Subgroups — C₄₁×#21009 #23797210

Order 10496.

1708 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₁×#568	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄₁×#3449	C₂	1	1	yes	maximal, characteristic
3	C₄₁×#2896	C₂	1	2	yes	maximal, complemented
4	C₂×C₄₁×#410	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₁×#1910	C₂	1	4	yes	maximal, complemented
6	C₄₁×#1909	C₂	1	4	yes	maximal, complemented
7	C₂×C₄₁×H(3,ℤ/4)	C₂	1	2	yes	maximal, complemented
8	C₂²×#41×C₄₁	C₂²	1	1	yes	characteristic
9	C₂²×#41×C₄₁	C₂²	1	1	yes	characteristic
10	C₄₁×#568	—	2	2	no	—
11	C₄₁×#568	—	2	4	no	—
12	C₄₁×#568	C₂²	1	4	yes	—
13	C₂×#131×C₄₁	—	2	4	no	—
14	C₂²×M₁₆×C₄₁	—	2	2	no	—
15	C₂²×M₁₆×C₄₁	C₂²	1	2	yes	—
16	C₄₁×#537	—	2	2	no	—
17	C₄₁×#536	C₄	1	2	yes	complemented
18	C₄₁×#536	C₂²	1	2	yes	—
19	C₄₁×#535	C₄	1	2	yes	complemented
20	C₄₁×#535	C₂²	1	2	yes	—
21	C₄₁×#534	—	2	2	no	—
22	C₄₁×#532	C₄	1	4	yes	complemented
23	C₄₁×#525	—	2	2	no	—
24	C₄₁×#525	—	2	2	no	—
25	C₂×#117×C₄₁	C₂²	1	2	yes	—
26	C₂×#117×C₄₁	C₂²	1	1	yes	characteristic
27	C₄₁×#419	C₂²	1	4	yes	complemented
28	C₄₁×#418	C₂²	1	4	yes	complemented
29	C₄₁×#417	—	2	4	no	—
30	C₄₁×#416	—	2	4	no	—
31	C₄₁×#410	—	2	2	no	—
32	C₄₁×#410	C₂²	1	4	yes	—
33	C₂×#99×C₄₁	—	2	2	no	—
34	C₄₁×H(3,ℤ/4)	C₂²	1	8	yes	complemented
35	C₂×#41×C₄₁	—	2	2	no	—
36	C₂×#41×C₄₁	—	2	2	no	—
37	C₂×#41×C₄₁	—	2	1	no	—
38	C₂×#41×C₄₁	—	2	1	no	—
39	C₂×#41×C₄₁	—	2	2	no	—
40	C₂×#41×C₄₁	—	2	2	no	—
41	C₂×#41×C₄₁	—	2	2	no	—
42	C₂×#41×C₄₁	—	2	2	no	—
43	C₂×#41×C₄₁	—	2	2	no	—
44	C₂×#41×C₄₁	—	2	2	no	—
45	C₂×#41×C₄₁	C₂×C₄	1	2	yes	—
46	C₂×#41×C₄₁	C₂×C₄	1	2	yes	—
47	C₂×#41×C₄₁	C₂×C₄	1	2	yes	—
48	C₂×#41×C₄₁	D₄	1	2	yes	—
49	C₂×#41×C₄₁	D₄	1	2	yes	—
50	C₂×#41×C₄₁	C₂³	1	2	yes	—
51	C₂²×Q₈×C₄₁	C₂×C₄	1	1	yes	characteristic
52	C₂²×Q₈×C₄₁	C₂³	1	1	yes	characteristic
53	C₂²×D₄×C₄₁	—	2	1	no	—
54	C₂²×D₄×C₄₁	C₂×C₄	1	1	yes	characteristic
55	C₂²×D₄×C₄₁	D₄	1	2	yes	—
56	C₂²×D₄×C₄₁	C₂³	1	1	yes	characteristic
57	C₂³×C₄×C₄₁	—	2	1	no	—
58	C₂³×C₄×C₄₁	D₄	1	2	yes	—
59	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
60	#131×C₄₁	—	2	16	no	—
61	#131×C₄₁	—	2	16	no	—
62	C₂×M₁₆×C₄₁	—	2	4	no	—
63	C₂×M₁₆×C₄₁	—	2	8	no	—
64	C₂×M₁₆×C₄₁	—	2	2	no	—
65	C₂×M₁₆×C₄₁	—	2	8	no	—
66	C₂×M₁₆×C₄₁	—	2	2	no	—
67	C₂×M₁₆×C₄₁	—	2	2	no	—
68	C₂×M₁₆×C₄₁	—	2	2	no	—
69	C₂×M₁₆×C₄₁	D₄	1	4	yes	complemented
70	C₂×M₁₆×C₄₁	C₂³	1	4	yes	—
71	C₂²×C₈×C₄₁	—	2	4	no	—
72	C₂²×C₈×C₄₁	D₄	1	4	yes	complemented
73	C₄⋊Q₈×C₄₁	C₂×C₄	1	4	yes	complemented
74	#127×C₄₁	C₂×C₄	1	4	yes	complemented
75	#124×C₄₁	C₂×C₄	1	4	yes	complemented
76	#124×C₄₁	C₂×C₄	1	4	yes	complemented
77	#123×C₄₁	—	2	4	no	—
78	#123×C₄₁	—	2	4	no	—
79	C₂²⋊Q₈×C₄₁	—	2	4	no	—
80	C₂²⋊Q₈×C₄₁	—	2	4	no	—
81	#121×C₄₁	—	2	4	no	—
82	#121×C₄₁	—	2	8	no	—
83	#121×C₄₁	—	2	4	no	—
84	#120×C₄₁	—	2	4	no	—
85	#120×C₄₁	—	2	4	no	—
86	C₄×D₄×C₄₁	—	2	8	no	—
87	#117×C₄₁	—	2	1	no	—
88	#117×C₄₁	—	2	1	no	—
89	#117×C₄₁	—	2	2	no	—
90	#117×C₄₁	—	2	2	no	—
91	#117×C₄₁	—	2	2	no	—
92	#117×C₄₁	C₂×C₄	1	2	yes	—
93	#117×C₄₁	C₂³	1	4	yes	—
94	#117×C₄₁	C₂³	1	2	yes	—
95	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
96	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
97	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
98	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
99	C₂×C₄²×C₄₁	—	2	2	no	—
100	C₂×C₄²×C₄₁	C₂×C₄	1	2	yes	—
101	#103×C₄₁	—	2	8	no	—
102	#102×C₄₁	—	2	8	no	—
103	#99×C₄₁	—	2	8	no	—
104	C₂⁴×C₄₁	—	2	1	no	—
105	C₂⁴×C₄₁	C₂²⋊C₄	1	2	yes	—
106	C₂⁴×C₄₁	C₂×D₄	1	1	yes	characteristic
107	#41×C₄₁	—	2	4	no	—
108	#41×C₄₁	—	2	4	no	—
109	#41×C₄₁	—	2	4	no	—
110	#41×C₄₁	—	2	4	no	—
111	#41×C₄₁	—	2	4	no	—
112	#41×C₄₁	—	2	4	no	—
113	#41×C₄₁	—	2	4	no	—
114	#41×C₄₁	—	2	4	no	—
115	#41×C₄₁	—	2	4	no	—
116	#41×C₄₁	—	2	4	no	—
117	#41×C₄₁	—	2	4	no	—
118	#41×C₄₁	—	2	4	no	—
119	#41×C₄₁	—	4	2	no	—
120	#41×C₄₁	—	4	1	no	—
121	#41×C₄₁	—	4	1	no	—
122	#41×C₄₁	—	4	1	no	—
123	#41×C₄₁	—	4	2	no	—
124	#41×C₄₁	—	4	1	no	—
125	C₂×Q₈×C₄₁	—	2	2	no	—
126	C₂×Q₈×C₄₁	—	2	2	no	—
127	C₂×Q₈×C₄₁	—	2	1	no	—
128	C₂×Q₈×C₄₁	—	2	2	no	—
129	C₂×Q₈×C₄₁	—	2	2	no	—
130	C₂×Q₈×C₄₁	C₂²⋊C₄	1	2	yes	—
131	C₂×Q₈×C₄₁	C₂²×C₄	1	2	yes	—
132	C₂×Q₈×C₄₁	C₂²×C₄	1	2	yes	—
133	C₂×D₄×C₄₁	—	2	4	no	—
134	C₂×D₄×C₄₁	—	2	4	no	—
135	C₂×D₄×C₄₁	—	2	2	no	—
136	C₂×D₄×C₄₁	—	2	2	no	—
137	C₂×D₄×C₄₁	—	2	8	no	—
138	C₂×D₄×C₄₁	—	2	2	no	—
139	C₂×D₄×C₄₁	—	2	2	no	—
140	C₂×D₄×C₄₁	—	2	2	no	—
141	C₂×D₄×C₄₁	—	2	1	no	—
142	C₂×D₄×C₄₁	—	2	2	no	—
143	C₂×D₄×C₄₁	—	4	2	no	—
144	C₂×D₄×C₄₁	—	4	2	no	—
145	C₂×D₄×C₄₁	C₂²⋊C₄	1	2	yes	—
146	C₂×D₄×C₄₁	C₂²⋊C₄	1	4	yes	—
147	C₂×D₄×C₄₁	C₂²×C₄	1	2	yes	—
148	C₂×D₄×C₄₁	C₂²×C₄	1	2	yes	—
149	C₂×D₄×C₄₁	C₂×D₄	1	4	yes	—
150	C₂²×C₄×C₄₁	—	2	2	no	—
151	C₂²×C₄×C₄₁	—	2	2	no	—
152	C₂²×C₄×C₄₁	—	2	2	no	—
153	C₂²×C₄×C₄₁	—	2	2	no	—
154	C₂²×C₄×C₄₁	—	2	1	no	—
155	C₂²×C₄×C₄₁	—	2	2	no	—
156	C₂²×C₄×C₄₁	—	2	2	no	—
157	C₂²×C₄×C₄₁	—	2	2	no	—
158	C₂²×C₄×C₄₁	—	4	2	no	—
159	C₂²×C₄×C₄₁	—	4	2	no	—
160	C₂²×C₄×C₄₁	—	4	2	no	—
161	C₂²×C₄×C₄₁	C₂²⋊C₄	1	4	yes	—
162	C₂²×C₄×C₄₁	C₂²⋊C₄	1	2	yes	—
163	C₂²×C₄×C₄₁	C₂²×C₄	1	1	yes	characteristic
164	C₂²×C₄×C₄₁	C₂²×C₄	1	1	yes	characteristic
165	C₂²×C₄×C₄₁	C₂×D₄	1	4	yes	—
166	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
167	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
168	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
169	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
170	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
171	C₂²×C₄×C₄₁	#41	1	2	yes	—
172	C₂²×C₄×C₄₁	#41	1	2	yes	—
173	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
174	M₁₆×C₄₁	—	2	16	no	—
175	M₁₆×C₄₁	—	2	4	no	—
176	M₁₆×C₄₁	—	2	4	no	—
177	M₁₆×C₄₁	—	2	4	no	—
178	M₁₆×C₄₁	—	2	4	no	—
179	C₂×C₈×C₄₁	—	2	16	no	—
180	C₂×C₈×C₄₁	—	2	4	no	—
181	C₂×C₈×C₄₁	—	2	4	no	—
182	C₂×C₈×C₄₁	C₂×D₄	1	8	yes	—
183	C₄⋊C₄×C₄₁	—	2	2	no	—
184	C₄⋊C₄×C₄₁	—	2	8	no	—
185	C₄⋊C₄×C₄₁	—	2	2	no	—
186	C₄⋊C₄×C₄₁	—	2	4	no	—
187	C₄⋊C₄×C₄₁	—	4	2	no	—
188	C₂²⋊C₄×C₄₁	—	2	2	no	—
189	C₂²⋊C₄×C₄₁	—	2	8	no	—
190	C₂²⋊C₄×C₄₁	—	2	2	no	—
191	C₂²⋊C₄×C₄₁	—	2	8	no	—
192	C₂²⋊C₄×C₄₁	—	2	4	no	—
193	C₂²⋊C₄×C₄₁	—	4	2	no	—
194	C₄²×C₄₁	—	2	2	no	—
195	C₄²×C₄₁	—	2	4	no	—
196	C₄²×C₄₁	—	4	2	no	—
197	C₄²×C₄₁	C₂²×C₄	1	4	yes	—
198	C₂³×C₄₁	—	2	2	no	—
199	C₂³×C₄₁	—	2	2	no	—
200	C₂³×C₄₁	—	2	2	no	—
201	C₂³×C₄₁	—	4	2	no	—
202	C₂³×C₄₁	—	8	1	no	—
203	C₂³×C₄₁	—	8	2	no	—
204	C₂³×C₄₁	—	8	2	no	—
205	C₂³×C₄₁	C₂×C₂²⋊C₄	1	4	yes	—
206	C₂³×C₄₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
207	C₂³×C₄₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
208	C₂³×C₄₁	#121	1	2	yes	—
209	C₂³×C₄₁	#121	1	2	yes	—
210	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
211	Q₈×C₄₁	—	2	4	no	—
212	Q₈×C₄₁	—	2	4	no	—
213	Q₈×C₄₁	—	2	4	no	—
214	Q₈×C₄₁	—	4	1	no	—
215	Q₈×C₄₁	—	4	1	no	—
216	D₄×C₄₁	—	2	8	no	—
217	D₄×C₄₁	—	2	8	no	—
218	D₄×C₄₁	—	2	4	no	—
219	D₄×C₄₁	—	2	4	no	—
220	D₄×C₄₁	—	2	4	no	—
221	D₄×C₄₁	—	4	2	no	—
222	D₄×C₄₁	—	4	2	no	—
223	D₄×C₄₁	—	4	4	no	—
224	D₄×C₄₁	—	4	1	no	—
225	D₄×C₄₁	—	4	1	no	—
226	D₄×C₄₁	—	8	8	no	—
227	C₂×C₄×C₄₁	—	2	2	no	—
228	C₂×C₄×C₄₁	—	2	2	no	—
229	C₂×C₄×C₄₁	—	2	4	no	—
230	C₂×C₄×C₄₁	—	2	4	no	—
231	C₂×C₄×C₄₁	—	2	4	no	—
232	C₂×C₄×C₄₁	—	2	4	no	—
233	C₂×C₄×C₄₁	—	2	4	no	—
234	C₂×C₄×C₄₁	—	2	2	no	—
235	C₂×C₄×C₄₁	—	4	2	no	—
236	C₂×C₄×C₄₁	—	4	2	no	—
237	C₂×C₄×C₄₁	—	4	4	no	—
238	C₂×C₄×C₄₁	—	4	2	no	—
239	C₂×C₄×C₄₁	—	4	4	no	—
240	C₂×C₄×C₄₁	—	8	2	no	—
241	C₂×C₄×C₄₁	—	8	4	no	—
242	C₂×C₄×C₄₁	C₂×C₂²⋊C₄	1	4	yes	—
243	C₂×C₄×C₄₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
244	C₂×C₄×C₄₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
245	C₂×C₄×C₄₁	C₄×D₄	1	2	yes	—
246	C₂×C₄×C₄₁	C₄×D₄	1	2	yes	—
247	C₂×C₄×C₄₁	C₄×D₄	1	2	yes	—
248	C₂×C₄×C₄₁	C₄×D₄	1	2	yes	—
249	C₂×C₄×C₄₁	#120	1	2	yes	—
250	C₂×C₄×C₄₁	#120	1	1	yes	characteristic
251	C₂×C₄×C₄₁	#120	1	1	yes	characteristic
252	C₂×C₄×C₄₁	#121	1	2	yes	—
253	C₂×C₄×C₄₁	#121	1	2	yes	—
254	C₂×C₄×C₄₁	#123	1	1	yes	characteristic
255	C₂×C₄×C₄₁	#123	1	2	yes	—
256	C₂×C₄×C₄₁	#123	1	1	yes	characteristic
257	C₂×C₄×C₄₁	C₂³×C₄	1	1	yes	characteristic
258	C₂×C₄×C₄₁	C₂²×D₄	1	2	yes	—
259	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
260	C₂×C₄×C₄₁	C₂×#41	1	2	yes	—
261	C₈×C₄₁	—	2	8	no	—
262	#21009	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
263	C₂²×C₄₁	—	2	4	no	—
264	C₂²×C₄₁	—	4	1	no	—
265	C₂²×C₄₁	—	4	2	no	—
266	C₂²×C₄₁	—	4	1	no	—
267	C₂²×C₄₁	—	4	1	no	—
268	C₂²×C₄₁	—	4	2	no	—
269	C₂²×C₄₁	—	4	4	no	—
270	C₂²×C₄₁	—	4	4	no	—
271	C₂²×C₄₁	—	4	4	no	—
272	C₂²×C₄₁	—	4	2	no	—
273	C₂²×C₄₁	—	8	2	no	—
274	C₂²×C₄₁	—	8	4	no	—
275	C₂²×C₄₁	#386	1	1	yes	characteristic
276	C₂²×C₄₁	#386	1	1	yes	characteristic
277	C₂²×C₄₁	#386	1	2	yes	—
278	C₂²×C₄₁	C₂²×C₂²⋊C₄	1	1	yes	characteristic
279	C₂²×C₄₁	C₂×#121	1	2	yes	—
280	C₄×C₄₁	—	2	4	no	—
281	C₄×C₄₁	—	4	4	no	—
282	C₄×C₄₁	—	4	2	no	—
283	C₄×C₄₁	—	8	4	no	—
284	C₄×C₄₁	#386	1	1	yes	characteristic
285	C₄×C₄₁	#386	1	2	yes	—
286	C₄×C₄₁	#386	1	1	yes	characteristic
287	C₄×C₄₁	C₂×C₄×D₄	1	2	yes	—
288	C₄×C₄₁	C₂×#120	1	1	yes	characteristic
289	C₄×C₄₁	C₂×#123	1	1	yes	characteristic
290	C₂×#568	C₂×C₄₁	1	1	yes	characteristic, complemented
291	#3449	C₂×C₄₁	1	1	yes	characteristic
292	#2896	C₂×C₄₁	1	2	yes	complemented
293	C₂×#410	C₂×C₄₁	1	1	yes	characteristic, complemented
294	#1910	C₂×C₄₁	1	4	yes	complemented
295	#1909	C₂×C₄₁	1	4	yes	complemented
296	C₂×H(3,ℤ/4)	C₂×C₄₁	1	2	yes	complemented
297	C₂×C₄₁	—	2	1	no	—
298	C₂×C₄₁	—	2	2	no	—
299	C₂×C₄₁	—	2	1	no	—
300	C₂×C₄₁	—	2	1	no	—
301	C₂×C₄₁	—	2	2	no	—
302	C₂×C₄₁	—	4	4	no	—
303	C₂×C₄₁	—	8	2	no	—
304	C₂×C₄₁	C₂×#386	1	1	yes	characteristic
305	C₂²×#41	C₂²×C₄₁	1	1	yes	characteristic
306	C₂²×#41	C₂²×C₄₁	1	1	yes	characteristic
307	#568	—	2	2	no	—
308	#568	—	2	4	no	—
309	#568	C₂²×C₄₁	1	4	yes	—
310	C₂×#131	—	2	4	no	—
311	C₂²×M₁₆	—	2	2	no	—
312	C₂²×M₁₆	C₂²×C₄₁	1	2	yes	—
313	#537	—	2	2	no	—
314	#536	C₄×C₄₁	1	2	yes	complemented
315	#536	C₂²×C₄₁	1	2	yes	—
316	#535	C₄×C₄₁	1	2	yes	complemented
317	#535	C₂²×C₄₁	1	2	yes	—
318	#534	—	2	2	no	—
319	#532	C₄×C₄₁	1	4	yes	complemented
320	#525	—	2	2	no	—
321	#525	—	2	2	no	—
322	C₂×#117	C₂²×C₄₁	1	2	yes	—
323	C₂×#117	C₂²×C₄₁	1	1	yes	characteristic
324	#419	C₂²×C₄₁	1	4	yes	complemented
325	#418	C₂²×C₄₁	1	4	yes	complemented
326	#417	—	2	4	no	—
327	#416	—	2	4	no	—
328	#410	—	2	2	no	—
329	#410	C₂²×C₄₁	1	4	yes	—
330	C₂×#99	—	2	2	no	—
331	H(3,ℤ/4)	C₂²×C₄₁	1	8	yes	complemented
332	C₄₁	#21009	1	1	yes	characteristic, direct product factor, Sylow
333	C₂×#41	—	2	2	no	—
334	C₂×#41	—	2	2	no	—
335	C₂×#41	—	2	1	no	—
336	C₂×#41	—	2	1	no	—
337	C₂×#41	—	2	2	no	—
338	C₂×#41	—	2	2	no	—
339	C₂×#41	—	2	2	no	—
340	C₂×#41	—	2	2	no	—
341	C₂×#41	—	2	2	no	—
342	C₂×#41	—	2	2	no	—
343	C₂×#41	C₂×C₄×C₄₁	1	2	yes	—
344	C₂×#41	C₂×C₄×C₄₁	1	2	yes	—
345	C₂×#41	C₂×C₄×C₄₁	1	2	yes	—
346	C₂×#41	D₄×C₄₁	1	2	yes	—
347	C₂×#41	D₄×C₄₁	1	2	yes	—
348	C₂×#41	C₂³×C₄₁	1	2	yes	—
349	C₂²×Q₈	C₂×C₄×C₄₁	1	1	yes	characteristic
350	C₂²×Q₈	C₂³×C₄₁	1	1	yes	characteristic
351	C₂²×D₄	—	2	1	no	—
352	C₂²×D₄	C₂×C₄×C₄₁	1	1	yes	characteristic
353	C₂²×D₄	D₄×C₄₁	1	2	yes	—
354	C₂²×D₄	C₂³×C₄₁	1	1	yes	characteristic
355	C₂³×C₄	—	2	1	no	—
356	C₂³×C₄	D₄×C₄₁	1	2	yes	—
357	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
358	#131	—	2	16	no	—
359	#131	—	2	16	no	—
360	C₂×M₁₆	—	2	4	no	—
361	C₂×M₁₆	—	2	8	no	—
362	C₂×M₁₆	—	2	2	no	—
363	C₂×M₁₆	—	2	8	no	—
364	C₂×M₁₆	—	2	2	no	—
365	C₂×M₁₆	—	2	2	no	—
366	C₂×M₁₆	—	2	2	no	—
367	C₂×M₁₆	D₄×C₄₁	1	4	yes	complemented
368	C₂×M₁₆	C₂³×C₄₁	1	4	yes	—
369	C₂²×C₈	—	2	4	no	—
370	C₂²×C₈	D₄×C₄₁	1	4	yes	complemented
371	C₄⋊Q₈	C₂×C₄×C₄₁	1	4	yes	complemented
372	#127	C₂×C₄×C₄₁	1	4	yes	complemented
373	#124	C₂×C₄×C₄₁	1	4	yes	complemented
374	#124	C₂×C₄×C₄₁	1	4	yes	complemented
375	#123	—	2	4	no	—
376	#123	—	2	4	no	—
377	C₂²⋊Q₈	—	2	4	no	—
378	C₂²⋊Q₈	—	2	4	no	—
379	#121	—	2	4	no	—
380	#121	—	2	8	no	—
381	#121	—	2	4	no	—
382	#120	—	2	4	no	—
383	#120	—	2	4	no	—
384	C₄×D₄	—	2	8	no	—
385	#117	—	2	1	no	—
386	#117	—	2	1	no	—
387	#117	—	2	2	no	—
388	#117	—	2	2	no	—
389	#117	—	2	2	no	—
390	#117	C₂×C₄×C₄₁	1	2	yes	—
391	#117	C₂³×C₄₁	1	4	yes	—
392	#117	C₂³×C₄₁	1	2	yes	—
393	C₂×C₄⋊C₄	—	2	1	no	—
394	C₂×C₄⋊C₄	—	2	2	no	—
395	C₂×C₂²⋊C₄	—	2	1	no	—
396	C₂×C₂²⋊C₄	—	2	2	no	—
397	C₂×C₄²	—	2	2	no	—
398	C₂×C₄²	C₂×C₄×C₄₁	1	2	yes	—
399	#103	—	2	8	no	—
400	#102	—	2	8	no	—
401	#99	—	2	8	no	—
402	C₂⁴	—	2	1	no	—
403	C₂⁴	C₂²⋊C₄×C₄₁	1	2	yes	—
404	C₂⁴	C₂×D₄×C₄₁	1	1	yes	characteristic
405	#41	—	2	4	no	—
406	#41	—	2	4	no	—
407	#41	—	2	4	no	—
408	#41	—	2	4	no	—
409	#41	—	2	4	no	—
410	#41	—	2	4	no	—
411	#41	—	2	4	no	—
412	#41	—	2	4	no	—
413	#41	—	2	4	no	—
414	#41	—	2	4	no	—
415	#41	—	2	4	no	—
416	#41	—	2	4	no	—
417	#41	—	4	1	no	—
418	#41	—	4	2	no	—
419	#41	—	4	1	no	—
420	#41	—	4	1	no	—
421	#41	—	4	1	no	—
422	#41	—	4	2	no	—
423	C₂×Q₈	—	2	2	no	—
424	C₂×Q₈	—	2	2	no	—
425	C₂×Q₈	—	2	1	no	—
426	C₂×Q₈	—	2	2	no	—
427	C₂×Q₈	—	2	2	no	—
428	C₂×Q₈	C₂²⋊C₄×C₄₁	1	2	yes	—
429	C₂×Q₈	C₂²×C₄×C₄₁	1	2	yes	—
430	C₂×Q₈	C₂²×C₄×C₄₁	1	2	yes	—
431	C₂×D₄	—	2	4	no	—
432	C₂×D₄	—	2	4	no	—
433	C₂×D₄	—	2	2	no	—
434	C₂×D₄	—	2	2	no	—
435	C₂×D₄	—	2	8	no	—
436	C₂×D₄	—	2	2	no	—
437	C₂×D₄	—	2	2	no	—
438	C₂×D₄	—	2	2	no	—
439	C₂×D₄	—	2	1	no	—
440	C₂×D₄	—	2	2	no	—
441	C₂×D₄	—	4	2	no	—
442	C₂×D₄	—	4	2	no	—
443	C₂×D₄	C₂²⋊C₄×C₄₁	1	2	yes	—
444	C₂×D₄	C₂²⋊C₄×C₄₁	1	4	yes	—
445	C₂×D₄	C₂²×C₄×C₄₁	1	2	yes	—
446	C₂×D₄	C₂²×C₄×C₄₁	1	2	yes	—
447	C₂×D₄	C₂×D₄×C₄₁	1	4	yes	—
448	C₂²×C₄	—	2	2	no	—
449	C₂²×C₄	—	2	2	no	—
450	C₂²×C₄	—	2	2	no	—
451	C₂²×C₄	—	2	2	no	—
452	C₂²×C₄	—	2	1	no	—
453	C₂²×C₄	—	2	2	no	—
454	C₂²×C₄	—	2	2	no	—
455	C₂²×C₄	—	2	2	no	—
456	C₂²×C₄	—	4	2	no	—
457	C₂²×C₄	—	4	2	no	—
458	C₂²×C₄	—	4	2	no	—
459	C₂²×C₄	C₂²⋊C₄×C₄₁	1	4	yes	—
460	C₂²×C₄	C₂²⋊C₄×C₄₁	1	2	yes	—
461	C₂²×C₄	C₂²×C₄×C₄₁	1	1	yes	characteristic
462	C₂²×C₄	C₂²×C₄×C₄₁	1	1	yes	characteristic
463	C₂²×C₄	C₂×D₄×C₄₁	1	4	yes	—
464	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
465	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
466	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
467	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
468	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
469	C₂²×C₄	#41×C₄₁	1	2	yes	—
470	C₂²×C₄	#41×C₄₁	1	2	yes	—
471	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
472	M₁₆	—	2	16	no	—
473	M₁₆	—	2	4	no	—
474	M₁₆	—	2	4	no	—
475	M₁₆	—	2	4	no	—
476	M₁₆	—	2	4	no	—
477	C₂×C₈	—	2	16	no	—
478	C₂×C₈	—	2	4	no	—
479	C₂×C₈	—	2	4	no	—
480	C₂×C₈	C₂×D₄×C₄₁	1	8	yes	—
481	C₄⋊C₄	—	2	2	no	—
482	C₄⋊C₄	—	2	8	no	—
483	C₄⋊C₄	—	2	2	no	—
484	C₄⋊C₄	—	2	4	no	—
485	C₄⋊C₄	—	4	2	no	—
486	C₂²⋊C₄	—	2	2	no	—
487	C₂²⋊C₄	—	2	8	no	—
488	C₂²⋊C₄	—	2	2	no	—
489	C₂²⋊C₄	—	2	8	no	—
490	C₂²⋊C₄	—	2	4	no	—
491	C₂²⋊C₄	—	4	2	no	—
492	C₄²	—	2	2	no	—
493	C₄²	—	2	4	no	—
494	C₄²	—	4	2	no	—
495	C₄²	C₂²×C₄×C₄₁	1	4	yes	—
496	C₂³	—	2	2	no	—
497	C₂³	—	2	2	no	—
498	C₂³	—	2	2	no	—
499	C₂³	—	4	2	no	—
500	C₂³	—	8	1	no	—
501	C₂³	—	8	2	no	—
502	C₂³	—	8	2	no	—
503	C₂³	C₂×C₂²⋊C₄×C₄₁	1	4	yes	—
504	C₂³	C₂×C₂²⋊C₄×C₄₁	1	1	yes	characteristic
505	C₂³	C₂×C₂²⋊C₄×C₄₁	1	1	yes	characteristic
506	C₂³	#121×C₄₁	1	2	yes	—
507	C₂³	#121×C₄₁	1	2	yes	—
508	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
509	Q₈	—	2	4	no	—
510	Q₈	—	2	4	no	—
511	Q₈	—	2	4	no	—
512	Q₈	—	4	1	no	—
513	Q₈	—	4	1	no	—
514	D₄	—	2	8	no	—
515	D₄	—	2	8	no	—
516	D₄	—	2	4	no	—
517	D₄	—	2	4	no	—
518	D₄	—	2	4	no	—
519	D₄	—	4	2	no	—
520	D₄	—	4	2	no	—
521	D₄	—	4	4	no	—
522	D₄	—	4	1	no	—
523	D₄	—	4	1	no	—
524	D₄	—	8	8	no	—
525	C₂×C₄	—	2	2	no	—
526	C₂×C₄	—	2	2	no	—
527	C₂×C₄	—	2	4	no	—
528	C₂×C₄	—	2	4	no	—
529	C₂×C₄	—	2	4	no	—
530	C₂×C₄	—	2	4	no	—
531	C₂×C₄	—	2	4	no	—
532	C₂×C₄	—	2	2	no	—
533	C₂×C₄	—	4	2	no	—
534	C₂×C₄	—	4	2	no	—
535	C₂×C₄	—	4	2	no	—
536	C₂×C₄	—	4	4	no	—
537	C₂×C₄	—	4	4	no	—
538	C₂×C₄	—	8	2	no	—
539	C₂×C₄	—	8	4	no	—
540	C₂×C₄	C₂×C₂²⋊C₄×C₄₁	1	4	yes	—
541	C₂×C₄	C₂×C₂²⋊C₄×C₄₁	1	1	yes	characteristic
542	C₂×C₄	C₂×C₂²⋊C₄×C₄₁	1	1	yes	characteristic
543	C₂×C₄	C₄×D₄×C₄₁	1	2	yes	—
544	C₂×C₄	C₄×D₄×C₄₁	1	2	yes	—
545	C₂×C₄	C₄×D₄×C₄₁	1	2	yes	—
546	C₂×C₄	C₄×D₄×C₄₁	1	2	yes	—
547	C₂×C₄	#120×C₄₁	1	1	yes	characteristic
548	C₂×C₄	#120×C₄₁	1	2	yes	—
549	C₂×C₄	#120×C₄₁	1	1	yes	characteristic
550	C₂×C₄	#121×C₄₁	1	2	yes	—
551	C₂×C₄	#121×C₄₁	1	2	yes	—
552	C₂×C₄	#123×C₄₁	1	1	yes	characteristic
553	C₂×C₄	#123×C₄₁	1	1	yes	characteristic
554	C₂×C₄	#123×C₄₁	1	2	yes	—
555	C₂×C₄	C₂³×C₄×C₄₁	1	1	yes	characteristic
556	C₂×C₄	C₂²×D₄×C₄₁	1	2	yes	—
557	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
558	C₂×C₄	C₂×#41×C₄₁	1	2	yes	—
559	C₈	—	2	8	no	—
560	C₂²	—	2	4	no	—
561	C₂²	—	4	1	no	—
562	C₂²	—	4	2	no	—
563	C₂²	—	4	1	no	—
564	C₂²	—	4	1	no	—
565	C₂²	—	4	2	no	—
566	C₂²	—	4	4	no	—
567	C₂²	—	4	4	no	—
568	C₂²	—	4	4	no	—
569	C₂²	—	4	2	no	—
570	C₂²	—	8	2	no	—
571	C₂²	—	8	4	no	—
572	C₂²	C₄₁×#386	1	1	yes	characteristic
573	C₂²	C₄₁×#386	1	1	yes	characteristic
574	C₂²	C₄₁×#386	1	2	yes	—
575	C₂²	C₂²×C₂²⋊C₄×C₄₁	1	1	yes	characteristic
576	C₂²	C₂×#121×C₄₁	1	2	yes	—
577	C₄	—	2	4	no	—
578	C₄	—	4	4	no	—
579	C₄	—	4	2	no	—
580	C₄	—	8	4	no	—
581	C₄	C₄₁×#386	1	1	yes	characteristic
582	C₄	C₄₁×#386	1	1	yes	characteristic
583	C₄	C₄₁×#386	1	2	yes	—
584	C₄	C₂×C₄×D₄×C₄₁	1	2	yes	—
585	C₄	C₂×#120×C₄₁	1	1	yes	characteristic
586	C₄	C₂×#123×C₄₁	1	1	yes	characteristic
587	C₂	—	2	1	no	—
588	C₂	—	2	2	no	—
589	C₂	—	2	1	no	—
590	C₂	—	2	1	no	—
591	C₂	—	2	2	no	—
592	C₂	—	4	4	no	—
593	C₂	—	8	2	no	—
594	C₂	C₂×C₄₁×#386	1	1	yes	characteristic

	subgroup	G/H
center	C₄×C₄₁	#386
commutator	C₂×C₄	C₂³×C₄×C₄₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₁
socle	C₂×C₄₁	C₂×#386
prime radical	C₄₁×#3449	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₄₁ ◁ C₂³×C₄×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₄₁×#568	C₂	semidirect
3. C₄₁×#2896	C₂	semidirect
4. C₂×C₄₁×#410	C₂	semidirect
5. C₄₁×#1910	C₂	semidirect
6. C₄₁×#1909	C₂	semidirect
7. C₂×C₄₁×H(3,ℤ/4)	C₂	semidirect
17. C₄₁×#536	C₄	semidirect
19. C₄₁×#535	C₄	semidirect
22. C₄₁×#532	C₄	semidirect
27. C₄₁×#419	C₂²	semidirect
28. C₄₁×#418	C₂²	semidirect
34. C₄₁×H(3,ℤ/4)	C₂²	semidirect
69. C₂×M₁₆×C₄₁	D₄	semidirect
72. C₂²×C₈×C₄₁	D₄	semidirect
73. C₄⋊Q₈×C₄₁	C₂×C₄	semidirect
74. #127×C₄₁	C₂×C₄	semidirect
75. #124×C₄₁	C₂×C₄	semidirect
76. #124×C₄₁	C₂×C₄	semidirect
262. #21009	C₄₁	direct (N × H)
290. C₂×#568	C₂×C₄₁	semidirect
292. #2896	C₂×C₄₁	semidirect
293. C₂×#410	C₂×C₄₁	semidirect
294. #1910	C₂×C₄₁	semidirect
295. #1909	C₂×C₄₁	semidirect
296. C₂×H(3,ℤ/4)	C₂×C₄₁	semidirect
314. #536	C₄×C₄₁	semidirect
316. #535	C₄×C₄₁	semidirect
319. #532	C₄×C₄₁	semidirect
324. #419	C₂²×C₄₁	semidirect
325. #418	C₂²×C₄₁	semidirect
331. H(3,ℤ/4)	C₂²×C₄₁	semidirect
332. C₄₁	#21009	direct (N × H)
367. C₂×M₁₆	D₄×C₄₁	semidirect
370. C₂²×C₈	D₄×C₄₁	semidirect
371. C₄⋊Q₈	C₂×C₄×C₄₁	semidirect
372. #127	C₂×C₄×C₄₁	semidirect
373. #124	C₂×C₄×C₄₁	semidirect
374. #124	C₂×C₄×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×#568	2
C₄₁×#3449	2
C₄₁×#2896	2
C₂×C₄₁×#410	2
C₄₁×#1910	2
C₄₁×#1909	2
C₂×C₄₁×H(3,ℤ/4)	2
#21009	41

Subgroups — C41×#21009 #23797210

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#21009 #23797210