Subgroups — #21459892

Order 7808.

1042 conjugacy classes of subgroups.

The subgroup lattice has 646 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16840484	C₂	1	1	yes	maximal, characteristic, complemented
2	#16840473	C₂	1	1	yes	maximal, characteristic, complemented
3	#16840463	C₂	1	2	yes	maximal, complemented
4	#16840456	C₂	1	1	yes	maximal, characteristic, complemented
5	#16840453	C₂	1	2	yes	maximal, complemented
6	#16840451	C₂	1	1	yes	maximal, characteristic, complemented
7	#16840442	C₂	1	2	yes	maximal, complemented
8	#16840437	C₂	1	2	yes	maximal, complemented
9	#16840414	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	#16840386	C₂	1	1	yes	maximal, characteristic, complemented
13	#16840372	C₂	1	1	yes	maximal, characteristic, complemented
14	#16840353	C₂	1	2	yes	maximal, complemented
15	#16840346	C₂	1	2	yes	maximal, complemented
16	#16840299	C₂	1	2	yes	maximal, complemented
17	#16840298	C₂	1	1	yes	maximal, characteristic, complemented
18	#16840292	C₂	1	1	yes	maximal, characteristic, complemented
19	#126×D₆₁	C₂	1	2	yes	maximal, complemented
20	#16840244	C₂	1	1	yes	maximal, characteristic, complemented
21	#16840236	C₂	1	1	yes	maximal, characteristic, complemented
22	#16840230	C₂	1	1	yes	maximal, characteristic, complemented
23	C₆₁×#556	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#11758226	C₂²	1	1	yes	characteristic
25	C₂×#11758222	C₂²	1	1	yes	characteristic
26	C₂²×D₂₄₄	C₂²	1	1	yes	characteristic
27	#14519775	C₂²	1	1	yes	characteristic, complemented
28	#14519772	C₂²	1	2	yes	complemented
29	#14519772	C₂²	1	2	yes	complemented
30	#14519772	C₂²	1	2	yes	complemented
31	#14519772	C₂²	1	1	yes	characteristic, complemented
32	#14519771	C₂²	1	2	yes	complemented
33	#14519771	C₂²	1	2	yes	complemented
34	#14519770	C₂²	1	2	yes	—
35	#14519770	C₂²	1	1	yes	characteristic
36	#14519770	C₂²	1	2	yes	—
37	#14519770	C₂²	1	2	yes	—
38	#14519769	C₂²	1	2	yes	complemented
39	#14519768	C₂²	1	1	yes	characteristic, complemented
40	#14519768	C₂²	1	1	yes	characteristic, complemented
41	#14519768	C₂²	1	2	yes	complemented
42	#14519767	C₂²	1	1	yes	characteristic, complemented
43	#14519767	C₂²	1	2	yes	complemented
44	#14519766	C₂²	1	1	yes	characteristic
45	#14519766	C₂²	1	2	yes	complemented
46	#14519765	C₂²	1	1	yes	characteristic
47	#14519763	C₂²	1	1	yes	characteristic
48	#14519762	C₂²	1	2	yes	—
49	#14519762	C₂²	1	2	yes	—
50	#14519762	C₂²	1	2	yes	complemented
51	#14519762	C₂²	1	2	yes	complemented
52	#14519761	C₂²	1	1	yes	characteristic, complemented
53	#14519761	C₂²	1	2	yes	complemented
54	#14519759	C₂²	1	2	yes	—
55	#14519759	C₂²	1	2	yes	complemented
56	#14519759	C₂²	1	2	yes	complemented
57	#14519758	C₂²	1	1	yes	characteristic
58	#14519757	C₂²	1	1	yes	characteristic, complemented
59	#14519757	C₂²	1	2	yes	complemented
60	#14519756	C₂²	1	1	yes	characteristic
61	#14519755	C₂²	1	2	yes	complemented
62	#14519754	C₂²	1	1	yes	characteristic, complemented
63	#14519753	C₂²	1	2	yes	complemented
64	#14519753	C₂²	1	2	yes	complemented
65	#14519753	C₂²	1	2	yes	complemented
66	#14519752	C₂²	1	1	yes	characteristic
67	#14519752	C₂²	1	2	yes	—
68	#14519751	C₂²	1	1	yes	characteristic
69	#14519750	C₂²	1	2	yes	—
70	#14519750	C₂²	1	2	yes	complemented
71	#14519750	C₂²	1	2	yes	complemented
72	#14519749	C₂²	1	1	yes	characteristic
73	#14519747	C₂²	1	2	yes	—
74	#14519745	C₂²	1	2	yes	—
75	Q₈×Dic₆₁	C₂²	1	1	yes	characteristic, complemented
76	C₄×Dic₁₂₂	C₂²	1	1	yes	characteristic, complemented
77	#14519742	C₂²	1	1	yes	characteristic, complemented
78	#14519742	C₂²	1	1	yes	characteristic, complemented
79	C₄×D₂₄₄	C₂²	1	2	yes	—
80	C₄×D₂₄₄	C₂²	1	1	yes	characteristic
81	C₄×D₂₄₄	C₂²	1	2	yes	—
82	C₄×D₂₄₄	C₂²	1	2	yes	complemented
83	C₄×D₂₄₄	C₂²	1	2	yes	complemented
84	#14519739	C₂²	1	1	yes	characteristic
85	#14519739	C₂²	1	1	yes	characteristic
86	#14519739	C₂²	1	1	yes	characteristic
87	#14519739	C₂²	1	1	yes	characteristic
88	#14519739	C₂²	1	1	yes	characteristic
89	#14519739	C₂²	1	2	yes	complemented
90	C₄×C₂²⋊D₆₁	C₂²	1	1	yes	characteristic
91	C₄×C₂²⋊D₆₁	C₂²	1	1	yes	characteristic, complemented
92	#14519737	C₂²	1	2	yes	complemented
93	#14519737	C₂²	1	2	yes	complemented
94	#14519737	C₂²	1	2	yes	complemented
95	#14519736	C₂²	1	1	yes	characteristic
96	#14519735	C₂²	1	2	yes	complemented
97	#14519734	C₂²	1	2	yes	complemented
98	#14519734	C₂²	1	2	yes	complemented
99	#14519734	C₂²	1	2	yes	complemented
100	#14519734	C₂²	1	2	yes	complemented
101	#14519734	C₂²	1	1	yes	characteristic, complemented
102	C₄⋊C₄×D₆₁	C₂²	1	1	yes	characteristic, complemented
103	C₄⋊C₄×D₆₁	C₂²	1	2	yes	complemented
104	C₄⋊C₄×D₆₁	C₂²	1	2	yes	complemented
105	C₄⋊C₄×D₆₁	C₂²	1	2	yes	complemented
106	C₂²⋊C₄×D₆₁	C₂²	1	2	yes	—
107	C₂²⋊C₄×D₆₁	C₂²	1	2	yes	—
108	C₂²⋊C₄×D₆₁	C₂²	1	2	yes	—
109	C₂²⋊C₄×D₆₁	C₂²	1	2	yes	—
110	C₂×C₄×Dic₆₁	C₂²	1	1	yes	characteristic, complemented
111	C₄²×D₆₁	C₂²	1	2	yes	complemented
112	C₄⋊Q₈×C₆₁	C₂²	1	1	yes	characteristic, complemented
113	#126×C₆₁	C₂²	1	2	yes	—
114	#126×C₆₁	C₂²	1	2	yes	complemented
115	#124×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	2	yes	complemented
119	C₄×Q₈×C₆₁	C₂²	1	1	yes	characteristic, complemented
120	C₄×D₄×C₆₁	C₂²	1	1	yes	characteristic
121	#117×C₆₁	C₂²	1	1	yes	characteristic
122	#117×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×Q₈×C₆₁	C₂³	1	2	yes	—
126	C₂×D₄×C₆₁	C₂³	1	1	yes	characteristic
127	C₂²×C₄×C₆₁	C₂³	1	1	yes	characteristic
128	C₂²×C₄×C₆₁	C₂³	1	1	yes	characteristic
129	C₂×C₂²⋊D₆₁	C₂³	1	2	yes	—
130	C₂×C₂²⋊D₆₁	C₂³	1	2	yes	—
131	C₂×C₂²⋊D₆₁	C₂³	1	1	yes	characteristic
132	C₂×C₂²⋊D₆₁	C₂³	1	1	yes	characteristic
133	C₂²×Dic₆₁	C₂³	1	1	yes	characteristic
134	C₂²×Dic₆₁	C₂³	1	1	yes	characteristic
135	#11758226	—	2	4	no	—
136	#11758222	—	2	4	no	—
137	C₂×D₂₄₄	—	2	4	no	—
138	C₂×D₂₄₄	C₂³	1	1	yes	characteristic
139	C₂×D₂₄₄	C₂³	1	2	yes	—
140	C₂×D₂₄₄	C₂³	1	2	yes	—
141	C₂×D₂₄₄	C₂³	1	2	yes	—
142	C₂×D₂₄₄	C₂³	1	1	yes	characteristic
143	C₂×C₄×D₆₁	C₂³	1	2	yes	—
144	C₂×C₄×D₆₁	C₂³	1	2	yes	—
145	C₂×C₄×D₆₁	C₂³	1	1	yes	characteristic
146	C₂×C₄×D₆₁	C₂³	1	2	yes	—
147	C₂×C₄×D₆₁	C₂³	1	2	yes	—
148	C₂×C₄×D₆₁	C₂³	1	2	yes	—
149	C₂×C₄×D₆₁	C₂³	1	2	yes	—
150	C₂×C₄×D₆₁	C₂³	1	2	yes	—
151	C₂×C₄×D₆₁	C₂³	1	2	yes	—
152	C₂×C₄×D₆₁	C₂³	1	2	yes	—
153	C₂×Dic₁₂₂	C₂³	1	1	yes	characteristic
154	C₂×Dic₁₂₂	C₂³	1	1	yes	characteristic
155	C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
156	C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
157	C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
158	C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
159	C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
160	C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
161	C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
162	C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
163	C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
164	C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
165	C₂²⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
166	C₂²⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
167	C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
168	C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
169	C₄²×C₆₁	C₂³	1	2	yes	—
170	C₄²×C₆₁	C₂³	1	2	yes	—
171	C₄²×C₆₁	C₂³	1	1	yes	characteristic
172	C₄²×C₆₁	C₂³	1	2	yes	—
173	C₂²⋊Dic₆₁	C₂³	1	1	yes	characteristic
174	C₂²⋊Dic₆₁	C₂³	1	1	yes	characteristic
175	C₂²⋊Dic₆₁	C₂³	1	1	yes	characteristic
176	C₂²⋊Dic₆₁	C₂³	1	2	yes	—
177	C₂²⋊Dic₆₁	C₂³	1	1	yes	characteristic
178	#11758198	C₂³	1	2	yes	—
179	#11758198	C₂³	1	2	yes	—
180	#11758198	C₂³	1	2	yes	—
181	#11758198	C₂³	1	2	yes	—
182	#11758198	C₂³	1	2	yes	—
183	#11758198	C₂³	1	2	yes	—
184	#11758198	C₂³	1	2	yes	—
185	#11758198	C₂³	1	2	yes	—
186	#11758198	C₂³	1	1	yes	characteristic
187	#11758198	C₂³	1	2	yes	—
188	#11758198	C₂³	1	1	yes	characteristic
189	#11758198	C₂³	1	2	yes	—
190	#11758198	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	1	yes	characteristic
195	C₄⋊Dic₆₁	C₂³	1	1	yes	characteristic
196	C₄⋊Dic₆₁	C₂³	1	1	yes	characteristic
197	C₄⋊Dic₆₁	C₂³	1	2	yes	—
198	C₄⋊Dic₆₁	C₂³	1	2	yes	—
199	C₄⋊Dic₆₁	C₂³	1	2	yes	—
200	C₄⋊Dic₆₁	C₂³	1	1	yes	characteristic
201	C₄⋊Dic₆₁	C₂³	1	1	yes	characteristic
202	C₄⋊Dic₆₁	C₂³	1	2	yes	—
203	#11758196	C₂³	1	1	yes	characteristic
204	#11758196	C₂³	1	2	yes	—
205	#11758196	C₂³	1	1	yes	characteristic
206	#11758196	C₂³	1	2	yes	—
207	#11758196	C₂³	1	2	yes	—
208	#11758196	C₂³	1	2	yes	—
209	#11758196	C₂³	1	1	yes	characteristic
210	#11758196	C₂³	1	1	yes	characteristic
211	#11758196	C₂³	1	2	yes	—
212	#11758196	C₂³	1	2	yes	—
213	#11758196	C₂³	1	2	yes	—
214	#11758196	C₂³	1	2	yes	—
215	#11758196	C₂³	1	1	yes	characteristic
216	#11758196	C₂³	1	1	yes	characteristic
217	C₄×Dic₆₁	C₂³	1	1	yes	characteristic
218	C₄×Dic₆₁	C₂³	1	2	yes	—
219	C₄×Dic₆₁	C₂³	1	2	yes	—
220	C₄×Dic₆₁	C₂³	1	1	yes	characteristic
221	C₄×Dic₆₁	C₂³	1	1	yes	characteristic
222	C₄×Dic₆₁	C₂³	1	1	yes	characteristic
223	C₄×Dic₆₁	C₂³	1	2	yes	—
224	C₄×Dic₆₁	C₂³	1	1	yes	characteristic
225	C₂³×C₆₁	C₂⁴	1	1	yes	characteristic
226	C₂³×C₆₁	C₂⁴	1	1	yes	characteristic
227	C₂²×D₆₁	—	2	4	no	—
228	C₂²×D₆₁	—	4	2	no	—
229	C₂²×D₆₁	—	4	2	no	—
230	C₂²×D₆₁	C₂⁴	1	2	yes	—
231	C₂²×D₆₁	C₂⁴	1	1	yes	characteristic
232	C₂²×D₆₁	C₂⁴	1	2	yes	—
233	Q₈×C₆₁	—	2	2	no	—
234	Q₈×C₆₁	—	4	2	no	—
235	D₄×C₆₁	—	4	1	no	—
236	C₂×C₄×C₆₁	—	2	2	no	—
237	C₂×C₄×C₆₁	—	2	2	no	—
238	C₂×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
239	C₂×C₄×C₆₁	C₂⁴	1	2	yes	—
240	C₂×C₄×C₆₁	C₂⁴	1	2	yes	—
241	C₂×C₄×C₆₁	C₂⁴	1	2	yes	—
242	C₂×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
243	C₂×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
244	C₂×C₄×C₆₁	C₂⁴	1	2	yes	—
245	C₂×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
246	C₂×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
247	C₂²⋊D₆₁	—	2	4	no	—
248	C₂²⋊D₆₁	—	4	1	no	—
249	C₂²⋊D₆₁	—	4	2	no	—
250	C₂²⋊D₆₁	—	4	1	no	—
251	C₂×Dic₆₁	—	4	1	no	—
252	C₂×Dic₆₁	—	4	1	no	—
253	C₂×Dic₆₁	C₂⁴	1	1	yes	characteristic
254	C₂×Dic₆₁	C₂⁴	1	1	yes	characteristic
255	C₂×Dic₆₁	C₂⁴	1	1	yes	characteristic
256	C₂×Dic₆₁	C₂⁴	1	2	yes	—
257	C₂×Dic₆₁	C₂⁴	1	1	yes	characteristic
258	C₂×Dic₆₁	C₂⁴	1	1	yes	characteristic
259	C₂×Dic₆₁	C₂⁴	1	2	yes	—
260	C₂×Dic₆₁	C₂⁴	1	1	yes	characteristic
261	C₂×Dic₆₁	C₂⁴	1	1	yes	characteristic
262	D₂₄₄	—	2	4	no	—
263	D₂₄₄	—	2	4	no	—
264	D₂₄₄	—	2	2	no	—
265	D₂₄₄	—	4	2	no	—
266	D₂₄₄	#41	1	4	yes	—
267	C₄×D₆₁	—	2	4	no	—
268	C₄×D₆₁	—	2	4	no	—
269	C₄×D₆₁	—	2	2	no	—
270	C₄×D₆₁	—	4	2	no	—
271	C₄×D₆₁	—	4	2	no	—
272	C₄×D₆₁	—	4	2	no	—
273	C₄×D₆₁	—	4	2	no	—
274	C₄×D₆₁	—	4	2	no	—
275	C₄×D₆₁	—	4	2	no	—
276	C₄×D₆₁	—	4	2	no	—
277	Dic₁₂₂	—	2	2	no	—
278	Dic₁₂₂	—	4	1	no	—
279	C₂²×C₆₁	—	2	1	no	—
280	C₂²×C₆₁	—	2	1	no	—
281	C₂²×C₆₁	—	2	1	no	—
282	C₂²×C₆₁	—	2	1	no	—
283	C₂²×C₆₁	—	2	1	no	—
284	C₂²×C₆₁	—	2	1	no	—
285	C₂²×C₆₁	C₂⁵	1	1	yes	characteristic
286	C₂×D₆₁	—	2	2	no	—
287	C₂×D₆₁	—	2	2	no	—
288	C₂×D₆₁	—	2	1	no	—
289	C₂×D₆₁	—	2	2	no	—
290	C₂×D₆₁	—	2	1	no	—
291	C₂×D₆₁	—	2	2	no	—
292	C₂×D₆₁	—	2	2	no	—
293	C₂×D₆₁	—	2	1	no	—
294	C₂×D₆₁	—	8	4	no	—
295	C₂×D₆₁	C₂×#41	1	4	yes	—
296	C₄×C₆₁	—	2	1	no	—
297	C₄×C₆₁	—	2	2	no	—
298	C₄×C₆₁	—	2	1	no	—
299	C₄×C₆₁	—	2	1	no	—
300	C₄×C₆₁	—	2	2	no	—
301	C₄×C₆₁	—	2	2	no	—
302	C₄×C₆₁	—	2	2	no	—
303	C₄×C₆₁	—	2	1	no	—
304	C₄×C₆₁	C₂×#41	1	2	yes	—
305	Dic₆₁	—	2	2	no	—
306	Dic₆₁	—	2	1	no	—
307	Dic₆₁	—	2	1	no	—
308	Dic₆₁	—	2	1	no	—
309	Dic₆₁	—	2	1	no	—
310	Dic₆₁	—	2	1	no	—
311	Dic₆₁	—	2	1	no	—
312	Dic₆₁	—	2	1	no	—
313	Dic₆₁	—	2	2	no	—
314	#3521	—	61	1	no	maximal, Sylow
315	C₂×C₆₁	—	4	1	no	—
316	C₂×C₆₁	—	4	1	no	—
317	C₂×C₆₁	C₂²×#41	1	1	yes	characteristic
318	C₂×C₆₁	#585	1	1	yes	characteristic
319	C₂×C₆₁	#585	1	1	yes	characteristic
320	D₆₁	—	2	4	no	—
321	D₆₁	—	4	1	no	—
322	D₆₁	—	4	2	no	—
323	#556	—	61	1	no	—
324	#556	D₆₁	1	1	yes	characteristic, complemented
325	#554	—	61	1	no	—
326	#553	—	61	2	no	—
327	#553	—	61	1	no	—
328	#552	—	61	2	no	—
329	#552	—	61	1	no	—
330	#551	—	61	2	no	—
331	#551	—	61	2	no	—
332	#547	—	61	1	no	—
333	#546	—	61	1	no	—
334	#546	—	61	1	no	—
335	#542	—	61	1	no	—
336	#541	—	61	1	no	—
337	#539	—	61	2	no	—
338	#538	—	61	2	no	—
339	#529	—	61	1	no	—
340	#529	—	61	2	no	—
341	#529	—	61	1	no	—
342	C₂×#126	—	61	2	no	—
343	#520	—	61	1	no	—
344	#518	—	61	1	no	—
345	C₄×#41	—	61	1	no	—
346	C₆₁	#3521	1	1	yes	characteristic, complemented, Sylow
347	C₂×#41	—	61	1	no	—
348	C₂×#41	—	61	1	no	—
349	C₂²×D₄	—	61	1	no	—
350	C₄⋊Q₈	—	61	1	no	—
351	C₄⋊Q₈	C₂×D₆₁	1	1	yes	characteristic, complemented
352	#126	—	61	2	no	—
353	#126	—	61	2	no	—
354	#126	—	61	2	no	—
355	#126	—	61	1	no	—
356	#126	—	61	1	no	—
357	#126	—	61	2	no	—
358	#126	—	61	2	no	—
359	#126	—	61	2	no	—
360	#126	—	61	2	no	—
361	#126	—	61	2	no	—
362	#126	C₂×D₆₁	1	2	yes	—
363	#126	C₂×D₆₁	1	2	yes	complemented
364	#125	—	61	2	no	—
365	#125	—	61	1	no	—
366	#125	—	61	1	no	—
367	#125	—	61	2	no	—
368	#125	—	61	1	no	—
369	#125	—	61	2	no	—
370	#124	—	61	2	no	—
371	#124	—	61	1	no	—
372	#124	—	61	1	no	—
373	#124	—	61	1	no	—
374	#124	C₂×D₆₁	1	2	yes	—
375	#123	—	61	1	no	—
376	#123	—	61	2	no	—
377	#123	—	61	2	no	—
378	#123	—	61	2	no	—
379	#123	—	61	2	no	—
380	#123	—	61	2	no	—
381	#123	—	61	1	no	—
382	#123	—	61	2	no	—
383	#123	—	61	2	no	—
384	#123	—	61	2	no	—
385	C₂²⋊Q₈	—	61	2	no	—
386	C₂²⋊Q₈	—	61	2	no	—
387	C₂²⋊Q₈	—	61	2	no	—
388	C₂²⋊Q₈	—	61	1	no	—
389	C₂²⋊Q₈	—	61	2	no	—
390	C₂²⋊Q₈	—	61	2	no	—
391	C₂²⋊Q₈	—	61	1	no	—
392	C₂²⋊Q₈	—	61	1	no	—
393	C₂²⋊Q₈	C₂×D₆₁	1	1	yes	characteristic
394	C₂²⋊Q₈	C₂×D₆₁	1	1	yes	characteristic, complemented
395	#121	—	61	1	no	—
396	#121	—	61	1	no	—
397	#121	—	61	2	no	—
398	#121	—	61	1	no	—
399	#121	—	61	2	no	—
400	#121	—	61	2	no	—
401	#121	—	61	2	no	—
402	#120	—	61	2	no	—
403	#120	—	61	2	no	—
404	C₄×Q₈	—	61	1	no	—
405	C₄×Q₈	—	61	1	no	—
406	C₄×Q₈	—	61	1	no	—
407	C₄×Q₈	—	61	1	no	—
408	C₄×Q₈	C₂×D₆₁	1	1	yes	characteristic, complemented
409	C₄×Q₈	C₂×D₆₁	1	2	yes	complemented
410	C₄×D₄	—	61	1	no	—
411	C₄×D₄	—	61	1	no	—
412	C₄×D₄	—	61	1	no	—
413	C₄×D₄	—	61	1	no	—
414	C₄×D₄	—	61	1	no	—
415	C₄×D₄	—	61	1	no	—
416	C₄×D₄	—	61	1	no	—
417	C₄×D₄	—	61	2	no	—
418	C₄×D₄	—	61	2	no	—
419	C₄×D₄	—	61	2	no	—
420	C₄×D₄	—	61	2	no	—
421	C₄×D₄	—	61	2	no	—
422	C₄×D₄	—	61	2	no	—
423	C₄×D₄	—	61	2	no	—
424	C₄×D₄	—	61	1	no	—
425	C₄×D₄	—	61	2	no	—
426	C₄×D₄	C₂×D₆₁	1	1	yes	characteristic
427	#117	—	61	1	no	—
428	#117	—	61	2	no	—
429	#117	—	61	2	no	—
430	#117	—	61	1	no	—
431	#117	—	61	2	no	—
432	#117	—	61	2	no	—
433	#117	—	61	2	no	—
434	#117	C₂×D₆₁	1	1	yes	characteristic
435	#117	C₂×D₆₁	1	1	yes	characteristic, complemented
436	C₂×C₄⋊C₄	—	61	2	no	—
437	C₂×C₄⋊C₄	—	61	1	no	—
438	C₂×C₄⋊C₄	—	61	2	no	—
439	C₂×C₄⋊C₄	—	61	2	no	—
440	C₂×C₂²⋊C₄	—	61	2	no	—
441	C₂×C₂²⋊C₄	—	61	2	no	—
442	C₂×C₂²⋊C₄	—	61	2	no	—
443	C₂×C₂²⋊C₄	—	61	2	no	—
444	C₂×C₄²	—	61	1	no	—
445	C₂×C₄²	—	61	2	no	—
446	C₂⁴	—	61	2	no	—
447	#41	—	122	4	no	—
448	#41	—	122	4	no	—
449	C₂×Q₈	—	61	1	no	—
450	C₂×Q₈	—	61	1	no	—
451	C₂×Q₈	C₂²×D₆₁	1	1	yes	characteristic
452	C₂×Q₈	C₂²×D₆₁	1	2	yes	—
453	C₂×D₄	—	61	2	no	—
454	C₂×D₄	—	61	1	no	—
455	C₂×D₄	—	61	2	no	—
456	C₂×D₄	—	61	1	no	—
457	C₂×D₄	—	61	1	no	—
458	C₂×D₄	—	61	2	no	—
459	C₂×D₄	—	61	2	no	—
460	C₂×D₄	—	61	1	no	—
461	C₂×D₄	—	61	2	no	—
462	C₂×D₄	—	122	4	no	—
463	C₂×D₄	C₂²×D₆₁	1	1	yes	characteristic
464	C₂²×C₄	—	61	1	no	—
465	C₂²×C₄	—	61	1	no	—
466	C₂²×C₄	—	61	2	no	—
467	C₂²×C₄	—	61	2	no	—
468	C₂²×C₄	—	61	1	no	—
469	C₂²×C₄	—	61	2	no	—
470	C₂²×C₄	—	61	2	no	—
471	C₂²×C₄	—	61	2	no	—
472	C₂²×C₄	—	61	2	no	—
473	C₂²×C₄	—	61	2	no	—
474	C₂²×C₄	—	61	2	no	—
475	C₂²×C₄	—	61	2	no	—
476	C₂²×C₄	C₂²×D₆₁	1	1	yes	characteristic
477	C₂²×C₄	C₂²×D₆₁	1	1	yes	characteristic
478	C₄⋊C₄	—	61	1	no	—
479	C₄⋊C₄	—	61	2	no	—
480	C₄⋊C₄	—	61	1	no	—
481	C₄⋊C₄	—	61	1	no	—
482	C₄⋊C₄	—	61	2	no	—
483	C₄⋊C₄	—	61	2	no	—
484	C₄⋊C₄	—	61	2	no	—
485	C₄⋊C₄	—	61	1	no	—
486	C₄⋊C₄	—	61	2	no	—
487	C₄⋊C₄	—	61	2	no	—
488	C₄⋊C₄	—	61	1	no	—
489	C₄⋊C₄	—	61	1	no	—
490	C₄⋊C₄	—	61	2	no	—
491	C₄⋊C₄	—	61	2	no	—
492	C₄⋊C₄	—	61	2	no	—
493	C₄⋊C₄	—	61	2	no	—
494	C₄⋊C₄	—	61	1	no	—
495	C₄⋊C₄	—	61	1	no	—
496	C₄⋊C₄	—	61	1	no	—
497	C₄⋊C₄	—	61	1	no	—
498	C₄⋊C₄	—	61	2	no	—
499	C₄⋊C₄	—	61	2	no	—
500	C₄⋊C₄	C₂²×D₆₁	1	2	yes	—
501	C₄⋊C₄	C₂²×D₆₁	1	1	yes	characteristic
502	C₄⋊C₄	C₂²×D₆₁	1	2	yes	—
503	C₄⋊C₄	C₂²×D₆₁	1	2	yes	—
504	C₄⋊C₄	C₂²×D₆₁	1	1	yes	characteristic
505	C₄⋊C₄	C₂²×D₆₁	1	1	yes	characteristic
506	C₄⋊C₄	C₂²×D₆₁	1	1	yes	characteristic
507	C₄⋊C₄	C₂²×D₆₁	1	2	yes	—
508	C₂²⋊C₄	—	61	1	no	—
509	C₂²⋊C₄	—	61	1	no	—
510	C₂²⋊C₄	—	61	1	no	—
511	C₂²⋊C₄	—	61	2	no	—
512	C₂²⋊C₄	—	61	1	no	—
513	C₂²⋊C₄	—	61	2	no	—
514	C₂²⋊C₄	—	61	2	no	—
515	C₂²⋊C₄	—	61	2	no	—
516	C₂²⋊C₄	—	61	2	no	—
517	C₂²⋊C₄	—	61	2	no	—
518	C₂²⋊C₄	—	61	2	no	—
519	C₂²⋊C₄	—	61	2	no	—
520	C₂²⋊C₄	—	61	2	no	—
521	C₂²⋊C₄	—	61	1	no	—
522	C₂²⋊C₄	—	61	2	no	—
523	C₂²⋊C₄	—	61	2	no	—
524	C₂²⋊C₄	—	61	1	no	—
525	C₂²⋊C₄	—	61	1	no	—
526	C₂²⋊C₄	—	61	2	no	—
527	C₂²⋊C₄	—	61	2	no	—
528	C₂²⋊C₄	—	61	2	no	—
529	C₂²⋊C₄	—	61	1	no	—
530	C₂²⋊C₄	C₂²×D₆₁	1	2	yes	—
531	C₂²⋊C₄	C₂²×D₆₁	1	1	yes	characteristic
532	C₂²⋊C₄	C₂²×D₆₁	1	2	yes	—
533	C₂²⋊C₄	C₂²×D₆₁	1	2	yes	—
534	C₂²⋊C₄	C₂²×D₆₁	1	2	yes	—
535	C₂²⋊C₄	C₂²×D₆₁	1	1	yes	characteristic
536	C₄²	—	61	1	no	—
537	C₄²	—	61	1	no	—
538	C₄²	—	61	1	no	—
539	C₄²	—	61	2	no	—
540	C₄²	—	61	1	no	—
541	C₄²	—	61	2	no	—
542	C₄²	—	61	2	no	—
543	C₄²	—	61	1	no	—
544	C₄²	C₂²×D₆₁	1	2	yes	—
545	C₄²	C₂²×D₆₁	1	2	yes	—
546	C₄²	C₂²×D₆₁	1	2	yes	—
547	C₄²	C₂²×D₆₁	1	1	yes	characteristic
548	C₂³	—	61	2	no	—
549	C₂³	—	61	2	no	—
550	C₂³	—	61	1	no	—
551	C₂³	—	122	4	no	—
552	C₂³	—	244	2	no	—
553	C₂³	—	244	2	no	—
554	C₂³	C₂³×D₆₁	1	1	yes	characteristic
555	C₂³	C₂³×D₆₁	1	1	yes	characteristic
556	Q₈	—	2	2	no	—
557	Q₈	—	4	2	no	—
558	Q₈	—	122	2	no	—
559	Q₈	—	244	1	no	—
560	D₄	—	4	1	no	—
561	D₄	—	61	4	no	—
562	D₄	—	122	4	no	—
563	D₄	—	122	4	no	—
564	D₄	—	122	4	no	—
565	D₄	—	122	2	no	—
566	D₄	—	244	2	no	—
567	D₄	—	244	1	no	—
568	D₄	—	244	2	no	—
569	D₄	—	244	1	no	—
570	C₂×C₄	—	2	2	no	—
571	C₂×C₄	—	2	2	no	—
572	C₂×C₄	—	61	1	no	—
573	C₂×C₄	—	61	1	no	—
574	C₂×C₄	—	61	1	no	—
575	C₂×C₄	—	61	2	no	—
576	C₂×C₄	—	61	1	no	—
577	C₂×C₄	—	61	1	no	—
578	C₂×C₄	—	61	1	no	—
579	C₂×C₄	—	61	2	no	—
580	C₂×C₄	—	61	1	no	—
581	C₂×C₄	—	122	4	no	—
582	C₂×C₄	—	122	4	no	—
583	C₂×C₄	—	122	2	no	—
584	C₂×C₄	—	244	2	no	—
585	C₂×C₄	—	244	2	no	—
586	C₂×C₄	—	244	2	no	—
587	C₂×C₄	—	244	2	no	—
588	C₂×C₄	—	244	2	no	—
589	C₂×C₄	—	244	2	no	—
590	C₂×C₄	—	244	2	no	—
591	C₂×C₄	—	244	1	no	—
592	C₂×C₄	—	244	1	no	—
593	C₂×C₄	C₂³×D₆₁	1	1	yes	characteristic
594	C₂×C₄	C₂³×D₆₁	1	2	yes	—
595	C₂×C₄	C₂³×D₆₁	1	2	yes	—
596	C₂×C₄	C₂³×D₆₁	1	2	yes	—
597	C₂×C₄	C₂³×D₆₁	1	1	yes	characteristic
598	C₂×C₄	C₂³×D₆₁	1	1	yes	characteristic
599	C₂×C₄	C₂³×D₆₁	1	2	yes	—
600	C₂×C₄	C₂³×D₆₁	1	1	yes	characteristic
601	C₂×C₄	C₂³×D₆₁	1	1	yes	characteristic
602	C₂²	—	2	1	no	—
603	C₂²	—	2	1	no	—
604	C₂²	—	2	1	no	—
605	C₂²	—	2	1	no	—
606	C₂²	—	2	1	no	—
607	C₂²	—	2	1	no	—
608	C₂²	—	61	4	no	—
609	C₂²	—	122	2	no	—
610	C₂²	—	122	2	no	—
611	C₂²	—	122	1	no	—
612	C₂²	—	122	2	no	—
613	C₂²	—	122	2	no	—
614	C₂²	—	122	1	no	—
615	C₂²	—	122	1	no	—
616	C₂²	—	122	2	no	—
617	C₂²	—	488	4	no	—
618	C₂²	C₂⁴×D₆₁	1	1	yes	characteristic
619	C₄	—	2	1	no	—
620	C₄	—	2	1	no	—
621	C₄	—	2	2	no	—
622	C₄	—	2	2	no	—
623	C₄	—	2	2	no	—
624	C₄	—	2	1	no	—
625	C₄	—	2	2	no	—
626	C₄	—	2	1	no	—
627	C₄	—	122	1	no	—
628	C₄	—	122	2	no	—
629	C₄	—	122	1	no	—
630	C₄	—	122	1	no	—
631	C₄	—	122	1	no	—
632	C₄	—	122	1	no	—
633	C₄	—	122	2	no	—
634	C₄	—	122	1	no	—
635	C₄	—	122	1	no	—
636	C₄	#41×D₆₁	1	2	yes	—
637	C₂	—	4	1	no	—
638	C₂	—	4	1	no	—
639	C₂	—	122	4	no	—
640	C₂	—	244	2	no	—
641	C₂	—	244	1	no	—
642	C₂	C₂×#41×D₆₁	1	1	yes	characteristic
643	C₂	#16840598	1	1	yes	characteristic
644	C₂	#16840599	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₆₁
commutator, socle	C₂²×C₆₁	C₂⁵
Fitting	C₆₁×#556	C₂
hypercenter	#556	D₆₁
hypocenter	C₆₁	#3521
LCS	G ▷ C₂²×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂² ◁ #556

Complements

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

N	H ≅ G/N	type
1. #16840484	C₂	semidirect
2. #16840473	C₂	semidirect
3. #16840463	C₂	semidirect
4. #16840456	C₂	semidirect
5. #16840453	C₂	semidirect
6. #16840451	C₂	semidirect
7. #16840442	C₂	semidirect
8. #16840437	C₂	semidirect
9. #16840414	C₂	semidirect
10. #16840408	C₂	semidirect
11. #16840403	C₂	semidirect
12. #16840386	C₂	semidirect
13. #16840372	C₂	semidirect
14. #16840353	C₂	semidirect
15. #16840346	C₂	semidirect
16. #16840299	C₂	semidirect
17. #16840298	C₂	semidirect
18. #16840292	C₂	semidirect
19. #126×D₆₁	C₂	semidirect
20. #16840244	C₂	semidirect
21. #16840236	C₂	semidirect
22. #16840230	C₂	semidirect
23. C₆₁×#556	C₂	semidirect
27. #14519775	C₂²	semidirect
28. #14519772	C₂²	semidirect
29. #14519772	C₂²	semidirect
30. #14519772	C₂²	semidirect
31. #14519772	C₂²	semidirect
32. #14519771	C₂²	semidirect
33. #14519771	C₂²	semidirect
38. #14519769	C₂²	semidirect
39. #14519768	C₂²	semidirect
40. #14519768	C₂²	semidirect
41. #14519768	C₂²	semidirect
42. #14519767	C₂²	semidirect
43. #14519767	C₂²	semidirect
45. #14519766	C₂²	semidirect
50. #14519762	C₂²	semidirect
51. #14519762	C₂²	semidirect
52. #14519761	C₂²	semidirect
53. #14519761	C₂²	semidirect
55. #14519759	C₂²	semidirect
56. #14519759	C₂²	semidirect
58. #14519757	C₂²	semidirect
59. #14519757	C₂²	semidirect
61. #14519755	C₂²	semidirect
62. #14519754	C₂²	semidirect
63. #14519753	C₂²	semidirect
64. #14519753	C₂²	semidirect
65. #14519753	C₂²	semidirect
70. #14519750	C₂²	semidirect
71. #14519750	C₂²	semidirect
75. Q₈×Dic₆₁	C₂²	semidirect
76. C₄×Dic₁₂₂	C₂²	semidirect
77. #14519742	C₂²	semidirect
78. #14519742	C₂²	semidirect
82. C₄×D₂₄₄	C₂²	semidirect
83. C₄×D₂₄₄	C₂²	semidirect
89. #14519739	C₂²	semidirect
91. C₄×C₂²⋊D₆₁	C₂²	semidirect
92. #14519737	C₂²	semidirect
93. #14519737	C₂²	semidirect
94. #14519737	C₂²	semidirect
96. #14519735	C₂²	semidirect
97. #14519734	C₂²	semidirect
98. #14519734	C₂²	semidirect
99. #14519734	C₂²	semidirect
100. #14519734	C₂²	semidirect
101. #14519734	C₂²	semidirect
102. C₄⋊C₄×D₆₁	C₂²	semidirect
103. C₄⋊C₄×D₆₁	C₂²	semidirect
104. C₄⋊C₄×D₆₁	C₂²	semidirect
105. C₄⋊C₄×D₆₁	C₂²	semidirect
110. C₂×C₄×Dic₆₁	C₂²	semidirect
111. C₄²×D₆₁	C₂²	semidirect
112. C₄⋊Q₈×C₆₁	C₂²	semidirect
114. #126×C₆₁	C₂²	semidirect
117. C₂²⋊Q₈×C₆₁	C₂²	semidirect
118. C₄×Q₈×C₆₁	C₂²	semidirect
119. C₄×Q₈×C₆₁	C₂²	semidirect
122. #117×C₆₁	C₂²	semidirect
324. #556	D₆₁	semidirect
346. C₆₁	#3521	semidirect
351. C₄⋊Q₈	C₂×D₆₁	semidirect
363. #126	C₂×D₆₁	semidirect
394. C₂²⋊Q₈	C₂×D₆₁	semidirect
408. C₄×Q₈	C₂×D₆₁	semidirect
409. C₄×Q₈	C₂×D₆₁	semidirect
435. #117	C₂×D₆₁	semidirect