Subgroups — C₁₁×#24799 #14601992

Order 2816.

890 conjugacy classes of subgroups.

The subgroup lattice has 534 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₁×#472	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₁×#3058	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₁×#3045	C₂	1	2	yes	maximal, complemented
4	C₂×C₁₁×#444	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₁×#2912	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₁×#2063	C₂	1	2	yes	maximal, complemented
7	C₁₁×#2037	C₂	1	2	yes	maximal, complemented
8	C₁₁×#1972	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₁×#1946	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₁×#1883	C₂	1	2	yes	maximal, complemented
11	C₁₁×#1815	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₁×AGL(1,ℤ/8)	C₂²	1	2	yes	—
13	C₂×C₁₁×#135	C₂²	1	1	yes	characteristic
14	C₂²×C₁₁×D₈	C₂²	1	1	yes	characteristic
15	C₂×C₁₁×#131	C₂²	1	1	yes	characteristic
16	C₂×C₁₁×#131	C₂²	1	1	yes	characteristic
17	C₁₁×#535	C₂²	1	2	yes	—
18	C₁₁×#520	C₂²	1	2	yes	—
19	C₁₁×#472	—	2	4	no	—
20	C₁₁×#469	—	2	1	no	—
21	C₁₁×#469	—	2	1	no	—
22	C₁₁×#466	—	2	2	no	—
23	C₁₁×#464	—	2	2	no	—
24	C₁₁×#463	—	2	2	no	—
25	C₁₁×#460	—	2	2	no	—
26	C₁₁×#459	—	2	2	no	—
27	C₁₁×#444	—	2	4	no	—
28	C₂×C₁₁×#108	C₂²	1	1	yes	characteristic
29	C₂×C₁₁×#108	C₂²	1	1	yes	characteristic
30	C₁₁×#428	—	2	2	no	—
31	C₁₁×#428	C₂²	1	2	yes	—
32	C₁₁×#427	—	2	1	no	—
33	C₁₁×#427	C₂²	1	1	yes	characteristic
34	C₂×C₁₁×#106	—	2	1	no	—
35	C₂×C₁₁×#106	C₂²	1	1	yes	characteristic
36	C₁₁×#424	C₂²	1	2	yes	—
37	C₂×C₁₁×#104	C₂²	1	1	yes	characteristic
38	C₂×C₁₁×#104	C₂²	1	1	yes	characteristic
39	C₁₁×#418	C₂²	1	2	yes	—
40	C₁₁×#417	C₂²	1	2	yes	—
41	C₂×C₁₁×#102	C₂²	1	2	yes	—
42	C₂×C₁₁×#100	C₂²	1	2	yes	—
43	C₂×C₁₁×#97	C₂²	1	1	yes	characteristic
44	C₁₁×#390	C₂²	1	2	yes	—
45	C₁₁×#343	C₂²	1	2	yes	—
46	C₁₁×#339	C₂²	1	2	yes	—
47	C₂×C₁₁×#41	C₂³	1	1	yes	characteristic
48	C₂×C₁₁×#41	C₂³	1	1	yes	characteristic
49	C₂²×D₄×C₁₁	C₂³	1	2	yes	—
50	C₁₁×AGL(1,ℤ/8)	—	2	4	no	—
51	C₁₁×AGL(1,ℤ/8)	—	2	4	no	—
52	C₁₁×#135	—	2	2	no	—
53	C₁₁×#135	—	2	2	no	—
54	C₂×C₁₁×Q₁₆	D₄	1	1	yes	characteristic
55	C₂×C₁₁×SD₁₆	—	2	2	no	—
56	C₂×C₁₁×SD₁₆	D₄	1	1	yes	characteristic
57	C₂×C₁₁×SD₁₆	D₄	1	1	yes	characteristic
58	C₂×C₁₁×D₈	—	2	2	no	—
59	C₂×C₁₁×D₈	—	2	1	no	—
60	C₂×C₁₁×D₈	—	2	1	no	—
61	C₂×C₁₁×D₈	—	2	2	no	—
62	C₂×C₁₁×D₈	—	2	2	no	—
63	C₂×C₁₁×D₈	D₄	1	1	yes	characteristic
64	C₁₁×#131	—	2	2	no	—
65	C₁₁×#131	—	2	2	no	—
66	C₁₁×#131	—	2	2	no	—
67	C₁₁×#131	D₄	1	4	yes	complemented
68	C₂×C₁₁×M₁₆	—	2	1	no	—
69	C₂×C₁₁×M₁₆	—	2	1	no	—
70	C₂×C₁₁×M₁₆	C₂³	1	2	yes	—
71	C₂×C₁₁×M₁₆	C₂³	1	1	yes	characteristic
72	C₂×C₁₁×M₁₆	C₂³	1	1	yes	characteristic
73	C₂²×C₈×C₁₁	—	2	1	no	—
74	C₂²×C₈×C₁₁	—	2	1	no	—
75	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
76	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
77	C₁₁×#127	—	2	2	no	—
78	C₁₁×#124	—	2	2	no	—
79	C₁₁×#121	—	2	2	no	—
80	C₁₁×#121	—	2	2	no	—
81	C₁₁×#120	—	4	2	no	—
82	C₄×Q₈×C₁₁	—	2	2	no	—
83	C₄×D₄×C₁₁	—	2	2	no	—
84	C₄×D₄×C₁₁	—	4	2	no	—
85	C₁₁×#117	—	2	2	no	—
86	C₁₁×#117	C₂³	1	2	yes	—
87	C₂×C₁₁×C₄⋊C₄	—	2	2	no	—
88	C₂×C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
89	C₂×C₁₁×C₂²⋊C₄	—	4	2	no	—
90	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
91	C₁₁×#108	—	2	2	no	—
92	C₁₁×#108	—	2	2	no	—
93	C₁₁×#107	—	2	2	no	—
94	C₁₁×#107	D₄	1	2	yes	—
95	C₁₁×#106	—	2	1	no	—
96	C₁₁×#106	—	2	1	no	—
97	C₁₁×#106	—	2	2	no	—
98	C₁₁×#106	D₄	1	1	yes	characteristic
99	C₁₁×#106	D₄	1	1	yes	characteristic
100	C₁₁×C₄⋊C₈	—	2	2	no	—
101	C₁₁×C₄⋊C₈	—	2	2	no	—
102	C₁₁×#104	—	2	2	no	—
103	C₁₁×#104	—	2	2	no	—
104	C₁₁×#103	—	2	2	no	—
105	C₁₁×#102	—	2	2	no	—
106	C₁₁×#102	—	2	2	no	—
107	C₁₁×#102	—	2	2	no	—
108	C₁₁×#102	—	2	2	no	—
109	C₁₁×#102	—	2	2	no	—
110	C₁₁×#100	—	2	4	no	—
111	C₁₁×#97	—	2	2	no	—
112	#24799	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
113	C₂⁴×C₁₁	—	2	2	no	—
114	C₁₁×#41	—	2	1	no	—
115	C₁₁×#41	—	2	1	no	—
116	C₁₁×#41	—	2	1	no	—
117	C₁₁×#41	—	2	1	no	—
118	C₁₁×#41	—	2	1	no	—
119	C₁₁×#41	—	2	1	no	—
120	C₁₁×#41	C₂×D₄	1	2	yes	—
121	C₁₁×#41	#41	1	2	yes	—
122	C₂×Q₈×C₁₁	C₂×D₄	1	1	yes	characteristic
123	C₂×Q₈×C₁₁	C₂×D₄	1	1	yes	characteristic
124	C₂×D₄×C₁₁	—	2	1	no	—
125	C₂×D₄×C₁₁	—	2	1	no	—
126	C₂×D₄×C₁₁	—	2	2	no	—
127	C₂×D₄×C₁₁	—	2	2	no	—
128	C₂×D₄×C₁₁	—	2	2	no	—
129	C₂×D₄×C₁₁	—	2	2	no	—
130	C₂×D₄×C₁₁	—	2	2	no	—
131	C₂×D₄×C₁₁	—	2	2	no	—
132	C₂×D₄×C₁₁	—	4	2	no	—
133	C₂×D₄×C₁₁	—	4	2	no	—
134	C₂×D₄×C₁₁	C₂×D₄	1	1	yes	characteristic
135	C₂×D₄×C₁₁	C₂×D₄	1	1	yes	characteristic
136	C₂²×C₄×C₁₁	—	2	1	no	—
137	C₂²×C₄×C₁₁	—	2	1	no	—
138	C₂²×C₄×C₁₁	—	2	1	no	—
139	C₂²×C₄×C₁₁	—	2	2	no	—
140	C₂²×C₄×C₁₁	—	4	2	no	—
141	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
142	C₁₁×Q₁₆	—	2	2	no	—
143	C₁₁×SD₁₆	—	2	2	no	—
144	C₁₁×SD₁₆	—	2	2	no	—
145	C₁₁×SD₁₆	—	4	4	no	—
146	C₁₁×D₈	—	2	2	no	—
147	C₁₁×D₈	—	4	2	no	—
148	C₁₁×D₈	—	4	2	no	—
149	C₁₁×D₈	—	4	4	no	—
150	C₁₁×M₁₆	—	2	4	no	—
151	C₁₁×M₁₆	—	2	2	no	—
152	C₁₁×M₁₆	—	2	1	no	—
153	C₁₁×M₁₆	—	2	1	no	—
154	C₁₁×M₁₆	—	2	1	no	—
155	C₁₁×M₁₆	—	2	2	no	—
156	C₁₁×M₁₆	—	4	2	no	—
157	C₁₁×M₁₆	C₂×D₄	1	2	yes	—
158	C₂×C₈×C₁₁	—	2	4	no	—
159	C₂×C₈×C₁₁	—	2	1	no	—
160	C₂×C₈×C₁₁	—	2	1	no	—
161	C₂×C₈×C₁₁	—	2	1	no	—
162	C₂×C₈×C₁₁	—	2	2	no	—
163	C₂×C₈×C₁₁	—	2	1	no	—
164	C₂×C₈×C₁₁	—	4	2	no	—
165	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
166	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
167	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
168	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
169	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
170	C₂×C₈×C₁₁	#41	1	2	yes	—
171	C₁₁×C₄⋊C₄	—	2	2	no	—
172	C₁₁×C₄⋊C₄	—	2	2	no	—
173	C₁₁×C₄⋊C₄	—	4	2	no	—
174	C₁₁×C₄⋊C₄	C₂×D₄	1	2	yes	—
175	C₁₁×C₄⋊C₄	C₂×D₄	1	2	yes	—
176	C₁₁×C₂²⋊C₄	—	2	2	no	—
177	C₁₁×C₂²⋊C₄	—	4	2	no	—
178	C₁₁×C₂²⋊C₄	—	4	2	no	—
179	C₁₁×C₂²⋊C₄	—	4	2	no	—
180	C₁₁×C₂²⋊C₄	—	8	4	no	—
181	C₄²×C₁₁	—	2	2	no	—
182	C₄²×C₁₁	—	2	1	no	—
183	C₄²×C₁₁	—	2	1	no	—
184	C₄²×C₁₁	—	4	2	no	—
185	C₂×#472	C₂×C₁₁	1	1	yes	characteristic, complemented
186	#3058	C₂×C₁₁	1	1	yes	characteristic, complemented
187	#3045	C₂×C₁₁	1	2	yes	complemented
188	C₂×#444	C₂×C₁₁	1	1	yes	characteristic, complemented
189	#2912	C₂×C₁₁	1	1	yes	characteristic, complemented
190	#2063	C₂×C₁₁	1	2	yes	complemented
191	#2037	C₂×C₁₁	1	2	yes	complemented
192	#1972	C₂×C₁₁	1	1	yes	characteristic, complemented
193	#1946	C₂×C₁₁	1	1	yes	characteristic, complemented
194	#1883	C₂×C₁₁	1	2	yes	complemented
195	#1815	C₂×C₁₁	1	1	yes	characteristic, complemented
196	C₂³×C₁₁	—	2	1	no	—
197	C₂³×C₁₁	—	2	1	no	—
198	C₂³×C₁₁	—	4	2	no	—
199	C₂³×C₁₁	—	4	2	no	—
200	C₂³×C₁₁	—	4	2	no	—
201	C₂³×C₁₁	—	8	2	no	—
202	C₂³×C₁₁	—	8	2	no	—
203	C₂³×C₁₁	H(5,𝔽₂)	1	1	yes	characteristic
204	Q₈×C₁₁	—	2	1	no	—
205	Q₈×C₁₁	—	2	1	no	—
206	Q₈×C₁₁	—	2	1	no	—
207	Q₈×C₁₁	#121	1	2	yes	—
208	D₄×C₁₁	—	2	2	no	—
209	D₄×C₁₁	—	2	2	no	—
210	D₄×C₁₁	—	2	1	no	—
211	D₄×C₁₁	—	2	1	no	—
212	D₄×C₁₁	—	2	1	no	—
213	D₄×C₁₁	—	4	1	no	—
214	D₄×C₁₁	—	4	1	no	—
215	D₄×C₁₁	—	4	2	no	—
216	D₄×C₁₁	—	4	2	no	—
217	D₄×C₁₁	—	4	2	no	—
218	D₄×C₁₁	—	4	2	no	—
219	D₄×C₁₁	—	16	2	no	—
220	D₄×C₁₁	—	16	2	no	—
221	D₄×C₁₁	#121	1	2	yes	—
222	C₂×C₄×C₁₁	—	2	1	no	—
223	C₂×C₄×C₁₁	—	2	2	no	—
224	C₂×C₄×C₁₁	—	2	2	no	—
225	C₂×C₄×C₁₁	—	2	2	no	—
226	C₂×C₄×C₁₁	—	2	2	no	—
227	C₂×C₄×C₁₁	—	2	1	no	—
228	C₂×C₄×C₁₁	—	4	1	no	—
229	C₂×C₄×C₁₁	—	4	1	no	—
230	C₂×C₄×C₁₁	—	4	2	no	—
231	C₂×C₄×C₁₁	—	4	1	no	—
232	C₂×C₄×C₁₁	—	4	2	no	—
233	C₂×C₄×C₁₁	—	8	2	no	—
234	C₂×C₄×C₁₁	—	16	2	no	—
235	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
236	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
237	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
238	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
239	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
240	C₂×C₄×C₁₁	2₋¹⁺⁴	1	1	yes	characteristic
241	C₈×C₁₁	—	2	2	no	—
242	C₈×C₁₁	—	2	1	no	—
243	C₈×C₁₁	—	2	1	no	—
244	C₈×C₁₁	—	4	1	no	—
245	C₈×C₁₁	—	4	2	no	—
246	C₈×C₁₁	#121	1	2	yes	—
247	C₈×C₁₁	#121	1	2	yes	—
248	C₂×AGL(1,ℤ/8)	C₂²×C₁₁	1	2	yes	—
249	C₂×#135	C₂²×C₁₁	1	1	yes	characteristic
250	C₂²×D₈	C₂²×C₁₁	1	1	yes	characteristic
251	C₂×#131	C₂²×C₁₁	1	1	yes	characteristic
252	C₂×#131	C₂²×C₁₁	1	1	yes	characteristic
253	#535	C₂²×C₁₁	1	2	yes	—
254	#520	C₂²×C₁₁	1	2	yes	—
255	#472	—	2	4	no	—
256	#469	—	2	1	no	—
257	#469	—	2	1	no	—
258	#466	—	2	2	no	—
259	#464	—	2	2	no	—
260	#463	—	2	2	no	—
261	#460	—	2	2	no	—
262	#459	—	2	2	no	—
263	#444	—	2	4	no	—
264	C₂×#108	C₂²×C₁₁	1	1	yes	characteristic
265	C₂×#108	C₂²×C₁₁	1	1	yes	characteristic
266	#428	—	2	2	no	—
267	#428	C₂²×C₁₁	1	2	yes	—
268	#427	—	2	1	no	—
269	#427	C₂²×C₁₁	1	1	yes	characteristic
270	C₂×#106	—	2	1	no	—
271	C₂×#106	C₂²×C₁₁	1	1	yes	characteristic
272	#424	C₂²×C₁₁	1	2	yes	—
273	C₂×#104	C₂²×C₁₁	1	1	yes	characteristic
274	C₂×#104	C₂²×C₁₁	1	1	yes	characteristic
275	#418	C₂²×C₁₁	1	2	yes	—
276	#417	C₂²×C₁₁	1	2	yes	—
277	C₂×#102	C₂²×C₁₁	1	2	yes	—
278	C₂×#100	C₂²×C₁₁	1	2	yes	—
279	C₂×#97	C₂²×C₁₁	1	1	yes	characteristic
280	#390	C₂²×C₁₁	1	2	yes	—
281	#343	C₂²×C₁₁	1	2	yes	—
282	#339	C₂²×C₁₁	1	2	yes	—
283	C₂²×C₁₁	—	2	2	no	—
284	C₂²×C₁₁	—	2	2	no	—
285	C₂²×C₁₁	—	4	2	no	—
286	C₂²×C₁₁	—	4	1	no	—
287	C₂²×C₁₁	—	4	2	no	—
288	C₂²×C₁₁	—	8	4	no	—
289	C₂²×C₁₁	—	8	2	no	—
290	C₂²×C₁₁	—	8	2	no	—
291	C₂²×C₁₁	—	8	2	no	—
292	C₂²×C₁₁	—	16	2	no	—
293	C₂²×C₁₁	#537	1	1	yes	characteristic
294	C₂²×C₁₁	D₄²	1	1	yes	characteristic
295	C₂²×C₁₁	#553	1	1	yes	characteristic
296	C₄×C₁₁	—	2	2	no	—
297	C₄×C₁₁	—	4	1	no	—
298	C₄×C₁₁	—	4	2	no	—
299	C₄×C₁₁	—	4	2	no	—
300	C₄×C₁₁	—	8	1	no	—
301	C₄×C₁₁	—	8	2	no	—
302	C₄×C₁₁	C₂×#121	1	1	yes	characteristic
303	C₄×C₁₁	C₂×#121	1	1	yes	characteristic
304	C₄×C₁₁	#547	1	1	yes	characteristic
305	C₄×C₁₁	#548	1	1	yes	characteristic
306	C₂×#41	C₂³×C₁₁	1	1	yes	characteristic
307	C₂×#41	C₂³×C₁₁	1	1	yes	characteristic
308	C₂²×D₄	C₂³×C₁₁	1	2	yes	—
309	AGL(1,ℤ/8)	—	2	4	no	—
310	AGL(1,ℤ/8)	—	2	4	no	—
311	#135	—	2	2	no	—
312	#135	—	2	2	no	—
313	C₂×Q₁₆	D₄×C₁₁	1	1	yes	characteristic
314	C₂×SD₁₆	—	2	2	no	—
315	C₂×SD₁₆	D₄×C₁₁	1	1	yes	characteristic
316	C₂×SD₁₆	D₄×C₁₁	1	1	yes	characteristic
317	C₂×D₈	—	2	2	no	—
318	C₂×D₈	—	2	1	no	—
319	C₂×D₈	—	2	1	no	—
320	C₂×D₈	—	2	2	no	—
321	C₂×D₈	—	2	2	no	—
322	C₂×D₈	D₄×C₁₁	1	1	yes	characteristic
323	#131	—	2	2	no	—
324	#131	—	2	2	no	—
325	#131	—	2	2	no	—
326	#131	D₄×C₁₁	1	4	yes	complemented
327	C₂×M₁₆	—	2	1	no	—
328	C₂×M₁₆	—	2	1	no	—
329	C₂×M₁₆	C₂³×C₁₁	1	1	yes	characteristic
330	C₂×M₁₆	C₂³×C₁₁	1	2	yes	—
331	C₂×M₁₆	C₂³×C₁₁	1	1	yes	characteristic
332	C₂²×C₈	—	2	1	no	—
333	C₂²×C₈	—	2	1	no	—
334	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
335	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
336	#127	—	2	2	no	—
337	#124	—	2	2	no	—
338	#121	—	2	2	no	—
339	#121	—	2	2	no	—
340	#120	—	4	2	no	—
341	C₄×Q₈	—	2	2	no	—
342	C₄×D₄	—	2	2	no	—
343	C₄×D₄	—	4	2	no	—
344	#117	—	2	2	no	—
345	#117	C₂³×C₁₁	1	2	yes	—
346	C₂×C₄⋊C₄	—	2	2	no	—
347	C₂×C₄⋊C₄	C₂³×C₁₁	1	2	yes	—
348	C₂×C₂²⋊C₄	—	4	2	no	—
349	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
350	#108	—	2	2	no	—
351	#108	—	2	2	no	—
352	#107	—	2	2	no	—
353	#107	D₄×C₁₁	1	2	yes	—
354	#106	—	2	1	no	—
355	#106	—	2	1	no	—
356	#106	—	2	2	no	—
357	#106	D₄×C₁₁	1	1	yes	characteristic
358	#106	D₄×C₁₁	1	1	yes	characteristic
359	C₄⋊C₈	—	2	2	no	—
360	C₄⋊C₈	—	2	2	no	—
361	#104	—	2	2	no	—
362	#104	—	2	2	no	—
363	#103	—	2	2	no	—
364	#102	—	2	2	no	—
365	#102	—	2	2	no	—
366	#102	—	2	2	no	—
367	#102	—	2	2	no	—
368	#102	—	2	2	no	—
369	#100	—	2	4	no	—
370	#97	—	2	2	no	—
371	C₂×C₁₁	—	2	1	no	—
372	C₂×C₁₁	—	2	1	no	—
373	C₂×C₁₁	—	4	2	no	—
374	C₂×C₁₁	—	8	1	no	—
375	C₂×C₁₁	—	16	2	no	—
376	C₂×C₁₁	#2416	1	1	yes	characteristic
377	C₂×C₁₁	#3288	1	2	yes	—
378	C₂⁴	—	2	2	no	—
379	#41	—	2	1	no	—
380	#41	—	2	1	no	—
381	#41	—	2	1	no	—
382	#41	—	2	1	no	—
383	#41	—	2	1	no	—
384	#41	—	2	1	no	—
385	#41	C₂×D₄×C₁₁	1	2	yes	—
386	#41	C₁₁×#41	1	2	yes	—
387	C₂×Q₈	C₂×D₄×C₁₁	1	1	yes	characteristic
388	C₂×Q₈	C₂×D₄×C₁₁	1	1	yes	characteristic
389	C₂×D₄	—	2	1	no	—
390	C₂×D₄	—	2	1	no	—
391	C₂×D₄	—	2	2	no	—
392	C₂×D₄	—	2	2	no	—
393	C₂×D₄	—	2	2	no	—
394	C₂×D₄	—	2	2	no	—
395	C₂×D₄	—	2	2	no	—
396	C₂×D₄	—	2	2	no	—
397	C₂×D₄	—	4	2	no	—
398	C₂×D₄	—	4	2	no	—
399	C₂×D₄	C₂×D₄×C₁₁	1	1	yes	characteristic
400	C₂×D₄	C₂×D₄×C₁₁	1	1	yes	characteristic
401	C₂²×C₄	—	2	1	no	—
402	C₂²×C₄	—	2	1	no	—
403	C₂²×C₄	—	2	1	no	—
404	C₂²×C₄	—	2	2	no	—
405	C₂²×C₄	—	4	2	no	—
406	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
407	Q₁₆	—	2	2	no	—
408	SD₁₆	—	2	2	no	—
409	SD₁₆	—	2	2	no	—
410	SD₁₆	—	4	4	no	—
411	D₈	—	2	2	no	—
412	D₈	—	4	4	no	—
413	D₈	—	4	2	no	—
414	D₈	—	4	2	no	—
415	M₁₆	—	2	1	no	—
416	M₁₆	—	2	4	no	—
417	M₁₆	—	2	2	no	—
418	M₁₆	—	2	1	no	—
419	M₁₆	—	2	1	no	—
420	M₁₆	—	2	2	no	—
421	M₁₆	—	4	2	no	—
422	M₁₆	C₂×D₄×C₁₁	1	2	yes	—
423	C₂×C₈	—	2	1	no	—
424	C₂×C₈	—	2	1	no	—
425	C₂×C₈	—	2	1	no	—
426	C₂×C₈	—	2	4	no	—
427	C₂×C₈	—	2	1	no	—
428	C₂×C₈	—	2	2	no	—
429	C₂×C₈	—	4	2	no	—
430	C₂×C₈	C₂×D₄×C₁₁	1	1	yes	characteristic
431	C₂×C₈	C₂×D₄×C₁₁	1	1	yes	characteristic
432	C₂×C₈	C₂×D₄×C₁₁	1	2	yes	—
433	C₂×C₈	C₂×D₄×C₁₁	1	1	yes	characteristic
434	C₂×C₈	C₂×D₄×C₁₁	1	1	yes	characteristic
435	C₂×C₈	C₁₁×#41	1	2	yes	—
436	C₄⋊C₄	—	2	2	no	—
437	C₄⋊C₄	—	2	2	no	—
438	C₄⋊C₄	—	4	2	no	—
439	C₄⋊C₄	C₂×D₄×C₁₁	1	2	yes	—
440	C₄⋊C₄	C₂×D₄×C₁₁	1	2	yes	—
441	C₂²⋊C₄	—	2	2	no	—
442	C₂²⋊C₄	—	4	2	no	—
443	C₂²⋊C₄	—	4	2	no	—
444	C₂²⋊C₄	—	4	2	no	—
445	C₂²⋊C₄	—	8	4	no	—
446	C₄²	—	2	2	no	—
447	C₄²	—	2	1	no	—
448	C₄²	—	2	1	no	—
449	C₄²	—	4	2	no	—
450	C₁₁	#24799	1	1	yes	characteristic, direct product factor, Sylow
451	C₂³	—	2	1	no	—
452	C₂³	—	2	1	no	—
453	C₂³	—	4	2	no	—
454	C₂³	—	4	2	no	—
455	C₂³	—	4	2	no	—
456	C₂³	—	8	2	no	—
457	C₂³	—	8	2	no	—
458	C₂³	C₁₁×H(5,𝔽₂)	1	1	yes	characteristic
459	Q₈	—	2	1	no	—
460	Q₈	—	2	1	no	—
461	Q₈	—	2	1	no	—
462	Q₈	C₁₁×#121	1	2	yes	—
463	D₄	—	2	2	no	—
464	D₄	—	2	2	no	—
465	D₄	—	2	1	no	—
466	D₄	—	2	1	no	—
467	D₄	—	2	1	no	—
468	D₄	—	4	1	no	—
469	D₄	—	4	1	no	—
470	D₄	—	4	2	no	—
471	D₄	—	4	2	no	—
472	D₄	—	4	2	no	—
473	D₄	—	4	2	no	—
474	D₄	—	16	2	no	—
475	D₄	—	16	2	no	—
476	D₄	C₁₁×#121	1	2	yes	—
477	C₂×C₄	—	2	1	no	—
478	C₂×C₄	—	2	2	no	—
479	C₂×C₄	—	2	2	no	—
480	C₂×C₄	—	2	2	no	—
481	C₂×C₄	—	2	2	no	—
482	C₂×C₄	—	2	1	no	—
483	C₂×C₄	—	4	1	no	—
484	C₂×C₄	—	4	1	no	—
485	C₂×C₄	—	4	2	no	—
486	C₂×C₄	—	4	1	no	—
487	C₂×C₄	—	4	2	no	—
488	C₂×C₄	—	8	2	no	—
489	C₂×C₄	—	16	2	no	—
490	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
491	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
492	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
493	C₂×C₄	C₂×C₁₁×#41	1	1	yes	characteristic
494	C₂×C₄	C₂×C₁₁×#41	1	1	yes	characteristic
495	C₂×C₄	C₁₁×2₋¹⁺⁴	1	1	yes	characteristic
496	C₈	—	2	2	no	—
497	C₈	—	2	1	no	—
498	C₈	—	2	1	no	—
499	C₈	—	4	1	no	—
500	C₈	—	4	2	no	—
501	C₈	C₁₁×#121	1	2	yes	—
502	C₈	C₁₁×#121	1	2	yes	—
503	C₂²	—	2	2	no	—
504	C₂²	—	2	2	no	—
505	C₂²	—	4	2	no	—
506	C₂²	—	4	1	no	—
507	C₂²	—	4	2	no	—
508	C₂²	—	8	4	no	—
509	C₂²	—	8	2	no	—
510	C₂²	—	8	2	no	—
511	C₂²	—	8	2	no	—
512	C₂²	—	16	2	no	—
513	C₂²	C₁₁×#537	1	1	yes	characteristic
514	C₂²	D₄²×C₁₁	1	1	yes	characteristic
515	C₂²	C₁₁×#553	1	1	yes	characteristic
516	C₄	—	2	2	no	—
517	C₄	—	4	1	no	—
518	C₄	—	4	2	no	—
519	C₄	—	4	2	no	—
520	C₄	—	8	1	no	—
521	C₄	—	8	2	no	—
522	C₄	C₂×C₁₁×#121	1	1	yes	characteristic
523	C₄	C₂×C₁₁×#121	1	1	yes	characteristic
524	C₄	C₁₁×#547	1	1	yes	characteristic
525	C₄	C₁₁×#548	1	1	yes	characteristic
526	C₂	—	2	1	no	—
527	C₂	—	2	1	no	—
528	C₂	—	4	2	no	—
529	C₂	—	8	1	no	—
530	C₂	—	16	2	no	—
531	C₂	C₁₁×#2416	1	1	yes	characteristic
532	C₂	C₁₁×#3288	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₁	D₄²
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₁
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₁ ◁ C₂²×C₄×C₁₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₁×#472	C₂	semidirect
2. C₁₁×#3058	C₂	semidirect
3. C₁₁×#3045	C₂	semidirect
4. C₂×C₁₁×#444	C₂	semidirect
5. C₁₁×#2912	C₂	semidirect
6. C₁₁×#2063	C₂	semidirect
7. C₁₁×#2037	C₂	semidirect
8. C₁₁×#1972	C₂	semidirect
9. C₁₁×#1946	C₂	semidirect
10. C₁₁×#1883	C₂	semidirect
11. C₁₁×#1815	C₂	semidirect
67. C₁₁×#131	D₄	semidirect
112. #24799	C₁₁	direct (N × H)
185. C₂×#472	C₂×C₁₁	semidirect
186. #3058	C₂×C₁₁	semidirect
187. #3045	C₂×C₁₁	semidirect
188. C₂×#444	C₂×C₁₁	semidirect
189. #2912	C₂×C₁₁	semidirect
190. #2063	C₂×C₁₁	semidirect
191. #2037	C₂×C₁₁	semidirect
192. #1972	C₂×C₁₁	semidirect
193. #1946	C₂×C₁₁	semidirect
194. #1883	C₂×C₁₁	semidirect
195. #1815	C₂×C₁₁	semidirect
326. #131	D₄×C₁₁	semidirect
450. C₁₁	#24799	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×#472	2
C₁₁×#3058	2
C₁₁×#3045	2
C₂×C₁₁×#444	2
C₁₁×#2912	2
C₁₁×#2063	2
C₁₁×#2037	2
C₁₁×#1972	2
C₁₁×#1946	2
C₁₁×#1883	2
C₁₁×#1815	2
#24799	11

Subgroups — C11×#24799 #14601992

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#24799 #14601992