Subgroups — C₂×C₄₁×#1753 #23796582

Order 10496.

1830 conjugacy classes of subgroups.

The subgroup lattice has 450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×M₁₆×C₄₁	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₂²⋊C₈×C₄₁	C₂	1	1	yes	maximal, characteristic
3	C₂²×#97×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×C₄×C₈×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₄×C₂²⋊C₄×C₄₁	C₂	1	1	yes	maximal, characteristic
6	C₄₁×#1753	C₂	1	8	yes	maximal, direct product factor
7	C₂×C₄₁×#336	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₄₁×#336	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂⁴×C₄×C₄₁	C₂²	1	1	yes	characteristic
10	C₂²×M₁₆×C₄₁	—	2	4	no	—
11	C₂²×M₁₆×C₄₁	—	2	4	no	—
12	C₂²×M₁₆×C₄₁	C₄	1	8	yes	complemented
13	C₂²×M₁₆×C₄₁	C₂²	1	4	yes	—
14	C₂³×C₈×C₄₁	C₂²	1	1	yes	characteristic
15	C₂³×C₈×C₄₁	C₂²	1	1	yes	characteristic
16	C₂³×C₈×C₄₁	C₂²	1	1	yes	characteristic
17	C₂³×C₈×C₄₁	C₂²	1	1	yes	characteristic
18	C₂²×C₂²⋊C₄×C₄₁	C₄	1	2	yes	—
19	C₂²×C₄²×C₄₁	C₂²	1	1	yes	characteristic
20	C₂²×C₄²×C₄₁	C₂²	1	1	yes	characteristic
21	C₂×C₂²⋊C₈×C₄₁	C₄	1	8	yes	complemented
22	C₂×C₂²⋊C₈×C₄₁	C₂²	1	4	yes	—
23	C₂×#97×C₄₁	—	2	4	no	—
24	C₂×#97×C₄₁	C₂²	1	4	yes	complemented
25	C₂×C₄×C₈×C₄₁	—	2	4	no	—
26	C₂×C₄×C₈×C₄₁	C₂²	1	4	yes	complemented
27	C₄×C₂²⋊C₄×C₄₁	C₄	1	4	yes	—
28	C₄×C₂²⋊C₄×C₄₁	C₂²	1	4	yes	—
29	C₂×#95×C₄₁	C₄	1	2	yes	—
30	C₄₁×#336	C₂²	1	4	yes	complemented
31	C₄₁×#336	C₂²	1	4	yes	complemented
32	C₂⁵×C₄₁	C₂×C₄	1	1	yes	characteristic
33	C₂³×C₄×C₄₁	—	2	2	no	—
34	C₂³×C₄×C₄₁	—	2	2	no	—
35	C₂³×C₄×C₄₁	—	2	2	no	—
36	C₂³×C₄×C₄₁	—	2	2	no	—
37	C₂³×C₄×C₄₁	C₂×C₄	1	2	yes	—
38	C₂³×C₄×C₄₁	C₂×C₄	1	1	yes	characteristic
39	C₂³×C₄×C₄₁	C₂×C₄	1	2	yes	—
40	C₂³×C₄×C₄₁	C₂×C₄	1	4	yes	—
41	C₂³×C₄×C₄₁	C₂×C₄	1	4	yes	—
42	C₂³×C₄×C₄₁	C₂×C₄	1	2	yes	—
43	C₂³×C₄×C₄₁	C₂³	1	2	yes	—
44	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
45	C₂×M₁₆×C₄₁	—	2	32	no	—
46	C₂×M₁₆×C₄₁	—	2	8	no	—
47	C₂×M₁₆×C₄₁	—	2	8	no	—
48	C₂×M₁₆×C₄₁	C₂×C₄	1	16	yes	complemented
49	C₂²×C₈×C₄₁	—	2	2	no	—
50	C₂²×C₈×C₄₁	—	2	2	no	—
51	C₂²×C₈×C₄₁	—	2	2	no	—
52	C₂²×C₈×C₄₁	—	2	2	no	—
53	C₂²×C₈×C₄₁	—	2	2	no	—
54	C₂²×C₈×C₄₁	—	2	2	no	—
55	C₂²×C₈×C₄₁	C₂×C₄	1	4	yes	—
56	C₂²×C₈×C₄₁	C₂×C₄	1	4	yes	—
57	C₂²×C₈×C₄₁	C₂×C₄	1	4	yes	—
58	C₂²×C₈×C₄₁	C₂×C₄	1	4	yes	—
59	C₂²×C₈×C₄₁	D₄	1	4	yes	—
60	C₂²×C₈×C₄₁	D₄	1	4	yes	—
61	C₂²×C₈×C₄₁	C₂³	1	2	yes	—
62	C₂²×C₈×C₄₁	C₂³	1	2	yes	—
63	C₂²×C₈×C₄₁	C₂³	1	2	yes	—
64	C₂²×C₈×C₄₁	C₂³	1	2	yes	—
65	C₂×C₂²⋊C₄×C₄₁	—	2	8	no	—
66	C₂×C₂²⋊C₄×C₄₁	C₂×C₄	1	8	yes	—
67	C₂×C₄²×C₄₁	—	2	2	no	—
68	C₂×C₄²×C₄₁	—	2	2	no	—
69	C₂×C₄²×C₄₁	—	2	2	no	—
70	C₂×C₄²×C₄₁	—	2	2	no	—
71	C₂×C₄²×C₄₁	C₂×C₄	1	2	yes	—
72	C₂×C₄²×C₄₁	C₂×C₄	1	2	yes	—
73	C₂×C₄²×C₄₁	C₂³	1	2	yes	—
74	C₂×C₄²×C₄₁	C₂³	1	2	yes	—
75	C₂²⋊C₈×C₄₁	C₂×C₄	1	16	yes	complemented
76	#97×C₄₁	—	2	8	no	—
77	C₄×C₈×C₄₁	—	2	8	no	—
78	#95×C₄₁	C₂×C₄	1	8	yes	—
79	C₂⁴×C₄₁	—	2	2	no	—
80	C₂⁴×C₄₁	—	2	2	no	—
81	C₂⁴×C₄₁	—	2	4	no	—
82	C₂⁴×C₄₁	—	2	4	no	—
83	C₂⁴×C₄₁	C₄²	1	4	yes	—
84	C₂⁴×C₄₁	C₂²×C₄	1	2	yes	—
85	C₂⁴×C₄₁	C₂²×C₄	1	1	yes	characteristic
86	C₂²×C₄×C₄₁	—	2	4	no	—
87	C₂²×C₄×C₄₁	—	2	2	no	—
88	C₂²×C₄×C₄₁	—	2	2	no	—
89	C₂²×C₄×C₄₁	—	2	4	no	—
90	C₂²×C₄×C₄₁	—	2	8	no	—
91	C₂²×C₄×C₄₁	—	2	8	no	—
92	C₂²×C₄×C₄₁	—	2	4	no	—
93	C₂²×C₄×C₄₁	—	2	4	no	—
94	C₂²×C₄×C₄₁	—	2	8	no	—
95	C₂²×C₄×C₄₁	—	2	8	no	—
96	C₂²×C₄×C₄₁	—	2	2	no	—
97	C₂²×C₄×C₄₁	—	2	2	no	—
98	C₂²×C₄×C₄₁	—	2	2	no	—
99	C₂²×C₄×C₄₁	—	2	2	no	—
100	C₂²×C₄×C₄₁	—	2	4	no	—
101	C₂²×C₄×C₄₁	—	2	4	no	—
102	C₂²×C₄×C₄₁	—	2	4	no	—
103	C₂²×C₄×C₄₁	C₄²	1	4	yes	—
104	C₂²×C₄×C₄₁	C₄²	1	8	yes	—
105	C₂²×C₄×C₄₁	M₁₆	1	8	yes	complemented
106	C₂²×C₄×C₄₁	C₂²×C₄	1	4	yes	—
107	C₂²×C₄×C₄₁	C₂²×C₄	1	2	yes	—
108	C₂²×C₄×C₄₁	C₂²×C₄	1	4	yes	—
109	C₂²×C₄×C₄₁	C₂²×C₄	1	4	yes	—
110	C₂²×C₄×C₄₁	C₂²×C₄	1	4	yes	—
111	C₂²×C₄×C₄₁	C₂²×C₄	1	1	yes	characteristic
112	C₂²×C₄×C₄₁	C₂²×C₄	1	2	yes	—
113	C₂²×C₄×C₄₁	C₂²×C₄	1	2	yes	—
114	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
115	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
116	C₂²×C₄×C₄₁	#41	1	2	yes	—
117	C₂²×C₄×C₄₁	#41	1	2	yes	—
118	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
119	M₁₆×C₄₁	—	2	32	no	—
120	C₂×C₈×C₄₁	—	2	8	no	—
121	C₂×C₈×C₄₁	—	2	8	no	—
122	C₂×C₈×C₄₁	—	2	8	no	—
123	C₂×C₈×C₄₁	—	2	2	no	—
124	C₂×C₈×C₄₁	—	2	2	no	—
125	C₂×C₈×C₄₁	—	2	2	no	—
126	C₂×C₈×C₄₁	—	2	2	no	—
127	C₂×C₈×C₄₁	—	2	2	no	—
128	C₂×C₈×C₄₁	—	2	2	no	—
129	C₂×C₈×C₄₁	C₂²⋊C₄	1	16	yes	complemented
130	C₂×C₈×C₄₁	C₂²×C₄	1	4	yes	—
131	C₂×C₈×C₄₁	C₂²×C₄	1	4	yes	—
132	C₂×C₈×C₄₁	C₂²×C₄	1	4	yes	—
133	C₂×C₈×C₄₁	C₂²×C₄	1	4	yes	—
134	C₂×C₈×C₄₁	C₂×D₄	1	4	yes	—
135	C₂×C₈×C₄₁	C₂×D₄	1	4	yes	—
136	C₂²⋊C₄×C₄₁	—	2	16	no	—
137	C₄²×C₄₁	—	2	4	no	—
138	C₄²×C₄₁	—	2	4	no	—
139	C₄²×C₄₁	—	2	2	no	—
140	C₄²×C₄₁	—	2	2	no	—
141	C₄²×C₄₁	—	2	2	no	—
142	C₄²×C₄₁	—	2	2	no	—
143	C₂³×C₄₁	—	2	2	no	—
144	C₂³×C₄₁	—	2	2	no	—
145	C₂³×C₄₁	—	2	4	no	—
146	C₂³×C₄₁	—	2	4	no	—
147	C₂³×C₄₁	—	2	8	no	—
148	C₂³×C₄₁	—	2	8	no	—
149	C₂³×C₄₁	—	2	8	no	—
150	C₂³×C₄₁	—	4	8	no	—
151	C₂³×C₄₁	—	4	8	no	—
152	C₂³×C₄₁	C₂×C₄²	1	4	yes	—
153	C₂³×C₄₁	C₂×C₄²	1	2	yes	—
154	C₂³×C₄₁	C₄×D₄	1	2	yes	—
155	C₂³×C₄₁	C₄×D₄	1	2	yes	—
156	C₂³×C₄₁	C₂×M₁₆	1	4	yes	—
157	C₂³×C₄₁	#131	1	4	yes	—
158	C₂³×C₄₁	C₂³×C₄	1	1	yes	characteristic
159	C₂×C₄×C₄₁	—	2	4	no	—
160	C₂×C₄×C₄₁	—	2	2	no	—
161	C₂×C₄×C₄₁	—	2	2	no	—
162	C₂×C₄×C₄₁	—	2	4	no	—
163	C₂×C₄×C₄₁	—	2	8	no	—
164	C₂×C₄×C₄₁	—	2	16	no	—
165	C₂×C₄×C₄₁	—	2	4	no	—
166	C₂×C₄×C₄₁	—	2	4	no	—
167	C₂×C₄×C₄₁	—	2	4	no	—
168	C₂×C₄×C₄₁	—	2	4	no	—
169	C₂×C₄×C₄₁	—	2	16	no	—
170	C₂×C₄×C₄₁	—	2	4	no	—
171	C₂×C₄×C₄₁	—	2	4	no	—
172	C₂×C₄×C₄₁	—	2	4	no	—
173	C₂×C₄×C₄₁	—	4	8	no	—
174	C₂×C₄×C₄₁	C₂×C₄²	1	4	yes	—
175	C₂×C₄×C₄₁	C₂×C₄²	1	2	yes	—
176	C₂×C₄×C₄₁	C₂×C₂²⋊C₄	1	4	yes	—
177	C₂×C₄×C₄₁	#117	1	4	yes	—
178	C₂×C₄×C₄₁	C₄×D₄	1	4	yes	—
179	C₂×C₄×C₄₁	C₄×D₄	1	4	yes	—
180	C₂×C₄×C₄₁	C₄×D₄	1	2	yes	—
181	C₂×C₄×C₄₁	C₄×D₄	1	2	yes	—
182	C₂×C₄×C₄₁	C₂×M₁₆	1	8	yes	complemented
183	C₂×C₄×C₄₁	C₂³×C₄	1	1	yes	characteristic
184	C₂×C₄×C₄₁	C₂³×C₄	1	1	yes	characteristic
185	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
186	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
187	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
188	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
189	C₈×C₄₁	—	2	4	no	—
190	C₈×C₄₁	—	2	4	no	—
191	C₈×C₄₁	—	2	4	no	—
192	C₈×C₄₁	C₂×C₂²⋊C₄	1	8	yes	complemented
193	C₂×#1753	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
194	C₂²×C₄₁	—	2	4	no	—
195	C₂²×C₄₁	—	2	4	no	—
196	C₂²×C₄₁	—	2	4	no	—
197	C₂²×C₄₁	—	4	4	no	—
198	C₂²×C₄₁	—	4	4	no	—
199	C₂²×C₄₁	—	4	16	no	—
200	C₂²×C₄₁	C₄×C₂²⋊C₄	1	4	yes	—
201	C₂²×C₄₁	C₄×M₁₆	1	4	yes	—
202	C₂²×C₄₁	#405	1	4	yes	—
203	C₂²×C₄₁	#435	1	8	yes	—
204	C₂²×C₄₁	#436	1	8	yes	—
205	C₂²×C₄₁	C₂²×C₄²	1	1	yes	characteristic
206	C₂²×C₄₁	C₂×C₄×D₄	1	1	yes	characteristic
207	C₂²×C₄₁	C₂×C₄×D₄	1	1	yes	characteristic
208	C₂²×C₄₁	C₂²×M₁₆	1	2	yes	—
209	C₂²×C₄₁	C₂×#131	1	2	yes	—
210	C₄×C₄₁	—	2	8	no	—
211	C₄×C₄₁	—	2	4	no	—
212	C₄×C₄₁	—	4	4	no	—
213	C₄×C₄₁	C₄×C₂²⋊C₄	1	4	yes	—
214	C₄×C₄₁	C₂²×C₂²⋊C₄	1	1	yes	characteristic
215	C₄×C₄₁	C₂×#117	1	1	yes	characteristic
216	C₄×C₄₁	C₂×C₄×D₄	1	1	yes	characteristic
217	C₄×C₄₁	C₂×C₄×D₄	1	1	yes	characteristic
218	C₂³×M₁₆	C₂×C₄₁	1	1	yes	characteristic
219	C₂²×C₂²⋊C₈	C₂×C₄₁	1	1	yes	characteristic
220	C₂²×#97	C₂×C₄₁	1	1	yes	characteristic, complemented
221	C₂²×C₄×C₈	C₂×C₄₁	1	1	yes	characteristic, complemented
222	C₂×C₄×C₂²⋊C₄	C₂×C₄₁	1	1	yes	characteristic
223	#1753	C₂×C₄₁	1	8	yes	direct product factor
224	C₂×#336	C₂×C₄₁	1	1	yes	characteristic, complemented
225	C₂×#336	C₂×C₄₁	1	1	yes	characteristic, complemented
226	C₂×C₄₁	—	4	4	no	—
227	C₂×C₄₁	#1753	1	8	yes	direct product factor
228	C₂×C₄₁	C₂×C₄×C₂²⋊C₄	1	1	yes	characteristic
229	C₂×C₄₁	C₂×C₄×M₁₆	1	1	yes	characteristic
230	C₂×C₄₁	C₂×#405	1	1	yes	characteristic
231	C₂×C₄₁	C₂×#435	1	2	yes	—
232	C₂×C₄₁	C₂×#436	1	2	yes	—
233	C₂⁴×C₄	C₂²×C₄₁	1	1	yes	characteristic
234	C₂²×M₁₆	—	2	4	no	—
235	C₂²×M₁₆	—	2	4	no	—
236	C₂²×M₁₆	C₄×C₄₁	1	8	yes	complemented
237	C₂²×M₁₆	C₂²×C₄₁	1	4	yes	—
238	C₂³×C₈	C₂²×C₄₁	1	1	yes	characteristic
239	C₂³×C₈	C₂²×C₄₁	1	1	yes	characteristic
240	C₂³×C₈	C₂²×C₄₁	1	1	yes	characteristic
241	C₂³×C₈	C₂²×C₄₁	1	1	yes	characteristic
242	C₂²×C₂²⋊C₄	C₄×C₄₁	1	2	yes	—
243	C₂²×C₄²	C₂²×C₄₁	1	1	yes	characteristic
244	C₂²×C₄²	C₂²×C₄₁	1	1	yes	characteristic
245	C₂×C₂²⋊C₈	C₄×C₄₁	1	8	yes	complemented
246	C₂×C₂²⋊C₈	C₂²×C₄₁	1	4	yes	—
247	C₂×#97	—	2	4	no	—
248	C₂×#97	C₂²×C₄₁	1	4	yes	complemented
249	C₂×C₄×C₈	—	2	4	no	—
250	C₂×C₄×C₈	C₂²×C₄₁	1	4	yes	complemented
251	C₄×C₂²⋊C₄	C₄×C₄₁	1	4	yes	—
252	C₄×C₂²⋊C₄	C₂²×C₄₁	1	4	yes	—
253	C₂×#95	C₄×C₄₁	1	2	yes	—
254	#336	C₂²×C₄₁	1	4	yes	complemented
255	#336	C₂²×C₄₁	1	4	yes	complemented
256	C₄₁	C₂×#1753	1	1	yes	characteristic, direct product factor, Sylow
257	C₂⁵	C₂×C₄×C₄₁	1	1	yes	characteristic
258	C₂³×C₄	—	2	2	no	—
259	C₂³×C₄	—	2	2	no	—
260	C₂³×C₄	—	2	2	no	—
261	C₂³×C₄	—	2	2	no	—
262	C₂³×C₄	C₂×C₄×C₄₁	1	2	yes	—
263	C₂³×C₄	C₂×C₄×C₄₁	1	1	yes	characteristic
264	C₂³×C₄	C₂×C₄×C₄₁	1	2	yes	—
265	C₂³×C₄	C₂×C₄×C₄₁	1	4	yes	—
266	C₂³×C₄	C₂×C₄×C₄₁	1	4	yes	—
267	C₂³×C₄	C₂×C₄×C₄₁	1	2	yes	—
268	C₂³×C₄	C₂³×C₄₁	1	2	yes	—
269	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
270	C₂×M₁₆	—	2	32	no	—
271	C₂×M₁₆	—	2	8	no	—
272	C₂×M₁₆	—	2	8	no	—
273	C₂×M₁₆	C₂×C₄×C₄₁	1	16	yes	complemented
274	C₂²×C₈	—	2	2	no	—
275	C₂²×C₈	—	2	2	no	—
276	C₂²×C₈	—	2	2	no	—
277	C₂²×C₈	—	2	2	no	—
278	C₂²×C₈	—	2	2	no	—
279	C₂²×C₈	—	2	2	no	—
280	C₂²×C₈	C₂×C₄×C₄₁	1	4	yes	—
281	C₂²×C₈	C₂×C₄×C₄₁	1	4	yes	—
282	C₂²×C₈	C₂×C₄×C₄₁	1	4	yes	—
283	C₂²×C₈	C₂×C₄×C₄₁	1	4	yes	—
284	C₂²×C₈	D₄×C₄₁	1	4	yes	—
285	C₂²×C₈	D₄×C₄₁	1	4	yes	—
286	C₂²×C₈	C₂³×C₄₁	1	2	yes	—
287	C₂²×C₈	C₂³×C₄₁	1	2	yes	—
288	C₂²×C₈	C₂³×C₄₁	1	2	yes	—
289	C₂²×C₈	C₂³×C₄₁	1	2	yes	—
290	C₂×C₂²⋊C₄	—	2	8	no	—
291	C₂×C₂²⋊C₄	C₂×C₄×C₄₁	1	8	yes	—
292	C₂×C₄²	—	2	2	no	—
293	C₂×C₄²	—	2	2	no	—
294	C₂×C₄²	—	2	2	no	—
295	C₂×C₄²	—	2	2	no	—
296	C₂×C₄²	C₂×C₄×C₄₁	1	2	yes	—
297	C₂×C₄²	C₂×C₄×C₄₁	1	2	yes	—
298	C₂×C₄²	C₂³×C₄₁	1	2	yes	—
299	C₂×C₄²	C₂³×C₄₁	1	2	yes	—
300	C₂²⋊C₈	C₂×C₄×C₄₁	1	16	yes	complemented
301	#97	—	2	8	no	—
302	C₄×C₈	—	2	8	no	—
303	#95	C₂×C₄×C₄₁	1	8	yes	—
304	C₂⁴	—	2	2	no	—
305	C₂⁴	—	2	2	no	—
306	C₂⁴	—	2	4	no	—
307	C₂⁴	—	2	4	no	—
308	C₂⁴	C₄²×C₄₁	1	4	yes	—
309	C₂⁴	C₂²×C₄×C₄₁	1	2	yes	—
310	C₂⁴	C₂²×C₄×C₄₁	1	1	yes	characteristic
311	C₂²×C₄	—	2	4	no	—
312	C₂²×C₄	—	2	2	no	—
313	C₂²×C₄	—	2	2	no	—
314	C₂²×C₄	—	2	4	no	—
315	C₂²×C₄	—	2	8	no	—
316	C₂²×C₄	—	2	8	no	—
317	C₂²×C₄	—	2	4	no	—
318	C₂²×C₄	—	2	4	no	—
319	C₂²×C₄	—	2	8	no	—
320	C₂²×C₄	—	2	8	no	—
321	C₂²×C₄	—	2	2	no	—
322	C₂²×C₄	—	2	2	no	—
323	C₂²×C₄	—	2	2	no	—
324	C₂²×C₄	—	2	2	no	—
325	C₂²×C₄	—	2	4	no	—
326	C₂²×C₄	—	2	4	no	—
327	C₂²×C₄	—	2	4	no	—
328	C₂²×C₄	C₄²×C₄₁	1	4	yes	—
329	C₂²×C₄	C₄²×C₄₁	1	8	yes	—
330	C₂²×C₄	M₁₆×C₄₁	1	8	yes	complemented
331	C₂²×C₄	C₂²×C₄×C₄₁	1	4	yes	—
332	C₂²×C₄	C₂²×C₄×C₄₁	1	2	yes	—
333	C₂²×C₄	C₂²×C₄×C₄₁	1	4	yes	—
334	C₂²×C₄	C₂²×C₄×C₄₁	1	4	yes	—
335	C₂²×C₄	C₂²×C₄×C₄₁	1	4	yes	—
336	C₂²×C₄	C₂²×C₄×C₄₁	1	1	yes	characteristic
337	C₂²×C₄	C₂²×C₄×C₄₁	1	2	yes	—
338	C₂²×C₄	C₂²×C₄×C₄₁	1	2	yes	—
339	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
340	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
341	C₂²×C₄	#41×C₄₁	1	2	yes	—
342	C₂²×C₄	#41×C₄₁	1	2	yes	—
343	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
344	M₁₆	—	2	32	no	—
345	C₂×C₈	—	2	8	no	—
346	C₂×C₈	—	2	8	no	—
347	C₂×C₈	—	2	8	no	—
348	C₂×C₈	—	2	2	no	—
349	C₂×C₈	—	2	2	no	—
350	C₂×C₈	—	2	2	no	—
351	C₂×C₈	—	2	2	no	—
352	C₂×C₈	—	2	2	no	—
353	C₂×C₈	—	2	2	no	—
354	C₂×C₈	C₂²⋊C₄×C₄₁	1	16	yes	complemented
355	C₂×C₈	C₂²×C₄×C₄₁	1	4	yes	—
356	C₂×C₈	C₂²×C₄×C₄₁	1	4	yes	—
357	C₂×C₈	C₂²×C₄×C₄₁	1	4	yes	—
358	C₂×C₈	C₂²×C₄×C₄₁	1	4	yes	—
359	C₂×C₈	C₂×D₄×C₄₁	1	4	yes	—
360	C₂×C₈	C₂×D₄×C₄₁	1	4	yes	—
361	C₂²⋊C₄	—	2	16	no	—
362	C₄²	—	2	4	no	—
363	C₄²	—	2	4	no	—
364	C₄²	—	2	2	no	—
365	C₄²	—	2	2	no	—
366	C₄²	—	2	2	no	—
367	C₄²	—	2	2	no	—
368	C₂³	—	2	2	no	—
369	C₂³	—	2	2	no	—
370	C₂³	—	2	4	no	—
371	C₂³	—	2	4	no	—
372	C₂³	—	2	8	no	—
373	C₂³	—	2	8	no	—
374	C₂³	—	2	8	no	—
375	C₂³	—	4	8	no	—
376	C₂³	—	4	8	no	—
377	C₂³	C₂×C₄²×C₄₁	1	4	yes	—
378	C₂³	C₂×C₄²×C₄₁	1	2	yes	—
379	C₂³	C₄×D₄×C₄₁	1	2	yes	—
380	C₂³	C₄×D₄×C₄₁	1	2	yes	—
381	C₂³	C₂×M₁₆×C₄₁	1	4	yes	—
382	C₂³	#131×C₄₁	1	4	yes	—
383	C₂³	C₂³×C₄×C₄₁	1	1	yes	characteristic
384	C₂×C₄	—	2	4	no	—
385	C₂×C₄	—	2	2	no	—
386	C₂×C₄	—	2	2	no	—
387	C₂×C₄	—	2	4	no	—
388	C₂×C₄	—	2	8	no	—
389	C₂×C₄	—	2	16	no	—
390	C₂×C₄	—	2	4	no	—
391	C₂×C₄	—	2	4	no	—
392	C₂×C₄	—	2	4	no	—
393	C₂×C₄	—	2	4	no	—
394	C₂×C₄	—	2	16	no	—
395	C₂×C₄	—	2	4	no	—
396	C₂×C₄	—	2	4	no	—
397	C₂×C₄	—	2	4	no	—
398	C₂×C₄	—	4	8	no	—
399	C₂×C₄	C₂×C₄²×C₄₁	1	4	yes	—
400	C₂×C₄	C₂×C₄²×C₄₁	1	2	yes	—
401	C₂×C₄	C₂×C₂²⋊C₄×C₄₁	1	4	yes	—
402	C₂×C₄	#117×C₄₁	1	4	yes	—
403	C₂×C₄	C₄×D₄×C₄₁	1	4	yes	—
404	C₂×C₄	C₄×D₄×C₄₁	1	4	yes	—
405	C₂×C₄	C₄×D₄×C₄₁	1	2	yes	—
406	C₂×C₄	C₄×D₄×C₄₁	1	2	yes	—
407	C₂×C₄	C₂×M₁₆×C₄₁	1	8	yes	complemented
408	C₂×C₄	C₂³×C₄×C₄₁	1	1	yes	characteristic
409	C₂×C₄	C₂³×C₄×C₄₁	1	1	yes	characteristic
410	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
411	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
412	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
413	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
414	C₈	—	2	4	no	—
415	C₈	—	2	4	no	—
416	C₈	—	2	4	no	—
417	C₈	C₂×C₂²⋊C₄×C₄₁	1	8	yes	complemented
418	C₂²	—	2	4	no	—
419	C₂²	—	2	4	no	—
420	C₂²	—	2	4	no	—
421	C₂²	—	4	4	no	—
422	C₂²	—	4	4	no	—
423	C₂²	—	4	16	no	—
424	C₂²	C₄×C₂²⋊C₄×C₄₁	1	4	yes	—
425	C₂²	C₄×M₁₆×C₄₁	1	4	yes	—
426	C₂²	C₄₁×#405	1	4	yes	—
427	C₂²	C₄₁×#435	1	8	yes	—
428	C₂²	C₄₁×#436	1	8	yes	—
429	C₂²	C₂²×C₄²×C₄₁	1	1	yes	characteristic
430	C₂²	C₂×C₄×D₄×C₄₁	1	1	yes	characteristic
431	C₂²	C₂×C₄×D₄×C₄₁	1	1	yes	characteristic
432	C₂²	C₂²×M₁₆×C₄₁	1	2	yes	—
433	C₂²	C₂×#131×C₄₁	1	2	yes	—
434	C₄	—	2	4	no	—
435	C₄	—	2	8	no	—
436	C₄	—	4	4	no	—
437	C₄	C₄×C₂²⋊C₄×C₄₁	1	4	yes	—
438	C₄	C₂²×C₂²⋊C₄×C₄₁	1	1	yes	characteristic
439	C₄	C₂×#117×C₄₁	1	1	yes	characteristic
440	C₄	C₂×C₄×D₄×C₄₁	1	1	yes	characteristic
441	C₄	C₂×C₄×D₄×C₄₁	1	1	yes	characteristic
442	C₂	—	4	4	no	—
443	C₂	C₄₁×#1753	1	8	yes	direct product factor
444	C₂	C₂×C₄×C₂²⋊C₄×C₄₁	1	1	yes	characteristic
445	C₂	C₂×C₄×M₁₆×C₄₁	1	1	yes	characteristic
446	C₂	C₂×C₄₁×#405	1	1	yes	characteristic
447	C₂	C₂×C₄₁×#435	1	2	yes	—
448	C₂	C₂×C₄₁×#436	1	2	yes	—

	subgroup	G/H
center	C₂³×C₄×C₄₁	C₂³
commutator	C₂²	C₂²×C₄²×C₄₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₁
socle	C₂⁴×C₄₁	C₂²×C₄
prime radical	C₂⁵×C₄₁	C₂×C₄
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₄×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₂²×#97×C₄₁	C₂	semidirect
4. C₂²×C₄×C₈×C₄₁	C₂	semidirect
6. C₄₁×#1753	C₂	direct (N × H)
7. C₂×C₄₁×#336	C₂	semidirect
8. C₂×C₄₁×#336	C₂	semidirect
12. C₂²×M₁₆×C₄₁	C₄	semidirect
21. C₂×C₂²⋊C₈×C₄₁	C₄	semidirect
24. C₂×#97×C₄₁	C₂²	semidirect
26. C₂×C₄×C₈×C₄₁	C₂²	semidirect
30. C₄₁×#336	C₂²	semidirect
31. C₄₁×#336	C₂²	semidirect
48. C₂×M₁₆×C₄₁	C₂×C₄	semidirect
75. C₂²⋊C₈×C₄₁	C₂×C₄	semidirect
105. C₂²×C₄×C₄₁	M₁₆	semidirect
129. C₂×C₈×C₄₁	C₂²⋊C₄	semidirect
182. C₂×C₄×C₄₁	C₂×M₁₆	semidirect
192. C₈×C₄₁	C₂×C₂²⋊C₄	semidirect
193. C₂×#1753	C₄₁	direct (N × H)
220. C₂²×#97	C₂×C₄₁	semidirect
221. C₂²×C₄×C₈	C₂×C₄₁	semidirect
223. #1753	C₂×C₄₁	direct (N × H)
224. C₂×#336	C₂×C₄₁	semidirect
225. C₂×#336	C₂×C₄₁	semidirect
227. C₂×C₄₁	#1753	direct (N × H)
236. C₂²×M₁₆	C₄×C₄₁	semidirect
245. C₂×C₂²⋊C₈	C₄×C₄₁	semidirect
248. C₂×#97	C₂²×C₄₁	semidirect
250. C₂×C₄×C₈	C₂²×C₄₁	semidirect
254. #336	C₂²×C₄₁	semidirect
255. #336	C₂²×C₄₁	semidirect
256. C₄₁	C₂×#1753	direct (N × H)
273. C₂×M₁₆	C₂×C₄×C₄₁	semidirect
300. C₂²⋊C₈	C₂×C₄×C₄₁	semidirect
330. C₂²×C₄	M₁₆×C₄₁	semidirect
354. C₂×C₈	C₂²⋊C₄×C₄₁	semidirect
407. C₂×C₄	C₂×M₁₆×C₄₁	semidirect
417. C₈	C₂×C₂²⋊C₄×C₄₁	semidirect
443. C₂	C₄₁×#1753	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×M₁₆×C₄₁	2
C₂²×C₂²⋊C₈×C₄₁	2
C₂²×#97×C₄₁	2
C₂²×C₄×C₈×C₄₁	2
C₂×C₄×C₂²⋊C₄×C₄₁	2
C₄₁×#1753	2
C₂×C₄₁×#336	2
C₂×#1753	41

Subgroups — C2×C41×#1753 #23796582

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄₁×#1753 #23796582