Subgroups — #30612313

Order 15616.

714 conjugacy classes of subgroups.

The subgroup lattice has 582 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
2	Q₈×D₆₁⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
3	#21461413	C₂	1	1	yes	maximal, characteristic, complemented
4	#21461412	C₂	1	1	yes	maximal, characteristic, complemented
5	#21461411	C₂	1	1	yes	maximal, characteristic, complemented
6	#21461409	C₂	1	1	yes	maximal, characteristic, complemented
7	#21461406	C₂	1	1	yes	maximal, characteristic, complemented
8	Q₁₆×#92420	C₂	1	1	yes	maximal, characteristic, complemented
9	#21461404	C₂	1	1	yes	maximal, characteristic, complemented
10	#21461403	C₂	1	1	yes	maximal, characteristic, complemented
11	#21461371	C₂	1	1	yes	maximal, characteristic, complemented
12	#21461122	C₂	1	1	yes	maximal, characteristic, complemented
13	#21461117	C₂	1	1	yes	maximal, characteristic
14	#21461017	C₂	1	1	yes	maximal, characteristic, complemented
15	#21454635	C₂	1	1	yes	maximal, characteristic
16	#16840811	—	2	1	no	—
17	#16840811	—	2	1	no	—
18	#16840811	C₂²	1	1	yes	characteristic
19	#16840811	C₂²	1	1	yes	characteristic
20	Q₈×#92420	C₂²	1	1	yes	characteristic
21	Q₈×#92420	C₂²	1	1	yes	characteristic
22	Q₈×#92420	C₂²	1	1	yes	characteristic
23	Q₈×#92420	C₂²	1	1	yes	characteristic
24	#16840790	—	2	1	no	—
25	#16840790	—	2	1	no	—
26	#16840790	C₂²	1	1	yes	characteristic
27	#16840790	C₂²	1	1	yes	characteristic
28	#16840781	—	2	1	no	—
29	#16840781	C₂²	1	1	yes	characteristic
30	#16840780	C₂²	1	1	yes	characteristic
31	D₆₁⋊(C₄⋊C₈)	—	2	1	no	—
32	D₆₁⋊(C₄⋊C₈)	C₂²	1	1	yes	characteristic
33	C₄×D₆₁⋊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
37	#16840625	C₂²	1	1	yes	characteristic
38	#16840624	C₂²	1	1	yes	characteristic
39	#16840623	C₂²	1	1	yes	characteristic
40	#16840612	C₂²	1	1	yes	characteristic
41	#16840612	C₂²	1	1	yes	characteristic
42	Q₈⋊#92420	C₂²	1	1	yes	characteristic
43	Q₈⋊#92420	C₂²	1	1	yes	characteristic
44	Q₈⋊#92420	C₂²	1	1	yes	characteristic
45	Q₈⋊#92420	C₂²	1	1	yes	characteristic
46	#16840610	C₂²	1	1	yes	characteristic
47	#16840610	C₂²	1	1	yes	characteristic
48	#16840603	C₂²	1	1	yes	characteristic
49	#16840603	C₂²	1	1	yes	characteristic
50	C₈×#92420	C₂²	1	1	yes	characteristic
51	C₈×#92420	C₂²	1	1	yes	characteristic
52	C₂×#14519809	C₄	1	1	yes	characteristic
53	C₄×#11758226	C₂²	1	1	yes	characteristic
54	C₄×Q₈×D₆₁	C₂²	1	1	yes	characteristic
55	#16839867	C₄	1	1	yes	characteristic
56	#16839864	C₄	1	1	yes	characteristic
57	#16839860	C₄	1	1	yes	characteristic
58	Q₁₆×Dic₆₁	C₂²	1	1	yes	characteristic
59	#16839854	C₂²	1	1	yes	characteristic
60	#16839849	C₂²	1	1	yes	characteristic
61	#16839847	C₂²	1	1	yes	characteristic
62	#16839801	C₄	1	1	yes	characteristic
63	#16839769	C₄	1	1	yes	characteristic
64	#16839762	C₄	1	1	yes	characteristic
65	#16839714	C₂²	1	1	yes	characteristic
66	C₆₁×#441	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	D₄	1	1	yes	characteristic
71	C₂×D₆₁⋊C₈	D₄	1	1	yes	characteristic
72	#14519844	—	2	1	no	—
73	#14519844	—	2	1	no	—
74	#14519844	—	2	1	no	—
75	#14519844	—	2	1	no	—
76	C₄⋊#92420	—	2	1	no	—
77	C₄⋊#92420	—	2	1	no	—
78	C₄⋊#92420	—	2	1	no	—
79	C₄⋊#92420	—	2	1	no	—
80	C₄⋊#92420	C₂³	1	1	yes	characteristic
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	#14519834	—	2	1	no	—
85	#14519834	—	2	1	no	—
86	#14519834	—	2	1	no	—
87	#14519834	—	2	1	no	—
88	C₄×#92420	—	2	1	no	—
89	C₄×#92420	—	2	1	no	—
90	C₄×#92420	—	2	1	no	—
91	C₄×#92420	—	2	1	no	—
92	C₄×#92420	—	2	1	no	—
93	C₄×#92420	—	2	1	no	—
94	C₄×#92420	—	2	1	no	—
95	C₄×#92420	D₄	1	1	yes	characteristic
96	C₄×#92420	D₄	1	1	yes	characteristic
97	C₄×#92420	C₂³	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	C₂×#11758226	C₂×C₄	1	1	yes	characteristic
102	C₂×Q₈×D₆₁	C₂×C₄	1	1	yes	characteristic
103	#14519809	C₈	1	8	yes	complemented
104	C₂×#11758202	C₂×C₄	1	1	yes	characteristic
105	C₂×#11758190	C₂×C₄	1	1	yes	characteristic
106	C₂×#11758201	C₂×C₄	1	1	yes	characteristic
107	C₂×#11758189	C₂×C₄	1	1	yes	characteristic
108	C₂×#11758189	C₂×C₄	1	1	yes	characteristic
109	Q₈×Dic₆₁	C₂³	1	1	yes	characteristic
110	Q₈×Dic₆₁	C₂³	1	1	yes	characteristic
111	C₄×Dic₁₂₂	—	2	1	no	—
112	C₄×Dic₁₂₂	C₂×C₄	1	1	yes	characteristic
113	#14519742	—	2	1	no	—
114	#14519742	C₂³	1	1	yes	characteristic
115	C₄×D₂₄₄	—	2	1	no	—
116	C₄×D₂₄₄	C₂×C₄	1	1	yes	characteristic
117	#14519739	—	2	1	no	—
118	#14519739	C₂³	1	1	yes	characteristic
119	#14519735	—	2	1	no	—
120	#14519735	C₂×C₄	1	1	yes	characteristic
121	C₄⋊C₄×D₆₁	—	2	1	no	—
122	C₄⋊C₄×D₆₁	C₂×C₄	1	1	yes	characteristic
123	C₄²×D₆₁	—	2	1	no	—
124	C₄²×D₆₁	—	2	1	no	—
125	C₄²×D₆₁	C₂³	1	1	yes	characteristic
126	#14519711	C₂×C₄	1	1	yes	characteristic
127	#14519710	C₂×C₄	1	1	yes	characteristic
128	#14519708	C₂×C₄	1	1	yes	characteristic
129	#14519702	C₂×C₄	1	1	yes	characteristic
130	#14519701	C₂×C₄	1	1	yes	characteristic
131	#14519701	C₂×C₄	1	1	yes	characteristic
132	#14519700	C₂×C₄	1	1	yes	characteristic
133	#14519699	C₂×C₄	1	1	yes	characteristic
134	#14519697	C₂×C₄	1	1	yes	characteristic
135	#14519688	C₂×C₄	1	1	yes	characteristic
136	C₈×Dic₆₁	C₂³	1	1	yes	characteristic
137	C₈×Dic₆₁	C₂³	1	1	yes	characteristic
138	C₂×Q₁₆×C₆₁	C₂×C₄	1	1	yes	characteristic
139	C₄×Q₈×C₆₁	C₂×C₄	1	1	yes	characteristic
140	C₄×Q₈×C₆₁	C₂×C₄	1	1	yes	characteristic
141	#106×C₆₁	C₂×C₄	1	1	yes	characteristic
142	#103×C₆₁	C₂×C₄	1	1	yes	characteristic
143	#103×C₆₁	C₂×C₄	1	1	yes	characteristic
144	#97×C₆₁	C₂×C₄	1	1	yes	characteristic
145	C₂×Q₈×C₆₁	C₂²×C₄	1	1	yes	characteristic
146	C₂×Q₈×C₆₁	C₂²×C₄	1	1	yes	characteristic
147	#11758226	—	2	2	no	—
148	#11758226	C₂×C₈	1	4	yes	—
149	Q₈×D₆₁	—	2	2	no	—
150	Q₈×D₆₁	C₂×C₈	1	4	yes	complemented
151	C₂×D₂₄₄	—	2	1	no	—
152	C₂×D₂₄₄	C₂²×C₄	1	1	yes	characteristic
153	C₂×C₄×D₆₁	—	2	1	no	—
154	C₂×C₄×D₆₁	—	2	1	no	—
155	C₂×C₄×D₆₁	—	2	1	no	—
156	C₂×C₄×D₆₁	—	2	1	no	—
157	C₂×C₄×D₆₁	—	2	1	no	—
158	C₂×C₄×D₆₁	C₂²×C₄	1	1	yes	characteristic
159	C₂×C₄×D₆₁	C₂×D₄	1	1	yes	characteristic
160	C₂×C₄×D₆₁	#41	1	1	yes	characteristic
161	C₂×Dic₁₂₂	—	2	1	no	—
162	C₂×Dic₁₂₂	C₂²×C₄	1	1	yes	characteristic
163	C₂×#92420	—	2	1	no	—
164	C₂×#92420	—	2	1	no	—
165	C₂×#92420	—	2	1	no	—
166	C₂×#92420	—	2	1	no	—
167	C₂×#92420	—	2	1	no	—
168	C₂×#92420	—	2	1	no	—
169	C₂×#92420	C₂×D₄	1	1	yes	characteristic
170	C₂×#92420	C₂×D₄	1	1	yes	characteristic
171	C₂×#92420	C₂×D₄	1	1	yes	characteristic
172	C₂×#92420	C₂×D₄	1	1	yes	characteristic
173	D₆₁⋊C₈	—	2	2	no	—
174	D₆₁⋊C₈	—	4	1	no	—
175	D₆₁⋊C₈	—	4	2	no	—
176	D₆₁⋊C₈	—	4	2	no	—
177	D₆₁⋊C₈	—	4	2	no	—
178	Q₁₆×C₆₁	C₂×C₈	1	4	yes	complemented
179	C₂×C₈×C₆₁	C₂²×C₄	1	1	yes	characteristic
180	C₂×C₈×C₆₁	C₂²×C₄	1	1	yes	characteristic
181	C₄⋊C₄×C₆₁	—	2	1	no	—
182	C₄⋊C₄×C₆₁	—	2	1	no	—
183	C₄⋊C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
184	C₄⋊C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
185	C₄²×C₆₁	—	2	1	no	—
186	C₄²×C₆₁	—	2	1	no	—
187	C₄²×C₆₁	C₂²×C₄	1	1	yes	characteristic
188	#11758202	C₂×C₈	1	4	yes	complemented
189	#11758201	C₂×C₈	1	4	yes	complemented
190	#11758198	—	2	1	no	—
191	#11758198	—	2	1	no	—
192	#11758198	—	2	1	no	—
193	C₄⋊Dic₆₁	—	2	1	no	—
194	C₄⋊Dic₆₁	—	2	1	no	—
195	C₄⋊Dic₆₁	C₂²×C₄	1	1	yes	characteristic
196	C₄⋊Dic₆₁	C₂²×C₄	1	1	yes	characteristic
197	#11758196	—	2	1	no	—
198	#11758196	—	2	1	no	—
199	#11758196	—	2	1	no	—
200	C₄×Dic₆₁	—	2	1	no	—
201	C₄×Dic₆₁	—	2	1	no	—
202	C₄×Dic₆₁	—	2	1	no	—
203	C₄×Dic₆₁	—	2	1	no	—
204	C₄×Dic₆₁	—	2	1	no	—
205	C₄×Dic₆₁	C₂×D₄	1	1	yes	characteristic
206	C₄×Dic₆₁	#41	1	1	yes	characteristic
207	C₄×Dic₆₁	C₂⁴	1	1	yes	characteristic
208	C₂×#92418	C₂²×C₄	1	1	yes	characteristic
209	C₂×#92418	C₂²×C₄	1	1	yes	characteristic
210	#11758190	C₂×C₈	1	4	yes	complemented
211	#11758189	—	2	2	no	—
212	#11758189	C₂×C₈	1	4	yes	complemented
213	C₂²×D₆₁	—	2	1	no	—
214	C₂²×D₆₁	C₄×D₄	1	1	yes	characteristic
215	Q₈×C₆₁	—	2	1	no	—
216	Q₈×C₆₁	—	2	1	no	—
217	Q₈×C₆₁	C₂²×C₈	1	2	yes	—
218	Q₈×C₆₁	C₂²×C₈	1	2	yes	—
219	C₂×C₄×C₆₁	—	2	1	no	—
220	C₂×C₄×C₆₁	—	2	1	no	—
221	C₂×C₄×C₆₁	—	2	1	no	—
222	C₂×C₄×C₆₁	—	2	1	no	—
223	C₂×C₄×C₆₁	C₄×D₄	1	1	yes	characteristic
224	C₂×C₄×C₆₁	C₄×D₄	1	1	yes	characteristic
225	C₂×C₄×C₆₁	C₂³×C₄	1	1	yes	characteristic
226	C₂×Dic₆₁	—	2	1	no	—
227	C₂×Dic₆₁	—	2	1	no	—
228	C₂×Dic₆₁	—	2	1	no	—
229	C₂×Dic₆₁	C₄×D₄	1	1	yes	characteristic
230	C₂×Dic₆₁	C₂²×D₄	1	1	yes	characteristic
231	C₂×Dic₆₁	C₂×#41	1	1	yes	characteristic
232	D₂₄₄	—	2	4	no	—
233	D₂₄₄	—	2	1	no	—
234	D₂₄₄	C₂²×C₈	1	2	yes	—
235	C₄×D₆₁	—	2	4	no	—
236	C₄×D₆₁	—	2	1	no	—
237	C₄×D₆₁	—	2	1	no	—
238	C₄×D₆₁	—	2	4	no	—
239	C₄×D₆₁	—	4	1	no	—
240	C₄×D₆₁	—	4	2	no	—
241	C₄×D₆₁	—	4	2	no	—
242	C₄×D₆₁	—	4	1	no	—
243	C₄×D₆₁	—	4	1	no	—
244	C₄×D₆₁	C₂²×C₈	1	2	yes	—
245	C₄×D₆₁	#131	1	2	yes	—
246	Dic₁₂₂	—	2	1	no	—
247	Dic₁₂₂	—	2	4	no	—
248	Dic₁₂₂	C₂²×C₈	1	2	yes	—
249	#92420	—	2	1	no	—
250	#92420	—	2	1	no	—
251	#92420	—	2	1	no	—
252	#92420	—	4	1	no	—
253	#92420	—	4	1	no	—
254	#92420	—	4	1	no	—
255	#92420	—	4	1	no	—
256	#92420	—	4	1	no	—
257	#92420	—	4	1	no	—
258	#92420	#137	1	2	yes	complemented
259	C₈×C₆₁	—	2	1	no	—
260	C₈×C₆₁	C₂²×C₈	1	2	yes	—
261	#92418	—	2	1	no	—
262	#92418	C₂²×C₈	1	2	yes	—
263	C₈×#137	—	61	1	no	maximal, Sylow
264	C₂²×C₆₁	C₂×C₄×D₄	1	1	yes	characteristic
265	C₂×D₆₁	—	2	1	no	—
266	C₂×D₆₁	—	2	1	no	—
267	C₂×D₆₁	—	2	2	no	—
268	C₂×D₆₁	—	4	1	no	—
269	C₂×D₆₁	—	4	1	no	—
270	C₂×D₆₁	C₈×D₄	1	2	yes	—
271	C₄×C₆₁	—	2	2	no	—
272	C₄×C₆₁	—	2	2	no	—
273	C₄×C₆₁	—	2	1	no	—
274	C₄×C₆₁	—	2	1	no	—
275	C₄×C₆₁	—	4	1	no	—
276	C₄×C₆₁	—	4	1	no	—
277	C₄×C₆₁	C₂³×C₈	1	1	yes	characteristic
278	C₄×C₆₁	C₂×#131	1	1	yes	characteristic
279	Dic₆₁	—	2	2	no	—
280	Dic₆₁	—	2	1	no	—
281	Dic₆₁	—	4	1	no	—
282	Dic₆₁	—	4	1	no	—
283	Dic₆₁	C₈×D₄	1	2	yes	—
284	Dic₆₁	C₂×#137	1	1	yes	characteristic
285	Dic₆₁	#575	1	1	yes	characteristic
286	C₈×#41	—	61	1	no	—
287	C₂×C₈×Q₈	—	61	1	no	—
288	C₄×#137	—	61	1	no	—
289	#1579	—	61	1	no	—
290	#1579	—	61	1	no	—
291	SD₁₆⋊C₈	—	61	1	no	—
292	SD₁₆⋊C₈	—	61	1	no	—
293	C₈×Q₁₆	—	61	1	no	—
294	C₈×Q₁₆	—	61	1	no	—
295	C₈×SD₁₆	—	61	1	no	—
296	C₈×SD₁₆	—	61	1	no	—
297	#1565	—	61	1	no	—
298	#1479	—	61	1	no	—
299	#1477	—	61	1	no	—
300	C₈×M₁₆	—	61	1	no	—
301	C₂×C₆₁	C₂×C₈×D₄	1	1	yes	characteristic
302	C₂×C₆₁	C₄×#137	1	1	yes	characteristic
303	C₂×C₆₁	#2955	1	1	yes	characteristic
304	D₆₁	—	2	2	no	—
305	D₆₁	—	4	2	no	—
306	C₂×#137	—	61	1	no	—
307	C₄×#41	—	61	1	no	—
308	C₂×C₄×Q₈	—	61	1	no	—
309	C₈×Q₈	—	61	1	no	—
310	C₈×Q₈	—	61	1	no	—
311	C₈×Q₈	—	61	1	no	—
312	C₈×Q₈	—	61	1	no	—
313	C₈×Q₈	—	61	1	no	—
314	C₈×Q₈	—	61	1	no	—
315	C₈×Q₈	—	122	1	no	—
316	C₈×Q₈	—	122	1	no	—
317	#441	—	61	1	no	—
318	#441	#6923	1	1	yes	characteristic
319	#440	—	61	1	no	—
320	#440	—	61	1	no	—
321	C₄×Q₁₆	—	61	1	no	—
322	C₄×Q₁₆	—	61	1	no	—
323	C₄×SD₁₆	—	61	1	no	—
324	C₄×SD₁₆	—	61	1	no	—
325	C₈×D₄	—	61	1	no	—
326	C₈×D₄	—	61	1	no	—
327	C₈×D₄	—	122	1	no	—
328	C₈×D₄	—	122	1	no	—
329	#431	—	61	1	no	—
330	#431	—	61	1	no	—
331	#431	—	122	1	no	—
332	#428	—	61	1	no	—
333	C₂×C₄⋊C₈	—	61	1	no	—
334	C₂×C₄⋊C₈	—	122	1	no	—
335	#419	—	61	1	no	—
336	#417	—	61	1	no	—
337	C₄×M₁₆	—	61	1	no	—
338	C₂×C₄×C₈	—	61	1	no	—
339	C₂×C₄×C₈	—	122	1	no	—
340	C₂×C₄×C₈	—	122	1	no	—
341	#335	—	61	1	no	—
342	#335	—	61	1	no	—
343	#334	—	61	1	no	—
344	#334	—	61	1	no	—
345	Q₈⋊C₈	—	61	1	no	—
346	Q₈⋊C₈	—	61	1	no	—
347	Q₈⋊C₈	—	61	1	no	—
348	Q₈⋊C₈	—	61	1	no	—
349	Q₈⋊C₈	—	61	1	no	—
350	Q₈⋊C₈	—	61	1	no	—
351	D₄⋊C₈	—	61	1	no	—
352	D₄⋊C₈	—	61	1	no	—
353	#322	—	61	1	no	—
354	#322	—	61	1	no	—
355	C₈²	—	61	1	no	—
356	C₈²	—	61	1	no	—
357	C₆₁	C₈×#137	1	1	yes	characteristic, complemented, Sylow
358	C₂×#41	—	61	1	no	—
359	C₂²×Q₈	—	61	1	no	—
360	#137	—	61	8	no	—
361	C₂×Q₁₆	—	61	1	no	—
362	C₂×Q₁₆	C₂×#6923	1	1	yes	characteristic
363	C₂×SD₁₆	—	61	1	no	—
364	C₂×SD₁₆	—	61	1	no	—
365	C₂×M₁₆	—	61	1	no	—
366	C₂×M₁₆	—	61	1	no	—
367	C₂²×C₈	—	61	1	no	—
368	C₂²×C₈	—	61	1	no	—
369	C₂²×C₈	—	122	1	no	—
370	C₂²×C₈	—	122	1	no	—
371	C₂²×C₈	—	122	1	no	—
372	C₄×Q₈	—	61	1	no	—
373	C₄×Q₈	—	61	1	no	—
374	C₄×Q₈	—	61	1	no	—
375	C₄×Q₈	—	61	1	no	—
376	C₄×Q₈	—	122	1	no	—
377	C₄×Q₈	—	122	1	no	—
378	C₄×Q₈	C₂×#6923	1	1	yes	characteristic
379	C₄×Q₈	C₂×#6923	1	1	yes	characteristic
380	C₄×D₄	—	61	1	no	—
381	C₄×D₄	—	61	1	no	—
382	C₄×D₄	—	122	1	no	—
383	C₄×D₄	—	122	1	no	—
384	#117	—	61	1	no	—
385	#117	—	122	1	no	—
386	C₂×C₄⋊C₄	—	61	1	no	—
387	C₂×C₄⋊C₄	—	122	1	no	—
388	C₂×C₄²	—	61	1	no	—
389	C₂×C₄²	—	122	1	no	—
390	C₂×C₄²	—	122	1	no	—
391	#107	—	61	1	no	—
392	#107	—	61	1	no	—
393	#106	—	61	1	no	—
394	#106	C₂×#6923	1	1	yes	characteristic
395	C₄⋊C₈	—	61	1	no	—
396	C₄⋊C₈	—	61	1	no	—
397	C₄⋊C₈	—	61	1	no	—
398	C₄⋊C₈	—	61	1	no	—
399	C₄⋊C₈	—	122	1	no	—
400	C₄⋊C₈	—	122	1	no	—
401	C₄⋊C₈	—	122	1	no	—
402	C₄⋊C₈	—	122	1	no	—
403	C₄⋊C₈	—	122	1	no	—
404	C₄⋊C₈	—	122	1	no	—
405	C₄⋊C₈	—	122	1	no	—
406	C₄⋊C₈	—	122	1	no	—
407	#103	—	61	1	no	—
408	#103	—	61	1	no	—
409	#103	—	61	1	no	—
410	#103	—	61	1	no	—
411	#103	C₂×#6923	1	1	yes	characteristic
412	#103	C₂×#6923	1	1	yes	characteristic
413	#102	—	61	1	no	—
414	#102	—	61	1	no	—
415	C₂²⋊C₈	—	122	1	no	—
416	C₂²⋊C₈	—	122	1	no	—
417	C₂²⋊C₈	—	122	1	no	—
418	C₂²⋊C₈	—	122	1	no	—
419	#97	—	61	1	no	—
420	#97	C₂×#6923	1	1	yes	characteristic
421	C₄×C₈	—	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	—	61	1	no	—
427	C₄×C₈	—	61	1	no	—
428	C₄×C₈	—	61	1	no	—
429	C₄×C₈	—	122	1	no	—
430	C₄×C₈	—	122	1	no	—
431	C₄×C₈	—	122	1	no	—
432	C₄×C₈	—	122	1	no	—
433	C₄×C₈	—	122	1	no	—
434	C₄×C₈	—	122	1	no	—
435	C₄×C₈	—	122	1	no	—
436	#41	—	61	4	no	—
437	#41	—	122	2	no	—
438	C₂×Q₈	—	61	4	no	—
439	C₂×Q₈	—	61	1	no	—
440	C₂×Q₈	—	122	1	no	—
441	C₂×Q₈	—	122	2	no	—
442	C₂×Q₈	C₂²×#6923	1	1	yes	characteristic
443	C₂×Q₈	C₂²×#6923	1	1	yes	characteristic
444	C₂×D₄	—	61	1	no	—
445	C₂×D₄	—	122	1	no	—
446	C₂²×C₄	—	61	1	no	—
447	C₂²×C₄	—	61	1	no	—
448	C₂²×C₄	—	61	1	no	—
449	C₂²×C₄	—	122	1	no	—
450	C₂²×C₄	—	122	1	no	—
451	C₂²×C₄	—	122	1	no	—
452	C₂²×C₄	—	122	1	no	—
453	C₂²×C₄	—	122	1	no	—
454	Q₁₆	—	61	4	no	—
455	Q₁₆	D₆₁⋊C₈	1	4	yes	complemented
456	SD₁₆	—	61	4	no	—
457	SD₁₆	—	61	4	no	—
458	M₁₆	—	61	4	no	—
459	M₁₆	—	122	2	no	—
460	C₂×C₈	—	61	1	no	—
461	C₂×C₈	—	61	1	no	—
462	C₂×C₈	—	61	1	no	—
463	C₂×C₈	—	61	1	no	—
464	C₂×C₈	—	61	1	no	—
465	C₂×C₈	—	61	1	no	—
466	C₂×C₈	—	122	2	no	—
467	C₂×C₈	—	122	1	no	—
468	C₂×C₈	—	122	1	no	—
469	C₂×C₈	—	122	1	no	—
470	C₂×C₈	—	122	1	no	—
471	C₂×C₈	—	122	1	no	—
472	C₂×C₈	—	122	1	no	—
473	C₂×C₈	—	244	2	no	—
474	C₂×C₈	—	244	1	no	—
475	C₂×C₈	—	244	2	no	—
476	C₂×C₈	—	244	2	no	—
477	C₂×C₈	C₂²×#6923	1	1	yes	characteristic
478	C₂×C₈	C₂²×#6923	1	1	yes	characteristic
479	C₄⋊C₄	—	2	1	no	—
480	C₄⋊C₄	—	2	1	no	—
481	C₄⋊C₄	—	61	1	no	—
482	C₄⋊C₄	—	61	1	no	—
483	C₄⋊C₄	—	122	1	no	—
484	C₄⋊C₄	—	122	1	no	—
485	C₄⋊C₄	—	122	1	no	—
486	C₄⋊C₄	—	122	1	no	—
487	C₄⋊C₄	—	122	1	no	—
488	C₄⋊C₄	C₂²×#6923	1	1	yes	characteristic
489	C₄⋊C₄	C₂²×#6923	1	1	yes	characteristic
490	C₂²⋊C₄	—	122	1	no	—
491	C₂²⋊C₄	—	122	1	no	—
492	C₂²⋊C₄	—	122	1	no	—
493	C₄²	—	2	1	no	—
494	C₄²	—	2	1	no	—
495	C₄²	—	61	1	no	—
496	C₄²	—	61	1	no	—
497	C₄²	—	61	1	no	—
498	C₄²	—	122	1	no	—
499	C₄²	—	122	1	no	—
500	C₄²	—	122	1	no	—
501	C₄²	—	122	1	no	—
502	C₄²	—	122	1	no	—
503	C₄²	C₂²×#6923	1	1	yes	characteristic
504	C₂³	—	61	1	no	—
505	C₂³	—	122	1	no	—
506	Q₈	—	2	1	no	—
507	Q₈	—	2	1	no	—
508	Q₈	—	61	2	no	—
509	Q₈	—	122	4	no	—
510	Q₈	—	122	1	no	—
511	Q₈	C₂×D₆₁⋊C₈	1	2	yes	—
512	Q₈	C₂×D₆₁⋊C₈	1	2	yes	—
513	D₄	—	61	2	no	—
514	D₄	—	122	4	no	—
515	D₄	—	122	1	no	—
516	C₂×C₄	—	2	1	no	—
517	C₂×C₄	—	2	1	no	—
518	C₂×C₄	—	2	1	no	—
519	C₂×C₄	—	2	1	no	—
520	C₂×C₄	—	61	1	no	—
521	C₂×C₄	—	61	1	no	—
522	C₂×C₄	—	61	2	no	—
523	C₂×C₄	—	61	2	no	—
524	C₂×C₄	—	61	1	no	—
525	C₂×C₄	—	122	1	no	—
526	C₂×C₄	—	122	1	no	—
527	C₂×C₄	—	122	4	no	—
528	C₂×C₄	—	122	4	no	—
529	C₂×C₄	—	122	1	no	—
530	C₂×C₄	—	122	1	no	—
531	C₂×C₄	—	122	1	no	—
532	C₂×C₄	—	244	1	no	—
533	C₂×C₄	—	244	2	no	—
534	C₂×C₄	—	244	1	no	—
535	C₂×C₄	—	244	1	no	—
536	C₂×C₄	—	244	2	no	—
537	C₂×C₄	D₄×#6923	1	1	yes	characteristic
538	C₂×C₄	D₄×#6923	1	1	yes	characteristic
539	C₂×C₄	C₂³×#6923	1	1	yes	characteristic
540	C₈	—	2	1	no	—
541	C₈	—	61	2	no	—
542	C₈	—	61	2	no	—
543	C₈	—	122	1	no	—
544	C₈	—	122	1	no	—
545	C₈	—	122	1	no	—
546	C₈	—	122	1	no	—
547	C₈	—	244	1	no	—
548	C₈	—	244	1	no	—
549	C₈	—	244	1	no	—
550	C₈	—	244	1	no	—
551	C₈	—	244	1	no	—
552	C₈	—	244	1	no	—
553	C₈	C₂×D₆₁⋊C₈	1	2	yes	—
554	C₂²	—	61	2	no	—
555	C₂²	—	122	1	no	—
556	C₂²	—	122	1	no	—
557	C₂²	—	122	2	no	—
558	C₂²	—	244	1	no	—
559	C₂²	—	244	1	no	—
560	C₂²	C₂×D₄×#6923	1	1	yes	characteristic
561	C₄	—	2	1	no	—
562	C₄	—	2	1	no	—
563	C₄	—	2	2	no	—
564	C₄	—	2	2	no	—
565	C₄	—	4	1	no	—
566	C₄	—	4	1	no	—
567	C₄	—	61	1	no	—
568	C₄	—	61	1	no	—
569	C₄	—	61	2	no	—
570	C₄	—	122	1	no	—
571	C₄	—	122	2	no	—
572	C₄	—	244	1	no	—
573	C₄	—	244	1	no	—
574	C₄	C₂²×D₆₁⋊C₈	1	1	yes	characteristic
575	C₄	D₆₁⋊#131	1	1	yes	characteristic
576	C₂	—	122	2	no	—
577	C₂	—	244	2	no	—
578	C₂	D₄×D₆₁⋊C₈	1	1	yes	characteristic
579	C₂	#137×#6923	1	1	yes	characteristic
580	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×#441	C₄
socle	C₂²×C₆₁	C₂×C₄×D₄
prime radical	C₂×#11758226	C₂×C₄
cosocle	C₄×Dic₆₁	C₂⁴
hypercenter	#441	#6923
hypocenter	C₆₁	C₈×#137
LCS	G ▷ C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #441

Complements

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

N	H ≅ G/N	type
2. Q₈×D₆₁⋊C₈	C₂	semidirect
3. #21461413	C₂	semidirect
4. #21461412	C₂	semidirect
5. #21461411	C₂	semidirect
6. #21461409	C₂	semidirect
7. #21461406	C₂	semidirect
8. Q₁₆×#92420	C₂	semidirect
9. #21461404	C₂	semidirect
10. #21461403	C₂	semidirect
11. #21461371	C₂	semidirect
12. #21461122	C₂	semidirect
14. #21461017	C₂	semidirect
103. #14519809	C₈	semidirect
150. Q₈×D₆₁	C₂×C₈	semidirect
178. Q₁₆×C₆₁	C₂×C₈	semidirect
188. #11758202	C₂×C₈	semidirect
189. #11758201	C₂×C₈	semidirect
210. #11758190	C₂×C₈	semidirect
212. #11758189	C₂×C₈	semidirect
258. #92420	#137	semidirect
357. C₆₁	C₈×#137	semidirect
455. Q₁₆	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
Q₈×D₆₁⋊C₈	2
#21461413	2
#21461412	2
#21461411	2
#21461409	2
#21461406	2
Q₁₆×#92420	2
#21461404	2
#21461403	2
#21461371	2
#21461122	2
#21461117	2
#21461017	2
#21454635	2
C₈×#137	61