Subgroups — #29833693

Order 15616.

536 conjugacy classes of subgroups.

The subgroup lattice has 494 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈×#11758224	C₂	1	1	yes	maximal, characteristic
2	#21447726	C₂	1	1	yes	maximal, characteristic, complemented
3	#21447725	C₂	1	1	yes	maximal, characteristic, complemented
4	#21447647	C₂	1	1	yes	maximal, characteristic, complemented
5	#21447645	C₂	1	1	yes	maximal, characteristic, complemented
6	#21447642	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₆×C₂²⋊D₆₁	C₂	1	1	yes	maximal, characteristic, complemented
8	#21447636	C₂	1	1	yes	maximal, characteristic, complemented
9	#21447620	C₂	1	1	yes	maximal, characteristic, complemented
10	#21447619	C₂	1	1	yes	maximal, characteristic, complemented
11	#21447615	C₂	1	1	yes	maximal, characteristic, complemented
12	#21447574	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×#16839580	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄⋊C₁₆×D₆₁	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₁×#2168	C₂	1	1	yes	maximal, characteristic, complemented
16	C₄×#11758224	C₄	1	1	yes	characteristic
17	C₂×#14519717	C₂²	1	1	yes	characteristic
18	C₂²×#11758185	C₂²	1	1	yes	characteristic
19	C₂×C₁₆×D₆₁	C₂²	1	1	yes	characteristic
20	C₂×C₁₆×D₆₁	C₂²	1	1	yes	characteristic
21	C₈×Dic₁₂₂	C₂²	1	1	yes	characteristic
22	#16839886	C₄	1	1	yes	characteristic
23	D₄×#92418	C₄	1	1	yes	characteristic
24	C₈×C₂²⋊D₆₁	C₂²	1	1	yes	characteristic
25	C₈×C₂²⋊D₆₁	C₂²	1	1	yes	characteristic
26	#16839825	C₄	1	1	yes	characteristic
27	#16839825	C₄	1	1	yes	characteristic
28	#16839814	C₄	1	1	yes	characteristic
29	#16839812	C₄	1	1	yes	characteristic
30	#16839812	C₄	1	1	yes	characteristic
31	C₂×C₈×Dic₆₁	C₂²	1	1	yes	characteristic
32	C₂×C₈×Dic₆₁	C₂²	1	1	yes	characteristic
33	C₄×C₈×D₆₁	C₂²	1	1	yes	characteristic
34	C₄⋊#11758185	C₂²	1	1	yes	characteristic
35	#16839580	C₂²	1	1	yes	characteristic
36	#16839580	C₂²	1	1	yes	characteristic
37	#16839580	C₂²	1	1	yes	characteristic
38	#16839580	C₂²	1	1	yes	characteristic
39	#16839580	C₂²	1	1	yes	characteristic
40	#16839580	C₂²	1	1	yes	characteristic
41	#16839580	C₂²	1	1	yes	characteristic
42	#16839580	C₂²	1	1	yes	characteristic
43	C₂²⋊#11758185	C₂²	1	1	yes	characteristic
44	C₂²⋊#11758185	C₂²	1	1	yes	characteristic
45	#16839541	C₂²	1	1	yes	characteristic
46	#16839541	C₂²	1	1	yes	characteristic
47	#16839538	C₂²	1	1	yes	characteristic
48	#16839537	C₂²	1	1	yes	characteristic
49	#16839537	C₂²	1	1	yes	characteristic
50	C₁₆×Dic₆₁	C₂²	1	1	yes	characteristic
51	C₁₆×Dic₆₁	C₂²	1	1	yes	characteristic
52	C₂×M₃₂×C₆₁	C₂²	1	1	yes	characteristic
53	C₂²×C₁₆×C₆₁	C₂²	1	1	yes	characteristic
54	C₈×D₄×C₆₁	C₂²	1	1	yes	characteristic
55	C₆₁×C₄⋊C₁₆	C₂²	1	1	yes	characteristic
56	C₆₁×C₂²⋊C₁₆	C₂²	1	1	yes	characteristic
57	C₆₁×C₂²⋊C₁₆	C₂²	1	1	yes	characteristic
58	C₆₁×#346	C₂²	1	1	yes	characteristic
59	C₂×#11758224	C₈	1	1	yes	characteristic
60	C₂²×#92418	C₂×C₄	1	1	yes	characteristic
61	C₂²×#92418	C₂×C₄	1	1	yes	characteristic
62	C₂×C₈×D₆₁	C₂×C₄	1	1	yes	characteristic
63	C₂×C₈×D₆₁	C₂³	1	1	yes	characteristic
64	C₄×Dic₁₂₂	C₂×C₄	1	1	yes	characteristic
65	#14519742	C₈	1	1	yes	characteristic
66	D₄×Dic₆₁	C₈	1	1	yes	characteristic
67	C₄×C₂²⋊D₆₁	C₂×C₄	1	1	yes	characteristic
68	C₄×C₂²⋊D₆₁	C₂×C₄	1	1	yes	characteristic
69	#14519737	C₈	1	1	yes	characteristic
70	#14519737	C₈	1	1	yes	characteristic
71	#14519735	C₈	1	1	yes	characteristic
72	#14519733	C₈	1	1	yes	characteristic
73	#14519733	C₈	1	1	yes	characteristic
74	C₂×C₄×Dic₆₁	C₂×C₄	1	1	yes	characteristic
75	C₂×C₄×Dic₆₁	C₂×C₄	1	1	yes	characteristic
76	C₄²×D₆₁	C₂×C₄	1	1	yes	characteristic
77	#14519717	—	4	1	no	—
78	C₂×#11758185	—	4	1	no	—
79	C₂×#11758185	C₂³	1	1	yes	characteristic
80	C₂×#11758185	C₂³	1	1	yes	characteristic
81	C₂×#11758185	C₂³	1	1	yes	characteristic
82	C₂×#11758185	C₂³	1	1	yes	characteristic
83	C₁₆×D₆₁	—	4	1	no	—
84	C₁₆×D₆₁	—	4	1	no	—
85	C₄⋊#92418	C₂×C₄	1	1	yes	characteristic
86	#14519706	C₂×C₄	1	1	yes	characteristic
87	#14519706	C₂×C₄	1	1	yes	characteristic
88	#14519706	C₂×C₄	1	1	yes	characteristic
89	#14519706	C₂×C₄	1	1	yes	characteristic
90	C₂²⋊#92418	C₂×C₄	1	1	yes	characteristic
91	C₂²⋊#92418	C₂×C₄	1	1	yes	characteristic
92	#14519689	C₂×C₄	1	1	yes	characteristic
93	#14519689	C₂×C₄	1	1	yes	characteristic
94	C₄×#92418	C₂×C₄	1	1	yes	characteristic
95	C₈×Dic₆₁	C₂×C₄	1	1	yes	characteristic
96	C₈×Dic₆₁	C₂×C₄	1	1	yes	characteristic
97	C₈×Dic₆₁	C₂×C₄	1	1	yes	characteristic
98	C₈×Dic₆₁	C₂×C₄	1	1	yes	characteristic
99	C₈×Dic₆₁	C₂×C₄	1	1	yes	characteristic
100	C₈×Dic₆₁	C₂³	1	1	yes	characteristic
101	C₈×Dic₆₁	C₂³	1	1	yes	characteristic
102	C₈×Dic₆₁	C₂³	1	1	yes	characteristic
103	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
104	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
105	C₄×D₄×C₆₁	C₂×C₄	1	1	yes	characteristic
106	M₃₂×C₆₁	—	4	1	no	—
107	C₂×C₁₆×C₆₁	—	4	1	no	—
108	C₂×C₁₆×C₆₁	C₂³	1	1	yes	characteristic
109	C₂×C₁₆×C₆₁	C₂³	1	1	yes	characteristic
110	C₂×C₁₆×C₆₁	C₂³	1	1	yes	characteristic
111	C₂×C₁₆×C₆₁	C₂³	1	1	yes	characteristic
112	C₄⋊C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
113	C₂²⋊C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
114	C₂²⋊C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
115	C₄×C₈×C₆₁	C₂³	1	1	yes	characteristic
116	C₂×D₄×C₆₁	C₂×C₈	1	1	yes	characteristic
117	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
118	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
119	C₂×C₂²⋊D₆₁	C₂×C₈	1	1	yes	characteristic
120	C₂×C₂²⋊D₆₁	C₂×C₈	1	1	yes	characteristic
121	C₂²×Dic₆₁	C₂×C₈	1	1	yes	characteristic
122	C₂²×Dic₆₁	C₂×C₈	1	1	yes	characteristic
123	C₂²×Dic₆₁	C₂×C₈	1	1	yes	characteristic
124	C₂²×Dic₆₁	C₂×C₈	1	1	yes	characteristic
125	#11758224	—	2	4	no	—
126	C₂×C₄×D₆₁	C₂×C₈	1	1	yes	characteristic
127	C₂×C₄×D₆₁	C₂×C₈	1	1	yes	characteristic
128	C₂×C₄×D₆₁	C₂²×C₄	1	1	yes	characteristic
129	C₂×Dic₁₂₂	C₂×C₈	1	1	yes	characteristic
130	C₂×C₈×C₆₁	—	2	1	no	—
131	C₂×C₈×C₆₁	—	2	1	no	—
132	C₂×C₈×C₆₁	—	2	1	no	—
133	C₂×C₈×C₆₁	—	2	1	no	—
134	C₂×C₈×C₆₁	C₂²×C₄	1	1	yes	characteristic
135	C₂×C₈×C₆₁	C₂²×C₄	1	1	yes	characteristic
136	C₂×C₈×C₆₁	C₂²×C₄	1	1	yes	characteristic
137	C₂×C₈×C₆₁	C₂⁴	1	1	yes	characteristic
138	C₄⋊C₄×C₆₁	C₂×C₈	1	1	yes	characteristic
139	C₂²⋊C₄×C₆₁	C₂×C₈	1	1	yes	characteristic
140	C₂²⋊C₄×C₆₁	C₂×C₈	1	1	yes	characteristic
141	C₄²×C₆₁	C₂²×C₄	1	1	yes	characteristic
142	C₂²⋊Dic₆₁	C₂×C₈	1	1	yes	characteristic
143	C₂²⋊Dic₆₁	C₂×C₈	1	1	yes	characteristic
144	#11758198	C₂×C₈	1	1	yes	characteristic
145	#11758198	C₂×C₈	1	1	yes	characteristic
146	C₄⋊Dic₆₁	C₂×C₈	1	1	yes	characteristic
147	#11758196	C₂×C₈	1	1	yes	characteristic
148	#11758196	C₂×C₈	1	1	yes	characteristic
149	#11758196	C₂×C₈	1	1	yes	characteristic
150	#11758196	C₂×C₈	1	1	yes	characteristic
151	C₄×Dic₆₁	C₂×C₈	1	1	yes	characteristic
152	C₄×Dic₆₁	C₂×C₈	1	1	yes	characteristic
153	C₄×Dic₆₁	C₂×C₈	1	1	yes	characteristic
154	C₄×Dic₆₁	C₂×C₈	1	1	yes	characteristic
155	C₄×Dic₆₁	C₂×C₈	1	1	yes	characteristic
156	C₄×Dic₆₁	C₂×C₈	1	1	yes	characteristic
157	C₄×Dic₆₁	C₂²×C₄	1	1	yes	characteristic
158	C₄×Dic₆₁	C₂²×C₄	1	1	yes	characteristic
159	C₄×Dic₆₁	C₂²×C₄	1	1	yes	characteristic
160	C₂×#92418	—	4	1	no	—
161	C₂×#92418	—	4	1	no	—
162	C₂×#92418	C₂²×C₄	1	1	yes	characteristic
163	C₂×#92418	C₂²×C₄	1	1	yes	characteristic
164	C₂×#92418	C₂²×C₄	1	1	yes	characteristic
165	C₂×#92418	C₂²×C₄	1	1	yes	characteristic
166	C₈×D₆₁	—	2	1	no	—
167	C₈×D₆₁	—	2	1	no	—
168	C₈×D₆₁	—	4	1	no	—
169	C₁₆×C₆₁	—	2	1	no	—
170	C₁₆×C₆₁	—	2	1	no	—
171	C₁₆×C₆₁	—	2	1	no	—
172	C₁₆×C₆₁	—	2	1	no	—
173	#11758185	—	2	1	no	—
174	#11758185	—	2	1	no	—
175	#11758185	—	2	1	no	—
176	#11758185	—	2	1	no	—
177	C₂³×C₆₁	C₂²×C₈	1	1	yes	characteristic
178	C₂³×C₆₁	C₂²×C₈	1	1	yes	characteristic
179	C₂²×D₆₁	C₂²×C₈	1	1	yes	characteristic
180	D₄×C₆₁	—	2	2	no	—
181	C₂×C₄×C₆₁	—	2	1	no	—
182	C₂×C₄×C₆₁	—	2	1	no	—
183	C₂×C₄×C₆₁	—	2	1	no	—
184	C₂×C₄×C₆₁	—	2	1	no	—
185	C₂×C₄×C₆₁	C₂²×C₈	1	1	yes	characteristic
186	C₂×C₄×C₆₁	C₂²×C₈	1	1	yes	characteristic
187	C₂×C₄×C₆₁	C₂²×C₈	1	1	yes	characteristic
188	C₂×C₄×C₆₁	C₂²×C₈	1	1	yes	characteristic
189	C₂×C₄×C₆₁	C₂³×C₄	1	1	yes	characteristic
190	C₂²⋊D₆₁	—	2	2	no	—
191	C₂²⋊D₆₁	M₃₂	1	4	yes	complemented
192	C₂×Dic₆₁	—	2	2	no	—
193	C₂×Dic₆₁	—	2	2	no	—
194	C₂×Dic₆₁	—	2	2	no	—
195	C₂×Dic₆₁	—	2	2	no	—
196	C₂×Dic₆₁	C₂²×C₈	1	1	yes	characteristic
197	C₂×Dic₆₁	C₂²×C₈	1	1	yes	characteristic
198	C₂×Dic₆₁	C₂²×C₈	1	1	yes	characteristic
199	C₂×Dic₆₁	C₂²×C₈	1	1	yes	characteristic
200	C₂×Dic₆₁	C₂²×C₈	1	1	yes	characteristic
201	C₂×Dic₆₁	C₂²×C₈	1	1	yes	characteristic
202	C₂×Dic₆₁	C₂²×C₈	1	1	yes	characteristic
203	C₄×D₆₁	—	2	2	no	—
204	C₄×D₆₁	—	2	1	no	—
205	C₄×D₆₁	—	2	1	no	—
206	C₄×D₆₁	—	2	2	no	—
207	Dic₁₂₂	—	2	2	no	—
208	C₈×C₆₁	—	2	1	no	—
209	C₈×C₆₁	—	2	1	no	—
210	C₈×C₆₁	—	2	1	no	—
211	C₈×C₆₁	H(5,𝔽₂)	1	1	yes	characteristic
212	C₈×C₆₁	2₋¹⁺⁴	1	1	yes	characteristic
213	#92418	—	2	1	no	—
214	#92418	—	2	1	no	—
215	#92418	—	2	1	no	—
216	#92418	—	2	1	no	—
217	#33504	—	61	1	no	maximal, Sylow
218	C₂²×C₆₁	—	2	1	no	—
219	C₂²×C₆₁	—	2	1	no	—
220	C₂²×C₆₁	—	2	1	no	—
221	C₂²×C₆₁	—	2	1	no	—
222	C₂²×C₆₁	—	2	1	no	—
223	C₂²×C₆₁	C₂×M₃₂	1	2	yes	—
224	C₂²×C₆₁	C₂³×C₈	1	1	yes	characteristic
225	C₂×D₆₁	—	2	1	no	—
226	C₂×D₆₁	—	2	1	no	—
227	C₂×D₆₁	C₂×M₃₂	1	2	yes	—
228	C₄×C₆₁	—	2	1	no	—
229	C₄×C₆₁	—	2	1	no	—
230	C₄×C₆₁	—	2	1	no	—
231	C₄×C₆₁	—	2	1	no	—
232	C₄×C₆₁	#520	1	1	yes	characteristic
233	C₄×C₆₁	#568	1	1	yes	characteristic
234	Dic₆₁	—	2	1	no	—
235	Dic₆₁	—	2	1	no	—
236	Dic₆₁	—	2	1	no	—
237	Dic₆₁	—	2	1	no	—
238	Dic₆₁	—	2	1	no	—
239	Dic₆₁	C₂×M₃₂	1	2	yes	—
240	Dic₆₁	#504	1	2	yes	—
241	C₈×#41	—	61	1	no	—
242	#2183	—	61	1	no	—
243	#2183	—	61	1	no	—
244	#2168	—	61	1	no	—
245	#2168	—	61	1	no	—
246	#2168	—	61	1	no	—
247	#2168	D₆₁	1	1	yes	characteristic, complemented
248	D₄×C₁₆	—	61	1	no	—
249	D₄×C₁₆	—	61	1	no	—
250	#2163	—	61	1	no	—
251	#2163	—	61	1	no	—
252	#2162	—	61	1	no	—
253	#2150	—	61	1	no	—
254	C₂×C₄⋊C₁₆	—	61	1	no	—
255	C₂×C₄⋊C₁₆	—	61	1	no	—
256	C₂×C₆₁	—	2	2	no	—
257	C₂×C₆₁	—	4	1	no	—
258	C₂×C₆₁	#2988	1	1	yes	characteristic
259	C₂×C₆₁	C₂²×M₃₂	1	1	yes	characteristic
260	C₂×C₆₁	C₂×#504	1	1	yes	characteristic
261	D₆₁	—	2	2	no	—
262	C₄×#41	—	61	1	no	—
263	C₂×M₃₂	—	61	1	no	—
264	C₂×M₃₂	C₂×D₆₁	1	1	yes	characteristic
265	C₂²×C₁₆	—	61	1	no	—
266	C₂²×C₁₆	—	61	1	no	—
267	C₂²×C₁₆	—	61	1	no	—
268	C₂²×C₁₆	C₂×D₆₁	1	1	yes	characteristic
269	C₈×Q₈	—	61	1	no	—
270	C₈×Q₈	—	61	1	no	—
271	C₈×D₄	—	61	1	no	—
272	C₈×D₄	—	61	1	no	—
273	C₈×D₄	—	61	1	no	—
274	C₈×D₄	—	61	1	no	—
275	C₈×D₄	—	61	1	no	—
276	C₈×D₄	C₂×D₆₁	1	1	yes	characteristic
277	#431	—	61	1	no	—
278	#431	—	61	1	no	—
279	#431	—	61	1	no	—
280	C₂×C₄×C₈	—	61	1	no	—
281	C₂×C₄×C₈	—	61	1	no	—
282	C₂×C₄×C₈	—	61	1	no	—
283	C₄⋊C₁₆	—	61	1	no	—
284	C₄⋊C₁₆	—	61	1	no	—
285	C₄⋊C₁₆	—	61	1	no	—
286	C₄⋊C₁₆	—	61	1	no	—
287	C₄⋊C₁₆	—	61	1	no	—
288	C₄⋊C₁₆	—	61	1	no	—
289	C₄⋊C₁₆	—	61	1	no	—
290	C₄⋊C₁₆	—	61	1	no	—
291	C₄⋊C₁₆	—	61	1	no	—
292	C₄⋊C₁₆	C₂×D₆₁	1	1	yes	characteristic
293	C₂²⋊C₁₆	—	61	1	no	—
294	C₂²⋊C₁₆	—	61	1	no	—
295	C₂²⋊C₁₆	—	61	1	no	—
296	C₂²⋊C₁₆	—	61	1	no	—
297	C₂²⋊C₁₆	C₂×D₆₁	1	1	yes	characteristic
298	C₂²⋊C₁₆	C₂×D₆₁	1	1	yes	characteristic
299	#346	—	61	1	no	—
300	#346	—	61	1	no	—
301	#346	—	61	1	no	—
302	#346	C₂×D₆₁	1	1	yes	characteristic
303	C₄×C₁₆	—	61	1	no	—
304	C₄×C₁₆	—	61	1	no	—
305	C₆₁	#33504	1	1	yes	characteristic, complemented, Sylow
306	C₂×#41	—	61	1	no	—
307	C₂²×C₈	—	61	1	no	—
308	C₂²×C₈	—	61	1	no	—
309	C₂²×C₈	—	61	1	no	—
310	C₂²×C₈	—	61	1	no	—
311	C₂²×C₈	C₂²×D₆₁	1	1	yes	characteristic
312	C₂²×C₈	C₂²×D₆₁	1	1	yes	characteristic
313	C₄×Q₈	—	61	1	no	—
314	C₄×Q₈	—	61	1	no	—
315	C₄×D₄	—	61	1	no	—
316	C₄×D₄	—	61	1	no	—
317	C₄×D₄	—	61	1	no	—
318	C₄×D₄	—	61	1	no	—
319	C₄×D₄	—	61	1	no	—
320	C₄×D₄	C₄×D₆₁	1	1	yes	characteristic
321	#117	—	61	1	no	—
322	#117	—	61	1	no	—
323	#117	—	61	1	no	—
324	C₂×C₄²	—	61	1	no	—
325	C₂×C₄²	—	61	1	no	—
326	C₂×C₄²	—	61	1	no	—
327	M₃₂	—	4	1	no	—
328	M₃₂	—	244	1	no	—
329	C₂×C₁₆	—	4	1	no	—
330	C₂×C₁₆	—	61	1	no	—
331	C₂×C₁₆	—	61	1	no	—
332	C₂×C₁₆	—	61	1	no	—
333	C₂×C₁₆	—	61	1	no	—
334	C₂×C₁₆	—	244	1	no	—
335	C₂×C₁₆	—	244	1	no	—
336	C₂×C₁₆	—	244	1	no	—
337	C₂×C₁₆	C₂²×D₆₁	1	1	yes	characteristic
338	C₂×C₁₆	C₂²×D₆₁	1	1	yes	characteristic
339	C₂×C₁₆	C₂²×D₆₁	1	1	yes	characteristic
340	C₂×C₁₆	C₂²×D₆₁	1	1	yes	characteristic
341	C₄⋊C₈	—	61	1	no	—
342	C₄⋊C₈	—	61	1	no	—
343	C₄⋊C₈	—	61	1	no	—
344	C₄⋊C₈	—	61	1	no	—
345	C₄⋊C₈	—	61	1	no	—
346	C₄⋊C₈	C₄×D₆₁	1	1	yes	characteristic
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	C₄×D₆₁	1	1	yes	characteristic
352	C₂²⋊C₈	C₄×D₆₁	1	1	yes	characteristic
353	C₄×C₈	—	61	1	no	—
354	C₄×C₈	—	61	1	no	—
355	C₄×C₈	—	61	1	no	—
356	C₄×C₈	—	61	1	no	—
357	C₄×C₈	—	61	1	no	—
358	C₄×C₈	—	61	1	no	—
359	C₄×C₈	—	61	1	no	—
360	C₄×C₈	—	61	1	no	—
361	C₄×C₈	—	61	1	no	—
362	C₄×C₈	C₂²×D₆₁	1	1	yes	characteristic
363	#41	—	122	4	no	—
364	C₂×Q₈	—	61	1	no	—
365	C₂×D₄	—	61	1	no	—
366	C₂×D₄	—	61	1	no	—
367	C₂×D₄	C₈×D₆₁	1	1	yes	characteristic
368	C₂²×C₄	—	61	1	no	—
369	C₂²×C₄	—	61	1	no	—
370	C₂²×C₄	—	61	1	no	—
371	C₂²×C₄	—	61	1	no	—
372	C₂²×C₄	—	61	1	no	—
373	C₂²×C₄	—	61	1	no	—
374	C₂²×C₄	—	61	1	no	—
375	C₂²×C₄	C₂×C₄×D₆₁	1	1	yes	characteristic
376	C₂²×C₄	C₂×C₄×D₆₁	1	1	yes	characteristic
377	C₂×C₈	—	2	1	no	—
378	C₂×C₈	—	2	1	no	—
379	C₂×C₈	—	2	1	no	—
380	C₂×C₈	—	2	1	no	—
381	C₂×C₈	—	61	1	no	—
382	C₂×C₈	—	61	1	no	—
383	C₂×C₈	—	61	1	no	—
384	C₂×C₈	—	61	1	no	—
385	C₂×C₈	—	122	1	no	—
386	C₂×C₈	—	122	1	no	—
387	C₂×C₈	—	244	1	no	—
388	C₂×C₈	—	244	1	no	—
389	C₂×C₈	—	244	1	no	—
390	C₂×C₈	C₂×C₄×D₆₁	1	1	yes	characteristic
391	C₂×C₈	C₂×C₄×D₆₁	1	1	yes	characteristic
392	C₂×C₈	C₂×C₄×D₆₁	1	1	yes	characteristic
393	C₂×C₈	C₂³×D₆₁	1	1	yes	characteristic
394	C₄⋊C₄	—	61	1	no	—
395	C₄⋊C₄	—	61	1	no	—
396	C₄⋊C₄	—	61	1	no	—
397	C₄⋊C₄	—	61	1	no	—
398	C₄⋊C₄	—	61	1	no	—
399	C₄⋊C₄	C₈×D₆₁	1	1	yes	characteristic
400	C₂²⋊C₄	—	61	1	no	—
401	C₂²⋊C₄	—	61	1	no	—
402	C₂²⋊C₄	—	61	1	no	—
403	C₂²⋊C₄	—	61	1	no	—
404	C₂²⋊C₄	C₈×D₆₁	1	1	yes	characteristic
405	C₂²⋊C₄	C₈×D₆₁	1	1	yes	characteristic
406	C₄²	—	61	1	no	—
407	C₄²	—	61	1	no	—
408	C₄²	—	61	1	no	—
409	C₄²	—	61	1	no	—
410	C₄²	—	61	1	no	—
411	C₄²	—	61	1	no	—
412	C₄²	—	61	1	no	—
413	C₄²	—	61	1	no	—
414	C₄²	—	61	1	no	—
415	C₄²	C₂×C₄×D₆₁	1	1	yes	characteristic
416	C₁₆	—	2	1	no	—
417	C₁₆	—	2	1	no	—
418	C₁₆	—	2	1	no	—
419	C₁₆	—	2	1	no	—
420	C₁₆	—	122	1	no	—
421	C₁₆	—	122	1	no	—
422	C₁₆	—	122	1	no	—
423	C₁₆	—	122	1	no	—
424	C₂³	—	61	1	no	—
425	C₂³	C₂×C₈×D₆₁	1	1	yes	characteristic
426	C₂³	C₂×C₈×D₆₁	1	1	yes	characteristic
427	Q₈	—	122	2	no	—
428	D₄	—	2	2	no	—
429	D₄	—	61	4	no	—
430	D₄	—	122	2	no	—
431	C₂×C₄	—	2	1	no	—
432	C₂×C₄	—	2	1	no	—
433	C₂×C₄	—	2	1	no	—
434	C₂×C₄	—	2	1	no	—
435	C₂×C₄	—	61	1	no	—
436	C₂×C₄	—	61	1	no	—
437	C₂×C₄	—	61	1	no	—
438	C₂×C₄	—	61	1	no	—
439	C₂×C₄	—	61	1	no	—
440	C₂×C₄	—	61	1	no	—
441	C₂×C₄	—	61	1	no	—
442	C₂×C₄	—	122	2	no	—
443	C₂×C₄	—	122	2	no	—
444	C₂×C₄	—	122	2	no	—
445	C₂×C₄	—	122	2	no	—
446	C₂×C₄	—	122	2	no	—
447	C₂×C₄	—	122	2	no	—
448	C₂×C₄	—	122	1	no	—
449	C₂×C₄	—	122	1	no	—
450	C₂×C₄	C₂×C₈×D₆₁	1	1	yes	characteristic
451	C₂×C₄	C₂×C₈×D₆₁	1	1	yes	characteristic
452	C₂×C₄	C₂×C₈×D₆₁	1	1	yes	characteristic
453	C₂×C₄	C₂×C₈×D₆₁	1	1	yes	characteristic
454	C₂×C₄	C₂²×C₄×D₆₁	1	1	yes	characteristic
455	C₈	—	2	1	no	—
456	C₈	—	2	1	no	—
457	C₈	—	2	1	no	—
458	C₈	—	122	1	no	—
459	C₈	—	122	1	no	—
460	C₈	—	122	1	no	—
461	C₈	—	122	1	no	—
462	C₈	#14519822	1	1	yes	characteristic
463	C₈	#14519824	1	1	yes	characteristic
464	C₂²	—	2	1	no	—
465	C₂²	—	2	1	no	—
466	C₂²	—	2	1	no	—
467	C₂²	—	2	1	no	—
468	C₂²	—	2	1	no	—
469	C₂²	—	61	2	no	—
470	C₂²	—	122	1	no	—
471	C₂²	—	122	1	no	—
472	C₂²	M₃₂×D₆₁	1	2	yes	—
473	C₂²	C₂²×C₈×D₆₁	1	1	yes	characteristic
474	C₄	—	2	1	no	—
475	C₄	—	2	1	no	—
476	C₄	—	2	1	no	—
477	C₄	—	2	1	no	—
478	C₄	—	61	2	no	—
479	C₄	—	61	2	no	—
480	C₄	—	122	1	no	—
481	C₄	—	122	1	no	—
482	C₄	—	122	1	no	—
483	C₄	—	122	1	no	—
484	C₄	—	122	1	no	—
485	C₄	#16840241	1	1	yes	characteristic
486	C₄	#16840527	1	1	yes	characteristic
487	C₂	—	2	2	no	—
488	C₂	—	4	1	no	—
489	C₂	—	122	2	no	—
490	C₂	#21454926	1	1	yes	characteristic
491	C₂	C₂×M₃₂×D₆₁	1	1	yes	characteristic
492	C₂	#504×D₆₁	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	C₂×#11758224	C₈
cosocle	C₂×C₈×C₆₁	C₂⁴
hypercenter	#2168	D₆₁
hypocenter	C₆₁	#33504
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. #21447726	C₂	semidirect
3. #21447725	C₂	semidirect
4. #21447647	C₂	semidirect
5. #21447645	C₂	semidirect
6. #21447642	C₂	semidirect
7. C₁₆×C₂²⋊D₆₁	C₂	semidirect
8. #21447636	C₂	semidirect
9. #21447620	C₂	semidirect
10. #21447619	C₂	semidirect
11. #21447615	C₂	semidirect
12. #21447574	C₂	semidirect
13. C₂×#16839580	C₂	semidirect
14. C₄⋊C₁₆×D₆₁	C₂	semidirect
15. C₆₁×#2168	C₂	semidirect
191. C₂²⋊D₆₁	M₃₂	semidirect
247. #2168	D₆₁	semidirect
305. C₆₁	#33504	semidirect

Maximal subgroups

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

subgroup	index
C₈×#11758224	2
#21447726	2
#21447725	2
#21447647	2
#21447645	2
#21447642	2
C₁₆×C₂²⋊D₆₁	2
#21447636	2
#21447620	2
#21447619	2
#21447615	2
#21447574	2
C₂×#16839580	2
C₄⋊C₁₆×D₆₁	2
C₆₁×#2168	2
#33504	61