Subgroups — #14719409

Order 2816.

742 conjugacy classes of subgroups.

The subgroup lattice has 446 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13077247	C₂	1	1	yes	maximal, characteristic
2	#13077244	C₂	1	1	yes	maximal, characteristic
3	C₂×#10622298	C₂	1	1	yes	maximal, characteristic
4	#13066917	C₂	1	2	yes	maximal, complemented
5	#13066917	C₂	1	2	yes	maximal, complemented
6	#13066914	C₂	1	2	yes	maximal, complemented
7	#13066912	C₂	1	2	yes	maximal, complemented
8	#13066905	C₂	1	1	yes	maximal, characteristic, complemented
9	#13066897	C₂	1	1	yes	maximal, characteristic, complemented
10	M₁₆×C₁₁⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₁×#1451	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₄²×D₁₁	C₂²	1	1	yes	characteristic
13	C₁₁×#431	C₂²	1	1	yes	characteristic
14	C₄×C₁₁×M₁₆	C₂²	1	1	yes	characteristic
15	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
16	#10622739	C₄	1	2	yes	—
17	#10622731	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	#10622318	C₄	1	2	yes	—
28	#10622318	C₄	1	2	yes	—
29	C₄×#4313	C₂²	1	2	yes	—
30	#10622298	C₄	1	2	yes	—
31	#10622298	C₄	1	2	yes	—
32	#10622298	C₂²	1	1	yes	characteristic
33	#10622298	C₂²	1	2	yes	—
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	#10622298	C₂²	1	2	yes	—
39	C₁₁×#322	C₂²	1	2	yes	complemented
40	C₁₁×#322	C₂²	1	2	yes	complemented
41	#10622093	C₂²	1	2	yes	complemented
42	#10622093	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	C₂×#4313	C₂×C₄	1	4	yes	—
59	C₄²×D₁₁	C₂×C₄	1	1	yes	characteristic
60	C₄²×D₁₁	C₂×C₄	1	1	yes	characteristic
61	C₄²×D₁₁	C₂×C₄	1	1	yes	characteristic
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	C₂³	1	1	yes	characteristic
66	C₄²×D₁₁	C₂³	1	1	yes	characteristic
67	C₁₁×C₄⋊C₈	C₂×C₄	1	2	yes	—
68	C₁₁×C₂²⋊C₈	C₂×C₄	1	2	yes	—
69	C₁₁×#97	C₂×C₄	1	2	yes	—
70	C₄×C₈×C₁₁	C₂×C₄	1	2	yes	—
71	C₄×C₈×C₁₁	C₂³	1	2	yes	—
72	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
73	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
74	C₄×C₈×C₁₁	C₂³	1	2	yes	—
75	C₂²⋊(C₁₁⋊C₈)	C₂×C₄	1	2	yes	—
76	(C₂×D₁₁)⋊C₈	C₂×C₄	1	2	yes	—
77	(C₂×D₁₁)⋊C₈	C₂×C₄	1	2	yes	—
78	(C₂×D₁₁)⋊C₈	C₂×C₄	1	2	yes	—
79	(C₂×D₁₁)⋊C₈	C₂×C₄	1	2	yes	—
80	(C₂×D₁₁)⋊C₈	C₂×C₄	1	4	yes	—
81	(C₂×D₁₁)⋊C₈	C₂×C₄	1	4	yes	—
82	(C₂×D₁₁)⋊C₈	C₂×C₄	1	4	yes	—
83	#66879	C₂×C₄	1	4	yes	—
84	Dic₁₁⋊C₈	C₂×C₄	1	4	yes	—
85	Dic₁₁⋊C₈	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	C₄⋊(C₁₁⋊C₈)	C₂×C₄	1	2	yes	—
92	#66867	C₂×C₄	1	2	yes	—
93	C₄×C₁₁⋊C₈	C₂×C₄	1	2	yes	—
94	C₄×C₁₁⋊C₈	C₂³	1	1	yes	characteristic
95	C₄×C₁₁⋊C₈	C₂³	1	1	yes	characteristic
96	C₄×C₁₁⋊C₈	C₂³	1	2	yes	—
97	C₄×C₁₁⋊C₈	C₂³	1	2	yes	—
98	#17324	—	11	1	no	maximal, Sylow
99	C₂³×D₁₁	C₄²	1	1	yes	characteristic
100	C₂²×C₄×C₁₁	C₂²×C₄	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×Dic₁₁	C₄²	1	1	yes	characteristic
104	C₂²×Dic₁₁	C₄²	1	1	yes	characteristic
105	C₂²×Dic₁₁	C₄²	1	1	yes	characteristic
106	C₂×C₄×D₁₁	—	2	4	no	—
107	C₂×C₄×D₁₁	—	4	2	no	—
108	C₂×C₄×D₁₁	—	4	2	no	—
109	C₂×C₄×D₁₁	C₄²	1	1	yes	characteristic
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	C₂²×C₄	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	C₁₁×M₁₆	—	2	4	no	—
122	C₂×C₈×C₁₁	—	4	2	no	—
123	C₂×C₈×C₁₁	C₂²×C₄	1	2	yes	—
124	C₂×C₈×C₁₁	C₂²×C₄	1	2	yes	—
125	C₂×C₈×C₁₁	C₂²×C₄	1	4	yes	—
126	C₂×C₈×C₁₁	C₂²×C₄	1	4	yes	—
127	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
128	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
129	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
130	C₄²×C₁₁	C₂⁴	1	1	yes	characteristic
131	C₄×Dic₁₁	C₄²	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	C₂²×C₄	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	#4318	—	2	4	no	—
144	C₂×C₁₁⋊C₈	—	4	2	no	—
145	C₂×C₁₁⋊C₈	C₂²×C₄	1	2	yes	—
146	C₂×C₁₁⋊C₈	C₂²×C₄	1	2	yes	—
147	C₂×C₁₁⋊C₈	C₂²×C₄	1	4	yes	—
148	C₂×C₁₁⋊C₈	C₂²×C₄	1	4	yes	—
149	#4313	—	4	4	no	—
150	#2920	—	11	1	no	—
151	#2920	—	11	1	no	—
152	C₂×#431	—	11	1	no	—
153	#1454	—	11	2	no	—
154	#1454	—	11	2	no	—
155	#1453	—	11	2	no	—
156	#1453	—	11	2	no	—
157	#1451	—	11	1	no	—
158	#1451	D₁₁	1	1	yes	characteristic, complemented
159	C₈×M₁₆	—	11	1	no	—
160	C₈×M₁₆	—	11	1	no	—
161	C₂³×C₁₁	C₂×C₄²	1	1	yes	characteristic
162	C₂²×D₁₁	—	2	2	no	—
163	C₂²×D₁₁	—	4	1	no	—
164	C₂²×D₁₁	—	4	1	no	—
165	C₂²×D₁₁	C₂×C₄²	1	1	yes	characteristic
166	C₂²×D₁₁	C₂×C₄²	1	1	yes	characteristic
167	C₂×C₄×C₁₁	—	2	2	no	—
168	C₂×C₄×C₁₁	—	2	2	no	—
169	C₂×C₄×C₁₁	C₂×C₄²	1	1	yes	characteristic
170	C₂×C₄×C₁₁	C₂×C₄²	1	1	yes	characteristic
171	C₂×C₄×C₁₁	C₂×C₄²	1	1	yes	characteristic
172	C₂×C₄×C₁₁	#131	1	4	yes	—
173	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
174	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
175	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
176	C₂×Dic₁₁	—	2	2	no	—
177	C₂×Dic₁₁	—	4	1	no	—
178	C₂×Dic₁₁	—	4	1	no	—
179	C₂×Dic₁₁	C₂×C₄²	1	1	yes	characteristic
180	C₂×Dic₁₁	C₂×C₄²	1	1	yes	characteristic
181	C₂×Dic₁₁	C₂×C₄²	1	1	yes	characteristic
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	C₄×D₁₁	—	2	2	no	—
186	C₄×D₁₁	—	2	2	no	—
187	C₄×D₁₁	—	2	2	no	—
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	—	4	1	no	—
194	C₄×D₁₁	—	4	1	no	—
195	C₄×D₁₁	—	4	1	no	—
196	C₄×D₁₁	—	4	1	no	—
197	C₈×C₁₁	—	2	4	no	—
198	C₈×C₁₁	—	2	4	no	—
199	C₈×C₁₁	—	2	2	no	—
200	C₈×C₁₁	—	2	2	no	—
201	C₁₁⋊C₈	—	2	4	no	—
202	C₁₁⋊C₈	—	2	4	no	—
203	C₁₁⋊C₈	—	2	2	no	—
204	C₁₁⋊C₈	—	2	2	no	—
205	C₂²×C₄²	—	11	1	no	—
206	#432	—	11	2	no	—
207	#432	—	11	2	no	—
208	#432	—	11	2	no	—
209	#432	—	11	2	no	—
210	#431	—	11	1	no	—
211	#431	—	11	1	no	—
212	#431	—	11	1	no	—
213	#431	—	11	1	no	—
214	#431	—	11	1	no	—
215	#431	—	11	2	no	—
216	#431	—	11	2	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	#423	—	11	2	no	—
223	C₂×C₄⋊C₈	—	11	2	no	—
224	#407	—	11	2	no	—
225	#407	—	11	2	no	—
226	C₂×C₂²⋊C₈	—	11	2	no	—
227	C₄×M₁₆	—	11	1	no	—
228	C₄×M₁₆	—	11	2	no	—
229	C₄×M₁₆	C₂×D₁₁	1	1	yes	characteristic
230	C₂×C₄×C₈	—	11	1	no	—
231	C₂×C₄×C₈	C₂×D₁₁	1	1	yes	characteristic
232	#322	—	11	2	no	—
233	#322	—	11	2	no	—
234	#322	—	11	2	no	—
235	#322	—	11	2	no	—
236	#322	C₂×D₁₁	1	2	yes	complemented
237	#322	C₂×D₁₁	1	2	yes	complemented
238	C₈²	—	11	2	no	—
239	C₈²	—	11	2	no	—
240	C₂²×C₁₁	—	2	1	no	—
241	C₂²×C₁₁	—	2	1	no	—
242	C₂²×C₁₁	#405	1	2	yes	—
243	C₂²×C₁₁	C₂²×C₄²	1	1	yes	characteristic
244	C₂×D₁₁	—	2	1	no	—
245	C₂×D₁₁	—	2	1	no	—
246	C₂×D₁₁	—	2	1	no	—
247	C₂×D₁₁	—	2	1	no	—
248	C₂×D₁₁	—	2	1	no	—
249	C₂×D₁₁	—	2	1	no	—
250	C₂×D₁₁	—	4	4	no	—
251	C₄×C₁₁	—	2	1	no	—
252	C₄×C₁₁	—	2	1	no	—
253	C₄×C₁₁	#405	1	2	yes	—
254	C₄×C₁₁	C₂×#131	1	2	yes	—
255	C₄×C₁₁	#568	1	2	yes	—
256	C₄×C₁₁	#568	1	2	yes	—
257	Dic₁₁	—	2	1	no	—
258	Dic₁₁	—	2	1	no	—
259	Dic₁₁	—	2	1	no	—
260	Dic₁₁	—	2	1	no	—
261	Dic₁₁	—	2	1	no	—
262	Dic₁₁	—	2	1	no	—
263	C₂³×C₄	—	11	1	no	—
264	C₂³×C₄	—	11	1	no	—
265	C₂³×C₄	—	11	1	no	—
266	C₂×M₁₆	—	11	2	no	—
267	C₂×M₁₆	—	11	4	no	—
268	C₂×M₁₆	C₄×D₁₁	1	2	yes	—
269	C₂²×C₈	—	11	2	no	—
270	C₂²×C₈	C₄×D₁₁	1	2	yes	—
271	C₂×C₄²	—	11	1	no	—
272	C₂×C₄²	—	11	1	no	—
273	C₂×C₄²	—	11	1	no	—
274	C₂×C₄²	—	11	1	no	—
275	C₂×C₄²	—	11	1	no	—
276	C₂×C₄²	—	11	1	no	—
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	C₂²×D₁₁	1	1	yes	characteristic
283	C₄⋊C₈	—	11	2	no	—
284	C₄⋊C₈	—	11	2	no	—
285	C₄⋊C₈	—	11	2	no	—
286	C₄⋊C₈	—	11	2	no	—
287	C₄⋊C₈	—	11	4	no	—
288	C₄⋊C₈	—	11	4	no	—
289	C₄⋊C₈	—	11	4	no	—
290	C₄⋊C₈	—	11	2	no	—
291	C₄⋊C₈	C₄×D₁₁	1	2	yes	—
292	C₂²⋊C₈	—	11	2	no	—
293	C₂²⋊C₈	—	11	2	no	—
294	C₂²⋊C₈	—	11	2	no	—
295	C₂²⋊C₈	—	11	2	no	—
296	C₂²⋊C₈	—	11	2	no	—
297	C₂²⋊C₈	—	11	4	no	—
298	C₂²⋊C₈	—	11	4	no	—
299	C₂²⋊C₈	—	11	4	no	—
300	C₂²⋊C₈	C₄×D₁₁	1	2	yes	—
301	#97	—	11	4	no	—
302	#97	—	11	2	no	—
303	#97	C₄×D₁₁	1	2	yes	—
304	C₄×C₈	—	11	2	no	—
305	C₄×C₈	—	11	1	no	—
306	C₄×C₈	—	11	1	no	—
307	C₄×C₈	—	11	2	no	—
308	C₄×C₈	—	11	2	no	—
309	C₄×C₈	C₄×D₁₁	1	2	yes	—
310	C₄×C₈	C₂²×D₁₁	1	2	yes	—
311	C₄×C₈	C₂²×D₁₁	1	2	yes	—
312	C₄×C₈	C₂²×D₁₁	1	1	yes	characteristic
313	C₄×C₈	C₂²×D₁₁	1	1	yes	characteristic
314	C₂×C₁₁	—	2	2	no	—
315	C₂×C₁₁	C₂×#405	1	1	yes	characteristic
316	C₂×C₁₁	#2873	1	1	yes	characteristic
317	C₂×C₁₁	#2873	1	1	yes	characteristic
318	D₁₁	—	4	1	no	—
319	D₁₁	—	4	1	no	—
320	C₂⁴	—	11	1	no	—
321	C₂²×C₄	—	11	1	no	—
322	C₂²×C₄	—	11	1	no	—
323	C₂²×C₄	—	11	1	no	—
324	C₂²×C₄	—	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	—	22	4	no	—
337	C₂²×C₄	—	44	2	no	—
338	C₂²×C₄	—	44	2	no	—
339	C₂²×C₄	C₂×C₄×D₁₁	1	1	yes	characteristic
340	C₂²×C₄	C₂×C₄×D₁₁	1	1	yes	characteristic
341	C₂²×C₄	C₂×C₄×D₁₁	1	1	yes	characteristic
342	M₁₆	—	2	4	no	—
343	M₁₆	—	22	4	no	—
344	M₁₆	—	44	4	no	—
345	C₂×C₈	—	4	2	no	—
346	C₂×C₈	—	11	2	no	—
347	C₂×C₈	—	11	2	no	—
348	C₂×C₈	—	11	4	no	—
349	C₂×C₈	—	11	4	no	—
350	C₂×C₈	—	44	2	no	—
351	C₂×C₈	C₂×C₄×D₁₁	1	2	yes	—
352	C₂×C₈	C₂×C₄×D₁₁	1	2	yes	—
353	C₂×C₈	C₂×C₄×D₁₁	1	4	yes	—
354	C₂×C₈	C₂×C₄×D₁₁	1	4	yes	—
355	C₄²	—	11	1	no	—
356	C₄²	—	11	1	no	—
357	C₄²	—	11	1	no	—
358	C₄²	—	11	1	no	—
359	C₄²	—	11	1	no	—
360	C₄²	—	11	1	no	—
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	C₂×C₄×D₁₁	1	1	yes	characteristic
368	C₄²	C₂×C₄×D₁₁	1	1	yes	characteristic
369	C₄²	C₂×C₄×D₁₁	1	1	yes	characteristic
370	C₄²	C₂³×D₁₁	1	1	yes	characteristic
371	C₁₁	#17324	1	1	yes	characteristic, complemented, Sylow
372	C₂³	—	11	1	no	—
373	C₂³	—	11	1	no	—
374	C₂³	—	22	2	no	—
375	C₂³	—	44	1	no	—
376	C₂³	—	44	1	no	—
377	C₂³	C₄²×D₁₁	1	1	yes	characteristic
378	C₂×C₄	—	2	2	no	—
379	C₂×C₄	—	2	2	no	—
380	C₂×C₄	—	11	1	no	—
381	C₂×C₄	—	11	1	no	—
382	C₂×C₄	—	11	1	no	—
383	C₂×C₄	—	11	1	no	—
384	C₂×C₄	—	11	1	no	—
385	C₂×C₄	—	11	1	no	—
386	C₂×C₄	—	22	2	no	—
387	C₂×C₄	—	22	2	no	—
388	C₂×C₄	—	22	2	no	—
389	C₂×C₄	—	22	2	no	—
390	C₂×C₄	—	22	2	no	—
391	C₂×C₄	—	22	2	no	—
392	C₂×C₄	—	22	2	no	—
393	C₂×C₄	—	22	2	no	—
394	C₂×C₄	—	22	2	no	—
395	C₂×C₄	—	44	1	no	—
396	C₂×C₄	—	44	1	no	—
397	C₂×C₄	—	44	1	no	—
398	C₂×C₄	—	44	1	no	—
399	C₂×C₄	—	44	1	no	—
400	C₂×C₄	—	44	1	no	—
401	C₂×C₄	C₄²×D₁₁	1	1	yes	characteristic
402	C₂×C₄	C₄²×D₁₁	1	1	yes	characteristic
403	C₂×C₄	C₄²×D₁₁	1	1	yes	characteristic
404	C₂×C₄	#66960	1	4	yes	—
405	C₂×C₄	C₂²×C₄×D₁₁	1	1	yes	characteristic
406	C₂×C₄	C₂²×C₄×D₁₁	1	1	yes	characteristic
407	C₂×C₄	C₂²×C₄×D₁₁	1	1	yes	characteristic
408	C₈	—	2	4	no	—
409	C₈	—	2	2	no	—
410	C₈	—	2	2	no	—
411	C₈	—	2	4	no	—
412	C₈	—	22	4	no	—
413	C₈	—	22	2	no	—
414	C₈	—	22	2	no	—
415	C₈	—	22	4	no	—
416	C₂²	—	2	1	no	—
417	C₂²	—	2	1	no	—
418	C₂²	—	22	1	no	—
419	C₂²	—	22	1	no	—
420	C₂²	—	22	1	no	—
421	C₂²	—	22	1	no	—
422	C₂²	—	22	1	no	—
423	C₂²	—	22	1	no	—
424	C₂²	—	44	4	no	—
425	C₂²	#10622321	1	2	yes	—
426	C₂²	C₂×C₄²×D₁₁	1	1	yes	characteristic
427	C₄	—	2	1	no	—
428	C₄	—	2	1	no	—
429	C₄	—	22	1	no	—
430	C₄	—	22	1	no	—
431	C₄	—	22	1	no	—
432	C₄	—	22	1	no	—
433	C₄	—	22	1	no	—
434	C₄	—	22	1	no	—
435	C₄	#10622321	1	2	yes	—
436	C₄	C₂×#66960	1	2	yes	—
437	C₄	#10623276	1	2	yes	—
438	C₄	#10623281	1	2	yes	—
439	C₂	—	2	2	no	—
440	C₂	—	44	1	no	—
441	C₂	—	44	1	no	—
442	C₂	C₂×#10622321	1	1	yes	characteristic
443	C₂	#13077032	1	1	yes	characteristic
444	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	#17324
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. #13066917	C₂	semidirect
5. #13066917	C₂	semidirect
6. #13066914	C₂	semidirect
7. #13066912	C₂	semidirect
8. #13066905	C₂	semidirect
9. #13066897	C₂	semidirect
10. M₁₆×C₁₁⋊C₈	C₂	semidirect
11. C₁₁×#1451	C₂	semidirect
39. C₁₁×#322	C₂²	semidirect
40. C₁₁×#322	C₂²	semidirect
41. #10622093	C₂²	semidirect
42. #10622093	C₂²	semidirect
43. #10622092	C₂²	semidirect
44. #10622092	C₂²	semidirect
45. C₈×C₁₁⋊C₈	C₂²	semidirect
46. C₈×C₁₁⋊C₈	C₂²	semidirect
158. #1451	D₁₁	semidirect
236. #322	C₂×D₁₁	semidirect
237. #322	C₂×D₁₁	semidirect
371. C₁₁	#17324	semidirect

Maximal subgroups

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

subgroup	index
#13077247	2
#13077244	2
C₂×#10622298	2
#13066917	2
#13066914	2
#13066912	2
#13066905	2
#13066897	2
M₁₆×C₁₁⋊C₈	2
C₁₁×#1451	2
#17324	11