Subgroups — C₄₁×#33010 #23809211

Order 10496.

1314 conjugacy classes of subgroups.

The subgroup lattice has 414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄×Q₈×C₄₁	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄₁×#484	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄₁×#451	C₂	1	1	yes	maximal, characteristic
4	C₄₁×#2855	C₂	1	1	yes	maximal, characteristic
5	C₄₁×#1878	C₂	1	4	yes	maximal, complemented
6	C₄₁×#1863	C₂	1	4	yes	maximal, complemented
7	C₄₁×#1824	C₂	1	1	yes	maximal, characteristic
8	C₄₁×#1817	C₂	1	1	yes	maximal, characteristic
9	C₄₁×#1787	C₂	1	1	yes	maximal, characteristic
10	C₂³×Q₈×C₄₁	C₂²	1	1	yes	characteristic
11	C₂²×Q₁₆×C₄₁	C₂²	1	2	yes	—
12	C₂×C₂²⋊Q₈×C₄₁	C₂²	1	1	yes	characteristic
13	C₂×C₄×Q₈×C₄₁	—	2	4	no	—
14	C₂×C₄×Q₈×C₄₁	—	2	4	no	—
15	C₂×C₄×Q₈×C₄₁	—	2	2	no	—
16	C₂×C₄×Q₈×C₄₁	C₂²	1	4	yes	—
17	C₂²×C₄⋊C₄×C₄₁	—	2	1	no	—
18	C₂²×C₄⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
19	C₂²×C₄²×C₄₁	—	2	1	no	—
20	C₂²×C₄²×C₄₁	C₂²	1	1	yes	characteristic
21	C₄₁×#484	—	2	4	no	—
22	C₄₁×#451	—	2	4	no	—
23	C₂×#107×C₄₁	C₂²	1	2	yes	—
24	C₂×#103×C₄₁	C₂²	1	4	yes	—
25	C₂×#103×C₄₁	C₂²	1	2	yes	—
26	C₂×#103×C₄₁	C₂²	1	2	yes	—
27	C₂×C₂²⋊C₈×C₄₁	C₂²	1	1	yes	characteristic
28	C₂×C₂²⋊C₈×C₄₁	C₂²	1	1	yes	characteristic
29	C₄₁×#391	C₂²	1	2	yes	—
30	C₄₁×#389	C₂²	1	2	yes	—
31	C₄₁×#387	—	2	2	no	—
32	C₄₁×#385	—	2	1	no	—
33	C₄₁×#381	—	2	1	no	—
34	C₄₁×#380	C₂²	1	1	yes	characteristic
35	C₄₁×#340	C₂²	1	4	yes	—
36	C₄₁×#336	C₂²	1	4	yes	—
37	C₂²×Q₈×C₄₁	—	2	8	no	—
38	C₂²×Q₈×C₄₁	—	2	2	no	—
39	C₂²×Q₈×C₄₁	—	2	1	no	—
40	C₂²×Q₈×C₄₁	D₄	1	4	yes	—
41	C₂²×Q₈×C₄₁	C₂³	1	1	yes	characteristic
42	C₂²×Q₈×C₄₁	C₂³	1	2	yes	—
43	C₂³×C₄×C₄₁	—	2	1	no	—
44	C₂³×C₄×C₄₁	—	2	1	no	—
45	C₂³×C₄×C₄₁	D₄	1	1	yes	characteristic
46	C₂³×C₄×C₄₁	D₄	1	1	yes	characteristic
47	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
48	C₂×Q₁₆×C₄₁	—	2	4	no	—
49	C₂×Q₁₆×C₄₁	—	2	8	no	—
50	C₂²×C₈×C₄₁	C₂³	1	2	yes	—
51	C₂²×C₈×C₄₁	C₂³	1	2	yes	—
52	C₂²⋊Q₈×C₄₁	—	2	2	no	—
53	C₂²⋊Q₈×C₄₁	—	2	2	no	—
54	C₄×Q₈×C₄₁	—	2	16	no	—
55	C₄×Q₈×C₄₁	—	2	8	no	—
56	C₄×Q₈×C₄₁	—	2	8	no	—
57	C₂×C₄⋊C₄×C₄₁	—	2	8	no	—
58	C₂×C₄⋊C₄×C₄₁	—	2	4	no	—
59	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
60	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
61	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
62	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
63	C₂×C₄⋊C₄×C₄₁	D₄	1	4	yes	—
64	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
65	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
66	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
67	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
68	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
69	C₂×C₄²×C₄₁	—	2	8	no	—
70	C₂×C₄²×C₄₁	—	2	4	no	—
71	C₂×C₄²×C₄₁	—	2	2	no	—
72	C₂×C₄²×C₄₁	—	2	2	no	—
73	C₂×C₄²×C₄₁	D₄	1	2	yes	—
74	C₂×C₄²×C₄₁	C₂³	1	2	yes	—
75	#107×C₄₁	—	2	4	no	—
76	#103×C₄₁	—	2	4	no	—
77	#103×C₄₁	—	2	8	no	—
78	#103×C₄₁	—	2	4	no	—
79	C₂²⋊C₈×C₄₁	—	2	2	no	—
80	C₂²⋊C₈×C₄₁	—	2	2	no	—
81	#95×C₄₁	—	2	1	no	—
82	#95×C₄₁	—	2	2	no	—
83	#95×C₄₁	—	2	2	no	—
84	#95×C₄₁	—	2	2	no	—
85	C₂⁴×C₄₁	C₂×D₄	1	1	yes	characteristic
86	C₂×Q₈×C₄₁	—	2	16	no	—
87	C₂×Q₈×C₄₁	—	2	8	no	—
88	C₂×Q₈×C₄₁	—	2	16	no	—
89	C₂×Q₈×C₄₁	—	2	4	no	—
90	C₂×Q₈×C₄₁	—	2	2	no	—
91	C₂×Q₈×C₄₁	—	2	4	no	—
92	C₂×Q₈×C₄₁	—	2	1	no	—
93	C₂×Q₈×C₄₁	—	2	1	no	—
94	C₂×Q₈×C₄₁	—	2	4	no	—
95	C₂×Q₈×C₄₁	C₂×D₄	1	4	yes	—
96	C₂×Q₈×C₄₁	#41	1	8	yes	—
97	C₂²×C₄×C₄₁	—	2	8	no	—
98	C₂²×C₄×C₄₁	—	2	2	no	—
99	C₂²×C₄×C₄₁	—	2	4	no	—
100	C₂²×C₄×C₄₁	—	2	2	no	—
101	C₂²×C₄×C₄₁	—	2	2	no	—
102	C₂²×C₄×C₄₁	—	2	4	no	—
103	C₂²×C₄×C₄₁	—	2	2	no	—
104	C₂²×C₄×C₄₁	—	2	4	no	—
105	C₂²×C₄×C₄₁	—	2	2	no	—
106	C₂²×C₄×C₄₁	—	2	2	no	—
107	C₂²×C₄×C₄₁	—	2	1	no	—
108	C₂²×C₄×C₄₁	—	2	1	no	—
109	C₂²×C₄×C₄₁	—	4	2	no	—
110	C₂²×C₄×C₄₁	—	4	4	no	—
111	C₂²×C₄×C₄₁	Q₁₆	1	4	yes	complemented
112	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
113	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
114	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
115	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
116	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
117	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
118	Q₁₆×C₄₁	—	4	8	no	—
119	C₂×C₈×C₄₁	—	2	2	no	—
120	C₂×C₈×C₄₁	—	2	2	no	—
121	C₂×C₈×C₄₁	—	2	4	no	—
122	C₂×C₈×C₄₁	—	2	4	no	—
123	C₄⋊C₄×C₄₁	—	2	16	no	—
124	C₄⋊C₄×C₄₁	—	2	4	no	—
125	C₄⋊C₄×C₄₁	—	2	2	no	—
126	C₄⋊C₄×C₄₁	—	2	1	no	—
127	C₄⋊C₄×C₄₁	—	2	1	no	—
128	C₄⋊C₄×C₄₁	—	2	4	no	—
129	C₄⋊C₄×C₄₁	—	4	4	no	—
130	C₄⋊C₄×C₄₁	—	4	2	no	—
131	C₄⋊C₄×C₄₁	C₂×D₄	1	4	yes	—
132	C₂²⋊C₄×C₄₁	—	4	2	no	—
133	C₂²⋊C₄×C₄₁	—	4	2	no	—
134	C₄²×C₄₁	—	2	16	no	—
135	C₄²×C₄₁	—	2	4	no	—
136	C₄²×C₄₁	—	2	2	no	—
137	C₄²×C₄₁	—	2	2	no	—
138	C₂³×C₄₁	—	2	2	no	—
139	C₂³×C₄₁	—	2	2	no	—
140	C₂³×C₄₁	#120	1	2	yes	—
141	C₂³×C₄₁	C₂×Q₁₆	1	2	yes	—
142	C₂³×C₄₁	#137	1	2	yes	—
143	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
144	Q₈×C₄₁	—	2	16	no	—
145	Q₈×C₄₁	—	2	4	no	—
146	Q₈×C₄₁	—	2	8	no	—
147	Q₈×C₄₁	—	4	2	no	—
148	Q₈×C₄₁	—	4	2	no	—
149	Q₈×C₄₁	#123	1	8	yes	—
150	C₂×C₄×C₄₁	—	2	16	no	—
151	C₂×C₄×C₄₁	—	2	2	no	—
152	C₂×C₄×C₄₁	—	2	4	no	—
153	C₂×C₄×C₄₁	—	2	8	no	—
154	C₂×C₄×C₄₁	—	2	2	no	—
155	C₂×C₄×C₄₁	—	2	2	no	—
156	C₂×C₄×C₄₁	—	2	8	no	—
157	C₂×C₄×C₄₁	—	2	4	no	—
158	C₂×C₄×C₄₁	—	2	4	no	—
159	C₂×C₄×C₄₁	—	2	2	no	—
160	C₂×C₄×C₄₁	—	2	4	no	—
161	C₂×C₄×C₄₁	—	2	2	no	—
162	C₂×C₄×C₄₁	—	2	2	no	—
163	C₂×C₄×C₄₁	—	4	4	no	—
164	C₂×C₄×C₄₁	—	4	8	no	—
165	C₂×C₄×C₄₁	—	4	4	no	—
166	C₂×C₄×C₄₁	—	4	1	no	—
167	C₂×C₄×C₄₁	—	4	1	no	—
168	C₂×C₄×C₄₁	—	4	2	no	—
169	C₂×C₄×C₄₁	—	4	2	no	—
170	C₂×C₄×C₄₁	—	4	2	no	—
171	C₂×C₄×C₄₁	—	4	2	no	—
172	C₂×C₄×C₄₁	—	4	2	no	—
173	C₂×C₄×C₄₁	#120	1	2	yes	—
174	C₂×C₄×C₄₁	C₂×Q₁₆	1	4	yes	—
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	4	yes	—
178	C₈×C₄₁	—	4	2	no	—
179	C₈×C₄₁	—	4	2	no	—
180	#33010	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
181	C₂²×C₄₁	—	2	4	no	—
182	C₂²×C₄₁	—	2	2	no	—
183	C₂²×C₄₁	—	2	4	no	—
184	C₂²×C₄₁	—	2	2	no	—
185	C₂²×C₄₁	#451	1	4	yes	—
186	C₂²×C₄₁	C₂×#120	1	1	yes	characteristic
187	C₂²×C₄₁	#525	1	2	yes	—
188	C₂²×C₄₁	C₂²×Q₁₆	1	1	yes	characteristic
189	C₂²×C₄₁	C₂×#137	1	1	yes	characteristic
190	C₂²×C₄₁	#575	1	2	yes	—
191	C₄×C₄₁	—	2	8	no	—
192	C₄×C₄₁	—	2	2	no	—
193	C₄×C₄₁	—	2	4	no	—
194	C₄×C₄₁	—	4	2	no	—
195	C₄×C₄₁	—	4	4	no	—
196	C₄×C₄₁	—	8	1	no	—
197	C₄×C₄₁	—	8	2	no	—
198	C₄×C₄₁	—	8	1	no	—
199	C₄×C₄₁	C₂×#123	1	2	yes	—
200	C₄×C₄₁	#525	1	2	yes	—
201	C₂²×C₄×Q₈	C₂×C₄₁	1	1	yes	characteristic
202	C₂×#484	C₂×C₄₁	1	1	yes	characteristic
203	C₂×#451	C₂×C₄₁	1	1	yes	characteristic
204	#2855	C₂×C₄₁	1	1	yes	characteristic
205	#1878	C₂×C₄₁	1	4	yes	complemented
206	#1863	C₂×C₄₁	1	4	yes	complemented
207	#1824	C₂×C₄₁	1	1	yes	characteristic
208	#1817	C₂×C₄₁	1	1	yes	characteristic
209	#1787	C₂×C₄₁	1	1	yes	characteristic
210	C₂×C₄₁	—	2	4	no	—
211	C₂×C₄₁	#2849	1	1	yes	characteristic
212	C₂×C₄₁	C₂×#451	1	1	yes	characteristic
213	C₂×C₄₁	#3005	1	1	yes	characteristic
214	C₂×C₄₁	#3104	1	2	yes	—
215	C₂×C₄₁	#3117	1	2	yes	—
216	C₂³×Q₈	C₂²×C₄₁	1	1	yes	characteristic
217	C₂²×Q₁₆	C₂²×C₄₁	1	2	yes	—
218	C₂×C₂²⋊Q₈	C₂²×C₄₁	1	1	yes	characteristic
219	C₂×C₄×Q₈	—	2	4	no	—
220	C₂×C₄×Q₈	—	2	4	no	—
221	C₂×C₄×Q₈	—	2	2	no	—
222	C₂×C₄×Q₈	C₂²×C₄₁	1	4	yes	—
223	C₂²×C₄⋊C₄	—	2	1	no	—
224	C₂²×C₄⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
225	C₂²×C₄²	—	2	1	no	—
226	C₂²×C₄²	C₂²×C₄₁	1	1	yes	characteristic
227	#484	—	2	4	no	—
228	#451	—	2	4	no	—
229	C₂×#107	C₂²×C₄₁	1	2	yes	—
230	C₂×#103	C₂²×C₄₁	1	2	yes	—
231	C₂×#103	C₂²×C₄₁	1	2	yes	—
232	C₂×#103	C₂²×C₄₁	1	4	yes	—
233	C₂×C₂²⋊C₈	C₂²×C₄₁	1	1	yes	characteristic
234	C₂×C₂²⋊C₈	C₂²×C₄₁	1	1	yes	characteristic
235	#391	C₂²×C₄₁	1	2	yes	—
236	#389	C₂²×C₄₁	1	2	yes	—
237	#387	—	2	2	no	—
238	#385	—	2	1	no	—
239	#381	—	2	1	no	—
240	#380	C₂²×C₄₁	1	1	yes	characteristic
241	#340	C₂²×C₄₁	1	4	yes	—
242	#336	C₂²×C₄₁	1	4	yes	—
243	C₄₁	#33010	1	1	yes	characteristic, direct product factor, Sylow
244	C₂²×Q₈	—	2	8	no	—
245	C₂²×Q₈	—	2	2	no	—
246	C₂²×Q₈	—	2	1	no	—
247	C₂²×Q₈	D₄×C₄₁	1	4	yes	—
248	C₂²×Q₈	C₂³×C₄₁	1	1	yes	characteristic
249	C₂²×Q₈	C₂³×C₄₁	1	2	yes	—
250	C₂³×C₄	—	2	1	no	—
251	C₂³×C₄	—	2	1	no	—
252	C₂³×C₄	D₄×C₄₁	1	1	yes	characteristic
253	C₂³×C₄	D₄×C₄₁	1	1	yes	characteristic
254	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
255	C₂×Q₁₆	—	2	4	no	—
256	C₂×Q₁₆	—	2	8	no	—
257	C₂²×C₈	C₂³×C₄₁	1	2	yes	—
258	C₂²×C₈	C₂³×C₄₁	1	2	yes	—
259	C₂²⋊Q₈	—	2	2	no	—
260	C₂²⋊Q₈	—	2	2	no	—
261	C₄×Q₈	—	2	16	no	—
262	C₄×Q₈	—	2	8	no	—
263	C₄×Q₈	—	2	8	no	—
264	C₂×C₄⋊C₄	—	2	8	no	—
265	C₂×C₄⋊C₄	—	2	4	no	—
266	C₂×C₄⋊C₄	—	2	1	no	—
267	C₂×C₄⋊C₄	—	2	2	no	—
268	C₂×C₄⋊C₄	—	2	1	no	—
269	C₂×C₄⋊C₄	—	2	2	no	—
270	C₂×C₄⋊C₄	D₄×C₄₁	1	4	yes	—
271	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
272	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
273	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
274	C₂×C₂²⋊C₄	—	2	1	no	—
275	C₂×C₂²⋊C₄	—	2	1	no	—
276	C₂×C₄²	—	2	8	no	—
277	C₂×C₄²	—	2	2	no	—
278	C₂×C₄²	—	2	2	no	—
279	C₂×C₄²	—	2	4	no	—
280	C₂×C₄²	D₄×C₄₁	1	2	yes	—
281	C₂×C₄²	C₂³×C₄₁	1	2	yes	—
282	#107	—	2	4	no	—
283	#103	—	2	4	no	—
284	#103	—	2	8	no	—
285	#103	—	2	4	no	—
286	C₂²⋊C₈	—	2	2	no	—
287	C₂²⋊C₈	—	2	2	no	—
288	#95	—	2	1	no	—
289	#95	—	2	2	no	—
290	#95	—	2	2	no	—
291	#95	—	2	2	no	—
292	C₂⁴	C₂×D₄×C₄₁	1	1	yes	characteristic
293	C₂×Q₈	—	2	16	no	—
294	C₂×Q₈	—	2	8	no	—
295	C₂×Q₈	—	2	16	no	—
296	C₂×Q₈	—	2	4	no	—
297	C₂×Q₈	—	2	2	no	—
298	C₂×Q₈	—	2	4	no	—
299	C₂×Q₈	—	2	1	no	—
300	C₂×Q₈	—	2	1	no	—
301	C₂×Q₈	—	2	4	no	—
302	C₂×Q₈	C₂×D₄×C₄₁	1	4	yes	—
303	C₂×Q₈	#41×C₄₁	1	8	yes	—
304	C₂²×C₄	—	2	8	no	—
305	C₂²×C₄	—	2	2	no	—
306	C₂²×C₄	—	2	4	no	—
307	C₂²×C₄	—	2	2	no	—
308	C₂²×C₄	—	2	2	no	—
309	C₂²×C₄	—	2	4	no	—
310	C₂²×C₄	—	2	2	no	—
311	C₂²×C₄	—	2	4	no	—
312	C₂²×C₄	—	2	2	no	—
313	C₂²×C₄	—	2	2	no	—
314	C₂²×C₄	—	2	1	no	—
315	C₂²×C₄	—	2	1	no	—
316	C₂²×C₄	—	4	2	no	—
317	C₂²×C₄	—	4	4	no	—
318	C₂²×C₄	Q₁₆×C₄₁	1	4	yes	complemented
319	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
320	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
321	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
322	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
323	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
324	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
325	Q₁₆	—	4	8	no	—
326	C₂×C₈	—	2	2	no	—
327	C₂×C₈	—	2	2	no	—
328	C₂×C₈	—	2	4	no	—
329	C₂×C₈	—	2	4	no	—
330	C₄⋊C₄	—	2	16	no	—
331	C₄⋊C₄	—	2	4	no	—
332	C₄⋊C₄	—	2	2	no	—
333	C₄⋊C₄	—	2	1	no	—
334	C₄⋊C₄	—	2	1	no	—
335	C₄⋊C₄	—	2	4	no	—
336	C₄⋊C₄	—	4	4	no	—
337	C₄⋊C₄	—	4	2	no	—
338	C₄⋊C₄	C₂×D₄×C₄₁	1	4	yes	—
339	C₂²⋊C₄	—	4	2	no	—
340	C₂²⋊C₄	—	4	2	no	—
341	C₄²	—	2	16	no	—
342	C₄²	—	2	4	no	—
343	C₄²	—	2	2	no	—
344	C₄²	—	2	2	no	—
345	C₂³	—	2	2	no	—
346	C₂³	—	2	2	no	—
347	C₂³	#120×C₄₁	1	2	yes	—
348	C₂³	C₂×Q₁₆×C₄₁	1	2	yes	—
349	C₂³	#137×C₄₁	1	2	yes	—
350	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
351	Q₈	—	2	16	no	—
352	Q₈	—	2	4	no	—
353	Q₈	—	2	8	no	—
354	Q₈	—	4	2	no	—
355	Q₈	—	4	2	no	—
356	Q₈	#123×C₄₁	1	8	yes	—
357	C₂×C₄	—	2	16	no	—
358	C₂×C₄	—	2	2	no	—
359	C₂×C₄	—	2	4	no	—
360	C₂×C₄	—	2	8	no	—
361	C₂×C₄	—	2	2	no	—
362	C₂×C₄	—	2	2	no	—
363	C₂×C₄	—	2	8	no	—
364	C₂×C₄	—	2	4	no	—
365	C₂×C₄	—	2	4	no	—
366	C₂×C₄	—	2	2	no	—
367	C₂×C₄	—	2	4	no	—
368	C₂×C₄	—	2	2	no	—
369	C₂×C₄	—	2	2	no	—
370	C₂×C₄	—	4	4	no	—
371	C₂×C₄	—	4	8	no	—
372	C₂×C₄	—	4	4	no	—
373	C₂×C₄	—	4	1	no	—
374	C₂×C₄	—	4	1	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	#120×C₄₁	1	2	yes	—
381	C₂×C₄	C₂×Q₁₆×C₄₁	1	4	yes	—
382	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
383	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
384	C₂×C₄	C₂×#41×C₄₁	1	4	yes	—
385	C₈	—	4	2	no	—
386	C₈	—	4	2	no	—
387	C₂²	—	2	4	no	—
388	C₂²	—	2	2	no	—
389	C₂²	—	2	4	no	—
390	C₂²	—	2	2	no	—
391	C₂²	C₄₁×#451	1	4	yes	—
392	C₂²	C₂×#120×C₄₁	1	1	yes	characteristic
393	C₂²	C₄₁×#525	1	2	yes	—
394	C₂²	C₂²×Q₁₆×C₄₁	1	1	yes	characteristic
395	C₂²	C₂×#137×C₄₁	1	1	yes	characteristic
396	C₂²	C₄₁×#575	1	2	yes	—
397	C₄	—	2	8	no	—
398	C₄	—	2	2	no	—
399	C₄	—	2	4	no	—
400	C₄	—	4	2	no	—
401	C₄	—	4	4	no	—
402	C₄	—	8	1	no	—
403	C₄	—	8	2	no	—
404	C₄	—	8	1	no	—
405	C₄	C₂×#123×C₄₁	1	2	yes	—
406	C₄	C₄₁×#525	1	2	yes	—
407	C₂	—	2	4	no	—
408	C₂	C₄₁×#2849	1	1	yes	characteristic
409	C₂	C₂×C₄₁×#451	1	1	yes	characteristic
410	C₂	C₄₁×#3005	1	1	yes	characteristic
411	C₂	C₄₁×#3104	1	2	yes	—
412	C₂	C₄₁×#3117	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₄₁	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₁
prime radical	C₂⁴×C₄₁	C₂×D₄
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₄₁ ◁ C₂²×C₄²×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
5. C₄₁×#1878	C₂	semidirect
6. C₄₁×#1863	C₂	semidirect
111. C₂²×C₄×C₄₁	Q₁₆	semidirect
180. #33010	C₄₁	direct (N × H)
205. #1878	C₂×C₄₁	semidirect
206. #1863	C₂×C₄₁	semidirect
243. C₄₁	#33010	direct (N × H)
318. C₂²×C₄	Q₁₆×C₄₁	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₄×Q₈×C₄₁	2
C₂×C₄₁×#484	2
C₂×C₄₁×#451	2
C₄₁×#2855	2
C₄₁×#1878	2
C₄₁×#1863	2
C₄₁×#1824	2
C₄₁×#1817	2
C₄₁×#1787	2
#33010	41

Subgroups — C41×#33010 #23809211

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#33010 #23809211