Subgroups — C₄₁×#23133 #23799334

Order 10496.

898 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₁×#467	C₂	1	1	yes	maximal, characteristic
2	C₄₁×#2360	C₂	1	2	yes	maximal
3	C₄₁×#1935	C₂	1	2	yes	maximal, complemented
4	C₄₁×#1918	C₂	1	2	yes	maximal, complemented
5	C₄₁×#1878	C₂	1	2	yes	maximal, complemented
6	C₄₁×#1872	C₂	1	2	yes	maximal
7	C₄₁×#1763	C₂	1	2	yes	maximal, complemented
8	C₄₁×#1752	C₂	1	1	yes	maximal, characteristic
9	C₂×C₄₁×#340	C₂	1	1	yes	maximal, characteristic
10	C₂²×Q₁₆×C₄₁	C₂²	1	1	yes	characteristic
11	C₂³×C₈×C₄₁	C₂²	1	1	yes	characteristic
12	C₂×C₂²⋊Q₈×C₄₁	C₂²	1	2	yes	—
13	C₂×C₄×Q₈×C₄₁	C₂²	1	2	yes	—
14	C₂²×C₄⋊C₄×C₄₁	C₂²	1	2	yes	—
15	C₄₁×#467	C₄	1	8	yes	complemented
16	C₂×#107×C₄₁	C₂²	1	1	yes	characteristic
17	C₂×#103×C₄₁	C₂²	1	2	yes	—
18	C₂×#103×C₄₁	C₂²	1	2	yes	—
19	C₂×#103×C₄₁	C₂²	1	2	yes	—
20	C₂×C₂²⋊C₈×C₄₁	C₂²	1	1	yes	characteristic
21	C₂×#97×C₄₁	C₂²	1	2	yes	—
22	C₄₁×#391	C₂²	1	2	yes	—
23	C₄₁×#389	—	2	2	no	—
24	C₄₁×#389	C₂²	1	2	yes	—
25	C₄₁×#387	—	2	2	no	—
26	C₄₁×#385	—	2	2	no	—
27	C₄×C₄⋊C₄×C₄₁	C₂²	1	2	yes	—
28	C₄×C₂²⋊C₄×C₄₁	—	2	2	no	—
29	C₄×C₂²⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
30	C₄₁×#340	C₂²	1	1	yes	characteristic
31	C₄₁×#340	C₂²	1	2	yes	—
32	C₄₁×#340	C₂²	1	2	yes	—
33	C₄₁×#340	C₂²	1	2	yes	—
34	C₄₁×#340	C₂²	1	1	yes	characteristic
35	C₄₁×#336	C₂²	1	2	yes	—
36	C₂²×Q₈×C₄₁	C₂³	1	2	yes	—
37	C₂³×C₄×C₄₁	—	2	2	no	—
38	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
39	C₂×Q₁₆×C₄₁	—	4	2	no	—
40	C₂×Q₁₆×C₄₁	C₂×C₄	1	4	yes	complemented
41	C₂²×C₈×C₄₁	—	4	2	no	—
42	C₂²×C₈×C₄₁	C₂×C₄	1	4	yes	—
43	C₂²×C₈×C₄₁	C₂³	1	2	yes	—
44	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
45	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
46	C₂²⋊Q₈×C₄₁	—	2	4	no	—
47	C₂²⋊Q₈×C₄₁	C₂×C₄	1	8	yes	—
48	C₄×Q₈×C₄₁	—	2	4	no	—
49	C₄×Q₈×C₄₁	—	4	2	no	—
50	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
51	C₂×C₄⋊C₄×C₄₁	—	2	4	no	—
52	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
53	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
54	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
55	C₂×C₄⋊C₄×C₄₁	—	4	2	no	—
56	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
57	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
58	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
59	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
60	C₂×C₂²⋊C₄×C₄₁	D₄	1	2	yes	—
61	C₂×C₄²×C₄₁	—	2	2	no	—
62	C₂×C₄²×C₄₁	—	2	2	no	—
63	C₂×C₄²×C₄₁	C₂³	1	2	yes	—
64	#107×C₄₁	C₂×C₄	1	4	yes	complemented
65	#103×C₄₁	—	2	4	no	—
66	#103×C₄₁	—	4	2	no	—
67	#103×C₄₁	C₂×C₄	1	8	yes	complemented
68	C₂²⋊C₈×C₄₁	—	2	2	no	—
69	#97×C₄₁	—	4	2	no	—
70	#95×C₄₁	—	2	2	no	—
71	#95×C₄₁	—	2	2	no	—
72	#95×C₄₁	—	2	2	no	—
73	#95×C₄₁	—	2	2	no	—
74	#95×C₄₁	D₄	1	1	yes	characteristic
75	#95×C₄₁	D₄	1	1	yes	characteristic
76	C₂⁴×C₄₁	C₂×D₄	1	1	yes	characteristic
77	C₂×Q₈×C₄₁	—	2	2	no	—
78	C₂×Q₈×C₄₁	—	2	2	no	—
79	C₂×Q₈×C₄₁	—	2	2	no	—
80	C₂×Q₈×C₄₁	—	2	2	no	—
81	C₂×Q₈×C₄₁	—	2	2	no	—
82	C₂×Q₈×C₄₁	C₂²×C₄	1	4	yes	—
83	C₂²×C₄×C₄₁	—	2	2	no	—
84	C₂²×C₄×C₄₁	—	2	2	no	—
85	C₂²×C₄×C₄₁	—	2	2	no	—
86	C₂²×C₄×C₄₁	—	2	2	no	—
87	C₂²×C₄×C₄₁	—	2	2	no	—
88	C₂²×C₄×C₄₁	—	2	2	no	—
89	C₂²×C₄×C₄₁	—	4	4	no	—
90	C₂²×C₄×C₄₁	—	4	4	no	—
91	C₂²×C₄×C₄₁	—	8	2	no	—
92	C₂²×C₄×C₄₁	C₂²×C₄	1	2	yes	—
93	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
94	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
95	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
96	C₂²×C₄×C₄₁	#41	1	2	yes	—
97	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
98	Q₁₆×C₄₁	—	4	4	no	—
99	C₂×C₈×C₄₁	—	2	2	no	—
100	C₂×C₈×C₄₁	—	2	2	no	—
101	C₂×C₈×C₄₁	—	2	2	no	—
102	C₂×C₈×C₄₁	—	2	2	no	—
103	C₂×C₈×C₄₁	—	2	2	no	—
104	C₂×C₈×C₄₁	—	4	4	no	—
105	C₂×C₈×C₄₁	C₂²×C₄	1	2	yes	—
106	C₂×C₈×C₄₁	C₂²×C₄	1	2	yes	—
107	C₄⋊C₄×C₄₁	—	2	8	no	—
108	C₄⋊C₄×C₄₁	—	2	2	no	—
109	C₄⋊C₄×C₄₁	—	2	2	no	—
110	C₄⋊C₄×C₄₁	—	2	2	no	—
111	C₄⋊C₄×C₄₁	—	2	2	no	—
112	C₄⋊C₄×C₄₁	—	4	4	no	—
113	C₄⋊C₄×C₄₁	—	4	4	no	—
114	C₄⋊C₄×C₄₁	—	8	2	no	—
115	C₄⋊C₄×C₄₁	C₂²×C₄	1	4	yes	—
116	C₄⋊C₄×C₄₁	#41	1	4	yes	—
117	C₂²⋊C₄×C₄₁	—	2	8	no	—
118	C₂²⋊C₄×C₄₁	—	2	4	no	—
119	C₄²×C₄₁	—	2	2	no	—
120	C₄²×C₄₁	—	2	2	no	—
121	C₄²×C₄₁	—	4	4	no	—
122	C₄²×C₄₁	—	8	2	no	—
123	C₂³×C₄₁	—	2	2	no	—
124	C₂³×C₄₁	—	2	1	no	—
125	C₂³×C₄₁	—	2	1	no	—
126	C₂³×C₄₁	C₄×D₄	1	2	yes	—
127	C₂³×C₄₁	#137	1	4	yes	—
128	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
129	Q₈×C₄₁	—	2	4	no	—
130	Q₈×C₄₁	—	2	4	no	—
131	Q₈×C₄₁	—	4	2	no	—
132	Q₈×C₄₁	—	4	2	no	—
133	C₂×C₄×C₄₁	—	2	2	no	—
134	C₂×C₄×C₄₁	—	2	2	no	—
135	C₂×C₄×C₄₁	—	2	2	no	—
136	C₂×C₄×C₄₁	—	2	4	no	—
137	C₂×C₄×C₄₁	—	2	4	no	—
138	C₂×C₄×C₄₁	—	2	4	no	—
139	C₂×C₄×C₄₁	—	2	2	no	—
140	C₂×C₄×C₄₁	—	2	2	no	—
141	C₂×C₄×C₄₁	—	2	4	no	—
142	C₂×C₄×C₄₁	—	2	2	no	—
143	C₂×C₄×C₄₁	—	2	2	no	—
144	C₂×C₄×C₄₁	—	2	2	no	—
145	C₂×C₄×C₄₁	—	2	2	no	—
146	C₂×C₄×C₄₁	—	4	2	no	—
147	C₂×C₄×C₄₁	—	4	2	no	—
148	C₂×C₄×C₄₁	—	4	2	no	—
149	C₂×C₄×C₄₁	—	4	2	no	—
150	C₂×C₄×C₄₁	—	4	2	no	—
151	C₂×C₄×C₄₁	—	4	2	no	—
152	C₂×C₄×C₄₁	—	4	2	no	—
153	C₂×C₄×C₄₁	—	4	2	no	—
154	C₂×C₄×C₄₁	—	4	2	no	—
155	C₂×C₄×C₄₁	—	8	8	no	—
156	C₂×C₄×C₄₁	C₄×D₄	1	2	yes	—
157	C₂×C₄×C₄₁	C₂³×C₄	1	1	yes	characteristic
158	C₂×C₄×C₄₁	C₂×#41	1	2	yes	—
159	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
160	C₂×C₄×C₄₁	H(5,𝔽₂)	1	2	yes	—
161	C₈×C₄₁	—	2	2	no	—
162	C₈×C₄₁	—	2	2	no	—
163	C₈×C₄₁	—	4	2	no	—
164	#23133	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
165	C₂²×C₄₁	—	2	2	no	—
166	C₂²×C₄₁	—	2	2	no	—
167	C₂²×C₄₁	—	2	4	no	—
168	C₂²×C₄₁	—	2	4	no	—
169	C₂²×C₄₁	#441	1	4	yes	—
170	C₂²×C₄₁	C₂×C₄×D₄	1	1	yes	characteristic
171	C₂²×C₄₁	#546	1	2	yes	—
172	C₂²×C₄₁	C₂×#137	1	2	yes	—
173	C₂²×C₄₁	#576	1	1	yes	characteristic
174	C₂²×C₄₁	#578	1	1	yes	characteristic
175	C₄×C₄₁	—	2	2	no	—
176	C₄×C₄₁	—	4	4	no	—
177	C₄×C₄₁	—	4	4	no	—
178	C₄×C₄₁	—	4	2	no	—
179	C₄×C₄₁	—	4	2	no	—
180	C₄×C₄₁	—	4	4	no	—
181	C₄×C₄₁	—	8	2	no	—
182	C₄×C₄₁	C₄×#41	1	1	yes	characteristic
183	C₄×C₄₁	#518	1	1	yes	characteristic
184	C₄×C₄₁	#553	1	2	yes	—
185	C₂×#467	C₂×C₄₁	1	1	yes	characteristic
186	#2360	C₂×C₄₁	1	2	yes	—
187	#1935	C₂×C₄₁	1	2	yes	complemented
188	#1918	C₂×C₄₁	1	2	yes	complemented
189	#1878	C₂×C₄₁	1	2	yes	complemented
190	#1872	C₂×C₄₁	1	2	yes	—
191	#1763	C₂×C₄₁	1	2	yes	complemented
192	#1752	C₂×C₄₁	1	1	yes	characteristic
193	C₂×#340	C₂×C₄₁	1	1	yes	characteristic
194	C₂×C₄₁	—	2	4	no	—
195	C₂×C₄₁	#2364	1	1	yes	characteristic
196	C₂×C₄₁	C₂×#441	1	1	yes	characteristic
197	C₂×C₄₁	#2951	1	1	yes	characteristic
198	C₂×C₄₁	#3312	1	2	yes	—
199	C₂×C₄₁	#3314	1	2	yes	—
200	C₂²×Q₁₆	C₂²×C₄₁	1	1	yes	characteristic
201	C₂³×C₈	C₂²×C₄₁	1	1	yes	characteristic
202	C₂×C₂²⋊Q₈	C₂²×C₄₁	1	2	yes	—
203	C₂×C₄×Q₈	C₂²×C₄₁	1	2	yes	—
204	C₂²×C₄⋊C₄	C₂²×C₄₁	1	2	yes	—
205	#467	C₄×C₄₁	1	8	yes	complemented
206	C₂×#107	C₂²×C₄₁	1	1	yes	characteristic
207	C₂×#103	C₂²×C₄₁	1	2	yes	—
208	C₂×#103	C₂²×C₄₁	1	2	yes	—
209	C₂×#103	C₂²×C₄₁	1	2	yes	—
210	C₂×C₂²⋊C₈	C₂²×C₄₁	1	1	yes	characteristic
211	C₂×#97	C₂²×C₄₁	1	2	yes	—
212	#391	C₂²×C₄₁	1	2	yes	—
213	#389	—	2	2	no	—
214	#389	C₂²×C₄₁	1	2	yes	—
215	#387	—	2	2	no	—
216	#385	—	2	2	no	—
217	C₄×C₄⋊C₄	C₂²×C₄₁	1	2	yes	—
218	C₄×C₂²⋊C₄	—	2	2	no	—
219	C₄×C₂²⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
220	#340	C₂²×C₄₁	1	2	yes	—
221	#340	C₂²×C₄₁	1	2	yes	—
222	#340	C₂²×C₄₁	1	2	yes	—
223	#340	C₂²×C₄₁	1	1	yes	characteristic
224	#340	C₂²×C₄₁	1	1	yes	characteristic
225	#336	C₂²×C₄₁	1	2	yes	—
226	C₄₁	#23133	1	1	yes	characteristic, direct product factor, Sylow
227	C₂²×Q₈	C₂³×C₄₁	1	2	yes	—
228	C₂³×C₄	—	2	2	no	—
229	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
230	C₂×Q₁₆	—	4	2	no	—
231	C₂×Q₁₆	C₂×C₄×C₄₁	1	4	yes	complemented
232	C₂²×C₈	—	4	2	no	—
233	C₂²×C₈	C₂×C₄×C₄₁	1	4	yes	—
234	C₂²×C₈	C₂³×C₄₁	1	2	yes	—
235	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
236	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
237	C₂²⋊Q₈	—	2	4	no	—
238	C₂²⋊Q₈	C₂×C₄×C₄₁	1	8	yes	—
239	C₄×Q₈	—	2	4	no	—
240	C₄×Q₈	—	4	2	no	—
241	C₂×C₄⋊C₄	—	2	2	no	—
242	C₂×C₄⋊C₄	—	2	4	no	—
243	C₂×C₄⋊C₄	—	2	2	no	—
244	C₂×C₄⋊C₄	—	2	2	no	—
245	C₂×C₄⋊C₄	—	2	2	no	—
246	C₂×C₄⋊C₄	—	4	2	no	—
247	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
248	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
249	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
250	C₂×C₂²⋊C₄	—	2	2	no	—
251	C₂×C₂²⋊C₄	D₄×C₄₁	1	2	yes	—
252	C₂×C₄²	—	2	2	no	—
253	C₂×C₄²	—	2	2	no	—
254	C₂×C₄²	C₂³×C₄₁	1	2	yes	—
255	#107	C₂×C₄×C₄₁	1	4	yes	complemented
256	#103	—	2	4	no	—
257	#103	—	4	2	no	—
258	#103	C₂×C₄×C₄₁	1	8	yes	complemented
259	C₂²⋊C₈	—	2	2	no	—
260	#97	—	4	2	no	—
261	#95	—	2	2	no	—
262	#95	—	2	2	no	—
263	#95	—	2	2	no	—
264	#95	—	2	2	no	—
265	#95	D₄×C₄₁	1	1	yes	characteristic
266	#95	D₄×C₄₁	1	1	yes	characteristic
267	C₂⁴	C₂×D₄×C₄₁	1	1	yes	characteristic
268	C₂×Q₈	—	2	2	no	—
269	C₂×Q₈	—	2	2	no	—
270	C₂×Q₈	—	2	2	no	—
271	C₂×Q₈	—	2	2	no	—
272	C₂×Q₈	—	2	2	no	—
273	C₂×Q₈	C₂²×C₄×C₄₁	1	4	yes	—
274	C₂²×C₄	—	2	2	no	—
275	C₂²×C₄	—	2	2	no	—
276	C₂²×C₄	—	2	2	no	—
277	C₂²×C₄	—	2	2	no	—
278	C₂²×C₄	—	2	2	no	—
279	C₂²×C₄	—	2	2	no	—
280	C₂²×C₄	—	4	4	no	—
281	C₂²×C₄	—	4	4	no	—
282	C₂²×C₄	—	8	2	no	—
283	C₂²×C₄	C₂²×C₄×C₄₁	1	2	yes	—
284	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
285	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
286	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
287	C₂²×C₄	#41×C₄₁	1	2	yes	—
288	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
289	Q₁₆	—	4	4	no	—
290	C₂×C₈	—	2	2	no	—
291	C₂×C₈	—	2	2	no	—
292	C₂×C₈	—	2	2	no	—
293	C₂×C₈	—	2	2	no	—
294	C₂×C₈	—	2	2	no	—
295	C₂×C₈	—	4	4	no	—
296	C₂×C₈	C₂²×C₄×C₄₁	1	2	yes	—
297	C₂×C₈	C₂²×C₄×C₄₁	1	2	yes	—
298	C₄⋊C₄	—	2	8	no	—
299	C₄⋊C₄	—	2	2	no	—
300	C₄⋊C₄	—	2	2	no	—
301	C₄⋊C₄	—	2	2	no	—
302	C₄⋊C₄	—	2	2	no	—
303	C₄⋊C₄	—	4	4	no	—
304	C₄⋊C₄	—	4	4	no	—
305	C₄⋊C₄	—	8	2	no	—
306	C₄⋊C₄	C₂²×C₄×C₄₁	1	4	yes	—
307	C₄⋊C₄	#41×C₄₁	1	4	yes	—
308	C₂²⋊C₄	—	2	8	no	—
309	C₂²⋊C₄	—	2	4	no	—
310	C₄²	—	2	2	no	—
311	C₄²	—	2	2	no	—
312	C₄²	—	4	4	no	—
313	C₄²	—	8	2	no	—
314	C₂³	—	2	2	no	—
315	C₂³	—	2	1	no	—
316	C₂³	—	2	1	no	—
317	C₂³	C₄×D₄×C₄₁	1	2	yes	—
318	C₂³	#137×C₄₁	1	4	yes	—
319	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
320	Q₈	—	2	4	no	—
321	Q₈	—	2	4	no	—
322	Q₈	—	4	2	no	—
323	Q₈	—	4	2	no	—
324	C₂×C₄	—	2	2	no	—
325	C₂×C₄	—	2	2	no	—
326	C₂×C₄	—	2	2	no	—
327	C₂×C₄	—	2	4	no	—
328	C₂×C₄	—	2	4	no	—
329	C₂×C₄	—	2	4	no	—
330	C₂×C₄	—	2	2	no	—
331	C₂×C₄	—	2	2	no	—
332	C₂×C₄	—	2	4	no	—
333	C₂×C₄	—	2	2	no	—
334	C₂×C₄	—	2	2	no	—
335	C₂×C₄	—	2	2	no	—
336	C₂×C₄	—	2	2	no	—
337	C₂×C₄	—	4	2	no	—
338	C₂×C₄	—	4	2	no	—
339	C₂×C₄	—	4	2	no	—
340	C₂×C₄	—	4	2	no	—
341	C₂×C₄	—	4	2	no	—
342	C₂×C₄	—	4	2	no	—
343	C₂×C₄	—	4	2	no	—
344	C₂×C₄	—	4	2	no	—
345	C₂×C₄	—	4	2	no	—
346	C₂×C₄	—	8	8	no	—
347	C₂×C₄	C₄×D₄×C₄₁	1	2	yes	—
348	C₂×C₄	C₂³×C₄×C₄₁	1	1	yes	characteristic
349	C₂×C₄	C₂×#41×C₄₁	1	2	yes	—
350	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
351	C₂×C₄	H(5,𝔽₂)×C₄₁	1	2	yes	—
352	C₈	—	2	2	no	—
353	C₈	—	2	2	no	—
354	C₈	—	4	2	no	—
355	C₂²	—	2	4	no	—
356	C₂²	—	2	4	no	—
357	C₂²	—	2	2	no	—
358	C₂²	—	2	2	no	—
359	C₂²	C₄₁×#441	1	4	yes	—
360	C₂²	C₂×C₄×D₄×C₄₁	1	1	yes	characteristic
361	C₂²	C₄₁×#546	1	2	yes	—
362	C₂²	C₂×#137×C₄₁	1	2	yes	—
363	C₂²	C₄₁×#576	1	1	yes	characteristic
364	C₂²	C₄₁×#578	1	1	yes	characteristic
365	C₄	—	2	2	no	—
366	C₄	—	4	2	no	—
367	C₄	—	4	2	no	—
368	C₄	—	4	4	no	—
369	C₄	—	4	4	no	—
370	C₄	—	4	4	no	—
371	C₄	—	8	2	no	—
372	C₄	C₄×#41×C₄₁	1	1	yes	characteristic
373	C₄	C₄₁×#518	1	1	yes	characteristic
374	C₄	C₄₁×#553	1	2	yes	—
375	C₂	—	2	4	no	—
376	C₂	C₄₁×#2364	1	1	yes	characteristic
377	C₂	C₂×C₄₁×#441	1	1	yes	characteristic
378	C₂	C₄₁×#2951	1	1	yes	characteristic
379	C₂	C₄₁×#3312	1	2	yes	—
380	C₂	C₄₁×#3314	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	C₂⁴×C₄₁	C₂×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₄₁ ◁ C₄×C₂²⋊C₄×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₄₁×#1935	C₂	semidirect
4. C₄₁×#1918	C₂	semidirect
5. C₄₁×#1878	C₂	semidirect
7. C₄₁×#1763	C₂	semidirect
15. C₄₁×#467	C₄	semidirect
40. C₂×Q₁₆×C₄₁	C₂×C₄	semidirect
64. #107×C₄₁	C₂×C₄	semidirect
67. #103×C₄₁	C₂×C₄	semidirect
164. #23133	C₄₁	direct (N × H)
187. #1935	C₂×C₄₁	semidirect
188. #1918	C₂×C₄₁	semidirect
189. #1878	C₂×C₄₁	semidirect
191. #1763	C₂×C₄₁	semidirect
205. #467	C₄×C₄₁	semidirect
226. C₄₁	#23133	direct (N × H)
231. C₂×Q₁₆	C₂×C₄×C₄₁	semidirect
255. #107	C₂×C₄×C₄₁	semidirect
258. #103	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
C₂×C₄₁×#467	2
C₄₁×#2360	2
C₄₁×#1935	2
C₄₁×#1918	2
C₄₁×#1878	2
C₄₁×#1872	2
C₄₁×#1763	2
C₄₁×#1752	2
C₂×C₄₁×#340	2
#23133	41

Subgroups — C41×#23133 #23799334

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#23133 #23799334