Subgroups — #14725543

Order 2816.

654 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13079175	C₂	1	1	yes	maximal, characteristic
2	#13077563	C₂	1	1	yes	maximal, characteristic, complemented
3	#13077362	C₂	1	1	yes	maximal, characteristic
4	#13067508	C₂	1	2	yes	maximal, complemented
5	#13067461	C₂	1	2	yes	maximal, complemented
6	#13067454	C₂	1	2	yes	maximal, complemented
7	C₈×#4314	C₂	1	2	yes	maximal, complemented
8	C₂×#10622095	C₂	1	1	yes	maximal, characteristic, complemented
9	#13067020	C₂	1	1	yes	maximal, characteristic, complemented
10	#13067016	C₂	1	1	yes	maximal, characteristic
11	C₈×C₁₁×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#66960	—	2	1	no	—
13	#10623008	C₂²	1	1	yes	characteristic
14	#10623001	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	#10622742	—	2	1	no	—
19	#10622735	—	2	1	no	—
20	#10622732	—	2	1	no	—
21	#10622727	C₄	1	2	yes	—
22	#10622727	C₄	1	2	yes	—
23	C₂×C₄⋊(C₁₁⋊C₈)	C₂²	1	1	yes	characteristic
24	C₂×C₄⋊(C₁₁⋊C₈)	C₂²	1	1	yes	characteristic
25	#10622319	—	2	2	no	—
26	#10622314	—	2	2	no	—
27	#10622307	C₄	1	1	yes	characteristic
28	#10622306	C₄	1	1	yes	characteristic
29	C₄×#4314	C₂²	1	2	yes	—
30	C₄×#4314	C₂²	1	2	yes	—
31	#10622301	C₂²	1	2	yes	—
32	C₈×D₄₄	C₂²	1	2	yes	—
33	#10622294	C₄	1	1	yes	characteristic
34	#10622293	C₄	1	1	yes	characteristic
35	#10622292	C₂²	1	2	yes	—
36	C₈×Dic₂₂	C₂²	1	2	yes	—
37	C₁₁×#322	C₂²	1	2	yes	—
38	C₈²×C₁₁	C₂²	1	2	yes	—
39	#10622097	C₂²	1	2	yes	—
40	#10622097	C₂²	1	2	yes	—
41	#10622095	C₂²	1	1	yes	characteristic
42	#10622095	C₂²	1	1	yes	characteristic
43	#10622095	C₂²	1	1	yes	characteristic
44	#10622095	C₂²	1	1	yes	characteristic
45	#10622094	C₂²	1	2	yes	—
46	#10622094	C₂²	1	2	yes	—
47	C₂×#4339	—	2	1	no	—
48	C₂×C₁₁×M₁₆	D₄	1	1	yes	characteristic
49	C₂×C₁₁×M₁₆	D₄	1	1	yes	characteristic
50	C₂²×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
51	C₂²×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
52	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
53	#66983	—	2	1	no	—
54	#66983	C₂×C₄	1	2	yes	—
55	#66979	—	2	1	no	—
56	#66977	—	2	1	no	—
57	#66977	C₂×C₄	1	2	yes	—
58	C₂²×C₁₁⋊C₈	—	2	1	no	—
59	C₂²×C₁₁⋊C₈	—	2	1	no	—
60	#66960	—	4	4	no	—
61	C₂×#4314	C₂×C₄	1	2	yes	—
62	C₂×#4314	C₂×C₄	1	2	yes	—
63	C₂×#4313	—	2	2	no	—
64	C₂×C₈×D₁₁	—	2	2	no	—
65	#66928	—	2	1	no	—
66	#66927	C₂×C₄	1	1	yes	characteristic
67	C₄×D₄₄	—	2	1	no	—
68	C₄×D₄₄	C₂³	1	2	yes	—
69	#66923	—	2	1	no	—
70	#66922	C₂×C₄	1	1	yes	characteristic
71	#66922	C₂×C₄	1	1	yes	characteristic
72	#66922	C₂×C₄	1	1	yes	characteristic
73	C₄×Dic₂₂	—	2	1	no	—
74	C₄×Dic₂₂	C₂³	1	2	yes	—
75	C₁₁×C₄⋊C₈	—	2	1	no	—
76	C₁₁×C₂²⋊C₈	—	2	1	no	—
77	C₁₁×#97	D₄	1	2	yes	—
78	C₄×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
79	C₄×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
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	C₄×C₈×C₁₁	C₂³	1	2	yes	—
84	#66885	C₂×C₄	1	2	yes	—
85	#66885	C₂×C₄	1	2	yes	—
86	(C₂×D₁₁)⋊C₈	—	2	2	no	—
87	(C₂×D₁₁)⋊C₈	—	2	2	no	—
88	#66881	C₂×C₄	1	2	yes	—
89	#66881	C₂×C₄	1	2	yes	—
90	#66880	C₂×C₄	1	2	yes	—
91	#66880	C₂×C₄	1	2	yes	—
92	#66879	—	2	2	no	—
93	Dic₁₁⋊C₈	—	2	2	no	—
94	Dic₁₁⋊C₈	—	2	2	no	—
95	C₈×Dic₁₁	—	2	2	no	—
96	C₄⋊(C₁₁⋊C₈)	—	2	1	no	—
97	C₄⋊(C₁₁⋊C₈)	—	2	1	no	—
98	C₄⋊(C₁₁⋊C₈)	C₂³	1	1	yes	characteristic
99	C₄⋊(C₁₁⋊C₈)	C₂³	1	1	yes	characteristic
100	C₄⋊(C₁₁⋊C₈)	C₂³	1	1	yes	characteristic
101	C₄⋊(C₁₁⋊C₈)	C₂³	1	1	yes	characteristic
102	#18067	—	11	1	no	maximal, Sylow
103	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
104	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
105	C₂²×C₄×C₁₁	#41	1	1	yes	characteristic
106	C₂×C₂²⋊D₁₁	—	2	2	no	—
107	#4339	—	4	2	no	—
108	#4339	—	4	2	no	—
109	C₂×D₄₄	—	2	1	no	—
110	C₂×D₄₄	—	2	1	no	—
111	C₂×D₄₄	C₂²×C₄	1	2	yes	—
112	C₂×C₄×D₁₁	—	2	2	no	—
113	C₂×Dic₂₂	—	2	1	no	—
114	C₂×Dic₂₂	—	2	1	no	—
115	C₂×Dic₂₂	C₂²×C₄	1	2	yes	—
116	C₁₁×M₁₆	—	2	2	no	—
117	C₁₁×M₁₆	SD₁₆	1	4	yes	complemented
118	C₂×C₈×C₁₁	—	2	2	no	—
119	C₂×C₈×C₁₁	—	2	2	no	—
120	C₂×C₈×C₁₁	—	4	1	no	—
121	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
122	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
123	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
124	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
125	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
126	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
127	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
128	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
129	C₄²×C₁₁	#41	1	1	yes	characteristic
130	C₄²×C₁₁	C₂⁴	1	1	yes	characteristic
131	C₂²⋊Dic₁₁	—	2	2	no	—
132	(C₂×D₁₁)⋊C₄	—	2	2	no	—
133	(C₂×D₁₁)⋊C₄	—	2	2	no	—
134	C₄⋊Dic₁₁	—	2	1	no	—
135	C₄⋊Dic₁₁	—	2	1	no	—
136	C₄⋊Dic₁₁	—	2	1	no	—
137	C₄⋊Dic₁₁	—	2	1	no	—
138	C₄⋊Dic₁₁	C₂²×C₄	1	2	yes	—
139	C₄⋊Dic₁₁	C₂²×C₄	1	2	yes	—
140	Dic₁₁⋊C₄	—	2	2	no	—
141	Dic₁₁⋊C₄	—	2	2	no	—
142	C₄×Dic₁₁	—	2	2	no	—
143	C₂×C₁₁⋊C₈	—	2	1	no	—
144	C₂×C₁₁⋊C₈	—	2	1	no	—
145	C₂×C₁₁⋊C₈	—	2	1	no	—
146	C₂×C₁₁⋊C₈	—	2	1	no	—
147	C₂×C₁₁⋊C₈	—	4	2	no	—
148	C₂×C₁₁⋊C₈	—	4	2	no	—
149	#4314	—	2	4	no	—
150	#4314	—	4	2	no	—
151	#4313	—	4	4	no	—
152	C₈×D₁₁	—	4	4	no	—
153	#3167	—	11	1	no	—
154	#2962	—	11	1	no	—
155	#2935	—	11	1	no	—
156	#1590	—	11	2	no	—
157	#1583	—	11	2	no	—
158	#1582	—	11	2	no	—
159	C₈×SD₁₆	—	11	2	no	—
160	C₂×#334	—	11	1	no	—
161	#1481	—	11	1	no	—
162	#1480	—	11	1	no	—
163	C₈×M₁₆	D₁₁	1	1	yes	characteristic, complemented
164	C₂³×C₁₁	C₄×D₄	1	1	yes	characteristic
165	C₂²×D₁₁	—	2	2	no	—
166	C₂×C₄×C₁₁	—	2	1	no	—
167	C₂×C₄×C₁₁	—	2	1	no	—
168	C₂×C₄×C₁₁	—	4	1	no	—
169	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
170	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
171	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
172	C₂×C₄×C₁₁	C₂×SD₁₆	1	2	yes	—
173	C₂×C₄×C₁₁	#135	1	2	yes	—
174	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
175	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
176	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
177	C₂²⋊D₁₁	—	4	4	no	—
178	C₂×Dic₁₁	—	2	2	no	—
179	C₂×Dic₁₁	—	2	2	no	—
180	C₂×Dic₁₁	—	2	2	no	—
181	D₄₄	—	2	2	no	—
182	D₄₄	—	2	2	no	—
183	D₄₄	—	4	2	no	—
184	D₄₄	—	8	1	no	—
185	C₄×D₁₁	—	4	2	no	—
186	C₄×D₁₁	—	4	2	no	—
187	Dic₂₂	—	2	2	no	—
188	Dic₂₂	—	2	2	no	—
189	Dic₂₂	—	4	2	no	—
190	Dic₂₂	—	8	1	no	—
191	C₈×C₁₁	—	2	1	no	—
192	C₈×C₁₁	—	2	1	no	—
193	C₈×C₁₁	—	2	1	no	—
194	C₈×C₁₁	—	2	2	no	—
195	C₈×C₁₁	—	4	2	no	—
196	C₈×C₁₁	#131	1	2	yes	complemented
197	C₈×C₁₁	C₂×SD₁₆	1	4	yes	—
198	C₁₁⋊C₈	—	4	1	no	—
199	C₁₁⋊C₈	—	4	1	no	—
200	C₁₁⋊C₈	—	4	1	no	—
201	C₁₁⋊C₈	—	4	1	no	—
202	C₂×#131	—	22	1	no	—
203	#533	—	11	1	no	—
204	#532	—	11	1	no	—
205	#498	—	11	1	no	—
206	#492	—	11	1	no	—
207	#487	—	11	1	no	—
208	#486	—	11	1	no	—
209	#465	—	11	2	no	—
210	#465	—	11	2	no	—
211	#446	—	11	2	no	—
212	#446	—	22	2	no	—
213	C₈×Q₈	—	11	2	no	—
214	C₄×SD₁₆	—	11	2	no	—
215	C₄×SD₁₆	—	11	2	no	—
216	#436	—	11	2	no	—
217	#435	—	22	2	no	—
218	C₈×D₄	—	11	2	no	—
219	#431	C₂×D₁₁	1	1	yes	characteristic
220	#424	—	22	1	no	—
221	C₂×C₄⋊C₈	—	11	1	no	—
222	C₂×C₄⋊C₈	—	11	1	no	—
223	#408	—	22	1	no	—
224	#405	—	22	1	no	—
225	C₄×M₁₆	C₂×D₁₁	1	1	yes	characteristic
226	C₂×C₄×C₈	C₂×D₁₁	1	1	yes	characteristic
227	#334	—	11	1	no	—
228	#334	—	11	1	no	—
229	#334	—	11	1	no	—
230	#334	—	11	1	no	—
231	Q₈⋊C₈	—	11	2	no	—
232	Q₈⋊C₈	—	11	2	no	—
233	D₄⋊C₈	—	11	2	no	—
234	D₄⋊C₈	—	11	2	no	—
235	#322	C₂×D₁₁	1	2	yes	—
236	C₈²	C₂×D₁₁	1	2	yes	—
237	C₂²×C₁₁	—	2	1	no	—
238	C₂²×C₁₁	—	2	1	no	—
239	C₂²×C₁₁	C₄×SD₁₆	1	2	yes	—
240	C₂²×C₁₁	C₂×C₄×D₄	1	1	yes	characteristic
241	C₂×D₁₁	—	4	2	no	—
242	C₂×D₁₁	—	4	2	no	—
243	C₂×D₁₁	—	4	2	no	—
244	C₄×C₁₁	—	2	1	no	—
245	C₄×C₁₁	—	2	1	no	—
246	C₄×C₁₁	—	2	1	no	—
247	C₄×C₁₁	C₄×SD₁₆	1	2	yes	—
248	C₄×C₁₁	C₂×#131	1	1	yes	characteristic
249	C₄×C₁₁	#568	1	1	yes	characteristic
250	C₄×C₁₁	C₂²×SD₁₆	1	1	yes	characteristic
251	C₄×C₁₁	C₂×#135	1	1	yes	characteristic
252	Dic₁₁	—	4	2	no	—
253	Dic₁₁	—	4	2	no	—
254	Dic₁₁	—	4	2	no	—
255	C₂×#41	—	22	1	no	—
256	C₂×SD₁₆	—	11	2	no	—
257	C₂×SD₁₆	—	11	2	no	—
258	#131	—	44	4	no	—
259	C₂×M₁₆	—	22	2	no	—
260	C₂×M₁₆	D₄₄	1	1	yes	characteristic
261	C₂×M₁₆	D₄₄	1	1	yes	characteristic
262	C₂²×C₈	—	22	1	no	—
263	C₂²×C₈	—	22	1	no	—
264	C₂²×C₈	—	22	2	no	—
265	C₂²×C₈	C₄×D₁₁	1	1	yes	characteristic
266	C₂²×C₈	C₄×D₁₁	1	1	yes	characteristic
267	C₄⋊Q₈	—	11	1	no	—
268	C₄⋊Q₈	—	11	1	no	—
269	C₄⋊Q₈	—	11	1	no	—
270	#127	—	11	1	no	—
271	#125	—	22	1	no	—
272	#124	—	22	1	no	—
273	C₂²⋊Q₈	—	11	2	no	—
274	C₂²⋊Q₈	—	22	1	no	—
275	#121	—	11	2	no	—
276	#121	—	22	1	no	—
277	C₄×Q₈	—	11	2	no	—
278	C₄×Q₈	—	22	1	no	—
279	C₄×D₄	—	11	2	no	—
280	C₄×D₄	—	22	1	no	—
281	#117	—	22	1	no	—
282	C₂×C₄²	C₂²×D₁₁	1	1	yes	characteristic
283	#106	—	11	2	no	—
284	#106	—	11	2	no	—
285	C₄⋊C₈	—	2	1	no	—
286	C₄⋊C₈	—	11	1	no	—
287	C₄⋊C₈	—	11	1	no	—
288	C₄⋊C₈	—	11	1	no	—
289	C₄⋊C₈	—	11	1	no	—
290	C₄⋊C₈	—	22	2	no	—
291	C₄⋊C₈	—	22	2	no	—
292	C₄⋊C₈	—	22	1	no	—
293	C₄⋊C₈	—	22	1	no	—
294	#103	—	11	2	no	—
295	#103	—	11	2	no	—
296	#102	—	11	2	no	—
297	#102	—	11	2	no	—
298	C₂²⋊C₈	—	2	1	no	—
299	C₂²⋊C₈	—	22	2	no	—
300	C₂²⋊C₈	—	22	2	no	—
301	#97	—	22	2	no	—
302	#97	D₄₄	1	2	yes	—
303	C₄×C₈	—	22	2	no	—
304	C₄×C₈	C₄×D₁₁	1	1	yes	characteristic
305	C₄×C₈	C₄×D₁₁	1	1	yes	characteristic
306	C₄×C₈	C₂²×D₁₁	1	2	yes	—
307	C₄×C₈	C₂²×D₁₁	1	1	yes	characteristic
308	C₄×C₈	C₂²×D₁₁	1	1	yes	characteristic
309	C₄×C₈	C₂²×D₁₁	1	2	yes	—
310	C₂×C₁₁	—	2	2	no	—
311	C₂×C₁₁	#2935	1	1	yes	characteristic
312	C₂×C₁₁	C₂×C₄×SD₁₆	1	1	yes	characteristic
313	C₂×C₁₁	#2957	1	1	yes	characteristic
314	D₁₁	—	8	2	no	—
315	#41	—	44	2	no	—
316	#41	—	44	2	no	—
317	C₂×Q₈	—	11	2	no	—
318	C₂×Q₈	—	22	1	no	—
319	C₂×Q₈	—	22	1	no	—
320	C₂×D₄	—	11	2	no	—
321	C₂×D₄	—	22	2	no	—
322	C₂×D₄	—	22	1	no	—
323	C₂×D₄	—	22	1	no	—
324	C₂²×C₄	—	22	2	no	—
325	C₂²×C₄	C₂×C₄×D₁₁	1	1	yes	characteristic
326	C₂²×C₄	C₂×D₄₄	1	1	yes	characteristic
327	C₂²×C₄	#4339	1	1	yes	characteristic
328	SD₁₆	—	22	4	no	—
329	SD₁₆	—	44	2	no	—
330	M₁₆	—	2	2	no	—
331	M₁₆	—	44	4	no	—
332	M₁₆	#4314	1	4	yes	complemented
333	C₂×C₈	—	2	2	no	—
334	C₂×C₈	—	2	2	no	—
335	C₂×C₈	—	4	1	no	—
336	C₂×C₈	—	22	1	no	—
337	C₂×C₈	—	22	1	no	—
338	C₂×C₈	—	22	1	no	—
339	C₂×C₈	—	22	1	no	—
340	C₂×C₈	—	44	2	no	—
341	C₂×C₈	—	44	2	no	—
342	C₂×C₈	—	44	4	no	—
343	C₂×C₈	C₂×C₄×D₁₁	1	1	yes	characteristic
344	C₂×C₈	C₂×C₄×D₁₁	1	1	yes	characteristic
345	C₂×C₈	C₂×C₄×D₁₁	1	1	yes	characteristic
346	C₂×C₈	C₂×C₄×D₁₁	1	1	yes	characteristic
347	C₂×C₈	C₂×D₄₄	1	2	yes	—
348	C₂×C₈	C₂×D₄₄	1	2	yes	—
349	C₄⋊C₄	—	11	2	no	—
350	C₄⋊C₄	—	11	2	no	—
351	C₄⋊C₄	—	22	1	no	—
352	C₄⋊C₄	—	22	1	no	—
353	C₄⋊C₄	—	22	1	no	—
354	C₄⋊C₄	—	22	2	no	—
355	C₄⋊C₄	—	22	1	no	—
356	C₄⋊C₄	—	22	2	no	—
357	C₂²⋊C₄	—	22	2	no	—
358	C₂²⋊C₄	—	22	2	no	—
359	C₂²⋊C₄	—	22	2	no	—
360	C₄²	—	22	2	no	—
361	C₄²	C₂×C₄×D₁₁	1	1	yes	characteristic
362	C₄²	C₂×D₄₄	1	1	yes	characteristic
363	C₄²	#4339	1	1	yes	characteristic
364	C₄²	C₂³×D₁₁	1	1	yes	characteristic
365	C₁₁	#18067	1	1	yes	characteristic, complemented, Sylow
366	C₂³	—	22	2	no	—
367	C₂³	C₄×D₄₄	1	1	yes	characteristic
368	Q₈	—	22	2	no	—
369	Q₈	—	22	2	no	—
370	Q₈	—	44	2	no	—
371	Q₈	—	88	1	no	—
372	D₄	—	22	2	no	—
373	D₄	—	22	2	no	—
374	D₄	—	44	4	no	—
375	D₄	—	44	2	no	—
376	D₄	—	88	1	no	—
377	C₂×C₄	—	2	1	no	—
378	C₂×C₄	—	2	1	no	—
379	C₂×C₄	—	4	1	no	—
380	C₂×C₄	—	22	2	no	—
381	C₂×C₄	—	22	2	no	—
382	C₂×C₄	—	22	2	no	—
383	C₂×C₄	—	44	2	no	—
384	C₂×C₄	—	44	2	no	—
385	C₂×C₄	C₄×D₄₄	1	1	yes	characteristic
386	C₂×C₄	C₄×D₄₄	1	1	yes	characteristic
387	C₂×C₄	C₄×D₄₄	1	1	yes	characteristic
388	C₂×C₄	C₂×#4314	1	2	yes	—
389	C₂×C₄	#66957	1	2	yes	—
390	C₂×C₄	C₂²×C₄×D₁₁	1	1	yes	characteristic
391	C₂×C₄	C₂²×D₄₄	1	1	yes	characteristic
392	C₂×C₄	C₂×#4339	1	1	yes	characteristic
393	C₈	—	2	2	no	—
394	C₈	—	2	1	no	—
395	C₈	—	2	1	no	—
396	C₈	—	2	1	no	—
397	C₈	—	4	2	no	—
398	C₈	—	44	1	no	—
399	C₈	—	44	1	no	—
400	C₈	—	44	1	no	—
401	C₈	—	44	1	no	—
402	C₈	C₂×#4314	1	4	yes	—
403	C₈	#66960	1	2	yes	complemented
404	C₂²	—	2	1	no	—
405	C₂²	—	2	1	no	—
406	C₂²	—	44	2	no	—
407	C₂²	—	44	2	no	—
408	C₂²	—	44	2	no	—
409	C₂²	C₄×#4314	1	2	yes	—
410	C₂²	C₂×C₄×D₄₄	1	1	yes	characteristic
411	C₄	—	2	1	no	—
412	C₄	—	2	1	no	—
413	C₄	—	2	1	no	—
414	C₄	—	44	2	no	—
415	C₄	—	44	2	no	—
416	C₄	—	44	2	no	—
417	C₄	C₄×#4314	1	2	yes	—
418	C₄	C₂²×#4314	1	1	yes	characteristic
419	C₄	C₂×#66957	1	1	yes	characteristic
420	C₄	C₂×#66960	1	1	yes	characteristic
421	C₄	#10623276	1	1	yes	characteristic
422	C₂	—	2	2	no	—
423	C₂	—	88	2	no	—
424	C₂	#13077362	1	1	yes	characteristic
425	C₂	C₂×C₄×#4314	1	1	yes	characteristic
426	C₂	#13077534	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×D₄₄
commutator	C₂×C₄×C₁₁	C₂³×C₄
Frattini	C₄²	C₂³×D₁₁
Fitting	C₈×C₁₁×M₁₆	C₂
socle	C₂²×C₁₁	C₂×C₄×D₄
prime radical	#10623008	C₂²
cosocle	C₄²×C₁₁	C₂⁴
hypercenter	C₈×M₁₆	D₁₁
hypocenter	C₁₁	#18067
LCS	G ▷ C₂×C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂×C₄ ◁ C₄×M₁₆ ◁ C₈×M₁₆

Complements

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

N	H ≅ G/N	type
2. #13077563	C₂	semidirect
4. #13067508	C₂	semidirect
5. #13067461	C₂	semidirect
6. #13067454	C₂	semidirect
7. C₈×#4314	C₂	semidirect
8. C₂×#10622095	C₂	semidirect
9. #13067020	C₂	semidirect
11. C₈×C₁₁×M₁₆	C₂	semidirect
117. C₁₁×M₁₆	SD₁₆	semidirect
163. C₈×M₁₆	D₁₁	semidirect
196. C₈×C₁₁	#131	semidirect
332. M₁₆	#4314	semidirect
365. C₁₁	#18067	semidirect
403. C₈	#66960	semidirect

Maximal subgroups

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

subgroup	index
#13079175	2
#13077563	2
#13077362	2
#13067508	2
#13067461	2
#13067454	2
C₈×#4314	2
C₂×#10622095	2
#13067020	2
#13067016	2
C₈×C₁₁×M₁₆	2
#18067	11