Subgroups — C₁₁×#22523 #14599716

Order 2816.

1250 conjugacy classes of subgroups.

The subgroup lattice has 502 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₄×Q₈×C₁₁	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₁×#446	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₁×#2355	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₁×#1993	C₂	1	2	yes	maximal, complemented
5	C₁₁×#1990	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₁×#1988	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₁×#1987	C₂	1	2	yes	maximal, complemented
8	C₁₁×#1804	C₂	1	2	yes	maximal
9	C₁₁×#1802	C₂	1	1	yes	maximal, characteristic
10	C₁₁×#1762	C₂	1	2	yes	maximal
11	C₄×C₁₁×#102	C₂	1	1	yes	maximal, characteristic
12	C₂³×Q₈×C₁₁	—	2	1	no	—
13	D₄×Q₈×C₁₁	—	2	4	no	—
14	D₄×Q₈×C₁₁	C₄	1	8	yes	complemented
15	C₂×C₁₁×C₄⋊Q₈	C₂²	1	2	yes	—
16	C₂×C₁₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic
17	C₂×C₁₁×C₂²⋊Q₈	—	2	1	no	—
18	C₂×C₁₁×C₂²⋊Q₈	—	2	2	no	—
19	C₂×C₄×Q₈×C₁₁	C₂²	1	1	yes	characteristic
20	C₂×C₄×D₄×C₁₁	C₂²	1	1	yes	characteristic
21	C₂×C₄×D₄×C₁₁	C₂²	1	2	yes	—
22	C₁₁×#446	—	2	4	no	—
23	C₂×C₁₁×C₄⋊C₈	C₂²	1	2	yes	—
24	C₂×C₁₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
25	C₂×C₁₁×#102	C₂²	1	1	yes	characteristic
26	C₂×C₁₁×#102	C₂²	1	2	yes	—
27	C₂×C₁₁×#102	C₂²	1	1	yes	characteristic
28	C₂×C₁₁×#97	C₂²	1	2	yes	—
29	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
30	C₁₁×#391	—	2	1	no	—
31	C₁₁×#387	—	2	2	no	—
32	C₁₁×#384	C₂²	1	1	yes	characteristic
33	C₁₁×#382	C₂²	1	2	yes	—
34	C₄×C₁₁×C₄⋊C₄	—	2	1	no	—
35	C₄×C₁₁×C₄⋊C₄	C₂²	1	2	yes	—
36	C₄×C₁₁×C₄⋊C₄	C₂²	1	1	yes	characteristic
37	C₁₁×#340	C₂²	1	1	yes	characteristic
38	C₁₁×#340	C₂²	1	2	yes	—
39	C₁₁×#340	C₂²	1	2	yes	—
40	C₁₁×#340	C₂²	1	2	yes	—
41	C₁₁×#340	C₂²	1	2	yes	—
42	C₁₁×#340	C₂²	1	2	yes	—
43	C₁₁×#340	C₂²	1	1	yes	characteristic
44	C₂²×Q₈×C₁₁	—	2	8	no	—
45	C₂²×Q₈×C₁₁	—	2	2	no	—
46	C₂²×Q₈×C₁₁	—	2	1	no	—
47	C₂²×Q₈×C₁₁	—	4	4	no	—
48	C₂²×Q₈×C₁₁	—	4	4	no	—
49	C₂²×Q₈×C₁₁	D₄	1	1	yes	characteristic
50	C₂²×D₄×C₁₁	C₂³	1	1	yes	characteristic
51	C₂³×C₄×C₁₁	—	2	2	no	—
52	C₂³×C₄×C₁₁	—	2	1	no	—
53	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
54	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
55	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
56	C₁₁×C₄⋊Q₈	—	2	2	no	—
57	C₁₁×C₄⋊Q₈	—	2	4	no	—
58	C₁₁×C₄⋊Q₈	C₂×C₄	1	8	yes	—
59	C₁₁×C₄⋊Q₈	C₂×C₄	1	4	yes	—
60	C₁₁×C₂²⋊Q₈	—	2	16	no	—
61	C₁₁×C₂²⋊Q₈	—	2	8	no	—
62	C₄×Q₈×C₁₁	C₂×C₄	1	4	yes	—
63	C₄×Q₈×C₁₁	D₄	1	4	yes	—
64	C₄×D₄×C₁₁	—	2	2	no	—
65	C₄×D₄×C₁₁	—	2	4	no	—
66	C₄×D₄×C₁₁	C₂×C₄	1	4	yes	—
67	C₄×D₄×C₁₁	C₂×C₄	1	8	yes	—
68	C₂×C₁₁×C₄⋊C₄	—	2	2	no	—
69	C₂×C₁₁×C₄⋊C₄	—	2	1	no	—
70	C₂×C₁₁×C₄⋊C₄	—	2	1	no	—
71	C₂×C₁₁×C₄⋊C₄	—	2	1	no	—
72	C₂×C₁₁×C₄⋊C₄	D₄	1	1	yes	characteristic
73	C₂×C₁₁×C₄⋊C₄	D₄	1	2	yes	—
74	C₂×C₁₁×C₄⋊C₄	C₂³	1	1	yes	characteristic
75	C₂×C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
76	C₂×C₁₁×C₄⋊C₄	C₂³	1	1	yes	characteristic
77	C₂×C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
78	C₂×C₁₁×C₄⋊C₄	C₂³	1	1	yes	characteristic
79	C₂×C₁₁×C₂²⋊C₄	—	2	2	no	—
80	C₂×C₁₁×C₂²⋊C₄	—	2	1	no	—
81	C₂×C₄²×C₁₁	—	2	1	no	—
82	C₂×C₄²×C₁₁	—	2	2	no	—
83	C₂×C₄²×C₁₁	C₂³	1	2	yes	—
84	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
85	C₁₁×C₄⋊C₈	—	2	2	no	—
86	C₁₁×C₄⋊C₈	—	2	4	no	—
87	C₁₁×#102	—	2	2	no	—
88	C₁₁×#102	—	2	4	no	—
89	C₁₁×#102	Q₈	1	4	yes	complemented
90	C₁₁×#97	—	2	4	no	—
91	C₄×C₈×C₁₁	—	2	2	no	—
92	C₁₁×#95	—	2	2	no	—
93	C₁₁×#95	—	2	1	no	—
94	C₁₁×#95	—	2	2	no	—
95	C₁₁×#95	—	2	2	no	—
96	#22523	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
97	C₂⁴×C₁₁	—	2	1	no	—
98	C₂×Q₈×C₁₁	—	2	8	no	—
99	C₂×Q₈×C₁₁	—	2	4	no	—
100	C₂×Q₈×C₁₁	—	2	2	no	—
101	C₂×Q₈×C₁₁	—	2	2	no	—
102	C₂×Q₈×C₁₁	—	4	4	no	—
103	C₂×Q₈×C₁₁	—	4	4	no	—
104	C₂×Q₈×C₁₁	—	4	32	no	—
105	C₂×Q₈×C₁₁	—	4	2	no	—
106	C₂×Q₈×C₁₁	—	4	2	no	—
107	C₂×Q₈×C₁₁	C₂²⋊C₄	1	4	yes	—
108	C₂×D₄×C₁₁	—	2	1	no	—
109	C₂×D₄×C₁₁	—	2	1	no	—
110	C₂×D₄×C₁₁	—	2	1	no	—
111	C₂×D₄×C₁₁	C₂²×C₄	1	2	yes	—
112	C₂×D₄×C₁₁	C₂×Q₈	1	2	yes	—
113	C₂×D₄×C₁₁	#41	1	2	yes	—
114	C₂²×C₄×C₁₁	—	2	1	no	—
115	C₂²×C₄×C₁₁	—	2	2	no	—
116	C₂²×C₄×C₁₁	—	2	1	no	—
117	C₂²×C₄×C₁₁	—	2	8	no	—
118	C₂²×C₄×C₁₁	—	2	4	no	—
119	C₂²×C₄×C₁₁	—	2	1	no	—
120	C₂²×C₄×C₁₁	—	2	2	no	—
121	C₂²×C₄×C₁₁	—	4	4	no	—
122	C₂²×C₄×C₁₁	—	4	4	no	—
123	C₂²×C₄×C₁₁	—	4	2	no	—
124	C₂²×C₄×C₁₁	—	4	2	no	—
125	C₂²×C₄×C₁₁	C₂×D₄	1	2	yes	—
126	C₂²×C₄×C₁₁	C₂×D₄	1	2	yes	—
127	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
128	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
129	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
130	C₂×C₈×C₁₁	—	2	1	no	—
131	C₂×C₈×C₁₁	—	2	1	no	—
132	C₂×C₈×C₁₁	—	2	2	no	—
133	C₂×C₈×C₁₁	—	2	1	no	—
134	C₂×C₈×C₁₁	—	2	2	no	—
135	C₂×C₈×C₁₁	—	2	1	no	—
136	C₂×C₈×C₁₁	—	2	1	no	—
137	C₂×C₈×C₁₁	—	2	2	no	—
138	C₂×C₈×C₁₁	C₂×Q₈	1	2	yes	complemented
139	C₁₁×C₄⋊C₄	—	2	4	no	—
140	C₁₁×C₄⋊C₄	—	2	8	no	—
141	C₁₁×C₄⋊C₄	—	2	1	no	—
142	C₁₁×C₄⋊C₄	—	2	2	no	—
143	C₁₁×C₄⋊C₄	—	2	1	no	—
144	C₁₁×C₄⋊C₄	—	2	1	no	—
145	C₁₁×C₄⋊C₄	—	2	2	no	—
146	C₁₁×C₄⋊C₄	—	2	1	no	—
147	C₁₁×C₄⋊C₄	—	2	2	no	—
148	C₁₁×C₄⋊C₄	—	4	2	no	—
149	C₁₁×C₄⋊C₄	—	8	1	no	—
150	C₁₁×C₄⋊C₄	C₂²⋊C₄	1	8	yes	—
151	C₁₁×C₄⋊C₄	C₂²⋊C₄	1	4	yes	—
152	C₁₁×C₄⋊C₄	C₂²×C₄	1	2	yes	—
153	C₁₁×C₄⋊C₄	C₂²×C₄	1	4	yes	—
154	C₁₁×C₄⋊C₄	C₂×Q₈	1	2	yes	complemented
155	C₁₁×C₂²⋊C₄	—	2	4	no	—
156	C₁₁×C₂²⋊C₄	—	2	8	no	—
157	C₄²×C₁₁	—	4	2	no	—
158	C₄²×C₁₁	—	8	2	no	—
159	C₄²×C₁₁	C₂²×C₄	1	4	yes	—
160	C₄²×C₁₁	C₂²×C₄	1	2	yes	—
161	C₄²×C₁₁	C₂×D₄	1	2	yes	—
162	C₄²×C₁₁	C₂×D₄	1	4	yes	—
163	C₂×D₄×Q₈	C₂×C₁₁	1	1	yes	characteristic
164	C₂×#446	C₂×C₁₁	1	1	yes	characteristic, complemented
165	#2355	C₂×C₁₁	1	1	yes	characteristic, complemented
166	#1993	C₂×C₁₁	1	2	yes	complemented
167	#1990	C₂×C₁₁	1	1	yes	characteristic, complemented
168	#1988	C₂×C₁₁	1	1	yes	characteristic, complemented
169	#1987	C₂×C₁₁	1	2	yes	complemented
170	#1804	C₂×C₁₁	1	2	yes	—
171	#1802	C₂×C₁₁	1	1	yes	characteristic
172	#1762	C₂×C₁₁	1	2	yes	—
173	C₄×#102	C₂×C₁₁	1	1	yes	characteristic
174	C₂³×C₁₁	—	2	2	no	—
175	C₂³×C₁₁	—	2	2	no	—
176	C₂³×C₁₁	—	2	2	no	—
177	C₂³×C₁₁	—	4	1	no	—
178	C₂³×C₁₁	—	4	1	no	—
179	C₂³×C₁₁	—	4	1	no	—
180	C₂³×C₁₁	—	4	1	no	—
181	C₂³×C₁₁	C₂²×D₄	1	1	yes	characteristic
182	Q₈×C₁₁	—	2	8	no	—
183	Q₈×C₁₁	—	4	16	no	—
184	Q₈×C₁₁	—	4	8	no	—
185	D₄×C₁₁	—	2	2	no	—
186	D₄×C₁₁	—	2	2	no	—
187	D₄×C₁₁	—	2	2	no	—
188	D₄×C₁₁	C₄×Q₈	1	4	yes	—
189	C₂×C₄×C₁₁	—	2	2	no	—
190	C₂×C₄×C₁₁	—	2	2	no	—
191	C₂×C₄×C₁₁	—	2	2	no	—
192	C₂×C₄×C₁₁	—	2	1	no	—
193	C₂×C₄×C₁₁	—	2	2	no	—
194	C₂×C₄×C₁₁	—	2	1	no	—
195	C₂×C₄×C₁₁	—	2	4	no	—
196	C₂×C₄×C₁₁	—	2	2	no	—
197	C₂×C₄×C₁₁	—	2	2	no	—
198	C₂×C₄×C₁₁	—	4	16	no	—
199	C₂×C₄×C₁₁	—	4	1	no	—
200	C₂×C₄×C₁₁	—	4	2	no	—
201	C₂×C₄×C₁₁	—	4	1	no	—
202	C₂×C₄×C₁₁	—	4	2	no	—
203	C₂×C₄×C₁₁	—	4	1	no	—
204	C₂×C₄×C₁₁	—	4	1	no	—
205	C₂×C₄×C₁₁	—	4	8	no	—
206	C₂×C₄×C₁₁	—	4	1	no	—
207	C₂×C₄×C₁₁	—	4	2	no	—
208	C₂×C₄×C₁₁	—	4	1	no	—
209	C₂×C₄×C₁₁	—	4	2	no	—
210	C₂×C₄×C₁₁	—	4	2	no	—
211	C₂×C₄×C₁₁	—	4	1	no	—
212	C₂×C₄×C₁₁	C₂×C₂²⋊C₄	1	2	yes	—
213	C₂×C₄×C₁₁	C₂×C₂²⋊C₄	1	4	yes	—
214	C₂×C₄×C₁₁	C₂×C₂²⋊C₄	1	4	yes	—
215	C₂×C₄×C₁₁	C₂×C₂²⋊C₄	1	2	yes	—
216	C₂×C₄×C₁₁	AGL(1,ℤ/8)	1	2	yes	—
217	C₂×C₄×C₁₁	AGL(1,ℤ/8)	1	2	yes	—
218	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
219	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
220	C₂×C₄×C₁₁	C₂²×Q₈	1	1	yes	characteristic
221	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
222	C₂×C₄×C₁₁	2₋¹⁺⁴	1	1	yes	characteristic
223	C₂×C₄×C₁₁	2₋¹⁺⁴	1	1	yes	characteristic
224	C₈×C₁₁	—	2	2	no	—
225	C₈×C₁₁	—	4	1	no	—
226	C₈×C₁₁	—	4	2	no	—
227	C₂³×Q₈	—	2	1	no	—
228	D₄×Q₈	—	2	4	no	—
229	D₄×Q₈	C₄×C₁₁	1	8	yes	complemented
230	C₂×C₄⋊Q₈	C₂²×C₁₁	1	2	yes	—
231	C₂×C₄⋊Q₈	C₂²×C₁₁	1	1	yes	characteristic
232	C₂×C₂²⋊Q₈	—	2	1	no	—
233	C₂×C₂²⋊Q₈	—	2	2	no	—
234	C₂×C₄×Q₈	C₂²×C₁₁	1	1	yes	characteristic
235	C₂×C₄×D₄	C₂²×C₁₁	1	1	yes	characteristic
236	C₂×C₄×D₄	C₂²×C₁₁	1	2	yes	—
237	#446	—	2	4	no	—
238	C₂×C₄⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
239	C₂×C₄⋊C₈	C₂²×C₁₁	1	2	yes	—
240	C₂×#102	C₂²×C₁₁	1	2	yes	—
241	C₂×#102	C₂²×C₁₁	1	1	yes	characteristic
242	C₂×#102	C₂²×C₁₁	1	1	yes	characteristic
243	C₂×#97	C₂²×C₁₁	1	2	yes	—
244	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
245	#391	—	2	1	no	—
246	#387	—	2	2	no	—
247	#384	C₂²×C₁₁	1	1	yes	characteristic
248	#382	C₂²×C₁₁	1	2	yes	—
249	C₄×C₄⋊C₄	—	2	1	no	—
250	C₄×C₄⋊C₄	C₂²×C₁₁	1	2	yes	—
251	C₄×C₄⋊C₄	C₂²×C₁₁	1	1	yes	characteristic
252	#340	C₂²×C₁₁	1	2	yes	—
253	#340	C₂²×C₁₁	1	2	yes	—
254	#340	C₂²×C₁₁	1	2	yes	—
255	#340	C₂²×C₁₁	1	1	yes	characteristic
256	#340	C₂²×C₁₁	1	2	yes	—
257	#340	C₂²×C₁₁	1	2	yes	—
258	#340	C₂²×C₁₁	1	1	yes	characteristic
259	C₂²×C₁₁	—	2	4	no	—
260	C₂²×C₁₁	—	4	2	no	—
261	C₂²×C₁₁	—	4	2	no	—
262	C₂²×C₁₁	—	4	2	no	—
263	C₂²×C₁₁	—	4	2	no	—
264	C₂²×C₁₁	—	4	2	no	—
265	C₂²×C₁₁	—	4	2	no	—
266	C₂²×C₁₁	C₂²×C₂²⋊C₄	1	1	yes	characteristic
267	C₂²×C₁₁	#548	1	1	yes	characteristic
268	C₂²×C₁₁	D₄×Q₈	1	1	yes	characteristic
269	C₂²×C₁₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
270	C₂²×C₁₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
271	C₂²×C₁₁	#577	1	1	yes	characteristic
272	C₂²×C₁₁	#578	1	1	yes	characteristic
273	C₄×C₁₁	—	2	4	no	—
274	C₄×C₁₁	—	2	4	no	—
275	C₄×C₁₁	—	2	2	no	—
276	C₄×C₁₁	—	4	2	no	—
277	C₄×C₁₁	—	4	4	no	—
278	C₄×C₁₁	—	4	2	no	—
279	C₄×C₁₁	—	8	1	no	—
280	C₄×C₁₁	—	8	2	no	—
281	C₄×C₁₁	#418	1	4	yes	—
282	C₄×C₁₁	C₂×C₄×Q₈	1	1	yes	characteristic
283	C₄×C₁₁	#519	1	1	yes	characteristic
284	C₄×C₁₁	#548	1	1	yes	characteristic
285	C₄×C₁₁	D₄×Q₈	1	1	yes	characteristic
286	C₂²×Q₈	—	2	8	no	—
287	C₂²×Q₈	—	2	2	no	—
288	C₂²×Q₈	—	2	1	no	—
289	C₂²×Q₈	—	4	4	no	—
290	C₂²×Q₈	—	4	4	no	—
291	C₂²×Q₈	D₄×C₁₁	1	1	yes	characteristic
292	C₂²×D₄	C₂³×C₁₁	1	1	yes	characteristic
293	C₂³×C₄	—	2	2	no	—
294	C₂³×C₄	—	2	1	no	—
295	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
296	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
297	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
298	C₄⋊Q₈	—	2	2	no	—
299	C₄⋊Q₈	—	2	4	no	—
300	C₄⋊Q₈	C₂×C₄×C₁₁	1	8	yes	—
301	C₄⋊Q₈	C₂×C₄×C₁₁	1	4	yes	—
302	C₂²⋊Q₈	—	2	16	no	—
303	C₂²⋊Q₈	—	2	8	no	—
304	C₄×Q₈	C₂×C₄×C₁₁	1	4	yes	—
305	C₄×Q₈	D₄×C₁₁	1	4	yes	—
306	C₄×D₄	—	2	2	no	—
307	C₄×D₄	—	2	4	no	—
308	C₄×D₄	C₂×C₄×C₁₁	1	4	yes	—
309	C₄×D₄	C₂×C₄×C₁₁	1	8	yes	—
310	C₂×C₄⋊C₄	—	2	2	no	—
311	C₂×C₄⋊C₄	—	2	1	no	—
312	C₂×C₄⋊C₄	—	2	1	no	—
313	C₂×C₄⋊C₄	—	2	1	no	—
314	C₂×C₄⋊C₄	D₄×C₁₁	1	1	yes	characteristic
315	C₂×C₄⋊C₄	D₄×C₁₁	1	2	yes	—
316	C₂×C₄⋊C₄	C₂³×C₁₁	1	1	yes	characteristic
317	C₂×C₄⋊C₄	C₂³×C₁₁	1	2	yes	—
318	C₂×C₄⋊C₄	C₂³×C₁₁	1	1	yes	characteristic
319	C₂×C₄⋊C₄	C₂³×C₁₁	1	2	yes	—
320	C₂×C₄⋊C₄	C₂³×C₁₁	1	1	yes	characteristic
321	C₂×C₂²⋊C₄	—	2	2	no	—
322	C₂×C₂²⋊C₄	—	2	1	no	—
323	C₂×C₄²	—	2	1	no	—
324	C₂×C₄²	—	2	2	no	—
325	C₂×C₄²	C₂³×C₁₁	1	2	yes	—
326	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
327	C₄⋊C₈	—	2	2	no	—
328	C₄⋊C₈	—	2	4	no	—
329	#102	—	2	4	no	—
330	#102	—	2	2	no	—
331	#102	Q₈×C₁₁	1	4	yes	complemented
332	#97	—	2	4	no	—
333	C₄×C₈	—	2	2	no	—
334	#95	—	2	2	no	—
335	#95	—	2	1	no	—
336	#95	—	2	2	no	—
337	#95	—	2	2	no	—
338	C₂×C₁₁	—	4	4	no	—
339	C₂×C₁₁	Q₈×C₂²⋊C₄	1	1	yes	characteristic
340	C₂×C₁₁	C₂×#418	1	1	yes	characteristic
341	C₂×C₁₁	#2898	1	1	yes	characteristic
342	C₂×C₁₁	#3367	1	1	yes	characteristic
343	C₂×C₁₁	#3373	1	1	yes	characteristic
344	C₂×C₁₁	#3384	1	1	yes	characteristic
345	C₂×C₁₁	#3386	1	1	yes	characteristic
346	C₂⁴	—	2	1	no	—
347	C₂×Q₈	—	2	8	no	—
348	C₂×Q₈	—	2	4	no	—
349	C₂×Q₈	—	2	2	no	—
350	C₂×Q₈	—	2	2	no	—
351	C₂×Q₈	—	4	4	no	—
352	C₂×Q₈	—	4	4	no	—
353	C₂×Q₈	—	4	32	no	—
354	C₂×Q₈	—	4	2	no	—
355	C₂×Q₈	—	4	2	no	—
356	C₂×Q₈	C₁₁×C₂²⋊C₄	1	4	yes	—
357	C₂×D₄	—	2	1	no	—
358	C₂×D₄	—	2	1	no	—
359	C₂×D₄	—	2	1	no	—
360	C₂×D₄	C₂²×C₄×C₁₁	1	2	yes	—
361	C₂×D₄	C₂×Q₈×C₁₁	1	2	yes	—
362	C₂×D₄	C₁₁×#41	1	2	yes	—
363	C₂²×C₄	—	2	1	no	—
364	C₂²×C₄	—	2	2	no	—
365	C₂²×C₄	—	2	1	no	—
366	C₂²×C₄	—	2	8	no	—
367	C₂²×C₄	—	2	4	no	—
368	C₂²×C₄	—	2	1	no	—
369	C₂²×C₄	—	2	2	no	—
370	C₂²×C₄	—	4	4	no	—
371	C₂²×C₄	—	4	4	no	—
372	C₂²×C₄	—	4	2	no	—
373	C₂²×C₄	—	4	2	no	—
374	C₂²×C₄	C₂×D₄×C₁₁	1	2	yes	—
375	C₂²×C₄	C₂×D₄×C₁₁	1	2	yes	—
376	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
377	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
378	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
379	C₂×C₈	—	2	1	no	—
380	C₂×C₈	—	2	1	no	—
381	C₂×C₈	—	2	1	no	—
382	C₂×C₈	—	2	2	no	—
383	C₂×C₈	—	2	1	no	—
384	C₂×C₈	—	2	2	no	—
385	C₂×C₈	—	2	1	no	—
386	C₂×C₈	—	2	2	no	—
387	C₂×C₈	C₂×Q₈×C₁₁	1	2	yes	complemented
388	C₄⋊C₄	—	2	4	no	—
389	C₄⋊C₄	—	2	8	no	—
390	C₄⋊C₄	—	2	1	no	—
391	C₄⋊C₄	—	2	2	no	—
392	C₄⋊C₄	—	2	1	no	—
393	C₄⋊C₄	—	2	1	no	—
394	C₄⋊C₄	—	2	2	no	—
395	C₄⋊C₄	—	2	1	no	—
396	C₄⋊C₄	—	2	2	no	—
397	C₄⋊C₄	—	4	2	no	—
398	C₄⋊C₄	—	8	1	no	—
399	C₄⋊C₄	C₁₁×C₂²⋊C₄	1	8	yes	—
400	C₄⋊C₄	C₁₁×C₂²⋊C₄	1	4	yes	—
401	C₄⋊C₄	C₂²×C₄×C₁₁	1	2	yes	—
402	C₄⋊C₄	C₂²×C₄×C₁₁	1	4	yes	—
403	C₄⋊C₄	C₂×Q₈×C₁₁	1	2	yes	complemented
404	C₂²⋊C₄	—	2	4	no	—
405	C₂²⋊C₄	—	2	8	no	—
406	C₄²	—	4	2	no	—
407	C₄²	—	8	2	no	—
408	C₄²	C₂²×C₄×C₁₁	1	4	yes	—
409	C₄²	C₂²×C₄×C₁₁	1	2	yes	—
410	C₄²	C₂×D₄×C₁₁	1	2	yes	—
411	C₄²	C₂×D₄×C₁₁	1	4	yes	—
412	C₁₁	#22523	1	1	yes	characteristic, direct product factor, Sylow
413	C₂³	—	2	2	no	—
414	C₂³	—	2	2	no	—
415	C₂³	—	2	2	no	—
416	C₂³	—	4	1	no	—
417	C₂³	—	4	1	no	—
418	C₂³	—	4	1	no	—
419	C₂³	—	4	1	no	—
420	C₂³	C₂²×D₄×C₁₁	1	1	yes	characteristic
421	Q₈	—	2	8	no	—
422	Q₈	—	4	16	no	—
423	Q₈	—	4	8	no	—
424	D₄	—	2	2	no	—
425	D₄	—	2	2	no	—
426	D₄	—	2	2	no	—
427	D₄	C₄×Q₈×C₁₁	1	4	yes	—
428	C₂×C₄	—	2	2	no	—
429	C₂×C₄	—	2	2	no	—
430	C₂×C₄	—	2	2	no	—
431	C₂×C₄	—	2	1	no	—
432	C₂×C₄	—	2	2	no	—
433	C₂×C₄	—	2	1	no	—
434	C₂×C₄	—	2	4	no	—
435	C₂×C₄	—	2	2	no	—
436	C₂×C₄	—	2	2	no	—
437	C₂×C₄	—	4	16	no	—
438	C₂×C₄	—	4	1	no	—
439	C₂×C₄	—	4	2	no	—
440	C₂×C₄	—	4	1	no	—
441	C₂×C₄	—	4	2	no	—
442	C₂×C₄	—	4	1	no	—
443	C₂×C₄	—	4	1	no	—
444	C₂×C₄	—	4	8	no	—
445	C₂×C₄	—	4	1	no	—
446	C₂×C₄	—	4	2	no	—
447	C₂×C₄	—	4	1	no	—
448	C₂×C₄	—	4	2	no	—
449	C₂×C₄	—	4	2	no	—
450	C₂×C₄	—	4	1	no	—
451	C₂×C₄	C₂×C₁₁×C₂²⋊C₄	1	2	yes	—
452	C₂×C₄	C₂×C₁₁×C₂²⋊C₄	1	4	yes	—
453	C₂×C₄	C₂×C₁₁×C₂²⋊C₄	1	4	yes	—
454	C₂×C₄	C₂×C₁₁×C₂²⋊C₄	1	2	yes	—
455	C₂×C₄	C₁₁×AGL(1,ℤ/8)	1	2	yes	—
456	C₂×C₄	C₁₁×AGL(1,ℤ/8)	1	2	yes	—
457	C₂×C₄	C₂³×C₄×C₁₁	1	1	yes	characteristic
458	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
459	C₂×C₄	C₂²×Q₈×C₁₁	1	1	yes	characteristic
460	C₂×C₄	C₂×C₁₁×#41	1	1	yes	characteristic
461	C₂×C₄	C₁₁×2₋¹⁺⁴	1	1	yes	characteristic
462	C₂×C₄	C₁₁×2₋¹⁺⁴	1	1	yes	characteristic
463	C₈	—	2	2	no	—
464	C₈	—	4	1	no	—
465	C₈	—	4	2	no	—
466	C₂²	—	2	4	no	—
467	C₂²	—	4	2	no	—
468	C₂²	—	4	2	no	—
469	C₂²	—	4	2	no	—
470	C₂²	—	4	2	no	—
471	C₂²	—	4	2	no	—
472	C₂²	—	4	2	no	—
473	C₂²	C₂²×C₁₁×C₂²⋊C₄	1	1	yes	characteristic
474	C₂²	C₁₁×#548	1	1	yes	characteristic
475	C₂²	D₄×Q₈×C₁₁	1	1	yes	characteristic
476	C₂²	C₂×C₁₁×AGL(1,ℤ/8)	1	1	yes	characteristic
477	C₂²	C₂×C₁₁×AGL(1,ℤ/8)	1	1	yes	characteristic
478	C₂²	C₁₁×#577	1	1	yes	characteristic
479	C₂²	C₁₁×#578	1	1	yes	characteristic
480	C₄	—	2	4	no	—
481	C₄	—	2	4	no	—
482	C₄	—	2	2	no	—
483	C₄	—	4	4	no	—
484	C₄	—	4	2	no	—
485	C₄	—	4	2	no	—
486	C₄	—	8	1	no	—
487	C₄	—	8	2	no	—
488	C₄	C₁₁×#418	1	4	yes	—
489	C₄	C₂×C₄×Q₈×C₁₁	1	1	yes	characteristic
490	C₄	C₁₁×#519	1	1	yes	characteristic
491	C₄	C₁₁×#548	1	1	yes	characteristic
492	C₄	D₄×Q₈×C₁₁	1	1	yes	characteristic
493	C₂	—	4	4	no	—
494	C₂	Q₈×C₁₁×C₂²⋊C₄	1	1	yes	characteristic
495	C₂	C₂×C₁₁×#418	1	1	yes	characteristic
496	C₂	C₁₁×#2898	1	1	yes	characteristic
497	C₂	C₁₁×#3367	1	1	yes	characteristic
498	C₂	C₁₁×#3373	1	1	yes	characteristic
499	C₂	C₁₁×#3384	1	1	yes	characteristic
500	C₂	C₁₁×#3386	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×D₄×C₁₁	C₂³
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₁ ◁ C₂×C₄×Q₈×C₁₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₁×#446	C₂	semidirect
3. C₁₁×#2355	C₂	semidirect
4. C₁₁×#1993	C₂	semidirect
5. C₁₁×#1990	C₂	semidirect
6. C₁₁×#1988	C₂	semidirect
7. C₁₁×#1987	C₂	semidirect
14. D₄×Q₈×C₁₁	C₄	semidirect
89. C₁₁×#102	Q₈	semidirect
96. #22523	C₁₁	direct (N × H)
138. C₂×C₈×C₁₁	C₂×Q₈	semidirect
154. C₁₁×C₄⋊C₄	C₂×Q₈	semidirect
164. C₂×#446	C₂×C₁₁	semidirect
165. #2355	C₂×C₁₁	semidirect
166. #1993	C₂×C₁₁	semidirect
167. #1990	C₂×C₁₁	semidirect
168. #1988	C₂×C₁₁	semidirect
169. #1987	C₂×C₁₁	semidirect
229. D₄×Q₈	C₄×C₁₁	semidirect
331. #102	Q₈×C₁₁	semidirect
387. C₂×C₈	C₂×Q₈×C₁₁	semidirect
403. C₄⋊C₄	C₂×Q₈×C₁₁	semidirect
412. C₁₁	#22523	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×D₄×Q₈×C₁₁	2
C₂×C₁₁×#446	2
C₁₁×#2355	2
C₁₁×#1993	2
C₁₁×#1990	2
C₁₁×#1988	2
C₁₁×#1987	2
C₁₁×#1804	2
C₁₁×#1802	2
C₁₁×#1762	2
C₄×C₁₁×#102	2
#22523	11

Subgroups — C11×#22523 #14599716

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#22523 #14599716