Subgroups — C₄₁×#22197 #23798398

Order 10496.

822 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	C₂×C₄₁×#467	C₂	1	1	yes	maximal, characteristic
2	C₄₁×#2323	C₂	1	2	yes	maximal
3	C₄₁×#1928	C₂	1	2	yes	maximal, complemented
4	C₄₁×#1918	C₂	1	2	yes	maximal, complemented
5	C₄₁×#1894	C₂	1	2	yes	maximal
6	C₄₁×#1878	C₂	1	2	yes	maximal, complemented
7	C₄₁×#1863	C₂	1	2	yes	maximal, complemented
8	C₄₁×#1808	C₂	1	1	yes	maximal, characteristic
9	C₄₁×#1729	C₂	1	1	yes	maximal, characteristic
10	C₂²×Q₁₆×C₄₁	C₂²	1	1	yes	characteristic
11	C₂²×M₁₆×C₄₁	C₂²	1	1	yes	characteristic
12	C₂³×C₈×C₄₁	C₂²	1	1	yes	characteristic
13	C₂×C₂²⋊Q₈×C₄₁	C₂²	1	2	yes	—
14	C₂×C₄×Q₈×C₄₁	C₂²	1	2	yes	—
15	C₂×#117×C₄₁	C₂²	1	1	yes	characteristic
16	C₄₁×#467	C₄	1	8	yes	complemented
17	C₂×#107×C₄₁	C₂²	1	1	yes	characteristic
18	C₂×#107×C₄₁	C₂²	1	1	yes	characteristic
19	C₂×#107×C₄₁	C₂²	1	1	yes	characteristic
20	C₂×#103×C₄₁	C₂²	1	2	yes	—
21	C₂×#103×C₄₁	C₂²	1	2	yes	—
22	C₂×#103×C₄₁	C₂²	1	2	yes	—
23	C₄₁×#391	C₂²	1	2	yes	—
24	C₄₁×#389	—	2	2	no	—
25	C₄₁×#389	C₂²	1	2	yes	—
26	C₄₁×#388	—	2	2	no	—
27	C₄₁×#388	—	2	2	no	—
28	C₄₁×#387	—	2	2	no	—
29	C₄₁×#380	C₂²	1	2	yes	—
30	C₄×C₄⋊C₄×C₄₁	C₂²	1	2	yes	—
31	C₄₁×#340	C₂²	1	2	yes	—
32	C₄₁×#340	C₂²	1	2	yes	—
33	C₄₁×#340	C₂²	1	2	yes	—
34	C₄₁×#336	C₂²	1	2	yes	—
35	C₄₁×#336	C₂²	1	2	yes	—
36	C₂²×Q₈×C₄₁	C₂³	1	2	yes	—
37	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
38	C₂×Q₁₆×C₄₁	—	4	1	no	—
39	C₂×Q₁₆×C₄₁	—	4	1	no	—
40	C₂×Q₁₆×C₄₁	C₂×C₄	1	4	yes	—
41	C₂×M₁₆×C₄₁	—	2	2	no	—
42	C₂×M₁₆×C₄₁	—	4	1	no	—
43	C₂×M₁₆×C₄₁	—	4	1	no	—
44	C₂²×C₈×C₄₁	—	4	1	no	—
45	C₂²×C₈×C₄₁	—	4	1	no	—
46	C₂²×C₈×C₄₁	C₂×C₄	1	4	yes	—
47	C₂²×C₈×C₄₁	C₂³	1	2	yes	—
48	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
49	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
50	C₂²⋊Q₈×C₄₁	—	2	4	no	—
51	C₂²⋊Q₈×C₄₁	C₂×C₄	1	8	yes	—
52	C₄×Q₈×C₄₁	—	4	2	no	—
53	C₄×Q₈×C₄₁	—	4	2	no	—
54	#117×C₄₁	—	4	1	no	—
55	#117×C₄₁	—	4	1	no	—
56	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
57	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
58	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
59	C₂×C₄⋊C₄×C₄₁	D₄	1	1	yes	characteristic
60	C₂×C₄⋊C₄×C₄₁	D₄	1	1	yes	characteristic
61	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
62	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
63	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
64	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
65	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
66	C₂×C₂²⋊C₄×C₄₁	D₄	1	2	yes	—
67	C₂×C₄²×C₄₁	—	2	2	no	—
68	C₂×C₄²×C₄₁	—	2	2	no	—
69	C₂×C₄²×C₄₁	C₂³	1	2	yes	—
70	#107×C₄₁	—	4	1	no	—
71	#107×C₄₁	—	4	1	no	—
72	#107×C₄₁	C₂×C₄	1	4	yes	—
73	#103×C₄₁	—	4	2	no	—
74	#103×C₄₁	—	4	2	no	—
75	#103×C₄₁	C₂×C₄	1	8	yes	—
76	#95×C₄₁	—	2	2	no	—
77	#95×C₄₁	—	2	2	no	—
78	#95×C₄₁	—	2	2	no	—
79	#95×C₄₁	—	2	2	no	—
80	#95×C₄₁	—	2	2	no	—
81	C₂⁴×C₄₁	C₂×D₄	1	1	yes	characteristic
82	C₂×Q₈×C₄₁	—	2	2	no	—
83	C₂×Q₈×C₄₁	—	2	2	no	—
84	C₂×Q₈×C₄₁	—	2	2	no	—
85	C₂×Q₈×C₄₁	—	2	2	no	—
86	C₂×Q₈×C₄₁	—	2	2	no	—
87	C₂×Q₈×C₄₁	C₂²×C₄	1	4	yes	—
88	C₂²×C₄×C₄₁	—	2	1	no	—
89	C₂²×C₄×C₄₁	—	2	1	no	—
90	C₂²×C₄×C₄₁	—	2	1	no	—
91	C₂²×C₄×C₄₁	—	2	1	no	—
92	C₂²×C₄×C₄₁	—	2	2	no	—
93	C₂²×C₄×C₄₁	—	2	2	no	—
94	C₂²×C₄×C₄₁	—	2	2	no	—
95	C₂²×C₄×C₄₁	—	2	2	no	—
96	C₂²×C₄×C₄₁	C₂²×C₄	1	2	yes	—
97	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
98	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
99	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
100	C₂²×C₄×C₄₁	#41	1	2	yes	—
101	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
102	Q₁₆×C₄₁	—	4	4	no	—
103	M₁₆×C₄₁	—	4	4	no	—
104	C₂×C₈×C₄₁	—	2	1	no	—
105	C₂×C₈×C₄₁	—	2	1	no	—
106	C₂×C₈×C₄₁	—	2	1	no	—
107	C₂×C₈×C₄₁	—	2	1	no	—
108	C₂×C₈×C₄₁	—	2	2	no	—
109	C₂×C₈×C₄₁	—	2	2	no	—
110	C₂×C₈×C₄₁	—	2	2	no	—
111	C₂×C₈×C₄₁	—	4	4	no	—
112	C₂×C₈×C₄₁	C₂²×C₄	1	2	yes	—
113	C₂×C₈×C₄₁	C₂²×C₄	1	2	yes	—
114	C₄⋊C₄×C₄₁	—	2	8	no	—
115	C₄⋊C₄×C₄₁	—	2	2	no	—
116	C₄⋊C₄×C₄₁	—	2	2	no	—
117	C₄⋊C₄×C₄₁	—	2	2	no	—
118	C₄⋊C₄×C₄₁	—	2	2	no	—
119	C₄⋊C₄×C₄₁	—	2	2	no	—
120	C₄⋊C₄×C₄₁	—	4	1	no	—
121	C₄⋊C₄×C₄₁	—	4	1	no	—
122	C₄⋊C₄×C₄₁	—	4	4	no	—
123	C₄⋊C₄×C₄₁	—	8	2	no	—
124	C₄⋊C₄×C₄₁	C₂²×C₄	1	4	yes	—
125	C₂²⋊C₄×C₄₁	—	2	8	no	—
126	C₂²⋊C₄×C₄₁	—	4	2	no	—
127	C₂²⋊C₄×C₄₁	—	8	2	no	—
128	C₄²×C₄₁	—	2	2	no	—
129	C₄²×C₄₁	—	2	2	no	—
130	C₄²×C₄₁	—	4	4	no	—
131	C₄²×C₄₁	—	8	2	no	—
132	C₂³×C₄₁	—	2	1	no	—
133	C₂³×C₄₁	—	2	1	no	—
134	C₂³×C₄₁	—	2	1	no	—
135	C₂³×C₄₁	—	2	1	no	—
136	C₂³×C₄₁	—	2	1	no	—
137	C₂³×C₄₁	—	2	1	no	—
138	C₂³×C₄₁	C₄×D₄	1	2	yes	—
139	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
140	Q₈×C₄₁	—	2	4	no	—
141	Q₈×C₄₁	—	2	4	no	—
142	Q₈×C₄₁	—	4	2	no	—
143	Q₈×C₄₁	—	4	2	no	—
144	C₂×C₄×C₄₁	—	2	1	no	—
145	C₂×C₄×C₄₁	—	2	1	no	—
146	C₂×C₄×C₄₁	—	2	2	no	—
147	C₂×C₄×C₄₁	—	2	2	no	—
148	C₂×C₄×C₄₁	—	2	2	no	—
149	C₂×C₄×C₄₁	—	2	2	no	—
150	C₂×C₄×C₄₁	—	2	4	no	—
151	C₂×C₄×C₄₁	—	2	4	no	—
152	C₂×C₄×C₄₁	—	2	2	no	—
153	C₂×C₄×C₄₁	—	2	2	no	—
154	C₂×C₄×C₄₁	—	2	2	no	—
155	C₂×C₄×C₄₁	—	2	2	no	—
156	C₂×C₄×C₄₁	—	2	2	no	—
157	C₂×C₄×C₄₁	—	2	2	no	—
158	C₂×C₄×C₄₁	—	4	2	no	—
159	C₂×C₄×C₄₁	—	4	2	no	—
160	C₂×C₄×C₄₁	—	4	2	no	—
161	C₂×C₄×C₄₁	—	4	2	no	—
162	C₂×C₄×C₄₁	—	4	2	no	—
163	C₂×C₄×C₄₁	—	4	2	no	—
164	C₂×C₄×C₄₁	—	4	2	no	—
165	C₂×C₄×C₄₁	—	4	2	no	—
166	C₂×C₄×C₄₁	—	4	2	no	—
167	C₂×C₄×C₄₁	—	4	2	no	—
168	C₂×C₄×C₄₁	C₄×D₄	1	2	yes	—
169	C₂×C₄×C₄₁	C₂³×C₄	1	1	yes	characteristic
170	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
171	C₂×C₄×C₄₁	H(5,𝔽₂)	1	1	yes	characteristic
172	C₂×C₄×C₄₁	H(5,𝔽₂)	1	1	yes	characteristic
173	C₂×C₄×C₄₁	H(5,𝔽₂)	1	1	yes	characteristic
174	C₂×C₄×C₄₁	2₋¹⁺⁴	1	1	yes	characteristic
175	C₈×C₄₁	—	2	2	no	—
176	C₈×C₄₁	—	2	2	no	—
177	C₈×C₄₁	—	4	2	no	—
178	#22197	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
179	C₂²×C₄₁	—	2	2	no	—
180	C₂²×C₄₁	—	2	2	no	—
181	C₂²×C₄₁	—	2	2	no	—
182	C₂²×C₄₁	—	4	1	no	—
183	C₂²×C₄₁	—	4	1	no	—
184	C₂²×C₄₁	—	4	1	no	—
185	C₂²×C₄₁	—	4	1	no	—
186	C₂²×C₄₁	C₂×C₄×D₄	1	1	yes	characteristic
187	C₂²×C₄₁	#534	1	1	yes	characteristic
188	C₂²×C₄₁	#537	1	1	yes	characteristic
189	C₂²×C₄₁	#576	1	1	yes	characteristic
190	C₂²×C₄₁	#578	1	1	yes	characteristic
191	C₂²×C₄₁	#578	1	1	yes	characteristic
192	C₂²×C₄₁	#578	1	1	yes	characteristic
193	C₄×C₄₁	—	2	2	no	—
194	C₄×C₄₁	—	4	4	no	—
195	C₄×C₄₁	—	4	2	no	—
196	C₄×C₄₁	—	4	2	no	—
197	C₄×C₄₁	—	4	4	no	—
198	C₄×C₄₁	—	8	2	no	—
199	C₄×C₄₁	—	8	2	no	—
200	C₄×C₄₁	#518	1	1	yes	characteristic
201	C₄×C₄₁	#520	1	1	yes	characteristic
202	C₄×C₄₁	#538	1	1	yes	characteristic
203	C₄×C₄₁	#539	1	1	yes	characteristic
204	C₂×#467	C₂×C₄₁	1	1	yes	characteristic
205	#2323	C₂×C₄₁	1	2	yes	—
206	#1928	C₂×C₄₁	1	2	yes	complemented
207	#1918	C₂×C₄₁	1	2	yes	complemented
208	#1894	C₂×C₄₁	1	2	yes	—
209	#1878	C₂×C₄₁	1	2	yes	complemented
210	#1863	C₂×C₄₁	1	2	yes	complemented
211	#1808	C₂×C₄₁	1	1	yes	characteristic
212	#1729	C₂×C₄₁	1	1	yes	characteristic
213	C₂×C₄₁	—	4	2	no	—
214	C₂×C₄₁	#2325	1	1	yes	characteristic
215	C₂×C₄₁	#2950	1	1	yes	characteristic
216	C₂×C₄₁	#2951	1	1	yes	characteristic
217	C₂×C₄₁	#3202	1	1	yes	characteristic
218	C₂×C₄₁	#3203	1	1	yes	characteristic
219	C₂×C₄₁	#3261	1	1	yes	characteristic
220	C₂×C₄₁	#3262	1	1	yes	characteristic
221	C₂²×Q₁₆	C₂²×C₄₁	1	1	yes	characteristic
222	C₂²×M₁₆	C₂²×C₄₁	1	1	yes	characteristic
223	C₂³×C₈	C₂²×C₄₁	1	1	yes	characteristic
224	C₂×C₂²⋊Q₈	C₂²×C₄₁	1	2	yes	—
225	C₂×C₄×Q₈	C₂²×C₄₁	1	2	yes	—
226	C₂×#117	C₂²×C₄₁	1	1	yes	characteristic
227	#467	C₄×C₄₁	1	8	yes	complemented
228	C₂×#107	C₂²×C₄₁	1	1	yes	characteristic
229	C₂×#107	C₂²×C₄₁	1	1	yes	characteristic
230	C₂×#107	C₂²×C₄₁	1	1	yes	characteristic
231	C₂×#103	C₂²×C₄₁	1	2	yes	—
232	C₂×#103	C₂²×C₄₁	1	2	yes	—
233	C₂×#103	C₂²×C₄₁	1	2	yes	—
234	#391	C₂²×C₄₁	1	2	yes	—
235	#389	—	2	2	no	—
236	#389	C₂²×C₄₁	1	2	yes	—
237	#388	—	2	2	no	—
238	#388	—	2	2	no	—
239	#387	—	2	2	no	—
240	#380	C₂²×C₄₁	1	2	yes	—
241	C₄×C₄⋊C₄	C₂²×C₄₁	1	2	yes	—
242	#340	C₂²×C₄₁	1	2	yes	—
243	#340	C₂²×C₄₁	1	2	yes	—
244	#340	C₂²×C₄₁	1	2	yes	—
245	#336	C₂²×C₄₁	1	2	yes	—
246	#336	C₂²×C₄₁	1	2	yes	—
247	C₄₁	#22197	1	1	yes	characteristic, direct product factor, Sylow
248	C₂²×Q₈	C₂³×C₄₁	1	2	yes	—
249	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
250	C₂×Q₁₆	—	4	1	no	—
251	C₂×Q₁₆	—	4	1	no	—
252	C₂×Q₁₆	C₂×C₄×C₄₁	1	4	yes	—
253	C₂×M₁₆	—	2	2	no	—
254	C₂×M₁₆	—	4	1	no	—
255	C₂×M₁₆	—	4	1	no	—
256	C₂²×C₈	—	4	1	no	—
257	C₂²×C₈	—	4	1	no	—
258	C₂²×C₈	C₂×C₄×C₄₁	1	4	yes	—
259	C₂²×C₈	C₂³×C₄₁	1	2	yes	—
260	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
261	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
262	C₂²⋊Q₈	—	2	4	no	—
263	C₂²⋊Q₈	C₂×C₄×C₄₁	1	8	yes	—
264	C₄×Q₈	—	4	2	no	—
265	C₄×Q₈	—	4	2	no	—
266	#117	—	4	1	no	—
267	#117	—	4	1	no	—
268	C₂×C₄⋊C₄	—	2	2	no	—
269	C₂×C₄⋊C₄	—	2	2	no	—
270	C₂×C₄⋊C₄	—	2	2	no	—
271	C₂×C₄⋊C₄	D₄×C₄₁	1	1	yes	characteristic
272	C₂×C₄⋊C₄	D₄×C₄₁	1	1	yes	characteristic
273	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
274	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
275	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
276	C₂×C₂²⋊C₄	—	2	2	no	—
277	C₂×C₂²⋊C₄	—	2	2	no	—
278	C₂×C₂²⋊C₄	D₄×C₄₁	1	2	yes	—
279	C₂×C₄²	—	2	2	no	—
280	C₂×C₄²	—	2	2	no	—
281	C₂×C₄²	C₂³×C₄₁	1	2	yes	—
282	#107	—	4	1	no	—
283	#107	—	4	1	no	—
284	#107	C₂×C₄×C₄₁	1	4	yes	—
285	#103	—	4	2	no	—
286	#103	—	4	2	no	—
287	#103	C₂×C₄×C₄₁	1	8	yes	—
288	#95	—	2	2	no	—
289	#95	—	2	2	no	—
290	#95	—	2	2	no	—
291	#95	—	2	2	no	—
292	#95	—	2	2	no	—
293	C₂⁴	C₂×D₄×C₄₁	1	1	yes	characteristic
294	C₂×Q₈	—	2	2	no	—
295	C₂×Q₈	—	2	2	no	—
296	C₂×Q₈	—	2	2	no	—
297	C₂×Q₈	—	2	2	no	—
298	C₂×Q₈	—	2	2	no	—
299	C₂×Q₈	C₂²×C₄×C₄₁	1	4	yes	—
300	C₂²×C₄	—	2	1	no	—
301	C₂²×C₄	—	2	1	no	—
302	C₂²×C₄	—	2	1	no	—
303	C₂²×C₄	—	2	1	no	—
304	C₂²×C₄	—	2	2	no	—
305	C₂²×C₄	—	2	2	no	—
306	C₂²×C₄	—	2	2	no	—
307	C₂²×C₄	—	2	2	no	—
308	C₂²×C₄	C₂²×C₄×C₄₁	1	2	yes	—
309	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
310	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
311	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
312	C₂²×C₄	#41×C₄₁	1	2	yes	—
313	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
314	Q₁₆	—	4	4	no	—
315	M₁₆	—	4	4	no	—
316	C₂×C₈	—	2	1	no	—
317	C₂×C₈	—	2	1	no	—
318	C₂×C₈	—	2	1	no	—
319	C₂×C₈	—	2	1	no	—
320	C₂×C₈	—	2	2	no	—
321	C₂×C₈	—	2	2	no	—
322	C₂×C₈	—	2	2	no	—
323	C₂×C₈	—	4	4	no	—
324	C₂×C₈	C₂²×C₄×C₄₁	1	2	yes	—
325	C₂×C₈	C₂²×C₄×C₄₁	1	2	yes	—
326	C₄⋊C₄	—	2	8	no	—
327	C₄⋊C₄	—	2	2	no	—
328	C₄⋊C₄	—	2	2	no	—
329	C₄⋊C₄	—	2	2	no	—
330	C₄⋊C₄	—	2	2	no	—
331	C₄⋊C₄	—	2	2	no	—
332	C₄⋊C₄	—	4	1	no	—
333	C₄⋊C₄	—	4	1	no	—
334	C₄⋊C₄	—	4	4	no	—
335	C₄⋊C₄	—	8	2	no	—
336	C₄⋊C₄	C₂²×C₄×C₄₁	1	4	yes	—
337	C₂²⋊C₄	—	2	8	no	—
338	C₂²⋊C₄	—	4	2	no	—
339	C₂²⋊C₄	—	8	2	no	—
340	C₄²	—	2	2	no	—
341	C₄²	—	2	2	no	—
342	C₄²	—	4	4	no	—
343	C₄²	—	8	2	no	—
344	C₂³	—	2	1	no	—
345	C₂³	—	2	1	no	—
346	C₂³	—	2	1	no	—
347	C₂³	—	2	1	no	—
348	C₂³	—	2	1	no	—
349	C₂³	—	2	1	no	—
350	C₂³	C₄×D₄×C₄₁	1	2	yes	—
351	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
352	Q₈	—	2	4	no	—
353	Q₈	—	2	4	no	—
354	Q₈	—	4	2	no	—
355	Q₈	—	4	2	no	—
356	C₂×C₄	—	2	1	no	—
357	C₂×C₄	—	2	1	no	—
358	C₂×C₄	—	2	2	no	—
359	C₂×C₄	—	2	2	no	—
360	C₂×C₄	—	2	2	no	—
361	C₂×C₄	—	2	2	no	—
362	C₂×C₄	—	2	4	no	—
363	C₂×C₄	—	2	4	no	—
364	C₂×C₄	—	2	2	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	—	2	2	no	—
370	C₂×C₄	—	4	2	no	—
371	C₂×C₄	—	4	2	no	—
372	C₂×C₄	—	4	2	no	—
373	C₂×C₄	—	4	2	no	—
374	C₂×C₄	—	4	2	no	—
375	C₂×C₄	—	4	2	no	—
376	C₂×C₄	—	4	2	no	—
377	C₂×C₄	—	4	2	no	—
378	C₂×C₄	—	4	2	no	—
379	C₂×C₄	—	4	2	no	—
380	C₂×C₄	C₄×D₄×C₄₁	1	2	yes	—
381	C₂×C₄	C₂³×C₄×C₄₁	1	1	yes	characteristic
382	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
383	C₂×C₄	H(5,𝔽₂)×C₄₁	1	1	yes	characteristic
384	C₂×C₄	H(5,𝔽₂)×C₄₁	1	1	yes	characteristic
385	C₂×C₄	H(5,𝔽₂)×C₄₁	1	1	yes	characteristic
386	C₂×C₄	2₋¹⁺⁴×C₄₁	1	1	yes	characteristic
387	C₈	—	2	2	no	—
388	C₈	—	2	2	no	—
389	C₈	—	4	2	no	—
390	C₂²	—	2	2	no	—
391	C₂²	—	2	2	no	—
392	C₂²	—	2	2	no	—
393	C₂²	—	4	1	no	—
394	C₂²	—	4	1	no	—
395	C₂²	—	4	1	no	—
396	C₂²	—	4	1	no	—
397	C₂²	C₂×C₄×D₄×C₄₁	1	1	yes	characteristic
398	C₂²	C₄₁×#534	1	1	yes	characteristic
399	C₂²	C₄₁×#537	1	1	yes	characteristic
400	C₂²	C₄₁×#576	1	1	yes	characteristic
401	C₂²	C₄₁×#578	1	1	yes	characteristic
402	C₂²	C₄₁×#578	1	1	yes	characteristic
403	C₂²	C₄₁×#578	1	1	yes	characteristic
404	C₄	—	2	2	no	—
405	C₄	—	4	4	no	—
406	C₄	—	4	2	no	—
407	C₄	—	4	2	no	—
408	C₄	—	4	4	no	—
409	C₄	—	8	2	no	—
410	C₄	—	8	2	no	—
411	C₄	C₄₁×#518	1	1	yes	characteristic
412	C₄	C₄₁×#520	1	1	yes	characteristic
413	C₄	C₄₁×#538	1	1	yes	characteristic
414	C₄	C₄₁×#539	1	1	yes	characteristic
415	C₂	—	4	2	no	—
416	C₂	C₄₁×#2325	1	1	yes	characteristic
417	C₂	C₄₁×#2950	1	1	yes	characteristic
418	C₂	C₄₁×#2951	1	1	yes	characteristic
419	C₂	C₄₁×#3202	1	1	yes	characteristic
420	C₂	C₄₁×#3203	1	1	yes	characteristic
421	C₂	C₄₁×#3261	1	1	yes	characteristic
422	C₂	C₄₁×#3262	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₄₁	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₄₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₁
prime radical	C₂⁴×C₄₁	C₂×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₄₁ ◁ C₂×#117×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₄₁×#1928	C₂	semidirect
4. C₄₁×#1918	C₂	semidirect
6. C₄₁×#1878	C₂	semidirect
7. C₄₁×#1863	C₂	semidirect
16. C₄₁×#467	C₄	semidirect
178. #22197	C₄₁	direct (N × H)
206. #1928	C₂×C₄₁	semidirect
207. #1918	C₂×C₄₁	semidirect
209. #1878	C₂×C₄₁	semidirect
210. #1863	C₂×C₄₁	semidirect
227. #467	C₄×C₄₁	semidirect
247. C₄₁	#22197	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×#467	2
C₄₁×#2323	2
C₄₁×#1928	2
C₄₁×#1918	2
C₄₁×#1894	2
C₄₁×#1878	2
C₄₁×#1863	2
C₄₁×#1808	2
C₄₁×#1729	2
#22197	41

Subgroups — C41×#22197 #23798398

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#22197 #23798398