Subgroups — C₄₁×#24827 #23801028

Order 10496.

880 conjugacy classes of subgroups.

The subgroup lattice has 466 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₁×#477	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄₁×#440	C₂	1	1	yes	maximal, characteristic
3	C₄₁×#2542	C₂	1	1	yes	maximal, characteristic
4	C₄₁×#2351	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₁×#2083	C₂	1	2	yes	maximal, complemented
6	C₄₁×#2067	C₂	1	2	yes	maximal
7	C₄₁×#1993	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄₁×#1940	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄₁×#1880	C₂	1	2	yes	maximal
10	C₄₁×#1804	C₂	1	1	yes	maximal, characteristic
11	C₄₁×#1803	C₂	1	2	yes	maximal, complemented
12	C₂²×SD₁₆×C₄₁	C₂²	1	1	yes	characteristic
13	C₂×C₄⋊Q₈×C₄₁	C₂²	1	1	yes	characteristic
14	C₂×C₂²⋊Q₈×C₄₁	—	2	2	no	—
15	C₂×C₄×Q₈×C₄₁	C₂²	1	2	yes	—
16	C₂×C₄×Q₈×C₄₁	C₂²	1	1	yes	characteristic
17	C₂×C₄×D₄×C₄₁	C₂²	1	1	yes	characteristic
18	C₄₁×#477	—	2	4	no	—
19	C₄₁×#440	—	2	4	no	—
20	C₂×#107×C₄₁	C₂²	1	2	yes	—
21	C₂×#107×C₄₁	C₂²	1	1	yes	characteristic
22	C₂×C₄⋊C₈×C₄₁	C₂²	1	1	yes	characteristic
23	C₂×C₄⋊C₈×C₄₁	C₂²	1	2	yes	—
24	C₂×#103×C₄₁	C₂²	1	2	yes	—
25	C₂×#103×C₄₁	C₂²	1	1	yes	characteristic
26	C₂×#102×C₄₁	C₂²	1	1	yes	characteristic
27	C₂×#102×C₄₁	C₂²	1	2	yes	—
28	C₂×#97×C₄₁	C₂²	1	1	yes	characteristic
29	C₄₁×#399	—	2	1	no	—
30	C₄₁×#399	—	2	1	no	—
31	C₄₁×#390	C₂²	1	2	yes	—
32	C₄₁×#389	—	2	2	no	—
33	C₄₁×#389	C₂²	1	2	yes	—
34	C₄₁×#384	C₂²	1	2	yes	—
35	C₄₁×#382	—	2	1	no	—
36	C₄₁×#382	C₂²	1	1	yes	characteristic
37	C₄×C₄⋊C₄×C₄₁	—	2	1	no	—
38	C₄×C₄⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
39	C₄₁×#340	C₂²	1	2	yes	—
40	C₄₁×#340	C₂²	1	2	yes	—
41	C₄₁×#340	C₂²	1	2	yes	—
42	C₄₁×#336	C₂²	1	2	yes	—
43	C₂²×Q₈×C₄₁	—	2	1	no	—
44	C₂²×Q₈×C₄₁	C₂³	1	1	yes	characteristic
45	C₂²×D₄×C₄₁	C₂³	1	1	yes	characteristic
46	C₂³×C₄×C₄₁	—	2	1	no	—
47	C₂×SD₁₆×C₄₁	—	2	2	no	—
48	C₂×SD₁₆×C₄₁	—	2	2	no	—
49	C₂×SD₁₆×C₄₁	Q₈	1	4	yes	complemented
50	C₂²×C₈×C₄₁	C₂³	1	2	yes	—
51	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
52	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
53	C₄⋊Q₈×C₄₁	—	2	2	no	—
54	C₄⋊Q₈×C₄₁	—	2	2	no	—
55	C₂²⋊Q₈×C₄₁	—	4	8	no	—
56	C₄×Q₈×C₄₁	—	2	2	no	—
57	C₄×Q₈×C₄₁	—	2	4	no	—
58	C₄×Q₈×C₄₁	—	4	2	no	—
59	C₄×Q₈×C₄₁	D₄	1	4	yes	—
60	C₄×D₄×C₄₁	—	2	2	no	—
61	C₄×D₄×C₄₁	—	2	2	no	—
62	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
63	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
64	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
65	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
66	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
67	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
68	C₂×C₄⋊C₄×C₄₁	D₄	1	2	yes	—
69	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
70	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
71	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
72	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
73	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
74	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
75	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
76	C₂×C₄²×C₄₁	—	2	1	no	—
77	C₂×C₄²×C₄₁	—	2	2	no	—
78	C₂×C₄²×C₄₁	C₂³	1	2	yes	—
79	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
80	#107×C₄₁	—	2	2	no	—
81	#107×C₄₁	—	2	4	no	—
82	C₄⋊C₈×C₄₁	—	2	2	no	—
83	C₄⋊C₈×C₄₁	—	4	2	no	—
84	#103×C₄₁	—	2	2	no	—
85	#103×C₄₁	—	2	4	no	—
86	#102×C₄₁	—	2	2	no	—
87	#102×C₄₁	—	4	2	no	—
88	#97×C₄₁	—	2	2	no	—
89	#95×C₄₁	—	2	1	no	—
90	#95×C₄₁	—	2	2	no	—
91	#95×C₄₁	—	2	1	no	—
92	#95×C₄₁	D₄	1	1	yes	characteristic
93	#95×C₄₁	D₄	1	1	yes	characteristic
94	C₂⁴×C₄₁	—	2	1	no	—
95	C₂×Q₈×C₄₁	—	2	1	no	—
96	C₂×Q₈×C₄₁	—	2	1	no	—
97	C₂×Q₈×C₄₁	—	2	1	no	—
98	C₂×Q₈×C₄₁	—	4	4	no	—
99	C₂×Q₈×C₄₁	—	4	2	no	—
100	C₂×Q₈×C₄₁	C₂×D₄	1	2	yes	—
101	C₂×Q₈×C₄₁	C₂×Q₈	1	2	yes	—
102	C₂×Q₈×C₄₁	#41	1	2	yes	—
103	C₂×D₄×C₄₁	—	2	1	no	—
104	C₂×D₄×C₄₁	—	2	1	no	—
105	C₂×D₄×C₄₁	—	2	1	no	—
106	C₂×D₄×C₄₁	—	2	1	no	—
107	C₂×D₄×C₄₁	—	2	1	no	—
108	C₂×D₄×C₄₁	C₂×Q₈	1	2	yes	—
109	C₂²×C₄×C₄₁	—	2	1	no	—
110	C₂²×C₄×C₄₁	—	2	1	no	—
111	C₂²×C₄×C₄₁	—	2	2	no	—
112	C₂²×C₄×C₄₁	—	2	2	no	—
113	C₂²×C₄×C₄₁	—	2	1	no	—
114	C₂²×C₄×C₄₁	—	4	4	no	—
115	C₂²×C₄×C₄₁	—	4	2	no	—
116	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
117	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
118	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
119	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
120	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
121	SD₁₆×C₄₁	—	2	8	no	—
122	C₂×C₈×C₄₁	—	2	1	no	—
123	C₂×C₈×C₄₁	—	2	1	no	—
124	C₂×C₈×C₄₁	—	2	1	no	—
125	C₂×C₈×C₄₁	—	2	2	no	—
126	C₂×C₈×C₄₁	—	2	2	no	—
127	C₂×C₈×C₄₁	—	2	1	no	—
128	C₂×C₈×C₄₁	—	2	2	no	—
129	C₂×C₈×C₄₁	—	2	1	no	—
130	C₂×C₈×C₄₁	C₂×Q₈	1	2	yes	—
131	C₄⋊C₄×C₄₁	—	2	4	no	—
132	C₄⋊C₄×C₄₁	—	2	4	no	—
133	C₄⋊C₄×C₄₁	—	2	1	no	—
134	C₄⋊C₄×C₄₁	—	2	1	no	—
135	C₄⋊C₄×C₄₁	—	2	2	no	—
136	C₄⋊C₄×C₄₁	—	2	1	no	—
137	C₄⋊C₄×C₄₁	—	2	2	no	—
138	C₄⋊C₄×C₄₁	—	2	2	no	—
139	C₄⋊C₄×C₄₁	—	2	2	no	—
140	C₄⋊C₄×C₄₁	—	4	4	no	—
141	C₄⋊C₄×C₄₁	—	4	4	no	—
142	C₄⋊C₄×C₄₁	—	4	2	no	—
143	C₄⋊C₄×C₄₁	—	4	4	no	—
144	C₄⋊C₄×C₄₁	—	4	4	no	—
145	C₄⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
146	C₂²⋊C₄×C₄₁	—	4	4	no	—
147	C₂²⋊C₄×C₄₁	—	4	2	no	—
148	C₂²⋊C₄×C₄₁	—	4	4	no	—
149	C₄²×C₄₁	—	2	4	no	—
150	C₄²×C₄₁	—	2	2	no	—
151	C₄²×C₄₁	—	2	2	no	—
152	C₄²×C₄₁	—	4	4	no	—
153	C₄²×C₄₁	C₂×D₄	1	2	yes	—
154	C₄²×C₄₁	#41	1	2	yes	—
155	C₂³×C₄₁	—	2	2	no	—
156	C₂³×C₄₁	—	4	1	no	—
157	C₂³×C₄₁	—	4	1	no	—
158	C₂³×C₄₁	—	4	2	no	—
159	C₂³×C₄₁	—	4	2	no	—
160	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
161	Q₈×C₄₁	—	2	2	no	—
162	Q₈×C₄₁	—	2	2	no	—
163	Q₈×C₄₁	—	2	2	no	—
164	Q₈×C₄₁	—	8	4	no	—
165	Q₈×C₄₁	C₂²⋊Q₈	1	4	yes	complemented
166	D₄×C₄₁	—	2	2	no	—
167	D₄×C₄₁	—	2	2	no	—
168	D₄×C₄₁	—	4	1	no	—
169	D₄×C₄₁	—	4	1	no	—
170	C₂×C₄×C₄₁	—	2	2	no	—
171	C₂×C₄×C₄₁	—	2	2	no	—
172	C₂×C₄×C₄₁	—	2	2	no	—
173	C₂×C₄×C₄₁	—	2	2	no	—
174	C₂×C₄×C₄₁	—	2	2	no	—
175	C₂×C₄×C₄₁	—	2	2	no	—
176	C₂×C₄×C₄₁	—	2	2	no	—
177	C₂×C₄×C₄₁	—	2	2	no	—
178	C₂×C₄×C₄₁	—	2	2	no	—
179	C₂×C₄×C₄₁	—	2	2	no	—
180	C₂×C₄×C₄₁	—	2	2	no	—
181	C₂×C₄×C₄₁	—	4	2	no	—
182	C₂×C₄×C₄₁	—	4	1	no	—
183	C₂×C₄×C₄₁	—	4	2	no	—
184	C₂×C₄×C₄₁	—	4	2	no	—
185	C₂×C₄×C₄₁	—	4	2	no	—
186	C₂×C₄×C₄₁	—	4	2	no	—
187	C₂×C₄×C₄₁	—	4	2	no	—
188	C₂×C₄×C₄₁	—	4	2	no	—
189	C₂×C₄×C₄₁	—	4	2	no	—
190	C₂×C₄×C₄₁	—	8	4	no	—
191	C₂×C₄×C₄₁	#121	1	2	yes	—
192	C₂×C₄×C₄₁	#121	1	2	yes	—
193	C₂×C₄×C₄₁	AGL(1,ℤ/8)	1	4	yes	—
194	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
195	C₂×C₄×C₄₁	C₂²×Q₈	1	1	yes	characteristic
196	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
197	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
198	C₂×C₄×C₄₁	H(5,𝔽₂)	1	1	yes	characteristic
199	C₂×C₄×C₄₁	2₋¹⁺⁴	1	1	yes	characteristic
200	C₈×C₄₁	—	2	2	no	—
201	C₈×C₄₁	—	4	1	no	—
202	C₈×C₄₁	—	4	2	no	—
203	#24827	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
204	C₂²×C₄₁	—	4	4	no	—
205	C₂²×C₄₁	—	4	2	no	—
206	C₂²×C₄₁	—	8	1	no	—
207	C₂²×C₄₁	—	8	1	no	—
208	C₂²×C₄₁	—	8	2	no	—
209	C₂²×C₄₁	C₂×#121	1	1	yes	characteristic
210	C₂²×C₄₁	#546	1	1	yes	characteristic
211	C₂²×C₄₁	D₄×Q₈	1	1	yes	characteristic
212	C₂²×C₄₁	C₂×AGL(1,ℤ/8)	1	2	yes	—
213	C₂²×C₄₁	#578	1	2	yes	—
214	C₄×C₄₁	—	2	4	no	—
215	C₄×C₄₁	—	2	2	no	—
216	C₄×C₄₁	—	2	2	no	—
217	C₄×C₄₁	—	2	4	no	—
218	C₄×C₄₁	—	4	2	no	—
219	C₄×C₄₁	—	4	2	no	—
220	C₄×C₄₁	—	8	1	no	—
221	C₄×C₄₁	—	8	2	no	—
222	C₄×C₄₁	—	8	2	no	—
223	C₄×C₄₁	C₂×C₂²⋊Q₈	1	1	yes	characteristic
224	C₄×C₄₁	#537	1	1	yes	characteristic
225	C₄×C₄₁	#552	1	1	yes	characteristic
226	C₄×C₄₁	#554	1	1	yes	characteristic
227	C₂×#477	C₂×C₄₁	1	1	yes	characteristic, complemented
228	C₂×#440	C₂×C₄₁	1	1	yes	characteristic
229	#2542	C₂×C₄₁	1	1	yes	characteristic
230	#2351	C₂×C₄₁	1	1	yes	characteristic, complemented
231	#2083	C₂×C₄₁	1	2	yes	complemented
232	#2067	C₂×C₄₁	1	2	yes	—
233	#1993	C₂×C₄₁	1	1	yes	characteristic, complemented
234	#1940	C₂×C₄₁	1	1	yes	characteristic, complemented
235	#1880	C₂×C₄₁	1	2	yes	—
236	#1804	C₂×C₄₁	1	1	yes	characteristic
237	#1803	C₂×C₄₁	1	2	yes	complemented
238	C₂×C₄₁	—	8	2	no	—
239	C₂×C₄₁	#2417	1	1	yes	characteristic
240	C₂×C₄₁	#3038	1	1	yes	characteristic
241	C₂×C₄₁	#3044	1	1	yes	characteristic
242	C₂×C₄₁	#3308	1	2	yes	—
243	C₂×C₄₁	#3386	1	2	yes	—
244	C₂²×SD₁₆	C₂²×C₄₁	1	1	yes	characteristic
245	C₂×C₄⋊Q₈	C₂²×C₄₁	1	1	yes	characteristic
246	C₂×C₂²⋊Q₈	—	2	2	no	—
247	C₂×C₄×Q₈	C₂²×C₄₁	1	2	yes	—
248	C₂×C₄×Q₈	C₂²×C₄₁	1	1	yes	characteristic
249	C₂×C₄×D₄	C₂²×C₄₁	1	1	yes	characteristic
250	#477	—	2	4	no	—
251	#440	—	2	4	no	—
252	C₂×#107	C₂²×C₄₁	1	2	yes	—
253	C₂×#107	C₂²×C₄₁	1	1	yes	characteristic
254	C₂×C₄⋊C₈	C₂²×C₄₁	1	1	yes	characteristic
255	C₂×C₄⋊C₈	C₂²×C₄₁	1	2	yes	—
256	C₂×#103	C₂²×C₄₁	1	2	yes	—
257	C₂×#103	C₂²×C₄₁	1	1	yes	characteristic
258	C₂×#102	C₂²×C₄₁	1	1	yes	characteristic
259	C₂×#102	C₂²×C₄₁	1	2	yes	—
260	C₂×#97	C₂²×C₄₁	1	1	yes	characteristic
261	#399	—	2	1	no	—
262	#399	—	2	1	no	—
263	#390	C₂²×C₄₁	1	2	yes	—
264	#389	—	2	2	no	—
265	#389	C₂²×C₄₁	1	2	yes	—
266	#384	C₂²×C₄₁	1	2	yes	—
267	#382	—	2	1	no	—
268	#382	C₂²×C₄₁	1	1	yes	characteristic
269	C₄×C₄⋊C₄	—	2	1	no	—
270	C₄×C₄⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
271	#340	C₂²×C₄₁	1	2	yes	—
272	#340	C₂²×C₄₁	1	2	yes	—
273	#340	C₂²×C₄₁	1	2	yes	—
274	#336	C₂²×C₄₁	1	2	yes	—
275	C₄₁	#24827	1	1	yes	characteristic, direct product factor, Sylow
276	C₂²×Q₈	—	2	1	no	—
277	C₂²×Q₈	C₂³×C₄₁	1	1	yes	characteristic
278	C₂²×D₄	C₂³×C₄₁	1	1	yes	characteristic
279	C₂³×C₄	—	2	1	no	—
280	C₂×SD₁₆	—	2	2	no	—
281	C₂×SD₁₆	—	2	2	no	—
282	C₂×SD₁₆	Q₈×C₄₁	1	4	yes	complemented
283	C₂²×C₈	C₂³×C₄₁	1	2	yes	—
284	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
285	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
286	C₄⋊Q₈	—	2	2	no	—
287	C₄⋊Q₈	—	2	2	no	—
288	C₂²⋊Q₈	—	4	8	no	—
289	C₄×Q₈	—	2	2	no	—
290	C₄×Q₈	—	2	4	no	—
291	C₄×Q₈	—	4	2	no	—
292	C₄×Q₈	D₄×C₄₁	1	4	yes	—
293	C₄×D₄	—	2	2	no	—
294	C₄×D₄	—	2	2	no	—
295	C₂×C₄⋊C₄	—	2	1	no	—
296	C₂×C₄⋊C₄	—	2	2	no	—
297	C₂×C₄⋊C₄	—	2	2	no	—
298	C₂×C₄⋊C₄	—	2	2	no	—
299	C₂×C₄⋊C₄	—	2	1	no	—
300	C₂×C₄⋊C₄	—	2	2	no	—
301	C₂×C₄⋊C₄	D₄×C₄₁	1	2	yes	—
302	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
303	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
304	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
305	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
306	C₂×C₂²⋊C₄	—	2	1	no	—
307	C₂×C₂²⋊C₄	—	2	2	no	—
308	C₂×C₂²⋊C₄	—	2	2	no	—
309	C₂×C₄²	—	2	1	no	—
310	C₂×C₄²	—	2	2	no	—
311	C₂×C₄²	C₂³×C₄₁	1	2	yes	—
312	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
313	#107	—	2	2	no	—
314	#107	—	2	4	no	—
315	C₄⋊C₈	—	2	2	no	—
316	C₄⋊C₈	—	4	2	no	—
317	#103	—	2	2	no	—
318	#103	—	2	4	no	—
319	#102	—	2	2	no	—
320	#102	—	4	2	no	—
321	#97	—	2	2	no	—
322	#95	—	2	1	no	—
323	#95	—	2	2	no	—
324	#95	—	2	1	no	—
325	#95	D₄×C₄₁	1	1	yes	characteristic
326	#95	D₄×C₄₁	1	1	yes	characteristic
327	C₂⁴	—	2	1	no	—
328	C₂×Q₈	—	2	1	no	—
329	C₂×Q₈	—	2	1	no	—
330	C₂×Q₈	—	2	1	no	—
331	C₂×Q₈	—	4	4	no	—
332	C₂×Q₈	—	4	2	no	—
333	C₂×Q₈	C₂×D₄×C₄₁	1	2	yes	—
334	C₂×Q₈	C₂×Q₈×C₄₁	1	2	yes	—
335	C₂×Q₈	#41×C₄₁	1	2	yes	—
336	C₂×D₄	—	2	1	no	—
337	C₂×D₄	—	2	1	no	—
338	C₂×D₄	—	2	1	no	—
339	C₂×D₄	—	2	1	no	—
340	C₂×D₄	—	2	1	no	—
341	C₂×D₄	C₂×Q₈×C₄₁	1	2	yes	—
342	C₂²×C₄	—	2	1	no	—
343	C₂²×C₄	—	2	1	no	—
344	C₂²×C₄	—	2	2	no	—
345	C₂²×C₄	—	2	2	no	—
346	C₂²×C₄	—	2	1	no	—
347	C₂²×C₄	—	4	4	no	—
348	C₂²×C₄	—	4	2	no	—
349	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
350	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
351	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
352	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
353	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
354	SD₁₆	—	2	8	no	—
355	C₂×C₈	—	2	1	no	—
356	C₂×C₈	—	2	1	no	—
357	C₂×C₈	—	2	1	no	—
358	C₂×C₈	—	2	2	no	—
359	C₂×C₈	—	2	2	no	—
360	C₂×C₈	—	2	1	no	—
361	C₂×C₈	—	2	2	no	—
362	C₂×C₈	—	2	1	no	—
363	C₂×C₈	C₂×Q₈×C₄₁	1	2	yes	—
364	C₄⋊C₄	—	2	4	no	—
365	C₄⋊C₄	—	2	4	no	—
366	C₄⋊C₄	—	2	1	no	—
367	C₄⋊C₄	—	2	1	no	—
368	C₄⋊C₄	—	2	2	no	—
369	C₄⋊C₄	—	2	1	no	—
370	C₄⋊C₄	—	2	2	no	—
371	C₄⋊C₄	—	2	2	no	—
372	C₄⋊C₄	—	2	2	no	—
373	C₄⋊C₄	—	4	4	no	—
374	C₄⋊C₄	—	4	4	no	—
375	C₄⋊C₄	—	4	2	no	—
376	C₄⋊C₄	—	4	4	no	—
377	C₄⋊C₄	—	4	4	no	—
378	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
379	C₂²⋊C₄	—	4	4	no	—
380	C₂²⋊C₄	—	4	2	no	—
381	C₂²⋊C₄	—	4	4	no	—
382	C₄²	—	2	4	no	—
383	C₄²	—	2	2	no	—
384	C₄²	—	2	2	no	—
385	C₄²	—	4	4	no	—
386	C₄²	C₂×D₄×C₄₁	1	2	yes	—
387	C₄²	#41×C₄₁	1	2	yes	—
388	C₂³	—	2	2	no	—
389	C₂³	—	4	1	no	—
390	C₂³	—	4	1	no	—
391	C₂³	—	4	2	no	—
392	C₂³	—	4	2	no	—
393	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
394	Q₈	—	2	2	no	—
395	Q₈	—	2	2	no	—
396	Q₈	—	2	2	no	—
397	Q₈	—	8	4	no	—
398	Q₈	C₂²⋊Q₈×C₄₁	1	4	yes	complemented
399	D₄	—	2	2	no	—
400	D₄	—	2	2	no	—
401	D₄	—	4	1	no	—
402	D₄	—	4	1	no	—
403	C₂×C₄	—	2	2	no	—
404	C₂×C₄	—	2	2	no	—
405	C₂×C₄	—	2	2	no	—
406	C₂×C₄	—	2	2	no	—
407	C₂×C₄	—	2	2	no	—
408	C₂×C₄	—	2	2	no	—
409	C₂×C₄	—	2	2	no	—
410	C₂×C₄	—	2	2	no	—
411	C₂×C₄	—	2	2	no	—
412	C₂×C₄	—	2	2	no	—
413	C₂×C₄	—	2	2	no	—
414	C₂×C₄	—	4	2	no	—
415	C₂×C₄	—	4	1	no	—
416	C₂×C₄	—	4	2	no	—
417	C₂×C₄	—	4	2	no	—
418	C₂×C₄	—	4	2	no	—
419	C₂×C₄	—	4	2	no	—
420	C₂×C₄	—	4	2	no	—
421	C₂×C₄	—	4	2	no	—
422	C₂×C₄	—	4	2	no	—
423	C₂×C₄	—	8	4	no	—
424	C₂×C₄	#121×C₄₁	1	2	yes	—
425	C₂×C₄	#121×C₄₁	1	2	yes	—
426	C₂×C₄	AGL(1,ℤ/8)×C₄₁	1	4	yes	—
427	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
428	C₂×C₄	C₂²×Q₈×C₄₁	1	1	yes	characteristic
429	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
430	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
431	C₂×C₄	H(5,𝔽₂)×C₄₁	1	1	yes	characteristic
432	C₂×C₄	2₋¹⁺⁴×C₄₁	1	1	yes	characteristic
433	C₈	—	2	2	no	—
434	C₈	—	4	1	no	—
435	C₈	—	4	2	no	—
436	C₂²	—	4	4	no	—
437	C₂²	—	4	2	no	—
438	C₂²	—	8	1	no	—
439	C₂²	—	8	1	no	—
440	C₂²	—	8	2	no	—
441	C₂²	C₂×#121×C₄₁	1	1	yes	characteristic
442	C₂²	C₄₁×#546	1	1	yes	characteristic
443	C₂²	D₄×Q₈×C₄₁	1	1	yes	characteristic
444	C₂²	C₂×AGL(1,ℤ/8)×C₄₁	1	2	yes	—
445	C₂²	C₄₁×#578	1	2	yes	—
446	C₄	—	2	2	no	—
447	C₄	—	2	2	no	—
448	C₄	—	2	4	no	—
449	C₄	—	2	4	no	—
450	C₄	—	4	2	no	—
451	C₄	—	4	2	no	—
452	C₄	—	8	1	no	—
453	C₄	—	8	2	no	—
454	C₄	—	8	2	no	—
455	C₄	C₂×C₂²⋊Q₈×C₄₁	1	1	yes	characteristic
456	C₄	C₄₁×#537	1	1	yes	characteristic
457	C₄	C₄₁×#552	1	1	yes	characteristic
458	C₄	C₄₁×#554	1	1	yes	characteristic
459	C₂	—	8	2	no	—
460	C₂	C₄₁×#2417	1	1	yes	characteristic
461	C₂	C₄₁×#3038	1	1	yes	characteristic
462	C₂	C₄₁×#3044	1	1	yes	characteristic
463	C₂	C₄₁×#3308	1	2	yes	—
464	C₂	C₄₁×#3386	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
1. C₂×C₄₁×#477	C₂	semidirect
4. C₄₁×#2351	C₂	semidirect
5. C₄₁×#2083	C₂	semidirect
7. C₄₁×#1993	C₂	semidirect
8. C₄₁×#1940	C₂	semidirect
11. C₄₁×#1803	C₂	semidirect
49. C₂×SD₁₆×C₄₁	Q₈	semidirect
165. Q₈×C₄₁	C₂²⋊Q₈	semidirect
203. #24827	C₄₁	direct (N × H)
227. C₂×#477	C₂×C₄₁	semidirect
230. #2351	C₂×C₄₁	semidirect
231. #2083	C₂×C₄₁	semidirect
233. #1993	C₂×C₄₁	semidirect
234. #1940	C₂×C₄₁	semidirect
237. #1803	C₂×C₄₁	semidirect
275. C₄₁	#24827	direct (N × H)
282. C₂×SD₁₆	Q₈×C₄₁	semidirect
398. Q₈	C₂²⋊Q₈×C₄₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄₁×#477	2
C₂×C₄₁×#440	2
C₄₁×#2542	2
C₄₁×#2351	2
C₄₁×#2083	2
C₄₁×#2067	2
C₄₁×#1993	2
C₄₁×#1940	2
C₄₁×#1880	2
C₄₁×#1804	2
C₄₁×#1803	2
#24827	41

Subgroups — C41×#24827 #23801028

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#24827 #23801028