Subgroups — C₁₁×#22060 #14599253

Order 2816.

926 conjugacy classes of subgroups.

The subgroup lattice has 602 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×#3002	C₂	1	1	yes	maximal, characteristic
2	C₁₁×#2929	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₁×#408	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₁×#1974	C₂	1	2	yes	maximal, complemented
5	C₁₁×#1937	C₂	1	2	yes	maximal, complemented
6	C₁₁×#1929	C₂	1	2	yes	maximal, complemented
7	C₁₁×#1876	C₂	1	2	yes	maximal, complemented
8	C₁₁×#1871	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₁×#1855	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₁×#1789	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈×C₁₁×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₁₁×#41	C₂²	1	1	yes	characteristic
13	C₂×C₁₁×#135	C₂²	1	2	yes	—
14	C₂×C₁₁×#131	C₂²	1	1	yes	characteristic, complemented
15	C₂²×C₁₁×M₁₆	C₂²	1	1	yes	characteristic
16	C₂³×C₈×C₁₁	C₂²	1	1	yes	characteristic
17	C₁₁×#525	C₂²	1	1	yes	characteristic
18	C₁₁×#452	C₄	1	2	yes	complemented
19	C₁₁×#451	C₄	1	1	yes	characteristic, complemented
20	C₁₁×#450	C₄	1	1	yes	characteristic, complemented
21	C₁₁×#449	C₄	1	2	yes	complemented
22	C₁₁×#448	C₄	1	1	yes	characteristic, complemented
23	C₁₁×#447	C₄	1	1	yes	characteristic, complemented
24	C₁₁×#435	—	2	1	no	—
25	C₁₁×#435	—	2	1	no	—
26	C₈×D₄×C₁₁	—	2	1	no	—
27	C₈×D₄×C₁₁	—	2	1	no	—
28	C₂×C₁₁×#108	C₂²	1	2	yes	complemented
29	C₁₁×#424	C₂²	1	1	yes	characteristic, complemented
30	C₂×C₁₁×#104	C₂²	1	2	yes	—
31	C₂×C₁₁×#104	C₂²	1	2	yes	—
32	C₂×C₁₁×#104	C₂²	1	2	yes	complemented
33	C₁₁×#416	C₂²	1	2	yes	—
34	C₁₁×#408	—	2	1	no	—
35	C₁₁×#408	—	2	1	no	—
36	C₁₁×#408	C₂²	1	2	yes	—
37	C₁₁×#408	C₂²	1	2	yes	—
38	C₁₁×#408	C₂²	1	1	yes	characteristic, complemented
39	C₁₁×#407	C₂²	1	1	yes	characteristic
40	C₂×C₁₁×C₂²⋊C₈	—	2	1	no	—
41	C₂×C₁₁×C₂²⋊C₈	—	2	1	no	—
42	C₂×C₁₁×C₂²⋊C₈	C₂²	1	1	yes	characteristic
43	C₁₁×#405	C₂²	1	1	yes	characteristic, complemented
44	C₂×C₄×C₈×C₁₁	C₂²	1	2	yes	complemented
45	C₄×C₁₁×C₂²⋊C₄	C₂²	1	1	yes	characteristic
46	C₁₁×#341	C₂²	1	2	yes	complemented
47	C₁₁×#339	C₂²	1	2	yes	complemented
48	C₁₁×#336	C₂²	1	2	yes	complemented
49	C₂×C₁₁×#41	—	2	1	no	—
50	C₂×C₁₁×#41	—	2	1	no	—
51	C₂×C₁₁×#41	—	4	2	no	—
52	C₂×C₁₁×#41	—	4	2	no	—
53	C₂×C₁₁×#41	C₂×C₄	1	2	yes	—
54	C₂×C₁₁×#41	C₂³	1	1	yes	characteristic
55	C₂×C₁₁×#41	C₂³	1	2	yes	—
56	C₂²×Q₈×C₁₁	C₂×C₄	1	1	yes	characteristic
57	C₂²×D₄×C₁₁	—	2	1	no	—
58	C₂²×D₄×C₁₁	C₂×C₄	1	1	yes	characteristic
59	C₂³×C₄×C₁₁	—	2	1	no	—
60	C₂³×C₄×C₁₁	C₂³	1	1	yes	characteristic
61	C₁₁×#135	—	4	2	no	—
62	C₁₁×#135	—	4	2	no	—
63	C₂×C₁₁×Q₁₆	C₂×C₄	1	2	yes	—
64	C₂×C₁₁×SD₁₆	C₂×C₄	1	2	yes	—
65	C₂×C₁₁×SD₁₆	C₂×C₄	1	2	yes	—
66	C₂×C₁₁×D₈	C₂×C₄	1	2	yes	—
67	C₁₁×#131	—	4	2	no	—
68	C₂×C₁₁×M₁₆	—	2	1	no	—
69	C₂×C₁₁×M₁₆	—	2	1	no	—
70	C₂×C₁₁×M₁₆	—	4	2	no	—
71	C₂×C₁₁×M₁₆	C₂³	1	2	yes	—
72	C₂×C₁₁×M₁₆	C₂³	1	1	yes	characteristic
73	C₂×C₁₁×M₁₆	C₂³	1	1	yes	characteristic
74	C₂²×C₈×C₁₁	—	2	1	no	—
75	C₂²×C₈×C₁₁	—	2	1	no	—
76	C₂²×C₈×C₁₁	—	4	2	no	—
77	C₂²×C₈×C₁₁	D₄	1	1	yes	characteristic
78	C₂²×C₈×C₁₁	D₄	1	1	yes	characteristic
79	C₂²×C₈×C₁₁	D₄	1	1	yes	characteristic
80	C₂²×C₈×C₁₁	D₄	1	1	yes	characteristic
81	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
82	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
83	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
84	C₁₁×#123	—	2	1	no	—
85	C₁₁×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
86	C₁₁×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
87	C₁₁×#121	C₂×C₄	1	1	yes	characteristic
88	C₁₁×#121	C₂×C₄	1	1	yes	characteristic
89	C₁₁×#120	—	2	1	no	—
90	C₄×D₄×C₁₁	—	2	1	no	—
91	C₄×D₄×C₁₁	—	2	1	no	—
92	C₁₁×#117	C₂³	1	1	yes	characteristic
93	C₂×C₁₁×C₂²⋊C₄	—	2	1	no	—
94	C₂×C₄²×C₁₁	C₂³	1	2	yes	—
95	C₁₁×#108	—	4	2	no	—
96	C₁₁×C₄⋊C₈	—	2	1	no	—
97	C₁₁×C₄⋊C₈	—	2	1	no	—
98	C₁₁×#104	—	4	2	no	—
99	C₁₁×#104	—	4	2	no	—
100	C₁₁×#104	—	4	2	no	—
101	C₁₁×#103	C₂×C₄	1	2	yes	—
102	C₁₁×#103	C₂×C₄	1	2	yes	—
103	C₁₁×#102	C₂×C₄	1	2	yes	—
104	C₁₁×#102	C₂×C₄	1	2	yes	—
105	C₁₁×C₂²⋊C₈	—	2	1	no	—
106	C₁₁×C₂²⋊C₈	—	2	1	no	—
107	C₁₁×C₂²⋊C₈	—	2	2	no	—
108	C₁₁×C₂²⋊C₈	—	2	2	no	—
109	C₁₁×C₂²⋊C₈	—	2	2	no	—
110	C₁₁×C₂²⋊C₈	—	2	2	no	—
111	C₁₁×C₂²⋊C₈	—	2	1	no	—
112	C₁₁×C₂²⋊C₈	—	2	1	no	—
113	C₁₁×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
114	C₁₁×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
115	C₁₁×C₂²⋊C₈	C₂×C₄	1	2	yes	—
116	C₁₁×#97	—	2	1	no	—
117	C₄×C₈×C₁₁	—	2	1	no	—
118	C₄×C₈×C₁₁	—	4	2	no	—
119	C₁₁×#95	—	2	1	no	—
120	#22060	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
121	C₂⁴×C₁₁	—	2	1	no	—
122	C₂⁴×C₁₁	#41	1	1	yes	characteristic
123	C₁₁×#41	—	2	2	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	2	no	—
129	C₁₁×#41	—	4	2	no	—
130	C₁₁×#41	—	4	2	no	—
131	C₁₁×#41	—	4	4	no	—
132	C₁₁×#41	—	4	2	no	—
133	C₁₁×#41	—	4	2	no	—
134	C₂×Q₈×C₁₁	—	2	1	no	—
135	C₂×Q₈×C₁₁	—	4	2	no	—
136	C₂×Q₈×C₁₁	C₂²×C₄	1	2	yes	—
137	C₂×Q₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
138	C₂×D₄×C₁₁	—	2	1	no	—
139	C₂×D₄×C₁₁	—	2	1	no	—
140	C₂×D₄×C₁₁	—	2	2	no	—
141	C₂×D₄×C₁₁	—	2	1	no	—
142	C₂×D₄×C₁₁	—	2	2	no	—
143	C₂×D₄×C₁₁	—	2	1	no	—
144	C₂×D₄×C₁₁	—	4	2	no	—
145	C₂×D₄×C₁₁	—	4	4	no	—
146	C₂×D₄×C₁₁	C₂²×C₄	1	2	yes	—
147	C₂×D₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
148	C₂²×C₄×C₁₁	—	2	2	no	—
149	C₂²×C₄×C₁₁	—	2	2	no	—
150	C₂²×C₄×C₁₁	—	2	1	no	—
151	C₂²×C₄×C₁₁	—	2	2	no	—
152	C₂²×C₄×C₁₁	—	2	2	no	—
153	C₂²×C₄×C₁₁	—	2	2	no	—
154	C₂²×C₄×C₁₁	—	2	1	no	—
155	C₂²×C₄×C₁₁	—	4	2	no	—
156	C₂²×C₄×C₁₁	—	4	2	no	—
157	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
158	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
159	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
160	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
161	C₂²×C₄×C₁₁	#41	1	1	yes	characteristic
162	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
163	C₁₁×Q₁₆	—	4	2	no	—
164	C₁₁×SD₁₆	—	4	2	no	—
165	C₁₁×SD₁₆	—	4	2	no	—
166	C₁₁×D₈	—	4	2	no	—
167	C₁₁×M₁₆	—	2	2	no	—
168	C₁₁×M₁₆	—	2	2	no	—
169	C₁₁×M₁₆	—	2	2	no	—
170	C₁₁×M₁₆	—	2	2	no	—
171	C₁₁×M₁₆	—	4	2	no	—
172	C₁₁×M₁₆	—	4	2	no	—
173	C₂×C₈×C₁₁	—	2	1	no	—
174	C₂×C₈×C₁₁	—	2	2	no	—
175	C₂×C₈×C₁₁	—	2	1	no	—
176	C₂×C₈×C₁₁	—	2	2	no	—
177	C₂×C₈×C₁₁	—	2	2	no	—
178	C₂×C₈×C₁₁	—	2	2	no	—
179	C₂×C₈×C₁₁	—	2	2	no	—
180	C₂×C₈×C₁₁	—	4	1	no	—
181	C₂×C₈×C₁₁	—	4	1	no	—
182	C₂×C₈×C₁₁	—	4	1	no	—
183	C₂×C₈×C₁₁	—	4	1	no	—
184	C₂×C₈×C₁₁	—	4	2	no	—
185	C₂×C₈×C₁₁	—	4	2	no	—
186	C₂×C₈×C₁₁	C₂²×C₄	1	2	yes	—
187	C₂×C₈×C₁₁	C₂²×C₄	1	2	yes	—
188	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
189	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
190	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
191	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
192	C₁₁×C₄⋊C₄	—	2	1	no	—
193	C₁₁×C₄⋊C₄	—	2	1	no	—
194	C₁₁×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
195	C₁₁×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
196	C₁₁×C₂²⋊C₄	—	2	4	no	—
197	C₁₁×C₂²⋊C₄	—	2	1	no	—
198	C₁₁×C₂²⋊C₄	—	2	1	no	—
199	C₁₁×C₂²⋊C₄	—	2	1	no	—
200	C₁₁×C₂²⋊C₄	—	2	1	no	—
201	C₁₁×C₂²⋊C₄	—	2	1	no	—
202	C₄²×C₁₁	—	2	1	no	—
203	C₄²×C₁₁	—	2	2	no	—
204	C₄²×C₁₁	—	2	2	no	—
205	#3002	C₂×C₁₁	1	1	yes	characteristic
206	#2929	C₂×C₁₁	1	1	yes	characteristic, complemented
207	C₂×#408	C₂×C₁₁	1	1	yes	characteristic, complemented
208	#1974	C₂×C₁₁	1	2	yes	complemented
209	#1937	C₂×C₁₁	1	2	yes	complemented
210	#1929	C₂×C₁₁	1	2	yes	complemented
211	#1876	C₂×C₁₁	1	2	yes	complemented
212	#1871	C₂×C₁₁	1	1	yes	characteristic, complemented
213	#1855	C₂×C₁₁	1	1	yes	characteristic, complemented
214	#1789	C₂×C₁₁	1	1	yes	characteristic, complemented
215	C₈×C₂²⋊C₄	C₂×C₁₁	1	1	yes	characteristic, complemented
216	C₂³×C₁₁	—	2	2	no	—
217	C₂³×C₁₁	—	2	2	no	—
218	C₂³×C₁₁	—	2	1	no	—
219	C₂³×C₁₁	—	2	2	no	—
220	C₂³×C₁₁	—	4	1	no	—
221	C₂³×C₁₁	—	4	2	no	—
222	C₂³×C₁₁	—	4	2	no	—
223	C₂³×C₁₁	—	4	2	no	—
224	C₂³×C₁₁	C₄×D₄	1	1	yes	characteristic
225	C₂³×C₁₁	C₄×D₄	1	1	yes	characteristic
226	C₂³×C₁₁	C₂×#41	1	1	yes	characteristic
227	Q₈×C₁₁	—	2	2	no	—
228	Q₈×C₁₁	—	2	2	no	—
229	Q₈×C₁₁	—	2	2	no	—
230	Q₈×C₁₁	—	4	2	no	—
231	D₄×C₁₁	—	2	2	no	—
232	D₄×C₁₁	—	2	2	no	—
233	D₄×C₁₁	—	2	2	no	—
234	D₄×C₁₁	—	4	2	no	—
235	D₄×C₁₁	—	4	2	no	—
236	D₄×C₁₁	—	4	4	no	—
237	D₄×C₁₁	—	4	2	no	—
238	D₄×C₁₁	—	4	2	no	—
239	D₄×C₁₁	—	4	2	no	—
240	D₄×C₁₁	—	4	2	no	—
241	C₂×C₄×C₁₁	—	2	2	no	—
242	C₂×C₄×C₁₁	—	2	2	no	—
243	C₂×C₄×C₁₁	—	2	2	no	—
244	C₂×C₄×C₁₁	—	2	1	no	—
245	C₂×C₄×C₁₁	—	2	1	no	—
246	C₂×C₄×C₁₁	—	2	1	no	—
247	C₂×C₄×C₁₁	—	2	1	no	—
248	C₂×C₄×C₁₁	—	2	4	no	—
249	C₂×C₄×C₁₁	—	2	1	no	—
250	C₂×C₄×C₁₁	—	2	1	no	—
251	C₂×C₄×C₁₁	—	2	1	no	—
252	C₂×C₄×C₁₁	—	2	2	no	—
253	C₂×C₄×C₁₁	—	4	4	no	—
254	C₂×C₄×C₁₁	—	4	2	no	—
255	C₂×C₄×C₁₁	—	4	2	no	—
256	C₂×C₄×C₁₁	—	4	2	no	—
257	C₂×C₄×C₁₁	—	4	1	no	—
258	C₂×C₄×C₁₁	—	4	2	no	—
259	C₂×C₄×C₁₁	—	4	2	no	—
260	C₂×C₄×C₁₁	—	4	1	no	—
261	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
262	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
263	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
264	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
265	C₂×C₄×C₁₁	H(5,𝔽₂)	1	2	yes	—
266	C₂×C₄×C₁₁	H(5,𝔽₂)	1	2	yes	—
267	C₈×C₁₁	—	2	2	no	—
268	C₈×C₁₁	—	2	2	no	—
269	C₈×C₁₁	—	2	1	no	—
270	C₈×C₁₁	—	2	1	no	—
271	C₈×C₁₁	—	2	1	no	—
272	C₈×C₁₁	—	2	1	no	—
273	C₈×C₁₁	—	4	1	no	—
274	C₈×C₁₁	—	4	2	no	—
275	C₈×C₁₁	—	4	1	no	—
276	C₂²×#41	C₂²×C₁₁	1	1	yes	characteristic
277	C₂×#135	C₂²×C₁₁	1	2	yes	—
278	C₂×#131	C₂²×C₁₁	1	1	yes	characteristic, complemented
279	C₂²×M₁₆	C₂²×C₁₁	1	1	yes	characteristic
280	C₂³×C₈	C₂²×C₁₁	1	1	yes	characteristic
281	#525	C₂²×C₁₁	1	1	yes	characteristic
282	#452	C₄×C₁₁	1	2	yes	complemented
283	#451	C₄×C₁₁	1	1	yes	characteristic, complemented
284	#450	C₄×C₁₁	1	1	yes	characteristic, complemented
285	#449	C₄×C₁₁	1	2	yes	complemented
286	#448	C₄×C₁₁	1	1	yes	characteristic, complemented
287	#447	C₄×C₁₁	1	1	yes	characteristic, complemented
288	#435	—	2	1	no	—
289	#435	—	2	1	no	—
290	C₈×D₄	—	2	1	no	—
291	C₈×D₄	—	2	1	no	—
292	C₂×#108	C₂²×C₁₁	1	2	yes	complemented
293	#424	C₂²×C₁₁	1	1	yes	characteristic, complemented
294	C₂×#104	C₂²×C₁₁	1	2	yes	—
295	C₂×#104	C₂²×C₁₁	1	2	yes	—
296	C₂×#104	C₂²×C₁₁	1	2	yes	complemented
297	#416	C₂²×C₁₁	1	2	yes	—
298	#408	—	2	1	no	—
299	#408	—	2	1	no	—
300	#408	C₂²×C₁₁	1	2	yes	—
301	#408	C₂²×C₁₁	1	2	yes	—
302	#408	C₂²×C₁₁	1	1	yes	characteristic, complemented
303	#407	C₂²×C₁₁	1	1	yes	characteristic
304	C₂×C₂²⋊C₈	—	2	1	no	—
305	C₂×C₂²⋊C₈	—	2	1	no	—
306	C₂×C₂²⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
307	#405	C₂²×C₁₁	1	1	yes	characteristic, complemented
308	C₂×C₄×C₈	C₂²×C₁₁	1	2	yes	complemented
309	C₄×C₂²⋊C₄	C₂²×C₁₁	1	1	yes	characteristic
310	#341	C₂²×C₁₁	1	2	yes	complemented
311	#339	C₂²×C₁₁	1	2	yes	complemented
312	#336	C₂²×C₁₁	1	2	yes	complemented
313	C₂²×C₁₁	—	2	1	no	—
314	C₂²×C₁₁	—	2	1	no	—
315	C₂²×C₁₁	—	2	1	no	—
316	C₂²×C₁₁	—	2	1	no	—
317	C₂²×C₁₁	—	2	1	no	—
318	C₂²×C₁₁	—	2	1	no	—
319	C₂²×C₁₁	—	2	1	no	—
320	C₂²×C₁₁	—	4	4	no	—
321	C₂²×C₁₁	—	4	2	no	—
322	C₂²×C₁₁	—	4	1	no	—
323	C₂²×C₁₁	—	4	1	no	—
324	C₂²×C₁₁	—	4	2	no	—
325	C₂²×C₁₁	—	4	1	no	—
326	C₂²×C₁₁	—	4	2	no	—
327	C₂²×C₁₁	—	8	4	no	—
328	C₂²×C₁₁	#443	1	2	yes	—
329	C₂²×C₁₁	C₂×C₄×D₄	1	1	yes	characteristic
330	C₂²×C₁₁	#538	1	2	yes	—
331	C₄×C₁₁	—	2	1	no	—
332	C₄×C₁₁	—	2	1	no	—
333	C₄×C₁₁	—	4	4	no	—
334	C₄×C₁₁	—	4	2	no	—
335	C₄×C₁₁	—	4	1	no	—
336	C₄×C₁₁	—	4	1	no	—
337	C₄×C₁₁	—	4	1	no	—
338	C₄×C₁₁	#518	1	2	yes	—
339	C₄×C₁₁	#534	1	1	yes	characteristic
340	C₄×C₁₁	#535	1	1	yes	characteristic
341	C₂×#41	—	2	1	no	—
342	C₂×#41	—	2	1	no	—
343	C₂×#41	—	4	2	no	—
344	C₂×#41	—	4	2	no	—
345	C₂×#41	C₂×C₄×C₁₁	1	2	yes	—
346	C₂×#41	C₂³×C₁₁	1	1	yes	characteristic
347	C₂×#41	C₂³×C₁₁	1	2	yes	—
348	C₂²×Q₈	C₂×C₄×C₁₁	1	1	yes	characteristic
349	C₂²×D₄	—	2	1	no	—
350	C₂²×D₄	C₂×C₄×C₁₁	1	1	yes	characteristic
351	C₂³×C₄	—	2	1	no	—
352	C₂³×C₄	C₂³×C₁₁	1	1	yes	characteristic
353	#135	—	4	2	no	—
354	#135	—	4	2	no	—
355	C₂×Q₁₆	C₂×C₄×C₁₁	1	2	yes	—
356	C₂×SD₁₆	C₂×C₄×C₁₁	1	2	yes	—
357	C₂×SD₁₆	C₂×C₄×C₁₁	1	2	yes	—
358	C₂×D₈	C₂×C₄×C₁₁	1	2	yes	—
359	#131	—	4	2	no	—
360	C₂×M₁₆	—	2	1	no	—
361	C₂×M₁₆	—	2	1	no	—
362	C₂×M₁₆	—	4	2	no	—
363	C₂×M₁₆	C₂³×C₁₁	1	2	yes	—
364	C₂×M₁₆	C₂³×C₁₁	1	1	yes	characteristic
365	C₂×M₁₆	C₂³×C₁₁	1	1	yes	characteristic
366	C₂²×C₈	—	2	1	no	—
367	C₂²×C₈	—	2	1	no	—
368	C₂²×C₈	—	4	2	no	—
369	C₂²×C₈	D₄×C₁₁	1	1	yes	characteristic
370	C₂²×C₈	D₄×C₁₁	1	1	yes	characteristic
371	C₂²×C₈	D₄×C₁₁	1	1	yes	characteristic
372	C₂²×C₈	D₄×C₁₁	1	1	yes	characteristic
373	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
374	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
375	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
376	#123	—	2	1	no	—
377	C₂²⋊Q₈	C₂×C₄×C₁₁	1	1	yes	characteristic
378	C₂²⋊Q₈	C₂×C₄×C₁₁	1	1	yes	characteristic
379	#121	C₂×C₄×C₁₁	1	1	yes	characteristic
380	#121	C₂×C₄×C₁₁	1	1	yes	characteristic
381	#120	—	2	1	no	—
382	C₄×D₄	—	2	1	no	—
383	C₄×D₄	—	2	1	no	—
384	#117	C₂³×C₁₁	1	1	yes	characteristic
385	C₂×C₂²⋊C₄	—	2	1	no	—
386	C₂×C₄²	C₂³×C₁₁	1	2	yes	—
387	#108	—	4	2	no	—
388	C₄⋊C₈	—	2	1	no	—
389	C₄⋊C₈	—	2	1	no	—
390	#104	—	4	2	no	—
391	#104	—	4	2	no	—
392	#104	—	4	2	no	—
393	#103	C₂×C₄×C₁₁	1	2	yes	—
394	#103	C₂×C₄×C₁₁	1	2	yes	—
395	#102	C₂×C₄×C₁₁	1	2	yes	—
396	#102	C₂×C₄×C₁₁	1	2	yes	—
397	C₂²⋊C₈	—	2	1	no	—
398	C₂²⋊C₈	—	2	1	no	—
399	C₂²⋊C₈	—	2	2	no	—
400	C₂²⋊C₈	—	2	2	no	—
401	C₂²⋊C₈	—	2	2	no	—
402	C₂²⋊C₈	—	2	2	no	—
403	C₂²⋊C₈	—	2	1	no	—
404	C₂²⋊C₈	—	2	1	no	—
405	C₂²⋊C₈	C₂×C₄×C₁₁	1	1	yes	characteristic
406	C₂²⋊C₈	C₂×C₄×C₁₁	1	1	yes	characteristic
407	C₂²⋊C₈	C₂×C₄×C₁₁	1	2	yes	—
408	#97	—	2	1	no	—
409	C₄×C₈	—	2	1	no	—
410	C₄×C₈	—	4	2	no	—
411	#95	—	2	1	no	—
412	C₂×C₁₁	—	2	2	no	—
413	C₂×C₁₁	—	2	2	no	—
414	C₂×C₁₁	—	4	1	no	—
415	C₂×C₁₁	—	8	1	no	—
416	C₂×C₁₁	—	8	2	no	—
417	C₂×C₁₁	#2321	1	1	yes	characteristic
418	C₂×C₁₁	C₂×#443	1	1	yes	characteristic
419	C₂×C₁₁	#2955	1	1	yes	characteristic
420	C₂⁴	—	2	1	no	—
421	C₂⁴	C₁₁×#41	1	1	yes	characteristic
422	#41	—	2	2	no	—
423	#41	—	2	2	no	—
424	#41	—	2	2	no	—
425	#41	—	2	2	no	—
426	#41	—	2	2	no	—
427	#41	—	2	2	no	—
428	#41	—	4	2	no	—
429	#41	—	4	2	no	—
430	#41	—	4	4	no	—
431	#41	—	4	2	no	—
432	#41	—	4	2	no	—
433	C₂×Q₈	—	2	1	no	—
434	C₂×Q₈	—	4	2	no	—
435	C₂×Q₈	C₂²×C₄×C₁₁	1	2	yes	—
436	C₂×Q₈	C₂²×C₄×C₁₁	1	1	yes	characteristic
437	C₂×D₄	—	2	1	no	—
438	C₂×D₄	—	2	1	no	—
439	C₂×D₄	—	2	2	no	—
440	C₂×D₄	—	2	1	no	—
441	C₂×D₄	—	2	2	no	—
442	C₂×D₄	—	2	1	no	—
443	C₂×D₄	—	4	2	no	—
444	C₂×D₄	—	4	4	no	—
445	C₂×D₄	C₂²×C₄×C₁₁	1	2	yes	—
446	C₂×D₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
447	C₂²×C₄	—	2	2	no	—
448	C₂²×C₄	—	2	2	no	—
449	C₂²×C₄	—	2	1	no	—
450	C₂²×C₄	—	2	2	no	—
451	C₂²×C₄	—	2	2	no	—
452	C₂²×C₄	—	2	2	no	—
453	C₂²×C₄	—	2	1	no	—
454	C₂²×C₄	—	4	2	no	—
455	C₂²×C₄	—	4	2	no	—
456	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
457	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
458	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
459	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
460	C₂²×C₄	C₁₁×#41	1	1	yes	characteristic
461	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
462	Q₁₆	—	4	2	no	—
463	SD₁₆	—	4	2	no	—
464	SD₁₆	—	4	2	no	—
465	D₈	—	4	2	no	—
466	M₁₆	—	2	2	no	—
467	M₁₆	—	2	2	no	—
468	M₁₆	—	2	2	no	—
469	M₁₆	—	2	2	no	—
470	M₁₆	—	4	2	no	—
471	M₁₆	—	4	2	no	—
472	C₂×C₈	—	2	2	no	—
473	C₂×C₈	—	2	2	no	—
474	C₂×C₈	—	2	2	no	—
475	C₂×C₈	—	2	2	no	—
476	C₂×C₈	—	2	1	no	—
477	C₂×C₈	—	2	2	no	—
478	C₂×C₈	—	2	1	no	—
479	C₂×C₈	—	4	1	no	—
480	C₂×C₈	—	4	1	no	—
481	C₂×C₈	—	4	1	no	—
482	C₂×C₈	—	4	1	no	—
483	C₂×C₈	—	4	2	no	—
484	C₂×C₈	—	4	2	no	—
485	C₂×C₈	C₂²×C₄×C₁₁	1	2	yes	—
486	C₂×C₈	C₂²×C₄×C₁₁	1	2	yes	—
487	C₂×C₈	C₂×D₄×C₁₁	1	1	yes	characteristic
488	C₂×C₈	C₂×D₄×C₁₁	1	1	yes	characteristic
489	C₂×C₈	C₂×D₄×C₁₁	1	1	yes	characteristic
490	C₂×C₈	C₂×D₄×C₁₁	1	1	yes	characteristic
491	C₄⋊C₄	—	2	1	no	—
492	C₄⋊C₄	—	2	1	no	—
493	C₄⋊C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
494	C₄⋊C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
495	C₂²⋊C₄	—	2	4	no	—
496	C₂²⋊C₄	—	2	1	no	—
497	C₂²⋊C₄	—	2	1	no	—
498	C₂²⋊C₄	—	2	1	no	—
499	C₂²⋊C₄	—	2	1	no	—
500	C₂²⋊C₄	—	2	1	no	—
501	C₄²	—	2	1	no	—
502	C₄²	—	2	2	no	—
503	C₄²	—	2	2	no	—
504	C₁₁	#22060	1	1	yes	characteristic, direct product factor, Sylow
505	C₂³	—	2	2	no	—
506	C₂³	—	2	2	no	—
507	C₂³	—	2	1	no	—
508	C₂³	—	2	2	no	—
509	C₂³	—	4	1	no	—
510	C₂³	—	4	2	no	—
511	C₂³	—	4	2	no	—
512	C₂³	—	4	2	no	—
513	C₂³	C₄×D₄×C₁₁	1	1	yes	characteristic
514	C₂³	C₄×D₄×C₁₁	1	1	yes	characteristic
515	C₂³	C₂×C₁₁×#41	1	1	yes	characteristic
516	Q₈	—	2	2	no	—
517	Q₈	—	2	2	no	—
518	Q₈	—	2	2	no	—
519	Q₈	—	4	2	no	—
520	D₄	—	2	2	no	—
521	D₄	—	2	2	no	—
522	D₄	—	2	2	no	—
523	D₄	—	4	2	no	—
524	D₄	—	4	2	no	—
525	D₄	—	4	4	no	—
526	D₄	—	4	2	no	—
527	D₄	—	4	2	no	—
528	D₄	—	4	2	no	—
529	D₄	—	4	2	no	—
530	C₂×C₄	—	2	2	no	—
531	C₂×C₄	—	2	2	no	—
532	C₂×C₄	—	2	2	no	—
533	C₂×C₄	—	2	1	no	—
534	C₂×C₄	—	2	1	no	—
535	C₂×C₄	—	2	1	no	—
536	C₂×C₄	—	2	1	no	—
537	C₂×C₄	—	2	4	no	—
538	C₂×C₄	—	2	1	no	—
539	C₂×C₄	—	2	1	no	—
540	C₂×C₄	—	2	1	no	—
541	C₂×C₄	—	2	2	no	—
542	C₂×C₄	—	4	4	no	—
543	C₂×C₄	—	4	2	no	—
544	C₂×C₄	—	4	2	no	—
545	C₂×C₄	—	4	2	no	—
546	C₂×C₄	—	4	1	no	—
547	C₂×C₄	—	4	2	no	—
548	C₂×C₄	—	4	2	no	—
549	C₂×C₄	—	4	1	no	—
550	C₂×C₄	C₄×D₄×C₁₁	1	1	yes	characteristic
551	C₂×C₄	C₄×D₄×C₁₁	1	1	yes	characteristic
552	C₂×C₄	C₂³×C₄×C₁₁	1	1	yes	characteristic
553	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
554	C₂×C₄	C₁₁×H(5,𝔽₂)	1	2	yes	—
555	C₂×C₄	C₁₁×H(5,𝔽₂)	1	2	yes	—
556	C₈	—	2	2	no	—
557	C₈	—	2	2	no	—
558	C₈	—	2	1	no	—
559	C₈	—	2	1	no	—
560	C₈	—	2	1	no	—
561	C₈	—	2	1	no	—
562	C₈	—	4	1	no	—
563	C₈	—	4	2	no	—
564	C₈	—	4	1	no	—
565	C₂²	—	2	1	no	—
566	C₂²	—	2	1	no	—
567	C₂²	—	2	1	no	—
568	C₂²	—	2	1	no	—
569	C₂²	—	2	1	no	—
570	C₂²	—	2	1	no	—
571	C₂²	—	2	1	no	—
572	C₂²	—	4	4	no	—
573	C₂²	—	4	1	no	—
574	C₂²	—	4	2	no	—
575	C₂²	—	4	1	no	—
576	C₂²	—	4	2	no	—
577	C₂²	—	4	2	no	—
578	C₂²	—	4	1	no	—
579	C₂²	—	8	4	no	—
580	C₂²	C₁₁×#443	1	2	yes	—
581	C₂²	C₂×C₄×D₄×C₁₁	1	1	yes	characteristic
582	C₂²	C₁₁×#538	1	2	yes	—
583	C₄	—	2	1	no	—
584	C₄	—	2	1	no	—
585	C₄	—	4	4	no	—
586	C₄	—	4	1	no	—
587	C₄	—	4	1	no	—
588	C₄	—	4	2	no	—
589	C₄	—	4	1	no	—
590	C₄	C₁₁×#518	1	2	yes	—
591	C₄	C₁₁×#534	1	1	yes	characteristic
592	C₄	C₁₁×#535	1	1	yes	characteristic
593	C₂	—	2	2	no	—
594	C₂	—	2	2	no	—
595	C₂	—	4	1	no	—
596	C₂	—	8	2	no	—
597	C₂	—	8	1	no	—
598	C₂	C₁₁×#2321	1	1	yes	characteristic
599	C₂	C₂×C₁₁×#443	1	1	yes	characteristic
600	C₂	C₁₁×#2955	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₁	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₁
socle	C₂²×C₁₁	C₂×C₄×D₄
prime radical	C₁₁×#3002	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₁ ◁ C₂³×C₈×C₁₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₁×#2929	C₂	semidirect
3. C₂×C₁₁×#408	C₂	semidirect
4. C₁₁×#1974	C₂	semidirect
5. C₁₁×#1937	C₂	semidirect
6. C₁₁×#1929	C₂	semidirect
7. C₁₁×#1876	C₂	semidirect
8. C₁₁×#1871	C₂	semidirect
9. C₁₁×#1855	C₂	semidirect
10. C₁₁×#1789	C₂	semidirect
11. C₈×C₁₁×C₂²⋊C₄	C₂	semidirect
14. C₂×C₁₁×#131	C₂²	semidirect
18. C₁₁×#452	C₄	semidirect
19. C₁₁×#451	C₄	semidirect
20. C₁₁×#450	C₄	semidirect
21. C₁₁×#449	C₄	semidirect
22. C₁₁×#448	C₄	semidirect
23. C₁₁×#447	C₄	semidirect
28. C₂×C₁₁×#108	C₂²	semidirect
29. C₁₁×#424	C₂²	semidirect
32. C₂×C₁₁×#104	C₂²	semidirect
38. C₁₁×#408	C₂²	semidirect
43. C₁₁×#405	C₂²	semidirect
44. C₂×C₄×C₈×C₁₁	C₂²	semidirect
46. C₁₁×#341	C₂²	semidirect
47. C₁₁×#339	C₂²	semidirect
48. C₁₁×#336	C₂²	semidirect
120. #22060	C₁₁	direct (N × H)
206. #2929	C₂×C₁₁	semidirect
207. C₂×#408	C₂×C₁₁	semidirect
208. #1974	C₂×C₁₁	semidirect
209. #1937	C₂×C₁₁	semidirect
210. #1929	C₂×C₁₁	semidirect
211. #1876	C₂×C₁₁	semidirect
212. #1871	C₂×C₁₁	semidirect
213. #1855	C₂×C₁₁	semidirect
214. #1789	C₂×C₁₁	semidirect
215. C₈×C₂²⋊C₄	C₂×C₁₁	semidirect
278. C₂×#131	C₂²×C₁₁	semidirect
282. #452	C₄×C₁₁	semidirect
283. #451	C₄×C₁₁	semidirect
284. #450	C₄×C₁₁	semidirect
285. #449	C₄×C₁₁	semidirect
286. #448	C₄×C₁₁	semidirect
287. #447	C₄×C₁₁	semidirect
292. C₂×#108	C₂²×C₁₁	semidirect
293. #424	C₂²×C₁₁	semidirect
296. C₂×#104	C₂²×C₁₁	semidirect
302. #408	C₂²×C₁₁	semidirect
307. #405	C₂²×C₁₁	semidirect
308. C₂×C₄×C₈	C₂²×C₁₁	semidirect
310. #341	C₂²×C₁₁	semidirect
311. #339	C₂²×C₁₁	semidirect
312. #336	C₂²×C₁₁	semidirect
504. C₁₁	#22060	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×#3002	2
C₁₁×#2929	2
C₂×C₁₁×#408	2
C₁₁×#1974	2
C₁₁×#1937	2
C₁₁×#1929	2
C₁₁×#1876	2
C₁₁×#1871	2
C₁₁×#1855	2
C₁₁×#1789	2
C₈×C₁₁×C₂²⋊C₄	2
#22060	11

Subgroups — C11×#22060 #14599253

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#22060 #14599253