Subgroups — C₄₁×#11030 #23787231

Order 10496.

1422 conjugacy classes of subgroups.

The subgroup lattice has 778 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×AGL(1,ℤ/8)×C₄₁	C₂	1	1	yes	maximal, characteristic
2	C₄₁×#2896	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄₁×#418	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₄₁×#410	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₁×#2309	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₄₁×#344	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₁×#1733	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×#41×C₄₁	C₂²	1	1	yes	characteristic
9	C₂³×D₄×C₄₁	C₂²	1	1	yes	characteristic
10	C₂×AGL(1,ℤ/8)×C₄₁	—	2	2	no	—
11	C₂×AGL(1,ℤ/8)×C₄₁	—	2	2	no	—
12	C₂×AGL(1,ℤ/8)×C₄₁	—	2	2	no	—
13	C₂×AGL(1,ℤ/8)×C₄₁	—	2	2	no	—
14	C₂×AGL(1,ℤ/8)×C₄₁	—	2	2	no	—
15	C₂×AGL(1,ℤ/8)×C₄₁	C₄	1	4	yes	complemented
16	C₂²×SD₁₆×C₄₁	—	2	1	no	—
17	C₂²×D₈×C₄₁	—	2	1	no	—
18	C₂²×M₁₆×C₄₁	C₂²	1	1	yes	characteristic
19	C₂²×M₁₆×C₄₁	C₂²	1	1	yes	characteristic
20	C₂×#117×C₄₁	C₂²	1	1	yes	characteristic
21	C₂×#117×C₄₁	C₂²	1	1	yes	characteristic
22	C₂×#117×C₄₁	C₂²	1	1	yes	characteristic
23	C₄₁×#419	—	2	1	no	—
24	C₄₁×#418	—	2	2	no	—
25	C₄₁×#418	—	2	1	no	—
26	C₄₁×#418	—	2	2	no	—
27	C₄₁×#417	—	2	2	no	—
28	C₄₁×#416	—	2	2	no	—
29	C₂×#102×C₄₁	—	2	2	no	—
30	C₄₁×#410	—	2	2	no	—
31	C₄₁×#410	—	2	2	no	—
32	C₂×#99×C₄₁	—	2	2	no	—
33	C₄₁×#390	—	2	2	no	—
34	C₄₁×#390	—	2	2	no	—
35	C₄₁×#379	—	2	2	no	—
36	C₄₁×#344	—	2	2	no	—
37	C₄₁×#339	—	2	2	no	—
38	C₂⁵×C₄₁	—	2	1	no	—
39	C₂×#41×C₄₁	—	2	1	no	—
40	C₂×#41×C₄₁	—	2	1	no	—
41	C₂×#41×C₄₁	—	2	1	no	—
42	C₂×#41×C₄₁	—	2	1	no	—
43	C₂×#41×C₄₁	—	2	1	no	—
44	C₂×#41×C₄₁	—	2	1	no	—
45	C₂×#41×C₄₁	—	2	1	no	—
46	C₂×#41×C₄₁	—	2	1	no	—
47	C₂×#41×C₄₁	—	2	1	no	—
48	C₂×#41×C₄₁	—	2	1	no	—
49	C₂×#41×C₄₁	C₂×C₄	1	2	yes	—
50	C₂×#41×C₄₁	D₄	1	2	yes	—
51	C₂²×Q₈×C₄₁	D₄	1	1	yes	characteristic
52	C₂²×D₄×C₄₁	—	2	1	no	—
53	C₂²×D₄×C₄₁	—	2	1	no	—
54	C₂²×D₄×C₄₁	—	2	1	no	—
55	C₂²×D₄×C₄₁	—	2	1	no	—
56	C₂²×D₄×C₄₁	—	2	1	no	—
57	C₂²×D₄×C₄₁	—	2	1	no	—
58	C₂²×D₄×C₄₁	—	2	1	no	—
59	C₂²×D₄×C₄₁	—	2	1	no	—
60	C₂²×D₄×C₄₁	—	2	1	no	—
61	C₂²×D₄×C₄₁	—	2	1	no	—
62	C₂²×D₄×C₄₁	—	2	1	no	—
63	C₂²×D₄×C₄₁	—	2	1	no	—
64	C₂²×D₄×C₄₁	C₂×C₄	1	2	yes	—
65	C₂²×D₄×C₄₁	D₄	1	2	yes	—
66	C₂²×D₄×C₄₁	D₄	1	2	yes	—
67	C₂²×D₄×C₄₁	D₄	1	1	yes	characteristic
68	C₂³×C₄×C₄₁	—	2	1	no	—
69	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
70	AGL(1,ℤ/8)×C₄₁	—	2	8	no	—
71	AGL(1,ℤ/8)×C₄₁	—	2	8	no	—
72	AGL(1,ℤ/8)×C₄₁	—	2	8	no	—
73	AGL(1,ℤ/8)×C₄₁	—	2	8	no	—
74	C₂×SD₁₆×C₄₁	—	2	4	no	—
75	C₂×SD₁₆×C₄₁	—	2	4	no	—
76	C₂×SD₁₆×C₄₁	—	2	4	no	—
77	C₂×D₈×C₄₁	—	2	4	no	—
78	C₂×D₈×C₄₁	—	2	4	no	—
79	C₂×D₈×C₄₁	—	2	4	no	—
80	C₂×M₁₆×C₄₁	—	2	1	no	—
81	C₂×M₁₆×C₄₁	—	2	1	no	—
82	C₂×M₁₆×C₄₁	—	2	1	no	—
83	C₂×M₁₆×C₄₁	—	2	1	no	—
84	C₂×M₁₆×C₄₁	—	2	1	no	—
85	C₂×M₁₆×C₄₁	—	2	1	no	—
86	C₂×M₁₆×C₄₁	—	2	1	no	—
87	C₂×M₁₆×C₄₁	—	2	1	no	—
88	C₂×M₁₆×C₄₁	—	2	1	no	—
89	C₂×M₁₆×C₄₁	C₂×C₄	1	2	yes	—
90	C₂×M₁₆×C₄₁	D₄	1	2	yes	—
91	C₂×M₁₆×C₄₁	D₄	1	2	yes	—
92	C₂²×C₈×C₄₁	—	2	1	no	—
93	C₂²×C₈×C₄₁	D₄	1	2	yes	—
94	#117×C₄₁	—	2	1	no	—
95	#117×C₄₁	—	2	1	no	—
96	#117×C₄₁	—	2	1	no	—
97	#117×C₄₁	—	2	1	no	—
98	#117×C₄₁	—	2	1	no	—
99	#117×C₄₁	—	2	1	no	—
100	#117×C₄₁	—	2	1	no	—
101	#117×C₄₁	—	2	1	no	—
102	#117×C₄₁	—	2	1	no	—
103	#117×C₄₁	—	2	1	no	—
104	#117×C₄₁	—	2	1	no	—
105	#117×C₄₁	D₄	1	2	yes	—
106	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
107	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
108	C₂×C₄⋊C₄×C₄₁	D₄	1	2	yes	—
109	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
110	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
111	C₂×C₂²⋊C₄×C₄₁	—	2	8	no	—
112	C₂×C₂²⋊C₄×C₄₁	D₄	1	2	yes	—
113	C₂×C₄²×C₄₁	—	2	1	no	—
114	C₂×C₄²×C₄₁	—	2	1	no	—
115	C₂×C₄²×C₄₁	—	2	1	no	—
116	#103×C₄₁	—	2	4	no	—
117	#102×C₄₁	—	2	8	no	—
118	#102×C₄₁	—	2	4	no	—
119	#99×C₄₁	—	2	8	no	—
120	C₂⁴×C₄₁	—	2	2	no	—
121	C₂⁴×C₄₁	—	2	2	no	—
122	C₂⁴×C₄₁	—	2	1	no	—
123	C₂⁴×C₄₁	—	2	2	no	—
124	C₂⁴×C₄₁	—	4	1	no	—
125	C₂⁴×C₄₁	—	4	1	no	—
126	C₂⁴×C₄₁	—	4	1	no	—
127	C₂⁴×C₄₁	—	4	1	no	—
128	C₂⁴×C₄₁	—	8	4	no	—
129	C₂⁴×C₄₁	C₂×D₄	1	1	yes	characteristic
130	#41×C₄₁	—	2	2	no	—
131	#41×C₄₁	—	2	2	no	—
132	#41×C₄₁	—	2	2	no	—
133	#41×C₄₁	—	2	2	no	—
134	#41×C₄₁	—	2	2	no	—
135	#41×C₄₁	—	2	2	no	—
136	#41×C₄₁	—	2	2	no	—
137	#41×C₄₁	—	2	2	no	—
138	#41×C₄₁	—	4	1	no	—
139	#41×C₄₁	—	4	1	no	—
140	#41×C₄₁	—	4	1	no	—
141	#41×C₄₁	—	4	1	no	—
142	#41×C₄₁	—	4	1	no	—
143	#41×C₄₁	—	4	1	no	—
144	#41×C₄₁	—	4	1	no	—
145	#41×C₄₁	—	4	1	no	—
146	C₂×Q₈×C₄₁	—	2	1	no	—
147	C₂×Q₈×C₄₁	—	2	1	no	—
148	C₂×Q₈×C₄₁	—	2	1	no	—
149	C₂×Q₈×C₄₁	—	2	1	no	—
150	C₂×Q₈×C₄₁	—	2	1	no	—
151	C₂×Q₈×C₄₁	C₂²⋊C₄	1	2	yes	complemented
152	C₂×D₄×C₄₁	—	2	2	no	—
153	C₂×D₄×C₄₁	—	2	2	no	—
154	C₂×D₄×C₄₁	—	2	2	no	—
155	C₂×D₄×C₄₁	—	2	2	no	—
156	C₂×D₄×C₄₁	—	2	2	no	—
157	C₂×D₄×C₄₁	—	2	2	no	—
158	C₂×D₄×C₄₁	—	2	2	no	—
159	C₂×D₄×C₄₁	—	2	2	no	—
160	C₂×D₄×C₄₁	—	2	1	no	—
161	C₂×D₄×C₄₁	—	2	1	no	—
162	C₂×D₄×C₄₁	—	2	1	no	—
163	C₂×D₄×C₄₁	—	2	2	no	—
164	C₂×D₄×C₄₁	—	2	2	no	—
165	C₂×D₄×C₄₁	—	2	2	no	—
166	C₂×D₄×C₄₁	—	2	2	no	—
167	C₂×D₄×C₄₁	—	2	2	no	—
168	C₂×D₄×C₄₁	—	2	2	no	—
169	C₂×D₄×C₄₁	—	2	2	no	—
170	C₂×D₄×C₄₁	—	2	1	no	—
171	C₂×D₄×C₄₁	—	2	2	no	—
172	C₂×D₄×C₄₁	—	2	1	no	—
173	C₂×D₄×C₄₁	—	2	2	no	—
174	C₂×D₄×C₄₁	—	4	1	no	—
175	C₂×D₄×C₄₁	—	4	1	no	—
176	C₂×D₄×C₄₁	—	4	1	no	—
177	C₂×D₄×C₄₁	—	4	1	no	—
178	C₂×D₄×C₄₁	—	4	1	no	—
179	C₂×D₄×C₄₁	—	4	1	no	—
180	C₂×D₄×C₄₁	—	4	1	no	—
181	C₂×D₄×C₄₁	—	4	1	no	—
182	C₂×D₄×C₄₁	—	4	1	no	—
183	C₂×D₄×C₄₁	—	4	1	no	—
184	C₂×D₄×C₄₁	—	4	1	no	—
185	C₂×D₄×C₄₁	—	4	1	no	—
186	C₂×D₄×C₄₁	—	4	1	no	—
187	C₂×D₄×C₄₁	—	4	1	no	—
188	C₂×D₄×C₄₁	—	4	1	no	—
189	C₂×D₄×C₄₁	—	4	1	no	—
190	C₂×D₄×C₄₁	C₂²⋊C₄	1	4	yes	—
191	C₂×D₄×C₄₁	C₂²⋊C₄	1	2	yes	complemented
192	C₂²×C₄×C₄₁	—	2	1	no	—
193	C₂²×C₄×C₄₁	—	2	2	no	—
194	C₂²×C₄×C₄₁	—	2	2	no	—
195	C₂²×C₄×C₄₁	—	2	2	no	—
196	C₂²×C₄×C₄₁	—	2	2	no	—
197	C₂²×C₄×C₄₁	—	4	1	no	—
198	C₂²×C₄×C₄₁	—	4	1	no	—
199	C₂²×C₄×C₄₁	—	4	1	no	—
200	C₂²×C₄×C₄₁	—	4	1	no	—
201	C₂²×C₄×C₄₁	—	4	1	no	—
202	C₂²×C₄×C₄₁	C₂²×C₄	1	1	yes	characteristic
203	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
204	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
205	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
206	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
207	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
208	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
209	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
210	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
211	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
212	C₂²×C₄×C₄₁	#41	1	1	yes	characteristic
213	C₂²×C₄×C₄₁	#41	1	1	yes	characteristic
214	C₂²×C₄×C₄₁	#41	1	1	yes	characteristic
215	C₂²×C₄×C₄₁	#41	1	1	yes	characteristic
216	SD₁₆×C₄₁	—	2	16	no	—
217	D₈×C₄₁	—	2	16	no	—
218	M₁₆×C₄₁	—	2	2	no	—
219	M₁₆×C₄₁	—	2	2	no	—
220	M₁₆×C₄₁	—	2	2	no	—
221	M₁₆×C₄₁	—	4	1	no	—
222	M₁₆×C₄₁	—	4	1	no	—
223	M₁₆×C₄₁	—	4	1	no	—
224	M₁₆×C₄₁	—	4	1	no	—
225	M₁₆×C₄₁	C₂²⋊C₄	1	4	yes	complemented
226	C₂×C₈×C₄₁	—	2	2	no	—
227	C₂×C₈×C₄₁	—	2	2	no	—
228	C₂×C₈×C₄₁	—	2	2	no	—
229	C₂×C₈×C₄₁	—	2	2	no	—
230	C₂×C₈×C₄₁	—	2	2	no	—
231	C₂×C₈×C₄₁	—	2	2	no	—
232	C₄⋊C₄×C₄₁	—	2	2	no	—
233	C₄⋊C₄×C₄₁	—	2	2	no	—
234	C₄⋊C₄×C₄₁	—	2	2	no	—
235	C₄⋊C₄×C₄₁	—	4	1	no	—
236	C₄⋊C₄×C₄₁	—	4	1	no	—
237	C₄⋊C₄×C₄₁	—	4	1	no	—
238	C₂²⋊C₄×C₄₁	—	2	2	no	—
239	C₂²⋊C₄×C₄₁	—	2	2	no	—
240	C₂²⋊C₄×C₄₁	—	2	2	no	—
241	C₂²⋊C₄×C₄₁	—	4	1	no	—
242	C₂²⋊C₄×C₄₁	—	4	1	no	—
243	C₂²⋊C₄×C₄₁	—	4	1	no	—
244	C₂²⋊C₄×C₄₁	—	8	8	no	—
245	C₄²×C₄₁	—	2	2	no	—
246	C₄²×C₄₁	—	4	1	no	—
247	C₄²×C₄₁	—	4	1	no	—
248	C₄²×C₄₁	—	4	1	no	—
249	C₄²×C₄₁	—	4	1	no	—
250	C₄²×C₄₁	—	4	1	no	—
251	C₂³×C₄₁	—	2	4	no	—
252	C₂³×C₄₁	—	2	2	no	—
253	C₂³×C₄₁	—	4	2	no	—
254	C₂³×C₄₁	—	4	8	no	—
255	C₂³×C₄₁	—	4	2	no	—
256	C₂³×C₄₁	—	4	2	no	—
257	C₂³×C₄₁	—	4	2	no	—
258	C₂³×C₄₁	—	4	2	no	—
259	C₂³×C₄₁	—	4	1	no	—
260	C₂³×C₄₁	—	4	2	no	—
261	C₂³×C₄₁	—	4	1	no	—
262	C₂³×C₄₁	—	4	2	no	—
263	C₂³×C₄₁	—	8	2	no	—
264	C₂³×C₄₁	—	8	4	no	—
265	C₂³×C₄₁	—	8	4	no	—
266	C₂³×C₄₁	—	8	4	no	—
267	C₂³×C₄₁	—	8	4	no	—
268	C₂³×C₄₁	—	8	4	no	—
269	C₂³×C₄₁	—	8	4	no	—
270	C₂³×C₄₁	C₄×D₄	1	1	yes	characteristic
271	C₂³×C₄₁	#120	1	1	yes	characteristic
272	C₂³×C₄₁	#120	1	1	yes	characteristic
273	C₂³×C₄₁	#121	1	1	yes	characteristic
274	C₂³×C₄₁	#121	1	1	yes	characteristic
275	C₂³×C₄₁	#121	1	1	yes	characteristic
276	C₂³×C₄₁	#127	1	1	yes	characteristic
277	Q₈×C₄₁	—	2	2	no	—
278	Q₈×C₄₁	—	2	2	no	—
279	Q₈×C₄₁	—	4	1	no	—
280	Q₈×C₄₁	—	4	1	no	—
281	D₄×C₄₁	—	2	2	no	—
282	D₄×C₄₁	—	2	4	no	—
283	D₄×C₄₁	—	2	4	no	—
284	D₄×C₄₁	—	2	2	no	—
285	D₄×C₄₁	—	4	2	no	—
286	D₄×C₄₁	—	4	2	no	—
287	D₄×C₄₁	—	4	2	no	—
288	D₄×C₄₁	—	4	2	no	—
289	D₄×C₄₁	—	4	2	no	—
290	D₄×C₄₁	—	4	2	no	—
291	D₄×C₄₁	—	4	2	no	—
292	D₄×C₄₁	—	4	1	no	—
293	D₄×C₄₁	—	4	2	no	—
294	D₄×C₄₁	—	4	2	no	—
295	D₄×C₄₁	—	4	2	no	—
296	D₄×C₄₁	—	4	1	no	—
297	C₂×C₄×C₄₁	—	2	2	no	—
298	C₂×C₄×C₄₁	—	4	1	no	—
299	C₂×C₄×C₄₁	—	4	1	no	—
300	C₂×C₄×C₄₁	—	4	2	no	—
301	C₂×C₄×C₄₁	—	4	2	no	—
302	C₂×C₄×C₄₁	—	4	2	no	—
303	C₂×C₄×C₄₁	—	4	2	no	—
304	C₂×C₄×C₄₁	—	4	4	no	—
305	C₂×C₄×C₄₁	—	4	4	no	—
306	C₂×C₄×C₄₁	—	4	2	no	—
307	C₂×C₄×C₄₁	—	4	2	no	—
308	C₂×C₄×C₄₁	—	4	2	no	—
309	C₂×C₄×C₄₁	—	8	2	no	—
310	C₂×C₄×C₄₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
311	C₂×C₄×C₄₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
312	C₂×C₄×C₄₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
313	C₂×C₄×C₄₁	C₄×D₄	1	1	yes	characteristic
314	C₂×C₄×C₄₁	C₄×D₄	1	1	yes	characteristic
315	C₂×C₄×C₄₁	C₄×D₄	1	1	yes	characteristic
316	C₂×C₄×C₄₁	#120	1	1	yes	characteristic
317	C₂×C₄×C₄₁	#120	1	1	yes	characteristic
318	C₂×C₄×C₄₁	#120	1	1	yes	characteristic
319	C₂×C₄×C₄₁	#120	1	1	yes	characteristic
320	C₂×C₄×C₄₁	#120	1	1	yes	characteristic
321	C₂×C₄×C₄₁	#120	1	1	yes	characteristic
322	C₂×C₄×C₄₁	#121	1	1	yes	characteristic
323	C₂×C₄×C₄₁	#121	1	1	yes	characteristic
324	C₂×C₄×C₄₁	#121	1	1	yes	characteristic
325	C₂×C₄×C₄₁	#121	1	1	yes	characteristic
326	C₂×C₄×C₄₁	#121	1	1	yes	characteristic
327	C₂×C₄×C₄₁	#121	1	1	yes	characteristic
328	C₂×C₄×C₄₁	#121	1	1	yes	characteristic
329	C₂×C₄×C₄₁	#121	1	1	yes	characteristic
330	C₂×C₄×C₄₁	#121	1	1	yes	characteristic
331	C₂×C₄×C₄₁	#123	1	1	yes	characteristic
332	C₂×C₄×C₄₁	#123	1	1	yes	characteristic
333	C₂×C₄×C₄₁	#123	1	1	yes	characteristic
334	C₂×C₄×C₄₁	#123	1	1	yes	characteristic
335	C₂×C₄×C₄₁	#124	1	1	yes	characteristic
336	C₂×C₄×C₄₁	#124	1	1	yes	characteristic
337	C₂×C₄×C₄₁	#127	1	1	yes	characteristic
338	C₈×C₄₁	—	2	4	no	—
339	C₈×C₄₁	—	4	2	no	—
340	#11030	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
341	C₂²×C₄₁	—	2	2	no	—
342	C₂²×C₄₁	—	2	2	no	—
343	C₂²×C₄₁	—	2	2	no	—
344	C₂²×C₄₁	—	4	1	no	—
345	C₂²×C₄₁	—	4	1	no	—
346	C₂²×C₄₁	—	4	1	no	—
347	C₂²×C₄₁	—	4	1	no	—
348	C₂²×C₄₁	—	4	8	no	—
349	C₂²×C₄₁	—	4	2	no	—
350	C₂²×C₄₁	—	4	4	no	—
351	C₂²×C₄₁	—	8	2	no	—
352	C₂²×C₄₁	—	8	4	no	—
353	C₂²×C₄₁	—	8	2	no	—
354	C₂²×C₄₁	—	8	4	no	—
355	C₂²×C₄₁	—	8	4	no	—
356	C₂²×C₄₁	—	8	4	no	—
357	C₂²×C₄₁	—	8	4	no	—
358	C₂²×C₄₁	—	8	4	no	—
359	C₂²×C₄₁	—	8	2	no	—
360	C₂²×C₄₁	#386	1	1	yes	characteristic
361	C₂²×C₄₁	#386	1	1	yes	characteristic
362	C₂²×C₄₁	#390	1	1	yes	characteristic
363	C₂²×C₄₁	#392	1	1	yes	characteristic
364	C₂²×C₄₁	#392	1	1	yes	characteristic
365	C₂²×C₄₁	#392	1	1	yes	characteristic
366	C₂²×C₄₁	#394	1	1	yes	characteristic
367	C₄×C₄₁	—	4	2	no	—
368	C₄×C₄₁	—	8	2	no	—
369	C₄×C₄₁	—	8	2	no	—
370	C₄×C₄₁	—	8	2	no	—
371	C₄×C₄₁	#379	1	1	yes	characteristic
372	C₄×C₄₁	#386	1	1	yes	characteristic
373	C₄×C₄₁	#386	1	1	yes	characteristic
374	C₄×C₄₁	#390	1	1	yes	characteristic
375	C₄×C₄₁	#392	1	1	yes	characteristic
376	C₄×C₄₁	#394	1	1	yes	characteristic
377	C₄×C₄₁	#394	1	1	yes	characteristic
378	C₄×C₄₁	#394	1	1	yes	characteristic
379	C₂²×AGL(1,ℤ/8)	C₂×C₄₁	1	1	yes	characteristic
380	#2896	C₂×C₄₁	1	1	yes	characteristic, complemented
381	C₂×#418	C₂×C₄₁	1	1	yes	characteristic, complemented
382	C₂×#410	C₂×C₄₁	1	1	yes	characteristic, complemented
383	#2309	C₂×C₄₁	1	1	yes	characteristic, complemented
384	C₂×#344	C₂×C₄₁	1	1	yes	characteristic, complemented
385	#1733	C₂×C₄₁	1	1	yes	characteristic, complemented
386	C₂×C₄₁	—	2	1	no	—
387	C₂×C₄₁	—	2	1	no	—
388	C₂×C₄₁	—	2	1	no	—
389	C₂×C₄₁	—	2	1	no	—
390	C₂×C₄₁	—	2	1	no	—
391	C₂×C₄₁	—	2	1	no	—
392	C₂×C₄₁	—	8	4	no	—
393	C₂×C₄₁	—	8	2	no	—
394	C₂×C₄₁	#1438	1	1	yes	characteristic
395	C₂×C₄₁	#2008	1	2	yes	—
396	C₂²×#41	C₂²×C₄₁	1	1	yes	characteristic
397	C₂³×D₄	C₂²×C₄₁	1	1	yes	characteristic
398	C₂×AGL(1,ℤ/8)	—	2	2	no	—
399	C₂×AGL(1,ℤ/8)	—	2	2	no	—
400	C₂×AGL(1,ℤ/8)	—	2	2	no	—
401	C₂×AGL(1,ℤ/8)	—	2	2	no	—
402	C₂×AGL(1,ℤ/8)	—	2	2	no	—
403	C₂×AGL(1,ℤ/8)	C₄×C₄₁	1	4	yes	complemented
404	C₂²×SD₁₆	—	2	1	no	—
405	C₂²×D₈	—	2	1	no	—
406	C₂²×M₁₆	C₂²×C₄₁	1	1	yes	characteristic
407	C₂²×M₁₆	C₂²×C₄₁	1	1	yes	characteristic
408	C₂×#117	C₂²×C₄₁	1	1	yes	characteristic
409	C₂×#117	C₂²×C₄₁	1	1	yes	characteristic
410	C₂×#117	C₂²×C₄₁	1	1	yes	characteristic
411	#419	—	2	1	no	—
412	#418	—	2	2	no	—
413	#418	—	2	1	no	—
414	#418	—	2	2	no	—
415	#417	—	2	2	no	—
416	#416	—	2	2	no	—
417	C₂×#102	—	2	2	no	—
418	#410	—	2	2	no	—
419	#410	—	2	2	no	—
420	C₂×#99	—	2	2	no	—
421	#390	—	2	2	no	—
422	#390	—	2	2	no	—
423	#379	—	2	2	no	—
424	#344	—	2	2	no	—
425	#339	—	2	2	no	—
426	C₄₁	#11030	1	1	yes	characteristic, direct product factor, Sylow
427	C₂⁵	—	2	1	no	—
428	C₂×#41	—	2	1	no	—
429	C₂×#41	—	2	1	no	—
430	C₂×#41	—	2	1	no	—
431	C₂×#41	—	2	1	no	—
432	C₂×#41	—	2	1	no	—
433	C₂×#41	—	2	1	no	—
434	C₂×#41	—	2	1	no	—
435	C₂×#41	—	2	1	no	—
436	C₂×#41	—	2	1	no	—
437	C₂×#41	—	2	1	no	—
438	C₂×#41	C₂×C₄×C₄₁	1	2	yes	—
439	C₂×#41	D₄×C₄₁	1	2	yes	—
440	C₂²×Q₈	D₄×C₄₁	1	1	yes	characteristic
441	C₂²×D₄	—	2	1	no	—
442	C₂²×D₄	—	2	1	no	—
443	C₂²×D₄	—	2	1	no	—
444	C₂²×D₄	—	2	1	no	—
445	C₂²×D₄	—	2	1	no	—
446	C₂²×D₄	—	2	1	no	—
447	C₂²×D₄	—	2	1	no	—
448	C₂²×D₄	—	2	1	no	—
449	C₂²×D₄	—	2	1	no	—
450	C₂²×D₄	—	2	1	no	—
451	C₂²×D₄	—	2	1	no	—
452	C₂²×D₄	—	2	1	no	—
453	C₂²×D₄	C₂×C₄×C₄₁	1	2	yes	—
454	C₂²×D₄	D₄×C₄₁	1	2	yes	—
455	C₂²×D₄	D₄×C₄₁	1	2	yes	—
456	C₂²×D₄	D₄×C₄₁	1	1	yes	characteristic
457	C₂³×C₄	—	2	1	no	—
458	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
459	AGL(1,ℤ/8)	—	2	8	no	—
460	AGL(1,ℤ/8)	—	2	8	no	—
461	AGL(1,ℤ/8)	—	2	8	no	—
462	AGL(1,ℤ/8)	—	2	8	no	—
463	C₂×SD₁₆	—	2	4	no	—
464	C₂×SD₁₆	—	2	4	no	—
465	C₂×SD₁₆	—	2	4	no	—
466	C₂×D₈	—	2	4	no	—
467	C₂×D₈	—	2	4	no	—
468	C₂×D₈	—	2	4	no	—
469	C₂×M₁₆	—	2	1	no	—
470	C₂×M₁₆	—	2	1	no	—
471	C₂×M₁₆	—	2	1	no	—
472	C₂×M₁₆	—	2	1	no	—
473	C₂×M₁₆	—	2	1	no	—
474	C₂×M₁₆	—	2	1	no	—
475	C₂×M₁₆	—	2	1	no	—
476	C₂×M₁₆	—	2	1	no	—
477	C₂×M₁₆	—	2	1	no	—
478	C₂×M₁₆	C₂×C₄×C₄₁	1	2	yes	—
479	C₂×M₁₆	D₄×C₄₁	1	2	yes	—
480	C₂×M₁₆	D₄×C₄₁	1	2	yes	—
481	C₂²×C₈	—	2	1	no	—
482	C₂²×C₈	D₄×C₄₁	1	2	yes	—
483	#117	—	2	1	no	—
484	#117	—	2	1	no	—
485	#117	—	2	1	no	—
486	#117	—	2	1	no	—
487	#117	—	2	1	no	—
488	#117	—	2	1	no	—
489	#117	—	2	1	no	—
490	#117	—	2	1	no	—
491	#117	—	2	1	no	—
492	#117	—	2	1	no	—
493	#117	—	2	1	no	—
494	#117	D₄×C₄₁	1	2	yes	—
495	C₂×C₄⋊C₄	—	2	1	no	—
496	C₂×C₄⋊C₄	—	2	1	no	—
497	C₂×C₄⋊C₄	D₄×C₄₁	1	2	yes	—
498	C₂×C₂²⋊C₄	—	2	1	no	—
499	C₂×C₂²⋊C₄	—	2	1	no	—
500	C₂×C₂²⋊C₄	—	2	8	no	—
501	C₂×C₂²⋊C₄	D₄×C₄₁	1	2	yes	—
502	C₂×C₄²	—	2	1	no	—
503	C₂×C₄²	—	2	1	no	—
504	C₂×C₄²	—	2	1	no	—
505	#103	—	2	4	no	—
506	#102	—	2	8	no	—
507	#102	—	2	4	no	—
508	#99	—	2	8	no	—
509	C₂⁴	—	2	2	no	—
510	C₂⁴	—	2	2	no	—
511	C₂⁴	—	2	1	no	—
512	C₂⁴	—	2	2	no	—
513	C₂⁴	—	4	1	no	—
514	C₂⁴	—	4	1	no	—
515	C₂⁴	—	4	1	no	—
516	C₂⁴	—	4	1	no	—
517	C₂⁴	—	8	4	no	—
518	C₂⁴	C₂×D₄×C₄₁	1	1	yes	characteristic
519	#41	—	2	2	no	—
520	#41	—	2	2	no	—
521	#41	—	2	2	no	—
522	#41	—	2	2	no	—
523	#41	—	2	2	no	—
524	#41	—	2	2	no	—
525	#41	—	2	2	no	—
526	#41	—	2	2	no	—
527	#41	—	4	1	no	—
528	#41	—	4	1	no	—
529	#41	—	4	1	no	—
530	#41	—	4	1	no	—
531	#41	—	4	1	no	—
532	#41	—	4	1	no	—
533	#41	—	4	1	no	—
534	#41	—	4	1	no	—
535	C₂×Q₈	—	2	1	no	—
536	C₂×Q₈	—	2	1	no	—
537	C₂×Q₈	—	2	1	no	—
538	C₂×Q₈	—	2	1	no	—
539	C₂×Q₈	—	2	1	no	—
540	C₂×Q₈	C₂²⋊C₄×C₄₁	1	2	yes	complemented
541	C₂×D₄	—	2	2	no	—
542	C₂×D₄	—	2	2	no	—
543	C₂×D₄	—	2	2	no	—
544	C₂×D₄	—	2	2	no	—
545	C₂×D₄	—	2	2	no	—
546	C₂×D₄	—	2	2	no	—
547	C₂×D₄	—	2	2	no	—
548	C₂×D₄	—	2	2	no	—
549	C₂×D₄	—	2	1	no	—
550	C₂×D₄	—	2	1	no	—
551	C₂×D₄	—	2	1	no	—
552	C₂×D₄	—	2	2	no	—
553	C₂×D₄	—	2	2	no	—
554	C₂×D₄	—	2	2	no	—
555	C₂×D₄	—	2	2	no	—
556	C₂×D₄	—	2	2	no	—
557	C₂×D₄	—	2	2	no	—
558	C₂×D₄	—	2	2	no	—
559	C₂×D₄	—	2	1	no	—
560	C₂×D₄	—	2	2	no	—
561	C₂×D₄	—	2	1	no	—
562	C₂×D₄	—	2	2	no	—
563	C₂×D₄	—	4	1	no	—
564	C₂×D₄	—	4	1	no	—
565	C₂×D₄	—	4	1	no	—
566	C₂×D₄	—	4	1	no	—
567	C₂×D₄	—	4	1	no	—
568	C₂×D₄	—	4	1	no	—
569	C₂×D₄	—	4	1	no	—
570	C₂×D₄	—	4	1	no	—
571	C₂×D₄	—	4	1	no	—
572	C₂×D₄	—	4	1	no	—
573	C₂×D₄	—	4	1	no	—
574	C₂×D₄	—	4	1	no	—
575	C₂×D₄	—	4	1	no	—
576	C₂×D₄	—	4	1	no	—
577	C₂×D₄	—	4	1	no	—
578	C₂×D₄	—	4	1	no	—
579	C₂×D₄	C₂²⋊C₄×C₄₁	1	4	yes	—
580	C₂×D₄	C₂²⋊C₄×C₄₁	1	2	yes	complemented
581	C₂²×C₄	—	2	1	no	—
582	C₂²×C₄	—	2	2	no	—
583	C₂²×C₄	—	2	2	no	—
584	C₂²×C₄	—	2	2	no	—
585	C₂²×C₄	—	2	2	no	—
586	C₂²×C₄	—	4	1	no	—
587	C₂²×C₄	—	4	1	no	—
588	C₂²×C₄	—	4	1	no	—
589	C₂²×C₄	—	4	1	no	—
590	C₂²×C₄	—	4	1	no	—
591	C₂²×C₄	C₂²×C₄×C₄₁	1	1	yes	characteristic
592	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
593	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
594	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
595	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
596	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
597	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
598	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
599	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
600	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
601	C₂²×C₄	#41×C₄₁	1	1	yes	characteristic
602	C₂²×C₄	#41×C₄₁	1	1	yes	characteristic
603	C₂²×C₄	#41×C₄₁	1	1	yes	characteristic
604	C₂²×C₄	#41×C₄₁	1	1	yes	characteristic
605	SD₁₆	—	2	16	no	—
606	D₈	—	2	16	no	—
607	M₁₆	—	2	2	no	—
608	M₁₆	—	2	2	no	—
609	M₁₆	—	2	2	no	—
610	M₁₆	—	4	1	no	—
611	M₁₆	—	4	1	no	—
612	M₁₆	—	4	1	no	—
613	M₁₆	—	4	1	no	—
614	M₁₆	C₂²⋊C₄×C₄₁	1	4	yes	complemented
615	C₂×C₈	—	2	2	no	—
616	C₂×C₈	—	2	2	no	—
617	C₂×C₈	—	2	2	no	—
618	C₂×C₈	—	2	2	no	—
619	C₂×C₈	—	2	2	no	—
620	C₂×C₈	—	2	2	no	—
621	C₄⋊C₄	—	2	2	no	—
622	C₄⋊C₄	—	2	2	no	—
623	C₄⋊C₄	—	2	2	no	—
624	C₄⋊C₄	—	4	1	no	—
625	C₄⋊C₄	—	4	1	no	—
626	C₄⋊C₄	—	4	1	no	—
627	C₂²⋊C₄	—	2	2	no	—
628	C₂²⋊C₄	—	2	2	no	—
629	C₂²⋊C₄	—	2	2	no	—
630	C₂²⋊C₄	—	4	1	no	—
631	C₂²⋊C₄	—	4	1	no	—
632	C₂²⋊C₄	—	4	1	no	—
633	C₂²⋊C₄	—	8	8	no	—
634	C₄²	—	2	2	no	—
635	C₄²	—	4	1	no	—
636	C₄²	—	4	1	no	—
637	C₄²	—	4	1	no	—
638	C₄²	—	4	1	no	—
639	C₄²	—	4	1	no	—
640	C₂³	—	2	4	no	—
641	C₂³	—	2	2	no	—
642	C₂³	—	4	2	no	—
643	C₂³	—	4	8	no	—
644	C₂³	—	4	2	no	—
645	C₂³	—	4	2	no	—
646	C₂³	—	4	1	no	—
647	C₂³	—	4	2	no	—
648	C₂³	—	4	2	no	—
649	C₂³	—	4	2	no	—
650	C₂³	—	4	1	no	—
651	C₂³	—	4	2	no	—
652	C₂³	—	8	2	no	—
653	C₂³	—	8	4	no	—
654	C₂³	—	8	4	no	—
655	C₂³	—	8	4	no	—
656	C₂³	—	8	4	no	—
657	C₂³	—	8	4	no	—
658	C₂³	—	8	4	no	—
659	C₂³	C₄×D₄×C₄₁	1	1	yes	characteristic
660	C₂³	#120×C₄₁	1	1	yes	characteristic
661	C₂³	#120×C₄₁	1	1	yes	characteristic
662	C₂³	#121×C₄₁	1	1	yes	characteristic
663	C₂³	#121×C₄₁	1	1	yes	characteristic
664	C₂³	#121×C₄₁	1	1	yes	characteristic
665	C₂³	#127×C₄₁	1	1	yes	characteristic
666	Q₈	—	2	2	no	—
667	Q₈	—	2	2	no	—
668	Q₈	—	4	1	no	—
669	Q₈	—	4	1	no	—
670	D₄	—	2	2	no	—
671	D₄	—	2	4	no	—
672	D₄	—	2	4	no	—
673	D₄	—	2	2	no	—
674	D₄	—	4	2	no	—
675	D₄	—	4	2	no	—
676	D₄	—	4	2	no	—
677	D₄	—	4	2	no	—
678	D₄	—	4	2	no	—
679	D₄	—	4	2	no	—
680	D₄	—	4	2	no	—
681	D₄	—	4	1	no	—
682	D₄	—	4	2	no	—
683	D₄	—	4	2	no	—
684	D₄	—	4	2	no	—
685	D₄	—	4	1	no	—
686	C₂×C₄	—	2	2	no	—
687	C₂×C₄	—	4	1	no	—
688	C₂×C₄	—	4	1	no	—
689	C₂×C₄	—	4	2	no	—
690	C₂×C₄	—	4	2	no	—
691	C₂×C₄	—	4	2	no	—
692	C₂×C₄	—	4	2	no	—
693	C₂×C₄	—	4	4	no	—
694	C₂×C₄	—	4	4	no	—
695	C₂×C₄	—	4	2	no	—
696	C₂×C₄	—	4	2	no	—
697	C₂×C₄	—	4	2	no	—
698	C₂×C₄	—	8	2	no	—
699	C₂×C₄	C₂×C₂²⋊C₄×C₄₁	1	1	yes	characteristic
700	C₂×C₄	C₂×C₂²⋊C₄×C₄₁	1	1	yes	characteristic
701	C₂×C₄	C₂×C₂²⋊C₄×C₄₁	1	1	yes	characteristic
702	C₂×C₄	C₄×D₄×C₄₁	1	1	yes	characteristic
703	C₂×C₄	C₄×D₄×C₄₁	1	1	yes	characteristic
704	C₂×C₄	C₄×D₄×C₄₁	1	1	yes	characteristic
705	C₂×C₄	#120×C₄₁	1	1	yes	characteristic
706	C₂×C₄	#120×C₄₁	1	1	yes	characteristic
707	C₂×C₄	#120×C₄₁	1	1	yes	characteristic
708	C₂×C₄	#120×C₄₁	1	1	yes	characteristic
709	C₂×C₄	#120×C₄₁	1	1	yes	characteristic
710	C₂×C₄	#120×C₄₁	1	1	yes	characteristic
711	C₂×C₄	#121×C₄₁	1	1	yes	characteristic
712	C₂×C₄	#121×C₄₁	1	1	yes	characteristic
713	C₂×C₄	#121×C₄₁	1	1	yes	characteristic
714	C₂×C₄	#121×C₄₁	1	1	yes	characteristic
715	C₂×C₄	#121×C₄₁	1	1	yes	characteristic
716	C₂×C₄	#121×C₄₁	1	1	yes	characteristic
717	C₂×C₄	#121×C₄₁	1	1	yes	characteristic
718	C₂×C₄	#121×C₄₁	1	1	yes	characteristic
719	C₂×C₄	#121×C₄₁	1	1	yes	characteristic
720	C₂×C₄	#123×C₄₁	1	1	yes	characteristic
721	C₂×C₄	#123×C₄₁	1	1	yes	characteristic
722	C₂×C₄	#123×C₄₁	1	1	yes	characteristic
723	C₂×C₄	#123×C₄₁	1	1	yes	characteristic
724	C₂×C₄	#124×C₄₁	1	1	yes	characteristic
725	C₂×C₄	#124×C₄₁	1	1	yes	characteristic
726	C₂×C₄	#127×C₄₁	1	1	yes	characteristic
727	C₈	—	2	4	no	—
728	C₈	—	4	2	no	—
729	C₂²	—	2	2	no	—
730	C₂²	—	2	2	no	—
731	C₂²	—	2	2	no	—
732	C₂²	—	4	1	no	—
733	C₂²	—	4	1	no	—
734	C₂²	—	4	1	no	—
735	C₂²	—	4	1	no	—
736	C₂²	—	4	8	no	—
737	C₂²	—	4	2	no	—
738	C₂²	—	4	4	no	—
739	C₂²	—	8	2	no	—
740	C₂²	—	8	4	no	—
741	C₂²	—	8	4	no	—
742	C₂²	—	8	4	no	—
743	C₂²	—	8	4	no	—
744	C₂²	—	8	4	no	—
745	C₂²	—	8	2	no	—
746	C₂²	—	8	4	no	—
747	C₂²	—	8	2	no	—
748	C₂²	C₄₁×#386	1	1	yes	characteristic
749	C₂²	C₄₁×#386	1	1	yes	characteristic
750	C₂²	C₄₁×#390	1	1	yes	characteristic
751	C₂²	C₄₁×#392	1	1	yes	characteristic
752	C₂²	C₄₁×#392	1	1	yes	characteristic
753	C₂²	C₄₁×#392	1	1	yes	characteristic
754	C₂²	C₄₁×#394	1	1	yes	characteristic
755	C₄	—	4	2	no	—
756	C₄	—	8	2	no	—
757	C₄	—	8	2	no	—
758	C₄	—	8	2	no	—
759	C₄	C₄₁×#379	1	1	yes	characteristic
760	C₄	C₄₁×#386	1	1	yes	characteristic
761	C₄	C₄₁×#386	1	1	yes	characteristic
762	C₄	C₄₁×#390	1	1	yes	characteristic
763	C₄	C₄₁×#392	1	1	yes	characteristic
764	C₄	C₄₁×#394	1	1	yes	characteristic
765	C₄	C₄₁×#394	1	1	yes	characteristic
766	C₄	C₄₁×#394	1	1	yes	characteristic
767	C₂	—	2	1	no	—
768	C₂	—	2	1	no	—
769	C₂	—	2	1	no	—
770	C₂	—	2	1	no	—
771	C₂	—	2	1	no	—
772	C₂	—	2	1	no	—
773	C₂	—	8	4	no	—
774	C₂	—	8	2	no	—
775	C₂	C₄₁×#1438	1	1	yes	characteristic
776	C₂	C₄₁×#2008	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₄₁	#392
commutator	C₂²×C₄	C₂²×C₄×C₄₁
Frattini, cosocle	C₂³×C₄	C₂³×C₄₁
prime radical	C₂²×AGL(1,ℤ/8)×C₄₁	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄₁ ◁ C₂³×C₄×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₄₁×#2896	C₂	semidirect
3. C₂×C₄₁×#418	C₂	semidirect
4. C₂×C₄₁×#410	C₂	semidirect
5. C₄₁×#2309	C₂	semidirect
6. C₂×C₄₁×#344	C₂	semidirect
7. C₄₁×#1733	C₂	semidirect
15. C₂×AGL(1,ℤ/8)×C₄₁	C₄	semidirect
151. C₂×Q₈×C₄₁	C₂²⋊C₄	semidirect
191. C₂×D₄×C₄₁	C₂²⋊C₄	semidirect
225. M₁₆×C₄₁	C₂²⋊C₄	semidirect
340. #11030	C₄₁	direct (N × H)
380. #2896	C₂×C₄₁	semidirect
381. C₂×#418	C₂×C₄₁	semidirect
382. C₂×#410	C₂×C₄₁	semidirect
383. #2309	C₂×C₄₁	semidirect
384. C₂×#344	C₂×C₄₁	semidirect
385. #1733	C₂×C₄₁	semidirect
403. C₂×AGL(1,ℤ/8)	C₄×C₄₁	semidirect
426. C₄₁	#11030	direct (N × H)
540. C₂×Q₈	C₂²⋊C₄×C₄₁	semidirect
580. C₂×D₄	C₂²⋊C₄×C₄₁	semidirect
614. M₁₆	C₂²⋊C₄×C₄₁	semidirect

Maximal subgroups

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

subgroup	index
C₂²×AGL(1,ℤ/8)×C₄₁	2
C₄₁×#2896	2
C₂×C₄₁×#418	2
C₂×C₄₁×#410	2
C₄₁×#2309	2
C₂×C₄₁×#344	2
C₄₁×#1733	2
#11030	41

Subgroups — C41×#11030 #23787231

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#11030 #23787231