Subgroups — C₁₁×#34269 #14611462

Order 2816.

3426 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₁×#535	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₁×#518	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄×C₁₁×#41	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₁×#2367	C₂	1	4	yes	maximal, complemented
5	C₁₁×#2366	C₂	1	4	yes	maximal, complemented
6	C₁₁×#2358	C₂	1	8	yes	maximal, complemented
7	C₁₁×#2324	C₂	1	4	yes	maximal, complemented
8	C₁₁×#2311	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄×C₁₁×#121	C₂	1	4	yes	maximal, complemented
10	C₁₁×#2296	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₁₁×#390	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₁×#2274	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂²×C₁₁×#41	C₂²	1	1	yes	characteristic
14	C₂³×D₄×C₁₁	C₂²	1	1	yes	characteristic
15	C₁₁×#535	C₄	1	16	yes	complemented
16	C₂×C₁₁×#127	C₂²	1	2	yes	—
17	C₂×C₁₁×#124	C₂²	1	2	yes	—
18	C₂×C₁₁×#121	C₂²	1	4	yes	—
19	C₂×C₁₁×#120	C₂²	1	4	yes	—
20	C₁₁×#518	—	2	8	no	—
21	C₄×C₁₁×#41	—	2	8	no	—
22	C₂×C₄×Q₈×C₁₁	C₂²	1	2	yes	complemented
23	C₂×C₄×D₄×C₁₁	C₂²	1	4	yes	—
24	C₂×C₄×D₄×C₁₁	C₂²	1	4	yes	—
25	C₂×C₄×D₄×C₁₁	C₂²	1	4	yes	—
26	C₂×C₄×D₄×C₁₁	C₂²	1	2	yes	complemented
27	C₂×C₄×D₄×C₁₁	C₂²	1	8	yes	complemented
28	C₂×C₁₁×#117	C₂²	1	1	yes	characteristic
29	C₂×C₁₁×#117	C₂²	1	1	yes	characteristic
30	C₂×C₁₁×#117	C₂²	1	1	yes	characteristic
31	C₂×C₁₁×#117	C₂²	1	2	yes	complemented
32	C₂²×C₁₁×C₄⋊C₄	C₂²	1	1	yes	characteristic
33	C₂²×C₁₁×C₂²⋊C₄	C₂²	1	4	yes	—
34	C₂²×C₁₁×C₂²⋊C₄	C₂²	1	4	yes	—
35	C₂²×C₄²×C₁₁	C₂²	1	1	yes	characteristic
36	C₂²×C₄²×C₁₁	C₂²	1	2	yes	complemented
37	C₁₁×#391	C₂²	1	2	yes	complemented
38	C₁₁×#390	C₂²	1	2	yes	—
39	C₁₁×#390	C₂²	1	2	yes	—
40	C₁₁×#390	C₂²	1	4	yes	—
41	C₁₁×#390	C₂²	1	2	yes	complemented
42	C₁₁×#390	C₂²	1	8	yes	complemented
43	C₁₁×#389	C₂²	1	2	yes	complemented
44	C₁₁×#389	C₂²	1	2	yes	complemented
45	C₁₁×#388	C₂²	1	8	yes	complemented
46	C₁₁×#388	C₂²	1	8	yes	complemented
47	C₁₁×#386	C₂²	1	4	yes	—
48	C₁₁×#386	C₂²	1	8	yes	complemented
49	C₁₁×#386	C₂²	1	8	yes	complemented
50	C₁₁×#385	C₂²	1	4	yes	—
51	C₁₁×#385	C₂²	1	8	yes	complemented
52	C₁₁×#380	C₂²	1	4	yes	complemented
53	C₄×C₁₁×C₄⋊C₄	C₂²	1	4	yes	complemented
54	C₄×C₁₁×C₄⋊C₄	C₂²	1	4	yes	complemented
55	C₄×C₁₁×C₄⋊C₄	C₂²	1	4	yes	complemented
56	C₄×C₁₁×C₂²⋊C₄	C₂²	1	4	yes	—
57	C₄×C₁₁×C₂²⋊C₄	C₂²	1	8	yes	complemented
58	C₂⁵×C₁₁	C₂³	1	2	yes	—
59	C₂×C₁₁×#41	—	2	4	no	—
60	C₂×C₁₁×#41	—	2	4	no	—
61	C₂×C₁₁×#41	C₂×C₄	1	8	yes	complemented
62	C₂²×Q₈×C₁₁	C₂³	1	1	yes	characteristic
63	C₂²×D₄×C₁₁	—	2	4	no	—
64	C₂²×D₄×C₁₁	—	2	4	no	—
65	C₂²×D₄×C₁₁	C₂×C₄	1	8	yes	complemented
66	C₂²×D₄×C₁₁	C₂³	1	2	yes	—
67	C₂²×D₄×C₁₁	C₂³	1	2	yes	—
68	C₂²×D₄×C₁₁	C₂³	1	2	yes	—
69	C₂²×D₄×C₁₁	C₂³	1	1	yes	characteristic
70	C₂²×D₄×C₁₁	C₂³	1	8	yes	—
71	C₂³×C₄×C₁₁	C₂³	1	2	yes	—
72	C₂³×C₄×C₁₁	C₂³	1	4	yes	—
73	C₂³×C₄×C₁₁	C₂³	1	2	yes	—
74	C₂³×C₄×C₁₁	C₂³	1	2	yes	—
75	C₂³×C₄×C₁₁	C₂³	1	8	yes	—
76	C₂³×C₄×C₁₁	C₂³	1	1	yes	characteristic
77	C₁₁×#127	C₂×C₄	1	16	yes	complemented
78	C₁₁×#124	C₂×C₄	1	16	yes	complemented
79	C₁₁×#121	C₂×C₄	1	32	yes	complemented
80	C₁₁×#120	C₂×C₄	1	32	yes	complemented
81	C₄×Q₈×C₁₁	—	2	8	no	—
82	C₄×D₄×C₁₁	—	2	16	no	—
83	C₄×D₄×C₁₁	—	2	8	no	—
84	C₄×D₄×C₁₁	—	2	16	no	—
85	C₄×D₄×C₁₁	—	2	16	no	—
86	C₄×D₄×C₁₁	—	4	16	no	—
87	C₁₁×#117	—	2	4	no	—
88	C₁₁×#117	—	2	8	no	—
89	C₁₁×#117	C₂×C₄	1	8	yes	complemented
90	C₁₁×#117	D₄	1	8	yes	complemented
91	C₂×C₁₁×C₄⋊C₄	—	2	4	no	—
92	C₂×C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
93	C₂×C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
94	C₂×C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
95	C₂×C₁₁×C₄⋊C₄	C₂³	1	4	yes	—
96	C₂×C₁₁×C₄⋊C₄	C₂³	1	4	yes	—
97	C₂×C₁₁×C₄⋊C₄	C₂³	1	4	yes	—
98	C₂×C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
99	C₂×C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
100	C₂×C₁₁×C₂²⋊C₄	—	2	16	no	—
101	C₂×C₁₁×C₂²⋊C₄	—	4	8	no	—
102	C₂×C₁₁×C₂²⋊C₄	C₂³	1	2	yes	—
103	C₂×C₁₁×C₂²⋊C₄	C₂³	1	8	yes	—
104	C₂×C₁₁×C₂²⋊C₄	C₂³	1	8	yes	—
105	C₂×C₁₁×C₂²⋊C₄	C₂³	1	4	yes	—
106	C₂×C₁₁×C₂²⋊C₄	C₂³	1	8	yes	—
107	C₂×C₁₁×C₂²⋊C₄	C₂³	1	8	yes	—
108	C₂×C₁₁×C₂²⋊C₄	C₂³	1	2	yes	—
109	C₂×C₁₁×C₂²⋊C₄	C₂³	1	8	yes	—
110	C₂×C₁₁×C₂²⋊C₄	C₂³	1	2	yes	—
111	C₂×C₄²×C₁₁	—	2	4	no	—
112	C₂×C₄²×C₁₁	—	2	8	no	—
113	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
114	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
115	C₂×C₄²×C₁₁	C₂³	1	2	yes	—
116	C₂×C₄²×C₁₁	C₂³	1	4	yes	—
117	C₂×C₄²×C₁₁	C₂³	1	2	yes	—
118	C₂×C₄²×C₁₁	C₂³	1	8	yes	—
119	C₂×C₄²×C₁₁	C₂³	1	2	yes	—
120	C₂×C₄²×C₁₁	C₂³	1	2	yes	—
121	C₁₁×#95	C₂³	1	8	yes	—
122	C₁₁×#95	C₂³	1	4	yes	—
123	C₁₁×#95	C₂³	1	8	yes	—
124	C₁₁×#95	C₂³	1	4	yes	—
125	#34269	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
126	C₂⁴×C₁₁	—	2	4	no	—
127	C₂⁴×C₁₁	—	2	4	no	—
128	C₂⁴×C₁₁	—	4	4	no	—
129	C₂⁴×C₁₁	—	4	4	no	—
130	C₂⁴×C₁₁	C₂²×C₄	1	8	yes	—
131	C₂⁴×C₁₁	C₂⁴	1	4	yes	—
132	C₂⁴×C₁₁	C₂⁴	1	2	yes	—
133	C₂⁴×C₁₁	C₂⁴	1	1	yes	characteristic
134	C₁₁×#41	—	2	32	no	—
135	C₂×Q₈×C₁₁	—	2	2	no	—
136	C₂×Q₈×C₁₁	—	2	2	no	—
137	C₂×Q₈×C₁₁	C₂²×C₄	1	4	yes	—
138	C₂×D₄×C₁₁	—	2	4	no	—
139	C₂×D₄×C₁₁	—	2	4	no	—
140	C₂×D₄×C₁₁	—	2	32	no	—
141	C₂×D₄×C₁₁	—	2	4	no	—
142	C₂×D₄×C₁₁	—	2	4	no	—
143	C₂×D₄×C₁₁	—	2	2	no	—
144	C₂×D₄×C₁₁	—	2	4	no	—
145	C₂×D₄×C₁₁	—	2	4	no	—
146	C₂×D₄×C₁₁	—	2	2	no	—
147	C₂×D₄×C₁₁	—	4	8	no	—
148	C₂×D₄×C₁₁	—	4	8	no	—
149	C₂×D₄×C₁₁	C₂²×C₄	1	8	yes	—
150	C₂×D₄×C₁₁	C₂²×C₄	1	8	yes	—
151	C₂×D₄×C₁₁	C₂²×C₄	1	8	yes	—
152	C₂×D₄×C₁₁	C₂²×C₄	1	4	yes	—
153	C₂×D₄×C₁₁	C₂²×C₄	1	32	yes	—
154	C₂²×C₄×C₁₁	—	2	4	no	—
155	C₂²×C₄×C₁₁	—	2	4	no	—
156	C₂²×C₄×C₁₁	—	2	4	no	—
157	C₂²×C₄×C₁₁	—	2	4	no	—
158	C₂²×C₄×C₁₁	—	2	8	no	—
159	C₂²×C₄×C₁₁	—	2	4	no	—
160	C₂²×C₄×C₁₁	—	2	8	no	—
161	C₂²×C₄×C₁₁	—	2	16	no	—
162	C₂²×C₄×C₁₁	—	4	4	no	—
163	C₂²×C₄×C₁₁	—	4	2	no	—
164	C₂²×C₄×C₁₁	—	4	4	no	—
165	C₂²×C₄×C₁₁	—	4	8	no	—
166	C₂²×C₄×C₁₁	—	4	8	no	—
167	C₂²×C₄×C₁₁	C₂²×C₄	1	8	yes	—
168	C₂²×C₄×C₁₁	C₂²×C₄	1	4	yes	—
169	C₂²×C₄×C₁₁	C₂×D₄	1	4	yes	—
170	C₂²×C₄×C₁₁	#41	1	4	yes	—
171	C₂²×C₄×C₁₁	C₂⁴	1	4	yes	—
172	C₂²×C₄×C₁₁	C₂⁴	1	4	yes	—
173	C₂²×C₄×C₁₁	C₂⁴	1	2	yes	—
174	C₂²×C₄×C₁₁	C₂⁴	1	4	yes	—
175	C₂²×C₄×C₁₁	C₂⁴	1	2	yes	—
176	C₂²×C₄×C₁₁	C₂⁴	1	4	yes	—
177	C₂²×C₄×C₁₁	C₂⁴	1	2	yes	—
178	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
179	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
180	C₁₁×C₄⋊C₄	—	2	4	no	—
181	C₁₁×C₄⋊C₄	—	2	8	no	—
182	C₁₁×C₄⋊C₄	—	2	4	no	—
183	C₁₁×C₄⋊C₄	—	2	4	no	—
184	C₁₁×C₄⋊C₄	—	2	8	no	—
185	C₁₁×C₄⋊C₄	—	4	4	no	—
186	C₁₁×C₄⋊C₄	C₂²×C₄	1	8	yes	—
187	C₁₁×C₄⋊C₄	C₂×D₄	1	8	yes	—
188	C₁₁×C₂²⋊C₄	—	2	4	no	—
189	C₁₁×C₂²⋊C₄	—	2	16	no	—
190	C₁₁×C₂²⋊C₄	—	2	8	no	—
191	C₁₁×C₂²⋊C₄	—	2	16	no	—
192	C₁₁×C₂²⋊C₄	—	4	8	no	—
193	C₁₁×C₂²⋊C₄	—	4	8	no	—
194	C₁₁×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
195	C₁₁×C₂²⋊C₄	C₂²×C₄	1	32	yes	—
196	C₁₁×C₂²⋊C₄	C₂×D₄	1	8	yes	—
197	C₄²×C₁₁	—	2	2	no	—
198	C₄²×C₁₁	—	2	2	no	—
199	C₄²×C₁₁	—	2	8	no	—
200	C₄²×C₁₁	—	2	4	no	—
201	C₄²×C₁₁	—	2	4	no	—
202	C₄²×C₁₁	—	4	8	no	—
203	C₄²×C₁₁	C₂²×C₄	1	8	yes	—
204	C₄²×C₁₁	C₂×D₄	1	8	yes	—
205	C₂×#535	C₂×C₁₁	1	1	yes	characteristic
206	C₂×#518	C₂×C₁₁	1	1	yes	characteristic, complemented
207	C₂×C₄×#41	C₂×C₁₁	1	1	yes	characteristic, complemented
208	#2367	C₂×C₁₁	1	4	yes	complemented
209	#2366	C₂×C₁₁	1	4	yes	complemented
210	#2358	C₂×C₁₁	1	8	yes	complemented
211	#2324	C₂×C₁₁	1	4	yes	complemented
212	#2311	C₂×C₁₁	1	1	yes	characteristic, complemented
213	C₄×#121	C₂×C₁₁	1	4	yes	complemented
214	#2296	C₂×C₁₁	1	1	yes	characteristic, complemented
215	C₂×#390	C₂×C₁₁	1	1	yes	characteristic, complemented
216	#2274	C₂×C₁₁	1	1	yes	characteristic, complemented
217	C₂³×C₁₁	—	2	2	no	—
218	C₂³×C₁₁	—	2	2	no	—
219	C₂³×C₁₁	—	2	2	no	—
220	C₂³×C₁₁	—	2	4	no	—
221	C₂³×C₁₁	—	2	2	no	—
222	C₂³×C₁₁	—	2	4	no	—
223	C₂³×C₁₁	—	2	8	no	—
224	C₂³×C₁₁	—	2	4	no	—
225	C₂³×C₁₁	—	2	4	no	—
226	C₂³×C₁₁	—	2	8	no	—
227	C₂³×C₁₁	—	2	16	no	—
228	C₂³×C₁₁	—	4	16	no	—
229	C₂³×C₁₁	—	8	8	no	—
230	C₂³×C₁₁	—	8	4	no	—
231	C₂³×C₁₁	—	8	4	no	—
232	C₂³×C₁₁	C₂³×C₄	1	8	yes	—
233	C₂³×C₁₁	C₂³×C₄	1	4	yes	—
234	C₂³×C₁₁	C₂³×C₄	1	2	yes	—
235	C₂³×C₁₁	C₂²×D₄	1	2	yes	—
236	C₂³×C₁₁	C₂×#41	1	2	yes	—
237	C₂³×C₁₁	C₂⁵	1	1	yes	characteristic
238	Q₈×C₁₁	—	2	8	no	—
239	D₄×C₁₁	—	2	16	no	—
240	D₄×C₁₁	—	2	16	no	—
241	D₄×C₁₁	—	2	16	no	—
242	D₄×C₁₁	—	2	8	no	—
243	D₄×C₁₁	—	4	32	no	—
244	C₂×C₄×C₁₁	—	2	2	no	—
245	C₂×C₄×C₁₁	—	2	2	no	—
246	C₂×C₄×C₁₁	—	2	2	no	—
247	C₂×C₄×C₁₁	—	2	4	no	—
248	C₂×C₄×C₁₁	—	2	4	no	—
249	C₂×C₄×C₁₁	—	2	4	no	—
250	C₂×C₄×C₁₁	—	2	2	no	—
251	C₂×C₄×C₁₁	—	2	4	no	—
252	C₂×C₄×C₁₁	—	2	16	no	—
253	C₂×C₄×C₁₁	—	2	2	no	—
254	C₂×C₄×C₁₁	—	2	4	no	—
255	C₂×C₄×C₁₁	—	2	4	no	—
256	C₂×C₄×C₁₁	—	2	8	no	—
257	C₂×C₄×C₁₁	—	2	2	no	—
258	C₂×C₄×C₁₁	—	2	4	no	—
259	C₂×C₄×C₁₁	—	2	2	no	—
260	C₂×C₄×C₁₁	—	2	4	no	—
261	C₂×C₄×C₁₁	—	4	16	no	—
262	C₂×C₄×C₁₁	—	4	8	no	—
263	C₂×C₄×C₁₁	—	8	16	no	—
264	C₂×C₄×C₁₁	—	8	4	no	—
265	C₂×C₄×C₁₁	C₄×D₄	1	16	yes	complemented
266	C₂×C₄×C₁₁	C₂³×C₄	1	8	yes	—
267	C₂×C₄×C₁₁	C₂³×C₄	1	4	yes	—
268	C₂×C₄×C₁₁	C₂³×C₄	1	2	yes	—
269	C₂×C₄×C₁₁	C₂³×C₄	1	2	yes	—
270	C₂×C₄×C₁₁	C₂²×D₄	1	8	yes	—
271	C₂×C₄×C₁₁	C₂²×D₄	1	2	yes	—
272	C₂×C₄×C₁₁	C₂²×D₄	1	2	yes	—
273	C₂×C₄×C₁₁	C₂×#41	1	2	yes	—
274	C₂×C₄×C₁₁	C₂×#41	1	2	yes	—
275	C₂×C₄×C₁₁	H(5,𝔽₂)	1	4	yes	—
276	C₂²×#41	C₂²×C₁₁	1	1	yes	characteristic
277	C₂³×D₄	C₂²×C₁₁	1	1	yes	characteristic
278	#535	C₄×C₁₁	1	16	yes	complemented
279	C₂×#127	C₂²×C₁₁	1	2	yes	—
280	C₂×#124	C₂²×C₁₁	1	2	yes	—
281	C₂×#121	C₂²×C₁₁	1	4	yes	—
282	C₂×#120	C₂²×C₁₁	1	4	yes	—
283	#518	—	2	8	no	—
284	C₄×#41	—	2	8	no	—
285	C₂×C₄×Q₈	C₂²×C₁₁	1	2	yes	complemented
286	C₂×C₄×D₄	C₂²×C₁₁	1	4	yes	—
287	C₂×C₄×D₄	C₂²×C₁₁	1	4	yes	—
288	C₂×C₄×D₄	C₂²×C₁₁	1	4	yes	—
289	C₂×C₄×D₄	C₂²×C₁₁	1	2	yes	complemented
290	C₂×C₄×D₄	C₂²×C₁₁	1	8	yes	complemented
291	C₂×#117	C₂²×C₁₁	1	1	yes	characteristic
292	C₂×#117	C₂²×C₁₁	1	1	yes	characteristic
293	C₂×#117	C₂²×C₁₁	1	1	yes	characteristic
294	C₂×#117	C₂²×C₁₁	1	2	yes	complemented
295	C₂²×C₄⋊C₄	C₂²×C₁₁	1	1	yes	characteristic
296	C₂²×C₂²⋊C₄	C₂²×C₁₁	1	4	yes	—
297	C₂²×C₂²⋊C₄	C₂²×C₁₁	1	4	yes	—
298	C₂²×C₄²	C₂²×C₁₁	1	1	yes	characteristic
299	C₂²×C₄²	C₂²×C₁₁	1	2	yes	complemented
300	#391	C₂²×C₁₁	1	2	yes	complemented
301	#390	C₂²×C₁₁	1	2	yes	—
302	#390	C₂²×C₁₁	1	4	yes	—
303	#390	C₂²×C₁₁	1	2	yes	—
304	#390	C₂²×C₁₁	1	2	yes	complemented
305	#390	C₂²×C₁₁	1	8	yes	complemented
306	#389	C₂²×C₁₁	1	2	yes	complemented
307	#389	C₂²×C₁₁	1	2	yes	complemented
308	#388	C₂²×C₁₁	1	8	yes	complemented
309	#388	C₂²×C₁₁	1	8	yes	complemented
310	#386	C₂²×C₁₁	1	4	yes	—
311	#386	C₂²×C₁₁	1	8	yes	complemented
312	#386	C₂²×C₁₁	1	8	yes	complemented
313	#385	C₂²×C₁₁	1	4	yes	—
314	#385	C₂²×C₁₁	1	8	yes	complemented
315	#380	C₂²×C₁₁	1	4	yes	complemented
316	C₄×C₄⋊C₄	C₂²×C₁₁	1	4	yes	complemented
317	C₄×C₄⋊C₄	C₂²×C₁₁	1	4	yes	complemented
318	C₄×C₄⋊C₄	C₂²×C₁₁	1	4	yes	complemented
319	C₄×C₂²⋊C₄	C₂²×C₁₁	1	4	yes	—
320	C₄×C₂²⋊C₄	C₂²×C₁₁	1	8	yes	complemented
321	C₂²×C₁₁	—	2	4	no	—
322	C₂²×C₁₁	—	2	4	no	—
323	C₂²×C₁₁	—	2	2	no	—
324	C₂²×C₁₁	—	2	2	no	—
325	C₂²×C₁₁	—	2	4	no	—
326	C₂²×C₁₁	—	2	8	no	—
327	C₂²×C₁₁	—	2	8	no	—
328	C₂²×C₁₁	—	2	16	no	—
329	C₂²×C₁₁	—	4	4	no	—
330	C₂²×C₁₁	—	4	8	no	—
331	C₂²×C₁₁	—	4	2	no	—
332	C₂²×C₁₁	—	4	4	no	—
333	C₂²×C₁₁	—	4	2	no	—
334	C₂²×C₁₁	—	4	4	no	—
335	C₂²×C₁₁	—	8	16	no	—
336	C₂²×C₁₁	C₂×C₄×D₄	1	4	yes	—
337	C₂²×C₁₁	C₂⁴×C₄	1	1	yes	characteristic
338	C₂²×C₁₁	C₂³×D₄	1	1	yes	characteristic
339	C₂²×C₁₁	C₂²×#41	1	1	yes	characteristic
340	C₂²×C₁₁	C₂×H(5,𝔽₂)	1	2	yes	—
341	C₂²×C₁₁	#585	1	2	yes	—
342	C₄×C₁₁	—	2	4	no	—
343	C₄×C₁₁	—	2	8	no	—
344	C₄×C₁₁	—	2	4	no	—
345	C₄×C₁₁	—	2	8	no	—
346	C₄×C₁₁	—	4	2	no	—
347	C₄×C₁₁	—	4	4	no	—
348	C₄×C₁₁	—	4	4	no	—
349	C₄×C₁₁	C₂×C₄×D₄	1	4	yes	—
350	C₄×C₁₁	C₂×C₄×D₄	1	4	yes	—
351	C₂⁵	C₂³×C₁₁	1	2	yes	—
352	C₂×#41	—	2	4	no	—
353	C₂×#41	—	2	4	no	—
354	C₂×#41	C₂×C₄×C₁₁	1	8	yes	complemented
355	C₂²×Q₈	C₂³×C₁₁	1	1	yes	characteristic
356	C₂²×D₄	—	2	4	no	—
357	C₂²×D₄	—	2	4	no	—
358	C₂²×D₄	C₂×C₄×C₁₁	1	8	yes	complemented
359	C₂²×D₄	C₂³×C₁₁	1	2	yes	—
360	C₂²×D₄	C₂³×C₁₁	1	2	yes	—
361	C₂²×D₄	C₂³×C₁₁	1	2	yes	—
362	C₂²×D₄	C₂³×C₁₁	1	1	yes	characteristic
363	C₂²×D₄	C₂³×C₁₁	1	8	yes	—
364	C₂³×C₄	C₂³×C₁₁	1	2	yes	—
365	C₂³×C₄	C₂³×C₁₁	1	4	yes	—
366	C₂³×C₄	C₂³×C₁₁	1	2	yes	—
367	C₂³×C₄	C₂³×C₁₁	1	2	yes	—
368	C₂³×C₄	C₂³×C₁₁	1	8	yes	—
369	C₂³×C₄	C₂³×C₁₁	1	1	yes	characteristic
370	#127	C₂×C₄×C₁₁	1	16	yes	complemented
371	#124	C₂×C₄×C₁₁	1	16	yes	complemented
372	#121	C₂×C₄×C₁₁	1	32	yes	complemented
373	#120	C₂×C₄×C₁₁	1	32	yes	complemented
374	C₄×Q₈	—	2	8	no	—
375	C₄×D₄	—	2	16	no	—
376	C₄×D₄	—	2	8	no	—
377	C₄×D₄	—	2	16	no	—
378	C₄×D₄	—	2	16	no	—
379	C₄×D₄	—	4	16	no	—
380	#117	—	2	4	no	—
381	#117	—	2	8	no	—
382	#117	C₂×C₄×C₁₁	1	8	yes	complemented
383	#117	D₄×C₁₁	1	8	yes	complemented
384	C₂×C₄⋊C₄	—	2	4	no	—
385	C₂×C₄⋊C₄	C₂³×C₁₁	1	2	yes	—
386	C₂×C₄⋊C₄	C₂³×C₁₁	1	2	yes	—
387	C₂×C₄⋊C₄	C₂³×C₁₁	1	2	yes	—
388	C₂×C₄⋊C₄	C₂³×C₁₁	1	4	yes	—
389	C₂×C₄⋊C₄	C₂³×C₁₁	1	4	yes	—
390	C₂×C₄⋊C₄	C₂³×C₁₁	1	4	yes	—
391	C₂×C₄⋊C₄	C₂³×C₁₁	1	2	yes	—
392	C₂×C₄⋊C₄	C₂³×C₁₁	1	2	yes	—
393	C₂×C₂²⋊C₄	—	2	16	no	—
394	C₂×C₂²⋊C₄	—	4	8	no	—
395	C₂×C₂²⋊C₄	C₂³×C₁₁	1	2	yes	—
396	C₂×C₂²⋊C₄	C₂³×C₁₁	1	8	yes	—
397	C₂×C₂²⋊C₄	C₂³×C₁₁	1	8	yes	—
398	C₂×C₂²⋊C₄	C₂³×C₁₁	1	4	yes	—
399	C₂×C₂²⋊C₄	C₂³×C₁₁	1	8	yes	—
400	C₂×C₂²⋊C₄	C₂³×C₁₁	1	8	yes	—
401	C₂×C₂²⋊C₄	C₂³×C₁₁	1	2	yes	—
402	C₂×C₂²⋊C₄	C₂³×C₁₁	1	8	yes	—
403	C₂×C₂²⋊C₄	C₂³×C₁₁	1	2	yes	—
404	C₂×C₄²	—	2	4	no	—
405	C₂×C₄²	—	2	8	no	—
406	C₂×C₄²	C₂³×C₁₁	1	2	yes	—
407	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
408	C₂×C₄²	C₂³×C₁₁	1	4	yes	—
409	C₂×C₄²	C₂³×C₁₁	1	2	yes	—
410	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
411	C₂×C₄²	C₂³×C₁₁	1	8	yes	—
412	C₂×C₄²	C₂³×C₁₁	1	2	yes	—
413	C₂×C₄²	C₂³×C₁₁	1	2	yes	—
414	#95	C₂³×C₁₁	1	8	yes	—
415	#95	C₂³×C₁₁	1	4	yes	—
416	#95	C₂³×C₁₁	1	8	yes	—
417	#95	C₂³×C₁₁	1	4	yes	—
418	C₂×C₁₁	—	2	4	no	—
419	C₂×C₁₁	—	4	4	no	—
420	C₂×C₁₁	—	4	8	no	—
421	C₂×C₁₁	C₂²×C₄×D₄	1	1	yes	characteristic
422	C₂×C₁₁	C₄×H(5,𝔽₂)	1	2	yes	—
423	C₂×C₁₁	#3488	1	2	yes	—
424	C₂×C₁₁	#3508	1	1	yes	characteristic
425	C₂×C₁₁	#3510	1	1	yes	characteristic
426	C₂⁴	—	2	4	no	—
427	C₂⁴	—	2	4	no	—
428	C₂⁴	—	4	4	no	—
429	C₂⁴	—	4	4	no	—
430	C₂⁴	C₂²×C₄×C₁₁	1	8	yes	—
431	C₂⁴	C₂⁴×C₁₁	1	4	yes	—
432	C₂⁴	C₂⁴×C₁₁	1	2	yes	—
433	C₂⁴	C₂⁴×C₁₁	1	1	yes	characteristic
434	#41	—	2	32	no	—
435	C₂×Q₈	—	2	2	no	—
436	C₂×Q₈	—	2	2	no	—
437	C₂×Q₈	C₂²×C₄×C₁₁	1	4	yes	—
438	C₂×D₄	—	2	4	no	—
439	C₂×D₄	—	2	4	no	—
440	C₂×D₄	—	2	32	no	—
441	C₂×D₄	—	2	4	no	—
442	C₂×D₄	—	2	4	no	—
443	C₂×D₄	—	2	2	no	—
444	C₂×D₄	—	2	4	no	—
445	C₂×D₄	—	2	4	no	—
446	C₂×D₄	—	2	2	no	—
447	C₂×D₄	—	4	8	no	—
448	C₂×D₄	—	4	8	no	—
449	C₂×D₄	C₂²×C₄×C₁₁	1	8	yes	—
450	C₂×D₄	C₂²×C₄×C₁₁	1	8	yes	—
451	C₂×D₄	C₂²×C₄×C₁₁	1	8	yes	—
452	C₂×D₄	C₂²×C₄×C₁₁	1	4	yes	—
453	C₂×D₄	C₂²×C₄×C₁₁	1	32	yes	—
454	C₂²×C₄	—	2	4	no	—
455	C₂²×C₄	—	2	4	no	—
456	C₂²×C₄	—	2	4	no	—
457	C₂²×C₄	—	2	4	no	—
458	C₂²×C₄	—	2	8	no	—
459	C₂²×C₄	—	2	4	no	—
460	C₂²×C₄	—	2	8	no	—
461	C₂²×C₄	—	2	16	no	—
462	C₂²×C₄	—	4	4	no	—
463	C₂²×C₄	—	4	2	no	—
464	C₂²×C₄	—	4	4	no	—
465	C₂²×C₄	—	4	8	no	—
466	C₂²×C₄	—	4	8	no	—
467	C₂²×C₄	C₂²×C₄×C₁₁	1	8	yes	—
468	C₂²×C₄	C₂²×C₄×C₁₁	1	4	yes	—
469	C₂²×C₄	C₂×D₄×C₁₁	1	4	yes	—
470	C₂²×C₄	C₁₁×#41	1	4	yes	—
471	C₂²×C₄	C₂⁴×C₁₁	1	4	yes	—
472	C₂²×C₄	C₂⁴×C₁₁	1	4	yes	—
473	C₂²×C₄	C₂⁴×C₁₁	1	2	yes	—
474	C₂²×C₄	C₂⁴×C₁₁	1	4	yes	—
475	C₂²×C₄	C₂⁴×C₁₁	1	2	yes	—
476	C₂²×C₄	C₂⁴×C₁₁	1	4	yes	—
477	C₂²×C₄	C₂⁴×C₁₁	1	2	yes	—
478	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
479	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
480	C₄⋊C₄	—	2	4	no	—
481	C₄⋊C₄	—	2	8	no	—
482	C₄⋊C₄	—	2	4	no	—
483	C₄⋊C₄	—	2	4	no	—
484	C₄⋊C₄	—	2	8	no	—
485	C₄⋊C₄	—	4	4	no	—
486	C₄⋊C₄	C₂²×C₄×C₁₁	1	8	yes	—
487	C₄⋊C₄	C₂×D₄×C₁₁	1	8	yes	—
488	C₂²⋊C₄	—	2	4	no	—
489	C₂²⋊C₄	—	2	16	no	—
490	C₂²⋊C₄	—	2	8	no	—
491	C₂²⋊C₄	—	2	16	no	—
492	C₂²⋊C₄	—	4	8	no	—
493	C₂²⋊C₄	—	4	8	no	—
494	C₂²⋊C₄	C₂²×C₄×C₁₁	1	8	yes	—
495	C₂²⋊C₄	C₂²×C₄×C₁₁	1	32	yes	—
496	C₂²⋊C₄	C₂×D₄×C₁₁	1	8	yes	—
497	C₄²	—	2	2	no	—
498	C₄²	—	2	2	no	—
499	C₄²	—	2	8	no	—
500	C₄²	—	2	4	no	—
501	C₄²	—	2	4	no	—
502	C₄²	—	4	8	no	—
503	C₄²	C₂²×C₄×C₁₁	1	8	yes	—
504	C₄²	C₂×D₄×C₁₁	1	8	yes	—
505	C₁₁	#34269	1	1	yes	characteristic, direct product factor, Sylow
506	C₂³	—	2	2	no	—
507	C₂³	—	2	2	no	—
508	C₂³	—	2	2	no	—
509	C₂³	—	2	4	no	—
510	C₂³	—	2	2	no	—
511	C₂³	—	2	4	no	—
512	C₂³	—	2	8	no	—
513	C₂³	—	2	4	no	—
514	C₂³	—	2	4	no	—
515	C₂³	—	2	8	no	—
516	C₂³	—	2	16	no	—
517	C₂³	—	4	16	no	—
518	C₂³	—	8	8	no	—
519	C₂³	—	8	4	no	—
520	C₂³	—	8	4	no	—
521	C₂³	C₂³×C₄×C₁₁	1	8	yes	—
522	C₂³	C₂³×C₄×C₁₁	1	4	yes	—
523	C₂³	C₂³×C₄×C₁₁	1	2	yes	—
524	C₂³	C₂²×D₄×C₁₁	1	2	yes	—
525	C₂³	C₂×C₁₁×#41	1	2	yes	—
526	C₂³	C₂⁵×C₁₁	1	1	yes	characteristic
527	Q₈	—	2	8	no	—
528	D₄	—	2	16	no	—
529	D₄	—	2	16	no	—
530	D₄	—	2	16	no	—
531	D₄	—	2	8	no	—
532	D₄	—	4	32	no	—
533	C₂×C₄	—	2	2	no	—
534	C₂×C₄	—	2	2	no	—
535	C₂×C₄	—	2	2	no	—
536	C₂×C₄	—	2	4	no	—
537	C₂×C₄	—	2	4	no	—
538	C₂×C₄	—	2	4	no	—
539	C₂×C₄	—	2	2	no	—
540	C₂×C₄	—	2	4	no	—
541	C₂×C₄	—	2	16	no	—
542	C₂×C₄	—	2	2	no	—
543	C₂×C₄	—	2	4	no	—
544	C₂×C₄	—	2	4	no	—
545	C₂×C₄	—	2	8	no	—
546	C₂×C₄	—	2	2	no	—
547	C₂×C₄	—	2	4	no	—
548	C₂×C₄	—	2	2	no	—
549	C₂×C₄	—	2	4	no	—
550	C₂×C₄	—	4	16	no	—
551	C₂×C₄	—	4	8	no	—
552	C₂×C₄	—	8	16	no	—
553	C₂×C₄	—	8	4	no	—
554	C₂×C₄	C₄×D₄×C₁₁	1	16	yes	complemented
555	C₂×C₄	C₂³×C₄×C₁₁	1	8	yes	—
556	C₂×C₄	C₂³×C₄×C₁₁	1	4	yes	—
557	C₂×C₄	C₂³×C₄×C₁₁	1	2	yes	—
558	C₂×C₄	C₂³×C₄×C₁₁	1	2	yes	—
559	C₂×C₄	C₂²×D₄×C₁₁	1	8	yes	—
560	C₂×C₄	C₂²×D₄×C₁₁	1	2	yes	—
561	C₂×C₄	C₂²×D₄×C₁₁	1	2	yes	—
562	C₂×C₄	C₂×C₁₁×#41	1	2	yes	—
563	C₂×C₄	C₂×C₁₁×#41	1	2	yes	—
564	C₂×C₄	C₁₁×H(5,𝔽₂)	1	4	yes	—
565	C₂²	—	2	4	no	—
566	C₂²	—	2	4	no	—
567	C₂²	—	2	2	no	—
568	C₂²	—	2	2	no	—
569	C₂²	—	2	4	no	—
570	C₂²	—	2	8	no	—
571	C₂²	—	2	8	no	—
572	C₂²	—	2	16	no	—
573	C₂²	—	4	4	no	—
574	C₂²	—	4	8	no	—
575	C₂²	—	4	4	no	—
576	C₂²	—	4	2	no	—
577	C₂²	—	4	4	no	—
578	C₂²	—	4	2	no	—
579	C₂²	—	8	16	no	—
580	C₂²	C₂×C₄×D₄×C₁₁	1	4	yes	—
581	C₂²	C₂⁴×C₄×C₁₁	1	1	yes	characteristic
582	C₂²	C₂³×D₄×C₁₁	1	1	yes	characteristic
583	C₂²	C₂²×C₁₁×#41	1	1	yes	characteristic
584	C₂²	C₂×C₁₁×H(5,𝔽₂)	1	2	yes	—
585	C₂²	C₁₁×#585	1	2	yes	—
586	C₄	—	2	4	no	—
587	C₄	—	2	8	no	—
588	C₄	—	2	4	no	—
589	C₄	—	2	8	no	—
590	C₄	—	4	2	no	—
591	C₄	—	4	4	no	—
592	C₄	—	4	4	no	—
593	C₄	C₂×C₄×D₄×C₁₁	1	4	yes	—
594	C₄	C₂×C₄×D₄×C₁₁	1	4	yes	—
595	C₂	—	2	4	no	—
596	C₂	—	4	8	no	—
597	C₂	—	4	4	no	—
598	C₂	C₂²×C₄×D₄×C₁₁	1	1	yes	characteristic
599	C₂	C₄×C₁₁×H(5,𝔽₂)	1	2	yes	—
600	C₂	C₁₁×#3488	1	2	yes	—
601	C₂	C₁₁×#3508	1	1	yes	characteristic
602	C₂	C₁₁×#3510	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₁	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₁₁
Frattini, cosocle	C₂³	C₂⁵×C₁₁
prime radical	C₂×C₁₁×#535	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. C₂×C₁₁×#518	C₂	semidirect
3. C₂×C₄×C₁₁×#41	C₂	semidirect
4. C₁₁×#2367	C₂	semidirect
5. C₁₁×#2366	C₂	semidirect
6. C₁₁×#2358	C₂	semidirect
7. C₁₁×#2324	C₂	semidirect
8. C₁₁×#2311	C₂	semidirect
9. C₄×C₁₁×#121	C₂	semidirect
10. C₁₁×#2296	C₂	semidirect
11. C₂×C₁₁×#390	C₂	semidirect
12. C₁₁×#2274	C₂	semidirect
15. C₁₁×#535	C₄	semidirect
22. C₂×C₄×Q₈×C₁₁	C₂²	semidirect
26. C₂×C₄×D₄×C₁₁	C₂²	semidirect
27. C₂×C₄×D₄×C₁₁	C₂²	semidirect
31. C₂×C₁₁×#117	C₂²	semidirect
36. C₂²×C₄²×C₁₁	C₂²	semidirect
37. C₁₁×#391	C₂²	semidirect
41. C₁₁×#390	C₂²	semidirect
42. C₁₁×#390	C₂²	semidirect
43. C₁₁×#389	C₂²	semidirect
44. C₁₁×#389	C₂²	semidirect
45. C₁₁×#388	C₂²	semidirect
46. C₁₁×#388	C₂²	semidirect
48. C₁₁×#386	C₂²	semidirect
49. C₁₁×#386	C₂²	semidirect
51. C₁₁×#385	C₂²	semidirect
52. C₁₁×#380	C₂²	semidirect
53. C₄×C₁₁×C₄⋊C₄	C₂²	semidirect
54. C₄×C₁₁×C₄⋊C₄	C₂²	semidirect
55. C₄×C₁₁×C₄⋊C₄	C₂²	semidirect
57. C₄×C₁₁×C₂²⋊C₄	C₂²	semidirect
61. C₂×C₁₁×#41	C₂×C₄	semidirect
65. C₂²×D₄×C₁₁	C₂×C₄	semidirect
77. C₁₁×#127	C₂×C₄	semidirect
78. C₁₁×#124	C₂×C₄	semidirect
79. C₁₁×#121	C₂×C₄	semidirect
80. C₁₁×#120	C₂×C₄	semidirect
89. C₁₁×#117	C₂×C₄	semidirect
90. C₁₁×#117	D₄	semidirect
125. #34269	C₁₁	direct (N × H)
206. C₂×#518	C₂×C₁₁	semidirect
207. C₂×C₄×#41	C₂×C₁₁	semidirect
208. #2367	C₂×C₁₁	semidirect
209. #2366	C₂×C₁₁	semidirect
210. #2358	C₂×C₁₁	semidirect
211. #2324	C₂×C₁₁	semidirect
212. #2311	C₂×C₁₁	semidirect
213. C₄×#121	C₂×C₁₁	semidirect
214. #2296	C₂×C₁₁	semidirect
215. C₂×#390	C₂×C₁₁	semidirect
216. #2274	C₂×C₁₁	semidirect
265. C₂×C₄×C₁₁	C₄×D₄	semidirect
278. #535	C₄×C₁₁	semidirect
285. C₂×C₄×Q₈	C₂²×C₁₁	semidirect
289. C₂×C₄×D₄	C₂²×C₁₁	semidirect
290. C₂×C₄×D₄	C₂²×C₁₁	semidirect
294. C₂×#117	C₂²×C₁₁	semidirect
299. C₂²×C₄²	C₂²×C₁₁	semidirect
300. #391	C₂²×C₁₁	semidirect
304. #390	C₂²×C₁₁	semidirect
305. #390	C₂²×C₁₁	semidirect
306. #389	C₂²×C₁₁	semidirect
307. #389	C₂²×C₁₁	semidirect
308. #388	C₂²×C₁₁	semidirect
309. #388	C₂²×C₁₁	semidirect
311. #386	C₂²×C₁₁	semidirect
312. #386	C₂²×C₁₁	semidirect
314. #385	C₂²×C₁₁	semidirect
315. #380	C₂²×C₁₁	semidirect
316. C₄×C₄⋊C₄	C₂²×C₁₁	semidirect
317. C₄×C₄⋊C₄	C₂²×C₁₁	semidirect
318. C₄×C₄⋊C₄	C₂²×C₁₁	semidirect
320. C₄×C₂²⋊C₄	C₂²×C₁₁	semidirect
354. C₂×#41	C₂×C₄×C₁₁	semidirect
358. C₂²×D₄	C₂×C₄×C₁₁	semidirect
370. #127	C₂×C₄×C₁₁	semidirect
371. #124	C₂×C₄×C₁₁	semidirect
372. #121	C₂×C₄×C₁₁	semidirect
373. #120	C₂×C₄×C₁₁	semidirect
382. #117	C₂×C₄×C₁₁	semidirect
383. #117	D₄×C₁₁	semidirect
505. C₁₁	#34269	direct (N × H)
554. C₂×C₄	C₄×D₄×C₁₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₁×#535	2
C₂×C₁₁×#518	2
C₂×C₄×C₁₁×#41	2
C₁₁×#2367	2
C₁₁×#2366	2
C₁₁×#2358	2
C₁₁×#2324	2
C₁₁×#2311	2
C₄×C₁₁×#121	2
C₁₁×#2296	2
C₂×C₁₁×#390	2
C₁₁×#2274	2
#34269	11

Subgroups — C11×#34269 #14611462

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#34269 #14611462