Subgroups — C₁₁×#23029 #14600222

Order 2816.

1138 conjugacy classes of subgroups.

The subgroup lattice has 478 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₁×#466	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₁×#442	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₁₁×#106	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₁×#2361	C₂	1	2	yes	maximal, complemented
5	C₁₁×#1972	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₁×#1943	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₁×#1926	C₂	1	2	yes	maximal, complemented
8	C₁₁×#1874	C₂	1	2	yes	maximal, complemented
9	C₁₁×#1864	C₂	1	2	yes	maximal, complemented
10	C₁₁×#1776	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₁×#1752	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₁₁×D₈	C₂²	1	1	yes	characteristic
13	C₂³×C₈×C₁₁	C₂²	1	1	yes	characteristic
14	C₂×C₁₁×#121	C₂²	1	2	yes	—
15	C₂×C₄×D₄×C₁₁	—	2	2	no	—
16	C₂×C₄×D₄×C₁₁	C₂²	1	2	yes	—
17	C₂²×C₁₁×C₄⋊C₄	C₂²	1	2	yes	—
18	C₁₁×#466	C₄	1	8	yes	complemented
19	C₁₁×#442	—	2	4	no	—
20	C₂×C₁₁×#107	C₂²	1	1	yes	characteristic
21	C₂×C₁₁×#106	—	2	4	no	—
22	C₂×C₁₁×#106	C₂²	1	2	yes	—
23	C₂×C₁₁×#106	C₂²	1	1	yes	characteristic
24	C₂×C₁₁×#106	C₂²	1	1	yes	characteristic
25	C₂×C₁₁×#102	C₂²	1	2	yes	—
26	C₂×C₁₁×#102	C₂²	1	2	yes	—
27	C₂×C₁₁×#102	C₂²	1	2	yes	—
28	C₂×C₁₁×C₂²⋊C₈	C₂²	1	1	yes	characteristic
29	C₂×C₁₁×#97	C₂²	1	1	yes	characteristic
30	C₂×C₁₁×#97	C₂²	1	1	yes	characteristic
31	C₁₁×#390	C₂²	1	2	yes	—
32	C₁₁×#389	C₂²	1	2	yes	—
33	C₁₁×#388	—	2	2	no	—
34	C₁₁×#386	—	2	2	no	—
35	C₁₁×#385	—	2	2	no	—
36	C₄×C₁₁×C₄⋊C₄	C₂²	1	2	yes	—
37	C₄×C₁₁×C₂²⋊C₄	C₂²	1	1	yes	characteristic
38	C₁₁×#340	C₂²	1	2	yes	—
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×D₄×C₁₁	—	2	2	no	—
43	C₂²×D₄×C₁₁	C₂³	1	2	yes	—
44	C₂³×C₄×C₁₁	—	2	2	no	—
45	C₂³×C₄×C₁₁	—	2	2	no	—
46	C₂³×C₄×C₁₁	C₂³	1	1	yes	characteristic
47	C₂×C₁₁×D₈	—	2	2	no	—
48	C₂×C₁₁×D₈	—	2	2	no	—
49	C₂×C₁₁×D₈	C₂×C₄	1	4	yes	complemented
50	C₂²×C₈×C₁₁	—	2	2	no	—
51	C₂²×C₈×C₁₁	—	2	2	no	—
52	C₂²×C₈×C₁₁	C₂×C₄	1	4	yes	complemented
53	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
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	C₁₁×#121	—	2	4	no	—
58	C₁₁×#121	C₂×C₄	1	8	yes	complemented
59	C₄×D₄×C₁₁	—	2	4	no	—
60	C₄×D₄×C₁₁	—	4	2	no	—
61	C₄×D₄×C₁₁	—	4	8	no	—
62	C₂×C₁₁×C₄⋊C₄	—	2	4	no	—
63	C₂×C₁₁×C₄⋊C₄	—	2	2	no	—
64	C₂×C₁₁×C₄⋊C₄	—	2	2	no	—
65	C₂×C₁₁×C₄⋊C₄	—	4	2	no	—
66	C₂×C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
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	D₄	1	2	yes	—
74	C₂×C₄²×C₁₁	—	2	2	no	—
75	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
76	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
77	C₁₁×#107	C₂×C₄	1	4	yes	complemented
78	C₁₁×#106	—	2	2	no	—
79	C₁₁×#106	—	2	4	no	—
80	C₁₁×#106	D₄	1	4	yes	complemented
81	C₁₁×#102	—	2	4	no	—
82	C₁₁×#102	—	4	2	no	—
83	C₁₁×#102	C₂×C₄	1	8	yes	complemented
84	C₁₁×C₂²⋊C₈	—	2	2	no	—
85	C₁₁×#97	—	2	2	no	—
86	C₁₁×#97	—	2	2	no	—
87	C₁₁×#95	—	2	2	no	—
88	C₁₁×#95	—	2	2	no	—
89	C₁₁×#95	D₄	1	2	yes	—
90	#23029	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
91	C₂⁴×C₁₁	—	2	2	no	—
92	C₂⁴×C₁₁	C₂×D₄	1	1	yes	characteristic
93	C₂×D₄×C₁₁	—	2	8	no	—
94	C₂×D₄×C₁₁	—	2	2	no	—
95	C₂×D₄×C₁₁	—	2	2	no	—
96	C₂×D₄×C₁₁	—	2	2	no	—
97	C₂×D₄×C₁₁	—	2	2	no	—
98	C₂×D₄×C₁₁	—	2	2	no	—
99	C₂×D₄×C₁₁	—	4	4	no	—
100	C₂×D₄×C₁₁	—	4	4	no	—
101	C₂×D₄×C₁₁	C₂²×C₄	1	4	yes	—
102	C₂²×C₄×C₁₁	—	2	1	no	—
103	C₂²×C₄×C₁₁	—	2	1	no	—
104	C₂²×C₄×C₁₁	—	2	1	no	—
105	C₂²×C₄×C₁₁	—	2	1	no	—
106	C₂²×C₄×C₁₁	—	2	2	no	—
107	C₂²×C₄×C₁₁	—	2	2	no	—
108	C₂²×C₄×C₁₁	—	2	2	no	—
109	C₂²×C₄×C₁₁	—	4	4	no	—
110	C₂²×C₄×C₁₁	—	4	4	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	—	8	2	no	—
115	C₂²×C₄×C₁₁	C₂²×C₄	1	2	yes	—
116	C₂²×C₄×C₁₁	C₂×D₄	1	2	yes	—
117	C₂²×C₄×C₁₁	C₂×D₄	1	2	yes	—
118	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
119	C₂²×C₄×C₁₁	#41	1	2	yes	—
120	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
121	C₁₁×D₈	—	2	8	no	—
122	C₂×C₈×C₁₁	—	2	8	no	—
123	C₂×C₈×C₁₁	—	2	1	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	C₂²×C₄	1	2	yes	—
132	C₂×C₈×C₁₁	C₂²×C₄	1	2	yes	—
133	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
134	C₂×C₈×C₁₁	#41	1	2	yes	—
135	C₁₁×C₄⋊C₄	—	2	2	no	—
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	—	4	4	no	—
140	C₁₁×C₄⋊C₄	—	4	4	no	—
141	C₁₁×C₄⋊C₄	C₂²×C₄	1	4	yes	—
142	C₁₁×C₄⋊C₄	C₂×D₄	1	4	yes	—
143	C₁₁×C₂²⋊C₄	—	2	4	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	C₂×#466	C₂×C₁₁	1	1	yes	characteristic
154	C₂×#442	C₂×C₁₁	1	1	yes	characteristic, complemented
155	C₂²×#106	C₂×C₁₁	1	1	yes	characteristic, complemented
156	#2361	C₂×C₁₁	1	2	yes	complemented
157	#1972	C₂×C₁₁	1	1	yes	characteristic, complemented
158	#1943	C₂×C₁₁	1	1	yes	characteristic, complemented
159	#1926	C₂×C₁₁	1	2	yes	complemented
160	#1874	C₂×C₁₁	1	2	yes	complemented
161	#1864	C₂×C₁₁	1	2	yes	complemented
162	#1776	C₂×C₁₁	1	1	yes	characteristic, complemented
163	#1752	C₂×C₁₁	1	1	yes	characteristic, complemented
164	C₂³×C₁₁	—	2	1	no	—
165	C₂³×C₁₁	—	2	1	no	—
166	C₂³×C₁₁	—	2	2	no	—
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	C₄×D₄	1	2	yes	—
175	C₂³×C₁₁	AGL(1,ℤ/8)	1	4	yes	—
176	C₂³×C₁₁	C₂²×D₄	1	1	yes	characteristic
177	D₄×C₁₁	—	2	4	no	—
178	D₄×C₁₁	—	2	4	no	—
179	D₄×C₁₁	—	4	16	no	—
180	D₄×C₁₁	—	4	2	no	—
181	D₄×C₁₁	—	4	2	no	—
182	C₂×C₄×C₁₁	—	2	1	no	—
183	C₂×C₄×C₁₁	—	2	1	no	—
184	C₂×C₄×C₁₁	—	2	2	no	—
185	C₂×C₄×C₁₁	—	2	2	no	—
186	C₂×C₄×C₁₁	—	2	2	no	—
187	C₂×C₄×C₁₁	—	2	2	no	—
188	C₂×C₄×C₁₁	—	2	4	no	—
189	C₂×C₄×C₁₁	—	2	2	no	—
190	C₂×C₄×C₁₁	—	2	4	no	—
191	C₂×C₄×C₁₁	—	2	2	no	—
192	C₂×C₄×C₁₁	—	2	2	no	—
193	C₂×C₄×C₁₁	—	2	2	no	—
194	C₂×C₄×C₁₁	—	2	2	no	—
195	C₂×C₄×C₁₁	—	2	2	no	—
196	C₂×C₄×C₁₁	—	4	2	no	—
197	C₂×C₄×C₁₁	—	4	2	no	—
198	C₂×C₄×C₁₁	—	4	2	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	—	8	8	no	—
204	C₂×C₄×C₁₁	—	8	8	no	—
205	C₂×C₄×C₁₁	C₄×D₄	1	2	yes	—
206	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
207	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
208	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
209	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
210	C₂×C₄×C₁₁	H(5,𝔽₂)	1	1	yes	characteristic
211	C₂×C₄×C₁₁	2₋¹⁺⁴	1	1	yes	characteristic
212	C₈×C₁₁	—	2	2	no	—
213	C₈×C₁₁	—	4	1	no	—
214	C₈×C₁₁	—	4	1	no	—
215	C₈×C₁₁	C₄×D₄	1	4	yes	complemented
216	C₂²×D₈	C₂²×C₁₁	1	1	yes	characteristic
217	C₂³×C₈	C₂²×C₁₁	1	1	yes	characteristic
218	C₂×#121	C₂²×C₁₁	1	2	yes	—
219	C₂×C₄×D₄	—	2	2	no	—
220	C₂×C₄×D₄	C₂²×C₁₁	1	2	yes	—
221	C₂²×C₄⋊C₄	C₂²×C₁₁	1	2	yes	—
222	#466	C₄×C₁₁	1	8	yes	complemented
223	#442	—	2	4	no	—
224	C₂×#107	C₂²×C₁₁	1	1	yes	characteristic
225	C₂×#106	—	2	4	no	—
226	C₂×#106	C₂²×C₁₁	1	2	yes	—
227	C₂×#106	C₂²×C₁₁	1	1	yes	characteristic
228	C₂×#106	C₂²×C₁₁	1	1	yes	characteristic
229	C₂×#102	C₂²×C₁₁	1	2	yes	—
230	C₂×#102	C₂²×C₁₁	1	2	yes	—
231	C₂×#102	C₂²×C₁₁	1	2	yes	—
232	C₂×C₂²⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
233	C₂×#97	C₂²×C₁₁	1	1	yes	characteristic
234	C₂×#97	C₂²×C₁₁	1	1	yes	characteristic
235	#390	C₂²×C₁₁	1	2	yes	—
236	#389	C₂²×C₁₁	1	2	yes	—
237	#388	—	2	2	no	—
238	#386	—	2	2	no	—
239	#385	—	2	2	no	—
240	C₄×C₄⋊C₄	C₂²×C₁₁	1	2	yes	—
241	C₄×C₂²⋊C₄	C₂²×C₁₁	1	1	yes	characteristic
242	#340	C₂²×C₁₁	1	2	yes	—
243	#340	C₂²×C₁₁	1	2	yes	—
244	#336	C₂²×C₁₁	1	1	yes	characteristic
245	#336	C₂²×C₁₁	1	1	yes	characteristic
246	C₂²×C₁₁	—	2	4	no	—
247	C₂²×C₁₁	—	2	2	no	—
248	C₂²×C₁₁	—	2	2	no	—
249	C₂²×C₁₁	—	2	4	no	—
250	C₂²×C₁₁	—	4	4	no	—
251	C₂²×C₁₁	—	4	4	no	—
252	C₂²×C₁₁	—	4	4	no	—
253	C₂²×C₁₁	—	8	2	no	—
254	C₂²×C₁₁	—	8	2	no	—
255	C₂²×C₁₁	—	8	2	no	—
256	C₂²×C₁₁	—	8	2	no	—
257	C₂²×C₁₁	#442	1	4	yes	complemented
258	C₂²×C₁₁	C₂×C₄×D₄	1	1	yes	characteristic
259	C₂²×C₁₁	D₄²	1	1	yes	characteristic
260	C₂²×C₁₁	#547	1	1	yes	characteristic
261	C₂²×C₁₁	C₂×AGL(1,ℤ/8)	1	2	yes	—
262	C₂²×C₁₁	#577	1	2	yes	—
263	C₄×C₁₁	—	2	2	no	—
264	C₄×C₁₁	—	4	2	no	—
265	C₄×C₁₁	—	4	4	no	—
266	C₄×C₁₁	—	4	2	no	—
267	C₄×C₁₁	—	4	4	no	—
268	C₄×C₁₁	—	8	2	no	—
269	C₄×C₁₁	C₂×C₄×D₄	1	1	yes	characteristic
270	C₄×C₁₁	#520	1	1	yes	characteristic
271	C₄×C₁₁	#548	1	1	yes	characteristic
272	C₄×C₁₁	#553	1	1	yes	characteristic
273	C₂²×D₄	—	2	2	no	—
274	C₂²×D₄	C₂³×C₁₁	1	2	yes	—
275	C₂³×C₄	—	2	2	no	—
276	C₂³×C₄	—	2	2	no	—
277	C₂³×C₄	C₂³×C₁₁	1	1	yes	characteristic
278	C₂×D₈	—	2	2	no	—
279	C₂×D₈	—	2	2	no	—
280	C₂×D₈	C₂×C₄×C₁₁	1	4	yes	complemented
281	C₂²×C₈	—	2	2	no	—
282	C₂²×C₈	—	2	2	no	—
283	C₂²×C₈	C₂×C₄×C₁₁	1	4	yes	complemented
284	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
285	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
286	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
287	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
288	#121	—	2	4	no	—
289	#121	C₂×C₄×C₁₁	1	8	yes	complemented
290	C₄×D₄	—	2	4	no	—
291	C₄×D₄	—	4	2	no	—
292	C₄×D₄	—	4	8	no	—
293	C₂×C₄⋊C₄	—	2	4	no	—
294	C₂×C₄⋊C₄	—	2	2	no	—
295	C₂×C₄⋊C₄	—	2	2	no	—
296	C₂×C₄⋊C₄	—	4	2	no	—
297	C₂×C₄⋊C₄	C₂³×C₁₁	1	2	yes	—
298	C₂×C₄⋊C₄	C₂³×C₁₁	1	2	yes	—
299	C₂×C₄⋊C₄	C₂³×C₁₁	1	2	yes	—
300	C₂×C₂²⋊C₄	—	2	2	no	—
301	C₂×C₂²⋊C₄	—	2	2	no	—
302	C₂×C₂²⋊C₄	—	2	2	no	—
303	C₂×C₂²⋊C₄	—	2	2	no	—
304	C₂×C₂²⋊C₄	D₄×C₁₁	1	2	yes	—
305	C₂×C₄²	—	2	2	no	—
306	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
307	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
308	#107	C₂×C₄×C₁₁	1	4	yes	complemented
309	#106	—	2	2	no	—
310	#106	—	2	4	no	—
311	#106	D₄×C₁₁	1	4	yes	complemented
312	#102	—	2	4	no	—
313	#102	—	4	2	no	—
314	#102	C₂×C₄×C₁₁	1	8	yes	complemented
315	C₂²⋊C₈	—	2	2	no	—
316	#97	—	2	2	no	—
317	#97	—	2	2	no	—
318	#95	—	2	2	no	—
319	#95	—	2	2	no	—
320	#95	D₄×C₁₁	1	2	yes	—
321	C₂×C₁₁	—	2	4	no	—
322	C₂×C₁₁	—	8	4	no	—
323	C₂×C₁₁	#2361	1	1	yes	characteristic
324	C₂×C₁₁	C₂×#442	1	1	yes	characteristic
325	C₂×C₁₁	#2952	1	1	yes	characteristic
326	C₂×C₁₁	#3265	1	2	yes	—
327	C₂×C₁₁	#3345	1	2	yes	—
328	C₂⁴	—	2	2	no	—
329	C₂⁴	C₂×D₄×C₁₁	1	1	yes	characteristic
330	C₂×D₄	—	2	8	no	—
331	C₂×D₄	—	2	2	no	—
332	C₂×D₄	—	2	2	no	—
333	C₂×D₄	—	2	2	no	—
334	C₂×D₄	—	2	2	no	—
335	C₂×D₄	—	2	2	no	—
336	C₂×D₄	—	4	4	no	—
337	C₂×D₄	—	4	4	no	—
338	C₂×D₄	C₂²×C₄×C₁₁	1	4	yes	—
339	C₂²×C₄	—	2	1	no	—
340	C₂²×C₄	—	2	1	no	—
341	C₂²×C₄	—	2	1	no	—
342	C₂²×C₄	—	2	1	no	—
343	C₂²×C₄	—	2	2	no	—
344	C₂²×C₄	—	2	2	no	—
345	C₂²×C₄	—	2	2	no	—
346	C₂²×C₄	—	4	4	no	—
347	C₂²×C₄	—	4	4	no	—
348	C₂²×C₄	—	4	4	no	—
349	C₂²×C₄	—	4	4	no	—
350	C₂²×C₄	—	8	2	no	—
351	C₂²×C₄	—	8	2	no	—
352	C₂²×C₄	C₂²×C₄×C₁₁	1	2	yes	—
353	C₂²×C₄	C₂×D₄×C₁₁	1	2	yes	—
354	C₂²×C₄	C₂×D₄×C₁₁	1	2	yes	—
355	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
356	C₂²×C₄	C₁₁×#41	1	2	yes	—
357	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
358	D₈	—	2	8	no	—
359	C₂×C₈	—	2	1	no	—
360	C₂×C₈	—	2	1	no	—
361	C₂×C₈	—	2	8	no	—
362	C₂×C₈	—	2	1	no	—
363	C₂×C₈	—	2	1	no	—
364	C₂×C₈	—	2	1	no	—
365	C₂×C₈	—	2	1	no	—
366	C₂×C₈	—	2	1	no	—
367	C₂×C₈	—	2	1	no	—
368	C₂×C₈	C₂²×C₄×C₁₁	1	2	yes	—
369	C₂×C₈	C₂²×C₄×C₁₁	1	2	yes	—
370	C₂×C₈	C₂×D₄×C₁₁	1	2	yes	—
371	C₂×C₈	C₁₁×#41	1	2	yes	—
372	C₄⋊C₄	—	2	2	no	—
373	C₄⋊C₄	—	2	2	no	—
374	C₄⋊C₄	—	2	2	no	—
375	C₄⋊C₄	—	2	2	no	—
376	C₄⋊C₄	—	4	4	no	—
377	C₄⋊C₄	—	4	4	no	—
378	C₄⋊C₄	C₂²×C₄×C₁₁	1	4	yes	—
379	C₄⋊C₄	C₂×D₄×C₁₁	1	4	yes	—
380	C₂²⋊C₄	—	2	4	no	—
381	C₂²⋊C₄	—	2	8	no	—
382	C₂²⋊C₄	—	4	4	no	—
383	C₂²⋊C₄	—	4	4	no	—
384	C₂²⋊C₄	—	8	2	no	—
385	C₄²	—	2	1	no	—
386	C₄²	—	2	1	no	—
387	C₄²	—	2	1	no	—
388	C₄²	—	2	1	no	—
389	C₄²	—	4	4	no	—
390	C₁₁	#23029	1	1	yes	characteristic, direct product factor, Sylow
391	C₂³	—	2	1	no	—
392	C₂³	—	2	1	no	—
393	C₂³	—	2	2	no	—
394	C₂³	—	2	4	no	—
395	C₂³	—	4	2	no	—
396	C₂³	—	4	2	no	—
397	C₂³	—	4	2	no	—
398	C₂³	—	4	2	no	—
399	C₂³	—	4	2	no	—
400	C₂³	—	4	2	no	—
401	C₂³	C₄×D₄×C₁₁	1	2	yes	—
402	C₂³	C₁₁×AGL(1,ℤ/8)	1	4	yes	—
403	C₂³	C₂²×D₄×C₁₁	1	1	yes	characteristic
404	D₄	—	2	4	no	—
405	D₄	—	2	4	no	—
406	D₄	—	4	16	no	—
407	D₄	—	4	2	no	—
408	D₄	—	4	2	no	—
409	C₂×C₄	—	2	1	no	—
410	C₂×C₄	—	2	1	no	—
411	C₂×C₄	—	2	2	no	—
412	C₂×C₄	—	2	2	no	—
413	C₂×C₄	—	2	2	no	—
414	C₂×C₄	—	2	2	no	—
415	C₂×C₄	—	2	4	no	—
416	C₂×C₄	—	2	2	no	—
417	C₂×C₄	—	2	4	no	—
418	C₂×C₄	—	2	2	no	—
419	C₂×C₄	—	2	2	no	—
420	C₂×C₄	—	2	2	no	—
421	C₂×C₄	—	2	2	no	—
422	C₂×C₄	—	2	2	no	—
423	C₂×C₄	—	4	2	no	—
424	C₂×C₄	—	4	2	no	—
425	C₂×C₄	—	4	2	no	—
426	C₂×C₄	—	4	2	no	—
427	C₂×C₄	—	4	2	no	—
428	C₂×C₄	—	4	2	no	—
429	C₂×C₄	—	4	2	no	—
430	C₂×C₄	—	8	8	no	—
431	C₂×C₄	—	8	8	no	—
432	C₂×C₄	C₄×D₄×C₁₁	1	2	yes	—
433	C₂×C₄	C₂³×C₄×C₁₁	1	1	yes	characteristic
434	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
435	C₂×C₄	C₂×C₁₁×#41	1	1	yes	characteristic
436	C₂×C₄	C₂×C₁₁×#41	1	1	yes	characteristic
437	C₂×C₄	C₁₁×H(5,𝔽₂)	1	1	yes	characteristic
438	C₂×C₄	C₁₁×2₋¹⁺⁴	1	1	yes	characteristic
439	C₈	—	2	2	no	—
440	C₈	—	4	1	no	—
441	C₈	—	4	1	no	—
442	C₈	C₄×D₄×C₁₁	1	4	yes	complemented
443	C₂²	—	2	2	no	—
444	C₂²	—	2	4	no	—
445	C₂²	—	2	4	no	—
446	C₂²	—	2	2	no	—
447	C₂²	—	4	4	no	—
448	C₂²	—	4	4	no	—
449	C₂²	—	4	4	no	—
450	C₂²	—	8	2	no	—
451	C₂²	—	8	2	no	—
452	C₂²	—	8	2	no	—
453	C₂²	—	8	2	no	—
454	C₂²	C₁₁×#442	1	4	yes	complemented
455	C₂²	C₂×C₄×D₄×C₁₁	1	1	yes	characteristic
456	C₂²	D₄²×C₁₁	1	1	yes	characteristic
457	C₂²	C₁₁×#547	1	1	yes	characteristic
458	C₂²	C₂×C₁₁×AGL(1,ℤ/8)	1	2	yes	—
459	C₂²	C₁₁×#577	1	2	yes	—
460	C₄	—	2	2	no	—
461	C₄	—	4	4	no	—
462	C₄	—	4	2	no	—
463	C₄	—	4	4	no	—
464	C₄	—	4	2	no	—
465	C₄	—	8	2	no	—
466	C₄	C₂×C₄×D₄×C₁₁	1	1	yes	characteristic
467	C₄	C₁₁×#520	1	1	yes	characteristic
468	C₄	C₁₁×#548	1	1	yes	characteristic
469	C₄	C₁₁×#553	1	1	yes	characteristic
470	C₂	—	2	4	no	—
471	C₂	—	8	4	no	—
472	C₂	C₁₁×#2361	1	1	yes	characteristic
473	C₂	C₂×C₁₁×#442	1	1	yes	characteristic
474	C₂	C₁₁×#2952	1	1	yes	characteristic
475	C₂	C₁₁×#3265	1	2	yes	—
476	C₂	C₁₁×#3345	1	2	yes	—

	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×#466	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₁ ◁ C₄×C₁₁×C₂²⋊C₄ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₁×#442	C₂	semidirect
3. C₂²×C₁₁×#106	C₂	semidirect
4. C₁₁×#2361	C₂	semidirect
5. C₁₁×#1972	C₂	semidirect
6. C₁₁×#1943	C₂	semidirect
7. C₁₁×#1926	C₂	semidirect
8. C₁₁×#1874	C₂	semidirect
9. C₁₁×#1864	C₂	semidirect
10. C₁₁×#1776	C₂	semidirect
11. C₁₁×#1752	C₂	semidirect
18. C₁₁×#466	C₄	semidirect
49. C₂×C₁₁×D₈	C₂×C₄	semidirect
52. C₂²×C₈×C₁₁	C₂×C₄	semidirect
58. C₁₁×#121	C₂×C₄	semidirect
77. C₁₁×#107	C₂×C₄	semidirect
80. C₁₁×#106	D₄	semidirect
83. C₁₁×#102	C₂×C₄	semidirect
90. #23029	C₁₁	direct (N × H)
154. C₂×#442	C₂×C₁₁	semidirect
155. C₂²×#106	C₂×C₁₁	semidirect
156. #2361	C₂×C₁₁	semidirect
157. #1972	C₂×C₁₁	semidirect
158. #1943	C₂×C₁₁	semidirect
159. #1926	C₂×C₁₁	semidirect
160. #1874	C₂×C₁₁	semidirect
161. #1864	C₂×C₁₁	semidirect
162. #1776	C₂×C₁₁	semidirect
163. #1752	C₂×C₁₁	semidirect
215. C₈×C₁₁	C₄×D₄	semidirect
222. #466	C₄×C₁₁	semidirect
257. C₂²×C₁₁	#442	semidirect
280. C₂×D₈	C₂×C₄×C₁₁	semidirect
283. C₂²×C₈	C₂×C₄×C₁₁	semidirect
289. #121	C₂×C₄×C₁₁	semidirect
308. #107	C₂×C₄×C₁₁	semidirect
311. #106	D₄×C₁₁	semidirect
314. #102	C₂×C₄×C₁₁	semidirect
390. C₁₁	#23029	direct (N × H)
442. C₈	C₄×D₄×C₁₁	semidirect
454. C₂²	C₁₁×#442	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₁×#466	2
C₂×C₁₁×#442	2
C₂²×C₁₁×#106	2
C₁₁×#2361	2
C₁₁×#1972	2
C₁₁×#1943	2
C₁₁×#1926	2
C₁₁×#1874	2
C₁₁×#1864	2
C₁₁×#1776	2
C₁₁×#1752	2
#23029	11

Subgroups — C11×#23029 #14600222

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#23029 #14600222