Subgroups — C₄₁×#20933 #23797134

Order 10496.

1906 conjugacy classes of subgroups.

The subgroup lattice has 476 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×SD₁₆×C₄₁	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄₁×#518	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄₁×#419	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₄₁×#418	C₂	1	1	yes	maximal, characteristic
5	C₄₁×#2310	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄₁×#1877	C₂	1	8	yes	maximal, complemented
7	C₄₁×#1735	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄₁×#1729	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂³×Q₈×C₄₁	C₂²	1	1	yes	characteristic
10	C₂³×D₄×C₄₁	C₂²	1	1	yes	characteristic
11	C₂²×SD₁₆×C₄₁	—	2	4	no	—
12	C₂²×SD₁₆×C₄₁	—	2	4	no	—
13	C₂²×SD₁₆×C₄₁	C₄	1	8	yes	complemented
14	C₂²×SD₁₆×C₄₁	C₂²	1	4	yes	—
15	C₂²×M₁₆×C₄₁	C₂²	1	1	yes	characteristic
16	C₂³×C₈×C₄₁	C₂²	1	1	yes	characteristic
17	C₄₁×#518	—	2	4	no	—
18	C₄₁×#518	—	2	4	no	—
19	C₂×C₄×D₄×C₄₁	—	2	2	no	—
20	C₂×C₄×D₄×C₄₁	C₂²	1	4	yes	—
21	C₂×#117×C₄₁	C₂²	1	1	yes	characteristic
22	C₂×#117×C₄₁	C₂²	1	1	yes	characteristic
23	C₂×#117×C₄₁	C₂²	1	1	yes	characteristic
24	C₂²×C₂²⋊C₄×C₄₁	—	2	2	no	—
25	C₄₁×#419	—	2	4	no	—
26	C₄₁×#418	—	2	4	no	—
27	C₂×#103×C₄₁	C₂²	1	4	yes	complemented
28	C₂×#102×C₄₁	C₂²	1	4	yes	—
29	C₄₁×#391	—	2	2	no	—
30	C₄₁×#391	C₂²	1	4	yes	complemented
31	C₄₁×#381	—	2	2	no	—
32	C₄₁×#340	C₂²	1	4	yes	complemented
33	C₄₁×#336	C₂²	1	4	yes	complemented
34	C₂⁵×C₄₁	—	2	1	no	—
35	C₂²×Q₈×C₄₁	—	2	1	no	—
36	C₂²×Q₈×C₄₁	—	2	2	no	—
37	C₂²×Q₈×C₄₁	—	2	2	no	—
38	C₂²×Q₈×C₄₁	—	2	2	no	—
39	C₂²×Q₈×C₄₁	—	2	2	no	—
40	C₂²×Q₈×C₄₁	—	2	2	no	—
41	C₂²×Q₈×C₄₁	C₂×C₄	1	4	yes	complemented
42	C₂²×Q₈×C₄₁	C₂³	1	2	yes	—
43	C₂²×D₄×C₄₁	—	2	1	no	—
44	C₂²×D₄×C₄₁	—	2	2	no	—
45	C₂²×D₄×C₄₁	—	2	2	no	—
46	C₂²×D₄×C₄₁	—	2	2	no	—
47	C₂²×D₄×C₄₁	C₂×C₄	1	4	yes	—
48	C₂²×D₄×C₄₁	D₄	1	4	yes	—
49	C₂²×D₄×C₄₁	D₄	1	4	yes	—
50	C₂²×D₄×C₄₁	C₂³	1	2	yes	—
51	C₂³×C₄×C₄₁	—	2	1	no	—
52	C₂³×C₄×C₄₁	—	2	4	no	—
53	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
54	C₂×SD₁₆×C₄₁	—	2	32	no	—
55	C₂×SD₁₆×C₄₁	—	2	8	no	—
56	C₂×SD₁₆×C₄₁	—	2	8	no	—
57	C₂×SD₁₆×C₄₁	C₂×C₄	1	16	yes	complemented
58	C₂×M₁₆×C₄₁	—	2	2	no	—
59	C₂×M₁₆×C₄₁	—	2	2	no	—
60	C₂×M₁₆×C₄₁	—	2	2	no	—
61	C₂²×C₈×C₄₁	—	2	2	no	—
62	C₂²×C₈×C₄₁	—	2	2	no	—
63	C₂²×C₈×C₄₁	C₂×C₄	1	4	yes	complemented
64	C₂²×C₈×C₄₁	C₂³	1	2	yes	—
65	C₂²×C₈×C₄₁	C₂³	1	2	yes	—
66	C₄×D₄×C₄₁	—	2	16	no	—
67	C₄×D₄×C₄₁	—	2	8	no	—
68	C₄×D₄×C₄₁	—	2	8	no	—
69	#117×C₄₁	—	2	2	no	—
70	#117×C₄₁	—	2	2	no	—
71	#117×C₄₁	—	2	2	no	—
72	#117×C₄₁	—	2	2	no	—
73	#117×C₄₁	—	2	2	no	—
74	#117×C₄₁	D₄	1	4	yes	—
75	C₂×C₄⋊C₄×C₄₁	D₄	1	2	yes	—
76	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
77	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
78	C₂×C₂²⋊C₄×C₄₁	—	2	16	no	—
79	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
80	C₂×C₂²⋊C₄×C₄₁	—	2	4	no	—
81	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
82	C₂×C₂²⋊C₄×C₄₁	D₄	1	2	yes	—
83	C₂×C₄²×C₄₁	—	2	1	no	—
84	C₂×C₄²×C₄₁	—	2	1	no	—
85	C₂×C₄²×C₄₁	C₂³	1	2	yes	—
86	#103×C₄₁	—	2	8	no	—
87	#102×C₄₁	—	2	8	no	—
88	#95×C₄₁	—	2	8	no	—
89	C₂⁴×C₄₁	—	2	2	no	—
90	C₂⁴×C₄₁	—	2	4	no	—
91	C₂⁴×C₄₁	—	2	4	no	—
92	C₂⁴×C₄₁	—	2	4	no	—
93	C₂⁴×C₄₁	—	8	4	no	—
94	C₂⁴×C₄₁	C₂×D₄	1	1	yes	characteristic
95	C₂×Q₈×C₄₁	—	2	4	no	—
96	C₂×Q₈×C₄₁	—	2	2	no	—
97	C₂×Q₈×C₄₁	—	2	8	no	—
98	C₂×Q₈×C₄₁	—	2	8	no	—
99	C₂×Q₈×C₄₁	—	2	2	no	—
100	C₂×Q₈×C₄₁	—	2	2	no	—
101	C₂×Q₈×C₄₁	—	2	2	no	—
102	C₂×Q₈×C₄₁	—	2	2	no	—
103	C₂×Q₈×C₄₁	—	4	2	no	—
104	C₂×Q₈×C₄₁	—	4	2	no	—
105	C₂×Q₈×C₄₁	—	4	4	no	—
106	C₂×Q₈×C₄₁	—	4	4	no	—
107	C₂×Q₈×C₄₁	C₂²×C₄	1	4	yes	—
108	C₂×D₄×C₄₁	—	2	8	no	—
109	C₂×D₄×C₄₁	—	2	4	no	—
110	C₂×D₄×C₄₁	—	2	4	no	—
111	C₂×D₄×C₄₁	—	2	8	no	—
112	C₂×D₄×C₄₁	—	2	4	no	—
113	C₂×D₄×C₄₁	—	2	8	no	—
114	C₂×D₄×C₄₁	—	2	2	no	—
115	C₂×D₄×C₄₁	—	2	2	no	—
116	C₂×D₄×C₄₁	—	2	2	no	—
117	C₂×D₄×C₄₁	C₂²⋊C₄	1	16	yes	—
118	C₂×D₄×C₄₁	C₂²×C₄	1	4	yes	—
119	C₂×D₄×C₄₁	C₂×D₄	1	4	yes	—
120	C₂×D₄×C₄₁	C₂×D₄	1	4	yes	—
121	C₂²×C₄×C₄₁	—	2	4	no	—
122	C₂²×C₄×C₄₁	—	2	2	no	—
123	C₂²×C₄×C₄₁	—	2	2	no	—
124	C₂²×C₄×C₄₁	—	2	16	no	—
125	C₂²×C₄×C₄₁	—	2	2	no	—
126	C₂²×C₄×C₄₁	—	4	2	no	—
127	C₂²×C₄×C₄₁	—	4	2	no	—
128	C₂²×C₄×C₄₁	—	8	8	no	—
129	C₂²×C₄×C₄₁	C₂²×C₄	1	2	yes	—
130	C₂²×C₄×C₄₁	C₂×D₄	1	4	yes	—
131	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
132	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
133	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
134	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
135	C₂²×C₄×C₄₁	#41	1	2	yes	—
136	C₂²×C₄×C₄₁	#41	1	2	yes	—
137	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
138	SD₁₆×C₄₁	—	2	32	no	—
139	M₁₆×C₄₁	—	4	4	no	—
140	C₂×C₈×C₄₁	—	2	8	no	—
141	C₂×C₈×C₄₁	—	2	2	no	—
142	C₂×C₈×C₄₁	—	2	2	no	—
143	C₂×C₈×C₄₁	—	2	2	no	—
144	C₂×C₈×C₄₁	—	2	2	no	—
145	C₂×C₈×C₄₁	—	2	2	no	—
146	C₂×C₈×C₄₁	C₂²×C₄	1	4	yes	—
147	C₄⋊C₄×C₄₁	—	2	4	no	—
148	C₄⋊C₄×C₄₁	—	2	2	no	—
149	C₄⋊C₄×C₄₁	—	2	2	no	—
150	C₄⋊C₄×C₄₁	—	2	2	no	—
151	C₄⋊C₄×C₄₁	C₂×D₄	1	4	yes	—
152	C₂²⋊C₄×C₄₁	—	2	16	no	—
153	C₂²⋊C₄×C₄₁	—	2	4	no	—
154	C₂²⋊C₄×C₄₁	—	2	4	no	—
155	C₂²⋊C₄×C₄₁	—	4	2	no	—
156	C₄²×C₄₁	—	2	4	no	—
157	C₄²×C₄₁	—	2	2	no	—
158	C₄²×C₄₁	—	2	2	no	—
159	C₄²×C₄₁	—	4	2	no	—
160	C₂³×C₄₁	—	2	4	no	—
161	C₂³×C₄₁	—	2	4	no	—
162	C₂³×C₄₁	—	2	4	no	—
163	C₂³×C₄₁	—	2	4	no	—
164	C₂³×C₄₁	—	2	16	no	—
165	C₂³×C₄₁	—	4	8	no	—
166	C₂³×C₄₁	—	8	8	no	—
167	C₂³×C₄₁	—	8	8	no	—
168	C₂³×C₄₁	—	8	8	no	—
169	C₂³×C₄₁	C₄×D₄	1	2	yes	—
170	C₂³×C₄₁	#120	1	2	yes	—
171	C₂³×C₄₁	#121	1	2	yes	—
172	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
173	Q₈×C₄₁	—	2	4	no	—
174	Q₈×C₄₁	—	2	4	no	—
175	Q₈×C₄₁	—	4	2	no	—
176	Q₈×C₄₁	—	4	2	no	—
177	Q₈×C₄₁	—	4	8	no	—
178	D₄×C₄₁	—	2	4	no	—
179	D₄×C₄₁	—	2	4	no	—
180	D₄×C₄₁	—	2	4	no	—
181	D₄×C₄₁	—	2	16	no	—
182	D₄×C₄₁	C₂×C₂²⋊C₄	1	8	yes	—
183	C₂×C₄×C₄₁	—	2	4	no	—
184	C₂×C₄×C₄₁	—	2	4	no	—
185	C₂×C₄×C₄₁	—	2	4	no	—
186	C₂×C₄×C₄₁	—	2	8	no	—
187	C₂×C₄×C₄₁	—	4	2	no	—
188	C₂×C₄×C₄₁	—	4	2	no	—
189	C₂×C₄×C₄₁	—	4	4	no	—
190	C₂×C₄×C₄₁	—	4	8	no	—
191	C₂×C₄×C₄₁	—	4	2	no	—
192	C₂×C₄×C₄₁	—	4	4	no	—
193	C₂×C₄×C₄₁	—	8	16	no	—
194	C₂×C₄×C₄₁	C₂×C₂²⋊C₄	1	4	yes	—
195	C₂×C₄×C₄₁	C₄×D₄	1	4	yes	—
196	C₂×C₄×C₄₁	C₄×D₄	1	2	yes	—
197	C₂×C₄×C₄₁	#120	1	2	yes	—
198	C₂×C₄×C₄₁	#121	1	4	yes	—
199	C₂×C₄×C₄₁	#121	1	2	yes	—
200	C₂×C₄×C₄₁	#123	1	4	yes	—
201	C₂×C₄×C₄₁	C₂³×C₄	1	1	yes	characteristic
202	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
203	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
204	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
205	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
206	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
207	C₈×C₄₁	—	2	4	no	—
208	C₈×C₄₁	—	4	2	no	—
209	#20933	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
210	C₂²×C₄₁	—	2	4	no	—
211	C₂²×C₄₁	—	2	4	no	—
212	C₂²×C₄₁	—	2	4	no	—
213	C₂²×C₄₁	—	2	8	no	—
214	C₂²×C₄₁	—	4	8	no	—
215	C₂²×C₄₁	—	4	8	no	—
216	C₂²×C₄₁	—	4	8	no	—
217	C₂²×C₄₁	—	8	16	no	—
218	C₂²×C₄₁	#386	1	4	yes	—
219	C₂²×C₄₁	C₂×C₄×D₄	1	1	yes	characteristic
220	C₂²×C₄₁	C₂×#120	1	1	yes	characteristic
221	C₂²×C₄₁	C₂×#121	1	1	yes	characteristic
222	C₂²×C₄₁	#577	1	4	yes	—
223	C₄×C₄₁	—	4	4	no	—
224	C₄×C₄₁	—	4	4	no	—
225	C₄×C₄₁	—	4	4	no	—
226	C₄×C₄₁	—	8	2	no	—
227	C₄×C₄₁	#386	1	4	yes	—
228	C₄×C₄₁	C₂²×C₂²⋊C₄	1	1	yes	characteristic
229	C₄×C₄₁	C₂×C₄×D₄	1	1	yes	characteristic
230	C₄×C₄₁	C₂×#121	1	1	yes	characteristic
231	C₄×C₄₁	C₂×#123	1	1	yes	characteristic
232	C₂³×SD₁₆	C₂×C₄₁	1	1	yes	characteristic
233	C₂×#518	C₂×C₄₁	1	1	yes	characteristic
234	C₂×#419	C₂×C₄₁	1	1	yes	characteristic, complemented
235	C₂×#418	C₂×C₄₁	1	1	yes	characteristic
236	#2310	C₂×C₄₁	1	1	yes	characteristic, complemented
237	#1877	C₂×C₄₁	1	8	yes	complemented
238	#1735	C₂×C₄₁	1	1	yes	characteristic, complemented
239	#1729	C₂×C₄₁	1	1	yes	characteristic, complemented
240	C₂×C₄₁	—	2	4	no	—
241	C₂×C₄₁	—	4	8	no	—
242	C₂×C₄₁	C₂×#386	1	1	yes	characteristic
243	C₂×C₄₁	#2949	1	2	yes	—
244	C₂×C₄₁	#3009	1	2	yes	—
245	C₂×C₄₁	#3042	1	2	yes	—
246	C₂³×Q₈	C₂²×C₄₁	1	1	yes	characteristic
247	C₂³×D₄	C₂²×C₄₁	1	1	yes	characteristic
248	C₂²×SD₁₆	—	2	4	no	—
249	C₂²×SD₁₆	—	2	4	no	—
250	C₂²×SD₁₆	C₄×C₄₁	1	8	yes	complemented
251	C₂²×SD₁₆	C₂²×C₄₁	1	4	yes	—
252	C₂²×M₁₆	C₂²×C₄₁	1	1	yes	characteristic
253	C₂³×C₈	C₂²×C₄₁	1	1	yes	characteristic
254	#518	—	2	4	no	—
255	#518	—	2	4	no	—
256	C₂×C₄×D₄	—	2	2	no	—
257	C₂×C₄×D₄	C₂²×C₄₁	1	4	yes	—
258	C₂×#117	C₂²×C₄₁	1	1	yes	characteristic
259	C₂×#117	C₂²×C₄₁	1	1	yes	characteristic
260	C₂×#117	C₂²×C₄₁	1	1	yes	characteristic
261	C₂²×C₂²⋊C₄	—	2	2	no	—
262	#419	—	2	4	no	—
263	#418	—	2	4	no	—
264	C₂×#103	C₂²×C₄₁	1	4	yes	complemented
265	C₂×#102	C₂²×C₄₁	1	4	yes	—
266	#391	—	2	2	no	—
267	#391	C₂²×C₄₁	1	4	yes	complemented
268	#381	—	2	2	no	—
269	#340	C₂²×C₄₁	1	4	yes	complemented
270	#336	C₂²×C₄₁	1	4	yes	complemented
271	C₄₁	#20933	1	1	yes	characteristic, direct product factor, Sylow
272	C₂⁵	—	2	1	no	—
273	C₂²×Q₈	—	2	1	no	—
274	C₂²×Q₈	—	2	2	no	—
275	C₂²×Q₈	—	2	2	no	—
276	C₂²×Q₈	—	2	2	no	—
277	C₂²×Q₈	—	2	2	no	—
278	C₂²×Q₈	—	2	2	no	—
279	C₂²×Q₈	C₂×C₄×C₄₁	1	4	yes	complemented
280	C₂²×Q₈	C₂³×C₄₁	1	2	yes	—
281	C₂²×D₄	—	2	1	no	—
282	C₂²×D₄	—	2	2	no	—
283	C₂²×D₄	—	2	2	no	—
284	C₂²×D₄	—	2	2	no	—
285	C₂²×D₄	C₂×C₄×C₄₁	1	4	yes	—
286	C₂²×D₄	D₄×C₄₁	1	4	yes	—
287	C₂²×D₄	D₄×C₄₁	1	4	yes	—
288	C₂²×D₄	C₂³×C₄₁	1	2	yes	—
289	C₂³×C₄	—	2	1	no	—
290	C₂³×C₄	—	2	4	no	—
291	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
292	C₂×SD₁₆	—	2	32	no	—
293	C₂×SD₁₆	—	2	8	no	—
294	C₂×SD₁₆	—	2	8	no	—
295	C₂×SD₁₆	C₂×C₄×C₄₁	1	16	yes	complemented
296	C₂×M₁₆	—	2	2	no	—
297	C₂×M₁₆	—	2	2	no	—
298	C₂×M₁₆	—	2	2	no	—
299	C₂²×C₈	—	2	2	no	—
300	C₂²×C₈	—	2	2	no	—
301	C₂²×C₈	C₂×C₄×C₄₁	1	4	yes	complemented
302	C₂²×C₈	C₂³×C₄₁	1	2	yes	—
303	C₂²×C₈	C₂³×C₄₁	1	2	yes	—
304	C₄×D₄	—	2	16	no	—
305	C₄×D₄	—	2	8	no	—
306	C₄×D₄	—	2	8	no	—
307	#117	—	2	2	no	—
308	#117	—	2	2	no	—
309	#117	—	2	2	no	—
310	#117	—	2	2	no	—
311	#117	—	2	2	no	—
312	#117	D₄×C₄₁	1	4	yes	—
313	C₂×C₄⋊C₄	D₄×C₄₁	1	2	yes	—
314	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
315	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
316	C₂×C₂²⋊C₄	—	2	16	no	—
317	C₂×C₂²⋊C₄	—	2	1	no	—
318	C₂×C₂²⋊C₄	—	2	4	no	—
319	C₂×C₂²⋊C₄	—	2	1	no	—
320	C₂×C₂²⋊C₄	D₄×C₄₁	1	2	yes	—
321	C₂×C₄²	—	2	1	no	—
322	C₂×C₄²	—	2	1	no	—
323	C₂×C₄²	C₂³×C₄₁	1	2	yes	—
324	#103	—	2	8	no	—
325	#102	—	2	8	no	—
326	#95	—	2	8	no	—
327	C₂⁴	—	2	2	no	—
328	C₂⁴	—	2	4	no	—
329	C₂⁴	—	2	4	no	—
330	C₂⁴	—	2	4	no	—
331	C₂⁴	—	8	4	no	—
332	C₂⁴	C₂×D₄×C₄₁	1	1	yes	characteristic
333	C₂×Q₈	—	2	4	no	—
334	C₂×Q₈	—	2	2	no	—
335	C₂×Q₈	—	2	8	no	—
336	C₂×Q₈	—	2	8	no	—
337	C₂×Q₈	—	2	2	no	—
338	C₂×Q₈	—	2	2	no	—
339	C₂×Q₈	—	2	2	no	—
340	C₂×Q₈	—	2	2	no	—
341	C₂×Q₈	—	4	2	no	—
342	C₂×Q₈	—	4	2	no	—
343	C₂×Q₈	—	4	4	no	—
344	C₂×Q₈	—	4	4	no	—
345	C₂×Q₈	C₂²×C₄×C₄₁	1	4	yes	—
346	C₂×D₄	—	2	8	no	—
347	C₂×D₄	—	2	4	no	—
348	C₂×D₄	—	2	4	no	—
349	C₂×D₄	—	2	8	no	—
350	C₂×D₄	—	2	4	no	—
351	C₂×D₄	—	2	8	no	—
352	C₂×D₄	—	2	2	no	—
353	C₂×D₄	—	2	2	no	—
354	C₂×D₄	—	2	2	no	—
355	C₂×D₄	C₂²⋊C₄×C₄₁	1	16	yes	—
356	C₂×D₄	C₂²×C₄×C₄₁	1	4	yes	—
357	C₂×D₄	C₂×D₄×C₄₁	1	4	yes	—
358	C₂×D₄	C₂×D₄×C₄₁	1	4	yes	—
359	C₂²×C₄	—	2	4	no	—
360	C₂²×C₄	—	2	2	no	—
361	C₂²×C₄	—	2	2	no	—
362	C₂²×C₄	—	2	16	no	—
363	C₂²×C₄	—	2	2	no	—
364	C₂²×C₄	—	4	2	no	—
365	C₂²×C₄	—	4	2	no	—
366	C₂²×C₄	—	8	8	no	—
367	C₂²×C₄	C₂²×C₄×C₄₁	1	2	yes	—
368	C₂²×C₄	C₂×D₄×C₄₁	1	4	yes	—
369	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
370	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
371	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
372	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
373	C₂²×C₄	#41×C₄₁	1	2	yes	—
374	C₂²×C₄	#41×C₄₁	1	2	yes	—
375	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
376	SD₁₆	—	2	32	no	—
377	M₁₆	—	4	4	no	—
378	C₂×C₈	—	2	8	no	—
379	C₂×C₈	—	2	2	no	—
380	C₂×C₈	—	2	2	no	—
381	C₂×C₈	—	2	2	no	—
382	C₂×C₈	—	2	2	no	—
383	C₂×C₈	—	2	2	no	—
384	C₂×C₈	C₂²×C₄×C₄₁	1	4	yes	—
385	C₄⋊C₄	—	2	4	no	—
386	C₄⋊C₄	—	2	2	no	—
387	C₄⋊C₄	—	2	2	no	—
388	C₄⋊C₄	—	2	2	no	—
389	C₄⋊C₄	C₂×D₄×C₄₁	1	4	yes	—
390	C₂²⋊C₄	—	2	16	no	—
391	C₂²⋊C₄	—	2	4	no	—
392	C₂²⋊C₄	—	2	4	no	—
393	C₂²⋊C₄	—	4	2	no	—
394	C₄²	—	2	4	no	—
395	C₄²	—	2	2	no	—
396	C₄²	—	2	2	no	—
397	C₄²	—	4	2	no	—
398	C₂³	—	2	4	no	—
399	C₂³	—	2	4	no	—
400	C₂³	—	2	4	no	—
401	C₂³	—	2	4	no	—
402	C₂³	—	2	16	no	—
403	C₂³	—	4	8	no	—
404	C₂³	—	8	8	no	—
405	C₂³	—	8	8	no	—
406	C₂³	—	8	8	no	—
407	C₂³	C₄×D₄×C₄₁	1	2	yes	—
408	C₂³	#120×C₄₁	1	2	yes	—
409	C₂³	#121×C₄₁	1	2	yes	—
410	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
411	Q₈	—	2	4	no	—
412	Q₈	—	2	4	no	—
413	Q₈	—	4	2	no	—
414	Q₈	—	4	2	no	—
415	Q₈	—	4	8	no	—
416	D₄	—	2	4	no	—
417	D₄	—	2	4	no	—
418	D₄	—	2	4	no	—
419	D₄	—	2	16	no	—
420	D₄	C₂×C₂²⋊C₄×C₄₁	1	8	yes	—
421	C₂×C₄	—	2	4	no	—
422	C₂×C₄	—	2	4	no	—
423	C₂×C₄	—	2	4	no	—
424	C₂×C₄	—	2	8	no	—
425	C₂×C₄	—	4	2	no	—
426	C₂×C₄	—	4	2	no	—
427	C₂×C₄	—	4	4	no	—
428	C₂×C₄	—	4	8	no	—
429	C₂×C₄	—	4	2	no	—
430	C₂×C₄	—	4	4	no	—
431	C₂×C₄	—	8	16	no	—
432	C₂×C₄	C₂×C₂²⋊C₄×C₄₁	1	4	yes	—
433	C₂×C₄	C₄×D₄×C₄₁	1	4	yes	—
434	C₂×C₄	C₄×D₄×C₄₁	1	2	yes	—
435	C₂×C₄	#120×C₄₁	1	2	yes	—
436	C₂×C₄	#121×C₄₁	1	4	yes	—
437	C₂×C₄	#121×C₄₁	1	2	yes	—
438	C₂×C₄	#123×C₄₁	1	4	yes	—
439	C₂×C₄	C₂³×C₄×C₄₁	1	1	yes	characteristic
440	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
441	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
442	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
443	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
444	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
445	C₈	—	2	4	no	—
446	C₈	—	4	2	no	—
447	C₂²	—	2	4	no	—
448	C₂²	—	2	4	no	—
449	C₂²	—	2	4	no	—
450	C₂²	—	2	8	no	—
451	C₂²	—	4	8	no	—
452	C₂²	—	4	8	no	—
453	C₂²	—	4	8	no	—
454	C₂²	—	8	16	no	—
455	C₂²	C₄₁×#386	1	4	yes	—
456	C₂²	C₂×C₄×D₄×C₄₁	1	1	yes	characteristic
457	C₂²	C₂×#120×C₄₁	1	1	yes	characteristic
458	C₂²	C₂×#121×C₄₁	1	1	yes	characteristic
459	C₂²	C₄₁×#577	1	4	yes	—
460	C₄	—	4	4	no	—
461	C₄	—	4	4	no	—
462	C₄	—	4	4	no	—
463	C₄	—	8	2	no	—
464	C₄	C₄₁×#386	1	4	yes	—
465	C₄	C₂²×C₂²⋊C₄×C₄₁	1	1	yes	characteristic
466	C₄	C₂×C₄×D₄×C₄₁	1	1	yes	characteristic
467	C₄	C₂×#121×C₄₁	1	1	yes	characteristic
468	C₄	C₂×#123×C₄₁	1	1	yes	characteristic
469	C₂	—	2	4	no	—
470	C₂	—	4	8	no	—
471	C₂	C₂×C₄₁×#386	1	1	yes	characteristic
472	C₂	C₄₁×#2949	1	2	yes	—
473	C₂	C₄₁×#3009	1	2	yes	—
474	C₂	C₄₁×#3042	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₄₁	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₄₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₁
prime radical	C₂³×D₄×C₄₁	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₄₁ ◁ C₂×#117×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₂×C₄₁×#419	C₂	semidirect
5. C₄₁×#2310	C₂	semidirect
6. C₄₁×#1877	C₂	semidirect
7. C₄₁×#1735	C₂	semidirect
8. C₄₁×#1729	C₂	semidirect
13. C₂²×SD₁₆×C₄₁	C₄	semidirect
27. C₂×#103×C₄₁	C₂²	semidirect
30. C₄₁×#391	C₂²	semidirect
32. C₄₁×#340	C₂²	semidirect
33. C₄₁×#336	C₂²	semidirect
41. C₂²×Q₈×C₄₁	C₂×C₄	semidirect
57. C₂×SD₁₆×C₄₁	C₂×C₄	semidirect
63. C₂²×C₈×C₄₁	C₂×C₄	semidirect
209. #20933	C₄₁	direct (N × H)
234. C₂×#419	C₂×C₄₁	semidirect
236. #2310	C₂×C₄₁	semidirect
237. #1877	C₂×C₄₁	semidirect
238. #1735	C₂×C₄₁	semidirect
239. #1729	C₂×C₄₁	semidirect
250. C₂²×SD₁₆	C₄×C₄₁	semidirect
264. C₂×#103	C₂²×C₄₁	semidirect
267. #391	C₂²×C₄₁	semidirect
269. #340	C₂²×C₄₁	semidirect
270. #336	C₂²×C₄₁	semidirect
271. C₄₁	#20933	direct (N × H)
279. C₂²×Q₈	C₂×C₄×C₄₁	semidirect
295. C₂×SD₁₆	C₂×C₄×C₄₁	semidirect
301. C₂²×C₈	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
C₂³×SD₁₆×C₄₁	2
C₂×C₄₁×#518	2
C₂×C₄₁×#419	2
C₂×C₄₁×#418	2
C₄₁×#2310	2
C₄₁×#1877	2
C₄₁×#1735	2
C₄₁×#1729	2
#20933	41

Subgroups — C41×#20933 #23797134

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#20933 #23797134