Subgroups — C₄₁×#25368 #23801569

Order 10496.

1086 conjugacy classes of subgroups.

The subgroup lattice has 538 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₁×#492	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄₁×#460	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄₁×#461	C₂	1	2	yes	maximal, complemented
4	C₄₁×#2546	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₁×#2366	C₂	1	1	yes	maximal, characteristic
6	C₄₁×#2055	C₂	1	2	yes	maximal, complemented
7	C₄₁×#2013	C₂	1	2	yes	maximal, complemented
8	C₄₁×#1981	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄₁×#1939	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄₁×#1877	C₂	1	2	yes	maximal, complemented
11	C₄×#103×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×SD₁₆×C₄₁	C₂²	1	2	yes	—
13	C₂²×SD₁₆×C₄₁	C₂²	1	2	yes	—
14	C₂²×SD₁₆×C₄₁	C₂²	1	2	yes	—
15	C₂×C₄⋊Q₈×C₄₁	C₂²	1	1	yes	characteristic
16	C₂×C₄⋊Q₈×C₄₁	C₂²	1	2	yes	—
17	C₂×#127×C₄₁	C₂²	1	1	yes	characteristic
18	C₂×C₄×Q₈×C₄₁	C₂²	1	1	yes	characteristic
19	C₂×C₄×D₄×C₄₁	—	2	1	no	—
20	C₂×C₄×D₄×C₄₁	C₂²	1	2	yes	—
21	C₄₁×#492	—	2	4	no	—
22	C₄₁×#461	—	2	8	no	—
23	C₄₁×#460	—	2	4	no	—
24	C₂×C₄⋊C₈×C₄₁	C₂²	1	2	yes	—
25	C₂×C₄⋊C₈×C₄₁	C₂²	1	1	yes	characteristic
26	C₂×#103×C₄₁	C₂²	1	1	yes	characteristic
27	C₂×#103×C₄₁	C₂²	1	2	yes	—
28	C₂×#103×C₄₁	C₂²	1	2	yes	—
29	C₂×#103×C₄₁	C₂²	1	1	yes	characteristic
30	C₂×#102×C₄₁	C₂²	1	2	yes	—
31	C₂×C₄×C₈×C₄₁	C₂²	1	1	yes	characteristic
32	C₄₁×#398	—	2	2	no	—
33	C₄₁×#391	C₂²	1	2	yes	—
34	C₄₁×#390	—	2	1	no	—
35	C₄₁×#390	C₂²	1	2	yes	—
36	C₄₁×#389	—	2	1	no	—
37	C₄₁×#389	—	2	1	no	—
38	C₄₁×#386	—	2	2	no	—
39	C₄×C₄⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
40	C₄×C₄⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
41	C₄₁×#340	C₂²	1	1	yes	characteristic
42	C₄₁×#340	C₂²	1	1	yes	characteristic
43	C₄₁×#336	C₂²	1	2	yes	—
44	C₂²×Q₈×C₄₁	C₂³	1	2	yes	—
45	C₂²×Q₈×C₄₁	C₂³	1	1	yes	characteristic
46	C₂²×D₄×C₄₁	—	2	1	no	—
47	C₂²×D₄×C₄₁	—	2	1	no	—
48	C₂²×D₄×C₄₁	C₂³	1	2	yes	—
49	C₂³×C₄×C₄₁	—	2	2	no	—
50	C₂×SD₁₆×C₄₁	—	2	4	no	—
51	C₂×SD₁₆×C₄₁	—	2	4	no	—
52	C₂×SD₁₆×C₄₁	—	2	4	no	—
53	C₂×SD₁₆×C₄₁	—	2	4	no	—
54	C₂×SD₁₆×C₄₁	—	2	4	no	—
55	C₂×SD₁₆×C₄₁	—	2	4	no	—
56	C₂×SD₁₆×C₄₁	—	4	2	no	—
57	C₂×SD₁₆×C₄₁	—	4	2	no	—
58	C₂×SD₁₆×C₄₁	—	4	2	no	—
59	C₂²×C₈×C₄₁	C₂³	1	2	yes	—
60	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
61	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
62	C₄⋊Q₈×C₄₁	—	2	4	no	—
63	C₄⋊Q₈×C₄₁	—	2	2	no	—
64	C₄⋊Q₈×C₄₁	—	2	2	no	—
65	C₄⋊Q₈×C₄₁	—	4	2	no	—
66	#127×C₄₁	—	2	2	no	—
67	#127×C₄₁	D₄	1	4	yes	—
68	C₄×Q₈×C₄₁	—	2	2	no	—
69	C₄×Q₈×C₄₁	—	2	2	no	—
70	C₄×D₄×C₄₁	—	2	4	no	—
71	C₄×D₄×C₄₁	—	4	2	no	—
72	C₄×D₄×C₄₁	—	4	4	no	—
73	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
74	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
75	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
76	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
77	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
78	C₂×C₄⋊C₄×C₄₁	D₄	1	1	yes	characteristic
79	C₂×C₄⋊C₄×C₄₁	D₄	1	1	yes	characteristic
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×C₂²⋊C₄×C₄₁	—	2	2	no	—
84	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
85	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
86	C₂×C₄²×C₄₁	—	2	1	no	—
87	C₂×C₄²×C₄₁	—	2	1	no	—
88	C₂×C₄²×C₄₁	C₂³	1	2	yes	—
89	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
90	C₄⋊C₈×C₄₁	—	2	4	no	—
91	C₄⋊C₈×C₄₁	—	2	2	no	—
92	#103×C₄₁	—	2	2	no	—
93	#103×C₄₁	—	2	4	no	—
94	#103×C₄₁	—	4	2	no	—
95	#103×C₄₁	D₄	1	4	yes	complemented
96	#102×C₄₁	—	2	4	no	—
97	C₄×C₈×C₄₁	—	2	2	no	—
98	#95×C₄₁	—	2	1	no	—
99	#95×C₄₁	—	2	2	no	—
100	#95×C₄₁	—	2	2	no	—
101	#95×C₄₁	D₄	1	2	yes	—
102	C₂⁴×C₄₁	—	2	2	no	—
103	C₂×Q₈×C₄₁	—	2	1	no	—
104	C₂×Q₈×C₄₁	—	2	1	no	—
105	C₂×Q₈×C₄₁	—	2	2	no	—
106	C₂×Q₈×C₄₁	—	2	2	no	—
107	C₂×Q₈×C₄₁	—	2	1	no	—
108	C₂×Q₈×C₄₁	—	2	1	no	—
109	C₂×Q₈×C₄₁	—	2	2	no	—
110	C₂×Q₈×C₄₁	—	2	2	no	—
111	C₂×Q₈×C₄₁	—	2	1	no	—
112	C₂×Q₈×C₄₁	—	2	2	no	—
113	C₂×Q₈×C₄₁	—	2	2	no	—
114	C₂×Q₈×C₄₁	C₂×D₄	1	2	yes	—
115	C₂×D₄×C₄₁	—	2	4	no	—
116	C₂×D₄×C₄₁	—	2	4	no	—
117	C₂×D₄×C₄₁	—	2	2	no	—
118	C₂×D₄×C₄₁	—	2	2	no	—
119	C₂×D₄×C₄₁	—	2	2	no	—
120	C₂×D₄×C₄₁	—	2	2	no	—
121	C₂×D₄×C₄₁	—	2	2	no	—
122	C₂×D₄×C₄₁	—	4	2	no	—
123	C₂×D₄×C₄₁	—	4	2	no	—
124	C₂×D₄×C₄₁	—	8	1	no	—
125	C₂×D₄×C₄₁	—	8	1	no	—
126	C₂×D₄×C₄₁	C₂×D₄	1	4	yes	—
127	C₂²×C₄×C₄₁	—	2	1	no	—
128	C₂²×C₄×C₄₁	—	2	1	no	—
129	C₂²×C₄×C₄₁	—	2	1	no	—
130	C₂²×C₄×C₄₁	—	2	2	no	—
131	C₂²×C₄×C₄₁	—	2	1	no	—
132	C₂²×C₄×C₄₁	—	4	4	no	—
133	C₂²×C₄×C₄₁	—	4	4	no	—
134	C₂²×C₄×C₄₁	—	8	2	no	—
135	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
136	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
137	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
138	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
139	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
140	SD₁₆×C₄₁	—	4	8	no	—
141	SD₁₆×C₄₁	—	4	8	no	—
142	SD₁₆×C₄₁	—	4	8	no	—
143	C₂×C₈×C₄₁	—	2	1	no	—
144	C₂×C₈×C₄₁	—	2	1	no	—
145	C₂×C₈×C₄₁	—	2	1	no	—
146	C₂×C₈×C₄₁	—	2	1	no	—
147	C₂×C₈×C₄₁	—	2	2	no	—
148	C₂×C₈×C₄₁	—	2	2	no	—
149	C₂×C₈×C₄₁	—	2	2	no	—
150	C₂×C₈×C₄₁	C₂×D₄	1	2	yes	—
151	C₂×C₈×C₄₁	#41	1	2	yes	—
152	C₄⋊C₄×C₄₁	—	2	2	no	—
153	C₄⋊C₄×C₄₁	—	2	1	no	—
154	C₄⋊C₄×C₄₁	—	2	1	no	—
155	C₄⋊C₄×C₄₁	—	2	1	no	—
156	C₄⋊C₄×C₄₁	—	2	1	no	—
157	C₄⋊C₄×C₄₁	—	2	1	no	—
158	C₄⋊C₄×C₄₁	—	4	4	no	—
159	C₄⋊C₄×C₄₁	—	4	4	no	—
160	C₄⋊C₄×C₄₁	—	4	2	no	—
161	C₄⋊C₄×C₄₁	—	4	2	no	—
162	C₄⋊C₄×C₄₁	—	4	2	no	—
163	C₄⋊C₄×C₄₁	SD₁₆	1	4	yes	complemented
164	C₄⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
165	C₂²⋊C₄×C₄₁	—	4	4	no	—
166	C₂²⋊C₄×C₄₁	—	4	4	no	—
167	C₂²⋊C₄×C₄₁	—	8	2	no	—
168	C₄²×C₄₁	—	2	2	no	—
169	C₄²×C₄₁	—	2	2	no	—
170	C₄²×C₄₁	—	4	2	no	—
171	C₄²×C₄₁	—	4	2	no	—
172	C₄²×C₄₁	C₂×D₄	1	2	yes	—
173	C₄²×C₄₁	#41	1	2	yes	—
174	C₂³×C₄₁	—	2	4	no	—
175	C₂³×C₄₁	—	4	2	no	—
176	C₂³×C₄₁	—	4	2	no	—
177	C₂³×C₄₁	—	4	2	no	—
178	C₂³×C₄₁	—	4	2	no	—
179	C₂³×C₄₁	—	4	2	no	—
180	C₂³×C₄₁	—	4	2	no	—
181	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
182	Q₈×C₄₁	—	2	2	no	—
183	Q₈×C₄₁	—	2	2	no	—
184	Q₈×C₄₁	—	4	1	no	—
185	Q₈×C₄₁	—	4	1	no	—
186	Q₈×C₄₁	—	4	2	no	—
187	Q₈×C₄₁	—	4	2	no	—
188	Q₈×C₄₁	—	4	2	no	—
189	Q₈×C₄₁	—	4	2	no	—
190	D₄×C₄₁	—	2	4	no	—
191	D₄×C₄₁	—	2	4	no	—
192	D₄×C₄₁	—	4	2	no	—
193	D₄×C₄₁	—	4	2	no	—
194	D₄×C₄₁	—	4	8	no	—
195	D₄×C₄₁	—	8	4	no	—
196	C₂×C₄×C₄₁	—	2	2	no	—
197	C₂×C₄×C₄₁	—	2	2	no	—
198	C₂×C₄×C₄₁	—	2	1	no	—
199	C₂×C₄×C₄₁	—	2	1	no	—
200	C₂×C₄×C₄₁	—	2	2	no	—
201	C₂×C₄×C₄₁	—	2	2	no	—
202	C₂×C₄×C₄₁	—	2	2	no	—
203	C₂×C₄×C₄₁	—	2	2	no	—
204	C₂×C₄×C₄₁	—	2	2	no	—
205	C₂×C₄×C₄₁	—	4	1	no	—
206	C₂×C₄×C₄₁	—	4	1	no	—
207	C₂×C₄×C₄₁	—	4	1	no	—
208	C₂×C₄×C₄₁	—	4	1	no	—
209	C₂×C₄×C₄₁	—	4	1	no	—
210	C₂×C₄×C₄₁	—	4	2	no	—
211	C₂×C₄×C₄₁	—	4	2	no	—
212	C₂×C₄×C₄₁	—	4	1	no	—
213	C₂×C₄×C₄₁	—	4	2	no	—
214	C₂×C₄×C₄₁	—	4	1	no	—
215	C₂×C₄×C₄₁	—	4	1	no	—
216	C₂×C₄×C₄₁	—	4	1	no	—
217	C₂×C₄×C₄₁	—	4	1	no	—
218	C₂×C₄×C₄₁	—	8	8	no	—
219	C₂×C₄×C₄₁	#121	1	2	yes	—
220	C₂×C₄×C₄₁	#121	1	2	yes	—
221	C₂×C₄×C₄₁	C₂×SD₁₆	1	4	yes	—
222	C₂×C₄×C₄₁	C₂×SD₁₆	1	2	yes	—
223	C₂×C₄×C₄₁	#137	1	2	yes	—
224	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
225	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
226	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
227	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
228	C₂×C₄×C₄₁	H(5,𝔽₂)	1	1	yes	characteristic
229	C₂×C₄×C₄₁	H(5,𝔽₂)	1	1	yes	characteristic
230	C₈×C₄₁	—	2	2	no	—
231	C₈×C₄₁	—	2	2	no	—
232	C₈×C₄₁	—	4	2	no	—
233	#25368	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
234	C₂²×C₄₁	—	4	4	no	—
235	C₂²×C₄₁	—	4	4	no	—
236	C₂²×C₄₁	—	4	4	no	—
237	C₂²×C₄₁	—	8	2	no	—
238	C₂²×C₄₁	—	8	2	no	—
239	C₂²×C₄₁	—	8	2	no	—
240	C₂²×C₄₁	—	8	2	no	—
241	C₂²×C₄₁	C₂×#121	1	1	yes	characteristic
242	C₂²×C₄₁	D₄²	1	1	yes	characteristic
243	C₂²×C₄₁	#550	1	1	yes	characteristic
244	C₂²×C₄₁	C₂²×SD₁₆	1	1	yes	characteristic
245	C₂²×C₄₁	C₂×#137	1	1	yes	characteristic
246	C₂²×C₄₁	#577	1	1	yes	characteristic
247	C₂²×C₄₁	#577	1	1	yes	characteristic
248	C₄×C₄₁	—	2	4	no	—
249	C₄×C₄₁	—	2	2	no	—
250	C₄×C₄₁	—	4	2	no	—
251	C₄×C₄₁	—	4	2	no	—
252	C₄×C₄₁	—	4	2	no	—
253	C₄×C₄₁	—	8	1	no	—
254	C₄×C₄₁	—	8	2	no	—
255	C₄×C₄₁	—	8	1	no	—
256	C₄×C₄₁	#461	1	4	yes	complemented
257	C₄×C₄₁	#532	1	1	yes	characteristic
258	C₄×C₄₁	#540	1	1	yes	characteristic
259	C₄×C₄₁	D₄²	1	1	yes	characteristic
260	C₄×C₄₁	#546	1	1	yes	characteristic
261	C₂×#492	C₂×C₄₁	1	1	yes	characteristic
262	C₂×#460	C₂×C₄₁	1	1	yes	characteristic
263	C₂×#461	C₂×C₄₁	1	2	yes	complemented
264	#2546	C₂×C₄₁	1	1	yes	characteristic, complemented
265	#2366	C₂×C₄₁	1	1	yes	characteristic
266	#2055	C₂×C₄₁	1	2	yes	complemented
267	#2013	C₂×C₄₁	1	2	yes	complemented
268	#1981	C₂×C₄₁	1	1	yes	characteristic, complemented
269	#1939	C₂×C₄₁	1	1	yes	characteristic, complemented
270	#1877	C₂×C₄₁	1	2	yes	complemented
271	C₄×#103	C₂×C₄₁	1	1	yes	characteristic, complemented
272	C₂×C₄₁	—	8	4	no	—
273	C₂×C₄₁	#2428	1	1	yes	characteristic
274	C₂×C₄₁	C₂×#461	1	1	yes	characteristic
275	C₂×C₄₁	#3042	1	1	yes	characteristic
276	C₂×C₄₁	#3278	1	1	yes	characteristic
277	C₂×C₄₁	D₄×SD₁₆	1	1	yes	characteristic
278	C₂×C₄₁	#3392	1	1	yes	characteristic
279	C₂×C₄₁	#3400	1	1	yes	characteristic
280	C₂²×SD₁₆	C₂²×C₄₁	1	2	yes	—
281	C₂²×SD₁₆	C₂²×C₄₁	1	2	yes	—
282	C₂²×SD₁₆	C₂²×C₄₁	1	2	yes	—
283	C₂×C₄⋊Q₈	C₂²×C₄₁	1	1	yes	characteristic
284	C₂×C₄⋊Q₈	C₂²×C₄₁	1	2	yes	—
285	C₂×#127	C₂²×C₄₁	1	1	yes	characteristic
286	C₂×C₄×Q₈	C₂²×C₄₁	1	1	yes	characteristic
287	C₂×C₄×D₄	—	2	1	no	—
288	C₂×C₄×D₄	C₂²×C₄₁	1	2	yes	—
289	#492	—	2	4	no	—
290	#461	—	2	8	no	—
291	#460	—	2	4	no	—
292	C₂×C₄⋊C₈	C₂²×C₄₁	1	2	yes	—
293	C₂×C₄⋊C₈	C₂²×C₄₁	1	1	yes	characteristic
294	C₂×#103	C₂²×C₄₁	1	2	yes	—
295	C₂×#103	C₂²×C₄₁	1	1	yes	characteristic
296	C₂×#103	C₂²×C₄₁	1	2	yes	—
297	C₂×#103	C₂²×C₄₁	1	1	yes	characteristic
298	C₂×#102	C₂²×C₄₁	1	2	yes	—
299	C₂×C₄×C₈	C₂²×C₄₁	1	1	yes	characteristic
300	#398	—	2	2	no	—
301	#391	C₂²×C₄₁	1	2	yes	—
302	#390	—	2	1	no	—
303	#390	C₂²×C₄₁	1	2	yes	—
304	#389	—	2	1	no	—
305	#389	—	2	1	no	—
306	#386	—	2	2	no	—
307	C₄×C₄⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
308	C₄×C₄⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
309	#340	C₂²×C₄₁	1	1	yes	characteristic
310	#340	C₂²×C₄₁	1	1	yes	characteristic
311	#336	C₂²×C₄₁	1	2	yes	—
312	C₄₁	#25368	1	1	yes	characteristic, direct product factor, Sylow
313	C₂²×Q₈	C₂³×C₄₁	1	2	yes	—
314	C₂²×Q₈	C₂³×C₄₁	1	1	yes	characteristic
315	C₂²×D₄	—	2	1	no	—
316	C₂²×D₄	—	2	1	no	—
317	C₂²×D₄	C₂³×C₄₁	1	2	yes	—
318	C₂³×C₄	—	2	2	no	—
319	C₂×SD₁₆	—	2	4	no	—
320	C₂×SD₁₆	—	2	4	no	—
321	C₂×SD₁₆	—	2	4	no	—
322	C₂×SD₁₆	—	2	4	no	—
323	C₂×SD₁₆	—	2	4	no	—
324	C₂×SD₁₆	—	2	4	no	—
325	C₂×SD₁₆	—	4	2	no	—
326	C₂×SD₁₆	—	4	2	no	—
327	C₂×SD₁₆	—	4	2	no	—
328	C₂²×C₈	C₂³×C₄₁	1	2	yes	—
329	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
330	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
331	C₄⋊Q₈	—	2	4	no	—
332	C₄⋊Q₈	—	2	2	no	—
333	C₄⋊Q₈	—	2	2	no	—
334	C₄⋊Q₈	—	4	2	no	—
335	#127	—	2	2	no	—
336	#127	D₄×C₄₁	1	4	yes	—
337	C₄×Q₈	—	2	2	no	—
338	C₄×Q₈	—	2	2	no	—
339	C₄×D₄	—	2	4	no	—
340	C₄×D₄	—	4	2	no	—
341	C₄×D₄	—	4	4	no	—
342	C₂×C₄⋊C₄	—	2	1	no	—
343	C₂×C₄⋊C₄	—	2	1	no	—
344	C₂×C₄⋊C₄	—	2	2	no	—
345	C₂×C₄⋊C₄	—	2	2	no	—
346	C₂×C₄⋊C₄	—	2	1	no	—
347	C₂×C₄⋊C₄	D₄×C₄₁	1	1	yes	characteristic
348	C₂×C₄⋊C₄	D₄×C₄₁	1	1	yes	characteristic
349	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
350	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
351	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
352	C₂×C₂²⋊C₄	—	2	2	no	—
353	C₂×C₂²⋊C₄	—	2	2	no	—
354	C₂×C₂²⋊C₄	—	2	2	no	—
355	C₂×C₄²	—	2	1	no	—
356	C₂×C₄²	—	2	1	no	—
357	C₂×C₄²	C₂³×C₄₁	1	2	yes	—
358	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
359	C₄⋊C₈	—	2	4	no	—
360	C₄⋊C₈	—	2	2	no	—
361	#103	—	2	2	no	—
362	#103	—	2	4	no	—
363	#103	—	4	2	no	—
364	#103	D₄×C₄₁	1	4	yes	complemented
365	#102	—	2	4	no	—
366	C₄×C₈	—	2	2	no	—
367	#95	—	2	1	no	—
368	#95	—	2	2	no	—
369	#95	—	2	2	no	—
370	#95	D₄×C₄₁	1	2	yes	—
371	C₂⁴	—	2	2	no	—
372	C₂×Q₈	—	2	1	no	—
373	C₂×Q₈	—	2	1	no	—
374	C₂×Q₈	—	2	2	no	—
375	C₂×Q₈	—	2	2	no	—
376	C₂×Q₈	—	2	1	no	—
377	C₂×Q₈	—	2	1	no	—
378	C₂×Q₈	—	2	2	no	—
379	C₂×Q₈	—	2	2	no	—
380	C₂×Q₈	—	2	1	no	—
381	C₂×Q₈	—	2	2	no	—
382	C₂×Q₈	—	2	2	no	—
383	C₂×Q₈	C₂×D₄×C₄₁	1	2	yes	—
384	C₂×D₄	—	2	4	no	—
385	C₂×D₄	—	2	4	no	—
386	C₂×D₄	—	2	2	no	—
387	C₂×D₄	—	2	2	no	—
388	C₂×D₄	—	2	2	no	—
389	C₂×D₄	—	2	2	no	—
390	C₂×D₄	—	2	2	no	—
391	C₂×D₄	—	4	2	no	—
392	C₂×D₄	—	4	2	no	—
393	C₂×D₄	—	8	1	no	—
394	C₂×D₄	—	8	1	no	—
395	C₂×D₄	C₂×D₄×C₄₁	1	4	yes	—
396	C₂²×C₄	—	2	1	no	—
397	C₂²×C₄	—	2	1	no	—
398	C₂²×C₄	—	2	1	no	—
399	C₂²×C₄	—	2	2	no	—
400	C₂²×C₄	—	2	1	no	—
401	C₂²×C₄	—	4	4	no	—
402	C₂²×C₄	—	4	4	no	—
403	C₂²×C₄	—	8	2	no	—
404	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
405	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
406	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
407	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
408	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
409	SD₁₆	—	4	8	no	—
410	SD₁₆	—	4	8	no	—
411	SD₁₆	—	4	8	no	—
412	C₂×C₈	—	2	1	no	—
413	C₂×C₈	—	2	1	no	—
414	C₂×C₈	—	2	1	no	—
415	C₂×C₈	—	2	1	no	—
416	C₂×C₈	—	2	2	no	—
417	C₂×C₈	—	2	2	no	—
418	C₂×C₈	—	2	2	no	—
419	C₂×C₈	C₂×D₄×C₄₁	1	2	yes	—
420	C₂×C₈	#41×C₄₁	1	2	yes	—
421	C₄⋊C₄	—	2	2	no	—
422	C₄⋊C₄	—	2	1	no	—
423	C₄⋊C₄	—	2	1	no	—
424	C₄⋊C₄	—	2	1	no	—
425	C₄⋊C₄	—	2	1	no	—
426	C₄⋊C₄	—	2	1	no	—
427	C₄⋊C₄	—	4	4	no	—
428	C₄⋊C₄	—	4	4	no	—
429	C₄⋊C₄	—	4	2	no	—
430	C₄⋊C₄	—	4	2	no	—
431	C₄⋊C₄	—	4	2	no	—
432	C₄⋊C₄	SD₁₆×C₄₁	1	4	yes	complemented
433	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
434	C₂²⋊C₄	—	4	4	no	—
435	C₂²⋊C₄	—	4	4	no	—
436	C₂²⋊C₄	—	8	2	no	—
437	C₄²	—	2	2	no	—
438	C₄²	—	2	2	no	—
439	C₄²	—	4	2	no	—
440	C₄²	—	4	2	no	—
441	C₄²	C₂×D₄×C₄₁	1	2	yes	—
442	C₄²	#41×C₄₁	1	2	yes	—
443	C₂³	—	2	4	no	—
444	C₂³	—	4	2	no	—
445	C₂³	—	4	2	no	—
446	C₂³	—	4	2	no	—
447	C₂³	—	4	2	no	—
448	C₂³	—	4	2	no	—
449	C₂³	—	4	2	no	—
450	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
451	Q₈	—	2	2	no	—
452	Q₈	—	2	2	no	—
453	Q₈	—	4	1	no	—
454	Q₈	—	4	1	no	—
455	Q₈	—	4	2	no	—
456	Q₈	—	4	2	no	—
457	Q₈	—	4	2	no	—
458	Q₈	—	4	2	no	—
459	D₄	—	2	4	no	—
460	D₄	—	2	4	no	—
461	D₄	—	4	2	no	—
462	D₄	—	4	2	no	—
463	D₄	—	4	8	no	—
464	D₄	—	8	4	no	—
465	C₂×C₄	—	2	2	no	—
466	C₂×C₄	—	2	2	no	—
467	C₂×C₄	—	2	1	no	—
468	C₂×C₄	—	2	1	no	—
469	C₂×C₄	—	2	2	no	—
470	C₂×C₄	—	2	2	no	—
471	C₂×C₄	—	2	2	no	—
472	C₂×C₄	—	2	2	no	—
473	C₂×C₄	—	2	2	no	—
474	C₂×C₄	—	4	1	no	—
475	C₂×C₄	—	4	1	no	—
476	C₂×C₄	—	4	1	no	—
477	C₂×C₄	—	4	1	no	—
478	C₂×C₄	—	4	1	no	—
479	C₂×C₄	—	4	2	no	—
480	C₂×C₄	—	4	2	no	—
481	C₂×C₄	—	4	1	no	—
482	C₂×C₄	—	4	2	no	—
483	C₂×C₄	—	4	1	no	—
484	C₂×C₄	—	4	1	no	—
485	C₂×C₄	—	4	1	no	—
486	C₂×C₄	—	4	1	no	—
487	C₂×C₄	—	8	8	no	—
488	C₂×C₄	#121×C₄₁	1	2	yes	—
489	C₂×C₄	#121×C₄₁	1	2	yes	—
490	C₂×C₄	C₂×SD₁₆×C₄₁	1	4	yes	—
491	C₂×C₄	C₂×SD₁₆×C₄₁	1	2	yes	—
492	C₂×C₄	#137×C₄₁	1	2	yes	—
493	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
494	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
495	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
496	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
497	C₂×C₄	H(5,𝔽₂)×C₄₁	1	1	yes	characteristic
498	C₂×C₄	H(5,𝔽₂)×C₄₁	1	1	yes	characteristic
499	C₈	—	2	2	no	—
500	C₈	—	2	2	no	—
501	C₈	—	4	2	no	—
502	C₂²	—	4	4	no	—
503	C₂²	—	4	4	no	—
504	C₂²	—	4	4	no	—
505	C₂²	—	8	2	no	—
506	C₂²	—	8	2	no	—
507	C₂²	—	8	2	no	—
508	C₂²	—	8	2	no	—
509	C₂²	C₂×#121×C₄₁	1	1	yes	characteristic
510	C₂²	D₄²×C₄₁	1	1	yes	characteristic
511	C₂²	C₄₁×#550	1	1	yes	characteristic
512	C₂²	C₂²×SD₁₆×C₄₁	1	1	yes	characteristic
513	C₂²	C₂×#137×C₄₁	1	1	yes	characteristic
514	C₂²	C₄₁×#577	1	1	yes	characteristic
515	C₂²	C₄₁×#577	1	1	yes	characteristic
516	C₄	—	2	2	no	—
517	C₄	—	2	4	no	—
518	C₄	—	4	2	no	—
519	C₄	—	4	2	no	—
520	C₄	—	4	2	no	—
521	C₄	—	8	1	no	—
522	C₄	—	8	1	no	—
523	C₄	—	8	2	no	—
524	C₄	C₄₁×#461	1	4	yes	complemented
525	C₄	C₄₁×#532	1	1	yes	characteristic
526	C₄	C₄₁×#540	1	1	yes	characteristic
527	C₄	D₄²×C₄₁	1	1	yes	characteristic
528	C₄	C₄₁×#546	1	1	yes	characteristic
529	C₂	—	8	4	no	—
530	C₂	C₄₁×#2428	1	1	yes	characteristic
531	C₂	C₂×C₄₁×#461	1	1	yes	characteristic
532	C₂	C₄₁×#3042	1	1	yes	characteristic
533	C₂	C₄₁×#3278	1	1	yes	characteristic
534	C₂	D₄×SD₁₆×C₄₁	1	1	yes	characteristic
535	C₂	C₄₁×#3392	1	1	yes	characteristic
536	C₂	C₄₁×#3400	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₄₁	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₁
prime radical	C₂×#127×C₄₁	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₄₁ ◁ C₄×C₄⋊C₄×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₂×C₄₁×#461	C₂	semidirect
4. C₄₁×#2546	C₂	semidirect
6. C₄₁×#2055	C₂	semidirect
7. C₄₁×#2013	C₂	semidirect
8. C₄₁×#1981	C₂	semidirect
9. C₄₁×#1939	C₂	semidirect
10. C₄₁×#1877	C₂	semidirect
11. C₄×#103×C₄₁	C₂	semidirect
95. #103×C₄₁	D₄	semidirect
163. C₄⋊C₄×C₄₁	SD₁₆	semidirect
233. #25368	C₄₁	direct (N × H)
256. C₄×C₄₁	#461	semidirect
263. C₂×#461	C₂×C₄₁	semidirect
264. #2546	C₂×C₄₁	semidirect
266. #2055	C₂×C₄₁	semidirect
267. #2013	C₂×C₄₁	semidirect
268. #1981	C₂×C₄₁	semidirect
269. #1939	C₂×C₄₁	semidirect
270. #1877	C₂×C₄₁	semidirect
271. C₄×#103	C₂×C₄₁	semidirect
312. C₄₁	#25368	direct (N × H)
364. #103	D₄×C₄₁	semidirect
432. C₄⋊C₄	SD₁₆×C₄₁	semidirect
524. C₄	C₄₁×#461	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄₁×#492	2
C₂×C₄₁×#460	2
C₂×C₄₁×#461	2
C₄₁×#2546	2
C₄₁×#2366	2
C₄₁×#2055	2
C₄₁×#2013	2
C₄₁×#1981	2
C₄₁×#1939	2
C₄₁×#1877	2
C₄×#103×C₄₁	2
#25368	41

Subgroups — C41×#25368 #23801569

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#25368 #23801569