Subgroups — C₄₁×#24361 #23800562

Order 10496.

1408 conjugacy classes of subgroups.

The subgroup lattice has 558 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×Q₁₆×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄₁×#464	C₂	1	2	yes	maximal, complemented
3	C₂×C₄₁×#448	C₂	1	1	yes	maximal, characteristic
4	C₄₁×#2436	C₂	1	1	yes	maximal, characteristic
5	Q₈×C₂²⋊C₄×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄₁×#2056	C₂	1	2	yes	maximal, complemented
7	C₄₁×#2015	C₂	1	2	yes	maximal, complemented
8	C₄₁×#1893	C₂	1	1	yes	maximal, characteristic
9	C₄₁×#1878	C₂	1	2	yes	maximal, complemented
10	C₄₁×#1850	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₁×#1787	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂³×Q₈×C₄₁	C₂²	1	1	yes	characteristic
13	C₂³×Q₈×C₄₁	C₂²	1	1	yes	characteristic
14	C₂²×Q₁₆×C₄₁	—	2	4	no	—
15	C₂²×Q₁₆×C₄₁	—	2	8	no	—
16	C₂²×Q₁₆×C₄₁	C₂²	1	2	yes	—
17	C₂²×Q₁₆×C₄₁	C₂²	1	2	yes	—
18	C₂²×SD₁₆×C₄₁	C₂²	1	1	yes	characteristic
19	C₂²×SD₁₆×C₄₁	C₂²	1	1	yes	characteristic
20	C₂³×C₈×C₄₁	C₂²	1	1	yes	characteristic
21	C₂×#124×C₄₁	C₂²	1	2	yes	—
22	C₂×#121×C₄₁	C₂²	1	1	yes	characteristic
23	C₂×C₄×Q₈×C₄₁	C₂²	1	2	yes	—
24	C₄₁×#464	—	2	8	no	—
25	C₄₁×#448	—	2	4	no	—
26	C₂×C₄⋊C₈×C₄₁	C₂²	1	2	yes	—
27	C₂×#103×C₄₁	C₂²	1	2	yes	—
28	C₂×#103×C₄₁	C₂²	1	1	yes	characteristic
29	C₂×#103×C₄₁	C₂²	1	1	yes	characteristic
30	C₂×#103×C₄₁	C₂²	1	2	yes	—
31	C₂×#102×C₄₁	C₂²	1	2	yes	—
32	C₂×C₂²⋊C₈×C₄₁	C₂²	1	1	yes	characteristic
33	C₄₁×#393	—	2	2	no	—
34	C₄₁×#391	—	2	2	no	—
35	C₄₁×#391	C₂²	1	2	yes	—
36	C₄₁×#391	C₂²	1	2	yes	—
37	C₄₁×#386	—	2	1	no	—
38	C₄₁×#386	—	2	1	no	—
39	C₄₁×#380	—	2	1	no	—
40	C₄₁×#380	C₂²	1	1	yes	characteristic
41	C₄×C₂²⋊C₄×C₄₁	—	2	1	no	—
42	C₄×C₂²⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
43	C₄₁×#340	C₂²	1	2	yes	—
44	C₄₁×#336	C₂²	1	2	yes	—
45	C₂²×Q₈×C₄₁	—	2	1	no	—
46	C₂²×Q₈×C₄₁	—	2	1	no	—
47	C₂²×Q₈×C₄₁	—	2	2	no	—
48	C₂²×Q₈×C₄₁	—	2	4	no	—
49	C₂²×Q₈×C₄₁	—	2	4	no	—
50	C₂²×Q₈×C₄₁	—	2	2	no	—
51	C₂²×Q₈×C₄₁	—	2	2	no	—
52	C₂²×Q₈×C₄₁	—	4	2	no	—
53	C₂²×Q₈×C₄₁	—	4	2	no	—
54	C₂²×Q₈×C₄₁	D₄	1	4	yes	—
55	C₂²×Q₈×C₄₁	C₂³	1	2	yes	—
56	C₂²×Q₈×C₄₁	C₂³	1	1	yes	characteristic
57	C₂²×Q₈×C₄₁	C₂³	1	1	yes	characteristic
58	C₂²×D₄×C₄₁	—	2	1	no	—
59	C₂²×D₄×C₄₁	C₂³	1	1	yes	characteristic
60	C₂³×C₄×C₄₁	—	2	1	no	—
61	C₂³×C₄×C₄₁	—	2	1	no	—
62	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
63	C₂×Q₁₆×C₄₁	—	2	32	no	—
64	C₂×Q₁₆×C₄₁	—	2	4	no	—
65	C₂×Q₁₆×C₄₁	—	2	4	no	—
66	C₂×Q₁₆×C₄₁	—	2	4	no	—
67	C₂×Q₁₆×C₄₁	—	2	4	no	—
68	C₂×Q₁₆×C₄₁	—	2	4	no	—
69	C₂×Q₁₆×C₄₁	D₄	1	8	yes	complemented
70	C₂×SD₁₆×C₄₁	—	2	2	no	—
71	C₂×SD₁₆×C₄₁	—	2	2	no	—
72	C₂×SD₁₆×C₄₁	—	2	4	no	—
73	C₂×SD₁₆×C₄₁	—	4	2	no	—
74	C₂²×C₈×C₄₁	—	2	2	no	—
75	C₂²×C₈×C₄₁	—	2	4	no	—
76	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
77	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
78	C₂²×C₈×C₄₁	C₂³	1	2	yes	—
79	#124×C₄₁	—	2	4	no	—
80	#124×C₄₁	—	4	2	no	—
81	#121×C₄₁	—	2	2	no	—
82	#121×C₄₁	—	2	2	no	—
83	C₄×Q₈×C₄₁	—	2	4	no	—
84	C₄×Q₈×C₄₁	—	4	2	no	—
85	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
86	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
87	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
88	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
89	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
90	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
91	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
92	C₂×C₂²⋊C₄×C₄₁	D₄	1	1	yes	characteristic
93	C₂×C₂²⋊C₄×C₄₁	D₄	1	1	yes	characteristic
94	C₂×C₄²×C₄₁	—	2	2	no	—
95	C₂×C₄²×C₄₁	C₂³	1	2	yes	—
96	C₄⋊C₈×C₄₁	—	2	4	no	—
97	#103×C₄₁	—	2	2	no	—
98	#103×C₄₁	—	2	2	no	—
99	#103×C₄₁	—	2	4	no	—
100	#103×C₄₁	—	4	2	no	—
101	#102×C₄₁	—	2	4	no	—
102	C₂²⋊C₈×C₄₁	—	2	2	no	—
103	#95×C₄₁	—	2	2	no	—
104	#95×C₄₁	—	2	2	no	—
105	#95×C₄₁	—	2	1	no	—
106	#95×C₄₁	—	2	2	no	—
107	#95×C₄₁	—	2	2	no	—
108	#95×C₄₁	D₄	1	2	yes	—
109	C₂⁴×C₄₁	—	2	1	no	—
110	C₂⁴×C₄₁	C₂×D₄	1	1	yes	characteristic
111	C₂×Q₈×C₄₁	—	2	4	no	—
112	C₂×Q₈×C₄₁	—	2	1	no	—
113	C₂×Q₈×C₄₁	—	2	1	no	—
114	C₂×Q₈×C₄₁	—	2	2	no	—
115	C₂×Q₈×C₄₁	—	2	2	no	—
116	C₂×Q₈×C₄₁	—	2	8	no	—
117	C₂×Q₈×C₄₁	—	2	8	no	—
118	C₂×Q₈×C₄₁	—	2	2	no	—
119	C₂×Q₈×C₄₁	—	2	2	no	—
120	C₂×Q₈×C₄₁	—	2	2	no	—
121	C₂×Q₈×C₄₁	—	2	2	no	—
122	C₂×Q₈×C₄₁	—	2	2	no	—
123	C₂×Q₈×C₄₁	—	2	2	no	—
124	C₂×Q₈×C₄₁	—	4	4	no	—
125	C₂×Q₈×C₄₁	—	4	4	no	—
126	C₂×Q₈×C₄₁	—	4	4	no	—
127	C₂×Q₈×C₄₁	—	4	8	no	—
128	C₂×Q₈×C₄₁	—	4	8	no	—
129	C₂×Q₈×C₄₁	—	4	4	no	—
130	C₂×Q₈×C₄₁	—	4	2	no	—
131	C₂×Q₈×C₄₁	C₂×D₄	1	4	yes	—
132	C₂×Q₈×C₄₁	C₂×D₄	1	2	yes	—
133	C₂×Q₈×C₄₁	C₂×D₄	1	2	yes	—
134	C₂×Q₈×C₄₁	C₂×D₄	1	4	yes	—
135	C₂×D₄×C₄₁	—	2	2	no	—
136	C₂×D₄×C₄₁	—	2	1	no	—
137	C₂×D₄×C₄₁	—	2	1	no	—
138	C₂×D₄×C₄₁	—	2	2	no	—
139	C₂×D₄×C₄₁	—	4	2	no	—
140	C₂×D₄×C₄₁	—	4	2	no	—
141	C₂×D₄×C₄₁	—	4	2	no	—
142	C₂²×C₄×C₄₁	—	2	1	no	—
143	C₂²×C₄×C₄₁	—	2	2	no	—
144	C₂²×C₄×C₄₁	—	2	2	no	—
145	C₂²×C₄×C₄₁	—	2	4	no	—
146	C₂²×C₄×C₄₁	—	2	1	no	—
147	C₂²×C₄×C₄₁	—	2	2	no	—
148	C₂²×C₄×C₄₁	—	2	1	no	—
149	C₂²×C₄×C₄₁	—	2	2	no	—
150	C₂²×C₄×C₄₁	—	4	4	no	—
151	C₂²×C₄×C₄₁	—	4	4	no	—
152	C₂²×C₄×C₄₁	—	4	2	no	—
153	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
154	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
155	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
156	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
157	C₂²×C₄×C₄₁	#41	1	2	yes	—
158	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
159	Q₁₆×C₄₁	—	2	16	no	—
160	Q₁₆×C₄₁	—	2	16	no	—
161	SD₁₆×C₄₁	—	4	4	no	—
162	SD₁₆×C₄₁	—	4	4	no	—
163	C₂×C₈×C₄₁	—	2	8	no	—
164	C₂×C₈×C₄₁	—	2	2	no	—
165	C₂×C₈×C₄₁	—	2	2	no	—
166	C₂×C₈×C₄₁	—	2	1	no	—
167	C₂×C₈×C₄₁	—	2	1	no	—
168	C₂×C₈×C₄₁	—	2	2	no	—
169	C₂×C₈×C₄₁	—	2	2	no	—
170	C₂×C₈×C₄₁	C₂×D₄	1	4	yes	—
171	C₄⋊C₄×C₄₁	—	2	2	no	—
172	C₄⋊C₄×C₄₁	—	2	1	no	—
173	C₄⋊C₄×C₄₁	—	2	1	no	—
174	C₄⋊C₄×C₄₁	—	2	2	no	—
175	C₄⋊C₄×C₄₁	—	4	4	no	—
176	C₂²⋊C₄×C₄₁	—	2	2	no	—
177	C₂²⋊C₄×C₄₁	—	2	2	no	—
178	C₂²⋊C₄×C₄₁	—	4	4	no	—
179	C₂²⋊C₄×C₄₁	—	4	4	no	—
180	C₂²⋊C₄×C₄₁	—	4	2	no	—
181	C₂²⋊C₄×C₄₁	—	4	2	no	—
182	C₄²×C₄₁	—	2	2	no	—
183	C₄²×C₄₁	—	2	2	no	—
184	C₄²×C₄₁	—	4	4	no	—
185	C₂³×C₄₁	—	2	2	no	—
186	C₂³×C₄₁	—	2	2	no	—
187	C₂³×C₄₁	—	4	1	no	—
188	C₂³×C₄₁	—	4	2	no	—
189	C₂³×C₄₁	—	4	1	no	—
190	C₂³×C₄₁	—	4	1	no	—
191	C₂³×C₄₁	—	4	2	no	—
192	C₂³×C₄₁	#121	1	2	yes	—
193	C₂³×C₄₁	#135	1	2	yes	—
194	C₂³×C₄₁	#137	1	2	yes	—
195	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
196	Q₈×C₄₁	—	2	2	no	—
197	Q₈×C₄₁	—	2	4	no	—
198	Q₈×C₄₁	—	2	2	no	—
199	Q₈×C₄₁	—	2	4	no	—
200	Q₈×C₄₁	—	2	2	no	—
201	Q₈×C₄₁	—	2	4	no	—
202	Q₈×C₄₁	—	4	8	no	—
203	Q₈×C₄₁	—	4	8	no	—
204	Q₈×C₄₁	—	4	2	no	—
205	Q₈×C₄₁	—	4	2	no	—
206	Q₈×C₄₁	—	4	2	no	—
207	Q₈×C₄₁	#120	1	4	yes	—
208	D₄×C₄₁	—	4	1	no	—
209	D₄×C₄₁	—	4	1	no	—
210	D₄×C₄₁	—	4	2	no	—
211	D₄×C₄₁	—	8	4	no	—
212	C₂×C₄×C₄₁	—	2	2	no	—
213	C₂×C₄×C₄₁	—	2	4	no	—
214	C₂×C₄×C₄₁	—	2	2	no	—
215	C₂×C₄×C₄₁	—	2	2	no	—
216	C₂×C₄×C₄₁	—	2	2	no	—
217	C₂×C₄×C₄₁	—	2	4	no	—
218	C₂×C₄×C₄₁	—	2	2	no	—
219	C₂×C₄×C₄₁	—	2	2	no	—
220	C₂×C₄×C₄₁	—	2	2	no	—
221	C₂×C₄×C₄₁	—	2	4	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	—	4	8	no	—
227	C₂×C₄×C₄₁	—	4	8	no	—
228	C₂×C₄×C₄₁	—	4	2	no	—
229	C₂×C₄×C₄₁	—	4	2	no	—
230	C₂×C₄×C₄₁	—	4	2	no	—
231	C₂×C₄×C₄₁	—	4	1	no	—
232	C₂×C₄×C₄₁	—	4	2	no	—
233	C₂×C₄×C₄₁	—	4	2	no	—
234	C₂×C₄×C₄₁	—	4	1	no	—
235	C₂×C₄×C₄₁	—	4	1	no	—
236	C₂×C₄×C₄₁	—	4	2	no	—
237	C₂×C₄×C₄₁	#121	1	2	yes	—
238	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
239	C₂×C₄×C₄₁	C₂²×D₄	1	2	yes	—
240	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
241	C₂×C₄×C₄₁	H(5,𝔽₂)	1	2	yes	—
242	C₈×C₄₁	—	2	4	no	—
243	C₈×C₄₁	—	4	1	no	—
244	C₈×C₄₁	—	4	1	no	—
245	#24361	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
246	C₂²×C₄₁	—	2	2	no	—
247	C₂²×C₄₁	—	2	4	no	—
248	C₂²×C₄₁	—	2	4	no	—
249	C₂²×C₄₁	—	2	2	no	—
250	C₂²×C₄₁	—	8	1	no	—
251	C₂²×C₄₁	—	8	2	no	—
252	C₂²×C₄₁	—	8	2	no	—
253	C₂²×C₄₁	—	8	1	no	—
254	C₂²×C₄₁	—	8	1	no	—
255	C₂²×C₄₁	#464	1	4	yes	complemented
256	C₂²×C₄₁	C₂×#121	1	1	yes	characteristic
257	C₂²×C₄₁	D₄²	1	2	yes	—
258	C₂²×C₄₁	C₂×#135	1	1	yes	characteristic
259	C₂²×C₄₁	C₂×#137	1	1	yes	characteristic
260	C₂²×C₄₁	#578	1	2	yes	—
261	C₄×C₄₁	—	2	2	no	—
262	C₄×C₄₁	—	2	4	no	—
263	C₄×C₄₁	—	4	2	no	—
264	C₄×C₄₁	—	4	4	no	—
265	C₄×C₄₁	—	4	2	no	—
266	C₄×C₄₁	—	4	2	no	—
267	C₄×C₄₁	—	8	2	no	—
268	C₄×C₄₁	—	8	1	no	—
269	C₄×C₄₁	C₂×#120	1	1	yes	characteristic
270	C₄×C₄₁	#534	1	1	yes	characteristic
271	C₄×C₄₁	#546	1	2	yes	—
272	C₂³×Q₁₆	C₂×C₄₁	1	1	yes	characteristic, complemented
273	C₂×#464	C₂×C₄₁	1	2	yes	complemented
274	C₂×#448	C₂×C₄₁	1	1	yes	characteristic
275	#2436	C₂×C₄₁	1	1	yes	characteristic
276	Q₈×C₂²⋊C₄	C₂×C₄₁	1	1	yes	characteristic, complemented
277	#2056	C₂×C₄₁	1	2	yes	complemented
278	#2015	C₂×C₄₁	1	2	yes	complemented
279	#1893	C₂×C₄₁	1	1	yes	characteristic
280	#1878	C₂×C₄₁	1	2	yes	complemented
281	#1850	C₂×C₄₁	1	1	yes	characteristic, complemented
282	#1787	C₂×C₄₁	1	1	yes	characteristic, complemented
283	C₂×C₄₁	—	2	4	no	—
284	C₂×C₄₁	—	16	1	no	—
285	C₂×C₄₁	#2410	1	1	yes	characteristic
286	C₂×C₄₁	C₂×#464	1	1	yes	characteristic
287	C₂×C₄₁	#3044	1	1	yes	characteristic
288	C₂×C₄₁	#3270	1	2	yes	—
289	C₂×C₄₁	#3285	1	2	yes	—
290	C₂³×Q₈	C₂²×C₄₁	1	1	yes	characteristic
291	C₂³×Q₈	C₂²×C₄₁	1	1	yes	characteristic
292	C₂²×Q₁₆	—	2	4	no	—
293	C₂²×Q₁₆	—	2	8	no	—
294	C₂²×Q₁₆	C₂²×C₄₁	1	2	yes	—
295	C₂²×Q₁₆	C₂²×C₄₁	1	2	yes	—
296	C₂²×SD₁₆	C₂²×C₄₁	1	1	yes	characteristic
297	C₂²×SD₁₆	C₂²×C₄₁	1	1	yes	characteristic
298	C₂³×C₈	C₂²×C₄₁	1	1	yes	characteristic
299	C₂×#124	C₂²×C₄₁	1	2	yes	—
300	C₂×#121	C₂²×C₄₁	1	1	yes	characteristic
301	C₂×C₄×Q₈	C₂²×C₄₁	1	2	yes	—
302	#464	—	2	8	no	—
303	#448	—	2	4	no	—
304	C₂×C₄⋊C₈	C₂²×C₄₁	1	2	yes	—
305	C₂×#103	C₂²×C₄₁	1	1	yes	characteristic
306	C₂×#103	C₂²×C₄₁	1	2	yes	—
307	C₂×#103	C₂²×C₄₁	1	1	yes	characteristic
308	C₂×#103	C₂²×C₄₁	1	2	yes	—
309	C₂×#102	C₂²×C₄₁	1	2	yes	—
310	C₂×C₂²⋊C₈	C₂²×C₄₁	1	1	yes	characteristic
311	#393	—	2	2	no	—
312	#391	—	2	2	no	—
313	#391	C₂²×C₄₁	1	2	yes	—
314	#391	C₂²×C₄₁	1	2	yes	—
315	#386	—	2	1	no	—
316	#386	—	2	1	no	—
317	#380	—	2	1	no	—
318	#380	C₂²×C₄₁	1	1	yes	characteristic
319	C₄×C₂²⋊C₄	—	2	1	no	—
320	C₄×C₂²⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
321	#340	C₂²×C₄₁	1	2	yes	—
322	#336	C₂²×C₄₁	1	2	yes	—
323	C₄₁	#24361	1	1	yes	characteristic, direct product factor, Sylow
324	C₂²×Q₈	—	2	1	no	—
325	C₂²×Q₈	—	2	1	no	—
326	C₂²×Q₈	—	2	2	no	—
327	C₂²×Q₈	—	2	4	no	—
328	C₂²×Q₈	—	2	4	no	—
329	C₂²×Q₈	—	2	2	no	—
330	C₂²×Q₈	—	2	2	no	—
331	C₂²×Q₈	—	4	2	no	—
332	C₂²×Q₈	—	4	2	no	—
333	C₂²×Q₈	D₄×C₄₁	1	4	yes	—
334	C₂²×Q₈	C₂³×C₄₁	1	2	yes	—
335	C₂²×Q₈	C₂³×C₄₁	1	1	yes	characteristic
336	C₂²×Q₈	C₂³×C₄₁	1	1	yes	characteristic
337	C₂²×D₄	—	2	1	no	—
338	C₂²×D₄	C₂³×C₄₁	1	1	yes	characteristic
339	C₂³×C₄	—	2	1	no	—
340	C₂³×C₄	—	2	1	no	—
341	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
342	C₂×Q₁₆	—	2	32	no	—
343	C₂×Q₁₆	—	2	4	no	—
344	C₂×Q₁₆	—	2	4	no	—
345	C₂×Q₁₆	—	2	4	no	—
346	C₂×Q₁₆	—	2	4	no	—
347	C₂×Q₁₆	—	2	4	no	—
348	C₂×Q₁₆	D₄×C₄₁	1	8	yes	complemented
349	C₂×SD₁₆	—	2	2	no	—
350	C₂×SD₁₆	—	2	2	no	—
351	C₂×SD₁₆	—	2	4	no	—
352	C₂×SD₁₆	—	4	2	no	—
353	C₂²×C₈	—	2	2	no	—
354	C₂²×C₈	—	2	4	no	—
355	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
356	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
357	C₂²×C₈	C₂³×C₄₁	1	2	yes	—
358	#124	—	2	4	no	—
359	#124	—	4	2	no	—
360	#121	—	2	2	no	—
361	#121	—	2	2	no	—
362	C₄×Q₈	—	2	4	no	—
363	C₄×Q₈	—	4	2	no	—
364	C₂×C₄⋊C₄	—	2	2	no	—
365	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
366	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
367	C₂×C₂²⋊C₄	—	2	1	no	—
368	C₂×C₂²⋊C₄	—	2	1	no	—
369	C₂×C₂²⋊C₄	—	2	2	no	—
370	C₂×C₂²⋊C₄	—	2	2	no	—
371	C₂×C₂²⋊C₄	D₄×C₄₁	1	1	yes	characteristic
372	C₂×C₂²⋊C₄	D₄×C₄₁	1	1	yes	characteristic
373	C₂×C₄²	—	2	2	no	—
374	C₂×C₄²	C₂³×C₄₁	1	2	yes	—
375	C₄⋊C₈	—	2	4	no	—
376	#103	—	2	2	no	—
377	#103	—	2	2	no	—
378	#103	—	2	4	no	—
379	#103	—	4	2	no	—
380	#102	—	2	4	no	—
381	C₂²⋊C₈	—	2	2	no	—
382	#95	—	2	2	no	—
383	#95	—	2	2	no	—
384	#95	—	2	1	no	—
385	#95	—	2	2	no	—
386	#95	—	2	2	no	—
387	#95	D₄×C₄₁	1	2	yes	—
388	C₂⁴	—	2	1	no	—
389	C₂⁴	C₂×D₄×C₄₁	1	1	yes	characteristic
390	C₂×Q₈	—	2	4	no	—
391	C₂×Q₈	—	2	1	no	—
392	C₂×Q₈	—	2	1	no	—
393	C₂×Q₈	—	2	2	no	—
394	C₂×Q₈	—	2	2	no	—
395	C₂×Q₈	—	2	8	no	—
396	C₂×Q₈	—	2	8	no	—
397	C₂×Q₈	—	2	2	no	—
398	C₂×Q₈	—	2	2	no	—
399	C₂×Q₈	—	2	2	no	—
400	C₂×Q₈	—	2	2	no	—
401	C₂×Q₈	—	2	2	no	—
402	C₂×Q₈	—	2	2	no	—
403	C₂×Q₈	—	4	4	no	—
404	C₂×Q₈	—	4	4	no	—
405	C₂×Q₈	—	4	4	no	—
406	C₂×Q₈	—	4	8	no	—
407	C₂×Q₈	—	4	8	no	—
408	C₂×Q₈	—	4	4	no	—
409	C₂×Q₈	—	4	2	no	—
410	C₂×Q₈	C₂×D₄×C₄₁	1	4	yes	—
411	C₂×Q₈	C₂×D₄×C₄₁	1	2	yes	—
412	C₂×Q₈	C₂×D₄×C₄₁	1	2	yes	—
413	C₂×Q₈	C₂×D₄×C₄₁	1	4	yes	—
414	C₂×D₄	—	2	2	no	—
415	C₂×D₄	—	2	1	no	—
416	C₂×D₄	—	2	1	no	—
417	C₂×D₄	—	2	2	no	—
418	C₂×D₄	—	4	2	no	—
419	C₂×D₄	—	4	2	no	—
420	C₂×D₄	—	4	2	no	—
421	C₂²×C₄	—	2	1	no	—
422	C₂²×C₄	—	2	2	no	—
423	C₂²×C₄	—	2	2	no	—
424	C₂²×C₄	—	2	4	no	—
425	C₂²×C₄	—	2	1	no	—
426	C₂²×C₄	—	2	2	no	—
427	C₂²×C₄	—	2	1	no	—
428	C₂²×C₄	—	2	2	no	—
429	C₂²×C₄	—	4	4	no	—
430	C₂²×C₄	—	4	4	no	—
431	C₂²×C₄	—	4	2	no	—
432	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
433	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
434	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
435	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
436	C₂²×C₄	#41×C₄₁	1	2	yes	—
437	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
438	Q₁₆	—	2	16	no	—
439	Q₁₆	—	2	16	no	—
440	SD₁₆	—	4	4	no	—
441	SD₁₆	—	4	4	no	—
442	C₂×C₈	—	2	8	no	—
443	C₂×C₈	—	2	2	no	—
444	C₂×C₈	—	2	2	no	—
445	C₂×C₈	—	2	1	no	—
446	C₂×C₈	—	2	1	no	—
447	C₂×C₈	—	2	2	no	—
448	C₂×C₈	—	2	2	no	—
449	C₂×C₈	C₂×D₄×C₄₁	1	4	yes	—
450	C₄⋊C₄	—	2	2	no	—
451	C₄⋊C₄	—	2	1	no	—
452	C₄⋊C₄	—	2	1	no	—
453	C₄⋊C₄	—	2	2	no	—
454	C₄⋊C₄	—	4	4	no	—
455	C₂²⋊C₄	—	2	2	no	—
456	C₂²⋊C₄	—	2	2	no	—
457	C₂²⋊C₄	—	4	4	no	—
458	C₂²⋊C₄	—	4	4	no	—
459	C₂²⋊C₄	—	4	2	no	—
460	C₂²⋊C₄	—	4	2	no	—
461	C₄²	—	2	2	no	—
462	C₄²	—	2	2	no	—
463	C₄²	—	4	4	no	—
464	C₂³	—	2	2	no	—
465	C₂³	—	2	2	no	—
466	C₂³	—	4	1	no	—
467	C₂³	—	4	2	no	—
468	C₂³	—	4	1	no	—
469	C₂³	—	4	1	no	—
470	C₂³	—	4	2	no	—
471	C₂³	#121×C₄₁	1	2	yes	—
472	C₂³	#135×C₄₁	1	2	yes	—
473	C₂³	#137×C₄₁	1	2	yes	—
474	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
475	Q₈	—	2	2	no	—
476	Q₈	—	2	4	no	—
477	Q₈	—	2	2	no	—
478	Q₈	—	2	4	no	—
479	Q₈	—	2	2	no	—
480	Q₈	—	2	4	no	—
481	Q₈	—	4	8	no	—
482	Q₈	—	4	8	no	—
483	Q₈	—	4	2	no	—
484	Q₈	—	4	2	no	—
485	Q₈	—	4	2	no	—
486	Q₈	#120×C₄₁	1	4	yes	—
487	D₄	—	4	1	no	—
488	D₄	—	4	1	no	—
489	D₄	—	4	2	no	—
490	D₄	—	8	4	no	—
491	C₂×C₄	—	2	2	no	—
492	C₂×C₄	—	2	4	no	—
493	C₂×C₄	—	2	2	no	—
494	C₂×C₄	—	2	2	no	—
495	C₂×C₄	—	2	2	no	—
496	C₂×C₄	—	2	4	no	—
497	C₂×C₄	—	2	2	no	—
498	C₂×C₄	—	2	2	no	—
499	C₂×C₄	—	2	2	no	—
500	C₂×C₄	—	2	4	no	—
501	C₂×C₄	—	2	2	no	—
502	C₂×C₄	—	2	2	no	—
503	C₂×C₄	—	2	2	no	—
504	C₂×C₄	—	2	2	no	—
505	C₂×C₄	—	4	8	no	—
506	C₂×C₄	—	4	8	no	—
507	C₂×C₄	—	4	2	no	—
508	C₂×C₄	—	4	2	no	—
509	C₂×C₄	—	4	2	no	—
510	C₂×C₄	—	4	1	no	—
511	C₂×C₄	—	4	2	no	—
512	C₂×C₄	—	4	2	no	—
513	C₂×C₄	—	4	1	no	—
514	C₂×C₄	—	4	1	no	—
515	C₂×C₄	—	4	2	no	—
516	C₂×C₄	#121×C₄₁	1	2	yes	—
517	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
518	C₂×C₄	C₂²×D₄×C₄₁	1	2	yes	—
519	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
520	C₂×C₄	H(5,𝔽₂)×C₄₁	1	2	yes	—
521	C₈	—	2	4	no	—
522	C₈	—	4	1	no	—
523	C₈	—	4	1	no	—
524	C₂²	—	2	2	no	—
525	C₂²	—	2	2	no	—
526	C₂²	—	2	4	no	—
527	C₂²	—	2	4	no	—
528	C₂²	—	8	1	no	—
529	C₂²	—	8	1	no	—
530	C₂²	—	8	2	no	—
531	C₂²	—	8	2	no	—
532	C₂²	—	8	1	no	—
533	C₂²	C₄₁×#464	1	4	yes	complemented
534	C₂²	C₂×#121×C₄₁	1	1	yes	characteristic
535	C₂²	D₄²×C₄₁	1	2	yes	—
536	C₂²	C₂×#135×C₄₁	1	1	yes	characteristic
537	C₂²	C₂×#137×C₄₁	1	1	yes	characteristic
538	C₂²	C₄₁×#578	1	2	yes	—
539	C₄	—	2	2	no	—
540	C₄	—	2	4	no	—
541	C₄	—	4	2	no	—
542	C₄	—	4	4	no	—
543	C₄	—	4	2	no	—
544	C₄	—	4	2	no	—
545	C₄	—	8	2	no	—
546	C₄	—	8	1	no	—
547	C₄	C₂×#120×C₄₁	1	1	yes	characteristic
548	C₄	C₄₁×#534	1	1	yes	characteristic
549	C₄	C₄₁×#546	1	2	yes	—
550	C₂	—	2	4	no	—
551	C₂	—	16	1	no	—
552	C₂	C₄₁×#2410	1	1	yes	characteristic
553	C₂	C₂×C₄₁×#464	1	1	yes	characteristic
554	C₂	C₄₁×#3044	1	1	yes	characteristic
555	C₂	C₄₁×#3270	1	2	yes	—
556	C₂	C₄₁×#3285	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₄₁	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₁
prime radical	C₂×#121×C₄₁	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₄₁ ◁ C₄×C₂²⋊C₄×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂³×Q₁₆×C₄₁	C₂	semidirect
2. C₂×C₄₁×#464	C₂	semidirect
5. Q₈×C₂²⋊C₄×C₄₁	C₂	semidirect
6. C₄₁×#2056	C₂	semidirect
7. C₄₁×#2015	C₂	semidirect
9. C₄₁×#1878	C₂	semidirect
10. C₄₁×#1850	C₂	semidirect
11. C₄₁×#1787	C₂	semidirect
69. C₂×Q₁₆×C₄₁	D₄	semidirect
245. #24361	C₄₁	direct (N × H)
255. C₂²×C₄₁	#464	semidirect
272. C₂³×Q₁₆	C₂×C₄₁	semidirect
273. C₂×#464	C₂×C₄₁	semidirect
276. Q₈×C₂²⋊C₄	C₂×C₄₁	semidirect
277. #2056	C₂×C₄₁	semidirect
278. #2015	C₂×C₄₁	semidirect
280. #1878	C₂×C₄₁	semidirect
281. #1850	C₂×C₄₁	semidirect
282. #1787	C₂×C₄₁	semidirect
323. C₄₁	#24361	direct (N × H)
348. C₂×Q₁₆	D₄×C₄₁	semidirect
533. C₂²	C₄₁×#464	semidirect

Maximal subgroups

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

subgroup	index
C₂³×Q₁₆×C₄₁	2
C₂×C₄₁×#464	2
C₂×C₄₁×#448	2
C₄₁×#2436	2
Q₈×C₂²⋊C₄×C₄₁	2
C₄₁×#2056	2
C₄₁×#2015	2
C₄₁×#1893	2
C₄₁×#1878	2
C₄₁×#1850	2
C₄₁×#1787	2
#24361	41

Subgroups — C41×#24361 #23800562

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#24361 #23800562