Subgroups — #14722801

Order 2816.

756 conjugacy classes of subgroups.

The subgroup lattice has 462 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13077248	C₂	1	1	yes	maximal, characteristic
2	D₁₁×#423	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×#4313	C₂	1	1	yes	maximal, characteristic
4	#13067382	C₂	1	4	yes	maximal, complemented
5	#13067374	C₂	1	1	yes	maximal, characteristic, complemented
6	#13067372	C₂	1	1	yes	maximal, characteristic, complemented
7	#13067371	C₂	1	1	yes	maximal, characteristic, complemented
8	#13067367	C₂	1	4	yes	maximal, complemented
9	C₁₁×#1567	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×M₁₆×D₁₁	—	2	1	no	—
11	C₂²×#4313	C₄	1	2	yes	—
12	C₂×C₄²×D₁₁	C₂²	1	1	yes	characteristic
13	C₁₁×#423	C₂²	1	1	yes	characteristic
14	C₁₁×#423	C₂²	1	1	yes	characteristic
15	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
16	#10622739	—	2	1	no	—
17	#10622731	—	2	1	no	—
18	M₁₆×Dic₁₁	—	2	1	no	—
19	C₂×#66879	C₄	1	2	yes	—
20	#10622537	C₂²	1	1	yes	characteristic
21	#10622537	C₂²	1	1	yes	characteristic
22	C₂×C₄×C₁₁⋊C₈	C₂²	1	1	yes	characteristic
23	#10622450	—	2	1	no	—
24	#10622450	C₂²	1	2	yes	—
25	#10622448	—	2	1	no	—
26	#10622448	C₂²	1	2	yes	—
27	#10622446	—	2	1	no	—
28	#10622446	C₂²	1	2	yes	—
29	D₁₁×C₄⋊C₈	—	2	1	no	—
30	D₁₁×C₄⋊C₈	C₂²	1	2	yes	—
31	C₄×#4313	C₄	1	1	yes	characteristic
32	C₄×#4313	C₄	1	1	yes	characteristic
33	C₄×#4313	C₄	1	1	yes	characteristic
34	C₄×#4313	C₄	1	1	yes	characteristic
35	C₄×#4313	C₂²	1	2	yes	—
36	C₄×#4313	C₂²	1	2	yes	—
37	C₁₁×#335	C₂²	1	4	yes	complemented
38	#10622118	C₂²	1	4	yes	complemented
39	#10622117	C₂²	1	4	yes	complemented
40	#10622095	C₂²	1	4	yes	complemented
41	C₂²×C₄×D₁₁	C₂×C₄	1	1	yes	characteristic
42	C₂²×C₄×D₁₁	D₄	1	1	yes	characteristic
43	C₂²×C₄×D₁₁	Q₈	1	1	yes	characteristic
44	C₂×C₁₁×M₁₆	—	2	1	no	—
45	C₂×C₁₁×M₁₆	—	2	1	no	—
46	C₂²×C₈×C₁₁	C₂×C₄	1	2	yes	—
47	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
48	C₂×C₄×Dic₁₁	C₂×C₄	1	1	yes	characteristic
49	C₂×C₄×Dic₁₁	D₄	1	1	yes	characteristic
50	C₂×C₄×Dic₁₁	Q₈	1	1	yes	characteristic
51	C₂×#4318	—	2	1	no	—
52	C₂×#4318	—	2	1	no	—
53	C₂²×C₁₁⋊C₈	C₂×C₄	1	2	yes	—
54	M₁₆×D₁₁	—	4	4	no	—
55	C₂×#4313	—	2	8	no	—
56	C₂×#4313	—	2	2	no	—
57	C₂×#4313	C₂×C₄	1	2	yes	—
58	C₂×#4313	C₂×C₄	1	2	yes	—
59	C₂×#4313	C₂×C₄	1	2	yes	—
60	C₂×#4313	C₂×C₄	1	2	yes	—
61	C₂×C₈×D₁₁	—	2	2	no	—
62	C₄²×D₁₁	C₂×C₄	1	1	yes	characteristic
63	C₄²×D₁₁	C₂×C₄	1	1	yes	characteristic
64	C₄²×D₁₁	D₄	1	1	yes	characteristic
65	C₄²×D₁₁	D₄	1	1	yes	characteristic
66	C₄²×D₁₁	Q₈	1	1	yes	characteristic
67	C₄²×D₁₁	Q₈	1	1	yes	characteristic
68	C₄²×D₁₁	C₂³	1	1	yes	characteristic
69	C₄²×D₁₁	C₂³	1	1	yes	characteristic
70	C₁₁×C₄⋊C₈	—	2	1	no	—
71	C₁₁×C₄⋊C₈	—	2	1	no	—
72	C₁₁×C₄⋊C₈	C₂³	1	2	yes	—
73	C₁₁×C₄⋊C₈	C₂³	1	2	yes	—
74	C₄×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
75	C₄×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
76	C₄×C₈×C₁₁	C₂³	1	2	yes	—
77	(C₂×D₁₁)⋊C₈	—	2	2	no	—
78	(C₂×D₁₁)⋊C₈	—	2	2	no	—
79	#66879	—	2	2	no	—
80	#66879	C₂×C₄	1	2	yes	—
81	#66879	C₂×C₄	1	2	yes	—
82	#66879	C₂×C₄	1	2	yes	—
83	#66879	C₂×C₄	1	2	yes	—
84	Dic₁₁⋊C₈	—	2	2	no	—
85	Dic₁₁⋊C₈	—	2	2	no	—
86	C₈×Dic₁₁	—	2	2	no	—
87	C₄⋊(C₁₁⋊C₈)	—	2	1	no	—
88	C₄⋊(C₁₁⋊C₈)	—	2	1	no	—
89	C₄⋊(C₁₁⋊C₈)	C₂³	1	2	yes	—
90	C₄⋊(C₁₁⋊C₈)	C₂³	1	2	yes	—
91	C₄×C₁₁⋊C₈	C₂×C₄	1	1	yes	characteristic
92	C₄×C₁₁⋊C₈	C₂×C₄	1	1	yes	characteristic
93	C₄×C₁₁⋊C₈	C₂³	1	2	yes	—
94	#17796	—	11	1	no	maximal, Sylow
95	C₂³×D₁₁	C₄⋊C₄	1	1	yes	characteristic
96	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
97	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
98	C₂²×C₄×C₁₁	C₂×Q₈	1	1	yes	characteristic
99	C₂²×Dic₁₁	C₄⋊C₄	1	1	yes	characteristic
100	C₂²×Dic₁₁	C₄⋊C₄	1	1	yes	characteristic
101	C₂²×Dic₁₁	C₄⋊C₄	1	1	yes	characteristic
102	C₂×C₄×D₁₁	—	2	4	no	—
103	C₂×C₄×D₁₁	—	2	2	no	—
104	C₂×C₄×D₁₁	—	2	2	no	—
105	C₂×C₄×D₁₁	—	4	2	no	—
106	C₂×C₄×D₁₁	C₄⋊C₄	1	1	yes	characteristic
107	C₂×C₄×D₁₁	C₄⋊C₄	1	1	yes	characteristic
108	C₂×C₄×D₁₁	C₄⋊C₄	1	1	yes	characteristic
109	C₂×C₄×D₁₁	C₄⋊C₄	1	1	yes	characteristic
110	C₂×C₄×D₁₁	C₄⋊C₄	1	1	yes	characteristic
111	C₂×C₄×D₁₁	C₄⋊C₄	1	1	yes	characteristic
112	C₂×C₄×D₁₁	C₂²×C₄	1	1	yes	characteristic
113	C₂×C₄×D₁₁	C₂²×C₄	1	1	yes	characteristic
114	C₂×C₄×D₁₁	C₂×D₄	1	1	yes	characteristic
115	C₂×C₄×D₁₁	C₂×D₄	1	1	yes	characteristic
116	C₂×C₄×D₁₁	C₂×Q₈	1	1	yes	characteristic
117	C₂×C₄×D₁₁	C₂×Q₈	1	1	yes	characteristic
118	C₁₁×M₁₆	—	4	2	no	—
119	C₁₁×M₁₆	—	4	2	no	—
120	C₂×C₈×C₁₁	—	2	4	no	—
121	C₂×C₈×C₁₁	—	2	2	no	—
122	C₂×C₈×C₁₁	—	2	2	no	—
123	C₂×C₈×C₁₁	C₂²×C₄	1	2	yes	—
124	C₂×C₈×C₁₁	C₂²×C₄	1	2	yes	—
125	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
126	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
127	C₄²×C₁₁	C₂×Q₈	1	1	yes	characteristic
128	C₄²×C₁₁	C₂⁴	1	1	yes	characteristic
129	C₄×Dic₁₁	C₄⋊C₄	1	1	yes	characteristic
130	C₄×Dic₁₁	C₄⋊C₄	1	1	yes	characteristic
131	C₄×Dic₁₁	C₄⋊C₄	1	1	yes	characteristic
132	C₄×Dic₁₁	C₄⋊C₄	1	1	yes	characteristic
133	C₄×Dic₁₁	C₄⋊C₄	1	1	yes	characteristic
134	C₄×Dic₁₁	C₄⋊C₄	1	1	yes	characteristic
135	C₄×Dic₁₁	C₂²×C₄	1	1	yes	characteristic
136	C₄×Dic₁₁	C₂²×C₄	1	1	yes	characteristic
137	C₄×Dic₁₁	C₂×D₄	1	1	yes	characteristic
138	C₄×Dic₁₁	C₂×D₄	1	1	yes	characteristic
139	C₄×Dic₁₁	C₂×Q₈	1	1	yes	characteristic
140	C₄×Dic₁₁	C₂×Q₈	1	1	yes	characteristic
141	#4318	—	4	2	no	—
142	#4318	—	4	2	no	—
143	C₂×C₁₁⋊C₈	—	2	4	no	—
144	C₂×C₁₁⋊C₈	—	2	2	no	—
145	C₂×C₁₁⋊C₈	—	2	2	no	—
146	C₂×C₁₁⋊C₈	C₂²×C₄	1	2	yes	—
147	C₂×C₁₁⋊C₈	C₂²×C₄	1	2	yes	—
148	#4313	—	2	4	no	—
149	#4313	—	2	4	no	—
150	#4313	—	2	4	no	—
151	#4313	—	4	4	no	—
152	#4313	M₁₆	1	8	yes	complemented
153	C₈×D₁₁	—	4	4	no	—
154	#2920	—	11	1	no	—
155	C₂×#423	—	11	1	no	—
156	C₂×C₄×M₁₆	—	11	1	no	—
157	#1569	—	11	4	no	—
158	#1567	—	11	1	no	—
159	#1567	D₁₁	1	1	yes	characteristic, complemented
160	#1566	—	11	1	no	—
161	#1566	—	11	1	no	—
162	#1565	—	11	4	no	—
163	C₂³×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
164	C₂²×D₁₁	—	2	2	no	—
165	C₂²×D₁₁	—	2	2	no	—
166	C₂²×D₁₁	—	4	1	no	—
167	C₂²×D₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
168	C₂²×D₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
169	C₂×C₄×C₁₁	—	2	2	no	—
170	C₂×C₄×C₁₁	—	2	2	no	—
171	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
172	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
173	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
174	C₂×C₄×C₁₁	AGL(1,ℤ/8)	1	2	yes	—
175	C₂×C₄×C₁₁	#137	1	2	yes	—
176	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
177	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
178	C₂×C₄×C₁₁	C₂²×Q₈	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×C₄⋊C₄	1	1	yes	characteristic
183	C₂×Dic₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
184	C₂×Dic₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
185	C₂×Dic₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
186	C₂×Dic₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
187	C₂×Dic₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
188	C₄×D₁₁	—	2	2	no	—
189	C₄×D₁₁	—	2	2	no	—
190	C₄×D₁₁	—	2	1	no	—
191	C₄×D₁₁	—	2	1	no	—
192	C₄×D₁₁	—	2	1	no	—
193	C₄×D₁₁	—	2	1	no	—
194	C₄×D₁₁	—	2	2	no	—
195	C₄×D₁₁	—	2	2	no	—
196	C₄×D₁₁	—	2	2	no	—
197	C₄×D₁₁	—	2	2	no	—
198	C₄×D₁₁	—	2	2	no	—
199	C₄×D₁₁	—	4	1	no	—
200	C₄×D₁₁	—	4	1	no	—
201	C₄×D₁₁	C₂×M₁₆	1	4	yes	—
202	C₈×C₁₁	—	2	2	no	—
203	C₈×C₁₁	—	4	2	no	—
204	C₈×C₁₁	—	4	2	no	—
205	C₈×C₁₁	C₂×M₁₆	1	4	yes	complemented
206	C₁₁⋊C₈	—	2	2	no	—
207	C₁₁⋊C₈	—	4	2	no	—
208	C₁₁⋊C₈	—	4	2	no	—
209	C₁₁⋊C₈	C₂×M₁₆	1	4	yes	complemented
210	C₂²×M₁₆	—	11	2	no	—
211	C₂²×M₁₆	—	22	1	no	—
212	C₂²×C₄²	—	11	1	no	—
213	#432	—	11	2	no	—
214	#432	—	22	1	no	—
215	#431	—	11	2	no	—
216	#431	—	22	1	no	—
217	#423	—	11	1	no	—
218	#423	—	11	1	no	—
219	#423	—	11	2	no	—
220	#423	—	22	1	no	—
221	#423	—	22	1	no	—
222	#423	C₂×D₁₁	1	1	yes	characteristic
223	#423	C₂×D₁₁	1	1	yes	characteristic
224	C₂×C₄⋊C₈	—	11	2	no	—
225	C₂×C₄⋊C₈	—	22	1	no	—
226	#407	—	22	1	no	—
227	C₄×M₁₆	—	11	2	no	—
228	C₄×M₁₆	—	11	2	no	—
229	C₄×M₁₆	—	11	1	no	—
230	C₄×M₁₆	—	11	1	no	—
231	C₄×M₁₆	—	11	1	no	—
232	C₄×M₁₆	—	11	1	no	—
233	C₄×M₁₆	—	22	1	no	—
234	C₂×#97	—	11	2	no	—
235	C₂×C₄×C₈	—	11	1	no	—
236	C₂×C₄×C₈	C₂×D₁₁	1	1	yes	characteristic
237	#335	—	11	4	no	—
238	#335	C₂×D₁₁	1	4	yes	complemented
239	#334	—	11	4	no	—
240	#334	—	11	4	no	—
241	C₂²×C₁₁	—	2	1	no	—
242	C₂²×C₁₁	—	2	1	no	—
243	C₂²×C₁₁	#428	1	2	yes	—
244	C₂²×C₁₁	C₂²×C₄⋊C₄	1	1	yes	characteristic
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	C₂×D₁₁	#423	1	2	yes	—
252	C₄×C₁₁	—	2	1	no	—
253	C₄×C₁₁	—	2	1	no	—
254	C₄×C₁₁	#428	1	2	yes	—
255	C₄×C₁₁	#430	1	2	yes	—
256	C₄×C₁₁	C₂²×M₁₆	1	2	yes	—
257	C₄×C₁₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
258	C₄×C₁₁	C₂×#137	1	1	yes	characteristic
259	Dic₁₁	—	2	1	no	—
260	Dic₁₁	—	2	1	no	—
261	Dic₁₁	—	2	1	no	—
262	Dic₁₁	—	2	1	no	—
263	Dic₁₁	—	2	1	no	—
264	Dic₁₁	#423	1	2	yes	—
265	C₂³×C₄	—	11	1	no	—
266	C₂³×C₄	—	11	1	no	—
267	C₂³×C₄	—	11	1	no	—
268	C₂×M₁₆	—	2	1	no	—
269	C₂×M₁₆	—	2	1	no	—
270	C₂×M₁₆	—	11	2	no	—
271	C₂×M₁₆	—	11	2	no	—
272	C₂×M₁₆	—	11	2	no	—
273	C₂×M₁₆	—	11	2	no	—
274	C₂×M₁₆	—	22	8	no	—
275	C₂×M₁₆	—	22	2	no	—
276	C₂×M₁₆	—	22	1	no	—
277	C₂×M₁₆	—	22	1	no	—
278	C₂×M₁₆	—	44	4	no	—
279	C₂²×C₈	—	11	2	no	—
280	C₂²×C₈	—	22	2	no	—
281	C₂²×C₈	C₄×D₁₁	1	2	yes	—
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	—	11	1	no	—
289	C₂×C₄²	—	11	1	no	—
290	C₂×C₄²	—	11	1	no	—
291	C₂×C₄²	—	11	1	no	—
292	C₂×C₄²	—	11	1	no	—
293	C₂×C₄²	C₂²×D₁₁	1	1	yes	characteristic
294	C₄⋊C₈	—	2	1	no	—
295	C₄⋊C₈	—	2	1	no	—
296	C₄⋊C₈	—	11	2	no	—
297	C₄⋊C₈	—	11	2	no	—
298	C₄⋊C₈	—	22	2	no	—
299	C₄⋊C₈	—	22	2	no	—
300	C₄⋊C₈	—	22	1	no	—
301	C₄⋊C₈	—	22	1	no	—
302	C₄⋊C₈	C₂²×D₁₁	1	2	yes	—
303	C₄⋊C₈	C₂²×D₁₁	1	2	yes	—
304	C₂²⋊C₈	—	22	2	no	—
305	C₂²⋊C₈	—	22	2	no	—
306	#97	—	11	2	no	—
307	#97	—	11	2	no	—
308	#97	—	11	2	no	—
309	#97	—	11	2	no	—
310	#97	—	22	2	no	—
311	C₄×C₈	—	11	1	no	—
312	C₄×C₈	—	11	1	no	—
313	C₄×C₈	—	11	2	no	—
314	C₄×C₈	—	22	2	no	—
315	C₄×C₈	C₄×D₁₁	1	1	yes	characteristic
316	C₄×C₈	C₄×D₁₁	1	1	yes	characteristic
317	C₄×C₈	C₂²×D₁₁	1	2	yes	—
318	C₂×C₁₁	—	2	2	no	—
319	C₂×C₁₁	C₂×#423	1	1	yes	characteristic
320	C₂×C₁₁	C₂×#428	1	1	yes	characteristic
321	C₂×C₁₁	C₂×#430	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	2	no	—
342	C₂²×C₄	—	22	2	no	—
343	C₂²×C₄	—	44	2	no	—
344	C₂²×C₄	C₂×C₄×D₁₁	1	1	yes	characteristic
345	C₂²×C₄	D₄×D₁₁	1	1	yes	characteristic
346	C₂²×C₄	Q₈×D₁₁	1	1	yes	characteristic
347	M₁₆	—	4	2	no	—
348	M₁₆	—	4	2	no	—
349	M₁₆	—	11	8	no	—
350	M₁₆	—	22	4	no	—
351	M₁₆	—	22	4	no	—
352	M₁₆	—	22	4	no	—
353	M₁₆	—	44	4	no	—
354	M₁₆	—	44	2	no	—
355	M₁₆	—	44	2	no	—
356	C₂×C₈	—	2	4	no	—
357	C₂×C₈	—	2	2	no	—
358	C₂×C₈	—	2	2	no	—
359	C₂×C₈	—	11	2	no	—
360	C₂×C₈	—	11	2	no	—
361	C₂×C₈	—	22	4	no	—
362	C₂×C₈	—	22	2	no	—
363	C₂×C₈	—	22	2	no	—
364	C₂×C₈	—	44	4	no	—
365	C₂×C₈	C₂×C₄×D₁₁	1	2	yes	—
366	C₂×C₈	C₂×C₄×D₁₁	1	2	yes	—
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	—	11	1	no	—
374	C₄²	—	11	1	no	—
375	C₄²	—	11	1	no	—
376	C₄²	—	11	1	no	—
377	C₄²	—	11	1	no	—
378	C₄²	—	11	1	no	—
379	C₄²	C₂×C₄×D₁₁	1	1	yes	characteristic
380	C₄²	D₄×D₁₁	1	1	yes	characteristic
381	C₄²	Q₈×D₁₁	1	1	yes	characteristic
382	C₄²	C₂³×D₁₁	1	1	yes	characteristic
383	C₁₁	#17796	1	1	yes	characteristic, complemented, Sylow
384	C₂³	—	11	1	no	—
385	C₂³	—	11	1	no	—
386	C₂³	—	22	2	no	—
387	C₂³	—	22	2	no	—
388	C₂³	—	44	1	no	—
389	C₂³	C₄⋊C₄×D₁₁	1	1	yes	characteristic
390	C₂×C₄	—	2	2	no	—
391	C₂×C₄	—	2	2	no	—
392	C₂×C₄	—	11	1	no	—
393	C₂×C₄	—	11	4	no	—
394	C₂×C₄	—	11	1	no	—
395	C₂×C₄	—	11	1	no	—
396	C₂×C₄	—	11	1	no	—
397	C₂×C₄	—	11	1	no	—
398	C₂×C₄	—	11	1	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	—	22	2	no	—
405	C₂×C₄	—	22	2	no	—
406	C₂×C₄	—	22	2	no	—
407	C₂×C₄	—	22	2	no	—
408	C₂×C₄	—	22	1	no	—
409	C₂×C₄	—	22	1	no	—
410	C₂×C₄	—	22	1	no	—
411	C₂×C₄	—	22	1	no	—
412	C₂×C₄	—	44	1	no	—
413	C₂×C₄	—	44	1	no	—
414	C₂×C₄	—	44	1	no	—
415	C₂×C₄	C₄⋊C₄×D₁₁	1	1	yes	characteristic
416	C₂×C₄	C₄⋊C₄×D₁₁	1	1	yes	characteristic
417	C₂×C₄	C₄⋊C₄×D₁₁	1	1	yes	characteristic
418	C₂×C₄	#66964	1	2	yes	—
419	C₂×C₄	#66971	1	2	yes	—
420	C₂×C₄	C₂²×C₄×D₁₁	1	1	yes	characteristic
421	C₂×C₄	C₂×D₄×D₁₁	1	1	yes	characteristic
422	C₂×C₄	C₂×Q₈×D₁₁	1	1	yes	characteristic
423	C₈	—	2	2	no	—
424	C₈	—	4	2	no	—
425	C₈	—	4	2	no	—
426	C₈	—	11	4	no	—
427	C₈	—	22	2	no	—
428	C₈	—	44	2	no	—
429	C₈	—	44	2	no	—
430	C₈	M₁₆×D₁₁	1	4	yes	complemented
431	C₂²	—	2	1	no	—
432	C₂²	—	2	1	no	—
433	C₂²	—	11	2	no	—
434	C₂²	—	22	1	no	—
435	C₂²	—	22	1	no	—
436	C₂²	—	22	1	no	—
437	C₂²	—	22	1	no	—
438	C₂²	—	22	1	no	—
439	C₂²	—	44	4	no	—
440	C₂²	#10622494	1	2	yes	—
441	C₂²	C₂×C₄⋊C₄×D₁₁	1	1	yes	characteristic
442	C₄	—	2	1	no	—
443	C₄	—	2	1	no	—
444	C₄	—	11	2	no	—
445	C₄	—	22	1	no	—
446	C₄	—	22	1	no	—
447	C₄	—	22	1	no	—
448	C₄	—	22	1	no	—
449	C₄	—	22	1	no	—
450	C₄	#10622494	1	2	yes	—
451	C₄	#10622506	1	2	yes	—
452	C₄	C₂×M₁₆×D₁₁	1	2	yes	—
453	C₄	C₂×#66964	1	1	yes	characteristic
454	C₄	C₂×#66971	1	1	yes	characteristic
455	C₂	—	2	2	no	—
456	C₂	—	22	2	no	—
457	C₂	—	44	1	no	—
458	C₂	D₁₁×#423	1	1	yes	characteristic
459	C₂	C₂×#10622494	1	1	yes	characteristic
460	C₂	C₂×#10622506	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₁₁
commutator	C₂×C₄×C₁₁	C₂³×C₄
Frattini	C₄²	C₂³×D₁₁
Fitting	C₁₁×#1567	C₂
socle	C₂²×C₁₁	C₂²×C₄⋊C₄
prime radical	C₂³×D₁₁	C₄⋊C₄
cosocle	C₄²×C₁₁	C₂⁴
hypercenter	#1567	D₁₁
hypocenter	C₁₁	#17796
LCS	G ▷ C₂×C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1567

Complements

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

N	H ≅ G/N	type
4. #13067382	C₂	semidirect
5. #13067374	C₂	semidirect
6. #13067372	C₂	semidirect
7. #13067371	C₂	semidirect
8. #13067367	C₂	semidirect
9. C₁₁×#1567	C₂	semidirect
37. C₁₁×#335	C₂²	semidirect
38. #10622118	C₂²	semidirect
39. #10622117	C₂²	semidirect
40. #10622095	C₂²	semidirect
152. #4313	M₁₆	semidirect
159. #1567	D₁₁	semidirect
205. C₈×C₁₁	C₂×M₁₆	semidirect
209. C₁₁⋊C₈	C₂×M₁₆	semidirect
238. #335	C₂×D₁₁	semidirect
383. C₁₁	#17796	semidirect
430. C₈	M₁₆×D₁₁	semidirect

Maximal subgroups

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

subgroup	index
#13077248	2
D₁₁×#423	2
C₂×C₄×#4313	2
#13067382	2
#13067374	2
#13067372	2
#13067371	2
#13067367	2
C₁₁×#1567	2
#17796	11