Subgroups — #14643290

Order 2816.

700 conjugacy classes of subgroups.

The subgroup lattice has 366 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13077249	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×#4318	C₂	1	1	yes	maximal, characteristic
3	#13066454	C₂	1	4	yes	maximal, complemented
4	C₂×C₄×C₁₁×M₁₆	C₂	1	1	yes	maximal, characteristic
5	C₂²×C₁₁×M₁₆	C₄	1	2	yes	—
6	C₂²×C₄²×C₁₁	C₂²	1	1	yes	characteristic
7	C₂²×#4318	—	2	1	no	—
8	C₄×C₁₁×M₁₆	—	2	1	no	—
9	C₄×C₁₁×M₁₆	—	2	1	no	—
10	C₄×C₁₁×M₁₆	C₄	1	2	yes	—
11	C₄×C₁₁×M₁₆	C₂²	1	2	yes	—
12	C₂×C₁₁×#97	—	2	1	no	—
13	C₂×C₄×C₈×C₁₁	—	2	1	no	—
14	#10622820	—	2	1	no	—
15	#10622539	—	2	1	no	—
16	#10622539	C₄	1	2	yes	—
17	#10622538	—	2	1	no	—
18	#10622538	C₂²	1	2	yes	—
19	#10622537	C₄	1	2	yes	—
20	C₄×#4318	—	2	1	no	—
21	C₄×#4318	—	2	1	no	—
22	C₄×#4318	—	2	1	no	—
23	C₄×#4318	C₄	1	2	yes	—
24	C₄×#4318	C₄	1	2	yes	—
25	C₂×#66867	—	2	1	no	—
26	C₂×C₄×C₁₁⋊C₈	C₂²	1	2	yes	—
27	C₂³×C₄×C₁₁	C₂×C₄	1	1	yes	characteristic
28	C₂³×C₄×C₁₁	D₄	1	1	yes	characteristic
29	C₂³×C₄×C₁₁	Q₈	1	1	yes	characteristic
30	C₂×C₁₁×M₁₆	—	2	2	no	—
31	C₂×C₁₁×M₁₆	—	2	8	no	—
32	C₂×C₁₁×M₁₆	C₂×C₄	1	4	yes	—
33	C₂²×C₈×C₁₁	—	2	2	no	—
34	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
35	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
36	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
37	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
38	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
39	C₂×C₄²×C₁₁	D₄	1	1	yes	characteristic
40	C₂×C₄²×C₁₁	D₄	1	1	yes	characteristic
41	C₂×C₄²×C₁₁	D₄	1	1	yes	characteristic
42	C₂×C₄²×C₁₁	D₄	1	1	yes	characteristic
43	C₂×C₄²×C₁₁	D₄	1	1	yes	characteristic
44	C₂×C₄²×C₁₁	Q₈	1	1	yes	characteristic
45	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
46	C₂×#4318	—	2	8	no	—
47	C₂×#4318	—	2	2	no	—
48	C₂×#4318	—	2	2	no	—
49	C₂×#4318	—	2	2	no	—
50	C₂²×C₁₁⋊C₈	—	2	2	no	—
51	C₁₁×#97	—	2	2	no	—
52	C₁₁×#97	—	2	2	no	—
53	C₄×C₈×C₁₁	—	2	2	no	—
54	C₄×C₈×C₁₁	—	2	2	no	—
55	C₂²⋊(C₁₁⋊C₈)	—	2	2	no	—
56	C₂²⋊(C₁₁⋊C₈)	—	2	2	no	—
57	C₄⋊(C₁₁⋊C₈)	—	2	2	no	—
58	C₄⋊(C₁₁⋊C₈)	C₂×C₄	1	4	yes	—
59	#66867	—	2	2	no	—
60	#66867	—	2	2	no	—
61	#66867	—	2	2	no	—
62	C₄×C₁₁⋊C₈	—	2	2	no	—
63	C₄×C₁₁⋊C₈	—	2	2	no	—
64	C₄×C₁₁⋊C₈	C₂×C₄	1	4	yes	—
65	#7887	—	11	1	no	maximal, Sylow
66	C₂⁴×C₁₁	C₄⋊C₄	1	1	yes	characteristic
67	C₂²×C₄×C₁₁	—	2	4	no	—
68	C₂²×C₄×C₁₁	—	2	4	no	—
69	C₂²×C₄×C₁₁	—	4	2	no	—
70	C₂²×C₄×C₁₁	C₄²	1	1	yes	characteristic
71	C₂²×C₄×C₁₁	C₄²	1	1	yes	characteristic
72	C₂²×C₄×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
73	C₂²×C₄×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
74	C₂²×C₄×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
75	C₂²×C₄×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
76	C₂²×C₄×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
77	C₂²×C₄×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
78	C₂²×C₄×C₁₁	C₄⋊C₄	1	1	yes	characteristic
79	C₂²×C₄×C₁₁	C₄⋊C₄	1	1	yes	characteristic
80	C₂²×C₄×C₁₁	C₄⋊C₄	1	1	yes	characteristic
81	C₂²×C₄×C₁₁	C₄⋊C₄	1	1	yes	characteristic
82	C₂²×C₄×C₁₁	C₄⋊C₄	1	1	yes	characteristic
83	C₂²×C₄×C₁₁	C₄⋊C₄	1	1	yes	characteristic
84	C₂²×C₄×C₁₁	C₄⋊C₄	1	1	yes	characteristic
85	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
86	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
87	C₂²×C₄×C₁₁	C₂×Q₈	1	1	yes	characteristic
88	C₁₁×M₁₆	—	2	8	no	—
89	C₁₁×M₁₆	—	2	4	no	—
90	C₁₁×M₁₆	M₁₆	1	8	yes	complemented
91	C₂×C₈×C₁₁	—	2	8	no	—
92	C₂×C₈×C₁₁	—	2	4	no	—
93	C₄²×C₁₁	C₄²	1	1	yes	characteristic
94	C₄²×C₁₁	C₄²	1	1	yes	characteristic
95	C₄²×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
96	C₄²×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
97	C₄²×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
98	C₄²×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
99	C₄²×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
100	C₄²×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
101	C₄²×C₁₁	C₄⋊C₄	1	1	yes	characteristic
102	C₄²×C₁₁	C₄⋊C₄	1	1	yes	characteristic
103	C₄²×C₁₁	C₄⋊C₄	1	1	yes	characteristic
104	C₄²×C₁₁	C₄⋊C₄	1	1	yes	characteristic
105	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
106	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
107	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
108	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
109	#4318	—	2	8	no	—
110	#4318	—	2	8	no	—
111	#4318	—	4	4	no	—
112	C₂×C₁₁⋊C₈	—	2	8	no	—
113	C₂×C₁₁⋊C₈	—	2	4	no	—
114	C₂×C₁₁⋊C₈	—	2	4	no	—
115	#2920	—	11	1	no	—
116	C₂×C₄×M₁₆	—	11	1	no	—
117	C₂×C₄×M₁₆	D₁₁	1	1	yes	characteristic
118	#1278	—	11	4	no	—
119	C₂³×C₁₁	—	2	2	no	—
120	C₂³×C₁₁	—	2	2	no	—
121	C₂³×C₁₁	—	4	1	no	—
122	C₂³×C₁₁	#95	1	1	yes	characteristic
123	C₂³×C₁₁	#95	1	1	yes	characteristic
124	C₂³×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
125	C₂×C₄×C₁₁	—	2	2	no	—
126	C₂×C₄×C₁₁	—	2	2	no	—
127	C₂×C₄×C₁₁	—	2	2	no	—
128	C₂×C₄×C₁₁	—	2	2	no	—
129	C₂×C₄×C₁₁	—	2	2	no	—
130	C₂×C₄×C₁₁	—	2	2	no	—
131	C₂×C₄×C₁₁	—	2	2	no	—
132	C₂×C₄×C₁₁	—	2	2	no	—
133	C₂×C₄×C₁₁	—	2	2	no	—
134	C₂×C₄×C₁₁	—	2	2	no	—
135	C₂×C₄×C₁₁	—	2	2	no	—
136	C₂×C₄×C₁₁	—	2	2	no	—
137	C₂×C₄×C₁₁	—	2	2	no	—
138	C₂×C₄×C₁₁	—	4	1	no	—
139	C₂×C₄×C₁₁	—	4	1	no	—
140	C₂×C₄×C₁₁	—	4	1	no	—
141	C₂×C₄×C₁₁	#95	1	1	yes	characteristic
142	C₂×C₄×C₁₁	#95	1	1	yes	characteristic
143	C₂×C₄×C₁₁	#95	1	1	yes	characteristic
144	C₂×C₄×C₁₁	#95	1	1	yes	characteristic
145	C₂×C₄×C₁₁	#95	1	1	yes	characteristic
146	C₂×C₄×C₁₁	#95	1	1	yes	characteristic
147	C₂×C₄×C₁₁	#104	1	4	yes	—
148	C₂×C₄×C₁₁	C₂×C₄²	1	1	yes	characteristic
149	C₂×C₄×C₁₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
150	C₂×C₄×C₁₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
151	C₂×C₄×C₁₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
152	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
153	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
154	C₂×C₄×C₁₁	C₂×M₁₆	1	4	yes	—
155	C₈×C₁₁	—	2	8	no	—
156	C₁₁⋊C₈	—	2	8	no	—
157	C₁₁⋊C₈	—	4	4	no	—
158	C₂²×M₁₆	—	22	1	no	—
159	C₂²×M₁₆	Dic₁₁	1	2	yes	—
160	C₂²×C₄²	C₂×D₁₁	1	1	yes	characteristic
161	#432	—	11	2	no	—
162	#432	—	22	1	no	—
163	#431	—	11	2	no	—
164	#431	—	22	1	no	—
165	#423	—	11	2	no	—
166	#407	—	22	1	no	—
167	C₄×M₁₆	—	2	1	no	—
168	C₄×M₁₆	—	2	1	no	—
169	C₄×M₁₆	—	11	2	no	—
170	C₄×M₁₆	—	11	2	no	—
171	C₄×M₁₆	—	22	1	no	—
172	C₄×M₁₆	—	22	1	no	—
173	C₄×M₁₆	—	22	1	no	—
174	C₄×M₁₆	Dic₁₁	1	2	yes	—
175	C₄×M₁₆	C₂×D₁₁	1	2	yes	—
176	C₂×#97	—	2	1	no	—
177	C₂×#97	—	22	1	no	—
178	C₂×C₄×C₈	—	2	1	no	—
179	C₂×C₄×C₈	—	11	2	no	—
180	C₂²×C₁₁	—	2	1	no	—
181	C₂²×C₁₁	—	2	1	no	—
182	C₂²×C₁₁	—	2	1	no	—
183	C₂²×C₁₁	—	2	1	no	—
184	C₂²×C₁₁	—	2	1	no	—
185	C₂²×C₁₁	—	2	1	no	—
186	C₂²×C₁₁	—	2	1	no	—
187	C₂²×C₁₁	—	4	4	no	—
188	C₂²×C₁₁	#339	1	2	yes	—
189	C₂²×C₁₁	C₂×#95	1	1	yes	characteristic
190	C₂²×C₁₁	#423	1	2	yes	—
191	C₄×C₁₁	—	2	1	no	—
192	C₄×C₁₁	—	2	1	no	—
193	C₄×C₁₁	—	2	1	no	—
194	C₄×C₁₁	—	2	1	no	—
195	C₄×C₁₁	—	2	1	no	—
196	C₄×C₁₁	—	2	1	no	—
197	C₄×C₁₁	—	2	1	no	—
198	C₄×C₁₁	#339	1	2	yes	—
199	C₄×C₁₁	C₄×M₁₆	1	2	yes	—
200	C₄×C₁₁	#407	1	2	yes	—
201	C₄×C₁₁	C₂×#104	1	2	yes	—
202	C₄×C₁₁	#430	1	2	yes	—
203	C₂³×C₄	Dic₂₂	1	1	yes	characteristic
204	C₂³×C₄	D₄₄	1	1	yes	characteristic
205	C₂³×C₄	C₂×Dic₁₁	1	1	yes	characteristic
206	C₂×M₁₆	—	2	2	no	—
207	C₂×M₁₆	—	2	8	no	—
208	C₂×M₁₆	—	22	8	no	—
209	C₂×M₁₆	—	22	2	no	—
210	C₂×M₁₆	—	22	2	no	—
211	C₂×M₁₆	—	22	2	no	—
212	C₂×M₁₆	C₂×Dic₁₁	1	4	yes	—
213	C₂²×C₈	—	2	2	no	—
214	C₂²×C₈	—	22	2	no	—
215	C₂×C₄²	Dic₂₂	1	1	yes	characteristic
216	C₂×C₄²	C₄×D₁₁	1	1	yes	characteristic
217	C₂×C₄²	C₄×D₁₁	1	1	yes	characteristic
218	C₂×C₄²	C₄×D₁₁	1	1	yes	characteristic
219	C₂×C₄²	C₄×D₁₁	1	1	yes	characteristic
220	C₂×C₄²	D₄₄	1	1	yes	characteristic
221	C₂×C₄²	C₂×Dic₁₁	1	1	yes	characteristic
222	C₂×C₄²	C₂²⋊D₁₁	1	1	yes	characteristic
223	C₂×C₄²	C₂²⋊D₁₁	1	1	yes	characteristic
224	C₂×C₄²	C₂²⋊D₁₁	1	1	yes	characteristic
225	C₂×C₄²	C₂²⋊D₁₁	1	1	yes	characteristic
226	C₂×C₄²	C₂²×D₁₁	1	1	yes	characteristic
227	C₄⋊C₈	—	11	4	no	—
228	C₄⋊C₈	—	22	2	no	—
229	C₂²⋊C₈	—	22	2	no	—
230	C₂²⋊C₈	—	22	2	no	—
231	#97	—	2	2	no	—
232	#97	—	2	2	no	—
233	#97	—	22	2	no	—
234	#97	—	22	2	no	—
235	#97	—	22	2	no	—
236	C₄×C₈	—	2	2	no	—
237	C₄×C₈	—	2	2	no	—
238	C₄×C₈	—	11	4	no	—
239	C₄×C₈	—	22	2	no	—
240	C₄×C₈	—	22	2	no	—
241	C₂×C₁₁	—	2	2	no	—
242	C₂×C₁₁	—	2	2	no	—
243	C₂×C₁₁	—	4	1	no	—
244	C₂×C₁₁	#1728	1	1	yes	characteristic
245	C₂×C₁₁	C₂×#339	1	1	yes	characteristic
246	C₂×C₁₁	#1738	1	1	yes	characteristic
247	C₂⁴	C₄⋊Dic₁₁	1	1	yes	characteristic
248	C₂²×C₄	—	2	4	no	—
249	C₂²×C₄	—	2	4	no	—
250	C₂²×C₄	—	4	2	no	—
251	C₂²×C₄	C₄×Dic₁₁	1	1	yes	characteristic
252	C₂²×C₄	C₄×Dic₁₁	1	1	yes	characteristic
253	C₂²×C₄	Dic₁₁⋊C₄	1	1	yes	characteristic
254	C₂²×C₄	Dic₁₁⋊C₄	1	1	yes	characteristic
255	C₂²×C₄	Dic₁₁⋊C₄	1	1	yes	characteristic
256	C₂²×C₄	Dic₁₁⋊C₄	1	1	yes	characteristic
257	C₂²×C₄	C₄⋊Dic₁₁	1	1	yes	characteristic
258	C₂²×C₄	C₄⋊Dic₁₁	1	1	yes	characteristic
259	C₂²×C₄	C₄⋊Dic₁₁	1	1	yes	characteristic
260	C₂²×C₄	(C₂×D₁₁)⋊C₄	1	1	yes	characteristic
261	C₂²×C₄	(C₂×D₁₁)⋊C₄	1	1	yes	characteristic
262	C₂²×C₄	(C₂×D₁₁)⋊C₄	1	1	yes	characteristic
263	C₂²×C₄	(C₂×D₁₁)⋊C₄	1	1	yes	characteristic
264	C₂²×C₄	C₂²⋊Dic₁₁	1	1	yes	characteristic
265	C₂²×C₄	C₂²⋊Dic₁₁	1	1	yes	characteristic
266	C₂²×C₄	C₂×Dic₂₂	1	1	yes	characteristic
267	C₂²×C₄	C₂×D₄₄	1	1	yes	characteristic
268	C₂²×C₄	C₂²×Dic₁₁	1	1	yes	characteristic
269	M₁₆	—	2	8	no	—
270	M₁₆	—	2	4	no	—
271	M₁₆	—	22	8	no	—
272	M₁₆	—	22	8	no	—
273	M₁₆	—	44	4	no	—
274	M₁₆	#4318	1	8	yes	complemented
275	C₂×C₈	—	2	8	no	—
276	C₂×C₈	—	2	4	no	—
277	C₂×C₈	—	22	8	no	—
278	C₂×C₈	—	22	4	no	—
279	C₂×C₈	—	22	4	no	—
280	C₄²	C₄×Dic₁₁	1	1	yes	characteristic
281	C₄²	C₄×Dic₁₁	1	1	yes	characteristic
282	C₄²	Dic₁₁⋊C₄	1	1	yes	characteristic
283	C₄²	Dic₁₁⋊C₄	1	1	yes	characteristic
284	C₄²	Dic₁₁⋊C₄	1	1	yes	characteristic
285	C₄²	Dic₁₁⋊C₄	1	1	yes	characteristic
286	C₄²	(C₂×D₁₁)⋊C₄	1	1	yes	characteristic
287	C₄²	(C₂×D₁₁)⋊C₄	1	1	yes	characteristic
288	C₄²	(C₂×D₁₁)⋊C₄	1	1	yes	characteristic
289	C₄²	(C₂×D₁₁)⋊C₄	1	1	yes	characteristic
290	C₄²	C₂²⋊Dic₁₁	1	1	yes	characteristic
291	C₄²	C₂²⋊Dic₁₁	1	1	yes	characteristic
292	C₄²	C₂×C₄×D₁₁	1	1	yes	characteristic
293	C₄²	C₂×C₄×D₁₁	1	1	yes	characteristic
294	C₄²	C₂×C₂²⋊D₁₁	1	1	yes	characteristic
295	C₄²	C₂×C₂²⋊D₁₁	1	1	yes	characteristic
296	C₁₁	#7887	1	1	yes	characteristic, complemented, Sylow
297	C₂³	—	2	2	no	—
298	C₂³	—	2	2	no	—
299	C₂³	—	4	1	no	—
300	C₂³	C₁₁⋊#95	1	1	yes	characteristic
301	C₂³	C₁₁⋊#95	1	1	yes	characteristic
302	C₂³	C₂×C₄⋊Dic₁₁	1	1	yes	characteristic
303	C₂×C₄	—	2	2	no	—
304	C₂×C₄	—	2	2	no	—
305	C₂×C₄	—	2	2	no	—
306	C₂×C₄	—	2	2	no	—
307	C₂×C₄	—	2	2	no	—
308	C₂×C₄	—	2	2	no	—
309	C₂×C₄	—	2	2	no	—
310	C₂×C₄	—	2	2	no	—
311	C₂×C₄	—	2	2	no	—
312	C₂×C₄	—	2	2	no	—
313	C₂×C₄	—	2	2	no	—
314	C₂×C₄	—	2	2	no	—
315	C₂×C₄	—	2	2	no	—
316	C₂×C₄	—	4	1	no	—
317	C₂×C₄	—	4	1	no	—
318	C₂×C₄	—	4	1	no	—
319	C₂×C₄	#66889	1	4	yes	—
320	C₂×C₄	C₁₁⋊#95	1	1	yes	characteristic
321	C₂×C₄	C₁₁⋊#95	1	1	yes	characteristic
322	C₂×C₄	C₁₁⋊#95	1	1	yes	characteristic
323	C₂×C₄	C₁₁⋊#95	1	1	yes	characteristic
324	C₂×C₄	C₁₁⋊#95	1	1	yes	characteristic
325	C₂×C₄	C₁₁⋊#95	1	1	yes	characteristic
326	C₂×C₄	C₂×#4318	1	4	yes	—
327	C₂×C₄	C₂×C₄×Dic₁₁	1	1	yes	characteristic
328	C₂×C₄	C₂×Dic₁₁⋊C₄	1	1	yes	characteristic
329	C₂×C₄	C₂×Dic₁₁⋊C₄	1	1	yes	characteristic
330	C₂×C₄	C₂×(C₂×D₁₁)⋊C₄	1	1	yes	characteristic
331	C₂×C₄	C₂×(C₂×D₁₁)⋊C₄	1	1	yes	characteristic
332	C₂×C₄	C₂×C₂²⋊Dic₁₁	1	1	yes	characteristic
333	C₈	—	2	8	no	—
334	C₈	—	22	8	no	—
335	C₈	—	44	4	no	—
336	C₂²	—	2	1	no	—
337	C₂²	—	2	1	no	—
338	C₂²	—	2	1	no	—
339	C₂²	—	2	1	no	—
340	C₂²	—	2	1	no	—
341	C₂²	—	2	1	no	—
342	C₂²	—	2	1	no	—
343	C₂²	—	4	4	no	—
344	C₂²	#10622193	1	2	yes	—
345	C₂²	#10622537	1	2	yes	—
346	C₂²	C₂×C₁₁⋊#95	1	1	yes	characteristic
347	C₄	—	2	1	no	—
348	C₄	—	2	1	no	—
349	C₄	—	2	1	no	—
350	C₄	—	2	1	no	—
351	C₄	—	2	1	no	—
352	C₄	—	2	1	no	—
353	C₄	—	2	1	no	—
354	C₄	#10622193	1	2	yes	—
355	C₄	C₄×#4318	1	2	yes	—
356	C₄	#10622737	1	2	yes	—
357	C₄	C₂×#66889	1	2	yes	—
358	C₄	#10622820	1	2	yes	—
359	C₂	—	2	2	no	—
360	C₂	—	2	2	no	—
361	C₂	—	4	1	no	—
362	C₂	#13068310	1	1	yes	characteristic
363	C₂	C₂×#10622193	1	1	yes	characteristic
364	C₂	#13068342	1	1	yes	characteristic

	subgroup	G/H
center	C₄²	C₂×C₂²⋊D₁₁
commutator	C₂×C₄×C₁₁	C₂×C₄²
Frattini	C₂×C₄²	C₂²×D₁₁
Fitting	C₂×C₄×C₁₁×M₁₆	C₂
socle	C₂²×C₁₁	C₂×#95
prime radical	C₂⁴×C₁₁	C₄⋊C₄
cosocle	C₂×C₄²×C₁₁	C₂³
hypercenter	C₂×C₄×M₁₆	D₁₁
hypocenter	C₁₁	#7887
LCS	G ▷ C₂×C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₄² ◁ C₂²×C₄² ◁ C₂×C₄×M₁₆

Complements

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

N	H ≅ G/N	type
3. #13066454	C₂	semidirect
90. C₁₁×M₁₆	M₁₆	semidirect
274. M₁₆	#4318	semidirect
296. C₁₁	#7887	semidirect

Maximal subgroups

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

subgroup	index
#13077249	2
C₂×C₄×#4318	2
#13066454	2
C₂×C₄×C₁₁×M₁₆	2
#7887	11