Subgroups — #29648833

Order 15616.

918 conjugacy classes of subgroups.

The subgroup lattice has 732 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#21454936	C₂	1	1	yes	maximal, characteristic, complemented
2	#21454485	C₂	1	1	yes	maximal, characteristic, complemented
3	#21444554	C₂	1	1	yes	maximal, characteristic, complemented
4	#21444549	C₂	1	1	yes	maximal, characteristic, complemented
5	#21444545	C₂	1	1	yes	maximal, characteristic, complemented
6	#21444541	C₂	1	1	yes	maximal, characteristic, complemented
7	#21444529	C₂	1	1	yes	maximal, characteristic, complemented
8	#21444524	C₂	1	1	yes	maximal, characteristic, complemented
9	#21444514	C₂	1	1	yes	maximal, characteristic, complemented
10	#21444514	C₂	1	1	yes	maximal, characteristic, complemented
11	#21444509	C₂	1	1	yes	maximal, characteristic, complemented
12	#21444500	C₂	1	1	yes	maximal, characteristic, complemented
13	#21444481	C₂	1	1	yes	maximal, characteristic, complemented
14	#21444476	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₁×#3511	C₂	1	1	yes	maximal, characteristic
16	#16839893	—	2	1	no	—
17	#16839840	—	2	1	no	—
18	#16839834	—	2	1	no	—
19	#16839834	—	2	1	no	—
20	#16839823	—	2	1	no	—
21	#16839823	—	2	1	no	—
22	#16839819	C₂²	1	1	yes	characteristic
23	#16839819	C₂²	1	1	yes	characteristic
24	#16839819	C₂²	1	1	yes	characteristic
25	#16839819	C₂²	1	1	yes	characteristic
26	#16839815	C₂²	1	1	yes	characteristic
27	#16839815	C₂²	1	1	yes	characteristic
28	#16839815	C₂²	1	1	yes	characteristic
29	#16839786	C₂²	1	1	yes	characteristic
30	#16839786	C₂²	1	1	yes	characteristic
31	#16839786	C₂²	1	1	yes	characteristic
32	C₂×C₄⋊#92418	C₂²	1	1	yes	characteristic
33	C₂×C₄⋊#92418	C₂²	1	1	yes	characteristic
34	#16839729	—	2	1	no	—
35	#16839718	—	2	1	no	—
36	#16839511	C₂²	1	1	yes	characteristic
37	#16839511	C₂²	1	1	yes	characteristic
38	#16839511	C₂²	1	1	yes	characteristic
39	#16839511	C₂²	1	1	yes	characteristic
40	#16839511	C₂²	1	1	yes	characteristic
41	#16839511	C₂²	1	1	yes	characteristic
42	#16839511	C₂²	1	1	yes	characteristic
43	#16839511	C₂²	1	1	yes	characteristic
44	#16839508	C₂²	1	1	yes	characteristic
45	#16839508	C₂²	1	1	yes	characteristic
46	#16839508	C₂²	1	1	yes	characteristic
47	#16839508	C₂²	1	1	yes	characteristic
48	#16839506	C₂²	1	1	yes	characteristic
49	#16839506	C₂²	1	1	yes	characteristic
50	#16839506	C₂²	1	1	yes	characteristic
51	#16839506	C₂²	1	1	yes	characteristic
52	C₆₁×#556	C₄	1	2	yes	—
53	C₆₁×#555	—	2	1	no	—
54	C₆₁×#554	—	2	1	no	—
55	C₆₁×#553	—	2	1	no	—
56	C₆₁×#553	—	2	1	no	—
57	C₆₁×#548	C₄	1	2	yes	—
58	C₆₁×#548	C₄	1	2	yes	—
59	C₆₁×#547	C₄	1	2	yes	—
60	C₆₁×#542	—	2	1	no	—
61	C₆₁×#542	—	2	1	no	—
62	C₆₁×#537	—	2	1	no	—
63	C₆₁×#533	C₂²	1	1	yes	characteristic
64	C₆₁×#533	C₂²	1	1	yes	characteristic
65	C₆₁×#532	C₂²	1	1	yes	characteristic
66	C₆₁×#532	C₂²	1	1	yes	characteristic
67	C₆₁×#532	C₂²	1	1	yes	characteristic
68	C₂×C₄⋊Q₈×C₆₁	C₂²	1	1	yes	characteristic
69	C₆₁×#520	—	2	1	no	—
70	C₄×#41×C₆₁	C₂²	1	1	yes	characteristic
71	C₂×#11758194	—	2	1	no	—
72	C₂×#11758194	—	2	1	no	—
73	C₂×#11758194	—	2	1	no	—
74	C₂²×#92418	—	2	1	no	—
75	C₂²×#92418	—	2	1	no	—
76	C₄⋊#92418	—	2	1	no	—
77	C₄⋊#92418	—	2	1	no	—
78	C₄⋊#92418	—	2	1	no	—
79	C₄⋊#92418	—	2	1	no	—
80	C₄⋊#92418	—	2	1	no	—
81	C₄⋊#92418	C₂³	1	1	yes	characteristic
82	C₄⋊#92418	C₂³	1	1	yes	characteristic
83	C₄⋊#92418	C₂³	1	1	yes	characteristic
84	C₄⋊#92418	C₂³	1	1	yes	characteristic
85	C₄⋊#92418	C₂³	1	1	yes	characteristic
86	C₄⋊#92418	C₂³	1	1	yes	characteristic
87	C₄⋊#92418	C₂³	1	1	yes	characteristic
88	C₄⋊#92418	C₂³	1	1	yes	characteristic
89	C₂²⋊#92418	—	2	1	no	—
90	C₂²⋊#92418	—	2	1	no	—
91	C₂²⋊#92418	—	2	1	no	—
92	C₂²⋊#92418	—	2	1	no	—
93	C₂²⋊#92418	—	2	1	no	—
94	C₂²⋊#92418	—	2	1	no	—
95	C₂²⋊#92418	—	2	1	no	—
96	#14519688	—	2	1	no	—
97	#14519688	—	2	1	no	—
98	#14519688	—	2	1	no	—
99	#14519688	—	2	1	no	—
100	C₄×#92418	—	2	1	no	—
101	C₄×#92418	—	2	1	no	—
102	C₄×#92418	—	2	1	no	—
103	C₂×#41×C₆₁	—	2	1	no	—
104	C₂×#41×C₆₁	C₂×C₄	1	2	yes	—
105	C₂×#41×C₆₁	C₂×C₄	1	2	yes	—
106	C₂×#41×C₆₁	D₄	1	1	yes	characteristic
107	C₂²×Q₈×C₆₁	C₂×C₄	1	2	yes	—
108	C₄⋊Q₈×C₆₁	—	2	1	no	—
109	C₄⋊Q₈×C₆₁	—	2	1	no	—
110	C₄⋊Q₈×C₆₁	C₂×C₄	1	2	yes	—
111	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
112	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
113	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
114	#127×C₆₁	C₂³	1	1	yes	characteristic
115	#126×C₆₁	—	2	2	no	—
116	#126×C₆₁	—	2	2	no	—
117	#125×C₆₁	—	2	1	no	—
118	#125×C₆₁	—	2	1	no	—
119	#124×C₆₁	—	2	2	no	—
120	#124×C₆₁	—	2	2	no	—
121	#124×C₆₁	—	2	1	no	—
122	#124×C₆₁	C₂×C₄	1	2	yes	—
123	#124×C₆₁	C₂×C₄	1	2	yes	—
124	#123×C₆₁	—	2	2	no	—
125	#123×C₆₁	—	2	2	no	—
126	C₂²⋊Q₈×C₆₁	—	2	2	no	—
127	C₂²⋊Q₈×C₆₁	—	2	1	no	—
128	C₂²⋊Q₈×C₆₁	—	2	1	no	—
129	C₂²⋊Q₈×C₆₁	—	2	2	no	—
130	C₂²⋊Q₈×C₆₁	—	2	2	no	—
131	C₂²⋊Q₈×C₆₁	C₂×C₄	1	2	yes	—
132	C₂²⋊Q₈×C₆₁	C₂×C₄	1	2	yes	—
133	#121×C₆₁	—	2	2	no	—
134	#121×C₆₁	—	2	2	no	—
135	#121×C₆₁	—	2	2	no	—
136	#121×C₆₁	—	2	1	no	—
137	#121×C₆₁	—	2	1	no	—
138	#121×C₆₁	—	2	1	no	—
139	#121×C₆₁	—	2	1	no	—
140	#121×C₆₁	—	2	1	no	—
141	#121×C₆₁	C₂×C₄	1	2	yes	—
142	C₄×Q₈×C₆₁	—	2	1	no	—
143	C₄×Q₈×C₆₁	—	2	1	no	—
144	C₄×Q₈×C₆₁	C₂×C₄	1	2	yes	—
145	C₄×Q₈×C₆₁	C₂×C₄	1	2	yes	—
146	C₄×Q₈×C₆₁	C₂×C₄	1	1	yes	characteristic
147	C₄×Q₈×C₆₁	D₄	1	1	yes	characteristic
148	C₄×D₄×C₆₁	—	2	2	no	—
149	C₄×D₄×C₆₁	—	2	2	no	—
150	C₄×D₄×C₆₁	—	2	1	no	—
151	C₄×D₄×C₆₁	—	2	1	no	—
152	C₄×D₄×C₆₁	—	2	1	no	—
153	C₄×D₄×C₆₁	—	2	1	no	—
154	C₄×D₄×C₆₁	—	2	1	no	—
155	C₄×D₄×C₆₁	C₂×C₄	1	2	yes	—
156	C₄×D₄×C₆₁	C₂×C₄	1	1	yes	characteristic
157	C₄×D₄×C₆₁	C₂×C₄	1	1	yes	characteristic
158	C₄×D₄×C₆₁	C₂×C₄	1	1	yes	characteristic
159	C₄×D₄×C₆₁	D₄	1	1	yes	characteristic
160	C₄×D₄×C₆₁	D₄	1	1	yes	characteristic
161	C₄×D₄×C₆₁	D₄	1	1	yes	characteristic
162	#117×C₆₁	—	2	1	no	—
163	#117×C₆₁	—	2	1	no	—
164	#117×C₆₁	—	2	2	no	—
165	#117×C₆₁	D₄	1	1	yes	characteristic
166	#117×C₆₁	D₄	1	1	yes	characteristic
167	#117×C₆₁	D₄	1	1	yes	characteristic
168	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
169	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
170	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
171	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
172	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
173	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
174	#41×C₆₁	—	4	1	no	—
175	#41×C₆₁	—	4	1	no	—
176	#41×C₆₁	—	4	2	no	—
177	#41×C₆₁	—	4	2	no	—
178	#41×C₆₁	—	8	2	no	—
179	#41×C₆₁	—	8	2	no	—
180	C₂×Q₈×C₆₁	—	2	2	no	—
181	C₂×Q₈×C₆₁	—	2	1	no	—
182	C₂×Q₈×C₆₁	—	8	2	no	—
183	C₂×Q₈×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
184	C₂×Q₈×C₆₁	C₂²×C₄	1	2	yes	—
185	C₂×Q₈×C₆₁	C₂²×C₄	1	2	yes	—
186	C₂×D₄×C₆₁	—	2	2	no	—
187	C₂×D₄×C₆₁	—	2	2	no	—
188	C₂×D₄×C₆₁	—	2	2	no	—
189	C₂×D₄×C₆₁	—	2	1	no	—
190	C₂×D₄×C₆₁	—	2	1	no	—
191	C₂×D₄×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
192	C₂×D₄×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
193	C₂×D₄×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
194	C₂×D₄×C₆₁	C₂²×C₄	1	2	yes	—
195	C₂²×C₄×C₆₁	—	2	2	no	—
196	C₂²×C₄×C₆₁	—	2	2	no	—
197	C₂²×C₄×C₆₁	—	2	2	no	—
198	C₂²×C₄×C₆₁	—	2	2	no	—
199	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
200	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
201	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
202	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
203	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
204	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
205	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
206	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
207	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
208	C₄⋊C₄×C₆₁	—	2	2	no	—
209	C₄⋊C₄×C₆₁	—	2	2	no	—
210	C₄⋊C₄×C₆₁	—	2	2	no	—
211	C₄⋊C₄×C₆₁	—	2	2	no	—
212	C₄⋊C₄×C₆₁	—	2	2	no	—
213	C₄⋊C₄×C₆₁	—	2	2	no	—
214	C₄⋊C₄×C₆₁	—	2	1	no	—
215	C₄⋊C₄×C₆₁	—	2	1	no	—
216	C₄⋊C₄×C₆₁	—	2	1	no	—
217	C₄⋊C₄×C₆₁	—	2	1	no	—
218	C₄⋊C₄×C₆₁	—	2	1	no	—
219	C₄⋊C₄×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
220	C₄⋊C₄×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
221	C₄⋊C₄×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
222	C₄⋊C₄×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
223	C₄⋊C₄×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
224	C₄⋊C₄×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
225	C₄⋊C₄×C₆₁	C₂²×C₄	1	2	yes	—
226	C₂²⋊C₄×C₆₁	—	2	2	no	—
227	C₂²⋊C₄×C₆₁	—	2	2	no	—
228	C₂²⋊C₄×C₆₁	—	2	2	no	—
229	C₂²⋊C₄×C₆₁	—	2	2	no	—
230	C₂²⋊C₄×C₆₁	—	2	2	no	—
231	C₂²⋊C₄×C₆₁	—	2	2	no	—
232	C₂²⋊C₄×C₆₁	—	2	2	no	—
233	C₂²⋊C₄×C₆₁	—	2	2	no	—
234	C₂²⋊C₄×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
235	C₂²⋊C₄×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
236	C₂²⋊C₄×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
237	C₂²⋊C₄×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
238	C₂²⋊C₄×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
239	C₂²⋊C₄×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
240	C₄²×C₆₁	—	2	2	no	—
241	C₄²×C₆₁	—	2	2	no	—
242	C₄²×C₆₁	C₂²×C₄	1	1	yes	characteristic
243	C₄²×C₆₁	C₂²×C₄	1	1	yes	characteristic
244	C₄²×C₆₁	C₂²×C₄	1	1	yes	characteristic
245	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
246	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
247	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
248	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
249	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
250	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
251	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
252	#11758194	—	4	2	no	—
253	#11758194	—	8	1	no	—
254	#11758194	—	8	1	no	—
255	C₂×#92418	—	2	1	no	—
256	C₂×#92418	—	2	1	no	—
257	C₂×#92418	—	2	1	no	—
258	C₂×#92418	—	2	1	no	—
259	C₂×#92418	—	2	1	no	—
260	C₂×#92418	—	2	1	no	—
261	C₂×#92418	—	2	1	no	—
262	C₂×#92418	—	2	1	no	—
263	C₂×#92418	—	4	2	no	—
264	C₂×#92418	—	8	1	no	—
265	C₂³×C₆₁	—	2	2	no	—
266	C₂³×C₆₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
267	C₂³×C₆₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
268	C₂³×C₆₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
269	Q₈×C₆₁	—	4	1	no	—
270	Q₈×C₆₁	—	4	2	no	—
271	Q₈×C₆₁	—	4	2	no	—
272	Q₈×C₆₁	—	4	1	no	—
273	Q₈×C₆₁	—	4	1	no	—
274	Q₈×C₆₁	—	8	2	no	—
275	D₄×C₆₁	—	4	1	no	—
276	D₄×C₆₁	—	4	1	no	—
277	D₄×C₆₁	—	4	1	no	—
278	D₄×C₆₁	—	4	2	no	—
279	D₄×C₆₁	—	4	4	no	—
280	D₄×C₆₁	—	4	1	no	—
281	D₄×C₆₁	—	4	1	no	—
282	D₄×C₆₁	—	4	1	no	—
283	D₄×C₆₁	—	4	1	no	—
284	D₄×C₆₁	—	8	2	no	—
285	D₄×C₆₁	—	8	2	no	—
286	C₂×C₄×C₆₁	—	2	1	no	—
287	C₂×C₄×C₆₁	—	2	1	no	—
288	C₂×C₄×C₆₁	—	2	1	no	—
289	C₂×C₄×C₆₁	—	2	1	no	—
290	C₂×C₄×C₆₁	—	2	1	no	—
291	C₂×C₄×C₆₁	—	2	1	no	—
292	C₂×C₄×C₆₁	—	2	1	no	—
293	C₂×C₄×C₆₁	—	2	1	no	—
294	C₂×C₄×C₆₁	—	2	1	no	—
295	C₂×C₄×C₆₁	—	2	1	no	—
296	C₂×C₄×C₆₁	—	2	1	no	—
297	C₂×C₄×C₆₁	—	2	1	no	—
298	C₂×C₄×C₆₁	—	2	2	no	—
299	C₂×C₄×C₆₁	—	2	2	no	—
300	C₂×C₄×C₆₁	—	2	2	no	—
301	C₂×C₄×C₆₁	—	4	1	no	—
302	C₂×C₄×C₆₁	—	4	1	no	—
303	C₂×C₄×C₆₁	—	4	1	no	—
304	C₂×C₄×C₆₁	—	4	4	no	—
305	C₂×C₄×C₆₁	—	8	2	no	—
306	C₂×C₄×C₆₁	—	8	2	no	—
307	C₂×C₄×C₆₁	—	8	2	no	—
308	C₂×C₄×C₆₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
309	C₂×C₄×C₆₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
310	C₂×C₄×C₆₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
311	C₂×C₄×C₆₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
312	C₂×C₄×C₆₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
313	C₂×C₄×C₆₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
314	C₂×C₄×C₆₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
315	C₂×C₄×C₆₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
316	C₂×C₄×C₆₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
317	C₂×C₄×C₆₁	C₂³×C₄	1	1	yes	characteristic
318	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
319	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
320	#92418	—	4	1	no	—
321	#92418	—	4	1	no	—
322	#92418	—	4	1	no	—
323	#92418	—	4	1	no	—
324	#92418	—	4	1	no	—
325	#92418	—	4	1	no	—
326	#92418	—	4	1	no	—
327	#92418	—	4	1	no	—
328	#17768	—	61	1	no	maximal, Sylow
329	C₂²×C₆₁	—	2	1	no	—
330	C₂²×C₆₁	—	2	1	no	—
331	C₂²×C₆₁	—	2	1	no	—
332	C₂²×C₆₁	—	2	1	no	—
333	C₂²×C₆₁	—	2	1	no	—
334	C₂²×C₆₁	—	2	1	no	—
335	C₂²×C₆₁	—	2	1	no	—
336	C₂²×C₆₁	—	2	1	no	—
337	C₂²×C₆₁	—	2	1	no	—
338	C₂²×C₆₁	—	4	2	no	—
339	C₂²×C₆₁	—	4	2	no	—
340	C₂²×C₆₁	—	4	2	no	—
341	C₂²×C₆₁	C₂²×C₂²⋊C₄	1	1	yes	characteristic
342	C₄×C₆₁	—	2	1	no	—
343	C₄×C₆₁	—	2	1	no	—
344	C₄×C₆₁	—	2	1	no	—
345	C₄×C₆₁	—	2	1	no	—
346	C₄×C₆₁	—	2	1	no	—
347	C₄×C₆₁	—	2	1	no	—
348	C₄×C₆₁	—	2	1	no	—
349	C₄×C₆₁	—	2	1	no	—
350	C₄×C₆₁	—	2	1	no	—
351	C₄×C₆₁	—	2	1	no	—
352	C₄×C₆₁	—	4	2	no	—
353	C₄×C₆₁	—	4	2	no	—
354	C₄×C₆₁	—	4	2	no	—
355	C₄×C₆₁	#575	1	1	yes	characteristic
356	C₄×C₆₁	#575	1	1	yes	characteristic
357	C₄×C₆₁	#577	1	1	yes	characteristic
358	C₄×C₆₁	#578	1	1	yes	characteristic
359	#3511	D₆₁	1	1	yes	characteristic
360	#2989	—	61	1	no	—
361	#2925	—	61	1	no	—
362	#1560	—	61	1	no	—
363	#1559	—	61	1	no	—
364	#1558	—	61	1	no	—
365	#1557	—	61	1	no	—
366	#1554	—	61	1	no	—
367	#1553	—	61	1	no	—
368	#1551	—	61	1	no	—
369	#1551	—	61	1	no	—
370	#1550	—	61	1	no	—
371	#1548	—	61	1	no	—
372	#1543	—	61	1	no	—
373	#1542	—	61	1	no	—
374	C₂×C₆₁	—	4	1	no	—
375	C₂×C₆₁	—	4	1	no	—
376	C₂×C₆₁	—	4	1	no	—
377	C₂×C₆₁	—	8	2	no	—
378	C₂×C₆₁	#2888	1	1	yes	characteristic
379	C₂×C₆₁	#2896	1	1	yes	characteristic
380	C₂×C₆₁	#2898	1	1	yes	characteristic
381	#556	Dic₆₁	1	2	yes	—
382	#555	—	2	1	no	—
383	#554	—	2	1	no	—
384	#553	—	2	1	no	—
385	#553	—	2	1	no	—
386	#548	Dic₆₁	1	2	yes	—
387	#548	Dic₆₁	1	2	yes	—
388	#547	Dic₆₁	1	2	yes	—
389	#542	—	2	1	no	—
390	#542	—	2	1	no	—
391	#537	—	2	1	no	—
392	#533	C₂×D₆₁	1	1	yes	characteristic
393	#533	C₂×D₆₁	1	1	yes	characteristic
394	#532	C₂×D₆₁	1	1	yes	characteristic
395	#532	C₂×D₆₁	1	1	yes	characteristic
396	#532	C₂×D₆₁	1	1	yes	characteristic
397	C₂×C₄⋊Q₈	C₂×D₆₁	1	1	yes	characteristic
398	#520	—	2	1	no	—
399	C₄×#41	C₂×D₆₁	1	1	yes	characteristic
400	#446	—	122	1	no	—
401	#436	—	122	1	no	—
402	#435	—	122	1	no	—
403	#435	—	122	1	no	—
404	#433	—	122	1	no	—
405	#433	—	122	1	no	—
406	#432	—	61	1	no	—
407	#432	—	61	1	no	—
408	#432	—	61	1	no	—
409	#432	—	61	1	no	—
410	#431	—	61	1	no	—
411	#431	—	61	1	no	—
412	#431	—	61	1	no	—
413	#423	—	61	1	no	—
414	#423	—	61	1	no	—
415	#423	—	61	1	no	—
416	C₂×C₄⋊C₈	—	61	1	no	—
417	C₂×C₄⋊C₈	—	61	1	no	—
418	#408	—	122	1	no	—
419	#405	—	122	1	no	—
420	#333	—	61	1	no	—
421	#333	—	61	1	no	—
422	#333	—	61	1	no	—
423	#333	—	61	1	no	—
424	#333	—	61	1	no	—
425	#333	—	61	1	no	—
426	#333	—	61	1	no	—
427	#333	—	61	1	no	—
428	#332	—	61	1	no	—
429	#332	—	61	1	no	—
430	#332	—	61	1	no	—
431	#332	—	61	1	no	—
432	#331	—	61	1	no	—
433	#331	—	61	1	no	—
434	#331	—	61	1	no	—
435	#331	—	61	1	no	—
436	C₆₁	#17768	1	1	yes	characteristic, complemented, Sylow
437	C₂×#41	—	2	1	no	—
438	C₂×#41	C₂×Dic₆₁	1	2	yes	—
439	C₂×#41	C₂×Dic₆₁	1	2	yes	—
440	C₂×#41	C₂²⋊D₆₁	1	1	yes	characteristic
441	C₂²×Q₈	C₂×Dic₆₁	1	2	yes	—
442	C₂×M₁₆	—	122	1	no	—
443	C₂×M₁₆	—	122	1	no	—
444	C₂×M₁₆	—	122	1	no	—
445	C₂²×C₈	—	122	1	no	—
446	C₂²×C₈	—	122	1	no	—
447	C₄⋊Q₈	—	2	1	no	—
448	C₄⋊Q₈	—	2	1	no	—
449	C₄⋊Q₈	C₂×Dic₆₁	1	2	yes	—
450	C₄⋊Q₈	C₂²×D₆₁	1	1	yes	characteristic
451	C₄⋊Q₈	C₂²×D₆₁	1	1	yes	characteristic
452	C₄⋊Q₈	C₂²×D₆₁	1	1	yes	characteristic
453	#127	C₂²×D₆₁	1	1	yes	characteristic
454	#126	—	2	2	no	—
455	#126	—	2	2	no	—
456	#125	—	2	1	no	—
457	#125	—	2	1	no	—
458	#124	—	2	2	no	—
459	#124	—	2	2	no	—
460	#124	—	2	1	no	—
461	#124	C₂×Dic₆₁	1	2	yes	—
462	#124	C₂×Dic₆₁	1	2	yes	—
463	#123	—	2	2	no	—
464	#123	—	2	2	no	—
465	C₂²⋊Q₈	—	2	2	no	—
466	C₂²⋊Q₈	—	2	1	no	—
467	C₂²⋊Q₈	—	2	1	no	—
468	C₂²⋊Q₈	—	2	2	no	—
469	C₂²⋊Q₈	—	2	2	no	—
470	C₂²⋊Q₈	C₂×Dic₆₁	1	2	yes	—
471	C₂²⋊Q₈	C₂×Dic₆₁	1	2	yes	—
472	#121	—	2	2	no	—
473	#121	—	2	2	no	—
474	#121	—	2	2	no	—
475	#121	—	2	1	no	—
476	#121	—	2	1	no	—
477	#121	—	2	1	no	—
478	#121	—	2	1	no	—
479	#121	—	2	1	no	—
480	#121	C₂×Dic₆₁	1	2	yes	—
481	C₄×Q₈	—	2	1	no	—
482	C₄×Q₈	—	2	1	no	—
483	C₄×Q₈	C₂×Dic₆₁	1	2	yes	—
484	C₄×Q₈	C₂×Dic₆₁	1	2	yes	—
485	C₄×Q₈	C₂×Dic₆₁	1	1	yes	characteristic
486	C₄×Q₈	C₂²⋊D₆₁	1	1	yes	characteristic
487	C₄×D₄	—	2	2	no	—
488	C₄×D₄	—	2	2	no	—
489	C₄×D₄	—	2	1	no	—
490	C₄×D₄	—	2	1	no	—
491	C₄×D₄	—	2	1	no	—
492	C₄×D₄	—	2	1	no	—
493	C₄×D₄	—	2	1	no	—
494	C₄×D₄	C₂×Dic₆₁	1	2	yes	—
495	C₄×D₄	C₂×Dic₆₁	1	1	yes	characteristic
496	C₄×D₄	C₂×Dic₆₁	1	1	yes	characteristic
497	C₄×D₄	C₂×Dic₆₁	1	1	yes	characteristic
498	C₄×D₄	C₂²⋊D₆₁	1	1	yes	characteristic
499	C₄×D₄	C₂²⋊D₆₁	1	1	yes	characteristic
500	C₄×D₄	C₂²⋊D₆₁	1	1	yes	characteristic
501	#117	—	2	1	no	—
502	#117	—	2	1	no	—
503	#117	—	2	2	no	—
504	#117	C₂²⋊D₆₁	1	1	yes	characteristic
505	#117	C₂²⋊D₆₁	1	1	yes	characteristic
506	#117	C₂²⋊D₆₁	1	1	yes	characteristic
507	C₂×C₄⋊C₄	—	2	1	no	—
508	C₂×C₄⋊C₄	—	2	1	no	—
509	C₂×C₄⋊C₄	—	2	2	no	—
510	C₂×C₄²	C₂²×D₆₁	1	1	yes	characteristic
511	C₂×C₄²	C₂²×D₆₁	1	1	yes	characteristic
512	C₂×C₄²	C₂²×D₆₁	1	1	yes	characteristic
513	C₄⋊C₈	—	61	1	no	—
514	C₄⋊C₈	—	61	1	no	—
515	C₄⋊C₈	—	61	1	no	—
516	C₄⋊C₈	—	61	1	no	—
517	C₄⋊C₈	—	61	1	no	—
518	C₄⋊C₈	—	61	1	no	—
519	C₄⋊C₈	—	61	1	no	—
520	C₄⋊C₈	—	61	1	no	—
521	C₄⋊C₈	—	122	1	no	—
522	C₄⋊C₈	—	122	1	no	—
523	C₄⋊C₈	—	122	1	no	—
524	C₄⋊C₈	—	122	1	no	—
525	C₄⋊C₈	—	122	1	no	—
526	C₂²⋊C₈	—	122	1	no	—
527	C₂²⋊C₈	—	122	1	no	—
528	C₂²⋊C₈	—	122	1	no	—
529	C₂²⋊C₈	—	122	1	no	—
530	C₂²⋊C₈	—	122	1	no	—
531	C₂²⋊C₈	—	122	1	no	—
532	C₂²⋊C₈	—	122	1	no	—
533	#97	—	122	1	no	—
534	#97	—	122	1	no	—
535	#97	—	122	1	no	—
536	#97	—	122	1	no	—
537	C₄×C₈	—	122	1	no	—
538	C₄×C₈	—	122	1	no	—
539	C₄×C₈	—	122	1	no	—
540	#41	—	4	1	no	—
541	#41	—	4	1	no	—
542	#41	—	4	2	no	—
543	#41	—	4	2	no	—
544	#41	—	8	2	no	—
545	#41	—	8	2	no	—
546	C₂×Q₈	—	2	1	no	—
547	C₂×Q₈	—	2	2	no	—
548	C₂×Q₈	—	8	2	no	—
549	C₂×Q₈	C₂²⋊Dic₆₁	1	1	yes	characteristic
550	C₂×Q₈	C₂²×Dic₆₁	1	2	yes	—
551	C₂×Q₈	C₂²×Dic₆₁	1	2	yes	—
552	C₂×D₄	—	2	2	no	—
553	C₂×D₄	—	2	2	no	—
554	C₂×D₄	—	2	2	no	—
555	C₂×D₄	—	2	1	no	—
556	C₂×D₄	—	2	1	no	—
557	C₂×D₄	C₂²⋊Dic₆₁	1	1	yes	characteristic
558	C₂×D₄	C₂²⋊Dic₆₁	1	1	yes	characteristic
559	C₂×D₄	C₂²⋊Dic₆₁	1	1	yes	characteristic
560	C₂×D₄	C₂²×Dic₆₁	1	2	yes	—
561	C₂²×C₄	—	2	2	no	—
562	C₂²×C₄	—	2	2	no	—
563	C₂²×C₄	—	2	2	no	—
564	C₂²×C₄	—	2	2	no	—
565	C₂²×C₄	C₂²×Dic₆₁	1	1	yes	characteristic
566	C₂²×C₄	C₂²×Dic₆₁	1	1	yes	characteristic
567	C₂²×C₄	C₂²×Dic₆₁	1	1	yes	characteristic
568	C₂²×C₄	C₂×C₂²⋊D₆₁	1	1	yes	characteristic
569	C₂²×C₄	C₂×C₂²⋊D₆₁	1	1	yes	characteristic
570	C₂²×C₄	C₂×C₂²⋊D₆₁	1	1	yes	characteristic
571	C₂²×C₄	C₂×C₂²⋊D₆₁	1	1	yes	characteristic
572	C₂²×C₄	C₂×C₂²⋊D₆₁	1	1	yes	characteristic
573	C₂²×C₄	C₂×C₂²⋊D₆₁	1	1	yes	characteristic
574	M₁₆	—	488	1	no	—
575	M₁₆	—	488	1	no	—
576	M₁₆	—	244	2	no	—
577	C₂×C₈	—	122	1	no	—
578	C₂×C₈	—	122	1	no	—
579	C₂×C₈	—	122	1	no	—
580	C₂×C₈	—	122	1	no	—
581	C₂×C₈	—	122	1	no	—
582	C₂×C₈	—	122	1	no	—
583	C₂×C₈	—	122	1	no	—
584	C₂×C₈	—	122	1	no	—
585	C₂×C₈	—	488	1	no	—
586	C₂×C₈	—	244	2	no	—
587	C₄⋊C₄	—	2	1	no	—
588	C₄⋊C₄	—	2	1	no	—
589	C₄⋊C₄	—	2	1	no	—
590	C₄⋊C₄	—	2	1	no	—
591	C₄⋊C₄	—	2	1	no	—
592	C₄⋊C₄	—	2	2	no	—
593	C₄⋊C₄	—	2	2	no	—
594	C₄⋊C₄	—	2	2	no	—
595	C₄⋊C₄	—	2	2	no	—
596	C₄⋊C₄	—	2	2	no	—
597	C₄⋊C₄	—	2	2	no	—
598	C₄⋊C₄	C₂²⋊Dic₆₁	1	1	yes	characteristic
599	C₄⋊C₄	C₂²⋊Dic₆₁	1	1	yes	characteristic
600	C₄⋊C₄	C₂²⋊Dic₆₁	1	1	yes	characteristic
601	C₄⋊C₄	C₂²⋊Dic₆₁	1	1	yes	characteristic
602	C₄⋊C₄	C₂²⋊Dic₆₁	1	1	yes	characteristic
603	C₄⋊C₄	C₂²⋊Dic₆₁	1	1	yes	characteristic
604	C₄⋊C₄	C₂²×Dic₆₁	1	2	yes	—
605	C₂²⋊C₄	—	2	2	no	—
606	C₂²⋊C₄	—	2	2	no	—
607	C₂²⋊C₄	—	2	2	no	—
608	C₂²⋊C₄	—	2	2	no	—
609	C₂²⋊C₄	—	2	2	no	—
610	C₂²⋊C₄	—	2	2	no	—
611	C₂²⋊C₄	—	2	2	no	—
612	C₂²⋊C₄	—	2	2	no	—
613	C₂²⋊C₄	C₂²⋊Dic₆₁	1	1	yes	characteristic
614	C₂²⋊C₄	C₂²⋊Dic₆₁	1	1	yes	characteristic
615	C₂²⋊C₄	C₂²⋊Dic₆₁	1	1	yes	characteristic
616	C₂²⋊C₄	C₂²⋊Dic₆₁	1	1	yes	characteristic
617	C₂²⋊C₄	C₂²⋊Dic₆₁	1	1	yes	characteristic
618	C₂²⋊C₄	C₂²⋊Dic₆₁	1	1	yes	characteristic
619	C₄²	—	2	2	no	—
620	C₄²	—	2	2	no	—
621	C₄²	C₂²×Dic₆₁	1	1	yes	characteristic
622	C₄²	C₂²×Dic₆₁	1	1	yes	characteristic
623	C₄²	C₂²×Dic₆₁	1	1	yes	characteristic
624	C₄²	C₂×C₂²⋊D₆₁	1	1	yes	characteristic
625	C₄²	C₂×C₂²⋊D₆₁	1	1	yes	characteristic
626	C₄²	C₂×C₂²⋊D₆₁	1	1	yes	characteristic
627	C₄²	C₂×C₂²⋊D₆₁	1	1	yes	characteristic
628	C₄²	C₂×C₂²⋊D₆₁	1	1	yes	characteristic
629	C₄²	C₂×C₂²⋊D₆₁	1	1	yes	characteristic
630	C₄²	C₂³×D₆₁	1	1	yes	characteristic
631	C₂³	—	2	2	no	—
632	C₂³	C₂×C₂²⋊Dic₆₁	1	1	yes	characteristic
633	C₂³	C₂×C₂²⋊Dic₆₁	1	1	yes	characteristic
634	C₂³	C₂×C₂²⋊Dic₆₁	1	1	yes	characteristic
635	Q₈	—	4	1	no	—
636	Q₈	—	4	2	no	—
637	Q₈	—	4	2	no	—
638	Q₈	—	4	1	no	—
639	Q₈	—	4	1	no	—
640	Q₈	—	8	2	no	—
641	D₄	—	4	1	no	—
642	D₄	—	4	1	no	—
643	D₄	—	4	1	no	—
644	D₄	—	4	2	no	—
645	D₄	—	4	4	no	—
646	D₄	—	4	1	no	—
647	D₄	—	4	1	no	—
648	D₄	—	4	1	no	—
649	D₄	—	4	1	no	—
650	D₄	—	8	2	no	—
651	D₄	—	8	2	no	—
652	C₂×C₄	—	2	1	no	—
653	C₂×C₄	—	2	1	no	—
654	C₂×C₄	—	2	1	no	—
655	C₂×C₄	—	2	1	no	—
656	C₂×C₄	—	2	1	no	—
657	C₂×C₄	—	2	1	no	—
658	C₂×C₄	—	2	1	no	—
659	C₂×C₄	—	2	1	no	—
660	C₂×C₄	—	2	1	no	—
661	C₂×C₄	—	2	1	no	—
662	C₂×C₄	—	2	1	no	—
663	C₂×C₄	—	2	1	no	—
664	C₂×C₄	—	2	2	no	—
665	C₂×C₄	—	2	2	no	—
666	C₂×C₄	—	2	2	no	—
667	C₂×C₄	—	4	1	no	—
668	C₂×C₄	—	4	1	no	—
669	C₂×C₄	—	4	1	no	—
670	C₂×C₄	—	4	4	no	—
671	C₂×C₄	—	8	2	no	—
672	C₂×C₄	—	8	2	no	—
673	C₂×C₄	—	8	2	no	—
674	C₂×C₄	C₂×C₂²⋊Dic₆₁	1	1	yes	characteristic
675	C₂×C₄	C₂×C₂²⋊Dic₆₁	1	1	yes	characteristic
676	C₂×C₄	C₂×C₂²⋊Dic₆₁	1	1	yes	characteristic
677	C₂×C₄	C₂×C₂²⋊Dic₆₁	1	1	yes	characteristic
678	C₂×C₄	C₂×C₂²⋊Dic₆₁	1	1	yes	characteristic
679	C₂×C₄	C₂×C₂²⋊Dic₆₁	1	1	yes	characteristic
680	C₂×C₄	C₂×C₂²⋊Dic₆₁	1	1	yes	characteristic
681	C₂×C₄	C₂×C₂²⋊Dic₆₁	1	1	yes	characteristic
682	C₂×C₄	C₂×C₂²⋊Dic₆₁	1	1	yes	characteristic
683	C₂×C₄	C₂³×Dic₆₁	1	1	yes	characteristic
684	C₂×C₄	C₂²×C₂²⋊D₆₁	1	1	yes	characteristic
685	C₂×C₄	C₂²×C₂²⋊D₆₁	1	1	yes	characteristic
686	C₈	—	244	1	no	—
687	C₈	—	244	1	no	—
688	C₈	—	244	1	no	—
689	C₈	—	244	1	no	—
690	C₈	—	244	1	no	—
691	C₈	—	244	1	no	—
692	C₈	—	244	1	no	—
693	C₈	—	244	1	no	—
694	C₂²	—	2	1	no	—
695	C₂²	—	2	1	no	—
696	C₂²	—	2	1	no	—
697	C₂²	—	2	1	no	—
698	C₂²	—	2	1	no	—
699	C₂²	—	2	1	no	—
700	C₂²	—	2	1	no	—
701	C₂²	—	2	1	no	—
702	C₂²	—	2	1	no	—
703	C₂²	—	4	2	no	—
704	C₂²	—	4	2	no	—
705	C₂²	—	4	2	no	—
706	C₂²	C₂²×C₂²⋊Dic₆₁	1	1	yes	characteristic
707	C₄	—	2	1	no	—
708	C₄	—	2	1	no	—
709	C₄	—	2	1	no	—
710	C₄	—	2	1	no	—
711	C₄	—	2	1	no	—
712	C₄	—	2	1	no	—
713	C₄	—	2	1	no	—
714	C₄	—	2	1	no	—
715	C₄	—	2	1	no	—
716	C₄	—	2	1	no	—
717	C₄	—	4	2	no	—
718	C₄	—	4	2	no	—
719	C₄	—	4	2	no	—
720	C₄	#16840560	1	1	yes	characteristic
721	C₄	#16840560	1	1	yes	characteristic
722	C₄	#16840570	1	1	yes	characteristic
723	C₄	#16840577	1	1	yes	characteristic
724	C₂	—	4	1	no	—
725	C₂	—	4	1	no	—
726	C₂	—	4	1	no	—
727	C₂	—	8	2	no	—
728	C₂	#21454298	1	1	yes	characteristic
729	C₂	#21454338	1	1	yes	characteristic
730	C₂	#21454352	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²×C₂²⋊Dic₆₁
commutator	C₂×C₄×C₆₁	C₂³×C₄
Frattini	C₄²	C₂³×D₆₁
Fitting, prime radical	C₆₁×#3511	C₂
socle	C₂²×C₆₁	C₂²×C₂²⋊C₄
cosocle	C₄²×C₆₁	C₂⁴
hypercenter	#3511	D₆₁
hypocenter	C₆₁	#17768
LCS	G ▷ C₂×C₄×C₆₁ ▷ C₂²×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂² ◁ C₄×#41 ◁ #3511

Complements

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

N	H ≅ G/N	type
1. #21454936	C₂	semidirect
2. #21454485	C₂	semidirect
3. #21444554	C₂	semidirect
4. #21444549	C₂	semidirect
5. #21444545	C₂	semidirect
6. #21444541	C₂	semidirect
7. #21444529	C₂	semidirect
8. #21444524	C₂	semidirect
9. #21444514	C₂	semidirect
10. #21444514	C₂	semidirect
11. #21444509	C₂	semidirect
12. #21444500	C₂	semidirect
13. #21444481	C₂	semidirect
14. #21444476	C₂	semidirect
436. C₆₁	#17768	semidirect

Maximal subgroups

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

subgroup	index
#21454936	2
#21454485	2
#21444554	2
#21444549	2
#21444545	2
#21444541	2
#21444529	2
#21444524	2
#21444514	2
#21444509	2
#21444500	2
#21444481	2
#21444476	2
C₆₁×#3511	2
#17768	61