Subgroups — D₆₁⋊#2155 #30624116

Order 15616.

658 conjugacy classes of subgroups.

The subgroup lattice has 434 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₆₁⋊#108	C₂	1	1	yes	maximal, characteristic
2	C₂×#16840772	C₂	1	1	yes	maximal, characteristic
3	#21462167	C₂	1	4	yes	maximal, complemented
4	#21462166	C₂	1	4	yes	maximal, complemented
5	D₆₁⋊#365	C₂	1	4	yes	maximal, complemented
6	C₂×M₃₂×D₆₁	C₂	1	1	yes	maximal, characteristic
7	C₂×D₆₁⋊M₁₆	—	2	1	no	—
8	C₂×#14519856	—	2	1	no	—
9	C₂×#14519848	—	2	1	no	—
10	D₆₁⋊#108	—	2	1	no	—
11	D₆₁⋊#108	—	2	1	no	—
12	D₆₁⋊#108	C₂²	1	2	yes	—
13	D₆₁⋊#108	C₂²	1	2	yes	—
14	C₂×#14519847	C₂²	1	2	yes	—
15	#16840772	—	2	1	no	—
16	#16840772	—	2	1	no	—
17	#16840772	C₂²	1	2	yes	—
18	#16840772	C₂²	1	2	yes	—
19	C₂×#14519846	—	2	1	no	—
20	C₂×#14519845	C₂²	1	2	yes	—
21	#16840687	C₂²	1	8	yes	complemented
22	#16840686	C₂²	1	8	yes	complemented
23	C₂²×C₈×D₆₁	C₂²	1	1	yes	characteristic
24	C₂×#14519717	C₄	1	1	yes	characteristic, complemented
25	C₂×#14519716	C₂²	1	2	yes	—
26	M₃₂×D₆₁	C₄	1	2	yes	complemented
27	M₃₂×D₆₁	C₄	1	2	yes	complemented
28	M₃₂×D₆₁	C₂²	1	2	yes	—
29	M₃₂×D₆₁	C₂²	1	2	yes	—
30	C₂×C₁₆×D₆₁	C₄	1	2	yes	complemented
31	C₂×M₃₂×C₆₁	C₄	1	1	yes	characteristic, complemented
32	C₂×#11758213	—	2	2	no	—
33	D₆₁⋊M₁₆	—	2	2	no	—
34	D₆₁⋊M₁₆	—	2	2	no	—
35	D₆₁⋊M₁₆	—	4	1	no	—
36	D₆₁⋊M₁₆	—	4	1	no	—
37	C₂×#11758217	—	4	1	no	—
38	C₂×D₆₁⋊C₈	—	4	1	no	—
39	#14519856	—	2	2	no	—
40	#14519856	—	2	2	no	—
41	#14519856	—	4	1	no	—
42	#14519856	—	4	1	no	—
43	C₂×C₄⋊#6923	—	2	2	no	—
44	C₂×C₂²⋊#6923	—	4	1	no	—
45	C₂×C₄×#6923	—	4	1	no	—
46	#14519848	—	2	2	no	—
47	#14519848	—	2	2	no	—
48	#14519847	—	2	2	no	—
49	#14519847	C₂³	1	4	yes	—
50	#14519846	—	2	2	no	—
51	#14519846	—	2	2	no	—
52	#14519845	—	2	2	no	—
53	#14519845	C₂³	1	4	yes	—
54	C₂²×C₄×D₆₁	D₄	1	1	yes	characteristic
55	C₂²×#92418	Q₈	1	1	yes	characteristic
56	C₂×C₈×D₆₁	C₂×C₄	1	1	yes	characteristic
57	C₂×C₈×D₆₁	C₂×C₄	1	1	yes	characteristic
58	C₂×C₈×D₆₁	C₂×C₄	1	1	yes	characteristic
59	C₂×C₈×D₆₁	D₄	1	1	yes	characteristic
60	C₂×C₈×D₆₁	D₄	1	1	yes	characteristic
61	C₂×C₈×D₆₁	D₄	1	1	yes	characteristic
62	C₂×C₈×D₆₁	Q₈	1	1	yes	characteristic
63	C₂×C₈×D₆₁	Q₈	1	1	yes	characteristic
64	C₂×C₈×D₆₁	Q₈	1	1	yes	characteristic
65	C₂×C₈×D₆₁	C₂³	1	1	yes	characteristic
66	C₂×C₈×D₆₁	C₂³	1	1	yes	characteristic
67	C₂×C₈×D₆₁	C₂³	1	1	yes	characteristic
68	#14519717	C₂×C₄	1	2	yes	—
69	#14519717	C₂×C₄	1	2	yes	complemented
70	#14519716	C₂×C₄	1	4	yes	complemented
71	#14519716	C₂³	1	4	yes	—
72	C₂×#11758185	C₂×C₄	1	2	yes	complemented
73	C₁₆×D₆₁	C₂×C₄	1	4	yes	—
74	C₁₆×D₆₁	C₂×C₄	1	4	yes	complemented
75	C₂²×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
76	M₃₂×C₆₁	C₂×C₄	1	2	yes	—
77	M₃₂×C₆₁	C₂×C₄	1	2	yes	complemented
78	C₂×C₁₆×C₆₁	C₂×C₄	1	2	yes	complemented
79	C₂³×D₆₁	SD₁₆	1	1	yes	characteristic
80	C₂²×#6923	—	4	2	no	—
81	C₂²×C₄×C₆₁	C₄⋊C₄	1	1	yes	characteristic
82	C₂²×Dic₆₁	SD₁₆	1	1	yes	characteristic
83	C₂×C₄×D₆₁	C₄⋊C₄	1	1	yes	characteristic
84	C₂×C₄×D₆₁	C₄⋊C₄	1	1	yes	characteristic
85	C₂×C₄×D₆₁	C₄⋊C₄	1	1	yes	characteristic
86	C₂×C₄×D₆₁	SD₁₆	1	1	yes	characteristic
87	C₂×C₄×D₆₁	SD₁₆	1	1	yes	characteristic
88	C₂×C₄×D₆₁	SD₁₆	1	1	yes	characteristic
89	C₂×C₄×D₆₁	SD₁₆	1	1	yes	characteristic
90	C₂×C₄×D₆₁	SD₁₆	1	1	yes	characteristic
91	C₂×C₄×D₆₁	SD₁₆	1	1	yes	characteristic
92	C₂×C₄×D₆₁	C₂×D₄	1	1	yes	characteristic
93	C₂×C₄×D₆₁	C₂×D₄	1	1	yes	characteristic
94	C₂×C₄×D₆₁	C₂×D₄	1	1	yes	characteristic
95	C₂²⋊#6923	—	4	2	no	—
96	C₂²⋊#6923	—	4	2	no	—
97	#11758217	—	4	2	no	—
98	#11758217	—	4	2	no	—
99	C₂×#92420	—	4	2	no	—
100	C₄⋊#6923	—	2	4	no	—
101	C₄⋊#6923	—	4	2	no	—
102	C₄×#6923	—	4	2	no	—
103	C₄×#6923	—	4	2	no	—
104	#11758213	—	2	4	no	—
105	#11758213	—	4	2	no	—
106	D₆₁⋊C₈	—	4	2	no	—
107	D₆₁⋊C₈	—	4	2	no	—
108	C₂×C₈×C₆₁	C₄⋊C₄	1	1	yes	characteristic
109	C₂×C₈×C₆₁	C₄⋊C₄	1	1	yes	characteristic
110	C₂×C₈×C₆₁	C₄⋊C₄	1	1	yes	characteristic
111	C₂×C₈×C₆₁	C₂²×C₄	1	1	yes	characteristic
112	C₂×C₈×C₆₁	C₂²×C₄	1	1	yes	characteristic
113	C₂×C₈×C₆₁	C₂²×C₄	1	1	yes	characteristic
114	C₂×#92418	C₄⋊C₄	1	1	yes	characteristic
115	C₂×#92418	C₄⋊C₄	1	1	yes	characteristic
116	C₂×#92418	C₄⋊C₄	1	1	yes	characteristic
117	C₂×#92418	C₂×Q₈	1	1	yes	characteristic
118	C₂×#92418	C₂×Q₈	1	1	yes	characteristic
119	C₂×#92418	C₂×Q₈	1	1	yes	characteristic
120	C₈×D₆₁	C₄⋊C₄	1	1	yes	characteristic
121	C₈×D₆₁	C₄⋊C₄	1	1	yes	characteristic
122	C₈×D₆₁	C₄⋊C₄	1	1	yes	characteristic
123	C₈×D₆₁	C₄⋊C₄	1	1	yes	characteristic
124	C₈×D₆₁	C₄⋊C₄	1	1	yes	characteristic
125	C₈×D₆₁	C₄⋊C₄	1	1	yes	characteristic
126	C₈×D₆₁	C₂²×C₄	1	1	yes	characteristic
127	C₈×D₆₁	C₂²×C₄	1	1	yes	characteristic
128	C₈×D₆₁	C₂²×C₄	1	1	yes	characteristic
129	C₈×D₆₁	C₂×D₄	1	1	yes	characteristic
130	C₈×D₆₁	C₂×D₄	1	1	yes	characteristic
131	C₈×D₆₁	C₂×D₄	1	1	yes	characteristic
132	C₈×D₆₁	C₂×Q₈	1	1	yes	characteristic
133	C₈×D₆₁	C₂×Q₈	1	1	yes	characteristic
134	C₈×D₆₁	C₂×Q₈	1	1	yes	characteristic
135	C₈×D₆₁	C₂⁴	1	1	yes	characteristic
136	C₁₆×C₆₁	C₂²×C₄	1	4	yes	—
137	#11758185	C₂²×C₄	1	4	yes	—
138	C₂³×C₆₁	#106	1	1	yes	characteristic
139	C₂²×D₆₁	—	4	2	no	—
140	C₂²×D₆₁	#106	1	1	yes	characteristic
141	C₂²×D₆₁	#106	1	1	yes	characteristic
142	C₂²×D₆₁	#106	1	1	yes	characteristic
143	C₂²×D₆₁	C₂×SD₁₆	1	1	yes	characteristic
144	C₂²×D₆₁	C₂×SD₁₆	1	1	yes	characteristic
145	C₂²×D₆₁	C₂×SD₁₆	1	1	yes	characteristic
146	C₂×#6923	—	4	4	no	—
147	C₂×#6923	—	8	4	no	—
148	C₂×C₄×C₆₁	#106	1	1	yes	characteristic
149	C₂×C₄×C₆₁	#106	1	1	yes	characteristic
150	C₂×C₄×C₆₁	#106	1	1	yes	characteristic
151	C₂×C₄×C₆₁	C₂×C₄⋊C₄	1	1	yes	characteristic
152	C₂×C₄×C₆₁	C₂×C₄⋊C₄	1	1	yes	characteristic
153	C₂×C₄×C₆₁	C₂×C₄⋊C₄	1	1	yes	characteristic
154	C₂×Dic₆₁	#106	1	1	yes	characteristic
155	C₂×Dic₆₁	#106	1	1	yes	characteristic
156	C₂×Dic₆₁	#106	1	1	yes	characteristic
157	C₂×Dic₆₁	C₂×SD₁₆	1	1	yes	characteristic
158	C₂×Dic₆₁	C₂×SD₁₆	1	1	yes	characteristic
159	C₂×Dic₆₁	C₂×SD₁₆	1	1	yes	characteristic
160	C₄×D₆₁	#106	1	1	yes	characteristic
161	C₄×D₆₁	#106	1	1	yes	characteristic
162	C₄×D₆₁	#106	1	1	yes	characteristic
163	C₄×D₆₁	#106	1	1	yes	characteristic
164	C₄×D₆₁	#106	1	1	yes	characteristic
165	C₄×D₆₁	#106	1	1	yes	characteristic
166	C₄×D₆₁	C₂×C₄⋊C₄	1	1	yes	characteristic
167	C₄×D₆₁	C₂×C₄⋊C₄	1	1	yes	characteristic
168	C₄×D₆₁	C₂×C₄⋊C₄	1	1	yes	characteristic
169	C₄×D₆₁	C₂×SD₁₆	1	1	yes	characteristic
170	C₄×D₆₁	C₂×SD₁₆	1	1	yes	characteristic
171	C₄×D₆₁	C₂×SD₁₆	1	1	yes	characteristic
172	C₄×D₆₁	C₂×SD₁₆	1	1	yes	characteristic
173	C₄×D₆₁	C₂×SD₁₆	1	1	yes	characteristic
174	C₄×D₆₁	C₂×SD₁₆	1	1	yes	characteristic
175	C₄×D₆₁	C₂²×D₄	1	1	yes	characteristic
176	#92420	—	4	4	no	—
177	C₈×C₆₁	C₂×C₄⋊C₄	1	1	yes	characteristic
178	C₈×C₆₁	C₂×C₄⋊C₄	1	1	yes	characteristic
179	C₈×C₆₁	C₂×C₄⋊C₄	1	1	yes	characteristic
180	C₈×C₆₁	C₂³×C₄	1	1	yes	characteristic
181	#92418	C₂×C₄⋊C₄	1	1	yes	characteristic
182	#92418	C₂×C₄⋊C₄	1	1	yes	characteristic
183	#92418	C₂×C₄⋊C₄	1	1	yes	characteristic
184	#92418	C₂²×Q₈	1	1	yes	characteristic
185	C₂×#2155	—	61	1	no	maximal, Sylow
186	C₂²×C₆₁	—	4	1	no	—
187	C₂²×C₆₁	C₂×#106	1	1	yes	characteristic
188	C₂²×C₆₁	C₂×#106	1	1	yes	characteristic
189	C₂²×C₆₁	C₂×#106	1	1	yes	characteristic
190	C₂×D₆₁	—	2	2	no	—
191	C₂×D₆₁	—	2	2	no	—
192	C₂×D₆₁	—	2	2	no	—
193	C₂×D₆₁	—	4	1	no	—
194	C₂×D₆₁	—	4	1	no	—
195	C₂×D₆₁	—	4	1	no	—
196	C₂×D₆₁	C₂×#106	1	1	yes	characteristic
197	C₂×D₆₁	C₂×#106	1	1	yes	characteristic
198	C₂×D₆₁	C₂×#106	1	1	yes	characteristic
199	C₂×D₆₁	C₂²×SD₁₆	1	1	yes	characteristic
200	#6923	—	8	4	no	—
201	C₄×C₆₁	C₂×#106	1	1	yes	characteristic
202	C₄×C₆₁	C₂×#106	1	1	yes	characteristic
203	C₄×C₆₁	C₂×#106	1	1	yes	characteristic
204	C₄×C₆₁	C₂²×C₄⋊C₄	1	1	yes	characteristic
205	Dic₆₁	C₂×#106	1	1	yes	characteristic
206	Dic₆₁	C₂×#106	1	1	yes	characteristic
207	Dic₆₁	C₂×#106	1	1	yes	characteristic
208	Dic₆₁	C₂²×SD₁₆	1	1	yes	characteristic
209	C₂²×M₃₂	—	61	1	no	—
210	C₂²×#108	—	61	1	no	—
211	C₂×#427	—	61	1	no	—
212	#2155	—	61	4	no	—
213	#2155	—	61	4	no	—
214	C₂×#365	—	61	4	no	—
215	C₂×C₆₁	—	2	1	no	—
216	C₂×C₆₁	—	2	1	no	—
217	C₂×C₆₁	—	2	1	no	—
218	C₂×C₆₁	C₂²×#106	1	1	yes	characteristic
219	D₆₁	—	2	1	no	—
220	D₆₁	—	2	1	no	—
221	D₆₁	—	2	1	no	—
222	D₆₁	#2155	1	2	yes	complemented
223	C₂²×M₁₆	—	122	1	no	—
224	C₂³×C₈	—	61	1	no	—
225	C₂×#117	—	122	1	no	—
226	C₂×M₃₂	—	61	1	no	—
227	C₂×M₃₂	—	61	2	no	—
228	C₂×M₃₂	—	61	2	no	—
229	C₂×M₃₂	—	61	2	no	—
230	C₂×M₃₂	—	61	2	no	—
231	C₂×M₃₂	—	61	2	no	—
232	C₂×M₃₂	#6923	1	1	yes	characteristic, complemented
233	C₂²×C₁₆	—	61	2	no	—
234	C₂×#108	—	61	2	no	—
235	C₂×#108	—	61	2	no	—
236	C₂×#108	—	61	2	no	—
237	C₂×#108	—	122	1	no	—
238	C₂×#108	—	122	1	no	—
239	C₂×#108	—	122	1	no	—
240	#427	—	61	2	no	—
241	#427	—	61	2	no	—
242	#427	—	122	1	no	—
243	#427	—	122	1	no	—
244	C₂×#107	—	122	1	no	—
245	C₂×#106	—	61	2	no	—
246	#365	—	61	8	no	—
247	#365	—	61	8	no	—
248	C₆₁	C₂×#2155	1	1	yes	characteristic, complemented, Sylow
249	C₂³×C₄	—	61	1	no	—
250	C₂×M₁₆	—	122	2	no	—
251	C₂×M₁₆	—	122	2	no	—
252	C₂×M₁₆	—	122	2	no	—
253	C₂×M₁₆	—	244	1	no	—
254	C₂×M₁₆	—	244	1	no	—
255	C₂×M₁₆	—	244	1	no	—
256	C₂²×C₈	—	61	1	no	—
257	C₂²×C₈	—	61	1	no	—
258	C₂²×C₈	—	61	1	no	—
259	C₂²×C₈	—	61	1	no	—
260	C₂²×C₈	—	61	1	no	—
261	C₂²×C₈	—	61	1	no	—
262	C₂²×C₈	—	61	1	no	—
263	C₂²×C₈	—	61	1	no	—
264	C₂²×C₈	—	61	1	no	—
265	C₂²×C₈	—	61	1	no	—
266	C₂²×C₈	—	61	1	no	—
267	C₂²×C₈	—	61	1	no	—
268	C₂²×C₈	—	61	1	no	—
269	C₂²×C₈	—	244	1	no	—
270	C₂²×C₈	C₂×#6923	1	1	yes	characteristic
271	#117	—	122	2	no	—
272	#117	—	122	2	no	—
273	#117	—	244	1	no	—
274	#117	—	244	1	no	—
275	C₂×C₄⋊C₄	—	122	2	no	—
276	C₂×C₂²⋊C₄	—	244	1	no	—
277	C₂×C₄²	—	244	1	no	—
278	M₃₂	—	61	2	no	—
279	M₃₂	—	61	2	no	—
280	M₃₂	—	61	4	no	—
281	M₃₂	—	61	4	no	—
282	M₃₂	C₂×#6923	1	2	yes	—
283	M₃₂	C₂×#6923	1	2	yes	complemented
284	C₂×C₁₆	—	61	2	no	—
285	C₂×C₁₆	—	61	4	no	—
286	C₂×C₁₆	—	61	4	no	—
287	C₂×C₁₆	C₂×#6923	1	2	yes	complemented
288	#108	—	61	4	no	—
289	#108	—	122	2	no	—
290	#108	—	122	2	no	—
291	#108	—	122	2	no	—
292	#107	—	122	2	no	—
293	#107	—	122	2	no	—
294	#106	—	61	4	no	—
295	#106	—	122	2	no	—
296	C₂⁴	—	61	1	no	—
297	C₂²×C₄	—	61	1	no	—
298	C₂²×C₄	—	61	1	no	—
299	C₂²×C₄	—	61	1	no	—
300	C₂²×C₄	—	61	1	no	—
301	C₂²×C₄	—	61	1	no	—
302	C₂²×C₄	—	61	1	no	—
303	C₂²×C₄	—	61	1	no	—
304	C₂²×C₄	—	61	1	no	—
305	C₂²×C₄	—	61	1	no	—
306	C₂²×C₄	—	61	1	no	—
307	C₂²×C₄	—	61	1	no	—
308	C₂²×C₄	—	61	1	no	—
309	C₂²×C₄	—	61	1	no	—
310	C₂²×C₄	—	244	2	no	—
311	C₂²×C₄	C₄⋊#6923	1	1	yes	characteristic
312	M₁₆	—	122	4	no	—
313	M₁₆	—	244	2	no	—
314	M₁₆	—	244	2	no	—
315	M₁₆	—	244	2	no	—
316	C₂×C₈	—	61	1	no	—
317	C₂×C₈	—	61	1	no	—
318	C₂×C₈	—	61	1	no	—
319	C₂×C₈	—	61	1	no	—
320	C₂×C₈	—	61	1	no	—
321	C₂×C₈	—	61	1	no	—
322	C₂×C₈	—	61	1	no	—
323	C₂×C₈	—	61	1	no	—
324	C₂×C₈	—	61	1	no	—
325	C₂×C₈	—	61	1	no	—
326	C₂×C₈	—	61	1	no	—
327	C₂×C₈	—	61	1	no	—
328	C₂×C₈	—	61	1	no	—
329	C₂×C₈	—	61	1	no	—
330	C₂×C₈	—	61	1	no	—
331	C₂×C₈	—	61	1	no	—
332	C₂×C₈	—	61	1	no	—
333	C₂×C₈	—	61	1	no	—
334	C₂×C₈	—	61	1	no	—
335	C₂×C₈	—	61	1	no	—
336	C₂×C₈	—	61	1	no	—
337	C₂×C₈	—	61	1	no	—
338	C₂×C₈	—	244	2	no	—
339	C₂×C₈	—	244	2	no	—
340	C₂×C₈	—	244	2	no	—
341	C₂×C₈	C₄⋊#6923	1	1	yes	characteristic
342	C₂×C₈	C₄⋊#6923	1	1	yes	characteristic
343	C₂×C₈	C₄⋊#6923	1	1	yes	characteristic
344	C₂×C₈	C₂²×#6923	1	1	yes	characteristic
345	C₂×C₈	C₂²×#6923	1	1	yes	characteristic
346	C₂×C₈	C₂²×#6923	1	1	yes	characteristic
347	C₄⋊C₄	—	122	4	no	—
348	C₄⋊C₄	—	244	2	no	—
349	C₂²⋊C₄	—	244	2	no	—
350	C₂²⋊C₄	—	244	2	no	—
351	C₄²	—	244	2	no	—
352	C₄²	—	244	2	no	—
353	C₁₆	—	61	4	no	—
354	C₁₆	C₂²×#6923	1	4	yes	—
355	C₂³	—	61	1	no	—
356	C₂³	—	61	1	no	—
357	C₂³	—	61	1	no	—
358	C₂³	—	61	1	no	—
359	C₂³	—	61	1	no	—
360	C₂³	—	61	1	no	—
361	C₂³	—	244	2	no	—
362	C₂³	#14519845	1	1	yes	characteristic
363	C₂×C₄	—	61	1	no	—
364	C₂×C₄	—	61	1	no	—
365	C₂×C₄	—	61	1	no	—
366	C₂×C₄	—	61	1	no	—
367	C₂×C₄	—	61	1	no	—
368	C₂×C₄	—	61	1	no	—
369	C₂×C₄	—	61	1	no	—
370	C₂×C₄	—	61	1	no	—
371	C₂×C₄	—	61	1	no	—
372	C₂×C₄	—	61	1	no	—
373	C₂×C₄	—	61	1	no	—
374	C₂×C₄	—	61	1	no	—
375	C₂×C₄	—	61	1	no	—
376	C₂×C₄	—	61	1	no	—
377	C₂×C₄	—	61	1	no	—
378	C₂×C₄	—	61	1	no	—
379	C₂×C₄	—	61	1	no	—
380	C₂×C₄	—	61	1	no	—
381	C₂×C₄	—	61	1	no	—
382	C₂×C₄	—	61	1	no	—
383	C₂×C₄	—	61	1	no	—
384	C₂×C₄	—	61	1	no	—
385	C₂×C₄	—	488	4	no	—
386	C₂×C₄	—	244	4	no	—
387	C₂×C₄	#14519845	1	1	yes	characteristic
388	C₂×C₄	#14519845	1	1	yes	characteristic
389	C₂×C₄	#14519845	1	1	yes	characteristic
390	C₂×C₄	C₂×C₄⋊#6923	1	1	yes	characteristic
391	C₂×C₄	C₂×C₄⋊#6923	1	1	yes	characteristic
392	C₂×C₄	C₂×C₄⋊#6923	1	1	yes	characteristic
393	C₈	—	61	1	no	—
394	C₈	—	61	1	no	—
395	C₈	—	61	1	no	—
396	C₈	—	61	1	no	—
397	C₈	—	244	4	no	—
398	C₈	C₂×C₄⋊#6923	1	1	yes	characteristic
399	C₈	C₂×C₄⋊#6923	1	1	yes	characteristic
400	C₈	C₂×C₄⋊#6923	1	1	yes	characteristic
401	C₈	C₂³×#6923	1	1	yes	characteristic
402	C₂²	—	4	1	no	—
403	C₂²	—	61	1	no	—
404	C₂²	—	61	1	no	—
405	C₂²	—	61	1	no	—
406	C₂²	—	61	1	no	—
407	C₂²	—	122	2	no	—
408	C₂²	—	122	2	no	—
409	C₂²	—	122	2	no	—
410	C₂²	—	244	1	no	—
411	C₂²	—	244	1	no	—
412	C₂²	—	244	1	no	—
413	C₂²	C₂×#14519845	1	1	yes	characteristic
414	C₂²	C₂×#14519845	1	1	yes	characteristic
415	C₂²	C₂×#14519845	1	1	yes	characteristic
416	C₄	—	61	1	no	—
417	C₄	—	61	1	no	—
418	C₄	—	61	1	no	—
419	C₄	—	61	1	no	—
420	C₄	—	488	4	no	—
421	C₄	C₂×#14519845	1	1	yes	characteristic
422	C₄	C₂×#14519845	1	1	yes	characteristic
423	C₄	C₂×#14519845	1	1	yes	characteristic
424	C₄	C₂²×C₄⋊#6923	1	1	yes	characteristic
425	C₂	—	2	1	no	—
426	C₂	—	2	1	no	—
427	C₂	—	2	1	no	—
428	C₂	—	61	2	no	—
429	C₂	—	122	1	no	—
430	C₂	—	122	1	no	—
431	C₂	—	122	1	no	—
432	C₂	C₂²×#14519845	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₂×#14519845
commutator	C₈×C₆₁	C₂³×C₄
Frattini	C₈	C₂³×#6923
Fitting	C₂×M₃₂×C₆₁	C₄
socle	C₂×C₆₁	C₂²×#106
prime radical	C₂³×D₆₁	SD₁₆
cosocle	C₈×D₆₁	C₂⁴
hypercenter	C₂×M₃₂	#6923
hypocenter	C₆₁	C₂×#2155
LCS	G ▷ C₈×C₆₁ ▷ C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂×M₃₂

Complements

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

N	H ≅ G/N	type
3. #21462167	C₂	semidirect
4. #21462166	C₂	semidirect
5. D₆₁⋊#365	C₂	semidirect
21. #16840687	C₂²	semidirect
22. #16840686	C₂²	semidirect
24. C₂×#14519717	C₄	semidirect
26. M₃₂×D₆₁	C₄	semidirect
27. M₃₂×D₆₁	C₄	semidirect
30. C₂×C₁₆×D₆₁	C₄	semidirect
31. C₂×M₃₂×C₆₁	C₄	semidirect
69. #14519717	C₂×C₄	semidirect
70. #14519716	C₂×C₄	semidirect
72. C₂×#11758185	C₂×C₄	semidirect
74. C₁₆×D₆₁	C₂×C₄	semidirect
77. M₃₂×C₆₁	C₂×C₄	semidirect
78. C₂×C₁₆×C₆₁	C₂×C₄	semidirect
222. D₆₁	#2155	semidirect
232. C₂×M₃₂	#6923	semidirect
248. C₆₁	C₂×#2155	semidirect
283. M₃₂	C₂×#6923	semidirect
287. C₂×C₁₆	C₂×#6923	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₆₁⋊#108	2
C₂×#16840772	2
#21462167	2
#21462166	2
D₆₁⋊#365	2
C₂×M₃₂×D₆₁	2
C₂×#2155	61

Subgroups — D61⋊#2155 #30624116

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₆₁⋊#2155 #30624116