Subgroups — C₄₁×#23046 #23799247

Order 10496.

896 conjugacy classes of subgroups.

The subgroup lattice has 488 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₁×#472	C₂	1	1	yes	maximal, characteristic
2	C₄₁×#2948	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₁×#2946	C₂	1	2	yes	maximal, complemented
4	C₄₁×#2913	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₁×#1970	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄₁×#1952	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₁×#1931	C₂	1	2	yes	maximal, complemented
8	C₄₁×#1883	C₂	1	2	yes	maximal, complemented
9	C₄₁×#1856	C₂	1	2	yes	maximal, complemented
10	C₄₁×#1772	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₁×#1764	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×AGL(1,ℤ/8)×C₄₁	C₂²	1	2	yes	—
13	C₂²×D₈×C₄₁	C₂²	1	1	yes	characteristic
14	C₂×#131×C₄₁	C₂²	1	1	yes	characteristic
15	C₄₁×#520	C₂²	1	2	yes	—
16	C₄₁×#518	C₂²	1	2	yes	—
17	C₄₁×#472	C₄	1	8	yes	complemented
18	C₄₁×#442	—	2	2	no	—
19	C₄₁×#442	—	2	2	no	—
20	C₄₁×#440	—	2	2	no	—
21	C₄×SD₁₆×C₄₁	—	2	2	no	—
22	C₄×D₈×C₄₁	—	2	1	no	—
23	C₄×D₈×C₄₁	—	2	1	no	—
24	C₄×D₈×C₄₁	—	2	2	no	—
25	C₂×#108×C₄₁	C₂²	1	1	yes	characteristic
26	C₄₁×#428	—	2	2	no	—
27	C₄₁×#428	C₂²	1	2	yes	—
28	C₄₁×#428	C₂²	1	2	yes	—
29	C₄₁×#427	—	2	1	no	—
30	C₄₁×#427	C₂²	1	1	yes	characteristic
31	C₂×#107×C₄₁	—	2	1	no	—
32	C₂×#107×C₄₁	C₂²	1	1	yes	characteristic
33	C₂×#104×C₄₁	C₂²	1	1	yes	characteristic
34	C₄₁×#418	C₂²	1	2	yes	—
35	C₄₁×#416	C₂²	1	1	yes	characteristic
36	C₂×#102×C₄₁	C₂²	1	2	yes	—
37	C₂×#100×C₄₁	C₂²	1	2	yes	—
38	C₄₁×#405	C₂²	1	1	yes	characteristic
39	C₄₁×#405	C₂²	1	2	yes	—
40	C₂×C₄×C₈×C₄₁	C₂²	1	1	yes	characteristic
41	C₄₁×#390	C₂²	1	2	yes	—
42	C₄₁×#343	C₂²	1	2	yes	—
43	C₄₁×#341	C₂²	1	1	yes	characteristic
44	C₄₁×#339	C₂²	1	1	yes	characteristic
45	C₄₁×#339	C₂²	1	2	yes	—
46	C₂×#41×C₄₁	C₂³	1	1	yes	characteristic
47	C₂²×D₄×C₄₁	C₂³	1	2	yes	—
48	AGL(1,ℤ/8)×C₄₁	—	2	4	no	—
49	AGL(1,ℤ/8)×C₄₁	C₂×C₄	1	8	yes	complemented
50	C₂×SD₁₆×C₄₁	—	2	2	no	—
51	C₂×D₈×C₄₁	—	2	2	no	—
52	C₂×D₈×C₄₁	—	2	1	no	—
53	C₂×D₈×C₄₁	—	2	1	no	—
54	C₂×D₈×C₄₁	—	2	2	no	—
55	C₂×D₈×C₄₁	C₂×C₄	1	4	yes	complemented
56	#131×C₄₁	—	2	2	no	—
57	#131×C₄₁	C₂×C₄	1	4	yes	complemented
58	C₂×M₁₆×C₄₁	—	2	1	no	—
59	C₂×M₁₆×C₄₁	C₂³	1	1	yes	characteristic
60	C₂×M₁₆×C₄₁	C₂³	1	1	yes	characteristic
61	C₂×M₁₆×C₄₁	C₂³	1	2	yes	—
62	C₂²×C₈×C₄₁	—	2	1	no	—
63	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
64	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
65	C₄×Q₈×C₄₁	—	2	2	no	—
66	C₄×D₄×C₄₁	—	2	2	no	—
67	C₄×D₄×C₄₁	—	2	2	no	—
68	C₄×D₄×C₄₁	—	2	2	no	—
69	C₄×D₄×C₄₁	—	2	2	no	—
70	C₄×D₄×C₄₁	—	2	2	no	—
71	C₄×D₄×C₄₁	—	4	2	no	—
72	#117×C₄₁	—	2	2	no	—
73	#117×C₄₁	C₂³	1	1	yes	characteristic
74	#117×C₄₁	C₂³	1	2	yes	—
75	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
76	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
77	C₂×C₂²⋊C₄×C₄₁	—	4	2	no	—
78	C₂×C₂²⋊C₄×C₄₁	—	4	2	no	—
79	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
80	#108×C₄₁	C₂×C₄	1	4	yes	complemented
81	#107×C₄₁	—	2	1	no	—
82	#107×C₄₁	—	2	1	no	—
83	#107×C₄₁	—	2	2	no	—
84	#107×C₄₁	—	2	2	no	—
85	#107×C₄₁	D₄	1	1	yes	characteristic
86	#107×C₄₁	D₄	1	1	yes	characteristic
87	#106×C₄₁	—	2	2	no	—
88	#106×C₄₁	—	2	2	no	—
89	#106×C₄₁	D₄	1	2	yes	—
90	#104×C₄₁	—	2	2	no	—
91	#103×C₄₁	D₄	1	1	yes	characteristic
92	#103×C₄₁	D₄	1	1	yes	characteristic
93	#102×C₄₁	—	2	2	no	—
94	#102×C₄₁	—	2	2	no	—
95	#102×C₄₁	—	2	2	no	—
96	#102×C₄₁	—	2	2	no	—
97	#102×C₄₁	D₄	1	1	yes	characteristic
98	#102×C₄₁	D₄	1	1	yes	characteristic
99	#100×C₄₁	C₂×C₄	1	8	yes	complemented
100	#97×C₄₁	—	2	2	no	—
101	#97×C₄₁	—	2	1	no	—
102	C₄×C₈×C₄₁	—	2	1	no	—
103	C₄×C₈×C₄₁	—	2	2	no	—
104	C₄×C₈×C₄₁	—	2	2	no	—
105	C₂⁴×C₄₁	—	2	2	no	—
106	#41×C₄₁	—	2	1	no	—
107	#41×C₄₁	—	2	1	no	—
108	#41×C₄₁	C₂²×C₄	1	2	yes	—
109	#41×C₄₁	#41	1	2	yes	—
110	C₂×Q₈×C₄₁	C₂×D₄	1	1	yes	characteristic
111	C₂×D₄×C₄₁	—	2	1	no	—
112	C₂×D₄×C₄₁	—	2	2	no	—
113	C₂×D₄×C₄₁	—	2	2	no	—
114	C₂×D₄×C₄₁	—	2	2	no	—
115	C₂×D₄×C₄₁	—	2	2	no	—
116	C₂×D₄×C₄₁	—	2	2	no	—
117	C₂×D₄×C₄₁	C₂²×C₄	1	4	yes	—
118	C₂×D₄×C₄₁	C₂×D₄	1	1	yes	characteristic
119	C₂²×C₄×C₄₁	—	2	1	no	—
120	C₂²×C₄×C₄₁	—	2	1	no	—
121	C₂²×C₄×C₄₁	—	2	2	no	—
122	C₂²×C₄×C₄₁	—	4	2	no	—
123	C₂²×C₄×C₄₁	—	4	2	no	—
124	C₂²×C₄×C₄₁	—	4	2	no	—
125	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
126	SD₁₆×C₄₁	—	2	8	no	—
127	D₈×C₄₁	—	2	8	no	—
128	D₈×C₄₁	—	2	4	no	—
129	D₈×C₄₁	—	2	4	no	—
130	M₁₆×C₄₁	—	2	1	no	—
131	M₁₆×C₄₁	—	2	2	no	—
132	M₁₆×C₄₁	—	2	4	no	—
133	M₁₆×C₄₁	—	2	1	no	—
134	M₁₆×C₄₁	—	2	1	no	—
135	M₁₆×C₄₁	C₂²×C₄	1	2	yes	—
136	M₁₆×C₄₁	C₂²×C₄	1	4	yes	—
137	C₂×C₈×C₄₁	—	2	2	no	—
138	C₂×C₈×C₄₁	—	2	1	no	—
139	C₂×C₈×C₄₁	—	2	1	no	—
140	C₂×C₈×C₄₁	—	2	1	no	—
141	C₂×C₈×C₄₁	—	2	4	no	—
142	C₂×C₈×C₄₁	—	2	1	no	—
143	C₂×C₈×C₄₁	C₂²×C₄	1	2	yes	—
144	C₂×C₈×C₄₁	C₂×D₄	1	1	yes	characteristic
145	C₂×C₈×C₄₁	C₂×D₄	1	1	yes	characteristic
146	C₂×C₈×C₄₁	C₂×D₄	1	1	yes	characteristic
147	C₂×C₈×C₄₁	C₂×D₄	1	1	yes	characteristic
148	C₂×C₈×C₄₁	#41	1	2	yes	—
149	C₄⋊C₄×C₄₁	—	2	2	no	—
150	C₄⋊C₄×C₄₁	—	2	2	no	—
151	C₄⋊C₄×C₄₁	—	4	2	no	—
152	C₄⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
153	C₄⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
154	C₄⋊C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
155	C₄⋊C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
156	C₂²⋊C₄×C₄₁	—	2	1	no	—
157	C₂²⋊C₄×C₄₁	—	2	2	no	—
158	C₂²⋊C₄×C₄₁	—	4	2	no	—
159	C₂²⋊C₄×C₄₁	—	4	2	no	—
160	C₂²⋊C₄×C₄₁	—	4	2	no	—
161	C₂²⋊C₄×C₄₁	—	8	4	no	—
162	C₄²×C₄₁	—	2	1	no	—
163	C₄²×C₄₁	—	2	2	no	—
164	C₄²×C₄₁	—	2	1	no	—
165	C₄²×C₄₁	—	2	1	no	—
166	C₄²×C₄₁	—	4	2	no	—
167	C₂³×C₄₁	—	2	1	no	—
168	C₂³×C₄₁	—	2	4	no	—
169	C₂³×C₄₁	—	4	2	no	—
170	C₂³×C₄₁	—	4	2	no	—
171	C₂³×C₄₁	—	8	2	no	—
172	C₂³×C₄₁	—	8	2	no	—
173	C₂³×C₄₁	H(5,𝔽₂)	1	1	yes	characteristic
174	Q₈×C₄₁	—	2	1	no	—
175	Q₈×C₄₁	C₄×D₄	1	2	yes	—
176	D₄×C₄₁	—	2	2	no	—
177	D₄×C₄₁	—	2	2	no	—
178	D₄×C₄₁	—	2	4	no	—
179	D₄×C₄₁	—	2	4	no	—
180	D₄×C₄₁	—	2	1	no	—
181	D₄×C₄₁	—	4	2	no	—
182	D₄×C₄₁	—	4	2	no	—
183	D₄×C₄₁	C₄×D₄	1	2	yes	—
184	C₂×C₄×C₄₁	—	2	1	no	—
185	C₂×C₄×C₄₁	—	2	2	no	—
186	C₂×C₄×C₄₁	—	2	2	no	—
187	C₂×C₄×C₄₁	—	2	2	no	—
188	C₂×C₄×C₄₁	—	2	2	no	—
189	C₂×C₄×C₄₁	—	2	1	no	—
190	C₂×C₄×C₄₁	—	2	1	no	—
191	C₂×C₄×C₄₁	—	2	2	no	—
192	C₂×C₄×C₄₁	—	4	1	no	—
193	C₂×C₄×C₄₁	—	4	1	no	—
194	C₂×C₄×C₄₁	—	4	2	no	—
195	C₂×C₄×C₄₁	—	8	2	no	—
196	C₂×C₄×C₄₁	—	16	2	no	—
197	C₂×C₄×C₄₁	—	16	2	no	—
198	C₂×C₄×C₄₁	—	16	2	no	—
199	C₂×C₄×C₄₁	C₂³×C₄	1	1	yes	characteristic
200	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
201	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
202	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
203	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
204	C₂×C₄×C₄₁	2₋¹⁺⁴	1	1	yes	characteristic
205	C₈×C₄₁	—	2	2	no	—
206	C₈×C₄₁	—	2	4	no	—
207	C₈×C₄₁	—	2	1	no	—
208	C₈×C₄₁	—	2	1	no	—
209	C₈×C₄₁	—	4	1	no	—
210	C₈×C₄₁	C₄×D₄	1	2	yes	—
211	C₈×C₄₁	C₄×D₄	1	2	yes	—
212	#23046	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
213	C₂²×C₄₁	—	2	1	no	—
214	C₂²×C₄₁	—	2	1	no	—
215	C₂²×C₄₁	—	2	2	no	—
216	C₂²×C₄₁	—	4	1	no	—
217	C₂²×C₄₁	—	4	1	no	—
218	C₂²×C₄₁	—	4	4	no	—
219	C₂²×C₄₁	—	8	4	no	—
220	C₂²×C₄₁	—	8	2	no	—
221	C₂²×C₄₁	—	8	2	no	—
222	C₂²×C₄₁	—	16	2	no	—
223	C₂²×C₄₁	#520	1	1	yes	characteristic
224	C₂²×C₄₁	D₄²	1	1	yes	characteristic
225	C₂²×C₄₁	#553	1	1	yes	characteristic
226	C₄×C₄₁	—	2	2	no	—
227	C₄×C₄₁	—	4	2	no	—
228	C₄×C₄₁	—	4	2	no	—
229	C₄×C₄₁	—	4	1	no	—
230	C₄×C₄₁	—	4	1	no	—
231	C₄×C₄₁	—	4	2	no	—
232	C₄×C₄₁	—	8	2	no	—
233	C₄×C₄₁	C₂×C₄×D₄	1	1	yes	characteristic
234	C₄×C₄₁	C₂×C₄×D₄	1	1	yes	characteristic
235	C₄×C₄₁	#547	1	1	yes	characteristic
236	C₄×C₄₁	#548	1	1	yes	characteristic
237	C₂×#472	C₂×C₄₁	1	1	yes	characteristic
238	#2948	C₂×C₄₁	1	1	yes	characteristic, complemented
239	#2946	C₂×C₄₁	1	2	yes	complemented
240	#2913	C₂×C₄₁	1	1	yes	characteristic, complemented
241	#1970	C₂×C₄₁	1	1	yes	characteristic, complemented
242	#1952	C₂×C₄₁	1	1	yes	characteristic, complemented
243	#1931	C₂×C₄₁	1	2	yes	complemented
244	#1883	C₂×C₄₁	1	2	yes	complemented
245	#1856	C₂×C₄₁	1	2	yes	complemented
246	#1772	C₂×C₄₁	1	1	yes	characteristic, complemented
247	#1764	C₂×C₄₁	1	1	yes	characteristic, complemented
248	C₂×C₄₁	—	2	1	no	—
249	C₂×C₄₁	—	2	1	no	—
250	C₂×C₄₁	—	4	2	no	—
251	C₂×C₄₁	—	8	4	no	—
252	C₂×C₄₁	#2361	1	1	yes	characteristic
253	C₂×C₄₁	#3290	1	1	yes	characteristic
254	C₂×C₄₁	#3292	1	1	yes	characteristic
255	C₂×AGL(1,ℤ/8)	C₂²×C₄₁	1	2	yes	—
256	C₂²×D₈	C₂²×C₄₁	1	1	yes	characteristic
257	C₂×#131	C₂²×C₄₁	1	1	yes	characteristic
258	#520	C₂²×C₄₁	1	2	yes	—
259	#518	C₂²×C₄₁	1	2	yes	—
260	#472	C₄×C₄₁	1	8	yes	complemented
261	#442	—	2	2	no	—
262	#442	—	2	2	no	—
263	#440	—	2	2	no	—
264	C₄×SD₁₆	—	2	2	no	—
265	C₄×D₈	—	2	1	no	—
266	C₄×D₈	—	2	1	no	—
267	C₄×D₈	—	2	2	no	—
268	C₂×#108	C₂²×C₄₁	1	1	yes	characteristic
269	#428	—	2	2	no	—
270	#428	C₂²×C₄₁	1	2	yes	—
271	#428	C₂²×C₄₁	1	2	yes	—
272	#427	—	2	1	no	—
273	#427	C₂²×C₄₁	1	1	yes	characteristic
274	C₂×#107	—	2	1	no	—
275	C₂×#107	C₂²×C₄₁	1	1	yes	characteristic
276	C₂×#104	C₂²×C₄₁	1	1	yes	characteristic
277	#418	C₂²×C₄₁	1	2	yes	—
278	#416	C₂²×C₄₁	1	1	yes	characteristic
279	C₂×#102	C₂²×C₄₁	1	2	yes	—
280	C₂×#100	C₂²×C₄₁	1	2	yes	—
281	#405	C₂²×C₄₁	1	2	yes	—
282	#405	C₂²×C₄₁	1	1	yes	characteristic
283	C₂×C₄×C₈	C₂²×C₄₁	1	1	yes	characteristic
284	#390	C₂²×C₄₁	1	2	yes	—
285	#343	C₂²×C₄₁	1	2	yes	—
286	#341	C₂²×C₄₁	1	1	yes	characteristic
287	#339	C₂²×C₄₁	1	1	yes	characteristic
288	#339	C₂²×C₄₁	1	2	yes	—
289	C₄₁	#23046	1	1	yes	characteristic, direct product factor, Sylow
290	C₂×#41	C₂³×C₄₁	1	1	yes	characteristic
291	C₂²×D₄	C₂³×C₄₁	1	2	yes	—
292	AGL(1,ℤ/8)	—	2	4	no	—
293	AGL(1,ℤ/8)	C₂×C₄×C₄₁	1	8	yes	complemented
294	C₂×SD₁₆	—	2	2	no	—
295	C₂×D₈	—	2	2	no	—
296	C₂×D₈	—	2	1	no	—
297	C₂×D₈	—	2	1	no	—
298	C₂×D₈	—	2	2	no	—
299	C₂×D₈	C₂×C₄×C₄₁	1	4	yes	complemented
300	#131	—	2	2	no	—
301	#131	C₂×C₄×C₄₁	1	4	yes	complemented
302	C₂×M₁₆	—	2	1	no	—
303	C₂×M₁₆	C₂³×C₄₁	1	1	yes	characteristic
304	C₂×M₁₆	C₂³×C₄₁	1	1	yes	characteristic
305	C₂×M₁₆	C₂³×C₄₁	1	2	yes	—
306	C₂²×C₈	—	2	1	no	—
307	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
308	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
309	C₄×Q₈	—	2	2	no	—
310	C₄×D₄	—	2	2	no	—
311	C₄×D₄	—	2	2	no	—
312	C₄×D₄	—	2	2	no	—
313	C₄×D₄	—	2	2	no	—
314	C₄×D₄	—	2	2	no	—
315	C₄×D₄	—	4	2	no	—
316	#117	—	2	2	no	—
317	#117	C₂³×C₄₁	1	1	yes	characteristic
318	#117	C₂³×C₄₁	1	2	yes	—
319	C₂×C₄⋊C₄	—	2	2	no	—
320	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
321	C₂×C₂²⋊C₄	—	4	2	no	—
322	C₂×C₂²⋊C₄	—	4	2	no	—
323	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
324	#108	C₂×C₄×C₄₁	1	4	yes	complemented
325	#107	—	2	1	no	—
326	#107	—	2	1	no	—
327	#107	—	2	2	no	—
328	#107	—	2	2	no	—
329	#107	D₄×C₄₁	1	1	yes	characteristic
330	#107	D₄×C₄₁	1	1	yes	characteristic
331	#106	—	2	2	no	—
332	#106	—	2	2	no	—
333	#106	D₄×C₄₁	1	2	yes	—
334	#104	—	2	2	no	—
335	#103	D₄×C₄₁	1	1	yes	characteristic
336	#103	D₄×C₄₁	1	1	yes	characteristic
337	#102	—	2	2	no	—
338	#102	—	2	2	no	—
339	#102	—	2	2	no	—
340	#102	—	2	2	no	—
341	#102	D₄×C₄₁	1	1	yes	characteristic
342	#102	D₄×C₄₁	1	1	yes	characteristic
343	#100	C₂×C₄×C₄₁	1	8	yes	complemented
344	#97	—	2	2	no	—
345	#97	—	2	1	no	—
346	C₄×C₈	—	2	1	no	—
347	C₄×C₈	—	2	2	no	—
348	C₄×C₈	—	2	2	no	—
349	C₂⁴	—	2	2	no	—
350	#41	—	2	1	no	—
351	#41	—	2	1	no	—
352	#41	C₂²×C₄×C₄₁	1	2	yes	—
353	#41	#41×C₄₁	1	2	yes	—
354	C₂×Q₈	C₂×D₄×C₄₁	1	1	yes	characteristic
355	C₂×D₄	—	2	1	no	—
356	C₂×D₄	—	2	2	no	—
357	C₂×D₄	—	2	2	no	—
358	C₂×D₄	—	2	2	no	—
359	C₂×D₄	—	2	2	no	—
360	C₂×D₄	—	2	2	no	—
361	C₂×D₄	C₂²×C₄×C₄₁	1	4	yes	—
362	C₂×D₄	C₂×D₄×C₄₁	1	1	yes	characteristic
363	C₂²×C₄	—	2	1	no	—
364	C₂²×C₄	—	2	1	no	—
365	C₂²×C₄	—	2	2	no	—
366	C₂²×C₄	—	4	2	no	—
367	C₂²×C₄	—	4	2	no	—
368	C₂²×C₄	—	4	2	no	—
369	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
370	SD₁₆	—	2	8	no	—
371	D₈	—	2	8	no	—
372	D₈	—	2	4	no	—
373	D₈	—	2	4	no	—
374	M₁₆	—	2	1	no	—
375	M₁₆	—	2	2	no	—
376	M₁₆	—	2	4	no	—
377	M₁₆	—	2	1	no	—
378	M₁₆	—	2	1	no	—
379	M₁₆	C₂²×C₄×C₄₁	1	2	yes	—
380	M₁₆	C₂²×C₄×C₄₁	1	4	yes	—
381	C₂×C₈	—	2	2	no	—
382	C₂×C₈	—	2	1	no	—
383	C₂×C₈	—	2	1	no	—
384	C₂×C₈	—	2	1	no	—
385	C₂×C₈	—	2	4	no	—
386	C₂×C₈	—	2	1	no	—
387	C₂×C₈	C₂²×C₄×C₄₁	1	2	yes	—
388	C₂×C₈	C₂×D₄×C₄₁	1	1	yes	characteristic
389	C₂×C₈	C₂×D₄×C₄₁	1	1	yes	characteristic
390	C₂×C₈	C₂×D₄×C₄₁	1	1	yes	characteristic
391	C₂×C₈	C₂×D₄×C₄₁	1	1	yes	characteristic
392	C₂×C₈	#41×C₄₁	1	2	yes	—
393	C₄⋊C₄	—	2	2	no	—
394	C₄⋊C₄	—	2	2	no	—
395	C₄⋊C₄	—	4	2	no	—
396	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
397	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
398	C₄⋊C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
399	C₄⋊C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
400	C₂²⋊C₄	—	2	1	no	—
401	C₂²⋊C₄	—	2	2	no	—
402	C₂²⋊C₄	—	4	2	no	—
403	C₂²⋊C₄	—	4	2	no	—
404	C₂²⋊C₄	—	4	2	no	—
405	C₂²⋊C₄	—	8	4	no	—
406	C₄²	—	2	1	no	—
407	C₄²	—	2	2	no	—
408	C₄²	—	2	1	no	—
409	C₄²	—	2	1	no	—
410	C₄²	—	4	2	no	—
411	C₂³	—	2	1	no	—
412	C₂³	—	2	4	no	—
413	C₂³	—	4	2	no	—
414	C₂³	—	4	2	no	—
415	C₂³	—	8	2	no	—
416	C₂³	—	8	2	no	—
417	C₂³	H(5,𝔽₂)×C₄₁	1	1	yes	characteristic
418	Q₈	—	2	1	no	—
419	Q₈	C₄×D₄×C₄₁	1	2	yes	—
420	D₄	—	2	2	no	—
421	D₄	—	2	2	no	—
422	D₄	—	2	4	no	—
423	D₄	—	2	4	no	—
424	D₄	—	2	1	no	—
425	D₄	—	4	2	no	—
426	D₄	—	4	2	no	—
427	D₄	C₄×D₄×C₄₁	1	2	yes	—
428	C₂×C₄	—	2	1	no	—
429	C₂×C₄	—	2	2	no	—
430	C₂×C₄	—	2	2	no	—
431	C₂×C₄	—	2	2	no	—
432	C₂×C₄	—	2	2	no	—
433	C₂×C₄	—	2	1	no	—
434	C₂×C₄	—	2	1	no	—
435	C₂×C₄	—	2	2	no	—
436	C₂×C₄	—	4	1	no	—
437	C₂×C₄	—	4	1	no	—
438	C₂×C₄	—	4	2	no	—
439	C₂×C₄	—	8	2	no	—
440	C₂×C₄	—	16	2	no	—
441	C₂×C₄	—	16	2	no	—
442	C₂×C₄	—	16	2	no	—
443	C₂×C₄	C₂³×C₄×C₄₁	1	1	yes	characteristic
444	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
445	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
446	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
447	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
448	C₂×C₄	2₋¹⁺⁴×C₄₁	1	1	yes	characteristic
449	C₈	—	2	2	no	—
450	C₈	—	2	4	no	—
451	C₈	—	2	1	no	—
452	C₈	—	2	1	no	—
453	C₈	—	4	1	no	—
454	C₈	C₄×D₄×C₄₁	1	2	yes	—
455	C₈	C₄×D₄×C₄₁	1	2	yes	—
456	C₂²	—	2	1	no	—
457	C₂²	—	2	1	no	—
458	C₂²	—	2	2	no	—
459	C₂²	—	4	1	no	—
460	C₂²	—	4	1	no	—
461	C₂²	—	4	4	no	—
462	C₂²	—	8	4	no	—
463	C₂²	—	8	2	no	—
464	C₂²	—	8	2	no	—
465	C₂²	—	16	2	no	—
466	C₂²	C₄₁×#520	1	1	yes	characteristic
467	C₂²	D₄²×C₄₁	1	1	yes	characteristic
468	C₂²	C₄₁×#553	1	1	yes	characteristic
469	C₄	—	2	2	no	—
470	C₄	—	4	2	no	—
471	C₄	—	4	1	no	—
472	C₄	—	4	2	no	—
473	C₄	—	4	1	no	—
474	C₄	—	4	2	no	—
475	C₄	—	8	2	no	—
476	C₄	C₂×C₄×D₄×C₄₁	1	1	yes	characteristic
477	C₄	C₂×C₄×D₄×C₄₁	1	1	yes	characteristic
478	C₄	C₄₁×#547	1	1	yes	characteristic
479	C₄	C₄₁×#548	1	1	yes	characteristic
480	C₂	—	2	1	no	—
481	C₂	—	2	1	no	—
482	C₂	—	4	2	no	—
483	C₂	—	8	4	no	—
484	C₂	C₄₁×#2361	1	1	yes	characteristic
485	C₂	C₄₁×#3290	1	1	yes	characteristic
486	C₂	C₄₁×#3292	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₄₁	D₄²
commutator	C₂×C₄	C₂³×C₄×C₄₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₁
prime radical	C₂×C₄₁×#472	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄₁ ◁ C₂²×C₄×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₄₁×#2948	C₂	semidirect
3. C₄₁×#2946	C₂	semidirect
4. C₄₁×#2913	C₂	semidirect
5. C₄₁×#1970	C₂	semidirect
6. C₄₁×#1952	C₂	semidirect
7. C₄₁×#1931	C₂	semidirect
8. C₄₁×#1883	C₂	semidirect
9. C₄₁×#1856	C₂	semidirect
10. C₄₁×#1772	C₂	semidirect
11. C₄₁×#1764	C₂	semidirect
17. C₄₁×#472	C₄	semidirect
49. AGL(1,ℤ/8)×C₄₁	C₂×C₄	semidirect
55. C₂×D₈×C₄₁	C₂×C₄	semidirect
57. #131×C₄₁	C₂×C₄	semidirect
80. #108×C₄₁	C₂×C₄	semidirect
99. #100×C₄₁	C₂×C₄	semidirect
212. #23046	C₄₁	direct (N × H)
238. #2948	C₂×C₄₁	semidirect
239. #2946	C₂×C₄₁	semidirect
240. #2913	C₂×C₄₁	semidirect
241. #1970	C₂×C₄₁	semidirect
242. #1952	C₂×C₄₁	semidirect
243. #1931	C₂×C₄₁	semidirect
244. #1883	C₂×C₄₁	semidirect
245. #1856	C₂×C₄₁	semidirect
246. #1772	C₂×C₄₁	semidirect
247. #1764	C₂×C₄₁	semidirect
260. #472	C₄×C₄₁	semidirect
289. C₄₁	#23046	direct (N × H)
293. AGL(1,ℤ/8)	C₂×C₄×C₄₁	semidirect
299. C₂×D₈	C₂×C₄×C₄₁	semidirect
301. #131	C₂×C₄×C₄₁	semidirect
324. #108	C₂×C₄×C₄₁	semidirect
343. #100	C₂×C₄×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×#472	2
C₄₁×#2948	2
C₄₁×#2946	2
C₄₁×#2913	2
C₄₁×#1970	2
C₄₁×#1952	2
C₄₁×#1931	2
C₄₁×#1883	2
C₄₁×#1856	2
C₄₁×#1772	2
C₄₁×#1764	2
#23046	41

Subgroups — C41×#23046 #23799247

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#23046 #23799247