Subgroups — C₄₁×#24814 #23801015

Order 10496.

838 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×#477	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄×SD₁₆×C₄₁	C₂	1	1	yes	maximal, characteristic
3	C₄₁×#2563	C₂	1	1	yes	maximal, characteristic
4	Q₈×C₄⋊C₄×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₁×#2085	C₂	1	2	yes	maximal, complemented
6	C₄₁×#2067	C₂	1	2	yes	maximal
7	C₄₁×#1990	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄₁×#1939	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄₁×#1880	C₂	1	2	yes	maximal
10	C₄₁×#1805	C₂	1	2	yes	maximal, complemented
11	C₄₁×#1802	C₂	1	1	yes	maximal, characteristic
12	C₂²×SD₁₆×C₄₁	C₂²	1	1	yes	characteristic
13	C₂×C₄⋊Q₈×C₄₁	C₂²	1	1	yes	characteristic
14	C₂×C₄×Q₈×C₄₁	C₂²	1	2	yes	—
15	C₂×C₄×Q₈×C₄₁	C₂²	1	1	yes	characteristic
16	C₂×C₄×D₄×C₄₁	C₂²	1	1	yes	characteristic
17	C₄₁×#477	—	2	4	no	—
18	C₄×SD₁₆×C₄₁	—	2	4	no	—
19	C₂×#107×C₄₁	C₂²	1	2	yes	—
20	C₂×#106×C₄₁	C₂²	1	1	yes	characteristic
21	C₂×C₄⋊C₈×C₄₁	C₂²	1	1	yes	characteristic
22	C₂×C₄⋊C₈×C₄₁	C₂²	1	2	yes	—
23	C₂×#103×C₄₁	C₂²	1	2	yes	—
24	C₂×#103×C₄₁	C₂²	1	1	yes	characteristic
25	C₂×#102×C₄₁	C₂²	1	1	yes	characteristic
26	C₂×#102×C₄₁	C₂²	1	2	yes	—
27	C₂×C₄×C₈×C₄₁	C₂²	1	1	yes	characteristic
28	C₄₁×#393	—	2	2	no	—
29	C₄₁×#390	C₂²	1	2	yes	—
30	C₄₁×#389	—	2	2	no	—
31	C₄₁×#389	C₂²	1	2	yes	—
32	C₄₁×#384	—	2	1	no	—
33	C₄₁×#384	C₂²	1	1	yes	characteristic
34	C₄₁×#382	C₂²	1	2	yes	—
35	C₄₁×#380	—	2	1	no	—
36	C₄₁×#380	—	2	1	no	—
37	C₄×C₄⋊C₄×C₄₁	—	2	1	no	—
38	C₄×C₄⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
39	C₄₁×#340	C₂²	1	2	yes	—
40	C₄₁×#340	C₂²	1	2	yes	—
41	C₄₁×#340	C₂²	1	2	yes	—
42	C₄₁×#336	C₂²	1	2	yes	—
43	C₂²×Q₈×C₄₁	—	2	1	no	—
44	C₂²×Q₈×C₄₁	C₂³	1	1	yes	characteristic
45	C₂²×D₄×C₄₁	C₂³	1	1	yes	characteristic
46	C₂³×C₄×C₄₁	—	2	1	no	—
47	C₂×SD₁₆×C₄₁	—	2	2	no	—
48	C₂×SD₁₆×C₄₁	—	2	2	no	—
49	C₂×SD₁₆×C₄₁	Q₈	1	4	yes	complemented
50	C₂²×C₈×C₄₁	C₂³	1	2	yes	—
51	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
52	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
53	C₄⋊Q₈×C₄₁	—	2	2	no	—
54	C₄⋊Q₈×C₄₁	—	2	2	no	—
55	C₄×Q₈×C₄₁	—	2	2	no	—
56	C₄×Q₈×C₄₁	—	2	4	no	—
57	C₄×Q₈×C₄₁	—	4	2	no	—
58	C₄×Q₈×C₄₁	D₄	1	4	yes	—
59	C₄×D₄×C₄₁	—	2	2	no	—
60	C₄×D₄×C₄₁	—	2	2	no	—
61	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
62	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
63	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
64	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
65	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
66	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
67	C₂×C₄⋊C₄×C₄₁	D₄	1	1	yes	characteristic
68	C₂×C₄⋊C₄×C₄₁	D₄	1	1	yes	characteristic
69	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
70	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
71	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
72	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
73	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
74	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
75	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
76	C₂×C₄²×C₄₁	—	2	1	no	—
77	C₂×C₄²×C₄₁	—	2	2	no	—
78	C₂×C₄²×C₄₁	C₂³	1	2	yes	—
79	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
80	#107×C₄₁	—	2	4	no	—
81	#106×C₄₁	—	2	2	no	—
82	C₄⋊C₈×C₄₁	—	2	2	no	—
83	C₄⋊C₈×C₄₁	—	4	2	no	—
84	#103×C₄₁	—	2	2	no	—
85	#103×C₄₁	—	2	4	no	—
86	#102×C₄₁	—	2	2	no	—
87	#102×C₄₁	—	4	2	no	—
88	C₄×C₈×C₄₁	—	2	2	no	—
89	#95×C₄₁	—	2	2	no	—
90	#95×C₄₁	—	2	2	no	—
91	#95×C₄₁	—	2	2	no	—
92	#95×C₄₁	D₄	1	2	yes	—
93	C₂⁴×C₄₁	—	2	1	no	—
94	C₂×Q₈×C₄₁	—	2	1	no	—
95	C₂×Q₈×C₄₁	—	2	1	no	—
96	C₂×Q₈×C₄₁	—	2	1	no	—
97	C₂×Q₈×C₄₁	—	4	2	no	—
98	C₂×Q₈×C₄₁	—	8	1	no	—
99	C₂×Q₈×C₄₁	—	8	1	no	—
100	C₂×Q₈×C₄₁	C₂×D₄	1	2	yes	—
101	C₂×Q₈×C₄₁	C₂×Q₈	1	2	yes	—
102	C₂×Q₈×C₄₁	#41	1	2	yes	—
103	C₂×D₄×C₄₁	—	2	1	no	—
104	C₂×D₄×C₄₁	—	2	1	no	—
105	C₂×D₄×C₄₁	—	2	1	no	—
106	C₂×D₄×C₄₁	—	2	1	no	—
107	C₂×D₄×C₄₁	—	2	1	no	—
108	C₂×D₄×C₄₁	C₂×Q₈	1	2	yes	—
109	C₂²×C₄×C₄₁	—	2	1	no	—
110	C₂²×C₄×C₄₁	—	2	1	no	—
111	C₂²×C₄×C₄₁	—	2	1	no	—
112	C₂²×C₄×C₄₁	—	2	2	no	—
113	C₂²×C₄×C₄₁	—	2	2	no	—
114	C₂²×C₄×C₄₁	—	4	2	no	—
115	C₂²×C₄×C₄₁	—	4	2	no	—
116	C₂²×C₄×C₄₁	—	4	2	no	—
117	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
118	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
119	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
120	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
121	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
122	SD₁₆×C₄₁	—	2	8	no	—
123	C₂×C₈×C₄₁	—	2	1	no	—
124	C₂×C₈×C₄₁	—	2	1	no	—
125	C₂×C₈×C₄₁	—	2	1	no	—
126	C₂×C₈×C₄₁	—	2	2	no	—
127	C₂×C₈×C₄₁	—	2	2	no	—
128	C₂×C₈×C₄₁	—	2	1	no	—
129	C₂×C₈×C₄₁	—	2	2	no	—
130	C₂×C₈×C₄₁	—	2	1	no	—
131	C₂×C₈×C₄₁	C₂×Q₈	1	2	yes	—
132	C₄⋊C₄×C₄₁	—	2	4	no	—
133	C₄⋊C₄×C₄₁	—	2	2	no	—
134	C₄⋊C₄×C₄₁	—	2	2	no	—
135	C₄⋊C₄×C₄₁	—	2	1	no	—
136	C₄⋊C₄×C₄₁	—	2	1	no	—
137	C₄⋊C₄×C₄₁	—	2	2	no	—
138	C₄⋊C₄×C₄₁	—	2	1	no	—
139	C₄⋊C₄×C₄₁	—	2	2	no	—
140	C₄⋊C₄×C₄₁	—	2	2	no	—
141	C₄⋊C₄×C₄₁	—	2	2	no	—
142	C₄⋊C₄×C₄₁	—	4	4	no	—
143	C₄⋊C₄×C₄₁	—	4	2	no	—
144	C₄⋊C₄×C₄₁	—	4	2	no	—
145	C₄⋊C₄×C₄₁	—	8	1	no	—
146	C₄⋊C₄×C₄₁	—	8	2	no	—
147	C₄⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
148	C₂²⋊C₄×C₄₁	—	4	2	no	—
149	C₂²⋊C₄×C₄₁	—	8	2	no	—
150	C₂²⋊C₄×C₄₁	—	8	2	no	—
151	C₄²×C₄₁	—	2	4	no	—
152	C₄²×C₄₁	—	2	2	no	—
153	C₄²×C₄₁	—	2	2	no	—
154	C₄²×C₄₁	—	4	4	no	—
155	C₄²×C₄₁	C₂×D₄	1	2	yes	—
156	C₄²×C₄₁	#41	1	2	yes	—
157	C₂³×C₄₁	—	2	2	no	—
158	C₂³×C₄₁	—	4	1	no	—
159	C₂³×C₄₁	—	4	1	no	—
160	C₂³×C₄₁	—	4	1	no	—
161	C₂³×C₄₁	—	4	1	no	—
162	C₂³×C₄₁	—	4	1	no	—
163	C₂³×C₄₁	—	4	1	no	—
164	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
165	Q₈×C₄₁	—	2	2	no	—
166	Q₈×C₄₁	—	2	2	no	—
167	Q₈×C₄₁	—	2	2	no	—
168	Q₈×C₄₁	—	8	4	no	—
169	Q₈×C₄₁	C₂²⋊Q₈	1	4	yes	—
170	D₄×C₄₁	—	2	2	no	—
171	D₄×C₄₁	—	2	2	no	—
172	D₄×C₄₁	—	4	1	no	—
173	D₄×C₄₁	—	4	1	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	—	2	1	no	—
178	C₂×C₄×C₄₁	—	2	1	no	—
179	C₂×C₄×C₄₁	—	2	2	no	—
180	C₂×C₄×C₄₁	—	2	2	no	—
181	C₂×C₄×C₄₁	—	2	2	no	—
182	C₂×C₄×C₄₁	—	2	2	no	—
183	C₂×C₄×C₄₁	—	2	2	no	—
184	C₂×C₄×C₄₁	—	2	2	no	—
185	C₂×C₄×C₄₁	—	2	2	no	—
186	C₂×C₄×C₄₁	—	4	1	no	—
187	C₂×C₄×C₄₁	—	4	1	no	—
188	C₂×C₄×C₄₁	—	4	1	no	—
189	C₂×C₄×C₄₁	—	4	2	no	—
190	C₂×C₄×C₄₁	—	4	2	no	—
191	C₂×C₄×C₄₁	—	4	2	no	—
192	C₂×C₄×C₄₁	—	4	1	no	—
193	C₂×C₄×C₄₁	—	4	1	no	—
194	C₂×C₄×C₄₁	—	4	2	no	—
195	C₂×C₄×C₄₁	—	4	2	no	—
196	C₂×C₄×C₄₁	—	4	2	no	—
197	C₂×C₄×C₄₁	—	8	4	no	—
198	C₂×C₄×C₄₁	#121	1	2	yes	—
199	C₂×C₄×C₄₁	#121	1	2	yes	—
200	C₂×C₄×C₄₁	#135	1	2	yes	—
201	C₂×C₄×C₄₁	#137	1	2	yes	—
202	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
203	C₂×C₄×C₄₁	C₂²×Q₈	1	1	yes	characteristic
204	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
205	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
206	C₂×C₄×C₄₁	H(5,𝔽₂)	1	1	yes	characteristic
207	C₂×C₄×C₄₁	2₋¹⁺⁴	1	1	yes	characteristic
208	C₈×C₄₁	—	2	2	no	—
209	C₈×C₄₁	—	4	1	no	—
210	C₈×C₄₁	—	4	2	no	—
211	#24814	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
212	C₂²×C₄₁	—	4	2	no	—
213	C₂²×C₄₁	—	4	2	no	—
214	C₂²×C₄₁	—	4	2	no	—
215	C₂²×C₄₁	—	8	1	no	—
216	C₂²×C₄₁	—	8	1	no	—
217	C₂²×C₄₁	—	8	1	no	—
218	C₂²×C₄₁	—	8	1	no	—
219	C₂²×C₄₁	C₂×#121	1	1	yes	characteristic
220	C₂²×C₄₁	#546	1	1	yes	characteristic
221	C₂²×C₄₁	D₄×Q₈	1	1	yes	characteristic
222	C₂²×C₄₁	C₂×#135	1	1	yes	characteristic
223	C₂²×C₄₁	C₂×#137	1	1	yes	characteristic
224	C₂²×C₄₁	#576	1	1	yes	characteristic
225	C₂²×C₄₁	#577	1	1	yes	characteristic
226	C₄×C₄₁	—	2	4	no	—
227	C₄×C₄₁	—	2	2	no	—
228	C₄×C₄₁	—	4	2	no	—
229	C₄×C₄₁	—	4	2	no	—
230	C₄×C₄₁	—	4	2	no	—
231	C₄×C₄₁	—	8	1	no	—
232	C₄×C₄₁	—	8	2	no	—
233	C₄×C₄₁	—	8	2	no	—
234	C₄×C₄₁	#464	1	4	yes	—
235	C₄×C₄₁	C₂×C₂²⋊Q₈	1	1	yes	characteristic
236	C₄×C₄₁	#537	1	1	yes	characteristic
237	C₄×C₄₁	#552	1	1	yes	characteristic
238	C₄×C₄₁	#554	1	1	yes	characteristic
239	C₂×#477	C₂×C₄₁	1	1	yes	characteristic, complemented
240	C₂×C₄×SD₁₆	C₂×C₄₁	1	1	yes	characteristic
241	#2563	C₂×C₄₁	1	1	yes	characteristic
242	Q₈×C₄⋊C₄	C₂×C₄₁	1	1	yes	characteristic, complemented
243	#2085	C₂×C₄₁	1	2	yes	complemented
244	#2067	C₂×C₄₁	1	2	yes	—
245	#1990	C₂×C₄₁	1	1	yes	characteristic, complemented
246	#1939	C₂×C₄₁	1	1	yes	characteristic, complemented
247	#1880	C₂×C₄₁	1	2	yes	—
248	#1805	C₂×C₄₁	1	2	yes	complemented
249	#1802	C₂×C₄₁	1	1	yes	characteristic
250	C₂×C₄₁	—	8	2	no	—
251	C₂×C₄₁	#2417	1	1	yes	characteristic
252	C₂×C₄₁	C₂×#464	1	1	yes	characteristic
253	C₂×C₄₁	#3045	1	1	yes	characteristic
254	C₂×C₄₁	#3305	1	1	yes	characteristic
255	C₂×C₄₁	#3329	1	1	yes	characteristic
256	C₂×C₄₁	#3381	1	1	yes	characteristic
257	C₂×C₄₁	#3385	1	1	yes	characteristic
258	C₂²×SD₁₆	C₂²×C₄₁	1	1	yes	characteristic
259	C₂×C₄⋊Q₈	C₂²×C₄₁	1	1	yes	characteristic
260	C₂×C₄×Q₈	C₂²×C₄₁	1	2	yes	—
261	C₂×C₄×Q₈	C₂²×C₄₁	1	1	yes	characteristic
262	C₂×C₄×D₄	C₂²×C₄₁	1	1	yes	characteristic
263	#477	—	2	4	no	—
264	C₄×SD₁₆	—	2	4	no	—
265	C₂×#107	C₂²×C₄₁	1	2	yes	—
266	C₂×#106	C₂²×C₄₁	1	1	yes	characteristic
267	C₂×C₄⋊C₈	C₂²×C₄₁	1	1	yes	characteristic
268	C₂×C₄⋊C₈	C₂²×C₄₁	1	2	yes	—
269	C₂×#103	C₂²×C₄₁	1	2	yes	—
270	C₂×#103	C₂²×C₄₁	1	1	yes	characteristic
271	C₂×#102	C₂²×C₄₁	1	1	yes	characteristic
272	C₂×#102	C₂²×C₄₁	1	2	yes	—
273	C₂×C₄×C₈	C₂²×C₄₁	1	1	yes	characteristic
274	#393	—	2	2	no	—
275	#390	C₂²×C₄₁	1	2	yes	—
276	#389	—	2	2	no	—
277	#389	C₂²×C₄₁	1	2	yes	—
278	#384	—	2	1	no	—
279	#384	C₂²×C₄₁	1	1	yes	characteristic
280	#382	C₂²×C₄₁	1	2	yes	—
281	#380	—	2	1	no	—
282	#380	—	2	1	no	—
283	C₄×C₄⋊C₄	—	2	1	no	—
284	C₄×C₄⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
285	#340	C₂²×C₄₁	1	2	yes	—
286	#340	C₂²×C₄₁	1	2	yes	—
287	#340	C₂²×C₄₁	1	2	yes	—
288	#336	C₂²×C₄₁	1	2	yes	—
289	C₄₁	#24814	1	1	yes	characteristic, direct product factor, Sylow
290	C₂²×Q₈	—	2	1	no	—
291	C₂²×Q₈	C₂³×C₄₁	1	1	yes	characteristic
292	C₂²×D₄	C₂³×C₄₁	1	1	yes	characteristic
293	C₂³×C₄	—	2	1	no	—
294	C₂×SD₁₆	—	2	2	no	—
295	C₂×SD₁₆	—	2	2	no	—
296	C₂×SD₁₆	Q₈×C₄₁	1	4	yes	complemented
297	C₂²×C₈	C₂³×C₄₁	1	2	yes	—
298	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
299	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
300	C₄⋊Q₈	—	2	2	no	—
301	C₄⋊Q₈	—	2	2	no	—
302	C₄×Q₈	—	2	2	no	—
303	C₄×Q₈	—	2	4	no	—
304	C₄×Q₈	—	4	2	no	—
305	C₄×Q₈	D₄×C₄₁	1	4	yes	—
306	C₄×D₄	—	2	2	no	—
307	C₄×D₄	—	2	2	no	—
308	C₂×C₄⋊C₄	—	2	1	no	—
309	C₂×C₄⋊C₄	—	2	2	no	—
310	C₂×C₄⋊C₄	—	2	1	no	—
311	C₂×C₄⋊C₄	—	2	1	no	—
312	C₂×C₄⋊C₄	—	2	2	no	—
313	C₂×C₄⋊C₄	—	2	1	no	—
314	C₂×C₄⋊C₄	D₄×C₄₁	1	1	yes	characteristic
315	C₂×C₄⋊C₄	D₄×C₄₁	1	1	yes	characteristic
316	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
317	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
318	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
319	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
320	C₂×C₂²⋊C₄	—	2	1	no	—
321	C₂×C₂²⋊C₄	—	2	2	no	—
322	C₂×C₂²⋊C₄	—	2	2	no	—
323	C₂×C₄²	—	2	1	no	—
324	C₂×C₄²	—	2	2	no	—
325	C₂×C₄²	C₂³×C₄₁	1	2	yes	—
326	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
327	#107	—	2	4	no	—
328	#106	—	2	2	no	—
329	C₄⋊C₈	—	2	2	no	—
330	C₄⋊C₈	—	4	2	no	—
331	#103	—	2	2	no	—
332	#103	—	2	4	no	—
333	#102	—	2	2	no	—
334	#102	—	4	2	no	—
335	C₄×C₈	—	2	2	no	—
336	#95	—	2	2	no	—
337	#95	—	2	2	no	—
338	#95	—	2	2	no	—
339	#95	D₄×C₄₁	1	2	yes	—
340	C₂⁴	—	2	1	no	—
341	C₂×Q₈	—	2	1	no	—
342	C₂×Q₈	—	2	1	no	—
343	C₂×Q₈	—	2	1	no	—
344	C₂×Q₈	—	4	2	no	—
345	C₂×Q₈	—	8	1	no	—
346	C₂×Q₈	—	8	1	no	—
347	C₂×Q₈	C₂×D₄×C₄₁	1	2	yes	—
348	C₂×Q₈	C₂×Q₈×C₄₁	1	2	yes	—
349	C₂×Q₈	#41×C₄₁	1	2	yes	—
350	C₂×D₄	—	2	1	no	—
351	C₂×D₄	—	2	1	no	—
352	C₂×D₄	—	2	1	no	—
353	C₂×D₄	—	2	1	no	—
354	C₂×D₄	—	2	1	no	—
355	C₂×D₄	C₂×Q₈×C₄₁	1	2	yes	—
356	C₂²×C₄	—	2	1	no	—
357	C₂²×C₄	—	2	1	no	—
358	C₂²×C₄	—	2	1	no	—
359	C₂²×C₄	—	2	2	no	—
360	C₂²×C₄	—	2	2	no	—
361	C₂²×C₄	—	4	2	no	—
362	C₂²×C₄	—	4	2	no	—
363	C₂²×C₄	—	4	2	no	—
364	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
365	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
366	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
367	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
368	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
369	SD₁₆	—	2	8	no	—
370	C₂×C₈	—	2	1	no	—
371	C₂×C₈	—	2	1	no	—
372	C₂×C₈	—	2	1	no	—
373	C₂×C₈	—	2	2	no	—
374	C₂×C₈	—	2	2	no	—
375	C₂×C₈	—	2	1	no	—
376	C₂×C₈	—	2	2	no	—
377	C₂×C₈	—	2	1	no	—
378	C₂×C₈	C₂×Q₈×C₄₁	1	2	yes	—
379	C₄⋊C₄	—	2	4	no	—
380	C₄⋊C₄	—	2	2	no	—
381	C₄⋊C₄	—	2	2	no	—
382	C₄⋊C₄	—	2	1	no	—
383	C₄⋊C₄	—	2	1	no	—
384	C₄⋊C₄	—	2	2	no	—
385	C₄⋊C₄	—	2	1	no	—
386	C₄⋊C₄	—	2	2	no	—
387	C₄⋊C₄	—	2	2	no	—
388	C₄⋊C₄	—	2	2	no	—
389	C₄⋊C₄	—	4	4	no	—
390	C₄⋊C₄	—	4	2	no	—
391	C₄⋊C₄	—	4	2	no	—
392	C₄⋊C₄	—	8	1	no	—
393	C₄⋊C₄	—	8	2	no	—
394	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
395	C₂²⋊C₄	—	4	2	no	—
396	C₂²⋊C₄	—	8	2	no	—
397	C₂²⋊C₄	—	8	2	no	—
398	C₄²	—	2	4	no	—
399	C₄²	—	2	2	no	—
400	C₄²	—	2	2	no	—
401	C₄²	—	4	4	no	—
402	C₄²	C₂×D₄×C₄₁	1	2	yes	—
403	C₄²	#41×C₄₁	1	2	yes	—
404	C₂³	—	2	2	no	—
405	C₂³	—	4	1	no	—
406	C₂³	—	4	1	no	—
407	C₂³	—	4	1	no	—
408	C₂³	—	4	1	no	—
409	C₂³	—	4	1	no	—
410	C₂³	—	4	1	no	—
411	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
412	Q₈	—	2	2	no	—
413	Q₈	—	2	2	no	—
414	Q₈	—	2	2	no	—
415	Q₈	—	8	4	no	—
416	Q₈	C₂²⋊Q₈×C₄₁	1	4	yes	—
417	D₄	—	2	2	no	—
418	D₄	—	2	2	no	—
419	D₄	—	4	1	no	—
420	D₄	—	4	1	no	—
421	C₂×C₄	—	2	2	no	—
422	C₂×C₄	—	2	2	no	—
423	C₂×C₄	—	2	2	no	—
424	C₂×C₄	—	2	1	no	—
425	C₂×C₄	—	2	1	no	—
426	C₂×C₄	—	2	2	no	—
427	C₂×C₄	—	2	2	no	—
428	C₂×C₄	—	2	2	no	—
429	C₂×C₄	—	2	2	no	—
430	C₂×C₄	—	2	2	no	—
431	C₂×C₄	—	2	2	no	—
432	C₂×C₄	—	2	2	no	—
433	C₂×C₄	—	4	1	no	—
434	C₂×C₄	—	4	1	no	—
435	C₂×C₄	—	4	1	no	—
436	C₂×C₄	—	4	2	no	—
437	C₂×C₄	—	4	2	no	—
438	C₂×C₄	—	4	2	no	—
439	C₂×C₄	—	4	1	no	—
440	C₂×C₄	—	4	1	no	—
441	C₂×C₄	—	4	2	no	—
442	C₂×C₄	—	4	2	no	—
443	C₂×C₄	—	4	2	no	—
444	C₂×C₄	—	8	4	no	—
445	C₂×C₄	#121×C₄₁	1	2	yes	—
446	C₂×C₄	#121×C₄₁	1	2	yes	—
447	C₂×C₄	#135×C₄₁	1	2	yes	—
448	C₂×C₄	#137×C₄₁	1	2	yes	—
449	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
450	C₂×C₄	C₂²×Q₈×C₄₁	1	1	yes	characteristic
451	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
452	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
453	C₂×C₄	H(5,𝔽₂)×C₄₁	1	1	yes	characteristic
454	C₂×C₄	2₋¹⁺⁴×C₄₁	1	1	yes	characteristic
455	C₈	—	2	2	no	—
456	C₈	—	4	1	no	—
457	C₈	—	4	2	no	—
458	C₂²	—	4	2	no	—
459	C₂²	—	4	2	no	—
460	C₂²	—	4	2	no	—
461	C₂²	—	8	1	no	—
462	C₂²	—	8	1	no	—
463	C₂²	—	8	1	no	—
464	C₂²	—	8	1	no	—
465	C₂²	C₂×#121×C₄₁	1	1	yes	characteristic
466	C₂²	C₄₁×#546	1	1	yes	characteristic
467	C₂²	D₄×Q₈×C₄₁	1	1	yes	characteristic
468	C₂²	C₂×#135×C₄₁	1	1	yes	characteristic
469	C₂²	C₂×#137×C₄₁	1	1	yes	characteristic
470	C₂²	C₄₁×#576	1	1	yes	characteristic
471	C₂²	C₄₁×#577	1	1	yes	characteristic
472	C₄	—	2	2	no	—
473	C₄	—	2	4	no	—
474	C₄	—	4	2	no	—
475	C₄	—	4	2	no	—
476	C₄	—	4	2	no	—
477	C₄	—	8	2	no	—
478	C₄	—	8	2	no	—
479	C₄	—	8	1	no	—
480	C₄	C₄₁×#464	1	4	yes	—
481	C₄	C₂×C₂²⋊Q₈×C₄₁	1	1	yes	characteristic
482	C₄	C₄₁×#537	1	1	yes	characteristic
483	C₄	C₄₁×#552	1	1	yes	characteristic
484	C₄	C₄₁×#554	1	1	yes	characteristic
485	C₂	—	8	2	no	—
486	C₂	C₄₁×#2417	1	1	yes	characteristic
487	C₂	C₂×C₄₁×#464	1	1	yes	characteristic
488	C₂	C₄₁×#3045	1	1	yes	characteristic
489	C₂	C₄₁×#3305	1	1	yes	characteristic
490	C₂	C₄₁×#3329	1	1	yes	characteristic
491	C₂	C₄₁×#3381	1	1	yes	characteristic
492	C₂	C₄₁×#3385	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₂×C₄₁×#477	C₂	semidirect
4. Q₈×C₄⋊C₄×C₄₁	C₂	semidirect
5. C₄₁×#2085	C₂	semidirect
7. C₄₁×#1990	C₂	semidirect
8. C₄₁×#1939	C₂	semidirect
10. C₄₁×#1805	C₂	semidirect
49. C₂×SD₁₆×C₄₁	Q₈	semidirect
211. #24814	C₄₁	direct (N × H)
239. C₂×#477	C₂×C₄₁	semidirect
242. Q₈×C₄⋊C₄	C₂×C₄₁	semidirect
243. #2085	C₂×C₄₁	semidirect
245. #1990	C₂×C₄₁	semidirect
246. #1939	C₂×C₄₁	semidirect
248. #1805	C₂×C₄₁	semidirect
289. C₄₁	#24814	direct (N × H)
296. C₂×SD₁₆	Q₈×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×#477	2
C₂×C₄×SD₁₆×C₄₁	2
C₄₁×#2563	2
Q₈×C₄⋊C₄×C₄₁	2
C₄₁×#2085	2
C₄₁×#2067	2
C₄₁×#1990	2
C₄₁×#1939	2
C₄₁×#1880	2
C₄₁×#1805	2
C₄₁×#1802	2
#24814	41

Subgroups — C41×#24814 #23801015

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#24814 #23801015