Subgroups — C₄₁×#33084 #23809285

Order 10496.

852 conjugacy classes of subgroups.

The subgroup lattice has 618 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₁×#2863	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄²×D₄×C₄₁	C₂	1	1	yes	maximal, characteristic
3	C₄₁×#1928	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₁×#1928	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₁×#1927	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄₁×#1921	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₁×#1919	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄₁×#1918	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄₁×#1877	C₂	1	1	yes	maximal, characteristic
10	C₄₁×#1877	C₂	1	1	yes	maximal, characteristic
11	C₄₁×#1877	C₂	1	1	yes	maximal, characteristic
12	C₄₁×#1864	C₂	1	1	yes	maximal, characteristic
13	C₄₁×#1862	C₂	1	1	yes	maximal, characteristic
14	C₄₁×#1862	C₂	1	1	yes	maximal, characteristic
15	C₄₁×#1839	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×SD₁₆×C₄₁	C₂²	1	1	yes	characteristic
17	C₂×C₄×D₄×C₄₁	C₂²	1	1	yes	characteristic
18	C₂×C₄×D₄×C₄₁	C₂²	1	1	yes	characteristic
19	C₂×C₄×D₄×C₄₁	C₂²	1	1	yes	characteristic
20	C₂²×C₄²×C₄₁	—	2	1	no	—
21	C₂×#107×C₄₁	C₂²	1	1	yes	characteristic
22	C₂×#107×C₄₁	C₂²	1	1	yes	characteristic
23	C₂×#106×C₄₁	C₂²	1	1	yes	characteristic
24	C₂×#103×C₄₁	C₂²	1	1	yes	characteristic
25	C₂×#103×C₄₁	C₂²	1	1	yes	characteristic
26	C₂×#103×C₄₁	C₂²	1	1	yes	characteristic
27	C₂×#102×C₄₁	C₂²	1	1	yes	characteristic
28	C₂×#102×C₄₁	C₂²	1	1	yes	characteristic
29	C₂×#102×C₄₁	C₂²	1	1	yes	characteristic
30	C₄₁×#391	C₂²	1	1	yes	characteristic
31	C₄₁×#391	C₂²	1	1	yes	characteristic
32	C₄₁×#391	C₂²	1	1	yes	characteristic
33	C₄₁×#389	C₂²	1	1	yes	characteristic
34	C₄₁×#389	C₂²	1	1	yes	characteristic
35	C₄₁×#389	C₂²	1	1	yes	characteristic
36	C₄₁×#387	—	2	1	no	—
37	C₄₁×#387	—	2	1	no	—
38	C₄₁×#387	—	2	1	no	—
39	C₄₁×#383	—	2	1	no	—
40	C₄×C₄⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
41	C₄×C₄⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
42	C₄×C₄⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
43	C₄×C₂²⋊C₄×C₄₁	—	2	1	no	—
44	C₄×C₂²⋊C₄×C₄₁	—	2	1	no	—
45	C₄×C₂²⋊C₄×C₄₁	—	2	1	no	—
46	C₄³×C₄₁	C₂²	1	1	yes	characteristic
47	C₄₁×#340	C₂²	1	1	yes	characteristic
48	C₄₁×#340	C₂²	1	1	yes	characteristic
49	C₄₁×#340	C₂²	1	1	yes	characteristic
50	C₄₁×#340	C₂²	1	1	yes	characteristic
51	C₄₁×#340	C₂²	1	1	yes	characteristic
52	C₄₁×#340	C₂²	1	1	yes	characteristic
53	C₄₁×#336	C₂²	1	1	yes	characteristic
54	C₄₁×#336	C₂²	1	1	yes	characteristic
55	C₄₁×#336	C₂²	1	1	yes	characteristic
56	C₄₁×#336	C₂²	1	1	yes	characteristic
57	C₄₁×#336	C₂²	1	1	yes	characteristic
58	C₄₁×#336	C₂²	1	1	yes	characteristic
59	C₂²×Q₈×C₄₁	C₂³	1	1	yes	characteristic
60	C₂²×D₄×C₄₁	C₂³	1	1	yes	characteristic
61	C₂³×C₄×C₄₁	—	2	1	no	—
62	C₂³×C₄×C₄₁	—	2	1	no	—
63	C₂³×C₄×C₄₁	—	2	1	no	—
64	C₂×SD₁₆×C₄₁	—	2	2	no	—
65	C₂×SD₁₆×C₄₁	—	2	2	no	—
66	C₂×SD₁₆×C₄₁	—	2	2	no	—
67	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
68	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
69	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
70	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
71	C₄×D₄×C₄₁	—	2	2	no	—
72	C₄×D₄×C₄₁	—	2	2	no	—
73	C₄×D₄×C₄₁	—	2	2	no	—
74	C₄×D₄×C₄₁	—	2	2	no	—
75	C₄×D₄×C₄₁	—	2	2	no	—
76	C₄×D₄×C₄₁	—	2	2	no	—
77	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
78	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
79	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
80	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
81	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
82	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
83	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
84	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
85	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
86	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
87	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
88	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
89	C₂×C₄²×C₄₁	—	2	1	no	—
90	C₂×C₄²×C₄₁	—	2	1	no	—
91	C₂×C₄²×C₄₁	—	2	1	no	—
92	C₂×C₄²×C₄₁	—	4	4	no	—
93	C₂×C₄²×C₄₁	D₄	1	1	yes	characteristic
94	C₂×C₄²×C₄₁	D₄	1	1	yes	characteristic
95	C₂×C₄²×C₄₁	D₄	1	1	yes	characteristic
96	C₂×C₄²×C₄₁	D₄	1	1	yes	characteristic
97	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
98	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
99	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
100	#107×C₄₁	—	2	2	no	—
101	#107×C₄₁	—	2	2	no	—
102	#106×C₄₁	—	2	2	no	—
103	#103×C₄₁	—	2	2	no	—
104	#103×C₄₁	—	2	2	no	—
105	#103×C₄₁	—	2	2	no	—
106	#102×C₄₁	—	2	2	no	—
107	#102×C₄₁	—	2	2	no	—
108	#102×C₄₁	—	2	2	no	—
109	#95×C₄₁	—	2	1	no	—
110	#95×C₄₁	—	2	1	no	—
111	#95×C₄₁	—	2	1	no	—
112	#95×C₄₁	—	2	1	no	—
113	#95×C₄₁	—	2	1	no	—
114	#95×C₄₁	—	2	1	no	—
115	#95×C₄₁	—	2	1	no	—
116	#95×C₄₁	—	2	1	no	—
117	#95×C₄₁	—	2	1	no	—
118	#95×C₄₁	—	2	1	no	—
119	#95×C₄₁	—	2	1	no	—
120	#95×C₄₁	—	2	1	no	—
121	C₂⁴×C₄₁	—	2	1	no	—
122	C₂×Q₈×C₄₁	—	2	1	no	—
123	C₂×Q₈×C₄₁	—	2	1	no	—
124	C₂×Q₈×C₄₁	—	2	1	no	—
125	C₂×Q₈×C₄₁	—	2	1	no	—
126	C₂×Q₈×C₄₁	—	2	1	no	—
127	C₂×Q₈×C₄₁	—	2	1	no	—
128	C₂×D₄×C₄₁	—	2	1	no	—
129	C₂×D₄×C₄₁	—	2	1	no	—
130	C₂×D₄×C₄₁	—	2	1	no	—
131	C₂×D₄×C₄₁	#41	1	2	yes	—
132	C₂×D₄×C₄₁	#41	1	2	yes	—
133	C₂×D₄×C₄₁	#41	1	2	yes	—
134	C₂²×C₄×C₄₁	—	2	4	no	—
135	C₂²×C₄×C₄₁	—	2	4	no	—
136	C₂²×C₄×C₄₁	—	2	4	no	—
137	C₂²×C₄×C₄₁	—	2	1	no	—
138	C₂²×C₄×C₄₁	—	2	1	no	—
139	C₂²×C₄×C₄₁	—	2	1	no	—
140	C₂²×C₄×C₄₁	—	2	1	no	—
141	C₂²×C₄×C₄₁	—	2	1	no	—
142	C₂²×C₄×C₄₁	—	2	1	no	—
143	C₂²×C₄×C₄₁	—	2	1	no	—
144	C₂²×C₄×C₄₁	—	4	2	no	—
145	C₂²×C₄×C₄₁	—	4	2	no	—
146	C₂²×C₄×C₄₁	—	4	2	no	—
147	C₂²×C₄×C₄₁	—	4	2	no	—
148	C₂²×C₄×C₄₁	—	4	2	no	—
149	C₂²×C₄×C₄₁	—	4	2	no	—
150	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
151	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
152	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
153	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
154	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
155	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
156	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
157	SD₁₆×C₄₁	—	4	4	no	—
158	C₂×C₈×C₄₁	—	2	1	no	—
159	C₂×C₈×C₄₁	—	2	1	no	—
160	C₂×C₈×C₄₁	—	2	1	no	—
161	C₂×C₈×C₄₁	—	2	1	no	—
162	C₂×C₈×C₄₁	—	2	1	no	—
163	C₂×C₈×C₄₁	—	2	1	no	—
164	C₂×C₈×C₄₁	—	2	1	no	—
165	C₂×C₈×C₄₁	—	2	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	C₄⋊C₄×C₄₁	—	2	1	no	—
171	C₄⋊C₄×C₄₁	—	2	1	no	—
172	C₄⋊C₄×C₄₁	—	2	1	no	—
173	C₄⋊C₄×C₄₁	—	2	1	no	—
174	C₄⋊C₄×C₄₁	—	2	1	no	—
175	C₄⋊C₄×C₄₁	—	2	1	no	—
176	C₄⋊C₄×C₄₁	—	2	1	no	—
177	C₄⋊C₄×C₄₁	—	2	1	no	—
178	C₄⋊C₄×C₄₁	—	2	1	no	—
179	C₄⋊C₄×C₄₁	—	4	2	no	—
180	C₄⋊C₄×C₄₁	—	4	2	no	—
181	C₄⋊C₄×C₄₁	—	4	2	no	—
182	C₄⋊C₄×C₄₁	#41	1	2	yes	—
183	C₄⋊C₄×C₄₁	#41	1	2	yes	—
184	C₄⋊C₄×C₄₁	#41	1	2	yes	—
185	C₂²⋊C₄×C₄₁	—	2	4	no	—
186	C₂²⋊C₄×C₄₁	—	2	4	no	—
187	C₂²⋊C₄×C₄₁	—	2	4	no	—
188	C₄²×C₄₁	—	2	2	no	—
189	C₄²×C₄₁	—	2	2	no	—
190	C₄²×C₄₁	—	2	2	no	—
191	C₄²×C₄₁	—	2	1	no	—
192	C₄²×C₄₁	—	2	1	no	—
193	C₄²×C₄₁	—	2	1	no	—
194	C₄²×C₄₁	—	2	1	no	—
195	C₄²×C₄₁	—	2	1	no	—
196	C₄²×C₄₁	—	2	1	no	—
197	C₄²×C₄₁	—	4	1	no	—
198	C₄²×C₄₁	—	4	2	no	—
199	C₄²×C₄₁	—	4	2	no	—
200	C₄²×C₄₁	—	4	2	no	—
201	C₂³×C₄₁	—	2	2	no	—
202	C₂³×C₄₁	—	2	2	no	—
203	C₂³×C₄₁	—	2	2	no	—
204	C₂³×C₄₁	—	4	1	no	—
205	C₂³×C₄₁	—	4	1	no	—
206	C₂³×C₄₁	—	4	1	no	—
207	C₂³×C₄₁	—	4	1	no	—
208	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
209	Q₈×C₄₁	—	4	1	no	—
210	Q₈×C₄₁	—	4	1	no	—
211	Q₈×C₄₁	—	4	1	no	—
212	Q₈×C₄₁	—	4	1	no	—
213	D₄×C₄₁	—	2	2	no	—
214	D₄×C₄₁	—	2	2	no	—
215	D₄×C₄₁	—	2	2	no	—
216	D₄×C₄₁	#126	1	4	yes	—
217	C₂×C₄×C₄₁	—	2	1	no	—
218	C₂×C₄×C₄₁	—	2	1	no	—
219	C₂×C₄×C₄₁	—	2	1	no	—
220	C₂×C₄×C₄₁	—	2	1	no	—
221	C₂×C₄×C₄₁	—	2	1	no	—
222	C₂×C₄×C₄₁	—	2	1	no	—
223	C₂×C₄×C₄₁	—	2	1	no	—
224	C₂×C₄×C₄₁	—	2	1	no	—
225	C₂×C₄×C₄₁	—	2	1	no	—
226	C₂×C₄×C₄₁	—	2	2	no	—
227	C₂×C₄×C₄₁	—	2	2	no	—
228	C₂×C₄×C₄₁	—	2	2	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	—	2	1	no	—
235	C₂×C₄×C₄₁	—	4	8	no	—
236	C₂×C₄×C₄₁	—	4	8	no	—
237	C₂×C₄×C₄₁	—	4	8	no	—
238	C₂×C₄×C₄₁	—	4	1	no	—
239	C₂×C₄×C₄₁	—	4	1	no	—
240	C₂×C₄×C₄₁	—	4	1	no	—
241	C₂×C₄×C₄₁	—	4	1	no	—
242	C₂×C₄×C₄₁	—	4	1	no	—
243	C₂×C₄×C₄₁	—	4	1	no	—
244	C₂×C₄×C₄₁	—	4	1	no	—
245	C₂×C₄×C₄₁	—	4	1	no	—
246	C₂×C₄×C₄₁	—	4	1	no	—
247	C₂×C₄×C₄₁	—	4	1	no	—
248	C₂×C₄×C₄₁	—	4	1	no	—
249	C₂×C₄×C₄₁	—	4	1	no	—
250	C₂×C₄×C₄₁	—	4	1	no	—
251	C₂×C₄×C₄₁	—	4	1	no	—
252	C₂×C₄×C₄₁	—	4	1	no	—
253	C₂×C₄×C₄₁	—	4	1	no	—
254	C₂×C₄×C₄₁	—	4	1	no	—
255	C₂×C₄×C₄₁	—	4	1	no	—
256	C₂×C₄×C₄₁	#135	1	2	yes	—
257	C₂×C₄×C₄₁	AGL(1,ℤ/8)	1	2	yes	—
258	C₂×C₄×C₄₁	#137	1	2	yes	—
259	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
260	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
261	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
262	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
263	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
264	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
265	C₈×C₄₁	—	4	1	no	—
266	C₈×C₄₁	—	4	1	no	—
267	C₈×C₄₁	—	4	1	no	—
268	C₈×C₄₁	—	4	1	no	—
269	#33084	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
270	C₂²×C₄₁	—	2	4	no	—
271	C₂²×C₄₁	—	4	2	no	—
272	C₂²×C₄₁	—	4	2	no	—
273	C₂²×C₄₁	—	4	2	no	—
274	C₂²×C₄₁	—	4	2	no	—
275	C₂²×C₄₁	—	4	2	no	—
276	C₂²×C₄₁	—	4	2	no	—
277	C₂²×C₄₁	#525	1	1	yes	characteristic
278	C₂²×C₄₁	#525	1	1	yes	characteristic
279	C₂²×C₄₁	#525	1	1	yes	characteristic
280	C₂²×C₄₁	C₂×#135	1	1	yes	characteristic
281	C₂²×C₄₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
282	C₂²×C₄₁	C₂×#137	1	1	yes	characteristic
283	C₂²×C₄₁	#575	1	1	yes	characteristic
284	C₄×C₄₁	—	2	2	no	—
285	C₄×C₄₁	—	2	2	no	—
286	C₄×C₄₁	—	2	2	no	—
287	C₄×C₄₁	—	4	1	no	—
288	C₄×C₄₁	—	4	2	no	—
289	C₄×C₄₁	—	4	1	no	—
290	C₄×C₄₁	—	4	2	no	—
291	C₄×C₄₁	—	4	2	no	—
292	C₄×C₄₁	—	4	1	no	—
293	C₄×C₄₁	—	8	1	no	—
294	C₄×C₄₁	—	8	1	no	—
295	C₄×C₄₁	—	8	1	no	—
296	C₄×C₄₁	—	8	1	no	—
297	C₄×C₄₁	C₂×#126	1	1	yes	characteristic
298	C₄×C₄₁	#529	1	1	yes	characteristic
299	C₄×C₄₁	#529	1	1	yes	characteristic
300	C₄×C₄₁	#529	1	1	yes	characteristic
301	#2863	C₂×C₄₁	1	1	yes	characteristic, complemented
302	C₄²×D₄	C₂×C₄₁	1	1	yes	characteristic
303	#1928	C₂×C₄₁	1	1	yes	characteristic, complemented
304	#1928	C₂×C₄₁	1	1	yes	characteristic, complemented
305	#1927	C₂×C₄₁	1	1	yes	characteristic, complemented
306	#1921	C₂×C₄₁	1	1	yes	characteristic, complemented
307	#1919	C₂×C₄₁	1	1	yes	characteristic, complemented
308	#1918	C₂×C₄₁	1	1	yes	characteristic, complemented
309	#1877	C₂×C₄₁	1	1	yes	characteristic
310	#1877	C₂×C₄₁	1	1	yes	characteristic
311	#1877	C₂×C₄₁	1	1	yes	characteristic
312	#1864	C₂×C₄₁	1	1	yes	characteristic
313	#1862	C₂×C₄₁	1	1	yes	characteristic
314	#1862	C₂×C₄₁	1	1	yes	characteristic
315	#1839	C₂×C₄₁	1	1	yes	characteristic, complemented
316	C₂×C₄₁	—	4	4	no	—
317	C₂×C₄₁	#2852	1	1	yes	characteristic
318	C₂×C₄₁	#3102	1	1	yes	characteristic
319	C₂×C₄₁	#3105	1	1	yes	characteristic
320	C₂×C₄₁	#3107	1	1	yes	characteristic
321	C₂×C₄₁	#3110	1	1	yes	characteristic
322	C₂×C₄₁	#3114	1	1	yes	characteristic
323	C₂×C₄₁	#3116	1	1	yes	characteristic
324	C₂²×SD₁₆	C₂²×C₄₁	1	1	yes	characteristic
325	C₂×C₄×D₄	C₂²×C₄₁	1	1	yes	characteristic
326	C₂×C₄×D₄	C₂²×C₄₁	1	1	yes	characteristic
327	C₂×C₄×D₄	C₂²×C₄₁	1	1	yes	characteristic
328	C₂²×C₄²	—	2	1	no	—
329	C₂×#107	C₂²×C₄₁	1	1	yes	characteristic
330	C₂×#107	C₂²×C₄₁	1	1	yes	characteristic
331	C₂×#106	C₂²×C₄₁	1	1	yes	characteristic
332	C₂×#103	C₂²×C₄₁	1	1	yes	characteristic
333	C₂×#103	C₂²×C₄₁	1	1	yes	characteristic
334	C₂×#103	C₂²×C₄₁	1	1	yes	characteristic
335	C₂×#102	C₂²×C₄₁	1	1	yes	characteristic
336	C₂×#102	C₂²×C₄₁	1	1	yes	characteristic
337	C₂×#102	C₂²×C₄₁	1	1	yes	characteristic
338	#391	C₂²×C₄₁	1	1	yes	characteristic
339	#391	C₂²×C₄₁	1	1	yes	characteristic
340	#391	C₂²×C₄₁	1	1	yes	characteristic
341	#389	C₂²×C₄₁	1	1	yes	characteristic
342	#389	C₂²×C₄₁	1	1	yes	characteristic
343	#389	C₂²×C₄₁	1	1	yes	characteristic
344	#387	—	2	1	no	—
345	#387	—	2	1	no	—
346	#387	—	2	1	no	—
347	#383	—	2	1	no	—
348	C₄×C₄⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
349	C₄×C₄⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
350	C₄×C₄⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
351	C₄×C₂²⋊C₄	—	2	1	no	—
352	C₄×C₂²⋊C₄	—	2	1	no	—
353	C₄×C₂²⋊C₄	—	2	1	no	—
354	C₄³	C₂²×C₄₁	1	1	yes	characteristic
355	#340	C₂²×C₄₁	1	1	yes	characteristic
356	#340	C₂²×C₄₁	1	1	yes	characteristic
357	#340	C₂²×C₄₁	1	1	yes	characteristic
358	#340	C₂²×C₄₁	1	1	yes	characteristic
359	#340	C₂²×C₄₁	1	1	yes	characteristic
360	#340	C₂²×C₄₁	1	1	yes	characteristic
361	#336	C₂²×C₄₁	1	1	yes	characteristic
362	#336	C₂²×C₄₁	1	1	yes	characteristic
363	#336	C₂²×C₄₁	1	1	yes	characteristic
364	#336	C₂²×C₄₁	1	1	yes	characteristic
365	#336	C₂²×C₄₁	1	1	yes	characteristic
366	#336	C₂²×C₄₁	1	1	yes	characteristic
367	C₄₁	#33084	1	1	yes	characteristic, direct product factor, Sylow
368	C₂²×Q₈	C₂³×C₄₁	1	1	yes	characteristic
369	C₂²×D₄	C₂³×C₄₁	1	1	yes	characteristic
370	C₂³×C₄	—	2	1	no	—
371	C₂³×C₄	—	2	1	no	—
372	C₂³×C₄	—	2	1	no	—
373	C₂×SD₁₆	—	2	2	no	—
374	C₂×SD₁₆	—	2	2	no	—
375	C₂×SD₁₆	—	2	2	no	—
376	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
377	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
378	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
379	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
380	C₄×D₄	—	2	2	no	—
381	C₄×D₄	—	2	2	no	—
382	C₄×D₄	—	2	2	no	—
383	C₄×D₄	—	2	2	no	—
384	C₄×D₄	—	2	2	no	—
385	C₄×D₄	—	2	2	no	—
386	C₂×C₄⋊C₄	—	2	1	no	—
387	C₂×C₄⋊C₄	—	2	1	no	—
388	C₂×C₄⋊C₄	—	2	1	no	—
389	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
390	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
391	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
392	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
393	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
394	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
395	C₂×C₂²⋊C₄	—	2	1	no	—
396	C₂×C₂²⋊C₄	—	2	1	no	—
397	C₂×C₂²⋊C₄	—	2	1	no	—
398	C₂×C₄²	—	2	1	no	—
399	C₂×C₄²	—	2	1	no	—
400	C₂×C₄²	—	2	1	no	—
401	C₂×C₄²	—	4	4	no	—
402	C₂×C₄²	D₄×C₄₁	1	1	yes	characteristic
403	C₂×C₄²	D₄×C₄₁	1	1	yes	characteristic
404	C₂×C₄²	D₄×C₄₁	1	1	yes	characteristic
405	C₂×C₄²	D₄×C₄₁	1	1	yes	characteristic
406	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
407	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
408	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
409	#107	—	2	2	no	—
410	#107	—	2	2	no	—
411	#106	—	2	2	no	—
412	#103	—	2	2	no	—
413	#103	—	2	2	no	—
414	#103	—	2	2	no	—
415	#102	—	2	2	no	—
416	#102	—	2	2	no	—
417	#102	—	2	2	no	—
418	#95	—	2	1	no	—
419	#95	—	2	1	no	—
420	#95	—	2	1	no	—
421	#95	—	2	1	no	—
422	#95	—	2	1	no	—
423	#95	—	2	1	no	—
424	#95	—	2	1	no	—
425	#95	—	2	1	no	—
426	#95	—	2	1	no	—
427	#95	—	2	1	no	—
428	#95	—	2	1	no	—
429	#95	—	2	1	no	—
430	C₂⁴	—	2	1	no	—
431	C₂×Q₈	—	2	1	no	—
432	C₂×Q₈	—	2	1	no	—
433	C₂×Q₈	—	2	1	no	—
434	C₂×Q₈	—	2	1	no	—
435	C₂×Q₈	—	2	1	no	—
436	C₂×Q₈	—	2	1	no	—
437	C₂×D₄	—	2	1	no	—
438	C₂×D₄	—	2	1	no	—
439	C₂×D₄	—	2	1	no	—
440	C₂×D₄	#41×C₄₁	1	2	yes	—
441	C₂×D₄	#41×C₄₁	1	2	yes	—
442	C₂×D₄	#41×C₄₁	1	2	yes	—
443	C₂²×C₄	—	2	4	no	—
444	C₂²×C₄	—	2	4	no	—
445	C₂²×C₄	—	2	4	no	—
446	C₂²×C₄	—	2	1	no	—
447	C₂²×C₄	—	2	1	no	—
448	C₂²×C₄	—	2	1	no	—
449	C₂²×C₄	—	2	1	no	—
450	C₂²×C₄	—	2	1	no	—
451	C₂²×C₄	—	2	1	no	—
452	C₂²×C₄	—	2	1	no	—
453	C₂²×C₄	—	4	2	no	—
454	C₂²×C₄	—	4	2	no	—
455	C₂²×C₄	—	4	2	no	—
456	C₂²×C₄	—	4	2	no	—
457	C₂²×C₄	—	4	2	no	—
458	C₂²×C₄	—	4	2	no	—
459	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
460	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
461	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
462	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
463	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
464	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
465	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
466	SD₁₆	—	4	4	no	—
467	C₂×C₈	—	2	1	no	—
468	C₂×C₈	—	2	1	no	—
469	C₂×C₈	—	2	1	no	—
470	C₂×C₈	—	2	1	no	—
471	C₂×C₈	—	2	1	no	—
472	C₂×C₈	—	2	1	no	—
473	C₂×C₈	—	2	1	no	—
474	C₂×C₈	—	2	1	no	—
475	C₂×C₈	—	2	1	no	—
476	C₂×C₈	—	2	1	no	—
477	C₂×C₈	—	2	1	no	—
478	C₂×C₈	—	2	1	no	—
479	C₄⋊C₄	—	2	1	no	—
480	C₄⋊C₄	—	2	1	no	—
481	C₄⋊C₄	—	2	1	no	—
482	C₄⋊C₄	—	2	1	no	—
483	C₄⋊C₄	—	2	1	no	—
484	C₄⋊C₄	—	2	1	no	—
485	C₄⋊C₄	—	2	1	no	—
486	C₄⋊C₄	—	2	1	no	—
487	C₄⋊C₄	—	2	1	no	—
488	C₄⋊C₄	—	4	2	no	—
489	C₄⋊C₄	—	4	2	no	—
490	C₄⋊C₄	—	4	2	no	—
491	C₄⋊C₄	#41×C₄₁	1	2	yes	—
492	C₄⋊C₄	#41×C₄₁	1	2	yes	—
493	C₄⋊C₄	#41×C₄₁	1	2	yes	—
494	C₂²⋊C₄	—	2	4	no	—
495	C₂²⋊C₄	—	2	4	no	—
496	C₂²⋊C₄	—	2	4	no	—
497	C₄²	—	2	2	no	—
498	C₄²	—	2	2	no	—
499	C₄²	—	2	2	no	—
500	C₄²	—	2	1	no	—
501	C₄²	—	2	1	no	—
502	C₄²	—	2	1	no	—
503	C₄²	—	2	1	no	—
504	C₄²	—	2	1	no	—
505	C₄²	—	2	1	no	—
506	C₄²	—	4	1	no	—
507	C₄²	—	4	2	no	—
508	C₄²	—	4	2	no	—
509	C₄²	—	4	2	no	—
510	C₂³	—	2	2	no	—
511	C₂³	—	2	2	no	—
512	C₂³	—	2	2	no	—
513	C₂³	—	4	1	no	—
514	C₂³	—	4	1	no	—
515	C₂³	—	4	1	no	—
516	C₂³	—	4	1	no	—
517	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
518	Q₈	—	4	1	no	—
519	Q₈	—	4	1	no	—
520	Q₈	—	4	1	no	—
521	Q₈	—	4	1	no	—
522	D₄	—	2	2	no	—
523	D₄	—	2	2	no	—
524	D₄	—	2	2	no	—
525	D₄	#126×C₄₁	1	4	yes	—
526	C₂×C₄	—	2	1	no	—
527	C₂×C₄	—	2	1	no	—
528	C₂×C₄	—	2	1	no	—
529	C₂×C₄	—	2	1	no	—
530	C₂×C₄	—	2	1	no	—
531	C₂×C₄	—	2	1	no	—
532	C₂×C₄	—	2	1	no	—
533	C₂×C₄	—	2	1	no	—
534	C₂×C₄	—	2	1	no	—
535	C₂×C₄	—	2	2	no	—
536	C₂×C₄	—	2	2	no	—
537	C₂×C₄	—	2	2	no	—
538	C₂×C₄	—	2	1	no	—
539	C₂×C₄	—	2	1	no	—
540	C₂×C₄	—	2	1	no	—
541	C₂×C₄	—	2	1	no	—
542	C₂×C₄	—	2	1	no	—
543	C₂×C₄	—	2	1	no	—
544	C₂×C₄	—	4	8	no	—
545	C₂×C₄	—	4	8	no	—
546	C₂×C₄	—	4	8	no	—
547	C₂×C₄	—	4	1	no	—
548	C₂×C₄	—	4	1	no	—
549	C₂×C₄	—	4	1	no	—
550	C₂×C₄	—	4	1	no	—
551	C₂×C₄	—	4	1	no	—
552	C₂×C₄	—	4	1	no	—
553	C₂×C₄	—	4	1	no	—
554	C₂×C₄	—	4	1	no	—
555	C₂×C₄	—	4	1	no	—
556	C₂×C₄	—	4	1	no	—
557	C₂×C₄	—	4	1	no	—
558	C₂×C₄	—	4	1	no	—
559	C₂×C₄	—	4	1	no	—
560	C₂×C₄	—	4	1	no	—
561	C₂×C₄	—	4	1	no	—
562	C₂×C₄	—	4	1	no	—
563	C₂×C₄	—	4	1	no	—
564	C₂×C₄	—	4	1	no	—
565	C₂×C₄	#135×C₄₁	1	2	yes	—
566	C₂×C₄	AGL(1,ℤ/8)×C₄₁	1	2	yes	—
567	C₂×C₄	#137×C₄₁	1	2	yes	—
568	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
569	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
570	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
571	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
572	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
573	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
574	C₈	—	4	1	no	—
575	C₈	—	4	1	no	—
576	C₈	—	4	1	no	—
577	C₈	—	4	1	no	—
578	C₂²	—	2	4	no	—
579	C₂²	—	4	2	no	—
580	C₂²	—	4	2	no	—
581	C₂²	—	4	2	no	—
582	C₂²	—	4	2	no	—
583	C₂²	—	4	2	no	—
584	C₂²	—	4	2	no	—
585	C₂²	C₄₁×#525	1	1	yes	characteristic
586	C₂²	C₄₁×#525	1	1	yes	characteristic
587	C₂²	C₄₁×#525	1	1	yes	characteristic
588	C₂²	C₂×#135×C₄₁	1	1	yes	characteristic
589	C₂²	C₂×AGL(1,ℤ/8)×C₄₁	1	1	yes	characteristic
590	C₂²	C₂×#137×C₄₁	1	1	yes	characteristic
591	C₂²	C₄₁×#575	1	1	yes	characteristic
592	C₄	—	2	2	no	—
593	C₄	—	2	2	no	—
594	C₄	—	2	2	no	—
595	C₄	—	4	1	no	—
596	C₄	—	4	2	no	—
597	C₄	—	4	1	no	—
598	C₄	—	4	2	no	—
599	C₄	—	4	2	no	—
600	C₄	—	4	1	no	—
601	C₄	—	8	1	no	—
602	C₄	—	8	1	no	—
603	C₄	—	8	1	no	—
604	C₄	—	8	1	no	—
605	C₄	C₂×#126×C₄₁	1	1	yes	characteristic
606	C₄	C₄₁×#529	1	1	yes	characteristic
607	C₄	C₄₁×#529	1	1	yes	characteristic
608	C₄	C₄₁×#529	1	1	yes	characteristic
609	C₂	—	4	4	no	—
610	C₂	C₄₁×#2852	1	1	yes	characteristic
611	C₂	C₄₁×#3102	1	1	yes	characteristic
612	C₂	C₄₁×#3105	1	1	yes	characteristic
613	C₂	C₄₁×#3107	1	1	yes	characteristic
614	C₂	C₄₁×#3110	1	1	yes	characteristic
615	C₂	C₄₁×#3114	1	1	yes	characteristic
616	C₂	C₄₁×#3116	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₄₁	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₁
prime radical	C₂²×D₄×C₄₁	C₂³
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₄₁ ◁ C₄³×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₄₁×#2863	C₂	semidirect
3. C₄₁×#1928	C₂	semidirect
4. C₄₁×#1928	C₂	semidirect
5. C₄₁×#1927	C₂	semidirect
6. C₄₁×#1921	C₂	semidirect
7. C₄₁×#1919	C₂	semidirect
8. C₄₁×#1918	C₂	semidirect
15. C₄₁×#1839	C₂	semidirect
269. #33084	C₄₁	direct (N × H)
301. #2863	C₂×C₄₁	semidirect
303. #1928	C₂×C₄₁	semidirect
304. #1928	C₂×C₄₁	semidirect
305. #1927	C₂×C₄₁	semidirect
306. #1921	C₂×C₄₁	semidirect
307. #1919	C₂×C₄₁	semidirect
308. #1918	C₂×C₄₁	semidirect
315. #1839	C₂×C₄₁	semidirect
367. C₄₁	#33084	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×#2863	2
C₄²×D₄×C₄₁	2
C₄₁×#1928	2
C₄₁×#1927	2
C₄₁×#1921	2
C₄₁×#1919	2
C₄₁×#1918	2
C₄₁×#1877	2
C₄₁×#1864	2
C₄₁×#1862	2
C₄₁×#1839	2
#33084	41

Subgroups — C41×#33084 #23809285

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#33084 #23809285