Subgroups — C₁₁×#23182 #14600375

Order 2816.

1098 conjugacy classes of subgroups.

The subgroup lattice has 508 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₁×#492	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×C₁₁×SD₁₆	C₂	1	2	yes	maximal, complemented
3	C₁₁×#2366	C₂	1	1	yes	maximal, characteristic
4	C₁₁×#2365	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₁×#1982	C₂	1	1	yes	maximal, characteristic
6	C₁₁×#1981	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₁×#1968	C₂	1	2	yes	maximal, complemented
8	C₁₁×#1880	C₂	1	2	yes	maximal, complemented
9	C₁₁×#1877	C₂	1	2	yes	maximal, complemented
10	C₄×C₁₁×#106	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈×C₁₁×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₁₁×SD₁₆	C₂²	1	2	yes	—
13	C₂²×C₁₁×SD₁₆	C₂²	1	2	yes	—
14	C₂×C₁₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic
15	C₂×C₁₁×#127	C₂²	1	1	yes	characteristic
16	C₂×C₄×Q₈×C₁₁	C₂²	1	2	yes	—
17	C₂×C₄×D₄×C₁₁	—	2	1	no	—
18	C₂×C₄×D₄×C₁₁	C₂²	1	2	yes	—
19	C₁₁×#492	C₄	1	8	yes	complemented
20	C₄×C₁₁×SD₁₆	—	2	8	no	—
21	C₂×C₁₁×#106	C₂²	1	1	yes	characteristic
22	C₂×C₁₁×#106	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	2	yes	—
29	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
30	C₁₁×#391	C₂²	1	2	yes	—
31	C₁₁×#390	—	2	1	no	—
32	C₁₁×#390	C₂²	1	2	yes	—
33	C₁₁×#389	—	2	1	no	—
34	C₁₁×#387	—	2	2	no	—
35	C₁₁×#386	—	2	2	no	—
36	C₄×C₁₁×C₄⋊C₄	—	2	1	no	—
37	C₄×C₁₁×C₄⋊C₄	C₂²	1	1	yes	characteristic
38	C₄×C₁₁×C₄⋊C₄	C₂²	1	1	yes	characteristic
39	C₄×C₁₁×C₄⋊C₄	C₂²	1	1	yes	characteristic
40	C₁₁×#340	C₂²	1	1	yes	characteristic
41	C₁₁×#340	C₂²	1	1	yes	characteristic
42	C₁₁×#336	C₂²	1	2	yes	—
43	C₂²×Q₈×C₁₁	C₂³	1	2	yes	—
44	C₂²×D₄×C₁₁	—	2	1	no	—
45	C₂²×D₄×C₁₁	—	2	1	no	—
46	C₂²×D₄×C₁₁	C₂³	1	2	yes	—
47	C₂³×C₄×C₁₁	—	2	2	no	—
48	C₂×C₁₁×SD₁₆	—	2	4	no	—
49	C₂×C₁₁×SD₁₆	—	2	4	no	—
50	C₂×C₁₁×SD₁₆	—	4	2	no	—
51	C₂×C₁₁×SD₁₆	—	4	2	no	—
52	C₂×C₁₁×SD₁₆	C₂×C₄	1	8	yes	complemented
53	C₂×C₁₁×SD₁₆	C₂×C₄	1	8	yes	complemented
54	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
55	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
56	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
57	C₁₁×C₄⋊Q₈	—	2	2	no	—
58	C₁₁×C₄⋊Q₈	C₂×C₄	1	4	yes	complemented
59	C₁₁×#127	—	2	2	no	—
60	C₁₁×#127	C₂×C₄	1	4	yes	—
61	C₄×Q₈×C₁₁	—	2	4	no	—
62	C₄×Q₈×C₁₁	—	4	2	no	—
63	C₄×D₄×C₁₁	—	2	4	no	—
64	C₄×D₄×C₁₁	—	4	2	no	—
65	C₄×D₄×C₁₁	—	4	4	no	—
66	C₂×C₁₁×C₄⋊C₄	—	2	1	no	—
67	C₂×C₁₁×C₄⋊C₄	—	2	1	no	—
68	C₂×C₁₁×C₄⋊C₄	—	2	2	no	—
69	C₂×C₁₁×C₄⋊C₄	D₄	1	1	yes	characteristic
70	C₂×C₁₁×C₄⋊C₄	D₄	1	1	yes	characteristic
71	C₂×C₁₁×C₄⋊C₄	C₂³	1	1	yes	characteristic
72	C₂×C₁₁×C₄⋊C₄	C₂³	1	1	yes	characteristic
73	C₂×C₁₁×C₄⋊C₄	C₂³	1	1	yes	characteristic
74	C₂×C₁₁×C₄⋊C₄	C₂³	1	1	yes	characteristic
75	C₂×C₁₁×C₂²⋊C₄	—	2	2	no	—
76	C₂×C₁₁×C₂²⋊C₄	—	2	2	no	—
77	C₂×C₁₁×C₂²⋊C₄	—	2	2	no	—
78	C₂×C₄²×C₁₁	—	2	1	no	—
79	C₂×C₄²×C₁₁	—	2	1	no	—
80	C₂×C₄²×C₁₁	—	2	2	no	—
81	C₂×C₄²×C₁₁	C₂³	1	2	yes	—
82	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
83	C₁₁×#106	—	2	2	no	—
84	C₁₁×#106	D₄	1	4	yes	complemented
85	C₁₁×C₄⋊C₈	—	2	2	no	—
86	C₁₁×#103	—	2	4	no	—
87	C₁₁×#103	—	4	2	no	—
88	C₁₁×#102	—	2	4	no	—
89	C₁₁×#102	—	4	2	no	—
90	C₄×C₈×C₁₁	—	2	4	no	—
91	C₄×C₈×C₁₁	C₂×C₄	1	4	yes	complemented
92	C₁₁×#95	—	2	2	no	—
93	C₁₁×#95	—	2	1	no	—
94	C₁₁×#95	—	2	1	no	—
95	C₁₁×#95	—	2	2	no	—
96	C₁₁×#95	D₄	1	2	yes	—
97	#23182	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
98	C₂⁴×C₁₁	—	2	2	no	—
99	C₂×Q₈×C₁₁	—	2	2	no	—
100	C₂×Q₈×C₁₁	—	2	2	no	—
101	C₂×Q₈×C₁₁	—	2	2	no	—
102	C₂×Q₈×C₁₁	—	2	2	no	—
103	C₂×Q₈×C₁₁	—	2	2	no	—
104	C₂×Q₈×C₁₁	C₂²×C₄	1	4	yes	—
105	C₂×D₄×C₁₁	—	2	4	no	—
106	C₂×D₄×C₁₁	—	2	4	no	—
107	C₂×D₄×C₁₁	—	2	2	no	—
108	C₂×D₄×C₁₁	—	2	2	no	—
109	C₂×D₄×C₁₁	—	2	2	no	—
110	C₂×D₄×C₁₁	—	2	2	no	—
111	C₂×D₄×C₁₁	—	2	2	no	—
112	C₂×D₄×C₁₁	—	4	2	no	—
113	C₂×D₄×C₁₁	—	4	2	no	—
114	C₂×D₄×C₁₁	—	8	1	no	—
115	C₂×D₄×C₁₁	—	8	1	no	—
116	C₂×D₄×C₁₁	C₂²×C₄	1	4	yes	—
117	C₂²×C₄×C₁₁	—	2	2	no	—
118	C₂²×C₄×C₁₁	—	2	1	no	—
119	C₂²×C₄×C₁₁	—	2	1	no	—
120	C₂²×C₄×C₁₁	—	2	1	no	—
121	C₂²×C₄×C₁₁	—	2	1	no	—
122	C₂²×C₄×C₁₁	—	4	4	no	—
123	C₂²×C₄×C₁₁	—	4	4	no	—
124	C₂²×C₄×C₁₁	—	8	2	no	—
125	C₂²×C₄×C₁₁	C₂×D₄	1	2	yes	—
126	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
127	C₂²×C₄×C₁₁	C₂×D₄	1	2	yes	—
128	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
129	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
130	C₁₁×SD₁₆	—	2	16	no	—
131	C₁₁×SD₁₆	—	4	8	no	—
132	C₂×C₈×C₁₁	—	2	2	no	—
133	C₂×C₈×C₁₁	—	2	2	no	—
134	C₂×C₈×C₁₁	—	2	1	no	—
135	C₂×C₈×C₁₁	—	2	1	no	—
136	C₂×C₈×C₁₁	—	2	2	no	—
137	C₂×C₈×C₁₁	C₂²×C₄	1	2	yes	—
138	C₂×C₈×C₁₁	C₂²×C₄	1	2	yes	—
139	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
140	C₂×C₈×C₁₁	#41	1	2	yes	—
141	C₁₁×C₄⋊C₄	—	2	4	no	—
142	C₁₁×C₄⋊C₄	—	2	4	no	—
143	C₁₁×C₄⋊C₄	—	2	2	no	—
144	C₁₁×C₄⋊C₄	—	2	1	no	—
145	C₁₁×C₄⋊C₄	—	2	1	no	—
146	C₁₁×C₄⋊C₄	—	2	1	no	—
147	C₁₁×C₄⋊C₄	—	2	1	no	—
148	C₁₁×C₄⋊C₄	—	2	1	no	—
149	C₁₁×C₄⋊C₄	—	2	1	no	—
150	C₁₁×C₄⋊C₄	—	4	4	no	—
151	C₁₁×C₄⋊C₄	SD₁₆	1	4	yes	complemented
152	C₁₁×C₄⋊C₄	C₂×D₄	1	2	yes	—
153	C₁₁×C₄⋊C₄	C₂×D₄	1	2	yes	—
154	C₁₁×C₂²⋊C₄	—	4	4	no	—
155	C₁₁×C₂²⋊C₄	—	4	4	no	—
156	C₁₁×C₂²⋊C₄	—	8	2	no	—
157	C₄²×C₁₁	—	2	2	no	—
158	C₄²×C₁₁	—	2	2	no	—
159	C₄²×C₁₁	—	4	4	no	—
160	C₄²×C₁₁	—	4	2	no	—
161	C₄²×C₁₁	—	4	2	no	—
162	C₄²×C₁₁	C₂²×C₄	1	2	yes	—
163	C₄²×C₁₁	#41	1	2	yes	—
164	C₂×#492	C₂×C₁₁	1	1	yes	characteristic
165	C₂×C₄×SD₁₆	C₂×C₁₁	1	2	yes	complemented
166	#2366	C₂×C₁₁	1	1	yes	characteristic
167	#2365	C₂×C₁₁	1	1	yes	characteristic, complemented
168	#1982	C₂×C₁₁	1	1	yes	characteristic
169	#1981	C₂×C₁₁	1	1	yes	characteristic, complemented
170	#1968	C₂×C₁₁	1	2	yes	complemented
171	#1880	C₂×C₁₁	1	2	yes	complemented
172	#1877	C₂×C₁₁	1	2	yes	complemented
173	C₄×#106	C₂×C₁₁	1	1	yes	characteristic, complemented
174	C₈×C₄⋊C₄	C₂×C₁₁	1	1	yes	characteristic, complemented
175	C₂³×C₁₁	—	2	4	no	—
176	C₂³×C₁₁	—	4	2	no	—
177	C₂³×C₁₁	—	4	2	no	—
178	C₂³×C₁₁	—	4	2	no	—
179	C₂³×C₁₁	—	4	2	no	—
180	C₂³×C₁₁	—	4	2	no	—
181	C₂³×C₁₁	—	4	2	no	—
182	C₂³×C₁₁	C₂²×D₄	1	1	yes	characteristic
183	Q₈×C₁₁	—	2	4	no	—
184	Q₈×C₁₁	—	2	4	no	—
185	Q₈×C₁₁	—	4	2	no	—
186	Q₈×C₁₁	—	4	2	no	—
187	D₄×C₁₁	—	2	4	no	—
188	D₄×C₁₁	—	2	4	no	—
189	D₄×C₁₁	—	4	2	no	—
190	D₄×C₁₁	—	4	2	no	—
191	D₄×C₁₁	—	4	8	no	—
192	D₄×C₁₁	—	8	4	no	—
193	C₂×C₄×C₁₁	—	2	2	no	—
194	C₂×C₄×C₁₁	—	2	2	no	—
195	C₂×C₄×C₁₁	—	2	1	no	—
196	C₂×C₄×C₁₁	—	2	1	no	—
197	C₂×C₄×C₁₁	—	2	4	no	—
198	C₂×C₄×C₁₁	—	2	2	no	—
199	C₂×C₄×C₁₁	—	2	2	no	—
200	C₂×C₄×C₁₁	—	2	2	no	—
201	C₂×C₄×C₁₁	—	2	2	no	—
202	C₂×C₄×C₁₁	—	2	2	no	—
203	C₂×C₄×C₁₁	—	4	2	no	—
204	C₂×C₄×C₁₁	—	4	2	no	—
205	C₂×C₄×C₁₁	—	4	1	no	—
206	C₂×C₄×C₁₁	—	4	1	no	—
207	C₂×C₄×C₁₁	—	4	1	no	—
208	C₂×C₄×C₁₁	—	4	1	no	—
209	C₂×C₄×C₁₁	—	4	1	no	—
210	C₂×C₄×C₁₁	—	4	1	no	—
211	C₂×C₄×C₁₁	—	4	1	no	—
212	C₂×C₄×C₁₁	—	4	1	no	—
213	C₂×C₄×C₁₁	—	4	1	no	—
214	C₂×C₄×C₁₁	—	4	1	no	—
215	C₂×C₄×C₁₁	—	8	8	no	—
216	C₂×C₄×C₁₁	C₄×D₄	1	2	yes	—
217	C₂×C₄×C₁₁	C₄×D₄	1	2	yes	—
218	C₂×C₄×C₁₁	C₂×SD₁₆	1	4	yes	—
219	C₂×C₄×C₁₁	C₂×SD₁₆	1	2	yes	—
220	C₂×C₄×C₁₁	#135	1	2	yes	—
221	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
222	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
223	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
224	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
225	C₂×C₄×C₁₁	H(5,𝔽₂)	1	1	yes	characteristic
226	C₂×C₄×C₁₁	H(5,𝔽₂)	1	1	yes	characteristic
227	C₈×C₁₁	—	2	2	no	—
228	C₈×C₁₁	—	4	2	no	—
229	C₈×C₁₁	C₄×D₄	1	4	yes	complemented
230	C₂²×SD₁₆	C₂²×C₁₁	1	2	yes	—
231	C₂²×SD₁₆	C₂²×C₁₁	1	2	yes	—
232	C₂×C₄⋊Q₈	C₂²×C₁₁	1	1	yes	characteristic
233	C₂×#127	C₂²×C₁₁	1	1	yes	characteristic
234	C₂×C₄×Q₈	C₂²×C₁₁	1	2	yes	—
235	C₂×C₄×D₄	—	2	1	no	—
236	C₂×C₄×D₄	C₂²×C₁₁	1	2	yes	—
237	#492	C₄×C₁₁	1	8	yes	complemented
238	C₄×SD₁₆	—	2	8	no	—
239	C₂×#106	C₂²×C₁₁	1	1	yes	characteristic
240	C₂×#106	C₂²×C₁₁	1	1	yes	characteristic
241	C₂×C₄⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
242	C₂×#103	C₂²×C₁₁	1	2	yes	—
243	C₂×#103	C₂²×C₁₁	1	2	yes	—
244	C₂×#102	C₂²×C₁₁	1	2	yes	—
245	C₂×#102	C₂²×C₁₁	1	2	yes	—
246	C₂×C₄×C₈	C₂²×C₁₁	1	2	yes	—
247	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
248	#391	C₂²×C₁₁	1	2	yes	—
249	#390	—	2	1	no	—
250	#390	C₂²×C₁₁	1	2	yes	—
251	#389	—	2	1	no	—
252	#387	—	2	2	no	—
253	#386	—	2	2	no	—
254	C₄×C₄⋊C₄	—	2	1	no	—
255	C₄×C₄⋊C₄	C₂²×C₁₁	1	1	yes	characteristic
256	C₄×C₄⋊C₄	C₂²×C₁₁	1	1	yes	characteristic
257	C₄×C₄⋊C₄	C₂²×C₁₁	1	1	yes	characteristic
258	#340	C₂²×C₁₁	1	1	yes	characteristic
259	#340	C₂²×C₁₁	1	1	yes	characteristic
260	#336	C₂²×C₁₁	1	2	yes	—
261	C₂²×C₁₁	—	4	4	no	—
262	C₂²×C₁₁	—	4	4	no	—
263	C₂²×C₁₁	—	4	4	no	—
264	C₂²×C₁₁	—	8	2	no	—
265	C₂²×C₁₁	—	8	2	no	—
266	C₂²×C₁₁	—	8	2	no	—
267	C₂²×C₁₁	—	8	2	no	—
268	C₂²×C₁₁	C₂×C₄×D₄	1	1	yes	characteristic
269	C₂²×C₁₁	D₄²	1	1	yes	characteristic
270	C₂²×C₁₁	#550	1	1	yes	characteristic
271	C₂²×C₁₁	C₂²×SD₁₆	1	1	yes	characteristic
272	C₂²×C₁₁	C₂×#135	1	1	yes	characteristic
273	C₂²×C₁₁	#577	1	1	yes	characteristic
274	C₂²×C₁₁	#577	1	1	yes	characteristic
275	C₄×C₁₁	—	2	2	no	—
276	C₄×C₁₁	—	2	4	no	—
277	C₄×C₁₁	—	4	4	no	—
278	C₄×C₁₁	—	4	2	no	—
279	C₄×C₁₁	—	4	2	no	—
280	C₄×C₁₁	—	4	2	no	—
281	C₄×C₁₁	—	8	1	no	—
282	C₄×C₁₁	—	8	1	no	—
283	C₄×C₁₁	C₄×SD₁₆	1	4	yes	complemented
284	C₄×C₁₁	C₂×C₄×D₄	1	1	yes	characteristic
285	C₄×C₁₁	#518	1	1	yes	characteristic
286	C₄×C₁₁	#550	1	1	yes	characteristic
287	C₄×C₁₁	#559	1	1	yes	characteristic
288	C₂²×Q₈	C₂³×C₁₁	1	2	yes	—
289	C₂²×D₄	—	2	1	no	—
290	C₂²×D₄	—	2	1	no	—
291	C₂²×D₄	C₂³×C₁₁	1	2	yes	—
292	C₂³×C₄	—	2	2	no	—
293	C₂×SD₁₆	—	2	4	no	—
294	C₂×SD₁₆	—	2	4	no	—
295	C₂×SD₁₆	—	4	2	no	—
296	C₂×SD₁₆	—	4	2	no	—
297	C₂×SD₁₆	C₂×C₄×C₁₁	1	8	yes	complemented
298	C₂×SD₁₆	C₂×C₄×C₁₁	1	8	yes	complemented
299	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
300	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
301	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
302	C₄⋊Q₈	—	2	2	no	—
303	C₄⋊Q₈	C₂×C₄×C₁₁	1	4	yes	complemented
304	#127	—	2	2	no	—
305	#127	C₂×C₄×C₁₁	1	4	yes	—
306	C₄×Q₈	—	2	4	no	—
307	C₄×Q₈	—	4	2	no	—
308	C₄×D₄	—	2	4	no	—
309	C₄×D₄	—	4	2	no	—
310	C₄×D₄	—	4	4	no	—
311	C₂×C₄⋊C₄	—	2	1	no	—
312	C₂×C₄⋊C₄	—	2	1	no	—
313	C₂×C₄⋊C₄	—	2	2	no	—
314	C₂×C₄⋊C₄	D₄×C₁₁	1	1	yes	characteristic
315	C₂×C₄⋊C₄	D₄×C₁₁	1	1	yes	characteristic
316	C₂×C₄⋊C₄	C₂³×C₁₁	1	1	yes	characteristic
317	C₂×C₄⋊C₄	C₂³×C₁₁	1	1	yes	characteristic
318	C₂×C₄⋊C₄	C₂³×C₁₁	1	1	yes	characteristic
319	C₂×C₄⋊C₄	C₂³×C₁₁	1	1	yes	characteristic
320	C₂×C₂²⋊C₄	—	2	2	no	—
321	C₂×C₂²⋊C₄	—	2	2	no	—
322	C₂×C₂²⋊C₄	—	2	2	no	—
323	C₂×C₄²	—	2	1	no	—
324	C₂×C₄²	—	2	2	no	—
325	C₂×C₄²	—	2	1	no	—
326	C₂×C₄²	C₂³×C₁₁	1	2	yes	—
327	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
328	#106	—	2	2	no	—
329	#106	D₄×C₁₁	1	4	yes	complemented
330	C₄⋊C₈	—	2	2	no	—
331	#103	—	2	4	no	—
332	#103	—	4	2	no	—
333	#102	—	2	4	no	—
334	#102	—	4	2	no	—
335	C₄×C₈	—	2	4	no	—
336	C₄×C₈	C₂×C₄×C₁₁	1	4	yes	complemented
337	#95	—	2	2	no	—
338	#95	—	2	1	no	—
339	#95	—	2	1	no	—
340	#95	—	2	2	no	—
341	#95	D₄×C₁₁	1	2	yes	—
342	C₂×C₁₁	—	8	4	no	—
343	C₂×C₁₁	#2366	1	1	yes	characteristic
344	C₂×C₁₁	C₂×C₄×SD₁₆	1	1	yes	characteristic
345	C₂×C₁₁	#2949	1	1	yes	characteristic
346	C₂×C₁₁	D₄×SD₁₆	1	1	yes	characteristic
347	C₂×C₁₁	#3284	1	1	yes	characteristic
348	C₂×C₁₁	#3392	1	1	yes	characteristic
349	C₂×C₁₁	#3394	1	1	yes	characteristic
350	C₂⁴	—	2	2	no	—
351	C₂×Q₈	—	2	2	no	—
352	C₂×Q₈	—	2	2	no	—
353	C₂×Q₈	—	2	2	no	—
354	C₂×Q₈	—	2	2	no	—
355	C₂×Q₈	—	2	2	no	—
356	C₂×Q₈	C₂²×C₄×C₁₁	1	4	yes	—
357	C₂×D₄	—	2	4	no	—
358	C₂×D₄	—	2	4	no	—
359	C₂×D₄	—	2	2	no	—
360	C₂×D₄	—	2	2	no	—
361	C₂×D₄	—	2	2	no	—
362	C₂×D₄	—	2	2	no	—
363	C₂×D₄	—	2	2	no	—
364	C₂×D₄	—	4	2	no	—
365	C₂×D₄	—	4	2	no	—
366	C₂×D₄	—	8	1	no	—
367	C₂×D₄	—	8	1	no	—
368	C₂×D₄	C₂²×C₄×C₁₁	1	4	yes	—
369	C₂²×C₄	—	2	2	no	—
370	C₂²×C₄	—	2	1	no	—
371	C₂²×C₄	—	2	1	no	—
372	C₂²×C₄	—	2	1	no	—
373	C₂²×C₄	—	2	1	no	—
374	C₂²×C₄	—	4	4	no	—
375	C₂²×C₄	—	4	4	no	—
376	C₂²×C₄	—	8	2	no	—
377	C₂²×C₄	C₂×D₄×C₁₁	1	2	yes	—
378	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
379	C₂²×C₄	C₂×D₄×C₁₁	1	2	yes	—
380	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
381	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
382	SD₁₆	—	2	16	no	—
383	SD₁₆	—	4	8	no	—
384	C₂×C₈	—	2	1	no	—
385	C₂×C₈	—	2	1	no	—
386	C₂×C₈	—	2	2	no	—
387	C₂×C₈	—	2	2	no	—
388	C₂×C₈	—	2	2	no	—
389	C₂×C₈	C₂²×C₄×C₁₁	1	2	yes	—
390	C₂×C₈	C₂²×C₄×C₁₁	1	2	yes	—
391	C₂×C₈	C₂×D₄×C₁₁	1	2	yes	—
392	C₂×C₈	C₁₁×#41	1	2	yes	—
393	C₄⋊C₄	—	2	4	no	—
394	C₄⋊C₄	—	2	4	no	—
395	C₄⋊C₄	—	2	2	no	—
396	C₄⋊C₄	—	2	1	no	—
397	C₄⋊C₄	—	2	1	no	—
398	C₄⋊C₄	—	2	1	no	—
399	C₄⋊C₄	—	2	1	no	—
400	C₄⋊C₄	—	2	1	no	—
401	C₄⋊C₄	—	2	1	no	—
402	C₄⋊C₄	—	4	4	no	—
403	C₄⋊C₄	C₁₁×SD₁₆	1	4	yes	complemented
404	C₄⋊C₄	C₂×D₄×C₁₁	1	2	yes	—
405	C₄⋊C₄	C₂×D₄×C₁₁	1	2	yes	—
406	C₂²⋊C₄	—	4	4	no	—
407	C₂²⋊C₄	—	4	4	no	—
408	C₂²⋊C₄	—	8	2	no	—
409	C₄²	—	2	2	no	—
410	C₄²	—	2	2	no	—
411	C₄²	—	4	4	no	—
412	C₄²	—	4	2	no	—
413	C₄²	—	4	2	no	—
414	C₄²	C₂²×C₄×C₁₁	1	2	yes	—
415	C₄²	C₁₁×#41	1	2	yes	—
416	C₁₁	#23182	1	1	yes	characteristic, direct product factor, Sylow
417	C₂³	—	2	4	no	—
418	C₂³	—	4	2	no	—
419	C₂³	—	4	2	no	—
420	C₂³	—	4	2	no	—
421	C₂³	—	4	2	no	—
422	C₂³	—	4	2	no	—
423	C₂³	—	4	2	no	—
424	C₂³	C₂²×D₄×C₁₁	1	1	yes	characteristic
425	Q₈	—	2	4	no	—
426	Q₈	—	2	4	no	—
427	Q₈	—	4	2	no	—
428	Q₈	—	4	2	no	—
429	D₄	—	2	4	no	—
430	D₄	—	2	4	no	—
431	D₄	—	4	2	no	—
432	D₄	—	4	2	no	—
433	D₄	—	4	8	no	—
434	D₄	—	8	4	no	—
435	C₂×C₄	—	2	2	no	—
436	C₂×C₄	—	2	2	no	—
437	C₂×C₄	—	2	1	no	—
438	C₂×C₄	—	2	1	no	—
439	C₂×C₄	—	2	4	no	—
440	C₂×C₄	—	2	2	no	—
441	C₂×C₄	—	2	2	no	—
442	C₂×C₄	—	2	2	no	—
443	C₂×C₄	—	2	2	no	—
444	C₂×C₄	—	2	2	no	—
445	C₂×C₄	—	4	2	no	—
446	C₂×C₄	—	4	2	no	—
447	C₂×C₄	—	4	1	no	—
448	C₂×C₄	—	4	1	no	—
449	C₂×C₄	—	4	1	no	—
450	C₂×C₄	—	4	1	no	—
451	C₂×C₄	—	4	1	no	—
452	C₂×C₄	—	4	1	no	—
453	C₂×C₄	—	4	1	no	—
454	C₂×C₄	—	4	1	no	—
455	C₂×C₄	—	4	1	no	—
456	C₂×C₄	—	4	1	no	—
457	C₂×C₄	—	8	8	no	—
458	C₂×C₄	C₄×D₄×C₁₁	1	2	yes	—
459	C₂×C₄	C₄×D₄×C₁₁	1	2	yes	—
460	C₂×C₄	C₂×C₁₁×SD₁₆	1	4	yes	—
461	C₂×C₄	C₂×C₁₁×SD₁₆	1	2	yes	—
462	C₂×C₄	C₁₁×#135	1	2	yes	—
463	C₂×C₄	C₂³×C₄×C₁₁	1	1	yes	characteristic
464	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
465	C₂×C₄	C₂×C₁₁×#41	1	1	yes	characteristic
466	C₂×C₄	C₂×C₁₁×#41	1	1	yes	characteristic
467	C₂×C₄	C₁₁×H(5,𝔽₂)	1	1	yes	characteristic
468	C₂×C₄	C₁₁×H(5,𝔽₂)	1	1	yes	characteristic
469	C₈	—	2	2	no	—
470	C₈	—	4	2	no	—
471	C₈	C₄×D₄×C₁₁	1	4	yes	complemented
472	C₂²	—	4	4	no	—
473	C₂²	—	4	4	no	—
474	C₂²	—	4	4	no	—
475	C₂²	—	8	2	no	—
476	C₂²	—	8	2	no	—
477	C₂²	—	8	2	no	—
478	C₂²	—	8	2	no	—
479	C₂²	C₂×C₄×D₄×C₁₁	1	1	yes	characteristic
480	C₂²	D₄²×C₁₁	1	1	yes	characteristic
481	C₂²	C₁₁×#550	1	1	yes	characteristic
482	C₂²	C₂²×C₁₁×SD₁₆	1	1	yes	characteristic
483	C₂²	C₂×C₁₁×#135	1	1	yes	characteristic
484	C₂²	C₁₁×#577	1	1	yes	characteristic
485	C₂²	C₁₁×#577	1	1	yes	characteristic
486	C₄	—	2	2	no	—
487	C₄	—	2	4	no	—
488	C₄	—	4	2	no	—
489	C₄	—	4	2	no	—
490	C₄	—	4	2	no	—
491	C₄	—	4	4	no	—
492	C₄	—	8	1	no	—
493	C₄	—	8	1	no	—
494	C₄	C₄×C₁₁×SD₁₆	1	4	yes	complemented
495	C₄	C₂×C₄×D₄×C₁₁	1	1	yes	characteristic
496	C₄	C₁₁×#518	1	1	yes	characteristic
497	C₄	C₁₁×#550	1	1	yes	characteristic
498	C₄	C₁₁×#559	1	1	yes	characteristic
499	C₂	—	8	4	no	—
500	C₂	C₁₁×#2366	1	1	yes	characteristic
501	C₂	C₂×C₄×C₁₁×SD₁₆	1	1	yes	characteristic
502	C₂	C₁₁×#2949	1	1	yes	characteristic
503	C₂	D₄×C₁₁×SD₁₆	1	1	yes	characteristic
504	C₂	C₁₁×#3284	1	1	yes	characteristic
505	C₂	C₁₁×#3392	1	1	yes	characteristic
506	C₂	C₁₁×#3394	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	C₂×C₁₁×#127	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×SD₁₆	C₂	semidirect
4. C₁₁×#2365	C₂	semidirect
6. C₁₁×#1981	C₂	semidirect
7. C₁₁×#1968	C₂	semidirect
8. C₁₁×#1880	C₂	semidirect
9. C₁₁×#1877	C₂	semidirect
10. C₄×C₁₁×#106	C₂	semidirect
11. C₈×C₁₁×C₄⋊C₄	C₂	semidirect
19. C₁₁×#492	C₄	semidirect
52. C₂×C₁₁×SD₁₆	C₂×C₄	semidirect
53. C₂×C₁₁×SD₁₆	C₂×C₄	semidirect
58. C₁₁×C₄⋊Q₈	C₂×C₄	semidirect
84. C₁₁×#106	D₄	semidirect
91. C₄×C₈×C₁₁	C₂×C₄	semidirect
97. #23182	C₁₁	direct (N × H)
151. C₁₁×C₄⋊C₄	SD₁₆	semidirect
165. C₂×C₄×SD₁₆	C₂×C₁₁	semidirect
167. #2365	C₂×C₁₁	semidirect
169. #1981	C₂×C₁₁	semidirect
170. #1968	C₂×C₁₁	semidirect
171. #1880	C₂×C₁₁	semidirect
172. #1877	C₂×C₁₁	semidirect
173. C₄×#106	C₂×C₁₁	semidirect
174. C₈×C₄⋊C₄	C₂×C₁₁	semidirect
229. C₈×C₁₁	C₄×D₄	semidirect
237. #492	C₄×C₁₁	semidirect
283. C₄×C₁₁	C₄×SD₁₆	semidirect
297. C₂×SD₁₆	C₂×C₄×C₁₁	semidirect
298. C₂×SD₁₆	C₂×C₄×C₁₁	semidirect
303. C₄⋊Q₈	C₂×C₄×C₁₁	semidirect
329. #106	D₄×C₁₁	semidirect
336. C₄×C₈	C₂×C₄×C₁₁	semidirect
403. C₄⋊C₄	C₁₁×SD₁₆	semidirect
416. C₁₁	#23182	direct (N × H)
471. C₈	C₄×D₄×C₁₁	semidirect
494. C₄	C₄×C₁₁×SD₁₆	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₁×#492	2
C₂×C₄×C₁₁×SD₁₆	2
C₁₁×#2366	2
C₁₁×#2365	2
C₁₁×#1982	2
C₁₁×#1981	2
C₁₁×#1968	2
C₁₁×#1880	2
C₁₁×#1877	2
C₄×C₁₁×#106	2
C₈×C₁₁×C₄⋊C₄	2
#23182	11

Subgroups — C11×#23182 #14600375

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#23182 #14600375