Subgroups — C₁₁×#34356 #14611549

Order 2816.

4134 conjugacy classes of subgroups.

The subgroup lattice has 562 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₁×#120	C₂	1	1	yes	maximal, characteristic
2	C₁₁×#2375	C₂	1	4	yes	maximal, complemented
3	C₁₁×#2358	C₂	1	4	yes	maximal, complemented
4	C₁₁×#2342	C₂	1	4	yes	maximal, complemented
5	D₄×C₁₁×C₂²⋊C₄	C₂	1	4	yes	maximal, complemented
6	C₁₁×#2321	C₂	1	8	yes	maximal, complemented
7	C₁₁×#2312	C₂	1	2	yes	maximal, complemented
8	C₁₁×#2309	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₁×#2308	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₁₁×#379	C₂	1	2	yes	maximal, complemented
11	C₂⁶×C₁₁	C₂²	1	1	yes	characteristic
12	C₂³×D₄×C₁₁	C₂²	1	1	yes	characteristic
13	C₂³×D₄×C₁₁	C₂²	1	2	yes	—
14	C₂×C₁₁×#120	C₄	1	16	yes	complemented
15	C₂×C₁₁×#120	C₂²	1	4	yes	—
16	C₂×C₁₁×#120	C₂²	1	2	yes	—
17	C₂×C₁₁×#120	C₂²	1	2	yes	—
18	C₂×C₄×D₄×C₁₁	C₂²	1	8	yes	complemented
19	C₂×C₁₁×#117	C₂²	1	2	yes	complemented
20	C₂²×C₁₁×C₂²⋊C₄	C₂²	1	4	yes	—
21	C₂²×C₁₁×C₂²⋊C₄	C₂²	1	1	yes	characteristic
22	C₂²×C₁₁×C₂²⋊C₄	C₂²	1	2	yes	—
23	C₂²×C₁₁×C₂²⋊C₄	C₂²	1	4	yes	complemented
24	C₂²×C₁₁×C₂²⋊C₄	C₂²	1	4	yes	complemented
25	C₂²×C₁₁×C₂²⋊C₄	C₂²	1	2	yes	complemented
26	C₁₁×#390	C₂²	1	4	yes	complemented
27	C₁₁×#390	C₂²	1	4	yes	complemented
28	C₁₁×#390	C₂²	1	8	yes	complemented
29	C₁₁×#388	C₂²	1	8	yes	complemented
30	C₁₁×#388	C₂²	1	8	yes	complemented
31	C₁₁×#388	C₂²	1	8	yes	complemented
32	C₁₁×#388	C₂²	1	8	yes	complemented
33	C₁₁×#386	C₂²	1	4	yes	complemented
34	C₁₁×#386	C₂²	1	4	yes	complemented
35	C₁₁×#386	C₂²	1	8	yes	complemented
36	C₁₁×#386	C₂²	1	8	yes	complemented
37	C₁₁×#385	C₂²	1	8	yes	complemented
38	C₁₁×#381	C₂²	1	2	yes	complemented
39	C₁₁×#380	C₂²	1	4	yes	complemented
40	C₁₁×#379	C₂²	1	2	yes	—
41	C₁₁×#379	C₂²	1	2	yes	—
42	C₁₁×#379	C₂²	1	4	yes	—
43	C₁₁×#379	C₂²	1	4	yes	complemented
44	C₁₁×#379	C₂²	1	4	yes	complemented
45	C₁₁×#379	C₂²	1	2	yes	complemented
46	C₄×C₁₁×C₂²⋊C₄	C₂²	1	4	yes	complemented
47	C₄×C₁₁×C₂²⋊C₄	C₂²	1	8	yes	complemented
48	C₂⁵×C₁₁	—	4	4	no	—
49	C₂⁵×C₁₁	—	4	8	no	—
50	C₂⁵×C₁₁	C₂×C₄	1	8	yes	complemented
51	C₂⁵×C₁₁	C₂³	1	2	yes	—
52	C₂⁵×C₁₁	C₂³	1	1	yes	characteristic
53	C₂⁵×C₁₁	C₂³	1	1	yes	characteristic
54	C₂⁵×C₁₁	C₂³	1	2	yes	—
55	C₂⁵×C₁₁	C₂³	1	1	yes	characteristic
56	C₂⁵×C₁₁	C₂³	1	1	yes	characteristic
57	C₂²×D₄×C₁₁	—	4	4	no	—
58	C₂²×D₄×C₁₁	—	4	8	no	—
59	C₂²×D₄×C₁₁	C₂×C₄	1	8	yes	complemented
60	C₂²×D₄×C₁₁	C₂×C₄	1	16	yes	complemented
61	C₂²×D₄×C₁₁	C₂³	1	4	yes	—
62	C₂²×D₄×C₁₁	C₂³	1	2	yes	—
63	C₂²×D₄×C₁₁	C₂³	1	4	yes	—
64	C₂²×D₄×C₁₁	C₂³	1	2	yes	—
65	C₂³×C₄×C₁₁	C₂³	1	1	yes	characteristic
66	C₂³×C₄×C₁₁	C₂³	1	8	yes	—
67	C₂³×C₄×C₁₁	C₂³	1	2	yes	—
68	C₂³×C₄×C₁₁	C₂³	1	4	yes	complemented
69	C₁₁×#120	C₂×C₄	1	16	yes	complemented
70	C₁₁×#120	C₂×C₄	1	32	yes	complemented
71	C₁₁×#120	C₂×C₄	1	16	yes	complemented
72	C₄×D₄×C₁₁	—	4	16	no	—
73	C₁₁×#117	—	4	4	no	—
74	C₂×C₁₁×C₄⋊C₄	C₂³	1	4	yes	complemented
75	C₂×C₁₁×C₄⋊C₄	C₂³	1	8	yes	complemented
76	C₂×C₁₁×C₂²⋊C₄	—	4	8	no	—
77	C₂×C₁₁×C₂²⋊C₄	—	4	4	no	—
78	C₂×C₁₁×C₂²⋊C₄	—	4	8	no	—
79	C₂×C₁₁×C₂²⋊C₄	—	4	8	no	—
80	C₂×C₁₁×C₂²⋊C₄	C₂×C₄	1	16	yes	complemented
81	C₂×C₁₁×C₂²⋊C₄	C₂×C₄	1	8	yes	complemented
82	C₂×C₁₁×C₂²⋊C₄	C₂³	1	4	yes	—
83	C₂×C₁₁×C₂²⋊C₄	C₂³	1	4	yes	—
84	C₂×C₁₁×C₂²⋊C₄	C₂³	1	8	yes	—
85	C₂×C₁₁×C₂²⋊C₄	C₂³	1	8	yes	—
86	C₂×C₁₁×C₂²⋊C₄	C₂³	1	4	yes	—
87	C₂×C₁₁×C₂²⋊C₄	C₂³	1	4	yes	—
88	C₂×C₁₁×C₂²⋊C₄	C₂³	1	8	yes	—
89	C₂×C₁₁×C₂²⋊C₄	C₂³	1	4	yes	—
90	C₂×C₁₁×C₂²⋊C₄	C₂³	1	4	yes	—
91	C₂×C₁₁×C₂²⋊C₄	C₂³	1	4	yes	—
92	C₂×C₁₁×C₂²⋊C₄	C₂³	1	2	yes	—
93	C₂×C₁₁×C₂²⋊C₄	C₂³	1	2	yes	—
94	C₂×C₁₁×C₂²⋊C₄	C₂³	1	4	yes	—
95	C₂×C₁₁×C₂²⋊C₄	C₂³	1	4	yes	complemented
96	C₂×C₁₁×C₂²⋊C₄	C₂³	1	8	yes	complemented
97	C₂×C₄²×C₁₁	C₂³	1	4	yes	complemented
98	C₂×C₄²×C₁₁	C₂³	1	8	yes	complemented
99	C₁₁×#95	C₂³	1	8	yes	complemented
100	C₁₁×#95	C₂³	1	8	yes	complemented
101	C₁₁×#95	C₂³	1	8	yes	complemented
102	#34356	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
103	C₂⁴×C₁₁	—	2	8	no	—
104	C₂⁴×C₁₁	—	2	8	no	—
105	C₂⁴×C₁₁	—	2	8	no	—
106	C₂⁴×C₁₁	—	2	8	no	—
107	C₂⁴×C₁₁	—	2	4	no	—
108	C₂⁴×C₁₁	—	2	4	no	—
109	C₂⁴×C₁₁	—	4	32	no	—
110	C₂⁴×C₁₁	—	4	16	no	—
111	C₂⁴×C₁₁	—	4	2	no	—
112	C₂⁴×C₁₁	—	4	4	no	—
113	C₂⁴×C₁₁	—	4	4	no	—
114	C₂⁴×C₁₁	—	4	4	no	—
115	C₂⁴×C₁₁	—	4	4	no	—
116	C₂⁴×C₁₁	—	4	2	no	—
117	C₂⁴×C₁₁	—	4	4	no	—
118	C₂⁴×C₁₁	—	4	4	no	—
119	C₂⁴×C₁₁	—	4	64	no	—
120	C₂⁴×C₁₁	C₂²×C₄	1	8	yes	—
121	C₂⁴×C₁₁	C₂²×C₄	1	4	yes	—
122	C₂⁴×C₁₁	C₂²×C₄	1	4	yes	—
123	C₂⁴×C₁₁	C₂²×C₄	1	8	yes	—
124	C₂⁴×C₁₁	C₂²×C₄	1	4	yes	—
125	C₂⁴×C₁₁	C₂²×C₄	1	4	yes	—
126	C₂⁴×C₁₁	C₂⁴	1	2	yes	—
127	C₂⁴×C₁₁	C₂⁴	1	1	yes	characteristic
128	C₂⁴×C₁₁	C₂⁴	1	1	yes	characteristic
129	C₂⁴×C₁₁	C₂⁴	1	2	yes	—
130	C₂⁴×C₁₁	C₂⁴	1	1	yes	characteristic
131	C₂⁴×C₁₁	C₂⁴	1	2	yes	—
132	C₂×D₄×C₁₁	—	2	16	no	—
133	C₂×D₄×C₁₁	—	4	16	no	—
134	C₂×D₄×C₁₁	—	4	2	no	—
135	C₂×D₄×C₁₁	—	4	2	no	—
136	C₂×D₄×C₁₁	—	4	8	no	—
137	C₂×D₄×C₁₁	—	4	2	no	—
138	C₂×D₄×C₁₁	—	4	2	no	—
139	C₂×D₄×C₁₁	—	4	32	no	—
140	C₂×D₄×C₁₁	C₂²×C₄	1	16	yes	—
141	C₂×D₄×C₁₁	C₂²×C₄	1	8	yes	—
142	C₂×D₄×C₁₁	C₂²×C₄	1	8	yes	—
143	C₂×D₄×C₁₁	C₂²×C₄	1	16	yes	—
144	C₂²×C₄×C₁₁	—	2	4	no	—
145	C₂²×C₄×C₁₁	—	2	16	no	—
146	C₂²×C₄×C₁₁	—	4	4	no	—
147	C₂²×C₄×C₁₁	—	4	8	no	—
148	C₂²×C₄×C₁₁	—	4	8	no	—
149	C₂²×C₄×C₁₁	—	4	4	no	—
150	C₂²×C₄×C₁₁	—	4	8	no	—
151	C₂²×C₄×C₁₁	C₂²×C₄	1	4	yes	—
152	C₂²×C₄×C₁₁	C₂²×C₄	1	8	yes	—
153	C₂²×C₄×C₁₁	C₂⁴	1	8	yes	—
154	C₂²×C₄×C₁₁	C₂⁴	1	8	yes	—
155	C₂²×C₄×C₁₁	C₂⁴	1	2	yes	—
156	C₂²×C₄×C₁₁	C₂⁴	1	4	yes	—
157	C₁₁×C₄⋊C₄	—	4	4	no	—
158	C₁₁×C₄⋊C₄	—	4	8	no	—
159	C₁₁×C₂²⋊C₄	—	2	8	no	—
160	C₁₁×C₂²⋊C₄	—	2	8	no	—
161	C₁₁×C₂²⋊C₄	—	2	16	no	—
162	C₁₁×C₂²⋊C₄	—	4	4	no	—
163	C₁₁×C₂²⋊C₄	—	4	8	no	—
164	C₁₁×C₂²⋊C₄	—	4	4	no	—
165	C₁₁×C₂²⋊C₄	—	4	8	no	—
166	C₁₁×C₂²⋊C₄	—	4	4	no	—
167	C₁₁×C₂²⋊C₄	—	4	4	no	—
168	C₁₁×C₂²⋊C₄	—	4	4	no	—
169	C₁₁×C₂²⋊C₄	—	4	8	no	—
170	C₁₁×C₂²⋊C₄	C₂²×C₄	1	16	yes	—
171	C₁₁×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
172	C₁₁×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
173	C₁₁×C₂²⋊C₄	C₂²×C₄	1	16	yes	—
174	C₄²×C₁₁	—	4	4	no	—
175	C₄²×C₁₁	—	4	8	no	—
176	C₂²×#120	C₂×C₁₁	1	1	yes	characteristic
177	#2375	C₂×C₁₁	1	4	yes	complemented
178	#2358	C₂×C₁₁	1	4	yes	complemented
179	#2342	C₂×C₁₁	1	4	yes	complemented
180	D₄×C₂²⋊C₄	C₂×C₁₁	1	4	yes	complemented
181	#2321	C₂×C₁₁	1	8	yes	complemented
182	#2312	C₂×C₁₁	1	2	yes	complemented
183	#2309	C₂×C₁₁	1	1	yes	characteristic, complemented
184	#2308	C₂×C₁₁	1	1	yes	characteristic, complemented
185	C₂×#379	C₂×C₁₁	1	2	yes	complemented
186	C₂³×C₁₁	—	2	4	no	—
187	C₂³×C₁₁	—	2	4	no	—
188	C₂³×C₁₁	—	2	4	no	—
189	C₂³×C₁₁	—	2	16	no	—
190	C₂³×C₁₁	—	2	8	no	—
191	C₂³×C₁₁	—	2	16	no	—
192	C₂³×C₁₁	—	2	16	no	—
193	C₂³×C₁₁	—	2	16	no	—
194	C₂³×C₁₁	—	2	2	no	—
195	C₂³×C₁₁	—	2	4	no	—
196	C₂³×C₁₁	—	2	4	no	—
197	C₂³×C₁₁	—	2	4	no	—
198	C₂³×C₁₁	—	2	4	no	—
199	C₂³×C₁₁	—	2	8	no	—
200	C₂³×C₁₁	—	2	2	no	—
201	C₂³×C₁₁	—	2	2	no	—
202	C₂³×C₁₁	—	2	4	no	—
203	C₂³×C₁₁	—	2	2	no	—
204	C₂³×C₁₁	—	2	8	no	—
205	C₂³×C₁₁	—	4	8	no	—
206	C₂³×C₁₁	—	4	8	no	—
207	C₂³×C₁₁	—	4	4	no	—
208	C₂³×C₁₁	—	4	8	no	—
209	C₂³×C₁₁	—	4	8	no	—
210	C₂³×C₁₁	—	4	4	no	—
211	C₂³×C₁₁	—	4	8	no	—
212	C₂³×C₁₁	—	4	8	no	—
213	C₂³×C₁₁	—	4	16	no	—
214	C₂³×C₁₁	—	4	32	no	—
215	C₂³×C₁₁	—	4	32	no	—
216	C₂³×C₁₁	—	4	16	no	—
217	C₂³×C₁₁	—	4	128	no	—
218	C₂³×C₁₁	—	4	16	no	—
219	C₂³×C₁₁	—	8	8	no	—
220	C₂³×C₁₁	C₂³×C₄	1	4	yes	—
221	C₂³×C₁₁	C₂³×C₄	1	2	yes	—
222	C₂³×C₁₁	C₂³×C₄	1	2	yes	—
223	C₂³×C₁₁	C₂³×C₄	1	4	yes	—
224	C₂³×C₁₁	C₂³×C₄	1	4	yes	—
225	C₂³×C₁₁	C₂³×C₄	1	2	yes	—
226	C₂³×C₁₁	H(5,𝔽₂)	1	4	yes	—
227	C₂³×C₁₁	H(5,𝔽₂)	1	8	yes	—
228	C₂³×C₁₁	C₂⁵	1	1	yes	characteristic
229	D₄×C₁₁	—	2	32	no	—
230	D₄×C₁₁	—	4	8	no	—
231	D₄×C₁₁	—	4	8	no	—
232	D₄×C₁₁	—	4	16	no	—
233	C₂×C₄×C₁₁	—	2	8	no	—
234	C₂×C₄×C₁₁	—	2	2	no	—
235	C₂×C₄×C₁₁	—	2	8	no	—
236	C₂×C₄×C₁₁	—	2	2	no	—
237	C₂×C₄×C₁₁	—	2	8	no	—
238	C₂×C₄×C₁₁	—	2	8	no	—
239	C₂×C₄×C₁₁	—	2	8	no	—
240	C₂×C₄×C₁₁	—	2	8	no	—
241	C₂×C₄×C₁₁	—	2	8	no	—
242	C₂×C₄×C₁₁	—	2	8	no	—
243	C₂×C₄×C₁₁	—	4	8	no	—
244	C₂×C₄×C₁₁	—	8	16	no	—
245	C₂×C₄×C₁₁	—	8	8	no	—
246	C₂×C₄×C₁₁	C₂³×C₄	1	4	yes	—
247	C₂×C₄×C₁₁	C₂³×C₄	1	8	yes	—
248	C₂⁶	C₂²×C₁₁	1	1	yes	characteristic
249	C₂³×D₄	C₂²×C₁₁	1	1	yes	characteristic
250	C₂³×D₄	C₂²×C₁₁	1	2	yes	—
251	C₂×#120	C₄×C₁₁	1	16	yes	complemented
252	C₂×#120	C₂²×C₁₁	1	4	yes	—
253	C₂×#120	C₂²×C₁₁	1	2	yes	—
254	C₂×#120	C₂²×C₁₁	1	2	yes	—
255	C₂×C₄×D₄	C₂²×C₁₁	1	8	yes	complemented
256	C₂×#117	C₂²×C₁₁	1	2	yes	complemented
257	C₂²×C₂²⋊C₄	C₂²×C₁₁	1	4	yes	—
258	C₂²×C₂²⋊C₄	C₂²×C₁₁	1	1	yes	characteristic
259	C₂²×C₂²⋊C₄	C₂²×C₁₁	1	2	yes	—
260	C₂²×C₂²⋊C₄	C₂²×C₁₁	1	4	yes	complemented
261	C₂²×C₂²⋊C₄	C₂²×C₁₁	1	4	yes	complemented
262	C₂²×C₂²⋊C₄	C₂²×C₁₁	1	2	yes	complemented
263	#390	C₂²×C₁₁	1	4	yes	complemented
264	#390	C₂²×C₁₁	1	4	yes	complemented
265	#390	C₂²×C₁₁	1	8	yes	complemented
266	#388	C₂²×C₁₁	1	8	yes	complemented
267	#388	C₂²×C₁₁	1	8	yes	complemented
268	#388	C₂²×C₁₁	1	8	yes	complemented
269	#388	C₂²×C₁₁	1	8	yes	complemented
270	#386	C₂²×C₁₁	1	4	yes	complemented
271	#386	C₂²×C₁₁	1	4	yes	complemented
272	#386	C₂²×C₁₁	1	8	yes	complemented
273	#386	C₂²×C₁₁	1	8	yes	complemented
274	#385	C₂²×C₁₁	1	8	yes	complemented
275	#381	C₂²×C₁₁	1	2	yes	complemented
276	#380	C₂²×C₁₁	1	4	yes	complemented
277	#379	C₂²×C₁₁	1	2	yes	—
278	#379	C₂²×C₁₁	1	2	yes	—
279	#379	C₂²×C₁₁	1	4	yes	—
280	#379	C₂²×C₁₁	1	4	yes	complemented
281	#379	C₂²×C₁₁	1	4	yes	complemented
282	#379	C₂²×C₁₁	1	2	yes	complemented
283	C₄×C₂²⋊C₄	C₂²×C₁₁	1	4	yes	complemented
284	C₄×C₂²⋊C₄	C₂²×C₁₁	1	8	yes	complemented
285	C₂²×C₁₁	—	2	4	no	—
286	C₂²×C₁₁	—	2	4	no	—
287	C₂²×C₁₁	—	2	4	no	—
288	C₂²×C₁₁	—	2	16	no	—
289	C₂²×C₁₁	—	2	8	no	—
290	C₂²×C₁₁	—	2	8	no	—
291	C₂²×C₁₁	—	2	2	no	—
292	C₂²×C₁₁	—	2	4	no	—
293	C₂²×C₁₁	—	2	2	no	—
294	C₂²×C₁₁	—	2	4	no	—
295	C₂²×C₁₁	—	2	4	no	—
296	C₂²×C₁₁	—	2	4	no	—
297	C₂²×C₁₁	—	2	4	no	—
298	C₂²×C₁₁	—	2	4	no	—
299	C₂²×C₁₁	—	4	32	no	—
300	C₂²×C₁₁	—	4	16	no	—
301	C₂²×C₁₁	—	4	16	no	—
302	C₂²×C₁₁	—	4	32	no	—
303	C₂²×C₁₁	—	4	16	no	—
304	C₂²×C₁₁	—	4	4	no	—
305	C₂²×C₁₁	—	4	4	no	—
306	C₂²×C₁₁	—	4	8	no	—
307	C₂²×C₁₁	—	4	4	no	—
308	C₂²×C₁₁	—	4	4	no	—
309	C₂²×C₁₁	—	8	8	no	—
310	C₂²×C₁₁	#518	1	4	yes	—
311	C₂²×C₁₁	#518	1	8	yes	—
312	C₂²×C₁₁	C₂⁴×C₄	1	1	yes	characteristic
313	C₂²×C₁₁	C₂×H(5,𝔽₂)	1	2	yes	—
314	C₂²×C₁₁	C₂×H(5,𝔽₂)	1	4	yes	—
315	C₄×C₁₁	—	2	4	no	—
316	C₄×C₁₁	—	2	8	no	—
317	C₄×C₁₁	—	4	8	no	—
318	C₄×C₁₁	—	4	8	no	—
319	C₂⁵	—	4	4	no	—
320	C₂⁵	—	4	8	no	—
321	C₂⁵	C₂×C₄×C₁₁	1	8	yes	complemented
322	C₂⁵	C₂³×C₁₁	1	2	yes	—
323	C₂⁵	C₂³×C₁₁	1	1	yes	characteristic
324	C₂⁵	C₂³×C₁₁	1	1	yes	characteristic
325	C₂⁵	C₂³×C₁₁	1	2	yes	—
326	C₂⁵	C₂³×C₁₁	1	1	yes	characteristic
327	C₂⁵	C₂³×C₁₁	1	1	yes	characteristic
328	C₂²×D₄	—	4	4	no	—
329	C₂²×D₄	—	4	8	no	—
330	C₂²×D₄	C₂×C₄×C₁₁	1	8	yes	complemented
331	C₂²×D₄	C₂×C₄×C₁₁	1	16	yes	complemented
332	C₂²×D₄	C₂³×C₁₁	1	4	yes	—
333	C₂²×D₄	C₂³×C₁₁	1	2	yes	—
334	C₂²×D₄	C₂³×C₁₁	1	4	yes	—
335	C₂²×D₄	C₂³×C₁₁	1	2	yes	—
336	C₂³×C₄	C₂³×C₁₁	1	1	yes	characteristic
337	C₂³×C₄	C₂³×C₁₁	1	8	yes	—
338	C₂³×C₄	C₂³×C₁₁	1	2	yes	—
339	C₂³×C₄	C₂³×C₁₁	1	4	yes	complemented
340	#120	C₂×C₄×C₁₁	1	16	yes	complemented
341	#120	C₂×C₄×C₁₁	1	32	yes	complemented
342	#120	C₂×C₄×C₁₁	1	16	yes	complemented
343	C₄×D₄	—	4	16	no	—
344	#117	—	4	4	no	—
345	C₂×C₄⋊C₄	C₂³×C₁₁	1	4	yes	complemented
346	C₂×C₄⋊C₄	C₂³×C₁₁	1	8	yes	complemented
347	C₂×C₂²⋊C₄	—	4	8	no	—
348	C₂×C₂²⋊C₄	—	4	4	no	—
349	C₂×C₂²⋊C₄	—	4	8	no	—
350	C₂×C₂²⋊C₄	—	4	8	no	—
351	C₂×C₂²⋊C₄	C₂×C₄×C₁₁	1	16	yes	complemented
352	C₂×C₂²⋊C₄	C₂×C₄×C₁₁	1	8	yes	complemented
353	C₂×C₂²⋊C₄	C₂³×C₁₁	1	4	yes	—
354	C₂×C₂²⋊C₄	C₂³×C₁₁	1	4	yes	—
355	C₂×C₂²⋊C₄	C₂³×C₁₁	1	8	yes	—
356	C₂×C₂²⋊C₄	C₂³×C₁₁	1	8	yes	—
357	C₂×C₂²⋊C₄	C₂³×C₁₁	1	4	yes	—
358	C₂×C₂²⋊C₄	C₂³×C₁₁	1	4	yes	—
359	C₂×C₂²⋊C₄	C₂³×C₁₁	1	8	yes	—
360	C₂×C₂²⋊C₄	C₂³×C₁₁	1	4	yes	—
361	C₂×C₂²⋊C₄	C₂³×C₁₁	1	4	yes	—
362	C₂×C₂²⋊C₄	C₂³×C₁₁	1	4	yes	—
363	C₂×C₂²⋊C₄	C₂³×C₁₁	1	2	yes	—
364	C₂×C₂²⋊C₄	C₂³×C₁₁	1	2	yes	—
365	C₂×C₂²⋊C₄	C₂³×C₁₁	1	4	yes	—
366	C₂×C₂²⋊C₄	C₂³×C₁₁	1	4	yes	complemented
367	C₂×C₂²⋊C₄	C₂³×C₁₁	1	8	yes	complemented
368	C₂×C₄²	C₂³×C₁₁	1	4	yes	complemented
369	C₂×C₄²	C₂³×C₁₁	1	8	yes	complemented
370	#95	C₂³×C₁₁	1	8	yes	complemented
371	#95	C₂³×C₁₁	1	8	yes	complemented
372	#95	C₂³×C₁₁	1	8	yes	complemented
373	C₂×C₁₁	—	2	4	no	—
374	C₂×C₁₁	—	2	8	no	—
375	C₂×C₁₁	—	4	4	no	—
376	C₂×C₁₁	—	4	2	no	—
377	C₂×C₁₁	—	4	2	no	—
378	C₂×C₁₁	—	4	4	no	—
379	C₂×C₁₁	C₂×#518	1	1	yes	characteristic
380	C₂×C₁₁	C₂×#518	1	2	yes	—
381	C₂×C₁₁	#3532	1	4	yes	—
382	C₂⁴	—	2	8	no	—
383	C₂⁴	—	2	8	no	—
384	C₂⁴	—	2	8	no	—
385	C₂⁴	—	2	8	no	—
386	C₂⁴	—	2	4	no	—
387	C₂⁴	—	2	4	no	—
388	C₂⁴	—	4	32	no	—
389	C₂⁴	—	4	16	no	—
390	C₂⁴	—	4	2	no	—
391	C₂⁴	—	4	4	no	—
392	C₂⁴	—	4	4	no	—
393	C₂⁴	—	4	4	no	—
394	C₂⁴	—	4	4	no	—
395	C₂⁴	—	4	2	no	—
396	C₂⁴	—	4	4	no	—
397	C₂⁴	—	4	4	no	—
398	C₂⁴	—	4	64	no	—
399	C₂⁴	C₂²×C₄×C₁₁	1	8	yes	—
400	C₂⁴	C₂²×C₄×C₁₁	1	4	yes	—
401	C₂⁴	C₂²×C₄×C₁₁	1	4	yes	—
402	C₂⁴	C₂²×C₄×C₁₁	1	8	yes	—
403	C₂⁴	C₂²×C₄×C₁₁	1	4	yes	—
404	C₂⁴	C₂²×C₄×C₁₁	1	4	yes	—
405	C₂⁴	C₂⁴×C₁₁	1	2	yes	—
406	C₂⁴	C₂⁴×C₁₁	1	1	yes	characteristic
407	C₂⁴	C₂⁴×C₁₁	1	1	yes	characteristic
408	C₂⁴	C₂⁴×C₁₁	1	2	yes	—
409	C₂⁴	C₂⁴×C₁₁	1	1	yes	characteristic
410	C₂⁴	C₂⁴×C₁₁	1	2	yes	—
411	C₂×D₄	—	2	16	no	—
412	C₂×D₄	—	4	16	no	—
413	C₂×D₄	—	4	2	no	—
414	C₂×D₄	—	4	2	no	—
415	C₂×D₄	—	4	8	no	—
416	C₂×D₄	—	4	2	no	—
417	C₂×D₄	—	4	2	no	—
418	C₂×D₄	—	4	32	no	—
419	C₂×D₄	C₂²×C₄×C₁₁	1	16	yes	—
420	C₂×D₄	C₂²×C₄×C₁₁	1	8	yes	—
421	C₂×D₄	C₂²×C₄×C₁₁	1	8	yes	—
422	C₂×D₄	C₂²×C₄×C₁₁	1	16	yes	—
423	C₂²×C₄	—	2	4	no	—
424	C₂²×C₄	—	2	16	no	—
425	C₂²×C₄	—	4	4	no	—
426	C₂²×C₄	—	4	8	no	—
427	C₂²×C₄	—	4	8	no	—
428	C₂²×C₄	—	4	4	no	—
429	C₂²×C₄	—	4	8	no	—
430	C₂²×C₄	C₂²×C₄×C₁₁	1	4	yes	—
431	C₂²×C₄	C₂²×C₄×C₁₁	1	8	yes	—
432	C₂²×C₄	C₂⁴×C₁₁	1	8	yes	—
433	C₂²×C₄	C₂⁴×C₁₁	1	8	yes	—
434	C₂²×C₄	C₂⁴×C₁₁	1	2	yes	—
435	C₂²×C₄	C₂⁴×C₁₁	1	4	yes	—
436	C₄⋊C₄	—	4	4	no	—
437	C₄⋊C₄	—	4	8	no	—
438	C₂²⋊C₄	—	2	8	no	—
439	C₂²⋊C₄	—	2	8	no	—
440	C₂²⋊C₄	—	2	16	no	—
441	C₂²⋊C₄	—	4	4	no	—
442	C₂²⋊C₄	—	4	8	no	—
443	C₂²⋊C₄	—	4	4	no	—
444	C₂²⋊C₄	—	4	8	no	—
445	C₂²⋊C₄	—	4	4	no	—
446	C₂²⋊C₄	—	4	4	no	—
447	C₂²⋊C₄	—	4	4	no	—
448	C₂²⋊C₄	—	4	8	no	—
449	C₂²⋊C₄	C₂²×C₄×C₁₁	1	16	yes	—
450	C₂²⋊C₄	C₂²×C₄×C₁₁	1	8	yes	—
451	C₂²⋊C₄	C₂²×C₄×C₁₁	1	8	yes	—
452	C₂²⋊C₄	C₂²×C₄×C₁₁	1	16	yes	—
453	C₄²	—	4	4	no	—
454	C₄²	—	4	8	no	—
455	C₁₁	#34356	1	1	yes	characteristic, direct product factor, Sylow
456	C₂³	—	2	4	no	—
457	C₂³	—	2	4	no	—
458	C₂³	—	2	4	no	—
459	C₂³	—	2	16	no	—
460	C₂³	—	2	8	no	—
461	C₂³	—	2	16	no	—
462	C₂³	—	2	16	no	—
463	C₂³	—	2	16	no	—
464	C₂³	—	2	2	no	—
465	C₂³	—	2	4	no	—
466	C₂³	—	2	4	no	—
467	C₂³	—	2	4	no	—
468	C₂³	—	2	4	no	—
469	C₂³	—	2	8	no	—
470	C₂³	—	2	2	no	—
471	C₂³	—	2	2	no	—
472	C₂³	—	2	4	no	—
473	C₂³	—	2	2	no	—
474	C₂³	—	2	8	no	—
475	C₂³	—	4	8	no	—
476	C₂³	—	4	8	no	—
477	C₂³	—	4	4	no	—
478	C₂³	—	4	8	no	—
479	C₂³	—	4	8	no	—
480	C₂³	—	4	4	no	—
481	C₂³	—	4	8	no	—
482	C₂³	—	4	8	no	—
483	C₂³	—	4	16	no	—
484	C₂³	—	4	32	no	—
485	C₂³	—	4	32	no	—
486	C₂³	—	4	16	no	—
487	C₂³	—	4	128	no	—
488	C₂³	—	4	16	no	—
489	C₂³	—	8	8	no	—
490	C₂³	C₂³×C₄×C₁₁	1	4	yes	—
491	C₂³	C₂³×C₄×C₁₁	1	2	yes	—
492	C₂³	C₂³×C₄×C₁₁	1	2	yes	—
493	C₂³	C₂³×C₄×C₁₁	1	4	yes	—
494	C₂³	C₂³×C₄×C₁₁	1	4	yes	—
495	C₂³	C₂³×C₄×C₁₁	1	2	yes	—
496	C₂³	C₁₁×H(5,𝔽₂)	1	4	yes	—
497	C₂³	C₁₁×H(5,𝔽₂)	1	8	yes	—
498	C₂³	C₂⁵×C₁₁	1	1	yes	characteristic
499	D₄	—	2	32	no	—
500	D₄	—	4	8	no	—
501	D₄	—	4	8	no	—
502	D₄	—	4	16	no	—
503	C₂×C₄	—	2	8	no	—
504	C₂×C₄	—	2	2	no	—
505	C₂×C₄	—	2	8	no	—
506	C₂×C₄	—	2	2	no	—
507	C₂×C₄	—	2	8	no	—
508	C₂×C₄	—	2	8	no	—
509	C₂×C₄	—	2	8	no	—
510	C₂×C₄	—	2	8	no	—
511	C₂×C₄	—	2	8	no	—
512	C₂×C₄	—	2	8	no	—
513	C₂×C₄	—	4	8	no	—
514	C₂×C₄	—	8	16	no	—
515	C₂×C₄	—	8	8	no	—
516	C₂×C₄	C₂³×C₄×C₁₁	1	4	yes	—
517	C₂×C₄	C₂³×C₄×C₁₁	1	8	yes	—
518	C₂²	—	2	4	no	—
519	C₂²	—	2	4	no	—
520	C₂²	—	2	4	no	—
521	C₂²	—	2	16	no	—
522	C₂²	—	2	8	no	—
523	C₂²	—	2	8	no	—
524	C₂²	—	2	2	no	—
525	C₂²	—	2	4	no	—
526	C₂²	—	2	2	no	—
527	C₂²	—	2	4	no	—
528	C₂²	—	2	4	no	—
529	C₂²	—	2	4	no	—
530	C₂²	—	2	4	no	—
531	C₂²	—	2	4	no	—
532	C₂²	—	4	32	no	—
533	C₂²	—	4	16	no	—
534	C₂²	—	4	16	no	—
535	C₂²	—	4	32	no	—
536	C₂²	—	4	16	no	—
537	C₂²	—	4	4	no	—
538	C₂²	—	4	4	no	—
539	C₂²	—	4	8	no	—
540	C₂²	—	4	4	no	—
541	C₂²	—	4	4	no	—
542	C₂²	—	8	8	no	—
543	C₂²	C₁₁×#518	1	4	yes	—
544	C₂²	C₁₁×#518	1	8	yes	—
545	C₂²	C₂⁴×C₄×C₁₁	1	1	yes	characteristic
546	C₂²	C₂×C₁₁×H(5,𝔽₂)	1	2	yes	—
547	C₂²	C₂×C₁₁×H(5,𝔽₂)	1	4	yes	—
548	C₄	—	2	4	no	—
549	C₄	—	2	8	no	—
550	C₄	—	4	8	no	—
551	C₄	—	4	8	no	—
552	C₂	—	2	4	no	—
553	C₂	—	2	8	no	—
554	C₂	—	4	4	no	—
555	C₂	—	4	2	no	—
556	C₂	—	4	2	no	—
557	C₂	—	4	4	no	—
558	C₂	C₂×C₁₁×#518	1	1	yes	characteristic
559	C₂	C₂×C₁₁×#518	1	2	yes	—
560	C₂	C₁₁×#3532	1	4	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₁	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₁₁
Frattini, cosocle	C₂³	C₂⁵×C₁₁
prime radical	C₂²×C₁₁×#120	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₁ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
2. C₁₁×#2375	C₂	semidirect
3. C₁₁×#2358	C₂	semidirect
4. C₁₁×#2342	C₂	semidirect
5. D₄×C₁₁×C₂²⋊C₄	C₂	semidirect
6. C₁₁×#2321	C₂	semidirect
7. C₁₁×#2312	C₂	semidirect
8. C₁₁×#2309	C₂	semidirect
9. C₁₁×#2308	C₂	semidirect
10. C₂×C₁₁×#379	C₂	semidirect
14. C₂×C₁₁×#120	C₄	semidirect
18. C₂×C₄×D₄×C₁₁	C₂²	semidirect
19. C₂×C₁₁×#117	C₂²	semidirect
23. C₂²×C₁₁×C₂²⋊C₄	C₂²	semidirect
24. C₂²×C₁₁×C₂²⋊C₄	C₂²	semidirect
25. C₂²×C₁₁×C₂²⋊C₄	C₂²	semidirect
26. C₁₁×#390	C₂²	semidirect
27. C₁₁×#390	C₂²	semidirect
28. C₁₁×#390	C₂²	semidirect
29. C₁₁×#388	C₂²	semidirect
30. C₁₁×#388	C₂²	semidirect
31. C₁₁×#388	C₂²	semidirect
32. C₁₁×#388	C₂²	semidirect
33. C₁₁×#386	C₂²	semidirect
34. C₁₁×#386	C₂²	semidirect
35. C₁₁×#386	C₂²	semidirect
36. C₁₁×#386	C₂²	semidirect
37. C₁₁×#385	C₂²	semidirect
38. C₁₁×#381	C₂²	semidirect
39. C₁₁×#380	C₂²	semidirect
43. C₁₁×#379	C₂²	semidirect
44. C₁₁×#379	C₂²	semidirect
45. C₁₁×#379	C₂²	semidirect
46. C₄×C₁₁×C₂²⋊C₄	C₂²	semidirect
47. C₄×C₁₁×C₂²⋊C₄	C₂²	semidirect
50. C₂⁵×C₁₁	C₂×C₄	semidirect
59. C₂²×D₄×C₁₁	C₂×C₄	semidirect
60. C₂²×D₄×C₁₁	C₂×C₄	semidirect
68. C₂³×C₄×C₁₁	C₂³	semidirect
69. C₁₁×#120	C₂×C₄	semidirect
70. C₁₁×#120	C₂×C₄	semidirect
71. C₁₁×#120	C₂×C₄	semidirect
74. C₂×C₁₁×C₄⋊C₄	C₂³	semidirect
75. C₂×C₁₁×C₄⋊C₄	C₂³	semidirect
80. C₂×C₁₁×C₂²⋊C₄	C₂×C₄	semidirect
81. C₂×C₁₁×C₂²⋊C₄	C₂×C₄	semidirect
95. C₂×C₁₁×C₂²⋊C₄	C₂³	semidirect
96. C₂×C₁₁×C₂²⋊C₄	C₂³	semidirect
97. C₂×C₄²×C₁₁	C₂³	semidirect
98. C₂×C₄²×C₁₁	C₂³	semidirect
99. C₁₁×#95	C₂³	semidirect
100. C₁₁×#95	C₂³	semidirect
101. C₁₁×#95	C₂³	semidirect
102. #34356	C₁₁	direct (N × H)
177. #2375	C₂×C₁₁	semidirect
178. #2358	C₂×C₁₁	semidirect
179. #2342	C₂×C₁₁	semidirect
180. D₄×C₂²⋊C₄	C₂×C₁₁	semidirect
181. #2321	C₂×C₁₁	semidirect
182. #2312	C₂×C₁₁	semidirect
183. #2309	C₂×C₁₁	semidirect
184. #2308	C₂×C₁₁	semidirect
185. C₂×#379	C₂×C₁₁	semidirect
251. C₂×#120	C₄×C₁₁	semidirect
255. C₂×C₄×D₄	C₂²×C₁₁	semidirect
256. C₂×#117	C₂²×C₁₁	semidirect
260. C₂²×C₂²⋊C₄	C₂²×C₁₁	semidirect
261. C₂²×C₂²⋊C₄	C₂²×C₁₁	semidirect
262. C₂²×C₂²⋊C₄	C₂²×C₁₁	semidirect
263. #390	C₂²×C₁₁	semidirect
264. #390	C₂²×C₁₁	semidirect
265. #390	C₂²×C₁₁	semidirect
266. #388	C₂²×C₁₁	semidirect
267. #388	C₂²×C₁₁	semidirect
268. #388	C₂²×C₁₁	semidirect
269. #388	C₂²×C₁₁	semidirect
270. #386	C₂²×C₁₁	semidirect
271. #386	C₂²×C₁₁	semidirect
272. #386	C₂²×C₁₁	semidirect
273. #386	C₂²×C₁₁	semidirect
274. #385	C₂²×C₁₁	semidirect
275. #381	C₂²×C₁₁	semidirect
276. #380	C₂²×C₁₁	semidirect
280. #379	C₂²×C₁₁	semidirect
281. #379	C₂²×C₁₁	semidirect
282. #379	C₂²×C₁₁	semidirect
283. C₄×C₂²⋊C₄	C₂²×C₁₁	semidirect
284. C₄×C₂²⋊C₄	C₂²×C₁₁	semidirect
321. C₂⁵	C₂×C₄×C₁₁	semidirect
330. C₂²×D₄	C₂×C₄×C₁₁	semidirect
331. C₂²×D₄	C₂×C₄×C₁₁	semidirect
339. C₂³×C₄	C₂³×C₁₁	semidirect
340. #120	C₂×C₄×C₁₁	semidirect
341. #120	C₂×C₄×C₁₁	semidirect
342. #120	C₂×C₄×C₁₁	semidirect
345. C₂×C₄⋊C₄	C₂³×C₁₁	semidirect
346. C₂×C₄⋊C₄	C₂³×C₁₁	semidirect
351. C₂×C₂²⋊C₄	C₂×C₄×C₁₁	semidirect
352. C₂×C₂²⋊C₄	C₂×C₄×C₁₁	semidirect
366. C₂×C₂²⋊C₄	C₂³×C₁₁	semidirect
367. C₂×C₂²⋊C₄	C₂³×C₁₁	semidirect
368. C₂×C₄²	C₂³×C₁₁	semidirect
369. C₂×C₄²	C₂³×C₁₁	semidirect
370. #95	C₂³×C₁₁	semidirect
371. #95	C₂³×C₁₁	semidirect
372. #95	C₂³×C₁₁	semidirect
455. C₁₁	#34356	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂²×C₁₁×#120	2
C₁₁×#2375	2
C₁₁×#2358	2
C₁₁×#2342	2
D₄×C₁₁×C₂²⋊C₄	2
C₁₁×#2321	2
C₁₁×#2312	2
C₁₁×#2309	2
C₁₁×#2308	2
C₂×C₁₁×#379	2
#34356	11

Subgroups — C11×#34356 #14611549

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#34356 #14611549