Subgroups — #21460247

Order 7808.

1050 conjugacy classes of subgroups.

The subgroup lattice has 688 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16840516	C₂	1	2	yes	maximal, complemented
2	#16840502	C₂	1	2	yes	maximal, complemented
3	#16840475	C₂	1	2	yes	maximal, complemented
4	#16840465	C₂	1	1	yes	maximal, characteristic, complemented
5	#16840460	C₂	1	1	yes	maximal, characteristic, complemented
6	#16840451	C₂	1	1	yes	maximal, characteristic, complemented
7	#16840437	C₂	1	2	yes	maximal, complemented
8	#16840424	C₂	1	1	yes	maximal, characteristic, complemented
9	#16840422	C₂	1	1	yes	maximal, characteristic, complemented
10	#16840408	C₂	1	1	yes	maximal, characteristic, complemented
11	#16840403	C₂	1	1	yes	maximal, characteristic, complemented
12	#16840368	C₂	1	2	yes	maximal, complemented
13	#16840367	C₂	1	2	yes	maximal, complemented
14	#16840351	C₂	1	2	yes	maximal, complemented
15	#16840348	C₂	1	2	yes	maximal, complemented
16	#16840343	C₂	1	1	yes	maximal, characteristic, complemented
17	#16840342	C₂	1	1	yes	maximal, characteristic, complemented
18	#16840335	C₂	1	1	yes	maximal, characteristic, complemented
19	#16840331	C₂	1	1	yes	maximal, characteristic, complemented
20	#16840309	C₂	1	1	yes	maximal, characteristic, complemented
21	#16840299	C₂	1	1	yes	maximal, characteristic, complemented
22	#16840297	C₂	1	1	yes	maximal, characteristic, complemented
23	C₆₁×#552	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#11758226	C₂²	1	1	yes	characteristic
25	C₂×#11758222	C₂²	1	1	yes	characteristic
26	C₂×#11758222	C₂²	1	1	yes	characteristic
27	C₂×#11758222	C₂²	1	1	yes	characteristic, complemented
28	C₂×Q₈×D₆₁	C₂²	1	1	yes	characteristic, complemented
29	C₂²×D₂₄₄	C₂²	1	1	yes	characteristic
30	#14519776	C₂²	1	2	yes	complemented
31	#14519776	C₂²	1	1	yes	characteristic, complemented
32	#14519774	C₂²	1	2	yes	—
33	#14519773	C₂²	1	1	yes	characteristic
34	#14519772	C₂²	1	2	yes	complemented
35	#14519772	C₂²	1	2	yes	complemented
36	#14519772	C₂²	1	2	yes	complemented
37	#14519772	C₂²	1	2	yes	complemented
38	#14519770	C₂²	1	2	yes	—
39	#14519769	C₂²	1	2	yes	complemented
40	#14519768	C₂²	1	1	yes	characteristic, complemented
41	#14519766	C₂²	1	1	yes	characteristic
42	#14519765	C₂²	1	2	yes	—
43	#14519765	C₂²	1	1	yes	characteristic
44	#14519765	C₂²	1	2	yes	complemented
45	#14519763	C₂²	1	1	yes	characteristic
46	#14519763	C₂²	1	2	yes	—
47	#14519763	C₂²	1	1	yes	characteristic, complemented
48	#14519763	C₂²	1	2	yes	complemented
49	#14519762	C₂²	1	2	yes	—
50	#14519762	C₂²	1	2	yes	—
51	#14519762	C₂²	1	2	yes	complemented
52	#14519762	C₂²	1	2	yes	complemented
53	#14519762	C₂²	1	2	yes	complemented
54	#14519762	C₂²	1	2	yes	complemented
55	#14519762	C₂²	1	2	yes	complemented
56	#14519759	C₂²	1	2	yes	—
57	#14519759	C₂²	1	2	yes	—
58	#14519757	C₂²	1	1	yes	characteristic, complemented
59	#14519757	C₂²	1	2	yes	complemented
60	#14519757	C₂²	1	2	yes	complemented
61	#14519757	C₂²	1	1	yes	characteristic, complemented
62	#14519756	C₂²	1	1	yes	characteristic
63	#14519755	C₂²	1	2	yes	complemented
64	#14519755	C₂²	1	2	yes	complemented
65	#14519753	C₂²	1	1	yes	characteristic, complemented
66	#14519752	C₂²	1	1	yes	characteristic
67	#14519752	C₂²	1	1	yes	characteristic
68	#14519752	C₂²	1	1	yes	characteristic
69	#14519752	C₂²	1	2	yes	—
70	#14519752	C₂²	1	1	yes	characteristic
71	#14519752	C₂²	1	1	yes	characteristic
72	#14519752	C₂²	1	2	yes	complemented
73	#14519752	C₂²	1	2	yes	complemented
74	#14519752	C₂²	1	1	yes	characteristic, complemented
75	#14519752	C₂²	1	2	yes	complemented
76	#14519752	C₂²	1	2	yes	complemented
77	#14519751	C₂²	1	1	yes	characteristic
78	#14519751	C₂²	1	2	yes	complemented
79	#14519751	C₂²	1	2	yes	complemented
80	#14519751	C₂²	1	2	yes	complemented
81	#14519750	C₂²	1	2	yes	—
82	#14519750	C₂²	1	1	yes	characteristic
83	#14519750	C₂²	1	2	yes	complemented
84	#14519750	C₂²	1	2	yes	complemented
85	#14519750	C₂²	1	1	yes	characteristic, complemented
86	#14519750	C₂²	1	2	yes	complemented
87	#14519748	C₂²	1	1	yes	characteristic
88	#14519747	C₂²	1	2	yes	—
89	#14519747	C₂²	1	2	yes	—
90	#14519747	C₂²	1	2	yes	—
91	#14519745	C₂²	1	2	yes	—
92	#14519742	C₂²	1	1	yes	characteristic, complemented
93	C₄×D₂₄₄	C₂²	1	1	yes	characteristic
94	C₄×D₂₄₄	C₂²	1	1	yes	characteristic, complemented
95	C₄×D₂₄₄	C₂²	1	2	yes	complemented
96	C₄×D₂₄₄	C₂²	1	2	yes	complemented
97	#14519739	C₂²	1	1	yes	characteristic
98	#14519739	C₂²	1	2	yes	complemented
99	#14519739	C₂²	1	2	yes	complemented
100	#14519739	C₂²	1	2	yes	complemented
101	C₄×C₂²⋊D₆₁	C₂²	1	1	yes	characteristic
102	C₄×C₂²⋊D₆₁	C₂²	1	2	yes	complemented
103	C₄×C₂²⋊D₆₁	C₂²	1	1	yes	characteristic, complemented
104	#14519735	C₂²	1	1	yes	characteristic, complemented
105	#14519735	C₂²	1	2	yes	complemented
106	#14519734	C₂²	1	2	yes	complemented
107	#14519734	C₂²	1	2	yes	complemented
108	C₄⋊C₄×D₆₁	C₂²	1	1	yes	characteristic, complemented
109	C₂²⋊C₄×D₆₁	C₂²	1	2	yes	—
110	C₂²⋊C₄×D₆₁	C₂²	1	2	yes	—
111	C₄²×D₆₁	C₂²	1	1	yes	characteristic, complemented
112	#126×C₆₁	C₂²	1	2	yes	—
113	#125×C₆₁	C₂²	1	1	yes	characteristic, complemented
114	#125×C₆₁	C₂²	1	2	yes	complemented
115	#123×C₆₁	C₂²	1	2	yes	—
116	C₂²⋊Q₈×C₆₁	C₂²	1	1	yes	characteristic
117	C₂²⋊Q₈×C₆₁	C₂²	1	1	yes	characteristic, complemented
118	C₄×Q₈×C₆₁	C₂²	1	1	yes	characteristic, complemented
119	C₄×D₄×C₆₁	C₂²	1	1	yes	characteristic
120	#117×C₆₁	C₂²	1	1	yes	characteristic
121	#117×C₆₁	C₂²	1	2	yes	complemented
122	C₂×C₄⋊C₄×C₆₁	C₂²	1	1	yes	characteristic, complemented
123	C₂³×D₆₁	C₂³	1	2	yes	—
124	C₂×Q₈×C₆₁	C₂³	1	1	yes	characteristic
125	C₂×D₄×C₆₁	C₂³	1	1	yes	characteristic
126	C₂²×C₄×C₆₁	C₂³	1	1	yes	characteristic
127	C₂²×C₄×C₆₁	C₂³	1	1	yes	characteristic
128	C₂²×C₄×C₆₁	C₂³	1	2	yes	—
129	C₂×C₂²⋊D₆₁	C₂³	1	2	yes	—
130	C₂×C₂²⋊D₆₁	C₂³	1	1	yes	characteristic
131	C₂×C₂²⋊D₆₁	C₂³	1	1	yes	characteristic
132	C₂×C₂²⋊D₆₁	C₂³	1	1	yes	characteristic
133	C₂×C₂²⋊D₆₁	C₂³	1	1	yes	characteristic
134	C₂×C₂²⋊D₆₁	C₂³	1	1	yes	characteristic
135	C₂×C₂²⋊D₆₁	C₂³	1	2	yes	—
136	C₂×C₂²⋊D₆₁	C₂³	1	1	yes	characteristic
137	#11758226	—	4	2	no	—
138	Q₈×D₆₁	—	4	2	no	—
139	#11758222	—	4	2	no	—
140	#11758222	—	4	2	no	—
141	#11758222	—	4	2	no	—
142	C₂×D₂₄₄	—	4	2	no	—
143	C₂×D₂₄₄	C₂³	1	1	yes	characteristic
144	C₂×D₂₄₄	C₂³	1	1	yes	characteristic
145	C₂×D₂₄₄	C₂³	1	2	yes	—
146	C₂×D₂₄₄	C₂³	1	1	yes	characteristic
147	C₂×D₂₄₄	C₂³	1	1	yes	characteristic
148	C₂×D₂₄₄	C₂³	1	2	yes	—
149	C₂×D₂₄₄	C₂³	1	2	yes	—
150	C₂×D₂₄₄	C₂³	1	2	yes	—
151	C₂×D₂₄₄	C₂³	1	2	yes	—
152	C₂×D₂₄₄	C₂³	1	2	yes	—
153	C₂×D₂₄₄	C₂³	1	2	yes	—
154	C₂×D₂₄₄	C₂³	1	1	yes	characteristic
155	C₂×C₄×D₆₁	C₂³	1	1	yes	characteristic
156	C₂×C₄×D₆₁	C₂³	1	1	yes	characteristic
157	C₂×C₄×D₆₁	C₂³	1	1	yes	characteristic
158	C₂×C₄×D₆₁	C₂³	1	2	yes	—
159	C₂×C₄×D₆₁	C₂³	1	2	yes	—
160	C₂×C₄×D₆₁	C₂³	1	2	yes	—
161	C₂×C₄×D₆₁	C₂³	1	1	yes	characteristic
162	C₂×C₄×D₆₁	C₂³	1	1	yes	characteristic
163	C₂×C₄×D₆₁	C₂³	1	2	yes	—
164	C₂×C₄×D₆₁	C₂³	1	2	yes	—
165	C₂×C₄×D₆₁	C₂³	1	2	yes	—
166	C₂×Dic₁₂₂	C₂³	1	1	yes	characteristic
167	C₂×Dic₁₂₂	C₂³	1	2	yes	—
168	C₂×Dic₁₂₂	C₂³	1	1	yes	characteristic
169	C₂×Dic₁₂₂	C₂³	1	1	yes	characteristic
170	C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
171	C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
172	C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
173	C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
174	C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
175	C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
176	C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
177	C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
178	C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
179	C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
180	C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
181	C₂²⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
182	C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
183	C₂²⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
184	C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
185	C₄²×C₆₁	C₂³	1	2	yes	—
186	C₄²×C₆₁	C₂³	1	2	yes	—
187	C₄²×C₆₁	C₂³	1	1	yes	characteristic
188	C₂²⋊Dic₆₁	C₂³	1	1	yes	characteristic
189	C₂²⋊Dic₆₁	C₂³	1	2	yes	—
190	C₂²⋊Dic₆₁	C₂³	1	1	yes	characteristic
191	#11758198	C₂³	1	2	yes	—
192	#11758198	C₂³	1	2	yes	—
193	#11758198	C₂³	1	2	yes	—
194	#11758198	C₂³	1	2	yes	—
195	#11758198	C₂³	1	1	yes	characteristic
196	#11758198	C₂³	1	2	yes	—
197	#11758198	C₂³	1	2	yes	—
198	#11758198	C₂³	1	2	yes	—
199	#11758198	C₂³	1	2	yes	—
200	#11758198	C₂³	1	1	yes	characteristic
201	#11758198	C₂³	1	2	yes	—
202	#11758198	C₂³	1	2	yes	—
203	#11758198	C₂³	1	1	yes	characteristic
204	#11758198	C₂³	1	2	yes	—
205	#11758198	C₂³	1	2	yes	—
206	#11758198	C₂³	1	2	yes	—
207	#11758198	C₂³	1	2	yes	—
208	#11758198	C₂³	1	1	yes	characteristic
209	#11758198	C₂³	1	2	yes	—
210	#11758198	C₂³	1	2	yes	—
211	C₄⋊Dic₆₁	C₂³	1	1	yes	characteristic
212	C₄⋊Dic₆₁	C₂³	1	2	yes	—
213	C₄⋊Dic₆₁	C₂³	1	1	yes	characteristic
214	C₄⋊Dic₆₁	C₂³	1	2	yes	—
215	C₄⋊Dic₆₁	C₂³	1	2	yes	—
216	#11758196	C₂³	1	2	yes	—
217	#11758196	C₂³	1	2	yes	—
218	#11758196	C₂³	1	2	yes	—
219	#11758196	C₂³	1	2	yes	—
220	#11758196	C₂³	1	1	yes	characteristic
221	#11758196	C₂³	1	1	yes	characteristic
222	#11758196	C₂³	1	2	yes	—
223	C₄×Dic₆₁	C₂³	1	1	yes	characteristic
224	C₄×Dic₆₁	C₂³	1	1	yes	characteristic
225	C₄×Dic₆₁	C₂³	1	1	yes	characteristic
226	C₄×Dic₆₁	C₂³	1	2	yes	—
227	C₄×Dic₆₁	C₂³	1	2	yes	—
228	C₂³×C₆₁	C₂⁴	1	1	yes	characteristic
229	C₂³×C₆₁	C₂⁴	1	1	yes	characteristic
230	C₂²×D₆₁	—	4	2	no	—
231	C₂²×D₆₁	—	4	2	no	—
232	C₂²×D₆₁	—	4	2	no	—
233	C₂²×D₆₁	C₂⁴	1	2	yes	—
234	C₂²×D₆₁	C₂⁴	1	2	yes	—
235	C₂²×D₆₁	C₂⁴	1	1	yes	characteristic
236	C₂²×D₆₁	C₂⁴	1	1	yes	characteristic
237	C₂²×D₆₁	C₂⁴	1	1	yes	characteristic
238	Q₈×C₆₁	—	2	2	no	—
239	D₄×C₆₁	—	4	1	no	—
240	C₂×C₄×C₆₁	—	2	2	no	—
241	C₂×C₄×C₆₁	—	2	2	no	—
242	C₂×C₄×C₆₁	—	4	2	no	—
243	C₂×C₄×C₆₁	C₂⁴	1	2	yes	—
244	C₂×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
245	C₂×C₄×C₆₁	C₂⁴	1	2	yes	—
246	C₂×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
247	C₂×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
248	C₂×C₄×C₆₁	C₂⁴	1	2	yes	—
249	C₂×C₄×C₆₁	C₂⁴	1	2	yes	—
250	C₂×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
251	C₂×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
252	C₂²⋊D₆₁	—	4	2	no	—
253	C₂²⋊D₆₁	—	4	1	no	—
254	C₂²⋊D₆₁	—	4	1	no	—
255	C₂²⋊D₆₁	—	4	1	no	—
256	C₂²⋊D₆₁	—	4	1	no	—
257	C₂²⋊D₆₁	—	4	2	no	—
258	C₂²⋊D₆₁	—	4	1	no	—
259	C₂²⋊D₆₁	—	4	1	no	—
260	C₂×Dic₆₁	C₂⁴	1	1	yes	characteristic
261	C₂×Dic₆₁	C₂⁴	1	1	yes	characteristic
262	C₂×Dic₆₁	C₂⁴	1	1	yes	characteristic
263	C₂×Dic₆₁	C₂⁴	1	1	yes	characteristic
264	C₂×Dic₆₁	C₂⁴	1	2	yes	—
265	C₂×Dic₆₁	C₂⁴	1	2	yes	—
266	C₂×Dic₆₁	C₂⁴	1	1	yes	characteristic
267	D₂₄₄	—	2	2	no	—
268	D₂₄₄	—	2	2	no	—
269	D₂₄₄	—	4	2	no	—
270	D₂₄₄	—	4	2	no	—
271	D₂₄₄	—	4	2	no	—
272	D₂₄₄	—	4	2	no	—
273	D₂₄₄	—	4	1	no	—
274	D₂₄₄	—	4	2	no	—
275	D₂₄₄	—	4	2	no	—
276	D₂₄₄	—	4	1	no	—
277	D₂₄₄	—	4	1	no	—
278	D₂₄₄	—	4	2	no	—
279	C₄×D₆₁	—	2	2	no	—
280	C₄×D₆₁	—	2	2	no	—
281	C₄×D₆₁	—	2	2	no	—
282	C₄×D₆₁	—	4	2	no	—
283	C₄×D₆₁	—	4	1	no	—
284	C₄×D₆₁	—	4	2	no	—
285	C₄×D₆₁	—	4	2	no	—
286	C₄×D₆₁	—	4	1	no	—
287	C₄×D₆₁	—	4	2	no	—
288	C₄×D₆₁	—	4	2	no	—
289	C₄×D₆₁	—	4	2	no	—
290	Dic₁₂₂	—	2	2	no	—
291	Dic₁₂₂	—	4	1	no	—
292	Dic₁₂₂	—	4	1	no	—
293	Dic₁₂₂	—	4	2	no	—
294	C₂²×C₆₁	—	2	1	no	—
295	C₂²×C₆₁	—	2	1	no	—
296	C₂²×C₆₁	—	2	1	no	—
297	C₂²×C₆₁	—	2	1	no	—
298	C₂²×C₆₁	—	2	1	no	—
299	C₂²×C₆₁	—	2	1	no	—
300	C₂²×C₆₁	C₂⁵	1	1	yes	characteristic
301	C₂×D₆₁	—	2	1	no	—
302	C₂×D₆₁	—	2	1	no	—
303	C₂×D₆₁	—	2	1	no	—
304	C₂×D₆₁	—	2	2	no	—
305	C₂×D₆₁	—	2	2	no	—
306	C₂×D₆₁	—	2	1	no	—
307	C₂×D₆₁	—	2	1	no	—
308	C₂×D₆₁	—	2	1	no	—
309	C₂×D₆₁	—	2	2	no	—
310	C₂×D₆₁	—	2	2	no	—
311	C₂×D₆₁	—	2	1	no	—
312	C₂×D₆₁	—	2	1	no	—
313	C₂×D₆₁	—	2	1	no	—
314	C₂×D₆₁	—	2	2	no	—
315	C₂×D₆₁	—	2	2	no	—
316	C₂×D₆₁	—	8	4	no	—
317	C₄×C₆₁	—	2	1	no	—
318	C₄×C₆₁	—	2	2	no	—
319	C₄×C₆₁	—	2	1	no	—
320	C₄×C₆₁	—	2	1	no	—
321	C₄×C₆₁	—	2	2	no	—
322	C₄×C₆₁	—	2	2	no	—
323	C₄×C₆₁	—	2	1	no	—
324	C₄×C₆₁	—	2	2	no	—
325	C₄×C₆₁	H(5,𝔽₂)	1	2	yes	—
326	Dic₆₁	—	2	2	no	—
327	Dic₆₁	—	2	1	no	—
328	Dic₆₁	—	2	1	no	—
329	Dic₆₁	—	2	1	no	—
330	Dic₆₁	—	2	1	no	—
331	Dic₆₁	—	2	2	no	—
332	Dic₆₁	—	2	1	no	—
333	#3551	—	61	1	no	maximal, Sylow
334	C₂×C₆₁	—	4	1	no	—
335	C₂×C₆₁	—	4	1	no	—
336	C₂×C₆₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
337	C₂×C₆₁	#585	1	1	yes	characteristic
338	C₂×C₆₁	#585	1	1	yes	characteristic
339	D₆₁	—	4	1	no	—
340	D₆₁	—	4	1	no	—
341	D₆₁	—	4	1	no	—
342	D₆₁	—	4	2	no	—
343	D₆₁	—	4	2	no	—
344	#563	—	61	2	no	—
345	#560	—	61	2	no	—
346	#555	—	61	2	no	—
347	#553	—	61	1	no	—
348	#553	—	61	1	no	—
349	#552	—	61	1	no	—
350	#552	D₆₁	1	1	yes	characteristic, complemented
351	#551	—	61	2	no	—
352	#548	—	61	1	no	—
353	#548	—	61	1	no	—
354	#546	—	61	1	no	—
355	#546	—	61	1	no	—
356	#540	—	61	2	no	—
357	#540	—	61	2	no	—
358	#538	—	61	2	no	—
359	#538	—	61	2	no	—
360	#537	—	61	1	no	—
361	#537	—	61	1	no	—
362	#536	—	61	1	no	—
363	#535	—	61	1	no	—
364	#532	—	61	1	no	—
365	#529	—	61	1	no	—
366	#529	—	61	1	no	—
367	C₆₁	#3551	1	1	yes	characteristic, complemented, Sylow
368	C₂×#41	—	61	1	no	—
369	C₂×#41	—	61	1	no	—
370	C₂×#41	—	61	1	no	—
371	C₂×#41	—	61	1	no	—
372	C₂²×Q₈	—	61	1	no	—
373	C₂²×D₄	—	61	1	no	—
374	C₄⋊Q₈	—	61	1	no	—
375	C₄⋊Q₈	—	61	2	no	—
376	#127	—	61	1	no	—
377	#127	—	61	2	no	—
378	#126	—	61	2	no	—
379	#126	—	61	2	no	—
380	#126	—	61	2	no	—
381	#126	—	61	2	no	—
382	#126	—	61	2	no	—
383	#126	C₂×D₆₁	1	2	yes	—
384	#125	—	61	1	no	—
385	#125	—	61	2	no	—
386	#125	C₂×D₆₁	1	1	yes	characteristic, complemented
387	#125	C₂×D₆₁	1	2	yes	complemented
388	#124	—	61	1	no	—
389	#124	—	61	1	no	—
390	#124	—	61	1	no	—
391	#124	—	61	2	no	—
392	#124	—	61	2	no	—
393	#124	—	61	1	no	—
394	#124	—	61	2	no	—
395	#124	—	61	2	no	—
396	#123	—	61	2	no	—
397	#123	—	61	2	no	—
398	#123	—	61	2	no	—
399	#123	—	61	2	no	—
400	#123	—	61	2	no	—
401	#123	—	61	2	no	—
402	#123	—	61	2	no	—
403	#123	—	61	2	no	—
404	#123	—	61	2	no	—
405	#123	C₂×D₆₁	1	2	yes	—
406	C₂²⋊Q₈	—	61	1	no	—
407	C₂²⋊Q₈	—	61	1	no	—
408	C₂²⋊Q₈	—	61	1	no	—
409	C₂²⋊Q₈	—	61	1	no	—
410	C₂²⋊Q₈	—	61	2	no	—
411	C₂²⋊Q₈	—	61	2	no	—
412	C₂²⋊Q₈	—	61	2	no	—
413	C₂²⋊Q₈	—	61	2	no	—
414	C₂²⋊Q₈	C₂×D₆₁	1	1	yes	characteristic
415	C₂²⋊Q₈	C₂×D₆₁	1	1	yes	characteristic, complemented
416	#121	—	61	1	no	—
417	#121	—	61	2	no	—
418	#121	—	61	1	no	—
419	#121	—	61	2	no	—
420	#121	—	61	2	no	—
421	#121	—	61	1	no	—
422	#121	—	61	1	no	—
423	#121	—	61	1	no	—
424	#121	—	61	1	no	—
425	#121	—	61	1	no	—
426	#121	—	61	2	no	—
427	#121	—	61	2	no	—
428	#121	—	61	1	no	—
429	#121	—	61	2	no	—
430	#121	—	61	2	no	—
431	#121	—	61	2	no	—
432	#121	—	61	1	no	—
433	#121	—	61	1	no	—
434	#121	—	61	2	no	—
435	#121	—	61	2	no	—
436	#121	—	61	2	no	—
437	#121	—	61	2	no	—
438	#120	—	61	2	no	—
439	#120	—	61	2	no	—
440	#120	—	61	2	no	—
441	#120	—	61	2	no	—
442	C₄×Q₈	—	61	1	no	—
443	C₄×Q₈	C₂×D₆₁	1	1	yes	characteristic, complemented
444	C₄×D₄	—	61	1	no	—
445	C₄×D₄	—	61	1	no	—
446	C₄×D₄	—	61	2	no	—
447	C₄×D₄	—	61	2	no	—
448	C₄×D₄	—	61	1	no	—
449	C₄×D₄	—	61	2	no	—
450	C₄×D₄	—	61	2	no	—
451	C₄×D₄	—	61	2	no	—
452	C₄×D₄	—	61	1	no	—
453	C₄×D₄	—	61	1	no	—
454	C₄×D₄	—	61	2	no	—
455	C₄×D₄	C₂×D₆₁	1	1	yes	characteristic
456	#117	—	61	2	no	—
457	#117	—	61	1	no	—
458	#117	—	61	2	no	—
459	#117	—	61	2	no	—
460	#117	C₂×D₆₁	1	1	yes	characteristic
461	#117	C₂×D₆₁	1	2	yes	complemented
462	C₂×C₄⋊C₄	—	61	1	no	—
463	C₂×C₄⋊C₄	C₂×D₆₁	1	1	yes	characteristic, complemented
464	C₂×C₂²⋊C₄	—	61	2	no	—
465	C₂×C₂²⋊C₄	—	61	2	no	—
466	C₂×C₄²	—	61	1	no	—
467	C₂⁴	—	61	2	no	—
468	#41	—	244	2	no	—
469	#41	—	244	2	no	—
470	#41	—	244	2	no	—
471	#41	—	244	2	no	—
472	C₂×Q₈	—	61	1	no	—
473	C₂×Q₈	—	61	1	no	—
474	C₂×Q₈	—	61	2	no	—
475	C₂×Q₈	—	61	1	no	—
476	C₂×Q₈	—	244	2	no	—
477	C₂×Q₈	C₂²×D₆₁	1	1	yes	characteristic
478	C₂×D₄	—	61	1	no	—
479	C₂×D₄	—	61	2	no	—
480	C₂×D₄	—	61	1	no	—
481	C₂×D₄	—	61	1	no	—
482	C₂×D₄	—	61	1	no	—
483	C₂×D₄	—	61	2	no	—
484	C₂×D₄	—	61	1	no	—
485	C₂×D₄	—	61	1	no	—
486	C₂×D₄	—	61	1	no	—
487	C₂×D₄	—	61	1	no	—
488	C₂×D₄	—	61	2	no	—
489	C₂×D₄	—	61	2	no	—
490	C₂×D₄	—	61	2	no	—
491	C₂×D₄	—	61	2	no	—
492	C₂×D₄	—	61	2	no	—
493	C₂×D₄	—	61	1	no	—
494	C₂×D₄	—	61	2	no	—
495	C₂×D₄	—	61	1	no	—
496	C₂×D₄	—	61	2	no	—
497	C₂×D₄	—	61	1	no	—
498	C₂×D₄	—	244	2	no	—
499	C₂×D₄	C₂²×D₆₁	1	1	yes	characteristic
500	C₂²×C₄	—	61	1	no	—
501	C₂²×C₄	—	61	1	no	—
502	C₂²×C₄	—	61	1	no	—
503	C₂²×C₄	—	61	1	no	—
504	C₂²×C₄	—	61	1	no	—
505	C₂²×C₄	—	61	2	no	—
506	C₂²×C₄	—	61	2	no	—
507	C₂²×C₄	—	61	2	no	—
508	C₂²×C₄	—	61	2	no	—
509	C₂²×C₄	—	61	2	no	—
510	C₂²×C₄	—	61	2	no	—
511	C₂²×C₄	C₂²×D₆₁	1	1	yes	characteristic
512	C₂²×C₄	C₂²×D₆₁	1	1	yes	characteristic
513	C₂²×C₄	C₂²×D₆₁	1	2	yes	—
514	C₄⋊C₄	—	61	2	no	—
515	C₄⋊C₄	—	61	1	no	—
516	C₄⋊C₄	—	61	2	no	—
517	C₄⋊C₄	—	61	2	no	—
518	C₄⋊C₄	—	61	2	no	—
519	C₄⋊C₄	—	61	1	no	—
520	C₄⋊C₄	—	61	1	no	—
521	C₄⋊C₄	—	61	2	no	—
522	C₄⋊C₄	—	61	2	no	—
523	C₄⋊C₄	—	61	2	no	—
524	C₄⋊C₄	—	61	1	no	—
525	C₄⋊C₄	—	61	2	no	—
526	C₄⋊C₄	C₂²×D₆₁	1	1	yes	characteristic
527	C₄⋊C₄	C₂²×D₆₁	1	1	yes	characteristic
528	C₄⋊C₄	C₂²×D₆₁	1	1	yes	characteristic
529	C₄⋊C₄	C₂²×D₆₁	1	2	yes	—
530	C₄⋊C₄	C₂²×D₆₁	1	2	yes	—
531	C₄⋊C₄	C₂²×D₆₁	1	2	yes	—
532	C₄⋊C₄	C₂²×D₆₁	1	2	yes	—
533	C₄⋊C₄	C₂²×D₆₁	1	2	yes	—
534	C₄⋊C₄	C₂²×D₆₁	1	1	yes	characteristic
535	C₄⋊C₄	C₂²×D₆₁	1	2	yes	—
536	C₂²⋊C₄	—	61	1	no	—
537	C₂²⋊C₄	—	61	2	no	—
538	C₂²⋊C₄	—	61	1	no	—
539	C₂²⋊C₄	—	61	2	no	—
540	C₂²⋊C₄	—	61	2	no	—
541	C₂²⋊C₄	—	61	2	no	—
542	C₂²⋊C₄	—	61	2	no	—
543	C₂²⋊C₄	—	61	1	no	—
544	C₂²⋊C₄	—	61	2	no	—
545	C₂²⋊C₄	—	61	2	no	—
546	C₂²⋊C₄	—	61	2	no	—
547	C₂²⋊C₄	—	61	2	no	—
548	C₂²⋊C₄	—	61	1	no	—
549	C₂²⋊C₄	—	61	1	no	—
550	C₂²⋊C₄	—	61	1	no	—
551	C₂²⋊C₄	—	61	2	no	—
552	C₂²⋊C₄	—	61	2	no	—
553	C₂²⋊C₄	—	61	2	no	—
554	C₂²⋊C₄	—	61	2	no	—
555	C₂²⋊C₄	—	61	2	no	—
556	C₂²⋊C₄	—	61	2	no	—
557	C₂²⋊C₄	—	61	2	no	—
558	C₂²⋊C₄	—	61	2	no	—
559	C₂²⋊C₄	C₂²×D₆₁	1	1	yes	characteristic
560	C₂²⋊C₄	C₂²×D₆₁	1	2	yes	—
561	C₂²⋊C₄	C₂²×D₆₁	1	2	yes	—
562	C₂²⋊C₄	C₂²×D₆₁	1	1	yes	characteristic
563	C₂²⋊C₄	C₂²×D₆₁	1	2	yes	—
564	C₄²	—	61	1	no	—
565	C₄²	—	61	1	no	—
566	C₄²	—	61	1	no	—
567	C₄²	—	61	2	no	—
568	C₄²	—	61	2	no	—
569	C₄²	C₂²×D₆₁	1	1	yes	characteristic
570	C₄²	C₂²×D₆₁	1	2	yes	—
571	C₄²	C₂²×D₆₁	1	2	yes	—
572	C₂³	—	61	2	no	—
573	C₂³	—	61	2	no	—
574	C₂³	—	61	1	no	—
575	C₂³	—	61	1	no	—
576	C₂³	—	61	1	no	—
577	C₂³	—	244	2	no	—
578	C₂³	—	244	2	no	—
579	C₂³	—	244	2	no	—
580	C₂³	C₂³×D₆₁	1	1	yes	characteristic
581	C₂³	C₂³×D₆₁	1	1	yes	characteristic
582	Q₈	—	2	2	no	—
583	Q₈	—	122	2	no	—
584	Q₈	—	244	2	no	—
585	Q₈	—	244	1	no	—
586	Q₈	—	244	1	no	—
587	D₄	—	4	1	no	—
588	D₄	—	122	2	no	—
589	D₄	—	122	2	no	—
590	D₄	—	244	2	no	—
591	D₄	—	244	2	no	—
592	D₄	—	244	2	no	—
593	D₄	—	244	1	no	—
594	D₄	—	244	2	no	—
595	D₄	—	244	2	no	—
596	D₄	—	244	2	no	—
597	D₄	—	244	1	no	—
598	D₄	—	244	1	no	—
599	D₄	—	244	2	no	—
600	D₄	—	244	2	no	—
601	D₄	—	244	1	no	—
602	D₄	—	244	1	no	—
603	D₄	—	244	1	no	—
604	D₄	—	244	1	no	—
605	D₄	—	244	1	no	—
606	D₄	—	244	1	no	—
607	D₄	—	244	2	no	—
608	C₂×C₄	—	2	2	no	—
609	C₂×C₄	—	2	2	no	—
610	C₂×C₄	—	4	2	no	—
611	C₂×C₄	—	61	1	no	—
612	C₂×C₄	—	61	1	no	—
613	C₂×C₄	—	61	1	no	—
614	C₂×C₄	—	61	1	no	—
615	C₂×C₄	—	61	2	no	—
616	C₂×C₄	—	61	2	no	—
617	C₂×C₄	—	61	1	no	—
618	C₂×C₄	—	122	2	no	—
619	C₂×C₄	—	122	2	no	—
620	C₂×C₄	—	122	2	no	—
621	C₂×C₄	—	244	2	no	—
622	C₂×C₄	—	244	1	no	—
623	C₂×C₄	—	244	2	no	—
624	C₂×C₄	—	244	1	no	—
625	C₂×C₄	—	244	2	no	—
626	C₂×C₄	—	244	2	no	—
627	C₂×C₄	—	244	2	no	—
628	C₂×C₄	—	244	2	no	—
629	C₂×C₄	C₂³×D₆₁	1	1	yes	characteristic
630	C₂×C₄	C₂³×D₆₁	1	1	yes	characteristic
631	C₂×C₄	C₂³×D₆₁	1	2	yes	—
632	C₂×C₄	C₂³×D₆₁	1	2	yes	—
633	C₂×C₄	C₂³×D₆₁	1	2	yes	—
634	C₂×C₄	C₂³×D₆₁	1	1	yes	characteristic
635	C₂×C₄	C₂³×D₆₁	1	2	yes	—
636	C₂×C₄	C₂³×D₆₁	1	1	yes	characteristic
637	C₂×C₄	C₂³×D₆₁	1	1	yes	characteristic
638	C₂²	—	2	1	no	—
639	C₂²	—	2	1	no	—
640	C₂²	—	2	1	no	—
641	C₂²	—	2	1	no	—
642	C₂²	—	2	1	no	—
643	C₂²	—	2	1	no	—
644	C₂²	—	122	1	no	—
645	C₂²	—	122	1	no	—
646	C₂²	—	122	1	no	—
647	C₂²	—	122	2	no	—
648	C₂²	—	122	2	no	—
649	C₂²	—	122	1	no	—
650	C₂²	—	122	2	no	—
651	C₂²	—	122	1	no	—
652	C₂²	—	122	1	no	—
653	C₂²	—	122	2	no	—
654	C₂²	—	122	1	no	—
655	C₂²	—	122	1	no	—
656	C₂²	—	122	2	no	—
657	C₂²	—	122	1	no	—
658	C₂²	—	122	2	no	—
659	C₂²	—	488	4	no	—
660	C₂²	C₂⁴×D₆₁	1	1	yes	characteristic
661	C₄	—	2	1	no	—
662	C₄	—	2	1	no	—
663	C₄	—	2	2	no	—
664	C₄	—	2	2	no	—
665	C₄	—	2	2	no	—
666	C₄	—	2	1	no	—
667	C₄	—	2	1	no	—
668	C₄	—	2	2	no	—
669	C₄	—	122	1	no	—
670	C₄	—	122	1	no	—
671	C₄	—	122	1	no	—
672	C₄	—	122	2	no	—
673	C₄	—	122	1	no	—
674	C₄	—	122	2	no	—
675	C₄	—	122	1	no	—
676	C₄	#14519823	1	2	yes	—
677	C₂	—	4	1	no	—
678	C₂	—	4	1	no	—
679	C₂	—	244	2	no	—
680	C₂	—	244	2	no	—
681	C₂	—	244	1	no	—
682	C₂	—	244	1	no	—
683	C₂	—	244	1	no	—
684	C₂	C₂×#14519823	1	1	yes	characteristic
685	C₂	#16840598	1	1	yes	characteristic
686	C₂	#16840599	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₆₁
commutator, socle	C₂²×C₆₁	C₂⁵
Fitting	C₆₁×#552	C₂
hypercenter	#552	D₆₁
hypocenter	C₆₁	#3551
LCS	G ▷ C₂²×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂² ◁ #552

Complements

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

N	H ≅ G/N	type
1. #16840516	C₂	semidirect
2. #16840502	C₂	semidirect
3. #16840475	C₂	semidirect
4. #16840465	C₂	semidirect
5. #16840460	C₂	semidirect
6. #16840451	C₂	semidirect
7. #16840437	C₂	semidirect
8. #16840424	C₂	semidirect
9. #16840422	C₂	semidirect
10. #16840408	C₂	semidirect
11. #16840403	C₂	semidirect
12. #16840368	C₂	semidirect
13. #16840367	C₂	semidirect
14. #16840351	C₂	semidirect
15. #16840348	C₂	semidirect
16. #16840343	C₂	semidirect
17. #16840342	C₂	semidirect
18. #16840335	C₂	semidirect
19. #16840331	C₂	semidirect
20. #16840309	C₂	semidirect
21. #16840299	C₂	semidirect
22. #16840297	C₂	semidirect
23. C₆₁×#552	C₂	semidirect
27. C₂×#11758222	C₂²	semidirect
28. C₂×Q₈×D₆₁	C₂²	semidirect
30. #14519776	C₂²	semidirect
31. #14519776	C₂²	semidirect
34. #14519772	C₂²	semidirect
35. #14519772	C₂²	semidirect
36. #14519772	C₂²	semidirect
37. #14519772	C₂²	semidirect
39. #14519769	C₂²	semidirect
40. #14519768	C₂²	semidirect
44. #14519765	C₂²	semidirect
47. #14519763	C₂²	semidirect
48. #14519763	C₂²	semidirect
51. #14519762	C₂²	semidirect
52. #14519762	C₂²	semidirect
53. #14519762	C₂²	semidirect
54. #14519762	C₂²	semidirect
55. #14519762	C₂²	semidirect
58. #14519757	C₂²	semidirect
59. #14519757	C₂²	semidirect
60. #14519757	C₂²	semidirect
61. #14519757	C₂²	semidirect
63. #14519755	C₂²	semidirect
64. #14519755	C₂²	semidirect
65. #14519753	C₂²	semidirect
72. #14519752	C₂²	semidirect
73. #14519752	C₂²	semidirect
74. #14519752	C₂²	semidirect
75. #14519752	C₂²	semidirect
76. #14519752	C₂²	semidirect
78. #14519751	C₂²	semidirect
79. #14519751	C₂²	semidirect
80. #14519751	C₂²	semidirect
83. #14519750	C₂²	semidirect
84. #14519750	C₂²	semidirect
85. #14519750	C₂²	semidirect
86. #14519750	C₂²	semidirect
92. #14519742	C₂²	semidirect
94. C₄×D₂₄₄	C₂²	semidirect
95. C₄×D₂₄₄	C₂²	semidirect
96. C₄×D₂₄₄	C₂²	semidirect
98. #14519739	C₂²	semidirect
99. #14519739	C₂²	semidirect
100. #14519739	C₂²	semidirect
102. C₄×C₂²⋊D₆₁	C₂²	semidirect
103. C₄×C₂²⋊D₆₁	C₂²	semidirect
104. #14519735	C₂²	semidirect
105. #14519735	C₂²	semidirect
106. #14519734	C₂²	semidirect
107. #14519734	C₂²	semidirect
108. C₄⋊C₄×D₆₁	C₂²	semidirect
111. C₄²×D₆₁	C₂²	semidirect
113. #125×C₆₁	C₂²	semidirect
114. #125×C₆₁	C₂²	semidirect
117. C₂²⋊Q₈×C₆₁	C₂²	semidirect
118. C₄×Q₈×C₆₁	C₂²	semidirect
121. #117×C₆₁	C₂²	semidirect
122. C₂×C₄⋊C₄×C₆₁	C₂²	semidirect
350. #552	D₆₁	semidirect
367. C₆₁	#3551	semidirect
386. #125	C₂×D₆₁	semidirect
387. #125	C₂×D₆₁	semidirect
415. C₂²⋊Q₈	C₂×D₆₁	semidirect
443. C₄×Q₈	C₂×D₆₁	semidirect
461. #117	C₂×D₆₁	semidirect
463. C₂×C₄⋊C₄	C₂×D₆₁	semidirect