Subgroups — #29833211

Order 15616.

692 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#16840178	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×#14519717	C₂	1	1	yes	maximal, characteristic, complemented
3	#21454513	C₂	1	1	yes	maximal, characteristic
4	#21447648	C₂	1	2	yes	maximal, complemented
5	#21447647	C₂	1	2	yes	maximal, complemented
6	#21447641	C₂	1	2	yes	maximal, complemented
7	#21447636	C₂	1	2	yes	maximal, complemented
8	#21447577	C₂	1	1	yes	maximal, characteristic, complemented
9	#21447432	C₂	1	1	yes	maximal, characteristic, complemented
10	#21447415	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₆₁×C₂²⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#14519783	C₂²	1	1	yes	characteristic
13	#16840273	C₄	1	1	yes	characteristic
14	#16840178	—	2	4	no	—
15	C₂×#14519717	—	2	4	no	—
16	C₂×#14519717	C₂²	1	1	yes	characteristic
17	C₂×#14519717	C₂²	1	2	yes	—
18	C₂×#14519717	C₂²	1	1	yes	characteristic
19	C₂×#14519716	C₂²	1	2	yes	complemented
20	C₂²×#11758185	C₂²	1	2	yes	—
21	C₂×C₁₆×D₆₁	C₂²	1	2	yes	complemented
22	#16839833	C₄	1	2	yes	—
23	#16839833	C₄	1	2	yes	—
24	C₈×C₂²⋊D₆₁	C₂²	1	2	yes	—
25	C₈×C₂²⋊D₆₁	C₂²	1	2	yes	—
26	#16839788	C₄	1	1	yes	characteristic
27	#16839728	C₄	1	1	yes	characteristic
28	#16839726	C₄	1	1	yes	characteristic
29	#16839717	C₂²	1	1	yes	characteristic
30	#16839580	C₂²	1	2	yes	complemented
31	#16839580	C₂²	1	2	yes	complemented
32	#16839541	C₂²	1	2	yes	complemented
33	#16839541	C₂²	1	2	yes	complemented
34	#16839537	C₂²	1	2	yes	complemented
35	C₁₆×Dic₆₁	C₂²	1	2	yes	complemented
36	C₂³×C₈×C₆₁	C₂²	1	1	yes	characteristic
37	C₂²×C₁₆×C₆₁	C₂²	1	1	yes	characteristic
38	C₂²×C₁₆×C₆₁	C₂²	1	1	yes	characteristic
39	C₆₁×C₂²⋊C₁₆	C₂²	1	1	yes	characteristic
40	C₆₁×C₂²⋊C₁₆	C₂²	1	1	yes	characteristic
41	C₆₁×C₂²⋊C₁₆	C₂²	1	1	yes	characteristic
42	C₆₁×C₂²⋊C₁₆	C₂²	1	1	yes	characteristic
43	C₂×#11758222	C₂×C₄	1	1	yes	characteristic
44	#14519783	—	2	2	no	—
45	#14519783	—	2	2	no	—
46	C₂×#11758194	C₂×C₄	1	1	yes	characteristic
47	C₂×#11758194	C₂×C₄	1	1	yes	characteristic
48	C₂×#11758189	C₂×C₄	1	2	yes	—
49	C₂×C₈×D₆₁	C₂³	1	2	yes	—
50	#14519760	C₈	1	2	yes	—
51	#14519756	C₈	1	1	yes	characteristic
52	#14519756	C₈	1	1	yes	characteristic
53	#14519751	C₈	1	1	yes	characteristic
54	#14519751	C₈	1	1	yes	characteristic
55	#14519746	C₈	1	2	yes	—
56	C₄×C₂²⋊D₆₁	C₂×C₄	1	2	yes	—
57	C₄×C₂²⋊D₆₁	C₂×C₄	1	2	yes	—
58	#14519736	C₂×C₄	1	1	yes	characteristic
59	#14519717	—	2	2	no	—
60	#14519717	—	2	4	no	—
61	#14519717	D₄	1	4	yes	complemented
62	#14519716	—	2	4	no	—
63	C₂×#11758185	—	2	4	no	—
64	C₂×#11758185	C₂³	1	2	yes	—
65	C₂×#11758185	C₂³	1	2	yes	—
66	C₁₆×D₆₁	—	2	4	no	—
67	#14519706	C₂×C₄	1	2	yes	—
68	#14519706	C₂×C₄	1	2	yes	—
69	C₂²⋊#92418	C₂×C₄	1	2	yes	—
70	C₂²⋊#92418	C₂×C₄	1	2	yes	—
71	#14519689	C₂×C₄	1	2	yes	—
72	#14519689	C₂×C₄	1	2	yes	—
73	#14519687	C₂×C₄	1	2	yes	—
74	C₈×Dic₆₁	C₂³	1	2	yes	—
75	C₂³×C₄×C₆₁	C₂×C₄	1	1	yes	characteristic
76	C₂²×C₈×C₆₁	—	2	2	no	—
77	C₂²×C₈×C₆₁	—	2	2	no	—
78	C₂²×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
79	C₂²×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
80	C₂²×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
81	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
82	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
83	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
84	C₂×C₁₆×C₆₁	—	2	2	no	—
85	C₂×C₁₆×C₆₁	—	2	2	no	—
86	C₂×C₁₆×C₆₁	C₂³	1	1	yes	characteristic
87	C₂×C₁₆×C₆₁	C₂³	1	1	yes	characteristic
88	C₂×C₁₆×C₆₁	C₂³	1	1	yes	characteristic
89	C₂×C₁₆×C₆₁	C₂³	1	1	yes	characteristic
90	C₂⁴×C₆₁	C₂×C₈	1	1	yes	characteristic
91	C₂²×C₄×C₆₁	—	2	2	no	—
92	C₂²×C₄×C₆₁	—	2	2	no	—
93	C₂²×C₄×C₆₁	C₂×C₈	1	1	yes	characteristic
94	C₂²×C₄×C₆₁	C₂×C₈	1	1	yes	characteristic
95	C₂²×C₄×C₆₁	C₂×C₈	1	1	yes	characteristic
96	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
97	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
98	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
99	C₂×C₂²⋊D₆₁	C₂×C₈	1	2	yes	—
100	C₂×C₂²⋊D₆₁	C₂×C₈	1	2	yes	—
101	C₂×C₂²⋊D₆₁	C₂×C₈	1	2	yes	—
102	#11758222	—	2	2	no	—
103	#11758222	—	2	2	no	—
104	C₂×D₂₄₄	C₂×C₈	1	1	yes	characteristic
105	C₂×C₄×D₆₁	C₂²×C₄	1	2	yes	—
106	C₂×Dic₁₂₂	C₂×C₈	1	1	yes	characteristic
107	C₂×C₈×C₆₁	—	2	2	no	—
108	C₂×C₈×C₆₁	—	2	2	no	—
109	C₂×C₈×C₆₁	—	2	2	no	—
110	C₂×C₈×C₆₁	—	2	1	no	—
111	C₂×C₈×C₆₁	—	2	1	no	—
112	C₂×C₈×C₆₁	—	2	1	no	—
113	C₂×C₈×C₆₁	—	2	1	no	—
114	C₂×C₈×C₆₁	C₂²×C₄	1	1	yes	characteristic
115	C₂×C₈×C₆₁	C₂²×C₄	1	1	yes	characteristic
116	C₂×C₈×C₆₁	C₂²×C₄	1	1	yes	characteristic
117	C₂×C₈×C₆₁	C₂×D₄	1	2	yes	—
118	C₂×C₈×C₆₁	#41	1	2	yes	—
119	C₂×C₈×C₆₁	C₂⁴	1	1	yes	characteristic
120	C₂²⋊Dic₆₁	C₂×C₈	1	2	yes	—
121	C₂²⋊Dic₆₁	C₂×C₈	1	2	yes	—
122	C₂²⋊Dic₆₁	C₂×C₈	1	2	yes	—
123	#11758198	C₂×C₈	1	2	yes	—
124	#11758198	C₂×C₈	1	2	yes	—
125	C₄⋊Dic₆₁	C₂×C₈	1	1	yes	characteristic
126	C₄⋊Dic₆₁	C₂×C₈	1	1	yes	characteristic
127	#11758196	C₂×C₈	1	2	yes	—
128	#11758196	C₂×C₈	1	2	yes	—
129	C₄×Dic₆₁	C₂²×C₄	1	2	yes	—
130	#11758194	—	2	2	no	—
131	#11758194	—	2	2	no	—
132	C₂×#92418	C₂²×C₄	1	2	yes	—
133	C₂×#92418	C₂²×C₄	1	2	yes	—
134	#11758189	—	2	4	no	—
135	C₈×D₆₁	—	2	2	no	—
136	C₈×D₆₁	—	2	2	no	—
137	C₁₆×C₆₁	—	2	1	no	—
138	C₁₆×C₆₁	—	2	1	no	—
139	C₁₆×C₆₁	—	2	1	no	—
140	C₁₆×C₆₁	—	2	1	no	—
141	#11758185	—	2	2	no	—
142	#11758185	C₂×D₄	1	4	yes	—
143	C₂³×C₆₁	—	2	2	no	—
144	C₂³×C₆₁	—	2	2	no	—
145	C₂³×C₆₁	—	4	1	no	—
146	C₂³×C₆₁	C₂²×C₈	1	1	yes	characteristic
147	C₂³×C₆₁	C₂²×C₈	1	1	yes	characteristic
148	C₂³×C₆₁	C₂²×C₈	1	1	yes	characteristic
149	C₂²×D₆₁	C₂²×C₈	1	2	yes	—
150	C₂×C₄×C₆₁	—	2	2	no	—
151	C₂×C₄×C₆₁	—	2	1	no	—
152	C₂×C₄×C₆₁	—	2	1	no	—
153	C₂×C₄×C₆₁	—	2	1	no	—
154	C₂×C₄×C₆₁	—	2	1	no	—
155	C₂×C₄×C₆₁	—	2	2	no	—
156	C₂×C₄×C₆₁	—	2	2	no	—
157	C₂×C₄×C₆₁	C₄×D₄	1	2	yes	—
158	C₂×C₄×C₆₁	C₂²×C₈	1	1	yes	characteristic
159	C₂×C₄×C₆₁	C₂²×C₈	1	1	yes	characteristic
160	C₂×C₄×C₆₁	C₂²×C₈	1	1	yes	characteristic
161	C₂×C₄×C₆₁	#131	1	2	yes	—
162	C₂×C₄×C₆₁	C₂³×C₄	1	1	yes	characteristic
163	C₂²⋊D₆₁	—	2	4	no	—
164	C₂²⋊D₆₁	—	2	4	no	—
165	C₂²⋊D₆₁	—	4	2	no	—
166	C₂×Dic₆₁	C₂²×C₈	1	2	yes	—
167	C₂×Dic₆₁	C₂²×C₈	1	2	yes	—
168	C₂×Dic₆₁	C₂²×C₈	1	2	yes	—
169	D₂₄₄	—	2	2	no	—
170	C₄×D₆₁	—	2	2	no	—
171	C₄×D₆₁	—	2	2	no	—
172	Dic₁₂₂	—	2	2	no	—
173	C₈×C₆₁	—	2	1	no	—
174	C₈×C₆₁	—	2	1	no	—
175	C₈×C₆₁	C₄×D₄	1	2	yes	—
176	C₈×C₆₁	C₂²×D₄	1	1	yes	characteristic
177	C₈×C₆₁	C₂×#41	1	1	yes	characteristic
178	#92418	—	2	2	no	—
179	#92418	—	2	2	no	—
180	#33436	—	61	1	no	maximal, Sylow
181	C₂²×C₆₁	—	2	1	no	—
182	C₂²×C₆₁	—	2	1	no	—
183	C₂²×C₆₁	—	2	1	no	—
184	C₂²×C₆₁	—	2	1	no	—
185	C₂²×C₆₁	—	2	1	no	—
186	C₂²×C₆₁	—	2	1	no	—
187	C₂²×C₆₁	—	2	1	no	—
188	C₂²×C₆₁	—	4	4	no	—
189	C₂²×C₆₁	C₈×D₄	1	2	yes	—
190	C₂²×C₆₁	#504	1	2	yes	complemented
191	C₂²×C₆₁	C₂³×C₈	1	1	yes	characteristic
192	C₂×D₆₁	—	2	2	no	—
193	C₂×D₆₁	—	2	2	no	—
194	C₂×D₆₁	—	2	2	no	—
195	C₄×C₆₁	—	2	1	no	—
196	C₄×C₆₁	—	2	1	no	—
197	C₄×C₆₁	C₈×D₄	1	2	yes	—
198	C₄×C₆₁	C₂×C₄×D₄	1	1	yes	characteristic
199	C₄×C₆₁	C₂×#131	1	1	yes	characteristic
200	Dic₆₁	—	2	2	no	—
201	Dic₆₁	—	2	2	no	—
202	Dic₆₁	—	2	2	no	—
203	C₂×#504	—	61	1	no	—
204	C₂²×M₃₂	—	61	1	no	—
205	#2929	—	61	1	no	—
206	#2169	—	61	2	no	—
207	#2168	—	61	2	no	—
208	#2168	—	61	2	no	—
209	D₄×C₁₆	—	61	2	no	—
210	#2151	—	61	1	no	—
211	#2113	—	61	1	no	—
212	C₂×C₂²⋊C₁₆	D₆₁	1	1	yes	characteristic, complemented
213	#2108	—	61	1	no	—
214	C₂×C₆₁	—	2	2	no	—
215	C₂×C₆₁	—	2	2	no	—
216	C₂×C₆₁	—	4	1	no	—
217	C₂×C₆₁	C₂×C₈×D₄	1	1	yes	characteristic
218	C₂×C₆₁	C₂×#504	1	1	yes	characteristic
219	C₂×C₆₁	#3407	1	1	yes	characteristic
220	D₆₁	—	4	2	no	—
221	C₂×#131	—	61	1	no	—
222	C₂³×C₈	C₂×D₆₁	1	1	yes	characteristic
223	#525	—	61	1	no	—
224	#504	—	122	4	no	—
225	C₂×M₃₂	—	61	1	no	—
226	C₂×M₃₂	—	61	1	no	—
227	C₂×M₃₂	—	61	2	no	—
228	C₂×M₃₂	—	61	2	no	—
229	C₂×M₃₂	—	122	4	no	—
230	C₂²×C₁₆	—	61	2	no	—
231	C₂²×C₁₆	—	61	2	no	—
232	C₂²×C₁₆	C₂×D₆₁	1	1	yes	characteristic
233	C₂²×C₁₆	C₂×D₆₁	1	1	yes	characteristic
234	#435	—	61	2	no	—
235	#435	—	61	2	no	—
236	C₈×D₄	—	61	2	no	—
237	C₈×D₄	—	61	2	no	—
238	#424	—	61	1	no	—
239	#408	—	61	1	no	—
240	#407	—	61	1	no	—
241	#405	—	61	1	no	—
242	C₄⋊C₁₆	—	61	2	no	—
243	C₄⋊C₁₆	—	61	2	no	—
244	C₂²⋊C₁₆	—	61	2	no	—
245	C₂²⋊C₁₆	—	61	2	no	—
246	C₂²⋊C₁₆	C₂×D₆₁	1	1	yes	characteristic
247	C₂²⋊C₁₆	C₂×D₆₁	1	1	yes	characteristic
248	C₂²⋊C₁₆	C₂×D₆₁	1	1	yes	characteristic
249	C₂²⋊C₁₆	C₂×D₆₁	1	1	yes	characteristic
250	#346	—	61	2	no	—
251	C₄×C₁₆	—	61	2	no	—
252	C₆₁	#33436	1	1	yes	characteristic, complemented, Sylow
253	C₂×#41	—	61	1	no	—
254	C₂³×C₄	C₄×D₆₁	1	1	yes	characteristic
255	#131	—	122	2	no	—
256	#131	—	122	2	no	—
257	C₂×M₁₆	—	61	1	no	—
258	C₂×M₁₆	—	61	1	no	—
259	C₂×M₁₆	—	61	2	no	—
260	C₂²×C₈	—	2	2	no	—
261	C₂²×C₈	—	2	2	no	—
262	C₂²×C₈	—	61	2	no	—
263	C₂²×C₈	C₄×D₆₁	1	1	yes	characteristic
264	C₂²×C₈	C₄×D₆₁	1	1	yes	characteristic
265	C₂²×C₈	C₄×D₆₁	1	1	yes	characteristic
266	C₂²×C₈	C₂²×D₆₁	1	1	yes	characteristic
267	C₂²×C₈	C₂²×D₆₁	1	1	yes	characteristic
268	C₂²×C₈	C₂²×D₆₁	1	1	yes	characteristic
269	#123	—	61	2	no	—
270	C₂²⋊Q₈	—	61	1	no	—
271	C₂²⋊Q₈	—	61	1	no	—
272	#121	—	61	1	no	—
273	#121	—	61	1	no	—
274	#120	—	61	2	no	—
275	C₄×D₄	—	61	2	no	—
276	C₄×D₄	—	61	2	no	—
277	#117	—	61	1	no	—
278	M₃₂	—	61	4	no	—
279	M₃₂	—	122	4	no	—
280	M₃₂	—	122	4	no	—
281	M₃₂	—	122	2	no	—
282	C₂×C₁₆	—	2	2	no	—
283	C₂×C₁₆	—	2	2	no	—
284	C₂×C₁₆	—	61	2	no	—
285	C₂×C₁₆	—	61	2	no	—
286	C₂×C₁₆	—	122	4	no	—
287	C₂×C₁₆	—	122	4	no	—
288	C₂×C₁₆	C₂²×D₆₁	1	1	yes	characteristic
289	C₂×C₁₆	C₂²×D₆₁	1	1	yes	characteristic
290	C₂×C₁₆	C₂²×D₆₁	1	1	yes	characteristic
291	C₂×C₁₆	C₂²×D₆₁	1	1	yes	characteristic
292	C₄⋊C₈	—	61	2	no	—
293	C₄⋊C₈	—	61	2	no	—
294	C₂²⋊C₈	—	61	2	no	—
295	C₂²⋊C₈	—	61	2	no	—
296	C₂²⋊C₈	—	61	2	no	—
297	C₂²⋊C₈	—	61	2	no	—
298	#97	—	61	2	no	—
299	C₄×C₈	—	61	2	no	—
300	C₂⁴	C₈×D₆₁	1	1	yes	characteristic
301	#41	—	122	2	no	—
302	#41	—	122	2	no	—
303	C₂×Q₈	—	61	1	no	—
304	C₂×D₄	—	61	2	no	—
305	C₂×D₄	—	61	2	no	—
306	C₂×D₄	—	61	2	no	—
307	C₂×D₄	—	61	1	no	—
308	C₂²×C₄	—	2	2	no	—
309	C₂²×C₄	—	2	2	no	—
310	C₂²×C₄	—	61	2	no	—
311	C₂²×C₄	C₈×D₆₁	1	1	yes	characteristic
312	C₂²×C₄	C₈×D₆₁	1	1	yes	characteristic
313	C₂²×C₄	C₈×D₆₁	1	1	yes	characteristic
314	C₂²×C₄	C₂×C₄×D₆₁	1	1	yes	characteristic
315	C₂²×C₄	C₂×C₄×D₆₁	1	1	yes	characteristic
316	C₂²×C₄	C₂×C₄×D₆₁	1	1	yes	characteristic
317	M₁₆	—	122	2	no	—
318	M₁₆	—	122	2	no	—
319	M₁₆	—	122	4	no	—
320	C₂×C₈	—	2	2	no	—
321	C₂×C₈	—	2	1	no	—
322	C₂×C₈	—	2	1	no	—
323	C₂×C₈	—	2	1	no	—
324	C₂×C₈	—	2	1	no	—
325	C₂×C₈	—	2	2	no	—
326	C₂×C₈	—	2	2	no	—
327	C₂×C₈	—	61	2	no	—
328	C₂×C₈	—	61	2	no	—
329	C₂×C₈	—	122	2	no	—
330	C₂×C₈	—	122	2	no	—
331	C₂×C₈	C₂×C₄×D₆₁	1	1	yes	characteristic
332	C₂×C₈	C₂×C₄×D₆₁	1	1	yes	characteristic
333	C₂×C₈	C₂×C₄×D₆₁	1	1	yes	characteristic
334	C₂×C₈	D₄×D₆₁	1	2	yes	—
335	C₂×C₈	#11758224	1	2	yes	—
336	C₂×C₈	C₂³×D₆₁	1	1	yes	characteristic
337	C₄⋊C₄	—	61	2	no	—
338	C₄⋊C₄	—	61	2	no	—
339	C₄⋊C₄	—	61	1	no	—
340	C₄⋊C₄	—	61	1	no	—
341	C₂²⋊C₄	—	61	2	no	—
342	C₂²⋊C₄	—	61	2	no	—
343	C₂²⋊C₄	—	61	2	no	—
344	C₂²⋊C₄	—	61	2	no	—
345	C₂²⋊C₄	—	61	2	no	—
346	C₄²	—	61	2	no	—
347	C₁₆	—	2	1	no	—
348	C₁₆	—	2	1	no	—
349	C₁₆	—	2	1	no	—
350	C₁₆	—	2	1	no	—
351	C₁₆	—	61	4	no	—
352	C₁₆	—	122	2	no	—
353	C₂³	—	2	2	no	—
354	C₂³	—	2	2	no	—
355	C₂³	—	4	1	no	—
356	C₂³	—	61	2	no	—
357	C₂³	C₂×C₈×D₆₁	1	1	yes	characteristic
358	C₂³	C₂×C₈×D₆₁	1	1	yes	characteristic
359	C₂³	C₂×C₈×D₆₁	1	1	yes	characteristic
360	Q₈	—	122	2	no	—
361	D₄	—	122	4	no	—
362	D₄	—	122	4	no	—
363	D₄	—	122	2	no	—
364	D₄	—	244	2	no	—
365	C₂×C₄	—	2	2	no	—
366	C₂×C₄	—	2	1	no	—
367	C₂×C₄	—	2	1	no	—
368	C₂×C₄	—	2	1	no	—
369	C₂×C₄	—	2	1	no	—
370	C₂×C₄	—	2	2	no	—
371	C₂×C₄	—	2	2	no	—
372	C₂×C₄	—	61	2	no	—
373	C₂×C₄	—	61	2	no	—
374	C₂×C₄	—	61	2	no	—
375	C₂×C₄	—	122	2	no	—
376	C₂×C₄	—	122	2	no	—
377	C₂×C₄	#14519737	1	2	yes	—
378	C₂×C₄	C₂×C₈×D₆₁	1	1	yes	characteristic
379	C₂×C₄	C₂×C₈×D₆₁	1	1	yes	characteristic
380	C₂×C₄	C₂×C₈×D₆₁	1	1	yes	characteristic
381	C₂×C₄	#14519785	1	2	yes	—
382	C₂×C₄	C₂²×C₄×D₆₁	1	1	yes	characteristic
383	C₈	—	2	1	no	—
384	C₈	—	2	1	no	—
385	C₈	—	122	2	no	—
386	C₈	—	122	2	no	—
387	C₈	#14519737	1	2	yes	—
388	C₈	C₂×D₄×D₆₁	1	1	yes	characteristic
389	C₈	C₂×#11758224	1	1	yes	characteristic
390	C₂²	—	2	1	no	—
391	C₂²	—	2	1	no	—
392	C₂²	—	2	1	no	—
393	C₂²	—	2	1	no	—
394	C₂²	—	2	1	no	—
395	C₂²	—	2	1	no	—
396	C₂²	—	2	1	no	—
397	C₂²	—	4	4	no	—
398	C₂²	—	122	2	no	—
399	C₂²	—	122	2	no	—
400	C₂²	—	122	2	no	—
401	C₂²	#16839825	1	2	yes	—
402	C₂²	#16840178	1	2	yes	complemented
403	C₂²	C₂²×C₈×D₆₁	1	1	yes	characteristic
404	C₄	—	2	1	no	—
405	C₄	—	2	1	no	—
406	C₄	—	122	2	no	—
407	C₄	—	122	2	no	—
408	C₄	—	122	2	no	—
409	C₄	#16839825	1	2	yes	—
410	C₄	C₂×#14519737	1	1	yes	characteristic
411	C₄	C₂×#14519785	1	1	yes	characteristic
412	C₂	—	2	2	no	—
413	C₂	—	2	2	no	—
414	C₂	—	4	1	no	—
415	C₂	—	244	2	no	—
416	C₂	C₂×#16839825	1	1	yes	characteristic
417	C₂	C₂×#16840178	1	1	yes	characteristic
418	C₂	#21458921	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₈	C₂³×D₆₁
commutator, socle	C₂²×C₆₁	C₂³×C₈
Fitting	C₂×C₆₁×C₂²⋊C₁₆	C₂
prime radical	#16840273	C₄
cosocle	C₂×C₈×C₆₁	C₂⁴
hypercenter	C₂×C₂²⋊C₁₆	D₆₁
hypocenter	C₆₁	#33436
LCS	G ▷ C₂²×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂×C₈ ◁ C₂×C₂²⋊C₁₆

Complements

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

N	H ≅ G/N	type
1. C₂×#16840178	C₂	semidirect
2. C₂²×#14519717	C₂	semidirect
4. #21447648	C₂	semidirect
5. #21447647	C₂	semidirect
6. #21447641	C₂	semidirect
7. #21447636	C₂	semidirect
8. #21447577	C₂	semidirect
9. #21447432	C₂	semidirect
10. #21447415	C₂	semidirect
11. C₂×C₆₁×C₂²⋊C₁₆	C₂	semidirect
19. C₂×#14519716	C₂²	semidirect
21. C₂×C₁₆×D₆₁	C₂²	semidirect
30. #16839580	C₂²	semidirect
31. #16839580	C₂²	semidirect
32. #16839541	C₂²	semidirect
33. #16839541	C₂²	semidirect
34. #16839537	C₂²	semidirect
35. C₁₆×Dic₆₁	C₂²	semidirect
61. #14519717	D₄	semidirect
190. C₂²×C₆₁	#504	semidirect
212. C₂×C₂²⋊C₁₆	D₆₁	semidirect
252. C₆₁	#33436	semidirect
402. C₂²	#16840178	semidirect

Maximal subgroups

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

subgroup	index
C₂×#16840178	2
C₂²×#14519717	2
#21454513	2
#21447648	2
#21447647	2
#21447641	2
#21447636	2
#21447577	2
#21447432	2
#21447415	2
C₂×C₆₁×C₂²⋊C₁₆	2
#33436	61