Subgroups — C₄₁×#60142 #23836343

Order 10496.

2714 conjugacy classes of subgroups.

The subgroup lattice has 600 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	C₂²×#131×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₁×#3449	C₂	1	1	yes	maximal, characteristic
4	C₄₁×#2935	C₂	1	8	yes	maximal, complemented
5	C₄₁×#2933	C₂	1	8	yes	maximal, complemented
6	C₄₁×#2930	C₂	1	4	yes	maximal, complemented
7	C₄₁×#2929	C₂	1	4	yes	maximal, complemented
8	C₂×C₄₁×#424	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄₁×#2879	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₄₁×#408	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₁×#2873	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×#41×C₄₁	C₂²	1	1	yes	characteristic
13	C₂²×#41×C₄₁	C₂²	1	1	yes	characteristic
14	C₄₁×#568	—	2	8	no	—
15	C₂×#131×C₄₁	—	2	8	no	—
16	C₂×#131×C₄₁	C₂²	1	4	yes	—
17	C₂×#131×C₄₁	C₂²	1	4	yes	—
18	C₂×#131×C₄₁	C₂²	1	4	yes	complemented
19	C₂×#131×C₄₁	C₂²	1	4	yes	complemented
20	C₂²×M₁₆×C₄₁	C₂²	1	1	yes	characteristic
21	C₂²×M₁₆×C₄₁	C₂²	1	1	yes	characteristic
22	C₂²×M₁₆×C₄₁	C₂²	1	1	yes	characteristic
23	C₂²×M₁₆×C₄₁	C₂²	1	2	yes	complemented
24	C₂²×M₁₆×C₄₁	C₂²	1	4	yes	complemented
25	C₂³×C₈×C₄₁	C₂²	1	1	yes	characteristic
26	C₂³×C₈×C₄₁	C₂²	1	2	yes	complemented
27	C₄₁×#537	C₄	1	4	yes	—
28	C₄₁×#536	C₄	1	2	yes	—
29	C₄₁×#536	C₄	1	2	yes	—
30	C₄₁×#535	C₄	1	2	yes	—
31	C₄₁×#535	C₄	1	2	yes	—
32	C₄₁×#534	C₄	1	4	yes	—
33	C₄₁×#532	C₂²	1	4	yes	—
34	C₄₁×#525	C₂²	1	4	yes	—
35	C₄₁×#525	C₂²	1	4	yes	—
36	C₂×#117×C₄₁	C₂²	1	1	yes	characteristic
37	C₄₁×#436	C₂²	1	16	yes	complemented
38	C₄₁×#435	C₂²	1	16	yes	complemented
39	C₄₁×#435	C₂²	1	16	yes	complemented
40	C₈×D₄×C₄₁	C₂²	1	16	yes	complemented
41	C₄₁×#424	C₂²	1	2	yes	complemented
42	C₄₁×#424	C₂²	1	2	yes	complemented
43	C₄₁×#424	C₂²	1	4	yes	complemented
44	C₂×C₄⋊C₈×C₄₁	C₂²	1	4	yes	complemented
45	C₄₁×#408	C₂²	1	2	yes	—
46	C₄₁×#408	C₂²	1	2	yes	—
47	C₄₁×#408	C₂²	1	4	yes	—
48	C₄₁×#408	C₂²	1	4	yes	complemented
49	C₄₁×#408	C₂²	1	4	yes	complemented
50	C₄₁×#407	C₂²	1	4	yes	complemented
51	C₂×C₂²⋊C₈×C₄₁	C₂²	1	4	yes	complemented
52	C₄₁×#405	C₂²	1	4	yes	complemented
53	C₄₁×#405	C₂²	1	4	yes	complemented
54	C₄×M₁₆×C₄₁	C₂²	1	4	yes	complemented
55	C₂×#41×C₄₁	—	2	4	no	—
56	C₂×#41×C₄₁	—	2	4	no	—
57	C₂×#41×C₄₁	—	2	4	no	—
58	C₂×#41×C₄₁	—	2	4	no	—
59	C₂×#41×C₄₁	C₂×C₄	1	2	yes	—
60	C₂×#41×C₄₁	C₂×C₄	1	2	yes	—
61	C₂×#41×C₄₁	C₂×C₄	1	2	yes	—
62	C₂×#41×C₄₁	C₂×C₄	1	2	yes	—
63	C₂×#41×C₄₁	C₂³	1	2	yes	—
64	C₂×#41×C₄₁	C₂³	1	2	yes	—
65	C₂×#41×C₄₁	C₂³	1	2	yes	—
66	C₂×#41×C₄₁	C₂³	1	2	yes	—
67	C₂²×Q₈×C₄₁	C₂×C₄	1	1	yes	characteristic
68	C₂²×Q₈×C₄₁	C₂×C₄	1	1	yes	characteristic
69	C₂²×D₄×C₄₁	C₂×C₄	1	2	yes	—
70	C₂²×D₄×C₄₁	C₂×C₄	1	2	yes	—
71	C₂²×D₄×C₄₁	C₂×C₄	1	1	yes	characteristic
72	C₂²×D₄×C₄₁	C₂×C₄	1	1	yes	characteristic
73	C₂³×C₄×C₄₁	C₂³	1	2	yes	—
74	C₂³×C₄×C₄₁	C₂³	1	2	yes	—
75	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
76	#131×C₄₁	—	2	16	no	—
77	#131×C₄₁	—	2	16	no	—
78	#131×C₄₁	—	2	16	no	—
79	#131×C₄₁	—	2	16	no	—
80	C₂×M₁₆×C₄₁	—	2	4	no	—
81	C₂×M₁₆×C₄₁	—	2	4	no	—
82	C₂×M₁₆×C₄₁	—	2	16	no	—
83	C₂×M₁₆×C₄₁	—	2	8	no	—
84	C₂×M₁₆×C₄₁	D₄	1	8	yes	complemented
85	C₂×M₁₆×C₄₁	C₂³	1	2	yes	—
86	C₂×M₁₆×C₄₁	C₂³	1	2	yes	—
87	C₂×M₁₆×C₄₁	C₂³	1	2	yes	—
88	C₂×M₁₆×C₄₁	C₂³	1	2	yes	—
89	C₂×M₁₆×C₄₁	C₂³	1	8	yes	—
90	C₂×M₁₆×C₄₁	C₂³	1	8	yes	—
91	C₂×M₁₆×C₄₁	C₂³	1	2	yes	—
92	C₂×M₁₆×C₄₁	C₂³	1	2	yes	—
93	C₂²×C₈×C₄₁	—	2	4	no	—
94	C₂²×C₈×C₄₁	—	2	8	no	—
95	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
96	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
97	C₂²×C₈×C₄₁	C₂³	1	2	yes	—
98	C₂²×C₈×C₄₁	C₂³	1	2	yes	—
99	C₂²×C₈×C₄₁	C₂³	1	8	yes	—
100	C₂²×C₈×C₄₁	C₂³	1	2	yes	—
101	C₂²×C₈×C₄₁	C₂³	1	2	yes	—
102	C₂²×C₈×C₄₁	C₂³	1	8	yes	—
103	C₂²×C₈×C₄₁	C₂³	1	2	yes	—
104	C₄⋊Q₈×C₄₁	C₂×C₄	1	4	yes	—
105	#127×C₄₁	C₂×C₄	1	4	yes	—
106	#124×C₄₁	C₂×C₄	1	4	yes	—
107	#124×C₄₁	C₂×C₄	1	4	yes	—
108	#123×C₄₁	C₂×C₄	1	8	yes	—
109	#123×C₄₁	C₂×C₄	1	8	yes	—
110	C₂²⋊Q₈×C₄₁	C₂×C₄	1	8	yes	—
111	C₂²⋊Q₈×C₄₁	C₂×C₄	1	8	yes	—
112	#121×C₄₁	C₂×C₄	1	8	yes	—
113	#121×C₄₁	C₂×C₄	1	8	yes	—
114	#121×C₄₁	C₂×C₄	1	16	yes	—
115	#120×C₄₁	C₂×C₄	1	8	yes	—
116	#120×C₄₁	C₂×C₄	1	8	yes	—
117	C₄×D₄×C₄₁	C₂³	1	16	yes	—
118	#117×C₄₁	C₂×C₄	1	2	yes	—
119	#117×C₄₁	C₂×C₄	1	2	yes	—
120	#117×C₄₁	C₂³	1	2	yes	—
121	#117×C₄₁	C₂³	1	2	yes	—
122	C₂×C₄⋊C₄×C₄₁	C₂×C₄	1	2	yes	—
123	C₂×C₂²⋊C₄×C₄₁	C₂×C₄	1	2	yes	—
124	C₂×C₄²×C₄₁	C₂³	1	2	yes	—
125	C₄⋊C₈×C₄₁	C₂³	1	8	yes	—
126	C₄⋊C₈×C₄₁	C₂³	1	8	yes	—
127	C₂²⋊C₈×C₄₁	C₂³	1	8	yes	—
128	C₂²⋊C₈×C₄₁	C₂³	1	8	yes	—
129	C₂²⋊C₈×C₄₁	C₂³	1	16	yes	—
130	#97×C₄₁	C₂³	1	8	yes	—
131	C₄×C₈×C₄₁	C₂³	1	8	yes	—
132	C₂⁴×C₄₁	C₂²×C₄	1	2	yes	—
133	C₂⁴×C₄₁	C₂²×C₄	1	2	yes	—
134	C₂⁴×C₄₁	C₂²×C₄	1	1	yes	characteristic
135	#41×C₄₁	—	2	8	no	—
136	#41×C₄₁	—	2	8	no	—
137	#41×C₄₁	—	2	8	no	—
138	#41×C₄₁	—	2	8	no	—
139	#41×C₄₁	—	2	4	no	—
140	#41×C₄₁	—	2	4	no	—
141	#41×C₄₁	—	2	4	no	—
142	#41×C₄₁	—	2	4	no	—
143	#41×C₄₁	—	2	4	no	—
144	#41×C₄₁	—	2	4	no	—
145	#41×C₄₁	—	2	4	no	—
146	#41×C₄₁	—	2	4	no	—
147	C₂×Q₈×C₄₁	—	2	4	no	—
148	C₂×Q₈×C₄₁	—	2	4	no	—
149	C₂×Q₈×C₄₁	C₂²×C₄	1	2	yes	—
150	C₂×Q₈×C₄₁	C₂²×C₄	1	2	yes	—
151	C₂×Q₈×C₄₁	C₂²×C₄	1	2	yes	—
152	C₂×Q₈×C₄₁	C₂²×C₄	1	2	yes	—
153	C₂×D₄×C₄₁	—	2	8	no	—
154	C₂×D₄×C₄₁	—	2	8	no	—
155	C₂×D₄×C₄₁	—	2	4	no	—
156	C₂×D₄×C₄₁	—	2	4	no	—
157	C₂×D₄×C₄₁	C₂²×C₄	1	4	yes	—
158	C₂×D₄×C₄₁	C₂²×C₄	1	4	yes	—
159	C₂×D₄×C₄₁	C₂²×C₄	1	4	yes	—
160	C₂×D₄×C₄₁	C₂²×C₄	1	4	yes	—
161	C₂×D₄×C₄₁	C₂²×C₄	1	2	yes	—
162	C₂×D₄×C₄₁	C₂²×C₄	1	2	yes	—
163	C₂×D₄×C₄₁	C₂²×C₄	1	2	yes	—
164	C₂×D₄×C₄₁	C₂²×C₄	1	2	yes	—
165	C₂×D₄×C₄₁	C₂²×C₄	1	16	yes	—
166	C₂²×C₄×C₄₁	—	2	4	no	—
167	C₂²×C₄×C₄₁	—	2	4	no	—
168	C₂²×C₄×C₄₁	—	2	4	no	—
169	C₂²×C₄×C₄₁	—	2	4	no	—
170	C₂²×C₄×C₄₁	C₂²×C₄	1	4	yes	—
171	C₂²×C₄×C₄₁	C₂²×C₄	1	4	yes	—
172	C₂²×C₄×C₄₁	C₂²×C₄	1	2	yes	—
173	C₂²×C₄×C₄₁	C₂²×C₄	1	2	yes	—
174	C₂²×C₄×C₄₁	C₂²×C₄	1	4	yes	—
175	C₂²×C₄×C₄₁	C₂²×C₄	1	1	yes	characteristic
176	C₂²×C₄×C₄₁	C₂²×C₄	1	1	yes	characteristic
177	C₂²×C₄×C₄₁	C₂²×C₄	1	1	yes	characteristic
178	C₂²×C₄×C₄₁	C₂×D₄	1	4	yes	—
179	C₂²×C₄×C₄₁	#41	1	4	yes	—
180	C₂²×C₄×C₄₁	C₂⁴	1	4	yes	—
181	C₂²×C₄×C₄₁	C₂⁴	1	4	yes	—
182	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
183	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
184	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
185	M₁₆×C₄₁	—	2	4	no	—
186	M₁₆×C₄₁	—	2	4	no	—
187	M₁₆×C₄₁	—	2	4	no	—
188	M₁₆×C₄₁	—	2	4	no	—
189	M₁₆×C₄₁	—	2	16	no	—
190	M₁₆×C₄₁	—	2	16	no	—
191	M₁₆×C₄₁	C₂×D₄	1	8	yes	—
192	M₁₆×C₄₁	C₂×D₄	1	8	yes	—
193	C₂×C₈×C₄₁	—	2	2	no	—
194	C₂×C₈×C₄₁	—	2	2	no	—
195	C₂×C₈×C₄₁	—	2	4	no	—
196	C₂×C₈×C₄₁	—	2	4	no	—
197	C₂×C₈×C₄₁	—	2	4	no	—
198	C₂×C₈×C₄₁	—	2	4	no	—
199	C₂×C₈×C₄₁	—	2	16	no	—
200	C₂×C₈×C₄₁	—	2	16	no	—
201	C₂×C₈×C₄₁	C₂×D₄	1	8	yes	—
202	C₂×C₈×C₄₁	C₂⁴	1	4	yes	—
203	C₂×C₈×C₄₁	C₂⁴	1	2	yes	—
204	C₂×C₈×C₄₁	C₂⁴	1	2	yes	—
205	C₂×C₈×C₄₁	C₂⁴	1	4	yes	—
206	C₂×C₈×C₄₁	C₂⁴	1	4	yes	—
207	C₄⋊C₄×C₄₁	C₂²×C₄	1	4	yes	—
208	C₄⋊C₄×C₄₁	C₂²×C₄	1	4	yes	—
209	C₄⋊C₄×C₄₁	C₂²×C₄	1	16	yes	—
210	C₂²⋊C₄×C₄₁	C₂²×C₄	1	4	yes	—
211	C₂²⋊C₄×C₄₁	C₂²×C₄	1	4	yes	—
212	C₂²⋊C₄×C₄₁	C₂²×C₄	1	16	yes	—
213	C₂²⋊C₄×C₄₁	C₂²×C₄	1	16	yes	—
214	C₄²×C₄₁	C₂²×C₄	1	4	yes	—
215	C₄²×C₄₁	C₂⁴	1	4	yes	—
216	C₂³×C₄₁	—	2	4	no	—
217	C₂³×C₄₁	—	2	4	no	—
218	C₂³×C₄₁	—	4	2	no	—
219	C₂³×C₄₁	—	4	4	no	—
220	C₂³×C₄₁	—	4	4	no	—
221	C₂³×C₄₁	C₄×D₄	1	4	yes	—
222	C₂³×C₄₁	C₂³×C₄	1	4	yes	—
223	C₂³×C₄₁	C₂³×C₄	1	4	yes	—
224	C₂³×C₄₁	C₂³×C₄	1	1	yes	characteristic
225	C₂³×C₄₁	C₂³×C₄	1	1	yes	characteristic
226	C₂³×C₄₁	C₂³×C₄	1	1	yes	characteristic
227	Q₈×C₄₁	—	2	4	no	—
228	Q₈×C₄₁	—	2	4	no	—
229	Q₈×C₄₁	—	2	4	no	—
230	Q₈×C₄₁	—	2	4	no	—
231	D₄×C₄₁	—	2	8	no	—
232	D₄×C₄₁	—	2	8	no	—
233	D₄×C₄₁	—	2	8	no	—
234	D₄×C₄₁	—	2	8	no	—
235	D₄×C₄₁	—	2	4	no	—
236	D₄×C₄₁	—	2	4	no	—
237	D₄×C₄₁	—	2	4	no	—
238	D₄×C₄₁	—	2	4	no	—
239	D₄×C₄₁	—	4	16	no	—
240	C₂×C₄×C₄₁	—	2	4	no	—
241	C₂×C₄×C₄₁	—	2	4	no	—
242	C₂×C₄×C₄₁	—	2	8	no	—
243	C₂×C₄×C₄₁	—	2	8	no	—
244	C₂×C₄×C₄₁	—	2	4	no	—
245	C₂×C₄×C₄₁	—	2	4	no	—
246	C₂×C₄×C₄₁	—	2	4	no	—
247	C₂×C₄×C₄₁	—	2	4	no	—
248	C₂×C₄×C₄₁	—	4	4	no	—
249	C₂×C₄×C₄₁	C₄×D₄	1	4	yes	—
250	C₂×C₄×C₄₁	C₄×D₄	1	4	yes	—
251	C₂×C₄×C₄₁	C₄×D₄	1	4	yes	—
252	C₂×C₄×C₄₁	C₂³×C₄	1	8	yes	—
253	C₂×C₄×C₄₁	C₂³×C₄	1	4	yes	—
254	C₂×C₄×C₄₁	C₂³×C₄	1	4	yes	—
255	C₂×C₄×C₄₁	C₂³×C₄	1	1	yes	characteristic
256	C₂×C₄×C₄₁	C₂³×C₄	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	2	yes	—
260	C₂×C₄×C₄₁	C₂²×D₄	1	2	yes	—
261	C₂×C₄×C₄₁	C₂×#41	1	2	yes	—
262	C₂×C₄×C₄₁	C₂×#41	1	2	yes	—
263	C₂×C₄×C₄₁	C₂×#41	1	2	yes	—
264	C₂×C₄×C₄₁	C₂⁵	1	1	yes	characteristic
265	C₈×C₄₁	—	2	2	no	—
266	C₈×C₄₁	—	2	2	no	—
267	C₈×C₄₁	—	2	4	no	—
268	C₈×C₄₁	—	2	4	no	—
269	C₈×C₄₁	C₂²×D₄	1	8	yes	—
270	#60142	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
271	C₂²×C₄₁	—	2	2	no	—
272	C₂²×C₄₁	—	2	2	no	—
273	C₂²×C₄₁	—	2	2	no	—
274	C₂²×C₄₁	—	2	4	no	—
275	C₂²×C₄₁	—	2	4	no	—
276	C₂²×C₄₁	—	2	8	no	—
277	C₂²×C₄₁	—	2	8	no	—
278	C₂²×C₄₁	—	4	4	no	—
279	C₂²×C₄₁	—	4	8	no	—
280	C₂²×C₄₁	—	8	4	no	—
281	C₂²×C₄₁	C₂×C₄×D₄	1	2	yes	—
282	C₂²×C₄₁	C₂×C₄×D₄	1	2	yes	—
283	C₂²×C₄₁	C₂×C₄×D₄	1	2	yes	—
284	C₂²×C₄₁	C₂⁴×C₄	1	1	yes	characteristic
285	C₄×C₄₁	—	2	4	no	—
286	C₄×C₄₁	—	2	4	no	—
287	C₄×C₄₁	—	2	8	no	—
288	C₄×C₄₁	C₂×C₄×D₄	1	2	yes	—
289	C₄×C₄₁	C₂×C₄×D₄	1	2	yes	—
290	C₄×C₄₁	C₂×C₄×D₄	1	2	yes	—
291	C₄×C₄₁	C₂³×D₄	1	1	yes	characteristic
292	C₄×C₄₁	C₂²×#41	1	1	yes	characteristic
293	C₂×#568	C₂×C₄₁	1	1	yes	characteristic, complemented
294	C₂²×#131	C₂×C₄₁	1	1	yes	characteristic, complemented
295	#3449	C₂×C₄₁	1	1	yes	characteristic
296	#2935	C₂×C₄₁	1	8	yes	complemented
297	#2933	C₂×C₄₁	1	8	yes	complemented
298	#2930	C₂×C₄₁	1	4	yes	complemented
299	#2929	C₂×C₄₁	1	4	yes	complemented
300	C₂×#424	C₂×C₄₁	1	1	yes	characteristic, complemented
301	#2879	C₂×C₄₁	1	1	yes	characteristic, complemented
302	C₂×#408	C₂×C₄₁	1	1	yes	characteristic, complemented
303	#2873	C₂×C₄₁	1	1	yes	characteristic, complemented
304	C₂×C₄₁	—	2	2	no	—
305	C₂×C₄₁	—	2	2	no	—
306	C₂×C₄₁	—	2	2	no	—
307	C₂×C₄₁	—	4	4	no	—
308	C₂×C₄₁	—	4	4	no	—
309	C₂×C₄₁	C₂²×C₄×D₄	1	1	yes	characteristic
310	C₂×C₄₁	#3573	1	2	yes	—
311	C₂²×#41	C₂²×C₄₁	1	1	yes	characteristic
312	C₂²×#41	C₂²×C₄₁	1	1	yes	characteristic
313	#568	—	2	8	no	—
314	C₂×#131	—	2	8	no	—
315	C₂×#131	C₂²×C₄₁	1	4	yes	—
316	C₂×#131	C₂²×C₄₁	1	4	yes	—
317	C₂×#131	C₂²×C₄₁	1	4	yes	complemented
318	C₂×#131	C₂²×C₄₁	1	4	yes	complemented
319	C₂²×M₁₆	C₂²×C₄₁	1	1	yes	characteristic
320	C₂²×M₁₆	C₂²×C₄₁	1	1	yes	characteristic
321	C₂²×M₁₆	C₂²×C₄₁	1	1	yes	characteristic
322	C₂²×M₁₆	C₂²×C₄₁	1	2	yes	complemented
323	C₂²×M₁₆	C₂²×C₄₁	1	4	yes	complemented
324	C₂³×C₈	C₂²×C₄₁	1	1	yes	characteristic
325	C₂³×C₈	C₂²×C₄₁	1	2	yes	complemented
326	#537	C₄×C₄₁	1	4	yes	—
327	#536	C₄×C₄₁	1	2	yes	—
328	#536	C₄×C₄₁	1	2	yes	—
329	#535	C₄×C₄₁	1	2	yes	—
330	#535	C₄×C₄₁	1	2	yes	—
331	#534	C₄×C₄₁	1	4	yes	—
332	#532	C₂²×C₄₁	1	4	yes	—
333	#525	C₂²×C₄₁	1	4	yes	—
334	#525	C₂²×C₄₁	1	4	yes	—
335	C₂×#117	C₂²×C₄₁	1	1	yes	characteristic
336	#436	C₂²×C₄₁	1	16	yes	complemented
337	#435	C₂²×C₄₁	1	16	yes	complemented
338	#435	C₂²×C₄₁	1	16	yes	complemented
339	C₈×D₄	C₂²×C₄₁	1	16	yes	complemented
340	#424	C₂²×C₄₁	1	2	yes	complemented
341	#424	C₂²×C₄₁	1	2	yes	complemented
342	#424	C₂²×C₄₁	1	4	yes	complemented
343	C₂×C₄⋊C₈	C₂²×C₄₁	1	4	yes	complemented
344	#408	C₂²×C₄₁	1	2	yes	—
345	#408	C₂²×C₄₁	1	2	yes	—
346	#408	C₂²×C₄₁	1	4	yes	—
347	#408	C₂²×C₄₁	1	4	yes	complemented
348	#408	C₂²×C₄₁	1	4	yes	complemented
349	#407	C₂²×C₄₁	1	4	yes	complemented
350	C₂×C₂²⋊C₈	C₂²×C₄₁	1	4	yes	complemented
351	#405	C₂²×C₄₁	1	4	yes	complemented
352	#405	C₂²×C₄₁	1	4	yes	complemented
353	C₄×M₁₆	C₂²×C₄₁	1	4	yes	complemented
354	C₄₁	#60142	1	1	yes	characteristic, direct product factor, Sylow
355	C₂×#41	—	2	4	no	—
356	C₂×#41	—	2	4	no	—
357	C₂×#41	—	2	4	no	—
358	C₂×#41	—	2	4	no	—
359	C₂×#41	C₂×C₄×C₄₁	1	2	yes	—
360	C₂×#41	C₂×C₄×C₄₁	1	2	yes	—
361	C₂×#41	C₂×C₄×C₄₁	1	2	yes	—
362	C₂×#41	C₂×C₄×C₄₁	1	2	yes	—
363	C₂×#41	C₂³×C₄₁	1	2	yes	—
364	C₂×#41	C₂³×C₄₁	1	2	yes	—
365	C₂×#41	C₂³×C₄₁	1	2	yes	—
366	C₂×#41	C₂³×C₄₁	1	2	yes	—
367	C₂²×Q₈	C₂×C₄×C₄₁	1	1	yes	characteristic
368	C₂²×Q₈	C₂×C₄×C₄₁	1	1	yes	characteristic
369	C₂²×D₄	C₂×C₄×C₄₁	1	2	yes	—
370	C₂²×D₄	C₂×C₄×C₄₁	1	2	yes	—
371	C₂²×D₄	C₂×C₄×C₄₁	1	1	yes	characteristic
372	C₂²×D₄	C₂×C₄×C₄₁	1	1	yes	characteristic
373	C₂³×C₄	C₂³×C₄₁	1	2	yes	—
374	C₂³×C₄	C₂³×C₄₁	1	2	yes	—
375	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
376	#131	—	2	16	no	—
377	#131	—	2	16	no	—
378	#131	—	2	16	no	—
379	#131	—	2	16	no	—
380	C₂×M₁₆	—	2	4	no	—
381	C₂×M₁₆	—	2	4	no	—
382	C₂×M₁₆	—	2	16	no	—
383	C₂×M₁₆	—	2	8	no	—
384	C₂×M₁₆	D₄×C₄₁	1	8	yes	complemented
385	C₂×M₁₆	C₂³×C₄₁	1	2	yes	—
386	C₂×M₁₆	C₂³×C₄₁	1	2	yes	—
387	C₂×M₁₆	C₂³×C₄₁	1	2	yes	—
388	C₂×M₁₆	C₂³×C₄₁	1	2	yes	—
389	C₂×M₁₆	C₂³×C₄₁	1	8	yes	—
390	C₂×M₁₆	C₂³×C₄₁	1	8	yes	—
391	C₂×M₁₆	C₂³×C₄₁	1	2	yes	—
392	C₂×M₁₆	C₂³×C₄₁	1	2	yes	—
393	C₂²×C₈	—	2	4	no	—
394	C₂²×C₈	—	2	8	no	—
395	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
396	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
397	C₂²×C₈	C₂³×C₄₁	1	2	yes	—
398	C₂²×C₈	C₂³×C₄₁	1	2	yes	—
399	C₂²×C₈	C₂³×C₄₁	1	8	yes	—
400	C₂²×C₈	C₂³×C₄₁	1	2	yes	—
401	C₂²×C₈	C₂³×C₄₁	1	2	yes	—
402	C₂²×C₈	C₂³×C₄₁	1	8	yes	—
403	C₂²×C₈	C₂³×C₄₁	1	2	yes	—
404	C₄⋊Q₈	C₂×C₄×C₄₁	1	4	yes	—
405	#127	C₂×C₄×C₄₁	1	4	yes	—
406	#124	C₂×C₄×C₄₁	1	4	yes	—
407	#124	C₂×C₄×C₄₁	1	4	yes	—
408	#123	C₂×C₄×C₄₁	1	8	yes	—
409	#123	C₂×C₄×C₄₁	1	8	yes	—
410	C₂²⋊Q₈	C₂×C₄×C₄₁	1	8	yes	—
411	C₂²⋊Q₈	C₂×C₄×C₄₁	1	8	yes	—
412	#121	C₂×C₄×C₄₁	1	8	yes	—
413	#121	C₂×C₄×C₄₁	1	8	yes	—
414	#121	C₂×C₄×C₄₁	1	16	yes	—
415	#120	C₂×C₄×C₄₁	1	8	yes	—
416	#120	C₂×C₄×C₄₁	1	8	yes	—
417	C₄×D₄	C₂³×C₄₁	1	16	yes	—
418	#117	C₂×C₄×C₄₁	1	2	yes	—
419	#117	C₂×C₄×C₄₁	1	2	yes	—
420	#117	C₂³×C₄₁	1	2	yes	—
421	#117	C₂³×C₄₁	1	2	yes	—
422	C₂×C₄⋊C₄	C₂×C₄×C₄₁	1	2	yes	—
423	C₂×C₂²⋊C₄	C₂×C₄×C₄₁	1	2	yes	—
424	C₂×C₄²	C₂³×C₄₁	1	2	yes	—
425	C₄⋊C₈	C₂³×C₄₁	1	8	yes	—
426	C₄⋊C₈	C₂³×C₄₁	1	8	yes	—
427	C₂²⋊C₈	C₂³×C₄₁	1	8	yes	—
428	C₂²⋊C₈	C₂³×C₄₁	1	8	yes	—
429	C₂²⋊C₈	C₂³×C₄₁	1	16	yes	—
430	#97	C₂³×C₄₁	1	8	yes	—
431	C₄×C₈	C₂³×C₄₁	1	8	yes	—
432	C₂⁴	C₂²×C₄×C₄₁	1	2	yes	—
433	C₂⁴	C₂²×C₄×C₄₁	1	2	yes	—
434	C₂⁴	C₂²×C₄×C₄₁	1	1	yes	characteristic
435	#41	—	2	8	no	—
436	#41	—	2	8	no	—
437	#41	—	2	8	no	—
438	#41	—	2	8	no	—
439	#41	—	2	4	no	—
440	#41	—	2	4	no	—
441	#41	—	2	4	no	—
442	#41	—	2	4	no	—
443	#41	—	2	4	no	—
444	#41	—	2	4	no	—
445	#41	—	2	4	no	—
446	#41	—	2	4	no	—
447	C₂×Q₈	—	2	4	no	—
448	C₂×Q₈	—	2	4	no	—
449	C₂×Q₈	C₂²×C₄×C₄₁	1	2	yes	—
450	C₂×Q₈	C₂²×C₄×C₄₁	1	2	yes	—
451	C₂×Q₈	C₂²×C₄×C₄₁	1	2	yes	—
452	C₂×Q₈	C₂²×C₄×C₄₁	1	2	yes	—
453	C₂×D₄	—	2	8	no	—
454	C₂×D₄	—	2	8	no	—
455	C₂×D₄	—	2	4	no	—
456	C₂×D₄	—	2	4	no	—
457	C₂×D₄	C₂²×C₄×C₄₁	1	4	yes	—
458	C₂×D₄	C₂²×C₄×C₄₁	1	4	yes	—
459	C₂×D₄	C₂²×C₄×C₄₁	1	4	yes	—
460	C₂×D₄	C₂²×C₄×C₄₁	1	4	yes	—
461	C₂×D₄	C₂²×C₄×C₄₁	1	2	yes	—
462	C₂×D₄	C₂²×C₄×C₄₁	1	2	yes	—
463	C₂×D₄	C₂²×C₄×C₄₁	1	2	yes	—
464	C₂×D₄	C₂²×C₄×C₄₁	1	2	yes	—
465	C₂×D₄	C₂²×C₄×C₄₁	1	16	yes	—
466	C₂²×C₄	—	2	4	no	—
467	C₂²×C₄	—	2	4	no	—
468	C₂²×C₄	—	2	4	no	—
469	C₂²×C₄	—	2	4	no	—
470	C₂²×C₄	C₂²×C₄×C₄₁	1	4	yes	—
471	C₂²×C₄	C₂²×C₄×C₄₁	1	4	yes	—
472	C₂²×C₄	C₂²×C₄×C₄₁	1	2	yes	—
473	C₂²×C₄	C₂²×C₄×C₄₁	1	2	yes	—
474	C₂²×C₄	C₂²×C₄×C₄₁	1	4	yes	—
475	C₂²×C₄	C₂²×C₄×C₄₁	1	1	yes	characteristic
476	C₂²×C₄	C₂²×C₄×C₄₁	1	1	yes	characteristic
477	C₂²×C₄	C₂²×C₄×C₄₁	1	1	yes	characteristic
478	C₂²×C₄	C₂×D₄×C₄₁	1	4	yes	—
479	C₂²×C₄	#41×C₄₁	1	4	yes	—
480	C₂²×C₄	C₂⁴×C₄₁	1	4	yes	—
481	C₂²×C₄	C₂⁴×C₄₁	1	4	yes	—
482	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
483	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
484	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
485	M₁₆	—	2	4	no	—
486	M₁₆	—	2	4	no	—
487	M₁₆	—	2	4	no	—
488	M₁₆	—	2	4	no	—
489	M₁₆	—	2	16	no	—
490	M₁₆	—	2	16	no	—
491	M₁₆	C₂×D₄×C₄₁	1	8	yes	—
492	M₁₆	C₂×D₄×C₄₁	1	8	yes	—
493	C₂×C₈	—	2	2	no	—
494	C₂×C₈	—	2	2	no	—
495	C₂×C₈	—	2	4	no	—
496	C₂×C₈	—	2	4	no	—
497	C₂×C₈	—	2	4	no	—
498	C₂×C₈	—	2	4	no	—
499	C₂×C₈	—	2	16	no	—
500	C₂×C₈	—	2	16	no	—
501	C₂×C₈	C₂×D₄×C₄₁	1	8	yes	—
502	C₂×C₈	C₂⁴×C₄₁	1	4	yes	—
503	C₂×C₈	C₂⁴×C₄₁	1	2	yes	—
504	C₂×C₈	C₂⁴×C₄₁	1	2	yes	—
505	C₂×C₈	C₂⁴×C₄₁	1	4	yes	—
506	C₂×C₈	C₂⁴×C₄₁	1	4	yes	—
507	C₄⋊C₄	C₂²×C₄×C₄₁	1	4	yes	—
508	C₄⋊C₄	C₂²×C₄×C₄₁	1	4	yes	—
509	C₄⋊C₄	C₂²×C₄×C₄₁	1	16	yes	—
510	C₂²⋊C₄	C₂²×C₄×C₄₁	1	4	yes	—
511	C₂²⋊C₄	C₂²×C₄×C₄₁	1	4	yes	—
512	C₂²⋊C₄	C₂²×C₄×C₄₁	1	16	yes	—
513	C₂²⋊C₄	C₂²×C₄×C₄₁	1	16	yes	—
514	C₄²	C₂²×C₄×C₄₁	1	4	yes	—
515	C₄²	C₂⁴×C₄₁	1	4	yes	—
516	C₂³	—	2	4	no	—
517	C₂³	—	2	4	no	—
518	C₂³	—	4	2	no	—
519	C₂³	—	4	4	no	—
520	C₂³	—	4	4	no	—
521	C₂³	C₄×D₄×C₄₁	1	4	yes	—
522	C₂³	C₂³×C₄×C₄₁	1	4	yes	—
523	C₂³	C₂³×C₄×C₄₁	1	4	yes	—
524	C₂³	C₂³×C₄×C₄₁	1	1	yes	characteristic
525	C₂³	C₂³×C₄×C₄₁	1	1	yes	characteristic
526	C₂³	C₂³×C₄×C₄₁	1	1	yes	characteristic
527	Q₈	—	2	4	no	—
528	Q₈	—	2	4	no	—
529	Q₈	—	2	4	no	—
530	Q₈	—	2	4	no	—
531	D₄	—	2	8	no	—
532	D₄	—	2	8	no	—
533	D₄	—	2	8	no	—
534	D₄	—	2	8	no	—
535	D₄	—	2	4	no	—
536	D₄	—	2	4	no	—
537	D₄	—	2	4	no	—
538	D₄	—	2	4	no	—
539	D₄	—	4	16	no	—
540	C₂×C₄	—	2	4	no	—
541	C₂×C₄	—	2	4	no	—
542	C₂×C₄	—	2	8	no	—
543	C₂×C₄	—	2	8	no	—
544	C₂×C₄	—	2	4	no	—
545	C₂×C₄	—	2	4	no	—
546	C₂×C₄	—	2	4	no	—
547	C₂×C₄	—	2	4	no	—
548	C₂×C₄	—	4	4	no	—
549	C₂×C₄	C₄×D₄×C₄₁	1	4	yes	—
550	C₂×C₄	C₄×D₄×C₄₁	1	4	yes	—
551	C₂×C₄	C₄×D₄×C₄₁	1	4	yes	—
552	C₂×C₄	C₂³×C₄×C₄₁	1	8	yes	—
553	C₂×C₄	C₂³×C₄×C₄₁	1	4	yes	—
554	C₂×C₄	C₂³×C₄×C₄₁	1	4	yes	—
555	C₂×C₄	C₂³×C₄×C₄₁	1	1	yes	characteristic
556	C₂×C₄	C₂³×C₄×C₄₁	1	1	yes	characteristic
557	C₂×C₄	C₂³×C₄×C₄₁	1	1	yes	characteristic
558	C₂×C₄	C₂²×D₄×C₄₁	1	2	yes	—
559	C₂×C₄	C₂²×D₄×C₄₁	1	2	yes	—
560	C₂×C₄	C₂²×D₄×C₄₁	1	2	yes	—
561	C₂×C₄	C₂×#41×C₄₁	1	2	yes	—
562	C₂×C₄	C₂×#41×C₄₁	1	2	yes	—
563	C₂×C₄	C₂×#41×C₄₁	1	2	yes	—
564	C₂×C₄	C₂⁵×C₄₁	1	1	yes	characteristic
565	C₈	—	2	2	no	—
566	C₈	—	2	2	no	—
567	C₈	—	2	4	no	—
568	C₈	—	2	4	no	—
569	C₈	C₂²×D₄×C₄₁	1	8	yes	—
570	C₂²	—	2	2	no	—
571	C₂²	—	2	2	no	—
572	C₂²	—	2	2	no	—
573	C₂²	—	2	8	no	—
574	C₂²	—	2	8	no	—
575	C₂²	—	2	4	no	—
576	C₂²	—	2	4	no	—
577	C₂²	—	4	4	no	—
578	C₂²	—	4	8	no	—
579	C₂²	—	8	4	no	—
580	C₂²	C₂×C₄×D₄×C₄₁	1	2	yes	—
581	C₂²	C₂×C₄×D₄×C₄₁	1	2	yes	—
582	C₂²	C₂×C₄×D₄×C₄₁	1	2	yes	—
583	C₂²	C₂⁴×C₄×C₄₁	1	1	yes	characteristic
584	C₄	—	2	8	no	—
585	C₄	—	2	4	no	—
586	C₄	—	2	4	no	—
587	C₄	C₂×C₄×D₄×C₄₁	1	2	yes	—
588	C₄	C₂×C₄×D₄×C₄₁	1	2	yes	—
589	C₄	C₂×C₄×D₄×C₄₁	1	2	yes	—
590	C₄	C₂³×D₄×C₄₁	1	1	yes	characteristic
591	C₄	C₂²×#41×C₄₁	1	1	yes	characteristic
592	C₂	—	2	2	no	—
593	C₂	—	2	2	no	—
594	C₂	—	2	2	no	—
595	C₂	—	4	4	no	—
596	C₂	—	4	4	no	—
597	C₂	C₂²×C₄×D₄×C₄₁	1	1	yes	characteristic
598	C₂	C₄₁×#3573	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₄₁	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₄₁
Frattini, cosocle	C₂×C₄	C₂⁵×C₄₁
socle	C₂²×C₄₁	C₂⁴×C₄
prime radical	C₄₁×#3449	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×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
2. C₂²×#131×C₄₁	C₂	semidirect
4. C₄₁×#2935	C₂	semidirect
5. C₄₁×#2933	C₂	semidirect
6. C₄₁×#2930	C₂	semidirect
7. C₄₁×#2929	C₂	semidirect
8. C₂×C₄₁×#424	C₂	semidirect
9. C₄₁×#2879	C₂	semidirect
10. C₂×C₄₁×#408	C₂	semidirect
11. C₄₁×#2873	C₂	semidirect
18. C₂×#131×C₄₁	C₂²	semidirect
19. C₂×#131×C₄₁	C₂²	semidirect
23. C₂²×M₁₆×C₄₁	C₂²	semidirect
24. C₂²×M₁₆×C₄₁	C₂²	semidirect
26. C₂³×C₈×C₄₁	C₂²	semidirect
37. C₄₁×#436	C₂²	semidirect
38. C₄₁×#435	C₂²	semidirect
39. C₄₁×#435	C₂²	semidirect
40. C₈×D₄×C₄₁	C₂²	semidirect
41. C₄₁×#424	C₂²	semidirect
42. C₄₁×#424	C₂²	semidirect
43. C₄₁×#424	C₂²	semidirect
44. C₂×C₄⋊C₈×C₄₁	C₂²	semidirect
48. C₄₁×#408	C₂²	semidirect
49. C₄₁×#408	C₂²	semidirect
50. C₄₁×#407	C₂²	semidirect
51. C₂×C₂²⋊C₈×C₄₁	C₂²	semidirect
52. C₄₁×#405	C₂²	semidirect
53. C₄₁×#405	C₂²	semidirect
54. C₄×M₁₆×C₄₁	C₂²	semidirect
84. C₂×M₁₆×C₄₁	D₄	semidirect
270. #60142	C₄₁	direct (N × H)
293. C₂×#568	C₂×C₄₁	semidirect
294. C₂²×#131	C₂×C₄₁	semidirect
296. #2935	C₂×C₄₁	semidirect
297. #2933	C₂×C₄₁	semidirect
298. #2930	C₂×C₄₁	semidirect
299. #2929	C₂×C₄₁	semidirect
300. C₂×#424	C₂×C₄₁	semidirect
301. #2879	C₂×C₄₁	semidirect
302. C₂×#408	C₂×C₄₁	semidirect
303. #2873	C₂×C₄₁	semidirect
317. C₂×#131	C₂²×C₄₁	semidirect
318. C₂×#131	C₂²×C₄₁	semidirect
322. C₂²×M₁₆	C₂²×C₄₁	semidirect
323. C₂²×M₁₆	C₂²×C₄₁	semidirect
325. C₂³×C₈	C₂²×C₄₁	semidirect
336. #436	C₂²×C₄₁	semidirect
337. #435	C₂²×C₄₁	semidirect
338. #435	C₂²×C₄₁	semidirect
339. C₈×D₄	C₂²×C₄₁	semidirect
340. #424	C₂²×C₄₁	semidirect
341. #424	C₂²×C₄₁	semidirect
342. #424	C₂²×C₄₁	semidirect
343. C₂×C₄⋊C₈	C₂²×C₄₁	semidirect
347. #408	C₂²×C₄₁	semidirect
348. #408	C₂²×C₄₁	semidirect
349. #407	C₂²×C₄₁	semidirect
350. C₂×C₂²⋊C₈	C₂²×C₄₁	semidirect
351. #405	C₂²×C₄₁	semidirect
352. #405	C₂²×C₄₁	semidirect
353. C₄×M₁₆	C₂²×C₄₁	semidirect
354. C₄₁	#60142	direct (N × H)
384. C₂×M₁₆	D₄×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
C₂²×#131×C₄₁	2
C₄₁×#3449	2
C₄₁×#2935	2
C₄₁×#2933	2
C₄₁×#2930	2
C₄₁×#2929	2
C₂×C₄₁×#424	2
C₄₁×#2879	2
C₂×C₄₁×#408	2
C₄₁×#2873	2
#60142	41

Subgroups — C41×#60142 #23836343

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#60142 #23836343