Subgroups — C₄₁×#21862 #23798063

Order 10496.

1138 conjugacy classes of subgroups.

The subgroup lattice has 470 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₁×#529	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄₁×#431	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₁×#2285	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₁×#1991	C₂	1	2	yes	maximal, complemented
5	C₄₁×#1958	C₂	1	2	yes	maximal, complemented
6	C₄₁×#1875	C₂	1	2	yes	maximal
7	C₄₁×#1873	C₂	1	2	yes	maximal, complemented
8	C₄₁×#1803	C₂	1	2	yes	maximal, complemented
9	C₄₁×#1802	C₂	1	2	yes	maximal, complemented
10	C₄₁×#529	—	2	4	no	—
11	C₄₁×#529	C₄	1	8	yes	complemented
12	C₂×#126×C₄₁	—	2	1	no	—
13	C₂×#125×C₄₁	C₂²	1	1	yes	characteristic
14	C₂×#124×C₄₁	C₂²	1	1	yes	characteristic
15	C₂×#123×C₄₁	—	2	1	no	—
16	C₂×C₂²⋊Q₈×C₄₁	C₂²	1	1	yes	characteristic
17	C₂×#121×C₄₁	C₂²	1	1	yes	characteristic
18	C₂×C₄×Q₈×C₄₁	C₂²	1	1	yes	characteristic
19	C₂×C₄×D₄×C₄₁	—	2	1	no	—
20	C₂×C₄×D₄×C₄₁	C₂²	1	1	yes	characteristic
21	C₂×#117×C₄₁	—	2	1	no	—
22	C₂×#117×C₄₁	C₂²	1	2	yes	—
23	C₂²×C₄²×C₄₁	C₂²	1	1	yes	characteristic
24	C₄₁×#431	—	2	4	no	—
25	C₂×C₄⋊C₈×C₄₁	C₂²	1	2	yes	—
26	C₂×#103×C₄₁	C₂²	1	4	yes	—
27	C₂×#102×C₄₁	C₂²	1	4	yes	—
28	C₂×C₂²⋊C₈×C₄₁	C₂²	1	2	yes	—
29	C₂×C₄×C₈×C₄₁	C₂²	1	2	yes	—
30	C₄₁×#384	C₂²	1	2	yes	—
31	C₄₁×#382	C₂²	1	2	yes	—
32	C₄₁×#380	—	2	1	no	—
33	C₄₁×#380	—	2	1	no	—
34	C₄×C₄⋊C₄×C₄₁	—	2	1	no	—
35	C₄×C₄⋊C₄×C₄₁	—	2	1	no	—
36	C₄₁×#340	C₂²	1	4	yes	—
37	C₄₁×#340	C₂²	1	4	yes	—
38	C₂²×Q₈×C₄₁	C₂³	1	1	yes	characteristic
39	C₂²×D₄×C₄₁	—	2	1	no	—
40	C₂²×D₄×C₄₁	C₂³	1	1	yes	characteristic
41	C₂³×C₄×C₄₁	—	2	1	no	—
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	C₂³	1	4	yes	—
46	#126×C₄₁	—	2	8	no	—
47	#125×C₄₁	—	2	2	no	—
48	#125×C₄₁	C₂×C₄	1	4	yes	—
49	#124×C₄₁	—	2	2	no	—
50	#124×C₄₁	C₂×C₄	1	4	yes	—
51	#123×C₄₁	—	2	8	no	—
52	C₂²⋊Q₈×C₄₁	—	2	2	no	—
53	C₂²⋊Q₈×C₄₁	C₂×C₄	1	4	yes	—
54	#121×C₄₁	—	2	2	no	—
55	#121×C₄₁	C₂×C₄	1	4	yes	—
56	C₄×Q₈×C₄₁	—	2	2	no	—
57	C₄×Q₈×C₄₁	C₂×C₄	1	4	yes	—
58	C₄×D₄×C₄₁	—	2	8	no	—
59	C₄×D₄×C₄₁	—	2	2	no	—
60	C₄×D₄×C₄₁	C₂×C₄	1	4	yes	—
61	#117×C₄₁	—	2	8	no	—
62	#117×C₄₁	—	4	4	no	—
63	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
64	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
65	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
66	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
67	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
68	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
69	C₂×C₄⋊C₄×C₄₁	C₂³	1	4	yes	—
70	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
71	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
72	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
73	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
74	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
75	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
76	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
77	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
78	C₂×C₄²×C₄₁	—	2	1	no	—
79	C₂×C₄²×C₄₁	—	2	2	no	—
80	C₂×C₄²×C₄₁	C₂×C₄	1	4	yes	—
81	C₂×C₄²×C₄₁	D₄	1	1	yes	characteristic
82	C₂×C₄²×C₄₁	D₄	1	1	yes	characteristic
83	C₂×C₄²×C₄₁	D₄	1	4	yes	—
84	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
85	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
86	C₄⋊C₈×C₄₁	—	2	4	no	—
87	#103×C₄₁	—	4	4	no	—
88	#102×C₄₁	—	4	4	no	—
89	C₂²⋊C₈×C₄₁	—	2	4	no	—
90	C₄×C₈×C₄₁	—	2	4	no	—
91	#95×C₄₁	—	2	2	no	—
92	#95×C₄₁	—	2	2	no	—
93	C₂⁴×C₄₁	—	2	1	no	—
94	C₂⁴×C₄₁	C₂×D₄	1	1	yes	characteristic
95	C₂×Q₈×C₄₁	—	2	1	no	—
96	C₂×Q₈×C₄₁	—	2	2	no	—
97	C₂×Q₈×C₄₁	—	2	2	no	—
98	C₂×Q₈×C₄₁	C₂²×C₄	1	2	yes	—
99	C₂×D₄×C₄₁	—	2	4	no	—
100	C₂×D₄×C₄₁	—	2	1	no	—
101	C₂×D₄×C₄₁	—	2	2	no	—
102	C₂×D₄×C₄₁	—	2	2	no	—
103	C₂×D₄×C₄₁	—	4	4	no	—
104	C₂×D₄×C₄₁	C₂²×C₄	1	2	yes	—
105	C₂²×C₄×C₄₁	—	2	4	no	—
106	C₂²×C₄×C₄₁	—	2	2	no	—
107	C₂²×C₄×C₄₁	—	2	2	no	—
108	C₂²×C₄×C₄₁	—	2	1	no	—
109	C₂²×C₄×C₄₁	—	2	1	no	—
110	C₂²×C₄×C₄₁	—	2	1	no	—
111	C₂²×C₄×C₄₁	—	2	4	no	—
112	C₂²×C₄×C₄₁	—	2	4	no	—
113	C₂²×C₄×C₄₁	—	4	2	no	—
114	C₂²×C₄×C₄₁	—	4	4	no	—
115	C₂²×C₄×C₄₁	C₂²⋊C₄	1	4	yes	—
116	C₂²×C₄×C₄₁	C₂²⋊C₄	1	4	yes	—
117	C₂²×C₄×C₄₁	C₂²×C₄	1	2	yes	—
118	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
119	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
120	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
121	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
122	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
123	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
124	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
125	C₂×C₈×C₄₁	—	2	4	no	—
126	C₂×C₈×C₄₁	—	2	4	no	—
127	C₂×C₈×C₄₁	—	2	4	no	—
128	C₄⋊C₄×C₄₁	—	2	4	no	—
129	C₄⋊C₄×C₄₁	—	2	4	no	—
130	C₄⋊C₄×C₄₁	—	2	4	no	—
131	C₄⋊C₄×C₄₁	—	2	4	no	—
132	C₄⋊C₄×C₄₁	—	2	1	no	—
133	C₄⋊C₄×C₄₁	—	2	1	no	—
134	C₄⋊C₄×C₄₁	—	2	4	no	—
135	C₄⋊C₄×C₄₁	—	2	4	no	—
136	C₄⋊C₄×C₄₁	—	4	4	no	—
137	C₄⋊C₄×C₄₁	—	4	4	no	—
138	C₄⋊C₄×C₄₁	C₂²×C₄	1	2	yes	—
139	C₄⋊C₄×C₄₁	C₂²×C₄	1	2	yes	—
140	C₂²⋊C₄×C₄₁	—	2	4	no	—
141	C₂²⋊C₄×C₄₁	—	2	4	no	—
142	C₂²⋊C₄×C₄₁	—	2	4	no	—
143	C₂²⋊C₄×C₄₁	—	2	4	no	—
144	C₂²⋊C₄×C₄₁	—	2	4	no	—
145	C₂²⋊C₄×C₄₁	—	4	4	no	—
146	C₄²×C₄₁	—	2	4	no	—
147	C₄²×C₄₁	—	4	4	no	—
148	C₄²×C₄₁	C₂²⋊C₄	1	4	yes	—
149	C₄²×C₄₁	C₂²⋊C₄	1	4	yes	—
150	C₄²×C₄₁	C₂²×C₄	1	2	yes	—
151	C₄²×C₄₁	C₂²×C₄	1	2	yes	—
152	C₄²×C₄₁	C₂×D₄	1	2	yes	—
153	C₄²×C₄₁	C₂×D₄	1	2	yes	—
154	C₂³×C₄₁	—	2	1	no	—
155	C₂³×C₄₁	—	2	1	no	—
156	C₂³×C₄₁	—	2	2	no	—
157	C₂³×C₄₁	—	2	2	no	—
158	C₂³×C₄₁	—	2	2	no	—
159	C₂³×C₄₁	—	4	1	no	—
160	C₂³×C₄₁	—	4	1	no	—
161	C₂³×C₄₁	—	4	2	no	—
162	C₂³×C₄₁	—	4	2	no	—
163	C₂³×C₄₁	C₂×C₂²⋊C₄	1	2	yes	—
164	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
165	Q₈×C₄₁	—	2	4	no	—
166	Q₈×C₄₁	—	4	2	no	—
167	D₄×C₄₁	—	2	4	no	—
168	D₄×C₄₁	—	4	8	no	—
169	D₄×C₄₁	—	4	2	no	—
170	C₂×C₄×C₄₁	—	2	1	no	—
171	C₂×C₄×C₄₁	—	2	1	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	4	no	—
176	C₂×C₄×C₄₁	—	2	4	no	—
177	C₂×C₄×C₄₁	—	2	8	no	—
178	C₂×C₄×C₄₁	—	2	2	no	—
179	C₂×C₄×C₄₁	—	2	2	no	—
180	C₂×C₄×C₄₁	—	2	2	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	2	no	—
186	C₂×C₄×C₄₁	—	4	8	no	—
187	C₂×C₄×C₄₁	—	4	4	no	—
188	C₂×C₄×C₄₁	—	4	4	no	—
189	C₂×C₄×C₄₁	—	4	4	no	—
190	C₂×C₄×C₄₁	C₂×C₂²⋊C₄	1	2	yes	—
191	C₂×C₄×C₄₁	C₂×C₂²⋊C₄	1	2	yes	—
192	C₂×C₄×C₄₁	C₂×C₂²⋊C₄	1	2	yes	—
193	C₂×C₄×C₄₁	C₂×C₂²⋊C₄	1	2	yes	—
194	C₂×C₄×C₄₁	C₂×C₂²⋊C₄	1	2	yes	—
195	C₂×C₄×C₄₁	#135	1	4	yes	—
196	C₂×C₄×C₄₁	C₂³×C₄	1	1	yes	characteristic
197	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
198	C₂×C₄×C₄₁	H(5,𝔽₂)	1	2	yes	—
199	C₂×C₄×C₄₁	2₋¹⁺⁴	1	2	yes	—
200	C₈×C₄₁	—	4	4	no	—
201	#21862	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
202	C₂²×C₄₁	—	2	2	no	—
203	C₂²×C₄₁	—	2	2	no	—
204	C₂²×C₄₁	—	2	2	no	—
205	C₂²×C₄₁	—	4	2	no	—
206	C₂²×C₄₁	—	4	2	no	—
207	C₂²×C₄₁	—	4	2	no	—
208	C₂²×C₄₁	—	4	2	no	—
209	C₂²×C₄₁	—	4	2	no	—
210	C₂²×C₄₁	—	8	2	no	—
211	C₂²×C₄₁	—	8	2	no	—
212	C₂²×C₄₁	C₂²×C₂²⋊C₄	1	1	yes	characteristic
213	C₂²×C₄₁	#535	1	1	yes	characteristic
214	C₂²×C₄₁	#536	1	1	yes	characteristic
215	C₂²×C₄₁	C₂×#135	1	2	yes	—
216	C₂²×C₄₁	#575	1	2	yes	—
217	C₄×C₄₁	—	2	2	no	—
218	C₄×C₄₁	—	2	2	no	—
219	C₄×C₄₁	—	2	2	no	—
220	C₄×C₄₁	—	2	2	no	—
221	C₄×C₄₁	—	4	2	no	—
222	C₄×C₄₁	—	4	2	no	—
223	C₄×C₄₁	—	4	2	no	—
224	C₄×C₄₁	—	8	4	no	—
225	C₄×C₄₁	#416	1	4	yes	—
226	C₄×C₄₁	#520	1	2	yes	—
227	C₄×C₄₁	#537	1	2	yes	—
228	C₂×#529	C₂×C₄₁	1	1	yes	characteristic
229	C₂×#431	C₂×C₄₁	1	1	yes	characteristic, complemented
230	#2285	C₂×C₄₁	1	1	yes	characteristic, complemented
231	#1991	C₂×C₄₁	1	2	yes	complemented
232	#1958	C₂×C₄₁	1	2	yes	complemented
233	#1875	C₂×C₄₁	1	2	yes	—
234	#1873	C₂×C₄₁	1	2	yes	complemented
235	#1803	C₂×C₄₁	1	2	yes	complemented
236	#1802	C₂×C₄₁	1	2	yes	complemented
237	C₂×C₄₁	—	4	2	no	—
238	C₂×C₄₁	—	8	2	no	—
239	C₂×C₄₁	#2311	1	1	yes	characteristic
240	C₂×C₄₁	C₂×#416	1	1	yes	characteristic
241	C₂×C₄₁	#2896	1	1	yes	characteristic
242	C₂×C₄₁	#3212	1	2	yes	—
243	C₂×C₄₁	#3233	1	2	yes	—
244	#529	—	2	4	no	—
245	#529	C₄×C₄₁	1	8	yes	complemented
246	C₂×#126	—	2	1	no	—
247	C₂×#125	C₂²×C₄₁	1	1	yes	characteristic
248	C₂×#124	C₂²×C₄₁	1	1	yes	characteristic
249	C₂×#123	—	2	1	no	—
250	C₂×C₂²⋊Q₈	C₂²×C₄₁	1	1	yes	characteristic
251	C₂×#121	C₂²×C₄₁	1	1	yes	characteristic
252	C₂×C₄×Q₈	C₂²×C₄₁	1	1	yes	characteristic
253	C₂×C₄×D₄	—	2	1	no	—
254	C₂×C₄×D₄	C₂²×C₄₁	1	1	yes	characteristic
255	C₂×#117	—	2	1	no	—
256	C₂×#117	C₂²×C₄₁	1	2	yes	—
257	C₂²×C₄²	C₂²×C₄₁	1	1	yes	characteristic
258	#431	—	2	4	no	—
259	C₂×C₄⋊C₈	C₂²×C₄₁	1	2	yes	—
260	C₂×#103	C₂²×C₄₁	1	4	yes	—
261	C₂×#102	C₂²×C₄₁	1	4	yes	—
262	C₂×C₂²⋊C₈	C₂²×C₄₁	1	2	yes	—
263	C₂×C₄×C₈	C₂²×C₄₁	1	2	yes	—
264	#384	C₂²×C₄₁	1	2	yes	—
265	#382	C₂²×C₄₁	1	2	yes	—
266	#380	—	2	1	no	—
267	#380	—	2	1	no	—
268	C₄×C₄⋊C₄	—	2	1	no	—
269	C₄×C₄⋊C₄	—	2	1	no	—
270	#340	C₂²×C₄₁	1	4	yes	—
271	#340	C₂²×C₄₁	1	4	yes	—
272	C₄₁	#21862	1	1	yes	characteristic, direct product factor, Sylow
273	C₂²×Q₈	C₂³×C₄₁	1	1	yes	characteristic
274	C₂²×D₄	—	2	1	no	—
275	C₂²×D₄	C₂³×C₄₁	1	1	yes	characteristic
276	C₂³×C₄	—	2	1	no	—
277	C₂³×C₄	D₄×C₄₁	1	1	yes	characteristic
278	C₂³×C₄	D₄×C₄₁	1	1	yes	characteristic
279	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
280	C₂²×C₈	C₂³×C₄₁	1	4	yes	—
281	#126	—	2	8	no	—
282	#125	—	2	2	no	—
283	#125	C₂×C₄×C₄₁	1	4	yes	—
284	#124	—	2	2	no	—
285	#124	C₂×C₄×C₄₁	1	4	yes	—
286	#123	—	2	8	no	—
287	C₂²⋊Q₈	—	2	2	no	—
288	C₂²⋊Q₈	C₂×C₄×C₄₁	1	4	yes	—
289	#121	—	2	2	no	—
290	#121	C₂×C₄×C₄₁	1	4	yes	—
291	C₄×Q₈	—	2	2	no	—
292	C₄×Q₈	C₂×C₄×C₄₁	1	4	yes	—
293	C₄×D₄	—	2	8	no	—
294	C₄×D₄	—	2	2	no	—
295	C₄×D₄	C₂×C₄×C₄₁	1	4	yes	—
296	#117	—	2	8	no	—
297	#117	—	4	4	no	—
298	C₂×C₄⋊C₄	—	2	1	no	—
299	C₂×C₄⋊C₄	—	2	1	no	—
300	C₂×C₄⋊C₄	—	2	1	no	—
301	C₂×C₄⋊C₄	—	2	1	no	—
302	C₂×C₄⋊C₄	—	2	2	no	—
303	C₂×C₄⋊C₄	—	2	2	no	—
304	C₂×C₄⋊C₄	C₂³×C₄₁	1	4	yes	—
305	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
306	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
307	C₂×C₂²⋊C₄	—	2	1	no	—
308	C₂×C₂²⋊C₄	—	2	1	no	—
309	C₂×C₂²⋊C₄	—	2	1	no	—
310	C₂×C₂²⋊C₄	—	2	1	no	—
311	C₂×C₂²⋊C₄	—	2	1	no	—
312	C₂×C₂²⋊C₄	—	2	2	no	—
313	C₂×C₄²	—	2	1	no	—
314	C₂×C₄²	—	2	2	no	—
315	C₂×C₄²	C₂×C₄×C₄₁	1	4	yes	—
316	C₂×C₄²	D₄×C₄₁	1	1	yes	characteristic
317	C₂×C₄²	D₄×C₄₁	1	1	yes	characteristic
318	C₂×C₄²	D₄×C₄₁	1	4	yes	—
319	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
320	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
321	C₄⋊C₈	—	2	4	no	—
322	#103	—	4	4	no	—
323	#102	—	4	4	no	—
324	C₂²⋊C₈	—	2	4	no	—
325	C₄×C₈	—	2	4	no	—
326	#95	—	2	2	no	—
327	#95	—	2	2	no	—
328	C₂⁴	—	2	1	no	—
329	C₂⁴	C₂×D₄×C₄₁	1	1	yes	characteristic
330	C₂×Q₈	—	2	1	no	—
331	C₂×Q₈	—	2	2	no	—
332	C₂×Q₈	—	2	2	no	—
333	C₂×Q₈	C₂²×C₄×C₄₁	1	2	yes	—
334	C₂×D₄	—	2	4	no	—
335	C₂×D₄	—	2	1	no	—
336	C₂×D₄	—	2	2	no	—
337	C₂×D₄	—	2	2	no	—
338	C₂×D₄	—	4	4	no	—
339	C₂×D₄	C₂²×C₄×C₄₁	1	2	yes	—
340	C₂²×C₄	—	2	4	no	—
341	C₂²×C₄	—	2	2	no	—
342	C₂²×C₄	—	2	2	no	—
343	C₂²×C₄	—	2	1	no	—
344	C₂²×C₄	—	2	1	no	—
345	C₂²×C₄	—	2	1	no	—
346	C₂²×C₄	—	2	4	no	—
347	C₂²×C₄	—	2	4	no	—
348	C₂²×C₄	—	4	2	no	—
349	C₂²×C₄	—	4	4	no	—
350	C₂²×C₄	C₂²⋊C₄×C₄₁	1	4	yes	—
351	C₂²×C₄	C₂²⋊C₄×C₄₁	1	4	yes	—
352	C₂²×C₄	C₂²×C₄×C₄₁	1	2	yes	—
353	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
354	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
355	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
356	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
357	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
358	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
359	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
360	C₂×C₈	—	2	4	no	—
361	C₂×C₈	—	2	4	no	—
362	C₂×C₈	—	2	4	no	—
363	C₄⋊C₄	—	2	4	no	—
364	C₄⋊C₄	—	2	4	no	—
365	C₄⋊C₄	—	2	4	no	—
366	C₄⋊C₄	—	2	4	no	—
367	C₄⋊C₄	—	2	1	no	—
368	C₄⋊C₄	—	2	1	no	—
369	C₄⋊C₄	—	2	4	no	—
370	C₄⋊C₄	—	2	4	no	—
371	C₄⋊C₄	—	4	4	no	—
372	C₄⋊C₄	—	4	4	no	—
373	C₄⋊C₄	C₂²×C₄×C₄₁	1	2	yes	—
374	C₄⋊C₄	C₂²×C₄×C₄₁	1	2	yes	—
375	C₂²⋊C₄	—	2	4	no	—
376	C₂²⋊C₄	—	2	4	no	—
377	C₂²⋊C₄	—	2	4	no	—
378	C₂²⋊C₄	—	2	4	no	—
379	C₂²⋊C₄	—	2	4	no	—
380	C₂²⋊C₄	—	4	4	no	—
381	C₄²	—	2	4	no	—
382	C₄²	—	4	4	no	—
383	C₄²	C₂²⋊C₄×C₄₁	1	4	yes	—
384	C₄²	C₂²⋊C₄×C₄₁	1	4	yes	—
385	C₄²	C₂²×C₄×C₄₁	1	2	yes	—
386	C₄²	C₂²×C₄×C₄₁	1	2	yes	—
387	C₄²	C₂×D₄×C₄₁	1	2	yes	—
388	C₄²	C₂×D₄×C₄₁	1	2	yes	—
389	C₂³	—	2	1	no	—
390	C₂³	—	2	1	no	—
391	C₂³	—	2	2	no	—
392	C₂³	—	2	2	no	—
393	C₂³	—	2	2	no	—
394	C₂³	—	4	1	no	—
395	C₂³	—	4	1	no	—
396	C₂³	—	4	2	no	—
397	C₂³	—	4	2	no	—
398	C₂³	C₂×C₂²⋊C₄×C₄₁	1	2	yes	—
399	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
400	Q₈	—	2	4	no	—
401	Q₈	—	4	2	no	—
402	D₄	—	2	4	no	—
403	D₄	—	4	8	no	—
404	D₄	—	4	2	no	—
405	C₂×C₄	—	2	1	no	—
406	C₂×C₄	—	2	1	no	—
407	C₂×C₄	—	2	2	no	—
408	C₂×C₄	—	2	2	no	—
409	C₂×C₄	—	2	2	no	—
410	C₂×C₄	—	2	4	no	—
411	C₂×C₄	—	2	4	no	—
412	C₂×C₄	—	2	8	no	—
413	C₂×C₄	—	2	2	no	—
414	C₂×C₄	—	2	2	no	—
415	C₂×C₄	—	2	2	no	—
416	C₂×C₄	—	4	4	no	—
417	C₂×C₄	—	4	1	no	—
418	C₂×C₄	—	4	1	no	—
419	C₂×C₄	—	4	2	no	—
420	C₂×C₄	—	4	2	no	—
421	C₂×C₄	—	4	8	no	—
422	C₂×C₄	—	4	4	no	—
423	C₂×C₄	—	4	4	no	—
424	C₂×C₄	—	4	4	no	—
425	C₂×C₄	C₂×C₂²⋊C₄×C₄₁	1	2	yes	—
426	C₂×C₄	C₂×C₂²⋊C₄×C₄₁	1	2	yes	—
427	C₂×C₄	C₂×C₂²⋊C₄×C₄₁	1	2	yes	—
428	C₂×C₄	C₂×C₂²⋊C₄×C₄₁	1	2	yes	—
429	C₂×C₄	C₂×C₂²⋊C₄×C₄₁	1	2	yes	—
430	C₂×C₄	#135×C₄₁	1	4	yes	—
431	C₂×C₄	C₂³×C₄×C₄₁	1	1	yes	characteristic
432	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
433	C₂×C₄	H(5,𝔽₂)×C₄₁	1	2	yes	—
434	C₂×C₄	2₋¹⁺⁴×C₄₁	1	2	yes	—
435	C₈	—	4	4	no	—
436	C₂²	—	2	2	no	—
437	C₂²	—	2	2	no	—
438	C₂²	—	2	2	no	—
439	C₂²	—	4	2	no	—
440	C₂²	—	4	2	no	—
441	C₂²	—	4	2	no	—
442	C₂²	—	4	2	no	—
443	C₂²	—	4	2	no	—
444	C₂²	—	8	2	no	—
445	C₂²	—	8	2	no	—
446	C₂²	C₂²×C₂²⋊C₄×C₄₁	1	1	yes	characteristic
447	C₂²	C₄₁×#535	1	1	yes	characteristic
448	C₂²	C₄₁×#536	1	1	yes	characteristic
449	C₂²	C₂×#135×C₄₁	1	2	yes	—
450	C₂²	C₄₁×#575	1	2	yes	—
451	C₄	—	2	2	no	—
452	C₄	—	2	2	no	—
453	C₄	—	2	2	no	—
454	C₄	—	2	2	no	—
455	C₄	—	4	2	no	—
456	C₄	—	4	2	no	—
457	C₄	—	4	2	no	—
458	C₄	—	8	4	no	—
459	C₄	C₄₁×#416	1	4	yes	—
460	C₄	C₄₁×#520	1	2	yes	—
461	C₄	C₄₁×#537	1	2	yes	—
462	C₂	—	4	2	no	—
463	C₂	—	8	2	no	—
464	C₂	C₄₁×#2311	1	1	yes	characteristic
465	C₂	C₂×C₄₁×#416	1	1	yes	characteristic
466	C₂	C₄₁×#2896	1	1	yes	characteristic
467	C₂	C₄₁×#3212	1	2	yes	—
468	C₂	C₄₁×#3233	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₄₁	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₄₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₁
prime radical	C₂×#121×C₄₁	C₂²
LCS	G ▷ C₂×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
2. C₂×C₄₁×#431	C₂	semidirect
3. C₄₁×#2285	C₂	semidirect
4. C₄₁×#1991	C₂	semidirect
5. C₄₁×#1958	C₂	semidirect
7. C₄₁×#1873	C₂	semidirect
8. C₄₁×#1803	C₂	semidirect
9. C₄₁×#1802	C₂	semidirect
11. C₄₁×#529	C₄	semidirect
201. #21862	C₄₁	direct (N × H)
229. C₂×#431	C₂×C₄₁	semidirect
230. #2285	C₂×C₄₁	semidirect
231. #1991	C₂×C₄₁	semidirect
232. #1958	C₂×C₄₁	semidirect
234. #1873	C₂×C₄₁	semidirect
235. #1803	C₂×C₄₁	semidirect
236. #1802	C₂×C₄₁	semidirect
245. #529	C₄×C₄₁	semidirect
272. C₄₁	#21862	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₄₁×#529	2
C₂×C₄₁×#431	2
C₄₁×#2285	2
C₄₁×#1991	2
C₄₁×#1958	2
C₄₁×#1875	2
C₄₁×#1873	2
C₄₁×#1803	2
C₄₁×#1802	2
#21862	41

Subgroups — C41×#21862 #23798063

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#21862 #23798063