Subgroups — C₄₁×#61825 #23838026

Order 10496.

1990 conjugacy classes of subgroups.

The subgroup lattice has 462 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₁×#3497	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄₁×#554	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₁×#3384	C₂	1	8	yes	maximal, complemented
4	C₄₁×#3366	C₂	1	8	yes	maximal, complemented
5	C₄₁×#3234	C₂	1	4	yes	maximal, complemented
6	C₄₁×#3227	C₂	1	2	yes	maximal, complemented
7	C₄₁×#3109	C₂	1	4	yes	maximal, complemented
8	C₄₁×#3100	C₂	1	2	yes	maximal, complemented
9	C₄₁×#2983	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×2₋¹⁺⁴×C₄₁	—	2	1	no	—
11	C₄₁×#554	—	2	4	no	—
12	C₄₁×#554	C₂²	1	8	yes	—
13	C₄₁×#550	C₂²	1	4	yes	complemented
14	D₄×Q₈×C₄₁	C₂²	1	4	yes	complemented
15	C₄₁×#548	—	2	4	no	—
16	C₄₁×#537	—	2	1	no	—
17	C₄₁×#537	—	2	2	no	—
18	C₄₁×#532	C₂²	1	2	yes	—
19	C₄₁×#532	C₂²	1	4	yes	—
20	C₂×C₄⋊Q₈×C₄₁	C₂²	1	1	yes	characteristic
21	C₂×#125×C₄₁	C₂²	1	2	yes	—
22	C₂×C₂²⋊Q₈×C₄₁	—	2	1	no	—
23	C₂×C₂²⋊Q₈×C₄₁	—	2	2	no	—
24	C₂×C₄×Q₈×C₄₁	C₂²	1	1	yes	characteristic
25	C₂×C₄×D₄×C₄₁	C₂²	1	1	yes	characteristic
26	C₂×C₄×D₄×C₄₁	C₂²	1	2	yes	—
27	C₂²×C₄⋊C₄×C₄₁	—	2	1	no	—
28	C₄₁×#501	C₂²	1	8	yes	complemented
29	C₄₁×#498	C₂²	1	4	yes	complemented
30	C₄₁×#490	C₂²	1	8	yes	complemented
31	C₄₁×#486	C₂²	1	4	yes	complemented
32	C₄₁×#481	C₂²	1	8	yes	—
33	C₄₁×#480	C₂²	1	4	yes	—
34	C₄₁×#478	C₂²	1	16	yes	complemented
35	C₄₁×#476	C₂²	1	8	yes	—
36	C₄₁×#476	C₂²	1	8	yes	complemented
37	C₄₁×#474	C₂²	1	4	yes	—
38	C₄₁×#459	C₂²	1	4	yes	—
39	C₄₁×#459	C₂²	1	8	yes	—
40	C₄₁×#447	C₂²	1	4	yes	—
41	C₄₁×#446	C₂²	1	8	yes	complemented
42	C₄₁×#442	C₂²	1	16	yes	—
43	C₄×D₈×C₄₁	C₂²	1	8	yes	—
44	C₄₁×#432	C₂²	1	4	yes	—
45	C₄₁×#431	C₂²	1	2	yes	—
46	2₋¹⁺⁴×C₄₁	—	4	8	no	—
47	C₂×#41×C₄₁	—	2	4	no	—
48	C₂×#41×C₄₁	—	2	4	no	—
49	C₂×#41×C₄₁	—	2	2	no	—
50	C₂²×Q₈×C₄₁	—	2	4	no	—
51	C₂²×Q₈×C₄₁	—	2	1	no	—
52	C₂²×Q₈×C₄₁	D₄	1	1	yes	characteristic
53	C₂²×D₄×C₄₁	C₂³	1	1	yes	characteristic
54	C₂³×C₄×C₄₁	—	2	1	no	—
55	C₂³×C₄×C₄₁	—	2	2	no	—
56	C₂×D₈×C₄₁	C₂³	1	8	yes	—
57	C₄⋊Q₈×C₄₁	—	2	2	no	—
58	C₄⋊Q₈×C₄₁	C₂³	1	4	yes	—
59	C₄⋊Q₈×C₄₁	C₂³	1	4	yes	—
60	C₄⋊Q₈×C₄₁	C₂³	1	2	yes	—
61	#127×C₄₁	C₂³	1	2	yes	—
62	#127×C₄₁	C₂³	1	4	yes	—
63	#125×C₄₁	—	2	4	no	—
64	#125×C₄₁	C₂³	1	8	yes	—
65	#124×C₄₁	—	2	4	no	—
66	#124×C₄₁	—	2	2	no	—
67	C₂²⋊Q₈×C₄₁	—	2	8	no	—
68	C₂²⋊Q₈×C₄₁	—	2	16	no	—
69	C₂²⋊Q₈×C₄₁	—	2	4	no	—
70	C₂²⋊Q₈×C₄₁	—	2	8	no	—
71	#121×C₄₁	—	2	2	no	—
72	#121×C₄₁	—	2	4	no	—
73	#121×C₄₁	—	2	4	no	—
74	#121×C₄₁	—	2	8	no	—
75	#121×C₄₁	C₂³	1	4	yes	—
76	C₄×Q₈×C₄₁	D₄	1	4	yes	—
77	C₄×Q₈×C₄₁	C₂³	1	4	yes	—
78	C₄×D₄×C₄₁	—	2	4	no	—
79	C₄×D₄×C₄₁	—	2	2	no	—
80	C₄×D₄×C₄₁	—	2	4	no	—
81	C₄×D₄×C₄₁	—	2	2	no	—
82	C₄×D₄×C₄₁	C₂³	1	4	yes	—
83	C₄×D₄×C₄₁	C₂³	1	8	yes	—
84	C₄×D₄×C₄₁	C₂³	1	4	yes	—
85	C₄×D₄×C₄₁	C₂³	1	8	yes	—
86	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
87	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
88	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
89	C₂×C₄⋊C₄×C₄₁	—	2	8	no	—
90	C₂×C₄⋊C₄×C₄₁	D₄	1	1	yes	characteristic
91	C₂×C₄⋊C₄×C₄₁	D₄	1	2	yes	—
92	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
93	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
94	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
95	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
96	C₂×C₄²×C₄₁	C₂³	1	2	yes	—
97	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
98	#107×C₄₁	C₂³	1	8	yes	—
99	#106×C₄₁	C₂³	1	16	yes	—
100	C₄⋊C₈×C₄₁	C₂³	1	4	yes	—
101	C₄⋊C₈×C₄₁	C₂³	1	8	yes	—
102	#102×C₄₁	C₂³	1	8	yes	—
103	#102×C₄₁	C₂³	1	8	yes	—
104	#102×C₄₁	C₂³	1	16	yes	—
105	C₂²⋊C₈×C₄₁	C₂³	1	4	yes	—
106	#97×C₄₁	C₂³	1	8	yes	—
107	C₄×C₈×C₄₁	C₂³	1	4	yes	—
108	C₂⁴×C₄₁	—	2	1	no	—
109	#41×C₄₁	—	4	16	no	—
110	#41×C₄₁	—	4	16	no	—
111	#41×C₄₁	—	4	8	no	—
112	C₂×Q₈×C₄₁	—	2	4	no	—
113	C₂×Q₈×C₄₁	—	2	4	no	—
114	C₂×Q₈×C₄₁	—	2	2	no	—
115	C₂×Q₈×C₄₁	—	2	4	no	—
116	C₂×Q₈×C₄₁	—	4	16	no	—
117	C₂×Q₈×C₄₁	—	8	2	no	—
118	C₂×Q₈×C₄₁	C₂×D₄	1	4	yes	—
119	C₂×D₄×C₄₁	—	2	4	no	—
120	C₂×D₄×C₄₁	—	2	4	no	—
121	C₂×D₄×C₄₁	—	2	1	no	—
122	C₂×D₄×C₄₁	—	2	4	no	—
123	C₂×D₄×C₄₁	—	2	2	no	—
124	C₂×D₄×C₄₁	—	2	2	no	—
125	C₂×D₄×C₄₁	—	2	4	no	—
126	C₂×D₄×C₄₁	C₂⁴	1	4	yes	—
127	C₂×D₄×C₄₁	C₂⁴	1	2	yes	—
128	C₂²×C₄×C₄₁	—	2	1	no	—
129	C₂²×C₄×C₄₁	—	2	2	no	—
130	C₂²×C₄×C₄₁	—	2	4	no	—
131	C₂²×C₄×C₄₁	—	2	8	no	—
132	C₂²×C₄×C₄₁	—	2	4	no	—
133	C₂²×C₄×C₄₁	—	2	8	no	—
134	C₂²×C₄×C₄₁	—	4	4	no	—
135	C₂²×C₄×C₄₁	—	8	4	no	—
136	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
137	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
138	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
139	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
140	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
141	D₈×C₄₁	—	2	16	no	—
142	C₂×C₈×C₄₁	C₂⁴	1	8	yes	—
143	C₄⋊C₄×C₄₁	—	2	8	no	—
144	C₄⋊C₄×C₄₁	—	2	4	no	—
145	C₄⋊C₄×C₄₁	—	2	8	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	4	no	—
150	C₄⋊C₄×C₄₁	C₂×D₄	1	4	yes	—
151	C₄⋊C₄×C₄₁	C₂×D₄	1	8	yes	—
152	C₄⋊C₄×C₄₁	C₂⁴	1	4	yes	—
153	C₄⋊C₄×C₄₁	C₂⁴	1	2	yes	—
154	C₄⋊C₄×C₄₁	C₂⁴	1	4	yes	—
155	C₂²⋊C₄×C₄₁	—	2	4	no	—
156	C₂²⋊C₄×C₄₁	—	2	8	no	—
157	C₂²⋊C₄×C₄₁	—	2	4	no	—
158	C₂²⋊C₄×C₄₁	—	2	4	no	—
159	C₂²⋊C₄×C₄₁	—	2	8	no	—
160	C₄²×C₄₁	C₂×D₄	1	4	yes	—
161	C₄²×C₄₁	C₂×D₄	1	2	yes	—
162	C₄²×C₄₁	C₂⁴	1	2	yes	—
163	C₄²×C₄₁	C₂⁴	1	4	yes	—
164	C₂³×C₄₁	—	2	4	no	—
165	C₂³×C₄₁	—	2	2	no	—
166	C₂³×C₄₁	—	2	4	no	—
167	C₂³×C₄₁	—	4	2	no	—
168	C₂³×C₄₁	—	4	2	no	—
169	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
170	Q₈×C₄₁	—	2	8	no	—
171	Q₈×C₄₁	—	4	8	no	—
172	Q₈×C₄₁	—	4	4	no	—
173	Q₈×C₄₁	—	8	4	no	—
174	D₄×C₄₁	—	2	4	no	—
175	D₄×C₄₁	—	2	2	no	—
176	D₄×C₄₁	—	2	8	no	—
177	D₄×C₄₁	—	4	8	no	—
178	D₄×C₄₁	—	4	8	no	—
179	D₄×C₄₁	—	4	4	no	—
180	D₄×C₄₁	—	8	4	no	—
181	D₄×C₄₁	—	8	2	no	—
182	D₄×C₄₁	2₋¹⁺⁴	1	4	yes	complemented
183	C₂×C₄×C₄₁	—	2	4	no	—
184	C₂×C₄×C₄₁	—	2	2	no	—
185	C₂×C₄×C₄₁	—	2	4	no	—
186	C₂×C₄×C₄₁	—	2	2	no	—
187	C₂×C₄×C₄₁	—	2	4	no	—
188	C₂×C₄×C₄₁	—	4	2	no	—
189	C₂×C₄×C₄₁	—	4	1	no	—
190	C₂×C₄×C₄₁	—	4	16	no	—
191	C₂×C₄×C₄₁	—	4	4	no	—
192	C₂×C₄×C₄₁	—	4	2	no	—
193	C₂×C₄×C₄₁	—	4	8	no	—
194	C₂×C₄×C₄₁	—	4	8	no	—
195	C₂×C₄×C₄₁	—	8	8	no	—
196	C₂×C₄×C₄₁	AGL(1,ℤ/8)	1	4	yes	—
197	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
198	C₂×C₄×C₄₁	C₂²×D₄	1	2	yes	—
199	C₂×C₄×C₄₁	C₂²×D₄	1	4	yes	—
200	C₂×C₄×C₄₁	C₂²×D₄	1	4	yes	—
201	C₂×C₄×C₄₁	C₂²×D₄	1	2	yes	—
202	C₂×C₄×C₄₁	C₂⁵	1	1	yes	characteristic
203	C₈×C₄₁	—	2	8	no	—
204	#61825	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
205	C₂²×C₄₁	—	2	1	no	—
206	C₂²×C₄₁	—	2	1	no	—
207	C₂²×C₄₁	—	2	4	no	—
208	C₂²×C₄₁	—	4	8	no	—
209	C₂²×C₄₁	—	4	2	no	—
210	C₂²×C₄₁	—	4	2	no	—
211	C₂²×C₄₁	—	4	4	no	—
212	C₂²×C₄₁	—	4	4	no	—
213	C₂²×C₄₁	—	4	4	no	—
214	C₂²×C₄₁	C₂×AGL(1,ℤ/8)	1	2	yes	—
215	C₂²×C₄₁	C₂³×D₄	1	1	yes	characteristic
216	C₄×C₄₁	—	2	4	no	—
217	C₄×C₄₁	—	2	2	no	—
218	C₄×C₄₁	—	2	1	no	—
219	C₄×C₄₁	—	2	4	no	—
220	C₄×C₄₁	—	4	4	no	—
221	C₄×C₄₁	—	4	2	no	—
222	C₄×C₄₁	—	4	4	no	—
223	C₄×C₄₁	C₂×AGL(1,ℤ/8)	1	4	yes	—
224	C₄×C₄₁	C₂×2₋¹⁺⁴	1	2	yes	—
225	#3497	C₂×C₄₁	1	1	yes	characteristic, complemented
226	C₂×#554	C₂×C₄₁	1	1	yes	characteristic, complemented
227	#3384	C₂×C₄₁	1	8	yes	complemented
228	#3366	C₂×C₄₁	1	8	yes	complemented
229	#3234	C₂×C₄₁	1	4	yes	complemented
230	#3227	C₂×C₄₁	1	2	yes	complemented
231	#3109	C₂×C₄₁	1	4	yes	complemented
232	#3100	C₂×C₄₁	1	2	yes	complemented
233	#2983	C₂×C₄₁	1	1	yes	characteristic, complemented
234	C₂×C₄₁	—	2	2	no	—
235	C₂×C₄₁	—	4	4	no	—
236	C₂×C₄₁	—	8	4	no	—
237	C₂×C₄₁	#3486	1	1	yes	characteristic
238	C₂×C₄₁	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
239	C₂×C₄₁	#3585	1	1	yes	characteristic
240	C₂×2₋¹⁺⁴	—	2	1	no	—
241	#554	—	2	4	no	—
242	#554	C₂²×C₄₁	1	8	yes	—
243	#550	C₂²×C₄₁	1	4	yes	complemented
244	D₄×Q₈	C₂²×C₄₁	1	4	yes	complemented
245	#548	—	2	4	no	—
246	#537	—	2	1	no	—
247	#537	—	2	2	no	—
248	#532	C₂²×C₄₁	1	2	yes	—
249	#532	C₂²×C₄₁	1	4	yes	—
250	C₂×C₄⋊Q₈	C₂²×C₄₁	1	1	yes	characteristic
251	C₂×#125	C₂²×C₄₁	1	2	yes	—
252	C₂×C₂²⋊Q₈	—	2	1	no	—
253	C₂×C₂²⋊Q₈	—	2	2	no	—
254	C₂×C₄×Q₈	C₂²×C₄₁	1	1	yes	characteristic
255	C₂×C₄×D₄	C₂²×C₄₁	1	1	yes	characteristic
256	C₂×C₄×D₄	C₂²×C₄₁	1	2	yes	—
257	C₂²×C₄⋊C₄	—	2	1	no	—
258	#501	C₂²×C₄₁	1	8	yes	complemented
259	#498	C₂²×C₄₁	1	4	yes	complemented
260	#490	C₂²×C₄₁	1	8	yes	complemented
261	#486	C₂²×C₄₁	1	4	yes	complemented
262	#481	C₂²×C₄₁	1	8	yes	—
263	#480	C₂²×C₄₁	1	4	yes	—
264	#478	C₂²×C₄₁	1	16	yes	complemented
265	#476	C₂²×C₄₁	1	8	yes	—
266	#476	C₂²×C₄₁	1	8	yes	complemented
267	#474	C₂²×C₄₁	1	4	yes	—
268	#459	C₂²×C₄₁	1	4	yes	—
269	#459	C₂²×C₄₁	1	8	yes	—
270	#447	C₂²×C₄₁	1	4	yes	—
271	#446	C₂²×C₄₁	1	8	yes	complemented
272	#442	C₂²×C₄₁	1	16	yes	—
273	C₄×D₈	C₂²×C₄₁	1	8	yes	—
274	#432	C₂²×C₄₁	1	4	yes	—
275	#431	C₂²×C₄₁	1	2	yes	—
276	C₄₁	#61825	1	1	yes	characteristic, direct product factor, Sylow
277	2₋¹⁺⁴	—	4	8	no	—
278	C₂×#41	—	2	4	no	—
279	C₂×#41	—	2	4	no	—
280	C₂×#41	—	2	2	no	—
281	C₂²×Q₈	—	2	4	no	—
282	C₂²×Q₈	—	2	1	no	—
283	C₂²×Q₈	D₄×C₄₁	1	1	yes	characteristic
284	C₂²×D₄	C₂³×C₄₁	1	1	yes	characteristic
285	C₂³×C₄	—	2	1	no	—
286	C₂³×C₄	—	2	2	no	—
287	C₂×D₈	C₂³×C₄₁	1	8	yes	—
288	C₄⋊Q₈	—	2	2	no	—
289	C₄⋊Q₈	C₂³×C₄₁	1	4	yes	—
290	C₄⋊Q₈	C₂³×C₄₁	1	2	yes	—
291	C₄⋊Q₈	C₂³×C₄₁	1	4	yes	—
292	#127	C₂³×C₄₁	1	2	yes	—
293	#127	C₂³×C₄₁	1	4	yes	—
294	#125	—	2	4	no	—
295	#125	C₂³×C₄₁	1	8	yes	—
296	#124	—	2	4	no	—
297	#124	—	2	2	no	—
298	C₂²⋊Q₈	—	2	8	no	—
299	C₂²⋊Q₈	—	2	16	no	—
300	C₂²⋊Q₈	—	2	4	no	—
301	C₂²⋊Q₈	—	2	8	no	—
302	#121	—	2	2	no	—
303	#121	—	2	4	no	—
304	#121	—	2	4	no	—
305	#121	—	2	8	no	—
306	#121	C₂³×C₄₁	1	4	yes	—
307	C₄×Q₈	D₄×C₄₁	1	4	yes	—
308	C₄×Q₈	C₂³×C₄₁	1	4	yes	—
309	C₄×D₄	—	2	4	no	—
310	C₄×D₄	—	2	2	no	—
311	C₄×D₄	—	2	4	no	—
312	C₄×D₄	—	2	2	no	—
313	C₄×D₄	C₂³×C₄₁	1	4	yes	—
314	C₄×D₄	C₂³×C₄₁	1	8	yes	—
315	C₄×D₄	C₂³×C₄₁	1	4	yes	—
316	C₄×D₄	C₂³×C₄₁	1	8	yes	—
317	C₂×C₄⋊C₄	—	2	2	no	—
318	C₂×C₄⋊C₄	—	2	1	no	—
319	C₂×C₄⋊C₄	—	2	2	no	—
320	C₂×C₄⋊C₄	—	2	8	no	—
321	C₂×C₄⋊C₄	D₄×C₄₁	1	1	yes	characteristic
322	C₂×C₄⋊C₄	D₄×C₄₁	1	2	yes	—
323	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
324	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
325	C₂×C₂²⋊C₄	—	2	1	no	—
326	C₂×C₂²⋊C₄	—	2	2	no	—
327	C₂×C₄²	C₂³×C₄₁	1	2	yes	—
328	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
329	#107	C₂³×C₄₁	1	8	yes	—
330	#106	C₂³×C₄₁	1	16	yes	—
331	C₄⋊C₈	C₂³×C₄₁	1	4	yes	—
332	C₄⋊C₈	C₂³×C₄₁	1	8	yes	—
333	#102	C₂³×C₄₁	1	8	yes	—
334	#102	C₂³×C₄₁	1	8	yes	—
335	#102	C₂³×C₄₁	1	16	yes	—
336	C₂²⋊C₈	C₂³×C₄₁	1	4	yes	—
337	#97	C₂³×C₄₁	1	8	yes	—
338	C₄×C₈	C₂³×C₄₁	1	4	yes	—
339	C₂⁴	—	2	1	no	—
340	#41	—	4	16	no	—
341	#41	—	4	16	no	—
342	#41	—	4	8	no	—
343	C₂×Q₈	—	2	4	no	—
344	C₂×Q₈	—	2	4	no	—
345	C₂×Q₈	—	2	2	no	—
346	C₂×Q₈	—	2	4	no	—
347	C₂×Q₈	—	4	16	no	—
348	C₂×Q₈	—	8	2	no	—
349	C₂×Q₈	C₂×D₄×C₄₁	1	4	yes	—
350	C₂×D₄	—	2	4	no	—
351	C₂×D₄	—	2	4	no	—
352	C₂×D₄	—	2	1	no	—
353	C₂×D₄	—	2	4	no	—
354	C₂×D₄	—	2	2	no	—
355	C₂×D₄	—	2	2	no	—
356	C₂×D₄	—	2	4	no	—
357	C₂×D₄	C₂⁴×C₄₁	1	4	yes	—
358	C₂×D₄	C₂⁴×C₄₁	1	2	yes	—
359	C₂²×C₄	—	2	1	no	—
360	C₂²×C₄	—	2	2	no	—
361	C₂²×C₄	—	2	4	no	—
362	C₂²×C₄	—	2	8	no	—
363	C₂²×C₄	—	2	4	no	—
364	C₂²×C₄	—	2	8	no	—
365	C₂²×C₄	—	4	4	no	—
366	C₂²×C₄	—	8	4	no	—
367	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
368	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
369	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
370	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
371	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
372	D₈	—	2	16	no	—
373	C₂×C₈	C₂⁴×C₄₁	1	8	yes	—
374	C₄⋊C₄	—	2	8	no	—
375	C₄⋊C₄	—	2	4	no	—
376	C₄⋊C₄	—	2	8	no	—
377	C₄⋊C₄	—	2	1	no	—
378	C₄⋊C₄	—	2	2	no	—
379	C₄⋊C₄	—	2	2	no	—
380	C₄⋊C₄	—	2	4	no	—
381	C₄⋊C₄	C₂×D₄×C₄₁	1	4	yes	—
382	C₄⋊C₄	C₂×D₄×C₄₁	1	8	yes	—
383	C₄⋊C₄	C₂⁴×C₄₁	1	4	yes	—
384	C₄⋊C₄	C₂⁴×C₄₁	1	2	yes	—
385	C₄⋊C₄	C₂⁴×C₄₁	1	4	yes	—
386	C₂²⋊C₄	—	2	4	no	—
387	C₂²⋊C₄	—	2	8	no	—
388	C₂²⋊C₄	—	2	4	no	—
389	C₂²⋊C₄	—	2	4	no	—
390	C₂²⋊C₄	—	2	8	no	—
391	C₄²	C₂×D₄×C₄₁	1	4	yes	—
392	C₄²	C₂×D₄×C₄₁	1	2	yes	—
393	C₄²	C₂⁴×C₄₁	1	2	yes	—
394	C₄²	C₂⁴×C₄₁	1	4	yes	—
395	C₂³	—	2	4	no	—
396	C₂³	—	2	2	no	—
397	C₂³	—	2	4	no	—
398	C₂³	—	4	2	no	—
399	C₂³	—	4	2	no	—
400	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
401	Q₈	—	2	8	no	—
402	Q₈	—	4	8	no	—
403	Q₈	—	4	4	no	—
404	Q₈	—	8	4	no	—
405	D₄	—	2	4	no	—
406	D₄	—	2	2	no	—
407	D₄	—	2	8	no	—
408	D₄	—	4	8	no	—
409	D₄	—	4	8	no	—
410	D₄	—	4	4	no	—
411	D₄	—	8	4	no	—
412	D₄	—	8	2	no	—
413	D₄	2₋¹⁺⁴×C₄₁	1	4	yes	complemented
414	C₂×C₄	—	2	4	no	—
415	C₂×C₄	—	2	2	no	—
416	C₂×C₄	—	2	4	no	—
417	C₂×C₄	—	2	2	no	—
418	C₂×C₄	—	2	4	no	—
419	C₂×C₄	—	4	2	no	—
420	C₂×C₄	—	4	1	no	—
421	C₂×C₄	—	4	16	no	—
422	C₂×C₄	—	4	4	no	—
423	C₂×C₄	—	4	2	no	—
424	C₂×C₄	—	4	8	no	—
425	C₂×C₄	—	4	8	no	—
426	C₂×C₄	—	8	8	no	—
427	C₂×C₄	AGL(1,ℤ/8)×C₄₁	1	4	yes	—
428	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
429	C₂×C₄	C₂²×D₄×C₄₁	1	2	yes	—
430	C₂×C₄	C₂²×D₄×C₄₁	1	4	yes	—
431	C₂×C₄	C₂²×D₄×C₄₁	1	4	yes	—
432	C₂×C₄	C₂²×D₄×C₄₁	1	2	yes	—
433	C₂×C₄	C₂⁵×C₄₁	1	1	yes	characteristic
434	C₈	—	2	8	no	—
435	C₂²	—	2	1	no	—
436	C₂²	—	2	1	no	—
437	C₂²	—	2	4	no	—
438	C₂²	—	4	8	no	—
439	C₂²	—	4	2	no	—
440	C₂²	—	4	2	no	—
441	C₂²	—	4	4	no	—
442	C₂²	—	4	4	no	—
443	C₂²	—	4	4	no	—
444	C₂²	C₂×AGL(1,ℤ/8)×C₄₁	1	2	yes	—
445	C₂²	C₂³×D₄×C₄₁	1	1	yes	characteristic
446	C₄	—	2	4	no	—
447	C₄	—	2	4	no	—
448	C₄	—	2	2	no	—
449	C₄	—	2	1	no	—
450	C₄	—	4	4	no	—
451	C₄	—	4	2	no	—
452	C₄	—	4	4	no	—
453	C₄	C₂×AGL(1,ℤ/8)×C₄₁	1	4	yes	—
454	C₄	C₂×2₋¹⁺⁴×C₄₁	1	2	yes	—
455	C₂	—	2	2	no	—
456	C₂	—	4	4	no	—
457	C₂	—	8	4	no	—
458	C₂	C₄₁×#3486	1	1	yes	characteristic
459	C₂	C₂²×AGL(1,ℤ/8)×C₄₁	1	1	yes	characteristic
460	C₂	C₄₁×#3585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₄₁	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₄₁
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄₁ ◁ C₂×C₄×Q₈×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₄₁×#3497	C₂	semidirect
2. C₂×C₄₁×#554	C₂	semidirect
3. C₄₁×#3384	C₂	semidirect
4. C₄₁×#3366	C₂	semidirect
5. C₄₁×#3234	C₂	semidirect
6. C₄₁×#3227	C₂	semidirect
7. C₄₁×#3109	C₂	semidirect
8. C₄₁×#3100	C₂	semidirect
9. C₄₁×#2983	C₂	semidirect
13. C₄₁×#550	C₂²	semidirect
14. D₄×Q₈×C₄₁	C₂²	semidirect
28. C₄₁×#501	C₂²	semidirect
29. C₄₁×#498	C₂²	semidirect
30. C₄₁×#490	C₂²	semidirect
31. C₄₁×#486	C₂²	semidirect
34. C₄₁×#478	C₂²	semidirect
36. C₄₁×#476	C₂²	semidirect
41. C₄₁×#446	C₂²	semidirect
182. D₄×C₄₁	2₋¹⁺⁴	semidirect
204. #61825	C₄₁	direct (N × H)
225. #3497	C₂×C₄₁	semidirect
226. C₂×#554	C₂×C₄₁	semidirect
227. #3384	C₂×C₄₁	semidirect
228. #3366	C₂×C₄₁	semidirect
229. #3234	C₂×C₄₁	semidirect
230. #3227	C₂×C₄₁	semidirect
231. #3109	C₂×C₄₁	semidirect
232. #3100	C₂×C₄₁	semidirect
233. #2983	C₂×C₄₁	semidirect
243. #550	C₂²×C₄₁	semidirect
244. D₄×Q₈	C₂²×C₄₁	semidirect
258. #501	C₂²×C₄₁	semidirect
259. #498	C₂²×C₄₁	semidirect
260. #490	C₂²×C₄₁	semidirect
261. #486	C₂²×C₄₁	semidirect
264. #478	C₂²×C₄₁	semidirect
266. #476	C₂²×C₄₁	semidirect
271. #446	C₂²×C₄₁	semidirect
276. C₄₁	#61825	direct (N × H)
413. D₄	2₋¹⁺⁴×C₄₁	semidirect

Maximal subgroups

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

subgroup	index
C₄₁×#3497	2
C₂×C₄₁×#554	2
C₄₁×#3384	2
C₄₁×#3366	2
C₄₁×#3234	2
C₄₁×#3227	2
C₄₁×#3109	2
C₄₁×#3100	2
C₄₁×#2983	2
#61825	41

Subgroups — C41×#61825 #23838026

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#61825 #23838026