Subgroups — C₄₁×#11060 #23787261

Order 10496.

938 conjugacy classes of subgroups.

The subgroup lattice has 620 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#104×C₄₁	C₂	1	1	yes	maximal, characteristic
2	C₄₁×#2896	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄₁×#410	C₂	1	1	yes	maximal, characteristic
4	C₄₁×#2296	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₄₁×#344	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄₁×#1733	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₄₁×#339	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×#41×C₄₁	C₂²	1	1	yes	characteristic
9	C₂²×M₁₆×C₄₁	C₂²	1	1	yes	characteristic
10	C₂²×M₁₆×C₄₁	C₂²	1	1	yes	characteristic
11	C₂×#117×C₄₁	C₂²	1	1	yes	characteristic
12	C₂×#117×C₄₁	C₂²	1	1	yes	characteristic
13	C₂×#117×C₄₁	C₂²	1	1	yes	characteristic
14	C₂²×C₄²×C₄₁	C₂²	1	1	yes	characteristic
15	C₂×#104×C₄₁	—	2	2	no	—
16	C₂×#104×C₄₁	—	2	2	no	—
17	C₂×#104×C₄₁	—	2	2	no	—
18	C₄₁×#419	C₄	1	2	yes	complemented
19	C₄₁×#418	C₄	1	2	yes	complemented
20	C₄₁×#417	—	2	2	no	—
21	C₄₁×#416	—	2	2	no	—
22	C₄₁×#410	—	2	2	no	—
23	C₄₁×#410	—	2	2	no	—
24	C₂×#99×C₄₁	—	2	2	no	—
25	C₄₁×#389	—	2	2	no	—
26	C₄₁×#385	—	2	2	no	—
27	C₄×C₄⋊C₄×C₄₁	—	2	2	no	—
28	C₄₁×#344	—	2	2	no	—
29	C₄₁×#339	—	2	2	no	—
30	C₄₁×#339	—	2	2	no	—
31	C₂×#41×C₄₁	—	2	1	no	—
32	C₂×#41×C₄₁	—	2	1	no	—
33	C₂×#41×C₄₁	—	2	1	no	—
34	C₂×#41×C₄₁	—	2	1	no	—
35	C₂×#41×C₄₁	—	2	1	no	—
36	C₂×#41×C₄₁	—	2	1	no	—
37	C₂×#41×C₄₁	—	2	1	no	—
38	C₂×#41×C₄₁	—	2	1	no	—
39	C₂×#41×C₄₁	—	2	1	no	—
40	C₂×#41×C₄₁	—	2	1	no	—
41	C₂×#41×C₄₁	D₄	1	2	yes	—
42	C₂×#41×C₄₁	Q₈	1	2	yes	—
43	C₂²×Q₈×C₄₁	C₂×C₄	1	1	yes	characteristic
44	C₂²×D₄×C₄₁	—	2	1	no	—
45	C₂²×D₄×C₄₁	C₂×C₄	1	1	yes	characteristic
46	C₂³×C₄×C₄₁	—	2	1	no	—
47	C₂³×C₄×C₄₁	—	2	1	no	—
48	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
49	C₂×M₁₆×C₄₁	—	2	1	no	—
50	C₂×M₁₆×C₄₁	—	2	1	no	—
51	C₂×M₁₆×C₄₁	—	2	1	no	—
52	C₂×M₁₆×C₄₁	—	2	1	no	—
53	C₂×M₁₆×C₄₁	—	2	1	no	—
54	C₂×M₁₆×C₄₁	—	2	1	no	—
55	C₂×M₁₆×C₄₁	—	2	1	no	—
56	C₂×M₁₆×C₄₁	—	2	1	no	—
57	C₂×M₁₆×C₄₁	—	2	1	no	—
58	C₂×M₁₆×C₄₁	—	2	1	no	—
59	C₂×M₁₆×C₄₁	C₂×C₄	1	2	yes	—
60	C₂×M₁₆×C₄₁	D₄	1	2	yes	—
61	C₂²×C₈×C₄₁	—	2	1	no	—
62	C₂²×C₈×C₄₁	—	2	1	no	—
63	#117×C₄₁	—	2	1	no	—
64	#117×C₄₁	—	2	1	no	—
65	#117×C₄₁	—	2	1	no	—
66	#117×C₄₁	—	2	1	no	—
67	#117×C₄₁	—	2	1	no	—
68	#117×C₄₁	—	2	1	no	—
69	#117×C₄₁	—	2	1	no	—
70	#117×C₄₁	—	2	1	no	—
71	#117×C₄₁	—	2	1	no	—
72	#117×C₄₁	C₂×C₄	1	2	yes	—
73	#117×C₄₁	D₄	1	2	yes	—
74	#117×C₄₁	D₄	1	2	yes	—
75	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
76	C₂×C₄⋊C₄×C₄₁	—	2	4	no	—
77	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
78	C₂×C₄⋊C₄×C₄₁	D₄	1	2	yes	—
79	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
80	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
81	C₂×C₂²⋊C₄×C₄₁	D₄	1	2	yes	—
82	C₂×C₄²×C₄₁	—	2	1	no	—
83	C₂×C₄²×C₄₁	—	2	1	no	—
84	C₂×C₄²×C₄₁	—	2	1	no	—
85	C₂×C₄²×C₄₁	—	2	1	no	—
86	C₂×C₄²×C₄₁	—	2	1	no	—
87	C₂×C₄²×C₄₁	—	2	1	no	—
88	C₂×C₄²×C₄₁	—	2	1	no	—
89	C₂×C₄²×C₄₁	—	2	1	no	—
90	C₂×C₄²×C₄₁	D₄	1	2	yes	—
91	#104×C₄₁	—	2	8	no	—
92	#103×C₄₁	—	2	4	no	—
93	#102×C₄₁	—	2	4	no	—
94	#99×C₄₁	—	2	8	no	—
95	#95×C₄₁	—	2	4	no	—
96	C₂⁴×C₄₁	—	2	1	no	—
97	C₂⁴×C₄₁	C₂×D₄	1	1	yes	characteristic
98	#41×C₄₁	—	2	2	no	—
99	#41×C₄₁	—	2	2	no	—
100	#41×C₄₁	—	2	2	no	—
101	#41×C₄₁	—	2	2	no	—
102	#41×C₄₁	—	2	2	no	—
103	#41×C₄₁	—	2	2	no	—
104	#41×C₄₁	—	2	2	no	—
105	#41×C₄₁	—	2	2	no	—
106	#41×C₄₁	—	4	1	no	—
107	#41×C₄₁	—	4	1	no	—
108	#41×C₄₁	—	4	1	no	—
109	#41×C₄₁	—	4	1	no	—
110	#41×C₄₁	—	4	1	no	—
111	#41×C₄₁	—	4	1	no	—
112	#41×C₄₁	—	4	1	no	—
113	#41×C₄₁	—	4	1	no	—
114	C₂×Q₈×C₄₁	—	2	1	no	—
115	C₂×Q₈×C₄₁	—	2	1	no	—
116	C₂×Q₈×C₄₁	—	2	1	no	—
117	C₂×Q₈×C₄₁	—	2	1	no	—
118	C₂×Q₈×C₄₁	—	2	1	no	—
119	C₂×Q₈×C₄₁	C₄⋊C₄	1	2	yes	complemented
120	C₂×D₄×C₄₁	—	2	2	no	—
121	C₂×D₄×C₄₁	—	2	2	no	—
122	C₂×D₄×C₄₁	—	2	1	no	—
123	C₂×D₄×C₄₁	—	2	1	no	—
124	C₂×D₄×C₄₁	—	2	1	no	—
125	C₂×D₄×C₄₁	—	2	1	no	—
126	C₂×D₄×C₄₁	—	2	1	no	—
127	C₂×D₄×C₄₁	—	4	1	no	—
128	C₂×D₄×C₄₁	—	4	1	no	—
129	C₂×D₄×C₄₁	—	4	1	no	—
130	C₂×D₄×C₄₁	—	4	1	no	—
131	C₂×D₄×C₄₁	C₄⋊C₄	1	2	yes	complemented
132	C₂²×C₄×C₄₁	—	2	1	no	—
133	C₂²×C₄×C₄₁	—	2	2	no	—
134	C₂²×C₄×C₄₁	—	2	2	no	—
135	C₂²×C₄×C₄₁	—	2	2	no	—
136	C₂²×C₄×C₄₁	—	2	2	no	—
137	C₂²×C₄×C₄₁	—	2	2	no	—
138	C₂²×C₄×C₄₁	—	4	4	no	—
139	C₂²×C₄×C₄₁	—	4	1	no	—
140	C₂²×C₄×C₄₁	—	4	1	no	—
141	C₂²×C₄×C₄₁	—	4	1	no	—
142	C₂²×C₄×C₄₁	—	4	1	no	—
143	C₂²×C₄×C₄₁	—	4	1	no	—
144	C₂²×C₄×C₄₁	—	4	1	no	—
145	C₂²×C₄×C₄₁	—	4	1	no	—
146	C₂²×C₄×C₄₁	C₂²×C₄	1	1	yes	characteristic
147	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
148	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
149	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
150	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
151	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
152	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
153	C₂²×C₄×C₄₁	C₂×Q₈	1	1	yes	characteristic
154	C₂²×C₄×C₄₁	#41	1	1	yes	characteristic
155	C₂²×C₄×C₄₁	#41	1	1	yes	characteristic
156	C₂²×C₄×C₄₁	#41	1	1	yes	characteristic
157	C₂²×C₄×C₄₁	#41	1	1	yes	characteristic
158	C₂²×C₄×C₄₁	#41	1	1	yes	characteristic
159	C₂²×C₄×C₄₁	#41	1	1	yes	characteristic
160	M₁₆×C₄₁	—	2	2	no	—
161	M₁₆×C₄₁	—	2	2	no	—
162	M₁₆×C₄₁	—	2	2	no	—
163	M₁₆×C₄₁	—	2	2	no	—
164	M₁₆×C₄₁	—	4	1	no	—
165	M₁₆×C₄₁	—	4	1	no	—
166	M₁₆×C₄₁	—	4	1	no	—
167	M₁₆×C₄₁	—	4	1	no	—
168	C₂×C₈×C₄₁	—	2	2	no	—
169	C₂×C₈×C₄₁	—	2	2	no	—
170	C₂×C₈×C₄₁	—	4	1	no	—
171	C₂×C₈×C₄₁	—	4	1	no	—
172	C₂×C₈×C₄₁	—	4	1	no	—
173	C₂×C₈×C₄₁	—	4	1	no	—
174	C₄⋊C₄×C₄₁	—	2	2	no	—
175	C₄⋊C₄×C₄₁	—	2	2	no	—
176	C₄⋊C₄×C₄₁	—	4	8	no	—
177	C₄⋊C₄×C₄₁	—	4	1	no	—
178	C₄⋊C₄×C₄₁	—	4	1	no	—
179	C₄⋊C₄×C₄₁	—	4	1	no	—
180	C₄⋊C₄×C₄₁	C₂²⋊C₄	1	4	yes	—
181	C₂²⋊C₄×C₄₁	—	2	2	no	—
182	C₂²⋊C₄×C₄₁	—	2	2	no	—
183	C₂²⋊C₄×C₄₁	—	2	2	no	—
184	C₂²⋊C₄×C₄₁	—	2	2	no	—
185	C₂²⋊C₄×C₄₁	—	2	2	no	—
186	C₂²⋊C₄×C₄₁	—	4	1	no	—
187	C₄²×C₄₁	—	2	2	no	—
188	C₄²×C₄₁	—	2	2	no	—
189	C₄²×C₄₁	—	2	2	no	—
190	C₄²×C₄₁	—	2	2	no	—
191	C₄²×C₄₁	—	2	2	no	—
192	C₄²×C₄₁	—	4	1	no	—
193	C₄²×C₄₁	—	4	1	no	—
194	C₄²×C₄₁	—	4	1	no	—
195	C₄²×C₄₁	—	4	1	no	—
196	C₄²×C₄₁	—	4	1	no	—
197	C₂³×C₄₁	—	2	2	no	—
198	C₂³×C₄₁	—	4	2	no	—
199	C₂³×C₄₁	—	4	1	no	—
200	C₂³×C₄₁	—	4	1	no	—
201	C₂³×C₄₁	—	8	2	no	—
202	C₂³×C₄₁	C₄×D₄	1	1	yes	characteristic
203	C₂³×C₄₁	#120	1	1	yes	characteristic
204	C₂³×C₄₁	#120	1	1	yes	characteristic
205	C₂³×C₄₁	#121	1	1	yes	characteristic
206	C₂³×C₄₁	#121	1	1	yes	characteristic
207	C₂³×C₄₁	C₂²⋊Q₈	1	1	yes	characteristic
208	C₂³×C₄₁	#124	1	1	yes	characteristic
209	Q₈×C₄₁	—	2	2	no	—
210	Q₈×C₄₁	—	2	2	no	—
211	Q₈×C₄₁	—	4	1	no	—
212	Q₈×C₄₁	—	4	1	no	—
213	D₄×C₄₁	—	2	2	no	—
214	D₄×C₄₁	—	2	2	no	—
215	D₄×C₄₁	—	4	2	no	—
216	D₄×C₄₁	—	4	2	no	—
217	D₄×C₄₁	—	4	2	no	—
218	D₄×C₄₁	—	4	2	no	—
219	D₄×C₄₁	—	4	1	no	—
220	D₄×C₄₁	—	4	1	no	—
221	C₂×C₄×C₄₁	—	2	4	no	—
222	C₂×C₄×C₄₁	—	2	2	no	—
223	C₂×C₄×C₄₁	—	2	4	no	—
224	C₂×C₄×C₄₁	—	4	4	no	—
225	C₂×C₄×C₄₁	—	4	2	no	—
226	C₂×C₄×C₄₁	—	4	4	no	—
227	C₂×C₄×C₄₁	—	4	4	no	—
228	C₂×C₄×C₄₁	—	4	1	no	—
229	C₂×C₄×C₄₁	—	4	1	no	—
230	C₂×C₄×C₄₁	—	4	2	no	—
231	C₂×C₄×C₄₁	—	4	2	no	—
232	C₂×C₄×C₄₁	—	4	2	no	—
233	C₂×C₄×C₄₁	—	4	2	no	—
234	C₂×C₄×C₄₁	—	4	2	no	—
235	C₂×C₄×C₄₁	—	4	4	no	—
236	C₂×C₄×C₄₁	—	4	2	no	—
237	C₂×C₄×C₄₁	—	4	2	no	—
238	C₂×C₄×C₄₁	—	8	2	no	—
239	C₂×C₄×C₄₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
240	C₂×C₄×C₄₁	C₂×C₄⋊C₄	1	1	yes	characteristic
241	C₂×C₄×C₄₁	#117	1	1	yes	characteristic
242	C₂×C₄×C₄₁	C₄×D₄	1	1	yes	characteristic
243	C₂×C₄×C₄₁	C₄×D₄	1	1	yes	characteristic
244	C₂×C₄×C₄₁	C₄×D₄	1	1	yes	characteristic
245	C₂×C₄×C₄₁	#120	1	1	yes	characteristic
246	C₂×C₄×C₄₁	#121	1	1	yes	characteristic
247	C₂×C₄×C₄₁	#121	1	1	yes	characteristic
248	C₂×C₄×C₄₁	#121	1	1	yes	characteristic
249	C₂×C₄×C₄₁	#121	1	1	yes	characteristic
250	C₂×C₄×C₄₁	#121	1	1	yes	characteristic
251	C₂×C₄×C₄₁	#121	1	1	yes	characteristic
252	C₂×C₄×C₄₁	C₂²⋊Q₈	1	1	yes	characteristic
253	C₂×C₄×C₄₁	C₂²⋊Q₈	1	1	yes	characteristic
254	C₂×C₄×C₄₁	C₂²⋊Q₈	1	1	yes	characteristic
255	C₂×C₄×C₄₁	C₂²⋊Q₈	1	1	yes	characteristic
256	C₂×C₄×C₄₁	C₂²⋊Q₈	1	1	yes	characteristic
257	C₂×C₄×C₄₁	#123	1	1	yes	characteristic
258	C₂×C₄×C₄₁	#123	1	1	yes	characteristic
259	C₂×C₄×C₄₁	#123	1	1	yes	characteristic
260	C₂×C₄×C₄₁	#123	1	1	yes	characteristic
261	C₂×C₄×C₄₁	#123	1	1	yes	characteristic
262	C₂×C₄×C₄₁	#124	1	1	yes	characteristic
263	C₂×C₄×C₄₁	#124	1	1	yes	characteristic
264	C₂×C₄×C₄₁	#126	1	1	yes	characteristic
265	C₂×C₄×C₄₁	#126	1	1	yes	characteristic
266	C₂×C₄×C₄₁	#127	1	1	yes	characteristic
267	C₈×C₄₁	—	4	2	no	—
268	C₈×C₄₁	—	4	2	no	—
269	#11060	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
270	C₂²×C₄₁	—	2	2	no	—
271	C₂²×C₄₁	—	2	2	no	—
272	C₂²×C₄₁	—	2	2	no	—
273	C₂²×C₄₁	—	4	1	no	—
274	C₂²×C₄₁	—	4	1	no	—
275	C₂²×C₄₁	—	4	1	no	—
276	C₂²×C₄₁	—	4	1	no	—
277	C₂²×C₄₁	—	4	2	no	—
278	C₂²×C₄₁	—	8	2	no	—
279	C₂²×C₄₁	—	8	2	no	—
280	C₂²×C₄₁	—	8	2	no	—
281	C₂²×C₄₁	#385	1	1	yes	characteristic
282	C₂²×C₄₁	#386	1	1	yes	characteristic
283	C₂²×C₄₁	#388	1	1	yes	characteristic
284	C₂²×C₄₁	#392	1	1	yes	characteristic
285	C₂²×C₄₁	#393	1	1	yes	characteristic
286	C₂²×C₄₁	#394	1	1	yes	characteristic
287	C₂²×C₄₁	#396	1	1	yes	characteristic
288	C₄×C₄₁	—	4	4	no	—
289	C₄×C₄₁	—	4	4	no	—
290	C₄×C₄₁	—	4	2	no	—
291	C₄×C₄₁	—	8	2	no	—
292	C₄×C₄₁	—	8	2	no	—
293	C₄×C₄₁	#380	1	1	yes	characteristic
294	C₄×C₄₁	#385	1	1	yes	characteristic
295	C₄×C₄₁	#388	1	1	yes	characteristic
296	C₄×C₄₁	#390	1	1	yes	characteristic
297	C₄×C₄₁	#394	1	1	yes	characteristic
298	C₄×C₄₁	#396	1	1	yes	characteristic
299	C₄×C₄₁	#397	1	1	yes	characteristic
300	C₄×C₄₁	#399	1	1	yes	characteristic
301	C₂²×#104	C₂×C₄₁	1	1	yes	characteristic
302	#2896	C₂×C₄₁	1	1	yes	characteristic
303	C₂×#410	C₂×C₄₁	1	1	yes	characteristic
304	#2296	C₂×C₄₁	1	1	yes	characteristic, complemented
305	C₂×#344	C₂×C₄₁	1	1	yes	characteristic, complemented
306	#1733	C₂×C₄₁	1	1	yes	characteristic, complemented
307	C₂×#339	C₂×C₄₁	1	1	yes	characteristic, complemented
308	C₂×C₄₁	—	2	1	no	—
309	C₂×C₄₁	—	2	1	no	—
310	C₂×C₄₁	—	2	1	no	—
311	C₂×C₄₁	—	2	1	no	—
312	C₂×C₄₁	—	2	1	no	—
313	C₂×C₄₁	—	2	1	no	—
314	C₂×C₄₁	—	8	2	no	—
315	C₂×C₄₁	#1439	1	1	yes	characteristic
316	C₂×C₄₁	#1906	1	2	yes	—
317	C₂²×#41	C₂²×C₄₁	1	1	yes	characteristic
318	C₂²×M₁₆	C₂²×C₄₁	1	1	yes	characteristic
319	C₂²×M₁₆	C₂²×C₄₁	1	1	yes	characteristic
320	C₂×#117	C₂²×C₄₁	1	1	yes	characteristic
321	C₂×#117	C₂²×C₄₁	1	1	yes	characteristic
322	C₂×#117	C₂²×C₄₁	1	1	yes	characteristic
323	C₂²×C₄²	C₂²×C₄₁	1	1	yes	characteristic
324	C₂×#104	—	2	2	no	—
325	C₂×#104	—	2	2	no	—
326	C₂×#104	—	2	2	no	—
327	#419	C₄×C₄₁	1	2	yes	complemented
328	#418	C₄×C₄₁	1	2	yes	complemented
329	#417	—	2	2	no	—
330	#416	—	2	2	no	—
331	#410	—	2	2	no	—
332	#410	—	2	2	no	—
333	C₂×#99	—	2	2	no	—
334	#389	—	2	2	no	—
335	#385	—	2	2	no	—
336	C₄×C₄⋊C₄	—	2	2	no	—
337	#344	—	2	2	no	—
338	#339	—	2	2	no	—
339	#339	—	2	2	no	—
340	C₄₁	#11060	1	1	yes	characteristic, direct product factor, Sylow
341	C₂×#41	—	2	1	no	—
342	C₂×#41	—	2	1	no	—
343	C₂×#41	—	2	1	no	—
344	C₂×#41	—	2	1	no	—
345	C₂×#41	—	2	1	no	—
346	C₂×#41	—	2	1	no	—
347	C₂×#41	—	2	1	no	—
348	C₂×#41	—	2	1	no	—
349	C₂×#41	—	2	1	no	—
350	C₂×#41	—	2	1	no	—
351	C₂×#41	D₄×C₄₁	1	2	yes	—
352	C₂×#41	Q₈×C₄₁	1	2	yes	—
353	C₂²×Q₈	C₂×C₄×C₄₁	1	1	yes	characteristic
354	C₂²×D₄	—	2	1	no	—
355	C₂²×D₄	C₂×C₄×C₄₁	1	1	yes	characteristic
356	C₂³×C₄	—	2	1	no	—
357	C₂³×C₄	—	2	1	no	—
358	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
359	C₂×M₁₆	—	2	1	no	—
360	C₂×M₁₆	—	2	1	no	—
361	C₂×M₁₆	—	2	1	no	—
362	C₂×M₁₆	—	2	1	no	—
363	C₂×M₁₆	—	2	1	no	—
364	C₂×M₁₆	—	2	1	no	—
365	C₂×M₁₆	—	2	1	no	—
366	C₂×M₁₆	—	2	1	no	—
367	C₂×M₁₆	—	2	1	no	—
368	C₂×M₁₆	—	2	1	no	—
369	C₂×M₁₆	C₂×C₄×C₄₁	1	2	yes	—
370	C₂×M₁₆	D₄×C₄₁	1	2	yes	—
371	C₂²×C₈	—	2	1	no	—
372	C₂²×C₈	—	2	1	no	—
373	#117	—	2	1	no	—
374	#117	—	2	1	no	—
375	#117	—	2	1	no	—
376	#117	—	2	1	no	—
377	#117	—	2	1	no	—
378	#117	—	2	1	no	—
379	#117	—	2	1	no	—
380	#117	—	2	1	no	—
381	#117	—	2	1	no	—
382	#117	C₂×C₄×C₄₁	1	2	yes	—
383	#117	D₄×C₄₁	1	2	yes	—
384	#117	D₄×C₄₁	1	2	yes	—
385	C₂×C₄⋊C₄	—	2	1	no	—
386	C₂×C₄⋊C₄	—	2	4	no	—
387	C₂×C₄⋊C₄	—	2	1	no	—
388	C₂×C₄⋊C₄	D₄×C₄₁	1	2	yes	—
389	C₂×C₂²⋊C₄	—	2	1	no	—
390	C₂×C₂²⋊C₄	—	2	1	no	—
391	C₂×C₂²⋊C₄	D₄×C₄₁	1	2	yes	—
392	C₂×C₄²	—	2	1	no	—
393	C₂×C₄²	—	2	1	no	—
394	C₂×C₄²	—	2	1	no	—
395	C₂×C₄²	—	2	1	no	—
396	C₂×C₄²	—	2	1	no	—
397	C₂×C₄²	—	2	1	no	—
398	C₂×C₄²	—	2	1	no	—
399	C₂×C₄²	—	2	1	no	—
400	C₂×C₄²	D₄×C₄₁	1	2	yes	—
401	#104	—	2	8	no	—
402	#103	—	2	4	no	—
403	#102	—	2	4	no	—
404	#99	—	2	8	no	—
405	#95	—	2	4	no	—
406	C₂⁴	—	2	1	no	—
407	C₂⁴	C₂×D₄×C₄₁	1	1	yes	characteristic
408	#41	—	2	2	no	—
409	#41	—	2	2	no	—
410	#41	—	2	2	no	—
411	#41	—	2	2	no	—
412	#41	—	2	2	no	—
413	#41	—	2	2	no	—
414	#41	—	2	2	no	—
415	#41	—	2	2	no	—
416	#41	—	4	1	no	—
417	#41	—	4	1	no	—
418	#41	—	4	1	no	—
419	#41	—	4	1	no	—
420	#41	—	4	1	no	—
421	#41	—	4	1	no	—
422	#41	—	4	1	no	—
423	#41	—	4	1	no	—
424	C₂×Q₈	—	2	1	no	—
425	C₂×Q₈	—	2	1	no	—
426	C₂×Q₈	—	2	1	no	—
427	C₂×Q₈	—	2	1	no	—
428	C₂×Q₈	—	2	1	no	—
429	C₂×Q₈	C₄⋊C₄×C₄₁	1	2	yes	complemented
430	C₂×D₄	—	2	2	no	—
431	C₂×D₄	—	2	2	no	—
432	C₂×D₄	—	2	1	no	—
433	C₂×D₄	—	2	1	no	—
434	C₂×D₄	—	2	1	no	—
435	C₂×D₄	—	2	1	no	—
436	C₂×D₄	—	2	1	no	—
437	C₂×D₄	—	4	1	no	—
438	C₂×D₄	—	4	1	no	—
439	C₂×D₄	—	4	1	no	—
440	C₂×D₄	—	4	1	no	—
441	C₂×D₄	C₄⋊C₄×C₄₁	1	2	yes	complemented
442	C₂²×C₄	—	2	1	no	—
443	C₂²×C₄	—	2	2	no	—
444	C₂²×C₄	—	2	2	no	—
445	C₂²×C₄	—	2	2	no	—
446	C₂²×C₄	—	2	2	no	—
447	C₂²×C₄	—	2	2	no	—
448	C₂²×C₄	—	4	4	no	—
449	C₂²×C₄	—	4	1	no	—
450	C₂²×C₄	—	4	1	no	—
451	C₂²×C₄	—	4	1	no	—
452	C₂²×C₄	—	4	1	no	—
453	C₂²×C₄	—	4	1	no	—
454	C₂²×C₄	—	4	1	no	—
455	C₂²×C₄	—	4	1	no	—
456	C₂²×C₄	C₂²×C₄×C₄₁	1	1	yes	characteristic
457	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
458	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
459	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
460	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
461	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
462	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
463	C₂²×C₄	C₂×Q₈×C₄₁	1	1	yes	characteristic
464	C₂²×C₄	#41×C₄₁	1	1	yes	characteristic
465	C₂²×C₄	#41×C₄₁	1	1	yes	characteristic
466	C₂²×C₄	#41×C₄₁	1	1	yes	characteristic
467	C₂²×C₄	#41×C₄₁	1	1	yes	characteristic
468	C₂²×C₄	#41×C₄₁	1	1	yes	characteristic
469	C₂²×C₄	#41×C₄₁	1	1	yes	characteristic
470	M₁₆	—	2	2	no	—
471	M₁₆	—	2	2	no	—
472	M₁₆	—	2	2	no	—
473	M₁₆	—	2	2	no	—
474	M₁₆	—	4	1	no	—
475	M₁₆	—	4	1	no	—
476	M₁₆	—	4	1	no	—
477	M₁₆	—	4	1	no	—
478	C₂×C₈	—	2	2	no	—
479	C₂×C₈	—	2	2	no	—
480	C₂×C₈	—	4	1	no	—
481	C₂×C₈	—	4	1	no	—
482	C₂×C₈	—	4	1	no	—
483	C₂×C₈	—	4	1	no	—
484	C₄⋊C₄	—	2	2	no	—
485	C₄⋊C₄	—	2	2	no	—
486	C₄⋊C₄	—	4	8	no	—
487	C₄⋊C₄	—	4	1	no	—
488	C₄⋊C₄	—	4	1	no	—
489	C₄⋊C₄	—	4	1	no	—
490	C₄⋊C₄	C₂²⋊C₄×C₄₁	1	4	yes	—
491	C₂²⋊C₄	—	2	2	no	—
492	C₂²⋊C₄	—	2	2	no	—
493	C₂²⋊C₄	—	2	2	no	—
494	C₂²⋊C₄	—	2	2	no	—
495	C₂²⋊C₄	—	2	2	no	—
496	C₂²⋊C₄	—	4	1	no	—
497	C₄²	—	2	2	no	—
498	C₄²	—	2	2	no	—
499	C₄²	—	2	2	no	—
500	C₄²	—	2	2	no	—
501	C₄²	—	2	2	no	—
502	C₄²	—	4	1	no	—
503	C₄²	—	4	1	no	—
504	C₄²	—	4	1	no	—
505	C₄²	—	4	1	no	—
506	C₄²	—	4	1	no	—
507	C₂³	—	2	2	no	—
508	C₂³	—	4	2	no	—
509	C₂³	—	4	1	no	—
510	C₂³	—	4	1	no	—
511	C₂³	—	8	2	no	—
512	C₂³	C₄×D₄×C₄₁	1	1	yes	characteristic
513	C₂³	#120×C₄₁	1	1	yes	characteristic
514	C₂³	#120×C₄₁	1	1	yes	characteristic
515	C₂³	#121×C₄₁	1	1	yes	characteristic
516	C₂³	#121×C₄₁	1	1	yes	characteristic
517	C₂³	C₂²⋊Q₈×C₄₁	1	1	yes	characteristic
518	C₂³	#124×C₄₁	1	1	yes	characteristic
519	Q₈	—	2	2	no	—
520	Q₈	—	2	2	no	—
521	Q₈	—	4	1	no	—
522	Q₈	—	4	1	no	—
523	D₄	—	2	2	no	—
524	D₄	—	2	2	no	—
525	D₄	—	4	2	no	—
526	D₄	—	4	2	no	—
527	D₄	—	4	2	no	—
528	D₄	—	4	2	no	—
529	D₄	—	4	1	no	—
530	D₄	—	4	1	no	—
531	C₂×C₄	—	2	4	no	—
532	C₂×C₄	—	2	2	no	—
533	C₂×C₄	—	2	4	no	—
534	C₂×C₄	—	4	4	no	—
535	C₂×C₄	—	4	2	no	—
536	C₂×C₄	—	4	4	no	—
537	C₂×C₄	—	4	4	no	—
538	C₂×C₄	—	4	1	no	—
539	C₂×C₄	—	4	1	no	—
540	C₂×C₄	—	4	2	no	—
541	C₂×C₄	—	4	2	no	—
542	C₂×C₄	—	4	2	no	—
543	C₂×C₄	—	4	2	no	—
544	C₂×C₄	—	4	2	no	—
545	C₂×C₄	—	4	4	no	—
546	C₂×C₄	—	4	2	no	—
547	C₂×C₄	—	4	2	no	—
548	C₂×C₄	—	8	2	no	—
549	C₂×C₄	C₂×C₂²⋊C₄×C₄₁	1	1	yes	characteristic
550	C₂×C₄	C₂×C₄⋊C₄×C₄₁	1	1	yes	characteristic
551	C₂×C₄	#117×C₄₁	1	1	yes	characteristic
552	C₂×C₄	C₄×D₄×C₄₁	1	1	yes	characteristic
553	C₂×C₄	C₄×D₄×C₄₁	1	1	yes	characteristic
554	C₂×C₄	C₄×D₄×C₄₁	1	1	yes	characteristic
555	C₂×C₄	#120×C₄₁	1	1	yes	characteristic
556	C₂×C₄	#121×C₄₁	1	1	yes	characteristic
557	C₂×C₄	#121×C₄₁	1	1	yes	characteristic
558	C₂×C₄	#121×C₄₁	1	1	yes	characteristic
559	C₂×C₄	#121×C₄₁	1	1	yes	characteristic
560	C₂×C₄	#121×C₄₁	1	1	yes	characteristic
561	C₂×C₄	#121×C₄₁	1	1	yes	characteristic
562	C₂×C₄	C₂²⋊Q₈×C₄₁	1	1	yes	characteristic
563	C₂×C₄	C₂²⋊Q₈×C₄₁	1	1	yes	characteristic
564	C₂×C₄	C₂²⋊Q₈×C₄₁	1	1	yes	characteristic
565	C₂×C₄	C₂²⋊Q₈×C₄₁	1	1	yes	characteristic
566	C₂×C₄	C₂²⋊Q₈×C₄₁	1	1	yes	characteristic
567	C₂×C₄	#123×C₄₁	1	1	yes	characteristic
568	C₂×C₄	#123×C₄₁	1	1	yes	characteristic
569	C₂×C₄	#123×C₄₁	1	1	yes	characteristic
570	C₂×C₄	#123×C₄₁	1	1	yes	characteristic
571	C₂×C₄	#123×C₄₁	1	1	yes	characteristic
572	C₂×C₄	#124×C₄₁	1	1	yes	characteristic
573	C₂×C₄	#124×C₄₁	1	1	yes	characteristic
574	C₂×C₄	#126×C₄₁	1	1	yes	characteristic
575	C₂×C₄	#126×C₄₁	1	1	yes	characteristic
576	C₂×C₄	#127×C₄₁	1	1	yes	characteristic
577	C₈	—	4	2	no	—
578	C₈	—	4	2	no	—
579	C₂²	—	2	2	no	—
580	C₂²	—	2	2	no	—
581	C₂²	—	2	2	no	—
582	C₂²	—	4	1	no	—
583	C₂²	—	4	1	no	—
584	C₂²	—	4	1	no	—
585	C₂²	—	4	1	no	—
586	C₂²	—	4	2	no	—
587	C₂²	—	8	2	no	—
588	C₂²	—	8	2	no	—
589	C₂²	—	8	2	no	—
590	C₂²	C₄₁×#385	1	1	yes	characteristic
591	C₂²	C₄₁×#386	1	1	yes	characteristic
592	C₂²	C₄₁×#388	1	1	yes	characteristic
593	C₂²	C₄₁×#392	1	1	yes	characteristic
594	C₂²	C₄₁×#393	1	1	yes	characteristic
595	C₂²	C₄₁×#394	1	1	yes	characteristic
596	C₂²	C₄₁×#396	1	1	yes	characteristic
597	C₄	—	4	4	no	—
598	C₄	—	4	4	no	—
599	C₄	—	4	2	no	—
600	C₄	—	8	2	no	—
601	C₄	—	8	2	no	—
602	C₄	C₄₁×#380	1	1	yes	characteristic
603	C₄	C₄₁×#385	1	1	yes	characteristic
604	C₄	C₄₁×#388	1	1	yes	characteristic
605	C₄	C₄₁×#390	1	1	yes	characteristic
606	C₄	C₄₁×#394	1	1	yes	characteristic
607	C₄	C₄₁×#396	1	1	yes	characteristic
608	C₄	C₄₁×#397	1	1	yes	characteristic
609	C₄	C₄₁×#399	1	1	yes	characteristic
610	C₂	—	2	1	no	—
611	C₂	—	2	1	no	—
612	C₂	—	2	1	no	—
613	C₂	—	2	1	no	—
614	C₂	—	2	1	no	—
615	C₂	—	2	1	no	—
616	C₂	—	8	2	no	—
617	C₂	C₄₁×#1439	1	1	yes	characteristic
618	C₂	C₄₁×#1906	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₄₁	#121
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
4. C₄₁×#2296	C₂	semidirect
5. C₂×C₄₁×#344	C₂	semidirect
6. C₄₁×#1733	C₂	semidirect
7. C₂×C₄₁×#339	C₂	semidirect
18. C₄₁×#419	C₄	semidirect
19. C₄₁×#418	C₄	semidirect
119. C₂×Q₈×C₄₁	C₄⋊C₄	semidirect
131. C₂×D₄×C₄₁	C₄⋊C₄	semidirect
269. #11060	C₄₁	direct (N × H)
304. #2296	C₂×C₄₁	semidirect
305. C₂×#344	C₂×C₄₁	semidirect
306. #1733	C₂×C₄₁	semidirect
307. C₂×#339	C₂×C₄₁	semidirect
327. #419	C₄×C₄₁	semidirect
328. #418	C₄×C₄₁	semidirect
340. C₄₁	#11060	direct (N × H)
429. C₂×Q₈	C₄⋊C₄×C₄₁	semidirect
441. C₂×D₄	C₄⋊C₄×C₄₁	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#104×C₄₁	2
C₄₁×#2896	2
C₂×C₄₁×#410	2
C₄₁×#2296	2
C₂×C₄₁×#344	2
C₄₁×#1733	2
C₂×C₄₁×#339	2
#11060	41

Subgroups — C41×#11060 #23787261

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#11060 #23787261