Subgroups — C₄₁×#61916 #23838117

Order 10496.

1696 conjugacy classes of subgroups.

The subgroup lattice has 726 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₁×#3550	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄₁×#3507	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₁×#3401	C₂	1	4	yes	maximal, complemented
4	C₄₁×#3398	C₂	1	2	yes	maximal, complemented
5	C₄₁×#3394	C₂	1	2	yes	maximal, complemented
6	C₄₁×#3373	C₂	1	2	yes	maximal, complemented
7	C₄₁×#3369	C₂	1	4	yes	maximal, complemented
8	C₄₁×#3359	C₂	1	2	yes	maximal, complemented
9	C₄₁×#3225	C₂	1	4	yes	maximal, complemented
10	C₄₁×#3214	C₂	1	1	yes	maximal, characteristic
11	C₄₁×#3210	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄₁×#3125	C₂	1	4	yes	maximal, complemented
13	C₄₁×#3113	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄₁×#3103	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄₁×#2985	C₂	1	1	yes	maximal, characteristic, complemented
16	C₄₁×#563	—	2	2	no	—
17	C₄₁×#559	C₂²	1	2	yes	—
18	C₄₁×#559	C₂²	1	2	yes	—
19	Q₈²×C₄₁	C₂²	1	2	yes	—
20	C₄₁×#557	C₂²	1	2	yes	—
21	C₄₁×#556	—	2	1	no	—
22	C₄₁×#556	—	2	1	no	—
23	C₄₁×#556	C₂²	1	2	yes	—
24	C₄₁×#556	C₂²	1	4	yes	—
25	C₄₁×#554	—	2	1	no	—
26	C₄₁×#552	—	2	2	no	—
27	D₄×Q₈×C₄₁	—	2	1	no	—
28	D₄×Q₈×C₄₁	C₂²	1	2	yes	—
29	C₄₁×#542	—	2	2	no	—
30	C₄₁×#542	C₂²	1	4	yes	—
31	C₄₁×#539	—	2	2	no	—
32	C₄₁×#536	—	2	2	no	—
33	C₄₁×#536	C₂²	1	2	yes	—
34	C₄₁×#533	C₂²	1	1	yes	characteristic
35	C₄₁×#533	C₂²	1	1	yes	characteristic
36	C₄₁×#532	C₂²	1	1	yes	characteristic
37	C₄₁×#532	C₂²	1	1	yes	characteristic
38	C₄₁×#529	—	2	2	no	—
39	C₄₁×#520	C₂²	1	2	yes	—
40	C₂×C₄×Q₈×C₄₁	C₂²	1	1	yes	characteristic
41	C₄₁×#497	C₂²	1	4	yes	—
42	C₄₁×#496	C₂²	1	2	yes	—
43	C₄₁×#495	C₂²	1	4	yes	—
44	C₄₁×#494	C₂²	1	1	yes	characteristic
45	C₄₁×#492	C₂²	1	1	yes	characteristic
46	C₄₁×#489	C₂²	1	2	yes	—
47	C₄₁×#489	C₂²	1	4	yes	—
48	C₄₁×#487	C₂²	1	1	yes	characteristic
49	C₄₁×#487	C₂²	1	4	yes	—
50	C₄₁×#486	C₂²	1	1	yes	characteristic
51	C₄₁×#483	C₂²	1	2	yes	—
52	C₄₁×#481	C₂²	1	2	yes	—
53	C₄₁×#476	C₂²	1	4	yes	—
54	C₄₁×#475	C₂²	1	2	yes	—
55	C₄₁×#475	C₂²	1	2	yes	—
56	C₄₁×#475	C₂²	1	4	yes	—
57	C₄₁×#464	C₂²	1	4	yes	—
58	C₄₁×#464	C₂²	1	4	yes	—
59	C₄₁×#464	C₂²	1	4	yes	—
60	C₄₁×#463	C₂²	1	4	yes	—
61	C₄₁×#463	C₂²	1	4	yes	—
62	C₄₁×#462	C₂²	1	2	yes	—
63	C₄₁×#462	C₂²	1	4	yes	—
64	C₄₁×#461	C₂²	1	2	yes	—
65	C₄₁×#461	C₂²	1	4	yes	—
66	C₄₁×#460	C₂²	1	2	yes	—
67	C₄₁×#459	C₂²	1	2	yes	—
68	C₄₁×#452	C₂²	1	4	yes	—
69	C₄₁×#451	C₂²	1	2	yes	—
70	C₄₁×#449	C₂²	1	4	yes	—
71	C₄₁×#448	C₂²	1	2	yes	—
72	C₄₁×#446	C₂²	1	4	yes	—
73	C₄₁×#446	C₂²	1	2	yes	—
74	C₈×Q₈×C₄₁	C₂²	1	2	yes	—
75	C₄₁×#442	C₂²	1	4	yes	—
76	C₄₁×#441	C₂²	1	4	yes	—
77	C₄₁×#441	C₂²	1	4	yes	—
78	C₄×SD₁₆×C₄₁	C₂²	1	2	yes	—
79	C₄×SD₁₆×C₄₁	C₂²	1	2	yes	—
80	C₄×SD₁₆×C₄₁	C₂²	1	4	yes	—
81	C₄×SD₁₆×C₄₁	C₂²	1	4	yes	—
82	C₄₁×#433	C₂²	1	4	yes	—
83	C₄₁×#432	C₂²	1	1	yes	characteristic
84	C₄₁×#431	C₂²	1	1	yes	characteristic
85	C₂×#41×C₄₁	—	2	1	no	—
86	C₂×#41×C₄₁	C₂³	1	2	yes	—
87	C₂²×Q₈×C₄₁	—	2	2	no	—
88	C₂²×Q₈×C₄₁	C₂³	1	1	yes	characteristic
89	C₂×Q₁₆×C₄₁	C₂³	1	4	yes	—
90	C₂×Q₁₆×C₄₁	C₂³	1	4	yes	—
91	C₂×SD₁₆×C₄₁	C₂³	1	2	yes	—
92	C₂×SD₁₆×C₄₁	C₂³	1	2	yes	—
93	C₂×SD₁₆×C₄₁	C₂³	1	4	yes	—
94	C₂×SD₁₆×C₄₁	C₂³	1	4	yes	—
95	C₂×D₈×C₄₁	C₂³	1	4	yes	—
96	C₄⋊Q₈×C₄₁	—	2	4	no	—
97	C₄⋊Q₈×C₄₁	—	2	2	no	—
98	C₄⋊Q₈×C₄₁	D₄	1	1	yes	characteristic
99	C₄⋊Q₈×C₄₁	D₄	1	1	yes	characteristic
100	C₄⋊Q₈×C₄₁	C₂³	1	1	yes	characteristic
101	C₄⋊Q₈×C₄₁	C₂³	1	1	yes	characteristic
102	C₄⋊Q₈×C₄₁	C₂³	1	4	yes	—
103	C₄⋊Q₈×C₄₁	C₂³	1	1	yes	characteristic
104	C₄⋊Q₈×C₄₁	C₂³	1	1	yes	characteristic
105	C₄⋊Q₈×C₄₁	C₂³	1	4	yes	—
106	#127×C₄₁	C₂³	1	1	yes	characteristic
107	#127×C₄₁	C₂³	1	1	yes	characteristic
108	#126×C₄₁	—	2	4	no	—
109	#126×C₄₁	—	2	4	no	—
110	#126×C₄₁	—	2	4	no	—
111	#126×C₄₁	—	2	4	no	—
112	#125×C₄₁	—	2	2	no	—
113	#125×C₄₁	—	2	4	no	—
114	#125×C₄₁	—	2	1	no	—
115	#125×C₄₁	D₄	1	2	yes	—
116	#124×C₄₁	—	2	2	no	—
117	#124×C₄₁	—	2	2	no	—
118	#124×C₄₁	—	2	4	no	—
119	#124×C₄₁	—	2	1	no	—
120	#124×C₄₁	C₂³	1	2	yes	—
121	#124×C₄₁	C₂³	1	4	yes	—
122	#124×C₄₁	C₂³	1	4	yes	—
123	#123×C₄₁	—	2	4	no	—
124	#123×C₄₁	—	2	4	no	—
125	#123×C₄₁	—	2	4	no	—
126	#123×C₄₁	—	2	4	no	—
127	C₂²⋊Q₈×C₄₁	—	2	2	no	—
128	C₂²⋊Q₈×C₄₁	—	2	4	no	—
129	C₂²⋊Q₈×C₄₁	—	2	1	no	—
130	C₂²⋊Q₈×C₄₁	—	2	2	no	—
131	C₂²⋊Q₈×C₄₁	—	2	2	no	—
132	C₂²⋊Q₈×C₄₁	—	2	2	no	—
133	C₂²⋊Q₈×C₄₁	—	2	4	no	—
134	C₂²⋊Q₈×C₄₁	—	2	4	no	—
135	C₂²⋊Q₈×C₄₁	D₄	1	2	yes	—
136	C₂²⋊Q₈×C₄₁	D₄	1	2	yes	—
137	C₂²⋊Q₈×C₄₁	C₂³	1	2	yes	—
138	#121×C₄₁	—	2	1	no	—
139	#121×C₄₁	—	2	1	no	—
140	#121×C₄₁	—	2	1	no	—
141	#121×C₄₁	C₂³	1	2	yes	—
142	C₄×Q₈×C₄₁	—	2	2	no	—
143	C₄×Q₈×C₄₁	—	2	2	no	—
144	C₄×Q₈×C₄₁	—	2	1	no	—
145	C₄×Q₈×C₄₁	—	2	1	no	—
146	C₄×Q₈×C₄₁	—	2	1	no	—
147	C₄×Q₈×C₄₁	C₂³	1	2	yes	—
148	C₄×Q₈×C₄₁	C₂³	1	2	yes	—
149	C₄×Q₈×C₄₁	C₂³	1	4	yes	—
150	C₄×Q₈×C₄₁	C₂³	1	2	yes	—
151	C₄×Q₈×C₄₁	C₂³	1	4	yes	—
152	C₄×Q₈×C₄₁	C₂³	1	2	yes	—
153	C₄×Q₈×C₄₁	C₂³	1	2	yes	—
154	C₄×D₄×C₄₁	—	2	2	no	—
155	C₄×D₄×C₄₁	—	2	2	no	—
156	C₄×D₄×C₄₁	—	2	4	no	—
157	C₄×D₄×C₄₁	—	2	1	no	—
158	C₄×D₄×C₄₁	—	2	1	no	—
159	C₄×D₄×C₄₁	—	2	1	no	—
160	C₄×D₄×C₄₁	C₂³	1	4	yes	—
161	C₄×D₄×C₄₁	C₂³	1	2	yes	—
162	C₄×D₄×C₄₁	C₂³	1	4	yes	—
163	#117×C₄₁	—	2	1	no	—
164	#117×C₄₁	—	2	2	no	—
165	#117×C₄₁	—	2	4	no	—
166	#117×C₄₁	—	2	2	no	—
167	#117×C₄₁	C₂³	1	2	yes	—
168	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
169	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
170	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
171	C₂×C₄²×C₄₁	—	2	1	no	—
172	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
173	#106×C₄₁	C₂³	1	2	yes	—
174	#106×C₄₁	C₂³	1	2	yes	—
175	#106×C₄₁	C₂³	1	4	yes	—
176	C₄⋊C₈×C₄₁	C₂³	1	2	yes	—
177	C₄⋊C₈×C₄₁	C₂³	1	2	yes	—
178	C₄⋊C₈×C₄₁	C₂³	1	4	yes	—
179	C₄⋊C₈×C₄₁	C₂³	1	4	yes	—
180	#103×C₄₁	C₂³	1	4	yes	—
181	#103×C₄₁	C₂³	1	2	yes	—
182	#103×C₄₁	C₂³	1	2	yes	—
183	#103×C₄₁	C₂³	1	4	yes	—
184	#103×C₄₁	C₂³	1	4	yes	—
185	#103×C₄₁	C₂³	1	4	yes	—
186	#102×C₄₁	C₂³	1	2	yes	—
187	#102×C₄₁	C₂³	1	2	yes	—
188	#102×C₄₁	C₂³	1	4	yes	—
189	#102×C₄₁	C₂³	1	4	yes	—
190	C₂²⋊C₈×C₄₁	C₂³	1	2	yes	—
191	C₂²⋊C₈×C₄₁	C₂³	1	2	yes	—
192	#97×C₄₁	C₂³	1	2	yes	—
193	#97×C₄₁	C₂³	1	4	yes	—
194	C₄×C₈×C₄₁	C₂³	1	1	yes	characteristic
195	C₄×C₈×C₄₁	C₂³	1	1	yes	characteristic
196	C₄×C₈×C₄₁	C₂³	1	4	yes	—
197	#41×C₄₁	—	4	4	no	—
198	#41×C₄₁	—	8	2	no	—
199	C₂×Q₈×C₄₁	—	2	1	no	—
200	C₂×Q₈×C₄₁	—	2	1	no	—
201	C₂×Q₈×C₄₁	—	2	4	no	—
202	C₂×Q₈×C₄₁	—	2	1	no	—
203	C₂×Q₈×C₄₁	—	4	2	no	—
204	C₂×Q₈×C₄₁	—	8	4	no	—
205	C₂×Q₈×C₄₁	C₂×D₄	1	2	yes	—
206	C₂×Q₈×C₄₁	C₂×D₄	1	2	yes	—
207	C₂×Q₈×C₄₁	C₂⁴	1	2	yes	—
208	C₂×Q₈×C₄₁	C₂⁴	1	2	yes	—
209	C₂×Q₈×C₄₁	C₂⁴	1	2	yes	—
210	C₂×D₄×C₄₁	—	2	2	no	—
211	C₂×D₄×C₄₁	—	2	2	no	—
212	C₂×D₄×C₄₁	—	2	1	no	—
213	C₂×D₄×C₄₁	—	2	1	no	—
214	C₂×D₄×C₄₁	—	2	1	no	—
215	C₂×D₄×C₄₁	—	2	1	no	—
216	C₂×D₄×C₄₁	C₂⁴	1	2	yes	—
217	C₂×D₄×C₄₁	C₂⁴	1	2	yes	—
218	C₂²×C₄×C₄₁	—	2	1	no	—
219	C₂²×C₄×C₄₁	—	2	1	no	—
220	C₂²×C₄×C₄₁	—	2	2	no	—
221	C₂²×C₄×C₄₁	—	2	2	no	—
222	C₂²×C₄×C₄₁	—	2	4	no	—
223	C₂²×C₄×C₄₁	—	2	4	no	—
224	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
225	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
226	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
227	Q₁₆×C₄₁	—	4	4	no	—
228	Q₁₆×C₄₁	—	4	4	no	—
229	SD₁₆×C₄₁	—	4	4	no	—
230	SD₁₆×C₄₁	—	4	4	no	—
231	SD₁₆×C₄₁	—	4	2	no	—
232	SD₁₆×C₄₁	—	4	2	no	—
233	D₈×C₄₁	—	4	4	no	—
234	C₂×C₈×C₄₁	C₂⁴	1	2	yes	—
235	C₂×C₈×C₄₁	C₂⁴	1	2	yes	—
236	C₂×C₈×C₄₁	C₂⁴	1	4	yes	—
237	C₄⋊C₄×C₄₁	—	2	1	no	—
238	C₄⋊C₄×C₄₁	—	2	4	no	—
239	C₄⋊C₄×C₄₁	—	2	2	no	—
240	C₄⋊C₄×C₄₁	—	2	2	no	—
241	C₄⋊C₄×C₄₁	—	2	1	no	—
242	C₄⋊C₄×C₄₁	—	2	1	no	—
243	C₄⋊C₄×C₄₁	—	2	4	no	—
244	C₄⋊C₄×C₄₁	—	2	1	no	—
245	C₄⋊C₄×C₄₁	—	2	1	no	—
246	C₄⋊C₄×C₄₁	—	2	1	no	—
247	C₄⋊C₄×C₄₁	—	2	1	no	—
248	C₄⋊C₄×C₄₁	—	2	2	no	—
249	C₄⋊C₄×C₄₁	—	2	4	no	—
250	C₄⋊C₄×C₄₁	—	2	4	no	—
251	C₄⋊C₄×C₄₁	—	2	4	no	—
252	C₄⋊C₄×C₄₁	—	2	2	no	—
253	C₄⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
254	C₄⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
255	C₄⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
256	C₄⋊C₄×C₄₁	C₂×D₄	1	4	yes	—
257	C₄⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
258	C₄⋊C₄×C₄₁	C₂×D₄	1	4	yes	—
259	C₄⋊C₄×C₄₁	C₂⁴	1	2	yes	—
260	C₄⋊C₄×C₄₁	C₂⁴	1	2	yes	—
261	C₄⋊C₄×C₄₁	C₂⁴	1	2	yes	—
262	C₂²⋊C₄×C₄₁	—	2	2	no	—
263	C₂²⋊C₄×C₄₁	—	2	2	no	—
264	C₂²⋊C₄×C₄₁	—	2	4	no	—
265	C₂²⋊C₄×C₄₁	—	2	4	no	—
266	C₂²⋊C₄×C₄₁	—	2	4	no	—
267	C₂²⋊C₄×C₄₁	—	2	2	no	—
268	C₂²⋊C₄×C₄₁	—	2	2	no	—
269	C₂²⋊C₄×C₄₁	—	2	4	no	—
270	C₂²⋊C₄×C₄₁	—	2	4	no	—
271	C₂²⋊C₄×C₄₁	—	2	2	no	—
272	C₂²⋊C₄×C₄₁	—	2	4	no	—
273	C₂²⋊C₄×C₄₁	C₂×D₄	1	4	yes	—
274	C₄²×C₄₁	—	2	2	no	—
275	C₄²×C₄₁	—	2	2	no	—
276	C₄²×C₄₁	—	2	4	no	—
277	C₄²×C₄₁	—	2	2	no	—
278	C₄²×C₄₁	—	2	4	no	—
279	C₄²×C₄₁	C₂×D₄	1	1	yes	characteristic
280	C₄²×C₄₁	C₂×D₄	1	1	yes	characteristic
281	C₄²×C₄₁	C₂⁴	1	1	yes	characteristic
282	C₄²×C₄₁	C₂⁴	1	4	yes	—
283	C₄²×C₄₁	C₂⁴	1	1	yes	characteristic
284	C₂³×C₄₁	—	2	2	no	—
285	C₂³×C₄₁	—	2	2	no	—
286	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
287	Q₈×C₄₁	—	2	4	no	—
288	Q₈×C₄₁	—	2	2	no	—
289	Q₈×C₄₁	—	2	4	no	—
290	Q₈×C₄₁	—	2	4	no	—
291	Q₈×C₄₁	—	2	2	no	—
292	Q₈×C₄₁	—	4	2	no	—
293	Q₈×C₄₁	—	4	2	no	—
294	Q₈×C₄₁	—	4	2	no	—
295	Q₈×C₄₁	—	8	4	no	—
296	Q₈×C₄₁	—	8	1	no	—
297	D₄×C₄₁	—	2	2	no	—
298	D₄×C₄₁	—	2	4	no	—
299	D₄×C₄₁	—	2	2	no	—
300	D₄×C₄₁	—	4	2	no	—
301	D₄×C₄₁	—	4	4	no	—
302	D₄×C₄₁	—	4	2	no	—
303	D₄×C₄₁	—	8	1	no	—
304	D₄×C₄₁	—	8	1	no	—
305	D₄×C₄₁	—	8	2	no	—
306	C₂×C₄×C₄₁	—	2	2	no	—
307	C₂×C₄×C₄₁	—	2	2	no	—
308	C₂×C₄×C₄₁	—	2	2	no	—
309	C₂×C₄×C₄₁	—	2	2	no	—
310	C₂×C₄×C₄₁	—	2	2	no	—
311	C₂×C₄×C₄₁	—	2	2	no	—
312	C₂×C₄×C₄₁	—	2	2	no	—
313	C₂×C₄×C₄₁	—	2	2	no	—
314	C₂×C₄×C₄₁	—	4	1	no	—
315	C₂×C₄×C₄₁	—	4	4	no	—
316	C₂×C₄×C₄₁	—	4	2	no	—
317	C₂×C₄×C₄₁	—	4	4	no	—
318	C₂×C₄×C₄₁	—	8	4	no	—
319	C₂×C₄×C₄₁	—	8	4	no	—
320	C₂×C₄×C₄₁	—	8	1	no	—
321	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
322	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
323	C₂×C₄×C₄₁	C₂²×D₄	1	4	yes	—
324	C₂×C₄×C₄₁	C₂²×D₄	1	4	yes	—
325	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
326	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
327	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
328	C₂×C₄×C₄₁	C₂⁵	1	1	yes	characteristic
329	C₈×C₄₁	—	2	4	no	—
330	C₈×C₄₁	—	2	2	no	—
331	C₈×C₄₁	—	2	2	no	—
332	#61916	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
333	C₂²×C₄₁	—	2	1	no	—
334	C₂²×C₄₁	—	2	1	no	—
335	C₂²×C₄₁	—	2	1	no	—
336	C₂²×C₄₁	—	4	2	no	—
337	C₂²×C₄₁	—	4	2	no	—
338	C₂²×C₄₁	—	4	2	no	—
339	C₂²×C₄₁	—	4	2	no	—
340	C₂²×C₄₁	—	4	2	no	—
341	C₂²×C₄₁	—	4	2	no	—
342	C₂²×C₄₁	C₂³×D₄	1	1	yes	characteristic
343	C₄×C₄₁	—	2	1	no	—
344	C₄×C₄₁	—	2	1	no	—
345	C₄×C₄₁	—	2	4	no	—
346	C₄×C₄₁	—	2	1	no	—
347	C₄×C₄₁	—	2	1	no	—
348	C₄×C₄₁	—	2	4	no	—
349	C₄×C₄₁	—	4	2	no	—
350	C₄×C₄₁	—	4	2	no	—
351	C₄×C₄₁	—	4	2	no	—
352	C₄×C₄₁	—	4	2	no	—
353	C₄×C₄₁	—	4	2	no	—
354	C₄×C₄₁	—	4	2	no	—
355	C₄×C₄₁	#577	1	2	yes	—
356	C₄×C₄₁	#585	1	2	yes	—
357	#3550	C₂×C₄₁	1	1	yes	characteristic, complemented
358	#3507	C₂×C₄₁	1	1	yes	characteristic, complemented
359	#3401	C₂×C₄₁	1	4	yes	complemented
360	#3398	C₂×C₄₁	1	2	yes	complemented
361	#3394	C₂×C₄₁	1	2	yes	complemented
362	#3373	C₂×C₄₁	1	2	yes	complemented
363	#3369	C₂×C₄₁	1	4	yes	complemented
364	#3359	C₂×C₄₁	1	2	yes	complemented
365	#3225	C₂×C₄₁	1	4	yes	complemented
366	#3214	C₂×C₄₁	1	1	yes	characteristic
367	#3210	C₂×C₄₁	1	1	yes	characteristic, complemented
368	#3125	C₂×C₄₁	1	4	yes	complemented
369	#3113	C₂×C₄₁	1	1	yes	characteristic, complemented
370	#3103	C₂×C₄₁	1	1	yes	characteristic, complemented
371	#2985	C₂×C₄₁	1	1	yes	characteristic, complemented
372	C₂×C₄₁	—	4	1	no	—
373	C₂×C₄₁	—	8	2	no	—
374	C₂×C₄₁	—	8	2	no	—
375	C₂×C₄₁	#3487	1	1	yes	characteristic
376	C₂×C₄₁	C₂×#577	1	1	yes	characteristic
377	C₂×C₄₁	#3586	1	1	yes	characteristic
378	#563	—	2	2	no	—
379	#559	C₂²×C₄₁	1	2	yes	—
380	#559	C₂²×C₄₁	1	2	yes	—
381	Q₈²	C₂²×C₄₁	1	2	yes	—
382	#557	C₂²×C₄₁	1	2	yes	—
383	#556	—	2	1	no	—
384	#556	—	2	1	no	—
385	#556	C₂²×C₄₁	1	4	yes	—
386	#556	C₂²×C₄₁	1	2	yes	—
387	#554	—	2	1	no	—
388	#552	—	2	2	no	—
389	D₄×Q₈	—	2	1	no	—
390	D₄×Q₈	C₂²×C₄₁	1	2	yes	—
391	#542	—	2	2	no	—
392	#542	C₂²×C₄₁	1	4	yes	—
393	#539	—	2	2	no	—
394	#536	—	2	2	no	—
395	#536	C₂²×C₄₁	1	2	yes	—
396	#533	C₂²×C₄₁	1	1	yes	characteristic
397	#533	C₂²×C₄₁	1	1	yes	characteristic
398	#532	C₂²×C₄₁	1	1	yes	characteristic
399	#532	C₂²×C₄₁	1	1	yes	characteristic
400	#529	—	2	2	no	—
401	#520	C₂²×C₄₁	1	2	yes	—
402	C₂×C₄×Q₈	C₂²×C₄₁	1	1	yes	characteristic
403	#497	C₂²×C₄₁	1	4	yes	—
404	#496	C₂²×C₄₁	1	2	yes	—
405	#495	C₂²×C₄₁	1	4	yes	—
406	#494	C₂²×C₄₁	1	1	yes	characteristic
407	#492	C₂²×C₄₁	1	1	yes	characteristic
408	#489	C₂²×C₄₁	1	2	yes	—
409	#489	C₂²×C₄₁	1	4	yes	—
410	#487	C₂²×C₄₁	1	1	yes	characteristic
411	#487	C₂²×C₄₁	1	4	yes	—
412	#486	C₂²×C₄₁	1	1	yes	characteristic
413	#483	C₂²×C₄₁	1	2	yes	—
414	#481	C₂²×C₄₁	1	2	yes	—
415	#476	C₂²×C₄₁	1	4	yes	—
416	#475	C₂²×C₄₁	1	2	yes	—
417	#475	C₂²×C₄₁	1	2	yes	—
418	#475	C₂²×C₄₁	1	4	yes	—
419	#464	C₂²×C₄₁	1	4	yes	—
420	#464	C₂²×C₄₁	1	4	yes	—
421	#464	C₂²×C₄₁	1	4	yes	—
422	#463	C₂²×C₄₁	1	4	yes	—
423	#463	C₂²×C₄₁	1	4	yes	—
424	#462	C₂²×C₄₁	1	2	yes	—
425	#462	C₂²×C₄₁	1	4	yes	—
426	#461	C₂²×C₄₁	1	2	yes	—
427	#461	C₂²×C₄₁	1	4	yes	—
428	#460	C₂²×C₄₁	1	2	yes	—
429	#459	C₂²×C₄₁	1	2	yes	—
430	#452	C₂²×C₄₁	1	4	yes	—
431	#451	C₂²×C₄₁	1	2	yes	—
432	#449	C₂²×C₄₁	1	4	yes	—
433	#448	C₂²×C₄₁	1	2	yes	—
434	#446	C₂²×C₄₁	1	4	yes	—
435	#446	C₂²×C₄₁	1	2	yes	—
436	C₈×Q₈	C₂²×C₄₁	1	2	yes	—
437	#442	C₂²×C₄₁	1	4	yes	—
438	#441	C₂²×C₄₁	1	4	yes	—
439	#441	C₂²×C₄₁	1	4	yes	—
440	C₄×SD₁₆	C₂²×C₄₁	1	2	yes	—
441	C₄×SD₁₆	C₂²×C₄₁	1	2	yes	—
442	C₄×SD₁₆	C₂²×C₄₁	1	4	yes	—
443	C₄×SD₁₆	C₂²×C₄₁	1	4	yes	—
444	#433	C₂²×C₄₁	1	4	yes	—
445	#432	C₂²×C₄₁	1	1	yes	characteristic
446	#431	C₂²×C₄₁	1	1	yes	characteristic
447	C₄₁	#61916	1	1	yes	characteristic, direct product factor, Sylow
448	C₂×#41	—	2	1	no	—
449	C₂×#41	C₂³×C₄₁	1	2	yes	—
450	C₂²×Q₈	—	2	2	no	—
451	C₂²×Q₈	C₂³×C₄₁	1	1	yes	characteristic
452	C₂×Q₁₆	C₂³×C₄₁	1	4	yes	—
453	C₂×Q₁₆	C₂³×C₄₁	1	4	yes	—
454	C₂×SD₁₆	C₂³×C₄₁	1	2	yes	—
455	C₂×SD₁₆	C₂³×C₄₁	1	2	yes	—
456	C₂×SD₁₆	C₂³×C₄₁	1	4	yes	—
457	C₂×SD₁₆	C₂³×C₄₁	1	4	yes	—
458	C₂×D₈	C₂³×C₄₁	1	4	yes	—
459	C₄⋊Q₈	—	2	4	no	—
460	C₄⋊Q₈	—	2	2	no	—
461	C₄⋊Q₈	D₄×C₄₁	1	1	yes	characteristic
462	C₄⋊Q₈	D₄×C₄₁	1	1	yes	characteristic
463	C₄⋊Q₈	C₂³×C₄₁	1	1	yes	characteristic
464	C₄⋊Q₈	C₂³×C₄₁	1	1	yes	characteristic
465	C₄⋊Q₈	C₂³×C₄₁	1	4	yes	—
466	C₄⋊Q₈	C₂³×C₄₁	1	1	yes	characteristic
467	C₄⋊Q₈	C₂³×C₄₁	1	1	yes	characteristic
468	C₄⋊Q₈	C₂³×C₄₁	1	4	yes	—
469	#127	C₂³×C₄₁	1	1	yes	characteristic
470	#127	C₂³×C₄₁	1	1	yes	characteristic
471	#126	—	2	4	no	—
472	#126	—	2	4	no	—
473	#126	—	2	4	no	—
474	#126	—	2	4	no	—
475	#125	—	2	2	no	—
476	#125	—	2	4	no	—
477	#125	—	2	1	no	—
478	#125	D₄×C₄₁	1	2	yes	—
479	#124	—	2	2	no	—
480	#124	—	2	2	no	—
481	#124	—	2	4	no	—
482	#124	—	2	1	no	—
483	#124	C₂³×C₄₁	1	2	yes	—
484	#124	C₂³×C₄₁	1	4	yes	—
485	#124	C₂³×C₄₁	1	4	yes	—
486	#123	—	2	4	no	—
487	#123	—	2	4	no	—
488	#123	—	2	4	no	—
489	#123	—	2	4	no	—
490	C₂²⋊Q₈	—	2	2	no	—
491	C₂²⋊Q₈	—	2	4	no	—
492	C₂²⋊Q₈	—	2	1	no	—
493	C₂²⋊Q₈	—	2	2	no	—
494	C₂²⋊Q₈	—	2	2	no	—
495	C₂²⋊Q₈	—	2	2	no	—
496	C₂²⋊Q₈	—	2	4	no	—
497	C₂²⋊Q₈	—	2	4	no	—
498	C₂²⋊Q₈	D₄×C₄₁	1	2	yes	—
499	C₂²⋊Q₈	D₄×C₄₁	1	2	yes	—
500	C₂²⋊Q₈	C₂³×C₄₁	1	2	yes	—
501	#121	—	2	1	no	—
502	#121	—	2	1	no	—
503	#121	—	2	1	no	—
504	#121	C₂³×C₄₁	1	2	yes	—
505	C₄×Q₈	—	2	2	no	—
506	C₄×Q₈	—	2	2	no	—
507	C₄×Q₈	—	2	1	no	—
508	C₄×Q₈	—	2	1	no	—
509	C₄×Q₈	—	2	1	no	—
510	C₄×Q₈	C₂³×C₄₁	1	2	yes	—
511	C₄×Q₈	C₂³×C₄₁	1	2	yes	—
512	C₄×Q₈	C₂³×C₄₁	1	4	yes	—
513	C₄×Q₈	C₂³×C₄₁	1	2	yes	—
514	C₄×Q₈	C₂³×C₄₁	1	4	yes	—
515	C₄×Q₈	C₂³×C₄₁	1	2	yes	—
516	C₄×Q₈	C₂³×C₄₁	1	2	yes	—
517	C₄×D₄	—	2	2	no	—
518	C₄×D₄	—	2	2	no	—
519	C₄×D₄	—	2	4	no	—
520	C₄×D₄	—	2	1	no	—
521	C₄×D₄	—	2	1	no	—
522	C₄×D₄	—	2	1	no	—
523	C₄×D₄	C₂³×C₄₁	1	4	yes	—
524	C₄×D₄	C₂³×C₄₁	1	2	yes	—
525	C₄×D₄	C₂³×C₄₁	1	4	yes	—
526	#117	—	2	1	no	—
527	#117	—	2	2	no	—
528	#117	—	2	4	no	—
529	#117	—	2	2	no	—
530	#117	C₂³×C₄₁	1	2	yes	—
531	C₂×C₄⋊C₄	—	2	1	no	—
532	C₂×C₄⋊C₄	—	2	2	no	—
533	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
534	C₂×C₄²	—	2	1	no	—
535	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
536	#106	C₂³×C₄₁	1	2	yes	—
537	#106	C₂³×C₄₁	1	2	yes	—
538	#106	C₂³×C₄₁	1	4	yes	—
539	C₄⋊C₈	C₂³×C₄₁	1	2	yes	—
540	C₄⋊C₈	C₂³×C₄₁	1	2	yes	—
541	C₄⋊C₈	C₂³×C₄₁	1	4	yes	—
542	C₄⋊C₈	C₂³×C₄₁	1	4	yes	—
543	#103	C₂³×C₄₁	1	4	yes	—
544	#103	C₂³×C₄₁	1	2	yes	—
545	#103	C₂³×C₄₁	1	2	yes	—
546	#103	C₂³×C₄₁	1	4	yes	—
547	#103	C₂³×C₄₁	1	4	yes	—
548	#103	C₂³×C₄₁	1	4	yes	—
549	#102	C₂³×C₄₁	1	2	yes	—
550	#102	C₂³×C₄₁	1	2	yes	—
551	#102	C₂³×C₄₁	1	4	yes	—
552	#102	C₂³×C₄₁	1	4	yes	—
553	C₂²⋊C₈	C₂³×C₄₁	1	2	yes	—
554	C₂²⋊C₈	C₂³×C₄₁	1	2	yes	—
555	#97	C₂³×C₄₁	1	2	yes	—
556	#97	C₂³×C₄₁	1	4	yes	—
557	C₄×C₈	C₂³×C₄₁	1	1	yes	characteristic
558	C₄×C₈	C₂³×C₄₁	1	1	yes	characteristic
559	C₄×C₈	C₂³×C₄₁	1	4	yes	—
560	#41	—	4	4	no	—
561	#41	—	8	2	no	—
562	C₂×Q₈	—	2	1	no	—
563	C₂×Q₈	—	2	1	no	—
564	C₂×Q₈	—	2	4	no	—
565	C₂×Q₈	—	2	1	no	—
566	C₂×Q₈	—	4	2	no	—
567	C₂×Q₈	—	8	4	no	—
568	C₂×Q₈	C₂×D₄×C₄₁	1	2	yes	—
569	C₂×Q₈	C₂×D₄×C₄₁	1	2	yes	—
570	C₂×Q₈	C₂⁴×C₄₁	1	2	yes	—
571	C₂×Q₈	C₂⁴×C₄₁	1	2	yes	—
572	C₂×Q₈	C₂⁴×C₄₁	1	2	yes	—
573	C₂×D₄	—	2	2	no	—
574	C₂×D₄	—	2	2	no	—
575	C₂×D₄	—	2	1	no	—
576	C₂×D₄	—	2	1	no	—
577	C₂×D₄	—	2	1	no	—
578	C₂×D₄	—	2	1	no	—
579	C₂×D₄	C₂⁴×C₄₁	1	2	yes	—
580	C₂×D₄	C₂⁴×C₄₁	1	2	yes	—
581	C₂²×C₄	—	2	1	no	—
582	C₂²×C₄	—	2	1	no	—
583	C₂²×C₄	—	2	2	no	—
584	C₂²×C₄	—	2	2	no	—
585	C₂²×C₄	—	2	4	no	—
586	C₂²×C₄	—	2	4	no	—
587	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
588	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
589	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
590	Q₁₆	—	4	4	no	—
591	Q₁₆	—	4	4	no	—
592	SD₁₆	—	4	4	no	—
593	SD₁₆	—	4	4	no	—
594	SD₁₆	—	4	2	no	—
595	SD₁₆	—	4	2	no	—
596	D₈	—	4	4	no	—
597	C₂×C₈	C₂⁴×C₄₁	1	2	yes	—
598	C₂×C₈	C₂⁴×C₄₁	1	2	yes	—
599	C₂×C₈	C₂⁴×C₄₁	1	4	yes	—
600	C₄⋊C₄	—	2	1	no	—
601	C₄⋊C₄	—	2	4	no	—
602	C₄⋊C₄	—	2	2	no	—
603	C₄⋊C₄	—	2	2	no	—
604	C₄⋊C₄	—	2	1	no	—
605	C₄⋊C₄	—	2	1	no	—
606	C₄⋊C₄	—	2	4	no	—
607	C₄⋊C₄	—	2	1	no	—
608	C₄⋊C₄	—	2	1	no	—
609	C₄⋊C₄	—	2	1	no	—
610	C₄⋊C₄	—	2	1	no	—
611	C₄⋊C₄	—	2	2	no	—
612	C₄⋊C₄	—	2	4	no	—
613	C₄⋊C₄	—	2	4	no	—
614	C₄⋊C₄	—	2	4	no	—
615	C₄⋊C₄	—	2	2	no	—
616	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
617	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
618	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
619	C₄⋊C₄	C₂×D₄×C₄₁	1	4	yes	—
620	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
621	C₄⋊C₄	C₂×D₄×C₄₁	1	4	yes	—
622	C₄⋊C₄	C₂⁴×C₄₁	1	2	yes	—
623	C₄⋊C₄	C₂⁴×C₄₁	1	2	yes	—
624	C₄⋊C₄	C₂⁴×C₄₁	1	2	yes	—
625	C₂²⋊C₄	—	2	2	no	—
626	C₂²⋊C₄	—	2	2	no	—
627	C₂²⋊C₄	—	2	4	no	—
628	C₂²⋊C₄	—	2	4	no	—
629	C₂²⋊C₄	—	2	4	no	—
630	C₂²⋊C₄	—	2	2	no	—
631	C₂²⋊C₄	—	2	2	no	—
632	C₂²⋊C₄	—	2	4	no	—
633	C₂²⋊C₄	—	2	4	no	—
634	C₂²⋊C₄	—	2	2	no	—
635	C₂²⋊C₄	—	2	4	no	—
636	C₂²⋊C₄	C₂×D₄×C₄₁	1	4	yes	—
637	C₄²	—	2	2	no	—
638	C₄²	—	2	2	no	—
639	C₄²	—	2	4	no	—
640	C₄²	—	2	2	no	—
641	C₄²	—	2	4	no	—
642	C₄²	C₂×D₄×C₄₁	1	1	yes	characteristic
643	C₄²	C₂×D₄×C₄₁	1	1	yes	characteristic
644	C₄²	C₂⁴×C₄₁	1	1	yes	characteristic
645	C₄²	C₂⁴×C₄₁	1	4	yes	—
646	C₄²	C₂⁴×C₄₁	1	1	yes	characteristic
647	C₂³	—	2	2	no	—
648	C₂³	—	2	2	no	—
649	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
650	Q₈	—	2	4	no	—
651	Q₈	—	2	2	no	—
652	Q₈	—	2	4	no	—
653	Q₈	—	2	4	no	—
654	Q₈	—	2	2	no	—
655	Q₈	—	4	2	no	—
656	Q₈	—	4	2	no	—
657	Q₈	—	4	2	no	—
658	Q₈	—	8	4	no	—
659	Q₈	—	8	1	no	—
660	D₄	—	2	2	no	—
661	D₄	—	2	4	no	—
662	D₄	—	2	2	no	—
663	D₄	—	4	2	no	—
664	D₄	—	4	4	no	—
665	D₄	—	4	2	no	—
666	D₄	—	8	1	no	—
667	D₄	—	8	1	no	—
668	D₄	—	8	2	no	—
669	C₂×C₄	—	2	2	no	—
670	C₂×C₄	—	2	2	no	—
671	C₂×C₄	—	2	2	no	—
672	C₂×C₄	—	2	2	no	—
673	C₂×C₄	—	2	2	no	—
674	C₂×C₄	—	2	2	no	—
675	C₂×C₄	—	2	2	no	—
676	C₂×C₄	—	2	2	no	—
677	C₂×C₄	—	4	1	no	—
678	C₂×C₄	—	4	4	no	—
679	C₂×C₄	—	4	2	no	—
680	C₂×C₄	—	4	4	no	—
681	C₂×C₄	—	8	4	no	—
682	C₂×C₄	—	8	4	no	—
683	C₂×C₄	—	8	1	no	—
684	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
685	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
686	C₂×C₄	C₂²×D₄×C₄₁	1	4	yes	—
687	C₂×C₄	C₂²×D₄×C₄₁	1	4	yes	—
688	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
689	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
690	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
691	C₂×C₄	C₂⁵×C₄₁	1	1	yes	characteristic
692	C₈	—	2	4	no	—
693	C₈	—	2	2	no	—
694	C₈	—	2	2	no	—
695	C₂²	—	2	1	no	—
696	C₂²	—	2	1	no	—
697	C₂²	—	2	1	no	—
698	C₂²	—	4	2	no	—
699	C₂²	—	4	2	no	—
700	C₂²	—	4	2	no	—
701	C₂²	—	4	2	no	—
702	C₂²	—	4	2	no	—
703	C₂²	—	4	2	no	—
704	C₂²	C₂³×D₄×C₄₁	1	1	yes	characteristic
705	C₄	—	2	1	no	—
706	C₄	—	2	4	no	—
707	C₄	—	2	1	no	—
708	C₄	—	2	1	no	—
709	C₄	—	2	4	no	—
710	C₄	—	2	1	no	—
711	C₄	—	4	2	no	—
712	C₄	—	4	2	no	—
713	C₄	—	4	2	no	—
714	C₄	—	4	2	no	—
715	C₄	—	4	2	no	—
716	C₄	—	4	2	no	—
717	C₄	C₄₁×#577	1	2	yes	—
718	C₄	C₄₁×#585	1	2	yes	—
719	C₂	—	4	1	no	—
720	C₂	—	8	2	no	—
721	C₂	—	8	2	no	—
722	C₂	C₄₁×#3487	1	1	yes	characteristic
723	C₂	C₂×C₄₁×#577	1	1	yes	characteristic
724	C₂	C₄₁×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₄₁	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₄₁
prime radical	C₄₁×#3214	C₂
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×#3550	C₂	semidirect
2. C₄₁×#3507	C₂	semidirect
3. C₄₁×#3401	C₂	semidirect
4. C₄₁×#3398	C₂	semidirect
5. C₄₁×#3394	C₂	semidirect
6. C₄₁×#3373	C₂	semidirect
7. C₄₁×#3369	C₂	semidirect
8. C₄₁×#3359	C₂	semidirect
9. C₄₁×#3225	C₂	semidirect
11. C₄₁×#3210	C₂	semidirect
12. C₄₁×#3125	C₂	semidirect
13. C₄₁×#3113	C₂	semidirect
14. C₄₁×#3103	C₂	semidirect
15. C₄₁×#2985	C₂	semidirect
332. #61916	C₄₁	direct (N × H)
357. #3550	C₂×C₄₁	semidirect
358. #3507	C₂×C₄₁	semidirect
359. #3401	C₂×C₄₁	semidirect
360. #3398	C₂×C₄₁	semidirect
361. #3394	C₂×C₄₁	semidirect
362. #3373	C₂×C₄₁	semidirect
363. #3369	C₂×C₄₁	semidirect
364. #3359	C₂×C₄₁	semidirect
365. #3225	C₂×C₄₁	semidirect
367. #3210	C₂×C₄₁	semidirect
368. #3125	C₂×C₄₁	semidirect
369. #3113	C₂×C₄₁	semidirect
370. #3103	C₂×C₄₁	semidirect
371. #2985	C₂×C₄₁	semidirect
447. C₄₁	#61916	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×#3550	2
C₄₁×#3507	2
C₄₁×#3401	2
C₄₁×#3398	2
C₄₁×#3394	2
C₄₁×#3373	2
C₄₁×#3369	2
C₄₁×#3359	2
C₄₁×#3225	2
C₄₁×#3214	2
C₄₁×#3210	2
C₄₁×#3125	2
C₄₁×#3113	2
C₄₁×#3103	2
C₄₁×#2985	2
#61916	41

Subgroups — C41×#61916 #23838117

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#61916 #23838117