Subgroups — C₄₁×#33116 #23809317

Order 10496.

930 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₁×#482	C₂	1	2	yes	maximal, complemented
2	C₄₁×#2619	C₂	1	1	yes	maximal, characteristic
3	C₄₁×#2274	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₁×#1982	C₂	1	2	yes	maximal, complemented
5	C₄₁×#1949	C₂	1	2	yes	maximal, complemented
6	C₄₁×#1926	C₂	1	2	yes	maximal, complemented
7	C₄₁×#1925	C₂	1	2	yes	maximal, complemented
8	C₄₁×#1874	C₂	1	2	yes	maximal, complemented
9	C₄₁×#1798	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#127×C₄₁	C₂²	1	1	yes	characteristic
11	C₂×#121×C₄₁	C₂²	1	2	yes	—
12	C₂×#117×C₄₁	C₂²	1	1	yes	characteristic
13	C₂×#117×C₄₁	C₂²	1	1	yes	characteristic
14	C₂²×C₄⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
15	C₄₁×#482	—	2	8	no	—
16	C₂×#107×C₄₁	C₂²	1	2	yes	—
17	C₂×#106×C₄₁	C₂²	1	2	yes	—
18	C₂×C₄⋊C₈×C₄₁	C₂²	1	2	yes	—
19	C₂×#102×C₄₁	C₂²	1	2	yes	—
20	C₂×#102×C₄₁	C₂²	1	2	yes	—
21	C₂×#102×C₄₁	C₂²	1	2	yes	—
22	C₂×#102×C₄₁	C₂²	1	2	yes	—
23	C₂×C₂²⋊C₈×C₄₁	C₂²	1	2	yes	—
24	C₄₁×#394	—	2	2	no	—
25	C₄₁×#392	—	2	2	no	—
26	C₄₁×#390	C₂²	1	2	yes	—
27	C₄₁×#382	C₂²	1	1	yes	characteristic
28	C₄×C₄⋊C₄×C₄₁	—	2	2	no	—
29	C₄×C₄⋊C₄×C₄₁	C₂²	1	2	yes	—
30	C₄×C₄⋊C₄×C₄₁	C₂²	1	2	yes	—
31	C₄×C₂²⋊C₄×C₄₁	—	2	2	no	—
32	C₄₁×#340	C₂²	1	2	yes	—
33	C₄₁×#340	C₂²	1	2	yes	—
34	C₄₁×#336	C₂²	1	1	yes	characteristic
35	C₄₁×#336	C₂²	1	1	yes	characteristic
36	C₂²×D₄×C₄₁	—	2	2	no	—
37	C₂²×D₄×C₄₁	—	2	2	no	—
38	C₂²×D₄×C₄₁	C₂³	1	2	yes	—
39	C₂³×C₄×C₄₁	—	2	1	no	—
40	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
41	C₂²×C₈×C₄₁	C₂³	1	2	yes	—
42	C₂²×C₈×C₄₁	C₂³	1	2	yes	—
43	#127×C₄₁	—	2	4	no	—
44	#121×C₄₁	—	2	4	no	—
45	#121×C₄₁	—	2	4	no	—
46	#117×C₄₁	—	2	2	no	—
47	#117×C₄₁	—	2	4	no	—
48	#117×C₄₁	D₄	1	4	yes	complemented
49	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
50	C₂×C₄⋊C₄×C₄₁	—	2	4	no	—
51	C₂×C₄⋊C₄×C₄₁	D₄	1	2	yes	—
52	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
53	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
54	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
55	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
56	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
57	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
58	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
59	C₂×C₂²⋊C₄×C₄₁	D₄	1	2	yes	—
60	C₂×C₄²×C₄₁	—	2	1	no	—
61	C₂×C₄²×C₄₁	—	2	2	no	—
62	C₂×C₄²×C₄₁	—	2	2	no	—
63	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
64	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
65	#107×C₄₁	—	2	4	no	—
66	#106×C₄₁	—	2	4	no	—
67	C₄⋊C₈×C₄₁	—	2	4	no	—
68	#102×C₄₁	—	2	4	no	—
69	#102×C₄₁	—	2	4	no	—
70	#102×C₄₁	—	2	4	no	—
71	#102×C₄₁	—	2	4	no	—
72	C₂²⋊C₈×C₄₁	—	2	4	no	—
73	#95×C₄₁	—	2	2	no	—
74	#95×C₄₁	—	2	2	no	—
75	#95×C₄₁	—	2	2	no	—
76	C₂⁴×C₄₁	—	2	2	no	—
77	C₂⁴×C₄₁	C₂×D₄	1	1	yes	characteristic
78	C₂×D₄×C₄₁	—	2	2	no	—
79	C₂×D₄×C₄₁	—	2	2	no	—
80	C₂×D₄×C₄₁	—	2	2	no	—
81	C₂×D₄×C₄₁	—	2	2	no	—
82	C₂×D₄×C₄₁	—	2	2	no	—
83	C₂×D₄×C₄₁	—	2	2	no	—
84	C₂×D₄×C₄₁	—	4	4	no	—
85	C₂×D₄×C₄₁	—	4	4	no	—
86	C₂×D₄×C₄₁	—	8	2	no	—
87	C₂×D₄×C₄₁	—	8	2	no	—
88	C₂×D₄×C₄₁	—	8	2	no	—
89	C₂×D₄×C₄₁	—	8	2	no	—
90	C₂²×C₄×C₄₁	—	2	2	no	—
91	C₂²×C₄×C₄₁	—	2	2	no	—
92	C₂²×C₄×C₄₁	—	2	2	no	—
93	C₂²×C₄×C₄₁	—	2	2	no	—
94	C₂²×C₄×C₄₁	—	2	4	no	—
95	C₂²×C₄×C₄₁	—	2	2	no	—
96	C₂²×C₄×C₄₁	—	8	2	no	—
97	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
98	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
99	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
100	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
101	C₂²×C₄×C₄₁	#41	1	2	yes	—
102	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
103	C₂×C₈×C₄₁	—	2	2	no	—
104	C₂×C₈×C₄₁	—	2	2	no	—
105	C₂×C₈×C₄₁	—	2	2	no	—
106	C₂×C₈×C₄₁	—	2	2	no	—
107	C₂×C₈×C₄₁	—	2	2	no	—
108	C₂×C₈×C₄₁	—	2	2	no	—
109	C₄⋊C₄×C₄₁	—	2	4	no	—
110	C₄⋊C₄×C₄₁	—	2	4	no	—
111	C₄⋊C₄×C₄₁	—	2	2	no	—
112	C₄⋊C₄×C₄₁	—	2	2	no	—
113	C₄⋊C₄×C₄₁	—	2	2	no	—
114	C₄⋊C₄×C₄₁	—	2	2	no	—
115	C₄⋊C₄×C₄₁	C₂×D₄	1	4	yes	—
116	C₄⋊C₄×C₄₁	#41	1	4	yes	—
117	C₂²⋊C₄×C₄₁	—	2	4	no	—
118	C₂²⋊C₄×C₄₁	—	2	4	no	—
119	C₂²⋊C₄×C₄₁	—	4	4	no	—
120	C₂²⋊C₄×C₄₁	—	8	2	no	—
121	C₂²⋊C₄×C₄₁	—	8	2	no	—
122	C₄²×C₄₁	—	2	4	no	—
123	C₄²×C₄₁	—	2	2	no	—
124	C₄²×C₄₁	—	8	2	no	—
125	C₄²×C₄₁	—	8	2	no	—
126	C₄²×C₄₁	#41	1	4	yes	—
127	C₂³×C₄₁	—	2	1	no	—
128	C₂³×C₄₁	—	2	1	no	—
129	C₂³×C₄₁	—	2	2	no	—
130	C₂³×C₄₁	—	2	2	no	—
131	C₂³×C₄₁	—	4	2	no	—
132	C₂³×C₄₁	—	4	2	no	—
133	C₂³×C₄₁	—	4	2	no	—
134	C₂³×C₄₁	—	4	2	no	—
135	C₂³×C₄₁	—	4	2	no	—
136	C₂³×C₄₁	—	4	2	no	—
137	C₂³×C₄₁	—	4	2	no	—
138	C₂³×C₄₁	#121	1	2	yes	—
139	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
140	D₄×C₄₁	—	4	2	no	—
141	D₄×C₄₁	—	4	2	no	—
142	D₄×C₄₁	—	4	2	no	—
143	D₄×C₄₁	—	4	2	no	—
144	D₄×C₄₁	—	8	8	no	—
145	D₄×C₄₁	—	8	8	no	—
146	C₂×C₄×C₄₁	—	2	1	no	—
147	C₂×C₄×C₄₁	—	2	1	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	4	no	—
153	C₂×C₄×C₄₁	—	2	2	no	—
154	C₂×C₄×C₄₁	—	2	4	no	—
155	C₂×C₄×C₄₁	—	2	2	no	—
156	C₂×C₄×C₄₁	—	2	2	no	—
157	C₂×C₄×C₄₁	—	4	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	—	8	4	no	—
165	C₂×C₄×C₄₁	#121	1	2	yes	—
166	C₂×C₄×C₄₁	#123	1	4	yes	—
167	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
168	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
169	C₂×C₄×C₄₁	C₂×#41	1	2	yes	—
170	C₂×C₄×C₄₁	C₂×#41	1	2	yes	—
171	C₈×C₄₁	—	4	2	no	—
172	C₈×C₄₁	—	4	2	no	—
173	#33116	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
174	C₂²×C₄₁	—	2	2	no	—
175	C₂²×C₄₁	—	2	4	no	—
176	C₂²×C₄₁	—	4	2	no	—
177	C₂²×C₄₁	—	4	1	no	—
178	C₂²×C₄₁	—	4	1	no	—
179	C₂²×C₄₁	—	8	2	no	—
180	C₂²×C₄₁	—	8	2	no	—
181	C₂²×C₄₁	—	8	2	no	—
182	C₂²×C₄₁	—	8	2	no	—
183	C₂²×C₄₁	—	8	2	no	—
184	C₂²×C₄₁	—	8	2	no	—
185	C₂²×C₄₁	—	8	2	no	—
186	C₂²×C₄₁	C₂×#121	1	1	yes	characteristic
187	C₂²×C₄₁	C₂×#123	1	1	yes	characteristic
188	C₂²×C₄₁	#525	1	1	yes	characteristic
189	C₂²×C₄₁	#576	1	2	yes	—
190	C₂²×C₄₁	#577	1	2	yes	—
191	C₄×C₄₁	—	2	4	no	—
192	C₄×C₄₁	—	2	2	no	—
193	C₄×C₄₁	—	4	2	no	—
194	C₄×C₄₁	—	4	4	no	—
195	C₄×C₄₁	—	4	4	no	—
196	C₄×C₄₁	—	8	2	no	—
197	C₄×C₄₁	#529	1	2	yes	—
198	C₄×C₄₁	#532	1	2	yes	—
199	C₂×#482	C₂×C₄₁	1	2	yes	complemented
200	#2619	C₂×C₄₁	1	1	yes	characteristic
201	#2274	C₂×C₄₁	1	1	yes	characteristic, complemented
202	#1982	C₂×C₄₁	1	2	yes	complemented
203	#1949	C₂×C₄₁	1	2	yes	complemented
204	#1926	C₂×C₄₁	1	2	yes	complemented
205	#1925	C₂×C₄₁	1	2	yes	complemented
206	#1874	C₂×C₄₁	1	2	yes	complemented
207	#1798	C₂×C₄₁	1	1	yes	characteristic, complemented
208	C₂×C₄₁	—	4	2	no	—
209	C₂×C₄₁	—	16	2	no	—
210	C₂×C₄₁	#2854	1	1	yes	characteristic
211	C₂×C₄₁	#3045	1	2	yes	—
212	C₂×C₄₁	#3096	1	2	yes	—
213	C₂×C₄₁	#3122	1	1	yes	characteristic
214	C₂×C₄₁	#3126	1	1	yes	characteristic
215	C₂×#127	C₂²×C₄₁	1	1	yes	characteristic
216	C₂×#121	C₂²×C₄₁	1	2	yes	—
217	C₂×#117	C₂²×C₄₁	1	1	yes	characteristic
218	C₂×#117	C₂²×C₄₁	1	1	yes	characteristic
219	C₂²×C₄⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
220	#482	—	2	8	no	—
221	C₂×#107	C₂²×C₄₁	1	2	yes	—
222	C₂×#106	C₂²×C₄₁	1	2	yes	—
223	C₂×C₄⋊C₈	C₂²×C₄₁	1	2	yes	—
224	C₂×#102	C₂²×C₄₁	1	2	yes	—
225	C₂×#102	C₂²×C₄₁	1	2	yes	—
226	C₂×#102	C₂²×C₄₁	1	2	yes	—
227	C₂×#102	C₂²×C₄₁	1	2	yes	—
228	C₂×C₂²⋊C₈	C₂²×C₄₁	1	2	yes	—
229	#394	—	2	2	no	—
230	#392	—	2	2	no	—
231	#390	C₂²×C₄₁	1	2	yes	—
232	#382	C₂²×C₄₁	1	1	yes	characteristic
233	C₄×C₄⋊C₄	—	2	2	no	—
234	C₄×C₄⋊C₄	C₂²×C₄₁	1	2	yes	—
235	C₄×C₄⋊C₄	C₂²×C₄₁	1	2	yes	—
236	C₄×C₂²⋊C₄	—	2	2	no	—
237	#340	C₂²×C₄₁	1	2	yes	—
238	#340	C₂²×C₄₁	1	2	yes	—
239	#336	C₂²×C₄₁	1	1	yes	characteristic
240	#336	C₂²×C₄₁	1	1	yes	characteristic
241	C₄₁	#33116	1	1	yes	characteristic, direct product factor, Sylow
242	C₂²×D₄	—	2	2	no	—
243	C₂²×D₄	—	2	2	no	—
244	C₂²×D₄	C₂³×C₄₁	1	2	yes	—
245	C₂³×C₄	—	2	1	no	—
246	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
247	C₂²×C₈	C₂³×C₄₁	1	2	yes	—
248	C₂²×C₈	C₂³×C₄₁	1	2	yes	—
249	#127	—	2	4	no	—
250	#121	—	2	4	no	—
251	#121	—	2	4	no	—
252	#117	—	2	2	no	—
253	#117	—	2	4	no	—
254	#117	D₄×C₄₁	1	4	yes	complemented
255	C₂×C₄⋊C₄	—	2	1	no	—
256	C₂×C₄⋊C₄	—	2	4	no	—
257	C₂×C₄⋊C₄	D₄×C₄₁	1	2	yes	—
258	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
259	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
260	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
261	C₂×C₂²⋊C₄	—	2	1	no	—
262	C₂×C₂²⋊C₄	—	2	2	no	—
263	C₂×C₂²⋊C₄	—	2	2	no	—
264	C₂×C₂²⋊C₄	—	2	2	no	—
265	C₂×C₂²⋊C₄	D₄×C₄₁	1	2	yes	—
266	C₂×C₄²	—	2	1	no	—
267	C₂×C₄²	—	2	2	no	—
268	C₂×C₄²	—	2	2	no	—
269	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
270	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
271	#107	—	2	4	no	—
272	#106	—	2	4	no	—
273	C₄⋊C₈	—	2	4	no	—
274	#102	—	2	4	no	—
275	#102	—	2	4	no	—
276	#102	—	2	4	no	—
277	#102	—	2	4	no	—
278	C₂²⋊C₈	—	2	4	no	—
279	#95	—	2	2	no	—
280	#95	—	2	2	no	—
281	#95	—	2	2	no	—
282	C₂⁴	—	2	2	no	—
283	C₂⁴	C₂×D₄×C₄₁	1	1	yes	characteristic
284	C₂×D₄	—	2	2	no	—
285	C₂×D₄	—	2	2	no	—
286	C₂×D₄	—	2	2	no	—
287	C₂×D₄	—	2	2	no	—
288	C₂×D₄	—	2	2	no	—
289	C₂×D₄	—	2	2	no	—
290	C₂×D₄	—	4	4	no	—
291	C₂×D₄	—	4	4	no	—
292	C₂×D₄	—	8	2	no	—
293	C₂×D₄	—	8	2	no	—
294	C₂×D₄	—	8	2	no	—
295	C₂×D₄	—	8	2	no	—
296	C₂²×C₄	—	2	2	no	—
297	C₂²×C₄	—	2	2	no	—
298	C₂²×C₄	—	2	2	no	—
299	C₂²×C₄	—	2	2	no	—
300	C₂²×C₄	—	2	4	no	—
301	C₂²×C₄	—	2	2	no	—
302	C₂²×C₄	—	8	2	no	—
303	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
304	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
305	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
306	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
307	C₂²×C₄	#41×C₄₁	1	2	yes	—
308	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
309	C₂×C₈	—	2	2	no	—
310	C₂×C₈	—	2	2	no	—
311	C₂×C₈	—	2	2	no	—
312	C₂×C₈	—	2	2	no	—
313	C₂×C₈	—	2	2	no	—
314	C₂×C₈	—	2	2	no	—
315	C₄⋊C₄	—	2	4	no	—
316	C₄⋊C₄	—	2	4	no	—
317	C₄⋊C₄	—	2	2	no	—
318	C₄⋊C₄	—	2	2	no	—
319	C₄⋊C₄	—	2	2	no	—
320	C₄⋊C₄	—	2	2	no	—
321	C₄⋊C₄	C₂×D₄×C₄₁	1	4	yes	—
322	C₄⋊C₄	#41×C₄₁	1	4	yes	—
323	C₂²⋊C₄	—	2	4	no	—
324	C₂²⋊C₄	—	2	4	no	—
325	C₂²⋊C₄	—	4	4	no	—
326	C₂²⋊C₄	—	8	2	no	—
327	C₂²⋊C₄	—	8	2	no	—
328	C₄²	—	2	4	no	—
329	C₄²	—	2	2	no	—
330	C₄²	—	8	2	no	—
331	C₄²	—	8	2	no	—
332	C₄²	#41×C₄₁	1	4	yes	—
333	C₂³	—	2	1	no	—
334	C₂³	—	2	1	no	—
335	C₂³	—	2	2	no	—
336	C₂³	—	2	2	no	—
337	C₂³	—	4	2	no	—
338	C₂³	—	4	2	no	—
339	C₂³	—	4	2	no	—
340	C₂³	—	4	2	no	—
341	C₂³	—	4	2	no	—
342	C₂³	—	4	2	no	—
343	C₂³	—	4	2	no	—
344	C₂³	#121×C₄₁	1	2	yes	—
345	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
346	D₄	—	4	2	no	—
347	D₄	—	4	2	no	—
348	D₄	—	4	2	no	—
349	D₄	—	4	2	no	—
350	D₄	—	8	8	no	—
351	D₄	—	8	8	no	—
352	C₂×C₄	—	2	1	no	—
353	C₂×C₄	—	2	1	no	—
354	C₂×C₄	—	2	2	no	—
355	C₂×C₄	—	2	2	no	—
356	C₂×C₄	—	2	4	no	—
357	C₂×C₄	—	2	4	no	—
358	C₂×C₄	—	2	4	no	—
359	C₂×C₄	—	2	2	no	—
360	C₂×C₄	—	2	4	no	—
361	C₂×C₄	—	2	2	no	—
362	C₂×C₄	—	2	2	no	—
363	C₂×C₄	—	4	2	no	—
364	C₂×C₄	—	4	2	no	—
365	C₂×C₄	—	4	2	no	—
366	C₂×C₄	—	4	2	no	—
367	C₂×C₄	—	4	2	no	—
368	C₂×C₄	—	4	2	no	—
369	C₂×C₄	—	4	2	no	—
370	C₂×C₄	—	8	4	no	—
371	C₂×C₄	#121×C₄₁	1	2	yes	—
372	C₂×C₄	#123×C₄₁	1	4	yes	—
373	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
374	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
375	C₂×C₄	C₂×#41×C₄₁	1	2	yes	—
376	C₂×C₄	C₂×#41×C₄₁	1	2	yes	—
377	C₈	—	4	2	no	—
378	C₈	—	4	2	no	—
379	C₂²	—	2	4	no	—
380	C₂²	—	2	2	no	—
381	C₂²	—	4	2	no	—
382	C₂²	—	4	1	no	—
383	C₂²	—	4	1	no	—
384	C₂²	—	8	2	no	—
385	C₂²	—	8	2	no	—
386	C₂²	—	8	2	no	—
387	C₂²	—	8	2	no	—
388	C₂²	—	8	2	no	—
389	C₂²	—	8	2	no	—
390	C₂²	—	8	2	no	—
391	C₂²	C₂×#121×C₄₁	1	1	yes	characteristic
392	C₂²	C₂×#123×C₄₁	1	1	yes	characteristic
393	C₂²	C₄₁×#525	1	1	yes	characteristic
394	C₂²	C₄₁×#576	1	2	yes	—
395	C₂²	C₄₁×#577	1	2	yes	—
396	C₄	—	2	4	no	—
397	C₄	—	2	2	no	—
398	C₄	—	4	4	no	—
399	C₄	—	4	2	no	—
400	C₄	—	4	4	no	—
401	C₄	—	8	2	no	—
402	C₄	C₄₁×#529	1	2	yes	—
403	C₄	C₄₁×#532	1	2	yes	—
404	C₂	—	4	2	no	—
405	C₂	—	16	2	no	—
406	C₂	C₄₁×#2854	1	1	yes	characteristic
407	C₂	C₄₁×#3045	1	2	yes	—
408	C₂	C₄₁×#3096	1	2	yes	—
409	C₂	C₄₁×#3122	1	1	yes	characteristic
410	C₂	C₄₁×#3126	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₄₁	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₁
prime radical	C₄₁×#2619	C₂
LCS	G ▷ C₂²×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
1. C₂×C₄₁×#482	C₂	semidirect
3. C₄₁×#2274	C₂	semidirect
4. C₄₁×#1982	C₂	semidirect
5. C₄₁×#1949	C₂	semidirect
6. C₄₁×#1926	C₂	semidirect
7. C₄₁×#1925	C₂	semidirect
8. C₄₁×#1874	C₂	semidirect
9. C₄₁×#1798	C₂	semidirect
48. #117×C₄₁	D₄	semidirect
173. #33116	C₄₁	direct (N × H)
199. C₂×#482	C₂×C₄₁	semidirect
201. #2274	C₂×C₄₁	semidirect
202. #1982	C₂×C₄₁	semidirect
203. #1949	C₂×C₄₁	semidirect
204. #1926	C₂×C₄₁	semidirect
205. #1925	C₂×C₄₁	semidirect
206. #1874	C₂×C₄₁	semidirect
207. #1798	C₂×C₄₁	semidirect
241. C₄₁	#33116	direct (N × H)
254. #117	D₄×C₄₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄₁×#482	2
C₄₁×#2619	2
C₄₁×#2274	2
C₄₁×#1982	2
C₄₁×#1949	2
C₄₁×#1926	2
C₄₁×#1925	2
C₄₁×#1874	2
C₄₁×#1798	2
#33116	41

Subgroups — C41×#33116 #23809317

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#33116 #23809317