Subgroups — C₄×C₄₁×#451 #23797650

Order 10496.

1448 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	C₂²×C₄×Q₈×C₄₁	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄₁×#451	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×Q₁₆×C₄₁	C₂	1	2	yes	maximal, complemented
4	C₄×C₂²⋊Q₈×C₄₁	C₂	1	1	yes	maximal, characteristic
5	C₄₁×#1878	C₂	1	2	yes	maximal, complemented
6	C₄₁×#1872	C₂	1	1	yes	maximal, characteristic
7	C₄₁×#1863	C₂	1	2	yes	maximal, complemented
8	C₄₁×#1852	C₂	1	1	yes	maximal, characteristic
9	C₄₁×#1787	C₂	1	1	yes	maximal, characteristic
10	C₄×#103×C₄₁	C₂	1	2	yes	maximal, complemented
11	C₄×C₂²⋊C₈×C₄₁	C₂	1	1	yes	maximal, characteristic
12	C₂³×Q₈×C₄₁	C₂²	1	1	yes	characteristic
13	C₂²×Q₁₆×C₄₁	C₂²	1	2	yes	—
14	C₂×C₂²⋊Q₈×C₄₁	C₂²	1	1	yes	characteristic
15	C₂×C₄×Q₈×C₄₁	—	2	8	no	—
16	C₂×C₄×Q₈×C₄₁	—	2	1	no	—
17	C₂×C₄×Q₈×C₄₁	—	2	1	no	—
18	C₂×C₄×Q₈×C₄₁	C₂²	1	1	yes	characteristic
19	C₂×C₄×Q₈×C₄₁	C₂²	1	2	yes	—
20	C₂×C₄×Q₈×C₄₁	C₂²	1	2	yes	—
21	C₂²×C₄⋊C₄×C₄₁	—	2	1	no	—
22	C₂²×C₄⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
23	C₂²×C₄²×C₄₁	—	2	1	no	—
24	C₂²×C₄²×C₄₁	C₂²	1	1	yes	characteristic
25	C₄₁×#451	C₄	1	8	yes	direct product factor
26	C₄×Q₁₆×C₄₁	—	2	8	no	—
27	C₂×#107×C₄₁	C₂²	1	2	yes	—
28	C₂×#103×C₄₁	C₂²	1	2	yes	—
29	C₂×#103×C₄₁	C₂²	1	2	yes	—
30	C₂×#103×C₄₁	C₂²	1	2	yes	—
31	C₂×#103×C₄₁	C₂²	1	2	yes	—
32	C₂×C₂²⋊C₈×C₄₁	C₂²	1	1	yes	characteristic
33	C₂×C₂²⋊C₈×C₄₁	C₂²	1	1	yes	characteristic
34	C₂×C₄×C₈×C₄₁	C₂²	1	2	yes	—
35	C₄₁×#391	C₂²	1	1	yes	characteristic
36	C₄₁×#389	C₂²	1	1	yes	characteristic
37	C₄₁×#387	—	2	1	no	—
38	C₄₁×#385	—	2	1	no	—
39	C₄₁×#380	C₂²	1	1	yes	characteristic
40	C₄×C₄⋊C₄×C₄₁	—	2	1	no	—
41	C₄×C₄⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
42	C₄×C₂²⋊C₄×C₄₁	—	2	1	no	—
43	C₄₁×#340	C₂²	1	2	yes	—
44	C₄₁×#340	C₂²	1	2	yes	—
45	C₄₁×#336	C₂²	1	2	yes	—
46	C₂²×Q₈×C₄₁	—	2	4	no	—
47	C₂²×Q₈×C₄₁	—	2	4	no	—
48	C₂²×Q₈×C₄₁	—	2	1	no	—
49	C₂²×Q₈×C₄₁	—	2	2	no	—
50	C₂²×Q₈×C₄₁	C₂×C₄	1	4	yes	—
51	C₂²×Q₈×C₄₁	C₂³	1	1	yes	characteristic
52	C₂²×Q₈×C₄₁	C₂³	1	2	yes	—
53	C₂³×C₄×C₄₁	—	2	1	no	—
54	C₂³×C₄×C₄₁	—	2	1	no	—
55	C₂³×C₄×C₄₁	D₄	1	1	yes	characteristic
56	C₂³×C₄×C₄₁	D₄	1	1	yes	characteristic
57	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
58	C₂×Q₁₆×C₄₁	—	2	4	no	—
59	C₂×Q₁₆×C₄₁	—	2	4	no	—
60	C₂×Q₁₆×C₄₁	C₂×C₄	1	8	yes	complemented
61	C₂²×C₈×C₄₁	C₂³	1	2	yes	—
62	C₂²×C₈×C₄₁	C₂³	1	2	yes	—
63	C₂²⋊Q₈×C₄₁	—	2	2	no	—
64	C₂²⋊Q₈×C₄₁	C₂×C₄	1	4	yes	—
65	C₄×Q₈×C₄₁	—	2	8	no	—
66	C₄×Q₈×C₄₁	—	2	8	no	—
67	C₄×Q₈×C₄₁	—	2	4	no	—
68	C₄×Q₈×C₄₁	—	2	4	no	—
69	C₄×Q₈×C₄₁	—	2	4	no	—
70	C₄×Q₈×C₄₁	—	2	4	no	—
71	C₄×Q₈×C₄₁	D₄	1	8	yes	—
72	C₂×C₄⋊C₄×C₄₁	—	2	8	no	—
73	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
74	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
75	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
76	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
77	C₂×C₄⋊C₄×C₄₁	—	2	4	no	—
78	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
79	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
80	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
81	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
82	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
83	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
84	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
85	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
86	C₂×C₄²×C₄₁	—	2	8	no	—
87	C₂×C₄²×C₄₁	—	2	2	no	—
88	C₂×C₄²×C₄₁	—	2	2	no	—
89	C₂×C₄²×C₄₁	—	2	4	no	—
90	C₂×C₄²×C₄₁	—	2	1	no	—
91	C₂×C₄²×C₄₁	—	2	1	no	—
92	C₂×C₄²×C₄₁	D₄	1	1	yes	characteristic
93	C₂×C₄²×C₄₁	D₄	1	1	yes	characteristic
94	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
95	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
96	#107×C₄₁	—	2	4	no	—
97	#103×C₄₁	—	2	4	no	—
98	#103×C₄₁	—	2	4	no	—
99	#103×C₄₁	—	2	4	no	—
100	#103×C₄₁	C₂×C₄	1	8	yes	complemented
101	C₂²⋊C₈×C₄₁	—	2	2	no	—
102	C₂²⋊C₈×C₄₁	C₂×C₄	1	4	yes	—
103	C₄×C₈×C₄₁	—	2	4	no	—
104	#95×C₄₁	—	2	1	no	—
105	#95×C₄₁	—	2	1	no	—
106	#95×C₄₁	—	2	1	no	—
107	#95×C₄₁	—	2	1	no	—
108	#95×C₄₁	—	2	1	no	—
109	C₂⁴×C₄₁	C₂×D₄	1	1	yes	characteristic
110	C₂×Q₈×C₄₁	—	2	4	no	—
111	C₂×Q₈×C₄₁	—	2	16	no	—
112	C₂×Q₈×C₄₁	—	2	4	no	—
113	C₂×Q₈×C₄₁	—	2	16	no	—
114	C₂×Q₈×C₄₁	—	2	4	no	—
115	C₂×Q₈×C₄₁	—	2	2	no	—
116	C₂×Q₈×C₄₁	—	2	2	no	—
117	C₂×Q₈×C₄₁	—	2	2	no	—
118	C₂×Q₈×C₄₁	—	2	1	no	—
119	C₂×Q₈×C₄₁	—	2	2	no	—
120	C₂×Q₈×C₄₁	—	2	2	no	—
121	C₂×Q₈×C₄₁	C₂²×C₄	1	2	yes	—
122	C₂×Q₈×C₄₁	C₂²×C₄	1	4	yes	—
123	C₂×Q₈×C₄₁	C₂×D₄	1	4	yes	—
124	C₂×Q₈×C₄₁	#41	1	4	yes	—
125	C₂²×C₄×C₄₁	—	2	4	no	—
126	C₂²×C₄×C₄₁	—	2	4	no	—
127	C₂²×C₄×C₄₁	—	2	4	no	—
128	C₂²×C₄×C₄₁	—	2	2	no	—
129	C₂²×C₄×C₄₁	—	2	2	no	—
130	C₂²×C₄×C₄₁	—	2	2	no	—
131	C₂²×C₄×C₄₁	—	2	2	no	—
132	C₂²×C₄×C₄₁	—	2	2	no	—
133	C₂²×C₄×C₄₁	—	2	4	no	—
134	C₂²×C₄×C₄₁	—	2	2	no	—
135	C₂²×C₄×C₄₁	—	2	1	no	—
136	C₂²×C₄×C₄₁	—	2	1	no	—
137	C₂²×C₄×C₄₁	—	2	2	no	—
138	C₂²×C₄×C₄₁	—	2	2	no	—
139	C₂²×C₄×C₄₁	—	2	1	no	—
140	C₂²×C₄×C₄₁	—	2	1	no	—
141	C₂²×C₄×C₄₁	—	4	1	no	—
142	C₂²×C₄×C₄₁	—	4	2	no	—
143	C₂²×C₄×C₄₁	—	4	2	no	—
144	C₂²×C₄×C₄₁	Q₁₆	1	4	yes	complemented
145	C₂²×C₄×C₄₁	C₂²×C₄	1	2	yes	—
146	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
147	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
148	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
149	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
150	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
151	C₂²×C₄×C₄₁	#41	1	2	yes	—
152	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
153	Q₁₆×C₄₁	—	2	16	no	—
154	C₂×C₈×C₄₁	—	2	2	no	—
155	C₂×C₈×C₄₁	—	2	2	no	—
156	C₂×C₈×C₄₁	—	2	2	no	—
157	C₂×C₈×C₄₁	—	2	2	no	—
158	C₂×C₈×C₄₁	—	2	2	no	—
159	C₂×C₈×C₄₁	C₂²×C₄	1	4	yes	—
160	C₄⋊C₄×C₄₁	—	2	8	no	—
161	C₄⋊C₄×C₄₁	—	2	4	no	—
162	C₄⋊C₄×C₄₁	—	2	4	no	—
163	C₄⋊C₄×C₄₁	—	2	8	no	—
164	C₄⋊C₄×C₄₁	—	2	2	no	—
165	C₄⋊C₄×C₄₁	—	2	1	no	—
166	C₄⋊C₄×C₄₁	—	2	2	no	—
167	C₄⋊C₄×C₄₁	—	2	2	no	—
168	C₄⋊C₄×C₄₁	—	4	2	no	—
169	C₄⋊C₄×C₄₁	—	4	2	no	—
170	C₄⋊C₄×C₄₁	C₂²×C₄	1	2	yes	—
171	C₄⋊C₄×C₄₁	C₂×D₄	1	4	yes	—
172	C₂²⋊C₄×C₄₁	—	2	4	no	—
173	C₂²⋊C₄×C₄₁	—	4	2	no	—
174	C₄²×C₄₁	—	2	8	no	—
175	C₄²×C₄₁	—	2	8	no	—
176	C₄²×C₄₁	—	2	2	no	—
177	C₄²×C₄₁	—	2	2	no	—
178	C₄²×C₄₁	—	2	2	no	—
179	C₄²×C₄₁	—	4	2	no	—
180	C₄²×C₄₁	—	4	2	no	—
181	C₄²×C₄₁	C₂×D₄	1	4	yes	—
182	C₂³×C₄₁	—	2	1	no	—
183	C₂³×C₄₁	—	2	1	no	—
184	C₂³×C₄₁	—	2	1	no	—
185	C₂³×C₄₁	—	2	1	no	—
186	C₂³×C₄₁	C₄×D₄	1	2	yes	—
187	C₂³×C₄₁	C₂×Q₁₆	1	2	yes	—
188	C₂³×C₄₁	#135	1	2	yes	—
189	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
190	Q₈×C₄₁	—	2	16	no	—
191	Q₈×C₄₁	—	2	4	no	—
192	Q₈×C₄₁	—	2	4	no	—
193	Q₈×C₄₁	—	2	4	no	—
194	Q₈×C₄₁	—	2	4	no	—
195	Q₈×C₄₁	—	4	2	no	—
196	Q₈×C₄₁	C₄×D₄	1	8	yes	—
197	C₂×C₄×C₄₁	—	2	16	no	—
198	C₂×C₄×C₄₁	—	2	4	no	—
199	C₂×C₄×C₄₁	—	2	1	no	—
200	C₂×C₄×C₄₁	—	2	4	no	—
201	C₂×C₄×C₄₁	—	2	1	no	—
202	C₂×C₄×C₄₁	—	2	4	no	—
203	C₂×C₄×C₄₁	—	2	1	no	—
204	C₂×C₄×C₄₁	—	2	1	no	—
205	C₂×C₄×C₄₁	—	2	1	no	—
206	C₂×C₄×C₄₁	—	2	1	no	—
207	C₂×C₄×C₄₁	—	2	4	no	—
208	C₂×C₄×C₄₁	—	2	4	no	—
209	C₂×C₄×C₄₁	—	2	8	no	—
210	C₂×C₄×C₄₁	—	2	2	no	—
211	C₂×C₄×C₄₁	—	2	2	no	—
212	C₂×C₄×C₄₁	—	2	1	no	—
213	C₂×C₄×C₄₁	—	2	4	no	—
214	C₂×C₄×C₄₁	—	2	1	no	—
215	C₂×C₄×C₄₁	—	2	1	no	—
216	C₂×C₄×C₄₁	—	4	4	no	—
217	C₂×C₄×C₄₁	—	4	8	no	—
218	C₂×C₄×C₄₁	—	4	1	no	—
219	C₂×C₄×C₄₁	—	4	1	no	—
220	C₂×C₄×C₄₁	—	4	2	no	—
221	C₂×C₄×C₄₁	—	4	1	no	—
222	C₂×C₄×C₄₁	—	4	1	no	—
223	C₂×C₄×C₄₁	—	4	2	no	—
224	C₂×C₄×C₄₁	—	4	1	no	—
225	C₂×C₄×C₄₁	—	4	1	no	—
226	C₂×C₄×C₄₁	—	4	1	no	—
227	C₂×C₄×C₄₁	—	4	1	no	—
228	C₂×C₄×C₄₁	—	4	1	no	—
229	C₂×C₄×C₄₁	—	4	1	no	—
230	C₂×C₄×C₄₁	C₄×D₄	1	2	yes	—
231	C₂×C₄×C₄₁	#120	1	2	yes	—
232	C₂×C₄×C₄₁	#120	1	2	yes	—
233	C₂×C₄×C₄₁	C₂×Q₁₆	1	2	yes	—
234	C₂×C₄×C₄₁	C₂×Q₁₆	1	2	yes	—
235	C₂×C₄×C₄₁	#137	1	2	yes	—
236	C₂×C₄×C₄₁	C₂³×C₄	1	1	yes	characteristic
237	C₂×C₄×C₄₁	C₂²×D₄	1	2	yes	—
238	C₂×C₄×C₄₁	C₂×#41	1	2	yes	—
239	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
240	C₈×C₄₁	—	2	4	no	—
241	C₈×C₄₁	—	4	2	no	—
242	C₄×#451	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
243	C₂²×C₄₁	—	2	2	no	—
244	C₂²×C₄₁	—	2	2	no	—
245	C₂²×C₄₁	—	2	2	no	—
246	C₂²×C₄₁	—	2	2	no	—
247	C₂²×C₄₁	—	2	2	no	—
248	C₂²×C₄₁	—	2	2	no	—
249	C₂²×C₄₁	C₄×Q₁₆	1	4	yes	complemented
250	C₂²×C₄₁	C₂×C₄×D₄	1	1	yes	characteristic
251	C₂²×C₄₁	C₂×#120	1	1	yes	characteristic
252	C₂²×C₄₁	#525	1	1	yes	characteristic
253	C₂²×C₄₁	C₂²×Q₁₆	1	1	yes	characteristic
254	C₂²×C₄₁	C₂×#135	1	1	yes	characteristic
255	C₂²×C₄₁	C₂×#137	1	1	yes	characteristic
256	C₂²×C₄₁	#575	1	1	yes	characteristic
257	C₄×C₄₁	—	2	2	no	—
258	C₄×C₄₁	—	2	2	no	—
259	C₄×C₄₁	—	2	8	no	—
260	C₄×C₄₁	—	2	2	no	—
261	C₄×C₄₁	—	4	2	no	—
262	C₄×C₄₁	—	4	1	no	—
263	C₄×C₄₁	—	4	4	no	—
264	C₄×C₄₁	—	4	2	no	—
265	C₄×C₄₁	—	8	1	no	—
266	C₄×C₄₁	—	8	1	no	—
267	C₄×C₄₁	#451	1	4	yes	direct product factor
268	C₄×C₄₁	C₂×C₄×D₄	1	2	yes	—
269	C₄×C₄₁	#525	1	2	yes	—
270	C₂²×C₄×Q₈	C₂×C₄₁	1	1	yes	characteristic
271	C₂×#451	C₂×C₄₁	1	1	yes	characteristic
272	C₂×C₄×Q₁₆	C₂×C₄₁	1	2	yes	complemented
273	C₄×C₂²⋊Q₈	C₂×C₄₁	1	1	yes	characteristic
274	#1878	C₂×C₄₁	1	2	yes	complemented
275	#1872	C₂×C₄₁	1	1	yes	characteristic
276	#1863	C₂×C₄₁	1	2	yes	complemented
277	#1852	C₂×C₄₁	1	1	yes	characteristic
278	#1787	C₂×C₄₁	1	1	yes	characteristic
279	C₄×#103	C₂×C₄₁	1	2	yes	complemented
280	C₄×C₂²⋊C₈	C₂×C₄₁	1	1	yes	characteristic
281	C₂×C₄₁	—	2	4	no	—
282	C₂×C₄₁	C₄×#120	1	1	yes	characteristic
283	C₂×C₄₁	C₂×C₄×Q₁₆	1	1	yes	characteristic
284	C₂×C₄₁	C₄×#137	1	1	yes	characteristic
285	C₂×C₄₁	C₂×#451	1	1	yes	characteristic
286	C₂×C₄₁	#3002	1	1	yes	characteristic
287	C₂×C₄₁	#3104	1	1	yes	characteristic
288	C₂×C₄₁	#3108	1	1	yes	characteristic
289	C₂³×Q₈	C₂²×C₄₁	1	1	yes	characteristic
290	C₂²×Q₁₆	C₂²×C₄₁	1	2	yes	—
291	C₂×C₂²⋊Q₈	C₂²×C₄₁	1	1	yes	characteristic
292	C₂×C₄×Q₈	—	2	8	no	—
293	C₂×C₄×Q₈	—	2	1	no	—
294	C₂×C₄×Q₈	—	2	1	no	—
295	C₂×C₄×Q₈	C₂²×C₄₁	1	2	yes	—
296	C₂×C₄×Q₈	C₂²×C₄₁	1	1	yes	characteristic
297	C₂×C₄×Q₈	C₂²×C₄₁	1	2	yes	—
298	C₂²×C₄⋊C₄	—	2	1	no	—
299	C₂²×C₄⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
300	C₂²×C₄²	—	2	1	no	—
301	C₂²×C₄²	C₂²×C₄₁	1	1	yes	characteristic
302	#451	C₄×C₄₁	1	8	yes	direct product factor
303	C₄×Q₁₆	—	2	8	no	—
304	C₂×#107	C₂²×C₄₁	1	2	yes	—
305	C₂×#103	C₂²×C₄₁	1	2	yes	—
306	C₂×#103	C₂²×C₄₁	1	2	yes	—
307	C₂×#103	C₂²×C₄₁	1	2	yes	—
308	C₂×#103	C₂²×C₄₁	1	2	yes	—
309	C₂×C₂²⋊C₈	C₂²×C₄₁	1	1	yes	characteristic
310	C₂×C₂²⋊C₈	C₂²×C₄₁	1	1	yes	characteristic
311	C₂×C₄×C₈	C₂²×C₄₁	1	2	yes	—
312	#391	C₂²×C₄₁	1	1	yes	characteristic
313	#389	C₂²×C₄₁	1	1	yes	characteristic
314	#387	—	2	1	no	—
315	#385	—	2	1	no	—
316	#380	C₂²×C₄₁	1	1	yes	characteristic
317	C₄×C₄⋊C₄	—	2	1	no	—
318	C₄×C₄⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
319	C₄×C₂²⋊C₄	—	2	1	no	—
320	#340	C₂²×C₄₁	1	2	yes	—
321	#340	C₂²×C₄₁	1	2	yes	—
322	#336	C₂²×C₄₁	1	2	yes	—
323	C₄₁	C₄×#451	1	1	yes	characteristic, direct product factor, Sylow
324	C₂²×Q₈	—	2	4	no	—
325	C₂²×Q₈	—	2	4	no	—
326	C₂²×Q₈	—	2	1	no	—
327	C₂²×Q₈	—	2	2	no	—
328	C₂²×Q₈	C₂×C₄×C₄₁	1	4	yes	—
329	C₂²×Q₈	C₂³×C₄₁	1	1	yes	characteristic
330	C₂²×Q₈	C₂³×C₄₁	1	2	yes	—
331	C₂³×C₄	—	2	1	no	—
332	C₂³×C₄	—	2	1	no	—
333	C₂³×C₄	D₄×C₄₁	1	1	yes	characteristic
334	C₂³×C₄	D₄×C₄₁	1	1	yes	characteristic
335	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
336	C₂×Q₁₆	—	2	4	no	—
337	C₂×Q₁₆	—	2	4	no	—
338	C₂×Q₁₆	C₂×C₄×C₄₁	1	8	yes	complemented
339	C₂²×C₈	C₂³×C₄₁	1	2	yes	—
340	C₂²×C₈	C₂³×C₄₁	1	2	yes	—
341	C₂²⋊Q₈	—	2	2	no	—
342	C₂²⋊Q₈	C₂×C₄×C₄₁	1	4	yes	—
343	C₄×Q₈	—	2	8	no	—
344	C₄×Q₈	—	2	8	no	—
345	C₄×Q₈	—	2	4	no	—
346	C₄×Q₈	—	2	4	no	—
347	C₄×Q₈	—	2	4	no	—
348	C₄×Q₈	—	2	4	no	—
349	C₄×Q₈	D₄×C₄₁	1	8	yes	—
350	C₂×C₄⋊C₄	—	2	8	no	—
351	C₂×C₄⋊C₄	—	2	2	no	—
352	C₂×C₄⋊C₄	—	2	2	no	—
353	C₂×C₄⋊C₄	—	2	1	no	—
354	C₂×C₄⋊C₄	—	2	1	no	—
355	C₂×C₄⋊C₄	—	2	4	no	—
356	C₂×C₄⋊C₄	—	2	1	no	—
357	C₂×C₄⋊C₄	—	2	1	no	—
358	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
359	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
360	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
361	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
362	C₂×C₂²⋊C₄	—	2	1	no	—
363	C₂×C₂²⋊C₄	—	2	1	no	—
364	C₂×C₄²	—	2	8	no	—
365	C₂×C₄²	—	2	2	no	—
366	C₂×C₄²	—	2	2	no	—
367	C₂×C₄²	—	2	4	no	—
368	C₂×C₄²	—	2	1	no	—
369	C₂×C₄²	—	2	1	no	—
370	C₂×C₄²	D₄×C₄₁	1	1	yes	characteristic
371	C₂×C₄²	D₄×C₄₁	1	1	yes	characteristic
372	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
373	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
374	#107	—	2	4	no	—
375	#103	—	2	4	no	—
376	#103	—	2	4	no	—
377	#103	—	2	4	no	—
378	#103	C₂×C₄×C₄₁	1	8	yes	complemented
379	C₂²⋊C₈	—	2	2	no	—
380	C₂²⋊C₈	C₂×C₄×C₄₁	1	4	yes	—
381	C₄×C₈	—	2	4	no	—
382	#95	—	2	1	no	—
383	#95	—	2	1	no	—
384	#95	—	2	1	no	—
385	#95	—	2	1	no	—
386	#95	—	2	1	no	—
387	C₂⁴	C₂×D₄×C₄₁	1	1	yes	characteristic
388	C₂×Q₈	—	2	4	no	—
389	C₂×Q₈	—	2	16	no	—
390	C₂×Q₈	—	2	4	no	—
391	C₂×Q₈	—	2	16	no	—
392	C₂×Q₈	—	2	4	no	—
393	C₂×Q₈	—	2	2	no	—
394	C₂×Q₈	—	2	2	no	—
395	C₂×Q₈	—	2	2	no	—
396	C₂×Q₈	—	2	1	no	—
397	C₂×Q₈	—	2	2	no	—
398	C₂×Q₈	—	2	2	no	—
399	C₂×Q₈	C₂²×C₄×C₄₁	1	2	yes	—
400	C₂×Q₈	C₂²×C₄×C₄₁	1	4	yes	—
401	C₂×Q₈	C₂×D₄×C₄₁	1	4	yes	—
402	C₂×Q₈	#41×C₄₁	1	4	yes	—
403	C₂²×C₄	—	2	4	no	—
404	C₂²×C₄	—	2	4	no	—
405	C₂²×C₄	—	2	4	no	—
406	C₂²×C₄	—	2	2	no	—
407	C₂²×C₄	—	2	2	no	—
408	C₂²×C₄	—	2	2	no	—
409	C₂²×C₄	—	2	2	no	—
410	C₂²×C₄	—	2	2	no	—
411	C₂²×C₄	—	2	4	no	—
412	C₂²×C₄	—	2	2	no	—
413	C₂²×C₄	—	2	1	no	—
414	C₂²×C₄	—	2	1	no	—
415	C₂²×C₄	—	2	2	no	—
416	C₂²×C₄	—	2	2	no	—
417	C₂²×C₄	—	2	1	no	—
418	C₂²×C₄	—	2	1	no	—
419	C₂²×C₄	—	4	1	no	—
420	C₂²×C₄	—	4	2	no	—
421	C₂²×C₄	—	4	2	no	—
422	C₂²×C₄	Q₁₆×C₄₁	1	4	yes	complemented
423	C₂²×C₄	C₂²×C₄×C₄₁	1	2	yes	—
424	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
425	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
426	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
427	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
428	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
429	C₂²×C₄	#41×C₄₁	1	2	yes	—
430	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
431	Q₁₆	—	2	16	no	—
432	C₂×C₈	—	2	2	no	—
433	C₂×C₈	—	2	2	no	—
434	C₂×C₈	—	2	2	no	—
435	C₂×C₈	—	2	2	no	—
436	C₂×C₈	—	2	2	no	—
437	C₂×C₈	C₂²×C₄×C₄₁	1	4	yes	—
438	C₄⋊C₄	—	2	8	no	—
439	C₄⋊C₄	—	2	4	no	—
440	C₄⋊C₄	—	2	4	no	—
441	C₄⋊C₄	—	2	8	no	—
442	C₄⋊C₄	—	2	2	no	—
443	C₄⋊C₄	—	2	1	no	—
444	C₄⋊C₄	—	2	2	no	—
445	C₄⋊C₄	—	2	2	no	—
446	C₄⋊C₄	—	4	2	no	—
447	C₄⋊C₄	—	4	2	no	—
448	C₄⋊C₄	C₂²×C₄×C₄₁	1	2	yes	—
449	C₄⋊C₄	C₂×D₄×C₄₁	1	4	yes	—
450	C₂²⋊C₄	—	2	4	no	—
451	C₂²⋊C₄	—	4	2	no	—
452	C₄²	—	2	8	no	—
453	C₄²	—	2	8	no	—
454	C₄²	—	2	2	no	—
455	C₄²	—	2	2	no	—
456	C₄²	—	2	2	no	—
457	C₄²	—	4	2	no	—
458	C₄²	—	4	2	no	—
459	C₄²	C₂×D₄×C₄₁	1	4	yes	—
460	C₂³	—	2	1	no	—
461	C₂³	—	2	1	no	—
462	C₂³	—	2	1	no	—
463	C₂³	—	2	1	no	—
464	C₂³	C₄×D₄×C₄₁	1	2	yes	—
465	C₂³	C₂×Q₁₆×C₄₁	1	2	yes	—
466	C₂³	#135×C₄₁	1	2	yes	—
467	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
468	Q₈	—	2	16	no	—
469	Q₈	—	2	4	no	—
470	Q₈	—	2	4	no	—
471	Q₈	—	2	4	no	—
472	Q₈	—	2	4	no	—
473	Q₈	—	4	2	no	—
474	Q₈	C₄×D₄×C₄₁	1	8	yes	—
475	C₂×C₄	—	2	16	no	—
476	C₂×C₄	—	2	4	no	—
477	C₂×C₄	—	2	1	no	—
478	C₂×C₄	—	2	4	no	—
479	C₂×C₄	—	2	1	no	—
480	C₂×C₄	—	2	4	no	—
481	C₂×C₄	—	2	1	no	—
482	C₂×C₄	—	2	1	no	—
483	C₂×C₄	—	2	1	no	—
484	C₂×C₄	—	2	1	no	—
485	C₂×C₄	—	2	4	no	—
486	C₂×C₄	—	2	4	no	—
487	C₂×C₄	—	2	8	no	—
488	C₂×C₄	—	2	2	no	—
489	C₂×C₄	—	2	2	no	—
490	C₂×C₄	—	2	1	no	—
491	C₂×C₄	—	2	4	no	—
492	C₂×C₄	—	2	1	no	—
493	C₂×C₄	—	2	1	no	—
494	C₂×C₄	—	4	4	no	—
495	C₂×C₄	—	4	8	no	—
496	C₂×C₄	—	4	1	no	—
497	C₂×C₄	—	4	1	no	—
498	C₂×C₄	—	4	2	no	—
499	C₂×C₄	—	4	1	no	—
500	C₂×C₄	—	4	1	no	—
501	C₂×C₄	—	4	2	no	—
502	C₂×C₄	—	4	1	no	—
503	C₂×C₄	—	4	1	no	—
504	C₂×C₄	—	4	1	no	—
505	C₂×C₄	—	4	1	no	—
506	C₂×C₄	—	4	1	no	—
507	C₂×C₄	—	4	1	no	—
508	C₂×C₄	C₄×D₄×C₄₁	1	2	yes	—
509	C₂×C₄	#120×C₄₁	1	2	yes	—
510	C₂×C₄	#120×C₄₁	1	2	yes	—
511	C₂×C₄	C₂×Q₁₆×C₄₁	1	2	yes	—
512	C₂×C₄	C₂×Q₁₆×C₄₁	1	2	yes	—
513	C₂×C₄	#137×C₄₁	1	2	yes	—
514	C₂×C₄	C₂³×C₄×C₄₁	1	1	yes	characteristic
515	C₂×C₄	C₂²×D₄×C₄₁	1	2	yes	—
516	C₂×C₄	C₂×#41×C₄₁	1	2	yes	—
517	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
518	C₈	—	2	4	no	—
519	C₈	—	4	2	no	—
520	C₂²	—	2	2	no	—
521	C₂²	—	2	2	no	—
522	C₂²	—	2	2	no	—
523	C₂²	—	2	2	no	—
524	C₂²	—	2	2	no	—
525	C₂²	—	2	2	no	—
526	C₂²	C₄×Q₁₆×C₄₁	1	4	yes	complemented
527	C₂²	C₂×C₄×D₄×C₄₁	1	1	yes	characteristic
528	C₂²	C₂×#120×C₄₁	1	1	yes	characteristic
529	C₂²	C₄₁×#525	1	1	yes	characteristic
530	C₂²	C₂²×Q₁₆×C₄₁	1	1	yes	characteristic
531	C₂²	C₂×#135×C₄₁	1	1	yes	characteristic
532	C₂²	C₂×#137×C₄₁	1	1	yes	characteristic
533	C₂²	C₄₁×#575	1	1	yes	characteristic
534	C₄	—	2	8	no	—
535	C₄	—	2	2	no	—
536	C₄	—	2	2	no	—
537	C₄	—	2	2	no	—
538	C₄	—	4	2	no	—
539	C₄	—	4	2	no	—
540	C₄	—	4	1	no	—
541	C₄	—	4	4	no	—
542	C₄	—	8	1	no	—
543	C₄	—	8	1	no	—
544	C₄	C₄₁×#451	1	4	yes	direct product factor
545	C₄	C₂×C₄×D₄×C₄₁	1	2	yes	—
546	C₄	C₄₁×#525	1	2	yes	—
547	C₂	—	2	4	no	—
548	C₂	C₄×#120×C₄₁	1	1	yes	characteristic
549	C₂	C₂×C₄×Q₁₆×C₄₁	1	1	yes	characteristic
550	C₂	C₄×#137×C₄₁	1	1	yes	characteristic
551	C₂	C₂×C₄₁×#451	1	1	yes	characteristic
552	C₂	C₄₁×#3002	1	1	yes	characteristic
553	C₂	C₄₁×#3104	1	1	yes	characteristic
554	C₂	C₄₁×#3108	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₄₁	C₂×D₄
commutator	C₂×C₄	C₂³×C₄×C₄₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₁
socle	C₂³×C₄₁	C₂²×D₄
prime radical	C₂⁴×C₄₁	C₂×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₄₁ ◁ C₂²×C₄²×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₂×C₄×Q₁₆×C₄₁	C₂	semidirect
5. C₄₁×#1878	C₂	semidirect
7. C₄₁×#1863	C₂	semidirect
10. C₄×#103×C₄₁	C₂	semidirect
25. C₄₁×#451	C₄	direct (N × H)
60. C₂×Q₁₆×C₄₁	C₂×C₄	semidirect
100. #103×C₄₁	C₂×C₄	semidirect
144. C₂²×C₄×C₄₁	Q₁₆	semidirect
242. C₄×#451	C₄₁	direct (N × H)
249. C₂²×C₄₁	C₄×Q₁₆	semidirect
267. C₄×C₄₁	#451	direct (N × H)
272. C₂×C₄×Q₁₆	C₂×C₄₁	semidirect
274. #1878	C₂×C₄₁	semidirect
276. #1863	C₂×C₄₁	semidirect
279. C₄×#103	C₂×C₄₁	semidirect
302. #451	C₄×C₄₁	direct (N × H)
323. C₄₁	C₄×#451	direct (N × H)
338. C₂×Q₁₆	C₂×C₄×C₄₁	semidirect
378. #103	C₂×C₄×C₄₁	semidirect
422. C₂²×C₄	Q₁₆×C₄₁	semidirect
526. C₂²	C₄×Q₁₆×C₄₁	semidirect
544. C₄	C₄₁×#451	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₄×Q₈×C₄₁	2
C₂×C₄₁×#451	2
C₂×C₄×Q₁₆×C₄₁	2
C₄×C₂²⋊Q₈×C₄₁	2
C₄₁×#1878	2
C₄₁×#1872	2
C₄₁×#1863	2
C₄₁×#1852	2
C₄₁×#1787	2
C₄×#103×C₄₁	2
C₄×C₂²⋊C₈×C₄₁	2
C₄×#451	41

Subgroups — C4×C41×#451 #23797650

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×C₄₁×#451 #23797650