Subgroups — C₄₁×#33042 #23809243

Order 10496.

1106 conjugacy classes of subgroups.

The subgroup lattice has 488 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₁×#486	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₄×C₈×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₁×#2857	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₁×#2856	C₂	1	1	yes	maximal, characteristic
5	C₄₁×#1990	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄₁×#1957	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₁×#1934	C₂	1	4	yes	maximal, complemented
8	C₄₁×#1893	C₂	1	4	yes	maximal, complemented
9	C₄₁×#1834	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂³×C₈×C₄₁	C₂²	1	2	yes	—
11	C₂×C₄⋊Q₈×C₄₁	C₂²	1	1	yes	characteristic
12	C₂×#127×C₄₁	C₂²	1	1	yes	characteristic
13	C₂×C₂²⋊Q₈×C₄₁	—	2	1	no	—
14	C₂×#121×C₄₁	—	2	1	no	—
15	C₂×#121×C₄₁	—	2	1	no	—
16	C₂×#121×C₄₁	C₂²	1	2	yes	—
17	C₂²×C₄²×C₄₁	C₂²	1	1	yes	characteristic
18	C₄₁×#486	—	2	4	no	—
19	C₂×#102×C₄₁	C₂²	1	4	yes	—
20	C₂×#102×C₄₁	C₂²	1	4	yes	—
21	C₂×C₄×C₈×C₄₁	—	2	4	no	—
22	C₂×C₄×C₈×C₄₁	C₂²	1	2	yes	—
23	C₂×C₄×C₈×C₄₁	C₂²	1	1	yes	characteristic
24	C₂×C₄×C₈×C₄₁	C₂²	1	1	yes	characteristic
25	C₄₁×#391	—	2	1	no	—
26	C₄₁×#390	—	2	1	no	—
27	C₄₁×#390	—	2	1	no	—
28	C₄₁×#390	C₂²	1	2	yes	—
29	C₄₁×#389	—	2	1	no	—
30	C₄₁×#389	C₂²	1	2	yes	—
31	C₄₁×#384	C₂²	1	1	yes	characteristic
32	C₄₁×#384	C₂²	1	1	yes	characteristic
33	C₄₁×#380	—	2	1	no	—
34	C₄₁×#380	C₂²	1	2	yes	—
35	C₄₁×#340	C₂²	1	4	yes	—
36	C₄₁×#340	C₂²	1	4	yes	—
37	C₂²×Q₈×C₄₁	—	2	1	no	—
38	C₂²×D₄×C₄₁	—	2	2	no	—
39	C₂²×D₄×C₄₁	—	2	1	no	—
40	C₂²×D₄×C₄₁	—	2	1	no	—
41	C₂²×D₄×C₄₁	C₂³	1	2	yes	—
42	C₂³×C₄×C₄₁	D₄	1	1	yes	characteristic
43	C₂³×C₄×C₄₁	D₄	1	1	yes	characteristic
44	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
45	C₂²×C₈×C₄₁	—	2	4	no	—
46	C₂²×C₈×C₄₁	—	2	4	no	—
47	C₂²×C₈×C₄₁	—	2	4	no	—
48	C₂²×C₈×C₄₁	C₂³	1	2	yes	—
49	C₂²×C₈×C₄₁	C₂³	1	2	yes	—
50	C₄⋊Q₈×C₄₁	—	2	2	no	—
51	C₄⋊Q₈×C₄₁	—	2	2	no	—
52	#127×C₄₁	—	2	2	no	—
53	#127×C₄₁	—	2	2	no	—
54	C₂²⋊Q₈×C₄₁	—	4	4	no	—
55	#121×C₄₁	—	2	8	no	—
56	#121×C₄₁	—	4	4	no	—
57	#121×C₄₁	—	4	4	no	—
58	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
59	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
60	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
61	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
62	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
63	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
64	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
65	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
66	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
67	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
68	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
69	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
70	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
71	C₂×C₄²×C₄₁	—	2	2	no	—
72	C₂×C₄²×C₄₁	—	2	2	no	—
73	C₂×C₄²×C₄₁	D₄	1	1	yes	characteristic
74	C₂×C₄²×C₄₁	D₄	1	1	yes	characteristic
75	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
76	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
77	#102×C₄₁	—	2	8	no	—
78	#102×C₄₁	—	2	8	no	—
79	C₄×C₈×C₄₁	—	2	4	no	—
80	C₄×C₈×C₄₁	—	2	2	no	—
81	C₄×C₈×C₄₁	D₄	1	4	yes	complemented
82	#95×C₄₁	—	2	2	no	—
83	#95×C₄₁	—	2	2	no	—
84	C₂⁴×C₄₁	—	2	2	no	—
85	C₂⁴×C₄₁	C₂×D₄	1	1	yes	characteristic
86	C₂×Q₈×C₄₁	—	4	2	no	—
87	C₂×Q₈×C₄₁	—	4	2	no	—
88	C₂×Q₈×C₄₁	—	4	2	no	—
89	C₂×D₄×C₄₁	—	2	2	no	—
90	C₂×D₄×C₄₁	—	2	4	no	—
91	C₂×D₄×C₄₁	—	2	4	no	—
92	C₂×D₄×C₄₁	—	2	2	no	—
93	C₂×D₄×C₄₁	—	4	4	no	—
94	C₂×D₄×C₄₁	—	4	4	no	—
95	C₂×D₄×C₄₁	—	4	4	no	—
96	C₂×D₄×C₄₁	—	4	2	no	—
97	C₂×D₄×C₄₁	—	4	2	no	—
98	C₂×D₄×C₄₁	—	4	2	no	—
99	C₂×D₄×C₄₁	—	4	2	no	—
100	C₂×D₄×C₄₁	—	4	2	no	—
101	C₂×D₄×C₄₁	—	4	2	no	—
102	C₂²×C₄×C₄₁	—	2	2	no	—
103	C₂²×C₄×C₄₁	—	2	2	no	—
104	C₂²×C₄×C₄₁	—	2	2	no	—
105	C₂²×C₄×C₄₁	—	2	2	no	—
106	C₂²×C₄×C₄₁	—	2	1	no	—
107	C₂²×C₄×C₄₁	—	2	1	no	—
108	C₂²×C₄×C₄₁	—	2	2	no	—
109	C₂²×C₄×C₄₁	—	2	2	no	—
110	C₂²×C₄×C₄₁	—	2	2	no	—
111	C₂²×C₄×C₄₁	—	2	2	no	—
112	C₂²×C₄×C₄₁	D₈	1	4	yes	—
113	C₂²×C₄×C₄₁	SD₁₆	1	4	yes	—
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	C₂×D₄	1	1	yes	characteristic
118	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
119	C₂²×C₄×C₄₁	#41	1	4	yes	—
120	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
121	C₂×C₈×C₄₁	—	2	16	no	—
122	C₂×C₈×C₄₁	—	2	2	no	—
123	C₂×C₈×C₄₁	—	2	2	no	—
124	C₂×C₈×C₄₁	—	2	2	no	—
125	C₂×C₈×C₄₁	—	2	2	no	—
126	C₂×C₈×C₄₁	C₂×D₄	1	4	yes	—
127	C₂×C₈×C₄₁	#41	1	4	yes	—
128	C₄⋊C₄×C₄₁	—	2	2	no	—
129	C₄⋊C₄×C₄₁	—	2	4	no	—
130	C₄⋊C₄×C₄₁	—	2	4	no	—
131	C₄⋊C₄×C₄₁	—	2	2	no	—
132	C₄⋊C₄×C₄₁	—	4	2	no	—
133	C₄⋊C₄×C₄₁	—	4	2	no	—
134	C₄⋊C₄×C₄₁	—	4	2	no	—
135	C₄⋊C₄×C₄₁	—	4	4	no	—
136	C₄⋊C₄×C₄₁	—	4	2	no	—
137	C₄⋊C₄×C₄₁	—	4	2	no	—
138	C₂²⋊C₄×C₄₁	—	4	4	no	—
139	C₂²⋊C₄×C₄₁	—	4	4	no	—
140	C₂²⋊C₄×C₄₁	—	4	4	no	—
141	C₂²⋊C₄×C₄₁	—	4	4	no	—
142	C₄²×C₄₁	—	2	2	no	—
143	C₄²×C₄₁	—	2	2	no	—
144	C₄²×C₄₁	—	2	1	no	—
145	C₄²×C₄₁	—	2	1	no	—
146	C₄²×C₄₁	C₂×D₄	1	2	yes	—
147	C₄²×C₄₁	#41	1	2	yes	—
148	C₂³×C₄₁	—	2	1	no	—
149	C₂³×C₄₁	—	2	1	no	—
150	C₂³×C₄₁	—	2	1	no	—
151	C₂³×C₄₁	—	2	1	no	—
152	C₂³×C₄₁	—	4	2	no	—
153	C₂³×C₄₁	—	4	2	no	—
154	C₂³×C₄₁	—	4	2	no	—
155	C₂³×C₄₁	—	4	2	no	—
156	C₂³×C₄₁	—	4	2	no	—
157	C₂³×C₄₁	—	4	2	no	—
158	C₂³×C₄₁	—	4	2	no	—
159	C₂³×C₄₁	#124	1	2	yes	—
160	C₂³×C₄₁	C₂×D₈	1	2	yes	—
161	C₂³×C₄₁	C₂×SD₁₆	1	2	yes	—
162	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
163	Q₈×C₄₁	—	8	4	no	—
164	D₄×C₄₁	—	4	4	no	—
165	D₄×C₄₁	—	4	4	no	—
166	D₄×C₄₁	—	8	8	no	—
167	D₄×C₄₁	—	8	4	no	—
168	D₄×C₄₁	—	8	4	no	—
169	C₂×C₄×C₄₁	—	2	1	no	—
170	C₂×C₄×C₄₁	—	2	1	no	—
171	C₂×C₄×C₄₁	—	2	1	no	—
172	C₂×C₄×C₄₁	—	2	1	no	—
173	C₂×C₄×C₄₁	—	2	1	no	—
174	C₂×C₄×C₄₁	—	2	1	no	—
175	C₂×C₄×C₄₁	—	2	4	no	—
176	C₂×C₄×C₄₁	—	2	4	no	—
177	C₂×C₄×C₄₁	—	2	8	no	—
178	C₂×C₄×C₄₁	—	2	8	no	—
179	C₂×C₄×C₄₁	—	4	2	no	—
180	C₂×C₄×C₄₁	—	4	2	no	—
181	C₂×C₄×C₄₁	—	4	2	no	—
182	C₂×C₄×C₄₁	—	4	2	no	—
183	C₂×C₄×C₄₁	—	4	2	no	—
184	C₂×C₄×C₄₁	—	4	2	no	—
185	C₂×C₄×C₄₁	—	4	2	no	—
186	C₂×C₄×C₄₁	—	4	2	no	—
187	C₂×C₄×C₄₁	—	4	2	no	—
188	C₂×C₄×C₄₁	#121	1	2	yes	—
189	C₂×C₄×C₄₁	#121	1	2	yes	—
190	C₂×C₄×C₄₁	#124	1	2	yes	—
191	C₂×C₄×C₄₁	C₂×D₈	1	2	yes	—
192	C₂×C₄×C₄₁	C₂×D₈	1	2	yes	—
193	C₂×C₄×C₄₁	C₂×SD₁₆	1	2	yes	—
194	C₂×C₄×C₄₁	C₂×SD₁₆	1	2	yes	—
195	C₂×C₄×C₄₁	#135	1	2	yes	—
196	C₂×C₄×C₄₁	#135	1	2	yes	—
197	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
198	C₂×C₄×C₄₁	C₂×#41	1	2	yes	—
199	C₂×C₄×C₄₁	C₂×#41	1	2	yes	—
200	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
201	C₈×C₄₁	—	2	4	no	—
202	C₈×C₄₁	—	2	4	no	—
203	#33042	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
204	C₂²×C₄₁	—	2	2	no	—
205	C₂²×C₄₁	—	2	2	no	—
206	C₂²×C₄₁	—	2	2	no	—
207	C₂²×C₄₁	—	2	2	no	—
208	C₂²×C₄₁	—	2	2	no	—
209	C₂²×C₄₁	—	2	2	no	—
210	C₂²×C₄₁	—	8	2	no	—
211	C₂²×C₄₁	—	8	2	no	—
212	C₂²×C₄₁	—	8	2	no	—
213	C₂²×C₄₁	—	8	2	no	—
214	C₂²×C₄₁	—	8	2	no	—
215	C₂²×C₄₁	—	8	2	no	—
216	C₂²×C₄₁	—	8	2	no	—
217	C₂²×C₄₁	#486	1	4	yes	complemented
218	C₂²×C₄₁	C₂×#121	1	1	yes	characteristic
219	C₂²×C₄₁	C₂×#124	1	1	yes	characteristic
220	C₂²×C₄₁	#532	1	1	yes	characteristic
221	C₂²×C₄₁	C₂²×D₈	1	1	yes	characteristic
222	C₂²×C₄₁	C₂²×SD₁₆	1	1	yes	characteristic
223	C₂²×C₄₁	C₂×#135	1	1	yes	characteristic
224	C₂²×C₄₁	C₂×#135	1	1	yes	characteristic
225	C₄×C₄₁	—	2	2	no	—
226	C₄×C₄₁	—	2	2	no	—
227	C₄×C₄₁	—	2	2	no	—
228	C₄×C₄₁	—	8	2	no	—
229	C₄×C₄₁	—	8	2	no	—
230	C₄×C₄₁	—	8	2	no	—
231	C₄×C₄₁	#465	1	4	yes	—
232	C₄×C₄₁	#466	1	4	yes	—
233	C₄×C₄₁	#525	1	2	yes	—
234	C₄×C₄₁	#529	1	2	yes	—
235	C₂×#486	C₂×C₄₁	1	1	yes	characteristic, complemented
236	C₂²×C₄×C₈	C₂×C₄₁	1	1	yes	characteristic, complemented
237	#2857	C₂×C₄₁	1	1	yes	characteristic, complemented
238	#2856	C₂×C₄₁	1	1	yes	characteristic
239	#1990	C₂×C₄₁	1	1	yes	characteristic, complemented
240	#1957	C₂×C₄₁	1	1	yes	characteristic, complemented
241	#1934	C₂×C₄₁	1	4	yes	complemented
242	#1893	C₂×C₄₁	1	4	yes	complemented
243	#1834	C₂×C₄₁	1	1	yes	characteristic, complemented
244	C₂×C₄₁	—	2	4	no	—
245	C₂×C₄₁	—	16	2	no	—
246	C₂×C₄₁	#2850	1	1	yes	characteristic
247	C₂×C₄₁	C₂×#465	1	1	yes	characteristic
248	C₂×C₄₁	C₂×#466	1	1	yes	characteristic
249	C₂×C₄₁	C₂×#486	1	1	yes	characteristic
250	C₂×C₄₁	#3131	1	1	yes	characteristic
251	C₂×C₄₁	#3167	1	1	yes	characteristic
252	C₂×C₄₁	#3169	1	1	yes	characteristic
253	C₂³×C₈	C₂²×C₄₁	1	2	yes	—
254	C₂×C₄⋊Q₈	C₂²×C₄₁	1	1	yes	characteristic
255	C₂×#127	C₂²×C₄₁	1	1	yes	characteristic
256	C₂×C₂²⋊Q₈	—	2	1	no	—
257	C₂×#121	—	2	1	no	—
258	C₂×#121	—	2	1	no	—
259	C₂×#121	C₂²×C₄₁	1	2	yes	—
260	C₂²×C₄²	C₂²×C₄₁	1	1	yes	characteristic
261	#486	—	2	4	no	—
262	C₂×#102	C₂²×C₄₁	1	4	yes	—
263	C₂×#102	C₂²×C₄₁	1	4	yes	—
264	C₂×C₄×C₈	—	2	4	no	—
265	C₂×C₄×C₈	C₂²×C₄₁	1	2	yes	—
266	C₂×C₄×C₈	C₂²×C₄₁	1	1	yes	characteristic
267	C₂×C₄×C₈	C₂²×C₄₁	1	1	yes	characteristic
268	#391	—	2	1	no	—
269	#390	—	2	1	no	—
270	#390	—	2	1	no	—
271	#390	C₂²×C₄₁	1	2	yes	—
272	#389	—	2	1	no	—
273	#389	C₂²×C₄₁	1	2	yes	—
274	#384	C₂²×C₄₁	1	1	yes	characteristic
275	#384	C₂²×C₄₁	1	1	yes	characteristic
276	#380	—	2	1	no	—
277	#380	C₂²×C₄₁	1	2	yes	—
278	#340	C₂²×C₄₁	1	4	yes	—
279	#340	C₂²×C₄₁	1	4	yes	—
280	C₄₁	#33042	1	1	yes	characteristic, direct product factor, Sylow
281	C₂²×Q₈	—	2	1	no	—
282	C₂²×D₄	—	2	2	no	—
283	C₂²×D₄	—	2	1	no	—
284	C₂²×D₄	—	2	1	no	—
285	C₂²×D₄	C₂³×C₄₁	1	2	yes	—
286	C₂³×C₄	D₄×C₄₁	1	1	yes	characteristic
287	C₂³×C₄	D₄×C₄₁	1	1	yes	characteristic
288	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
289	C₂²×C₈	—	2	4	no	—
290	C₂²×C₈	—	2	4	no	—
291	C₂²×C₈	—	2	4	no	—
292	C₂²×C₈	C₂³×C₄₁	1	2	yes	—
293	C₂²×C₈	C₂³×C₄₁	1	2	yes	—
294	C₄⋊Q₈	—	2	2	no	—
295	C₄⋊Q₈	—	2	2	no	—
296	#127	—	2	2	no	—
297	#127	—	2	2	no	—
298	C₂²⋊Q₈	—	4	4	no	—
299	#121	—	2	8	no	—
300	#121	—	4	4	no	—
301	#121	—	4	4	no	—
302	C₂×C₄⋊C₄	—	2	1	no	—
303	C₂×C₄⋊C₄	—	2	1	no	—
304	C₂×C₄⋊C₄	—	2	1	no	—
305	C₂×C₄⋊C₄	—	2	2	no	—
306	C₂×C₄⋊C₄	—	2	1	no	—
307	C₂×C₄⋊C₄	—	2	1	no	—
308	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
309	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
310	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
311	C₂×C₂²⋊C₄	—	2	2	no	—
312	C₂×C₂²⋊C₄	—	2	2	no	—
313	C₂×C₂²⋊C₄	—	2	2	no	—
314	C₂×C₂²⋊C₄	—	2	2	no	—
315	C₂×C₄²	—	2	2	no	—
316	C₂×C₄²	—	2	2	no	—
317	C₂×C₄²	D₄×C₄₁	1	1	yes	characteristic
318	C₂×C₄²	D₄×C₄₁	1	1	yes	characteristic
319	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
320	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
321	#102	—	2	8	no	—
322	#102	—	2	8	no	—
323	C₄×C₈	—	2	4	no	—
324	C₄×C₈	—	2	2	no	—
325	C₄×C₈	D₄×C₄₁	1	4	yes	complemented
326	#95	—	2	2	no	—
327	#95	—	2	2	no	—
328	C₂⁴	—	2	2	no	—
329	C₂⁴	C₂×D₄×C₄₁	1	1	yes	characteristic
330	C₂×Q₈	—	4	2	no	—
331	C₂×Q₈	—	4	2	no	—
332	C₂×Q₈	—	4	2	no	—
333	C₂×D₄	—	2	2	no	—
334	C₂×D₄	—	2	4	no	—
335	C₂×D₄	—	2	4	no	—
336	C₂×D₄	—	2	2	no	—
337	C₂×D₄	—	4	4	no	—
338	C₂×D₄	—	4	4	no	—
339	C₂×D₄	—	4	4	no	—
340	C₂×D₄	—	4	2	no	—
341	C₂×D₄	—	4	2	no	—
342	C₂×D₄	—	4	2	no	—
343	C₂×D₄	—	4	2	no	—
344	C₂×D₄	—	4	2	no	—
345	C₂×D₄	—	4	2	no	—
346	C₂²×C₄	—	2	2	no	—
347	C₂²×C₄	—	2	2	no	—
348	C₂²×C₄	—	2	2	no	—
349	C₂²×C₄	—	2	2	no	—
350	C₂²×C₄	—	2	1	no	—
351	C₂²×C₄	—	2	1	no	—
352	C₂²×C₄	—	2	2	no	—
353	C₂²×C₄	—	2	2	no	—
354	C₂²×C₄	—	2	2	no	—
355	C₂²×C₄	—	2	2	no	—
356	C₂²×C₄	D₈×C₄₁	1	4	yes	—
357	C₂²×C₄	SD₁₆×C₄₁	1	4	yes	—
358	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
359	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
360	C₂²×C₄	C₂×D₄×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	#41×C₄₁	1	4	yes	—
364	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
365	C₂×C₈	—	2	16	no	—
366	C₂×C₈	—	2	2	no	—
367	C₂×C₈	—	2	2	no	—
368	C₂×C₈	—	2	2	no	—
369	C₂×C₈	—	2	2	no	—
370	C₂×C₈	C₂×D₄×C₄₁	1	4	yes	—
371	C₂×C₈	#41×C₄₁	1	4	yes	—
372	C₄⋊C₄	—	2	2	no	—
373	C₄⋊C₄	—	2	4	no	—
374	C₄⋊C₄	—	2	4	no	—
375	C₄⋊C₄	—	2	2	no	—
376	C₄⋊C₄	—	4	2	no	—
377	C₄⋊C₄	—	4	2	no	—
378	C₄⋊C₄	—	4	2	no	—
379	C₄⋊C₄	—	4	4	no	—
380	C₄⋊C₄	—	4	2	no	—
381	C₄⋊C₄	—	4	2	no	—
382	C₂²⋊C₄	—	4	4	no	—
383	C₂²⋊C₄	—	4	4	no	—
384	C₂²⋊C₄	—	4	4	no	—
385	C₂²⋊C₄	—	4	4	no	—
386	C₄²	—	2	2	no	—
387	C₄²	—	2	2	no	—
388	C₄²	—	2	1	no	—
389	C₄²	—	2	1	no	—
390	C₄²	C₂×D₄×C₄₁	1	2	yes	—
391	C₄²	#41×C₄₁	1	2	yes	—
392	C₂³	—	2	1	no	—
393	C₂³	—	2	1	no	—
394	C₂³	—	2	1	no	—
395	C₂³	—	2	1	no	—
396	C₂³	—	4	2	no	—
397	C₂³	—	4	2	no	—
398	C₂³	—	4	2	no	—
399	C₂³	—	4	2	no	—
400	C₂³	—	4	2	no	—
401	C₂³	—	4	2	no	—
402	C₂³	—	4	2	no	—
403	C₂³	#124×C₄₁	1	2	yes	—
404	C₂³	C₂×D₈×C₄₁	1	2	yes	—
405	C₂³	C₂×SD₁₆×C₄₁	1	2	yes	—
406	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
407	Q₈	—	8	4	no	—
408	D₄	—	4	4	no	—
409	D₄	—	4	4	no	—
410	D₄	—	8	8	no	—
411	D₄	—	8	4	no	—
412	D₄	—	8	4	no	—
413	C₂×C₄	—	2	1	no	—
414	C₂×C₄	—	2	1	no	—
415	C₂×C₄	—	2	1	no	—
416	C₂×C₄	—	2	1	no	—
417	C₂×C₄	—	2	1	no	—
418	C₂×C₄	—	2	1	no	—
419	C₂×C₄	—	2	4	no	—
420	C₂×C₄	—	2	4	no	—
421	C₂×C₄	—	2	8	no	—
422	C₂×C₄	—	2	8	no	—
423	C₂×C₄	—	4	2	no	—
424	C₂×C₄	—	4	2	no	—
425	C₂×C₄	—	4	2	no	—
426	C₂×C₄	—	4	2	no	—
427	C₂×C₄	—	4	2	no	—
428	C₂×C₄	—	4	2	no	—
429	C₂×C₄	—	4	2	no	—
430	C₂×C₄	—	4	2	no	—
431	C₂×C₄	—	4	2	no	—
432	C₂×C₄	#121×C₄₁	1	2	yes	—
433	C₂×C₄	#121×C₄₁	1	2	yes	—
434	C₂×C₄	#124×C₄₁	1	2	yes	—
435	C₂×C₄	C₂×D₈×C₄₁	1	2	yes	—
436	C₂×C₄	C₂×D₈×C₄₁	1	2	yes	—
437	C₂×C₄	C₂×SD₁₆×C₄₁	1	2	yes	—
438	C₂×C₄	C₂×SD₁₆×C₄₁	1	2	yes	—
439	C₂×C₄	#135×C₄₁	1	2	yes	—
440	C₂×C₄	#135×C₄₁	1	2	yes	—
441	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
442	C₂×C₄	C₂×#41×C₄₁	1	2	yes	—
443	C₂×C₄	C₂×#41×C₄₁	1	2	yes	—
444	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
445	C₈	—	2	4	no	—
446	C₈	—	2	4	no	—
447	C₂²	—	2	2	no	—
448	C₂²	—	2	2	no	—
449	C₂²	—	2	2	no	—
450	C₂²	—	2	2	no	—
451	C₂²	—	2	2	no	—
452	C₂²	—	2	2	no	—
453	C₂²	—	8	2	no	—
454	C₂²	—	8	2	no	—
455	C₂²	—	8	2	no	—
456	C₂²	—	8	2	no	—
457	C₂²	—	8	2	no	—
458	C₂²	—	8	2	no	—
459	C₂²	—	8	2	no	—
460	C₂²	C₄₁×#486	1	4	yes	complemented
461	C₂²	C₂×#121×C₄₁	1	1	yes	characteristic
462	C₂²	C₂×#124×C₄₁	1	1	yes	characteristic
463	C₂²	C₄₁×#532	1	1	yes	characteristic
464	C₂²	C₂²×D₈×C₄₁	1	1	yes	characteristic
465	C₂²	C₂²×SD₁₆×C₄₁	1	1	yes	characteristic
466	C₂²	C₂×#135×C₄₁	1	1	yes	characteristic
467	C₂²	C₂×#135×C₄₁	1	1	yes	characteristic
468	C₄	—	2	2	no	—
469	C₄	—	2	2	no	—
470	C₄	—	2	2	no	—
471	C₄	—	8	2	no	—
472	C₄	—	8	2	no	—
473	C₄	—	8	2	no	—
474	C₄	C₄₁×#465	1	4	yes	—
475	C₄	C₄₁×#466	1	4	yes	—
476	C₄	C₄₁×#525	1	2	yes	—
477	C₄	C₄₁×#529	1	2	yes	—
478	C₂	—	2	4	no	—
479	C₂	—	16	2	no	—
480	C₂	C₄₁×#2850	1	1	yes	characteristic
481	C₂	C₂×C₄₁×#465	1	1	yes	characteristic
482	C₂	C₂×C₄₁×#466	1	1	yes	characteristic
483	C₂	C₂×C₄₁×#486	1	1	yes	characteristic
484	C₂	C₄₁×#3131	1	1	yes	characteristic
485	C₂	C₄₁×#3167	1	1	yes	characteristic
486	C₂	C₄₁×#3169	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₄₁	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₁
prime radical	C₄₁×#2856	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₄₁ ◁ C₂²×C₄²×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₄₁×#486	C₂	semidirect
2. C₂²×C₄×C₈×C₄₁	C₂	semidirect
3. C₄₁×#2857	C₂	semidirect
5. C₄₁×#1990	C₂	semidirect
6. C₄₁×#1957	C₂	semidirect
7. C₄₁×#1934	C₂	semidirect
8. C₄₁×#1893	C₂	semidirect
9. C₄₁×#1834	C₂	semidirect
81. C₄×C₈×C₄₁	D₄	semidirect
203. #33042	C₄₁	direct (N × H)
217. C₂²×C₄₁	#486	semidirect
235. C₂×#486	C₂×C₄₁	semidirect
236. C₂²×C₄×C₈	C₂×C₄₁	semidirect
237. #2857	C₂×C₄₁	semidirect
239. #1990	C₂×C₄₁	semidirect
240. #1957	C₂×C₄₁	semidirect
241. #1934	C₂×C₄₁	semidirect
242. #1893	C₂×C₄₁	semidirect
243. #1834	C₂×C₄₁	semidirect
280. C₄₁	#33042	direct (N × H)
325. C₄×C₈	D₄×C₄₁	semidirect
460. C₂²	C₄₁×#486	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄₁×#486	2
C₂²×C₄×C₈×C₄₁	2
C₄₁×#2857	2
C₄₁×#2856	2
C₄₁×#1990	2
C₄₁×#1957	2
C₄₁×#1934	2
C₄₁×#1893	2
C₄₁×#1834	2
#33042	41

Subgroups — C41×#33042 #23809243

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#33042 #23809243