Subgroups — #30624176

Order 15616.

600 conjugacy classes of subgroups.

The subgroup lattice has 450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#21462185	C₂	1	2	yes	maximal, complemented
2	#21462184	C₂	1	2	yes	maximal, complemented
3	#21462183	C₂	1	1	yes	maximal, characteristic, complemented
4	#21462182	C₂	1	1	yes	maximal, characteristic, complemented
5	#21462179	C₂	1	1	yes	maximal, characteristic, complemented
6	#21462178	C₂	1	1	yes	maximal, characteristic, complemented
7	#21462155	C₂	1	2	yes	maximal, complemented
8	#21462047	C₂	1	1	yes	maximal, characteristic
9	D₆₁⋊(C₂²⋊C₁₆)	C₂	1	1	yes	maximal, characteristic
10	#21462029	C₂	1	2	yes	maximal, complemented
11	#405×D₆₁	C₂	1	1	yes	maximal, characteristic
12	C₂×#14519852	C₂²	1	2	yes	—
13	C₂×D₆₁⋊C₁₆	C₂²	1	2	yes	—
14	#16840683	C₂²	1	2	yes	complemented
15	#16840683	C₂²	1	2	yes	complemented
16	C₄⋊#11758187	C₂²	1	2	yes	complemented
17	C₄⋊#11758187	C₂²	1	2	yes	complemented
18	#16840657	C₂²	1	1	yes	characteristic
19	#16840657	C₂²	1	1	yes	characteristic
20	#16840657	C₂²	1	1	yes	characteristic
21	#16840657	C₂²	1	1	yes	characteristic
22	C₂²⋊#11758187	C₂²	1	2	yes	—
23	C₂²⋊#11758187	C₂²	1	2	yes	—
24	#16840651	C₂²	1	2	yes	complemented
25	#16840650	C₂²	1	2	yes	complemented
26	#16840648	C₂²	1	2	yes	complemented
27	C₄×#11758187	C₂²	1	2	yes	complemented
28	C₂×M₁₆×D₆₁	C₄	1	1	yes	characteristic
29	C₂²×C₈×D₆₁	C₂²	1	1	yes	characteristic
30	#117×D₆₁	C₄	1	1	yes	characteristic
31	#16839720	C₂²	1	1	yes	characteristic
32	#16839719	C₂²	1	1	yes	characteristic
33	#16839719	C₂²	1	1	yes	characteristic
34	#16839718	C₂²	1	1	yes	characteristic
35	#16839717	C₄	1	1	yes	characteristic
36	#16839716	C₄	1	1	yes	characteristic
37	#16839716	C₄	1	1	yes	characteristic
38	#97×D₆₁	C₄	1	1	yes	characteristic
39	#97×D₆₁	C₄	1	1	yes	characteristic
40	C₄×C₈×D₆₁	C₂²	1	1	yes	characteristic
41	C₄×C₈×D₆₁	C₂²	1	1	yes	characteristic
42	C₆₁×#405	C₄	1	1	yes	characteristic
43	#14519852	—	2	4	no	—
44	D₆₁⋊C₁₆	—	2	4	no	—
45	C₂×#11758187	C₂³	1	2	yes	—
46	C₂×#11758187	C₂³	1	2	yes	—
47	C₂×#11758187	C₂³	1	2	yes	—
48	C₂×#11758187	C₂³	1	2	yes	—
49	C₂²×C₄×D₆₁	C₂×C₄	1	1	yes	characteristic
50	C₂×#11758194	C₂×C₄	1	1	yes	characteristic
51	C₂×#11758189	C₂×C₄	1	1	yes	characteristic
52	C₂×#11758189	C₂×C₄	1	1	yes	characteristic
53	M₁₆×D₆₁	—	2	4	no	—
54	C₂²×#92418	C₂³	1	1	yes	characteristic
55	C₂×C₈×D₆₁	—	2	4	no	—
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	C₂×C₄	1	1	yes	characteristic
60	C₂×C₈×D₆₁	C₂³	1	1	yes	characteristic
61	C₂×C₈×D₆₁	C₂³	1	1	yes	characteristic
62	#14519736	C₂×C₄	1	1	yes	characteristic
63	#14519735	C₈	1	1	yes	characteristic
64	#14519735	C₈	1	1	yes	characteristic
65	#14519734	C₂×C₄	1	1	yes	characteristic
66	#14519734	C₂×C₄	1	1	yes	characteristic
67	#14519733	C₈	1	1	yes	characteristic
68	#14519733	C₈	1	1	yes	characteristic
69	C₄⋊C₄×D₆₁	C₈	1	1	yes	characteristic
70	C₄⋊C₄×D₆₁	C₈	1	1	yes	characteristic
71	C₂²⋊C₄×D₆₁	C₈	1	1	yes	characteristic
72	C₂²⋊C₄×D₆₁	C₈	1	1	yes	characteristic
73	C₄²×D₆₁	C₂×C₄	1	1	yes	characteristic
74	C₄²×D₆₁	C₂×C₄	1	1	yes	characteristic
75	#14519688	C₂×C₄	1	1	yes	characteristic
76	#14519688	C₂×C₄	1	1	yes	characteristic
77	#14519687	C₂×C₄	1	1	yes	characteristic
78	#14519687	C₂×C₄	1	1	yes	characteristic
79	#14519687	C₂×C₄	1	1	yes	characteristic
80	#14519687	C₂×C₄	1	1	yes	characteristic
81	C₄×#92418	C₂³	1	1	yes	characteristic
82	C₄×#92418	C₂³	1	1	yes	characteristic
83	C₈×Dic₆₁	C₂×C₄	1	1	yes	characteristic
84	C₈×Dic₆₁	C₂×C₄	1	1	yes	characteristic
85	C₈×Dic₆₁	C₂³	1	1	yes	characteristic
86	C₈×Dic₆₁	C₂³	1	1	yes	characteristic
87	C₂×M₁₆×C₆₁	C₂×C₄	1	1	yes	characteristic
88	C₂²×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
89	#117×C₆₁	C₂×C₄	1	1	yes	characteristic
90	#97×C₆₁	C₂×C₄	1	1	yes	characteristic
91	#97×C₆₁	C₂×C₄	1	1	yes	characteristic
92	C₄×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
93	C₄×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
94	C₂³×D₆₁	C₂×C₈	1	1	yes	characteristic
95	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
96	C₂²×Dic₆₁	C₂×C₈	1	1	yes	characteristic
97	C₂×C₄×D₆₁	—	2	2	no	—
98	C₂×C₄×D₆₁	—	2	2	no	—
99	C₂×C₄×D₆₁	C₂×C₈	1	1	yes	characteristic
100	C₂×C₄×D₆₁	C₂×C₈	1	1	yes	characteristic
101	C₂×C₄×D₆₁	C₂×C₈	1	1	yes	characteristic
102	C₂×C₄×D₆₁	C₂×C₈	1	1	yes	characteristic
103	C₂×C₄×D₆₁	C₂×C₈	1	1	yes	characteristic
104	C₂×C₄×D₆₁	C₂×C₈	1	1	yes	characteristic
105	C₂×C₄×D₆₁	C₂²×C₄	1	1	yes	characteristic
106	C₂×C₄×D₆₁	C₂²×C₄	1	1	yes	characteristic
107	M₁₆×C₆₁	—	2	2	no	—
108	C₂×C₈×C₆₁	—	2	2	no	—
109	C₂×C₈×C₆₁	C₂²×C₄	1	1	yes	characteristic
110	C₂×C₈×C₆₁	C₂²×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	C₄⋊C₄×C₆₁	C₂×C₈	1	1	yes	characteristic
114	C₄⋊C₄×C₆₁	C₂×C₈	1	1	yes	characteristic
115	C₂²⋊C₄×C₆₁	C₂×C₈	1	1	yes	characteristic
116	C₂²⋊C₄×C₆₁	C₂×C₈	1	1	yes	characteristic
117	C₄²×C₆₁	C₂²×C₄	1	1	yes	characteristic
118	C₄²×C₆₁	C₂²×C₄	1	1	yes	characteristic
119	C₂²⋊Dic₆₁	C₂×C₈	1	1	yes	characteristic
120	C₂²⋊Dic₆₁	C₂×C₈	1	1	yes	characteristic
121	#11758198	C₂×C₈	1	1	yes	characteristic
122	#11758198	C₂×C₈	1	1	yes	characteristic
123	#11758198	C₂×C₈	1	1	yes	characteristic
124	#11758198	C₂×C₈	1	1	yes	characteristic
125	C₄⋊Dic₆₁	C₂×C₈	1	1	yes	characteristic
126	C₄⋊Dic₆₁	C₂×C₈	1	1	yes	characteristic
127	#11758196	C₂×C₈	1	1	yes	characteristic
128	#11758196	C₂×C₈	1	1	yes	characteristic
129	#11758196	C₂×C₈	1	1	yes	characteristic
130	#11758196	C₂×C₈	1	1	yes	characteristic
131	C₄×Dic₆₁	C₂×C₈	1	1	yes	characteristic
132	C₄×Dic₆₁	C₂×C₈	1	1	yes	characteristic
133	C₄×Dic₆₁	C₂×C₈	1	1	yes	characteristic
134	C₄×Dic₆₁	C₂×C₈	1	1	yes	characteristic
135	C₄×Dic₆₁	C₂²×C₄	1	1	yes	characteristic
136	C₄×Dic₆₁	C₂²×C₄	1	1	yes	characteristic
137	#11758194	—	2	2	no	—
138	C₂×#92418	—	2	2	no	—
139	C₂×#92418	C₂²×C₄	1	1	yes	characteristic
140	C₂×#92418	C₂²×C₄	1	1	yes	characteristic
141	C₂×#92418	C₂²×C₄	1	1	yes	characteristic
142	C₂×#92418	C₂⁴	1	1	yes	characteristic
143	#11758189	—	2	2	no	—
144	#11758189	M₁₆	1	4	yes	—
145	C₈×D₆₁	—	2	2	no	—
146	C₈×D₆₁	—	2	2	no	—
147	C₈×D₆₁	—	2	2	no	—
148	C₈×D₆₁	—	2	2	no	—
149	C₈×D₆₁	—	2	2	no	—
150	C₈×D₆₁	#41	1	4	yes	—
151	#11758187	—	2	2	no	—
152	#11758187	—	2	2	no	—
153	#11758187	—	2	2	no	—
154	#11758187	—	2	2	no	—
155	C₂³×C₆₁	C₂²×C₈	1	1	yes	characteristic
156	C₂²×D₆₁	—	2	2	no	—
157	C₂²×D₆₁	—	2	2	no	—
158	C₂²×D₆₁	—	4	1	no	—
159	C₂²×D₆₁	C₂²×C₈	1	1	yes	characteristic
160	C₂²×D₆₁	C₂²×C₈	1	1	yes	characteristic
161	C₂×C₄×C₆₁	—	2	1	no	—
162	C₂×C₄×C₆₁	—	2	1	no	—
163	C₂×C₄×C₆₁	C₂²×C₈	1	1	yes	characteristic
164	C₂×C₄×C₆₁	C₂²×C₈	1	1	yes	characteristic
165	C₂×C₄×C₆₁	C₂²×C₈	1	1	yes	characteristic
166	C₂×C₄×C₆₁	C₂²×C₈	1	1	yes	characteristic
167	C₂×C₄×C₆₁	C₂²×C₈	1	1	yes	characteristic
168	C₂×C₄×C₆₁	C₂³×C₄	1	1	yes	characteristic
169	C₂×Dic₆₁	—	2	2	no	—
170	C₂×Dic₆₁	C₂²×C₈	1	1	yes	characteristic
171	C₂×Dic₆₁	C₂²×C₈	1	1	yes	characteristic
172	C₂×Dic₆₁	C₂²×C₈	1	1	yes	characteristic
173	C₂×Dic₆₁	C₂²×C₈	1	1	yes	characteristic
174	C₂×Dic₆₁	C₂²×C₈	1	1	yes	characteristic
175	C₂×Dic₆₁	C₂²×C₈	1	1	yes	characteristic
176	C₄×D₆₁	—	2	2	no	—
177	C₄×D₆₁	—	2	2	no	—
178	C₄×D₆₁	—	2	2	no	—
179	C₄×D₆₁	—	2	1	no	—
180	C₄×D₆₁	—	2	1	no	—
181	C₄×D₆₁	—	2	2	no	—
182	C₄×D₆₁	—	4	1	no	—
183	C₄×D₆₁	—	4	1	no	—
184	C₄×D₆₁	#117	1	2	yes	—
185	C₄×D₆₁	C₂×M₁₆	1	2	yes	—
186	C₈×C₆₁	—	2	1	no	—
187	C₈×C₆₁	—	2	1	no	—
188	C₈×C₆₁	#117	1	2	yes	—
189	C₈×C₆₁	C₂×M₁₆	1	2	yes	—
190	#92418	—	2	1	no	—
191	#92418	—	2	1	no	—
192	#92418	C₂×M₁₆	1	2	yes	—
193	#92418	C₂×#41	1	2	yes	—
194	#33422	—	61	1	no	maximal, Sylow
195	C₂²×C₆₁	—	2	1	no	—
196	C₂²×C₆₁	—	2	1	no	—
197	C₂²×C₆₁	—	2	1	no	—
198	C₂²×C₆₁	C₂³×C₈	1	1	yes	characteristic
199	C₂×D₆₁	—	2	1	no	—
200	C₂×D₆₁	—	2	1	no	—
201	C₂×D₆₁	—	2	1	no	—
202	C₂×D₆₁	—	2	1	no	—
203	C₂×D₆₁	—	4	4	no	—
204	C₂×D₆₁	#431	1	2	yes	—
205	C₂×D₆₁	#504	1	2	yes	—
206	C₄×C₆₁	—	2	1	no	—
207	C₄×C₆₁	—	2	1	no	—
208	C₄×C₆₁	—	2	1	no	—
209	C₄×C₆₁	—	2	1	no	—
210	C₄×C₆₁	—	2	1	no	—
211	C₄×C₆₁	C₂×#117	1	1	yes	characteristic
212	C₄×C₆₁	C₂²×M₁₆	1	1	yes	characteristic
213	Dic₆₁	—	2	1	no	—
214	Dic₆₁	—	2	1	no	—
215	Dic₆₁	—	2	1	no	—
216	Dic₆₁	—	2	1	no	—
217	Dic₆₁	—	2	1	no	—
218	Dic₆₁	#431	1	2	yes	—
219	C₂×#405	—	61	1	no	—
220	#2164	—	61	2	no	—
221	#2164	—	61	2	no	—
222	#2163	—	61	1	no	—
223	#2163	—	61	1	no	—
224	#2162	—	61	1	no	—
225	#2162	—	61	1	no	—
226	#2151	—	61	2	no	—
227	#2112	—	61	1	no	—
228	C₂×C₂²⋊C₁₆	—	61	1	no	—
229	#2108	—	61	2	no	—
230	C₂×C₆₁	—	4	1	no	—
231	C₂×C₆₁	C₂×#431	1	1	yes	characteristic
232	C₂×C₆₁	C₂×#504	1	1	yes	characteristic
233	C₂×C₆₁	#3407	1	1	yes	characteristic
234	D₆₁	—	2	2	no	—
235	D₆₁	—	2	2	no	—
236	C₂²×M₁₆	—	61	1	no	—
237	C₂³×C₈	—	61	1	no	—
238	C₂×#117	—	61	1	no	—
239	C₂×M₃₂	—	61	2	no	—
240	C₂²×C₁₆	—	61	2	no	—
241	#405	—	61	1	no	—
242	#405	—	61	1	no	—
243	#405	—	61	1	no	—
244	#405	—	61	1	no	—
245	#405	—	61	1	no	—
246	#405	—	61	1	no	—
247	#405	—	61	1	no	—
248	#405	#6923	1	1	yes	characteristic
249	C₂×#97	—	61	1	no	—
250	C₂×#97	—	61	1	no	—
251	C₂×C₄×C₈	—	61	1	no	—
252	C₂×C₄×C₈	—	61	1	no	—
253	C₄⋊C₁₆	—	61	2	no	—
254	C₄⋊C₁₆	—	61	2	no	—
255	C₄⋊C₁₆	—	61	2	no	—
256	C₄⋊C₁₆	—	61	2	no	—
257	C₂²⋊C₁₆	—	61	1	no	—
258	C₂²⋊C₁₆	—	61	1	no	—
259	C₂²⋊C₁₆	—	61	2	no	—
260	C₂²⋊C₁₆	—	61	1	no	—
261	C₂²⋊C₁₆	—	61	1	no	—
262	C₂²⋊C₁₆	—	61	2	no	—
263	#346	—	61	2	no	—
264	#346	—	61	2	no	—
265	C₄×C₁₆	—	61	2	no	—
266	C₄×C₁₆	—	61	2	no	—
267	C₆₁	#33422	1	1	yes	characteristic, complemented, Sylow
268	C₂³×C₄	—	61	1	no	—
269	C₂×M₁₆	—	61	1	no	—
270	C₂×M₁₆	—	61	1	no	—
271	C₂×M₁₆	—	61	1	no	—
272	C₂×M₁₆	—	122	4	no	—
273	C₂×M₁₆	C₂×#6923	1	1	yes	characteristic
274	C₂²×C₈	—	61	1	no	—
275	C₂²×C₈	—	61	1	no	—
276	C₂²×C₈	—	61	1	no	—
277	C₂²×C₈	—	61	1	no	—
278	C₂²×C₈	—	61	1	no	—
279	C₂²×C₈	—	61	1	no	—
280	C₂²×C₈	—	61	1	no	—
281	C₂²×C₈	—	122	4	no	—
282	C₂²×C₈	C₂×#6923	1	1	yes	characteristic
283	#117	—	61	1	no	—
284	#117	—	61	1	no	—
285	#117	—	61	1	no	—
286	#117	—	61	1	no	—
287	#117	—	61	1	no	—
288	#117	—	61	1	no	—
289	#117	—	61	1	no	—
290	#117	C₂×#6923	1	1	yes	characteristic
291	C₂×C₄⋊C₄	—	61	1	no	—
292	C₂×C₄⋊C₄	—	61	1	no	—
293	C₂×C₂²⋊C₄	—	61	1	no	—
294	C₂×C₂²⋊C₄	—	61	1	no	—
295	C₂×C₄²	—	61	1	no	—
296	C₂×C₄²	—	61	1	no	—
297	M₃₂	—	122	4	no	—
298	C₂×C₁₆	—	61	2	no	—
299	C₂×C₁₆	—	61	2	no	—
300	C₂×C₁₆	—	61	2	no	—
301	C₂×C₁₆	—	61	2	no	—
302	C₂×C₁₆	—	122	4	no	—
303	#97	—	61	1	no	—
304	#97	—	61	1	no	—
305	#97	—	61	1	no	—
306	#97	—	61	1	no	—
307	#97	—	61	1	no	—
308	#97	—	61	1	no	—
309	#97	C₂×#6923	1	1	yes	characteristic
310	#97	C₂×#6923	1	1	yes	characteristic
311	C₄×C₈	—	61	1	no	—
312	C₄×C₈	—	61	1	no	—
313	C₄×C₈	—	61	1	no	—
314	C₄×C₈	—	61	1	no	—
315	C₄×C₈	—	61	1	no	—
316	C₄×C₈	—	61	1	no	—
317	C₄×C₈	C₂×#6923	1	1	yes	characteristic
318	C₄×C₈	C₂×#6923	1	1	yes	characteristic
319	C₂⁴	—	61	1	no	—
320	C₂²×C₄	—	61	1	no	—
321	C₂²×C₄	—	61	1	no	—
322	C₂²×C₄	—	61	1	no	—
323	C₂²×C₄	—	61	1	no	—
324	C₂²×C₄	—	61	1	no	—
325	C₂²×C₄	—	61	1	no	—
326	C₂²×C₄	—	61	1	no	—
327	C₂²×C₄	—	61	1	no	—
328	C₂²×C₄	—	61	1	no	—
329	C₂²×C₄	—	122	2	no	—
330	C₂²×C₄	—	122	2	no	—
331	C₂²×C₄	C₂²×#6923	1	1	yes	characteristic
332	M₁₆	—	2	2	no	—
333	M₁₆	—	61	4	no	—
334	M₁₆	—	122	2	no	—
335	M₁₆	—	122	2	no	—
336	C₂×C₈	—	2	2	no	—
337	C₂×C₈	—	61	1	no	—
338	C₂×C₈	—	61	1	no	—
339	C₂×C₈	—	61	4	no	—
340	C₂×C₈	—	61	1	no	—
341	C₂×C₈	—	61	1	no	—
342	C₂×C₈	—	122	2	no	—
343	C₂×C₈	—	122	2	no	—
344	C₂×C₈	—	122	2	no	—
345	C₂×C₈	—	122	2	no	—
346	C₂×C₈	—	122	2	no	—
347	C₂×C₈	—	122	2	no	—
348	C₂×C₈	C₂²×#6923	1	1	yes	characteristic
349	C₂×C₈	C₂²×#6923	1	1	yes	characteristic
350	C₂×C₈	C₂²×#6923	1	1	yes	characteristic
351	C₂×C₈	C₂²×#6923	1	1	yes	characteristic
352	C₄⋊C₄	—	61	1	no	—
353	C₄⋊C₄	—	61	1	no	—
354	C₄⋊C₄	—	61	1	no	—
355	C₄⋊C₄	—	61	1	no	—
356	C₄⋊C₄	—	61	1	no	—
357	C₄⋊C₄	—	61	1	no	—
358	C₄⋊C₄	D₆₁⋊C₈	1	1	yes	characteristic
359	C₄⋊C₄	D₆₁⋊C₈	1	1	yes	characteristic
360	C₂²⋊C₄	—	61	1	no	—
361	C₂²⋊C₄	—	61	1	no	—
362	C₂²⋊C₄	—	61	1	no	—
363	C₂²⋊C₄	—	61	1	no	—
364	C₂²⋊C₄	—	61	1	no	—
365	C₂²⋊C₄	—	61	1	no	—
366	C₂²⋊C₄	D₆₁⋊C₈	1	1	yes	characteristic
367	C₂²⋊C₄	D₆₁⋊C₈	1	1	yes	characteristic
368	C₄²	—	61	1	no	—
369	C₄²	—	61	1	no	—
370	C₄²	—	61	1	no	—
371	C₄²	—	61	1	no	—
372	C₄²	—	61	1	no	—
373	C₄²	—	61	1	no	—
374	C₄²	C₂²×#6923	1	1	yes	characteristic
375	C₄²	C₂²×#6923	1	1	yes	characteristic
376	C₁₆	—	122	2	no	—
377	C₁₆	—	122	2	no	—
378	C₁₆	—	122	2	no	—
379	C₁₆	—	122	2	no	—
380	C₂³	—	61	1	no	—
381	C₂³	—	61	1	no	—
382	C₂³	—	122	2	no	—
383	C₂³	—	122	2	no	—
384	C₂³	—	244	1	no	—
385	C₂³	C₂×D₆₁⋊C₈	1	1	yes	characteristic
386	C₂×C₄	—	2	1	no	—
387	C₂×C₄	—	2	1	no	—
388	C₂×C₄	—	61	1	no	—
389	C₂×C₄	—	61	2	no	—
390	C₂×C₄	—	61	2	no	—
391	C₂×C₄	—	61	1	no	—
392	C₂×C₄	—	61	1	no	—
393	C₂×C₄	—	61	1	no	—
394	C₂×C₄	—	61	1	no	—
395	C₂×C₄	—	61	1	no	—
396	C₂×C₄	—	122	2	no	—
397	C₂×C₄	—	122	2	no	—
398	C₂×C₄	—	122	2	no	—
399	C₂×C₄	—	122	2	no	—
400	C₂×C₄	—	122	2	no	—
401	C₂×C₄	—	122	1	no	—
402	C₂×C₄	—	122	1	no	—
403	C₂×C₄	—	244	1	no	—
404	C₂×C₄	—	244	1	no	—
405	C₂×C₄	C₂×D₆₁⋊C₈	1	1	yes	characteristic
406	C₂×C₄	C₂×D₆₁⋊C₈	1	1	yes	characteristic
407	C₂×C₄	C₂×D₆₁⋊C₈	1	1	yes	characteristic
408	C₂×C₄	C₂×D₆₁⋊C₈	1	1	yes	characteristic
409	C₂×C₄	C₂×D₆₁⋊C₈	1	1	yes	characteristic
410	C₂×C₄	C₂³×#6923	1	1	yes	characteristic
411	C₈	—	2	1	no	—
412	C₈	—	2	1	no	—
413	C₈	—	61	2	no	—
414	C₈	—	61	2	no	—
415	C₈	—	122	1	no	—
416	C₈	—	122	1	no	—
417	C₈	#14519856	1	2	yes	—
418	C₈	D₆₁⋊M₁₆	1	2	yes	—
419	C₂²	—	2	1	no	—
420	C₂²	—	2	1	no	—
421	C₂²	—	2	1	no	—
422	C₂²	—	61	2	no	—
423	C₂²	—	61	2	no	—
424	C₂²	—	122	1	no	—
425	C₂²	—	122	1	no	—
426	C₂²	—	122	1	no	—
427	C₂²	—	122	1	no	—
428	C₂²	—	244	4	no	—
429	C₂²	C₂²×D₆₁⋊C₈	1	1	yes	characteristic
430	C₄	—	2	1	no	—
431	C₄	—	2	1	no	—
432	C₄	—	2	1	no	—
433	C₄	—	2	1	no	—
434	C₄	—	2	1	no	—
435	C₄	—	61	2	no	—
436	C₄	—	122	1	no	—
437	C₄	—	122	1	no	—
438	C₄	—	122	1	no	—
439	C₄	—	122	1	no	—
440	C₄	—	122	1	no	—
441	C₄	C₂×#14519856	1	1	yes	characteristic
442	C₄	C₂×D₆₁⋊M₁₆	1	1	yes	characteristic
443	C₂	—	4	1	no	—
444	C₂	—	122	2	no	—
445	C₂	—	122	2	no	—
446	C₂	D₆₁⋊#431	1	1	yes	characteristic
447	C₂	D₆₁⋊#504	1	1	yes	characteristic
448	C₂	#21462787	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂³×#6923
commutator, socle	C₂²×C₆₁	C₂³×C₈
Fitting	C₆₁×#405	C₄
prime radical	C₂³×D₆₁	C₂×C₈
cosocle	C₂×#92418	C₂⁴
hypercenter	#405	#6923
hypocenter	C₆₁	#33422
LCS	G ▷ C₂²×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂×C₄ ◁ #405

Complements

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

N	H ≅ G/N	type
1. #21462185	C₂	semidirect
2. #21462184	C₂	semidirect
3. #21462183	C₂	semidirect
4. #21462182	C₂	semidirect
5. #21462179	C₂	semidirect
6. #21462178	C₂	semidirect
7. #21462155	C₂	semidirect
10. #21462029	C₂	semidirect
14. #16840683	C₂²	semidirect
15. #16840683	C₂²	semidirect
16. C₄⋊#11758187	C₂²	semidirect
17. C₄⋊#11758187	C₂²	semidirect
24. #16840651	C₂²	semidirect
25. #16840650	C₂²	semidirect
26. #16840648	C₂²	semidirect
27. C₄×#11758187	C₂²	semidirect
267. C₆₁	#33422	semidirect

Maximal subgroups

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

subgroup	index
#21462185	2
#21462184	2
#21462183	2
#21462182	2
#21462179	2
#21462178	2
#21462155	2
#21462047	2
D₆₁⋊(C₂²⋊C₁₆)	2
#21462029	2
#405×D₆₁	2
#33422	61