Subgroups — #29833620

Order 15616.

574 conjugacy classes of subgroups.

The subgroup lattice has 558 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#21454508	C₂	1	1	yes	maximal, characteristic
2	#21447651	C₂	1	1	yes	maximal, characteristic, complemented
3	#21447648	C₂	1	1	yes	maximal, characteristic, complemented
4	#21447647	C₂	1	1	yes	maximal, characteristic, complemented
5	#21447646	C₂	1	1	yes	maximal, characteristic, complemented
6	#21447642	C₂	1	1	yes	maximal, characteristic, complemented
7	#21447638	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₆×C₂²⋊D₆₁	C₂	1	1	yes	maximal, characteristic, complemented
9	#21447627	C₂	1	1	yes	maximal, characteristic, complemented
10	#21447625	C₂	1	1	yes	maximal, characteristic, complemented
11	#21447432	C₂	1	1	yes	maximal, characteristic, complemented
12	#21447431	C₂	1	1	yes	maximal, characteristic, complemented
13	#21447429	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂²⋊C₁₆×D₆₁	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₁×#2168	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#14519783	C₂²	1	1	yes	characteristic
17	C₂²×C₈×D₆₁	C₂²	1	1	yes	characteristic
18	#16840271	C₄	1	1	yes	characteristic
19	C₂×#14519717	C₂²	1	1	yes	characteristic
20	C₂×#14519717	C₂²	1	1	yes	characteristic, complemented
21	C₂×#14519716	C₂²	1	1	yes	characteristic, complemented
22	C₂×C₁₆×D₆₁	C₂²	1	1	yes	characteristic
23	C₂×C₁₆×D₆₁	C₂²	1	1	yes	characteristic
24	C₂×C₁₆×D₆₁	C₂²	1	1	yes	characteristic, complemented
25	#16839836	C₄	1	1	yes	characteristic
26	#16839834	C₄	1	1	yes	characteristic
27	#16839832	C₄	1	1	yes	characteristic
28	#16839830	C₄	1	1	yes	characteristic
29	C₈×D₂₄₄	C₂²	1	1	yes	characteristic
30	C₈×C₂²⋊D₆₁	C₂²	1	1	yes	characteristic
31	C₈×C₂²⋊D₆₁	C₂²	1	1	yes	characteristic
32	#16839787	C₄	1	1	yes	characteristic
33	#16839727	C₄	1	1	yes	characteristic
34	#16839724	C₄	1	1	yes	characteristic
35	#16839716	C₂²	1	1	yes	characteristic
36	C₄⋊#11758185	C₂²	1	1	yes	characteristic, complemented
37	#16839580	C₂²	1	1	yes	characteristic, complemented
38	#16839580	C₂²	1	1	yes	characteristic, complemented
39	C₂²⋊#11758185	C₂²	1	1	yes	characteristic
40	C₂²⋊#11758185	C₂²	1	1	yes	characteristic, complemented
41	#16839541	C₂²	1	1	yes	characteristic
42	#16839541	C₂²	1	1	yes	characteristic
43	#16839541	C₂²	1	1	yes	characteristic
44	#16839541	C₂²	1	1	yes	characteristic
45	#16839541	C₂²	1	1	yes	characteristic
46	#16839541	C₂²	1	1	yes	characteristic
47	#16839541	C₂²	1	1	yes	characteristic, complemented
48	#16839541	C₂²	1	1	yes	characteristic, complemented
49	#16839537	C₂²	1	1	yes	characteristic, complemented
50	C₄×#11758185	C₂²	1	1	yes	characteristic, complemented
51	C₁₆×Dic₆₁	C₂²	1	1	yes	characteristic, complemented
52	C₂×M₃₂×C₆₁	C₂²	1	1	yes	characteristic
53	C₂²×C₁₆×C₆₁	C₂²	1	1	yes	characteristic, complemented
54	C₈×D₄×C₆₁	C₂²	1	1	yes	characteristic
55	C₆₁×C₄⋊C₁₆	C₂²	1	1	yes	characteristic, complemented
56	C₆₁×C₂²⋊C₁₆	C₂²	1	1	yes	characteristic
57	C₆₁×C₂²⋊C₁₆	C₂²	1	1	yes	characteristic, complemented
58	C₆₁×#346	C₂²	1	1	yes	characteristic, complemented
59	C₂×#11758222	C₂×C₄	1	1	yes	characteristic
60	C₂²×C₄×D₆₁	C₂×C₄	1	1	yes	characteristic
61	#14519783	—	4	1	no	—
62	#14519783	—	4	1	no	—
63	C₂×#11758194	C₂×C₄	1	1	yes	characteristic
64	C₂×#11758189	C₂×C₄	1	1	yes	characteristic
65	C₂×#11758189	C₂×C₄	1	1	yes	characteristic
66	C₂×#11758189	C₂×C₄	1	1	yes	characteristic
67	C₂²×#92418	C₂×C₄	1	1	yes	characteristic
68	C₂×C₈×D₆₁	—	4	1	no	—
69	C₂×C₈×D₆₁	—	4	1	no	—
70	C₂×C₈×D₆₁	C₂×C₄	1	1	yes	characteristic
71	C₂×C₈×D₆₁	C₂×C₄	1	1	yes	characteristic
72	C₂×C₈×D₆₁	C₂³	1	1	yes	characteristic
73	C₂×C₈×D₆₁	C₂³	1	1	yes	characteristic
74	C₂×C₈×D₆₁	C₂³	1	1	yes	characteristic
75	#14519762	C₈	1	1	yes	characteristic
76	#14519759	C₈	1	1	yes	characteristic
77	#14519755	C₈	1	1	yes	characteristic
78	#14519754	C₈	1	1	yes	characteristic
79	#14519750	C₈	1	1	yes	characteristic
80	#14519749	C₈	1	1	yes	characteristic
81	#14519747	C₈	1	1	yes	characteristic
82	#14519745	C₈	1	1	yes	characteristic
83	C₄×D₂₄₄	C₂×C₄	1	1	yes	characteristic
84	C₄×C₂²⋊D₆₁	C₂×C₄	1	1	yes	characteristic
85	C₄×C₂²⋊D₆₁	C₂×C₄	1	1	yes	characteristic
86	#14519734	C₂×C₄	1	1	yes	characteristic
87	#14519717	—	4	1	no	—
88	#14519717	—	4	1	no	—
89	#14519716	—	4	1	no	—
90	C₂×#11758185	C₂³	1	1	yes	characteristic
91	C₂×#11758185	C₂³	1	1	yes	characteristic
92	C₂×#11758185	C₂³	1	1	yes	characteristic
93	C₂×#11758185	C₂³	1	1	yes	characteristic
94	C₁₆×D₆₁	—	4	1	no	—
95	C₁₆×D₆₁	—	4	1	no	—
96	C₁₆×D₆₁	—	4	1	no	—
97	C₄⋊#92418	C₂×C₄	1	1	yes	characteristic
98	#14519706	C₂×C₄	1	1	yes	characteristic
99	#14519706	C₂×C₄	1	1	yes	characteristic
100	C₂²⋊#92418	C₂×C₄	1	1	yes	characteristic
101	C₂²⋊#92418	C₂×C₄	1	1	yes	characteristic
102	#14519689	C₂×C₄	1	1	yes	characteristic
103	#14519689	C₂×C₄	1	1	yes	characteristic
104	#14519689	C₂×C₄	1	1	yes	characteristic
105	#14519689	C₂×C₄	1	1	yes	characteristic
106	#14519688	C₂×C₄	1	1	yes	characteristic
107	#14519687	C₂×C₄	1	1	yes	characteristic
108	C₈×Dic₆₁	C₂³	1	1	yes	characteristic
109	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
110	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
111	C₄×D₄×C₆₁	C₂×C₄	1	1	yes	characteristic
112	M₃₂×C₆₁	—	4	1	no	—
113	C₂×C₁₆×C₆₁	—	4	1	no	—
114	C₂×C₁₆×C₆₁	C₂³	1	1	yes	characteristic
115	C₂×C₁₆×C₆₁	C₂³	1	1	yes	characteristic
116	C₂×C₁₆×C₆₁	C₂³	1	1	yes	characteristic
117	C₂×C₁₆×C₆₁	C₂³	1	1	yes	characteristic
118	C₄⋊C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
119	C₂²⋊C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
120	C₂²⋊C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
121	C₄×C₈×C₆₁	C₂³	1	1	yes	characteristic
122	C₂³×D₆₁	C₂×C₈	1	1	yes	characteristic
123	C₂×D₄×C₆₁	C₂×C₈	1	1	yes	characteristic
124	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
125	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
126	C₂×C₂²⋊D₆₁	C₂×C₈	1	1	yes	characteristic
127	C₂×C₂²⋊D₆₁	C₂×C₈	1	1	yes	characteristic
128	C₂×C₂²⋊D₆₁	C₂×C₈	1	1	yes	characteristic
129	C₂×C₂²⋊D₆₁	C₂×C₈	1	1	yes	characteristic
130	C₂²×Dic₆₁	C₂×C₈	1	1	yes	characteristic
131	#11758222	—	4	1	no	—
132	#11758222	—	4	1	no	—
133	C₂×D₂₄₄	C₂×C₈	1	1	yes	characteristic
134	C₂×D₂₄₄	C₂×C₈	1	1	yes	characteristic
135	C₂×C₄×D₆₁	—	4	1	no	—
136	C₂×C₄×D₆₁	—	4	1	no	—
137	C₂×C₄×D₆₁	C₂×C₈	1	1	yes	characteristic
138	C₂×C₄×D₆₁	C₂×C₈	1	1	yes	characteristic
139	C₂×C₄×D₆₁	C₂²×C₄	1	1	yes	characteristic
140	C₂×C₄×D₆₁	C₂²×C₄	1	1	yes	characteristic
141	C₂×C₄×D₆₁	C₂²×C₄	1	1	yes	characteristic
142	C₂×Dic₁₂₂	C₂×C₈	1	1	yes	characteristic
143	C₂×C₈×C₆₁	—	2	1	no	—
144	C₂×C₈×C₆₁	—	2	1	no	—
145	C₂×C₈×C₆₁	—	2	1	no	—
146	C₂×C₈×C₆₁	—	2	1	no	—
147	C₂×C₈×C₆₁	C₂²×C₄	1	1	yes	characteristic
148	C₂×C₈×C₆₁	C₂²×C₄	1	1	yes	characteristic
149	C₂×C₈×C₆₁	C₂²×C₄	1	1	yes	characteristic
150	C₂×C₈×C₆₁	C₂⁴	1	1	yes	characteristic
151	C₄⋊C₄×C₆₁	C₂×C₈	1	1	yes	characteristic
152	C₂²⋊C₄×C₆₁	C₂×C₈	1	1	yes	characteristic
153	C₂²⋊C₄×C₆₁	C₂×C₈	1	1	yes	characteristic
154	C₄²×C₆₁	C₂²×C₄	1	1	yes	characteristic
155	C₂²⋊Dic₆₁	C₂×C₈	1	1	yes	characteristic
156	C₂²⋊Dic₆₁	C₂×C₈	1	1	yes	characteristic
157	#11758198	C₂×C₈	1	1	yes	characteristic
158	#11758198	C₂×C₈	1	1	yes	characteristic
159	#11758198	C₂×C₈	1	1	yes	characteristic
160	#11758198	C₂×C₈	1	1	yes	characteristic
161	#11758198	C₂×C₈	1	1	yes	characteristic
162	#11758198	C₂×C₈	1	1	yes	characteristic
163	C₄⋊Dic₆₁	C₂×C₈	1	1	yes	characteristic
164	#11758196	C₂×C₈	1	1	yes	characteristic
165	#11758196	C₂×C₈	1	1	yes	characteristic
166	#11758196	C₂×C₈	1	1	yes	characteristic
167	#11758196	C₂×C₈	1	1	yes	characteristic
168	C₄×Dic₆₁	C₂²×C₄	1	1	yes	characteristic
169	#11758194	—	4	1	no	—
170	C₂×#92418	—	4	1	no	—
171	C₂×#92418	C₂²×C₄	1	1	yes	characteristic
172	C₂×#92418	C₂²×C₄	1	1	yes	characteristic
173	C₂×#92418	C₂²×C₄	1	1	yes	characteristic
174	C₂×#92418	C₂²×C₄	1	1	yes	characteristic
175	#11758189	—	4	1	no	—
176	#11758189	—	4	1	no	—
177	#11758189	—	4	1	no	—
178	C₈×D₆₁	—	2	1	no	—
179	C₈×D₆₁	—	2	1	no	—
180	C₈×D₆₁	—	2	1	no	—
181	C₈×D₆₁	—	2	1	no	—
182	C₈×D₆₁	—	2	1	no	—
183	C₈×D₆₁	—	2	1	no	—
184	C₈×D₆₁	—	4	1	no	—
185	C₈×D₆₁	—	4	1	no	—
186	C₁₆×C₆₁	—	2	1	no	—
187	C₁₆×C₆₁	—	2	1	no	—
188	C₁₆×C₆₁	—	2	1	no	—
189	C₁₆×C₆₁	—	2	1	no	—
190	#11758185	—	2	1	no	—
191	#11758185	—	2	1	no	—
192	#11758185	—	2	1	no	—
193	#11758185	—	2	1	no	—
194	C₂³×C₆₁	C₂²×C₈	1	1	yes	characteristic
195	C₂³×C₆₁	C₂²×C₈	1	1	yes	characteristic
196	C₂²×D₆₁	—	2	2	no	—
197	C₂²×D₆₁	—	4	1	no	—
198	C₂²×D₆₁	—	4	1	no	—
199	C₂²×D₆₁	C₂²×C₈	1	1	yes	characteristic
200	C₂²×D₆₁	C₂²×C₈	1	1	yes	characteristic
201	C₂²×D₆₁	C₂²×C₈	1	1	yes	characteristic
202	D₄×C₆₁	—	4	1	no	—
203	C₂×C₄×C₆₁	—	2	1	no	—
204	C₂×C₄×C₆₁	—	2	1	no	—
205	C₂×C₄×C₆₁	—	2	1	no	—
206	C₂×C₄×C₆₁	—	2	1	no	—
207	C₂×C₄×C₆₁	C₂²×C₈	1	1	yes	characteristic
208	C₂×C₄×C₆₁	C₂²×C₈	1	1	yes	characteristic
209	C₂×C₄×C₆₁	C₂²×C₈	1	1	yes	characteristic
210	C₂×C₄×C₆₁	C₂²×C₈	1	1	yes	characteristic
211	C₂×C₄×C₆₁	C₂³×C₄	1	1	yes	characteristic
212	C₂²⋊D₆₁	—	2	2	no	—
213	C₂²⋊D₆₁	—	4	1	no	—
214	C₂²⋊D₆₁	—	4	1	no	—
215	C₂²⋊D₆₁	—	4	1	no	—
216	C₂×Dic₆₁	—	4	1	no	—
217	C₂×Dic₆₁	C₂²×C₈	1	1	yes	characteristic
218	C₂×Dic₆₁	C₂²×C₈	1	1	yes	characteristic
219	C₂×Dic₆₁	C₂²×C₈	1	1	yes	characteristic
220	C₂×Dic₆₁	C₂²×C₈	1	1	yes	characteristic
221	C₂×Dic₆₁	C₂²×C₈	1	1	yes	characteristic
222	D₂₄₄	—	2	2	no	—
223	D₂₄₄	—	4	1	no	—
224	C₄×D₆₁	—	2	1	no	—
225	C₄×D₆₁	—	2	1	no	—
226	C₄×D₆₁	—	2	1	no	—
227	C₄×D₆₁	—	2	1	no	—
228	C₄×D₆₁	—	2	1	no	—
229	C₄×D₆₁	—	2	1	no	—
230	C₄×D₆₁	—	4	1	no	—
231	C₄×D₆₁	—	4	1	no	—
232	Dic₁₂₂	—	4	1	no	—
233	C₈×C₆₁	—	2	1	no	—
234	C₈×C₆₁	—	2	1	no	—
235	C₈×C₆₁	—	2	1	no	—
236	C₈×C₆₁	H(5,𝔽₂)	1	1	yes	characteristic
237	C₈×C₆₁	H(5,𝔽₂)	1	1	yes	characteristic
238	#92418	—	2	1	no	—
239	#92418	—	2	1	no	—
240	#92418	—	2	1	no	—
241	#92418	—	2	1	no	—
242	#33490	—	61	1	no	maximal, Sylow
243	C₂²×C₆₁	—	2	1	no	—
244	C₂²×C₆₁	—	2	1	no	—
245	C₂²×C₆₁	—	2	1	no	—
246	C₂²×C₆₁	—	2	1	no	—
247	C₂²×C₆₁	—	2	1	no	—
248	C₂²×C₆₁	—	2	1	no	—
249	C₂²×C₆₁	C₂³×C₈	1	1	yes	characteristic
250	C₂×D₆₁	—	2	1	no	—
251	C₂×D₆₁	—	2	1	no	—
252	C₂×D₆₁	—	2	1	no	—
253	C₂×D₆₁	—	2	1	no	—
254	C₂×D₆₁	—	2	1	no	—
255	C₂×D₆₁	—	2	1	no	—
256	C₂×D₆₁	—	2	1	no	—
257	C₂×D₆₁	—	2	1	no	—
258	C₂×D₆₁	—	4	4	no	—
259	C₂×D₆₁	#504	1	2	yes	—
260	C₄×C₆₁	—	2	1	no	—
261	C₄×C₆₁	—	2	1	no	—
262	C₄×C₆₁	—	2	1	no	—
263	C₄×C₆₁	—	2	1	no	—
264	C₄×C₆₁	#518	1	1	yes	characteristic
265	C₄×C₆₁	#568	1	1	yes	characteristic
266	Dic₆₁	—	2	1	no	—
267	Dic₆₁	—	2	1	no	—
268	Dic₆₁	—	2	1	no	—
269	Dic₆₁	—	2	1	no	—
270	Dic₆₁	—	2	1	no	—
271	#2929	—	61	1	no	—
272	#2169	—	61	1	no	—
273	#2169	—	61	1	no	—
274	#2168	—	61	1	no	—
275	#2168	—	61	1	no	—
276	#2168	—	61	1	no	—
277	#2168	D₆₁	1	1	yes	characteristic, complemented
278	D₄×C₁₆	—	61	1	no	—
279	D₄×C₁₆	—	61	1	no	—
280	#2164	—	61	1	no	—
281	#2164	—	61	1	no	—
282	#2113	—	61	1	no	—
283	#2113	—	61	1	no	—
284	#2112	—	61	1	no	—
285	C₂×C₂²⋊C₁₆	—	61	1	no	—
286	C₂×C₆₁	—	4	1	no	—
287	C₂×C₆₁	—	4	1	no	—
288	C₂×C₆₁	#2972	1	1	yes	characteristic
289	C₂×C₆₁	C₂×#504	1	1	yes	characteristic
290	C₂×C₆₁	#3407	1	1	yes	characteristic
291	D₆₁	—	2	2	no	—
292	D₆₁	—	4	1	no	—
293	D₆₁	—	4	1	no	—
294	C₂×#131	—	61	1	no	—
295	C₂³×C₈	—	61	1	no	—
296	#525	—	61	1	no	—
297	C₂×M₃₂	—	61	1	no	—
298	C₂×M₃₂	—	61	1	no	—
299	C₂×M₃₂	—	61	1	no	—
300	C₂×M₃₂	C₂×D₆₁	1	1	yes	characteristic
301	C₂²×C₁₆	—	61	1	no	—
302	C₂²×C₁₆	—	61	1	no	—
303	C₂²×C₁₆	—	61	1	no	—
304	C₂²×C₁₆	C₂×D₆₁	1	1	yes	characteristic, complemented
305	#435	—	61	1	no	—
306	#435	—	61	1	no	—
307	#435	—	61	1	no	—
308	#435	—	61	1	no	—
309	C₈×D₄	—	61	1	no	—
310	C₈×D₄	—	61	1	no	—
311	C₈×D₄	—	61	1	no	—
312	C₈×D₄	C₂×D₆₁	1	1	yes	characteristic
313	#424	—	61	1	no	—
314	#408	—	61	1	no	—
315	#407	—	61	1	no	—
316	#405	—	61	1	no	—
317	C₄⋊C₁₆	—	61	1	no	—
318	C₄⋊C₁₆	—	61	1	no	—
319	C₄⋊C₁₆	—	61	1	no	—
320	C₄⋊C₁₆	C₂×D₆₁	1	1	yes	characteristic, complemented
321	C₂²⋊C₁₆	—	61	1	no	—
322	C₂²⋊C₁₆	—	61	1	no	—
323	C₂²⋊C₁₆	—	61	1	no	—
324	C₂²⋊C₁₆	—	61	1	no	—
325	C₂²⋊C₁₆	—	61	1	no	—
326	C₂²⋊C₁₆	—	61	1	no	—
327	C₂²⋊C₁₆	—	61	1	no	—
328	C₂²⋊C₁₆	—	61	1	no	—
329	C₂²⋊C₁₆	—	61	1	no	—
330	C₂²⋊C₁₆	—	61	1	no	—
331	C₂²⋊C₁₆	C₂×D₆₁	1	1	yes	characteristic
332	C₂²⋊C₁₆	C₂×D₆₁	1	1	yes	characteristic, complemented
333	#346	—	61	1	no	—
334	#346	C₂×D₆₁	1	1	yes	characteristic, complemented
335	C₄×C₁₆	—	61	1	no	—
336	C₄×C₁₆	—	61	1	no	—
337	C₆₁	#33490	1	1	yes	characteristic, complemented, Sylow
338	C₂×#41	—	61	1	no	—
339	C₂³×C₄	—	61	1	no	—
340	#131	—	244	1	no	—
341	#131	—	244	1	no	—
342	C₂×M₁₆	—	61	1	no	—
343	C₂×M₁₆	—	61	1	no	—
344	C₂×M₁₆	—	61	1	no	—
345	C₂×M₁₆	—	61	1	no	—
346	C₂²×C₈	—	61	1	no	—
347	C₂²×C₈	—	61	1	no	—
348	C₂²×C₈	—	61	1	no	—
349	C₂²×C₈	—	61	1	no	—
350	C₂²×C₈	—	61	1	no	—
351	C₂²×C₈	—	61	1	no	—
352	C₂²×C₈	—	244	1	no	—
353	C₂²×C₈	—	244	1	no	—
354	C₂²×C₈	C₂²×D₆₁	1	1	yes	characteristic
355	C₂²×C₈	C₂²×D₆₁	1	1	yes	characteristic
356	#123	—	61	1	no	—
357	#123	—	61	1	no	—
358	C₂²⋊Q₈	—	61	1	no	—
359	C₂²⋊Q₈	—	61	1	no	—
360	#121	—	61	1	no	—
361	#121	—	61	1	no	—
362	#120	—	61	1	no	—
363	#120	—	61	1	no	—
364	C₄×D₄	—	61	1	no	—
365	C₄×D₄	—	61	1	no	—
366	C₄×D₄	—	61	1	no	—
367	C₄×D₄	C₄×D₆₁	1	1	yes	characteristic
368	#117	—	61	1	no	—
369	M₃₂	—	4	1	no	—
370	M₃₂	—	244	1	no	—
371	M₃₂	—	244	1	no	—
372	M₃₂	—	244	1	no	—
373	C₂×C₁₆	—	4	1	no	—
374	C₂×C₁₆	—	61	1	no	—
375	C₂×C₁₆	—	61	1	no	—
376	C₂×C₁₆	—	61	1	no	—
377	C₂×C₁₆	—	61	1	no	—
378	C₂×C₁₆	—	244	1	no	—
379	C₂×C₁₆	—	244	1	no	—
380	C₂×C₁₆	—	244	1	no	—
381	C₂×C₁₆	C₂²×D₆₁	1	1	yes	characteristic
382	C₂×C₁₆	C₂²×D₆₁	1	1	yes	characteristic
383	C₂×C₁₆	C₂²×D₆₁	1	1	yes	characteristic
384	C₂×C₁₆	C₂²×D₆₁	1	1	yes	characteristic
385	C₄⋊C₈	—	61	1	no	—
386	C₄⋊C₈	—	61	1	no	—
387	C₄⋊C₈	—	61	1	no	—
388	C₄⋊C₈	C₄×D₆₁	1	1	yes	characteristic
389	C₂²⋊C₈	—	61	1	no	—
390	C₂²⋊C₈	—	61	1	no	—
391	C₂²⋊C₈	—	61	1	no	—
392	C₂²⋊C₈	—	61	1	no	—
393	C₂²⋊C₈	—	61	1	no	—
394	C₂²⋊C₈	—	61	1	no	—
395	C₂²⋊C₈	C₄×D₆₁	1	1	yes	characteristic
396	C₂²⋊C₈	C₄×D₆₁	1	1	yes	characteristic
397	#97	—	61	1	no	—
398	#97	—	61	1	no	—
399	C₄×C₈	—	61	1	no	—
400	C₄×C₈	C₂²×D₆₁	1	1	yes	characteristic
401	C₂⁴	—	61	1	no	—
402	#41	—	244	1	no	—
403	#41	—	244	1	no	—
404	C₂×Q₈	—	61	1	no	—
405	C₂×D₄	—	61	1	no	—
406	C₂×D₄	—	61	1	no	—
407	C₂×D₄	—	61	1	no	—
408	C₂×D₄	—	61	1	no	—
409	C₂×D₄	—	61	1	no	—
410	C₂×D₄	—	61	1	no	—
411	C₂×D₄	C₈×D₆₁	1	1	yes	characteristic
412	C₂²×C₄	—	61	1	no	—
413	C₂²×C₄	—	61	1	no	—
414	C₂²×C₄	—	61	1	no	—
415	C₂²×C₄	—	61	1	no	—
416	C₂²×C₄	—	61	1	no	—
417	C₂²×C₄	—	61	1	no	—
418	C₂²×C₄	—	244	1	no	—
419	C₂²×C₄	—	244	1	no	—
420	C₂²×C₄	C₂×C₄×D₆₁	1	1	yes	characteristic
421	C₂²×C₄	C₂×C₄×D₆₁	1	1	yes	characteristic
422	M₁₆	—	244	1	no	—
423	M₁₆	—	244	1	no	—
424	M₁₆	—	244	1	no	—
425	M₁₆	—	244	1	no	—
426	C₂×C₈	—	2	1	no	—
427	C₂×C₈	—	2	1	no	—
428	C₂×C₈	—	2	1	no	—
429	C₂×C₈	—	2	1	no	—
430	C₂×C₈	—	61	1	no	—
431	C₂×C₈	—	61	1	no	—
432	C₂×C₈	—	61	1	no	—
433	C₂×C₈	—	61	1	no	—
434	C₂×C₈	—	122	1	no	—
435	C₂×C₈	—	122	1	no	—
436	C₂×C₈	—	122	1	no	—
437	C₂×C₈	—	122	1	no	—
438	C₂×C₈	—	122	1	no	—
439	C₂×C₈	—	122	1	no	—
440	C₂×C₈	—	244	1	no	—
441	C₂×C₈	—	244	1	no	—
442	C₂×C₈	—	244	1	no	—
443	C₂×C₈	C₂×C₄×D₆₁	1	1	yes	characteristic
444	C₂×C₈	C₂×C₄×D₆₁	1	1	yes	characteristic
445	C₂×C₈	C₂×C₄×D₆₁	1	1	yes	characteristic
446	C₂×C₈	C₂³×D₆₁	1	1	yes	characteristic
447	C₄⋊C₄	—	61	1	no	—
448	C₄⋊C₄	—	61	1	no	—
449	C₄⋊C₄	—	61	1	no	—
450	C₄⋊C₄	—	61	1	no	—
451	C₄⋊C₄	—	61	1	no	—
452	C₄⋊C₄	C₈×D₆₁	1	1	yes	characteristic
453	C₂²⋊C₄	—	61	1	no	—
454	C₂²⋊C₄	—	61	1	no	—
455	C₂²⋊C₄	—	61	1	no	—
456	C₂²⋊C₄	—	61	1	no	—
457	C₂²⋊C₄	—	61	1	no	—
458	C₂²⋊C₄	—	61	1	no	—
459	C₂²⋊C₄	—	61	1	no	—
460	C₂²⋊C₄	—	61	1	no	—
461	C₂²⋊C₄	C₈×D₆₁	1	1	yes	characteristic
462	C₂²⋊C₄	C₈×D₆₁	1	1	yes	characteristic
463	C₄²	—	61	1	no	—
464	C₄²	C₂×C₄×D₆₁	1	1	yes	characteristic
465	C₁₆	—	2	1	no	—
466	C₁₆	—	2	1	no	—
467	C₁₆	—	2	1	no	—
468	C₁₆	—	2	1	no	—
469	C₁₆	—	122	1	no	—
470	C₁₆	—	122	1	no	—
471	C₁₆	—	122	1	no	—
472	C₁₆	—	122	1	no	—
473	C₂³	—	61	1	no	—
474	C₂³	—	61	1	no	—
475	C₂³	—	61	1	no	—
476	C₂³	—	122	2	no	—
477	C₂³	—	244	1	no	—
478	C₂³	—	244	1	no	—
479	C₂³	C₂×C₈×D₆₁	1	1	yes	characteristic
480	C₂³	C₂×C₈×D₆₁	1	1	yes	characteristic
481	Q₈	—	244	1	no	—
482	D₄	—	4	1	no	—
483	D₄	—	122	2	no	—
484	D₄	—	122	2	no	—
485	D₄	—	244	1	no	—
486	D₄	—	244	1	no	—
487	D₄	—	244	1	no	—
488	D₄	—	244	1	no	—
489	C₂×C₄	—	2	1	no	—
490	C₂×C₄	—	2	1	no	—
491	C₂×C₄	—	2	1	no	—
492	C₂×C₄	—	2	1	no	—
493	C₂×C₄	—	61	1	no	—
494	C₂×C₄	—	61	1	no	—
495	C₂×C₄	—	61	1	no	—
496	C₂×C₄	—	61	1	no	—
497	C₂×C₄	—	61	1	no	—
498	C₂×C₄	—	122	1	no	—
499	C₂×C₄	—	122	1	no	—
500	C₂×C₄	—	122	1	no	—
501	C₂×C₄	—	122	1	no	—
502	C₂×C₄	—	122	1	no	—
503	C₂×C₄	—	122	1	no	—
504	C₂×C₄	—	244	1	no	—
505	C₂×C₄	—	244	1	no	—
506	C₂×C₄	—	244	1	no	—
507	C₂×C₄	C₂×C₈×D₆₁	1	1	yes	characteristic
508	C₂×C₄	C₂×C₈×D₆₁	1	1	yes	characteristic
509	C₂×C₄	C₂×C₈×D₆₁	1	1	yes	characteristic
510	C₂×C₄	C₂×C₈×D₆₁	1	1	yes	characteristic
511	C₂×C₄	C₂²×C₄×D₆₁	1	1	yes	characteristic
512	C₈	—	2	1	no	—
513	C₈	—	2	1	no	—
514	C₈	—	2	1	no	—
515	C₈	—	122	1	no	—
516	C₈	—	122	1	no	—
517	C₈	—	122	1	no	—
518	C₈	—	122	1	no	—
519	C₈	#14519822	1	1	yes	characteristic
520	C₈	#14519823	1	1	yes	characteristic
521	C₂²	—	2	1	no	—
522	C₂²	—	2	1	no	—
523	C₂²	—	2	1	no	—
524	C₂²	—	2	1	no	—
525	C₂²	—	2	1	no	—
526	C₂²	—	2	1	no	—
527	C₂²	—	61	2	no	—
528	C₂²	—	122	1	no	—
529	C₂²	—	122	1	no	—
530	C₂²	—	122	1	no	—
531	C₂²	—	122	1	no	—
532	C₂²	—	122	1	no	—
533	C₂²	—	122	1	no	—
534	C₂²	—	122	1	no	—
535	C₂²	—	122	1	no	—
536	C₂²	—	244	4	no	—
537	C₂²	C₂²×C₈×D₆₁	1	1	yes	characteristic
538	C₄	—	2	1	no	—
539	C₄	—	2	1	no	—
540	C₄	—	2	1	no	—
541	C₄	—	2	1	no	—
542	C₄	—	122	1	no	—
543	C₄	—	122	1	no	—
544	C₄	—	122	1	no	—
545	C₄	—	122	1	no	—
546	C₄	—	122	1	no	—
547	C₄	#16840234	1	1	yes	characteristic
548	C₄	#16840527	1	1	yes	characteristic
549	C₂	—	4	1	no	—
550	C₂	—	4	1	no	—
551	C₂	—	122	2	no	—
552	C₂	—	244	1	no	—
553	C₂	—	244	1	no	—
554	C₂	#21454840	1	1	yes	characteristic
555	C₂	#504×D₆₁	1	1	yes	characteristic
556	C₂	#21458921	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₈	C₂³×D₆₁
commutator, socle	C₂²×C₆₁	C₂³×C₈
Fitting	C₆₁×#2168	C₂
prime radical	#16840271	C₄
cosocle	C₂×C₈×C₆₁	C₂⁴
hypercenter	#2168	D₆₁
hypocenter	C₆₁	#33490
LCS	G ▷ C₂²×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂×C₈ ◁ #2168

Complements

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

N	H ≅ G/N	type
2. #21447651	C₂	semidirect
3. #21447648	C₂	semidirect
4. #21447647	C₂	semidirect
5. #21447646	C₂	semidirect
6. #21447642	C₂	semidirect
7. #21447638	C₂	semidirect
8. C₁₆×C₂²⋊D₆₁	C₂	semidirect
9. #21447627	C₂	semidirect
10. #21447625	C₂	semidirect
11. #21447432	C₂	semidirect
12. #21447431	C₂	semidirect
13. #21447429	C₂	semidirect
14. C₂²⋊C₁₆×D₆₁	C₂	semidirect
15. C₆₁×#2168	C₂	semidirect
20. C₂×#14519717	C₂²	semidirect
21. C₂×#14519716	C₂²	semidirect
24. C₂×C₁₆×D₆₁	C₂²	semidirect
36. C₄⋊#11758185	C₂²	semidirect
37. #16839580	C₂²	semidirect
38. #16839580	C₂²	semidirect
40. C₂²⋊#11758185	C₂²	semidirect
47. #16839541	C₂²	semidirect
48. #16839541	C₂²	semidirect
49. #16839537	C₂²	semidirect
50. C₄×#11758185	C₂²	semidirect
51. C₁₆×Dic₆₁	C₂²	semidirect
53. C₂²×C₁₆×C₆₁	C₂²	semidirect
55. C₆₁×C₄⋊C₁₆	C₂²	semidirect
57. C₆₁×C₂²⋊C₁₆	C₂²	semidirect
58. C₆₁×#346	C₂²	semidirect
277. #2168	D₆₁	semidirect
304. C₂²×C₁₆	C₂×D₆₁	semidirect
320. C₄⋊C₁₆	C₂×D₆₁	semidirect
332. C₂²⋊C₁₆	C₂×D₆₁	semidirect
334. #346	C₂×D₆₁	semidirect
337. C₆₁	#33490	semidirect

Maximal subgroups

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

subgroup	index
#21454508	2
#21447651	2
#21447648	2
#21447647	2
#21447646	2
#21447642	2
#21447638	2
C₁₆×C₂²⋊D₆₁	2
#21447627	2
#21447625	2
#21447432	2
#21447431	2
#21447429	2
C₂²⋊C₁₆×D₆₁	2
C₆₁×#2168	2
#33490	61