Subgroups — C₁₁×#36591 #14613784

Order 2816.

1838 conjugacy classes of subgroups.

The subgroup lattice has 680 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×#2861	C₂	1	2	yes	maximal, complemented
2	C₁₁×#2858	C₂	1	1	yes	maximal, characteristic
3	C₁₁×#2595	C₂	1	4	yes	maximal, complemented
4	C₁₁×#2568	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₁×#2548	C₂	1	1	yes	maximal, characteristic
6	C₁₁×#2516	C₂	1	4	yes	maximal, complemented
7	C₁₁×#2513	C₂	1	2	yes	maximal, complemented
8	C₁₁×#2448	C₂	1	2	yes	maximal, complemented
9	C₁₁×#2448	C₂	1	2	yes	maximal, complemented
10	C₁₁×#2447	C₂	1	2	yes	maximal, complemented
11	C₁₁×#2367	C₂	1	2	yes	maximal, complemented
12	C₁₁×#2366	C₂	1	1	yes	maximal, characteristic
13	C₁₁×#2365	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₁×#2357	C₂	1	2	yes	maximal, complemented
15	C₄×C₁₁×#125	C₂	1	1	yes	maximal, characteristic, complemented
16	C₄×C₁₁×#124	C₂	1	2	yes	maximal, complemented
17	C₄²×Q₈×C₁₁	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×C₁₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic
19	C₂×C₁₁×#127	C₂²	1	1	yes	characteristic
20	C₂×C₁₁×#125	C₂²	1	1	yes	characteristic
21	C₂×C₁₁×#124	C₂²	1	2	yes	—
22	C₂×C₁₁×#124	C₂²	1	2	yes	—
23	C₂×C₁₁×#124	C₂²	1	2	yes	—
24	C₂×C₄×Q₈×C₁₁	C₂²	1	1	yes	characteristic
25	C₂×C₄×Q₈×C₁₁	C₂²	1	1	yes	characteristic
26	C₂×C₄×Q₈×C₁₁	C₂²	1	1	yes	characteristic
27	C₂×C₄×Q₈×C₁₁	C₂²	1	2	yes	—
28	C₂×C₄×D₄×C₁₁	C₂²	1	2	yes	—
29	C₂×C₄×D₄×C₁₁	C₂²	1	2	yes	—
30	C₁₁×#400	C₂²	1	4	yes	—
31	C₁₁×#399	C₂²	1	4	yes	—
32	C₁₁×#397	C₂²	1	4	yes	—
33	C₁₁×#397	C₂²	1	4	yes	—
34	C₁₁×#397	C₂²	1	4	yes	—
35	C₁₁×#394	C₂²	1	4	yes	—
36	C₁₁×#391	C₂²	1	2	yes	—
37	C₁₁×#391	C₂²	1	2	yes	—
38	C₁₁×#391	C₂²	1	2	yes	—
39	C₁₁×#391	C₂²	1	2	yes	—
40	C₁₁×#390	C₂²	1	2	yes	—
41	C₁₁×#390	C₂²	1	2	yes	—
42	C₁₁×#390	C₂²	1	2	yes	—
43	C₁₁×#390	C₂²	1	2	yes	—
44	C₁₁×#390	C₂²	1	2	yes	—
45	C₁₁×#390	C₂²	1	2	yes	—
46	C₁₁×#390	C₂²	1	2	yes	—
47	C₁₁×#390	C₂²	1	2	yes	—
48	C₁₁×#390	C₂²	1	2	yes	—
49	C₁₁×#389	C₂²	1	1	yes	characteristic
50	C₁₁×#389	C₂²	1	1	yes	characteristic
51	C₁₁×#389	C₂²	1	2	yes	—
52	C₁₁×#388	C₂²	1	4	yes	—
53	C₁₁×#388	C₂²	1	4	yes	—
54	C₁₁×#388	C₂²	1	4	yes	—
55	C₁₁×#388	C₂²	1	4	yes	—
56	C₁₁×#388	C₂²	1	4	yes	—
57	C₁₁×#388	C₂²	1	4	yes	—
58	C₁₁×#388	C₂²	1	4	yes	—
59	C₁₁×#388	C₂²	1	4	yes	—
60	C₁₁×#387	C₂²	1	2	yes	—
61	C₁₁×#387	C₂²	1	4	yes	—
62	C₁₁×#387	C₂²	1	2	yes	—
63	C₁₁×#386	C₂²	1	4	yes	—
64	C₁₁×#385	C₂²	1	4	yes	—
65	C₁₁×#382	C₂²	1	2	yes	—
66	C₁₁×#382	C₂²	1	1	yes	characteristic
67	C₁₁×#381	C₂²	1	4	yes	—
68	C₄×C₁₁×C₄⋊C₄	C₂²	1	2	yes	—
69	C₄×C₁₁×C₄⋊C₄	C₂²	1	2	yes	—
70	C₄×C₁₁×C₄⋊C₄	C₂²	1	1	yes	characteristic
71	C₄×C₁₁×C₄⋊C₄	C₂²	1	2	yes	—
72	C₄×C₁₁×C₄⋊C₄	C₂²	1	2	yes	—
73	C₄×C₁₁×C₄⋊C₄	C₂²	1	2	yes	—
74	C₄×C₁₁×C₄⋊C₄	C₂²	1	1	yes	characteristic
75	C₄×C₁₁×C₄⋊C₄	C₂²	1	1	yes	characteristic
76	C₄×C₁₁×C₄⋊C₄	C₂²	1	1	yes	characteristic
77	C₄×C₁₁×C₄⋊C₄	C₂²	1	1	yes	characteristic
78	C₄×C₁₁×C₄⋊C₄	C₂²	1	2	yes	—
79	C₄×C₁₁×C₂²⋊C₄	C₂²	1	4	yes	—
80	C₄×C₁₁×C₂²⋊C₄	C₂²	1	4	yes	—
81	C₄³×C₁₁	C₂²	1	2	yes	—
82	C₄³×C₁₁	C₂²	1	1	yes	characteristic
83	C₂²×Q₈×C₁₁	C₂³	1	2	yes	—
84	C₂²×Q₈×C₁₁	C₂³	1	1	yes	characteristic
85	C₂²×D₄×C₁₁	C₂³	1	2	yes	—
86	C₂²×D₄×C₁₁	C₂³	1	2	yes	—
87	C₂²×D₄×C₁₁	C₂³	1	2	yes	—
88	C₂³×C₄×C₁₁	C₂³	1	4	yes	—
89	C₁₁×C₄⋊Q₈	—	2	4	no	—
90	C₁₁×#127	—	2	4	no	—
91	C₁₁×#125	—	2	4	no	—
92	C₁₁×#124	—	2	8	no	—
93	C₁₁×#124	—	2	8	no	—
94	C₁₁×#124	—	4	4	no	—
95	C₄×Q₈×C₁₁	—	2	4	no	—
96	C₄×Q₈×C₁₁	—	2	4	no	—
97	C₄×Q₈×C₁₁	—	2	4	no	—
98	C₄×Q₈×C₁₁	—	4	4	no	—
99	C₄×D₄×C₁₁	—	2	8	no	—
100	C₄×D₄×C₁₁	—	4	4	no	—
101	C₂×C₁₁×C₄⋊C₄	C₂³	1	1	yes	characteristic
102	C₂×C₁₁×C₄⋊C₄	C₂³	1	1	yes	characteristic
103	C₂×C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
104	C₂×C₁₁×C₄⋊C₄	C₂³	1	1	yes	characteristic
105	C₂×C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
106	C₂×C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
107	C₂×C₁₁×C₄⋊C₄	C₂³	1	1	yes	characteristic
108	C₂×C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
109	C₂×C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
110	C₂×C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
111	C₂×C₁₁×C₄⋊C₄	C₂³	1	1	yes	characteristic
112	C₂×C₁₁×C₄⋊C₄	C₂³	1	1	yes	characteristic
113	C₂×C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
114	C₂×C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
115	C₂×C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
116	C₂×C₁₁×C₄⋊C₄	C₂³	1	4	yes	—
117	C₂×C₁₁×C₄⋊C₄	C₂³	1	1	yes	characteristic
118	C₂×C₁₁×C₂²⋊C₄	C₂³	1	4	yes	—
119	C₂×C₁₁×C₂²⋊C₄	C₂³	1	4	yes	—
120	C₂×C₁₁×C₂²⋊C₄	C₂³	1	4	yes	—
121	C₂×C₁₁×C₂²⋊C₄	C₂³	1	4	yes	—
122	C₂×C₁₁×C₂²⋊C₄	C₂³	1	4	yes	—
123	C₂×C₁₁×C₂²⋊C₄	C₂³	1	4	yes	—
124	C₂×C₁₁×C₂²⋊C₄	C₂³	1	4	yes	—
125	C₂×C₁₁×C₂²⋊C₄	C₂³	1	4	yes	—
126	C₂×C₁₁×C₂²⋊C₄	C₂³	1	4	yes	—
127	C₂×C₁₁×C₂²⋊C₄	C₂³	1	4	yes	—
128	C₂×C₁₁×C₂²⋊C₄	C₂³	1	4	yes	—
129	C₂×C₄²×C₁₁	C₂³	1	2	yes	—
130	C₂×C₄²×C₁₁	C₂³	1	2	yes	—
131	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
132	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
133	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
134	C₂×C₄²×C₁₁	C₂³	1	2	yes	—
135	C₂×C₄²×C₁₁	C₂³	1	2	yes	—
136	C₂×C₄²×C₁₁	C₂³	1	2	yes	—
137	C₂×C₄²×C₁₁	C₂³	1	2	yes	—
138	C₂×C₄²×C₁₁	C₂³	1	2	yes	—
139	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
140	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
141	C₂×C₄²×C₁₁	C₂³	1	2	yes	—
142	C₂×C₄²×C₁₁	C₂³	1	4	yes	—
143	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
144	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
145	C₁₁×#95	C₂³	1	2	yes	—
146	C₁₁×#95	C₂³	1	2	yes	—
147	C₁₁×#95	C₂³	1	4	yes	—
148	C₁₁×#95	C₂³	1	4	yes	—
149	C₁₁×#95	C₂³	1	2	yes	—
150	C₁₁×#95	C₂³	1	2	yes	—
151	C₁₁×#95	C₂³	1	2	yes	—
152	C₁₁×#95	C₂³	1	2	yes	—
153	C₁₁×#95	C₂³	1	4	yes	—
154	C₁₁×#95	C₂³	1	2	yes	—
155	C₁₁×#95	C₂³	1	2	yes	—
156	C₁₁×#95	C₂³	1	2	yes	—
157	C₁₁×#95	C₂³	1	4	yes	—
158	C₁₁×#95	C₂³	1	4	yes	—
159	C₁₁×#95	C₂³	1	4	yes	—
160	#36591	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
161	C₂⁴×C₁₁	C₂⁴	1	4	yes	—
162	C₂×Q₈×C₁₁	—	2	2	no	—
163	C₂×Q₈×C₁₁	—	2	2	no	—
164	C₂×Q₈×C₁₁	—	2	4	no	—
165	C₂×Q₈×C₁₁	—	2	4	no	—
166	C₂×Q₈×C₁₁	—	2	4	no	—
167	C₂×Q₈×C₁₁	#41	1	4	yes	—
168	C₂×D₄×C₁₁	—	2	4	no	—
169	C₂×D₄×C₁₁	—	2	4	no	—
170	C₂×D₄×C₁₁	—	2	4	no	—
171	C₂×D₄×C₁₁	—	2	4	no	—
172	C₂×D₄×C₁₁	—	2	4	no	—
173	C₂×D₄×C₁₁	—	2	4	no	—
174	C₂×D₄×C₁₁	—	2	4	no	—
175	C₂×D₄×C₁₁	—	4	2	no	—
176	C₂×D₄×C₁₁	—	4	2	no	—
177	C₂²×C₄×C₁₁	—	2	8	no	—
178	C₂²×C₄×C₁₁	—	4	4	no	—
179	C₂²×C₄×C₁₁	—	4	4	no	—
180	C₂²×C₄×C₁₁	C₂⁴	1	2	yes	—
181	C₂²×C₄×C₁₁	C₂⁴	1	2	yes	—
182	C₂²×C₄×C₁₁	C₂⁴	1	2	yes	—
183	C₂²×C₄×C₁₁	C₂⁴	1	2	yes	—
184	C₂²×C₄×C₁₁	C₂⁴	1	4	yes	—
185	C₂²×C₄×C₁₁	C₂⁴	1	2	yes	—
186	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
187	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
188	C₂²×C₄×C₁₁	C₂⁴	1	2	yes	—
189	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
190	C₂²×C₄×C₁₁	C₂⁴	1	2	yes	—
191	C₂²×C₄×C₁₁	C₂⁴	1	2	yes	—
192	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
193	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
194	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
195	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
196	C₁₁×C₄⋊C₄	—	2	4	no	—
197	C₁₁×C₄⋊C₄	—	2	4	no	—
198	C₁₁×C₄⋊C₄	—	2	4	no	—
199	C₁₁×C₄⋊C₄	—	2	2	no	—
200	C₁₁×C₄⋊C₄	—	2	2	no	—
201	C₁₁×C₄⋊C₄	—	2	4	no	—
202	C₁₁×C₄⋊C₄	—	2	4	no	—
203	C₁₁×C₄⋊C₄	—	2	2	no	—
204	C₁₁×C₄⋊C₄	—	2	2	no	—
205	C₁₁×C₄⋊C₄	—	2	4	no	—
206	C₁₁×C₄⋊C₄	—	2	4	no	—
207	C₁₁×C₄⋊C₄	—	2	2	no	—
208	C₁₁×C₄⋊C₄	—	2	2	no	—
209	C₁₁×C₄⋊C₄	—	4	2	no	—
210	C₁₁×C₄⋊C₄	—	4	2	no	—
211	C₁₁×C₄⋊C₄	—	4	4	no	—
212	C₁₁×C₄⋊C₄	#41	1	4	yes	—
213	C₁₁×C₂²⋊C₄	—	2	8	no	—
214	C₁₁×C₂²⋊C₄	—	2	8	no	—
215	C₁₁×C₂²⋊C₄	—	2	8	no	—
216	C₁₁×C₂²⋊C₄	—	2	8	no	—
217	C₁₁×C₂²⋊C₄	—	2	8	no	—
218	C₁₁×C₂²⋊C₄	—	4	4	no	—
219	C₁₁×C₂²⋊C₄	—	4	4	no	—
220	C₁₁×C₂²⋊C₄	—	4	4	no	—
221	C₁₁×C₂²⋊C₄	—	4	4	no	—
222	C₁₁×C₂²⋊C₄	—	4	4	no	—
223	C₁₁×C₂²⋊C₄	—	4	4	no	—
224	C₄²×C₁₁	—	2	4	no	—
225	C₄²×C₁₁	—	2	4	no	—
226	C₄²×C₁₁	—	2	4	no	—
227	C₄²×C₁₁	—	2	2	no	—
228	C₄²×C₁₁	—	2	2	no	—
229	C₄²×C₁₁	—	2	4	no	—
230	C₄²×C₁₁	—	2	4	no	—
231	C₄²×C₁₁	—	2	4	no	—
232	C₄²×C₁₁	—	2	2	no	—
233	C₄²×C₁₁	—	4	2	no	—
234	C₄²×C₁₁	—	4	1	no	—
235	C₄²×C₁₁	—	4	1	no	—
236	C₄²×C₁₁	—	4	2	no	—
237	C₄²×C₁₁	—	4	4	no	—
238	C₄²×C₁₁	#41	1	4	yes	—
239	C₄²×C₁₁	#41	1	4	yes	—
240	#2861	C₂×C₁₁	1	2	yes	complemented
241	#2858	C₂×C₁₁	1	1	yes	characteristic
242	#2595	C₂×C₁₁	1	4	yes	complemented
243	#2568	C₂×C₁₁	1	1	yes	characteristic, complemented
244	#2548	C₂×C₁₁	1	1	yes	characteristic
245	#2516	C₂×C₁₁	1	4	yes	complemented
246	#2513	C₂×C₁₁	1	2	yes	complemented
247	#2448	C₂×C₁₁	1	2	yes	complemented
248	#2448	C₂×C₁₁	1	2	yes	complemented
249	#2447	C₂×C₁₁	1	2	yes	complemented
250	#2367	C₂×C₁₁	1	2	yes	complemented
251	#2366	C₂×C₁₁	1	1	yes	characteristic
252	#2365	C₂×C₁₁	1	1	yes	characteristic, complemented
253	#2357	C₂×C₁₁	1	2	yes	complemented
254	C₄×#125	C₂×C₁₁	1	1	yes	characteristic, complemented
255	C₄×#124	C₂×C₁₁	1	2	yes	complemented
256	C₄²×Q₈	C₂×C₁₁	1	1	yes	characteristic, complemented
257	C₂³×C₁₁	—	2	4	no	—
258	C₂³×C₁₁	—	2	4	no	—
259	C₂³×C₁₁	—	2	4	no	—
260	C₂³×C₁₁	—	2	4	no	—
261	C₂³×C₁₁	—	2	4	no	—
262	C₂³×C₁₁	—	2	4	no	—
263	C₂³×C₁₁	—	2	4	no	—
264	C₂³×C₁₁	C₂⁵	1	1	yes	characteristic
265	Q₈×C₁₁	—	2	8	no	—
266	Q₈×C₁₁	—	4	8	no	—
267	D₄×C₁₁	—	4	8	no	—
268	D₄×C₁₁	—	4	8	no	—
269	D₄×C₁₁	—	8	4	no	—
270	C₂×C₄×C₁₁	—	2	1	no	—
271	C₂×C₄×C₁₁	—	2	1	no	—
272	C₂×C₄×C₁₁	—	2	2	no	—
273	C₂×C₄×C₁₁	—	2	2	no	—
274	C₂×C₄×C₁₁	—	2	2	no	—
275	C₂×C₄×C₁₁	—	2	1	no	—
276	C₂×C₄×C₁₁	—	2	1	no	—
277	C₂×C₄×C₁₁	—	2	2	no	—
278	C₂×C₄×C₁₁	—	2	1	no	—
279	C₂×C₄×C₁₁	—	2	1	no	—
280	C₂×C₄×C₁₁	—	2	2	no	—
281	C₂×C₄×C₁₁	—	2	2	no	—
282	C₂×C₄×C₁₁	—	2	2	no	—
283	C₂×C₄×C₁₁	—	2	2	no	—
284	C₂×C₄×C₁₁	—	2	1	no	—
285	C₂×C₄×C₁₁	—	2	1	no	—
286	C₂×C₄×C₁₁	—	2	2	no	—
287	C₂×C₄×C₁₁	—	2	2	no	—
288	C₂×C₄×C₁₁	—	2	4	no	—
289	C₂×C₄×C₁₁	—	2	2	no	—
290	C₂×C₄×C₁₁	—	2	2	no	—
291	C₂×C₄×C₁₁	—	2	4	no	—
292	C₂×C₄×C₁₁	—	2	1	no	—
293	C₂×C₄×C₁₁	—	2	1	no	—
294	C₂×C₄×C₁₁	—	2	2	no	—
295	C₂×C₄×C₁₁	—	2	2	no	—
296	C₂×C₄×C₁₁	—	2	4	no	—
297	C₂×C₄×C₁₁	—	2	2	no	—
298	C₂×C₄×C₁₁	—	2	2	no	—
299	C₂×C₄×C₁₁	—	2	2	no	—
300	C₂×C₄×C₁₁	—	2	2	no	—
301	C₂×C₄×C₁₁	—	2	1	no	—
302	C₂×C₄×C₁₁	—	2	1	no	—
303	C₂×C₄×C₁₁	—	2	2	no	—
304	C₂×C₄×C₁₁	—	2	2	no	—
305	C₂×C₄×C₁₁	—	2	2	no	—
306	C₂×C₄×C₁₁	—	2	2	no	—
307	C₂×C₄×C₁₁	—	8	8	no	—
308	C₂×C₄×C₁₁	C₂×#41	1	4	yes	—
309	C₂×C₄×C₁₁	C₂×#41	1	4	yes	—
310	C₂×C₄×C₁₁	C₂×#41	1	2	yes	—
311	C₂×C₄×C₁₁	C₂×#41	1	2	yes	—
312	C₂×C₄×C₁₁	C₂×#41	1	2	yes	—
313	C₂×C₄×C₁₁	C₂×#41	1	2	yes	—
314	C₂×C₄×C₁₁	C₂×#41	1	2	yes	—
315	C₂×C₄×C₁₁	C₂×#41	1	2	yes	—
316	C₂×C₄×C₁₁	C₂×#41	1	2	yes	—
317	C₂×C₄×C₁₁	C₂×#41	1	2	yes	—
318	C₂×C₄×C₁₁	H(5,𝔽₂)	1	2	yes	—
319	C₂×C₄⋊Q₈	C₂²×C₁₁	1	1	yes	characteristic
320	C₂×#127	C₂²×C₁₁	1	1	yes	characteristic
321	C₂×#125	C₂²×C₁₁	1	1	yes	characteristic
322	C₂×#124	C₂²×C₁₁	1	2	yes	—
323	C₂×#124	C₂²×C₁₁	1	2	yes	—
324	C₂×#124	C₂²×C₁₁	1	2	yes	—
325	C₂×C₄×Q₈	C₂²×C₁₁	1	1	yes	characteristic
326	C₂×C₄×Q₈	C₂²×C₁₁	1	1	yes	characteristic
327	C₂×C₄×Q₈	C₂²×C₁₁	1	1	yes	characteristic
328	C₂×C₄×Q₈	C₂²×C₁₁	1	2	yes	—
329	C₂×C₄×D₄	C₂²×C₁₁	1	2	yes	—
330	C₂×C₄×D₄	C₂²×C₁₁	1	2	yes	—
331	#400	C₂²×C₁₁	1	4	yes	—
332	#399	C₂²×C₁₁	1	4	yes	—
333	#397	C₂²×C₁₁	1	4	yes	—
334	#397	C₂²×C₁₁	1	4	yes	—
335	#397	C₂²×C₁₁	1	4	yes	—
336	#394	C₂²×C₁₁	1	4	yes	—
337	#391	C₂²×C₁₁	1	2	yes	—
338	#391	C₂²×C₁₁	1	2	yes	—
339	#391	C₂²×C₁₁	1	2	yes	—
340	#391	C₂²×C₁₁	1	2	yes	—
341	#390	C₂²×C₁₁	1	2	yes	—
342	#390	C₂²×C₁₁	1	2	yes	—
343	#390	C₂²×C₁₁	1	2	yes	—
344	#390	C₂²×C₁₁	1	2	yes	—
345	#390	C₂²×C₁₁	1	2	yes	—
346	#390	C₂²×C₁₁	1	2	yes	—
347	#390	C₂²×C₁₁	1	2	yes	—
348	#390	C₂²×C₁₁	1	2	yes	—
349	#390	C₂²×C₁₁	1	2	yes	—
350	#389	C₂²×C₁₁	1	1	yes	characteristic
351	#389	C₂²×C₁₁	1	1	yes	characteristic
352	#389	C₂²×C₁₁	1	2	yes	—
353	#388	C₂²×C₁₁	1	4	yes	—
354	#388	C₂²×C₁₁	1	4	yes	—
355	#388	C₂²×C₁₁	1	4	yes	—
356	#388	C₂²×C₁₁	1	4	yes	—
357	#388	C₂²×C₁₁	1	4	yes	—
358	#388	C₂²×C₁₁	1	4	yes	—
359	#388	C₂²×C₁₁	1	4	yes	—
360	#388	C₂²×C₁₁	1	4	yes	—
361	#387	C₂²×C₁₁	1	2	yes	—
362	#387	C₂²×C₁₁	1	2	yes	—
363	#387	C₂²×C₁₁	1	4	yes	—
364	#386	C₂²×C₁₁	1	4	yes	—
365	#385	C₂²×C₁₁	1	4	yes	—
366	#382	C₂²×C₁₁	1	1	yes	characteristic
367	#382	C₂²×C₁₁	1	2	yes	—
368	#381	C₂²×C₁₁	1	4	yes	—
369	C₄×C₄⋊C₄	C₂²×C₁₁	1	1	yes	characteristic
370	C₄×C₄⋊C₄	C₂²×C₁₁	1	2	yes	—
371	C₄×C₄⋊C₄	C₂²×C₁₁	1	1	yes	characteristic
372	C₄×C₄⋊C₄	C₂²×C₁₁	1	2	yes	—
373	C₄×C₄⋊C₄	C₂²×C₁₁	1	2	yes	—
374	C₄×C₄⋊C₄	C₂²×C₁₁	1	1	yes	characteristic
375	C₄×C₄⋊C₄	C₂²×C₁₁	1	2	yes	—
376	C₄×C₄⋊C₄	C₂²×C₁₁	1	1	yes	characteristic
377	C₄×C₄⋊C₄	C₂²×C₁₁	1	2	yes	—
378	C₄×C₄⋊C₄	C₂²×C₁₁	1	1	yes	characteristic
379	C₄×C₄⋊C₄	C₂²×C₁₁	1	2	yes	—
380	C₄×C₂²⋊C₄	C₂²×C₁₁	1	4	yes	—
381	C₄×C₂²⋊C₄	C₂²×C₁₁	1	4	yes	—
382	C₄³	C₂²×C₁₁	1	1	yes	characteristic
383	C₄³	C₂²×C₁₁	1	2	yes	—
384	C₂²×C₁₁	—	4	4	no	—
385	C₂²×C₁₁	—	4	4	no	—
386	C₂²×C₁₁	—	4	4	no	—
387	C₂²×C₁₁	—	4	4	no	—
388	C₂²×C₁₁	—	4	4	no	—
389	C₂²×C₁₁	—	4	4	no	—
390	C₂²×C₁₁	—	4	4	no	—
391	C₂²×C₁₁	C₂²×#41	1	1	yes	characteristic
392	C₂²×C₁₁	C₂²×#41	1	1	yes	characteristic
393	C₂²×C₁₁	C₂²×#41	1	1	yes	characteristic
394	C₂²×C₁₁	C₂²×#41	1	1	yes	characteristic
395	C₂²×C₁₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
396	C₂²×C₁₁	#585	1	1	yes	characteristic
397	C₂²×C₁₁	#585	1	1	yes	characteristic
398	C₄×C₁₁	—	2	4	no	—
399	C₄×C₁₁	—	2	2	no	—
400	C₄×C₁₁	—	2	2	no	—
401	C₄×C₁₁	—	2	2	no	—
402	C₄×C₁₁	—	2	4	no	—
403	C₄×C₁₁	—	4	4	no	—
404	C₄×C₁₁	—	4	2	no	—
405	C₄×C₁₁	—	4	2	no	—
406	C₄×C₁₁	—	4	2	no	—
407	C₄×C₁₁	—	4	1	no	—
408	C₄×C₁₁	—	4	2	no	—
409	C₄×C₁₁	—	4	2	no	—
410	C₄×C₁₁	—	4	1	no	—
411	C₄×C₁₁	—	4	2	no	—
412	C₄×C₁₁	#529	1	4	yes	—
413	C₄×C₁₁	#559	1	4	yes	—
414	C₂²×Q₈	C₂³×C₁₁	1	2	yes	—
415	C₂²×Q₈	C₂³×C₁₁	1	1	yes	characteristic
416	C₂²×D₄	C₂³×C₁₁	1	2	yes	—
417	C₂²×D₄	C₂³×C₁₁	1	2	yes	—
418	C₂²×D₄	C₂³×C₁₁	1	2	yes	—
419	C₂³×C₄	C₂³×C₁₁	1	4	yes	—
420	C₄⋊Q₈	—	2	4	no	—
421	#127	—	2	4	no	—
422	#125	—	2	4	no	—
423	#124	—	2	8	no	—
424	#124	—	2	8	no	—
425	#124	—	4	4	no	—
426	C₄×Q₈	—	2	4	no	—
427	C₄×Q₈	—	2	4	no	—
428	C₄×Q₈	—	2	4	no	—
429	C₄×Q₈	—	4	4	no	—
430	C₄×D₄	—	2	8	no	—
431	C₄×D₄	—	4	4	no	—
432	C₂×C₄⋊C₄	C₂³×C₁₁	1	1	yes	characteristic
433	C₂×C₄⋊C₄	C₂³×C₁₁	1	1	yes	characteristic
434	C₂×C₄⋊C₄	C₂³×C₁₁	1	1	yes	characteristic
435	C₂×C₄⋊C₄	C₂³×C₁₁	1	2	yes	—
436	C₂×C₄⋊C₄	C₂³×C₁₁	1	1	yes	characteristic
437	C₂×C₄⋊C₄	C₂³×C₁₁	1	2	yes	—
438	C₂×C₄⋊C₄	C₂³×C₁₁	1	2	yes	—
439	C₂×C₄⋊C₄	C₂³×C₁₁	1	2	yes	—
440	C₂×C₄⋊C₄	C₂³×C₁₁	1	2	yes	—
441	C₂×C₄⋊C₄	C₂³×C₁₁	1	1	yes	characteristic
442	C₂×C₄⋊C₄	C₂³×C₁₁	1	1	yes	characteristic
443	C₂×C₄⋊C₄	C₂³×C₁₁	1	2	yes	—
444	C₂×C₄⋊C₄	C₂³×C₁₁	1	2	yes	—
445	C₂×C₄⋊C₄	C₂³×C₁₁	1	4	yes	—
446	C₂×C₄⋊C₄	C₂³×C₁₁	1	2	yes	—
447	C₂×C₄⋊C₄	C₂³×C₁₁	1	2	yes	—
448	C₂×C₄⋊C₄	C₂³×C₁₁	1	1	yes	characteristic
449	C₂×C₂²⋊C₄	C₂³×C₁₁	1	4	yes	—
450	C₂×C₂²⋊C₄	C₂³×C₁₁	1	4	yes	—
451	C₂×C₂²⋊C₄	C₂³×C₁₁	1	4	yes	—
452	C₂×C₂²⋊C₄	C₂³×C₁₁	1	4	yes	—
453	C₂×C₂²⋊C₄	C₂³×C₁₁	1	4	yes	—
454	C₂×C₂²⋊C₄	C₂³×C₁₁	1	4	yes	—
455	C₂×C₂²⋊C₄	C₂³×C₁₁	1	4	yes	—
456	C₂×C₂²⋊C₄	C₂³×C₁₁	1	4	yes	—
457	C₂×C₂²⋊C₄	C₂³×C₁₁	1	4	yes	—
458	C₂×C₂²⋊C₄	C₂³×C₁₁	1	4	yes	—
459	C₂×C₂²⋊C₄	C₂³×C₁₁	1	4	yes	—
460	C₂×C₄²	C₂³×C₁₁	1	2	yes	—
461	C₂×C₄²	C₂³×C₁₁	1	2	yes	—
462	C₂×C₄²	C₂³×C₁₁	1	2	yes	—
463	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
464	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
465	C₂×C₄²	C₂³×C₁₁	1	2	yes	—
466	C₂×C₄²	C₂³×C₁₁	1	2	yes	—
467	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
468	C₂×C₄²	C₂³×C₁₁	1	2	yes	—
469	C₂×C₄²	C₂³×C₁₁	1	4	yes	—
470	C₂×C₄²	C₂³×C₁₁	1	2	yes	—
471	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
472	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
473	C₂×C₄²	C₂³×C₁₁	1	2	yes	—
474	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
475	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
476	#95	C₂³×C₁₁	1	2	yes	—
477	#95	C₂³×C₁₁	1	2	yes	—
478	#95	C₂³×C₁₁	1	4	yes	—
479	#95	C₂³×C₁₁	1	4	yes	—
480	#95	C₂³×C₁₁	1	2	yes	—
481	#95	C₂³×C₁₁	1	2	yes	—
482	#95	C₂³×C₁₁	1	2	yes	—
483	#95	C₂³×C₁₁	1	2	yes	—
484	#95	C₂³×C₁₁	1	4	yes	—
485	#95	C₂³×C₁₁	1	2	yes	—
486	#95	C₂³×C₁₁	1	2	yes	—
487	#95	C₂³×C₁₁	1	2	yes	—
488	#95	C₂³×C₁₁	1	4	yes	—
489	#95	C₂³×C₁₁	1	4	yes	—
490	#95	C₂³×C₁₁	1	4	yes	—
491	C₂×C₁₁	—	8	4	no	—
492	C₂×C₁₁	C₂×#529	1	1	yes	characteristic
493	C₂×C₁₁	C₂×#559	1	1	yes	characteristic
494	C₂×C₁₁	#3480	1	1	yes	characteristic
495	C₂×C₁₁	#3480	1	1	yes	characteristic
496	C₂×C₁₁	#3510	1	1	yes	characteristic
497	C₂×C₁₁	#3514	1	1	yes	characteristic
498	C₂×C₁₁	#3517	1	1	yes	characteristic
499	C₂⁴	C₂⁴×C₁₁	1	4	yes	—
500	C₂×Q₈	—	2	2	no	—
501	C₂×Q₈	—	2	2	no	—
502	C₂×Q₈	—	2	4	no	—
503	C₂×Q₈	—	2	4	no	—
504	C₂×Q₈	—	2	4	no	—
505	C₂×Q₈	C₁₁×#41	1	4	yes	—
506	C₂×D₄	—	2	4	no	—
507	C₂×D₄	—	2	4	no	—
508	C₂×D₄	—	2	4	no	—
509	C₂×D₄	—	2	4	no	—
510	C₂×D₄	—	2	4	no	—
511	C₂×D₄	—	2	4	no	—
512	C₂×D₄	—	2	4	no	—
513	C₂×D₄	—	4	2	no	—
514	C₂×D₄	—	4	2	no	—
515	C₂²×C₄	—	2	8	no	—
516	C₂²×C₄	—	4	4	no	—
517	C₂²×C₄	—	4	4	no	—
518	C₂²×C₄	C₂⁴×C₁₁	1	2	yes	—
519	C₂²×C₄	C₂⁴×C₁₁	1	2	yes	—
520	C₂²×C₄	C₂⁴×C₁₁	1	2	yes	—
521	C₂²×C₄	C₂⁴×C₁₁	1	2	yes	—
522	C₂²×C₄	C₂⁴×C₁₁	1	4	yes	—
523	C₂²×C₄	C₂⁴×C₁₁	1	2	yes	—
524	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
525	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
526	C₂²×C₄	C₂⁴×C₁₁	1	2	yes	—
527	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
528	C₂²×C₄	C₂⁴×C₁₁	1	2	yes	—
529	C₂²×C₄	C₂⁴×C₁₁	1	2	yes	—
530	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
531	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
532	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
533	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
534	C₄⋊C₄	—	2	4	no	—
535	C₄⋊C₄	—	2	4	no	—
536	C₄⋊C₄	—	2	4	no	—
537	C₄⋊C₄	—	2	2	no	—
538	C₄⋊C₄	—	2	2	no	—
539	C₄⋊C₄	—	2	4	no	—
540	C₄⋊C₄	—	2	4	no	—
541	C₄⋊C₄	—	2	2	no	—
542	C₄⋊C₄	—	2	2	no	—
543	C₄⋊C₄	—	2	4	no	—
544	C₄⋊C₄	—	2	4	no	—
545	C₄⋊C₄	—	2	2	no	—
546	C₄⋊C₄	—	2	2	no	—
547	C₄⋊C₄	—	4	4	no	—
548	C₄⋊C₄	—	4	2	no	—
549	C₄⋊C₄	—	4	2	no	—
550	C₄⋊C₄	C₁₁×#41	1	4	yes	—
551	C₂²⋊C₄	—	2	8	no	—
552	C₂²⋊C₄	—	2	8	no	—
553	C₂²⋊C₄	—	2	8	no	—
554	C₂²⋊C₄	—	2	8	no	—
555	C₂²⋊C₄	—	2	8	no	—
556	C₂²⋊C₄	—	4	4	no	—
557	C₂²⋊C₄	—	4	4	no	—
558	C₂²⋊C₄	—	4	4	no	—
559	C₂²⋊C₄	—	4	4	no	—
560	C₂²⋊C₄	—	4	4	no	—
561	C₂²⋊C₄	—	4	4	no	—
562	C₄²	—	2	4	no	—
563	C₄²	—	2	4	no	—
564	C₄²	—	2	4	no	—
565	C₄²	—	2	2	no	—
566	C₄²	—	2	2	no	—
567	C₄²	—	2	4	no	—
568	C₄²	—	2	4	no	—
569	C₄²	—	2	4	no	—
570	C₄²	—	2	2	no	—
571	C₄²	—	4	4	no	—
572	C₄²	—	4	2	no	—
573	C₄²	—	4	1	no	—
574	C₄²	—	4	1	no	—
575	C₄²	—	4	2	no	—
576	C₄²	C₁₁×#41	1	4	yes	—
577	C₄²	C₁₁×#41	1	4	yes	—
578	C₁₁	#36591	1	1	yes	characteristic, direct product factor, Sylow
579	C₂³	—	2	4	no	—
580	C₂³	—	2	4	no	—
581	C₂³	—	2	4	no	—
582	C₂³	—	2	4	no	—
583	C₂³	—	2	4	no	—
584	C₂³	—	2	4	no	—
585	C₂³	—	2	4	no	—
586	C₂³	C₂⁵×C₁₁	1	1	yes	characteristic
587	Q₈	—	2	8	no	—
588	Q₈	—	4	8	no	—
589	D₄	—	4	8	no	—
590	D₄	—	4	8	no	—
591	D₄	—	8	4	no	—
592	C₂×C₄	—	2	1	no	—
593	C₂×C₄	—	2	1	no	—
594	C₂×C₄	—	2	2	no	—
595	C₂×C₄	—	2	2	no	—
596	C₂×C₄	—	2	2	no	—
597	C₂×C₄	—	2	1	no	—
598	C₂×C₄	—	2	1	no	—
599	C₂×C₄	—	2	2	no	—
600	C₂×C₄	—	2	1	no	—
601	C₂×C₄	—	2	1	no	—
602	C₂×C₄	—	2	2	no	—
603	C₂×C₄	—	2	2	no	—
604	C₂×C₄	—	2	2	no	—
605	C₂×C₄	—	2	2	no	—
606	C₂×C₄	—	2	1	no	—
607	C₂×C₄	—	2	1	no	—
608	C₂×C₄	—	2	2	no	—
609	C₂×C₄	—	2	2	no	—
610	C₂×C₄	—	2	4	no	—
611	C₂×C₄	—	2	2	no	—
612	C₂×C₄	—	2	2	no	—
613	C₂×C₄	—	2	4	no	—
614	C₂×C₄	—	2	1	no	—
615	C₂×C₄	—	2	1	no	—
616	C₂×C₄	—	2	2	no	—
617	C₂×C₄	—	2	2	no	—
618	C₂×C₄	—	2	4	no	—
619	C₂×C₄	—	2	2	no	—
620	C₂×C₄	—	2	2	no	—
621	C₂×C₄	—	2	2	no	—
622	C₂×C₄	—	2	2	no	—
623	C₂×C₄	—	2	1	no	—
624	C₂×C₄	—	2	1	no	—
625	C₂×C₄	—	2	2	no	—
626	C₂×C₄	—	2	2	no	—
627	C₂×C₄	—	2	2	no	—
628	C₂×C₄	—	2	2	no	—
629	C₂×C₄	—	8	8	no	—
630	C₂×C₄	C₂×C₁₁×#41	1	4	yes	—
631	C₂×C₄	C₂×C₁₁×#41	1	4	yes	—
632	C₂×C₄	C₂×C₁₁×#41	1	2	yes	—
633	C₂×C₄	C₂×C₁₁×#41	1	2	yes	—
634	C₂×C₄	C₂×C₁₁×#41	1	2	yes	—
635	C₂×C₄	C₂×C₁₁×#41	1	2	yes	—
636	C₂×C₄	C₂×C₁₁×#41	1	2	yes	—
637	C₂×C₄	C₂×C₁₁×#41	1	2	yes	—
638	C₂×C₄	C₂×C₁₁×#41	1	2	yes	—
639	C₂×C₄	C₂×C₁₁×#41	1	2	yes	—
640	C₂×C₄	C₁₁×H(5,𝔽₂)	1	2	yes	—
641	C₂²	—	4	4	no	—
642	C₂²	—	4	4	no	—
643	C₂²	—	4	4	no	—
644	C₂²	—	4	4	no	—
645	C₂²	—	4	4	no	—
646	C₂²	—	4	4	no	—
647	C₂²	—	4	4	no	—
648	C₂²	C₂²×C₁₁×#41	1	1	yes	characteristic
649	C₂²	C₂²×C₁₁×#41	1	1	yes	characteristic
650	C₂²	C₂²×C₁₁×#41	1	1	yes	characteristic
651	C₂²	C₂²×C₁₁×#41	1	1	yes	characteristic
652	C₂²	C₂×C₁₁×H(5,𝔽₂)	1	1	yes	characteristic
653	C₂²	C₁₁×#585	1	1	yes	characteristic
654	C₂²	C₁₁×#585	1	1	yes	characteristic
655	C₄	—	2	4	no	—
656	C₄	—	2	2	no	—
657	C₄	—	2	2	no	—
658	C₄	—	2	2	no	—
659	C₄	—	2	4	no	—
660	C₄	—	4	4	no	—
661	C₄	—	4	2	no	—
662	C₄	—	4	2	no	—
663	C₄	—	4	2	no	—
664	C₄	—	4	2	no	—
665	C₄	—	4	1	no	—
666	C₄	—	4	2	no	—
667	C₄	—	4	1	no	—
668	C₄	—	4	2	no	—
669	C₄	C₁₁×#529	1	4	yes	—
670	C₄	C₁₁×#559	1	4	yes	—
671	C₂	—	8	4	no	—
672	C₂	C₂×C₁₁×#529	1	1	yes	characteristic
673	C₂	C₂×C₁₁×#559	1	1	yes	characteristic
674	C₂	C₁₁×#3480	1	1	yes	characteristic
675	C₂	C₁₁×#3480	1	1	yes	characteristic
676	C₂	C₁₁×#3510	1	1	yes	characteristic
677	C₂	C₁₁×#3514	1	1	yes	characteristic
678	C₂	C₁₁×#3517	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₁	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₁
prime radical	C₂×C₁₁×#127	C₂²
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₁×#2861	C₂	semidirect
3. C₁₁×#2595	C₂	semidirect
4. C₁₁×#2568	C₂	semidirect
6. C₁₁×#2516	C₂	semidirect
7. C₁₁×#2513	C₂	semidirect
8. C₁₁×#2448	C₂	semidirect
9. C₁₁×#2448	C₂	semidirect
10. C₁₁×#2447	C₂	semidirect
11. C₁₁×#2367	C₂	semidirect
13. C₁₁×#2365	C₂	semidirect
14. C₁₁×#2357	C₂	semidirect
15. C₄×C₁₁×#125	C₂	semidirect
16. C₄×C₁₁×#124	C₂	semidirect
17. C₄²×Q₈×C₁₁	C₂	semidirect
160. #36591	C₁₁	direct (N × H)
240. #2861	C₂×C₁₁	semidirect
242. #2595	C₂×C₁₁	semidirect
243. #2568	C₂×C₁₁	semidirect
245. #2516	C₂×C₁₁	semidirect
246. #2513	C₂×C₁₁	semidirect
247. #2448	C₂×C₁₁	semidirect
248. #2448	C₂×C₁₁	semidirect
249. #2447	C₂×C₁₁	semidirect
250. #2367	C₂×C₁₁	semidirect
252. #2365	C₂×C₁₁	semidirect
253. #2357	C₂×C₁₁	semidirect
254. C₄×#125	C₂×C₁₁	semidirect
255. C₄×#124	C₂×C₁₁	semidirect
256. C₄²×Q₈	C₂×C₁₁	semidirect
578. C₁₁	#36591	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₁×#2861	2
C₁₁×#2858	2
C₁₁×#2595	2
C₁₁×#2568	2
C₁₁×#2548	2
C₁₁×#2516	2
C₁₁×#2513	2
C₁₁×#2448	2
C₁₁×#2447	2
C₁₁×#2367	2
C₁₁×#2366	2
C₁₁×#2365	2
C₁₁×#2357	2
C₄×C₁₁×#125	2
C₄×C₁₁×#124	2
C₄²×Q₈×C₁₁	2
#36591	11

Subgroups — C11×#36591 #14613784

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#36591 #14613784