Subgroups — C₁₁×#60704 #14637897

Order 2816.

1974 conjugacy classes of subgroups.

The subgroup lattice has 550 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×#3455	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₁×#540	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₁×#3179	C₂	1	8	yes	maximal, complemented
4	C₁₁×#3176	C₂	1	4	yes	maximal, complemented
5	C₁₁×#3174	C₂	1	4	yes	maximal, complemented
6	C₁₁×#3166	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₁×#3151	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₁×#3142	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₁×#3138	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₁×#3055	C₂	1	4	yes	maximal, complemented
11	C₄×C₁₁×AGL(1,ℤ/8)	C₂	1	4	yes	maximal, complemented
12	C₁₁×#2873	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₁₁×AGL(1,ℤ/8)	C₂²	1	4	yes	—
14	C₂²×C₁₁×M₁₆	C₂²	1	2	yes	—
15	C₁₁×#542	C₂²	1	4	yes	complemented
16	C₁₁×#541	C₂²	1	2	yes	complemented
17	C₁₁×#540	—	2	4	no	—
18	C₁₁×#540	C₂²	1	4	yes	—
19	C₁₁×#540	C₂²	1	4	yes	—
20	C₁₁×#540	C₂²	1	2	yes	complemented
21	C₁₁×#539	—	2	2	no	—
22	C₁₁×#538	—	2	2	no	—
23	C₁₁×#533	C₂²	1	1	yes	characteristic
24	C₁₁×#532	C₂²	1	1	yes	characteristic
25	C₂×C₁₁×#127	C₂²	1	1	yes	characteristic
26	C₁₁×#529	—	2	4	no	—
27	C₂×C₁₁×#125	C₂²	1	1	yes	characteristic
28	C₁₁×#525	C₂²	1	2	yes	—
29	C₂×C₁₁×#123	—	2	2	no	—
30	C₂×C₁₁×#121	—	2	2	no	—
31	C₂×C₁₁×#121	C₂²	1	2	yes	—
32	C₄×C₁₁×#41	C₂²	1	2	yes	—
33	C₂×C₄×D₄×C₁₁	C₂²	1	2	yes	—
34	C₂×C₁₁×#117	C₂²	1	1	yes	characteristic
35	C₁₁×#501	C₂²	1	4	yes	complemented
36	C₁₁×#499	C₂²	1	4	yes	complemented
37	C₁₁×#496	C₂²	1	4	yes	complemented
38	C₁₁×#493	C₂²	1	2	yes	complemented
39	C₁₁×#492	C₂²	1	2	yes	complemented
40	C₁₁×#491	C₂²	1	2	yes	complemented
41	C₁₁×#490	C₂²	1	4	yes	complemented
42	C₁₁×#490	C₂²	1	2	yes	complemented
43	C₁₁×#488	C₂²	1	4	yes	complemented
44	C₁₁×#486	C₂²	1	4	yes	complemented
45	C₁₁×#469	C₂²	1	8	yes	complemented
46	C₁₁×#468	C₂²	1	8	yes	complemented
47	C₁₁×#466	C₂²	1	8	yes	complemented
48	C₁₁×#465	C₂²	1	8	yes	complemented
49	C₁₁×#442	C₂²	1	8	yes	complemented
50	C₁₁×#440	C₂²	1	8	yes	complemented
51	C₄×C₁₁×SD₁₆	C₂²	1	8	yes	complemented
52	C₄×C₁₁×D₈	C₂²	1	8	yes	complemented
53	C₁₁×#428	C₂²	1	4	yes	—
54	C₁₁×#418	C₂²	1	4	yes	—
55	C₁₁×#417	C₂²	1	4	yes	—
56	C₁₁×#405	C₂²	1	4	yes	complemented
57	C₁₁×#405	C₂²	1	4	yes	complemented
58	C₄×C₁₁×M₁₆	C₂²	1	1	yes	characteristic
59	C₄×C₁₁×M₁₆	C₂²	1	2	yes	—
60	C₄×C₁₁×M₁₆	C₂²	1	1	yes	characteristic
61	C₂×C₁₁×#41	C₂³	1	2	yes	—
62	C₂²×D₄×C₁₁	—	2	2	no	—
63	C₂²×D₄×C₁₁	—	2	2	no	—
64	C₂²×D₄×C₁₁	C₂³	1	2	yes	—
65	C₂³×C₄×C₁₁	—	2	2	no	—
66	C₂³×C₄×C₁₁	C₂³	1	1	yes	characteristic
67	C₁₁×AGL(1,ℤ/8)	—	2	16	no	—
68	C₂×C₁₁×SD₁₆	C₂³	1	8	yes	—
69	C₂×C₁₁×D₈	C₂³	1	8	yes	—
70	C₂×C₁₁×M₁₆	—	2	8	no	—
71	C₂×C₁₁×M₁₆	C₂³	1	2	yes	—
72	C₂×C₁₁×M₁₆	C₂³	1	4	yes	—
73	C₂×C₁₁×M₁₆	C₂³	1	2	yes	—
74	C₂²×C₈×C₁₁	C₂³	1	4	yes	—
75	C₁₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
76	C₁₁×C₄⋊Q₈	C₂³	1	2	yes	—
77	C₁₁×#127	—	2	2	no	—
78	C₁₁×#127	C₂³	1	2	yes	—
79	C₁₁×#127	C₂³	1	1	yes	characteristic
80	C₁₁×#127	C₂³	1	2	yes	—
81	C₁₁×#126	—	2	4	no	—
82	C₁₁×#126	—	2	4	no	—
83	C₁₁×#125	—	2	4	no	—
84	C₁₁×#125	—	2	2	no	—
85	C₁₁×#125	C₂³	1	2	yes	—
86	C₁₁×#125	C₂³	1	2	yes	—
87	C₁₁×#125	C₂³	1	2	yes	—
88	C₁₁×#124	—	2	4	no	—
89	C₁₁×#124	C₂³	1	2	yes	—
90	C₁₁×#123	—	2	2	no	—
91	C₁₁×#123	—	2	8	no	—
92	C₁₁×#123	—	2	8	no	—
93	C₁₁×#123	—	2	4	no	—
94	C₁₁×#123	—	2	4	no	—
95	C₁₁×C₂²⋊Q₈	—	2	2	no	—
96	C₁₁×C₂²⋊Q₈	—	2	4	no	—
97	C₁₁×C₂²⋊Q₈	C₂³	1	4	yes	—
98	C₁₁×#121	—	2	4	no	—
99	C₁₁×#121	—	2	2	no	—
100	C₁₁×#121	—	2	8	no	—
101	C₁₁×#121	—	2	8	no	—
102	C₁₁×#121	—	2	4	no	—
103	C₁₁×#121	C₂³	1	8	yes	—
104	C₁₁×#121	C₂³	1	4	yes	—
105	C₁₁×#120	—	2	2	no	—
106	C₄×Q₈×C₁₁	—	2	2	no	—
107	C₄×Q₈×C₁₁	C₂³	1	4	yes	—
108	C₄×D₄×C₁₁	—	2	4	no	—
109	C₄×D₄×C₁₁	—	2	4	no	—
110	C₄×D₄×C₁₁	—	2	4	no	—
111	C₄×D₄×C₁₁	—	2	2	no	—
112	C₄×D₄×C₁₁	C₂³	1	8	yes	—
113	C₄×D₄×C₁₁	C₂³	1	4	yes	—
114	C₁₁×#117	—	2	2	no	—
115	C₁₁×#117	D₄	1	4	yes	—
116	C₁₁×#117	C₂³	1	2	yes	—
117	C₁₁×#117	C₂³	1	2	yes	—
118	C₁₁×#117	C₂³	1	2	yes	—
119	C₂×C₁₁×C₄⋊C₄	—	2	2	no	—
120	C₂×C₁₁×C₄⋊C₄	D₄	1	2	yes	—
121	C₂×C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
122	C₂×C₁₁×C₂²⋊C₄	—	2	2	no	—
123	C₂×C₁₁×C₂²⋊C₄	—	2	2	no	—
124	C₂×C₁₁×C₂²⋊C₄	D₄	1	2	yes	—
125	C₂×C₄²×C₁₁	—	2	2	no	—
126	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
127	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
128	C₁₁×#107	C₂³	1	8	yes	—
129	C₁₁×#106	C₂³	1	8	yes	—
130	C₁₁×#103	C₂³	1	8	yes	—
131	C₁₁×#102	C₂³	1	8	yes	—
132	C₁₁×#102	C₂³	1	8	yes	—
133	C₁₁×#102	C₂³	1	8	yes	—
134	C₁₁×#97	C₂³	1	2	yes	—
135	C₁₁×#97	C₂³	1	2	yes	—
136	C₁₁×#97	C₂³	1	4	yes	—
137	C₄×C₈×C₁₁	C₂³	1	2	yes	—
138	C₄×C₈×C₁₁	C₂³	1	4	yes	—
139	C₄×C₈×C₁₁	C₂³	1	2	yes	—
140	#60704	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
141	C₂⁴×C₁₁	—	2	2	no	—
142	C₂⁴×C₁₁	C₂×D₄	1	1	yes	characteristic
143	C₁₁×#41	—	2	8	no	—
144	C₂×Q₈×C₁₁	—	2	2	no	—
145	C₂×Q₈×C₁₁	C₂⁴	1	2	yes	—
146	C₂×D₄×C₁₁	—	2	2	no	—
147	C₂×D₄×C₁₁	—	2	4	no	—
148	C₂×D₄×C₁₁	—	2	8	no	—
149	C₂×D₄×C₁₁	—	2	2	no	—
150	C₂×D₄×C₁₁	—	2	2	no	—
151	C₂×D₄×C₁₁	—	2	4	no	—
152	C₂×D₄×C₁₁	—	2	4	no	—
153	C₂×D₄×C₁₁	—	2	8	no	—
154	C₂×D₄×C₁₁	—	8	4	no	—
155	C₂×D₄×C₁₁	—	8	4	no	—
156	C₂×D₄×C₁₁	C₂⁴	1	2	yes	—
157	C₂×D₄×C₁₁	C₂⁴	1	4	yes	—
158	C₂²×C₄×C₁₁	—	2	4	no	—
159	C₂²×C₄×C₁₁	—	2	2	no	—
160	C₂²×C₄×C₁₁	—	2	2	no	—
161	C₂²×C₄×C₁₁	—	2	4	no	—
162	C₂²×C₄×C₁₁	—	2	8	no	—
163	C₂²×C₄×C₁₁	—	8	4	no	—
164	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
165	C₂²×C₄×C₁₁	C₂×D₄	1	2	yes	—
166	C₂²×C₄×C₁₁	C₂×D₄	1	2	yes	—
167	C₂²×C₄×C₁₁	C₂×D₄	1	2	yes	—
168	C₂²×C₄×C₁₁	C₂⁴	1	2	yes	—
169	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
170	C₁₁×SD₁₆	—	2	16	no	—
171	C₁₁×D₈	—	2	16	no	—
172	C₁₁×M₁₆	—	2	8	no	—
173	C₁₁×M₁₆	—	2	4	no	—
174	C₁₁×M₁₆	#41	1	8	yes	—
175	C₂×C₈×C₁₁	—	2	8	no	—
176	C₂×C₈×C₁₁	C₂⁴	1	4	yes	—
177	C₂×C₈×C₁₁	C₂⁴	1	4	yes	—
178	C₁₁×C₄⋊C₄	—	2	4	no	—
179	C₁₁×C₄⋊C₄	—	2	4	no	—
180	C₁₁×C₄⋊C₄	—	2	2	no	—
181	C₁₁×C₄⋊C₄	—	2	4	no	—
182	C₁₁×C₄⋊C₄	—	2	2	no	—
183	C₁₁×C₄⋊C₄	—	2	4	no	—
184	C₁₁×C₄⋊C₄	—	2	4	no	—
185	C₁₁×C₄⋊C₄	—	2	2	no	—
186	C₁₁×C₄⋊C₄	C₂×D₄	1	4	yes	—
187	C₁₁×C₄⋊C₄	C₂×D₄	1	4	yes	—
188	C₁₁×C₄⋊C₄	C₂⁴	1	4	yes	—
189	C₁₁×C₄⋊C₄	C₂⁴	1	4	yes	—
190	C₁₁×C₂²⋊C₄	—	2	2	no	—
191	C₁₁×C₂²⋊C₄	—	2	4	no	—
192	C₁₁×C₂²⋊C₄	—	2	8	no	—
193	C₁₁×C₂²⋊C₄	—	2	8	no	—
194	C₁₁×C₂²⋊C₄	—	2	4	no	—
195	C₁₁×C₂²⋊C₄	—	2	4	no	—
196	C₁₁×C₂²⋊C₄	—	2	4	no	—
197	C₁₁×C₂²⋊C₄	C₂×D₄	1	4	yes	—
198	C₁₁×C₂²⋊C₄	C₂×D₄	1	4	yes	—
199	C₄²×C₁₁	—	2	2	no	—
200	C₄²×C₁₁	—	2	4	no	—
201	C₄²×C₁₁	C₂×D₄	1	2	yes	—
202	C₄²×C₁₁	C₂×D₄	1	2	yes	—
203	C₄²×C₁₁	C₂⁴	1	2	yes	—
204	C₄²×C₁₁	C₂⁴	1	1	yes	characteristic
205	C₄²×C₁₁	C₂⁴	1	1	yes	characteristic
206	#3455	C₂×C₁₁	1	1	yes	characteristic, complemented
207	C₂×#540	C₂×C₁₁	1	1	yes	characteristic, complemented
208	#3179	C₂×C₁₁	1	8	yes	complemented
209	#3176	C₂×C₁₁	1	4	yes	complemented
210	#3174	C₂×C₁₁	1	4	yes	complemented
211	#3166	C₂×C₁₁	1	1	yes	characteristic, complemented
212	#3151	C₂×C₁₁	1	1	yes	characteristic, complemented
213	#3142	C₂×C₁₁	1	1	yes	characteristic, complemented
214	#3138	C₂×C₁₁	1	1	yes	characteristic, complemented
215	#3055	C₂×C₁₁	1	4	yes	complemented
216	C₄×AGL(1,ℤ/8)	C₂×C₁₁	1	4	yes	complemented
217	#2873	C₂×C₁₁	1	1	yes	characteristic, complemented
218	C₂³×C₁₁	—	2	2	no	—
219	C₂³×C₁₁	—	2	2	no	—
220	C₂³×C₁₁	—	2	4	no	—
221	C₂³×C₁₁	—	4	2	no	—
222	C₂³×C₁₁	—	4	4	no	—
223	C₂³×C₁₁	—	4	4	no	—
224	C₂³×C₁₁	—	4	4	no	—
225	C₂³×C₁₁	C₂²×D₄	1	2	yes	—
226	C₂³×C₁₁	C₂²×D₄	1	1	yes	characteristic
227	Q₈×C₁₁	—	2	4	no	—
228	Q₈×C₁₁	—	8	2	no	—
229	D₄×C₁₁	—	2	4	no	—
230	D₄×C₁₁	—	2	8	no	—
231	D₄×C₁₁	—	4	4	no	—
232	D₄×C₁₁	—	4	4	no	—
233	D₄×C₁₁	—	8	2	no	—
234	D₄×C₁₁	—	8	4	no	—
235	D₄×C₁₁	—	8	4	no	—
236	D₄×C₁₁	—	8	4	no	—
237	D₄×C₁₁	—	8	8	no	—
238	C₂×C₄×C₁₁	—	2	2	no	—
239	C₂×C₄×C₁₁	—	2	4	no	—
240	C₂×C₄×C₁₁	—	2	2	no	—
241	C₂×C₄×C₁₁	—	2	2	no	—
242	C₂×C₄×C₁₁	—	2	2	no	—
243	C₂×C₄×C₁₁	—	2	4	no	—
244	C₂×C₄×C₁₁	—	2	4	no	—
245	C₂×C₄×C₁₁	—	4	2	no	—
246	C₂×C₄×C₁₁	—	4	2	no	—
247	C₂×C₄×C₁₁	—	4	4	no	—
248	C₂×C₄×C₁₁	—	4	4	no	—
249	C₂×C₄×C₁₁	—	8	4	no	—
250	C₂×C₄×C₁₁	—	8	8	no	—
251	C₂×C₄×C₁₁	C₂²×D₄	1	4	yes	—
252	C₂×C₄×C₁₁	C₂²×D₄	1	2	yes	—
253	C₂×C₄×C₁₁	C₂²×D₄	1	2	yes	—
254	C₂×C₄×C₁₁	C₂²×D₄	1	2	yes	—
255	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
256	C₂×C₄×C₁₁	C₂×#41	1	4	yes	—
257	C₂×C₄×C₁₁	C₂⁵	1	1	yes	characteristic
258	C₈×C₁₁	—	2	4	no	—
259	C₈×C₁₁	C₂×#41	1	8	yes	—
260	C₂×AGL(1,ℤ/8)	C₂²×C₁₁	1	4	yes	—
261	C₂²×M₁₆	C₂²×C₁₁	1	2	yes	—
262	#542	C₂²×C₁₁	1	4	yes	complemented
263	#541	C₂²×C₁₁	1	2	yes	complemented
264	#540	—	2	4	no	—
265	#540	C₂²×C₁₁	1	4	yes	—
266	#540	C₂²×C₁₁	1	4	yes	—
267	#540	C₂²×C₁₁	1	2	yes	complemented
268	#539	—	2	2	no	—
269	#538	—	2	2	no	—
270	#533	C₂²×C₁₁	1	1	yes	characteristic
271	#532	C₂²×C₁₁	1	1	yes	characteristic
272	C₂×#127	C₂²×C₁₁	1	1	yes	characteristic
273	#529	—	2	4	no	—
274	C₂×#125	C₂²×C₁₁	1	1	yes	characteristic
275	#525	C₂²×C₁₁	1	2	yes	—
276	C₂×#123	—	2	2	no	—
277	C₂×#121	—	2	2	no	—
278	C₂×#121	C₂²×C₁₁	1	2	yes	—
279	C₄×#41	C₂²×C₁₁	1	2	yes	—
280	C₂×C₄×D₄	C₂²×C₁₁	1	2	yes	—
281	C₂×#117	C₂²×C₁₁	1	1	yes	characteristic
282	#501	C₂²×C₁₁	1	4	yes	complemented
283	#499	C₂²×C₁₁	1	4	yes	complemented
284	#496	C₂²×C₁₁	1	4	yes	complemented
285	#493	C₂²×C₁₁	1	2	yes	complemented
286	#492	C₂²×C₁₁	1	2	yes	complemented
287	#491	C₂²×C₁₁	1	2	yes	complemented
288	#490	C₂²×C₁₁	1	4	yes	complemented
289	#490	C₂²×C₁₁	1	2	yes	complemented
290	#488	C₂²×C₁₁	1	4	yes	complemented
291	#486	C₂²×C₁₁	1	4	yes	complemented
292	#469	C₂²×C₁₁	1	8	yes	complemented
293	#468	C₂²×C₁₁	1	8	yes	complemented
294	#466	C₂²×C₁₁	1	8	yes	complemented
295	#465	C₂²×C₁₁	1	8	yes	complemented
296	#442	C₂²×C₁₁	1	8	yes	complemented
297	#440	C₂²×C₁₁	1	8	yes	complemented
298	C₄×SD₁₆	C₂²×C₁₁	1	8	yes	complemented
299	C₄×D₈	C₂²×C₁₁	1	8	yes	complemented
300	#428	C₂²×C₁₁	1	4	yes	—
301	#418	C₂²×C₁₁	1	4	yes	—
302	#417	C₂²×C₁₁	1	4	yes	—
303	#405	C₂²×C₁₁	1	4	yes	complemented
304	#405	C₂²×C₁₁	1	4	yes	complemented
305	C₄×M₁₆	C₂²×C₁₁	1	1	yes	characteristic
306	C₄×M₁₆	C₂²×C₁₁	1	1	yes	characteristic
307	C₄×M₁₆	C₂²×C₁₁	1	2	yes	—
308	C₂²×C₁₁	—	2	2	no	—
309	C₂²×C₁₁	—	2	4	no	—
310	C₂²×C₁₁	—	2	2	no	—
311	C₂²×C₁₁	—	4	4	no	—
312	C₂²×C₁₁	—	4	4	no	—
313	C₂²×C₁₁	—	4	4	no	—
314	C₂²×C₁₁	—	4	2	no	—
315	C₂²×C₁₁	—	4	4	no	—
316	C₂²×C₁₁	—	8	2	no	—
317	C₂²×C₁₁	—	8	8	no	—
318	C₂²×C₁₁	#532	1	2	yes	—
319	C₂²×C₁₁	C₂³×D₄	1	1	yes	characteristic
320	C₄×C₁₁	—	2	4	no	—
321	C₄×C₁₁	—	2	2	no	—
322	C₄×C₁₁	—	2	2	no	—
323	C₄×C₁₁	—	2	2	no	—
324	C₄×C₁₁	—	4	4	no	—
325	C₄×C₁₁	—	4	4	no	—
326	C₄×C₁₁	—	4	2	no	—
327	C₄×C₁₁	#532	1	2	yes	—
328	C₄×C₁₁	C₂²×#41	1	2	yes	—
329	C₂×#41	C₂³×C₁₁	1	2	yes	—
330	C₂²×D₄	—	2	2	no	—
331	C₂²×D₄	—	2	2	no	—
332	C₂²×D₄	C₂³×C₁₁	1	2	yes	—
333	C₂³×C₄	—	2	2	no	—
334	C₂³×C₄	C₂³×C₁₁	1	1	yes	characteristic
335	AGL(1,ℤ/8)	—	2	16	no	—
336	C₂×SD₁₆	C₂³×C₁₁	1	8	yes	—
337	C₂×D₈	C₂³×C₁₁	1	8	yes	—
338	C₂×M₁₆	—	2	8	no	—
339	C₂×M₁₆	C₂³×C₁₁	1	2	yes	—
340	C₂×M₁₆	C₂³×C₁₁	1	4	yes	—
341	C₂×M₁₆	C₂³×C₁₁	1	2	yes	—
342	C₂²×C₈	C₂³×C₁₁	1	4	yes	—
343	C₄⋊Q₈	C₂³×C₁₁	1	1	yes	characteristic
344	C₄⋊Q₈	C₂³×C₁₁	1	2	yes	—
345	#127	—	2	2	no	—
346	#127	C₂³×C₁₁	1	2	yes	—
347	#127	C₂³×C₁₁	1	2	yes	—
348	#127	C₂³×C₁₁	1	1	yes	characteristic
349	#126	—	2	4	no	—
350	#126	—	2	4	no	—
351	#125	—	2	4	no	—
352	#125	—	2	2	no	—
353	#125	C₂³×C₁₁	1	2	yes	—
354	#125	C₂³×C₁₁	1	2	yes	—
355	#125	C₂³×C₁₁	1	2	yes	—
356	#124	—	2	4	no	—
357	#124	C₂³×C₁₁	1	2	yes	—
358	#123	—	2	2	no	—
359	#123	—	2	8	no	—
360	#123	—	2	8	no	—
361	#123	—	2	4	no	—
362	#123	—	2	4	no	—
363	C₂²⋊Q₈	—	2	2	no	—
364	C₂²⋊Q₈	—	2	4	no	—
365	C₂²⋊Q₈	C₂³×C₁₁	1	4	yes	—
366	#121	—	2	4	no	—
367	#121	—	2	2	no	—
368	#121	—	2	8	no	—
369	#121	—	2	8	no	—
370	#121	—	2	4	no	—
371	#121	C₂³×C₁₁	1	8	yes	—
372	#121	C₂³×C₁₁	1	4	yes	—
373	#120	—	2	2	no	—
374	C₄×Q₈	—	2	2	no	—
375	C₄×Q₈	C₂³×C₁₁	1	4	yes	—
376	C₄×D₄	—	2	4	no	—
377	C₄×D₄	—	2	4	no	—
378	C₄×D₄	—	2	4	no	—
379	C₄×D₄	—	2	2	no	—
380	C₄×D₄	C₂³×C₁₁	1	8	yes	—
381	C₄×D₄	C₂³×C₁₁	1	4	yes	—
382	#117	—	2	2	no	—
383	#117	D₄×C₁₁	1	4	yes	—
384	#117	C₂³×C₁₁	1	2	yes	—
385	#117	C₂³×C₁₁	1	2	yes	—
386	#117	C₂³×C₁₁	1	2	yes	—
387	C₂×C₄⋊C₄	—	2	2	no	—
388	C₂×C₄⋊C₄	D₄×C₁₁	1	2	yes	—
389	C₂×C₄⋊C₄	C₂³×C₁₁	1	2	yes	—
390	C₂×C₂²⋊C₄	—	2	2	no	—
391	C₂×C₂²⋊C₄	—	2	2	no	—
392	C₂×C₂²⋊C₄	D₄×C₁₁	1	2	yes	—
393	C₂×C₄²	—	2	2	no	—
394	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
395	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
396	#107	C₂³×C₁₁	1	8	yes	—
397	#106	C₂³×C₁₁	1	8	yes	—
398	#103	C₂³×C₁₁	1	8	yes	—
399	#102	C₂³×C₁₁	1	8	yes	—
400	#102	C₂³×C₁₁	1	8	yes	—
401	#102	C₂³×C₁₁	1	8	yes	—
402	#97	C₂³×C₁₁	1	4	yes	—
403	#97	C₂³×C₁₁	1	2	yes	—
404	#97	C₂³×C₁₁	1	2	yes	—
405	C₄×C₈	C₂³×C₁₁	1	4	yes	—
406	C₄×C₈	C₂³×C₁₁	1	2	yes	—
407	C₄×C₈	C₂³×C₁₁	1	2	yes	—
408	C₂×C₁₁	—	2	2	no	—
409	C₂×C₁₁	—	4	2	no	—
410	C₂×C₁₁	—	8	2	no	—
411	C₂×C₁₁	—	8	4	no	—
412	C₂×C₁₁	C₂×#532	1	1	yes	characteristic
413	C₂×C₁₁	#3585	1	2	yes	—
414	C₂⁴	—	2	2	no	—
415	C₂⁴	C₂×D₄×C₁₁	1	1	yes	characteristic
416	#41	—	2	8	no	—
417	C₂×Q₈	—	2	2	no	—
418	C₂×Q₈	C₂⁴×C₁₁	1	2	yes	—
419	C₂×D₄	—	2	2	no	—
420	C₂×D₄	—	2	4	no	—
421	C₂×D₄	—	2	8	no	—
422	C₂×D₄	—	2	2	no	—
423	C₂×D₄	—	2	2	no	—
424	C₂×D₄	—	2	4	no	—
425	C₂×D₄	—	2	4	no	—
426	C₂×D₄	—	2	8	no	—
427	C₂×D₄	—	8	4	no	—
428	C₂×D₄	—	8	4	no	—
429	C₂×D₄	C₂⁴×C₁₁	1	2	yes	—
430	C₂×D₄	C₂⁴×C₁₁	1	4	yes	—
431	C₂²×C₄	—	2	4	no	—
432	C₂²×C₄	—	2	2	no	—
433	C₂²×C₄	—	2	2	no	—
434	C₂²×C₄	—	2	4	no	—
435	C₂²×C₄	—	2	8	no	—
436	C₂²×C₄	—	8	4	no	—
437	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
438	C₂²×C₄	C₂×D₄×C₁₁	1	2	yes	—
439	C₂²×C₄	C₂×D₄×C₁₁	1	2	yes	—
440	C₂²×C₄	C₂×D₄×C₁₁	1	2	yes	—
441	C₂²×C₄	C₂⁴×C₁₁	1	2	yes	—
442	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
443	SD₁₆	—	2	16	no	—
444	D₈	—	2	16	no	—
445	M₁₆	—	2	4	no	—
446	M₁₆	—	2	8	no	—
447	M₁₆	C₁₁×#41	1	8	yes	—
448	C₂×C₈	—	2	8	no	—
449	C₂×C₈	C₂⁴×C₁₁	1	4	yes	—
450	C₂×C₈	C₂⁴×C₁₁	1	4	yes	—
451	C₄⋊C₄	—	2	4	no	—
452	C₄⋊C₄	—	2	4	no	—
453	C₄⋊C₄	—	2	2	no	—
454	C₄⋊C₄	—	2	4	no	—
455	C₄⋊C₄	—	2	2	no	—
456	C₄⋊C₄	—	2	4	no	—
457	C₄⋊C₄	—	2	4	no	—
458	C₄⋊C₄	—	2	2	no	—
459	C₄⋊C₄	C₂×D₄×C₁₁	1	4	yes	—
460	C₄⋊C₄	C₂×D₄×C₁₁	1	4	yes	—
461	C₄⋊C₄	C₂⁴×C₁₁	1	4	yes	—
462	C₄⋊C₄	C₂⁴×C₁₁	1	4	yes	—
463	C₂²⋊C₄	—	2	2	no	—
464	C₂²⋊C₄	—	2	4	no	—
465	C₂²⋊C₄	—	2	8	no	—
466	C₂²⋊C₄	—	2	8	no	—
467	C₂²⋊C₄	—	2	4	no	—
468	C₂²⋊C₄	—	2	4	no	—
469	C₂²⋊C₄	—	2	4	no	—
470	C₂²⋊C₄	C₂×D₄×C₁₁	1	4	yes	—
471	C₂²⋊C₄	C₂×D₄×C₁₁	1	4	yes	—
472	C₄²	—	2	2	no	—
473	C₄²	—	2	4	no	—
474	C₄²	C₂×D₄×C₁₁	1	2	yes	—
475	C₄²	C₂×D₄×C₁₁	1	2	yes	—
476	C₄²	C₂⁴×C₁₁	1	2	yes	—
477	C₄²	C₂⁴×C₁₁	1	1	yes	characteristic
478	C₄²	C₂⁴×C₁₁	1	1	yes	characteristic
479	C₁₁	#60704	1	1	yes	characteristic, direct product factor, Sylow
480	C₂³	—	2	2	no	—
481	C₂³	—	2	2	no	—
482	C₂³	—	2	4	no	—
483	C₂³	—	4	2	no	—
484	C₂³	—	4	4	no	—
485	C₂³	—	4	4	no	—
486	C₂³	—	4	4	no	—
487	C₂³	C₂²×D₄×C₁₁	1	2	yes	—
488	C₂³	C₂²×D₄×C₁₁	1	1	yes	characteristic
489	Q₈	—	2	4	no	—
490	Q₈	—	8	2	no	—
491	D₄	—	2	4	no	—
492	D₄	—	2	8	no	—
493	D₄	—	4	4	no	—
494	D₄	—	4	4	no	—
495	D₄	—	8	2	no	—
496	D₄	—	8	4	no	—
497	D₄	—	8	4	no	—
498	D₄	—	8	4	no	—
499	D₄	—	8	8	no	—
500	C₂×C₄	—	2	2	no	—
501	C₂×C₄	—	2	4	no	—
502	C₂×C₄	—	2	2	no	—
503	C₂×C₄	—	2	2	no	—
504	C₂×C₄	—	2	2	no	—
505	C₂×C₄	—	2	4	no	—
506	C₂×C₄	—	2	4	no	—
507	C₂×C₄	—	4	2	no	—
508	C₂×C₄	—	4	2	no	—
509	C₂×C₄	—	4	4	no	—
510	C₂×C₄	—	4	4	no	—
511	C₂×C₄	—	8	4	no	—
512	C₂×C₄	—	8	8	no	—
513	C₂×C₄	C₂²×D₄×C₁₁	1	4	yes	—
514	C₂×C₄	C₂²×D₄×C₁₁	1	2	yes	—
515	C₂×C₄	C₂²×D₄×C₁₁	1	2	yes	—
516	C₂×C₄	C₂²×D₄×C₁₁	1	2	yes	—
517	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
518	C₂×C₄	C₂×C₁₁×#41	1	4	yes	—
519	C₂×C₄	C₂⁵×C₁₁	1	1	yes	characteristic
520	C₈	—	2	4	no	—
521	C₈	C₂×C₁₁×#41	1	8	yes	—
522	C₂²	—	2	2	no	—
523	C₂²	—	2	2	no	—
524	C₂²	—	2	4	no	—
525	C₂²	—	4	2	no	—
526	C₂²	—	4	4	no	—
527	C₂²	—	4	4	no	—
528	C₂²	—	4	4	no	—
529	C₂²	—	4	4	no	—
530	C₂²	—	8	2	no	—
531	C₂²	—	8	8	no	—
532	C₂²	C₁₁×#532	1	2	yes	—
533	C₂²	C₂³×D₄×C₁₁	1	1	yes	characteristic
534	C₄	—	2	2	no	—
535	C₄	—	2	4	no	—
536	C₄	—	2	2	no	—
537	C₄	—	2	2	no	—
538	C₄	—	4	2	no	—
539	C₄	—	4	4	no	—
540	C₄	—	4	4	no	—
541	C₄	C₁₁×#532	1	2	yes	—
542	C₄	C₂²×C₁₁×#41	1	2	yes	—
543	C₂	—	2	2	no	—
544	C₂	—	4	2	no	—
545	C₂	—	8	4	no	—
546	C₂	—	8	2	no	—
547	C₂	C₂×C₁₁×#532	1	1	yes	characteristic
548	C₂	C₁₁×#3585	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 ◁ C₂×C₁₁×#117 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₁×#3455	C₂	semidirect
2. C₂×C₁₁×#540	C₂	semidirect
3. C₁₁×#3179	C₂	semidirect
4. C₁₁×#3176	C₂	semidirect
5. C₁₁×#3174	C₂	semidirect
6. C₁₁×#3166	C₂	semidirect
7. C₁₁×#3151	C₂	semidirect
8. C₁₁×#3142	C₂	semidirect
9. C₁₁×#3138	C₂	semidirect
10. C₁₁×#3055	C₂	semidirect
11. C₄×C₁₁×AGL(1,ℤ/8)	C₂	semidirect
12. C₁₁×#2873	C₂	semidirect
15. C₁₁×#542	C₂²	semidirect
16. C₁₁×#541	C₂²	semidirect
20. C₁₁×#540	C₂²	semidirect
35. C₁₁×#501	C₂²	semidirect
36. C₁₁×#499	C₂²	semidirect
37. C₁₁×#496	C₂²	semidirect
38. C₁₁×#493	C₂²	semidirect
39. C₁₁×#492	C₂²	semidirect
40. C₁₁×#491	C₂²	semidirect
41. C₁₁×#490	C₂²	semidirect
42. C₁₁×#490	C₂²	semidirect
43. C₁₁×#488	C₂²	semidirect
44. C₁₁×#486	C₂²	semidirect
45. C₁₁×#469	C₂²	semidirect
46. C₁₁×#468	C₂²	semidirect
47. C₁₁×#466	C₂²	semidirect
48. C₁₁×#465	C₂²	semidirect
49. C₁₁×#442	C₂²	semidirect
50. C₁₁×#440	C₂²	semidirect
51. C₄×C₁₁×SD₁₆	C₂²	semidirect
52. C₄×C₁₁×D₈	C₂²	semidirect
56. C₁₁×#405	C₂²	semidirect
57. C₁₁×#405	C₂²	semidirect
140. #60704	C₁₁	direct (N × H)
206. #3455	C₂×C₁₁	semidirect
207. C₂×#540	C₂×C₁₁	semidirect
208. #3179	C₂×C₁₁	semidirect
209. #3176	C₂×C₁₁	semidirect
210. #3174	C₂×C₁₁	semidirect
211. #3166	C₂×C₁₁	semidirect
212. #3151	C₂×C₁₁	semidirect
213. #3142	C₂×C₁₁	semidirect
214. #3138	C₂×C₁₁	semidirect
215. #3055	C₂×C₁₁	semidirect
216. C₄×AGL(1,ℤ/8)	C₂×C₁₁	semidirect
217. #2873	C₂×C₁₁	semidirect
262. #542	C₂²×C₁₁	semidirect
263. #541	C₂²×C₁₁	semidirect
267. #540	C₂²×C₁₁	semidirect
282. #501	C₂²×C₁₁	semidirect
283. #499	C₂²×C₁₁	semidirect
284. #496	C₂²×C₁₁	semidirect
285. #493	C₂²×C₁₁	semidirect
286. #492	C₂²×C₁₁	semidirect
287. #491	C₂²×C₁₁	semidirect
288. #490	C₂²×C₁₁	semidirect
289. #490	C₂²×C₁₁	semidirect
290. #488	C₂²×C₁₁	semidirect
291. #486	C₂²×C₁₁	semidirect
292. #469	C₂²×C₁₁	semidirect
293. #468	C₂²×C₁₁	semidirect
294. #466	C₂²×C₁₁	semidirect
295. #465	C₂²×C₁₁	semidirect
296. #442	C₂²×C₁₁	semidirect
297. #440	C₂²×C₁₁	semidirect
298. C₄×SD₁₆	C₂²×C₁₁	semidirect
299. C₄×D₈	C₂²×C₁₁	semidirect
303. #405	C₂²×C₁₁	semidirect
304. #405	C₂²×C₁₁	semidirect
479. C₁₁	#60704	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×#3455	2
C₂×C₁₁×#540	2
C₁₁×#3179	2
C₁₁×#3176	2
C₁₁×#3174	2
C₁₁×#3166	2
C₁₁×#3151	2
C₁₁×#3142	2
C₁₁×#3138	2
C₁₁×#3055	2
C₄×C₁₁×AGL(1,ℤ/8)	2
C₁₁×#2873	2
#60704	11

Subgroups — C11×#60704 #14637897

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#60704 #14637897