Subgroups — C₄₁×#33101 #23809302

Order 10496.

770 conjugacy classes of subgroups.

The subgroup lattice has 610 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₁×#2855	C₂	1	1	yes	maximal, characteristic
2	C₄×#117×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×#1927	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₁×#1921	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄₁×#1920	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄₁×#1919	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄₁×#1918	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₁×#1873	C₂	1	1	yes	maximal, characteristic
12	C₄₁×#1873	C₂	1	1	yes	maximal, characteristic
13	C₄₁×#1854	C₂	1	1	yes	maximal, characteristic
14	C₄₁×#1854	C₂	1	1	yes	maximal, characteristic
15	C₄₁×#1817	C₂	1	1	yes	maximal, characteristic
16	C₂×C₂²⋊Q₈×C₄₁	C₂²	1	1	yes	characteristic
17	C₂×#117×C₄₁	C₂²	1	1	yes	characteristic
18	C₂×#117×C₄₁	C₂²	1	1	yes	characteristic
19	C₂²×C₄²×C₄₁	C₂²	1	1	yes	characteristic
20	C₂×#107×C₄₁	C₂²	1	1	yes	characteristic
21	C₂×#107×C₄₁	C₂²	1	1	yes	characteristic
22	C₂×#106×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×#103×C₄₁	C₂²	1	1	yes	characteristic
28	C₂×C₂²⋊C₈×C₄₁	C₂²	1	1	yes	characteristic
29	C₂×C₂²⋊C₈×C₄₁	C₂²	1	1	yes	characteristic
30	C₄₁×#391	C₂²	1	1	yes	characteristic
31	C₄₁×#391	C₂²	1	1	yes	characteristic
32	C₄₁×#389	C₂²	1	1	yes	characteristic
33	C₄₁×#389	C₂²	1	1	yes	characteristic
34	C₄₁×#387	—	2	1	no	—
35	C₄₁×#387	—	2	1	no	—
36	C₄₁×#385	—	2	1	no	—
37	C₄₁×#381	—	2	1	no	—
38	C₄₁×#380	C₂²	1	1	yes	characteristic
39	C₄×C₄⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
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	C₄₁×#376	—	2	1	no	—
46	C₄³×C₄₁	—	2	1	no	—
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×#340	C₂²	1	1	yes	characteristic
54	C₄₁×#340	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	C₂³×C₄×C₄₁	D₄	1	1	yes	characteristic
61	C₂³×C₄×C₄₁	D₄	1	1	yes	characteristic
62	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
63	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
64	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
65	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
66	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
67	C₂²⋊Q₈×C₄₁	—	2	2	no	—
68	C₂²⋊Q₈×C₄₁	—	2	2	no	—
69	#117×C₄₁	—	2	2	no	—
70	#117×C₄₁	—	2	2	no	—
71	#117×C₄₁	—	2	2	no	—
72	#117×C₄₁	—	2	2	no	—
73	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
74	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
75	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
76	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
77	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
78	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
79	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
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×C₂²⋊C₄×C₄₁	—	2	1	no	—
84	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
85	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
86	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
87	C₂×C₄²×C₄₁	—	2	1	no	—
88	C₂×C₄²×C₄₁	—	2	1	no	—
89	C₂×C₄²×C₄₁	—	2	2	no	—
90	C₂×C₄²×C₄₁	—	2	2	no	—
91	C₂×C₄²×C₄₁	—	2	1	no	—
92	C₂×C₄²×C₄₁	—	2	1	no	—
93	C₂×C₄²×C₄₁	—	2	1	no	—
94	C₂×C₄²×C₄₁	—	2	1	no	—
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	#107×C₄₁	—	2	2	no	—
100	#107×C₄₁	—	2	2	no	—
101	#106×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	#103×C₄₁	—	2	2	no	—
107	C₂²⋊C₈×C₄₁	—	2	2	no	—
108	C₂²⋊C₈×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	C₂⁴×C₄₁	C₂×D₄	1	1	yes	characteristic
121	C₂×Q₈×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	C₂²×C₄×C₄₁	—	2	1	no	—
128	C₂²×C₄×C₄₁	—	2	1	no	—
129	C₂²×C₄×C₄₁	—	2	1	no	—
130	C₂²×C₄×C₄₁	—	2	1	no	—
131	C₂²×C₄×C₄₁	—	2	2	no	—
132	C₂²×C₄×C₄₁	—	2	2	no	—
133	C₂²×C₄×C₄₁	—	2	1	no	—
134	C₂²×C₄×C₄₁	—	2	1	no	—
135	C₂²×C₄×C₄₁	—	2	1	no	—
136	C₂²×C₄×C₄₁	—	2	1	no	—
137	C₂²×C₄×C₄₁	—	2	2	no	—
138	C₂²×C₄×C₄₁	—	2	2	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	—	4	1	no	—
144	C₂²×C₄×C₄₁	—	4	1	no	—
145	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
146	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
147	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
148	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
149	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
150	C₂²×C₄×C₄₁	#41	1	2	yes	—
151	C₂²×C₄×C₄₁	#41	1	2	yes	—
152	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
153	C₂×C₈×C₄₁	—	2	1	no	—
154	C₂×C₈×C₄₁	—	2	1	no	—
155	C₂×C₈×C₄₁	—	2	1	no	—
156	C₂×C₈×C₄₁	—	2	1	no	—
157	C₂×C₈×C₄₁	—	2	1	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	C₄⋊C₄×C₄₁	—	2	1	no	—
166	C₄⋊C₄×C₄₁	—	2	1	no	—
167	C₄⋊C₄×C₄₁	—	2	1	no	—
168	C₄⋊C₄×C₄₁	—	2	1	no	—
169	C₄⋊C₄×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	—	4	2	no	—
176	C₄⋊C₄×C₄₁	—	4	2	no	—
177	C₄⋊C₄×C₄₁	—	4	2	no	—
178	C₄⋊C₄×C₄₁	#41	1	2	yes	—
179	C₄⋊C₄×C₄₁	#41	1	2	yes	—
180	C₄⋊C₄×C₄₁	#41	1	2	yes	—
181	C₄⋊C₄×C₄₁	#41	1	2	yes	—
182	C₂²⋊C₄×C₄₁	—	2	4	no	—
183	C₂²⋊C₄×C₄₁	—	2	4	no	—
184	C₂²⋊C₄×C₄₁	—	4	2	no	—
185	C₂²⋊C₄×C₄₁	—	4	2	no	—
186	C₄²×C₄₁	—	2	4	no	—
187	C₄²×C₄₁	—	2	4	no	—
188	C₄²×C₄₁	—	2	2	no	—
189	C₄²×C₄₁	—	2	2	no	—
190	C₄²×C₄₁	—	2	1	no	—
191	C₄²×C₄₁	—	2	1	no	—
192	C₄²×C₄₁	—	2	1	no	—
193	C₄²×C₄₁	—	2	1	no	—
194	C₄²×C₄₁	—	4	2	no	—
195	C₄²×C₄₁	—	4	2	no	—
196	C₄²×C₄₁	—	4	2	no	—
197	C₄²×C₄₁	—	4	2	no	—
198	C₂³×C₄₁	—	2	1	no	—
199	C₂³×C₄₁	—	2	1	no	—
200	C₂³×C₄₁	—	2	1	no	—
201	C₂³×C₄₁	—	2	1	no	—
202	C₂³×C₄₁	—	2	1	no	—
203	C₂³×C₄₁	—	2	1	no	—
204	C₂³×C₄₁	#123	1	2	yes	—
205	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
206	Q₈×C₄₁	—	4	1	no	—
207	Q₈×C₄₁	—	4	1	no	—
208	Q₈×C₄₁	—	4	1	no	—
209	Q₈×C₄₁	—	4	1	no	—
210	C₂×C₄×C₄₁	—	2	1	no	—
211	C₂×C₄×C₄₁	—	2	1	no	—
212	C₂×C₄×C₄₁	—	2	1	no	—
213	C₂×C₄×C₄₁	—	2	1	no	—
214	C₂×C₄×C₄₁	—	2	1	no	—
215	C₂×C₄×C₄₁	—	2	1	no	—
216	C₂×C₄×C₄₁	—	2	2	no	—
217	C₂×C₄×C₄₁	—	2	2	no	—
218	C₂×C₄×C₄₁	—	2	2	no	—
219	C₂×C₄×C₄₁	—	2	2	no	—
220	C₂×C₄×C₄₁	—	2	1	no	—
221	C₂×C₄×C₄₁	—	2	1	no	—
222	C₂×C₄×C₄₁	—	2	2	no	—
223	C₂×C₄×C₄₁	—	2	2	no	—
224	C₂×C₄×C₄₁	—	2	2	no	—
225	C₂×C₄×C₄₁	—	2	2	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	—	4	4	no	—
231	C₂×C₄×C₄₁	—	4	4	no	—
232	C₂×C₄×C₄₁	—	4	1	no	—
233	C₂×C₄×C₄₁	—	4	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	—	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	#123	1	2	yes	—
253	C₂×C₄×C₄₁	#135	1	2	yes	—
254	C₂×C₄×C₄₁	#137	1	2	yes	—
255	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
256	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
257	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
258	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
259	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
260	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
261	C₈×C₄₁	—	4	1	no	—
262	C₈×C₄₁	—	4	1	no	—
263	C₈×C₄₁	—	4	1	no	—
264	C₈×C₄₁	—	4	1	no	—
265	#33101	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
266	C₂²×C₄₁	—	2	2	no	—
267	C₂²×C₄₁	—	2	2	no	—
268	C₂²×C₄₁	—	2	2	no	—
269	C₂²×C₄₁	—	4	1	no	—
270	C₂²×C₄₁	—	4	1	no	—
271	C₂²×C₄₁	—	4	1	no	—
272	C₂²×C₄₁	—	4	1	no	—
273	C₂²×C₄₁	C₂×#123	1	1	yes	characteristic
274	C₂²×C₄₁	#525	1	1	yes	characteristic
275	C₂²×C₄₁	#525	1	1	yes	characteristic
276	C₂²×C₄₁	C₂×#135	1	1	yes	characteristic
277	C₂²×C₄₁	C₂×#137	1	1	yes	characteristic
278	C₂²×C₄₁	#575	1	1	yes	characteristic
279	C₂²×C₄₁	#575	1	1	yes	characteristic
280	C₄×C₄₁	—	2	2	no	—
281	C₄×C₄₁	—	2	2	no	—
282	C₄×C₄₁	—	2	2	no	—
283	C₄×C₄₁	—	4	1	no	—
284	C₄×C₄₁	—	4	1	no	—
285	C₄×C₄₁	—	4	2	no	—
286	C₄×C₄₁	—	4	2	no	—
287	C₄×C₄₁	—	4	2	no	—
288	C₄×C₄₁	—	4	2	no	—
289	C₄×C₄₁	—	8	1	no	—
290	C₄×C₄₁	—	8	1	no	—
291	C₄×C₄₁	—	8	1	no	—
292	C₄×C₄₁	—	8	1	no	—
293	C₄×C₄₁	#529	1	1	yes	characteristic
294	C₄×C₄₁	#529	1	1	yes	characteristic
295	C₄×C₄₁	#529	1	1	yes	characteristic
296	C₄×C₄₁	#529	1	1	yes	characteristic
297	#2855	C₂×C₄₁	1	1	yes	characteristic
298	C₄×#117	C₂×C₄₁	1	1	yes	characteristic
299	#1928	C₂×C₄₁	1	1	yes	characteristic, complemented
300	#1928	C₂×C₄₁	1	1	yes	characteristic, complemented
301	#1927	C₂×C₄₁	1	1	yes	characteristic, complemented
302	#1927	C₂×C₄₁	1	1	yes	characteristic, complemented
303	#1921	C₂×C₄₁	1	1	yes	characteristic, complemented
304	#1920	C₂×C₄₁	1	1	yes	characteristic, complemented
305	#1919	C₂×C₄₁	1	1	yes	characteristic, complemented
306	#1918	C₂×C₄₁	1	1	yes	characteristic, complemented
307	#1873	C₂×C₄₁	1	1	yes	characteristic
308	#1873	C₂×C₄₁	1	1	yes	characteristic
309	#1854	C₂×C₄₁	1	1	yes	characteristic
310	#1854	C₂×C₄₁	1	1	yes	characteristic
311	#1817	C₂×C₄₁	1	1	yes	characteristic
312	C₂×C₄₁	—	4	2	no	—
313	C₂×C₄₁	#2853	1	1	yes	characteristic
314	C₂×C₄₁	#3091	1	1	yes	characteristic
315	C₂×C₄₁	#3095	1	1	yes	characteristic
316	C₂×C₄₁	#3102	1	1	yes	characteristic
317	C₂×C₄₁	#3107	1	1	yes	characteristic
318	C₂×C₄₁	#3111	1	1	yes	characteristic
319	C₂×C₄₁	#3116	1	1	yes	characteristic
320	C₂×C₂²⋊Q₈	C₂²×C₄₁	1	1	yes	characteristic
321	C₂×#117	C₂²×C₄₁	1	1	yes	characteristic
322	C₂×#117	C₂²×C₄₁	1	1	yes	characteristic
323	C₂²×C₄²	C₂²×C₄₁	1	1	yes	characteristic
324	C₂×#107	C₂²×C₄₁	1	1	yes	characteristic
325	C₂×#107	C₂²×C₄₁	1	1	yes	characteristic
326	C₂×#106	C₂²×C₄₁	1	1	yes	characteristic
327	C₂×#106	C₂²×C₄₁	1	1	yes	characteristic
328	C₂×#103	C₂²×C₄₁	1	1	yes	characteristic
329	C₂×#103	C₂²×C₄₁	1	1	yes	characteristic
330	C₂×#103	C₂²×C₄₁	1	1	yes	characteristic
331	C₂×#103	C₂²×C₄₁	1	1	yes	characteristic
332	C₂×C₂²⋊C₈	C₂²×C₄₁	1	1	yes	characteristic
333	C₂×C₂²⋊C₈	C₂²×C₄₁	1	1	yes	characteristic
334	#391	C₂²×C₄₁	1	1	yes	characteristic
335	#391	C₂²×C₄₁	1	1	yes	characteristic
336	#389	C₂²×C₄₁	1	1	yes	characteristic
337	#389	C₂²×C₄₁	1	1	yes	characteristic
338	#387	—	2	1	no	—
339	#387	—	2	1	no	—
340	#385	—	2	1	no	—
341	#381	—	2	1	no	—
342	#380	C₂²×C₄₁	1	1	yes	characteristic
343	C₄×C₄⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
344	C₄×C₄⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
345	C₄×C₄⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
346	C₄×C₄⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
347	C₄×C₂²⋊C₄	—	2	1	no	—
348	C₄×C₂²⋊C₄	—	2	1	no	—
349	#376	—	2	1	no	—
350	C₄³	—	2	1	no	—
351	#340	C₂²×C₄₁	1	1	yes	characteristic
352	#340	C₂²×C₄₁	1	1	yes	characteristic
353	#340	C₂²×C₄₁	1	1	yes	characteristic
354	#340	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	#336	C₂²×C₄₁	1	1	yes	characteristic
360	#336	C₂²×C₄₁	1	1	yes	characteristic
361	#336	C₂²×C₄₁	1	1	yes	characteristic
362	#336	C₂²×C₄₁	1	1	yes	characteristic
363	C₄₁	#33101	1	1	yes	characteristic, direct product factor, Sylow
364	C₂²×Q₈	C₂³×C₄₁	1	1	yes	characteristic
365	C₂³×C₄	D₄×C₄₁	1	1	yes	characteristic
366	C₂³×C₄	D₄×C₄₁	1	1	yes	characteristic
367	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
368	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
369	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
370	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
371	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
372	C₂²⋊Q₈	—	2	2	no	—
373	C₂²⋊Q₈	—	2	2	no	—
374	#117	—	2	2	no	—
375	#117	—	2	2	no	—
376	#117	—	2	2	no	—
377	#117	—	2	2	no	—
378	C₂×C₄⋊C₄	—	2	1	no	—
379	C₂×C₄⋊C₄	—	2	1	no	—
380	C₂×C₄⋊C₄	—	2	1	no	—
381	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
382	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
383	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
384	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
385	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
386	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
387	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
388	C₂×C₂²⋊C₄	—	2	1	no	—
389	C₂×C₂²⋊C₄	—	2	1	no	—
390	C₂×C₂²⋊C₄	—	2	1	no	—
391	C₂×C₂²⋊C₄	—	2	1	no	—
392	C₂×C₄²	—	2	1	no	—
393	C₂×C₄²	—	2	1	no	—
394	C₂×C₄²	—	2	2	no	—
395	C₂×C₄²	—	2	2	no	—
396	C₂×C₄²	—	2	1	no	—
397	C₂×C₄²	—	2	1	no	—
398	C₂×C₄²	—	2	1	no	—
399	C₂×C₄²	—	2	1	no	—
400	C₂×C₄²	D₄×C₄₁	1	1	yes	characteristic
401	C₂×C₄²	D₄×C₄₁	1	1	yes	characteristic
402	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
403	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
404	#107	—	2	2	no	—
405	#107	—	2	2	no	—
406	#106	—	2	2	no	—
407	#106	—	2	2	no	—
408	#103	—	2	2	no	—
409	#103	—	2	2	no	—
410	#103	—	2	2	no	—
411	#103	—	2	2	no	—
412	C₂²⋊C₈	—	2	2	no	—
413	C₂²⋊C₈	—	2	2	no	—
414	#95	—	2	1	no	—
415	#95	—	2	1	no	—
416	#95	—	2	1	no	—
417	#95	—	2	1	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	C₂⁴	C₂×D₄×C₄₁	1	1	yes	characteristic
426	C₂×Q₈	—	2	1	no	—
427	C₂×Q₈	—	2	1	no	—
428	C₂×Q₈	—	2	1	no	—
429	C₂×Q₈	—	2	1	no	—
430	C₂×Q₈	—	2	1	no	—
431	C₂×Q₈	—	2	1	no	—
432	C₂²×C₄	—	2	1	no	—
433	C₂²×C₄	—	2	1	no	—
434	C₂²×C₄	—	2	1	no	—
435	C₂²×C₄	—	2	1	no	—
436	C₂²×C₄	—	2	2	no	—
437	C₂²×C₄	—	2	2	no	—
438	C₂²×C₄	—	2	1	no	—
439	C₂²×C₄	—	2	1	no	—
440	C₂²×C₄	—	2	1	no	—
441	C₂²×C₄	—	2	1	no	—
442	C₂²×C₄	—	2	2	no	—
443	C₂²×C₄	—	2	2	no	—
444	C₂²×C₄	—	2	1	no	—
445	C₂²×C₄	—	2	1	no	—
446	C₂²×C₄	—	2	1	no	—
447	C₂²×C₄	—	2	1	no	—
448	C₂²×C₄	—	4	1	no	—
449	C₂²×C₄	—	4	1	no	—
450	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
451	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
452	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
453	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
454	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
455	C₂²×C₄	#41×C₄₁	1	2	yes	—
456	C₂²×C₄	#41×C₄₁	1	2	yes	—
457	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
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	—	2	1	no	—
464	C₂×C₈	—	2	1	no	—
465	C₂×C₈	—	2	1	no	—
466	C₂×C₈	—	2	1	no	—
467	C₂×C₈	—	2	1	no	—
468	C₂×C₈	—	2	1	no	—
469	C₂×C₈	—	2	1	no	—
470	C₄⋊C₄	—	2	1	no	—
471	C₄⋊C₄	—	2	1	no	—
472	C₄⋊C₄	—	2	1	no	—
473	C₄⋊C₄	—	2	1	no	—
474	C₄⋊C₄	—	2	1	no	—
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	—	4	2	no	—
481	C₄⋊C₄	—	4	2	no	—
482	C₄⋊C₄	—	4	2	no	—
483	C₄⋊C₄	#41×C₄₁	1	2	yes	—
484	C₄⋊C₄	#41×C₄₁	1	2	yes	—
485	C₄⋊C₄	#41×C₄₁	1	2	yes	—
486	C₄⋊C₄	#41×C₄₁	1	2	yes	—
487	C₂²⋊C₄	—	2	4	no	—
488	C₂²⋊C₄	—	2	4	no	—
489	C₂²⋊C₄	—	4	2	no	—
490	C₂²⋊C₄	—	4	2	no	—
491	C₄²	—	2	4	no	—
492	C₄²	—	2	4	no	—
493	C₄²	—	2	2	no	—
494	C₄²	—	2	2	no	—
495	C₄²	—	2	1	no	—
496	C₄²	—	2	1	no	—
497	C₄²	—	2	1	no	—
498	C₄²	—	2	1	no	—
499	C₄²	—	4	2	no	—
500	C₄²	—	4	2	no	—
501	C₄²	—	4	2	no	—
502	C₄²	—	4	2	no	—
503	C₂³	—	2	1	no	—
504	C₂³	—	2	1	no	—
505	C₂³	—	2	1	no	—
506	C₂³	—	2	1	no	—
507	C₂³	—	2	1	no	—
508	C₂³	—	2	1	no	—
509	C₂³	#123×C₄₁	1	2	yes	—
510	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
511	Q₈	—	4	1	no	—
512	Q₈	—	4	1	no	—
513	Q₈	—	4	1	no	—
514	Q₈	—	4	1	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	2	no	—
522	C₂×C₄	—	2	2	no	—
523	C₂×C₄	—	2	2	no	—
524	C₂×C₄	—	2	2	no	—
525	C₂×C₄	—	2	1	no	—
526	C₂×C₄	—	2	1	no	—
527	C₂×C₄	—	2	2	no	—
528	C₂×C₄	—	2	2	no	—
529	C₂×C₄	—	2	2	no	—
530	C₂×C₄	—	2	2	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	—	4	4	no	—
536	C₂×C₄	—	4	4	no	—
537	C₂×C₄	—	4	1	no	—
538	C₂×C₄	—	4	1	no	—
539	C₂×C₄	—	4	1	no	—
540	C₂×C₄	—	4	1	no	—
541	C₂×C₄	—	4	1	no	—
542	C₂×C₄	—	4	1	no	—
543	C₂×C₄	—	4	1	no	—
544	C₂×C₄	—	4	1	no	—
545	C₂×C₄	—	4	1	no	—
546	C₂×C₄	—	4	1	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	#123×C₄₁	1	2	yes	—
558	C₂×C₄	#135×C₄₁	1	2	yes	—
559	C₂×C₄	#137×C₄₁	1	2	yes	—
560	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
561	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
562	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
563	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
564	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
565	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
566	C₈	—	4	1	no	—
567	C₈	—	4	1	no	—
568	C₈	—	4	1	no	—
569	C₈	—	4	1	no	—
570	C₂²	—	2	2	no	—
571	C₂²	—	2	2	no	—
572	C₂²	—	2	2	no	—
573	C₂²	—	4	1	no	—
574	C₂²	—	4	1	no	—
575	C₂²	—	4	1	no	—
576	C₂²	—	4	1	no	—
577	C₂²	C₂×#123×C₄₁	1	1	yes	characteristic
578	C₂²	C₄₁×#525	1	1	yes	characteristic
579	C₂²	C₄₁×#525	1	1	yes	characteristic
580	C₂²	C₂×#135×C₄₁	1	1	yes	characteristic
581	C₂²	C₂×#137×C₄₁	1	1	yes	characteristic
582	C₂²	C₄₁×#575	1	1	yes	characteristic
583	C₂²	C₄₁×#575	1	1	yes	characteristic
584	C₄	—	2	2	no	—
585	C₄	—	2	2	no	—
586	C₄	—	2	2	no	—
587	C₄	—	4	1	no	—
588	C₄	—	4	1	no	—
589	C₄	—	4	2	no	—
590	C₄	—	4	2	no	—
591	C₄	—	4	2	no	—
592	C₄	—	4	2	no	—
593	C₄	—	8	1	no	—
594	C₄	—	8	1	no	—
595	C₄	—	8	1	no	—
596	C₄	—	8	1	no	—
597	C₄	C₄₁×#529	1	1	yes	characteristic
598	C₄	C₄₁×#529	1	1	yes	characteristic
599	C₄	C₄₁×#529	1	1	yes	characteristic
600	C₄	C₄₁×#529	1	1	yes	characteristic
601	C₂	—	4	2	no	—
602	C₂	C₄₁×#2853	1	1	yes	characteristic
603	C₂	C₄₁×#3091	1	1	yes	characteristic
604	C₂	C₄₁×#3095	1	1	yes	characteristic
605	C₂	C₄₁×#3102	1	1	yes	characteristic
606	C₂	C₄₁×#3107	1	1	yes	characteristic
607	C₂	C₄₁×#3111	1	1	yes	characteristic
608	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	C₂⁴×C₄₁	C₂×D₄
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₄₁ ◁ C₂²×C₄²×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₄₁×#1928	C₂	semidirect
4. C₄₁×#1928	C₂	semidirect
5. C₄₁×#1927	C₂	semidirect
6. C₄₁×#1927	C₂	semidirect
7. C₄₁×#1921	C₂	semidirect
8. C₄₁×#1920	C₂	semidirect
9. C₄₁×#1919	C₂	semidirect
10. C₄₁×#1918	C₂	semidirect
265. #33101	C₄₁	direct (N × H)
299. #1928	C₂×C₄₁	semidirect
300. #1928	C₂×C₄₁	semidirect
301. #1927	C₂×C₄₁	semidirect
302. #1927	C₂×C₄₁	semidirect
303. #1921	C₂×C₄₁	semidirect
304. #1920	C₂×C₄₁	semidirect
305. #1919	C₂×C₄₁	semidirect
306. #1918	C₂×C₄₁	semidirect
363. C₄₁	#33101	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×#2855	2
C₄×#117×C₄₁	2
C₄₁×#1928	2
C₄₁×#1927	2
C₄₁×#1921	2
C₄₁×#1920	2
C₄₁×#1919	2
C₄₁×#1918	2
C₄₁×#1873	2
C₄₁×#1854	2
C₄₁×#1817	2
#33101	41

Subgroups — C41×#33101 #23809302

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#33101 #23809302