Subgroups — C₄₁×#11101 #23787302

Order 10496.

974 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₁×#430	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄₁×#407	C₂	1	2	yes	maximal
3	C₂×C₄₁×#407	C₂	1	1	yes	maximal, characteristic
4	C₄₁×#1738	C₂	1	2	yes	maximal, complemented
5	C₂×C₄₁×#338	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂⁴×C₄×C₄₁	C₂²	1	1	yes	characteristic
7	C₂²×M₁₆×C₄₁	C₂²	1	1	yes	characteristic
8	C₂²×M₁₆×C₄₁	C₂²	1	2	yes	—
9	C₂²×M₁₆×C₄₁	C₂²	1	2	yes	—
10	C₂²×M₁₆×C₄₁	C₂²	1	1	yes	characteristic
11	C₄₁×#430	—	2	4	no	—
12	C₂×#108×C₄₁	—	2	2	no	—
13	C₄₁×#407	—	2	4	no	—
14	C₄₁×#407	—	2	4	no	—
15	C₄₁×#407	—	2	2	no	—
16	C₄₁×#407	C₄	1	4	yes	—
17	C₂×C₂²⋊C₈×C₄₁	—	2	4	no	—
18	C₂×C₂²⋊C₈×C₄₁	—	2	2	no	—
19	C₄₁×#341	—	2	4	no	—
20	C₄₁×#338	—	2	2	no	—
21	C₂⁵×C₄₁	Q₈	1	1	yes	characteristic
22	C₂³×C₄×C₄₁	—	2	1	no	—
23	C₂³×C₄×C₄₁	—	2	2	no	—
24	C₂³×C₄×C₄₁	—	2	1	no	—
25	C₂³×C₄×C₄₁	—	2	2	no	—
26	C₂³×C₄×C₄₁	—	2	1	no	—
27	C₂³×C₄×C₄₁	—	2	1	no	—
28	C₂³×C₄×C₄₁	—	2	2	no	—
29	C₂³×C₄×C₄₁	—	2	2	no	—
30	C₂³×C₄×C₄₁	C₂×C₄	1	2	yes	—
31	C₂³×C₄×C₄₁	D₄	1	2	yes	—
32	C₂³×C₄×C₄₁	Q₈	1	1	yes	characteristic
33	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
34	C₂×M₁₆×C₄₁	—	2	2	no	—
35	C₂×M₁₆×C₄₁	—	2	2	no	—
36	C₂×M₁₆×C₄₁	—	2	2	no	—
37	C₂×M₁₆×C₄₁	—	2	1	no	—
38	C₂×M₁₆×C₄₁	—	2	2	no	—
39	C₂×M₁₆×C₄₁	—	2	2	no	—
40	C₂×M₁₆×C₄₁	—	2	2	no	—
41	C₂×M₁₆×C₄₁	—	2	2	no	—
42	C₂×M₁₆×C₄₁	—	2	2	no	—
43	C₂×M₁₆×C₄₁	—	2	2	no	—
44	C₂×M₁₆×C₄₁	—	2	2	no	—
45	C₂×M₁₆×C₄₁	—	2	2	no	—
46	C₂×M₁₆×C₄₁	—	2	2	no	—
47	C₂×M₁₆×C₄₁	—	2	2	no	—
48	C₂×M₁₆×C₄₁	—	2	2	no	—
49	C₂×M₁₆×C₄₁	—	2	2	no	—
50	C₂×M₁₆×C₄₁	C₂×C₄	1	2	yes	—
51	C₂×M₁₆×C₄₁	C₂×C₄	1	2	yes	—
52	C₂×M₁₆×C₄₁	D₄	1	4	yes	—
53	C₂×M₁₆×C₄₁	D₄	1	2	yes	—
54	C₂²×C₈×C₄₁	—	2	1	no	—
55	C₂²×C₈×C₄₁	—	2	2	no	—
56	C₂²×C₈×C₄₁	D₄	1	4	yes	—
57	C₂²×C₈×C₄₁	D₄	1	2	yes	—
58	#108×C₄₁	—	2	8	no	—
59	C₂²⋊C₈×C₄₁	—	2	16	no	—
60	C₂²⋊C₈×C₄₁	—	2	8	no	—
61	C₂⁴×C₄₁	—	2	1	no	—
62	C₂⁴×C₄₁	—	2	2	no	—
63	C₂⁴×C₄₁	—	2	1	no	—
64	C₂⁴×C₄₁	—	2	2	no	—
65	C₂⁴×C₄₁	—	4	4	no	—
66	C₂⁴×C₄₁	C₄⋊C₄	1	2	yes	—
67	C₂⁴×C₄₁	C₂×Q₈	1	1	yes	characteristic
68	C₂²×C₄×C₄₁	—	2	1	no	—
69	C₂²×C₄×C₄₁	—	2	1	no	—
70	C₂²×C₄×C₄₁	—	2	2	no	—
71	C₂²×C₄×C₄₁	—	2	2	no	—
72	C₂²×C₄×C₄₁	—	2	2	no	—
73	C₂²×C₄×C₄₁	—	2	2	no	—
74	C₂²×C₄×C₄₁	—	2	4	no	—
75	C₂²×C₄×C₄₁	—	2	4	no	—
76	C₂²×C₄×C₄₁	—	2	4	no	—
77	C₂²×C₄×C₄₁	—	2	2	no	—
78	C₂²×C₄×C₄₁	—	2	2	no	—
79	C₂²×C₄×C₄₁	—	2	4	no	—
80	C₂²×C₄×C₄₁	—	4	1	no	—
81	C₂²×C₄×C₄₁	—	4	2	no	—
82	C₂²×C₄×C₄₁	—	4	2	no	—
83	C₂²×C₄×C₄₁	—	4	2	no	—
84	C₂²×C₄×C₄₁	—	4	1	no	—
85	C₂²×C₄×C₄₁	—	4	2	no	—
86	C₂²×C₄×C₄₁	—	4	2	no	—
87	C₂²×C₄×C₄₁	—	4	1	no	—
88	C₂²×C₄×C₄₁	—	4	2	no	—
89	C₂²×C₄×C₄₁	—	4	1	no	—
90	C₂²×C₄×C₄₁	C₄⋊C₄	1	2	yes	—
91	C₂²×C₄×C₄₁	C₂²×C₄	1	1	yes	characteristic
92	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
93	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
94	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
95	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
96	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
97	C₂²×C₄×C₄₁	#41	1	1	yes	characteristic
98	C₂²×C₄×C₄₁	#41	1	1	yes	characteristic
99	C₂²×C₄×C₄₁	#41	1	2	yes	—
100	C₂²×C₄×C₄₁	#41	1	2	yes	—
101	M₁₆×C₄₁	—	2	4	no	—
102	M₁₆×C₄₁	—	2	4	no	—
103	M₁₆×C₄₁	—	2	4	no	—
104	M₁₆×C₄₁	—	2	4	no	—
105	M₁₆×C₄₁	—	2	4	no	—
106	M₁₆×C₄₁	—	4	2	no	—
107	M₁₆×C₄₁	—	4	2	no	—
108	M₁₆×C₄₁	—	4	2	no	—
109	M₁₆×C₄₁	—	4	2	no	—
110	M₁₆×C₄₁	—	4	2	no	—
111	M₁₆×C₄₁	—	4	2	no	—
112	M₁₆×C₄₁	—	4	2	no	—
113	C₂×C₈×C₄₁	—	2	2	no	—
114	C₂×C₈×C₄₁	—	2	2	no	—
115	C₂×C₈×C₄₁	—	2	2	no	—
116	C₂×C₈×C₄₁	—	2	4	no	—
117	C₂×C₈×C₄₁	—	2	4	no	—
118	C₂×C₈×C₄₁	—	2	4	no	—
119	C₂×C₈×C₄₁	—	2	4	no	—
120	C₂×C₈×C₄₁	—	4	2	no	—
121	C₂×C₈×C₄₁	—	4	1	no	—
122	C₂×C₈×C₄₁	—	4	1	no	—
123	C₂×C₈×C₄₁	—	4	2	no	—
124	C₂×C₈×C₄₁	C₂²⋊C₄	1	4	yes	—
125	C₂³×C₄₁	—	2	4	no	—
126	C₂³×C₄₁	—	2	8	no	—
127	C₂³×C₄₁	—	2	2	no	—
128	C₂³×C₄₁	—	2	4	no	—
129	C₂³×C₄₁	—	4	4	no	—
130	C₂³×C₄₁	—	4	2	no	—
131	C₂³×C₄₁	—	4	2	no	—
132	C₂³×C₄₁	—	4	4	no	—
133	C₂³×C₄₁	—	4	4	no	—
134	C₂³×C₄₁	—	4	8	no	—
135	C₂³×C₄₁	—	4	1	no	—
136	C₂³×C₄₁	—	4	2	no	—
137	C₂³×C₄₁	—	4	1	no	—
138	C₂³×C₄₁	C₂×C₄⋊C₄	1	1	yes	characteristic
139	C₂³×C₄₁	C₂²⋊Q₈	1	1	yes	characteristic
140	C₂³×C₄₁	C₂²⋊Q₈	1	2	yes	—
141	C₂³×C₄₁	C₂²⋊Q₈	1	1	yes	characteristic
142	C₂³×C₄₁	C₂²⋊Q₈	1	2	yes	—
143	C₂×C₄×C₄₁	—	2	2	no	—
144	C₂×C₄×C₄₁	—	2	4	no	—
145	C₂×C₄×C₄₁	—	4	1	no	—
146	C₂×C₄×C₄₁	—	4	2	no	—
147	C₂×C₄×C₄₁	—	4	1	no	—
148	C₂×C₄×C₄₁	—	4	2	no	—
149	C₂×C₄×C₄₁	—	4	4	no	—
150	C₂×C₄×C₄₁	—	4	2	no	—
151	C₂×C₄×C₄₁	—	4	2	no	—
152	C₂×C₄×C₄₁	—	4	4	no	—
153	C₂×C₄×C₄₁	—	4	2	no	—
154	C₂×C₄×C₄₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
155	C₂×C₄×C₄₁	#117	1	1	yes	characteristic
156	C₂×C₄×C₄₁	C₄×D₄	1	2	yes	—
157	C₂×C₄×C₄₁	C₄×D₄	1	2	yes	—
158	C₂×C₄×C₄₁	#120	1	1	yes	characteristic
159	C₂×C₄×C₄₁	#120	1	2	yes	—
160	C₂×C₄×C₄₁	#121	1	2	yes	—
161	C₂×C₄×C₄₁	#121	1	2	yes	—
162	C₂×C₄×C₄₁	#121	1	2	yes	—
163	C₂×C₄×C₄₁	#121	1	1	yes	characteristic
164	C₂×C₄×C₄₁	#121	1	1	yes	characteristic
165	C₂×C₄×C₄₁	#123	1	1	yes	characteristic
166	C₂×C₄×C₄₁	#123	1	2	yes	—
167	C₂×C₄×C₄₁	#123	1	2	yes	—
168	C₂×C₄×C₄₁	#124	1	2	yes	—
169	C₂×C₄×C₄₁	#124	1	1	yes	characteristic
170	C₂×C₄×C₄₁	#126	1	2	yes	—
171	C₂×C₄×C₄₁	#127	1	1	yes	characteristic
172	C₈×C₄₁	—	2	4	no	—
173	C₈×C₄₁	—	4	2	no	—
174	C₈×C₄₁	—	4	4	no	—
175	C₈×C₄₁	—	4	4	no	—
176	#11101	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
177	C₂²×C₄₁	—	2	2	no	—
178	C₂²×C₄₁	—	2	4	no	—
179	C₂²×C₄₁	—	2	4	no	—
180	C₂²×C₄₁	—	2	8	no	—
181	C₂²×C₄₁	—	4	1	no	—
182	C₂²×C₄₁	—	4	1	no	—
183	C₂²×C₄₁	—	4	2	no	—
184	C₂²×C₄₁	—	4	2	no	—
185	C₂²×C₄₁	—	4	4	no	—
186	C₂²×C₄₁	—	4	4	no	—
187	C₂²×C₄₁	—	4	8	no	—
188	C₂²×C₄₁	—	4	4	no	—
189	C₂²×C₄₁	—	4	2	no	—
190	C₂²×C₄₁	#380	1	1	yes	characteristic
191	C₂²×C₄₁	#385	1	2	yes	—
192	C₂²×C₄₁	#393	1	1	yes	characteristic
193	C₂²×C₄₁	#396	1	2	yes	—
194	C₂²×C₄₁	#399	1	1	yes	characteristic
195	C₄×C₄₁	—	4	2	no	—
196	C₄×C₄₁	#386	1	1	yes	characteristic
197	C₄×C₄₁	#388	1	2	yes	—
198	C₄×C₄₁	#390	1	1	yes	characteristic
199	C₄×C₄₁	#392	1	1	yes	characteristic
200	C₄×C₄₁	#394	1	2	yes	—
201	C₄×C₄₁	#397	1	1	yes	characteristic
202	C₂×#430	C₂×C₄₁	1	1	yes	characteristic, complemented
203	C₂×#407	C₂×C₄₁	1	2	yes	—
204	C₂×#407	C₂×C₄₁	1	1	yes	characteristic
205	#1738	C₂×C₄₁	1	2	yes	complemented
206	C₂×#338	C₂×C₄₁	1	1	yes	characteristic, complemented
207	C₂×C₄₁	—	2	1	no	—
208	C₂×C₄₁	—	2	2	no	—
209	C₂×C₄₁	—	2	1	no	—
210	C₂×C₄₁	—	2	2	no	—
211	C₂×C₄₁	—	4	4	no	—
212	C₂×C₄₁	#1439	1	1	yes	characteristic
213	C₂×C₄₁	#2091	1	2	yes	—
214	C₂⁴×C₄	C₂²×C₄₁	1	1	yes	characteristic
215	C₂²×M₁₆	C₂²×C₄₁	1	1	yes	characteristic
216	C₂²×M₁₆	C₂²×C₄₁	1	2	yes	—
217	C₂²×M₁₆	C₂²×C₄₁	1	2	yes	—
218	C₂²×M₁₆	C₂²×C₄₁	1	1	yes	characteristic
219	#430	—	2	4	no	—
220	C₂×#108	—	2	2	no	—
221	#407	—	2	4	no	—
222	#407	—	2	4	no	—
223	#407	—	2	2	no	—
224	#407	C₄×C₄₁	1	4	yes	—
225	C₂×C₂²⋊C₈	—	2	4	no	—
226	C₂×C₂²⋊C₈	—	2	2	no	—
227	#341	—	2	4	no	—
228	#338	—	2	2	no	—
229	C₄₁	#11101	1	1	yes	characteristic, direct product factor, Sylow
230	C₂⁵	Q₈×C₄₁	1	1	yes	characteristic
231	C₂³×C₄	—	2	1	no	—
232	C₂³×C₄	—	2	2	no	—
233	C₂³×C₄	—	2	1	no	—
234	C₂³×C₄	—	2	2	no	—
235	C₂³×C₄	—	2	1	no	—
236	C₂³×C₄	—	2	1	no	—
237	C₂³×C₄	—	2	2	no	—
238	C₂³×C₄	—	2	2	no	—
239	C₂³×C₄	C₂×C₄×C₄₁	1	2	yes	—
240	C₂³×C₄	D₄×C₄₁	1	2	yes	—
241	C₂³×C₄	Q₈×C₄₁	1	1	yes	characteristic
242	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
243	C₂×M₁₆	—	2	2	no	—
244	C₂×M₁₆	—	2	2	no	—
245	C₂×M₁₆	—	2	2	no	—
246	C₂×M₁₆	—	2	1	no	—
247	C₂×M₁₆	—	2	2	no	—
248	C₂×M₁₆	—	2	2	no	—
249	C₂×M₁₆	—	2	2	no	—
250	C₂×M₁₆	—	2	2	no	—
251	C₂×M₁₆	—	2	2	no	—
252	C₂×M₁₆	—	2	2	no	—
253	C₂×M₁₆	—	2	2	no	—
254	C₂×M₁₆	—	2	2	no	—
255	C₂×M₁₆	—	2	2	no	—
256	C₂×M₁₆	—	2	2	no	—
257	C₂×M₁₆	—	2	2	no	—
258	C₂×M₁₆	—	2	2	no	—
259	C₂×M₁₆	C₂×C₄×C₄₁	1	2	yes	—
260	C₂×M₁₆	C₂×C₄×C₄₁	1	2	yes	—
261	C₂×M₁₆	D₄×C₄₁	1	4	yes	—
262	C₂×M₁₆	D₄×C₄₁	1	2	yes	—
263	C₂²×C₈	—	2	1	no	—
264	C₂²×C₈	—	2	2	no	—
265	C₂²×C₈	D₄×C₄₁	1	4	yes	—
266	C₂²×C₈	D₄×C₄₁	1	2	yes	—
267	#108	—	2	8	no	—
268	C₂²⋊C₈	—	2	16	no	—
269	C₂²⋊C₈	—	2	8	no	—
270	C₂⁴	—	2	1	no	—
271	C₂⁴	—	2	2	no	—
272	C₂⁴	—	2	1	no	—
273	C₂⁴	—	2	2	no	—
274	C₂⁴	—	4	4	no	—
275	C₂⁴	C₄⋊C₄×C₄₁	1	2	yes	—
276	C₂⁴	C₂×Q₈×C₄₁	1	1	yes	characteristic
277	C₂²×C₄	—	2	1	no	—
278	C₂²×C₄	—	2	1	no	—
279	C₂²×C₄	—	2	2	no	—
280	C₂²×C₄	—	2	2	no	—
281	C₂²×C₄	—	2	2	no	—
282	C₂²×C₄	—	2	2	no	—
283	C₂²×C₄	—	2	4	no	—
284	C₂²×C₄	—	2	4	no	—
285	C₂²×C₄	—	2	4	no	—
286	C₂²×C₄	—	2	2	no	—
287	C₂²×C₄	—	2	2	no	—
288	C₂²×C₄	—	2	4	no	—
289	C₂²×C₄	—	4	1	no	—
290	C₂²×C₄	—	4	2	no	—
291	C₂²×C₄	—	4	2	no	—
292	C₂²×C₄	—	4	2	no	—
293	C₂²×C₄	—	4	1	no	—
294	C₂²×C₄	—	4	2	no	—
295	C₂²×C₄	—	4	2	no	—
296	C₂²×C₄	—	4	1	no	—
297	C₂²×C₄	—	4	2	no	—
298	C₂²×C₄	—	4	1	no	—
299	C₂²×C₄	C₄⋊C₄×C₄₁	1	2	yes	—
300	C₂²×C₄	C₂²×C₄×C₄₁	1	1	yes	characteristic
301	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
302	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
303	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
304	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
305	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
306	C₂²×C₄	#41×C₄₁	1	1	yes	characteristic
307	C₂²×C₄	#41×C₄₁	1	1	yes	characteristic
308	C₂²×C₄	#41×C₄₁	1	2	yes	—
309	C₂²×C₄	#41×C₄₁	1	2	yes	—
310	M₁₆	—	2	4	no	—
311	M₁₆	—	2	4	no	—
312	M₁₆	—	2	4	no	—
313	M₁₆	—	2	4	no	—
314	M₁₆	—	2	4	no	—
315	M₁₆	—	4	2	no	—
316	M₁₆	—	4	2	no	—
317	M₁₆	—	4	2	no	—
318	M₁₆	—	4	2	no	—
319	M₁₆	—	4	2	no	—
320	M₁₆	—	4	2	no	—
321	M₁₆	—	4	2	no	—
322	C₂×C₈	—	2	2	no	—
323	C₂×C₈	—	2	2	no	—
324	C₂×C₈	—	2	2	no	—
325	C₂×C₈	—	2	4	no	—
326	C₂×C₈	—	2	4	no	—
327	C₂×C₈	—	2	4	no	—
328	C₂×C₈	—	2	4	no	—
329	C₂×C₈	—	4	2	no	—
330	C₂×C₈	—	4	1	no	—
331	C₂×C₈	—	4	1	no	—
332	C₂×C₈	—	4	2	no	—
333	C₂×C₈	C₂²⋊C₄×C₄₁	1	4	yes	—
334	C₂³	—	2	4	no	—
335	C₂³	—	2	8	no	—
336	C₂³	—	2	2	no	—
337	C₂³	—	2	4	no	—
338	C₂³	—	4	4	no	—
339	C₂³	—	4	2	no	—
340	C₂³	—	4	2	no	—
341	C₂³	—	4	4	no	—
342	C₂³	—	4	4	no	—
343	C₂³	—	4	8	no	—
344	C₂³	—	4	1	no	—
345	C₂³	—	4	2	no	—
346	C₂³	—	4	1	no	—
347	C₂³	C₂×C₄⋊C₄×C₄₁	1	1	yes	characteristic
348	C₂³	C₂²⋊Q₈×C₄₁	1	1	yes	characteristic
349	C₂³	C₂²⋊Q₈×C₄₁	1	2	yes	—
350	C₂³	C₂²⋊Q₈×C₄₁	1	1	yes	characteristic
351	C₂³	C₂²⋊Q₈×C₄₁	1	2	yes	—
352	C₂×C₄	—	2	2	no	—
353	C₂×C₄	—	2	4	no	—
354	C₂×C₄	—	4	1	no	—
355	C₂×C₄	—	4	2	no	—
356	C₂×C₄	—	4	1	no	—
357	C₂×C₄	—	4	2	no	—
358	C₂×C₄	—	4	4	no	—
359	C₂×C₄	—	4	2	no	—
360	C₂×C₄	—	4	2	no	—
361	C₂×C₄	—	4	4	no	—
362	C₂×C₄	—	4	2	no	—
363	C₂×C₄	C₂×C₂²⋊C₄×C₄₁	1	1	yes	characteristic
364	C₂×C₄	#117×C₄₁	1	1	yes	characteristic
365	C₂×C₄	C₄×D₄×C₄₁	1	2	yes	—
366	C₂×C₄	C₄×D₄×C₄₁	1	2	yes	—
367	C₂×C₄	#120×C₄₁	1	1	yes	characteristic
368	C₂×C₄	#120×C₄₁	1	2	yes	—
369	C₂×C₄	#121×C₄₁	1	2	yes	—
370	C₂×C₄	#121×C₄₁	1	2	yes	—
371	C₂×C₄	#121×C₄₁	1	2	yes	—
372	C₂×C₄	#121×C₄₁	1	1	yes	characteristic
373	C₂×C₄	#121×C₄₁	1	1	yes	characteristic
374	C₂×C₄	#123×C₄₁	1	1	yes	characteristic
375	C₂×C₄	#123×C₄₁	1	2	yes	—
376	C₂×C₄	#123×C₄₁	1	2	yes	—
377	C₂×C₄	#124×C₄₁	1	2	yes	—
378	C₂×C₄	#124×C₄₁	1	1	yes	characteristic
379	C₂×C₄	#126×C₄₁	1	2	yes	—
380	C₂×C₄	#127×C₄₁	1	1	yes	characteristic
381	C₈	—	2	4	no	—
382	C₈	—	4	2	no	—
383	C₈	—	4	4	no	—
384	C₈	—	4	4	no	—
385	C₂²	—	2	2	no	—
386	C₂²	—	2	4	no	—
387	C₂²	—	2	4	no	—
388	C₂²	—	2	8	no	—
389	C₂²	—	4	1	no	—
390	C₂²	—	4	1	no	—
391	C₂²	—	4	2	no	—
392	C₂²	—	4	2	no	—
393	C₂²	—	4	4	no	—
394	C₂²	—	4	4	no	—
395	C₂²	—	4	8	no	—
396	C₂²	—	4	4	no	—
397	C₂²	—	4	2	no	—
398	C₂²	C₄₁×#380	1	1	yes	characteristic
399	C₂²	C₄₁×#385	1	2	yes	—
400	C₂²	C₄₁×#393	1	1	yes	characteristic
401	C₂²	C₄₁×#396	1	2	yes	—
402	C₂²	C₄₁×#399	1	1	yes	characteristic
403	C₄	—	4	2	no	—
404	C₄	C₄₁×#386	1	1	yes	characteristic
405	C₄	C₄₁×#388	1	2	yes	—
406	C₄	C₄₁×#390	1	1	yes	characteristic
407	C₄	C₄₁×#392	1	1	yes	characteristic
408	C₄	C₄₁×#394	1	2	yes	—
409	C₄	C₄₁×#397	1	1	yes	characteristic
410	C₂	—	2	1	no	—
411	C₂	—	2	2	no	—
412	C₂	—	2	1	no	—
413	C₂	—	2	2	no	—
414	C₂	—	4	4	no	—
415	C₂	C₄₁×#1439	1	1	yes	characteristic
416	C₂	C₄₁×#2091	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₄₁	#127
commutator	C₂²×C₄	C₂²×C₄×C₄₁
Frattini, cosocle	C₂³×C₄	C₂³×C₄₁
socle	C₂²×C₄₁	#399
prime radical	C₂⁵×C₄₁	Q₈
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₄₁ ◁ C₂³×C₄×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₄₁×#430	C₂	semidirect
4. C₄₁×#1738	C₂	semidirect
5. C₂×C₄₁×#338	C₂	semidirect
176. #11101	C₄₁	direct (N × H)
202. C₂×#430	C₂×C₄₁	semidirect
205. #1738	C₂×C₄₁	semidirect
206. C₂×#338	C₂×C₄₁	semidirect
229. C₄₁	#11101	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₄₁×#430	2
C₂×C₄₁×#407	2
C₄₁×#1738	2
C₂×C₄₁×#338	2
#11101	41

Subgroups — C41×#11101 #23787302

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#11101 #23787302