Subgroups — #14719429

Order 2816.

836 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13077244	C₂	1	1	yes	maximal, characteristic
2	C₂×#10622298	C₂	1	1	yes	maximal, characteristic
3	C₄×M₁₆×D₁₁	C₂	1	1	yes	maximal, characteristic
4	#13066912	C₂	1	2	yes	maximal, complemented
5	#13066912	C₂	1	2	yes	maximal, complemented
6	#13066904	C₂	1	2	yes	maximal, complemented
7	#13066903	C₂	1	1	yes	maximal, characteristic, complemented
8	#13066897	C₂	1	1	yes	maximal, characteristic, complemented
9	C₈×#4318	C₂	1	1	yes	maximal, characteristic, complemented
10	#13066895	C₂	1	2	yes	maximal, complemented
11	C₁₁×#1451	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×M₁₆×D₁₁	C₄	1	2	yes	—
13	C₂×C₄²×D₁₁	C₂²	1	1	yes	characteristic
14	C₁₁×#431	C₂²	1	1	yes	characteristic
15	C₄×C₁₁×M₁₆	C₂²	1	1	yes	characteristic
16	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
17	M₁₆×Dic₁₁	C₄	1	2	yes	—
18	C₂×(C₂×D₁₁)⋊C₈	C₄	1	2	yes	—
19	C₂×Dic₁₁⋊C₈	C₄	1	2	yes	—
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	#10622450	C₄	1	2	yes	—
24	#10622448	C₄	1	2	yes	—
25	#10622339	C₄	1	2	yes	—
26	#10622332	C₄	1	2	yes	—
27	#10622320	C₄	1	2	yes	—
28	D₁₁×#97	C₄	1	2	yes	—
29	C₄×#4313	C₂²	1	2	yes	—
30	C₄×#4313	C₂²	1	2	yes	—
31	#10622298	C₄	1	2	yes	—
32	#10622298	C₄	1	2	yes	—
33	#10622298	C₂²	1	1	yes	characteristic
34	#10622298	C₂²	1	1	yes	characteristic
35	#10622298	C₂²	1	1	yes	characteristic
36	#10622298	C₂²	1	1	yes	characteristic
37	#10622298	C₂²	1	2	yes	—
38	C₄×C₈×D₁₁	C₂²	1	2	yes	—
39	C₁₁×#322	C₂²	1	2	yes	complemented
40	C₁₁×#322	C₂²	1	2	yes	complemented
41	#10622092	C₂²	1	2	yes	complemented
42	#10622092	C₂²	1	2	yes	complemented
43	#10622092	C₂²	1	2	yes	complemented
44	#10622092	C₂²	1	2	yes	complemented
45	C₈×C₁₁⋊C₈	C₂²	1	2	yes	complemented
46	C₈×C₁₁⋊C₈	C₂²	1	2	yes	complemented
47	C₂²×C₄×D₁₁	C₂×C₄	1	1	yes	characteristic
48	C₂²×C₄×D₁₁	C₂×C₄	1	1	yes	characteristic
49	C₂²×C₄×D₁₁	C₂×C₄	1	1	yes	characteristic
50	C₂×C₁₁×M₁₆	C₂×C₄	1	2	yes	—
51	C₂²×C₈×C₁₁	C₂×C₄	1	2	yes	—
52	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
53	C₂×C₄×Dic₁₁	C₂×C₄	1	1	yes	characteristic
54	C₂×C₄×Dic₁₁	C₂×C₄	1	1	yes	characteristic
55	C₂×C₄×Dic₁₁	C₂×C₄	1	1	yes	characteristic
56	C₂×#4318	C₂×C₄	1	2	yes	—
57	C₂²×C₁₁⋊C₈	C₂×C₄	1	2	yes	—
58	M₁₆×D₁₁	—	2	8	no	—
59	C₂×#4313	C₂×C₄	1	4	yes	—
60	C₂×#4313	C₂×C₄	1	4	yes	—
61	C₂×C₈×D₁₁	C₂×C₄	1	4	yes	—
62	C₄²×D₁₁	C₂×C₄	1	1	yes	characteristic
63	C₄²×D₁₁	C₂×C₄	1	1	yes	characteristic
64	C₄²×D₁₁	C₂×C₄	1	1	yes	characteristic
65	C₄²×D₁₁	C₂×C₄	1	1	yes	characteristic
66	C₄²×D₁₁	C₂×C₄	1	1	yes	characteristic
67	C₄²×D₁₁	C₂×C₄	1	1	yes	characteristic
68	C₄²×D₁₁	C₂³	1	1	yes	characteristic
69	C₄²×D₁₁	C₂³	1	1	yes	characteristic
70	C₁₁×C₄⋊C₈	C₂×C₄	1	2	yes	—
71	C₁₁×C₂²⋊C₈	C₂×C₄	1	2	yes	—
72	C₁₁×#97	C₂×C₄	1	2	yes	—
73	C₄×C₈×C₁₁	C₂×C₄	1	2	yes	—
74	C₄×C₈×C₁₁	C₂³	1	2	yes	—
75	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
76	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
77	C₄×C₈×C₁₁	C₂³	1	2	yes	—
78	C₂²⋊(C₁₁⋊C₈)	C₂×C₄	1	2	yes	—
79	(C₂×D₁₁)⋊C₈	C₂×C₄	1	2	yes	—
80	(C₂×D₁₁)⋊C₈	C₂×C₄	1	2	yes	—
81	(C₂×D₁₁)⋊C₈	C₂×C₄	1	2	yes	—
82	(C₂×D₁₁)⋊C₈	C₂×C₄	1	2	yes	—
83	(C₂×D₁₁)⋊C₈	C₂×C₄	1	4	yes	—
84	#66879	C₂×C₄	1	4	yes	—
85	#66879	C₂×C₄	1	4	yes	—
86	Dic₁₁⋊C₈	C₂×C₄	1	2	yes	—
87	Dic₁₁⋊C₈	C₂×C₄	1	2	yes	—
88	Dic₁₁⋊C₈	C₂×C₄	1	2	yes	—
89	Dic₁₁⋊C₈	C₂×C₄	1	2	yes	—
90	Dic₁₁⋊C₈	C₂×C₄	1	4	yes	—
91	C₈×Dic₁₁	C₂×C₄	1	4	yes	—
92	C₄⋊(C₁₁⋊C₈)	C₂×C₄	1	2	yes	—
93	#66867	C₂×C₄	1	2	yes	—
94	C₄×C₁₁⋊C₈	C₂×C₄	1	2	yes	—
95	C₄×C₁₁⋊C₈	C₂³	1	1	yes	characteristic
96	C₄×C₁₁⋊C₈	C₂³	1	1	yes	characteristic
97	C₄×C₁₁⋊C₈	C₂³	1	2	yes	—
98	C₄×C₁₁⋊C₈	C₂³	1	2	yes	—
99	#17327	—	11	1	no	maximal, Sylow
100	C₂³×D₁₁	C₄²	1	1	yes	characteristic
101	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
102	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
103	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
104	C₂²×Dic₁₁	C₄²	1	1	yes	characteristic
105	C₂²×Dic₁₁	C₄²	1	1	yes	characteristic
106	C₂²×Dic₁₁	C₄²	1	1	yes	characteristic
107	C₂×C₄×D₁₁	—	2	4	no	—
108	C₂×C₄×D₁₁	—	2	4	no	—
109	C₂×C₄×D₁₁	—	4	2	no	—
110	C₂×C₄×D₁₁	C₄²	1	1	yes	characteristic
111	C₂×C₄×D₁₁	C₄²	1	1	yes	characteristic
112	C₂×C₄×D₁₁	C₄²	1	1	yes	characteristic
113	C₂×C₄×D₁₁	C₄²	1	1	yes	characteristic
114	C₂×C₄×D₁₁	C₄²	1	1	yes	characteristic
115	C₂×C₄×D₁₁	C₄²	1	1	yes	characteristic
116	C₂×C₄×D₁₁	C₂²×C₄	1	1	yes	characteristic
117	C₂×C₄×D₁₁	C₂²×C₄	1	1	yes	characteristic
118	C₂×C₄×D₁₁	C₂²×C₄	1	1	yes	characteristic
119	C₂×C₄×D₁₁	C₂²×C₄	1	1	yes	characteristic
120	C₂×C₄×D₁₁	C₂²×C₄	1	1	yes	characteristic
121	C₂×C₄×D₁₁	C₂²×C₄	1	1	yes	characteristic
122	C₁₁×M₁₆	—	2	4	no	—
123	C₂×C₈×C₁₁	—	4	2	no	—
124	C₂×C₈×C₁₁	C₂²×C₄	1	4	yes	—
125	C₂×C₈×C₁₁	C₂²×C₄	1	2	yes	—
126	C₂×C₈×C₁₁	C₂²×C₄	1	2	yes	—
127	C₂×C₈×C₁₁	C₂²×C₄	1	4	yes	—
128	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
129	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
130	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
131	C₄²×C₁₁	C₂⁴	1	1	yes	characteristic
132	C₄×Dic₁₁	C₄²	1	1	yes	characteristic
133	C₄×Dic₁₁	C₄²	1	1	yes	characteristic
134	C₄×Dic₁₁	C₄²	1	1	yes	characteristic
135	C₄×Dic₁₁	C₄²	1	1	yes	characteristic
136	C₄×Dic₁₁	C₄²	1	1	yes	characteristic
137	C₄×Dic₁₁	C₄²	1	1	yes	characteristic
138	C₄×Dic₁₁	C₂²×C₄	1	1	yes	characteristic
139	C₄×Dic₁₁	C₂²×C₄	1	1	yes	characteristic
140	C₄×Dic₁₁	C₂²×C₄	1	1	yes	characteristic
141	C₄×Dic₁₁	C₂²×C₄	1	1	yes	characteristic
142	C₄×Dic₁₁	C₂²×C₄	1	1	yes	characteristic
143	C₄×Dic₁₁	C₂²×C₄	1	1	yes	characteristic
144	#4318	M₁₆	1	8	yes	complemented
145	C₂×C₁₁⋊C₈	—	4	2	no	—
146	C₂×C₁₁⋊C₈	C₂²×C₄	1	2	yes	—
147	C₂×C₁₁⋊C₈	C₂²×C₄	1	2	yes	—
148	C₂×C₁₁⋊C₈	C₂²×C₄	1	4	yes	—
149	C₂×C₁₁⋊C₈	C₂²×C₄	1	4	yes	—
150	#4313	—	2	8	no	—
151	#4313	—	2	8	no	—
152	C₈×D₁₁	—	2	8	no	—
153	#2920	—	11	1	no	—
154	C₂×#431	—	11	1	no	—
155	C₂×C₄×M₁₆	—	11	1	no	—
156	#1453	—	11	2	no	—
157	#1453	—	11	2	no	—
158	#1451	—	11	1	no	—
159	#1451	—	11	2	no	—
160	#1451	D₁₁	1	1	yes	characteristic, complemented
161	C₈×M₁₆	—	11	1	no	—
162	C₈×M₁₆	—	11	1	no	—
163	C₈×M₁₆	—	11	2	no	—
164	C₂³×C₁₁	C₂×C₄²	1	1	yes	characteristic
165	C₂²×D₁₁	—	2	2	no	—
166	C₂²×D₁₁	—	2	2	no	—
167	C₂²×D₁₁	—	4	1	no	—
168	C₂²×D₁₁	C₂×C₄²	1	1	yes	characteristic
169	C₂²×D₁₁	C₂×C₄²	1	1	yes	characteristic
170	C₂×C₄×C₁₁	—	2	2	no	—
171	C₂×C₄×C₁₁	—	2	2	no	—
172	C₂×C₄×C₁₁	C₂×C₄²	1	1	yes	characteristic
173	C₂×C₄×C₁₁	C₂×C₄²	1	1	yes	characteristic
174	C₂×C₄×C₁₁	C₂×C₄²	1	1	yes	characteristic
175	C₂×C₄×C₁₁	C₂×M₁₆	1	4	yes	—
176	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
177	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
178	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
179	C₂×Dic₁₁	—	2	2	no	—
180	C₂×Dic₁₁	—	2	2	no	—
181	C₂×Dic₁₁	—	4	1	no	—
182	C₂×Dic₁₁	C₂×C₄²	1	1	yes	characteristic
183	C₂×Dic₁₁	C₂×C₄²	1	1	yes	characteristic
184	C₂×Dic₁₁	C₂×C₄²	1	1	yes	characteristic
185	C₂×Dic₁₁	C₂×C₄²	1	1	yes	characteristic
186	C₂×Dic₁₁	C₂×C₄²	1	1	yes	characteristic
187	C₂×Dic₁₁	C₂×C₄²	1	1	yes	characteristic
188	C₄×D₁₁	—	2	2	no	—
189	C₄×D₁₁	—	2	2	no	—
190	C₄×D₁₁	—	2	2	no	—
191	C₄×D₁₁	—	2	2	no	—
192	C₄×D₁₁	—	2	2	no	—
193	C₄×D₁₁	—	2	2	no	—
194	C₄×D₁₁	—	2	2	no	—
195	C₄×D₁₁	—	2	2	no	—
196	C₄×D₁₁	—	2	2	no	—
197	C₄×D₁₁	—	4	1	no	—
198	C₄×D₁₁	—	4	1	no	—
199	C₄×D₁₁	#131	1	4	yes	—
200	C₈×C₁₁	—	2	4	no	—
201	C₈×C₁₁	—	2	4	no	—
202	C₈×C₁₁	—	2	2	no	—
203	C₈×C₁₁	—	2	2	no	—
204	C₁₁⋊C₈	—	2	4	no	—
205	C₁₁⋊C₈	—	2	2	no	—
206	C₁₁⋊C₈	—	2	2	no	—
207	C₁₁⋊C₈	C₂×M₁₆	1	8	yes	—
208	C₂²×M₁₆	—	11	2	no	—
209	C₂²×C₄²	—	11	1	no	—
210	#432	—	11	2	no	—
211	#432	—	11	2	no	—
212	#431	—	11	1	no	—
213	#431	—	11	1	no	—
214	#431	—	11	1	no	—
215	#431	—	11	1	no	—
216	#431	—	11	1	no	—
217	#431	—	11	2	no	—
218	#431	—	11	2	no	—
219	#431	—	11	2	no	—
220	#431	C₂×D₁₁	1	1	yes	characteristic
221	#423	—	11	2	no	—
222	C₂×C₄⋊C₈	—	11	2	no	—
223	#407	—	11	2	no	—
224	C₂×C₂²⋊C₈	—	11	2	no	—
225	C₄×M₁₆	—	11	2	no	—
226	C₄×M₁₆	—	11	1	no	—
227	C₄×M₁₆	—	11	2	no	—
228	C₄×M₁₆	—	11	2	no	—
229	C₄×M₁₆	—	11	2	no	—
230	C₄×M₁₆	C₂×D₁₁	1	1	yes	characteristic
231	C₂×#97	—	11	2	no	—
232	C₂×C₄×C₈	—	11	1	no	—
233	C₂×C₄×C₈	—	11	2	no	—
234	C₂×C₄×C₈	C₂×D₁₁	1	1	yes	characteristic
235	#322	—	11	2	no	—
236	#322	—	11	2	no	—
237	#322	—	11	2	no	—
238	#322	—	11	2	no	—
239	#322	C₂×D₁₁	1	2	yes	complemented
240	#322	C₂×D₁₁	1	2	yes	complemented
241	C₈²	—	11	2	no	—
242	C₈²	—	11	2	no	—
243	C₂²×C₁₁	—	2	1	no	—
244	C₂²×C₁₁	—	2	1	no	—
245	C₂²×C₁₁	C₄×M₁₆	1	2	yes	—
246	C₂²×C₁₁	C₂²×C₄²	1	1	yes	characteristic
247	C₂×D₁₁	—	2	1	no	—
248	C₂×D₁₁	—	2	1	no	—
249	C₂×D₁₁	—	2	1	no	—
250	C₂×D₁₁	—	2	1	no	—
251	C₂×D₁₁	—	2	1	no	—
252	C₂×D₁₁	—	4	4	no	—
253	C₂×D₁₁	#405	1	2	yes	—
254	C₄×C₁₁	—	2	1	no	—
255	C₄×C₁₁	—	2	1	no	—
256	C₄×C₁₁	C₄×M₁₆	1	2	yes	—
257	C₄×C₁₁	C₂²×M₁₆	1	2	yes	—
258	C₄×C₁₁	C₂×#131	1	2	yes	—
259	C₄×C₁₁	#568	1	2	yes	—
260	Dic₁₁	—	2	1	no	—
261	Dic₁₁	—	2	1	no	—
262	Dic₁₁	—	2	1	no	—
263	Dic₁₁	—	2	1	no	—
264	Dic₁₁	—	2	1	no	—
265	Dic₁₁	#405	1	2	yes	—
266	C₂³×C₄	—	11	1	no	—
267	C₂³×C₄	—	11	1	no	—
268	C₂³×C₄	—	11	1	no	—
269	C₂×M₁₆	—	11	2	no	—
270	C₂×M₁₆	—	11	4	no	—
271	C₂×M₁₆	—	11	4	no	—
272	C₂×M₁₆	—	22	8	no	—
273	C₂×M₁₆	C₄×D₁₁	1	2	yes	—
274	C₂²×C₈	—	11	2	no	—
275	C₂²×C₈	—	11	4	no	—
276	C₂²×C₈	C₄×D₁₁	1	2	yes	—
277	C₂×C₄²	—	11	1	no	—
278	C₂×C₄²	—	11	1	no	—
279	C₂×C₄²	—	11	1	no	—
280	C₂×C₄²	—	11	1	no	—
281	C₂×C₄²	—	11	1	no	—
282	C₂×C₄²	—	11	1	no	—
283	C₂×C₄²	—	11	1	no	—
284	C₂×C₄²	—	11	1	no	—
285	C₂×C₄²	—	11	1	no	—
286	C₂×C₄²	—	11	1	no	—
287	C₂×C₄²	—	11	1	no	—
288	C₂×C₄²	C₂²×D₁₁	1	1	yes	characteristic
289	C₄⋊C₈	—	11	2	no	—
290	C₄⋊C₈	—	11	2	no	—
291	C₄⋊C₈	—	11	2	no	—
292	C₄⋊C₈	—	11	2	no	—
293	C₄⋊C₈	—	11	4	no	—
294	C₄⋊C₈	—	11	2	no	—
295	C₄⋊C₈	C₄×D₁₁	1	2	yes	—
296	C₂²⋊C₈	—	11	2	no	—
297	C₂²⋊C₈	—	11	2	no	—
298	C₂²⋊C₈	—	11	2	no	—
299	C₂²⋊C₈	—	11	2	no	—
300	C₂²⋊C₈	—	11	2	no	—
301	C₂²⋊C₈	—	11	4	no	—
302	C₂²⋊C₈	C₄×D₁₁	1	2	yes	—
303	#97	—	11	4	no	—
304	#97	—	11	4	no	—
305	#97	—	11	2	no	—
306	#97	C₄×D₁₁	1	2	yes	—
307	C₄×C₈	—	11	4	no	—
308	C₄×C₈	—	11	2	no	—
309	C₄×C₈	—	11	2	no	—
310	C₄×C₈	—	11	1	no	—
311	C₄×C₈	—	11	2	no	—
312	C₄×C₈	—	11	1	no	—
313	C₄×C₈	C₄×D₁₁	1	2	yes	—
314	C₄×C₈	C₂²×D₁₁	1	1	yes	characteristic
315	C₄×C₈	C₂²×D₁₁	1	2	yes	—
316	C₄×C₈	C₂²×D₁₁	1	2	yes	—
317	C₄×C₈	C₂²×D₁₁	1	1	yes	characteristic
318	C₂×C₁₁	—	2	2	no	—
319	C₂×C₁₁	C₂×C₄×M₁₆	1	1	yes	characteristic
320	C₂×C₁₁	C₂×#405	1	1	yes	characteristic
321	C₂×C₁₁	#2873	1	1	yes	characteristic
322	D₁₁	—	2	2	no	—
323	D₁₁	—	4	1	no	—
324	C₂⁴	—	11	1	no	—
325	C₂²×C₄	—	11	1	no	—
326	C₂²×C₄	—	11	1	no	—
327	C₂²×C₄	—	11	1	no	—
328	C₂²×C₄	—	11	1	no	—
329	C₂²×C₄	—	11	1	no	—
330	C₂²×C₄	—	11	1	no	—
331	C₂²×C₄	—	11	1	no	—
332	C₂²×C₄	—	11	1	no	—
333	C₂²×C₄	—	11	1	no	—
334	C₂²×C₄	—	11	1	no	—
335	C₂²×C₄	—	11	1	no	—
336	C₂²×C₄	—	11	1	no	—
337	C₂²×C₄	—	11	1	no	—
338	C₂²×C₄	—	11	1	no	—
339	C₂²×C₄	—	11	1	no	—
340	C₂²×C₄	—	22	4	no	—
341	C₂²×C₄	—	22	4	no	—
342	C₂²×C₄	—	44	2	no	—
343	C₂²×C₄	C₂×C₄×D₁₁	1	1	yes	characteristic
344	C₂²×C₄	C₂×C₄×D₁₁	1	1	yes	characteristic
345	C₂²×C₄	C₂×C₄×D₁₁	1	1	yes	characteristic
346	M₁₆	—	2	4	no	—
347	M₁₆	—	11	8	no	—
348	M₁₆	—	22	8	no	—
349	M₁₆	—	22	8	no	—
350	C₂×C₈	—	4	2	no	—
351	C₂×C₈	—	11	4	no	—
352	C₂×C₈	—	11	2	no	—
353	C₂×C₈	—	11	2	no	—
354	C₂×C₈	—	11	4	no	—
355	C₂×C₈	—	22	8	no	—
356	C₂×C₈	—	44	2	no	—
357	C₂×C₈	C₂×C₄×D₁₁	1	4	yes	—
358	C₂×C₈	C₂×C₄×D₁₁	1	2	yes	—
359	C₂×C₈	C₂×C₄×D₁₁	1	2	yes	—
360	C₂×C₈	C₂×C₄×D₁₁	1	4	yes	—
361	C₄²	—	11	1	no	—
362	C₄²	—	11	1	no	—
363	C₄²	—	11	1	no	—
364	C₄²	—	11	1	no	—
365	C₄²	—	11	1	no	—
366	C₄²	—	11	1	no	—
367	C₄²	—	11	1	no	—
368	C₄²	—	11	1	no	—
369	C₄²	—	11	1	no	—
370	C₄²	—	11	1	no	—
371	C₄²	—	11	1	no	—
372	C₄²	—	11	1	no	—
373	C₄²	C₂×C₄×D₁₁	1	1	yes	characteristic
374	C₄²	C₂×C₄×D₁₁	1	1	yes	characteristic
375	C₄²	C₂×C₄×D₁₁	1	1	yes	characteristic
376	C₄²	C₂³×D₁₁	1	1	yes	characteristic
377	C₁₁	#17327	1	1	yes	characteristic, complemented, Sylow
378	C₂³	—	11	1	no	—
379	C₂³	—	11	1	no	—
380	C₂³	—	22	2	no	—
381	C₂³	—	22	2	no	—
382	C₂³	—	44	1	no	—
383	C₂³	C₄²×D₁₁	1	1	yes	characteristic
384	C₂×C₄	—	2	2	no	—
385	C₂×C₄	—	2	2	no	—
386	C₂×C₄	—	11	1	no	—
387	C₂×C₄	—	11	4	no	—
388	C₂×C₄	—	11	1	no	—
389	C₂×C₄	—	11	1	no	—
390	C₂×C₄	—	11	1	no	—
391	C₂×C₄	—	11	1	no	—
392	C₂×C₄	—	11	1	no	—
393	C₂×C₄	—	22	2	no	—
394	C₂×C₄	—	22	2	no	—
395	C₂×C₄	—	22	2	no	—
396	C₂×C₄	—	22	2	no	—
397	C₂×C₄	—	22	2	no	—
398	C₂×C₄	—	22	2	no	—
399	C₂×C₄	—	22	2	no	—
400	C₂×C₄	—	22	2	no	—
401	C₂×C₄	—	22	2	no	—
402	C₂×C₄	—	22	2	no	—
403	C₂×C₄	—	22	2	no	—
404	C₂×C₄	—	44	1	no	—
405	C₂×C₄	—	44	1	no	—
406	C₂×C₄	—	44	1	no	—
407	C₂×C₄	C₄²×D₁₁	1	1	yes	characteristic
408	C₂×C₄	C₄²×D₁₁	1	1	yes	characteristic
409	C₂×C₄	C₄²×D₁₁	1	1	yes	characteristic
410	C₂×C₄	M₁₆×D₁₁	1	4	yes	—
411	C₂×C₄	C₂²×C₄×D₁₁	1	1	yes	characteristic
412	C₂×C₄	C₂²×C₄×D₁₁	1	1	yes	characteristic
413	C₂×C₄	C₂²×C₄×D₁₁	1	1	yes	characteristic
414	C₈	—	2	4	no	—
415	C₈	—	2	2	no	—
416	C₈	—	2	2	no	—
417	C₈	—	2	4	no	—
418	C₈	—	11	8	no	—
419	C₈	—	22	2	no	—
420	C₈	—	22	2	no	—
421	C₈	—	22	4	no	—
422	C₂²	—	2	1	no	—
423	C₂²	—	2	1	no	—
424	C₂²	—	11	2	no	—
425	C₂²	—	22	1	no	—
426	C₂²	—	22	1	no	—
427	C₂²	—	22	1	no	—
428	C₂²	—	22	1	no	—
429	C₂²	—	22	1	no	—
430	C₂²	—	44	4	no	—
431	C₂²	#10622320	1	2	yes	—
432	C₂²	C₂×C₄²×D₁₁	1	1	yes	characteristic
433	C₄	—	2	1	no	—
434	C₄	—	2	1	no	—
435	C₄	—	11	2	no	—
436	C₄	—	22	1	no	—
437	C₄	—	22	1	no	—
438	C₄	—	22	1	no	—
439	C₄	—	22	1	no	—
440	C₄	—	22	1	no	—
441	C₄	#10622320	1	2	yes	—
442	C₄	C₂×M₁₆×D₁₁	1	2	yes	—
443	C₄	#10623276	1	2	yes	—
444	C₄	D₁₁×#131	1	2	yes	—
445	C₂	—	2	2	no	—
446	C₂	—	22	2	no	—
447	C₂	—	44	1	no	—
448	C₂	C₂×#10622320	1	1	yes	characteristic
449	C₂	D₁₁×#405	1	1	yes	characteristic
450	C₂	#13077033	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₄²	C₂³×D₁₁
commutator, socle	C₂²×C₁₁	C₂²×C₄²
Fitting	C₁₁×#1451	C₂
prime radical	C₂³×D₁₁	C₄²
cosocle	C₄²×C₁₁	C₂⁴
hypercenter	#1451	D₁₁
hypocenter	C₁₁	#17327
LCS	G ▷ C₂²×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₄² ◁ #1451

Complements

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

N	H ≅ G/N	type
4. #13066912	C₂	semidirect
5. #13066912	C₂	semidirect
6. #13066904	C₂	semidirect
7. #13066903	C₂	semidirect
8. #13066897	C₂	semidirect
9. C₈×#4318	C₂	semidirect
10. #13066895	C₂	semidirect
11. C₁₁×#1451	C₂	semidirect
39. C₁₁×#322	C₂²	semidirect
40. C₁₁×#322	C₂²	semidirect
41. #10622092	C₂²	semidirect
42. #10622092	C₂²	semidirect
43. #10622092	C₂²	semidirect
44. #10622092	C₂²	semidirect
45. C₈×C₁₁⋊C₈	C₂²	semidirect
46. C₈×C₁₁⋊C₈	C₂²	semidirect
144. #4318	M₁₆	semidirect
160. #1451	D₁₁	semidirect
239. #322	C₂×D₁₁	semidirect
240. #322	C₂×D₁₁	semidirect
377. C₁₁	#17327	semidirect

Maximal subgroups

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

subgroup	index
#13077244	2
C₂×#10622298	2
C₄×M₁₆×D₁₁	2
#13066912	2
#13066904	2
#13066903	2
#13066897	2
C₈×#4318	2
#13066895	2
C₁₁×#1451	2
#17327	11