Subgroups — C₂×C₁₁×#3137 #14637804

Order 2816.

2070 conjugacy classes of subgroups.

The subgroup lattice has 566 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₁×#544	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₁×#536	C₂	1	1	yes	maximal, characteristic
3	C₁₁×#3137	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₁₁×#491	C₂	1	2	yes	maximal, complemented
5	C₂×C₁₁×#489	C₂	1	2	yes	maximal, complemented
6	C₂×C₁₁×#488	C₂	1	2	yes	maximal, complemented
7	C₂×C₁₁×#487	C₂	1	2	yes	maximal, complemented
8	C₂×C₁₁×#417	C₂	1	1	yes	maximal, characteristic
9	C₂×C₁₁×#419	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₁₁×#416	C₂	1	1	yes	maximal, characteristic
11	C₂²×C₁₁×#103	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₁×#405	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂²×C₁₁×#41	C₂²	1	1	yes	characteristic
14	C₂³×Q₈×C₁₁	C₂²	1	1	yes	characteristic
15	C₂²×C₁₁×M₁₆	C₂²	1	1	yes	characteristic
16	C₂³×C₈×C₁₁	C₂²	1	1	yes	characteristic
17	C₁₁×#544	—	2	4	no	—
18	C₁₁×#544	C₂²	1	8	yes	complemented
19	C₁₁×#536	—	2	4	no	—
20	C₁₁×#536	C₂²	1	8	yes	—
21	C₂×C₁₁×C₄⋊Q₈	—	2	1	no	—
22	C₂×C₁₁×C₄⋊Q₈	C₂²	1	2	yes	—
23	C₂×C₁₁×C₄⋊Q₈	C₂²	1	2	yes	—
24	C₂×C₁₁×#125	—	2	1	no	—
25	C₂×C₁₁×#125	C₂²	1	2	yes	—
26	C₂×C₁₁×#124	C₂²	1	2	yes	—
27	C₂×C₁₁×#123	—	2	2	no	—
28	C₂×C₁₁×C₂²⋊Q₈	—	2	1	no	—
29	C₂×C₁₁×C₂²⋊Q₈	—	2	1	no	—
30	C₂×C₁₁×C₂²⋊Q₈	—	2	2	no	—
31	C₂×C₁₁×#117	C₂²	1	1	yes	characteristic
32	C₂×C₁₁×#117	C₂²	1	1	yes	characteristic
33	C₂²×C₁₁×C₄⋊C₄	C₂²	1	1	yes	characteristic
34	C₁₁×#491	C₂²	1	16	yes	complemented
35	C₁₁×#489	C₂²	1	16	yes	complemented
36	C₁₁×#488	C₂²	1	16	yes	complemented
37	C₁₁×#487	C₂²	1	16	yes	complemented
38	C₁₁×#419	C₂²	1	8	yes	complemented
39	C₁₁×#417	C₂²	1	8	yes	—
40	C₁₁×#416	C₂²	1	8	yes	—
41	C₂×C₁₁×#103	C₂²	1	2	yes	—
42	C₂×C₁₁×#103	C₂²	1	2	yes	—
43	C₂×C₁₁×#103	C₂²	1	1	yes	characteristic
44	C₂×C₁₁×#103	C₂²	1	1	yes	characteristic
45	C₂×C₁₁×#103	C₂²	1	2	yes	—
46	C₂×C₁₁×#103	C₂²	1	2	yes	—
47	C₂×C₁₁×#103	C₂²	1	2	yes	—
48	C₂×C₁₁×#103	C₂²	1	8	yes	complemented
49	C₂×C₁₁×#102	C₂²	1	1	yes	characteristic
50	C₂×C₁₁×#102	C₂²	1	1	yes	characteristic
51	C₂×C₁₁×#102	C₂²	1	2	yes	—
52	C₁₁×#405	C₂²	1	8	yes	complemented
53	C₂×C₁₁×#97	C₂²	1	2	yes	—
54	C₂×C₄×C₈×C₁₁	C₂²	1	2	yes	—
55	C₂×C₁₁×#41	—	2	2	no	—
56	C₂×C₁₁×#41	—	2	4	no	—
57	C₂×C₁₁×#41	—	2	4	no	—
58	C₂×C₁₁×#41	C₂³	1	4	yes	—
59	C₂²×Q₈×C₁₁	—	2	1	no	—
60	C₂²×Q₈×C₁₁	—	2	2	no	—
61	C₂²×Q₈×C₁₁	—	2	2	no	—
62	C₂²×Q₈×C₁₁	—	2	4	no	—
63	C₂²×Q₈×C₁₁	—	2	4	no	—
64	C₂²×Q₈×C₁₁	C₂³	1	2	yes	—
65	C₂²×Q₈×C₁₁	C₂³	1	1	yes	characteristic
66	C₂²×Q₈×C₁₁	C₂³	1	4	yes	—
67	C₂²×D₄×C₁₁	—	2	1	no	—
68	C₂²×D₄×C₁₁	C₂³	1	1	yes	characteristic
69	C₂³×C₄×C₁₁	—	2	1	no	—
70	C₂³×C₄×C₁₁	—	2	1	no	—
71	C₂³×C₄×C₁₁	—	2	1	no	—
72	C₂³×C₄×C₁₁	C₂³	1	1	yes	characteristic
73	C₂×C₁₁×M₁₆	—	2	4	no	—
74	C₂×C₁₁×M₁₆	C₂³	1	4	yes	—
75	C₂²×C₈×C₁₁	—	2	4	no	—
76	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
77	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
78	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
79	C₂²×C₈×C₁₁	C₂³	1	4	yes	—
80	C₁₁×C₄⋊Q₈	—	2	8	no	—
81	C₁₁×C₄⋊Q₈	—	2	4	no	—
82	C₁₁×C₄⋊Q₈	—	2	4	no	—
83	C₁₁×C₄⋊Q₈	C₂³	1	8	yes	—
84	C₁₁×C₄⋊Q₈	C₂³	1	8	yes	—
85	C₁₁×#125	—	2	8	no	—
86	C₁₁×#125	—	2	4	no	—
87	C₁₁×#125	C₂³	1	8	yes	—
88	C₁₁×#124	—	2	4	no	—
89	C₁₁×#124	C₂³	1	8	yes	—
90	C₁₁×#123	—	2	16	no	—
91	C₁₁×C₂²⋊Q₈	—	2	8	no	—
92	C₁₁×C₂²⋊Q₈	—	2	8	no	—
93	C₁₁×C₂²⋊Q₈	—	2	16	no	—
94	C₁₁×#117	—	2	2	no	—
95	C₁₁×#117	D₄	1	4	yes	—
96	C₁₁×#117	C₂³	1	4	yes	—
97	C₁₁×#117	C₂³	1	4	yes	—
98	C₂×C₁₁×C₄⋊C₄	—	2	1	no	—
99	C₂×C₁₁×C₄⋊C₄	—	2	2	no	—
100	C₂×C₁₁×C₄⋊C₄	—	2	2	no	—
101	C₂×C₁₁×C₄⋊C₄	—	2	2	no	—
102	C₂×C₁₁×C₄⋊C₄	—	2	2	no	—
103	C₂×C₁₁×C₄⋊C₄	—	2	2	no	—
104	C₂×C₁₁×C₄⋊C₄	—	2	2	no	—
105	C₂×C₁₁×C₄⋊C₄	D₄	1	1	yes	characteristic
106	C₂×C₁₁×C₄⋊C₄	D₄	1	1	yes	characteristic
107	C₂×C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
108	C₂×C₁₁×C₄⋊C₄	C₂³	1	4	yes	—
109	C₂×C₁₁×C₄⋊C₄	C₂³	1	1	yes	characteristic
110	C₂×C₁₁×C₄⋊C₄	C₂³	1	1	yes	characteristic
111	C₂×C₁₁×C₂²⋊C₄	—	2	1	no	—
112	C₂×C₁₁×C₂²⋊C₄	—	2	2	no	—
113	C₂×C₁₁×C₂²⋊C₄	—	2	2	no	—
114	C₂×C₁₁×C₂²⋊C₄	D₄	1	2	yes	—
115	C₂×C₄²×C₁₁	—	2	1	no	—
116	C₂×C₄²×C₁₁	C₂³	1	2	yes	—
117	C₁₁×#103	C₂³	1	8	yes	—
118	C₁₁×#103	C₂³	1	8	yes	—
119	C₁₁×#103	C₂³	1	4	yes	—
120	C₁₁×#103	C₂³	1	8	yes	—
121	C₁₁×#103	C₂³	1	8	yes	—
122	C₁₁×#103	C₂³	1	8	yes	—
123	C₁₁×#103	C₂³	1	4	yes	—
124	C₁₁×#102	C₂³	1	4	yes	—
125	C₁₁×#102	C₂³	1	8	yes	—
126	C₁₁×#102	C₂³	1	4	yes	—
127	C₁₁×#97	C₂³	1	8	yes	—
128	C₄×C₈×C₁₁	C₂³	1	8	yes	—
129	C₂×#3137	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
130	C₂⁴×C₁₁	—	2	1	no	—
131	C₂⁴×C₁₁	C₂×D₄	1	1	yes	characteristic
132	C₁₁×#41	—	2	8	no	—
133	C₁₁×#41	—	2	8	no	—
134	C₁₁×#41	—	4	8	no	—
135	C₂×Q₈×C₁₁	—	2	4	no	—
136	C₂×Q₈×C₁₁	—	2	2	no	—
137	C₂×Q₈×C₁₁	—	2	1	no	—
138	C₂×Q₈×C₁₁	—	2	8	no	—
139	C₂×Q₈×C₁₁	—	2	4	no	—
140	C₂×Q₈×C₁₁	—	2	4	no	—
141	C₂×Q₈×C₁₁	—	2	8	no	—
142	C₂×Q₈×C₁₁	—	2	8	no	—
143	C₂×Q₈×C₁₁	—	2	2	no	—
144	C₂×Q₈×C₁₁	—	2	2	no	—
145	C₂×Q₈×C₁₁	—	4	4	no	—
146	C₂×Q₈×C₁₁	—	4	8	no	—
147	C₂×Q₈×C₁₁	—	8	4	no	—
148	C₂×Q₈×C₁₁	C₂⁴	1	4	yes	—
149	C₂×Q₈×C₁₁	C₂⁴	1	2	yes	—
150	C₂×D₄×C₁₁	—	2	4	no	—
151	C₂×D₄×C₁₁	—	2	1	no	—
152	C₂×D₄×C₁₁	—	2	2	no	—
153	C₂×D₄×C₁₁	—	2	2	no	—
154	C₂×D₄×C₁₁	—	4	4	no	—
155	C₂×D₄×C₁₁	C₂⁴	1	2	yes	—
156	C₂²×C₄×C₁₁	—	2	4	no	—
157	C₂²×C₄×C₁₁	—	2	1	no	—
158	C₂²×C₄×C₁₁	—	2	1	no	—
159	C₂²×C₄×C₁₁	—	2	2	no	—
160	C₂²×C₄×C₁₁	—	2	2	no	—
161	C₂²×C₄×C₁₁	—	2	1	no	—
162	C₂²×C₄×C₁₁	—	2	4	no	—
163	C₂²×C₄×C₁₁	—	2	4	no	—
164	C₂²×C₄×C₁₁	—	4	4	no	—
165	C₂²×C₄×C₁₁	—	4	4	no	—
166	C₂²×C₄×C₁₁	—	8	2	no	—
167	C₂²×C₄×C₁₁	C₂×D₄	1	2	yes	—
168	C₂²×C₄×C₁₁	C₂×D₄	1	2	yes	—
169	C₂²×C₄×C₁₁	C₂×D₄	1	2	yes	—
170	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
171	C₂²×C₄×C₁₁	#41	1	4	yes	—
172	C₂²×C₄×C₁₁	#41	1	4	yes	—
173	C₂²×C₄×C₁₁	C₂⁴	1	2	yes	—
174	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
175	C₁₁×M₁₆	—	2	8	no	—
176	C₂×C₈×C₁₁	—	2	2	no	—
177	C₂×C₈×C₁₁	—	2	2	no	—
178	C₂×C₈×C₁₁	—	2	8	no	—
179	C₂×C₈×C₁₁	—	2	4	no	—
180	C₂×C₈×C₁₁	C₂⁴	1	2	yes	—
181	C₂×C₈×C₁₁	C₂⁴	1	4	yes	—
182	C₂×C₈×C₁₁	C₂⁴	1	2	yes	—
183	C₁₁×C₄⋊C₄	—	2	4	no	—
184	C₁₁×C₄⋊C₄	—	2	2	no	—
185	C₁₁×C₄⋊C₄	—	2	8	no	—
186	C₁₁×C₄⋊C₄	—	2	8	no	—
187	C₁₁×C₄⋊C₄	—	2	8	no	—
188	C₁₁×C₄⋊C₄	—	2	8	no	—
189	C₁₁×C₄⋊C₄	—	2	8	no	—
190	C₁₁×C₄⋊C₄	—	2	1	no	—
191	C₁₁×C₄⋊C₄	—	2	1	no	—
192	C₁₁×C₄⋊C₄	C₂×D₄	1	4	yes	—
193	C₁₁×C₄⋊C₄	C₂×D₄	1	4	yes	—
194	C₁₁×C₄⋊C₄	C₂⁴	1	4	yes	—
195	C₁₁×C₄⋊C₄	C₂⁴	1	2	yes	—
196	C₁₁×C₄⋊C₄	C₂⁴	1	2	yes	—
197	C₁₁×C₂²⋊C₄	—	2	4	no	—
198	C₁₁×C₂²⋊C₄	—	2	8	no	—
199	C₁₁×C₂²⋊C₄	—	2	8	no	—
200	C₁₁×C₂²⋊C₄	C₂×D₄	1	8	yes	—
201	C₄²×C₁₁	—	2	4	no	—
202	C₄²×C₁₁	C₂×D₄	1	4	yes	—
203	C₄²×C₁₁	C₂⁴	1	4	yes	—
204	C₂×#544	C₂×C₁₁	1	1	yes	characteristic, complemented
205	C₂×#536	C₂×C₁₁	1	1	yes	characteristic
206	#3137	C₂×C₁₁	1	16	yes	direct product factor
207	C₂×#491	C₂×C₁₁	1	2	yes	complemented
208	C₂×#489	C₂×C₁₁	1	2	yes	complemented
209	C₂×#488	C₂×C₁₁	1	2	yes	complemented
210	C₂×#487	C₂×C₁₁	1	2	yes	complemented
211	C₂×#417	C₂×C₁₁	1	1	yes	characteristic
212	C₂×#419	C₂×C₁₁	1	1	yes	characteristic, complemented
213	C₂×#416	C₂×C₁₁	1	1	yes	characteristic
214	C₂²×#103	C₂×C₁₁	1	1	yes	characteristic, complemented
215	C₂×#405	C₂×C₁₁	1	1	yes	characteristic, complemented
216	C₂³×C₁₁	—	2	2	no	—
217	C₂³×C₁₁	—	2	2	no	—
218	C₂³×C₁₁	—	2	2	no	—
219	C₂³×C₁₁	—	4	2	no	—
220	C₂³×C₁₁	—	4	2	no	—
221	C₂³×C₁₁	—	4	2	no	—
222	C₂³×C₁₁	#124	1	4	yes	—
223	C₂³×C₁₁	C₂²×D₄	1	2	yes	—
224	C₂³×C₁₁	C₂²×D₄	1	1	yes	characteristic
225	Q₈×C₁₁	—	2	4	no	—
226	Q₈×C₁₁	—	2	4	no	—
227	Q₈×C₁₁	—	2	2	no	—
228	Q₈×C₁₁	—	2	2	no	—
229	Q₈×C₁₁	—	4	8	no	—
230	Q₈×C₁₁	—	4	4	no	—
231	Q₈×C₁₁	—	4	2	no	—
232	Q₈×C₁₁	—	8	8	no	—
233	D₄×C₁₁	—	2	2	no	—
234	D₄×C₁₁	—	2	2	no	—
235	D₄×C₁₁	—	4	8	no	—
236	D₄×C₁₁	—	4	2	no	—
237	C₂×C₄×C₁₁	—	2	4	no	—
238	C₂×C₄×C₁₁	—	2	4	no	—
239	C₂×C₄×C₁₁	—	2	2	no	—
240	C₂×C₄×C₁₁	—	2	2	no	—
241	C₂×C₄×C₁₁	—	2	4	no	—
242	C₂×C₄×C₁₁	—	2	4	no	—
243	C₂×C₄×C₁₁	—	2	2	no	—
244	C₂×C₄×C₁₁	—	4	2	no	—
245	C₂×C₄×C₁₁	—	4	8	no	—
246	C₂×C₄×C₁₁	—	4	4	no	—
247	C₂×C₄×C₁₁	—	4	4	no	—
248	C₂×C₄×C₁₁	—	4	2	no	—
249	C₂×C₄×C₁₁	—	4	2	no	—
250	C₂×C₄×C₁₁	—	4	8	no	—
251	C₂×C₄×C₁₁	—	8	4	no	—
252	C₂×C₄×C₁₁	#124	1	4	yes	—
253	C₂×C₄×C₁₁	#124	1	8	yes	—
254	C₂×C₄×C₁₁	C₂²×D₄	1	4	yes	—
255	C₂×C₄×C₁₁	C₂²×D₄	1	4	yes	—
256	C₂×C₄×C₁₁	C₂²×D₄	1	2	yes	—
257	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
258	C₂×C₄×C₁₁	C₂×#41	1	2	yes	—
259	C₂×C₄×C₁₁	C₂×#41	1	2	yes	—
260	C₂×C₄×C₁₁	C₂×#41	1	4	yes	—
261	C₂×C₄×C₁₁	C₂×#41	1	4	yes	—
262	C₂×C₄×C₁₁	C₂⁵	1	1	yes	characteristic
263	C₈×C₁₁	—	2	2	no	—
264	C₈×C₁₁	—	2	2	no	—
265	C₈×C₁₁	—	2	4	no	—
266	C₂²×#41	C₂²×C₁₁	1	1	yes	characteristic
267	C₂³×Q₈	C₂²×C₁₁	1	1	yes	characteristic
268	C₂²×M₁₆	C₂²×C₁₁	1	1	yes	characteristic
269	C₂³×C₈	C₂²×C₁₁	1	1	yes	characteristic
270	#544	—	2	4	no	—
271	#544	C₂²×C₁₁	1	8	yes	complemented
272	#536	—	2	4	no	—
273	#536	C₂²×C₁₁	1	8	yes	—
274	C₂×C₄⋊Q₈	—	2	1	no	—
275	C₂×C₄⋊Q₈	C₂²×C₁₁	1	2	yes	—
276	C₂×C₄⋊Q₈	C₂²×C₁₁	1	2	yes	—
277	C₂×#125	—	2	1	no	—
278	C₂×#125	C₂²×C₁₁	1	2	yes	—
279	C₂×#124	C₂²×C₁₁	1	2	yes	—
280	C₂×#123	—	2	2	no	—
281	C₂×C₂²⋊Q₈	—	2	1	no	—
282	C₂×C₂²⋊Q₈	—	2	1	no	—
283	C₂×C₂²⋊Q₈	—	2	2	no	—
284	C₂×#117	C₂²×C₁₁	1	1	yes	characteristic
285	C₂×#117	C₂²×C₁₁	1	1	yes	characteristic
286	C₂²×C₄⋊C₄	C₂²×C₁₁	1	1	yes	characteristic
287	#491	C₂²×C₁₁	1	16	yes	complemented
288	#489	C₂²×C₁₁	1	16	yes	complemented
289	#488	C₂²×C₁₁	1	16	yes	complemented
290	#487	C₂²×C₁₁	1	16	yes	complemented
291	#419	C₂²×C₁₁	1	8	yes	complemented
292	#417	C₂²×C₁₁	1	8	yes	—
293	#416	C₂²×C₁₁	1	8	yes	—
294	C₂×#103	C₂²×C₁₁	1	1	yes	characteristic
295	C₂×#103	C₂²×C₁₁	1	2	yes	—
296	C₂×#103	C₂²×C₁₁	1	2	yes	—
297	C₂×#103	C₂²×C₁₁	1	2	yes	—
298	C₂×#103	C₂²×C₁₁	1	2	yes	—
299	C₂×#103	C₂²×C₁₁	1	2	yes	—
300	C₂×#103	C₂²×C₁₁	1	1	yes	characteristic
301	C₂×#103	C₂²×C₁₁	1	8	yes	complemented
302	C₂×#102	C₂²×C₁₁	1	1	yes	characteristic
303	C₂×#102	C₂²×C₁₁	1	2	yes	—
304	C₂×#102	C₂²×C₁₁	1	1	yes	characteristic
305	#405	C₂²×C₁₁	1	8	yes	complemented
306	C₂×#97	C₂²×C₁₁	1	2	yes	—
307	C₂×C₄×C₈	C₂²×C₁₁	1	2	yes	—
308	C₂²×C₁₁	—	2	8	no	—
309	C₂²×C₁₁	—	2	2	no	—
310	C₂²×C₁₁	—	2	2	no	—
311	C₂²×C₁₁	—	4	2	no	—
312	C₂²×C₁₁	—	4	2	no	—
313	C₂²×C₁₁	—	4	2	no	—
314	C₂²×C₁₁	—	8	4	no	—
315	C₂²×C₁₁	C₂×#124	1	4	yes	—
316	C₂²×C₁₁	C₂×#124	1	2	yes	—
317	C₂²×C₁₁	#577	1	2	yes	—
318	C₂²×C₁₁	#578	1	2	yes	—
319	C₂²×C₁₁	C₂³×D₄	1	1	yes	characteristic
320	C₄×C₁₁	—	2	4	no	—
321	C₄×C₁₁	—	2	4	no	—
322	C₄×C₁₁	—	4	2	no	—
323	C₄×C₁₁	—	4	4	no	—
324	C₄×C₁₁	—	4	4	no	—
325	C₄×C₁₁	—	4	2	no	—
326	C₄×C₁₁	—	4	2	no	—
327	C₄×C₁₁	C₂×#124	1	4	yes	—
328	C₄×C₁₁	C₂×#124	1	2	yes	—
329	C₄×C₁₁	C₂²×#41	1	1	yes	characteristic
330	C₄×C₁₁	C₂²×#41	1	1	yes	characteristic
331	C₂×#41	—	2	2	no	—
332	C₂×#41	—	2	4	no	—
333	C₂×#41	—	2	4	no	—
334	C₂×#41	C₂³×C₁₁	1	4	yes	—
335	C₂²×Q₈	—	2	1	no	—
336	C₂²×Q₈	—	2	2	no	—
337	C₂²×Q₈	—	2	2	no	—
338	C₂²×Q₈	—	2	4	no	—
339	C₂²×Q₈	—	2	4	no	—
340	C₂²×Q₈	C₂³×C₁₁	1	2	yes	—
341	C₂²×Q₈	C₂³×C₁₁	1	1	yes	characteristic
342	C₂²×Q₈	C₂³×C₁₁	1	4	yes	—
343	C₂²×D₄	—	2	1	no	—
344	C₂²×D₄	C₂³×C₁₁	1	1	yes	characteristic
345	C₂³×C₄	—	2	1	no	—
346	C₂³×C₄	—	2	1	no	—
347	C₂³×C₄	—	2	1	no	—
348	C₂³×C₄	C₂³×C₁₁	1	1	yes	characteristic
349	C₂×M₁₆	—	2	4	no	—
350	C₂×M₁₆	C₂³×C₁₁	1	4	yes	—
351	C₂²×C₈	—	2	4	no	—
352	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
353	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
354	C₂²×C₈	C₂³×C₁₁	1	4	yes	—
355	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
356	C₄⋊Q₈	—	2	8	no	—
357	C₄⋊Q₈	—	2	4	no	—
358	C₄⋊Q₈	—	2	4	no	—
359	C₄⋊Q₈	C₂³×C₁₁	1	8	yes	—
360	C₄⋊Q₈	C₂³×C₁₁	1	8	yes	—
361	#125	—	2	8	no	—
362	#125	—	2	4	no	—
363	#125	C₂³×C₁₁	1	8	yes	—
364	#124	—	2	4	no	—
365	#124	C₂³×C₁₁	1	8	yes	—
366	#123	—	2	16	no	—
367	C₂²⋊Q₈	—	2	8	no	—
368	C₂²⋊Q₈	—	2	8	no	—
369	C₂²⋊Q₈	—	2	16	no	—
370	#117	—	2	2	no	—
371	#117	D₄×C₁₁	1	4	yes	—
372	#117	C₂³×C₁₁	1	4	yes	—
373	#117	C₂³×C₁₁	1	4	yes	—
374	C₂×C₄⋊C₄	—	2	1	no	—
375	C₂×C₄⋊C₄	—	2	2	no	—
376	C₂×C₄⋊C₄	—	2	2	no	—
377	C₂×C₄⋊C₄	—	2	2	no	—
378	C₂×C₄⋊C₄	—	2	2	no	—
379	C₂×C₄⋊C₄	—	2	2	no	—
380	C₂×C₄⋊C₄	—	2	2	no	—
381	C₂×C₄⋊C₄	D₄×C₁₁	1	1	yes	characteristic
382	C₂×C₄⋊C₄	D₄×C₁₁	1	1	yes	characteristic
383	C₂×C₄⋊C₄	C₂³×C₁₁	1	2	yes	—
384	C₂×C₄⋊C₄	C₂³×C₁₁	1	4	yes	—
385	C₂×C₄⋊C₄	C₂³×C₁₁	1	1	yes	characteristic
386	C₂×C₄⋊C₄	C₂³×C₁₁	1	1	yes	characteristic
387	C₂×C₂²⋊C₄	—	2	1	no	—
388	C₂×C₂²⋊C₄	—	2	2	no	—
389	C₂×C₂²⋊C₄	—	2	2	no	—
390	C₂×C₂²⋊C₄	D₄×C₁₁	1	2	yes	—
391	C₂×C₄²	—	2	1	no	—
392	C₂×C₄²	C₂³×C₁₁	1	2	yes	—
393	#103	C₂³×C₁₁	1	8	yes	—
394	#103	C₂³×C₁₁	1	8	yes	—
395	#103	C₂³×C₁₁	1	4	yes	—
396	#103	C₂³×C₁₁	1	4	yes	—
397	#103	C₂³×C₁₁	1	8	yes	—
398	#103	C₂³×C₁₁	1	8	yes	—
399	#103	C₂³×C₁₁	1	8	yes	—
400	#102	C₂³×C₁₁	1	4	yes	—
401	#102	C₂³×C₁₁	1	4	yes	—
402	#102	C₂³×C₁₁	1	8	yes	—
403	#97	C₂³×C₁₁	1	8	yes	—
404	C₄×C₈	C₂³×C₁₁	1	8	yes	—
405	C₂×C₁₁	—	2	4	no	—
406	C₂×C₁₁	—	8	2	no	—
407	C₂×C₁₁	#3137	1	4	yes	direct product factor
408	C₂×C₁₁	C₂²×#124	1	1	yes	characteristic
409	C₂×C₁₁	C₂×#577	1	1	yes	characteristic
410	C₂×C₁₁	C₂×#578	1	1	yes	characteristic
411	C₂⁴	—	2	1	no	—
412	C₂⁴	C₂×D₄×C₁₁	1	1	yes	characteristic
413	#41	—	2	8	no	—
414	#41	—	2	8	no	—
415	#41	—	4	8	no	—
416	C₂×Q₈	—	2	4	no	—
417	C₂×Q₈	—	2	2	no	—
418	C₂×Q₈	—	2	1	no	—
419	C₂×Q₈	—	2	8	no	—
420	C₂×Q₈	—	2	4	no	—
421	C₂×Q₈	—	2	4	no	—
422	C₂×Q₈	—	2	8	no	—
423	C₂×Q₈	—	2	8	no	—
424	C₂×Q₈	—	2	2	no	—
425	C₂×Q₈	—	2	2	no	—
426	C₂×Q₈	—	4	4	no	—
427	C₂×Q₈	—	4	8	no	—
428	C₂×Q₈	—	8	4	no	—
429	C₂×Q₈	C₂⁴×C₁₁	1	4	yes	—
430	C₂×Q₈	C₂⁴×C₁₁	1	2	yes	—
431	C₂×D₄	—	2	4	no	—
432	C₂×D₄	—	2	1	no	—
433	C₂×D₄	—	2	2	no	—
434	C₂×D₄	—	2	2	no	—
435	C₂×D₄	—	4	4	no	—
436	C₂×D₄	C₂⁴×C₁₁	1	2	yes	—
437	C₂²×C₄	—	2	1	no	—
438	C₂²×C₄	—	2	1	no	—
439	C₂²×C₄	—	2	2	no	—
440	C₂²×C₄	—	2	2	no	—
441	C₂²×C₄	—	2	1	no	—
442	C₂²×C₄	—	2	4	no	—
443	C₂²×C₄	—	2	4	no	—
444	C₂²×C₄	—	2	4	no	—
445	C₂²×C₄	—	4	4	no	—
446	C₂²×C₄	—	4	4	no	—
447	C₂²×C₄	—	8	2	no	—
448	C₂²×C₄	C₂×D₄×C₁₁	1	2	yes	—
449	C₂²×C₄	C₂×D₄×C₁₁	1	2	yes	—
450	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
451	C₂²×C₄	C₂×D₄×C₁₁	1	2	yes	—
452	C₂²×C₄	C₁₁×#41	1	4	yes	—
453	C₂²×C₄	C₁₁×#41	1	4	yes	—
454	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
455	C₂²×C₄	C₂⁴×C₁₁	1	2	yes	—
456	M₁₆	—	2	8	no	—
457	C₂×C₈	—	2	2	no	—
458	C₂×C₈	—	2	2	no	—
459	C₂×C₈	—	2	8	no	—
460	C₂×C₈	—	2	4	no	—
461	C₂×C₈	C₂⁴×C₁₁	1	2	yes	—
462	C₂×C₈	C₂⁴×C₁₁	1	4	yes	—
463	C₂×C₈	C₂⁴×C₁₁	1	2	yes	—
464	C₄⋊C₄	—	2	4	no	—
465	C₄⋊C₄	—	2	2	no	—
466	C₄⋊C₄	—	2	8	no	—
467	C₄⋊C₄	—	2	8	no	—
468	C₄⋊C₄	—	2	8	no	—
469	C₄⋊C₄	—	2	8	no	—
470	C₄⋊C₄	—	2	8	no	—
471	C₄⋊C₄	—	2	1	no	—
472	C₄⋊C₄	—	2	1	no	—
473	C₄⋊C₄	C₂×D₄×C₁₁	1	4	yes	—
474	C₄⋊C₄	C₂×D₄×C₁₁	1	4	yes	—
475	C₄⋊C₄	C₂⁴×C₁₁	1	4	yes	—
476	C₄⋊C₄	C₂⁴×C₁₁	1	2	yes	—
477	C₄⋊C₄	C₂⁴×C₁₁	1	2	yes	—
478	C₂²⋊C₄	—	2	4	no	—
479	C₂²⋊C₄	—	2	8	no	—
480	C₂²⋊C₄	—	2	8	no	—
481	C₂²⋊C₄	C₂×D₄×C₁₁	1	8	yes	—
482	C₄²	—	2	4	no	—
483	C₄²	C₂×D₄×C₁₁	1	4	yes	—
484	C₄²	C₂⁴×C₁₁	1	4	yes	—
485	C₁₁	C₂×#3137	1	1	yes	characteristic, direct product factor, Sylow
486	C₂³	—	2	2	no	—
487	C₂³	—	2	2	no	—
488	C₂³	—	2	2	no	—
489	C₂³	—	4	2	no	—
490	C₂³	—	4	2	no	—
491	C₂³	—	4	2	no	—
492	C₂³	C₁₁×#124	1	4	yes	—
493	C₂³	C₂²×D₄×C₁₁	1	2	yes	—
494	C₂³	C₂²×D₄×C₁₁	1	1	yes	characteristic
495	Q₈	—	2	4	no	—
496	Q₈	—	2	4	no	—
497	Q₈	—	2	2	no	—
498	Q₈	—	2	2	no	—
499	Q₈	—	4	8	no	—
500	Q₈	—	4	4	no	—
501	Q₈	—	4	2	no	—
502	Q₈	—	8	8	no	—
503	D₄	—	2	2	no	—
504	D₄	—	2	2	no	—
505	D₄	—	4	8	no	—
506	D₄	—	4	2	no	—
507	C₂×C₄	—	2	4	no	—
508	C₂×C₄	—	2	4	no	—
509	C₂×C₄	—	2	2	no	—
510	C₂×C₄	—	2	2	no	—
511	C₂×C₄	—	2	4	no	—
512	C₂×C₄	—	2	4	no	—
513	C₂×C₄	—	2	2	no	—
514	C₂×C₄	—	4	2	no	—
515	C₂×C₄	—	4	8	no	—
516	C₂×C₄	—	4	4	no	—
517	C₂×C₄	—	4	4	no	—
518	C₂×C₄	—	4	2	no	—
519	C₂×C₄	—	4	2	no	—
520	C₂×C₄	—	4	8	no	—
521	C₂×C₄	—	8	4	no	—
522	C₂×C₄	C₁₁×#124	1	4	yes	—
523	C₂×C₄	C₁₁×#124	1	8	yes	—
524	C₂×C₄	C₂²×D₄×C₁₁	1	4	yes	—
525	C₂×C₄	C₂²×D₄×C₁₁	1	4	yes	—
526	C₂×C₄	C₂²×D₄×C₁₁	1	2	yes	—
527	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
528	C₂×C₄	C₂×C₁₁×#41	1	2	yes	—
529	C₂×C₄	C₂×C₁₁×#41	1	2	yes	—
530	C₂×C₄	C₂×C₁₁×#41	1	4	yes	—
531	C₂×C₄	C₂×C₁₁×#41	1	4	yes	—
532	C₂×C₄	C₂⁵×C₁₁	1	1	yes	characteristic
533	C₈	—	2	2	no	—
534	C₈	—	2	2	no	—
535	C₈	—	2	4	no	—
536	C₂²	—	2	2	no	—
537	C₂²	—	2	2	no	—
538	C₂²	—	2	8	no	—
539	C₂²	—	4	2	no	—
540	C₂²	—	4	2	no	—
541	C₂²	—	4	2	no	—
542	C₂²	—	8	4	no	—
543	C₂²	C₂×C₁₁×#124	1	4	yes	—
544	C₂²	C₂×C₁₁×#124	1	2	yes	—
545	C₂²	C₁₁×#577	1	2	yes	—
546	C₂²	C₁₁×#578	1	2	yes	—
547	C₂²	C₂³×D₄×C₁₁	1	1	yes	characteristic
548	C₄	—	2	4	no	—
549	C₄	—	2	4	no	—
550	C₄	—	4	2	no	—
551	C₄	—	4	4	no	—
552	C₄	—	4	4	no	—
553	C₄	—	4	2	no	—
554	C₄	—	4	2	no	—
555	C₄	C₂×C₁₁×#124	1	4	yes	—
556	C₄	C₂×C₁₁×#124	1	2	yes	—
557	C₄	C₂²×C₁₁×#41	1	1	yes	characteristic
558	C₄	C₂²×C₁₁×#41	1	1	yes	characteristic
559	C₂	—	2	4	no	—
560	C₂	—	8	2	no	—
561	C₂	C₁₁×#3137	1	4	yes	direct product factor
562	C₂	C₂²×C₁₁×#124	1	1	yes	characteristic
563	C₂	C₂×C₁₁×#577	1	1	yes	characteristic
564	C₂	C₂×C₁₁×#578	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₁	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₁
prime radical	C₂²×C₁₁×#41	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₁ ◁ C₂×C₁₁×#117 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₁×#544	C₂	semidirect
3. C₁₁×#3137	C₂	direct (N × H)
4. C₂×C₁₁×#491	C₂	semidirect
5. C₂×C₁₁×#489	C₂	semidirect
6. C₂×C₁₁×#488	C₂	semidirect
7. C₂×C₁₁×#487	C₂	semidirect
9. C₂×C₁₁×#419	C₂	semidirect
11. C₂²×C₁₁×#103	C₂	semidirect
12. C₂×C₁₁×#405	C₂	semidirect
18. C₁₁×#544	C₂²	semidirect
34. C₁₁×#491	C₂²	semidirect
35. C₁₁×#489	C₂²	semidirect
36. C₁₁×#488	C₂²	semidirect
37. C₁₁×#487	C₂²	semidirect
38. C₁₁×#419	C₂²	semidirect
48. C₂×C₁₁×#103	C₂²	semidirect
52. C₁₁×#405	C₂²	semidirect
129. C₂×#3137	C₁₁	direct (N × H)
204. C₂×#544	C₂×C₁₁	semidirect
206. #3137	C₂×C₁₁	direct (N × H)
207. C₂×#491	C₂×C₁₁	semidirect
208. C₂×#489	C₂×C₁₁	semidirect
209. C₂×#488	C₂×C₁₁	semidirect
210. C₂×#487	C₂×C₁₁	semidirect
212. C₂×#419	C₂×C₁₁	semidirect
214. C₂²×#103	C₂×C₁₁	semidirect
215. C₂×#405	C₂×C₁₁	semidirect
271. #544	C₂²×C₁₁	semidirect
287. #491	C₂²×C₁₁	semidirect
288. #489	C₂²×C₁₁	semidirect
289. #488	C₂²×C₁₁	semidirect
290. #487	C₂²×C₁₁	semidirect
291. #419	C₂²×C₁₁	semidirect
301. C₂×#103	C₂²×C₁₁	semidirect
305. #405	C₂²×C₁₁	semidirect
407. C₂×C₁₁	#3137	direct (N × H)
485. C₁₁	C₂×#3137	direct (N × H)
561. C₂	C₁₁×#3137	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×#544	2
C₂×C₁₁×#536	2
C₁₁×#3137	2
C₂×C₁₁×#491	2
C₂×C₁₁×#489	2
C₂×C₁₁×#488	2
C₂×C₁₁×#487	2
C₂×C₁₁×#417	2
C₂×C₁₁×#419	2
C₂×C₁₁×#416	2
C₂²×C₁₁×#103	2
C₂×C₁₁×#405	2
C₂×#3137	11

Subgroups — C2×C11×#3137 #14637804

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₁×#3137 #14637804