Subgroups — C₄₁×#21089 #23797290

Order 10496.

1234 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₁×#418	C₂	1	1	yes	maximal, characteristic
2	C₂²×#102×C₄₁	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄₁×#405	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₁×#2316	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₁×#2309	C₂	1	1	yes	maximal, characteristic
6	C₄₁×#1936	C₂	1	4	yes	maximal, complemented
7	C₄₁×#1934	C₂	1	4	yes	maximal, complemented
8	C₄₁×#1736	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄₁×#1735	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂³×D₄×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×#117×C₄₁	C₂²	1	1	yes	characteristic
14	C₂×#117×C₄₁	C₂²	1	1	yes	characteristic
15	C₂×#117×C₄₁	C₂²	1	1	yes	characteristic
16	C₂²×C₄⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
17	C₄₁×#418	—	2	4	no	—
18	C₂×#102×C₄₁	C₄	1	8	yes	complemented
19	C₂×#102×C₄₁	C₂²	1	4	yes	—
20	C₂×#102×C₄₁	C₂²	1	2	yes	—
21	C₂×#102×C₄₁	C₂²	1	2	yes	—
22	C₄₁×#405	—	2	4	no	—
23	C₂×#97×C₄₁	C₂²	1	2	yes	complemented
24	C₂×C₄×C₈×C₄₁	C₂²	1	2	yes	complemented
25	C₄₁×#390	—	2	2	no	—
26	C₄₁×#390	C₂²	1	4	yes	—
27	C₄₁×#389	—	2	2	no	—
28	C₄₁×#389	C₂²	1	4	yes	complemented
29	C₄₁×#380	—	2	2	no	—
30	C₄₁×#379	—	2	2	no	—
31	C₄₁×#340	C₂²	1	2	yes	complemented
32	C₄₁×#340	C₂²	1	4	yes	complemented
33	C₄₁×#340	C₂²	1	2	yes	complemented
34	C₂⁵×C₄₁	—	2	1	no	—
35	C₂²×D₄×C₄₁	—	2	2	no	—
36	C₂²×D₄×C₄₁	—	2	1	no	—
37	C₂²×D₄×C₄₁	—	2	2	no	—
38	C₂²×D₄×C₄₁	—	2	2	no	—
39	C₂²×D₄×C₄₁	—	2	2	no	—
40	C₂²×D₄×C₄₁	—	2	2	no	—
41	C₂²×D₄×C₄₁	C₂×C₄	1	4	yes	—
42	C₂²×D₄×C₄₁	C₂³	1	2	yes	—
43	C₂³×C₄×C₄₁	—	2	1	no	—
44	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
45	C₂×M₁₆×C₄₁	—	2	2	no	—
46	C₂×M₁₆×C₄₁	—	2	2	no	—
47	C₂×M₁₆×C₄₁	D₄	1	4	yes	—
48	C₂²×C₈×C₄₁	—	2	2	no	—
49	C₂²×C₈×C₄₁	—	2	2	no	—
50	C₂²×C₈×C₄₁	C₂×C₄	1	4	yes	—
51	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
52	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
53	C₂²×C₈×C₄₁	C₂³	1	2	yes	—
54	#117×C₄₁	—	2	2	no	—
55	#117×C₄₁	—	2	2	no	—
56	#117×C₄₁	—	2	2	no	—
57	#117×C₄₁	—	2	2	no	—
58	#117×C₄₁	—	2	2	no	—
59	#117×C₄₁	—	2	2	no	—
60	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
61	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
62	C₂×C₄⋊C₄×C₄₁	—	2	4	no	—
63	C₂×C₄⋊C₄×C₄₁	C₂×C₄	1	4	yes	—
64	C₂×C₄⋊C₄×C₄₁	D₄	1	2	yes	—
65	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
66	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
67	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
68	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
69	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
70	C₂×C₂²⋊C₄×C₄₁	—	2	4	no	—
71	C₂×C₂²⋊C₄×C₄₁	—	2	4	no	—
72	C₂×C₂²⋊C₄×C₄₁	D₄	1	2	yes	—
73	C₂×C₄²×C₄₁	—	2	1	no	—
74	C₂×C₄²×C₄₁	—	2	1	no	—
75	C₂×C₄²×C₄₁	C₂³	1	2	yes	—
76	#102×C₄₁	—	2	8	no	—
77	#102×C₄₁	C₂×C₄	1	8	yes	—
78	#102×C₄₁	C₂×C₄	1	8	yes	—
79	#97×C₄₁	—	2	4	no	—
80	C₄×C₈×C₄₁	—	2	4	no	—
81	#95×C₄₁	—	2	4	no	—
82	C₂⁴×C₄₁	—	2	2	no	—
83	C₂⁴×C₄₁	—	2	4	no	—
84	C₂⁴×C₄₁	—	4	2	no	—
85	C₂⁴×C₄₁	—	4	2	no	—
86	C₂⁴×C₄₁	—	8	2	no	—
87	C₂⁴×C₄₁	—	8	2	no	—
88	C₂⁴×C₄₁	C₂×D₄	1	1	yes	characteristic
89	C₂×D₄×C₄₁	—	2	8	no	—
90	C₂×D₄×C₄₁	—	2	8	no	—
91	C₂×D₄×C₄₁	—	2	4	no	—
92	C₂×D₄×C₄₁	—	2	2	no	—
93	C₂×D₄×C₄₁	—	2	2	no	—
94	C₂×D₄×C₄₁	—	2	2	no	—
95	C₂×D₄×C₄₁	—	2	2	no	—
96	C₂×D₄×C₄₁	—	2	2	no	—
97	C₂×D₄×C₄₁	—	4	2	no	—
98	C₂×D₄×C₄₁	—	4	4	no	—
99	C₂×D₄×C₄₁	—	4	2	no	—
100	C₂×D₄×C₄₁	—	4	4	no	—
101	C₂×D₄×C₄₁	C₂²×C₄	1	4	yes	—
102	C₂²×C₄×C₄₁	—	2	2	no	—
103	C₂²×C₄×C₄₁	—	2	4	no	—
104	C₂²×C₄×C₄₁	—	2	2	no	—
105	C₂²×C₄×C₄₁	—	2	2	no	—
106	C₂²×C₄×C₄₁	—	8	2	no	—
107	C₂²×C₄×C₄₁	C₂²×C₄	1	2	yes	—
108	C₂²×C₄×C₄₁	C₂×D₄	1	4	yes	—
109	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
110	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
111	C₂²×C₄×C₄₁	#41	1	2	yes	—
112	C₂²×C₄×C₄₁	#41	1	2	yes	—
113	C₂²×C₄×C₄₁	#41	1	2	yes	—
114	C₂²×C₄×C₄₁	#41	1	2	yes	—
115	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
116	M₁₆×C₄₁	—	2	8	no	—
117	C₂×C₈×C₄₁	—	2	8	no	—
118	C₂×C₈×C₄₁	—	2	1	no	—
119	C₂×C₈×C₄₁	—	2	1	no	—
120	C₂×C₈×C₄₁	—	2	1	no	—
121	C₂×C₈×C₄₁	—	2	1	no	—
122	C₂×C₈×C₄₁	—	2	2	no	—
123	C₂×C₈×C₄₁	—	2	2	no	—
124	C₂×C₈×C₄₁	C₂²×C₄	1	2	yes	—
125	C₂×C₈×C₄₁	C₂²×C₄	1	2	yes	—
126	C₂×C₈×C₄₁	C₂×D₄	1	4	yes	—
127	C₄⋊C₄×C₄₁	—	2	4	no	—
128	C₄⋊C₄×C₄₁	—	2	4	no	—
129	C₄⋊C₄×C₄₁	—	2	2	no	—
130	C₄⋊C₄×C₄₁	—	2	2	no	—
131	C₄⋊C₄×C₄₁	—	2	2	no	—
132	C₄⋊C₄×C₄₁	—	2	2	no	—
133	C₄⋊C₄×C₄₁	—	2	2	no	—
134	C₄⋊C₄×C₄₁	—	8	4	no	—
135	C₄⋊C₄×C₄₁	C₂²×C₄	1	4	yes	—
136	C₂²⋊C₄×C₄₁	—	2	4	no	—
137	C₂²⋊C₄×C₄₁	—	4	2	no	—
138	C₂²⋊C₄×C₄₁	—	4	2	no	—
139	C₂²⋊C₄×C₄₁	—	8	4	no	—
140	C₂²⋊C₄×C₄₁	—	8	4	no	—
141	C₄²×C₄₁	—	2	2	no	—
142	C₄²×C₄₁	—	2	2	no	—
143	C₄²×C₄₁	—	4	2	no	—
144	C₄²×C₄₁	—	4	2	no	—
145	C₂³×C₄₁	—	2	2	no	—
146	C₂³×C₄₁	—	2	2	no	—
147	C₂³×C₄₁	—	2	4	no	—
148	C₂³×C₄₁	—	4	2	no	—
149	C₂³×C₄₁	—	4	2	no	—
150	C₂³×C₄₁	—	4	4	no	—
151	C₂³×C₄₁	—	4	4	no	—
152	C₂³×C₄₁	—	4	8	no	—
153	C₂³×C₄₁	—	8	4	no	—
154	C₂³×C₄₁	—	8	4	no	—
155	C₂³×C₄₁	—	8	8	no	—
156	C₂³×C₄₁	—	8	8	no	—
157	C₂³×C₄₁	C₄×D₄	1	2	yes	—
158	C₂³×C₄₁	#121	1	2	yes	—
159	C₂³×C₄₁	#124	1	2	yes	—
160	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
161	D₄×C₄₁	—	2	4	no	—
162	D₄×C₄₁	—	2	4	no	—
163	D₄×C₄₁	—	4	2	no	—
164	D₄×C₄₁	—	4	2	no	—
165	D₄×C₄₁	—	4	8	no	—
166	C₂×C₄×C₄₁	—	2	4	no	—
167	C₂×C₄×C₄₁	—	2	4	no	—
168	C₂×C₄×C₄₁	—	2	4	no	—
169	C₂×C₄×C₄₁	—	2	4	no	—
170	C₂×C₄×C₄₁	—	4	4	no	—
171	C₂×C₄×C₄₁	—	4	2	no	—
172	C₂×C₄×C₄₁	—	4	2	no	—
173	C₂×C₄×C₄₁	—	4	2	no	—
174	C₂×C₄×C₄₁	—	4	2	no	—
175	C₂×C₄×C₄₁	—	4	2	no	—
176	C₂×C₄×C₄₁	—	4	2	no	—
177	C₂×C₄×C₄₁	—	8	4	no	—
178	C₂×C₄×C₄₁	#117	1	4	yes	—
179	C₂×C₄×C₄₁	C₄×D₄	1	4	yes	—
180	C₂×C₄×C₄₁	C₄×D₄	1	2	yes	—
181	C₂×C₄×C₄₁	#121	1	2	yes	—
182	C₂×C₄×C₄₁	#123	1	4	yes	—
183	C₂×C₄×C₄₁	#124	1	2	yes	—
184	C₂×C₄×C₄₁	#126	1	4	yes	—
185	C₂×C₄×C₄₁	C₂³×C₄	1	1	yes	characteristic
186	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
187	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
188	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
189	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
190	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
191	C₈×C₄₁	—	2	2	no	—
192	C₈×C₄₁	—	2	2	no	—
193	C₈×C₄₁	—	2	4	no	—
194	#21089	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
195	C₂²×C₄₁	—	2	4	no	—
196	C₂²×C₄₁	—	2	2	no	—
197	C₂²×C₄₁	—	2	2	no	—
198	C₂²×C₄₁	—	2	4	no	—
199	C₂²×C₄₁	—	4	4	no	—
200	C₂²×C₄₁	—	4	4	no	—
201	C₂²×C₄₁	—	4	4	no	—
202	C₂²×C₄₁	—	8	16	no	—
203	C₂²×C₄₁	—	8	4	no	—
204	C₂²×C₄₁	—	8	4	no	—
205	C₂²×C₄₁	#388	1	4	yes	—
206	C₂²×C₄₁	C₂×C₄×D₄	1	1	yes	characteristic
207	C₂²×C₄₁	C₂×#121	1	1	yes	characteristic
208	C₂²×C₄₁	C₂×#124	1	1	yes	characteristic
209	C₂²×C₄₁	#576	1	2	yes	—
210	C₂²×C₄₁	#577	1	2	yes	—
211	C₄×C₄₁	—	4	4	no	—
212	C₄×C₄₁	—	4	4	no	—
213	C₄×C₄₁	—	8	2	no	—
214	C₄×C₄₁	—	8	2	no	—
215	C₄×C₄₁	#388	1	4	yes	—
216	C₄×C₄₁	C₂×#117	1	1	yes	characteristic
217	C₄×C₄₁	C₂×C₄×D₄	1	1	yes	characteristic
218	C₄×C₄₁	C₂×#123	1	1	yes	characteristic
219	C₄×C₄₁	C₂×#126	1	1	yes	characteristic
220	C₂×#418	C₂×C₄₁	1	1	yes	characteristic
221	C₂²×#102	C₂×C₄₁	1	1	yes	characteristic
222	C₂×#405	C₂×C₄₁	1	1	yes	characteristic, complemented
223	#2316	C₂×C₄₁	1	1	yes	characteristic, complemented
224	#2309	C₂×C₄₁	1	1	yes	characteristic
225	#1936	C₂×C₄₁	1	4	yes	complemented
226	#1934	C₂×C₄₁	1	4	yes	complemented
227	#1736	C₂×C₄₁	1	1	yes	characteristic, complemented
228	#1735	C₂×C₄₁	1	1	yes	characteristic, complemented
229	C₂×C₄₁	—	2	4	no	—
230	C₂×C₄₁	—	8	4	no	—
231	C₂×C₄₁	C₂×#388	1	1	yes	characteristic
232	C₂×C₄₁	#2948	1	1	yes	characteristic
233	C₂×C₄₁	#2949	1	1	yes	characteristic
234	C₂×C₄₁	#3062	1	2	yes	—
235	C₂×C₄₁	#3136	1	2	yes	—
236	C₂³×D₄	C₂²×C₄₁	1	1	yes	characteristic
237	C₂²×M₁₆	C₂²×C₄₁	1	1	yes	characteristic
238	C₂³×C₈	C₂²×C₄₁	1	1	yes	characteristic
239	C₂×#117	C₂²×C₄₁	1	1	yes	characteristic
240	C₂×#117	C₂²×C₄₁	1	1	yes	characteristic
241	C₂×#117	C₂²×C₄₁	1	1	yes	characteristic
242	C₂²×C₄⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
243	#418	—	2	4	no	—
244	C₂×#102	C₄×C₄₁	1	8	yes	complemented
245	C₂×#102	C₂²×C₄₁	1	4	yes	—
246	C₂×#102	C₂²×C₄₁	1	2	yes	—
247	C₂×#102	C₂²×C₄₁	1	2	yes	—
248	#405	—	2	4	no	—
249	C₂×#97	C₂²×C₄₁	1	2	yes	complemented
250	C₂×C₄×C₈	C₂²×C₄₁	1	2	yes	complemented
251	#390	—	2	2	no	—
252	#390	C₂²×C₄₁	1	4	yes	—
253	#389	—	2	2	no	—
254	#389	C₂²×C₄₁	1	4	yes	complemented
255	#380	—	2	2	no	—
256	#379	—	2	2	no	—
257	#340	C₂²×C₄₁	1	2	yes	complemented
258	#340	C₂²×C₄₁	1	4	yes	complemented
259	#340	C₂²×C₄₁	1	2	yes	complemented
260	C₄₁	#21089	1	1	yes	characteristic, direct product factor, Sylow
261	C₂⁵	—	2	1	no	—
262	C₂²×D₄	—	2	2	no	—
263	C₂²×D₄	—	2	1	no	—
264	C₂²×D₄	—	2	2	no	—
265	C₂²×D₄	—	2	2	no	—
266	C₂²×D₄	—	2	2	no	—
267	C₂²×D₄	—	2	2	no	—
268	C₂²×D₄	C₂×C₄×C₄₁	1	4	yes	—
269	C₂²×D₄	C₂³×C₄₁	1	2	yes	—
270	C₂³×C₄	—	2	1	no	—
271	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
272	C₂×M₁₆	—	2	2	no	—
273	C₂×M₁₆	—	2	2	no	—
274	C₂×M₁₆	D₄×C₄₁	1	4	yes	—
275	C₂²×C₈	—	2	2	no	—
276	C₂²×C₈	—	2	2	no	—
277	C₂²×C₈	C₂×C₄×C₄₁	1	4	yes	—
278	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
279	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
280	C₂²×C₈	C₂³×C₄₁	1	2	yes	—
281	#117	—	2	2	no	—
282	#117	—	2	2	no	—
283	#117	—	2	2	no	—
284	#117	—	2	2	no	—
285	#117	—	2	2	no	—
286	#117	—	2	2	no	—
287	C₂×C₄⋊C₄	—	2	1	no	—
288	C₂×C₄⋊C₄	—	2	2	no	—
289	C₂×C₄⋊C₄	—	2	4	no	—
290	C₂×C₄⋊C₄	C₂×C₄×C₄₁	1	4	yes	—
291	C₂×C₄⋊C₄	D₄×C₄₁	1	2	yes	—
292	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
293	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
294	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
295	C₂×C₂²⋊C₄	—	2	1	no	—
296	C₂×C₂²⋊C₄	—	2	1	no	—
297	C₂×C₂²⋊C₄	—	2	4	no	—
298	C₂×C₂²⋊C₄	—	2	4	no	—
299	C₂×C₂²⋊C₄	D₄×C₄₁	1	2	yes	—
300	C₂×C₄²	—	2	1	no	—
301	C₂×C₄²	—	2	1	no	—
302	C₂×C₄²	C₂³×C₄₁	1	2	yes	—
303	#102	—	2	8	no	—
304	#102	C₂×C₄×C₄₁	1	8	yes	—
305	#102	C₂×C₄×C₄₁	1	8	yes	—
306	#97	—	2	4	no	—
307	C₄×C₈	—	2	4	no	—
308	#95	—	2	4	no	—
309	C₂⁴	—	2	2	no	—
310	C₂⁴	—	2	4	no	—
311	C₂⁴	—	4	2	no	—
312	C₂⁴	—	4	2	no	—
313	C₂⁴	—	8	2	no	—
314	C₂⁴	—	8	2	no	—
315	C₂⁴	C₂×D₄×C₄₁	1	1	yes	characteristic
316	C₂×D₄	—	2	8	no	—
317	C₂×D₄	—	2	8	no	—
318	C₂×D₄	—	2	4	no	—
319	C₂×D₄	—	2	2	no	—
320	C₂×D₄	—	2	2	no	—
321	C₂×D₄	—	2	2	no	—
322	C₂×D₄	—	2	2	no	—
323	C₂×D₄	—	2	2	no	—
324	C₂×D₄	—	4	2	no	—
325	C₂×D₄	—	4	4	no	—
326	C₂×D₄	—	4	2	no	—
327	C₂×D₄	—	4	4	no	—
328	C₂×D₄	C₂²×C₄×C₄₁	1	4	yes	—
329	C₂²×C₄	—	2	2	no	—
330	C₂²×C₄	—	2	4	no	—
331	C₂²×C₄	—	2	2	no	—
332	C₂²×C₄	—	2	2	no	—
333	C₂²×C₄	—	8	2	no	—
334	C₂²×C₄	C₂²×C₄×C₄₁	1	2	yes	—
335	C₂²×C₄	C₂×D₄×C₄₁	1	4	yes	—
336	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
337	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
338	C₂²×C₄	#41×C₄₁	1	2	yes	—
339	C₂²×C₄	#41×C₄₁	1	2	yes	—
340	C₂²×C₄	#41×C₄₁	1	2	yes	—
341	C₂²×C₄	#41×C₄₁	1	2	yes	—
342	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
343	M₁₆	—	2	8	no	—
344	C₂×C₈	—	2	8	no	—
345	C₂×C₈	—	2	1	no	—
346	C₂×C₈	—	2	1	no	—
347	C₂×C₈	—	2	1	no	—
348	C₂×C₈	—	2	1	no	—
349	C₂×C₈	—	2	2	no	—
350	C₂×C₈	—	2	2	no	—
351	C₂×C₈	C₂²×C₄×C₄₁	1	2	yes	—
352	C₂×C₈	C₂²×C₄×C₄₁	1	2	yes	—
353	C₂×C₈	C₂×D₄×C₄₁	1	4	yes	—
354	C₄⋊C₄	—	2	4	no	—
355	C₄⋊C₄	—	2	4	no	—
356	C₄⋊C₄	—	2	2	no	—
357	C₄⋊C₄	—	2	2	no	—
358	C₄⋊C₄	—	2	2	no	—
359	C₄⋊C₄	—	2	2	no	—
360	C₄⋊C₄	—	2	2	no	—
361	C₄⋊C₄	—	8	4	no	—
362	C₄⋊C₄	C₂²×C₄×C₄₁	1	4	yes	—
363	C₂²⋊C₄	—	2	4	no	—
364	C₂²⋊C₄	—	4	2	no	—
365	C₂²⋊C₄	—	4	2	no	—
366	C₂²⋊C₄	—	8	4	no	—
367	C₂²⋊C₄	—	8	4	no	—
368	C₄²	—	2	2	no	—
369	C₄²	—	2	2	no	—
370	C₄²	—	4	2	no	—
371	C₄²	—	4	2	no	—
372	C₂³	—	2	2	no	—
373	C₂³	—	2	2	no	—
374	C₂³	—	2	4	no	—
375	C₂³	—	4	2	no	—
376	C₂³	—	4	2	no	—
377	C₂³	—	4	4	no	—
378	C₂³	—	4	4	no	—
379	C₂³	—	4	8	no	—
380	C₂³	—	8	4	no	—
381	C₂³	—	8	4	no	—
382	C₂³	—	8	8	no	—
383	C₂³	—	8	8	no	—
384	C₂³	C₄×D₄×C₄₁	1	2	yes	—
385	C₂³	#121×C₄₁	1	2	yes	—
386	C₂³	#124×C₄₁	1	2	yes	—
387	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
388	D₄	—	2	4	no	—
389	D₄	—	2	4	no	—
390	D₄	—	4	2	no	—
391	D₄	—	4	2	no	—
392	D₄	—	4	8	no	—
393	C₂×C₄	—	2	4	no	—
394	C₂×C₄	—	2	4	no	—
395	C₂×C₄	—	2	4	no	—
396	C₂×C₄	—	2	4	no	—
397	C₂×C₄	—	4	4	no	—
398	C₂×C₄	—	4	2	no	—
399	C₂×C₄	—	4	2	no	—
400	C₂×C₄	—	4	2	no	—
401	C₂×C₄	—	4	2	no	—
402	C₂×C₄	—	4	2	no	—
403	C₂×C₄	—	4	2	no	—
404	C₂×C₄	—	8	4	no	—
405	C₂×C₄	#117×C₄₁	1	4	yes	—
406	C₂×C₄	C₄×D₄×C₄₁	1	4	yes	—
407	C₂×C₄	C₄×D₄×C₄₁	1	2	yes	—
408	C₂×C₄	#121×C₄₁	1	2	yes	—
409	C₂×C₄	#123×C₄₁	1	4	yes	—
410	C₂×C₄	#124×C₄₁	1	2	yes	—
411	C₂×C₄	#126×C₄₁	1	4	yes	—
412	C₂×C₄	C₂³×C₄×C₄₁	1	1	yes	characteristic
413	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
414	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
415	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
416	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
417	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
418	C₈	—	2	2	no	—
419	C₈	—	2	2	no	—
420	C₈	—	2	4	no	—
421	C₂²	—	2	4	no	—
422	C₂²	—	2	4	no	—
423	C₂²	—	2	2	no	—
424	C₂²	—	2	2	no	—
425	C₂²	—	4	4	no	—
426	C₂²	—	4	4	no	—
427	C₂²	—	4	4	no	—
428	C₂²	—	8	16	no	—
429	C₂²	—	8	4	no	—
430	C₂²	—	8	4	no	—
431	C₂²	C₄₁×#388	1	4	yes	—
432	C₂²	C₂×C₄×D₄×C₄₁	1	1	yes	characteristic
433	C₂²	C₂×#121×C₄₁	1	1	yes	characteristic
434	C₂²	C₂×#124×C₄₁	1	1	yes	characteristic
435	C₂²	C₄₁×#576	1	2	yes	—
436	C₂²	C₄₁×#577	1	2	yes	—
437	C₄	—	4	4	no	—
438	C₄	—	4	4	no	—
439	C₄	—	8	2	no	—
440	C₄	—	8	2	no	—
441	C₄	C₄₁×#388	1	4	yes	—
442	C₄	C₂×#117×C₄₁	1	1	yes	characteristic
443	C₄	C₂×C₄×D₄×C₄₁	1	1	yes	characteristic
444	C₄	C₂×#123×C₄₁	1	1	yes	characteristic
445	C₄	C₂×#126×C₄₁	1	1	yes	characteristic
446	C₂	—	2	4	no	—
447	C₂	—	8	4	no	—
448	C₂	C₂×C₄₁×#388	1	1	yes	characteristic
449	C₂	C₄₁×#2948	1	1	yes	characteristic
450	C₂	C₄₁×#2949	1	1	yes	characteristic
451	C₂	C₄₁×#3062	1	2	yes	—
452	C₂	C₄₁×#3136	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₄₁	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₄₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₁
prime radical	C₂³×D₄×C₄₁	C₂²
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. C₂×C₄₁×#405	C₂	semidirect
4. C₄₁×#2316	C₂	semidirect
6. C₄₁×#1936	C₂	semidirect
7. C₄₁×#1934	C₂	semidirect
8. C₄₁×#1736	C₂	semidirect
9. C₄₁×#1735	C₂	semidirect
18. C₂×#102×C₄₁	C₄	semidirect
23. C₂×#97×C₄₁	C₂²	semidirect
24. C₂×C₄×C₈×C₄₁	C₂²	semidirect
28. C₄₁×#389	C₂²	semidirect
31. C₄₁×#340	C₂²	semidirect
32. C₄₁×#340	C₂²	semidirect
33. C₄₁×#340	C₂²	semidirect
194. #21089	C₄₁	direct (N × H)
222. C₂×#405	C₂×C₄₁	semidirect
223. #2316	C₂×C₄₁	semidirect
225. #1936	C₂×C₄₁	semidirect
226. #1934	C₂×C₄₁	semidirect
227. #1736	C₂×C₄₁	semidirect
228. #1735	C₂×C₄₁	semidirect
244. C₂×#102	C₄×C₄₁	semidirect
249. C₂×#97	C₂²×C₄₁	semidirect
250. C₂×C₄×C₈	C₂²×C₄₁	semidirect
254. #389	C₂²×C₄₁	semidirect
257. #340	C₂²×C₄₁	semidirect
258. #340	C₂²×C₄₁	semidirect
259. #340	C₂²×C₄₁	semidirect
260. C₄₁	#21089	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×#418	2
C₂²×#102×C₄₁	2
C₂×C₄₁×#405	2
C₄₁×#2316	2
C₄₁×#2309	2
C₄₁×#1936	2
C₄₁×#1934	2
C₄₁×#1736	2
C₄₁×#1735	2
#21089	41

Subgroups — C41×#21089 #23797290

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#21089 #23797290