Subgroups — #14719474

Order 2816.

734 conjugacy classes of subgroups.

The subgroup lattice has 502 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13077580	C₂	1	1	yes	maximal, characteristic
2	#13077572	C₂	1	1	yes	maximal, characteristic
3	#13077255	C₂	1	1	yes	maximal, characteristic
4	#13066917	C₂	1	1	yes	maximal, characteristic, complemented
5	#13066912	C₂	1	1	yes	maximal, characteristic, complemented
6	#13066911	C₂	1	1	yes	maximal, characteristic, complemented
7	#13066909	C₂	1	1	yes	maximal, characteristic, complemented
8	#13066907	C₂	1	1	yes	maximal, characteristic, complemented
9	#13066902	C₂	1	1	yes	maximal, characteristic, complemented
10	#13066898	C₂	1	1	yes	maximal, characteristic, complemented
11	#13066897	C₂	1	1	yes	maximal, characteristic, complemented
12	#13066895	C₂	1	1	yes	maximal, characteristic, complemented
13	C₈×#4313	C₂	1	1	yes	maximal, characteristic, complemented
14	D₁₁×#322	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₁×#1454	C₂	1	1	yes	maximal, characteristic, complemented
16	C₄×#4339	C₂²	1	1	yes	characteristic
17	C₁₁×#431	C₂²	1	1	yes	characteristic
18	C₁₁×#431	C₂²	1	1	yes	characteristic
19	C₁₁×#431	C₂²	1	1	yes	characteristic
20	#10622538	C₂²	1	1	yes	characteristic
21	C₄×#4318	C₂²	1	1	yes	characteristic
22	C₂×C₄×C₁₁⋊C₈	C₂²	1	1	yes	characteristic
23	#10622453	C₄	1	2	yes	—
24	#10622452	C₄	1	2	yes	—
25	#10622449	C₄	1	2	yes	—
26	#10622447	C₄	1	2	yes	—
27	#10622443	C₄	1	2	yes	—
28	#10622441	C₄	1	2	yes	—
29	#10622342	C₄	1	2	yes	—
30	#10622341	C₄	1	2	yes	—
31	#10622340	C₄	1	2	yes	—
32	(C₂²⋊D₁₁)⋊C₈	C₄	1	2	yes	—
33	(C₂²⋊D₁₁)⋊C₈	C₄	1	2	yes	—
34	#10622333	C₄	1	2	yes	—
35	C₄×#4313	C₂²	1	1	yes	characteristic
36	C₄×#4313	C₂²	1	1	yes	characteristic
37	#10622298	C₂²	1	1	yes	characteristic
38	#10622298	C₂²	1	1	yes	characteristic
39	#10622298	C₂²	1	1	yes	characteristic
40	#10622298	C₂²	1	1	yes	characteristic
41	#10622298	C₂²	1	1	yes	characteristic
42	#10622298	C₂²	1	1	yes	characteristic
43	C₄×C₈×D₁₁	C₂²	1	1	yes	characteristic
44	C₄×C₈×D₁₁	C₂²	1	1	yes	characteristic
45	C₄×C₈×D₁₁	C₂²	1	1	yes	characteristic
46	C₄×C₈×D₁₁	C₂²	1	1	yes	characteristic
47	C₁₁×#322	C₂²	1	1	yes	characteristic
48	C₁₁×#322	C₂²	1	1	yes	characteristic
49	C₁₁×#322	C₂²	1	1	yes	characteristic
50	C₈²×C₁₁	C₂²	1	1	yes	characteristic
51	#10622093	C₂²	1	1	yes	characteristic
52	#10622093	C₂²	1	1	yes	characteristic
53	#10622093	C₂²	1	1	yes	characteristic
54	#10622092	C₂²	1	1	yes	characteristic
55	#10622092	C₂²	1	1	yes	characteristic
56	#10622092	C₂²	1	1	yes	characteristic
57	#10622092	C₂²	1	1	yes	characteristic
58	#10622092	C₂²	1	1	yes	characteristic
59	#10622092	C₂²	1	1	yes	characteristic
60	C₈×C₁₁⋊C₈	C₂²	1	1	yes	characteristic
61	C₈×C₁₁⋊C₈	C₂²	1	1	yes	characteristic
62	C₈×C₁₁⋊C₈	C₂²	1	1	yes	characteristic
63	C₂×#4339	C₂×C₄	1	1	yes	characteristic
64	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
65	C₄×C₂²⋊D₁₁	C₂×C₄	1	1	yes	characteristic
66	C₄×C₂²⋊D₁₁	C₂×C₄	1	1	yes	characteristic
67	C₄×C₂²⋊D₁₁	C₂×C₄	1	1	yes	characteristic
68	C₄×C₂²⋊D₁₁	C₂×C₄	1	1	yes	characteristic
69	#66979	C₂×C₄	1	1	yes	characteristic
70	C₂×#4318	C₂×C₄	1	2	yes	—
71	C₂²×C₁₁⋊C₈	C₂×C₄	1	2	yes	—
72	C₂×#4313	C₂×C₄	1	2	yes	—
73	C₂×#4313	C₂×C₄	1	2	yes	—
74	C₂×C₈×D₁₁	C₂×C₄	1	2	yes	—
75	C₂×C₈×D₁₁	C₂×C₄	1	2	yes	—
76	C₂×C₈×D₁₁	C₂×C₄	1	2	yes	—
77	C₂×C₈×D₁₁	C₂×C₄	1	2	yes	—
78	C₄×D₄₄	C₂×C₄	1	1	yes	characteristic
79	C₄×D₄₄	C₂×C₄	1	1	yes	characteristic
80	#66925	C₂×C₄	1	1	yes	characteristic
81	#66925	C₂×C₄	1	1	yes	characteristic
82	C₄²×D₁₁	C₂³	1	1	yes	characteristic
83	C₄²×D₁₁	C₂³	1	1	yes	characteristic
84	C₄×Dic₂₂	C₂×C₄	1	1	yes	characteristic
85	C₄×Dic₂₂	C₂×C₄	1	1	yes	characteristic
86	C₁₁×C₄⋊C₈	C₂×C₄	1	2	yes	—
87	C₁₁×C₄⋊C₈	C₂×C₄	1	2	yes	—
88	C₁₁×C₄⋊C₈	C₂×C₄	1	2	yes	—
89	C₁₁×C₂²⋊C₈	C₂×C₄	1	2	yes	—
90	C₁₁×C₂²⋊C₈	C₂×C₄	1	2	yes	—
91	C₁₁×C₂²⋊C₈	C₂×C₄	1	2	yes	—
92	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
93	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
94	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
95	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
96	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
97	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
98	C₂²⋊(C₁₁⋊C₈)	C₂×C₄	1	2	yes	—
99	(C₂×D₁₁)⋊C₈	C₂×C₄	1	2	yes	—
100	(C₂×D₁₁)⋊C₈	C₂×C₄	1	2	yes	—
101	(C₂×D₁₁)⋊C₈	C₂×C₄	1	2	yes	—
102	(C₂×D₁₁)⋊C₈	C₂×C₄	1	2	yes	—
103	(C₂×D₁₁)⋊C₈	C₂×C₄	1	2	yes	—
104	(C₂×D₁₁)⋊C₈	C₂×C₄	1	2	yes	—
105	#66879	C₂×C₄	1	2	yes	—
106	#66879	C₂×C₄	1	2	yes	—
107	Dic₁₁⋊C₈	C₂×C₄	1	2	yes	—
108	Dic₁₁⋊C₈	C₂×C₄	1	2	yes	—
109	Dic₁₁⋊C₈	C₂×C₄	1	2	yes	—
110	Dic₁₁⋊C₈	C₂×C₄	1	2	yes	—
111	Dic₁₁⋊C₈	C₂×C₄	1	2	yes	—
112	Dic₁₁⋊C₈	C₂×C₄	1	2	yes	—
113	C₈×Dic₁₁	C₂×C₄	1	2	yes	—
114	C₈×Dic₁₁	C₂×C₄	1	2	yes	—
115	C₈×Dic₁₁	C₂×C₄	1	2	yes	—
116	C₈×Dic₁₁	C₂×C₄	1	2	yes	—
117	C₄⋊(C₁₁⋊C₈)	C₂×C₄	1	2	yes	—
118	#66867	C₂×C₄	1	2	yes	—
119	C₄×C₁₁⋊C₈	C₂×C₄	1	2	yes	—
120	C₄×C₁₁⋊C₈	C₂³	1	1	yes	characteristic
121	C₄×C₁₁⋊C₈	C₂³	1	1	yes	characteristic
122	C₄×C₁₁⋊C₈	C₂³	1	1	yes	characteristic
123	C₄×C₁₁⋊C₈	C₂³	1	1	yes	characteristic
124	C₄×C₁₁⋊C₈	C₂³	1	1	yes	characteristic
125	C₄×C₁₁⋊C₈	C₂³	1	1	yes	characteristic
126	#17331	—	11	1	no	maximal, Sylow
127	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
128	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
129	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
130	C₂×C₂²⋊D₁₁	C₄²	1	1	yes	characteristic
131	C₂×C₂²⋊D₁₁	C₄²	1	1	yes	characteristic
132	#4339	—	2	4	no	—
133	C₂×D₄₄	C₄²	1	1	yes	characteristic
134	C₂×C₄×D₁₁	C₂²×C₄	1	1	yes	characteristic
135	C₂×C₄×D₁₁	C₂²×C₄	1	1	yes	characteristic
136	C₂×C₄×D₁₁	C₂²×C₄	1	1	yes	characteristic
137	C₂×C₄×D₁₁	C₂²×C₄	1	1	yes	characteristic
138	C₂×C₄×D₁₁	C₂²×C₄	1	1	yes	characteristic
139	C₂×C₄×D₁₁	C₂²×C₄	1	1	yes	characteristic
140	C₂×Dic₂₂	C₄²	1	1	yes	characteristic
141	C₂×C₈×C₁₁	C₂²×C₄	1	2	yes	—
142	C₂×C₈×C₁₁	C₂²×C₄	1	2	yes	—
143	C₂×C₈×C₁₁	C₂²×C₄	1	2	yes	—
144	C₂×C₈×C₁₁	C₂²×C₄	1	2	yes	—
145	C₂×C₈×C₁₁	C₂²×C₄	1	2	yes	—
146	C₂×C₈×C₁₁	C₂²×C₄	1	2	yes	—
147	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
148	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
149	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
150	C₄²×C₁₁	C₂⁴	1	1	yes	characteristic
151	C₂²⋊Dic₁₁	C₄²	1	1	yes	characteristic
152	C₂²⋊Dic₁₁	C₄²	1	1	yes	characteristic
153	(C₂×D₁₁)⋊C₄	C₄²	1	1	yes	characteristic
154	(C₂×D₁₁)⋊C₄	C₄²	1	1	yes	characteristic
155	(C₂×D₁₁)⋊C₄	C₄²	1	1	yes	characteristic
156	(C₂×D₁₁)⋊C₄	C₄²	1	1	yes	characteristic
157	C₄⋊Dic₁₁	C₄²	1	1	yes	characteristic
158	C₄⋊Dic₁₁	C₄²	1	1	yes	characteristic
159	Dic₁₁⋊C₄	C₄²	1	1	yes	characteristic
160	Dic₁₁⋊C₄	C₄²	1	1	yes	characteristic
161	Dic₁₁⋊C₄	C₄²	1	1	yes	characteristic
162	Dic₁₁⋊C₄	C₄²	1	1	yes	characteristic
163	C₄×Dic₁₁	C₂²×C₄	1	1	yes	characteristic
164	C₄×Dic₁₁	C₂²×C₄	1	1	yes	characteristic
165	C₄×Dic₁₁	C₂²×C₄	1	1	yes	characteristic
166	C₄×Dic₁₁	C₂²×C₄	1	1	yes	characteristic
167	C₄×Dic₁₁	C₂²×C₄	1	1	yes	characteristic
168	C₄×Dic₁₁	C₂²×C₄	1	1	yes	characteristic
169	#4318	—	2	4	no	—
170	C₂×C₁₁⋊C₈	—	4	2	no	—
171	C₂×C₁₁⋊C₈	C₂²×C₄	1	2	yes	—
172	C₂×C₁₁⋊C₈	C₂²×C₄	1	2	yes	—
173	C₂×C₁₁⋊C₈	C₂²×C₄	1	2	yes	—
174	C₂×C₁₁⋊C₈	C₂²×C₄	1	2	yes	—
175	C₂×C₁₁⋊C₈	C₂²×C₄	1	2	yes	—
176	C₂×C₁₁⋊C₈	C₂²×C₄	1	2	yes	—
177	#4313	—	2	4	no	—
178	#4313	—	2	4	no	—
179	C₈×D₁₁	—	2	4	no	—
180	C₈×D₁₁	—	2	4	no	—
181	C₈×D₁₁	—	4	2	no	—
182	C₈×D₁₁	—	4	2	no	—
183	#2965	—	11	1	no	—
184	C₈×#41	—	11	1	no	—
185	#2922	—	11	1	no	—
186	#1454	—	11	1	no	—
187	#1454	D₁₁	1	1	yes	characteristic, complemented
188	#1453	—	11	1	no	—
189	#1453	—	11	1	no	—
190	#1452	—	11	1	no	—
191	#1452	—	11	1	no	—
192	#1451	—	11	1	no	—
193	#1450	—	11	1	no	—
194	C₈×M₁₆	—	11	1	no	—
195	C₈×M₁₆	—	11	1	no	—
196	C₈×M₁₆	—	11	1	no	—
197	C₂×#322	—	11	1	no	—
198	C₂³×C₁₁	C₂×C₄²	1	1	yes	characteristic
199	C₂²×D₁₁	C₂×C₄²	1	1	yes	characteristic
200	C₂²×D₁₁	C₂×C₄²	1	1	yes	characteristic
201	C₂×C₄×C₁₁	—	2	2	no	—
202	C₂×C₄×C₁₁	—	2	2	no	—
203	C₂×C₄×C₁₁	—	2	2	no	—
204	C₂×C₄×C₁₁	C₂×C₄²	1	1	yes	characteristic
205	C₂×C₄×C₁₁	C₂×C₄²	1	1	yes	characteristic
206	C₂×C₄×C₁₁	C₂×C₄²	1	1	yes	characteristic
207	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
208	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
209	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
210	C₂²⋊D₁₁	—	2	2	no	—
211	C₂²⋊D₁₁	—	2	2	no	—
212	C₂×Dic₁₁	C₂×C₄²	1	1	yes	characteristic
213	C₂×Dic₁₁	C₂×C₄²	1	1	yes	characteristic
214	C₂×Dic₁₁	C₂×C₄²	1	1	yes	characteristic
215	C₂×Dic₁₁	C₂×C₄²	1	1	yes	characteristic
216	C₂×Dic₁₁	C₂×C₄²	1	1	yes	characteristic
217	C₂×Dic₁₁	C₂×C₄²	1	1	yes	characteristic
218	D₄₄	—	2	2	no	—
219	C₄×D₁₁	—	2	2	no	—
220	C₄×D₁₁	—	2	2	no	—
221	C₄×D₁₁	—	2	2	no	—
222	C₄×D₁₁	—	2	2	no	—
223	C₄×D₁₁	—	2	2	no	—
224	C₄×D₁₁	#131	1	4	yes	—
225	Dic₂₂	—	2	2	no	—
226	C₈×C₁₁	—	2	2	no	—
227	C₈×C₁₁	—	2	2	no	—
228	C₈×C₁₁	—	2	2	no	—
229	C₈×C₁₁	—	2	2	no	—
230	C₈×C₁₁	—	2	2	no	—
231	C₈×C₁₁	—	2	2	no	—
232	C₁₁⋊C₈	—	2	2	no	—
233	C₁₁⋊C₈	—	2	2	no	—
234	C₁₁⋊C₈	—	2	2	no	—
235	C₁₁⋊C₈	—	2	2	no	—
236	C₁₁⋊C₈	—	2	2	no	—
237	C₁₁⋊C₈	#131	1	4	yes	—
238	C₄×#41	—	11	1	no	—
239	#446	—	11	2	no	—
240	C₈×Q₈	—	11	2	no	—
241	#436	—	11	2	no	—
242	#435	—	11	2	no	—
243	#435	—	11	2	no	—
244	C₈×D₄	—	11	2	no	—
245	C₈×D₄	—	11	2	no	—
246	C₈×D₄	—	11	2	no	—
247	#433	—	11	2	no	—
248	#433	—	11	2	no	—
249	#431	—	11	1	no	—
250	#431	—	11	1	no	—
251	#431	—	11	1	no	—
252	#431	—	11	1	no	—
253	#431	—	11	1	no	—
254	#431	—	11	1	no	—
255	#431	—	11	1	no	—
256	#431	C₂×D₁₁	1	1	yes	characteristic
257	#431	C₂×D₁₁	1	1	yes	characteristic
258	#431	C₂×D₁₁	1	1	yes	characteristic
259	#424	—	11	2	no	—
260	#408	—	11	2	no	—
261	C₄×M₁₆	—	11	1	no	—
262	C₄×M₁₆	—	11	1	no	—
263	C₄×M₁₆	—	11	1	no	—
264	C₂×C₄×C₈	—	11	1	no	—
265	C₂×C₄×C₈	—	11	1	no	—
266	C₂×C₄×C₈	—	11	1	no	—
267	C₂×C₄×C₈	—	11	1	no	—
268	C₂×C₄×C₈	—	11	1	no	—
269	#322	—	11	1	no	—
270	#322	—	11	1	no	—
271	#322	—	11	1	no	—
272	#322	—	11	1	no	—
273	#322	—	11	1	no	—
274	#322	—	11	1	no	—
275	#322	—	11	1	no	—
276	#322	—	11	1	no	—
277	#322	—	11	1	no	—
278	#322	C₂×D₁₁	1	1	yes	characteristic
279	#322	C₂×D₁₁	1	1	yes	characteristic
280	#322	C₂×D₁₁	1	1	yes	characteristic
281	C₈²	—	11	1	no	—
282	C₈²	—	11	1	no	—
283	C₈²	—	11	1	no	—
284	C₈²	C₂×D₁₁	1	1	yes	characteristic
285	C₂²×C₁₁	—	2	1	no	—
286	C₂²×C₁₁	—	2	1	no	—
287	C₂²×C₁₁	—	2	1	no	—
288	C₂²×C₁₁	C₂²×C₄²	1	1	yes	characteristic
289	C₂×D₁₁	—	2	1	no	—
290	C₂×D₁₁	—	2	1	no	—
291	C₂×D₁₁	—	2	1	no	—
292	C₂×D₁₁	—	2	1	no	—
293	C₂×D₁₁	—	2	1	no	—
294	C₂×D₁₁	#405	1	2	yes	—
295	C₄×C₁₁	—	2	1	no	—
296	C₄×C₁₁	—	2	1	no	—
297	C₄×C₁₁	—	2	1	no	—
298	C₄×C₁₁	C₂×#131	1	2	yes	—
299	C₄×C₁₁	C₂×#131	1	2	yes	—
300	C₄×C₁₁	#568	1	2	yes	—
301	Dic₁₁	—	2	1	no	—
302	Dic₁₁	—	2	1	no	—
303	Dic₁₁	—	2	1	no	—
304	Dic₁₁	—	2	1	no	—
305	Dic₁₁	—	2	1	no	—
306	Dic₁₁	#405	1	2	yes	—
307	C₂×#41	—	11	1	no	—
308	C₂×M₁₆	—	11	2	no	—
309	C₂×M₁₆	—	11	2	no	—
310	C₂×M₁₆	—	11	2	no	—
311	C₂²×C₈	—	11	2	no	—
312	C₂²×C₈	—	11	2	no	—
313	C₂²×C₈	—	11	2	no	—
314	C₂²×C₈	—	11	2	no	—
315	C₂²×C₈	—	11	2	no	—
316	C₄×Q₈	—	11	1	no	—
317	C₄×Q₈	—	11	1	no	—
318	C₄×D₄	—	11	1	no	—
319	C₄×D₄	—	11	1	no	—
320	C₄×D₄	—	11	1	no	—
321	C₄×D₄	—	11	1	no	—
322	C₄×D₄	—	11	1	no	—
323	C₄×D₄	—	11	1	no	—
324	#117	—	11	1	no	—
325	#117	—	11	1	no	—
326	#117	—	11	1	no	—
327	C₂×C₄²	—	11	1	no	—
328	C₂×C₄²	—	11	1	no	—
329	C₂×C₄²	C₂²×D₁₁	1	1	yes	characteristic
330	C₄⋊C₈	—	11	2	no	—
331	C₄⋊C₈	—	11	2	no	—
332	C₄⋊C₈	—	11	2	no	—
333	C₄⋊C₈	—	11	2	no	—
334	C₄⋊C₈	—	11	2	no	—
335	C₄⋊C₈	—	11	2	no	—
336	C₄⋊C₈	—	11	2	no	—
337	C₄⋊C₈	C₄×D₁₁	1	2	yes	—
338	C₄⋊C₈	C₄×D₁₁	1	2	yes	—
339	C₄⋊C₈	C₄×D₁₁	1	2	yes	—
340	C₂²⋊C₈	—	11	2	no	—
341	C₂²⋊C₈	—	11	2	no	—
342	C₂²⋊C₈	—	11	2	no	—
343	C₂²⋊C₈	—	11	2	no	—
344	C₂²⋊C₈	—	11	2	no	—
345	C₂²⋊C₈	—	11	2	no	—
346	C₂²⋊C₈	—	11	2	no	—
347	C₂²⋊C₈	C₄×D₁₁	1	2	yes	—
348	C₂²⋊C₈	C₄×D₁₁	1	2	yes	—
349	C₂²⋊C₈	C₄×D₁₁	1	2	yes	—
350	#97	—	11	2	no	—
351	#97	—	11	2	no	—
352	#97	—	11	2	no	—
353	C₄×C₈	—	11	2	no	—
354	C₄×C₈	—	11	2	no	—
355	C₄×C₈	—	11	2	no	—
356	C₄×C₈	—	11	2	no	—
357	C₄×C₈	—	11	2	no	—
358	C₄×C₈	—	11	1	no	—
359	C₄×C₈	—	11	1	no	—
360	C₄×C₈	—	11	1	no	—
361	C₄×C₈	—	11	1	no	—
362	C₄×C₈	—	11	1	no	—
363	C₄×C₈	—	11	1	no	—
364	C₄×C₈	C₂²×D₁₁	1	1	yes	characteristic
365	C₄×C₈	C₂²×D₁₁	1	1	yes	characteristic
366	C₄×C₈	C₂²×D₁₁	1	1	yes	characteristic
367	C₄×C₈	C₂²×D₁₁	1	1	yes	characteristic
368	C₄×C₈	C₂²×D₁₁	1	1	yes	characteristic
369	C₄×C₈	C₂²×D₁₁	1	1	yes	characteristic
370	C₂×C₁₁	—	4	1	no	—
371	C₂×C₁₁	C₂×#405	1	1	yes	characteristic
372	C₂×C₁₁	C₄×#131	1	1	yes	characteristic
373	C₂×C₁₁	#2875	1	1	yes	characteristic
374	D₁₁	—	2	2	no	—
375	D₁₁	—	4	1	no	—
376	#41	—	22	4	no	—
377	C₂×Q₈	—	11	1	no	—
378	C₂×D₄	—	11	1	no	—
379	C₂×D₄	—	11	1	no	—
380	C₂×D₄	—	11	1	no	—
381	C₂²×C₄	—	11	1	no	—
382	C₂²×C₄	—	11	1	no	—
383	C₂²×C₄	—	11	1	no	—
384	C₂²×C₄	—	11	1	no	—
385	C₂²×C₄	—	11	1	no	—
386	C₂²×C₄	—	11	1	no	—
387	C₂²×C₄	C₂×C₄×D₁₁	1	1	yes	characteristic
388	C₂²×C₄	C₂×C₄×D₁₁	1	1	yes	characteristic
389	C₂²×C₄	C₂×C₄×D₁₁	1	1	yes	characteristic
390	M₁₆	—	22	4	no	—
391	M₁₆	—	22	4	no	—
392	M₁₆	—	22	4	no	—
393	C₂×C₈	—	11	2	no	—
394	C₂×C₈	—	11	2	no	—
395	C₂×C₈	—	11	2	no	—
396	C₂×C₈	—	11	2	no	—
397	C₂×C₈	—	11	2	no	—
398	C₂×C₈	—	11	2	no	—
399	C₂×C₈	—	22	4	no	—
400	C₂×C₈	—	22	4	no	—
401	C₂×C₈	—	44	2	no	—
402	C₂×C₈	—	44	2	no	—
403	C₂×C₈	—	44	2	no	—
404	C₂×C₈	C₂×C₄×D₁₁	1	2	yes	—
405	C₂×C₈	C₂×C₄×D₁₁	1	2	yes	—
406	C₂×C₈	C₂×C₄×D₁₁	1	2	yes	—
407	C₂×C₈	C₂×C₄×D₁₁	1	2	yes	—
408	C₂×C₈	C₂×C₄×D₁₁	1	2	yes	—
409	C₂×C₈	C₂×C₄×D₁₁	1	2	yes	—
410	C₄⋊C₄	—	11	1	no	—
411	C₄⋊C₄	—	11	1	no	—
412	C₄⋊C₄	—	11	1	no	—
413	C₄⋊C₄	—	11	1	no	—
414	C₄⋊C₄	—	11	1	no	—
415	C₄⋊C₄	—	11	1	no	—
416	C₂²⋊C₄	—	11	1	no	—
417	C₂²⋊C₄	—	11	1	no	—
418	C₂²⋊C₄	—	11	1	no	—
419	C₂²⋊C₄	—	11	1	no	—
420	C₂²⋊C₄	—	11	1	no	—
421	C₂²⋊C₄	—	11	1	no	—
422	C₄²	—	11	1	no	—
423	C₄²	—	11	1	no	—
424	C₄²	—	11	1	no	—
425	C₄²	—	11	1	no	—
426	C₄²	—	11	1	no	—
427	C₄²	—	11	1	no	—
428	C₄²	C₂×C₄×D₁₁	1	1	yes	characteristic
429	C₄²	C₂×C₄×D₁₁	1	1	yes	characteristic
430	C₄²	C₂×C₄×D₁₁	1	1	yes	characteristic
431	C₄²	C₂³×D₁₁	1	1	yes	characteristic
432	C₁₁	#17331	1	1	yes	characteristic, complemented, Sylow
433	C₂³	—	11	1	no	—
434	C₂³	—	11	1	no	—
435	C₂³	C₄²×D₁₁	1	1	yes	characteristic
436	Q₈	—	22	2	no	—
437	D₄	—	22	2	no	—
438	D₄	—	22	2	no	—
439	D₄	—	22	2	no	—
440	C₂×C₄	—	2	2	no	—
441	C₂×C₄	—	2	2	no	—
442	C₂×C₄	—	2	2	no	—
443	C₂×C₄	—	11	1	no	—
444	C₂×C₄	—	11	4	no	—
445	C₂×C₄	—	11	1	no	—
446	C₂×C₄	—	11	1	no	—
447	C₂×C₄	—	11	1	no	—
448	C₂×C₄	—	11	1	no	—
449	C₂×C₄	—	11	1	no	—
450	C₂×C₄	—	22	2	no	—
451	C₂×C₄	—	22	2	no	—
452	C₂×C₄	—	22	2	no	—
453	C₂×C₄	—	22	2	no	—
454	C₂×C₄	—	22	2	no	—
455	C₂×C₄	C₄²×D₁₁	1	1	yes	characteristic
456	C₂×C₄	C₄²×D₁₁	1	1	yes	characteristic
457	C₂×C₄	C₄²×D₁₁	1	1	yes	characteristic
458	C₂×C₄	C₂²×C₄×D₁₁	1	1	yes	characteristic
459	C₂×C₄	C₂²×C₄×D₁₁	1	1	yes	characteristic
460	C₂×C₄	C₂²×C₄×D₁₁	1	1	yes	characteristic
461	C₈	—	2	2	no	—
462	C₈	—	2	2	no	—
463	C₈	—	2	2	no	—
464	C₈	—	2	2	no	—
465	C₈	—	2	2	no	—
466	C₈	—	2	2	no	—
467	C₈	—	11	4	no	—
468	C₈	—	22	2	no	—
469	C₈	—	22	2	no	—
470	C₈	—	22	2	no	—
471	C₈	—	22	2	no	—
472	C₈	—	22	2	no	—
473	C₂²	—	2	1	no	—
474	C₂²	—	2	1	no	—
475	C₂²	—	2	1	no	—
476	C₂²	—	11	2	no	—
477	C₂²	—	22	1	no	—
478	C₂²	—	22	1	no	—
479	C₂²	—	22	1	no	—
480	C₂²	—	22	1	no	—
481	C₂²	—	22	1	no	—
482	C₂²	C₂×C₄²×D₁₁	1	1	yes	characteristic
483	C₄	—	2	1	no	—
484	C₄	—	2	1	no	—
485	C₄	—	2	1	no	—
486	C₄	—	11	2	no	—
487	C₄	—	22	1	no	—
488	C₄	—	22	1	no	—
489	C₄	—	22	1	no	—
490	C₄	—	22	1	no	—
491	C₄	—	22	1	no	—
492	C₄	D₁₁×#131	1	2	yes	—
493	C₄	D₁₁×#131	1	2	yes	—
494	C₄	#10623281	1	2	yes	—
495	C₂	—	4	1	no	—
496	C₂	—	22	2	no	—
497	C₂	—	44	1	no	—
498	C₂	D₁₁×#405	1	1	yes	characteristic
499	C₂	#13077038	1	1	yes	characteristic
500	C₂	#13077043	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₄²	C₂³×D₁₁
commutator, socle	C₂²×C₁₁	C₂²×C₄²
Fitting	C₁₁×#1454	C₂
prime radical	C₂×#4339	C₂×C₄
cosocle	C₄²×C₁₁	C₂⁴
hypercenter	#1454	D₁₁
hypocenter	C₁₁	#17331
LCS	G ▷ C₂²×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₄² ◁ #1454

Complements

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

N	H ≅ G/N	type
4. #13066917	C₂	semidirect
5. #13066912	C₂	semidirect
6. #13066911	C₂	semidirect
7. #13066909	C₂	semidirect
8. #13066907	C₂	semidirect
9. #13066902	C₂	semidirect
10. #13066898	C₂	semidirect
11. #13066897	C₂	semidirect
12. #13066895	C₂	semidirect
13. C₈×#4313	C₂	semidirect
14. D₁₁×#322	C₂	semidirect
15. C₁₁×#1454	C₂	semidirect
187. #1454	D₁₁	semidirect
432. C₁₁	#17331	semidirect

Maximal subgroups

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

subgroup	index
#13077580	2
#13077572	2
#13077255	2
#13066917	2
#13066912	2
#13066911	2
#13066909	2
#13066907	2
#13066902	2
#13066898	2
#13066897	2
#13066895	2
C₈×#4313	2
D₁₁×#322	2
C₁₁×#1454	2
#17331	11