Subgroups — C₄₁×#21403 #23797604

Order 10496.

1218 conjugacy classes of subgroups.

The subgroup lattice has 472 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×C₄×M₁₆×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₁×#2285	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₁×#1992	C₂	1	2	yes	maximal, complemented
5	C₄₁×#1959	C₂	1	2	yes	maximal, complemented
6	C₄₁×#1895	C₂	1	2	yes	maximal
7	C₄₁×#1894	C₂	1	2	yes	maximal, complemented
8	C₄×#103×C₄₁	C₂	1	2	yes	maximal, complemented
9	C₄×#102×C₄₁	C₂	1	2	yes	maximal, complemented
10	C₂²×M₁₆×C₄₁	C₂²	1	2	yes	—
11	C₄₁×#529	—	2	4	no	—
12	C₄₁×#529	C₄	1	8	yes	complemented
13	C₂×#126×C₄₁	—	2	1	no	—
14	C₂×#125×C₄₁	C₂²	1	1	yes	characteristic
15	C₂×#124×C₄₁	C₂²	1	1	yes	characteristic
16	C₂×#123×C₄₁	—	2	1	no	—
17	C₂×C₂²⋊Q₈×C₄₁	C₂²	1	1	yes	characteristic
18	C₂×#121×C₄₁	C₂²	1	1	yes	characteristic
19	C₂×C₄×Q₈×C₄₁	C₂²	1	1	yes	characteristic
20	C₂×C₄×D₄×C₄₁	—	2	1	no	—
21	C₂×C₄×D₄×C₄₁	C₂²	1	1	yes	characteristic
22	C₂×#117×C₄₁	—	2	1	no	—
23	C₂×#117×C₄₁	—	2	1	no	—
24	C₂²×C₄²×C₄₁	C₂²	1	1	yes	characteristic
25	C₂×#103×C₄₁	C₂²	1	4	yes	—
26	C₂×#102×C₄₁	C₂²	1	4	yes	—
27	C₄×M₁₆×C₄₁	—	2	4	no	—
28	C₂×#97×C₄₁	C₂²	1	2	yes	—
29	C₂×C₄×C₈×C₄₁	C₂²	1	2	yes	—
30	C₄₁×#384	C₂²	1	2	yes	—
31	C₄₁×#382	—	2	1	no	—
32	C₄₁×#380	—	2	1	no	—
33	C₄₁×#380	C₂²	1	2	yes	—
34	C₄×C₄⋊C₄×C₄₁	—	2	1	no	—
35	C₄×C₄⋊C₄×C₄₁	C₂²	1	2	yes	—
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	C₂×M₁₆×C₄₁	—	2	4	no	—
46	C₂×M₁₆×C₄₁	—	2	8	no	—
47	C₂²×C₈×C₄₁	C₂³	1	4	yes	—
48	#126×C₄₁	—	2	8	no	—
49	#125×C₄₁	—	2	2	no	—
50	#125×C₄₁	C₂×C₄	1	4	yes	—
51	#124×C₄₁	—	2	2	no	—
52	#124×C₄₁	C₂×C₄	1	4	yes	—
53	#123×C₄₁	—	2	8	no	—
54	C₂²⋊Q₈×C₄₁	—	2	2	no	—
55	C₂²⋊Q₈×C₄₁	C₂×C₄	1	4	yes	—
56	#121×C₄₁	—	2	2	no	—
57	#121×C₄₁	C₂×C₄	1	4	yes	—
58	C₄×Q₈×C₄₁	—	2	2	no	—
59	C₄×Q₈×C₄₁	C₂×C₄	1	4	yes	—
60	C₄×D₄×C₄₁	—	2	8	no	—
61	C₄×D₄×C₄₁	—	2	2	no	—
62	C₄×D₄×C₄₁	C₂×C₄	1	4	yes	—
63	#117×C₄₁	—	2	8	no	—
64	#117×C₄₁	—	4	4	no	—
65	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
66	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
67	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
68	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
69	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
70	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
71	C₂×C₄⋊C₄×C₄₁	C₂³	1	4	yes	—
72	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
73	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
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	1	no	—
78	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
79	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
80	C₂×C₄²×C₄₁	—	2	1	no	—
81	C₂×C₄²×C₄₁	—	2	2	no	—
82	C₂×C₄²×C₄₁	C₂×C₄	1	4	yes	—
83	C₂×C₄²×C₄₁	D₄	1	1	yes	characteristic
84	C₂×C₄²×C₄₁	D₄	1	1	yes	characteristic
85	C₂×C₄²×C₄₁	D₄	1	4	yes	—
86	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
87	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
88	#103×C₄₁	—	2	8	no	—
89	#102×C₄₁	—	2	8	no	—
90	#97×C₄₁	—	2	4	no	—
91	C₄×C₈×C₄₁	—	2	4	no	—
92	#95×C₄₁	—	2	2	no	—
93	#95×C₄₁	—	2	2	no	—
94	C₂⁴×C₄₁	—	2	1	no	—
95	C₂⁴×C₄₁	C₂×D₄	1	1	yes	characteristic
96	C₂×Q₈×C₄₁	—	2	1	no	—
97	C₂×Q₈×C₄₁	—	2	4	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	4	no	—
102	C₂×D₄×C₄₁	—	4	4	no	—
103	C₂×D₄×C₄₁	C₂²×C₄	1	2	yes	—
104	C₂²×C₄×C₄₁	—	2	2	no	—
105	C₂²×C₄×C₄₁	—	2	2	no	—
106	C₂²×C₄×C₄₁	—	2	4	no	—
107	C₂²×C₄×C₄₁	—	2	1	no	—
108	C₂²×C₄×C₄₁	—	2	1	no	—
109	C₂²×C₄×C₄₁	—	2	1	no	—
110	C₂²×C₄×C₄₁	—	2	4	no	—
111	C₂²×C₄×C₄₁	—	2	4	no	—
112	C₂²×C₄×C₄₁	—	4	2	no	—
113	C₂²×C₄×C₄₁	—	4	2	no	—
114	C₂²×C₄×C₄₁	—	4	2	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	M₁₆×C₄₁	—	2	16	no	—
126	C₂×C₈×C₄₁	—	2	4	no	—
127	C₂×C₈×C₄₁	—	2	4	no	—
128	C₂×C₈×C₄₁	#41	1	8	yes	—
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	4	no	—
133	C₄⋊C₄×C₄₁	—	2	1	no	—
134	C₄⋊C₄×C₄₁	—	2	1	no	—
135	C₄⋊C₄×C₄₁	—	2	4	no	—
136	C₄⋊C₄×C₄₁	—	2	4	no	—
137	C₄⋊C₄×C₄₁	—	4	4	no	—
138	C₄⋊C₄×C₄₁	—	4	4	no	—
139	C₄⋊C₄×C₄₁	C₂²×C₄	1	2	yes	—
140	C₄⋊C₄×C₄₁	C₂²×C₄	1	2	yes	—
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	—	2	4	no	—
146	C₂²⋊C₄×C₄₁	—	4	4	no	—
147	C₄²×C₄₁	—	2	4	no	—
148	C₄²×C₄₁	—	4	4	no	—
149	C₄²×C₄₁	C₂²⋊C₄	1	4	yes	—
150	C₄²×C₄₁	C₂²⋊C₄	1	4	yes	—
151	C₄²×C₄₁	C₂²×C₄	1	2	yes	—
152	C₄²×C₄₁	C₂²×C₄	1	2	yes	—
153	C₄²×C₄₁	C₂×D₄	1	2	yes	—
154	C₄²×C₄₁	C₂×D₄	1	2	yes	—
155	C₂³×C₄₁	—	2	2	no	—
156	C₂³×C₄₁	—	2	1	no	—
157	C₂³×C₄₁	—	2	1	no	—
158	C₂³×C₄₁	—	2	2	no	—
159	C₂³×C₄₁	—	2	2	no	—
160	C₂³×C₄₁	—	4	2	no	—
161	C₂³×C₄₁	—	4	1	no	—
162	C₂³×C₄₁	—	4	1	no	—
163	C₂³×C₄₁	—	4	2	no	—
164	C₂³×C₄₁	C₂×C₂²⋊C₄	1	2	yes	—
165	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
166	Q₈×C₄₁	—	2	4	no	—
167	Q₈×C₄₁	—	4	2	no	—
168	D₄×C₄₁	—	2	4	no	—
169	D₄×C₄₁	—	4	8	no	—
170	D₄×C₄₁	—	4	2	no	—
171	C₂×C₄×C₄₁	—	2	2	no	—
172	C₂×C₄×C₄₁	—	2	1	no	—
173	C₂×C₄×C₄₁	—	2	1	no	—
174	C₂×C₄×C₄₁	—	2	2	no	—
175	C₂×C₄×C₄₁	—	2	2	no	—
176	C₂×C₄×C₄₁	—	2	4	no	—
177	C₂×C₄×C₄₁	—	2	4	no	—
178	C₂×C₄×C₄₁	—	2	8	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	—	4	4	no	—
183	C₂×C₄×C₄₁	—	4	2	no	—
184	C₂×C₄×C₄₁	—	4	1	no	—
185	C₂×C₄×C₄₁	—	4	1	no	—
186	C₂×C₄×C₄₁	—	4	2	no	—
187	C₂×C₄×C₄₁	—	4	8	no	—
188	C₂×C₄×C₄₁	—	4	4	no	—
189	C₂×C₄×C₄₁	—	4	4	no	—
190	C₂×C₄×C₄₁	—	4	4	no	—
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	C₂×C₂²⋊C₄	1	2	yes	—
196	C₂×C₄×C₄₁	AGL(1,ℤ/8)	1	2	yes	—
197	C₂×C₄×C₄₁	#137	1	2	yes	—
198	C₂×C₄×C₄₁	C₂³×C₄	1	1	yes	characteristic
199	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
200	C₂×C₄×C₄₁	C₂×#41	1	4	yes	—
201	C₈×C₄₁	—	2	8	no	—
202	#21403	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
203	C₂²×C₄₁	—	2	2	no	—
204	C₂²×C₄₁	—	2	2	no	—
205	C₂²×C₄₁	—	2	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	—	4	2	no	—
211	C₂²×C₄₁	—	8	2	no	—
212	C₂²×C₄₁	—	8	2	no	—
213	C₂²×C₄₁	C₂²×C₂²⋊C₄	1	1	yes	characteristic
214	C₂²×C₄₁	#532	1	2	yes	—
215	C₂²×C₄₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
216	C₂²×C₄₁	C₂×#137	1	1	yes	characteristic
217	C₂²×C₄₁	#575	1	2	yes	—
218	C₄×C₄₁	—	2	2	no	—
219	C₄×C₄₁	—	2	2	no	—
220	C₄×C₄₁	—	2	2	no	—
221	C₄×C₄₁	—	2	2	no	—
222	C₄×C₄₁	—	4	2	no	—
223	C₄×C₄₁	—	4	2	no	—
224	C₄×C₄₁	—	4	2	no	—
225	C₄×C₄₁	—	8	4	no	—
226	C₄×C₄₁	#417	1	4	yes	—
227	C₄×C₄₁	C₄×#41	1	2	yes	—
228	C₄×C₄₁	#525	1	2	yes	—
229	C₂×#529	C₂×C₄₁	1	1	yes	characteristic
230	C₂×C₄×M₁₆	C₂×C₄₁	1	1	yes	characteristic, complemented
231	#2285	C₂×C₄₁	1	1	yes	characteristic, complemented
232	#1992	C₂×C₄₁	1	2	yes	complemented
233	#1959	C₂×C₄₁	1	2	yes	complemented
234	#1895	C₂×C₄₁	1	2	yes	—
235	#1894	C₂×C₄₁	1	2	yes	complemented
236	C₄×#103	C₂×C₄₁	1	2	yes	complemented
237	C₄×#102	C₂×C₄₁	1	2	yes	complemented
238	C₂×C₄₁	—	4	2	no	—
239	C₂×C₄₁	—	8	2	no	—
240	C₂×C₄₁	#2297	1	1	yes	characteristic
241	C₂×C₄₁	C₂×#417	1	1	yes	characteristic
242	C₂×C₄₁	#2896	1	1	yes	characteristic
243	C₂×C₄₁	#3171	1	2	yes	—
244	C₂×C₄₁	#3172	1	2	yes	—
245	C₂²×M₁₆	C₂²×C₄₁	1	2	yes	—
246	#529	—	2	4	no	—
247	#529	C₄×C₄₁	1	8	yes	complemented
248	C₂×#126	—	2	1	no	—
249	C₂×#125	C₂²×C₄₁	1	1	yes	characteristic
250	C₂×#124	C₂²×C₄₁	1	1	yes	characteristic
251	C₂×#123	—	2	1	no	—
252	C₂×C₂²⋊Q₈	C₂²×C₄₁	1	1	yes	characteristic
253	C₂×#121	C₂²×C₄₁	1	1	yes	characteristic
254	C₂×C₄×Q₈	C₂²×C₄₁	1	1	yes	characteristic
255	C₂×C₄×D₄	—	2	1	no	—
256	C₂×C₄×D₄	C₂²×C₄₁	1	1	yes	characteristic
257	C₂×#117	—	2	1	no	—
258	C₂×#117	—	2	1	no	—
259	C₂²×C₄²	C₂²×C₄₁	1	1	yes	characteristic
260	C₂×#103	C₂²×C₄₁	1	4	yes	—
261	C₂×#102	C₂²×C₄₁	1	4	yes	—
262	C₄×M₁₆	—	2	4	no	—
263	C₂×#97	C₂²×C₄₁	1	2	yes	—
264	C₂×C₄×C₈	C₂²×C₄₁	1	2	yes	—
265	#384	C₂²×C₄₁	1	2	yes	—
266	#382	—	2	1	no	—
267	#380	—	2	1	no	—
268	#380	C₂²×C₄₁	1	2	yes	—
269	C₄×C₄⋊C₄	—	2	1	no	—
270	C₄×C₄⋊C₄	C₂²×C₄₁	1	2	yes	—
271	#340	C₂²×C₄₁	1	4	yes	—
272	#340	C₂²×C₄₁	1	4	yes	—
273	C₄₁	#21403	1	1	yes	characteristic, direct product factor, Sylow
274	C₂²×Q₈	C₂³×C₄₁	1	1	yes	characteristic
275	C₂²×D₄	—	2	1	no	—
276	C₂²×D₄	C₂³×C₄₁	1	1	yes	characteristic
277	C₂³×C₄	—	2	1	no	—
278	C₂³×C₄	D₄×C₄₁	1	1	yes	characteristic
279	C₂³×C₄	D₄×C₄₁	1	1	yes	characteristic
280	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
281	C₂×M₁₆	—	2	4	no	—
282	C₂×M₁₆	—	2	8	no	—
283	C₂²×C₈	C₂³×C₄₁	1	4	yes	—
284	#126	—	2	8	no	—
285	#125	—	2	2	no	—
286	#125	C₂×C₄×C₄₁	1	4	yes	—
287	#124	—	2	2	no	—
288	#124	C₂×C₄×C₄₁	1	4	yes	—
289	#123	—	2	8	no	—
290	C₂²⋊Q₈	—	2	2	no	—
291	C₂²⋊Q₈	C₂×C₄×C₄₁	1	4	yes	—
292	#121	—	2	2	no	—
293	#121	C₂×C₄×C₄₁	1	4	yes	—
294	C₄×Q₈	—	2	2	no	—
295	C₄×Q₈	C₂×C₄×C₄₁	1	4	yes	—
296	C₄×D₄	—	2	8	no	—
297	C₄×D₄	—	2	2	no	—
298	C₄×D₄	C₂×C₄×C₄₁	1	4	yes	—
299	#117	—	2	8	no	—
300	#117	—	4	4	no	—
301	C₂×C₄⋊C₄	—	2	1	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	2	no	—
307	C₂×C₄⋊C₄	C₂³×C₄₁	1	4	yes	—
308	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
309	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
310	C₂×C₂²⋊C₄	—	2	1	no	—
311	C₂×C₂²⋊C₄	—	2	1	no	—
312	C₂×C₂²⋊C₄	—	2	1	no	—
313	C₂×C₂²⋊C₄	—	2	1	no	—
314	C₂×C₂²⋊C₄	—	2	1	no	—
315	C₂×C₂²⋊C₄	—	2	2	no	—
316	C₂×C₄²	—	2	1	no	—
317	C₂×C₄²	—	2	2	no	—
318	C₂×C₄²	C₂×C₄×C₄₁	1	4	yes	—
319	C₂×C₄²	D₄×C₄₁	1	1	yes	characteristic
320	C₂×C₄²	D₄×C₄₁	1	1	yes	characteristic
321	C₂×C₄²	D₄×C₄₁	1	4	yes	—
322	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
323	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
324	#103	—	2	8	no	—
325	#102	—	2	8	no	—
326	#97	—	2	4	no	—
327	C₄×C₈	—	2	4	no	—
328	#95	—	2	2	no	—
329	#95	—	2	2	no	—
330	C₂⁴	—	2	1	no	—
331	C₂⁴	C₂×D₄×C₄₁	1	1	yes	characteristic
332	C₂×Q₈	—	2	1	no	—
333	C₂×Q₈	—	2	4	no	—
334	C₂×Q₈	C₂²×C₄×C₄₁	1	2	yes	—
335	C₂×D₄	—	2	4	no	—
336	C₂×D₄	—	2	1	no	—
337	C₂×D₄	—	2	4	no	—
338	C₂×D₄	—	4	4	no	—
339	C₂×D₄	C₂²×C₄×C₄₁	1	2	yes	—
340	C₂²×C₄	—	2	2	no	—
341	C₂²×C₄	—	2	2	no	—
342	C₂²×C₄	—	2	4	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	2	no	—
350	C₂²×C₄	—	4	2	no	—
351	C₂²×C₄	C₂²⋊C₄×C₄₁	1	4	yes	—
352	C₂²×C₄	C₂²⋊C₄×C₄₁	1	4	yes	—
353	C₂²×C₄	C₂²×C₄×C₄₁	1	2	yes	—
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	1	yes	characteristic
358	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
359	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
360	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
361	M₁₆	—	2	16	no	—
362	C₂×C₈	—	2	4	no	—
363	C₂×C₈	—	2	4	no	—
364	C₂×C₈	#41×C₄₁	1	8	yes	—
365	C₄⋊C₄	—	2	4	no	—
366	C₄⋊C₄	—	2	4	no	—
367	C₄⋊C₄	—	2	4	no	—
368	C₄⋊C₄	—	2	4	no	—
369	C₄⋊C₄	—	2	1	no	—
370	C₄⋊C₄	—	2	1	no	—
371	C₄⋊C₄	—	2	4	no	—
372	C₄⋊C₄	—	2	4	no	—
373	C₄⋊C₄	—	4	4	no	—
374	C₄⋊C₄	—	4	4	no	—
375	C₄⋊C₄	C₂²×C₄×C₄₁	1	2	yes	—
376	C₄⋊C₄	C₂²×C₄×C₄₁	1	2	yes	—
377	C₂²⋊C₄	—	2	4	no	—
378	C₂²⋊C₄	—	2	4	no	—
379	C₂²⋊C₄	—	2	4	no	—
380	C₂²⋊C₄	—	2	4	no	—
381	C₂²⋊C₄	—	2	4	no	—
382	C₂²⋊C₄	—	4	4	no	—
383	C₄²	—	2	4	no	—
384	C₄²	—	4	4	no	—
385	C₄²	C₂²⋊C₄×C₄₁	1	4	yes	—
386	C₄²	C₂²⋊C₄×C₄₁	1	4	yes	—
387	C₄²	C₂²×C₄×C₄₁	1	2	yes	—
388	C₄²	C₂²×C₄×C₄₁	1	2	yes	—
389	C₄²	C₂×D₄×C₄₁	1	2	yes	—
390	C₄²	C₂×D₄×C₄₁	1	2	yes	—
391	C₂³	—	2	2	no	—
392	C₂³	—	2	1	no	—
393	C₂³	—	2	1	no	—
394	C₂³	—	2	2	no	—
395	C₂³	—	2	2	no	—
396	C₂³	—	4	2	no	—
397	C₂³	—	4	1	no	—
398	C₂³	—	4	1	no	—
399	C₂³	—	4	2	no	—
400	C₂³	C₂×C₂²⋊C₄×C₄₁	1	2	yes	—
401	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
402	Q₈	—	2	4	no	—
403	Q₈	—	4	2	no	—
404	D₄	—	2	4	no	—
405	D₄	—	4	8	no	—
406	D₄	—	4	2	no	—
407	C₂×C₄	—	2	2	no	—
408	C₂×C₄	—	2	1	no	—
409	C₂×C₄	—	2	1	no	—
410	C₂×C₄	—	2	2	no	—
411	C₂×C₄	—	2	2	no	—
412	C₂×C₄	—	2	4	no	—
413	C₂×C₄	—	2	4	no	—
414	C₂×C₄	—	2	8	no	—
415	C₂×C₄	—	2	2	no	—
416	C₂×C₄	—	2	2	no	—
417	C₂×C₄	—	2	2	no	—
418	C₂×C₄	—	4	4	no	—
419	C₂×C₄	—	4	2	no	—
420	C₂×C₄	—	4	1	no	—
421	C₂×C₄	—	4	1	no	—
422	C₂×C₄	—	4	2	no	—
423	C₂×C₄	—	4	8	no	—
424	C₂×C₄	—	4	4	no	—
425	C₂×C₄	—	4	4	no	—
426	C₂×C₄	—	4	4	no	—
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	C₂×C₂²⋊C₄×C₄₁	1	2	yes	—
431	C₂×C₄	C₂×C₂²⋊C₄×C₄₁	1	2	yes	—
432	C₂×C₄	AGL(1,ℤ/8)×C₄₁	1	2	yes	—
433	C₂×C₄	#137×C₄₁	1	2	yes	—
434	C₂×C₄	C₂³×C₄×C₄₁	1	1	yes	characteristic
435	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
436	C₂×C₄	C₂×#41×C₄₁	1	4	yes	—
437	C₈	—	2	8	no	—
438	C₂²	—	2	2	no	—
439	C₂²	—	2	2	no	—
440	C₂²	—	2	2	no	—
441	C₂²	—	4	2	no	—
442	C₂²	—	4	2	no	—
443	C₂²	—	4	2	no	—
444	C₂²	—	4	2	no	—
445	C₂²	—	4	2	no	—
446	C₂²	—	8	2	no	—
447	C₂²	—	8	2	no	—
448	C₂²	C₂²×C₂²⋊C₄×C₄₁	1	1	yes	characteristic
449	C₂²	C₄₁×#532	1	2	yes	—
450	C₂²	C₂×AGL(1,ℤ/8)×C₄₁	1	1	yes	characteristic
451	C₂²	C₂×#137×C₄₁	1	1	yes	characteristic
452	C₂²	C₄₁×#575	1	2	yes	—
453	C₄	—	2	2	no	—
454	C₄	—	2	2	no	—
455	C₄	—	2	2	no	—
456	C₄	—	2	2	no	—
457	C₄	—	4	2	no	—
458	C₄	—	4	2	no	—
459	C₄	—	4	2	no	—
460	C₄	—	8	4	no	—
461	C₄	C₄₁×#417	1	4	yes	—
462	C₄	C₄×#41×C₄₁	1	2	yes	—
463	C₄	C₄₁×#525	1	2	yes	—
464	C₂	—	4	2	no	—
465	C₂	—	8	2	no	—
466	C₂	C₄₁×#2297	1	1	yes	characteristic
467	C₂	C₂×C₄₁×#417	1	1	yes	characteristic
468	C₂	C₄₁×#2896	1	1	yes	characteristic
469	C₂	C₄₁×#3171	1	2	yes	—
470	C₂	C₄₁×#3172	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄×C₄₁	C₂×D₄
commutator	C₂×C₄	C₂³×C₄×C₄₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₁
socle	C₂³×C₄₁	C₂²×D₄
prime radical	C₂×#121×C₄₁	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₄₁ ◁ C₂²×C₄²×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₄×M₁₆×C₄₁	C₂	semidirect
3. C₄₁×#2285	C₂	semidirect
4. C₄₁×#1992	C₂	semidirect
5. C₄₁×#1959	C₂	semidirect
7. C₄₁×#1894	C₂	semidirect
8. C₄×#103×C₄₁	C₂	semidirect
9. C₄×#102×C₄₁	C₂	semidirect
12. C₄₁×#529	C₄	semidirect
202. #21403	C₄₁	direct (N × H)
230. C₂×C₄×M₁₆	C₂×C₄₁	semidirect
231. #2285	C₂×C₄₁	semidirect
232. #1992	C₂×C₄₁	semidirect
233. #1959	C₂×C₄₁	semidirect
235. #1894	C₂×C₄₁	semidirect
236. C₄×#103	C₂×C₄₁	semidirect
237. C₄×#102	C₂×C₄₁	semidirect
247. #529	C₄×C₄₁	semidirect
273. C₄₁	#21403	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×C₄×M₁₆×C₄₁	2
C₄₁×#2285	2
C₄₁×#1992	2
C₄₁×#1959	2
C₄₁×#1895	2
C₄₁×#1894	2
C₄×#103×C₄₁	2
C₄×#102×C₄₁	2
#21403	41

Subgroups — C41×#21403 #23797604

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#21403 #23797604