Subgroups — C₄₁×#18646 #23794847

Order 10496.

1024 conjugacy classes of subgroups.

The subgroup lattice has 552 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×#486	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₁×#3038	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₁×#1628	C₂	1	4	yes	maximal, complemented
6	C₄₁×#1625	C₂	1	4	yes	maximal, complemented
7	C₄₁×#1549	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	C₄₁×#556	C₂²	1	2	yes	complemented
12	C₄₁×#555	—	2	1	no	—
13	C₄₁×#554	—	2	1	no	—
14	C₄₁×#553	—	2	2	no	—
15	C₄₁×#548	—	2	2	no	—
16	C₄₁×#547	C₂²	1	2	yes	complemented
17	C₄₁×#542	—	2	2	no	—
18	C₄₁×#537	—	2	1	no	—
19	C₄₁×#533	—	2	1	no	—
20	C₄₁×#532	—	2	1	no	—
21	C₄₁×#532	C₂²	1	1	yes	characteristic
22	C₂×C₄⋊Q₈×C₄₁	C₂²	1	1	yes	characteristic
23	C₂×#127×C₄₁	C₂²	1	1	yes	characteristic
24	C₄₁×#520	—	2	1	no	—
25	C₄×#41×C₄₁	C₂²	1	1	yes	characteristic
26	C₄₁×#493	—	2	1	no	—
27	C₄₁×#486	—	2	2	no	—
28	C₄₁×#486	—	2	1	no	—
29	C₄₁×#486	C₂²	1	4	yes	—
30	C₄₁×#460	—	2	1	no	—
31	C₄₁×#460	C₂²	1	2	yes	—
32	C₄₁×#459	—	2	1	no	—
33	C₄₁×#459	C₂²	1	2	yes	—
34	C₄₁×#459	C₂²	1	4	yes	—
35	C₄₁×#447	—	2	2	no	—
36	C₄₁×#431	C₂²	1	1	yes	characteristic
37	C₄₁×#423	C₂²	1	1	yes	characteristic
38	C₄₁×#418	—	2	1	no	—
39	C₂×#102×C₄₁	—	2	2	no	—
40	C₂×C₄×C₈×C₄₁	C₂²	1	1	yes	characteristic
41	C₄₁×#332	C₂²	1	4	yes	complemented
42	C₄₁×Q₈⋊C₈	C₂²	1	2	yes	complemented
43	C₄₁×D₄⋊C₈	C₂²	1	2	yes	complemented
44	C₄₁×D₄⋊C₈	C₂²	1	4	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	—	2	1	no	—
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	2	no	—
54	C₂×D₈×C₄₁	—	2	2	no	—
55	C₂×D₈×C₄₁	—	2	4	no	—
56	C₂×M₁₆×C₄₁	—	2	1	no	—
57	C₂²×C₈×C₄₁	—	2	1	no	—
58	C₄⋊Q₈×C₄₁	—	2	1	no	—
59	C₄⋊Q₈×C₄₁	—	2	1	no	—
60	C₄⋊Q₈×C₄₁	D₄	1	2	yes	—
61	C₄⋊Q₈×C₄₁	D₄	1	1	yes	characteristic
62	C₄⋊Q₈×C₄₁	C₂³	1	2	yes	—
63	#127×C₄₁	—	2	1	no	—
64	#127×C₄₁	—	2	1	no	—
65	#127×C₄₁	—	2	1	no	—
66	#127×C₄₁	D₄	1	1	yes	characteristic
67	#127×C₄₁	C₂³	1	2	yes	—
68	#126×C₄₁	—	2	4	no	—
69	#125×C₄₁	—	2	2	no	—
70	#124×C₄₁	—	2	4	no	—
71	#124×C₄₁	—	2	2	no	—
72	#124×C₄₁	—	2	1	no	—
73	#123×C₄₁	—	2	4	no	—
74	C₂²⋊Q₈×C₄₁	—	2	2	no	—
75	C₂²⋊Q₈×C₄₁	—	2	4	no	—
76	C₂²⋊Q₈×C₄₁	—	2	2	no	—
77	C₂²⋊Q₈×C₄₁	—	2	2	no	—
78	#121×C₄₁	—	2	2	no	—
79	#121×C₄₁	—	2	2	no	—
80	#121×C₄₁	—	2	4	no	—
81	#121×C₄₁	—	2	2	no	—
82	#121×C₄₁	—	2	1	no	—
83	#121×C₄₁	D₄	1	2	yes	—
84	C₄×Q₈×C₄₁	—	2	2	no	—
85	C₄×Q₈×C₄₁	—	2	2	no	—
86	C₄×Q₈×C₄₁	D₄	1	1	yes	characteristic
87	C₄×Q₈×C₄₁	C₂³	1	1	yes	characteristic
88	C₄×D₄×C₄₁	—	2	2	no	—
89	C₄×D₄×C₄₁	—	2	4	no	—
90	C₄×D₄×C₄₁	—	2	2	no	—
91	C₄×D₄×C₄₁	—	2	1	no	—
92	C₄×D₄×C₄₁	—	2	1	no	—
93	C₄×D₄×C₄₁	—	2	1	no	—
94	C₄×D₄×C₄₁	D₄	1	1	yes	characteristic
95	C₄×D₄×C₄₁	C₂³	1	1	yes	characteristic
96	C₄×D₄×C₄₁	C₂³	1	2	yes	—
97	#117×C₄₁	—	2	2	no	—
98	#117×C₄₁	—	2	2	no	—
99	#117×C₄₁	—	2	1	no	—
100	#117×C₄₁	D₄	1	1	yes	characteristic
101	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
102	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
103	C₂×C₄⋊C₄×C₄₁	D₄	1	2	yes	—
104	C₂×C₄²×C₄₁	—	2	1	no	—
105	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
106	C₄⋊C₈×C₄₁	—	2	1	no	—
107	C₄⋊C₈×C₄₁	C₂³	1	2	yes	—
108	C₄⋊C₈×C₄₁	C₂³	1	2	yes	—
109	#102×C₄₁	—	2	8	no	—
110	#102×C₄₁	—	2	2	no	—
111	#102×C₄₁	—	2	2	no	—
112	#102×C₄₁	—	2	4	no	—
113	C₂²⋊C₈×C₄₁	—	2	1	no	—
114	C₄×C₈×C₄₁	—	2	1	no	—
115	C₄×C₈×C₄₁	—	2	1	no	—
116	C₄×C₈×C₄₁	C₂³	1	2	yes	—
117	C₂⁴×C₄₁	—	4	1	no	—
118	#41×C₄₁	—	2	2	no	—
119	#41×C₄₁	—	2	2	no	—
120	#41×C₄₁	—	4	2	no	—
121	#41×C₄₁	—	4	2	no	—
122	#41×C₄₁	—	8	4	no	—
123	C₂×Q₈×C₄₁	—	2	1	no	—
124	C₂×Q₈×C₄₁	—	2	2	no	—
125	C₂×Q₈×C₄₁	—	2	2	no	—
126	C₂×Q₈×C₄₁	—	8	2	no	—
127	C₂×Q₈×C₄₁	C₂×D₄	1	1	yes	characteristic
128	C₂×D₄×C₄₁	—	2	1	no	—
129	C₂×D₄×C₄₁	—	2	2	no	—
130	C₂×D₄×C₄₁	—	2	4	no	—
131	C₂×D₄×C₄₁	—	2	1	no	—
132	C₂×D₄×C₄₁	—	2	1	no	—
133	C₂×D₄×C₄₁	—	2	2	no	—
134	C₂×D₄×C₄₁	—	2	2	no	—
135	C₂×D₄×C₄₁	—	2	2	no	—
136	C₂×D₄×C₄₁	—	4	4	no	—
137	C₂×D₄×C₄₁	—	4	1	no	—
138	C₂×D₄×C₄₁	—	4	1	no	—
139	C₂×D₄×C₄₁	—	4	1	no	—
140	C₂×D₄×C₄₁	—	4	2	no	—
141	C₂×D₄×C₄₁	—	4	2	no	—
142	C₂×D₄×C₄₁	—	8	2	no	—
143	C₂×D₄×C₄₁	C₂×D₄	1	1	yes	characteristic
144	C₂×D₄×C₄₁	C₂×D₄	1	2	yes	—
145	C₂²×C₄×C₄₁	—	2	4	no	—
146	C₂²×C₄×C₄₁	—	2	2	no	—
147	C₂²×C₄×C₄₁	—	2	1	no	—
148	C₂²×C₄×C₄₁	—	2	1	no	—
149	C₂²×C₄×C₄₁	—	2	1	no	—
150	C₂²×C₄×C₄₁	—	2	2	no	—
151	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
152	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
153	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
154	SD₁₆×C₄₁	—	4	4	no	—
155	D₈×C₄₁	—	4	4	no	—
156	D₈×C₄₁	—	8	4	no	—
157	M₁₆×C₄₁	—	4	2	no	—
158	C₂×C₈×C₄₁	—	2	2	no	—
159	C₂×C₈×C₄₁	—	2	2	no	—
160	C₂×C₈×C₄₁	—	2	2	no	—
161	C₂×C₈×C₄₁	—	4	2	no	—
162	C₄⋊C₄×C₄₁	—	2	4	no	—
163	C₄⋊C₄×C₄₁	—	2	4	no	—
164	C₄⋊C₄×C₄₁	—	2	2	no	—
165	C₄⋊C₄×C₄₁	—	2	2	no	—
166	C₄⋊C₄×C₄₁	—	2	1	no	—
167	C₄⋊C₄×C₄₁	—	2	1	no	—
168	C₄⋊C₄×C₄₁	—	2	2	no	—
169	C₄⋊C₄×C₄₁	—	2	1	no	—
170	C₄⋊C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
171	C₄⋊C₄×C₄₁	C₂×D₄	1	4	yes	—
172	C₄⋊C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
173	C₄⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
174	C₂²⋊C₄×C₄₁	—	2	4	no	—
175	C₂²⋊C₄×C₄₁	—	2	4	no	—
176	C₂²⋊C₄×C₄₁	—	2	4	no	—
177	C₂²⋊C₄×C₄₁	—	2	1	no	—
178	C₂²⋊C₄×C₄₁	—	2	1	no	—
179	C₂²⋊C₄×C₄₁	—	2	2	no	—
180	C₂²⋊C₄×C₄₁	—	2	1	no	—
181	C₂²⋊C₄×C₄₁	—	2	2	no	—
182	C₄²×C₄₁	—	2	4	no	—
183	C₄²×C₄₁	—	2	1	no	—
184	C₄²×C₄₁	—	2	1	no	—
185	C₄²×C₄₁	—	2	1	no	—
186	C₄²×C₄₁	C₂×D₄	1	1	yes	characteristic
187	C₄²×C₄₁	C₂×D₄	1	1	yes	characteristic
188	C₄²×C₄₁	C₂×D₄	1	1	yes	characteristic
189	C₄²×C₄₁	C₂⁴	1	1	yes	characteristic
190	C₂³×C₄₁	—	2	1	no	—
191	C₂³×C₄₁	—	2	2	no	—
192	C₂³×C₄₁	—	4	2	no	—
193	C₂³×C₄₁	—	8	2	no	—
194	C₂³×C₄₁	—	8	2	no	—
195	C₂³×C₄₁	—	8	2	no	—
196	C₂³×C₄₁	#120	1	1	yes	characteristic
197	Q₈×C₄₁	—	2	1	no	—
198	Q₈×C₄₁	—	2	1	no	—
199	Q₈×C₄₁	—	4	4	no	—
200	Q₈×C₄₁	—	4	2	no	—
201	Q₈×C₄₁	—	8	2	no	—
202	D₄×C₄₁	—	2	1	no	—
203	D₄×C₄₁	—	2	1	no	—
204	D₄×C₄₁	—	2	4	no	—
205	D₄×C₄₁	—	4	4	no	—
206	D₄×C₄₁	—	4	2	no	—
207	D₄×C₄₁	—	4	4	no	—
208	D₄×C₄₁	—	4	2	no	—
209	D₄×C₄₁	—	4	2	no	—
210	D₄×C₄₁	—	4	4	no	—
211	D₄×C₄₁	—	4	2	no	—
212	D₄×C₄₁	—	4	2	no	—
213	D₄×C₄₁	—	8	2	no	—
214	D₄×C₄₁	—	8	4	no	—
215	D₄×C₄₁	—	8	2	no	—
216	D₄×C₄₁	—	8	2	no	—
217	C₂×C₄×C₄₁	—	2	2	no	—
218	C₂×C₄×C₄₁	—	2	2	no	—
219	C₂×C₄×C₄₁	—	2	1	no	—
220	C₂×C₄×C₄₁	—	2	1	no	—
221	C₂×C₄×C₄₁	—	2	2	no	—
222	C₂×C₄×C₄₁	—	2	1	no	—
223	C₂×C₄×C₄₁	—	2	4	no	—
224	C₂×C₄×C₄₁	—	4	2	no	—
225	C₂×C₄×C₄₁	—	4	2	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	—	8	2	no	—
230	C₂×C₄×C₄₁	—	8	4	no	—
231	C₂×C₄×C₄₁	#120	1	1	yes	characteristic
232	C₂×C₄×C₄₁	#120	1	1	yes	characteristic
233	C₂×C₄×C₄₁	#120	1	1	yes	characteristic
234	C₂×C₄×C₄₁	#135	1	2	yes	—
235	C₂×C₄×C₄₁	AGL(1,ℤ/8)	1	2	yes	—
236	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
237	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
238	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
239	C₈×C₄₁	—	4	2	no	—
240	C₈×C₄₁	—	4	2	no	—
241	C₈×C₄₁	—	4	2	no	—
242	#18646	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
243	C₂²×C₄₁	—	2	1	no	—
244	C₂²×C₄₁	—	2	1	no	—
245	C₂²×C₄₁	—	4	1	no	—
246	C₂²×C₄₁	—	4	2	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	—	8	2	no	—
252	C₂²×C₄₁	—	8	2	no	—
253	C₂²×C₄₁	—	8	2	no	—
254	C₂²×C₄₁	—	16	4	no	—
255	C₂²×C₄₁	#449	1	2	yes	—
256	C₂²×C₄₁	C₂×#120	1	1	yes	characteristic
257	C₄×C₄₁	—	2	1	no	—
258	C₄×C₄₁	—	2	1	no	—
259	C₄×C₄₁	—	4	1	no	—
260	C₄×C₄₁	—	4	2	no	—
261	C₄×C₄₁	—	4	1	no	—
262	C₄×C₄₁	—	4	4	no	—
263	C₄×C₄₁	—	4	1	no	—
264	C₄×C₄₁	#449	1	2	yes	—
265	C₄×C₄₁	#454	1	2	yes	—
266	C₄×C₄₁	C₂×#135	1	1	yes	characteristic
267	C₄×C₄₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
268	C₄×C₄₁	#576	1	2	yes	—
269	#3511	C₂×C₄₁	1	1	yes	characteristic, complemented
270	#3205	C₂×C₄₁	1	1	yes	characteristic, complemented
271	C₂×#486	C₂×C₄₁	1	1	yes	characteristic, complemented
272	#3038	C₂×C₄₁	1	1	yes	characteristic, complemented
273	#1628	C₂×C₄₁	1	4	yes	complemented
274	#1625	C₂×C₄₁	1	4	yes	complemented
275	#1549	C₂×C₄₁	1	1	yes	characteristic, complemented
276	#1492	C₂×C₄₁	1	1	yes	characteristic, complemented
277	#1476	C₂×C₄₁	1	1	yes	characteristic, complemented
278	C₂×C₄₁	—	2	2	no	—
279	C₂×C₄₁	—	8	1	no	—
280	C₂×C₄₁	—	8	2	no	—
281	C₂×C₄₁	—	16	2	no	—
282	C₂×C₄₁	C₂×#449	1	1	yes	characteristic
283	C₂×C₄₁	#3008	1	1	yes	characteristic
284	C₂×C₄₁	C₂×#454	1	1	yes	characteristic
285	C₂×AGL(1,ℤ/8)	—	2	1	no	—
286	#556	C₂²×C₄₁	1	2	yes	complemented
287	#555	—	2	1	no	—
288	#554	—	2	1	no	—
289	#553	—	2	2	no	—
290	#548	—	2	2	no	—
291	#547	C₂²×C₄₁	1	2	yes	complemented
292	#542	—	2	2	no	—
293	#537	—	2	1	no	—
294	#533	—	2	1	no	—
295	#532	—	2	1	no	—
296	#532	C₂²×C₄₁	1	1	yes	characteristic
297	C₂×C₄⋊Q₈	C₂²×C₄₁	1	1	yes	characteristic
298	C₂×#127	C₂²×C₄₁	1	1	yes	characteristic
299	#520	—	2	1	no	—
300	C₄×#41	C₂²×C₄₁	1	1	yes	characteristic
301	#493	—	2	1	no	—
302	#486	—	2	2	no	—
303	#486	—	2	1	no	—
304	#486	C₂²×C₄₁	1	4	yes	—
305	#460	—	2	1	no	—
306	#460	C₂²×C₄₁	1	2	yes	—
307	#459	—	2	1	no	—
308	#459	C₂²×C₄₁	1	2	yes	—
309	#459	C₂²×C₄₁	1	4	yes	—
310	#447	—	2	2	no	—
311	#431	C₂²×C₄₁	1	1	yes	characteristic
312	#423	C₂²×C₄₁	1	1	yes	characteristic
313	#418	—	2	1	no	—
314	C₂×#102	—	2	2	no	—
315	C₂×C₄×C₈	C₂²×C₄₁	1	1	yes	characteristic
316	#332	C₂²×C₄₁	1	4	yes	complemented
317	Q₈⋊C₈	C₂²×C₄₁	1	2	yes	complemented
318	D₄⋊C₈	C₂²×C₄₁	1	2	yes	complemented
319	D₄⋊C₈	C₂²×C₄₁	1	4	yes	complemented
320	C₄₁	#18646	1	1	yes	characteristic, direct product factor, Sylow
321	C₂×#41	—	2	2	no	—
322	C₂×#41	—	2	1	no	—
323	C₂×#41	D₄×C₄₁	1	1	yes	characteristic
324	C₂²×Q₈	—	2	1	no	—
325	C₂²×D₄	—	2	1	no	—
326	C₂²×D₄	—	2	1	no	—
327	C₂²×D₄	—	2	1	no	—
328	AGL(1,ℤ/8)	—	4	4	no	—
329	C₂×SD₁₆	—	2	2	no	—
330	C₂×D₈	—	2	2	no	—
331	C₂×D₈	—	2	4	no	—
332	C₂×M₁₆	—	2	1	no	—
333	C₂²×C₈	—	2	1	no	—
334	C₄⋊Q₈	—	2	1	no	—
335	C₄⋊Q₈	—	2	1	no	—
336	C₄⋊Q₈	D₄×C₄₁	1	2	yes	—
337	C₄⋊Q₈	D₄×C₄₁	1	1	yes	characteristic
338	C₄⋊Q₈	C₂³×C₄₁	1	2	yes	—
339	#127	—	2	1	no	—
340	#127	—	2	1	no	—
341	#127	—	2	1	no	—
342	#127	D₄×C₄₁	1	1	yes	characteristic
343	#127	C₂³×C₄₁	1	2	yes	—
344	#126	—	2	4	no	—
345	#125	—	2	2	no	—
346	#124	—	2	4	no	—
347	#124	—	2	2	no	—
348	#124	—	2	1	no	—
349	#123	—	2	4	no	—
350	C₂²⋊Q₈	—	2	2	no	—
351	C₂²⋊Q₈	—	2	4	no	—
352	C₂²⋊Q₈	—	2	2	no	—
353	C₂²⋊Q₈	—	2	2	no	—
354	#121	—	2	2	no	—
355	#121	—	2	2	no	—
356	#121	—	2	4	no	—
357	#121	—	2	2	no	—
358	#121	—	2	1	no	—
359	#121	D₄×C₄₁	1	2	yes	—
360	C₄×Q₈	—	2	2	no	—
361	C₄×Q₈	—	2	2	no	—
362	C₄×Q₈	D₄×C₄₁	1	1	yes	characteristic
363	C₄×Q₈	C₂³×C₄₁	1	1	yes	characteristic
364	C₄×D₄	—	2	2	no	—
365	C₄×D₄	—	2	4	no	—
366	C₄×D₄	—	2	2	no	—
367	C₄×D₄	—	2	1	no	—
368	C₄×D₄	—	2	1	no	—
369	C₄×D₄	—	2	1	no	—
370	C₄×D₄	D₄×C₄₁	1	1	yes	characteristic
371	C₄×D₄	C₂³×C₄₁	1	1	yes	characteristic
372	C₄×D₄	C₂³×C₄₁	1	2	yes	—
373	#117	—	2	2	no	—
374	#117	—	2	2	no	—
375	#117	—	2	1	no	—
376	#117	D₄×C₄₁	1	1	yes	characteristic
377	C₂×C₄⋊C₄	—	2	1	no	—
378	C₂×C₄⋊C₄	—	2	2	no	—
379	C₂×C₄⋊C₄	D₄×C₄₁	1	2	yes	—
380	C₂×C₄²	—	2	1	no	—
381	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
382	C₄⋊C₈	—	2	1	no	—
383	C₄⋊C₈	C₂³×C₄₁	1	2	yes	—
384	C₄⋊C₈	C₂³×C₄₁	1	2	yes	—
385	#102	—	2	8	no	—
386	#102	—	2	2	no	—
387	#102	—	2	2	no	—
388	#102	—	2	4	no	—
389	C₂²⋊C₈	—	2	1	no	—
390	C₄×C₈	—	2	1	no	—
391	C₄×C₈	—	2	1	no	—
392	C₄×C₈	C₂³×C₄₁	1	2	yes	—
393	C₂⁴	—	4	1	no	—
394	#41	—	2	2	no	—
395	#41	—	2	2	no	—
396	#41	—	4	2	no	—
397	#41	—	4	2	no	—
398	#41	—	8	4	no	—
399	C₂×Q₈	—	2	1	no	—
400	C₂×Q₈	—	2	2	no	—
401	C₂×Q₈	—	2	2	no	—
402	C₂×Q₈	—	8	2	no	—
403	C₂×Q₈	C₂×D₄×C₄₁	1	1	yes	characteristic
404	C₂×D₄	—	2	1	no	—
405	C₂×D₄	—	2	2	no	—
406	C₂×D₄	—	2	4	no	—
407	C₂×D₄	—	2	1	no	—
408	C₂×D₄	—	2	1	no	—
409	C₂×D₄	—	2	2	no	—
410	C₂×D₄	—	2	2	no	—
411	C₂×D₄	—	2	2	no	—
412	C₂×D₄	—	4	4	no	—
413	C₂×D₄	—	4	1	no	—
414	C₂×D₄	—	4	1	no	—
415	C₂×D₄	—	4	1	no	—
416	C₂×D₄	—	4	2	no	—
417	C₂×D₄	—	4	2	no	—
418	C₂×D₄	—	8	2	no	—
419	C₂×D₄	C₂×D₄×C₄₁	1	1	yes	characteristic
420	C₂×D₄	C₂×D₄×C₄₁	1	2	yes	—
421	C₂²×C₄	—	2	4	no	—
422	C₂²×C₄	—	2	2	no	—
423	C₂²×C₄	—	2	1	no	—
424	C₂²×C₄	—	2	1	no	—
425	C₂²×C₄	—	2	1	no	—
426	C₂²×C₄	—	2	2	no	—
427	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
428	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
429	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
430	SD₁₆	—	4	4	no	—
431	D₈	—	4	4	no	—
432	D₈	—	8	4	no	—
433	M₁₆	—	4	2	no	—
434	C₂×C₈	—	2	2	no	—
435	C₂×C₈	—	2	2	no	—
436	C₂×C₈	—	2	2	no	—
437	C₂×C₈	—	4	2	no	—
438	C₄⋊C₄	—	2	4	no	—
439	C₄⋊C₄	—	2	4	no	—
440	C₄⋊C₄	—	2	2	no	—
441	C₄⋊C₄	—	2	2	no	—
442	C₄⋊C₄	—	2	1	no	—
443	C₄⋊C₄	—	2	1	no	—
444	C₄⋊C₄	—	2	2	no	—
445	C₄⋊C₄	—	2	1	no	—
446	C₄⋊C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
447	C₄⋊C₄	C₂×D₄×C₄₁	1	4	yes	—
448	C₄⋊C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
449	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
450	C₂²⋊C₄	—	2	4	no	—
451	C₂²⋊C₄	—	2	4	no	—
452	C₂²⋊C₄	—	2	4	no	—
453	C₂²⋊C₄	—	2	1	no	—
454	C₂²⋊C₄	—	2	1	no	—
455	C₂²⋊C₄	—	2	2	no	—
456	C₂²⋊C₄	—	2	1	no	—
457	C₂²⋊C₄	—	2	2	no	—
458	C₄²	—	2	4	no	—
459	C₄²	—	2	1	no	—
460	C₄²	—	2	1	no	—
461	C₄²	—	2	1	no	—
462	C₄²	C₂×D₄×C₄₁	1	1	yes	characteristic
463	C₄²	C₂×D₄×C₄₁	1	1	yes	characteristic
464	C₄²	C₂×D₄×C₄₁	1	1	yes	characteristic
465	C₄²	C₂⁴×C₄₁	1	1	yes	characteristic
466	C₂³	—	2	1	no	—
467	C₂³	—	2	2	no	—
468	C₂³	—	4	2	no	—
469	C₂³	—	8	2	no	—
470	C₂³	—	8	2	no	—
471	C₂³	—	8	2	no	—
472	C₂³	#120×C₄₁	1	1	yes	characteristic
473	Q₈	—	2	1	no	—
474	Q₈	—	2	1	no	—
475	Q₈	—	4	4	no	—
476	Q₈	—	4	2	no	—
477	Q₈	—	8	2	no	—
478	D₄	—	2	1	no	—
479	D₄	—	2	1	no	—
480	D₄	—	2	4	no	—
481	D₄	—	4	4	no	—
482	D₄	—	4	2	no	—
483	D₄	—	4	4	no	—
484	D₄	—	4	2	no	—
485	D₄	—	4	2	no	—
486	D₄	—	4	4	no	—
487	D₄	—	4	2	no	—
488	D₄	—	4	2	no	—
489	D₄	—	8	2	no	—
490	D₄	—	8	4	no	—
491	D₄	—	8	2	no	—
492	D₄	—	8	2	no	—
493	C₂×C₄	—	2	2	no	—
494	C₂×C₄	—	2	2	no	—
495	C₂×C₄	—	2	1	no	—
496	C₂×C₄	—	2	1	no	—
497	C₂×C₄	—	2	2	no	—
498	C₂×C₄	—	2	1	no	—
499	C₂×C₄	—	2	4	no	—
500	C₂×C₄	—	4	2	no	—
501	C₂×C₄	—	4	2	no	—
502	C₂×C₄	—	4	2	no	—
503	C₂×C₄	—	4	2	no	—
504	C₂×C₄	—	4	2	no	—
505	C₂×C₄	—	8	2	no	—
506	C₂×C₄	—	8	4	no	—
507	C₂×C₄	#120×C₄₁	1	1	yes	characteristic
508	C₂×C₄	#120×C₄₁	1	1	yes	characteristic
509	C₂×C₄	#120×C₄₁	1	1	yes	characteristic
510	C₂×C₄	#135×C₄₁	1	2	yes	—
511	C₂×C₄	AGL(1,ℤ/8)×C₄₁	1	2	yes	—
512	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
513	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
514	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
515	C₈	—	4	2	no	—
516	C₈	—	4	2	no	—
517	C₈	—	4	2	no	—
518	C₂²	—	2	1	no	—
519	C₂²	—	2	1	no	—
520	C₂²	—	4	1	no	—
521	C₂²	—	4	2	no	—
522	C₂²	—	4	1	no	—
523	C₂²	—	4	2	no	—
524	C₂²	—	4	1	no	—
525	C₂²	—	4	2	no	—
526	C₂²	—	8	2	no	—
527	C₂²	—	8	2	no	—
528	C₂²	—	8	2	no	—
529	C₂²	—	16	4	no	—
530	C₂²	C₄₁×#449	1	2	yes	—
531	C₂²	C₂×#120×C₄₁	1	1	yes	characteristic
532	C₄	—	2	1	no	—
533	C₄	—	2	1	no	—
534	C₄	—	4	1	no	—
535	C₄	—	4	2	no	—
536	C₄	—	4	1	no	—
537	C₄	—	4	4	no	—
538	C₄	—	4	1	no	—
539	C₄	C₄₁×#449	1	2	yes	—
540	C₄	C₄₁×#454	1	2	yes	—
541	C₄	C₂×#135×C₄₁	1	1	yes	characteristic
542	C₄	C₂×AGL(1,ℤ/8)×C₄₁	1	1	yes	characteristic
543	C₄	C₄₁×#576	1	2	yes	—
544	C₂	—	2	2	no	—
545	C₂	—	8	1	no	—
546	C₂	—	8	2	no	—
547	C₂	—	16	2	no	—
548	C₂	C₂×C₄₁×#449	1	1	yes	characteristic
549	C₂	C₄₁×#3008	1	1	yes	characteristic
550	C₂	C₂×C₄₁×#454	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×#486	C₂	semidirect
4. C₄₁×#3038	C₂	semidirect
5. C₄₁×#1628	C₂	semidirect
6. C₄₁×#1625	C₂	semidirect
7. C₄₁×#1549	C₂	semidirect
8. C₄₁×#1492	C₂	semidirect
9. C₄₁×#1476	C₂	semidirect
11. C₄₁×#556	C₂²	semidirect
16. C₄₁×#547	C₂²	semidirect
41. C₄₁×#332	C₂²	semidirect
42. C₄₁×Q₈⋊C₈	C₂²	semidirect
43. C₄₁×D₄⋊C₈	C₂²	semidirect
44. C₄₁×D₄⋊C₈	C₂²	semidirect
242. #18646	C₄₁	direct (N × H)
269. #3511	C₂×C₄₁	semidirect
270. #3205	C₂×C₄₁	semidirect
271. C₂×#486	C₂×C₄₁	semidirect
272. #3038	C₂×C₄₁	semidirect
273. #1628	C₂×C₄₁	semidirect
274. #1625	C₂×C₄₁	semidirect
275. #1549	C₂×C₄₁	semidirect
276. #1492	C₂×C₄₁	semidirect
277. #1476	C₂×C₄₁	semidirect
286. #556	C₂²×C₄₁	semidirect
291. #547	C₂²×C₄₁	semidirect
316. #332	C₂²×C₄₁	semidirect
317. Q₈⋊C₈	C₂²×C₄₁	semidirect
318. D₄⋊C₈	C₂²×C₄₁	semidirect
319. D₄⋊C₈	C₂²×C₄₁	semidirect
320. C₄₁	#18646	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×#486	2
C₄₁×#3038	2
C₄₁×#1628	2
C₄₁×#1625	2
C₄₁×#1549	2
C₄₁×#1492	2
C₄₁×#1476	2
#18646	41

Subgroups — C41×#18646 #23794847

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#18646 #23794847