Subgroups — C₄₁×#21098 #23797299

Order 10496.

1022 conjugacy classes of subgroups.

The subgroup lattice has 490 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₁×#2905	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄₁×#421	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄₁×#416	C₂	1	1	yes	maximal, characteristic
4	C₄₁×#2879	C₂	1	1	yes	maximal, characteristic
5	C₂×C₄₁×#405	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄₁×#1938	C₂	1	4	yes	maximal, complemented
7	C₄₁×#1937	C₂	1	4	yes	maximal, complemented
8	C₂×C₄₁×#341	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄₁×#1733	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×#41×C₄₁	C₂²	1	1	yes	characteristic
11	C₂²×M₁₆×C₄₁	C₂²	1	1	yes	characteristic
12	C₂²×M₁₆×C₄₁	C₂²	1	1	yes	characteristic
13	C₂²×M₁₆×C₄₁	C₂²	1	1	yes	characteristic
14	C₂³×C₈×C₄₁	C₂²	1	1	yes	characteristic
15	C₂×#117×C₄₁	C₂²	1	1	yes	characteristic
16	C₂×#117×C₄₁	C₂²	1	1	yes	characteristic
17	C₄₁×#424	—	2	2	no	—
18	C₄₁×#424	C₂²	1	4	yes	complemented
19	C₄₁×#423	—	2	2	no	—
20	C₄₁×#421	—	2	4	no	—
21	C₂×#104×C₄₁	C₂²	1	4	yes	—
22	C₄₁×#416	C₄	1	4	yes	complemented
23	C₄₁×#416	C₂²	1	2	yes	—
24	C₄₁×#416	C₂²	1	2	yes	—
25	C₂×#103×C₄₁	C₄	1	2	yes	complemented
26	C₂×#102×C₄₁	C₄	1	2	yes	complemented
27	C₄₁×#408	—	2	2	no	—
28	C₄₁×#408	C₂²	1	4	yes	—
29	C₄₁×#407	—	2	2	no	—
30	C₄₁×#405	—	2	4	no	—
31	C₂×#97×C₄₁	C₂²	1	2	yes	complemented
32	C₂×C₄×C₈×C₄₁	C₂²	1	2	yes	complemented
33	C₄₁×#341	C₂²	1	2	yes	complemented
34	C₄₁×#341	C₂²	1	2	yes	complemented
35	C₄₁×#339	C₂²	1	4	yes	complemented
36	C₂×#41×C₄₁	—	2	1	no	—
37	C₂×#41×C₄₁	—	2	1	no	—
38	C₂×#41×C₄₁	—	2	2	no	—
39	C₂×#41×C₄₁	—	2	2	no	—
40	C₂×#41×C₄₁	—	2	2	no	—
41	C₂×#41×C₄₁	—	2	2	no	—
42	C₂×#41×C₄₁	C₂×C₄	1	2	yes	—
43	C₂×#41×C₄₁	C₂³	1	2	yes	—
44	C₂²×Q₈×C₄₁	C₂×C₄	1	1	yes	characteristic
45	C₂²×D₄×C₄₁	—	2	1	no	—
46	C₂²×D₄×C₄₁	C₂×C₄	1	1	yes	characteristic
47	C₂³×C₄×C₄₁	—	2	1	no	—
48	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
49	C₂×M₁₆×C₄₁	—	2	2	no	—
50	C₂×M₁₆×C₄₁	—	2	2	no	—
51	C₂×M₁₆×C₄₁	—	2	1	no	—
52	C₂×M₁₆×C₄₁	—	2	1	no	—
53	C₂×M₁₆×C₄₁	—	2	2	no	—
54	C₂×M₁₆×C₄₁	—	2	2	no	—
55	C₂×M₁₆×C₄₁	—	2	2	no	—
56	C₂×M₁₆×C₄₁	—	2	2	no	—
57	C₂×M₁₆×C₄₁	D₄	1	2	yes	—
58	C₂×M₁₆×C₄₁	D₄	1	2	yes	—
59	C₂×M₁₆×C₄₁	C₂³	1	2	yes	—
60	C₂×M₁₆×C₄₁	C₂³	1	2	yes	—
61	C₂²×C₈×C₄₁	—	2	2	no	—
62	C₂²×C₈×C₄₁	—	2	2	no	—
63	C₂²×C₈×C₄₁	—	2	1	no	—
64	C₂²×C₈×C₄₁	—	2	1	no	—
65	C₂²×C₈×C₄₁	C₂×C₄	1	2	yes	—
66	C₂²×C₈×C₄₁	C₂×C₄	1	2	yes	—
67	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
68	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
69	C₂²×C₈×C₄₁	C₂³	1	2	yes	—
70	#117×C₄₁	—	2	1	no	—
71	#117×C₄₁	—	2	1	no	—
72	#117×C₄₁	—	2	2	no	—
73	#117×C₄₁	C₂×C₄	1	2	yes	—
74	#117×C₄₁	D₄	1	4	yes	—
75	#117×C₄₁	C₂³	1	2	yes	—
76	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
77	C₂×C₄⋊C₄×C₄₁	C₂×C₄	1	2	yes	—
78	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
79	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
80	C₂×C₄²×C₄₁	—	2	1	no	—
81	C₂×C₄²×C₄₁	C₂³	1	2	yes	—
82	C₄⋊C₈×C₄₁	—	2	8	no	—
83	#104×C₄₁	—	2	8	no	—
84	#103×C₄₁	C₂×C₄	1	4	yes	—
85	#103×C₄₁	C₂×C₄	1	4	yes	—
86	#102×C₄₁	C₂×C₄	1	4	yes	—
87	#102×C₄₁	C₂×C₄	1	4	yes	—
88	C₂²⋊C₈×C₄₁	—	2	8	no	—
89	#97×C₄₁	—	2	4	no	—
90	C₄×C₈×C₄₁	—	2	4	no	—
91	C₂⁴×C₄₁	—	2	1	no	—
92	C₂⁴×C₄₁	#41	1	1	yes	characteristic
93	#41×C₄₁	—	2	4	no	—
94	#41×C₄₁	—	2	4	no	—
95	#41×C₄₁	—	2	2	no	—
96	#41×C₄₁	—	2	2	no	—
97	#41×C₄₁	—	2	2	no	—
98	#41×C₄₁	—	2	2	no	—
99	#41×C₄₁	—	4	2	no	—
100	#41×C₄₁	—	4	2	no	—
101	#41×C₄₁	—	4	2	no	—
102	#41×C₄₁	—	4	2	no	—
103	C₂×Q₈×C₄₁	—	2	1	no	—
104	C₂×Q₈×C₄₁	—	2	2	no	—
105	C₂×Q₈×C₄₁	—	2	2	no	—
106	C₂×Q₈×C₄₁	C₂²×C₄	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	—	2	2	no	—
111	C₂×D₄×C₄₁	—	2	1	no	—
112	C₂×D₄×C₄₁	—	4	2	no	—
113	C₂×D₄×C₄₁	—	4	2	no	—
114	C₂×D₄×C₄₁	C₂²×C₄	1	2	yes	—
115	C₂²×C₄×C₄₁	—	2	1	no	—
116	C₂²×C₄×C₄₁	—	2	2	no	—
117	C₂²×C₄×C₄₁	—	2	2	no	—
118	C₂²×C₄×C₄₁	—	2	2	no	—
119	C₂²×C₄×C₄₁	—	2	2	no	—
120	C₂²×C₄×C₄₁	—	4	2	no	—
121	C₂²×C₄×C₄₁	—	4	2	no	—
122	C₂²×C₄×C₄₁	C₂²×C₄	1	1	yes	characteristic
123	C₂²×C₄×C₄₁	C₂²×C₄	1	1	yes	characteristic
124	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
125	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
126	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
127	C₂²×C₄×C₄₁	#41	1	2	yes	—
128	C₂²×C₄×C₄₁	#41	1	2	yes	—
129	C₂²×C₄×C₄₁	#41	1	1	yes	characteristic
130	C₂²×C₄×C₄₁	#41	1	2	yes	—
131	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
132	M₁₆×C₄₁	—	2	4	no	—
133	M₁₆×C₄₁	—	2	4	no	—
134	M₁₆×C₄₁	—	2	2	no	—
135	M₁₆×C₄₁	—	2	2	no	—
136	M₁₆×C₄₁	—	2	2	no	—
137	M₁₆×C₄₁	—	2	2	no	—
138	M₁₆×C₄₁	—	4	2	no	—
139	M₁₆×C₄₁	—	4	2	no	—
140	C₂×C₈×C₄₁	—	2	4	no	—
141	C₂×C₈×C₄₁	—	2	4	no	—
142	C₂×C₈×C₄₁	—	2	1	no	—
143	C₂×C₈×C₄₁	—	2	2	no	—
144	C₂×C₈×C₄₁	—	2	1	no	—
145	C₂×C₈×C₄₁	—	2	1	no	—
146	C₂×C₈×C₄₁	—	2	1	no	—
147	C₂×C₈×C₄₁	—	2	2	no	—
148	C₂×C₈×C₄₁	—	2	2	no	—
149	C₂×C₈×C₄₁	—	2	2	no	—
150	C₂×C₈×C₄₁	—	4	2	no	—
151	C₂×C₈×C₄₁	—	4	2	no	—
152	C₂×C₈×C₄₁	C₂²×C₄	1	2	yes	—
153	C₂×C₈×C₄₁	C₂²×C₄	1	2	yes	—
154	C₂×C₈×C₄₁	C₂×D₄	1	4	yes	—
155	C₄⋊C₄×C₄₁	—	2	2	no	—
156	C₄⋊C₄×C₄₁	—	2	4	no	—
157	C₄⋊C₄×C₄₁	C₂²×C₄	1	4	yes	—
158	C₂²⋊C₄×C₄₁	—	2	2	no	—
159	C₂²⋊C₄×C₄₁	—	2	4	no	—
160	C₂²⋊C₄×C₄₁	—	2	2	no	—
161	C₄²×C₄₁	—	2	2	no	—
162	C₄²×C₄₁	—	2	2	no	—
163	C₄²×C₄₁	—	2	2	no	—
164	C₄²×C₄₁	C₂×D₄	1	4	yes	—
165	C₂³×C₄₁	—	2	2	no	—
166	C₂³×C₄₁	—	4	2	no	—
167	C₂³×C₄₁	—	4	2	no	—
168	C₂³×C₄₁	—	8	2	no	—
169	C₂³×C₄₁	C₄×D₄	1	1	yes	characteristic
170	C₂³×C₄₁	C₄×D₄	1	1	yes	characteristic
171	C₂³×C₄₁	#123	1	2	yes	—
172	C₂³×C₄₁	#126	1	2	yes	—
173	C₂³×C₄₁	C₂×#41	1	1	yes	characteristic
174	Q₈×C₄₁	—	2	2	no	—
175	Q₈×C₄₁	—	2	2	no	—
176	Q₈×C₄₁	—	4	2	no	—
177	D₄×C₄₁	—	2	2	no	—
178	D₄×C₄₁	—	2	2	no	—
179	D₄×C₄₁	—	4	2	no	—
180	D₄×C₄₁	—	4	2	no	—
181	D₄×C₄₁	—	4	4	no	—
182	D₄×C₄₁	—	4	2	no	—
183	C₂×C₄×C₄₁	—	2	4	no	—
184	C₂×C₄×C₄₁	—	2	2	no	—
185	C₂×C₄×C₄₁	—	2	4	no	—
186	C₂×C₄×C₄₁	—	4	4	no	—
187	C₂×C₄×C₄₁	—	4	2	no	—
188	C₂×C₄×C₄₁	—	4	2	no	—
189	C₂×C₄×C₄₁	—	4	2	no	—
190	C₂×C₄×C₄₁	—	4	4	no	—
191	C₂×C₄×C₄₁	—	8	2	no	—
192	C₂×C₄×C₄₁	#117	1	2	yes	—
193	C₂×C₄×C₄₁	#117	1	2	yes	—
194	C₂×C₄×C₄₁	C₄×D₄	1	2	yes	—
195	C₂×C₄×C₄₁	C₄×D₄	1	2	yes	—
196	C₂×C₄×C₄₁	C₄×D₄	1	1	yes	characteristic
197	C₂×C₄×C₄₁	C₄×D₄	1	1	yes	characteristic
198	C₂×C₄×C₄₁	#121	1	2	yes	—
199	C₂×C₄×C₄₁	#121	1	2	yes	—
200	C₂×C₄×C₄₁	#123	1	2	yes	—
201	C₂×C₄×C₄₁	#124	1	2	yes	—
202	C₂×C₄×C₄₁	#124	1	2	yes	—
203	C₂×C₄×C₄₁	#126	1	2	yes	—
204	C₂×C₄×C₄₁	C₂³×C₄	1	1	yes	characteristic
205	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
206	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
207	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
208	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
209	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
210	C₈×C₄₁	—	2	2	no	—
211	C₈×C₄₁	—	2	2	no	—
212	C₈×C₄₁	—	2	4	no	—
213	C₈×C₄₁	—	4	2	no	—
214	C₈×C₄₁	—	4	2	no	—
215	#21098	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
216	C₂²×C₄₁	—	2	2	no	—
217	C₂²×C₄₁	—	2	2	no	—
218	C₂²×C₄₁	—	2	2	no	—
219	C₂²×C₄₁	—	4	2	no	—
220	C₂²×C₄₁	—	4	2	no	—
221	C₂²×C₄₁	—	4	4	no	—
222	C₂²×C₄₁	—	4	2	no	—
223	C₂²×C₄₁	—	8	4	no	—
224	C₂²×C₄₁	#388	1	2	yes	—
225	C₂²×C₄₁	#388	1	2	yes	—
226	C₂²×C₄₁	C₂×C₄×D₄	1	1	yes	characteristic
227	C₂²×C₄₁	C₂×#123	1	1	yes	characteristic
228	C₂²×C₄₁	C₂×#126	1	1	yes	characteristic
229	C₄×C₄₁	—	4	4	no	—
230	C₄×C₄₁	—	4	4	no	—
231	C₄×C₄₁	—	4	2	no	—
232	C₄×C₄₁	#388	1	2	yes	—
233	C₄×C₄₁	#388	1	2	yes	—
234	C₄×C₄₁	C₂×#117	1	1	yes	characteristic
235	C₄×C₄₁	C₂×C₄×D₄	1	1	yes	characteristic
236	C₄×C₄₁	C₂×#121	1	1	yes	characteristic
237	C₄×C₄₁	C₂×#124	1	1	yes	characteristic
238	#2905	C₂×C₄₁	1	1	yes	characteristic, complemented
239	C₂×#421	C₂×C₄₁	1	1	yes	characteristic
240	C₂×#416	C₂×C₄₁	1	1	yes	characteristic
241	#2879	C₂×C₄₁	1	1	yes	characteristic
242	C₂×#405	C₂×C₄₁	1	1	yes	characteristic, complemented
243	#1938	C₂×C₄₁	1	4	yes	complemented
244	#1937	C₂×C₄₁	1	4	yes	complemented
245	C₂×#341	C₂×C₄₁	1	1	yes	characteristic, complemented
246	#1733	C₂×C₄₁	1	1	yes	characteristic, complemented
247	C₂×C₄₁	—	2	1	no	—
248	C₂×C₄₁	—	2	2	no	—
249	C₂×C₄₁	—	2	1	no	—
250	C₂×C₄₁	—	2	2	no	—
251	C₂×C₄₁	—	8	2	no	—
252	C₂×C₄₁	C₂×#388	1	1	yes	characteristic
253	C₂×C₄₁	#2957	1	2	yes	—
254	C₂²×#41	C₂²×C₄₁	1	1	yes	characteristic
255	C₂²×M₁₆	C₂²×C₄₁	1	1	yes	characteristic
256	C₂²×M₁₆	C₂²×C₄₁	1	1	yes	characteristic
257	C₂²×M₁₆	C₂²×C₄₁	1	1	yes	characteristic
258	C₂³×C₈	C₂²×C₄₁	1	1	yes	characteristic
259	C₂×#117	C₂²×C₄₁	1	1	yes	characteristic
260	C₂×#117	C₂²×C₄₁	1	1	yes	characteristic
261	#424	—	2	2	no	—
262	#424	C₂²×C₄₁	1	4	yes	complemented
263	#423	—	2	2	no	—
264	#421	—	2	4	no	—
265	C₂×#104	C₂²×C₄₁	1	4	yes	—
266	#416	C₄×C₄₁	1	4	yes	complemented
267	#416	C₂²×C₄₁	1	2	yes	—
268	#416	C₂²×C₄₁	1	2	yes	—
269	C₂×#103	C₄×C₄₁	1	2	yes	complemented
270	C₂×#102	C₄×C₄₁	1	2	yes	complemented
271	#408	—	2	2	no	—
272	#408	C₂²×C₄₁	1	4	yes	—
273	#407	—	2	2	no	—
274	#405	—	2	4	no	—
275	C₂×#97	C₂²×C₄₁	1	2	yes	complemented
276	C₂×C₄×C₈	C₂²×C₄₁	1	2	yes	complemented
277	#341	C₂²×C₄₁	1	2	yes	complemented
278	#341	C₂²×C₄₁	1	2	yes	complemented
279	#339	C₂²×C₄₁	1	4	yes	complemented
280	C₄₁	#21098	1	1	yes	characteristic, direct product factor, Sylow
281	C₂×#41	—	2	1	no	—
282	C₂×#41	—	2	1	no	—
283	C₂×#41	—	2	2	no	—
284	C₂×#41	—	2	2	no	—
285	C₂×#41	—	2	2	no	—
286	C₂×#41	—	2	2	no	—
287	C₂×#41	C₂×C₄×C₄₁	1	2	yes	—
288	C₂×#41	C₂³×C₄₁	1	2	yes	—
289	C₂²×Q₈	C₂×C₄×C₄₁	1	1	yes	characteristic
290	C₂²×D₄	—	2	1	no	—
291	C₂²×D₄	C₂×C₄×C₄₁	1	1	yes	characteristic
292	C₂³×C₄	—	2	1	no	—
293	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
294	C₂×M₁₆	—	2	2	no	—
295	C₂×M₁₆	—	2	2	no	—
296	C₂×M₁₆	—	2	1	no	—
297	C₂×M₁₆	—	2	1	no	—
298	C₂×M₁₆	—	2	2	no	—
299	C₂×M₁₆	—	2	2	no	—
300	C₂×M₁₆	—	2	2	no	—
301	C₂×M₁₆	—	2	2	no	—
302	C₂×M₁₆	D₄×C₄₁	1	2	yes	—
303	C₂×M₁₆	D₄×C₄₁	1	2	yes	—
304	C₂×M₁₆	C₂³×C₄₁	1	2	yes	—
305	C₂×M₁₆	C₂³×C₄₁	1	2	yes	—
306	C₂²×C₈	—	2	2	no	—
307	C₂²×C₈	—	2	2	no	—
308	C₂²×C₈	—	2	1	no	—
309	C₂²×C₈	—	2	1	no	—
310	C₂²×C₈	C₂×C₄×C₄₁	1	2	yes	—
311	C₂²×C₈	C₂×C₄×C₄₁	1	2	yes	—
312	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
313	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
314	C₂²×C₈	C₂³×C₄₁	1	2	yes	—
315	#117	—	2	1	no	—
316	#117	—	2	1	no	—
317	#117	—	2	2	no	—
318	#117	C₂×C₄×C₄₁	1	2	yes	—
319	#117	D₄×C₄₁	1	4	yes	—
320	#117	C₂³×C₄₁	1	2	yes	—
321	C₂×C₄⋊C₄	—	2	1	no	—
322	C₂×C₄⋊C₄	C₂×C₄×C₄₁	1	2	yes	—
323	C₂×C₂²⋊C₄	—	2	1	no	—
324	C₂×C₂²⋊C₄	—	2	1	no	—
325	C₂×C₄²	—	2	1	no	—
326	C₂×C₄²	C₂³×C₄₁	1	2	yes	—
327	C₄⋊C₈	—	2	8	no	—
328	#104	—	2	8	no	—
329	#103	C₂×C₄×C₄₁	1	4	yes	—
330	#103	C₂×C₄×C₄₁	1	4	yes	—
331	#102	C₂×C₄×C₄₁	1	4	yes	—
332	#102	C₂×C₄×C₄₁	1	4	yes	—
333	C₂²⋊C₈	—	2	8	no	—
334	#97	—	2	4	no	—
335	C₄×C₈	—	2	4	no	—
336	C₂⁴	—	2	1	no	—
337	C₂⁴	#41×C₄₁	1	1	yes	characteristic
338	#41	—	2	4	no	—
339	#41	—	2	4	no	—
340	#41	—	2	2	no	—
341	#41	—	2	2	no	—
342	#41	—	2	2	no	—
343	#41	—	2	2	no	—
344	#41	—	4	2	no	—
345	#41	—	4	2	no	—
346	#41	—	4	2	no	—
347	#41	—	4	2	no	—
348	C₂×Q₈	—	2	1	no	—
349	C₂×Q₈	—	2	2	no	—
350	C₂×Q₈	—	2	2	no	—
351	C₂×Q₈	C₂²×C₄×C₄₁	1	2	yes	—
352	C₂×D₄	—	2	2	no	—
353	C₂×D₄	—	2	2	no	—
354	C₂×D₄	—	2	2	no	—
355	C₂×D₄	—	2	2	no	—
356	C₂×D₄	—	2	1	no	—
357	C₂×D₄	—	4	2	no	—
358	C₂×D₄	—	4	2	no	—
359	C₂×D₄	C₂²×C₄×C₄₁	1	2	yes	—
360	C₂²×C₄	—	2	1	no	—
361	C₂²×C₄	—	2	2	no	—
362	C₂²×C₄	—	2	2	no	—
363	C₂²×C₄	—	2	2	no	—
364	C₂²×C₄	—	2	2	no	—
365	C₂²×C₄	—	4	2	no	—
366	C₂²×C₄	—	4	2	no	—
367	C₂²×C₄	C₂²×C₄×C₄₁	1	1	yes	characteristic
368	C₂²×C₄	C₂²×C₄×C₄₁	1	1	yes	characteristic
369	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
370	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
371	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
372	C₂²×C₄	#41×C₄₁	1	2	yes	—
373	C₂²×C₄	#41×C₄₁	1	2	yes	—
374	C₂²×C₄	#41×C₄₁	1	1	yes	characteristic
375	C₂²×C₄	#41×C₄₁	1	2	yes	—
376	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
377	M₁₆	—	2	4	no	—
378	M₁₆	—	2	4	no	—
379	M₁₆	—	2	2	no	—
380	M₁₆	—	2	2	no	—
381	M₁₆	—	2	2	no	—
382	M₁₆	—	2	2	no	—
383	M₁₆	—	4	2	no	—
384	M₁₆	—	4	2	no	—
385	C₂×C₈	—	2	4	no	—
386	C₂×C₈	—	2	4	no	—
387	C₂×C₈	—	2	1	no	—
388	C₂×C₈	—	2	2	no	—
389	C₂×C₈	—	2	1	no	—
390	C₂×C₈	—	2	1	no	—
391	C₂×C₈	—	2	1	no	—
392	C₂×C₈	—	2	2	no	—
393	C₂×C₈	—	2	2	no	—
394	C₂×C₈	—	2	2	no	—
395	C₂×C₈	—	4	2	no	—
396	C₂×C₈	—	4	2	no	—
397	C₂×C₈	C₂²×C₄×C₄₁	1	2	yes	—
398	C₂×C₈	C₂²×C₄×C₄₁	1	2	yes	—
399	C₂×C₈	C₂×D₄×C₄₁	1	4	yes	—
400	C₄⋊C₄	—	2	2	no	—
401	C₄⋊C₄	—	2	4	no	—
402	C₄⋊C₄	C₂²×C₄×C₄₁	1	4	yes	—
403	C₂²⋊C₄	—	2	2	no	—
404	C₂²⋊C₄	—	2	4	no	—
405	C₂²⋊C₄	—	2	2	no	—
406	C₄²	—	2	2	no	—
407	C₄²	—	2	2	no	—
408	C₄²	—	2	2	no	—
409	C₄²	C₂×D₄×C₄₁	1	4	yes	—
410	C₂³	—	2	2	no	—
411	C₂³	—	4	2	no	—
412	C₂³	—	4	2	no	—
413	C₂³	—	8	2	no	—
414	C₂³	C₄×D₄×C₄₁	1	1	yes	characteristic
415	C₂³	C₄×D₄×C₄₁	1	1	yes	characteristic
416	C₂³	#123×C₄₁	1	2	yes	—
417	C₂³	#126×C₄₁	1	2	yes	—
418	C₂³	C₂×#41×C₄₁	1	1	yes	characteristic
419	Q₈	—	2	2	no	—
420	Q₈	—	2	2	no	—
421	Q₈	—	4	2	no	—
422	D₄	—	2	2	no	—
423	D₄	—	2	2	no	—
424	D₄	—	4	2	no	—
425	D₄	—	4	2	no	—
426	D₄	—	4	4	no	—
427	D₄	—	4	2	no	—
428	C₂×C₄	—	2	4	no	—
429	C₂×C₄	—	2	2	no	—
430	C₂×C₄	—	2	4	no	—
431	C₂×C₄	—	4	4	no	—
432	C₂×C₄	—	4	2	no	—
433	C₂×C₄	—	4	2	no	—
434	C₂×C₄	—	4	2	no	—
435	C₂×C₄	—	4	4	no	—
436	C₂×C₄	—	8	2	no	—
437	C₂×C₄	#117×C₄₁	1	2	yes	—
438	C₂×C₄	#117×C₄₁	1	2	yes	—
439	C₂×C₄	C₄×D₄×C₄₁	1	2	yes	—
440	C₂×C₄	C₄×D₄×C₄₁	1	2	yes	—
441	C₂×C₄	C₄×D₄×C₄₁	1	1	yes	characteristic
442	C₂×C₄	C₄×D₄×C₄₁	1	1	yes	characteristic
443	C₂×C₄	#121×C₄₁	1	2	yes	—
444	C₂×C₄	#121×C₄₁	1	2	yes	—
445	C₂×C₄	#123×C₄₁	1	2	yes	—
446	C₂×C₄	#124×C₄₁	1	2	yes	—
447	C₂×C₄	#124×C₄₁	1	2	yes	—
448	C₂×C₄	#126×C₄₁	1	2	yes	—
449	C₂×C₄	C₂³×C₄×C₄₁	1	1	yes	characteristic
450	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
451	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
452	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
453	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
454	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
455	C₈	—	2	2	no	—
456	C₈	—	2	2	no	—
457	C₈	—	2	4	no	—
458	C₈	—	4	2	no	—
459	C₈	—	4	2	no	—
460	C₂²	—	2	2	no	—
461	C₂²	—	2	2	no	—
462	C₂²	—	2	2	no	—
463	C₂²	—	4	2	no	—
464	C₂²	—	4	2	no	—
465	C₂²	—	4	2	no	—
466	C₂²	—	4	4	no	—
467	C₂²	—	8	4	no	—
468	C₂²	C₄₁×#388	1	2	yes	—
469	C₂²	C₄₁×#388	1	2	yes	—
470	C₂²	C₂×C₄×D₄×C₄₁	1	1	yes	characteristic
471	C₂²	C₂×#123×C₄₁	1	1	yes	characteristic
472	C₂²	C₂×#126×C₄₁	1	1	yes	characteristic
473	C₄	—	4	4	no	—
474	C₄	—	4	2	no	—
475	C₄	—	4	4	no	—
476	C₄	C₄₁×#388	1	2	yes	—
477	C₄	C₄₁×#388	1	2	yes	—
478	C₄	C₂×#117×C₄₁	1	1	yes	characteristic
479	C₄	C₂×C₄×D₄×C₄₁	1	1	yes	characteristic
480	C₄	C₂×#121×C₄₁	1	1	yes	characteristic
481	C₄	C₂×#124×C₄₁	1	1	yes	characteristic
482	C₂	—	2	1	no	—
483	C₂	—	2	2	no	—
484	C₂	—	2	1	no	—
485	C₂	—	2	2	no	—
486	C₂	—	8	2	no	—
487	C₂	C₂×C₄₁×#388	1	1	yes	characteristic
488	C₂	C₄₁×#2957	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₄₁	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₄₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₁
socle	C₂²×C₄₁	C₂×C₄×D₄
prime radical	C₂²×#41×C₄₁	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₄₁ ◁ C₂²×M₁₆×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₄₁×#2905	C₂	semidirect
5. C₂×C₄₁×#405	C₂	semidirect
6. C₄₁×#1938	C₂	semidirect
7. C₄₁×#1937	C₂	semidirect
8. C₂×C₄₁×#341	C₂	semidirect
9. C₄₁×#1733	C₂	semidirect
18. C₄₁×#424	C₂²	semidirect
22. C₄₁×#416	C₄	semidirect
25. C₂×#103×C₄₁	C₄	semidirect
26. C₂×#102×C₄₁	C₄	semidirect
31. C₂×#97×C₄₁	C₂²	semidirect
32. C₂×C₄×C₈×C₄₁	C₂²	semidirect
33. C₄₁×#341	C₂²	semidirect
34. C₄₁×#341	C₂²	semidirect
35. C₄₁×#339	C₂²	semidirect
215. #21098	C₄₁	direct (N × H)
238. #2905	C₂×C₄₁	semidirect
242. C₂×#405	C₂×C₄₁	semidirect
243. #1938	C₂×C₄₁	semidirect
244. #1937	C₂×C₄₁	semidirect
245. C₂×#341	C₂×C₄₁	semidirect
246. #1733	C₂×C₄₁	semidirect
262. #424	C₂²×C₄₁	semidirect
266. #416	C₄×C₄₁	semidirect
269. C₂×#103	C₄×C₄₁	semidirect
270. C₂×#102	C₄×C₄₁	semidirect
275. C₂×#97	C₂²×C₄₁	semidirect
276. C₂×C₄×C₈	C₂²×C₄₁	semidirect
277. #341	C₂²×C₄₁	semidirect
278. #341	C₂²×C₄₁	semidirect
279. #339	C₂²×C₄₁	semidirect
280. C₄₁	#21098	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×#2905	2
C₂×C₄₁×#421	2
C₂×C₄₁×#416	2
C₄₁×#2879	2
C₂×C₄₁×#405	2
C₄₁×#1938	2
C₄₁×#1937	2
C₂×C₄₁×#341	2
C₄₁×#1733	2
#21098	41

Subgroups — C41×#21098 #23797299

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#21098 #23797299