Subgroups — #29686952

Order 15616.

876 conjugacy classes of subgroups.

The subgroup lattice has 534 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#21455539	C₂	1	1	yes	maximal, characteristic
2	#21454720	C₂	1	2	yes	maximal, complemented
3	C₂×#16839880	C₂	1	1	yes	maximal, characteristic, complemented
4	#21446717	C₂	1	1	yes	maximal, characteristic, complemented
5	#21446609	C₂	1	1	yes	maximal, characteristic, complemented
6	#21446488	C₂	1	2	yes	maximal, complemented
7	#21446320	C₂	1	2	yes	maximal, complemented
8	#21445873	C₂	1	1	yes	maximal, characteristic, complemented
9	#21445698	C₂	1	1	yes	maximal, characteristic, complemented
10	#21445620	C₂	1	2	yes	maximal, complemented
11	C₄×#131×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
12	#16840560	C₂²	1	2	yes	—
13	C₂×#14519799	C₂²	1	1	yes	characteristic
14	C₂×#14519783	C₂²	1	2	yes	—
15	#16840037	C₄	1	2	yes	complemented
16	#16840032	C₄	1	2	yes	complemented
17	#16840025	C₄	1	4	yes	complemented
18	#16839882	—	2	4	no	—
19	#16839880	—	2	1	no	—
20	#16839880	—	2	1	no	—
21	#16839880	—	2	1	no	—
22	#16839880	—	2	1	no	—
23	#16839877	—	2	4	no	—
24	#16839810	C₂²	1	2	yes	—
25	C₂×#14519713	C₂²	1	1	yes	characteristic
26	C₂×#14519713	C₂²	1	1	yes	characteristic
27	#16839800	C₂²	1	1	yes	characteristic
28	#16839779	C₂²	1	2	yes	—
29	#16839778	C₂²	1	2	yes	—
30	C₂×#14519705	C₂²	1	2	yes	—
31	#16839744	C₂²	1	2	yes	—
32	#16839735	C₂²	1	2	yes	—
33	#16839717	C₂²	1	2	yes	—
34	#16839534	C₂²	1	2	yes	—
35	#16839532	C₂²	1	2	yes	—
36	#16839522	C₂²	1	2	yes	—
37	C₂×#131×C₆₁	C₂²	1	1	yes	characteristic
38	C₂×#131×C₆₁	C₂²	1	1	yes	characteristic
39	C₄×#41×C₆₁	C₂²	1	1	yes	characteristic
40	C₆₁×#405	—	2	1	no	—
41	C₆₁×#405	—	2	1	no	—
42	C₆₁×#405	C₂²	1	1	yes	characteristic
43	C₆₁×#405	C₂²	1	1	yes	characteristic
44	C₄×M₁₆×C₆₁	—	2	1	no	—
45	C₄×M₁₆×C₆₁	C₂²	1	1	yes	characteristic
46	C₂×C₄×C₈×C₆₁	—	2	1	no	—
47	C₂×C₄×C₈×C₆₁	C₂²	1	1	yes	characteristic
48	C₂×#11758222	C₂³	1	2	yes	—
49	#14519808	—	2	2	no	—
50	#14519807	C₂×C₄	1	4	yes	—
51	#14519803	—	2	2	no	—
52	#14519802	C₂×C₄	1	4	yes	—
53	#14519799	—	2	1	no	—
54	#14519799	—	2	1	no	—
55	#14519799	—	2	1	no	—
56	#14519799	—	2	1	no	—
57	#14519797	—	2	4	no	—
58	C₂×Dic₂₄₄	C₂×C₄	1	1	yes	characteristic, complemented
59	C₂×#11758190	C₂×C₄	1	2	yes	complemented
60	C₂×D₄₈₈	C₂×C₄	1	1	yes	characteristic, complemented
61	#14519783	—	2	2	no	—
62	#14519783	—	2	2	no	—
63	#14519783	—	2	2	no	—
64	#14519783	—	2	2	no	—
65	C₂×#11758194	C₂³	1	2	yes	—
66	C₂×#11758194	C₂³	1	2	yes	—
67	C₂×#11758189	—	2	2	no	—
68	C₂×C₈×D₆₁	—	2	2	no	—
69	#14519736	C₂³	1	2	yes	—
70	#14519713	—	2	1	no	—
71	#14519713	—	2	1	no	—
72	#14519713	C₂×C₄	1	2	yes	complemented
73	#14519713	C₂×C₄	1	2	yes	complemented
74	#14519712	—	2	4	no	—
75	#14519711	—	2	1	no	—
76	#14519709	—	2	1	no	—
77	#14519705	—	2	2	no	—
78	#14519705	—	2	2	no	—
79	#14519704	—	2	4	no	—
80	#14519703	—	2	4	no	—
81	#14519695	C₂×C₄	1	4	yes	complemented
82	#14519693	C₂×C₄	1	4	yes	complemented
83	#14519691	—	2	4	no	—
84	#14519687	—	2	2	no	—
85	C₈×Dic₆₁	—	2	2	no	—
86	C₂×#41×C₆₁	C₂³	1	1	yes	characteristic
87	#131×C₆₁	—	2	1	no	—
88	#131×C₆₁	—	2	1	no	—
89	#131×C₆₁	—	2	1	no	—
90	#131×C₆₁	—	2	1	no	—
91	#131×C₆₁	C₂×C₄	1	2	yes	—
92	#131×C₆₁	C₂×C₄	1	2	yes	—
93	#131×C₆₁	D₄	1	2	yes	—
94	#131×C₆₁	D₄	1	2	yes	—
95	C₂×M₁₆×C₆₁	—	2	1	no	—
96	C₂×M₁₆×C₆₁	—	2	1	no	—
97	C₂×M₁₆×C₆₁	C₂³	1	1	yes	characteristic
98	C₂×M₁₆×C₆₁	C₂³	1	1	yes	characteristic
99	C₂²×C₈×C₆₁	—	2	1	no	—
100	C₂²×C₈×C₆₁	—	2	1	no	—
101	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
102	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
103	C₄×Q₈×C₆₁	—	2	1	no	—
104	C₄×D₄×C₆₁	—	2	1	no	—
105	C₄×D₄×C₆₁	—	2	2	no	—
106	#117×C₆₁	—	2	1	no	—
107	#117×C₆₁	C₂³	1	1	yes	characteristic
108	C₂×C₄²×C₆₁	—	2	1	no	—
109	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
110	#97×C₆₁	—	2	1	no	—
111	#97×C₆₁	—	2	1	no	—
112	#97×C₆₁	—	2	1	no	—
113	C₄×C₈×C₆₁	—	2	1	no	—
114	C₄×C₈×C₆₁	—	2	1	no	—
115	C₄×C₈×C₆₁	—	2	1	no	—
116	C₄×C₈×C₆₁	D₄	1	1	yes	characteristic
117	C₄×C₈×C₆₁	D₄	1	1	yes	characteristic
118	C₄×C₈×C₆₁	D₄	1	1	yes	characteristic
119	C₄×C₈×C₆₁	D₄	1	1	yes	characteristic
120	#41×C₆₁	—	2	1	no	—
121	#41×C₆₁	—	2	1	no	—
122	#41×C₆₁	C₂²×C₄	1	2	yes	—
123	#41×C₆₁	C₂×D₄	1	2	yes	—
124	C₂×Q₈×C₆₁	#41	1	1	yes	characteristic
125	C₂×D₄×C₆₁	—	2	1	no	—
126	C₂×D₄×C₆₁	#41	1	1	yes	characteristic
127	C₂²×C₄×C₆₁	—	2	1	no	—
128	C₂²×C₄×C₆₁	—	2	2	no	—
129	C₂²×C₄×C₆₁	—	2	1	no	—
130	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
131	C₂×C₂²⋊D₆₁	—	2	2	no	—
132	#11758222	—	2	2	no	—
133	#11758222	—	2	2	no	—
134	#11758222	—	2	2	no	—
135	#11758222	—	2	2	no	—
136	C₂×D₂₄₄	C₂²×C₄	1	2	yes	—
137	C₂×C₄×D₆₁	—	2	2	no	—
138	C₂×Dic₁₂₂	C₂²×C₄	1	2	yes	—
139	M₁₆×C₆₁	—	2	1	no	—
140	M₁₆×C₆₁	—	2	1	no	—
141	M₁₆×C₆₁	—	2	2	no	—
142	M₁₆×C₆₁	—	2	2	no	—
143	M₁₆×C₆₁	—	2	2	no	—
144	M₁₆×C₆₁	—	2	2	no	—
145	M₁₆×C₆₁	C₂²×C₄	1	2	yes	—
146	M₁₆×C₆₁	C₂×D₄	1	2	yes	—
147	C₂×C₈×C₆₁	—	2	1	no	—
148	C₂×C₈×C₆₁	—	2	1	no	—
149	C₂×C₈×C₆₁	—	2	2	no	—
150	C₂×C₈×C₆₁	—	2	2	no	—
151	C₂×C₈×C₆₁	—	2	2	no	—
152	C₂×C₈×C₆₁	—	2	2	no	—
153	C₂×C₈×C₆₁	C₂²×C₄	1	1	yes	characteristic
154	C₂×C₈×C₆₁	C₂²×C₄	1	1	yes	characteristic
155	C₂×C₈×C₆₁	C₂×D₄	1	1	yes	characteristic
156	C₂×C₈×C₆₁	C₂×D₄	1	1	yes	characteristic
157	C₂×C₈×C₆₁	C₂×D₄	1	1	yes	characteristic
158	C₂×C₈×C₆₁	C₂×D₄	1	1	yes	characteristic
159	C₂×C₈×C₆₁	C₂×D₄	1	1	yes	characteristic
160	C₂×C₈×C₆₁	C₂×D₄	1	1	yes	characteristic
161	C₂×C₈×C₆₁	#41	1	1	yes	characteristic
162	C₂×C₈×C₆₁	#41	1	1	yes	characteristic
163	C₂×C₈×C₆₁	#41	1	1	yes	characteristic
164	C₂×C₈×C₆₁	#41	1	1	yes	characteristic
165	C₄⋊C₄×C₆₁	—	2	2	no	—
166	C₄⋊C₄×C₆₁	—	2	1	no	—
167	C₂²⋊C₄×C₆₁	—	2	2	no	—
168	C₂²⋊C₄×C₆₁	#41	1	2	yes	—
169	C₄²×C₆₁	—	2	2	no	—
170	C₄²×C₆₁	—	2	1	no	—
171	C₄²×C₆₁	—	2	1	no	—
172	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
173	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
174	C₂²⋊Dic₆₁	—	2	2	no	—
175	#11758202	—	2	4	no	—
176	#11758201	—	2	4	no	—
177	#11758200	—	2	4	no	—
178	#11758199	—	2	4	no	—
179	C₄⋊Dic₆₁	—	2	2	no	—
180	C₄×Dic₆₁	—	2	2	no	—
181	#11758194	—	2	2	no	—
182	#11758194	—	2	2	no	—
183	#11758194	—	2	2	no	—
184	#11758194	C₂²×C₄	1	4	yes	—
185	C₂×#92418	—	2	2	no	—
186	C₂×#92418	—	2	2	no	—
187	Dic₂₄₄	—	2	1	no	—
188	Dic₂₄₄	—	2	1	no	—
189	D₄₈₈	—	2	1	no	—
190	D₄₈₈	—	2	1	no	—
191	#11758190	—	2	2	no	—
192	#11758190	—	2	2	no	—
193	#11758189	—	4	2	no	—
194	#11758189	—	4	2	no	—
195	C₈×D₆₁	—	4	2	no	—
196	C₈×D₆₁	—	4	2	no	—
197	C₂³×C₆₁	—	2	1	no	—
198	C₂³×C₆₁	C₂×#41	1	1	yes	characteristic
199	C₂²×D₆₁	—	2	2	no	—
200	Q₈×C₆₁	—	2	1	no	—
201	Q₈×C₆₁	C₄×D₄	1	2	yes	—
202	D₄×C₆₁	—	2	2	no	—
203	D₄×C₆₁	—	2	2	no	—
204	D₄×C₆₁	—	2	1	no	—
205	D₄×C₆₁	C₄×D₄	1	2	yes	—
206	C₂×C₄×C₆₁	—	2	1	no	—
207	C₂×C₄×C₆₁	—	2	1	no	—
208	C₂×C₄×C₆₁	—	2	2	no	—
209	C₂×C₄×C₆₁	—	2	2	no	—
210	C₂×C₄×C₆₁	—	2	2	no	—
211	C₂×C₄×C₆₁	—	2	1	no	—
212	C₂×C₄×C₆₁	—	4	2	no	—
213	C₂×C₄×C₆₁	—	4	4	no	—
214	C₂×C₄×C₆₁	C₂³×C₄	1	1	yes	characteristic
215	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
216	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
217	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
218	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
219	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
220	C₂²⋊D₆₁	—	4	2	no	—
221	C₂²⋊D₆₁	—	4	2	no	—
222	C₂×Dic₆₁	—	2	2	no	—
223	C₂×Dic₆₁	—	4	2	no	—
224	D₂₄₄	—	2	2	no	—
225	D₂₄₄	—	2	2	no	—
226	C₄×D₆₁	—	4	2	no	—
227	C₄×D₆₁	—	4	2	no	—
228	Dic₁₂₂	—	2	2	no	—
229	Dic₁₂₂	—	2	2	no	—
230	C₈×C₆₁	—	2	2	no	—
231	C₈×C₆₁	—	2	2	no	—
232	C₈×C₆₁	C₄×D₄	1	1	yes	characteristic
233	C₈×C₆₁	C₄×D₄	1	1	yes	characteristic
234	C₈×C₆₁	C₄×D₄	1	1	yes	characteristic
235	C₈×C₆₁	C₄×D₄	1	1	yes	characteristic
236	C₈×C₆₁	#121	1	1	yes	characteristic
237	C₈×C₆₁	#121	1	1	yes	characteristic
238	C₈×C₆₁	#121	1	1	yes	characteristic
239	C₈×C₆₁	#121	1	1	yes	characteristic
240	#92418	—	2	4	no	—
241	#92418	—	4	2	no	—
242	#21558	—	61	1	no	maximal, Sylow
243	C₂²×C₆₁	—	2	2	no	—
244	C₂²×C₆₁	—	4	1	no	—
245	C₂²×C₆₁	—	4	2	no	—
246	C₂²×C₆₁	C₄×#41	1	1	yes	characteristic
247	C₂²×C₆₁	#525	1	1	yes	characteristic
248	C₂²×C₆₁	#532	1	1	yes	characteristic
249	C₂×D₆₁	—	4	2	no	—
250	C₂×D₆₁	—	8	2	no	—
251	C₄×C₆₁	—	2	2	no	—
252	C₄×C₆₁	—	2	2	no	—
253	C₄×C₆₁	—	4	2	no	—
254	C₄×C₆₁	—	4	1	no	—
255	C₄×C₆₁	C₂×C₄×D₄	1	1	yes	characteristic
256	C₄×C₆₁	C₂×C₄×D₄	1	1	yes	characteristic
257	C₄×C₆₁	C₂×#121	1	1	yes	characteristic
258	C₄×C₆₁	#529	1	1	yes	characteristic
259	Dic₆₁	—	4	2	no	—
260	Dic₆₁	—	8	2	no	—
261	#3067	—	61	1	no	—
262	#2955	—	61	2	no	—
263	C₂×#443	—	61	1	no	—
264	C₄×#131	D₆₁	1	1	yes	characteristic, complemented
265	#1976	—	61	1	no	—
266	#1953	—	61	1	no	—
267	#1932	—	61	2	no	—
268	#1906	—	61	2	no	—
269	#1814	—	61	1	no	—
270	#1772	—	61	1	no	—
271	#1757	—	61	2	no	—
272	C₂×C₆₁	—	2	1	no	—
273	C₂×C₆₁	—	2	1	no	—
274	C₂×C₆₁	—	2	1	no	—
275	C₂×C₆₁	—	4	2	no	—
276	C₂×C₆₁	C₄×#121	1	1	yes	characteristic
277	D₆₁	—	8	2	no	—
278	#575	—	61	2	no	—
279	C₂×#135	—	61	1	no	—
280	C₂×#131	—	61	2	no	—
281	C₂×#131	C₂×D₆₁	1	1	yes	characteristic
282	C₂×#131	C₂×D₆₁	1	1	yes	characteristic
283	C₄×#41	C₂×D₆₁	1	1	yes	characteristic
284	#473	—	61	2	no	—
285	#472	—	61	2	no	—
286	#471	—	61	4	no	—
287	#444	—	122	4	no	—
288	#443	—	122	4	no	—
289	#443	—	122	1	no	—
290	#443	—	122	1	no	—
291	#443	—	122	1	no	—
292	#443	—	122	1	no	—
293	#430	—	61	2	no	—
294	C₂×#108	—	61	1	no	—
295	C₂×#108	—	61	1	no	—
296	#427	—	61	1	no	—
297	#421	—	61	2	no	—
298	#421	—	61	2	no	—
299	C₂×#104	—	61	2	no	—
300	#413	—	61	2	no	—
301	#410	—	61	2	no	—
302	#405	—	2	1	no	—
303	#405	—	2	1	no	—
304	#405	—	61	2	no	—
305	#405	C₂×D₆₁	1	1	yes	characteristic
306	#405	C₂×D₆₁	1	1	yes	characteristic
307	C₄×M₁₆	—	2	1	no	—
308	C₄×M₁₆	C₂×D₆₁	1	1	yes	characteristic
309	C₂×C₄×C₈	—	2	1	no	—
310	C₂×C₄×C₈	C₂×D₆₁	1	1	yes	characteristic
311	#344	—	61	2	no	—
312	#344	—	61	2	no	—
313	#339	—	61	2	no	—
314	C₆₁	#21558	1	1	yes	characteristic, complemented, Sylow
315	C₂×#41	—	61	2	no	—
316	C₂×#41	C₂²×D₆₁	1	1	yes	characteristic
317	#137	—	61	4	no	—
318	#137	—	122	2	no	—
319	AGL(1,ℤ/8)	—	61	4	no	—
320	AGL(1,ℤ/8)	—	122	2	no	—
321	#135	—	122	4	no	—
322	#135	—	122	1	no	—
323	#135	—	122	1	no	—
324	#135	—	122	1	no	—
325	#135	—	122	1	no	—
326	C₂×Q₁₆	—	61	1	no	—
327	C₂×SD₁₆	—	61	2	no	—
328	C₂×D₈	—	61	1	no	—
329	#131	—	2	1	no	—
330	#131	—	2	1	no	—
331	#131	—	2	1	no	—
332	#131	—	2	1	no	—
333	#131	—	122	2	no	—
334	#131	—	122	2	no	—
335	#131	—	122	2	no	—
336	#131	—	122	2	no	—
337	#131	C₄×D₆₁	1	2	yes	—
338	#131	C₄×D₆₁	1	2	yes	—
339	#131	D₂₄₄	1	2	yes	—
340	#131	D₂₄₄	1	2	yes	—
341	C₂×M₁₆	—	2	1	no	—
342	C₂×M₁₆	—	2	1	no	—
343	C₂×M₁₆	—	61	2	no	—
344	C₂×M₁₆	—	61	2	no	—
345	C₂×M₁₆	—	122	2	no	—
346	C₂×M₁₆	C₂²×D₆₁	1	1	yes	characteristic
347	C₂×M₁₆	C₂²×D₆₁	1	1	yes	characteristic
348	C₂²×C₈	—	2	1	no	—
349	C₂²×C₈	—	2	1	no	—
350	C₂²×C₈	—	122	2	no	—
351	C₂²×C₈	C₂²×D₆₁	1	1	yes	characteristic
352	C₂²×C₈	C₂²×D₆₁	1	1	yes	characteristic
353	C₄×Q₈	—	2	1	no	—
354	C₄×D₄	—	2	1	no	—
355	C₄×D₄	—	2	2	no	—
356	#117	—	2	1	no	—
357	#117	—	61	2	no	—
358	#117	C₂²×D₆₁	1	1	yes	characteristic
359	C₂×C₄²	—	2	1	no	—
360	C₂×C₄²	C₂²×D₆₁	1	1	yes	characteristic
361	#108	—	61	2	no	—
362	#108	—	61	2	no	—
363	#108	—	122	4	no	—
364	#108	—	122	1	no	—
365	#108	—	122	1	no	—
366	#107	—	122	1	no	—
367	#106	—	122	1	no	—
368	#104	—	122	4	no	—
369	#104	—	122	4	no	—
370	#104	—	122	2	no	—
371	#104	—	122	2	no	—
372	#101	—	61	4	no	—
373	#100	—	61	4	no	—
374	#99	—	122	4	no	—
375	#97	—	2	1	no	—
376	#97	—	2	1	no	—
377	#97	—	2	1	no	—
378	#97	—	122	2	no	—
379	C₄×C₈	—	2	1	no	—
380	C₄×C₈	—	2	1	no	—
381	C₄×C₈	—	2	1	no	—
382	C₄×C₈	—	122	2	no	—
383	C₄×C₈	C₂²⋊D₆₁	1	1	yes	characteristic
384	C₄×C₈	C₂²⋊D₆₁	1	1	yes	characteristic
385	C₄×C₈	C₂²⋊D₆₁	1	1	yes	characteristic
386	C₄×C₈	C₂²⋊D₆₁	1	1	yes	characteristic
387	#41	—	2	1	no	—
388	#41	—	2	1	no	—
389	#41	—	122	2	no	—
390	#41	—	122	2	no	—
391	#41	—	122	2	no	—
392	#41	—	122	2	no	—
393	#41	C₂×C₄×D₆₁	1	2	yes	—
394	#41	C₂×D₂₄₄	1	2	yes	—
395	C₂×Q₈	—	61	2	no	—
396	C₂×Q₈	#11758222	1	1	yes	characteristic
397	C₂×D₄	—	2	1	no	—
398	C₂×D₄	—	61	2	no	—
399	C₂×D₄	—	122	2	no	—
400	C₂×D₄	#11758222	1	1	yes	characteristic
401	C₂²×C₄	—	2	1	no	—
402	C₂²×C₄	—	2	2	no	—
403	C₂²×C₄	—	2	1	no	—
404	C₂²×C₄	—	122	2	no	—
405	C₂²×C₄	C₂³×D₆₁	1	1	yes	characteristic
406	Q₁₆	—	122	4	no	—
407	Q₁₆	—	122	1	no	—
408	Q₁₆	—	122	1	no	—
409	SD₁₆	—	122	4	no	—
410	SD₁₆	—	122	4	no	—
411	SD₁₆	—	122	2	no	—
412	SD₁₆	—	122	2	no	—
413	D₈	—	122	4	no	—
414	D₈	—	122	1	no	—
415	D₈	—	122	1	no	—
416	M₁₆	—	2	1	no	—
417	M₁₆	—	2	1	no	—
418	M₁₆	—	2	2	no	—
419	M₁₆	—	2	2	no	—
420	M₁₆	—	2	2	no	—
421	M₁₆	—	2	2	no	—
422	M₁₆	—	61	4	no	—
423	M₁₆	—	122	2	no	—
424	M₁₆	—	122	2	no	—
425	M₁₆	—	122	2	no	—
426	M₁₆	—	244	2	no	—
427	M₁₆	—	244	2	no	—
428	M₁₆	C₂×C₄×D₆₁	1	2	yes	—
429	M₁₆	C₂×D₂₄₄	1	2	yes	—
430	C₂×C₈	—	2	1	no	—
431	C₂×C₈	—	2	1	no	—
432	C₂×C₈	—	2	2	no	—
433	C₂×C₈	—	2	2	no	—
434	C₂×C₈	—	2	2	no	—
435	C₂×C₈	—	2	2	no	—
436	C₂×C₈	—	122	2	no	—
437	C₂×C₈	—	122	2	no	—
438	C₂×C₈	—	244	2	no	—
439	C₂×C₈	—	244	2	no	—
440	C₂×C₈	C₂×C₄×D₆₁	1	1	yes	characteristic
441	C₂×C₈	C₂×C₄×D₆₁	1	1	yes	characteristic
442	C₂×C₈	C₂×D₂₄₄	1	1	yes	characteristic
443	C₂×C₈	C₂×D₂₄₄	1	1	yes	characteristic
444	C₂×C₈	#11758222	1	1	yes	characteristic
445	C₂×C₈	#11758222	1	1	yes	characteristic
446	C₂×C₈	#11758222	1	1	yes	characteristic
447	C₂×C₈	#11758222	1	1	yes	characteristic
448	C₂×C₈	C₂×C₂²⋊D₆₁	1	1	yes	characteristic
449	C₂×C₈	C₂×C₂²⋊D₆₁	1	1	yes	characteristic
450	C₂×C₈	C₂×C₂²⋊D₆₁	1	1	yes	characteristic
451	C₂×C₈	C₂×C₂²⋊D₆₁	1	1	yes	characteristic
452	C₄⋊C₄	—	2	2	no	—
453	C₄⋊C₄	—	2	1	no	—
454	C₄⋊C₄	—	122	2	no	—
455	C₂²⋊C₄	—	2	2	no	—
456	C₂²⋊C₄	—	122	2	no	—
457	C₂²⋊C₄	#11758222	1	2	yes	—
458	C₄²	—	2	2	no	—
459	C₄²	—	2	1	no	—
460	C₄²	—	2	1	no	—
461	C₄²	—	122	2	no	—
462	C₄²	C₂×C₂²⋊D₆₁	1	1	yes	characteristic
463	C₄²	C₂×C₂²⋊D₆₁	1	1	yes	characteristic
464	C₂³	—	2	1	no	—
465	C₂³	—	122	2	no	—
466	C₂³	C₂×#11758222	1	1	yes	characteristic
467	Q₈	—	2	1	no	—
468	Q₈	—	122	2	no	—
469	Q₈	—	122	2	no	—
470	Q₈	C₄×D₂₄₄	1	2	yes	—
471	D₄	—	2	2	no	—
472	D₄	—	2	2	no	—
473	D₄	—	2	1	no	—
474	D₄	—	122	2	no	—
475	D₄	—	122	2	no	—
476	D₄	—	244	2	no	—
477	D₄	—	244	2	no	—
478	D₄	C₄×D₂₄₄	1	2	yes	—
479	C₂×C₄	—	2	1	no	—
480	C₂×C₄	—	2	1	no	—
481	C₂×C₄	—	2	2	no	—
482	C₂×C₄	—	2	2	no	—
483	C₂×C₄	—	2	2	no	—
484	C₂×C₄	—	2	1	no	—
485	C₂×C₄	—	4	2	no	—
486	C₂×C₄	—	4	4	no	—
487	C₂×C₄	—	122	2	no	—
488	C₂×C₄	—	244	2	no	—
489	C₂×C₄	—	244	2	no	—
490	C₂×C₄	—	244	2	no	—
491	C₂×C₄	C₂²×C₄×D₆₁	1	1	yes	characteristic
492	C₂×C₄	C₂²×C₂²⋊D₆₁	1	1	yes	characteristic
493	C₂×C₄	C₂²×D₂₄₄	1	1	yes	characteristic
494	C₂×C₄	C₂×#11758222	1	1	yes	characteristic
495	C₂×C₄	C₂×#11758222	1	1	yes	characteristic
496	C₂×C₄	C₂×#11758222	1	1	yes	characteristic
497	C₈	—	2	2	no	—
498	C₈	—	2	2	no	—
499	C₈	—	122	4	no	—
500	C₈	—	244	2	no	—
501	C₈	C₄×C₂²⋊D₆₁	1	1	yes	characteristic
502	C₈	C₄×C₂²⋊D₆₁	1	1	yes	characteristic
503	C₈	C₄×C₂²⋊D₆₁	1	1	yes	characteristic
504	C₈	C₄×C₂²⋊D₆₁	1	1	yes	characteristic
505	C₈	#14519751	1	1	yes	characteristic
506	C₈	#14519751	1	1	yes	characteristic
507	C₈	#14519751	1	1	yes	characteristic
508	C₈	#14519751	1	1	yes	characteristic
509	C₂²	—	2	2	no	—
510	C₂²	—	4	1	no	—
511	C₂²	—	4	2	no	—
512	C₂²	—	488	2	no	—
513	C₂²	—	244	2	no	—
514	C₂²	C₄×#11758222	1	1	yes	characteristic
515	C₂²	#16840273	1	1	yes	characteristic
516	C₂²	#16840312	1	1	yes	characteristic
517	C₄	—	2	2	no	—
518	C₄	—	2	2	no	—
519	C₄	—	4	2	no	—
520	C₄	—	4	1	no	—
521	C₄	—	488	2	no	—
522	C₄	—	244	2	no	—
523	C₄	C₂×C₄×C₂²⋊D₆₁	1	1	yes	characteristic
524	C₄	C₂×C₄×D₂₄₄	1	1	yes	characteristic
525	C₄	C₂×#14519751	1	1	yes	characteristic
526	C₄	#16840296	1	1	yes	characteristic
527	C₂	—	2	1	no	—
528	C₂	—	2	1	no	—
529	C₂	—	2	1	no	—
530	C₂	—	4	2	no	—
531	C₂	—	488	2	no	—
532	C₂	C₄×#14519751	1	1	yes	characteristic

	subgroup	G/H
center	C₈	#14519751
commutator	C₂×C₄×C₆₁	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₆₁
Fitting	C₄×#131×C₆₁	C₂
socle	C₂×C₆₁	C₄×#121
prime radical	#21455539	C₂
cosocle	C₂²×C₄×C₆₁	C₂⁴
hypercenter	C₄×#131	D₆₁
hypocenter	C₆₁	#21558
LCS	G ▷ C₂×C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₈ ◁ C₂²×C₈ ◁ C₄×#131

Complements

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

N	H ≅ G/N	type
2. #21454720	C₂	semidirect
3. C₂×#16839880	C₂	semidirect
4. #21446717	C₂	semidirect
5. #21446609	C₂	semidirect
6. #21446488	C₂	semidirect
7. #21446320	C₂	semidirect
8. #21445873	C₂	semidirect
9. #21445698	C₂	semidirect
10. #21445620	C₂	semidirect
11. C₄×#131×C₆₁	C₂	semidirect
15. #16840037	C₄	semidirect
16. #16840032	C₄	semidirect
17. #16840025	C₄	semidirect
58. C₂×Dic₂₄₄	C₂×C₄	semidirect
59. C₂×#11758190	C₂×C₄	semidirect
60. C₂×D₄₈₈	C₂×C₄	semidirect
72. #14519713	C₂×C₄	semidirect
73. #14519713	C₂×C₄	semidirect
81. #14519695	C₂×C₄	semidirect
82. #14519693	C₂×C₄	semidirect
264. C₄×#131	D₆₁	semidirect
314. C₆₁	#21558	semidirect

Maximal subgroups

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

subgroup	index
#21455539	2
#21454720	2
C₂×#16839880	2
#21446717	2
#21446609	2
#21446488	2
#21446320	2
#21445873	2
#21445698	2
#21445620	2
C₄×#131×C₆₁	2
#21558	61