Subgroups — C₄₁×#25450 #23801651

Order 10496.

778 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₁×#500	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄₁×#476	C₂	1	1	yes	maximal, characteristic
3	C₄₁×#2563	C₂	1	1	yes	maximal, characteristic
4	C₄₁×#2369	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₁×#2085	C₂	1	2	yes	maximal, complemented
6	C₄₁×#2067	C₂	1	2	yes	maximal
7	C₄₁×#1987	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄₁×#1949	C₂	1	2	yes	maximal, complemented
9	C₄₁×#1939	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄₁×#1925	C₂	1	2	yes	maximal
11	C₄×#102×C₄₁	C₂	1	1	yes	maximal, characteristic
12	C₂×C₄⋊Q₈×C₄₁	C₂²	1	1	yes	characteristic
13	C₂×C₄⋊Q₈×C₄₁	C₂²	1	1	yes	characteristic
14	C₂×C₄×D₄×C₄₁	C₂²	1	1	yes	characteristic
15	C₄₁×#500	—	2	4	no	—
16	C₄₁×#476	—	2	4	no	—
17	C₂×#107×C₄₁	C₂²	1	2	yes	—
18	C₂×#107×C₄₁	C₂²	1	2	yes	—
19	C₂×#106×C₄₁	C₂²	1	2	yes	—
20	C₂×C₄⋊C₈×C₄₁	C₂²	1	1	yes	characteristic
21	C₂×C₄⋊C₈×C₄₁	C₂²	1	2	yes	—
22	C₂×#102×C₄₁	C₂²	1	1	yes	characteristic
23	C₂×#102×C₄₁	C₂²	1	2	yes	—
24	C₂×#102×C₄₁	C₂²	1	1	yes	characteristic
25	C₂×C₄×C₈×C₄₁	C₂²	1	1	yes	characteristic
26	C₄₁×#393	—	2	2	no	—
27	C₄₁×#391	—	2	2	no	—
28	C₄₁×#390	C₂²	1	2	yes	—
29	C₄₁×#389	—	2	1	no	—
30	C₄₁×#389	C₂²	1	2	yes	—
31	C₄₁×#382	C₂²	1	2	yes	—
32	C₄₁×#380	—	2	1	no	—
33	C₄₁×#380	—	2	1	no	—
34	C₄×C₄⋊C₄×C₄₁	—	2	1	no	—
35	C₄×C₄⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
36	C₄×C₄⋊C₄×C₄₁	C₂²	1	2	yes	—
37	C₄×C₄⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
38	C₄₁×#340	C₂²	1	1	yes	characteristic
39	C₄₁×#340	C₂²	1	1	yes	characteristic
40	C₄₁×#340	C₂²	1	2	yes	—
41	C₄₁×#340	C₂²	1	2	yes	—
42	C₄₁×#336	C₂²	1	2	yes	—
43	C₂²×Q₈×C₄₁	—	2	1	no	—
44	C₂²×Q₈×C₄₁	—	2	1	no	—
45	C₂²×D₄×C₄₁	C₂³	1	1	yes	characteristic
46	C₂³×C₄×C₄₁	—	2	1	no	—
47	C₂²×C₈×C₄₁	C₂³	1	2	yes	—
48	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
49	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
50	C₄⋊Q₈×C₄₁	—	2	2	no	—
51	C₄⋊Q₈×C₄₁	—	2	2	no	—
52	C₄⋊Q₈×C₄₁	—	2	2	no	—
53	C₄⋊Q₈×C₄₁	D₄	1	4	yes	—
54	C₄×D₄×C₄₁	—	2	2	no	—
55	C₄×D₄×C₄₁	—	2	2	no	—
56	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
57	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
58	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
59	C₂×C₄⋊C₄×C₄₁	D₄	1	1	yes	characteristic
60	C₂×C₄⋊C₄×C₄₁	D₄	1	1	yes	characteristic
61	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
62	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
63	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
64	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
65	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
66	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
67	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
68	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
69	C₂×C₄²×C₄₁	—	2	1	no	—
70	C₂×C₄²×C₄₁	—	2	2	no	—
71	C₂×C₄²×C₄₁	C₂³	1	2	yes	—
72	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
73	#107×C₄₁	—	2	4	no	—
74	#107×C₄₁	—	2	4	no	—
75	#106×C₄₁	—	2	4	no	—
76	C₄⋊C₈×C₄₁	—	2	4	no	—
77	C₄⋊C₈×C₄₁	—	2	2	no	—
78	#102×C₄₁	—	2	2	no	—
79	#102×C₄₁	—	2	4	no	—
80	#102×C₄₁	Q₈	1	4	yes	complemented
81	C₄×C₈×C₄₁	—	2	2	no	—
82	#95×C₄₁	—	2	2	no	—
83	#95×C₄₁	—	2	2	no	—
84	#95×C₄₁	—	2	1	no	—
85	#95×C₄₁	—	2	2	no	—
86	#95×C₄₁	—	2	2	no	—
87	#95×C₄₁	D₄	1	2	yes	—
88	C₂⁴×C₄₁	—	2	1	no	—
89	C₂×Q₈×C₄₁	—	2	4	no	—
90	C₂×Q₈×C₄₁	—	4	2	no	—
91	C₂×Q₈×C₄₁	—	8	1	no	—
92	C₂×Q₈×C₄₁	—	8	1	no	—
93	C₂×Q₈×C₄₁	—	8	1	no	—
94	C₂×Q₈×C₄₁	—	8	1	no	—
95	C₂×D₄×C₄₁	—	2	1	no	—
96	C₂×D₄×C₄₁	—	2	1	no	—
97	C₂×D₄×C₄₁	—	2	1	no	—
98	C₂×D₄×C₄₁	—	2	1	no	—
99	C₂×D₄×C₄₁	—	2	1	no	—
100	C₂×D₄×C₄₁	C₂×Q₈	1	2	yes	—
101	C₂²×C₄×C₄₁	—	2	1	no	—
102	C₂²×C₄×C₄₁	—	2	2	no	—
103	C₂²×C₄×C₄₁	—	2	1	no	—
104	C₂²×C₄×C₄₁	—	2	1	no	—
105	C₂²×C₄×C₄₁	—	2	2	no	—
106	C₂²×C₄×C₄₁	—	4	2	no	—
107	C₂²×C₄×C₄₁	—	4	2	no	—
108	C₂²×C₄×C₄₁	—	4	2	no	—
109	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
110	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
111	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
112	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
113	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
114	C₂×C₈×C₄₁	—	2	1	no	—
115	C₂×C₈×C₄₁	—	2	1	no	—
116	C₂×C₈×C₄₁	—	2	1	no	—
117	C₂×C₈×C₄₁	—	2	1	no	—
118	C₂×C₈×C₄₁	—	2	2	no	—
119	C₂×C₈×C₄₁	—	2	2	no	—
120	C₂×C₈×C₄₁	—	2	2	no	—
121	C₂×C₈×C₄₁	C₂×Q₈	1	2	yes	—
122	C₂×C₈×C₄₁	#41	1	2	yes	—
123	C₄⋊C₄×C₄₁	—	2	4	no	—
124	C₄⋊C₄×C₄₁	—	2	2	no	—
125	C₄⋊C₄×C₄₁	—	2	2	no	—
126	C₄⋊C₄×C₄₁	—	2	2	no	—
127	C₄⋊C₄×C₄₁	—	2	1	no	—
128	C₄⋊C₄×C₄₁	—	2	1	no	—
129	C₄⋊C₄×C₄₁	—	2	2	no	—
130	C₄⋊C₄×C₄₁	—	2	1	no	—
131	C₄⋊C₄×C₄₁	—	2	1	no	—
132	C₄⋊C₄×C₄₁	—	2	2	no	—
133	C₄⋊C₄×C₄₁	—	2	1	no	—
134	C₄⋊C₄×C₄₁	—	4	2	no	—
135	C₄⋊C₄×C₄₁	—	8	2	no	—
136	C₄⋊C₄×C₄₁	C₂×D₄	1	4	yes	—
137	C₄⋊C₄×C₄₁	C₂×Q₈	1	2	yes	—
138	C₂²⋊C₄×C₄₁	—	4	2	no	—
139	C₂²⋊C₄×C₄₁	—	8	2	no	—
140	C₂²⋊C₄×C₄₁	—	8	2	no	—
141	C₄²×C₄₁	—	2	2	no	—
142	C₄²×C₄₁	—	2	2	no	—
143	C₄²×C₄₁	—	4	2	no	—
144	C₄²×C₄₁	—	8	2	no	—
145	C₄²×C₄₁	C₂×D₄	1	2	yes	—
146	C₄²×C₄₁	#41	1	2	yes	—
147	C₂³×C₄₁	—	2	2	no	—
148	C₂³×C₄₁	—	4	1	no	—
149	C₂³×C₄₁	—	4	1	no	—
150	C₂³×C₄₁	—	4	1	no	—
151	C₂³×C₄₁	—	4	1	no	—
152	C₂³×C₄₁	—	4	1	no	—
153	C₂³×C₄₁	—	4	1	no	—
154	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
155	Q₈×C₄₁	—	8	4	no	—
156	Q₈×C₄₁	—	8	4	no	—
157	D₄×C₄₁	—	2	2	no	—
158	D₄×C₄₁	—	2	2	no	—
159	D₄×C₄₁	—	4	1	no	—
160	D₄×C₄₁	—	4	1	no	—
161	C₂×C₄×C₄₁	—	2	1	no	—
162	C₂×C₄×C₄₁	—	2	1	no	—
163	C₂×C₄×C₄₁	—	2	4	no	—
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	2	no	—
171	C₂×C₄×C₄₁	—	4	1	no	—
172	C₂×C₄×C₄₁	—	4	1	no	—
173	C₂×C₄×C₄₁	—	4	2	no	—
174	C₂×C₄×C₄₁	—	4	2	no	—
175	C₂×C₄×C₄₁	—	4	1	no	—
176	C₂×C₄×C₄₁	—	4	2	no	—
177	C₂×C₄×C₄₁	—	4	1	no	—
178	C₂×C₄×C₄₁	—	4	1	no	—
179	C₂×C₄×C₄₁	—	4	1	no	—
180	C₂×C₄×C₄₁	—	4	1	no	—
181	C₂×C₄×C₄₁	—	4	2	no	—
182	C₂×C₄×C₄₁	—	4	2	no	—
183	C₂×C₄×C₄₁	—	4	1	no	—
184	C₂×C₄×C₄₁	—	8	4	no	—
185	C₂×C₄×C₄₁	#121	1	2	yes	—
186	C₂×C₄×C₄₁	#121	1	2	yes	—
187	C₂×C₄×C₄₁	#135	1	2	yes	—
188	C₂×C₄×C₄₁	#137	1	2	yes	—
189	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
190	C₂×C₄×C₄₁	C₂²×Q₈	1	1	yes	characteristic
191	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
192	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
193	C₂×C₄×C₄₁	2₋¹⁺⁴	1	1	yes	characteristic
194	C₂×C₄×C₄₁	2₋¹⁺⁴	1	1	yes	characteristic
195	C₈×C₄₁	—	2	2	no	—
196	C₈×C₄₁	—	2	2	no	—
197	C₈×C₄₁	—	4	2	no	—
198	#25450	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
199	C₂²×C₄₁	—	4	2	no	—
200	C₂²×C₄₁	—	4	2	no	—
201	C₂²×C₄₁	—	4	2	no	—
202	C₂²×C₄₁	—	8	1	no	—
203	C₂²×C₄₁	—	8	1	no	—
204	C₂²×C₄₁	—	8	1	no	—
205	C₂²×C₄₁	—	8	1	no	—
206	C₂²×C₄₁	C₂×#121	1	1	yes	characteristic
207	C₂²×C₄₁	#547	1	1	yes	characteristic
208	C₂²×C₄₁	D₄×Q₈	1	1	yes	characteristic
209	C₂²×C₄₁	C₂×#135	1	1	yes	characteristic
210	C₂²×C₄₁	C₂×#137	1	1	yes	characteristic
211	C₂²×C₄₁	#576	1	1	yes	characteristic
212	C₂²×C₄₁	#576	1	1	yes	characteristic
213	C₄×C₄₁	—	2	2	no	—
214	C₄×C₄₁	—	4	2	no	—
215	C₄×C₄₁	—	4	2	no	—
216	C₄×C₄₁	—	4	2	no	—
217	C₄×C₄₁	—	4	4	no	—
218	C₄×C₄₁	—	8	1	no	—
219	C₄×C₄₁	—	8	1	no	—
220	C₄×C₄₁	—	8	2	no	—
221	C₄×C₄₁	#464	1	4	yes	—
222	C₄×C₄₁	#533	1	1	yes	characteristic
223	C₄×C₄₁	#541	1	1	yes	characteristic
224	C₄×C₄₁	#548	1	1	yes	characteristic
225	C₄×C₄₁	D₄×Q₈	1	1	yes	characteristic
226	C₂×#500	C₂×C₄₁	1	1	yes	characteristic, complemented
227	C₂×#476	C₂×C₄₁	1	1	yes	characteristic
228	#2563	C₂×C₄₁	1	1	yes	characteristic
229	#2369	C₂×C₄₁	1	1	yes	characteristic, complemented
230	#2085	C₂×C₄₁	1	2	yes	complemented
231	#2067	C₂×C₄₁	1	2	yes	—
232	#1987	C₂×C₄₁	1	1	yes	characteristic, complemented
233	#1949	C₂×C₄₁	1	2	yes	complemented
234	#1939	C₂×C₄₁	1	1	yes	characteristic, complemented
235	#1925	C₂×C₄₁	1	2	yes	—
236	C₄×#102	C₂×C₄₁	1	1	yes	characteristic
237	C₂×C₄₁	—	8	2	no	—
238	C₂×C₄₁	#2429	1	1	yes	characteristic
239	C₂×C₄₁	C₂×#464	1	1	yes	characteristic
240	C₂×C₄₁	#3041	1	1	yes	characteristic
241	C₂×C₄₁	#3341	1	1	yes	characteristic
242	C₂×C₄₁	#3357	1	1	yes	characteristic
243	C₂×C₄₁	#3380	1	1	yes	characteristic
244	C₂×C₄₁	#3385	1	1	yes	characteristic
245	C₂×C₄⋊Q₈	C₂²×C₄₁	1	1	yes	characteristic
246	C₂×C₄⋊Q₈	C₂²×C₄₁	1	1	yes	characteristic
247	C₂×C₄×D₄	C₂²×C₄₁	1	1	yes	characteristic
248	#500	—	2	4	no	—
249	#476	—	2	4	no	—
250	C₂×#107	C₂²×C₄₁	1	2	yes	—
251	C₂×#107	C₂²×C₄₁	1	2	yes	—
252	C₂×#106	C₂²×C₄₁	1	2	yes	—
253	C₂×C₄⋊C₈	C₂²×C₄₁	1	2	yes	—
254	C₂×C₄⋊C₈	C₂²×C₄₁	1	1	yes	characteristic
255	C₂×#102	C₂²×C₄₁	1	1	yes	characteristic
256	C₂×#102	C₂²×C₄₁	1	2	yes	—
257	C₂×#102	C₂²×C₄₁	1	1	yes	characteristic
258	C₂×C₄×C₈	C₂²×C₄₁	1	1	yes	characteristic
259	#393	—	2	2	no	—
260	#391	—	2	2	no	—
261	#390	C₂²×C₄₁	1	2	yes	—
262	#389	—	2	1	no	—
263	#389	C₂²×C₄₁	1	2	yes	—
264	#382	C₂²×C₄₁	1	2	yes	—
265	#380	—	2	1	no	—
266	#380	—	2	1	no	—
267	C₄×C₄⋊C₄	—	2	1	no	—
268	C₄×C₄⋊C₄	C₂²×C₄₁	1	2	yes	—
269	C₄×C₄⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
270	C₄×C₄⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
271	#340	C₂²×C₄₁	1	2	yes	—
272	#340	C₂²×C₄₁	1	1	yes	characteristic
273	#340	C₂²×C₄₁	1	2	yes	—
274	#340	C₂²×C₄₁	1	1	yes	characteristic
275	#336	C₂²×C₄₁	1	2	yes	—
276	C₄₁	#25450	1	1	yes	characteristic, direct product factor, Sylow
277	C₂²×Q₈	—	2	1	no	—
278	C₂²×Q₈	—	2	1	no	—
279	C₂²×D₄	C₂³×C₄₁	1	1	yes	characteristic
280	C₂³×C₄	—	2	1	no	—
281	C₂²×C₈	C₂³×C₄₁	1	2	yes	—
282	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
283	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
284	C₄⋊Q₈	—	2	2	no	—
285	C₄⋊Q₈	—	2	2	no	—
286	C₄⋊Q₈	—	2	2	no	—
287	C₄⋊Q₈	D₄×C₄₁	1	4	yes	—
288	C₄×D₄	—	2	2	no	—
289	C₄×D₄	—	2	2	no	—
290	C₂×C₄⋊C₄	—	2	1	no	—
291	C₂×C₄⋊C₄	—	2	1	no	—
292	C₂×C₄⋊C₄	—	2	2	no	—
293	C₂×C₄⋊C₄	D₄×C₄₁	1	1	yes	characteristic
294	C₂×C₄⋊C₄	D₄×C₄₁	1	1	yes	characteristic
295	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
296	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
297	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
298	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
299	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
300	C₂×C₂²⋊C₄	—	2	1	no	—
301	C₂×C₂²⋊C₄	—	2	2	no	—
302	C₂×C₂²⋊C₄	—	2	2	no	—
303	C₂×C₄²	—	2	1	no	—
304	C₂×C₄²	—	2	2	no	—
305	C₂×C₄²	C₂³×C₄₁	1	2	yes	—
306	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
307	#107	—	2	4	no	—
308	#107	—	2	4	no	—
309	#106	—	2	4	no	—
310	C₄⋊C₈	—	2	4	no	—
311	C₄⋊C₈	—	2	2	no	—
312	#102	—	2	2	no	—
313	#102	—	2	4	no	—
314	#102	Q₈×C₄₁	1	4	yes	complemented
315	C₄×C₈	—	2	2	no	—
316	#95	—	2	2	no	—
317	#95	—	2	2	no	—
318	#95	—	2	1	no	—
319	#95	—	2	2	no	—
320	#95	—	2	2	no	—
321	#95	D₄×C₄₁	1	2	yes	—
322	C₂⁴	—	2	1	no	—
323	C₂×Q₈	—	2	4	no	—
324	C₂×Q₈	—	4	2	no	—
325	C₂×Q₈	—	8	1	no	—
326	C₂×Q₈	—	8	1	no	—
327	C₂×Q₈	—	8	1	no	—
328	C₂×Q₈	—	8	1	no	—
329	C₂×D₄	—	2	1	no	—
330	C₂×D₄	—	2	1	no	—
331	C₂×D₄	—	2	1	no	—
332	C₂×D₄	—	2	1	no	—
333	C₂×D₄	—	2	1	no	—
334	C₂×D₄	C₂×Q₈×C₄₁	1	2	yes	—
335	C₂²×C₄	—	2	1	no	—
336	C₂²×C₄	—	2	2	no	—
337	C₂²×C₄	—	2	1	no	—
338	C₂²×C₄	—	2	1	no	—
339	C₂²×C₄	—	2	2	no	—
340	C₂²×C₄	—	4	2	no	—
341	C₂²×C₄	—	4	2	no	—
342	C₂²×C₄	—	4	2	no	—
343	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
344	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
345	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
346	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
347	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
348	C₂×C₈	—	2	1	no	—
349	C₂×C₈	—	2	1	no	—
350	C₂×C₈	—	2	1	no	—
351	C₂×C₈	—	2	1	no	—
352	C₂×C₈	—	2	2	no	—
353	C₂×C₈	—	2	2	no	—
354	C₂×C₈	—	2	2	no	—
355	C₂×C₈	C₂×Q₈×C₄₁	1	2	yes	—
356	C₂×C₈	#41×C₄₁	1	2	yes	—
357	C₄⋊C₄	—	2	4	no	—
358	C₄⋊C₄	—	2	2	no	—
359	C₄⋊C₄	—	2	2	no	—
360	C₄⋊C₄	—	2	2	no	—
361	C₄⋊C₄	—	2	1	no	—
362	C₄⋊C₄	—	2	1	no	—
363	C₄⋊C₄	—	2	2	no	—
364	C₄⋊C₄	—	2	1	no	—
365	C₄⋊C₄	—	2	1	no	—
366	C₄⋊C₄	—	2	2	no	—
367	C₄⋊C₄	—	2	1	no	—
368	C₄⋊C₄	—	4	2	no	—
369	C₄⋊C₄	—	8	2	no	—
370	C₄⋊C₄	C₂×D₄×C₄₁	1	4	yes	—
371	C₄⋊C₄	C₂×Q₈×C₄₁	1	2	yes	—
372	C₂²⋊C₄	—	4	2	no	—
373	C₂²⋊C₄	—	8	2	no	—
374	C₂²⋊C₄	—	8	2	no	—
375	C₄²	—	2	2	no	—
376	C₄²	—	2	2	no	—
377	C₄²	—	4	2	no	—
378	C₄²	—	8	2	no	—
379	C₄²	C₂×D₄×C₄₁	1	2	yes	—
380	C₄²	#41×C₄₁	1	2	yes	—
381	C₂³	—	2	2	no	—
382	C₂³	—	4	1	no	—
383	C₂³	—	4	1	no	—
384	C₂³	—	4	1	no	—
385	C₂³	—	4	1	no	—
386	C₂³	—	4	1	no	—
387	C₂³	—	4	1	no	—
388	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
389	Q₈	—	8	4	no	—
390	Q₈	—	8	4	no	—
391	D₄	—	2	2	no	—
392	D₄	—	2	2	no	—
393	D₄	—	4	1	no	—
394	D₄	—	4	1	no	—
395	C₂×C₄	—	2	1	no	—
396	C₂×C₄	—	2	1	no	—
397	C₂×C₄	—	2	4	no	—
398	C₂×C₄	—	2	2	no	—
399	C₂×C₄	—	2	2	no	—
400	C₂×C₄	—	2	2	no	—
401	C₂×C₄	—	2	2	no	—
402	C₂×C₄	—	2	2	no	—
403	C₂×C₄	—	2	2	no	—
404	C₂×C₄	—	2	2	no	—
405	C₂×C₄	—	4	1	no	—
406	C₂×C₄	—	4	1	no	—
407	C₂×C₄	—	4	2	no	—
408	C₂×C₄	—	4	2	no	—
409	C₂×C₄	—	4	1	no	—
410	C₂×C₄	—	4	2	no	—
411	C₂×C₄	—	4	1	no	—
412	C₂×C₄	—	4	1	no	—
413	C₂×C₄	—	4	1	no	—
414	C₂×C₄	—	4	1	no	—
415	C₂×C₄	—	4	2	no	—
416	C₂×C₄	—	4	2	no	—
417	C₂×C₄	—	4	1	no	—
418	C₂×C₄	—	8	4	no	—
419	C₂×C₄	#121×C₄₁	1	2	yes	—
420	C₂×C₄	#121×C₄₁	1	2	yes	—
421	C₂×C₄	#135×C₄₁	1	2	yes	—
422	C₂×C₄	#137×C₄₁	1	2	yes	—
423	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
424	C₂×C₄	C₂²×Q₈×C₄₁	1	1	yes	characteristic
425	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
426	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
427	C₂×C₄	2₋¹⁺⁴×C₄₁	1	1	yes	characteristic
428	C₂×C₄	2₋¹⁺⁴×C₄₁	1	1	yes	characteristic
429	C₈	—	2	2	no	—
430	C₈	—	2	2	no	—
431	C₈	—	4	2	no	—
432	C₂²	—	4	2	no	—
433	C₂²	—	4	2	no	—
434	C₂²	—	4	2	no	—
435	C₂²	—	8	1	no	—
436	C₂²	—	8	1	no	—
437	C₂²	—	8	1	no	—
438	C₂²	—	8	1	no	—
439	C₂²	C₂×#121×C₄₁	1	1	yes	characteristic
440	C₂²	C₄₁×#547	1	1	yes	characteristic
441	C₂²	D₄×Q₈×C₄₁	1	1	yes	characteristic
442	C₂²	C₂×#135×C₄₁	1	1	yes	characteristic
443	C₂²	C₂×#137×C₄₁	1	1	yes	characteristic
444	C₂²	C₄₁×#576	1	1	yes	characteristic
445	C₂²	C₄₁×#576	1	1	yes	characteristic
446	C₄	—	2	2	no	—
447	C₄	—	4	4	no	—
448	C₄	—	4	2	no	—
449	C₄	—	4	2	no	—
450	C₄	—	4	2	no	—
451	C₄	—	8	2	no	—
452	C₄	—	8	1	no	—
453	C₄	—	8	1	no	—
454	C₄	C₄₁×#464	1	4	yes	—
455	C₄	C₄₁×#533	1	1	yes	characteristic
456	C₄	C₄₁×#541	1	1	yes	characteristic
457	C₄	C₄₁×#548	1	1	yes	characteristic
458	C₄	D₄×Q₈×C₄₁	1	1	yes	characteristic
459	C₂	—	8	2	no	—
460	C₂	C₄₁×#2429	1	1	yes	characteristic
461	C₂	C₂×C₄₁×#464	1	1	yes	characteristic
462	C₂	C₄₁×#3041	1	1	yes	characteristic
463	C₂	C₄₁×#3341	1	1	yes	characteristic
464	C₂	C₄₁×#3357	1	1	yes	characteristic
465	C₂	C₄₁×#3380	1	1	yes	characteristic
466	C₂	C₄₁×#3385	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₂×C₄₁×#500	C₂	semidirect
4. C₄₁×#2369	C₂	semidirect
5. C₄₁×#2085	C₂	semidirect
7. C₄₁×#1987	C₂	semidirect
8. C₄₁×#1949	C₂	semidirect
9. C₄₁×#1939	C₂	semidirect
80. #102×C₄₁	Q₈	semidirect
198. #25450	C₄₁	direct (N × H)
226. C₂×#500	C₂×C₄₁	semidirect
229. #2369	C₂×C₄₁	semidirect
230. #2085	C₂×C₄₁	semidirect
232. #1987	C₂×C₄₁	semidirect
233. #1949	C₂×C₄₁	semidirect
234. #1939	C₂×C₄₁	semidirect
276. C₄₁	#25450	direct (N × H)
314. #102	Q₈×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×#500	2
C₂×C₄₁×#476	2
C₄₁×#2563	2
C₄₁×#2369	2
C₄₁×#2085	2
C₄₁×#2067	2
C₄₁×#1987	2
C₄₁×#1949	2
C₄₁×#1939	2
C₄₁×#1925	2
C₄×#102×C₄₁	2
#25450	41

Subgroups — C41×#25450 #23801651

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#25450 #23801651