Subgroups — C₄₁×#11056 #23787257

Order 10496.

942 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₁×#2905	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄₁×#421	C₂	1	2	yes	maximal
3	C₄₁×#2297	C₂	1	1	yes	maximal, characteristic
4	C₄₁×#1740	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₄₁×#339	C₂	1	2	yes	maximal, complemented
6	C₂²×#41×C₄₁	C₂²	1	1	yes	characteristic
7	C₂²×M₁₆×C₄₁	C₂²	1	2	yes	—
8	C₂×#117×C₄₁	C₂²	1	2	yes	—
9	C₂×#117×C₄₁	C₂²	1	1	yes	characteristic
10	C₂²×C₄²×C₄₁	C₂²	1	1	yes	characteristic
11	C₄₁×#424	—	2	4	no	—
12	C₄₁×#423	—	2	2	no	—
13	C₄₁×#421	—	2	4	no	—
14	C₄₁×#421	—	2	4	no	—
15	C₂×#104×C₄₁	—	2	4	no	—
16	C₄₁×#391	C₄	1	2	yes	complemented
17	C₄₁×#390	C₄	1	2	yes	complemented
18	C₄₁×#386	—	2	2	no	—
19	C₄×C₂²⋊C₄×C₄₁	—	2	2	no	—
20	C₄₁×#342	—	2	2	no	—
21	C₄₁×#339	—	2	4	no	—
22	C₂×#41×C₄₁	—	2	1	no	—
23	C₂×#41×C₄₁	—	2	1	no	—
24	C₂×#41×C₄₁	—	2	2	no	—
25	C₂×#41×C₄₁	—	2	2	no	—
26	C₂×#41×C₄₁	—	2	2	no	—
27	C₂×#41×C₄₁	—	2	2	no	—
28	C₂×#41×C₄₁	D₄	1	2	yes	—
29	C₂×#41×C₄₁	Q₈	1	2	yes	—
30	C₂²×Q₈×C₄₁	C₂×C₄	1	1	yes	characteristic
31	C₂²×D₄×C₄₁	—	2	1	no	—
32	C₂²×D₄×C₄₁	C₂×C₄	1	1	yes	characteristic
33	C₂³×C₄×C₄₁	—	2	1	no	—
34	C₂³×C₄×C₄₁	—	2	1	no	—
35	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
36	C₂×M₁₆×C₄₁	—	2	2	no	—
37	C₂×M₁₆×C₄₁	—	2	2	no	—
38	C₂×M₁₆×C₄₁	—	2	2	no	—
39	C₂×M₁₆×C₄₁	—	2	2	no	—
40	C₂×M₁₆×C₄₁	—	2	2	no	—
41	C₂×M₁₆×C₄₁	D₄	1	4	yes	—
42	C₂²×C₈×C₄₁	—	2	2	no	—
43	#117×C₄₁	—	2	2	no	—
44	#117×C₄₁	—	2	2	no	—
45	#117×C₄₁	—	2	2	no	—
46	#117×C₄₁	—	2	2	no	—
47	#117×C₄₁	—	2	2	no	—
48	#117×C₄₁	D₄	1	4	yes	—
49	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
50	C₂×C₄⋊C₄×C₄₁	C₂×C₄	1	2	yes	—
51	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
52	C₂×C₂²⋊C₄×C₄₁	—	2	4	no	—
53	C₂×C₂²⋊C₄×C₄₁	D₄	1	2	yes	—
54	C₂×C₄²×C₄₁	—	2	2	no	—
55	C₂×C₄²×C₄₁	—	2	2	no	—
56	C₂×C₄²×C₄₁	—	2	2	no	—
57	C₂×C₄²×C₄₁	—	2	1	no	—
58	C₂×C₄²×C₄₁	C₂×C₄	1	2	yes	—
59	C₂×C₄²×C₄₁	D₄	1	2	yes	—
60	C₄⋊C₈×C₄₁	—	2	8	no	—
61	#104×C₄₁	—	2	16	no	—
62	#95×C₄₁	—	2	4	no	—
63	C₂⁴×C₄₁	—	2	1	no	—
64	C₂⁴×C₄₁	C₂×D₄	1	1	yes	characteristic
65	#41×C₄₁	—	2	4	no	—
66	#41×C₄₁	—	2	4	no	—
67	#41×C₄₁	—	2	4	no	—
68	#41×C₄₁	—	2	4	no	—
69	#41×C₄₁	—	4	2	no	—
70	#41×C₄₁	—	4	2	no	—
71	#41×C₄₁	—	4	2	no	—
72	#41×C₄₁	—	4	2	no	—
73	C₂×Q₈×C₄₁	—	2	1	no	—
74	C₂×Q₈×C₄₁	—	2	2	no	—
75	C₂×Q₈×C₄₁	—	2	2	no	—
76	C₂×Q₈×C₄₁	C₄⋊C₄	1	2	yes	—
77	C₂×D₄×C₄₁	—	2	2	no	—
78	C₂×D₄×C₄₁	—	2	2	no	—
79	C₂×D₄×C₄₁	—	2	1	no	—
80	C₂×D₄×C₄₁	—	2	2	no	—
81	C₂×D₄×C₄₁	—	2	2	no	—
82	C₂×D₄×C₄₁	—	4	2	no	—
83	C₂×D₄×C₄₁	—	4	2	no	—
84	C₂×D₄×C₄₁	C₄⋊C₄	1	2	yes	—
85	C₂²×C₄×C₄₁	—	2	1	no	—
86	C₂²×C₄×C₄₁	—	2	2	no	—
87	C₂²×C₄×C₄₁	—	2	2	no	—
88	C₂²×C₄×C₄₁	—	2	2	no	—
89	C₂²×C₄×C₄₁	—	4	4	no	—
90	C₂²×C₄×C₄₁	—	4	2	no	—
91	C₂²×C₄×C₄₁	—	4	1	no	—
92	C₂²×C₄×C₄₁	—	4	1	no	—
93	C₂²×C₄×C₄₁	—	4	1	no	—
94	C₂²×C₄×C₄₁	—	4	1	no	—
95	C₂²×C₄×C₄₁	—	4	2	no	—
96	C₂²×C₄×C₄₁	C₂²⋊C₄	1	4	yes	—
97	C₂²×C₄×C₄₁	C₂²×C₄	1	1	yes	characteristic
98	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
99	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
100	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
101	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
102	C₂²×C₄×C₄₁	C₂×Q₈	1	1	yes	characteristic
103	C₂²×C₄×C₄₁	#41	1	1	yes	characteristic
104	C₂²×C₄×C₄₁	#41	1	1	yes	characteristic
105	C₂²×C₄×C₄₁	#41	1	2	yes	—
106	C₂²×C₄×C₄₁	#41	1	2	yes	—
107	M₁₆×C₄₁	—	2	4	no	—
108	M₁₆×C₄₁	—	2	4	no	—
109	M₁₆×C₄₁	—	4	2	no	—
110	M₁₆×C₄₁	—	4	2	no	—
111	C₂×C₈×C₄₁	—	2	4	no	—
112	C₂×C₈×C₄₁	—	4	2	no	—
113	C₂×C₈×C₄₁	—	4	2	no	—
114	C₄⋊C₄×C₄₁	—	2	4	no	—
115	C₄⋊C₄×C₄₁	—	2	4	no	—
116	C₄⋊C₄×C₄₁	—	4	2	no	—
117	C₂²⋊C₄×C₄₁	—	2	4	no	—
118	C₂²⋊C₄×C₄₁	—	2	4	no	—
119	C₂²⋊C₄×C₄₁	—	4	8	no	—
120	C₂²⋊C₄×C₄₁	—	4	2	no	—
121	C₄²×C₄₁	—	2	2	no	—
122	C₄²×C₄₁	—	2	2	no	—
123	C₄²×C₄₁	—	2	4	no	—
124	C₄²×C₄₁	—	2	4	no	—
125	C₄²×C₄₁	—	4	1	no	—
126	C₄²×C₄₁	—	4	2	no	—
127	C₄²×C₄₁	—	4	1	no	—
128	C₂³×C₄₁	—	2	2	no	—
129	C₂³×C₄₁	—	4	2	no	—
130	C₂³×C₄₁	—	4	4	no	—
131	C₂³×C₄₁	—	4	1	no	—
132	C₂³×C₄₁	—	4	1	no	—
133	C₂³×C₄₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
134	C₂³×C₄₁	#121	1	2	yes	—
135	C₂³×C₄₁	#121	1	1	yes	characteristic
136	C₂³×C₄₁	#121	1	2	yes	—
137	C₂³×C₄₁	C₂²⋊Q₈	1	1	yes	characteristic
138	Q₈×C₄₁	—	2	4	no	—
139	Q₈×C₄₁	—	4	2	no	—
140	D₄×C₄₁	—	2	4	no	—
141	D₄×C₄₁	—	4	4	no	—
142	D₄×C₄₁	—	4	4	no	—
143	D₄×C₄₁	—	4	2	no	—
144	C₂×C₄×C₄₁	—	2	4	no	—
145	C₂×C₄×C₄₁	—	2	2	no	—
146	C₂×C₄×C₄₁	—	2	4	no	—
147	C₂×C₄×C₄₁	—	4	2	no	—
148	C₂×C₄×C₄₁	—	4	8	no	—
149	C₂×C₄×C₄₁	—	4	1	no	—
150	C₂×C₄×C₄₁	—	4	2	no	—
151	C₂×C₄×C₄₁	—	4	1	no	—
152	C₂×C₄×C₄₁	—	4	2	no	—
153	C₂×C₄×C₄₁	—	4	2	no	—
154	C₂×C₄×C₄₁	—	4	2	no	—
155	C₂×C₄×C₄₁	—	4	2	no	—
156	C₂×C₄×C₄₁	—	4	4	no	—
157	C₂×C₄×C₄₁	—	4	4	no	—
158	C₂×C₄×C₄₁	—	8	4	no	—
159	C₂×C₄×C₄₁	C₂×C₄⋊C₄	1	1	yes	characteristic
160	C₂×C₄×C₄₁	#117	1	1	yes	characteristic
161	C₂×C₄×C₄₁	C₄×D₄	1	2	yes	—
162	C₂×C₄×C₄₁	C₄×D₄	1	2	yes	—
163	C₂×C₄×C₄₁	#120	1	2	yes	—
164	C₂×C₄×C₄₁	#120	1	1	yes	characteristic
165	C₂×C₄×C₄₁	#121	1	2	yes	—
166	C₂×C₄×C₄₁	#121	1	1	yes	characteristic
167	C₂×C₄×C₄₁	C₂²⋊Q₈	1	2	yes	—
168	C₂×C₄×C₄₁	C₂²⋊Q₈	1	2	yes	—
169	C₂×C₄×C₄₁	C₂²⋊Q₈	1	1	yes	characteristic
170	C₂×C₄×C₄₁	#123	1	2	yes	—
171	C₂×C₄×C₄₁	#123	1	2	yes	—
172	C₂×C₄×C₄₁	#123	1	1	yes	characteristic
173	C₂×C₄×C₄₁	#124	1	2	yes	—
174	C₂×C₄×C₄₁	#124	1	1	yes	characteristic
175	C₂×C₄×C₄₁	#126	1	2	yes	—
176	C₂×C₄×C₄₁	#127	1	1	yes	characteristic
177	C₈×C₄₁	—	4	4	no	—
178	#11056	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
179	C₂²×C₄₁	—	2	2	no	—
180	C₂²×C₄₁	—	2	4	no	—
181	C₂²×C₄₁	—	4	2	no	—
182	C₂²×C₄₁	—	4	1	no	—
183	C₂²×C₄₁	—	4	1	no	—
184	C₂²×C₄₁	—	4	4	no	—
185	C₂²×C₄₁	—	4	2	no	—
186	C₂²×C₄₁	—	8	2	no	—
187	C₂²×C₄₁	—	8	2	no	—
188	C₂²×C₄₁	#380	1	1	yes	characteristic
189	C₂²×C₄₁	#386	1	1	yes	characteristic
190	C₂²×C₄₁	#390	1	1	yes	characteristic
191	C₂²×C₄₁	#394	1	2	yes	—
192	C₂²×C₄₁	#396	1	2	yes	—
193	C₄×C₄₁	—	4	4	no	—
194	C₄×C₄₁	—	4	4	no	—
195	C₄×C₄₁	—	4	2	no	—
196	C₄×C₄₁	—	8	4	no	—
197	C₄×C₄₁	#385	1	2	yes	—
198	C₄×C₄₁	#388	1	2	yes	—
199	C₄×C₄₁	#392	1	1	yes	characteristic
200	C₄×C₄₁	#393	1	1	yes	characteristic
201	C₄×C₄₁	#397	1	1	yes	characteristic
202	C₄×C₄₁	#399	1	1	yes	characteristic
203	#2905	C₂×C₄₁	1	1	yes	characteristic, complemented
204	C₂×#421	C₂×C₄₁	1	2	yes	—
205	#2297	C₂×C₄₁	1	1	yes	characteristic
206	#1740	C₂×C₄₁	1	1	yes	characteristic, complemented
207	C₂×#339	C₂×C₄₁	1	2	yes	complemented
208	C₂×C₄₁	—	2	1	no	—
209	C₂×C₄₁	—	2	2	no	—
210	C₂×C₄₁	—	2	1	no	—
211	C₂×C₄₁	—	2	2	no	—
212	C₂×C₄₁	—	8	2	no	—
213	C₂×C₄₁	#1439	1	1	yes	characteristic
214	C₂×C₄₁	#1884	1	2	yes	—
215	C₂²×#41	C₂²×C₄₁	1	1	yes	characteristic
216	C₂²×M₁₆	C₂²×C₄₁	1	2	yes	—
217	C₂×#117	C₂²×C₄₁	1	2	yes	—
218	C₂×#117	C₂²×C₄₁	1	1	yes	characteristic
219	C₂²×C₄²	C₂²×C₄₁	1	1	yes	characteristic
220	#424	—	2	4	no	—
221	#423	—	2	2	no	—
222	#421	—	2	4	no	—
223	#421	—	2	4	no	—
224	C₂×#104	—	2	4	no	—
225	#391	C₄×C₄₁	1	2	yes	complemented
226	#390	C₄×C₄₁	1	2	yes	complemented
227	#386	—	2	2	no	—
228	C₄×C₂²⋊C₄	—	2	2	no	—
229	#342	—	2	2	no	—
230	#339	—	2	4	no	—
231	C₄₁	#11056	1	1	yes	characteristic, direct product factor, Sylow
232	C₂×#41	—	2	1	no	—
233	C₂×#41	—	2	1	no	—
234	C₂×#41	—	2	2	no	—
235	C₂×#41	—	2	2	no	—
236	C₂×#41	—	2	2	no	—
237	C₂×#41	—	2	2	no	—
238	C₂×#41	D₄×C₄₁	1	2	yes	—
239	C₂×#41	Q₈×C₄₁	1	2	yes	—
240	C₂²×Q₈	C₂×C₄×C₄₁	1	1	yes	characteristic
241	C₂²×D₄	—	2	1	no	—
242	C₂²×D₄	C₂×C₄×C₄₁	1	1	yes	characteristic
243	C₂³×C₄	—	2	1	no	—
244	C₂³×C₄	—	2	1	no	—
245	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
246	C₂×M₁₆	—	2	2	no	—
247	C₂×M₁₆	—	2	2	no	—
248	C₂×M₁₆	—	2	2	no	—
249	C₂×M₁₆	—	2	2	no	—
250	C₂×M₁₆	—	2	2	no	—
251	C₂×M₁₆	D₄×C₄₁	1	4	yes	—
252	C₂²×C₈	—	2	2	no	—
253	#117	—	2	2	no	—
254	#117	—	2	2	no	—
255	#117	—	2	2	no	—
256	#117	—	2	2	no	—
257	#117	—	2	2	no	—
258	#117	D₄×C₄₁	1	4	yes	—
259	C₂×C₄⋊C₄	—	2	2	no	—
260	C₂×C₄⋊C₄	C₂×C₄×C₄₁	1	2	yes	—
261	C₂×C₂²⋊C₄	—	2	2	no	—
262	C₂×C₂²⋊C₄	—	2	4	no	—
263	C₂×C₂²⋊C₄	D₄×C₄₁	1	2	yes	—
264	C₂×C₄²	—	2	2	no	—
265	C₂×C₄²	—	2	2	no	—
266	C₂×C₄²	—	2	2	no	—
267	C₂×C₄²	—	2	1	no	—
268	C₂×C₄²	C₂×C₄×C₄₁	1	2	yes	—
269	C₂×C₄²	D₄×C₄₁	1	2	yes	—
270	C₄⋊C₈	—	2	8	no	—
271	#104	—	2	16	no	—
272	#95	—	2	4	no	—
273	C₂⁴	—	2	1	no	—
274	C₂⁴	C₂×D₄×C₄₁	1	1	yes	characteristic
275	#41	—	2	4	no	—
276	#41	—	2	4	no	—
277	#41	—	2	4	no	—
278	#41	—	2	4	no	—
279	#41	—	4	2	no	—
280	#41	—	4	2	no	—
281	#41	—	4	2	no	—
282	#41	—	4	2	no	—
283	C₂×Q₈	—	2	1	no	—
284	C₂×Q₈	—	2	2	no	—
285	C₂×Q₈	—	2	2	no	—
286	C₂×Q₈	C₄⋊C₄×C₄₁	1	2	yes	—
287	C₂×D₄	—	2	2	no	—
288	C₂×D₄	—	2	2	no	—
289	C₂×D₄	—	2	1	no	—
290	C₂×D₄	—	2	2	no	—
291	C₂×D₄	—	2	2	no	—
292	C₂×D₄	—	4	2	no	—
293	C₂×D₄	—	4	2	no	—
294	C₂×D₄	C₄⋊C₄×C₄₁	1	2	yes	—
295	C₂²×C₄	—	2	1	no	—
296	C₂²×C₄	—	2	2	no	—
297	C₂²×C₄	—	2	2	no	—
298	C₂²×C₄	—	2	2	no	—
299	C₂²×C₄	—	4	4	no	—
300	C₂²×C₄	—	4	2	no	—
301	C₂²×C₄	—	4	1	no	—
302	C₂²×C₄	—	4	1	no	—
303	C₂²×C₄	—	4	1	no	—
304	C₂²×C₄	—	4	1	no	—
305	C₂²×C₄	—	4	2	no	—
306	C₂²×C₄	C₂²⋊C₄×C₄₁	1	4	yes	—
307	C₂²×C₄	C₂²×C₄×C₄₁	1	1	yes	characteristic
308	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
309	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
310	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
311	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
312	C₂²×C₄	C₂×Q₈×C₄₁	1	1	yes	characteristic
313	C₂²×C₄	#41×C₄₁	1	1	yes	characteristic
314	C₂²×C₄	#41×C₄₁	1	1	yes	characteristic
315	C₂²×C₄	#41×C₄₁	1	2	yes	—
316	C₂²×C₄	#41×C₄₁	1	2	yes	—
317	M₁₆	—	2	4	no	—
318	M₁₆	—	2	4	no	—
319	M₁₆	—	4	2	no	—
320	M₁₆	—	4	2	no	—
321	C₂×C₈	—	2	4	no	—
322	C₂×C₈	—	4	2	no	—
323	C₂×C₈	—	4	2	no	—
324	C₄⋊C₄	—	2	4	no	—
325	C₄⋊C₄	—	2	4	no	—
326	C₄⋊C₄	—	4	2	no	—
327	C₂²⋊C₄	—	2	4	no	—
328	C₂²⋊C₄	—	2	4	no	—
329	C₂²⋊C₄	—	4	8	no	—
330	C₂²⋊C₄	—	4	2	no	—
331	C₄²	—	2	2	no	—
332	C₄²	—	2	2	no	—
333	C₄²	—	2	4	no	—
334	C₄²	—	2	4	no	—
335	C₄²	—	4	1	no	—
336	C₄²	—	4	2	no	—
337	C₄²	—	4	1	no	—
338	C₂³	—	2	2	no	—
339	C₂³	—	4	2	no	—
340	C₂³	—	4	4	no	—
341	C₂³	—	4	1	no	—
342	C₂³	—	4	1	no	—
343	C₂³	C₂×C₂²⋊C₄×C₄₁	1	1	yes	characteristic
344	C₂³	#121×C₄₁	1	2	yes	—
345	C₂³	#121×C₄₁	1	1	yes	characteristic
346	C₂³	#121×C₄₁	1	2	yes	—
347	C₂³	C₂²⋊Q₈×C₄₁	1	1	yes	characteristic
348	Q₈	—	2	4	no	—
349	Q₈	—	4	2	no	—
350	D₄	—	2	4	no	—
351	D₄	—	4	4	no	—
352	D₄	—	4	4	no	—
353	D₄	—	4	2	no	—
354	C₂×C₄	—	2	4	no	—
355	C₂×C₄	—	2	2	no	—
356	C₂×C₄	—	2	4	no	—
357	C₂×C₄	—	4	2	no	—
358	C₂×C₄	—	4	8	no	—
359	C₂×C₄	—	4	1	no	—
360	C₂×C₄	—	4	2	no	—
361	C₂×C₄	—	4	1	no	—
362	C₂×C₄	—	4	2	no	—
363	C₂×C₄	—	4	2	no	—
364	C₂×C₄	—	4	2	no	—
365	C₂×C₄	—	4	2	no	—
366	C₂×C₄	—	4	4	no	—
367	C₂×C₄	—	4	4	no	—
368	C₂×C₄	—	8	4	no	—
369	C₂×C₄	C₂×C₄⋊C₄×C₄₁	1	1	yes	characteristic
370	C₂×C₄	#117×C₄₁	1	1	yes	characteristic
371	C₂×C₄	C₄×D₄×C₄₁	1	2	yes	—
372	C₂×C₄	C₄×D₄×C₄₁	1	2	yes	—
373	C₂×C₄	#120×C₄₁	1	2	yes	—
374	C₂×C₄	#120×C₄₁	1	1	yes	characteristic
375	C₂×C₄	#121×C₄₁	1	2	yes	—
376	C₂×C₄	#121×C₄₁	1	1	yes	characteristic
377	C₂×C₄	C₂²⋊Q₈×C₄₁	1	2	yes	—
378	C₂×C₄	C₂²⋊Q₈×C₄₁	1	2	yes	—
379	C₂×C₄	C₂²⋊Q₈×C₄₁	1	1	yes	characteristic
380	C₂×C₄	#123×C₄₁	1	2	yes	—
381	C₂×C₄	#123×C₄₁	1	2	yes	—
382	C₂×C₄	#123×C₄₁	1	1	yes	characteristic
383	C₂×C₄	#124×C₄₁	1	2	yes	—
384	C₂×C₄	#124×C₄₁	1	1	yes	characteristic
385	C₂×C₄	#126×C₄₁	1	2	yes	—
386	C₂×C₄	#127×C₄₁	1	1	yes	characteristic
387	C₈	—	4	4	no	—
388	C₂²	—	2	2	no	—
389	C₂²	—	2	4	no	—
390	C₂²	—	4	2	no	—
391	C₂²	—	4	1	no	—
392	C₂²	—	4	1	no	—
393	C₂²	—	4	4	no	—
394	C₂²	—	4	2	no	—
395	C₂²	—	8	2	no	—
396	C₂²	—	8	2	no	—
397	C₂²	C₄₁×#380	1	1	yes	characteristic
398	C₂²	C₄₁×#386	1	1	yes	characteristic
399	C₂²	C₄₁×#390	1	1	yes	characteristic
400	C₂²	C₄₁×#394	1	2	yes	—
401	C₂²	C₄₁×#396	1	2	yes	—
402	C₄	—	4	4	no	—
403	C₄	—	4	4	no	—
404	C₄	—	4	2	no	—
405	C₄	—	8	4	no	—
406	C₄	C₄₁×#385	1	2	yes	—
407	C₄	C₄₁×#388	1	2	yes	—
408	C₄	C₄₁×#392	1	1	yes	characteristic
409	C₄	C₄₁×#393	1	1	yes	characteristic
410	C₄	C₄₁×#397	1	1	yes	characteristic
411	C₄	C₄₁×#399	1	1	yes	characteristic
412	C₂	—	2	1	no	—
413	C₂	—	2	2	no	—
414	C₂	—	2	1	no	—
415	C₂	—	2	2	no	—
416	C₂	—	8	2	no	—
417	C₂	C₄₁×#1439	1	1	yes	characteristic
418	C₂	C₄₁×#1884	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₄₁	#120
commutator	C₂²×C₄	C₂²×C₄×C₄₁
Frattini, cosocle	C₂³×C₄	C₂³×C₄₁
socle	C₂²×C₄₁	#386
prime radical	C₂²×#41×C₄₁	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₄₁ ◁ C₂³×C₄×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₄₁×#2905	C₂	semidirect
4. C₄₁×#1740	C₂	semidirect
5. C₂×C₄₁×#339	C₂	semidirect
16. C₄₁×#391	C₄	semidirect
17. C₄₁×#390	C₄	semidirect
178. #11056	C₄₁	direct (N × H)
203. #2905	C₂×C₄₁	semidirect
206. #1740	C₂×C₄₁	semidirect
207. C₂×#339	C₂×C₄₁	semidirect
225. #391	C₄×C₄₁	semidirect
226. #390	C₄×C₄₁	semidirect
231. C₄₁	#11056	direct (N × H)

Maximal subgroups

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

subgroup	index
C₄₁×#2905	2
C₂×C₄₁×#421	2
C₄₁×#2297	2
C₄₁×#1740	2
C₂×C₄₁×#339	2
#11056	41

Subgroups — C41×#11056 #23787257

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#11056 #23787257