Subgroups — C₄₁×#18527 #23794728

Order 10496.

1176 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₁×#3481	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄₁×#3151	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₁×#3038	C₂	1	2	yes	maximal, complemented
4	C₄₁×#1622	C₂	1	4	yes	maximal, complemented
5	C₄₁×#1620	C₂	1	2	yes	maximal, complemented
6	C₄₁×#1619	C₂	1	2	yes	maximal, complemented
7	C₄₁×#1560	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄₁×#1489	C₂	1	2	yes	maximal, complemented
9	C₂×AGL(1,ℤ/8)×C₄₁	—	2	2	no	—
10	C₂×AGL(1,ℤ/8)×C₄₁	—	2	2	no	—
11	C₄₁×#559	C₂²	1	1	yes	characteristic, complemented
12	C₄₁×#554	C₂²	1	2	yes	complemented
13	C₄₁×#553	—	2	2	no	—
14	C₄₁×#551	—	2	2	no	—
15	C₄₁×#546	—	2	2	no	—
16	D₄²×C₄₁	C₂²	1	1	yes	characteristic, complemented
17	C₄₁×#532	C₂²	1	1	yes	characteristic
18	C₂×#127×C₄₁	C₂²	1	1	yes	characteristic, complemented
19	C₄₁×#529	—	2	2	no	—
20	C₄₁×#525	—	2	2	no	—
21	C₄×#41×C₄₁	C₂²	1	2	yes	—
22	C₂×C₄×D₄×C₄₁	—	2	2	no	—
23	C₄₁×#496	—	2	2	no	—
24	C₄₁×#493	C₂²	1	2	yes	—
25	C₄₁×#492	C₂²	1	2	yes	complemented
26	C₄₁×#460	—	2	2	no	—
27	C₄₁×#460	C₂²	1	4	yes	complemented
28	C₄₁×#459	—	2	2	no	—
29	C₄₁×#459	C₂²	1	4	yes	—
30	C₄₁×#423	C₂²	1	2	yes	complemented
31	C₄₁×#418	—	2	2	no	—
32	C₄×M₁₆×C₄₁	C₂²	1	1	yes	characteristic, complemented
33	C₄₁×#333	C₂²	1	2	yes	complemented
34	C₄₁×#331	C₂²	1	2	yes	complemented
35	C₄₁×Q₈⋊C₈	C₂²	1	4	yes	complemented
36	C₄₁×D₄⋊C₈	C₂²	1	4	yes	complemented
37	C₂×#41×C₄₁	D₄	1	2	yes	—
38	C₂×#41×C₄₁	D₄	1	2	yes	—
39	C₂²×D₄×C₄₁	—	2	2	no	—
40	C₂²×D₄×C₄₁	—	2	1	no	—
41	C₂²×D₄×C₄₁	—	2	2	no	—
42	C₂³×C₄×C₄₁	—	2	2	no	—
43	AGL(1,ℤ/8)×C₄₁	—	4	8	no	—
44	AGL(1,ℤ/8)×C₄₁	—	4	8	no	—
45	C₂×SD₁₆×C₄₁	—	2	4	no	—
46	C₂×SD₁₆×C₄₁	—	2	4	no	—
47	C₂×D₈×C₄₁	—	2	4	no	—
48	C₂×D₈×C₄₁	—	2	4	no	—
49	C₂×M₁₆×C₄₁	—	2	1	no	—
50	C₂×M₁₆×C₄₁	—	2	2	no	—
51	C₄⋊Q₈×C₄₁	C₂³	1	1	yes	characteristic
52	#127×C₄₁	—	2	2	no	—
53	#127×C₄₁	—	2	1	no	—
54	#127×C₄₁	C₂³	1	2	yes	—
55	#127×C₄₁	C₂³	1	1	yes	characteristic
56	#126×C₄₁	—	2	4	no	—
57	#125×C₄₁	—	2	2	no	—
58	#124×C₄₁	—	2	2	no	—
59	#124×C₄₁	D₄	1	2	yes	—
60	#123×C₄₁	—	2	2	no	—
61	#123×C₄₁	—	2	4	no	—
62	#123×C₄₁	—	2	2	no	—
63	C₂²⋊Q₈×C₄₁	—	2	4	no	—
64	C₂²⋊Q₈×C₄₁	—	2	2	no	—
65	#121×C₄₁	—	2	4	no	—
66	#121×C₄₁	—	2	2	no	—
67	#121×C₄₁	—	2	2	no	—
68	#120×C₄₁	—	2	2	no	—
69	#120×C₄₁	—	2	2	no	—
70	C₄×Q₈×C₄₁	D₄	1	2	yes	—
71	C₄×Q₈×C₄₁	C₂³	1	2	yes	—
72	C₄×D₄×C₄₁	—	2	4	no	—
73	C₄×D₄×C₄₁	—	2	4	no	—
74	C₄×D₄×C₄₁	—	2	2	no	—
75	C₄×D₄×C₄₁	—	2	2	no	—
76	C₄×D₄×C₄₁	—	2	2	no	—
77	C₄×D₄×C₄₁	—	2	2	no	—
78	C₄×D₄×C₄₁	—	2	2	no	—
79	C₄×D₄×C₄₁	D₄	1	2	yes	—
80	C₄×D₄×C₄₁	C₂³	1	2	yes	—
81	#117×C₄₁	—	2	2	no	—
82	#117×C₄₁	—	2	2	no	—
83	#117×C₄₁	D₄	1	2	yes	—
84	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
85	C₂×C₂²⋊C₄×C₄₁	—	2	4	no	—
86	C₂×C₄²×C₄₁	—	2	2	no	—
87	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
88	C₄⋊C₈×C₄₁	—	2	2	no	—
89	C₄⋊C₈×C₄₁	C₂³	1	4	yes	—
90	#102×C₄₁	—	2	4	no	—
91	#102×C₄₁	—	2	4	no	—
92	#97×C₄₁	—	2	1	no	—
93	C₄×C₈×C₄₁	C₂³	1	2	yes	—
94	C₂⁴×C₄₁	—	2	2	no	—
95	C₂⁴×C₄₁	—	4	1	no	—
96	#41×C₄₁	—	2	4	no	—
97	#41×C₄₁	—	4	2	no	—
98	#41×C₄₁	—	4	4	no	—
99	C₂×Q₈×C₄₁	C₂×D₄	1	2	yes	—
100	C₂×Q₈×C₄₁	C₂×D₄	1	2	yes	—
101	C₂×D₄×C₄₁	—	2	4	no	—
102	C₂×D₄×C₄₁	—	2	2	no	—
103	C₂×D₄×C₄₁	—	2	2	no	—
104	C₂×D₄×C₄₁	—	2	2	no	—
105	C₂×D₄×C₄₁	—	2	4	no	—
106	C₂×D₄×C₄₁	—	2	2	no	—
107	C₂×D₄×C₄₁	—	4	4	no	—
108	C₂×D₄×C₄₁	—	4	4	no	—
109	C₂×D₄×C₄₁	—	4	4	no	—
110	C₂×D₄×C₄₁	—	4	4	no	—
111	C₂×D₄×C₄₁	—	4	4	no	—
112	C₂×D₄×C₄₁	—	4	2	no	—
113	C₂×D₄×C₄₁	—	4	1	no	—
114	C₂×D₄×C₄₁	C₂×D₄	1	2	yes	—
115	C₂×D₄×C₄₁	C₂×D₄	1	2	yes	—
116	C₂²×C₄×C₄₁	—	2	4	no	—
117	C₂²×C₄×C₄₁	—	2	2	no	—
118	C₂²×C₄×C₄₁	—	2	2	no	—
119	C₂²×C₄×C₄₁	—	2	2	no	—
120	C₂²×C₄×C₄₁	—	2	2	no	—
121	C₂²×C₄×C₄₁	—	2	2	no	—
122	C₂²×C₄×C₄₁	—	8	4	no	—
123	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
124	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
125	SD₁₆×C₄₁	—	4	8	no	—
126	SD₁₆×C₄₁	—	4	8	no	—
127	D₈×C₄₁	—	4	8	no	—
128	D₈×C₄₁	—	4	8	no	—
129	M₁₆×C₄₁	—	2	4	no	—
130	M₁₆×C₄₁	—	4	4	no	—
131	C₂×C₈×C₄₁	—	2	2	no	—
132	C₂×C₈×C₄₁	—	2	4	no	—
133	C₄⋊C₄×C₄₁	—	2	4	no	—
134	C₄⋊C₄×C₄₁	—	2	4	no	—
135	C₄⋊C₄×C₄₁	—	2	2	no	—
136	C₄⋊C₄×C₄₁	—	2	2	no	—
137	C₄⋊C₄×C₄₁	—	2	2	no	—
138	C₄⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
139	C₄⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
140	C₂²⋊C₄×C₄₁	—	2	4	no	—
141	C₂²⋊C₄×C₄₁	—	2	4	no	—
142	C₂²⋊C₄×C₄₁	—	2	2	no	—
143	C₂²⋊C₄×C₄₁	—	2	2	no	—
144	C₂²⋊C₄×C₄₁	—	2	2	no	—
145	C₂²⋊C₄×C₄₁	—	2	2	no	—
146	C₂²⋊C₄×C₄₁	—	2	4	no	—
147	C₂²⋊C₄×C₄₁	—	2	2	no	—
148	C₄²×C₄₁	—	2	2	no	—
149	C₄²×C₄₁	—	2	2	no	—
150	C₄²×C₄₁	—	2	2	no	—
151	C₄²×C₄₁	C₂×D₄	1	1	yes	characteristic
152	C₄²×C₄₁	C₂×D₄	1	2	yes	—
153	C₄²×C₄₁	C₂⁴	1	1	yes	characteristic
154	C₂³×C₄₁	—	2	2	no	—
155	C₂³×C₄₁	—	2	2	no	—
156	C₂³×C₄₁	—	4	8	no	—
157	C₂³×C₄₁	—	4	2	no	—
158	C₂³×C₄₁	—	8	4	no	—
159	C₂³×C₄₁	—	8	2	no	—
160	C₂³×C₄₁	—	8	2	no	—
161	C₂³×C₄₁	#120	1	1	yes	characteristic
162	Q₈×C₄₁	—	2	2	no	—
163	Q₈×C₄₁	—	2	2	no	—
164	Q₈×C₄₁	—	4	2	no	—
165	D₄×C₄₁	—	2	2	no	—
166	D₄×C₄₁	—	4	2	no	—
167	D₄×C₄₁	—	4	4	no	—
168	D₄×C₄₁	—	4	4	no	—
169	D₄×C₄₁	—	4	8	no	—
170	D₄×C₄₁	—	4	2	no	—
171	D₄×C₄₁	—	4	4	no	—
172	D₄×C₄₁	—	4	2	no	—
173	D₄×C₄₁	—	4	4	no	—
174	D₄×C₄₁	—	8	4	no	—
175	D₄×C₄₁	—	8	2	no	—
176	D₄×C₄₁	—	8	2	no	—
177	D₄×C₄₁	AGL(1,ℤ/8)	1	4	yes	complemented
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	—	2	2	no	—
182	C₂×C₄×C₄₁	—	2	2	no	—
183	C₂×C₄×C₄₁	—	2	2	no	—
184	C₂×C₄×C₄₁	—	2	2	no	—
185	C₂×C₄×C₄₁	—	4	4	no	—
186	C₂×C₄×C₄₁	—	4	2	no	—
187	C₂×C₄×C₄₁	—	4	2	no	—
188	C₂×C₄×C₄₁	—	4	4	no	—
189	C₂×C₄×C₄₁	—	4	4	no	—
190	C₂×C₄×C₄₁	—	8	2	no	—
191	C₂×C₄×C₄₁	—	8	4	no	—
192	C₂×C₄×C₄₁	#120	1	2	yes	—
193	C₂×C₄×C₄₁	#120	1	1	yes	characteristic
194	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
195	C₂×C₄×C₄₁	C₂²×D₄	1	2	yes	—
196	C₈×C₄₁	—	2	4	no	—
197	C₈×C₄₁	—	4	4	no	—
198	#18527	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
199	C₂²×C₄₁	—	2	2	no	—
200	C₂²×C₄₁	—	2	4	no	—
201	C₂²×C₄₁	—	2	1	no	—
202	C₂²×C₄₁	—	4	2	no	—
203	C₂²×C₄₁	—	4	2	no	—
204	C₂²×C₄₁	—	4	4	no	—
205	C₂²×C₄₁	—	4	2	no	—
206	C₂²×C₄₁	—	8	8	no	—
207	C₂²×C₄₁	—	8	4	no	—
208	C₂²×C₄₁	—	8	2	no	—
209	C₂²×C₄₁	—	16	4	no	—
210	C₂²×C₄₁	C₂×#120	1	1	yes	characteristic
211	C₄×C₄₁	—	2	2	no	—
212	C₄×C₄₁	—	2	1	no	—
213	C₄×C₄₁	—	4	2	no	—
214	C₄×C₄₁	—	4	2	no	—
215	C₄×C₄₁	—	4	2	no	—
216	C₄×C₄₁	—	4	2	no	—
217	C₄×C₄₁	#453	1	2	yes	—
218	C₄×C₄₁	C₂×AGL(1,ℤ/8)	1	2	yes	—
219	C₄×C₄₁	#575	1	2	yes	—
220	#3481	C₂×C₄₁	1	1	yes	characteristic, complemented
221	#3151	C₂×C₄₁	1	1	yes	characteristic, complemented
222	#3038	C₂×C₄₁	1	2	yes	complemented
223	#1622	C₂×C₄₁	1	4	yes	complemented
224	#1620	C₂×C₄₁	1	2	yes	complemented
225	#1619	C₂×C₄₁	1	2	yes	complemented
226	#1560	C₂×C₄₁	1	1	yes	characteristic, complemented
227	#1489	C₂×C₄₁	1	2	yes	complemented
228	C₂×C₄₁	—	4	1	no	—
229	C₂×C₄₁	—	4	4	no	—
230	C₂×C₄₁	—	8	2	no	—
231	C₂×C₄₁	—	16	2	no	—
232	C₂×C₄₁	#3006	1	2	yes	—
233	C₂×C₄₁	C₂×#453	1	1	yes	characteristic
234	C₂×AGL(1,ℤ/8)	—	2	2	no	—
235	C₂×AGL(1,ℤ/8)	—	2	2	no	—
236	#559	C₂²×C₄₁	1	1	yes	characteristic, complemented
237	#554	C₂²×C₄₁	1	2	yes	complemented
238	#553	—	2	2	no	—
239	#551	—	2	2	no	—
240	#546	—	2	2	no	—
241	D₄²	C₂²×C₄₁	1	1	yes	characteristic, complemented
242	#532	C₂²×C₄₁	1	1	yes	characteristic
243	C₂×#127	C₂²×C₄₁	1	1	yes	characteristic, complemented
244	#529	—	2	2	no	—
245	#525	—	2	2	no	—
246	C₄×#41	C₂²×C₄₁	1	2	yes	—
247	C₂×C₄×D₄	—	2	2	no	—
248	#496	—	2	2	no	—
249	#493	C₂²×C₄₁	1	2	yes	—
250	#492	C₂²×C₄₁	1	2	yes	complemented
251	#460	—	2	2	no	—
252	#460	C₂²×C₄₁	1	4	yes	complemented
253	#459	—	2	2	no	—
254	#459	C₂²×C₄₁	1	4	yes	—
255	#423	C₂²×C₄₁	1	2	yes	complemented
256	#418	—	2	2	no	—
257	C₄×M₁₆	C₂²×C₄₁	1	1	yes	characteristic, complemented
258	#333	C₂²×C₄₁	1	2	yes	complemented
259	#331	C₂²×C₄₁	1	2	yes	complemented
260	Q₈⋊C₈	C₂²×C₄₁	1	4	yes	complemented
261	D₄⋊C₈	C₂²×C₄₁	1	4	yes	complemented
262	C₄₁	#18527	1	1	yes	characteristic, direct product factor, Sylow
263	C₂×#41	D₄×C₄₁	1	2	yes	—
264	C₂×#41	D₄×C₄₁	1	2	yes	—
265	C₂²×D₄	—	2	2	no	—
266	C₂²×D₄	—	2	1	no	—
267	C₂²×D₄	—	2	2	no	—
268	C₂³×C₄	—	2	2	no	—
269	AGL(1,ℤ/8)	—	4	8	no	—
270	AGL(1,ℤ/8)	—	4	8	no	—
271	C₂×SD₁₆	—	2	4	no	—
272	C₂×SD₁₆	—	2	4	no	—
273	C₂×D₈	—	2	4	no	—
274	C₂×D₈	—	2	4	no	—
275	C₂×M₁₆	—	2	1	no	—
276	C₂×M₁₆	—	2	2	no	—
277	C₄⋊Q₈	C₂³×C₄₁	1	1	yes	characteristic
278	#127	—	2	2	no	—
279	#127	—	2	1	no	—
280	#127	C₂³×C₄₁	1	2	yes	—
281	#127	C₂³×C₄₁	1	1	yes	characteristic
282	#126	—	2	4	no	—
283	#125	—	2	2	no	—
284	#124	—	2	2	no	—
285	#124	D₄×C₄₁	1	2	yes	—
286	#123	—	2	2	no	—
287	#123	—	2	4	no	—
288	#123	—	2	2	no	—
289	C₂²⋊Q₈	—	2	4	no	—
290	C₂²⋊Q₈	—	2	2	no	—
291	#121	—	2	4	no	—
292	#121	—	2	2	no	—
293	#121	—	2	2	no	—
294	#120	—	2	2	no	—
295	#120	—	2	2	no	—
296	C₄×Q₈	D₄×C₄₁	1	2	yes	—
297	C₄×Q₈	C₂³×C₄₁	1	2	yes	—
298	C₄×D₄	—	2	4	no	—
299	C₄×D₄	—	2	4	no	—
300	C₄×D₄	—	2	2	no	—
301	C₄×D₄	—	2	2	no	—
302	C₄×D₄	—	2	2	no	—
303	C₄×D₄	—	2	2	no	—
304	C₄×D₄	—	2	2	no	—
305	C₄×D₄	D₄×C₄₁	1	2	yes	—
306	C₄×D₄	C₂³×C₄₁	1	2	yes	—
307	#117	—	2	2	no	—
308	#117	—	2	2	no	—
309	#117	D₄×C₄₁	1	2	yes	—
310	C₂×C₄⋊C₄	—	2	2	no	—
311	C₂×C₂²⋊C₄	—	2	4	no	—
312	C₂×C₄²	—	2	2	no	—
313	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
314	C₄⋊C₈	—	2	2	no	—
315	C₄⋊C₈	C₂³×C₄₁	1	4	yes	—
316	#102	—	2	4	no	—
317	#102	—	2	4	no	—
318	#97	—	2	1	no	—
319	C₄×C₈	C₂³×C₄₁	1	2	yes	—
320	C₂⁴	—	2	2	no	—
321	C₂⁴	—	4	1	no	—
322	#41	—	2	4	no	—
323	#41	—	4	2	no	—
324	#41	—	4	4	no	—
325	C₂×Q₈	C₂×D₄×C₄₁	1	2	yes	—
326	C₂×Q₈	C₂×D₄×C₄₁	1	2	yes	—
327	C₂×D₄	—	2	4	no	—
328	C₂×D₄	—	2	2	no	—
329	C₂×D₄	—	2	2	no	—
330	C₂×D₄	—	2	2	no	—
331	C₂×D₄	—	2	4	no	—
332	C₂×D₄	—	2	2	no	—
333	C₂×D₄	—	4	4	no	—
334	C₂×D₄	—	4	4	no	—
335	C₂×D₄	—	4	4	no	—
336	C₂×D₄	—	4	4	no	—
337	C₂×D₄	—	4	4	no	—
338	C₂×D₄	—	4	2	no	—
339	C₂×D₄	—	4	1	no	—
340	C₂×D₄	C₂×D₄×C₄₁	1	2	yes	—
341	C₂×D₄	C₂×D₄×C₄₁	1	2	yes	—
342	C₂²×C₄	—	2	4	no	—
343	C₂²×C₄	—	2	2	no	—
344	C₂²×C₄	—	2	2	no	—
345	C₂²×C₄	—	2	2	no	—
346	C₂²×C₄	—	2	2	no	—
347	C₂²×C₄	—	2	2	no	—
348	C₂²×C₄	—	8	4	no	—
349	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
350	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
351	SD₁₆	—	4	8	no	—
352	SD₁₆	—	4	8	no	—
353	D₈	—	4	8	no	—
354	D₈	—	4	8	no	—
355	M₁₆	—	2	4	no	—
356	M₁₆	—	4	4	no	—
357	C₂×C₈	—	2	2	no	—
358	C₂×C₈	—	2	4	no	—
359	C₄⋊C₄	—	2	4	no	—
360	C₄⋊C₄	—	2	4	no	—
361	C₄⋊C₄	—	2	2	no	—
362	C₄⋊C₄	—	2	2	no	—
363	C₄⋊C₄	—	2	2	no	—
364	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
365	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
366	C₂²⋊C₄	—	2	4	no	—
367	C₂²⋊C₄	—	2	4	no	—
368	C₂²⋊C₄	—	2	2	no	—
369	C₂²⋊C₄	—	2	2	no	—
370	C₂²⋊C₄	—	2	2	no	—
371	C₂²⋊C₄	—	2	2	no	—
372	C₂²⋊C₄	—	2	4	no	—
373	C₂²⋊C₄	—	2	2	no	—
374	C₄²	—	2	2	no	—
375	C₄²	—	2	2	no	—
376	C₄²	—	2	2	no	—
377	C₄²	C₂×D₄×C₄₁	1	1	yes	characteristic
378	C₄²	C₂×D₄×C₄₁	1	2	yes	—
379	C₄²	C₂⁴×C₄₁	1	1	yes	characteristic
380	C₂³	—	2	2	no	—
381	C₂³	—	2	2	no	—
382	C₂³	—	4	8	no	—
383	C₂³	—	4	2	no	—
384	C₂³	—	8	4	no	—
385	C₂³	—	8	2	no	—
386	C₂³	—	8	2	no	—
387	C₂³	#120×C₄₁	1	1	yes	characteristic
388	Q₈	—	2	2	no	—
389	Q₈	—	2	2	no	—
390	Q₈	—	4	2	no	—
391	D₄	—	2	2	no	—
392	D₄	—	4	2	no	—
393	D₄	—	4	4	no	—
394	D₄	—	4	4	no	—
395	D₄	—	4	8	no	—
396	D₄	—	4	2	no	—
397	D₄	—	4	4	no	—
398	D₄	—	4	2	no	—
399	D₄	—	4	4	no	—
400	D₄	—	8	4	no	—
401	D₄	—	8	2	no	—
402	D₄	—	8	2	no	—
403	D₄	AGL(1,ℤ/8)×C₄₁	1	4	yes	complemented
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	—	4	4	no	—
412	C₂×C₄	—	4	2	no	—
413	C₂×C₄	—	4	2	no	—
414	C₂×C₄	—	4	4	no	—
415	C₂×C₄	—	4	4	no	—
416	C₂×C₄	—	8	2	no	—
417	C₂×C₄	—	8	4	no	—
418	C₂×C₄	#120×C₄₁	1	2	yes	—
419	C₂×C₄	#120×C₄₁	1	1	yes	characteristic
420	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
421	C₂×C₄	C₂²×D₄×C₄₁	1	2	yes	—
422	C₈	—	2	4	no	—
423	C₈	—	4	4	no	—
424	C₂²	—	2	2	no	—
425	C₂²	—	2	4	no	—
426	C₂²	—	2	1	no	—
427	C₂²	—	4	2	no	—
428	C₂²	—	4	2	no	—
429	C₂²	—	4	4	no	—
430	C₂²	—	4	2	no	—
431	C₂²	—	8	8	no	—
432	C₂²	—	8	4	no	—
433	C₂²	—	8	2	no	—
434	C₂²	—	16	4	no	—
435	C₂²	C₂×#120×C₄₁	1	1	yes	characteristic
436	C₄	—	2	2	no	—
437	C₄	—	2	1	no	—
438	C₄	—	4	2	no	—
439	C₄	—	4	2	no	—
440	C₄	—	4	2	no	—
441	C₄	—	4	2	no	—
442	C₄	C₄₁×#453	1	2	yes	—
443	C₄	C₂×AGL(1,ℤ/8)×C₄₁	1	2	yes	—
444	C₄	C₄₁×#575	1	2	yes	—
445	C₂	—	4	1	no	—
446	C₂	—	4	4	no	—
447	C₂	—	8	2	no	—
448	C₂	—	16	2	no	—
449	C₂	C₄₁×#3006	1	2	yes	—
450	C₂	C₂×C₄₁×#453	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₄₁	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₄₁
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₄₁ ◁ C₂×C₄²×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₄₁×#3481	C₂	semidirect
2. C₄₁×#3151	C₂	semidirect
3. C₄₁×#3038	C₂	semidirect
4. C₄₁×#1622	C₂	semidirect
5. C₄₁×#1620	C₂	semidirect
6. C₄₁×#1619	C₂	semidirect
7. C₄₁×#1560	C₂	semidirect
8. C₄₁×#1489	C₂	semidirect
11. C₄₁×#559	C₂²	semidirect
12. C₄₁×#554	C₂²	semidirect
16. D₄²×C₄₁	C₂²	semidirect
18. C₂×#127×C₄₁	C₂²	semidirect
25. C₄₁×#492	C₂²	semidirect
27. C₄₁×#460	C₂²	semidirect
30. C₄₁×#423	C₂²	semidirect
32. C₄×M₁₆×C₄₁	C₂²	semidirect
33. C₄₁×#333	C₂²	semidirect
34. C₄₁×#331	C₂²	semidirect
35. C₄₁×Q₈⋊C₈	C₂²	semidirect
36. C₄₁×D₄⋊C₈	C₂²	semidirect
177. D₄×C₄₁	AGL(1,ℤ/8)	semidirect
198. #18527	C₄₁	direct (N × H)
220. #3481	C₂×C₄₁	semidirect
221. #3151	C₂×C₄₁	semidirect
222. #3038	C₂×C₄₁	semidirect
223. #1622	C₂×C₄₁	semidirect
224. #1620	C₂×C₄₁	semidirect
225. #1619	C₂×C₄₁	semidirect
226. #1560	C₂×C₄₁	semidirect
227. #1489	C₂×C₄₁	semidirect
236. #559	C₂²×C₄₁	semidirect
237. #554	C₂²×C₄₁	semidirect
241. D₄²	C₂²×C₄₁	semidirect
243. C₂×#127	C₂²×C₄₁	semidirect
250. #492	C₂²×C₄₁	semidirect
252. #460	C₂²×C₄₁	semidirect
255. #423	C₂²×C₄₁	semidirect
257. C₄×M₁₆	C₂²×C₄₁	semidirect
258. #333	C₂²×C₄₁	semidirect
259. #331	C₂²×C₄₁	semidirect
260. Q₈⋊C₈	C₂²×C₄₁	semidirect
261. D₄⋊C₈	C₂²×C₄₁	semidirect
262. C₄₁	#18527	direct (N × H)
403. D₄	AGL(1,ℤ/8)×C₄₁	semidirect

Maximal subgroups

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

subgroup	index
C₄₁×#3481	2
C₄₁×#3151	2
C₄₁×#3038	2
C₄₁×#1622	2
C₄₁×#1620	2
C₄₁×#1619	2
C₄₁×#1560	2
C₄₁×#1489	2
#18527	41

Subgroups — C41×#18527 #23794728

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#18527 #23794728