Subgroups — #29648818

Order 15616.

862 conjugacy classes of subgroups.

The subgroup lattice has 704 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
2	#21454485	C₂	1	1	yes	maximal, characteristic
3	#21444557	C₂	1	1	yes	maximal, characteristic, complemented
4	#21444549	C₂	1	1	yes	maximal, characteristic, complemented
5	#21444549	C₂	1	1	yes	maximal, characteristic, complemented
6	#21444536	C₂	1	1	yes	maximal, characteristic, complemented
7	#21444529	C₂	1	1	yes	maximal, characteristic, complemented
8	#21444529	C₂	1	1	yes	maximal, characteristic, complemented
9	#21444519	C₂	1	1	yes	maximal, characteristic, complemented
10	#21444519	C₂	1	1	yes	maximal, characteristic, complemented
11	#21444509	C₂	1	1	yes	maximal, characteristic, complemented
12	#21444504	C₂	1	1	yes	maximal, characteristic, complemented
13	#21444484	C₂	1	1	yes	maximal, characteristic, complemented
14	#21444476	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₁×#3509	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	#16839508	C₂²	1	1	yes	characteristic
41	#16839508	C₂²	1	1	yes	characteristic
42	#16839508	C₂²	1	1	yes	characteristic
43	#16839508	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	#16839508	C₂²	1	1	yes	characteristic
49	#16839508	C₂²	1	1	yes	characteristic
50	#16839508	C₂²	1	1	yes	characteristic
51	#16839508	C₂²	1	1	yes	characteristic
52	C₆₁×#557	—	2	1	no	—
53	C₆₁×#557	C₄	1	2	yes	—
54	C₆₁×#556	—	2	1	no	—
55	C₆₁×#556	C₄	1	2	yes	—
56	C₆₁×#552	—	2	1	no	—
57	C₆₁×#552	—	2	1	no	—
58	C₆₁×#552	C₄	1	2	yes	—
59	C₆₁×#552	C₄	1	2	yes	—
60	C₆₁×#541	—	2	1	no	—
61	C₆₁×#541	—	2	1	no	—
62	C₆₁×#536	—	2	1	no	—
63	C₆₁×#533	C₂²	1	1	yes	characteristic
64	C₆₁×#533	C₂²	1	1	yes	characteristic
65	C₆₁×#533	C₂²	1	1	yes	characteristic
66	C₆₁×#533	C₂²	1	1	yes	characteristic
67	C₆₁×#533	C₂²	1	1	yes	characteristic
68	C₂×C₄⋊Q₈×C₆₁	C₂²	1	1	yes	characteristic
69	C₆₁×#519	—	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	D₄	1	1	yes	characteristic
104	C₂²×Q₈×C₆₁	—	2	1	no	—
105	C₄⋊Q₈×C₆₁	—	2	2	no	—
106	C₄⋊Q₈×C₆₁	—	2	1	no	—
107	C₄⋊Q₈×C₆₁	—	2	1	no	—
108	C₄⋊Q₈×C₆₁	C₂×C₄	1	2	yes	—
109	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
110	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
111	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
112	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
113	#126×C₆₁	—	2	2	no	—
114	#126×C₆₁	—	2	2	no	—
115	#126×C₆₁	—	2	2	no	—
116	#126×C₆₁	—	2	2	no	—
117	#125×C₆₁	—	2	2	no	—
118	#125×C₆₁	—	2	2	no	—
119	#125×C₆₁	—	2	2	no	—
120	#125×C₆₁	—	2	2	no	—
121	#125×C₆₁	—	2	1	no	—
122	#125×C₆₁	—	2	1	no	—
123	#125×C₆₁	—	2	1	no	—
124	#125×C₆₁	C₂×C₄	1	2	yes	—
125	#125×C₆₁	C₂×C₄	1	2	yes	—
126	#124×C₆₁	—	2	2	no	—
127	#123×C₆₁	—	2	2	no	—
128	#123×C₆₁	—	2	2	no	—
129	C₂²⋊Q₈×C₆₁	—	2	1	no	—
130	C₂²⋊Q₈×C₆₁	—	2	1	no	—
131	C₂²⋊Q₈×C₆₁	—	2	1	no	—
132	C₂²⋊Q₈×C₆₁	—	2	1	no	—
133	C₂²⋊Q₈×C₆₁	—	2	1	no	—
134	C₂²⋊Q₈×C₆₁	—	2	1	no	—
135	C₂²⋊Q₈×C₆₁	—	2	1	no	—
136	C₂²⋊Q₈×C₆₁	C₂×C₄	1	2	yes	—
137	C₂²⋊Q₈×C₆₁	C₂×C₄	1	2	yes	—
138	C₂²⋊Q₈×C₆₁	C₂×C₄	1	2	yes	—
139	C₄×Q₈×C₆₁	—	2	2	no	—
140	C₄×Q₈×C₆₁	—	2	2	no	—
141	C₄×Q₈×C₆₁	—	2	1	no	—
142	C₄×Q₈×C₆₁	—	2	1	no	—
143	C₄×Q₈×C₆₁	—	2	1	no	—
144	C₄×Q₈×C₆₁	—	2	1	no	—
145	C₄×Q₈×C₆₁	—	2	1	no	—
146	C₄×Q₈×C₆₁	—	2	1	no	—
147	C₄×Q₈×C₆₁	—	2	1	no	—
148	C₄×Q₈×C₆₁	C₂×C₄	1	2	yes	—
149	C₄×Q₈×C₆₁	C₂×C₄	1	2	yes	—
150	C₄×Q₈×C₆₁	C₂×C₄	1	2	yes	—
151	C₄×Q₈×C₆₁	C₂×C₄	1	1	yes	characteristic
152	C₄×Q₈×C₆₁	D₄	1	1	yes	characteristic
153	C₄×D₄×C₆₁	C₂×C₄	1	1	yes	characteristic
154	C₄×D₄×C₆₁	C₂×C₄	1	1	yes	characteristic
155	C₄×D₄×C₆₁	C₂×C₄	1	1	yes	characteristic
156	C₄×D₄×C₆₁	D₄	1	1	yes	characteristic
157	C₄×D₄×C₆₁	D₄	1	1	yes	characteristic
158	C₄×D₄×C₆₁	D₄	1	1	yes	characteristic
159	#117×C₆₁	—	2	1	no	—
160	#117×C₆₁	—	2	1	no	—
161	#117×C₆₁	—	2	1	no	—
162	#117×C₆₁	—	2	2	no	—
163	#117×C₆₁	—	2	2	no	—
164	#117×C₆₁	C₂×C₄	1	2	yes	—
165	#117×C₆₁	C₂×C₄	1	2	yes	—
166	#117×C₆₁	D₄	1	1	yes	characteristic
167	#117×C₆₁	D₄	1	1	yes	characteristic
168	#117×C₆₁	D₄	1	1	yes	characteristic
169	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
170	C₂×C₄⋊C₄×C₆₁	C₂×C₄	1	2	yes	—
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	C₂×Q₈×C₆₁	—	2	2	no	—
177	C₂×Q₈×C₆₁	—	2	1	no	—
178	C₂×Q₈×C₆₁	—	2	1	no	—
179	C₂×Q₈×C₆₁	—	2	1	no	—
180	C₂×Q₈×C₆₁	—	4	2	no	—
181	C₂×Q₈×C₆₁	—	4	2	no	—
182	C₂×Q₈×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
183	C₂×Q₈×C₆₁	C₂²×C₄	1	2	yes	—
184	C₂×D₄×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
185	C₂×D₄×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
186	C₂×D₄×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
187	C₂²×C₄×C₆₁	—	2	2	no	—
188	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
189	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
190	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
191	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
192	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
193	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
194	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
195	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
196	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
197	C₄⋊C₄×C₆₁	—	2	2	no	—
198	C₄⋊C₄×C₆₁	—	2	2	no	—
199	C₄⋊C₄×C₆₁	—	2	2	no	—
200	C₄⋊C₄×C₆₁	—	2	2	no	—
201	C₄⋊C₄×C₆₁	—	2	2	no	—
202	C₄⋊C₄×C₆₁	—	2	2	no	—
203	C₄⋊C₄×C₆₁	—	2	2	no	—
204	C₄⋊C₄×C₆₁	—	2	2	no	—
205	C₄⋊C₄×C₆₁	—	2	2	no	—
206	C₄⋊C₄×C₆₁	—	2	2	no	—
207	C₄⋊C₄×C₆₁	—	2	2	no	—
208	C₄⋊C₄×C₆₁	—	2	2	no	—
209	C₄⋊C₄×C₆₁	—	2	1	no	—
210	C₄⋊C₄×C₆₁	—	2	1	no	—
211	C₄⋊C₄×C₆₁	—	2	1	no	—
212	C₄⋊C₄×C₆₁	—	2	1	no	—
213	C₄⋊C₄×C₆₁	—	2	1	no	—
214	C₄⋊C₄×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
215	C₄⋊C₄×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
216	C₄⋊C₄×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
217	C₄⋊C₄×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
218	C₄⋊C₄×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
219	C₄⋊C₄×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
220	C₄⋊C₄×C₆₁	C₂²×C₄	1	2	yes	—
221	C₄⋊C₄×C₆₁	C₂²×C₄	1	2	yes	—
222	C₄⋊C₄×C₆₁	C₂²×C₄	1	2	yes	—
223	C₂²⋊C₄×C₆₁	—	2	2	no	—
224	C₂²⋊C₄×C₆₁	—	2	2	no	—
225	C₂²⋊C₄×C₆₁	—	2	2	no	—
226	C₂²⋊C₄×C₆₁	—	2	2	no	—
227	C₂²⋊C₄×C₆₁	—	2	2	no	—
228	C₂²⋊C₄×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
229	C₂²⋊C₄×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
230	C₂²⋊C₄×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
231	C₂²⋊C₄×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
232	C₂²⋊C₄×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
233	C₂²⋊C₄×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
234	C₄²×C₆₁	—	2	2	no	—
235	C₄²×C₆₁	—	2	2	no	—
236	C₄²×C₆₁	—	2	2	no	—
237	C₄²×C₆₁	—	2	2	no	—
238	C₄²×C₆₁	—	2	2	no	—
239	C₄²×C₆₁	C₂²×C₄	1	1	yes	characteristic
240	C₄²×C₆₁	C₂²×C₄	1	1	yes	characteristic
241	C₄²×C₆₁	C₂²×C₄	1	1	yes	characteristic
242	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
243	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
244	C₄²×C₆₁	C₂×D₄	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	C₂⁴	1	1	yes	characteristic
249	#11758194	—	4	2	no	—
250	#11758194	—	8	1	no	—
251	#11758194	—	8	1	no	—
252	C₂×#92418	—	2	1	no	—
253	C₂×#92418	—	2	1	no	—
254	C₂×#92418	—	2	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	—	4	2	no	—
261	C₂×#92418	—	8	1	no	—
262	C₂³×C₆₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
263	C₂³×C₆₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
264	C₂³×C₆₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
265	Q₈×C₆₁	—	4	1	no	—
266	Q₈×C₆₁	—	4	4	no	—
267	Q₈×C₆₁	—	4	2	no	—
268	Q₈×C₆₁	—	4	1	no	—
269	Q₈×C₆₁	—	4	1	no	—
270	Q₈×C₆₁	—	4	1	no	—
271	Q₈×C₆₁	—	4	1	no	—
272	Q₈×C₆₁	—	4	1	no	—
273	Q₈×C₆₁	—	4	1	no	—
274	D₄×C₆₁	—	4	1	no	—
275	D₄×C₆₁	—	4	1	no	—
276	D₄×C₆₁	—	4	1	no	—
277	C₂×C₄×C₆₁	—	2	1	no	—
278	C₂×C₄×C₆₁	—	2	1	no	—
279	C₂×C₄×C₆₁	—	2	1	no	—
280	C₂×C₄×C₆₁	—	2	1	no	—
281	C₂×C₄×C₆₁	—	2	1	no	—
282	C₂×C₄×C₆₁	—	2	1	no	—
283	C₂×C₄×C₆₁	—	2	1	no	—
284	C₂×C₄×C₆₁	—	2	1	no	—
285	C₂×C₄×C₆₁	—	2	1	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	2	no	—
290	C₂×C₄×C₆₁	—	2	2	no	—
291	C₂×C₄×C₆₁	—	2	2	no	—
292	C₂×C₄×C₆₁	—	2	2	no	—
293	C₂×C₄×C₆₁	—	4	1	no	—
294	C₂×C₄×C₆₁	—	4	1	no	—
295	C₂×C₄×C₆₁	—	4	1	no	—
296	C₂×C₄×C₆₁	—	4	4	no	—
297	C₂×C₄×C₆₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
298	C₂×C₄×C₆₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
299	C₂×C₄×C₆₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
300	C₂×C₄×C₆₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
301	C₂×C₄×C₆₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
302	C₂×C₄×C₆₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
303	C₂×C₄×C₆₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
304	C₂×C₄×C₆₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
305	C₂×C₄×C₆₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
306	C₂×C₄×C₆₁	C₂³×C₄	1	1	yes	characteristic
307	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
308	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
309	#92418	—	4	1	no	—
310	#92418	—	4	1	no	—
311	#92418	—	4	1	no	—
312	#92418	—	4	1	no	—
313	#92418	—	4	1	no	—
314	#92418	—	4	1	no	—
315	#92418	—	4	1	no	—
316	#92418	—	4	1	no	—
317	#17767	—	61	1	no	maximal, Sylow
318	C₂²×C₆₁	—	2	1	no	—
319	C₂²×C₆₁	—	2	1	no	—
320	C₂²×C₆₁	—	2	1	no	—
321	C₂²×C₆₁	—	2	1	no	—
322	C₂²×C₆₁	—	2	1	no	—
323	C₂²×C₆₁	—	2	1	no	—
324	C₂²×C₆₁	—	2	1	no	—
325	C₂²×C₆₁	—	2	1	no	—
326	C₂²×C₆₁	—	2	1	no	—
327	C₂²×C₆₁	C₂²×C₂²⋊C₄	1	1	yes	characteristic
328	C₄×C₆₁	—	2	1	no	—
329	C₄×C₆₁	—	2	1	no	—
330	C₄×C₆₁	—	2	1	no	—
331	C₄×C₆₁	—	2	1	no	—
332	C₄×C₆₁	—	2	1	no	—
333	C₄×C₆₁	—	2	1	no	—
334	C₄×C₆₁	—	2	1	no	—
335	C₄×C₆₁	—	2	1	no	—
336	C₄×C₆₁	—	2	1	no	—
337	C₄×C₆₁	—	2	1	no	—
338	C₄×C₆₁	—	4	2	no	—
339	C₄×C₆₁	—	4	2	no	—
340	C₄×C₆₁	—	4	2	no	—
341	C₄×C₆₁	—	4	2	no	—
342	C₄×C₆₁	#575	1	1	yes	characteristic
343	C₄×C₆₁	#575	1	1	yes	characteristic
344	C₄×C₆₁	#577	1	1	yes	characteristic
345	C₄×C₆₁	#578	1	1	yes	characteristic
346	#3509	D₆₁	1	1	yes	characteristic
347	#2989	—	61	1	no	—
348	#2925	—	61	1	no	—
349	#1561	—	61	1	no	—
350	#1559	—	61	1	no	—
351	#1559	—	61	1	no	—
352	#1556	—	61	1	no	—
353	#1554	—	61	1	no	—
354	#1554	—	61	1	no	—
355	#1552	—	61	1	no	—
356	#1552	—	61	1	no	—
357	#1550	—	61	1	no	—
358	#1549	—	61	1	no	—
359	#1544	—	61	1	no	—
360	#1542	—	61	1	no	—
361	C₂×C₆₁	—	4	1	no	—
362	C₂×C₆₁	—	4	1	no	—
363	C₂×C₆₁	—	4	1	no	—
364	C₂×C₆₁	#2889	1	1	yes	characteristic
365	C₂×C₆₁	#2896	1	1	yes	characteristic
366	C₂×C₆₁	#2898	1	1	yes	characteristic
367	#557	—	2	1	no	—
368	#557	Dic₆₁	1	2	yes	—
369	#556	—	2	1	no	—
370	#556	Dic₆₁	1	2	yes	—
371	#552	—	2	1	no	—
372	#552	—	2	1	no	—
373	#552	Dic₆₁	1	2	yes	—
374	#552	Dic₆₁	1	2	yes	—
375	#541	—	2	1	no	—
376	#541	—	2	1	no	—
377	#536	—	2	1	no	—
378	#533	C₂×D₆₁	1	1	yes	characteristic
379	#533	C₂×D₆₁	1	1	yes	characteristic
380	#533	C₂×D₆₁	1	1	yes	characteristic
381	#533	C₂×D₆₁	1	1	yes	characteristic
382	#533	C₂×D₆₁	1	1	yes	characteristic
383	C₂×C₄⋊Q₈	C₂×D₆₁	1	1	yes	characteristic
384	#519	—	2	1	no	—
385	C₄×#41	C₂×D₆₁	1	1	yes	characteristic
386	#446	—	122	1	no	—
387	#436	—	122	1	no	—
388	#435	—	122	1	no	—
389	#435	—	122	1	no	—
390	#433	—	122	1	no	—
391	#433	—	122	1	no	—
392	#432	—	61	1	no	—
393	#432	—	61	1	no	—
394	#432	—	61	1	no	—
395	#432	—	61	1	no	—
396	#431	—	61	1	no	—
397	#431	—	61	1	no	—
398	#431	—	61	1	no	—
399	#423	—	61	1	no	—
400	#423	—	61	1	no	—
401	#423	—	61	1	no	—
402	C₂×C₄⋊C₈	—	61	1	no	—
403	C₂×C₄⋊C₈	—	61	1	no	—
404	#408	—	122	1	no	—
405	#405	—	122	1	no	—
406	#333	—	61	1	no	—
407	#333	—	61	1	no	—
408	#333	—	61	1	no	—
409	#333	—	61	1	no	—
410	#332	—	61	1	no	—
411	#332	—	61	1	no	—
412	#332	—	61	1	no	—
413	#332	—	61	1	no	—
414	#332	—	61	1	no	—
415	#332	—	61	1	no	—
416	#332	—	61	1	no	—
417	#332	—	61	1	no	—
418	#332	—	61	1	no	—
419	#332	—	61	1	no	—
420	#332	—	61	1	no	—
421	#332	—	61	1	no	—
422	C₆₁	#17767	1	1	yes	characteristic, complemented, Sylow
423	C₂×#41	C₂²⋊D₆₁	1	1	yes	characteristic
424	C₂²×Q₈	—	2	1	no	—
425	C₂×M₁₆	—	122	1	no	—
426	C₂×M₁₆	—	122	1	no	—
427	C₂×M₁₆	—	122	1	no	—
428	C₂²×C₈	—	122	1	no	—
429	C₂²×C₈	—	122	1	no	—
430	C₄⋊Q₈	—	2	2	no	—
431	C₄⋊Q₈	—	2	1	no	—
432	C₄⋊Q₈	—	2	1	no	—
433	C₄⋊Q₈	C₂×Dic₆₁	1	2	yes	—
434	C₄⋊Q₈	C₂²×D₆₁	1	1	yes	characteristic
435	C₄⋊Q₈	C₂²×D₆₁	1	1	yes	characteristic
436	C₄⋊Q₈	C₂²×D₆₁	1	1	yes	characteristic
437	C₄⋊Q₈	C₂²×D₆₁	1	1	yes	characteristic
438	#126	—	2	2	no	—
439	#126	—	2	2	no	—
440	#126	—	2	2	no	—
441	#126	—	2	2	no	—
442	#125	—	2	2	no	—
443	#125	—	2	2	no	—
444	#125	—	2	2	no	—
445	#125	—	2	2	no	—
446	#125	—	2	1	no	—
447	#125	—	2	1	no	—
448	#125	—	2	1	no	—
449	#125	C₂×Dic₆₁	1	2	yes	—
450	#125	C₂×Dic₆₁	1	2	yes	—
451	#124	—	2	2	no	—
452	#123	—	2	2	no	—
453	#123	—	2	2	no	—
454	C₂²⋊Q₈	—	2	1	no	—
455	C₂²⋊Q₈	—	2	1	no	—
456	C₂²⋊Q₈	—	2	1	no	—
457	C₂²⋊Q₈	—	2	1	no	—
458	C₂²⋊Q₈	—	2	1	no	—
459	C₂²⋊Q₈	—	2	1	no	—
460	C₂²⋊Q₈	—	2	1	no	—
461	C₂²⋊Q₈	C₂×Dic₆₁	1	2	yes	—
462	C₂²⋊Q₈	C₂×Dic₆₁	1	2	yes	—
463	C₂²⋊Q₈	C₂×Dic₆₁	1	2	yes	—
464	C₄×Q₈	—	2	2	no	—
465	C₄×Q₈	—	2	2	no	—
466	C₄×Q₈	—	2	1	no	—
467	C₄×Q₈	—	2	1	no	—
468	C₄×Q₈	—	2	1	no	—
469	C₄×Q₈	—	2	1	no	—
470	C₄×Q₈	—	2	1	no	—
471	C₄×Q₈	—	2	1	no	—
472	C₄×Q₈	—	2	1	no	—
473	C₄×Q₈	C₂×Dic₆₁	1	2	yes	—
474	C₄×Q₈	C₂×Dic₆₁	1	2	yes	—
475	C₄×Q₈	C₂×Dic₆₁	1	2	yes	—
476	C₄×Q₈	C₂×Dic₆₁	1	1	yes	characteristic
477	C₄×Q₈	C₂²⋊D₆₁	1	1	yes	characteristic
478	C₄×D₄	C₂×Dic₆₁	1	1	yes	characteristic
479	C₄×D₄	C₂×Dic₆₁	1	1	yes	characteristic
480	C₄×D₄	C₂×Dic₆₁	1	1	yes	characteristic
481	C₄×D₄	C₂²⋊D₆₁	1	1	yes	characteristic
482	C₄×D₄	C₂²⋊D₆₁	1	1	yes	characteristic
483	C₄×D₄	C₂²⋊D₆₁	1	1	yes	characteristic
484	#117	—	2	1	no	—
485	#117	—	2	1	no	—
486	#117	—	2	1	no	—
487	#117	—	2	2	no	—
488	#117	—	2	2	no	—
489	#117	C₂×Dic₆₁	1	2	yes	—
490	#117	C₂×Dic₆₁	1	2	yes	—
491	#117	C₂²⋊D₆₁	1	1	yes	characteristic
492	#117	C₂²⋊D₆₁	1	1	yes	characteristic
493	#117	C₂²⋊D₆₁	1	1	yes	characteristic
494	C₂×C₄⋊C₄	—	2	1	no	—
495	C₂×C₄⋊C₄	C₂×Dic₆₁	1	2	yes	—
496	C₂×C₄²	C₂²×D₆₁	1	1	yes	characteristic
497	C₂×C₄²	C₂²×D₆₁	1	1	yes	characteristic
498	C₂×C₄²	C₂²×D₆₁	1	1	yes	characteristic
499	C₄⋊C₈	—	61	1	no	—
500	C₄⋊C₈	—	61	1	no	—
501	C₄⋊C₈	—	61	1	no	—
502	C₄⋊C₈	—	61	1	no	—
503	C₄⋊C₈	—	61	1	no	—
504	C₄⋊C₈	—	61	1	no	—
505	C₄⋊C₈	—	61	1	no	—
506	C₄⋊C₈	—	61	1	no	—
507	C₄⋊C₈	—	122	1	no	—
508	C₄⋊C₈	—	122	1	no	—
509	C₄⋊C₈	—	122	1	no	—
510	C₄⋊C₈	—	122	1	no	—
511	C₄⋊C₈	—	122	1	no	—
512	C₂²⋊C₈	—	122	1	no	—
513	C₂²⋊C₈	—	122	1	no	—
514	C₂²⋊C₈	—	122	1	no	—
515	C₂²⋊C₈	—	122	1	no	—
516	C₂²⋊C₈	—	122	1	no	—
517	C₂²⋊C₈	—	122	1	no	—
518	C₂²⋊C₈	—	122	1	no	—
519	#97	—	122	1	no	—
520	#97	—	122	1	no	—
521	#97	—	122	1	no	—
522	#97	—	122	1	no	—
523	C₄×C₈	—	122	1	no	—
524	C₄×C₈	—	122	1	no	—
525	C₄×C₈	—	122	1	no	—
526	#41	—	4	1	no	—
527	#41	—	4	1	no	—
528	C₂×Q₈	—	2	1	no	—
529	C₂×Q₈	—	2	1	no	—
530	C₂×Q₈	—	2	1	no	—
531	C₂×Q₈	—	2	2	no	—
532	C₂×Q₈	—	4	2	no	—
533	C₂×Q₈	—	4	2	no	—
534	C₂×Q₈	C₂²⋊Dic₆₁	1	1	yes	characteristic
535	C₂×Q₈	C₂²×Dic₆₁	1	2	yes	—
536	C₂×D₄	C₂²⋊Dic₆₁	1	1	yes	characteristic
537	C₂×D₄	C₂²⋊Dic₆₁	1	1	yes	characteristic
538	C₂×D₄	C₂²⋊Dic₆₁	1	1	yes	characteristic
539	C₂²×C₄	—	2	2	no	—
540	C₂²×C₄	C₂²×Dic₆₁	1	1	yes	characteristic
541	C₂²×C₄	C₂²×Dic₆₁	1	1	yes	characteristic
542	C₂²×C₄	C₂²×Dic₆₁	1	1	yes	characteristic
543	C₂²×C₄	C₂×C₂²⋊D₆₁	1	1	yes	characteristic
544	C₂²×C₄	C₂×C₂²⋊D₆₁	1	1	yes	characteristic
545	C₂²×C₄	C₂×C₂²⋊D₆₁	1	1	yes	characteristic
546	C₂²×C₄	C₂×C₂²⋊D₆₁	1	1	yes	characteristic
547	C₂²×C₄	C₂×C₂²⋊D₆₁	1	1	yes	characteristic
548	C₂²×C₄	C₂×C₂²⋊D₆₁	1	1	yes	characteristic
549	M₁₆	—	488	1	no	—
550	M₁₆	—	488	1	no	—
551	M₁₆	—	244	2	no	—
552	C₂×C₈	—	122	1	no	—
553	C₂×C₈	—	122	1	no	—
554	C₂×C₈	—	122	1	no	—
555	C₂×C₈	—	122	1	no	—
556	C₂×C₈	—	122	1	no	—
557	C₂×C₈	—	122	1	no	—
558	C₂×C₈	—	122	1	no	—
559	C₂×C₈	—	122	1	no	—
560	C₂×C₈	—	488	1	no	—
561	C₂×C₈	—	244	2	no	—
562	C₄⋊C₄	—	2	1	no	—
563	C₄⋊C₄	—	2	1	no	—
564	C₄⋊C₄	—	2	1	no	—
565	C₄⋊C₄	—	2	1	no	—
566	C₄⋊C₄	—	2	1	no	—
567	C₄⋊C₄	—	2	2	no	—
568	C₄⋊C₄	—	2	2	no	—
569	C₄⋊C₄	—	2	2	no	—
570	C₄⋊C₄	—	2	2	no	—
571	C₄⋊C₄	—	2	2	no	—
572	C₄⋊C₄	—	2	2	no	—
573	C₄⋊C₄	—	2	2	no	—
574	C₄⋊C₄	—	2	2	no	—
575	C₄⋊C₄	—	2	2	no	—
576	C₄⋊C₄	—	2	2	no	—
577	C₄⋊C₄	—	2	2	no	—
578	C₄⋊C₄	—	2	2	no	—
579	C₄⋊C₄	C₂²⋊Dic₆₁	1	1	yes	characteristic
580	C₄⋊C₄	C₂²⋊Dic₆₁	1	1	yes	characteristic
581	C₄⋊C₄	C₂²⋊Dic₆₁	1	1	yes	characteristic
582	C₄⋊C₄	C₂²⋊Dic₆₁	1	1	yes	characteristic
583	C₄⋊C₄	C₂²⋊Dic₆₁	1	1	yes	characteristic
584	C₄⋊C₄	C₂²⋊Dic₆₁	1	1	yes	characteristic
585	C₄⋊C₄	C₂²×Dic₆₁	1	2	yes	—
586	C₄⋊C₄	C₂²×Dic₆₁	1	2	yes	—
587	C₄⋊C₄	C₂²×Dic₆₁	1	2	yes	—
588	C₂²⋊C₄	—	2	2	no	—
589	C₂²⋊C₄	—	2	2	no	—
590	C₂²⋊C₄	—	2	2	no	—
591	C₂²⋊C₄	—	2	2	no	—
592	C₂²⋊C₄	—	2	2	no	—
593	C₂²⋊C₄	C₂²⋊Dic₆₁	1	1	yes	characteristic
594	C₂²⋊C₄	C₂²⋊Dic₆₁	1	1	yes	characteristic
595	C₂²⋊C₄	C₂²⋊Dic₆₁	1	1	yes	characteristic
596	C₂²⋊C₄	C₂²⋊Dic₆₁	1	1	yes	characteristic
597	C₂²⋊C₄	C₂²⋊Dic₆₁	1	1	yes	characteristic
598	C₂²⋊C₄	C₂²⋊Dic₆₁	1	1	yes	characteristic
599	C₄²	—	2	2	no	—
600	C₄²	—	2	2	no	—
601	C₄²	—	2	2	no	—
602	C₄²	—	2	2	no	—
603	C₄²	—	2	2	no	—
604	C₄²	C₂²×Dic₆₁	1	1	yes	characteristic
605	C₄²	C₂²×Dic₆₁	1	1	yes	characteristic
606	C₄²	C₂²×Dic₆₁	1	1	yes	characteristic
607	C₄²	C₂×C₂²⋊D₆₁	1	1	yes	characteristic
608	C₄²	C₂×C₂²⋊D₆₁	1	1	yes	characteristic
609	C₄²	C₂×C₂²⋊D₆₁	1	1	yes	characteristic
610	C₄²	C₂×C₂²⋊D₆₁	1	1	yes	characteristic
611	C₄²	C₂×C₂²⋊D₆₁	1	1	yes	characteristic
612	C₄²	C₂×C₂²⋊D₆₁	1	1	yes	characteristic
613	C₄²	C₂³×D₆₁	1	1	yes	characteristic
614	C₂³	C₂×C₂²⋊Dic₆₁	1	1	yes	characteristic
615	C₂³	C₂×C₂²⋊Dic₆₁	1	1	yes	characteristic
616	C₂³	C₂×C₂²⋊Dic₆₁	1	1	yes	characteristic
617	Q₈	—	4	1	no	—
618	Q₈	—	4	2	no	—
619	Q₈	—	4	4	no	—
620	Q₈	—	4	1	no	—
621	Q₈	—	4	1	no	—
622	Q₈	—	4	1	no	—
623	Q₈	—	4	1	no	—
624	Q₈	—	4	1	no	—
625	Q₈	—	4	1	no	—
626	D₄	—	4	1	no	—
627	D₄	—	4	1	no	—
628	D₄	—	4	1	no	—
629	C₂×C₄	—	2	1	no	—
630	C₂×C₄	—	2	1	no	—
631	C₂×C₄	—	2	1	no	—
632	C₂×C₄	—	2	1	no	—
633	C₂×C₄	—	2	1	no	—
634	C₂×C₄	—	2	1	no	—
635	C₂×C₄	—	2	1	no	—
636	C₂×C₄	—	2	1	no	—
637	C₂×C₄	—	2	1	no	—
638	C₂×C₄	—	2	1	no	—
639	C₂×C₄	—	2	1	no	—
640	C₂×C₄	—	2	1	no	—
641	C₂×C₄	—	2	2	no	—
642	C₂×C₄	—	2	2	no	—
643	C₂×C₄	—	2	2	no	—
644	C₂×C₄	—	2	2	no	—
645	C₂×C₄	—	4	1	no	—
646	C₂×C₄	—	4	1	no	—
647	C₂×C₄	—	4	1	no	—
648	C₂×C₄	—	4	4	no	—
649	C₂×C₄	C₂×C₂²⋊Dic₆₁	1	1	yes	characteristic
650	C₂×C₄	C₂×C₂²⋊Dic₆₁	1	1	yes	characteristic
651	C₂×C₄	C₂×C₂²⋊Dic₆₁	1	1	yes	characteristic
652	C₂×C₄	C₂×C₂²⋊Dic₆₁	1	1	yes	characteristic
653	C₂×C₄	C₂×C₂²⋊Dic₆₁	1	1	yes	characteristic
654	C₂×C₄	C₂×C₂²⋊Dic₆₁	1	1	yes	characteristic
655	C₂×C₄	C₂×C₂²⋊Dic₆₁	1	1	yes	characteristic
656	C₂×C₄	C₂×C₂²⋊Dic₆₁	1	1	yes	characteristic
657	C₂×C₄	C₂×C₂²⋊Dic₆₁	1	1	yes	characteristic
658	C₂×C₄	C₂³×Dic₆₁	1	1	yes	characteristic
659	C₂×C₄	C₂²×C₂²⋊D₆₁	1	1	yes	characteristic
660	C₂×C₄	C₂²×C₂²⋊D₆₁	1	1	yes	characteristic
661	C₈	—	244	1	no	—
662	C₈	—	244	1	no	—
663	C₈	—	244	1	no	—
664	C₈	—	244	1	no	—
665	C₈	—	244	1	no	—
666	C₈	—	244	1	no	—
667	C₈	—	244	1	no	—
668	C₈	—	244	1	no	—
669	C₂²	—	2	1	no	—
670	C₂²	—	2	1	no	—
671	C₂²	—	2	1	no	—
672	C₂²	—	2	1	no	—
673	C₂²	—	2	1	no	—
674	C₂²	—	2	1	no	—
675	C₂²	—	2	1	no	—
676	C₂²	—	2	1	no	—
677	C₂²	—	2	1	no	—
678	C₂²	C₂²×C₂²⋊Dic₆₁	1	1	yes	characteristic
679	C₄	—	2	1	no	—
680	C₄	—	2	1	no	—
681	C₄	—	2	1	no	—
682	C₄	—	2	1	no	—
683	C₄	—	2	1	no	—
684	C₄	—	2	1	no	—
685	C₄	—	2	1	no	—
686	C₄	—	2	1	no	—
687	C₄	—	2	1	no	—
688	C₄	—	2	1	no	—
689	C₄	—	4	2	no	—
690	C₄	—	4	2	no	—
691	C₄	—	4	2	no	—
692	C₄	—	4	2	no	—
693	C₄	#16840560	1	1	yes	characteristic
694	C₄	#16840560	1	1	yes	characteristic
695	C₄	#16840570	1	1	yes	characteristic
696	C₄	#16840577	1	1	yes	characteristic
697	C₂	—	4	1	no	—
698	C₂	—	4	1	no	—
699	C₂	—	4	1	no	—
700	C₂	#21454302	1	1	yes	characteristic
701	C₂	#21454338	1	1	yes	characteristic
702	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	C₆₁×#3509	C₂
socle	C₂²×C₆₁	C₂²×C₂²⋊C₄
prime radical	C₂×#41×C₆₁	D₄
cosocle	C₄²×C₆₁	C₂⁴
hypercenter	#3509	D₆₁
hypocenter	C₆₁	#17767
LCS	G ▷ C₂×C₄×C₆₁ ▷ C₂²×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂² ◁ C₄×#41 ◁ #3509

Complements

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

N	H ≅ G/N	type
3. #21444557	C₂	semidirect
4. #21444549	C₂	semidirect
5. #21444549	C₂	semidirect
6. #21444536	C₂	semidirect
7. #21444529	C₂	semidirect
8. #21444529	C₂	semidirect
9. #21444519	C₂	semidirect
10. #21444519	C₂	semidirect
11. #21444509	C₂	semidirect
12. #21444504	C₂	semidirect
13. #21444484	C₂	semidirect
14. #21444476	C₂	semidirect
422. C₆₁	#17767	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
#21444557	2
#21444549	2
#21444536	2
#21444529	2
#21444519	2
#21444509	2
#21444504	2
#21444484	2
#21444476	2
C₆₁×#3509	2
#17767	61