C₂×C₄	—	4	1	no	—
428	C₂×C₄	—	4	1	no	—
429	C₂×C₄	—	4	4	no	—
430	C₂×C₄	C₄×D₄×C₁₁	1	2	yes	—
431	C₂×C₄	C₄×D₄×C₁₁	1	2	yes	—
432	C₂×C₄	C₂×C₁₁×M₁₆	1	4	yes	—
433	C₂×C₄	C₂×C₁₁×M₁₆	1	2	yes	—
434	C₂×C₄	C₁₁×#131	1	2	yes	—
435	C₂×C₄	C₁₁×#131	1	2	yes	—
436	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
437	C₂×C₄	C₂×C₁₁×#41	1	1	yes	characteristic
438	C₂×C₄	C₁₁×H(5,𝔽₂)	1	1	yes	characteristic
439	C₂×C₄	C₁₁×2₋¹⁺⁴	1	1	yes	characteristic
440	C₂×C₄	C₁₁×2₋¹⁺⁴	1	1	yes	characteristic
441	C₂×C₄	C₁₁×2₋¹⁺⁴	1	1	yes	characteristic
442	C₈	—	2	2	no	—
443	C₈	—	2	2	no	—
444	C₈	—	4	1	no	—
445	C₈	—	4	1	no	—
446	C₈	—	4	2	no	—
447	C₈	—	4	2	no	—
448	C₂²	—	2	2	no	—
449	C₂²	—	2	2	no	—
450	C₂²	—	2	2	no	—
451	C₂²	—	4	1	no	—
452	C₂²	—	4	1	no	—
453	C₂²	—	4	1	no	—
454	C₂²	—	4	1	no	—
455	C₂²	C₂×C₄×D₄×C₁₁	1	1	yes	characteristic
456	C₂²	C₁₁×#519	1	1	yes	characteristic
457	C₂²	C₁₁×#520	1	1	yes	characteristic
458	C₂²	C₂²×C₁₁×M₁₆	1	1	yes	characteristic
459	C₂²	C₂×C₁₁×#131	1	1	yes	characteristic
460	C₂²	C₂×C₁₁×#131	1	1	yes	characteristic
461	C₂²	C₂×C₁₁×#131	1	1	yes	characteristic
462	C₄	—	2	2	no	—
463	C₄	—	2	2	no	—
464	C₄	—	2	4	no	—
465	C₄	—	4	1	no	—
466	C₄	—	4	2	no	—
467	C₄	—	4	2	no	—
468	C₄	—	4	2	no	—
469	C₄	—	4	1	no	—
470	C₄	C₁₁×#436	1	4	yes	—
471	C₄	C₁₁×#536	1	1	yes	characteristic
472	C₄	C₁₁×#537	1	1	yes	characteristic
473	C₄	C₁₁×#541	1	1	yes	characteristic
474	C₄	C₁₁×#542	1	1	yes	characteristic
475	C₂	—	4	2	no	—
476	C₂	C₁₁×#2323	1	1	yes	characteristic
477	C₂	C₂×C₁₁×#436	1	1	yes	characteristic
478	C₂	C₁₁×#2929	1	1	yes	characteristic
479	C₂	C₁₁×#2984	1	1	yes	characteristic
480	C₂	C₁₁×#2986	1	1	yes	characteristic
481	C₂	C₁₁×#2990	1	1	yes	characteristic
482	C₂	C₁₁×#2994	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	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
1. C₂×C₁₁×#446	C₂	semidirect
4. C₁₁×#1984	C₂	semidirect
5. C₁₁×#1939	C₂	semidirect
6. C₁₁×#1939	C₂	semidirect
9. C₁₁×#1917	C₂	semidirect
11. C₈×C₁₁×C₄⋊C₄	C₂	semidirect
90. #22102	C₁₁	direct (N × H)
153. C₂×#446	C₂×C₁₁	semidirect
156. #1984	C₂×C₁₁	semidirect
157. #1939	C₂×C₁₁	semidirect
158. #1939	C₂×C₁₁	semidirect
161. #1917	C₂×C₁₁	semidirect
163. C₈×C₄⋊C₄	C₂×C₁₁	semidirect
393. C₁₁	#22102	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×#446	2
C₂×C₁₁×#431	2
C₄×C₁₁×C₂²⋊Q₈	2
C₁₁×#1984	2
C₁₁×#1939	2
C₁₁×#1924	2
C₁₁×#1923	2
C₁₁×#1917	2
C₁₁×#1797	2
C₈×C₁₁×C₄⋊C₄	2
#22102	11

Subgroups — C11×#22102 #14599295

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#22102 #14599295