Subgroups — C₄₁×#21099 #23797300

Order 10496.

1054 conjugacy classes of subgroups.

The subgroup lattice has 496 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	C₂²×#104×C₄₁	C₂	1	1	yes	maximal, characteristic
3	C₄₁×#2896	C₂	1	1	yes	maximal, characteristic
4	C₄₁×#2879	C₂	1	1	yes	maximal, characteristic
5	C₂×C₄×M₁₆×C₄₁	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	C₄₁×#1738	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₄₁×#339	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	C₂²×M₁₆×C₄₁	C₂²	1	1	yes	characteristic
15	C₂×#117×C₄₁	C₂²	1	1	yes	characteristic
16	C₂²×C₄²×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	C₂×#104×C₄₁	—	2	4	no	—
21	C₂×#104×C₄₁	C₂²	1	2	yes	—
22	C₂×#104×C₄₁	C₂²	1	2	yes	—
23	C₄₁×#419	C₄	1	2	yes	complemented
24	C₄₁×#418	C₄	1	2	yes	complemented
25	C₄₁×#417	C₄	1	4	yes	complemented
26	C₄₁×#416	C₂²	1	4	yes	—
27	C₄₁×#408	—	2	2	no	—
28	C₄₁×#408	C₂²	1	4	yes	—
29	C₄₁×#407	—	2	2	no	—
30	C₄×M₁₆×C₄₁	—	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	4	yes	complemented
34	C₄₁×#339	C₂²	1	2	yes	complemented
35	C₄₁×#339	C₂²	1	2	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	—	2	1	no	—
49	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
50	C₂×M₁₆×C₄₁	—	2	2	no	—
51	C₂×M₁₆×C₄₁	—	2	2	no	—
52	C₂×M₁₆×C₄₁	—	2	2	no	—
53	C₂×M₁₆×C₄₁	—	2	2	no	—
54	C₂×M₁₆×C₄₁	—	2	1	no	—
55	C₂×M₁₆×C₄₁	—	2	1	no	—
56	C₂×M₁₆×C₄₁	—	2	2	no	—
57	C₂×M₁₆×C₄₁	—	2	2	no	—
58	C₂×M₁₆×C₄₁	—	2	2	no	—
59	C₂×M₁₆×C₄₁	—	2	2	no	—
60	C₂×M₁₆×C₄₁	C₂×C₄	1	2	yes	—
61	C₂×M₁₆×C₄₁	C₂×C₄	1	2	yes	—
62	C₂×M₁₆×C₄₁	D₄	1	2	yes	—
63	C₂×M₁₆×C₄₁	D₄	1	2	yes	—
64	C₂×M₁₆×C₄₁	C₂³	1	2	yes	—
65	C₂×M₁₆×C₄₁	C₂³	1	2	yes	—
66	C₂²×C₈×C₄₁	—	2	1	no	—
67	C₂²×C₈×C₄₁	—	2	1	no	—
68	C₂²×C₈×C₄₁	C₂³	1	2	yes	—
69	C₂²×C₈×C₄₁	C₂³	1	2	yes	—
70	#117×C₄₁	—	2	1	no	—
71	#117×C₄₁	—	2	1	no	—
72	#117×C₄₁	C₂×C₄	1	2	yes	—
73	#117×C₄₁	C₂³	1	2	yes	—
74	C₂×C₄⋊C₄×C₄₁	C₂×C₄	1	2	yes	—
75	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
76	C₂×C₄²×C₄₁	—	2	1	no	—
77	C₂×C₄²×C₄₁	—	2	1	no	—
78	C₂×C₄²×C₄₁	—	2	2	no	—
79	C₂×C₄²×C₄₁	D₄	1	4	yes	—
80	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
81	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
82	C₄⋊C₈×C₄₁	—	2	8	no	—
83	#104×C₄₁	—	2	4	no	—
84	#104×C₄₁	—	2	4	no	—
85	#103×C₄₁	C₂×C₄	1	8	yes	complemented
86	#102×C₄₁	C₂×C₄	1	8	yes	complemented
87	C₂²⋊C₈×C₄₁	—	2	8	no	—
88	#97×C₄₁	—	2	4	no	—
89	C₄×C₈×C₄₁	—	2	4	no	—
90	C₂⁴×C₄₁	—	2	1	no	—
91	C₂⁴×C₄₁	#41	1	1	yes	characteristic
92	#41×C₄₁	—	2	4	no	—
93	#41×C₄₁	—	2	4	no	—
94	#41×C₄₁	—	2	2	no	—
95	#41×C₄₁	—	2	2	no	—
96	#41×C₄₁	—	2	2	no	—
97	#41×C₄₁	—	2	2	no	—
98	#41×C₄₁	—	4	2	no	—
99	#41×C₄₁	—	4	2	no	—
100	#41×C₄₁	—	4	2	no	—
101	#41×C₄₁	—	4	2	no	—
102	C₂×Q₈×C₄₁	—	2	1	no	—
103	C₂×Q₈×C₄₁	—	2	2	no	—
104	C₂×Q₈×C₄₁	—	2	2	no	—
105	C₂×Q₈×C₄₁	C₂²×C₄	1	2	yes	—
106	C₂×D₄×C₄₁	—	2	2	no	—
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	1	no	—
111	C₂×D₄×C₄₁	—	4	2	no	—
112	C₂×D₄×C₄₁	—	4	2	no	—
113	C₂×D₄×C₄₁	C₂²×C₄	1	2	yes	—
114	C₂²×C₄×C₄₁	—	2	1	no	—
115	C₂²×C₄×C₄₁	—	2	1	no	—
116	C₂²×C₄×C₄₁	—	2	4	no	—
117	C₂²×C₄×C₄₁	—	2	1	no	—
118	C₂²×C₄×C₄₁	—	2	2	no	—
119	C₂²×C₄×C₄₁	—	2	2	no	—
120	C₂²×C₄×C₄₁	—	2	2	no	—
121	C₂²×C₄×C₄₁	—	4	4	no	—
122	C₂²×C₄×C₄₁	—	4	2	no	—
123	C₂²×C₄×C₄₁	—	4	2	no	—
124	C₂²×C₄×C₄₁	C₂²×C₄	1	1	yes	characteristic
125	C₂²×C₄×C₄₁	C₂²×C₄	1	1	yes	characteristic
126	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
127	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
128	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
129	C₂²×C₄×C₄₁	#41	1	2	yes	—
130	C₂²×C₄×C₄₁	#41	1	2	yes	—
131	C₂²×C₄×C₄₁	#41	1	1	yes	characteristic
132	C₂²×C₄×C₄₁	#41	1	2	yes	—
133	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
134	M₁₆×C₄₁	—	2	4	no	—
135	M₁₆×C₄₁	—	2	4	no	—
136	M₁₆×C₄₁	—	2	4	no	—
137	M₁₆×C₄₁	—	2	4	no	—
138	M₁₆×C₄₁	—	2	2	no	—
139	M₁₆×C₄₁	—	2	2	no	—
140	M₁₆×C₄₁	—	2	2	no	—
141	M₁₆×C₄₁	—	2	2	no	—
142	M₁₆×C₄₁	—	4	2	no	—
143	M₁₆×C₄₁	—	4	2	no	—
144	C₂×C₈×C₄₁	—	2	2	no	—
145	C₂×C₈×C₄₁	—	2	2	no	—
146	C₂×C₈×C₄₁	—	2	2	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	4	yes	—
153	C₂×C₈×C₄₁	C₂×D₄	1	4	yes	—
154	C₄⋊C₄×C₄₁	—	2	2	no	—
155	C₄⋊C₄×C₄₁	C₂²×C₄	1	4	yes	—
156	C₂²⋊C₄×C₄₁	—	2	2	no	—
157	C₂²⋊C₄×C₄₁	—	2	2	no	—
158	C₄²×C₄₁	—	2	2	no	—
159	C₄²×C₄₁	—	2	4	no	—
160	C₄²×C₄₁	—	2	2	no	—
161	C₄²×C₄₁	—	2	1	no	—
162	C₄²×C₄₁	—	2	1	no	—
163	C₄²×C₄₁	C₂×D₄	1	2	yes	—
164	C₄²×C₄₁	C₂×D₄	1	2	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	—	2	2	no	—
187	C₂×C₄×C₄₁	—	2	2	no	—
188	C₂×C₄×C₄₁	—	4	8	no	—
189	C₂×C₄×C₄₁	—	4	2	no	—
190	C₂×C₄×C₄₁	—	4	2	no	—
191	C₂×C₄×C₄₁	—	4	2	no	—
192	C₂×C₄×C₄₁	—	4	2	no	—
193	C₂×C₄×C₄₁	—	4	4	no	—
194	C₂×C₄×C₄₁	—	8	2	no	—
195	C₂×C₄×C₄₁	#117	1	2	yes	—
196	C₂×C₄×C₄₁	#117	1	2	yes	—
197	C₂×C₄×C₄₁	C₄×D₄	1	2	yes	—
198	C₂×C₄×C₄₁	C₄×D₄	1	2	yes	—
199	C₂×C₄×C₄₁	C₄×D₄	1	1	yes	characteristic
200	C₂×C₄×C₄₁	C₄×D₄	1	1	yes	characteristic
201	C₂×C₄×C₄₁	#121	1	2	yes	—
202	C₂×C₄×C₄₁	#121	1	2	yes	—
203	C₂×C₄×C₄₁	#123	1	2	yes	—
204	C₂×C₄×C₄₁	#124	1	2	yes	—
205	C₂×C₄×C₄₁	#124	1	2	yes	—
206	C₂×C₄×C₄₁	#126	1	2	yes	—
207	C₂×C₄×C₄₁	C₂³×C₄	1	1	yes	characteristic
208	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
209	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
210	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
211	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
212	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
213	C₈×C₄₁	—	2	4	no	—
214	C₈×C₄₁	—	2	4	no	—
215	C₈×C₄₁	—	4	2	no	—
216	C₈×C₄₁	—	4	2	no	—
217	#21099	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
218	C₂²×C₄₁	—	2	2	no	—
219	C₂²×C₄₁	—	2	2	no	—
220	C₂²×C₄₁	—	2	2	no	—
221	C₂²×C₄₁	—	4	2	no	—
222	C₂²×C₄₁	—	4	2	no	—
223	C₂²×C₄₁	—	4	4	no	—
224	C₂²×C₄₁	—	4	2	no	—
225	C₂²×C₄₁	—	8	4	no	—
226	C₂²×C₄₁	#388	1	2	yes	—
227	C₂²×C₄₁	#388	1	2	yes	—
228	C₂²×C₄₁	C₂×C₄×D₄	1	1	yes	characteristic
229	C₂²×C₄₁	C₂×#123	1	1	yes	characteristic
230	C₂²×C₄₁	C₂×#126	1	1	yes	characteristic
231	C₄×C₄₁	—	2	4	no	—
232	C₄×C₄₁	—	4	2	no	—
233	C₄×C₄₁	—	4	4	no	—
234	C₄×C₄₁	—	4	2	no	—
235	C₄×C₄₁	#388	1	2	yes	—
236	C₄×C₄₁	#388	1	2	yes	—
237	C₄×C₄₁	C₂×#117	1	1	yes	characteristic
238	C₄×C₄₁	C₂×C₄×D₄	1	1	yes	characteristic
239	C₄×C₄₁	C₂×#121	1	1	yes	characteristic
240	C₄×C₄₁	C₂×#124	1	1	yes	characteristic
241	#2905	C₂×C₄₁	1	1	yes	characteristic, complemented
242	C₂²×#104	C₂×C₄₁	1	1	yes	characteristic
243	#2896	C₂×C₄₁	1	1	yes	characteristic
244	#2879	C₂×C₄₁	1	1	yes	characteristic
245	C₂×C₄×M₁₆	C₂×C₄₁	1	1	yes	characteristic, complemented
246	#1938	C₂×C₄₁	1	4	yes	complemented
247	#1937	C₂×C₄₁	1	4	yes	complemented
248	#1738	C₂×C₄₁	1	1	yes	characteristic, complemented
249	C₂×#339	C₂×C₄₁	1	1	yes	characteristic, complemented
250	C₂×C₄₁	—	2	1	no	—
251	C₂×C₄₁	—	2	2	no	—
252	C₂×C₄₁	—	2	1	no	—
253	C₂×C₄₁	—	2	2	no	—
254	C₂×C₄₁	—	8	2	no	—
255	C₂×C₄₁	C₂×#388	1	1	yes	characteristic
256	C₂×C₄₁	#2956	1	2	yes	—
257	C₂²×#41	C₂²×C₄₁	1	1	yes	characteristic
258	C₂²×M₁₆	C₂²×C₄₁	1	1	yes	characteristic
259	C₂²×M₁₆	C₂²×C₄₁	1	1	yes	characteristic
260	C₂²×M₁₆	C₂²×C₄₁	1	1	yes	characteristic
261	C₂²×M₁₆	C₂²×C₄₁	1	1	yes	characteristic
262	C₂×#117	C₂²×C₄₁	1	1	yes	characteristic
263	C₂²×C₄²	C₂²×C₄₁	1	1	yes	characteristic
264	#424	—	2	2	no	—
265	#424	C₂²×C₄₁	1	4	yes	complemented
266	#423	—	2	2	no	—
267	C₂×#104	—	2	4	no	—
268	C₂×#104	C₂²×C₄₁	1	2	yes	—
269	C₂×#104	C₂²×C₄₁	1	2	yes	—
270	#419	C₄×C₄₁	1	2	yes	complemented
271	#418	C₄×C₄₁	1	2	yes	complemented
272	#417	C₄×C₄₁	1	4	yes	complemented
273	#416	C₂²×C₄₁	1	4	yes	—
274	#408	—	2	2	no	—
275	#408	C₂²×C₄₁	1	4	yes	—
276	#407	—	2	2	no	—
277	C₄×M₁₆	—	2	4	no	—
278	C₂×#97	C₂²×C₄₁	1	2	yes	complemented
279	C₂×C₄×C₈	C₂²×C₄₁	1	2	yes	complemented
280	#341	C₂²×C₄₁	1	4	yes	complemented
281	#339	C₂²×C₄₁	1	2	yes	complemented
282	#339	C₂²×C₄₁	1	2	yes	complemented
283	C₄₁	#21099	1	1	yes	characteristic, direct product factor, Sylow
284	C₂×#41	—	2	1	no	—
285	C₂×#41	—	2	1	no	—
286	C₂×#41	—	2	2	no	—
287	C₂×#41	—	2	2	no	—
288	C₂×#41	—	2	2	no	—
289	C₂×#41	—	2	2	no	—
290	C₂×#41	C₂×C₄×C₄₁	1	2	yes	—
291	C₂×#41	C₂³×C₄₁	1	2	yes	—
292	C₂²×Q₈	C₂×C₄×C₄₁	1	1	yes	characteristic
293	C₂²×D₄	—	2	1	no	—
294	C₂²×D₄	C₂×C₄×C₄₁	1	1	yes	characteristic
295	C₂³×C₄	—	2	1	no	—
296	C₂³×C₄	—	2	1	no	—
297	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
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	—	2	1	no	—
303	C₂×M₁₆	—	2	1	no	—
304	C₂×M₁₆	—	2	2	no	—
305	C₂×M₁₆	—	2	2	no	—
306	C₂×M₁₆	—	2	2	no	—
307	C₂×M₁₆	—	2	2	no	—
308	C₂×M₁₆	C₂×C₄×C₄₁	1	2	yes	—
309	C₂×M₁₆	C₂×C₄×C₄₁	1	2	yes	—
310	C₂×M₁₆	D₄×C₄₁	1	2	yes	—
311	C₂×M₁₆	D₄×C₄₁	1	2	yes	—
312	C₂×M₁₆	C₂³×C₄₁	1	2	yes	—
313	C₂×M₁₆	C₂³×C₄₁	1	2	yes	—
314	C₂²×C₈	—	2	1	no	—
315	C₂²×C₈	—	2	1	no	—
316	C₂²×C₈	C₂³×C₄₁	1	2	yes	—
317	C₂²×C₈	C₂³×C₄₁	1	2	yes	—
318	#117	—	2	1	no	—
319	#117	—	2	1	no	—
320	#117	C₂×C₄×C₄₁	1	2	yes	—
321	#117	C₂³×C₄₁	1	2	yes	—
322	C₂×C₄⋊C₄	C₂×C₄×C₄₁	1	2	yes	—
323	C₂×C₂²⋊C₄	—	2	1	no	—
324	C₂×C₄²	—	2	1	no	—
325	C₂×C₄²	—	2	1	no	—
326	C₂×C₄²	—	2	2	no	—
327	C₂×C₄²	D₄×C₄₁	1	4	yes	—
328	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
329	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
330	C₄⋊C₈	—	2	8	no	—
331	#104	—	2	4	no	—
332	#104	—	2	4	no	—
333	#103	C₂×C₄×C₄₁	1	8	yes	complemented
334	#102	C₂×C₄×C₄₁	1	8	yes	complemented
335	C₂²⋊C₈	—	2	8	no	—
336	#97	—	2	4	no	—
337	C₄×C₈	—	2	4	no	—
338	C₂⁴	—	2	1	no	—
339	C₂⁴	#41×C₄₁	1	1	yes	characteristic
340	#41	—	2	4	no	—
341	#41	—	2	4	no	—
342	#41	—	2	2	no	—
343	#41	—	2	2	no	—
344	#41	—	2	2	no	—
345	#41	—	2	2	no	—
346	#41	—	4	2	no	—
347	#41	—	4	2	no	—
348	#41	—	4	2	no	—
349	#41	—	4	2	no	—
350	C₂×Q₈	—	2	1	no	—
351	C₂×Q₈	—	2	2	no	—
352	C₂×Q₈	—	2	2	no	—
353	C₂×Q₈	C₂²×C₄×C₄₁	1	2	yes	—
354	C₂×D₄	—	2	2	no	—
355	C₂×D₄	—	2	2	no	—
356	C₂×D₄	—	2	2	no	—
357	C₂×D₄	—	2	2	no	—
358	C₂×D₄	—	2	1	no	—
359	C₂×D₄	—	4	2	no	—
360	C₂×D₄	—	4	2	no	—
361	C₂×D₄	C₂²×C₄×C₄₁	1	2	yes	—
362	C₂²×C₄	—	2	1	no	—
363	C₂²×C₄	—	2	1	no	—
364	C₂²×C₄	—	2	4	no	—
365	C₂²×C₄	—	2	1	no	—
366	C₂²×C₄	—	2	2	no	—
367	C₂²×C₄	—	2	2	no	—
368	C₂²×C₄	—	2	2	no	—
369	C₂²×C₄	—	4	4	no	—
370	C₂²×C₄	—	4	2	no	—
371	C₂²×C₄	—	4	2	no	—
372	C₂²×C₄	C₂²×C₄×C₄₁	1	1	yes	characteristic
373	C₂²×C₄	C₂²×C₄×C₄₁	1	1	yes	characteristic
374	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
375	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
376	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
377	C₂²×C₄	#41×C₄₁	1	2	yes	—
378	C₂²×C₄	#41×C₄₁	1	2	yes	—
379	C₂²×C₄	#41×C₄₁	1	1	yes	characteristic
380	C₂²×C₄	#41×C₄₁	1	2	yes	—
381	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
382	M₁₆	—	2	4	no	—
383	M₁₆	—	2	4	no	—
384	M₁₆	—	2	4	no	—
385	M₁₆	—	2	4	no	—
386	M₁₆	—	2	2	no	—
387	M₁₆	—	2	2	no	—
388	M₁₆	—	2	2	no	—
389	M₁₆	—	2	2	no	—
390	M₁₆	—	4	2	no	—
391	M₁₆	—	4	2	no	—
392	C₂×C₈	—	2	2	no	—
393	C₂×C₈	—	2	2	no	—
394	C₂×C₈	—	2	2	no	—
395	C₂×C₈	—	2	2	no	—
396	C₂×C₈	—	2	2	no	—
397	C₂×C₈	—	2	2	no	—
398	C₂×C₈	—	4	2	no	—
399	C₂×C₈	—	4	2	no	—
400	C₂×C₈	C₂²×C₄×C₄₁	1	4	yes	—
401	C₂×C₈	C₂×D₄×C₄₁	1	4	yes	—
402	C₄⋊C₄	—	2	2	no	—
403	C₄⋊C₄	C₂²×C₄×C₄₁	1	4	yes	—
404	C₂²⋊C₄	—	2	2	no	—
405	C₂²⋊C₄	—	2	2	no	—
406	C₄²	—	2	2	no	—
407	C₄²	—	2	4	no	—
408	C₄²	—	2	2	no	—
409	C₄²	—	2	1	no	—
410	C₄²	—	2	1	no	—
411	C₄²	C₂×D₄×C₄₁	1	2	yes	—
412	C₄²	C₂×D₄×C₄₁	1	2	yes	—
413	C₂³	—	2	2	no	—
414	C₂³	—	4	2	no	—
415	C₂³	—	4	2	no	—
416	C₂³	—	8	2	no	—
417	C₂³	C₄×D₄×C₄₁	1	1	yes	characteristic
418	C₂³	C₄×D₄×C₄₁	1	1	yes	characteristic
419	C₂³	#123×C₄₁	1	2	yes	—
420	C₂³	#126×C₄₁	1	2	yes	—
421	C₂³	C₂×#41×C₄₁	1	1	yes	characteristic
422	Q₈	—	2	2	no	—
423	Q₈	—	2	2	no	—
424	Q₈	—	4	2	no	—
425	D₄	—	2	2	no	—
426	D₄	—	2	2	no	—
427	D₄	—	4	2	no	—
428	D₄	—	4	2	no	—
429	D₄	—	4	4	no	—
430	D₄	—	4	2	no	—
431	C₂×C₄	—	2	4	no	—
432	C₂×C₄	—	2	2	no	—
433	C₂×C₄	—	2	4	no	—
434	C₂×C₄	—	2	2	no	—
435	C₂×C₄	—	2	2	no	—
436	C₂×C₄	—	4	8	no	—
437	C₂×C₄	—	4	2	no	—
438	C₂×C₄	—	4	2	no	—
439	C₂×C₄	—	4	2	no	—
440	C₂×C₄	—	4	2	no	—
441	C₂×C₄	—	4	4	no	—
442	C₂×C₄	—	8	2	no	—
443	C₂×C₄	#117×C₄₁	1	2	yes	—
444	C₂×C₄	#117×C₄₁	1	2	yes	—
445	C₂×C₄	C₄×D₄×C₄₁	1	2	yes	—
446	C₂×C₄	C₄×D₄×C₄₁	1	2	yes	—
447	C₂×C₄	C₄×D₄×C₄₁	1	1	yes	characteristic
448	C₂×C₄	C₄×D₄×C₄₁	1	1	yes	characteristic
449	C₂×C₄	#121×C₄₁	1	2	yes	—
450	C₂×C₄	#121×C₄₁	1	2	yes	—
451	C₂×C₄	#123×C₄₁	1	2	yes	—
452	C₂×C₄	#124×C₄₁	1	2	yes	—
453	C₂×C₄	#124×C₄₁	1	2	yes	—
454	C₂×C₄	#126×C₄₁	1	2	yes	—
455	C₂×C₄	C₂³×C₄×C₄₁	1	1	yes	characteristic
456	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
457	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
458	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
459	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
460	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
461	C₈	—	2	4	no	—
462	C₈	—	2	4	no	—
463	C₈	—	4	2	no	—
464	C₈	—	4	2	no	—
465	C₂²	—	2	2	no	—
466	C₂²	—	2	2	no	—
467	C₂²	—	2	2	no	—
468	C₂²	—	4	2	no	—
469	C₂²	—	4	2	no	—
470	C₂²	—	4	2	no	—
471	C₂²	—	4	4	no	—
472	C₂²	—	8	4	no	—
473	C₂²	C₄₁×#388	1	2	yes	—
474	C₂²	C₄₁×#388	1	2	yes	—
475	C₂²	C₂×C₄×D₄×C₄₁	1	1	yes	characteristic
476	C₂²	C₂×#123×C₄₁	1	1	yes	characteristic
477	C₂²	C₂×#126×C₄₁	1	1	yes	characteristic
478	C₄	—	2	4	no	—
479	C₄	—	4	2	no	—
480	C₄	—	4	2	no	—
481	C₄	—	4	4	no	—
482	C₄	C₄₁×#388	1	2	yes	—
483	C₄	C₄₁×#388	1	2	yes	—
484	C₄	C₂×#117×C₄₁	1	1	yes	characteristic
485	C₄	C₂×C₄×D₄×C₄₁	1	1	yes	characteristic
486	C₄	C₂×#121×C₄₁	1	1	yes	characteristic
487	C₄	C₂×#124×C₄₁	1	1	yes	characteristic
488	C₂	—	2	1	no	—
489	C₂	—	2	2	no	—
490	C₂	—	2	1	no	—
491	C₂	—	2	2	no	—
492	C₂	—	8	2	no	—
493	C₂	C₂×C₄₁×#388	1	1	yes	characteristic
494	C₂	C₄₁×#2956	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×C₄×M₁₆×C₄₁	C₂	semidirect
6. C₄₁×#1938	C₂	semidirect
7. C₄₁×#1937	C₂	semidirect
8. C₄₁×#1738	C₂	semidirect
9. C₂×C₄₁×#339	C₂	semidirect
18. C₄₁×#424	C₂²	semidirect
23. C₄₁×#419	C₄	semidirect
24. C₄₁×#418	C₄	semidirect
25. C₄₁×#417	C₄	semidirect
31. C₂×#97×C₄₁	C₂²	semidirect
32. C₂×C₄×C₈×C₄₁	C₂²	semidirect
33. C₄₁×#341	C₂²	semidirect
34. C₄₁×#339	C₂²	semidirect
35. C₄₁×#339	C₂²	semidirect
85. #103×C₄₁	C₂×C₄	semidirect
86. #102×C₄₁	C₂×C₄	semidirect
217. #21099	C₄₁	direct (N × H)
241. #2905	C₂×C₄₁	semidirect
245. C₂×C₄×M₁₆	C₂×C₄₁	semidirect
246. #1938	C₂×C₄₁	semidirect
247. #1937	C₂×C₄₁	semidirect
248. #1738	C₂×C₄₁	semidirect
249. C₂×#339	C₂×C₄₁	semidirect
265. #424	C₂²×C₄₁	semidirect
270. #419	C₄×C₄₁	semidirect
271. #418	C₄×C₄₁	semidirect
272. #417	C₄×C₄₁	semidirect
278. C₂×#97	C₂²×C₄₁	semidirect
279. C₂×C₄×C₈	C₂²×C₄₁	semidirect
280. #341	C₂²×C₄₁	semidirect
281. #339	C₂²×C₄₁	semidirect
282. #339	C₂²×C₄₁	semidirect
283. C₄₁	#21099	direct (N × H)
333. #103	C₂×C₄×C₄₁	semidirect
334. #102	C₂×C₄×C₄₁	semidirect

Maximal subgroups

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

subgroup	index
C₄₁×#2905	2
C₂²×#104×C₄₁	2
C₄₁×#2896	2
C₄₁×#2879	2
C₂×C₄×M₁₆×C₄₁	2
C₄₁×#1938	2
C₄₁×#1937	2
C₄₁×#1738	2
C₂×C₄₁×#339	2
#21099	41

Subgroups — C41×#21099 #23797300

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#21099 #23797300