Subgroups — C₄₁×#61943 #23838144

Order 10496.

1650 conjugacy classes of subgroups.

The subgroup lattice has 598 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₁×#3556	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄₁×#3510	C₂	1	1	yes	maximal, characteristic
3	C₄₁×#3400	C₂	1	4	yes	maximal, complemented
4	C₄₁×#3398	C₂	1	4	yes	maximal, complemented
5	C₄₁×#3377	C₂	1	4	yes	maximal, complemented
6	C₄₁×#3371	C₂	1	4	yes	maximal, complemented
7	C₄₁×#3223	C₂	1	2	yes	maximal, complemented
8	C₄₁×#3222	C₂	1	2	yes	maximal
9	C₄₁×#3215	C₂	1	2	yes	maximal, complemented
10	C₄₁×#3127	C₂	1	2	yes	maximal, complemented
11	C₄₁×#3123	C₂	1	2	yes	maximal, complemented
12	C₄₁×#3116	C₂	1	2	yes	maximal, complemented
13	C₄₁×#2987	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄₁×#564	—	2	2	no	—
15	C₄₁×#559	C₂²	1	4	yes	—
16	C₄₁×#557	—	2	2	no	—
17	C₄₁×#557	C₂²	1	4	yes	complemented
18	C₄₁×#557	C₂²	1	4	yes	complemented
19	C₄₁×#556	C₂²	1	4	yes	—
20	C₄₁×#551	—	2	4	no	—
21	C₄₁×#542	—	2	2	no	—
22	C₄₁×#541	—	2	4	no	—
23	C₄₁×#541	C₂²	1	2	yes	—
24	C₄₁×#541	C₂²	1	2	yes	—
25	C₄₁×#536	C₂²	1	1	yes	characteristic
26	C₄₁×#535	C₂²	1	1	yes	characteristic
27	C₄₁×#533	C₂²	1	2	yes	—
28	C₄₁×#533	C₂²	1	1	yes	characteristic
29	C₄₁×#529	—	2	2	no	—
30	C₂×#124×C₄₁	C₂²	1	1	yes	characteristic
31	C₄₁×#519	C₂²	1	1	yes	characteristic
32	C₄₁×#518	C₂²	1	1	yes	characteristic
33	C₄×#41×C₄₁	C₂²	1	1	yes	characteristic
34	C₄₁×#497	C₂²	1	2	yes	—
35	C₄₁×#497	C₂²	1	4	yes	—
36	C₄₁×#497	C₂²	1	2	yes	complemented
37	C₄₁×#494	C₂²	1	2	yes	complemented
38	C₄₁×#492	C₂²	1	2	yes	—
39	C₄₁×#491	C₂²	1	2	yes	complemented
40	C₄₁×#490	C₂²	1	2	yes	—
41	C₄₁×#489	C₂²	1	4	yes	—
42	C₄₁×#488	C₂²	1	2	yes	—
43	C₄₁×#488	C₂²	1	2	yes	complemented
44	C₄₁×#485	C₂²	1	4	yes	—
45	C₄₁×#479	C₂²	1	4	yes	complemented
46	C₄₁×#478	C₂²	1	4	yes	—
47	C₄₁×#477	C₂²	1	2	yes	complemented
48	C₄₁×#476	C₂²	1	2	yes	complemented
49	C₄₁×#464	C₂²	1	4	yes	—
50	C₄₁×#464	C₂²	1	4	yes	—
51	C₄₁×#464	C₂²	1	4	yes	—
52	C₄₁×#464	C₂²	1	4	yes	complemented
53	C₄₁×#462	C₂²	1	2	yes	complemented
54	C₄₁×#462	C₂²	1	4	yes	complemented
55	C₄₁×#462	C₂²	1	4	yes	complemented
56	C₄₁×#461	C₂²	1	4	yes	—
57	C₄₁×#461	C₂²	1	2	yes	complemented
58	C₄₁×#460	C₂²	1	4	yes	—
59	C₄₁×#452	C₂²	1	4	yes	—
60	C₄₁×#451	C₂²	1	4	yes	—
61	C₄₁×#450	C₂²	1	4	yes	—
62	C₄₁×#446	C₂²	1	4	yes	complemented
63	C₄₁×#446	C₂²	1	4	yes	complemented
64	C₄₁×#441	C₂²	1	4	yes	complemented
65	C₄₁×#441	C₂²	1	4	yes	complemented
66	C₄₁×#440	C₂²	1	4	yes	—
67	C₄₁×#440	C₂²	1	4	yes	complemented
68	C₄×Q₁₆×C₄₁	C₂²	1	4	yes	complemented
69	C₄×SD₁₆×C₄₁	C₂²	1	4	yes	—
70	C₄₁×#433	C₂²	1	2	yes	—
71	C₄₁×#433	C₂²	1	2	yes	—
72	C₄₁×#432	C₂²	1	2	yes	—
73	C₂×#41×C₄₁	C₂³	1	1	yes	characteristic
74	C₂²×Q₈×C₄₁	C₂³	1	1	yes	characteristic
75	C₂²×D₄×C₄₁	C₂³	1	1	yes	characteristic
76	C₂×Q₁₆×C₄₁	C₂³	1	4	yes	—
77	C₂×Q₁₆×C₄₁	C₂³	1	4	yes	—
78	C₂×Q₁₆×C₄₁	C₂³	1	4	yes	—
79	C₂×SD₁₆×C₄₁	C₂³	1	4	yes	—
80	C₂×SD₁₆×C₄₁	C₂³	1	4	yes	—
81	C₂×SD₁₆×C₄₁	C₂³	1	4	yes	—
82	C₄⋊Q₈×C₄₁	—	2	4	no	—
83	C₄⋊Q₈×C₄₁	D₄	1	2	yes	—
84	C₄⋊Q₈×C₄₁	C₂³	1	2	yes	—
85	C₄⋊Q₈×C₄₁	C₂³	1	2	yes	—
86	C₄⋊Q₈×C₄₁	C₂³	1	2	yes	—
87	C₄⋊Q₈×C₄₁	C₂³	1	2	yes	—
88	C₄⋊Q₈×C₄₁	C₂³	1	2	yes	—
89	#127×C₄₁	C₂³	1	2	yes	—
90	#126×C₄₁	—	2	4	no	—
91	#126×C₄₁	—	2	4	no	—
92	#126×C₄₁	—	2	4	no	—
93	#126×C₄₁	—	2	4	no	—
94	#125×C₄₁	—	2	4	no	—
95	#125×C₄₁	—	2	4	no	—
96	#125×C₄₁	—	2	4	no	—
97	#125×C₄₁	—	2	4	no	—
98	#125×C₄₁	—	2	4	no	—
99	#125×C₄₁	—	2	4	no	—
100	#125×C₄₁	—	2	4	no	—
101	#125×C₄₁	—	2	2	no	—
102	#125×C₄₁	D₄	1	2	yes	—
103	#125×C₄₁	C₂³	1	2	yes	—
104	#125×C₄₁	C₂³	1	2	yes	—
105	#124×C₄₁	—	2	4	no	—
106	#124×C₄₁	—	2	1	no	—
107	#124×C₄₁	—	2	1	no	—
108	#124×C₄₁	C₂³	1	4	yes	—
109	#124×C₄₁	C₂³	1	2	yes	—
110	#124×C₄₁	C₂³	1	2	yes	—
111	#123×C₄₁	—	2	4	no	—
112	#123×C₄₁	—	2	4	no	—
113	#123×C₄₁	—	2	2	no	—
114	C₂²⋊Q₈×C₄₁	—	2	4	no	—
115	C₂²⋊Q₈×C₄₁	—	2	2	no	—
116	C₂²⋊Q₈×C₄₁	—	2	2	no	—
117	C₂²⋊Q₈×C₄₁	D₄	1	4	yes	—
118	C₂²⋊Q₈×C₄₁	C₂³	1	4	yes	—
119	#121×C₄₁	—	2	2	no	—
120	#120×C₄₁	—	2	2	no	—
121	C₄×Q₈×C₄₁	—	2	4	no	—
122	C₄×Q₈×C₄₁	—	2	2	no	—
123	C₄×Q₈×C₄₁	—	2	4	no	—
124	C₄×Q₈×C₄₁	—	2	2	no	—
125	C₄×Q₈×C₄₁	C₂³	1	2	yes	—
126	C₄×Q₈×C₄₁	C₂³	1	4	yes	—
127	C₄×Q₈×C₄₁	C₂³	1	4	yes	—
128	C₄×Q₈×C₄₁	C₂³	1	4	yes	—
129	C₄×Q₈×C₄₁	C₂³	1	4	yes	—
130	C₄×Q₈×C₄₁	C₂³	1	4	yes	—
131	C₄×D₄×C₄₁	—	2	2	no	—
132	C₄×D₄×C₄₁	—	2	2	no	—
133	C₄×D₄×C₄₁	—	2	4	no	—
134	C₄×D₄×C₄₁	C₂³	1	2	yes	—
135	C₄×D₄×C₄₁	C₂³	1	4	yes	—
136	#117×C₄₁	—	2	2	no	—
137	#117×C₄₁	—	2	4	no	—
138	#117×C₄₁	—	2	2	no	—
139	#117×C₄₁	—	2	1	no	—
140	#117×C₄₁	C₂³	1	1	yes	characteristic
141	#117×C₄₁	C₂³	1	1	yes	characteristic
142	#117×C₄₁	C₂³	1	1	yes	characteristic
143	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
144	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
145	C₂×C₄²×C₄₁	—	2	1	no	—
146	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
147	#107×C₄₁	C₂³	1	4	yes	—
148	#106×C₄₁	C₂³	1	4	yes	—
149	C₄⋊C₈×C₄₁	C₂³	1	2	yes	—
150	C₄⋊C₈×C₄₁	C₂³	1	2	yes	—
151	C₄⋊C₈×C₄₁	C₂³	1	4	yes	—
152	C₄⋊C₈×C₄₁	C₂³	1	4	yes	—
153	#103×C₄₁	C₂³	1	4	yes	—
154	#103×C₄₁	C₂³	1	4	yes	—
155	#103×C₄₁	C₂³	1	4	yes	—
156	#103×C₄₁	C₂³	1	4	yes	—
157	#103×C₄₁	C₂³	1	4	yes	—
158	#102×C₄₁	C₂³	1	4	yes	—
159	#102×C₄₁	C₂³	1	4	yes	—
160	#102×C₄₁	C₂³	1	4	yes	—
161	C₂²⋊C₈×C₄₁	C₂³	1	4	yes	—
162	#97×C₄₁	C₂³	1	4	yes	—
163	#97×C₄₁	C₂³	1	2	yes	—
164	#97×C₄₁	C₂³	1	2	yes	—
165	C₄×C₈×C₄₁	C₂³	1	2	yes	—
166	C₄×C₈×C₄₁	C₂³	1	2	yes	—
167	C₂⁴×C₄₁	—	2	1	no	—
168	#41×C₄₁	—	4	2	no	—
169	C₂×Q₈×C₄₁	—	2	2	no	—
170	C₂×Q₈×C₄₁	—	2	1	no	—
171	C₂×Q₈×C₄₁	—	4	2	no	—
172	C₂×Q₈×C₄₁	C₂×D₄	1	4	yes	—
173	C₂×Q₈×C₄₁	C₂⁴	1	2	yes	—
174	C₂×Q₈×C₄₁	C₂⁴	1	1	yes	characteristic
175	C₂×Q₈×C₄₁	C₂⁴	1	4	yes	—
176	C₂×D₄×C₄₁	—	2	1	no	—
177	C₂×D₄×C₄₁	—	2	1	no	—
178	C₂×D₄×C₄₁	—	2	4	no	—
179	C₂×D₄×C₄₁	—	4	2	no	—
180	C₂×D₄×C₄₁	C₂⁴	1	2	yes	—
181	C₂×D₄×C₄₁	C₂⁴	1	1	yes	characteristic
182	C₂²×C₄×C₄₁	—	2	1	no	—
183	C₂²×C₄×C₄₁	—	2	1	no	—
184	C₂²×C₄×C₄₁	—	2	2	no	—
185	C₂²×C₄×C₄₁	—	2	4	no	—
186	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
187	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
188	Q₁₆×C₄₁	—	4	4	no	—
189	Q₁₆×C₄₁	—	4	4	no	—
190	Q₁₆×C₄₁	—	4	4	no	—
191	SD₁₆×C₄₁	—	4	4	no	—
192	SD₁₆×C₄₁	—	4	4	no	—
193	SD₁₆×C₄₁	—	4	4	no	—
194	C₂×C₈×C₄₁	C₂⁴	1	4	yes	—
195	C₂×C₈×C₄₁	C₂⁴	1	4	yes	—
196	C₄⋊C₄×C₄₁	—	2	2	no	—
197	C₄⋊C₄×C₄₁	—	2	4	no	—
198	C₄⋊C₄×C₄₁	—	2	4	no	—
199	C₄⋊C₄×C₄₁	—	2	2	no	—
200	C₄⋊C₄×C₄₁	—	2	2	no	—
201	C₄⋊C₄×C₄₁	—	2	2	no	—
202	C₄⋊C₄×C₄₁	—	2	4	no	—
203	C₄⋊C₄×C₄₁	—	2	4	no	—
204	C₄⋊C₄×C₄₁	—	2	4	no	—
205	C₄⋊C₄×C₄₁	—	2	4	no	—
206	C₄⋊C₄×C₄₁	—	2	4	no	—
207	C₄⋊C₄×C₄₁	—	2	4	no	—
208	C₄⋊C₄×C₄₁	—	2	4	no	—
209	C₄⋊C₄×C₄₁	—	2	4	no	—
210	C₄⋊C₄×C₄₁	C₂×D₄	1	4	yes	—
211	C₄⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
212	C₄⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
213	C₄⋊C₄×C₄₁	C₂×D₄	1	4	yes	—
214	C₄⋊C₄×C₄₁	C₂×D₄	1	4	yes	—
215	C₄⋊C₄×C₄₁	C₂⁴	1	4	yes	—
216	C₄⋊C₄×C₄₁	C₂⁴	1	2	yes	—
217	C₂²⋊C₄×C₄₁	—	2	1	no	—
218	C₂²⋊C₄×C₄₁	—	2	4	no	—
219	C₂²⋊C₄×C₄₁	—	2	4	no	—
220	C₂²⋊C₄×C₄₁	—	2	4	no	—
221	C₂²⋊C₄×C₄₁	—	2	4	no	—
222	C₂²⋊C₄×C₄₁	—	2	2	no	—
223	C₂²⋊C₄×C₄₁	—	2	4	no	—
224	C₂²⋊C₄×C₄₁	—	2	4	no	—
225	C₂²⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
226	C₂²⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
227	C₄²×C₄₁	—	2	2	no	—
228	C₄²×C₄₁	—	2	1	no	—
229	C₄²×C₄₁	—	2	4	no	—
230	C₄²×C₄₁	—	2	4	no	—
231	C₄²×C₄₁	—	2	4	no	—
232	C₄²×C₄₁	—	2	4	no	—
233	C₄²×C₄₁	C₂×D₄	1	1	yes	characteristic
234	C₄²×C₄₁	C₂×D₄	1	1	yes	characteristic
235	C₄²×C₄₁	C₂⁴	1	2	yes	—
236	C₄²×C₄₁	C₂⁴	1	2	yes	—
237	C₄²×C₄₁	C₂⁴	1	2	yes	—
238	C₂³×C₄₁	—	2	2	no	—
239	C₂³×C₄₁	—	2	1	no	—
240	C₂³×C₄₁	—	4	2	no	—
241	C₂³×C₄₁	—	8	2	no	—
242	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
243	Q₈×C₄₁	—	2	4	no	—
244	Q₈×C₄₁	—	2	4	no	—
245	Q₈×C₄₁	—	2	4	no	—
246	Q₈×C₄₁	—	2	2	no	—
247	Q₈×C₄₁	—	4	4	no	—
248	Q₈×C₄₁	—	4	4	no	—
249	Q₈×C₄₁	—	4	2	no	—
250	D₄×C₄₁	—	2	4	no	—
251	D₄×C₄₁	—	2	2	no	—
252	D₄×C₄₁	—	4	2	no	—
253	D₄×C₄₁	—	4	2	no	—
254	D₄×C₄₁	—	8	4	no	—
255	C₂×C₄×C₄₁	—	2	2	no	—
256	C₂×C₄×C₄₁	—	2	2	no	—
257	C₂×C₄×C₄₁	—	2	4	no	—
258	C₂×C₄×C₄₁	—	2	4	no	—
259	C₂×C₄×C₄₁	—	2	2	no	—
260	C₂×C₄×C₄₁	—	2	1	no	—
261	C₂×C₄×C₄₁	—	4	2	no	—
262	C₂×C₄×C₄₁	—	4	2	no	—
263	C₂×C₄×C₄₁	—	4	2	no	—
264	C₂×C₄×C₄₁	—	8	2	no	—
265	C₂×C₄×C₄₁	—	8	4	no	—
266	C₂×C₄×C₄₁	C₂²×D₄	1	2	yes	—
267	C₂×C₄×C₄₁	C₂²×D₄	1	4	yes	—
268	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
269	C₂×C₄×C₄₁	C₂²×D₄	1	2	yes	—
270	C₂×C₄×C₄₁	C₂²×D₄	1	4	yes	—
271	C₂×C₄×C₄₁	C₂⁵	1	1	yes	characteristic
272	C₈×C₄₁	—	2	4	no	—
273	C₈×C₄₁	—	2	4	no	—
274	#61943	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
275	C₂²×C₄₁	—	2	2	no	—
276	C₂²×C₄₁	—	2	1	no	—
277	C₂²×C₄₁	—	4	2	no	—
278	C₂²×C₄₁	—	4	4	no	—
279	C₂²×C₄₁	—	4	1	no	—
280	C₂²×C₄₁	—	4	2	no	—
281	C₂²×C₄₁	—	16	2	no	—
282	C₂²×C₄₁	C₂³×D₄	1	1	yes	characteristic
283	C₄×C₄₁	—	2	2	no	—
284	C₄×C₄₁	—	2	2	no	—
285	C₄×C₄₁	—	2	4	no	—
286	C₄×C₄₁	—	2	4	no	—
287	C₄×C₄₁	—	2	1	no	—
288	C₄×C₄₁	—	4	2	no	—
289	C₄×C₄₁	—	4	4	no	—
290	C₄×C₄₁	—	4	1	no	—
291	C₄×C₄₁	—	4	2	no	—
292	C₄×C₄₁	—	4	4	no	—
293	C₄×C₄₁	#585	1	2	yes	—
294	#3556	C₂×C₄₁	1	1	yes	characteristic, complemented
295	#3510	C₂×C₄₁	1	1	yes	characteristic
296	#3400	C₂×C₄₁	1	4	yes	complemented
297	#3398	C₂×C₄₁	1	4	yes	complemented
298	#3377	C₂×C₄₁	1	4	yes	complemented
299	#3371	C₂×C₄₁	1	4	yes	complemented
300	#3223	C₂×C₄₁	1	2	yes	complemented
301	#3222	C₂×C₄₁	1	2	yes	—
302	#3215	C₂×C₄₁	1	2	yes	complemented
303	#3127	C₂×C₄₁	1	2	yes	complemented
304	#3123	C₂×C₄₁	1	2	yes	complemented
305	#3116	C₂×C₄₁	1	2	yes	complemented
306	#2987	C₂×C₄₁	1	1	yes	characteristic, complemented
307	C₂×C₄₁	—	4	1	no	—
308	C₂×C₄₁	—	8	1	no	—
309	C₂×C₄₁	—	8	2	no	—
310	C₂×C₄₁	#3487	1	1	yes	characteristic
311	C₂×C₄₁	#3586	1	2	yes	—
312	#564	—	2	2	no	—
313	#559	C₂²×C₄₁	1	4	yes	—
314	#557	—	2	2	no	—
315	#557	C₂²×C₄₁	1	4	yes	complemented
316	#557	C₂²×C₄₁	1	4	yes	complemented
317	#556	C₂²×C₄₁	1	4	yes	—
318	#551	—	2	4	no	—
319	#542	—	2	2	no	—
320	#541	—	2	4	no	—
321	#541	C₂²×C₄₁	1	2	yes	—
322	#541	C₂²×C₄₁	1	2	yes	—
323	#536	C₂²×C₄₁	1	1	yes	characteristic
324	#535	C₂²×C₄₁	1	1	yes	characteristic
325	#533	C₂²×C₄₁	1	2	yes	—
326	#533	C₂²×C₄₁	1	1	yes	characteristic
327	#529	—	2	2	no	—
328	C₂×#124	C₂²×C₄₁	1	1	yes	characteristic
329	#519	C₂²×C₄₁	1	1	yes	characteristic
330	#518	C₂²×C₄₁	1	1	yes	characteristic
331	C₄×#41	C₂²×C₄₁	1	1	yes	characteristic
332	#497	C₂²×C₄₁	1	2	yes	—
333	#497	C₂²×C₄₁	1	4	yes	—
334	#497	C₂²×C₄₁	1	2	yes	complemented
335	#494	C₂²×C₄₁	1	2	yes	complemented
336	#492	C₂²×C₄₁	1	2	yes	—
337	#491	C₂²×C₄₁	1	2	yes	complemented
338	#490	C₂²×C₄₁	1	2	yes	—
339	#489	C₂²×C₄₁	1	4	yes	—
340	#488	C₂²×C₄₁	1	2	yes	—
341	#488	C₂²×C₄₁	1	2	yes	complemented
342	#485	C₂²×C₄₁	1	4	yes	—
343	#479	C₂²×C₄₁	1	4	yes	complemented
344	#478	C₂²×C₄₁	1	4	yes	—
345	#477	C₂²×C₄₁	1	2	yes	complemented
346	#476	C₂²×C₄₁	1	2	yes	complemented
347	#464	C₂²×C₄₁	1	4	yes	—
348	#464	C₂²×C₄₁	1	4	yes	—
349	#464	C₂²×C₄₁	1	4	yes	—
350	#464	C₂²×C₄₁	1	4	yes	complemented
351	#462	C₂²×C₄₁	1	2	yes	complemented
352	#462	C₂²×C₄₁	1	4	yes	complemented
353	#462	C₂²×C₄₁	1	4	yes	complemented
354	#461	C₂²×C₄₁	1	4	yes	—
355	#461	C₂²×C₄₁	1	2	yes	complemented
356	#460	C₂²×C₄₁	1	4	yes	—
357	#452	C₂²×C₄₁	1	4	yes	—
358	#451	C₂²×C₄₁	1	4	yes	—
359	#450	C₂²×C₄₁	1	4	yes	—
360	#446	C₂²×C₄₁	1	4	yes	complemented
361	#446	C₂²×C₄₁	1	4	yes	complemented
362	#441	C₂²×C₄₁	1	4	yes	complemented
363	#441	C₂²×C₄₁	1	4	yes	complemented
364	#440	C₂²×C₄₁	1	4	yes	—
365	#440	C₂²×C₄₁	1	4	yes	complemented
366	C₄×Q₁₆	C₂²×C₄₁	1	4	yes	complemented
367	C₄×SD₁₆	C₂²×C₄₁	1	4	yes	—
368	#433	C₂²×C₄₁	1	2	yes	—
369	#433	C₂²×C₄₁	1	2	yes	—
370	#432	C₂²×C₄₁	1	2	yes	—
371	C₄₁	#61943	1	1	yes	characteristic, direct product factor, Sylow
372	C₂×#41	C₂³×C₄₁	1	1	yes	characteristic
373	C₂²×Q₈	C₂³×C₄₁	1	1	yes	characteristic
374	C₂²×D₄	C₂³×C₄₁	1	1	yes	characteristic
375	C₂×Q₁₆	C₂³×C₄₁	1	4	yes	—
376	C₂×Q₁₆	C₂³×C₄₁	1	4	yes	—
377	C₂×Q₁₆	C₂³×C₄₁	1	4	yes	—
378	C₂×SD₁₆	C₂³×C₄₁	1	4	yes	—
379	C₂×SD₁₆	C₂³×C₄₁	1	4	yes	—
380	C₂×SD₁₆	C₂³×C₄₁	1	4	yes	—
381	C₄⋊Q₈	—	2	4	no	—
382	C₄⋊Q₈	D₄×C₄₁	1	2	yes	—
383	C₄⋊Q₈	C₂³×C₄₁	1	2	yes	—
384	C₄⋊Q₈	C₂³×C₄₁	1	2	yes	—
385	C₄⋊Q₈	C₂³×C₄₁	1	2	yes	—
386	C₄⋊Q₈	C₂³×C₄₁	1	2	yes	—
387	C₄⋊Q₈	C₂³×C₄₁	1	2	yes	—
388	#127	C₂³×C₄₁	1	2	yes	—
389	#126	—	2	4	no	—
390	#126	—	2	4	no	—
391	#126	—	2	4	no	—
392	#126	—	2	4	no	—
393	#125	—	2	4	no	—
394	#125	—	2	4	no	—
395	#125	—	2	4	no	—
396	#125	—	2	4	no	—
397	#125	—	2	4	no	—
398	#125	—	2	4	no	—
399	#125	—	2	4	no	—
400	#125	—	2	2	no	—
401	#125	D₄×C₄₁	1	2	yes	—
402	#125	C₂³×C₄₁	1	2	yes	—
403	#125	C₂³×C₄₁	1	2	yes	—
404	#124	—	2	4	no	—
405	#124	—	2	1	no	—
406	#124	—	2	1	no	—
407	#124	C₂³×C₄₁	1	4	yes	—
408	#124	C₂³×C₄₁	1	2	yes	—
409	#124	C₂³×C₄₁	1	2	yes	—
410	#123	—	2	4	no	—
411	#123	—	2	4	no	—
412	#123	—	2	2	no	—
413	C₂²⋊Q₈	—	2	4	no	—
414	C₂²⋊Q₈	—	2	2	no	—
415	C₂²⋊Q₈	—	2	2	no	—
416	C₂²⋊Q₈	D₄×C₄₁	1	4	yes	—
417	C₂²⋊Q₈	C₂³×C₄₁	1	4	yes	—
418	#121	—	2	2	no	—
419	#120	—	2	2	no	—
420	C₄×Q₈	—	2	4	no	—
421	C₄×Q₈	—	2	2	no	—
422	C₄×Q₈	—	2	4	no	—
423	C₄×Q₈	—	2	2	no	—
424	C₄×Q₈	C₂³×C₄₁	1	2	yes	—
425	C₄×Q₈	C₂³×C₄₁	1	4	yes	—
426	C₄×Q₈	C₂³×C₄₁	1	4	yes	—
427	C₄×Q₈	C₂³×C₄₁	1	4	yes	—
428	C₄×Q₈	C₂³×C₄₁	1	4	yes	—
429	C₄×Q₈	C₂³×C₄₁	1	4	yes	—
430	C₄×D₄	—	2	2	no	—
431	C₄×D₄	—	2	2	no	—
432	C₄×D₄	—	2	4	no	—
433	C₄×D₄	C₂³×C₄₁	1	2	yes	—
434	C₄×D₄	C₂³×C₄₁	1	4	yes	—
435	#117	—	2	2	no	—
436	#117	—	2	4	no	—
437	#117	—	2	2	no	—
438	#117	—	2	1	no	—
439	#117	C₂³×C₄₁	1	1	yes	characteristic
440	#117	C₂³×C₄₁	1	1	yes	characteristic
441	#117	C₂³×C₄₁	1	1	yes	characteristic
442	C₂×C₂²⋊C₄	—	2	2	no	—
443	C₂×C₂²⋊C₄	—	2	2	no	—
444	C₂×C₄²	—	2	1	no	—
445	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
446	#107	C₂³×C₄₁	1	4	yes	—
447	#106	C₂³×C₄₁	1	4	yes	—
448	C₄⋊C₈	C₂³×C₄₁	1	2	yes	—
449	C₄⋊C₈	C₂³×C₄₁	1	2	yes	—
450	C₄⋊C₈	C₂³×C₄₁	1	4	yes	—
451	C₄⋊C₈	C₂³×C₄₁	1	4	yes	—
452	#103	C₂³×C₄₁	1	4	yes	—
453	#103	C₂³×C₄₁	1	4	yes	—
454	#103	C₂³×C₄₁	1	4	yes	—
455	#103	C₂³×C₄₁	1	4	yes	—
456	#103	C₂³×C₄₁	1	4	yes	—
457	#102	C₂³×C₄₁	1	4	yes	—
458	#102	C₂³×C₄₁	1	4	yes	—
459	#102	C₂³×C₄₁	1	4	yes	—
460	C₂²⋊C₈	C₂³×C₄₁	1	4	yes	—
461	#97	C₂³×C₄₁	1	4	yes	—
462	#97	C₂³×C₄₁	1	2	yes	—
463	#97	C₂³×C₄₁	1	2	yes	—
464	C₄×C₈	C₂³×C₄₁	1	2	yes	—
465	C₄×C₈	C₂³×C₄₁	1	2	yes	—
466	C₂⁴	—	2	1	no	—
467	#41	—	4	2	no	—
468	C₂×Q₈	—	2	2	no	—
469	C₂×Q₈	—	2	1	no	—
470	C₂×Q₈	—	4	2	no	—
471	C₂×Q₈	C₂×D₄×C₄₁	1	4	yes	—
472	C₂×Q₈	C₂⁴×C₄₁	1	2	yes	—
473	C₂×Q₈	C₂⁴×C₄₁	1	1	yes	characteristic
474	C₂×Q₈	C₂⁴×C₄₁	1	4	yes	—
475	C₂×D₄	—	2	1	no	—
476	C₂×D₄	—	2	1	no	—
477	C₂×D₄	—	2	4	no	—
478	C₂×D₄	—	4	2	no	—
479	C₂×D₄	C₂⁴×C₄₁	1	2	yes	—
480	C₂×D₄	C₂⁴×C₄₁	1	1	yes	characteristic
481	C₂²×C₄	—	2	1	no	—
482	C₂²×C₄	—	2	1	no	—
483	C₂²×C₄	—	2	2	no	—
484	C₂²×C₄	—	2	4	no	—
485	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
486	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
487	Q₁₆	—	4	4	no	—
488	Q₁₆	—	4	4	no	—
489	Q₁₆	—	4	4	no	—
490	SD₁₆	—	4	4	no	—
491	SD₁₆	—	4	4	no	—
492	SD₁₆	—	4	4	no	—
493	C₂×C₈	C₂⁴×C₄₁	1	4	yes	—
494	C₂×C₈	C₂⁴×C₄₁	1	4	yes	—
495	C₄⋊C₄	—	2	2	no	—
496	C₄⋊C₄	—	2	4	no	—
497	C₄⋊C₄	—	2	4	no	—
498	C₄⋊C₄	—	2	2	no	—
499	C₄⋊C₄	—	2	2	no	—
500	C₄⋊C₄	—	2	2	no	—
501	C₄⋊C₄	—	2	4	no	—
502	C₄⋊C₄	—	2	4	no	—
503	C₄⋊C₄	—	2	4	no	—
504	C₄⋊C₄	—	2	4	no	—
505	C₄⋊C₄	—	2	4	no	—
506	C₄⋊C₄	—	2	4	no	—
507	C₄⋊C₄	—	2	4	no	—
508	C₄⋊C₄	—	2	4	no	—
509	C₄⋊C₄	C₂×D₄×C₄₁	1	4	yes	—
510	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
511	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
512	C₄⋊C₄	C₂×D₄×C₄₁	1	4	yes	—
513	C₄⋊C₄	C₂×D₄×C₄₁	1	4	yes	—
514	C₄⋊C₄	C₂⁴×C₄₁	1	4	yes	—
515	C₄⋊C₄	C₂⁴×C₄₁	1	2	yes	—
516	C₂²⋊C₄	—	2	1	no	—
517	C₂²⋊C₄	—	2	4	no	—
518	C₂²⋊C₄	—	2	4	no	—
519	C₂²⋊C₄	—	2	4	no	—
520	C₂²⋊C₄	—	2	4	no	—
521	C₂²⋊C₄	—	2	2	no	—
522	C₂²⋊C₄	—	2	4	no	—
523	C₂²⋊C₄	—	2	4	no	—
524	C₂²⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
525	C₂²⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
526	C₄²	—	2	2	no	—
527	C₄²	—	2	1	no	—
528	C₄²	—	2	4	no	—
529	C₄²	—	2	4	no	—
530	C₄²	—	2	4	no	—
531	C₄²	—	2	4	no	—
532	C₄²	C₂×D₄×C₄₁	1	1	yes	characteristic
533	C₄²	C₂×D₄×C₄₁	1	1	yes	characteristic
534	C₄²	C₂⁴×C₄₁	1	2	yes	—
535	C₄²	C₂⁴×C₄₁	1	2	yes	—
536	C₄²	C₂⁴×C₄₁	1	2	yes	—
537	C₂³	—	2	2	no	—
538	C₂³	—	2	1	no	—
539	C₂³	—	4	2	no	—
540	C₂³	—	8	2	no	—
541	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
542	Q₈	—	2	4	no	—
543	Q₈	—	2	4	no	—
544	Q₈	—	2	4	no	—
545	Q₈	—	2	2	no	—
546	Q₈	—	4	4	no	—
547	Q₈	—	4	2	no	—
548	Q₈	—	4	4	no	—
549	D₄	—	2	4	no	—
550	D₄	—	2	2	no	—
551	D₄	—	4	2	no	—
552	D₄	—	4	2	no	—
553	D₄	—	8	4	no	—
554	C₂×C₄	—	2	2	no	—
555	C₂×C₄	—	2	2	no	—
556	C₂×C₄	—	2	4	no	—
557	C₂×C₄	—	2	4	no	—
558	C₂×C₄	—	2	2	no	—
559	C₂×C₄	—	2	1	no	—
560	C₂×C₄	—	4	2	no	—
561	C₂×C₄	—	4	2	no	—
562	C₂×C₄	—	4	2	no	—
563	C₂×C₄	—	8	2	no	—
564	C₂×C₄	—	8	4	no	—
565	C₂×C₄	C₂²×D₄×C₄₁	1	2	yes	—
566	C₂×C₄	C₂²×D₄×C₄₁	1	4	yes	—
567	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
568	C₂×C₄	C₂²×D₄×C₄₁	1	2	yes	—
569	C₂×C₄	C₂²×D₄×C₄₁	1	4	yes	—
570	C₂×C₄	C₂⁵×C₄₁	1	1	yes	characteristic
571	C₈	—	2	4	no	—
572	C₈	—	2	4	no	—
573	C₂²	—	2	2	no	—
574	C₂²	—	2	1	no	—
575	C₂²	—	4	2	no	—
576	C₂²	—	4	4	no	—
577	C₂²	—	4	1	no	—
578	C₂²	—	4	2	no	—
579	C₂²	—	16	2	no	—
580	C₂²	C₂³×D₄×C₄₁	1	1	yes	characteristic
581	C₄	—	2	2	no	—
582	C₄	—	2	2	no	—
583	C₄	—	2	4	no	—
584	C₄	—	2	4	no	—
585	C₄	—	2	1	no	—
586	C₄	—	4	2	no	—
587	C₄	—	4	4	no	—
588	C₄	—	4	1	no	—
589	C₄	—	4	2	no	—
590	C₄	—	4	4	no	—
591	C₄	C₄₁×#585	1	2	yes	—
592	C₂	—	4	1	no	—
593	C₂	—	8	2	no	—
594	C₂	—	8	1	no	—
595	C₂	C₄₁×#3487	1	1	yes	characteristic
596	C₂	C₄₁×#3586	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₄₁	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₄₁
prime radical	C₄₁×#535	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄₁ ◁ C₄₁×#533 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₄₁×#3556	C₂	semidirect
3. C₄₁×#3400	C₂	semidirect
4. C₄₁×#3398	C₂	semidirect
5. C₄₁×#3377	C₂	semidirect
6. C₄₁×#3371	C₂	semidirect
7. C₄₁×#3223	C₂	semidirect
9. C₄₁×#3215	C₂	semidirect
10. C₄₁×#3127	C₂	semidirect
11. C₄₁×#3123	C₂	semidirect
12. C₄₁×#3116	C₂	semidirect
13. C₄₁×#2987	C₂	semidirect
17. C₄₁×#557	C₂²	semidirect
18. C₄₁×#557	C₂²	semidirect
36. C₄₁×#497	C₂²	semidirect
37. C₄₁×#494	C₂²	semidirect
39. C₄₁×#491	C₂²	semidirect
43. C₄₁×#488	C₂²	semidirect
45. C₄₁×#479	C₂²	semidirect
47. C₄₁×#477	C₂²	semidirect
48. C₄₁×#476	C₂²	semidirect
52. C₄₁×#464	C₂²	semidirect
53. C₄₁×#462	C₂²	semidirect
54. C₄₁×#462	C₂²	semidirect
55. C₄₁×#462	C₂²	semidirect
57. C₄₁×#461	C₂²	semidirect
62. C₄₁×#446	C₂²	semidirect
63. C₄₁×#446	C₂²	semidirect
64. C₄₁×#441	C₂²	semidirect
65. C₄₁×#441	C₂²	semidirect
67. C₄₁×#440	C₂²	semidirect
68. C₄×Q₁₆×C₄₁	C₂²	semidirect
274. #61943	C₄₁	direct (N × H)
294. #3556	C₂×C₄₁	semidirect
296. #3400	C₂×C₄₁	semidirect
297. #3398	C₂×C₄₁	semidirect
298. #3377	C₂×C₄₁	semidirect
299. #3371	C₂×C₄₁	semidirect
300. #3223	C₂×C₄₁	semidirect
302. #3215	C₂×C₄₁	semidirect
303. #3127	C₂×C₄₁	semidirect
304. #3123	C₂×C₄₁	semidirect
305. #3116	C₂×C₄₁	semidirect
306. #2987	C₂×C₄₁	semidirect
315. #557	C₂²×C₄₁	semidirect
316. #557	C₂²×C₄₁	semidirect
334. #497	C₂²×C₄₁	semidirect
335. #494	C₂²×C₄₁	semidirect
337. #491	C₂²×C₄₁	semidirect
341. #488	C₂²×C₄₁	semidirect
343. #479	C₂²×C₄₁	semidirect
345. #477	C₂²×C₄₁	semidirect
346. #476	C₂²×C₄₁	semidirect
350. #464	C₂²×C₄₁	semidirect
351. #462	C₂²×C₄₁	semidirect
352. #462	C₂²×C₄₁	semidirect
353. #462	C₂²×C₄₁	semidirect
355. #461	C₂²×C₄₁	semidirect
360. #446	C₂²×C₄₁	semidirect
361. #446	C₂²×C₄₁	semidirect
362. #441	C₂²×C₄₁	semidirect
363. #441	C₂²×C₄₁	semidirect
365. #440	C₂²×C₄₁	semidirect
366. C₄×Q₁₆	C₂²×C₄₁	semidirect
371. C₄₁	#61943	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×#3556	2
C₄₁×#3510	2
C₄₁×#3400	2
C₄₁×#3398	2
C₄₁×#3377	2
C₄₁×#3371	2
C₄₁×#3223	2
C₄₁×#3222	2
C₄₁×#3215	2
C₄₁×#3127	2
C₄₁×#3123	2
C₄₁×#3116	2
C₄₁×#2987	2
#61943	41

Subgroups — C41×#61943 #23838144

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#61943 #23838144