Subgroups — C₄₁×#19400 #23795601

Order 10496.

610 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₁×#3210	C₂	1	1	yes	maximal, characteristic
2	C₄₁×#3113	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₁×#3103	C₂	1	1	yes	maximal, characteristic
4	C₄₁×#2982	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₁×#1682	C₂	1	2	yes	maximal, complemented
6	C₄₁×#1680	C₂	1	2	yes	maximal, complemented
7	C₄₁×#1670	C₂	1	2	yes	maximal, complemented
8	C₄₁×#1666	C₂	1	2	yes	maximal, complemented
9	C₄₁×#1572	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄₁×#1553	C₂	1	1	yes	maximal, characteristic
11	C₄₁×#1544	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄₁×#533	C₂²	1	1	yes	characteristic
13	C₄₁×#532	C₂²	1	1	yes	characteristic
14	C₂×C₄×Q₈×C₄₁	C₂²	1	1	yes	characteristic
15	C₄₁×#494	C₂²	1	1	yes	characteristic
16	C₄₁×#492	C₂²	1	1	yes	characteristic
17	C₄₁×#487	C₂²	1	1	yes	characteristic
18	C₄₁×#486	C₂²	1	1	yes	characteristic
19	C₄₁×#483	—	2	1	no	—
20	C₄₁×#481	—	2	1	no	—
21	C₄₁×#475	C₂²	1	2	yes	—
22	C₄₁×#475	C₂²	1	2	yes	—
23	C₄₁×#464	—	2	2	no	—
24	C₄₁×#462	C₂²	1	2	yes	—
25	C₄₁×#460	C₂²	1	2	yes	—
26	C₄₁×#452	—	2	2	no	—
27	C₄₁×#451	—	2	1	no	—
28	C₄₁×#448	—	2	1	no	—
29	C₈×Q₈×C₄₁	—	2	2	no	—
30	C₈×Q₈×C₄₁	C₂²	1	2	yes	—
31	C₈×Q₈×C₄₁	C₂²	1	2	yes	—
32	C₄₁×#441	—	2	2	no	—
33	C₄×SD₁₆×C₄₁	—	2	2	no	—
34	C₄₁×#432	C₂²	1	1	yes	characteristic
35	C₄₁×#431	—	2	2	no	—
36	C₄₁×#431	C₂²	1	1	yes	characteristic
37	C₄₁×#431	C₂²	1	1	yes	characteristic
38	C₄₁×#431	C₂²	1	1	yes	characteristic
39	C₄₁×#335	C₂²	1	2	yes	—
40	C₄₁×#334	C₂²	1	2	yes	—
41	C₄₁×#332	C₂²	1	2	yes	—
42	C₄₁×#332	C₂²	1	2	yes	—
43	C₄₁×#332	C₂²	1	2	yes	—
44	C₄₁×#331	C₂²	1	2	yes	—
45	C₂×#41×C₄₁	—	2	1	no	—
46	C₂²×Q₈×C₄₁	D₄	1	1	yes	characteristic
47	C₂×Q₁₆×C₄₁	—	2	2	no	—
48	C₂×Q₁₆×C₄₁	—	2	2	no	—
49	C₂×SD₁₆×C₄₁	—	2	2	no	—
50	C₂×SD₁₆×C₄₁	—	2	2	no	—
51	C₄⋊Q₈×C₄₁	C₂³	1	1	yes	characteristic
52	C₄⋊Q₈×C₄₁	C₂³	1	1	yes	characteristic
53	C₄⋊Q₈×C₄₁	C₂³	1	1	yes	characteristic
54	#127×C₄₁	C₂³	1	1	yes	characteristic
55	#125×C₄₁	—	2	1	no	—
56	#124×C₄₁	—	2	1	no	—
57	C₂²⋊Q₈×C₄₁	—	2	1	no	—
58	C₂²⋊Q₈×C₄₁	—	2	1	no	—
59	#121×C₄₁	—	2	1	no	—
60	#121×C₄₁	—	2	1	no	—
61	C₄×Q₈×C₄₁	—	2	1	no	—
62	C₄×Q₈×C₄₁	—	2	1	no	—
63	C₄×Q₈×C₄₁	—	2	1	no	—
64	C₄×Q₈×C₄₁	—	2	1	no	—
65	C₄×Q₈×C₄₁	D₄	1	2	yes	—
66	C₄×Q₈×C₄₁	C₂³	1	2	yes	—
67	C₄×D₄×C₄₁	—	2	1	no	—
68	C₄×D₄×C₄₁	—	2	1	no	—
69	#117×C₄₁	—	2	1	no	—
70	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
71	C₂×C₄⋊C₄×C₄₁	D₄	1	1	yes	characteristic
72	C₂×C₄²×C₄₁	—	2	1	no	—
73	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
74	#106×C₄₁	—	2	2	no	—
75	#106×C₄₁	—	2	2	no	—
76	C₄⋊C₈×C₄₁	—	2	2	no	—
77	C₄⋊C₈×C₄₁	—	2	2	no	—
78	C₄⋊C₈×C₄₁	D₄	1	2	yes	—
79	C₄⋊C₈×C₄₁	C₂³	1	2	yes	—
80	C₄⋊C₈×C₄₁	C₂³	1	2	yes	—
81	C₄⋊C₈×C₄₁	C₂³	1	2	yes	—
82	#103×C₄₁	—	2	2	no	—
83	#103×C₄₁	—	2	2	no	—
84	#103×C₄₁	—	2	2	no	—
85	#103×C₄₁	—	2	2	no	—
86	#102×C₄₁	—	2	2	no	—
87	#102×C₄₁	—	2	2	no	—
88	C₂²⋊C₈×C₄₁	—	2	1	no	—
89	C₂²⋊C₈×C₄₁	—	2	1	no	—
90	C₂²⋊C₈×C₄₁	—	2	1	no	—
91	C₂²⋊C₈×C₄₁	D₄	1	2	yes	—
92	#97×C₄₁	—	2	1	no	—
93	C₄×C₈×C₄₁	—	2	2	no	—
94	C₄×C₈×C₄₁	—	2	2	no	—
95	C₄×C₈×C₄₁	—	2	1	no	—
96	C₄×C₈×C₄₁	—	2	1	no	—
97	C₄×C₈×C₄₁	C₂³	1	1	yes	characteristic
98	C₄×C₈×C₄₁	C₂³	1	1	yes	characteristic
99	#41×C₄₁	—	8	2	no	—
100	C₂×Q₈×C₄₁	—	2	4	no	—
101	C₂×Q₈×C₄₁	—	2	1	no	—
102	C₂×Q₈×C₄₁	—	2	1	no	—
103	C₂×Q₈×C₄₁	—	2	1	no	—
104	C₂×Q₈×C₄₁	—	2	1	no	—
105	C₂×Q₈×C₄₁	C₂×D₄	1	2	yes	—
106	C₂×D₄×C₄₁	—	2	1	no	—
107	C₂×D₄×C₄₁	—	2	1	no	—
108	C₂×D₄×C₄₁	—	2	1	no	—
109	C₂×D₄×C₄₁	—	4	1	no	—
110	C₂²×C₄×C₄₁	—	2	1	no	—
111	C₂²×C₄×C₄₁	—	2	1	no	—
112	C₂²×C₄×C₄₁	—	4	1	no	—
113	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
114	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
115	C₂²×C₄×C₄₁	#41	1	1	yes	characteristic
116	Q₁₆×C₄₁	—	4	4	no	—
117	Q₁₆×C₄₁	—	8	2	no	—
118	SD₁₆×C₄₁	—	4	4	no	—
119	SD₁₆×C₄₁	—	8	2	no	—
120	C₂×C₈×C₄₁	—	2	2	no	—
121	C₂×C₈×C₄₁	—	2	2	no	—
122	C₂×C₈×C₄₁	—	2	2	no	—
123	C₂×C₈×C₄₁	C₂×D₄	1	2	yes	—
124	C₂×C₈×C₄₁	C₂×D₄	1	2	yes	—
125	C₄⋊C₄×C₄₁	—	2	2	no	—
126	C₄⋊C₄×C₄₁	—	2	1	no	—
127	C₄⋊C₄×C₄₁	—	2	2	no	—
128	C₄⋊C₄×C₄₁	—	2	1	no	—
129	C₄⋊C₄×C₄₁	—	2	1	no	—
130	C₄⋊C₄×C₄₁	—	2	1	no	—
131	C₄⋊C₄×C₄₁	—	2	1	no	—
132	C₄⋊C₄×C₄₁	—	2	1	no	—
133	C₄⋊C₄×C₄₁	—	2	1	no	—
134	C₄⋊C₄×C₄₁	—	4	1	no	—
135	C₄⋊C₄×C₄₁	—	4	1	no	—
136	C₄⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
137	C₂²⋊C₄×C₄₁	—	4	1	no	—
138	C₂²⋊C₄×C₄₁	—	4	1	no	—
139	C₂²⋊C₄×C₄₁	—	4	1	no	—
140	C₄²×C₄₁	—	2	2	no	—
141	C₄²×C₄₁	—	2	2	no	—
142	C₄²×C₄₁	—	4	1	no	—
143	C₄²×C₄₁	C₂×D₄	1	1	yes	characteristic
144	C₄²×C₄₁	C₂×D₄	1	1	yes	characteristic
145	C₄²×C₄₁	#41	1	1	yes	characteristic
146	C₄²×C₄₁	C₂⁴	1	1	yes	characteristic
147	C₂³×C₄₁	—	4	1	no	—
148	C₂³×C₄₁	#121	1	1	yes	characteristic
149	Q₈×C₄₁	—	2	4	no	—
150	Q₈×C₄₁	—	2	2	no	—
151	Q₈×C₄₁	—	4	2	no	—
152	Q₈×C₄₁	—	4	2	no	—
153	Q₈×C₄₁	—	4	2	no	—
154	Q₈×C₄₁	#135	1	4	yes	—
155	D₄×C₄₁	—	4	2	no	—
156	D₄×C₄₁	—	4	2	no	—
157	D₄×C₄₁	—	8	1	no	—
158	D₄×C₄₁	—	8	2	no	—
159	C₂×C₄×C₄₁	—	2	4	no	—
160	C₂×C₄×C₄₁	—	2	2	no	—
161	C₂×C₄×C₄₁	—	2	2	no	—
162	C₂×C₄×C₄₁	—	2	2	no	—
163	C₂×C₄×C₄₁	—	2	2	no	—
164	C₂×C₄×C₄₁	—	4	1	no	—
165	C₂×C₄×C₄₁	—	4	1	no	—
166	C₂×C₄×C₄₁	—	4	1	no	—
167	C₂×C₄×C₄₁	—	4	1	no	—
168	C₂×C₄×C₄₁	—	8	2	no	—
169	C₂×C₄×C₄₁	—	8	1	no	—
170	C₂×C₄×C₄₁	#121	1	1	yes	characteristic
171	C₂×C₄×C₄₁	#121	1	1	yes	characteristic
172	C₂×C₄×C₄₁	#121	1	1	yes	characteristic
173	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
174	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
175	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
176	C₈×C₄₁	—	2	2	no	—
177	C₈×C₄₁	—	2	2	no	—
178	C₈×C₄₁	—	4	2	no	—
179	C₈×C₄₁	—	4	2	no	—
180	C₈×C₄₁	—	4	2	no	—
181	#19400	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
182	C₂²×C₄₁	—	2	1	no	—
183	C₂²×C₄₁	—	2	1	no	—
184	C₂²×C₄₁	—	2	1	no	—
185	C₂²×C₄₁	—	8	1	no	—
186	C₂²×C₄₁	—	8	1	no	—
187	C₂²×C₄₁	—	8	1	no	—
188	C₂²×C₄₁	C₂×#121	1	1	yes	characteristic
189	C₄×C₄₁	—	2	1	no	—
190	C₄×C₄₁	—	2	4	no	—
191	C₄×C₄₁	—	2	1	no	—
192	C₄×C₄₁	—	2	1	no	—
193	C₄×C₄₁	—	2	1	no	—
194	C₄×C₄₁	—	4	2	no	—
195	C₄×C₄₁	—	8	1	no	—
196	C₄×C₄₁	—	8	1	no	—
197	C₄×C₄₁	—	8	1	no	—
198	C₄×C₄₁	C₂×#135	1	2	yes	—
199	C₄×C₄₁	#577	1	2	yes	—
200	#3210	C₂×C₄₁	1	1	yes	characteristic
201	#3113	C₂×C₄₁	1	1	yes	characteristic, complemented
202	#3103	C₂×C₄₁	1	1	yes	characteristic
203	#2982	C₂×C₄₁	1	1	yes	characteristic, complemented
204	#1682	C₂×C₄₁	1	2	yes	complemented
205	#1680	C₂×C₄₁	1	2	yes	complemented
206	#1670	C₂×C₄₁	1	2	yes	complemented
207	#1666	C₂×C₄₁	1	2	yes	complemented
208	#1572	C₂×C₄₁	1	1	yes	characteristic, complemented
209	#1553	C₂×C₄₁	1	1	yes	characteristic
210	#1544	C₂×C₄₁	1	1	yes	characteristic, complemented
211	C₂×C₄₁	—	4	1	no	—
212	C₂×C₄₁	—	16	1	no	—
213	C₂×C₄₁	#3043	1	1	yes	characteristic
214	C₂×C₄₁	#3050	1	1	yes	characteristic
215	C₂×C₄₁	#3069	1	1	yes	characteristic
216	#533	C₂²×C₄₁	1	1	yes	characteristic
217	#532	C₂²×C₄₁	1	1	yes	characteristic
218	C₂×C₄×Q₈	C₂²×C₄₁	1	1	yes	characteristic
219	#494	C₂²×C₄₁	1	1	yes	characteristic
220	#492	C₂²×C₄₁	1	1	yes	characteristic
221	#487	C₂²×C₄₁	1	1	yes	characteristic
222	#486	C₂²×C₄₁	1	1	yes	characteristic
223	#483	—	2	1	no	—
224	#481	—	2	1	no	—
225	#475	C₂²×C₄₁	1	2	yes	—
226	#475	C₂²×C₄₁	1	2	yes	—
227	#464	—	2	2	no	—
228	#462	C₂²×C₄₁	1	2	yes	—
229	#460	C₂²×C₄₁	1	2	yes	—
230	#452	—	2	2	no	—
231	#451	—	2	1	no	—
232	#448	—	2	1	no	—
233	C₈×Q₈	—	2	2	no	—
234	C₈×Q₈	C₂²×C₄₁	1	2	yes	—
235	C₈×Q₈	C₂²×C₄₁	1	2	yes	—
236	#441	—	2	2	no	—
237	C₄×SD₁₆	—	2	2	no	—
238	#432	C₂²×C₄₁	1	1	yes	characteristic
239	#431	—	2	2	no	—
240	#431	C₂²×C₄₁	1	1	yes	characteristic
241	#431	C₂²×C₄₁	1	1	yes	characteristic
242	#431	C₂²×C₄₁	1	1	yes	characteristic
243	#335	C₂²×C₄₁	1	2	yes	—
244	#334	C₂²×C₄₁	1	2	yes	—
245	#332	C₂²×C₄₁	1	2	yes	—
246	#332	C₂²×C₄₁	1	2	yes	—
247	#332	C₂²×C₄₁	1	2	yes	—
248	#331	C₂²×C₄₁	1	2	yes	—
249	C₄₁	#19400	1	1	yes	characteristic, direct product factor, Sylow
250	C₂×#41	—	2	1	no	—
251	C₂²×Q₈	D₄×C₄₁	1	1	yes	characteristic
252	C₂×Q₁₆	—	2	2	no	—
253	C₂×Q₁₆	—	2	2	no	—
254	C₂×SD₁₆	—	2	2	no	—
255	C₂×SD₁₆	—	2	2	no	—
256	C₄⋊Q₈	C₂³×C₄₁	1	1	yes	characteristic
257	C₄⋊Q₈	C₂³×C₄₁	1	1	yes	characteristic
258	C₄⋊Q₈	C₂³×C₄₁	1	1	yes	characteristic
259	#127	C₂³×C₄₁	1	1	yes	characteristic
260	#125	—	2	1	no	—
261	#124	—	2	1	no	—
262	C₂²⋊Q₈	—	2	1	no	—
263	C₂²⋊Q₈	—	2	1	no	—
264	#121	—	2	1	no	—
265	#121	—	2	1	no	—
266	C₄×Q₈	—	2	1	no	—
267	C₄×Q₈	—	2	1	no	—
268	C₄×Q₈	—	2	1	no	—
269	C₄×Q₈	—	2	1	no	—
270	C₄×Q₈	D₄×C₄₁	1	2	yes	—
271	C₄×Q₈	C₂³×C₄₁	1	2	yes	—
272	C₄×D₄	—	2	1	no	—
273	C₄×D₄	—	2	1	no	—
274	#117	—	2	1	no	—
275	C₂×C₄⋊C₄	—	2	1	no	—
276	C₂×C₄⋊C₄	D₄×C₄₁	1	1	yes	characteristic
277	C₂×C₄²	—	2	1	no	—
278	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
279	#106	—	2	2	no	—
280	#106	—	2	2	no	—
281	C₄⋊C₈	—	2	2	no	—
282	C₄⋊C₈	—	2	2	no	—
283	C₄⋊C₈	D₄×C₄₁	1	2	yes	—
284	C₄⋊C₈	C₂³×C₄₁	1	2	yes	—
285	C₄⋊C₈	C₂³×C₄₁	1	2	yes	—
286	C₄⋊C₈	C₂³×C₄₁	1	2	yes	—
287	#103	—	2	2	no	—
288	#103	—	2	2	no	—
289	#103	—	2	2	no	—
290	#103	—	2	2	no	—
291	#102	—	2	2	no	—
292	#102	—	2	2	no	—
293	C₂²⋊C₈	—	2	1	no	—
294	C₂²⋊C₈	—	2	1	no	—
295	C₂²⋊C₈	—	2	1	no	—
296	C₂²⋊C₈	D₄×C₄₁	1	2	yes	—
297	#97	—	2	1	no	—
298	C₄×C₈	—	2	2	no	—
299	C₄×C₈	—	2	2	no	—
300	C₄×C₈	—	2	1	no	—
301	C₄×C₈	—	2	1	no	—
302	C₄×C₈	C₂³×C₄₁	1	1	yes	characteristic
303	C₄×C₈	C₂³×C₄₁	1	1	yes	characteristic
304	#41	—	8	2	no	—
305	C₂×Q₈	—	2	4	no	—
306	C₂×Q₈	—	2	1	no	—
307	C₂×Q₈	—	2	1	no	—
308	C₂×Q₈	—	2	1	no	—
309	C₂×Q₈	—	2	1	no	—
310	C₂×Q₈	C₂×D₄×C₄₁	1	2	yes	—
311	C₂×D₄	—	2	1	no	—
312	C₂×D₄	—	2	1	no	—
313	C₂×D₄	—	2	1	no	—
314	C₂×D₄	—	4	1	no	—
315	C₂²×C₄	—	2	1	no	—
316	C₂²×C₄	—	2	1	no	—
317	C₂²×C₄	—	4	1	no	—
318	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
319	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
320	C₂²×C₄	#41×C₄₁	1	1	yes	characteristic
321	Q₁₆	—	4	4	no	—
322	Q₁₆	—	8	2	no	—
323	SD₁₆	—	4	4	no	—
324	SD₁₆	—	8	2	no	—
325	C₂×C₈	—	2	2	no	—
326	C₂×C₈	—	2	2	no	—
327	C₂×C₈	—	2	2	no	—
328	C₂×C₈	C₂×D₄×C₄₁	1	2	yes	—
329	C₂×C₈	C₂×D₄×C₄₁	1	2	yes	—
330	C₄⋊C₄	—	2	2	no	—
331	C₄⋊C₄	—	2	1	no	—
332	C₄⋊C₄	—	2	2	no	—
333	C₄⋊C₄	—	2	1	no	—
334	C₄⋊C₄	—	2	1	no	—
335	C₄⋊C₄	—	2	1	no	—
336	C₄⋊C₄	—	2	1	no	—
337	C₄⋊C₄	—	2	1	no	—
338	C₄⋊C₄	—	2	1	no	—
339	C₄⋊C₄	—	4	1	no	—
340	C₄⋊C₄	—	4	1	no	—
341	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
342	C₂²⋊C₄	—	4	1	no	—
343	C₂²⋊C₄	—	4	1	no	—
344	C₂²⋊C₄	—	4	1	no	—
345	C₄²	—	2	2	no	—
346	C₄²	—	2	2	no	—
347	C₄²	—	4	1	no	—
348	C₄²	C₂×D₄×C₄₁	1	1	yes	characteristic
349	C₄²	C₂×D₄×C₄₁	1	1	yes	characteristic
350	C₄²	#41×C₄₁	1	1	yes	characteristic
351	C₄²	C₂⁴×C₄₁	1	1	yes	characteristic
352	C₂³	—	4	1	no	—
353	C₂³	#121×C₄₁	1	1	yes	characteristic
354	Q₈	—	2	4	no	—
355	Q₈	—	2	2	no	—
356	Q₈	—	4	2	no	—
357	Q₈	—	4	2	no	—
358	Q₈	—	4	2	no	—
359	Q₈	#135×C₄₁	1	4	yes	—
360	D₄	—	4	2	no	—
361	D₄	—	4	2	no	—
362	D₄	—	8	1	no	—
363	D₄	—	8	2	no	—
364	C₂×C₄	—	2	4	no	—
365	C₂×C₄	—	2	2	no	—
366	C₂×C₄	—	2	2	no	—
367	C₂×C₄	—	2	2	no	—
368	C₂×C₄	—	2	2	no	—
369	C₂×C₄	—	4	1	no	—
370	C₂×C₄	—	4	1	no	—
371	C₂×C₄	—	4	1	no	—
372	C₂×C₄	—	4	1	no	—
373	C₂×C₄	—	8	2	no	—
374	C₂×C₄	—	8	1	no	—
375	C₂×C₄	#121×C₄₁	1	1	yes	characteristic
376	C₂×C₄	#121×C₄₁	1	1	yes	characteristic
377	C₂×C₄	#121×C₄₁	1	1	yes	characteristic
378	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
379	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
380	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
381	C₈	—	2	2	no	—
382	C₈	—	2	2	no	—
383	C₈	—	4	2	no	—
384	C₈	—	4	2	no	—
385	C₈	—	4	2	no	—
386	C₂²	—	2	1	no	—
387	C₂²	—	2	1	no	—
388	C₂²	—	2	1	no	—
389	C₂²	—	8	1	no	—
390	C₂²	—	8	1	no	—
391	C₂²	—	8	1	no	—
392	C₂²	C₂×#121×C₄₁	1	1	yes	characteristic
393	C₄	—	2	1	no	—
394	C₄	—	2	4	no	—
395	C₄	—	2	1	no	—
396	C₄	—	2	1	no	—
397	C₄	—	2	1	no	—
398	C₄	—	4	2	no	—
399	C₄	—	8	1	no	—
400	C₄	—	8	1	no	—
401	C₄	—	8	1	no	—
402	C₄	C₂×#135×C₄₁	1	2	yes	—
403	C₄	C₄₁×#577	1	2	yes	—
404	C₂	—	4	1	no	—
405	C₂	—	16	1	no	—
406	C₂	C₄₁×#3043	1	1	yes	characteristic
407	C₂	C₄₁×#3050	1	1	yes	characteristic
408	C₂	C₄₁×#3069	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₄₁	C₂×#121
commutator, Frattini, cosocle	C₄²	C₂⁴×C₄₁
prime radical	C₄₁×#532	C₂²
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
2. C₄₁×#3113	C₂	semidirect
4. C₄₁×#2982	C₂	semidirect
5. C₄₁×#1682	C₂	semidirect
6. C₄₁×#1680	C₂	semidirect
7. C₄₁×#1670	C₂	semidirect
8. C₄₁×#1666	C₂	semidirect
9. C₄₁×#1572	C₂	semidirect
11. C₄₁×#1544	C₂	semidirect
181. #19400	C₄₁	direct (N × H)
201. #3113	C₂×C₄₁	semidirect
203. #2982	C₂×C₄₁	semidirect
204. #1682	C₂×C₄₁	semidirect
205. #1680	C₂×C₄₁	semidirect
206. #1670	C₂×C₄₁	semidirect
207. #1666	C₂×C₄₁	semidirect
208. #1572	C₂×C₄₁	semidirect
210. #1544	C₂×C₄₁	semidirect
249. C₄₁	#19400	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×#3210	2
C₄₁×#3113	2
C₄₁×#3103	2
C₄₁×#2982	2
C₄₁×#1682	2
C₄₁×#1680	2
C₄₁×#1670	2
C₄₁×#1666	2
C₄₁×#1572	2
C₄₁×#1553	2
C₄₁×#1544	2
#19400	41

Subgroups — C41×#19400 #23795601

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#19400 #23795601