Subgroups — C₁₁×#22459 #14599652

Order 2816.

1312 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₁×#577	C₂	1	1	yes	maximal, characteristic
2	C₁₁×#2957	C₂	1	2	yes	maximal, complemented
3	C₁₁×#2889	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₁×#2888	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₁×#1977	C₂	1	2	yes	maximal, complemented
6	C₁₁×#1903	C₂	1	2	yes	maximal, complemented
7	C₁₁×#1902	C₂	1	2	yes	maximal, complemented
8	C₁₁×#1813	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₁×#1796	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₁×#1795	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₁×#1757	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₁×2₋¹⁺⁴	C₂²	1	1	yes	characteristic
13	C₂×C₁₁×H(5,𝔽₂)	C₂²	1	1	yes	characteristic
14	C₁₁×#577	—	2	4	no	—
15	C₁₁×#577	—	2	4	no	—
16	C₂×C₁₁×#137	C₄	1	2	yes	complemented
17	C₂×C₁₁×#137	C₂²	1	1	yes	characteristic
18	C₂×C₁₁×AGL(1,ℤ/8)	C₄	1	2	yes	complemented
19	C₂×C₁₁×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
20	C₂×C₁₁×#135	C₄	1	2	yes	complemented
21	C₂×C₁₁×#135	C₂²	1	1	yes	characteristic
22	C₂²×C₁₁×SD₁₆	C₄	1	2	yes	complemented
23	C₂²×C₁₁×SD₁₆	C₂²	1	1	yes	characteristic
24	C₁₁×#568	C₂²	1	2	yes	—
25	C₁₁×#568	C₂²	1	2	yes	complemented
26	C₂×C₁₁×#131	C₂²	1	1	yes	characteristic
27	C₁₁×#444	—	2	4	no	—
28	C₁₁×#443	—	2	4	no	—
29	C₂×C₁₁×#108	C₂²	1	2	yes	complemented
30	C₁₁×#421	C₂²	1	2	yes	—
31	C₁₁×#421	C₂²	1	2	yes	complemented
32	C₁₁×#419	C₂²	1	2	yes	complemented
33	C₁₁×#418	C₂²	1	2	yes	—
34	C₁₁×#413	—	2	2	no	—
35	C₁₁×#413	—	2	2	no	—
36	C₁₁×#413	C₂²	1	1	yes	characteristic
37	C₁₁×#413	C₂²	1	1	yes	characteristic
38	C₁₁×#413	C₂²	1	1	yes	characteristic
39	C₂×C₁₁×#101	—	2	2	no	—
40	C₂×C₁₁×#101	C₂²	1	2	yes	complemented
41	C₂×C₁₁×#100	—	2	2	no	—
42	C₂×C₁₁×#100	C₂²	1	2	yes	—
43	C₁₁×#410	C₂²	1	1	yes	characteristic
44	C₁₁×#405	C₂²	1	2	yes	complemented
45	C₁₁×#344	C₂²	1	2	yes	complemented
46	C₁₁×#338	C₂²	1	2	yes	complemented
47	C₁₁×2₋¹⁺⁴	—	2	4	no	—
48	C₁₁×2₋¹⁺⁴	—	4	2	no	—
49	C₁₁×H(5,𝔽₂)	—	2	4	no	—
50	C₁₁×H(5,𝔽₂)	—	4	2	no	—
51	C₂×C₁₁×#41	—	2	1	no	—
52	C₂×C₁₁×#41	—	2	1	no	—
53	C₂×C₁₁×#41	—	2	2	no	—
54	C₂×C₁₁×#41	C₂×C₄	1	2	yes	—
55	C₂×C₁₁×#41	C₂×C₄	1	2	yes	—
56	C₂×C₁₁×#41	C₂³	1	1	yes	characteristic
57	C₂×C₁₁×#41	C₂³	1	1	yes	characteristic
58	C₂×C₁₁×#41	C₂³	1	1	yes	characteristic
59	C₂²×Q₈×C₁₁	—	2	1	no	—
60	C₂²×Q₈×C₁₁	C₂×C₄	1	2	yes	—
61	C₂²×Q₈×C₁₁	C₂³	1	1	yes	characteristic
62	C₂²×D₄×C₁₁	—	2	1	no	—
63	C₂²×D₄×C₁₁	—	2	2	no	—
64	C₂²×D₄×C₁₁	C₂×C₄	1	2	yes	—
65	C₂²×D₄×C₁₁	C₂³	1	1	yes	characteristic
66	C₁₁×#137	—	2	4	no	—
67	C₁₁×#137	—	2	8	no	—
68	C₁₁×AGL(1,ℤ/8)	—	2	4	no	—
69	C₁₁×AGL(1,ℤ/8)	—	2	8	no	—
70	C₁₁×#135	—	2	4	no	—
71	C₁₁×#135	—	2	4	no	—
72	C₁₁×#135	D₄	1	4	yes	—
73	C₁₁×#135	D₄	1	4	yes	—
74	C₂×C₁₁×Q₁₆	C₂×C₄	1	2	yes	—
75	C₂×C₁₁×Q₁₆	C₂×C₄	1	1	yes	characteristic
76	C₂×C₁₁×SD₁₆	—	2	4	no	—
77	C₂×C₁₁×SD₁₆	—	2	4	no	—
78	C₂×C₁₁×SD₁₆	—	2	2	no	—
79	C₂×C₁₁×SD₁₆	—	2	2	no	—
80	C₂×C₁₁×SD₁₆	C₂×C₄	1	2	yes	—
81	C₂×C₁₁×SD₁₆	C₂×C₄	1	2	yes	—
82	C₂×C₁₁×SD₁₆	C₂×C₄	1	2	yes	—
83	C₂×C₁₁×SD₁₆	C₂×C₄	1	2	yes	—
84	C₂×C₁₁×SD₁₆	C₂×C₄	1	1	yes	characteristic
85	C₂×C₁₁×SD₁₆	C₂×C₄	1	1	yes	characteristic
86	C₂×C₁₁×D₈	C₂×C₄	1	2	yes	—
87	C₂×C₁₁×D₈	C₂×C₄	1	1	yes	characteristic
88	C₁₁×#131	—	2	2	no	—
89	C₁₁×#131	—	2	2	no	—
90	C₁₁×#131	—	2	4	no	—
91	C₁₁×#131	—	2	4	no	—
92	C₁₁×#131	—	4	2	no	—
93	C₁₁×#131	—	4	2	no	—
94	C₂×C₁₁×M₁₆	—	2	4	no	—
95	C₂×C₁₁×M₁₆	—	2	4	no	—
96	C₂×C₁₁×M₁₆	C₂×C₄	1	2	yes	—
97	C₂×C₁₁×M₁₆	C₂³	1	2	yes	—
98	C₂×C₁₁×M₁₆	C₂³	1	2	yes	—
99	C₂×C₁₁×M₁₆	C₂³	1	2	yes	—
100	C₂×C₁₁×M₁₆	C₂³	1	1	yes	characteristic
101	C₂²×C₈×C₁₁	C₂×C₄	1	2	yes	—
102	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
103	C₁₁×#117	C₂³	1	2	yes	—
104	C₁₁×#108	—	2	2	no	—
105	C₁₁×#108	—	2	2	no	—
106	C₁₁×#104	—	2	4	no	—
107	C₁₁×#104	—	2	4	no	—
108	C₁₁×#103	—	4	2	no	—
109	C₁₁×#102	—	4	2	no	—
110	C₁₁×#101	—	2	1	no	—
111	C₁₁×#101	—	2	1	no	—
112	C₁₁×#101	—	2	4	no	—
113	C₁₁×#101	D₄	1	2	yes	—
114	C₁₁×#100	—	2	1	no	—
115	C₁₁×#100	—	2	1	no	—
116	C₁₁×#100	—	2	4	no	—
117	C₁₁×#100	D₄	1	2	yes	—
118	C₁₁×#99	—	2	2	no	—
119	C₁₁×#97	—	2	2	no	—
120	C₄×C₈×C₁₁	—	2	2	no	—
121	#22459	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
122	C₂⁴×C₁₁	—	2	2	no	—
123	C₂⁴×C₁₁	—	2	1	no	—
124	C₁₁×#41	—	2	2	no	—
125	C₁₁×#41	—	2	2	no	—
126	C₁₁×#41	—	2	2	no	—
127	C₁₁×#41	—	2	2	no	—
128	C₁₁×#41	—	2	4	no	—
129	C₁₁×#41	—	2	4	no	—
130	C₁₁×#41	—	4	2	no	—
131	C₁₁×#41	—	4	2	no	—
132	C₁₁×#41	—	4	4	no	—
133	C₁₁×#41	—	4	4	no	—
134	C₁₁×#41	—	4	8	no	—
135	C₁₁×#41	C₂×D₄	1	4	yes	—
136	C₁₁×#41	C₂×D₄	1	4	yes	—
137	C₂×Q₈×C₁₁	—	2	2	no	—
138	C₂×Q₈×C₁₁	—	2	1	no	—
139	C₂×Q₈×C₁₁	—	2	4	no	—
140	C₂×Q₈×C₁₁	—	2	2	no	—
141	C₂×Q₈×C₁₁	—	2	2	no	—
142	C₂×Q₈×C₁₁	—	4	2	no	—
143	C₂×Q₈×C₁₁	—	4	4	no	—
144	C₂×Q₈×C₁₁	C₂²×C₄	1	2	yes	—
145	C₂×Q₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
146	C₂×Q₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
147	C₂×Q₈×C₁₁	C₂×D₄	1	1	yes	characteristic
148	C₂×D₄×C₁₁	—	2	1	no	—
149	C₂×D₄×C₁₁	—	2	1	no	—
150	C₂×D₄×C₁₁	—	2	4	no	—
151	C₂×D₄×C₁₁	—	2	2	no	—
152	C₂×D₄×C₁₁	—	2	2	no	—
153	C₂×D₄×C₁₁	—	2	2	no	—
154	C₂×D₄×C₁₁	—	2	2	no	—
155	C₂×D₄×C₁₁	—	2	1	no	—
156	C₂×D₄×C₁₁	—	2	2	no	—
157	C₂×D₄×C₁₁	—	4	2	no	—
158	C₂×D₄×C₁₁	—	4	4	no	—
159	C₂×D₄×C₁₁	—	4	8	no	—
160	C₂×D₄×C₁₁	C₂²×C₄	1	2	yes	—
161	C₂×D₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
162	C₂×D₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
163	C₂×D₄×C₁₁	C₂×D₄	1	1	yes	characteristic
164	C₂×D₄×C₁₁	#41	1	2	yes	—
165	C₂²×C₄×C₁₁	—	2	1	no	—
166	C₂²×C₄×C₁₁	—	2	1	no	—
167	C₂²×C₄×C₁₁	—	2	2	no	—
168	C₂²×C₄×C₁₁	—	2	1	no	—
169	C₂²×C₄×C₁₁	—	2	2	no	—
170	C₂²×C₄×C₁₁	—	2	2	no	—
171	C₂²×C₄×C₁₁	C₂²×C₄	1	2	yes	—
172	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
173	C₁₁×Q₁₆	—	2	4	no	—
174	C₁₁×Q₁₆	C₂²⋊C₄	1	4	yes	—
175	C₁₁×SD₁₆	—	2	2	no	—
176	C₁₁×SD₁₆	—	2	2	no	—
177	C₁₁×SD₁₆	—	2	4	no	—
178	C₁₁×SD₁₆	—	2	4	no	—
179	C₁₁×SD₁₆	—	2	4	no	—
180	C₁₁×SD₁₆	C₂²⋊C₄	1	2	yes	—
181	C₁₁×SD₁₆	C₂²⋊C₄	1	2	yes	—
182	C₁₁×SD₁₆	C₂²⋊C₄	1	2	yes	—
183	C₁₁×SD₁₆	C₂²⋊C₄	1	2	yes	—
184	C₁₁×D₈	—	2	4	no	—
185	C₁₁×D₈	C₂²⋊C₄	1	4	yes	—
186	C₁₁×M₁₆	—	2	4	no	—
187	C₁₁×M₁₆	—	2	2	no	—
188	C₁₁×M₁₆	—	2	2	no	—
189	C₁₁×M₁₆	—	2	2	no	—
190	C₁₁×M₁₆	—	2	2	no	—
191	C₁₁×M₁₆	—	2	2	no	—
192	C₁₁×M₁₆	—	2	2	no	—
193	C₁₁×M₁₆	—	4	4	no	—
194	C₁₁×M₁₆	—	4	4	no	—
195	C₁₁×M₁₆	C₂×D₄	1	4	yes	—
196	C₂×C₈×C₁₁	—	2	2	no	—
197	C₂×C₈×C₁₁	—	2	2	no	—
198	C₂×C₈×C₁₁	—	2	2	no	—
199	C₂×C₈×C₁₁	—	2	2	no	—
200	C₂×C₈×C₁₁	—	2	2	no	—
201	C₂×C₈×C₁₁	—	4	4	no	—
202	C₂×C₈×C₁₁	—	4	4	no	—
203	C₂×C₈×C₁₁	C₂²×C₄	1	2	yes	—
204	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
205	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
206	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
207	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
208	C₁₁×C₄⋊C₄	—	2	2	no	—
209	C₁₁×C₂²⋊C₄	—	2	2	no	—
210	C₄²×C₁₁	—	2	2	no	—
211	C₂×#577	C₂×C₁₁	1	1	yes	characteristic
212	#2957	C₂×C₁₁	1	2	yes	complemented
213	#2889	C₂×C₁₁	1	1	yes	characteristic, complemented
214	#2888	C₂×C₁₁	1	1	yes	characteristic, complemented
215	#1977	C₂×C₁₁	1	2	yes	complemented
216	#1903	C₂×C₁₁	1	2	yes	complemented
217	#1902	C₂×C₁₁	1	2	yes	complemented
218	#1813	C₂×C₁₁	1	1	yes	characteristic, complemented
219	#1796	C₂×C₁₁	1	1	yes	characteristic, complemented
220	#1795	C₂×C₁₁	1	1	yes	characteristic, complemented
221	#1757	C₂×C₁₁	1	1	yes	characteristic, complemented
222	C₂³×C₁₁	—	2	1	no	—
223	C₂³×C₁₁	—	2	1	no	—
224	C₂³×C₁₁	—	2	2	no	—
225	C₂³×C₁₁	—	4	4	no	—
226	C₂³×C₁₁	—	4	2	no	—
227	C₂³×C₁₁	—	16	1	no	—
228	C₂³×C₁₁	—	16	2	no	—
229	C₂³×C₁₁	C₄×D₄	1	2	yes	—
230	C₂³×C₁₁	C₂×#41	1	1	yes	characteristic
231	Q₈×C₁₁	—	2	1	no	—
232	Q₈×C₁₁	—	2	1	no	—
233	Q₈×C₁₁	—	2	2	no	—
234	Q₈×C₁₁	—	2	2	no	—
235	Q₈×C₁₁	—	2	2	no	—
236	Q₈×C₁₁	—	4	4	no	—
237	Q₈×C₁₁	—	4	2	no	—
238	Q₈×C₁₁	C₂×C₂²⋊C₄	1	2	yes	—
239	Q₈×C₁₁	C₂×C₂²⋊C₄	1	2	yes	—
240	D₄×C₁₁	—	2	4	no	—
241	D₄×C₁₁	—	2	4	no	—
242	D₄×C₁₁	—	2	4	no	—
243	D₄×C₁₁	—	2	2	no	—
244	D₄×C₁₁	—	2	1	no	—
245	D₄×C₁₁	—	2	1	no	—
246	D₄×C₁₁	—	2	2	no	—
247	D₄×C₁₁	—	2	2	no	—
248	D₄×C₁₁	—	4	4	no	—
249	D₄×C₁₁	—	4	4	no	—
250	D₄×C₁₁	—	4	4	no	—
251	D₄×C₁₁	—	4	2	no	—
252	D₄×C₁₁	C₂×C₂²⋊C₄	1	2	yes	—
253	D₄×C₁₁	C₂×C₂²⋊C₄	1	2	yes	—
254	C₂×C₄×C₁₁	—	2	1	no	—
255	C₂×C₄×C₁₁	—	2	1	no	—
256	C₂×C₄×C₁₁	—	2	2	no	—
257	C₂×C₄×C₁₁	—	2	2	no	—
258	C₂×C₄×C₁₁	—	2	4	no	—
259	C₂×C₄×C₁₁	—	2	4	no	—
260	C₂×C₄×C₁₁	—	2	2	no	—
261	C₂×C₄×C₁₁	—	4	4	no	—
262	C₂×C₄×C₁₁	—	4	4	no	—
263	C₂×C₄×C₁₁	—	4	4	no	—
264	C₂×C₄×C₁₁	—	4	2	no	—
265	C₂×C₄×C₁₁	—	4	2	no	—
266	C₂×C₄×C₁₁	C₄×D₄	1	2	yes	—
267	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
268	C₂×C₄×C₁₁	C₂²×D₄	1	2	yes	—
269	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
270	C₂×C₄×C₁₁	H(5,𝔽₂)	1	2	yes	—
271	C₈×C₁₁	—	2	2	no	—
272	C₈×C₁₁	—	2	4	no	—
273	C₈×C₁₁	—	4	2	no	—
274	C₈×C₁₁	—	4	2	no	—
275	C₈×C₁₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
276	C₈×C₁₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
277	C₈×C₁₁	C₂×C₂²⋊C₄	1	2	yes	—
278	C₂×2₋¹⁺⁴	C₂²×C₁₁	1	1	yes	characteristic
279	C₂×H(5,𝔽₂)	C₂²×C₁₁	1	1	yes	characteristic
280	#577	—	2	4	no	—
281	#577	—	2	4	no	—
282	C₂×#137	C₄×C₁₁	1	2	yes	complemented
283	C₂×#137	C₂²×C₁₁	1	1	yes	characteristic
284	C₂×AGL(1,ℤ/8)	C₄×C₁₁	1	2	yes	complemented
285	C₂×AGL(1,ℤ/8)	C₂²×C₁₁	1	1	yes	characteristic
286	C₂×#135	C₄×C₁₁	1	2	yes	complemented
287	C₂×#135	C₂²×C₁₁	1	1	yes	characteristic
288	C₂²×SD₁₆	C₄×C₁₁	1	2	yes	complemented
289	C₂²×SD₁₆	C₂²×C₁₁	1	1	yes	characteristic
290	#568	C₂²×C₁₁	1	2	yes	—
291	#568	C₂²×C₁₁	1	2	yes	complemented
292	C₂×#131	C₂²×C₁₁	1	1	yes	characteristic
293	#444	—	2	4	no	—
294	#443	—	2	4	no	—
295	C₂×#108	C₂²×C₁₁	1	2	yes	complemented
296	#421	C₂²×C₁₁	1	2	yes	—
297	#421	C₂²×C₁₁	1	2	yes	complemented
298	#419	C₂²×C₁₁	1	2	yes	complemented
299	#418	C₂²×C₁₁	1	2	yes	—
300	#413	—	2	2	no	—
301	#413	—	2	2	no	—
302	#413	C₂²×C₁₁	1	1	yes	characteristic
303	#413	C₂²×C₁₁	1	1	yes	characteristic
304	#413	C₂²×C₁₁	1	1	yes	characteristic
305	C₂×#101	—	2	2	no	—
306	C₂×#101	C₂²×C₁₁	1	2	yes	complemented
307	C₂×#100	—	2	2	no	—
308	C₂×#100	C₂²×C₁₁	1	2	yes	—
309	#410	C₂²×C₁₁	1	1	yes	characteristic
310	#405	C₂²×C₁₁	1	2	yes	complemented
311	#344	C₂²×C₁₁	1	2	yes	complemented
312	#338	C₂²×C₁₁	1	2	yes	complemented
313	C₂²×C₁₁	—	2	2	no	—
314	C₂²×C₁₁	—	2	2	no	—
315	C₂²×C₁₁	—	2	2	no	—
316	C₂²×C₁₁	—	4	1	no	—
317	C₂²×C₁₁	—	4	2	no	—
318	C₂²×C₁₁	—	4	2	no	—
319	C₂²×C₁₁	—	8	1	no	—
320	C₂²×C₁₁	—	8	1	no	—
321	C₂²×C₁₁	—	8	2	no	—
322	C₂²×C₁₁	—	16	2	no	—
323	C₂²×C₁₁	—	16	4	no	—
324	C₂²×C₁₁	C₂×C₄×D₄	1	1	yes	characteristic
325	C₂²×C₁₁	#546	1	2	yes	—
326	C₄×C₁₁	—	2	2	no	—
327	C₄×C₁₁	—	2	2	no	—
328	C₄×C₁₁	—	2	2	no	—
329	C₄×C₁₁	—	4	2	no	—
330	C₄×C₁₁	—	8	2	no	—
331	C₄×C₁₁	C₂²×C₂²⋊C₄	1	1	yes	characteristic
332	C₄×C₁₁	#518	1	1	yes	characteristic
333	C₄×C₁₁	D₄²	1	2	yes	—
334	2₋¹⁺⁴	—	2	4	no	—
335	2₋¹⁺⁴	—	4	2	no	—
336	H(5,𝔽₂)	—	2	4	no	—
337	H(5,𝔽₂)	—	4	2	no	—
338	C₂×#41	—	2	1	no	—
339	C₂×#41	—	2	1	no	—
340	C₂×#41	—	2	2	no	—
341	C₂×#41	C₂×C₄×C₁₁	1	2	yes	—
342	C₂×#41	C₂×C₄×C₁₁	1	2	yes	—
343	C₂×#41	C₂³×C₁₁	1	1	yes	characteristic
344	C₂×#41	C₂³×C₁₁	1	1	yes	characteristic
345	C₂×#41	C₂³×C₁₁	1	1	yes	characteristic
346	C₂²×Q₈	—	2	1	no	—
347	C₂²×Q₈	C₂×C₄×C₁₁	1	2	yes	—
348	C₂²×Q₈	C₂³×C₁₁	1	1	yes	characteristic
349	C₂²×D₄	—	2	1	no	—
350	C₂²×D₄	—	2	2	no	—
351	C₂²×D₄	C₂×C₄×C₁₁	1	2	yes	—
352	C₂²×D₄	C₂³×C₁₁	1	1	yes	characteristic
353	#137	—	2	4	no	—
354	#137	—	2	8	no	—
355	AGL(1,ℤ/8)	—	2	4	no	—
356	AGL(1,ℤ/8)	—	2	8	no	—
357	#135	—	2	4	no	—
358	#135	—	2	4	no	—
359	#135	D₄×C₁₁	1	4	yes	—
360	#135	D₄×C₁₁	1	4	yes	—
361	C₂×Q₁₆	C₂×C₄×C₁₁	1	2	yes	—
362	C₂×Q₁₆	C₂×C₄×C₁₁	1	1	yes	characteristic
363	C₂×SD₁₆	—	2	4	no	—
364	C₂×SD₁₆	—	2	4	no	—
365	C₂×SD₁₆	—	2	2	no	—
366	C₂×SD₁₆	—	2	2	no	—
367	C₂×SD₁₆	C₂×C₄×C₁₁	1	2	yes	—
368	C₂×SD₁₆	C₂×C₄×C₁₁	1	2	yes	—
369	C₂×SD₁₆	C₂×C₄×C₁₁	1	2	yes	—
370	C₂×SD₁₆	C₂×C₄×C₁₁	1	2	yes	—
371	C₂×SD₁₆	C₂×C₄×C₁₁	1	1	yes	characteristic
372	C₂×SD₁₆	C₂×C₄×C₁₁	1	1	yes	characteristic
373	C₂×D₈	C₂×C₄×C₁₁	1	2	yes	—
374	C₂×D₈	C₂×C₄×C₁₁	1	1	yes	characteristic
375	#131	—	2	2	no	—
376	#131	—	2	2	no	—
377	#131	—	2	4	no	—
378	#131	—	2	4	no	—
379	#131	—	4	2	no	—
380	#131	—	4	2	no	—
381	C₂×M₁₆	—	2	4	no	—
382	C₂×M₁₆	—	2	4	no	—
383	C₂×M₁₆	C₂×C₄×C₁₁	1	2	yes	—
384	C₂×M₁₆	C₂³×C₁₁	1	2	yes	—
385	C₂×M₁₆	C₂³×C₁₁	1	2	yes	—
386	C₂×M₁₆	C₂³×C₁₁	1	2	yes	—
387	C₂×M₁₆	C₂³×C₁₁	1	1	yes	characteristic
388	C₂²×C₈	C₂×C₄×C₁₁	1	2	yes	—
389	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
390	#117	C₂³×C₁₁	1	2	yes	—
391	#108	—	2	2	no	—
392	#108	—	2	2	no	—
393	#104	—	2	4	no	—
394	#104	—	2	4	no	—
395	#103	—	4	2	no	—
396	#102	—	4	2	no	—
397	#101	—	2	1	no	—
398	#101	—	2	1	no	—
399	#101	—	2	4	no	—
400	#101	D₄×C₁₁	1	2	yes	—
401	#100	—	2	1	no	—
402	#100	—	2	1	no	—
403	#100	—	2	4	no	—
404	#100	D₄×C₁₁	1	2	yes	—
405	#99	—	2	2	no	—
406	#97	—	2	2	no	—
407	C₄×C₈	—	2	2	no	—
408	C₂×C₁₁	—	2	2	no	—
409	C₂×C₁₁	—	2	1	no	—
410	C₂×C₁₁	—	4	2	no	—
411	C₂×C₁₁	—	4	2	no	—
412	C₂×C₁₁	—	4	2	no	—
413	C₂×C₁₁	—	8	2	no	—
414	C₂×C₁₁	D₄×C₂²⋊C₄	1	1	yes	characteristic
415	C₂⁴	—	2	2	no	—
416	C₂⁴	—	2	1	no	—
417	#41	—	2	2	no	—
418	#41	—	2	2	no	—
419	#41	—	2	2	no	—
420	#41	—	2	2	no	—
421	#41	—	2	4	no	—
422	#41	—	2	4	no	—
423	#41	—	4	2	no	—
424	#41	—	4	2	no	—
425	#41	—	4	4	no	—
426	#41	—	4	4	no	—
427	#41	—	4	8	no	—
428	#41	C₂×D₄×C₁₁	1	4	yes	—
429	#41	C₂×D₄×C₁₁	1	4	yes	—
430	C₂×Q₈	—	2	2	no	—
431	C₂×Q₈	—	2	1	no	—
432	C₂×Q₈	—	2	4	no	—
433	C₂×Q₈	—	2	2	no	—
434	C₂×Q₈	—	2	2	no	—
435	C₂×Q₈	—	4	2	no	—
436	C₂×Q₈	—	4	4	no	—
437	C₂×Q₈	C₂²×C₄×C₁₁	1	2	yes	—
438	C₂×Q₈	C₂²×C₄×C₁₁	1	1	yes	characteristic
439	C₂×Q₈	C₂²×C₄×C₁₁	1	1	yes	characteristic
440	C₂×Q₈	C₂×D₄×C₁₁	1	1	yes	characteristic
441	C₂×D₄	—	2	1	no	—
442	C₂×D₄	—	2	1	no	—
443	C₂×D₄	—	2	4	no	—
444	C₂×D₄	—	2	2	no	—
445	C₂×D₄	—	2	2	no	—
446	C₂×D₄	—	2	2	no	—
447	C₂×D₄	—	2	2	no	—
448	C₂×D₄	—	2	1	no	—
449	C₂×D₄	—	2	2	no	—
450	C₂×D₄	—	4	2	no	—
451	C₂×D₄	—	4	4	no	—
452	C₂×D₄	—	4	8	no	—
453	C₂×D₄	C₂²×C₄×C₁₁	1	2	yes	—
454	C₂×D₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
455	C₂×D₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
456	C₂×D₄	C₂×D₄×C₁₁	1	1	yes	characteristic
457	C₂×D₄	C₁₁×#41	1	2	yes	—
458	C₂²×C₄	—	2	1	no	—
459	C₂²×C₄	—	2	1	no	—
460	C₂²×C₄	—	2	2	no	—
461	C₂²×C₄	—	2	1	no	—
462	C₂²×C₄	—	2	2	no	—
463	C₂²×C₄	—	2	2	no	—
464	C₂²×C₄	C₂²×C₄×C₁₁	1	2	yes	—
465	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
466	Q₁₆	—	2	4	no	—
467	Q₁₆	C₁₁×C₂²⋊C₄	1	4	yes	—
468	SD₁₆	—	2	4	no	—
469	SD₁₆	—	2	4	no	—
470	SD₁₆	—	2	2	no	—
471	SD₁₆	—	2	2	no	—
472	SD₁₆	—	2	4	no	—
473	SD₁₆	C₁₁×C₂²⋊C₄	1	2	yes	—
474	SD₁₆	C₁₁×C₂²⋊C₄	1	2	yes	—
475	SD₁₆	C₁₁×C₂²⋊C₄	1	2	yes	—
476	SD₁₆	C₁₁×C₂²⋊C₄	1	2	yes	—
477	D₈	—	2	4	no	—
478	D₈	C₁₁×C₂²⋊C₄	1	4	yes	—
479	M₁₆	—	2	2	no	—
480	M₁₆	—	2	2	no	—
481	M₁₆	—	2	4	no	—
482	M₁₆	—	2	2	no	—
483	M₁₆	—	2	2	no	—
484	M₁₆	—	2	2	no	—
485	M₁₆	—	2	2	no	—
486	M₁₆	—	4	4	no	—
487	M₁₆	—	4	4	no	—
488	M₁₆	C₂×D₄×C₁₁	1	4	yes	—
489	C₂×C₈	—	2	2	no	—
490	C₂×C₈	—	2	2	no	—
491	C₂×C₈	—	2	2	no	—
492	C₂×C₈	—	2	2	no	—
493	C₂×C₈	—	2	2	no	—
494	C₂×C₈	—	4	4	no	—
495	C₂×C₈	—	4	4	no	—
496	C₂×C₈	C₂²×C₄×C₁₁	1	2	yes	—
497	C₂×C₈	C₂²×C₄×C₁₁	1	1	yes	characteristic
498	C₂×C₈	C₂²×C₄×C₁₁	1	1	yes	characteristic
499	C₂×C₈	C₂×D₄×C₁₁	1	2	yes	—
500	C₂×C₈	C₂×D₄×C₁₁	1	2	yes	—
501	C₄⋊C₄	—	2	2	no	—
502	C₂²⋊C₄	—	2	2	no	—
503	C₄²	—	2	2	no	—
504	C₁₁	#22459	1	1	yes	characteristic, direct product factor, Sylow
505	C₂³	—	2	1	no	—
506	C₂³	—	2	1	no	—
507	C₂³	—	2	2	no	—
508	C₂³	—	4	4	no	—
509	C₂³	—	4	2	no	—
510	C₂³	—	16	1	no	—
511	C₂³	—	16	2	no	—
512	C₂³	C₄×D₄×C₁₁	1	2	yes	—
513	C₂³	C₂×C₁₁×#41	1	1	yes	characteristic
514	Q₈	—	2	1	no	—
515	Q₈	—	2	1	no	—
516	Q₈	—	2	2	no	—
517	Q₈	—	2	2	no	—
518	Q₈	—	2	2	no	—
519	Q₈	—	4	4	no	—
520	Q₈	—	4	2	no	—
521	Q₈	C₂×C₁₁×C₂²⋊C₄	1	2	yes	—
522	Q₈	C₂×C₁₁×C₂²⋊C₄	1	2	yes	—
523	D₄	—	2	4	no	—
524	D₄	—	2	4	no	—
525	D₄	—	2	4	no	—
526	D₄	—	2	2	no	—
527	D₄	—	2	1	no	—
528	D₄	—	2	1	no	—
529	D₄	—	2	2	no	—
530	D₄	—	2	2	no	—
531	D₄	—	4	4	no	—
532	D₄	—	4	4	no	—
533	D₄	—	4	4	no	—
534	D₄	—	4	2	no	—
535	D₄	C₂×C₁₁×C₂²⋊C₄	1	2	yes	—
536	D₄	C₂×C₁₁×C₂²⋊C₄	1	2	yes	—
537	C₂×C₄	—	2	1	no	—
538	C₂×C₄	—	2	1	no	—
539	C₂×C₄	—	2	2	no	—
540	C₂×C₄	—	2	2	no	—
541	C₂×C₄	—	2	4	no	—
542	C₂×C₄	—	2	4	no	—
543	C₂×C₄	—	2	2	no	—
544	C₂×C₄	—	4	4	no	—
545	C₂×C₄	—	4	4	no	—
546	C₂×C₄	—	4	4	no	—
547	C₂×C₄	—	4	2	no	—
548	C₂×C₄	—	4	2	no	—
549	C₂×C₄	C₄×D₄×C₁₁	1	2	yes	—
550	C₂×C₄	C₂³×C₄×C₁₁	1	1	yes	characteristic
551	C₂×C₄	C₂²×D₄×C₁₁	1	2	yes	—
552	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
553	C₂×C₄	C₁₁×H(5,𝔽₂)	1	2	yes	—
554	C₈	—	2	2	no	—
555	C₈	—	2	4	no	—
556	C₈	—	4	2	no	—
557	C₈	—	4	2	no	—
558	C₈	C₂×C₁₁×C₂²⋊C₄	1	1	yes	characteristic
559	C₈	C₂×C₁₁×C₂²⋊C₄	1	1	yes	characteristic
560	C₈	C₂×C₁₁×C₂²⋊C₄	1	2	yes	—
561	C₂²	—	2	2	no	—
562	C₂²	—	2	2	no	—
563	C₂²	—	2	2	no	—
564	C₂²	—	4	1	no	—
565	C₂²	—	4	2	no	—
566	C₂²	—	4	2	no	—
567	C₂²	—	8	1	no	—
568	C₂²	—	8	1	no	—
569	C₂²	—	8	2	no	—
570	C₂²	—	16	2	no	—
571	C₂²	—	16	4	no	—
572	C₂²	C₂×C₄×D₄×C₁₁	1	1	yes	characteristic
573	C₂²	C₁₁×#546	1	2	yes	—
574	C₄	—	2	2	no	—
575	C₄	—	2	2	no	—
576	C₄	—	2	2	no	—
577	C₄	—	4	2	no	—
578	C₄	—	8	2	no	—
579	C₄	C₂²×C₁₁×C₂²⋊C₄	1	1	yes	characteristic
580	C₄	C₁₁×#518	1	1	yes	characteristic
581	C₄	D₄²×C₁₁	1	2	yes	—
582	C₂	—	2	2	no	—
583	C₂	—	2	1	no	—
584	C₂	—	4	2	no	—
585	C₂	—	4	2	no	—
586	C₂	—	4	2	no	—
587	C₂	—	8	2	no	—
588	C₂	D₄×C₁₁×C₂²⋊C₄	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₁₁	D₄×C₂²⋊C₄
commutator	C₂×C₄	C₂³×C₄×C₁₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₁
prime radical	C₂×C₁₁×#577	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₁ ◁ C₂²×C₄×C₁₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₁×#2957	C₂	semidirect
3. C₁₁×#2889	C₂	semidirect
4. C₁₁×#2888	C₂	semidirect
5. C₁₁×#1977	C₂	semidirect
6. C₁₁×#1903	C₂	semidirect
7. C₁₁×#1902	C₂	semidirect
8. C₁₁×#1813	C₂	semidirect
9. C₁₁×#1796	C₂	semidirect
10. C₁₁×#1795	C₂	semidirect
11. C₁₁×#1757	C₂	semidirect
16. C₂×C₁₁×#137	C₄	semidirect
18. C₂×C₁₁×AGL(1,ℤ/8)	C₄	semidirect
20. C₂×C₁₁×#135	C₄	semidirect
22. C₂²×C₁₁×SD₁₆	C₄	semidirect
25. C₁₁×#568	C₂²	semidirect
29. C₂×C₁₁×#108	C₂²	semidirect
31. C₁₁×#421	C₂²	semidirect
32. C₁₁×#419	C₂²	semidirect
40. C₂×C₁₁×#101	C₂²	semidirect
44. C₁₁×#405	C₂²	semidirect
45. C₁₁×#344	C₂²	semidirect
46. C₁₁×#338	C₂²	semidirect
121. #22459	C₁₁	direct (N × H)
212. #2957	C₂×C₁₁	semidirect
213. #2889	C₂×C₁₁	semidirect
214. #2888	C₂×C₁₁	semidirect
215. #1977	C₂×C₁₁	semidirect
216. #1903	C₂×C₁₁	semidirect
217. #1902	C₂×C₁₁	semidirect
218. #1813	C₂×C₁₁	semidirect
219. #1796	C₂×C₁₁	semidirect
220. #1795	C₂×C₁₁	semidirect
221. #1757	C₂×C₁₁	semidirect
282. C₂×#137	C₄×C₁₁	semidirect
284. C₂×AGL(1,ℤ/8)	C₄×C₁₁	semidirect
286. C₂×#135	C₄×C₁₁	semidirect
288. C₂²×SD₁₆	C₄×C₁₁	semidirect
291. #568	C₂²×C₁₁	semidirect
295. C₂×#108	C₂²×C₁₁	semidirect
297. #421	C₂²×C₁₁	semidirect
298. #419	C₂²×C₁₁	semidirect
306. C₂×#101	C₂²×C₁₁	semidirect
310. #405	C₂²×C₁₁	semidirect
311. #344	C₂²×C₁₁	semidirect
312. #338	C₂²×C₁₁	semidirect
504. C₁₁	#22459	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×#577	2
C₁₁×#2957	2
C₁₁×#2889	2
C₁₁×#2888	2
C₁₁×#1977	2
C₁₁×#1903	2
C₁₁×#1902	2
C₁₁×#1813	2
C₁₁×#1796	2
C₁₁×#1795	2
C₁₁×#1757	2
#22459	11

Subgroups — C11×#22459 #14599652

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#22459 #14599652