Subgroups — #15834685

Order 3328.

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	#13125396	C₂	1	1	yes	maximal, characteristic
2	#13123582	C₂	1	1	yes	maximal, characteristic
3	#13113726	C₂	1	2	yes	maximal, complemented
4	#13113679	C₂	1	2	yes	maximal, complemented
5	#13113670	C₂	1	2	yes	maximal, complemented
6	C₈×#6106	C₂	1	2	yes	maximal, complemented
7	C₂×#11718072	C₂	1	1	yes	maximal, characteristic, complemented
8	#13113239	C₂	1	1	yes	maximal, characteristic, complemented
9	#13113234	C₂	1	1	yes	maximal, characteristic
10	M₁₆×#1055	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#2962	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#533	C₂²	1	1	yes	characteristic
13	C₂×#88161	—	2	1	no	—
14	#11719182	C₂²	1	1	yes	characteristic
15	C₁₃×#446	—	2	2	no	—
16	C₁₃×#446	C₂²	1	2	yes	—
17	C₈×Q₈×C₁₃	C₂²	1	2	yes	—
18	C₁₃×#424	—	2	1	no	—
19	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
20	C₁₃×#405	—	2	1	no	—
21	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
22	#11718790	—	2	1	no	—
23	#11718749	C₄	1	1	yes	characteristic
24	#11718746	C₄	1	1	yes	characteristic
25	#11718742	C₄	1	1	yes	characteristic
26	#11718740	C₄	1	1	yes	characteristic
27	#11718709	C₄	1	2	yes	—
28	#11718709	C₄	1	2	yes	—
29	C₄×#6106	C₂²	1	2	yes	—
30	C₄×#6106	C₂²	1	2	yes	—
31	#11718586	C₂²	1	1	yes	characteristic
32	C₂×C₄⋊#1055	C₂²	1	1	yes	characteristic
33	C₂×C₄×#1055	C₂²	1	1	yes	characteristic
34	#11718367	—	2	2	no	—
35	#11718349	C₂²	1	2	yes	—
36	C₈×D₅₂	C₂²	1	2	yes	—
37	Q₈⋊#1055	C₂²	1	2	yes	—
38	Q₈⋊#1055	C₂²	1	2	yes	—
39	#11718075	C₂²	1	2	yes	—
40	#11718075	C₂²	1	2	yes	—
41	#11718072	C₂²	1	1	yes	characteristic
42	#11718072	C₂²	1	1	yes	characteristic
43	#11718072	C₂²	1	1	yes	characteristic
44	#11718072	C₂²	1	1	yes	characteristic
45	#11718047	C₂²	1	2	yes	—
46	C₈×#1055	C₂²	1	2	yes	—
47	C₂×#6127	—	2	1	no	—
48	C₂×C₁₃×M₁₆	D₄	1	1	yes	characteristic
49	C₂×C₁₃×M₁₆	D₄	1	1	yes	characteristic
50	C₂²×C₈×C₁₃	—	2	1	no	—
51	C₁₃×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
52	C₁₃×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
53	C₁₃×#125	—	2	1	no	—
54	C₁₃×C₂²⋊Q₈	—	2	1	no	—
55	C₁₃×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
56	C₄×Q₈×C₁₃	—	2	1	no	—
57	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
58	C₁₃×#117	—	2	1	no	—
59	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
60	C₂×#6106	C₂×C₄	1	2	yes	—
61	C₂×#6106	C₂×C₄	1	2	yes	—
62	#88184	—	2	1	no	—
63	#88184	C₂×C₄	1	2	yes	—
64	C₂²×#1055	—	2	1	no	—
65	C₂²×#1055	C₂×C₄	1	1	yes	characteristic
66	C₂²×#1055	C₂×C₄	1	1	yes	characteristic
67	#88161	—	4	4	no	—
68	C₂×#6094	—	2	2	no	—
69	C₂×C₈×D₁₃	—	2	2	no	—
70	#88129	—	2	1	no	—
71	#88128	C₂×C₄	1	1	yes	characteristic
72	C₄×D₅₂	—	2	1	no	—
73	C₄×D₅₂	C₂³	1	2	yes	—
74	#88123	C₂×C₄	1	1	yes	characteristic
75	C₁₃×C₄⋊C₈	—	2	2	no	—
76	C₁₃×C₄⋊C₈	—	2	2	no	—
77	C₁₃×C₄⋊C₈	—	2	1	no	—
78	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
79	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
80	C₁₃×#97	—	2	2	no	—
81	C₁₃×#97	D₄	1	2	yes	—
82	C₄×C₈×C₁₃	—	2	2	no	—
83	C₄×C₈×C₁₃	C₂³	1	2	yes	—
84	#88075	C₂×C₄	1	2	yes	—
85	#88075	C₂×C₄	1	2	yes	—
86	C₂²⋊#1055	—	2	1	no	—
87	#88060	—	2	2	no	—
88	#88060	—	2	2	no	—
89	#88049	C₂×C₄	1	2	yes	—
90	#88049	C₂×C₄	1	2	yes	—
91	#88048	C₂×C₄	1	2	yes	—
92	#88048	C₂×C₄	1	2	yes	—
93	C₄⋊#1055	—	2	1	no	—
94	C₄⋊#1055	—	2	1	no	—
95	C₄⋊#1055	C₂³	1	1	yes	characteristic
96	C₄⋊#1055	C₂³	1	1	yes	characteristic
97	C₄×#1055	C₂×C₄	1	1	yes	characteristic
98	C₄×#1055	C₂×C₄	1	1	yes	characteristic
99	C₄×#1055	C₂³	1	2	yes	—
100	C₄×#1055	C₂³	1	1	yes	characteristic
101	C₄×#1055	C₂³	1	1	yes	characteristic
102	#18067	—	13	1	no	maximal, Sylow
103	C₂×Q₈×C₁₃	—	2	1	no	—
104	C₂×Q₈×C₁₃	C₂²×C₄	1	2	yes	—
105	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
106	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
107	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
108	C₂×C₂²⋊D₁₃	—	2	2	no	—
109	#6127	—	4	2	no	—
110	#6127	—	4	2	no	—
111	C₂×D₅₂	—	2	1	no	—
112	C₂×D₅₂	—	2	1	no	—
113	C₂×D₅₂	C₂²×C₄	1	2	yes	—
114	C₂×C₄×D₁₃	—	2	2	no	—
115	C₂×Dic₂₆	—	2	1	no	—
116	C₁₃×M₁₆	—	2	2	no	—
117	C₁₃×M₁₆	SD₁₆	1	4	yes	complemented
118	C₂×C₈×C₁₃	—	2	1	no	—
119	C₂×C₈×C₁₃	—	2	1	no	—
120	C₂×C₈×C₁₃	—	4	2	no	—
121	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
122	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
123	C₁₃×C₄⋊C₄	—	2	1	no	—
124	C₁₃×C₄⋊C₄	—	2	1	no	—
125	C₁₃×C₄⋊C₄	—	2	1	no	—
126	C₁₃×C₄⋊C₄	—	2	2	no	—
127	C₁₃×C₄⋊C₄	—	2	2	no	—
128	C₁₃×C₄⋊C₄	C₂²×C₄	1	2	yes	—
129	C₁₃×C₂²⋊C₄	—	2	2	no	—
130	C₄²×C₁₃	—	2	2	no	—
131	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
132	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
133	C₄²×C₁₃	#41	1	1	yes	characteristic
134	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
135	#6106	—	2	4	no	—
136	#6106	—	4	2	no	—
137	#6103	—	2	2	no	—
138	#6103	—	2	2	no	—
139	C₄⋊Dic₁₃	—	2	1	no	—
140	C₄⋊Dic₁₃	C₂²×C₄	1	2	yes	—
141	C₂×#1055	—	2	2	no	—
142	C₂×#1055	—	2	1	no	—
143	C₂×#1055	—	2	1	no	—
144	C₂×#1055	—	2	2	no	—
145	C₂×#1055	—	4	1	no	—
146	C₂×#1055	—	4	2	no	—
147	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
148	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
149	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
150	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
151	#6094	—	4	4	no	—
152	C₈×D₁₃	—	4	4	no	—
153	#3167	—	13	1	no	—
154	#2962	D₁₃	1	1	yes	characteristic, complemented
155	#2935	—	13	1	no	—
156	#1590	—	13	2	no	—
157	#1583	—	13	2	no	—
158	#1582	—	13	2	no	—
159	C₈×SD₁₆	—	13	2	no	—
160	C₂×#334	—	13	1	no	—
161	#1481	—	13	1	no	—
162	#1480	—	13	1	no	—
163	C₈×M₁₆	—	13	1	no	—
164	C₂³×C₁₃	C₄×D₄	1	1	yes	characteristic
165	C₂²×D₁₃	—	2	2	no	—
166	Q₈×C₁₃	—	2	2	no	—
167	Q₈×C₁₃	—	2	2	no	—
168	Q₈×C₁₃	—	8	1	no	—
169	C₂×C₄×C₁₃	—	2	1	no	—
170	C₂×C₄×C₁₃	—	2	1	no	—
171	C₂×C₄×C₁₃	—	2	2	no	—
172	C₂×C₄×C₁₃	—	2	2	no	—
173	C₂×C₄×C₁₃	—	4	1	no	—
174	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
175	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
176	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
177	C₂×C₄×C₁₃	C₂×SD₁₆	1	2	yes	—
178	C₂×C₄×C₁₃	#135	1	2	yes	—
179	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
180	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
181	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
182	C₂²⋊D₁₃	—	4	4	no	—
183	C₂×Dic₁₃	—	2	2	no	—
184	D₅₂	—	2	2	no	—
185	D₅₂	—	2	2	no	—
186	D₅₂	—	4	2	no	—
187	D₅₂	—	8	1	no	—
188	C₄×D₁₃	—	4	2	no	—
189	C₄×D₁₃	—	4	2	no	—
190	Dic₂₆	—	4	2	no	—
191	C₈×C₁₃	—	2	2	no	—
192	C₈×C₁₃	—	4	1	no	—
193	C₈×C₁₃	—	4	1	no	—
194	C₈×C₁₃	C₂×SD₁₆	1	4	yes	—
195	#1055	—	2	1	no	—
196	#1055	—	2	1	no	—
197	#1055	—	2	1	no	—
198	#1055	—	4	2	no	—
199	#1055	—	4	1	no	—
200	#1055	—	4	1	no	—
201	#1055	#131	1	2	yes	complemented
202	C₂×#131	—	26	1	no	—
203	#533	C₂×D₁₃	1	1	yes	characteristic
204	#532	—	13	1	no	—
205	#498	—	13	1	no	—
206	#492	—	13	1	no	—
207	#487	—	13	1	no	—
208	#486	—	13	1	no	—
209	#465	—	13	2	no	—
210	#465	—	13	2	no	—
211	#446	—	2	2	no	—
212	#446	C₂×D₁₃	1	2	yes	—
213	C₈×Q₈	C₂×D₁₃	1	2	yes	—
214	C₄×SD₁₆	—	13	2	no	—
215	C₄×SD₁₆	—	13	2	no	—
216	#436	—	13	2	no	—
217	#435	—	26	2	no	—
218	C₈×D₄	—	13	2	no	—
219	#431	—	13	1	no	—
220	#424	—	2	1	no	—
221	C₂×C₄⋊C₈	—	13	1	no	—
222	C₂×C₄⋊C₈	C₂×D₁₃	1	1	yes	characteristic
223	#408	—	26	1	no	—
224	#405	—	2	1	no	—
225	C₄×M₁₆	C₂×D₁₃	1	1	yes	characteristic
226	C₂×C₄×C₈	—	13	1	no	—
227	#334	—	13	1	no	—
228	#334	—	13	1	no	—
229	#334	—	13	1	no	—
230	#334	—	13	1	no	—
231	Q₈⋊C₈	—	13	2	no	—
232	Q₈⋊C₈	—	13	2	no	—
233	D₄⋊C₈	—	13	2	no	—
234	D₄⋊C₈	—	13	2	no	—
235	#322	—	13	2	no	—
236	C₈²	—	13	2	no	—
237	C₂²×C₁₃	—	2	1	no	—
238	C₂²×C₁₃	—	2	1	no	—
239	C₂²×C₁₃	C₄×SD₁₆	1	2	yes	—
240	C₂²×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
241	C₂×D₁₃	—	4	2	no	—
242	C₂×D₁₃	—	4	2	no	—
243	C₂×D₁₃	—	4	2	no	—
244	C₄×C₁₃	—	2	1	no	—
245	C₄×C₁₃	—	2	1	no	—
246	C₄×C₁₃	—	2	1	no	—
247	C₄×C₁₃	—	4	2	no	—
248	C₄×C₁₃	—	4	2	no	—
249	C₄×C₁₃	C₄×SD₁₆	1	2	yes	—
250	C₄×C₁₃	C₂×#131	1	1	yes	characteristic
251	C₄×C₁₃	#568	1	1	yes	characteristic
252	C₄×C₁₃	C₂²×SD₁₆	1	1	yes	characteristic
253	C₄×C₁₃	C₂×#135	1	1	yes	characteristic
254	Dic₁₃	—	4	2	no	—
255	C₂×#41	—	26	1	no	—
256	C₂×SD₁₆	—	13	2	no	—
257	C₂×SD₁₆	—	13	2	no	—
258	#131	—	52	4	no	—
259	C₂×M₁₆	—	26	2	no	—
260	C₂×M₁₆	C₂²⋊D₁₃	1	1	yes	characteristic
261	C₂×M₁₆	C₂²⋊D₁₃	1	1	yes	characteristic
262	C₂²×C₈	—	2	1	no	—
263	C₂²×C₈	—	13	1	no	—
264	C₂²×C₈	—	13	1	no	—
265	C₂²×C₈	—	26	1	no	—
266	C₂²×C₈	—	26	2	no	—
267	C₄⋊Q₈	—	13	1	no	—
268	C₄⋊Q₈	C₄×D₁₃	1	1	yes	characteristic
269	C₄⋊Q₈	C₄×D₁₃	1	1	yes	characteristic
270	#127	—	13	1	no	—
271	#125	—	2	1	no	—
272	#124	—	26	1	no	—
273	C₂²⋊Q₈	—	2	1	no	—
274	C₂²⋊Q₈	C₄×D₁₃	1	2	yes	—
275	#121	—	13	2	no	—
276	#121	—	26	1	no	—
277	C₄×Q₈	—	2	1	no	—
278	C₄×Q₈	C₂²×D₁₃	1	2	yes	—
279	C₄×D₄	—	13	2	no	—
280	C₄×D₄	—	26	1	no	—
281	#117	—	2	1	no	—
282	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
283	#106	—	13	2	no	—
284	#106	—	13	2	no	—
285	C₄⋊C₈	—	2	2	no	—
286	C₄⋊C₈	—	2	2	no	—
287	C₄⋊C₈	—	2	1	no	—
288	C₄⋊C₈	—	13	1	no	—
289	C₄⋊C₈	—	13	1	no	—
290	C₄⋊C₈	—	26	1	no	—
291	C₄⋊C₈	—	26	1	no	—
292	C₄⋊C₈	C₂²×D₁₃	1	1	yes	characteristic
293	C₄⋊C₈	C₂²×D₁₃	1	1	yes	characteristic
294	#103	—	13	2	no	—
295	#103	—	13	2	no	—
296	#102	—	13	2	no	—
297	#102	—	13	2	no	—
298	C₂²⋊C₈	—	26	1	no	—
299	C₂²⋊C₈	—	26	2	no	—
300	C₂²⋊C₈	—	26	2	no	—
301	#97	—	2	2	no	—
302	#97	C₂²⋊D₁₃	1	2	yes	—
303	C₄×C₈	—	2	2	no	—
304	C₄×C₈	—	13	1	no	—
305	C₄×C₈	—	13	1	no	—
306	C₄×C₈	—	13	1	no	—
307	C₄×C₈	—	13	1	no	—
308	C₄×C₈	—	13	2	no	—
309	C₄×C₈	C₂²×D₁₃	1	2	yes	—
310	C₂×C₁₃	—	2	2	no	—
311	C₂×C₁₃	#2935	1	1	yes	characteristic
312	C₂×C₁₃	C₂×C₄×SD₁₆	1	1	yes	characteristic
313	C₂×C₁₃	#2957	1	1	yes	characteristic
314	D₁₃	—	8	2	no	—
315	#41	—	52	2	no	—
316	#41	—	52	2	no	—
317	C₂×Q₈	—	2	1	no	—
318	C₂×Q₈	—	26	1	no	—
319	C₂×Q₈	C₂×C₄×D₁₃	1	2	yes	—
320	C₂×D₄	—	13	2	no	—
321	C₂×D₄	—	26	2	no	—
322	C₂×D₄	—	26	1	no	—
323	C₂×D₄	—	26	1	no	—
324	C₂²×C₄	—	26	2	no	—
325	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
326	C₂²×C₄	#6127	1	1	yes	characteristic
327	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
328	SD₁₆	—	26	4	no	—
329	SD₁₆	—	52	2	no	—
330	M₁₆	—	2	2	no	—
331	M₁₆	—	52	4	no	—
332	M₁₆	#6106	1	4	yes	complemented
333	C₂×C₈	—	2	1	no	—
334	C₂×C₈	—	2	1	no	—
335	C₂×C₈	—	4	2	no	—
336	C₂×C₈	—	13	1	no	—
337	C₂×C₈	—	13	1	no	—
338	C₂×C₈	—	13	1	no	—
339	C₂×C₈	—	13	1	no	—
340	C₂×C₈	—	26	2	no	—
341	C₂×C₈	—	26	2	no	—
342	C₂×C₈	—	26	1	no	—
343	C₂×C₈	—	26	1	no	—
344	C₂×C₈	—	52	1	no	—
345	C₂×C₈	—	52	2	no	—
346	C₂×C₈	—	52	4	no	—
347	C₂×C₈	C₂×C₂²⋊D₁₃	1	2	yes	—
348	C₂×C₈	C₂×C₂²⋊D₁₃	1	2	yes	—
349	C₄⋊C₄	—	2	1	no	—
350	C₄⋊C₄	—	2	1	no	—
351	C₄⋊C₄	—	2	1	no	—
352	C₄⋊C₄	—	2	2	no	—
353	C₄⋊C₄	—	2	2	no	—
354	C₄⋊C₄	—	13	2	no	—
355	C₄⋊C₄	—	26	1	no	—
356	C₄⋊C₄	C₂×C₄×D₁₃	1	2	yes	—
357	C₂²⋊C₄	—	2	2	no	—
358	C₂²⋊C₄	—	26	2	no	—
359	C₂²⋊C₄	—	26	2	no	—
360	C₄²	—	2	2	no	—
361	C₄²	C₂×C₄×D₁₃	1	1	yes	characteristic
362	C₄²	#6127	1	1	yes	characteristic
363	C₄²	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
364	C₄²	C₂³×D₁₃	1	1	yes	characteristic
365	C₁₃	#18067	1	1	yes	characteristic, complemented, Sylow
366	C₂³	—	26	2	no	—
367	C₂³	C₄×C₂²⋊D₁₃	1	1	yes	characteristic
368	Q₈	—	2	2	no	—
369	Q₈	—	2	2	no	—
370	Q₈	—	8	1	no	—
371	Q₈	—	52	2	no	—
372	D₄	—	26	2	no	—
373	D₄	—	26	2	no	—
374	D₄	—	52	4	no	—
375	D₄	—	52	2	no	—
376	D₄	—	104	1	no	—
377	C₂×C₄	—	2	1	no	—
378	C₂×C₄	—	2	1	no	—
379	C₂×C₄	—	2	2	no	—
380	C₂×C₄	—	2	2	no	—
381	C₂×C₄	—	4	1	no	—
382	C₂×C₄	—	26	2	no	—
383	C₂×C₄	—	52	2	no	—
384	C₂×C₄	—	52	2	no	—
385	C₂×C₄	C₄×C₂²⋊D₁₃	1	1	yes	characteristic
386	C₂×C₄	C₄×C₂²⋊D₁₃	1	1	yes	characteristic
387	C₂×C₄	C₄×C₂²⋊D₁₃	1	1	yes	characteristic
388	C₂×C₄	C₂×#6106	1	2	yes	—
389	C₂×C₄	#88204	1	2	yes	—
390	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
391	C₂×C₄	C₂×#6127	1	1	yes	characteristic
392	C₂×C₄	C₂²×C₂²⋊D₁₃	1	1	yes	characteristic
393	C₈	—	2	2	no	—
394	C₈	—	4	1	no	—
395	C₈	—	4	1	no	—
396	C₈	—	13	2	no	—
397	C₈	—	26	1	no	—
398	C₈	—	26	1	no	—
399	C₈	—	26	1	no	—
400	C₈	—	52	2	no	—
401	C₈	—	52	1	no	—
402	C₈	—	52	1	no	—
403	C₈	C₂×#6106	1	4	yes	—
404	C₂²	—	2	1	no	—
405	C₂²	—	2	1	no	—
406	C₂²	—	52	2	no	—
407	C₂²	—	52	2	no	—
408	C₂²	—	52	2	no	—
409	C₂²	C₄×#6106	1	2	yes	—
410	C₂²	C₂×C₄×C₂²⋊D₁₃	1	1	yes	characteristic
411	C₄	—	2	1	no	—
412	C₄	—	2	1	no	—
413	C₄	—	2	1	no	—
414	C₄	—	4	2	no	—
415	C₄	—	4	2	no	—
416	C₄	—	52	2	no	—
417	C₄	C₄×#6106	1	2	yes	—
418	C₄	D₁₃×#131	1	1	yes	characteristic
419	C₄	#11719455	1	1	yes	characteristic
420	C₄	C₂²×#6106	1	1	yes	characteristic
421	C₄	C₂×#88204	1	1	yes	characteristic
422	C₂	—	2	2	no	—
423	C₂	—	104	2	no	—
424	C₂	#13123578	1	1	yes	characteristic
425	C₂	C₂×C₄×#6106	1	1	yes	characteristic
426	C₂	#13123751	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×C₂²⋊D₁₃
commutator	C₂×C₄×C₁₃	C₂³×C₄
Frattini	C₄²	C₂³×D₁₃
Fitting	C₁₃×#2962	C₂
socle	C₂²×C₁₃	C₂×C₄×D₄
prime radical	#11719182	C₂²
cosocle	C₄²×C₁₃	C₂⁴
hypercenter	#2962	D₁₃
hypocenter	C₁₃	#18067
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₄×M₁₆ ◁ #2962

Complements

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

N	H ≅ G/N	type
3. #13113726	C₂	semidirect
4. #13113679	C₂	semidirect
5. #13113670	C₂	semidirect
6. C₈×#6106	C₂	semidirect
7. C₂×#11718072	C₂	semidirect
8. #13113239	C₂	semidirect
10. M₁₆×#1055	C₂	semidirect
11. C₁₃×#2962	C₂	semidirect
117. C₁₃×M₁₆	SD₁₆	semidirect
154. #2962	D₁₃	semidirect
201. #1055	#131	semidirect
332. M₁₆	#6106	semidirect
365. C₁₃	#18067	semidirect

Maximal subgroups

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

subgroup	index
#13125396	2
#13123582	2
#13113726	2
#13113679	2
#13113670	2
C₈×#6106	2
C₂×#11718072	2
#13113239	2
#13113234	2
M₁₆×#1055	2
C₁₃×#2962	2
#18067	13