Subgroups — C₁₁×#60144 #14637337

Order 2816.

2778 conjugacy classes of subgroups.

The subgroup lattice has 500 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₁×#568	C₂	1	2	yes	maximal, complemented
2	C₂×C₁₁×#532	C₂	1	1	yes	maximal, characteristic
3	C₁₁×#2935	C₂	1	8	yes	maximal, complemented
4	D₄×C₁₁×M₁₆	C₂	1	8	yes	maximal, complemented
5	C₁₁×#2932	C₂	1	4	yes	maximal, complemented
6	C₁₁×#2931	C₂	1	4	yes	maximal, complemented
7	C₂×C₁₁×#423	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₁×#2879	C₂	1	2	yes	maximal, complemented
9	C₂×C₄×C₁₁×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×C₁₁×#41	C₂²	1	2	yes	—
11	C₁₁×#568	—	2	16	no	—
12	C₂×C₁₁×#131	C₂²	1	8	yes	complemented
13	C₂×C₁₁×#131	C₂²	1	8	yes	complemented
14	C₂²×C₁₁×M₁₆	C₂²	1	2	yes	—
15	C₂²×C₁₁×M₁₆	C₂²	1	8	yes	—
16	C₂²×C₁₁×M₁₆	C₂²	1	1	yes	characteristic
17	C₂²×C₁₁×M₁₆	C₂²	1	1	yes	characteristic
18	C₁₁×#532	C₄	1	2	yes	—
19	C₁₁×#532	C₄	1	4	yes	—
20	C₁₁×#532	C₄	1	2	yes	—
21	C₁₁×#532	C₂²	1	2	yes	—
22	C₁₁×#532	C₂²	1	2	yes	—
23	C₁₁×#532	C₂²	1	4	yes	—
24	C₂×C₁₁×C₄⋊Q₈	C₄	1	1	yes	characteristic
25	C₂×C₁₁×#127	C₄	1	1	yes	characteristic
26	C₂×C₁₁×#124	C₄	1	2	yes	—
27	C₂×C₁₁×#121	C₄	1	4	yes	—
28	C₂×C₄×D₄×C₁₁	C₂²	1	4	yes	—
29	C₂²×C₄²×C₁₁	C₂²	1	1	yes	characteristic
30	C₁₁×#436	C₂²	1	16	yes	complemented
31	C₁₁×#435	C₂²	1	32	yes	complemented
32	C₈×D₄×C₁₁	C₂²	1	16	yes	complemented
33	C₁₁×#423	C₂²	1	4	yes	—
34	C₁₁×#423	C₂²	1	2	yes	complemented
35	C₁₁×#423	C₂²	1	2	yes	complemented
36	C₂×C₁₁×C₄⋊C₈	C₂²	1	4	yes	complemented
37	C₁₁×#408	C₂²	1	8	yes	complemented
38	C₁₁×#408	C₂²	1	8	yes	complemented
39	C₁₁×#407	C₂²	1	8	yes	—
40	C₄×C₁₁×M₁₆	C₂²	1	4	yes	—
41	C₄×C₁₁×M₁₆	C₂²	1	4	yes	complemented
42	C₂×C₁₁×#97	C₂²	1	2	yes	complemented
43	C₂×C₄×C₈×C₁₁	C₂²	1	2	yes	complemented
44	C₂×C₁₁×#41	—	2	8	no	—
45	C₂×C₁₁×#41	—	2	8	no	—
46	C₂×C₁₁×#41	C₂×C₄	1	4	yes	—
47	C₂×C₁₁×#41	C₂×C₄	1	4	yes	—
48	C₂×C₁₁×#41	C₂³	1	4	yes	—
49	C₂×C₁₁×#41	C₂³	1	4	yes	—
50	C₂²×Q₈×C₁₁	C₂×C₄	1	2	yes	—
51	C₂²×D₄×C₁₁	C₂×C₄	1	4	yes	—
52	C₂²×D₄×C₁₁	C₂×C₄	1	2	yes	—
53	C₂²×D₄×C₁₁	C₂×C₄	1	4	yes	—
54	C₂³×C₄×C₁₁	C₂×C₄	1	2	yes	—
55	C₂³×C₄×C₁₁	C₂³	1	4	yes	—
56	C₂³×C₄×C₁₁	C₂³	1	1	yes	characteristic
57	C₁₁×#131	—	2	32	no	—
58	C₁₁×#131	—	2	32	no	—
59	C₂×C₁₁×M₁₆	—	2	8	no	—
60	C₂×C₁₁×M₁₆	—	2	4	no	—
61	C₂×C₁₁×M₁₆	—	2	32	no	—
62	C₂×C₁₁×M₁₆	D₄	1	8	yes	complemented
63	C₂×C₁₁×M₁₆	C₂³	1	2	yes	—
64	C₂×C₁₁×M₁₆	C₂³	1	2	yes	—
65	C₂×C₁₁×M₁₆	C₂³	1	4	yes	—
66	C₂×C₁₁×M₁₆	C₂³	1	4	yes	—
67	C₂×C₁₁×M₁₆	C₂³	1	16	yes	—
68	C₂×C₁₁×M₁₆	C₂³	1	2	yes	—
69	C₂×C₁₁×M₁₆	C₂³	1	2	yes	—
70	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
71	C₂²×C₈×C₁₁	C₂³	1	4	yes	—
72	C₂²×C₈×C₁₁	C₂³	1	16	yes	—
73	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
74	C₁₁×C₄⋊Q₈	C₂×C₄	1	2	yes	—
75	C₁₁×C₄⋊Q₈	C₂×C₄	1	2	yes	—
76	C₁₁×C₄⋊Q₈	C₂×C₄	1	4	yes	—
77	C₁₁×#127	C₂×C₄	1	2	yes	—
78	C₁₁×#127	C₂×C₄	1	4	yes	—
79	C₁₁×#127	C₂×C₄	1	2	yes	—
80	C₁₁×#124	C₂×C₄	1	4	yes	—
81	C₁₁×#124	C₂×C₄	1	4	yes	—
82	C₁₁×#124	C₂×C₄	1	8	yes	—
83	C₁₁×#121	C₂×C₄	1	8	yes	—
84	C₁₁×#121	C₂×C₄	1	8	yes	—
85	C₁₁×#121	C₂×C₄	1	8	yes	—
86	C₁₁×#121	C₂×C₄	1	8	yes	—
87	C₄×D₄×C₁₁	C₂×C₄	1	8	yes	—
88	C₄×D₄×C₁₁	C₂×C₄	1	8	yes	—
89	C₄×D₄×C₁₁	C₂³	1	8	yes	—
90	C₄×D₄×C₁₁	C₂³	1	8	yes	—
91	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	4	yes	—
92	C₂×C₁₁×C₂²⋊C₄	C₂×C₄	1	8	yes	—
93	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
94	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
95	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
96	C₂×C₄²×C₁₁	C₂×C₄	1	2	yes	—
97	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
98	C₂×C₄²×C₁₁	C₂³	1	2	yes	—
99	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
100	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
101	C₂×C₄²×C₁₁	C₂³	1	2	yes	—
102	C₁₁×C₄⋊C₈	C₂³	1	8	yes	—
103	C₁₁×C₄⋊C₈	C₂³	1	8	yes	—
104	C₁₁×C₂²⋊C₈	C₂³	1	32	yes	—
105	C₁₁×#97	C₂³	1	8	yes	—
106	C₄×C₈×C₁₁	C₂³	1	8	yes	—
107	#60144	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
108	C₂⁴×C₁₁	C₂²×C₄	1	4	yes	—
109	C₂⁴×C₁₁	C₂²×C₄	1	1	yes	characteristic
110	C₁₁×#41	—	2	16	no	—
111	C₁₁×#41	—	2	16	no	—
112	C₁₁×#41	—	2	8	no	—
113	C₁₁×#41	—	2	8	no	—
114	C₁₁×#41	—	2	8	no	—
115	C₁₁×#41	—	2	8	no	—
116	C₂×Q₈×C₁₁	—	2	8	no	—
117	C₂×Q₈×C₁₁	C₂²×C₄	1	4	yes	—
118	C₂×Q₈×C₁₁	C₂²×C₄	1	4	yes	—
119	C₂×D₄×C₁₁	—	2	16	no	—
120	C₂×D₄×C₁₁	—	2	8	no	—
121	C₂×D₄×C₁₁	—	4	8	no	—
122	C₂×D₄×C₁₁	C₂²×C₄	1	8	yes	—
123	C₂×D₄×C₁₁	C₂²×C₄	1	8	yes	—
124	C₂×D₄×C₁₁	C₂²×C₄	1	8	yes	—
125	C₂×D₄×C₁₁	C₂²×C₄	1	4	yes	—
126	C₂×D₄×C₁₁	C₂²×C₄	1	4	yes	—
127	C₂×D₄×C₁₁	C₂²×C₄	1	8	yes	—
128	C₂²×C₄×C₁₁	—	2	8	no	—
129	C₂²×C₄×C₁₁	—	2	8	no	—
130	C₂²×C₄×C₁₁	—	4	4	no	—
131	C₂²×C₄×C₁₁	C₂²×C₄	1	2	yes	—
132	C₂²×C₄×C₁₁	C₂²×C₄	1	2	yes	—
133	C₂²×C₄×C₁₁	C₂²×C₄	1	2	yes	—
134	C₂²×C₄×C₁₁	C₂²×C₄	1	4	yes	—
135	C₂²×C₄×C₁₁	C₂²×C₄	1	8	yes	—
136	C₂²×C₄×C₁₁	C₂²×C₄	1	2	yes	—
137	C₂²×C₄×C₁₁	C₂²×C₄	1	2	yes	—
138	C₂²×C₄×C₁₁	C₂²×C₄	1	2	yes	—
139	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
140	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
141	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
142	C₂²×C₄×C₁₁	C₂×D₄	1	4	yes	—
143	C₂²×C₄×C₁₁	#41	1	4	yes	—
144	C₂²×C₄×C₁₁	C₂⁴	1	8	yes	—
145	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
146	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
147	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
148	C₁₁×M₁₆	—	2	32	no	—
149	C₁₁×M₁₆	—	2	8	no	—
150	C₁₁×M₁₆	—	2	8	no	—
151	C₁₁×M₁₆	—	2	4	no	—
152	C₁₁×M₁₆	—	2	4	no	—
153	C₁₁×M₁₆	C₂×D₄	1	8	yes	—
154	C₁₁×M₁₆	C₂×D₄	1	8	yes	complemented
155	C₂×C₈×C₁₁	—	2	32	no	—
156	C₂×C₈×C₁₁	—	2	8	no	—
157	C₂×C₈×C₁₁	—	2	4	no	—
158	C₂×C₈×C₁₁	C₂×D₄	1	8	yes	complemented
159	C₂×C₈×C₁₁	C₂⁴	1	4	yes	—
160	C₂×C₈×C₁₁	C₂⁴	1	8	yes	—
161	C₂×C₈×C₁₁	C₂⁴	1	4	yes	—
162	C₁₁×C₄⋊C₄	C₂²×C₄	1	8	yes	—
163	C₁₁×C₄⋊C₄	C₂²×C₄	1	8	yes	—
164	C₁₁×C₂²⋊C₄	C₂²×C₄	1	16	yes	—
165	C₁₁×C₂²⋊C₄	C₂²×C₄	1	16	yes	—
166	C₄²×C₁₁	C₂²×C₄	1	2	yes	—
167	C₄²×C₁₁	C₂²×C₄	1	2	yes	—
168	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
169	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
170	C₄²×C₁₁	C₂²×C₄	1	2	yes	—
171	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
172	C₄²×C₁₁	C₂²×C₄	1	2	yes	—
173	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
174	C₄²×C₁₁	C₂⁴	1	2	yes	—
175	C₄²×C₁₁	C₂⁴	1	2	yes	—
176	C₂×#568	C₂×C₁₁	1	2	yes	complemented
177	C₂×#532	C₂×C₁₁	1	1	yes	characteristic
178	#2935	C₂×C₁₁	1	8	yes	complemented
179	D₄×M₁₆	C₂×C₁₁	1	8	yes	complemented
180	#2932	C₂×C₁₁	1	4	yes	complemented
181	#2931	C₂×C₁₁	1	4	yes	complemented
182	C₂×#423	C₂×C₁₁	1	1	yes	characteristic, complemented
183	#2879	C₂×C₁₁	1	2	yes	complemented
184	C₂×C₄×M₁₆	C₂×C₁₁	1	1	yes	characteristic, complemented
185	C₂³×C₁₁	—	2	8	no	—
186	C₂³×C₁₁	—	4	2	no	—
187	C₂³×C₁₁	—	4	8	no	—
188	C₂³×C₁₁	C₄×D₄	1	4	yes	—
189	C₂³×C₁₁	C₂³×C₄	1	8	yes	—
190	C₂³×C₁₁	C₂³×C₄	1	1	yes	characteristic
191	C₂³×C₁₁	C₂³×C₄	1	1	yes	characteristic
192	C₂³×C₁₁	C₂³×C₄	1	1	yes	characteristic
193	Q₈×C₁₁	—	2	8	no	—
194	Q₈×C₁₁	—	2	8	no	—
195	D₄×C₁₁	—	2	16	no	—
196	D₄×C₁₁	—	2	16	no	—
197	D₄×C₁₁	—	2	8	no	—
198	D₄×C₁₁	—	2	8	no	—
199	D₄×C₁₁	—	2	16	no	—
200	D₄×C₁₁	—	4	8	no	—
201	C₂×C₄×C₁₁	—	2	8	no	—
202	C₂×C₄×C₁₁	—	2	16	no	—
203	C₂×C₄×C₁₁	—	2	4	no	—
204	C₂×C₄×C₁₁	—	2	4	no	—
205	C₂×C₄×C₁₁	—	2	4	no	—
206	C₂×C₄×C₁₁	—	2	8	no	—
207	C₂×C₄×C₁₁	—	2	8	no	—
208	C₂×C₄×C₁₁	—	4	2	no	—
209	C₂×C₄×C₁₁	—	4	2	no	—
210	C₂×C₄×C₁₁	—	4	2	no	—
211	C₂×C₄×C₁₁	C₄×D₄	1	4	yes	—
212	C₂×C₄×C₁₁	C₄×D₄	1	4	yes	—
213	C₂×C₄×C₁₁	C₄×D₄	1	4	yes	—
214	C₂×C₄×C₁₁	C₂³×C₄	1	2	yes	—
215	C₂×C₄×C₁₁	C₂³×C₄	1	2	yes	—
216	C₂×C₄×C₁₁	C₂³×C₄	1	2	yes	—
217	C₂×C₄×C₁₁	C₂³×C₄	1	8	yes	—
218	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
219	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
220	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
221	C₂×C₄×C₁₁	C₂³×C₄	1	2	yes	—
222	C₂×C₄×C₁₁	C₂²×D₄	1	2	yes	—
223	C₂×C₄×C₁₁	C₂²×D₄	1	2	yes	—
224	C₂×C₄×C₁₁	C₂²×D₄	1	2	yes	—
225	C₂×C₄×C₁₁	C₂×#41	1	2	yes	—
226	C₂×C₄×C₁₁	C₂×#41	1	2	yes	—
227	C₂×C₄×C₁₁	C₂×#41	1	2	yes	—
228	C₂×C₄×C₁₁	C₂⁵	1	1	yes	characteristic
229	C₈×C₁₁	—	2	8	no	—
230	C₈×C₁₁	—	2	4	no	—
231	C₈×C₁₁	C₂²×D₄	1	8	yes	—
232	C₂²×#41	C₂²×C₁₁	1	2	yes	—
233	#568	—	2	16	no	—
234	C₂×#131	C₂²×C₁₁	1	8	yes	complemented
235	C₂×#131	C₂²×C₁₁	1	8	yes	complemented
236	C₂²×M₁₆	C₂²×C₁₁	1	1	yes	characteristic
237	C₂²×M₁₆	C₂²×C₁₁	1	2	yes	—
238	C₂²×M₁₆	C₂²×C₁₁	1	8	yes	—
239	C₂²×M₁₆	C₂²×C₁₁	1	1	yes	characteristic
240	#532	C₄×C₁₁	1	2	yes	—
241	#532	C₄×C₁₁	1	4	yes	—
242	#532	C₄×C₁₁	1	2	yes	—
243	#532	C₂²×C₁₁	1	2	yes	—
244	#532	C₂²×C₁₁	1	2	yes	—
245	#532	C₂²×C₁₁	1	4	yes	—
246	C₂×C₄⋊Q₈	C₄×C₁₁	1	1	yes	characteristic
247	C₂×#127	C₄×C₁₁	1	1	yes	characteristic
248	C₂×#124	C₄×C₁₁	1	2	yes	—
249	C₂×#121	C₄×C₁₁	1	4	yes	—
250	C₂×C₄×D₄	C₂²×C₁₁	1	4	yes	—
251	C₂²×C₄²	C₂²×C₁₁	1	1	yes	characteristic
252	#436	C₂²×C₁₁	1	16	yes	complemented
253	#435	C₂²×C₁₁	1	32	yes	complemented
254	C₈×D₄	C₂²×C₁₁	1	16	yes	complemented
255	#423	C₂²×C₁₁	1	4	yes	—
256	#423	C₂²×C₁₁	1	2	yes	complemented
257	#423	C₂²×C₁₁	1	2	yes	complemented
258	C₂×C₄⋊C₈	C₂²×C₁₁	1	4	yes	complemented
259	#408	C₂²×C₁₁	1	8	yes	complemented
260	#408	C₂²×C₁₁	1	8	yes	complemented
261	#407	C₂²×C₁₁	1	8	yes	—
262	C₄×M₁₆	C₂²×C₁₁	1	4	yes	—
263	C₄×M₁₆	C₂²×C₁₁	1	4	yes	complemented
264	C₂×#97	C₂²×C₁₁	1	2	yes	complemented
265	C₂×C₄×C₈	C₂²×C₁₁	1	2	yes	complemented
266	C₂²×C₁₁	—	2	2	no	—
267	C₂²×C₁₁	—	2	2	no	—
268	C₂²×C₁₁	—	2	2	no	—
269	C₂²×C₁₁	—	2	8	no	—
270	C₂²×C₁₁	—	2	16	no	—
271	C₂²×C₁₁	—	4	4	no	—
272	C₂²×C₁₁	—	8	8	no	—
273	C₂²×C₁₁	C₂×C₄×D₄	1	2	yes	—
274	C₂²×C₁₁	C₂×C₄×D₄	1	2	yes	—
275	C₂²×C₁₁	C₂×C₄×D₄	1	2	yes	—
276	C₂²×C₁₁	C₂⁴×C₄	1	1	yes	characteristic
277	C₄×C₁₁	—	2	8	no	—
278	C₄×C₁₁	—	2	2	no	—
279	C₄×C₁₁	—	2	2	no	—
280	C₄×C₁₁	—	2	2	no	—
281	C₄×C₁₁	C₂×C₄×D₄	1	2	yes	—
282	C₄×C₁₁	C₂×C₄×D₄	1	2	yes	—
283	C₄×C₁₁	C₂×C₄×D₄	1	2	yes	—
284	C₄×C₁₁	#568	1	4	yes	complemented
285	C₄×C₁₁	C₂³×D₄	1	1	yes	characteristic
286	C₄×C₁₁	C₂²×#41	1	1	yes	characteristic
287	C₂×#41	—	2	8	no	—
288	C₂×#41	—	2	8	no	—
289	C₂×#41	C₂×C₄×C₁₁	1	4	yes	—
290	C₂×#41	C₂×C₄×C₁₁	1	4	yes	—
291	C₂×#41	C₂³×C₁₁	1	4	yes	—
292	C₂×#41	C₂³×C₁₁	1	4	yes	—
293	C₂²×Q₈	C₂×C₄×C₁₁	1	2	yes	—
294	C₂²×D₄	C₂×C₄×C₁₁	1	4	yes	—
295	C₂²×D₄	C₂×C₄×C₁₁	1	2	yes	—
296	C₂²×D₄	C₂×C₄×C₁₁	1	4	yes	—
297	C₂³×C₄	C₂×C₄×C₁₁	1	2	yes	—
298	C₂³×C₄	C₂³×C₁₁	1	4	yes	—
299	C₂³×C₄	C₂³×C₁₁	1	1	yes	characteristic
300	#131	—	2	32	no	—
301	#131	—	2	32	no	—
302	C₂×M₁₆	—	2	8	no	—
303	C₂×M₁₆	—	2	4	no	—
304	C₂×M₁₆	—	2	32	no	—
305	C₂×M₁₆	D₄×C₁₁	1	8	yes	complemented
306	C₂×M₁₆	C₂³×C₁₁	1	4	yes	—
307	C₂×M₁₆	C₂³×C₁₁	1	4	yes	—
308	C₂×M₁₆	C₂³×C₁₁	1	16	yes	—
309	C₂×M₁₆	C₂³×C₁₁	1	2	yes	—
310	C₂×M₁₆	C₂³×C₁₁	1	2	yes	—
311	C₂×M₁₆	C₂³×C₁₁	1	2	yes	—
312	C₂×M₁₆	C₂³×C₁₁	1	2	yes	—
313	C₂²×C₈	C₂³×C₁₁	1	4	yes	—
314	C₂²×C₈	C₂³×C₁₁	1	16	yes	—
315	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
316	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
317	C₄⋊Q₈	C₂×C₄×C₁₁	1	2	yes	—
318	C₄⋊Q₈	C₂×C₄×C₁₁	1	2	yes	—
319	C₄⋊Q₈	C₂×C₄×C₁₁	1	4	yes	—
320	#127	C₂×C₄×C₁₁	1	2	yes	—
321	#127	C₂×C₄×C₁₁	1	4	yes	—
322	#127	C₂×C₄×C₁₁	1	2	yes	—
323	#124	C₂×C₄×C₁₁	1	4	yes	—
324	#124	C₂×C₄×C₁₁	1	4	yes	—
325	#124	C₂×C₄×C₁₁	1	8	yes	—
326	#121	C₂×C₄×C₁₁	1	8	yes	—
327	#121	C₂×C₄×C₁₁	1	8	yes	—
328	#121	C₂×C₄×C₁₁	1	8	yes	—
329	#121	C₂×C₄×C₁₁	1	8	yes	—
330	C₄×D₄	C₂×C₄×C₁₁	1	8	yes	—
331	C₄×D₄	C₂×C₄×C₁₁	1	8	yes	—
332	C₄×D₄	C₂³×C₁₁	1	8	yes	—
333	C₄×D₄	C₂³×C₁₁	1	8	yes	—
334	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	4	yes	—
335	C₂×C₂²⋊C₄	C₂×C₄×C₁₁	1	8	yes	—
336	C₂×C₄²	C₂×C₄×C₁₁	1	1	yes	characteristic
337	C₂×C₄²	C₂×C₄×C₁₁	1	1	yes	characteristic
338	C₂×C₄²	C₂×C₄×C₁₁	1	1	yes	characteristic
339	C₂×C₄²	C₂×C₄×C₁₁	1	2	yes	—
340	C₂×C₄²	C₂×C₄×C₁₁	1	1	yes	characteristic
341	C₂×C₄²	C₂³×C₁₁	1	2	yes	—
342	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
343	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
344	C₂×C₄²	C₂³×C₁₁	1	2	yes	—
345	C₄⋊C₈	C₂³×C₁₁	1	8	yes	—
346	C₄⋊C₈	C₂³×C₁₁	1	8	yes	—
347	C₂²⋊C₈	C₂³×C₁₁	1	32	yes	—
348	#97	C₂³×C₁₁	1	8	yes	—
349	C₄×C₈	C₂³×C₁₁	1	8	yes	—
350	C₂×C₁₁	—	2	2	no	—
351	C₂×C₁₁	—	2	2	no	—
352	C₂×C₁₁	—	2	2	no	—
353	C₂×C₁₁	—	4	8	no	—
354	C₂×C₁₁	C₂²×C₄×D₄	1	1	yes	characteristic
355	C₂×C₁₁	C₂×#568	1	2	yes	—
356	C₂⁴	C₂²×C₄×C₁₁	1	4	yes	—
357	C₂⁴	C₂²×C₄×C₁₁	1	1	yes	characteristic
358	#41	—	2	16	no	—
359	#41	—	2	16	no	—
360	#41	—	2	8	no	—
361	#41	—	2	8	no	—
362	#41	—	2	8	no	—
363	#41	—	2	8	no	—
364	C₂×Q₈	—	2	8	no	—
365	C₂×Q₈	C₂²×C₄×C₁₁	1	4	yes	—
366	C₂×Q₈	C₂²×C₄×C₁₁	1	4	yes	—
367	C₂×D₄	—	2	16	no	—
368	C₂×D₄	—	2	8	no	—
369	C₂×D₄	—	4	8	no	—
370	C₂×D₄	C₂²×C₄×C₁₁	1	8	yes	—
371	C₂×D₄	C₂²×C₄×C₁₁	1	8	yes	—
372	C₂×D₄	C₂²×C₄×C₁₁	1	8	yes	—
373	C₂×D₄	C₂²×C₄×C₁₁	1	4	yes	—
374	C₂×D₄	C₂²×C₄×C₁₁	1	4	yes	—
375	C₂×D₄	C₂²×C₄×C₁₁	1	8	yes	—
376	C₂²×C₄	—	2	8	no	—
377	C₂²×C₄	—	2	8	no	—
378	C₂²×C₄	—	4	4	no	—
379	C₂²×C₄	C₂²×C₄×C₁₁	1	2	yes	—
380	C₂²×C₄	C₂²×C₄×C₁₁	1	2	yes	—
381	C₂²×C₄	C₂²×C₄×C₁₁	1	2	yes	—
382	C₂²×C₄	C₂²×C₄×C₁₁	1	4	yes	—
383	C₂²×C₄	C₂²×C₄×C₁₁	1	8	yes	—
384	C₂²×C₄	C₂²×C₄×C₁₁	1	2	yes	—
385	C₂²×C₄	C₂²×C₄×C₁₁	1	2	yes	—
386	C₂²×C₄	C₂²×C₄×C₁₁	1	2	yes	—
387	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
388	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
389	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
390	C₂²×C₄	C₂×D₄×C₁₁	1	4	yes	—
391	C₂²×C₄	C₁₁×#41	1	4	yes	—
392	C₂²×C₄	C₂⁴×C₁₁	1	8	yes	—
393	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
394	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
395	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
396	M₁₆	—	2	8	no	—
397	M₁₆	—	2	8	no	—
398	M₁₆	—	2	4	no	—
399	M₁₆	—	2	4	no	—
400	M₁₆	—	2	32	no	—
401	M₁₆	C₂×D₄×C₁₁	1	8	yes	—
402	M₁₆	C₂×D₄×C₁₁	1	8	yes	complemented
403	C₂×C₈	—	2	8	no	—
404	C₂×C₈	—	2	4	no	—
405	C₂×C₈	—	2	32	no	—
406	C₂×C₈	C₂×D₄×C₁₁	1	8	yes	complemented
407	C₂×C₈	C₂⁴×C₁₁	1	4	yes	—
408	C₂×C₈	C₂⁴×C₁₁	1	8	yes	—
409	C₂×C₈	C₂⁴×C₁₁	1	4	yes	—
410	C₄⋊C₄	C₂²×C₄×C₁₁	1	8	yes	—
411	C₄⋊C₄	C₂²×C₄×C₁₁	1	8	yes	—
412	C₂²⋊C₄	C₂²×C₄×C₁₁	1	16	yes	—
413	C₂²⋊C₄	C₂²×C₄×C₁₁	1	16	yes	—
414	C₄²	C₂²×C₄×C₁₁	1	2	yes	—
415	C₄²	C₂²×C₄×C₁₁	1	2	yes	—
416	C₄²	C₂²×C₄×C₁₁	1	1	yes	characteristic
417	C₄²	C₂²×C₄×C₁₁	1	1	yes	characteristic
418	C₄²	C₂²×C₄×C₁₁	1	2	yes	—
419	C₄²	C₂²×C₄×C₁₁	1	1	yes	characteristic
420	C₄²	C₂²×C₄×C₁₁	1	2	yes	—
421	C₄²	C₂²×C₄×C₁₁	1	1	yes	characteristic
422	C₄²	C₂⁴×C₁₁	1	2	yes	—
423	C₄²	C₂⁴×C₁₁	1	2	yes	—
424	C₁₁	#60144	1	1	yes	characteristic, direct product factor, Sylow
425	C₂³	—	2	8	no	—
426	C₂³	—	4	2	no	—
427	C₂³	—	4	8	no	—
428	C₂³	C₄×D₄×C₁₁	1	4	yes	—
429	C₂³	C₂³×C₄×C₁₁	1	8	yes	—
430	C₂³	C₂³×C₄×C₁₁	1	1	yes	characteristic
431	C₂³	C₂³×C₄×C₁₁	1	1	yes	characteristic
432	C₂³	C₂³×C₄×C₁₁	1	1	yes	characteristic
433	Q₈	—	2	8	no	—
434	Q₈	—	2	8	no	—
435	D₄	—	2	16	no	—
436	D₄	—	2	16	no	—
437	D₄	—	2	8	no	—
438	D₄	—	2	8	no	—
439	D₄	—	2	16	no	—
440	D₄	—	4	8	no	—
441	C₂×C₄	—	2	8	no	—
442	C₂×C₄	—	2	16	no	—
443	C₂×C₄	—	2	4	no	—
444	C₂×C₄	—	2	4	no	—
445	C₂×C₄	—	2	4	no	—
446	C₂×C₄	—	2	8	no	—
447	C₂×C₄	—	2	8	no	—
448	C₂×C₄	—	4	2	no	—
449	C₂×C₄	—	4	2	no	—
450	C₂×C₄	—	4	2	no	—
451	C₂×C₄	C₄×D₄×C₁₁	1	4	yes	—
452	C₂×C₄	C₄×D₄×C₁₁	1	4	yes	—
453	C₂×C₄	C₄×D₄×C₁₁	1	4	yes	—
454	C₂×C₄	C₂³×C₄×C₁₁	1	2	yes	—
455	C₂×C₄	C₂³×C₄×C₁₁	1	2	yes	—
456	C₂×C₄	C₂³×C₄×C₁₁	1	2	yes	—
457	C₂×C₄	C₂³×C₄×C₁₁	1	8	yes	—
458	C₂×C₄	C₂³×C₄×C₁₁	1	1	yes	characteristic
459	C₂×C₄	C₂³×C₄×C₁₁	1	1	yes	characteristic
460	C₂×C₄	C₂³×C₄×C₁₁	1	1	yes	characteristic
461	C₂×C₄	C₂³×C₄×C₁₁	1	2	yes	—
462	C₂×C₄	C₂²×D₄×C₁₁	1	2	yes	—
463	C₂×C₄	C₂²×D₄×C₁₁	1	2	yes	—
464	C₂×C₄	C₂²×D₄×C₁₁	1	2	yes	—
465	C₂×C₄	C₂×C₁₁×#41	1	2	yes	—
466	C₂×C₄	C₂×C₁₁×#41	1	2	yes	—
467	C₂×C₄	C₂×C₁₁×#41	1	2	yes	—
468	C₂×C₄	C₂⁵×C₁₁	1	1	yes	characteristic
469	C₈	—	2	8	no	—
470	C₈	—	2	4	no	—
471	C₈	C₂²×D₄×C₁₁	1	8	yes	—
472	C₂²	—	2	2	no	—
473	C₂²	—	2	2	no	—
474	C₂²	—	2	2	no	—
475	C₂²	—	2	8	no	—
476	C₂²	—	2	16	no	—
477	C₂²	—	4	4	no	—
478	C₂²	—	8	8	no	—
479	C₂²	C₂×C₄×D₄×C₁₁	1	2	yes	—
480	C₂²	C₂×C₄×D₄×C₁₁	1	2	yes	—
481	C₂²	C₂×C₄×D₄×C₁₁	1	2	yes	—
482	C₂²	C₂⁴×C₄×C₁₁	1	1	yes	characteristic
483	C₄	—	2	8	no	—
484	C₄	—	2	2	no	—
485	C₄	—	2	2	no	—
486	C₄	—	2	2	no	—
487	C₄	C₂×C₄×D₄×C₁₁	1	2	yes	—
488	C₄	C₂×C₄×D₄×C₁₁	1	2	yes	—
489	C₄	C₂×C₄×D₄×C₁₁	1	2	yes	—
490	C₄	C₁₁×#568	1	4	yes	complemented
491	C₄	C₂³×D₄×C₁₁	1	1	yes	characteristic
492	C₄	C₂²×C₁₁×#41	1	1	yes	characteristic
493	C₂	—	2	2	no	—
494	C₂	—	2	2	no	—
495	C₂	—	2	2	no	—
496	C₂	—	4	8	no	—
497	C₂	C₂²×C₄×D₄×C₁₁	1	1	yes	characteristic
498	C₂	C₂×C₁₁×#568	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₁₁	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₁₁
Frattini, cosocle	C₂×C₄	C₂⁵×C₁₁
socle	C₂²×C₁₁	C₂⁴×C₄
prime radical	C₂×C₁₁×#532	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₁×#568	C₂	semidirect
3. C₁₁×#2935	C₂	semidirect
4. D₄×C₁₁×M₁₆	C₂	semidirect
5. C₁₁×#2932	C₂	semidirect
6. C₁₁×#2931	C₂	semidirect
7. C₂×C₁₁×#423	C₂	semidirect
8. C₁₁×#2879	C₂	semidirect
9. C₂×C₄×C₁₁×M₁₆	C₂	semidirect
12. C₂×C₁₁×#131	C₂²	semidirect
13. C₂×C₁₁×#131	C₂²	semidirect
30. C₁₁×#436	C₂²	semidirect
31. C₁₁×#435	C₂²	semidirect
32. C₈×D₄×C₁₁	C₂²	semidirect
34. C₁₁×#423	C₂²	semidirect
35. C₁₁×#423	C₂²	semidirect
36. C₂×C₁₁×C₄⋊C₈	C₂²	semidirect
37. C₁₁×#408	C₂²	semidirect
38. C₁₁×#408	C₂²	semidirect
41. C₄×C₁₁×M₁₆	C₂²	semidirect
42. C₂×C₁₁×#97	C₂²	semidirect
43. C₂×C₄×C₈×C₁₁	C₂²	semidirect
62. C₂×C₁₁×M₁₆	D₄	semidirect
107. #60144	C₁₁	direct (N × H)
154. C₁₁×M₁₆	C₂×D₄	semidirect
158. C₂×C₈×C₁₁	C₂×D₄	semidirect
176. C₂×#568	C₂×C₁₁	semidirect
178. #2935	C₂×C₁₁	semidirect
179. D₄×M₁₆	C₂×C₁₁	semidirect
180. #2932	C₂×C₁₁	semidirect
181. #2931	C₂×C₁₁	semidirect
182. C₂×#423	C₂×C₁₁	semidirect
183. #2879	C₂×C₁₁	semidirect
184. C₂×C₄×M₁₆	C₂×C₁₁	semidirect
234. C₂×#131	C₂²×C₁₁	semidirect
235. C₂×#131	C₂²×C₁₁	semidirect
252. #436	C₂²×C₁₁	semidirect
253. #435	C₂²×C₁₁	semidirect
254. C₈×D₄	C₂²×C₁₁	semidirect
256. #423	C₂²×C₁₁	semidirect
257. #423	C₂²×C₁₁	semidirect
258. C₂×C₄⋊C₈	C₂²×C₁₁	semidirect
259. #408	C₂²×C₁₁	semidirect
260. #408	C₂²×C₁₁	semidirect
263. C₄×M₁₆	C₂²×C₁₁	semidirect
264. C₂×#97	C₂²×C₁₁	semidirect
265. C₂×C₄×C₈	C₂²×C₁₁	semidirect
284. C₄×C₁₁	#568	semidirect
305. C₂×M₁₆	D₄×C₁₁	semidirect
402. M₁₆	C₂×D₄×C₁₁	semidirect
406. C₂×C₈	C₂×D₄×C₁₁	semidirect
424. C₁₁	#60144	direct (N × H)
490. C₄	C₁₁×#568	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₁×#568	2
C₂×C₁₁×#532	2
C₁₁×#2935	2
D₄×C₁₁×M₁₆	2
C₁₁×#2932	2
C₁₁×#2931	2
C₂×C₁₁×#423	2
C₁₁×#2879	2
C₂×C₄×C₁₁×M₁₆	2
#60144	11

Subgroups — C11×#60144 #14637337

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#60144 #14637337