Subgroups — C₄₁×#22869 #23799070

Order 10496.

1058 conjugacy classes of subgroups.

The subgroup lattice has 702 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₁×#451	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄₁×#441	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄₁×#419	C₂	1	1	yes	maximal, characteristic
4	C₄₁×#2362	C₂	1	1	yes	maximal, characteristic
5	Q₈×C₂²⋊C₄×C₄₁	C₂	1	1	yes	maximal, characteristic
6	C₄₁×#1969	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₁×#1935	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄₁×#1927	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄₁×#1894	C₂	1	1	yes	maximal, characteristic
10	C₄₁×#1878	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₁×#1878	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄₁×#1863	C₂	1	1	yes	maximal, characteristic, complemented
13	C₄₁×#1854	C₂	1	1	yes	maximal, characteristic
14	C₄×#103×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄₁×#1753	C₂	1	1	yes	maximal, characteristic
16	C₂³×Q₈×C₄₁	C₂²	1	1	yes	characteristic
17	C₂²×Q₁₆×C₄₁	C₂²	1	1	yes	characteristic
18	C₂²×Q₁₆×C₄₁	C₂²	1	1	yes	characteristic
19	C₂²×M₁₆×C₄₁	C₂²	1	1	yes	characteristic
20	C₂×C₂²⋊Q₈×C₄₁	C₂²	1	1	yes	characteristic
21	C₂×C₄×Q₈×C₄₁	C₂²	1	1	yes	characteristic
22	C₂×C₄×Q₈×C₄₁	C₂²	1	1	yes	characteristic
23	C₂×C₄×Q₈×C₄₁	C₂²	1	1	yes	characteristic
24	C₂×#117×C₄₁	C₂²	1	1	yes	characteristic
25	C₄₁×#451	C₄	1	8	yes	complemented
26	C₄₁×#441	—	2	4	no	—
27	C₂×#107×C₄₁	C₂²	1	1	yes	characteristic
28	C₂×#106×C₄₁	C₂²	1	1	yes	characteristic
29	C₄₁×#419	—	2	4	no	—
30	C₂×#103×C₄₁	C₂²	1	1	yes	characteristic
31	C₂×#103×C₄₁	C₂²	1	1	yes	characteristic
32	C₂×#103×C₄₁	C₂²	1	1	yes	characteristic
33	C₂×#103×C₄₁	C₂²	1	1	yes	characteristic
34	C₂×#103×C₄₁	C₂²	1	1	yes	characteristic
35	C₂×#103×C₄₁	C₂²	1	1	yes	characteristic
36	C₂×#103×C₄₁	C₂²	1	1	yes	characteristic
37	C₂×#103×C₄₁	C₂²	1	1	yes	characteristic
38	C₂×C₂²⋊C₈×C₄₁	C₂²	1	1	yes	characteristic
39	C₂×#97×C₄₁	C₂²	1	1	yes	characteristic
40	C₂×C₄×C₈×C₄₁	C₂²	1	1	yes	characteristic
41	C₄₁×#391	—	2	1	no	—
42	C₄₁×#391	—	2	1	no	—
43	C₄₁×#391	C₂²	1	1	yes	characteristic
44	C₄₁×#391	C₂²	1	1	yes	characteristic
45	C₄₁×#391	C₂²	1	1	yes	characteristic
46	C₄₁×#389	C₂²	1	1	yes	characteristic
47	C₄₁×#388	—	2	1	no	—
48	C₄₁×#388	—	2	1	no	—
49	C₄₁×#387	—	2	1	no	—
50	C₄₁×#380	—	2	1	no	—
51	C₄₁×#380	C₂²	1	1	yes	characteristic
52	C₄×C₄⋊C₄×C₄₁	—	2	1	no	—
53	C₄×C₄⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
54	C₄×C₂²⋊C₄×C₄₁	—	2	1	no	—
55	C₄×C₂²⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
56	C₄₁×#340	C₂²	1	1	yes	characteristic
57	C₄₁×#340	C₂²	1	1	yes	characteristic
58	C₄₁×#340	C₂²	1	1	yes	characteristic
59	C₄₁×#340	C₂²	1	1	yes	characteristic
60	C₄₁×#336	C₂²	1	1	yes	characteristic
61	C₄₁×#336	C₂²	1	1	yes	characteristic
62	C₂²×Q₈×C₄₁	—	2	1	no	—
63	C₂²×Q₈×C₄₁	—	2	2	no	—
64	C₂²×Q₈×C₄₁	—	2	2	no	—
65	C₂²×Q₈×C₄₁	—	2	2	no	—
66	C₂²×Q₈×C₄₁	—	4	1	no	—
67	C₂²×Q₈×C₄₁	—	4	1	no	—
68	C₂²×Q₈×C₄₁	C₂×C₄	1	4	yes	—
69	C₂²×Q₈×C₄₁	C₂³	1	1	yes	characteristic
70	C₂²×Q₈×C₄₁	C₂³	1	1	yes	characteristic
71	C₂²×Q₈×C₄₁	C₂³	1	1	yes	characteristic
72	C₂³×C₄×C₄₁	—	2	1	no	—
73	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
74	C₂×Q₁₆×C₄₁	—	2	2	no	—
75	C₂×Q₁₆×C₄₁	—	2	2	no	—
76	C₂×Q₁₆×C₄₁	—	4	1	no	—
77	C₂×Q₁₆×C₄₁	—	4	1	no	—
78	C₂×Q₁₆×C₄₁	C₂×C₄	1	4	yes	—
79	C₂×Q₁₆×C₄₁	C₂×C₄	1	4	yes	—
80	C₂×M₁₆×C₄₁	—	2	2	no	—
81	C₂×M₁₆×C₄₁	—	2	2	no	—
82	C₂×M₁₆×C₄₁	—	4	1	no	—
83	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
84	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
85	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
86	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
87	C₂²⋊Q₈×C₄₁	—	2	2	no	—
88	C₂²⋊Q₈×C₄₁	C₂×C₄	1	4	yes	—
89	C₄×Q₈×C₄₁	—	2	2	no	—
90	C₄×Q₈×C₄₁	—	2	2	no	—
91	C₄×Q₈×C₄₁	—	2	2	no	—
92	C₄×Q₈×C₄₁	—	4	1	no	—
93	C₄×Q₈×C₄₁	—	4	1	no	—
94	C₄×Q₈×C₄₁	—	4	1	no	—
95	#117×C₄₁	—	2	2	no	—
96	#117×C₄₁	—	4	1	no	—
97	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
98	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
99	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
100	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
101	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
102	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
103	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
104	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
105	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
106	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
107	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
108	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
109	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
110	C₂×C₂²⋊C₄×C₄₁	D₄	1	1	yes	characteristic
111	C₂×C₂²⋊C₄×C₄₁	D₄	1	1	yes	characteristic
112	C₂×C₄²×C₄₁	—	2	1	no	—
113	C₂×C₄²×C₄₁	—	2	1	no	—
114	C₂×C₄²×C₄₁	—	2	1	no	—
115	C₂×C₄²×C₄₁	—	2	1	no	—
116	C₂×C₄²×C₄₁	—	2	1	no	—
117	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
118	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
119	#107×C₄₁	—	4	1	no	—
120	#106×C₄₁	—	2	2	no	—
121	#103×C₄₁	—	2	2	no	—
122	#103×C₄₁	—	2	2	no	—
123	#103×C₄₁	—	2	2	no	—
124	#103×C₄₁	—	2	2	no	—
125	#103×C₄₁	—	4	1	no	—
126	#103×C₄₁	C₂×C₄	1	4	yes	—
127	#103×C₄₁	C₂×C₄	1	4	yes	—
128	#103×C₄₁	D₄	1	4	yes	—
129	C₂²⋊C₈×C₄₁	C₂×C₄	1	4	yes	—
130	#97×C₄₁	—	2	2	no	—
131	C₄×C₈×C₄₁	—	4	1	no	—
132	#95×C₄₁	—	2	1	no	—
133	#95×C₄₁	—	2	1	no	—
134	#95×C₄₁	—	2	1	no	—
135	#95×C₄₁	—	2	1	no	—
136	#95×C₄₁	—	2	1	no	—
137	#95×C₄₁	—	2	1	no	—
138	#95×C₄₁	—	2	1	no	—
139	#95×C₄₁	—	2	1	no	—
140	#95×C₄₁	—	2	1	no	—
141	#95×C₄₁	D₄	1	1	yes	characteristic
142	#95×C₄₁	D₄	1	1	yes	characteristic
143	C₂⁴×C₄₁	C₂×D₄	1	1	yes	characteristic
144	C₂×Q₈×C₄₁	—	2	4	no	—
145	C₂×Q₈×C₄₁	—	2	1	no	—
146	C₂×Q₈×C₄₁	—	2	1	no	—
147	C₂×Q₈×C₄₁	—	2	1	no	—
148	C₂×Q₈×C₄₁	—	2	1	no	—
149	C₂×Q₈×C₄₁	—	2	1	no	—
150	C₂×Q₈×C₄₁	—	2	8	no	—
151	C₂×Q₈×C₄₁	—	2	1	no	—
152	C₂×Q₈×C₄₁	—	2	1	no	—
153	C₂×Q₈×C₄₁	—	2	1	no	—
154	C₂×Q₈×C₄₁	—	2	1	no	—
155	C₂×Q₈×C₄₁	—	2	1	no	—
156	C₂×Q₈×C₄₁	—	2	1	no	—
157	C₂×Q₈×C₄₁	—	2	1	no	—
158	C₂×Q₈×C₄₁	—	2	1	no	—
159	C₂×Q₈×C₄₁	—	4	2	no	—
160	C₂×Q₈×C₄₁	—	4	2	no	—
161	C₂×Q₈×C₄₁	—	4	4	no	—
162	C₂×Q₈×C₄₁	—	4	4	no	—
163	C₂×Q₈×C₄₁	—	4	4	no	—
164	C₂×Q₈×C₄₁	C₂²×C₄	1	2	yes	—
165	C₂×Q₈×C₄₁	C₂²×C₄	1	2	yes	—
166	C₂×Q₈×C₄₁	C₂²×C₄	1	2	yes	—
167	C₂×Q₈×C₄₁	C₂×D₄	1	2	yes	—
168	C₂×Q₈×C₄₁	#41	1	2	yes	—
169	C₂²×C₄×C₄₁	—	2	1	no	—
170	C₂²×C₄×C₄₁	—	2	1	no	—
171	C₂²×C₄×C₄₁	—	2	1	no	—
172	C₂²×C₄×C₄₁	—	2	1	no	—
173	C₂²×C₄×C₄₁	—	2	1	no	—
174	C₂²×C₄×C₄₁	—	2	4	no	—
175	C₂²×C₄×C₄₁	—	2	1	no	—
176	C₂²×C₄×C₄₁	—	2	1	no	—
177	C₂²×C₄×C₄₁	—	2	1	no	—
178	C₂²×C₄×C₄₁	—	2	1	no	—
179	C₂²×C₄×C₄₁	—	2	1	no	—
180	C₂²×C₄×C₄₁	—	2	1	no	—
181	C₂²×C₄×C₄₁	—	2	1	no	—
182	C₂²×C₄×C₄₁	—	4	2	no	—
183	C₂²×C₄×C₄₁	—	4	2	no	—
184	C₂²×C₄×C₄₁	C₂²×C₄	1	2	yes	—
185	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
186	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
187	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
188	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
189	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
190	C₂²×C₄×C₄₁	#41	1	2	yes	—
191	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
192	Q₁₆×C₄₁	—	2	8	no	—
193	Q₁₆×C₄₁	—	4	4	no	—
194	M₁₆×C₄₁	—	4	4	no	—
195	C₂×C₈×C₄₁	—	2	1	no	—
196	C₂×C₈×C₄₁	—	2	1	no	—
197	C₂×C₈×C₄₁	—	2	1	no	—
198	C₂×C₈×C₄₁	—	2	1	no	—
199	C₂×C₈×C₄₁	—	2	1	no	—
200	C₂×C₈×C₄₁	—	2	1	no	—
201	C₂×C₈×C₄₁	—	2	1	no	—
202	C₂×C₈×C₄₁	—	2	1	no	—
203	C₂×C₈×C₄₁	—	2	1	no	—
204	C₂×C₈×C₄₁	C₂²×C₄	1	2	yes	—
205	C₂×C₈×C₄₁	C₂²×C₄	1	2	yes	—
206	C₂×C₈×C₄₁	C₂×D₄	1	2	yes	—
207	C₄⋊C₄×C₄₁	—	2	4	no	—
208	C₄⋊C₄×C₄₁	—	2	1	no	—
209	C₄⋊C₄×C₄₁	—	2	1	no	—
210	C₄⋊C₄×C₄₁	—	2	1	no	—
211	C₄⋊C₄×C₄₁	—	2	1	no	—
212	C₄⋊C₄×C₄₁	—	2	1	no	—
213	C₄⋊C₄×C₄₁	—	2	1	no	—
214	C₄⋊C₄×C₄₁	—	2	1	no	—
215	C₄⋊C₄×C₄₁	—	2	1	no	—
216	C₄⋊C₄×C₄₁	—	4	2	no	—
217	C₄⋊C₄×C₄₁	—	4	2	no	—
218	C₄⋊C₄×C₄₁	—	4	2	no	—
219	C₄⋊C₄×C₄₁	—	4	2	no	—
220	C₄⋊C₄×C₄₁	C₂²×C₄	1	2	yes	—
221	C₄⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
222	C₂²⋊C₄×C₄₁	—	2	4	no	—
223	C₂²⋊C₄×C₄₁	—	2	2	no	—
224	C₂²⋊C₄×C₄₁	—	4	1	no	—
225	C₂²⋊C₄×C₄₁	—	4	2	no	—
226	C₂²⋊C₄×C₄₁	—	4	2	no	—
227	C₄²×C₄₁	—	2	1	no	—
228	C₄²×C₄₁	—	2	1	no	—
229	C₄²×C₄₁	—	2	1	no	—
230	C₄²×C₄₁	—	2	1	no	—
231	C₄²×C₄₁	—	4	2	no	—
232	C₄²×C₄₁	—	4	2	no	—
233	C₄²×C₄₁	—	4	2	no	—
234	C₄²×C₄₁	—	4	2	no	—
235	C₄²×C₄₁	—	4	2	no	—
236	C₂³×C₄₁	—	2	1	no	—
237	C₂³×C₄₁	—	2	1	no	—
238	C₂³×C₄₁	—	2	1	no	—
239	C₂³×C₄₁	—	2	1	no	—
240	C₂³×C₄₁	—	2	1	no	—
241	C₂³×C₄₁	—	2	1	no	—
242	C₂³×C₄₁	C₄×D₄	1	2	yes	—
243	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
244	Q₈×C₄₁	—	2	2	no	—
245	Q₈×C₄₁	—	2	2	no	—
246	Q₈×C₄₁	—	2	2	no	—
247	Q₈×C₄₁	—	2	2	no	—
248	Q₈×C₄₁	—	2	2	no	—
249	Q₈×C₄₁	—	2	2	no	—
250	Q₈×C₄₁	—	2	2	no	—
251	Q₈×C₄₁	—	4	8	no	—
252	Q₈×C₄₁	—	4	1	no	—
253	Q₈×C₄₁	—	4	1	no	—
254	Q₈×C₄₁	—	4	1	no	—
255	Q₈×C₄₁	—	4	1	no	—
256	Q₈×C₄₁	C₄×D₄	1	4	yes	—
257	C₂×C₄×C₄₁	—	2	2	no	—
258	C₂×C₄×C₄₁	—	2	1	no	—
259	C₂×C₄×C₄₁	—	2	2	no	—
260	C₂×C₄×C₄₁	—	2	1	no	—
261	C₂×C₄×C₄₁	—	2	2	no	—
262	C₂×C₄×C₄₁	—	2	1	no	—
263	C₂×C₄×C₄₁	—	2	1	no	—
264	C₂×C₄×C₄₁	—	2	2	no	—
265	C₂×C₄×C₄₁	—	2	2	no	—
266	C₂×C₄×C₄₁	—	2	2	no	—
267	C₂×C₄×C₄₁	—	2	2	no	—
268	C₂×C₄×C₄₁	—	2	2	no	—
269	C₂×C₄×C₄₁	—	2	2	no	—
270	C₂×C₄×C₄₁	—	2	2	no	—
271	C₂×C₄×C₄₁	—	2	1	no	—
272	C₂×C₄×C₄₁	—	2	1	no	—
273	C₂×C₄×C₄₁	—	2	2	no	—
274	C₂×C₄×C₄₁	—	2	1	no	—
275	C₂×C₄×C₄₁	—	2	1	no	—
276	C₂×C₄×C₄₁	—	2	1	no	—
277	C₂×C₄×C₄₁	—	2	1	no	—
278	C₂×C₄×C₄₁	—	2	1	no	—
279	C₂×C₄×C₄₁	—	2	1	no	—
280	C₂×C₄×C₄₁	—	2	1	no	—
281	C₂×C₄×C₄₁	—	4	8	no	—
282	C₂×C₄×C₄₁	—	4	1	no	—
283	C₂×C₄×C₄₁	—	4	1	no	—
284	C₂×C₄×C₄₁	—	4	1	no	—
285	C₂×C₄×C₄₁	—	4	1	no	—
286	C₂×C₄×C₄₁	—	4	1	no	—
287	C₂×C₄×C₄₁	—	4	1	no	—
288	C₂×C₄×C₄₁	—	4	1	no	—
289	C₂×C₄×C₄₁	—	4	1	no	—
290	C₂×C₄×C₄₁	—	4	1	no	—
291	C₂×C₄×C₄₁	—	4	1	no	—
292	C₂×C₄×C₄₁	—	4	1	no	—
293	C₂×C₄×C₄₁	—	4	1	no	—
294	C₂×C₄×C₄₁	—	4	1	no	—
295	C₂×C₄×C₄₁	—	4	1	no	—
296	C₂×C₄×C₄₁	—	4	1	no	—
297	C₂×C₄×C₄₁	—	4	1	no	—
298	C₂×C₄×C₄₁	—	4	1	no	—
299	C₂×C₄×C₄₁	C₄×D₄	1	2	yes	—
300	C₂×C₄×C₄₁	#137	1	2	yes	—
301	C₂×C₄×C₄₁	C₂³×C₄	1	1	yes	characteristic
302	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
303	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
304	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
305	C₂×C₄×C₄₁	H(5,𝔽₂)	1	1	yes	characteristic
306	C₂×C₄×C₄₁	H(5,𝔽₂)	1	1	yes	characteristic
307	C₈×C₄₁	—	2	2	no	—
308	C₈×C₄₁	—	2	2	no	—
309	C₈×C₄₁	—	2	2	no	—
310	C₈×C₄₁	—	4	1	no	—
311	#22869	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
312	C₂²×C₄₁	—	2	2	no	—
313	C₂²×C₄₁	—	2	2	no	—
314	C₂²×C₄₁	—	2	2	no	—
315	C₂²×C₄₁	—	4	1	no	—
316	C₂²×C₄₁	—	4	1	no	—
317	C₂²×C₄₁	—	4	1	no	—
318	C₂²×C₄₁	—	4	1	no	—
319	C₂²×C₄₁	C₂×C₄×D₄	1	1	yes	characteristic
320	C₂²×C₄₁	D₄²	1	1	yes	characteristic
321	C₂²×C₄₁	#546	1	1	yes	characteristic
322	C₂²×C₄₁	C₂×#137	1	1	yes	characteristic
323	C₂²×C₄₁	#575	1	1	yes	characteristic
324	C₂²×C₄₁	#578	1	1	yes	characteristic
325	C₂²×C₄₁	#578	1	1	yes	characteristic
326	C₄×C₄₁	—	2	2	no	—
327	C₄×C₄₁	—	2	4	no	—
328	C₄×C₄₁	—	2	2	no	—
329	C₄×C₄₁	—	4	2	no	—
330	C₄×C₄₁	—	4	2	no	—
331	C₄×C₄₁	—	4	2	no	—
332	C₄×C₄₁	—	4	1	no	—
333	C₄×C₄₁	—	4	2	no	—
334	C₄×C₄₁	—	4	1	no	—
335	C₄×C₄₁	—	4	1	no	—
336	C₄×C₄₁	—	8	1	no	—
337	C₄×C₄₁	—	8	1	no	—
338	C₄×C₄₁	—	8	1	no	—
339	C₄×C₄₁	C₂×C₄×D₄	1	1	yes	characteristic
340	C₄×C₄₁	#518	1	1	yes	characteristic
341	C₄×C₄₁	#546	1	1	yes	characteristic
342	C₄×C₄₁	#551	1	1	yes	characteristic
343	C₂×#451	C₂×C₄₁	1	1	yes	characteristic
344	C₂×#441	C₂×C₄₁	1	1	yes	characteristic, complemented
345	C₂×#419	C₂×C₄₁	1	1	yes	characteristic
346	#2362	C₂×C₄₁	1	1	yes	characteristic
347	Q₈×C₂²⋊C₄	C₂×C₄₁	1	1	yes	characteristic
348	#1969	C₂×C₄₁	1	1	yes	characteristic, complemented
349	#1935	C₂×C₄₁	1	1	yes	characteristic, complemented
350	#1927	C₂×C₄₁	1	1	yes	characteristic, complemented
351	#1894	C₂×C₄₁	1	1	yes	characteristic
352	#1878	C₂×C₄₁	1	1	yes	characteristic, complemented
353	#1878	C₂×C₄₁	1	1	yes	characteristic, complemented
354	#1863	C₂×C₄₁	1	1	yes	characteristic, complemented
355	#1854	C₂×C₄₁	1	1	yes	characteristic
356	C₄×#103	C₂×C₄₁	1	1	yes	characteristic, complemented
357	#1753	C₂×C₄₁	1	1	yes	characteristic
358	C₂×C₄₁	—	4	2	no	—
359	C₂×C₄₁	#2358	1	1	yes	characteristic
360	C₂×C₄₁	C₄×#137	1	1	yes	characteristic
361	C₂×C₄₁	#2950	1	1	yes	characteristic
362	C₂×C₄₁	#3276	1	1	yes	characteristic
363	C₂×C₄₁	#3277	1	1	yes	characteristic
364	C₂×C₄₁	#3312	1	1	yes	characteristic
365	C₂×C₄₁	#3313	1	1	yes	characteristic
366	C₂³×Q₈	C₂²×C₄₁	1	1	yes	characteristic
367	C₂²×Q₁₆	C₂²×C₄₁	1	1	yes	characteristic
368	C₂²×Q₁₆	C₂²×C₄₁	1	1	yes	characteristic
369	C₂²×M₁₆	C₂²×C₄₁	1	1	yes	characteristic
370	C₂×C₂²⋊Q₈	C₂²×C₄₁	1	1	yes	characteristic
371	C₂×C₄×Q₈	C₂²×C₄₁	1	1	yes	characteristic
372	C₂×C₄×Q₈	C₂²×C₄₁	1	1	yes	characteristic
373	C₂×C₄×Q₈	C₂²×C₄₁	1	1	yes	characteristic
374	C₂×#117	C₂²×C₄₁	1	1	yes	characteristic
375	#451	C₄×C₄₁	1	8	yes	complemented
376	#441	—	2	4	no	—
377	C₂×#107	C₂²×C₄₁	1	1	yes	characteristic
378	C₂×#106	C₂²×C₄₁	1	1	yes	characteristic
379	#419	—	2	4	no	—
380	C₂×#103	C₂²×C₄₁	1	1	yes	characteristic
381	C₂×#103	C₂²×C₄₁	1	1	yes	characteristic
382	C₂×#103	C₂²×C₄₁	1	1	yes	characteristic
383	C₂×#103	C₂²×C₄₁	1	1	yes	characteristic
384	C₂×#103	C₂²×C₄₁	1	1	yes	characteristic
385	C₂×#103	C₂²×C₄₁	1	1	yes	characteristic
386	C₂×#103	C₂²×C₄₁	1	1	yes	characteristic
387	C₂×#103	C₂²×C₄₁	1	1	yes	characteristic
388	C₂×C₂²⋊C₈	C₂²×C₄₁	1	1	yes	characteristic
389	C₂×#97	C₂²×C₄₁	1	1	yes	characteristic
390	C₂×C₄×C₈	C₂²×C₄₁	1	1	yes	characteristic
391	#391	—	2	1	no	—
392	#391	—	2	1	no	—
393	#391	C₂²×C₄₁	1	1	yes	characteristic
394	#391	C₂²×C₄₁	1	1	yes	characteristic
395	#391	C₂²×C₄₁	1	1	yes	characteristic
396	#389	C₂²×C₄₁	1	1	yes	characteristic
397	#388	—	2	1	no	—
398	#388	—	2	1	no	—
399	#387	—	2	1	no	—
400	#380	—	2	1	no	—
401	#380	C₂²×C₄₁	1	1	yes	characteristic
402	C₄×C₄⋊C₄	—	2	1	no	—
403	C₄×C₄⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
404	C₄×C₂²⋊C₄	—	2	1	no	—
405	C₄×C₂²⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
406	#340	C₂²×C₄₁	1	1	yes	characteristic
407	#340	C₂²×C₄₁	1	1	yes	characteristic
408	#340	C₂²×C₄₁	1	1	yes	characteristic
409	#340	C₂²×C₄₁	1	1	yes	characteristic
410	#336	C₂²×C₄₁	1	1	yes	characteristic
411	#336	C₂²×C₄₁	1	1	yes	characteristic
412	C₄₁	#22869	1	1	yes	characteristic, direct product factor, Sylow
413	C₂²×Q₈	—	2	1	no	—
414	C₂²×Q₈	—	2	2	no	—
415	C₂²×Q₈	—	2	2	no	—
416	C₂²×Q₈	—	2	2	no	—
417	C₂²×Q₈	—	4	1	no	—
418	C₂²×Q₈	—	4	1	no	—
419	C₂²×Q₈	C₂×C₄×C₄₁	1	4	yes	—
420	C₂²×Q₈	C₂³×C₄₁	1	1	yes	characteristic
421	C₂²×Q₈	C₂³×C₄₁	1	1	yes	characteristic
422	C₂²×Q₈	C₂³×C₄₁	1	1	yes	characteristic
423	C₂³×C₄	—	2	1	no	—
424	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
425	C₂×Q₁₆	—	2	2	no	—
426	C₂×Q₁₆	—	2	2	no	—
427	C₂×Q₁₆	—	4	1	no	—
428	C₂×Q₁₆	—	4	1	no	—
429	C₂×Q₁₆	C₂×C₄×C₄₁	1	4	yes	—
430	C₂×Q₁₆	C₂×C₄×C₄₁	1	4	yes	—
431	C₂×M₁₆	—	2	2	no	—
432	C₂×M₁₆	—	2	2	no	—
433	C₂×M₁₆	—	4	1	no	—
434	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
435	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
436	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
437	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
438	C₂²⋊Q₈	—	2	2	no	—
439	C₂²⋊Q₈	C₂×C₄×C₄₁	1	4	yes	—
440	C₄×Q₈	—	2	2	no	—
441	C₄×Q₈	—	2	2	no	—
442	C₄×Q₈	—	2	2	no	—
443	C₄×Q₈	—	4	1	no	—
444	C₄×Q₈	—	4	1	no	—
445	C₄×Q₈	—	4	1	no	—
446	#117	—	2	2	no	—
447	#117	—	4	1	no	—
448	C₂×C₄⋊C₄	—	2	1	no	—
449	C₂×C₄⋊C₄	—	2	1	no	—
450	C₂×C₄⋊C₄	—	2	1	no	—
451	C₂×C₄⋊C₄	—	2	1	no	—
452	C₂×C₄⋊C₄	—	2	1	no	—
453	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
454	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
455	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
456	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
457	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
458	C₂×C₂²⋊C₄	—	2	1	no	—
459	C₂×C₂²⋊C₄	—	2	1	no	—
460	C₂×C₂²⋊C₄	—	2	1	no	—
461	C₂×C₂²⋊C₄	D₄×C₄₁	1	1	yes	characteristic
462	C₂×C₂²⋊C₄	D₄×C₄₁	1	1	yes	characteristic
463	C₂×C₄²	—	2	1	no	—
464	C₂×C₄²	—	2	1	no	—
465	C₂×C₄²	—	2	1	no	—
466	C₂×C₄²	—	2	1	no	—
467	C₂×C₄²	—	2	1	no	—
468	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
469	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
470	#107	—	4	1	no	—
471	#106	—	2	2	no	—
472	#103	—	2	2	no	—
473	#103	—	2	2	no	—
474	#103	—	2	2	no	—
475	#103	—	2	2	no	—
476	#103	—	4	1	no	—
477	#103	C₂×C₄×C₄₁	1	4	yes	—
478	#103	C₂×C₄×C₄₁	1	4	yes	—
479	#103	D₄×C₄₁	1	4	yes	—
480	C₂²⋊C₈	C₂×C₄×C₄₁	1	4	yes	—
481	#97	—	2	2	no	—
482	C₄×C₈	—	4	1	no	—
483	#95	—	2	1	no	—
484	#95	—	2	1	no	—
485	#95	—	2	1	no	—
486	#95	—	2	1	no	—
487	#95	—	2	1	no	—
488	#95	—	2	1	no	—
489	#95	—	2	1	no	—
490	#95	—	2	1	no	—
491	#95	—	2	1	no	—
492	#95	D₄×C₄₁	1	1	yes	characteristic
493	#95	D₄×C₄₁	1	1	yes	characteristic
494	C₂⁴	C₂×D₄×C₄₁	1	1	yes	characteristic
495	C₂×Q₈	—	2	4	no	—
496	C₂×Q₈	—	2	1	no	—
497	C₂×Q₈	—	2	1	no	—
498	C₂×Q₈	—	2	1	no	—
499	C₂×Q₈	—	2	1	no	—
500	C₂×Q₈	—	2	1	no	—
501	C₂×Q₈	—	2	8	no	—
502	C₂×Q₈	—	2	1	no	—
503	C₂×Q₈	—	2	1	no	—
504	C₂×Q₈	—	2	1	no	—
505	C₂×Q₈	—	2	1	no	—
506	C₂×Q₈	—	2	1	no	—
507	C₂×Q₈	—	2	1	no	—
508	C₂×Q₈	—	2	1	no	—
509	C₂×Q₈	—	2	1	no	—
510	C₂×Q₈	—	4	2	no	—
511	C₂×Q₈	—	4	2	no	—
512	C₂×Q₈	—	4	4	no	—
513	C₂×Q₈	—	4	4	no	—
514	C₂×Q₈	—	4	4	no	—
515	C₂×Q₈	C₂²×C₄×C₄₁	1	2	yes	—
516	C₂×Q₈	C₂²×C₄×C₄₁	1	2	yes	—
517	C₂×Q₈	C₂²×C₄×C₄₁	1	2	yes	—
518	C₂×Q₈	C₂×D₄×C₄₁	1	2	yes	—
519	C₂×Q₈	#41×C₄₁	1	2	yes	—
520	C₂²×C₄	—	2	1	no	—
521	C₂²×C₄	—	2	1	no	—
522	C₂²×C₄	—	2	1	no	—
523	C₂²×C₄	—	2	1	no	—
524	C₂²×C₄	—	2	1	no	—
525	C₂²×C₄	—	2	4	no	—
526	C₂²×C₄	—	2	1	no	—
527	C₂²×C₄	—	2	1	no	—
528	C₂²×C₄	—	2	1	no	—
529	C₂²×C₄	—	2	1	no	—
530	C₂²×C₄	—	2	1	no	—
531	C₂²×C₄	—	2	1	no	—
532	C₂²×C₄	—	2	1	no	—
533	C₂²×C₄	—	4	2	no	—
534	C₂²×C₄	—	4	2	no	—
535	C₂²×C₄	C₂²×C₄×C₄₁	1	2	yes	—
536	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
537	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
538	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
539	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
540	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
541	C₂²×C₄	#41×C₄₁	1	2	yes	—
542	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
543	Q₁₆	—	2	8	no	—
544	Q₁₆	—	4	4	no	—
545	M₁₆	—	4	4	no	—
546	C₂×C₈	—	2	1	no	—
547	C₂×C₈	—	2	1	no	—
548	C₂×C₈	—	2	1	no	—
549	C₂×C₈	—	2	1	no	—
550	C₂×C₈	—	2	1	no	—
551	C₂×C₈	—	2	1	no	—
552	C₂×C₈	—	2	1	no	—
553	C₂×C₈	—	2	1	no	—
554	C₂×C₈	—	2	1	no	—
555	C₂×C₈	C₂²×C₄×C₄₁	1	2	yes	—
556	C₂×C₈	C₂²×C₄×C₄₁	1	2	yes	—
557	C₂×C₈	C₂×D₄×C₄₁	1	2	yes	—
558	C₄⋊C₄	—	2	4	no	—
559	C₄⋊C₄	—	2	1	no	—
560	C₄⋊C₄	—	2	1	no	—
561	C₄⋊C₄	—	2	1	no	—
562	C₄⋊C₄	—	2	1	no	—
563	C₄⋊C₄	—	2	1	no	—
564	C₄⋊C₄	—	2	1	no	—
565	C₄⋊C₄	—	2	1	no	—
566	C₄⋊C₄	—	2	1	no	—
567	C₄⋊C₄	—	4	2	no	—
568	C₄⋊C₄	—	4	2	no	—
569	C₄⋊C₄	—	4	2	no	—
570	C₄⋊C₄	—	4	2	no	—
571	C₄⋊C₄	C₂²×C₄×C₄₁	1	2	yes	—
572	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
573	C₂²⋊C₄	—	2	4	no	—
574	C₂²⋊C₄	—	2	2	no	—
575	C₂²⋊C₄	—	4	1	no	—
576	C₂²⋊C₄	—	4	2	no	—
577	C₂²⋊C₄	—	4	2	no	—
578	C₄²	—	2	1	no	—
579	C₄²	—	2	1	no	—
580	C₄²	—	2	1	no	—
581	C₄²	—	2	1	no	—
582	C₄²	—	4	2	no	—
583	C₄²	—	4	2	no	—
584	C₄²	—	4	2	no	—
585	C₄²	—	4	2	no	—
586	C₄²	—	4	2	no	—
587	C₂³	—	2	1	no	—
588	C₂³	—	2	1	no	—
589	C₂³	—	2	1	no	—
590	C₂³	—	2	1	no	—
591	C₂³	—	2	1	no	—
592	C₂³	—	2	1	no	—
593	C₂³	C₄×D₄×C₄₁	1	2	yes	—
594	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
595	Q₈	—	2	2	no	—
596	Q₈	—	2	2	no	—
597	Q₈	—	2	2	no	—
598	Q₈	—	2	2	no	—
599	Q₈	—	2	2	no	—
600	Q₈	—	2	2	no	—
601	Q₈	—	2	2	no	—
602	Q₈	—	4	8	no	—
603	Q₈	—	4	1	no	—
604	Q₈	—	4	1	no	—
605	Q₈	—	4	1	no	—
606	Q₈	—	4	1	no	—
607	Q₈	C₄×D₄×C₄₁	1	4	yes	—
608	C₂×C₄	—	2	2	no	—
609	C₂×C₄	—	2	1	no	—
610	C₂×C₄	—	2	2	no	—
611	C₂×C₄	—	2	1	no	—
612	C₂×C₄	—	2	2	no	—
613	C₂×C₄	—	2	1	no	—
614	C₂×C₄	—	2	1	no	—
615	C₂×C₄	—	2	2	no	—
616	C₂×C₄	—	2	2	no	—
617	C₂×C₄	—	2	2	no	—
618	C₂×C₄	—	2	2	no	—
619	C₂×C₄	—	2	2	no	—
620	C₂×C₄	—	2	2	no	—
621	C₂×C₄	—	2	2	no	—
622	C₂×C₄	—	2	1	no	—
623	C₂×C₄	—	2	1	no	—
624	C₂×C₄	—	2	2	no	—
625	C₂×C₄	—	2	1	no	—
626	C₂×C₄	—	2	1	no	—
627	C₂×C₄	—	2	1	no	—
628	C₂×C₄	—	2	1	no	—
629	C₂×C₄	—	2	1	no	—
630	C₂×C₄	—	2	1	no	—
631	C₂×C₄	—	2	1	no	—
632	C₂×C₄	—	4	8	no	—
633	C₂×C₄	—	4	1	no	—
634	C₂×C₄	—	4	1	no	—
635	C₂×C₄	—	4	1	no	—
636	C₂×C₄	—	4	1	no	—
637	C₂×C₄	—	4	1	no	—
638	C₂×C₄	—	4	1	no	—
639	C₂×C₄	—	4	1	no	—
640	C₂×C₄	—	4	1	no	—
641	C₂×C₄	—	4	1	no	—
642	C₂×C₄	—	4	1	no	—
643	C₂×C₄	—	4	1	no	—
644	C₂×C₄	—	4	1	no	—
645	C₂×C₄	—	4	1	no	—
646	C₂×C₄	—	4	1	no	—
647	C₂×C₄	—	4	1	no	—
648	C₂×C₄	—	4	1	no	—
649	C₂×C₄	—	4	1	no	—
650	C₂×C₄	C₄×D₄×C₄₁	1	2	yes	—
651	C₂×C₄	#137×C₄₁	1	2	yes	—
652	C₂×C₄	C₂³×C₄×C₄₁	1	1	yes	characteristic
653	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
654	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
655	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
656	C₂×C₄	H(5,𝔽₂)×C₄₁	1	1	yes	characteristic
657	C₂×C₄	H(5,𝔽₂)×C₄₁	1	1	yes	characteristic
658	C₈	—	2	2	no	—
659	C₈	—	2	2	no	—
660	C₈	—	2	2	no	—
661	C₈	—	4	1	no	—
662	C₂²	—	2	2	no	—
663	C₂²	—	2	2	no	—
664	C₂²	—	2	2	no	—
665	C₂²	—	4	1	no	—
666	C₂²	—	4	1	no	—
667	C₂²	—	4	1	no	—
668	C₂²	—	4	1	no	—
669	C₂²	C₂×C₄×D₄×C₄₁	1	1	yes	characteristic
670	C₂²	D₄²×C₄₁	1	1	yes	characteristic
671	C₂²	C₄₁×#546	1	1	yes	characteristic
672	C₂²	C₂×#137×C₄₁	1	1	yes	characteristic
673	C₂²	C₄₁×#575	1	1	yes	characteristic
674	C₂²	C₄₁×#578	1	1	yes	characteristic
675	C₂²	C₄₁×#578	1	1	yes	characteristic
676	C₄	—	2	2	no	—
677	C₄	—	2	2	no	—
678	C₄	—	2	4	no	—
679	C₄	—	4	1	no	—
680	C₄	—	4	2	no	—
681	C₄	—	4	2	no	—
682	C₄	—	4	2	no	—
683	C₄	—	4	1	no	—
684	C₄	—	4	2	no	—
685	C₄	—	4	1	no	—
686	C₄	—	8	1	no	—
687	C₄	—	8	1	no	—
688	C₄	—	8	1	no	—
689	C₄	C₂×C₄×D₄×C₄₁	1	1	yes	characteristic
690	C₄	C₄₁×#518	1	1	yes	characteristic
691	C₄	C₄₁×#546	1	1	yes	characteristic
692	C₄	C₄₁×#551	1	1	yes	characteristic
693	C₂	—	4	2	no	—
694	C₂	C₄₁×#2358	1	1	yes	characteristic
695	C₂	C₄×#137×C₄₁	1	1	yes	characteristic
696	C₂	C₄₁×#2950	1	1	yes	characteristic
697	C₂	C₄₁×#3276	1	1	yes	characteristic
698	C₂	C₄₁×#3277	1	1	yes	characteristic
699	C₂	C₄₁×#3312	1	1	yes	characteristic
700	C₂	C₄₁×#3313	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
2. C₂×C₄₁×#441	C₂	semidirect
6. C₄₁×#1969	C₂	semidirect
7. C₄₁×#1935	C₂	semidirect
8. C₄₁×#1927	C₂	semidirect
10. C₄₁×#1878	C₂	semidirect
11. C₄₁×#1878	C₂	semidirect
12. C₄₁×#1863	C₂	semidirect
14. C₄×#103×C₄₁	C₂	semidirect
25. C₄₁×#451	C₄	semidirect
311. #22869	C₄₁	direct (N × H)
344. C₂×#441	C₂×C₄₁	semidirect
348. #1969	C₂×C₄₁	semidirect
349. #1935	C₂×C₄₁	semidirect
350. #1927	C₂×C₄₁	semidirect
352. #1878	C₂×C₄₁	semidirect
353. #1878	C₂×C₄₁	semidirect
354. #1863	C₂×C₄₁	semidirect
356. C₄×#103	C₂×C₄₁	semidirect
375. #451	C₄×C₄₁	semidirect
412. C₄₁	#22869	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₄₁×#451	2
C₂×C₄₁×#441	2
C₂×C₄₁×#419	2
C₄₁×#2362	2
Q₈×C₂²⋊C₄×C₄₁	2
C₄₁×#1969	2
C₄₁×#1935	2
C₄₁×#1927	2
C₄₁×#1894	2
C₄₁×#1878	2
C₄₁×#1863	2
C₄₁×#1854	2
C₄×#103×C₄₁	2
C₄₁×#1753	2
#22869	41

Subgroups — C41×#22869 #23799070

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#22869 #23799070