Subgroups — C₄₁×#9262 #23785463

Order 10496.

750 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	C₂×C₄₁×#448	C₂	1	1	yes	maximal, characteristic
2	Q₈×C₂²⋊C₄×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₁×#1964	C₂	1	1	yes	maximal, characteristic
4	C₄₁×#1787	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₁×#1519	C₂	1	1	yes	maximal, characteristic
6	C₄₁×#1289	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₁×#1282	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂³×Q₈×C₄₁	C₂²	1	1	yes	characteristic
9	C₂²×SD₁₆×C₄₁	C₄	1	2	yes	complemented
10	C₂×#121×C₄₁	C₂²	1	1	yes	characteristic
11	C₂×C₄×Q₈×C₄₁	—	2	1	no	—
12	C₄₁×#448	—	2	1	no	—
13	C₄₁×#448	—	2	2	no	—
14	C₄₁×#448	—	2	1	no	—
15	C₂×#103×C₄₁	—	2	2	no	—
16	C₂×#103×C₄₁	C₄	1	2	yes	complemented
17	C₂×#99×C₄₁	—	2	1	no	—
18	C₂×#99×C₄₁	—	2	1	no	—
19	C₂×C₂²⋊C₈×C₄₁	C₂²	1	1	yes	characteristic
20	C₂×C₂²⋊C₈×C₄₁	C₂²	1	1	yes	characteristic
21	C₄₁×#391	—	2	1	no	—
22	C₄₁×#391	—	2	2	no	—
23	C₄₁×#380	—	2	1	no	—
24	C₄₁×#380	C₂²	1	1	yes	characteristic
25	C₄₁×#380	C₂²	1	1	yes	characteristic
26	C₄×C₂²⋊C₄×C₄₁	—	2	1	no	—
27	C₄×C₂²⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
28	C₄₁×#327	—	2	2	no	—
29	C₂²×Q₈×C₄₁	—	2	1	no	—
30	C₂²×Q₈×C₄₁	—	2	1	no	—
31	C₂²×Q₈×C₄₁	—	2	1	no	—
32	C₂²×Q₈×C₄₁	—	4	4	no	—
33	C₂²×Q₈×C₄₁	C₂×C₄	1	2	yes	—
34	C₂²×Q₈×C₄₁	D₄	1	1	yes	characteristic
35	C₂²×Q₈×C₄₁	D₄	1	2	yes	—
36	C₂²×Q₈×C₄₁	D₄	1	1	yes	characteristic
37	C₂²×D₄×C₄₁	—	2	1	no	—
38	C₂²×D₄×C₄₁	C₂×C₄	1	1	yes	characteristic
39	C₂³×C₄×C₄₁	—	2	1	no	—
40	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
41	C₂×SD₁₆×C₄₁	—	2	2	no	—
42	C₂×SD₁₆×C₄₁	—	2	2	no	—
43	C₂×SD₁₆×C₄₁	—	4	4	no	—
44	C₂²×C₈×C₄₁	—	2	1	no	—
45	C₂²×C₈×C₄₁	C₂×C₄	1	2	yes	—
46	#121×C₄₁	—	2	1	no	—
47	#121×C₄₁	—	2	1	no	—
48	#121×C₄₁	—	2	1	no	—
49	#121×C₄₁	—	2	1	no	—
50	C₄×Q₈×C₄₁	—	4	4	no	—
51	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
52	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
53	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
54	C₂×C₄⋊C₄×C₄₁	C₂×C₄	1	1	yes	characteristic
55	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
56	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
57	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
58	C₂×C₂²⋊C₄×C₄₁	D₄	1	1	yes	characteristic
59	C₂×C₂²⋊C₄×C₄₁	D₄	1	1	yes	characteristic
60	C₂×C₄²×C₄₁	—	2	2	no	—
61	C₂×C₄²×C₄₁	—	2	1	no	—
62	#103×C₄₁	—	2	2	no	—
63	#103×C₄₁	—	2	2	no	—
64	#103×C₄₁	—	4	4	no	—
65	#99×C₄₁	—	4	2	no	—
66	#99×C₄₁	—	4	2	no	—
67	C₂²⋊C₈×C₄₁	—	2	1	no	—
68	C₂²⋊C₈×C₄₁	—	2	1	no	—
69	C₂²⋊C₈×C₄₁	—	2	1	no	—
70	C₂²⋊C₈×C₄₁	—	2	1	no	—
71	#95×C₄₁	—	2	2	no	—
72	#95×C₄₁	—	2	2	no	—
73	#95×C₄₁	—	2	1	no	—
74	#95×C₄₁	—	2	1	no	—
75	#95×C₄₁	D₄	1	2	yes	—
76	C₂⁴×C₄₁	—	2	1	no	—
77	C₂⁴×C₄₁	C₂×D₄	1	1	yes	characteristic
78	C₂×Q₈×C₄₁	—	2	4	no	—
79	C₂×Q₈×C₄₁	—	2	2	no	—
80	C₂×Q₈×C₄₁	—	2	2	no	—
81	C₂×Q₈×C₄₁	—	2	1	no	—
82	C₂×Q₈×C₄₁	—	2	1	no	—
83	C₂×Q₈×C₄₁	—	2	4	no	—
84	C₂×Q₈×C₄₁	—	2	4	no	—
85	C₂×Q₈×C₄₁	—	4	2	no	—
86	C₂×Q₈×C₄₁	—	4	2	no	—
87	C₂×Q₈×C₄₁	—	4	2	no	—
88	C₂×Q₈×C₄₁	—	4	4	no	—
89	C₂×Q₈×C₄₁	—	4	4	no	—
90	C₂×Q₈×C₄₁	—	4	4	no	—
91	C₂×Q₈×C₄₁	C₂²⋊C₄	1	2	yes	—
92	C₂×Q₈×C₄₁	C₂²⋊C₄	1	2	yes	—
93	C₂×D₄×C₄₁	—	2	1	no	—
94	C₂×D₄×C₄₁	—	2	1	no	—
95	C₂×D₄×C₄₁	—	4	2	no	—
96	C₂×D₄×C₄₁	—	4	1	no	—
97	C₂×D₄×C₄₁	—	4	1	no	—
98	C₂×D₄×C₄₁	—	4	1	no	—
99	C₂×D₄×C₄₁	—	4	1	no	—
100	C₂×D₄×C₄₁	—	4	1	no	—
101	C₂×D₄×C₄₁	—	4	1	no	—
102	C₂²×C₄×C₄₁	—	2	1	no	—
103	C₂²×C₄×C₄₁	—	2	2	no	—
104	C₂²×C₄×C₄₁	—	2	1	no	—
105	C₂²×C₄×C₄₁	—	2	1	no	—
106	C₂²×C₄×C₄₁	—	2	2	no	—
107	C₂²×C₄×C₄₁	—	2	1	no	—
108	C₂²×C₄×C₄₁	—	2	1	no	—
109	C₂²×C₄×C₄₁	—	2	2	no	—
110	C₂²×C₄×C₄₁	—	4	2	no	—
111	C₂²×C₄×C₄₁	—	4	4	no	—
112	C₂²×C₄×C₄₁	—	4	1	no	—
113	C₂²×C₄×C₄₁	C₂²×C₄	1	1	yes	characteristic
114	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
115	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
116	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
117	C₂²×C₄×C₄₁	#41	1	1	yes	characteristic
118	C₂²×C₄×C₄₁	#41	1	1	yes	characteristic
119	SD₁₆×C₄₁	—	4	4	no	—
120	SD₁₆×C₄₁	—	4	4	no	—
121	C₂×C₈×C₄₁	—	2	2	no	—
122	C₂×C₈×C₄₁	—	4	2	no	—
123	C₂×C₈×C₄₁	—	4	2	no	—
124	C₂×C₈×C₄₁	—	4	1	no	—
125	C₄⋊C₄×C₄₁	—	2	1	no	—
126	C₄⋊C₄×C₄₁	—	2	1	no	—
127	C₄⋊C₄×C₄₁	—	4	4	no	—
128	C₄⋊C₄×C₄₁	—	4	2	no	—
129	C₄⋊C₄×C₄₁	—	4	2	no	—
130	C₂²⋊C₄×C₄₁	—	2	1	no	—
131	C₂²⋊C₄×C₄₁	—	2	1	no	—
132	C₂²⋊C₄×C₄₁	—	2	1	no	—
133	C₂²⋊C₄×C₄₁	—	4	1	no	—
134	C₂²⋊C₄×C₄₁	—	4	1	no	—
135	C₂²⋊C₄×C₄₁	—	4	1	no	—
136	C₂²⋊C₄×C₄₁	—	4	1	no	—
137	C₂²⋊C₄×C₄₁	—	4	1	no	—
138	C₂²⋊C₄×C₄₁	—	4	1	no	—
139	C₂²⋊C₄×C₄₁	SD₁₆	1	2	yes	complemented
140	C₄²×C₄₁	—	4	4	no	—
141	C₄²×C₄₁	—	4	2	no	—
142	C₂³×C₄₁	—	4	1	no	—
143	C₂³×C₄₁	—	4	1	no	—
144	C₂³×C₄₁	—	4	1	no	—
145	C₂³×C₄₁	—	4	1	no	—
146	C₂³×C₄₁	—	4	1	no	—
147	C₂³×C₄₁	—	8	1	no	—
148	C₂³×C₄₁	—	8	1	no	—
149	C₂³×C₄₁	C₄×D₄	1	1	yes	characteristic
150	C₂³×C₄₁	#120	1	1	yes	characteristic
151	C₂³×C₄₁	#121	1	1	yes	characteristic
152	C₂³×C₄₁	C₂×SD₁₆	1	1	yes	characteristic
153	C₂³×C₄₁	#135	1	1	yes	characteristic
154	C₂³×C₄₁	AGL(1,ℤ/8)	1	1	yes	characteristic
155	C₂³×C₄₁	#137	1	1	yes	characteristic
156	Q₈×C₄₁	—	2	4	no	—
157	Q₈×C₄₁	—	2	2	no	—
158	Q₈×C₄₁	—	2	2	no	—
159	Q₈×C₄₁	—	2	2	no	—
160	Q₈×C₄₁	—	4	4	no	—
161	Q₈×C₄₁	—	4	4	no	—
162	Q₈×C₄₁	—	4	2	no	—
163	Q₈×C₄₁	#99	1	4	yes	complemented
164	D₄×C₄₁	—	4	2	no	—
165	D₄×C₄₁	—	8	1	no	—
166	D₄×C₄₁	—	8	1	no	—
167	D₄×C₄₁	—	8	1	no	—
168	D₄×C₄₁	—	8	1	no	—
169	D₄×C₄₁	—	8	1	no	—
170	C₂×C₄×C₄₁	—	2	4	no	—
171	C₂×C₄×C₄₁	—	2	2	no	—
172	C₂×C₄×C₄₁	—	2	2	no	—
173	C₂×C₄×C₄₁	—	2	2	no	—
174	C₂×C₄×C₄₁	—	2	2	no	—
175	C₂×C₄×C₄₁	—	2	2	no	—
176	C₂×C₄×C₄₁	—	2	2	no	—
177	C₂×C₄×C₄₁	—	4	1	no	—
178	C₂×C₄×C₄₁	—	4	1	no	—
179	C₂×C₄×C₄₁	—	4	1	no	—
180	C₂×C₄×C₄₁	—	4	4	no	—
181	C₂×C₄×C₄₁	—	4	4	no	—
182	C₂×C₄×C₄₁	—	4	1	no	—
183	C₂×C₄×C₄₁	—	4	1	no	—
184	C₂×C₄×C₄₁	—	4	2	no	—
185	C₂×C₄×C₄₁	—	4	1	no	—
186	C₂×C₄×C₄₁	—	4	2	no	—
187	C₂×C₄×C₄₁	—	4	1	no	—
188	C₂×C₄×C₄₁	—	4	2	no	—
189	C₂×C₄×C₄₁	—	4	1	no	—
190	C₂×C₄×C₄₁	—	4	1	no	—
191	C₂×C₄×C₄₁	—	4	1	no	—
192	C₂×C₄×C₄₁	—	4	1	no	—
193	C₂×C₄×C₄₁	—	4	2	no	—
194	C₂×C₄×C₄₁	—	8	1	no	—
195	C₂×C₄×C₄₁	—	8	1	no	—
196	C₂×C₄×C₄₁	—	8	1	no	—
197	C₂×C₄×C₄₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
198	C₂×C₄×C₄₁	C₄×D₄	1	1	yes	characteristic
199	C₂×C₄×C₄₁	#121	1	1	yes	characteristic
200	C₂×C₄×C₄₁	#123	1	1	yes	characteristic
201	C₈×C₄₁	—	4	2	no	—
202	C₈×C₄₁	—	8	1	no	—
203	#9262	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
204	C₂²×C₄₁	—	2	1	no	—
205	C₂²×C₄₁	—	2	1	no	—
206	C₂²×C₄₁	—	2	1	no	—
207	C₂²×C₄₁	—	2	1	no	—
208	C₂²×C₄₁	—	2	1	no	—
209	C₂²×C₄₁	—	2	1	no	—
210	C₂²×C₄₁	—	4	1	no	—
211	C₂²×C₄₁	—	4	1	no	—
212	C₂²×C₄₁	—	4	1	no	—
213	C₂²×C₄₁	—	4	1	no	—
214	C₂²×C₄₁	—	8	1	no	—
215	C₂²×C₄₁	—	8	1	no	—
216	C₂²×C₄₁	—	8	1	no	—
217	C₂²×C₄₁	—	16	1	no	—
218	C₂²×C₄₁	—	16	1	no	—
219	C₂²×C₄₁	#386	1	1	yes	characteristic
220	C₂²×C₄₁	C₄×SD₁₆	1	1	yes	characteristic
221	C₂²×C₄₁	#440	1	1	yes	characteristic
222	C₂²×C₄₁	#448	1	1	yes	characteristic
223	C₂²×C₄₁	#449	1	1	yes	characteristic
224	C₂²×C₄₁	#460	1	1	yes	characteristic
225	C₂²×C₄₁	#464	1	1	yes	characteristic
226	C₄×C₄₁	—	2	1	no	—
227	C₄×C₄₁	—	2	4	no	—
228	C₄×C₄₁	—	2	1	no	—
229	C₄×C₄₁	—	2	1	no	—
230	C₄×C₄₁	—	4	2	no	—
231	C₄×C₄₁	—	4	2	no	—
232	C₄×C₄₁	—	8	1	no	—
233	C₄×C₄₁	—	8	2	no	—
234	C₄×C₄₁	—	8	1	no	—
235	C₄×C₄₁	—	16	1	no	—
236	C₄×C₄₁	C₂×#99	1	2	yes	—
237	C₂×#448	C₂×C₄₁	1	1	yes	characteristic
238	Q₈×C₂²⋊C₄	C₂×C₄₁	1	1	yes	characteristic, complemented
239	#1964	C₂×C₄₁	1	1	yes	characteristic
240	#1787	C₂×C₄₁	1	1	yes	characteristic, complemented
241	#1519	C₂×C₄₁	1	1	yes	characteristic
242	#1289	C₂×C₄₁	1	1	yes	characteristic, complemented
243	#1282	C₂×C₄₁	1	1	yes	characteristic, complemented
244	C₂×C₄₁	—	2	1	no	—
245	C₂×C₄₁	—	2	1	no	—
246	C₂×C₄₁	—	2	1	no	—
247	C₂×C₄₁	—	2	1	no	—
248	C₂×C₄₁	—	2	1	no	—
249	C₂×C₄₁	—	2	1	no	—
250	C₂×C₄₁	—	16	1	no	—
251	C₂×C₄₁	#1880	1	1	yes	characteristic
252	C₂×C₄₁	#1898	1	1	yes	characteristic
253	C₂×C₄₁	#1905	1	1	yes	characteristic
254	C₂³×Q₈	C₂²×C₄₁	1	1	yes	characteristic
255	C₂²×SD₁₆	C₄×C₄₁	1	2	yes	complemented
256	C₂×#121	C₂²×C₄₁	1	1	yes	characteristic
257	C₂×C₄×Q₈	—	2	1	no	—
258	#448	—	2	1	no	—
259	#448	—	2	2	no	—
260	#448	—	2	1	no	—
261	C₂×#103	—	2	2	no	—
262	C₂×#103	C₄×C₄₁	1	2	yes	complemented
263	C₂×#99	—	2	1	no	—
264	C₂×#99	—	2	1	no	—
265	C₂×C₂²⋊C₈	C₂²×C₄₁	1	1	yes	characteristic
266	C₂×C₂²⋊C₈	C₂²×C₄₁	1	1	yes	characteristic
267	#391	—	2	1	no	—
268	#391	—	2	2	no	—
269	#380	—	2	1	no	—
270	#380	C₂²×C₄₁	1	1	yes	characteristic
271	#380	C₂²×C₄₁	1	1	yes	characteristic
272	C₄×C₂²⋊C₄	—	2	1	no	—
273	C₄×C₂²⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
274	#327	—	2	2	no	—
275	C₄₁	#9262	1	1	yes	characteristic, direct product factor, Sylow
276	C₂²×Q₈	—	2	1	no	—
277	C₂²×Q₈	—	2	1	no	—
278	C₂²×Q₈	—	2	1	no	—
279	C₂²×Q₈	—	4	4	no	—
280	C₂²×Q₈	C₂×C₄×C₄₁	1	2	yes	—
281	C₂²×Q₈	D₄×C₄₁	1	1	yes	characteristic
282	C₂²×Q₈	D₄×C₄₁	1	2	yes	—
283	C₂²×Q₈	D₄×C₄₁	1	1	yes	characteristic
284	C₂²×D₄	—	2	1	no	—
285	C₂²×D₄	C₂×C₄×C₄₁	1	1	yes	characteristic
286	C₂³×C₄	—	2	1	no	—
287	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
288	C₂×SD₁₆	—	2	2	no	—
289	C₂×SD₁₆	—	2	2	no	—
290	C₂×SD₁₆	—	4	4	no	—
291	C₂²×C₈	—	2	1	no	—
292	C₂²×C₈	C₂×C₄×C₄₁	1	2	yes	—
293	#121	—	2	1	no	—
294	#121	—	2	1	no	—
295	#121	—	2	1	no	—
296	#121	—	2	1	no	—
297	C₄×Q₈	—	4	4	no	—
298	C₂×C₄⋊C₄	—	2	2	no	—
299	C₂×C₄⋊C₄	—	2	1	no	—
300	C₂×C₄⋊C₄	—	2	1	no	—
301	C₂×C₄⋊C₄	C₂×C₄×C₄₁	1	1	yes	characteristic
302	C₂×C₂²⋊C₄	—	2	1	no	—
303	C₂×C₂²⋊C₄	—	2	1	no	—
304	C₂×C₂²⋊C₄	—	2	1	no	—
305	C₂×C₂²⋊C₄	D₄×C₄₁	1	1	yes	characteristic
306	C₂×C₂²⋊C₄	D₄×C₄₁	1	1	yes	characteristic
307	C₂×C₄²	—	2	2	no	—
308	C₂×C₄²	—	2	1	no	—
309	#103	—	2	2	no	—
310	#103	—	2	2	no	—
311	#103	—	4	4	no	—
312	#99	—	4	2	no	—
313	#99	—	4	2	no	—
314	C₂²⋊C₈	—	2	1	no	—
315	C₂²⋊C₈	—	2	1	no	—
316	C₂²⋊C₈	—	2	1	no	—
317	C₂²⋊C₈	—	2	1	no	—
318	#95	—	2	2	no	—
319	#95	—	2	2	no	—
320	#95	—	2	1	no	—
321	#95	—	2	1	no	—
322	#95	D₄×C₄₁	1	2	yes	—
323	C₂⁴	—	2	1	no	—
324	C₂⁴	C₂×D₄×C₄₁	1	1	yes	characteristic
325	C₂×Q₈	—	2	4	no	—
326	C₂×Q₈	—	2	2	no	—
327	C₂×Q₈	—	2	2	no	—
328	C₂×Q₈	—	2	1	no	—
329	C₂×Q₈	—	2	1	no	—
330	C₂×Q₈	—	2	4	no	—
331	C₂×Q₈	—	2	4	no	—
332	C₂×Q₈	—	4	2	no	—
333	C₂×Q₈	—	4	2	no	—
334	C₂×Q₈	—	4	2	no	—
335	C₂×Q₈	—	4	4	no	—
336	C₂×Q₈	—	4	4	no	—
337	C₂×Q₈	—	4	4	no	—
338	C₂×Q₈	C₂²⋊C₄×C₄₁	1	2	yes	—
339	C₂×Q₈	C₂²⋊C₄×C₄₁	1	2	yes	—
340	C₂×D₄	—	2	1	no	—
341	C₂×D₄	—	2	1	no	—
342	C₂×D₄	—	4	2	no	—
343	C₂×D₄	—	4	1	no	—
344	C₂×D₄	—	4	1	no	—
345	C₂×D₄	—	4	1	no	—
346	C₂×D₄	—	4	1	no	—
347	C₂×D₄	—	4	1	no	—
348	C₂×D₄	—	4	1	no	—
349	C₂²×C₄	—	2	1	no	—
350	C₂²×C₄	—	2	2	no	—
351	C₂²×C₄	—	2	1	no	—
352	C₂²×C₄	—	2	1	no	—
353	C₂²×C₄	—	2	2	no	—
354	C₂²×C₄	—	2	1	no	—
355	C₂²×C₄	—	2	1	no	—
356	C₂²×C₄	—	2	2	no	—
357	C₂²×C₄	—	4	2	no	—
358	C₂²×C₄	—	4	4	no	—
359	C₂²×C₄	—	4	1	no	—
360	C₂²×C₄	C₂²×C₄×C₄₁	1	1	yes	characteristic
361	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
362	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
363	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
364	C₂²×C₄	#41×C₄₁	1	1	yes	characteristic
365	C₂²×C₄	#41×C₄₁	1	1	yes	characteristic
366	SD₁₆	—	4	4	no	—
367	SD₁₆	—	4	4	no	—
368	C₂×C₈	—	2	2	no	—
369	C₂×C₈	—	4	2	no	—
370	C₂×C₈	—	4	2	no	—
371	C₂×C₈	—	4	1	no	—
372	C₄⋊C₄	—	2	1	no	—
373	C₄⋊C₄	—	2	1	no	—
374	C₄⋊C₄	—	4	4	no	—
375	C₄⋊C₄	—	4	2	no	—
376	C₄⋊C₄	—	4	2	no	—
377	C₂²⋊C₄	—	2	1	no	—
378	C₂²⋊C₄	—	2	1	no	—
379	C₂²⋊C₄	—	2	1	no	—
380	C₂²⋊C₄	—	4	1	no	—
381	C₂²⋊C₄	—	4	1	no	—
382	C₂²⋊C₄	—	4	1	no	—
383	C₂²⋊C₄	—	4	1	no	—
384	C₂²⋊C₄	—	4	1	no	—
385	C₂²⋊C₄	—	4	1	no	—
386	C₂²⋊C₄	SD₁₆×C₄₁	1	2	yes	complemented
387	C₄²	—	4	4	no	—
388	C₄²	—	4	2	no	—
389	C₂³	—	4	1	no	—
390	C₂³	—	4	1	no	—
391	C₂³	—	4	1	no	—
392	C₂³	—	4	1	no	—
393	C₂³	—	4	1	no	—
394	C₂³	—	8	1	no	—
395	C₂³	—	8	1	no	—
396	C₂³	C₄×D₄×C₄₁	1	1	yes	characteristic
397	C₂³	#120×C₄₁	1	1	yes	characteristic
398	C₂³	#121×C₄₁	1	1	yes	characteristic
399	C₂³	C₂×SD₁₆×C₄₁	1	1	yes	characteristic
400	C₂³	#135×C₄₁	1	1	yes	characteristic
401	C₂³	AGL(1,ℤ/8)×C₄₁	1	1	yes	characteristic
402	C₂³	#137×C₄₁	1	1	yes	characteristic
403	Q₈	—	2	4	no	—
404	Q₈	—	2	2	no	—
405	Q₈	—	2	2	no	—
406	Q₈	—	2	2	no	—
407	Q₈	—	4	4	no	—
408	Q₈	—	4	4	no	—
409	Q₈	—	4	2	no	—
410	Q₈	#99×C₄₁	1	4	yes	complemented
411	D₄	—	4	2	no	—
412	D₄	—	8	1	no	—
413	D₄	—	8	1	no	—
414	D₄	—	8	1	no	—
415	D₄	—	8	1	no	—
416	D₄	—	8	1	no	—
417	C₂×C₄	—	2	4	no	—
418	C₂×C₄	—	2	2	no	—
419	C₂×C₄	—	2	2	no	—
420	C₂×C₄	—	2	2	no	—
421	C₂×C₄	—	2	2	no	—
422	C₂×C₄	—	2	2	no	—
423	C₂×C₄	—	2	2	no	—
424	C₂×C₄	—	4	1	no	—
425	C₂×C₄	—	4	1	no	—
426	C₂×C₄	—	4	1	no	—
427	C₂×C₄	—	4	4	no	—
428	C₂×C₄	—	4	4	no	—
429	C₂×C₄	—	4	1	no	—
430	C₂×C₄	—	4	2	no	—
431	C₂×C₄	—	4	1	no	—
432	C₂×C₄	—	4	1	no	—
433	C₂×C₄	—	4	2	no	—
434	C₂×C₄	—	4	1	no	—
435	C₂×C₄	—	4	2	no	—
436	C₂×C₄	—	4	1	no	—
437	C₂×C₄	—	4	1	no	—
438	C₂×C₄	—	4	1	no	—
439	C₂×C₄	—	4	1	no	—
440	C₂×C₄	—	4	2	no	—
441	C₂×C₄	—	8	1	no	—
442	C₂×C₄	—	8	1	no	—
443	C₂×C₄	—	8	1	no	—
444	C₂×C₄	C₂×C₂²⋊C₄×C₄₁	1	1	yes	characteristic
445	C₂×C₄	C₄×D₄×C₄₁	1	1	yes	characteristic
446	C₂×C₄	#121×C₄₁	1	1	yes	characteristic
447	C₂×C₄	#123×C₄₁	1	1	yes	characteristic
448	C₈	—	4	2	no	—
449	C₈	—	8	1	no	—
450	C₂²	—	2	1	no	—
451	C₂²	—	2	1	no	—
452	C₂²	—	2	1	no	—
453	C₂²	—	2	1	no	—
454	C₂²	—	2	1	no	—
455	C₂²	—	2	1	no	—
456	C₂²	—	4	1	no	—
457	C₂²	—	4	1	no	—
458	C₂²	—	4	1	no	—
459	C₂²	—	4	1	no	—
460	C₂²	—	8	1	no	—
461	C₂²	—	8	1	no	—
462	C₂²	—	8	1	no	—
463	C₂²	—	16	1	no	—
464	C₂²	—	16	1	no	—
465	C₂²	C₄₁×#386	1	1	yes	characteristic
466	C₂²	C₄×SD₁₆×C₄₁	1	1	yes	characteristic
467	C₂²	C₄₁×#440	1	1	yes	characteristic
468	C₂²	C₄₁×#448	1	1	yes	characteristic
469	C₂²	C₄₁×#449	1	1	yes	characteristic
470	C₂²	C₄₁×#460	1	1	yes	characteristic
471	C₂²	C₄₁×#464	1	1	yes	characteristic
472	C₄	—	2	1	no	—
473	C₄	—	2	4	no	—
474	C₄	—	2	1	no	—
475	C₄	—	2	1	no	—
476	C₄	—	4	2	no	—
477	C₄	—	4	2	no	—
478	C₄	—	8	1	no	—
479	C₄	—	8	2	no	—
480	C₄	—	8	1	no	—
481	C₄	—	16	1	no	—
482	C₄	C₂×#99×C₄₁	1	2	yes	—
483	C₂	—	2	1	no	—
484	C₂	—	2	1	no	—
485	C₂	—	2	1	no	—
486	C₂	—	2	1	no	—
487	C₂	—	2	1	no	—
488	C₂	—	2	1	no	—
489	C₂	—	16	1	no	—
490	C₂	C₄₁×#1880	1	1	yes	characteristic
491	C₂	C₄₁×#1898	1	1	yes	characteristic
492	C₂	C₄₁×#1905	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₄₁	#386
commutator	C₂²×C₄	C₂²×C₄×C₄₁
Frattini, cosocle	C₂³×C₄	C₂³×C₄₁
prime radical	C₂×#121×C₄₁	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₄₁ ◁ C₂³×C₄×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. Q₈×C₂²⋊C₄×C₄₁	C₂	semidirect
4. C₄₁×#1787	C₂	semidirect
6. C₄₁×#1289	C₂	semidirect
7. C₄₁×#1282	C₂	semidirect
9. C₂²×SD₁₆×C₄₁	C₄	semidirect
16. C₂×#103×C₄₁	C₄	semidirect
139. C₂²⋊C₄×C₄₁	SD₁₆	semidirect
163. Q₈×C₄₁	#99	semidirect
203. #9262	C₄₁	direct (N × H)
238. Q₈×C₂²⋊C₄	C₂×C₄₁	semidirect
240. #1787	C₂×C₄₁	semidirect
242. #1289	C₂×C₄₁	semidirect
243. #1282	C₂×C₄₁	semidirect
255. C₂²×SD₁₆	C₄×C₄₁	semidirect
262. C₂×#103	C₄×C₄₁	semidirect
275. C₄₁	#9262	direct (N × H)
386. C₂²⋊C₄	SD₁₆×C₄₁	semidirect
410. Q₈	#99×C₄₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄₁×#448	2
Q₈×C₂²⋊C₄×C₄₁	2
C₄₁×#1964	2
C₄₁×#1787	2
C₄₁×#1519	2
C₄₁×#1289	2
C₄₁×#1282	2
#9262	41

Subgroups — C41×#9262 #23785463

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#9262 #23785463