Subgroups — C₄₁×#19361 #23795562

Order 10496.

570 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₁×#3252	C₂	1	2	yes	maximal
2	C₄₁×#3160	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₁×#2966	C₂	1	1	yes	maximal, characteristic
4	C₄₁×#1692	C₂	1	2	yes	maximal, complemented
5	C₄₁×#1691	C₂	1	2	yes	maximal, complemented
6	C₄₁×#1676	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₁×#1675	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄₁×#1674	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄₁×#1673	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄₁×#1567	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₁×#1559	C₂	1	2	yes	maximal, complemented
12	C₄₁×#533	C₂²	1	2	yes	—
13	C₄₁×#529	C₂²	1	1	yes	characteristic
14	C₄₁×#500	C₂²	1	1	yes	characteristic
15	C₄₁×#500	C₂²	1	1	yes	characteristic
16	C₄₁×#499	—	2	1	no	—
17	C₄₁×#499	—	2	1	no	—
18	C₄₁×#498	C₂²	1	2	yes	—
19	C₄₁×#479	—	2	2	no	—
20	C₄₁×#477	C₂²	1	2	yes	—
21	C₄₁×#476	C₂²	1	2	yes	—
22	C₄₁×#470	—	2	2	no	—
23	C₄₁×#468	—	2	2	no	—
24	C₄₁×#464	—	2	2	no	—
25	C₄₁×#462	C₂²	1	2	yes	—
26	C₄₁×#461	C₂²	1	2	yes	—
27	C₄₁×#446	C₂²	1	1	yes	characteristic
28	C₈×Q₈×C₄₁	C₂²	1	1	yes	characteristic
29	C₄₁×#436	C₂²	1	1	yes	characteristic
30	C₄₁×#435	—	2	1	no	—
31	C₈×D₄×C₄₁	—	2	1	no	—
32	C₈×D₄×C₄₁	C₂²	1	1	yes	characteristic
33	C₄₁×#433	—	2	1	no	—
34	C₄₁×#432	C₂²	1	1	yes	characteristic
35	C₄₁×#427	—	2	1	no	—
36	C₄₁×#427	—	2	1	no	—
37	C₄₁×#423	C₂²	1	2	yes	—
38	C₄₁×#405	—	2	1	no	—
39	C₂×C₄×C₈×C₄₁	C₂²	1	1	yes	characteristic
40	C₄₁×#335	C₂²	1	1	yes	characteristic
41	C₄₁×#335	C₂²	1	1	yes	characteristic
42	C₄₁×#335	C₂²	1	2	yes	—
43	C₄₁×#333	C₂²	1	2	yes	—
44	C₄₁×#333	C₂²	1	2	yes	—
45	C₄₁×#332	C₂²	1	2	yes	—
46	C₄₁×#332	C₂²	1	2	yes	—
47	C₂×Q₁₆×C₄₁	—	2	2	no	—
48	C₂×SD₁₆×C₄₁	—	2	2	no	—
49	C₂×M₁₆×C₄₁	—	2	2	no	—
50	C₂×M₁₆×C₄₁	—	2	1	no	—
51	C₂²×C₈×C₄₁	—	2	1	no	—
52	C₂²×C₈×C₄₁	D₄	1	1	yes	characteristic
53	C₂²×C₈×C₄₁	D₄	1	1	yes	characteristic
54	C₄⋊Q₈×C₄₁	C₂³	1	2	yes	—
55	C₄⋊Q₈×C₄₁	C₂³	1	2	yes	—
56	#126×C₄₁	—	2	1	no	—
57	#125×C₄₁	—	2	2	no	—
58	#125×C₄₁	D₄	1	1	yes	characteristic
59	#124×C₄₁	D₄	1	1	yes	characteristic
60	#123×C₄₁	—	2	1	no	—
61	C₂²⋊Q₈×C₄₁	—	2	2	no	—
62	C₂²⋊Q₈×C₄₁	—	2	2	no	—
63	C₂²⋊Q₈×C₄₁	D₄	1	1	yes	characteristic
64	#121×C₄₁	D₄	1	1	yes	characteristic
65	C₄×Q₈×C₄₁	—	2	2	no	—
66	C₄×Q₈×C₄₁	—	2	2	no	—
67	C₄×Q₈×C₄₁	C₂³	1	1	yes	characteristic
68	C₄×D₄×C₄₁	—	2	1	no	—
69	C₄×D₄×C₄₁	C₂³	1	1	yes	characteristic
70	#117×C₄₁	—	2	1	no	—
71	#117×C₄₁	—	2	2	no	—
72	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
73	#107×C₄₁	—	2	1	no	—
74	#107×C₄₁	—	2	1	no	—
75	#107×C₄₁	—	2	1	no	—
76	#107×C₄₁	—	2	1	no	—
77	#107×C₄₁	—	2	2	no	—
78	#106×C₄₁	—	2	2	no	—
79	#106×C₄₁	—	2	2	no	—
80	#106×C₄₁	—	2	2	no	—
81	C₄⋊C₈×C₄₁	—	2	1	no	—
82	C₄⋊C₈×C₄₁	—	2	1	no	—
83	C₄⋊C₈×C₄₁	—	2	2	no	—
84	C₄⋊C₈×C₄₁	C₂³	1	1	yes	characteristic
85	C₄⋊C₈×C₄₁	C₂³	1	1	yes	characteristic
86	C₄⋊C₈×C₄₁	C₂³	1	2	yes	—
87	C₄⋊C₈×C₄₁	C₂³	1	2	yes	—
88	#103×C₄₁	—	2	2	no	—
89	#103×C₄₁	—	2	2	no	—
90	#103×C₄₁	—	2	2	no	—
91	#102×C₄₁	—	2	2	no	—
92	C₂²⋊C₈×C₄₁	—	2	1	no	—
93	C₂²⋊C₈×C₄₁	—	2	1	no	—
94	C₂²⋊C₈×C₄₁	—	2	1	no	—
95	#97×C₄₁	—	2	1	no	—
96	#97×C₄₁	—	2	1	no	—
97	C₄×C₈×C₄₁	—	2	1	no	—
98	C₄×C₈×C₄₁	D₄	1	1	yes	characteristic
99	C₄×C₈×C₄₁	D₄	1	1	yes	characteristic
100	C₄×C₈×C₄₁	C₂³	1	1	yes	characteristic
101	C₄×C₈×C₄₁	C₂³	1	1	yes	characteristic
102	C₂×Q₈×C₄₁	—	2	2	no	—
103	C₂×Q₈×C₄₁	—	2	2	no	—
104	C₂×Q₈×C₄₁	C₂×D₄	1	1	yes	characteristic
105	C₂×D₄×C₄₁	—	2	1	no	—
106	C₂×D₄×C₄₁	C₂×D₄	1	1	yes	characteristic
107	C₂²×C₄×C₄₁	—	2	1	no	—
108	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
109	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
110	C₂²×C₄×C₄₁	#41	1	1	yes	characteristic
111	Q₁₆×C₄₁	—	8	2	no	—
112	SD₁₆×C₄₁	—	8	2	no	—
113	M₁₆×C₄₁	—	4	2	no	—
114	M₁₆×C₄₁	—	8	2	no	—
115	C₂×C₈×C₄₁	—	2	2	no	—
116	C₂×C₈×C₄₁	—	2	2	no	—
117	C₂×C₈×C₄₁	—	2	1	no	—
118	C₂×C₈×C₄₁	—	2	1	no	—
119	C₂×C₈×C₄₁	—	2	2	no	—
120	C₂×C₈×C₄₁	—	2	2	no	—
121	C₂×C₈×C₄₁	—	4	2	no	—
122	C₂×C₈×C₄₁	C₂×D₄	1	1	yes	characteristic
123	C₂×C₈×C₄₁	C₂×D₄	1	1	yes	characteristic
124	C₂×C₈×C₄₁	C₂×D₄	1	1	yes	characteristic
125	C₂×C₈×C₄₁	C₂×D₄	1	1	yes	characteristic
126	C₄⋊C₄×C₄₁	—	2	1	no	—
127	C₄⋊C₄×C₄₁	—	2	1	no	—
128	C₄⋊C₄×C₄₁	—	2	1	no	—
129	C₄⋊C₄×C₄₁	—	2	1	no	—
130	C₄⋊C₄×C₄₁	—	2	2	no	—
131	C₄⋊C₄×C₄₁	—	2	2	no	—
132	C₄⋊C₄×C₄₁	—	2	2	no	—
133	C₄⋊C₄×C₄₁	—	2	2	no	—
134	C₄⋊C₄×C₄₁	—	4	2	no	—
135	C₄⋊C₄×C₄₁	—	4	2	no	—
136	C₄⋊C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
137	C₄⋊C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
138	C₂²⋊C₄×C₄₁	—	2	1	no	—
139	C₂²⋊C₄×C₄₁	—	2	1	no	—
140	C₂²⋊C₄×C₄₁	—	2	1	no	—
141	C₂²⋊C₄×C₄₁	—	2	1	no	—
142	C₂²⋊C₄×C₄₁	—	2	1	no	—
143	C₂²⋊C₄×C₄₁	—	4	2	no	—
144	C₄²×C₄₁	—	2	1	no	—
145	C₄²×C₄₁	—	4	2	no	—
146	C₄²×C₄₁	C₂×D₄	1	1	yes	characteristic
147	C₄²×C₄₁	C₂×D₄	1	1	yes	characteristic
148	C₄²×C₄₁	#41	1	1	yes	characteristic
149	C₄²×C₄₁	C₂⁴	1	1	yes	characteristic
150	C₂³×C₄₁	—	2	1	no	—
151	C₂³×C₄₁	#121	1	1	yes	characteristic
152	Q₈×C₄₁	—	2	1	no	—
153	Q₈×C₄₁	—	2	1	no	—
154	Q₈×C₄₁	—	4	2	no	—
155	Q₈×C₄₁	—	4	2	no	—
156	Q₈×C₄₁	—	8	2	no	—
157	D₄×C₄₁	—	2	1	no	—
158	D₄×C₄₁	—	2	1	no	—
159	D₄×C₄₁	—	4	2	no	—
160	C₂×C₄×C₄₁	—	2	1	no	—
161	C₂×C₄×C₄₁	—	2	1	no	—
162	C₂×C₄×C₄₁	—	2	1	no	—
163	C₂×C₄×C₄₁	—	2	1	no	—
164	C₂×C₄×C₄₁	—	2	1	no	—
165	C₂×C₄×C₄₁	—	2	1	no	—
166	C₂×C₄×C₄₁	—	2	1	no	—
167	C₂×C₄×C₄₁	—	4	1	no	—
168	C₂×C₄×C₄₁	—	4	1	no	—
169	C₂×C₄×C₄₁	—	4	1	no	—
170	C₂×C₄×C₄₁	—	4	2	no	—
171	C₂×C₄×C₄₁	—	4	2	no	—
172	C₂×C₄×C₄₁	#121	1	1	yes	characteristic
173	C₂×C₄×C₄₁	#121	1	1	yes	characteristic
174	C₂×C₄×C₄₁	#121	1	1	yes	characteristic
175	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
176	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
177	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
178	C₈×C₄₁	—	2	1	no	—
179	C₈×C₄₁	—	2	1	no	—
180	C₈×C₄₁	—	4	1	no	—
181	C₈×C₄₁	—	4	1	no	—
182	C₈×C₄₁	—	4	2	no	—
183	C₈×C₄₁	—	4	2	no	—
184	C₈×C₄₁	#137	1	2	yes	—
185	C₈×C₄₁	#137	1	2	yes	—
186	#19361	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
187	C₂²×C₄₁	—	2	1	no	—
188	C₂²×C₄₁	—	2	1	no	—
189	C₂²×C₄₁	—	2	1	no	—
190	C₂²×C₄₁	—	4	1	no	—
191	C₂²×C₄₁	—	4	1	no	—
192	C₂²×C₄₁	—	4	1	no	—
193	C₂²×C₄₁	C₂×#121	1	1	yes	characteristic
194	C₄×C₄₁	—	2	1	no	—
195	C₄×C₄₁	—	2	1	no	—
196	C₄×C₄₁	—	2	1	no	—
197	C₄×C₄₁	—	2	1	no	—
198	C₄×C₄₁	—	4	1	no	—
199	C₄×C₄₁	—	4	1	no	—
200	C₄×C₄₁	—	4	1	no	—
201	C₄×C₄₁	—	8	2	no	—
202	C₄×C₄₁	—	8	2	no	—
203	C₄×C₄₁	C₂×#137	1	1	yes	characteristic
204	C₄×C₄₁	C₂×#137	1	1	yes	characteristic
205	C₄×C₄₁	#576	1	1	yes	characteristic
206	C₄×C₄₁	#578	1	1	yes	characteristic
207	#3252	C₂×C₄₁	1	2	yes	—
208	#3160	C₂×C₄₁	1	1	yes	characteristic, complemented
209	#2966	C₂×C₄₁	1	1	yes	characteristic
210	#1692	C₂×C₄₁	1	2	yes	complemented
211	#1691	C₂×C₄₁	1	2	yes	complemented
212	#1676	C₂×C₄₁	1	1	yes	characteristic, complemented
213	#1675	C₂×C₄₁	1	1	yes	characteristic, complemented
214	#1674	C₂×C₄₁	1	1	yes	characteristic, complemented
215	#1673	C₂×C₄₁	1	1	yes	characteristic, complemented
216	#1567	C₂×C₄₁	1	1	yes	characteristic, complemented
217	#1559	C₂×C₄₁	1	2	yes	complemented
218	C₂×C₄₁	—	4	1	no	—
219	C₂×C₄₁	—	8	1	no	—
220	C₂×C₄₁	#3039	1	1	yes	characteristic
221	C₂×C₄₁	#3061	1	1	yes	characteristic
222	C₂×C₄₁	#3067	1	1	yes	characteristic
223	#533	C₂²×C₄₁	1	2	yes	—
224	#529	C₂²×C₄₁	1	1	yes	characteristic
225	#500	C₂²×C₄₁	1	1	yes	characteristic
226	#500	C₂²×C₄₁	1	1	yes	characteristic
227	#499	—	2	1	no	—
228	#499	—	2	1	no	—
229	#498	C₂²×C₄₁	1	2	yes	—
230	#479	—	2	2	no	—
231	#477	C₂²×C₄₁	1	2	yes	—
232	#476	C₂²×C₄₁	1	2	yes	—
233	#470	—	2	2	no	—
234	#468	—	2	2	no	—
235	#464	—	2	2	no	—
236	#462	C₂²×C₄₁	1	2	yes	—
237	#461	C₂²×C₄₁	1	2	yes	—
238	#446	C₂²×C₄₁	1	1	yes	characteristic
239	C₈×Q₈	C₂²×C₄₁	1	1	yes	characteristic
240	#436	C₂²×C₄₁	1	1	yes	characteristic
241	#435	—	2	1	no	—
242	C₈×D₄	—	2	1	no	—
243	C₈×D₄	C₂²×C₄₁	1	1	yes	characteristic
244	#433	—	2	1	no	—
245	#432	C₂²×C₄₁	1	1	yes	characteristic
246	#427	—	2	1	no	—
247	#427	—	2	1	no	—
248	#423	C₂²×C₄₁	1	2	yes	—
249	#405	—	2	1	no	—
250	C₂×C₄×C₈	C₂²×C₄₁	1	1	yes	characteristic
251	#335	C₂²×C₄₁	1	1	yes	characteristic
252	#335	C₂²×C₄₁	1	1	yes	characteristic
253	#335	C₂²×C₄₁	1	2	yes	—
254	#333	C₂²×C₄₁	1	2	yes	—
255	#333	C₂²×C₄₁	1	2	yes	—
256	#332	C₂²×C₄₁	1	2	yes	—
257	#332	C₂²×C₄₁	1	2	yes	—
258	C₄₁	#19361	1	1	yes	characteristic, direct product factor, Sylow
259	C₂×Q₁₆	—	2	2	no	—
260	C₂×SD₁₆	—	2	2	no	—
261	C₂×M₁₆	—	2	2	no	—
262	C₂×M₁₆	—	2	1	no	—
263	C₂²×C₈	—	2	1	no	—
264	C₂²×C₈	D₄×C₄₁	1	1	yes	characteristic
265	C₂²×C₈	D₄×C₄₁	1	1	yes	characteristic
266	C₄⋊Q₈	C₂³×C₄₁	1	2	yes	—
267	C₄⋊Q₈	C₂³×C₄₁	1	2	yes	—
268	#126	—	2	1	no	—
269	#125	—	2	2	no	—
270	#125	D₄×C₄₁	1	1	yes	characteristic
271	#124	D₄×C₄₁	1	1	yes	characteristic
272	#123	—	2	1	no	—
273	C₂²⋊Q₈	—	2	2	no	—
274	C₂²⋊Q₈	—	2	2	no	—
275	C₂²⋊Q₈	D₄×C₄₁	1	1	yes	characteristic
276	#121	D₄×C₄₁	1	1	yes	characteristic
277	C₄×Q₈	—	2	2	no	—
278	C₄×Q₈	—	2	2	no	—
279	C₄×Q₈	C₂³×C₄₁	1	1	yes	characteristic
280	C₄×D₄	—	2	1	no	—
281	C₄×D₄	C₂³×C₄₁	1	1	yes	characteristic
282	#117	—	2	1	no	—
283	#117	—	2	2	no	—
284	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
285	#107	—	2	1	no	—
286	#107	—	2	1	no	—
287	#107	—	2	1	no	—
288	#107	—	2	1	no	—
289	#107	—	2	2	no	—
290	#106	—	2	2	no	—
291	#106	—	2	2	no	—
292	#106	—	2	2	no	—
293	C₄⋊C₈	—	2	1	no	—
294	C₄⋊C₈	—	2	1	no	—
295	C₄⋊C₈	—	2	2	no	—
296	C₄⋊C₈	C₂³×C₄₁	1	1	yes	characteristic
297	C₄⋊C₈	C₂³×C₄₁	1	1	yes	characteristic
298	C₄⋊C₈	C₂³×C₄₁	1	2	yes	—
299	C₄⋊C₈	C₂³×C₄₁	1	2	yes	—
300	#103	—	2	2	no	—
301	#103	—	2	2	no	—
302	#103	—	2	2	no	—
303	#102	—	2	2	no	—
304	C₂²⋊C₈	—	2	1	no	—
305	C₂²⋊C₈	—	2	1	no	—
306	C₂²⋊C₈	—	2	1	no	—
307	#97	—	2	1	no	—
308	#97	—	2	1	no	—
309	C₄×C₈	—	2	1	no	—
310	C₄×C₈	D₄×C₄₁	1	1	yes	characteristic
311	C₄×C₈	D₄×C₄₁	1	1	yes	characteristic
312	C₄×C₈	C₂³×C₄₁	1	1	yes	characteristic
313	C₄×C₈	C₂³×C₄₁	1	1	yes	characteristic
314	C₂×Q₈	—	2	2	no	—
315	C₂×Q₈	—	2	2	no	—
316	C₂×Q₈	C₂×D₄×C₄₁	1	1	yes	characteristic
317	C₂×D₄	—	2	1	no	—
318	C₂×D₄	C₂×D₄×C₄₁	1	1	yes	characteristic
319	C₂²×C₄	—	2	1	no	—
320	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
321	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
322	C₂²×C₄	#41×C₄₁	1	1	yes	characteristic
323	Q₁₆	—	8	2	no	—
324	SD₁₆	—	8	2	no	—
325	M₁₆	—	4	2	no	—
326	M₁₆	—	8	2	no	—
327	C₂×C₈	—	2	2	no	—
328	C₂×C₈	—	2	2	no	—
329	C₂×C₈	—	2	1	no	—
330	C₂×C₈	—	2	1	no	—
331	C₂×C₈	—	2	2	no	—
332	C₂×C₈	—	2	2	no	—
333	C₂×C₈	—	4	2	no	—
334	C₂×C₈	C₂×D₄×C₄₁	1	1	yes	characteristic
335	C₂×C₈	C₂×D₄×C₄₁	1	1	yes	characteristic
336	C₂×C₈	C₂×D₄×C₄₁	1	1	yes	characteristic
337	C₂×C₈	C₂×D₄×C₄₁	1	1	yes	characteristic
338	C₄⋊C₄	—	2	1	no	—
339	C₄⋊C₄	—	2	1	no	—
340	C₄⋊C₄	—	2	1	no	—
341	C₄⋊C₄	—	2	1	no	—
342	C₄⋊C₄	—	2	2	no	—
343	C₄⋊C₄	—	2	2	no	—
344	C₄⋊C₄	—	2	2	no	—
345	C₄⋊C₄	—	2	2	no	—
346	C₄⋊C₄	—	4	2	no	—
347	C₄⋊C₄	—	4	2	no	—
348	C₄⋊C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
349	C₄⋊C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
350	C₂²⋊C₄	—	2	1	no	—
351	C₂²⋊C₄	—	2	1	no	—
352	C₂²⋊C₄	—	2	1	no	—
353	C₂²⋊C₄	—	2	1	no	—
354	C₂²⋊C₄	—	2	1	no	—
355	C₂²⋊C₄	—	4	2	no	—
356	C₄²	—	2	1	no	—
357	C₄²	—	4	2	no	—
358	C₄²	C₂×D₄×C₄₁	1	1	yes	characteristic
359	C₄²	C₂×D₄×C₄₁	1	1	yes	characteristic
360	C₄²	#41×C₄₁	1	1	yes	characteristic
361	C₄²	C₂⁴×C₄₁	1	1	yes	characteristic
362	C₂³	—	2	1	no	—
363	C₂³	#121×C₄₁	1	1	yes	characteristic
364	Q₈	—	2	1	no	—
365	Q₈	—	2	1	no	—
366	Q₈	—	4	2	no	—
367	Q₈	—	4	2	no	—
368	Q₈	—	8	2	no	—
369	D₄	—	2	1	no	—
370	D₄	—	2	1	no	—
371	D₄	—	4	2	no	—
372	C₂×C₄	—	2	1	no	—
373	C₂×C₄	—	2	1	no	—
374	C₂×C₄	—	2	1	no	—
375	C₂×C₄	—	2	1	no	—
376	C₂×C₄	—	2	1	no	—
377	C₂×C₄	—	2	1	no	—
378	C₂×C₄	—	2	1	no	—
379	C₂×C₄	—	4	1	no	—
380	C₂×C₄	—	4	1	no	—
381	C₂×C₄	—	4	1	no	—
382	C₂×C₄	—	4	2	no	—
383	C₂×C₄	—	4	2	no	—
384	C₂×C₄	#121×C₄₁	1	1	yes	characteristic
385	C₂×C₄	#121×C₄₁	1	1	yes	characteristic
386	C₂×C₄	#121×C₄₁	1	1	yes	characteristic
387	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
388	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
389	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
390	C₈	—	2	1	no	—
391	C₈	—	2	1	no	—
392	C₈	—	4	1	no	—
393	C₈	—	4	1	no	—
394	C₈	—	4	2	no	—
395	C₈	—	4	2	no	—
396	C₈	#137×C₄₁	1	2	yes	—
397	C₈	#137×C₄₁	1	2	yes	—
398	C₂²	—	2	1	no	—
399	C₂²	—	2	1	no	—
400	C₂²	—	2	1	no	—
401	C₂²	—	4	1	no	—
402	C₂²	—	4	1	no	—
403	C₂²	—	4	1	no	—
404	C₂²	C₂×#121×C₄₁	1	1	yes	characteristic
405	C₄	—	2	1	no	—
406	C₄	—	2	1	no	—
407	C₄	—	2	1	no	—
408	C₄	—	2	1	no	—
409	C₄	—	4	1	no	—
410	C₄	—	4	1	no	—
411	C₄	—	4	1	no	—
412	C₄	—	8	2	no	—
413	C₄	—	8	2	no	—
414	C₄	C₂×#137×C₄₁	1	1	yes	characteristic
415	C₄	C₂×#137×C₄₁	1	1	yes	characteristic
416	C₄	C₄₁×#576	1	1	yes	characteristic
417	C₄	C₄₁×#578	1	1	yes	characteristic
418	C₂	—	4	1	no	—
419	C₂	—	8	1	no	—
420	C₂	C₄₁×#3039	1	1	yes	characteristic
421	C₂	C₄₁×#3061	1	1	yes	characteristic
422	C₂	C₄₁×#3067	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₄₁	C₂×#121
commutator, Frattini, cosocle	C₄²	C₂⁴×C₄₁
prime radical	#121×C₄₁	D₄
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×#3160	C₂	semidirect
4. C₄₁×#1692	C₂	semidirect
5. C₄₁×#1691	C₂	semidirect
6. C₄₁×#1676	C₂	semidirect
7. C₄₁×#1675	C₂	semidirect
8. C₄₁×#1674	C₂	semidirect
9. C₄₁×#1673	C₂	semidirect
10. C₄₁×#1567	C₂	semidirect
11. C₄₁×#1559	C₂	semidirect
186. #19361	C₄₁	direct (N × H)
208. #3160	C₂×C₄₁	semidirect
210. #1692	C₂×C₄₁	semidirect
211. #1691	C₂×C₄₁	semidirect
212. #1676	C₂×C₄₁	semidirect
213. #1675	C₂×C₄₁	semidirect
214. #1674	C₂×C₄₁	semidirect
215. #1673	C₂×C₄₁	semidirect
216. #1567	C₂×C₄₁	semidirect
217. #1559	C₂×C₄₁	semidirect
258. C₄₁	#19361	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×#3252	2
C₄₁×#3160	2
C₄₁×#2966	2
C₄₁×#1692	2
C₄₁×#1691	2
C₄₁×#1676	2
C₄₁×#1675	2
C₄₁×#1674	2
C₄₁×#1673	2
C₄₁×#1567	2
C₄₁×#1559	2
#19361	41

Subgroups — C41×#19361 #23795562

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#19361 #23795562