Subgroups — C₄₁×#24692 #23800893

Order 10496.

884 conjugacy classes of subgroups.

The subgroup lattice has 480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₁×#476	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄₁×#442	C₂	1	1	yes	maximal, characteristic
3	C₄₁×#2542	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₁×#2357	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₁×#2071	C₂	1	2	yes	maximal, complemented
6	C₄₁×#2054	C₂	1	2	yes	maximal
7	C₄₁×#1993	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄₁×#1948	C₂	1	2	yes	maximal, complemented
9	C₄₁×#1940	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄₁×#1926	C₂	1	2	yes	maximal, complemented
11	C₄₁×#1804	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×D₈×C₄₁	C₂²	1	1	yes	characteristic
13	C₂×C₄⋊Q₈×C₄₁	C₂²	1	1	yes	characteristic
14	C₂×C₂²⋊Q₈×C₄₁	—	2	2	no	—
15	C₂×C₄×D₄×C₄₁	C₂²	1	1	yes	characteristic
16	C₂×C₄×D₄×C₄₁	C₂²	1	1	yes	characteristic
17	C₄₁×#476	—	2	4	no	—
18	C₄₁×#442	—	2	4	no	—
19	C₂×#106×C₄₁	C₂²	1	2	yes	—
20	C₂×#106×C₄₁	C₂²	1	1	yes	characteristic
21	C₂×C₄⋊C₈×C₄₁	C₂²	1	1	yes	characteristic
22	C₂×C₄⋊C₈×C₄₁	C₂²	1	2	yes	—
23	C₂×#102×C₄₁	C₂²	1	2	yes	—
24	C₂×#102×C₄₁	C₂²	1	2	yes	—
25	C₂×#102×C₄₁	C₂²	1	1	yes	characteristic
26	C₂×#102×C₄₁	C₂²	1	1	yes	characteristic
27	C₂×#97×C₄₁	C₂²	1	1	yes	characteristic
28	C₄₁×#399	—	2	1	no	—
29	C₄₁×#399	—	2	1	no	—
30	C₄₁×#390	C₂²	1	2	yes	—
31	C₄₁×#390	C₂²	1	2	yes	—
32	C₄₁×#388	—	2	2	no	—
33	C₄₁×#384	C₂²	1	2	yes	—
34	C₄₁×#382	C₂²	1	1	yes	characteristic
35	C₄₁×#381	—	2	1	no	—
36	C₄×C₄⋊C₄×C₄₁	C₂²	1	2	yes	—
37	C₄×C₄⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
38	C₄×C₂²⋊C₄×C₄₁	—	2	1	no	—
39	C₄₁×#340	C₂²	1	2	yes	—
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×D₄×C₄₁	C₂³	1	1	yes	characteristic
45	C₂²×D₄×C₄₁	C₂³	1	1	yes	characteristic
46	C₂³×C₄×C₄₁	—	2	1	no	—
47	C₂³×C₄×C₄₁	—	2	1	no	—
48	C₂×D₈×C₄₁	—	2	2	no	—
49	C₂×D₈×C₄₁	—	2	2	no	—
50	C₂×D₈×C₄₁	—	2	2	no	—
51	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
52	C₂²×C₈×C₄₁	C₂³	1	2	yes	—
53	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
54	C₄⋊Q₈×C₄₁	—	2	2	no	—
55	C₄⋊Q₈×C₄₁	—	2	2	no	—
56	C₂²⋊Q₈×C₄₁	—	4	8	no	—
57	C₄×D₄×C₄₁	—	2	2	no	—
58	C₄×D₄×C₄₁	—	2	2	no	—
59	C₄×D₄×C₄₁	—	2	2	no	—
60	C₄×D₄×C₄₁	D₄	1	4	yes	—
61	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
62	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
63	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
64	C₂×C₄⋊C₄×C₄₁	D₄	1	2	yes	—
65	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
66	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
67	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
68	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
69	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
70	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
71	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
72	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
73	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
74	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
75	C₂×C₄²×C₄₁	—	2	2	no	—
76	C₂×C₄²×C₄₁	C₂³	1	2	yes	—
77	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
78	#106×C₄₁	—	2	2	no	—
79	#106×C₄₁	—	2	4	no	—
80	C₄⋊C₈×C₄₁	—	2	4	no	—
81	C₄⋊C₈×C₄₁	—	2	2	no	—
82	#102×C₄₁	—	2	2	no	—
83	#102×C₄₁	—	2	4	no	—
84	#102×C₄₁	—	2	4	no	—
85	#102×C₄₁	—	2	2	no	—
86	#97×C₄₁	—	2	2	no	—
87	#95×C₄₁	—	2	1	no	—
88	#95×C₄₁	—	2	2	no	—
89	#95×C₄₁	—	2	1	no	—
90	#95×C₄₁	D₄	1	1	yes	characteristic
91	#95×C₄₁	D₄	1	1	yes	characteristic
92	C₂⁴×C₄₁	—	2	1	no	—
93	C₂⁴×C₄₁	—	2	1	no	—
94	C₂×Q₈×C₄₁	—	4	4	no	—
95	C₂×Q₈×C₄₁	—	4	2	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	—	2	1	no	—
101	C₂×D₄×C₄₁	—	2	1	no	—
102	C₂×D₄×C₄₁	—	2	1	no	—
103	C₂×D₄×C₄₁	—	2	1	no	—
104	C₂×D₄×C₄₁	—	2	1	no	—
105	C₂×D₄×C₄₁	—	2	1	no	—
106	C₂×D₄×C₄₁	C₂×D₄	1	2	yes	—
107	C₂×D₄×C₄₁	#41	1	2	yes	—
108	C₂²×C₄×C₄₁	—	2	1	no	—
109	C₂²×C₄×C₄₁	—	2	4	no	—
110	C₂²×C₄×C₄₁	—	2	2	no	—
111	C₂²×C₄×C₄₁	—	2	2	no	—
112	C₂²×C₄×C₄₁	—	2	1	no	—
113	C₂²×C₄×C₄₁	—	4	4	no	—
114	C₂²×C₄×C₄₁	—	4	2	no	—
115	C₂²×C₄×C₄₁	—	8	2	no	—
116	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
117	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
118	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
119	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
120	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
121	D₈×C₄₁	—	2	8	no	—
122	C₂×C₈×C₄₁	—	2	1	no	—
123	C₂×C₈×C₄₁	—	2	1	no	—
124	C₂×C₈×C₄₁	—	2	1	no	—
125	C₂×C₈×C₄₁	—	2	2	no	—
126	C₂×C₈×C₄₁	—	2	2	no	—
127	C₂×C₈×C₄₁	—	2	2	no	—
128	C₂×C₈×C₄₁	—	2	1	no	—
129	C₂×C₈×C₄₁	—	2	1	no	—
130	C₂×C₈×C₄₁	#41	1	2	yes	—
131	C₄⋊C₄×C₄₁	—	2	4	no	—
132	C₄⋊C₄×C₄₁	—	2	1	no	—
133	C₄⋊C₄×C₄₁	—	2	1	no	—
134	C₄⋊C₄×C₄₁	—	2	2	no	—
135	C₄⋊C₄×C₄₁	—	2	2	no	—
136	C₄⋊C₄×C₄₁	—	2	1	no	—
137	C₄⋊C₄×C₄₁	—	2	2	no	—
138	C₄⋊C₄×C₄₁	—	2	2	no	—
139	C₄⋊C₄×C₄₁	—	4	4	no	—
140	C₄⋊C₄×C₄₁	—	4	2	no	—
141	C₄⋊C₄×C₄₁	—	4	4	no	—
142	C₄⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
143	C₂²⋊C₄×C₄₁	—	2	4	no	—
144	C₂²⋊C₄×C₄₁	—	4	4	no	—
145	C₂²⋊C₄×C₄₁	—	4	2	no	—
146	C₂²⋊C₄×C₄₁	—	4	4	no	—
147	C₂²⋊C₄×C₄₁	—	4	4	no	—
148	C₂²⋊C₄×C₄₁	—	8	2	no	—
149	C₄²×C₄₁	—	2	2	no	—
150	C₄²×C₄₁	—	2	2	no	—
151	C₄²×C₄₁	—	8	2	no	—
152	C₄²×C₄₁	C₂×D₄	1	2	yes	—
153	C₄²×C₄₁	#41	1	2	yes	—
154	C₂³×C₄₁	—	2	2	no	—
155	C₂³×C₄₁	—	2	2	no	—
156	C₂³×C₄₁	—	4	1	no	—
157	C₂³×C₄₁	—	4	1	no	—
158	C₂³×C₄₁	—	4	1	no	—
159	C₂³×C₄₁	—	4	1	no	—
160	C₂³×C₄₁	—	4	2	no	—
161	C₂³×C₄₁	—	4	2	no	—
162	C₂³×C₄₁	—	4	2	no	—
163	C₂³×C₄₁	—	4	2	no	—
164	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
165	Q₈×C₄₁	—	8	4	no	—
166	D₄×C₄₁	—	2	2	no	—
167	D₄×C₄₁	—	2	2	no	—
168	D₄×C₄₁	—	2	2	no	—
169	D₄×C₄₁	—	2	2	no	—
170	D₄×C₄₁	—	4	1	no	—
171	D₄×C₄₁	—	4	1	no	—
172	D₄×C₄₁	—	4	1	no	—
173	D₄×C₄₁	—	4	1	no	—
174	C₂×C₄×C₄₁	—	2	2	no	—
175	C₂×C₄×C₄₁	—	2	2	no	—
176	C₂×C₄×C₄₁	—	2	2	no	—
177	C₂×C₄×C₄₁	—	2	2	no	—
178	C₂×C₄×C₄₁	—	2	2	no	—
179	C₂×C₄×C₄₁	—	2	2	no	—
180	C₂×C₄×C₄₁	—	2	2	no	—
181	C₂×C₄×C₄₁	—	2	2	no	—
182	C₂×C₄×C₄₁	—	4	2	no	—
183	C₂×C₄×C₄₁	—	4	1	no	—
184	C₂×C₄×C₄₁	—	4	2	no	—
185	C₂×C₄×C₄₁	—	4	2	no	—
186	C₂×C₄×C₄₁	—	4	2	no	—
187	C₂×C₄×C₄₁	—	4	2	no	—
188	C₂×C₄×C₄₁	—	4	2	no	—
189	C₂×C₄×C₄₁	—	4	2	no	—
190	C₂×C₄×C₄₁	—	4	2	no	—
191	C₂×C₄×C₄₁	—	8	4	no	—
192	C₂×C₄×C₄₁	—	8	4	no	—
193	C₂×C₄×C₄₁	#121	1	2	yes	—
194	C₂×C₄×C₄₁	#121	1	2	yes	—
195	C₂×C₄×C₄₁	AGL(1,ℤ/8)	1	4	yes	—
196	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
197	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
198	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
199	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
200	C₂×C₄×C₄₁	2₋¹⁺⁴	1	1	yes	characteristic
201	C₂×C₄×C₄₁	2₋¹⁺⁴	1	1	yes	characteristic
202	C₈×C₄₁	—	2	2	no	—
203	C₈×C₄₁	—	4	2	no	—
204	C₈×C₄₁	—	4	1	no	—
205	#24692	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
206	C₂²×C₄₁	—	4	4	no	—
207	C₂²×C₄₁	—	4	2	no	—
208	C₂²×C₄₁	—	4	2	no	—
209	C₂²×C₄₁	—	4	2	no	—
210	C₂²×C₄₁	—	4	2	no	—
211	C₂²×C₄₁	—	8	2	no	—
212	C₂²×C₄₁	—	8	2	no	—
213	C₂²×C₄₁	—	8	2	no	—
214	C₂²×C₄₁	—	8	1	no	—
215	C₂²×C₄₁	—	8	1	no	—
216	C₂²×C₄₁	C₂×#121	1	1	yes	characteristic
217	C₂²×C₄₁	#547	1	1	yes	characteristic
218	C₂²×C₄₁	#548	1	1	yes	characteristic
219	C₂²×C₄₁	C₂×AGL(1,ℤ/8)	1	2	yes	—
220	C₂²×C₄₁	#577	1	2	yes	—
221	C₄×C₄₁	—	2	4	no	—
222	C₄×C₄₁	—	2	2	no	—
223	C₄×C₄₁	—	2	2	no	—
224	C₄×C₄₁	—	4	2	no	—
225	C₄×C₄₁	—	4	2	no	—
226	C₄×C₄₁	—	8	2	no	—
227	C₄×C₄₁	—	8	1	no	—
228	C₄×C₄₁	—	8	2	no	—
229	C₄×C₄₁	#525	1	1	yes	characteristic
230	C₄×C₄₁	#536	1	1	yes	characteristic
231	C₄×C₄₁	#552	1	1	yes	characteristic
232	C₄×C₄₁	#556	1	1	yes	characteristic
233	C₂×#476	C₂×C₄₁	1	1	yes	characteristic, complemented
234	C₂×#442	C₂×C₄₁	1	1	yes	characteristic
235	#2542	C₂×C₄₁	1	1	yes	characteristic, complemented
236	#2357	C₂×C₄₁	1	1	yes	characteristic, complemented
237	#2071	C₂×C₄₁	1	2	yes	complemented
238	#2054	C₂×C₄₁	1	2	yes	—
239	#1993	C₂×C₄₁	1	1	yes	characteristic, complemented
240	#1948	C₂×C₄₁	1	2	yes	complemented
241	#1940	C₂×C₄₁	1	1	yes	characteristic, complemented
242	#1926	C₂×C₄₁	1	2	yes	complemented
243	#1804	C₂×C₄₁	1	1	yes	characteristic, complemented
244	C₂×C₄₁	—	8	2	no	—
245	C₂×C₄₁	—	8	2	no	—
246	C₂×C₄₁	#2415	1	1	yes	characteristic
247	C₂×C₄₁	#3038	1	1	yes	characteristic
248	C₂×C₄₁	#3042	1	1	yes	characteristic
249	C₂×C₄₁	#3345	1	2	yes	—
250	C₂×C₄₁	#3373	1	2	yes	—
251	C₂²×D₈	C₂²×C₄₁	1	1	yes	characteristic
252	C₂×C₄⋊Q₈	C₂²×C₄₁	1	1	yes	characteristic
253	C₂×C₂²⋊Q₈	—	2	2	no	—
254	C₂×C₄×D₄	C₂²×C₄₁	1	1	yes	characteristic
255	C₂×C₄×D₄	C₂²×C₄₁	1	1	yes	characteristic
256	#476	—	2	4	no	—
257	#442	—	2	4	no	—
258	C₂×#106	C₂²×C₄₁	1	1	yes	characteristic
259	C₂×#106	C₂²×C₄₁	1	2	yes	—
260	C₂×C₄⋊C₈	C₂²×C₄₁	1	2	yes	—
261	C₂×C₄⋊C₈	C₂²×C₄₁	1	1	yes	characteristic
262	C₂×#102	C₂²×C₄₁	1	2	yes	—
263	C₂×#102	C₂²×C₄₁	1	2	yes	—
264	C₂×#102	C₂²×C₄₁	1	1	yes	characteristic
265	C₂×#102	C₂²×C₄₁	1	1	yes	characteristic
266	C₂×#97	C₂²×C₄₁	1	1	yes	characteristic
267	#399	—	2	1	no	—
268	#399	—	2	1	no	—
269	#390	C₂²×C₄₁	1	2	yes	—
270	#390	C₂²×C₄₁	1	2	yes	—
271	#388	—	2	2	no	—
272	#384	C₂²×C₄₁	1	2	yes	—
273	#382	C₂²×C₄₁	1	1	yes	characteristic
274	#381	—	2	1	no	—
275	C₄×C₄⋊C₄	C₂²×C₄₁	1	2	yes	—
276	C₄×C₄⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
277	C₄×C₂²⋊C₄	—	2	1	no	—
278	#340	C₂²×C₄₁	1	2	yes	—
279	#340	C₂²×C₄₁	1	2	yes	—
280	#340	C₂²×C₄₁	1	2	yes	—
281	#336	C₂²×C₄₁	1	2	yes	—
282	C₄₁	#24692	1	1	yes	characteristic, direct product factor, Sylow
283	C₂²×Q₈	—	2	1	no	—
284	C₂²×D₄	C₂³×C₄₁	1	1	yes	characteristic
285	C₂²×D₄	C₂³×C₄₁	1	1	yes	characteristic
286	C₂³×C₄	—	2	1	no	—
287	C₂³×C₄	—	2	1	no	—
288	C₂×D₈	—	2	2	no	—
289	C₂×D₈	—	2	2	no	—
290	C₂×D₈	—	2	2	no	—
291	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
292	C₂²×C₈	C₂³×C₄₁	1	2	yes	—
293	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
294	C₄⋊Q₈	—	2	2	no	—
295	C₄⋊Q₈	—	2	2	no	—
296	C₂²⋊Q₈	—	4	8	no	—
297	C₄×D₄	—	2	2	no	—
298	C₄×D₄	—	2	2	no	—
299	C₄×D₄	—	2	2	no	—
300	C₄×D₄	D₄×C₄₁	1	4	yes	—
301	C₂×C₄⋊C₄	—	2	2	no	—
302	C₂×C₄⋊C₄	—	2	2	no	—
303	C₂×C₄⋊C₄	—	2	1	no	—
304	C₂×C₄⋊C₄	D₄×C₄₁	1	2	yes	—
305	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
306	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
307	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
308	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
309	C₂×C₂²⋊C₄	—	2	1	no	—
310	C₂×C₂²⋊C₄	—	2	1	no	—
311	C₂×C₂²⋊C₄	—	2	2	no	—
312	C₂×C₂²⋊C₄	—	2	2	no	—
313	C₂×C₂²⋊C₄	—	2	2	no	—
314	C₂×C₂²⋊C₄	—	2	2	no	—
315	C₂×C₄²	—	2	2	no	—
316	C₂×C₄²	C₂³×C₄₁	1	2	yes	—
317	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
318	#106	—	2	2	no	—
319	#106	—	2	4	no	—
320	C₄⋊C₈	—	2	4	no	—
321	C₄⋊C₈	—	2	2	no	—
322	#102	—	2	2	no	—
323	#102	—	2	4	no	—
324	#102	—	2	4	no	—
325	#102	—	2	2	no	—
326	#97	—	2	2	no	—
327	#95	—	2	1	no	—
328	#95	—	2	2	no	—
329	#95	—	2	1	no	—
330	#95	D₄×C₄₁	1	1	yes	characteristic
331	#95	D₄×C₄₁	1	1	yes	characteristic
332	C₂⁴	—	2	1	no	—
333	C₂⁴	—	2	1	no	—
334	C₂×Q₈	—	4	4	no	—
335	C₂×Q₈	—	4	2	no	—
336	C₂×D₄	—	2	1	no	—
337	C₂×D₄	—	2	1	no	—
338	C₂×D₄	—	2	1	no	—
339	C₂×D₄	—	2	1	no	—
340	C₂×D₄	—	2	1	no	—
341	C₂×D₄	—	2	1	no	—
342	C₂×D₄	—	2	1	no	—
343	C₂×D₄	—	2	1	no	—
344	C₂×D₄	—	2	1	no	—
345	C₂×D₄	—	2	1	no	—
346	C₂×D₄	C₂×D₄×C₄₁	1	2	yes	—
347	C₂×D₄	#41×C₄₁	1	2	yes	—
348	C₂²×C₄	—	2	1	no	—
349	C₂²×C₄	—	2	4	no	—
350	C₂²×C₄	—	2	2	no	—
351	C₂²×C₄	—	2	2	no	—
352	C₂²×C₄	—	2	1	no	—
353	C₂²×C₄	—	4	4	no	—
354	C₂²×C₄	—	4	2	no	—
355	C₂²×C₄	—	8	2	no	—
356	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
357	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
358	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
359	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
360	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
361	D₈	—	2	8	no	—
362	C₂×C₈	—	2	1	no	—
363	C₂×C₈	—	2	1	no	—
364	C₂×C₈	—	2	1	no	—
365	C₂×C₈	—	2	2	no	—
366	C₂×C₈	—	2	2	no	—
367	C₂×C₈	—	2	2	no	—
368	C₂×C₈	—	2	1	no	—
369	C₂×C₈	—	2	1	no	—
370	C₂×C₈	#41×C₄₁	1	2	yes	—
371	C₄⋊C₄	—	2	4	no	—
372	C₄⋊C₄	—	2	1	no	—
373	C₄⋊C₄	—	2	1	no	—
374	C₄⋊C₄	—	2	2	no	—
375	C₄⋊C₄	—	2	2	no	—
376	C₄⋊C₄	—	2	1	no	—
377	C₄⋊C₄	—	2	2	no	—
378	C₄⋊C₄	—	2	2	no	—
379	C₄⋊C₄	—	4	4	no	—
380	C₄⋊C₄	—	4	2	no	—
381	C₄⋊C₄	—	4	4	no	—
382	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
383	C₂²⋊C₄	—	2	4	no	—
384	C₂²⋊C₄	—	4	4	no	—
385	C₂²⋊C₄	—	4	2	no	—
386	C₂²⋊C₄	—	4	4	no	—
387	C₂²⋊C₄	—	4	4	no	—
388	C₂²⋊C₄	—	8	2	no	—
389	C₄²	—	2	2	no	—
390	C₄²	—	2	2	no	—
391	C₄²	—	8	2	no	—
392	C₄²	C₂×D₄×C₄₁	1	2	yes	—
393	C₄²	#41×C₄₁	1	2	yes	—
394	C₂³	—	2	2	no	—
395	C₂³	—	2	2	no	—
396	C₂³	—	4	1	no	—
397	C₂³	—	4	1	no	—
398	C₂³	—	4	1	no	—
399	C₂³	—	4	1	no	—
400	C₂³	—	4	2	no	—
401	C₂³	—	4	2	no	—
402	C₂³	—	4	2	no	—
403	C₂³	—	4	2	no	—
404	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
405	Q₈	—	8	4	no	—
406	D₄	—	2	2	no	—
407	D₄	—	2	2	no	—
408	D₄	—	2	2	no	—
409	D₄	—	2	2	no	—
410	D₄	—	4	1	no	—
411	D₄	—	4	1	no	—
412	D₄	—	4	1	no	—
413	D₄	—	4	1	no	—
414	C₂×C₄	—	2	2	no	—
415	C₂×C₄	—	2	2	no	—
416	C₂×C₄	—	2	2	no	—
417	C₂×C₄	—	2	2	no	—
418	C₂×C₄	—	2	2	no	—
419	C₂×C₄	—	2	2	no	—
420	C₂×C₄	—	2	2	no	—
421	C₂×C₄	—	2	2	no	—
422	C₂×C₄	—	4	2	no	—
423	C₂×C₄	—	4	1	no	—
424	C₂×C₄	—	4	2	no	—
425	C₂×C₄	—	4	2	no	—
426	C₂×C₄	—	4	2	no	—
427	C₂×C₄	—	4	2	no	—
428	C₂×C₄	—	4	2	no	—
429	C₂×C₄	—	4	2	no	—
430	C₂×C₄	—	4	2	no	—
431	C₂×C₄	—	8	4	no	—
432	C₂×C₄	—	8	4	no	—
433	C₂×C₄	#121×C₄₁	1	2	yes	—
434	C₂×C₄	#121×C₄₁	1	2	yes	—
435	C₂×C₄	AGL(1,ℤ/8)×C₄₁	1	4	yes	—
436	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
437	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
438	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
439	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
440	C₂×C₄	2₋¹⁺⁴×C₄₁	1	1	yes	characteristic
441	C₂×C₄	2₋¹⁺⁴×C₄₁	1	1	yes	characteristic
442	C₈	—	2	2	no	—
443	C₈	—	4	2	no	—
444	C₈	—	4	1	no	—
445	C₂²	—	4	2	no	—
446	C₂²	—	4	2	no	—
447	C₂²	—	4	4	no	—
448	C₂²	—	4	2	no	—
449	C₂²	—	4	2	no	—
450	C₂²	—	8	1	no	—
451	C₂²	—	8	1	no	—
452	C₂²	—	8	2	no	—
453	C₂²	—	8	2	no	—
454	C₂²	—	8	2	no	—
455	C₂²	C₂×#121×C₄₁	1	1	yes	characteristic
456	C₂²	C₄₁×#547	1	1	yes	characteristic
457	C₂²	C₄₁×#548	1	1	yes	characteristic
458	C₂²	C₂×AGL(1,ℤ/8)×C₄₁	1	2	yes	—
459	C₂²	C₄₁×#577	1	2	yes	—
460	C₄	—	2	2	no	—
461	C₄	—	2	2	no	—
462	C₄	—	2	4	no	—
463	C₄	—	4	2	no	—
464	C₄	—	4	2	no	—
465	C₄	—	8	1	no	—
466	C₄	—	8	2	no	—
467	C₄	—	8	2	no	—
468	C₄	C₄₁×#525	1	1	yes	characteristic
469	C₄	C₄₁×#536	1	1	yes	characteristic
470	C₄	C₄₁×#552	1	1	yes	characteristic
471	C₄	C₄₁×#556	1	1	yes	characteristic
472	C₂	—	8	2	no	—
473	C₂	—	8	2	no	—
474	C₂	C₄₁×#2415	1	1	yes	characteristic
475	C₂	C₄₁×#3038	1	1	yes	characteristic
476	C₂	C₄₁×#3042	1	1	yes	characteristic
477	C₂	C₄₁×#3345	1	2	yes	—
478	C₂	C₄₁×#3373	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₄₁	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₁
prime radical	C₂²×D₈×C₄₁	C₂²
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×#476	C₂	semidirect
3. C₄₁×#2542	C₂	semidirect
4. C₄₁×#2357	C₂	semidirect
5. C₄₁×#2071	C₂	semidirect
7. C₄₁×#1993	C₂	semidirect
8. C₄₁×#1948	C₂	semidirect
9. C₄₁×#1940	C₂	semidirect
10. C₄₁×#1926	C₂	semidirect
11. C₄₁×#1804	C₂	semidirect
205. #24692	C₄₁	direct (N × H)
233. C₂×#476	C₂×C₄₁	semidirect
235. #2542	C₂×C₄₁	semidirect
236. #2357	C₂×C₄₁	semidirect
237. #2071	C₂×C₄₁	semidirect
239. #1993	C₂×C₄₁	semidirect
240. #1948	C₂×C₄₁	semidirect
241. #1940	C₂×C₄₁	semidirect
242. #1926	C₂×C₄₁	semidirect
243. #1804	C₂×C₄₁	semidirect
282. C₄₁	#24692	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×#476	2
C₂×C₄₁×#442	2
C₄₁×#2542	2
C₄₁×#2357	2
C₄₁×#2071	2
C₄₁×#2054	2
C₄₁×#1993	2
C₄₁×#1948	2
C₄₁×#1940	2
C₄₁×#1926	2
C₄₁×#1804	2
#24692	41

Subgroups — C41×#24692 #23800893

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#24692 #23800893