Subgroups — C₄₁×#21413 #23797614

Order 10496.

1070 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₁×#541	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄₁×#405	C₂	1	1	yes	maximal, characteristic
3	C₄₁×#2314	C₂	1	1	yes	maximal, characteristic
4	C₄₁×#1992	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₁×#1991	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄₁×#1960	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₁×#1956	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄₁×#1894	C₂	1	2	yes	maximal
9	C₄₁×#1892	C₂	1	2	yes	maximal
10	C₄₁×#1763	C₂	1	2	yes	maximal, complemented
11	C₄×#103×C₄₁	C₂	1	2	yes	maximal, complemented
12	C₂²×M₁₆×C₄₁	C₂²	1	1	yes	characteristic
13	C₂³×C₈×C₄₁	C₂²	1	1	yes	characteristic
14	C₄₁×#541	—	2	4	no	—
15	C₄₁×#541	C₄	1	8	yes	complemented
16	C₂×C₄⋊Q₈×C₄₁	C₂²	1	1	yes	characteristic
17	C₂×#126×C₄₁	—	2	2	no	—
18	C₂×#125×C₄₁	—	2	2	no	—
19	C₂×#125×C₄₁	C₂²	1	1	yes	characteristic
20	C₂×C₂²⋊Q₈×C₄₁	C₂²	1	2	yes	—
21	C₂×C₄×Q₈×C₄₁	C₂²	1	2	yes	—
22	C₂×#117×C₄₁	C₂²	1	1	yes	characteristic
23	C₂×#103×C₄₁	C₂²	1	2	yes	—
24	C₂×#103×C₄₁	C₂²	1	2	yes	—
25	C₂×#103×C₄₁	C₂²	1	2	yes	—
26	C₂×#103×C₄₁	C₂²	1	2	yes	—
27	C₄₁×#405	—	2	4	no	—
28	C₂×#97×C₄₁	C₂²	1	1	yes	characteristic
29	C₂×#97×C₄₁	C₂²	1	1	yes	characteristic
30	C₂×C₄×C₈×C₄₁	C₂²	1	1	yes	characteristic
31	C₂×C₄×C₈×C₄₁	C₂²	1	1	yes	characteristic
32	C₄₁×#388	—	2	2	no	—
33	C₄₁×#387	—	2	2	no	—
34	C₄₁×#384	C₂²	1	1	yes	characteristic
35	C₄₁×#382	C₂²	1	1	yes	characteristic
36	C₄₁×#380	C₂²	1	2	yes	—
37	C₄×C₄⋊C₄×C₄₁	C₂²	1	2	yes	—
38	C₄₁×#340	C₂²	1	2	yes	—
39	C₄₁×#340	C₂²	1	2	yes	—
40	C₄₁×#340	C₂²	1	2	yes	—
41	C₄₁×#340	C₂²	1	2	yes	—
42	C₂²×Q₈×C₄₁	C₂³	1	2	yes	—
43	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
44	C₂×M₁₆×C₄₁	—	2	2	no	—
45	C₂×M₁₆×C₄₁	—	2	2	no	—
46	C₂×M₁₆×C₄₁	—	2	2	no	—
47	C₂²×C₈×C₄₁	—	2	2	no	—
48	C₂²×C₈×C₄₁	—	2	2	no	—
49	C₂²×C₈×C₄₁	—	2	2	no	—
50	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
51	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
52	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
53	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
54	C₄⋊Q₈×C₄₁	—	2	2	no	—
55	C₄⋊Q₈×C₄₁	C₂×C₄	1	4	yes	—
56	#126×C₄₁	—	2	16	no	—
57	#125×C₄₁	—	2	16	no	—
58	#125×C₄₁	—	2	2	no	—
59	#125×C₄₁	C₂×C₄	1	4	yes	—
60	C₂²⋊Q₈×C₄₁	—	2	4	no	—
61	C₂²⋊Q₈×C₄₁	C₂×C₄	1	8	yes	—
62	C₄×Q₈×C₄₁	—	2	4	no	—
63	C₄×Q₈×C₄₁	C₂×C₄	1	8	yes	—
64	#117×C₄₁	C₂×C₄	1	4	yes	—
65	#117×C₄₁	D₄	1	4	yes	—
66	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
67	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
68	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
69	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
70	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
71	C₂×C₄⋊C₄×C₄₁	D₄	1	2	yes	—
72	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
73	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
74	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
75	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
76	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
77	C₂×C₂²⋊C₄×C₄₁	D₄	1	2	yes	—
78	C₂×C₄²×C₄₁	—	2	2	no	—
79	C₂×C₄²×C₄₁	—	2	2	no	—
80	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
81	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
82	#103×C₄₁	—	2	4	no	—
83	#103×C₄₁	—	2	4	no	—
84	#103×C₄₁	—	2	4	no	—
85	#103×C₄₁	—	2	4	no	—
86	#97×C₄₁	—	2	2	no	—
87	#97×C₄₁	—	2	2	no	—
88	C₄×C₈×C₄₁	—	2	2	no	—
89	C₄×C₈×C₄₁	—	2	2	no	—
90	#95×C₄₁	—	2	2	no	—
91	#95×C₄₁	—	2	2	no	—
92	#95×C₄₁	—	2	2	no	—
93	C₂⁴×C₄₁	C₂×D₄	1	1	yes	characteristic
94	C₂×Q₈×C₄₁	—	2	2	no	—
95	C₂×Q₈×C₄₁	—	2	2	no	—
96	C₂×Q₈×C₄₁	—	2	2	no	—
97	C₂×Q₈×C₄₁	—	2	2	no	—
98	C₂×Q₈×C₄₁	—	2	2	no	—
99	C₂×Q₈×C₄₁	C₂²×C₄	1	4	yes	—
100	C₂²×C₄×C₄₁	—	2	1	no	—
101	C₂²×C₄×C₄₁	—	2	1	no	—
102	C₂²×C₄×C₄₁	—	2	1	no	—
103	C₂²×C₄×C₄₁	—	2	1	no	—
104	C₂²×C₄×C₄₁	—	2	2	no	—
105	C₂²×C₄×C₄₁	—	2	2	no	—
106	C₂²×C₄×C₄₁	—	2	2	no	—
107	C₂²×C₄×C₄₁	—	2	2	no	—
108	C₂²×C₄×C₄₁	C₂²×C₄	1	2	yes	—
109	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
110	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
111	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
112	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
113	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
114	M₁₆×C₄₁	—	2	8	no	—
115	C₂×C₈×C₄₁	—	2	8	no	—
116	C₂×C₈×C₄₁	—	2	1	no	—
117	C₂×C₈×C₄₁	—	2	1	no	—
118	C₂×C₈×C₄₁	—	2	1	no	—
119	C₂×C₈×C₄₁	—	2	1	no	—
120	C₂×C₈×C₄₁	—	2	1	no	—
121	C₂×C₈×C₄₁	—	2	1	no	—
122	C₂×C₈×C₄₁	—	2	1	no	—
123	C₂×C₈×C₄₁	—	2	1	no	—
124	C₂×C₈×C₄₁	#41	1	2	yes	—
125	C₂×C₈×C₄₁	#41	1	2	yes	—
126	C₂×C₈×C₄₁	#41	1	2	yes	—
127	C₂×C₈×C₄₁	#41	1	2	yes	—
128	C₄⋊C₄×C₄₁	—	2	8	no	—
129	C₄⋊C₄×C₄₁	—	2	8	no	—
130	C₄⋊C₄×C₄₁	—	2	8	no	—
131	C₄⋊C₄×C₄₁	—	2	8	no	—
132	C₄⋊C₄×C₄₁	—	2	2	no	—
133	C₄⋊C₄×C₄₁	—	2	2	no	—
134	C₄⋊C₄×C₄₁	—	2	2	no	—
135	C₄⋊C₄×C₄₁	—	2	2	no	—
136	C₄⋊C₄×C₄₁	—	2	2	no	—
137	C₄⋊C₄×C₄₁	—	8	2	no	—
138	C₄⋊C₄×C₄₁	C₂²⋊C₄	1	8	yes	—
139	C₄⋊C₄×C₄₁	C₂²×C₄	1	4	yes	—
140	C₂²⋊C₄×C₄₁	—	2	8	no	—
141	C₂²⋊C₄×C₄₁	—	8	2	no	—
142	C₂²⋊C₄×C₄₁	C₂²⋊C₄	1	8	yes	—
143	C₄²×C₄₁	—	2	8	no	—
144	C₄²×C₄₁	—	8	2	no	—
145	C₄²×C₄₁	C₂²×C₄	1	2	yes	—
146	C₄²×C₄₁	C₂²×C₄	1	2	yes	—
147	C₄²×C₄₁	C₂×D₄	1	2	yes	—
148	C₄²×C₄₁	C₂×D₄	1	2	yes	—
149	C₂³×C₄₁	—	2	1	no	—
150	C₂³×C₄₁	—	2	1	no	—
151	C₂³×C₄₁	—	2	2	no	—
152	C₂³×C₄₁	—	2	2	no	—
153	C₂³×C₄₁	C₂×C₂²⋊C₄	1	2	yes	—
154	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
155	Q₈×C₄₁	—	2	4	no	—
156	Q₈×C₄₁	—	2	4	no	—
157	Q₈×C₄₁	—	4	2	no	—
158	Q₈×C₄₁	—	4	2	no	—
159	C₂×C₄×C₄₁	—	2	1	no	—
160	C₂×C₄×C₄₁	—	2	1	no	—
161	C₂×C₄×C₄₁	—	2	2	no	—
162	C₂×C₄×C₄₁	—	2	2	no	—
163	C₂×C₄×C₄₁	—	2	2	no	—
164	C₂×C₄×C₄₁	—	2	2	no	—
165	C₂×C₄×C₄₁	—	2	2	no	—
166	C₂×C₄×C₄₁	—	2	2	no	—
167	C₂×C₄×C₄₁	—	2	2	no	—
168	C₂×C₄×C₄₁	—	2	2	no	—
169	C₂×C₄×C₄₁	—	2	4	no	—
170	C₂×C₄×C₄₁	—	2	4	no	—
171	C₂×C₄×C₄₁	—	4	2	no	—
172	C₂×C₄×C₄₁	—	4	2	no	—
173	C₂×C₄×C₄₁	—	4	2	no	—
174	C₂×C₄×C₄₁	—	4	2	no	—
175	C₂×C₄×C₄₁	—	4	2	no	—
176	C₂×C₄×C₄₁	—	4	2	no	—
177	C₂×C₄×C₄₁	—	4	2	no	—
178	C₂×C₄×C₄₁	—	4	2	no	—
179	C₂×C₄×C₄₁	—	4	2	no	—
180	C₂×C₄×C₄₁	—	4	2	no	—
181	C₂×C₄×C₄₁	C₂×C₂²⋊C₄	1	4	yes	—
182	C₂×C₄×C₄₁	C₂×C₂²⋊C₄	1	4	yes	—
183	C₂×C₄×C₄₁	C₂×C₂²⋊C₄	1	2	yes	—
184	C₂×C₄×C₄₁	C₂³×C₄	1	1	yes	characteristic
185	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
186	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
187	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
188	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
189	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
190	C₈×C₄₁	—	2	2	no	—
191	C₈×C₄₁	—	2	2	no	—
192	C₈×C₄₁	—	2	2	no	—
193	C₈×C₄₁	—	2	2	no	—
194	#21413	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
195	C₂²×C₄₁	—	2	4	no	—
196	C₂²×C₄₁	—	2	2	no	—
197	C₂²×C₄₁	—	4	1	no	—
198	C₂²×C₄₁	—	4	1	no	—
199	C₂²×C₄₁	—	4	2	no	—
200	C₂²×C₄₁	C₂²×C₂²⋊C₄	1	1	yes	characteristic
201	C₂²×C₄₁	#532	1	1	yes	characteristic
202	C₂²×C₄₁	#532	1	1	yes	characteristic
203	C₂²×C₄₁	#577	1	2	yes	—
204	C₂²×C₄₁	#578	1	2	yes	—
205	C₄×C₄₁	—	2	4	no	—
206	C₄×C₄₁	—	2	4	no	—
207	C₄×C₄₁	—	2	2	no	—
208	C₄×C₄₁	—	4	4	no	—
209	C₄×C₄₁	—	4	4	no	—
210	C₄×C₄₁	—	8	2	no	—
211	C₄×C₄₁	—	8	2	no	—
212	C₄×C₄₁	C₄×#41	1	1	yes	characteristic
213	C₄×C₄₁	C₄×#41	1	1	yes	characteristic
214	C₄×C₄₁	#525	1	1	yes	characteristic
215	C₄×C₄₁	#525	1	1	yes	characteristic
216	C₂×#541	C₂×C₄₁	1	1	yes	characteristic
217	C₂×#405	C₂×C₄₁	1	1	yes	characteristic
218	#2314	C₂×C₄₁	1	1	yes	characteristic
219	#1992	C₂×C₄₁	1	1	yes	characteristic, complemented
220	#1991	C₂×C₄₁	1	1	yes	characteristic, complemented
221	#1960	C₂×C₄₁	1	1	yes	characteristic, complemented
222	#1956	C₂×C₄₁	1	1	yes	characteristic, complemented
223	#1894	C₂×C₄₁	1	2	yes	—
224	#1892	C₂×C₄₁	1	2	yes	—
225	#1763	C₂×C₄₁	1	2	yes	complemented
226	C₄×#103	C₂×C₄₁	1	2	yes	complemented
227	C₂×C₄₁	—	4	2	no	—
228	C₂×C₄₁	#2297	1	1	yes	characteristic
229	C₂×C₄₁	#2898	1	2	yes	—
230	C₂×C₄₁	#3174	1	1	yes	characteristic
231	C₂×C₄₁	#3177	1	1	yes	characteristic
232	C₂×C₄₁	#3178	1	2	yes	—
233	C₂²×M₁₆	C₂²×C₄₁	1	1	yes	characteristic
234	C₂³×C₈	C₂²×C₄₁	1	1	yes	characteristic
235	#541	—	2	4	no	—
236	#541	C₄×C₄₁	1	8	yes	complemented
237	C₂×C₄⋊Q₈	C₂²×C₄₁	1	1	yes	characteristic
238	C₂×#126	—	2	2	no	—
239	C₂×#125	—	2	2	no	—
240	C₂×#125	C₂²×C₄₁	1	1	yes	characteristic
241	C₂×C₂²⋊Q₈	C₂²×C₄₁	1	2	yes	—
242	C₂×C₄×Q₈	C₂²×C₄₁	1	2	yes	—
243	C₂×#117	C₂²×C₄₁	1	1	yes	characteristic
244	C₂×#103	C₂²×C₄₁	1	2	yes	—
245	C₂×#103	C₂²×C₄₁	1	2	yes	—
246	C₂×#103	C₂²×C₄₁	1	2	yes	—
247	C₂×#103	C₂²×C₄₁	1	2	yes	—
248	#405	—	2	4	no	—
249	C₂×#97	C₂²×C₄₁	1	1	yes	characteristic
250	C₂×#97	C₂²×C₄₁	1	1	yes	characteristic
251	C₂×C₄×C₈	C₂²×C₄₁	1	1	yes	characteristic
252	C₂×C₄×C₈	C₂²×C₄₁	1	1	yes	characteristic
253	#388	—	2	2	no	—
254	#387	—	2	2	no	—
255	#384	C₂²×C₄₁	1	1	yes	characteristic
256	#382	C₂²×C₄₁	1	1	yes	characteristic
257	#380	C₂²×C₄₁	1	2	yes	—
258	C₄×C₄⋊C₄	C₂²×C₄₁	1	2	yes	—
259	#340	C₂²×C₄₁	1	2	yes	—
260	#340	C₂²×C₄₁	1	2	yes	—
261	#340	C₂²×C₄₁	1	2	yes	—
262	#340	C₂²×C₄₁	1	2	yes	—
263	C₄₁	#21413	1	1	yes	characteristic, direct product factor, Sylow
264	C₂²×Q₈	C₂³×C₄₁	1	2	yes	—
265	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
266	C₂×M₁₆	—	2	2	no	—
267	C₂×M₁₆	—	2	2	no	—
268	C₂×M₁₆	—	2	2	no	—
269	C₂²×C₈	—	2	2	no	—
270	C₂²×C₈	—	2	2	no	—
271	C₂²×C₈	—	2	2	no	—
272	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
273	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
274	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
275	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
276	C₄⋊Q₈	—	2	2	no	—
277	C₄⋊Q₈	C₂×C₄×C₄₁	1	4	yes	—
278	#126	—	2	16	no	—
279	#125	—	2	16	no	—
280	#125	—	2	2	no	—
281	#125	C₂×C₄×C₄₁	1	4	yes	—
282	C₂²⋊Q₈	—	2	4	no	—
283	C₂²⋊Q₈	C₂×C₄×C₄₁	1	8	yes	—
284	C₄×Q₈	—	2	4	no	—
285	C₄×Q₈	C₂×C₄×C₄₁	1	8	yes	—
286	#117	C₂×C₄×C₄₁	1	4	yes	—
287	#117	D₄×C₄₁	1	4	yes	—
288	C₂×C₄⋊C₄	—	2	2	no	—
289	C₂×C₄⋊C₄	—	2	2	no	—
290	C₂×C₄⋊C₄	—	2	2	no	—
291	C₂×C₄⋊C₄	—	2	2	no	—
292	C₂×C₄⋊C₄	—	2	2	no	—
293	C₂×C₄⋊C₄	D₄×C₄₁	1	2	yes	—
294	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
295	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
296	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
297	C₂×C₂²⋊C₄	—	2	2	no	—
298	C₂×C₂²⋊C₄	—	2	2	no	—
299	C₂×C₂²⋊C₄	D₄×C₄₁	1	2	yes	—
300	C₂×C₄²	—	2	2	no	—
301	C₂×C₄²	—	2	2	no	—
302	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
303	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
304	#103	—	2	4	no	—
305	#103	—	2	4	no	—
306	#103	—	2	4	no	—
307	#103	—	2	4	no	—
308	#97	—	2	2	no	—
309	#97	—	2	2	no	—
310	C₄×C₈	—	2	2	no	—
311	C₄×C₈	—	2	2	no	—
312	#95	—	2	2	no	—
313	#95	—	2	2	no	—
314	#95	—	2	2	no	—
315	C₂⁴	C₂×D₄×C₄₁	1	1	yes	characteristic
316	C₂×Q₈	—	2	2	no	—
317	C₂×Q₈	—	2	2	no	—
318	C₂×Q₈	—	2	2	no	—
319	C₂×Q₈	—	2	2	no	—
320	C₂×Q₈	—	2	2	no	—
321	C₂×Q₈	C₂²×C₄×C₄₁	1	4	yes	—
322	C₂²×C₄	—	2	1	no	—
323	C₂²×C₄	—	2	1	no	—
324	C₂²×C₄	—	2	1	no	—
325	C₂²×C₄	—	2	1	no	—
326	C₂²×C₄	—	2	2	no	—
327	C₂²×C₄	—	2	2	no	—
328	C₂²×C₄	—	2	2	no	—
329	C₂²×C₄	—	2	2	no	—
330	C₂²×C₄	C₂²×C₄×C₄₁	1	2	yes	—
331	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
332	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
333	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
334	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
335	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
336	M₁₆	—	2	8	no	—
337	C₂×C₈	—	2	8	no	—
338	C₂×C₈	—	2	1	no	—
339	C₂×C₈	—	2	1	no	—
340	C₂×C₈	—	2	1	no	—
341	C₂×C₈	—	2	1	no	—
342	C₂×C₈	—	2	1	no	—
343	C₂×C₈	—	2	1	no	—
344	C₂×C₈	—	2	1	no	—
345	C₂×C₈	—	2	1	no	—
346	C₂×C₈	#41×C₄₁	1	2	yes	—
347	C₂×C₈	#41×C₄₁	1	2	yes	—
348	C₂×C₈	#41×C₄₁	1	2	yes	—
349	C₂×C₈	#41×C₄₁	1	2	yes	—
350	C₄⋊C₄	—	2	8	no	—
351	C₄⋊C₄	—	2	8	no	—
352	C₄⋊C₄	—	2	8	no	—
353	C₄⋊C₄	—	2	8	no	—
354	C₄⋊C₄	—	2	2	no	—
355	C₄⋊C₄	—	2	2	no	—
356	C₄⋊C₄	—	2	2	no	—
357	C₄⋊C₄	—	2	2	no	—
358	C₄⋊C₄	—	2	2	no	—
359	C₄⋊C₄	—	8	2	no	—
360	C₄⋊C₄	C₂²⋊C₄×C₄₁	1	8	yes	—
361	C₄⋊C₄	C₂²×C₄×C₄₁	1	4	yes	—
362	C₂²⋊C₄	—	2	8	no	—
363	C₂²⋊C₄	—	8	2	no	—
364	C₂²⋊C₄	C₂²⋊C₄×C₄₁	1	8	yes	—
365	C₄²	—	2	8	no	—
366	C₄²	—	8	2	no	—
367	C₄²	C₂²×C₄×C₄₁	1	2	yes	—
368	C₄²	C₂²×C₄×C₄₁	1	2	yes	—
369	C₄²	C₂×D₄×C₄₁	1	2	yes	—
370	C₄²	C₂×D₄×C₄₁	1	2	yes	—
371	C₂³	—	2	1	no	—
372	C₂³	—	2	1	no	—
373	C₂³	—	2	2	no	—
374	C₂³	—	2	2	no	—
375	C₂³	C₂×C₂²⋊C₄×C₄₁	1	2	yes	—
376	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
377	Q₈	—	2	4	no	—
378	Q₈	—	2	4	no	—
379	Q₈	—	4	2	no	—
380	Q₈	—	4	2	no	—
381	C₂×C₄	—	2	1	no	—
382	C₂×C₄	—	2	1	no	—
383	C₂×C₄	—	2	2	no	—
384	C₂×C₄	—	2	2	no	—
385	C₂×C₄	—	2	2	no	—
386	C₂×C₄	—	2	2	no	—
387	C₂×C₄	—	2	2	no	—
388	C₂×C₄	—	2	2	no	—
389	C₂×C₄	—	2	2	no	—
390	C₂×C₄	—	2	2	no	—
391	C₂×C₄	—	2	4	no	—
392	C₂×C₄	—	2	4	no	—
393	C₂×C₄	—	4	2	no	—
394	C₂×C₄	—	4	2	no	—
395	C₂×C₄	—	4	2	no	—
396	C₂×C₄	—	4	2	no	—
397	C₂×C₄	—	4	2	no	—
398	C₂×C₄	—	4	2	no	—
399	C₂×C₄	—	4	2	no	—
400	C₂×C₄	—	4	2	no	—
401	C₂×C₄	—	4	2	no	—
402	C₂×C₄	—	4	2	no	—
403	C₂×C₄	C₂×C₂²⋊C₄×C₄₁	1	4	yes	—
404	C₂×C₄	C₂×C₂²⋊C₄×C₄₁	1	4	yes	—
405	C₂×C₄	C₂×C₂²⋊C₄×C₄₁	1	2	yes	—
406	C₂×C₄	C₂³×C₄×C₄₁	1	1	yes	characteristic
407	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
408	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
409	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
410	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
411	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
412	C₈	—	2	2	no	—
413	C₈	—	2	2	no	—
414	C₈	—	2	2	no	—
415	C₈	—	2	2	no	—
416	C₂²	—	2	2	no	—
417	C₂²	—	2	4	no	—
418	C₂²	—	4	1	no	—
419	C₂²	—	4	1	no	—
420	C₂²	—	4	2	no	—
421	C₂²	C₂²×C₂²⋊C₄×C₄₁	1	1	yes	characteristic
422	C₂²	C₄₁×#532	1	1	yes	characteristic
423	C₂²	C₄₁×#532	1	1	yes	characteristic
424	C₂²	C₄₁×#577	1	2	yes	—
425	C₂²	C₄₁×#578	1	2	yes	—
426	C₄	—	2	2	no	—
427	C₄	—	2	4	no	—
428	C₄	—	2	4	no	—
429	C₄	—	4	4	no	—
430	C₄	—	4	4	no	—
431	C₄	—	8	2	no	—
432	C₄	—	8	2	no	—
433	C₄	C₄×#41×C₄₁	1	1	yes	characteristic
434	C₄	C₄×#41×C₄₁	1	1	yes	characteristic
435	C₄	C₄₁×#525	1	1	yes	characteristic
436	C₄	C₄₁×#525	1	1	yes	characteristic
437	C₂	—	4	2	no	—
438	C₂	C₄₁×#2297	1	1	yes	characteristic
439	C₂	C₄₁×#2898	1	2	yes	—
440	C₂	C₄₁×#3174	1	1	yes	characteristic
441	C₂	C₄₁×#3177	1	1	yes	characteristic
442	C₂	C₄₁×#3178	1	2	yes	—

	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 ◁ C₂×#117×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₄₁×#1992	C₂	semidirect
5. C₄₁×#1991	C₂	semidirect
6. C₄₁×#1960	C₂	semidirect
7. C₄₁×#1956	C₂	semidirect
10. C₄₁×#1763	C₂	semidirect
11. C₄×#103×C₄₁	C₂	semidirect
15. C₄₁×#541	C₄	semidirect
194. #21413	C₄₁	direct (N × H)
219. #1992	C₂×C₄₁	semidirect
220. #1991	C₂×C₄₁	semidirect
221. #1960	C₂×C₄₁	semidirect
222. #1956	C₂×C₄₁	semidirect
225. #1763	C₂×C₄₁	semidirect
226. C₄×#103	C₂×C₄₁	semidirect
236. #541	C₄×C₄₁	semidirect
263. C₄₁	#21413	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×#541	2
C₂×C₄₁×#405	2
C₄₁×#2314	2
C₄₁×#1992	2
C₄₁×#1991	2
C₄₁×#1960	2
C₄₁×#1956	2
C₄₁×#1894	2
C₄₁×#1892	2
C₄₁×#1763	2
C₄×#103×C₄₁	2
#21413	41

Subgroups — C41×#21413 #23797614

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#21413 #23797614