Subgroups — #29651778

Order 15616.

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	#21456378	C₂	1	1	yes	maximal, characteristic
2	#21454762	C₂	1	1	yes	maximal, characteristic, complemented
3	#21454562	C₂	1	1	yes	maximal, characteristic
4	#21444708	C₂	1	2	yes	maximal, complemented
5	#21444661	C₂	1	2	yes	maximal, complemented
6	#21444654	C₂	1	2	yes	maximal, complemented
7	#21444618	C₂	1	2	yes	maximal, complemented
8	#21444221	C₂	1	1	yes	maximal, characteristic, complemented
9	#21444217	C₂	1	1	yes	maximal, characteristic
10	C₈×#11758194	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₆₁×#334	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#14519783	—	2	1	no	—
13	#16840319	C₂²	1	1	yes	characteristic
14	#16840312	C₂²	1	1	yes	characteristic
15	#16840160	C₄	1	1	yes	characteristic
16	#16840135	C₄	1	1	yes	characteristic
17	#16840113	C₄	1	1	yes	characteristic
18	#16840109	C₄	1	1	yes	characteristic
19	#16839991	C₄	1	2	yes	—
20	#16839991	C₄	1	2	yes	—
21	#16839891	—	2	2	no	—
22	#16839889	C₂²	1	2	yes	—
23	#16839886	C₂²	1	2	yes	—
24	C₄×#11758190	C₂²	1	2	yes	—
25	C₄×#11758190	C₂²	1	2	yes	—
26	#16839839	C₂²	1	2	yes	—
27	#16839832	—	2	2	no	—
28	#16839827	C₂²	1	2	yes	—
29	#16839815	C₂²	1	1	yes	characteristic
30	#16839788	—	2	1	no	—
31	#16839728	—	2	1	no	—
32	#16839717	—	2	1	no	—
33	C₄×#11758194	C₂²	1	1	yes	characteristic
34	#16839492	C₂²	1	2	yes	—
35	#16839492	C₂²	1	2	yes	—
36	#16839489	C₂²	1	2	yes	—
37	#16839489	C₂²	1	2	yes	—
38	#16839484	C₂²	1	2	yes	—
39	C₈×#92418	C₂²	1	2	yes	—
40	C₂×C₄⋊C₈×C₆₁	C₂²	1	1	yes	characteristic
41	C₂×C₄⋊C₈×C₆₁	C₂²	1	1	yes	characteristic
42	C₂×C₄×C₈×C₆₁	C₂²	1	1	yes	characteristic
43	C₆₁×#334	C₂²	1	1	yes	characteristic
44	C₆₁×#334	C₂²	1	1	yes	characteristic
45	C₆₁×#334	C₂²	1	1	yes	characteristic
46	C₆₁×#334	C₂²	1	1	yes	characteristic
47	C₂×#11758222	—	2	1	no	—
48	C₂×#11758190	C₂×C₄	1	2	yes	—
49	C₂×#11758190	C₂×C₄	1	2	yes	—
50	#14519783	—	4	4	no	—
51	C₂×#11758194	D₄	1	1	yes	characteristic
52	C₂×#11758194	D₄	1	1	yes	characteristic
53	C₂×#11758189	—	2	2	no	—
54	C₂×C₈×D₆₁	—	2	2	no	—
55	#14519777	C₂×C₄	1	1	yes	characteristic
56	#14519777	C₂×C₄	1	1	yes	characteristic
57	#14519777	C₂×C₄	1	1	yes	characteristic
58	#14519774	C₂×C₄	1	1	yes	characteristic
59	#14519769	—	2	1	no	—
60	#14519765	—	2	1	no	—
61	#14519756	—	2	1	no	—
62	#14519756	C₂×C₄	1	2	yes	—
63	#14519751	—	2	1	no	—
64	#14519751	C₂×C₄	1	2	yes	—
65	C₄×Dic₁₂₂	—	2	1	no	—
66	C₄×Dic₁₂₂	C₂³	1	2	yes	—
67	C₄×D₂₄₄	—	2	1	no	—
68	C₄×D₂₄₄	C₂³	1	2	yes	—
69	#14519736	—	2	1	no	—
70	#14519709	C₂×C₄	1	2	yes	—
71	#14519709	C₂×C₄	1	2	yes	—
72	C₄⋊#92418	—	2	1	no	—
73	#14519706	—	2	2	no	—
74	#14519706	—	2	2	no	—
75	#14519702	C₂×C₄	1	2	yes	—
76	#14519702	C₂×C₄	1	2	yes	—
77	#14519699	C₂×C₄	1	2	yes	—
78	#14519699	C₂×C₄	1	2	yes	—
79	C₂²⋊#92418	—	2	1	no	—
80	#14519689	—	2	2	no	—
81	#14519689	—	2	2	no	—
82	#14519688	D₄	1	2	yes	—
83	#14519687	—	2	2	no	—
84	C₄×#92418	C₂³	1	2	yes	—
85	C₄×#92418	C₂³	1	2	yes	—
86	C₈×Dic₆₁	—	2	2	no	—
87	C₂²×C₈×C₆₁	—	2	1	no	—
88	C₂²×C₈×C₆₁	—	2	1	no	—
89	C₂²×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
90	C₂²×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
91	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
92	C₄⋊C₈×C₆₁	—	2	1	no	—
93	C₄⋊C₈×C₆₁	—	2	1	no	—
94	C₄⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
95	C₄⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
96	C₄⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
97	C₄⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
98	C₄×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
99	C₄×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
100	C₄×C₈×C₆₁	C₂³	1	1	yes	characteristic
101	C₄×C₈×C₆₁	C₂³	1	1	yes	characteristic
102	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
103	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
104	C₂²×C₄×C₆₁	#41	1	1	yes	characteristic
105	C₂×C₂²⋊D₆₁	—	2	2	no	—
106	#11758222	—	4	2	no	—
107	#11758222	—	4	2	no	—
108	C₂×D₂₄₄	—	2	1	no	—
109	C₂×D₂₄₄	—	2	1	no	—
110	C₂×D₂₄₄	C₂²×C₄	1	2	yes	—
111	C₂×C₄×D₆₁	—	2	2	no	—
112	C₂×Dic₁₂₂	—	2	1	no	—
113	C₂×Dic₁₂₂	—	2	1	no	—
114	C₂×Dic₁₂₂	C₂²×C₄	1	2	yes	—
115	C₂×C₈×C₆₁	—	2	2	no	—
116	C₂×C₈×C₆₁	—	2	1	no	—
117	C₂×C₈×C₆₁	—	2	1	no	—
118	C₂×C₈×C₆₁	—	2	1	no	—
119	C₂×C₈×C₆₁	—	2	1	no	—
120	C₂×C₈×C₆₁	—	4	1	no	—
121	C₂×C₈×C₆₁	—	4	2	no	—
122	C₂×C₈×C₆₁	—	4	2	no	—
123	C₂×C₈×C₆₁	C₂²×C₄	1	1	yes	characteristic
124	C₂×C₈×C₆₁	C₂²×C₄	1	1	yes	characteristic
125	C₂×C₈×C₆₁	C₂²×C₄	1	1	yes	characteristic
126	C₂×C₈×C₆₁	C₂²×C₄	1	1	yes	characteristic
127	C₄²×C₆₁	C₂²×C₄	1	1	yes	characteristic
128	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
129	C₄²×C₆₁	#41	1	1	yes	characteristic
130	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
131	C₂²⋊Dic₆₁	—	2	2	no	—
132	#11758198	—	2	2	no	—
133	#11758198	—	2	2	no	—
134	C₄⋊Dic₆₁	—	2	1	no	—
135	C₄⋊Dic₆₁	—	2	1	no	—
136	C₄⋊Dic₆₁	—	2	1	no	—
137	C₄⋊Dic₆₁	—	2	1	no	—
138	C₄⋊Dic₆₁	C₂²×C₄	1	2	yes	—
139	C₄⋊Dic₆₁	C₂²×C₄	1	2	yes	—
140	#11758196	—	2	2	no	—
141	#11758196	—	2	2	no	—
142	C₄×Dic₆₁	—	2	2	no	—
143	#11758194	—	2	2	no	—
144	#11758194	SD₁₆	1	4	yes	complemented
145	C₂×#92418	—	2	2	no	—
146	C₂×#92418	C₂×D₄	1	2	yes	—
147	C₂×#92418	C₂×D₄	1	2	yes	—
148	#11758190	—	2	4	no	—
149	#11758190	—	4	2	no	—
150	#11758189	—	4	4	no	—
151	C₈×D₆₁	—	4	4	no	—
152	C₂³×C₆₁	C₄×D₄	1	1	yes	characteristic
153	C₂²×D₆₁	—	2	2	no	—
154	C₂×C₄×C₆₁	—	2	1	no	—
155	C₂×C₄×C₆₁	—	2	1	no	—
156	C₂×C₄×C₆₁	—	4	1	no	—
157	C₂×C₄×C₆₁	C₄×D₄	1	1	yes	characteristic
158	C₂×C₄×C₆₁	C₄×D₄	1	1	yes	characteristic
159	C₂×C₄×C₆₁	C₄×D₄	1	1	yes	characteristic
160	C₂×C₄×C₆₁	C₂×SD₁₆	1	2	yes	—
161	C₂×C₄×C₆₁	#135	1	2	yes	—
162	C₂×C₄×C₆₁	C₂³×C₄	1	1	yes	characteristic
163	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
164	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
165	C₂²⋊D₆₁	—	4	4	no	—
166	C₂×Dic₆₁	—	2	2	no	—
167	C₂×Dic₆₁	—	2	2	no	—
168	C₂×Dic₆₁	—	2	2	no	—
169	D₂₄₄	—	2	2	no	—
170	D₂₄₄	—	2	2	no	—
171	D₂₄₄	—	4	2	no	—
172	D₂₄₄	—	8	1	no	—
173	C₄×D₆₁	—	4	2	no	—
174	C₄×D₆₁	—	4	2	no	—
175	Dic₁₂₂	—	2	2	no	—
176	Dic₁₂₂	—	2	2	no	—
177	Dic₁₂₂	—	4	2	no	—
178	Dic₁₂₂	—	8	1	no	—
179	C₈×C₆₁	—	2	1	no	—
180	C₈×C₆₁	—	2	1	no	—
181	C₈×C₆₁	—	2	1	no	—
182	C₈×C₆₁	—	4	1	no	—
183	C₈×C₆₁	—	4	1	no	—
184	C₈×C₆₁	—	4	1	no	—
185	C₈×C₆₁	—	4	1	no	—
186	C₈×C₆₁	#131	1	2	yes	complemented
187	#92418	—	2	2	no	—
188	#92418	—	4	2	no	—
189	#92418	C₂×SD₁₆	1	4	yes	—
190	#18067	—	61	1	no	maximal, Sylow
191	C₂²×C₆₁	—	2	1	no	—
192	C₂²×C₆₁	—	2	1	no	—
193	C₂²×C₆₁	C₄×SD₁₆	1	2	yes	—
194	C₂²×C₆₁	C₂×C₄×D₄	1	1	yes	characteristic
195	C₂×D₆₁	—	4	2	no	—
196	C₂×D₆₁	—	4	2	no	—
197	C₂×D₆₁	—	4	2	no	—
198	C₄×C₆₁	—	2	1	no	—
199	C₄×C₆₁	—	2	1	no	—
200	C₄×C₆₁	—	2	1	no	—
201	C₄×C₆₁	C₄×SD₁₆	1	2	yes	—
202	C₄×C₆₁	C₂×#131	1	1	yes	characteristic
203	C₄×C₆₁	#568	1	1	yes	characteristic
204	C₄×C₆₁	C₂²×SD₁₆	1	1	yes	characteristic
205	C₄×C₆₁	C₂×#135	1	1	yes	characteristic
206	Dic₆₁	—	4	2	no	—
207	Dic₆₁	—	4	2	no	—
208	Dic₆₁	—	4	2	no	—
209	#3167	—	61	1	no	—
210	#2962	—	61	1	no	—
211	#2935	—	61	1	no	—
212	#1590	—	61	2	no	—
213	#1583	—	61	2	no	—
214	#1582	—	61	2	no	—
215	C₈×SD₁₆	—	61	2	no	—
216	C₂×#334	D₆₁	1	1	yes	characteristic, complemented
217	#1481	—	61	1	no	—
218	#1480	—	61	1	no	—
219	C₈×M₁₆	—	61	1	no	—
220	C₂×C₆₁	—	2	2	no	—
221	C₂×C₆₁	#2935	1	1	yes	characteristic
222	C₂×C₆₁	C₂×C₄×SD₁₆	1	1	yes	characteristic
223	C₂×C₆₁	#2957	1	1	yes	characteristic
224	D₆₁	—	8	2	no	—
225	C₂×#131	—	122	1	no	—
226	#533	—	61	1	no	—
227	#532	—	61	1	no	—
228	#498	—	61	1	no	—
229	#492	—	61	1	no	—
230	#487	—	61	1	no	—
231	#486	—	61	1	no	—
232	#465	—	61	2	no	—
233	#465	—	61	2	no	—
234	#446	—	61	2	no	—
235	#446	—	122	2	no	—
236	C₈×Q₈	—	61	2	no	—
237	C₄×SD₁₆	—	61	2	no	—
238	C₄×SD₁₆	—	61	2	no	—
239	#436	—	61	2	no	—
240	#435	—	122	2	no	—
241	C₈×D₄	—	61	2	no	—
242	#431	—	61	1	no	—
243	#424	—	122	1	no	—
244	C₂×C₄⋊C₈	C₂×D₆₁	1	1	yes	characteristic
245	C₂×C₄⋊C₈	C₂×D₆₁	1	1	yes	characteristic
246	#408	—	122	1	no	—
247	#405	—	122	1	no	—
248	C₄×M₁₆	—	61	1	no	—
249	C₂×C₄×C₈	C₂×D₆₁	1	1	yes	characteristic
250	#334	C₂×D₆₁	1	1	yes	characteristic
251	#334	C₂×D₆₁	1	1	yes	characteristic
252	#334	C₂×D₆₁	1	1	yes	characteristic
253	#334	C₂×D₆₁	1	1	yes	characteristic
254	Q₈⋊C₈	—	61	2	no	—
255	Q₈⋊C₈	—	61	2	no	—
256	D₄⋊C₈	—	61	2	no	—
257	D₄⋊C₈	—	61	2	no	—
258	#322	—	61	2	no	—
259	C₈²	—	61	2	no	—
260	C₆₁	#18067	1	1	yes	characteristic, complemented, Sylow
261	C₂×#41	—	122	1	no	—
262	C₂×SD₁₆	—	61	2	no	—
263	C₂×SD₁₆	—	61	2	no	—
264	#131	—	244	4	no	—
265	C₂×M₁₆	—	61	1	no	—
266	C₂×M₁₆	—	61	1	no	—
267	C₂×M₁₆	—	122	2	no	—
268	C₂²×C₈	—	2	1	no	—
269	C₂²×C₈	—	2	1	no	—
270	C₂²×C₈	—	122	2	no	—
271	C₂²×C₈	C₄×D₆₁	1	1	yes	characteristic
272	C₂²×C₈	C₄×D₆₁	1	1	yes	characteristic
273	C₄⋊Q₈	—	61	1	no	—
274	C₄⋊Q₈	—	61	1	no	—
275	C₄⋊Q₈	—	61	1	no	—
276	#127	—	61	1	no	—
277	#125	—	122	1	no	—
278	#124	—	122	1	no	—
279	C₂²⋊Q₈	—	61	2	no	—
280	C₂²⋊Q₈	—	122	1	no	—
281	#121	—	61	2	no	—
282	#121	—	122	1	no	—
283	C₄×Q₈	—	61	2	no	—
284	C₄×Q₈	—	122	1	no	—
285	C₄×D₄	—	61	2	no	—
286	C₄×D₄	—	122	1	no	—
287	#117	—	122	1	no	—
288	C₂×C₄²	C₂²×D₆₁	1	1	yes	characteristic
289	#106	—	61	2	no	—
290	#106	—	61	2	no	—
291	C₄⋊C₈	—	2	1	no	—
292	C₄⋊C₈	—	2	1	no	—
293	C₄⋊C₈	—	122	2	no	—
294	C₄⋊C₈	—	122	2	no	—
295	C₄⋊C₈	—	122	1	no	—
296	C₄⋊C₈	C₂²×D₆₁	1	1	yes	characteristic
297	C₄⋊C₈	C₂²×D₆₁	1	1	yes	characteristic
298	C₄⋊C₈	C₂²×D₆₁	1	1	yes	characteristic
299	C₄⋊C₈	C₂²×D₆₁	1	1	yes	characteristic
300	#103	—	61	2	no	—
301	#103	—	61	2	no	—
302	#102	—	61	2	no	—
303	#102	—	61	2	no	—
304	C₂²⋊C₈	—	122	2	no	—
305	C₂²⋊C₈	—	122	2	no	—
306	C₂²⋊C₈	—	122	1	no	—
307	#97	—	61	2	no	—
308	#97	—	122	2	no	—
309	C₄×C₈	—	61	2	no	—
310	C₄×C₈	—	61	2	no	—
311	C₄×C₈	—	122	2	no	—
312	C₄×C₈	C₄×D₆₁	1	1	yes	characteristic
313	C₄×C₈	C₄×D₆₁	1	1	yes	characteristic
314	C₄×C₈	C₂²×D₆₁	1	1	yes	characteristic
315	C₄×C₈	C₂²×D₆₁	1	1	yes	characteristic
316	#41	—	244	2	no	—
317	#41	—	244	2	no	—
318	C₂×Q₈	—	61	2	no	—
319	C₂×Q₈	—	122	1	no	—
320	C₂×Q₈	—	122	1	no	—
321	C₂×D₄	—	61	2	no	—
322	C₂×D₄	—	122	2	no	—
323	C₂×D₄	—	122	1	no	—
324	C₂×D₄	—	122	1	no	—
325	C₂²×C₄	—	122	2	no	—
326	C₂²×C₄	C₂×C₄×D₆₁	1	1	yes	characteristic
327	C₂²×C₄	D₄×D₆₁	1	1	yes	characteristic
328	C₂²×C₄	#11758226	1	1	yes	characteristic
329	SD₁₆	—	122	4	no	—
330	SD₁₆	—	244	2	no	—
331	M₁₆	—	61	4	no	—
332	M₁₆	—	122	2	no	—
333	M₁₆	—	244	4	no	—
334	C₂×C₈	—	2	2	no	—
335	C₂×C₈	—	2	1	no	—
336	C₂×C₈	—	2	1	no	—
337	C₂×C₈	—	2	1	no	—
338	C₂×C₈	—	2	1	no	—
339	C₂×C₈	—	4	1	no	—
340	C₂×C₈	—	4	2	no	—
341	C₂×C₈	—	4	2	no	—
342	C₂×C₈	—	61	2	no	—
343	C₂×C₈	—	61	2	no	—
344	C₂×C₈	—	122	2	no	—
345	C₂×C₈	—	244	4	no	—
346	C₂×C₈	C₂×C₄×D₆₁	1	1	yes	characteristic
347	C₂×C₈	C₂×C₄×D₆₁	1	1	yes	characteristic
348	C₂×C₈	C₂×C₄×D₆₁	1	1	yes	characteristic
349	C₂×C₈	C₂×C₄×D₆₁	1	1	yes	characteristic
350	C₄⋊C₄	—	61	2	no	—
351	C₄⋊C₄	—	61	2	no	—
352	C₄⋊C₄	—	122	2	no	—
353	C₄⋊C₄	—	122	2	no	—
354	C₄⋊C₄	—	122	1	no	—
355	C₄⋊C₄	—	122	1	no	—
356	C₄⋊C₄	—	122	1	no	—
357	C₄⋊C₄	—	122	1	no	—
358	C₂²⋊C₄	—	122	2	no	—
359	C₂²⋊C₄	—	122	2	no	—
360	C₂²⋊C₄	—	122	2	no	—
361	C₄²	—	122	2	no	—
362	C₄²	C₂×C₄×D₆₁	1	1	yes	characteristic
363	C₄²	D₄×D₆₁	1	1	yes	characteristic
364	C₄²	#11758226	1	1	yes	characteristic
365	C₄²	C₂³×D₆₁	1	1	yes	characteristic
366	C₂³	—	122	2	no	—
367	C₂³	#14519739	1	1	yes	characteristic
368	Q₈	—	122	2	no	—
369	Q₈	—	122	2	no	—
370	Q₈	—	488	1	no	—
371	Q₈	—	244	2	no	—
372	D₄	—	122	2	no	—
373	D₄	—	122	2	no	—
374	D₄	—	488	1	no	—
375	D₄	—	244	4	no	—
376	D₄	—	244	2	no	—
377	C₂×C₄	—	2	1	no	—
378	C₂×C₄	—	2	1	no	—
379	C₂×C₄	—	4	1	no	—
380	C₂×C₄	—	122	2	no	—
381	C₂×C₄	—	122	2	no	—
382	C₂×C₄	—	122	2	no	—
383	C₂×C₄	—	244	2	no	—
384	C₂×C₄	—	244	2	no	—
385	C₂×C₄	#14519739	1	1	yes	characteristic
386	C₂×C₄	#14519739	1	1	yes	characteristic
387	C₂×C₄	#14519739	1	1	yes	characteristic
388	C₂×C₄	SD₁₆×D₆₁	1	2	yes	—
389	C₂×C₄	#14519798	1	2	yes	—
390	C₂×C₄	C₂²×C₄×D₆₁	1	1	yes	characteristic
391	C₂×C₄	C₂×D₄×D₆₁	1	1	yes	characteristic
392	C₂×C₄	C₂×#11758226	1	1	yes	characteristic
393	C₈	—	2	1	no	—
394	C₈	—	2	1	no	—
395	C₈	—	2	1	no	—
396	C₈	—	4	1	no	—
397	C₈	—	4	1	no	—
398	C₈	—	4	1	no	—
399	C₈	—	4	1	no	—
400	C₈	—	61	4	no	—
401	C₈	—	122	2	no	—
402	C₈	—	244	2	no	—
403	C₈	#14519783	1	2	yes	complemented
404	C₂²	—	2	1	no	—
405	C₂²	—	2	1	no	—
406	C₂²	—	244	2	no	—
407	C₂²	—	244	2	no	—
408	C₂²	—	244	2	no	—
409	C₂²	#16839849	1	2	yes	—
410	C₂²	C₂×#14519739	1	1	yes	characteristic
411	C₄	—	2	1	no	—
412	C₄	—	2	1	no	—
413	C₄	—	2	1	no	—
414	C₄	—	244	2	no	—
415	C₄	—	244	2	no	—
416	C₄	—	244	2	no	—
417	C₄	#16839849	1	2	yes	—
418	C₄	C₂×#14519783	1	1	yes	characteristic
419	C₄	#16840528	1	1	yes	characteristic
420	C₄	C₂×SD₁₆×D₆₁	1	1	yes	characteristic
421	C₄	C₂×#14519798	1	1	yes	characteristic
422	C₂	—	2	2	no	—
423	C₂	—	488	2	no	—
424	C₂	#21454562	1	1	yes	characteristic
425	C₂	C₂×#16839849	1	1	yes	characteristic
426	C₂	#21454735	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₆₁
commutator	C₂×C₄×C₆₁	C₂³×C₄
Frattini	C₄²	C₂³×D₆₁
Fitting	C₂×C₆₁×#334	C₂
socle	C₂²×C₆₁	C₂×C₄×D₄
prime radical	#16840312	C₂²
cosocle	C₄²×C₆₁	C₂⁴
hypercenter	C₂×#334	D₆₁
hypocenter	C₆₁	#18067
LCS	G ▷ C₂×C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₂×#334

Complements

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

N	H ≅ G/N	type
2. #21454762	C₂	semidirect
4. #21444708	C₂	semidirect
5. #21444661	C₂	semidirect
6. #21444654	C₂	semidirect
7. #21444618	C₂	semidirect
8. #21444221	C₂	semidirect
10. C₈×#11758194	C₂	semidirect
11. C₂×C₆₁×#334	C₂	semidirect
144. #11758194	SD₁₆	semidirect
186. C₈×C₆₁	#131	semidirect
216. C₂×#334	D₆₁	semidirect
260. C₆₁	#18067	semidirect
403. C₈	#14519783	semidirect

Maximal subgroups

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

subgroup	index
#21456378	2
#21454762	2
#21454562	2
#21444708	2
#21444661	2
#21444654	2
#21444618	2
#21444221	2
#21444217	2
C₈×#11758194	2
C₂×C₆₁×#334	2
#18067	61