Subgroups — C₁₁×#22134 #14599327

Order 2816.

916 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₈×D₄×C₁₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₁×#433	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₁×#2392	C₂	1	1	yes	maximal, characteristic
4	C₁₁×#1955	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₁×#1954	C₂	1	2	yes	maximal, complemented
6	C₁₁×#1940	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₁×#1923	C₂	1	2	yes	maximal, complemented
8	C₁₁×#1869	C₂	1	2	yes	maximal, complemented
9	C₁₁×#1850	C₂	1	2	yes	maximal, complemented
10	C₁₁×#1798	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈×C₁₁×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂³×C₈×C₁₁	C₂²	1	2	yes	—
13	C₂×C₄×D₄×C₁₁	C₂²	1	1	yes	characteristic
14	C₂×C₄×D₄×C₁₁	C₂²	1	2	yes	—
15	C₂×C₁₁×#117	C₂²	1	1	yes	characteristic
16	C₈×D₄×C₁₁	—	2	4	no	—
17	C₁₁×#433	—	2	4	no	—
18	C₂×C₁₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
19	C₂×C₁₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
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×C₂²⋊C₈	C₂²	1	2	yes	—
27	C₂×C₁₁×C₂²⋊C₈	C₂²	1	2	yes	—
28	C₂×C₁₁×C₂²⋊C₈	C₂²	1	2	yes	—
29	C₂×C₁₁×#97	C₂²	1	1	yes	characteristic
30	C₂×C₄×C₈×C₁₁	C₂²	1	2	yes	—
31	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
32	C₁₁×#398	C₄	1	1	yes	characteristic
33	C₁₁×#397	C₄	1	1	yes	characteristic
34	C₁₁×#396	C₄	1	2	yes	—
35	C₁₁×#394	C₄	1	2	yes	—
36	C₁₁×#394	C₄	1	1	yes	characteristic
37	C₁₁×#392	C₄	1	1	yes	characteristic
38	C₄×C₁₁×C₄⋊C₄	C₂²	1	1	yes	characteristic
39	C₄×C₁₁×C₂²⋊C₄	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×D₄×C₁₁	C₂×C₄	1	1	yes	characteristic
44	C₂²×D₄×C₁₁	C₂×C₄	1	2	yes	—
45	C₂³×C₄×C₁₁	C₂³	1	1	yes	characteristic
46	C₂³×C₄×C₁₁	C₂³	1	2	yes	—
47	C₂²×C₈×C₁₁	—	2	4	no	—
48	C₂²×C₈×C₁₁	—	4	2	no	—
49	C₂²×C₈×C₁₁	—	4	2	no	—
50	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
51	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
52	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
53	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
54	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
55	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
56	C₄×D₄×C₁₁	—	2	2	no	—
57	C₄×D₄×C₁₁	—	2	2	no	—
58	C₄×D₄×C₁₁	—	4	2	no	—
59	C₄×D₄×C₁₁	—	4	2	no	—
60	C₁₁×#117	—	2	2	no	—
61	C₁₁×#117	—	2	2	no	—
62	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
63	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
64	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
65	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	2	yes	—
66	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	2	yes	—
67	C₂×C₁₁×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
68	C₂×C₁₁×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
69	C₂×C₁₁×C₂²⋊C₄	C₂×C₄	1	2	yes	—
70	C₂×C₁₁×C₂²⋊C₄	C₂×C₄	1	2	yes	—
71	C₂×C₁₁×C₂²⋊C₄	C₂×C₄	1	2	yes	—
72	C₂×C₁₁×C₂²⋊C₄	C₂×C₄	1	2	yes	—
73	C₂×C₁₁×C₂²⋊C₄	C₂×C₄	1	2	yes	—
74	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
75	C₂×C₄²×C₁₁	C₂³	1	2	yes	—
76	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
77	C₁₁×C₄⋊C₈	—	2	2	no	—
78	C₁₁×C₄⋊C₈	—	2	2	no	—
79	C₁₁×C₄⋊C₈	—	2	2	no	—
80	C₁₁×C₄⋊C₈	—	2	2	no	—
81	C₁₁×C₄⋊C₈	—	4	2	no	—
82	C₁₁×C₂²⋊C₈	—	2	2	no	—
83	C₁₁×C₂²⋊C₈	—	2	2	no	—
84	C₁₁×C₂²⋊C₈	—	2	4	no	—
85	C₁₁×C₂²⋊C₈	—	4	2	no	—
86	C₁₁×C₂²⋊C₈	—	4	2	no	—
87	C₁₁×C₂²⋊C₈	—	4	2	no	—
88	C₁₁×#97	—	2	2	no	—
89	C₄×C₈×C₁₁	—	4	2	no	—
90	C₄×C₈×C₁₁	D₄	1	4	yes	complemented
91	C₁₁×#95	C₂×C₄	1	2	yes	—
92	C₁₁×#95	C₂×C₄	1	2	yes	—
93	C₁₁×#95	C₂×C₄	1	1	yes	characteristic
94	C₁₁×#95	C₂×C₄	1	1	yes	characteristic
95	#22134	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
96	C₂⁴×C₁₁	C₂²×C₄	1	1	yes	characteristic
97	C₂⁴×C₁₁	C₂²×C₄	1	2	yes	—
98	C₂×D₄×C₁₁	—	2	4	no	—
99	C₂×D₄×C₁₁	—	2	4	no	—
100	C₂×D₄×C₁₁	—	2	2	no	—
101	C₂×D₄×C₁₁	—	2	4	no	—
102	C₂×D₄×C₁₁	—	4	2	no	—
103	C₂²×C₄×C₁₁	—	2	1	no	—
104	C₂²×C₄×C₁₁	—	2	2	no	—
105	C₂²×C₄×C₁₁	—	2	1	no	—
106	C₂²×C₄×C₁₁	—	2	2	no	—
107	C₂²×C₄×C₁₁	—	2	1	no	—
108	C₂²×C₄×C₁₁	—	2	2	no	—
109	C₂²×C₄×C₁₁	—	2	2	no	—
110	C₂²×C₄×C₁₁	—	2	1	no	—
111	C₂²×C₄×C₁₁	—	2	1	no	—
112	C₂²×C₄×C₁₁	—	2	2	no	—
113	C₂²×C₄×C₁₁	—	2	2	no	—
114	C₂²×C₄×C₁₁	—	2	1	no	—
115	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
116	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
117	C₂²×C₄×C₁₁	C₂²×C₄	1	2	yes	—
118	C₂²×C₄×C₁₁	C₂²×C₄	1	2	yes	—
119	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
120	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
121	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
122	C₂²×C₄×C₁₁	C₂²×C₄	1	2	yes	—
123	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
124	C₂×C₈×C₁₁	—	2	1	no	—
125	C₂×C₈×C₁₁	—	2	1	no	—
126	C₂×C₈×C₁₁	—	2	2	no	—
127	C₂×C₈×C₁₁	—	2	2	no	—
128	C₂×C₈×C₁₁	—	2	1	no	—
129	C₂×C₈×C₁₁	—	2	1	no	—
130	C₂×C₈×C₁₁	—	2	1	no	—
131	C₂×C₈×C₁₁	—	2	2	no	—
132	C₂×C₈×C₁₁	—	2	1	no	—
133	C₂×C₈×C₁₁	—	2	2	no	—
134	C₂×C₈×C₁₁	—	2	1	no	—
135	C₂×C₈×C₁₁	—	2	2	no	—
136	C₂×C₈×C₁₁	—	2	1	no	—
137	C₂×C₈×C₁₁	—	2	2	no	—
138	C₂×C₈×C₁₁	—	2	1	no	—
139	C₂×C₈×C₁₁	—	2	1	no	—
140	C₂×C₈×C₁₁	—	4	8	no	—
141	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
142	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
143	C₁₁×C₄⋊C₄	—	2	2	no	—
144	C₁₁×C₄⋊C₄	—	2	2	no	—
145	C₁₁×C₄⋊C₄	—	2	2	no	—
146	C₁₁×C₄⋊C₄	—	2	4	no	—
147	C₁₁×C₄⋊C₄	—	4	2	no	—
148	C₁₁×C₂²⋊C₄	—	2	4	no	—
149	C₁₁×C₂²⋊C₄	—	2	2	no	—
150	C₁₁×C₂²⋊C₄	—	2	2	no	—
151	C₁₁×C₂²⋊C₄	—	2	4	no	—
152	C₁₁×C₂²⋊C₄	—	2	4	no	—
153	C₁₁×C₂²⋊C₄	—	4	2	no	—
154	C₁₁×C₂²⋊C₄	—	4	2	no	—
155	C₄²×C₁₁	—	2	1	no	—
156	C₄²×C₁₁	—	2	1	no	—
157	C₄²×C₁₁	—	2	2	no	—
158	C₄²×C₁₁	—	2	2	no	—
159	C₄²×C₁₁	C₂×D₄	1	2	yes	—
160	C₄²×C₁₁	#41	1	2	yes	—
161	C₂×C₈×D₄	C₂×C₁₁	1	1	yes	characteristic, complemented
162	C₂×#433	C₂×C₁₁	1	1	yes	characteristic, complemented
163	#2392	C₂×C₁₁	1	1	yes	characteristic
164	#1955	C₂×C₁₁	1	1	yes	characteristic, complemented
165	#1954	C₂×C₁₁	1	2	yes	complemented
166	#1940	C₂×C₁₁	1	1	yes	characteristic, complemented
167	#1923	C₂×C₁₁	1	2	yes	complemented
168	#1869	C₂×C₁₁	1	2	yes	complemented
169	#1850	C₂×C₁₁	1	2	yes	complemented
170	#1798	C₂×C₁₁	1	1	yes	characteristic, complemented
171	C₈×C₄⋊C₄	C₂×C₁₁	1	1	yes	characteristic, complemented
172	C₂³×C₁₁	—	2	2	no	—
173	C₂³×C₁₁	—	2	2	no	—
174	C₂³×C₁₁	—	2	2	no	—
175	C₂³×C₁₁	—	2	2	no	—
176	C₂³×C₁₁	—	2	2	no	—
177	C₂³×C₁₁	—	2	2	no	—
178	C₂³×C₁₁	—	2	1	no	—
179	C₂³×C₁₁	—	2	1	no	—
180	C₂³×C₁₁	—	2	1	no	—
181	C₂³×C₁₁	—	2	2	no	—
182	C₂³×C₁₁	—	2	2	no	—
183	C₂³×C₁₁	#131	1	4	yes	—
184	C₂³×C₁₁	C₂³×C₄	1	1	yes	characteristic
185	D₄×C₁₁	—	2	8	no	—
186	D₄×C₁₁	—	4	8	no	—
187	C₂×C₄×C₁₁	—	2	2	no	—
188	C₂×C₄×C₁₁	—	2	2	no	—
189	C₂×C₄×C₁₁	—	2	2	no	—
190	C₂×C₄×C₁₁	—	2	2	no	—
191	C₂×C₄×C₁₁	—	2	1	no	—
192	C₂×C₄×C₁₁	—	2	1	no	—
193	C₂×C₄×C₁₁	—	2	2	no	—
194	C₂×C₄×C₁₁	—	2	1	no	—
195	C₂×C₄×C₁₁	—	2	2	no	—
196	C₂×C₄×C₁₁	—	2	1	no	—
197	C₂×C₄×C₁₁	—	2	2	no	—
198	C₂×C₄×C₁₁	—	2	1	no	—
199	C₂×C₄×C₁₁	—	2	2	no	—
200	C₂×C₄×C₁₁	—	2	2	no	—
201	C₂×C₄×C₁₁	—	2	2	no	—
202	C₂×C₄×C₁₁	—	2	2	no	—
203	C₂×C₄×C₁₁	—	2	2	no	—
204	C₂×C₄×C₁₁	—	4	2	no	—
205	C₂×C₄×C₁₁	—	4	1	no	—
206	C₂×C₄×C₁₁	—	4	2	no	—
207	C₂×C₄×C₁₁	—	4	1	no	—
208	C₂×C₄×C₁₁	—	4	2	no	—
209	C₂×C₄×C₁₁	—	4	1	no	—
210	C₂×C₄×C₁₁	—	4	2	no	—
211	C₂×C₄×C₁₁	—	4	1	no	—
212	C₂×C₄×C₁₁	C₄×D₄	1	2	yes	—
213	C₂×C₄×C₁₁	C₄×D₄	1	2	yes	—
214	C₂×C₄×C₁₁	#131	1	4	yes	—
215	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
216	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
217	C₂×C₄×C₁₁	H(5,𝔽₂)	1	1	yes	characteristic
218	C₂×C₄×C₁₁	H(5,𝔽₂)	1	1	yes	characteristic
219	C₂×C₄×C₁₁	H(5,𝔽₂)	1	1	yes	characteristic
220	C₂×C₄×C₁₁	2₋¹⁺⁴	1	1	yes	characteristic
221	C₈×C₁₁	—	2	2	no	—
222	C₈×C₁₁	—	2	2	no	—
223	C₈×C₁₁	—	4	1	no	—
224	C₈×C₁₁	—	4	2	no	—
225	C₈×C₁₁	—	4	1	no	—
226	C₈×C₁₁	—	4	2	no	—
227	C₂³×C₈	C₂²×C₁₁	1	2	yes	—
228	C₂×C₄×D₄	C₂²×C₁₁	1	1	yes	characteristic
229	C₂×C₄×D₄	C₂²×C₁₁	1	2	yes	—
230	C₂×#117	C₂²×C₁₁	1	1	yes	characteristic
231	C₈×D₄	—	2	4	no	—
232	#433	—	2	4	no	—
233	C₂×C₄⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
234	C₂×C₄⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
235	C₂×C₄⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
236	C₂×C₄⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
237	C₂×C₄⋊C₈	C₂²×C₁₁	1	2	yes	—
238	C₂×C₂²⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
239	C₂×C₂²⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
240	C₂×C₂²⋊C₈	C₂²×C₁₁	1	2	yes	—
241	C₂×C₂²⋊C₈	C₂²×C₁₁	1	2	yes	—
242	C₂×C₂²⋊C₈	C₂²×C₁₁	1	2	yes	—
243	C₂×C₂²⋊C₈	C₂²×C₁₁	1	2	yes	—
244	C₂×#97	C₂²×C₁₁	1	1	yes	characteristic
245	C₂×C₄×C₈	C₂²×C₁₁	1	2	yes	—
246	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
247	#398	C₄×C₁₁	1	1	yes	characteristic
248	#397	C₄×C₁₁	1	1	yes	characteristic
249	#396	C₄×C₁₁	1	2	yes	—
250	#394	C₄×C₁₁	1	2	yes	—
251	#394	C₄×C₁₁	1	1	yes	characteristic
252	#392	C₄×C₁₁	1	1	yes	characteristic
253	C₄×C₄⋊C₄	C₂²×C₁₁	1	1	yes	characteristic
254	C₄×C₂²⋊C₄	C₂²×C₁₁	1	2	yes	—
255	#336	C₂²×C₁₁	1	2	yes	—
256	#336	C₂²×C₁₁	1	2	yes	—
257	#336	C₂²×C₁₁	1	2	yes	—
258	C₂²×C₁₁	—	2	4	no	—
259	C₂²×C₁₁	—	2	4	no	—
260	C₂²×C₁₁	—	2	4	no	—
261	C₂²×C₁₁	—	4	2	no	—
262	C₂²×C₁₁	—	4	2	no	—
263	C₂²×C₁₁	—	4	2	no	—
264	C₂²×C₁₁	—	4	2	no	—
265	C₂²×C₁₁	—	4	1	no	—
266	C₂²×C₁₁	—	4	1	no	—
267	C₂²×C₁₁	—	4	1	no	—
268	C₂²×C₁₁	—	4	2	no	—
269	C₂²×C₁₁	—	4	2	no	—
270	C₂²×C₁₁	C₂×C₄×D₄	1	1	yes	characteristic
271	C₂²×C₁₁	#518	1	1	yes	characteristic
272	C₂²×C₁₁	#520	1	1	yes	characteristic
273	C₂²×C₁₁	C₂×#131	1	2	yes	—
274	C₂²×C₁₁	C₂×#131	1	2	yes	—
275	C₄×C₁₁	—	2	2	no	—
276	C₄×C₁₁	—	2	2	no	—
277	C₄×C₁₁	—	2	4	no	—
278	C₄×C₁₁	—	4	2	no	—
279	C₄×C₁₁	—	4	1	no	—
280	C₄×C₁₁	—	4	1	no	—
281	C₄×C₁₁	—	4	1	no	—
282	C₄×C₁₁	—	4	2	no	—
283	C₄×C₁₁	#535	1	1	yes	characteristic
284	C₄×C₁₁	#537	1	1	yes	characteristic
285	C₄×C₁₁	#540	1	1	yes	characteristic
286	C₄×C₁₁	#542	1	1	yes	characteristic
287	C₂²×D₄	C₂×C₄×C₁₁	1	1	yes	characteristic
288	C₂²×D₄	C₂×C₄×C₁₁	1	2	yes	—
289	C₂³×C₄	C₂³×C₁₁	1	1	yes	characteristic
290	C₂³×C₄	C₂³×C₁₁	1	2	yes	—
291	C₂²×C₈	—	2	4	no	—
292	C₂²×C₈	—	4	2	no	—
293	C₂²×C₈	—	4	2	no	—
294	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
295	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
296	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
297	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
298	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
299	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
300	C₄×D₄	—	2	2	no	—
301	C₄×D₄	—	2	2	no	—
302	C₄×D₄	—	4	2	no	—
303	C₄×D₄	—	4	2	no	—
304	#117	—	2	2	no	—
305	#117	—	2	2	no	—
306	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
307	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
308	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
309	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	2	yes	—
310	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	2	yes	—
311	C₂×C₂²⋊C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
312	C₂×C₂²⋊C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
313	C₂×C₂²⋊C₄	C₂×C₄×C₁₁	1	2	yes	—
314	C₂×C₂²⋊C₄	C₂×C₄×C₁₁	1	2	yes	—
315	C₂×C₂²⋊C₄	C₂×C₄×C₁₁	1	2	yes	—
316	C₂×C₂²⋊C₄	C₂×C₄×C₁₁	1	2	yes	—
317	C₂×C₂²⋊C₄	C₂×C₄×C₁₁	1	2	yes	—
318	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
319	C₂×C₄²	C₂³×C₁₁	1	2	yes	—
320	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
321	C₄⋊C₈	—	2	2	no	—
322	C₄⋊C₈	—	2	2	no	—
323	C₄⋊C₈	—	2	2	no	—
324	C₄⋊C₈	—	2	2	no	—
325	C₄⋊C₈	—	4	2	no	—
326	C₂²⋊C₈	—	2	2	no	—
327	C₂²⋊C₈	—	2	2	no	—
328	C₂²⋊C₈	—	2	4	no	—
329	C₂²⋊C₈	—	4	2	no	—
330	C₂²⋊C₈	—	4	2	no	—
331	C₂²⋊C₈	—	4	2	no	—
332	#97	—	2	2	no	—
333	C₄×C₈	—	4	2	no	—
334	C₄×C₈	D₄×C₁₁	1	4	yes	complemented
335	#95	C₂×C₄×C₁₁	1	2	yes	—
336	#95	C₂×C₄×C₁₁	1	2	yes	—
337	#95	C₂×C₄×C₁₁	1	1	yes	characteristic
338	#95	C₂×C₄×C₁₁	1	1	yes	characteristic
339	C₂×C₁₁	—	4	4	no	—
340	C₂×C₁₁	—	8	1	no	—
341	C₂×C₁₁	#2324	1	1	yes	characteristic
342	C₂×C₁₁	#2929	1	1	yes	characteristic
343	C₂×C₁₁	#2931	1	1	yes	characteristic
344	C₂×C₁₁	#2977	1	2	yes	—
345	C₂×C₁₁	#2994	1	2	yes	—
346	C₂⁴	C₂²×C₄×C₁₁	1	1	yes	characteristic
347	C₂⁴	C₂²×C₄×C₁₁	1	2	yes	—
348	C₂×D₄	—	2	4	no	—
349	C₂×D₄	—	2	4	no	—
350	C₂×D₄	—	2	2	no	—
351	C₂×D₄	—	2	4	no	—
352	C₂×D₄	—	4	2	no	—
353	C₂²×C₄	—	2	1	no	—
354	C₂²×C₄	—	2	2	no	—
355	C₂²×C₄	—	2	1	no	—
356	C₂²×C₄	—	2	2	no	—
357	C₂²×C₄	—	2	1	no	—
358	C₂²×C₄	—	2	2	no	—
359	C₂²×C₄	—	2	2	no	—
360	C₂²×C₄	—	2	1	no	—
361	C₂²×C₄	—	2	1	no	—
362	C₂²×C₄	—	2	2	no	—
363	C₂²×C₄	—	2	2	no	—
364	C₂²×C₄	—	2	1	no	—
365	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
366	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
367	C₂²×C₄	C₂²×C₄×C₁₁	1	2	yes	—
368	C₂²×C₄	C₂²×C₄×C₁₁	1	2	yes	—
369	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
370	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
371	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
372	C₂²×C₄	C₂²×C₄×C₁₁	1	2	yes	—
373	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
374	C₂×C₈	—	2	1	no	—
375	C₂×C₈	—	2	1	no	—
376	C₂×C₈	—	2	1	no	—
377	C₂×C₈	—	2	1	no	—
378	C₂×C₈	—	2	1	no	—
379	C₂×C₈	—	2	1	no	—
380	C₂×C₈	—	2	2	no	—
381	C₂×C₈	—	2	2	no	—
382	C₂×C₈	—	2	2	no	—
383	C₂×C₈	—	2	1	no	—
384	C₂×C₈	—	2	1	no	—
385	C₂×C₈	—	2	2	no	—
386	C₂×C₈	—	2	2	no	—
387	C₂×C₈	—	2	1	no	—
388	C₂×C₈	—	2	2	no	—
389	C₂×C₈	—	2	1	no	—
390	C₂×C₈	—	4	8	no	—
391	C₂×C₈	C₂×D₄×C₁₁	1	2	yes	—
392	C₂×C₈	C₂×D₄×C₁₁	1	2	yes	—
393	C₄⋊C₄	—	2	2	no	—
394	C₄⋊C₄	—	2	2	no	—
395	C₄⋊C₄	—	2	2	no	—
396	C₄⋊C₄	—	2	4	no	—
397	C₄⋊C₄	—	4	2	no	—
398	C₂²⋊C₄	—	2	4	no	—
399	C₂²⋊C₄	—	2	2	no	—
400	C₂²⋊C₄	—	2	2	no	—
401	C₂²⋊C₄	—	2	4	no	—
402	C₂²⋊C₄	—	2	4	no	—
403	C₂²⋊C₄	—	4	2	no	—
404	C₂²⋊C₄	—	4	2	no	—
405	C₄²	—	2	1	no	—
406	C₄²	—	2	1	no	—
407	C₄²	—	2	2	no	—
408	C₄²	—	2	2	no	—
409	C₄²	C₂×D₄×C₁₁	1	2	yes	—
410	C₄²	C₁₁×#41	1	2	yes	—
411	C₁₁	#22134	1	1	yes	characteristic, direct product factor, Sylow
412	C₂³	—	2	2	no	—
413	C₂³	—	2	2	no	—
414	C₂³	—	2	2	no	—
415	C₂³	—	2	2	no	—
416	C₂³	—	2	2	no	—
417	C₂³	—	2	2	no	—
418	C₂³	—	2	1	no	—
419	C₂³	—	2	1	no	—
420	C₂³	—	2	1	no	—
421	C₂³	—	2	2	no	—
422	C₂³	—	2	2	no	—
423	C₂³	C₁₁×#131	1	4	yes	—
424	C₂³	C₂³×C₄×C₁₁	1	1	yes	characteristic
425	D₄	—	2	8	no	—
426	D₄	—	4	8	no	—
427	C₂×C₄	—	2	2	no	—
428	C₂×C₄	—	2	2	no	—
429	C₂×C₄	—	2	2	no	—
430	C₂×C₄	—	2	2	no	—
431	C₂×C₄	—	2	1	no	—
432	C₂×C₄	—	2	1	no	—
433	C₂×C₄	—	2	2	no	—
434	C₂×C₄	—	2	1	no	—
435	C₂×C₄	—	2	2	no	—
436	C₂×C₄	—	2	1	no	—
437	C₂×C₄	—	2	2	no	—
438	C₂×C₄	—	2	1	no	—
439	C₂×C₄	—	2	2	no	—
440	C₂×C₄	—	2	2	no	—
441	C₂×C₄	—	2	2	no	—
442	C₂×C₄	—	2	2	no	—
443	C₂×C₄	—	2	2	no	—
444	C₂×C₄	—	4	2	no	—
445	C₂×C₄	—	4	1	no	—
446	C₂×C₄	—	4	2	no	—
447	C₂×C₄	—	4	1	no	—
448	C₂×C₄	—	4	2	no	—
449	C₂×C₄	—	4	1	no	—
450	C₂×C₄	—	4	2	no	—
451	C₂×C₄	—	4	1	no	—
452	C₂×C₄	C₄×D₄×C₁₁	1	2	yes	—
453	C₂×C₄	C₄×D₄×C₁₁	1	2	yes	—
454	C₂×C₄	C₁₁×#131	1	4	yes	—
455	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
456	C₂×C₄	C₂×C₁₁×#41	1	1	yes	characteristic
457	C₂×C₄	C₁₁×H(5,𝔽₂)	1	1	yes	characteristic
458	C₂×C₄	C₁₁×H(5,𝔽₂)	1	1	yes	characteristic
459	C₂×C₄	C₁₁×H(5,𝔽₂)	1	1	yes	characteristic
460	C₂×C₄	C₁₁×2₋¹⁺⁴	1	1	yes	characteristic
461	C₈	—	2	2	no	—
462	C₈	—	2	2	no	—
463	C₈	—	4	2	no	—
464	C₈	—	4	1	no	—
465	C₈	—	4	1	no	—
466	C₈	—	4	2	no	—
467	C₂²	—	2	4	no	—
468	C₂²	—	2	4	no	—
469	C₂²	—	2	4	no	—
470	C₂²	—	4	2	no	—
471	C₂²	—	4	2	no	—
472	C₂²	—	4	2	no	—
473	C₂²	—	4	2	no	—
474	C₂²	—	4	1	no	—
475	C₂²	—	4	1	no	—
476	C₂²	—	4	2	no	—
477	C₂²	—	4	2	no	—
478	C₂²	—	4	1	no	—
479	C₂²	C₂×C₄×D₄×C₁₁	1	1	yes	characteristic
480	C₂²	C₁₁×#518	1	1	yes	characteristic
481	C₂²	C₁₁×#520	1	1	yes	characteristic
482	C₂²	C₂×C₁₁×#131	1	2	yes	—
483	C₂²	C₂×C₁₁×#131	1	2	yes	—
484	C₄	—	2	2	no	—
485	C₄	—	2	2	no	—
486	C₄	—	2	4	no	—
487	C₄	—	4	1	no	—
488	C₄	—	4	1	no	—
489	C₄	—	4	2	no	—
490	C₄	—	4	2	no	—
491	C₄	—	4	1	no	—
492	C₄	C₁₁×#535	1	1	yes	characteristic
493	C₄	C₁₁×#537	1	1	yes	characteristic
494	C₄	C₁₁×#540	1	1	yes	characteristic
495	C₄	C₁₁×#542	1	1	yes	characteristic
496	C₂	—	4	4	no	—
497	C₂	—	8	1	no	—
498	C₂	C₁₁×#2324	1	1	yes	characteristic
499	C₂	C₁₁×#2929	1	1	yes	characteristic
500	C₂	C₁₁×#2931	1	1	yes	characteristic
501	C₂	C₁₁×#2977	1	2	yes	—
502	C₂	C₁₁×#2994	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	C₁₁×#392	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×C₈×D₄×C₁₁	C₂	semidirect
2. C₂×C₁₁×#433	C₂	semidirect
4. C₁₁×#1955	C₂	semidirect
5. C₁₁×#1954	C₂	semidirect
6. C₁₁×#1940	C₂	semidirect
7. C₁₁×#1923	C₂	semidirect
8. C₁₁×#1869	C₂	semidirect
9. C₁₁×#1850	C₂	semidirect
10. C₁₁×#1798	C₂	semidirect
11. C₈×C₁₁×C₄⋊C₄	C₂	semidirect
90. C₄×C₈×C₁₁	D₄	semidirect
95. #22134	C₁₁	direct (N × H)
161. C₂×C₈×D₄	C₂×C₁₁	semidirect
162. C₂×#433	C₂×C₁₁	semidirect
164. #1955	C₂×C₁₁	semidirect
165. #1954	C₂×C₁₁	semidirect
166. #1940	C₂×C₁₁	semidirect
167. #1923	C₂×C₁₁	semidirect
168. #1869	C₂×C₁₁	semidirect
169. #1850	C₂×C₁₁	semidirect
170. #1798	C₂×C₁₁	semidirect
171. C₈×C₄⋊C₄	C₂×C₁₁	semidirect
334. C₄×C₈	D₄×C₁₁	semidirect
411. C₁₁	#22134	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×C₈×D₄×C₁₁	2
C₂×C₁₁×#433	2
C₁₁×#2392	2
C₁₁×#1955	2
C₁₁×#1954	2
C₁₁×#1940	2
C₁₁×#1923	2
C₁₁×#1869	2
C₁₁×#1850	2
C₁₁×#1798	2
C₈×C₁₁×C₄⋊C₄	2
#22134	11

Subgroups — C11×#22134 #14599327

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#22134 #14599327