Subgroups — C₄₁×#33046 #23809247

Order 10496.

830 conjugacy classes of subgroups.

The subgroup lattice has 472 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₁×#487	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄₁×#405	C₂	1	1	yes	maximal, characteristic
3	C₄₁×#2628	C₂	1	1	yes	maximal, characteristic
4	C₄₁×#2621	C₂	1	1	yes	maximal, characteristic
5	C₄₁×#1993	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄₁×#1960	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₁×#1935	C₂	1	2	yes	maximal, complemented
8	C₄₁×#1933	C₂	1	2	yes	maximal, complemented
9	C₄₁×#1894	C₂	1	2	yes	maximal
10	C₄₁×#1892	C₂	1	2	yes	maximal
11	C₄₁×#1835	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×M₁₆×C₄₁	C₂²	1	1	yes	characteristic
13	C₂³×C₈×C₄₁	C₂²	1	1	yes	characteristic
14	C₂×C₄⋊Q₈×C₄₁	C₂²	1	1	yes	characteristic
15	C₂×C₄⋊Q₈×C₄₁	C₂²	1	1	yes	characteristic
16	C₂×C₂²⋊Q₈×C₄₁	C₂²	1	2	yes	—
17	C₂×#117×C₄₁	C₂²	1	1	yes	characteristic
18	C₄₁×#487	—	2	4	no	—
19	C₂×#103×C₄₁	C₂²	1	2	yes	—
20	C₂×#103×C₄₁	C₂²	1	2	yes	—
21	C₂×#103×C₄₁	C₂²	1	2	yes	—
22	C₂×#103×C₄₁	C₂²	1	2	yes	—
23	C₄₁×#405	—	2	4	no	—
24	C₂×#97×C₄₁	C₂²	1	1	yes	characteristic
25	C₂×#97×C₄₁	C₂²	1	1	yes	characteristic
26	C₂×C₄×C₈×C₄₁	C₂²	1	1	yes	characteristic
27	C₂×C₄×C₈×C₄₁	C₂²	1	1	yes	characteristic
28	C₄₁×#400	—	2	1	no	—
29	C₄₁×#399	—	2	1	no	—
30	C₄₁×#398	—	2	1	no	—
31	C₄₁×#398	—	2	1	no	—
32	C₄₁×#397	—	2	1	no	—
33	C₄₁×#397	—	2	1	no	—
34	C₄₁×#395	—	2	1	no	—
35	C₄₁×#393	—	2	1	no	—
36	C₄₁×#391	C₂²	1	2	yes	—
37	C₄₁×#389	C₂²	1	2	yes	—
38	C₄₁×#382	C₂²	1	1	yes	characteristic
39	C₄₁×#382	C₂²	1	1	yes	characteristic
40	C₄₁×#380	C₂²	1	2	yes	—
41	C₄₁×#340	C₂²	1	2	yes	—
42	C₄₁×#340	C₂²	1	2	yes	—
43	C₄₁×#340	C₂²	1	2	yes	—
44	C₄₁×#340	C₂²	1	2	yes	—
45	C₂²×Q₈×C₄₁	—	2	1	no	—
46	C₂²×Q₈×C₄₁	C₂³	1	2	yes	—
47	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
48	C₂×M₁₆×C₄₁	—	2	2	no	—
49	C₂×M₁₆×C₄₁	—	2	2	no	—
50	C₂×M₁₆×C₄₁	—	2	2	no	—
51	C₂²×C₈×C₄₁	—	2	2	no	—
52	C₂²×C₈×C₄₁	—	2	2	no	—
53	C₂²×C₈×C₄₁	—	2	2	no	—
54	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
55	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
56	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
57	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
58	C₄⋊Q₈×C₄₁	—	2	2	no	—
59	C₄⋊Q₈×C₄₁	—	2	2	no	—
60	C₄⋊Q₈×C₄₁	—	2	2	no	—
61	C₄⋊Q₈×C₄₁	—	2	2	no	—
62	C₂²⋊Q₈×C₄₁	—	2	4	no	—
63	C₂²⋊Q₈×C₄₁	—	2	4	no	—
64	#117×C₄₁	—	2	2	no	—
65	#117×C₄₁	—	2	2	no	—
66	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
67	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
68	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
69	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
70	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
71	C₂×C₄⋊C₄×C₄₁	D₄	1	1	yes	characteristic
72	C₂×C₄⋊C₄×C₄₁	D₄	1	1	yes	characteristic
73	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
74	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
75	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
76	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
77	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
78	C₂×C₂²⋊C₄×C₄₁	D₄	1	1	yes	characteristic
79	C₂×C₂²⋊C₄×C₄₁	D₄	1	1	yes	characteristic
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	D₄	1	4	yes	—
90	#95×C₄₁	—	2	2	no	—
91	#95×C₄₁	—	2	1	no	—
92	#95×C₄₁	—	2	1	no	—
93	#95×C₄₁	—	2	1	no	—
94	#95×C₄₁	—	2	1	no	—
95	#95×C₄₁	—	2	2	no	—
96	#95×C₄₁	—	2	2	no	—
97	#95×C₄₁	—	2	2	no	—
98	C₂⁴×C₄₁	C₂×D₄	1	1	yes	characteristic
99	C₂×Q₈×C₄₁	—	2	2	no	—
100	C₂×Q₈×C₄₁	—	2	2	no	—
101	C₂×Q₈×C₄₁	—	2	2	no	—
102	C₂×Q₈×C₄₁	—	2	2	no	—
103	C₂×Q₈×C₄₁	—	2	2	no	—
104	C₂×Q₈×C₄₁	—	2	2	no	—
105	C₂×Q₈×C₄₁	—	4	2	no	—
106	C₂×Q₈×C₄₁	—	8	2	no	—
107	C₂²×C₄×C₄₁	—	2	1	no	—
108	C₂²×C₄×C₄₁	—	2	1	no	—
109	C₂²×C₄×C₄₁	—	2	1	no	—
110	C₂²×C₄×C₄₁	—	2	1	no	—
111	C₂²×C₄×C₄₁	—	2	2	no	—
112	C₂²×C₄×C₄₁	—	2	2	no	—
113	C₂²×C₄×C₄₁	—	2	2	no	—
114	C₂²×C₄×C₄₁	—	2	2	no	—
115	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
116	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
117	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
118	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
119	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
120	C₂²×C₄×C₄₁	#41	1	2	yes	—
121	C₂²×C₄×C₄₁	#41	1	2	yes	—
122	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
123	M₁₆×C₄₁	—	2	8	no	—
124	C₂×C₈×C₄₁	—	2	8	no	—
125	C₂×C₈×C₄₁	—	2	1	no	—
126	C₂×C₈×C₄₁	—	2	1	no	—
127	C₂×C₈×C₄₁	—	2	1	no	—
128	C₂×C₈×C₄₁	—	2	1	no	—
129	C₂×C₈×C₄₁	—	2	1	no	—
130	C₂×C₈×C₄₁	—	2	1	no	—
131	C₂×C₈×C₄₁	—	2	1	no	—
132	C₂×C₈×C₄₁	—	2	1	no	—
133	C₂×C₈×C₄₁	C₂×D₄	1	2	yes	—
134	C₂×C₈×C₄₁	C₂×D₄	1	2	yes	—
135	C₂×C₈×C₄₁	#41	1	2	yes	—
136	C₂×C₈×C₄₁	#41	1	2	yes	—
137	C₄⋊C₄×C₄₁	—	2	2	no	—
138	C₄⋊C₄×C₄₁	—	2	2	no	—
139	C₄⋊C₄×C₄₁	—	2	2	no	—
140	C₄⋊C₄×C₄₁	—	2	2	no	—
141	C₄⋊C₄×C₄₁	—	2	2	no	—
142	C₄⋊C₄×C₄₁	—	2	2	no	—
143	C₄⋊C₄×C₄₁	—	2	2	no	—
144	C₄⋊C₄×C₄₁	—	2	2	no	—
145	C₄⋊C₄×C₄₁	—	4	2	no	—
146	C₄⋊C₄×C₄₁	—	4	2	no	—
147	C₄⋊C₄×C₄₁	—	4	2	no	—
148	C₄⋊C₄×C₄₁	—	4	4	no	—
149	C₄⋊C₄×C₄₁	—	8	2	no	—
150	C₂²⋊C₄×C₄₁	—	2	2	no	—
151	C₂²⋊C₄×C₄₁	—	2	2	no	—
152	C₂²⋊C₄×C₄₁	—	4	4	no	—
153	C₂²⋊C₄×C₄₁	—	8	2	no	—
154	C₄²×C₄₁	—	2	1	no	—
155	C₄²×C₄₁	—	2	1	no	—
156	C₄²×C₄₁	C₂×D₄	1	2	yes	—
157	C₄²×C₄₁	#41	1	2	yes	—
158	C₂³×C₄₁	—	2	1	no	—
159	C₂³×C₄₁	—	2	1	no	—
160	C₂³×C₄₁	—	2	2	no	—
161	C₂³×C₄₁	—	2	2	no	—
162	C₂³×C₄₁	#124	1	2	yes	—
163	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
164	Q₈×C₄₁	—	4	2	no	—
165	Q₈×C₄₁	—	4	2	no	—
166	Q₈×C₄₁	—	4	2	no	—
167	Q₈×C₄₁	—	4	2	no	—
168	Q₈×C₄₁	—	8	4	no	—
169	C₂×C₄×C₄₁	—	2	1	no	—
170	C₂×C₄×C₄₁	—	2	1	no	—
171	C₂×C₄×C₄₁	—	2	2	no	—
172	C₂×C₄×C₄₁	—	2	2	no	—
173	C₂×C₄×C₄₁	—	2	2	no	—
174	C₂×C₄×C₄₁	—	2	2	no	—
175	C₂×C₄×C₄₁	—	2	2	no	—
176	C₂×C₄×C₄₁	—	2	2	no	—
177	C₂×C₄×C₄₁	—	2	1	no	—
178	C₂×C₄×C₄₁	—	2	1	no	—
179	C₂×C₄×C₄₁	—	2	2	no	—
180	C₂×C₄×C₄₁	—	2	2	no	—
181	C₂×C₄×C₄₁	—	4	2	no	—
182	C₂×C₄×C₄₁	—	4	2	no	—
183	C₂×C₄×C₄₁	—	4	2	no	—
184	C₂×C₄×C₄₁	—	4	2	no	—
185	C₂×C₄×C₄₁	—	4	2	no	—
186	C₂×C₄×C₄₁	—	4	2	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	2	no	—
191	C₂×C₄×C₄₁	—	4	2	no	—
192	C₂×C₄×C₄₁	—	4	2	no	—
193	C₂×C₄×C₄₁	#121	1	2	yes	—
194	C₂×C₄×C₄₁	#121	1	2	yes	—
195	C₂×C₄×C₄₁	#124	1	2	yes	—
196	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
197	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
198	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
199	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
200	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
201	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
202	C₈×C₄₁	—	2	2	no	—
203	C₈×C₄₁	—	2	2	no	—
204	C₈×C₄₁	—	2	2	no	—
205	C₈×C₄₁	—	2	2	no	—
206	#33046	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
207	C₂²×C₄₁	—	2	2	no	—
208	C₂²×C₄₁	—	2	4	no	—
209	C₂²×C₄₁	—	4	2	no	—
210	C₂²×C₄₁	—	4	1	no	—
211	C₂²×C₄₁	—	4	1	no	—
212	C₂²×C₄₁	C₂×#121	1	1	yes	characteristic
213	C₂²×C₄₁	C₂×#124	1	1	yes	characteristic
214	C₂²×C₄₁	#532	1	1	yes	characteristic
215	C₂²×C₄₁	#577	1	2	yes	—
216	C₂²×C₄₁	#578	1	2	yes	—
217	C₄×C₄₁	—	2	2	no	—
218	C₄×C₄₁	—	2	2	no	—
219	C₄×C₄₁	—	2	2	no	—
220	C₄×C₄₁	—	4	1	no	—
221	C₄×C₄₁	—	4	1	no	—
222	C₄×C₄₁	—	8	2	no	—
223	C₄×C₄₁	—	8	2	no	—
224	C₄×C₄₁	—	8	2	no	—
225	C₄×C₄₁	—	8	2	no	—
226	C₄×C₄₁	#525	1	1	yes	characteristic
227	C₄×C₄₁	#525	1	1	yes	characteristic
228	C₄×C₄₁	#529	1	1	yes	characteristic
229	C₄×C₄₁	#529	1	1	yes	characteristic
230	C₂×#487	C₂×C₄₁	1	1	yes	characteristic, complemented
231	C₂×#405	C₂×C₄₁	1	1	yes	characteristic
232	#2628	C₂×C₄₁	1	1	yes	characteristic
233	#2621	C₂×C₄₁	1	1	yes	characteristic
234	#1993	C₂×C₄₁	1	1	yes	characteristic, complemented
235	#1960	C₂×C₄₁	1	1	yes	characteristic, complemented
236	#1935	C₂×C₄₁	1	2	yes	complemented
237	#1933	C₂×C₄₁	1	2	yes	complemented
238	#1894	C₂×C₄₁	1	2	yes	—
239	#1892	C₂×C₄₁	1	2	yes	—
240	#1835	C₂×C₄₁	1	1	yes	characteristic, complemented
241	C₂×C₄₁	—	4	2	no	—
242	C₂×C₄₁	#2850	1	1	yes	characteristic
243	C₂×C₄₁	#3057	1	1	yes	characteristic
244	C₂×C₄₁	#3059	1	1	yes	characteristic
245	C₂×C₄₁	#3137	1	2	yes	—
246	C₂×C₄₁	#3178	1	2	yes	—
247	C₂²×M₁₆	C₂²×C₄₁	1	1	yes	characteristic
248	C₂³×C₈	C₂²×C₄₁	1	1	yes	characteristic
249	C₂×C₄⋊Q₈	C₂²×C₄₁	1	1	yes	characteristic
250	C₂×C₄⋊Q₈	C₂²×C₄₁	1	1	yes	characteristic
251	C₂×C₂²⋊Q₈	C₂²×C₄₁	1	2	yes	—
252	C₂×#117	C₂²×C₄₁	1	1	yes	characteristic
253	#487	—	2	4	no	—
254	C₂×#103	C₂²×C₄₁	1	2	yes	—
255	C₂×#103	C₂²×C₄₁	1	2	yes	—
256	C₂×#103	C₂²×C₄₁	1	2	yes	—
257	C₂×#103	C₂²×C₄₁	1	2	yes	—
258	#405	—	2	4	no	—
259	C₂×#97	C₂²×C₄₁	1	1	yes	characteristic
260	C₂×#97	C₂²×C₄₁	1	1	yes	characteristic
261	C₂×C₄×C₈	C₂²×C₄₁	1	1	yes	characteristic
262	C₂×C₄×C₈	C₂²×C₄₁	1	1	yes	characteristic
263	#400	—	2	1	no	—
264	#399	—	2	1	no	—
265	#398	—	2	1	no	—
266	#398	—	2	1	no	—
267	#397	—	2	1	no	—
268	#397	—	2	1	no	—
269	#395	—	2	1	no	—
270	#393	—	2	1	no	—
271	#391	C₂²×C₄₁	1	2	yes	—
272	#389	C₂²×C₄₁	1	2	yes	—
273	#382	C₂²×C₄₁	1	1	yes	characteristic
274	#382	C₂²×C₄₁	1	1	yes	characteristic
275	#380	C₂²×C₄₁	1	2	yes	—
276	#340	C₂²×C₄₁	1	2	yes	—
277	#340	C₂²×C₄₁	1	2	yes	—
278	#340	C₂²×C₄₁	1	2	yes	—
279	#340	C₂²×C₄₁	1	2	yes	—
280	C₄₁	#33046	1	1	yes	characteristic, direct product factor, Sylow
281	C₂²×Q₈	—	2	1	no	—
282	C₂²×Q₈	C₂³×C₄₁	1	2	yes	—
283	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
284	C₂×M₁₆	—	2	2	no	—
285	C₂×M₁₆	—	2	2	no	—
286	C₂×M₁₆	—	2	2	no	—
287	C₂²×C₈	—	2	2	no	—
288	C₂²×C₈	—	2	2	no	—
289	C₂²×C₈	—	2	2	no	—
290	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
291	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
292	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
293	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
294	C₄⋊Q₈	—	2	2	no	—
295	C₄⋊Q₈	—	2	2	no	—
296	C₄⋊Q₈	—	2	2	no	—
297	C₄⋊Q₈	—	2	2	no	—
298	C₂²⋊Q₈	—	2	4	no	—
299	C₂²⋊Q₈	—	2	4	no	—
300	#117	—	2	2	no	—
301	#117	—	2	2	no	—
302	C₂×C₄⋊C₄	—	2	2	no	—
303	C₂×C₄⋊C₄	—	2	1	no	—
304	C₂×C₄⋊C₄	—	2	1	no	—
305	C₂×C₄⋊C₄	—	2	1	no	—
306	C₂×C₄⋊C₄	—	2	2	no	—
307	C₂×C₄⋊C₄	D₄×C₄₁	1	1	yes	characteristic
308	C₂×C₄⋊C₄	D₄×C₄₁	1	1	yes	characteristic
309	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
310	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
311	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
312	C₂×C₂²⋊C₄	—	2	2	no	—
313	C₂×C₂²⋊C₄	—	2	2	no	—
314	C₂×C₂²⋊C₄	D₄×C₄₁	1	1	yes	characteristic
315	C₂×C₂²⋊C₄	D₄×C₄₁	1	1	yes	characteristic
316	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
317	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
318	#103	—	2	4	no	—
319	#103	—	2	4	no	—
320	#103	—	2	4	no	—
321	#103	—	2	4	no	—
322	#97	—	2	2	no	—
323	#97	—	2	2	no	—
324	C₄×C₈	—	2	2	no	—
325	C₄×C₈	D₄×C₄₁	1	4	yes	—
326	#95	—	2	2	no	—
327	#95	—	2	1	no	—
328	#95	—	2	1	no	—
329	#95	—	2	1	no	—
330	#95	—	2	1	no	—
331	#95	—	2	2	no	—
332	#95	—	2	2	no	—
333	#95	—	2	2	no	—
334	C₂⁴	C₂×D₄×C₄₁	1	1	yes	characteristic
335	C₂×Q₈	—	2	2	no	—
336	C₂×Q₈	—	2	2	no	—
337	C₂×Q₈	—	2	2	no	—
338	C₂×Q₈	—	2	2	no	—
339	C₂×Q₈	—	2	2	no	—
340	C₂×Q₈	—	2	2	no	—
341	C₂×Q₈	—	4	2	no	—
342	C₂×Q₈	—	8	2	no	—
343	C₂²×C₄	—	2	1	no	—
344	C₂²×C₄	—	2	1	no	—
345	C₂²×C₄	—	2	1	no	—
346	C₂²×C₄	—	2	1	no	—
347	C₂²×C₄	—	2	2	no	—
348	C₂²×C₄	—	2	2	no	—
349	C₂²×C₄	—	2	2	no	—
350	C₂²×C₄	—	2	2	no	—
351	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
352	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
353	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
354	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
355	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
356	C₂²×C₄	#41×C₄₁	1	2	yes	—
357	C₂²×C₄	#41×C₄₁	1	2	yes	—
358	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
359	M₁₆	—	2	8	no	—
360	C₂×C₈	—	2	8	no	—
361	C₂×C₈	—	2	1	no	—
362	C₂×C₈	—	2	1	no	—
363	C₂×C₈	—	2	1	no	—
364	C₂×C₈	—	2	1	no	—
365	C₂×C₈	—	2	1	no	—
366	C₂×C₈	—	2	1	no	—
367	C₂×C₈	—	2	1	no	—
368	C₂×C₈	—	2	1	no	—
369	C₂×C₈	C₂×D₄×C₄₁	1	2	yes	—
370	C₂×C₈	C₂×D₄×C₄₁	1	2	yes	—
371	C₂×C₈	#41×C₄₁	1	2	yes	—
372	C₂×C₈	#41×C₄₁	1	2	yes	—
373	C₄⋊C₄	—	2	2	no	—
374	C₄⋊C₄	—	2	2	no	—
375	C₄⋊C₄	—	2	2	no	—
376	C₄⋊C₄	—	2	2	no	—
377	C₄⋊C₄	—	2	2	no	—
378	C₄⋊C₄	—	2	2	no	—
379	C₄⋊C₄	—	2	2	no	—
380	C₄⋊C₄	—	2	2	no	—
381	C₄⋊C₄	—	4	2	no	—
382	C₄⋊C₄	—	4	2	no	—
383	C₄⋊C₄	—	4	2	no	—
384	C₄⋊C₄	—	4	4	no	—
385	C₄⋊C₄	—	8	2	no	—
386	C₂²⋊C₄	—	2	2	no	—
387	C₂²⋊C₄	—	2	2	no	—
388	C₂²⋊C₄	—	4	4	no	—
389	C₂²⋊C₄	—	8	2	no	—
390	C₄²	—	2	1	no	—
391	C₄²	—	2	1	no	—
392	C₄²	C₂×D₄×C₄₁	1	2	yes	—
393	C₄²	#41×C₄₁	1	2	yes	—
394	C₂³	—	2	1	no	—
395	C₂³	—	2	1	no	—
396	C₂³	—	2	2	no	—
397	C₂³	—	2	2	no	—
398	C₂³	#124×C₄₁	1	2	yes	—
399	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
400	Q₈	—	4	2	no	—
401	Q₈	—	4	2	no	—
402	Q₈	—	4	2	no	—
403	Q₈	—	4	2	no	—
404	Q₈	—	8	4	no	—
405	C₂×C₄	—	2	1	no	—
406	C₂×C₄	—	2	1	no	—
407	C₂×C₄	—	2	2	no	—
408	C₂×C₄	—	2	2	no	—
409	C₂×C₄	—	2	2	no	—
410	C₂×C₄	—	2	2	no	—
411	C₂×C₄	—	2	2	no	—
412	C₂×C₄	—	2	2	no	—
413	C₂×C₄	—	2	1	no	—
414	C₂×C₄	—	2	1	no	—
415	C₂×C₄	—	2	2	no	—
416	C₂×C₄	—	2	2	no	—
417	C₂×C₄	—	4	2	no	—
418	C₂×C₄	—	4	2	no	—
419	C₂×C₄	—	4	2	no	—
420	C₂×C₄	—	4	2	no	—
421	C₂×C₄	—	4	2	no	—
422	C₂×C₄	—	4	2	no	—
423	C₂×C₄	—	4	2	no	—
424	C₂×C₄	—	4	2	no	—
425	C₂×C₄	—	4	2	no	—
426	C₂×C₄	—	4	2	no	—
427	C₂×C₄	—	4	2	no	—
428	C₂×C₄	—	4	2	no	—
429	C₂×C₄	#121×C₄₁	1	2	yes	—
430	C₂×C₄	#121×C₄₁	1	2	yes	—
431	C₂×C₄	#124×C₄₁	1	2	yes	—
432	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
433	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
434	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
435	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
436	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
437	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
438	C₈	—	2	2	no	—
439	C₈	—	2	2	no	—
440	C₈	—	2	2	no	—
441	C₈	—	2	2	no	—
442	C₂²	—	2	2	no	—
443	C₂²	—	2	4	no	—
444	C₂²	—	4	1	no	—
445	C₂²	—	4	1	no	—
446	C₂²	—	4	2	no	—
447	C₂²	C₂×#121×C₄₁	1	1	yes	characteristic
448	C₂²	C₂×#124×C₄₁	1	1	yes	characteristic
449	C₂²	C₄₁×#532	1	1	yes	characteristic
450	C₂²	C₄₁×#577	1	2	yes	—
451	C₂²	C₄₁×#578	1	2	yes	—
452	C₄	—	2	2	no	—
453	C₄	—	2	2	no	—
454	C₄	—	2	2	no	—
455	C₄	—	4	1	no	—
456	C₄	—	4	1	no	—
457	C₄	—	8	2	no	—
458	C₄	—	8	2	no	—
459	C₄	—	8	2	no	—
460	C₄	—	8	2	no	—
461	C₄	C₄₁×#525	1	1	yes	characteristic
462	C₄	C₄₁×#525	1	1	yes	characteristic
463	C₄	C₄₁×#529	1	1	yes	characteristic
464	C₄	C₄₁×#529	1	1	yes	characteristic
465	C₂	—	4	2	no	—
466	C₂	C₄₁×#2850	1	1	yes	characteristic
467	C₂	C₄₁×#3057	1	1	yes	characteristic
468	C₂	C₄₁×#3059	1	1	yes	characteristic
469	C₂	C₄₁×#3137	1	2	yes	—
470	C₂	C₄₁×#3178	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₄₁	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₁
prime radical	C₂⁴×C₄₁	C₂×D₄
LCS	G ▷ C₂²×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
1. C₂×C₄₁×#487	C₂	semidirect
5. C₄₁×#1993	C₂	semidirect
6. C₄₁×#1960	C₂	semidirect
7. C₄₁×#1935	C₂	semidirect
8. C₄₁×#1933	C₂	semidirect
11. C₄₁×#1835	C₂	semidirect
206. #33046	C₄₁	direct (N × H)
230. C₂×#487	C₂×C₄₁	semidirect
234. #1993	C₂×C₄₁	semidirect
235. #1960	C₂×C₄₁	semidirect
236. #1935	C₂×C₄₁	semidirect
237. #1933	C₂×C₄₁	semidirect
240. #1835	C₂×C₄₁	semidirect
280. C₄₁	#33046	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×#487	2
C₂×C₄₁×#405	2
C₄₁×#2628	2
C₄₁×#2621	2
C₄₁×#1993	2
C₄₁×#1960	2
C₄₁×#1935	2
C₄₁×#1933	2
C₄₁×#1894	2
C₄₁×#1892	2
C₄₁×#1835	2
#33046	41

Subgroups — C41×#33046 #23809247

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#33046 #23809247