Subgroups — C₄₁×#33164 #23809365

Order 10496.

1246 conjugacy classes of subgroups.

The subgroup lattice has 448 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₁×#463	C₂	1	4	yes	maximal, complemented
2	C₂×C₄₁×#461	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄₁×#459	C₂	1	1	yes	maximal, characteristic
4	C₄₁×#2858	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄²×D₄×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄₁×#1983	C₂	1	4	yes	maximal, complemented
7	C₄₁×#1982	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄₁×#1981	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄₁×#1842	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×SD₁₆×C₄₁	C₂²	1	2	yes	—
11	C₂²×D₈×C₄₁	C₂²	1	2	yes	—
12	C₂×C₄⋊Q₈×C₄₁	C₂²	1	1	yes	characteristic
13	C₂×#127×C₄₁	C₂²	1	1	yes	characteristic
14	C₂×#124×C₄₁	C₂²	1	4	yes	—
15	C₂×C₄×D₄×C₄₁	C₂²	1	1	yes	characteristic
16	C₂×C₄×D₄×C₄₁	C₂²	1	2	yes	—
17	C₂²×C₄²×C₄₁	—	2	1	no	—
18	C₄₁×#463	—	2	16	no	—
19	C₄₁×#461	—	2	4	no	—
20	C₄₁×#459	—	2	4	no	—
21	C₂×C₄⋊C₈×C₄₁	C₂²	1	1	yes	characteristic
22	C₂×C₄⋊C₈×C₄₁	C₂²	1	1	yes	characteristic
23	C₂×C₄⋊C₈×C₄₁	C₂²	1	4	yes	—
24	C₂×#103×C₄₁	C₂²	1	4	yes	—
25	C₂×#103×C₄₁	C₂²	1	2	yes	—
26	C₂×#102×C₄₁	C₂²	1	4	yes	—
27	C₂×#102×C₄₁	C₂²	1	2	yes	—
28	C₄₁×#390	—	2	1	no	—
29	C₄₁×#390	—	2	1	no	—
30	C₄₁×#390	—	2	2	no	—
31	C₄×C₄⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
32	C₄×C₄⋊C₄×C₄₁	C₂²	1	2	yes	—
33	C₄×C₂²⋊C₄×C₄₁	—	2	1	no	—
34	C₄×C₂²⋊C₄×C₄₁	—	2	2	no	—
35	C₄³×C₄₁	C₂²	1	1	yes	characteristic
36	C₂²×Q₈×C₄₁	C₂³	1	2	yes	—
37	C₂²×D₄×C₄₁	—	2	1	no	—
38	C₂²×D₄×C₄₁	—	2	1	no	—
39	C₂²×D₄×C₄₁	C₂³	1	2	yes	—
40	C₂²×D₄×C₄₁	C₂³	1	1	yes	characteristic
41	C₂³×C₄×C₄₁	—	2	1	no	—
42	C₂³×C₄×C₄₁	—	2	2	no	—
43	C₂×SD₁₆×C₄₁	—	2	4	no	—
44	C₂×SD₁₆×C₄₁	—	2	8	no	—
45	C₂×D₈×C₄₁	—	2	4	no	—
46	C₂×D₈×C₄₁	—	2	8	no	—
47	C₂²×C₈×C₄₁	C₂³	1	2	yes	—
48	C₂²×C₈×C₄₁	C₂³	1	2	yes	—
49	C₄⋊Q₈×C₄₁	—	2	2	no	—
50	C₄⋊Q₈×C₄₁	—	2	2	no	—
51	#127×C₄₁	—	2	2	no	—
52	#127×C₄₁	—	2	2	no	—
53	#124×C₄₁	—	2	8	no	—
54	#124×C₄₁	—	2	8	no	—
55	C₄×D₄×C₄₁	—	2	4	no	—
56	C₄×D₄×C₄₁	—	2	2	no	—
57	C₄×D₄×C₄₁	D₄	1	4	yes	—
58	C₄×D₄×C₄₁	D₄	1	8	yes	complemented
59	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
60	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
61	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
62	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
63	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
64	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
65	C₂×C₂²⋊C₄×C₄₁	—	2	4	no	—
66	C₂×C₂²⋊C₄×C₄₁	—	2	4	no	—
67	C₂×C₄²×C₄₁	—	2	2	no	—
68	C₂×C₄²×C₄₁	—	2	1	no	—
69	C₂×C₄²×C₄₁	—	4	4	no	—
70	C₂×C₄²×C₄₁	D₄	1	1	yes	characteristic
71	C₂×C₄²×C₄₁	D₄	1	1	yes	characteristic
72	C₂×C₄²×C₄₁	D₄	1	2	yes	—
73	C₂×C₄²×C₄₁	C₂³	1	2	yes	—
74	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
75	C₄⋊C₈×C₄₁	—	2	2	no	—
76	C₄⋊C₈×C₄₁	—	2	2	no	—
77	C₄⋊C₈×C₄₁	—	2	8	no	—
78	#103×C₄₁	—	2	4	no	—
79	#103×C₄₁	—	2	8	no	—
80	#102×C₄₁	—	2	4	no	—
81	#102×C₄₁	—	2	8	no	—
82	#95×C₄₁	—	2	2	no	—
83	#95×C₄₁	—	2	1	no	—
84	C₂⁴×C₄₁	—	2	1	no	—
85	C₂⁴×C₄₁	—	2	2	no	—
86	C₂×Q₈×C₄₁	—	2	4	no	—
87	C₂×Q₈×C₄₁	—	2	2	no	—
88	C₂×Q₈×C₄₁	—	2	4	no	—
89	C₂×Q₈×C₄₁	—	2	2	no	—
90	C₂×D₄×C₄₁	—	2	4	no	—
91	C₂×D₄×C₄₁	—	2	2	no	—
92	C₂×D₄×C₄₁	—	2	1	no	—
93	C₂×D₄×C₄₁	—	2	2	no	—
94	C₂×D₄×C₄₁	—	2	4	no	—
95	C₂×D₄×C₄₁	—	2	2	no	—
96	C₂×D₄×C₄₁	—	4	4	no	—
97	C₂×D₄×C₄₁	—	4	2	no	—
98	C₂×D₄×C₄₁	—	4	2	no	—
99	C₂×D₄×C₄₁	—	4	2	no	—
100	C₂×D₄×C₄₁	—	4	2	no	—
101	C₂×D₄×C₄₁	C₂×D₄	1	2	yes	—
102	C₂×D₄×C₄₁	C₂×D₄	1	4	yes	—
103	C₂²×C₄×C₄₁	—	2	1	no	—
104	C₂²×C₄×C₄₁	—	2	2	no	—
105	C₂²×C₄×C₄₁	—	2	4	no	—
106	C₂²×C₄×C₄₁	—	2	8	no	—
107	C₂²×C₄×C₄₁	—	2	2	no	—
108	C₂²×C₄×C₄₁	—	4	4	no	—
109	C₂²×C₄×C₄₁	—	4	4	no	—
110	C₂²×C₄×C₄₁	—	4	2	no	—
111	C₂²×C₄×C₄₁	—	4	2	no	—
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	1	yes	characteristic
116	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
117	SD₁₆×C₄₁	—	4	8	no	—
118	D₈×C₄₁	—	4	8	no	—
119	C₂×C₈×C₄₁	—	2	2	no	—
120	C₂×C₈×C₄₁	—	2	4	no	—
121	C₂×C₈×C₄₁	—	2	4	no	—
122	C₂×C₈×C₄₁	—	2	2	no	—
123	C₄⋊C₄×C₄₁	—	2	1	no	—
124	C₄⋊C₄×C₄₁	—	2	2	no	—
125	C₄⋊C₄×C₄₁	—	4	2	no	—
126	C₄⋊C₄×C₄₁	—	4	2	no	—
127	C₄⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
128	C₄⋊C₄×C₄₁	C₂×D₄	1	4	yes	—
129	C₂²⋊C₄×C₄₁	—	2	4	no	—
130	C₂²⋊C₄×C₄₁	—	2	8	no	—
131	C₂²⋊C₄×C₄₁	—	4	8	no	—
132	C₂²⋊C₄×C₄₁	—	4	8	no	—
133	C₄²×C₄₁	—	2	2	no	—
134	C₄²×C₄₁	—	2	2	no	—
135	C₄²×C₄₁	—	4	2	no	—
136	C₄²×C₄₁	—	4	4	no	—
137	C₄²×C₄₁	—	4	2	no	—
138	C₄²×C₄₁	C₂×D₄	1	2	yes	—
139	C₄²×C₄₁	C₂×D₄	1	4	yes	—
140	C₄²×C₄₁	#41	1	4	yes	—
141	C₄²×C₄₁	#41	1	2	yes	—
142	C₂³×C₄₁	—	2	2	no	—
143	C₂³×C₄₁	—	2	4	no	—
144	C₂³×C₄₁	—	4	1	no	—
145	C₂³×C₄₁	—	4	1	no	—
146	C₂³×C₄₁	—	4	2	no	—
147	C₂³×C₄₁	—	4	4	no	—
148	C₂³×C₄₁	—	4	2	no	—
149	C₂³×C₄₁	—	4	2	no	—
150	C₂³×C₄₁	—	4	2	no	—
151	C₂³×C₄₁	—	4	4	no	—
152	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
153	Q₈×C₄₁	—	4	2	no	—
154	Q₈×C₄₁	—	4	4	no	—
155	Q₈×C₄₁	—	4	2	no	—
156	D₄×C₄₁	—	2	2	no	—
157	D₄×C₄₁	—	2	4	no	—
158	D₄×C₄₁	—	4	2	no	—
159	D₄×C₄₁	—	4	4	no	—
160	D₄×C₄₁	—	4	2	no	—
161	D₄×C₄₁	—	8	4	no	—
162	D₄×C₄₁	—	8	4	no	—
163	D₄×C₄₁	#127	1	4	yes	—
164	C₂×C₄×C₄₁	—	2	2	no	—
165	C₂×C₄×C₄₁	—	2	2	no	—
166	C₂×C₄×C₄₁	—	2	2	no	—
167	C₂×C₄×C₄₁	—	2	2	no	—
168	C₂×C₄×C₄₁	—	2	2	no	—
169	C₂×C₄×C₄₁	—	2	2	no	—
170	C₂×C₄×C₄₁	—	2	4	no	—
171	C₂×C₄×C₄₁	—	4	16	no	—
172	C₂×C₄×C₄₁	—	4	1	no	—
173	C₂×C₄×C₄₁	—	4	1	no	—
174	C₂×C₄×C₄₁	—	4	2	no	—
175	C₂×C₄×C₄₁	—	4	2	no	—
176	C₂×C₄×C₄₁	—	4	8	no	—
177	C₂×C₄×C₄₁	—	4	4	no	—
178	C₂×C₄×C₄₁	—	4	2	no	—
179	C₂×C₄×C₄₁	#121	1	4	yes	—
180	C₂×C₄×C₄₁	#121	1	2	yes	—
181	C₂×C₄×C₄₁	#121	1	4	yes	—
182	C₂×C₄×C₄₁	#121	1	2	yes	—
183	C₂×C₄×C₄₁	#135	1	2	yes	—
184	C₂×C₄×C₄₁	AGL(1,ℤ/8)	1	2	yes	—
185	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
186	C₂×C₄×C₄₁	C₂²×D₄	1	2	yes	—
187	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
188	C₂×C₄×C₄₁	C₂×#41	1	2	yes	—
189	C₈×C₄₁	—	4	2	no	—
190	C₈×C₄₁	—	4	2	no	—
191	#33164	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
192	C₂²×C₄₁	—	2	4	no	—
193	C₂²×C₄₁	—	4	2	no	—
194	C₂²×C₄₁	—	4	4	no	—
195	C₂²×C₄₁	—	4	4	no	—
196	C₂²×C₄₁	—	4	2	no	—
197	C₂²×C₄₁	—	8	2	no	—
198	C₂²×C₄₁	—	8	2	no	—
199	C₂²×C₄₁	—	8	4	no	—
200	C₂²×C₄₁	—	8	4	no	—
201	C₂²×C₄₁	—	8	2	no	—
202	C₂²×C₄₁	C₂×#121	1	1	yes	characteristic
203	C₂²×C₄₁	C₂×#121	1	2	yes	—
204	C₂²×C₄₁	C₂×#135	1	1	yes	characteristic
205	C₂²×C₄₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
206	C₂²×C₄₁	#575	1	2	yes	—
207	C₄×C₄₁	—	2	4	no	—
208	C₄×C₄₁	—	2	4	no	—
209	C₄×C₄₁	—	2	2	no	—
210	C₄×C₄₁	—	4	2	no	—
211	C₄×C₄₁	—	4	4	no	—
212	C₄×C₄₁	—	8	2	no	—
213	C₄×C₄₁	#463	1	4	yes	complemented
214	C₄×C₄₁	C₂×#127	1	1	yes	characteristic
215	C₄×C₄₁	#532	1	1	yes	characteristic
216	C₄×C₄₁	#532	1	2	yes	—
217	C₂×#463	C₂×C₄₁	1	4	yes	complemented
218	C₂×#461	C₂×C₄₁	1	1	yes	characteristic, complemented
219	C₂×#459	C₂×C₄₁	1	1	yes	characteristic
220	#2858	C₂×C₄₁	1	1	yes	characteristic, complemented
221	C₄²×D₄	C₂×C₄₁	1	1	yes	characteristic, complemented
222	#1983	C₂×C₄₁	1	4	yes	complemented
223	#1982	C₂×C₄₁	1	1	yes	characteristic, complemented
224	#1981	C₂×C₄₁	1	1	yes	characteristic, complemented
225	#1842	C₂×C₄₁	1	1	yes	characteristic, complemented
226	C₂×C₄₁	—	4	4	no	—
227	C₂×C₄₁	—	16	2	no	—
228	C₂×C₄₁	#2856	1	1	yes	characteristic
229	C₂×C₄₁	C₂×#463	1	1	yes	characteristic
230	C₂×C₄₁	#3035	1	2	yes	—
231	C₂×C₄₁	#3036	1	2	yes	—
232	C₂×C₄₁	#3040	1	1	yes	characteristic
233	C₂²×SD₁₆	C₂²×C₄₁	1	2	yes	—
234	C₂²×D₈	C₂²×C₄₁	1	2	yes	—
235	C₂×C₄⋊Q₈	C₂²×C₄₁	1	1	yes	characteristic
236	C₂×#127	C₂²×C₄₁	1	1	yes	characteristic
237	C₂×#124	C₂²×C₄₁	1	4	yes	—
238	C₂×C₄×D₄	C₂²×C₄₁	1	1	yes	characteristic
239	C₂×C₄×D₄	C₂²×C₄₁	1	2	yes	—
240	C₂²×C₄²	—	2	1	no	—
241	#463	—	2	16	no	—
242	#461	—	2	4	no	—
243	#459	—	2	4	no	—
244	C₂×C₄⋊C₈	C₂²×C₄₁	1	1	yes	characteristic
245	C₂×C₄⋊C₈	C₂²×C₄₁	1	1	yes	characteristic
246	C₂×C₄⋊C₈	C₂²×C₄₁	1	4	yes	—
247	C₂×#103	C₂²×C₄₁	1	4	yes	—
248	C₂×#103	C₂²×C₄₁	1	2	yes	—
249	C₂×#102	C₂²×C₄₁	1	4	yes	—
250	C₂×#102	C₂²×C₄₁	1	2	yes	—
251	#390	—	2	1	no	—
252	#390	—	2	1	no	—
253	#390	—	2	2	no	—
254	C₄×C₄⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
255	C₄×C₄⋊C₄	C₂²×C₄₁	1	2	yes	—
256	C₄×C₂²⋊C₄	—	2	1	no	—
257	C₄×C₂²⋊C₄	—	2	2	no	—
258	C₄³	C₂²×C₄₁	1	1	yes	characteristic
259	C₄₁	#33164	1	1	yes	characteristic, direct product factor, Sylow
260	C₂²×Q₈	C₂³×C₄₁	1	2	yes	—
261	C₂²×D₄	—	2	1	no	—
262	C₂²×D₄	—	2	1	no	—
263	C₂²×D₄	C₂³×C₄₁	1	2	yes	—
264	C₂²×D₄	C₂³×C₄₁	1	1	yes	characteristic
265	C₂³×C₄	—	2	1	no	—
266	C₂³×C₄	—	2	2	no	—
267	C₂×SD₁₆	—	2	4	no	—
268	C₂×SD₁₆	—	2	8	no	—
269	C₂×D₈	—	2	4	no	—
270	C₂×D₈	—	2	8	no	—
271	C₂²×C₈	C₂³×C₄₁	1	2	yes	—
272	C₂²×C₈	C₂³×C₄₁	1	2	yes	—
273	C₄⋊Q₈	—	2	2	no	—
274	C₄⋊Q₈	—	2	2	no	—
275	#127	—	2	2	no	—
276	#127	—	2	2	no	—
277	#124	—	2	8	no	—
278	#124	—	2	8	no	—
279	C₄×D₄	—	2	4	no	—
280	C₄×D₄	—	2	2	no	—
281	C₄×D₄	D₄×C₄₁	1	4	yes	—
282	C₄×D₄	D₄×C₄₁	1	8	yes	complemented
283	C₂×C₄⋊C₄	—	2	1	no	—
284	C₂×C₄⋊C₄	—	2	1	no	—
285	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
286	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
287	C₂×C₂²⋊C₄	—	2	1	no	—
288	C₂×C₂²⋊C₄	—	2	2	no	—
289	C₂×C₂²⋊C₄	—	2	4	no	—
290	C₂×C₂²⋊C₄	—	2	4	no	—
291	C₂×C₄²	—	2	2	no	—
292	C₂×C₄²	—	2	1	no	—
293	C₂×C₄²	—	4	4	no	—
294	C₂×C₄²	D₄×C₄₁	1	1	yes	characteristic
295	C₂×C₄²	D₄×C₄₁	1	1	yes	characteristic
296	C₂×C₄²	D₄×C₄₁	1	2	yes	—
297	C₂×C₄²	C₂³×C₄₁	1	2	yes	—
298	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
299	C₄⋊C₈	—	2	2	no	—
300	C₄⋊C₈	—	2	2	no	—
301	C₄⋊C₈	—	2	8	no	—
302	#103	—	2	4	no	—
303	#103	—	2	8	no	—
304	#102	—	2	4	no	—
305	#102	—	2	8	no	—
306	#95	—	2	2	no	—
307	#95	—	2	1	no	—
308	C₂⁴	—	2	1	no	—
309	C₂⁴	—	2	2	no	—
310	C₂×Q₈	—	2	4	no	—
311	C₂×Q₈	—	2	2	no	—
312	C₂×Q₈	—	2	4	no	—
313	C₂×Q₈	—	2	2	no	—
314	C₂×D₄	—	2	4	no	—
315	C₂×D₄	—	2	2	no	—
316	C₂×D₄	—	2	2	no	—
317	C₂×D₄	—	2	1	no	—
318	C₂×D₄	—	2	4	no	—
319	C₂×D₄	—	2	2	no	—
320	C₂×D₄	—	4	4	no	—
321	C₂×D₄	—	4	2	no	—
322	C₂×D₄	—	4	2	no	—
323	C₂×D₄	—	4	2	no	—
324	C₂×D₄	—	4	2	no	—
325	C₂×D₄	C₂×D₄×C₄₁	1	2	yes	—
326	C₂×D₄	C₂×D₄×C₄₁	1	4	yes	—
327	C₂²×C₄	—	2	1	no	—
328	C₂²×C₄	—	2	2	no	—
329	C₂²×C₄	—	2	4	no	—
330	C₂²×C₄	—	2	8	no	—
331	C₂²×C₄	—	2	2	no	—
332	C₂²×C₄	—	4	4	no	—
333	C₂²×C₄	—	4	4	no	—
334	C₂²×C₄	—	4	2	no	—
335	C₂²×C₄	—	4	2	no	—
336	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
337	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
338	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
339	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
340	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
341	SD₁₆	—	4	8	no	—
342	D₈	—	4	8	no	—
343	C₂×C₈	—	2	2	no	—
344	C₂×C₈	—	2	4	no	—
345	C₂×C₈	—	2	4	no	—
346	C₂×C₈	—	2	2	no	—
347	C₄⋊C₄	—	2	2	no	—
348	C₄⋊C₄	—	2	1	no	—
349	C₄⋊C₄	—	4	2	no	—
350	C₄⋊C₄	—	4	2	no	—
351	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
352	C₄⋊C₄	C₂×D₄×C₄₁	1	4	yes	—
353	C₂²⋊C₄	—	2	4	no	—
354	C₂²⋊C₄	—	2	8	no	—
355	C₂²⋊C₄	—	4	8	no	—
356	C₂²⋊C₄	—	4	8	no	—
357	C₄²	—	2	2	no	—
358	C₄²	—	2	2	no	—
359	C₄²	—	4	2	no	—
360	C₄²	—	4	4	no	—
361	C₄²	—	4	2	no	—
362	C₄²	C₂×D₄×C₄₁	1	2	yes	—
363	C₄²	C₂×D₄×C₄₁	1	4	yes	—
364	C₄²	#41×C₄₁	1	4	yes	—
365	C₄²	#41×C₄₁	1	2	yes	—
366	C₂³	—	2	4	no	—
367	C₂³	—	2	2	no	—
368	C₂³	—	4	1	no	—
369	C₂³	—	4	1	no	—
370	C₂³	—	4	2	no	—
371	C₂³	—	4	4	no	—
372	C₂³	—	4	2	no	—
373	C₂³	—	4	2	no	—
374	C₂³	—	4	2	no	—
375	C₂³	—	4	4	no	—
376	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
377	Q₈	—	4	2	no	—
378	Q₈	—	4	4	no	—
379	Q₈	—	4	2	no	—
380	D₄	—	2	2	no	—
381	D₄	—	2	4	no	—
382	D₄	—	4	2	no	—
383	D₄	—	4	4	no	—
384	D₄	—	4	2	no	—
385	D₄	—	8	4	no	—
386	D₄	—	8	4	no	—
387	D₄	#127×C₄₁	1	4	yes	—
388	C₂×C₄	—	2	2	no	—
389	C₂×C₄	—	2	2	no	—
390	C₂×C₄	—	2	2	no	—
391	C₂×C₄	—	2	2	no	—
392	C₂×C₄	—	2	2	no	—
393	C₂×C₄	—	2	4	no	—
394	C₂×C₄	—	2	2	no	—
395	C₂×C₄	—	4	16	no	—
396	C₂×C₄	—	4	1	no	—
397	C₂×C₄	—	4	2	no	—
398	C₂×C₄	—	4	1	no	—
399	C₂×C₄	—	4	2	no	—
400	C₂×C₄	—	4	8	no	—
401	C₂×C₄	—	4	4	no	—
402	C₂×C₄	—	4	2	no	—
403	C₂×C₄	#121×C₄₁	1	4	yes	—
404	C₂×C₄	#121×C₄₁	1	2	yes	—
405	C₂×C₄	#121×C₄₁	1	4	yes	—
406	C₂×C₄	#121×C₄₁	1	2	yes	—
407	C₂×C₄	#135×C₄₁	1	2	yes	—
408	C₂×C₄	AGL(1,ℤ/8)×C₄₁	1	2	yes	—
409	C₂×C₄	C₂²×D₄×C₄₁	1	2	yes	—
410	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
411	C₂×C₄	C₂×#41×C₄₁	1	2	yes	—
412	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
413	C₈	—	4	2	no	—
414	C₈	—	4	2	no	—
415	C₂²	—	2	4	no	—
416	C₂²	—	4	4	no	—
417	C₂²	—	4	2	no	—
418	C₂²	—	4	2	no	—
419	C₂²	—	4	4	no	—
420	C₂²	—	8	4	no	—
421	C₂²	—	8	2	no	—
422	C₂²	—	8	2	no	—
423	C₂²	—	8	2	no	—
424	C₂²	—	8	4	no	—
425	C₂²	C₂×#121×C₄₁	1	2	yes	—
426	C₂²	C₂×#121×C₄₁	1	1	yes	characteristic
427	C₂²	C₂×#135×C₄₁	1	1	yes	characteristic
428	C₂²	C₂×AGL(1,ℤ/8)×C₄₁	1	1	yes	characteristic
429	C₂²	C₄₁×#575	1	2	yes	—
430	C₄	—	2	4	no	—
431	C₄	—	2	2	no	—
432	C₄	—	2	4	no	—
433	C₄	—	4	4	no	—
434	C₄	—	4	2	no	—
435	C₄	—	8	2	no	—
436	C₄	C₄₁×#463	1	4	yes	complemented
437	C₄	C₂×#127×C₄₁	1	1	yes	characteristic
438	C₄	C₄₁×#532	1	2	yes	—
439	C₄	C₄₁×#532	1	1	yes	characteristic
440	C₂	—	4	4	no	—
441	C₂	—	16	2	no	—
442	C₂	C₄₁×#2856	1	1	yes	characteristic
443	C₂	C₂×C₄₁×#463	1	1	yes	characteristic
444	C₂	C₄₁×#3035	1	2	yes	—
445	C₂	C₄₁×#3036	1	2	yes	—
446	C₂	C₄₁×#3040	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₄₁	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₁
prime radical	C₂×C₄₁×#459	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₄₁ ◁ C₄³×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₄₁×#463	C₂	semidirect
2. C₂×C₄₁×#461	C₂	semidirect
4. C₄₁×#2858	C₂	semidirect
5. C₄²×D₄×C₄₁	C₂	semidirect
6. C₄₁×#1983	C₂	semidirect
7. C₄₁×#1982	C₂	semidirect
8. C₄₁×#1981	C₂	semidirect
9. C₄₁×#1842	C₂	semidirect
58. C₄×D₄×C₄₁	D₄	semidirect
191. #33164	C₄₁	direct (N × H)
213. C₄×C₄₁	#463	semidirect
217. C₂×#463	C₂×C₄₁	semidirect
218. C₂×#461	C₂×C₄₁	semidirect
220. #2858	C₂×C₄₁	semidirect
221. C₄²×D₄	C₂×C₄₁	semidirect
222. #1983	C₂×C₄₁	semidirect
223. #1982	C₂×C₄₁	semidirect
224. #1981	C₂×C₄₁	semidirect
225. #1842	C₂×C₄₁	semidirect
259. C₄₁	#33164	direct (N × H)
282. C₄×D₄	D₄×C₄₁	semidirect
436. C₄	C₄₁×#463	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄₁×#463	2
C₂×C₄₁×#461	2
C₂×C₄₁×#459	2
C₄₁×#2858	2
C₄²×D₄×C₄₁	2
C₄₁×#1983	2
C₄₁×#1982	2
C₄₁×#1981	2
C₄₁×#1842	2
#33164	41

Subgroups — C41×#33164 #23809365

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#33164 #23809365