Subgroups — C₄₁×#19242 #23795443

Order 10496.

636 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×#3249	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄₁×#3208	C₂	1	1	yes	maximal, characteristic
3	C₄₁×#3138	C₂	1	1	yes	maximal, characteristic
4	C₄₁×#2962	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₁×#1702	C₂	1	2	yes	maximal, complemented
6	C₄₁×#1698	C₂	1	2	yes	maximal, complemented
7	C₄₁×#1682	C₂	1	2	yes	maximal, complemented
8	C₄₁×#1678	C₂	1	2	yes	maximal, complemented
9	C₄₁×#1565	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄₁×#1542	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₄₁×#331	C₂	1	1	yes	maximal, characteristic
12	C₄₁×#533	C₂²	1	1	yes	characteristic
13	C₄₁×#533	C₂²	1	1	yes	characteristic
14	C₂×#127×C₄₁	C₂²	1	1	yes	characteristic
15	C₄₁×#492	—	2	1	no	—
16	C₄₁×#490	—	2	2	no	—
17	C₄₁×#486	—	2	1	no	—
18	C₄₁×#486	C₂²	1	2	yes	—
19	C₄₁×#486	C₂²	1	2	yes	—
20	C₄₁×#477	—	2	1	no	—
21	C₄₁×#477	C₂²	1	2	yes	complemented
22	C₄₁×#467	—	2	2	no	—
23	C₄₁×#462	—	2	1	no	—
24	C₄₁×#462	C₂²	1	2	yes	complemented
25	C₄₁×#460	C₂²	1	2	yes	—
26	C₄₁×#460	C₂²	1	2	yes	—
27	C₄₁×#450	—	2	2	no	—
28	C₄₁×#446	—	2	2	no	—
29	C₄₁×#446	C₂²	1	2	yes	complemented
30	C₈×Q₈×C₄₁	C₂²	1	2	yes	complemented
31	C₄₁×#431	C₂²	1	1	yes	characteristic
32	C₄₁×#424	—	2	1	no	—
33	C₂×C₄⋊C₈×C₄₁	C₂²	1	1	yes	characteristic
34	C₂×C₄⋊C₈×C₄₁	C₂²	1	1	yes	characteristic
35	C₄₁×#418	—	2	1	no	—
36	C₄₁×#418	—	2	1	no	—
37	C₄₁×#405	—	2	1	no	—
38	C₄×M₁₆×C₄₁	C₂²	1	1	yes	characteristic
39	C₄₁×#335	C₂²	1	2	yes	complemented
40	C₄₁×#334	C₂²	1	2	yes	complemented
41	C₄₁×#333	C₂²	1	1	yes	characteristic, complemented
42	C₄₁×#333	C₂²	1	1	yes	characteristic, complemented
43	C₄₁×#332	C₂²	1	1	yes	characteristic, complemented
44	C₄₁×#332	C₂²	1	1	yes	characteristic, complemented
45	C₄₁×#331	C₂²	1	2	yes	—
46	C₄₁×#331	C₂²	1	2	yes	—
47	C₂²×D₄×C₄₁	—	2	1	no	—
48	C₂²×D₄×C₄₁	—	2	1	no	—
49	C₂²×D₄×C₄₁	—	2	1	no	—
50	C₂×Q₁₆×C₄₁	—	2	2	no	—
51	C₂×SD₁₆×C₄₁	—	2	2	no	—
52	C₂×SD₁₆×C₄₁	—	2	2	no	—
53	C₂×M₁₆×C₄₁	D₄	1	1	yes	characteristic
54	C₂×M₁₆×C₄₁	D₄	1	1	yes	characteristic
55	C₂²×C₈×C₄₁	—	2	1	no	—
56	C₂²×C₈×C₄₁	—	2	1	no	—
57	C₄⋊Q₈×C₄₁	D₄	1	1	yes	characteristic
58	C₄⋊Q₈×C₄₁	D₄	1	1	yes	characteristic
59	C₄⋊Q₈×C₄₁	C₂³	1	1	yes	characteristic
60	C₄⋊Q₈×C₄₁	C₂³	1	1	yes	characteristic
61	#127×C₄₁	—	2	1	no	—
62	#127×C₄₁	—	2	1	no	—
63	#127×C₄₁	—	2	1	no	—
64	#127×C₄₁	C₂³	1	2	yes	—
65	#125×C₄₁	—	2	1	no	—
66	#125×C₄₁	—	2	1	no	—
67	C₂²⋊Q₈×C₄₁	—	2	1	no	—
68	C₂²⋊Q₈×C₄₁	—	2	1	no	—
69	C₂²⋊Q₈×C₄₁	—	2	1	no	—
70	C₂²⋊Q₈×C₄₁	D₄	1	2	yes	—
71	C₄×Q₈×C₄₁	—	2	1	no	—
72	C₄×Q₈×C₄₁	—	2	1	no	—
73	C₄×Q₈×C₄₁	—	2	1	no	—
74	C₄×Q₈×C₄₁	C₂³	1	2	yes	—
75	#117×C₄₁	—	2	1	no	—
76	#117×C₄₁	—	2	1	no	—
77	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
78	#107×C₄₁	—	2	2	no	—
79	C₄⋊C₈×C₄₁	—	2	2	no	—
80	C₄⋊C₈×C₄₁	—	2	2	no	—
81	C₄⋊C₈×C₄₁	—	2	1	no	—
82	C₄⋊C₈×C₄₁	—	2	1	no	—
83	C₄⋊C₈×C₄₁	C₂³	1	1	yes	characteristic
84	C₄⋊C₈×C₄₁	C₂³	1	1	yes	characteristic
85	C₄⋊C₈×C₄₁	C₂³	1	2	yes	—
86	C₄⋊C₈×C₄₁	C₂³	1	1	yes	characteristic
87	C₄⋊C₈×C₄₁	C₂³	1	1	yes	characteristic
88	#103×C₄₁	—	2	2	no	—
89	#103×C₄₁	—	2	2	no	—
90	#102×C₄₁	—	2	2	no	—
91	#102×C₄₁	—	2	2	no	—
92	#102×C₄₁	—	2	2	no	—
93	#102×C₄₁	—	2	2	no	—
94	#102×C₄₁	—	2	2	no	—
95	#102×C₄₁	—	2	2	no	—
96	C₂²⋊C₈×C₄₁	—	2	1	no	—
97	#97×C₄₁	—	2	2	no	—
98	#97×C₄₁	D₄	1	2	yes	—
99	C₄×C₈×C₄₁	—	2	2	no	—
100	C₄×C₈×C₄₁	—	2	1	no	—
101	C₄×C₈×C₄₁	C₂³	1	2	yes	—
102	C₂⁴×C₄₁	—	4	1	no	—
103	C₂×Q₈×C₄₁	—	2	1	no	—
104	C₂×Q₈×C₄₁	—	2	1	no	—
105	C₂×Q₈×C₄₁	—	2	1	no	—
106	C₂×Q₈×C₄₁	C₂×D₄	1	2	yes	—
107	C₂×D₄×C₄₁	—	2	2	no	—
108	C₂×D₄×C₄₁	—	2	2	no	—
109	C₂×D₄×C₄₁	—	2	2	no	—
110	C₂×D₄×C₄₁	—	4	1	no	—
111	C₂×D₄×C₄₁	—	4	1	no	—
112	C₂×D₄×C₄₁	—	4	1	no	—
113	C₂×D₄×C₄₁	—	4	2	no	—
114	C₂×D₄×C₄₁	—	4	2	no	—
115	C₂×D₄×C₄₁	—	8	1	no	—
116	C₂×D₄×C₄₁	—	8	1	no	—
117	C₂×D₄×C₄₁	—	8	2	no	—
118	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
119	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
120	C₂²×C₄×C₄₁	#41	1	1	yes	characteristic
121	Q₁₆×C₄₁	—	8	2	no	—
122	SD₁₆×C₄₁	—	8	2	no	—
123	SD₁₆×C₄₁	—	8	2	no	—
124	M₁₆×C₄₁	—	2	2	no	—
125	M₁₆×C₄₁	—	2	2	no	—
126	C₂×C₈×C₄₁	—	2	1	no	—
127	C₂×C₈×C₄₁	—	2	1	no	—
128	C₂×C₈×C₄₁	—	2	1	no	—
129	C₂×C₈×C₄₁	—	2	1	no	—
130	C₂×C₈×C₄₁	—	2	2	no	—
131	C₂×C₈×C₄₁	—	4	2	no	—
132	C₂×C₈×C₄₁	—	8	1	no	—
133	C₂×C₈×C₄₁	C₂×D₄	1	2	yes	—
134	C₂×C₈×C₄₁	C₂×D₄	1	2	yes	—
135	C₄⋊C₄×C₄₁	—	2	1	no	—
136	C₄⋊C₄×C₄₁	—	2	1	no	—
137	C₄⋊C₄×C₄₁	—	2	1	no	—
138	C₄⋊C₄×C₄₁	—	2	2	no	—
139	C₄⋊C₄×C₄₁	—	2	2	no	—
140	C₄⋊C₄×C₄₁	—	2	1	no	—
141	C₄⋊C₄×C₄₁	—	2	1	no	—
142	C₄⋊C₄×C₄₁	—	2	1	no	—
143	C₄⋊C₄×C₄₁	—	2	1	no	—
144	C₄⋊C₄×C₄₁	—	4	1	no	—
145	C₄⋊C₄×C₄₁	—	4	1	no	—
146	C₄⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
147	C₂²⋊C₄×C₄₁	—	2	2	no	—
148	C₂²⋊C₄×C₄₁	—	4	1	no	—
149	C₄²×C₄₁	—	2	2	no	—
150	C₄²×C₄₁	—	4	1	no	—
151	C₄²×C₄₁	C₂×D₄	1	1	yes	characteristic
152	C₄²×C₄₁	C₂×D₄	1	1	yes	characteristic
153	C₄²×C₄₁	#41	1	1	yes	characteristic
154	C₄²×C₄₁	C₂⁴	1	1	yes	characteristic
155	C₂³×C₄₁	—	4	2	no	—
156	C₂³×C₄₁	—	8	2	no	—
157	C₂³×C₄₁	—	8	2	no	—
158	C₂³×C₄₁	—	8	2	no	—
159	C₂³×C₄₁	#121	1	1	yes	characteristic
160	Q₈×C₄₁	—	2	2	no	—
161	Q₈×C₄₁	—	2	2	no	—
162	Q₈×C₄₁	—	4	1	no	—
163	Q₈×C₄₁	—	4	1	no	—
164	Q₈×C₄₁	—	8	1	no	—
165	Q₈×C₄₁	—	8	1	no	—
166	D₄×C₄₁	—	4	2	no	—
167	D₄×C₄₁	—	4	2	no	—
168	D₄×C₄₁	—	4	2	no	—
169	D₄×C₄₁	—	4	2	no	—
170	D₄×C₄₁	—	8	2	no	—
171	D₄×C₄₁	—	8	2	no	—
172	D₄×C₄₁	—	8	2	no	—
173	D₄×C₄₁	—	8	2	no	—
174	C₂×C₄×C₄₁	—	2	1	no	—
175	C₂×C₄×C₄₁	—	2	1	no	—
176	C₂×C₄×C₄₁	—	2	2	no	—
177	C₂×C₄×C₄₁	—	2	2	no	—
178	C₂×C₄×C₄₁	—	4	1	no	—
179	C₂×C₄×C₄₁	—	4	1	no	—
180	C₂×C₄×C₄₁	—	4	1	no	—
181	C₂×C₄×C₄₁	#121	1	1	yes	characteristic
182	C₂×C₄×C₄₁	#121	1	1	yes	characteristic
183	C₂×C₄×C₄₁	#121	1	1	yes	characteristic
184	C₂×C₄×C₄₁	#135	1	2	yes	—
185	C₂×C₄×C₄₁	#137	1	2	yes	—
186	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
187	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
188	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
189	C₈×C₄₁	—	2	2	no	—
190	C₈×C₄₁	—	2	2	no	—
191	C₈×C₄₁	—	4	1	no	—
192	C₈×C₄₁	—	4	1	no	—
193	C₈×C₄₁	—	4	2	no	—
194	C₈×C₄₁	—	4	1	no	—
195	C₈×C₄₁	—	4	1	no	—
196	#19242	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
197	C₂²×C₄₁	—	2	1	no	—
198	C₂²×C₄₁	—	2	1	no	—
199	C₂²×C₄₁	—	8	2	no	—
200	C₂²×C₄₁	—	8	2	no	—
201	C₂²×C₄₁	—	8	2	no	—
202	C₂²×C₄₁	—	16	4	no	—
203	C₂²×C₄₁	#464	1	2	yes	—
204	C₂²×C₄₁	C₂×#121	1	1	yes	characteristic
205	C₄×C₄₁	—	2	1	no	—
206	C₄×C₄₁	—	2	1	no	—
207	C₄×C₄₁	—	2	1	no	—
208	C₄×C₄₁	—	4	2	no	—
209	C₄×C₄₁	—	4	2	no	—
210	C₄×C₄₁	—	8	1	no	—
211	C₄×C₄₁	—	8	1	no	—
212	C₄×C₄₁	#464	1	2	yes	—
213	C₄×C₄₁	C₂×#135	1	1	yes	characteristic
214	C₄×C₄₁	C₂×#137	1	1	yes	characteristic
215	C₄×C₄₁	#576	1	1	yes	characteristic
216	C₄×C₄₁	#577	1	1	yes	characteristic
217	#3249	C₂×C₄₁	1	1	yes	characteristic, complemented
218	#3208	C₂×C₄₁	1	1	yes	characteristic
219	#3138	C₂×C₄₁	1	1	yes	characteristic
220	#2962	C₂×C₄₁	1	1	yes	characteristic, complemented
221	#1702	C₂×C₄₁	1	2	yes	complemented
222	#1698	C₂×C₄₁	1	2	yes	complemented
223	#1682	C₂×C₄₁	1	2	yes	complemented
224	#1678	C₂×C₄₁	1	2	yes	complemented
225	#1565	C₂×C₄₁	1	1	yes	characteristic, complemented
226	#1542	C₂×C₄₁	1	1	yes	characteristic, complemented
227	C₂×#331	C₂×C₄₁	1	1	yes	characteristic
228	C₂×C₄₁	—	2	2	no	—
229	C₂×C₄₁	—	16	2	no	—
230	C₂×C₄₁	C₂×#464	1	1	yes	characteristic
231	C₂×C₄₁	#3062	1	1	yes	characteristic
232	C₂×C₄₁	#3068	1	1	yes	characteristic
233	#533	C₂²×C₄₁	1	1	yes	characteristic
234	#533	C₂²×C₄₁	1	1	yes	characteristic
235	C₂×#127	C₂²×C₄₁	1	1	yes	characteristic
236	#492	—	2	1	no	—
237	#490	—	2	2	no	—
238	#486	—	2	1	no	—
239	#486	C₂²×C₄₁	1	2	yes	—
240	#486	C₂²×C₄₁	1	2	yes	—
241	#477	—	2	1	no	—
242	#477	C₂²×C₄₁	1	2	yes	complemented
243	#467	—	2	2	no	—
244	#462	—	2	1	no	—
245	#462	C₂²×C₄₁	1	2	yes	complemented
246	#460	C₂²×C₄₁	1	2	yes	—
247	#460	C₂²×C₄₁	1	2	yes	—
248	#450	—	2	2	no	—
249	#446	—	2	2	no	—
250	#446	C₂²×C₄₁	1	2	yes	complemented
251	C₈×Q₈	C₂²×C₄₁	1	2	yes	complemented
252	#431	C₂²×C₄₁	1	1	yes	characteristic
253	#424	—	2	1	no	—
254	C₂×C₄⋊C₈	C₂²×C₄₁	1	1	yes	characteristic
255	C₂×C₄⋊C₈	C₂²×C₄₁	1	1	yes	characteristic
256	#418	—	2	1	no	—
257	#418	—	2	1	no	—
258	#405	—	2	1	no	—
259	C₄×M₁₆	C₂²×C₄₁	1	1	yes	characteristic
260	#335	C₂²×C₄₁	1	2	yes	complemented
261	#334	C₂²×C₄₁	1	2	yes	complemented
262	#333	C₂²×C₄₁	1	1	yes	characteristic, complemented
263	#333	C₂²×C₄₁	1	1	yes	characteristic, complemented
264	#332	C₂²×C₄₁	1	1	yes	characteristic, complemented
265	#332	C₂²×C₄₁	1	1	yes	characteristic, complemented
266	#331	C₂²×C₄₁	1	2	yes	—
267	#331	C₂²×C₄₁	1	2	yes	—
268	C₄₁	#19242	1	1	yes	characteristic, direct product factor, Sylow
269	C₂²×D₄	—	2	1	no	—
270	C₂²×D₄	—	2	1	no	—
271	C₂²×D₄	—	2	1	no	—
272	C₂×Q₁₆	—	2	2	no	—
273	C₂×SD₁₆	—	2	2	no	—
274	C₂×SD₁₆	—	2	2	no	—
275	C₂×M₁₆	D₄×C₄₁	1	1	yes	characteristic
276	C₂×M₁₆	D₄×C₄₁	1	1	yes	characteristic
277	C₂²×C₈	—	2	1	no	—
278	C₂²×C₈	—	2	1	no	—
279	C₄⋊Q₈	D₄×C₄₁	1	1	yes	characteristic
280	C₄⋊Q₈	D₄×C₄₁	1	1	yes	characteristic
281	C₄⋊Q₈	C₂³×C₄₁	1	1	yes	characteristic
282	C₄⋊Q₈	C₂³×C₄₁	1	1	yes	characteristic
283	#127	—	2	1	no	—
284	#127	—	2	1	no	—
285	#127	—	2	1	no	—
286	#127	C₂³×C₄₁	1	2	yes	—
287	#125	—	2	1	no	—
288	#125	—	2	1	no	—
289	C₂²⋊Q₈	—	2	1	no	—
290	C₂²⋊Q₈	—	2	1	no	—
291	C₂²⋊Q₈	—	2	1	no	—
292	C₂²⋊Q₈	D₄×C₄₁	1	2	yes	—
293	C₄×Q₈	—	2	1	no	—
294	C₄×Q₈	—	2	1	no	—
295	C₄×Q₈	—	2	1	no	—
296	C₄×Q₈	C₂³×C₄₁	1	2	yes	—
297	#117	—	2	1	no	—
298	#117	—	2	1	no	—
299	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
300	#107	—	2	2	no	—
301	C₄⋊C₈	—	2	2	no	—
302	C₄⋊C₈	—	2	2	no	—
303	C₄⋊C₈	—	2	1	no	—
304	C₄⋊C₈	—	2	1	no	—
305	C₄⋊C₈	C₂³×C₄₁	1	1	yes	characteristic
306	C₄⋊C₈	C₂³×C₄₁	1	1	yes	characteristic
307	C₄⋊C₈	C₂³×C₄₁	1	2	yes	—
308	C₄⋊C₈	C₂³×C₄₁	1	1	yes	characteristic
309	C₄⋊C₈	C₂³×C₄₁	1	1	yes	characteristic
310	#103	—	2	2	no	—
311	#103	—	2	2	no	—
312	#102	—	2	2	no	—
313	#102	—	2	2	no	—
314	#102	—	2	2	no	—
315	#102	—	2	2	no	—
316	#102	—	2	2	no	—
317	#102	—	2	2	no	—
318	C₂²⋊C₈	—	2	1	no	—
319	#97	—	2	2	no	—
320	#97	D₄×C₄₁	1	2	yes	—
321	C₄×C₈	—	2	2	no	—
322	C₄×C₈	—	2	1	no	—
323	C₄×C₈	C₂³×C₄₁	1	2	yes	—
324	C₂⁴	—	4	1	no	—
325	C₂×Q₈	—	2	1	no	—
326	C₂×Q₈	—	2	1	no	—
327	C₂×Q₈	—	2	1	no	—
328	C₂×Q₈	C₂×D₄×C₄₁	1	2	yes	—
329	C₂×D₄	—	2	2	no	—
330	C₂×D₄	—	2	2	no	—
331	C₂×D₄	—	2	2	no	—
332	C₂×D₄	—	4	1	no	—
333	C₂×D₄	—	4	1	no	—
334	C₂×D₄	—	4	1	no	—
335	C₂×D₄	—	4	2	no	—
336	C₂×D₄	—	4	2	no	—
337	C₂×D₄	—	8	1	no	—
338	C₂×D₄	—	8	1	no	—
339	C₂×D₄	—	8	2	no	—
340	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
341	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
342	C₂²×C₄	#41×C₄₁	1	1	yes	characteristic
343	Q₁₆	—	8	2	no	—
344	SD₁₆	—	8	2	no	—
345	SD₁₆	—	8	2	no	—
346	M₁₆	—	2	2	no	—
347	M₁₆	—	2	2	no	—
348	C₂×C₈	—	2	1	no	—
349	C₂×C₈	—	2	1	no	—
350	C₂×C₈	—	2	1	no	—
351	C₂×C₈	—	2	1	no	—
352	C₂×C₈	—	2	2	no	—
353	C₂×C₈	—	4	2	no	—
354	C₂×C₈	—	8	1	no	—
355	C₂×C₈	C₂×D₄×C₄₁	1	2	yes	—
356	C₂×C₈	C₂×D₄×C₄₁	1	2	yes	—
357	C₄⋊C₄	—	2	1	no	—
358	C₄⋊C₄	—	2	1	no	—
359	C₄⋊C₄	—	2	1	no	—
360	C₄⋊C₄	—	2	2	no	—
361	C₄⋊C₄	—	2	2	no	—
362	C₄⋊C₄	—	2	1	no	—
363	C₄⋊C₄	—	2	1	no	—
364	C₄⋊C₄	—	2	1	no	—
365	C₄⋊C₄	—	2	1	no	—
366	C₄⋊C₄	—	4	1	no	—
367	C₄⋊C₄	—	4	1	no	—
368	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
369	C₂²⋊C₄	—	2	2	no	—
370	C₂²⋊C₄	—	4	1	no	—
371	C₄²	—	2	2	no	—
372	C₄²	—	4	1	no	—
373	C₄²	C₂×D₄×C₄₁	1	1	yes	characteristic
374	C₄²	C₂×D₄×C₄₁	1	1	yes	characteristic
375	C₄²	#41×C₄₁	1	1	yes	characteristic
376	C₄²	C₂⁴×C₄₁	1	1	yes	characteristic
377	C₂³	—	4	2	no	—
378	C₂³	—	8	2	no	—
379	C₂³	—	8	2	no	—
380	C₂³	—	8	2	no	—
381	C₂³	#121×C₄₁	1	1	yes	characteristic
382	Q₈	—	2	2	no	—
383	Q₈	—	2	2	no	—
384	Q₈	—	4	1	no	—
385	Q₈	—	4	1	no	—
386	Q₈	—	8	1	no	—
387	Q₈	—	8	1	no	—
388	D₄	—	4	2	no	—
389	D₄	—	4	2	no	—
390	D₄	—	4	2	no	—
391	D₄	—	4	2	no	—
392	D₄	—	8	2	no	—
393	D₄	—	8	2	no	—
394	D₄	—	8	2	no	—
395	D₄	—	8	2	no	—
396	C₂×C₄	—	2	1	no	—
397	C₂×C₄	—	2	1	no	—
398	C₂×C₄	—	2	2	no	—
399	C₂×C₄	—	2	2	no	—
400	C₂×C₄	—	4	1	no	—
401	C₂×C₄	—	4	1	no	—
402	C₂×C₄	—	4	1	no	—
403	C₂×C₄	#121×C₄₁	1	1	yes	characteristic
404	C₂×C₄	#121×C₄₁	1	1	yes	characteristic
405	C₂×C₄	#121×C₄₁	1	1	yes	characteristic
406	C₂×C₄	#135×C₄₁	1	2	yes	—
407	C₂×C₄	#137×C₄₁	1	2	yes	—
408	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
409	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
410	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
411	C₈	—	2	2	no	—
412	C₈	—	2	2	no	—
413	C₈	—	4	1	no	—
414	C₈	—	4	1	no	—
415	C₈	—	4	2	no	—
416	C₈	—	4	1	no	—
417	C₈	—	4	1	no	—
418	C₂²	—	2	1	no	—
419	C₂²	—	2	1	no	—
420	C₂²	—	8	2	no	—
421	C₂²	—	8	2	no	—
422	C₂²	—	8	2	no	—
423	C₂²	—	16	4	no	—
424	C₂²	C₄₁×#464	1	2	yes	—
425	C₂²	C₂×#121×C₄₁	1	1	yes	characteristic
426	C₄	—	2	1	no	—
427	C₄	—	2	1	no	—
428	C₄	—	2	1	no	—
429	C₄	—	4	2	no	—
430	C₄	—	4	2	no	—
431	C₄	—	8	1	no	—
432	C₄	—	8	1	no	—
433	C₄	C₄₁×#464	1	2	yes	—
434	C₄	C₂×#135×C₄₁	1	1	yes	characteristic
435	C₄	C₂×#137×C₄₁	1	1	yes	characteristic
436	C₄	C₄₁×#576	1	1	yes	characteristic
437	C₄	C₄₁×#577	1	1	yes	characteristic
438	C₂	—	2	2	no	—
439	C₂	—	16	2	no	—
440	C₂	C₂×C₄₁×#464	1	1	yes	characteristic
441	C₂	C₄₁×#3062	1	1	yes	characteristic
442	C₂	C₄₁×#3068	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₄₁	C₂×#121
commutator, Frattini, cosocle	C₄²	C₂⁴×C₄₁
prime radical	C₂×#127×C₄₁	C₂²
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
1. C₄₁×#3249	C₂	semidirect
4. C₄₁×#2962	C₂	semidirect
5. C₄₁×#1702	C₂	semidirect
6. C₄₁×#1698	C₂	semidirect
7. C₄₁×#1682	C₂	semidirect
8. C₄₁×#1678	C₂	semidirect
9. C₄₁×#1565	C₂	semidirect
10. C₄₁×#1542	C₂	semidirect
21. C₄₁×#477	C₂²	semidirect
24. C₄₁×#462	C₂²	semidirect
29. C₄₁×#446	C₂²	semidirect
30. C₈×Q₈×C₄₁	C₂²	semidirect
39. C₄₁×#335	C₂²	semidirect
40. C₄₁×#334	C₂²	semidirect
41. C₄₁×#333	C₂²	semidirect
42. C₄₁×#333	C₂²	semidirect
43. C₄₁×#332	C₂²	semidirect
44. C₄₁×#332	C₂²	semidirect
196. #19242	C₄₁	direct (N × H)
217. #3249	C₂×C₄₁	semidirect
220. #2962	C₂×C₄₁	semidirect
221. #1702	C₂×C₄₁	semidirect
222. #1698	C₂×C₄₁	semidirect
223. #1682	C₂×C₄₁	semidirect
224. #1678	C₂×C₄₁	semidirect
225. #1565	C₂×C₄₁	semidirect
226. #1542	C₂×C₄₁	semidirect
242. #477	C₂²×C₄₁	semidirect
245. #462	C₂²×C₄₁	semidirect
250. #446	C₂²×C₄₁	semidirect
251. C₈×Q₈	C₂²×C₄₁	semidirect
260. #335	C₂²×C₄₁	semidirect
261. #334	C₂²×C₄₁	semidirect
262. #333	C₂²×C₄₁	semidirect
263. #333	C₂²×C₄₁	semidirect
264. #332	C₂²×C₄₁	semidirect
265. #332	C₂²×C₄₁	semidirect
268. C₄₁	#19242	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×#3249	2
C₄₁×#3208	2
C₄₁×#3138	2
C₄₁×#2962	2
C₄₁×#1702	2
C₄₁×#1698	2
C₄₁×#1682	2
C₄₁×#1678	2
C₄₁×#1565	2
C₄₁×#1542	2
C₂×C₄₁×#331	2
#19242	41

Subgroups — C41×#19242 #23795443

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#19242 #23795443