Subgroups — C₄₁×#24237 #23800438

Order 10496.

1522 conjugacy classes of subgroups.

The subgroup lattice has 654 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₁×#547	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄₁×#461	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄₁×#449	C₂	1	2	yes	maximal, complemented
4	C₂×C₄×D₈×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₁×#2537	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄₁×#2036	C₂	1	2	yes	maximal, complemented
7	C₄₁×#2000	C₂	1	2	yes	maximal, complemented
8	C₄₁×#1956	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄₁×#1954	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄₁×#1802	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₁×#1788	C₂	1	2	yes	maximal, complemented
12	C₂²×#41×C₄₁	C₂²	1	2	yes	—
13	C₂²×SD₁₆×C₄₁	C₂²	1	2	yes	—
14	C₂²×D₈×C₄₁	C₂²	1	1	yes	characteristic
15	C₄₁×#547	—	2	4	no	—
16	C₄₁×#547	—	2	4	no	—
17	C₂×C₄⋊Q₈×C₄₁	C₂²	1	1	yes	characteristic
18	C₂×#123×C₄₁	—	2	2	no	—
19	C₂×C₂²⋊Q₈×C₄₁	C₂²	1	2	yes	—
20	C₂×#121×C₄₁	—	2	1	no	—
21	C₂×#121×C₄₁	—	2	1	no	—
22	C₂×#121×C₄₁	C₂²	1	2	yes	—
23	C₂×C₄×D₄×C₄₁	C₂²	1	1	yes	characteristic
24	C₂×C₄×D₄×C₄₁	C₂²	1	1	yes	characteristic
25	C₂×C₄×D₄×C₄₁	C₂²	1	1	yes	characteristic
26	C₂²×C₄⋊C₄×C₄₁	—	2	1	no	—
27	C₄₁×#461	—	2	4	no	—
28	C₄₁×#449	—	2	8	no	—
29	C₄×D₈×C₄₁	—	2	4	no	—
30	C₂×#107×C₄₁	C₂²	1	1	yes	characteristic
31	C₂×C₄⋊C₈×C₄₁	C₂²	1	1	yes	characteristic
32	C₂×#103×C₄₁	C₂²	1	2	yes	—
33	C₂×#103×C₄₁	C₂²	1	2	yes	—
34	C₂×#103×C₄₁	C₂²	1	2	yes	—
35	C₂×#102×C₄₁	C₂²	1	1	yes	characteristic
36	C₂×#102×C₄₁	C₂²	1	2	yes	—
37	C₂×#102×C₄₁	C₂²	1	1	yes	characteristic
38	C₂×C₂²⋊C₈×C₄₁	C₂²	1	2	yes	—
39	C₂×C₂²⋊C₈×C₄₁	C₂²	1	2	yes	—
40	C₂×C₄×C₈×C₄₁	C₂²	1	1	yes	characteristic
41	C₄₁×#394	—	2	2	no	—
42	C₄₁×#384	C₂²	1	1	yes	characteristic
43	C₄₁×#380	—	2	1	no	—
44	C₄₁×#380	C₂²	1	2	yes	—
45	C₄₁×#340	C₂²	1	2	yes	—
46	C₂×#41×C₄₁	—	2	4	no	—
47	C₂×#41×C₄₁	—	2	4	no	—
48	C₂×#41×C₄₁	—	2	4	no	—
49	C₂×#41×C₄₁	—	2	4	no	—
50	C₂×#41×C₄₁	—	4	2	no	—
51	C₂×#41×C₄₁	—	4	2	no	—
52	C₂²×Q₈×C₄₁	C₂³	1	2	yes	—
53	C₂²×D₄×C₄₁	—	2	2	no	—
54	C₂²×D₄×C₄₁	—	2	2	no	—
55	C₂²×D₄×C₄₁	D₄	1	1	yes	characteristic
56	C₂²×D₄×C₄₁	C₂³	1	1	yes	characteristic
57	C₂²×D₄×C₄₁	C₂³	1	1	yes	characteristic
58	C₂³×C₄×C₄₁	—	2	1	no	—
59	C₂³×C₄×C₄₁	—	2	2	no	—
60	C₂³×C₄×C₄₁	—	2	1	no	—
61	C₂³×C₄×C₄₁	C₂³	1	2	yes	—
62	C₂×SD₁₆×C₄₁	—	2	4	no	—
63	C₂×SD₁₆×C₄₁	—	2	4	no	—
64	C₂×SD₁₆×C₄₁	—	4	2	no	—
65	C₂×D₈×C₄₁	—	2	2	no	—
66	C₂×D₈×C₄₁	—	2	2	no	—
67	C₂×D₈×C₄₁	D₄	1	4	yes	complemented
68	C₂²×C₈×C₄₁	C₂³	1	2	yes	—
69	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
70	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
71	C₄⋊Q₈×C₄₁	—	2	2	no	—
72	C₄⋊Q₈×C₄₁	D₄	1	4	yes	complemented
73	#123×C₄₁	—	2	16	no	—
74	C₂²⋊Q₈×C₄₁	—	2	4	no	—
75	C₂²⋊Q₈×C₄₁	—	2	4	no	—
76	#121×C₄₁	—	2	8	no	—
77	#121×C₄₁	—	2	4	no	—
78	#121×C₄₁	—	4	2	no	—
79	#121×C₄₁	—	4	4	no	—
80	C₄×D₄×C₄₁	—	2	2	no	—
81	C₄×D₄×C₄₁	—	2	2	no	—
82	C₄×D₄×C₄₁	—	2	2	no	—
83	C₄×D₄×C₄₁	—	2	2	no	—
84	C₄×D₄×C₄₁	—	2	2	no	—
85	C₄×D₄×C₄₁	D₄	1	4	yes	complemented
86	C₂×C₄⋊C₄×C₄₁	—	2	8	no	—
87	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
88	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
89	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
90	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
91	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
92	C₂×C₄⋊C₄×C₄₁	D₄	1	1	yes	characteristic
93	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
94	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
95	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
96	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
97	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
98	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
99	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
100	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
101	C₂×C₂²⋊C₄×C₄₁	D₄	1	2	yes	—
102	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
103	#107×C₄₁	—	2	2	no	—
104	C₄⋊C₈×C₄₁	—	2	2	no	—
105	#103×C₄₁	—	2	4	no	—
106	#103×C₄₁	—	2	4	no	—
107	#103×C₄₁	—	4	2	no	—
108	#102×C₄₁	—	2	2	no	—
109	#102×C₄₁	—	2	4	no	—
110	#102×C₄₁	—	2	2	no	—
111	C₂²⋊C₈×C₄₁	—	2	4	no	—
112	C₂²⋊C₈×C₄₁	—	4	2	no	—
113	C₄×C₈×C₄₁	—	2	2	no	—
114	#95×C₄₁	—	2	2	no	—
115	C₂⁴×C₄₁	—	2	1	no	—
116	C₂⁴×C₄₁	—	2	1	no	—
117	C₂⁴×C₄₁	C₂×D₄	1	2	yes	—
118	#41×C₄₁	—	4	8	no	—
119	#41×C₄₁	—	4	8	no	—
120	#41×C₄₁	—	4	8	no	—
121	#41×C₄₁	—	4	8	no	—
122	C₂×Q₈×C₄₁	—	2	2	no	—
123	C₂×Q₈×C₄₁	—	2	2	no	—
124	C₂×Q₈×C₄₁	—	2	2	no	—
125	C₂×Q₈×C₄₁	—	2	2	no	—
126	C₂×Q₈×C₄₁	—	2	2	no	—
127	C₂×Q₈×C₄₁	C₂×D₄	1	4	yes	—
128	C₂×D₄×C₄₁	—	2	8	no	—
129	C₂×D₄×C₄₁	—	2	2	no	—
130	C₂×D₄×C₄₁	—	2	2	no	—
131	C₂×D₄×C₄₁	—	2	2	no	—
132	C₂×D₄×C₄₁	—	2	1	no	—
133	C₂×D₄×C₄₁	—	2	1	no	—
134	C₂×D₄×C₄₁	—	2	1	no	—
135	C₂×D₄×C₄₁	—	2	1	no	—
136	C₂×D₄×C₄₁	—	2	1	no	—
137	C₂×D₄×C₄₁	—	2	1	no	—
138	C₂×D₄×C₄₁	—	2	1	no	—
139	C₂×D₄×C₄₁	—	2	1	no	—
140	C₂×D₄×C₄₁	—	4	4	no	—
141	C₂×D₄×C₄₁	—	4	4	no	—
142	C₂×D₄×C₄₁	—	4	4	no	—
143	C₂×D₄×C₄₁	—	4	4	no	—
144	C₂×D₄×C₄₁	—	8	2	no	—
145	C₂×D₄×C₄₁	C₂×D₄	1	2	yes	—
146	C₂×D₄×C₄₁	C₂×D₄	1	2	yes	—
147	C₂×D₄×C₄₁	C₂×D₄	1	2	yes	—
148	C₂×D₄×C₄₁	#41	1	2	yes	—
149	C₂²×C₄×C₄₁	—	2	8	no	—
150	C₂²×C₄×C₄₁	—	2	1	no	—
151	C₂²×C₄×C₄₁	—	2	2	no	—
152	C₂²×C₄×C₄₁	—	2	4	no	—
153	C₂²×C₄×C₄₁	—	2	2	no	—
154	C₂²×C₄×C₄₁	—	2	2	no	—
155	C₂²×C₄×C₄₁	—	2	2	no	—
156	C₂²×C₄×C₄₁	—	2	2	no	—
157	C₂²×C₄×C₄₁	—	2	2	no	—
158	C₂²×C₄×C₄₁	—	2	2	no	—
159	C₂²×C₄×C₄₁	—	2	1	no	—
160	C₂²×C₄×C₄₁	—	2	2	no	—
161	C₂²×C₄×C₄₁	—	4	4	no	—
162	C₂²×C₄×C₄₁	—	4	4	no	—
163	C₂²×C₄×C₄₁	—	4	2	no	—
164	C₂²×C₄×C₄₁	—	4	2	no	—
165	C₂²×C₄×C₄₁	—	4	2	no	—
166	C₂²×C₄×C₄₁	—	4	2	no	—
167	C₂²×C₄×C₄₁	—	4	2	no	—
168	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
169	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
170	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
171	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
172	SD₁₆×C₄₁	—	4	8	no	—
173	D₈×C₄₁	—	2	8	no	—
174	C₂×C₈×C₄₁	—	2	1	no	—
175	C₂×C₈×C₄₁	—	2	1	no	—
176	C₂×C₈×C₄₁	—	2	1	no	—
177	C₂×C₈×C₄₁	—	2	2	no	—
178	C₂×C₈×C₄₁	—	2	2	no	—
179	C₂×C₈×C₄₁	—	2	1	no	—
180	C₂×C₈×C₄₁	—	2	2	no	—
181	C₂×C₈×C₄₁	—	2	1	no	—
182	C₂×C₈×C₄₁	C₂×D₄	1	2	yes	—
183	C₄⋊C₄×C₄₁	—	2	8	no	—
184	C₄⋊C₄×C₄₁	—	2	2	no	—
185	C₄⋊C₄×C₄₁	—	2	4	no	—
186	C₄⋊C₄×C₄₁	—	2	4	no	—
187	C₄⋊C₄×C₄₁	—	2	1	no	—
188	C₄⋊C₄×C₄₁	—	2	2	no	—
189	C₄⋊C₄×C₄₁	—	2	1	no	—
190	C₄⋊C₄×C₄₁	—	2	1	no	—
191	C₄⋊C₄×C₄₁	—	2	2	no	—
192	C₄⋊C₄×C₄₁	—	4	2	no	—
193	C₄⋊C₄×C₄₁	—	8	1	no	—
194	C₄⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
195	C₂²⋊C₄×C₄₁	—	2	8	no	—
196	C₂²⋊C₄×C₄₁	—	2	4	no	—
197	C₂²⋊C₄×C₄₁	—	2	4	no	—
198	C₂²⋊C₄×C₄₁	—	4	4	no	—
199	C₂²⋊C₄×C₄₁	—	4	4	no	—
200	C₂²⋊C₄×C₄₁	—	4	2	no	—
201	C₄²×C₄₁	C₂×D₄	1	2	yes	—
202	C₄²×C₄₁	C₂×D₄	1	2	yes	—
203	C₂³×C₄₁	—	2	2	no	—
204	C₂³×C₄₁	—	2	2	no	—
205	C₂³×C₄₁	—	2	2	no	—
206	C₂³×C₄₁	—	2	2	no	—
207	C₂³×C₄₁	—	2	2	no	—
208	C₂³×C₄₁	—	2	2	no	—
209	C₂³×C₄₁	—	2	2	no	—
210	C₂³×C₄₁	—	2	2	no	—
211	C₂³×C₄₁	—	2	2	no	—
212	C₂³×C₄₁	—	2	2	no	—
213	C₂³×C₄₁	—	2	2	no	—
214	C₂³×C₄₁	—	4	1	no	—
215	C₂³×C₄₁	—	4	1	no	—
216	C₂³×C₄₁	—	4	1	no	—
217	C₂³×C₄₁	—	4	1	no	—
218	C₂³×C₄₁	—	4	1	no	—
219	C₂³×C₄₁	—	4	1	no	—
220	C₂³×C₄₁	—	4	1	no	—
221	C₂³×C₄₁	—	4	1	no	—
222	C₂³×C₄₁	—	4	1	no	—
223	C₂³×C₄₁	—	4	1	no	—
224	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
225	Q₈×C₄₁	—	2	4	no	—
226	Q₈×C₄₁	—	2	4	no	—
227	Q₈×C₄₁	—	4	2	no	—
228	Q₈×C₄₁	—	4	2	no	—
229	D₄×C₄₁	—	2	2	no	—
230	D₄×C₄₁	—	2	2	no	—
231	D₄×C₄₁	—	2	2	no	—
232	D₄×C₄₁	—	2	2	no	—
233	D₄×C₄₁	—	2	2	no	—
234	D₄×C₄₁	—	4	16	no	—
235	D₄×C₄₁	—	4	1	no	—
236	D₄×C₄₁	—	4	1	no	—
237	D₄×C₄₁	—	4	4	no	—
238	D₄×C₄₁	—	8	8	no	—
239	D₄×C₄₁	#121	1	4	yes	complemented
240	C₂×C₄×C₄₁	—	2	1	no	—
241	C₂×C₄×C₄₁	—	2	1	no	—
242	C₂×C₄×C₄₁	—	2	2	no	—
243	C₂×C₄×C₄₁	—	2	2	no	—
244	C₂×C₄×C₄₁	—	2	4	no	—
245	C₂×C₄×C₄₁	—	2	2	no	—
246	C₂×C₄×C₄₁	—	2	2	no	—
247	C₂×C₄×C₄₁	—	4	16	no	—
248	C₂×C₄×C₄₁	—	4	2	no	—
249	C₂×C₄×C₄₁	—	4	2	no	—
250	C₂×C₄×C₄₁	—	4	1	no	—
251	C₂×C₄×C₄₁	—	4	1	no	—
252	C₂×C₄×C₄₁	—	4	2	no	—
253	C₂×C₄×C₄₁	—	4	2	no	—
254	C₂×C₄×C₄₁	—	4	2	no	—
255	C₂×C₄×C₄₁	—	4	2	no	—
256	C₂×C₄×C₄₁	—	4	8	no	—
257	C₂×C₄×C₄₁	—	4	1	no	—
258	C₂×C₄×C₄₁	—	4	2	no	—
259	C₂×C₄×C₄₁	—	4	1	no	—
260	C₂×C₄×C₄₁	—	4	1	no	—
261	C₂×C₄×C₄₁	—	4	2	no	—
262	C₂×C₄×C₄₁	—	4	2	no	—
263	C₂×C₄×C₄₁	—	8	4	no	—
264	C₂×C₄×C₄₁	#120	1	2	yes	—
265	C₂×C₄×C₄₁	#120	1	2	yes	—
266	C₂×C₄×C₄₁	#135	1	2	yes	—
267	C₂×C₄×C₄₁	AGL(1,ℤ/8)	1	2	yes	—
268	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
269	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
270	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
271	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
272	C₂×C₄×C₄₁	H(5,𝔽₂)	1	1	yes	characteristic
273	C₂×C₄×C₄₁	H(5,𝔽₂)	1	1	yes	characteristic
274	C₈×C₄₁	—	2	2	no	—
275	C₈×C₄₁	—	4	1	no	—
276	C₈×C₄₁	—	4	2	no	—
277	#24237	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
278	C₂²×C₄₁	—	2	4	no	—
279	C₂²×C₄₁	—	4	2	no	—
280	C₂²×C₄₁	—	4	2	no	—
281	C₂²×C₄₁	—	4	2	no	—
282	C₂²×C₄₁	—	4	2	no	—
283	C₂²×C₄₁	—	4	2	no	—
284	C₂²×C₄₁	—	4	2	no	—
285	C₂²×C₄₁	—	4	2	no	—
286	C₂²×C₄₁	—	4	2	no	—
287	C₂²×C₄₁	—	4	2	no	—
288	C₂²×C₄₁	—	4	2	no	—
289	C₂²×C₄₁	—	4	2	no	—
290	C₂²×C₄₁	—	4	2	no	—
291	C₂²×C₄₁	—	4	2	no	—
292	C₂²×C₄₁	—	4	2	no	—
293	C₂²×C₄₁	—	4	2	no	—
294	C₂²×C₄₁	—	4	2	no	—
295	C₂²×C₄₁	—	8	1	no	—
296	C₂²×C₄₁	—	8	1	no	—
297	C₂²×C₄₁	—	8	1	no	—
298	C₂²×C₄₁	—	8	1	no	—
299	C₂²×C₄₁	C₂×#120	1	1	yes	characteristic
300	C₂²×C₄₁	D₄²	1	1	yes	characteristic
301	C₂²×C₄₁	#546	1	1	yes	characteristic
302	C₂²×C₄₁	C₂×#135	1	1	yes	characteristic
303	C₂²×C₄₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
304	C₂²×C₄₁	#577	1	1	yes	characteristic
305	C₂²×C₄₁	#578	1	1	yes	characteristic
306	C₄×C₄₁	—	2	2	no	—
307	C₄×C₄₁	—	4	2	no	—
308	C₄×C₄₁	—	4	4	no	—
309	C₄×C₄₁	—	4	2	no	—
310	C₄×C₄₁	—	8	1	no	—
311	C₄×C₄₁	—	8	2	no	—
312	C₄×C₄₁	#449	1	4	yes	complemented
313	C₄×C₄₁	C₂×#121	1	1	yes	characteristic
314	C₄×C₄₁	#535	1	1	yes	characteristic
315	C₄×C₄₁	D₄²	1	1	yes	characteristic
316	C₄×C₄₁	#546	1	1	yes	characteristic
317	C₂×#547	C₂×C₄₁	1	1	yes	characteristic, complemented
318	C₂×#461	C₂×C₄₁	1	1	yes	characteristic, complemented
319	C₂×#449	C₂×C₄₁	1	2	yes	complemented
320	C₂×C₄×D₈	C₂×C₄₁	1	1	yes	characteristic, complemented
321	#2537	C₂×C₄₁	1	1	yes	characteristic, complemented
322	#2036	C₂×C₄₁	1	2	yes	complemented
323	#2000	C₂×C₄₁	1	2	yes	complemented
324	#1956	C₂×C₄₁	1	1	yes	characteristic, complemented
325	#1954	C₂×C₄₁	1	1	yes	characteristic, complemented
326	#1802	C₂×C₄₁	1	1	yes	characteristic, complemented
327	#1788	C₂×C₄₁	1	2	yes	complemented
328	C₂×C₄₁	—	4	4	no	—
329	C₂×C₄₁	—	8	2	no	—
330	C₂×C₄₁	—	8	2	no	—
331	C₂×C₄₁	#2408	1	1	yes	characteristic
332	C₂×C₄₁	C₂×#449	1	1	yes	characteristic
333	C₂×C₄₁	#3013	1	1	yes	characteristic
334	C₂×C₄₁	#3272	1	1	yes	characteristic
335	C₂×C₄₁	#3283	1	1	yes	characteristic
336	C₂×C₄₁	#3303	1	1	yes	characteristic
337	C₂×C₄₁	#3330	1	1	yes	characteristic
338	C₂²×#41	C₂²×C₄₁	1	2	yes	—
339	C₂²×SD₁₆	C₂²×C₄₁	1	2	yes	—
340	C₂²×D₈	C₂²×C₄₁	1	1	yes	characteristic
341	#547	—	2	4	no	—
342	#547	—	2	4	no	—
343	C₂×C₄⋊Q₈	C₂²×C₄₁	1	1	yes	characteristic
344	C₂×#123	—	2	2	no	—
345	C₂×C₂²⋊Q₈	C₂²×C₄₁	1	2	yes	—
346	C₂×#121	—	2	1	no	—
347	C₂×#121	—	2	1	no	—
348	C₂×#121	C₂²×C₄₁	1	2	yes	—
349	C₂×C₄×D₄	C₂²×C₄₁	1	1	yes	characteristic
350	C₂×C₄×D₄	C₂²×C₄₁	1	1	yes	characteristic
351	C₂×C₄×D₄	C₂²×C₄₁	1	1	yes	characteristic
352	C₂²×C₄⋊C₄	—	2	1	no	—
353	#461	—	2	4	no	—
354	#449	—	2	8	no	—
355	C₄×D₈	—	2	4	no	—
356	C₂×#107	C₂²×C₄₁	1	1	yes	characteristic
357	C₂×C₄⋊C₈	C₂²×C₄₁	1	1	yes	characteristic
358	C₂×#103	C₂²×C₄₁	1	2	yes	—
359	C₂×#103	C₂²×C₄₁	1	2	yes	—
360	C₂×#103	C₂²×C₄₁	1	2	yes	—
361	C₂×#102	C₂²×C₄₁	1	2	yes	—
362	C₂×#102	C₂²×C₄₁	1	1	yes	characteristic
363	C₂×#102	C₂²×C₄₁	1	1	yes	characteristic
364	C₂×C₂²⋊C₈	C₂²×C₄₁	1	2	yes	—
365	C₂×C₂²⋊C₈	C₂²×C₄₁	1	2	yes	—
366	C₂×C₄×C₈	C₂²×C₄₁	1	1	yes	characteristic
367	#394	—	2	2	no	—
368	#384	C₂²×C₄₁	1	1	yes	characteristic
369	#380	—	2	1	no	—
370	#380	C₂²×C₄₁	1	2	yes	—
371	#340	C₂²×C₄₁	1	2	yes	—
372	C₄₁	#24237	1	1	yes	characteristic, direct product factor, Sylow
373	C₂×#41	—	2	4	no	—
374	C₂×#41	—	2	4	no	—
375	C₂×#41	—	2	4	no	—
376	C₂×#41	—	2	4	no	—
377	C₂×#41	—	4	2	no	—
378	C₂×#41	—	4	2	no	—
379	C₂²×Q₈	C₂³×C₄₁	1	2	yes	—
380	C₂²×D₄	—	2	2	no	—
381	C₂²×D₄	—	2	2	no	—
382	C₂²×D₄	D₄×C₄₁	1	1	yes	characteristic
383	C₂²×D₄	C₂³×C₄₁	1	1	yes	characteristic
384	C₂²×D₄	C₂³×C₄₁	1	1	yes	characteristic
385	C₂³×C₄	—	2	1	no	—
386	C₂³×C₄	—	2	2	no	—
387	C₂³×C₄	—	2	1	no	—
388	C₂³×C₄	C₂³×C₄₁	1	2	yes	—
389	C₂×SD₁₆	—	2	4	no	—
390	C₂×SD₁₆	—	2	4	no	—
391	C₂×SD₁₆	—	4	2	no	—
392	C₂×D₈	—	2	2	no	—
393	C₂×D₈	—	2	2	no	—
394	C₂×D₈	D₄×C₄₁	1	4	yes	complemented
395	C₂²×C₈	C₂³×C₄₁	1	2	yes	—
396	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
397	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
398	C₄⋊Q₈	—	2	2	no	—
399	C₄⋊Q₈	D₄×C₄₁	1	4	yes	complemented
400	#123	—	2	16	no	—
401	C₂²⋊Q₈	—	2	4	no	—
402	C₂²⋊Q₈	—	2	4	no	—
403	#121	—	2	8	no	—
404	#121	—	2	4	no	—
405	#121	—	4	2	no	—
406	#121	—	4	4	no	—
407	C₄×D₄	—	2	2	no	—
408	C₄×D₄	—	2	2	no	—
409	C₄×D₄	—	2	2	no	—
410	C₄×D₄	—	2	2	no	—
411	C₄×D₄	—	2	2	no	—
412	C₄×D₄	D₄×C₄₁	1	4	yes	complemented
413	C₂×C₄⋊C₄	—	2	8	no	—
414	C₂×C₄⋊C₄	—	2	1	no	—
415	C₂×C₄⋊C₄	—	2	2	no	—
416	C₂×C₄⋊C₄	—	2	1	no	—
417	C₂×C₄⋊C₄	—	2	1	no	—
418	C₂×C₄⋊C₄	—	2	1	no	—
419	C₂×C₄⋊C₄	D₄×C₄₁	1	1	yes	characteristic
420	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
421	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
422	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
423	C₂×C₂²⋊C₄	—	2	2	no	—
424	C₂×C₂²⋊C₄	—	2	1	no	—
425	C₂×C₂²⋊C₄	—	2	2	no	—
426	C₂×C₂²⋊C₄	—	2	1	no	—
427	C₂×C₂²⋊C₄	—	2	2	no	—
428	C₂×C₂²⋊C₄	D₄×C₄₁	1	2	yes	—
429	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
430	#107	—	2	2	no	—
431	C₄⋊C₈	—	2	2	no	—
432	#103	—	2	4	no	—
433	#103	—	2	4	no	—
434	#103	—	4	2	no	—
435	#102	—	2	2	no	—
436	#102	—	2	4	no	—
437	#102	—	2	2	no	—
438	C₂²⋊C₈	—	2	4	no	—
439	C₂²⋊C₈	—	4	2	no	—
440	C₄×C₈	—	2	2	no	—
441	#95	—	2	2	no	—
442	C₂⁴	—	2	1	no	—
443	C₂⁴	—	2	1	no	—
444	C₂⁴	C₂×D₄×C₄₁	1	2	yes	—
445	#41	—	4	8	no	—
446	#41	—	4	8	no	—
447	#41	—	4	8	no	—
448	#41	—	4	8	no	—
449	C₂×Q₈	—	2	2	no	—
450	C₂×Q₈	—	2	2	no	—
451	C₂×Q₈	—	2	2	no	—
452	C₂×Q₈	—	2	2	no	—
453	C₂×Q₈	—	2	2	no	—
454	C₂×Q₈	C₂×D₄×C₄₁	1	4	yes	—
455	C₂×D₄	—	2	8	no	—
456	C₂×D₄	—	2	2	no	—
457	C₂×D₄	—	2	2	no	—
458	C₂×D₄	—	2	2	no	—
459	C₂×D₄	—	2	1	no	—
460	C₂×D₄	—	2	1	no	—
461	C₂×D₄	—	2	1	no	—
462	C₂×D₄	—	2	1	no	—
463	C₂×D₄	—	2	1	no	—
464	C₂×D₄	—	2	1	no	—
465	C₂×D₄	—	2	1	no	—
466	C₂×D₄	—	2	1	no	—
467	C₂×D₄	—	4	4	no	—
468	C₂×D₄	—	4	4	no	—
469	C₂×D₄	—	4	4	no	—
470	C₂×D₄	—	4	4	no	—
471	C₂×D₄	—	8	2	no	—
472	C₂×D₄	C₂×D₄×C₄₁	1	2	yes	—
473	C₂×D₄	C₂×D₄×C₄₁	1	2	yes	—
474	C₂×D₄	C₂×D₄×C₄₁	1	2	yes	—
475	C₂×D₄	#41×C₄₁	1	2	yes	—
476	C₂²×C₄	—	2	8	no	—
477	C₂²×C₄	—	2	1	no	—
478	C₂²×C₄	—	2	2	no	—
479	C₂²×C₄	—	2	4	no	—
480	C₂²×C₄	—	2	2	no	—
481	C₂²×C₄	—	2	2	no	—
482	C₂²×C₄	—	2	2	no	—
483	C₂²×C₄	—	2	2	no	—
484	C₂²×C₄	—	2	2	no	—
485	C₂²×C₄	—	2	2	no	—
486	C₂²×C₄	—	2	1	no	—
487	C₂²×C₄	—	2	2	no	—
488	C₂²×C₄	—	4	4	no	—
489	C₂²×C₄	—	4	4	no	—
490	C₂²×C₄	—	4	2	no	—
491	C₂²×C₄	—	4	2	no	—
492	C₂²×C₄	—	4	2	no	—
493	C₂²×C₄	—	4	2	no	—
494	C₂²×C₄	—	4	2	no	—
495	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
496	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
497	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
498	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
499	SD₁₆	—	4	8	no	—
500	D₈	—	2	8	no	—
501	C₂×C₈	—	2	1	no	—
502	C₂×C₈	—	2	1	no	—
503	C₂×C₈	—	2	1	no	—
504	C₂×C₈	—	2	2	no	—
505	C₂×C₈	—	2	2	no	—
506	C₂×C₈	—	2	1	no	—
507	C₂×C₈	—	2	2	no	—
508	C₂×C₈	—	2	1	no	—
509	C₂×C₈	C₂×D₄×C₄₁	1	2	yes	—
510	C₄⋊C₄	—	2	8	no	—
511	C₄⋊C₄	—	2	2	no	—
512	C₄⋊C₄	—	2	4	no	—
513	C₄⋊C₄	—	2	4	no	—
514	C₄⋊C₄	—	2	1	no	—
515	C₄⋊C₄	—	2	2	no	—
516	C₄⋊C₄	—	2	1	no	—
517	C₄⋊C₄	—	2	1	no	—
518	C₄⋊C₄	—	2	2	no	—
519	C₄⋊C₄	—	4	2	no	—
520	C₄⋊C₄	—	8	1	no	—
521	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
522	C₂²⋊C₄	—	2	8	no	—
523	C₂²⋊C₄	—	2	4	no	—
524	C₂²⋊C₄	—	2	4	no	—
525	C₂²⋊C₄	—	4	4	no	—
526	C₂²⋊C₄	—	4	4	no	—
527	C₂²⋊C₄	—	4	2	no	—
528	C₄²	C₂×D₄×C₄₁	1	2	yes	—
529	C₄²	C₂×D₄×C₄₁	1	2	yes	—
530	C₂³	—	2	2	no	—
531	C₂³	—	2	2	no	—
532	C₂³	—	2	2	no	—
533	C₂³	—	2	2	no	—
534	C₂³	—	2	2	no	—
535	C₂³	—	2	2	no	—
536	C₂³	—	2	2	no	—
537	C₂³	—	2	2	no	—
538	C₂³	—	2	2	no	—
539	C₂³	—	2	2	no	—
540	C₂³	—	2	2	no	—
541	C₂³	—	4	1	no	—
542	C₂³	—	4	1	no	—
543	C₂³	—	4	1	no	—
544	C₂³	—	4	1	no	—
545	C₂³	—	4	1	no	—
546	C₂³	—	4	1	no	—
547	C₂³	—	4	1	no	—
548	C₂³	—	4	1	no	—
549	C₂³	—	4	1	no	—
550	C₂³	—	4	1	no	—
551	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
552	Q₈	—	2	4	no	—
553	Q₈	—	2	4	no	—
554	Q₈	—	4	2	no	—
555	Q₈	—	4	2	no	—
556	D₄	—	2	2	no	—
557	D₄	—	2	2	no	—
558	D₄	—	2	2	no	—
559	D₄	—	2	2	no	—
560	D₄	—	2	2	no	—
561	D₄	—	4	16	no	—
562	D₄	—	4	1	no	—
563	D₄	—	4	1	no	—
564	D₄	—	4	4	no	—
565	D₄	—	8	8	no	—
566	D₄	#121×C₄₁	1	4	yes	complemented
567	C₂×C₄	—	2	1	no	—
568	C₂×C₄	—	2	1	no	—
569	C₂×C₄	—	2	2	no	—
570	C₂×C₄	—	2	2	no	—
571	C₂×C₄	—	2	4	no	—
572	C₂×C₄	—	2	2	no	—
573	C₂×C₄	—	2	2	no	—
574	C₂×C₄	—	4	16	no	—
575	C₂×C₄	—	4	2	no	—
576	C₂×C₄	—	4	2	no	—
577	C₂×C₄	—	4	1	no	—
578	C₂×C₄	—	4	1	no	—
579	C₂×C₄	—	4	2	no	—
580	C₂×C₄	—	4	2	no	—
581	C₂×C₄	—	4	2	no	—
582	C₂×C₄	—	4	2	no	—
583	C₂×C₄	—	4	8	no	—
584	C₂×C₄	—	4	1	no	—
585	C₂×C₄	—	4	2	no	—
586	C₂×C₄	—	4	1	no	—
587	C₂×C₄	—	4	1	no	—
588	C₂×C₄	—	4	2	no	—
589	C₂×C₄	—	4	2	no	—
590	C₂×C₄	—	8	4	no	—
591	C₂×C₄	#120×C₄₁	1	2	yes	—
592	C₂×C₄	#120×C₄₁	1	2	yes	—
593	C₂×C₄	#135×C₄₁	1	2	yes	—
594	C₂×C₄	AGL(1,ℤ/8)×C₄₁	1	2	yes	—
595	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
596	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
597	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
598	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
599	C₂×C₄	H(5,𝔽₂)×C₄₁	1	1	yes	characteristic
600	C₂×C₄	H(5,𝔽₂)×C₄₁	1	1	yes	characteristic
601	C₈	—	2	2	no	—
602	C₈	—	4	1	no	—
603	C₈	—	4	2	no	—
604	C₂²	—	2	4	no	—
605	C₂²	—	4	2	no	—
606	C₂²	—	4	2	no	—
607	C₂²	—	4	2	no	—
608	C₂²	—	4	2	no	—
609	C₂²	—	4	2	no	—
610	C₂²	—	4	2	no	—
611	C₂²	—	4	2	no	—
612	C₂²	—	4	2	no	—
613	C₂²	—	4	2	no	—
614	C₂²	—	4	2	no	—
615	C₂²	—	4	2	no	—
616	C₂²	—	4	2	no	—
617	C₂²	—	4	2	no	—
618	C₂²	—	4	2	no	—
619	C₂²	—	4	2	no	—
620	C₂²	—	4	2	no	—
621	C₂²	—	8	1	no	—
622	C₂²	—	8	1	no	—
623	C₂²	—	8	1	no	—
624	C₂²	—	8	1	no	—
625	C₂²	C₂×#120×C₄₁	1	1	yes	characteristic
626	C₂²	D₄²×C₄₁	1	1	yes	characteristic
627	C₂²	C₄₁×#546	1	1	yes	characteristic
628	C₂²	C₂×#135×C₄₁	1	1	yes	characteristic
629	C₂²	C₂×AGL(1,ℤ/8)×C₄₁	1	1	yes	characteristic
630	C₂²	C₄₁×#577	1	1	yes	characteristic
631	C₂²	C₄₁×#578	1	1	yes	characteristic
632	C₄	—	2	2	no	—
633	C₄	—	4	2	no	—
634	C₄	—	4	4	no	—
635	C₄	—	4	2	no	—
636	C₄	—	8	1	no	—
637	C₄	—	8	2	no	—
638	C₄	C₄₁×#449	1	4	yes	complemented
639	C₄	C₂×#121×C₄₁	1	1	yes	characteristic
640	C₄	C₄₁×#535	1	1	yes	characteristic
641	C₄	D₄²×C₄₁	1	1	yes	characteristic
642	C₄	C₄₁×#546	1	1	yes	characteristic
643	C₂	—	4	4	no	—
644	C₂	—	8	2	no	—
645	C₂	—	8	2	no	—
646	C₂	C₄₁×#2408	1	1	yes	characteristic
647	C₂	C₂×C₄₁×#449	1	1	yes	characteristic
648	C₂	C₄₁×#3013	1	1	yes	characteristic
649	C₂	C₄₁×#3272	1	1	yes	characteristic
650	C₂	C₄₁×#3283	1	1	yes	characteristic
651	C₂	C₄₁×#3303	1	1	yes	characteristic
652	C₂	C₄₁×#3330	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₂×C₄₁×#547	C₂	semidirect
2. C₂×C₄₁×#461	C₂	semidirect
3. C₂×C₄₁×#449	C₂	semidirect
4. C₂×C₄×D₈×C₄₁	C₂	semidirect
5. C₄₁×#2537	C₂	semidirect
6. C₄₁×#2036	C₂	semidirect
7. C₄₁×#2000	C₂	semidirect
8. C₄₁×#1956	C₂	semidirect
9. C₄₁×#1954	C₂	semidirect
10. C₄₁×#1802	C₂	semidirect
11. C₄₁×#1788	C₂	semidirect
67. C₂×D₈×C₄₁	D₄	semidirect
72. C₄⋊Q₈×C₄₁	D₄	semidirect
85. C₄×D₄×C₄₁	D₄	semidirect
239. D₄×C₄₁	#121	semidirect
277. #24237	C₄₁	direct (N × H)
312. C₄×C₄₁	#449	semidirect
317. C₂×#547	C₂×C₄₁	semidirect
318. C₂×#461	C₂×C₄₁	semidirect
319. C₂×#449	C₂×C₄₁	semidirect
320. C₂×C₄×D₈	C₂×C₄₁	semidirect
321. #2537	C₂×C₄₁	semidirect
322. #2036	C₂×C₄₁	semidirect
323. #2000	C₂×C₄₁	semidirect
324. #1956	C₂×C₄₁	semidirect
325. #1954	C₂×C₄₁	semidirect
326. #1802	C₂×C₄₁	semidirect
327. #1788	C₂×C₄₁	semidirect
372. C₄₁	#24237	direct (N × H)
394. C₂×D₈	D₄×C₄₁	semidirect
399. C₄⋊Q₈	D₄×C₄₁	semidirect
412. C₄×D₄	D₄×C₄₁	semidirect
566. D₄	#121×C₄₁	semidirect
638. C₄	C₄₁×#449	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄₁×#547	2
C₂×C₄₁×#461	2
C₂×C₄₁×#449	2
C₂×C₄×D₈×C₄₁	2
C₄₁×#2537	2
C₄₁×#2036	2
C₄₁×#2000	2
C₄₁×#1956	2
C₄₁×#1954	2
C₄₁×#1802	2
C₄₁×#1788	2
#24237	41

Subgroups — C41×#24237 #23800438

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#24237 #23800438