Subgroups — C₁₁×#36631 #14613824

Order 2816.

2670 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×#529	C₂	1	2	yes	maximal, complemented
2	C₁₁×#2861	C₂	1	2	yes	maximal, complemented
3	C₁₁×#2860	C₂	1	4	yes	maximal, complemented
4	C₁₁×#2859	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₁×#2858	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₁×#2857	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₁×#2856	C₂	1	1	yes	maximal, characteristic
8	C₁₁×#2854	C₂	1	4	yes	maximal, complemented
9	C₁₁×#2850	C₂	1	2	yes	maximal, complemented
10	C₄×C₁₁×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×C₁₁×#127	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄×C₁₁×#124	C₂	1	2	yes	maximal, complemented
13	C₄×C₁₁×#121	C₂	1	4	yes	maximal, complemented
14	C₁₁×#2293	C₂	1	4	yes	maximal, complemented
15	C₂×C₄³×C₁₁	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₁₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic
17	C₂×C₁₁×#127	C₂²	1	1	yes	characteristic
18	C₁₁×#529	—	2	16	no	—
19	C₂×C₁₁×#126	C₂²	1	4	yes	—
20	C₂×C₁₁×#125	C₂²	1	2	yes	—
21	C₂×C₁₁×#124	C₂²	1	2	yes	—
22	C₂×C₁₁×#124	C₂²	1	2	yes	—
23	C₂×C₁₁×#123	C₂²	1	4	yes	—
24	C₂×C₁₁×C₂²⋊Q₈	C₂²	1	2	yes	—
25	C₂×C₁₁×#121	C₂²	1	2	yes	—
26	C₂×C₁₁×#121	C₂²	1	4	yes	—
27	C₂×C₄×Q₈×C₁₁	C₂²	1	2	yes	—
28	C₂×C₄×D₄×C₁₁	C₂²	1	4	yes	—
29	C₂×C₄×D₄×C₁₁	C₂²	1	2	yes	—
30	C₂×C₄×D₄×C₁₁	C₂²	1	4	yes	—
31	C₂×C₁₁×#117	C₂²	1	4	yes	—
32	C₂²×C₄²×C₁₁	C₂²	1	2	yes	—
33	C₂²×C₄²×C₁₁	C₂²	1	1	yes	characteristic
34	C₂²×C₄²×C₁₁	C₂²	1	2	yes	—
35	C₂²×C₄²×C₁₁	C₂²	1	1	yes	characteristic
36	C₂²×C₄²×C₁₁	C₂²	1	1	yes	characteristic
37	C₁₁×#391	C₂²	1	2	yes	—
38	C₁₁×#391	C₂²	1	2	yes	—
39	C₁₁×#390	C₂²	1	4	yes	—
40	C₁₁×#390	C₂²	1	4	yes	—
41	C₁₁×#390	C₂²	1	4	yes	—
42	C₁₁×#390	C₂²	1	2	yes	—
43	C₁₁×#390	C₂²	1	2	yes	—
44	C₁₁×#390	C₂²	1	4	yes	—
45	C₁₁×#389	C₂²	1	4	yes	—
46	C₁₁×#389	C₂²	1	4	yes	—
47	C₁₁×#389	C₂²	1	4	yes	—
48	C₁₁×#389	C₂²	1	4	yes	—
49	C₁₁×#388	C₂²	1	8	yes	—
50	C₁₁×#388	C₂²	1	8	yes	—
51	C₁₁×#388	C₂²	1	8	yes	—
52	C₁₁×#388	C₂²	1	8	yes	—
53	C₁₁×#386	C₂²	1	8	yes	—
54	C₁₁×#384	C₂²	1	1	yes	characteristic
55	C₁₁×#384	C₂²	1	1	yes	characteristic
56	C₁₁×#382	C₂²	1	2	yes	—
57	C₁₁×#380	C₂²	1	4	yes	—
58	C₄×C₁₁×C₄⋊C₄	C₂²	1	4	yes	—
59	C₄×C₁₁×C₂²⋊C₄	C₂²	1	8	yes	—
60	C₄³×C₁₁	C₂²	1	2	yes	—
61	C₄³×C₁₁	C₂²	1	1	yes	characteristic
62	C₄³×C₁₁	C₂²	1	1	yes	characteristic
63	C₄³×C₁₁	C₂²	1	1	yes	characteristic
64	C₄³×C₁₁	C₂²	1	2	yes	—
65	C₄³×C₁₁	C₂²	1	1	yes	characteristic
66	C₂²×Q₈×C₁₁	C₂³	1	2	yes	—
67	C₂²×D₄×C₁₁	C₂³	1	4	yes	—
68	C₂²×D₄×C₁₁	C₂³	1	2	yes	—
69	C₂²×D₄×C₁₁	C₂³	1	4	yes	—
70	C₂³×C₄×C₁₁	C₂³	1	2	yes	—
71	C₂³×C₄×C₁₁	C₂³	1	4	yes	—
72	C₂³×C₄×C₁₁	C₂³	1	1	yes	characteristic
73	C₂³×C₄×C₁₁	C₂³	1	1	yes	characteristic
74	C₂³×C₄×C₁₁	C₂³	1	1	yes	characteristic
75	C₂³×C₄×C₁₁	C₂³	1	2	yes	—
76	C₁₁×C₄⋊Q₈	—	2	4	no	—
77	C₁₁×#127	—	2	4	no	—
78	C₁₁×#126	—	2	16	no	—
79	C₁₁×#125	—	2	8	no	—
80	C₁₁×#124	—	2	8	no	—
81	C₁₁×#124	—	2	8	no	—
82	C₁₁×#123	—	2	16	no	—
83	C₁₁×C₂²⋊Q₈	—	2	8	no	—
84	C₁₁×#121	—	2	8	no	—
85	C₁₁×#121	—	2	16	no	—
86	C₄×Q₈×C₁₁	—	2	8	no	—
87	C₄×D₄×C₁₁	—	2	16	no	—
88	C₄×D₄×C₁₁	—	2	8	no	—
89	C₄×D₄×C₁₁	—	2	16	no	—
90	C₁₁×#117	—	2	16	no	—
91	C₂×C₁₁×C₄⋊C₄	C₂³	1	4	yes	—
92	C₂×C₁₁×C₄⋊C₄	C₂³	1	4	yes	—
93	C₂×C₁₁×C₄⋊C₄	C₂³	1	4	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	4	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	8	yes	—
103	C₂×C₁₁×C₂²⋊C₄	C₂³	1	8	yes	—
104	C₂×C₁₁×C₂²⋊C₄	C₂³	1	4	yes	—
105	C₂×C₁₁×C₂²⋊C₄	C₂³	1	8	yes	—
106	C₂×C₁₁×C₂²⋊C₄	C₂³	1	4	yes	—
107	C₂×C₁₁×C₂²⋊C₄	C₂³	1	4	yes	—
108	C₂×C₄²×C₁₁	—	2	8	no	—
109	C₂×C₄²×C₁₁	—	2	8	no	—
110	C₂×C₄²×C₁₁	—	2	4	no	—
111	C₂×C₄²×C₁₁	—	2	4	no	—
112	C₂×C₄²×C₁₁	D₄	1	8	yes	complemented
113	C₂×C₄²×C₁₁	C₂³	1	2	yes	—
114	C₂×C₄²×C₁₁	C₂³	1	2	yes	—
115	C₂×C₄²×C₁₁	C₂³	1	2	yes	—
116	C₂×C₄²×C₁₁	C₂³	1	2	yes	—
117	C₂×C₄²×C₁₁	C₂³	1	2	yes	—
118	C₂×C₄²×C₁₁	C₂³	1	2	yes	—
119	C₂×C₄²×C₁₁	C₂³	1	2	yes	—
120	C₂×C₄²×C₁₁	C₂³	1	2	yes	—
121	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
122	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
123	C₂×C₄²×C₁₁	C₂³	1	2	yes	—
124	C₂×C₄²×C₁₁	C₂³	1	4	yes	—
125	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
126	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
127	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
128	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
129	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
130	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
131	C₂×C₄²×C₁₁	C₂³	1	2	yes	—
132	C₁₁×#95	C₂³	1	8	yes	—
133	C₁₁×#95	C₂³	1	8	yes	—
134	C₁₁×#95	C₂³	1	8	yes	—
135	#36631	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
136	C₂⁴×C₁₁	C₂⁴	1	4	yes	—
137	C₂⁴×C₁₁	C₂⁴	1	1	yes	characteristic
138	C₂×Q₈×C₁₁	—	2	4	no	—
139	C₂×Q₈×C₁₁	—	2	4	no	—
140	C₂×Q₈×C₁₁	—	2	4	no	—
141	C₂×D₄×C₁₁	—	2	8	no	—
142	C₂×D₄×C₁₁	—	2	16	no	—
143	C₂×D₄×C₁₁	—	2	4	no	—
144	C₂×D₄×C₁₁	—	2	8	no	—
145	C₂×D₄×C₁₁	—	2	8	no	—
146	C₂×D₄×C₁₁	—	2	4	no	—
147	C₂×D₄×C₁₁	—	2	8	no	—
148	C₂×D₄×C₁₁	—	2	4	no	—
149	C₂²×C₄×C₁₁	—	2	4	no	—
150	C₂²×C₄×C₁₁	—	2	4	no	—
151	C₂²×C₄×C₁₁	—	2	4	no	—
152	C₂²×C₄×C₁₁	—	2	4	no	—
153	C₂²×C₄×C₁₁	—	2	4	no	—
154	C₂²×C₄×C₁₁	—	2	4	no	—
155	C₂²×C₄×C₁₁	—	2	4	no	—
156	C₂²×C₄×C₁₁	—	2	2	no	—
157	C₂²×C₄×C₁₁	—	2	2	no	—
158	C₂²×C₄×C₁₁	—	2	8	no	—
159	C₂²×C₄×C₁₁	—	2	16	no	—
160	C₂²×C₄×C₁₁	C₂×D₄	1	4	yes	—
161	C₂²×C₄×C₁₁	C₂×D₄	1	4	yes	—
162	C₂²×C₄×C₁₁	C₂×D₄	1	4	yes	—
163	C₂²×C₄×C₁₁	#41	1	8	yes	—
164	C₂²×C₄×C₁₁	C₂⁴	1	4	yes	—
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	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
169	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
170	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
171	C₂²×C₄×C₁₁	C₂⁴	1	2	yes	—
172	C₂²×C₄×C₁₁	C₂⁴	1	2	yes	—
173	C₂²×C₄×C₁₁	C₂⁴	1	2	yes	—
174	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
175	C₂²×C₄×C₁₁	C₂⁴	1	2	yes	—
176	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
177	C₁₁×C₄⋊C₄	—	2	8	no	—
178	C₁₁×C₄⋊C₄	—	2	8	no	—
179	C₁₁×C₄⋊C₄	—	2	4	no	—
180	C₁₁×C₄⋊C₄	—	2	8	no	—
181	C₁₁×C₄⋊C₄	—	2	4	no	—
182	C₁₁×C₄⋊C₄	—	2	8	no	—
183	C₁₁×C₄⋊C₄	—	2	8	no	—
184	C₁₁×C₄⋊C₄	—	2	8	no	—
185	C₁₁×C₄⋊C₄	—	2	8	no	—
186	C₁₁×C₂²⋊C₄	—	2	8	no	—
187	C₁₁×C₂²⋊C₄	—	2	8	no	—
188	C₁₁×C₂²⋊C₄	—	2	8	no	—
189	C₁₁×C₂²⋊C₄	—	2	8	no	—
190	C₁₁×C₂²⋊C₄	—	2	8	no	—
191	C₁₁×C₂²⋊C₄	—	2	16	no	—
192	C₁₁×C₂²⋊C₄	—	2	16	no	—
193	C₁₁×C₂²⋊C₄	—	2	16	no	—
194	C₄²×C₁₁	—	2	8	no	—
195	C₄²×C₁₁	—	2	4	no	—
196	C₄²×C₁₁	—	2	4	no	—
197	C₄²×C₁₁	—	2	4	no	—
198	C₄²×C₁₁	—	2	4	no	—
199	C₄²×C₁₁	—	2	4	no	—
200	C₄²×C₁₁	—	2	4	no	—
201	C₄²×C₁₁	—	2	4	no	—
202	C₄²×C₁₁	—	2	4	no	—
203	C₄²×C₁₁	—	2	4	no	—
204	C₄²×C₁₁	—	2	2	no	—
205	C₄²×C₁₁	—	2	2	no	—
206	C₄²×C₁₁	C₂×D₄	1	4	yes	—
207	C₄²×C₁₁	C₂×D₄	1	4	yes	—
208	C₄²×C₁₁	C₂×D₄	1	4	yes	—
209	C₄²×C₁₁	C₂×D₄	1	4	yes	—
210	C₄²×C₁₁	#41	1	8	yes	—
211	C₄²×C₁₁	#41	1	4	yes	—
212	C₄²×C₁₁	#41	1	4	yes	—
213	C₂×#529	C₂×C₁₁	1	2	yes	complemented
214	#2861	C₂×C₁₁	1	2	yes	complemented
215	#2860	C₂×C₁₁	1	4	yes	complemented
216	#2859	C₂×C₁₁	1	1	yes	characteristic, complemented
217	#2858	C₂×C₁₁	1	1	yes	characteristic, complemented
218	#2857	C₂×C₁₁	1	1	yes	characteristic, complemented
219	#2856	C₂×C₁₁	1	1	yes	characteristic
220	#2854	C₂×C₁₁	1	4	yes	complemented
221	#2850	C₂×C₁₁	1	2	yes	complemented
222	C₄×C₄⋊Q₈	C₂×C₁₁	1	1	yes	characteristic, complemented
223	C₄×#127	C₂×C₁₁	1	1	yes	characteristic, complemented
224	C₄×#124	C₂×C₁₁	1	2	yes	complemented
225	C₄×#121	C₂×C₁₁	1	4	yes	complemented
226	#2293	C₂×C₁₁	1	4	yes	complemented
227	C₂×C₄³	C₂×C₁₁	1	1	yes	characteristic, complemented
228	C₂³×C₁₁	—	2	1	no	—
229	C₂³×C₁₁	—	2	2	no	—
230	C₂³×C₁₁	—	2	1	no	—
231	C₂³×C₁₁	—	2	4	no	—
232	C₂³×C₁₁	—	2	4	no	—
233	C₂³×C₁₁	—	2	8	no	—
234	C₂³×C₁₁	—	2	8	no	—
235	C₂³×C₁₁	—	2	4	no	—
236	C₂³×C₁₁	C₂²×D₄	1	2	yes	—
237	C₂³×C₁₁	C₂×#41	1	4	yes	—
238	C₂³×C₁₁	C₂⁵	1	1	yes	characteristic
239	Q₈×C₁₁	—	4	8	no	—
240	D₄×C₁₁	—	4	16	no	—
241	D₄×C₁₁	—	4	16	no	—
242	D₄×C₁₁	—	4	8	no	—
243	C₂×C₄×C₁₁	—	2	16	no	—
244	C₂×C₄×C₁₁	—	2	8	no	—
245	C₂×C₄×C₁₁	—	2	2	no	—
246	C₂×C₄×C₁₁	—	2	2	no	—
247	C₂×C₄×C₁₁	—	2	1	no	—
248	C₂×C₄×C₁₁	—	2	2	no	—
249	C₂×C₄×C₁₁	—	2	2	no	—
250	C₂×C₄×C₁₁	—	2	2	no	—
251	C₂×C₄×C₁₁	—	2	1	no	—
252	C₂×C₄×C₁₁	—	2	2	no	—
253	C₂×C₄×C₁₁	—	2	2	no	—
254	C₂×C₄×C₁₁	—	2	2	no	—
255	C₂×C₄×C₁₁	—	2	2	no	—
256	C₂×C₄×C₁₁	—	2	16	no	—
257	C₂×C₄×C₁₁	—	2	8	no	—
258	C₂×C₄×C₁₁	—	2	8	no	—
259	C₂×C₄×C₁₁	—	2	4	no	—
260	C₂×C₄×C₁₁	—	2	4	no	—
261	C₂×C₄×C₁₁	—	2	4	no	—
262	C₂×C₄×C₁₁	—	2	4	no	—
263	C₂×C₄×C₁₁	—	2	8	no	—
264	C₂×C₄×C₁₁	—	2	8	no	—
265	C₂×C₄×C₁₁	—	2	4	no	—
266	C₂×C₄×C₁₁	—	4	16	no	—
267	C₂×C₄×C₁₁	C₂²×D₄	1	2	yes	—
268	C₂×C₄×C₁₁	C₂²×D₄	1	2	yes	—
269	C₂×C₄×C₁₁	C₂²×D₄	1	2	yes	—
270	C₂×C₄×C₁₁	C₂²×D₄	1	2	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	4	yes	—
274	C₂×C₄×C₁₁	C₂×#41	1	4	yes	—
275	C₂×C₄×C₁₁	C₂×#41	1	4	yes	—
276	C₂×C₄×C₁₁	C₂×#41	1	4	yes	—
277	C₂×C₄×C₁₁	C₂×#41	1	4	yes	—
278	C₂×C₄×C₁₁	C₂×#41	1	4	yes	—
279	C₂×C₄×C₁₁	C₂×#41	1	4	yes	—
280	C₂×C₄×C₁₁	C₂×#41	1	2	yes	—
281	C₂×C₄×C₁₁	C₂×#41	1	2	yes	—
282	C₂×C₄⋊Q₈	C₂²×C₁₁	1	1	yes	characteristic
283	C₂×#127	C₂²×C₁₁	1	1	yes	characteristic
284	#529	—	2	16	no	—
285	C₂×#126	C₂²×C₁₁	1	4	yes	—
286	C₂×#125	C₂²×C₁₁	1	2	yes	—
287	C₂×#124	C₂²×C₁₁	1	2	yes	—
288	C₂×#124	C₂²×C₁₁	1	2	yes	—
289	C₂×#123	C₂²×C₁₁	1	4	yes	—
290	C₂×C₂²⋊Q₈	C₂²×C₁₁	1	2	yes	—
291	C₂×#121	C₂²×C₁₁	1	2	yes	—
292	C₂×#121	C₂²×C₁₁	1	4	yes	—
293	C₂×C₄×Q₈	C₂²×C₁₁	1	2	yes	—
294	C₂×C₄×D₄	C₂²×C₁₁	1	2	yes	—
295	C₂×C₄×D₄	C₂²×C₁₁	1	4	yes	—
296	C₂×C₄×D₄	C₂²×C₁₁	1	4	yes	—
297	C₂×#117	C₂²×C₁₁	1	4	yes	—
298	C₂²×C₄²	C₂²×C₁₁	1	1	yes	characteristic
299	C₂²×C₄²	C₂²×C₁₁	1	2	yes	—
300	C₂²×C₄²	C₂²×C₁₁	1	1	yes	characteristic
301	C₂²×C₄²	C₂²×C₁₁	1	2	yes	—
302	C₂²×C₄²	C₂²×C₁₁	1	1	yes	characteristic
303	#391	C₂²×C₁₁	1	2	yes	—
304	#391	C₂²×C₁₁	1	2	yes	—
305	#390	C₂²×C₁₁	1	2	yes	—
306	#390	C₂²×C₁₁	1	4	yes	—
307	#390	C₂²×C₁₁	1	4	yes	—
308	#390	C₂²×C₁₁	1	4	yes	—
309	#390	C₂²×C₁₁	1	2	yes	—
310	#390	C₂²×C₁₁	1	4	yes	—
311	#389	C₂²×C₁₁	1	4	yes	—
312	#389	C₂²×C₁₁	1	4	yes	—
313	#389	C₂²×C₁₁	1	4	yes	—
314	#389	C₂²×C₁₁	1	4	yes	—
315	#388	C₂²×C₁₁	1	8	yes	—
316	#388	C₂²×C₁₁	1	8	yes	—
317	#388	C₂²×C₁₁	1	8	yes	—
318	#388	C₂²×C₁₁	1	8	yes	—
319	#386	C₂²×C₁₁	1	8	yes	—
320	#384	C₂²×C₁₁	1	1	yes	characteristic
321	#384	C₂²×C₁₁	1	1	yes	characteristic
322	#382	C₂²×C₁₁	1	2	yes	—
323	#380	C₂²×C₁₁	1	4	yes	—
324	C₄×C₄⋊C₄	C₂²×C₁₁	1	4	yes	—
325	C₄×C₂²⋊C₄	C₂²×C₁₁	1	8	yes	—
326	C₄³	C₂²×C₁₁	1	1	yes	characteristic
327	C₄³	C₂²×C₁₁	1	1	yes	characteristic
328	C₄³	C₂²×C₁₁	1	2	yes	—
329	C₄³	C₂²×C₁₁	1	1	yes	characteristic
330	C₄³	C₂²×C₁₁	1	2	yes	—
331	C₄³	C₂²×C₁₁	1	1	yes	characteristic
332	C₂²×C₁₁	—	2	4	no	—
333	C₂²×C₁₁	—	2	2	no	—
334	C₂²×C₁₁	—	2	2	no	—
335	C₂²×C₁₁	—	2	4	no	—
336	C₂²×C₁₁	—	4	8	no	—
337	C₂²×C₁₁	—	4	4	no	—
338	C₂²×C₁₁	—	4	4	no	—
339	C₂²×C₁₁	—	4	4	no	—
340	C₂²×C₁₁	—	4	8	no	—
341	C₂²×C₁₁	#532	1	4	yes	—
342	C₂²×C₁₁	C₂³×D₄	1	1	yes	characteristic
343	C₂²×C₁₁	C₂²×#41	1	1	yes	characteristic
344	C₂²×C₁₁	C₂²×#41	1	2	yes	—
345	C₂²×C₁₁	C₂²×#41	1	2	yes	—
346	C₂²×C₁₁	C₂²×#41	1	1	yes	characteristic
347	C₄×C₁₁	—	2	4	no	—
348	C₄×C₁₁	—	2	2	no	—
349	C₄×C₁₁	—	2	2	no	—
350	C₄×C₁₁	—	2	2	no	—
351	C₄×C₁₁	—	2	2	no	—
352	C₄×C₁₁	—	2	4	no	—
353	C₄×C₁₁	—	2	4	no	—
354	C₄×C₁₁	—	4	4	no	—
355	C₄×C₁₁	—	4	4	no	—
356	C₄×C₁₁	—	4	4	no	—
357	C₄×C₁₁	#529	1	8	yes	complemented
358	C₄×C₁₁	#532	1	4	yes	—
359	C₄×C₁₁	#532	1	4	yes	—
360	C₂²×Q₈	C₂³×C₁₁	1	2	yes	—
361	C₂²×D₄	C₂³×C₁₁	1	4	yes	—
362	C₂²×D₄	C₂³×C₁₁	1	2	yes	—
363	C₂²×D₄	C₂³×C₁₁	1	4	yes	—
364	C₂³×C₄	C₂³×C₁₁	1	4	yes	—
365	C₂³×C₄	C₂³×C₁₁	1	2	yes	—
366	C₂³×C₄	C₂³×C₁₁	1	1	yes	characteristic
367	C₂³×C₄	C₂³×C₁₁	1	1	yes	characteristic
368	C₂³×C₄	C₂³×C₁₁	1	1	yes	characteristic
369	C₂³×C₄	C₂³×C₁₁	1	2	yes	—
370	C₄⋊Q₈	—	2	4	no	—
371	#127	—	2	4	no	—
372	#126	—	2	16	no	—
373	#125	—	2	8	no	—
374	#124	—	2	8	no	—
375	#124	—	2	8	no	—
376	#123	—	2	16	no	—
377	C₂²⋊Q₈	—	2	8	no	—
378	#121	—	2	8	no	—
379	#121	—	2	16	no	—
380	C₄×Q₈	—	2	8	no	—
381	C₄×D₄	—	2	16	no	—
382	C₄×D₄	—	2	8	no	—
383	C₄×D₄	—	2	16	no	—
384	#117	—	2	16	no	—
385	C₂×C₄⋊C₄	C₂³×C₁₁	1	4	yes	—
386	C₂×C₄⋊C₄	C₂³×C₁₁	1	4	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	2	yes	—
391	C₂×C₄⋊C₄	C₂³×C₁₁	1	4	yes	—
392	C₂×C₄⋊C₄	C₂³×C₁₁	1	4	yes	—
393	C₂×C₄⋊C₄	C₂³×C₁₁	1	4	yes	—
394	C₂×C₂²⋊C₄	C₂³×C₁₁	1	4	yes	—
395	C₂×C₂²⋊C₄	C₂³×C₁₁	1	4	yes	—
396	C₂×C₂²⋊C₄	C₂³×C₁₁	1	4	yes	—
397	C₂×C₂²⋊C₄	C₂³×C₁₁	1	4	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	8	yes	—
402	C₂×C₄²	—	2	8	no	—
403	C₂×C₄²	—	2	8	no	—
404	C₂×C₄²	—	2	4	no	—
405	C₂×C₄²	—	2	4	no	—
406	C₂×C₄²	D₄×C₁₁	1	8	yes	complemented
407	C₂×C₄²	C₂³×C₁₁	1	4	yes	—
408	C₂×C₄²	C₂³×C₁₁	1	2	yes	—
409	C₂×C₄²	C₂³×C₁₁	1	2	yes	—
410	C₂×C₄²	C₂³×C₁₁	1	2	yes	—
411	C₂×C₄²	C₂³×C₁₁	1	2	yes	—
412	C₂×C₄²	C₂³×C₁₁	1	2	yes	—
413	C₂×C₄²	C₂³×C₁₁	1	2	yes	—
414	C₂×C₄²	C₂³×C₁₁	1	2	yes	—
415	C₂×C₄²	C₂³×C₁₁	1	2	yes	—
416	C₂×C₄²	C₂³×C₁₁	1	2	yes	—
417	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
418	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
419	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
420	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
421	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
422	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
423	C₂×C₄²	C₂³×C₁₁	1	2	yes	—
424	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
425	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
426	#95	C₂³×C₁₁	1	8	yes	—
427	#95	C₂³×C₁₁	1	8	yes	—
428	#95	C₂³×C₁₁	1	8	yes	—
429	C₂×C₁₁	—	2	4	no	—
430	C₂×C₁₁	—	8	4	no	—
431	C₂×C₁₁	C₂×#529	1	2	yes	—
432	C₂×C₁₁	C₂×#532	1	1	yes	characteristic
433	C₂×C₁₁	C₂×#532	1	1	yes	characteristic
434	C₂×C₁₁	C₂×#532	1	1	yes	characteristic
435	C₂×C₁₁	#3444	1	2	yes	—
436	C₂⁴	C₂⁴×C₁₁	1	4	yes	—
437	C₂⁴	C₂⁴×C₁₁	1	1	yes	characteristic
438	C₂×Q₈	—	2	4	no	—
439	C₂×Q₈	—	2	4	no	—
440	C₂×Q₈	—	2	4	no	—
441	C₂×D₄	—	2	8	no	—
442	C₂×D₄	—	2	16	no	—
443	C₂×D₄	—	2	4	no	—
444	C₂×D₄	—	2	8	no	—
445	C₂×D₄	—	2	8	no	—
446	C₂×D₄	—	2	4	no	—
447	C₂×D₄	—	2	8	no	—
448	C₂×D₄	—	2	4	no	—
449	C₂²×C₄	—	2	4	no	—
450	C₂²×C₄	—	2	4	no	—
451	C₂²×C₄	—	2	4	no	—
452	C₂²×C₄	—	2	4	no	—
453	C₂²×C₄	—	2	4	no	—
454	C₂²×C₄	—	2	4	no	—
455	C₂²×C₄	—	2	4	no	—
456	C₂²×C₄	—	2	2	no	—
457	C₂²×C₄	—	2	2	no	—
458	C₂²×C₄	—	2	8	no	—
459	C₂²×C₄	—	2	16	no	—
460	C₂²×C₄	C₂×D₄×C₁₁	1	4	yes	—
461	C₂²×C₄	C₂×D₄×C₁₁	1	4	yes	—
462	C₂²×C₄	C₂×D₄×C₁₁	1	4	yes	—
463	C₂²×C₄	C₁₁×#41	1	8	yes	—
464	C₂²×C₄	C₂⁴×C₁₁	1	4	yes	—
465	C₂²×C₄	C₂⁴×C₁₁	1	4	yes	—
466	C₂²×C₄	C₂⁴×C₁₁	1	4	yes	—
467	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
468	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
469	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
470	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
471	C₂²×C₄	C₂⁴×C₁₁	1	2	yes	—
472	C₂²×C₄	C₂⁴×C₁₁	1	2	yes	—
473	C₂²×C₄	C₂⁴×C₁₁	1	2	yes	—
474	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
475	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
476	C₂²×C₄	C₂⁴×C₁₁	1	2	yes	—
477	C₄⋊C₄	—	2	8	no	—
478	C₄⋊C₄	—	2	8	no	—
479	C₄⋊C₄	—	2	4	no	—
480	C₄⋊C₄	—	2	8	no	—
481	C₄⋊C₄	—	2	4	no	—
482	C₄⋊C₄	—	2	8	no	—
483	C₄⋊C₄	—	2	8	no	—
484	C₄⋊C₄	—	2	8	no	—
485	C₄⋊C₄	—	2	8	no	—
486	C₂²⋊C₄	—	2	8	no	—
487	C₂²⋊C₄	—	2	8	no	—
488	C₂²⋊C₄	—	2	8	no	—
489	C₂²⋊C₄	—	2	8	no	—
490	C₂²⋊C₄	—	2	8	no	—
491	C₂²⋊C₄	—	2	16	no	—
492	C₂²⋊C₄	—	2	16	no	—
493	C₂²⋊C₄	—	2	16	no	—
494	C₄²	—	2	8	no	—
495	C₄²	—	2	4	no	—
496	C₄²	—	2	4	no	—
497	C₄²	—	2	4	no	—
498	C₄²	—	2	4	no	—
499	C₄²	—	2	4	no	—
500	C₄²	—	2	4	no	—
501	C₄²	—	2	4	no	—
502	C₄²	—	2	4	no	—
503	C₄²	—	2	4	no	—
504	C₄²	—	2	2	no	—
505	C₄²	—	2	2	no	—
506	C₄²	C₂×D₄×C₁₁	1	4	yes	—
507	C₄²	C₂×D₄×C₁₁	1	4	yes	—
508	C₄²	C₂×D₄×C₁₁	1	4	yes	—
509	C₄²	C₂×D₄×C₁₁	1	4	yes	—
510	C₄²	C₁₁×#41	1	8	yes	—
511	C₄²	C₁₁×#41	1	4	yes	—
512	C₄²	C₁₁×#41	1	4	yes	—
513	C₁₁	#36631	1	1	yes	characteristic, direct product factor, Sylow
514	C₂³	—	2	1	no	—
515	C₂³	—	2	2	no	—
516	C₂³	—	2	1	no	—
517	C₂³	—	2	4	no	—
518	C₂³	—	2	4	no	—
519	C₂³	—	2	8	no	—
520	C₂³	—	2	8	no	—
521	C₂³	—	2	4	no	—
522	C₂³	C₂²×D₄×C₁₁	1	2	yes	—
523	C₂³	C₂×C₁₁×#41	1	4	yes	—
524	C₂³	C₂⁵×C₁₁	1	1	yes	characteristic
525	Q₈	—	4	8	no	—
526	D₄	—	4	16	no	—
527	D₄	—	4	16	no	—
528	D₄	—	4	8	no	—
529	C₂×C₄	—	2	16	no	—
530	C₂×C₄	—	2	8	no	—
531	C₂×C₄	—	2	2	no	—
532	C₂×C₄	—	2	2	no	—
533	C₂×C₄	—	2	1	no	—
534	C₂×C₄	—	2	2	no	—
535	C₂×C₄	—	2	2	no	—
536	C₂×C₄	—	2	2	no	—
537	C₂×C₄	—	2	1	no	—
538	C₂×C₄	—	2	2	no	—
539	C₂×C₄	—	2	2	no	—
540	C₂×C₄	—	2	2	no	—
541	C₂×C₄	—	2	2	no	—
542	C₂×C₄	—	2	16	no	—
543	C₂×C₄	—	2	8	no	—
544	C₂×C₄	—	2	8	no	—
545	C₂×C₄	—	2	4	no	—
546	C₂×C₄	—	2	4	no	—
547	C₂×C₄	—	2	4	no	—
548	C₂×C₄	—	2	4	no	—
549	C₂×C₄	—	2	8	no	—
550	C₂×C₄	—	2	8	no	—
551	C₂×C₄	—	2	4	no	—
552	C₂×C₄	—	4	16	no	—
553	C₂×C₄	C₂²×D₄×C₁₁	1	2	yes	—
554	C₂×C₄	C₂²×D₄×C₁₁	1	2	yes	—
555	C₂×C₄	C₂²×D₄×C₁₁	1	2	yes	—
556	C₂×C₄	C₂²×D₄×C₁₁	1	2	yes	—
557	C₂×C₄	C₂²×D₄×C₁₁	1	2	yes	—
558	C₂×C₄	C₂²×D₄×C₁₁	1	2	yes	—
559	C₂×C₄	C₂×C₁₁×#41	1	4	yes	—
560	C₂×C₄	C₂×C₁₁×#41	1	4	yes	—
561	C₂×C₄	C₂×C₁₁×#41	1	4	yes	—
562	C₂×C₄	C₂×C₁₁×#41	1	4	yes	—
563	C₂×C₄	C₂×C₁₁×#41	1	4	yes	—
564	C₂×C₄	C₂×C₁₁×#41	1	4	yes	—
565	C₂×C₄	C₂×C₁₁×#41	1	4	yes	—
566	C₂×C₄	C₂×C₁₁×#41	1	2	yes	—
567	C₂×C₄	C₂×C₁₁×#41	1	2	yes	—
568	C₂²	—	2	4	no	—
569	C₂²	—	2	2	no	—
570	C₂²	—	2	2	no	—
571	C₂²	—	2	4	no	—
572	C₂²	—	4	8	no	—
573	C₂²	—	4	4	no	—
574	C₂²	—	4	4	no	—
575	C₂²	—	4	4	no	—
576	C₂²	—	4	8	no	—
577	C₂²	C₁₁×#532	1	4	yes	—
578	C₂²	C₂³×D₄×C₁₁	1	1	yes	characteristic
579	C₂²	C₂²×C₁₁×#41	1	1	yes	characteristic
580	C₂²	C₂²×C₁₁×#41	1	2	yes	—
581	C₂²	C₂²×C₁₁×#41	1	2	yes	—
582	C₂²	C₂²×C₁₁×#41	1	1	yes	characteristic
583	C₄	—	2	4	no	—
584	C₄	—	2	2	no	—
585	C₄	—	2	2	no	—
586	C₄	—	2	2	no	—
587	C₄	—	2	2	no	—
588	C₄	—	2	4	no	—
589	C₄	—	2	4	no	—
590	C₄	—	4	4	no	—
591	C₄	—	4	4	no	—
592	C₄	—	4	4	no	—
593	C₄	C₁₁×#529	1	8	yes	complemented
594	C₄	C₁₁×#532	1	4	yes	—
595	C₄	C₁₁×#532	1	4	yes	—
596	C₂	—	2	4	no	—
597	C₂	—	8	4	no	—
598	C₂	C₂×C₁₁×#529	1	2	yes	—
599	C₂	C₂×C₁₁×#532	1	1	yes	characteristic
600	C₂	C₂×C₁₁×#532	1	1	yes	characteristic
601	C₂	C₂×C₁₁×#532	1	1	yes	characteristic
602	C₂	C₁₁×#3444	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄×C₁₁	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₁
socle	C₂³×C₁₁	C₂⁵
prime radical	C₁₁×#2856	C₂
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×#529	C₂	semidirect
2. C₁₁×#2861	C₂	semidirect
3. C₁₁×#2860	C₂	semidirect
4. C₁₁×#2859	C₂	semidirect
5. C₁₁×#2858	C₂	semidirect
6. C₁₁×#2857	C₂	semidirect
8. C₁₁×#2854	C₂	semidirect
9. C₁₁×#2850	C₂	semidirect
10. C₄×C₁₁×C₄⋊Q₈	C₂	semidirect
11. C₄×C₁₁×#127	C₂	semidirect
12. C₄×C₁₁×#124	C₂	semidirect
13. C₄×C₁₁×#121	C₂	semidirect
14. C₁₁×#2293	C₂	semidirect
15. C₂×C₄³×C₁₁	C₂	semidirect
112. C₂×C₄²×C₁₁	D₄	semidirect
135. #36631	C₁₁	direct (N × H)
213. C₂×#529	C₂×C₁₁	semidirect
214. #2861	C₂×C₁₁	semidirect
215. #2860	C₂×C₁₁	semidirect
216. #2859	C₂×C₁₁	semidirect
217. #2858	C₂×C₁₁	semidirect
218. #2857	C₂×C₁₁	semidirect
220. #2854	C₂×C₁₁	semidirect
221. #2850	C₂×C₁₁	semidirect
222. C₄×C₄⋊Q₈	C₂×C₁₁	semidirect
223. C₄×#127	C₂×C₁₁	semidirect
224. C₄×#124	C₂×C₁₁	semidirect
225. C₄×#121	C₂×C₁₁	semidirect
226. #2293	C₂×C₁₁	semidirect
227. C₂×C₄³	C₂×C₁₁	semidirect
357. C₄×C₁₁	#529	semidirect
406. C₂×C₄²	D₄×C₁₁	semidirect
513. C₁₁	#36631	direct (N × H)
593. C₄	C₁₁×#529	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₁×#529	2
C₁₁×#2861	2
C₁₁×#2860	2
C₁₁×#2859	2
C₁₁×#2858	2
C₁₁×#2857	2
C₁₁×#2856	2
C₁₁×#2854	2
C₁₁×#2850	2
C₄×C₁₁×C₄⋊Q₈	2
C₄×C₁₁×#127	2
C₄×C₁₁×#124	2
C₄×C₁₁×#121	2
C₁₁×#2293	2
C₂×C₄³×C₁₁	2
#36631	11

Subgroups — C11×#36631 #14613824

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#36631 #14613824