Subgroups — C₁₁×#36538 #14613731

Order 2816.

2238 conjugacy classes of subgroups.

The subgroup lattice has 550 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₁×#559	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₁×#557	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₁×#2861	C₂	1	2	yes	maximal, complemented
4	C₁₁×#2858	C₂	1	1	yes	maximal, characteristic
5	C₁₁×#2568	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₁×#2566	C₂	1	2	yes	maximal, complemented
7	C₁₁×#2558	C₂	1	8	yes	maximal, complemented
8	C₁₁×#2548	C₂	1	1	yes	maximal, characteristic
9	C₁₁×#2545	C₂	1	2	yes	maximal, complemented
10	C₁₁×#2545	C₂	1	4	yes	maximal, complemented
11	C₁₁×#2367	C₂	1	4	yes	maximal, complemented
12	C₄×C₁₁×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
13	C₄×C₁₁×#124	C₂	1	2	yes	maximal, complemented
14	C₄²×Q₈×C₁₁	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₁×#559	—	2	8	no	—
16	C₁₁×#557	—	2	8	no	—
17	C₂×C₁₁×C₄⋊Q₈	C₂²	1	2	yes	—
18	C₂×C₁₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic
19	C₂×C₁₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic
20	C₂×C₁₁×#127	C₂²	1	1	yes	characteristic
21	C₂×C₁₁×#125	C₂²	1	4	yes	—
22	C₂×C₁₁×#125	C₂²	1	2	yes	—
23	C₂×C₁₁×#124	C₂²	1	2	yes	—
24	C₂×C₁₁×#124	C₂²	1	2	yes	—
25	C₂×C₁₁×#124	C₂²	1	2	yes	—
26	C₂×C₁₁×#124	C₂²	1	4	yes	—
27	C₂×C₁₁×#123	C₂²	1	4	yes	—
28	C₂×C₄×Q₈×C₁₁	C₂²	1	2	yes	—
29	C₂×C₄×Q₈×C₁₁	C₂²	1	1	yes	characteristic
30	C₂×C₄×Q₈×C₁₁	C₂²	1	2	yes	—
31	C₂×C₄×Q₈×C₁₁	C₂²	1	1	yes	characteristic
32	C₂×C₄×Q₈×C₁₁	C₂²	1	2	yes	—
33	C₂×C₄×Q₈×C₁₁	C₂²	1	1	yes	characteristic
34	C₂×C₄×D₄×C₁₁	C₂²	1	2	yes	—
35	C₂×C₄×D₄×C₁₁	C₂²	1	2	yes	—
36	C₁₁×#400	C₂²	1	4	yes	—
37	C₁₁×#396	C₂²	1	8	yes	—
38	C₁₁×#396	C₂²	1	8	yes	—
39	C₁₁×#394	C₂²	1	4	yes	—
40	C₁₁×#391	C₂²	1	2	yes	—
41	C₁₁×#391	C₂²	1	4	yes	—
42	C₁₁×#391	C₂²	1	1	yes	characteristic
43	C₁₁×#391	C₂²	1	1	yes	characteristic
44	C₁₁×#390	C₂²	1	4	yes	—
45	C₁₁×#390	C₂²	1	2	yes	—
46	C₁₁×#390	C₂²	1	2	yes	—
47	C₁₁×#390	C₂²	1	4	yes	—
48	C₁₁×#390	C₂²	1	2	yes	—
49	C₁₁×#389	C₂²	1	4	yes	—
50	C₁₁×#388	C₂²	1	8	yes	—
51	C₁₁×#388	C₂²	1	8	yes	—
52	C₁₁×#388	C₂²	1	8	yes	—
53	C₁₁×#388	C₂²	1	8	yes	—
54	C₁₁×#385	C₂²	1	8	yes	—
55	C₁₁×#384	C₂²	1	1	yes	characteristic
56	C₁₁×#382	C₂²	1	2	yes	—
57	C₄×C₁₁×C₄⋊C₄	C₂²	1	2	yes	—
58	C₄×C₁₁×C₄⋊C₄	C₂²	1	1	yes	characteristic
59	C₄×C₁₁×C₄⋊C₄	C₂²	1	4	yes	—
60	C₄×C₁₁×C₄⋊C₄	C₂²	1	2	yes	—
61	C₄×C₁₁×C₄⋊C₄	C₂²	1	4	yes	—
62	C₄×C₁₁×C₂²⋊C₄	C₂²	1	8	yes	—
63	C₄³×C₁₁	C₂²	1	2	yes	—
64	C₄³×C₁₁	C₂²	1	1	yes	characteristic
65	C₂²×Q₈×C₁₁	C₂³	1	1	yes	characteristic
66	C₂²×Q₈×C₁₁	C₂³	1	2	yes	—
67	C₂²×Q₈×C₁₁	C₂³	1	1	yes	characteristic
68	C₂²×Q₈×C₁₁	C₂³	1	1	yes	characteristic
69	C₂²×D₄×C₁₁	C₂³	1	2	yes	—
70	C₂²×D₄×C₁₁	C₂³	1	2	yes	—
71	C₂²×D₄×C₁₁	C₂³	1	2	yes	—
72	C₂³×C₄×C₁₁	C₂³	1	4	yes	—
73	C₁₁×C₄⋊Q₈	—	2	8	no	—
74	C₁₁×C₄⋊Q₈	—	2	4	no	—
75	C₁₁×C₄⋊Q₈	—	2	4	no	—
76	C₁₁×#127	—	2	4	no	—
77	C₁₁×#125	—	2	16	no	—
78	C₁₁×#125	—	2	8	no	—
79	C₁₁×#124	—	2	8	no	—
80	C₁₁×#124	—	2	8	no	—
81	C₁₁×#124	—	2	8	no	—
82	C₁₁×#124	—	2	16	no	—
83	C₁₁×#123	—	2	16	no	—
84	C₄×Q₈×C₁₁	—	2	8	no	—
85	C₄×Q₈×C₁₁	—	2	8	no	—
86	C₄×Q₈×C₁₁	—	2	4	no	—
87	C₄×Q₈×C₁₁	—	2	4	no	—
88	C₄×Q₈×C₁₁	—	2	8	no	—
89	C₄×Q₈×C₁₁	D₄	1	8	yes	—
90	C₄×D₄×C₁₁	—	2	8	no	—
91	C₄×D₄×C₁₁	—	2	8	no	—
92	C₂×C₁₁×C₄⋊C₄	C₂³	1	1	yes	characteristic
93	C₂×C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
94	C₂×C₁₁×C₄⋊C₄	C₂³	1	4	yes	—
95	C₂×C₁₁×C₄⋊C₄	C₂³	1	4	yes	—
96	C₂×C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
97	C₂×C₁₁×C₄⋊C₄	C₂³	1	1	yes	characteristic
98	C₂×C₁₁×C₄⋊C₄	C₂³	1	4	yes	—
99	C₂×C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
100	C₂×C₁₁×C₄⋊C₄	C₂³	1	4	yes	—
101	C₂×C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
102	C₂×C₁₁×C₄⋊C₄	C₂³	1	4	yes	—
103	C₂×C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
104	C₂×C₁₁×C₄⋊C₄	C₂³	1	4	yes	—
105	C₂×C₁₁×C₄⋊C₄	C₂³	1	1	yes	characteristic
106	C₂×C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
107	C₂×C₁₁×C₂²⋊C₄	C₂³	1	8	yes	—
108	C₂×C₁₁×C₂²⋊C₄	C₂³	1	8	yes	—
109	C₂×C₁₁×C₂²⋊C₄	C₂³	1	4	yes	—
110	C₂×C₁₁×C₂²⋊C₄	C₂³	1	4	yes	—
111	C₂×C₁₁×C₂²⋊C₄	C₂³	1	8	yes	—
112	C₂×C₁₁×C₂²⋊C₄	C₂³	1	4	yes	—
113	C₂×C₁₁×C₂²⋊C₄	C₂³	1	8	yes	—
114	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
115	C₂×C₄²×C₁₁	C₂³	1	2	yes	—
116	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
117	C₂×C₄²×C₁₁	C₂³	1	4	yes	—
118	C₂×C₄²×C₁₁	C₂³	1	4	yes	—
119	C₂×C₄²×C₁₁	C₂³	1	2	yes	—
120	C₂×C₄²×C₁₁	C₂³	1	2	yes	—
121	C₂×C₄²×C₁₁	C₂³	1	4	yes	—
122	C₂×C₄²×C₁₁	C₂³	1	2	yes	—
123	C₂×C₄²×C₁₁	C₂³	1	2	yes	—
124	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
125	C₂×C₄²×C₁₁	C₂³	1	2	yes	—
126	C₁₁×#95	C₂³	1	4	yes	—
127	C₁₁×#95	C₂³	1	8	yes	—
128	C₁₁×#95	C₂³	1	4	yes	—
129	C₁₁×#95	C₂³	1	2	yes	—
130	C₁₁×#95	C₂³	1	4	yes	—
131	C₁₁×#95	C₂³	1	8	yes	—
132	#36538	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
133	C₂⁴×C₁₁	C₂⁴	1	4	yes	—
134	C₂×Q₈×C₁₁	—	2	2	no	—
135	C₂×Q₈×C₁₁	—	2	2	no	—
136	C₂×Q₈×C₁₁	—	2	4	no	—
137	C₂×Q₈×C₁₁	—	2	4	no	—
138	C₂×Q₈×C₁₁	—	2	8	no	—
139	C₂×Q₈×C₁₁	—	2	2	no	—
140	C₂×Q₈×C₁₁	—	2	2	no	—
141	C₂×Q₈×C₁₁	—	2	2	no	—
142	C₂×Q₈×C₁₁	C₂×D₄	1	4	yes	—
143	C₂×Q₈×C₁₁	#41	1	4	yes	—
144	C₂×D₄×C₁₁	—	2	4	no	—
145	C₂×D₄×C₁₁	—	2	4	no	—
146	C₂×D₄×C₁₁	—	2	4	no	—
147	C₂×D₄×C₁₁	—	2	8	no	—
148	C₂×D₄×C₁₁	—	2	4	no	—
149	C₂×D₄×C₁₁	—	2	4	no	—
150	C₂×D₄×C₁₁	—	4	4	no	—
151	C₂²×C₄×C₁₁	—	2	8	no	—
152	C₂²×C₄×C₁₁	—	4	8	no	—
153	C₂²×C₄×C₁₁	C₂⁴	1	4	yes	—
154	C₂²×C₄×C₁₁	C₂⁴	1	2	yes	—
155	C₂²×C₄×C₁₁	C₂⁴	1	2	yes	—
156	C₂²×C₄×C₁₁	C₂⁴	1	4	yes	—
157	C₂²×C₄×C₁₁	C₂⁴	1	2	yes	—
158	C₂²×C₄×C₁₁	C₂⁴	1	2	yes	—
159	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
160	C₂²×C₄×C₁₁	C₂⁴	1	2	yes	—
161	C₂²×C₄×C₁₁	C₂⁴	1	2	yes	—
162	C₂²×C₄×C₁₁	C₂⁴	1	2	yes	—
163	C₂²×C₄×C₁₁	C₂⁴	1	2	yes	—
164	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
165	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
166	C₁₁×C₄⋊C₄	—	2	2	no	—
167	C₁₁×C₄⋊C₄	—	2	4	no	—
168	C₁₁×C₄⋊C₄	—	2	4	no	—
169	C₁₁×C₄⋊C₄	—	2	2	no	—
170	C₁₁×C₄⋊C₄	—	2	8	no	—
171	C₁₁×C₄⋊C₄	—	2	8	no	—
172	C₁₁×C₄⋊C₄	—	2	4	no	—
173	C₁₁×C₄⋊C₄	—	2	8	no	—
174	C₁₁×C₄⋊C₄	—	2	4	no	—
175	C₁₁×C₄⋊C₄	—	2	8	no	—
176	C₁₁×C₄⋊C₄	—	2	4	no	—
177	C₁₁×C₄⋊C₄	—	2	8	no	—
178	C₁₁×C₄⋊C₄	—	4	4	no	—
179	C₁₁×C₄⋊C₄	C₂×D₄	1	4	yes	—
180	C₁₁×C₄⋊C₄	C₂×D₄	1	8	yes	—
181	C₁₁×C₂²⋊C₄	—	2	8	no	—
182	C₁₁×C₂²⋊C₄	—	2	8	no	—
183	C₁₁×C₂²⋊C₄	—	2	8	no	—
184	C₁₁×C₂²⋊C₄	—	2	16	no	—
185	C₁₁×C₂²⋊C₄	—	2	16	no	—
186	C₁₁×C₂²⋊C₄	—	2	16	no	—
187	C₁₁×C₂²⋊C₄	—	4	8	no	—
188	C₄²×C₁₁	—	2	4	no	—
189	C₄²×C₁₁	—	2	8	no	—
190	C₄²×C₁₁	—	2	4	no	—
191	C₄²×C₁₁	—	2	8	no	—
192	C₄²×C₁₁	—	2	4	no	—
193	C₄²×C₁₁	—	2	2	no	—
194	C₄²×C₁₁	—	2	2	no	—
195	C₄²×C₁₁	—	4	2	no	—
196	C₄²×C₁₁	—	4	4	no	—
197	C₄²×C₁₁	C₂×D₄	1	8	yes	—
198	C₄²×C₁₁	C₂×D₄	1	4	yes	—
199	C₄²×C₁₁	#41	1	8	yes	—
200	C₂×#559	C₂×C₁₁	1	1	yes	characteristic
201	C₂×#557	C₂×C₁₁	1	1	yes	characteristic, complemented
202	#2861	C₂×C₁₁	1	2	yes	complemented
203	#2858	C₂×C₁₁	1	1	yes	characteristic
204	#2568	C₂×C₁₁	1	1	yes	characteristic, complemented
205	#2566	C₂×C₁₁	1	2	yes	complemented
206	#2558	C₂×C₁₁	1	8	yes	complemented
207	#2548	C₂×C₁₁	1	1	yes	characteristic
208	#2545	C₂×C₁₁	1	2	yes	complemented
209	#2545	C₂×C₁₁	1	4	yes	complemented
210	#2367	C₂×C₁₁	1	4	yes	complemented
211	C₄×C₄⋊Q₈	C₂×C₁₁	1	1	yes	characteristic, complemented
212	C₄×#124	C₂×C₁₁	1	2	yes	complemented
213	C₄²×Q₈	C₂×C₁₁	1	1	yes	characteristic, complemented
214	C₂³×C₁₁	—	2	4	no	—
215	C₂³×C₁₁	—	2	8	no	—
216	C₂³×C₁₁	—	2	4	no	—
217	C₂³×C₁₁	—	2	4	no	—
218	C₂³×C₁₁	—	2	8	no	—
219	C₂³×C₁₁	C₂⁵	1	1	yes	characteristic
220	Q₈×C₁₁	—	2	8	no	—
221	Q₈×C₁₁	—	2	8	no	—
222	Q₈×C₁₁	—	4	8	no	—
223	Q₈×C₁₁	—	4	4	no	—
224	D₄×C₁₁	—	4	8	no	—
225	D₄×C₁₁	—	4	8	no	—
226	D₄×C₁₁	—	8	4	no	—
227	C₂×C₄×C₁₁	—	2	2	no	—
228	C₂×C₄×C₁₁	—	2	2	no	—
229	C₂×C₄×C₁₁	—	2	4	no	—
230	C₂×C₄×C₁₁	—	2	2	no	—
231	C₂×C₄×C₁₁	—	2	2	no	—
232	C₂×C₄×C₁₁	—	2	2	no	—
233	C₂×C₄×C₁₁	—	2	2	no	—
234	C₂×C₄×C₁₁	—	2	4	no	—
235	C₂×C₄×C₁₁	—	2	2	no	—
236	C₂×C₄×C₁₁	—	2	2	no	—
237	C₂×C₄×C₁₁	—	2	2	no	—
238	C₂×C₄×C₁₁	—	2	2	no	—
239	C₂×C₄×C₁₁	—	2	4	no	—
240	C₂×C₄×C₁₁	—	2	4	no	—
241	C₂×C₄×C₁₁	—	2	4	no	—
242	C₂×C₄×C₁₁	—	2	8	no	—
243	C₂×C₄×C₁₁	—	2	2	no	—
244	C₂×C₄×C₁₁	—	2	2	no	—
245	C₂×C₄×C₁₁	—	2	4	no	—
246	C₂×C₄×C₁₁	—	2	4	no	—
247	C₂×C₄×C₁₁	—	2	4	no	—
248	C₂×C₄×C₁₁	—	8	8	no	—
249	C₂×C₄×C₁₁	C₂²×D₄	1	4	yes	—
250	C₂×C₄×C₁₁	C₂²×D₄	1	4	yes	—
251	C₂×C₄×C₁₁	C₂²×D₄	1	2	yes	—
252	C₂×C₄×C₁₁	C₂²×D₄	1	2	yes	—
253	C₂×C₄×C₁₁	C₂²×D₄	1	2	yes	—
254	C₂×C₄×C₁₁	C₂×#41	1	4	yes	—
255	C₂×C₄×C₁₁	C₂×#41	1	4	yes	—
256	C₂×C₄×C₁₁	C₂×#41	1	4	yes	—
257	C₂×C₄×C₁₁	C₂×#41	1	4	yes	—
258	C₂×C₄×C₁₁	C₂×#41	1	2	yes	—
259	C₂×C₄×C₁₁	2₋¹⁺⁴	1	2	yes	—
260	#559	—	2	8	no	—
261	#557	—	2	8	no	—
262	C₂×C₄⋊Q₈	C₂²×C₁₁	1	1	yes	characteristic
263	C₂×C₄⋊Q₈	C₂²×C₁₁	1	1	yes	characteristic
264	C₂×C₄⋊Q₈	C₂²×C₁₁	1	2	yes	—
265	C₂×#127	C₂²×C₁₁	1	1	yes	characteristic
266	C₂×#125	C₂²×C₁₁	1	2	yes	—
267	C₂×#125	C₂²×C₁₁	1	4	yes	—
268	C₂×#124	C₂²×C₁₁	1	4	yes	—
269	C₂×#124	C₂²×C₁₁	1	2	yes	—
270	C₂×#124	C₂²×C₁₁	1	2	yes	—
271	C₂×#124	C₂²×C₁₁	1	2	yes	—
272	C₂×#123	C₂²×C₁₁	1	4	yes	—
273	C₂×C₄×Q₈	C₂²×C₁₁	1	1	yes	characteristic
274	C₂×C₄×Q₈	C₂²×C₁₁	1	1	yes	characteristic
275	C₂×C₄×Q₈	C₂²×C₁₁	1	2	yes	—
276	C₂×C₄×Q₈	C₂²×C₁₁	1	2	yes	—
277	C₂×C₄×Q₈	C₂²×C₁₁	1	2	yes	—
278	C₂×C₄×Q₈	C₂²×C₁₁	1	1	yes	characteristic
279	C₂×C₄×D₄	C₂²×C₁₁	1	2	yes	—
280	C₂×C₄×D₄	C₂²×C₁₁	1	2	yes	—
281	#400	C₂²×C₁₁	1	4	yes	—
282	#396	C₂²×C₁₁	1	8	yes	—
283	#396	C₂²×C₁₁	1	8	yes	—
284	#394	C₂²×C₁₁	1	4	yes	—
285	#391	C₂²×C₁₁	1	1	yes	characteristic
286	#391	C₂²×C₁₁	1	1	yes	characteristic
287	#391	C₂²×C₁₁	1	2	yes	—
288	#391	C₂²×C₁₁	1	4	yes	—
289	#390	C₂²×C₁₁	1	2	yes	—
290	#390	C₂²×C₁₁	1	2	yes	—
291	#390	C₂²×C₁₁	1	2	yes	—
292	#390	C₂²×C₁₁	1	4	yes	—
293	#390	C₂²×C₁₁	1	4	yes	—
294	#389	C₂²×C₁₁	1	4	yes	—
295	#388	C₂²×C₁₁	1	8	yes	—
296	#388	C₂²×C₁₁	1	8	yes	—
297	#388	C₂²×C₁₁	1	8	yes	—
298	#388	C₂²×C₁₁	1	8	yes	—
299	#385	C₂²×C₁₁	1	8	yes	—
300	#384	C₂²×C₁₁	1	1	yes	characteristic
301	#382	C₂²×C₁₁	1	2	yes	—
302	C₄×C₄⋊C₄	C₂²×C₁₁	1	4	yes	—
303	C₄×C₄⋊C₄	C₂²×C₁₁	1	2	yes	—
304	C₄×C₄⋊C₄	C₂²×C₁₁	1	1	yes	characteristic
305	C₄×C₄⋊C₄	C₂²×C₁₁	1	2	yes	—
306	C₄×C₄⋊C₄	C₂²×C₁₁	1	4	yes	—
307	C₄×C₂²⋊C₄	C₂²×C₁₁	1	8	yes	—
308	C₄³	C₂²×C₁₁	1	1	yes	characteristic
309	C₄³	C₂²×C₁₁	1	2	yes	—
310	C₂²×C₁₁	—	4	4	no	—
311	C₂²×C₁₁	—	4	4	no	—
312	C₂²×C₁₁	—	4	8	no	—
313	C₂²×C₁₁	—	4	4	no	—
314	C₂²×C₁₁	—	4	8	no	—
315	C₂²×C₁₁	C₂³×D₄	1	1	yes	characteristic
316	C₂²×C₁₁	C₂²×#41	1	2	yes	—
317	C₂²×C₁₁	C₂²×#41	1	1	yes	characteristic
318	C₂²×C₁₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
319	C₂²×C₁₁	#585	1	2	yes	—
320	C₄×C₁₁	—	2	4	no	—
321	C₄×C₁₁	—	2	4	no	—
322	C₄×C₁₁	—	2	4	no	—
323	C₄×C₁₁	—	2	4	no	—
324	C₄×C₁₁	—	2	2	no	—
325	C₄×C₁₁	—	2	4	no	—
326	C₄×C₁₁	—	4	4	no	—
327	C₄×C₁₁	—	4	2	no	—
328	C₄×C₁₁	—	4	4	no	—
329	C₄×C₁₁	—	4	2	no	—
330	C₄×C₁₁	—	4	2	no	—
331	C₄×C₁₁	#532	1	4	yes	—
332	C₄×C₁₁	#548	1	4	yes	—
333	C₂²×Q₈	C₂³×C₁₁	1	2	yes	—
334	C₂²×Q₈	C₂³×C₁₁	1	1	yes	characteristic
335	C₂²×Q₈	C₂³×C₁₁	1	1	yes	characteristic
336	C₂²×Q₈	C₂³×C₁₁	1	1	yes	characteristic
337	C₂²×D₄	C₂³×C₁₁	1	2	yes	—
338	C₂²×D₄	C₂³×C₁₁	1	2	yes	—
339	C₂²×D₄	C₂³×C₁₁	1	2	yes	—
340	C₂³×C₄	C₂³×C₁₁	1	4	yes	—
341	C₄⋊Q₈	—	2	8	no	—
342	C₄⋊Q₈	—	2	4	no	—
343	C₄⋊Q₈	—	2	4	no	—
344	#127	—	2	4	no	—
345	#125	—	2	16	no	—
346	#125	—	2	8	no	—
347	#124	—	2	8	no	—
348	#124	—	2	8	no	—
349	#124	—	2	8	no	—
350	#124	—	2	16	no	—
351	#123	—	2	16	no	—
352	C₄×Q₈	—	2	8	no	—
353	C₄×Q₈	—	2	8	no	—
354	C₄×Q₈	—	2	4	no	—
355	C₄×Q₈	—	2	4	no	—
356	C₄×Q₈	—	2	8	no	—
357	C₄×Q₈	D₄×C₁₁	1	8	yes	—
358	C₄×D₄	—	2	8	no	—
359	C₄×D₄	—	2	8	no	—
360	C₂×C₄⋊C₄	C₂³×C₁₁	1	1	yes	characteristic
361	C₂×C₄⋊C₄	C₂³×C₁₁	1	2	yes	—
362	C₂×C₄⋊C₄	C₂³×C₁₁	1	1	yes	characteristic
363	C₂×C₄⋊C₄	C₂³×C₁₁	1	4	yes	—
364	C₂×C₄⋊C₄	C₂³×C₁₁	1	2	yes	—
365	C₂×C₄⋊C₄	C₂³×C₁₁	1	2	yes	—
366	C₂×C₄⋊C₄	C₂³×C₁₁	1	4	yes	—
367	C₂×C₄⋊C₄	C₂³×C₁₁	1	2	yes	—
368	C₂×C₄⋊C₄	C₂³×C₁₁	1	4	yes	—
369	C₂×C₄⋊C₄	C₂³×C₁₁	1	4	yes	—
370	C₂×C₄⋊C₄	C₂³×C₁₁	1	2	yes	—
371	C₂×C₄⋊C₄	C₂³×C₁₁	1	4	yes	—
372	C₂×C₄⋊C₄	C₂³×C₁₁	1	4	yes	—
373	C₂×C₄⋊C₄	C₂³×C₁₁	1	1	yes	characteristic
374	C₂×C₄⋊C₄	C₂³×C₁₁	1	2	yes	—
375	C₂×C₂²⋊C₄	C₂³×C₁₁	1	4	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	8	yes	—
379	C₂×C₂²⋊C₄	C₂³×C₁₁	1	8	yes	—
380	C₂×C₂²⋊C₄	C₂³×C₁₁	1	8	yes	—
381	C₂×C₂²⋊C₄	C₂³×C₁₁	1	8	yes	—
382	C₂×C₄²	C₂³×C₁₁	1	2	yes	—
383	C₂×C₄²	C₂³×C₁₁	1	4	yes	—
384	C₂×C₄²	C₂³×C₁₁	1	2	yes	—
385	C₂×C₄²	C₂³×C₁₁	1	4	yes	—
386	C₂×C₄²	C₂³×C₁₁	1	2	yes	—
387	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
388	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
389	C₂×C₄²	C₂³×C₁₁	1	4	yes	—
390	C₂×C₄²	C₂³×C₁₁	1	2	yes	—
391	C₂×C₄²	C₂³×C₁₁	1	2	yes	—
392	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
393	C₂×C₄²	C₂³×C₁₁	1	2	yes	—
394	#95	C₂³×C₁₁	1	4	yes	—
395	#95	C₂³×C₁₁	1	8	yes	—
396	#95	C₂³×C₁₁	1	4	yes	—
397	#95	C₂³×C₁₁	1	2	yes	—
398	#95	C₂³×C₁₁	1	4	yes	—
399	#95	C₂³×C₁₁	1	8	yes	—
400	C₂×C₁₁	—	8	4	no	—
401	C₂×C₁₁	C₂×#532	1	1	yes	characteristic
402	C₂×C₁₁	C₂×#548	1	1	yes	characteristic
403	C₂×C₁₁	#3480	1	2	yes	—
404	C₂×C₁₁	#3500	1	1	yes	characteristic
405	C₂×C₁₁	#3507	1	2	yes	—
406	C₂⁴	C₂⁴×C₁₁	1	4	yes	—
407	C₂×Q₈	—	2	2	no	—
408	C₂×Q₈	—	2	2	no	—
409	C₂×Q₈	—	2	4	no	—
410	C₂×Q₈	—	2	4	no	—
411	C₂×Q₈	—	2	8	no	—
412	C₂×Q₈	—	2	2	no	—
413	C₂×Q₈	—	2	2	no	—
414	C₂×Q₈	—	2	2	no	—
415	C₂×Q₈	C₂×D₄×C₁₁	1	4	yes	—
416	C₂×Q₈	C₁₁×#41	1	4	yes	—
417	C₂×D₄	—	2	4	no	—
418	C₂×D₄	—	2	4	no	—
419	C₂×D₄	—	2	4	no	—
420	C₂×D₄	—	2	8	no	—
421	C₂×D₄	—	2	4	no	—
422	C₂×D₄	—	2	4	no	—
423	C₂×D₄	—	4	4	no	—
424	C₂²×C₄	—	2	8	no	—
425	C₂²×C₄	—	4	8	no	—
426	C₂²×C₄	C₂⁴×C₁₁	1	4	yes	—
427	C₂²×C₄	C₂⁴×C₁₁	1	2	yes	—
428	C₂²×C₄	C₂⁴×C₁₁	1	2	yes	—
429	C₂²×C₄	C₂⁴×C₁₁	1	4	yes	—
430	C₂²×C₄	C₂⁴×C₁₁	1	2	yes	—
431	C₂²×C₄	C₂⁴×C₁₁	1	2	yes	—
432	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
433	C₂²×C₄	C₂⁴×C₁₁	1	2	yes	—
434	C₂²×C₄	C₂⁴×C₁₁	1	2	yes	—
435	C₂²×C₄	C₂⁴×C₁₁	1	2	yes	—
436	C₂²×C₄	C₂⁴×C₁₁	1	2	yes	—
437	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
438	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
439	C₄⋊C₄	—	2	2	no	—
440	C₄⋊C₄	—	2	4	no	—
441	C₄⋊C₄	—	2	4	no	—
442	C₄⋊C₄	—	2	2	no	—
443	C₄⋊C₄	—	2	8	no	—
444	C₄⋊C₄	—	2	8	no	—
445	C₄⋊C₄	—	2	4	no	—
446	C₄⋊C₄	—	2	8	no	—
447	C₄⋊C₄	—	2	4	no	—
448	C₄⋊C₄	—	2	8	no	—
449	C₄⋊C₄	—	2	4	no	—
450	C₄⋊C₄	—	2	8	no	—
451	C₄⋊C₄	—	4	4	no	—
452	C₄⋊C₄	C₂×D₄×C₁₁	1	4	yes	—
453	C₄⋊C₄	C₂×D₄×C₁₁	1	8	yes	—
454	C₂²⋊C₄	—	2	8	no	—
455	C₂²⋊C₄	—	2	8	no	—
456	C₂²⋊C₄	—	2	8	no	—
457	C₂²⋊C₄	—	2	16	no	—
458	C₂²⋊C₄	—	2	16	no	—
459	C₂²⋊C₄	—	2	16	no	—
460	C₂²⋊C₄	—	4	8	no	—
461	C₄²	—	2	4	no	—
462	C₄²	—	2	8	no	—
463	C₄²	—	2	4	no	—
464	C₄²	—	2	8	no	—
465	C₄²	—	2	4	no	—
466	C₄²	—	2	2	no	—
467	C₄²	—	2	2	no	—
468	C₄²	—	4	2	no	—
469	C₄²	—	4	4	no	—
470	C₄²	C₂×D₄×C₁₁	1	8	yes	—
471	C₄²	C₂×D₄×C₁₁	1	4	yes	—
472	C₄²	C₁₁×#41	1	8	yes	—
473	C₁₁	#36538	1	1	yes	characteristic, direct product factor, Sylow
474	C₂³	—	2	4	no	—
475	C₂³	—	2	8	no	—
476	C₂³	—	2	4	no	—
477	C₂³	—	2	4	no	—
478	C₂³	—	2	8	no	—
479	C₂³	C₂⁵×C₁₁	1	1	yes	characteristic
480	Q₈	—	2	8	no	—
481	Q₈	—	2	8	no	—
482	Q₈	—	4	8	no	—
483	Q₈	—	4	4	no	—
484	D₄	—	4	8	no	—
485	D₄	—	4	8	no	—
486	D₄	—	8	4	no	—
487	C₂×C₄	—	2	2	no	—
488	C₂×C₄	—	2	2	no	—
489	C₂×C₄	—	2	4	no	—
490	C₂×C₄	—	2	2	no	—
491	C₂×C₄	—	2	2	no	—
492	C₂×C₄	—	2	2	no	—
493	C₂×C₄	—	2	2	no	—
494	C₂×C₄	—	2	4	no	—
495	C₂×C₄	—	2	2	no	—
496	C₂×C₄	—	2	2	no	—
497	C₂×C₄	—	2	2	no	—
498	C₂×C₄	—	2	2	no	—
499	C₂×C₄	—	2	4	no	—
500	C₂×C₄	—	2	4	no	—
501	C₂×C₄	—	2	4	no	—
502	C₂×C₄	—	2	8	no	—
503	C₂×C₄	—	2	2	no	—
504	C₂×C₄	—	2	2	no	—
505	C₂×C₄	—	2	4	no	—
506	C₂×C₄	—	2	4	no	—
507	C₂×C₄	—	2	4	no	—
508	C₂×C₄	—	8	8	no	—
509	C₂×C₄	C₂²×D₄×C₁₁	1	4	yes	—
510	C₂×C₄	C₂²×D₄×C₁₁	1	4	yes	—
511	C₂×C₄	C₂²×D₄×C₁₁	1	2	yes	—
512	C₂×C₄	C₂²×D₄×C₁₁	1	2	yes	—
513	C₂×C₄	C₂²×D₄×C₁₁	1	2	yes	—
514	C₂×C₄	C₂×C₁₁×#41	1	4	yes	—
515	C₂×C₄	C₂×C₁₁×#41	1	4	yes	—
516	C₂×C₄	C₂×C₁₁×#41	1	4	yes	—
517	C₂×C₄	C₂×C₁₁×#41	1	4	yes	—
518	C₂×C₄	C₂×C₁₁×#41	1	2	yes	—
519	C₂×C₄	C₁₁×2₋¹⁺⁴	1	2	yes	—
520	C₂²	—	4	4	no	—
521	C₂²	—	4	4	no	—
522	C₂²	—	4	8	no	—
523	C₂²	—	4	4	no	—
524	C₂²	—	4	8	no	—
525	C₂²	C₂³×D₄×C₁₁	1	1	yes	characteristic
526	C₂²	C₂²×C₁₁×#41	1	2	yes	—
527	C₂²	C₂²×C₁₁×#41	1	1	yes	characteristic
528	C₂²	C₂×C₁₁×2₋¹⁺⁴	1	1	yes	characteristic
529	C₂²	C₁₁×#585	1	2	yes	—
530	C₄	—	2	4	no	—
531	C₄	—	2	4	no	—
532	C₄	—	2	4	no	—
533	C₄	—	2	4	no	—
534	C₄	—	2	2	no	—
535	C₄	—	2	4	no	—
536	C₄	—	4	4	no	—
537	C₄	—	4	2	no	—
538	C₄	—	4	4	no	—
539	C₄	—	4	2	no	—
540	C₄	—	4	2	no	—
541	C₄	C₁₁×#532	1	4	yes	—
542	C₄	C₁₁×#548	1	4	yes	—
543	C₂	—	8	4	no	—
544	C₂	C₂×C₁₁×#532	1	1	yes	characteristic
545	C₂	C₂×C₁₁×#548	1	1	yes	characteristic
546	C₂	C₁₁×#3480	1	2	yes	—
547	C₂	C₁₁×#3500	1	1	yes	characteristic
548	C₂	C₁₁×#3507	1	2	yes	—

	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
2. C₂×C₁₁×#557	C₂	semidirect
3. C₁₁×#2861	C₂	semidirect
5. C₁₁×#2568	C₂	semidirect
6. C₁₁×#2566	C₂	semidirect
7. C₁₁×#2558	C₂	semidirect
9. C₁₁×#2545	C₂	semidirect
10. C₁₁×#2545	C₂	semidirect
11. C₁₁×#2367	C₂	semidirect
12. C₄×C₁₁×C₄⋊Q₈	C₂	semidirect
13. C₄×C₁₁×#124	C₂	semidirect
14. C₄²×Q₈×C₁₁	C₂	semidirect
132. #36538	C₁₁	direct (N × H)
201. C₂×#557	C₂×C₁₁	semidirect
202. #2861	C₂×C₁₁	semidirect
204. #2568	C₂×C₁₁	semidirect
205. #2566	C₂×C₁₁	semidirect
206. #2558	C₂×C₁₁	semidirect
208. #2545	C₂×C₁₁	semidirect
209. #2545	C₂×C₁₁	semidirect
210. #2367	C₂×C₁₁	semidirect
211. C₄×C₄⋊Q₈	C₂×C₁₁	semidirect
212. C₄×#124	C₂×C₁₁	semidirect
213. C₄²×Q₈	C₂×C₁₁	semidirect
473. C₁₁	#36538	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₁₁×#559	2
C₂×C₁₁×#557	2
C₁₁×#2861	2
C₁₁×#2858	2
C₁₁×#2568	2
C₁₁×#2566	2
C₁₁×#2558	2
C₁₁×#2548	2
C₁₁×#2545	2
C₁₁×#2367	2
C₄×C₁₁×C₄⋊Q₈	2
C₄×C₁₁×#124	2
C₄²×Q₈×C₁₁	2
#36538	11

Subgroups — C11×#36538 #14613731

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#36538 #14613731