Subgroups — #30612307

Order 15616.

802 conjugacy classes of subgroups.

The subgroup lattice has 626 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#21462625	C₂	1	1	yes	maximal, characteristic, complemented
2	D₄×D₆₁⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
3	#21461417	C₂	1	1	yes	maximal, characteristic, complemented
4	#21461416	C₂	1	1	yes	maximal, characteristic, complemented
5	#21461409	C₂	1	1	yes	maximal, characteristic, complemented
6	SD₁₆⋊#92420	C₂	1	1	yes	maximal, characteristic, complemented
7	#21461403	C₂	1	1	yes	maximal, characteristic, complemented
8	SD₁₆×#92420	C₂	1	1	yes	maximal, characteristic, complemented
9	#21461400	C₂	1	1	yes	maximal, characteristic, complemented
10	#21461399	C₂	1	1	yes	maximal, characteristic, complemented
11	#21461371	C₂	1	1	yes	maximal, characteristic, complemented
12	#21461119	C₂	1	1	yes	maximal, characteristic, complemented
13	#21461117	C₂	1	1	yes	maximal, characteristic, complemented
14	#21461017	C₂	1	1	yes	maximal, characteristic, complemented
15	#21454624	C₂	1	1	yes	maximal, characteristic
16	C₂²×D₆₁⋊C₈	—	2	1	no	—
17	Q₈×#92420	C₂²	1	1	yes	characteristic, complemented
18	Q₈×#92420	C₂²	1	1	yes	characteristic, complemented
19	#16840790	—	2	1	no	—
20	#16840790	—	2	1	no	—
21	#16840790	C₂²	1	1	yes	characteristic
22	#16840790	C₂²	1	1	yes	characteristic
23	#16840790	C₂²	1	1	yes	characteristic, complemented
24	#16840790	C₂²	1	1	yes	characteristic, complemented
25	#16840789	—	2	1	no	—
26	#16840789	—	2	1	no	—
27	D₄×#92420	C₂²	1	1	yes	characteristic
28	D₄×#92420	C₂²	1	1	yes	characteristic
29	#16840781	—	2	1	no	—
30	#16840781	C₂²	1	1	yes	characteristic
31	#16840780	C₂²	1	1	yes	characteristic
32	D₆₁⋊(C₄⋊C₈)	C₂²	1	1	yes	characteristic
33	D₆₁⋊(C₂²⋊C₈)	—	2	1	no	—
34	C₄×D₆₁⋊C₈	—	2	1	no	—
35	C₄×D₆₁⋊C₈	C₂²	1	1	yes	characteristic
36	#16840626	C₂²	1	1	yes	characteristic, complemented
37	#16840625	C₂²	1	1	yes	characteristic, complemented
38	#16840624	C₂²	1	1	yes	characteristic, complemented
39	#16840623	C₂²	1	1	yes	characteristic, complemented
40	Q₈⋊#92420	C₂²	1	1	yes	characteristic, complemented
41	Q₈⋊#92420	C₂²	1	1	yes	characteristic, complemented
42	#16840610	C₂²	1	1	yes	characteristic
43	#16840610	C₂²	1	1	yes	characteristic
44	#16840610	C₂²	1	1	yes	characteristic, complemented
45	#16840610	C₂²	1	1	yes	characteristic, complemented
46	D₄⋊#92420	C₂²	1	1	yes	characteristic
47	D₄⋊#92420	C₂²	1	1	yes	characteristic
48	#16840603	C₂²	1	1	yes	characteristic, complemented
49	#16840603	C₂²	1	1	yes	characteristic, complemented
50	C₈×#92420	C₂²	1	1	yes	characteristic, complemented
51	C₈×#92420	C₂²	1	1	yes	characteristic, complemented
52	C₂×#14519804	C₄	1	1	yes	characteristic
53	C₄×#11758226	C₂²	1	1	yes	characteristic
54	C₄×D₄×D₆₁	C₂²	1	1	yes	characteristic
55	#16839875	C₄	1	1	yes	characteristic
56	#16839872	C₄	1	1	yes	characteristic
57	#16839860	C₄	1	1	yes	characteristic
58	SD₁₆×Dic₆₁	C₂²	1	1	yes	characteristic
59	#16839847	C₂²	1	1	yes	characteristic
60	#16839844	C₂²	1	1	yes	characteristic
61	#16839842	C₂²	1	1	yes	characteristic
62	#16839803	C₄	1	1	yes	characteristic
63	#16839765	C₄	1	1	yes	characteristic
64	#16839762	C₄	1	1	yes	characteristic
65	#16839714	C₂²	1	1	yes	characteristic
66	C₆₁×#440	C₄	1	1	yes	characteristic
67	C₂×D₆₁⋊C₈	—	2	1	no	—
68	C₂×D₆₁⋊C₈	—	2	1	no	—
69	C₂×D₆₁⋊C₈	—	2	1	no	—
70	C₂×D₆₁⋊C₈	—	2	1	no	—
71	C₂×D₆₁⋊C₈	—	2	1	no	—
72	C₂×D₆₁⋊C₈	—	4	4	no	—
73	C₂×D₆₁⋊C₈	D₄	1	1	yes	characteristic
74	C₂×D₆₁⋊C₈	D₄	1	1	yes	characteristic
75	C₂²×#92420	—	2	1	no	—
76	C₂²×#92420	—	2	1	no	—
77	#14519844	—	2	1	no	—
78	#14519844	—	2	1	no	—
79	C₄⋊#92420	—	2	1	no	—
80	C₄⋊#92420	—	2	1	no	—
81	C₄⋊#92420	C₂³	1	1	yes	characteristic
82	C₄⋊#92420	C₂³	1	1	yes	characteristic
83	C₄⋊#92420	C₂³	1	1	yes	characteristic
84	C₄⋊#92420	C₂³	1	1	yes	characteristic
85	#14519834	—	2	1	no	—
86	#14519834	—	2	1	no	—
87	#14519834	—	2	1	no	—
88	#14519834	—	2	1	no	—
89	#14519834	—	2	1	no	—
90	#14519834	—	2	1	no	—
91	C₂²⋊#92420	—	2	1	no	—
92	C₂²⋊#92420	—	2	1	no	—
93	C₄×#92420	—	2	1	no	—
94	C₄×#92420	—	2	1	no	—
95	C₄×#92420	—	2	1	no	—
96	C₄×#92420	D₄	1	1	yes	characteristic
97	C₄×#92420	D₄	1	1	yes	characteristic
98	C₄×#92420	C₂³	1	1	yes	characteristic
99	C₄×#92420	C₂³	1	1	yes	characteristic
100	C₄×#92420	C₂³	1	1	yes	characteristic
101	C₄×#92420	C₂³	1	1	yes	characteristic
102	C₂×#11758226	C₂×C₄	1	1	yes	characteristic
103	C₂×D₄×D₆₁	C₂×C₄	1	1	yes	characteristic
104	C₂²×C₄×D₆₁	—	2	1	no	—
105	#14519804	C₈	1	8	yes	complemented
106	C₂×#11758201	C₂×C₄	1	1	yes	characteristic
107	C₂×D₄₈₈	C₂×C₄	1	1	yes	characteristic
108	C₂×#11758199	C₂×C₄	1	1	yes	characteristic
109	C₂×#11758189	C₂×C₄	1	1	yes	characteristic
110	C₂×#11758189	C₂×C₄	1	1	yes	characteristic
111	Q₈×Dic₆₁	C₂³	1	1	yes	characteristic
112	C₄×D₂₄₄	—	2	1	no	—
113	C₄×D₂₄₄	C₂×C₄	1	1	yes	characteristic
114	C₄×D₂₄₄	C₂×C₄	1	1	yes	characteristic
115	D₄×Dic₆₁	C₂³	1	1	yes	characteristic
116	#14519739	—	2	1	no	—
117	#14519739	C₂³	1	1	yes	characteristic
118	#14519739	C₂³	1	1	yes	characteristic
119	C₄×C₂²⋊D₆₁	—	2	1	no	—
120	#14519737	—	2	1	no	—
121	#14519735	—	2	1	no	—
122	#14519735	C₂×C₄	1	1	yes	characteristic
123	C₄⋊C₄×D₆₁	C₂×C₄	1	1	yes	characteristic
124	C₂²⋊C₄×D₆₁	—	2	1	no	—
125	C₄²×D₆₁	—	2	1	no	—
126	C₄²×D₆₁	C₂³	1	1	yes	characteristic
127	#14519710	C₂×C₄	1	1	yes	characteristic
128	#14519709	C₂×C₄	1	1	yes	characteristic
129	#14519708	C₂×C₄	1	1	yes	characteristic
130	#14519701	C₂×C₄	1	1	yes	characteristic
131	#14519699	C₂×C₄	1	1	yes	characteristic
132	#14519699	C₂×C₄	1	1	yes	characteristic
133	#14519698	C₂×C₄	1	1	yes	characteristic
134	#14519697	C₂×C₄	1	1	yes	characteristic
135	#14519697	C₂×C₄	1	1	yes	characteristic
136	#14519688	C₂×C₄	1	1	yes	characteristic
137	C₈×Dic₆₁	C₂³	1	1	yes	characteristic
138	C₈×Dic₆₁	C₂³	1	1	yes	characteristic
139	C₂×SD₁₆×C₆₁	C₂×C₄	1	1	yes	characteristic
140	C₄×Q₈×C₆₁	C₂×C₄	1	1	yes	characteristic
141	C₄×D₄×C₆₁	C₂×C₄	1	1	yes	characteristic
142	#107×C₆₁	C₂×C₄	1	1	yes	characteristic
143	#103×C₆₁	C₂×C₄	1	1	yes	characteristic
144	#102×C₆₁	C₂×C₄	1	1	yes	characteristic
145	#97×C₆₁	C₂×C₄	1	1	yes	characteristic
146	C₂³×D₆₁	—	2	1	no	—
147	C₂×Q₈×C₆₁	C₂²×C₄	1	1	yes	characteristic
148	C₂×D₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
149	C₂²×C₄×C₆₁	—	2	1	no	—
150	C₂×C₂²⋊D₆₁	—	2	1	no	—
151	C₂²×Dic₆₁	—	2	1	no	—
152	#11758226	—	2	2	no	—
153	#11758226	C₂×C₈	1	4	yes	complemented
154	D₄×D₆₁	—	2	2	no	—
155	D₄×D₆₁	C₂×C₈	1	4	yes	complemented
156	C₂×D₂₄₄	—	2	1	no	—
157	C₂×D₂₄₄	C₂²×C₄	1	1	yes	characteristic
158	C₂×D₂₄₄	C₂²×C₄	1	1	yes	characteristic
159	C₂×C₄×D₆₁	—	2	1	no	—
160	C₂×C₄×D₆₁	—	2	1	no	—
161	C₂×C₄×D₆₁	—	2	1	no	—
162	C₂×C₄×D₆₁	—	2	1	no	—
163	C₂×C₄×D₆₁	—	2	1	no	—
164	C₂×C₄×D₆₁	—	2	1	no	—
165	C₂×C₄×D₆₁	—	4	2	no	—
166	C₂×C₄×D₆₁	—	4	2	no	—
167	C₂×C₄×D₆₁	C₂²×C₄	1	1	yes	characteristic
168	C₂×C₄×D₆₁	C₂×D₄	1	1	yes	characteristic
169	C₂×C₄×D₆₁	#41	1	1	yes	characteristic
170	C₂×#92420	—	2	1	no	—
171	C₂×#92420	—	2	1	no	—
172	C₂×#92420	—	2	1	no	—
173	C₂×#92420	—	2	1	no	—
174	C₂×#92420	—	2	1	no	—
175	C₂×#92420	—	2	1	no	—
176	C₂×#92420	—	4	2	no	—
177	C₂×#92420	—	4	2	no	—
178	C₂×#92420	C₂×D₄	1	1	yes	characteristic
179	C₂×#92420	C₂×D₄	1	1	yes	characteristic
180	C₂×#92420	C₂×D₄	1	1	yes	characteristic
181	C₂×#92420	C₂×D₄	1	1	yes	characteristic
182	D₆₁⋊C₈	—	2	2	no	—
183	D₆₁⋊C₈	—	4	1	no	—
184	D₆₁⋊C₈	—	4	2	no	—
185	D₆₁⋊C₈	—	4	2	no	—
186	D₆₁⋊C₈	—	4	2	no	—
187	D₆₁⋊C₈	—	4	2	no	—
188	D₆₁⋊C₈	—	4	2	no	—
189	SD₁₆×C₆₁	C₂×C₈	1	4	yes	complemented
190	C₂×C₈×C₆₁	C₂²×C₄	1	1	yes	characteristic
191	C₂×C₈×C₆₁	C₂²×C₄	1	1	yes	characteristic
192	C₄⋊C₄×C₆₁	—	2	1	no	—
193	C₄⋊C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
194	C₄⋊C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
195	C₂²⋊C₄×C₆₁	—	2	1	no	—
196	C₄²×C₆₁	—	2	1	no	—
197	C₄²×C₆₁	C₂²×C₄	1	1	yes	characteristic
198	C₂²⋊Dic₆₁	—	2	1	no	—
199	#11758201	C₂×C₈	1	4	yes	complemented
200	#11758199	C₂×C₈	1	4	yes	complemented
201	#11758198	—	2	1	no	—
202	#11758198	—	2	1	no	—
203	#11758198	—	2	1	no	—
204	#11758198	—	2	1	no	—
205	#11758198	—	2	1	no	—
206	C₄⋊Dic₆₁	—	2	1	no	—
207	C₄⋊Dic₆₁	C₂²×C₄	1	1	yes	characteristic
208	C₄⋊Dic₆₁	C₂²×C₄	1	1	yes	characteristic
209	#11758196	—	2	1	no	—
210	C₄×Dic₆₁	—	2	1	no	—
211	C₄×Dic₆₁	—	2	1	no	—
212	C₄×Dic₆₁	C₂×D₄	1	1	yes	characteristic
213	C₄×Dic₆₁	#41	1	1	yes	characteristic
214	C₄×Dic₆₁	C₂⁴	1	1	yes	characteristic
215	C₂×#92418	C₂²×C₄	1	1	yes	characteristic
216	C₂×#92418	C₂²×C₄	1	1	yes	characteristic
217	D₄₈₈	C₂×C₈	1	4	yes	complemented
218	#11758189	—	2	2	no	—
219	#11758189	C₂×C₈	1	4	yes	complemented
220	C₂³×C₆₁	—	2	1	no	—
221	C₂²×D₆₁	—	2	1	no	—
222	C₂²×D₆₁	—	2	1	no	—
223	C₂²×D₆₁	—	2	4	no	—
224	C₂²×D₆₁	—	4	2	no	—
225	C₂²×D₆₁	—	4	2	no	—
226	C₂²×D₆₁	C₄×D₄	1	1	yes	characteristic
227	Q₈×C₆₁	—	2	1	no	—
228	Q₈×C₆₁	C₂²×C₈	1	2	yes	complemented
229	D₄×C₆₁	—	2	1	no	—
230	D₄×C₆₁	C₂²×C₈	1	2	yes	—
231	C₂×C₄×C₆₁	—	2	1	no	—
232	C₂×C₄×C₆₁	—	2	1	no	—
233	C₂×C₄×C₆₁	—	2	1	no	—
234	C₂×C₄×C₆₁	—	4	2	no	—
235	C₂×C₄×C₆₁	C₄×D₄	1	1	yes	characteristic
236	C₂×C₄×C₆₁	C₄×D₄	1	1	yes	characteristic
237	C₂×C₄×C₆₁	C₂³×C₄	1	1	yes	characteristic
238	C₂²⋊D₆₁	—	2	4	no	—
239	C₂×Dic₆₁	—	2	1	no	—
240	C₂×Dic₆₁	—	2	1	no	—
241	C₂×Dic₆₁	—	4	1	no	—
242	C₂×Dic₆₁	—	4	1	no	—
243	C₂×Dic₆₁	C₄×D₄	1	1	yes	characteristic
244	C₂×Dic₆₁	C₂²×D₄	1	1	yes	characteristic
245	C₂×Dic₆₁	C₂×#41	1	1	yes	characteristic
246	D₂₄₄	—	2	4	no	—
247	D₂₄₄	—	2	1	no	—
248	D₂₄₄	—	2	1	no	—
249	D₂₄₄	C₂²×C₈	1	2	yes	—
250	D₂₄₄	C₂²×C₈	1	2	yes	complemented
251	C₄×D₆₁	—	2	1	no	—
252	C₄×D₆₁	—	2	1	no	—
253	C₄×D₆₁	—	2	4	no	—
254	C₄×D₆₁	—	4	1	no	—
255	C₄×D₆₁	—	4	2	no	—
256	C₄×D₆₁	—	4	2	no	—
257	C₄×D₆₁	—	4	2	no	—
258	C₄×D₆₁	—	4	1	no	—
259	C₄×D₆₁	—	4	1	no	—
260	C₄×D₆₁	—	4	1	no	—
261	C₄×D₆₁	—	4	1	no	—
262	C₄×D₆₁	C₂²×C₈	1	2	yes	—
263	C₄×D₆₁	#131	1	2	yes	—
264	#92420	—	2	1	no	—
265	#92420	—	2	1	no	—
266	#92420	—	2	1	no	—
267	#92420	—	4	1	no	—
268	#92420	—	4	1	no	—
269	#92420	—	4	1	no	—
270	#92420	—	4	1	no	—
271	#92420	—	4	1	no	—
272	#92420	—	4	1	no	—
273	#92420	AGL(1,ℤ/8)	1	2	yes	complemented
274	C₈×C₆₁	—	2	1	no	—
275	C₈×C₆₁	C₂²×C₈	1	2	yes	complemented
276	#92418	—	2	1	no	—
277	#92418	C₂²×C₈	1	2	yes	complemented
278	C₈×AGL(1,ℤ/8)	—	61	1	no	maximal, Sylow
279	C₂²×C₆₁	—	2	2	no	—
280	C₂²×C₆₁	—	4	1	no	—
281	C₂²×C₆₁	—	4	1	no	—
282	C₂²×C₆₁	C₂×C₄×D₄	1	1	yes	characteristic
283	C₂×D₆₁	—	2	1	no	—
284	C₂×D₆₁	—	2	1	no	—
285	C₂×D₆₁	—	2	2	no	—
286	C₂×D₆₁	—	2	2	no	—
287	C₂×D₆₁	—	4	8	no	—
288	C₂×D₆₁	—	4	1	no	—
289	C₂×D₆₁	—	4	1	no	—
290	C₂×D₆₁	—	4	1	no	—
291	C₂×D₆₁	—	4	1	no	—
292	C₂×D₆₁	C₈×D₄	1	2	yes	—
293	C₄×C₆₁	—	2	2	no	—
294	C₄×C₆₁	—	2	1	no	—
295	C₄×C₆₁	—	2	1	no	—
296	C₄×C₆₁	—	4	1	no	—
297	C₄×C₆₁	—	4	1	no	—
298	C₄×C₆₁	C₂³×C₈	1	1	yes	characteristic
299	C₄×C₆₁	C₂×#131	1	1	yes	characteristic
300	Dic₆₁	—	2	1	no	—
301	Dic₆₁	—	4	1	no	—
302	Dic₆₁	—	4	1	no	—
303	Dic₆₁	C₈×D₄	1	2	yes	—
304	Dic₆₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
305	Dic₆₁	#575	1	1	yes	characteristic
306	C₈×#41	—	61	1	no	—
307	C₄×AGL(1,ℤ/8)	—	61	1	no	—
308	C₂×C₈×D₄	—	61	1	no	—
309	#1580	—	61	1	no	—
310	#1580	—	61	1	no	—
311	SD₁₆⋊C₈	—	61	1	no	—
312	SD₁₆⋊C₈	—	61	1	no	—
313	C₈×SD₁₆	—	61	1	no	—
314	C₈×SD₁₆	—	61	1	no	—
315	C₈×D₈	—	61	1	no	—
316	C₈×D₈	—	61	1	no	—
317	#1565	—	61	1	no	—
318	#1478	—	61	1	no	—
319	#1477	—	61	1	no	—
320	C₈×M₁₆	—	61	1	no	—
321	C₂×C₆₁	—	4	2	no	—
322	C₂×C₆₁	C₂×C₈×D₄	1	1	yes	characteristic
323	C₂×C₆₁	C₄×AGL(1,ℤ/8)	1	1	yes	characteristic
324	C₂×C₆₁	#2955	1	1	yes	characteristic
325	D₆₁	—	2	2	no	—
326	D₆₁	—	4	2	no	—
327	D₆₁	—	4	2	no	—
328	C₂×AGL(1,ℤ/8)	—	61	1	no	—
329	C₂³×C₈	—	122	1	no	—
330	C₄×#41	—	61	1	no	—
331	C₂×C₄×D₄	—	61	1	no	—
332	C₈×Q₈	—	61	1	no	—
333	C₈×Q₈	—	61	1	no	—
334	#442	—	61	1	no	—
335	#442	—	61	1	no	—
336	#440	—	61	1	no	—
337	#440	#6923	1	1	yes	characteristic
338	C₄×SD₁₆	—	61	1	no	—
339	C₄×SD₁₆	—	61	1	no	—
340	C₄×D₈	—	61	1	no	—
341	C₄×D₈	—	61	1	no	—
342	C₈×D₄	—	61	1	no	—
343	C₈×D₄	—	61	1	no	—
344	C₈×D₄	—	61	1	no	—
345	C₈×D₄	—	61	1	no	—
346	C₈×D₄	—	61	1	no	—
347	C₈×D₄	—	61	1	no	—
348	C₈×D₄	—	122	1	no	—
349	C₈×D₄	—	122	1	no	—
350	C₈×D₄	—	122	1	no	—
351	C₈×D₄	—	122	1	no	—
352	#431	—	61	1	no	—
353	#431	—	61	1	no	—
354	#431	—	122	1	no	—
355	#428	—	61	1	no	—
356	C₂×C₄⋊C₈	—	61	1	no	—
357	#418	—	61	1	no	—
358	#417	—	61	1	no	—
359	C₂×C₂²⋊C₈	—	122	1	no	—
360	C₄×M₁₆	—	61	1	no	—
361	C₂×C₄×C₈	—	61	1	no	—
362	C₂×C₄×C₈	—	122	1	no	—
363	#335	—	61	1	no	—
364	#335	—	61	1	no	—
365	#334	—	61	1	no	—
366	#334	—	61	1	no	—
367	Q₈⋊C₈	—	61	1	no	—
368	Q₈⋊C₈	—	61	1	no	—
369	D₄⋊C₈	—	61	1	no	—
370	D₄⋊C₈	—	61	1	no	—
371	D₄⋊C₈	—	61	1	no	—
372	D₄⋊C₈	—	61	1	no	—
373	D₄⋊C₈	—	61	1	no	—
374	D₄⋊C₈	—	61	1	no	—
375	#322	—	61	1	no	—
376	#322	—	61	1	no	—
377	C₈²	—	61	1	no	—
378	C₈²	—	61	1	no	—
379	C₆₁	C₈×AGL(1,ℤ/8)	1	1	yes	characteristic, complemented, Sylow
380	C₂×#41	—	61	1	no	—
381	C₂²×D₄	—	61	1	no	—
382	C₂³×C₄	—	122	1	no	—
383	AGL(1,ℤ/8)	—	61	8	no	—
384	C₂×SD₁₆	—	61	1	no	—
385	C₂×SD₁₆	C₂×#6923	1	1	yes	characteristic
386	C₂×D₈	—	61	1	no	—
387	C₂×D₈	—	61	1	no	—
388	C₂×M₁₆	—	61	1	no	—
389	C₂×M₁₆	—	61	1	no	—
390	C₂²×C₈	—	61	1	no	—
391	C₂²×C₈	—	61	1	no	—
392	C₂²×C₈	—	122	1	no	—
393	C₂²×C₈	—	122	1	no	—
394	C₂²×C₈	—	122	1	no	—
395	C₂²×C₈	—	122	1	no	—
396	C₂²×C₈	—	122	1	no	—
397	C₂²×C₈	—	122	1	no	—
398	C₂²×C₈	—	122	1	no	—
399	C₂²×C₈	—	244	4	no	—
400	C₄×Q₈	—	61	1	no	—
401	C₄×Q₈	C₂×#6923	1	1	yes	characteristic
402	C₄×D₄	—	61	1	no	—
403	C₄×D₄	—	61	1	no	—
404	C₄×D₄	—	61	1	no	—
405	C₄×D₄	—	61	1	no	—
406	C₄×D₄	—	61	1	no	—
407	C₄×D₄	—	122	1	no	—
408	C₄×D₄	—	122	1	no	—
409	C₄×D₄	—	122	1	no	—
410	C₄×D₄	—	122	1	no	—
411	C₄×D₄	C₂×#6923	1	1	yes	characteristic
412	#117	—	61	1	no	—
413	#117	—	122	1	no	—
414	C₂×C₄⋊C₄	—	61	1	no	—
415	C₂×C₂²⋊C₄	—	122	1	no	—
416	C₂×C₄²	—	61	1	no	—
417	C₂×C₄²	—	122	1	no	—
418	#107	—	61	1	no	—
419	#107	C₂×#6923	1	1	yes	characteristic
420	#106	—	61	1	no	—
421	#106	—	61	1	no	—
422	C₄⋊C₈	—	61	1	no	—
423	C₄⋊C₈	—	61	1	no	—
424	C₄⋊C₈	—	61	1	no	—
425	C₄⋊C₈	—	61	1	no	—
426	C₄⋊C₈	—	122	1	no	—
427	C₄⋊C₈	—	122	1	no	—
428	C₄⋊C₈	—	122	1	no	—
429	C₄⋊C₈	—	122	1	no	—
430	#103	—	61	1	no	—
431	#103	C₂×#6923	1	1	yes	characteristic
432	#102	—	61	1	no	—
433	#102	—	61	1	no	—
434	#102	—	61	1	no	—
435	#102	—	61	1	no	—
436	#102	—	61	1	no	—
437	#102	C₂×#6923	1	1	yes	characteristic
438	C₂²⋊C₈	—	122	1	no	—
439	C₂²⋊C₈	—	122	1	no	—
440	C₂²⋊C₈	—	122	1	no	—
441	C₂²⋊C₈	—	122	1	no	—
442	C₂²⋊C₈	—	122	1	no	—
443	C₂²⋊C₈	—	122	1	no	—
444	C₂²⋊C₈	—	122	1	no	—
445	C₂²⋊C₈	—	122	1	no	—
446	#97	—	61	1	no	—
447	#97	C₂×#6923	1	1	yes	characteristic
448	C₄×C₈	—	61	1	no	—
449	C₄×C₈	—	61	1	no	—
450	C₄×C₈	—	61	1	no	—
451	C₄×C₈	—	61	1	no	—
452	C₄×C₈	—	61	1	no	—
453	C₄×C₈	—	61	1	no	—
454	C₄×C₈	—	61	1	no	—
455	C₄×C₈	—	61	1	no	—
456	C₄×C₈	—	122	1	no	—
457	C₄×C₈	—	122	1	no	—
458	C₄×C₈	—	122	1	no	—
459	C₂⁴	—	122	1	no	—
460	#41	—	61	4	no	—
461	#41	—	122	2	no	—
462	C₂×Q₈	C₂²×#6923	1	1	yes	characteristic
463	C₂×D₄	—	61	4	no	—
464	C₂×D₄	—	61	1	no	—
465	C₂×D₄	—	61	1	no	—
466	C₂×D₄	—	122	1	no	—
467	C₂×D₄	—	122	2	no	—
468	C₂×D₄	—	122	1	no	—
469	C₂×D₄	C₂²×#6923	1	1	yes	characteristic
470	C₂²×C₄	—	2	1	no	—
471	C₂²×C₄	—	61	1	no	—
472	C₂²×C₄	—	61	1	no	—
473	C₂²×C₄	—	61	1	no	—
474	C₂²×C₄	—	122	1	no	—
475	C₂²×C₄	—	122	1	no	—
476	C₂²×C₄	—	122	1	no	—
477	C₂²×C₄	—	122	1	no	—
478	C₂²×C₄	—	122	1	no	—
479	C₂²×C₄	—	122	1	no	—
480	C₂²×C₄	—	122	1	no	—
481	C₂²×C₄	—	244	2	no	—
482	C₂²×C₄	—	244	2	no	—
483	SD₁₆	—	61	4	no	—
484	SD₁₆	D₆₁⋊C₈	1	4	yes	complemented
485	D₈	—	61	4	no	—
486	D₈	—	61	4	no	—
487	M₁₆	—	61	4	no	—
488	M₁₆	—	122	2	no	—
489	C₂×C₈	—	61	1	no	—
490	C₂×C₈	—	61	1	no	—
491	C₂×C₈	—	61	1	no	—
492	C₂×C₈	—	61	1	no	—
493	C₂×C₈	—	61	1	no	—
494	C₂×C₈	—	61	1	no	—
495	C₂×C₈	—	122	2	no	—
496	C₂×C₈	—	122	1	no	—
497	C₂×C₈	—	122	1	no	—
498	C₂×C₈	—	122	1	no	—
499	C₂×C₈	—	122	1	no	—
500	C₂×C₈	—	122	1	no	—
501	C₂×C₈	—	122	1	no	—
502	C₂×C₈	—	244	2	no	—
503	C₂×C₈	—	244	2	no	—
504	C₂×C₈	—	244	2	no	—
505	C₂×C₈	—	244	1	no	—
506	C₂×C₈	—	244	2	no	—
507	C₂×C₈	—	244	2	no	—
508	C₂×C₈	—	244	2	no	—
509	C₂×C₈	—	244	2	no	—
510	C₂×C₈	C₂²×#6923	1	1	yes	characteristic
511	C₂×C₈	C₂²×#6923	1	1	yes	characteristic
512	C₄⋊C₄	—	2	1	no	—
513	C₄⋊C₄	—	61	1	no	—
514	C₄⋊C₄	—	61	1	no	—
515	C₄⋊C₄	—	122	1	no	—
516	C₄⋊C₄	—	122	1	no	—
517	C₄⋊C₄	C₂²×#6923	1	1	yes	characteristic
518	C₄⋊C₄	C₂²×#6923	1	1	yes	characteristic
519	C₂²⋊C₄	—	2	1	no	—
520	C₂²⋊C₄	—	122	1	no	—
521	C₂²⋊C₄	—	122	1	no	—
522	C₂²⋊C₄	—	122	1	no	—
523	C₂²⋊C₄	—	122	1	no	—
524	C₂²⋊C₄	—	122	1	no	—
525	C₂²⋊C₄	—	122	1	no	—
526	C₄²	—	2	1	no	—
527	C₄²	—	61	1	no	—
528	C₄²	—	61	1	no	—
529	C₄²	—	61	1	no	—
530	C₄²	—	122	1	no	—
531	C₄²	—	122	1	no	—
532	C₄²	C₂²×#6923	1	1	yes	characteristic
533	C₂³	—	2	1	no	—
534	C₂³	—	61	1	no	—
535	C₂³	—	122	4	no	—
536	C₂³	—	122	1	no	—
537	C₂³	—	122	1	no	—
538	C₂³	—	244	2	no	—
539	C₂³	—	244	2	no	—
540	Q₈	—	2	1	no	—
541	Q₈	C₂×D₆₁⋊C₈	1	2	yes	complemented
542	D₄	—	2	1	no	—
543	D₄	—	61	2	no	—
544	D₄	—	61	2	no	—
545	D₄	—	122	4	no	—
546	D₄	—	122	4	no	—
547	D₄	—	122	1	no	—
548	D₄	—	122	1	no	—
549	D₄	C₂×D₆₁⋊C₈	1	2	yes	—
550	C₂×C₄	—	2	1	no	—
551	C₂×C₄	—	2	1	no	—
552	C₂×C₄	—	2	1	no	—
553	C₂×C₄	—	4	2	no	—
554	C₂×C₄	—	61	1	no	—
555	C₂×C₄	—	61	1	no	—
556	C₂×C₄	—	61	2	no	—
557	C₂×C₄	—	61	2	no	—
558	C₂×C₄	—	61	1	no	—
559	C₂×C₄	—	122	1	no	—
560	C₂×C₄	—	122	1	no	—
561	C₂×C₄	—	122	4	no	—
562	C₂×C₄	—	122	1	no	—
563	C₂×C₄	—	122	1	no	—
564	C₂×C₄	—	244	1	no	—
565	C₂×C₄	—	244	2	no	—
566	C₂×C₄	—	244	2	no	—
567	C₂×C₄	—	244	1	no	—
568	C₂×C₄	—	244	1	no	—
569	C₂×C₄	—	244	1	no	—
570	C₂×C₄	—	244	1	no	—
571	C₂×C₄	—	244	2	no	—
572	C₂×C₄	—	244	1	no	—
573	C₂×C₄	—	244	1	no	—
574	C₂×C₄	D₄×#6923	1	1	yes	characteristic
575	C₂×C₄	D₄×#6923	1	1	yes	characteristic
576	C₂×C₄	C₂³×#6923	1	1	yes	characteristic
577	C₈	—	2	1	no	—
578	C₈	—	61	2	no	—
579	C₈	—	61	2	no	—
580	C₈	—	122	1	no	—
581	C₈	—	122	1	no	—
582	C₈	—	122	1	no	—
583	C₈	—	122	1	no	—
584	C₈	—	244	1	no	—
585	C₈	—	244	1	no	—
586	C₈	—	244	1	no	—
587	C₈	—	244	1	no	—
588	C₈	—	244	1	no	—
589	C₈	—	244	1	no	—
590	C₈	C₂×D₆₁⋊C₈	1	2	yes	complemented
591	C₂²	—	2	2	no	—
592	C₂²	—	4	1	no	—
593	C₂²	—	4	1	no	—
594	C₂²	—	61	2	no	—
595	C₂²	—	122	1	no	—
596	C₂²	—	122	1	no	—
597	C₂²	—	122	2	no	—
598	C₂²	—	122	2	no	—
599	C₂²	—	244	8	no	—
600	C₂²	—	244	1	no	—
601	C₂²	—	244	1	no	—
602	C₂²	—	244	1	no	—
603	C₂²	—	244	1	no	—
604	C₂²	C₂×D₄×#6923	1	1	yes	characteristic
605	C₄	—	2	1	no	—
606	C₄	—	2	1	no	—
607	C₄	—	2	2	no	—
608	C₄	—	4	1	no	—
609	C₄	—	4	1	no	—
610	C₄	—	61	1	no	—
611	C₄	—	61	1	no	—
612	C₄	—	61	2	no	—
613	C₄	—	122	1	no	—
614	C₄	—	244	1	no	—
615	C₄	—	244	1	no	—
616	C₄	C₂²×D₆₁⋊C₈	1	1	yes	characteristic
617	C₄	D₆₁⋊#131	1	1	yes	characteristic
618	C₂	—	4	2	no	—
619	C₂	—	122	2	no	—
620	C₂	—	244	2	no	—
621	C₂	—	244	2	no	—
622	C₂	D₄×D₆₁⋊C₈	1	1	yes	characteristic
623	C₂	AGL(1,ℤ/8)×#6923	1	1	yes	characteristic
624	C₂	#21462592	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₄×#6923
commutator	C₄×C₆₁	C₂³×C₈
Frattini	C₂×C₄	C₂³×#6923
Fitting	C₆₁×#440	C₄
socle	C₂²×C₆₁	C₂×C₄×D₄
prime radical	C₂×#14519804	C₄
cosocle	C₄×Dic₆₁	C₂⁴
hypercenter	#440	#6923
hypocenter	C₆₁	C₈×AGL(1,ℤ/8)
LCS	G ▷ C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #440

Complements

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

N	H ≅ G/N	type
1. #21462625	C₂	semidirect
2. D₄×D₆₁⋊C₈	C₂	semidirect
3. #21461417	C₂	semidirect
4. #21461416	C₂	semidirect
5. #21461409	C₂	semidirect
6. SD₁₆⋊#92420	C₂	semidirect
7. #21461403	C₂	semidirect
8. SD₁₆×#92420	C₂	semidirect
9. #21461400	C₂	semidirect
10. #21461399	C₂	semidirect
11. #21461371	C₂	semidirect
12. #21461119	C₂	semidirect
13. #21461117	C₂	semidirect
14. #21461017	C₂	semidirect
17. Q₈×#92420	C₂²	semidirect
18. Q₈×#92420	C₂²	semidirect
23. #16840790	C₂²	semidirect
24. #16840790	C₂²	semidirect
36. #16840626	C₂²	semidirect
37. #16840625	C₂²	semidirect
38. #16840624	C₂²	semidirect
39. #16840623	C₂²	semidirect
40. Q₈⋊#92420	C₂²	semidirect
41. Q₈⋊#92420	C₂²	semidirect
44. #16840610	C₂²	semidirect
45. #16840610	C₂²	semidirect
48. #16840603	C₂²	semidirect
49. #16840603	C₂²	semidirect
50. C₈×#92420	C₂²	semidirect
51. C₈×#92420	C₂²	semidirect
105. #14519804	C₈	semidirect
153. #11758226	C₂×C₈	semidirect
155. D₄×D₆₁	C₂×C₈	semidirect
189. SD₁₆×C₆₁	C₂×C₈	semidirect
199. #11758201	C₂×C₈	semidirect
200. #11758199	C₂×C₈	semidirect
217. D₄₈₈	C₂×C₈	semidirect
219. #11758189	C₂×C₈	semidirect
228. Q₈×C₆₁	C₂²×C₈	semidirect
250. D₂₄₄	C₂²×C₈	semidirect
273. #92420	AGL(1,ℤ/8)	semidirect
275. C₈×C₆₁	C₂²×C₈	semidirect
277. #92418	C₂²×C₈	semidirect
379. C₆₁	C₈×AGL(1,ℤ/8)	semidirect
484. SD₁₆	D₆₁⋊C₈	semidirect
541. Q₈	C₂×D₆₁⋊C₈	semidirect
590. C₈	C₂×D₆₁⋊C₈	semidirect

Maximal subgroups

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

subgroup	index
#21462625	2
D₄×D₆₁⋊C₈	2
#21461417	2
#21461416	2
#21461409	2
SD₁₆⋊#92420	2
#21461403	2
SD₁₆×#92420	2
#21461400	2
#21461399	2
#21461371	2
#21461119	2
#21461117	2
#21461017	2
#21454624	2
C₈×AGL(1,ℤ/8)	61