Subgroups — C₄₁×#17927 #23794128

Order 10496.

620 conjugacy classes of subgroups.

The subgroup lattice has 582 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₁×#3102	C₂	1	1	yes	maximal, characteristic
2	C₄₁×#2993	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₁×#2988	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₁×#1587	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₁×#1586	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄₁×#1583	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₁×#1582	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄₁×#1580	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄₁×#1579	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈×SD₁₆×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈×SD₁₆×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄₁×#1570	C₂	1	1	yes	maximal, characteristic, complemented
13	C₄₁×#1489	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄₁×#1483	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄₁×#1453	C₂	1	1	yes	maximal, characteristic, complemented
16	C₄₁×#529	C₂²	1	1	yes	characteristic
17	C₄×#41×C₄₁	C₂²	1	1	yes	characteristic
18	C₄₁×#485	C₄	1	1	yes	characteristic
19	C₄₁×#482	C₄	1	1	yes	characteristic
20	C₄₁×#479	C₄	1	1	yes	characteristic
21	C₄₁×#478	C₄	1	1	yes	characteristic
22	C₄₁×#464	C₄	1	1	yes	characteristic
23	C₄₁×#463	C₄	1	1	yes	characteristic
24	C₄₁×#452	C₄	1	1	yes	characteristic
25	C₄₁×#449	C₄	1	1	yes	characteristic
26	C₄₁×#446	C₂²	1	1	yes	characteristic
27	C₈×Q₈×C₄₁	C₂²	1	1	yes	characteristic
28	C₈×Q₈×C₄₁	C₂²	1	1	yes	characteristic
29	C₈×Q₈×C₄₁	C₂²	1	1	yes	characteristic
30	C₄×Q₁₆×C₄₁	C₂²	1	1	yes	characteristic
31	C₄×SD₁₆×C₄₁	C₂²	1	1	yes	characteristic
32	C₄×SD₁₆×C₄₁	C₂²	1	1	yes	characteristic
33	C₄×D₈×C₄₁	C₂²	1	1	yes	characteristic
34	C₄₁×#436	—	2	1	no	—
35	C₄₁×#436	C₂²	1	1	yes	characteristic
36	C₄₁×#435	—	2	1	no	—
37	C₈×D₄×C₄₁	—	2	1	no	—
38	C₈×D₄×C₄₁	—	2	1	no	—
39	C₈×D₄×C₄₁	C₂²	1	1	yes	characteristic
40	C₈×D₄×C₄₁	C₂²	1	1	yes	characteristic
41	C₈×D₄×C₄₁	C₂²	1	1	yes	characteristic
42	C₄₁×#433	—	2	1	no	—
43	C₄₁×#431	—	2	1	no	—
44	C₄₁×#431	C₂²	1	1	yes	characteristic
45	C₄₁×#431	C₂²	1	1	yes	characteristic
46	C₄₁×#424	—	2	1	no	—
47	C₄₁×#423	C₂²	1	1	yes	characteristic
48	C₂×C₄⋊C₈×C₄₁	—	2	1	no	—
49	C₂×C₄⋊C₈×C₄₁	C₂²	1	1	yes	characteristic
50	C₄×M₁₆×C₄₁	C₂²	1	1	yes	characteristic
51	C₄₁×#334	C₂²	1	1	yes	characteristic
52	C₄₁×#334	C₂²	1	1	yes	characteristic
53	C₄₁×#334	C₂²	1	1	yes	characteristic
54	C₄₁×#334	C₂²	1	1	yes	characteristic
55	C₄₁×Q₈⋊C₈	C₂²	1	1	yes	characteristic
56	C₄₁×Q₈⋊C₈	C₂²	1	1	yes	characteristic
57	C₄₁×Q₈⋊C₈	C₂²	1	1	yes	characteristic
58	C₄₁×Q₈⋊C₈	C₂²	1	1	yes	characteristic
59	C₄₁×D₄⋊C₈	C₂²	1	1	yes	characteristic
60	C₄₁×D₄⋊C₈	C₂²	1	1	yes	characteristic
61	C₄₁×D₄⋊C₈	C₂²	1	1	yes	characteristic
62	C₄₁×D₄⋊C₈	C₂²	1	1	yes	characteristic
63	C₄₁×#322	C₂²	1	1	yes	characteristic
64	C₄₁×#322	C₂²	1	1	yes	characteristic
65	C₄₁×#322	C₂²	1	1	yes	characteristic
66	C₈²×C₄₁	C₂²	1	1	yes	characteristic
67	C₂×#41×C₄₁	C₂×C₄	1	1	yes	characteristic
68	C₂×Q₁₆×C₄₁	C₂×C₄	1	1	yes	characteristic
69	C₂×SD₁₆×C₄₁	C₂×C₄	1	1	yes	characteristic
70	C₂×SD₁₆×C₄₁	C₂×C₄	1	1	yes	characteristic
71	C₂×D₈×C₄₁	C₂×C₄	1	1	yes	characteristic
72	C₂×M₁₆×C₄₁	—	2	1	no	—
73	C₂×M₁₆×C₄₁	—	2	1	no	—
74	C₂×M₁₆×C₄₁	—	2	1	no	—
75	C₂²×C₈×C₄₁	—	2	1	no	—
76	C₂²×C₈×C₄₁	—	2	1	no	—
77	C₂²×C₈×C₄₁	—	2	1	no	—
78	C₂²×C₈×C₄₁	—	2	1	no	—
79	#126×C₄₁	—	2	1	no	—
80	#125×C₄₁	C₂×C₄	1	1	yes	characteristic
81	#124×C₄₁	C₂×C₄	1	1	yes	characteristic
82	#123×C₄₁	—	2	1	no	—
83	C₂²⋊Q₈×C₄₁	C₂×C₄	1	1	yes	characteristic
84	#121×C₄₁	C₂×C₄	1	1	yes	characteristic
85	C₄×Q₈×C₄₁	C₂×C₄	1	1	yes	characteristic
86	C₄×Q₈×C₄₁	C₂³	1	1	yes	characteristic
87	C₄×Q₈×C₄₁	C₂³	1	1	yes	characteristic
88	C₄×D₄×C₄₁	—	2	1	no	—
89	C₄×D₄×C₄₁	—	2	1	no	—
90	C₄×D₄×C₄₁	—	2	1	no	—
91	C₄×D₄×C₄₁	C₂×C₄	1	1	yes	characteristic
92	C₄×D₄×C₄₁	C₂³	1	1	yes	characteristic
93	C₄×D₄×C₄₁	C₂³	1	1	yes	characteristic
94	#117×C₄₁	—	2	1	no	—
95	#117×C₄₁	—	2	1	no	—
96	#117×C₄₁	C₂×C₄	1	1	yes	characteristic
97	C₂×C₄²×C₄₁	—	2	1	no	—
98	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
99	#107×C₄₁	C₂×C₄	1	1	yes	characteristic
100	#107×C₄₁	C₂×C₄	1	1	yes	characteristic
101	#106×C₄₁	C₂×C₄	1	1	yes	characteristic
102	#106×C₄₁	C₂×C₄	1	1	yes	characteristic
103	C₄⋊C₈×C₄₁	—	2	1	no	—
104	C₄⋊C₈×C₄₁	—	2	1	no	—
105	C₄⋊C₈×C₄₁	—	2	1	no	—
106	C₄⋊C₈×C₄₁	—	2	1	no	—
107	C₄⋊C₈×C₄₁	—	2	1	no	—
108	C₄⋊C₈×C₄₁	—	2	1	no	—
109	C₄⋊C₈×C₄₁	C₂×C₄	1	1	yes	characteristic
110	C₄⋊C₈×C₄₁	C₂×C₄	1	1	yes	characteristic
111	C₄⋊C₈×C₄₁	D₄	1	1	yes	characteristic
112	C₄⋊C₈×C₄₁	D₄	1	1	yes	characteristic
113	C₄⋊C₈×C₄₁	C₂³	1	1	yes	characteristic
114	C₄⋊C₈×C₄₁	C₂³	1	1	yes	characteristic
115	C₄⋊C₈×C₄₁	C₂³	1	1	yes	characteristic
116	C₄⋊C₈×C₄₁	C₂³	1	1	yes	characteristic
117	#103×C₄₁	C₂×C₄	1	1	yes	characteristic
118	#103×C₄₁	C₂×C₄	1	1	yes	characteristic
119	#103×C₄₁	C₂×C₄	1	1	yes	characteristic
120	#103×C₄₁	C₂×C₄	1	1	yes	characteristic
121	#102×C₄₁	C₂×C₄	1	1	yes	characteristic
122	#102×C₄₁	C₂×C₄	1	1	yes	characteristic
123	#102×C₄₁	C₂×C₄	1	1	yes	characteristic
124	#102×C₄₁	C₂×C₄	1	1	yes	characteristic
125	C₂²⋊C₈×C₄₁	—	2	1	no	—
126	C₂²⋊C₈×C₄₁	—	2	1	no	—
127	C₂²⋊C₈×C₄₁	—	2	1	no	—
128	C₂²⋊C₈×C₄₁	—	2	1	no	—
129	C₂²⋊C₈×C₄₁	C₂×C₄	1	1	yes	characteristic
130	C₂²⋊C₈×C₄₁	C₂×C₄	1	1	yes	characteristic
131	C₂²⋊C₈×C₄₁	D₄	1	1	yes	characteristic
132	C₂²⋊C₈×C₄₁	D₄	1	1	yes	characteristic
133	#97×C₄₁	—	2	1	no	—
134	#97×C₄₁	—	2	1	no	—
135	C₄×C₈×C₄₁	—	2	1	no	—
136	C₄×C₈×C₄₁	—	2	1	no	—
137	C₄×C₈×C₄₁	—	2	1	no	—
138	C₄×C₈×C₄₁	C₂³	1	1	yes	characteristic
139	C₄×C₈×C₄₁	C₂³	1	1	yes	characteristic
140	C₄×C₈×C₄₁	C₂³	1	1	yes	characteristic
141	C₄×C₈×C₄₁	C₂³	1	1	yes	characteristic
142	C₄×C₈×C₄₁	C₂³	1	1	yes	characteristic
143	C₄×C₈×C₄₁	C₂³	1	1	yes	characteristic
144	#41×C₄₁	—	2	2	no	—
145	#41×C₄₁	—	2	2	no	—
146	C₂×Q₈×C₄₁	C₂²×C₄	1	1	yes	characteristic
147	C₂×Q₈×C₄₁	C₂²×C₄	1	1	yes	characteristic
148	C₂×D₄×C₄₁	—	2	1	no	—
149	C₂×D₄×C₄₁	—	2	1	no	—
150	C₂×D₄×C₄₁	C₂²×C₄	1	1	yes	characteristic
151	C₂×D₄×C₄₁	C₂²×C₄	1	1	yes	characteristic
152	C₂²×C₄×C₄₁	—	2	1	no	—
153	C₂²×C₄×C₄₁	—	2	1	no	—
154	C₂²×C₄×C₄₁	—	2	1	no	—
155	C₂²×C₄×C₄₁	—	2	1	no	—
156	C₂²×C₄×C₄₁	C₂²×C₄	1	1	yes	characteristic
157	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
158	C₂²×C₄×C₄₁	#41	1	1	yes	characteristic
159	Q₁₆×C₄₁	—	2	2	no	—
160	SD₁₆×C₄₁	—	2	2	no	—
161	SD₁₆×C₄₁	—	2	2	no	—
162	D₈×C₄₁	—	2	2	no	—
163	M₁₆×C₄₁	—	4	2	no	—
164	M₁₆×C₄₁	—	8	1	no	—
165	M₁₆×C₄₁	—	8	1	no	—
166	C₂×C₈×C₄₁	—	2	1	no	—
167	C₂×C₈×C₄₁	—	2	1	no	—
168	C₂×C₈×C₄₁	—	2	1	no	—
169	C₂×C₈×C₄₁	—	2	1	no	—
170	C₂×C₈×C₄₁	—	2	1	no	—
171	C₂×C₈×C₄₁	—	2	1	no	—
172	C₂×C₈×C₄₁	—	8	1	no	—
173	C₂×C₈×C₄₁	—	8	1	no	—
174	C₂×C₈×C₄₁	—	8	1	no	—
175	C₂×C₈×C₄₁	—	8	1	no	—
176	C₂×C₈×C₄₁	C₂²×C₄	1	1	yes	characteristic
177	C₂×C₈×C₄₁	C₂²×C₄	1	1	yes	characteristic
178	C₂×C₈×C₄₁	C₂²×C₄	1	1	yes	characteristic
179	C₂×C₈×C₄₁	C₂²×C₄	1	1	yes	characteristic
180	C₂×C₈×C₄₁	C₂×D₄	1	1	yes	characteristic
181	C₂×C₈×C₄₁	C₂×D₄	1	1	yes	characteristic
182	C₂×C₈×C₄₁	C₂×D₄	1	1	yes	characteristic
183	C₂×C₈×C₄₁	C₂×D₄	1	1	yes	characteristic
184	C₄⋊C₄×C₄₁	—	2	1	no	—
185	C₄⋊C₄×C₄₁	—	2	1	no	—
186	C₄⋊C₄×C₄₁	—	2	1	no	—
187	C₄⋊C₄×C₄₁	—	2	1	no	—
188	C₄⋊C₄×C₄₁	—	2	1	no	—
189	C₄⋊C₄×C₄₁	—	2	1	no	—
190	C₄⋊C₄×C₄₁	C₂²×C₄	1	1	yes	characteristic
191	C₄⋊C₄×C₄₁	C₂²×C₄	1	1	yes	characteristic
192	C₄⋊C₄×C₄₁	C₂²×C₄	1	1	yes	characteristic
193	C₄⋊C₄×C₄₁	C₂²×C₄	1	1	yes	characteristic
194	C₂²⋊C₄×C₄₁	—	2	1	no	—
195	C₂²⋊C₄×C₄₁	—	2	1	no	—
196	C₂²⋊C₄×C₄₁	—	2	1	no	—
197	C₂²⋊C₄×C₄₁	—	2	1	no	—
198	C₂²⋊C₄×C₄₁	—	2	1	no	—
199	C₂²⋊C₄×C₄₁	—	2	1	no	—
200	C₂²⋊C₄×C₄₁	—	2	1	no	—
201	C₂²⋊C₄×C₄₁	—	2	1	no	—
202	C₄²×C₄₁	—	2	1	no	—
203	C₄²×C₄₁	—	2	1	no	—
204	C₄²×C₄₁	—	2	1	no	—
205	C₄²×C₄₁	—	2	1	no	—
206	C₄²×C₄₁	C₂²×C₄	1	1	yes	characteristic
207	C₄²×C₄₁	C₂×D₄	1	1	yes	characteristic
208	C₄²×C₄₁	#41	1	1	yes	characteristic
209	C₄²×C₄₁	C₂⁴	1	1	yes	characteristic
210	C₂³×C₄₁	—	2	1	no	—
211	C₂³×C₄₁	—	2	1	no	—
212	C₂³×C₄₁	C₄×D₄	1	1	yes	characteristic
213	Q₈×C₄₁	—	2	1	no	—
214	Q₈×C₄₁	—	2	1	no	—
215	Q₈×C₄₁	—	2	1	no	—
216	Q₈×C₄₁	#131	1	2	yes	—
217	D₄×C₄₁	—	2	4	no	—
218	D₄×C₄₁	—	2	1	no	—
219	D₄×C₄₁	—	2	1	no	—
220	D₄×C₄₁	—	2	1	no	—
221	D₄×C₄₁	—	8	1	no	—
222	D₄×C₄₁	#131	1	2	yes	—
223	C₂×C₄×C₄₁	—	2	4	no	—
224	C₂×C₄×C₄₁	—	2	1	no	—
225	C₂×C₄×C₄₁	—	2	1	no	—
226	C₂×C₄×C₄₁	—	2	1	no	—
227	C₂×C₄×C₄₁	—	2	1	no	—
228	C₂×C₄×C₄₁	—	2	1	no	—
229	C₂×C₄×C₄₁	—	2	1	no	—
230	C₂×C₄×C₄₁	—	2	1	no	—
231	C₂×C₄×C₄₁	—	2	1	no	—
232	C₂×C₄×C₄₁	—	2	1	no	—
233	C₂×C₄×C₄₁	—	2	1	no	—
234	C₂×C₄×C₄₁	—	4	1	no	—
235	C₂×C₄×C₄₁	—	4	1	no	—
236	C₂×C₄×C₄₁	—	4	1	no	—
237	C₂×C₄×C₄₁	—	4	1	no	—
238	C₂×C₄×C₄₁	—	4	1	no	—
239	C₂×C₄×C₄₁	—	8	1	no	—
240	C₂×C₄×C₄₁	C₄×D₄	1	1	yes	characteristic
241	C₂×C₄×C₄₁	C₄×D₄	1	1	yes	characteristic
242	C₂×C₄×C₄₁	C₄×D₄	1	1	yes	characteristic
243	C₂×C₄×C₄₁	C₂³×C₄	1	1	yes	characteristic
244	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
245	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
246	C₈×C₄₁	—	2	2	no	—
247	C₈×C₄₁	—	2	1	no	—
248	C₈×C₄₁	—	2	1	no	—
249	C₈×C₄₁	—	2	1	no	—
250	C₈×C₄₁	—	2	1	no	—
251	C₈×C₄₁	—	2	1	no	—
252	C₈×C₄₁	—	2	1	no	—
253	C₈×C₄₁	—	2	1	no	—
254	C₈×C₄₁	—	2	1	no	—
255	C₈×C₄₁	—	4	1	no	—
256	C₈×C₄₁	—	4	1	no	—
257	C₈×C₄₁	—	4	1	no	—
258	C₈×C₄₁	—	4	1	no	—
259	C₈×C₄₁	—	4	1	no	—
260	#17927	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
261	C₂²×C₄₁	—	2	1	no	—
262	C₂²×C₄₁	—	2	2	no	—
263	C₂²×C₄₁	—	2	1	no	—
264	C₂²×C₄₁	—	2	1	no	—
265	C₂²×C₄₁	—	4	1	no	—
266	C₂²×C₄₁	—	4	1	no	—
267	C₂²×C₄₁	—	4	1	no	—
268	C₂²×C₄₁	—	4	1	no	—
269	C₂²×C₄₁	—	4	1	no	—
270	C₂²×C₄₁	C₂×C₄×D₄	1	1	yes	characteristic
271	C₄×C₄₁	—	2	1	no	—
272	C₄×C₄₁	—	2	2	no	—
273	C₄×C₄₁	—	2	1	no	—
274	C₄×C₄₁	—	2	1	no	—
275	C₄×C₄₁	—	2	1	no	—
276	C₄×C₄₁	—	4	1	no	—
277	C₄×C₄₁	—	4	1	no	—
278	C₄×C₄₁	—	4	1	no	—
279	C₄×C₄₁	—	4	1	no	—
280	C₄×C₄₁	—	4	1	no	—
281	C₄×C₄₁	C₂×#131	1	1	yes	characteristic
282	C₄×C₄₁	C₂×#131	1	1	yes	characteristic
283	C₄×C₄₁	#577	1	1	yes	characteristic
284	C₄×C₄₁	#577	1	1	yes	characteristic
285	#3102	C₂×C₄₁	1	1	yes	characteristic
286	#2993	C₂×C₄₁	1	1	yes	characteristic, complemented
287	#2988	C₂×C₄₁	1	1	yes	characteristic, complemented
288	#1587	C₂×C₄₁	1	1	yes	characteristic, complemented
289	#1586	C₂×C₄₁	1	1	yes	characteristic, complemented
290	#1583	C₂×C₄₁	1	1	yes	characteristic, complemented
291	#1582	C₂×C₄₁	1	1	yes	characteristic, complemented
292	#1580	C₂×C₄₁	1	1	yes	characteristic, complemented
293	#1579	C₂×C₄₁	1	1	yes	characteristic, complemented
294	C₈×SD₁₆	C₂×C₄₁	1	1	yes	characteristic, complemented
295	C₈×SD₁₆	C₂×C₄₁	1	1	yes	characteristic, complemented
296	#1570	C₂×C₄₁	1	1	yes	characteristic, complemented
297	#1489	C₂×C₄₁	1	1	yes	characteristic, complemented
298	#1483	C₂×C₄₁	1	1	yes	characteristic, complemented
299	#1453	C₂×C₄₁	1	1	yes	characteristic, complemented
300	C₂×C₄₁	—	4	1	no	—
301	C₂×C₄₁	—	4	2	no	—
302	C₂×C₄₁	—	8	1	no	—
303	C₂×C₄₁	#2929	1	1	yes	characteristic
304	C₂×C₄₁	#2952	1	1	yes	characteristic
305	C₂×C₄₁	#2956	1	1	yes	characteristic
306	#529	C₂²×C₄₁	1	1	yes	characteristic
307	C₄×#41	C₂²×C₄₁	1	1	yes	characteristic
308	#485	C₄×C₄₁	1	1	yes	characteristic
309	#482	C₄×C₄₁	1	1	yes	characteristic
310	#479	C₄×C₄₁	1	1	yes	characteristic
311	#478	C₄×C₄₁	1	1	yes	characteristic
312	#464	C₄×C₄₁	1	1	yes	characteristic
313	#463	C₄×C₄₁	1	1	yes	characteristic
314	#452	C₄×C₄₁	1	1	yes	characteristic
315	#449	C₄×C₄₁	1	1	yes	characteristic
316	#446	C₂²×C₄₁	1	1	yes	characteristic
317	C₈×Q₈	C₂²×C₄₁	1	1	yes	characteristic
318	C₈×Q₈	C₂²×C₄₁	1	1	yes	characteristic
319	C₈×Q₈	C₂²×C₄₁	1	1	yes	characteristic
320	C₄×Q₁₆	C₂²×C₄₁	1	1	yes	characteristic
321	C₄×SD₁₆	C₂²×C₄₁	1	1	yes	characteristic
322	C₄×SD₁₆	C₂²×C₄₁	1	1	yes	characteristic
323	C₄×D₈	C₂²×C₄₁	1	1	yes	characteristic
324	#436	—	2	1	no	—
325	#436	C₂²×C₄₁	1	1	yes	characteristic
326	#435	—	2	1	no	—
327	C₈×D₄	—	2	1	no	—
328	C₈×D₄	—	2	1	no	—
329	C₈×D₄	C₂²×C₄₁	1	1	yes	characteristic
330	C₈×D₄	C₂²×C₄₁	1	1	yes	characteristic
331	C₈×D₄	C₂²×C₄₁	1	1	yes	characteristic
332	#433	—	2	1	no	—
333	#431	—	2	1	no	—
334	#431	C₂²×C₄₁	1	1	yes	characteristic
335	#431	C₂²×C₄₁	1	1	yes	characteristic
336	#424	—	2	1	no	—
337	#423	C₂²×C₄₁	1	1	yes	characteristic
338	C₂×C₄⋊C₈	—	2	1	no	—
339	C₂×C₄⋊C₈	C₂²×C₄₁	1	1	yes	characteristic
340	C₄×M₁₆	C₂²×C₄₁	1	1	yes	characteristic
341	#334	C₂²×C₄₁	1	1	yes	characteristic
342	#334	C₂²×C₄₁	1	1	yes	characteristic
343	#334	C₂²×C₄₁	1	1	yes	characteristic
344	#334	C₂²×C₄₁	1	1	yes	characteristic
345	Q₈⋊C₈	C₂²×C₄₁	1	1	yes	characteristic
346	Q₈⋊C₈	C₂²×C₄₁	1	1	yes	characteristic
347	Q₈⋊C₈	C₂²×C₄₁	1	1	yes	characteristic
348	Q₈⋊C₈	C₂²×C₄₁	1	1	yes	characteristic
349	D₄⋊C₈	C₂²×C₄₁	1	1	yes	characteristic
350	D₄⋊C₈	C₂²×C₄₁	1	1	yes	characteristic
351	D₄⋊C₈	C₂²×C₄₁	1	1	yes	characteristic
352	D₄⋊C₈	C₂²×C₄₁	1	1	yes	characteristic
353	#322	C₂²×C₄₁	1	1	yes	characteristic
354	#322	C₂²×C₄₁	1	1	yes	characteristic
355	#322	C₂²×C₄₁	1	1	yes	characteristic
356	C₈²	C₂²×C₄₁	1	1	yes	characteristic
357	C₄₁	#17927	1	1	yes	characteristic, direct product factor, Sylow
358	C₂×#41	C₂×C₄×C₄₁	1	1	yes	characteristic
359	C₂×Q₁₆	C₂×C₄×C₄₁	1	1	yes	characteristic
360	C₂×SD₁₆	C₂×C₄×C₄₁	1	1	yes	characteristic
361	C₂×SD₁₆	C₂×C₄×C₄₁	1	1	yes	characteristic
362	C₂×D₈	C₂×C₄×C₄₁	1	1	yes	characteristic
363	C₂×M₁₆	—	2	1	no	—
364	C₂×M₁₆	—	2	1	no	—
365	C₂×M₁₆	—	2	1	no	—
366	C₂²×C₈	—	2	1	no	—
367	C₂²×C₈	—	2	1	no	—
368	C₂²×C₈	—	2	1	no	—
369	C₂²×C₈	—	2	1	no	—
370	#126	—	2	1	no	—
371	#125	C₂×C₄×C₄₁	1	1	yes	characteristic
372	#124	C₂×C₄×C₄₁	1	1	yes	characteristic
373	#123	—	2	1	no	—
374	C₂²⋊Q₈	C₂×C₄×C₄₁	1	1	yes	characteristic
375	#121	C₂×C₄×C₄₁	1	1	yes	characteristic
376	C₄×Q₈	C₂×C₄×C₄₁	1	1	yes	characteristic
377	C₄×Q₈	C₂³×C₄₁	1	1	yes	characteristic
378	C₄×Q₈	C₂³×C₄₁	1	1	yes	characteristic
379	C₄×D₄	—	2	1	no	—
380	C₄×D₄	—	2	1	no	—
381	C₄×D₄	—	2	1	no	—
382	C₄×D₄	C₂×C₄×C₄₁	1	1	yes	characteristic
383	C₄×D₄	C₂³×C₄₁	1	1	yes	characteristic
384	C₄×D₄	C₂³×C₄₁	1	1	yes	characteristic
385	#117	—	2	1	no	—
386	#117	—	2	1	no	—
387	#117	C₂×C₄×C₄₁	1	1	yes	characteristic
388	C₂×C₄²	—	2	1	no	—
389	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
390	#107	C₂×C₄×C₄₁	1	1	yes	characteristic
391	#107	C₂×C₄×C₄₁	1	1	yes	characteristic
392	#106	C₂×C₄×C₄₁	1	1	yes	characteristic
393	#106	C₂×C₄×C₄₁	1	1	yes	characteristic
394	C₄⋊C₈	—	2	1	no	—
395	C₄⋊C₈	—	2	1	no	—
396	C₄⋊C₈	—	2	1	no	—
397	C₄⋊C₈	—	2	1	no	—
398	C₄⋊C₈	—	2	1	no	—
399	C₄⋊C₈	—	2	1	no	—
400	C₄⋊C₈	C₂×C₄×C₄₁	1	1	yes	characteristic
401	C₄⋊C₈	C₂×C₄×C₄₁	1	1	yes	characteristic
402	C₄⋊C₈	D₄×C₄₁	1	1	yes	characteristic
403	C₄⋊C₈	D₄×C₄₁	1	1	yes	characteristic
404	C₄⋊C₈	C₂³×C₄₁	1	1	yes	characteristic
405	C₄⋊C₈	C₂³×C₄₁	1	1	yes	characteristic
406	C₄⋊C₈	C₂³×C₄₁	1	1	yes	characteristic
407	C₄⋊C₈	C₂³×C₄₁	1	1	yes	characteristic
408	#103	C₂×C₄×C₄₁	1	1	yes	characteristic
409	#103	C₂×C₄×C₄₁	1	1	yes	characteristic
410	#103	C₂×C₄×C₄₁	1	1	yes	characteristic
411	#103	C₂×C₄×C₄₁	1	1	yes	characteristic
412	#102	C₂×C₄×C₄₁	1	1	yes	characteristic
413	#102	C₂×C₄×C₄₁	1	1	yes	characteristic
414	#102	C₂×C₄×C₄₁	1	1	yes	characteristic
415	#102	C₂×C₄×C₄₁	1	1	yes	characteristic
416	C₂²⋊C₈	—	2	1	no	—
417	C₂²⋊C₈	—	2	1	no	—
418	C₂²⋊C₈	—	2	1	no	—
419	C₂²⋊C₈	—	2	1	no	—
420	C₂²⋊C₈	C₂×C₄×C₄₁	1	1	yes	characteristic
421	C₂²⋊C₈	C₂×C₄×C₄₁	1	1	yes	characteristic
422	C₂²⋊C₈	D₄×C₄₁	1	1	yes	characteristic
423	C₂²⋊C₈	D₄×C₄₁	1	1	yes	characteristic
424	#97	—	2	1	no	—
425	#97	—	2	1	no	—
426	C₄×C₈	—	2	1	no	—
427	C₄×C₈	—	2	1	no	—
428	C₄×C₈	—	2	1	no	—
429	C₄×C₈	C₂³×C₄₁	1	1	yes	characteristic
430	C₄×C₈	C₂³×C₄₁	1	1	yes	characteristic
431	C₄×C₈	C₂³×C₄₁	1	1	yes	characteristic
432	C₄×C₈	C₂³×C₄₁	1	1	yes	characteristic
433	C₄×C₈	C₂³×C₄₁	1	1	yes	characteristic
434	C₄×C₈	C₂³×C₄₁	1	1	yes	characteristic
435	#41	—	2	2	no	—
436	#41	—	2	2	no	—
437	C₂×Q₈	C₂²×C₄×C₄₁	1	1	yes	characteristic
438	C₂×Q₈	C₂²×C₄×C₄₁	1	1	yes	characteristic
439	C₂×D₄	—	2	1	no	—
440	C₂×D₄	—	2	1	no	—
441	C₂×D₄	C₂²×C₄×C₄₁	1	1	yes	characteristic
442	C₂×D₄	C₂²×C₄×C₄₁	1	1	yes	characteristic
443	C₂²×C₄	—	2	1	no	—
444	C₂²×C₄	—	2	1	no	—
445	C₂²×C₄	—	2	1	no	—
446	C₂²×C₄	—	2	1	no	—
447	C₂²×C₄	C₂²×C₄×C₄₁	1	1	yes	characteristic
448	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
449	C₂²×C₄	#41×C₄₁	1	1	yes	characteristic
450	Q₁₆	—	2	2	no	—
451	SD₁₆	—	2	2	no	—
452	SD₁₆	—	2	2	no	—
453	D₈	—	2	2	no	—
454	M₁₆	—	4	2	no	—
455	M₁₆	—	8	1	no	—
456	M₁₆	—	8	1	no	—
457	C₂×C₈	—	2	1	no	—
458	C₂×C₈	—	2	1	no	—
459	C₂×C₈	—	2	1	no	—
460	C₂×C₈	—	2	1	no	—
461	C₂×C₈	—	2	1	no	—
462	C₂×C₈	—	2	1	no	—
463	C₂×C₈	—	8	1	no	—
464	C₂×C₈	—	8	1	no	—
465	C₂×C₈	—	8	1	no	—
466	C₂×C₈	—	8	1	no	—
467	C₂×C₈	C₂²×C₄×C₄₁	1	1	yes	characteristic
468	C₂×C₈	C₂²×C₄×C₄₁	1	1	yes	characteristic
469	C₂×C₈	C₂²×C₄×C₄₁	1	1	yes	characteristic
470	C₂×C₈	C₂²×C₄×C₄₁	1	1	yes	characteristic
471	C₂×C₈	C₂×D₄×C₄₁	1	1	yes	characteristic
472	C₂×C₈	C₂×D₄×C₄₁	1	1	yes	characteristic
473	C₂×C₈	C₂×D₄×C₄₁	1	1	yes	characteristic
474	C₂×C₈	C₂×D₄×C₄₁	1	1	yes	characteristic
475	C₄⋊C₄	—	2	1	no	—
476	C₄⋊C₄	—	2	1	no	—
477	C₄⋊C₄	—	2	1	no	—
478	C₄⋊C₄	—	2	1	no	—
479	C₄⋊C₄	—	2	1	no	—
480	C₄⋊C₄	—	2	1	no	—
481	C₄⋊C₄	C₂²×C₄×C₄₁	1	1	yes	characteristic
482	C₄⋊C₄	C₂²×C₄×C₄₁	1	1	yes	characteristic
483	C₄⋊C₄	C₂²×C₄×C₄₁	1	1	yes	characteristic
484	C₄⋊C₄	C₂²×C₄×C₄₁	1	1	yes	characteristic
485	C₂²⋊C₄	—	2	1	no	—
486	C₂²⋊C₄	—	2	1	no	—
487	C₂²⋊C₄	—	2	1	no	—
488	C₂²⋊C₄	—	2	1	no	—
489	C₂²⋊C₄	—	2	1	no	—
490	C₂²⋊C₄	—	2	1	no	—
491	C₂²⋊C₄	—	2	1	no	—
492	C₂²⋊C₄	—	2	1	no	—
493	C₄²	—	2	1	no	—
494	C₄²	—	2	1	no	—
495	C₄²	—	2	1	no	—
496	C₄²	—	2	1	no	—
497	C₄²	C₂²×C₄×C₄₁	1	1	yes	characteristic
498	C₄²	C₂×D₄×C₄₁	1	1	yes	characteristic
499	C₄²	#41×C₄₁	1	1	yes	characteristic
500	C₄²	C₂⁴×C₄₁	1	1	yes	characteristic
501	C₂³	—	2	1	no	—
502	C₂³	—	2	1	no	—
503	C₂³	C₄×D₄×C₄₁	1	1	yes	characteristic
504	Q₈	—	2	1	no	—
505	Q₈	—	2	1	no	—
506	Q₈	—	2	1	no	—
507	Q₈	#131×C₄₁	1	2	yes	—
508	D₄	—	2	4	no	—
509	D₄	—	2	1	no	—
510	D₄	—	2	1	no	—
511	D₄	—	2	1	no	—
512	D₄	—	8	1	no	—
513	D₄	#131×C₄₁	1	2	yes	—
514	C₂×C₄	—	2	4	no	—
515	C₂×C₄	—	2	1	no	—
516	C₂×C₄	—	2	1	no	—
517	C₂×C₄	—	2	1	no	—
518	C₂×C₄	—	2	1	no	—
519	C₂×C₄	—	2	1	no	—
520	C₂×C₄	—	2	1	no	—
521	C₂×C₄	—	2	1	no	—
522	C₂×C₄	—	2	1	no	—
523	C₂×C₄	—	2	1	no	—
524	C₂×C₄	—	2	1	no	—
525	C₂×C₄	—	4	1	no	—
526	C₂×C₄	—	4	1	no	—
527	C₂×C₄	—	4	1	no	—
528	C₂×C₄	—	4	1	no	—
529	C₂×C₄	—	4	1	no	—
530	C₂×C₄	—	8	1	no	—
531	C₂×C₄	C₄×D₄×C₄₁	1	1	yes	characteristic
532	C₂×C₄	C₄×D₄×C₄₁	1	1	yes	characteristic
533	C₂×C₄	C₄×D₄×C₄₁	1	1	yes	characteristic
534	C₂×C₄	C₂³×C₄×C₄₁	1	1	yes	characteristic
535	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
536	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
537	C₈	—	2	2	no	—
538	C₈	—	2	1	no	—
539	C₈	—	2	1	no	—
540	C₈	—	2	1	no	—
541	C₈	—	2	1	no	—
542	C₈	—	2	1	no	—
543	C₈	—	2	1	no	—
544	C₈	—	2	1	no	—
545	C₈	—	2	1	no	—
546	C₈	—	4	1	no	—
547	C₈	—	4	1	no	—
548	C₈	—	4	1	no	—
549	C₈	—	4	1	no	—
550	C₈	—	4	1	no	—
551	C₂²	—	2	1	no	—
552	C₂²	—	2	2	no	—
553	C₂²	—	2	1	no	—
554	C₂²	—	2	1	no	—
555	C₂²	—	4	1	no	—
556	C₂²	—	4	1	no	—
557	C₂²	—	4	1	no	—
558	C₂²	—	4	1	no	—
559	C₂²	—	4	1	no	—
560	C₂²	C₂×C₄×D₄×C₄₁	1	1	yes	characteristic
561	C₄	—	2	1	no	—
562	C₄	—	2	2	no	—
563	C₄	—	2	1	no	—
564	C₄	—	2	1	no	—
565	C₄	—	2	1	no	—
566	C₄	—	4	1	no	—
567	C₄	—	4	1	no	—
568	C₄	—	4	1	no	—
569	C₄	—	4	1	no	—
570	C₄	—	4	1	no	—
571	C₄	C₂×#131×C₄₁	1	1	yes	characteristic
572	C₄	C₂×#131×C₄₁	1	1	yes	characteristic
573	C₄	C₄₁×#577	1	1	yes	characteristic
574	C₄	C₄₁×#577	1	1	yes	characteristic
575	C₂	—	4	1	no	—
576	C₂	—	4	2	no	—
577	C₂	—	8	1	no	—
578	C₂	C₄₁×#2929	1	1	yes	characteristic
579	C₂	C₄₁×#2952	1	1	yes	characteristic
580	C₂	C₄₁×#2956	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₄₁	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₄₁
Frattini, cosocle	C₄²	C₂⁴×C₄₁
socle	C₂²×C₄₁	C₂×C₄×D₄
prime radical	C₄₁×#449	C₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₄₁ ◁ C₄₁×#431 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₄₁×#2993	C₂	semidirect
3. C₄₁×#2988	C₂	semidirect
4. C₄₁×#1587	C₂	semidirect
5. C₄₁×#1586	C₂	semidirect
6. C₄₁×#1583	C₂	semidirect
7. C₄₁×#1582	C₂	semidirect
8. C₄₁×#1580	C₂	semidirect
9. C₄₁×#1579	C₂	semidirect
10. C₈×SD₁₆×C₄₁	C₂	semidirect
11. C₈×SD₁₆×C₄₁	C₂	semidirect
12. C₄₁×#1570	C₂	semidirect
13. C₄₁×#1489	C₂	semidirect
14. C₄₁×#1483	C₂	semidirect
15. C₄₁×#1453	C₂	semidirect
260. #17927	C₄₁	direct (N × H)
286. #2993	C₂×C₄₁	semidirect
287. #2988	C₂×C₄₁	semidirect
288. #1587	C₂×C₄₁	semidirect
289. #1586	C₂×C₄₁	semidirect
290. #1583	C₂×C₄₁	semidirect
291. #1582	C₂×C₄₁	semidirect
292. #1580	C₂×C₄₁	semidirect
293. #1579	C₂×C₄₁	semidirect
294. C₈×SD₁₆	C₂×C₄₁	semidirect
295. C₈×SD₁₆	C₂×C₄₁	semidirect
296. #1570	C₂×C₄₁	semidirect
297. #1489	C₂×C₄₁	semidirect
298. #1483	C₂×C₄₁	semidirect
299. #1453	C₂×C₄₁	semidirect
357. C₄₁	#17927	direct (N × H)

Maximal subgroups

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

subgroup	index
C₄₁×#3102	2
C₄₁×#2993	2
C₄₁×#2988	2
C₄₁×#1587	2
C₄₁×#1586	2
C₄₁×#1583	2
C₄₁×#1582	2
C₄₁×#1580	2
C₄₁×#1579	2
C₈×SD₁₆×C₄₁	2
C₄₁×#1570	2
C₄₁×#1489	2
C₄₁×#1483	2
C₄₁×#1453	2
#17927	41

Subgroups — C41×#17927 #23794128

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#17927 #23794128