Subgroups — C₄₁×#61932 #23838133

Order 10496.

1866 conjugacy classes of subgroups.

The subgroup lattice has 494 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₁×#3548	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄₁×#3508	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₁×#3399	C₂	1	4	yes	maximal, complemented
4	C₄₁×#3391	C₂	1	4	yes	maximal, complemented
5	C₄₁×#3366	C₂	1	4	yes	maximal, complemented
6	C₄₁×#3361	C₂	1	4	yes	maximal, complemented
7	C₄₁×#3220	C₂	1	4	yes	maximal, complemented
8	C₄₁×#3205	C₂	1	2	yes	maximal, complemented
9	C₄₁×#3122	C₂	1	4	yes	maximal, complemented
10	C₄₁×#3106	C₂	1	2	yes	maximal, complemented
11	C₄₁×#2986	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄₁×#562	—	2	2	no	—
13	C₄₁×#559	C₂²	1	4	yes	—
14	C₄₁×#554	C₂²	1	4	yes	complemented
15	C₄₁×#550	C₂²	1	4	yes	—
16	C₄₁×#550	C₂²	1	4	yes	complemented
17	C₄₁×#547	—	2	2	no	—
18	C₄₁×#546	—	2	4	no	—
19	C₄₁×#540	—	2	2	no	—
20	C₄₁×#540	C₂²	1	4	yes	—
21	C₄₁×#537	—	2	4	no	—
22	C₄₁×#535	C₂²	1	2	yes	—
23	C₄₁×#533	C₂²	1	1	yes	characteristic
24	C₄₁×#532	—	2	2	no	—
25	C₄₁×#532	C₂²	1	2	yes	—
26	C₂×#127×C₄₁	C₂²	1	1	yes	characteristic
27	C₄₁×#518	C₂²	1	2	yes	—
28	C₄×#41×C₄₁	C₂²	1	1	yes	characteristic
29	C₄₁×#496	C₂²	1	4	yes	complemented
30	C₄₁×#493	C₂²	1	4	yes	—
31	C₄₁×#493	C₂²	1	4	yes	complemented
32	C₄₁×#490	C₂²	1	4	yes	complemented
33	C₄₁×#488	C₂²	1	4	yes	complemented
34	C₄₁×#486	C₂²	1	4	yes	—
35	C₄₁×#482	C₂²	1	4	yes	—
36	C₄₁×#478	C₂²	1	8	yes	complemented
37	C₄₁×#477	C₂²	1	2	yes	complemented
38	C₄₁×#476	C₂²	1	2	yes	complemented
39	C₄₁×#463	C₂²	1	8	yes	complemented
40	C₄₁×#460	C₂²	1	2	yes	complemented
41	C₄₁×#459	C₂²	1	4	yes	—
42	C₄₁×#459	C₂²	1	4	yes	—
43	C₄₁×#459	C₂²	1	2	yes	complemented
44	C₄₁×#459	C₂²	1	8	yes	complemented
45	C₄₁×#459	C₂²	1	8	yes	complemented
46	C₄₁×#449	C₂²	1	4	yes	—
47	C₄₁×#447	C₂²	1	8	yes	—
48	C₄₁×#446	C₂²	1	4	yes	complemented
49	C₈×Q₈×C₄₁	C₂²	1	4	yes	complemented
50	C₄₁×#442	C₂²	1	8	yes	complemented
51	C₄×SD₁₆×C₄₁	C₂²	1	4	yes	complemented
52	C₄×D₈×C₄₁	C₂²	1	8	yes	complemented
53	C₄×D₈×C₄₁	C₂²	1	4	yes	complemented
54	C₄₁×#433	C₂²	1	4	yes	—
55	C₄₁×#431	C₂²	1	2	yes	—
56	C₂×#41×C₄₁	—	2	4	no	—
57	C₂×#41×C₄₁	—	2	4	no	—
58	C₂×#41×C₄₁	—	2	2	no	—
59	C₂×#41×C₄₁	C₂³	1	1	yes	characteristic
60	C₂²×D₄×C₄₁	—	2	2	no	—
61	C₂²×D₄×C₄₁	C₂³	1	2	yes	—
62	C₂×SD₁₆×C₄₁	C₂³	1	4	yes	—
63	C₂×D₈×C₄₁	C₂³	1	8	yes	—
64	C₂×D₈×C₄₁	C₂³	1	4	yes	—
65	C₂×D₈×C₄₁	C₂³	1	8	yes	—
66	C₄⋊Q₈×C₄₁	D₄	1	2	yes	—
67	C₄⋊Q₈×C₄₁	C₂³	1	2	yes	—
68	#127×C₄₁	—	2	1	no	—
69	#127×C₄₁	—	2	1	no	—
70	#127×C₄₁	C₂³	1	4	yes	—
71	#127×C₄₁	C₂³	1	2	yes	—
72	#127×C₄₁	C₂³	1	4	yes	—
73	#127×C₄₁	C₂³	1	4	yes	—
74	#125×C₄₁	D₄	1	2	yes	—
75	#125×C₄₁	C₂³	1	4	yes	—
76	#124×C₄₁	—	2	4	no	—
77	#124×C₄₁	—	2	2	no	—
78	#124×C₄₁	C₂³	1	4	yes	—
79	#123×C₄₁	—	2	8	no	—
80	#123×C₄₁	—	2	8	no	—
81	C₂²⋊Q₈×C₄₁	—	2	4	no	—
82	C₂²⋊Q₈×C₄₁	—	2	8	no	—
83	C₂²⋊Q₈×C₄₁	D₄	1	4	yes	—
84	#121×C₄₁	—	2	2	no	—
85	#121×C₄₁	—	2	4	no	—
86	#121×C₄₁	—	2	4	no	—
87	#121×C₄₁	—	2	4	no	—
88	#121×C₄₁	—	2	8	no	—
89	#121×C₄₁	—	2	8	no	—
90	#121×C₄₁	—	2	8	no	—
91	#121×C₄₁	C₂³	1	4	yes	—
92	#120×C₄₁	—	2	4	no	—
93	C₄×Q₈×C₄₁	C₂³	1	2	yes	—
94	C₄×Q₈×C₄₁	C₂³	1	4	yes	—
95	C₄×D₄×C₄₁	—	2	2	no	—
96	C₄×D₄×C₄₁	—	2	4	no	—
97	C₄×D₄×C₄₁	—	2	4	no	—
98	C₄×D₄×C₄₁	—	2	2	no	—
99	C₄×D₄×C₄₁	C₂³	1	2	yes	—
100	C₄×D₄×C₄₁	C₂³	1	8	yes	—
101	C₄×D₄×C₄₁	C₂³	1	4	yes	—
102	C₄×D₄×C₄₁	C₂³	1	8	yes	—
103	#117×C₄₁	—	2	1	no	—
104	#117×C₄₁	C₂³	1	1	yes	characteristic
105	#117×C₄₁	C₂³	1	2	yes	—
106	C₂×C₄⋊C₄×C₄₁	—	2	4	no	—
107	C₂×C₂²⋊C₄×C₄₁	—	2	4	no	—
108	C₂×C₄²×C₄₁	—	2	1	no	—
109	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
110	#107×C₄₁	C₂³	1	4	yes	—
111	#106×C₄₁	C₂³	1	4	yes	—
112	C₄⋊C₈×C₄₁	C₂³	1	2	yes	—
113	C₄⋊C₈×C₄₁	C₂³	1	2	yes	—
114	C₄⋊C₈×C₄₁	C₂³	1	8	yes	—
115	#103×C₄₁	C₂³	1	4	yes	—
116	#102×C₄₁	C₂³	1	4	yes	—
117	#102×C₄₁	C₂³	1	4	yes	—
118	#102×C₄₁	C₂³	1	8	yes	—
119	#102×C₄₁	C₂³	1	4	yes	—
120	#102×C₄₁	C₂³	1	8	yes	—
121	C₂²⋊C₈×C₄₁	C₂³	1	4	yes	—
122	#97×C₄₁	C₂³	1	4	yes	—
123	C₄×C₈×C₄₁	C₂³	1	4	yes	—
124	C₄×C₈×C₄₁	C₂³	1	4	yes	—
125	C₂⁴×C₄₁	—	2	2	no	—
126	#41×C₄₁	—	4	2	no	—
127	#41×C₄₁	—	8	4	no	—
128	#41×C₄₁	—	8	8	no	—
129	#41×C₄₁	—	8	8	no	—
130	C₂×Q₈×C₄₁	—	2	2	no	—
131	C₂×Q₈×C₄₁	C₂×D₄	1	4	yes	—
132	C₂×Q₈×C₄₁	C₂⁴	1	1	yes	characteristic
133	C₂×D₄×C₄₁	—	2	1	no	—
134	C₂×D₄×C₄₁	—	2	4	no	—
135	C₂×D₄×C₄₁	—	2	2	no	—
136	C₂×D₄×C₄₁	—	2	2	no	—
137	C₂×D₄×C₄₁	—	2	4	no	—
138	C₂×D₄×C₄₁	—	2	8	no	—
139	C₂×D₄×C₄₁	—	2	8	no	—
140	C₂×D₄×C₄₁	—	2	2	no	—
141	C₂×D₄×C₄₁	—	2	4	no	—
142	C₂×D₄×C₄₁	—	4	4	no	—
143	C₂×D₄×C₄₁	—	8	4	no	—
144	C₂×D₄×C₄₁	C₂⁴	1	4	yes	—
145	C₂×D₄×C₄₁	C₂⁴	1	1	yes	characteristic
146	C₂×D₄×C₄₁	C₂⁴	1	4	yes	—
147	C₂²×C₄×C₄₁	—	2	1	no	—
148	C₂²×C₄×C₄₁	—	2	2	no	—
149	C₂²×C₄×C₄₁	—	2	4	no	—
150	C₂²×C₄×C₄₁	—	2	8	no	—
151	C₂²×C₄×C₄₁	—	2	8	no	—
152	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
153	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
154	SD₁₆×C₄₁	—	4	4	no	—
155	D₈×C₄₁	—	4	4	no	—
156	D₈×C₄₁	—	4	8	no	—
157	D₈×C₄₁	—	4	8	no	—
158	C₂×C₈×C₄₁	C₂⁴	1	4	yes	—
159	C₂×C₈×C₄₁	C₂⁴	1	4	yes	—
160	C₄⋊C₄×C₄₁	—	2	2	no	—
161	C₄⋊C₄×C₄₁	—	2	8	no	—
162	C₄⋊C₄×C₄₁	—	2	2	no	—
163	C₄⋊C₄×C₄₁	C₂×D₄	1	4	yes	—
164	C₄⋊C₄×C₄₁	C₂×D₄	1	4	yes	—
165	C₄⋊C₄×C₄₁	C₂×D₄	1	8	yes	—
166	C₄⋊C₄×C₄₁	C₂⁴	1	4	yes	—
167	C₄⋊C₄×C₄₁	C₂⁴	1	2	yes	—
168	C₂²⋊C₄×C₄₁	—	2	1	no	—
169	C₂²⋊C₄×C₄₁	—	2	8	no	—
170	C₂²⋊C₄×C₄₁	—	2	2	no	—
171	C₂²⋊C₄×C₄₁	—	2	8	no	—
172	C₂²⋊C₄×C₄₁	—	2	4	no	—
173	C₂²⋊C₄×C₄₁	—	2	8	no	—
174	C₂²⋊C₄×C₄₁	—	2	4	no	—
175	C₂²⋊C₄×C₄₁	C₂×D₄	1	4	yes	—
176	C₄²×C₄₁	—	2	1	no	—
177	C₄²×C₄₁	—	2	2	no	—
178	C₄²×C₄₁	C₂×D₄	1	1	yes	characteristic
179	C₄²×C₄₁	C₂×D₄	1	1	yes	characteristic
180	C₄²×C₄₁	C₂⁴	1	2	yes	—
181	C₄²×C₄₁	C₂⁴	1	4	yes	—
182	C₂³×C₄₁	—	2	4	no	—
183	C₂³×C₄₁	—	2	4	no	—
184	C₂³×C₄₁	—	2	1	no	—
185	C₂³×C₄₁	—	4	4	no	—
186	C₂³×C₄₁	—	8	4	no	—
187	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
188	Q₈×C₄₁	—	2	8	no	—
189	Q₈×C₄₁	—	2	2	no	—
190	Q₈×C₄₁	—	8	2	no	—
191	D₄×C₄₁	—	2	4	no	—
192	D₄×C₄₁	—	2	4	no	—
193	D₄×C₄₁	—	2	8	no	—
194	D₄×C₄₁	—	2	2	no	—
195	D₄×C₄₁	—	4	4	no	—
196	D₄×C₄₁	—	4	2	no	—
197	D₄×C₄₁	—	4	8	no	—
198	D₄×C₄₁	—	4	4	no	—
199	D₄×C₄₁	—	8	4	no	—
200	D₄×C₄₁	—	8	2	no	—
201	D₄×C₄₁	—	8	8	no	—
202	D₄×C₄₁	—	8	8	no	—
203	D₄×C₄₁	—	8	4	no	—
204	C₂×C₄×C₄₁	—	2	4	no	—
205	C₂×C₄×C₄₁	—	2	2	no	—
206	C₂×C₄×C₄₁	—	2	1	no	—
207	C₂×C₄×C₄₁	—	2	2	no	—
208	C₂×C₄×C₄₁	—	2	4	no	—
209	C₂×C₄×C₄₁	—	4	2	no	—
210	C₂×C₄×C₄₁	—	4	4	no	—
211	C₂×C₄×C₄₁	—	4	8	no	—
212	C₂×C₄×C₄₁	—	8	8	no	—
213	C₂×C₄×C₄₁	—	8	8	no	—
214	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
215	C₂×C₄×C₄₁	C₂²×D₄	1	2	yes	—
216	C₂×C₄×C₄₁	C₂²×D₄	1	8	yes	—
217	C₂×C₄×C₄₁	C₂²×D₄	1	2	yes	—
218	C₂×C₄×C₄₁	C₂⁵	1	1	yes	characteristic
219	C₈×C₄₁	—	2	4	no	—
220	C₈×C₄₁	—	2	4	no	—
221	#61932	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
222	C₂²×C₄₁	—	2	1	no	—
223	C₂²×C₄₁	—	2	2	no	—
224	C₂²×C₄₁	—	4	1	no	—
225	C₂²×C₄₁	—	4	4	no	—
226	C₂²×C₄₁	—	4	4	no	—
227	C₂²×C₄₁	—	4	2	no	—
228	C₂²×C₄₁	—	4	4	no	—
229	C₂²×C₄₁	—	4	4	no	—
230	C₂²×C₄₁	—	4	8	no	—
231	C₂²×C₄₁	—	16	4	no	—
232	C₂²×C₄₁	C₂³×D₄	1	1	yes	characteristic
233	C₄×C₄₁	—	2	1	no	—
234	C₄×C₄₁	—	2	2	no	—
235	C₄×C₄₁	—	2	8	no	—
236	C₄×C₄₁	—	4	1	no	—
237	C₄×C₄₁	—	4	2	no	—
238	C₄×C₄₁	—	4	4	no	—
239	C₄×C₄₁	#576	1	4	yes	—
240	C₄×C₄₁	#585	1	2	yes	—
241	#3548	C₂×C₄₁	1	1	yes	characteristic, complemented
242	#3508	C₂×C₄₁	1	1	yes	characteristic, complemented
243	#3399	C₂×C₄₁	1	4	yes	complemented
244	#3391	C₂×C₄₁	1	4	yes	complemented
245	#3366	C₂×C₄₁	1	4	yes	complemented
246	#3361	C₂×C₄₁	1	4	yes	complemented
247	#3220	C₂×C₄₁	1	4	yes	complemented
248	#3205	C₂×C₄₁	1	2	yes	complemented
249	#3122	C₂×C₄₁	1	4	yes	complemented
250	#3106	C₂×C₄₁	1	2	yes	complemented
251	#2986	C₂×C₄₁	1	1	yes	characteristic, complemented
252	C₂×C₄₁	—	4	1	no	—
253	C₂×C₄₁	—	8	1	no	—
254	C₂×C₄₁	—	8	4	no	—
255	C₂×C₄₁	—	8	4	no	—
256	C₂×C₄₁	#3487	1	1	yes	characteristic
257	C₂×C₄₁	C₂×#576	1	2	yes	—
258	#562	—	2	2	no	—
259	#559	C₂²×C₄₁	1	4	yes	—
260	#554	C₂²×C₄₁	1	4	yes	complemented
261	#550	C₂²×C₄₁	1	4	yes	—
262	#550	C₂²×C₄₁	1	4	yes	complemented
263	#547	—	2	2	no	—
264	#546	—	2	4	no	—
265	#540	—	2	2	no	—
266	#540	C₂²×C₄₁	1	4	yes	—
267	#537	—	2	4	no	—
268	#535	C₂²×C₄₁	1	2	yes	—
269	#533	C₂²×C₄₁	1	1	yes	characteristic
270	#532	—	2	2	no	—
271	#532	C₂²×C₄₁	1	2	yes	—
272	C₂×#127	C₂²×C₄₁	1	1	yes	characteristic
273	#518	C₂²×C₄₁	1	2	yes	—
274	C₄×#41	C₂²×C₄₁	1	1	yes	characteristic
275	#496	C₂²×C₄₁	1	4	yes	complemented
276	#493	C₂²×C₄₁	1	4	yes	—
277	#493	C₂²×C₄₁	1	4	yes	complemented
278	#490	C₂²×C₄₁	1	4	yes	complemented
279	#488	C₂²×C₄₁	1	4	yes	complemented
280	#486	C₂²×C₄₁	1	4	yes	—
281	#482	C₂²×C₄₁	1	4	yes	—
282	#478	C₂²×C₄₁	1	8	yes	complemented
283	#477	C₂²×C₄₁	1	2	yes	complemented
284	#476	C₂²×C₄₁	1	2	yes	complemented
285	#463	C₂²×C₄₁	1	8	yes	complemented
286	#460	C₂²×C₄₁	1	2	yes	complemented
287	#459	C₂²×C₄₁	1	4	yes	—
288	#459	C₂²×C₄₁	1	4	yes	—
289	#459	C₂²×C₄₁	1	2	yes	complemented
290	#459	C₂²×C₄₁	1	8	yes	complemented
291	#459	C₂²×C₄₁	1	8	yes	complemented
292	#449	C₂²×C₄₁	1	4	yes	—
293	#447	C₂²×C₄₁	1	8	yes	—
294	#446	C₂²×C₄₁	1	4	yes	complemented
295	C₈×Q₈	C₂²×C₄₁	1	4	yes	complemented
296	#442	C₂²×C₄₁	1	8	yes	complemented
297	C₄×SD₁₆	C₂²×C₄₁	1	4	yes	complemented
298	C₄×D₈	C₂²×C₄₁	1	8	yes	complemented
299	C₄×D₈	C₂²×C₄₁	1	4	yes	complemented
300	#433	C₂²×C₄₁	1	4	yes	—
301	#431	C₂²×C₄₁	1	2	yes	—
302	C₄₁	#61932	1	1	yes	characteristic, direct product factor, Sylow
303	C₂×#41	—	2	4	no	—
304	C₂×#41	—	2	4	no	—
305	C₂×#41	—	2	2	no	—
306	C₂×#41	C₂³×C₄₁	1	1	yes	characteristic
307	C₂²×D₄	—	2	2	no	—
308	C₂²×D₄	C₂³×C₄₁	1	2	yes	—
309	C₂×SD₁₆	C₂³×C₄₁	1	4	yes	—
310	C₂×D₈	C₂³×C₄₁	1	8	yes	—
311	C₂×D₈	C₂³×C₄₁	1	4	yes	—
312	C₂×D₈	C₂³×C₄₁	1	8	yes	—
313	C₄⋊Q₈	D₄×C₄₁	1	2	yes	—
314	C₄⋊Q₈	C₂³×C₄₁	1	2	yes	—
315	#127	—	2	1	no	—
316	#127	—	2	1	no	—
317	#127	C₂³×C₄₁	1	4	yes	—
318	#127	C₂³×C₄₁	1	2	yes	—
319	#127	C₂³×C₄₁	1	4	yes	—
320	#127	C₂³×C₄₁	1	4	yes	—
321	#125	D₄×C₄₁	1	2	yes	—
322	#125	C₂³×C₄₁	1	4	yes	—
323	#124	—	2	4	no	—
324	#124	—	2	2	no	—
325	#124	C₂³×C₄₁	1	4	yes	—
326	#123	—	2	8	no	—
327	#123	—	2	8	no	—
328	C₂²⋊Q₈	—	2	4	no	—
329	C₂²⋊Q₈	—	2	8	no	—
330	C₂²⋊Q₈	D₄×C₄₁	1	4	yes	—
331	#121	—	2	2	no	—
332	#121	—	2	4	no	—
333	#121	—	2	4	no	—
334	#121	—	2	4	no	—
335	#121	—	2	8	no	—
336	#121	—	2	8	no	—
337	#121	—	2	8	no	—
338	#121	C₂³×C₄₁	1	4	yes	—
339	#120	—	2	4	no	—
340	C₄×Q₈	C₂³×C₄₁	1	2	yes	—
341	C₄×Q₈	C₂³×C₄₁	1	4	yes	—
342	C₄×D₄	—	2	2	no	—
343	C₄×D₄	—	2	4	no	—
344	C₄×D₄	—	2	4	no	—
345	C₄×D₄	—	2	2	no	—
346	C₄×D₄	C₂³×C₄₁	1	2	yes	—
347	C₄×D₄	C₂³×C₄₁	1	8	yes	—
348	C₄×D₄	C₂³×C₄₁	1	4	yes	—
349	C₄×D₄	C₂³×C₄₁	1	8	yes	—
350	#117	—	2	1	no	—
351	#117	C₂³×C₄₁	1	1	yes	characteristic
352	#117	C₂³×C₄₁	1	2	yes	—
353	C₂×C₄⋊C₄	—	2	4	no	—
354	C₂×C₂²⋊C₄	—	2	4	no	—
355	C₂×C₄²	—	2	1	no	—
356	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
357	#107	C₂³×C₄₁	1	4	yes	—
358	#106	C₂³×C₄₁	1	4	yes	—
359	C₄⋊C₈	C₂³×C₄₁	1	2	yes	—
360	C₄⋊C₈	C₂³×C₄₁	1	2	yes	—
361	C₄⋊C₈	C₂³×C₄₁	1	8	yes	—
362	#103	C₂³×C₄₁	1	4	yes	—
363	#102	C₂³×C₄₁	1	4	yes	—
364	#102	C₂³×C₄₁	1	4	yes	—
365	#102	C₂³×C₄₁	1	8	yes	—
366	#102	C₂³×C₄₁	1	4	yes	—
367	#102	C₂³×C₄₁	1	8	yes	—
368	C₂²⋊C₈	C₂³×C₄₁	1	4	yes	—
369	#97	C₂³×C₄₁	1	4	yes	—
370	C₄×C₈	C₂³×C₄₁	1	4	yes	—
371	C₄×C₈	C₂³×C₄₁	1	4	yes	—
372	C₂⁴	—	2	2	no	—
373	#41	—	4	2	no	—
374	#41	—	8	4	no	—
375	#41	—	8	8	no	—
376	#41	—	8	8	no	—
377	C₂×Q₈	—	2	2	no	—
378	C₂×Q₈	C₂×D₄×C₄₁	1	4	yes	—
379	C₂×Q₈	C₂⁴×C₄₁	1	1	yes	characteristic
380	C₂×D₄	—	2	1	no	—
381	C₂×D₄	—	2	4	no	—
382	C₂×D₄	—	2	2	no	—
383	C₂×D₄	—	2	2	no	—
384	C₂×D₄	—	2	4	no	—
385	C₂×D₄	—	2	8	no	—
386	C₂×D₄	—	2	8	no	—
387	C₂×D₄	—	2	2	no	—
388	C₂×D₄	—	2	4	no	—
389	C₂×D₄	—	4	4	no	—
390	C₂×D₄	—	8	4	no	—
391	C₂×D₄	C₂⁴×C₄₁	1	4	yes	—
392	C₂×D₄	C₂⁴×C₄₁	1	1	yes	characteristic
393	C₂×D₄	C₂⁴×C₄₁	1	4	yes	—
394	C₂²×C₄	—	2	1	no	—
395	C₂²×C₄	—	2	2	no	—
396	C₂²×C₄	—	2	4	no	—
397	C₂²×C₄	—	2	8	no	—
398	C₂²×C₄	—	2	8	no	—
399	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
400	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
401	SD₁₆	—	4	4	no	—
402	D₈	—	4	4	no	—
403	D₈	—	4	8	no	—
404	D₈	—	4	8	no	—
405	C₂×C₈	C₂⁴×C₄₁	1	4	yes	—
406	C₂×C₈	C₂⁴×C₄₁	1	4	yes	—
407	C₄⋊C₄	—	2	2	no	—
408	C₄⋊C₄	—	2	8	no	—
409	C₄⋊C₄	—	2	2	no	—
410	C₄⋊C₄	C₂×D₄×C₄₁	1	4	yes	—
411	C₄⋊C₄	C₂×D₄×C₄₁	1	4	yes	—
412	C₄⋊C₄	C₂×D₄×C₄₁	1	8	yes	—
413	C₄⋊C₄	C₂⁴×C₄₁	1	4	yes	—
414	C₄⋊C₄	C₂⁴×C₄₁	1	2	yes	—
415	C₂²⋊C₄	—	2	1	no	—
416	C₂²⋊C₄	—	2	8	no	—
417	C₂²⋊C₄	—	2	2	no	—
418	C₂²⋊C₄	—	2	8	no	—
419	C₂²⋊C₄	—	2	4	no	—
420	C₂²⋊C₄	—	2	8	no	—
421	C₂²⋊C₄	—	2	4	no	—
422	C₂²⋊C₄	C₂×D₄×C₄₁	1	4	yes	—
423	C₄²	—	2	1	no	—
424	C₄²	—	2	2	no	—
425	C₄²	C₂×D₄×C₄₁	1	1	yes	characteristic
426	C₄²	C₂×D₄×C₄₁	1	1	yes	characteristic
427	C₄²	C₂⁴×C₄₁	1	2	yes	—
428	C₄²	C₂⁴×C₄₁	1	4	yes	—
429	C₂³	—	2	4	no	—
430	C₂³	—	2	4	no	—
431	C₂³	—	2	1	no	—
432	C₂³	—	4	4	no	—
433	C₂³	—	8	4	no	—
434	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
435	Q₈	—	2	8	no	—
436	Q₈	—	2	2	no	—
437	Q₈	—	8	2	no	—
438	D₄	—	2	4	no	—
439	D₄	—	2	4	no	—
440	D₄	—	2	8	no	—
441	D₄	—	2	2	no	—
442	D₄	—	4	4	no	—
443	D₄	—	4	2	no	—
444	D₄	—	4	8	no	—
445	D₄	—	4	4	no	—
446	D₄	—	8	4	no	—
447	D₄	—	8	2	no	—
448	D₄	—	8	8	no	—
449	D₄	—	8	8	no	—
450	D₄	—	8	4	no	—
451	C₂×C₄	—	2	4	no	—
452	C₂×C₄	—	2	2	no	—
453	C₂×C₄	—	2	1	no	—
454	C₂×C₄	—	2	2	no	—
455	C₂×C₄	—	2	4	no	—
456	C₂×C₄	—	4	2	no	—
457	C₂×C₄	—	4	4	no	—
458	C₂×C₄	—	4	8	no	—
459	C₂×C₄	—	8	8	no	—
460	C₂×C₄	—	8	8	no	—
461	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
462	C₂×C₄	C₂²×D₄×C₄₁	1	2	yes	—
463	C₂×C₄	C₂²×D₄×C₄₁	1	8	yes	—
464	C₂×C₄	C₂²×D₄×C₄₁	1	2	yes	—
465	C₂×C₄	C₂⁵×C₄₁	1	1	yes	characteristic
466	C₈	—	2	4	no	—
467	C₈	—	2	4	no	—
468	C₂²	—	2	2	no	—
469	C₂²	—	2	1	no	—
470	C₂²	—	4	2	no	—
471	C₂²	—	4	4	no	—
472	C₂²	—	4	4	no	—
473	C₂²	—	4	8	no	—
474	C₂²	—	4	1	no	—
475	C₂²	—	4	4	no	—
476	C₂²	—	4	4	no	—
477	C₂²	—	16	4	no	—
478	C₂²	C₂³×D₄×C₄₁	1	1	yes	characteristic
479	C₄	—	2	2	no	—
480	C₄	—	2	8	no	—
481	C₄	—	2	1	no	—
482	C₄	—	4	2	no	—
483	C₄	—	4	4	no	—
484	C₄	—	4	1	no	—
485	C₄	C₄₁×#576	1	4	yes	—
486	C₄	C₄₁×#585	1	2	yes	—
487	C₂	—	4	1	no	—
488	C₂	—	8	4	no	—
489	C₂	—	8	1	no	—
490	C₂	—	8	4	no	—
491	C₂	C₄₁×#3487	1	1	yes	characteristic
492	C₂	C₂×C₄₁×#576	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₄₁	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₄₁
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄₁ ◁ C₄₁×#533 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₄₁×#3548	C₂	semidirect
2. C₄₁×#3508	C₂	semidirect
3. C₄₁×#3399	C₂	semidirect
4. C₄₁×#3391	C₂	semidirect
5. C₄₁×#3366	C₂	semidirect
6. C₄₁×#3361	C₂	semidirect
7. C₄₁×#3220	C₂	semidirect
8. C₄₁×#3205	C₂	semidirect
9. C₄₁×#3122	C₂	semidirect
10. C₄₁×#3106	C₂	semidirect
11. C₄₁×#2986	C₂	semidirect
14. C₄₁×#554	C₂²	semidirect
16. C₄₁×#550	C₂²	semidirect
29. C₄₁×#496	C₂²	semidirect
31. C₄₁×#493	C₂²	semidirect
32. C₄₁×#490	C₂²	semidirect
33. C₄₁×#488	C₂²	semidirect
36. C₄₁×#478	C₂²	semidirect
37. C₄₁×#477	C₂²	semidirect
38. C₄₁×#476	C₂²	semidirect
39. C₄₁×#463	C₂²	semidirect
40. C₄₁×#460	C₂²	semidirect
43. C₄₁×#459	C₂²	semidirect
44. C₄₁×#459	C₂²	semidirect
45. C₄₁×#459	C₂²	semidirect
48. C₄₁×#446	C₂²	semidirect
49. C₈×Q₈×C₄₁	C₂²	semidirect
50. C₄₁×#442	C₂²	semidirect
51. C₄×SD₁₆×C₄₁	C₂²	semidirect
52. C₄×D₈×C₄₁	C₂²	semidirect
53. C₄×D₈×C₄₁	C₂²	semidirect
221. #61932	C₄₁	direct (N × H)
241. #3548	C₂×C₄₁	semidirect
242. #3508	C₂×C₄₁	semidirect
243. #3399	C₂×C₄₁	semidirect
244. #3391	C₂×C₄₁	semidirect
245. #3366	C₂×C₄₁	semidirect
246. #3361	C₂×C₄₁	semidirect
247. #3220	C₂×C₄₁	semidirect
248. #3205	C₂×C₄₁	semidirect
249. #3122	C₂×C₄₁	semidirect
250. #3106	C₂×C₄₁	semidirect
251. #2986	C₂×C₄₁	semidirect
260. #554	C₂²×C₄₁	semidirect
262. #550	C₂²×C₄₁	semidirect
275. #496	C₂²×C₄₁	semidirect
277. #493	C₂²×C₄₁	semidirect
278. #490	C₂²×C₄₁	semidirect
279. #488	C₂²×C₄₁	semidirect
282. #478	C₂²×C₄₁	semidirect
283. #477	C₂²×C₄₁	semidirect
284. #476	C₂²×C₄₁	semidirect
285. #463	C₂²×C₄₁	semidirect
286. #460	C₂²×C₄₁	semidirect
289. #459	C₂²×C₄₁	semidirect
290. #459	C₂²×C₄₁	semidirect
291. #459	C₂²×C₄₁	semidirect
294. #446	C₂²×C₄₁	semidirect
295. C₈×Q₈	C₂²×C₄₁	semidirect
296. #442	C₂²×C₄₁	semidirect
297. C₄×SD₁₆	C₂²×C₄₁	semidirect
298. C₄×D₈	C₂²×C₄₁	semidirect
299. C₄×D₈	C₂²×C₄₁	semidirect
302. C₄₁	#61932	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×#3548	2
C₄₁×#3508	2
C₄₁×#3399	2
C₄₁×#3391	2
C₄₁×#3366	2
C₄₁×#3361	2
C₄₁×#3220	2
C₄₁×#3205	2
C₄₁×#3122	2
C₄₁×#3106	2
C₄₁×#2986	2
#61932	41

Subgroups — C41×#61932 #23838133

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#61932 #23838133