Subgroups — C₄₁×#24376 #23800577

Order 10496.

1424 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#137×C₄₁	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄₁×#461	C₂	1	2	yes	maximal, complemented
3	C₂×C₄₁×#452	C₂	1	1	yes	maximal, characteristic
4	C₄₁×#2434	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₁×#2339	C₂	1	1	yes	maximal, characteristic
6	C₄₁×#2056	C₂	1	2	yes	maximal, complemented
7	C₄₁×#2016	C₂	1	2	yes	maximal, complemented
8	C₄₁×#1894	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄₁×#1877	C₂	1	2	yes	maximal, complemented
10	C₄₁×#1851	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₁×#1787	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×#41×C₄₁	C₂²	1	1	yes	characteristic
13	C₂³×Q₈×C₄₁	C₂²	1	1	yes	characteristic
14	C₂×#137×C₄₁	—	2	4	no	—
15	C₂×#137×C₄₁	—	2	8	no	—
16	C₂²×Q₁₆×C₄₁	C₂²	1	2	yes	—
17	C₂²×Q₁₆×C₄₁	C₂²	1	1	yes	characteristic
18	C₂²×SD₁₆×C₄₁	C₂²	1	1	yes	characteristic
19	C₂²×SD₁₆×C₄₁	C₂²	1	2	yes	—
20	C₂²×M₁₆×C₄₁	C₂²	1	1	yes	characteristic
21	C₂×C₄⋊Q₈×C₄₁	C₂²	1	2	yes	—
22	C₂×C₂²⋊Q₈×C₄₁	C₂²	1	1	yes	characteristic
23	C₂×C₄×D₄×C₄₁	C₂²	1	2	yes	—
24	C₄₁×#461	—	2	8	no	—
25	C₄₁×#452	—	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	2	yes	—
29	C₂×#103×C₄₁	C₂²	1	1	yes	characteristic
30	C₂×#103×C₄₁	C₂²	1	2	yes	—
31	C₂×#102×C₄₁	C₂²	1	1	yes	characteristic
32	C₂×C₂²⋊C₈×C₄₁	C₂²	1	1	yes	characteristic
33	C₄₁×#395	—	2	1	no	—
34	C₄₁×#395	—	2	1	no	—
35	C₄₁×#391	C₂²	1	2	yes	—
36	C₄₁×#391	C₂²	1	2	yes	—
37	C₄₁×#386	—	2	2	no	—
38	C₄₁×#385	—	2	2	no	—
39	C₄₁×#381	—	2	1	no	—
40	C₄₁×#380	C₂²	1	1	yes	characteristic
41	C₄×C₂²⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
42	C₂×#95×C₄₁	—	2	1	no	—
43	C₄₁×#340	C₂²	1	2	yes	—
44	C₄₁×#336	C₂²	1	2	yes	—
45	C₂×#41×C₄₁	—	2	2	no	—
46	C₂×#41×C₄₁	—	2	4	no	—
47	C₂×#41×C₄₁	—	4	2	no	—
48	C₂×#41×C₄₁	D₄	1	4	yes	—
49	C₂²×Q₈×C₄₁	—	2	1	no	—
50	C₂²×Q₈×C₄₁	—	2	4	no	—
51	C₂²×Q₈×C₄₁	—	2	2	no	—
52	C₂²×Q₈×C₄₁	—	2	2	no	—
53	C₂²×Q₈×C₄₁	—	4	2	no	—
54	C₂²×Q₈×C₄₁	C₂³	1	1	yes	characteristic
55	C₂²×Q₈×C₄₁	C₂³	1	2	yes	—
56	C₂²×Q₈×C₄₁	C₂³	1	1	yes	characteristic
57	C₂²×D₄×C₄₁	—	2	1	no	—
58	C₂²×D₄×C₄₁	C₂³	1	1	yes	characteristic
59	C₂³×C₄×C₄₁	—	2	1	no	—
60	C₂³×C₄×C₄₁	—	2	1	no	—
61	C₂³×C₄×C₄₁	—	2	2	no	—
62	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
63	#137×C₄₁	—	2	32	no	—
64	C₂×Q₁₆×C₄₁	—	2	4	no	—
65	C₂×Q₁₆×C₄₁	—	2	4	no	—
66	C₂×Q₁₆×C₄₁	—	2	2	no	—
67	C₂×Q₁₆×C₄₁	—	2	4	no	—
68	C₂×Q₁₆×C₄₁	—	4	2	no	—
69	C₂×SD₁₆×C₄₁	—	2	4	no	—
70	C₂×SD₁₆×C₄₁	—	2	4	no	—
71	C₂×SD₁₆×C₄₁	—	2	2	no	—
72	C₂×SD₁₆×C₄₁	—	2	4	no	—
73	C₂×SD₁₆×C₄₁	D₄	1	8	yes	—
74	C₂×M₁₆×C₄₁	—	2	2	no	—
75	C₂×M₁₆×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	C₄⋊Q₈×C₄₁	—	2	4	no	—
80	C₄⋊Q₈×C₄₁	—	4	2	no	—
81	C₂²⋊Q₈×C₄₁	—	2	2	no	—
82	C₂²⋊Q₈×C₄₁	—	2	2	no	—
83	C₄×D₄×C₄₁	—	2	4	no	—
84	C₄×D₄×C₄₁	—	4	2	no	—
85	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
86	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
87	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
88	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
89	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
90	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
91	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
92	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
93	C₂×C₂²⋊C₄×C₄₁	D₄	1	2	yes	—
94	C₂×C₄²×C₄₁	C₂³	1	2	yes	—
95	C₄⋊C₈×C₄₁	—	2	4	no	—
96	#103×C₄₁	—	2	2	no	—
97	#103×C₄₁	—	2	4	no	—
98	#103×C₄₁	—	2	4	no	—
99	#103×C₄₁	—	4	2	no	—
100	#102×C₄₁	—	2	2	no	—
101	C₂²⋊C₈×C₄₁	—	2	2	no	—
102	#95×C₄₁	—	2	1	no	—
103	#95×C₄₁	—	2	2	no	—
104	#95×C₄₁	—	2	2	no	—
105	#95×C₄₁	—	2	2	no	—
106	#95×C₄₁	—	2	2	no	—
107	#95×C₄₁	D₄	1	1	yes	characteristic
108	#95×C₄₁	D₄	1	1	yes	characteristic
109	C₂⁴×C₄₁	—	2	1	no	—
110	C₂⁴×C₄₁	C₂×D₄	1	1	yes	characteristic
111	#41×C₄₁	—	2	8	no	—
112	#41×C₄₁	—	4	4	no	—
113	#41×C₄₁	—	4	8	no	—
114	C₂×Q₈×C₄₁	—	2	1	no	—
115	C₂×Q₈×C₄₁	—	2	2	no	—
116	C₂×Q₈×C₄₁	—	2	8	no	—
117	C₂×Q₈×C₄₁	—	2	2	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	1	no	—
122	C₂×Q₈×C₄₁	—	2	2	no	—
123	C₂×Q₈×C₄₁	—	2	1	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	—	4	4	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×D₄×C₄₁	—	2	4	no	—
134	C₂×D₄×C₄₁	—	2	1	no	—
135	C₂×D₄×C₄₁	—	2	2	no	—
136	C₂×D₄×C₄₁	—	4	4	no	—
137	C₂×D₄×C₄₁	C₂×D₄	1	2	yes	—
138	C₂×D₄×C₄₁	C₂×D₄	1	4	yes	—
139	C₂²×C₄×C₄₁	—	2	2	no	—
140	C₂²×C₄×C₄₁	—	2	2	no	—
141	C₂²×C₄×C₄₁	—	2	1	no	—
142	C₂²×C₄×C₄₁	—	2	2	no	—
143	C₂²×C₄×C₄₁	—	2	4	no	—
144	C₂²×C₄×C₄₁	—	2	1	no	—
145	C₂²×C₄×C₄₁	—	2	2	no	—
146	C₂²×C₄×C₄₁	—	2	1	no	—
147	C₂²×C₄×C₄₁	—	4	4	no	—
148	C₂²×C₄×C₄₁	—	4	4	no	—
149	C₂²×C₄×C₄₁	—	4	4	no	—
150	C₂²×C₄×C₄₁	—	4	2	no	—
151	C₂²×C₄×C₄₁	—	4	4	no	—
152	C₂²×C₄×C₄₁	—	8	2	no	—
153	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
154	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
155	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
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	—	4	4	no	—
161	SD₁₆×C₄₁	—	2	16	no	—
162	SD₁₆×C₄₁	—	4	4	no	—
163	M₁₆×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	1	no	—
172	C₄⋊C₄×C₄₁	—	2	2	no	—
173	C₄⋊C₄×C₄₁	—	2	1	no	—
174	C₄⋊C₄×C₄₁	—	2	2	no	—
175	C₄⋊C₄×C₄₁	—	4	4	no	—
176	C₄⋊C₄×C₄₁	—	4	4	no	—
177	C₄⋊C₄×C₄₁	—	4	2	no	—
178	C₂²⋊C₄×C₄₁	—	2	4	no	—
179	C₂²⋊C₄×C₄₁	—	4	4	no	—
180	C₂²⋊C₄×C₄₁	—	4	2	no	—
181	C₂²⋊C₄×C₄₁	—	8	1	no	—
182	C₄²×C₄₁	—	2	2	no	—
183	C₄²×C₄₁	—	2	2	no	—
184	C₂³×C₄₁	—	2	2	no	—
185	C₂³×C₄₁	—	2	4	no	—
186	C₂³×C₄₁	—	2	2	no	—
187	C₂³×C₄₁	—	2	2	no	—
188	C₂³×C₄₁	—	2	1	no	—
189	C₂³×C₄₁	—	2	1	no	—
190	C₂³×C₄₁	—	4	2	no	—
191	C₂³×C₄₁	—	4	1	no	—
192	C₂³×C₄₁	—	4	1	no	—
193	C₂³×C₄₁	#121	1	2	yes	—
194	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
195	Q₈×C₄₁	—	2	4	no	—
196	Q₈×C₄₁	—	2	2	no	—
197	Q₈×C₄₁	—	2	2	no	—
198	Q₈×C₄₁	—	2	4	no	—
199	Q₈×C₄₁	—	4	8	no	—
200	Q₈×C₄₁	—	4	2	no	—
201	Q₈×C₄₁	—	4	2	no	—
202	Q₈×C₄₁	—	4	2	no	—
203	Q₈×C₄₁	—	4	1	no	—
204	Q₈×C₄₁	—	4	1	no	—
205	Q₈×C₄₁	—	4	2	no	—
206	D₄×C₄₁	—	2	2	no	—
207	D₄×C₄₁	—	2	4	no	—
208	D₄×C₄₁	—	4	8	no	—
209	D₄×C₄₁	#120	1	4	yes	—
210	C₂×C₄×C₄₁	—	2	2	no	—
211	C₂×C₄×C₄₁	—	2	2	no	—
212	C₂×C₄×C₄₁	—	2	2	no	—
213	C₂×C₄×C₄₁	—	2	2	no	—
214	C₂×C₄×C₄₁	—	2	2	no	—
215	C₂×C₄×C₄₁	—	2	4	no	—
216	C₂×C₄×C₄₁	—	2	2	no	—
217	C₂×C₄×C₄₁	—	2	2	no	—
218	C₂×C₄×C₄₁	—	2	4	no	—
219	C₂×C₄×C₄₁	—	2	2	no	—
220	C₂×C₄×C₄₁	—	2	2	no	—
221	C₂×C₄×C₄₁	—	4	8	no	—
222	C₂×C₄×C₄₁	—	4	8	no	—
223	C₂×C₄×C₄₁	—	4	2	no	—
224	C₂×C₄×C₄₁	—	4	2	no	—
225	C₂×C₄×C₄₁	—	4	2	no	—
226	C₂×C₄×C₄₁	—	4	1	no	—
227	C₂×C₄×C₄₁	—	4	1	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	2	no	—
232	C₂×C₄×C₄₁	—	4	1	no	—
233	C₂×C₄×C₄₁	—	4	1	no	—
234	C₂×C₄×C₄₁	—	8	8	no	—
235	C₂×C₄×C₄₁	#121	1	2	yes	—
236	C₂×C₄×C₄₁	#137	1	4	yes	complemented
237	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
238	C₂×C₄×C₄₁	C₂²×D₄	1	2	yes	—
239	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
240	C₂×C₄×C₄₁	H(5,𝔽₂)	1	2	yes	—
241	C₈×C₄₁	—	2	4	no	—
242	C₈×C₄₁	—	4	1	no	—
243	C₈×C₄₁	—	4	1	no	—
244	#24376	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
245	C₂²×C₄₁	—	2	2	no	—
246	C₂²×C₄₁	—	2	4	no	—
247	C₂²×C₄₁	—	2	2	no	—
248	C₂²×C₄₁	—	2	2	no	—
249	C₂²×C₄₁	—	4	4	no	—
250	C₂²×C₄₁	—	4	2	no	—
251	C₂²×C₄₁	—	4	2	no	—
252	C₂²×C₄₁	—	4	4	no	—
253	C₂²×C₄₁	—	4	2	no	—
254	C₂²×C₄₁	—	4	2	no	—
255	C₂²×C₄₁	C₂×#121	1	1	yes	characteristic
256	C₂²×C₄₁	D₄²	1	2	yes	—
257	C₂²×C₄₁	C₂×#137	1	2	yes	—
258	C₂²×C₄₁	#577	1	1	yes	characteristic
259	C₂²×C₄₁	#578	1	1	yes	characteristic
260	C₄×C₄₁	—	2	2	no	—
261	C₄×C₄₁	—	2	4	no	—
262	C₄×C₄₁	—	4	2	no	—
263	C₄×C₄₁	—	4	4	no	—
264	C₄×C₄₁	—	4	2	no	—
265	C₄×C₄₁	—	8	1	no	—
266	C₄×C₄₁	—	8	2	no	—
267	C₄×C₄₁	—	8	1	no	—
268	C₄×C₄₁	C₂×#120	1	1	yes	characteristic
269	C₄×C₄₁	#534	1	1	yes	characteristic
270	C₄×C₄₁	#546	1	2	yes	—
271	C₂²×#137	C₂×C₄₁	1	1	yes	characteristic
272	C₂×#461	C₂×C₄₁	1	2	yes	complemented
273	C₂×#452	C₂×C₄₁	1	1	yes	characteristic
274	#2434	C₂×C₄₁	1	1	yes	characteristic, complemented
275	#2339	C₂×C₄₁	1	1	yes	characteristic
276	#2056	C₂×C₄₁	1	2	yes	complemented
277	#2016	C₂×C₄₁	1	2	yes	complemented
278	#1894	C₂×C₄₁	1	1	yes	characteristic, complemented
279	#1877	C₂×C₄₁	1	2	yes	complemented
280	#1851	C₂×C₄₁	1	1	yes	characteristic, complemented
281	#1787	C₂×C₄₁	1	1	yes	characteristic, complemented
282	C₂×C₄₁	—	4	2	no	—
283	C₂×C₄₁	—	4	4	no	—
284	C₂×C₄₁	#2410	1	1	yes	characteristic
285	C₂×C₄₁	#3039	1	1	yes	characteristic
286	C₂×C₄₁	#3046	1	1	yes	characteristic
287	C₂×C₄₁	#3266	1	2	yes	—
288	C₂×C₄₁	#3276	1	2	yes	—
289	C₂²×#41	C₂²×C₄₁	1	1	yes	characteristic
290	C₂³×Q₈	C₂²×C₄₁	1	1	yes	characteristic
291	C₂×#137	—	2	4	no	—
292	C₂×#137	—	2	8	no	—
293	C₂²×Q₁₆	C₂²×C₄₁	1	2	yes	—
294	C₂²×Q₁₆	C₂²×C₄₁	1	1	yes	characteristic
295	C₂²×SD₁₆	C₂²×C₄₁	1	1	yes	characteristic
296	C₂²×SD₁₆	C₂²×C₄₁	1	2	yes	—
297	C₂²×M₁₆	C₂²×C₄₁	1	1	yes	characteristic
298	C₂×C₄⋊Q₈	C₂²×C₄₁	1	2	yes	—
299	C₂×C₂²⋊Q₈	C₂²×C₄₁	1	1	yes	characteristic
300	C₂×C₄×D₄	C₂²×C₄₁	1	2	yes	—
301	#461	—	2	8	no	—
302	#452	—	2	4	no	—
303	C₂×C₄⋊C₈	C₂²×C₄₁	1	2	yes	—
304	C₂×#103	C₂²×C₄₁	1	1	yes	characteristic
305	C₂×#103	C₂²×C₄₁	1	2	yes	—
306	C₂×#103	C₂²×C₄₁	1	2	yes	—
307	C₂×#103	C₂²×C₄₁	1	2	yes	—
308	C₂×#102	C₂²×C₄₁	1	1	yes	characteristic
309	C₂×C₂²⋊C₈	C₂²×C₄₁	1	1	yes	characteristic
310	#395	—	2	1	no	—
311	#395	—	2	1	no	—
312	#391	C₂²×C₄₁	1	2	yes	—
313	#391	C₂²×C₄₁	1	2	yes	—
314	#386	—	2	2	no	—
315	#385	—	2	2	no	—
316	#381	—	2	1	no	—
317	#380	C₂²×C₄₁	1	1	yes	characteristic
318	C₄×C₂²⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
319	C₂×#95	—	2	1	no	—
320	#340	C₂²×C₄₁	1	2	yes	—
321	#336	C₂²×C₄₁	1	2	yes	—
322	C₄₁	#24376	1	1	yes	characteristic, direct product factor, Sylow
323	C₂×#41	—	2	2	no	—
324	C₂×#41	—	2	4	no	—
325	C₂×#41	—	4	2	no	—
326	C₂×#41	D₄×C₄₁	1	4	yes	—
327	C₂²×Q₈	—	2	1	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	C₂³×C₄₁	1	1	yes	characteristic
333	C₂²×Q₈	C₂³×C₄₁	1	2	yes	—
334	C₂²×Q₈	C₂³×C₄₁	1	1	yes	characteristic
335	C₂²×D₄	—	2	1	no	—
336	C₂²×D₄	C₂³×C₄₁	1	1	yes	characteristic
337	C₂³×C₄	—	2	1	no	—
338	C₂³×C₄	—	2	1	no	—
339	C₂³×C₄	—	2	2	no	—
340	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
341	#137	—	2	32	no	—
342	C₂×Q₁₆	—	2	4	no	—
343	C₂×Q₁₆	—	2	4	no	—
344	C₂×Q₁₆	—	2	2	no	—
345	C₂×Q₁₆	—	2	4	no	—
346	C₂×Q₁₆	—	4	2	no	—
347	C₂×SD₁₆	—	2	4	no	—
348	C₂×SD₁₆	—	2	4	no	—
349	C₂×SD₁₆	—	2	2	no	—
350	C₂×SD₁₆	—	2	4	no	—
351	C₂×SD₁₆	D₄×C₄₁	1	8	yes	—
352	C₂×M₁₆	—	2	2	no	—
353	C₂×M₁₆	—	2	4	no	—
354	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
355	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
356	C₂²×C₈	C₂³×C₄₁	1	2	yes	—
357	C₄⋊Q₈	—	2	4	no	—
358	C₄⋊Q₈	—	4	2	no	—
359	C₂²⋊Q₈	—	2	2	no	—
360	C₂²⋊Q₈	—	2	2	no	—
361	C₄×D₄	—	2	4	no	—
362	C₄×D₄	—	4	2	no	—
363	C₂×C₄⋊C₄	—	2	1	no	—
364	C₂×C₄⋊C₄	—	2	2	no	—
365	C₂×C₄⋊C₄	—	2	2	no	—
366	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
367	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
368	C₂×C₂²⋊C₄	—	2	1	no	—
369	C₂×C₂²⋊C₄	—	2	2	no	—
370	C₂×C₂²⋊C₄	—	2	1	no	—
371	C₂×C₂²⋊C₄	D₄×C₄₁	1	2	yes	—
372	C₂×C₄²	C₂³×C₄₁	1	2	yes	—
373	C₄⋊C₈	—	2	4	no	—
374	#103	—	2	2	no	—
375	#103	—	2	4	no	—
376	#103	—	2	4	no	—
377	#103	—	4	2	no	—
378	#102	—	2	2	no	—
379	C₂²⋊C₈	—	2	2	no	—
380	#95	—	2	1	no	—
381	#95	—	2	2	no	—
382	#95	—	2	2	no	—
383	#95	—	2	2	no	—
384	#95	—	2	2	no	—
385	#95	D₄×C₄₁	1	1	yes	characteristic
386	#95	D₄×C₄₁	1	1	yes	characteristic
387	C₂⁴	—	2	1	no	—
388	C₂⁴	C₂×D₄×C₄₁	1	1	yes	characteristic
389	#41	—	2	8	no	—
390	#41	—	4	4	no	—
391	#41	—	4	8	no	—
392	C₂×Q₈	—	2	1	no	—
393	C₂×Q₈	—	2	2	no	—
394	C₂×Q₈	—	2	8	no	—
395	C₂×Q₈	—	2	2	no	—
396	C₂×Q₈	—	2	2	no	—
397	C₂×Q₈	—	2	2	no	—
398	C₂×Q₈	—	2	2	no	—
399	C₂×Q₈	—	2	1	no	—
400	C₂×Q₈	—	2	2	no	—
401	C₂×Q₈	—	2	1	no	—
402	C₂×Q₈	—	2	2	no	—
403	C₂×Q₈	—	2	2	no	—
404	C₂×Q₈	—	2	2	no	—
405	C₂×Q₈	—	4	4	no	—
406	C₂×Q₈	—	4	8	no	—
407	C₂×Q₈	—	4	4	no	—
408	C₂×Q₈	—	4	2	no	—
409	C₂×Q₈	C₂×D₄×C₄₁	1	4	yes	—
410	C₂×Q₈	C₂×D₄×C₄₁	1	2	yes	—
411	C₂×D₄	—	2	4	no	—
412	C₂×D₄	—	2	1	no	—
413	C₂×D₄	—	2	2	no	—
414	C₂×D₄	—	4	4	no	—
415	C₂×D₄	C₂×D₄×C₄₁	1	2	yes	—
416	C₂×D₄	C₂×D₄×C₄₁	1	4	yes	—
417	C₂²×C₄	—	2	2	no	—
418	C₂²×C₄	—	2	2	no	—
419	C₂²×C₄	—	2	1	no	—
420	C₂²×C₄	—	2	2	no	—
421	C₂²×C₄	—	2	4	no	—
422	C₂²×C₄	—	2	1	no	—
423	C₂²×C₄	—	2	2	no	—
424	C₂²×C₄	—	2	1	no	—
425	C₂²×C₄	—	4	4	no	—
426	C₂²×C₄	—	4	4	no	—
427	C₂²×C₄	—	4	4	no	—
428	C₂²×C₄	—	4	2	no	—
429	C₂²×C₄	—	4	4	no	—
430	C₂²×C₄	—	8	2	no	—
431	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
432	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
433	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
434	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
435	C₂²×C₄	#41×C₄₁	1	2	yes	—
436	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
437	Q₁₆	—	2	16	no	—
438	Q₁₆	—	4	4	no	—
439	SD₁₆	—	2	16	no	—
440	SD₁₆	—	4	4	no	—
441	M₁₆	—	2	8	no	—
442	C₂×C₈	—	2	2	no	—
443	C₂×C₈	—	2	2	no	—
444	C₂×C₈	—	2	1	no	—
445	C₂×C₈	—	2	1	no	—
446	C₂×C₈	—	2	2	no	—
447	C₂×C₈	—	2	2	no	—
448	C₂×C₈	C₂×D₄×C₄₁	1	4	yes	—
449	C₄⋊C₄	—	2	1	no	—
450	C₄⋊C₄	—	2	2	no	—
451	C₄⋊C₄	—	2	1	no	—
452	C₄⋊C₄	—	2	2	no	—
453	C₄⋊C₄	—	4	4	no	—
454	C₄⋊C₄	—	4	4	no	—
455	C₄⋊C₄	—	4	2	no	—
456	C₂²⋊C₄	—	2	4	no	—
457	C₂²⋊C₄	—	4	4	no	—
458	C₂²⋊C₄	—	4	2	no	—
459	C₂²⋊C₄	—	8	1	no	—
460	C₄²	—	2	2	no	—
461	C₄²	—	2	2	no	—
462	C₂³	—	2	2	no	—
463	C₂³	—	2	4	no	—
464	C₂³	—	2	2	no	—
465	C₂³	—	2	2	no	—
466	C₂³	—	2	1	no	—
467	C₂³	—	2	1	no	—
468	C₂³	—	4	2	no	—
469	C₂³	—	4	1	no	—
470	C₂³	—	4	1	no	—
471	C₂³	#121×C₄₁	1	2	yes	—
472	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
473	Q₈	—	2	4	no	—
474	Q₈	—	2	2	no	—
475	Q₈	—	2	2	no	—
476	Q₈	—	2	4	no	—
477	Q₈	—	4	8	no	—
478	Q₈	—	4	2	no	—
479	Q₈	—	4	2	no	—
480	Q₈	—	4	2	no	—
481	Q₈	—	4	1	no	—
482	Q₈	—	4	1	no	—
483	Q₈	—	4	2	no	—
484	D₄	—	2	2	no	—
485	D₄	—	2	4	no	—
486	D₄	—	4	8	no	—
487	D₄	#120×C₄₁	1	4	yes	—
488	C₂×C₄	—	2	2	no	—
489	C₂×C₄	—	2	2	no	—
490	C₂×C₄	—	2	2	no	—
491	C₂×C₄	—	2	2	no	—
492	C₂×C₄	—	2	2	no	—
493	C₂×C₄	—	2	4	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	—	4	8	no	—
500	C₂×C₄	—	4	8	no	—
501	C₂×C₄	—	4	2	no	—
502	C₂×C₄	—	4	2	no	—
503	C₂×C₄	—	4	2	no	—
504	C₂×C₄	—	4	1	no	—
505	C₂×C₄	—	4	1	no	—
506	C₂×C₄	—	4	2	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	1	no	—
512	C₂×C₄	—	8	8	no	—
513	C₂×C₄	#121×C₄₁	1	2	yes	—
514	C₂×C₄	#137×C₄₁	1	4	yes	complemented
515	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
516	C₂×C₄	C₂²×D₄×C₄₁	1	2	yes	—
517	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
518	C₂×C₄	H(5,𝔽₂)×C₄₁	1	2	yes	—
519	C₈	—	2	4	no	—
520	C₈	—	4	1	no	—
521	C₈	—	4	1	no	—
522	C₂²	—	2	2	no	—
523	C₂²	—	2	2	no	—
524	C₂²	—	2	2	no	—
525	C₂²	—	2	4	no	—
526	C₂²	—	4	2	no	—
527	C₂²	—	4	2	no	—
528	C₂²	—	4	4	no	—
529	C₂²	—	4	2	no	—
530	C₂²	—	4	2	no	—
531	C₂²	—	4	4	no	—
532	C₂²	C₂×#121×C₄₁	1	1	yes	characteristic
533	C₂²	D₄²×C₄₁	1	2	yes	—
534	C₂²	C₂×#137×C₄₁	1	2	yes	—
535	C₂²	C₄₁×#577	1	1	yes	characteristic
536	C₂²	C₄₁×#578	1	1	yes	characteristic
537	C₄	—	2	2	no	—
538	C₄	—	2	4	no	—
539	C₄	—	4	2	no	—
540	C₄	—	4	4	no	—
541	C₄	—	4	2	no	—
542	C₄	—	8	1	no	—
543	C₄	—	8	1	no	—
544	C₄	—	8	2	no	—
545	C₄	C₂×#120×C₄₁	1	1	yes	characteristic
546	C₄	C₄₁×#534	1	1	yes	characteristic
547	C₄	C₄₁×#546	1	2	yes	—
548	C₂	—	4	2	no	—
549	C₂	—	4	4	no	—
550	C₂	C₄₁×#2410	1	1	yes	characteristic
551	C₂	C₄₁×#3039	1	1	yes	characteristic
552	C₂	C₄₁×#3046	1	1	yes	characteristic
553	C₂	C₄₁×#3266	1	2	yes	—
554	C₂	C₄₁×#3276	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₄₁	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₁
prime radical	C₂²×#41×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
2. C₂×C₄₁×#461	C₂	semidirect
4. C₄₁×#2434	C₂	semidirect
6. C₄₁×#2056	C₂	semidirect
7. C₄₁×#2016	C₂	semidirect
8. C₄₁×#1894	C₂	semidirect
9. C₄₁×#1877	C₂	semidirect
10. C₄₁×#1851	C₂	semidirect
11. C₄₁×#1787	C₂	semidirect
236. C₂×C₄×C₄₁	#137	semidirect
244. #24376	C₄₁	direct (N × H)
272. C₂×#461	C₂×C₄₁	semidirect
274. #2434	C₂×C₄₁	semidirect
276. #2056	C₂×C₄₁	semidirect
277. #2016	C₂×C₄₁	semidirect
278. #1894	C₂×C₄₁	semidirect
279. #1877	C₂×C₄₁	semidirect
280. #1851	C₂×C₄₁	semidirect
281. #1787	C₂×C₄₁	semidirect
322. C₄₁	#24376	direct (N × H)
514. C₂×C₄	#137×C₄₁	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#137×C₄₁	2
C₂×C₄₁×#461	2
C₂×C₄₁×#452	2
C₄₁×#2434	2
C₄₁×#2339	2
C₄₁×#2056	2
C₄₁×#2016	2
C₄₁×#1894	2
C₄₁×#1877	2
C₄₁×#1851	2
C₄₁×#1787	2
#24376	41

Subgroups — C41×#24376 #23800577

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#24376 #23800577