Subgroups — C₄₁×#18623 #23794824

Order 10496.

970 conjugacy classes of subgroups.

The subgroup lattice has 500 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₁×#3503	C₂	1	1	yes	maximal, characteristic
2	C₄₁×#3230	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄₁×#494	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₁×#3079	C₂	1	1	yes	maximal, characteristic
5	C₄₁×#1633	C₂	1	4	yes	maximal, complemented
6	C₄₁×#1632	C₂	1	4	yes	maximal, complemented
7	C₄₁×#1548	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄₁×#1493	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄₁×#1476	C₂	1	1	yes	maximal, characteristic
10	C₂²×Q₁₆×C₄₁	—	2	2	no	—
11	Q₈²×C₄₁	C₂²	1	2	yes	—
12	C₄₁×#557	—	2	1	no	—
13	C₄₁×#554	—	2	2	no	—
14	C₄₁×#554	C₂²	1	2	yes	—
15	D₄×Q₈×C₄₁	—	2	2	no	—
16	D₄×Q₈×C₄₁	—	2	1	no	—
17	C₄₁×#544	—	2	2	no	—
18	C₄₁×#544	—	2	1	no	—
19	C₄₁×#533	—	2	1	no	—
20	C₄₁×#533	C₂²	1	1	yes	characteristic
21	C₂×C₄⋊Q₈×C₄₁	—	2	1	no	—
22	C₂×C₄⋊Q₈×C₄₁	C₂²	1	1	yes	characteristic
23	C₂×C₄⋊Q₈×C₄₁	C₂²	1	1	yes	characteristic
24	C₄₁×#520	—	2	1	no	—
25	C₄×#41×C₄₁	C₂²	1	1	yes	characteristic
26	C₄₁×#500	—	2	1	no	—
27	C₄₁×#494	—	2	2	no	—
28	C₄₁×#494	C₂²	1	4	yes	—
29	C₄₁×#487	—	2	1	no	—
30	C₄₁×#484	—	2	2	no	—
31	C₄₁×#477	C₂²	1	2	yes	—
32	C₄₁×#477	C₂²	1	4	yes	—
33	C₄₁×#476	C₂²	1	2	yes	—
34	C₄₁×#475	—	2	1	no	—
35	C₄₁×#474	—	2	1	no	—
36	C₄₁×#431	C₂²	1	1	yes	characteristic
37	C₄₁×#428	—	2	1	no	—
38	C₄₁×#423	C₂²	1	1	yes	characteristic
39	C₄₁×#417	—	2	1	no	—
40	C₂×C₄×C₈×C₄₁	C₂²	1	1	yes	characteristic
41	C₄₁×#333	C₂²	1	4	yes	—
42	C₄₁×Q₈⋊C₈	C₂²	1	4	yes	—
43	C₄₁×Q₈⋊C₈	C₂²	1	2	yes	—
44	C₄₁×D₄⋊C₈	C₂²	1	2	yes	—
45	C₂×#41×C₄₁	D₄	1	1	yes	characteristic
46	C₂²×Q₈×C₄₁	—	2	2	no	—
47	C₂²×Q₈×C₄₁	—	2	1	no	—
48	C₂²×Q₈×C₄₁	D₄	1	2	yes	—
49	C₂×Q₁₆×C₄₁	—	2	8	no	—
50	C₂×Q₁₆×C₄₁	—	4	8	no	—
51	C₂×M₁₆×C₄₁	—	2	1	no	—
52	C₂²×C₈×C₄₁	—	2	1	no	—
53	C₄⋊Q₈×C₄₁	—	2	2	no	—
54	C₄⋊Q₈×C₄₁	—	2	2	no	—
55	C₄⋊Q₈×C₄₁	—	2	4	no	—
56	C₄⋊Q₈×C₄₁	—	2	2	no	—
57	C₄⋊Q₈×C₄₁	—	2	2	no	—
58	C₄⋊Q₈×C₄₁	—	2	1	no	—
59	C₄⋊Q₈×C₄₁	—	2	1	no	—
60	C₄⋊Q₈×C₄₁	—	2	1	no	—
61	C₄⋊Q₈×C₄₁	—	2	1	no	—
62	C₄⋊Q₈×C₄₁	—	2	1	no	—
63	C₄⋊Q₈×C₄₁	D₄	1	2	yes	—
64	C₄⋊Q₈×C₄₁	D₄	1	1	yes	characteristic
65	C₄⋊Q₈×C₄₁	D₄	1	1	yes	characteristic
66	C₄⋊Q₈×C₄₁	C₂³	1	2	yes	—
67	C₄⋊Q₈×C₄₁	C₂³	1	2	yes	—
68	#125×C₄₁	—	2	2	no	—
69	#125×C₄₁	—	2	4	no	—
70	#125×C₄₁	—	2	2	no	—
71	#125×C₄₁	—	2	1	no	—
72	C₂²⋊Q₈×C₄₁	—	2	2	no	—
73	C₂²⋊Q₈×C₄₁	—	2	4	no	—
74	C₂²⋊Q₈×C₄₁	—	2	4	no	—
75	C₂²⋊Q₈×C₄₁	—	2	2	no	—
76	C₂²⋊Q₈×C₄₁	—	2	4	no	—
77	C₂²⋊Q₈×C₄₁	—	2	1	no	—
78	C₂²⋊Q₈×C₄₁	D₄	1	2	yes	—
79	C₄×Q₈×C₄₁	—	2	2	no	—
80	C₄×Q₈×C₄₁	—	2	2	no	—
81	C₄×Q₈×C₄₁	—	2	2	no	—
82	C₄×Q₈×C₄₁	—	2	1	no	—
83	C₄×Q₈×C₄₁	D₄	1	1	yes	characteristic
84	C₄×Q₈×C₄₁	C₂³	1	1	yes	characteristic
85	C₄×Q₈×C₄₁	C₂³	1	2	yes	—
86	C₄×D₄×C₄₁	—	2	4	no	—
87	C₄×D₄×C₄₁	—	2	2	no	—
88	C₄×D₄×C₄₁	—	2	1	no	—
89	C₄×D₄×C₄₁	—	2	1	no	—
90	C₄×D₄×C₄₁	D₄	1	1	yes	characteristic
91	C₄×D₄×C₄₁	C₂³	1	1	yes	characteristic
92	#117×C₄₁	—	2	2	no	—
93	#117×C₄₁	—	2	1	no	—
94	#117×C₄₁	—	2	1	no	—
95	#117×C₄₁	D₄	1	1	yes	characteristic
96	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
97	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
98	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
99	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
100	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
101	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
102	C₂×C₄²×C₄₁	—	2	1	no	—
103	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
104	#107×C₄₁	—	2	4	no	—
105	#107×C₄₁	—	2	2	no	—
106	#106×C₄₁	—	2	2	no	—
107	C₄⋊C₈×C₄₁	—	2	1	no	—
108	C₄⋊C₈×C₄₁	C₂³	1	2	yes	—
109	C₄⋊C₈×C₄₁	C₂³	1	2	yes	—
110	#103×C₄₁	—	2	2	no	—
111	#103×C₄₁	—	2	4	no	—
112	#102×C₄₁	—	2	2	no	—
113	C₂²⋊C₈×C₄₁	—	2	1	no	—
114	C₄×C₈×C₄₁	—	2	1	no	—
115	C₄×C₈×C₄₁	—	2	1	no	—
116	C₄×C₈×C₄₁	C₂³	1	2	yes	—
117	#41×C₄₁	—	2	2	no	—
118	#41×C₄₁	Q₁₆	1	4	yes	complemented
119	C₂×Q₈×C₄₁	—	2	4	no	—
120	C₂×Q₈×C₄₁	—	2	2	no	—
121	C₂×Q₈×C₄₁	—	2	1	no	—
122	C₂×Q₈×C₄₁	—	2	2	no	—
123	C₂×Q₈×C₄₁	—	4	4	no	—
124	C₂×Q₈×C₄₁	—	4	4	no	—
125	C₂×Q₈×C₄₁	—	4	1	no	—
126	C₂×Q₈×C₄₁	—	8	4	no	—
127	C₂×Q₈×C₄₁	C₂×D₄	1	2	yes	—
128	C₂×Q₈×C₄₁	C₂×D₄	1	1	yes	characteristic
129	C₂×Q₈×C₄₁	C₂×D₄	1	4	yes	—
130	C₂×D₄×C₄₁	—	2	1	no	—
131	C₂×D₄×C₄₁	C₂×D₄	1	1	yes	characteristic
132	C₂²×C₄×C₄₁	—	2	1	no	—
133	C₂²×C₄×C₄₁	—	2	4	no	—
134	C₂²×C₄×C₄₁	—	2	2	no	—
135	C₂²×C₄×C₄₁	—	2	1	no	—
136	C₂²×C₄×C₄₁	—	2	1	no	—
137	C₂²×C₄×C₄₁	—	4	1	no	—
138	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
139	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
140	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
141	Q₁₆×C₄₁	—	4	16	no	—
142	M₁₆×C₄₁	—	4	2	no	—
143	C₂×C₈×C₄₁	—	2	4	no	—
144	C₂×C₈×C₄₁	—	2	2	no	—
145	C₂×C₈×C₄₁	—	2	2	no	—
146	C₂×C₈×C₄₁	—	2	2	no	—
147	C₄⋊C₄×C₄₁	—	2	4	no	—
148	C₄⋊C₄×C₄₁	—	2	4	no	—
149	C₄⋊C₄×C₄₁	—	2	4	no	—
150	C₄⋊C₄×C₄₁	—	2	4	no	—
151	C₄⋊C₄×C₄₁	—	2	2	no	—
152	C₄⋊C₄×C₄₁	—	2	1	no	—
153	C₄⋊C₄×C₄₁	—	2	2	no	—
154	C₄⋊C₄×C₄₁	—	2	1	no	—
155	C₄⋊C₄×C₄₁	—	2	1	no	—
156	C₄⋊C₄×C₄₁	—	2	1	no	—
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	—	2	1	no	—
161	C₄⋊C₄×C₄₁	—	2	2	no	—
162	C₄⋊C₄×C₄₁	—	2	2	no	—
163	C₄⋊C₄×C₄₁	—	2	2	no	—
164	C₄⋊C₄×C₄₁	—	4	1	no	—
165	C₄⋊C₄×C₄₁	—	4	1	no	—
166	C₄⋊C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
167	C₄⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
168	C₄⋊C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
169	C₂²⋊C₄×C₄₁	—	2	4	no	—
170	C₂²⋊C₄×C₄₁	—	2	2	no	—
171	C₂²⋊C₄×C₄₁	—	2	1	no	—
172	C₂²⋊C₄×C₄₁	—	2	1	no	—
173	C₂²⋊C₄×C₄₁	—	2	1	no	—
174	C₄²×C₄₁	—	2	4	no	—
175	C₄²×C₄₁	—	2	1	no	—
176	C₄²×C₄₁	—	2	1	no	—
177	C₄²×C₄₁	—	2	1	no	—
178	C₄²×C₄₁	—	2	2	no	—
179	C₄²×C₄₁	C₂×D₄	1	1	yes	characteristic
180	C₄²×C₄₁	C₂×D₄	1	1	yes	characteristic
181	C₄²×C₄₁	C₂×D₄	1	1	yes	characteristic
182	C₄²×C₄₁	C₂⁴	1	1	yes	characteristic
183	C₂³×C₄₁	—	2	1	no	—
184	C₂³×C₄₁	#120	1	1	yes	characteristic
185	Q₈×C₄₁	—	2	1	no	—
186	Q₈×C₄₁	—	2	4	no	—
187	Q₈×C₄₁	—	4	4	no	—
188	Q₈×C₄₁	—	4	4	no	—
189	Q₈×C₄₁	—	4	4	no	—
190	Q₈×C₄₁	—	4	2	no	—
191	Q₈×C₄₁	—	8	4	no	—
192	Q₈×C₄₁	—	8	2	no	—
193	Q₈×C₄₁	C₂×Q₁₆	1	2	yes	complemented
194	D₄×C₄₁	—	2	4	no	—
195	D₄×C₄₁	—	2	1	no	—
196	D₄×C₄₁	C₂×Q₁₆	1	2	yes	complemented
197	C₂×C₄×C₄₁	—	2	1	no	—
198	C₂×C₄×C₄₁	—	2	2	no	—
199	C₂×C₄×C₄₁	—	2	4	no	—
200	C₂×C₄×C₄₁	—	2	2	no	—
201	C₂×C₄×C₄₁	—	2	2	no	—
202	C₂×C₄×C₄₁	—	2	1	no	—
203	C₂×C₄×C₄₁	—	2	1	no	—
204	C₂×C₄×C₄₁	—	2	4	no	—
205	C₂×C₄×C₄₁	—	2	2	no	—
206	C₂×C₄×C₄₁	—	4	2	no	—
207	C₂×C₄×C₄₁	—	4	2	no	—
208	C₂×C₄×C₄₁	—	4	2	no	—
209	C₂×C₄×C₄₁	—	8	2	no	—
210	C₂×C₄×C₄₁	—	8	4	no	—
211	C₂×C₄×C₄₁	—	8	2	no	—
212	C₂×C₄×C₄₁	#120	1	1	yes	characteristic
213	C₂×C₄×C₄₁	#120	1	1	yes	characteristic
214	C₂×C₄×C₄₁	#120	1	1	yes	characteristic
215	C₂×C₄×C₄₁	C₂×Q₁₆	1	2	yes	—
216	C₂×C₄×C₄₁	#137	1	2	yes	—
217	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
218	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
219	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
220	C₈×C₄₁	—	2	4	no	—
221	C₈×C₄₁	—	4	2	no	—
222	C₈×C₄₁	—	4	2	no	—
223	#18623	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
224	C₂²×C₄₁	—	2	1	no	—
225	C₂²×C₄₁	—	2	1	no	—
226	C₂²×C₄₁	—	2	2	no	—
227	C₂²×C₄₁	—	4	1	no	—
228	C₂²×C₄₁	—	4	1	no	—
229	C₂²×C₄₁	#451	1	2	yes	—
230	C₂²×C₄₁	C₂×#120	1	1	yes	characteristic
231	C₄×C₄₁	—	2	2	no	—
232	C₄×C₄₁	—	2	1	no	—
233	C₄×C₄₁	—	2	1	no	—
234	C₄×C₄₁	—	4	1	no	—
235	C₄×C₄₁	—	4	2	no	—
236	C₄×C₄₁	—	4	1	no	—
237	C₄×C₄₁	—	4	4	no	—
238	C₄×C₄₁	—	4	2	no	—
239	C₄×C₄₁	—	8	2	no	—
240	C₄×C₄₁	#451	1	2	yes	—
241	C₄×C₄₁	#453	1	2	yes	—
242	C₄×C₄₁	C₂²×Q₁₆	1	1	yes	characteristic
243	C₄×C₄₁	C₂×#137	1	1	yes	characteristic
244	C₄×C₄₁	#578	1	2	yes	—
245	#3503	C₂×C₄₁	1	1	yes	characteristic
246	#3230	C₂×C₄₁	1	1	yes	characteristic, complemented
247	C₂×#494	C₂×C₄₁	1	1	yes	characteristic, complemented
248	#3079	C₂×C₄₁	1	1	yes	characteristic
249	#1633	C₂×C₄₁	1	4	yes	complemented
250	#1632	C₂×C₄₁	1	4	yes	complemented
251	#1548	C₂×C₄₁	1	1	yes	characteristic, complemented
252	#1493	C₂×C₄₁	1	1	yes	characteristic, complemented
253	#1476	C₂×C₄₁	1	1	yes	characteristic
254	C₂×C₄₁	—	2	2	no	—
255	C₂×C₄₁	—	4	2	no	—
256	C₂×C₄₁	C₂×#451	1	1	yes	characteristic
257	C₂×C₄₁	#3011	1	1	yes	characteristic
258	C₂×C₄₁	C₂×#453	1	1	yes	characteristic
259	C₂²×Q₁₆	—	2	2	no	—
260	Q₈²	C₂²×C₄₁	1	2	yes	—
261	#557	—	2	1	no	—
262	#554	—	2	2	no	—
263	#554	C₂²×C₄₁	1	2	yes	—
264	D₄×Q₈	—	2	2	no	—
265	D₄×Q₈	—	2	1	no	—
266	#544	—	2	2	no	—
267	#544	—	2	1	no	—
268	#533	—	2	1	no	—
269	#533	C₂²×C₄₁	1	1	yes	characteristic
270	C₂×C₄⋊Q₈	—	2	1	no	—
271	C₂×C₄⋊Q₈	C₂²×C₄₁	1	1	yes	characteristic
272	C₂×C₄⋊Q₈	C₂²×C₄₁	1	1	yes	characteristic
273	#520	—	2	1	no	—
274	C₄×#41	C₂²×C₄₁	1	1	yes	characteristic
275	#500	—	2	1	no	—
276	#494	—	2	2	no	—
277	#494	C₂²×C₄₁	1	4	yes	—
278	#487	—	2	1	no	—
279	#484	—	2	2	no	—
280	#477	C₂²×C₄₁	1	2	yes	—
281	#477	C₂²×C₄₁	1	4	yes	—
282	#476	C₂²×C₄₁	1	2	yes	—
283	#475	—	2	1	no	—
284	#474	—	2	1	no	—
285	#431	C₂²×C₄₁	1	1	yes	characteristic
286	#428	—	2	1	no	—
287	#423	C₂²×C₄₁	1	1	yes	characteristic
288	#417	—	2	1	no	—
289	C₂×C₄×C₈	C₂²×C₄₁	1	1	yes	characteristic
290	#333	C₂²×C₄₁	1	4	yes	—
291	Q₈⋊C₈	C₂²×C₄₁	1	4	yes	—
292	Q₈⋊C₈	C₂²×C₄₁	1	2	yes	—
293	D₄⋊C₈	C₂²×C₄₁	1	2	yes	—
294	C₄₁	#18623	1	1	yes	characteristic, direct product factor, Sylow
295	C₂×#41	D₄×C₄₁	1	1	yes	characteristic
296	C₂²×Q₈	—	2	2	no	—
297	C₂²×Q₈	—	2	1	no	—
298	C₂²×Q₈	D₄×C₄₁	1	2	yes	—
299	C₂×Q₁₆	—	2	8	no	—
300	C₂×Q₁₆	—	4	8	no	—
301	C₂×M₁₆	—	2	1	no	—
302	C₂²×C₈	—	2	1	no	—
303	C₄⋊Q₈	—	2	2	no	—
304	C₄⋊Q₈	—	2	2	no	—
305	C₄⋊Q₈	—	2	4	no	—
306	C₄⋊Q₈	—	2	2	no	—
307	C₄⋊Q₈	—	2	2	no	—
308	C₄⋊Q₈	—	2	1	no	—
309	C₄⋊Q₈	—	2	1	no	—
310	C₄⋊Q₈	—	2	1	no	—
311	C₄⋊Q₈	—	2	1	no	—
312	C₄⋊Q₈	—	2	1	no	—
313	C₄⋊Q₈	D₄×C₄₁	1	2	yes	—
314	C₄⋊Q₈	D₄×C₄₁	1	1	yes	characteristic
315	C₄⋊Q₈	D₄×C₄₁	1	1	yes	characteristic
316	C₄⋊Q₈	C₂³×C₄₁	1	2	yes	—
317	C₄⋊Q₈	C₂³×C₄₁	1	2	yes	—
318	#125	—	2	2	no	—
319	#125	—	2	4	no	—
320	#125	—	2	2	no	—
321	#125	—	2	1	no	—
322	C₂²⋊Q₈	—	2	2	no	—
323	C₂²⋊Q₈	—	2	4	no	—
324	C₂²⋊Q₈	—	2	4	no	—
325	C₂²⋊Q₈	—	2	2	no	—
326	C₂²⋊Q₈	—	2	4	no	—
327	C₂²⋊Q₈	—	2	1	no	—
328	C₂²⋊Q₈	D₄×C₄₁	1	2	yes	—
329	C₄×Q₈	—	2	2	no	—
330	C₄×Q₈	—	2	2	no	—
331	C₄×Q₈	—	2	2	no	—
332	C₄×Q₈	—	2	1	no	—
333	C₄×Q₈	D₄×C₄₁	1	1	yes	characteristic
334	C₄×Q₈	C₂³×C₄₁	1	1	yes	characteristic
335	C₄×Q₈	C₂³×C₄₁	1	2	yes	—
336	C₄×D₄	—	2	4	no	—
337	C₄×D₄	—	2	2	no	—
338	C₄×D₄	—	2	1	no	—
339	C₄×D₄	—	2	1	no	—
340	C₄×D₄	D₄×C₄₁	1	1	yes	characteristic
341	C₄×D₄	C₂³×C₄₁	1	1	yes	characteristic
342	#117	—	2	2	no	—
343	#117	—	2	1	no	—
344	#117	—	2	1	no	—
345	#117	D₄×C₄₁	1	1	yes	characteristic
346	C₂×C₄⋊C₄	—	2	2	no	—
347	C₂×C₄⋊C₄	—	2	1	no	—
348	C₂×C₄⋊C₄	—	2	1	no	—
349	C₂×C₄⋊C₄	—	2	2	no	—
350	C₂×C₄⋊C₄	—	2	1	no	—
351	C₂×C₄⋊C₄	—	2	1	no	—
352	C₂×C₄²	—	2	1	no	—
353	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
354	#107	—	2	2	no	—
355	#107	—	2	4	no	—
356	#106	—	2	2	no	—
357	C₄⋊C₈	—	2	1	no	—
358	C₄⋊C₈	C₂³×C₄₁	1	2	yes	—
359	C₄⋊C₈	C₂³×C₄₁	1	2	yes	—
360	#103	—	2	2	no	—
361	#103	—	2	4	no	—
362	#102	—	2	2	no	—
363	C₂²⋊C₈	—	2	1	no	—
364	C₄×C₈	—	2	1	no	—
365	C₄×C₈	—	2	1	no	—
366	C₄×C₈	C₂³×C₄₁	1	2	yes	—
367	#41	—	2	2	no	—
368	#41	Q₁₆×C₄₁	1	4	yes	complemented
369	C₂×Q₈	—	2	4	no	—
370	C₂×Q₈	—	2	2	no	—
371	C₂×Q₈	—	2	1	no	—
372	C₂×Q₈	—	2	2	no	—
373	C₂×Q₈	—	4	4	no	—
374	C₂×Q₈	—	4	4	no	—
375	C₂×Q₈	—	4	1	no	—
376	C₂×Q₈	—	8	4	no	—
377	C₂×Q₈	C₂×D₄×C₄₁	1	2	yes	—
378	C₂×Q₈	C₂×D₄×C₄₁	1	1	yes	characteristic
379	C₂×Q₈	C₂×D₄×C₄₁	1	4	yes	—
380	C₂×D₄	—	2	1	no	—
381	C₂×D₄	C₂×D₄×C₄₁	1	1	yes	characteristic
382	C₂²×C₄	—	2	1	no	—
383	C₂²×C₄	—	2	4	no	—
384	C₂²×C₄	—	2	2	no	—
385	C₂²×C₄	—	2	1	no	—
386	C₂²×C₄	—	2	1	no	—
387	C₂²×C₄	—	4	1	no	—
388	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
389	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
390	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
391	Q₁₆	—	4	16	no	—
392	M₁₆	—	4	2	no	—
393	C₂×C₈	—	2	4	no	—
394	C₂×C₈	—	2	2	no	—
395	C₂×C₈	—	2	2	no	—
396	C₂×C₈	—	2	2	no	—
397	C₄⋊C₄	—	2	4	no	—
398	C₄⋊C₄	—	2	4	no	—
399	C₄⋊C₄	—	2	4	no	—
400	C₄⋊C₄	—	2	4	no	—
401	C₄⋊C₄	—	2	2	no	—
402	C₄⋊C₄	—	2	1	no	—
403	C₄⋊C₄	—	2	2	no	—
404	C₄⋊C₄	—	2	1	no	—
405	C₄⋊C₄	—	2	1	no	—
406	C₄⋊C₄	—	2	1	no	—
407	C₄⋊C₄	—	2	2	no	—
408	C₄⋊C₄	—	2	2	no	—
409	C₄⋊C₄	—	2	2	no	—
410	C₄⋊C₄	—	2	1	no	—
411	C₄⋊C₄	—	2	2	no	—
412	C₄⋊C₄	—	2	2	no	—
413	C₄⋊C₄	—	2	2	no	—
414	C₄⋊C₄	—	4	1	no	—
415	C₄⋊C₄	—	4	1	no	—
416	C₄⋊C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
417	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
418	C₄⋊C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
419	C₂²⋊C₄	—	2	4	no	—
420	C₂²⋊C₄	—	2	2	no	—
421	C₂²⋊C₄	—	2	1	no	—
422	C₂²⋊C₄	—	2	1	no	—
423	C₂²⋊C₄	—	2	1	no	—
424	C₄²	—	2	4	no	—
425	C₄²	—	2	1	no	—
426	C₄²	—	2	1	no	—
427	C₄²	—	2	1	no	—
428	C₄²	—	2	2	no	—
429	C₄²	C₂×D₄×C₄₁	1	1	yes	characteristic
430	C₄²	C₂×D₄×C₄₁	1	1	yes	characteristic
431	C₄²	C₂×D₄×C₄₁	1	1	yes	characteristic
432	C₄²	C₂⁴×C₄₁	1	1	yes	characteristic
433	C₂³	—	2	1	no	—
434	C₂³	#120×C₄₁	1	1	yes	characteristic
435	Q₈	—	2	1	no	—
436	Q₈	—	2	4	no	—
437	Q₈	—	4	4	no	—
438	Q₈	—	4	4	no	—
439	Q₈	—	4	4	no	—
440	Q₈	—	4	2	no	—
441	Q₈	—	8	4	no	—
442	Q₈	—	8	2	no	—
443	Q₈	C₂×Q₁₆×C₄₁	1	2	yes	complemented
444	D₄	—	2	4	no	—
445	D₄	—	2	1	no	—
446	D₄	C₂×Q₁₆×C₄₁	1	2	yes	complemented
447	C₂×C₄	—	2	1	no	—
448	C₂×C₄	—	2	2	no	—
449	C₂×C₄	—	2	4	no	—
450	C₂×C₄	—	2	2	no	—
451	C₂×C₄	—	2	2	no	—
452	C₂×C₄	—	2	1	no	—
453	C₂×C₄	—	2	1	no	—
454	C₂×C₄	—	2	4	no	—
455	C₂×C₄	—	2	2	no	—
456	C₂×C₄	—	4	2	no	—
457	C₂×C₄	—	4	2	no	—
458	C₂×C₄	—	4	2	no	—
459	C₂×C₄	—	8	2	no	—
460	C₂×C₄	—	8	4	no	—
461	C₂×C₄	—	8	2	no	—
462	C₂×C₄	#120×C₄₁	1	1	yes	characteristic
463	C₂×C₄	#120×C₄₁	1	1	yes	characteristic
464	C₂×C₄	#120×C₄₁	1	1	yes	characteristic
465	C₂×C₄	C₂×Q₁₆×C₄₁	1	2	yes	—
466	C₂×C₄	#137×C₄₁	1	2	yes	—
467	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
468	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
469	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
470	C₈	—	2	4	no	—
471	C₈	—	4	2	no	—
472	C₈	—	4	2	no	—
473	C₂²	—	2	1	no	—
474	C₂²	—	2	1	no	—
475	C₂²	—	2	2	no	—
476	C₂²	—	4	1	no	—
477	C₂²	—	4	1	no	—
478	C₂²	C₄₁×#451	1	2	yes	—
479	C₂²	C₂×#120×C₄₁	1	1	yes	characteristic
480	C₄	—	2	2	no	—
481	C₄	—	2	1	no	—
482	C₄	—	2	1	no	—
483	C₄	—	4	1	no	—
484	C₄	—	4	2	no	—
485	C₄	—	4	1	no	—
486	C₄	—	4	4	no	—
487	C₄	—	4	2	no	—
488	C₄	—	8	2	no	—
489	C₄	C₄₁×#451	1	2	yes	—
490	C₄	C₄₁×#453	1	2	yes	—
491	C₄	C₂²×Q₁₆×C₄₁	1	1	yes	characteristic
492	C₄	C₂×#137×C₄₁	1	1	yes	characteristic
493	C₄	C₄₁×#578	1	2	yes	—
494	C₂	—	2	2	no	—
495	C₂	—	4	2	no	—
496	C₂	C₂×C₄₁×#451	1	1	yes	characteristic
497	C₂	C₄₁×#3011	1	1	yes	characteristic
498	C₂	C₂×C₄₁×#453	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₄₁	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₄₁
prime radical	C₂×#41×C₄₁	D₄
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₄₁ ◁ C₂×C₄²×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₄₁×#3230	C₂	semidirect
3. C₂×C₄₁×#494	C₂	semidirect
5. C₄₁×#1633	C₂	semidirect
6. C₄₁×#1632	C₂	semidirect
7. C₄₁×#1548	C₂	semidirect
8. C₄₁×#1493	C₂	semidirect
118. #41×C₄₁	Q₁₆	semidirect
193. Q₈×C₄₁	C₂×Q₁₆	semidirect
196. D₄×C₄₁	C₂×Q₁₆	semidirect
223. #18623	C₄₁	direct (N × H)
246. #3230	C₂×C₄₁	semidirect
247. C₂×#494	C₂×C₄₁	semidirect
249. #1633	C₂×C₄₁	semidirect
250. #1632	C₂×C₄₁	semidirect
251. #1548	C₂×C₄₁	semidirect
252. #1493	C₂×C₄₁	semidirect
294. C₄₁	#18623	direct (N × H)
368. #41	Q₁₆×C₄₁	semidirect
443. Q₈	C₂×Q₁₆×C₄₁	semidirect
446. D₄	C₂×Q₁₆×C₄₁	semidirect

Maximal subgroups

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

subgroup	index
C₄₁×#3503	2
C₄₁×#3230	2
C₂×C₄₁×#494	2
C₄₁×#3079	2
C₄₁×#1633	2
C₄₁×#1632	2
C₄₁×#1548	2
C₄₁×#1493	2
C₄₁×#1476	2
#18623	41

Subgroups — C41×#18623 #23794824

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#18623 #23794824