Subgroups — C₄₁×#22895 #23799096

Order 10496.

1008 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₁×#454	C₂	1	1	yes	maximal, characteristic
2	C₄₁×#2946	C₂	1	2	yes	maximal, complemented
3	C₄₁×#2898	C₂	1	2	yes	maximal, complemented
4	C₄₁×#1958	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₁×#1930	C₂	1	2	yes	maximal, complemented
6	C₄₁×#1907	C₂	1	2	yes	maximal, complemented
7	C₄₁×#1885	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄₁×#1860	C₂	1	2	yes	maximal, complemented
9	C₄₁×#1764	C₂	1	2	yes	maximal, complemented
10	C₂×2₋¹⁺⁴×C₄₁	C₂²	1	1	yes	characteristic
11	C₂×AGL(1,ℤ/8)×C₄₁	C₂²	1	2	yes	—
12	C₂×#131×C₄₁	C₂²	1	2	yes	—
13	C₂×#124×C₄₁	C₂²	1	1	yes	characteristic
14	C₄₁×#520	C₂²	1	2	yes	—
15	C₄₁×#518	C₂²	1	1	yes	characteristic
16	C₄₁×#454	C₄	1	8	yes	complemented
17	C₄₁×#442	—	2	2	no	—
18	C₄₁×#440	—	2	2	no	—
19	C₄×SD₁₆×C₄₁	—	2	2	no	—
20	C₄×D₈×C₄₁	—	2	2	no	—
21	C₄₁×#428	C₂²	1	2	yes	—
22	C₂×#104×C₄₁	C₂²	1	2	yes	—
23	C₄₁×#419	—	2	2	no	—
24	C₄₁×#419	C₂²	1	2	yes	—
25	C₄₁×#417	—	2	2	no	—
26	C₄₁×#417	C₂²	1	2	yes	—
27	C₄₁×#416	—	2	2	no	—
28	C₄₁×#416	C₂²	1	2	yes	—
29	C₂×#103×C₄₁	—	2	2	no	—
30	C₂×#103×C₄₁	C₂²	1	2	yes	—
31	C₂×#102×C₄₁	C₂²	1	2	yes	—
32	C₂×#101×C₄₁	C₂²	1	1	yes	characteristic
33	C₂×#100×C₄₁	C₂²	1	1	yes	characteristic
34	C₄₁×#405	C₂²	1	2	yes	—
35	C₂×C₄×C₈×C₄₁	C₂²	1	1	yes	characteristic
36	C₄₁×#382	C₂²	1	1	yes	characteristic
37	C₄₁×#343	C₂²	1	2	yes	—
38	C₄₁×#341	C₂²	1	2	yes	—
39	C₄₁×#339	C₂²	1	2	yes	—
40	2₋¹⁺⁴×C₄₁	—	2	4	no	—
41	2₋¹⁺⁴×C₄₁	—	4	1	no	—
42	2₋¹⁺⁴×C₄₁	C₂×C₄	1	4	yes	complemented
43	C₂×#41×C₄₁	—	2	2	no	—
44	C₂×#41×C₄₁	—	4	1	no	—
45	C₂×#41×C₄₁	C₂³	1	2	yes	—
46	C₂²×Q₈×C₄₁	—	2	2	no	—
47	C₂²×Q₈×C₄₁	C₂³	1	1	yes	characteristic
48	C₂²×D₄×C₄₁	C₂³	1	1	yes	characteristic
49	AGL(1,ℤ/8)×C₄₁	—	2	4	no	—
50	AGL(1,ℤ/8)×C₄₁	C₂×C₄	1	8	yes	complemented
51	C₂×SD₁₆×C₄₁	—	2	2	no	—
52	C₂×D₈×C₄₁	—	2	2	no	—
53	#131×C₄₁	—	2	4	no	—
54	#131×C₄₁	—	4	2	no	—
55	C₂×M₁₆×C₄₁	—	2	2	no	—
56	C₂×M₁₆×C₄₁	C₂³	1	2	yes	—
57	C₂×M₁₆×C₄₁	C₂³	1	2	yes	—
58	C₂²×C₈×C₄₁	—	2	2	no	—
59	C₂²×C₈×C₄₁	C₂³	1	2	yes	—
60	#124×C₄₁	—	4	1	no	—
61	#124×C₄₁	C₂×C₄	1	4	yes	complemented
62	C₄×Q₈×C₄₁	—	2	2	no	—
63	C₄×D₄×C₄₁	—	2	2	no	—
64	C₄×D₄×C₄₁	—	2	2	no	—
65	C₄×D₄×C₄₁	—	2	2	no	—
66	C₄×D₄×C₄₁	—	4	2	no	—
67	#117×C₄₁	—	2	2	no	—
68	#117×C₄₁	C₂³	1	2	yes	—
69	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
70	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
71	C₂×C₂²⋊C₄×C₄₁	—	4	1	no	—
72	C₂×C₂²⋊C₄×C₄₁	—	4	1	no	—
73	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
74	#107×C₄₁	—	2	2	no	—
75	#106×C₄₁	—	2	2	no	—
76	#104×C₄₁	C₂×C₄	1	8	yes	complemented
77	#103×C₄₁	—	2	2	no	—
78	#103×C₄₁	—	2	2	no	—
79	#103×C₄₁	—	2	2	no	—
80	#103×C₄₁	—	2	2	no	—
81	#103×C₄₁	—	2	2	no	—
82	#103×C₄₁	D₄	1	2	yes	—
83	#103×C₄₁	D₄	1	2	yes	—
84	#102×C₄₁	—	2	2	no	—
85	#102×C₄₁	—	2	2	no	—
86	#102×C₄₁	—	2	2	no	—
87	#102×C₄₁	D₄	1	2	yes	—
88	#102×C₄₁	D₄	1	2	yes	—
89	#101×C₄₁	C₂×C₄	1	4	yes	complemented
90	#100×C₄₁	—	4	1	no	—
91	#97×C₄₁	—	2	2	no	—
92	C₄×C₈×C₄₁	—	2	2	no	—
93	C₄×C₈×C₄₁	—	4	1	no	—
94	#95×C₄₁	—	4	1	no	—
95	C₂⁴×C₄₁	—	2	1	no	—
96	#41×C₄₁	—	2	2	no	—
97	#41×C₄₁	—	2	2	no	—
98	#41×C₄₁	—	2	8	no	—
99	#41×C₄₁	—	4	4	no	—
100	#41×C₄₁	—	4	4	no	—
101	#41×C₄₁	—	4	4	no	—
102	#41×C₄₁	C₂²×C₄	1	4	yes	—
103	#41×C₄₁	#41	1	4	yes	—
104	C₂×Q₈×C₄₁	—	2	1	no	—
105	C₂×Q₈×C₄₁	—	2	8	no	—
106	C₂×Q₈×C₄₁	—	2	2	no	—
107	C₂×Q₈×C₄₁	—	2	2	no	—
108	C₂×Q₈×C₄₁	—	4	1	no	—
109	C₂×Q₈×C₄₁	—	4	4	no	—
110	C₂×Q₈×C₄₁	C₂²×C₄	1	2	yes	—
111	C₂×Q₈×C₄₁	C₂×D₄	1	2	yes	—
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	1	no	—
116	C₂×D₄×C₄₁	—	4	1	no	—
117	C₂×D₄×C₄₁	C₂²×C₄	1	2	yes	—
118	C₂×D₄×C₄₁	C₂×D₄	1	2	yes	—
119	C₂²×C₄×C₄₁	—	2	2	no	—
120	C₂²×C₄×C₄₁	—	2	1	no	—
121	C₂²×C₄×C₄₁	—	2	1	no	—
122	C₂²×C₄×C₄₁	—	2	2	no	—
123	C₂²×C₄×C₄₁	—	4	2	no	—
124	C₂²×C₄×C₄₁	—	4	2	no	—
125	C₂²×C₄×C₄₁	—	4	2	no	—
126	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
127	SD₁₆×C₄₁	—	2	8	no	—
128	D₈×C₄₁	—	2	8	no	—
129	M₁₆×C₄₁	—	2	2	no	—
130	M₁₆×C₄₁	—	2	2	no	—
131	M₁₆×C₄₁	—	2	2	no	—
132	M₁₆×C₄₁	—	4	4	no	—
133	M₁₆×C₄₁	C₂²×C₄	1	4	yes	—
134	C₂×C₈×C₄₁	—	2	2	no	—
135	C₂×C₈×C₄₁	—	2	2	no	—
136	C₂×C₈×C₄₁	—	2	2	no	—
137	C₂×C₈×C₄₁	—	2	2	no	—
138	C₂×C₈×C₄₁	—	4	4	no	—
139	C₂×C₈×C₄₁	C₂×D₄	1	2	yes	—
140	C₂×C₈×C₄₁	C₂×D₄	1	2	yes	—
141	C₄⋊C₄×C₄₁	—	2	2	no	—
142	C₄⋊C₄×C₄₁	—	2	2	no	—
143	C₄⋊C₄×C₄₁	—	4	2	no	—
144	C₄⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
145	C₄⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
146	C₂²⋊C₄×C₄₁	—	2	2	no	—
147	C₂²⋊C₄×C₄₁	—	4	4	no	—
148	C₂²⋊C₄×C₄₁	—	4	1	no	—
149	C₂²⋊C₄×C₄₁	—	4	1	no	—
150	C₂²⋊C₄×C₄₁	—	4	2	no	—
151	C₄²×C₄₁	—	2	2	no	—
152	C₄²×C₄₁	—	2	1	no	—
153	C₄²×C₄₁	—	4	2	no	—
154	C₄²×C₄₁	C₂²×C₄	1	2	yes	—
155	C₂³×C₄₁	—	2	2	no	—
156	C₂³×C₄₁	—	2	2	no	—
157	C₂³×C₄₁	—	4	1	no	—
158	C₂³×C₄₁	—	4	1	no	—
159	C₂³×C₄₁	—	8	2	no	—
160	C₂³×C₄₁	H(5,𝔽₂)	1	1	yes	characteristic
161	Q₈×C₄₁	—	2	2	no	—
162	Q₈×C₄₁	—	2	4	no	—
163	Q₈×C₄₁	—	4	4	no	—
164	Q₈×C₄₁	—	4	2	no	—
165	Q₈×C₄₁	C₄×D₄	1	4	yes	—
166	D₄×C₄₁	—	2	4	no	—
167	D₄×C₄₁	—	2	4	no	—
168	D₄×C₄₁	—	2	4	no	—
169	D₄×C₄₁	—	2	2	no	—
170	D₄×C₄₁	—	4	4	no	—
171	D₄×C₄₁	—	4	2	no	—
172	D₄×C₄₁	C₄×D₄	1	4	yes	—
173	C₂×C₄×C₄₁	—	2	2	no	—
174	C₂×C₄×C₄₁	—	2	4	no	—
175	C₂×C₄×C₄₁	—	2	4	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	—	4	8	no	—
181	C₂×C₄×C₄₁	—	4	2	no	—
182	C₂×C₄×C₄₁	—	4	1	no	—
183	C₂×C₄×C₄₁	—	4	1	no	—
184	C₂×C₄×C₄₁	—	4	2	no	—
185	C₂×C₄×C₄₁	—	8	2	no	—
186	C₂×C₄×C₄₁	—	16	2	no	—
187	C₂×C₄×C₄₁	—	16	2	no	—
188	C₂×C₄×C₄₁	C₂³×C₄	1	1	yes	characteristic
189	C₂×C₄×C₄₁	C₂²×D₄	1	2	yes	—
190	C₂×C₄×C₄₁	C₂×#41	1	2	yes	—
191	C₂×C₄×C₄₁	H(5,𝔽₂)	1	1	yes	characteristic
192	C₈×C₄₁	—	2	4	no	—
193	C₈×C₄₁	—	2	2	no	—
194	C₈×C₄₁	—	2	2	no	—
195	C₈×C₄₁	—	4	2	no	—
196	#22895	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
197	C₂²×C₄₁	—	2	2	no	—
198	C₂²×C₄₁	—	2	4	no	—
199	C₂²×C₄₁	—	4	2	no	—
200	C₂²×C₄₁	—	4	2	no	—
201	C₂²×C₄₁	—	4	2	no	—
202	C₂²×C₄₁	—	8	2	no	—
203	C₂²×C₄₁	—	8	2	no	—
204	C₂²×C₄₁	—	16	1	no	—
205	C₂²×C₄₁	#518	1	1	yes	characteristic
206	C₂²×C₄₁	D₄²	1	1	yes	characteristic
207	C₂²×C₄₁	#551	1	1	yes	characteristic
208	C₄×C₄₁	—	2	4	no	—
209	C₄×C₄₁	—	4	2	no	—
210	C₄×C₄₁	—	4	2	no	—
211	C₄×C₄₁	—	4	2	no	—
212	C₄×C₄₁	—	4	2	no	—
213	C₄×C₄₁	—	8	2	no	—
214	C₄×C₄₁	C₂×C₄×D₄	1	2	yes	—
215	C₄×C₄₁	#546	1	2	yes	—
216	C₂×#454	C₂×C₄₁	1	1	yes	characteristic
217	#2946	C₂×C₄₁	1	2	yes	complemented
218	#2898	C₂×C₄₁	1	2	yes	complemented
219	#1958	C₂×C₄₁	1	1	yes	characteristic, complemented
220	#1930	C₂×C₄₁	1	2	yes	complemented
221	#1907	C₂×C₄₁	1	2	yes	complemented
222	#1885	C₂×C₄₁	1	1	yes	characteristic, complemented
223	#1860	C₂×C₄₁	1	2	yes	complemented
224	#1764	C₂×C₄₁	1	2	yes	complemented
225	C₂×C₄₁	—	2	1	no	—
226	C₂×C₄₁	—	2	1	no	—
227	C₂×C₄₁	—	4	4	no	—
228	C₂×C₄₁	—	8	2	no	—
229	C₂×C₄₁	#2358	1	1	yes	characteristic
230	C₂×C₄₁	#3290	1	2	yes	—
231	C₂×2₋¹⁺⁴	C₂²×C₄₁	1	1	yes	characteristic
232	C₂×AGL(1,ℤ/8)	C₂²×C₄₁	1	2	yes	—
233	C₂×#131	C₂²×C₄₁	1	2	yes	—
234	C₂×#124	C₂²×C₄₁	1	1	yes	characteristic
235	#520	C₂²×C₄₁	1	2	yes	—
236	#518	C₂²×C₄₁	1	1	yes	characteristic
237	#454	C₄×C₄₁	1	8	yes	complemented
238	#442	—	2	2	no	—
239	#440	—	2	2	no	—
240	C₄×SD₁₆	—	2	2	no	—
241	C₄×D₈	—	2	2	no	—
242	#428	C₂²×C₄₁	1	2	yes	—
243	C₂×#104	C₂²×C₄₁	1	2	yes	—
244	#419	—	2	2	no	—
245	#419	C₂²×C₄₁	1	2	yes	—
246	#417	—	2	2	no	—
247	#417	C₂²×C₄₁	1	2	yes	—
248	#416	—	2	2	no	—
249	#416	C₂²×C₄₁	1	2	yes	—
250	C₂×#103	—	2	2	no	—
251	C₂×#103	C₂²×C₄₁	1	2	yes	—
252	C₂×#102	C₂²×C₄₁	1	2	yes	—
253	C₂×#101	C₂²×C₄₁	1	1	yes	characteristic
254	C₂×#100	C₂²×C₄₁	1	1	yes	characteristic
255	#405	C₂²×C₄₁	1	2	yes	—
256	C₂×C₄×C₈	C₂²×C₄₁	1	1	yes	characteristic
257	#382	C₂²×C₄₁	1	1	yes	characteristic
258	#343	C₂²×C₄₁	1	2	yes	—
259	#341	C₂²×C₄₁	1	2	yes	—
260	#339	C₂²×C₄₁	1	2	yes	—
261	C₄₁	#22895	1	1	yes	characteristic, direct product factor, Sylow
262	2₋¹⁺⁴	—	2	4	no	—
263	2₋¹⁺⁴	—	4	1	no	—
264	2₋¹⁺⁴	C₂×C₄×C₄₁	1	4	yes	complemented
265	C₂×#41	—	2	2	no	—
266	C₂×#41	—	4	1	no	—
267	C₂×#41	C₂³×C₄₁	1	2	yes	—
268	C₂²×Q₈	—	2	2	no	—
269	C₂²×Q₈	C₂³×C₄₁	1	1	yes	characteristic
270	C₂²×D₄	C₂³×C₄₁	1	1	yes	characteristic
271	AGL(1,ℤ/8)	—	2	4	no	—
272	AGL(1,ℤ/8)	C₂×C₄×C₄₁	1	8	yes	complemented
273	C₂×SD₁₆	—	2	2	no	—
274	C₂×D₈	—	2	2	no	—
275	#131	—	2	4	no	—
276	#131	—	4	2	no	—
277	C₂×M₁₆	—	2	2	no	—
278	C₂×M₁₆	C₂³×C₄₁	1	2	yes	—
279	C₂×M₁₆	C₂³×C₄₁	1	2	yes	—
280	C₂²×C₈	—	2	2	no	—
281	C₂²×C₈	C₂³×C₄₁	1	2	yes	—
282	#124	—	4	1	no	—
283	#124	C₂×C₄×C₄₁	1	4	yes	complemented
284	C₄×Q₈	—	2	2	no	—
285	C₄×D₄	—	2	2	no	—
286	C₄×D₄	—	2	2	no	—
287	C₄×D₄	—	2	2	no	—
288	C₄×D₄	—	4	2	no	—
289	#117	—	2	2	no	—
290	#117	C₂³×C₄₁	1	2	yes	—
291	C₂×C₄⋊C₄	—	2	2	no	—
292	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
293	C₂×C₂²⋊C₄	—	4	1	no	—
294	C₂×C₂²⋊C₄	—	4	1	no	—
295	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
296	#107	—	2	2	no	—
297	#106	—	2	2	no	—
298	#104	C₂×C₄×C₄₁	1	8	yes	complemented
299	#103	—	2	2	no	—
300	#103	—	2	2	no	—
301	#103	—	2	2	no	—
302	#103	—	2	2	no	—
303	#103	—	2	2	no	—
304	#103	D₄×C₄₁	1	2	yes	—
305	#103	D₄×C₄₁	1	2	yes	—
306	#102	—	2	2	no	—
307	#102	—	2	2	no	—
308	#102	—	2	2	no	—
309	#102	D₄×C₄₁	1	2	yes	—
310	#102	D₄×C₄₁	1	2	yes	—
311	#101	C₂×C₄×C₄₁	1	4	yes	complemented
312	#100	—	4	1	no	—
313	#97	—	2	2	no	—
314	C₄×C₈	—	2	2	no	—
315	C₄×C₈	—	4	1	no	—
316	#95	—	4	1	no	—
317	C₂⁴	—	2	1	no	—
318	#41	—	2	2	no	—
319	#41	—	2	2	no	—
320	#41	—	2	8	no	—
321	#41	—	4	4	no	—
322	#41	—	4	4	no	—
323	#41	—	4	4	no	—
324	#41	C₂²×C₄×C₄₁	1	4	yes	—
325	#41	#41×C₄₁	1	4	yes	—
326	C₂×Q₈	—	2	1	no	—
327	C₂×Q₈	—	2	8	no	—
328	C₂×Q₈	—	2	2	no	—
329	C₂×Q₈	—	2	2	no	—
330	C₂×Q₈	—	4	1	no	—
331	C₂×Q₈	—	4	4	no	—
332	C₂×Q₈	C₂²×C₄×C₄₁	1	2	yes	—
333	C₂×Q₈	C₂×D₄×C₄₁	1	2	yes	—
334	C₂×D₄	—	2	2	no	—
335	C₂×D₄	—	2	2	no	—
336	C₂×D₄	—	2	2	no	—
337	C₂×D₄	—	2	1	no	—
338	C₂×D₄	—	4	1	no	—
339	C₂×D₄	C₂²×C₄×C₄₁	1	2	yes	—
340	C₂×D₄	C₂×D₄×C₄₁	1	2	yes	—
341	C₂²×C₄	—	2	2	no	—
342	C₂²×C₄	—	2	1	no	—
343	C₂²×C₄	—	2	1	no	—
344	C₂²×C₄	—	2	2	no	—
345	C₂²×C₄	—	4	2	no	—
346	C₂²×C₄	—	4	2	no	—
347	C₂²×C₄	—	4	2	no	—
348	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
349	SD₁₆	—	2	8	no	—
350	D₈	—	2	8	no	—
351	M₁₆	—	2	2	no	—
352	M₁₆	—	2	2	no	—
353	M₁₆	—	2	2	no	—
354	M₁₆	—	4	4	no	—
355	M₁₆	C₂²×C₄×C₄₁	1	4	yes	—
356	C₂×C₈	—	2	2	no	—
357	C₂×C₈	—	2	2	no	—
358	C₂×C₈	—	2	2	no	—
359	C₂×C₈	—	2	2	no	—
360	C₂×C₈	—	4	4	no	—
361	C₂×C₈	C₂×D₄×C₄₁	1	2	yes	—
362	C₂×C₈	C₂×D₄×C₄₁	1	2	yes	—
363	C₄⋊C₄	—	2	2	no	—
364	C₄⋊C₄	—	2	2	no	—
365	C₄⋊C₄	—	4	2	no	—
366	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
367	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
368	C₂²⋊C₄	—	2	2	no	—
369	C₂²⋊C₄	—	4	4	no	—
370	C₂²⋊C₄	—	4	1	no	—
371	C₂²⋊C₄	—	4	1	no	—
372	C₂²⋊C₄	—	4	2	no	—
373	C₄²	—	2	2	no	—
374	C₄²	—	2	1	no	—
375	C₄²	—	4	2	no	—
376	C₄²	C₂²×C₄×C₄₁	1	2	yes	—
377	C₂³	—	2	2	no	—
378	C₂³	—	2	2	no	—
379	C₂³	—	4	1	no	—
380	C₂³	—	4	1	no	—
381	C₂³	—	8	2	no	—
382	C₂³	H(5,𝔽₂)×C₄₁	1	1	yes	characteristic
383	Q₈	—	2	2	no	—
384	Q₈	—	2	4	no	—
385	Q₈	—	4	4	no	—
386	Q₈	—	4	2	no	—
387	Q₈	C₄×D₄×C₄₁	1	4	yes	—
388	D₄	—	2	4	no	—
389	D₄	—	2	4	no	—
390	D₄	—	2	4	no	—
391	D₄	—	2	2	no	—
392	D₄	—	4	4	no	—
393	D₄	—	4	2	no	—
394	D₄	C₄×D₄×C₄₁	1	4	yes	—
395	C₂×C₄	—	2	2	no	—
396	C₂×C₄	—	2	4	no	—
397	C₂×C₄	—	2	4	no	—
398	C₂×C₄	—	2	2	no	—
399	C₂×C₄	—	2	2	no	—
400	C₂×C₄	—	2	2	no	—
401	C₂×C₄	—	2	2	no	—
402	C₂×C₄	—	4	8	no	—
403	C₂×C₄	—	4	2	no	—
404	C₂×C₄	—	4	1	no	—
405	C₂×C₄	—	4	1	no	—
406	C₂×C₄	—	4	2	no	—
407	C₂×C₄	—	8	2	no	—
408	C₂×C₄	—	16	2	no	—
409	C₂×C₄	—	16	2	no	—
410	C₂×C₄	C₂³×C₄×C₄₁	1	1	yes	characteristic
411	C₂×C₄	C₂²×D₄×C₄₁	1	2	yes	—
412	C₂×C₄	C₂×#41×C₄₁	1	2	yes	—
413	C₂×C₄	H(5,𝔽₂)×C₄₁	1	1	yes	characteristic
414	C₈	—	2	4	no	—
415	C₈	—	2	2	no	—
416	C₈	—	2	2	no	—
417	C₈	—	4	2	no	—
418	C₂²	—	2	2	no	—
419	C₂²	—	2	4	no	—
420	C₂²	—	4	2	no	—
421	C₂²	—	4	2	no	—
422	C₂²	—	4	2	no	—
423	C₂²	—	8	2	no	—
424	C₂²	—	8	2	no	—
425	C₂²	—	16	1	no	—
426	C₂²	C₄₁×#518	1	1	yes	characteristic
427	C₂²	D₄²×C₄₁	1	1	yes	characteristic
428	C₂²	C₄₁×#551	1	1	yes	characteristic
429	C₄	—	2	4	no	—
430	C₄	—	4	2	no	—
431	C₄	—	4	2	no	—
432	C₄	—	4	2	no	—
433	C₄	—	4	2	no	—
434	C₄	—	8	2	no	—
435	C₄	C₂×C₄×D₄×C₄₁	1	2	yes	—
436	C₄	C₄₁×#546	1	2	yes	—
437	C₂	—	2	1	no	—
438	C₂	—	2	1	no	—
439	C₂	—	4	4	no	—
440	C₂	—	8	2	no	—
441	C₂	C₄₁×#2358	1	1	yes	characteristic
442	C₂	C₄₁×#3290	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₄₁	D₄²
commutator	C₂×C₄	C₂³×C₄×C₄₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₁
prime radical	C₂×C₄₁×#454	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×#2946	C₂	semidirect
3. C₄₁×#2898	C₂	semidirect
4. C₄₁×#1958	C₂	semidirect
5. C₄₁×#1930	C₂	semidirect
6. C₄₁×#1907	C₂	semidirect
7. C₄₁×#1885	C₂	semidirect
8. C₄₁×#1860	C₂	semidirect
9. C₄₁×#1764	C₂	semidirect
16. C₄₁×#454	C₄	semidirect
42. 2₋¹⁺⁴×C₄₁	C₂×C₄	semidirect
50. AGL(1,ℤ/8)×C₄₁	C₂×C₄	semidirect
61. #124×C₄₁	C₂×C₄	semidirect
76. #104×C₄₁	C₂×C₄	semidirect
89. #101×C₄₁	C₂×C₄	semidirect
196. #22895	C₄₁	direct (N × H)
217. #2946	C₂×C₄₁	semidirect
218. #2898	C₂×C₄₁	semidirect
219. #1958	C₂×C₄₁	semidirect
220. #1930	C₂×C₄₁	semidirect
221. #1907	C₂×C₄₁	semidirect
222. #1885	C₂×C₄₁	semidirect
223. #1860	C₂×C₄₁	semidirect
224. #1764	C₂×C₄₁	semidirect
237. #454	C₄×C₄₁	semidirect
261. C₄₁	#22895	direct (N × H)
264. 2₋¹⁺⁴	C₂×C₄×C₄₁	semidirect
272. AGL(1,ℤ/8)	C₂×C₄×C₄₁	semidirect
283. #124	C₂×C₄×C₄₁	semidirect
298. #104	C₂×C₄×C₄₁	semidirect
311. #101	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×#454	2
C₄₁×#2946	2
C₄₁×#2898	2
C₄₁×#1958	2
C₄₁×#1930	2
C₄₁×#1907	2
C₄₁×#1885	2
C₄₁×#1860	2
C₄₁×#1764	2
#22895	41

Subgroups — C41×#22895 #23799096

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#22895 #23799096