Subgroups — C₁₁×#60717 #14637910

Order 2816.

1870 conjugacy classes of subgroups.

The subgroup lattice has 518 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×#3512	C₂	1	2	yes	maximal, complemented
2	C₁₁×#3183	C₂	1	4	yes	maximal, complemented
3	C₁₁×#3177	C₂	1	2	yes	maximal, complemented
4	C₁₁×#3176	C₂	1	2	yes	maximal, complemented
5	C₁₁×#3174	C₂	1	4	yes	maximal, complemented
6	C₁₁×#3168	C₂	1	4	yes	maximal, complemented
7	C₂×C₁₁×#499	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₁×#3147	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₁×#3142	C₂	1	2	yes	maximal, complemented
10	C₁₁×#3061	C₂	1	2	yes	maximal, complemented
11	C₁₁×#3060	C₂	1	2	yes	maximal, complemented
12	C₁₁×#2952	C₂	1	2	yes	maximal, complemented
13	C₁₁×#2951	C₂	1	2	yes	maximal, complemented
14	C₄×C₁₁×#131	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₁₁×#135	C₂²	1	2	yes	—
16	C₂×C₁₁×#135	C₂²	1	2	yes	—
17	C₂×C₁₁×#131	C₂²	1	1	yes	characteristic
18	C₂×C₁₁×#131	C₂²	1	1	yes	characteristic
19	C₁₁×#553	—	2	8	no	—
20	C₁₁×#553	—	2	4	no	—
21	C₁₁×#552	—	2	4	no	—
22	C₁₁×#541	C₂²	1	4	yes	—
23	C₁₁×#540	C₂²	1	4	yes	—
24	C₁₁×#537	C₂²	1	4	yes	—
25	C₁₁×#532	C₂²	1	2	yes	—
26	C₁₁×#529	C₂²	1	8	yes	—
27	C₂×C₁₁×#125	C₂²	1	2	yes	—
28	C₁₁×#520	C₂²	1	4	yes	—
29	C₄×C₁₁×#41	C₂²	1	1	yes	characteristic
30	C₁₁×#499	C₂²	1	2	yes	—
31	C₁₁×#499	C₂²	1	2	yes	—
32	C₁₁×#499	C₂²	1	2	yes	—
33	C₁₁×#499	C₂²	1	2	yes	—
34	C₁₁×#495	C₂²	1	2	yes	—
35	C₁₁×#495	C₂²	1	2	yes	—
36	C₁₁×#494	C₂²	1	1	yes	characteristic
37	C₁₁×#493	C₂²	1	1	yes	characteristic
38	C₁₁×#492	C₂²	1	2	yes	—
39	C₁₁×#491	C₂²	1	4	yes	—
40	C₁₁×#490	C₂²	1	4	yes	—
41	C₁₁×#488	C₂²	1	8	yes	—
42	C₁₁×#470	C₂²	1	4	yes	—
43	C₁₁×#469	C₂²	1	4	yes	—
44	C₁₁×#468	C₂²	1	8	yes	—
45	C₁₁×#467	C₂²	1	4	yes	—
46	C₁₁×#466	C₂²	1	4	yes	—
47	C₁₁×#465	C₂²	1	8	yes	—
48	C₁₁×#442	C₂²	1	4	yes	—
49	C₁₁×#441	C₂²	1	4	yes	—
50	C₁₁×#440	C₂²	1	8	yes	—
51	C₄×C₁₁×Q₁₆	C₂²	1	4	yes	—
52	C₄×C₁₁×SD₁₆	C₂²	1	8	yes	—
53	C₄×C₁₁×D₈	C₂²	1	4	yes	—
54	C₂×C₁₁×#107	C₂²	1	2	yes	—
55	C₂×C₁₁×#106	C₂²	1	2	yes	—
56	C₁₁×#417	C₂²	1	4	yes	—
57	C₁₁×#417	C₂²	1	4	yes	—
58	C₁₁×#405	C₂²	1	2	yes	—
59	C₁₁×#405	C₂²	1	2	yes	—
60	C₁₁×#405	C₂²	1	1	yes	characteristic
61	C₁₁×#405	C₂²	1	1	yes	characteristic
62	C₄×C₁₁×M₁₆	C₂²	1	2	yes	—
63	C₄×C₁₁×M₁₆	C₂²	1	1	yes	characteristic
64	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
65	C₂×C₄×C₈×C₁₁	C₂²	1	2	yes	—
66	C₂×C₁₁×#41	C₂³	1	4	yes	—
67	C₂×C₁₁×#41	C₂³	1	1	yes	characteristic
68	C₁₁×#135	—	2	8	no	—
69	C₁₁×#135	—	2	8	no	—
70	C₂×C₁₁×Q₁₆	C₂³	1	2	yes	—
71	C₂×C₁₁×Q₁₆	C₂³	1	2	yes	—
72	C₂×C₁₁×SD₁₆	C₂³	1	4	yes	—
73	C₂×C₁₁×SD₁₆	C₂³	1	4	yes	—
74	C₂×C₁₁×D₈	C₂³	1	2	yes	—
75	C₂×C₁₁×D₈	C₂³	1	2	yes	—
76	C₁₁×#131	—	2	4	no	—
77	C₁₁×#131	—	2	4	no	—
78	C₂×C₁₁×M₁₆	C₂³	1	1	yes	characteristic
79	C₂×C₁₁×M₁₆	C₂³	1	1	yes	characteristic
80	C₂×C₁₁×M₁₆	C₂³	1	2	yes	—
81	C₂×C₁₁×M₁₆	C₂³	1	2	yes	—
82	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
83	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
84	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
85	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
86	C₁₁×C₄⋊Q₈	C₂³	1	2	yes	—
87	C₁₁×#127	C₂³	1	2	yes	—
88	C₁₁×#126	—	2	8	no	—
89	C₁₁×#126	—	2	8	no	—
90	C₁₁×#125	—	2	8	no	—
91	C₁₁×#125	—	2	4	no	—
92	C₁₁×#125	C₂³	1	4	yes	—
93	C₁₁×#125	C₂³	1	4	yes	—
94	C₁₁×#124	C₂³	1	4	yes	—
95	C₁₁×#123	—	2	8	no	—
96	C₁₁×#123	—	2	8	no	—
97	C₁₁×C₂²⋊Q₈	—	2	4	no	—
98	C₁₁×C₂²⋊Q₈	C₂³	1	8	yes	—
99	C₁₁×#121	—	2	4	no	—
100	C₁₁×#121	—	2	8	no	—
101	C₁₁×#121	—	2	4	no	—
102	C₁₁×#121	—	2	8	no	—
103	C₁₁×#121	C₂³	1	8	yes	—
104	C₄×Q₈×C₁₁	D₄	1	2	yes	—
105	C₄×Q₈×C₁₁	C₂³	1	8	yes	—
106	C₄×D₄×C₁₁	—	2	8	no	—
107	C₄×D₄×C₁₁	—	2	8	no	—
108	C₄×D₄×C₁₁	—	2	4	no	—
109	C₄×D₄×C₁₁	D₄	1	4	yes	—
110	C₄×D₄×C₁₁	D₄	1	2	yes	—
111	C₄×D₄×C₁₁	C₂³	1	8	yes	—
112	C₁₁×#117	—	2	4	no	—
113	C₁₁×#117	—	2	8	no	—
114	C₁₁×#117	C₂³	1	1	yes	characteristic
115	C₁₁×#117	C₂³	1	2	yes	—
116	C₂×C₁₁×C₄⋊C₄	—	2	4	no	—
117	C₂×C₁₁×C₄⋊C₄	—	2	4	no	—
118	C₂×C₁₁×C₄⋊C₄	C₂³	1	4	yes	—
119	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
120	C₂×C₄²×C₁₁	C₂³	1	2	yes	—
121	C₁₁×#107	C₂³	1	4	yes	—
122	C₁₁×#107	C₂³	1	4	yes	—
123	C₁₁×#106	C₂³	1	4	yes	—
124	C₁₁×#106	C₂³	1	4	yes	—
125	C₁₁×#103	C₂³	1	8	yes	—
126	C₁₁×#103	C₂³	1	8	yes	—
127	C₁₁×#102	C₂³	1	8	yes	—
128	C₁₁×#102	C₂³	1	8	yes	—
129	C₁₁×#97	C₂³	1	2	yes	—
130	C₁₁×#97	C₂³	1	2	yes	—
131	C₁₁×#97	C₂³	1	2	yes	—
132	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
133	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
134	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
135	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
136	C₄×C₈×C₁₁	C₂³	1	2	yes	—
137	C₄×C₈×C₁₁	C₂³	1	2	yes	—
138	C₄×C₈×C₁₁	C₂³	1	2	yes	—
139	#60717	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
140	C₁₁×#41	—	2	2	no	—
141	C₁₁×#41	—	2	2	no	—
142	C₁₁×#41	—	2	8	no	—
143	C₁₁×#41	—	2	8	no	—
144	C₂×Q₈×C₁₁	C₂×D₄	1	1	yes	characteristic
145	C₂×Q₈×C₁₁	C₂⁴	1	4	yes	—
146	C₂×D₄×C₁₁	—	2	4	no	—
147	C₂×D₄×C₁₁	—	2	8	no	—
148	C₂×D₄×C₁₁	—	2	4	no	—
149	C₂×D₄×C₁₁	C₂×D₄	1	2	yes	—
150	C₂×D₄×C₁₁	C₂×D₄	1	1	yes	characteristic
151	C₂×D₄×C₁₁	C₂⁴	1	4	yes	—
152	C₂²×C₄×C₁₁	—	2	4	no	—
153	C₂²×C₄×C₁₁	—	2	4	no	—
154	C₂²×C₄×C₁₁	—	2	8	no	—
155	C₂²×C₄×C₁₁	C₂×D₄	1	2	yes	—
156	C₂²×C₄×C₁₁	C₂×D₄	1	4	yes	—
157	C₂²×C₄×C₁₁	C₂⁴	1	2	yes	—
158	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
159	C₁₁×Q₁₆	—	2	4	no	—
160	C₁₁×Q₁₆	—	2	4	no	—
161	C₁₁×SD₁₆	—	2	8	no	—
162	C₁₁×SD₁₆	—	2	8	no	—
163	C₁₁×D₈	—	2	4	no	—
164	C₁₁×D₈	—	2	4	no	—
165	C₁₁×M₁₆	—	2	4	no	—
166	C₁₁×M₁₆	—	2	4	no	—
167	C₁₁×M₁₆	—	2	2	no	—
168	C₁₁×M₁₆	—	2	2	no	—
169	C₂×C₈×C₁₁	—	2	4	no	—
170	C₂×C₈×C₁₁	—	2	4	no	—
171	C₂×C₈×C₁₁	#41	1	4	yes	—
172	C₂×C₈×C₁₁	#41	1	4	yes	—
173	C₂×C₈×C₁₁	C₂⁴	1	2	yes	—
174	C₂×C₈×C₁₁	C₂⁴	1	2	yes	—
175	C₂×C₈×C₁₁	C₂⁴	1	1	yes	characteristic
176	C₂×C₈×C₁₁	C₂⁴	1	1	yes	characteristic
177	C₂×C₈×C₁₁	C₂⁴	1	1	yes	characteristic
178	C₂×C₈×C₁₁	C₂⁴	1	1	yes	characteristic
179	C₁₁×C₄⋊C₄	—	2	4	no	—
180	C₁₁×C₄⋊C₄	—	2	8	no	—
181	C₁₁×C₄⋊C₄	—	2	8	no	—
182	C₁₁×C₄⋊C₄	—	2	8	no	—
183	C₁₁×C₄⋊C₄	—	2	8	no	—
184	C₁₁×C₄⋊C₄	—	2	4	no	—
185	C₁₁×C₄⋊C₄	C₂×D₄	1	2	yes	—
186	C₁₁×C₄⋊C₄	C₂×D₄	1	4	yes	—
187	C₁₁×C₄⋊C₄	C₂⁴	1	8	yes	—
188	C₁₁×C₂²⋊C₄	—	2	8	no	—
189	C₁₁×C₂²⋊C₄	—	2	4	no	—
190	C₁₁×C₂²⋊C₄	—	2	8	no	—
191	C₁₁×C₂²⋊C₄	—	2	8	no	—
192	C₁₁×C₂²⋊C₄	—	2	4	no	—
193	C₁₁×C₂²⋊C₄	C₂×D₄	1	2	yes	—
194	C₁₁×C₂²⋊C₄	C₂×D₄	1	4	yes	—
195	C₄²×C₁₁	—	2	8	no	—
196	C₄²×C₁₁	C₂×D₄	1	4	yes	—
197	C₄²×C₁₁	C₂×D₄	1	2	yes	—
198	C₄²×C₁₁	C₂⁴	1	1	yes	characteristic
199	C₄²×C₁₁	C₂⁴	1	2	yes	—
200	C₄²×C₁₁	C₂⁴	1	1	yes	characteristic
201	#3512	C₂×C₁₁	1	2	yes	complemented
202	#3183	C₂×C₁₁	1	4	yes	complemented
203	#3177	C₂×C₁₁	1	2	yes	complemented
204	#3176	C₂×C₁₁	1	2	yes	complemented
205	#3174	C₂×C₁₁	1	4	yes	complemented
206	#3168	C₂×C₁₁	1	4	yes	complemented
207	C₂×#499	C₂×C₁₁	1	1	yes	characteristic, complemented
208	#3147	C₂×C₁₁	1	1	yes	characteristic, complemented
209	#3142	C₂×C₁₁	1	2	yes	complemented
210	#3061	C₂×C₁₁	1	2	yes	complemented
211	#3060	C₂×C₁₁	1	2	yes	complemented
212	#2952	C₂×C₁₁	1	2	yes	complemented
213	#2951	C₂×C₁₁	1	2	yes	complemented
214	C₄×#131	C₂×C₁₁	1	1	yes	characteristic, complemented
215	C₂³×C₁₁	—	2	4	no	—
216	C₂³×C₁₁	C₂²×D₄	1	2	yes	—
217	C₂³×C₁₁	C₂²×D₄	1	1	yes	characteristic
218	Q₈×C₁₁	—	2	2	no	—
219	Q₈×C₁₁	—	2	4	no	—
220	Q₈×C₁₁	—	2	4	no	—
221	D₄×C₁₁	—	2	4	no	—
222	D₄×C₁₁	—	2	2	no	—
223	D₄×C₁₁	—	2	4	no	—
224	D₄×C₁₁	—	2	4	no	—
225	D₄×C₁₁	—	4	8	no	—
226	D₄×C₁₁	—	8	4	no	—
227	D₄×C₁₁	—	8	8	no	—
228	C₂×C₄×C₁₁	—	2	2	no	—
229	C₂×C₄×C₁₁	—	2	2	no	—
230	C₂×C₄×C₁₁	—	2	4	no	—
231	C₂×C₄×C₁₁	—	2	8	no	—
232	C₂×C₄×C₁₁	—	4	4	no	—
233	C₂×C₄×C₁₁	—	4	2	no	—
234	C₂×C₄×C₁₁	—	4	8	no	—
235	C₂×C₄×C₁₁	—	8	8	no	—
236	C₂×C₄×C₁₁	—	8	4	no	—
237	C₂×C₄×C₁₁	C₂²×D₄	1	4	yes	—
238	C₂×C₄×C₁₁	C₂²×D₄	1	2	yes	—
239	C₂×C₄×C₁₁	C₂²×D₄	1	2	yes	—
240	C₂×C₄×C₁₁	C₂²×D₄	1	2	yes	—
241	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
242	C₂×C₄×C₁₁	C₂×#41	1	2	yes	—
243	C₂×C₄×C₁₁	C₂×#41	1	2	yes	—
244	C₂×C₄×C₁₁	C₂⁵	1	1	yes	characteristic
245	C₈×C₁₁	—	2	2	no	—
246	C₈×C₁₁	—	2	2	no	—
247	C₈×C₁₁	C₂×#41	1	2	yes	—
248	C₈×C₁₁	C₂×#41	1	2	yes	—
249	C₈×C₁₁	C₂×#41	1	2	yes	—
250	C₈×C₁₁	C₂×#41	1	2	yes	—
251	C₂×#135	C₂²×C₁₁	1	2	yes	—
252	C₂×#135	C₂²×C₁₁	1	2	yes	—
253	C₂×#131	C₂²×C₁₁	1	1	yes	characteristic
254	C₂×#131	C₂²×C₁₁	1	1	yes	characteristic
255	#553	—	2	8	no	—
256	#553	—	2	4	no	—
257	#552	—	2	4	no	—
258	#541	C₂²×C₁₁	1	4	yes	—
259	#540	C₂²×C₁₁	1	4	yes	—
260	#537	C₂²×C₁₁	1	4	yes	—
261	#532	C₂²×C₁₁	1	2	yes	—
262	#529	C₂²×C₁₁	1	8	yes	—
263	C₂×#125	C₂²×C₁₁	1	2	yes	—
264	#520	C₂²×C₁₁	1	4	yes	—
265	C₄×#41	C₂²×C₁₁	1	1	yes	characteristic
266	#499	C₂²×C₁₁	1	2	yes	—
267	#499	C₂²×C₁₁	1	2	yes	—
268	#499	C₂²×C₁₁	1	2	yes	—
269	#499	C₂²×C₁₁	1	2	yes	—
270	#495	C₂²×C₁₁	1	2	yes	—
271	#495	C₂²×C₁₁	1	2	yes	—
272	#494	C₂²×C₁₁	1	1	yes	characteristic
273	#493	C₂²×C₁₁	1	1	yes	characteristic
274	#492	C₂²×C₁₁	1	2	yes	—
275	#491	C₂²×C₁₁	1	4	yes	—
276	#490	C₂²×C₁₁	1	4	yes	—
277	#488	C₂²×C₁₁	1	8	yes	—
278	#470	C₂²×C₁₁	1	4	yes	—
279	#469	C₂²×C₁₁	1	4	yes	—
280	#468	C₂²×C₁₁	1	8	yes	—
281	#467	C₂²×C₁₁	1	4	yes	—
282	#466	C₂²×C₁₁	1	4	yes	—
283	#465	C₂²×C₁₁	1	8	yes	—
284	#442	C₂²×C₁₁	1	4	yes	—
285	#441	C₂²×C₁₁	1	4	yes	—
286	#440	C₂²×C₁₁	1	8	yes	—
287	C₄×Q₁₆	C₂²×C₁₁	1	4	yes	—
288	C₄×SD₁₆	C₂²×C₁₁	1	8	yes	—
289	C₄×D₈	C₂²×C₁₁	1	4	yes	—
290	C₂×#107	C₂²×C₁₁	1	2	yes	—
291	C₂×#106	C₂²×C₁₁	1	2	yes	—
292	#417	C₂²×C₁₁	1	4	yes	—
293	#417	C₂²×C₁₁	1	4	yes	—
294	#405	C₂²×C₁₁	1	2	yes	—
295	#405	C₂²×C₁₁	1	2	yes	—
296	#405	C₂²×C₁₁	1	1	yes	characteristic
297	#405	C₂²×C₁₁	1	1	yes	characteristic
298	C₄×M₁₆	C₂²×C₁₁	1	1	yes	characteristic
299	C₄×M₁₆	C₂²×C₁₁	1	2	yes	—
300	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
301	C₂×C₄×C₈	C₂²×C₁₁	1	2	yes	—
302	C₂²×C₁₁	—	2	2	no	—
303	C₂²×C₁₁	—	2	4	no	—
304	C₂²×C₁₁	—	2	2	no	—
305	C₂²×C₁₁	—	4	4	no	—
306	C₂²×C₁₁	—	4	4	no	—
307	C₂²×C₁₁	—	4	4	no	—
308	C₂²×C₁₁	#532	1	2	yes	—
309	C₂²×C₁₁	C₂³×D₄	1	1	yes	characteristic
310	C₄×C₁₁	—	2	2	no	—
311	C₄×C₁₁	—	2	4	no	—
312	C₄×C₁₁	—	2	2	no	—
313	C₄×C₁₁	—	2	2	no	—
314	C₄×C₁₁	—	4	8	no	—
315	C₄×C₁₁	—	4	4	no	—
316	C₄×C₁₁	#532	1	2	yes	—
317	C₄×C₁₁	C₂²×#41	1	1	yes	characteristic
318	C₄×C₁₁	C₂²×#41	1	1	yes	characteristic
319	C₂×#41	C₂³×C₁₁	1	4	yes	—
320	C₂×#41	C₂³×C₁₁	1	1	yes	characteristic
321	#135	—	2	8	no	—
322	#135	—	2	8	no	—
323	C₂×Q₁₆	C₂³×C₁₁	1	2	yes	—
324	C₂×Q₁₆	C₂³×C₁₁	1	2	yes	—
325	C₂×SD₁₆	C₂³×C₁₁	1	4	yes	—
326	C₂×SD₁₆	C₂³×C₁₁	1	4	yes	—
327	C₂×D₈	C₂³×C₁₁	1	2	yes	—
328	C₂×D₈	C₂³×C₁₁	1	2	yes	—
329	#131	—	2	4	no	—
330	#131	—	2	4	no	—
331	C₂×M₁₆	C₂³×C₁₁	1	1	yes	characteristic
332	C₂×M₁₆	C₂³×C₁₁	1	1	yes	characteristic
333	C₂×M₁₆	C₂³×C₁₁	1	2	yes	—
334	C₂×M₁₆	C₂³×C₁₁	1	2	yes	—
335	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
336	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
337	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
338	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
339	C₄⋊Q₈	C₂³×C₁₁	1	2	yes	—
340	#127	C₂³×C₁₁	1	2	yes	—
341	#126	—	2	8	no	—
342	#126	—	2	8	no	—
343	#125	—	2	8	no	—
344	#125	—	2	4	no	—
345	#125	C₂³×C₁₁	1	4	yes	—
346	#125	C₂³×C₁₁	1	4	yes	—
347	#124	C₂³×C₁₁	1	4	yes	—
348	#123	—	2	8	no	—
349	#123	—	2	8	no	—
350	C₂²⋊Q₈	—	2	4	no	—
351	C₂²⋊Q₈	C₂³×C₁₁	1	8	yes	—
352	#121	—	2	4	no	—
353	#121	—	2	8	no	—
354	#121	—	2	4	no	—
355	#121	—	2	8	no	—
356	#121	C₂³×C₁₁	1	8	yes	—
357	C₄×Q₈	D₄×C₁₁	1	2	yes	—
358	C₄×Q₈	C₂³×C₁₁	1	8	yes	—
359	C₄×D₄	—	2	8	no	—
360	C₄×D₄	—	2	8	no	—
361	C₄×D₄	—	2	4	no	—
362	C₄×D₄	D₄×C₁₁	1	4	yes	—
363	C₄×D₄	D₄×C₁₁	1	2	yes	—
364	C₄×D₄	C₂³×C₁₁	1	8	yes	—
365	#117	—	2	4	no	—
366	#117	—	2	8	no	—
367	#117	C₂³×C₁₁	1	1	yes	characteristic
368	#117	C₂³×C₁₁	1	2	yes	—
369	C₂×C₄⋊C₄	—	2	4	no	—
370	C₂×C₄⋊C₄	—	2	4	no	—
371	C₂×C₄⋊C₄	C₂³×C₁₁	1	4	yes	—
372	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
373	C₂×C₄²	C₂³×C₁₁	1	2	yes	—
374	#107	C₂³×C₁₁	1	4	yes	—
375	#107	C₂³×C₁₁	1	4	yes	—
376	#106	C₂³×C₁₁	1	4	yes	—
377	#106	C₂³×C₁₁	1	4	yes	—
378	#103	C₂³×C₁₁	1	8	yes	—
379	#103	C₂³×C₁₁	1	8	yes	—
380	#102	C₂³×C₁₁	1	8	yes	—
381	#102	C₂³×C₁₁	1	8	yes	—
382	#97	C₂³×C₁₁	1	2	yes	—
383	#97	C₂³×C₁₁	1	2	yes	—
384	#97	C₂³×C₁₁	1	2	yes	—
385	C₄×C₈	C₂³×C₁₁	1	1	yes	characteristic
386	C₄×C₈	C₂³×C₁₁	1	2	yes	—
387	C₄×C₈	C₂³×C₁₁	1	1	yes	characteristic
388	C₄×C₈	C₂³×C₁₁	1	2	yes	—
389	C₄×C₈	C₂³×C₁₁	1	2	yes	—
390	C₄×C₈	C₂³×C₁₁	1	1	yes	characteristic
391	C₄×C₈	C₂³×C₁₁	1	1	yes	characteristic
392	C₂×C₁₁	—	2	2	no	—
393	C₂×C₁₁	—	4	2	no	—
394	C₂×C₁₁	—	8	4	no	—
395	C₂×C₁₁	C₂×#532	1	1	yes	characteristic
396	C₂×C₁₁	#3584	1	2	yes	—
397	#41	—	2	2	no	—
398	#41	—	2	2	no	—
399	#41	—	2	8	no	—
400	#41	—	2	8	no	—
401	C₂×Q₈	C₂×D₄×C₁₁	1	1	yes	characteristic
402	C₂×Q₈	C₂⁴×C₁₁	1	4	yes	—
403	C₂×D₄	—	2	4	no	—
404	C₂×D₄	—	2	8	no	—
405	C₂×D₄	—	2	4	no	—
406	C₂×D₄	C₂×D₄×C₁₁	1	2	yes	—
407	C₂×D₄	C₂×D₄×C₁₁	1	1	yes	characteristic
408	C₂×D₄	C₂⁴×C₁₁	1	4	yes	—
409	C₂²×C₄	—	2	4	no	—
410	C₂²×C₄	—	2	4	no	—
411	C₂²×C₄	—	2	8	no	—
412	C₂²×C₄	C₂×D₄×C₁₁	1	2	yes	—
413	C₂²×C₄	C₂×D₄×C₁₁	1	4	yes	—
414	C₂²×C₄	C₂⁴×C₁₁	1	2	yes	—
415	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
416	Q₁₆	—	2	4	no	—
417	Q₁₆	—	2	4	no	—
418	SD₁₆	—	2	8	no	—
419	SD₁₆	—	2	8	no	—
420	D₈	—	2	4	no	—
421	D₈	—	2	4	no	—
422	M₁₆	—	2	2	no	—
423	M₁₆	—	2	2	no	—
424	M₁₆	—	2	4	no	—
425	M₁₆	—	2	4	no	—
426	C₂×C₈	—	2	4	no	—
427	C₂×C₈	—	2	4	no	—
428	C₂×C₈	C₁₁×#41	1	4	yes	—
429	C₂×C₈	C₁₁×#41	1	4	yes	—
430	C₂×C₈	C₂⁴×C₁₁	1	2	yes	—
431	C₂×C₈	C₂⁴×C₁₁	1	2	yes	—
432	C₂×C₈	C₂⁴×C₁₁	1	1	yes	characteristic
433	C₂×C₈	C₂⁴×C₁₁	1	1	yes	characteristic
434	C₂×C₈	C₂⁴×C₁₁	1	1	yes	characteristic
435	C₂×C₈	C₂⁴×C₁₁	1	1	yes	characteristic
436	C₄⋊C₄	—	2	4	no	—
437	C₄⋊C₄	—	2	8	no	—
438	C₄⋊C₄	—	2	8	no	—
439	C₄⋊C₄	—	2	8	no	—
440	C₄⋊C₄	—	2	8	no	—
441	C₄⋊C₄	—	2	4	no	—
442	C₄⋊C₄	C₂×D₄×C₁₁	1	2	yes	—
443	C₄⋊C₄	C₂×D₄×C₁₁	1	4	yes	—
444	C₄⋊C₄	C₂⁴×C₁₁	1	8	yes	—
445	C₂²⋊C₄	—	2	8	no	—
446	C₂²⋊C₄	—	2	4	no	—
447	C₂²⋊C₄	—	2	8	no	—
448	C₂²⋊C₄	—	2	8	no	—
449	C₂²⋊C₄	—	2	4	no	—
450	C₂²⋊C₄	C₂×D₄×C₁₁	1	2	yes	—
451	C₂²⋊C₄	C₂×D₄×C₁₁	1	4	yes	—
452	C₄²	—	2	8	no	—
453	C₄²	C₂×D₄×C₁₁	1	4	yes	—
454	C₄²	C₂×D₄×C₁₁	1	2	yes	—
455	C₄²	C₂⁴×C₁₁	1	1	yes	characteristic
456	C₄²	C₂⁴×C₁₁	1	2	yes	—
457	C₄²	C₂⁴×C₁₁	1	1	yes	characteristic
458	C₁₁	#60717	1	1	yes	characteristic, direct product factor, Sylow
459	C₂³	—	2	4	no	—
460	C₂³	C₂²×D₄×C₁₁	1	2	yes	—
461	C₂³	C₂²×D₄×C₁₁	1	1	yes	characteristic
462	Q₈	—	2	2	no	—
463	Q₈	—	2	4	no	—
464	Q₈	—	2	4	no	—
465	D₄	—	2	4	no	—
466	D₄	—	2	2	no	—
467	D₄	—	2	4	no	—
468	D₄	—	2	4	no	—
469	D₄	—	4	8	no	—
470	D₄	—	8	4	no	—
471	D₄	—	8	8	no	—
472	C₂×C₄	—	2	2	no	—
473	C₂×C₄	—	2	2	no	—
474	C₂×C₄	—	2	4	no	—
475	C₂×C₄	—	2	8	no	—
476	C₂×C₄	—	4	4	no	—
477	C₂×C₄	—	4	2	no	—
478	C₂×C₄	—	4	8	no	—
479	C₂×C₄	—	8	8	no	—
480	C₂×C₄	—	8	4	no	—
481	C₂×C₄	C₂²×D₄×C₁₁	1	4	yes	—
482	C₂×C₄	C₂²×D₄×C₁₁	1	2	yes	—
483	C₂×C₄	C₂²×D₄×C₁₁	1	2	yes	—
484	C₂×C₄	C₂²×D₄×C₁₁	1	2	yes	—
485	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
486	C₂×C₄	C₂×C₁₁×#41	1	2	yes	—
487	C₂×C₄	C₂×C₁₁×#41	1	2	yes	—
488	C₂×C₄	C₂⁵×C₁₁	1	1	yes	characteristic
489	C₈	—	2	2	no	—
490	C₈	—	2	2	no	—
491	C₈	C₂×C₁₁×#41	1	2	yes	—
492	C₈	C₂×C₁₁×#41	1	2	yes	—
493	C₈	C₂×C₁₁×#41	1	2	yes	—
494	C₈	C₂×C₁₁×#41	1	2	yes	—
495	C₂²	—	2	2	no	—
496	C₂²	—	2	2	no	—
497	C₂²	—	2	4	no	—
498	C₂²	—	4	4	no	—
499	C₂²	—	4	4	no	—
500	C₂²	—	4	4	no	—
501	C₂²	C₁₁×#532	1	2	yes	—
502	C₂²	C₂³×D₄×C₁₁	1	1	yes	characteristic
503	C₄	—	2	2	no	—
504	C₄	—	2	2	no	—
505	C₄	—	2	4	no	—
506	C₄	—	2	2	no	—
507	C₄	—	4	4	no	—
508	C₄	—	4	8	no	—
509	C₄	C₁₁×#532	1	2	yes	—
510	C₄	C₂²×C₁₁×#41	1	1	yes	characteristic
511	C₄	C₂²×C₁₁×#41	1	1	yes	characteristic
512	C₂	—	2	2	no	—
513	C₂	—	4	2	no	—
514	C₂	—	8	4	no	—
515	C₂	C₂×C₁₁×#532	1	1	yes	characteristic
516	C₂	C₁₁×#3584	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
1. C₁₁×#3512	C₂	semidirect
2. C₁₁×#3183	C₂	semidirect
3. C₁₁×#3177	C₂	semidirect
4. C₁₁×#3176	C₂	semidirect
5. C₁₁×#3174	C₂	semidirect
6. C₁₁×#3168	C₂	semidirect
7. C₂×C₁₁×#499	C₂	semidirect
8. C₁₁×#3147	C₂	semidirect
9. C₁₁×#3142	C₂	semidirect
10. C₁₁×#3061	C₂	semidirect
11. C₁₁×#3060	C₂	semidirect
12. C₁₁×#2952	C₂	semidirect
13. C₁₁×#2951	C₂	semidirect
14. C₄×C₁₁×#131	C₂	semidirect
139. #60717	C₁₁	direct (N × H)
201. #3512	C₂×C₁₁	semidirect
202. #3183	C₂×C₁₁	semidirect
203. #3177	C₂×C₁₁	semidirect
204. #3176	C₂×C₁₁	semidirect
205. #3174	C₂×C₁₁	semidirect
206. #3168	C₂×C₁₁	semidirect
207. C₂×#499	C₂×C₁₁	semidirect
208. #3147	C₂×C₁₁	semidirect
209. #3142	C₂×C₁₁	semidirect
210. #3061	C₂×C₁₁	semidirect
211. #3060	C₂×C₁₁	semidirect
212. #2952	C₂×C₁₁	semidirect
213. #2951	C₂×C₁₁	semidirect
214. C₄×#131	C₂×C₁₁	semidirect
458. C₁₁	#60717	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₁×#3512	2
C₁₁×#3183	2
C₁₁×#3177	2
C₁₁×#3176	2
C₁₁×#3174	2
C₁₁×#3168	2
C₂×C₁₁×#499	2
C₁₁×#3147	2
C₁₁×#3142	2
C₁₁×#3061	2
C₁₁×#3060	2
C₁₁×#2952	2
C₁₁×#2951	2
C₄×C₁₁×#131	2
#60717	11

Subgroups — C11×#60717 #14637910

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#60717 #14637910