Subgroups — C₄₁×#8985 #23785186

Order 10496.

680 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₁×#461	C₂	1	1	yes	maximal, characteristic
2	D₄×C₄⋊C₄×C₄₁	C₂	1	1	yes	maximal, characteristic
3	C₄₁×#1990	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₁×#1988	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₄₁×D₄⋊C₈	C₂	1	1	yes	maximal, characteristic
6	C₄₁×#1296	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₁×#1279	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×SD₁₆×C₄₁	—	2	1	no	—
9	C₂×C₄⋊Q₈×C₄₁	C₂²	1	1	yes	characteristic
10	C₂×C₄×D₄×C₄₁	—	2	1	no	—
11	C₂×C₄×D₄×C₄₁	C₂²	1	1	yes	characteristic
12	C₂²×C₄⋊C₄×C₄₁	—	2	1	no	—
13	C₄₁×#461	—	2	2	no	—
14	C₄₁×#461	C₄	1	4	yes	complemented
15	C₂×C₄⋊C₈×C₄₁	C₂²	1	1	yes	characteristic
16	C₂×C₄⋊C₈×C₄₁	C₂²	1	1	yes	characteristic
17	C₂×#103×C₄₁	—	2	1	no	—
18	C₂×C₄×C₈×C₄₁	C₂²	1	1	yes	characteristic
19	C₄₁×#389	—	2	1	no	—
20	C₄₁×#385	—	2	2	no	—
21	C₄₁×#384	C₂²	1	1	yes	characteristic
22	C₄₁×#380	—	2	1	no	—
23	C₄×C₄⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
24	C₄₁×#340	—	2	1	no	—
25	C₄₁×#340	—	2	1	no	—
26	C₄₁×#340	—	2	2	no	—
27	C₄₁×D₄⋊C₈	—	2	2	no	—
28	C₂²×Q₈×C₄₁	—	2	1	no	—
29	C₂²×D₄×C₄₁	D₄	1	1	yes	characteristic
30	C₂³×C₄×C₄₁	—	2	1	no	—
31	C₂³×C₄×C₄₁	—	2	2	no	—
32	C₂×SD₁₆×C₄₁	—	2	4	no	—
33	C₂×SD₁₆×C₄₁	—	4	2	no	—
34	C₂×SD₁₆×C₄₁	—	4	2	no	—
35	C₂²×C₈×C₄₁	—	2	1	no	—
36	C₂²×C₈×C₄₁	—	2	1	no	—
37	C₂²×C₈×C₄₁	—	2	1	no	—
38	C₄⋊Q₈×C₄₁	—	2	1	no	—
39	C₄⋊Q₈×C₄₁	—	2	1	no	—
40	C₄⋊Q₈×C₄₁	—	2	1	no	—
41	C₄⋊Q₈×C₄₁	C₂×C₄	1	2	yes	complemented
42	C₄×D₄×C₄₁	—	2	1	no	—
43	C₄×D₄×C₄₁	—	2	1	no	—
44	C₄×D₄×C₄₁	—	4	2	no	—
45	C₄×D₄×C₄₁	—	4	2	no	—
46	C₄×D₄×C₄₁	C₂×C₄	1	2	yes	—
47	C₄×D₄×C₄₁	D₄	1	2	yes	—
48	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
49	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
50	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
51	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
52	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
53	C₂×C₄⋊C₄×C₄₁	—	4	2	no	—
54	C₂×C₄⋊C₄×C₄₁	—	4	2	no	—
55	C₂×C₄⋊C₄×C₄₁	D₄	1	1	yes	characteristic
56	C₂×C₄⋊C₄×C₄₁	D₄	1	1	yes	characteristic
57	C₂×C₄⋊C₄×C₄₁	D₄	1	1	yes	characteristic
58	C₂×C₄⋊C₄×C₄₁	D₄	1	2	yes	—
59	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
60	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
61	C₂×C₄²×C₄₁	—	2	1	no	—
62	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
63	C₄⋊C₈×C₄₁	—	2	1	no	—
64	C₄⋊C₈×C₄₁	—	2	1	no	—
65	C₄⋊C₈×C₄₁	—	2	1	no	—
66	C₄⋊C₈×C₄₁	C₂×C₄	1	2	yes	complemented
67	#103×C₄₁	—	2	4	no	—
68	C₄×C₈×C₄₁	—	2	1	no	—
69	C₄×C₈×C₄₁	—	2	1	no	—
70	#95×C₄₁	—	2	2	no	—
71	#95×C₄₁	—	2	1	no	—
72	C₂⁴×C₄₁	—	2	1	no	—
73	C₂×Q₈×C₄₁	—	2	2	no	—
74	C₂×Q₈×C₄₁	—	4	1	no	—
75	C₂×Q₈×C₄₁	—	4	1	no	—
76	C₂×Q₈×C₄₁	—	4	1	no	—
77	C₂×Q₈×C₄₁	—	4	1	no	—
78	C₂×Q₈×C₄₁	—	4	1	no	—
79	C₂×D₄×C₄₁	—	2	1	no	—
80	C₂×D₄×C₄₁	—	2	1	no	—
81	C₂×D₄×C₄₁	—	2	1	no	—
82	C₂×D₄×C₄₁	C₂²⋊C₄	1	2	yes	—
83	C₂×D₄×C₄₁	D₈	1	2	yes	—
84	C₂×D₄×C₄₁	SD₁₆	1	2	yes	—
85	C₂²×C₄×C₄₁	—	2	1	no	—
86	C₂²×C₄×C₄₁	—	2	1	no	—
87	C₂²×C₄×C₄₁	—	2	2	no	—
88	C₂²×C₄×C₄₁	—	2	2	no	—
89	C₂²×C₄×C₄₁	—	2	1	no	—
90	C₂²×C₄×C₄₁	—	2	2	no	—
91	C₂²×C₄×C₄₁	—	4	4	no	—
92	C₂²×C₄×C₄₁	—	4	1	no	—
93	C₂²×C₄×C₄₁	—	4	1	no	—
94	C₂²×C₄×C₄₁	—	4	1	no	—
95	C₂²×C₄×C₄₁	—	4	1	no	—
96	C₂²×C₄×C₄₁	—	4	4	no	—
97	C₂²×C₄×C₄₁	—	4	1	no	—
98	C₂²×C₄×C₄₁	—	8	2	no	—
99	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
100	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
101	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
102	SD₁₆×C₄₁	—	4	8	no	—
103	C₂×C₈×C₄₁	—	2	2	no	—
104	C₂×C₈×C₄₁	—	2	2	no	—
105	C₂×C₈×C₄₁	—	4	1	no	—
106	C₂×C₈×C₄₁	—	4	1	no	—
107	C₂×C₈×C₄₁	—	4	1	no	—
108	C₂×C₈×C₄₁	—	4	1	no	—
109	C₂×C₈×C₄₁	—	4	1	no	—
110	C₂×C₈×C₄₁	—	4	1	no	—
111	C₂×C₈×C₄₁	—	4	1	no	—
112	C₄⋊C₄×C₄₁	—	2	1	no	—
113	C₄⋊C₄×C₄₁	—	2	1	no	—
114	C₄⋊C₄×C₄₁	—	2	2	no	—
115	C₄⋊C₄×C₄₁	—	2	2	no	—
116	C₄⋊C₄×C₄₁	—	2	1	no	—
117	C₄⋊C₄×C₄₁	—	2	1	no	—
118	C₄⋊C₄×C₄₁	—	4	2	no	—
119	C₄⋊C₄×C₄₁	—	4	4	no	—
120	C₄⋊C₄×C₄₁	—	4	1	no	—
121	C₄⋊C₄×C₄₁	—	4	1	no	—
122	C₄⋊C₄×C₄₁	—	4	1	no	—
123	C₄⋊C₄×C₄₁	—	4	1	no	—
124	C₄⋊C₄×C₄₁	—	4	1	no	—
125	C₄⋊C₄×C₄₁	—	4	1	no	—
126	C₄⋊C₄×C₄₁	C₂²⋊C₄	1	2	yes	—
127	C₄⋊C₄×C₄₁	SD₁₆	1	2	yes	complemented
128	C₂²⋊C₄×C₄₁	—	2	2	no	—
129	C₂²⋊C₄×C₄₁	—	2	2	no	—
130	C₂²⋊C₄×C₄₁	—	4	4	no	—
131	C₄²×C₄₁	—	4	1	no	—
132	C₄²×C₄₁	—	4	1	no	—
133	C₄²×C₄₁	C₂²×C₄	1	1	yes	characteristic
134	C₄²×C₄₁	C₂×D₄	1	1	yes	characteristic
135	C₄²×C₄₁	#41	1	1	yes	characteristic
136	C₄²×C₄₁	#41	1	1	yes	characteristic
137	C₂³×C₄₁	—	2	2	no	—
138	C₂³×C₄₁	—	2	2	no	—
139	C₂³×C₄₁	—	2	2	no	—
140	C₂³×C₄₁	—	4	1	no	—
141	C₂³×C₄₁	—	4	1	no	—
142	C₂³×C₄₁	—	4	1	no	—
143	C₂³×C₄₁	—	4	1	no	—
144	C₂³×C₄₁	#120	1	1	yes	characteristic
145	Q₈×C₄₁	—	4	2	no	—
146	Q₈×C₄₁	—	4	2	no	—
147	Q₈×C₄₁	—	8	1	no	—
148	Q₈×C₄₁	—	8	1	no	—
149	D₄×C₄₁	—	2	2	no	—
150	D₄×C₄₁	—	2	2	no	—
151	D₄×C₄₁	—	2	2	no	—
152	D₄×C₄₁	#102	1	4	yes	—
153	C₂×C₄×C₄₁	—	2	1	no	—
154	C₂×C₄×C₄₁	—	2	1	no	—
155	C₂×C₄×C₄₁	—	2	2	no	—
156	C₂×C₄×C₄₁	—	2	2	no	—
157	C₂×C₄×C₄₁	—	4	1	no	—
158	C₂×C₄×C₄₁	—	4	1	no	—
159	C₂×C₄×C₄₁	—	4	1	no	—
160	C₂×C₄×C₄₁	—	4	1	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	1	no	—
167	C₂×C₄×C₄₁	—	4	2	no	—
168	C₂×C₄×C₄₁	—	4	2	no	—
169	C₂×C₄×C₄₁	—	4	1	no	—
170	C₂×C₄×C₄₁	—	4	2	no	—
171	C₂×C₄×C₄₁	—	4	1	no	—
172	C₂×C₄×C₄₁	—	8	8	no	—
173	C₂×C₄×C₄₁	—	8	1	no	—
174	C₂×C₄×C₄₁	—	8	1	no	—
175	C₂×C₄×C₄₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
176	C₂×C₄×C₄₁	C₄×D₄	1	1	yes	characteristic
177	C₂×C₄×C₄₁	C₄×D₄	1	1	yes	characteristic
178	C₂×C₄×C₄₁	#121	1	1	yes	characteristic
179	C₂×C₄×C₄₁	#121	1	1	yes	characteristic
180	C₂×C₄×C₄₁	#123	1	1	yes	characteristic
181	C₂×C₄×C₄₁	C₂×D₈	1	1	yes	characteristic
182	C₂×C₄×C₄₁	C₂×SD₁₆	1	1	yes	characteristic
183	C₂×C₄×C₄₁	C₂×SD₁₆	1	1	yes	characteristic
184	C₂×C₄×C₄₁	#135	1	1	yes	characteristic
185	C₂×C₄×C₄₁	AGL(1,ℤ/8)	1	1	yes	characteristic
186	C₂×C₄×C₄₁	AGL(1,ℤ/8)	1	1	yes	characteristic
187	C₂×C₄×C₄₁	#137	1	1	yes	characteristic
188	C₂×C₄×C₄₁	#137	1	1	yes	characteristic
189	C₈×C₄₁	—	4	2	no	—
190	C₈×C₄₁	—	4	2	no	—
191	C₈×C₄₁	—	8	1	no	—
192	#8985	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
193	C₂²×C₄₁	—	2	4	no	—
194	C₂²×C₄₁	—	4	2	no	—
195	C₂²×C₄₁	—	4	2	no	—
196	C₂²×C₄₁	—	4	2	no	—
197	C₂²×C₄₁	—	4	2	no	—
198	C₂²×C₄₁	—	4	2	no	—
199	C₂²×C₄₁	—	4	2	no	—
200	C₂²×C₄₁	#386	1	1	yes	characteristic
201	C₂²×C₄₁	#447	1	1	yes	characteristic
202	C₂²×C₄₁	#448	1	1	yes	characteristic
203	C₂²×C₄₁	#450	1	1	yes	characteristic
204	C₂²×C₄₁	#452	1	1	yes	characteristic
205	C₂²×C₄₁	#455	1	1	yes	characteristic
206	C₂²×C₄₁	#456	1	1	yes	characteristic
207	C₄×C₄₁	—	2	1	no	—
208	C₄×C₄₁	—	2	1	no	—
209	C₄×C₄₁	—	4	2	no	—
210	C₄×C₄₁	—	4	2	no	—
211	C₄×C₄₁	—	8	2	no	—
212	C₄×C₄₁	—	8	2	no	—
213	C₄×C₄₁	—	8	1	no	—
214	C₄×C₄₁	C₂×#102	1	1	yes	characteristic
215	C₄×C₄₁	#417	1	1	yes	characteristic
216	C₄×C₄₁	C₄×SD₁₆	1	1	yes	characteristic
217	C₄×C₄₁	#440	1	1	yes	characteristic
218	C₄×C₄₁	#461	1	1	yes	characteristic
219	C₄×C₄₁	#463	1	1	yes	characteristic
220	C₄×C₄₁	#480	1	1	yes	characteristic
221	C₄×C₄₁	#481	1	1	yes	characteristic
222	C₂×#461	C₂×C₄₁	1	1	yes	characteristic
223	D₄×C₄⋊C₄	C₂×C₄₁	1	1	yes	characteristic
224	#1990	C₂×C₄₁	1	1	yes	characteristic, complemented
225	#1988	C₂×C₄₁	1	1	yes	characteristic, complemented
226	C₂×D₄⋊C₈	C₂×C₄₁	1	1	yes	characteristic
227	#1296	C₂×C₄₁	1	1	yes	characteristic, complemented
228	#1279	C₂×C₄₁	1	1	yes	characteristic, complemented
229	C₂×C₄₁	—	4	4	no	—
230	C₂×C₄₁	#1639	1	1	yes	characteristic
231	C₂×C₄₁	#1643	1	1	yes	characteristic
232	C₂×C₄₁	#1647	1	1	yes	characteristic
233	C₂×C₄₁	#1651	1	1	yes	characteristic
234	C₂×C₄₁	#1874	1	1	yes	characteristic
235	C₂×C₄₁	#1877	1	1	yes	characteristic
236	C₂×C₄₁	#1882	1	1	yes	characteristic
237	C₂²×SD₁₆	—	2	1	no	—
238	C₂×C₄⋊Q₈	C₂²×C₄₁	1	1	yes	characteristic
239	C₂×C₄×D₄	—	2	1	no	—
240	C₂×C₄×D₄	C₂²×C₄₁	1	1	yes	characteristic
241	C₂²×C₄⋊C₄	—	2	1	no	—
242	#461	—	2	2	no	—
243	#461	C₄×C₄₁	1	4	yes	complemented
244	C₂×C₄⋊C₈	C₂²×C₄₁	1	1	yes	characteristic
245	C₂×C₄⋊C₈	C₂²×C₄₁	1	1	yes	characteristic
246	C₂×#103	—	2	1	no	—
247	C₂×C₄×C₈	C₂²×C₄₁	1	1	yes	characteristic
248	#389	—	2	1	no	—
249	#385	—	2	2	no	—
250	#384	C₂²×C₄₁	1	1	yes	characteristic
251	#380	—	2	1	no	—
252	C₄×C₄⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
253	#340	—	2	1	no	—
254	#340	—	2	1	no	—
255	#340	—	2	2	no	—
256	D₄⋊C₈	—	2	2	no	—
257	C₄₁	#8985	1	1	yes	characteristic, direct product factor, Sylow
258	C₂²×Q₈	—	2	1	no	—
259	C₂²×D₄	D₄×C₄₁	1	1	yes	characteristic
260	C₂³×C₄	—	2	1	no	—
261	C₂³×C₄	—	2	2	no	—
262	C₂×SD₁₆	—	2	4	no	—
263	C₂×SD₁₆	—	4	2	no	—
264	C₂×SD₁₆	—	4	2	no	—
265	C₂²×C₈	—	2	1	no	—
266	C₂²×C₈	—	2	1	no	—
267	C₂²×C₈	—	2	1	no	—
268	C₄⋊Q₈	—	2	1	no	—
269	C₄⋊Q₈	—	2	1	no	—
270	C₄⋊Q₈	—	2	1	no	—
271	C₄⋊Q₈	C₂×C₄×C₄₁	1	2	yes	complemented
272	C₄×D₄	—	2	1	no	—
273	C₄×D₄	—	2	1	no	—
274	C₄×D₄	—	4	2	no	—
275	C₄×D₄	—	4	2	no	—
276	C₄×D₄	C₂×C₄×C₄₁	1	2	yes	—
277	C₄×D₄	D₄×C₄₁	1	2	yes	—
278	C₂×C₄⋊C₄	—	2	1	no	—
279	C₂×C₄⋊C₄	—	2	1	no	—
280	C₂×C₄⋊C₄	—	2	2	no	—
281	C₂×C₄⋊C₄	—	2	1	no	—
282	C₂×C₄⋊C₄	—	2	1	no	—
283	C₂×C₄⋊C₄	—	4	2	no	—
284	C₂×C₄⋊C₄	—	4	2	no	—
285	C₂×C₄⋊C₄	D₄×C₄₁	1	1	yes	characteristic
286	C₂×C₄⋊C₄	D₄×C₄₁	1	1	yes	characteristic
287	C₂×C₄⋊C₄	D₄×C₄₁	1	1	yes	characteristic
288	C₂×C₄⋊C₄	D₄×C₄₁	1	2	yes	—
289	C₂×C₂²⋊C₄	—	2	1	no	—
290	C₂×C₂²⋊C₄	—	2	2	no	—
291	C₂×C₄²	—	2	1	no	—
292	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
293	C₄⋊C₈	—	2	1	no	—
294	C₄⋊C₈	—	2	1	no	—
295	C₄⋊C₈	—	2	1	no	—
296	C₄⋊C₈	C₂×C₄×C₄₁	1	2	yes	complemented
297	#103	—	2	4	no	—
298	C₄×C₈	—	2	1	no	—
299	C₄×C₈	—	2	1	no	—
300	#95	—	2	2	no	—
301	#95	—	2	1	no	—
302	C₂⁴	—	2	1	no	—
303	C₂×Q₈	—	2	2	no	—
304	C₂×Q₈	—	4	1	no	—
305	C₂×Q₈	—	4	1	no	—
306	C₂×Q₈	—	4	1	no	—
307	C₂×Q₈	—	4	1	no	—
308	C₂×Q₈	—	4	1	no	—
309	C₂×D₄	—	2	1	no	—
310	C₂×D₄	—	2	1	no	—
311	C₂×D₄	—	2	1	no	—
312	C₂×D₄	C₂²⋊C₄×C₄₁	1	2	yes	—
313	C₂×D₄	D₈×C₄₁	1	2	yes	—
314	C₂×D₄	SD₁₆×C₄₁	1	2	yes	—
315	C₂²×C₄	—	2	1	no	—
316	C₂²×C₄	—	2	1	no	—
317	C₂²×C₄	—	2	2	no	—
318	C₂²×C₄	—	2	2	no	—
319	C₂²×C₄	—	2	1	no	—
320	C₂²×C₄	—	2	2	no	—
321	C₂²×C₄	—	4	4	no	—
322	C₂²×C₄	—	4	1	no	—
323	C₂²×C₄	—	4	1	no	—
324	C₂²×C₄	—	4	1	no	—
325	C₂²×C₄	—	4	1	no	—
326	C₂²×C₄	—	4	4	no	—
327	C₂²×C₄	—	4	1	no	—
328	C₂²×C₄	—	8	2	no	—
329	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
330	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
331	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
332	SD₁₆	—	4	8	no	—
333	C₂×C₈	—	2	2	no	—
334	C₂×C₈	—	2	2	no	—
335	C₂×C₈	—	4	1	no	—
336	C₂×C₈	—	4	1	no	—
337	C₂×C₈	—	4	1	no	—
338	C₂×C₈	—	4	1	no	—
339	C₂×C₈	—	4	1	no	—
340	C₂×C₈	—	4	1	no	—
341	C₂×C₈	—	4	1	no	—
342	C₄⋊C₄	—	2	1	no	—
343	C₄⋊C₄	—	2	1	no	—
344	C₄⋊C₄	—	2	2	no	—
345	C₄⋊C₄	—	2	2	no	—
346	C₄⋊C₄	—	2	1	no	—
347	C₄⋊C₄	—	2	1	no	—
348	C₄⋊C₄	—	4	2	no	—
349	C₄⋊C₄	—	4	4	no	—
350	C₄⋊C₄	—	4	1	no	—
351	C₄⋊C₄	—	4	1	no	—
352	C₄⋊C₄	—	4	1	no	—
353	C₄⋊C₄	—	4	1	no	—
354	C₄⋊C₄	—	4	1	no	—
355	C₄⋊C₄	—	4	1	no	—
356	C₄⋊C₄	C₂²⋊C₄×C₄₁	1	2	yes	—
357	C₄⋊C₄	SD₁₆×C₄₁	1	2	yes	complemented
358	C₂²⋊C₄	—	2	2	no	—
359	C₂²⋊C₄	—	2	2	no	—
360	C₂²⋊C₄	—	4	4	no	—
361	C₄²	—	4	1	no	—
362	C₄²	—	4	1	no	—
363	C₄²	C₂²×C₄×C₄₁	1	1	yes	characteristic
364	C₄²	C₂×D₄×C₄₁	1	1	yes	characteristic
365	C₄²	#41×C₄₁	1	1	yes	characteristic
366	C₄²	#41×C₄₁	1	1	yes	characteristic
367	C₂³	—	2	2	no	—
368	C₂³	—	2	2	no	—
369	C₂³	—	2	2	no	—
370	C₂³	—	4	1	no	—
371	C₂³	—	4	1	no	—
372	C₂³	—	4	1	no	—
373	C₂³	—	4	1	no	—
374	C₂³	#120×C₄₁	1	1	yes	characteristic
375	Q₈	—	4	2	no	—
376	Q₈	—	4	2	no	—
377	Q₈	—	8	1	no	—
378	Q₈	—	8	1	no	—
379	D₄	—	2	2	no	—
380	D₄	—	2	2	no	—
381	D₄	—	2	2	no	—
382	D₄	#102×C₄₁	1	4	yes	—
383	C₂×C₄	—	2	1	no	—
384	C₂×C₄	—	2	1	no	—
385	C₂×C₄	—	2	2	no	—
386	C₂×C₄	—	2	2	no	—
387	C₂×C₄	—	4	1	no	—
388	C₂×C₄	—	4	1	no	—
389	C₂×C₄	—	4	1	no	—
390	C₂×C₄	—	4	1	no	—
391	C₂×C₄	—	4	2	no	—
392	C₂×C₄	—	4	2	no	—
393	C₂×C₄	—	4	2	no	—
394	C₂×C₄	—	4	2	no	—
395	C₂×C₄	—	4	2	no	—
396	C₂×C₄	—	4	1	no	—
397	C₂×C₄	—	4	2	no	—
398	C₂×C₄	—	4	2	no	—
399	C₂×C₄	—	4	1	no	—
400	C₂×C₄	—	4	2	no	—
401	C₂×C₄	—	4	1	no	—
402	C₂×C₄	—	8	8	no	—
403	C₂×C₄	—	8	1	no	—
404	C₂×C₄	—	8	1	no	—
405	C₂×C₄	C₂×C₂²⋊C₄×C₄₁	1	1	yes	characteristic
406	C₂×C₄	C₄×D₄×C₄₁	1	1	yes	characteristic
407	C₂×C₄	C₄×D₄×C₄₁	1	1	yes	characteristic
408	C₂×C₄	#121×C₄₁	1	1	yes	characteristic
409	C₂×C₄	#121×C₄₁	1	1	yes	characteristic
410	C₂×C₄	#123×C₄₁	1	1	yes	characteristic
411	C₂×C₄	C₂×D₈×C₄₁	1	1	yes	characteristic
412	C₂×C₄	C₂×SD₁₆×C₄₁	1	1	yes	characteristic
413	C₂×C₄	C₂×SD₁₆×C₄₁	1	1	yes	characteristic
414	C₂×C₄	#135×C₄₁	1	1	yes	characteristic
415	C₂×C₄	AGL(1,ℤ/8)×C₄₁	1	1	yes	characteristic
416	C₂×C₄	AGL(1,ℤ/8)×C₄₁	1	1	yes	characteristic
417	C₂×C₄	#137×C₄₁	1	1	yes	characteristic
418	C₂×C₄	#137×C₄₁	1	1	yes	characteristic
419	C₈	—	4	2	no	—
420	C₈	—	4	2	no	—
421	C₈	—	8	1	no	—
422	C₂²	—	2	4	no	—
423	C₂²	—	4	2	no	—
424	C₂²	—	4	2	no	—
425	C₂²	—	4	2	no	—
426	C₂²	—	4	2	no	—
427	C₂²	—	4	2	no	—
428	C₂²	—	4	2	no	—
429	C₂²	C₄₁×#386	1	1	yes	characteristic
430	C₂²	C₄₁×#447	1	1	yes	characteristic
431	C₂²	C₄₁×#448	1	1	yes	characteristic
432	C₂²	C₄₁×#450	1	1	yes	characteristic
433	C₂²	C₄₁×#452	1	1	yes	characteristic
434	C₂²	C₄₁×#455	1	1	yes	characteristic
435	C₂²	C₄₁×#456	1	1	yes	characteristic
436	C₄	—	2	1	no	—
437	C₄	—	2	1	no	—
438	C₄	—	4	2	no	—
439	C₄	—	4	2	no	—
440	C₄	—	8	2	no	—
441	C₄	—	8	2	no	—
442	C₄	—	8	1	no	—
443	C₄	C₂×#102×C₄₁	1	1	yes	characteristic
444	C₄	C₄₁×#417	1	1	yes	characteristic
445	C₄	C₄×SD₁₆×C₄₁	1	1	yes	characteristic
446	C₄	C₄₁×#440	1	1	yes	characteristic
447	C₄	C₄₁×#461	1	1	yes	characteristic
448	C₄	C₄₁×#463	1	1	yes	characteristic
449	C₄	C₄₁×#480	1	1	yes	characteristic
450	C₄	C₄₁×#481	1	1	yes	characteristic
451	C₂	—	4	4	no	—
452	C₂	C₄₁×#1639	1	1	yes	characteristic
453	C₂	C₄₁×#1643	1	1	yes	characteristic
454	C₂	C₄₁×#1647	1	1	yes	characteristic
455	C₂	C₄₁×#1651	1	1	yes	characteristic
456	C₂	C₄₁×#1874	1	1	yes	characteristic
457	C₂	C₄₁×#1877	1	1	yes	characteristic
458	C₂	C₄₁×#1882	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₄₁	#120
commutator	C₄²	C₂²×C₄×C₄₁
Frattini, cosocle	C₂×C₄²	C₂³×C₄₁
prime radical	C₂²×D₄×C₄₁	D₄
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₄₁ ◁ C₂×C₄²×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₄₁×#1990	C₂	semidirect
4. C₄₁×#1988	C₂	semidirect
6. C₄₁×#1296	C₂	semidirect
7. C₄₁×#1279	C₂	semidirect
14. C₄₁×#461	C₄	semidirect
41. C₄⋊Q₈×C₄₁	C₂×C₄	semidirect
66. C₄⋊C₈×C₄₁	C₂×C₄	semidirect
127. C₄⋊C₄×C₄₁	SD₁₆	semidirect
192. #8985	C₄₁	direct (N × H)
224. #1990	C₂×C₄₁	semidirect
225. #1988	C₂×C₄₁	semidirect
227. #1296	C₂×C₄₁	semidirect
228. #1279	C₂×C₄₁	semidirect
243. #461	C₄×C₄₁	semidirect
257. C₄₁	#8985	direct (N × H)
271. C₄⋊Q₈	C₂×C₄×C₄₁	semidirect
296. C₄⋊C₈	C₂×C₄×C₄₁	semidirect
357. C₄⋊C₄	SD₁₆×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×#461	2
D₄×C₄⋊C₄×C₄₁	2
C₄₁×#1990	2
C₄₁×#1988	2
C₂×C₄₁×D₄⋊C₈	2
C₄₁×#1296	2
C₄₁×#1279	2
#8985	41

Subgroups — C41×#8985 #23785186

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#8985 #23785186