Subgroups — C₄₁×#25922 #23802123

Order 10496.

1072 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₁×#3501	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄₁×#3140	C₂	1	2	yes	maximal, complemented
3	C₄₁×#2544	C₂	1	1	yes	maximal, characteristic
4	C₄₁×#2028	C₂	1	2	yes	maximal, complemented
5	C₄₁×#2027	C₂	1	2	yes	maximal, complemented
6	C₄₁×#1986	C₂	1	2	yes	maximal, complemented
7	C₄₁×#1887	C₂	1	2	yes	maximal
8	C₄₁×#1885	C₂	1	2	yes	maximal, complemented
9	C₄×#100×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄₁×#554	—	2	2	no	—
11	C₄₁×#554	—	2	4	no	—
12	D₄×Q₈×C₄₁	—	2	2	no	—
13	C₄₁×#544	C₂²	1	2	yes	—
14	C₄₁×#543	—	2	2	no	—
15	C₄₁×#533	C₂²	1	2	yes	—
16	C₂×#127×C₄₁	C₂²	1	1	yes	characteristic
17	C₂×#124×C₄₁	C₂²	1	1	yes	characteristic
18	C₂×#124×C₄₁	C₂²	1	1	yes	characteristic
19	C₂×C₂²⋊Q₈×C₄₁	—	2	2	no	—
20	C₄₁×#518	C₂²	1	2	yes	—
21	C₂×C₄×D₄×C₄₁	C₂²	1	1	yes	characteristic
22	C₄₁×#489	—	2	2	no	—
23	C₄₁×#489	—	2	2	no	—
24	C₄₁×#488	—	2	4	no	—
25	C₄₁×#419	C₂²	1	4	yes	—
26	C₄₁×#418	C₂²	1	4	yes	—
27	C₂×#100×C₄₁	C₂²	1	2	yes	—
28	C₄×M₁₆×C₄₁	C₂²	1	2	yes	—
29	C₄₁×#394	—	2	2	no	—
30	C₄₁×#391	C₂²	1	1	yes	characteristic
31	C₄₁×#390	C₂²	1	1	yes	characteristic
32	C₄₁×#386	—	2	2	no	—
33	C₄×C₄⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
34	C₄₁×#343	C₂²	1	2	yes	—
35	C₄₁×#339	C₂²	1	4	yes	—
36	C₄₁×#339	C₂²	1	4	yes	—
37	C₂²×Q₈×C₄₁	—	2	2	no	—
38	C₂²×Q₈×C₄₁	C₂³	1	1	yes	characteristic
39	C₂²×D₄×C₄₁	—	2	2	no	—
40	C₂²×D₄×C₄₁	C₂³	1	1	yes	characteristic
41	C₂²×D₄×C₄₁	C₂³	1	1	yes	characteristic
42	C₂³×C₄×C₄₁	D₄	1	2	yes	—
43	C₂×M₁₆×C₄₁	C₂³	1	4	yes	—
44	C₄⋊Q₈×C₄₁	—	2	4	no	—
45	C₄⋊Q₈×C₄₁	D₄	1	2	yes	complemented
46	C₄⋊Q₈×C₄₁	D₄	1	2	yes	complemented
47	#127×C₄₁	—	2	4	no	—
48	#125×C₄₁	—	2	4	no	—
49	#125×C₄₁	D₄	1	4	yes	complemented
50	#124×C₄₁	—	2	4	no	—
51	#124×C₄₁	—	2	2	no	—
52	#124×C₄₁	—	2	2	no	—
53	C₂²⋊Q₈×C₄₁	—	2	4	no	—
54	C₂²⋊Q₈×C₄₁	—	2	4	no	—
55	C₂²⋊Q₈×C₄₁	—	2	8	no	—
56	C₂²⋊Q₈×C₄₁	—	2	8	no	—
57	C₂²⋊Q₈×C₄₁	—	2	2	no	—
58	C₂²⋊Q₈×C₄₁	—	2	4	no	—
59	C₂²⋊Q₈×C₄₁	—	2	2	no	—
60	C₄×Q₈×C₄₁	—	2	2	no	—
61	C₄×Q₈×C₄₁	—	2	2	no	—
62	C₄×D₄×C₄₁	—	2	4	no	—
63	C₄×D₄×C₄₁	—	2	4	no	—
64	C₄×D₄×C₄₁	—	2	2	no	—
65	C₄×D₄×C₄₁	—	2	2	no	—
66	#117×C₄₁	C₂³	1	4	yes	—
67	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
68	C₂×C₄⋊C₄×C₄₁	—	2	4	no	—
69	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
70	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
71	C₂×C₂²⋊C₄×C₄₁	—	2	4	no	—
72	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
73	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
74	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
75	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
76	C₂×C₂²⋊C₄×C₄₁	D₄	1	2	yes	—
77	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
78	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
79	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
80	#103×C₄₁	—	2	4	no	—
81	#103×C₄₁	—	2	4	no	—
82	#102×C₄₁	—	2	4	no	—
83	#102×C₄₁	—	2	4	no	—
84	#100×C₄₁	—	2	4	no	—
85	#97×C₄₁	—	2	2	no	—
86	C₄×C₈×C₄₁	—	2	2	no	—
87	#95×C₄₁	—	2	1	no	—
88	#95×C₄₁	—	2	2	no	—
89	C₂⁴×C₄₁	—	2	1	no	—
90	C₂⁴×C₄₁	C₂×D₄	1	2	yes	—
91	C₂×Q₈×C₄₁	—	2	4	no	—
92	C₂×Q₈×C₄₁	—	2	2	no	—
93	C₂×Q₈×C₄₁	—	2	2	no	—
94	C₂×Q₈×C₄₁	—	2	2	no	—
95	C₂×Q₈×C₄₁	—	2	2	no	—
96	C₂×Q₈×C₄₁	—	2	2	no	—
97	C₂×Q₈×C₄₁	—	8	4	no	—
98	C₂×D₄×C₄₁	—	2	2	no	—
99	C₂×D₄×C₄₁	—	2	2	no	—
100	C₂×D₄×C₄₁	—	2	2	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	—	4	4	no	—
105	C₂×D₄×C₄₁	—	8	2	no	—
106	C₂×D₄×C₄₁	#41	1	4	yes	—
107	C₂²×C₄×C₄₁	—	2	1	no	—
108	C₂²×C₄×C₄₁	—	2	4	no	—
109	C₂²×C₄×C₄₁	—	2	4	no	—
110	C₂²×C₄×C₄₁	—	2	2	no	—
111	C₂²×C₄×C₄₁	—	2	2	no	—
112	C₂²×C₄×C₄₁	—	2	1	no	—
113	C₂²×C₄×C₄₁	—	2	1	no	—
114	C₂²×C₄×C₄₁	—	8	2	no	—
115	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
116	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
117	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
118	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
119	M₁₆×C₄₁	—	2	4	no	—
120	M₁₆×C₄₁	—	2	4	no	—
121	C₂×C₈×C₄₁	—	2	4	no	—
122	C₄⋊C₄×C₄₁	—	2	4	no	—
123	C₄⋊C₄×C₄₁	—	2	8	no	—
124	C₄⋊C₄×C₄₁	—	2	4	no	—
125	C₄⋊C₄×C₄₁	—	2	2	no	—
126	C₄⋊C₄×C₄₁	—	2	4	no	—
127	C₄⋊C₄×C₄₁	—	2	2	no	—
128	C₄⋊C₄×C₄₁	—	2	2	no	—
129	C₄⋊C₄×C₄₁	—	4	2	no	—
130	C₄⋊C₄×C₄₁	C₂×D₄	1	4	yes	—
131	C₄⋊C₄×C₄₁	C₂×D₄	1	4	yes	—
132	C₂²⋊C₄×C₄₁	—	2	8	no	—
133	C₂²⋊C₄×C₄₁	—	2	4	no	—
134	C₂²⋊C₄×C₄₁	—	2	4	no	—
135	C₂²⋊C₄×C₄₁	—	4	4	no	—
136	C₂²⋊C₄×C₄₁	—	4	2	no	—
137	C₂²⋊C₄×C₄₁	—	4	1	no	—
138	C₂²⋊C₄×C₄₁	—	4	1	no	—
139	C₂²⋊C₄×C₄₁	—	8	2	no	—
140	C₄²×C₄₁	—	2	4	no	—
141	C₄²×C₄₁	—	2	2	no	—
142	C₄²×C₄₁	—	2	2	no	—
143	C₄²×C₄₁	C₂×D₄	1	2	yes	—
144	C₄²×C₄₁	C₂×D₄	1	2	yes	—
145	C₂³×C₄₁	—	2	2	no	—
146	C₂³×C₄₁	—	2	2	no	—
147	C₂³×C₄₁	—	4	2	no	—
148	C₂³×C₄₁	—	4	2	no	—
149	C₂³×C₄₁	—	4	2	no	—
150	C₂³×C₄₁	—	4	2	no	—
151	C₂³×C₄₁	—	4	1	no	—
152	C₂³×C₄₁	—	4	1	no	—
153	C₂³×C₄₁	—	4	1	no	—
154	C₂³×C₄₁	#124	1	4	yes	—
155	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
156	Q₈×C₄₁	—	4	4	no	—
157	Q₈×C₄₁	—	4	4	no	—
158	Q₈×C₄₁	—	8	2	no	—
159	Q₈×C₄₁	—	8	4	no	—
160	D₄×C₄₁	—	2	8	no	—
161	D₄×C₄₁	—	4	4	no	—
162	D₄×C₄₁	—	8	8	no	—
163	C₂×C₄×C₄₁	—	2	2	no	—
164	C₂×C₄×C₄₁	—	2	4	no	—
165	C₂×C₄×C₄₁	—	2	4	no	—
166	C₂×C₄×C₄₁	—	2	2	no	—
167	C₂×C₄×C₄₁	—	4	1	no	—
168	C₂×C₄×C₄₁	—	4	1	no	—
169	C₂×C₄×C₄₁	—	4	4	no	—
170	C₂×C₄×C₄₁	—	4	1	no	—
171	C₂×C₄×C₄₁	—	4	1	no	—
172	C₂×C₄×C₄₁	—	4	2	no	—
173	C₂×C₄×C₄₁	—	4	1	no	—
174	C₂×C₄×C₄₁	—	4	1	no	—
175	C₂×C₄×C₄₁	—	4	1	no	—
176	C₂×C₄×C₄₁	—	4	1	no	—
177	C₂×C₄×C₄₁	—	4	1	no	—
178	C₂×C₄×C₄₁	—	4	1	no	—
179	C₂×C₄×C₄₁	—	8	2	no	—
180	C₂×C₄×C₄₁	—	8	4	no	—
181	C₂×C₄×C₄₁	—	8	4	no	—
182	C₂×C₄×C₄₁	#120	1	2	yes	—
183	C₂×C₄×C₄₁	#120	1	1	yes	characteristic
184	C₂×C₄×C₄₁	#120	1	1	yes	characteristic
185	C₂×C₄×C₄₁	C₂²×D₄	1	2	yes	—
186	C₂×C₄×C₄₁	C₂×#41	1	2	yes	—
187	C₂×C₄×C₄₁	2₋¹⁺⁴	1	2	yes	—
188	C₈×C₄₁	—	4	4	no	—
189	#25922	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
190	C₂²×C₄₁	—	2	1	no	—
191	C₂²×C₄₁	—	2	1	no	—
192	C₂²×C₄₁	—	2	4	no	—
193	C₂²×C₄₁	—	4	4	no	—
194	C₂²×C₄₁	—	4	2	no	—
195	C₂²×C₄₁	—	4	2	no	—
196	C₂²×C₄₁	—	8	2	no	—
197	C₂²×C₄₁	—	8	2	no	—
198	C₂²×C₄₁	—	8	2	no	—
199	C₂²×C₄₁	—	8	1	no	—
200	C₂²×C₄₁	—	8	1	no	—
201	C₂²×C₄₁	—	8	1	no	—
202	C₂²×C₄₁	C₂×#120	1	1	yes	characteristic
203	C₂²×C₄₁	C₂×#124	1	1	yes	characteristic
204	C₂²×C₄₁	#536	1	1	yes	characteristic
205	C₄×C₄₁	—	2	2	no	—
206	C₄×C₄₁	—	2	1	no	—
207	C₄×C₄₁	—	2	1	no	—
208	C₄×C₄₁	—	4	2	no	—
209	C₄×C₄₁	—	4	4	no	—
210	C₄×C₄₁	—	4	2	no	—
211	C₄×C₄₁	—	4	4	no	—
212	C₄×C₄₁	—	8	1	no	—
213	C₄×C₄₁	—	8	1	no	—
214	C₄×C₄₁	#548	1	4	yes	—
215	#3501	C₂×C₄₁	1	1	yes	characteristic, complemented
216	#3140	C₂×C₄₁	1	2	yes	complemented
217	#2544	C₂×C₄₁	1	1	yes	characteristic
218	#2028	C₂×C₄₁	1	2	yes	complemented
219	#2027	C₂×C₄₁	1	2	yes	complemented
220	#1986	C₂×C₄₁	1	2	yes	complemented
221	#1887	C₂×C₄₁	1	2	yes	—
222	#1885	C₂×C₄₁	1	2	yes	complemented
223	C₄×#100	C₂×C₄₁	1	1	yes	characteristic, complemented
224	C₂×C₄₁	—	2	1	no	—
225	C₂×C₄₁	—	2	1	no	—
226	C₂×C₄₁	—	4	4	no	—
227	C₂×C₄₁	—	16	1	no	—
228	C₂×C₄₁	#2436	1	1	yes	characteristic
229	C₂×C₄₁	#3018	1	1	yes	characteristic
230	C₂×C₄₁	#3019	1	1	yes	characteristic
231	#554	—	2	2	no	—
232	#554	—	2	4	no	—
233	D₄×Q₈	—	2	2	no	—
234	#544	C₂²×C₄₁	1	2	yes	—
235	#543	—	2	2	no	—
236	#533	C₂²×C₄₁	1	2	yes	—
237	C₂×#127	C₂²×C₄₁	1	1	yes	characteristic
238	C₂×#124	C₂²×C₄₁	1	1	yes	characteristic
239	C₂×#124	C₂²×C₄₁	1	1	yes	characteristic
240	C₂×C₂²⋊Q₈	—	2	2	no	—
241	#518	C₂²×C₄₁	1	2	yes	—
242	C₂×C₄×D₄	C₂²×C₄₁	1	1	yes	characteristic
243	#489	—	2	2	no	—
244	#489	—	2	2	no	—
245	#488	—	2	4	no	—
246	#419	C₂²×C₄₁	1	4	yes	—
247	#418	C₂²×C₄₁	1	4	yes	—
248	C₂×#100	C₂²×C₄₁	1	2	yes	—
249	C₄×M₁₆	C₂²×C₄₁	1	2	yes	—
250	#394	—	2	2	no	—
251	#391	C₂²×C₄₁	1	1	yes	characteristic
252	#390	C₂²×C₄₁	1	1	yes	characteristic
253	#386	—	2	2	no	—
254	C₄×C₄⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
255	#343	C₂²×C₄₁	1	2	yes	—
256	#339	C₂²×C₄₁	1	4	yes	—
257	#339	C₂²×C₄₁	1	4	yes	—
258	C₄₁	#25922	1	1	yes	characteristic, direct product factor, Sylow
259	C₂²×Q₈	—	2	2	no	—
260	C₂²×Q₈	C₂³×C₄₁	1	1	yes	characteristic
261	C₂²×D₄	—	2	2	no	—
262	C₂²×D₄	C₂³×C₄₁	1	1	yes	characteristic
263	C₂²×D₄	C₂³×C₄₁	1	1	yes	characteristic
264	C₂³×C₄	D₄×C₄₁	1	2	yes	—
265	C₂×M₁₆	C₂³×C₄₁	1	4	yes	—
266	C₄⋊Q₈	—	2	4	no	—
267	C₄⋊Q₈	D₄×C₄₁	1	2	yes	complemented
268	C₄⋊Q₈	D₄×C₄₁	1	2	yes	complemented
269	#127	—	2	4	no	—
270	#125	—	2	4	no	—
271	#125	D₄×C₄₁	1	4	yes	complemented
272	#124	—	2	4	no	—
273	#124	—	2	2	no	—
274	#124	—	2	2	no	—
275	C₂²⋊Q₈	—	2	4	no	—
276	C₂²⋊Q₈	—	2	4	no	—
277	C₂²⋊Q₈	—	2	8	no	—
278	C₂²⋊Q₈	—	2	8	no	—
279	C₂²⋊Q₈	—	2	2	no	—
280	C₂²⋊Q₈	—	2	4	no	—
281	C₂²⋊Q₈	—	2	2	no	—
282	C₄×Q₈	—	2	2	no	—
283	C₄×Q₈	—	2	2	no	—
284	C₄×D₄	—	2	4	no	—
285	C₄×D₄	—	2	4	no	—
286	C₄×D₄	—	2	2	no	—
287	C₄×D₄	—	2	2	no	—
288	#117	C₂³×C₄₁	1	4	yes	—
289	C₂×C₄⋊C₄	—	2	2	no	—
290	C₂×C₄⋊C₄	—	2	4	no	—
291	C₂×C₄⋊C₄	—	2	1	no	—
292	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
293	C₂×C₂²⋊C₄	—	2	4	no	—
294	C₂×C₂²⋊C₄	—	2	2	no	—
295	C₂×C₂²⋊C₄	—	2	1	no	—
296	C₂×C₂²⋊C₄	—	2	1	no	—
297	C₂×C₂²⋊C₄	—	2	2	no	—
298	C₂×C₂²⋊C₄	D₄×C₄₁	1	2	yes	—
299	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
300	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
301	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
302	#103	—	2	4	no	—
303	#103	—	2	4	no	—
304	#102	—	2	4	no	—
305	#102	—	2	4	no	—
306	#100	—	2	4	no	—
307	#97	—	2	2	no	—
308	C₄×C₈	—	2	2	no	—
309	#95	—	2	1	no	—
310	#95	—	2	2	no	—
311	C₂⁴	—	2	1	no	—
312	C₂⁴	C₂×D₄×C₄₁	1	2	yes	—
313	C₂×Q₈	—	2	4	no	—
314	C₂×Q₈	—	2	2	no	—
315	C₂×Q₈	—	2	2	no	—
316	C₂×Q₈	—	2	2	no	—
317	C₂×Q₈	—	2	2	no	—
318	C₂×Q₈	—	2	2	no	—
319	C₂×Q₈	—	8	4	no	—
320	C₂×D₄	—	2	2	no	—
321	C₂×D₄	—	2	2	no	—
322	C₂×D₄	—	2	2	no	—
323	C₂×D₄	—	2	2	no	—
324	C₂×D₄	—	2	2	no	—
325	C₂×D₄	—	4	4	no	—
326	C₂×D₄	—	4	4	no	—
327	C₂×D₄	—	8	2	no	—
328	C₂×D₄	#41×C₄₁	1	4	yes	—
329	C₂²×C₄	—	2	1	no	—
330	C₂²×C₄	—	2	4	no	—
331	C₂²×C₄	—	2	4	no	—
332	C₂²×C₄	—	2	2	no	—
333	C₂²×C₄	—	2	2	no	—
334	C₂²×C₄	—	2	1	no	—
335	C₂²×C₄	—	2	1	no	—
336	C₂²×C₄	—	8	2	no	—
337	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
338	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
339	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
340	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
341	M₁₆	—	2	4	no	—
342	M₁₆	—	2	4	no	—
343	C₂×C₈	—	2	4	no	—
344	C₄⋊C₄	—	2	4	no	—
345	C₄⋊C₄	—	2	8	no	—
346	C₄⋊C₄	—	2	4	no	—
347	C₄⋊C₄	—	2	2	no	—
348	C₄⋊C₄	—	2	4	no	—
349	C₄⋊C₄	—	2	2	no	—
350	C₄⋊C₄	—	2	2	no	—
351	C₄⋊C₄	—	4	2	no	—
352	C₄⋊C₄	C₂×D₄×C₄₁	1	4	yes	—
353	C₄⋊C₄	C₂×D₄×C₄₁	1	4	yes	—
354	C₂²⋊C₄	—	2	8	no	—
355	C₂²⋊C₄	—	2	4	no	—
356	C₂²⋊C₄	—	2	4	no	—
357	C₂²⋊C₄	—	4	4	no	—
358	C₂²⋊C₄	—	4	2	no	—
359	C₂²⋊C₄	—	4	1	no	—
360	C₂²⋊C₄	—	4	1	no	—
361	C₂²⋊C₄	—	8	2	no	—
362	C₄²	—	2	4	no	—
363	C₄²	—	2	2	no	—
364	C₄²	—	2	2	no	—
365	C₄²	C₂×D₄×C₄₁	1	2	yes	—
366	C₄²	C₂×D₄×C₄₁	1	2	yes	—
367	C₂³	—	2	2	no	—
368	C₂³	—	2	2	no	—
369	C₂³	—	4	2	no	—
370	C₂³	—	4	2	no	—
371	C₂³	—	4	2	no	—
372	C₂³	—	4	2	no	—
373	C₂³	—	4	1	no	—
374	C₂³	—	4	1	no	—
375	C₂³	—	4	1	no	—
376	C₂³	#124×C₄₁	1	4	yes	—
377	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
378	Q₈	—	4	4	no	—
379	Q₈	—	4	4	no	—
380	Q₈	—	8	2	no	—
381	Q₈	—	8	4	no	—
382	D₄	—	2	8	no	—
383	D₄	—	4	4	no	—
384	D₄	—	8	8	no	—
385	C₂×C₄	—	2	2	no	—
386	C₂×C₄	—	2	4	no	—
387	C₂×C₄	—	2	4	no	—
388	C₂×C₄	—	2	2	no	—
389	C₂×C₄	—	4	1	no	—
390	C₂×C₄	—	4	1	no	—
391	C₂×C₄	—	4	4	no	—
392	C₂×C₄	—	4	1	no	—
393	C₂×C₄	—	4	1	no	—
394	C₂×C₄	—	4	2	no	—
395	C₂×C₄	—	4	1	no	—
396	C₂×C₄	—	4	1	no	—
397	C₂×C₄	—	4	1	no	—
398	C₂×C₄	—	4	1	no	—
399	C₂×C₄	—	4	1	no	—
400	C₂×C₄	—	4	1	no	—
401	C₂×C₄	—	8	2	no	—
402	C₂×C₄	—	8	4	no	—
403	C₂×C₄	—	8	4	no	—
404	C₂×C₄	#120×C₄₁	1	2	yes	—
405	C₂×C₄	#120×C₄₁	1	1	yes	characteristic
406	C₂×C₄	#120×C₄₁	1	1	yes	characteristic
407	C₂×C₄	C₂²×D₄×C₄₁	1	2	yes	—
408	C₂×C₄	C₂×#41×C₄₁	1	2	yes	—
409	C₂×C₄	2₋¹⁺⁴×C₄₁	1	2	yes	—
410	C₈	—	4	4	no	—
411	C₂²	—	2	1	no	—
412	C₂²	—	2	1	no	—
413	C₂²	—	2	4	no	—
414	C₂²	—	4	4	no	—
415	C₂²	—	4	2	no	—
416	C₂²	—	4	2	no	—
417	C₂²	—	8	2	no	—
418	C₂²	—	8	2	no	—
419	C₂²	—	8	2	no	—
420	C₂²	—	8	1	no	—
421	C₂²	—	8	1	no	—
422	C₂²	—	8	1	no	—
423	C₂²	C₂×#120×C₄₁	1	1	yes	characteristic
424	C₂²	C₂×#124×C₄₁	1	1	yes	characteristic
425	C₂²	C₄₁×#536	1	1	yes	characteristic
426	C₄	—	2	2	no	—
427	C₄	—	2	1	no	—
428	C₄	—	2	1	no	—
429	C₄	—	4	2	no	—
430	C₄	—	4	4	no	—
431	C₄	—	4	2	no	—
432	C₄	—	4	4	no	—
433	C₄	—	8	1	no	—
434	C₄	—	8	1	no	—
435	C₄	C₄₁×#548	1	4	yes	—
436	C₂	—	2	1	no	—
437	C₂	—	2	1	no	—
438	C₂	—	4	4	no	—
439	C₂	—	16	1	no	—
440	C₂	C₄₁×#2436	1	1	yes	characteristic
441	C₂	C₄₁×#3018	1	1	yes	characteristic
442	C₂	C₄₁×#3019	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₄₁	C₂×#120
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₁
prime radical	C₂×#127×C₄₁	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄₁ ◁ C₂×C₄²×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₄₁×#3501	C₂	semidirect
2. C₄₁×#3140	C₂	semidirect
4. C₄₁×#2028	C₂	semidirect
5. C₄₁×#2027	C₂	semidirect
6. C₄₁×#1986	C₂	semidirect
8. C₄₁×#1885	C₂	semidirect
9. C₄×#100×C₄₁	C₂	semidirect
45. C₄⋊Q₈×C₄₁	D₄	semidirect
46. C₄⋊Q₈×C₄₁	D₄	semidirect
49. #125×C₄₁	D₄	semidirect
189. #25922	C₄₁	direct (N × H)
215. #3501	C₂×C₄₁	semidirect
216. #3140	C₂×C₄₁	semidirect
218. #2028	C₂×C₄₁	semidirect
219. #2027	C₂×C₄₁	semidirect
220. #1986	C₂×C₄₁	semidirect
222. #1885	C₂×C₄₁	semidirect
223. C₄×#100	C₂×C₄₁	semidirect
258. C₄₁	#25922	direct (N × H)
267. C₄⋊Q₈	D₄×C₄₁	semidirect
268. C₄⋊Q₈	D₄×C₄₁	semidirect
271. #125	D₄×C₄₁	semidirect

Maximal subgroups

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

subgroup	index
C₄₁×#3501	2
C₄₁×#3140	2
C₄₁×#2544	2
C₄₁×#2028	2
C₄₁×#2027	2
C₄₁×#1986	2
C₄₁×#1887	2
C₄₁×#1885	2
C₄×#100×C₄₁	2
#25922	41

Subgroups — C41×#25922 #23802123

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#25922 #23802123