Subgroups — C₄₁×#23182 #23799383

Order 10496.

1098 conjugacy classes of subgroups.

The subgroup lattice has 508 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×C₄×SD₁₆×C₄₁	C₂	1	2	yes	maximal, complemented
3	C₄₁×#2366	C₂	1	1	yes	maximal, characteristic
4	C₄₁×#2365	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₁×#1982	C₂	1	1	yes	maximal, characteristic
6	C₄₁×#1981	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₁×#1968	C₂	1	2	yes	maximal, complemented
8	C₄₁×#1880	C₂	1	2	yes	maximal, complemented
9	C₄₁×#1877	C₂	1	2	yes	maximal, complemented
10	C₄×#106×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈×C₄⋊C₄×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	C₂×C₄⋊Q₈×C₄₁	C₂²	1	1	yes	characteristic
15	C₂×#127×C₄₁	C₂²	1	1	yes	characteristic
16	C₂×C₄×Q₈×C₄₁	C₂²	1	2	yes	—
17	C₂×C₄×D₄×C₄₁	—	2	1	no	—
18	C₂×C₄×D₄×C₄₁	C₂²	1	2	yes	—
19	C₄₁×#492	C₄	1	8	yes	complemented
20	C₄×SD₁₆×C₄₁	—	2	8	no	—
21	C₂×#106×C₄₁	C₂²	1	1	yes	characteristic
22	C₂×#106×C₄₁	C₂²	1	1	yes	characteristic
23	C₂×C₄⋊C₈×C₄₁	C₂²	1	1	yes	characteristic
24	C₂×#103×C₄₁	C₂²	1	2	yes	—
25	C₂×#103×C₄₁	C₂²	1	2	yes	—
26	C₂×#102×C₄₁	C₂²	1	2	yes	—
27	C₂×#102×C₄₁	C₂²	1	2	yes	—
28	C₂×C₄×C₈×C₄₁	C₂²	1	2	yes	—
29	C₂×C₄×C₈×C₄₁	C₂²	1	1	yes	characteristic
30	C₄₁×#391	C₂²	1	2	yes	—
31	C₄₁×#390	—	2	1	no	—
32	C₄₁×#390	C₂²	1	2	yes	—
33	C₄₁×#389	—	2	1	no	—
34	C₄₁×#387	—	2	2	no	—
35	C₄₁×#386	—	2	2	no	—
36	C₄×C₄⋊C₄×C₄₁	—	2	1	no	—
37	C₄×C₄⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
38	C₄×C₄⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
39	C₄×C₄⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
40	C₄₁×#340	C₂²	1	1	yes	characteristic
41	C₄₁×#340	C₂²	1	1	yes	characteristic
42	C₄₁×#336	C₂²	1	2	yes	—
43	C₂²×Q₈×C₄₁	C₂³	1	2	yes	—
44	C₂²×D₄×C₄₁	—	2	1	no	—
45	C₂²×D₄×C₄₁	—	2	1	no	—
46	C₂²×D₄×C₄₁	C₂³	1	2	yes	—
47	C₂³×C₄×C₄₁	—	2	2	no	—
48	C₂×SD₁₆×C₄₁	—	2	4	no	—
49	C₂×SD₁₆×C₄₁	—	2	4	no	—
50	C₂×SD₁₆×C₄₁	—	4	2	no	—
51	C₂×SD₁₆×C₄₁	—	4	2	no	—
52	C₂×SD₁₆×C₄₁	C₂×C₄	1	8	yes	complemented
53	C₂×SD₁₆×C₄₁	C₂×C₄	1	8	yes	complemented
54	C₂²×C₈×C₄₁	C₂³	1	2	yes	—
55	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
56	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
57	C₄⋊Q₈×C₄₁	—	2	2	no	—
58	C₄⋊Q₈×C₄₁	C₂×C₄	1	4	yes	complemented
59	#127×C₄₁	—	2	2	no	—
60	#127×C₄₁	C₂×C₄	1	4	yes	—
61	C₄×Q₈×C₄₁	—	2	4	no	—
62	C₄×Q₈×C₄₁	—	4	2	no	—
63	C₄×D₄×C₄₁	—	2	4	no	—
64	C₄×D₄×C₄₁	—	4	2	no	—
65	C₄×D₄×C₄₁	—	4	4	no	—
66	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
67	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
68	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
69	C₂×C₄⋊C₄×C₄₁	D₄	1	1	yes	characteristic
70	C₂×C₄⋊C₄×C₄₁	D₄	1	1	yes	characteristic
71	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
72	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
73	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
74	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
75	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
76	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
77	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
78	C₂×C₄²×C₄₁	—	2	1	no	—
79	C₂×C₄²×C₄₁	—	2	2	no	—
80	C₂×C₄²×C₄₁	—	2	1	no	—
81	C₂×C₄²×C₄₁	C₂³	1	2	yes	—
82	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
83	#106×C₄₁	—	2	2	no	—
84	#106×C₄₁	D₄	1	4	yes	complemented
85	C₄⋊C₈×C₄₁	—	2	2	no	—
86	#103×C₄₁	—	2	4	no	—
87	#103×C₄₁	—	4	2	no	—
88	#102×C₄₁	—	2	4	no	—
89	#102×C₄₁	—	4	2	no	—
90	C₄×C₈×C₄₁	—	2	4	no	—
91	C₄×C₈×C₄₁	C₂×C₄	1	4	yes	complemented
92	#95×C₄₁	—	2	2	no	—
93	#95×C₄₁	—	2	1	no	—
94	#95×C₄₁	—	2	1	no	—
95	#95×C₄₁	—	2	2	no	—
96	#95×C₄₁	D₄	1	2	yes	—
97	C₂⁴×C₄₁	—	2	2	no	—
98	C₂×Q₈×C₄₁	—	2	2	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	C₂²×C₄	1	4	yes	—
104	C₂×D₄×C₄₁	—	2	4	no	—
105	C₂×D₄×C₄₁	—	2	4	no	—
106	C₂×D₄×C₄₁	—	2	2	no	—
107	C₂×D₄×C₄₁	—	2	2	no	—
108	C₂×D₄×C₄₁	—	2	2	no	—
109	C₂×D₄×C₄₁	—	2	2	no	—
110	C₂×D₄×C₄₁	—	2	2	no	—
111	C₂×D₄×C₄₁	—	4	2	no	—
112	C₂×D₄×C₄₁	—	4	2	no	—
113	C₂×D₄×C₄₁	—	8	1	no	—
114	C₂×D₄×C₄₁	—	8	1	no	—
115	C₂×D₄×C₄₁	C₂²×C₄	1	4	yes	—
116	C₂²×C₄×C₄₁	—	2	2	no	—
117	C₂²×C₄×C₄₁	—	2	1	no	—
118	C₂²×C₄×C₄₁	—	2	1	no	—
119	C₂²×C₄×C₄₁	—	2	1	no	—
120	C₂²×C₄×C₄₁	—	2	1	no	—
121	C₂²×C₄×C₄₁	—	4	4	no	—
122	C₂²×C₄×C₄₁	—	4	4	no	—
123	C₂²×C₄×C₄₁	—	8	2	no	—
124	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
125	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
126	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
127	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
128	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
129	SD₁₆×C₄₁	—	2	16	no	—
130	SD₁₆×C₄₁	—	4	8	no	—
131	C₂×C₈×C₄₁	—	2	1	no	—
132	C₂×C₈×C₄₁	—	2	1	no	—
133	C₂×C₈×C₄₁	—	2	2	no	—
134	C₂×C₈×C₄₁	—	2	2	no	—
135	C₂×C₈×C₄₁	—	2	2	no	—
136	C₂×C₈×C₄₁	C₂²×C₄	1	2	yes	—
137	C₂×C₈×C₄₁	C₂²×C₄	1	2	yes	—
138	C₂×C₈×C₄₁	C₂×D₄	1	2	yes	—
139	C₂×C₈×C₄₁	#41	1	2	yes	—
140	C₄⋊C₄×C₄₁	—	2	4	no	—
141	C₄⋊C₄×C₄₁	—	2	4	no	—
142	C₄⋊C₄×C₄₁	—	2	2	no	—
143	C₄⋊C₄×C₄₁	—	2	1	no	—
144	C₄⋊C₄×C₄₁	—	2	1	no	—
145	C₄⋊C₄×C₄₁	—	2	1	no	—
146	C₄⋊C₄×C₄₁	—	2	1	no	—
147	C₄⋊C₄×C₄₁	—	2	1	no	—
148	C₄⋊C₄×C₄₁	—	2	1	no	—
149	C₄⋊C₄×C₄₁	—	4	4	no	—
150	C₄⋊C₄×C₄₁	SD₁₆	1	4	yes	complemented
151	C₄⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
152	C₄⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
153	C₂²⋊C₄×C₄₁	—	4	4	no	—
154	C₂²⋊C₄×C₄₁	—	4	4	no	—
155	C₂²⋊C₄×C₄₁	—	8	2	no	—
156	C₄²×C₄₁	—	2	2	no	—
157	C₄²×C₄₁	—	2	2	no	—
158	C₄²×C₄₁	—	4	4	no	—
159	C₄²×C₄₁	—	4	2	no	—
160	C₄²×C₄₁	—	4	2	no	—
161	C₄²×C₄₁	C₂²×C₄	1	2	yes	—
162	C₄²×C₄₁	#41	1	2	yes	—
163	C₂³×C₄₁	—	2	4	no	—
164	C₂³×C₄₁	—	4	2	no	—
165	C₂³×C₄₁	—	4	2	no	—
166	C₂³×C₄₁	—	4	2	no	—
167	C₂³×C₄₁	—	4	2	no	—
168	C₂³×C₄₁	—	4	2	no	—
169	C₂³×C₄₁	—	4	2	no	—
170	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
171	Q₈×C₄₁	—	2	4	no	—
172	Q₈×C₄₁	—	2	4	no	—
173	Q₈×C₄₁	—	4	2	no	—
174	Q₈×C₄₁	—	4	2	no	—
175	D₄×C₄₁	—	2	4	no	—
176	D₄×C₄₁	—	2	4	no	—
177	D₄×C₄₁	—	4	2	no	—
178	D₄×C₄₁	—	4	2	no	—
179	D₄×C₄₁	—	4	8	no	—
180	D₄×C₄₁	—	8	4	no	—
181	C₂×C₄×C₄₁	—	2	2	no	—
182	C₂×C₄×C₄₁	—	2	2	no	—
183	C₂×C₄×C₄₁	—	2	1	no	—
184	C₂×C₄×C₄₁	—	2	1	no	—
185	C₂×C₄×C₄₁	—	2	4	no	—
186	C₂×C₄×C₄₁	—	2	2	no	—
187	C₂×C₄×C₄₁	—	2	2	no	—
188	C₂×C₄×C₄₁	—	2	2	no	—
189	C₂×C₄×C₄₁	—	2	2	no	—
190	C₂×C₄×C₄₁	—	2	2	no	—
191	C₂×C₄×C₄₁	—	4	2	no	—
192	C₂×C₄×C₄₁	—	4	2	no	—
193	C₂×C₄×C₄₁	—	4	1	no	—
194	C₂×C₄×C₄₁	—	4	1	no	—
195	C₂×C₄×C₄₁	—	4	1	no	—
196	C₂×C₄×C₄₁	—	4	1	no	—
197	C₂×C₄×C₄₁	—	4	1	no	—
198	C₂×C₄×C₄₁	—	4	1	no	—
199	C₂×C₄×C₄₁	—	4	1	no	—
200	C₂×C₄×C₄₁	—	4	1	no	—
201	C₂×C₄×C₄₁	—	4	1	no	—
202	C₂×C₄×C₄₁	—	4	1	no	—
203	C₂×C₄×C₄₁	—	8	8	no	—
204	C₂×C₄×C₄₁	C₄×D₄	1	2	yes	—
205	C₂×C₄×C₄₁	C₄×D₄	1	2	yes	—
206	C₂×C₄×C₄₁	C₂×SD₁₆	1	4	yes	—
207	C₂×C₄×C₄₁	C₂×SD₁₆	1	2	yes	—
208	C₂×C₄×C₄₁	#135	1	2	yes	—
209	C₂×C₄×C₄₁	C₂³×C₄	1	1	yes	characteristic
210	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
211	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
212	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
213	C₂×C₄×C₄₁	H(5,𝔽₂)	1	1	yes	characteristic
214	C₂×C₄×C₄₁	H(5,𝔽₂)	1	1	yes	characteristic
215	C₈×C₄₁	—	2	2	no	—
216	C₈×C₄₁	—	4	2	no	—
217	C₈×C₄₁	C₄×D₄	1	4	yes	complemented
218	#23182	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
219	C₂²×C₄₁	—	4	4	no	—
220	C₂²×C₄₁	—	4	4	no	—
221	C₂²×C₄₁	—	4	4	no	—
222	C₂²×C₄₁	—	8	2	no	—
223	C₂²×C₄₁	—	8	2	no	—
224	C₂²×C₄₁	—	8	2	no	—
225	C₂²×C₄₁	—	8	2	no	—
226	C₂²×C₄₁	C₂×C₄×D₄	1	1	yes	characteristic
227	C₂²×C₄₁	D₄²	1	1	yes	characteristic
228	C₂²×C₄₁	#550	1	1	yes	characteristic
229	C₂²×C₄₁	C₂²×SD₁₆	1	1	yes	characteristic
230	C₂²×C₄₁	C₂×#135	1	1	yes	characteristic
231	C₂²×C₄₁	#577	1	1	yes	characteristic
232	C₂²×C₄₁	#577	1	1	yes	characteristic
233	C₄×C₄₁	—	2	2	no	—
234	C₄×C₄₁	—	2	4	no	—
235	C₄×C₄₁	—	4	4	no	—
236	C₄×C₄₁	—	4	2	no	—
237	C₄×C₄₁	—	4	2	no	—
238	C₄×C₄₁	—	4	2	no	—
239	C₄×C₄₁	—	8	1	no	—
240	C₄×C₄₁	—	8	1	no	—
241	C₄×C₄₁	C₄×SD₁₆	1	4	yes	complemented
242	C₄×C₄₁	C₂×C₄×D₄	1	1	yes	characteristic
243	C₄×C₄₁	#518	1	1	yes	characteristic
244	C₄×C₄₁	#550	1	1	yes	characteristic
245	C₄×C₄₁	#559	1	1	yes	characteristic
246	C₂×#492	C₂×C₄₁	1	1	yes	characteristic
247	C₂×C₄×SD₁₆	C₂×C₄₁	1	2	yes	complemented
248	#2366	C₂×C₄₁	1	1	yes	characteristic
249	#2365	C₂×C₄₁	1	1	yes	characteristic, complemented
250	#1982	C₂×C₄₁	1	1	yes	characteristic
251	#1981	C₂×C₄₁	1	1	yes	characteristic, complemented
252	#1968	C₂×C₄₁	1	2	yes	complemented
253	#1880	C₂×C₄₁	1	2	yes	complemented
254	#1877	C₂×C₄₁	1	2	yes	complemented
255	C₄×#106	C₂×C₄₁	1	1	yes	characteristic, complemented
256	C₈×C₄⋊C₄	C₂×C₄₁	1	1	yes	characteristic, complemented
257	C₂×C₄₁	—	8	4	no	—
258	C₂×C₄₁	#2366	1	1	yes	characteristic
259	C₂×C₄₁	C₂×C₄×SD₁₆	1	1	yes	characteristic
260	C₂×C₄₁	#2949	1	1	yes	characteristic
261	C₂×C₄₁	D₄×SD₁₆	1	1	yes	characteristic
262	C₂×C₄₁	#3284	1	1	yes	characteristic
263	C₂×C₄₁	#3392	1	1	yes	characteristic
264	C₂×C₄₁	#3394	1	1	yes	characteristic
265	C₂²×SD₁₆	C₂²×C₄₁	1	2	yes	—
266	C₂²×SD₁₆	C₂²×C₄₁	1	2	yes	—
267	C₂×C₄⋊Q₈	C₂²×C₄₁	1	1	yes	characteristic
268	C₂×#127	C₂²×C₄₁	1	1	yes	characteristic
269	C₂×C₄×Q₈	C₂²×C₄₁	1	2	yes	—
270	C₂×C₄×D₄	—	2	1	no	—
271	C₂×C₄×D₄	C₂²×C₄₁	1	2	yes	—
272	#492	C₄×C₄₁	1	8	yes	complemented
273	C₄×SD₁₆	—	2	8	no	—
274	C₂×#106	C₂²×C₄₁	1	1	yes	characteristic
275	C₂×#106	C₂²×C₄₁	1	1	yes	characteristic
276	C₂×C₄⋊C₈	C₂²×C₄₁	1	1	yes	characteristic
277	C₂×#103	C₂²×C₄₁	1	2	yes	—
278	C₂×#103	C₂²×C₄₁	1	2	yes	—
279	C₂×#102	C₂²×C₄₁	1	2	yes	—
280	C₂×#102	C₂²×C₄₁	1	2	yes	—
281	C₂×C₄×C₈	C₂²×C₄₁	1	2	yes	—
282	C₂×C₄×C₈	C₂²×C₄₁	1	1	yes	characteristic
283	#391	C₂²×C₄₁	1	2	yes	—
284	#390	—	2	1	no	—
285	#390	C₂²×C₄₁	1	2	yes	—
286	#389	—	2	1	no	—
287	#387	—	2	2	no	—
288	#386	—	2	2	no	—
289	C₄×C₄⋊C₄	—	2	1	no	—
290	C₄×C₄⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
291	C₄×C₄⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
292	C₄×C₄⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
293	#340	C₂²×C₄₁	1	1	yes	characteristic
294	#340	C₂²×C₄₁	1	1	yes	characteristic
295	#336	C₂²×C₄₁	1	2	yes	—
296	C₄₁	#23182	1	1	yes	characteristic, direct product factor, Sylow
297	C₂²×Q₈	C₂³×C₄₁	1	2	yes	—
298	C₂²×D₄	—	2	1	no	—
299	C₂²×D₄	—	2	1	no	—
300	C₂²×D₄	C₂³×C₄₁	1	2	yes	—
301	C₂³×C₄	—	2	2	no	—
302	C₂×SD₁₆	—	2	4	no	—
303	C₂×SD₁₆	—	2	4	no	—
304	C₂×SD₁₆	—	4	2	no	—
305	C₂×SD₁₆	—	4	2	no	—
306	C₂×SD₁₆	C₂×C₄×C₄₁	1	8	yes	complemented
307	C₂×SD₁₆	C₂×C₄×C₄₁	1	8	yes	complemented
308	C₂²×C₈	C₂³×C₄₁	1	2	yes	—
309	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
310	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
311	C₄⋊Q₈	—	2	2	no	—
312	C₄⋊Q₈	C₂×C₄×C₄₁	1	4	yes	complemented
313	#127	—	2	2	no	—
314	#127	C₂×C₄×C₄₁	1	4	yes	—
315	C₄×Q₈	—	2	4	no	—
316	C₄×Q₈	—	4	2	no	—
317	C₄×D₄	—	2	4	no	—
318	C₄×D₄	—	4	2	no	—
319	C₄×D₄	—	4	4	no	—
320	C₂×C₄⋊C₄	—	2	1	no	—
321	C₂×C₄⋊C₄	—	2	1	no	—
322	C₂×C₄⋊C₄	—	2	2	no	—
323	C₂×C₄⋊C₄	D₄×C₄₁	1	1	yes	characteristic
324	C₂×C₄⋊C₄	D₄×C₄₁	1	1	yes	characteristic
325	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
326	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
327	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
328	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
329	C₂×C₂²⋊C₄	—	2	2	no	—
330	C₂×C₂²⋊C₄	—	2	2	no	—
331	C₂×C₂²⋊C₄	—	2	2	no	—
332	C₂×C₄²	—	2	1	no	—
333	C₂×C₄²	—	2	2	no	—
334	C₂×C₄²	—	2	1	no	—
335	C₂×C₄²	C₂³×C₄₁	1	2	yes	—
336	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
337	#106	—	2	2	no	—
338	#106	D₄×C₄₁	1	4	yes	complemented
339	C₄⋊C₈	—	2	2	no	—
340	#103	—	2	4	no	—
341	#103	—	4	2	no	—
342	#102	—	2	4	no	—
343	#102	—	4	2	no	—
344	C₄×C₈	—	2	4	no	—
345	C₄×C₈	C₂×C₄×C₄₁	1	4	yes	complemented
346	#95	—	2	2	no	—
347	#95	—	2	1	no	—
348	#95	—	2	1	no	—
349	#95	—	2	2	no	—
350	#95	D₄×C₄₁	1	2	yes	—
351	C₂⁴	—	2	2	no	—
352	C₂×Q₈	—	2	2	no	—
353	C₂×Q₈	—	2	2	no	—
354	C₂×Q₈	—	2	2	no	—
355	C₂×Q₈	—	2	2	no	—
356	C₂×Q₈	—	2	2	no	—
357	C₂×Q₈	C₂²×C₄×C₄₁	1	4	yes	—
358	C₂×D₄	—	2	4	no	—
359	C₂×D₄	—	2	4	no	—
360	C₂×D₄	—	2	2	no	—
361	C₂×D₄	—	2	2	no	—
362	C₂×D₄	—	2	2	no	—
363	C₂×D₄	—	2	2	no	—
364	C₂×D₄	—	2	2	no	—
365	C₂×D₄	—	4	2	no	—
366	C₂×D₄	—	4	2	no	—
367	C₂×D₄	—	8	1	no	—
368	C₂×D₄	—	8	1	no	—
369	C₂×D₄	C₂²×C₄×C₄₁	1	4	yes	—
370	C₂²×C₄	—	2	2	no	—
371	C₂²×C₄	—	2	1	no	—
372	C₂²×C₄	—	2	1	no	—
373	C₂²×C₄	—	2	1	no	—
374	C₂²×C₄	—	2	1	no	—
375	C₂²×C₄	—	4	4	no	—
376	C₂²×C₄	—	4	4	no	—
377	C₂²×C₄	—	8	2	no	—
378	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
379	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
380	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
381	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
382	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
383	SD₁₆	—	2	16	no	—
384	SD₁₆	—	4	8	no	—
385	C₂×C₈	—	2	1	no	—
386	C₂×C₈	—	2	1	no	—
387	C₂×C₈	—	2	2	no	—
388	C₂×C₈	—	2	2	no	—
389	C₂×C₈	—	2	2	no	—
390	C₂×C₈	C₂²×C₄×C₄₁	1	2	yes	—
391	C₂×C₈	C₂²×C₄×C₄₁	1	2	yes	—
392	C₂×C₈	C₂×D₄×C₄₁	1	2	yes	—
393	C₂×C₈	#41×C₄₁	1	2	yes	—
394	C₄⋊C₄	—	2	4	no	—
395	C₄⋊C₄	—	2	4	no	—
396	C₄⋊C₄	—	2	2	no	—
397	C₄⋊C₄	—	2	1	no	—
398	C₄⋊C₄	—	2	1	no	—
399	C₄⋊C₄	—	2	1	no	—
400	C₄⋊C₄	—	2	1	no	—
401	C₄⋊C₄	—	2	1	no	—
402	C₄⋊C₄	—	2	1	no	—
403	C₄⋊C₄	—	4	4	no	—
404	C₄⋊C₄	SD₁₆×C₄₁	1	4	yes	complemented
405	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
406	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
407	C₂²⋊C₄	—	4	4	no	—
408	C₂²⋊C₄	—	4	4	no	—
409	C₂²⋊C₄	—	8	2	no	—
410	C₄²	—	2	2	no	—
411	C₄²	—	2	2	no	—
412	C₄²	—	4	4	no	—
413	C₄²	—	4	2	no	—
414	C₄²	—	4	2	no	—
415	C₄²	C₂²×C₄×C₄₁	1	2	yes	—
416	C₄²	#41×C₄₁	1	2	yes	—
417	C₂³	—	2	4	no	—
418	C₂³	—	4	2	no	—
419	C₂³	—	4	2	no	—
420	C₂³	—	4	2	no	—
421	C₂³	—	4	2	no	—
422	C₂³	—	4	2	no	—
423	C₂³	—	4	2	no	—
424	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
425	Q₈	—	2	4	no	—
426	Q₈	—	2	4	no	—
427	Q₈	—	4	2	no	—
428	Q₈	—	4	2	no	—
429	D₄	—	2	4	no	—
430	D₄	—	2	4	no	—
431	D₄	—	4	2	no	—
432	D₄	—	4	2	no	—
433	D₄	—	4	8	no	—
434	D₄	—	8	4	no	—
435	C₂×C₄	—	2	2	no	—
436	C₂×C₄	—	2	2	no	—
437	C₂×C₄	—	2	1	no	—
438	C₂×C₄	—	2	1	no	—
439	C₂×C₄	—	2	4	no	—
440	C₂×C₄	—	2	2	no	—
441	C₂×C₄	—	2	2	no	—
442	C₂×C₄	—	2	2	no	—
443	C₂×C₄	—	2	2	no	—
444	C₂×C₄	—	2	2	no	—
445	C₂×C₄	—	4	2	no	—
446	C₂×C₄	—	4	2	no	—
447	C₂×C₄	—	4	1	no	—
448	C₂×C₄	—	4	1	no	—
449	C₂×C₄	—	4	1	no	—
450	C₂×C₄	—	4	1	no	—
451	C₂×C₄	—	4	1	no	—
452	C₂×C₄	—	4	1	no	—
453	C₂×C₄	—	4	1	no	—
454	C₂×C₄	—	4	1	no	—
455	C₂×C₄	—	4	1	no	—
456	C₂×C₄	—	4	1	no	—
457	C₂×C₄	—	8	8	no	—
458	C₂×C₄	C₄×D₄×C₄₁	1	2	yes	—
459	C₂×C₄	C₄×D₄×C₄₁	1	2	yes	—
460	C₂×C₄	C₂×SD₁₆×C₄₁	1	4	yes	—
461	C₂×C₄	C₂×SD₁₆×C₄₁	1	2	yes	—
462	C₂×C₄	#135×C₄₁	1	2	yes	—
463	C₂×C₄	C₂³×C₄×C₄₁	1	1	yes	characteristic
464	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
465	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
466	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
467	C₂×C₄	H(5,𝔽₂)×C₄₁	1	1	yes	characteristic
468	C₂×C₄	H(5,𝔽₂)×C₄₁	1	1	yes	characteristic
469	C₈	—	2	2	no	—
470	C₈	—	4	2	no	—
471	C₈	C₄×D₄×C₄₁	1	4	yes	complemented
472	C₂²	—	4	4	no	—
473	C₂²	—	4	4	no	—
474	C₂²	—	4	4	no	—
475	C₂²	—	8	2	no	—
476	C₂²	—	8	2	no	—
477	C₂²	—	8	2	no	—
478	C₂²	—	8	2	no	—
479	C₂²	C₂×C₄×D₄×C₄₁	1	1	yes	characteristic
480	C₂²	D₄²×C₄₁	1	1	yes	characteristic
481	C₂²	C₄₁×#550	1	1	yes	characteristic
482	C₂²	C₂²×SD₁₆×C₄₁	1	1	yes	characteristic
483	C₂²	C₂×#135×C₄₁	1	1	yes	characteristic
484	C₂²	C₄₁×#577	1	1	yes	characteristic
485	C₂²	C₄₁×#577	1	1	yes	characteristic
486	C₄	—	2	2	no	—
487	C₄	—	2	4	no	—
488	C₄	—	4	4	no	—
489	C₄	—	4	2	no	—
490	C₄	—	4	2	no	—
491	C₄	—	4	2	no	—
492	C₄	—	8	1	no	—
493	C₄	—	8	1	no	—
494	C₄	C₄×SD₁₆×C₄₁	1	4	yes	complemented
495	C₄	C₂×C₄×D₄×C₄₁	1	1	yes	characteristic
496	C₄	C₄₁×#518	1	1	yes	characteristic
497	C₄	C₄₁×#550	1	1	yes	characteristic
498	C₄	C₄₁×#559	1	1	yes	characteristic
499	C₂	—	8	4	no	—
500	C₂	C₄₁×#2366	1	1	yes	characteristic
501	C₂	C₂×C₄×SD₁₆×C₄₁	1	1	yes	characteristic
502	C₂	C₄₁×#2949	1	1	yes	characteristic
503	C₂	D₄×SD₁₆×C₄₁	1	1	yes	characteristic
504	C₂	C₄₁×#3284	1	1	yes	characteristic
505	C₂	C₄₁×#3392	1	1	yes	characteristic
506	C₂	C₄₁×#3394	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₄₁	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₄₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₁
prime radical	C₂×#127×C₄₁	C₂²
LCS	G ▷ C₂×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
2. C₂×C₄×SD₁₆×C₄₁	C₂	semidirect
4. C₄₁×#2365	C₂	semidirect
6. C₄₁×#1981	C₂	semidirect
7. C₄₁×#1968	C₂	semidirect
8. C₄₁×#1880	C₂	semidirect
9. C₄₁×#1877	C₂	semidirect
10. C₄×#106×C₄₁	C₂	semidirect
11. C₈×C₄⋊C₄×C₄₁	C₂	semidirect
19. C₄₁×#492	C₄	semidirect
52. C₂×SD₁₆×C₄₁	C₂×C₄	semidirect
53. C₂×SD₁₆×C₄₁	C₂×C₄	semidirect
58. C₄⋊Q₈×C₄₁	C₂×C₄	semidirect
84. #106×C₄₁	D₄	semidirect
91. C₄×C₈×C₄₁	C₂×C₄	semidirect
150. C₄⋊C₄×C₄₁	SD₁₆	semidirect
217. C₈×C₄₁	C₄×D₄	semidirect
218. #23182	C₄₁	direct (N × H)
241. C₄×C₄₁	C₄×SD₁₆	semidirect
247. C₂×C₄×SD₁₆	C₂×C₄₁	semidirect
249. #2365	C₂×C₄₁	semidirect
251. #1981	C₂×C₄₁	semidirect
252. #1968	C₂×C₄₁	semidirect
253. #1880	C₂×C₄₁	semidirect
254. #1877	C₂×C₄₁	semidirect
255. C₄×#106	C₂×C₄₁	semidirect
256. C₈×C₄⋊C₄	C₂×C₄₁	semidirect
272. #492	C₄×C₄₁	semidirect
296. C₄₁	#23182	direct (N × H)
306. C₂×SD₁₆	C₂×C₄×C₄₁	semidirect
307. C₂×SD₁₆	C₂×C₄×C₄₁	semidirect
312. C₄⋊Q₈	C₂×C₄×C₄₁	semidirect
338. #106	D₄×C₄₁	semidirect
345. C₄×C₈	C₂×C₄×C₄₁	semidirect
404. C₄⋊C₄	SD₁₆×C₄₁	semidirect
471. C₈	C₄×D₄×C₄₁	semidirect
494. C₄	C₄×SD₁₆×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×#492	2
C₂×C₄×SD₁₆×C₄₁	2
C₄₁×#2366	2
C₄₁×#2365	2
C₄₁×#1982	2
C₄₁×#1981	2
C₄₁×#1968	2
C₄₁×#1880	2
C₄₁×#1877	2
C₄×#106×C₄₁	2
C₈×C₄⋊C₄×C₄₁	2
#23182	41

Subgroups — C41×#23182 #23799383

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#23182 #23799383