Subgroups — M₁₆×#4313 #14719481

Order 2816.

900 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	#13077244	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×#4313	C₂	1	1	yes	maximal, characteristic
3	C₄×M₁₆×D₁₁	C₂	1	1	yes	maximal, characteristic
4	#13066920	C₂	1	2	yes	maximal, complemented
5	#13066918	C₂	1	2	yes	maximal, complemented
6	#13066906	C₂	1	1	yes	maximal, characteristic, complemented
7	#13066905	C₂	1	1	yes	maximal, characteristic, complemented
8	#13066902	C₂	1	2	yes	maximal, complemented
9	M₁₆×C₁₁⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈×#4313	C₂	1	2	yes	maximal, complemented
11	C₈×C₁₁×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×M₁₆×D₁₁	C₄	1	2	yes	—
13	C₂²×#4313	C₄	1	2	yes	—
14	C₂×C₄²×D₁₁	C₂²	1	1	yes	characteristic
15	C₁₁×#431	C₂²	1	1	yes	characteristic
16	C₄×C₁₁×M₁₆	C₂²	1	1	yes	characteristic
17	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
18	M₁₆×Dic₁₁	C₄	1	2	yes	—
19	C₂×#66879	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	C₄	1	2	yes	—
30	C₄×#4313	C₄	1	2	yes	—
31	C₄×#4313	C₂²	1	2	yes	—
32	C₄×#4313	C₂²	1	1	yes	characteristic
33	C₄×#4313	C₂²	1	1	yes	characteristic
34	C₄×#4313	C₂²	1	1	yes	characteristic
35	C₄×#4313	C₂²	1	1	yes	characteristic
36	C₄×#4313	C₂²	1	2	yes	—
37	#10622298	C₂²	1	2	yes	—
38	C₄×C₈×D₁₁	C₂²	1	2	yes	—
39	C₁₁×#322	C₂²	1	2	yes	complemented
40	C₈²×C₁₁	C₂²	1	2	yes	complemented
41	#10622093	C₂²	1	2	yes	complemented
42	#10622093	C₂²	1	2	yes	complemented
43	#10622093	C₂²	1	2	yes	complemented
44	#10622092	C₂²	1	2	yes	complemented
45	#10622092	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	—	2	8	no	—
60	C₂×#4313	C₂×C₄	1	2	yes	—
61	C₂×#4313	C₂×C₄	1	2	yes	—
62	C₂×#4313	C₂×C₄	1	2	yes	—
63	C₂×#4313	C₂×C₄	1	4	yes	—
64	C₂×#4313	C₂×C₄	1	4	yes	—
65	C₂×#4313	C₂×C₄	1	2	yes	—
66	C₂×C₈×D₁₁	C₂×C₄	1	4	yes	—
67	C₄²×D₁₁	C₂×C₄	1	1	yes	characteristic
68	C₄²×D₁₁	C₂×C₄	1	1	yes	characteristic
69	C₄²×D₁₁	C₂×C₄	1	1	yes	characteristic
70	C₄²×D₁₁	C₂×C₄	1	1	yes	characteristic
71	C₄²×D₁₁	C₂×C₄	1	1	yes	characteristic
72	C₄²×D₁₁	C₂×C₄	1	1	yes	characteristic
73	C₄²×D₁₁	C₂³	1	1	yes	characteristic
74	C₄²×D₁₁	C₂³	1	1	yes	characteristic
75	C₁₁×C₄⋊C₈	C₂×C₄	1	2	yes	—
76	C₁₁×C₂²⋊C₈	C₂×C₄	1	2	yes	—
77	C₁₁×#97	C₂×C₄	1	2	yes	—
78	C₄×C₈×C₁₁	C₂×C₄	1	2	yes	—
79	C₄×C₈×C₁₁	C₂³	1	2	yes	—
80	C₄×C₈×C₁₁	C₂³	1	2	yes	—
81	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
82	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
83	C₂²⋊(C₁₁⋊C₈)	C₂×C₄	1	2	yes	—
84	(C₂×D₁₁)⋊C₈	C₂×C₄	1	4	yes	—
85	#66879	C₂×C₄	1	4	yes	—
86	#66879	C₂×C₄	1	2	yes	—
87	#66879	C₂×C₄	1	2	yes	—
88	#66879	C₂×C₄	1	2	yes	—
89	#66879	C₂×C₄	1	2	yes	—
90	#66879	C₂×C₄	1	4	yes	—
91	Dic₁₁⋊C₈	C₂×C₄	1	4	yes	—
92	C₈×Dic₁₁	C₂×C₄	1	4	yes	—
93	C₄⋊(C₁₁⋊C₈)	C₂×C₄	1	2	yes	—
94	#66867	C₂×C₄	1	2	yes	—
95	C₄×C₁₁⋊C₈	C₂×C₄	1	2	yes	—
96	C₄×C₁₁⋊C₈	C₂³	1	1	yes	characteristic
97	C₄×C₁₁⋊C₈	C₂³	1	1	yes	characteristic
98	C₄×C₁₁⋊C₈	C₂³	1	2	yes	—
99	C₄×C₁₁⋊C₈	C₂³	1	2	yes	—
100	M₁₆²	—	11	1	no	maximal, Sylow
101	C₂³×D₁₁	C₄²	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×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
105	C₂²×Dic₁₁	C₄²	1	1	yes	characteristic
106	C₂²×Dic₁₁	C₄²	1	1	yes	characteristic
107	C₂²×Dic₁₁	C₄²	1	1	yes	characteristic
108	C₂×C₄×D₁₁	—	2	4	no	—
109	C₂×C₄×D₁₁	—	2	4	no	—
110	C₂×C₄×D₁₁	—	4	2	no	—
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	C₄²	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	C₂×C₄×D₁₁	C₂²×C₄	1	1	yes	characteristic
123	C₁₁×M₁₆	M₁₆	1	8	yes	complemented
124	C₂×C₈×C₁₁	—	2	4	no	—
125	C₂×C₈×C₁₁	C₂²×C₄	1	4	yes	—
126	C₂×C₈×C₁₁	C₂²×C₄	1	2	yes	—
127	C₂×C₈×C₁₁	C₂²×C₄	1	4	yes	—
128	C₂×C₈×C₁₁	C₂²×C₄	1	2	yes	—
129	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
130	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
131	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
132	C₄²×C₁₁	C₂⁴	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	C₄²	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	C₄×Dic₁₁	C₂²×C₄	1	1	yes	characteristic
145	#4318	—	2	4	no	—
146	C₂×C₁₁⋊C₈	—	2	4	no	—
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	C₂×C₁₁⋊C₈	C₂²×C₄	1	2	yes	—
151	#4313	—	2	4	no	—
152	#4313	—	2	4	no	—
153	#4313	—	2	8	no	—
154	#4313	—	2	4	no	—
155	#4313	—	4	4	no	—
156	#4313	M₁₆	1	8	yes	direct product factor
157	C₈×D₁₁	—	2	8	no	—
158	#2920	—	11	1	no	—
159	C₂×C₄×M₁₆	—	11	1	no	—
160	C₂×C₄×M₁₆	—	11	1	no	—
161	#1455	—	11	2	no	—
162	#1455	—	11	2	no	—
163	#1451	—	11	1	no	—
164	#1451	—	11	1	no	—
165	#1451	—	11	2	no	—
166	C₈×M₁₆	—	11	1	no	—
167	C₈×M₁₆	—	11	2	no	—
168	C₈×M₁₆	D₁₁	1	1	yes	characteristic, complemented
169	C₂³×C₁₁	C₂×C₄²	1	1	yes	characteristic
170	C₂²×D₁₁	—	2	2	no	—
171	C₂²×D₁₁	—	2	2	no	—
172	C₂²×D₁₁	—	4	1	no	—
173	C₂²×D₁₁	C₂×C₄²	1	1	yes	characteristic
174	C₂²×D₁₁	C₂×C₄²	1	1	yes	characteristic
175	C₂×C₄×C₁₁	—	2	2	no	—
176	C₂×C₄×C₁₁	—	2	2	no	—
177	C₂×C₄×C₁₁	C₂×C₄²	1	1	yes	characteristic
178	C₂×C₄×C₁₁	C₂×C₄²	1	1	yes	characteristic
179	C₂×C₄×C₁₁	C₂×C₄²	1	1	yes	characteristic
180	C₂×C₄×C₁₁	C₂×M₁₆	1	4	yes	—
181	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
182	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
183	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
184	C₂×Dic₁₁	—	2	2	no	—
185	C₂×Dic₁₁	—	2	2	no	—
186	C₂×Dic₁₁	—	4	1	no	—
187	C₂×Dic₁₁	C₂×C₄²	1	1	yes	characteristic
188	C₂×Dic₁₁	C₂×C₄²	1	1	yes	characteristic
189	C₂×Dic₁₁	C₂×C₄²	1	1	yes	characteristic
190	C₂×Dic₁₁	C₂×C₄²	1	1	yes	characteristic
191	C₂×Dic₁₁	C₂×C₄²	1	1	yes	characteristic
192	C₂×Dic₁₁	C₂×C₄²	1	1	yes	characteristic
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	—	2	2	no	—
198	C₄×D₁₁	—	2	2	no	—
199	C₄×D₁₁	—	2	2	no	—
200	C₄×D₁₁	—	2	2	no	—
201	C₄×D₁₁	—	2	2	no	—
202	C₄×D₁₁	—	4	1	no	—
203	C₄×D₁₁	—	4	1	no	—
204	C₄×D₁₁	C₂×M₁₆	1	4	yes	—
205	C₈×C₁₁	—	2	2	no	—
206	C₈×C₁₁	—	2	4	no	—
207	C₈×C₁₁	C₂×M₁₆	1	8	yes	complemented
208	C₈×C₁₁	C₂×M₁₆	1	4	yes	complemented
209	C₁₁⋊C₈	—	2	4	no	—
210	C₁₁⋊C₈	—	2	2	no	—
211	C₁₁⋊C₈	—	2	4	no	—
212	C₁₁⋊C₈	C₂×M₁₆	1	4	yes	complemented
213	C₂²×M₁₆	—	11	2	no	—
214	C₂²×M₁₆	—	11	2	no	—
215	C₂²×C₄²	—	11	1	no	—
216	#432	—	11	2	no	—
217	#432	—	11	2	no	—
218	#431	—	11	1	no	—
219	#431	—	11	2	no	—
220	#431	C₂×D₁₁	1	1	yes	characteristic
221	#423	—	11	2	no	—
222	#407	—	11	2	no	—
223	C₄×M₁₆	—	11	2	no	—
224	C₄×M₁₆	—	11	1	no	—
225	C₄×M₁₆	—	11	2	no	—
226	C₄×M₁₆	—	11	1	no	—
227	C₄×M₁₆	—	11	1	no	—
228	C₄×M₁₆	—	11	1	no	—
229	C₄×M₁₆	—	11	2	no	—
230	C₄×M₁₆	—	11	1	no	—
231	C₄×M₁₆	—	11	2	no	—
232	C₄×M₁₆	—	11	2	no	—
233	C₄×M₁₆	—	11	2	no	—
234	C₄×M₁₆	C₂×D₁₁	1	1	yes	characteristic
235	C₂×#97	—	11	2	no	—
236	C₂×#97	—	11	2	no	—
237	C₂×C₄×C₈	—	11	1	no	—
238	C₂×C₄×C₈	—	11	2	no	—
239	C₂×C₄×C₈	C₂×D₁₁	1	1	yes	characteristic
240	#322	—	11	2	no	—
241	#322	—	11	2	no	—
242	#322	—	11	2	no	—
243	#322	—	11	2	no	—
244	#322	—	11	2	no	—
245	#322	C₂×D₁₁	1	2	yes	complemented
246	C₈²	—	11	2	no	—
247	C₈²	C₂×D₁₁	1	2	yes	complemented
248	C₂²×C₁₁	—	2	1	no	—
249	C₂²×C₁₁	—	2	1	no	—
250	C₂²×C₁₁	C₄×M₁₆	1	2	yes	—
251	C₂²×C₁₁	C₂²×C₄²	1	1	yes	characteristic
252	C₂×D₁₁	—	2	1	no	—
253	C₂×D₁₁	—	2	1	no	—
254	C₂×D₁₁	—	2	1	no	—
255	C₂×D₁₁	—	2	1	no	—
256	C₂×D₁₁	—	2	1	no	—
257	C₂×D₁₁	—	4	4	no	—
258	C₂×D₁₁	C₄×M₁₆	1	2	yes	—
259	C₄×C₁₁	—	2	1	no	—
260	C₄×C₁₁	—	2	1	no	—
261	C₄×C₁₁	C₄×M₁₆	1	2	yes	—
262	C₄×C₁₁	C₂²×M₁₆	1	2	yes	—
263	C₄×C₁₁	C₂²×M₁₆	1	2	yes	—
264	C₄×C₁₁	#568	1	2	yes	—
265	Dic₁₁	—	2	1	no	—
266	Dic₁₁	—	2	1	no	—
267	Dic₁₁	—	2	1	no	—
268	Dic₁₁	—	2	1	no	—
269	Dic₁₁	—	2	1	no	—
270	Dic₁₁	C₄×M₁₆	1	2	yes	—
271	C₂³×C₄	—	11	1	no	—
272	C₂³×C₄	—	11	1	no	—
273	C₂³×C₄	—	11	1	no	—
274	C₂×M₁₆	—	11	2	no	—
275	C₂×M₁₆	—	11	2	no	—
276	C₂×M₁₆	—	11	2	no	—
277	C₂×M₁₆	—	11	2	no	—
278	C₂×M₁₆	—	11	4	no	—
279	C₂×M₁₆	—	11	2	no	—
280	C₂×M₁₆	—	11	4	no	—
281	C₂×M₁₆	—	22	8	no	—
282	C₂×M₁₆	—	22	8	no	—
283	C₂×M₁₆	C₄×D₁₁	1	2	yes	—
284	C₂²×C₈	—	11	2	no	—
285	C₂²×C₈	—	11	4	no	—
286	C₂²×C₈	C₄×D₁₁	1	2	yes	—
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	—	11	1	no	—
294	C₂×C₄²	—	11	1	no	—
295	C₂×C₄²	—	11	1	no	—
296	C₂×C₄²	—	11	1	no	—
297	C₂×C₄²	—	11	1	no	—
298	C₂×C₄²	C₂²×D₁₁	1	1	yes	characteristic
299	C₄⋊C₈	—	11	4	no	—
300	C₄⋊C₈	—	11	2	no	—
301	C₄⋊C₈	C₄×D₁₁	1	2	yes	—
302	C₂²⋊C₈	—	11	2	no	—
303	C₂²⋊C₈	—	11	4	no	—
304	C₂²⋊C₈	C₄×D₁₁	1	2	yes	—
305	#97	—	11	2	no	—
306	#97	—	11	2	no	—
307	#97	—	11	2	no	—
308	#97	—	11	4	no	—
309	#97	—	11	2	no	—
310	#97	—	11	4	no	—
311	#97	—	11	2	no	—
312	#97	C₄×D₁₁	1	2	yes	—
313	C₄×C₈	—	11	4	no	—
314	C₄×C₈	—	11	2	no	—
315	C₄×C₈	—	11	1	no	—
316	C₄×C₈	—	11	2	no	—
317	C₄×C₈	—	11	1	no	—
318	C₄×C₈	—	11	2	no	—
319	C₄×C₈	C₄×D₁₁	1	2	yes	—
320	C₄×C₈	C₂²×D₁₁	1	2	yes	—
321	C₄×C₈	C₂²×D₁₁	1	1	yes	characteristic
322	C₄×C₈	C₂²×D₁₁	1	2	yes	—
323	C₄×C₈	C₂²×D₁₁	1	1	yes	characteristic
324	C₂×C₁₁	—	2	2	no	—
325	C₂×C₁₁	C₂×C₄×M₁₆	1	1	yes	characteristic
326	C₂×C₁₁	C₂×C₄×M₁₆	1	1	yes	characteristic
327	C₂×C₁₁	#2873	1	1	yes	characteristic
328	D₁₁	—	2	2	no	—
329	D₁₁	—	4	1	no	—
330	C₂⁴	—	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	—	11	1	no	—
341	C₂²×C₄	—	11	1	no	—
342	C₂²×C₄	—	11	1	no	—
343	C₂²×C₄	—	11	1	no	—
344	C₂²×C₄	—	11	1	no	—
345	C₂²×C₄	—	11	1	no	—
346	C₂²×C₄	—	22	4	no	—
347	C₂²×C₄	—	22	4	no	—
348	C₂²×C₄	—	44	2	no	—
349	C₂²×C₄	C₂×C₄×D₁₁	1	1	yes	characteristic
350	C₂²×C₄	C₂×C₄×D₁₁	1	1	yes	characteristic
351	C₂²×C₄	C₂×C₄×D₁₁	1	1	yes	characteristic
352	M₁₆	—	11	8	no	—
353	M₁₆	—	22	4	no	—
354	M₁₆	—	22	4	no	—
355	M₁₆	—	22	4	no	—
356	M₁₆	—	22	8	no	—
357	M₁₆	—	22	4	no	—
358	M₁₆	—	44	4	no	—
359	M₁₆	#4313	1	8	yes	direct product factor
360	C₂×C₈	—	2	4	no	—
361	C₂×C₈	—	11	2	no	—
362	C₂×C₈	—	11	4	no	—
363	C₂×C₈	—	11	2	no	—
364	C₂×C₈	—	11	4	no	—
365	C₂×C₈	—	22	4	no	—
366	C₂×C₈	—	22	8	no	—
367	C₂×C₈	C₂×C₄×D₁₁	1	2	yes	—
368	C₂×C₈	C₂×C₄×D₁₁	1	4	yes	—
369	C₂×C₈	C₂×C₄×D₁₁	1	4	yes	—
370	C₂×C₈	C₂×C₄×D₁₁	1	2	yes	—
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	—	11	1	no	—
380	C₄²	—	11	1	no	—
381	C₄²	—	11	1	no	—
382	C₄²	—	11	1	no	—
383	C₄²	C₂×C₄×D₁₁	1	1	yes	characteristic
384	C₄²	C₂×C₄×D₁₁	1	1	yes	characteristic
385	C₄²	C₂×C₄×D₁₁	1	1	yes	characteristic
386	C₄²	C₂³×D₁₁	1	1	yes	characteristic
387	C₁₁	M₁₆²	1	1	yes	characteristic, complemented, Sylow
388	C₂³	—	11	1	no	—
389	C₂³	—	11	1	no	—
390	C₂³	—	22	2	no	—
391	C₂³	—	22	2	no	—
392	C₂³	—	44	1	no	—
393	C₂³	C₄²×D₁₁	1	1	yes	characteristic
394	C₂×C₄	—	2	2	no	—
395	C₂×C₄	—	2	2	no	—
396	C₂×C₄	—	11	1	no	—
397	C₂×C₄	—	11	4	no	—
398	C₂×C₄	—	11	1	no	—
399	C₂×C₄	—	11	1	no	—
400	C₂×C₄	—	11	1	no	—
401	C₂×C₄	—	11	1	no	—
402	C₂×C₄	—	11	1	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	2	no	—
409	C₂×C₄	—	22	2	no	—
410	C₂×C₄	—	22	2	no	—
411	C₂×C₄	—	22	2	no	—
412	C₂×C₄	—	22	2	no	—
413	C₂×C₄	—	22	2	no	—
414	C₂×C₄	—	44	1	no	—
415	C₂×C₄	—	44	1	no	—
416	C₂×C₄	—	44	1	no	—
417	C₂×C₄	C₄²×D₁₁	1	1	yes	characteristic
418	C₂×C₄	C₄²×D₁₁	1	1	yes	characteristic
419	C₂×C₄	C₄²×D₁₁	1	1	yes	characteristic
420	C₂×C₄	C₂×#4313	1	4	yes	—
421	C₂×C₄	C₂²×C₄×D₁₁	1	1	yes	characteristic
422	C₂×C₄	C₂²×C₄×D₁₁	1	1	yes	characteristic
423	C₂×C₄	C₂²×C₄×D₁₁	1	1	yes	characteristic
424	C₈	—	2	2	no	—
425	C₈	—	2	4	no	—
426	C₈	—	11	4	no	—
427	C₈	—	22	4	no	—
428	C₈	—	22	2	no	—
429	C₈	—	22	4	no	—
430	C₈	C₂×#4313	1	8	yes	complemented
431	C₈	M₁₆×D₁₁	1	4	yes	complemented
432	C₂²	—	2	1	no	—
433	C₂²	—	2	1	no	—
434	C₂²	—	11	2	no	—
435	C₂²	—	22	1	no	—
436	C₂²	—	22	1	no	—
437	C₂²	—	22	1	no	—
438	C₂²	—	22	1	no	—
439	C₂²	—	22	1	no	—
440	C₂²	—	44	4	no	—
441	C₂²	C₄×#4313	1	2	yes	—
442	C₂²	C₂×C₄²×D₁₁	1	1	yes	characteristic
443	C₄	—	2	1	no	—
444	C₄	—	2	1	no	—
445	C₄	—	11	2	no	—
446	C₄	—	22	1	no	—
447	C₄	—	22	1	no	—
448	C₄	—	22	1	no	—
449	C₄	—	22	1	no	—
450	C₄	—	22	1	no	—
451	C₄	C₄×#4313	1	2	yes	—
452	C₄	C₂²×#4313	1	2	yes	—
453	C₄	C₂×M₁₆×D₁₁	1	2	yes	—
454	C₄	#10623281	1	2	yes	—
455	C₂	—	2	2	no	—
456	C₂	—	22	2	no	—
457	C₂	—	44	1	no	—
458	C₂	C₄×M₁₆×D₁₁	1	1	yes	characteristic
459	C₂	C₂×C₄×#4313	1	1	yes	characteristic
460	C₂	#13077032	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₄²	C₂³×D₁₁
commutator, socle	C₂²×C₁₁	C₂²×C₄²
Fitting	C₈×C₁₁×M₁₆	C₂
prime radical	C₂³×D₁₁	C₄²
cosocle	C₄²×C₁₁	C₂⁴
hypercenter	C₈×M₁₆	D₁₁
hypocenter	C₁₁	M₁₆²
LCS	G ▷ C₂²×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₄² ◁ C₈×M₁₆

Complements

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

N	H ≅ G/N	type
4. #13066920	C₂	semidirect
5. #13066918	C₂	semidirect
6. #13066906	C₂	semidirect
7. #13066905	C₂	semidirect
8. #13066902	C₂	semidirect
9. M₁₆×C₁₁⋊C₈	C₂	semidirect
10. C₈×#4313	C₂	semidirect
11. C₈×C₁₁×M₁₆	C₂	semidirect
39. C₁₁×#322	C₂²	semidirect
40. C₈²×C₁₁	C₂²	semidirect
41. #10622093	C₂²	semidirect
42. #10622093	C₂²	semidirect
43. #10622093	C₂²	semidirect
44. #10622092	C₂²	semidirect
45. #10622092	C₂²	semidirect
46. C₈×C₁₁⋊C₈	C₂²	semidirect
123. C₁₁×M₁₆	M₁₆	semidirect
156. #4313	M₁₆	direct (N × H)
168. C₈×M₁₆	D₁₁	semidirect
207. C₈×C₁₁	C₂×M₁₆	semidirect
208. C₈×C₁₁	C₂×M₁₆	semidirect
212. C₁₁⋊C₈	C₂×M₁₆	semidirect
245. #322	C₂×D₁₁	semidirect
247. C₈²	C₂×D₁₁	semidirect
359. M₁₆	#4313	direct (N × H)
387. C₁₁	M₁₆²	semidirect
430. C₈	C₂×#4313	semidirect
431. 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
#13077244	2
C₂×C₄×#4313	2
C₄×M₁₆×D₁₁	2
#13066920	2
#13066918	2
#13066906	2
#13066905	2
#13066902	2
M₁₆×C₁₁⋊C₈	2
C₈×#4313	2
C₈×C₁₁×M₁₆	2
M₁₆²	11

Subgroups — M16×#4313 #14719481

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — M₁₆×#4313 #14719481