Subgroups — C₄₁×#23601 #23799802

Order 10496.

994 conjugacy classes of subgroups.

The subgroup lattice has 502 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#108×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄₁×#2911	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄₁×#424	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₁×#2896	C₂	1	1	yes	maximal, characteristic
5	C₂×C₄₁×#416	C₂	1	1	yes	maximal, characteristic
6	C₂×C₄₁×#413	C₂	1	1	yes	maximal, characteristic
7	C₄₁×#2064	C₂	1	4	yes	maximal, complemented
8	C₄₁×#2063	C₂	1	4	yes	maximal, complemented
9	C₄₁×#1742	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	C₂×#108×C₄₁	—	2	4	no	—
18	C₂×#108×C₄₁	C₂²	1	4	yes	—
19	C₄₁×#428	—	2	2	no	—
20	C₄₁×#428	C₂²	1	4	yes	—
21	C₄₁×#427	—	2	2	no	—
22	C₄₁×#424	—	2	2	no	—
23	C₄₁×#424	C₂²	1	4	yes	—
24	C₂×C₄⋊C₈×C₄₁	—	2	2	no	—
25	C₄₁×#419	C₂²	1	2	yes	—
26	C₄₁×#418	C₂²	1	2	yes	—
27	C₄₁×#417	—	2	2	no	—
28	C₄₁×#416	—	2	2	no	—
29	C₄₁×#416	—	2	2	no	—
30	C₄₁×#416	—	2	2	no	—
31	C₂×#103×C₄₁	C₂²	1	2	yes	—
32	C₂×#102×C₄₁	C₂²	1	2	yes	—
33	C₄₁×#413	—	2	4	no	—
34	C₂×#101×C₄₁	C₂²	1	2	yes	—
35	C₂×#100×C₄₁	C₂²	1	2	yes	—
36	C₄₁×#343	C₂²	1	4	yes	—
37	C₂×#41×C₄₁	—	2	2	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	—	2	1	no	—
42	C₂×#41×C₄₁	—	2	2	no	—
43	C₂×#41×C₄₁	—	2	2	no	—
44	C₂×#41×C₄₁	Q₈	1	4	yes	—
45	C₂²×Q₈×C₄₁	C₂³	1	1	yes	characteristic
46	C₂²×D₄×C₄₁	—	2	1	no	—
47	C₂²×D₄×C₄₁	C₂³	1	1	yes	characteristic
48	C₂³×C₄×C₄₁	—	2	1	no	—
49	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
50	C₂×M₁₆×C₄₁	—	2	1	no	—
51	C₂×M₁₆×C₄₁	—	2	2	no	—
52	C₂×M₁₆×C₄₁	—	2	1	no	—
53	C₂×M₁₆×C₄₁	—	2	1	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	—	2	2	no	—
58	C₂×M₁₆×C₄₁	D₄	1	4	yes	—
59	C₂×M₁₆×C₄₁	C₂³	1	2	yes	—
60	C₂×M₁₆×C₄₁	C₂³	1	2	yes	—
61	C₂×M₁₆×C₄₁	C₂³	1	2	yes	—
62	C₂²×C₈×C₄₁	—	2	2	no	—
63	C₂²×C₈×C₄₁	—	2	1	no	—
64	C₂²×C₈×C₄₁	—	2	2	no	—
65	C₂²×C₈×C₄₁	—	2	1	no	—
66	C₂²×C₈×C₄₁	—	2	1	no	—
67	C₂²×C₈×C₄₁	D₄	1	2	yes	—
68	C₂²×C₈×C₄₁	D₄	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	—	2	1	no	—
73	#117×C₄₁	—	2	1	no	—
74	#117×C₄₁	—	2	1	no	—
75	#117×C₄₁	—	2	1	no	—
76	#117×C₄₁	D₄	1	2	yes	—
77	#117×C₄₁	C₂³	1	2	yes	—
78	C₂×C₄⋊C₄×C₄₁	D₄	1	2	yes	—
79	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
80	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
81	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
82	C₂×C₄²×C₄₁	—	2	1	no	—
83	C₂×C₄²×C₄₁	—	2	1	no	—
84	#108×C₄₁	—	2	8	no	—
85	#107×C₄₁	—	2	4	no	—
86	#106×C₄₁	—	2	4	no	—
87	C₄⋊C₈×C₄₁	—	2	8	no	—
88	#103×C₄₁	—	2	4	no	—
89	#103×C₄₁	—	2	4	no	—
90	#102×C₄₁	—	2	4	no	—
91	#102×C₄₁	—	2	4	no	—
92	#101×C₄₁	—	2	4	no	—
93	#100×C₄₁	—	2	4	no	—
94	C₂⁴×C₄₁	—	2	1	no	—
95	C₂⁴×C₄₁	#41	1	1	yes	characteristic
96	#41×C₄₁	—	2	4	no	—
97	#41×C₄₁	—	2	4	no	—
98	#41×C₄₁	—	2	4	no	—
99	#41×C₄₁	—	2	4	no	—
100	#41×C₄₁	—	4	2	no	—
101	#41×C₄₁	—	4	2	no	—
102	#41×C₄₁	—	4	2	no	—
103	#41×C₄₁	—	4	2	no	—
104	C₂×Q₈×C₄₁	—	2	1	no	—
105	C₂×Q₈×C₄₁	—	2	1	no	—
106	C₂×Q₈×C₄₁	—	2	1	no	—
107	C₂×Q₈×C₄₁	—	2	1	no	—
108	C₂×Q₈×C₄₁	—	2	1	no	—
109	C₂×Q₈×C₄₁	C₂×Q₈	1	2	yes	—
110	C₂×D₄×C₄₁	—	2	4	no	—
111	C₂×D₄×C₄₁	—	2	1	no	—
112	C₂×D₄×C₄₁	—	2	1	no	—
113	C₂×D₄×C₄₁	—	2	1	no	—
114	C₂×D₄×C₄₁	—	2	1	no	—
115	C₂×D₄×C₄₁	—	2	1	no	—
116	C₂×D₄×C₄₁	—	4	1	no	—
117	C₂×D₄×C₄₁	—	4	1	no	—
118	C₂×D₄×C₄₁	—	4	2	no	—
119	C₂×D₄×C₄₁	C₂×Q₈	1	2	yes	—
120	C₂²×C₄×C₄₁	—	2	2	no	—
121	C₂²×C₄×C₄₁	—	2	1	no	—
122	C₂²×C₄×C₄₁	—	2	4	no	—
123	C₂²×C₄×C₄₁	—	2	2	no	—
124	C₂²×C₄×C₄₁	—	4	1	no	—
125	C₂²×C₄×C₄₁	—	4	1	no	—
126	C₂²×C₄×C₄₁	—	4	2	no	—
127	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
128	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
129	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
130	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
131	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
132	C₂²×C₄×C₄₁	C₂×Q₈	1	2	yes	—
133	C₂²×C₄×C₄₁	#41	1	2	yes	—
134	C₂²×C₄×C₄₁	#41	1	2	yes	—
135	C₂²×C₄×C₄₁	#41	1	1	yes	characteristic
136	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
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	—	2	2	no	—
143	M₁₆×C₄₁	—	4	2	no	—
144	M₁₆×C₄₁	—	4	2	no	—
145	M₁₆×C₄₁	C₂×D₄	1	4	yes	—
146	C₂×C₈×C₄₁	—	2	4	no	—
147	C₂×C₈×C₄₁	—	2	4	no	—
148	C₂×C₈×C₄₁	—	2	4	no	—
149	C₂×C₈×C₄₁	—	2	2	no	—
150	C₂×C₈×C₄₁	—	2	2	no	—
151	C₂×C₈×C₄₁	—	2	2	no	—
152	C₂×C₈×C₄₁	—	2	2	no	—
153	C₂×C₈×C₄₁	—	2	2	no	—
154	C₂×C₈×C₄₁	—	4	2	no	—
155	C₂×C₈×C₄₁	—	4	2	no	—
156	C₂×C₈×C₄₁	C₂×D₄	1	4	yes	—
157	C₄⋊C₄×C₄₁	—	2	2	no	—
158	C₄⋊C₄×C₄₁	—	2	2	no	—
159	C₄⋊C₄×C₄₁	—	2	2	no	—
160	C₄⋊C₄×C₄₁	C₂×D₄	1	4	yes	—
161	C₂²⋊C₄×C₄₁	—	2	2	no	—
162	C₂²⋊C₄×C₄₁	—	2	2	no	—
163	C₂²⋊C₄×C₄₁	—	4	1	no	—
164	C₂²⋊C₄×C₄₁	—	4	1	no	—
165	C₄²×C₄₁	—	2	2	no	—
166	C₄²×C₄₁	—	2	2	no	—
167	C₄²×C₄₁	—	4	1	no	—
168	C₄²×C₄₁	—	4	1	no	—
169	C₂³×C₄₁	—	2	2	no	—
170	C₂³×C₄₁	—	4	2	no	—
171	C₂³×C₄₁	—	4	1	no	—
172	C₂³×C₄₁	—	4	1	no	—
173	C₂³×C₄₁	—	8	2	no	—
174	C₂³×C₄₁	#121	1	1	yes	characteristic
175	C₂³×C₄₁	#121	1	1	yes	characteristic
176	C₂³×C₄₁	C₂²⋊Q₈	1	2	yes	—
177	C₂³×C₄₁	#126	1	2	yes	—
178	C₂³×C₄₁	C₂×#41	1	1	yes	characteristic
179	Q₈×C₄₁	—	2	2	no	—
180	Q₈×C₄₁	—	2	2	no	—
181	Q₈×C₄₁	—	4	1	no	—
182	Q₈×C₄₁	—	4	1	no	—
183	D₄×C₄₁	—	2	2	no	—
184	D₄×C₄₁	—	2	2	no	—
185	D₄×C₄₁	—	4	4	no	—
186	D₄×C₄₁	—	4	4	no	—
187	D₄×C₄₁	—	4	1	no	—
188	D₄×C₄₁	—	4	1	no	—
189	C₂×C₄×C₄₁	—	2	4	no	—
190	C₂×C₄×C₄₁	—	2	2	no	—
191	C₂×C₄×C₄₁	—	4	4	no	—
192	C₂×C₄×C₄₁	—	4	1	no	—
193	C₂×C₄×C₄₁	—	4	1	no	—
194	C₂×C₄×C₄₁	—	4	4	no	—
195	C₂×C₄×C₄₁	—	4	4	no	—
196	C₂×C₄×C₄₁	—	4	2	no	—
197	C₂×C₄×C₄₁	—	8	2	no	—
198	C₂×C₄×C₄₁	#121	1	2	yes	—
199	C₂×C₄×C₄₁	#121	1	2	yes	—
200	C₂×C₄×C₄₁	#121	1	2	yes	—
201	C₂×C₄×C₄₁	#121	1	2	yes	—
202	C₂×C₄×C₄₁	#121	1	1	yes	characteristic
203	C₂×C₄×C₄₁	#121	1	1	yes	characteristic
204	C₂×C₄×C₄₁	C₂²⋊Q₈	1	2	yes	—
205	C₂×C₄×C₄₁	C₂²⋊Q₈	1	2	yes	—
206	C₂×C₄×C₄₁	C₂²⋊Q₈	1	2	yes	—
207	C₂×C₄×C₄₁	C₂²⋊Q₈	1	2	yes	—
208	C₂×C₄×C₄₁	C₂²⋊Q₈	1	2	yes	—
209	C₂×C₄×C₄₁	#126	1	2	yes	—
210	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
211	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
212	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
213	C₂×C₄×C₄₁	C₂²×Q₈	1	1	yes	characteristic
214	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
215	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
216	C₈×C₄₁	—	2	4	no	—
217	C₈×C₄₁	—	2	4	no	—
218	C₈×C₄₁	—	4	2	no	—
219	C₈×C₄₁	—	4	2	no	—
220	#23601	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
221	C₂²×C₄₁	—	2	2	no	—
222	C₂²×C₄₁	—	2	2	no	—
223	C₂²×C₄₁	—	2	2	no	—
224	C₂²×C₄₁	—	4	2	no	—
225	C₂²×C₄₁	—	4	2	no	—
226	C₂²×C₄₁	—	4	2	no	—
227	C₂²×C₄₁	—	8	2	no	—
228	C₂²×C₄₁	—	8	2	no	—
229	C₂²×C₄₁	—	8	2	no	—
230	C₂²×C₄₁	#396	1	2	yes	—
231	C₂²×C₄₁	#396	1	2	yes	—
232	C₂²×C₄₁	C₂×#121	1	1	yes	characteristic
233	C₂²×C₄₁	C₂×C₂²⋊Q₈	1	1	yes	characteristic
234	C₂²×C₄₁	C₂×#126	1	1	yes	characteristic
235	C₄×C₄₁	—	4	2	no	—
236	C₄×C₄₁	—	4	4	no	—
237	C₄×C₄₁	—	8	2	no	—
238	C₄×C₄₁	#396	1	2	yes	—
239	C₄×C₄₁	#396	1	2	yes	—
240	C₄×C₄₁	C₂×#121	1	1	yes	characteristic
241	C₄×C₄₁	C₂×#121	1	1	yes	characteristic
242	C₄×C₄₁	C₂×C₂²⋊Q₈	1	1	yes	characteristic
243	C₄×C₄₁	C₂×C₂²⋊Q₈	1	1	yes	characteristic
244	C₂²×#108	C₂×C₄₁	1	1	yes	characteristic, complemented
245	#2911	C₂×C₄₁	1	1	yes	characteristic, complemented
246	C₂×#424	C₂×C₄₁	1	1	yes	characteristic, complemented
247	#2896	C₂×C₄₁	1	1	yes	characteristic
248	C₂×#416	C₂×C₄₁	1	1	yes	characteristic
249	C₂×#413	C₂×C₄₁	1	1	yes	characteristic
250	#2064	C₂×C₄₁	1	4	yes	complemented
251	#2063	C₂×C₄₁	1	4	yes	complemented
252	#1742	C₂×C₄₁	1	1	yes	characteristic, complemented
253	C₂×C₄₁	—	2	1	no	—
254	C₂×C₄₁	—	2	1	no	—
255	C₂×C₄₁	—	2	2	no	—
256	C₂×C₄₁	—	2	2	no	—
257	C₂×C₄₁	—	8	2	no	—
258	C₂×C₄₁	C₂×#396	1	1	yes	characteristic
259	C₂×C₄₁	#3067	1	2	yes	—
260	C₂²×#41	C₂²×C₄₁	1	1	yes	characteristic
261	C₂²×M₁₆	C₂²×C₄₁	1	1	yes	characteristic
262	C₂²×M₁₆	C₂²×C₄₁	1	1	yes	characteristic
263	C₂²×M₁₆	C₂²×C₄₁	1	1	yes	characteristic
264	C₂³×C₈	C₂²×C₄₁	1	1	yes	characteristic
265	C₂×#117	C₂²×C₄₁	1	1	yes	characteristic
266	C₂×#117	C₂²×C₄₁	1	1	yes	characteristic
267	C₂×#108	—	2	4	no	—
268	C₂×#108	C₂²×C₄₁	1	4	yes	—
269	#428	—	2	2	no	—
270	#428	C₂²×C₄₁	1	4	yes	—
271	#427	—	2	2	no	—
272	#424	—	2	2	no	—
273	#424	C₂²×C₄₁	1	4	yes	—
274	C₂×C₄⋊C₈	—	2	2	no	—
275	#419	C₂²×C₄₁	1	2	yes	—
276	#418	C₂²×C₄₁	1	2	yes	—
277	#417	—	2	2	no	—
278	#416	—	2	2	no	—
279	#416	—	2	2	no	—
280	#416	—	2	2	no	—
281	C₂×#103	C₂²×C₄₁	1	2	yes	—
282	C₂×#102	C₂²×C₄₁	1	2	yes	—
283	#413	—	2	4	no	—
284	C₂×#101	C₂²×C₄₁	1	2	yes	—
285	C₂×#100	C₂²×C₄₁	1	2	yes	—
286	#343	C₂²×C₄₁	1	4	yes	—
287	C₄₁	#23601	1	1	yes	characteristic, direct product factor, Sylow
288	C₂×#41	—	2	2	no	—
289	C₂×#41	—	2	1	no	—
290	C₂×#41	—	2	1	no	—
291	C₂×#41	—	2	1	no	—
292	C₂×#41	—	2	1	no	—
293	C₂×#41	—	2	2	no	—
294	C₂×#41	—	2	2	no	—
295	C₂×#41	Q₈×C₄₁	1	4	yes	—
296	C₂²×Q₈	C₂³×C₄₁	1	1	yes	characteristic
297	C₂²×D₄	—	2	1	no	—
298	C₂²×D₄	C₂³×C₄₁	1	1	yes	characteristic
299	C₂³×C₄	—	2	1	no	—
300	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
301	C₂×M₁₆	—	2	1	no	—
302	C₂×M₁₆	—	2	2	no	—
303	C₂×M₁₆	—	2	1	no	—
304	C₂×M₁₆	—	2	1	no	—
305	C₂×M₁₆	—	2	2	no	—
306	C₂×M₁₆	—	2	2	no	—
307	C₂×M₁₆	—	2	2	no	—
308	C₂×M₁₆	—	2	2	no	—
309	C₂×M₁₆	D₄×C₄₁	1	4	yes	—
310	C₂×M₁₆	C₂³×C₄₁	1	2	yes	—
311	C₂×M₁₆	C₂³×C₄₁	1	2	yes	—
312	C₂×M₁₆	C₂³×C₄₁	1	2	yes	—
313	C₂²×C₈	—	2	2	no	—
314	C₂²×C₈	—	2	1	no	—
315	C₂²×C₈	—	2	2	no	—
316	C₂²×C₈	—	2	1	no	—
317	C₂²×C₈	—	2	1	no	—
318	C₂²×C₈	D₄×C₄₁	1	2	yes	—
319	C₂²×C₈	D₄×C₄₁	1	2	yes	—
320	C₂²×C₈	C₂³×C₄₁	1	2	yes	—
321	#117	—	2	1	no	—
322	#117	—	2	1	no	—
323	#117	—	2	1	no	—
324	#117	—	2	1	no	—
325	#117	—	2	1	no	—
326	#117	—	2	1	no	—
327	#117	D₄×C₄₁	1	2	yes	—
328	#117	C₂³×C₄₁	1	2	yes	—
329	C₂×C₄⋊C₄	D₄×C₄₁	1	2	yes	—
330	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
331	C₂×C₂²⋊C₄	—	2	1	no	—
332	C₂×C₂²⋊C₄	—	2	1	no	—
333	C₂×C₄²	—	2	1	no	—
334	C₂×C₄²	—	2	1	no	—
335	#108	—	2	8	no	—
336	#107	—	2	4	no	—
337	#106	—	2	4	no	—
338	C₄⋊C₈	—	2	8	no	—
339	#103	—	2	4	no	—
340	#103	—	2	4	no	—
341	#102	—	2	4	no	—
342	#102	—	2	4	no	—
343	#101	—	2	4	no	—
344	#100	—	2	4	no	—
345	C₂⁴	—	2	1	no	—
346	C₂⁴	#41×C₄₁	1	1	yes	characteristic
347	#41	—	2	4	no	—
348	#41	—	2	4	no	—
349	#41	—	2	4	no	—
350	#41	—	2	4	no	—
351	#41	—	4	2	no	—
352	#41	—	4	2	no	—
353	#41	—	4	2	no	—
354	#41	—	4	2	no	—
355	C₂×Q₈	—	2	1	no	—
356	C₂×Q₈	—	2	1	no	—
357	C₂×Q₈	—	2	1	no	—
358	C₂×Q₈	—	2	1	no	—
359	C₂×Q₈	—	2	1	no	—
360	C₂×Q₈	C₂×Q₈×C₄₁	1	2	yes	—
361	C₂×D₄	—	2	4	no	—
362	C₂×D₄	—	2	1	no	—
363	C₂×D₄	—	2	1	no	—
364	C₂×D₄	—	2	1	no	—
365	C₂×D₄	—	2	1	no	—
366	C₂×D₄	—	2	1	no	—
367	C₂×D₄	—	4	1	no	—
368	C₂×D₄	—	4	1	no	—
369	C₂×D₄	—	4	2	no	—
370	C₂×D₄	C₂×Q₈×C₄₁	1	2	yes	—
371	C₂²×C₄	—	2	2	no	—
372	C₂²×C₄	—	2	1	no	—
373	C₂²×C₄	—	2	4	no	—
374	C₂²×C₄	—	2	2	no	—
375	C₂²×C₄	—	4	1	no	—
376	C₂²×C₄	—	4	1	no	—
377	C₂²×C₄	—	4	2	no	—
378	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
379	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
380	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
381	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
382	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
383	C₂²×C₄	C₂×Q₈×C₄₁	1	2	yes	—
384	C₂²×C₄	#41×C₄₁	1	1	yes	characteristic
385	C₂²×C₄	#41×C₄₁	1	2	yes	—
386	C₂²×C₄	#41×C₄₁	1	2	yes	—
387	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
388	M₁₆	—	2	4	no	—
389	M₁₆	—	2	2	no	—
390	M₁₆	—	2	2	no	—
391	M₁₆	—	2	2	no	—
392	M₁₆	—	2	2	no	—
393	M₁₆	—	2	2	no	—
394	M₁₆	—	4	2	no	—
395	M₁₆	—	4	2	no	—
396	M₁₆	C₂×D₄×C₄₁	1	4	yes	—
397	C₂×C₈	—	2	4	no	—
398	C₂×C₈	—	2	4	no	—
399	C₂×C₈	—	2	4	no	—
400	C₂×C₈	—	2	2	no	—
401	C₂×C₈	—	2	2	no	—
402	C₂×C₈	—	2	2	no	—
403	C₂×C₈	—	2	2	no	—
404	C₂×C₈	—	2	2	no	—
405	C₂×C₈	—	4	2	no	—
406	C₂×C₈	—	4	2	no	—
407	C₂×C₈	C₂×D₄×C₄₁	1	4	yes	—
408	C₄⋊C₄	—	2	2	no	—
409	C₄⋊C₄	—	2	2	no	—
410	C₄⋊C₄	—	2	2	no	—
411	C₄⋊C₄	C₂×D₄×C₄₁	1	4	yes	—
412	C₂²⋊C₄	—	2	2	no	—
413	C₂²⋊C₄	—	2	2	no	—
414	C₂²⋊C₄	—	4	1	no	—
415	C₂²⋊C₄	—	4	1	no	—
416	C₄²	—	2	2	no	—
417	C₄²	—	2	2	no	—
418	C₄²	—	4	1	no	—
419	C₄²	—	4	1	no	—
420	C₂³	—	2	2	no	—
421	C₂³	—	4	2	no	—
422	C₂³	—	4	1	no	—
423	C₂³	—	4	1	no	—
424	C₂³	—	8	2	no	—
425	C₂³	#121×C₄₁	1	1	yes	characteristic
426	C₂³	#121×C₄₁	1	1	yes	characteristic
427	C₂³	C₂²⋊Q₈×C₄₁	1	2	yes	—
428	C₂³	#126×C₄₁	1	2	yes	—
429	C₂³	C₂×#41×C₄₁	1	1	yes	characteristic
430	Q₈	—	2	2	no	—
431	Q₈	—	2	2	no	—
432	Q₈	—	4	1	no	—
433	Q₈	—	4	1	no	—
434	D₄	—	2	2	no	—
435	D₄	—	2	2	no	—
436	D₄	—	4	4	no	—
437	D₄	—	4	4	no	—
438	D₄	—	4	1	no	—
439	D₄	—	4	1	no	—
440	C₂×C₄	—	2	4	no	—
441	C₂×C₄	—	2	2	no	—
442	C₂×C₄	—	4	4	no	—
443	C₂×C₄	—	4	1	no	—
444	C₂×C₄	—	4	1	no	—
445	C₂×C₄	—	4	4	no	—
446	C₂×C₄	—	4	4	no	—
447	C₂×C₄	—	4	2	no	—
448	C₂×C₄	—	8	2	no	—
449	C₂×C₄	#121×C₄₁	1	2	yes	—
450	C₂×C₄	#121×C₄₁	1	2	yes	—
451	C₂×C₄	#121×C₄₁	1	2	yes	—
452	C₂×C₄	#121×C₄₁	1	2	yes	—
453	C₂×C₄	#121×C₄₁	1	1	yes	characteristic
454	C₂×C₄	#121×C₄₁	1	1	yes	characteristic
455	C₂×C₄	C₂²⋊Q₈×C₄₁	1	2	yes	—
456	C₂×C₄	C₂²⋊Q₈×C₄₁	1	2	yes	—
457	C₂×C₄	C₂²⋊Q₈×C₄₁	1	2	yes	—
458	C₂×C₄	C₂²⋊Q₈×C₄₁	1	2	yes	—
459	C₂×C₄	C₂²⋊Q₈×C₄₁	1	2	yes	—
460	C₂×C₄	#126×C₄₁	1	2	yes	—
461	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
462	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
463	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
464	C₂×C₄	C₂²×Q₈×C₄₁	1	1	yes	characteristic
465	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
466	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
467	C₈	—	2	4	no	—
468	C₈	—	2	4	no	—
469	C₈	—	4	2	no	—
470	C₈	—	4	2	no	—
471	C₂²	—	2	2	no	—
472	C₂²	—	2	2	no	—
473	C₂²	—	2	2	no	—
474	C₂²	—	4	2	no	—
475	C₂²	—	4	2	no	—
476	C₂²	—	4	2	no	—
477	C₂²	—	8	2	no	—
478	C₂²	—	8	2	no	—
479	C₂²	—	8	2	no	—
480	C₂²	C₄₁×#396	1	2	yes	—
481	C₂²	C₄₁×#396	1	2	yes	—
482	C₂²	C₂×#121×C₄₁	1	1	yes	characteristic
483	C₂²	C₂×C₂²⋊Q₈×C₄₁	1	1	yes	characteristic
484	C₂²	C₂×#126×C₄₁	1	1	yes	characteristic
485	C₄	—	4	4	no	—
486	C₄	—	4	2	no	—
487	C₄	—	8	2	no	—
488	C₄	C₄₁×#396	1	2	yes	—
489	C₄	C₄₁×#396	1	2	yes	—
490	C₄	C₂×#121×C₄₁	1	1	yes	characteristic
491	C₄	C₂×#121×C₄₁	1	1	yes	characteristic
492	C₄	C₂×C₂²⋊Q₈×C₄₁	1	1	yes	characteristic
493	C₄	C₂×C₂²⋊Q₈×C₄₁	1	1	yes	characteristic
494	C₂	—	2	1	no	—
495	C₂	—	2	1	no	—
496	C₂	—	2	2	no	—
497	C₂	—	2	2	no	—
498	C₂	—	8	2	no	—
499	C₂	C₂×C₄₁×#396	1	1	yes	characteristic
500	C₂	C₄₁×#3067	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₄₁	#121
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₁
socle	C₂²×C₄₁	C₂×#121
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
1. C₂²×#108×C₄₁	C₂	semidirect
2. C₄₁×#2911	C₂	semidirect
3. C₂×C₄₁×#424	C₂	semidirect
7. C₄₁×#2064	C₂	semidirect
8. C₄₁×#2063	C₂	semidirect
9. C₄₁×#1742	C₂	semidirect
220. #23601	C₄₁	direct (N × H)
244. C₂²×#108	C₂×C₄₁	semidirect
245. #2911	C₂×C₄₁	semidirect
246. C₂×#424	C₂×C₄₁	semidirect
250. #2064	C₂×C₄₁	semidirect
251. #2063	C₂×C₄₁	semidirect
252. #1742	C₂×C₄₁	semidirect
287. C₄₁	#23601	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×#108×C₄₁	2
C₄₁×#2911	2
C₂×C₄₁×#424	2
C₄₁×#2896	2
C₂×C₄₁×#416	2
C₂×C₄₁×#413	2
C₄₁×#2064	2
C₄₁×#2063	2
C₄₁×#1742	2
#23601	41

Subgroups — C41×#23601 #23799802

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#23601 #23799802