Subgroups — #29678564

Order 15616.

1046 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#16839877	C₂	1	1	yes	maximal, characteristic
2	C₂×#16839876	C₂	1	1	yes	maximal, characteristic
3	#21454587	C₂	1	1	yes	maximal, characteristic
4	#21454241	C₂	1	1	yes	maximal, characteristic, complemented
5	#131×Dic₆₁	C₂	1	1	yes	maximal, characteristic, complemented
6	#21445720	C₂	1	1	yes	maximal, characteristic, complemented
7	#21445699	C₂	1	1	yes	maximal, characteristic, complemented
8	#21445697	C₂	1	1	yes	maximal, characteristic, complemented
9	#21445659	C₂	1	1	yes	maximal, characteristic, complemented
10	#21445656	C₂	1	1	yes	maximal, characteristic, complemented
11	#21445655	C₂	1	1	yes	maximal, characteristic, complemented
12	#104×Dic₆₁	C₂	1	1	yes	maximal, characteristic, complemented
13	#21445623	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄×C₈×Dic₆₁	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₁×#1764	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#14519797	C₂²	1	1	yes	characteristic
17	C₂×#14519785	C₂²	1	1	yes	characteristic
18	C₂×#14519784	C₂²	1	1	yes	characteristic
19	C₂×#14519783	C₂²	1	1	yes	characteristic
20	#41×Dic₆₁	C₂²	1	1	yes	characteristic
21	#16840230	C₂²	1	1	yes	characteristic
22	#16839877	C₄	1	8	yes	complemented
23	#16839876	C₄	1	8	yes	complemented
24	#16839854	C₄	1	2	yes	complemented
25	#16839853	C₄	1	2	yes	complemented
26	#16839847	C₄	1	2	yes	complemented
27	#16839842	C₄	1	2	yes	complemented
28	C₂×#14519712	C₂²	1	1	yes	characteristic
29	C₂×#14519712	C₂²	1	1	yes	characteristic
30	#16839798	C₂²	1	1	yes	characteristic
31	C₂×#14519705	C₂²	1	1	yes	characteristic
32	C₂×#14519704	C₂²	1	1	yes	characteristic
33	C₂×#14519703	C₂²	1	1	yes	characteristic
34	#16839759	C₂²	1	1	yes	characteristic
35	#16839720	—	2	1	no	—
36	#16839720	C₂²	1	1	yes	characteristic
37	#16839719	—	2	1	no	—
38	#16839718	C₂²	1	1	yes	characteristic
39	#16839717	—	2	1	no	—
40	#16839717	C₂²	1	1	yes	characteristic
41	#16839716	—	2	1	no	—
42	#16839714	—	2	1	no	—
43	M₁₆×Dic₆₁	—	2	1	no	—
44	M₁₆×Dic₆₁	C₂²	1	1	yes	characteristic
45	M₁₆×Dic₆₁	C₂²	1	1	yes	characteristic
46	C₂×C₄×#92418	C₂²	1	1	yes	characteristic
47	C₂×C₈×Dic₆₁	—	2	1	no	—
48	C₂×C₈×Dic₆₁	C₂²	1	1	yes	characteristic
49	C₂×C₈×Dic₆₁	C₂²	1	1	yes	characteristic
50	C₂×C₈×Dic₆₁	C₂²	1	1	yes	characteristic
51	C₂×C₈×Dic₆₁	C₂²	1	1	yes	characteristic
52	C₄×C₈×D₆₁	—	2	1	no	—
53	C₄²×Dic₆₁	C₂²	1	1	yes	characteristic
54	#16839527	C₂²	1	1	yes	characteristic
55	#16839523	C₂²	1	1	yes	characteristic
56	#16839522	C₂²	1	1	yes	characteristic
57	#16839521	C₂²	1	1	yes	characteristic
58	C₂×#131×C₆₁	C₂²	1	1	yes	characteristic
59	C₂×#104×C₆₁	C₂²	1	1	yes	characteristic
60	C₆₁×#416	C₂²	1	1	yes	characteristic
61	C₆₁×#405	C₂²	1	1	yes	characteristic
62	C₂×C₄×C₈×C₆₁	C₂²	1	1	yes	characteristic
63	C₆₁×#341	C₂²	1	1	yes	characteristic
64	C₆₁×#339	C₂²	1	1	yes	characteristic
65	C₂×#11758222	C₂³	1	1	yes	characteristic
66	#14519797	C₂×C₄	1	4	yes	—
67	#14519797	C₂×C₄	1	4	yes	—
68	C₂×#11758202	C₂×C₄	1	1	yes	characteristic
69	C₂×#11758200	C₂×C₄	1	1	yes	characteristic
70	C₂×#11758201	C₂×C₄	1	1	yes	characteristic
71	C₂×#11758199	C₂×C₄	1	1	yes	characteristic
72	#14519785	—	2	2	no	—
73	#14519785	C₂×C₄	1	4	yes	complemented
74	#14519784	—	2	2	no	—
75	#14519784	C₂×C₄	1	4	yes	complemented
76	#14519783	—	2	2	no	—
77	#14519783	C₂×C₄	1	4	yes	complemented
78	C₂×#11758194	—	2	1	no	—
79	C₂×#11758194	C₂³	1	1	yes	characteristic
80	C₂×#11758194	C₂³	1	1	yes	characteristic
81	C₂×#11758189	—	2	1	no	—
82	C₂×#11758189	—	2	1	no	—
83	C₂²×#92418	—	2	1	no	—
84	C₂²×#92418	C₂³	1	1	yes	characteristic
85	C₂²×#92418	C₂³	1	1	yes	characteristic
86	C₂×C₈×D₆₁	—	2	1	no	—
87	C₂×C₈×D₆₁	—	2	1	no	—
88	Q₈×Dic₆₁	C₂×C₄	1	2	yes	—
89	#14519742	C₂×C₄	1	2	yes	—
90	D₄×Dic₆₁	—	2	2	no	—
91	D₄×Dic₆₁	C₂×C₄	1	2	yes	—
92	#14519739	C₂×C₄	1	2	yes	—
93	#14519737	—	2	2	no	—
94	#14519736	—	2	1	no	—
95	#14519736	C₂³	1	1	yes	characteristic
96	#14519734	—	2	1	no	—
97	C₂×C₄×Dic₆₁	—	2	2	no	—
98	C₂×C₄×Dic₆₁	—	2	1	no	—
99	C₂×C₄×Dic₆₁	C₂³	1	1	yes	characteristic
100	C₂×C₄×Dic₆₁	C₂³	1	1	yes	characteristic
101	C₄²×D₆₁	—	2	1	no	—
102	#14519712	C₂×C₄	1	4	yes	complemented
103	#14519712	C₂×C₄	1	4	yes	complemented
104	#14519710	C₂×C₄	1	2	yes	—
105	#14519708	C₂×C₄	1	2	yes	—
106	#14519705	C₂×C₄	1	4	yes	complemented
107	#14519704	C₂×C₄	1	4	yes	complemented
108	#14519703	C₂×C₄	1	4	yes	complemented
109	#14519702	C₂×C₄	1	2	yes	—
110	#14519699	C₂×C₄	1	2	yes	—
111	#14519688	—	2	1	no	—
112	#14519687	—	2	1	no	—
113	#14519687	—	2	1	no	—
114	#14519687	—	2	1	no	—
115	#14519687	—	2	1	no	—
116	C₄×#92418	—	2	1	no	—
117	C₄×#92418	C₂×C₄	1	4	yes	complemented
118	C₈×Dic₆₁	—	2	1	no	—
119	C₈×Dic₆₁	—	2	1	no	—
120	C₈×Dic₆₁	—	2	1	no	—
121	C₈×Dic₆₁	—	2	1	no	—
122	C₈×Dic₆₁	—	2	2	no	—
123	C₈×Dic₆₁	C₂×C₄	1	2	yes	—
124	C₈×Dic₆₁	C₂×C₄	1	2	yes	—
125	C₈×Dic₆₁	C₂×C₄	1	4	yes	complemented
126	C₈×Dic₆₁	D₄	1	1	yes	characteristic
127	C₈×Dic₆₁	D₄	1	1	yes	characteristic
128	C₈×Dic₆₁	D₄	1	1	yes	characteristic
129	C₈×Dic₆₁	D₄	1	1	yes	characteristic
130	C₂×#41×C₆₁	C₂³	1	1	yes	characteristic
131	#131×C₆₁	—	2	2	no	—
132	#131×C₆₁	C₂×C₄	1	4	yes	complemented
133	C₂×M₁₆×C₆₁	—	2	1	no	—
134	C₂×M₁₆×C₆₁	C₂³	1	1	yes	characteristic
135	C₂×M₁₆×C₆₁	C₂³	1	1	yes	characteristic
136	C₂²×C₈×C₆₁	—	2	1	no	—
137	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
138	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
139	#117×C₆₁	C₂³	1	1	yes	characteristic
140	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
141	#104×C₆₁	C₂×C₄	1	4	yes	complemented
142	#103×C₆₁	C₂×C₄	1	2	yes	—
143	#102×C₆₁	C₂×C₄	1	2	yes	—
144	#97×C₆₁	—	2	1	no	—
145	C₄×C₈×C₆₁	—	2	1	no	—
146	C₄×C₈×C₆₁	—	2	2	no	—
147	#41×C₆₁	—	2	1	no	—
148	#41×C₆₁	—	2	1	no	—
149	#41×C₆₁	C₂²×C₄	1	2	yes	—
150	#41×C₆₁	C₂²×C₄	1	2	yes	—
151	C₂×Q₈×C₆₁	C₂²×C₄	1	1	yes	characteristic
152	C₂×D₄×C₆₁	—	2	1	no	—
153	C₂×D₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
154	C₂²×C₄×C₆₁	—	2	1	no	—
155	C₂²×C₄×C₆₁	—	2	1	no	—
156	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
157	C₂×C₂²⋊D₆₁	—	2	1	no	—
158	C₂²×Dic₆₁	—	2	1	no	—
159	C₂²×Dic₆₁	—	2	2	no	—
160	C₂²×Dic₆₁	#41	1	2	yes	—
161	#11758222	—	2	1	no	—
162	#11758222	—	2	1	no	—
163	#11758222	C₂²×C₄	1	2	yes	—
164	#11758222	C₂²×C₄	1	2	yes	—
165	C₂×D₂₄₄	C₂²×C₄	1	1	yes	characteristic
166	C₂×C₄×D₆₁	—	2	1	no	—
167	C₂×C₄×D₆₁	—	2	2	no	—
168	C₂×Dic₁₂₂	C₂²×C₄	1	1	yes	characteristic
169	M₁₆×C₆₁	—	2	1	no	—
170	M₁₆×C₆₁	—	2	1	no	—
171	M₁₆×C₆₁	—	2	4	no	—
172	M₁₆×C₆₁	C₂²×C₄	1	2	yes	—
173	M₁₆×C₆₁	C₂²×C₄	1	2	yes	—
174	C₂×C₈×C₆₁	—	2	1	no	—
175	C₂×C₈×C₆₁	—	2	1	no	—
176	C₂×C₈×C₆₁	—	2	1	no	—
177	C₂×C₈×C₆₁	—	2	1	no	—
178	C₂×C₈×C₆₁	—	2	4	no	—
179	C₂×C₈×C₆₁	C₂²×C₄	1	2	yes	—
180	C₂×C₈×C₆₁	C₂²×C₄	1	2	yes	—
181	C₂×C₈×C₆₁	C₂×D₄	1	1	yes	characteristic
182	C₂×C₈×C₆₁	C₂×D₄	1	1	yes	characteristic
183	C₂×C₈×C₆₁	#41	1	2	yes	—
184	C₄⋊C₄×C₆₁	C₂²×C₄	1	2	yes	—
185	C₂²⋊C₄×C₆₁	—	2	1	no	—
186	C₄²×C₆₁	—	2	1	no	—
187	C₄²×C₆₁	—	2	1	no	—
188	C₄²×C₆₁	C₂²×C₄	1	2	yes	—
189	C₂²⋊Dic₆₁	—	2	1	no	—
190	C₂²⋊Dic₆₁	—	2	2	no	—
191	#11758202	C₄²	1	4	yes	complemented
192	#11758201	C₄²	1	4	yes	complemented
193	#11758200	C₄²	1	4	yes	complemented
194	#11758199	C₄²	1	4	yes	complemented
195	#11758198	—	2	2	no	—
196	C₄⋊Dic₆₁	—	2	2	no	—
197	C₄⋊Dic₆₁	C₂²×C₄	1	2	yes	—
198	#11758196	—	2	2	no	—
199	C₄×Dic₆₁	—	2	8	no	—
200	C₄×Dic₆₁	—	2	1	no	—
201	C₄×Dic₆₁	—	2	1	no	—
202	C₄×Dic₆₁	—	2	2	no	—
203	C₄×Dic₆₁	—	2	2	no	—
204	C₄×Dic₆₁	C₂²×C₄	1	2	yes	—
205	C₄×Dic₆₁	C₂²×C₄	1	2	yes	—
206	C₄×Dic₆₁	C₂×D₄	1	1	yes	characteristic
207	C₄×Dic₆₁	C₂×D₄	1	1	yes	characteristic
208	#11758194	—	2	1	no	—
209	#11758194	—	2	1	no	—
210	#11758194	—	2	4	no	—
211	#11758194	C₂²×C₄	1	2	yes	—
212	#11758194	C₂²×C₄	1	2	yes	—
213	C₂×#92418	—	2	1	no	—
214	C₂×#92418	—	2	1	no	—
215	C₂×#92418	—	2	4	no	—
216	C₂×#92418	C₂²×C₄	1	1	yes	characteristic
217	C₂×#92418	C₂²×C₄	1	1	yes	characteristic
218	C₂×#92418	C₂²×C₄	1	2	yes	—
219	C₂×#92418	C₂²×C₄	1	2	yes	—
220	C₂×#92418	C₂²×C₄	1	2	yes	—
221	C₂×#92418	C₂×D₄	1	1	yes	characteristic
222	C₂×#92418	C₂×D₄	1	1	yes	characteristic
223	C₂×#92418	#41	1	2	yes	—
224	#11758189	—	2	4	no	—
225	#11758189	—	2	4	no	—
226	C₈×D₆₁	—	2	4	no	—
227	C₈×D₆₁	—	2	4	no	—
228	C₂³×C₆₁	—	2	1	no	—
229	C₂³×C₆₁	C₂×#41	1	1	yes	characteristic
230	C₂²×D₆₁	—	2	1	no	—
231	Q₈×C₆₁	—	2	1	no	—
232	Q₈×C₆₁	C₂×C₄²	1	2	yes	—
233	D₄×C₆₁	—	2	2	no	—
234	D₄×C₆₁	—	2	2	no	—
235	D₄×C₆₁	—	2	1	no	—
236	D₄×C₆₁	C₂×C₄²	1	2	yes	—
237	C₂×C₄×C₆₁	—	2	4	no	—
238	C₂×C₄×C₆₁	—	2	1	no	—
239	C₂×C₄×C₆₁	—	2	2	no	—
240	C₂×C₄×C₆₁	—	2	2	no	—
241	C₂×C₄×C₆₁	—	2	2	no	—
242	C₂×C₄×C₆₁	—	2	2	no	—
243	C₂×C₄×C₆₁	C₂³×C₄	1	1	yes	characteristic
244	C₂×C₄×C₆₁	C₂³×C₄	1	1	yes	characteristic
245	C₂×C₄×C₆₁	C₂³×C₄	1	1	yes	characteristic
246	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
247	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
248	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
249	C₂²⋊D₆₁	—	2	2	no	—
250	C₂²⋊D₆₁	—	2	2	no	—
251	C₂×Dic₆₁	—	2	4	no	—
252	C₂×Dic₆₁	—	2	1	no	—
253	C₂×Dic₆₁	—	2	2	no	—
254	C₂×Dic₆₁	—	2	4	no	—
255	C₂×Dic₆₁	—	2	2	no	—
256	C₂×Dic₆₁	—	4	4	no	—
257	C₂×Dic₆₁	C₄×D₄	1	2	yes	—
258	C₂×Dic₆₁	C₄×D₄	1	2	yes	—
259	D₂₄₄	—	2	1	no	—
260	D₂₄₄	C₂×C₄²	1	2	yes	—
261	C₄×D₆₁	—	2	2	no	—
262	C₄×D₆₁	—	2	2	no	—
263	C₄×D₆₁	—	4	4	no	—
264	Dic₁₂₂	—	2	1	no	—
265	Dic₁₂₂	C₂×C₄²	1	2	yes	—
266	C₈×C₆₁	—	2	2	no	—
267	C₈×C₆₁	—	2	2	no	—
268	C₈×C₆₁	—	2	2	no	—
269	C₈×C₆₁	C₄×D₄	1	2	yes	—
270	C₈×C₆₁	C₄×D₄	1	2	yes	—
271	#92418	—	2	2	no	—
272	#92418	—	2	2	no	—
273	#92418	C₂×C₄²	1	2	yes	—
274	#92418	C₂×C₄²	1	2	yes	—
275	#92418	C₄×D₄	1	2	yes	—
276	#92418	C₄×D₄	1	2	yes	—
277	C₄×#443	—	61	1	no	maximal, Sylow
278	C₂²×C₆₁	—	2	2	no	—
279	C₂²×C₆₁	—	2	2	no	—
280	C₂²×C₆₁	—	4	2	no	—
281	C₂²×C₆₁	C₂×C₄×D₄	1	1	yes	characteristic
282	C₂²×C₆₁	C₄×#41	1	1	yes	characteristic
283	C₂²×C₆₁	C₄×#41	1	1	yes	characteristic
284	C₂×D₆₁	—	2	2	no	—
285	C₂×D₆₁	—	4	2	no	—
286	C₄×C₆₁	—	2	4	no	—
287	C₄×C₆₁	—	2	2	no	—
288	C₄×C₆₁	—	4	2	no	—
289	C₄×C₆₁	C₂²×C₄²	1	1	yes	characteristic
290	C₄×C₆₁	C₂×C₄×D₄	1	1	yes	characteristic
291	C₄×C₆₁	C₂×C₄×D₄	1	1	yes	characteristic
292	C₄×C₆₁	C₄×#41	1	1	yes	characteristic
293	Dic₆₁	—	2	4	no	—
294	Dic₆₁	—	2	2	no	—
295	Dic₆₁	—	2	2	no	—
296	Dic₆₁	—	4	2	no	—
297	Dic₆₁	#443	1	4	yes	complemented
298	C₂×#443	—	61	1	no	—
299	C₂×#443	—	61	1	no	—
300	C₄×#135	—	61	1	no	—
301	C₄×#131	—	61	1	no	—
302	C₄×#131	—	61	1	no	—
303	C₄×#108	—	61	1	no	—
304	#1772	—	61	1	no	—
305	#1772	—	61	1	no	—
306	#1764	—	61	1	no	—
307	#1764	—	61	1	no	—
308	#1764	—	61	1	no	—
309	#1764	D₆₁	1	1	yes	characteristic, complemented
310	C₄×#104	—	61	1	no	—
311	C₄×#104	—	61	1	no	—
312	C₄²×C₈	—	61	1	no	—
313	C₂×C₆₁	—	2	1	no	—
314	C₂×C₆₁	—	2	1	no	—
315	C₂×C₆₁	—	4	2	no	—
316	C₂×C₆₁	C₄²×D₄	1	1	yes	characteristic
317	C₂×C₆₁	C₂×#443	1	2	yes	—
318	D₆₁	—	4	2	no	—
319	C₂×#135	—	61	1	no	—
320	C₂×#131	—	61	1	no	—
321	C₂×#131	—	61	1	no	—
322	C₂×#131	—	61	1	no	—
323	C₂×#131	C₂×D₆₁	1	1	yes	characteristic
324	C₄×#41	—	61	1	no	—
325	C₄×#41	—	61	1	no	—
326	#443	—	61	8	no	—
327	#443	—	61	8	no	—
328	C₄×Q₁₆	—	61	2	no	—
329	C₄×SD₁₆	—	61	2	no	—
330	C₄×SD₁₆	—	61	2	no	—
331	C₄×D₈	—	61	2	no	—
332	C₂×#108	—	61	1	no	—
333	C₂×#108	—	61	1	no	—
334	#427	—	61	1	no	—
335	C₂×#104	—	61	1	no	—
336	C₂×#104	—	61	1	no	—
337	C₂×#104	—	61	1	no	—
338	C₂×#104	C₂×D₆₁	1	1	yes	characteristic
339	#416	—	61	1	no	—
340	#416	C₂×D₆₁	1	1	yes	characteristic
341	#405	—	61	1	no	—
342	#405	—	61	1	no	—
343	#405	—	61	1	no	—
344	#405	—	122	1	no	—
345	#405	—	122	1	no	—
346	#405	—	122	1	no	—
347	#405	—	122	1	no	—
348	#405	C₂×D₆₁	1	1	yes	characteristic
349	C₄×M₁₆	—	61	1	no	—
350	C₄×M₁₆	—	61	1	no	—
351	C₄×M₁₆	—	122	1	no	—
352	C₄×M₁₆	—	122	1	no	—
353	C₂×C₄×C₈	—	61	1	no	—
354	C₂×C₄×C₈	—	61	1	no	—
355	C₂×C₄×C₈	—	61	1	no	—
356	C₂×C₄×C₈	—	61	1	no	—
357	C₂×C₄×C₈	—	61	1	no	—
358	C₂×C₄×C₈	—	122	1	no	—
359	C₂×C₄×C₈	—	122	1	no	—
360	C₂×C₄×C₈	C₂×D₆₁	1	1	yes	characteristic
361	C₄³	—	61	1	no	—
362	#341	—	61	1	no	—
363	#341	C₂×D₆₁	1	1	yes	characteristic
364	#339	—	61	1	no	—
365	#339	—	61	1	no	—
366	#339	—	61	1	no	—
367	#339	C₂×D₆₁	1	1	yes	characteristic
368	C₆₁	C₄×#443	1	1	yes	characteristic, complemented, Sylow
369	C₂×#41	—	61	1	no	—
370	C₂×#41	C₂²×D₆₁	1	1	yes	characteristic
371	#135	—	61	4	no	—
372	#135	—	61	4	no	—
373	C₂×Q₁₆	—	61	1	no	—
374	C₂×SD₁₆	—	61	1	no	—
375	C₂×SD₁₆	—	61	1	no	—
376	C₂×D₈	—	61	1	no	—
377	#131	—	2	2	no	—
378	#131	—	61	4	no	—
379	#131	—	61	4	no	—
380	#131	—	61	4	no	—
381	#131	—	122	2	no	—
382	#131	—	122	2	no	—
383	#131	—	122	2	no	—
384	#131	C₄×D₆₁	1	4	yes	complemented
385	C₂×M₁₆	—	2	1	no	—
386	C₂×M₁₆	—	61	1	no	—
387	C₂×M₁₆	—	61	1	no	—
388	C₂×M₁₆	—	122	1	no	—
389	C₂×M₁₆	—	122	1	no	—
390	C₂×M₁₆	—	122	1	no	—
391	C₂×M₁₆	C₂²×D₆₁	1	1	yes	characteristic
392	C₂×M₁₆	C₂²×D₆₁	1	1	yes	characteristic
393	C₂²×C₈	—	2	1	no	—
394	C₂²×C₈	—	61	1	no	—
395	C₂²×C₈	—	61	1	no	—
396	C₂²×C₈	—	122	1	no	—
397	C₂²×C₈	—	122	1	no	—
398	C₂²×C₈	—	122	1	no	—
399	C₂²×C₈	C₂²×D₆₁	1	1	yes	characteristic
400	C₂²×C₈	C₂²×D₆₁	1	1	yes	characteristic
401	C₄×Q₈	—	61	2	no	—
402	C₄×Q₈	—	61	2	no	—
403	C₄×D₄	—	61	2	no	—
404	C₄×D₄	—	61	2	no	—
405	C₄×D₄	—	122	2	no	—
406	C₄×D₄	—	122	2	no	—
407	#117	—	61	1	no	—
408	#117	—	122	1	no	—
409	#117	—	122	1	no	—
410	#117	C₂²×D₆₁	1	1	yes	characteristic
411	C₂×C₄²	—	61	1	no	—
412	C₂×C₄²	—	61	1	no	—
413	C₂×C₄²	—	122	1	no	—
414	C₂×C₄²	—	122	1	no	—
415	C₂×C₄²	—	122	2	no	—
416	C₂×C₄²	C₂²×D₆₁	1	1	yes	characteristic
417	#108	—	61	4	no	—
418	#108	—	61	4	no	—
419	#107	—	61	2	no	—
420	#106	—	61	2	no	—
421	#104	—	61	4	no	—
422	#104	—	61	4	no	—
423	#104	—	61	4	no	—
424	#104	C₄×D₆₁	1	4	yes	complemented
425	#103	—	61	2	no	—
426	#103	C₄×D₆₁	1	2	yes	—
427	#102	—	61	2	no	—
428	#102	C₄×D₆₁	1	2	yes	—
429	#97	—	2	1	no	—
430	#97	—	122	1	no	—
431	#97	—	122	1	no	—
432	#97	—	122	1	no	—
433	#97	—	122	1	no	—
434	#97	—	122	1	no	—
435	C₄×C₈	—	2	1	no	—
436	C₄×C₈	—	2	2	no	—
437	C₄×C₈	—	61	2	no	—
438	C₄×C₈	—	61	2	no	—
439	C₄×C₈	—	61	4	no	—
440	C₄×C₈	—	61	1	no	—
441	C₄×C₈	—	61	1	no	—
442	C₄×C₈	—	61	1	no	—
443	C₄×C₈	—	61	1	no	—
444	C₄×C₈	—	61	4	no	—
445	C₄×C₈	—	122	1	no	—
446	C₄×C₈	—	122	1	no	—
447	C₄×C₈	—	122	1	no	—
448	C₄×C₈	—	122	2	no	—
449	C₄×C₈	—	122	1	no	—
450	C₄×C₈	—	122	1	no	—
451	#41	—	2	1	no	—
452	#41	—	2	1	no	—
453	#41	—	61	2	no	—
454	#41	—	61	2	no	—
455	#41	—	122	1	no	—
456	#41	—	122	1	no	—
457	#41	C₂×C₄×D₆₁	1	2	yes	—
458	#41	C₂×C₄×D₆₁	1	2	yes	—
459	C₂×Q₈	—	61	1	no	—
460	C₂×Q₈	C₂×C₄×D₆₁	1	1	yes	characteristic
461	C₂×D₄	—	2	1	no	—
462	C₂×D₄	—	61	1	no	—
463	C₂×D₄	—	122	1	no	—
464	C₂×D₄	C₂×C₄×D₆₁	1	1	yes	characteristic
465	C₂²×C₄	—	2	1	no	—
466	C₂²×C₄	—	2	1	no	—
467	C₂²×C₄	—	61	2	no	—
468	C₂²×C₄	—	122	2	no	—
469	C₂²×C₄	—	122	2	no	—
470	C₂²×C₄	—	122	1	no	—
471	C₂²×C₄	—	122	1	no	—
472	C₂²×C₄	C₂³×D₆₁	1	1	yes	characteristic
473	Q₁₆	—	61	4	no	—
474	SD₁₆	—	61	4	no	—
475	SD₁₆	—	61	4	no	—
476	D₈	—	61	4	no	—
477	M₁₆	—	2	1	no	—
478	M₁₆	—	2	1	no	—
479	M₁₆	—	2	4	no	—
480	M₁₆	—	61	2	no	—
481	M₁₆	—	61	2	no	—
482	M₁₆	—	122	4	no	—
483	M₁₆	—	122	4	no	—
484	M₁₆	—	122	1	no	—
485	M₁₆	—	122	1	no	—
486	M₁₆	—	122	4	no	—
487	M₁₆	C₂×C₄×D₆₁	1	2	yes	—
488	M₁₆	C₂×C₄×D₆₁	1	2	yes	—
489	C₂×C₈	—	2	1	no	—
490	C₂×C₈	—	2	1	no	—
491	C₂×C₈	—	2	1	no	—
492	C₂×C₈	—	2	1	no	—
493	C₂×C₈	—	2	4	no	—
494	C₂×C₈	—	61	1	no	—
495	C₂×C₈	—	61	1	no	—
496	C₂×C₈	—	61	2	no	—
497	C₂×C₈	—	61	2	no	—
498	C₂×C₈	—	61	2	no	—
499	C₂×C₈	—	61	1	no	—
500	C₂×C₈	—	61	1	no	—
501	C₂×C₈	—	61	2	no	—
502	C₂×C₈	—	122	4	no	—
503	C₂×C₈	—	122	4	no	—
504	C₂×C₈	—	122	1	no	—
505	C₂×C₈	—	122	1	no	—
506	C₂×C₈	—	122	4	no	—
507	C₂×C₈	C₂×C₄×D₆₁	1	2	yes	—
508	C₂×C₈	C₂×C₄×D₆₁	1	2	yes	—
509	C₂×C₈	D₄×D₆₁	1	1	yes	characteristic
510	C₂×C₈	D₄×D₆₁	1	1	yes	characteristic
511	C₂×C₈	#11758224	1	2	yes	—
512	C₄⋊C₄	—	61	2	no	—
513	C₄⋊C₄	—	122	2	no	—
514	C₄⋊C₄	—	122	2	no	—
515	C₄⋊C₄	C₂×C₄×D₆₁	1	2	yes	—
516	C₂²⋊C₄	—	2	1	no	—
517	C₂²⋊C₄	—	122	2	no	—
518	C₂²⋊C₄	—	122	2	no	—
519	C₂²⋊C₄	—	122	1	no	—
520	C₄²	—	2	1	no	—
521	C₄²	—	2	1	no	—
522	C₄²	—	61	2	no	—
523	C₄²	—	61	1	no	—
524	C₄²	—	61	1	no	—
525	C₄²	—	61	2	no	—
526	C₄²	—	122	2	no	—
527	C₄²	—	122	2	no	—
528	C₄²	—	122	8	no	—
529	C₄²	—	122	1	no	—
530	C₄²	—	122	1	no	—
531	C₄²	C₂×C₄×D₆₁	1	2	yes	—
532	C₂³	—	2	1	no	—
533	C₂³	—	122	1	no	—
534	C₂³	#41×D₆₁	1	1	yes	characteristic
535	Q₈	—	2	1	no	—
536	Q₈	—	61	2	no	—
537	Q₈	—	122	1	no	—
538	Q₈	C₄²×D₆₁	1	2	yes	—
539	D₄	—	2	2	no	—
540	D₄	—	2	2	no	—
541	D₄	—	2	1	no	—
542	D₄	—	61	2	no	—
543	D₄	—	122	2	no	—
544	D₄	—	122	2	no	—
545	D₄	—	122	1	no	—
546	D₄	C₄²×D₆₁	1	2	yes	—
547	C₂×C₄	—	2	4	no	—
548	C₂×C₄	—	2	1	no	—
549	C₂×C₄	—	2	2	no	—
550	C₂×C₄	—	2	2	no	—
551	C₂×C₄	—	2	2	no	—
552	C₂×C₄	—	2	2	no	—
553	C₂×C₄	—	61	2	no	—
554	C₂×C₄	—	61	2	no	—
555	C₂×C₄	—	122	4	no	—
556	C₂×C₄	—	122	4	no	—
557	C₂×C₄	—	122	1	no	—
558	C₂×C₄	—	122	2	no	—
559	C₂×C₄	—	122	2	no	—
560	C₂×C₄	—	122	2	no	—
561	C₂×C₄	—	122	2	no	—
562	C₂×C₄	—	244	4	no	—
563	C₂×C₄	—	244	4	no	—
564	C₂×C₄	C₂²×C₄×D₆₁	1	1	yes	characteristic
565	C₂×C₄	C₂²×C₄×D₆₁	1	1	yes	characteristic
566	C₂×C₄	C₂²×C₄×D₆₁	1	1	yes	characteristic
567	C₂×C₄	C₂×D₄×D₆₁	1	1	yes	characteristic
568	C₂×C₄	#41×D₆₁	1	1	yes	characteristic
569	C₂×C₄	C₂×#11758224	1	1	yes	characteristic
570	C₈	—	2	2	no	—
571	C₈	—	2	2	no	—
572	C₈	—	2	2	no	—
573	C₈	—	61	2	no	—
574	C₈	—	61	2	no	—
575	C₈	—	61	2	no	—
576	C₈	—	61	2	no	—
577	C₈	—	122	2	no	—
578	C₈	—	122	2	no	—
579	C₈	#14519737	1	2	yes	—
580	C₈	#14519737	1	2	yes	—
581	C₂²	—	2	2	no	—
582	C₂²	—	2	2	no	—
583	C₂²	—	4	2	no	—
584	C₂²	—	122	2	no	—
585	C₂²	—	244	2	no	—
586	C₂²	C₄×D₄×D₆₁	1	1	yes	characteristic
587	C₂²	C₄×#11758224	1	1	yes	characteristic
588	C₂²	#16840230	1	1	yes	characteristic
589	C₄	—	2	4	no	—
590	C₄	—	2	2	no	—
591	C₄	—	4	2	no	—
592	C₄	—	61	4	no	—
593	C₄	—	122	4	no	—
594	C₄	—	122	2	no	—
595	C₄	—	122	2	no	—
596	C₄	—	244	2	no	—
597	C₄	C₂×C₄²×D₆₁	1	1	yes	characteristic
598	C₄	C₄×D₄×D₆₁	1	1	yes	characteristic
599	C₄	C₂×#14519737	1	1	yes	characteristic
600	C₄	C₄×#11758224	1	1	yes	characteristic
601	C₂	—	2	1	no	—
602	C₂	—	2	1	no	—
603	C₂	—	4	2	no	—
604	C₂	—	244	2	no	—
605	C₂	C₄×#14519737	1	1	yes	characteristic
606	C₂	#443×D₆₁	1	2	yes	—

	subgroup	G/H
center	C₂×C₈	D₄×D₆₁
commutator	C₄×C₆₁	C₂²×C₄²
Frattini	C₂²×C₄	C₂³×D₆₁
Fitting	C₆₁×#1764	C₂
socle	C₂²×C₆₁	C₂×C₄×D₄
prime radical	C₂×#14519797	C₂²
cosocle	C₂²×C₄×C₆₁	C₂⁴
hypercenter	#1764	D₆₁
hypocenter	C₆₁	C₄×#443
LCS	G ▷ C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂×C₈ ◁ C₂²×C₈ ◁ #1764

Complements

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

N	H ≅ G/N	type
4. #21454241	C₂	semidirect
5. #131×Dic₆₁	C₂	semidirect
6. #21445720	C₂	semidirect
7. #21445699	C₂	semidirect
8. #21445697	C₂	semidirect
9. #21445659	C₂	semidirect
10. #21445656	C₂	semidirect
11. #21445655	C₂	semidirect
12. #104×Dic₆₁	C₂	semidirect
13. #21445623	C₂	semidirect
14. C₄×C₈×Dic₆₁	C₂	semidirect
15. C₆₁×#1764	C₂	semidirect
22. #16839877	C₄	semidirect
23. #16839876	C₄	semidirect
24. #16839854	C₄	semidirect
25. #16839853	C₄	semidirect
26. #16839847	C₄	semidirect
27. #16839842	C₄	semidirect
73. #14519785	C₂×C₄	semidirect
75. #14519784	C₂×C₄	semidirect
77. #14519783	C₂×C₄	semidirect
102. #14519712	C₂×C₄	semidirect
103. #14519712	C₂×C₄	semidirect
106. #14519705	C₂×C₄	semidirect
107. #14519704	C₂×C₄	semidirect
108. #14519703	C₂×C₄	semidirect
117. C₄×#92418	C₂×C₄	semidirect
125. C₈×Dic₆₁	C₂×C₄	semidirect
132. #131×C₆₁	C₂×C₄	semidirect
141. #104×C₆₁	C₂×C₄	semidirect
191. #11758202	C₄²	semidirect
192. #11758201	C₄²	semidirect
193. #11758200	C₄²	semidirect
194. #11758199	C₄²	semidirect
297. Dic₆₁	#443	semidirect
309. #1764	D₆₁	semidirect
368. C₆₁	C₄×#443	semidirect
384. #131	C₄×D₆₁	semidirect
424. #104	C₄×D₆₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×#16839877	2
C₂×#16839876	2
#21454587	2
#21454241	2
#131×Dic₆₁	2
#21445720	2
#21445699	2
#21445697	2
#21445659	2
#21445656	2
#21445655	2
#104×Dic₆₁	2
#21445623	2
C₄×C₈×Dic₆₁	2
C₆₁×#1764	2
C₄×#443	61