Subgroups — C₄₁×#24709 #23800910

Order 10496.

912 conjugacy classes of subgroups.

The subgroup lattice has 566 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₁×#474	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄₁×#432	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₁×#2857	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄×#121×C₄₁	C₂	1	1	yes	maximal, characteristic
5	C₄₁×#2076	C₂	1	2	yes	maximal, complemented
6	C₄₁×#2034	C₂	1	2	yes	maximal
7	C₄₁×#1988	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄₁×#1948	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄₁×#1944	C₂	1	2	yes	maximal, complemented
10	C₄₁×#1936	C₂	1	2	yes	maximal, complemented
11	C₄₁×#1802	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₄⋊Q₈×C₄₁	C₂²	1	1	yes	characteristic
13	C₂×C₂²⋊Q₈×C₄₁	—	2	1	no	—
14	C₂×#121×C₄₁	C₂²	1	1	yes	characteristic
15	C₂×C₄×D₄×C₄₁	—	2	1	no	—
16	C₂×C₄×D₄×C₄₁	C₂²	1	1	yes	characteristic
17	C₂²×C₄²×C₄₁	C₂²	1	1	yes	characteristic
18	C₄₁×#474	—	2	4	no	—
19	C₄₁×#432	—	2	4	no	—
20	C₂×#107×C₄₁	C₂²	1	2	yes	—
21	C₂×#106×C₄₁	C₂²	1	2	yes	—
22	C₂×C₄⋊C₈×C₄₁	C₂²	1	1	yes	characteristic
23	C₂×C₄⋊C₈×C₄₁	C₂²	1	1	yes	characteristic
24	C₂×#102×C₄₁	C₂²	1	2	yes	—
25	C₂×#102×C₄₁	C₂²	1	2	yes	—
26	C₂×C₂²⋊C₈×C₄₁	C₂²	1	2	yes	—
27	C₂×#97×C₄₁	C₂²	1	2	yes	—
28	C₄₁×#391	—	2	1	no	—
29	C₄₁×#390	C₂²	1	1	yes	characteristic
30	C₄₁×#389	—	2	1	no	—
31	C₄₁×#389	C₂²	1	1	yes	characteristic
32	C₄₁×#389	C₂²	1	2	yes	—
33	C₄₁×#388	—	2	1	no	—
34	C₄₁×#386	—	2	1	no	—
35	C₄₁×#384	C₂²	1	1	yes	characteristic
36	C₄₁×#380	—	2	1	no	—
37	C₄₁×#380	C₂²	1	2	yes	—
38	C₄₁×#380	C₂²	1	1	yes	characteristic
39	C₄×C₄⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
40	C₄×C₂²⋊C₄×C₄₁	—	2	1	no	—
41	C₄₁×#340	C₂²	1	2	yes	—
42	C₄₁×#340	C₂²	1	2	yes	—
43	C₄₁×#340	C₂²	1	2	yes	—
44	C₄₁×#340	C₂²	1	2	yes	—
45	C₂²×Q₈×C₄₁	—	2	1	no	—
46	C₂²×D₄×C₄₁	—	2	1	no	—
47	C₂²×D₄×C₄₁	C₂³	1	1	yes	characteristic
48	C₂³×C₄×C₄₁	—	2	1	no	—
49	C₂³×C₄×C₄₁	D₄	1	1	yes	characteristic
50	C₂³×C₄×C₄₁	D₄	1	1	yes	characteristic
51	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
52	C₂²×C₈×C₄₁	C₂³	1	2	yes	—
53	C₂²×C₈×C₄₁	C₂³	1	2	yes	—
54	C₄⋊Q₈×C₄₁	—	2	2	no	—
55	C₄⋊Q₈×C₄₁	—	2	2	no	—
56	C₂²⋊Q₈×C₄₁	—	4	4	no	—
57	#121×C₄₁	—	2	2	no	—
58	#121×C₄₁	—	2	2	no	—
59	C₄×D₄×C₄₁	—	2	2	no	—
60	C₄×D₄×C₄₁	—	2	2	no	—
61	C₄×D₄×C₄₁	—	4	4	no	—
62	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
63	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
64	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
65	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
66	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
67	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
68	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
69	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
70	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
71	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
72	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
73	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
74	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
75	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
76	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
77	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
78	C₂×C₄²×C₄₁	—	2	2	no	—
79	C₂×C₄²×C₄₁	—	2	2	no	—
80	C₂×C₄²×C₄₁	—	2	1	no	—
81	C₂×C₄²×C₄₁	D₄	1	1	yes	characteristic
82	C₂×C₄²×C₄₁	D₄	1	1	yes	characteristic
83	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
84	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
85	#107×C₄₁	—	2	4	no	—
86	#106×C₄₁	—	2	4	no	—
87	C₄⋊C₈×C₄₁	—	2	2	no	—
88	C₄⋊C₈×C₄₁	D₄	1	4	yes	complemented
89	#102×C₄₁	—	2	4	no	—
90	#102×C₄₁	—	2	4	no	—
91	C₂²⋊C₈×C₄₁	—	2	4	no	—
92	#97×C₄₁	—	2	4	no	—
93	#95×C₄₁	—	2	1	no	—
94	#95×C₄₁	—	2	1	no	—
95	#95×C₄₁	—	2	1	no	—
96	#95×C₄₁	—	2	2	no	—
97	#95×C₄₁	—	2	2	no	—
98	C₂⁴×C₄₁	—	2	1	no	—
99	C₂⁴×C₄₁	C₂×D₄	1	1	yes	characteristic
100	C₂×Q₈×C₄₁	—	4	2	no	—
101	C₂×Q₈×C₄₁	—	4	2	no	—
102	C₂×Q₈×C₄₁	—	4	2	no	—
103	C₂×D₄×C₄₁	—	2	4	no	—
104	C₂×D₄×C₄₁	—	2	1	no	—
105	C₂×D₄×C₄₁	—	2	1	no	—
106	C₂×D₄×C₄₁	—	2	1	no	—
107	C₂×D₄×C₄₁	—	2	1	no	—
108	C₂×D₄×C₄₁	—	2	1	no	—
109	C₂×D₄×C₄₁	—	4	2	no	—
110	C₂×D₄×C₄₁	—	4	2	no	—
111	C₂×D₄×C₄₁	#41	1	2	yes	—
112	C₂²×C₄×C₄₁	—	2	2	no	—
113	C₂²×C₄×C₄₁	—	2	1	no	—
114	C₂²×C₄×C₄₁	—	2	2	no	—
115	C₂²×C₄×C₄₁	—	2	2	no	—
116	C₂²×C₄×C₄₁	—	2	2	no	—
117	C₂²×C₄×C₄₁	—	2	2	no	—
118	C₂²×C₄×C₄₁	—	2	1	no	—
119	C₂²×C₄×C₄₁	—	2	1	no	—
120	C₂²×C₄×C₄₁	—	2	1	no	—
121	C₂²×C₄×C₄₁	—	2	1	no	—
122	C₂²×C₄×C₄₁	—	2	1	no	—
123	C₂²×C₄×C₄₁	—	2	1	no	—
124	C₂²×C₄×C₄₁	—	2	1	no	—
125	C₂²×C₄×C₄₁	—	2	1	no	—
126	C₂²×C₄×C₄₁	—	2	2	no	—
127	C₂²×C₄×C₄₁	—	2	2	no	—
128	C₂²×C₄×C₄₁	—	4	1	no	—
129	C₂²×C₄×C₄₁	—	4	2	no	—
130	C₂²×C₄×C₄₁	—	4	2	no	—
131	C₂²×C₄×C₄₁	—	4	2	no	—
132	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
133	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
134	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
135	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
136	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
137	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
138	C₂×C₈×C₄₁	—	2	2	no	—
139	C₂×C₈×C₄₁	—	2	2	no	—
140	C₂×C₈×C₄₁	—	2	2	no	—
141	C₂×C₈×C₄₁	—	2	2	no	—
142	C₂×C₈×C₄₁	—	2	2	no	—
143	C₂×C₈×C₄₁	C₂×D₄	1	4	yes	—
144	C₄⋊C₄×C₄₁	—	2	1	no	—
145	C₄⋊C₄×C₄₁	—	2	2	no	—
146	C₄⋊C₄×C₄₁	—	2	1	no	—
147	C₄⋊C₄×C₄₁	—	2	2	no	—
148	C₄⋊C₄×C₄₁	—	2	2	no	—
149	C₄⋊C₄×C₄₁	—	2	1	no	—
150	C₄⋊C₄×C₄₁	—	2	2	no	—
151	C₄⋊C₄×C₄₁	—	2	1	no	—
152	C₄⋊C₄×C₄₁	—	2	1	no	—
153	C₄⋊C₄×C₄₁	—	4	2	no	—
154	C₄⋊C₄×C₄₁	—	4	2	no	—
155	C₄⋊C₄×C₄₁	—	4	4	no	—
156	C₄⋊C₄×C₄₁	—	4	2	no	—
157	C₄⋊C₄×C₄₁	—	4	2	no	—
158	C₄⋊C₄×C₄₁	#41	1	2	yes	—
159	C₂²⋊C₄×C₄₁	—	2	4	no	—
160	C₂²⋊C₄×C₄₁	—	4	2	no	—
161	C₂²⋊C₄×C₄₁	—	4	2	no	—
162	C₂²⋊C₄×C₄₁	—	4	2	no	—
163	C₂²⋊C₄×C₄₁	—	4	4	no	—
164	C₂²⋊C₄×C₄₁	—	4	2	no	—
165	C₄²×C₄₁	—	2	2	no	—
166	C₄²×C₄₁	—	2	2	no	—
167	C₄²×C₄₁	—	2	1	no	—
168	C₄²×C₄₁	—	2	1	no	—
169	C₄²×C₄₁	—	4	2	no	—
170	C₄²×C₄₁	C₂×D₄	1	2	yes	—
171	C₄²×C₄₁	#41	1	2	yes	—
172	C₂³×C₄₁	—	2	1	no	—
173	C₂³×C₄₁	—	2	1	no	—
174	C₂³×C₄₁	—	2	1	no	—
175	C₂³×C₄₁	—	2	1	no	—
176	C₂³×C₄₁	—	2	1	no	—
177	C₂³×C₄₁	—	2	1	no	—
178	C₂³×C₄₁	—	2	2	no	—
179	C₂³×C₄₁	—	4	1	no	—
180	C₂³×C₄₁	—	4	1	no	—
181	C₂³×C₄₁	—	4	1	no	—
182	C₂³×C₄₁	—	4	1	no	—
183	C₂³×C₄₁	—	4	1	no	—
184	C₂³×C₄₁	—	4	1	no	—
185	C₂³×C₄₁	#137	1	2	yes	—
186	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
187	Q₈×C₄₁	—	8	4	no	—
188	D₄×C₄₁	—	2	2	no	—
189	D₄×C₄₁	—	2	2	no	—
190	D₄×C₄₁	—	4	8	no	—
191	D₄×C₄₁	—	4	1	no	—
192	D₄×C₄₁	—	4	1	no	—
193	C₂×C₄×C₄₁	—	2	1	no	—
194	C₂×C₄×C₄₁	—	2	1	no	—
195	C₂×C₄×C₄₁	—	2	1	no	—
196	C₂×C₄×C₄₁	—	2	1	no	—
197	C₂×C₄×C₄₁	—	2	1	no	—
198	C₂×C₄×C₄₁	—	2	1	no	—
199	C₂×C₄×C₄₁	—	2	2	no	—
200	C₂×C₄×C₄₁	—	2	1	no	—
201	C₂×C₄×C₄₁	—	2	1	no	—
202	C₂×C₄×C₄₁	—	2	1	no	—
203	C₂×C₄×C₄₁	—	2	1	no	—
204	C₂×C₄×C₄₁	—	2	1	no	—
205	C₂×C₄×C₄₁	—	4	4	no	—
206	C₂×C₄×C₄₁	—	4	1	no	—
207	C₂×C₄×C₄₁	—	4	1	no	—
208	C₂×C₄×C₄₁	—	4	1	no	—
209	C₂×C₄×C₄₁	—	4	1	no	—
210	C₂×C₄×C₄₁	—	4	1	no	—
211	C₂×C₄×C₄₁	—	4	1	no	—
212	C₂×C₄×C₄₁	—	4	4	no	—
213	C₂×C₄×C₄₁	—	4	1	no	—
214	C₂×C₄×C₄₁	—	4	2	no	—
215	C₂×C₄×C₄₁	—	4	2	no	—
216	C₂×C₄×C₄₁	—	4	1	no	—
217	C₂×C₄×C₄₁	—	4	1	no	—
218	C₂×C₄×C₄₁	—	4	2	no	—
219	C₂×C₄×C₄₁	—	4	1	no	—
220	C₂×C₄×C₄₁	—	4	2	no	—
221	C₂×C₄×C₄₁	—	4	1	no	—
222	C₂×C₄×C₄₁	—	4	2	no	—
223	C₂×C₄×C₄₁	—	4	1	no	—
224	C₂×C₄×C₄₁	—	4	2	no	—
225	C₂×C₄×C₄₁	—	8	4	no	—
226	C₂×C₄×C₄₁	#121	1	2	yes	—
227	C₂×C₄×C₄₁	#121	1	2	yes	—
228	C₂×C₄×C₄₁	AGL(1,ℤ/8)	1	2	yes	—
229	C₂×C₄×C₄₁	AGL(1,ℤ/8)	1	2	yes	—
230	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
231	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
232	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
233	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
234	C₂×C₄×C₄₁	2₋¹⁺⁴	1	1	yes	characteristic
235	C₂×C₄×C₄₁	2₋¹⁺⁴	1	1	yes	characteristic
236	C₈×C₄₁	—	2	4	no	—
237	C₈×C₄₁	—	4	2	no	—
238	#24709	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
239	C₂²×C₄₁	—	2	2	no	—
240	C₂²×C₄₁	—	2	2	no	—
241	C₂²×C₄₁	—	2	2	no	—
242	C₂²×C₄₁	—	4	1	no	—
243	C₂²×C₄₁	—	4	1	no	—
244	C₂²×C₄₁	—	4	1	no	—
245	C₂²×C₄₁	—	4	1	no	—
246	C₂²×C₄₁	—	4	2	no	—
247	C₂²×C₄₁	—	4	2	no	—
248	C₂²×C₄₁	—	4	2	no	—
249	C₂²×C₄₁	—	8	1	no	—
250	C₂²×C₄₁	—	8	1	no	—
251	C₂²×C₄₁	—	8	1	no	—
252	C₂²×C₄₁	—	8	1	no	—
253	C₂²×C₄₁	C₂×#121	1	1	yes	characteristic
254	C₂²×C₄₁	#525	1	1	yes	characteristic
255	C₂²×C₄₁	#536	1	1	yes	characteristic
256	C₂²×C₄₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
257	C₂²×C₄₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
258	C₂²×C₄₁	C₂×#137	1	1	yes	characteristic
259	C₂²×C₄₁	#575	1	1	yes	characteristic
260	C₄×C₄₁	—	2	2	no	—
261	C₄×C₄₁	—	4	2	no	—
262	C₄×C₄₁	—	4	1	no	—
263	C₄×C₄₁	—	4	1	no	—
264	C₄×C₄₁	—	4	1	no	—
265	C₄×C₄₁	—	8	2	no	—
266	C₄×C₄₁	—	8	1	no	—
267	C₄×C₄₁	—	8	1	no	—
268	C₄×C₄₁	—	8	2	no	—
269	C₄×C₄₁	#469	1	4	yes	—
270	C₄×C₄₁	#547	1	1	yes	characteristic
271	C₄×C₄₁	#548	1	1	yes	characteristic
272	C₄×C₄₁	#552	1	1	yes	characteristic
273	C₄×C₄₁	#556	1	1	yes	characteristic
274	C₂×#474	C₂×C₄₁	1	1	yes	characteristic, complemented
275	C₂×#432	C₂×C₄₁	1	1	yes	characteristic, complemented
276	#2857	C₂×C₄₁	1	1	yes	characteristic, complemented
277	C₄×#121	C₂×C₄₁	1	1	yes	characteristic
278	#2076	C₂×C₄₁	1	2	yes	complemented
279	#2034	C₂×C₄₁	1	2	yes	—
280	#1988	C₂×C₄₁	1	1	yes	characteristic, complemented
281	#1948	C₂×C₄₁	1	1	yes	characteristic, complemented
282	#1944	C₂×C₄₁	1	2	yes	complemented
283	#1936	C₂×C₄₁	1	2	yes	complemented
284	#1802	C₂×C₄₁	1	1	yes	characteristic, complemented
285	C₂×C₄₁	—	4	2	no	—
286	C₂×C₄₁	—	8	2	no	—
287	C₂×C₄₁	#2415	1	1	yes	characteristic
288	C₂×C₄₁	C₂×#469	1	1	yes	characteristic
289	C₂×C₄₁	#3056	1	1	yes	characteristic
290	C₂×C₄₁	#3110	1	1	yes	characteristic
291	C₂×C₄₁	#3115	1	1	yes	characteristic
292	C₂×C₄₁	#3235	1	1	yes	characteristic
293	C₂×C₄₁	#3239	1	1	yes	characteristic
294	C₂×C₄⋊Q₈	C₂²×C₄₁	1	1	yes	characteristic
295	C₂×C₂²⋊Q₈	—	2	1	no	—
296	C₂×#121	C₂²×C₄₁	1	1	yes	characteristic
297	C₂×C₄×D₄	—	2	1	no	—
298	C₂×C₄×D₄	C₂²×C₄₁	1	1	yes	characteristic
299	C₂²×C₄²	C₂²×C₄₁	1	1	yes	characteristic
300	#474	—	2	4	no	—
301	#432	—	2	4	no	—
302	C₂×#107	C₂²×C₄₁	1	2	yes	—
303	C₂×#106	C₂²×C₄₁	1	2	yes	—
304	C₂×C₄⋊C₈	C₂²×C₄₁	1	1	yes	characteristic
305	C₂×C₄⋊C₈	C₂²×C₄₁	1	1	yes	characteristic
306	C₂×#102	C₂²×C₄₁	1	2	yes	—
307	C₂×#102	C₂²×C₄₁	1	2	yes	—
308	C₂×C₂²⋊C₈	C₂²×C₄₁	1	2	yes	—
309	C₂×#97	C₂²×C₄₁	1	2	yes	—
310	#391	—	2	1	no	—
311	#390	C₂²×C₄₁	1	1	yes	characteristic
312	#389	—	2	1	no	—
313	#389	C₂²×C₄₁	1	2	yes	—
314	#389	C₂²×C₄₁	1	1	yes	characteristic
315	#388	—	2	1	no	—
316	#386	—	2	1	no	—
317	#384	C₂²×C₄₁	1	1	yes	characteristic
318	#380	—	2	1	no	—
319	#380	C₂²×C₄₁	1	1	yes	characteristic
320	#380	C₂²×C₄₁	1	2	yes	—
321	C₄×C₄⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
322	C₄×C₂²⋊C₄	—	2	1	no	—
323	#340	C₂²×C₄₁	1	2	yes	—
324	#340	C₂²×C₄₁	1	2	yes	—
325	#340	C₂²×C₄₁	1	2	yes	—
326	#340	C₂²×C₄₁	1	2	yes	—
327	C₄₁	#24709	1	1	yes	characteristic, direct product factor, Sylow
328	C₂²×Q₈	—	2	1	no	—
329	C₂²×D₄	—	2	1	no	—
330	C₂²×D₄	C₂³×C₄₁	1	1	yes	characteristic
331	C₂³×C₄	—	2	1	no	—
332	C₂³×C₄	D₄×C₄₁	1	1	yes	characteristic
333	C₂³×C₄	D₄×C₄₁	1	1	yes	characteristic
334	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
335	C₂²×C₈	C₂³×C₄₁	1	2	yes	—
336	C₂²×C₈	C₂³×C₄₁	1	2	yes	—
337	C₄⋊Q₈	—	2	2	no	—
338	C₄⋊Q₈	—	2	2	no	—
339	C₂²⋊Q₈	—	4	4	no	—
340	#121	—	2	2	no	—
341	#121	—	2	2	no	—
342	C₄×D₄	—	2	2	no	—
343	C₄×D₄	—	2	2	no	—
344	C₄×D₄	—	4	4	no	—
345	C₂×C₄⋊C₄	—	2	1	no	—
346	C₂×C₄⋊C₄	—	2	1	no	—
347	C₂×C₄⋊C₄	—	2	2	no	—
348	C₂×C₄⋊C₄	—	2	1	no	—
349	C₂×C₄⋊C₄	—	2	1	no	—
350	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
351	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
352	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
353	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
354	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
355	C₂×C₂²⋊C₄	—	2	1	no	—
356	C₂×C₂²⋊C₄	—	2	1	no	—
357	C₂×C₂²⋊C₄	—	2	2	no	—
358	C₂×C₂²⋊C₄	—	2	1	no	—
359	C₂×C₂²⋊C₄	—	2	1	no	—
360	C₂×C₂²⋊C₄	—	2	1	no	—
361	C₂×C₄²	—	2	2	no	—
362	C₂×C₄²	—	2	2	no	—
363	C₂×C₄²	—	2	1	no	—
364	C₂×C₄²	D₄×C₄₁	1	1	yes	characteristic
365	C₂×C₄²	D₄×C₄₁	1	1	yes	characteristic
366	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
367	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
368	#107	—	2	4	no	—
369	#106	—	2	4	no	—
370	C₄⋊C₈	—	2	2	no	—
371	C₄⋊C₈	D₄×C₄₁	1	4	yes	complemented
372	#102	—	2	4	no	—
373	#102	—	2	4	no	—
374	C₂²⋊C₈	—	2	4	no	—
375	#97	—	2	4	no	—
376	#95	—	2	1	no	—
377	#95	—	2	1	no	—
378	#95	—	2	1	no	—
379	#95	—	2	2	no	—
380	#95	—	2	2	no	—
381	C₂⁴	—	2	1	no	—
382	C₂⁴	C₂×D₄×C₄₁	1	1	yes	characteristic
383	C₂×Q₈	—	4	2	no	—
384	C₂×Q₈	—	4	2	no	—
385	C₂×Q₈	—	4	2	no	—
386	C₂×D₄	—	2	4	no	—
387	C₂×D₄	—	2	1	no	—
388	C₂×D₄	—	2	1	no	—
389	C₂×D₄	—	2	1	no	—
390	C₂×D₄	—	2	1	no	—
391	C₂×D₄	—	2	1	no	—
392	C₂×D₄	—	4	2	no	—
393	C₂×D₄	—	4	2	no	—
394	C₂×D₄	#41×C₄₁	1	2	yes	—
395	C₂²×C₄	—	2	2	no	—
396	C₂²×C₄	—	2	1	no	—
397	C₂²×C₄	—	2	2	no	—
398	C₂²×C₄	—	2	2	no	—
399	C₂²×C₄	—	2	2	no	—
400	C₂²×C₄	—	2	2	no	—
401	C₂²×C₄	—	2	1	no	—
402	C₂²×C₄	—	2	1	no	—
403	C₂²×C₄	—	2	1	no	—
404	C₂²×C₄	—	2	1	no	—
405	C₂²×C₄	—	2	1	no	—
406	C₂²×C₄	—	2	1	no	—
407	C₂²×C₄	—	2	1	no	—
408	C₂²×C₄	—	2	1	no	—
409	C₂²×C₄	—	2	2	no	—
410	C₂²×C₄	—	2	2	no	—
411	C₂²×C₄	—	4	1	no	—
412	C₂²×C₄	—	4	2	no	—
413	C₂²×C₄	—	4	2	no	—
414	C₂²×C₄	—	4	2	no	—
415	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
416	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
417	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
418	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
419	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
420	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
421	C₂×C₈	—	2	2	no	—
422	C₂×C₈	—	2	2	no	—
423	C₂×C₈	—	2	2	no	—
424	C₂×C₈	—	2	2	no	—
425	C₂×C₈	—	2	2	no	—
426	C₂×C₈	C₂×D₄×C₄₁	1	4	yes	—
427	C₄⋊C₄	—	2	1	no	—
428	C₄⋊C₄	—	2	2	no	—
429	C₄⋊C₄	—	2	1	no	—
430	C₄⋊C₄	—	2	2	no	—
431	C₄⋊C₄	—	2	2	no	—
432	C₄⋊C₄	—	2	1	no	—
433	C₄⋊C₄	—	2	2	no	—
434	C₄⋊C₄	—	2	1	no	—
435	C₄⋊C₄	—	2	1	no	—
436	C₄⋊C₄	—	4	2	no	—
437	C₄⋊C₄	—	4	4	no	—
438	C₄⋊C₄	—	4	2	no	—
439	C₄⋊C₄	—	4	2	no	—
440	C₄⋊C₄	—	4	2	no	—
441	C₄⋊C₄	#41×C₄₁	1	2	yes	—
442	C₂²⋊C₄	—	2	4	no	—
443	C₂²⋊C₄	—	4	2	no	—
444	C₂²⋊C₄	—	4	2	no	—
445	C₂²⋊C₄	—	4	2	no	—
446	C₂²⋊C₄	—	4	4	no	—
447	C₂²⋊C₄	—	4	2	no	—
448	C₄²	—	2	2	no	—
449	C₄²	—	2	2	no	—
450	C₄²	—	2	1	no	—
451	C₄²	—	2	1	no	—
452	C₄²	—	4	2	no	—
453	C₄²	C₂×D₄×C₄₁	1	2	yes	—
454	C₄²	#41×C₄₁	1	2	yes	—
455	C₂³	—	2	1	no	—
456	C₂³	—	2	1	no	—
457	C₂³	—	2	1	no	—
458	C₂³	—	2	1	no	—
459	C₂³	—	2	1	no	—
460	C₂³	—	2	1	no	—
461	C₂³	—	2	2	no	—
462	C₂³	—	4	1	no	—
463	C₂³	—	4	1	no	—
464	C₂³	—	4	1	no	—
465	C₂³	—	4	1	no	—
466	C₂³	—	4	1	no	—
467	C₂³	—	4	1	no	—
468	C₂³	#137×C₄₁	1	2	yes	—
469	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
470	Q₈	—	8	4	no	—
471	D₄	—	2	2	no	—
472	D₄	—	2	2	no	—
473	D₄	—	4	8	no	—
474	D₄	—	4	1	no	—
475	D₄	—	4	1	no	—
476	C₂×C₄	—	2	1	no	—
477	C₂×C₄	—	2	1	no	—
478	C₂×C₄	—	2	1	no	—
479	C₂×C₄	—	2	1	no	—
480	C₂×C₄	—	2	1	no	—
481	C₂×C₄	—	2	1	no	—
482	C₂×C₄	—	2	2	no	—
483	C₂×C₄	—	2	1	no	—
484	C₂×C₄	—	2	1	no	—
485	C₂×C₄	—	2	1	no	—
486	C₂×C₄	—	2	1	no	—
487	C₂×C₄	—	2	1	no	—
488	C₂×C₄	—	4	4	no	—
489	C₂×C₄	—	4	1	no	—
490	C₂×C₄	—	4	1	no	—
491	C₂×C₄	—	4	1	no	—
492	C₂×C₄	—	4	1	no	—
493	C₂×C₄	—	4	1	no	—
494	C₂×C₄	—	4	1	no	—
495	C₂×C₄	—	4	4	no	—
496	C₂×C₄	—	4	1	no	—
497	C₂×C₄	—	4	2	no	—
498	C₂×C₄	—	4	2	no	—
499	C₂×C₄	—	4	1	no	—
500	C₂×C₄	—	4	1	no	—
501	C₂×C₄	—	4	2	no	—
502	C₂×C₄	—	4	1	no	—
503	C₂×C₄	—	4	2	no	—
504	C₂×C₄	—	4	1	no	—
505	C₂×C₄	—	4	2	no	—
506	C₂×C₄	—	4	1	no	—
507	C₂×C₄	—	4	2	no	—
508	C₂×C₄	—	8	4	no	—
509	C₂×C₄	#121×C₄₁	1	2	yes	—
510	C₂×C₄	#121×C₄₁	1	2	yes	—
511	C₂×C₄	AGL(1,ℤ/8)×C₄₁	1	2	yes	—
512	C₂×C₄	AGL(1,ℤ/8)×C₄₁	1	2	yes	—
513	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
514	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
515	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
516	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
517	C₂×C₄	2₋¹⁺⁴×C₄₁	1	1	yes	characteristic
518	C₂×C₄	2₋¹⁺⁴×C₄₁	1	1	yes	characteristic
519	C₈	—	2	4	no	—
520	C₈	—	4	2	no	—
521	C₂²	—	2	2	no	—
522	C₂²	—	2	2	no	—
523	C₂²	—	2	2	no	—
524	C₂²	—	4	1	no	—
525	C₂²	—	4	1	no	—
526	C₂²	—	4	1	no	—
527	C₂²	—	4	1	no	—
528	C₂²	—	4	2	no	—
529	C₂²	—	4	2	no	—
530	C₂²	—	4	2	no	—
531	C₂²	—	8	1	no	—
532	C₂²	—	8	1	no	—
533	C₂²	—	8	1	no	—
534	C₂²	—	8	1	no	—
535	C₂²	C₂×#121×C₄₁	1	1	yes	characteristic
536	C₂²	C₄₁×#525	1	1	yes	characteristic
537	C₂²	C₄₁×#536	1	1	yes	characteristic
538	C₂²	C₂×AGL(1,ℤ/8)×C₄₁	1	1	yes	characteristic
539	C₂²	C₂×AGL(1,ℤ/8)×C₄₁	1	1	yes	characteristic
540	C₂²	C₂×#137×C₄₁	1	1	yes	characteristic
541	C₂²	C₄₁×#575	1	1	yes	characteristic
542	C₄	—	2	2	no	—
543	C₄	—	4	1	no	—
544	C₄	—	4	1	no	—
545	C₄	—	4	2	no	—
546	C₄	—	4	1	no	—
547	C₄	—	8	1	no	—
548	C₄	—	8	2	no	—
549	C₄	—	8	2	no	—
550	C₄	—	8	1	no	—
551	C₄	C₄₁×#469	1	4	yes	—
552	C₄	C₄₁×#547	1	1	yes	characteristic
553	C₄	C₄₁×#548	1	1	yes	characteristic
554	C₄	C₄₁×#552	1	1	yes	characteristic
555	C₄	C₄₁×#556	1	1	yes	characteristic
556	C₂	—	4	2	no	—
557	C₂	—	8	2	no	—
558	C₂	C₄₁×#2415	1	1	yes	characteristic
559	C₂	C₂×C₄₁×#469	1	1	yes	characteristic
560	C₂	C₄₁×#3056	1	1	yes	characteristic
561	C₂	C₄₁×#3110	1	1	yes	characteristic
562	C₂	C₄₁×#3115	1	1	yes	characteristic
563	C₂	C₄₁×#3235	1	1	yes	characteristic
564	C₂	C₄₁×#3239	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₄₁	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₁
prime radical	C₂×#121×C₄₁	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₄₁ ◁ C₂²×C₄²×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₄₁×#474	C₂	semidirect
2. C₂×C₄₁×#432	C₂	semidirect
3. C₄₁×#2857	C₂	semidirect
5. C₄₁×#2076	C₂	semidirect
7. C₄₁×#1988	C₂	semidirect
8. C₄₁×#1948	C₂	semidirect
9. C₄₁×#1944	C₂	semidirect
10. C₄₁×#1936	C₂	semidirect
11. C₄₁×#1802	C₂	semidirect
88. C₄⋊C₈×C₄₁	D₄	semidirect
238. #24709	C₄₁	direct (N × H)
274. C₂×#474	C₂×C₄₁	semidirect
275. C₂×#432	C₂×C₄₁	semidirect
276. #2857	C₂×C₄₁	semidirect
278. #2076	C₂×C₄₁	semidirect
280. #1988	C₂×C₄₁	semidirect
281. #1948	C₂×C₄₁	semidirect
282. #1944	C₂×C₄₁	semidirect
283. #1936	C₂×C₄₁	semidirect
284. #1802	C₂×C₄₁	semidirect
327. C₄₁	#24709	direct (N × H)
371. C₄⋊C₈	D₄×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×#474	2
C₂×C₄₁×#432	2
C₄₁×#2857	2
C₄×#121×C₄₁	2
C₄₁×#2076	2
C₄₁×#2034	2
C₄₁×#1988	2
C₄₁×#1948	2
C₄₁×#1944	2
C₄₁×#1936	2
C₄₁×#1802	2
#24709	41

Subgroups — C41×#24709 #23800910

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#24709 #23800910