Subgroups — C₁₁×#22216 #14599409

Order 2816.

844 conjugacy classes of subgroups.

The subgroup lattice has 684 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×#435	C₂	1	1	yes	maximal, characteristic
3	C₄×C₁₁×#124	C₂	1	1	yes	maximal, characteristic
4	C₁₁×#1985	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₁×#1955	C₂	1	1	yes	maximal, characteristic
6	C₁₁×#1924	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₁×#1924	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₁×#1923	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₁×#1923	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₁×#1851	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₁×#1851	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₁×#1850	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₁×#1850	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₁×#1842	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₁×#1745	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₁₁×M₁₆	C₂²	1	1	yes	characteristic
17	C₂³×C₈×C₁₁	C₂²	1	1	yes	characteristic
18	C₂×C₁₁×#124	C₄	1	1	yes	characteristic
19	C₂×C₄×Q₈×C₁₁	C₂²	1	1	yes	characteristic
20	C₂×C₄×D₄×C₁₁	C₂²	1	1	yes	characteristic
21	C₁₁×#446	—	2	4	no	—
22	C₁₁×#435	—	2	4	no	—
23	C₂×C₁₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
24	C₂×C₁₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
25	C₂×C₁₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
26	C₂×C₁₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
27	C₂×C₁₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
28	C₂×C₁₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
29	C₂×C₁₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
30	C₂×C₁₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
31	C₂×C₁₁×C₂²⋊C₈	C₂²	1	1	yes	characteristic
32	C₂×C₁₁×C₂²⋊C₈	C₂²	1	1	yes	characteristic
33	C₂×C₁₁×C₂²⋊C₈	C₂²	1	1	yes	characteristic
34	C₂×C₁₁×C₂²⋊C₈	C₂²	1	1	yes	characteristic
35	C₂×C₁₁×C₂²⋊C₈	C₂²	1	1	yes	characteristic
36	C₂×C₁₁×C₂²⋊C₈	C₂²	1	1	yes	characteristic
37	C₂×C₁₁×#97	C₂²	1	1	yes	characteristic
38	C₂×C₁₁×#97	C₂²	1	1	yes	characteristic
39	C₂×C₁₁×#97	C₂²	1	1	yes	characteristic
40	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
41	C₁₁×#391	C₄	1	1	yes	characteristic
42	C₁₁×#390	C₄	1	1	yes	characteristic
43	C₁₁×#388	C₄	1	1	yes	characteristic
44	C₁₁×#388	C₄	1	1	yes	characteristic
45	C₁₁×#388	C₄	1	1	yes	characteristic
46	C₁₁×#388	C₄	1	1	yes	characteristic
47	C₁₁×#382	C₄	1	1	yes	characteristic
48	C₄×C₁₁×C₂²⋊C₄	C₂²	1	1	yes	characteristic
49	C₄×C₁₁×C₂²⋊C₄	C₂²	1	1	yes	characteristic
50	C₄×C₁₁×C₂²⋊C₄	C₂²	1	1	yes	characteristic
51	C₄×C₁₁×C₂²⋊C₄	C₂²	1	1	yes	characteristic
52	C₄³×C₁₁	C₂²	1	1	yes	characteristic
53	C₁₁×#336	C₂²	1	1	yes	characteristic
54	C₁₁×#336	C₂²	1	1	yes	characteristic
55	C₁₁×#336	C₂²	1	1	yes	characteristic
56	C₁₁×#336	C₂²	1	1	yes	characteristic
57	C₁₁×#336	C₂²	1	1	yes	characteristic
58	C₁₁×#336	C₂²	1	1	yes	characteristic
59	C₁₁×#336	C₂²	1	1	yes	characteristic
60	C₁₁×#336	C₂²	1	1	yes	characteristic
61	C₂²×Q₈×C₁₁	C₂×C₄	1	1	yes	characteristic
62	C₂²×D₄×C₁₁	C₂×C₄	1	1	yes	characteristic
63	C₂³×C₄×C₁₁	C₂³	1	1	yes	characteristic
64	C₂³×C₄×C₁₁	C₂³	1	1	yes	characteristic
65	C₂×C₁₁×M₁₆	—	2	2	no	—
66	C₂×C₁₁×M₁₆	—	4	1	no	—
67	C₂×C₁₁×M₁₆	—	4	1	no	—
68	C₂²×C₈×C₁₁	—	2	2	no	—
69	C₂²×C₈×C₁₁	—	4	1	no	—
70	C₂²×C₈×C₁₁	—	4	1	no	—
71	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
72	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
73	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
74	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
75	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
76	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
77	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
78	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
79	C₁₁×#124	—	2	4	no	—
80	C₄×Q₈×C₁₁	—	2	2	no	—
81	C₄×Q₈×C₁₁	—	2	2	no	—
82	C₄×D₄×C₁₁	—	2	2	no	—
83	C₄×D₄×C₁₁	—	2	2	no	—
84	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
85	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
86	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
87	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
88	C₂×C₁₁×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
89	C₂×C₁₁×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
90	C₂×C₁₁×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
91	C₂×C₁₁×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
92	C₂×C₁₁×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
93	C₂×C₁₁×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
94	C₂×C₁₁×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
95	C₂×C₁₁×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
96	C₂×C₁₁×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
97	C₂×C₁₁×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
98	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
99	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
100	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
101	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
102	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
103	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
104	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
105	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
106	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
107	C₁₁×C₄⋊C₈	—	2	2	no	—
108	C₁₁×C₄⋊C₈	—	2	2	no	—
109	C₁₁×C₄⋊C₈	—	2	2	no	—
110	C₁₁×C₄⋊C₈	—	2	2	no	—
111	C₁₁×C₄⋊C₈	—	4	1	no	—
112	C₁₁×C₄⋊C₈	—	4	1	no	—
113	C₁₁×C₄⋊C₈	—	4	1	no	—
114	C₁₁×C₄⋊C₈	—	4	1	no	—
115	C₁₁×C₂²⋊C₈	—	2	2	no	—
116	C₁₁×C₂²⋊C₈	—	2	2	no	—
117	C₁₁×C₂²⋊C₈	—	4	1	no	—
118	C₁₁×C₂²⋊C₈	—	4	1	no	—
119	C₁₁×C₂²⋊C₈	—	4	1	no	—
120	C₁₁×C₂²⋊C₈	—	4	1	no	—
121	C₁₁×#97	—	2	2	no	—
122	C₁₁×#97	—	2	2	no	—
123	C₁₁×#97	D₄	1	4	yes	—
124	C₄×C₈×C₁₁	—	2	2	no	—
125	C₁₁×#95	C₂×C₄	1	1	yes	characteristic
126	C₁₁×#95	C₂×C₄	1	1	yes	characteristic
127	C₁₁×#95	C₂×C₄	1	1	yes	characteristic
128	C₁₁×#95	C₂×C₄	1	1	yes	characteristic
129	C₁₁×#95	C₂×C₄	1	1	yes	characteristic
130	C₁₁×#95	C₂×C₄	1	1	yes	characteristic
131	C₁₁×#95	C₂×C₄	1	1	yes	characteristic
132	C₁₁×#95	C₂×C₄	1	1	yes	characteristic
133	#22216	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
134	C₂⁴×C₁₁	C₂²×C₄	1	1	yes	characteristic
135	C₂⁴×C₁₁	C₂²×C₄	1	1	yes	characteristic
136	C₂×Q₈×C₁₁	—	2	2	no	—
137	C₂×Q₈×C₁₁	—	2	2	no	—
138	C₂×Q₈×C₁₁	—	4	1	no	—
139	C₂×D₄×C₁₁	—	2	2	no	—
140	C₂×D₄×C₁₁	—	2	2	no	—
141	C₂×D₄×C₁₁	—	4	1	no	—
142	C₂²×C₄×C₁₁	—	2	1	no	—
143	C₂²×C₄×C₁₁	—	2	1	no	—
144	C₂²×C₄×C₁₁	—	2	1	no	—
145	C₂²×C₄×C₁₁	—	2	1	no	—
146	C₂²×C₄×C₁₁	—	2	1	no	—
147	C₂²×C₄×C₁₁	—	2	1	no	—
148	C₂²×C₄×C₁₁	—	2	1	no	—
149	C₂²×C₄×C₁₁	—	2	1	no	—
150	C₂²×C₄×C₁₁	—	2	1	no	—
151	C₂²×C₄×C₁₁	—	2	1	no	—
152	C₂²×C₄×C₁₁	—	2	1	no	—
153	C₂²×C₄×C₁₁	—	2	1	no	—
154	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
155	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
156	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
157	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
158	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
159	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
160	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
161	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
162	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
163	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
164	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
165	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
166	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
167	C₁₁×M₁₆	—	4	4	no	—
168	C₂×C₈×C₁₁	—	2	1	no	—
169	C₂×C₈×C₁₁	—	2	1	no	—
170	C₂×C₈×C₁₁	—	2	1	no	—
171	C₂×C₈×C₁₁	—	2	1	no	—
172	C₂×C₈×C₁₁	—	2	1	no	—
173	C₂×C₈×C₁₁	—	2	1	no	—
174	C₂×C₈×C₁₁	—	2	1	no	—
175	C₂×C₈×C₁₁	—	2	1	no	—
176	C₂×C₈×C₁₁	—	2	1	no	—
177	C₂×C₈×C₁₁	—	2	1	no	—
178	C₂×C₈×C₁₁	—	2	1	no	—
179	C₂×C₈×C₁₁	—	2	1	no	—
180	C₂×C₈×C₁₁	—	2	1	no	—
181	C₂×C₈×C₁₁	—	2	1	no	—
182	C₂×C₈×C₁₁	—	2	1	no	—
183	C₂×C₈×C₁₁	—	2	1	no	—
184	C₂×C₈×C₁₁	—	2	1	no	—
185	C₂×C₈×C₁₁	—	2	1	no	—
186	C₂×C₈×C₁₁	—	2	1	no	—
187	C₂×C₈×C₁₁	—	2	1	no	—
188	C₂×C₈×C₁₁	—	2	1	no	—
189	C₂×C₈×C₁₁	—	2	1	no	—
190	C₂×C₈×C₁₁	—	4	4	no	—
191	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
192	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
193	C₁₁×C₄⋊C₄	—	2	2	no	—
194	C₁₁×C₄⋊C₄	—	2	2	no	—
195	C₁₁×C₄⋊C₄	—	2	2	no	—
196	C₁₁×C₄⋊C₄	—	2	2	no	—
197	C₁₁×C₂²⋊C₄	—	2	2	no	—
198	C₁₁×C₂²⋊C₄	—	2	2	no	—
199	C₁₁×C₂²⋊C₄	—	2	2	no	—
200	C₁₁×C₂²⋊C₄	—	2	2	no	—
201	C₁₁×C₂²⋊C₄	—	2	2	no	—
202	C₁₁×C₂²⋊C₄	—	2	2	no	—
203	C₁₁×C₂²⋊C₄	—	2	2	no	—
204	C₁₁×C₂²⋊C₄	—	4	1	no	—
205	C₁₁×C₂²⋊C₄	—	4	1	no	—
206	C₁₁×C₂²⋊C₄	M₁₆	1	4	yes	complemented
207	C₄²×C₁₁	—	2	2	no	—
208	C₄²×C₁₁	—	2	2	no	—
209	C₄²×C₁₁	—	2	1	no	—
210	C₄²×C₁₁	—	2	1	no	—
211	C₄²×C₁₁	—	2	1	no	—
212	C₄²×C₁₁	—	2	1	no	—
213	C₄²×C₁₁	—	2	1	no	—
214	C₄²×C₁₁	—	2	1	no	—
215	C₄²×C₁₁	—	2	1	no	—
216	C₄²×C₁₁	—	2	1	no	—
217	C₄²×C₁₁	—	4	1	no	—
218	C₄²×C₁₁	—	4	1	no	—
219	C₄²×C₁₁	C₂×D₄	1	2	yes	—
220	C₄²×C₁₁	#41	1	2	yes	—
221	C₂×#446	C₂×C₁₁	1	1	yes	characteristic, complemented
222	C₂×#435	C₂×C₁₁	1	1	yes	characteristic
223	C₄×#124	C₂×C₁₁	1	1	yes	characteristic
224	#1985	C₂×C₁₁	1	1	yes	characteristic, complemented
225	#1955	C₂×C₁₁	1	1	yes	characteristic
226	#1924	C₂×C₁₁	1	1	yes	characteristic, complemented
227	#1924	C₂×C₁₁	1	1	yes	characteristic, complemented
228	#1923	C₂×C₁₁	1	1	yes	characteristic, complemented
229	#1923	C₂×C₁₁	1	1	yes	characteristic, complemented
230	#1851	C₂×C₁₁	1	1	yes	characteristic, complemented
231	#1851	C₂×C₁₁	1	1	yes	characteristic, complemented
232	#1850	C₂×C₁₁	1	1	yes	characteristic, complemented
233	#1850	C₂×C₁₁	1	1	yes	characteristic, complemented
234	#1842	C₂×C₁₁	1	1	yes	characteristic, complemented
235	#1745	C₂×C₁₁	1	1	yes	characteristic, complemented
236	C₂³×C₁₁	—	2	1	no	—
237	C₂³×C₁₁	—	2	1	no	—
238	C₂³×C₁₁	—	2	1	no	—
239	C₂³×C₁₁	—	2	1	no	—
240	C₂³×C₁₁	—	2	1	no	—
241	C₂³×C₁₁	—	2	1	no	—
242	C₂³×C₁₁	—	2	1	no	—
243	C₂³×C₁₁	—	2	1	no	—
244	C₂³×C₁₁	—	2	1	no	—
245	C₂³×C₁₁	—	2	1	no	—
246	C₂³×C₁₁	—	2	1	no	—
247	C₂³×C₁₁	—	2	1	no	—
248	C₂³×C₁₁	—	2	1	no	—
249	C₂³×C₁₁	C₂×M₁₆	1	2	yes	—
250	C₂³×C₁₁	C₂³×C₄	1	1	yes	characteristic
251	Q₈×C₁₁	—	4	4	no	—
252	D₄×C₁₁	—	4	4	no	—
253	C₂×C₄×C₁₁	—	2	1	no	—
254	C₂×C₄×C₁₁	—	2	1	no	—
255	C₂×C₄×C₁₁	—	2	1	no	—
256	C₂×C₄×C₁₁	—	2	1	no	—
257	C₂×C₄×C₁₁	—	2	1	no	—
258	C₂×C₄×C₁₁	—	2	1	no	—
259	C₂×C₄×C₁₁	—	2	1	no	—
260	C₂×C₄×C₁₁	—	2	1	no	—
261	C₂×C₄×C₁₁	—	2	1	no	—
262	C₂×C₄×C₁₁	—	2	1	no	—
263	C₂×C₄×C₁₁	—	2	1	no	—
264	C₂×C₄×C₁₁	—	2	1	no	—
265	C₂×C₄×C₁₁	—	2	1	no	—
266	C₂×C₄×C₁₁	—	2	1	no	—
267	C₂×C₄×C₁₁	—	2	1	no	—
268	C₂×C₄×C₁₁	—	2	1	no	—
269	C₂×C₄×C₁₁	—	2	1	no	—
270	C₂×C₄×C₁₁	—	2	1	no	—
271	C₂×C₄×C₁₁	—	2	1	no	—
272	C₂×C₄×C₁₁	—	2	1	no	—
273	C₂×C₄×C₁₁	—	2	1	no	—
274	C₂×C₄×C₁₁	—	2	1	no	—
275	C₂×C₄×C₁₁	—	2	1	no	—
276	C₂×C₄×C₁₁	—	2	1	no	—
277	C₂×C₄×C₁₁	—	2	1	no	—
278	C₂×C₄×C₁₁	—	2	1	no	—
279	C₂×C₄×C₁₁	—	2	1	no	—
280	C₂×C₄×C₁₁	—	2	1	no	—
281	C₂×C₄×C₁₁	—	2	1	no	—
282	C₂×C₄×C₁₁	—	2	1	no	—
283	C₂×C₄×C₁₁	—	2	1	no	—
284	C₂×C₄×C₁₁	—	4	1	no	—
285	C₂×C₄×C₁₁	—	4	1	no	—
286	C₂×C₄×C₁₁	—	4	1	no	—
287	C₂×C₄×C₁₁	—	4	1	no	—
288	C₂×C₄×C₁₁	—	4	1	no	—
289	C₂×C₄×C₁₁	—	4	1	no	—
290	C₂×C₄×C₁₁	—	4	1	no	—
291	C₂×C₄×C₁₁	—	4	1	no	—
292	C₂×C₄×C₁₁	C₄×D₄	1	2	yes	—
293	C₂×C₄×C₁₁	C₄×D₄	1	2	yes	—
294	C₂×C₄×C₁₁	C₂×M₁₆	1	2	yes	—
295	C₂×C₄×C₁₁	C₂×M₁₆	1	2	yes	—
296	C₂×C₄×C₁₁	#131	1	2	yes	—
297	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
298	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
299	C₂×C₄×C₁₁	H(5,𝔽₂)	1	1	yes	characteristic
300	C₂×C₄×C₁₁	H(5,𝔽₂)	1	1	yes	characteristic
301	C₂×C₄×C₁₁	2₋¹⁺⁴	1	1	yes	characteristic
302	C₂×C₄×C₁₁	2₋¹⁺⁴	1	1	yes	characteristic
303	C₈×C₁₁	—	2	2	no	—
304	C₈×C₁₁	—	2	2	no	—
305	C₈×C₁₁	—	4	1	no	—
306	C₈×C₁₁	—	4	1	no	—
307	C₈×C₁₁	—	4	1	no	—
308	C₈×C₁₁	—	4	1	no	—
309	C₈×C₁₁	—	4	1	no	—
310	C₈×C₁₁	—	4	1	no	—
311	C₂²×M₁₆	C₂²×C₁₁	1	1	yes	characteristic
312	C₂³×C₈	C₂²×C₁₁	1	1	yes	characteristic
313	C₂×#124	C₄×C₁₁	1	1	yes	characteristic
314	C₂×C₄×Q₈	C₂²×C₁₁	1	1	yes	characteristic
315	C₂×C₄×D₄	C₂²×C₁₁	1	1	yes	characteristic
316	#446	—	2	4	no	—
317	#435	—	2	4	no	—
318	C₂×C₄⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
319	C₂×C₄⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
320	C₂×C₄⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
321	C₂×C₄⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
322	C₂×C₄⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
323	C₂×C₄⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
324	C₂×C₄⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
325	C₂×C₄⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
326	C₂×C₂²⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
327	C₂×C₂²⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
328	C₂×C₂²⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
329	C₂×C₂²⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
330	C₂×C₂²⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
331	C₂×C₂²⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
332	C₂×#97	C₂²×C₁₁	1	1	yes	characteristic
333	C₂×#97	C₂²×C₁₁	1	1	yes	characteristic
334	C₂×#97	C₂²×C₁₁	1	1	yes	characteristic
335	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
336	#391	C₄×C₁₁	1	1	yes	characteristic
337	#390	C₄×C₁₁	1	1	yes	characteristic
338	#388	C₄×C₁₁	1	1	yes	characteristic
339	#388	C₄×C₁₁	1	1	yes	characteristic
340	#388	C₄×C₁₁	1	1	yes	characteristic
341	#388	C₄×C₁₁	1	1	yes	characteristic
342	#382	C₄×C₁₁	1	1	yes	characteristic
343	C₄×C₂²⋊C₄	C₂²×C₁₁	1	1	yes	characteristic
344	C₄×C₂²⋊C₄	C₂²×C₁₁	1	1	yes	characteristic
345	C₄×C₂²⋊C₄	C₂²×C₁₁	1	1	yes	characteristic
346	C₄×C₂²⋊C₄	C₂²×C₁₁	1	1	yes	characteristic
347	C₄³	C₂²×C₁₁	1	1	yes	characteristic
348	#336	C₂²×C₁₁	1	1	yes	characteristic
349	#336	C₂²×C₁₁	1	1	yes	characteristic
350	#336	C₂²×C₁₁	1	1	yes	characteristic
351	#336	C₂²×C₁₁	1	1	yes	characteristic
352	#336	C₂²×C₁₁	1	1	yes	characteristic
353	#336	C₂²×C₁₁	1	1	yes	characteristic
354	#336	C₂²×C₁₁	1	1	yes	characteristic
355	#336	C₂²×C₁₁	1	1	yes	characteristic
356	C₂²×C₁₁	—	2	2	no	—
357	C₂²×C₁₁	—	2	2	no	—
358	C₂²×C₁₁	—	2	2	no	—
359	C₂²×C₁₁	—	4	1	no	—
360	C₂²×C₁₁	—	4	1	no	—
361	C₂²×C₁₁	—	4	1	no	—
362	C₂²×C₁₁	—	4	1	no	—
363	C₂²×C₁₁	—	4	1	no	—
364	C₂²×C₁₁	—	4	1	no	—
365	C₂²×C₁₁	—	4	1	no	—
366	C₂²×C₁₁	—	4	1	no	—
367	C₂²×C₁₁	—	4	1	no	—
368	C₂²×C₁₁	—	4	1	no	—
369	C₂²×C₁₁	—	4	1	no	—
370	C₂²×C₁₁	C₂×C₄×D₄	1	1	yes	characteristic
371	C₂²×C₁₁	#520	1	1	yes	characteristic
372	C₂²×C₁₁	#520	1	1	yes	characteristic
373	C₂²×C₁₁	C₂²×M₁₆	1	1	yes	characteristic
374	C₂²×C₁₁	C₂×#131	1	1	yes	characteristic
375	C₂²×C₁₁	#568	1	1	yes	characteristic
376	C₂²×C₁₁	#568	1	1	yes	characteristic
377	C₄×C₁₁	—	2	2	no	—
378	C₄×C₁₁	—	2	2	no	—
379	C₄×C₁₁	—	2	2	no	—
380	C₄×C₁₁	—	2	2	no	—
381	C₄×C₁₁	—	2	2	no	—
382	C₄×C₁₁	—	4	1	no	—
383	C₄×C₁₁	—	4	1	no	—
384	C₄×C₁₁	—	4	1	no	—
385	C₄×C₁₁	—	4	1	no	—
386	C₄×C₁₁	—	4	1	no	—
387	C₄×C₁₁	—	4	1	no	—
388	C₄×C₁₁	—	4	1	no	—
389	C₄×C₁₁	#535	1	1	yes	characteristic
390	C₄×C₁₁	#536	1	1	yes	characteristic
391	C₄×C₁₁	#542	1	1	yes	characteristic
392	C₄×C₁₁	#542	1	1	yes	characteristic
393	C₂²×Q₈	C₂×C₄×C₁₁	1	1	yes	characteristic
394	C₂²×D₄	C₂×C₄×C₁₁	1	1	yes	characteristic
395	C₂³×C₄	C₂³×C₁₁	1	1	yes	characteristic
396	C₂³×C₄	C₂³×C₁₁	1	1	yes	characteristic
397	C₂×M₁₆	—	2	2	no	—
398	C₂×M₁₆	—	4	1	no	—
399	C₂×M₁₆	—	4	1	no	—
400	C₂²×C₈	—	2	2	no	—
401	C₂²×C₈	—	4	1	no	—
402	C₂²×C₈	—	4	1	no	—
403	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
404	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
405	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
406	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
407	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
408	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
409	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
410	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
411	#124	—	2	4	no	—
412	C₄×Q₈	—	2	2	no	—
413	C₄×Q₈	—	2	2	no	—
414	C₄×D₄	—	2	2	no	—
415	C₄×D₄	—	2	2	no	—
416	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
417	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
418	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
419	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
420	C₂×C₂²⋊C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
421	C₂×C₂²⋊C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
422	C₂×C₂²⋊C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
423	C₂×C₂²⋊C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
424	C₂×C₂²⋊C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
425	C₂×C₂²⋊C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
426	C₂×C₂²⋊C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
427	C₂×C₂²⋊C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
428	C₂×C₂²⋊C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
429	C₂×C₂²⋊C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
430	C₂×C₄²	C₂×C₄×C₁₁	1	1	yes	characteristic
431	C₂×C₄²	C₂×C₄×C₁₁	1	1	yes	characteristic
432	C₂×C₄²	C₂×C₄×C₁₁	1	1	yes	characteristic
433	C₂×C₄²	C₂×C₄×C₁₁	1	1	yes	characteristic
434	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
435	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
436	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
437	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
438	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
439	C₄⋊C₈	—	2	2	no	—
440	C₄⋊C₈	—	2	2	no	—
441	C₄⋊C₈	—	2	2	no	—
442	C₄⋊C₈	—	2	2	no	—
443	C₄⋊C₈	—	4	1	no	—
444	C₄⋊C₈	—	4	1	no	—
445	C₄⋊C₈	—	4	1	no	—
446	C₄⋊C₈	—	4	1	no	—
447	C₂²⋊C₈	—	2	2	no	—
448	C₂²⋊C₈	—	2	2	no	—
449	C₂²⋊C₈	—	4	1	no	—
450	C₂²⋊C₈	—	4	1	no	—
451	C₂²⋊C₈	—	4	1	no	—
452	C₂²⋊C₈	—	4	1	no	—
453	#97	—	2	2	no	—
454	#97	—	2	2	no	—
455	#97	D₄×C₁₁	1	4	yes	—
456	C₄×C₈	—	2	2	no	—
457	#95	C₂×C₄×C₁₁	1	1	yes	characteristic
458	#95	C₂×C₄×C₁₁	1	1	yes	characteristic
459	#95	C₂×C₄×C₁₁	1	1	yes	characteristic
460	#95	C₂×C₄×C₁₁	1	1	yes	characteristic
461	#95	C₂×C₄×C₁₁	1	1	yes	characteristic
462	#95	C₂×C₄×C₁₁	1	1	yes	characteristic
463	#95	C₂×C₄×C₁₁	1	1	yes	characteristic
464	#95	C₂×C₄×C₁₁	1	1	yes	characteristic
465	C₂×C₁₁	—	4	2	no	—
466	C₂×C₁₁	—	8	1	no	—
467	C₂×C₁₁	#2326	1	1	yes	characteristic
468	C₂×C₁₁	D₄×M₁₆	1	1	yes	characteristic
469	C₂×C₁₁	#2935	1	1	yes	characteristic
470	C₂×C₁₁	#2989	1	1	yes	characteristic
471	C₂×C₁₁	#2990	1	1	yes	characteristic
472	C₂×C₁₁	#2992	1	1	yes	characteristic
473	C₂×C₁₁	#2995	1	1	yes	characteristic
474	C₂⁴	C₂²×C₄×C₁₁	1	1	yes	characteristic
475	C₂⁴	C₂²×C₄×C₁₁	1	1	yes	characteristic
476	C₂×Q₈	—	2	2	no	—
477	C₂×Q₈	—	2	2	no	—
478	C₂×Q₈	—	4	1	no	—
479	C₂×D₄	—	2	2	no	—
480	C₂×D₄	—	2	2	no	—
481	C₂×D₄	—	4	1	no	—
482	C₂²×C₄	—	2	1	no	—
483	C₂²×C₄	—	2	1	no	—
484	C₂²×C₄	—	2	1	no	—
485	C₂²×C₄	—	2	1	no	—
486	C₂²×C₄	—	2	1	no	—
487	C₂²×C₄	—	2	1	no	—
488	C₂²×C₄	—	2	1	no	—
489	C₂²×C₄	—	2	1	no	—
490	C₂²×C₄	—	2	1	no	—
491	C₂²×C₄	—	2	1	no	—
492	C₂²×C₄	—	2	1	no	—
493	C₂²×C₄	—	2	1	no	—
494	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
495	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
496	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
497	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
498	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
499	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
500	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
501	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
502	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
503	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
504	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
505	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
506	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
507	M₁₆	—	4	4	no	—
508	C₂×C₈	—	2	1	no	—
509	C₂×C₈	—	2	1	no	—
510	C₂×C₈	—	2	1	no	—
511	C₂×C₈	—	2	1	no	—
512	C₂×C₈	—	2	1	no	—
513	C₂×C₈	—	2	1	no	—
514	C₂×C₈	—	2	1	no	—
515	C₂×C₈	—	2	1	no	—
516	C₂×C₈	—	2	1	no	—
517	C₂×C₈	—	2	1	no	—
518	C₂×C₈	—	2	1	no	—
519	C₂×C₈	—	2	1	no	—
520	C₂×C₈	—	2	1	no	—
521	C₂×C₈	—	2	1	no	—
522	C₂×C₈	—	2	1	no	—
523	C₂×C₈	—	2	1	no	—
524	C₂×C₈	—	2	1	no	—
525	C₂×C₈	—	2	1	no	—
526	C₂×C₈	—	2	1	no	—
527	C₂×C₈	—	2	1	no	—
528	C₂×C₈	—	2	1	no	—
529	C₂×C₈	—	2	1	no	—
530	C₂×C₈	—	4	4	no	—
531	C₂×C₈	C₂×D₄×C₁₁	1	2	yes	—
532	C₂×C₈	C₂×D₄×C₁₁	1	2	yes	—
533	C₄⋊C₄	—	2	2	no	—
534	C₄⋊C₄	—	2	2	no	—
535	C₄⋊C₄	—	2	2	no	—
536	C₄⋊C₄	—	2	2	no	—
537	C₂²⋊C₄	—	2	2	no	—
538	C₂²⋊C₄	—	2	2	no	—
539	C₂²⋊C₄	—	2	2	no	—
540	C₂²⋊C₄	—	2	2	no	—
541	C₂²⋊C₄	—	2	2	no	—
542	C₂²⋊C₄	—	2	2	no	—
543	C₂²⋊C₄	—	2	2	no	—
544	C₂²⋊C₄	—	4	1	no	—
545	C₂²⋊C₄	—	4	1	no	—
546	C₂²⋊C₄	C₁₁×M₁₆	1	4	yes	complemented
547	C₄²	—	2	2	no	—
548	C₄²	—	2	2	no	—
549	C₄²	—	2	1	no	—
550	C₄²	—	2	1	no	—
551	C₄²	—	2	1	no	—
552	C₄²	—	2	1	no	—
553	C₄²	—	2	1	no	—
554	C₄²	—	2	1	no	—
555	C₄²	—	2	1	no	—
556	C₄²	—	2	1	no	—
557	C₄²	—	4	1	no	—
558	C₄²	—	4	1	no	—
559	C₄²	C₂×D₄×C₁₁	1	2	yes	—
560	C₄²	C₁₁×#41	1	2	yes	—
561	C₁₁	#22216	1	1	yes	characteristic, direct product factor, Sylow
562	C₂³	—	2	1	no	—
563	C₂³	—	2	1	no	—
564	C₂³	—	2	1	no	—
565	C₂³	—	2	1	no	—
566	C₂³	—	2	1	no	—
567	C₂³	—	2	1	no	—
568	C₂³	—	2	1	no	—
569	C₂³	—	2	1	no	—
570	C₂³	—	2	1	no	—
571	C₂³	—	2	1	no	—
572	C₂³	—	2	1	no	—
573	C₂³	—	2	1	no	—
574	C₂³	—	2	1	no	—
575	C₂³	C₂×C₁₁×M₁₆	1	2	yes	—
576	C₂³	C₂³×C₄×C₁₁	1	1	yes	characteristic
577	Q₈	—	4	4	no	—
578	D₄	—	4	4	no	—
579	C₂×C₄	—	2	1	no	—
580	C₂×C₄	—	2	1	no	—
581	C₂×C₄	—	2	1	no	—
582	C₂×C₄	—	2	1	no	—
583	C₂×C₄	—	2	1	no	—
584	C₂×C₄	—	2	1	no	—
585	C₂×C₄	—	2	1	no	—
586	C₂×C₄	—	2	1	no	—
587	C₂×C₄	—	2	1	no	—
588	C₂×C₄	—	2	1	no	—
589	C₂×C₄	—	2	1	no	—
590	C₂×C₄	—	2	1	no	—
591	C₂×C₄	—	2	1	no	—
592	C₂×C₄	—	2	1	no	—
593	C₂×C₄	—	2	1	no	—
594	C₂×C₄	—	2	1	no	—
595	C₂×C₄	—	2	1	no	—
596	C₂×C₄	—	2	1	no	—
597	C₂×C₄	—	2	1	no	—
598	C₂×C₄	—	2	1	no	—
599	C₂×C₄	—	2	1	no	—
600	C₂×C₄	—	2	1	no	—
601	C₂×C₄	—	2	1	no	—
602	C₂×C₄	—	2	1	no	—
603	C₂×C₄	—	2	1	no	—
604	C₂×C₄	—	2	1	no	—
605	C₂×C₄	—	2	1	no	—
606	C₂×C₄	—	2	1	no	—
607	C₂×C₄	—	2	1	no	—
608	C₂×C₄	—	2	1	no	—
609	C₂×C₄	—	2	1	no	—
610	C₂×C₄	—	4	1	no	—
611	C₂×C₄	—	4	1	no	—
612	C₂×C₄	—	4	1	no	—
613	C₂×C₄	—	4	1	no	—
614	C₂×C₄	—	4	1	no	—
615	C₂×C₄	—	4	1	no	—
616	C₂×C₄	—	4	1	no	—
617	C₂×C₄	—	4	1	no	—
618	C₂×C₄	C₄×D₄×C₁₁	1	2	yes	—
619	C₂×C₄	C₄×D₄×C₁₁	1	2	yes	—
620	C₂×C₄	C₂×C₁₁×M₁₆	1	2	yes	—
621	C₂×C₄	C₂×C₁₁×M₁₆	1	2	yes	—
622	C₂×C₄	C₁₁×#131	1	2	yes	—
623	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
624	C₂×C₄	C₂×C₁₁×#41	1	1	yes	characteristic
625	C₂×C₄	C₁₁×H(5,𝔽₂)	1	1	yes	characteristic
626	C₂×C₄	C₁₁×H(5,𝔽₂)	1	1	yes	characteristic
627	C₂×C₄	C₁₁×2₋¹⁺⁴	1	1	yes	characteristic
628	C₂×C₄	C₁₁×2₋¹⁺⁴	1	1	yes	characteristic
629	C₈	—	2	2	no	—
630	C₈	—	2	2	no	—
631	C₈	—	4	1	no	—
632	C₈	—	4	1	no	—
633	C₈	—	4	1	no	—
634	C₈	—	4	1	no	—
635	C₈	—	4	1	no	—
636	C₈	—	4	1	no	—
637	C₂²	—	2	2	no	—
638	C₂²	—	2	2	no	—
639	C₂²	—	2	2	no	—
640	C₂²	—	4	1	no	—
641	C₂²	—	4	1	no	—
642	C₂²	—	4	1	no	—
643	C₂²	—	4	1	no	—
644	C₂²	—	4	1	no	—
645	C₂²	—	4	1	no	—
646	C₂²	—	4	1	no	—
647	C₂²	—	4	1	no	—
648	C₂²	—	4	1	no	—
649	C₂²	—	4	1	no	—
650	C₂²	—	4	1	no	—
651	C₂²	C₂×C₄×D₄×C₁₁	1	1	yes	characteristic
652	C₂²	C₁₁×#520	1	1	yes	characteristic
653	C₂²	C₁₁×#520	1	1	yes	characteristic
654	C₂²	C₂²×C₁₁×M₁₆	1	1	yes	characteristic
655	C₂²	C₂×C₁₁×#131	1	1	yes	characteristic
656	C₂²	C₁₁×#568	1	1	yes	characteristic
657	C₂²	C₁₁×#568	1	1	yes	characteristic
658	C₄	—	2	2	no	—
659	C₄	—	2	2	no	—
660	C₄	—	2	2	no	—
661	C₄	—	2	2	no	—
662	C₄	—	2	2	no	—
663	C₄	—	4	1	no	—
664	C₄	—	4	1	no	—
665	C₄	—	4	1	no	—
666	C₄	—	4	1	no	—
667	C₄	—	4	1	no	—
668	C₄	—	4	1	no	—
669	C₄	—	4	1	no	—
670	C₄	C₁₁×#535	1	1	yes	characteristic
671	C₄	C₁₁×#536	1	1	yes	characteristic
672	C₄	C₁₁×#542	1	1	yes	characteristic
673	C₄	C₁₁×#542	1	1	yes	characteristic
674	C₂	—	4	2	no	—
675	C₂	—	8	1	no	—
676	C₂	C₁₁×#2326	1	1	yes	characteristic
677	C₂	D₄×C₁₁×M₁₆	1	1	yes	characteristic
678	C₂	C₁₁×#2935	1	1	yes	characteristic
679	C₂	C₁₁×#2989	1	1	yes	characteristic
680	C₂	C₁₁×#2990	1	1	yes	characteristic
681	C₂	C₁₁×#2992	1	1	yes	characteristic
682	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	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
1. C₂×C₁₁×#446	C₂	semidirect
4. C₁₁×#1985	C₂	semidirect
6. C₁₁×#1924	C₂	semidirect
7. C₁₁×#1924	C₂	semidirect
8. C₁₁×#1923	C₂	semidirect
9. C₁₁×#1923	C₂	semidirect
10. C₁₁×#1851	C₂	semidirect
11. C₁₁×#1851	C₂	semidirect
12. C₁₁×#1850	C₂	semidirect
13. C₁₁×#1850	C₂	semidirect
14. C₁₁×#1842	C₂	semidirect
15. C₁₁×#1745	C₂	semidirect
133. #22216	C₁₁	direct (N × H)
206. C₁₁×C₂²⋊C₄	M₁₆	semidirect
221. C₂×#446	C₂×C₁₁	semidirect
224. #1985	C₂×C₁₁	semidirect
226. #1924	C₂×C₁₁	semidirect
227. #1924	C₂×C₁₁	semidirect
228. #1923	C₂×C₁₁	semidirect
229. #1923	C₂×C₁₁	semidirect
230. #1851	C₂×C₁₁	semidirect
231. #1851	C₂×C₁₁	semidirect
232. #1850	C₂×C₁₁	semidirect
233. #1850	C₂×C₁₁	semidirect
234. #1842	C₂×C₁₁	semidirect
235. #1745	C₂×C₁₁	semidirect
546. C₂²⋊C₄	C₁₁×M₁₆	semidirect
561. C₁₁	#22216	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×#435	2
C₄×C₁₁×#124	2
C₁₁×#1985	2
C₁₁×#1955	2
C₁₁×#1924	2
C₁₁×#1923	2
C₁₁×#1851	2
C₁₁×#1850	2
C₁₁×#1842	2
C₁₁×#1745	2
#22216	11

Subgroups — C11×#22216 #14599409

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#22216 #14599409