Subgroups — C₄₁×#18626 #23794827

Order 10496.

1088 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₁×#3511	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄₁×#3205	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄₁×#492	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₁×#3038	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₁×#1624	C₂	1	4	yes	maximal, complemented
6	C₄₁×#1622	C₂	1	4	yes	maximal, complemented
7	C₄₁×#1548	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄₁×#1492	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄₁×#1476	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×AGL(1,ℤ/8)×C₄₁	—	2	1	no	—
11	C₂²×SD₁₆×C₄₁	—	2	2	no	—
12	C₄₁×#556	—	2	1	no	—
13	C₄₁×#555	C₂²	1	2	yes	complemented
14	C₄₁×#554	C₂²	1	2	yes	complemented
15	C₄₁×#553	—	2	2	no	—
16	C₄₁×#548	—	2	2	no	—
17	C₄₁×#547	—	2	1	no	—
18	C₄₁×#542	—	2	2	no	—
19	C₄₁×#537	—	2	1	no	—
20	C₄₁×#533	—	2	1	no	—
21	C₄₁×#532	—	2	1	no	—
22	C₄₁×#532	C₂²	1	1	yes	characteristic
23	C₂×C₄⋊Q₈×C₄₁	C₂²	1	1	yes	characteristic
24	C₂×#127×C₄₁	C₂²	1	1	yes	characteristic
25	C₄₁×#520	—	2	1	no	—
26	C₄×#41×C₄₁	C₂²	1	1	yes	characteristic
27	C₄₁×#493	—	2	1	no	—
28	C₄₁×#492	—	2	2	no	—
29	C₄₁×#492	C₂²	1	4	yes	—
30	C₄₁×#486	—	2	1	no	—
31	C₄₁×#460	—	2	1	no	—
32	C₄₁×#460	C₂²	1	2	yes	—
33	C₄₁×#459	—	2	1	no	—
34	C₄₁×#459	C₂²	1	2	yes	—
35	C₄₁×#459	C₂²	1	4	yes	—
36	C₄₁×#447	—	2	2	no	—
37	C₄₁×#431	C₂²	1	1	yes	characteristic
38	C₄₁×#423	C₂²	1	1	yes	characteristic
39	C₄₁×#418	—	2	1	no	—
40	C₂×C₄×C₈×C₄₁	C₂²	1	1	yes	characteristic
41	C₄₁×#333	C₂²	1	4	yes	complemented
42	C₄₁×Q₈⋊C₈	C₂²	1	2	yes	complemented
43	C₄₁×D₄⋊C₈	C₂²	1	4	yes	complemented
44	C₄₁×D₄⋊C₈	C₂²	1	2	yes	complemented
45	C₂×#41×C₄₁	—	2	2	no	—
46	C₂×#41×C₄₁	—	2	1	no	—
47	C₂×#41×C₄₁	D₄	1	1	yes	characteristic
48	C₂²×Q₈×C₄₁	D₄	1	2	yes	—
49	C₂²×D₄×C₄₁	—	2	1	no	—
50	C₂²×D₄×C₄₁	—	2	1	no	—
51	C₂²×D₄×C₄₁	—	2	1	no	—
52	AGL(1,ℤ/8)×C₄₁	—	4	4	no	—
53	C₂×SD₁₆×C₄₁	—	2	8	no	—
54	C₂×SD₁₆×C₄₁	—	2	2	no	—
55	C₂×SD₁₆×C₄₁	—	4	8	no	—
56	C₂×D₈×C₄₁	—	2	2	no	—
57	C₂×D₈×C₄₁	—	2	4	no	—
58	C₂×M₁₆×C₄₁	—	2	1	no	—
59	C₂²×C₈×C₄₁	—	2	1	no	—
60	C₄⋊Q₈×C₄₁	—	2	1	no	—
61	C₄⋊Q₈×C₄₁	—	2	1	no	—
62	C₄⋊Q₈×C₄₁	D₄	1	2	yes	—
63	C₄⋊Q₈×C₄₁	D₄	1	1	yes	characteristic
64	C₄⋊Q₈×C₄₁	C₂³	1	2	yes	—
65	#127×C₄₁	—	2	1	no	—
66	#127×C₄₁	—	2	1	no	—
67	#127×C₄₁	—	2	1	no	—
68	#127×C₄₁	D₄	1	1	yes	characteristic
69	#127×C₄₁	C₂³	1	2	yes	—
70	#126×C₄₁	—	2	4	no	—
71	#125×C₄₁	—	2	2	no	—
72	#124×C₄₁	—	2	2	no	—
73	#124×C₄₁	—	2	4	no	—
74	#124×C₄₁	—	2	1	no	—
75	#123×C₄₁	—	2	4	no	—
76	C₂²⋊Q₈×C₄₁	—	2	2	no	—
77	C₂²⋊Q₈×C₄₁	—	2	2	no	—
78	C₂²⋊Q₈×C₄₁	—	2	2	no	—
79	C₂²⋊Q₈×C₄₁	—	2	4	no	—
80	#121×C₄₁	—	2	2	no	—
81	#121×C₄₁	—	2	4	no	—
82	#121×C₄₁	—	2	2	no	—
83	#121×C₄₁	—	2	2	no	—
84	#121×C₄₁	—	2	1	no	—
85	#121×C₄₁	D₄	1	2	yes	—
86	C₄×Q₈×C₄₁	—	2	2	no	—
87	C₄×Q₈×C₄₁	—	2	2	no	—
88	C₄×Q₈×C₄₁	D₄	1	1	yes	characteristic
89	C₄×Q₈×C₄₁	C₂³	1	1	yes	characteristic
90	C₄×D₄×C₄₁	—	2	2	no	—
91	C₄×D₄×C₄₁	—	2	4	no	—
92	C₄×D₄×C₄₁	—	2	2	no	—
93	C₄×D₄×C₄₁	—	2	1	no	—
94	C₄×D₄×C₄₁	—	2	1	no	—
95	C₄×D₄×C₄₁	—	2	1	no	—
96	C₄×D₄×C₄₁	D₄	1	1	yes	characteristic
97	C₄×D₄×C₄₁	C₂³	1	1	yes	characteristic
98	C₄×D₄×C₄₁	C₂³	1	2	yes	—
99	#117×C₄₁	—	2	2	no	—
100	#117×C₄₁	—	2	2	no	—
101	#117×C₄₁	—	2	1	no	—
102	#117×C₄₁	D₄	1	1	yes	characteristic
103	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
104	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
105	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
106	C₂×C₄²×C₄₁	—	2	1	no	—
107	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
108	C₄⋊C₈×C₄₁	—	2	1	no	—
109	C₄⋊C₈×C₄₁	C₂³	1	2	yes	—
110	C₄⋊C₈×C₄₁	C₂³	1	2	yes	—
111	#102×C₄₁	—	2	2	no	—
112	#102×C₄₁	—	2	2	no	—
113	#102×C₄₁	—	2	4	no	—
114	C₂²⋊C₈×C₄₁	—	2	1	no	—
115	C₄×C₈×C₄₁	—	2	1	no	—
116	C₄×C₈×C₄₁	—	2	1	no	—
117	C₄×C₈×C₄₁	C₂³	1	2	yes	—
118	C₂⁴×C₄₁	—	4	1	no	—
119	#41×C₄₁	—	2	2	no	—
120	#41×C₄₁	—	2	2	no	—
121	#41×C₄₁	—	4	2	no	—
122	#41×C₄₁	—	4	2	no	—
123	#41×C₄₁	—	8	4	no	—
124	C₂×Q₈×C₄₁	—	2	1	no	—
125	C₂×Q₈×C₄₁	—	2	2	no	—
126	C₂×Q₈×C₄₁	—	4	4	no	—
127	C₂×Q₈×C₄₁	C₂×D₄	1	1	yes	characteristic
128	C₂×Q₈×C₄₁	C₂×D₄	1	4	yes	—
129	C₂×D₄×C₄₁	—	2	1	no	—
130	C₂×D₄×C₄₁	—	2	2	no	—
131	C₂×D₄×C₄₁	—	2	4	no	—
132	C₂×D₄×C₄₁	—	2	1	no	—
133	C₂×D₄×C₄₁	—	2	1	no	—
134	C₂×D₄×C₄₁	—	2	2	no	—
135	C₂×D₄×C₄₁	—	2	2	no	—
136	C₂×D₄×C₄₁	—	2	2	no	—
137	C₂×D₄×C₄₁	—	4	4	no	—
138	C₂×D₄×C₄₁	—	4	1	no	—
139	C₂×D₄×C₄₁	—	4	1	no	—
140	C₂×D₄×C₄₁	—	4	1	no	—
141	C₂×D₄×C₄₁	—	4	2	no	—
142	C₂×D₄×C₄₁	—	4	2	no	—
143	C₂×D₄×C₄₁	—	8	2	no	—
144	C₂×D₄×C₄₁	C₂×D₄	1	2	yes	—
145	C₂×D₄×C₄₁	C₂×D₄	1	1	yes	characteristic
146	C₂²×C₄×C₄₁	—	2	4	no	—
147	C₂²×C₄×C₄₁	—	2	2	no	—
148	C₂²×C₄×C₄₁	—	2	1	no	—
149	C₂²×C₄×C₄₁	—	2	1	no	—
150	C₂²×C₄×C₄₁	—	2	1	no	—
151	C₂²×C₄×C₄₁	—	2	2	no	—
152	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
153	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
154	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
155	SD₁₆×C₄₁	—	4	16	no	—
156	SD₁₆×C₄₁	—	4	4	no	—
157	D₈×C₄₁	—	4	4	no	—
158	D₈×C₄₁	—	8	4	no	—
159	M₁₆×C₄₁	—	4	2	no	—
160	C₂×C₈×C₄₁	—	2	4	no	—
161	C₂×C₈×C₄₁	—	2	2	no	—
162	C₂×C₈×C₄₁	—	2	2	no	—
163	C₂×C₈×C₄₁	—	2	2	no	—
164	C₄⋊C₄×C₄₁	—	2	4	no	—
165	C₄⋊C₄×C₄₁	—	2	4	no	—
166	C₄⋊C₄×C₄₁	—	2	2	no	—
167	C₄⋊C₄×C₄₁	—	2	2	no	—
168	C₄⋊C₄×C₄₁	—	2	1	no	—
169	C₄⋊C₄×C₄₁	—	2	1	no	—
170	C₄⋊C₄×C₄₁	—	2	2	no	—
171	C₄⋊C₄×C₄₁	—	2	2	no	—
172	C₄⋊C₄×C₄₁	—	2	1	no	—
173	C₄⋊C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
174	C₄⋊C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
175	C₄⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
176	C₂²⋊C₄×C₄₁	—	2	4	no	—
177	C₂²⋊C₄×C₄₁	—	2	4	no	—
178	C₂²⋊C₄×C₄₁	—	2	4	no	—
179	C₂²⋊C₄×C₄₁	—	2	1	no	—
180	C₂²⋊C₄×C₄₁	—	2	1	no	—
181	C₂²⋊C₄×C₄₁	—	2	2	no	—
182	C₂²⋊C₄×C₄₁	—	2	1	no	—
183	C₂²⋊C₄×C₄₁	—	2	2	no	—
184	C₄²×C₄₁	—	2	4	no	—
185	C₄²×C₄₁	—	2	1	no	—
186	C₄²×C₄₁	—	2	1	no	—
187	C₄²×C₄₁	—	2	1	no	—
188	C₄²×C₄₁	C₂×D₄	1	1	yes	characteristic
189	C₄²×C₄₁	C₂×D₄	1	1	yes	characteristic
190	C₄²×C₄₁	C₂×D₄	1	1	yes	characteristic
191	C₄²×C₄₁	C₂⁴	1	1	yes	characteristic
192	C₂³×C₄₁	—	2	1	no	—
193	C₂³×C₄₁	—	2	2	no	—
194	C₂³×C₄₁	—	4	2	no	—
195	C₂³×C₄₁	—	8	2	no	—
196	C₂³×C₄₁	—	8	2	no	—
197	C₂³×C₄₁	—	8	2	no	—
198	C₂³×C₄₁	#120	1	1	yes	characteristic
199	Q₈×C₄₁	—	2	1	no	—
200	Q₈×C₄₁	—	2	1	no	—
201	Q₈×C₄₁	—	4	4	no	—
202	Q₈×C₄₁	—	4	2	no	—
203	Q₈×C₄₁	—	4	4	no	—
204	D₄×C₄₁	—	2	1	no	—
205	D₄×C₄₁	—	2	1	no	—
206	D₄×C₄₁	—	2	4	no	—
207	D₄×C₄₁	—	4	4	no	—
208	D₄×C₄₁	—	4	2	no	—
209	D₄×C₄₁	—	4	4	no	—
210	D₄×C₄₁	—	4	2	no	—
211	D₄×C₄₁	—	4	2	no	—
212	D₄×C₄₁	—	4	4	no	—
213	D₄×C₄₁	—	4	2	no	—
214	D₄×C₄₁	—	4	2	no	—
215	D₄×C₄₁	—	8	2	no	—
216	D₄×C₄₁	—	8	4	no	—
217	D₄×C₄₁	—	8	2	no	—
218	D₄×C₄₁	—	8	2	no	—
219	C₂×C₄×C₄₁	—	2	2	no	—
220	C₂×C₄×C₄₁	—	2	2	no	—
221	C₂×C₄×C₄₁	—	2	1	no	—
222	C₂×C₄×C₄₁	—	2	1	no	—
223	C₂×C₄×C₄₁	—	2	2	no	—
224	C₂×C₄×C₄₁	—	2	1	no	—
225	C₂×C₄×C₄₁	—	2	4	no	—
226	C₂×C₄×C₄₁	—	4	2	no	—
227	C₂×C₄×C₄₁	—	4	2	no	—
228	C₂×C₄×C₄₁	—	4	2	no	—
229	C₂×C₄×C₄₁	—	4	2	no	—
230	C₂×C₄×C₄₁	—	4	2	no	—
231	C₂×C₄×C₄₁	—	8	2	no	—
232	C₂×C₄×C₄₁	—	8	4	no	—
233	C₂×C₄×C₄₁	#120	1	1	yes	characteristic
234	C₂×C₄×C₄₁	#120	1	1	yes	characteristic
235	C₂×C₄×C₄₁	#120	1	1	yes	characteristic
236	C₂×C₄×C₄₁	#135	1	2	yes	—
237	C₂×C₄×C₄₁	AGL(1,ℤ/8)	1	2	yes	—
238	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
239	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
240	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
241	C₈×C₄₁	—	2	4	no	—
242	C₈×C₄₁	—	4	2	no	—
243	C₈×C₄₁	—	4	2	no	—
244	#18626	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
245	C₂²×C₄₁	—	2	1	no	—
246	C₂²×C₄₁	—	2	1	no	—
247	C₂²×C₄₁	—	4	1	no	—
248	C₂²×C₄₁	—	4	2	no	—
249	C₂²×C₄₁	—	4	1	no	—
250	C₂²×C₄₁	—	4	2	no	—
251	C₂²×C₄₁	—	4	1	no	—
252	C₂²×C₄₁	—	4	2	no	—
253	C₂²×C₄₁	—	8	2	no	—
254	C₂²×C₄₁	—	8	2	no	—
255	C₂²×C₄₁	—	8	2	no	—
256	C₂²×C₄₁	—	16	4	no	—
257	C₂²×C₄₁	#449	1	2	yes	—
258	C₂²×C₄₁	C₂×#120	1	1	yes	characteristic
259	C₄×C₄₁	—	2	1	no	—
260	C₄×C₄₁	—	2	1	no	—
261	C₄×C₄₁	—	4	1	no	—
262	C₄×C₄₁	—	4	2	no	—
263	C₄×C₄₁	—	4	1	no	—
264	C₄×C₄₁	—	4	1	no	—
265	C₄×C₄₁	—	4	4	no	—
266	C₄×C₄₁	#449	1	2	yes	—
267	C₄×C₄₁	#453	1	2	yes	—
268	C₄×C₄₁	C₂×#135	1	1	yes	characteristic
269	C₄×C₄₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
270	C₄×C₄₁	#577	1	2	yes	—
271	#3511	C₂×C₄₁	1	1	yes	characteristic, complemented
272	#3205	C₂×C₄₁	1	1	yes	characteristic, complemented
273	C₂×#492	C₂×C₄₁	1	1	yes	characteristic, complemented
274	#3038	C₂×C₄₁	1	1	yes	characteristic, complemented
275	#1624	C₂×C₄₁	1	4	yes	complemented
276	#1622	C₂×C₄₁	1	4	yes	complemented
277	#1548	C₂×C₄₁	1	1	yes	characteristic, complemented
278	#1492	C₂×C₄₁	1	1	yes	characteristic, complemented
279	#1476	C₂×C₄₁	1	1	yes	characteristic, complemented
280	C₂×C₄₁	—	2	2	no	—
281	C₂×C₄₁	—	8	1	no	—
282	C₂×C₄₁	—	8	2	no	—
283	C₂×C₄₁	—	16	2	no	—
284	C₂×C₄₁	C₂×#449	1	1	yes	characteristic
285	C₂×C₄₁	#3010	1	1	yes	characteristic
286	C₂×C₄₁	C₂×#453	1	1	yes	characteristic
287	C₂×AGL(1,ℤ/8)	—	2	1	no	—
288	C₂²×SD₁₆	—	2	2	no	—
289	#556	—	2	1	no	—
290	#555	C₂²×C₄₁	1	2	yes	complemented
291	#554	C₂²×C₄₁	1	2	yes	complemented
292	#553	—	2	2	no	—
293	#548	—	2	2	no	—
294	#547	—	2	1	no	—
295	#542	—	2	2	no	—
296	#537	—	2	1	no	—
297	#533	—	2	1	no	—
298	#532	—	2	1	no	—
299	#532	C₂²×C₄₁	1	1	yes	characteristic
300	C₂×C₄⋊Q₈	C₂²×C₄₁	1	1	yes	characteristic
301	C₂×#127	C₂²×C₄₁	1	1	yes	characteristic
302	#520	—	2	1	no	—
303	C₄×#41	C₂²×C₄₁	1	1	yes	characteristic
304	#493	—	2	1	no	—
305	#492	—	2	2	no	—
306	#492	C₂²×C₄₁	1	4	yes	—
307	#486	—	2	1	no	—
308	#460	—	2	1	no	—
309	#460	C₂²×C₄₁	1	2	yes	—
310	#459	—	2	1	no	—
311	#459	C₂²×C₄₁	1	4	yes	—
312	#459	C₂²×C₄₁	1	2	yes	—
313	#447	—	2	2	no	—
314	#431	C₂²×C₄₁	1	1	yes	characteristic
315	#423	C₂²×C₄₁	1	1	yes	characteristic
316	#418	—	2	1	no	—
317	C₂×C₄×C₈	C₂²×C₄₁	1	1	yes	characteristic
318	#333	C₂²×C₄₁	1	4	yes	complemented
319	Q₈⋊C₈	C₂²×C₄₁	1	2	yes	complemented
320	D₄⋊C₈	C₂²×C₄₁	1	4	yes	complemented
321	D₄⋊C₈	C₂²×C₄₁	1	2	yes	complemented
322	C₄₁	#18626	1	1	yes	characteristic, direct product factor, Sylow
323	C₂×#41	—	2	2	no	—
324	C₂×#41	—	2	1	no	—
325	C₂×#41	D₄×C₄₁	1	1	yes	characteristic
326	C₂²×Q₈	D₄×C₄₁	1	2	yes	—
327	C₂²×D₄	—	2	1	no	—
328	C₂²×D₄	—	2	1	no	—
329	C₂²×D₄	—	2	1	no	—
330	AGL(1,ℤ/8)	—	4	4	no	—
331	C₂×SD₁₆	—	2	8	no	—
332	C₂×SD₁₆	—	2	2	no	—
333	C₂×SD₁₆	—	4	8	no	—
334	C₂×D₈	—	2	2	no	—
335	C₂×D₈	—	2	4	no	—
336	C₂×M₁₆	—	2	1	no	—
337	C₂²×C₈	—	2	1	no	—
338	C₄⋊Q₈	—	2	1	no	—
339	C₄⋊Q₈	—	2	1	no	—
340	C₄⋊Q₈	D₄×C₄₁	1	2	yes	—
341	C₄⋊Q₈	D₄×C₄₁	1	1	yes	characteristic
342	C₄⋊Q₈	C₂³×C₄₁	1	2	yes	—
343	#127	—	2	1	no	—
344	#127	—	2	1	no	—
345	#127	—	2	1	no	—
346	#127	D₄×C₄₁	1	1	yes	characteristic
347	#127	C₂³×C₄₁	1	2	yes	—
348	#126	—	2	4	no	—
349	#125	—	2	2	no	—
350	#124	—	2	2	no	—
351	#124	—	2	4	no	—
352	#124	—	2	1	no	—
353	#123	—	2	4	no	—
354	C₂²⋊Q₈	—	2	2	no	—
355	C₂²⋊Q₈	—	2	2	no	—
356	C₂²⋊Q₈	—	2	2	no	—
357	C₂²⋊Q₈	—	2	4	no	—
358	#121	—	2	2	no	—
359	#121	—	2	4	no	—
360	#121	—	2	2	no	—
361	#121	—	2	2	no	—
362	#121	—	2	1	no	—
363	#121	D₄×C₄₁	1	2	yes	—
364	C₄×Q₈	—	2	2	no	—
365	C₄×Q₈	—	2	2	no	—
366	C₄×Q₈	D₄×C₄₁	1	1	yes	characteristic
367	C₄×Q₈	C₂³×C₄₁	1	1	yes	characteristic
368	C₄×D₄	—	2	2	no	—
369	C₄×D₄	—	2	4	no	—
370	C₄×D₄	—	2	2	no	—
371	C₄×D₄	—	2	1	no	—
372	C₄×D₄	—	2	1	no	—
373	C₄×D₄	—	2	1	no	—
374	C₄×D₄	D₄×C₄₁	1	1	yes	characteristic
375	C₄×D₄	C₂³×C₄₁	1	1	yes	characteristic
376	C₄×D₄	C₂³×C₄₁	1	2	yes	—
377	#117	—	2	2	no	—
378	#117	—	2	2	no	—
379	#117	—	2	1	no	—
380	#117	D₄×C₄₁	1	1	yes	characteristic
381	C₂×C₄⋊C₄	—	2	1	no	—
382	C₂×C₄⋊C₄	—	2	1	no	—
383	C₂×C₄⋊C₄	—	2	2	no	—
384	C₂×C₄²	—	2	1	no	—
385	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
386	C₄⋊C₈	—	2	1	no	—
387	C₄⋊C₈	C₂³×C₄₁	1	2	yes	—
388	C₄⋊C₈	C₂³×C₄₁	1	2	yes	—
389	#102	—	2	2	no	—
390	#102	—	2	2	no	—
391	#102	—	2	4	no	—
392	C₂²⋊C₈	—	2	1	no	—
393	C₄×C₈	—	2	1	no	—
394	C₄×C₈	—	2	1	no	—
395	C₄×C₈	C₂³×C₄₁	1	2	yes	—
396	C₂⁴	—	4	1	no	—
397	#41	—	2	2	no	—
398	#41	—	2	2	no	—
399	#41	—	4	2	no	—
400	#41	—	4	2	no	—
401	#41	—	8	4	no	—
402	C₂×Q₈	—	2	1	no	—
403	C₂×Q₈	—	2	2	no	—
404	C₂×Q₈	—	4	4	no	—
405	C₂×Q₈	C₂×D₄×C₄₁	1	1	yes	characteristic
406	C₂×Q₈	C₂×D₄×C₄₁	1	4	yes	—
407	C₂×D₄	—	2	1	no	—
408	C₂×D₄	—	2	2	no	—
409	C₂×D₄	—	2	4	no	—
410	C₂×D₄	—	2	1	no	—
411	C₂×D₄	—	2	1	no	—
412	C₂×D₄	—	2	2	no	—
413	C₂×D₄	—	2	2	no	—
414	C₂×D₄	—	2	2	no	—
415	C₂×D₄	—	4	4	no	—
416	C₂×D₄	—	4	1	no	—
417	C₂×D₄	—	4	1	no	—
418	C₂×D₄	—	4	1	no	—
419	C₂×D₄	—	4	2	no	—
420	C₂×D₄	—	4	2	no	—
421	C₂×D₄	—	8	2	no	—
422	C₂×D₄	C₂×D₄×C₄₁	1	2	yes	—
423	C₂×D₄	C₂×D₄×C₄₁	1	1	yes	characteristic
424	C₂²×C₄	—	2	4	no	—
425	C₂²×C₄	—	2	2	no	—
426	C₂²×C₄	—	2	1	no	—
427	C₂²×C₄	—	2	1	no	—
428	C₂²×C₄	—	2	1	no	—
429	C₂²×C₄	—	2	2	no	—
430	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
431	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
432	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
433	SD₁₆	—	4	16	no	—
434	SD₁₆	—	4	4	no	—
435	D₈	—	4	4	no	—
436	D₈	—	8	4	no	—
437	M₁₆	—	4	2	no	—
438	C₂×C₈	—	2	4	no	—
439	C₂×C₈	—	2	2	no	—
440	C₂×C₈	—	2	2	no	—
441	C₂×C₈	—	2	2	no	—
442	C₄⋊C₄	—	2	4	no	—
443	C₄⋊C₄	—	2	4	no	—
444	C₄⋊C₄	—	2	2	no	—
445	C₄⋊C₄	—	2	2	no	—
446	C₄⋊C₄	—	2	1	no	—
447	C₄⋊C₄	—	2	1	no	—
448	C₄⋊C₄	—	2	2	no	—
449	C₄⋊C₄	—	2	2	no	—
450	C₄⋊C₄	—	2	1	no	—
451	C₄⋊C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
452	C₄⋊C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
453	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
454	C₂²⋊C₄	—	2	4	no	—
455	C₂²⋊C₄	—	2	4	no	—
456	C₂²⋊C₄	—	2	4	no	—
457	C₂²⋊C₄	—	2	1	no	—
458	C₂²⋊C₄	—	2	1	no	—
459	C₂²⋊C₄	—	2	2	no	—
460	C₂²⋊C₄	—	2	1	no	—
461	C₂²⋊C₄	—	2	2	no	—
462	C₄²	—	2	4	no	—
463	C₄²	—	2	1	no	—
464	C₄²	—	2	1	no	—
465	C₄²	—	2	1	no	—
466	C₄²	C₂×D₄×C₄₁	1	1	yes	characteristic
467	C₄²	C₂×D₄×C₄₁	1	1	yes	characteristic
468	C₄²	C₂×D₄×C₄₁	1	1	yes	characteristic
469	C₄²	C₂⁴×C₄₁	1	1	yes	characteristic
470	C₂³	—	2	1	no	—
471	C₂³	—	2	2	no	—
472	C₂³	—	4	2	no	—
473	C₂³	—	8	2	no	—
474	C₂³	—	8	2	no	—
475	C₂³	—	8	2	no	—
476	C₂³	#120×C₄₁	1	1	yes	characteristic
477	Q₈	—	2	1	no	—
478	Q₈	—	2	1	no	—
479	Q₈	—	4	4	no	—
480	Q₈	—	4	2	no	—
481	Q₈	—	4	4	no	—
482	D₄	—	2	1	no	—
483	D₄	—	2	1	no	—
484	D₄	—	2	4	no	—
485	D₄	—	4	4	no	—
486	D₄	—	4	2	no	—
487	D₄	—	4	4	no	—
488	D₄	—	4	2	no	—
489	D₄	—	4	2	no	—
490	D₄	—	4	4	no	—
491	D₄	—	4	2	no	—
492	D₄	—	4	2	no	—
493	D₄	—	8	2	no	—
494	D₄	—	8	4	no	—
495	D₄	—	8	2	no	—
496	D₄	—	8	2	no	—
497	C₂×C₄	—	2	2	no	—
498	C₂×C₄	—	2	2	no	—
499	C₂×C₄	—	2	1	no	—
500	C₂×C₄	—	2	1	no	—
501	C₂×C₄	—	2	2	no	—
502	C₂×C₄	—	2	1	no	—
503	C₂×C₄	—	2	4	no	—
504	C₂×C₄	—	4	2	no	—
505	C₂×C₄	—	4	2	no	—
506	C₂×C₄	—	4	2	no	—
507	C₂×C₄	—	4	2	no	—
508	C₂×C₄	—	4	2	no	—
509	C₂×C₄	—	8	2	no	—
510	C₂×C₄	—	8	4	no	—
511	C₂×C₄	#120×C₄₁	1	1	yes	characteristic
512	C₂×C₄	#120×C₄₁	1	1	yes	characteristic
513	C₂×C₄	#120×C₄₁	1	1	yes	characteristic
514	C₂×C₄	#135×C₄₁	1	2	yes	—
515	C₂×C₄	AGL(1,ℤ/8)×C₄₁	1	2	yes	—
516	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
517	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
518	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
519	C₈	—	2	4	no	—
520	C₈	—	4	2	no	—
521	C₈	—	4	2	no	—
522	C₂²	—	2	1	no	—
523	C₂²	—	2	1	no	—
524	C₂²	—	4	1	no	—
525	C₂²	—	4	2	no	—
526	C₂²	—	4	1	no	—
527	C₂²	—	4	2	no	—
528	C₂²	—	4	1	no	—
529	C₂²	—	4	2	no	—
530	C₂²	—	8	2	no	—
531	C₂²	—	8	2	no	—
532	C₂²	—	8	2	no	—
533	C₂²	—	16	4	no	—
534	C₂²	C₄₁×#449	1	2	yes	—
535	C₂²	C₂×#120×C₄₁	1	1	yes	characteristic
536	C₄	—	2	1	no	—
537	C₄	—	2	1	no	—
538	C₄	—	4	1	no	—
539	C₄	—	4	2	no	—
540	C₄	—	4	1	no	—
541	C₄	—	4	1	no	—
542	C₄	—	4	4	no	—
543	C₄	C₄₁×#449	1	2	yes	—
544	C₄	C₄₁×#453	1	2	yes	—
545	C₄	C₂×#135×C₄₁	1	1	yes	characteristic
546	C₄	C₂×AGL(1,ℤ/8)×C₄₁	1	1	yes	characteristic
547	C₄	C₄₁×#577	1	2	yes	—
548	C₂	—	2	2	no	—
549	C₂	—	8	1	no	—
550	C₂	—	8	2	no	—
551	C₂	—	16	2	no	—
552	C₂	C₂×C₄₁×#449	1	1	yes	characteristic
553	C₂	C₄₁×#3010	1	1	yes	characteristic
554	C₂	C₂×C₄₁×#453	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₄₁	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₄₁
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₄₁ ◁ C₂×C₄²×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₄₁×#3511	C₂	semidirect
2. C₄₁×#3205	C₂	semidirect
3. C₂×C₄₁×#492	C₂	semidirect
4. C₄₁×#3038	C₂	semidirect
5. C₄₁×#1624	C₂	semidirect
6. C₄₁×#1622	C₂	semidirect
7. C₄₁×#1548	C₂	semidirect
8. C₄₁×#1492	C₂	semidirect
9. C₄₁×#1476	C₂	semidirect
13. C₄₁×#555	C₂²	semidirect
14. C₄₁×#554	C₂²	semidirect
41. C₄₁×#333	C₂²	semidirect
42. C₄₁×Q₈⋊C₈	C₂²	semidirect
43. C₄₁×D₄⋊C₈	C₂²	semidirect
44. C₄₁×D₄⋊C₈	C₂²	semidirect
244. #18626	C₄₁	direct (N × H)
271. #3511	C₂×C₄₁	semidirect
272. #3205	C₂×C₄₁	semidirect
273. C₂×#492	C₂×C₄₁	semidirect
274. #3038	C₂×C₄₁	semidirect
275. #1624	C₂×C₄₁	semidirect
276. #1622	C₂×C₄₁	semidirect
277. #1548	C₂×C₄₁	semidirect
278. #1492	C₂×C₄₁	semidirect
279. #1476	C₂×C₄₁	semidirect
290. #555	C₂²×C₄₁	semidirect
291. #554	C₂²×C₄₁	semidirect
318. #333	C₂²×C₄₁	semidirect
319. Q₈⋊C₈	C₂²×C₄₁	semidirect
320. D₄⋊C₈	C₂²×C₄₁	semidirect
321. D₄⋊C₈	C₂²×C₄₁	semidirect
322. C₄₁	#18626	direct (N × H)

Maximal subgroups

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

subgroup	index
C₄₁×#3511	2
C₄₁×#3205	2
C₂×C₄₁×#492	2
C₄₁×#3038	2
C₄₁×#1624	2
C₄₁×#1622	2
C₄₁×#1548	2
C₄₁×#1492	2
C₄₁×#1476	2
#18626	41

Subgroups — C41×#18626 #23794827

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#18626 #23794827