Subgroups — C₄₁×#19085 #23795286

Order 10496.

842 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₁×#3553	C₂	1	1	yes	maximal, characteristic
2	C₄₁×#3181	C₂	1	2	yes	maximal, complemented
3	C₄₁×#3166	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₁×#1664	C₂	1	2	yes	maximal, complemented
5	C₄₁×#1663	C₂	1	2	yes	maximal, complemented
6	C₄₁×#1661	C₂	1	2	yes	maximal, complemented
7	C₄₁×#1660	C₂	1	2	yes	maximal, complemented
8	C₄₁×#1524	C₂	1	2	yes	maximal, complemented
9	C₂×C₄₁×#330	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄₁×#564	C₂²	1	1	yes	characteristic
11	C₄₁×#563	C₂²	1	2	yes	—
12	C₄₁×#562	C₂²	1	1	yes	characteristic
13	C₄₁×#554	—	2	2	no	—
14	C₄₁×#553	—	2	2	no	—
15	C₄₁×#552	—	2	2	no	—
16	C₄₁×#541	—	2	2	no	—
17	C₄₁×#539	—	2	2	no	—
18	C₄₁×#539	—	2	2	no	—
19	C₄₁×#533	C₂²	1	1	yes	characteristic
20	C₄₁×#529	C₂²	1	2	yes	—
21	C₂×#125×C₄₁	C₂²	1	1	yes	characteristic
22	C₄₁×#501	C₂²	1	2	yes	—
23	C₄₁×#501	C₂²	1	2	yes	—
24	C₄₁×#501	C₂²	1	2	yes	—
25	C₄₁×#499	—	2	2	no	—
26	C₄₁×#497	C₂²	1	2	yes	—
27	C₄₁×#491	C₂²	1	2	yes	—
28	C₄₁×#489	C₂²	1	2	yes	—
29	C₄₁×#467	—	2	2	no	—
30	C₄₁×#465	—	2	2	no	—
31	C₄₁×#441	—	2	2	no	—
32	C₄₁×#440	—	2	2	no	—
33	C₄₁×#428	—	2	2	no	—
34	C₄×M₁₆×C₄₁	C₂²	1	1	yes	characteristic
35	C₂×#97×C₄₁	C₂²	1	2	yes	—
36	C₄₁×#330	C₂²	1	1	yes	characteristic
37	C₄₁×#330	C₂²	1	2	yes	—
38	C₄₁×#330	C₂²	1	1	yes	characteristic
39	C₄₁×#330	C₂²	1	2	yes	—
40	C₄₁×#330	C₂²	1	2	yes	—
41	C₄₁×#329	C₂²	1	2	yes	—
42	C₄₁×#329	C₂²	1	2	yes	—
43	C₂×Q₁₆×C₄₁	—	2	2	no	—
44	C₂×SD₁₆×C₄₁	—	2	2	no	—
45	C₂×M₁₆×C₄₁	—	2	1	no	—
46	C₂²×C₈×C₄₁	—	2	2	no	—
47	C₄⋊Q₈×C₄₁	—	2	2	no	—
48	C₄⋊Q₈×C₄₁	C₂³	1	2	yes	—
49	#126×C₄₁	—	2	2	no	—
50	#126×C₄₁	—	2	2	no	—
51	#126×C₄₁	—	2	2	no	—
52	#126×C₄₁	—	2	2	no	—
53	#126×C₄₁	—	2	2	no	—
54	#125×C₄₁	—	2	2	no	—
55	#125×C₄₁	—	2	2	no	—
56	#125×C₄₁	—	2	2	no	—
57	#125×C₄₁	—	2	2	no	—
58	#125×C₄₁	—	2	2	no	—
59	#125×C₄₁	—	2	2	no	—
60	#125×C₄₁	—	2	1	no	—
61	#125×C₄₁	D₄	1	2	yes	—
62	#125×C₄₁	C₂³	1	1	yes	characteristic
63	#125×C₄₁	C₂³	1	1	yes	characteristic
64	#125×C₄₁	C₂³	1	2	yes	—
65	#124×C₄₁	C₂³	1	2	yes	—
66	#123×C₄₁	—	2	2	no	—
67	#123×C₄₁	—	2	2	no	—
68	#123×C₄₁	—	2	2	no	—
69	#123×C₄₁	—	2	2	no	—
70	#123×C₄₁	—	2	2	no	—
71	C₂²⋊Q₈×C₄₁	—	2	2	no	—
72	C₂²⋊Q₈×C₄₁	—	2	2	no	—
73	C₂²⋊Q₈×C₄₁	—	2	2	no	—
74	C₂²⋊Q₈×C₄₁	—	2	2	no	—
75	C₂²⋊Q₈×C₄₁	—	2	2	no	—
76	C₂²⋊Q₈×C₄₁	—	2	2	no	—
77	C₂²⋊Q₈×C₄₁	—	2	2	no	—
78	C₂²⋊Q₈×C₄₁	D₄	1	2	yes	—
79	#121×C₄₁	—	2	2	no	—
80	#121×C₄₁	—	2	2	no	—
81	#121×C₄₁	D₄	1	2	yes	—
82	C₄×Q₈×C₄₁	—	2	2	no	—
83	C₄×Q₈×C₄₁	—	2	2	no	—
84	C₄×Q₈×C₄₁	D₄	1	2	yes	—
85	C₄×D₄×C₄₁	—	2	2	no	—
86	C₄×D₄×C₄₁	—	2	2	no	—
87	C₄×D₄×C₄₁	—	2	2	no	—
88	C₄×D₄×C₄₁	—	2	2	no	—
89	C₄×D₄×C₄₁	D₄	1	2	yes	—
90	#117×C₄₁	—	2	2	no	—
91	#117×C₄₁	—	2	2	no	—
92	#117×C₄₁	—	2	1	no	—
93	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
94	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
95	C₂×C₄⋊C₄×C₄₁	D₄	1	2	yes	—
96	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
97	#107×C₄₁	—	2	2	no	—
98	#107×C₄₁	—	2	2	no	—
99	#107×C₄₁	—	2	2	no	—
100	#106×C₄₁	—	2	2	no	—
101	#106×C₄₁	—	2	2	no	—
102	#106×C₄₁	—	2	2	no	—
103	#103×C₄₁	—	2	2	no	—
104	#103×C₄₁	—	2	2	no	—
105	#103×C₄₁	—	2	2	no	—
106	#102×C₄₁	—	2	2	no	—
107	#97×C₄₁	—	2	2	no	—
108	#97×C₄₁	C₂³	1	2	yes	—
109	#97×C₄₁	C₂³	1	2	yes	—
110	#97×C₄₁	C₂³	1	2	yes	—
111	C₄×C₈×C₄₁	—	2	1	no	—
112	C₂×Q₈×C₄₁	—	2	2	no	—
113	C₂×Q₈×C₄₁	—	2	2	no	—
114	C₂×Q₈×C₄₁	C₂×D₄	1	2	yes	—
115	C₂×D₄×C₄₁	—	2	2	no	—
116	C₂×D₄×C₄₁	—	2	2	no	—
117	C₂×D₄×C₄₁	C₂×D₄	1	2	yes	—
118	C₂²×C₄×C₄₁	—	2	2	no	—
119	C₂²×C₄×C₄₁	—	2	2	no	—
120	C₂²×C₄×C₄₁	—	2	2	no	—
121	C₂²×C₄×C₄₁	—	2	2	no	—
122	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
123	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
124	Q₁₆×C₄₁	—	4	4	no	—
125	SD₁₆×C₄₁	—	4	4	no	—
126	M₁₆×C₄₁	—	2	4	no	—
127	C₂×C₈×C₄₁	—	2	2	no	—
128	C₂×C₈×C₄₁	—	2	2	no	—
129	C₂×C₈×C₄₁	—	2	2	no	—
130	C₂×C₈×C₄₁	—	4	4	no	—
131	C₄⋊C₄×C₄₁	—	2	2	no	—
132	C₄⋊C₄×C₄₁	—	2	2	no	—
133	C₄⋊C₄×C₄₁	—	2	2	no	—
134	C₄⋊C₄×C₄₁	—	2	2	no	—
135	C₄⋊C₄×C₄₁	—	2	2	no	—
136	C₄⋊C₄×C₄₁	—	2	2	no	—
137	C₄⋊C₄×C₄₁	—	2	2	no	—
138	C₄⋊C₄×C₄₁	—	2	2	no	—
139	C₄⋊C₄×C₄₁	—	2	2	no	—
140	C₄⋊C₄×C₄₁	—	2	2	no	—
141	C₄⋊C₄×C₄₁	—	2	2	no	—
142	C₄⋊C₄×C₄₁	—	2	2	no	—
143	C₄⋊C₄×C₄₁	—	2	2	no	—
144	C₄⋊C₄×C₄₁	—	2	2	no	—
145	C₄⋊C₄×C₄₁	—	2	2	no	—
146	C₄⋊C₄×C₄₁	—	2	2	no	—
147	C₄⋊C₄×C₄₁	—	2	2	no	—
148	C₄⋊C₄×C₄₁	—	4	2	no	—
149	C₄⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
150	C₄⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
151	C₄⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
152	C₄⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
153	C₂²⋊C₄×C₄₁	—	2	2	no	—
154	C₂²⋊C₄×C₄₁	—	2	2	no	—
155	C₂²⋊C₄×C₄₁	—	2	2	no	—
156	C₂²⋊C₄×C₄₁	—	2	2	no	—
157	C₂²⋊C₄×C₄₁	—	2	2	no	—
158	C₂²⋊C₄×C₄₁	—	2	2	no	—
159	C₂²⋊C₄×C₄₁	—	2	2	no	—
160	C₂²⋊C₄×C₄₁	—	2	2	no	—
161	C₂²⋊C₄×C₄₁	—	2	2	no	—
162	C₂²⋊C₄×C₄₁	—	4	1	no	—
163	C₄²×C₄₁	—	2	2	no	—
164	C₄²×C₄₁	—	2	2	no	—
165	C₄²×C₄₁	—	2	2	no	—
166	C₄²×C₄₁	—	4	1	no	—
167	C₄²×C₄₁	C₂×D₄	1	1	yes	characteristic
168	C₄²×C₄₁	C₂×D₄	1	2	yes	—
169	C₄²×C₄₁	C₂⁴	1	1	yes	characteristic
170	C₂³×C₄₁	—	2	2	no	—
171	C₂³×C₄₁	#120	1	1	yes	characteristic
172	Q₈×C₄₁	—	4	2	no	—
173	Q₈×C₄₁	—	4	2	no	—
174	Q₈×C₄₁	—	4	2	no	—
175	Q₈×C₄₁	—	8	2	no	—
176	D₄×C₄₁	—	4	2	no	—
177	D₄×C₄₁	—	4	4	no	—
178	D₄×C₄₁	—	8	2	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	—	2	2	no	—
183	C₂×C₄×C₄₁	—	2	2	no	—
184	C₂×C₄×C₄₁	—	2	2	no	—
185	C₂×C₄×C₄₁	—	4	2	no	—
186	C₂×C₄×C₄₁	—	4	2	no	—
187	C₂×C₄×C₄₁	—	8	2	no	—
188	C₂×C₄×C₄₁	—	8	2	no	—
189	C₂×C₄×C₄₁	—	8	2	no	—
190	C₂×C₄×C₄₁	—	8	2	no	—
191	C₂×C₄×C₄₁	#120	1	2	yes	—
192	C₂×C₄×C₄₁	#120	1	1	yes	characteristic
193	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
194	C₂×C₄×C₄₁	C₂²×D₄	1	2	yes	—
195	C₈×C₄₁	—	2	4	no	—
196	C₈×C₄₁	—	2	4	no	—
197	C₈×C₄₁	—	4	2	no	—
198	#19085	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
199	C₂²×C₄₁	—	2	2	no	—
200	C₂²×C₄₁	—	4	2	no	—
201	C₂²×C₄₁	—	4	2	no	—
202	C₂²×C₄₁	—	4	2	no	—
203	C₂²×C₄₁	#456	1	2	yes	—
204	C₂²×C₄₁	C₂×#120	1	1	yes	characteristic
205	C₄×C₄₁	—	2	1	no	—
206	C₄×C₄₁	—	2	1	no	—
207	C₄×C₄₁	—	2	2	no	—
208	C₄×C₄₁	—	2	2	no	—
209	C₄×C₄₁	—	4	2	no	—
210	C₄×C₄₁	—	4	2	no	—
211	C₄×C₄₁	—	4	2	no	—
212	C₄×C₄₁	—	4	2	no	—
213	C₄×C₄₁	—	4	2	no	—
214	C₄×C₄₁	—	8	2	no	—
215	#3553	C₂×C₄₁	1	1	yes	characteristic
216	#3181	C₂×C₄₁	1	2	yes	complemented
217	#3166	C₂×C₄₁	1	1	yes	characteristic, complemented
218	#1664	C₂×C₄₁	1	2	yes	complemented
219	#1663	C₂×C₄₁	1	2	yes	complemented
220	#1661	C₂×C₄₁	1	2	yes	complemented
221	#1660	C₂×C₄₁	1	2	yes	complemented
222	#1524	C₂×C₄₁	1	2	yes	complemented
223	C₂×#330	C₂×C₄₁	1	1	yes	characteristic, complemented
224	C₂×C₄₁	—	2	2	no	—
225	C₂×C₄₁	—	8	2	no	—
226	C₂×C₄₁	C₂×#456	1	1	yes	characteristic
227	C₂×C₄₁	#3018	1	2	yes	—
228	#564	C₂²×C₄₁	1	1	yes	characteristic
229	#563	C₂²×C₄₁	1	2	yes	—
230	#562	C₂²×C₄₁	1	1	yes	characteristic
231	#554	—	2	2	no	—
232	#553	—	2	2	no	—
233	#552	—	2	2	no	—
234	#541	—	2	2	no	—
235	#539	—	2	2	no	—
236	#539	—	2	2	no	—
237	#533	C₂²×C₄₁	1	1	yes	characteristic
238	#529	C₂²×C₄₁	1	2	yes	—
239	C₂×#125	C₂²×C₄₁	1	1	yes	characteristic
240	#501	C₂²×C₄₁	1	2	yes	—
241	#501	C₂²×C₄₁	1	2	yes	—
242	#501	C₂²×C₄₁	1	2	yes	—
243	#499	—	2	2	no	—
244	#497	C₂²×C₄₁	1	2	yes	—
245	#491	C₂²×C₄₁	1	2	yes	—
246	#489	C₂²×C₄₁	1	2	yes	—
247	#467	—	2	2	no	—
248	#465	—	2	2	no	—
249	#441	—	2	2	no	—
250	#440	—	2	2	no	—
251	#428	—	2	2	no	—
252	C₄×M₁₆	C₂²×C₄₁	1	1	yes	characteristic
253	C₂×#97	C₂²×C₄₁	1	2	yes	—
254	#330	C₂²×C₄₁	1	1	yes	characteristic
255	#330	C₂²×C₄₁	1	2	yes	—
256	#330	C₂²×C₄₁	1	2	yes	—
257	#330	C₂²×C₄₁	1	2	yes	—
258	#330	C₂²×C₄₁	1	1	yes	characteristic
259	#329	C₂²×C₄₁	1	2	yes	—
260	#329	C₂²×C₄₁	1	2	yes	—
261	C₄₁	#19085	1	1	yes	characteristic, direct product factor, Sylow
262	C₂×Q₁₆	—	2	2	no	—
263	C₂×SD₁₆	—	2	2	no	—
264	C₂×M₁₆	—	2	1	no	—
265	C₂²×C₈	—	2	2	no	—
266	C₄⋊Q₈	—	2	2	no	—
267	C₄⋊Q₈	C₂³×C₄₁	1	2	yes	—
268	#126	—	2	2	no	—
269	#126	—	2	2	no	—
270	#126	—	2	2	no	—
271	#126	—	2	2	no	—
272	#126	—	2	2	no	—
273	#125	—	2	2	no	—
274	#125	—	2	2	no	—
275	#125	—	2	2	no	—
276	#125	—	2	2	no	—
277	#125	—	2	2	no	—
278	#125	—	2	2	no	—
279	#125	—	2	1	no	—
280	#125	D₄×C₄₁	1	2	yes	—
281	#125	C₂³×C₄₁	1	1	yes	characteristic
282	#125	C₂³×C₄₁	1	1	yes	characteristic
283	#125	C₂³×C₄₁	1	2	yes	—
284	#124	C₂³×C₄₁	1	2	yes	—
285	#123	—	2	2	no	—
286	#123	—	2	2	no	—
287	#123	—	2	2	no	—
288	#123	—	2	2	no	—
289	#123	—	2	2	no	—
290	C₂²⋊Q₈	—	2	2	no	—
291	C₂²⋊Q₈	—	2	2	no	—
292	C₂²⋊Q₈	—	2	2	no	—
293	C₂²⋊Q₈	—	2	2	no	—
294	C₂²⋊Q₈	—	2	2	no	—
295	C₂²⋊Q₈	—	2	2	no	—
296	C₂²⋊Q₈	—	2	2	no	—
297	C₂²⋊Q₈	D₄×C₄₁	1	2	yes	—
298	#121	—	2	2	no	—
299	#121	—	2	2	no	—
300	#121	D₄×C₄₁	1	2	yes	—
301	C₄×Q₈	—	2	2	no	—
302	C₄×Q₈	—	2	2	no	—
303	C₄×Q₈	D₄×C₄₁	1	2	yes	—
304	C₄×D₄	—	2	2	no	—
305	C₄×D₄	—	2	2	no	—
306	C₄×D₄	—	2	2	no	—
307	C₄×D₄	—	2	2	no	—
308	C₄×D₄	D₄×C₄₁	1	2	yes	—
309	#117	—	2	2	no	—
310	#117	—	2	2	no	—
311	#117	—	2	1	no	—
312	C₂×C₄⋊C₄	—	2	2	no	—
313	C₂×C₄⋊C₄	—	2	2	no	—
314	C₂×C₄⋊C₄	D₄×C₄₁	1	2	yes	—
315	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
316	#107	—	2	2	no	—
317	#107	—	2	2	no	—
318	#107	—	2	2	no	—
319	#106	—	2	2	no	—
320	#106	—	2	2	no	—
321	#106	—	2	2	no	—
322	#103	—	2	2	no	—
323	#103	—	2	2	no	—
324	#103	—	2	2	no	—
325	#102	—	2	2	no	—
326	#97	—	2	2	no	—
327	#97	C₂³×C₄₁	1	2	yes	—
328	#97	C₂³×C₄₁	1	2	yes	—
329	#97	C₂³×C₄₁	1	2	yes	—
330	C₄×C₈	—	2	1	no	—
331	C₂×Q₈	—	2	2	no	—
332	C₂×Q₈	—	2	2	no	—
333	C₂×Q₈	C₂×D₄×C₄₁	1	2	yes	—
334	C₂×D₄	—	2	2	no	—
335	C₂×D₄	—	2	2	no	—
336	C₂×D₄	C₂×D₄×C₄₁	1	2	yes	—
337	C₂²×C₄	—	2	2	no	—
338	C₂²×C₄	—	2	2	no	—
339	C₂²×C₄	—	2	2	no	—
340	C₂²×C₄	—	2	2	no	—
341	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
342	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
343	Q₁₆	—	4	4	no	—
344	SD₁₆	—	4	4	no	—
345	M₁₆	—	2	4	no	—
346	C₂×C₈	—	2	2	no	—
347	C₂×C₈	—	2	2	no	—
348	C₂×C₈	—	2	2	no	—
349	C₂×C₈	—	4	4	no	—
350	C₄⋊C₄	—	2	2	no	—
351	C₄⋊C₄	—	2	2	no	—
352	C₄⋊C₄	—	2	2	no	—
353	C₄⋊C₄	—	2	2	no	—
354	C₄⋊C₄	—	2	2	no	—
355	C₄⋊C₄	—	2	2	no	—
356	C₄⋊C₄	—	2	2	no	—
357	C₄⋊C₄	—	2	2	no	—
358	C₄⋊C₄	—	2	2	no	—
359	C₄⋊C₄	—	2	2	no	—
360	C₄⋊C₄	—	2	2	no	—
361	C₄⋊C₄	—	2	2	no	—
362	C₄⋊C₄	—	2	2	no	—
363	C₄⋊C₄	—	2	2	no	—
364	C₄⋊C₄	—	2	2	no	—
365	C₄⋊C₄	—	2	2	no	—
366	C₄⋊C₄	—	2	2	no	—
367	C₄⋊C₄	—	4	2	no	—
368	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
369	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
370	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
371	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
372	C₂²⋊C₄	—	2	2	no	—
373	C₂²⋊C₄	—	2	2	no	—
374	C₂²⋊C₄	—	2	2	no	—
375	C₂²⋊C₄	—	2	2	no	—
376	C₂²⋊C₄	—	2	2	no	—
377	C₂²⋊C₄	—	2	2	no	—
378	C₂²⋊C₄	—	2	2	no	—
379	C₂²⋊C₄	—	2	2	no	—
380	C₂²⋊C₄	—	2	2	no	—
381	C₂²⋊C₄	—	4	1	no	—
382	C₄²	—	2	2	no	—
383	C₄²	—	2	2	no	—
384	C₄²	—	2	2	no	—
385	C₄²	—	4	1	no	—
386	C₄²	C₂×D₄×C₄₁	1	1	yes	characteristic
387	C₄²	C₂×D₄×C₄₁	1	2	yes	—
388	C₄²	C₂⁴×C₄₁	1	1	yes	characteristic
389	C₂³	—	2	2	no	—
390	C₂³	#120×C₄₁	1	1	yes	characteristic
391	Q₈	—	4	2	no	—
392	Q₈	—	4	2	no	—
393	Q₈	—	4	2	no	—
394	Q₈	—	8	2	no	—
395	D₄	—	4	2	no	—
396	D₄	—	4	4	no	—
397	D₄	—	8	2	no	—
398	C₂×C₄	—	2	2	no	—
399	C₂×C₄	—	2	2	no	—
400	C₂×C₄	—	2	2	no	—
401	C₂×C₄	—	2	2	no	—
402	C₂×C₄	—	2	2	no	—
403	C₂×C₄	—	2	2	no	—
404	C₂×C₄	—	4	2	no	—
405	C₂×C₄	—	4	2	no	—
406	C₂×C₄	—	8	2	no	—
407	C₂×C₄	—	8	2	no	—
408	C₂×C₄	—	8	2	no	—
409	C₂×C₄	—	8	2	no	—
410	C₂×C₄	#120×C₄₁	1	2	yes	—
411	C₂×C₄	#120×C₄₁	1	1	yes	characteristic
412	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
413	C₂×C₄	C₂²×D₄×C₄₁	1	2	yes	—
414	C₈	—	2	4	no	—
415	C₈	—	2	4	no	—
416	C₈	—	4	2	no	—
417	C₂²	—	2	2	no	—
418	C₂²	—	4	2	no	—
419	C₂²	—	4	2	no	—
420	C₂²	—	4	2	no	—
421	C₂²	C₄₁×#456	1	2	yes	—
422	C₂²	C₂×#120×C₄₁	1	1	yes	characteristic
423	C₄	—	2	1	no	—
424	C₄	—	2	1	no	—
425	C₄	—	2	2	no	—
426	C₄	—	2	2	no	—
427	C₄	—	4	2	no	—
428	C₄	—	4	2	no	—
429	C₄	—	4	2	no	—
430	C₄	—	4	2	no	—
431	C₄	—	4	2	no	—
432	C₄	—	8	2	no	—
433	C₂	—	2	2	no	—
434	C₂	—	8	2	no	—
435	C₂	C₂×C₄₁×#456	1	1	yes	characteristic
436	C₂	C₄₁×#3018	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₄₁	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₄₁
prime radical	C₄₁×#3553	C₂
LCS	G ▷ C₄² ▷ C₂² ▷ 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
2. C₄₁×#3181	C₂	semidirect
3. C₄₁×#3166	C₂	semidirect
4. C₄₁×#1664	C₂	semidirect
5. C₄₁×#1663	C₂	semidirect
6. C₄₁×#1661	C₂	semidirect
7. C₄₁×#1660	C₂	semidirect
8. C₄₁×#1524	C₂	semidirect
9. C₂×C₄₁×#330	C₂	semidirect
198. #19085	C₄₁	direct (N × H)
216. #3181	C₂×C₄₁	semidirect
217. #3166	C₂×C₄₁	semidirect
218. #1664	C₂×C₄₁	semidirect
219. #1663	C₂×C₄₁	semidirect
220. #1661	C₂×C₄₁	semidirect
221. #1660	C₂×C₄₁	semidirect
222. #1524	C₂×C₄₁	semidirect
223. C₂×#330	C₂×C₄₁	semidirect
261. C₄₁	#19085	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×#3553	2
C₄₁×#3181	2
C₄₁×#3166	2
C₄₁×#1664	2
C₄₁×#1663	2
C₄₁×#1661	2
C₄₁×#1660	2
C₄₁×#1524	2
C₂×C₄₁×#330	2
#19085	41

Subgroups — C41×#19085 #23795286

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#19085 #23795286