Subgroups — C₄₁×#33072 #23809273

Order 10496.

870 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₁×#2859	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄²×D₄×C₄₁	C₂	1	1	yes	maximal, characteristic
3	C₄₁×#1948	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₁×#1947	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₁×#1921	C₂	1	2	yes	maximal, complemented
6	C₄₁×#1919	C₂	1	2	yes	maximal, complemented
7	C₄₁×#1864	C₂	1	2	yes	maximal
8	C₄₁×#1862	C₂	1	2	yes	maximal
9	C₄₁×#1831	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄₁×#1802	C₂	1	1	yes	maximal, characteristic
11	C₄₁×#1802	C₂	1	1	yes	maximal, characteristic
12	C₂×#125×C₄₁	—	2	1	no	—
13	C₂×C₄×D₄×C₄₁	C₂²	1	1	yes	characteristic
14	C₂×C₄×D₄×C₄₁	C₂²	1	1	yes	characteristic
15	C₂×C₄×D₄×C₄₁	C₂²	1	1	yes	characteristic
16	C₂²×C₄²×C₄₁	—	2	1	no	—
17	C₂×#107×C₄₁	C₂²	1	2	yes	—
18	C₂×#106×C₄₁	C₂²	1	2	yes	—
19	C₂×C₄⋊C₈×C₄₁	C₂²	1	1	yes	characteristic
20	C₂×C₄⋊C₈×C₄₁	C₂²	1	1	yes	characteristic
21	C₂×#102×C₄₁	C₂²	1	2	yes	—
22	C₂×#102×C₄₁	C₂²	1	2	yes	—
23	C₄₁×#389	—	2	1	no	—
24	C₄₁×#389	—	2	1	no	—
25	C₄₁×#389	C₂²	1	2	yes	—
26	C₄₁×#389	C₂²	1	2	yes	—
27	C₄₁×#384	C₂²	1	1	yes	characteristic
28	C₄₁×#384	C₂²	1	1	yes	characteristic
29	C₄₁×#382	—	2	1	no	—
30	C₄×C₄⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
31	C₄×C₄⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
32	C₄×C₄⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
33	C₄×C₂²⋊C₄×C₄₁	—	2	1	no	—
34	C₄×C₂²⋊C₄×C₄₁	—	2	1	no	—
35	C₄×C₂²⋊C₄×C₄₁	—	2	1	no	—
36	C₄³×C₄₁	C₂²	1	1	yes	characteristic
37	C₄₁×#340	C₂²	1	2	yes	—
38	C₄₁×#340	C₂²	1	2	yes	—
39	C₄₁×#340	C₂²	1	2	yes	—
40	C₄₁×#340	C₂²	1	2	yes	—
41	C₄₁×#336	C₂²	1	2	yes	—
42	C₄₁×#336	C₂²	1	2	yes	—
43	C₂²×D₄×C₄₁	C₂³	1	1	yes	characteristic
44	C₂³×C₄×C₄₁	—	2	1	no	—
45	C₂³×C₄×C₄₁	—	2	1	no	—
46	C₂³×C₄×C₄₁	—	2	1	no	—
47	C₂²×C₈×C₄₁	C₂³	1	2	yes	—
48	C₂²×C₈×C₄₁	C₂³	1	2	yes	—
49	#125×C₄₁	—	4	4	no	—
50	C₄×D₄×C₄₁	—	2	2	no	—
51	C₄×D₄×C₄₁	—	2	2	no	—
52	C₄×D₄×C₄₁	—	2	2	no	—
53	C₄×D₄×C₄₁	—	2	2	no	—
54	C₄×D₄×C₄₁	—	2	2	no	—
55	C₄×D₄×C₄₁	Q₈	1	4	yes	—
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	—	2	2	no	—
60	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
61	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
62	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
63	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
64	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
65	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
66	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
67	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
68	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
69	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
70	C₂×C₄²×C₄₁	—	2	1	no	—
71	C₂×C₄²×C₄₁	—	2	1	no	—
72	C₂×C₄²×C₄₁	—	2	1	no	—
73	C₂×C₄²×C₄₁	—	4	4	no	—
74	C₂×C₄²×C₄₁	D₄	1	1	yes	characteristic
75	C₂×C₄²×C₄₁	D₄	1	1	yes	characteristic
76	C₂×C₄²×C₄₁	D₄	1	1	yes	characteristic
77	C₂×C₄²×C₄₁	D₄	1	1	yes	characteristic
78	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
79	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
80	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
81	#107×C₄₁	—	2	4	no	—
82	#106×C₄₁	—	2	4	no	—
83	C₄⋊C₈×C₄₁	—	2	2	no	—
84	C₄⋊C₈×C₄₁	—	2	2	no	—
85	#102×C₄₁	—	2	4	no	—
86	#102×C₄₁	—	2	4	no	—
87	#95×C₄₁	—	2	1	no	—
88	#95×C₄₁	—	2	1	no	—
89	#95×C₄₁	—	2	1	no	—
90	#95×C₄₁	—	2	2	no	—
91	#95×C₄₁	—	2	2	no	—
92	C₂⁴×C₄₁	—	2	1	no	—
93	C₂×D₄×C₄₁	—	2	1	no	—
94	C₂×D₄×C₄₁	—	2	1	no	—
95	C₂×D₄×C₄₁	—	2	1	no	—
96	C₂×D₄×C₄₁	C₂×Q₈	1	2	yes	—
97	C₂×D₄×C₄₁	#41	1	2	yes	—
98	C₂×D₄×C₄₁	#41	1	2	yes	—
99	C₂²×C₄×C₄₁	—	2	4	no	—
100	C₂²×C₄×C₄₁	—	2	4	no	—
101	C₂²×C₄×C₄₁	—	2	1	no	—
102	C₂²×C₄×C₄₁	—	2	1	no	—
103	C₂²×C₄×C₄₁	—	2	1	no	—
104	C₂²×C₄×C₄₁	—	2	4	no	—
105	C₂²×C₄×C₄₁	—	2	2	no	—
106	C₂²×C₄×C₄₁	—	2	2	no	—
107	C₂²×C₄×C₄₁	—	4	2	no	—
108	C₂²×C₄×C₄₁	—	4	2	no	—
109	C₂²×C₄×C₄₁	—	4	2	no	—
110	C₂²×C₄×C₄₁	—	4	2	no	—
111	C₂²×C₄×C₄₁	—	4	2	no	—
112	C₂²×C₄×C₄₁	—	4	2	no	—
113	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
114	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
115	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
116	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
117	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
118	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
119	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
120	C₂×C₈×C₄₁	—	2	2	no	—
121	C₂×C₈×C₄₁	—	2	2	no	—
122	C₂×C₈×C₄₁	—	2	2	no	—
123	C₂×C₈×C₄₁	—	2	2	no	—
124	C₂×C₈×C₄₁	—	2	2	no	—
125	C₂×C₈×C₄₁	—	2	2	no	—
126	C₄⋊C₄×C₄₁	—	2	1	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	2	no	—
131	C₄⋊C₄×C₄₁	—	2	2	no	—
132	C₄⋊C₄×C₄₁	—	2	2	no	—
133	C₄⋊C₄×C₄₁	—	4	2	no	—
134	C₄⋊C₄×C₄₁	—	4	2	no	—
135	C₄⋊C₄×C₄₁	—	4	4	no	—
136	C₄⋊C₄×C₄₁	—	4	2	no	—
137	C₄⋊C₄×C₄₁	—	4	2	no	—
138	C₄⋊C₄×C₄₁	—	4	4	no	—
139	C₄⋊C₄×C₄₁	C₂×Q₈	1	2	yes	—
140	C₄⋊C₄×C₄₁	#41	1	2	yes	—
141	C₄⋊C₄×C₄₁	#41	1	2	yes	—
142	C₂²⋊C₄×C₄₁	—	2	4	no	—
143	C₂²⋊C₄×C₄₁	—	2	4	no	—
144	C₂²⋊C₄×C₄₁	—	2	4	no	—
145	C₄²×C₄₁	—	2	2	no	—
146	C₄²×C₄₁	—	2	2	no	—
147	C₄²×C₄₁	—	2	2	no	—
148	C₄²×C₄₁	—	2	2	no	—
149	C₄²×C₄₁	—	2	1	no	—
150	C₄²×C₄₁	—	2	1	no	—
151	C₄²×C₄₁	—	2	1	no	—
152	C₄²×C₄₁	—	2	1	no	—
153	C₄²×C₄₁	—	4	2	no	—
154	C₄²×C₄₁	—	4	2	no	—
155	C₄²×C₄₁	—	4	2	no	—
156	C₄²×C₄₁	C₂×Q₈	1	2	yes	—
157	C₄²×C₄₁	#41	1	2	yes	—
158	C₂³×C₄₁	—	2	2	no	—
159	C₂³×C₄₁	—	2	2	no	—
160	C₂³×C₄₁	—	2	2	no	—
161	C₂³×C₄₁	—	4	1	no	—
162	C₂³×C₄₁	—	4	1	no	—
163	C₂³×C₄₁	—	4	1	no	—
164	C₂³×C₄₁	—	4	1	no	—
165	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
166	D₄×C₄₁	—	2	2	no	—
167	D₄×C₄₁	—	2	2	no	—
168	D₄×C₄₁	—	2	2	no	—
169	D₄×C₄₁	#125	1	4	yes	complemented
170	C₂×C₄×C₄₁	—	2	1	no	—
171	C₂×C₄×C₄₁	—	2	1	no	—
172	C₂×C₄×C₄₁	—	2	1	no	—
173	C₂×C₄×C₄₁	—	2	1	no	—
174	C₂×C₄×C₄₁	—	2	1	no	—
175	C₂×C₄×C₄₁	—	2	1	no	—
176	C₂×C₄×C₄₁	—	2	2	no	—
177	C₂×C₄×C₄₁	—	2	1	no	—
178	C₂×C₄×C₄₁	—	2	1	no	—
179	C₂×C₄×C₄₁	—	2	2	no	—
180	C₂×C₄×C₄₁	—	2	2	no	—
181	C₂×C₄×C₄₁	—	2	1	no	—
182	C₂×C₄×C₄₁	—	2	1	no	—
183	C₂×C₄×C₄₁	—	2	1	no	—
184	C₂×C₄×C₄₁	—	2	1	no	—
185	C₂×C₄×C₄₁	—	4	8	no	—
186	C₂×C₄×C₄₁	—	4	8	no	—
187	C₂×C₄×C₄₁	—	4	1	no	—
188	C₂×C₄×C₄₁	—	4	1	no	—
189	C₂×C₄×C₄₁	—	4	1	no	—
190	C₂×C₄×C₄₁	—	4	1	no	—
191	C₂×C₄×C₄₁	—	4	1	no	—
192	C₂×C₄×C₄₁	—	4	1	no	—
193	C₂×C₄×C₄₁	—	4	8	no	—
194	C₂×C₄×C₄₁	—	4	2	no	—
195	C₂×C₄×C₄₁	—	4	2	no	—
196	C₂×C₄×C₄₁	—	4	2	no	—
197	C₂×C₄×C₄₁	—	4	2	no	—
198	C₂×C₄×C₄₁	—	4	2	no	—
199	C₂×C₄×C₄₁	—	4	2	no	—
200	C₂×C₄×C₄₁	C₂²⋊Q₈	1	2	yes	—
201	C₂×C₄×C₄₁	C₂²⋊Q₈	1	2	yes	—
202	C₂×C₄×C₄₁	#135	1	2	yes	—
203	C₂×C₄×C₄₁	AGL(1,ℤ/8)	1	2	yes	—
204	C₂×C₄×C₄₁	AGL(1,ℤ/8)	1	2	yes	—
205	C₂×C₄×C₄₁	#137	1	2	yes	—
206	C₂×C₄×C₄₁	C₂²×Q₈	1	1	yes	characteristic
207	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
208	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
209	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
210	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
211	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
212	C₈×C₄₁	—	4	2	no	—
213	C₈×C₄₁	—	4	2	no	—
214	#33072	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
215	C₂²×C₄₁	—	2	4	no	—
216	C₂²×C₄₁	—	4	2	no	—
217	C₂²×C₄₁	—	4	2	no	—
218	C₂²×C₄₁	—	4	2	no	—
219	C₂²×C₄₁	—	4	2	no	—
220	C₂²×C₄₁	—	4	2	no	—
221	C₂²×C₄₁	—	4	2	no	—
222	C₂²×C₄₁	C₂×C₂²⋊Q₈	1	1	yes	characteristic
223	C₂²×C₄₁	#525	1	1	yes	characteristic
224	C₂²×C₄₁	#525	1	1	yes	characteristic
225	C₂²×C₄₁	C₂×#135	1	1	yes	characteristic
226	C₂²×C₄₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
227	C₂²×C₄₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
228	C₂²×C₄₁	C₂×#137	1	1	yes	characteristic
229	C₄×C₄₁	—	2	2	no	—
230	C₄×C₄₁	—	2	2	no	—
231	C₄×C₄₁	—	2	2	no	—
232	C₄×C₄₁	—	4	2	no	—
233	C₄×C₄₁	—	4	1	no	—
234	C₄×C₄₁	—	4	1	no	—
235	C₄×C₄₁	—	4	2	no	—
236	C₄×C₄₁	—	4	2	no	—
237	C₄×C₄₁	—	8	2	no	—
238	C₄×C₄₁	—	8	2	no	—
239	C₄×C₄₁	#478	1	4	yes	—
240	C₄×C₄₁	C₂×#125	1	1	yes	characteristic
241	C₄×C₄₁	#529	1	1	yes	characteristic
242	C₄×C₄₁	#529	1	1	yes	characteristic
243	C₄×C₄₁	#533	1	1	yes	characteristic
244	#2859	C₂×C₄₁	1	1	yes	characteristic, complemented
245	C₄²×D₄	C₂×C₄₁	1	1	yes	characteristic
246	#1948	C₂×C₄₁	1	1	yes	characteristic, complemented
247	#1947	C₂×C₄₁	1	1	yes	characteristic, complemented
248	#1921	C₂×C₄₁	1	2	yes	complemented
249	#1919	C₂×C₄₁	1	2	yes	complemented
250	#1864	C₂×C₄₁	1	2	yes	—
251	#1862	C₂×C₄₁	1	2	yes	—
252	#1831	C₂×C₄₁	1	1	yes	characteristic, complemented
253	#1802	C₂×C₄₁	1	1	yes	characteristic
254	#1802	C₂×C₄₁	1	1	yes	characteristic
255	C₂×C₄₁	—	4	4	no	—
256	C₂×C₄₁	#2851	1	1	yes	characteristic
257	C₂×C₄₁	C₂×#478	1	1	yes	characteristic
258	C₂×C₄₁	#3079	1	1	yes	characteristic
259	C₂×C₄₁	#3106	1	1	yes	characteristic
260	C₂×C₄₁	#3107	1	1	yes	characteristic
261	C₂×C₄₁	#3109	1	1	yes	characteristic
262	C₂×C₄₁	#3110	1	1	yes	characteristic
263	C₂×#125	—	2	1	no	—
264	C₂×C₄×D₄	C₂²×C₄₁	1	1	yes	characteristic
265	C₂×C₄×D₄	C₂²×C₄₁	1	1	yes	characteristic
266	C₂×C₄×D₄	C₂²×C₄₁	1	1	yes	characteristic
267	C₂²×C₄²	—	2	1	no	—
268	C₂×#107	C₂²×C₄₁	1	2	yes	—
269	C₂×#106	C₂²×C₄₁	1	2	yes	—
270	C₂×C₄⋊C₈	C₂²×C₄₁	1	1	yes	characteristic
271	C₂×C₄⋊C₈	C₂²×C₄₁	1	1	yes	characteristic
272	C₂×#102	C₂²×C₄₁	1	2	yes	—
273	C₂×#102	C₂²×C₄₁	1	2	yes	—
274	#389	—	2	1	no	—
275	#389	—	2	1	no	—
276	#389	C₂²×C₄₁	1	2	yes	—
277	#389	C₂²×C₄₁	1	2	yes	—
278	#384	C₂²×C₄₁	1	1	yes	characteristic
279	#384	C₂²×C₄₁	1	1	yes	characteristic
280	#382	—	2	1	no	—
281	C₄×C₄⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
282	C₄×C₄⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
283	C₄×C₄⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
284	C₄×C₂²⋊C₄	—	2	1	no	—
285	C₄×C₂²⋊C₄	—	2	1	no	—
286	C₄×C₂²⋊C₄	—	2	1	no	—
287	C₄³	C₂²×C₄₁	1	1	yes	characteristic
288	#340	C₂²×C₄₁	1	2	yes	—
289	#340	C₂²×C₄₁	1	2	yes	—
290	#340	C₂²×C₄₁	1	2	yes	—
291	#340	C₂²×C₄₁	1	2	yes	—
292	#336	C₂²×C₄₁	1	2	yes	—
293	#336	C₂²×C₄₁	1	2	yes	—
294	C₄₁	#33072	1	1	yes	characteristic, direct product factor, Sylow
295	C₂²×D₄	C₂³×C₄₁	1	1	yes	characteristic
296	C₂³×C₄	—	2	1	no	—
297	C₂³×C₄	—	2	1	no	—
298	C₂³×C₄	—	2	1	no	—
299	C₂²×C₈	C₂³×C₄₁	1	2	yes	—
300	C₂²×C₈	C₂³×C₄₁	1	2	yes	—
301	#125	—	4	4	no	—
302	C₄×D₄	—	2	2	no	—
303	C₄×D₄	—	2	2	no	—
304	C₄×D₄	—	2	2	no	—
305	C₄×D₄	—	2	2	no	—
306	C₄×D₄	—	2	2	no	—
307	C₄×D₄	Q₈×C₄₁	1	4	yes	—
308	C₂×C₄⋊C₄	—	2	1	no	—
309	C₂×C₄⋊C₄	—	2	1	no	—
310	C₂×C₄⋊C₄	—	2	2	no	—
311	C₂×C₄⋊C₄	—	2	2	no	—
312	C₂×C₄⋊C₄	—	2	1	no	—
313	C₂×C₄⋊C₄	—	2	1	no	—
314	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
315	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
316	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
317	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
318	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
319	C₂×C₂²⋊C₄	—	2	1	no	—
320	C₂×C₂²⋊C₄	—	2	1	no	—
321	C₂×C₂²⋊C₄	—	2	1	no	—
322	C₂×C₄²	—	2	1	no	—
323	C₂×C₄²	—	2	1	no	—
324	C₂×C₄²	—	2	1	no	—
325	C₂×C₄²	—	4	4	no	—
326	C₂×C₄²	D₄×C₄₁	1	1	yes	characteristic
327	C₂×C₄²	D₄×C₄₁	1	1	yes	characteristic
328	C₂×C₄²	D₄×C₄₁	1	1	yes	characteristic
329	C₂×C₄²	D₄×C₄₁	1	1	yes	characteristic
330	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
331	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
332	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
333	#107	—	2	4	no	—
334	#106	—	2	4	no	—
335	C₄⋊C₈	—	2	2	no	—
336	C₄⋊C₈	—	2	2	no	—
337	#102	—	2	4	no	—
338	#102	—	2	4	no	—
339	#95	—	2	1	no	—
340	#95	—	2	1	no	—
341	#95	—	2	1	no	—
342	#95	—	2	2	no	—
343	#95	—	2	2	no	—
344	C₂⁴	—	2	1	no	—
345	C₂×D₄	—	2	1	no	—
346	C₂×D₄	—	2	1	no	—
347	C₂×D₄	—	2	1	no	—
348	C₂×D₄	C₂×Q₈×C₄₁	1	2	yes	—
349	C₂×D₄	#41×C₄₁	1	2	yes	—
350	C₂×D₄	#41×C₄₁	1	2	yes	—
351	C₂²×C₄	—	2	4	no	—
352	C₂²×C₄	—	2	4	no	—
353	C₂²×C₄	—	2	1	no	—
354	C₂²×C₄	—	2	1	no	—
355	C₂²×C₄	—	2	1	no	—
356	C₂²×C₄	—	2	4	no	—
357	C₂²×C₄	—	2	2	no	—
358	C₂²×C₄	—	2	2	no	—
359	C₂²×C₄	—	4	2	no	—
360	C₂²×C₄	—	4	2	no	—
361	C₂²×C₄	—	4	2	no	—
362	C₂²×C₄	—	4	2	no	—
363	C₂²×C₄	—	4	2	no	—
364	C₂²×C₄	—	4	2	no	—
365	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
366	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
367	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
368	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
369	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
370	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
371	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
372	C₂×C₈	—	2	2	no	—
373	C₂×C₈	—	2	2	no	—
374	C₂×C₈	—	2	2	no	—
375	C₂×C₈	—	2	2	no	—
376	C₂×C₈	—	2	2	no	—
377	C₂×C₈	—	2	2	no	—
378	C₄⋊C₄	—	2	1	no	—
379	C₄⋊C₄	—	2	1	no	—
380	C₄⋊C₄	—	2	1	no	—
381	C₄⋊C₄	—	2	2	no	—
382	C₄⋊C₄	—	2	2	no	—
383	C₄⋊C₄	—	2	2	no	—
384	C₄⋊C₄	—	2	2	no	—
385	C₄⋊C₄	—	4	2	no	—
386	C₄⋊C₄	—	4	2	no	—
387	C₄⋊C₄	—	4	4	no	—
388	C₄⋊C₄	—	4	2	no	—
389	C₄⋊C₄	—	4	4	no	—
390	C₄⋊C₄	—	4	2	no	—
391	C₄⋊C₄	C₂×Q₈×C₄₁	1	2	yes	—
392	C₄⋊C₄	#41×C₄₁	1	2	yes	—
393	C₄⋊C₄	#41×C₄₁	1	2	yes	—
394	C₂²⋊C₄	—	2	4	no	—
395	C₂²⋊C₄	—	2	4	no	—
396	C₂²⋊C₄	—	2	4	no	—
397	C₄²	—	2	2	no	—
398	C₄²	—	2	2	no	—
399	C₄²	—	2	2	no	—
400	C₄²	—	2	2	no	—
401	C₄²	—	2	1	no	—
402	C₄²	—	2	1	no	—
403	C₄²	—	2	1	no	—
404	C₄²	—	2	1	no	—
405	C₄²	—	4	2	no	—
406	C₄²	—	4	2	no	—
407	C₄²	—	4	2	no	—
408	C₄²	C₂×Q₈×C₄₁	1	2	yes	—
409	C₄²	#41×C₄₁	1	2	yes	—
410	C₂³	—	2	2	no	—
411	C₂³	—	2	2	no	—
412	C₂³	—	2	2	no	—
413	C₂³	—	4	1	no	—
414	C₂³	—	4	1	no	—
415	C₂³	—	4	1	no	—
416	C₂³	—	4	1	no	—
417	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
418	D₄	—	2	2	no	—
419	D₄	—	2	2	no	—
420	D₄	—	2	2	no	—
421	D₄	#125×C₄₁	1	4	yes	complemented
422	C₂×C₄	—	2	1	no	—
423	C₂×C₄	—	2	1	no	—
424	C₂×C₄	—	2	1	no	—
425	C₂×C₄	—	2	1	no	—
426	C₂×C₄	—	2	1	no	—
427	C₂×C₄	—	2	1	no	—
428	C₂×C₄	—	2	2	no	—
429	C₂×C₄	—	2	1	no	—
430	C₂×C₄	—	2	1	no	—
431	C₂×C₄	—	2	2	no	—
432	C₂×C₄	—	2	2	no	—
433	C₂×C₄	—	2	1	no	—
434	C₂×C₄	—	2	1	no	—
435	C₂×C₄	—	2	1	no	—
436	C₂×C₄	—	2	1	no	—
437	C₂×C₄	—	4	8	no	—
438	C₂×C₄	—	4	8	no	—
439	C₂×C₄	—	4	1	no	—
440	C₂×C₄	—	4	1	no	—
441	C₂×C₄	—	4	1	no	—
442	C₂×C₄	—	4	1	no	—
443	C₂×C₄	—	4	1	no	—
444	C₂×C₄	—	4	1	no	—
445	C₂×C₄	—	4	8	no	—
446	C₂×C₄	—	4	2	no	—
447	C₂×C₄	—	4	2	no	—
448	C₂×C₄	—	4	2	no	—
449	C₂×C₄	—	4	2	no	—
450	C₂×C₄	—	4	2	no	—
451	C₂×C₄	—	4	2	no	—
452	C₂×C₄	C₂²⋊Q₈×C₄₁	1	2	yes	—
453	C₂×C₄	C₂²⋊Q₈×C₄₁	1	2	yes	—
454	C₂×C₄	#135×C₄₁	1	2	yes	—
455	C₂×C₄	AGL(1,ℤ/8)×C₄₁	1	2	yes	—
456	C₂×C₄	AGL(1,ℤ/8)×C₄₁	1	2	yes	—
457	C₂×C₄	#137×C₄₁	1	2	yes	—
458	C₂×C₄	C₂²×Q₈×C₄₁	1	1	yes	characteristic
459	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
460	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
461	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
462	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
463	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
464	C₈	—	4	2	no	—
465	C₈	—	4	2	no	—
466	C₂²	—	2	4	no	—
467	C₂²	—	4	2	no	—
468	C₂²	—	4	2	no	—
469	C₂²	—	4	2	no	—
470	C₂²	—	4	2	no	—
471	C₂²	—	4	2	no	—
472	C₂²	—	4	2	no	—
473	C₂²	C₂×C₂²⋊Q₈×C₄₁	1	1	yes	characteristic
474	C₂²	C₄₁×#525	1	1	yes	characteristic
475	C₂²	C₄₁×#525	1	1	yes	characteristic
476	C₂²	C₂×#135×C₄₁	1	1	yes	characteristic
477	C₂²	C₂×AGL(1,ℤ/8)×C₄₁	1	1	yes	characteristic
478	C₂²	C₂×AGL(1,ℤ/8)×C₄₁	1	1	yes	characteristic
479	C₂²	C₂×#137×C₄₁	1	1	yes	characteristic
480	C₄	—	2	2	no	—
481	C₄	—	2	2	no	—
482	C₄	—	2	2	no	—
483	C₄	—	4	2	no	—
484	C₄	—	4	1	no	—
485	C₄	—	4	1	no	—
486	C₄	—	4	2	no	—
487	C₄	—	4	2	no	—
488	C₄	—	8	2	no	—
489	C₄	—	8	2	no	—
490	C₄	C₄₁×#478	1	4	yes	—
491	C₄	C₂×#125×C₄₁	1	1	yes	characteristic
492	C₄	C₄₁×#529	1	1	yes	characteristic
493	C₄	C₄₁×#529	1	1	yes	characteristic
494	C₄	C₄₁×#533	1	1	yes	characteristic
495	C₂	—	4	4	no	—
496	C₂	C₄₁×#2851	1	1	yes	characteristic
497	C₂	C₂×C₄₁×#478	1	1	yes	characteristic
498	C₂	C₄₁×#3079	1	1	yes	characteristic
499	C₂	C₄₁×#3106	1	1	yes	characteristic
500	C₂	C₄₁×#3107	1	1	yes	characteristic
501	C₂	C₄₁×#3109	1	1	yes	characteristic
502	C₂	C₄₁×#3110	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 ◁ C₄³×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₄₁×#2859	C₂	semidirect
3. C₄₁×#1948	C₂	semidirect
4. C₄₁×#1947	C₂	semidirect
5. C₄₁×#1921	C₂	semidirect
6. C₄₁×#1919	C₂	semidirect
9. C₄₁×#1831	C₂	semidirect
169. D₄×C₄₁	#125	semidirect
214. #33072	C₄₁	direct (N × H)
244. #2859	C₂×C₄₁	semidirect
246. #1948	C₂×C₄₁	semidirect
247. #1947	C₂×C₄₁	semidirect
248. #1921	C₂×C₄₁	semidirect
249. #1919	C₂×C₄₁	semidirect
252. #1831	C₂×C₄₁	semidirect
294. C₄₁	#33072	direct (N × H)
421. D₄	#125×C₄₁	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₄₁×#2859	2
C₄²×D₄×C₄₁	2
C₄₁×#1948	2
C₄₁×#1947	2
C₄₁×#1921	2
C₄₁×#1919	2
C₄₁×#1864	2
C₄₁×#1862	2
C₄₁×#1831	2
C₄₁×#1802	2
#33072	41

Subgroups — C41×#33072 #23809273

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#33072 #23809273