Subgroups — C₄₁×#19257 #23795458

Order 10496.

716 conjugacy classes of subgroups.

The subgroup lattice has 480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₁×#3167	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄₁×#3110	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₁×#3109	C₂	1	1	yes	maximal, characteristic
4	C₂×C₈×D₄×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₁×#1683	C₂	1	2	yes	maximal, complemented
6	C₄₁×#1681	C₂	1	2	yes	maximal, complemented
7	C₄₁×#1671	C₂	1	2	yes	maximal, complemented
8	C₄₁×#1665	C₂	1	2	yes	maximal, complemented
9	C₄₁×#1568	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄₁×#1552	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₁×#1551	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂³×C₈×C₄₁	—	2	1	no	—
13	C₄₁×#533	C₂²	1	1	yes	characteristic
14	C₄₁×#532	C₂²	1	1	yes	characteristic
15	C₂×C₄×D₄×C₄₁	C₂²	1	1	yes	characteristic
16	C₄₁×#498	C₂²	1	1	yes	characteristic, complemented
17	C₄₁×#492	C₂²	1	1	yes	characteristic, complemented
18	C₄₁×#487	C₂²	1	1	yes	characteristic, complemented
19	C₄₁×#486	C₂²	1	1	yes	characteristic, complemented
20	C₄₁×#484	—	2	1	no	—
21	C₄₁×#481	—	2	1	no	—
22	C₄₁×#476	C₂²	1	2	yes	—
23	C₄₁×#474	C₂²	1	2	yes	—
24	C₄₁×#465	—	2	1	no	—
25	C₄₁×#465	—	2	1	no	—
26	C₄₁×#461	C₂²	1	2	yes	—
27	C₄₁×#459	C₂²	1	2	yes	—
28	C₄₁×#450	—	2	1	no	—
29	C₄₁×#447	—	2	1	no	—
30	C₄₁×#442	—	2	2	no	—
31	C₄₁×#440	—	2	2	no	—
32	C₄×SD₁₆×C₄₁	—	2	1	no	—
33	C₄×SD₁₆×C₄₁	—	2	1	no	—
34	C₈×D₄×C₄₁	—	2	1	no	—
35	C₈×D₄×C₄₁	—	2	1	no	—
36	C₈×D₄×C₄₁	C₂²	1	2	yes	—
37	C₈×D₄×C₄₁	C₂²	1	2	yes	—
38	C₄₁×#432	C₂²	1	1	yes	characteristic
39	C₄₁×#432	C₂²	1	1	yes	characteristic
40	C₂×C₄⋊C₈×C₄₁	C₂²	1	1	yes	characteristic
41	C₂×C₂²⋊C₈×C₄₁	—	2	1	no	—
42	C₂×C₄×C₈×C₄₁	C₂²	1	1	yes	characteristic
43	C₄₁×#335	C₂²	1	2	yes	complemented
44	C₄₁×#334	C₂²	1	2	yes	complemented
45	C₄₁×#333	C₂²	1	2	yes	complemented
46	C₄₁×#332	C₂²	1	2	yes	complemented
47	C₄₁×#332	C₂²	1	2	yes	complemented
48	C₄₁×#331	C₂²	1	2	yes	complemented
49	C₂×#41×C₄₁	—	2	1	no	—
50	C₂²×D₄×C₄₁	D₄	1	1	yes	characteristic
51	C₂³×C₄×C₄₁	—	2	1	no	—
52	C₂×SD₁₆×C₄₁	—	2	2	no	—
53	C₂×SD₁₆×C₄₁	—	2	1	no	—
54	C₂×SD₁₆×C₄₁	—	2	1	no	—
55	C₂×D₈×C₄₁	—	2	2	no	—
56	C₂²×C₈×C₄₁	—	2	1	no	—
57	C₂²×C₈×C₄₁	—	2	2	no	—
58	C₂²×C₈×C₄₁	—	2	2	no	—
59	C₂²×C₈×C₄₁	—	4	4	no	—
60	C₂²×C₈×C₄₁	D₄	1	1	yes	characteristic
61	C₂²×C₈×C₄₁	D₄	1	1	yes	characteristic
62	C₄⋊Q₈×C₄₁	C₂³	1	1	yes	characteristic
63	C₄⋊Q₈×C₄₁	C₂³	1	1	yes	characteristic
64	C₄⋊Q₈×C₄₁	C₂³	1	1	yes	characteristic
65	#127×C₄₁	C₂³	1	1	yes	characteristic
66	#125×C₄₁	—	2	1	no	—
67	#124×C₄₁	—	2	1	no	—
68	C₂²⋊Q₈×C₄₁	—	2	1	no	—
69	C₂²⋊Q₈×C₄₁	—	2	1	no	—
70	#121×C₄₁	—	2	1	no	—
71	#121×C₄₁	—	2	1	no	—
72	C₄×Q₈×C₄₁	—	2	1	no	—
73	C₄×Q₈×C₄₁	—	2	1	no	—
74	C₄×D₄×C₄₁	—	2	1	no	—
75	C₄×D₄×C₄₁	—	2	1	no	—
76	C₄×D₄×C₄₁	—	2	1	no	—
77	C₄×D₄×C₄₁	—	2	1	no	—
78	C₄×D₄×C₄₁	D₄	1	2	yes	—
79	C₄×D₄×C₄₁	C₂³	1	2	yes	—
80	#117×C₄₁	—	2	1	no	—
81	C₂×C₄⋊C₄×C₄₁	D₄	1	1	yes	characteristic
82	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
83	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
84	#107×C₄₁	—	2	2	no	—
85	#106×C₄₁	—	2	1	no	—
86	#106×C₄₁	—	2	1	no	—
87	#106×C₄₁	—	2	2	no	—
88	C₄⋊C₈×C₄₁	—	2	1	no	—
89	C₄⋊C₈×C₄₁	C₂³	1	2	yes	—
90	C₄⋊C₈×C₄₁	C₂³	1	2	yes	—
91	C₄⋊C₈×C₄₁	C₂³	1	2	yes	—
92	#103×C₄₁	—	2	1	no	—
93	#103×C₄₁	—	2	1	no	—
94	#103×C₄₁	—	2	2	no	—
95	#102×C₄₁	—	2	2	no	—
96	#102×C₄₁	—	2	2	no	—
97	#102×C₄₁	—	2	1	no	—
98	#102×C₄₁	—	2	1	no	—
99	#102×C₄₁	—	2	2	no	—
100	C₂²⋊C₈×C₄₁	—	2	1	no	—
101	C₂²⋊C₈×C₄₁	—	2	1	no	—
102	C₂²⋊C₈×C₄₁	—	2	2	no	—
103	C₂²⋊C₈×C₄₁	—	2	2	no	—
104	#97×C₄₁	—	2	1	no	—
105	#97×C₄₁	—	2	1	no	—
106	C₄×C₈×C₄₁	D₄	1	1	yes	characteristic
107	C₄×C₈×C₄₁	D₄	1	1	yes	characteristic
108	C₄×C₈×C₄₁	C₂³	1	1	yes	characteristic
109	C₄×C₈×C₄₁	C₂³	1	1	yes	characteristic
110	C₂⁴×C₄₁	—	2	1	no	—
111	#41×C₄₁	—	8	2	no	—
112	C₂×Q₈×C₄₁	—	2	1	no	—
113	C₂×Q₈×C₄₁	—	2	1	no	—
114	C₂×Q₈×C₄₁	—	2	1	no	—
115	C₂×D₄×C₄₁	—	2	4	no	—
116	C₂×D₄×C₄₁	—	2	1	no	—
117	C₂×D₄×C₄₁	—	2	1	no	—
118	C₂×D₄×C₄₁	—	2	1	no	—
119	C₂×D₄×C₄₁	—	2	1	no	—
120	C₂×D₄×C₄₁	—	4	1	no	—
121	C₂×D₄×C₄₁	C₂×D₄	1	2	yes	—
122	C₂²×C₄×C₄₁	—	2	1	no	—
123	C₂²×C₄×C₄₁	—	2	2	no	—
124	C₂²×C₄×C₄₁	—	2	2	no	—
125	C₂²×C₄×C₄₁	—	4	2	no	—
126	C₂²×C₄×C₄₁	—	4	2	no	—
127	C₂²×C₄×C₄₁	—	4	1	no	—
128	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
129	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
130	C₂²×C₄×C₄₁	#41	1	1	yes	characteristic
131	SD₁₆×C₄₁	—	4	2	no	—
132	SD₁₆×C₄₁	—	4	4	no	—
133	SD₁₆×C₄₁	—	4	2	no	—
134	D₈×C₄₁	—	4	4	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	—	2	2	no	—
139	C₂×C₈×C₄₁	—	4	1	no	—
140	C₂×C₈×C₄₁	—	4	4	no	—
141	C₂×C₈×C₄₁	—	4	2	no	—
142	C₂×C₈×C₄₁	—	4	4	no	—
143	C₂×C₈×C₄₁	C₂×D₄	1	1	yes	characteristic
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	C₄⋊C₄×C₄₁	—	2	1	no	—
148	C₄⋊C₄×C₄₁	—	2	1	no	—
149	C₄⋊C₄×C₄₁	—	2	1	no	—
150	C₄⋊C₄×C₄₁	—	2	1	no	—
151	C₄⋊C₄×C₄₁	—	2	1	no	—
152	C₄⋊C₄×C₄₁	—	2	1	no	—
153	C₄⋊C₄×C₄₁	—	2	1	no	—
154	C₄⋊C₄×C₄₁	—	4	1	no	—
155	C₄⋊C₄×C₄₁	—	4	1	no	—
156	C₄⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
157	C₂²⋊C₄×C₄₁	—	2	2	no	—
158	C₂²⋊C₄×C₄₁	—	2	2	no	—
159	C₂²⋊C₄×C₄₁	—	4	1	no	—
160	C₂²⋊C₄×C₄₁	—	4	1	no	—
161	C₂²⋊C₄×C₄₁	—	4	1	no	—
162	C₄²×C₄₁	—	4	1	no	—
163	C₄²×C₄₁	C₂×D₄	1	1	yes	characteristic
164	C₄²×C₄₁	C₂×D₄	1	1	yes	characteristic
165	C₄²×C₄₁	#41	1	1	yes	characteristic
166	C₄²×C₄₁	C₂⁴	1	1	yes	characteristic
167	C₂³×C₄₁	—	2	4	no	—
168	C₂³×C₄₁	—	2	2	no	—
169	C₂³×C₄₁	—	4	2	no	—
170	C₂³×C₄₁	—	4	2	no	—
171	C₂³×C₄₁	—	4	1	no	—
172	C₂³×C₄₁	#121	1	1	yes	characteristic
173	Q₈×C₄₁	—	4	2	no	—
174	Q₈×C₄₁	—	4	1	no	—
175	Q₈×C₄₁	—	4	1	no	—
176	Q₈×C₄₁	—	8	1	no	—
177	D₄×C₄₁	—	2	4	no	—
178	D₄×C₄₁	—	2	2	no	—
179	D₄×C₄₁	—	4	2	no	—
180	D₄×C₄₁	—	4	1	no	—
181	D₄×C₄₁	—	4	1	no	—
182	D₄×C₄₁	—	8	1	no	—
183	D₄×C₄₁	—	8	2	no	—
184	D₄×C₄₁	#135	1	4	yes	—
185	C₂×C₄×C₄₁	—	2	2	no	—
186	C₂×C₄×C₄₁	—	2	2	no	—
187	C₂×C₄×C₄₁	—	2	1	no	—
188	C₂×C₄×C₄₁	—	2	1	no	—
189	C₂×C₄×C₄₁	—	2	2	no	—
190	C₂×C₄×C₄₁	—	4	4	no	—
191	C₂×C₄×C₄₁	—	4	2	no	—
192	C₂×C₄×C₄₁	—	4	2	no	—
193	C₂×C₄×C₄₁	—	4	2	no	—
194	C₂×C₄×C₄₁	—	4	1	no	—
195	C₂×C₄×C₄₁	—	4	1	no	—
196	C₂×C₄×C₄₁	—	4	1	no	—
197	C₂×C₄×C₄₁	—	8	2	no	—
198	C₂×C₄×C₄₁	#121	1	1	yes	characteristic
199	C₂×C₄×C₄₁	#121	1	1	yes	characteristic
200	C₂×C₄×C₄₁	#121	1	1	yes	characteristic
201	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
202	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
203	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
204	C₈×C₄₁	—	2	1	no	—
205	C₈×C₄₁	—	2	1	no	—
206	C₈×C₄₁	—	2	1	no	—
207	C₈×C₄₁	—	4	2	no	—
208	C₈×C₄₁	—	4	2	no	—
209	C₈×C₄₁	—	4	2	no	—
210	C₈×C₄₁	AGL(1,ℤ/8)	1	2	yes	—
211	#19257	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
212	C₂²×C₄₁	—	2	1	no	—
213	C₂²×C₄₁	—	2	1	no	—
214	C₂²×C₄₁	—	2	4	no	—
215	C₂²×C₄₁	—	4	8	no	—
216	C₂²×C₄₁	—	4	2	no	—
217	C₂²×C₄₁	—	4	2	no	—
218	C₂²×C₄₁	—	8	1	no	—
219	C₂²×C₄₁	—	8	1	no	—
220	C₂²×C₄₁	—	8	1	no	—
221	C₂²×C₄₁	#471	1	2	yes	—
222	C₂²×C₄₁	C₂×#121	1	1	yes	characteristic
223	C₄×C₄₁	—	2	1	no	—
224	C₄×C₄₁	—	2	1	no	—
225	C₄×C₄₁	—	2	1	no	—
226	C₄×C₄₁	—	2	1	no	—
227	C₄×C₄₁	—	4	2	no	—
228	C₄×C₄₁	—	8	1	no	—
229	C₄×C₄₁	—	8	1	no	—
230	C₄×C₄₁	—	8	1	no	—
231	C₄×C₄₁	C₂×#135	1	2	yes	—
232	C₄×C₄₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
233	C₄×C₄₁	#575	1	1	yes	characteristic
234	#3167	C₂×C₄₁	1	1	yes	characteristic, complemented
235	#3110	C₂×C₄₁	1	1	yes	characteristic, complemented
236	#3109	C₂×C₄₁	1	1	yes	characteristic
237	C₂×C₈×D₄	C₂×C₄₁	1	1	yes	characteristic, complemented
238	#1683	C₂×C₄₁	1	2	yes	complemented
239	#1681	C₂×C₄₁	1	2	yes	complemented
240	#1671	C₂×C₄₁	1	2	yes	complemented
241	#1665	C₂×C₄₁	1	2	yes	complemented
242	#1568	C₂×C₄₁	1	1	yes	characteristic, complemented
243	#1552	C₂×C₄₁	1	1	yes	characteristic, complemented
244	#1551	C₂×C₄₁	1	1	yes	characteristic, complemented
245	C₂×C₄₁	—	2	2	no	—
246	C₂×C₄₁	—	4	4	no	—
247	C₂×C₄₁	—	16	1	no	—
248	C₂×C₄₁	#3036	1	1	yes	characteristic
249	C₂×C₄₁	#3050	1	1	yes	characteristic
250	C₂×C₄₁	C₂×#471	1	1	yes	characteristic
251	C₂³×C₈	—	2	1	no	—
252	#533	C₂²×C₄₁	1	1	yes	characteristic
253	#532	C₂²×C₄₁	1	1	yes	characteristic
254	C₂×C₄×D₄	C₂²×C₄₁	1	1	yes	characteristic
255	#498	C₂²×C₄₁	1	1	yes	characteristic, complemented
256	#492	C₂²×C₄₁	1	1	yes	characteristic, complemented
257	#487	C₂²×C₄₁	1	1	yes	characteristic, complemented
258	#486	C₂²×C₄₁	1	1	yes	characteristic, complemented
259	#484	—	2	1	no	—
260	#481	—	2	1	no	—
261	#476	C₂²×C₄₁	1	2	yes	—
262	#474	C₂²×C₄₁	1	2	yes	—
263	#465	—	2	1	no	—
264	#465	—	2	1	no	—
265	#461	C₂²×C₄₁	1	2	yes	—
266	#459	C₂²×C₄₁	1	2	yes	—
267	#450	—	2	1	no	—
268	#447	—	2	1	no	—
269	#442	—	2	2	no	—
270	#440	—	2	2	no	—
271	C₄×SD₁₆	—	2	1	no	—
272	C₄×SD₁₆	—	2	1	no	—
273	C₈×D₄	—	2	1	no	—
274	C₈×D₄	—	2	1	no	—
275	C₈×D₄	C₂²×C₄₁	1	2	yes	—
276	C₈×D₄	C₂²×C₄₁	1	2	yes	—
277	#432	C₂²×C₄₁	1	1	yes	characteristic
278	#432	C₂²×C₄₁	1	1	yes	characteristic
279	C₂×C₄⋊C₈	C₂²×C₄₁	1	1	yes	characteristic
280	C₂×C₂²⋊C₈	—	2	1	no	—
281	C₂×C₄×C₈	C₂²×C₄₁	1	1	yes	characteristic
282	#335	C₂²×C₄₁	1	2	yes	complemented
283	#334	C₂²×C₄₁	1	2	yes	complemented
284	#333	C₂²×C₄₁	1	2	yes	complemented
285	#332	C₂²×C₄₁	1	2	yes	complemented
286	#332	C₂²×C₄₁	1	2	yes	complemented
287	#331	C₂²×C₄₁	1	2	yes	complemented
288	C₄₁	#19257	1	1	yes	characteristic, direct product factor, Sylow
289	C₂×#41	—	2	1	no	—
290	C₂²×D₄	D₄×C₄₁	1	1	yes	characteristic
291	C₂³×C₄	—	2	1	no	—
292	C₂×SD₁₆	—	2	2	no	—
293	C₂×SD₁₆	—	2	1	no	—
294	C₂×SD₁₆	—	2	1	no	—
295	C₂×D₈	—	2	2	no	—
296	C₂²×C₈	—	2	1	no	—
297	C₂²×C₈	—	2	2	no	—
298	C₂²×C₈	—	2	2	no	—
299	C₂²×C₈	—	4	4	no	—
300	C₂²×C₈	D₄×C₄₁	1	1	yes	characteristic
301	C₂²×C₈	D₄×C₄₁	1	1	yes	characteristic
302	C₄⋊Q₈	C₂³×C₄₁	1	1	yes	characteristic
303	C₄⋊Q₈	C₂³×C₄₁	1	1	yes	characteristic
304	C₄⋊Q₈	C₂³×C₄₁	1	1	yes	characteristic
305	#127	C₂³×C₄₁	1	1	yes	characteristic
306	#125	—	2	1	no	—
307	#124	—	2	1	no	—
308	C₂²⋊Q₈	—	2	1	no	—
309	C₂²⋊Q₈	—	2	1	no	—
310	#121	—	2	1	no	—
311	#121	—	2	1	no	—
312	C₄×Q₈	—	2	1	no	—
313	C₄×Q₈	—	2	1	no	—
314	C₄×D₄	—	2	1	no	—
315	C₄×D₄	—	2	1	no	—
316	C₄×D₄	—	2	1	no	—
317	C₄×D₄	—	2	1	no	—
318	C₄×D₄	D₄×C₄₁	1	2	yes	—
319	C₄×D₄	C₂³×C₄₁	1	2	yes	—
320	#117	—	2	1	no	—
321	C₂×C₄⋊C₄	D₄×C₄₁	1	1	yes	characteristic
322	C₂×C₂²⋊C₄	—	2	1	no	—
323	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
324	#107	—	2	2	no	—
325	#106	—	2	1	no	—
326	#106	—	2	1	no	—
327	#106	—	2	2	no	—
328	C₄⋊C₈	—	2	1	no	—
329	C₄⋊C₈	C₂³×C₄₁	1	2	yes	—
330	C₄⋊C₈	C₂³×C₄₁	1	2	yes	—
331	C₄⋊C₈	C₂³×C₄₁	1	2	yes	—
332	#103	—	2	1	no	—
333	#103	—	2	1	no	—
334	#103	—	2	2	no	—
335	#102	—	2	2	no	—
336	#102	—	2	2	no	—
337	#102	—	2	1	no	—
338	#102	—	2	1	no	—
339	#102	—	2	2	no	—
340	C₂²⋊C₈	—	2	1	no	—
341	C₂²⋊C₈	—	2	1	no	—
342	C₂²⋊C₈	—	2	2	no	—
343	C₂²⋊C₈	—	2	2	no	—
344	#97	—	2	1	no	—
345	#97	—	2	1	no	—
346	C₄×C₈	D₄×C₄₁	1	1	yes	characteristic
347	C₄×C₈	D₄×C₄₁	1	1	yes	characteristic
348	C₄×C₈	C₂³×C₄₁	1	1	yes	characteristic
349	C₄×C₈	C₂³×C₄₁	1	1	yes	characteristic
350	C₂⁴	—	2	1	no	—
351	#41	—	8	2	no	—
352	C₂×Q₈	—	2	1	no	—
353	C₂×Q₈	—	2	1	no	—
354	C₂×Q₈	—	2	1	no	—
355	C₂×D₄	—	2	4	no	—
356	C₂×D₄	—	2	1	no	—
357	C₂×D₄	—	2	1	no	—
358	C₂×D₄	—	2	1	no	—
359	C₂×D₄	—	2	1	no	—
360	C₂×D₄	—	4	1	no	—
361	C₂×D₄	C₂×D₄×C₄₁	1	2	yes	—
362	C₂²×C₄	—	2	1	no	—
363	C₂²×C₄	—	2	2	no	—
364	C₂²×C₄	—	2	2	no	—
365	C₂²×C₄	—	4	2	no	—
366	C₂²×C₄	—	4	2	no	—
367	C₂²×C₄	—	4	1	no	—
368	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
369	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
370	C₂²×C₄	#41×C₄₁	1	1	yes	characteristic
371	SD₁₆	—	4	2	no	—
372	SD₁₆	—	4	4	no	—
373	SD₁₆	—	4	2	no	—
374	D₈	—	4	4	no	—
375	C₂×C₈	—	2	2	no	—
376	C₂×C₈	—	2	2	no	—
377	C₂×C₈	—	2	2	no	—
378	C₂×C₈	—	2	2	no	—
379	C₂×C₈	—	4	1	no	—
380	C₂×C₈	—	4	4	no	—
381	C₂×C₈	—	4	2	no	—
382	C₂×C₈	—	4	4	no	—
383	C₂×C₈	C₂×D₄×C₄₁	1	1	yes	characteristic
384	C₂×C₈	C₂×D₄×C₄₁	1	1	yes	characteristic
385	C₂×C₈	C₂×D₄×C₄₁	1	1	yes	characteristic
386	C₂×C₈	C₂×D₄×C₄₁	1	1	yes	characteristic
387	C₄⋊C₄	—	2	1	no	—
388	C₄⋊C₄	—	2	1	no	—
389	C₄⋊C₄	—	2	1	no	—
390	C₄⋊C₄	—	2	1	no	—
391	C₄⋊C₄	—	2	1	no	—
392	C₄⋊C₄	—	2	1	no	—
393	C₄⋊C₄	—	2	1	no	—
394	C₄⋊C₄	—	4	1	no	—
395	C₄⋊C₄	—	4	1	no	—
396	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
397	C₂²⋊C₄	—	2	2	no	—
398	C₂²⋊C₄	—	2	2	no	—
399	C₂²⋊C₄	—	4	1	no	—
400	C₂²⋊C₄	—	4	1	no	—
401	C₂²⋊C₄	—	4	1	no	—
402	C₄²	—	4	1	no	—
403	C₄²	C₂×D₄×C₄₁	1	1	yes	characteristic
404	C₄²	C₂×D₄×C₄₁	1	1	yes	characteristic
405	C₄²	#41×C₄₁	1	1	yes	characteristic
406	C₄²	C₂⁴×C₄₁	1	1	yes	characteristic
407	C₂³	—	2	4	no	—
408	C₂³	—	2	2	no	—
409	C₂³	—	4	2	no	—
410	C₂³	—	4	2	no	—
411	C₂³	—	4	1	no	—
412	C₂³	#121×C₄₁	1	1	yes	characteristic
413	Q₈	—	4	2	no	—
414	Q₈	—	4	1	no	—
415	Q₈	—	4	1	no	—
416	Q₈	—	8	1	no	—
417	D₄	—	2	4	no	—
418	D₄	—	2	2	no	—
419	D₄	—	4	2	no	—
420	D₄	—	4	1	no	—
421	D₄	—	4	1	no	—
422	D₄	—	8	1	no	—
423	D₄	—	8	2	no	—
424	D₄	#135×C₄₁	1	4	yes	—
425	C₂×C₄	—	2	2	no	—
426	C₂×C₄	—	2	2	no	—
427	C₂×C₄	—	2	1	no	—
428	C₂×C₄	—	2	1	no	—
429	C₂×C₄	—	2	2	no	—
430	C₂×C₄	—	4	4	no	—
431	C₂×C₄	—	4	2	no	—
432	C₂×C₄	—	4	2	no	—
433	C₂×C₄	—	4	2	no	—
434	C₂×C₄	—	4	1	no	—
435	C₂×C₄	—	4	1	no	—
436	C₂×C₄	—	4	1	no	—
437	C₂×C₄	—	8	2	no	—
438	C₂×C₄	#121×C₄₁	1	1	yes	characteristic
439	C₂×C₄	#121×C₄₁	1	1	yes	characteristic
440	C₂×C₄	#121×C₄₁	1	1	yes	characteristic
441	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
442	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
443	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
444	C₈	—	2	1	no	—
445	C₈	—	2	1	no	—
446	C₈	—	2	1	no	—
447	C₈	—	4	2	no	—
448	C₈	—	4	2	no	—
449	C₈	—	4	2	no	—
450	C₈	AGL(1,ℤ/8)×C₄₁	1	2	yes	—
451	C₂²	—	2	1	no	—
452	C₂²	—	2	1	no	—
453	C₂²	—	2	4	no	—
454	C₂²	—	4	8	no	—
455	C₂²	—	4	2	no	—
456	C₂²	—	4	2	no	—
457	C₂²	—	8	1	no	—
458	C₂²	—	8	1	no	—
459	C₂²	—	8	1	no	—
460	C₂²	C₄₁×#471	1	2	yes	—
461	C₂²	C₂×#121×C₄₁	1	1	yes	characteristic
462	C₄	—	2	1	no	—
463	C₄	—	2	1	no	—
464	C₄	—	2	1	no	—
465	C₄	—	2	1	no	—
466	C₄	—	4	2	no	—
467	C₄	—	8	1	no	—
468	C₄	—	8	1	no	—
469	C₄	—	8	1	no	—
470	C₄	C₂×#135×C₄₁	1	2	yes	—
471	C₄	C₂×AGL(1,ℤ/8)×C₄₁	1	1	yes	characteristic
472	C₄	C₄₁×#575	1	1	yes	characteristic
473	C₂	—	2	2	no	—
474	C₂	—	4	4	no	—
475	C₂	—	16	1	no	—
476	C₂	C₄₁×#3036	1	1	yes	characteristic
477	C₂	C₄₁×#3050	1	1	yes	characteristic
478	C₂	C₂×C₄₁×#471	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₄₁	C₂×#121
commutator, Frattini, cosocle	C₄²	C₂⁴×C₄₁
prime radical	C₄₁×#3109	C₂
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×#3167	C₂	semidirect
2. C₄₁×#3110	C₂	semidirect
4. C₂×C₈×D₄×C₄₁	C₂	semidirect
5. C₄₁×#1683	C₂	semidirect
6. C₄₁×#1681	C₂	semidirect
7. C₄₁×#1671	C₂	semidirect
8. C₄₁×#1665	C₂	semidirect
9. C₄₁×#1568	C₂	semidirect
10. C₄₁×#1552	C₂	semidirect
11. C₄₁×#1551	C₂	semidirect
16. C₄₁×#498	C₂²	semidirect
17. C₄₁×#492	C₂²	semidirect
18. C₄₁×#487	C₂²	semidirect
19. C₄₁×#486	C₂²	semidirect
43. C₄₁×#335	C₂²	semidirect
44. C₄₁×#334	C₂²	semidirect
45. C₄₁×#333	C₂²	semidirect
46. C₄₁×#332	C₂²	semidirect
47. C₄₁×#332	C₂²	semidirect
48. C₄₁×#331	C₂²	semidirect
211. #19257	C₄₁	direct (N × H)
234. #3167	C₂×C₄₁	semidirect
235. #3110	C₂×C₄₁	semidirect
237. C₂×C₈×D₄	C₂×C₄₁	semidirect
238. #1683	C₂×C₄₁	semidirect
239. #1681	C₂×C₄₁	semidirect
240. #1671	C₂×C₄₁	semidirect
241. #1665	C₂×C₄₁	semidirect
242. #1568	C₂×C₄₁	semidirect
243. #1552	C₂×C₄₁	semidirect
244. #1551	C₂×C₄₁	semidirect
255. #498	C₂²×C₄₁	semidirect
256. #492	C₂²×C₄₁	semidirect
257. #487	C₂²×C₄₁	semidirect
258. #486	C₂²×C₄₁	semidirect
282. #335	C₂²×C₄₁	semidirect
283. #334	C₂²×C₄₁	semidirect
284. #333	C₂²×C₄₁	semidirect
285. #332	C₂²×C₄₁	semidirect
286. #332	C₂²×C₄₁	semidirect
287. #331	C₂²×C₄₁	semidirect
288. C₄₁	#19257	direct (N × H)

Maximal subgroups

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

subgroup	index
C₄₁×#3167	2
C₄₁×#3110	2
C₄₁×#3109	2
C₂×C₈×D₄×C₄₁	2
C₄₁×#1683	2
C₄₁×#1681	2
C₄₁×#1671	2
C₄₁×#1665	2
C₄₁×#1568	2
C₄₁×#1552	2
C₄₁×#1551	2
#19257	41

Subgroups — C41×#19257 #23795458

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#19257 #23795458