Subgroups — C₁₁×#23186 #14600379

Order 2816.

1038 conjugacy classes of subgroups.

The subgroup lattice has 490 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₁×#495	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×C₁₁×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄×C₁₁×D₈	C₂	1	1	yes	maximal, characteristic
4	C₁₁×#2367	C₂	1	2	yes	maximal, complemented
5	C₁₁×#1983	C₂	1	2	yes	maximal, complemented
6	C₁₁×#1970	C₂	1	1	yes	maximal, characteristic
7	C₁₁×#1969	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₁×#1880	C₂	1	2	yes	maximal, complemented
9	C₁₁×#1877	C₂	1	2	yes	maximal, complemented
10	C₄×C₁₁×#107	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈×C₁₁×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₁₁×Q₁₆	C₂²	1	1	yes	characteristic
13	C₂²×C₁₁×SD₁₆	C₂²	1	2	yes	—
14	C₂²×C₁₁×D₈	C₂²	1	1	yes	characteristic
15	C₂×C₁₁×#124	C₂²	1	2	yes	—
16	C₂×C₄×Q₈×C₁₁	C₂²	1	2	yes	—
17	C₂×C₄×D₄×C₁₁	C₂²	1	2	yes	—
18	C₁₁×#495	C₄	1	8	yes	complemented
19	C₄×C₁₁×Q₁₆	—	2	4	no	—
20	C₄×C₁₁×D₈	—	2	4	no	—
21	C₂×C₁₁×#107	C₂²	1	1	yes	characteristic
22	C₂×C₁₁×#107	C₂²	1	1	yes	characteristic
23	C₂×C₁₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
24	C₂×C₁₁×#103	C₂²	1	2	yes	—
25	C₂×C₁₁×#103	C₂²	1	2	yes	—
26	C₂×C₁₁×#102	C₂²	1	2	yes	—
27	C₂×C₁₁×#102	C₂²	1	2	yes	—
28	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
29	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
30	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
31	C₁₁×#391	C₂²	1	2	yes	—
32	C₁₁×#390	C₂²	1	2	yes	—
33	C₁₁×#388	—	2	2	no	—
34	C₁₁×#388	—	2	2	no	—
35	C₁₁×#385	—	2	2	no	—
36	C₄×C₁₁×C₄⋊C₄	C₂²	1	2	yes	—
37	C₄×C₁₁×C₄⋊C₄	C₂²	1	1	yes	characteristic
38	C₄×C₁₁×C₂²⋊C₄	—	2	2	no	—
39	C₁₁×#340	C₂²	1	2	yes	—
40	C₁₁×#336	C₂²	1	1	yes	characteristic
41	C₁₁×#336	C₂²	1	1	yes	characteristic
42	C₂²×Q₈×C₁₁	C₂³	1	2	yes	—
43	C₂²×D₄×C₁₁	C₂³	1	2	yes	—
44	C₂³×C₄×C₁₁	—	2	2	no	—
45	C₂×C₁₁×Q₁₆	—	2	2	no	—
46	C₂×C₁₁×Q₁₆	—	2	2	no	—
47	C₂×C₁₁×Q₁₆	C₂×C₄	1	4	yes	complemented
48	C₂×C₁₁×SD₁₆	—	4	2	no	—
49	C₂×C₁₁×SD₁₆	—	4	2	no	—
50	C₂×C₁₁×SD₁₆	C₂×C₄	1	8	yes	complemented
51	C₂×C₁₁×D₈	—	2	2	no	—
52	C₂×C₁₁×D₈	—	2	2	no	—
53	C₂×C₁₁×D₈	C₂×C₄	1	4	yes	—
54	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
55	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
56	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
57	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
58	C₁₁×#124	—	2	4	no	—
59	C₁₁×#124	C₂×C₄	1	8	yes	complemented
60	C₄×Q₈×C₁₁	—	2	4	no	—
61	C₄×Q₈×C₁₁	—	4	2	no	—
62	C₄×D₄×C₁₁	—	2	4	no	—
63	C₄×D₄×C₁₁	—	4	2	no	—
64	C₂×C₁₁×C₄⋊C₄	—	2	2	no	—
65	C₂×C₁₁×C₄⋊C₄	D₄	1	1	yes	characteristic
66	C₂×C₁₁×C₄⋊C₄	D₄	1	1	yes	characteristic
67	C₂×C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
68	C₂×C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
69	C₂×C₁₁×C₂²⋊C₄	—	2	2	no	—
70	C₂×C₁₁×C₂²⋊C₄	—	2	2	no	—
71	C₂×C₁₁×C₂²⋊C₄	—	2	2	no	—
72	C₂×C₁₁×C₂²⋊C₄	—	2	2	no	—
73	C₂×C₁₁×C₂²⋊C₄	—	2	2	no	—
74	C₂×C₄²×C₁₁	—	2	2	no	—
75	C₂×C₄²×C₁₁	—	2	2	no	—
76	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
77	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
78	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
79	C₁₁×#107	—	2	2	no	—
80	C₁₁×#107	D₄	1	4	yes	—
81	C₁₁×C₄⋊C₈	—	2	2	no	—
82	C₁₁×#103	—	2	4	no	—
83	C₁₁×#103	—	4	2	no	—
84	C₁₁×#102	—	2	4	no	—
85	C₁₁×#102	—	4	2	no	—
86	C₄×C₈×C₁₁	—	2	2	no	—
87	C₄×C₈×C₁₁	—	2	2	no	—
88	C₄×C₈×C₁₁	C₂×C₄	1	4	yes	complemented
89	C₁₁×#95	—	2	2	no	—
90	C₁₁×#95	—	2	2	no	—
91	C₁₁×#95	—	2	2	no	—
92	C₁₁×#95	D₄	1	1	yes	characteristic
93	C₁₁×#95	D₄	1	1	yes	characteristic
94	#23186	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
95	C₂⁴×C₁₁	—	2	2	no	—
96	C₂×Q₈×C₁₁	—	2	2	no	—
97	C₂×Q₈×C₁₁	—	2	2	no	—
98	C₂×Q₈×C₁₁	—	2	2	no	—
99	C₂×Q₈×C₁₁	—	2	2	no	—
100	C₂×Q₈×C₁₁	—	2	2	no	—
101	C₂×Q₈×C₁₁	C₂²×C₄	1	4	yes	—
102	C₂×D₄×C₁₁	—	2	2	no	—
103	C₂×D₄×C₁₁	—	2	2	no	—
104	C₂×D₄×C₁₁	—	2	2	no	—
105	C₂×D₄×C₁₁	—	2	2	no	—
106	C₂×D₄×C₁₁	—	2	2	no	—
107	C₂×D₄×C₁₁	C₂²×C₄	1	4	yes	—
108	C₂²×C₄×C₁₁	—	2	2	no	—
109	C₂²×C₄×C₁₁	—	2	2	no	—
110	C₂²×C₄×C₁₁	—	2	2	no	—
111	C₂²×C₄×C₁₁	—	4	4	no	—
112	C₂²×C₄×C₁₁	—	4	4	no	—
113	C₂²×C₄×C₁₁	—	8	2	no	—
114	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
115	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
116	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
117	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
118	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
119	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
120	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
121	C₁₁×Q₁₆	—	2	8	no	—
122	C₁₁×SD₁₆	—	4	8	no	—
123	C₁₁×D₈	—	2	8	no	—
124	C₂×C₈×C₁₁	—	2	1	no	—
125	C₂×C₈×C₁₁	—	2	1	no	—
126	C₂×C₈×C₁₁	—	2	1	no	—
127	C₂×C₈×C₁₁	—	2	1	no	—
128	C₂×C₈×C₁₁	—	2	1	no	—
129	C₂×C₈×C₁₁	—	2	1	no	—
130	C₂×C₈×C₁₁	—	2	1	no	—
131	C₂×C₈×C₁₁	—	2	1	no	—
132	C₂×C₈×C₁₁	C₂²×C₄	1	2	yes	—
133	C₂×C₈×C₁₁	C₂²×C₄	1	2	yes	—
134	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
135	C₂×C₈×C₁₁	#41	1	2	yes	—
136	C₁₁×C₄⋊C₄	—	2	2	no	—
137	C₁₁×C₄⋊C₄	—	2	2	no	—
138	C₁₁×C₄⋊C₄	—	2	2	no	—
139	C₁₁×C₄⋊C₄	—	2	2	no	—
140	C₁₁×C₄⋊C₄	—	2	2	no	—
141	C₁₁×C₄⋊C₄	—	4	4	no	—
142	C₁₁×C₄⋊C₄	C₂×D₄	1	4	yes	—
143	C₁₁×C₂²⋊C₄	—	2	8	no	—
144	C₁₁×C₂²⋊C₄	—	2	8	no	—
145	C₁₁×C₂²⋊C₄	—	4	4	no	—
146	C₁₁×C₂²⋊C₄	—	4	4	no	—
147	C₁₁×C₂²⋊C₄	—	8	2	no	—
148	C₄²×C₁₁	—	2	1	no	—
149	C₄²×C₁₁	—	2	1	no	—
150	C₄²×C₁₁	—	2	1	no	—
151	C₄²×C₁₁	—	2	1	no	—
152	C₄²×C₁₁	—	4	4	no	—
153	C₄²×C₁₁	—	8	2	no	—
154	C₄²×C₁₁	C₂²×C₄	1	2	yes	—
155	C₄²×C₁₁	#41	1	2	yes	—
156	C₂×#495	C₂×C₁₁	1	1	yes	characteristic
157	C₂×C₄×Q₁₆	C₂×C₁₁	1	1	yes	characteristic, complemented
158	C₂×C₄×D₈	C₂×C₁₁	1	1	yes	characteristic
159	#2367	C₂×C₁₁	1	2	yes	complemented
160	#1983	C₂×C₁₁	1	2	yes	complemented
161	#1970	C₂×C₁₁	1	1	yes	characteristic
162	#1969	C₂×C₁₁	1	1	yes	characteristic, complemented
163	#1880	C₂×C₁₁	1	2	yes	complemented
164	#1877	C₂×C₁₁	1	2	yes	complemented
165	C₄×#107	C₂×C₁₁	1	1	yes	characteristic, complemented
166	C₈×C₄⋊C₄	C₂×C₁₁	1	1	yes	characteristic, complemented
167	C₂³×C₁₁	—	2	4	no	—
168	C₂³×C₁₁	—	4	2	no	—
169	C₂³×C₁₁	—	4	2	no	—
170	C₂³×C₁₁	—	4	2	no	—
171	C₂³×C₁₁	—	4	2	no	—
172	C₂³×C₁₁	—	4	2	no	—
173	C₂³×C₁₁	—	4	2	no	—
174	C₂³×C₁₁	C₂²×D₄	1	1	yes	characteristic
175	Q₈×C₁₁	—	2	4	no	—
176	Q₈×C₁₁	—	2	4	no	—
177	Q₈×C₁₁	—	4	2	no	—
178	Q₈×C₁₁	—	4	2	no	—
179	D₄×C₁₁	—	2	4	no	—
180	D₄×C₁₁	—	2	4	no	—
181	D₄×C₁₁	—	4	2	no	—
182	D₄×C₁₁	—	4	2	no	—
183	C₂×C₄×C₁₁	—	2	1	no	—
184	C₂×C₄×C₁₁	—	2	1	no	—
185	C₂×C₄×C₁₁	—	2	1	no	—
186	C₂×C₄×C₁₁	—	2	1	no	—
187	C₂×C₄×C₁₁	—	2	1	no	—
188	C₂×C₄×C₁₁	—	2	1	no	—
189	C₂×C₄×C₁₁	—	2	1	no	—
190	C₂×C₄×C₁₁	—	2	1	no	—
191	C₂×C₄×C₁₁	—	2	4	no	—
192	C₂×C₄×C₁₁	—	2	1	no	—
193	C₂×C₄×C₁₁	—	2	1	no	—
194	C₂×C₄×C₁₁	—	2	4	no	—
195	C₂×C₄×C₁₁	—	2	1	no	—
196	C₂×C₄×C₁₁	—	2	1	no	—
197	C₂×C₄×C₁₁	—	2	1	no	—
198	C₂×C₄×C₁₁	—	2	1	no	—
199	C₂×C₄×C₁₁	—	4	2	no	—
200	C₂×C₄×C₁₁	—	4	2	no	—
201	C₂×C₄×C₁₁	—	4	2	no	—
202	C₂×C₄×C₁₁	—	4	2	no	—
203	C₂×C₄×C₁₁	—	4	2	no	—
204	C₂×C₄×C₁₁	—	4	2	no	—
205	C₂×C₄×C₁₁	—	4	2	no	—
206	C₂×C₄×C₁₁	—	8	8	no	—
207	C₂×C₄×C₁₁	C₄×D₄	1	2	yes	—
208	C₂×C₄×C₁₁	C₄×D₄	1	2	yes	—
209	C₂×C₄×C₁₁	#135	1	2	yes	—
210	C₂×C₄×C₁₁	#135	1	2	yes	—
211	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
212	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
213	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
214	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
215	C₂×C₄×C₁₁	H(5,𝔽₂)	1	1	yes	characteristic
216	C₂×C₄×C₁₁	H(5,𝔽₂)	1	1	yes	characteristic
217	C₈×C₁₁	—	2	2	no	—
218	C₈×C₁₁	—	4	1	no	—
219	C₈×C₁₁	—	4	1	no	—
220	C₈×C₁₁	C₄×D₄	1	4	yes	—
221	C₂²×Q₁₆	C₂²×C₁₁	1	1	yes	characteristic
222	C₂²×SD₁₆	C₂²×C₁₁	1	2	yes	—
223	C₂²×D₈	C₂²×C₁₁	1	1	yes	characteristic
224	C₂×#124	C₂²×C₁₁	1	2	yes	—
225	C₂×C₄×Q₈	C₂²×C₁₁	1	2	yes	—
226	C₂×C₄×D₄	C₂²×C₁₁	1	2	yes	—
227	#495	C₄×C₁₁	1	8	yes	complemented
228	C₄×Q₁₆	—	2	4	no	—
229	C₄×D₈	—	2	4	no	—
230	C₂×#107	C₂²×C₁₁	1	1	yes	characteristic
231	C₂×#107	C₂²×C₁₁	1	1	yes	characteristic
232	C₂×C₄⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
233	C₂×#103	C₂²×C₁₁	1	2	yes	—
234	C₂×#103	C₂²×C₁₁	1	2	yes	—
235	C₂×#102	C₂²×C₁₁	1	2	yes	—
236	C₂×#102	C₂²×C₁₁	1	2	yes	—
237	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
238	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
239	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
240	#391	C₂²×C₁₁	1	2	yes	—
241	#390	C₂²×C₁₁	1	2	yes	—
242	#388	—	2	2	no	—
243	#388	—	2	2	no	—
244	#385	—	2	2	no	—
245	C₄×C₄⋊C₄	C₂²×C₁₁	1	2	yes	—
246	C₄×C₄⋊C₄	C₂²×C₁₁	1	1	yes	characteristic
247	C₄×C₂²⋊C₄	—	2	2	no	—
248	#340	C₂²×C₁₁	1	2	yes	—
249	#336	C₂²×C₁₁	1	1	yes	characteristic
250	#336	C₂²×C₁₁	1	1	yes	characteristic
251	C₂²×C₁₁	—	4	4	no	—
252	C₂²×C₁₁	—	4	4	no	—
253	C₂²×C₁₁	—	4	4	no	—
254	C₂²×C₁₁	—	8	2	no	—
255	C₂²×C₁₁	—	8	2	no	—
256	C₂²×C₁₁	—	8	2	no	—
257	C₂²×C₁₁	—	8	2	no	—
258	C₂²×C₁₁	C₂×C₄×D₄	1	1	yes	characteristic
259	C₂²×C₁₁	D₄²	1	1	yes	characteristic
260	C₂²×C₁₁	#550	1	1	yes	characteristic
261	C₂²×C₁₁	C₂×#135	1	1	yes	characteristic
262	C₂²×C₁₁	C₂×#135	1	1	yes	characteristic
263	C₂²×C₁₁	#576	1	1	yes	characteristic
264	C₂²×C₁₁	#578	1	1	yes	characteristic
265	C₄×C₁₁	—	2	2	no	—
266	C₄×C₁₁	—	2	2	no	—
267	C₄×C₁₁	—	2	2	no	—
268	C₄×C₁₁	—	2	2	no	—
269	C₄×C₁₁	—	4	4	no	—
270	C₄×C₁₁	—	4	1	no	—
271	C₄×C₁₁	—	4	4	no	—
272	C₄×C₁₁	—	4	1	no	—
273	C₄×C₁₁	—	8	2	no	—
274	C₄×C₁₁	C₂×C₄×D₄	1	1	yes	characteristic
275	C₄×C₁₁	#518	1	1	yes	characteristic
276	C₄×C₁₁	#550	1	1	yes	characteristic
277	C₄×C₁₁	#559	1	1	yes	characteristic
278	C₂²×Q₈	C₂³×C₁₁	1	2	yes	—
279	C₂²×D₄	C₂³×C₁₁	1	2	yes	—
280	C₂³×C₄	—	2	2	no	—
281	C₂×Q₁₆	—	2	2	no	—
282	C₂×Q₁₆	—	2	2	no	—
283	C₂×Q₁₆	C₂×C₄×C₁₁	1	4	yes	complemented
284	C₂×SD₁₆	—	4	2	no	—
285	C₂×SD₁₆	—	4	2	no	—
286	C₂×SD₁₆	C₂×C₄×C₁₁	1	8	yes	complemented
287	C₂×D₈	—	2	2	no	—
288	C₂×D₈	—	2	2	no	—
289	C₂×D₈	C₂×C₄×C₁₁	1	4	yes	—
290	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
291	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
292	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
293	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
294	#124	—	2	4	no	—
295	#124	C₂×C₄×C₁₁	1	8	yes	complemented
296	C₄×Q₈	—	2	4	no	—
297	C₄×Q₈	—	4	2	no	—
298	C₄×D₄	—	2	4	no	—
299	C₄×D₄	—	4	2	no	—
300	C₂×C₄⋊C₄	—	2	2	no	—
301	C₂×C₄⋊C₄	D₄×C₁₁	1	1	yes	characteristic
302	C₂×C₄⋊C₄	D₄×C₁₁	1	1	yes	characteristic
303	C₂×C₄⋊C₄	C₂³×C₁₁	1	2	yes	—
304	C₂×C₄⋊C₄	C₂³×C₁₁	1	2	yes	—
305	C₂×C₂²⋊C₄	—	2	2	no	—
306	C₂×C₂²⋊C₄	—	2	2	no	—
307	C₂×C₂²⋊C₄	—	2	2	no	—
308	C₂×C₂²⋊C₄	—	2	2	no	—
309	C₂×C₂²⋊C₄	—	2	2	no	—
310	C₂×C₄²	—	2	2	no	—
311	C₂×C₄²	—	2	2	no	—
312	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
313	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
314	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
315	#107	—	2	2	no	—
316	#107	D₄×C₁₁	1	4	yes	—
317	C₄⋊C₈	—	2	2	no	—
318	#103	—	2	4	no	—
319	#103	—	4	2	no	—
320	#102	—	2	4	no	—
321	#102	—	4	2	no	—
322	C₄×C₈	—	2	2	no	—
323	C₄×C₈	—	2	2	no	—
324	C₄×C₈	C₂×C₄×C₁₁	1	4	yes	complemented
325	#95	—	2	2	no	—
326	#95	—	2	2	no	—
327	#95	—	2	2	no	—
328	#95	D₄×C₁₁	1	1	yes	characteristic
329	#95	D₄×C₁₁	1	1	yes	characteristic
330	C₂×C₁₁	—	8	4	no	—
331	C₂×C₁₁	#2366	1	1	yes	characteristic
332	C₂×C₁₁	C₄×#135	1	1	yes	characteristic
333	C₂×C₁₁	#2951	1	1	yes	characteristic
334	C₂×C₁₁	#3280	1	1	yes	characteristic
335	C₂×C₁₁	#3285	1	1	yes	characteristic
336	C₂×C₁₁	#3393	1	1	yes	characteristic
337	C₂×C₁₁	#3396	1	1	yes	characteristic
338	C₂⁴	—	2	2	no	—
339	C₂×Q₈	—	2	2	no	—
340	C₂×Q₈	—	2	2	no	—
341	C₂×Q₈	—	2	2	no	—
342	C₂×Q₈	—	2	2	no	—
343	C₂×Q₈	—	2	2	no	—
344	C₂×Q₈	C₂²×C₄×C₁₁	1	4	yes	—
345	C₂×D₄	—	2	2	no	—
346	C₂×D₄	—	2	2	no	—
347	C₂×D₄	—	2	2	no	—
348	C₂×D₄	—	2	2	no	—
349	C₂×D₄	—	2	2	no	—
350	C₂×D₄	C₂²×C₄×C₁₁	1	4	yes	—
351	C₂²×C₄	—	2	2	no	—
352	C₂²×C₄	—	2	2	no	—
353	C₂²×C₄	—	2	2	no	—
354	C₂²×C₄	—	4	4	no	—
355	C₂²×C₄	—	4	4	no	—
356	C₂²×C₄	—	8	2	no	—
357	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
358	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
359	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
360	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
361	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
362	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
363	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
364	Q₁₆	—	2	8	no	—
365	SD₁₆	—	4	8	no	—
366	D₈	—	2	8	no	—
367	C₂×C₈	—	2	1	no	—
368	C₂×C₈	—	2	1	no	—
369	C₂×C₈	—	2	1	no	—
370	C₂×C₈	—	2	1	no	—
371	C₂×C₈	—	2	1	no	—
372	C₂×C₈	—	2	1	no	—
373	C₂×C₈	—	2	1	no	—
374	C₂×C₈	—	2	1	no	—
375	C₂×C₈	C₂²×C₄×C₁₁	1	2	yes	—
376	C₂×C₈	C₂²×C₄×C₁₁	1	2	yes	—
377	C₂×C₈	C₂×D₄×C₁₁	1	2	yes	—
378	C₂×C₈	C₁₁×#41	1	2	yes	—
379	C₄⋊C₄	—	2	2	no	—
380	C₄⋊C₄	—	2	2	no	—
381	C₄⋊C₄	—	2	2	no	—
382	C₄⋊C₄	—	2	2	no	—
383	C₄⋊C₄	—	2	2	no	—
384	C₄⋊C₄	—	4	4	no	—
385	C₄⋊C₄	C₂×D₄×C₁₁	1	4	yes	—
386	C₂²⋊C₄	—	2	8	no	—
387	C₂²⋊C₄	—	2	8	no	—
388	C₂²⋊C₄	—	4	4	no	—
389	C₂²⋊C₄	—	4	4	no	—
390	C₂²⋊C₄	—	8	2	no	—
391	C₄²	—	2	1	no	—
392	C₄²	—	2	1	no	—
393	C₄²	—	2	1	no	—
394	C₄²	—	2	1	no	—
395	C₄²	—	4	4	no	—
396	C₄²	—	8	2	no	—
397	C₄²	C₂²×C₄×C₁₁	1	2	yes	—
398	C₄²	C₁₁×#41	1	2	yes	—
399	C₁₁	#23186	1	1	yes	characteristic, direct product factor, Sylow
400	C₂³	—	2	4	no	—
401	C₂³	—	4	2	no	—
402	C₂³	—	4	2	no	—
403	C₂³	—	4	2	no	—
404	C₂³	—	4	2	no	—
405	C₂³	—	4	2	no	—
406	C₂³	—	4	2	no	—
407	C₂³	C₂²×D₄×C₁₁	1	1	yes	characteristic
408	Q₈	—	2	4	no	—
409	Q₈	—	2	4	no	—
410	Q₈	—	4	2	no	—
411	Q₈	—	4	2	no	—
412	D₄	—	2	4	no	—
413	D₄	—	2	4	no	—
414	D₄	—	4	2	no	—
415	D₄	—	4	2	no	—
416	C₂×C₄	—	2	1	no	—
417	C₂×C₄	—	2	1	no	—
418	C₂×C₄	—	2	1	no	—
419	C₂×C₄	—	2	1	no	—
420	C₂×C₄	—	2	1	no	—
421	C₂×C₄	—	2	1	no	—
422	C₂×C₄	—	2	1	no	—
423	C₂×C₄	—	2	1	no	—
424	C₂×C₄	—	2	4	no	—
425	C₂×C₄	—	2	1	no	—
426	C₂×C₄	—	2	1	no	—
427	C₂×C₄	—	2	4	no	—
428	C₂×C₄	—	2	1	no	—
429	C₂×C₄	—	2	1	no	—
430	C₂×C₄	—	2	1	no	—
431	C₂×C₄	—	2	1	no	—
432	C₂×C₄	—	4	2	no	—
433	C₂×C₄	—	4	2	no	—
434	C₂×C₄	—	4	2	no	—
435	C₂×C₄	—	4	2	no	—
436	C₂×C₄	—	4	2	no	—
437	C₂×C₄	—	4	2	no	—
438	C₂×C₄	—	4	2	no	—
439	C₂×C₄	—	8	8	no	—
440	C₂×C₄	C₄×D₄×C₁₁	1	2	yes	—
441	C₂×C₄	C₄×D₄×C₁₁	1	2	yes	—
442	C₂×C₄	C₁₁×#135	1	2	yes	—
443	C₂×C₄	C₁₁×#135	1	2	yes	—
444	C₂×C₄	C₂³×C₄×C₁₁	1	1	yes	characteristic
445	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
446	C₂×C₄	C₂×C₁₁×#41	1	1	yes	characteristic
447	C₂×C₄	C₂×C₁₁×#41	1	1	yes	characteristic
448	C₂×C₄	C₁₁×H(5,𝔽₂)	1	1	yes	characteristic
449	C₂×C₄	C₁₁×H(5,𝔽₂)	1	1	yes	characteristic
450	C₈	—	2	2	no	—
451	C₈	—	4	1	no	—
452	C₈	—	4	1	no	—
453	C₈	C₄×D₄×C₁₁	1	4	yes	—
454	C₂²	—	4	4	no	—
455	C₂²	—	4	4	no	—
456	C₂²	—	4	4	no	—
457	C₂²	—	8	2	no	—
458	C₂²	—	8	2	no	—
459	C₂²	—	8	2	no	—
460	C₂²	—	8	2	no	—
461	C₂²	C₂×C₄×D₄×C₁₁	1	1	yes	characteristic
462	C₂²	D₄²×C₁₁	1	1	yes	characteristic
463	C₂²	C₁₁×#550	1	1	yes	characteristic
464	C₂²	C₂×C₁₁×#135	1	1	yes	characteristic
465	C₂²	C₂×C₁₁×#135	1	1	yes	characteristic
466	C₂²	C₁₁×#576	1	1	yes	characteristic
467	C₂²	C₁₁×#578	1	1	yes	characteristic
468	C₄	—	2	2	no	—
469	C₄	—	2	2	no	—
470	C₄	—	2	2	no	—
471	C₄	—	2	2	no	—
472	C₄	—	4	1	no	—
473	C₄	—	4	4	no	—
474	C₄	—	4	1	no	—
475	C₄	—	4	4	no	—
476	C₄	—	8	2	no	—
477	C₄	C₂×C₄×D₄×C₁₁	1	1	yes	characteristic
478	C₄	C₁₁×#518	1	1	yes	characteristic
479	C₄	C₁₁×#550	1	1	yes	characteristic
480	C₄	C₁₁×#559	1	1	yes	characteristic
481	C₂	—	8	4	no	—
482	C₂	C₁₁×#2366	1	1	yes	characteristic
483	C₂	C₄×C₁₁×#135	1	1	yes	characteristic
484	C₂	C₁₁×#2951	1	1	yes	characteristic
485	C₂	C₁₁×#3280	1	1	yes	characteristic
486	C₂	C₁₁×#3285	1	1	yes	characteristic
487	C₂	C₁₁×#3393	1	1	yes	characteristic
488	C₂	C₁₁×#3396	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₁	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₁
prime radical	C₂²×C₁₁×D₈	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₁ ◁ C₄×C₁₁×C₄⋊C₄ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₄×C₁₁×Q₁₆	C₂	semidirect
4. C₁₁×#2367	C₂	semidirect
5. C₁₁×#1983	C₂	semidirect
7. C₁₁×#1969	C₂	semidirect
8. C₁₁×#1880	C₂	semidirect
9. C₁₁×#1877	C₂	semidirect
10. C₄×C₁₁×#107	C₂	semidirect
11. C₈×C₁₁×C₄⋊C₄	C₂	semidirect
18. C₁₁×#495	C₄	semidirect
47. C₂×C₁₁×Q₁₆	C₂×C₄	semidirect
50. C₂×C₁₁×SD₁₆	C₂×C₄	semidirect
59. C₁₁×#124	C₂×C₄	semidirect
88. C₄×C₈×C₁₁	C₂×C₄	semidirect
94. #23186	C₁₁	direct (N × H)
157. C₂×C₄×Q₁₆	C₂×C₁₁	semidirect
159. #2367	C₂×C₁₁	semidirect
160. #1983	C₂×C₁₁	semidirect
162. #1969	C₂×C₁₁	semidirect
163. #1880	C₂×C₁₁	semidirect
164. #1877	C₂×C₁₁	semidirect
165. C₄×#107	C₂×C₁₁	semidirect
166. C₈×C₄⋊C₄	C₂×C₁₁	semidirect
227. #495	C₄×C₁₁	semidirect
283. C₂×Q₁₆	C₂×C₄×C₁₁	semidirect
286. C₂×SD₁₆	C₂×C₄×C₁₁	semidirect
295. #124	C₂×C₄×C₁₁	semidirect
324. C₄×C₈	C₂×C₄×C₁₁	semidirect
399. C₁₁	#23186	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×#495	2
C₂×C₄×C₁₁×Q₁₆	2
C₂×C₄×C₁₁×D₈	2
C₁₁×#2367	2
C₁₁×#1983	2
C₁₁×#1970	2
C₁₁×#1969	2
C₁₁×#1880	2
C₁₁×#1877	2
C₄×C₁₁×#107	2
C₈×C₁₁×C₄⋊C₄	2
#23186	11

Subgroups — C11×#23186 #14600379

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#23186 #14600379