Subgroups — C₄₁×#24150 #23800351

Order 10496.

1478 conjugacy classes of subgroups.

The subgroup lattice has 668 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₁×#532	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄₁×#474	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄₁×#459	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄×#121×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₁×#2033	C₂	1	2	yes	maximal, complemented
6	C₄₁×#1999	C₂	1	2	yes	maximal, complemented
7	C₄₁×#1988	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄₁×#1982	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄₁×#1879	C₂	1	2	yes	maximal, complemented
10	C₄₁×#1862	C₂	1	2	yes	maximal, complemented
11	C₄₁×#1797	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×#41×C₄₁	—	2	1	no	—
13	C₂²×D₈×C₄₁	C₂²	1	2	yes	—
14	C₄₁×#532	—	2	4	no	—
15	C₄₁×#532	—	2	4	no	—
16	C₂×C₄⋊Q₈×C₄₁	C₂²	1	1	yes	characteristic
17	C₂×#127×C₄₁	C₂²	1	1	yes	characteristic
18	C₂×#124×C₄₁	—	2	1	no	—
19	C₂×#121×C₄₁	—	2	1	no	—
20	C₂×#121×C₄₁	C₂²	1	2	yes	—
21	C₂×#121×C₄₁	C₂²	1	1	yes	characteristic
22	C₂×C₄×D₄×C₄₁	—	2	1	no	—
23	C₂×C₄×D₄×C₄₁	—	2	1	no	—
24	C₂×C₄×D₄×C₄₁	C₂²	1	1	yes	characteristic
25	C₂×C₄×D₄×C₄₁	C₂²	1	2	yes	—
26	C₂²×C₄²×C₄₁	C₂²	1	1	yes	characteristic
27	C₄₁×#474	—	2	4	no	—
28	C₄₁×#459	—	2	4	no	—
29	C₂×#107×C₄₁	C₂²	1	2	yes	—
30	C₂×C₄⋊C₈×C₄₁	C₂²	1	1	yes	characteristic
31	C₂×C₄⋊C₈×C₄₁	C₂²	1	1	yes	characteristic
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×#102×C₄₁	C₂²	1	2	yes	—
36	C₂×C₂²⋊C₈×C₄₁	C₂²	1	2	yes	—
37	C₄₁×#390	C₂²	1	1	yes	characteristic
38	C₄₁×#389	C₂²	1	1	yes	characteristic
39	C₄₁×#388	—	2	1	no	—
40	C₄₁×#386	—	2	1	no	—
41	C₄₁×#380	C₂²	1	1	yes	characteristic
42	C₄×C₄⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
43	C₄×C₂²⋊C₄×C₄₁	—	2	1	no	—
44	C₄₁×#340	C₂²	1	2	yes	—
45	C₄₁×#340	C₂²	1	2	yes	—
46	C₄₁×#336	C₂²	1	2	yes	—
47	C₂×#41×C₄₁	—	2	8	no	—
48	C₂×#41×C₄₁	—	4	4	no	—
49	C₂×#41×C₄₁	—	4	4	no	—
50	C₂²×Q₈×C₄₁	—	2	1	no	—
51	C₂²×D₄×C₄₁	—	2	1	no	—
52	C₂²×D₄×C₄₁	—	2	2	no	—
53	C₂²×D₄×C₄₁	—	2	1	no	—
54	C₂²×D₄×C₄₁	—	2	1	no	—
55	C₂²×D₄×C₄₁	C₂³	1	2	yes	—
56	C₂²×D₄×C₄₁	C₂³	1	1	yes	characteristic
57	C₂³×C₄×C₄₁	—	2	2	no	—
58	C₂³×C₄×C₄₁	—	2	1	no	—
59	C₂³×C₄×C₄₁	D₄	1	1	yes	characteristic
60	C₂³×C₄×C₄₁	D₄	1	1	yes	characteristic
61	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
62	C₂×D₈×C₄₁	—	2	4	no	—
63	C₂×D₈×C₄₁	—	2	4	no	—
64	C₂×D₈×C₄₁	—	4	2	no	—
65	C₂²×C₈×C₄₁	C₂³	1	2	yes	—
66	C₂²×C₈×C₄₁	C₂³	1	2	yes	—
67	C₄⋊Q₈×C₄₁	—	2	2	no	—
68	C₄⋊Q₈×C₄₁	D₄	1	4	yes	complemented
69	#127×C₄₁	—	2	2	no	—
70	#127×C₄₁	D₄	1	4	yes	complemented
71	#124×C₄₁	—	2	8	no	—
72	#121×C₄₁	—	2	8	no	—
73	#121×C₄₁	—	2	4	no	—
74	#121×C₄₁	—	2	2	no	—
75	#121×C₄₁	—	2	4	no	—
76	#121×C₄₁	—	2	2	no	—
77	C₄×D₄×C₄₁	—	2	8	no	—
78	C₄×D₄×C₄₁	—	2	4	no	—
79	C₄×D₄×C₄₁	—	2	4	no	—
80	C₄×D₄×C₄₁	—	2	2	no	—
81	C₄×D₄×C₄₁	—	2	2	no	—
82	C₄×D₄×C₄₁	—	4	4	no	—
83	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
84	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
85	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
86	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
87	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
88	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
89	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
90	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
91	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
92	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
93	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
94	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
95	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
96	C₂×C₄²×C₄₁	—	2	2	no	—
97	C₂×C₄²×C₄₁	—	2	2	no	—
98	C₂×C₄²×C₄₁	—	2	1	no	—
99	C₂×C₄²×C₄₁	D₄	1	1	yes	characteristic
100	C₂×C₄²×C₄₁	D₄	1	1	yes	characteristic
101	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
102	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
103	#107×C₄₁	—	2	4	no	—
104	C₄⋊C₈×C₄₁	—	2	2	no	—
105	C₄⋊C₈×C₄₁	—	2	2	no	—
106	#102×C₄₁	—	2	4	no	—
107	#102×C₄₁	—	2	4	no	—
108	#102×C₄₁	—	2	4	no	—
109	#102×C₄₁	—	4	2	no	—
110	C₂²⋊C₈×C₄₁	—	4	2	no	—
111	#95×C₄₁	—	2	1	no	—
112	#95×C₄₁	—	2	1	no	—
113	#95×C₄₁	—	2	1	no	—
114	C₂⁴×C₄₁	—	2	1	no	—
115	C₂⁴×C₄₁	—	2	2	no	—
116	C₂⁴×C₄₁	C₂×D₄	1	1	yes	characteristic
117	#41×C₄₁	—	4	32	no	—
118	C₂×Q₈×C₄₁	—	2	4	no	—
119	C₂×Q₈×C₄₁	—	4	2	no	—
120	C₂×Q₈×C₄₁	—	4	2	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	4	no	—
125	C₂×D₄×C₄₁	—	2	1	no	—
126	C₂×D₄×C₄₁	—	2	1	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	1	no	—
131	C₂×D₄×C₄₁	—	2	2	no	—
132	C₂×D₄×C₄₁	—	2	1	no	—
133	C₂×D₄×C₄₁	—	2	2	no	—
134	C₂×D₄×C₄₁	—	2	1	no	—
135	C₂×D₄×C₄₁	—	4	2	no	—
136	C₂×D₄×C₄₁	—	4	2	no	—
137	C₂×D₄×C₄₁	—	4	2	no	—
138	C₂×D₄×C₄₁	—	4	4	no	—
139	C₂×D₄×C₄₁	—	4	2	no	—
140	C₂×D₄×C₄₁	—	4	4	no	—
141	C₂×D₄×C₄₁	—	4	2	no	—
142	C₂×D₄×C₄₁	—	4	2	no	—
143	C₂×D₄×C₄₁	C₂×D₄	1	4	yes	—
144	C₂×D₄×C₄₁	#41	1	2	yes	complemented
145	C₂²×C₄×C₄₁	—	2	2	no	—
146	C₂²×C₄×C₄₁	—	2	2	no	—
147	C₂²×C₄×C₄₁	—	2	8	no	—
148	C₂²×C₄×C₄₁	—	2	1	no	—
149	C₂²×C₄×C₄₁	—	2	2	no	—
150	C₂²×C₄×C₄₁	—	2	2	no	—
151	C₂²×C₄×C₄₁	—	2	1	no	—
152	C₂²×C₄×C₄₁	—	2	1	no	—
153	C₂²×C₄×C₄₁	—	2	1	no	—
154	C₂²×C₄×C₄₁	—	2	1	no	—
155	C₂²×C₄×C₄₁	—	2	1	no	—
156	C₂²×C₄×C₄₁	—	2	1	no	—
157	C₂²×C₄×C₄₁	—	2	1	no	—
158	C₂²×C₄×C₄₁	—	2	1	no	—
159	C₂²×C₄×C₄₁	—	4	1	no	—
160	C₂²×C₄×C₄₁	—	4	1	no	—
161	C₂²×C₄×C₄₁	—	4	4	no	—
162	C₂²×C₄×C₄₁	—	4	4	no	—
163	C₂²×C₄×C₄₁	—	4	2	no	—
164	C₂²×C₄×C₄₁	—	4	2	no	—
165	C₂²×C₄×C₄₁	—	4	2	no	—
166	C₂²×C₄×C₄₁	D₈	1	4	yes	complemented
167	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
168	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
169	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
170	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
171	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
172	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
173	D₈×C₄₁	—	4	8	no	—
174	C₂×C₈×C₄₁	—	2	2	no	—
175	C₂×C₈×C₄₁	—	2	2	no	—
176	C₂×C₈×C₄₁	—	2	2	no	—
177	C₂×C₈×C₄₁	—	2	2	no	—
178	C₂×C₈×C₄₁	—	2	2	no	—
179	C₂×C₈×C₄₁	—	2	2	no	—
180	C₄⋊C₄×C₄₁	—	2	4	no	—
181	C₄⋊C₄×C₄₁	—	2	2	no	—
182	C₄⋊C₄×C₄₁	—	2	1	no	—
183	C₄⋊C₄×C₄₁	—	2	1	no	—
184	C₄⋊C₄×C₄₁	—	2	1	no	—
185	C₄⋊C₄×C₄₁	—	2	1	no	—
186	C₄⋊C₄×C₄₁	—	2	1	no	—
187	C₄⋊C₄×C₄₁	—	4	2	no	—
188	C₄⋊C₄×C₄₁	C₂×D₄	1	4	yes	—
189	C₄⋊C₄×C₄₁	#41	1	2	yes	complemented
190	C₂²⋊C₄×C₄₁	—	2	8	no	—
191	C₂²⋊C₄×C₄₁	—	2	8	no	—
192	C₂²⋊C₄×C₄₁	—	2	4	no	—
193	C₂²⋊C₄×C₄₁	—	4	2	no	—
194	C₂²⋊C₄×C₄₁	—	4	2	no	—
195	C₂²⋊C₄×C₄₁	—	4	2	no	—
196	C₂²⋊C₄×C₄₁	—	4	2	no	—
197	C₄²×C₄₁	—	2	2	no	—
198	C₄²×C₄₁	—	2	2	no	—
199	C₄²×C₄₁	—	2	1	no	—
200	C₄²×C₄₁	—	2	1	no	—
201	C₄²×C₄₁	—	4	2	no	—
202	C₄²×C₄₁	C₂×D₄	1	2	yes	—
203	C₄²×C₄₁	C₂×D₄	1	2	yes	—
204	C₂³×C₄₁	—	2	1	no	—
205	C₂³×C₄₁	—	2	1	no	—
206	C₂³×C₄₁	—	2	1	no	—
207	C₂³×C₄₁	—	2	1	no	—
208	C₂³×C₄₁	—	2	1	no	—
209	C₂³×C₄₁	—	2	1	no	—
210	C₂³×C₄₁	—	2	4	no	—
211	C₂³×C₄₁	—	2	2	no	—
212	C₂³×C₄₁	—	4	1	no	—
213	C₂³×C₄₁	—	4	2	no	—
214	C₂³×C₄₁	—	4	2	no	—
215	C₂³×C₄₁	—	4	1	no	—
216	C₂³×C₄₁	—	4	1	no	—
217	C₂³×C₄₁	—	4	2	no	—
218	C₂³×C₄₁	—	4	2	no	—
219	C₂³×C₄₁	—	4	1	no	—
220	C₂³×C₄₁	—	4	1	no	—
221	C₂³×C₄₁	—	4	1	no	—
222	C₂³×C₄₁	—	4	2	no	—
223	C₂³×C₄₁	—	4	2	no	—
224	C₂³×C₄₁	C₂×D₈	1	2	yes	—
225	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
226	Q₈×C₄₁	—	4	8	no	—
227	D₄×C₄₁	—	2	2	no	—
228	D₄×C₄₁	—	2	4	no	—
229	D₄×C₄₁	—	2	4	no	—
230	D₄×C₄₁	—	2	2	no	—
231	D₄×C₄₁	—	4	8	no	—
232	D₄×C₄₁	—	4	8	no	—
233	D₄×C₄₁	—	4	16	no	—
234	D₄×C₄₁	—	4	1	no	—
235	D₄×C₄₁	—	4	2	no	—
236	D₄×C₄₁	—	4	1	no	—
237	D₄×C₄₁	—	4	2	no	—
238	D₄×C₄₁	—	4	8	no	—
239	C₂×C₄×C₄₁	—	2	1	no	—
240	C₂×C₄×C₄₁	—	2	1	no	—
241	C₂×C₄×C₄₁	—	2	1	no	—
242	C₂×C₄×C₄₁	—	2	1	no	—
243	C₂×C₄×C₄₁	—	2	8	no	—
244	C₂×C₄×C₄₁	—	2	1	no	—
245	C₂×C₄×C₄₁	—	2	1	no	—
246	C₂×C₄×C₄₁	—	2	4	no	—
247	C₂×C₄×C₄₁	—	2	1	no	—
248	C₂×C₄×C₄₁	—	2	2	no	—
249	C₂×C₄×C₄₁	—	2	1	no	—
250	C₂×C₄×C₄₁	—	2	1	no	—
251	C₂×C₄×C₄₁	—	2	1	no	—
252	C₂×C₄×C₄₁	—	4	4	no	—
253	C₂×C₄×C₄₁	—	4	16	no	—
254	C₂×C₄×C₄₁	—	4	1	no	—
255	C₂×C₄×C₄₁	—	4	2	no	—
256	C₂×C₄×C₄₁	—	4	2	no	—
257	C₂×C₄×C₄₁	—	4	1	no	—
258	C₂×C₄×C₄₁	—	4	1	no	—
259	C₂×C₄×C₄₁	—	4	1	no	—
260	C₂×C₄×C₄₁	—	4	1	no	—
261	C₂×C₄×C₄₁	—	4	1	no	—
262	C₂×C₄×C₄₁	—	4	1	no	—
263	C₂×C₄×C₄₁	—	4	1	no	—
264	C₂×C₄×C₄₁	—	4	1	no	—
265	C₂×C₄×C₄₁	—	4	1	no	—
266	C₂×C₄×C₄₁	—	4	1	no	—
267	C₂×C₄×C₄₁	—	4	1	no	—
268	C₂×C₄×C₄₁	—	8	4	no	—
269	C₂×C₄×C₄₁	#120	1	2	yes	—
270	C₂×C₄×C₄₁	#120	1	2	yes	—
271	C₂×C₄×C₄₁	C₂×D₈	1	2	yes	—
272	C₂×C₄×C₄₁	C₂×D₈	1	2	yes	—
273	C₂×C₄×C₄₁	AGL(1,ℤ/8)	1	2	yes	—
274	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
275	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
276	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
277	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
278	C₂×C₄×C₄₁	H(5,𝔽₂)	1	1	yes	characteristic
279	C₂×C₄×C₄₁	2₋¹⁺⁴	1	1	yes	characteristic
280	C₈×C₄₁	—	4	2	no	—
281	C₈×C₄₁	—	4	2	no	—
282	#24150	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
283	C₂²×C₄₁	—	2	2	no	—
284	C₂²×C₄₁	—	2	2	no	—
285	C₂²×C₄₁	—	2	2	no	—
286	C₂²×C₄₁	—	4	1	no	—
287	C₂²×C₄₁	—	4	1	no	—
288	C₂²×C₄₁	—	4	1	no	—
289	C₂²×C₄₁	—	4	1	no	—
290	C₂²×C₄₁	—	4	2	no	—
291	C₂²×C₄₁	—	4	2	no	—
292	C₂²×C₄₁	—	4	2	no	—
293	C₂²×C₄₁	—	4	4	no	—
294	C₂²×C₄₁	—	4	4	no	—
295	C₂²×C₄₁	—	4	4	no	—
296	C₂²×C₄₁	—	8	2	no	—
297	C₂²×C₄₁	—	8	2	no	—
298	C₂²×C₄₁	—	8	1	no	—
299	C₂²×C₄₁	—	8	2	no	—
300	C₂²×C₄₁	—	8	2	no	—
301	C₂²×C₄₁	—	8	1	no	—
302	C₂²×C₄₁	—	8	1	no	—
303	C₂²×C₄₁	—	8	1	no	—
304	C₂²×C₄₁	C₂×#120	1	1	yes	characteristic
305	C₂²×C₄₁	#525	1	1	yes	characteristic
306	C₂²×C₄₁	#537	1	1	yes	characteristic
307	C₂²×C₄₁	C₂²×D₈	1	1	yes	characteristic
308	C₂²×C₄₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
309	C₂²×C₄₁	#575	1	1	yes	characteristic
310	C₂²×C₄₁	#575	1	1	yes	characteristic
311	C₄×C₄₁	—	2	2	no	—
312	C₄×C₄₁	—	2	2	no	—
313	C₄×C₄₁	—	4	2	no	—
314	C₄×C₄₁	—	4	1	no	—
315	C₄×C₄₁	—	4	4	no	—
316	C₄×C₄₁	—	4	1	no	—
317	C₄×C₄₁	—	8	1	no	—
318	C₄×C₄₁	—	8	1	no	—
319	C₄×C₄₁	#447	1	4	yes	—
320	C₄×C₄₁	#546	1	1	yes	characteristic
321	C₄×C₄₁	#547	1	1	yes	characteristic
322	C₄×C₄₁	#548	1	1	yes	characteristic
323	C₄×C₄₁	#550	1	1	yes	characteristic
324	C₂×#532	C₂×C₄₁	1	1	yes	characteristic, complemented
325	C₂×#474	C₂×C₄₁	1	1	yes	characteristic, complemented
326	C₂×#459	C₂×C₄₁	1	1	yes	characteristic, complemented
327	C₄×#121	C₂×C₄₁	1	1	yes	characteristic, complemented
328	#2033	C₂×C₄₁	1	2	yes	complemented
329	#1999	C₂×C₄₁	1	2	yes	complemented
330	#1988	C₂×C₄₁	1	1	yes	characteristic, complemented
331	#1982	C₂×C₄₁	1	1	yes	characteristic, complemented
332	#1879	C₂×C₄₁	1	2	yes	complemented
333	#1862	C₂×C₄₁	1	2	yes	complemented
334	#1797	C₂×C₄₁	1	1	yes	characteristic, complemented
335	C₂×C₄₁	—	4	2	no	—
336	C₂×C₄₁	—	8	2	no	—
337	C₂×C₄₁	—	8	4	no	—
338	C₂×C₄₁	#2407	1	1	yes	characteristic
339	C₂×C₄₁	C₂×#447	1	1	yes	characteristic
340	C₂×C₄₁	#3005	1	1	yes	characteristic
341	C₂×C₄₁	#3100	1	1	yes	characteristic
342	C₂×C₄₁	#3115	1	1	yes	characteristic
343	C₂×C₄₁	#3245	1	1	yes	characteristic
344	C₂×C₄₁	#3251	1	1	yes	characteristic
345	C₂²×#41	—	2	1	no	—
346	C₂²×D₈	C₂²×C₄₁	1	2	yes	—
347	#532	—	2	4	no	—
348	#532	—	2	4	no	—
349	C₂×C₄⋊Q₈	C₂²×C₄₁	1	1	yes	characteristic
350	C₂×#127	C₂²×C₄₁	1	1	yes	characteristic
351	C₂×#124	—	2	1	no	—
352	C₂×#121	—	2	1	no	—
353	C₂×#121	C₂²×C₄₁	1	2	yes	—
354	C₂×#121	C₂²×C₄₁	1	1	yes	characteristic
355	C₂×C₄×D₄	—	2	1	no	—
356	C₂×C₄×D₄	—	2	1	no	—
357	C₂×C₄×D₄	C₂²×C₄₁	1	2	yes	—
358	C₂×C₄×D₄	C₂²×C₄₁	1	1	yes	characteristic
359	C₂²×C₄²	C₂²×C₄₁	1	1	yes	characteristic
360	#474	—	2	4	no	—
361	#459	—	2	4	no	—
362	C₂×#107	C₂²×C₄₁	1	2	yes	—
363	C₂×C₄⋊C₈	C₂²×C₄₁	1	1	yes	characteristic
364	C₂×C₄⋊C₈	C₂²×C₄₁	1	1	yes	characteristic
365	C₂×#102	C₂²×C₄₁	1	2	yes	—
366	C₂×#102	C₂²×C₄₁	1	2	yes	—
367	C₂×#102	C₂²×C₄₁	1	2	yes	—
368	C₂×#102	C₂²×C₄₁	1	2	yes	—
369	C₂×C₂²⋊C₈	C₂²×C₄₁	1	2	yes	—
370	#390	C₂²×C₄₁	1	1	yes	characteristic
371	#389	C₂²×C₄₁	1	1	yes	characteristic
372	#388	—	2	1	no	—
373	#386	—	2	1	no	—
374	#380	C₂²×C₄₁	1	1	yes	characteristic
375	C₄×C₄⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
376	C₄×C₂²⋊C₄	—	2	1	no	—
377	#340	C₂²×C₄₁	1	2	yes	—
378	#340	C₂²×C₄₁	1	2	yes	—
379	#336	C₂²×C₄₁	1	2	yes	—
380	C₄₁	#24150	1	1	yes	characteristic, direct product factor, Sylow
381	C₂×#41	—	2	8	no	—
382	C₂×#41	—	4	4	no	—
383	C₂×#41	—	4	4	no	—
384	C₂²×Q₈	—	2	1	no	—
385	C₂²×D₄	—	2	1	no	—
386	C₂²×D₄	—	2	2	no	—
387	C₂²×D₄	—	2	1	no	—
388	C₂²×D₄	—	2	1	no	—
389	C₂²×D₄	C₂³×C₄₁	1	2	yes	—
390	C₂²×D₄	C₂³×C₄₁	1	1	yes	characteristic
391	C₂³×C₄	—	2	2	no	—
392	C₂³×C₄	—	2	1	no	—
393	C₂³×C₄	D₄×C₄₁	1	1	yes	characteristic
394	C₂³×C₄	D₄×C₄₁	1	1	yes	characteristic
395	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
396	C₂×D₈	—	2	4	no	—
397	C₂×D₈	—	2	4	no	—
398	C₂×D₈	—	4	2	no	—
399	C₂²×C₈	C₂³×C₄₁	1	2	yes	—
400	C₂²×C₈	C₂³×C₄₁	1	2	yes	—
401	C₄⋊Q₈	—	2	2	no	—
402	C₄⋊Q₈	D₄×C₄₁	1	4	yes	complemented
403	#127	—	2	2	no	—
404	#127	D₄×C₄₁	1	4	yes	complemented
405	#124	—	2	8	no	—
406	#121	—	2	8	no	—
407	#121	—	2	4	no	—
408	#121	—	2	2	no	—
409	#121	—	2	4	no	—
410	#121	—	2	2	no	—
411	C₄×D₄	—	2	8	no	—
412	C₄×D₄	—	2	4	no	—
413	C₄×D₄	—	2	4	no	—
414	C₄×D₄	—	2	2	no	—
415	C₄×D₄	—	2	2	no	—
416	C₄×D₄	—	4	4	no	—
417	C₂×C₄⋊C₄	—	2	1	no	—
418	C₂×C₄⋊C₄	—	2	1	no	—
419	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
420	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
421	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
422	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
423	C₂×C₂²⋊C₄	—	2	2	no	—
424	C₂×C₂²⋊C₄	—	2	2	no	—
425	C₂×C₂²⋊C₄	—	2	1	no	—
426	C₂×C₂²⋊C₄	—	2	1	no	—
427	C₂×C₂²⋊C₄	—	2	1	no	—
428	C₂×C₂²⋊C₄	—	2	1	no	—
429	C₂×C₂²⋊C₄	—	2	1	no	—
430	C₂×C₄²	—	2	2	no	—
431	C₂×C₄²	—	2	2	no	—
432	C₂×C₄²	—	2	1	no	—
433	C₂×C₄²	D₄×C₄₁	1	1	yes	characteristic
434	C₂×C₄²	D₄×C₄₁	1	1	yes	characteristic
435	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
436	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
437	#107	—	2	4	no	—
438	C₄⋊C₈	—	2	2	no	—
439	C₄⋊C₈	—	2	2	no	—
440	#102	—	2	4	no	—
441	#102	—	2	4	no	—
442	#102	—	2	4	no	—
443	#102	—	4	2	no	—
444	C₂²⋊C₈	—	4	2	no	—
445	#95	—	2	1	no	—
446	#95	—	2	1	no	—
447	#95	—	2	1	no	—
448	C₂⁴	—	2	1	no	—
449	C₂⁴	—	2	2	no	—
450	C₂⁴	C₂×D₄×C₄₁	1	1	yes	characteristic
451	#41	—	4	32	no	—
452	C₂×Q₈	—	2	4	no	—
453	C₂×Q₈	—	4	2	no	—
454	C₂×Q₈	—	4	2	no	—
455	C₂×D₄	—	2	8	no	—
456	C₂×D₄	—	2	4	no	—
457	C₂×D₄	—	2	4	no	—
458	C₂×D₄	—	2	4	no	—
459	C₂×D₄	—	2	1	no	—
460	C₂×D₄	—	2	1	no	—
461	C₂×D₄	—	2	2	no	—
462	C₂×D₄	—	2	2	no	—
463	C₂×D₄	—	2	2	no	—
464	C₂×D₄	—	2	1	no	—
465	C₂×D₄	—	2	2	no	—
466	C₂×D₄	—	2	1	no	—
467	C₂×D₄	—	2	2	no	—
468	C₂×D₄	—	2	1	no	—
469	C₂×D₄	—	4	2	no	—
470	C₂×D₄	—	4	2	no	—
471	C₂×D₄	—	4	4	no	—
472	C₂×D₄	—	4	2	no	—
473	C₂×D₄	—	4	2	no	—
474	C₂×D₄	—	4	4	no	—
475	C₂×D₄	—	4	2	no	—
476	C₂×D₄	—	4	2	no	—
477	C₂×D₄	C₂×D₄×C₄₁	1	4	yes	—
478	C₂×D₄	#41×C₄₁	1	2	yes	complemented
479	C₂²×C₄	—	2	2	no	—
480	C₂²×C₄	—	2	2	no	—
481	C₂²×C₄	—	2	8	no	—
482	C₂²×C₄	—	2	1	no	—
483	C₂²×C₄	—	2	2	no	—
484	C₂²×C₄	—	2	2	no	—
485	C₂²×C₄	—	2	1	no	—
486	C₂²×C₄	—	2	1	no	—
487	C₂²×C₄	—	2	1	no	—
488	C₂²×C₄	—	2	1	no	—
489	C₂²×C₄	—	2	1	no	—
490	C₂²×C₄	—	2	1	no	—
491	C₂²×C₄	—	2	1	no	—
492	C₂²×C₄	—	2	1	no	—
493	C₂²×C₄	—	4	1	no	—
494	C₂²×C₄	—	4	1	no	—
495	C₂²×C₄	—	4	4	no	—
496	C₂²×C₄	—	4	4	no	—
497	C₂²×C₄	—	4	2	no	—
498	C₂²×C₄	—	4	2	no	—
499	C₂²×C₄	—	4	2	no	—
500	C₂²×C₄	D₈×C₄₁	1	4	yes	complemented
501	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
502	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
503	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
504	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
505	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
506	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
507	D₈	—	4	8	no	—
508	C₂×C₈	—	2	2	no	—
509	C₂×C₈	—	2	2	no	—
510	C₂×C₈	—	2	2	no	—
511	C₂×C₈	—	2	2	no	—
512	C₂×C₈	—	2	2	no	—
513	C₂×C₈	—	2	2	no	—
514	C₄⋊C₄	—	2	4	no	—
515	C₄⋊C₄	—	2	2	no	—
516	C₄⋊C₄	—	2	1	no	—
517	C₄⋊C₄	—	2	1	no	—
518	C₄⋊C₄	—	2	1	no	—
519	C₄⋊C₄	—	2	1	no	—
520	C₄⋊C₄	—	2	1	no	—
521	C₄⋊C₄	—	4	2	no	—
522	C₄⋊C₄	C₂×D₄×C₄₁	1	4	yes	—
523	C₄⋊C₄	#41×C₄₁	1	2	yes	complemented
524	C₂²⋊C₄	—	2	8	no	—
525	C₂²⋊C₄	—	2	8	no	—
526	C₂²⋊C₄	—	2	4	no	—
527	C₂²⋊C₄	—	4	2	no	—
528	C₂²⋊C₄	—	4	2	no	—
529	C₂²⋊C₄	—	4	2	no	—
530	C₂²⋊C₄	—	4	2	no	—
531	C₄²	—	2	2	no	—
532	C₄²	—	2	2	no	—
533	C₄²	—	2	1	no	—
534	C₄²	—	2	1	no	—
535	C₄²	—	4	2	no	—
536	C₄²	C₂×D₄×C₄₁	1	2	yes	—
537	C₄²	C₂×D₄×C₄₁	1	2	yes	—
538	C₂³	—	2	1	no	—
539	C₂³	—	2	1	no	—
540	C₂³	—	2	1	no	—
541	C₂³	—	2	1	no	—
542	C₂³	—	2	1	no	—
543	C₂³	—	2	1	no	—
544	C₂³	—	2	4	no	—
545	C₂³	—	2	2	no	—
546	C₂³	—	4	1	no	—
547	C₂³	—	4	2	no	—
548	C₂³	—	4	2	no	—
549	C₂³	—	4	1	no	—
550	C₂³	—	4	1	no	—
551	C₂³	—	4	2	no	—
552	C₂³	—	4	2	no	—
553	C₂³	—	4	1	no	—
554	C₂³	—	4	1	no	—
555	C₂³	—	4	1	no	—
556	C₂³	—	4	2	no	—
557	C₂³	—	4	2	no	—
558	C₂³	C₂×D₈×C₄₁	1	2	yes	—
559	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
560	Q₈	—	4	8	no	—
561	D₄	—	2	2	no	—
562	D₄	—	2	4	no	—
563	D₄	—	2	4	no	—
564	D₄	—	2	2	no	—
565	D₄	—	4	8	no	—
566	D₄	—	4	16	no	—
567	D₄	—	4	8	no	—
568	D₄	—	4	1	no	—
569	D₄	—	4	2	no	—
570	D₄	—	4	1	no	—
571	D₄	—	4	2	no	—
572	D₄	—	4	8	no	—
573	C₂×C₄	—	2	1	no	—
574	C₂×C₄	—	2	1	no	—
575	C₂×C₄	—	2	1	no	—
576	C₂×C₄	—	2	1	no	—
577	C₂×C₄	—	2	8	no	—
578	C₂×C₄	—	2	1	no	—
579	C₂×C₄	—	2	1	no	—
580	C₂×C₄	—	2	4	no	—
581	C₂×C₄	—	2	1	no	—
582	C₂×C₄	—	2	2	no	—
583	C₂×C₄	—	2	1	no	—
584	C₂×C₄	—	2	1	no	—
585	C₂×C₄	—	2	1	no	—
586	C₂×C₄	—	4	16	no	—
587	C₂×C₄	—	4	4	no	—
588	C₂×C₄	—	4	1	no	—
589	C₂×C₄	—	4	2	no	—
590	C₂×C₄	—	4	2	no	—
591	C₂×C₄	—	4	1	no	—
592	C₂×C₄	—	4	1	no	—
593	C₂×C₄	—	4	1	no	—
594	C₂×C₄	—	4	1	no	—
595	C₂×C₄	—	4	1	no	—
596	C₂×C₄	—	4	1	no	—
597	C₂×C₄	—	4	1	no	—
598	C₂×C₄	—	4	1	no	—
599	C₂×C₄	—	4	1	no	—
600	C₂×C₄	—	4	1	no	—
601	C₂×C₄	—	4	1	no	—
602	C₂×C₄	—	8	4	no	—
603	C₂×C₄	#120×C₄₁	1	2	yes	—
604	C₂×C₄	#120×C₄₁	1	2	yes	—
605	C₂×C₄	C₂×D₈×C₄₁	1	2	yes	—
606	C₂×C₄	C₂×D₈×C₄₁	1	2	yes	—
607	C₂×C₄	AGL(1,ℤ/8)×C₄₁	1	2	yes	—
608	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
609	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
610	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
611	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
612	C₂×C₄	H(5,𝔽₂)×C₄₁	1	1	yes	characteristic
613	C₂×C₄	2₋¹⁺⁴×C₄₁	1	1	yes	characteristic
614	C₈	—	4	2	no	—
615	C₈	—	4	2	no	—
616	C₂²	—	2	2	no	—
617	C₂²	—	2	2	no	—
618	C₂²	—	2	2	no	—
619	C₂²	—	4	1	no	—
620	C₂²	—	4	1	no	—
621	C₂²	—	4	1	no	—
622	C₂²	—	4	1	no	—
623	C₂²	—	4	2	no	—
624	C₂²	—	4	2	no	—
625	C₂²	—	4	2	no	—
626	C₂²	—	4	4	no	—
627	C₂²	—	4	4	no	—
628	C₂²	—	4	4	no	—
629	C₂²	—	8	2	no	—
630	C₂²	—	8	2	no	—
631	C₂²	—	8	1	no	—
632	C₂²	—	8	2	no	—
633	C₂²	—	8	2	no	—
634	C₂²	—	8	1	no	—
635	C₂²	—	8	1	no	—
636	C₂²	—	8	1	no	—
637	C₂²	C₂×#120×C₄₁	1	1	yes	characteristic
638	C₂²	C₄₁×#525	1	1	yes	characteristic
639	C₂²	C₄₁×#537	1	1	yes	characteristic
640	C₂²	C₂²×D₈×C₄₁	1	1	yes	characteristic
641	C₂²	C₂×AGL(1,ℤ/8)×C₄₁	1	1	yes	characteristic
642	C₂²	C₄₁×#575	1	1	yes	characteristic
643	C₂²	C₄₁×#575	1	1	yes	characteristic
644	C₄	—	2	2	no	—
645	C₄	—	2	2	no	—
646	C₄	—	4	2	no	—
647	C₄	—	4	1	no	—
648	C₄	—	4	4	no	—
649	C₄	—	4	1	no	—
650	C₄	—	8	1	no	—
651	C₄	—	8	1	no	—
652	C₄	C₄₁×#447	1	4	yes	—
653	C₄	C₄₁×#546	1	1	yes	characteristic
654	C₄	C₄₁×#547	1	1	yes	characteristic
655	C₄	C₄₁×#548	1	1	yes	characteristic
656	C₄	C₄₁×#550	1	1	yes	characteristic
657	C₂	—	4	2	no	—
658	C₂	—	8	2	no	—
659	C₂	—	8	4	no	—
660	C₂	C₄₁×#2407	1	1	yes	characteristic
661	C₂	C₂×C₄₁×#447	1	1	yes	characteristic
662	C₂	C₄₁×#3005	1	1	yes	characteristic
663	C₂	C₄₁×#3100	1	1	yes	characteristic
664	C₂	C₄₁×#3115	1	1	yes	characteristic
665	C₂	C₄₁×#3245	1	1	yes	characteristic
666	C₂	C₄₁×#3251	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₄₁	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₁
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×#532	C₂	semidirect
2. C₂×C₄₁×#474	C₂	semidirect
3. C₂×C₄₁×#459	C₂	semidirect
4. C₄×#121×C₄₁	C₂	semidirect
5. C₄₁×#2033	C₂	semidirect
6. C₄₁×#1999	C₂	semidirect
7. C₄₁×#1988	C₂	semidirect
8. C₄₁×#1982	C₂	semidirect
9. C₄₁×#1879	C₂	semidirect
10. C₄₁×#1862	C₂	semidirect
11. C₄₁×#1797	C₂	semidirect
68. C₄⋊Q₈×C₄₁	D₄	semidirect
70. #127×C₄₁	D₄	semidirect
144. C₂×D₄×C₄₁	#41	semidirect
166. C₂²×C₄×C₄₁	D₈	semidirect
189. C₄⋊C₄×C₄₁	#41	semidirect
282. #24150	C₄₁	direct (N × H)
324. C₂×#532	C₂×C₄₁	semidirect
325. C₂×#474	C₂×C₄₁	semidirect
326. C₂×#459	C₂×C₄₁	semidirect
327. C₄×#121	C₂×C₄₁	semidirect
328. #2033	C₂×C₄₁	semidirect
329. #1999	C₂×C₄₁	semidirect
330. #1988	C₂×C₄₁	semidirect
331. #1982	C₂×C₄₁	semidirect
332. #1879	C₂×C₄₁	semidirect
333. #1862	C₂×C₄₁	semidirect
334. #1797	C₂×C₄₁	semidirect
380. C₄₁	#24150	direct (N × H)
402. C₄⋊Q₈	D₄×C₄₁	semidirect
404. #127	D₄×C₄₁	semidirect
478. C₂×D₄	#41×C₄₁	semidirect
500. C₂²×C₄	D₈×C₄₁	semidirect
523. C₄⋊C₄	#41×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×#532	2
C₂×C₄₁×#474	2
C₂×C₄₁×#459	2
C₄×#121×C₄₁	2
C₄₁×#2033	2
C₄₁×#1999	2
C₄₁×#1988	2
C₄₁×#1982	2
C₄₁×#1879	2
C₄₁×#1862	2
C₄₁×#1797	2
#24150	41

Subgroups — C41×#24150 #23800351

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#24150 #23800351