Subgroups — C₄₁×#22432 #23798633

Order 10496.

1582 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₁×#550	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄₁×#436	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄₁×#417	C₂	1	2	yes	maximal, complemented
4	D₄×C₄⋊C₄×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₁×#1982	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄₁×#1957	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₁×#1895	C₂	1	2	yes	maximal, complemented
8	C₄₁×#1874	C₂	1	2	yes	maximal, complemented
9	C₄₁×#1803	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄₁×#1788	C₂	1	2	yes	maximal, complemented
11	C₄×#103×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×#41×C₄₁	C₂²	1	2	yes	—
13	C₂²×M₁₆×C₄₁	C₂²	1	2	yes	—
14	C₄₁×#550	—	2	4	no	—
15	C₄₁×#550	C₄	1	8	yes	complemented
16	C₂×#127×C₄₁	—	2	1	no	—
17	C₂×#127×C₄₁	C₂²	1	1	yes	characteristic
18	C₂×#121×C₄₁	—	2	2	no	—
19	C₂×#121×C₄₁	C₂²	1	2	yes	—
20	C₂×C₄×Q₈×C₄₁	C₂²	1	1	yes	characteristic
21	C₂×C₄×D₄×C₄₁	—	2	1	no	—
22	C₂×C₄×D₄×C₄₁	—	2	1	no	—
23	C₂×C₄×D₄×C₄₁	C₂²	1	1	yes	characteristic
24	C₂²×C₄⋊C₄×C₄₁	C₂²	1	2	yes	—
25	C₄₁×#436	—	2	4	no	—
26	C₂×C₄⋊C₈×C₄₁	C₂²	1	1	yes	characteristic
27	C₄₁×#417	—	2	8	no	—
28	C₂×#103×C₄₁	C₂²	1	1	yes	characteristic
29	C₂×#103×C₄₁	C₂²	1	2	yes	—
30	C₂×#103×C₄₁	C₂²	1	1	yes	characteristic
31	C₂×#102×C₄₁	C₂²	1	2	yes	—
32	C₂×#102×C₄₁	C₂²	1	2	yes	—
33	C₂×#102×C₄₁	C₂²	1	2	yes	—
34	C₂×#102×C₄₁	C₂²	1	2	yes	—
35	C₂×C₂²⋊C₈×C₄₁	C₂²	1	2	yes	—
36	C₂×C₄×C₈×C₄₁	C₂²	1	1	yes	characteristic
37	C₄₁×#389	—	2	1	no	—
38	C₄₁×#385	—	2	2	no	—
39	C₄₁×#384	C₂²	1	1	yes	characteristic
40	C₄₁×#380	C₂²	1	2	yes	—
41	C₄×C₄⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
42	C₄₁×#340	C₂²	1	1	yes	characteristic
43	C₄₁×#340	C₂²	1	1	yes	characteristic
44	C₄₁×#340	C₂²	1	2	yes	—
45	C₂×#41×C₄₁	—	2	4	no	—
46	C₂×#41×C₄₁	—	2	4	no	—
47	C₂×#41×C₄₁	—	2	4	no	—
48	C₂×#41×C₄₁	—	4	2	no	—
49	C₂×#41×C₄₁	—	4	2	no	—
50	C₂×#41×C₄₁	C₂×C₄	1	8	yes	complemented
51	C₂²×Q₈×C₄₁	C₂³	1	1	yes	characteristic
52	C₂²×D₄×C₄₁	—	2	2	no	—
53	C₂²×D₄×C₄₁	—	2	2	no	—
54	C₂²×D₄×C₄₁	—	2	1	no	—
55	C₂²×D₄×C₄₁	—	2	1	no	—
56	C₂²×D₄×C₄₁	D₄	1	1	yes	characteristic
57	C₂²×D₄×C₄₁	C₂³	1	2	yes	—
58	C₂³×C₄×C₄₁	—	2	2	no	—
59	C₂³×C₄×C₄₁	—	2	2	no	—
60	C₂³×C₄×C₄₁	C₂³	1	2	yes	—
61	C₂×M₁₆×C₄₁	—	2	4	no	—
62	C₂×M₁₆×C₄₁	—	2	4	no	—
63	C₂×M₁₆×C₄₁	—	4	2	no	—
64	C₂²×C₈×C₄₁	C₂³	1	2	yes	—
65	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
66	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
67	#127×C₄₁	—	2	8	no	—
68	#127×C₄₁	—	2	2	no	—
69	#127×C₄₁	C₂×C₄	1	4	yes	complemented
70	#121×C₄₁	—	2	4	no	—
71	#121×C₄₁	—	2	16	no	—
72	#121×C₄₁	C₂×C₄	1	8	yes	complemented
73	C₄×Q₈×C₄₁	—	2	2	no	—
74	C₄×Q₈×C₄₁	C₂×C₄	1	4	yes	complemented
75	C₄×D₄×C₄₁	—	2	8	no	—
76	C₄×D₄×C₄₁	—	4	4	no	—
77	C₄×D₄×C₄₁	C₂×C₄	1	4	yes	—
78	C₄×D₄×C₄₁	D₄	1	4	yes	—
79	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
80	C₂×C₄⋊C₄×C₄₁	—	2	4	no	—
81	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
82	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
83	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
84	C₂×C₄⋊C₄×C₄₁	—	4	2	no	—
85	C₂×C₄⋊C₄×C₄₁	D₄	1	1	yes	characteristic
86	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
87	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
88	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
89	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
90	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
91	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
92	C₂×C₂²⋊C₄×C₄₁	D₄	1	2	yes	—
93	C₂×C₄²×C₄₁	—	2	1	no	—
94	C₂×C₄²×C₄₁	—	2	1	no	—
95	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
96	C₄⋊C₈×C₄₁	—	2	2	no	—
97	#103×C₄₁	—	2	4	no	—
98	#103×C₄₁	—	2	2	no	—
99	#103×C₄₁	D₄	1	4	yes	complemented
100	#102×C₄₁	—	2	4	no	—
101	#102×C₄₁	—	2	4	no	—
102	#102×C₄₁	—	4	2	no	—
103	#102×C₄₁	—	4	2	no	—
104	C₂²⋊C₈×C₄₁	—	2	4	no	—
105	C₄×C₈×C₄₁	—	2	2	no	—
106	#95×C₄₁	—	2	1	no	—
107	#95×C₄₁	—	2	2	no	—
108	C₂⁴×C₄₁	—	2	2	no	—
109	C₂⁴×C₄₁	C₂×D₄	1	2	yes	—
110	#41×C₄₁	—	2	16	no	—
111	#41×C₄₁	—	4	8	no	—
112	#41×C₄₁	—	4	8	no	—
113	#41×C₄₁	—	4	8	no	—
114	C₂×Q₈×C₄₁	—	2	1	no	—
115	C₂×Q₈×C₄₁	—	2	1	no	—
116	C₂×Q₈×C₄₁	—	2	1	no	—
117	C₂×Q₈×C₄₁	C₂²×C₄	1	2	yes	—
118	C₂×Q₈×C₄₁	C₂×D₄	1	2	yes	—
119	C₂×Q₈×C₄₁	#41	1	2	yes	—
120	C₂×D₄×C₄₁	—	2	8	no	—
121	C₂×D₄×C₄₁	—	2	8	no	—
122	C₂×D₄×C₄₁	—	2	4	no	—
123	C₂×D₄×C₄₁	—	2	4	no	—
124	C₂×D₄×C₄₁	—	2	2	no	—
125	C₂×D₄×C₄₁	—	2	2	no	—
126	C₂×D₄×C₄₁	—	2	2	no	—
127	C₂×D₄×C₄₁	—	2	2	no	—
128	C₂×D₄×C₄₁	—	2	2	no	—
129	C₂×D₄×C₄₁	—	2	2	no	—
130	C₂×D₄×C₄₁	—	2	2	no	—
131	C₂×D₄×C₄₁	—	4	4	no	—
132	C₂×D₄×C₄₁	—	4	4	no	—
133	C₂×D₄×C₄₁	—	4	2	no	—
134	C₂×D₄×C₄₁	—	4	2	no	—
135	C₂×D₄×C₄₁	—	8	1	no	—
136	C₂×D₄×C₄₁	—	8	1	no	—
137	C₂×D₄×C₄₁	—	8	2	no	—
138	C₂×D₄×C₄₁	—	8	2	no	—
139	C₂×D₄×C₄₁	C₂²⋊C₄	1	4	yes	—
140	C₂×D₄×C₄₁	C₂²×C₄	1	4	yes	—
141	C₂²×C₄×C₄₁	—	2	1	no	—
142	C₂²×C₄×C₄₁	—	2	2	no	—
143	C₂²×C₄×C₄₁	—	2	2	no	—
144	C₂²×C₄×C₄₁	—	2	2	no	—
145	C₂²×C₄×C₄₁	—	2	2	no	—
146	C₂²×C₄×C₄₁	—	2	1	no	—
147	C₂²×C₄×C₄₁	—	2	1	no	—
148	C₂²×C₄×C₄₁	—	2	8	no	—
149	C₂²×C₄×C₄₁	—	2	1	no	—
150	C₂²×C₄×C₄₁	—	2	2	no	—
151	C₂²×C₄×C₄₁	—	4	4	no	—
152	C₂²×C₄×C₄₁	—	4	4	no	—
153	C₂²×C₄×C₄₁	—	4	4	no	—
154	C₂²×C₄×C₄₁	—	4	4	no	—
155	C₂²×C₄×C₄₁	—	8	2	no	—
156	C₂²×C₄×C₄₁	C₂²×C₄	1	4	yes	—
157	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
158	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
159	C₂²×C₄×C₄₁	C₂×D₄	1	4	yes	—
160	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
161	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
162	M₁₆×C₄₁	—	4	8	no	—
163	C₂×C₈×C₄₁	—	2	1	no	—
164	C₂×C₈×C₄₁	—	2	1	no	—
165	C₂×C₈×C₄₁	—	2	1	no	—
166	C₂×C₈×C₄₁	—	2	2	no	—
167	C₂×C₈×C₄₁	—	2	2	no	—
168	C₂×C₈×C₄₁	—	2	1	no	—
169	C₂×C₈×C₄₁	—	2	1	no	—
170	C₂×C₈×C₄₁	—	2	2	no	—
171	C₂×C₈×C₄₁	C₂×D₄	1	2	yes	—
172	C₄⋊C₄×C₄₁	—	2	4	no	—
173	C₄⋊C₄×C₄₁	—	2	1	no	—
174	C₄⋊C₄×C₄₁	—	2	1	no	—
175	C₄⋊C₄×C₄₁	—	2	2	no	—
176	C₄⋊C₄×C₄₁	—	2	1	no	—
177	C₄⋊C₄×C₄₁	—	2	1	no	—
178	C₄⋊C₄×C₄₁	—	2	2	no	—
179	C₄⋊C₄×C₄₁	—	4	4	no	—
180	C₄⋊C₄×C₄₁	—	4	2	no	—
181	C₄⋊C₄×C₄₁	—	8	1	no	—
182	C₄⋊C₄×C₄₁	C₂²⋊C₄	1	4	yes	—
183	C₄⋊C₄×C₄₁	C₂²×C₄	1	2	yes	—
184	C₄⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
185	C₂²⋊C₄×C₄₁	—	2	8	no	—
186	C₂²⋊C₄×C₄₁	—	4	4	no	—
187	C₂²⋊C₄×C₄₁	C₂²⋊C₄	1	8	yes	—
188	C₄²×C₄₁	—	2	4	no	—
189	C₄²×C₄₁	—	4	2	no	—
190	C₄²×C₄₁	C₂²×C₄	1	2	yes	—
191	C₄²×C₄₁	C₂×D₄	1	2	yes	—
192	C₂³×C₄₁	—	2	2	no	—
193	C₂³×C₄₁	—	2	2	no	—
194	C₂³×C₄₁	—	2	2	no	—
195	C₂³×C₄₁	—	2	2	no	—
196	C₂³×C₄₁	—	2	2	no	—
197	C₂³×C₄₁	—	2	2	no	—
198	C₂³×C₄₁	—	2	4	no	—
199	C₂³×C₄₁	—	4	2	no	—
200	C₂³×C₄₁	—	4	2	no	—
201	C₂³×C₄₁	—	4	2	no	—
202	C₂³×C₄₁	—	4	2	no	—
203	C₂³×C₄₁	—	4	2	no	—
204	C₂³×C₄₁	—	4	2	no	—
205	C₂³×C₄₁	C₂×C₂²⋊C₄	1	4	yes	—
206	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
207	Q₈×C₄₁	—	2	2	no	—
208	Q₈×C₄₁	—	2	2	no	—
209	Q₈×C₄₁	—	2	2	no	—
210	Q₈×C₄₁	C₄×D₄	1	4	yes	complemented
211	D₄×C₄₁	—	2	4	no	—
212	D₄×C₄₁	—	2	4	no	—
213	D₄×C₄₁	—	2	8	no	—
214	D₄×C₄₁	—	4	16	no	—
215	D₄×C₄₁	—	4	2	no	—
216	D₄×C₄₁	—	4	2	no	—
217	D₄×C₄₁	—	4	8	no	—
218	D₄×C₄₁	—	8	4	no	—
219	D₄×C₄₁	—	8	8	no	—
220	C₂×C₄×C₄₁	—	2	2	no	—
221	C₂×C₄×C₄₁	—	2	2	no	—
222	C₂×C₄×C₄₁	—	2	2	no	—
223	C₂×C₄×C₄₁	—	2	2	no	—
224	C₂×C₄×C₄₁	—	2	2	no	—
225	C₂×C₄×C₄₁	—	2	1	no	—
226	C₂×C₄×C₄₁	—	2	1	no	—
227	C₂×C₄×C₄₁	—	2	4	no	—
228	C₂×C₄×C₄₁	—	2	4	no	—
229	C₂×C₄×C₄₁	—	2	4	no	—
230	C₂×C₄×C₄₁	—	2	4	no	—
231	C₂×C₄×C₄₁	—	2	2	no	—
232	C₂×C₄×C₄₁	—	2	2	no	—
233	C₂×C₄×C₄₁	—	4	16	no	—
234	C₂×C₄×C₄₁	—	4	1	no	—
235	C₂×C₄×C₄₁	—	4	1	no	—
236	C₂×C₄×C₄₁	—	4	1	no	—
237	C₂×C₄×C₄₁	—	4	1	no	—
238	C₂×C₄×C₄₁	—	4	2	no	—
239	C₂×C₄×C₄₁	—	4	1	no	—
240	C₂×C₄×C₄₁	—	4	1	no	—
241	C₂×C₄×C₄₁	—	4	2	no	—
242	C₂×C₄×C₄₁	—	4	2	no	—
243	C₂×C₄×C₄₁	—	4	1	no	—
244	C₂×C₄×C₄₁	—	8	8	no	—
245	C₂×C₄×C₄₁	C₂×C₂²⋊C₄	1	2	yes	—
246	C₂×C₄×C₄₁	C₂×C₂²⋊C₄	1	4	yes	—
247	C₂×C₄×C₄₁	C₂×C₂²⋊C₄	1	2	yes	—
248	C₂×C₄×C₄₁	AGL(1,ℤ/8)	1	2	yes	—
249	C₂×C₄×C₄₁	#137	1	2	yes	—
250	C₂×C₄×C₄₁	C₂³×C₄	1	1	yes	characteristic
251	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
252	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
253	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
254	C₂×C₄×C₄₁	H(5,𝔽₂)	1	1	yes	characteristic
255	C₂×C₄×C₄₁	H(5,𝔽₂)	1	1	yes	characteristic
256	C₈×C₄₁	—	2	2	no	—
257	C₈×C₄₁	—	4	2	no	—
258	C₈×C₄₁	—	4	1	no	—
259	#22432	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
260	C₂²×C₄₁	—	2	4	no	—
261	C₂²×C₄₁	—	2	4	no	—
262	C₂²×C₄₁	—	2	4	no	—
263	C₂²×C₄₁	—	4	2	no	—
264	C₂²×C₄₁	—	4	2	no	—
265	C₂²×C₄₁	—	4	2	no	—
266	C₂²×C₄₁	—	4	2	no	—
267	C₂²×C₄₁	—	4	4	no	—
268	C₂²×C₄₁	—	4	4	no	—
269	C₂²×C₄₁	—	4	4	no	—
270	C₂²×C₄₁	—	8	2	no	—
271	C₂²×C₄₁	—	8	2	no	—
272	C₂²×C₄₁	—	8	2	no	—
273	C₂²×C₄₁	—	8	2	no	—
274	C₂²×C₄₁	C₂²×C₂²⋊C₄	1	1	yes	characteristic
275	C₂²×C₄₁	D₄²	1	1	yes	characteristic
276	C₂²×C₄₁	#546	1	1	yes	characteristic
277	C₂²×C₄₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
278	C₂²×C₄₁	C₂×#137	1	1	yes	characteristic
279	C₂²×C₄₁	#576	1	1	yes	characteristic
280	C₂²×C₄₁	#577	1	1	yes	characteristic
281	C₄×C₄₁	—	2	4	no	—
282	C₄×C₄₁	—	2	4	no	—
283	C₄×C₄₁	—	2	2	no	—
284	C₄×C₄₁	—	4	2	no	—
285	C₄×C₄₁	—	4	2	no	—
286	C₄×C₄₁	—	8	1	no	—
287	C₄×C₄₁	—	8	2	no	—
288	C₄×C₄₁	#417	1	4	yes	complemented
289	C₄×C₄₁	C₂×C₄×D₄	1	1	yes	characteristic
290	C₄×C₄₁	#518	1	1	yes	characteristic
291	C₄×C₄₁	D₄²	1	1	yes	characteristic
292	C₄×C₄₁	#546	1	1	yes	characteristic
293	C₂×#550	C₂×C₄₁	1	1	yes	characteristic
294	C₂×#436	C₂×C₄₁	1	1	yes	characteristic, complemented
295	C₂×#417	C₂×C₄₁	1	2	yes	complemented
296	D₄×C₄⋊C₄	C₂×C₄₁	1	1	yes	characteristic, complemented
297	#1982	C₂×C₄₁	1	1	yes	characteristic, complemented
298	#1957	C₂×C₄₁	1	1	yes	characteristic, complemented
299	#1895	C₂×C₄₁	1	2	yes	complemented
300	#1874	C₂×C₄₁	1	2	yes	complemented
301	#1803	C₂×C₄₁	1	1	yes	characteristic, complemented
302	#1788	C₂×C₄₁	1	2	yes	complemented
303	C₄×#103	C₂×C₄₁	1	1	yes	characteristic, complemented
304	C₂×C₄₁	—	4	4	no	—
305	C₂×C₄₁	—	8	4	no	—
306	C₂×C₄₁	D₄×C₂²⋊C₄	1	1	yes	characteristic
307	C₂×C₄₁	C₂×#417	1	1	yes	characteristic
308	C₂×C₄₁	#2897	1	1	yes	characteristic
309	C₂×C₄₁	#3274	1	1	yes	characteristic
310	C₂×C₄₁	#3278	1	1	yes	characteristic
311	C₂×C₄₁	#3332	1	1	yes	characteristic
312	C₂×C₄₁	#3333	1	1	yes	characteristic
313	C₂²×#41	C₂²×C₄₁	1	2	yes	—
314	C₂²×M₁₆	C₂²×C₄₁	1	2	yes	—
315	#550	—	2	4	no	—
316	#550	C₄×C₄₁	1	8	yes	complemented
317	C₂×#127	—	2	1	no	—
318	C₂×#127	C₂²×C₄₁	1	1	yes	characteristic
319	C₂×#121	—	2	2	no	—
320	C₂×#121	C₂²×C₄₁	1	2	yes	—
321	C₂×C₄×Q₈	C₂²×C₄₁	1	1	yes	characteristic
322	C₂×C₄×D₄	—	2	1	no	—
323	C₂×C₄×D₄	—	2	1	no	—
324	C₂×C₄×D₄	C₂²×C₄₁	1	1	yes	characteristic
325	C₂²×C₄⋊C₄	C₂²×C₄₁	1	2	yes	—
326	#436	—	2	4	no	—
327	C₂×C₄⋊C₈	C₂²×C₄₁	1	1	yes	characteristic
328	#417	—	2	8	no	—
329	C₂×#103	C₂²×C₄₁	1	2	yes	—
330	C₂×#103	C₂²×C₄₁	1	1	yes	characteristic
331	C₂×#103	C₂²×C₄₁	1	1	yes	characteristic
332	C₂×#102	C₂²×C₄₁	1	2	yes	—
333	C₂×#102	C₂²×C₄₁	1	2	yes	—
334	C₂×#102	C₂²×C₄₁	1	2	yes	—
335	C₂×#102	C₂²×C₄₁	1	2	yes	—
336	C₂×C₂²⋊C₈	C₂²×C₄₁	1	2	yes	—
337	C₂×C₄×C₈	C₂²×C₄₁	1	1	yes	characteristic
338	#389	—	2	1	no	—
339	#385	—	2	2	no	—
340	#384	C₂²×C₄₁	1	1	yes	characteristic
341	#380	C₂²×C₄₁	1	2	yes	—
342	C₄×C₄⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
343	#340	C₂²×C₄₁	1	2	yes	—
344	#340	C₂²×C₄₁	1	1	yes	characteristic
345	#340	C₂²×C₄₁	1	1	yes	characteristic
346	C₄₁	#22432	1	1	yes	characteristic, direct product factor, Sylow
347	C₂×#41	—	2	4	no	—
348	C₂×#41	—	2	4	no	—
349	C₂×#41	—	2	4	no	—
350	C₂×#41	—	4	2	no	—
351	C₂×#41	—	4	2	no	—
352	C₂×#41	C₂×C₄×C₄₁	1	8	yes	complemented
353	C₂²×Q₈	C₂³×C₄₁	1	1	yes	characteristic
354	C₂²×D₄	—	2	2	no	—
355	C₂²×D₄	—	2	2	no	—
356	C₂²×D₄	—	2	1	no	—
357	C₂²×D₄	—	2	1	no	—
358	C₂²×D₄	D₄×C₄₁	1	1	yes	characteristic
359	C₂²×D₄	C₂³×C₄₁	1	2	yes	—
360	C₂³×C₄	—	2	2	no	—
361	C₂³×C₄	—	2	2	no	—
362	C₂³×C₄	C₂³×C₄₁	1	2	yes	—
363	C₂×M₁₆	—	2	4	no	—
364	C₂×M₁₆	—	2	4	no	—
365	C₂×M₁₆	—	4	2	no	—
366	C₂²×C₈	C₂³×C₄₁	1	2	yes	—
367	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
368	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
369	#127	—	2	8	no	—
370	#127	—	2	2	no	—
371	#127	C₂×C₄×C₄₁	1	4	yes	complemented
372	#121	—	2	4	no	—
373	#121	—	2	16	no	—
374	#121	C₂×C₄×C₄₁	1	8	yes	complemented
375	C₄×Q₈	—	2	2	no	—
376	C₄×Q₈	C₂×C₄×C₄₁	1	4	yes	complemented
377	C₄×D₄	—	2	8	no	—
378	C₄×D₄	—	4	4	no	—
379	C₄×D₄	C₂×C₄×C₄₁	1	4	yes	—
380	C₄×D₄	D₄×C₄₁	1	4	yes	—
381	C₂×C₄⋊C₄	—	2	1	no	—
382	C₂×C₄⋊C₄	—	2	4	no	—
383	C₂×C₄⋊C₄	—	2	2	no	—
384	C₂×C₄⋊C₄	—	2	1	no	—
385	C₂×C₄⋊C₄	—	2	1	no	—
386	C₂×C₄⋊C₄	—	4	2	no	—
387	C₂×C₄⋊C₄	D₄×C₄₁	1	1	yes	characteristic
388	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
389	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
390	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
391	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
392	C₂×C₂²⋊C₄	—	2	2	no	—
393	C₂×C₂²⋊C₄	—	2	2	no	—
394	C₂×C₂²⋊C₄	D₄×C₄₁	1	2	yes	—
395	C₂×C₄²	—	2	1	no	—
396	C₂×C₄²	—	2	1	no	—
397	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
398	C₄⋊C₈	—	2	2	no	—
399	#103	—	2	4	no	—
400	#103	—	2	2	no	—
401	#103	D₄×C₄₁	1	4	yes	complemented
402	#102	—	2	4	no	—
403	#102	—	2	4	no	—
404	#102	—	4	2	no	—
405	#102	—	4	2	no	—
406	C₂²⋊C₈	—	2	4	no	—
407	C₄×C₈	—	2	2	no	—
408	#95	—	2	1	no	—
409	#95	—	2	2	no	—
410	C₂⁴	—	2	2	no	—
411	C₂⁴	C₂×D₄×C₄₁	1	2	yes	—
412	#41	—	2	16	no	—
413	#41	—	4	8	no	—
414	#41	—	4	8	no	—
415	#41	—	4	8	no	—
416	C₂×Q₈	—	2	1	no	—
417	C₂×Q₈	—	2	1	no	—
418	C₂×Q₈	—	2	1	no	—
419	C₂×Q₈	C₂²×C₄×C₄₁	1	2	yes	—
420	C₂×Q₈	C₂×D₄×C₄₁	1	2	yes	—
421	C₂×Q₈	#41×C₄₁	1	2	yes	—
422	C₂×D₄	—	2	8	no	—
423	C₂×D₄	—	2	8	no	—
424	C₂×D₄	—	2	4	no	—
425	C₂×D₄	—	2	4	no	—
426	C₂×D₄	—	2	2	no	—
427	C₂×D₄	—	2	2	no	—
428	C₂×D₄	—	2	2	no	—
429	C₂×D₄	—	2	2	no	—
430	C₂×D₄	—	2	2	no	—
431	C₂×D₄	—	2	2	no	—
432	C₂×D₄	—	2	2	no	—
433	C₂×D₄	—	4	4	no	—
434	C₂×D₄	—	4	4	no	—
435	C₂×D₄	—	4	2	no	—
436	C₂×D₄	—	4	2	no	—
437	C₂×D₄	—	8	1	no	—
438	C₂×D₄	—	8	1	no	—
439	C₂×D₄	—	8	2	no	—
440	C₂×D₄	—	8	2	no	—
441	C₂×D₄	C₂²⋊C₄×C₄₁	1	4	yes	—
442	C₂×D₄	C₂²×C₄×C₄₁	1	4	yes	—
443	C₂²×C₄	—	2	1	no	—
444	C₂²×C₄	—	2	2	no	—
445	C₂²×C₄	—	2	2	no	—
446	C₂²×C₄	—	2	2	no	—
447	C₂²×C₄	—	2	2	no	—
448	C₂²×C₄	—	2	1	no	—
449	C₂²×C₄	—	2	1	no	—
450	C₂²×C₄	—	2	8	no	—
451	C₂²×C₄	—	2	1	no	—
452	C₂²×C₄	—	2	2	no	—
453	C₂²×C₄	—	4	4	no	—
454	C₂²×C₄	—	4	4	no	—
455	C₂²×C₄	—	4	4	no	—
456	C₂²×C₄	—	4	4	no	—
457	C₂²×C₄	—	8	2	no	—
458	C₂²×C₄	C₂²×C₄×C₄₁	1	4	yes	—
459	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
460	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
461	C₂²×C₄	C₂×D₄×C₄₁	1	4	yes	—
462	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
463	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
464	M₁₆	—	4	8	no	—
465	C₂×C₈	—	2	1	no	—
466	C₂×C₈	—	2	1	no	—
467	C₂×C₈	—	2	1	no	—
468	C₂×C₈	—	2	2	no	—
469	C₂×C₈	—	2	2	no	—
470	C₂×C₈	—	2	1	no	—
471	C₂×C₈	—	2	1	no	—
472	C₂×C₈	—	2	2	no	—
473	C₂×C₈	C₂×D₄×C₄₁	1	2	yes	—
474	C₄⋊C₄	—	2	4	no	—
475	C₄⋊C₄	—	2	1	no	—
476	C₄⋊C₄	—	2	1	no	—
477	C₄⋊C₄	—	2	2	no	—
478	C₄⋊C₄	—	2	1	no	—
479	C₄⋊C₄	—	2	1	no	—
480	C₄⋊C₄	—	2	2	no	—
481	C₄⋊C₄	—	4	4	no	—
482	C₄⋊C₄	—	4	2	no	—
483	C₄⋊C₄	—	8	1	no	—
484	C₄⋊C₄	C₂²⋊C₄×C₄₁	1	4	yes	—
485	C₄⋊C₄	C₂²×C₄×C₄₁	1	2	yes	—
486	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
487	C₂²⋊C₄	—	2	8	no	—
488	C₂²⋊C₄	—	4	4	no	—
489	C₂²⋊C₄	C₂²⋊C₄×C₄₁	1	8	yes	—
490	C₄²	—	2	4	no	—
491	C₄²	—	4	2	no	—
492	C₄²	C₂²×C₄×C₄₁	1	2	yes	—
493	C₄²	C₂×D₄×C₄₁	1	2	yes	—
494	C₂³	—	2	2	no	—
495	C₂³	—	2	2	no	—
496	C₂³	—	2	2	no	—
497	C₂³	—	2	2	no	—
498	C₂³	—	2	2	no	—
499	C₂³	—	2	2	no	—
500	C₂³	—	2	4	no	—
501	C₂³	—	4	2	no	—
502	C₂³	—	4	2	no	—
503	C₂³	—	4	2	no	—
504	C₂³	—	4	2	no	—
505	C₂³	—	4	2	no	—
506	C₂³	—	4	2	no	—
507	C₂³	C₂×C₂²⋊C₄×C₄₁	1	4	yes	—
508	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
509	Q₈	—	2	2	no	—
510	Q₈	—	2	2	no	—
511	Q₈	—	2	2	no	—
512	Q₈	C₄×D₄×C₄₁	1	4	yes	complemented
513	D₄	—	2	4	no	—
514	D₄	—	2	4	no	—
515	D₄	—	2	8	no	—
516	D₄	—	4	16	no	—
517	D₄	—	4	2	no	—
518	D₄	—	4	2	no	—
519	D₄	—	4	8	no	—
520	D₄	—	8	4	no	—
521	D₄	—	8	8	no	—
522	C₂×C₄	—	2	2	no	—
523	C₂×C₄	—	2	2	no	—
524	C₂×C₄	—	2	2	no	—
525	C₂×C₄	—	2	2	no	—
526	C₂×C₄	—	2	2	no	—
527	C₂×C₄	—	2	1	no	—
528	C₂×C₄	—	2	1	no	—
529	C₂×C₄	—	2	4	no	—
530	C₂×C₄	—	2	4	no	—
531	C₂×C₄	—	2	4	no	—
532	C₂×C₄	—	2	4	no	—
533	C₂×C₄	—	2	2	no	—
534	C₂×C₄	—	2	2	no	—
535	C₂×C₄	—	4	16	no	—
536	C₂×C₄	—	4	1	no	—
537	C₂×C₄	—	4	1	no	—
538	C₂×C₄	—	4	1	no	—
539	C₂×C₄	—	4	1	no	—
540	C₂×C₄	—	4	2	no	—
541	C₂×C₄	—	4	1	no	—
542	C₂×C₄	—	4	1	no	—
543	C₂×C₄	—	4	2	no	—
544	C₂×C₄	—	4	2	no	—
545	C₂×C₄	—	4	1	no	—
546	C₂×C₄	—	8	8	no	—
547	C₂×C₄	C₂×C₂²⋊C₄×C₄₁	1	2	yes	—
548	C₂×C₄	C₂×C₂²⋊C₄×C₄₁	1	4	yes	—
549	C₂×C₄	C₂×C₂²⋊C₄×C₄₁	1	2	yes	—
550	C₂×C₄	AGL(1,ℤ/8)×C₄₁	1	2	yes	—
551	C₂×C₄	#137×C₄₁	1	2	yes	—
552	C₂×C₄	C₂³×C₄×C₄₁	1	1	yes	characteristic
553	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
554	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
555	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
556	C₂×C₄	H(5,𝔽₂)×C₄₁	1	1	yes	characteristic
557	C₂×C₄	H(5,𝔽₂)×C₄₁	1	1	yes	characteristic
558	C₈	—	2	2	no	—
559	C₈	—	4	2	no	—
560	C₈	—	4	1	no	—
561	C₂²	—	2	4	no	—
562	C₂²	—	2	4	no	—
563	C₂²	—	2	4	no	—
564	C₂²	—	4	2	no	—
565	C₂²	—	4	2	no	—
566	C₂²	—	4	2	no	—
567	C₂²	—	4	2	no	—
568	C₂²	—	4	4	no	—
569	C₂²	—	4	4	no	—
570	C₂²	—	4	4	no	—
571	C₂²	—	8	2	no	—
572	C₂²	—	8	2	no	—
573	C₂²	—	8	2	no	—
574	C₂²	—	8	2	no	—
575	C₂²	C₂²×C₂²⋊C₄×C₄₁	1	1	yes	characteristic
576	C₂²	D₄²×C₄₁	1	1	yes	characteristic
577	C₂²	C₄₁×#546	1	1	yes	characteristic
578	C₂²	C₂×AGL(1,ℤ/8)×C₄₁	1	1	yes	characteristic
579	C₂²	C₂×#137×C₄₁	1	1	yes	characteristic
580	C₂²	C₄₁×#576	1	1	yes	characteristic
581	C₂²	C₄₁×#577	1	1	yes	characteristic
582	C₄	—	2	4	no	—
583	C₄	—	2	4	no	—
584	C₄	—	2	2	no	—
585	C₄	—	4	2	no	—
586	C₄	—	4	2	no	—
587	C₄	—	8	1	no	—
588	C₄	—	8	2	no	—
589	C₄	C₄₁×#417	1	4	yes	complemented
590	C₄	C₂×C₄×D₄×C₄₁	1	1	yes	characteristic
591	C₄	C₄₁×#518	1	1	yes	characteristic
592	C₄	D₄²×C₄₁	1	1	yes	characteristic
593	C₄	C₄₁×#546	1	1	yes	characteristic
594	C₂	—	4	4	no	—
595	C₂	—	8	4	no	—
596	C₂	D₄×C₂²⋊C₄×C₄₁	1	1	yes	characteristic
597	C₂	C₂×C₄₁×#417	1	1	yes	characteristic
598	C₂	C₄₁×#2897	1	1	yes	characteristic
599	C₂	C₄₁×#3274	1	1	yes	characteristic
600	C₂	C₄₁×#3278	1	1	yes	characteristic
601	C₂	C₄₁×#3332	1	1	yes	characteristic
602	C₂	C₄₁×#3333	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₄₁	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₄₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₁
prime radical	C₂×C₄₁×#550	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₄₁ ◁ C₂×C₄×D₄×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₄₁×#436	C₂	semidirect
3. C₂×C₄₁×#417	C₂	semidirect
4. D₄×C₄⋊C₄×C₄₁	C₂	semidirect
5. C₄₁×#1982	C₂	semidirect
6. C₄₁×#1957	C₂	semidirect
7. C₄₁×#1895	C₂	semidirect
8. C₄₁×#1874	C₂	semidirect
9. C₄₁×#1803	C₂	semidirect
10. C₄₁×#1788	C₂	semidirect
11. C₄×#103×C₄₁	C₂	semidirect
15. C₄₁×#550	C₄	semidirect
50. C₂×#41×C₄₁	C₂×C₄	semidirect
69. #127×C₄₁	C₂×C₄	semidirect
72. #121×C₄₁	C₂×C₄	semidirect
74. C₄×Q₈×C₄₁	C₂×C₄	semidirect
99. #103×C₄₁	D₄	semidirect
210. Q₈×C₄₁	C₄×D₄	semidirect
259. #22432	C₄₁	direct (N × H)
288. C₄×C₄₁	#417	semidirect
294. C₂×#436	C₂×C₄₁	semidirect
295. C₂×#417	C₂×C₄₁	semidirect
296. D₄×C₄⋊C₄	C₂×C₄₁	semidirect
297. #1982	C₂×C₄₁	semidirect
298. #1957	C₂×C₄₁	semidirect
299. #1895	C₂×C₄₁	semidirect
300. #1874	C₂×C₄₁	semidirect
301. #1803	C₂×C₄₁	semidirect
302. #1788	C₂×C₄₁	semidirect
303. C₄×#103	C₂×C₄₁	semidirect
316. #550	C₄×C₄₁	semidirect
346. C₄₁	#22432	direct (N × H)
352. C₂×#41	C₂×C₄×C₄₁	semidirect
371. #127	C₂×C₄×C₄₁	semidirect
374. #121	C₂×C₄×C₄₁	semidirect
376. C₄×Q₈	C₂×C₄×C₄₁	semidirect
401. #103	D₄×C₄₁	semidirect
512. Q₈	C₄×D₄×C₄₁	semidirect
589. C₄	C₄₁×#417	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄₁×#550	2
C₂×C₄₁×#436	2
C₂×C₄₁×#417	2
D₄×C₄⋊C₄×C₄₁	2
C₄₁×#1982	2
C₄₁×#1957	2
C₄₁×#1895	2
C₄₁×#1874	2
C₄₁×#1803	2
C₄₁×#1788	2
C₄×#103×C₄₁	2
#22432	41

Subgroups — C41×#22432 #23798633

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#22432 #23798633