Subgroups — C₁₁×#34246 #14611439

Order 2816.

3194 conjugacy classes of subgroups.

The subgroup lattice has 570 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₁×#121	C₂	1	1	yes	maximal, characteristic
2	C₁₁×#2364	C₂	1	4	yes	maximal, complemented
3	C₁₁×#2363	C₂	1	4	yes	maximal, complemented
4	C₁₁×#2345	C₂	1	2	yes	maximal, complemented
5	D₄×C₁₁×C₂²⋊C₄	C₂	1	4	yes	maximal, complemented
6	D₄×C₁₁×C₂²⋊C₄	C₂	1	2	yes	maximal, complemented
7	C₁₁×#2333	C₂	1	4	yes	maximal, complemented
8	C₁₁×#2312	C₂	1	2	yes	maximal, complemented
9	C₄×C₁₁×#121	C₂	1	4	yes	maximal, complemented
10	C₁₁×#2280	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₁×#2273	C₂	1	2	yes	maximal, complemented
12	C₂×C₄×C₁₁×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂³×D₄×C₁₁	C₂²	1	1	yes	characteristic
14	C₂³×D₄×C₁₁	C₂²	1	2	yes	—
15	C₂⁴×C₄×C₁₁	C₂²	1	1	yes	characteristic
16	C₂×C₁₁×#121	C₄	1	16	yes	complemented
17	C₂×C₁₁×#121	C₂²	1	2	yes	—
18	C₂×C₁₁×#121	C₂²	1	2	yes	—
19	C₂×C₁₁×#121	C₂²	1	2	yes	—
20	C₂×C₁₁×#121	C₂²	1	2	yes	—
21	C₂×C₄×D₄×C₁₁	C₂²	1	4	yes	complemented
22	C₂×C₄×D₄×C₁₁	C₂²	1	8	yes	complemented
23	C₂×C₁₁×#117	C₂²	1	2	yes	complemented
24	C₂²×C₁₁×C₄⋊C₄	C₂²	1	1	yes	characteristic
25	C₂²×C₁₁×C₂²⋊C₄	C₂²	1	2	yes	—
26	C₂²×C₁₁×C₂²⋊C₄	C₂²	1	4	yes	—
27	C₂²×C₁₁×C₂²⋊C₄	C₂²	1	2	yes	—
28	C₂²×C₄²×C₁₁	C₂²	1	2	yes	complemented
29	C₁₁×#390	C₂²	1	4	yes	complemented
30	C₁₁×#390	C₂²	1	8	yes	complemented
31	C₁₁×#389	C₂²	1	4	yes	complemented
32	C₁₁×#388	C₂²	1	8	yes	complemented
33	C₁₁×#388	C₂²	1	8	yes	complemented
34	C₁₁×#387	C₂²	1	8	yes	complemented
35	C₁₁×#386	C₂²	1	8	yes	complemented
36	C₁₁×#386	C₂²	1	8	yes	complemented
37	C₁₁×#386	C₂²	1	8	yes	complemented
38	C₁₁×#381	C₂²	1	2	yes	complemented
39	C₁₁×#380	C₂²	1	2	yes	—
40	C₁₁×#380	C₂²	1	4	yes	—
41	C₁₁×#380	C₂²	1	2	yes	complemented
42	C₁₁×#379	C₂²	1	2	yes	—
43	C₁₁×#379	C₂²	1	4	yes	—
44	C₄×C₁₁×C₄⋊C₄	C₂²	1	4	yes	complemented
45	C₄×C₁₁×C₂²⋊C₄	C₂²	1	1	yes	characteristic
46	C₄×C₁₁×C₂²⋊C₄	C₂²	1	1	yes	characteristic
47	C₄×C₁₁×C₂²⋊C₄	C₂²	1	2	yes	—
48	C₄×C₁₁×C₂²⋊C₄	C₂²	1	2	yes	—
49	C₄×C₁₁×C₂²⋊C₄	C₂²	1	4	yes	—
50	C₄×C₁₁×C₂²⋊C₄	C₂²	1	2	yes	complemented
51	C₄×C₁₁×C₂²⋊C₄	C₂²	1	2	yes	complemented
52	C₄×C₁₁×C₂²⋊C₄	C₂²	1	8	yes	complemented
53	C₄×C₁₁×C₂²⋊C₄	C₂²	1	8	yes	complemented
54	C₄×C₁₁×C₂²⋊C₄	C₂²	1	2	yes	complemented
55	C₂×C₁₁×#95	C₂²	1	2	yes	complemented
56	C₂⁵×C₁₁	C₂³	1	1	yes	characteristic
57	C₂⁵×C₁₁	C₂³	1	2	yes	—
58	C₂²×D₄×C₁₁	—	4	4	no	—
59	C₂²×D₄×C₁₁	—	4	8	no	—
60	C₂²×D₄×C₁₁	C₂×C₄	1	8	yes	complemented
61	C₂²×D₄×C₁₁	C₂×C₄	1	16	yes	complemented
62	C₂²×D₄×C₁₁	C₂³	1	4	yes	—
63	C₂²×D₄×C₁₁	C₂³	1	2	yes	—
64	C₂²×D₄×C₁₁	C₂³	1	2	yes	—
65	C₂²×D₄×C₁₁	C₂³	1	4	yes	—
66	C₂³×C₄×C₁₁	—	4	4	no	—
67	C₂³×C₄×C₁₁	C₂×C₄	1	8	yes	complemented
68	C₂³×C₄×C₁₁	C₂³	1	4	yes	—
69	C₂³×C₄×C₁₁	C₂³	1	1	yes	characteristic
70	C₂³×C₄×C₁₁	C₂³	1	1	yes	characteristic
71	C₂³×C₄×C₁₁	C₂³	1	1	yes	characteristic
72	C₂³×C₄×C₁₁	C₂³	1	8	yes	—
73	C₂³×C₄×C₁₁	C₂³	1	1	yes	characteristic
74	C₂³×C₄×C₁₁	C₂³	1	2	yes	—
75	C₂³×C₄×C₁₁	C₂³	1	1	yes	characteristic
76	C₂³×C₄×C₁₁	C₂³	1	1	yes	characteristic
77	C₁₁×#121	C₂×C₄	1	16	yes	complemented
78	C₁₁×#121	C₂×C₄	1	16	yes	complemented
79	C₁₁×#121	C₂×C₄	1	16	yes	complemented
80	C₁₁×#121	C₂×C₄	1	16	yes	complemented
81	C₄×D₄×C₁₁	—	4	8	no	—
82	C₄×D₄×C₁₁	—	4	16	no	—
83	C₁₁×#117	—	4	4	no	—
84	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	8	yes	complemented
85	C₂×C₁₁×C₄⋊C₄	C₂³	1	4	yes	—
86	C₂×C₁₁×C₄⋊C₄	C₂³	1	8	yes	—
87	C₂×C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
88	C₂×C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
89	C₂×C₁₁×C₂²⋊C₄	—	2	8	no	—
90	C₂×C₁₁×C₂²⋊C₄	—	2	16	no	—
91	C₂×C₁₁×C₂²⋊C₄	C₂×C₄	1	16	yes	complemented
92	C₂×C₁₁×C₂²⋊C₄	C₂³	1	2	yes	—
93	C₂×C₁₁×C₂²⋊C₄	C₂³	1	4	yes	—
94	C₂×C₁₁×C₂²⋊C₄	C₂³	1	4	yes	—
95	C₂×C₁₁×C₂²⋊C₄	C₂³	1	8	yes	—
96	C₂×C₁₁×C₂²⋊C₄	C₂³	1	4	yes	—
97	C₂×C₁₁×C₂²⋊C₄	C₂³	1	4	yes	—
98	C₂×C₁₁×C₂²⋊C₄	C₂³	1	8	yes	—
99	C₂×C₁₁×C₂²⋊C₄	C₂³	1	8	yes	—
100	C₂×C₁₁×C₂²⋊C₄	C₂³	1	4	yes	—
101	C₂×C₁₁×C₂²⋊C₄	C₂³	1	4	yes	—
102	C₂×C₁₁×C₂²⋊C₄	C₂³	1	2	yes	—
103	C₂×C₄²×C₁₁	—	4	4	no	—
104	C₂×C₄²×C₁₁	C₂³	1	4	yes	—
105	C₂×C₄²×C₁₁	C₂³	1	2	yes	—
106	C₂×C₄²×C₁₁	C₂³	1	2	yes	—
107	C₂×C₄²×C₁₁	C₂³	1	4	yes	—
108	C₂×C₄²×C₁₁	C₂³	1	8	yes	—
109	C₁₁×#95	C₂³	1	2	yes	—
110	C₁₁×#95	C₂³	1	4	yes	—
111	C₁₁×#95	C₂³	1	2	yes	—
112	C₁₁×#95	C₂³	1	4	yes	—
113	C₁₁×#95	C₂³	1	8	yes	—
114	C₁₁×#95	C₂³	1	4	yes	—
115	C₁₁×#95	C₂³	1	8	yes	—
116	#34246	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
117	C₂⁴×C₁₁	—	2	4	no	—
118	C₂⁴×C₁₁	—	2	4	no	—
119	C₂⁴×C₁₁	—	2	8	no	—
120	C₂⁴×C₁₁	—	4	2	no	—
121	C₂⁴×C₁₁	—	4	4	no	—
122	C₂⁴×C₁₁	—	4	4	no	—
123	C₂⁴×C₁₁	C₂²×C₄	1	4	yes	—
124	C₂⁴×C₁₁	C₂²×C₄	1	8	yes	—
125	C₂⁴×C₁₁	C₂⁴	1	1	yes	characteristic
126	C₂⁴×C₁₁	C₂⁴	1	4	yes	—
127	C₂⁴×C₁₁	C₂⁴	1	1	yes	characteristic
128	C₂⁴×C₁₁	C₂⁴	1	1	yes	characteristic
129	C₂×D₄×C₁₁	—	2	16	no	—
130	C₂×D₄×C₁₁	—	2	8	no	—
131	C₂×D₄×C₁₁	—	4	16	no	—
132	C₂×D₄×C₁₁	—	4	8	no	—
133	C₂×D₄×C₁₁	—	4	4	no	—
134	C₂×D₄×C₁₁	—	4	32	no	—
135	C₂×D₄×C₁₁	C₂²×C₄	1	16	yes	—
136	C₂×D₄×C₁₁	C₂²×C₄	1	8	yes	—
137	C₂×D₄×C₁₁	C₂²×C₄	1	16	yes	—
138	C₂×D₄×C₁₁	C₂²×C₄	1	8	yes	—
139	C₂²×C₄×C₁₁	—	2	4	no	—
140	C₂²×C₄×C₁₁	—	2	4	no	—
141	C₂²×C₄×C₁₁	—	2	4	no	—
142	C₂²×C₄×C₁₁	—	2	8	no	—
143	C₂²×C₄×C₁₁	—	2	8	no	—
144	C₂²×C₄×C₁₁	—	2	16	no	—
145	C₂²×C₄×C₁₁	—	4	16	no	—
146	C₂²×C₄×C₁₁	—	4	4	no	—
147	C₂²×C₄×C₁₁	—	4	2	no	—
148	C₂²×C₄×C₁₁	—	4	2	no	—
149	C₂²×C₄×C₁₁	—	4	2	no	—
150	C₂²×C₄×C₁₁	—	4	4	no	—
151	C₂²×C₄×C₁₁	—	4	8	no	—
152	C₂²×C₄×C₁₁	—	4	8	no	—
153	C₂²×C₄×C₁₁	C₂²×C₄	1	4	yes	—
154	C₂²×C₄×C₁₁	C₂²×C₄	1	4	yes	—
155	C₂²×C₄×C₁₁	C₂²×C₄	1	4	yes	—
156	C₂²×C₄×C₁₁	C₂²×C₄	1	4	yes	—
157	C₂²×C₄×C₁₁	C₂²×C₄	1	8	yes	—
158	C₂²×C₄×C₁₁	C₂²×C₄	1	4	yes	—
159	C₂²×C₄×C₁₁	C₂²×C₄	1	4	yes	—
160	C₂²×C₄×C₁₁	C₂⁴	1	4	yes	—
161	C₂²×C₄×C₁₁	C₂⁴	1	8	yes	—
162	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
163	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
164	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
165	C₂²×C₄×C₁₁	C₂⁴	1	4	yes	—
166	C₂²×C₄×C₁₁	C₂⁴	1	4	yes	—
167	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
168	C₁₁×C₄⋊C₄	—	2	8	no	—
169	C₁₁×C₄⋊C₄	—	4	8	no	—
170	C₁₁×C₄⋊C₄	C₂²×C₄	1	8	yes	—
171	C₁₁×C₄⋊C₄	C₂²×C₄	1	8	yes	—
172	C₁₁×C₂²⋊C₄	—	2	4	no	—
173	C₁₁×C₂²⋊C₄	—	2	8	no	—
174	C₁₁×C₂²⋊C₄	—	2	8	no	—
175	C₁₁×C₂²⋊C₄	—	2	8	no	—
176	C₁₁×C₂²⋊C₄	—	2	16	no	—
177	C₁₁×C₂²⋊C₄	—	4	4	no	—
178	C₁₁×C₂²⋊C₄	—	4	8	no	—
179	C₁₁×C₂²⋊C₄	—	4	8	no	—
180	C₁₁×C₂²⋊C₄	C₂²×C₄	1	16	yes	—
181	C₁₁×C₂²⋊C₄	C₂²×C₄	1	16	yes	—
182	C₁₁×C₂²⋊C₄	#41	1	8	yes	—
183	C₄²×C₁₁	—	2	8	no	—
184	C₄²×C₁₁	—	4	2	no	—
185	C₄²×C₁₁	—	4	2	no	—
186	C₄²×C₁₁	—	4	4	no	—
187	C₄²×C₁₁	—	4	8	no	—
188	C₂²×#121	C₂×C₁₁	1	1	yes	characteristic
189	#2364	C₂×C₁₁	1	4	yes	complemented
190	#2363	C₂×C₁₁	1	4	yes	complemented
191	#2345	C₂×C₁₁	1	2	yes	complemented
192	D₄×C₂²⋊C₄	C₂×C₁₁	1	4	yes	complemented
193	D₄×C₂²⋊C₄	C₂×C₁₁	1	2	yes	complemented
194	#2333	C₂×C₁₁	1	4	yes	complemented
195	#2312	C₂×C₁₁	1	2	yes	complemented
196	C₄×#121	C₂×C₁₁	1	4	yes	complemented
197	#2280	C₂×C₁₁	1	1	yes	characteristic, complemented
198	#2273	C₂×C₁₁	1	2	yes	complemented
199	C₂×C₄×C₂²⋊C₄	C₂×C₁₁	1	1	yes	characteristic, complemented
200	C₂³×C₁₁	—	2	2	no	—
201	C₂³×C₁₁	—	2	2	no	—
202	C₂³×C₁₁	—	2	2	no	—
203	C₂³×C₁₁	—	2	2	no	—
204	C₂³×C₁₁	—	2	8	no	—
205	C₂³×C₁₁	—	2	8	no	—
206	C₂³×C₁₁	—	2	2	no	—
207	C₂³×C₁₁	—	2	4	no	—
208	C₂³×C₁₁	—	2	4	no	—
209	C₂³×C₁₁	—	2	2	no	—
210	C₂³×C₁₁	—	2	8	no	—
211	C₂³×C₁₁	—	2	8	no	—
212	C₂³×C₁₁	—	2	2	no	—
213	C₂³×C₁₁	—	2	16	no	—
214	C₂³×C₁₁	—	4	4	no	—
215	C₂³×C₁₁	—	4	8	no	—
216	C₂³×C₁₁	—	4	8	no	—
217	C₂³×C₁₁	—	4	16	no	—
218	C₂³×C₁₁	—	8	16	no	—
219	C₂³×C₁₁	C₂³×C₄	1	8	yes	—
220	C₂³×C₁₁	C₂³×C₄	1	2	yes	—
221	C₂³×C₁₁	C₂³×C₄	1	2	yes	—
222	C₂³×C₁₁	C₂³×C₄	1	2	yes	—
223	C₂³×C₁₁	C₂×#41	1	4	yes	—
224	C₂³×C₁₁	H(5,𝔽₂)	1	4	yes	—
225	C₂³×C₁₁	C₂⁵	1	1	yes	characteristic
226	D₄×C₁₁	—	2	32	no	—
227	D₄×C₁₁	—	2	16	no	—
228	D₄×C₁₁	—	4	8	no	—
229	D₄×C₁₁	—	4	16	no	—
230	C₂×C₄×C₁₁	—	2	4	no	—
231	C₂×C₄×C₁₁	—	2	2	no	—
232	C₂×C₄×C₁₁	—	2	2	no	—
233	C₂×C₄×C₁₁	—	2	4	no	—
234	C₂×C₄×C₁₁	—	2	8	no	—
235	C₂×C₄×C₁₁	—	2	2	no	—
236	C₂×C₄×C₁₁	—	2	8	no	—
237	C₂×C₄×C₁₁	—	2	8	no	—
238	C₂×C₄×C₁₁	—	2	8	no	—
239	C₂×C₄×C₁₁	—	2	4	no	—
240	C₂×C₄×C₁₁	—	2	8	no	—
241	C₂×C₄×C₁₁	—	2	4	no	—
242	C₂×C₄×C₁₁	—	2	8	no	—
243	C₂×C₄×C₁₁	—	2	8	no	—
244	C₂×C₄×C₁₁	—	2	4	no	—
245	C₂×C₄×C₁₁	—	4	4	no	—
246	C₂×C₄×C₁₁	—	4	4	no	—
247	C₂×C₄×C₁₁	—	4	4	no	—
248	C₂×C₄×C₁₁	—	4	8	no	—
249	C₂×C₄×C₁₁	—	4	16	no	—
250	C₂×C₄×C₁₁	—	8	16	no	—
251	C₂×C₄×C₁₁	C₂³×C₄	1	2	yes	—
252	C₂×C₄×C₁₁	C₂³×C₄	1	2	yes	—
253	C₂×C₄×C₁₁	C₂³×C₄	1	8	yes	—
254	C₂×C₄×C₁₁	C₂³×C₄	1	2	yes	—
255	C₂×C₄×C₁₁	C₂³×C₄	1	2	yes	—
256	C₂×C₄×C₁₁	C₂×#41	1	8	yes	—
257	C₂×C₄×C₁₁	H(5,𝔽₂)	1	4	yes	—
258	C₂³×D₄	C₂²×C₁₁	1	1	yes	characteristic
259	C₂³×D₄	C₂²×C₁₁	1	2	yes	—
260	C₂⁴×C₄	C₂²×C₁₁	1	1	yes	characteristic
261	C₂×#121	C₄×C₁₁	1	16	yes	complemented
262	C₂×#121	C₂²×C₁₁	1	2	yes	—
263	C₂×#121	C₂²×C₁₁	1	2	yes	—
264	C₂×#121	C₂²×C₁₁	1	2	yes	—
265	C₂×#121	C₂²×C₁₁	1	2	yes	—
266	C₂×C₄×D₄	C₂²×C₁₁	1	4	yes	complemented
267	C₂×C₄×D₄	C₂²×C₁₁	1	8	yes	complemented
268	C₂×#117	C₂²×C₁₁	1	2	yes	complemented
269	C₂²×C₄⋊C₄	C₂²×C₁₁	1	1	yes	characteristic
270	C₂²×C₂²⋊C₄	C₂²×C₁₁	1	2	yes	—
271	C₂²×C₂²⋊C₄	C₂²×C₁₁	1	4	yes	—
272	C₂²×C₂²⋊C₄	C₂²×C₁₁	1	2	yes	—
273	C₂²×C₄²	C₂²×C₁₁	1	2	yes	complemented
274	#390	C₂²×C₁₁	1	8	yes	complemented
275	#390	C₂²×C₁₁	1	4	yes	complemented
276	#389	C₂²×C₁₁	1	4	yes	complemented
277	#388	C₂²×C₁₁	1	8	yes	complemented
278	#388	C₂²×C₁₁	1	8	yes	complemented
279	#387	C₂²×C₁₁	1	8	yes	complemented
280	#386	C₂²×C₁₁	1	8	yes	complemented
281	#386	C₂²×C₁₁	1	8	yes	complemented
282	#386	C₂²×C₁₁	1	8	yes	complemented
283	#381	C₂²×C₁₁	1	2	yes	complemented
284	#380	C₂²×C₁₁	1	4	yes	—
285	#380	C₂²×C₁₁	1	2	yes	—
286	#380	C₂²×C₁₁	1	2	yes	complemented
287	#379	C₂²×C₁₁	1	4	yes	—
288	#379	C₂²×C₁₁	1	2	yes	—
289	C₄×C₄⋊C₄	C₂²×C₁₁	1	4	yes	complemented
290	C₄×C₂²⋊C₄	C₂²×C₁₁	1	1	yes	characteristic
291	C₄×C₂²⋊C₄	C₂²×C₁₁	1	2	yes	—
292	C₄×C₂²⋊C₄	C₂²×C₁₁	1	2	yes	—
293	C₄×C₂²⋊C₄	C₂²×C₁₁	1	4	yes	—
294	C₄×C₂²⋊C₄	C₂²×C₁₁	1	1	yes	characteristic
295	C₄×C₂²⋊C₄	C₂²×C₁₁	1	2	yes	complemented
296	C₄×C₂²⋊C₄	C₂²×C₁₁	1	8	yes	complemented
297	C₄×C₂²⋊C₄	C₂²×C₁₁	1	2	yes	complemented
298	C₄×C₂²⋊C₄	C₂²×C₁₁	1	8	yes	complemented
299	C₄×C₂²⋊C₄	C₂²×C₁₁	1	2	yes	complemented
300	C₂×#95	C₂²×C₁₁	1	2	yes	complemented
301	C₂²×C₁₁	—	2	2	no	—
302	C₂²×C₁₁	—	2	2	no	—
303	C₂²×C₁₁	—	2	2	no	—
304	C₂²×C₁₁	—	2	2	no	—
305	C₂²×C₁₁	—	2	8	no	—
306	C₂²×C₁₁	—	2	8	no	—
307	C₂²×C₁₁	—	2	2	no	—
308	C₂²×C₁₁	—	2	8	no	—
309	C₂²×C₁₁	—	2	2	no	—
310	C₂²×C₁₁	—	2	8	no	—
311	C₂²×C₁₁	—	2	8	no	—
312	C₂²×C₁₁	—	2	2	no	—
313	C₂²×C₁₁	—	4	16	no	—
314	C₂²×C₁₁	—	4	8	no	—
315	C₂²×C₁₁	—	4	4	no	—
316	C₂²×C₁₁	—	4	8	no	—
317	C₂²×C₁₁	—	8	16	no	—
318	C₂²×C₁₁	C₄×#41	1	4	yes	—
319	C₂²×C₁₁	#518	1	4	yes	—
320	C₂²×C₁₁	C₂⁴×C₄	1	1	yes	characteristic
321	C₂²×C₁₁	C₂²×#41	1	2	yes	—
322	C₂²×C₁₁	C₂×H(5,𝔽₂)	1	2	yes	—
323	C₂²×C₁₁	C₂×H(5,𝔽₂)	1	2	yes	—
324	C₄×C₁₁	—	2	2	no	—
325	C₄×C₁₁	—	2	2	no	—
326	C₄×C₁₁	—	2	2	no	—
327	C₄×C₁₁	—	2	8	no	—
328	C₄×C₁₁	—	2	8	no	—
329	C₄×C₁₁	—	4	4	no	—
330	C₄×C₁₁	—	4	8	no	—
331	C₄×C₁₁	#518	1	4	yes	—
332	C₂⁵	C₂³×C₁₁	1	1	yes	characteristic
333	C₂⁵	C₂³×C₁₁	1	2	yes	—
334	C₂²×D₄	—	4	4	no	—
335	C₂²×D₄	—	4	8	no	—
336	C₂²×D₄	C₂×C₄×C₁₁	1	8	yes	complemented
337	C₂²×D₄	C₂×C₄×C₁₁	1	16	yes	complemented
338	C₂²×D₄	C₂³×C₁₁	1	4	yes	—
339	C₂²×D₄	C₂³×C₁₁	1	2	yes	—
340	C₂²×D₄	C₂³×C₁₁	1	2	yes	—
341	C₂²×D₄	C₂³×C₁₁	1	4	yes	—
342	C₂³×C₄	—	4	4	no	—
343	C₂³×C₄	C₂×C₄×C₁₁	1	8	yes	complemented
344	C₂³×C₄	C₂³×C₁₁	1	4	yes	—
345	C₂³×C₄	C₂³×C₁₁	1	1	yes	characteristic
346	C₂³×C₄	C₂³×C₁₁	1	1	yes	characteristic
347	C₂³×C₄	C₂³×C₁₁	1	1	yes	characteristic
348	C₂³×C₄	C₂³×C₁₁	1	8	yes	—
349	C₂³×C₄	C₂³×C₁₁	1	1	yes	characteristic
350	C₂³×C₄	C₂³×C₁₁	1	2	yes	—
351	C₂³×C₄	C₂³×C₁₁	1	1	yes	characteristic
352	C₂³×C₄	C₂³×C₁₁	1	1	yes	characteristic
353	#121	C₂×C₄×C₁₁	1	16	yes	complemented
354	#121	C₂×C₄×C₁₁	1	16	yes	complemented
355	#121	C₂×C₄×C₁₁	1	16	yes	complemented
356	#121	C₂×C₄×C₁₁	1	16	yes	complemented
357	C₄×D₄	—	4	8	no	—
358	C₄×D₄	—	4	16	no	—
359	#117	—	4	4	no	—
360	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	8	yes	complemented
361	C₂×C₄⋊C₄	C₂³×C₁₁	1	4	yes	—
362	C₂×C₄⋊C₄	C₂³×C₁₁	1	8	yes	—
363	C₂×C₄⋊C₄	C₂³×C₁₁	1	2	yes	—
364	C₂×C₄⋊C₄	C₂³×C₁₁	1	2	yes	—
365	C₂×C₂²⋊C₄	—	2	8	no	—
366	C₂×C₂²⋊C₄	—	2	16	no	—
367	C₂×C₂²⋊C₄	C₂×C₄×C₁₁	1	16	yes	complemented
368	C₂×C₂²⋊C₄	C₂³×C₁₁	1	2	yes	—
369	C₂×C₂²⋊C₄	C₂³×C₁₁	1	4	yes	—
370	C₂×C₂²⋊C₄	C₂³×C₁₁	1	4	yes	—
371	C₂×C₂²⋊C₄	C₂³×C₁₁	1	8	yes	—
372	C₂×C₂²⋊C₄	C₂³×C₁₁	1	4	yes	—
373	C₂×C₂²⋊C₄	C₂³×C₁₁	1	4	yes	—
374	C₂×C₂²⋊C₄	C₂³×C₁₁	1	8	yes	—
375	C₂×C₂²⋊C₄	C₂³×C₁₁	1	8	yes	—
376	C₂×C₂²⋊C₄	C₂³×C₁₁	1	4	yes	—
377	C₂×C₂²⋊C₄	C₂³×C₁₁	1	4	yes	—
378	C₂×C₂²⋊C₄	C₂³×C₁₁	1	2	yes	—
379	C₂×C₄²	—	4	4	no	—
380	C₂×C₄²	C₂³×C₁₁	1	4	yes	—
381	C₂×C₄²	C₂³×C₁₁	1	4	yes	—
382	C₂×C₄²	C₂³×C₁₁	1	8	yes	—
383	C₂×C₄²	C₂³×C₁₁	1	2	yes	—
384	C₂×C₄²	C₂³×C₁₁	1	2	yes	—
385	#95	C₂³×C₁₁	1	2	yes	—
386	#95	C₂³×C₁₁	1	4	yes	—
387	#95	C₂³×C₁₁	1	2	yes	—
388	#95	C₂³×C₁₁	1	4	yes	—
389	#95	C₂³×C₁₁	1	8	yes	—
390	#95	C₂³×C₁₁	1	4	yes	—
391	#95	C₂³×C₁₁	1	8	yes	—
392	C₂×C₁₁	—	2	4	no	—
393	C₂×C₁₁	—	2	4	no	—
394	C₂×C₁₁	—	4	2	no	—
395	C₂×C₁₁	—	4	8	no	—
396	C₂×C₁₁	C₂×C₄×#41	1	1	yes	characteristic
397	C₂×C₁₁	C₂×#518	1	1	yes	characteristic
398	C₂×C₁₁	C₂×#518	1	1	yes	characteristic
399	C₂×C₁₁	#3519	1	4	yes	—
400	C₂⁴	—	2	4	no	—
401	C₂⁴	—	2	4	no	—
402	C₂⁴	—	2	8	no	—
403	C₂⁴	—	4	2	no	—
404	C₂⁴	—	4	4	no	—
405	C₂⁴	—	4	4	no	—
406	C₂⁴	C₂²×C₄×C₁₁	1	4	yes	—
407	C₂⁴	C₂²×C₄×C₁₁	1	8	yes	—
408	C₂⁴	C₂⁴×C₁₁	1	1	yes	characteristic
409	C₂⁴	C₂⁴×C₁₁	1	4	yes	—
410	C₂⁴	C₂⁴×C₁₁	1	1	yes	characteristic
411	C₂⁴	C₂⁴×C₁₁	1	1	yes	characteristic
412	C₂×D₄	—	2	16	no	—
413	C₂×D₄	—	2	8	no	—
414	C₂×D₄	—	4	16	no	—
415	C₂×D₄	—	4	8	no	—
416	C₂×D₄	—	4	4	no	—
417	C₂×D₄	—	4	32	no	—
418	C₂×D₄	C₂²×C₄×C₁₁	1	16	yes	—
419	C₂×D₄	C₂²×C₄×C₁₁	1	8	yes	—
420	C₂×D₄	C₂²×C₄×C₁₁	1	16	yes	—
421	C₂×D₄	C₂²×C₄×C₁₁	1	8	yes	—
422	C₂²×C₄	—	2	4	no	—
423	C₂²×C₄	—	2	4	no	—
424	C₂²×C₄	—	2	4	no	—
425	C₂²×C₄	—	2	8	no	—
426	C₂²×C₄	—	2	8	no	—
427	C₂²×C₄	—	2	16	no	—
428	C₂²×C₄	—	4	16	no	—
429	C₂²×C₄	—	4	4	no	—
430	C₂²×C₄	—	4	2	no	—
431	C₂²×C₄	—	4	2	no	—
432	C₂²×C₄	—	4	2	no	—
433	C₂²×C₄	—	4	4	no	—
434	C₂²×C₄	—	4	8	no	—
435	C₂²×C₄	—	4	8	no	—
436	C₂²×C₄	C₂²×C₄×C₁₁	1	4	yes	—
437	C₂²×C₄	C₂²×C₄×C₁₁	1	4	yes	—
438	C₂²×C₄	C₂²×C₄×C₁₁	1	4	yes	—
439	C₂²×C₄	C₂²×C₄×C₁₁	1	4	yes	—
440	C₂²×C₄	C₂²×C₄×C₁₁	1	8	yes	—
441	C₂²×C₄	C₂²×C₄×C₁₁	1	4	yes	—
442	C₂²×C₄	C₂²×C₄×C₁₁	1	4	yes	—
443	C₂²×C₄	C₂⁴×C₁₁	1	4	yes	—
444	C₂²×C₄	C₂⁴×C₁₁	1	8	yes	—
445	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
446	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
447	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
448	C₂²×C₄	C₂⁴×C₁₁	1	4	yes	—
449	C₂²×C₄	C₂⁴×C₁₁	1	4	yes	—
450	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
451	C₄⋊C₄	—	2	8	no	—
452	C₄⋊C₄	—	4	8	no	—
453	C₄⋊C₄	C₂²×C₄×C₁₁	1	8	yes	—
454	C₄⋊C₄	C₂²×C₄×C₁₁	1	8	yes	—
455	C₂²⋊C₄	—	2	4	no	—
456	C₂²⋊C₄	—	2	8	no	—
457	C₂²⋊C₄	—	2	8	no	—
458	C₂²⋊C₄	—	2	8	no	—
459	C₂²⋊C₄	—	2	16	no	—
460	C₂²⋊C₄	—	4	4	no	—
461	C₂²⋊C₄	—	4	8	no	—
462	C₂²⋊C₄	—	4	8	no	—
463	C₂²⋊C₄	C₂²×C₄×C₁₁	1	16	yes	—
464	C₂²⋊C₄	C₂²×C₄×C₁₁	1	16	yes	—
465	C₂²⋊C₄	C₁₁×#41	1	8	yes	—
466	C₄²	—	2	8	no	—
467	C₄²	—	4	2	no	—
468	C₄²	—	4	2	no	—
469	C₄²	—	4	4	no	—
470	C₄²	—	4	8	no	—
471	C₁₁	#34246	1	1	yes	characteristic, direct product factor, Sylow
472	C₂³	—	2	2	no	—
473	C₂³	—	2	2	no	—
474	C₂³	—	2	2	no	—
475	C₂³	—	2	2	no	—
476	C₂³	—	2	8	no	—
477	C₂³	—	2	8	no	—
478	C₂³	—	2	2	no	—
479	C₂³	—	2	4	no	—
480	C₂³	—	2	4	no	—
481	C₂³	—	2	2	no	—
482	C₂³	—	2	8	no	—
483	C₂³	—	2	8	no	—
484	C₂³	—	2	2	no	—
485	C₂³	—	2	16	no	—
486	C₂³	—	4	4	no	—
487	C₂³	—	4	8	no	—
488	C₂³	—	4	8	no	—
489	C₂³	—	4	16	no	—
490	C₂³	—	8	16	no	—
491	C₂³	C₂³×C₄×C₁₁	1	8	yes	—
492	C₂³	C₂³×C₄×C₁₁	1	2	yes	—
493	C₂³	C₂³×C₄×C₁₁	1	2	yes	—
494	C₂³	C₂³×C₄×C₁₁	1	2	yes	—
495	C₂³	C₂×C₁₁×#41	1	4	yes	—
496	C₂³	C₁₁×H(5,𝔽₂)	1	4	yes	—
497	C₂³	C₂⁵×C₁₁	1	1	yes	characteristic
498	D₄	—	2	32	no	—
499	D₄	—	2	16	no	—
500	D₄	—	4	8	no	—
501	D₄	—	4	16	no	—
502	C₂×C₄	—	2	4	no	—
503	C₂×C₄	—	2	2	no	—
504	C₂×C₄	—	2	2	no	—
505	C₂×C₄	—	2	4	no	—
506	C₂×C₄	—	2	8	no	—
507	C₂×C₄	—	2	2	no	—
508	C₂×C₄	—	2	8	no	—
509	C₂×C₄	—	2	8	no	—
510	C₂×C₄	—	2	8	no	—
511	C₂×C₄	—	2	4	no	—
512	C₂×C₄	—	2	8	no	—
513	C₂×C₄	—	2	4	no	—
514	C₂×C₄	—	2	8	no	—
515	C₂×C₄	—	2	8	no	—
516	C₂×C₄	—	2	4	no	—
517	C₂×C₄	—	4	4	no	—
518	C₂×C₄	—	4	4	no	—
519	C₂×C₄	—	4	4	no	—
520	C₂×C₄	—	4	8	no	—
521	C₂×C₄	—	4	16	no	—
522	C₂×C₄	—	8	16	no	—
523	C₂×C₄	C₂³×C₄×C₁₁	1	2	yes	—
524	C₂×C₄	C₂³×C₄×C₁₁	1	2	yes	—
525	C₂×C₄	C₂³×C₄×C₁₁	1	8	yes	—
526	C₂×C₄	C₂³×C₄×C₁₁	1	2	yes	—
527	C₂×C₄	C₂³×C₄×C₁₁	1	2	yes	—
528	C₂×C₄	C₂×C₁₁×#41	1	8	yes	—
529	C₂×C₄	C₁₁×H(5,𝔽₂)	1	4	yes	—
530	C₂²	—	2	2	no	—
531	C₂²	—	2	2	no	—
532	C₂²	—	2	2	no	—
533	C₂²	—	2	2	no	—
534	C₂²	—	2	8	no	—
535	C₂²	—	2	8	no	—
536	C₂²	—	2	2	no	—
537	C₂²	—	2	8	no	—
538	C₂²	—	2	2	no	—
539	C₂²	—	2	8	no	—
540	C₂²	—	2	8	no	—
541	C₂²	—	2	2	no	—
542	C₂²	—	4	16	no	—
543	C₂²	—	4	8	no	—
544	C₂²	—	4	4	no	—
545	C₂²	—	4	8	no	—
546	C₂²	—	8	16	no	—
547	C₂²	C₄×C₁₁×#41	1	4	yes	—
548	C₂²	C₁₁×#518	1	4	yes	—
549	C₂²	C₂⁴×C₄×C₁₁	1	1	yes	characteristic
550	C₂²	C₂²×C₁₁×#41	1	2	yes	—
551	C₂²	C₂×C₁₁×H(5,𝔽₂)	1	2	yes	—
552	C₂²	C₂×C₁₁×H(5,𝔽₂)	1	2	yes	—
553	C₄	—	2	2	no	—
554	C₄	—	2	2	no	—
555	C₄	—	2	2	no	—
556	C₄	—	2	8	no	—
557	C₄	—	2	8	no	—
558	C₄	—	4	4	no	—
559	C₄	—	4	8	no	—
560	C₄	C₁₁×#518	1	4	yes	—
561	C₂	—	2	4	no	—
562	C₂	—	2	4	no	—
563	C₂	—	4	2	no	—
564	C₂	—	4	8	no	—
565	C₂	C₂×C₄×C₁₁×#41	1	1	yes	characteristic
566	C₂	C₂×C₁₁×#518	1	1	yes	characteristic
567	C₂	C₂×C₁₁×#518	1	1	yes	characteristic
568	C₂	C₁₁×#3519	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×#121	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×#2364	C₂	semidirect
3. C₁₁×#2363	C₂	semidirect
4. C₁₁×#2345	C₂	semidirect
5. D₄×C₁₁×C₂²⋊C₄	C₂	semidirect
6. D₄×C₁₁×C₂²⋊C₄	C₂	semidirect
7. C₁₁×#2333	C₂	semidirect
8. C₁₁×#2312	C₂	semidirect
9. C₄×C₁₁×#121	C₂	semidirect
10. C₁₁×#2280	C₂	semidirect
11. C₁₁×#2273	C₂	semidirect
12. C₂×C₄×C₁₁×C₂²⋊C₄	C₂	semidirect
16. C₂×C₁₁×#121	C₄	semidirect
21. C₂×C₄×D₄×C₁₁	C₂²	semidirect
22. C₂×C₄×D₄×C₁₁	C₂²	semidirect
23. C₂×C₁₁×#117	C₂²	semidirect
28. C₂²×C₄²×C₁₁	C₂²	semidirect
29. C₁₁×#390	C₂²	semidirect
30. C₁₁×#390	C₂²	semidirect
31. C₁₁×#389	C₂²	semidirect
32. C₁₁×#388	C₂²	semidirect
33. C₁₁×#388	C₂²	semidirect
34. C₁₁×#387	C₂²	semidirect
35. C₁₁×#386	C₂²	semidirect
36. C₁₁×#386	C₂²	semidirect
37. C₁₁×#386	C₂²	semidirect
38. C₁₁×#381	C₂²	semidirect
41. C₁₁×#380	C₂²	semidirect
44. C₄×C₁₁×C₄⋊C₄	C₂²	semidirect
50. C₄×C₁₁×C₂²⋊C₄	C₂²	semidirect
51. C₄×C₁₁×C₂²⋊C₄	C₂²	semidirect
52. C₄×C₁₁×C₂²⋊C₄	C₂²	semidirect
53. C₄×C₁₁×C₂²⋊C₄	C₂²	semidirect
54. C₄×C₁₁×C₂²⋊C₄	C₂²	semidirect
55. C₂×C₁₁×#95	C₂²	semidirect
60. C₂²×D₄×C₁₁	C₂×C₄	semidirect
61. C₂²×D₄×C₁₁	C₂×C₄	semidirect
67. C₂³×C₄×C₁₁	C₂×C₄	semidirect
77. C₁₁×#121	C₂×C₄	semidirect
78. C₁₁×#121	C₂×C₄	semidirect
79. C₁₁×#121	C₂×C₄	semidirect
80. C₁₁×#121	C₂×C₄	semidirect
84. C₂×C₁₁×C₄⋊C₄	C₂×C₄	semidirect
91. C₂×C₁₁×C₂²⋊C₄	C₂×C₄	semidirect
116. #34246	C₁₁	direct (N × H)
189. #2364	C₂×C₁₁	semidirect
190. #2363	C₂×C₁₁	semidirect
191. #2345	C₂×C₁₁	semidirect
192. D₄×C₂²⋊C₄	C₂×C₁₁	semidirect
193. D₄×C₂²⋊C₄	C₂×C₁₁	semidirect
194. #2333	C₂×C₁₁	semidirect
195. #2312	C₂×C₁₁	semidirect
196. C₄×#121	C₂×C₁₁	semidirect
197. #2280	C₂×C₁₁	semidirect
198. #2273	C₂×C₁₁	semidirect
199. C₂×C₄×C₂²⋊C₄	C₂×C₁₁	semidirect
261. C₂×#121	C₄×C₁₁	semidirect
266. C₂×C₄×D₄	C₂²×C₁₁	semidirect
267. C₂×C₄×D₄	C₂²×C₁₁	semidirect
268. C₂×#117	C₂²×C₁₁	semidirect
273. C₂²×C₄²	C₂²×C₁₁	semidirect
274. #390	C₂²×C₁₁	semidirect
275. #390	C₂²×C₁₁	semidirect
276. #389	C₂²×C₁₁	semidirect
277. #388	C₂²×C₁₁	semidirect
278. #388	C₂²×C₁₁	semidirect
279. #387	C₂²×C₁₁	semidirect
280. #386	C₂²×C₁₁	semidirect
281. #386	C₂²×C₁₁	semidirect
282. #386	C₂²×C₁₁	semidirect
283. #381	C₂²×C₁₁	semidirect
286. #380	C₂²×C₁₁	semidirect
289. C₄×C₄⋊C₄	C₂²×C₁₁	semidirect
295. C₄×C₂²⋊C₄	C₂²×C₁₁	semidirect
296. C₄×C₂²⋊C₄	C₂²×C₁₁	semidirect
297. C₄×C₂²⋊C₄	C₂²×C₁₁	semidirect
298. C₄×C₂²⋊C₄	C₂²×C₁₁	semidirect
299. C₄×C₂²⋊C₄	C₂²×C₁₁	semidirect
300. C₂×#95	C₂²×C₁₁	semidirect
336. C₂²×D₄	C₂×C₄×C₁₁	semidirect
337. C₂²×D₄	C₂×C₄×C₁₁	semidirect
343. C₂³×C₄	C₂×C₄×C₁₁	semidirect
353. #121	C₂×C₄×C₁₁	semidirect
354. #121	C₂×C₄×C₁₁	semidirect
355. #121	C₂×C₄×C₁₁	semidirect
356. #121	C₂×C₄×C₁₁	semidirect
360. C₂×C₄⋊C₄	C₂×C₄×C₁₁	semidirect
367. C₂×C₂²⋊C₄	C₂×C₄×C₁₁	semidirect
471. C₁₁	#34246	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×#121	2
C₁₁×#2364	2
C₁₁×#2363	2
C₁₁×#2345	2
D₄×C₁₁×C₂²⋊C₄	2
C₁₁×#2333	2
C₁₁×#2312	2
C₄×C₁₁×#121	2
C₁₁×#2280	2
C₁₁×#2273	2
C₂×C₄×C₁₁×C₂²⋊C₄	2
#34246	11

Subgroups — C11×#34246 #14611439

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#34246 #14611439