Subgroups — C₄₁×#19390 #23795591

Order 10496.

674 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	C₄₁×#3229	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄₁×#3077	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄₁×#461	C₂	1	1	yes	maximal, characteristic
4	C₄₁×#2972	C₂	1	1	yes	maximal, characteristic
5	C₄₁×#1679	C₂	1	4	yes	maximal, complemented
6	C₄₁×#1671	C₂	1	4	yes	maximal, complemented
7	C₄₁×#1570	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄₁×#1546	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄₁×#1542	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×SD₁₆×C₄₁	—	2	1	no	—
11	C₄₁×#533	C₂²	1	1	yes	characteristic
12	C₂×C₄⋊Q₈×C₄₁	C₂²	1	1	yes	characteristic
13	C₂×C₄×D₄×C₄₁	C₂²	1	1	yes	characteristic
14	C₄₁×#498	C₂²	1	2	yes	complemented
15	C₄₁×#487	C₂²	1	2	yes	complemented
16	C₄₁×#483	—	2	2	no	—
17	C₄₁×#478	—	2	2	no	—
18	C₄₁×#476	C₂²	1	2	yes	—
19	C₄₁×#475	—	2	2	no	—
20	C₄₁×#474	C₂²	1	2	yes	—
21	C₄₁×#461	—	2	2	no	—
22	C₄₁×#461	C₂²	1	4	yes	—
23	C₈×D₄×C₄₁	—	2	2	no	—
24	C₈×D₄×C₄₁	C₂²	1	4	yes	—
25	C₄₁×#431	C₂²	1	1	yes	characteristic
26	C₄₁×#431	C₂²	1	1	yes	characteristic
27	C₄₁×#428	—	2	1	no	—
28	C₄₁×#423	C₂²	1	1	yes	characteristic
29	C₂×C₄⋊C₈×C₄₁	C₂²	1	1	yes	characteristic
30	C₄₁×#418	—	2	1	no	—
31	C₂×#103×C₄₁	—	2	1	no	—
32	C₂×C₂²⋊C₈×C₄₁	—	2	2	no	—
33	C₄₁×#334	C₂²	1	4	yes	complemented
34	C₄₁×#333	C₂²	1	2	yes	complemented
35	C₄₁×#332	C₂²	1	2	yes	complemented
36	C₄₁×#332	C₂²	1	4	yes	complemented
37	C₂²×Q₈×C₄₁	—	2	1	no	—
38	C₂²×D₄×C₄₁	D₄	1	1	yes	characteristic
39	C₂³×C₄×C₄₁	—	2	1	no	—
40	C₂×SD₁₆×C₄₁	—	2	4	no	—
41	C₂×SD₁₆×C₄₁	—	4	4	no	—
42	C₂×M₁₆×C₄₁	—	2	1	no	—
43	C₂²×C₈×C₄₁	—	2	1	no	—
44	C₂²×C₈×C₄₁	—	2	4	no	—
45	C₄⋊Q₈×C₄₁	—	2	1	no	—
46	C₄⋊Q₈×C₄₁	—	2	1	no	—
47	C₄⋊Q₈×C₄₁	—	2	1	no	—
48	C₄⋊Q₈×C₄₁	C₂³	1	2	yes	—
49	C₄⋊Q₈×C₄₁	C₂³	1	1	yes	characteristic
50	C₄⋊Q₈×C₄₁	C₂³	1	1	yes	characteristic
51	#125×C₄₁	—	2	1	no	—
52	C₂²⋊Q₈×C₄₁	—	2	1	no	—
53	C₂²⋊Q₈×C₄₁	—	2	1	no	—
54	C₄×Q₈×C₄₁	—	2	1	no	—
55	C₄×Q₈×C₄₁	—	2	1	no	—
56	C₄×D₄×C₄₁	—	2	1	no	—
57	C₄×D₄×C₄₁	—	2	1	no	—
58	C₄×D₄×C₄₁	D₄	1	2	yes	—
59	C₄×D₄×C₄₁	C₂³	1	2	yes	—
60	#117×C₄₁	—	2	1	no	—
61	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
62	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
63	C₂×C₄⋊C₄×C₄₁	D₄	1	1	yes	characteristic
64	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
65	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
66	#107×C₄₁	—	2	2	no	—
67	#106×C₄₁	—	2	4	no	—
68	#106×C₄₁	—	2	2	no	—
69	C₄⋊C₈×C₄₁	—	2	1	no	—
70	C₄⋊C₈×C₄₁	—	2	1	no	—
71	C₄⋊C₈×C₄₁	D₄	1	2	yes	—
72	C₄⋊C₈×C₄₁	C₂³	1	2	yes	—
73	C₄⋊C₈×C₄₁	C₂³	1	2	yes	—
74	C₄⋊C₈×C₄₁	C₂³	1	2	yes	—
75	#103×C₄₁	—	2	4	no	—
76	#103×C₄₁	—	2	4	no	—
77	#102×C₄₁	—	2	2	no	—
78	#102×C₄₁	—	2	2	no	—
79	C₂²⋊C₈×C₄₁	—	2	1	no	—
80	C₂²⋊C₈×C₄₁	—	2	4	no	—
81	C₂²⋊C₈×C₄₁	D₄	1	2	yes	—
82	C₄×C₈×C₄₁	—	2	1	no	—
83	C₄×C₈×C₄₁	C₂³	1	2	yes	—
84	C₂⁴×C₄₁	—	2	1	no	—
85	C₂×Q₈×C₄₁	—	2	1	no	—
86	C₂×Q₈×C₄₁	—	2	2	no	—
87	C₂×Q₈×C₄₁	—	2	1	no	—
88	C₂×Q₈×C₄₁	—	4	1	no	—
89	C₂×Q₈×C₄₁	—	4	2	no	—
90	C₂×Q₈×C₄₁	—	4	2	no	—
91	C₂×D₄×C₄₁	—	2	1	no	—
92	C₂×D₄×C₄₁	—	2	2	no	—
93	C₂×D₄×C₄₁	SD₁₆	1	4	yes	—
94	C₂×D₄×C₄₁	C₂×D₄	1	2	yes	—
95	C₂²×C₄×C₄₁	—	2	1	no	—
96	C₂²×C₄×C₄₁	—	2	2	no	—
97	C₂²×C₄×C₄₁	—	2	2	no	—
98	C₂²×C₄×C₄₁	—	4	1	no	—
99	C₂²×C₄×C₄₁	—	8	2	no	—
100	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
101	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
102	C₂²×C₄×C₄₁	#41	1	1	yes	characteristic
103	SD₁₆×C₄₁	—	4	8	no	—
104	M₁₆×C₄₁	—	4	2	no	—
105	C₂×C₈×C₄₁	—	2	2	no	—
106	C₂×C₈×C₄₁	—	2	2	no	—
107	C₂×C₈×C₄₁	—	2	2	no	—
108	C₂×C₈×C₄₁	—	4	2	no	—
109	C₂×C₈×C₄₁	—	8	4	no	—
110	C₂×C₈×C₄₁	C₂×D₄	1	4	yes	—
111	C₄⋊C₄×C₄₁	—	2	1	no	—
112	C₄⋊C₄×C₄₁	—	2	1	no	—
113	C₄⋊C₄×C₄₁	—	2	1	no	—
114	C₄⋊C₄×C₄₁	—	2	2	no	—
115	C₄⋊C₄×C₄₁	—	2	1	no	—
116	C₄⋊C₄×C₄₁	—	2	2	no	—
117	C₄⋊C₄×C₄₁	—	2	1	no	—
118	C₄⋊C₄×C₄₁	—	4	1	no	—
119	C₄⋊C₄×C₄₁	—	4	1	no	—
120	C₄⋊C₄×C₄₁	—	4	1	no	—
121	C₄⋊C₄×C₄₁	—	4	1	no	—
122	C₄⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
123	C₂²⋊C₄×C₄₁	—	2	2	no	—
124	C₂²⋊C₄×C₄₁	—	2	2	no	—
125	C₂²⋊C₄×C₄₁	—	4	1	no	—
126	C₄²×C₄₁	—	4	1	no	—
127	C₄²×C₄₁	C₂×D₄	1	1	yes	characteristic
128	C₄²×C₄₁	C₂×D₄	1	1	yes	characteristic
129	C₄²×C₄₁	#41	1	1	yes	characteristic
130	C₄²×C₄₁	C₂⁴	1	1	yes	characteristic
131	C₂³×C₄₁	—	2	2	no	—
132	C₂³×C₄₁	—	2	4	no	—
133	C₂³×C₄₁	—	8	1	no	—
134	C₂³×C₄₁	—	8	1	no	—
135	C₂³×C₄₁	#121	1	1	yes	characteristic
136	Q₈×C₄₁	—	4	2	no	—
137	Q₈×C₄₁	—	4	2	no	—
138	Q₈×C₄₁	—	4	2	no	—
139	Q₈×C₄₁	—	8	1	no	—
140	Q₈×C₄₁	—	8	2	no	—
141	D₄×C₄₁	—	2	2	no	—
142	D₄×C₄₁	—	2	4	no	—
143	D₄×C₄₁	C₂×SD₁₆	1	4	yes	—
144	C₂×C₄×C₄₁	—	2	2	no	—
145	C₂×C₄×C₄₁	—	2	2	no	—
146	C₂×C₄×C₄₁	—	4	1	no	—
147	C₂×C₄×C₄₁	—	4	4	no	—
148	C₂×C₄×C₄₁	—	4	1	no	—
149	C₂×C₄×C₄₁	—	4	1	no	—
150	C₂×C₄×C₄₁	—	4	2	no	—
151	C₂×C₄×C₄₁	—	8	2	no	—
152	C₂×C₄×C₄₁	—	8	1	no	—
153	C₂×C₄×C₄₁	—	8	2	no	—
154	C₂×C₄×C₄₁	#121	1	1	yes	characteristic
155	C₂×C₄×C₄₁	#121	1	1	yes	characteristic
156	C₂×C₄×C₄₁	#121	1	1	yes	characteristic
157	C₂×C₄×C₄₁	C₂×SD₁₆	1	2	yes	—
158	C₂×C₄×C₄₁	#135	1	2	yes	—
159	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
160	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
161	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
162	C₈×C₄₁	—	2	4	no	—
163	C₈×C₄₁	—	4	2	no	—
164	C₈×C₄₁	—	4	2	no	—
165	C₈×C₄₁	—	4	2	no	—
166	#19390	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
167	C₂²×C₄₁	—	2	1	no	—
168	C₂²×C₄₁	—	2	1	no	—
169	C₂²×C₄₁	—	2	4	no	—
170	C₂²×C₄₁	—	4	2	no	—
171	C₂²×C₄₁	—	4	2	no	—
172	C₂²×C₄₁	—	8	4	no	—
173	C₂²×C₄₁	#465	1	2	yes	—
174	C₂²×C₄₁	C₂×#121	1	1	yes	characteristic
175	C₄×C₄₁	—	2	1	no	—
176	C₄×C₄₁	—	2	1	no	—
177	C₄×C₄₁	—	2	1	no	—
178	C₄×C₄₁	—	4	2	no	—
179	C₄×C₄₁	—	8	1	no	—
180	C₄×C₄₁	—	8	2	no	—
181	C₄×C₄₁	—	8	1	no	—
182	C₄×C₄₁	#465	1	2	yes	—
183	C₄×C₄₁	C₂²×SD₁₆	1	1	yes	characteristic
184	C₄×C₄₁	C₂×#135	1	1	yes	characteristic
185	C₄×C₄₁	#577	1	2	yes	—
186	#3229	C₂×C₄₁	1	1	yes	characteristic, complemented
187	#3077	C₂×C₄₁	1	1	yes	characteristic
188	C₂×#461	C₂×C₄₁	1	1	yes	characteristic
189	#2972	C₂×C₄₁	1	1	yes	characteristic
190	#1679	C₂×C₄₁	1	4	yes	complemented
191	#1671	C₂×C₄₁	1	4	yes	complemented
192	#1570	C₂×C₄₁	1	1	yes	characteristic, complemented
193	#1546	C₂×C₄₁	1	1	yes	characteristic, complemented
194	#1542	C₂×C₄₁	1	1	yes	characteristic, complemented
195	C₂×C₄₁	—	2	2	no	—
196	C₂×C₄₁	—	4	4	no	—
197	C₂×C₄₁	#3042	1	1	yes	characteristic
198	C₂×C₄₁	C₂×#465	1	1	yes	characteristic
199	C₂×C₄₁	#3069	1	1	yes	characteristic
200	C₂²×SD₁₆	—	2	1	no	—
201	#533	C₂²×C₄₁	1	1	yes	characteristic
202	C₂×C₄⋊Q₈	C₂²×C₄₁	1	1	yes	characteristic
203	C₂×C₄×D₄	C₂²×C₄₁	1	1	yes	characteristic
204	#498	C₂²×C₄₁	1	2	yes	complemented
205	#487	C₂²×C₄₁	1	2	yes	complemented
206	#483	—	2	2	no	—
207	#478	—	2	2	no	—
208	#476	C₂²×C₄₁	1	2	yes	—
209	#475	—	2	2	no	—
210	#474	C₂²×C₄₁	1	2	yes	—
211	#461	—	2	2	no	—
212	#461	C₂²×C₄₁	1	4	yes	—
213	C₈×D₄	—	2	2	no	—
214	C₈×D₄	C₂²×C₄₁	1	4	yes	—
215	#431	C₂²×C₄₁	1	1	yes	characteristic
216	#431	C₂²×C₄₁	1	1	yes	characteristic
217	#428	—	2	1	no	—
218	#423	C₂²×C₄₁	1	1	yes	characteristic
219	C₂×C₄⋊C₈	C₂²×C₄₁	1	1	yes	characteristic
220	#418	—	2	1	no	—
221	C₂×#103	—	2	1	no	—
222	C₂×C₂²⋊C₈	—	2	2	no	—
223	#334	C₂²×C₄₁	1	4	yes	complemented
224	#333	C₂²×C₄₁	1	2	yes	complemented
225	#332	C₂²×C₄₁	1	2	yes	complemented
226	#332	C₂²×C₄₁	1	4	yes	complemented
227	C₄₁	#19390	1	1	yes	characteristic, direct product factor, Sylow
228	C₂²×Q₈	—	2	1	no	—
229	C₂²×D₄	D₄×C₄₁	1	1	yes	characteristic
230	C₂³×C₄	—	2	1	no	—
231	C₂×SD₁₆	—	2	4	no	—
232	C₂×SD₁₆	—	4	4	no	—
233	C₂×M₁₆	—	2	1	no	—
234	C₂²×C₈	—	2	1	no	—
235	C₂²×C₈	—	2	4	no	—
236	C₄⋊Q₈	—	2	1	no	—
237	C₄⋊Q₈	—	2	1	no	—
238	C₄⋊Q₈	—	2	1	no	—
239	C₄⋊Q₈	C₂³×C₄₁	1	2	yes	—
240	C₄⋊Q₈	C₂³×C₄₁	1	1	yes	characteristic
241	C₄⋊Q₈	C₂³×C₄₁	1	1	yes	characteristic
242	#125	—	2	1	no	—
243	C₂²⋊Q₈	—	2	1	no	—
244	C₂²⋊Q₈	—	2	1	no	—
245	C₄×Q₈	—	2	1	no	—
246	C₄×Q₈	—	2	1	no	—
247	C₄×D₄	—	2	1	no	—
248	C₄×D₄	—	2	1	no	—
249	C₄×D₄	D₄×C₄₁	1	2	yes	—
250	C₄×D₄	C₂³×C₄₁	1	2	yes	—
251	#117	—	2	1	no	—
252	C₂×C₄⋊C₄	—	2	1	no	—
253	C₂×C₄⋊C₄	—	2	1	no	—
254	C₂×C₄⋊C₄	D₄×C₄₁	1	1	yes	characteristic
255	C₂×C₂²⋊C₄	—	2	1	no	—
256	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
257	#107	—	2	2	no	—
258	#106	—	2	4	no	—
259	#106	—	2	2	no	—
260	C₄⋊C₈	—	2	1	no	—
261	C₄⋊C₈	—	2	1	no	—
262	C₄⋊C₈	D₄×C₄₁	1	2	yes	—
263	C₄⋊C₈	C₂³×C₄₁	1	2	yes	—
264	C₄⋊C₈	C₂³×C₄₁	1	2	yes	—
265	C₄⋊C₈	C₂³×C₄₁	1	2	yes	—
266	#103	—	2	4	no	—
267	#103	—	2	4	no	—
268	#102	—	2	2	no	—
269	#102	—	2	2	no	—
270	C₂²⋊C₈	—	2	1	no	—
271	C₂²⋊C₈	—	2	4	no	—
272	C₂²⋊C₈	D₄×C₄₁	1	2	yes	—
273	C₄×C₈	—	2	1	no	—
274	C₄×C₈	C₂³×C₄₁	1	2	yes	—
275	C₂⁴	—	2	1	no	—
276	C₂×Q₈	—	2	1	no	—
277	C₂×Q₈	—	2	2	no	—
278	C₂×Q₈	—	2	1	no	—
279	C₂×Q₈	—	4	1	no	—
280	C₂×Q₈	—	4	2	no	—
281	C₂×Q₈	—	4	2	no	—
282	C₂×D₄	—	2	1	no	—
283	C₂×D₄	—	2	2	no	—
284	C₂×D₄	SD₁₆×C₄₁	1	4	yes	—
285	C₂×D₄	C₂×D₄×C₄₁	1	2	yes	—
286	C₂²×C₄	—	2	1	no	—
287	C₂²×C₄	—	2	2	no	—
288	C₂²×C₄	—	2	2	no	—
289	C₂²×C₄	—	4	1	no	—
290	C₂²×C₄	—	8	2	no	—
291	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
292	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
293	C₂²×C₄	#41×C₄₁	1	1	yes	characteristic
294	SD₁₆	—	4	8	no	—
295	M₁₆	—	4	2	no	—
296	C₂×C₈	—	2	2	no	—
297	C₂×C₈	—	2	2	no	—
298	C₂×C₈	—	2	2	no	—
299	C₂×C₈	—	4	2	no	—
300	C₂×C₈	—	8	4	no	—
301	C₂×C₈	C₂×D₄×C₄₁	1	4	yes	—
302	C₄⋊C₄	—	2	1	no	—
303	C₄⋊C₄	—	2	1	no	—
304	C₄⋊C₄	—	2	1	no	—
305	C₄⋊C₄	—	2	2	no	—
306	C₄⋊C₄	—	2	1	no	—
307	C₄⋊C₄	—	2	2	no	—
308	C₄⋊C₄	—	2	1	no	—
309	C₄⋊C₄	—	4	1	no	—
310	C₄⋊C₄	—	4	1	no	—
311	C₄⋊C₄	—	4	1	no	—
312	C₄⋊C₄	—	4	1	no	—
313	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
314	C₂²⋊C₄	—	2	2	no	—
315	C₂²⋊C₄	—	2	2	no	—
316	C₂²⋊C₄	—	4	1	no	—
317	C₄²	—	4	1	no	—
318	C₄²	C₂×D₄×C₄₁	1	1	yes	characteristic
319	C₄²	C₂×D₄×C₄₁	1	1	yes	characteristic
320	C₄²	#41×C₄₁	1	1	yes	characteristic
321	C₄²	C₂⁴×C₄₁	1	1	yes	characteristic
322	C₂³	—	2	2	no	—
323	C₂³	—	2	4	no	—
324	C₂³	—	8	1	no	—
325	C₂³	—	8	1	no	—
326	C₂³	#121×C₄₁	1	1	yes	characteristic
327	Q₈	—	4	2	no	—
328	Q₈	—	4	2	no	—
329	Q₈	—	4	2	no	—
330	Q₈	—	8	1	no	—
331	Q₈	—	8	2	no	—
332	D₄	—	2	2	no	—
333	D₄	—	2	4	no	—
334	D₄	C₂×SD₁₆×C₄₁	1	4	yes	—
335	C₂×C₄	—	2	2	no	—
336	C₂×C₄	—	2	2	no	—
337	C₂×C₄	—	4	1	no	—
338	C₂×C₄	—	4	4	no	—
339	C₂×C₄	—	4	1	no	—
340	C₂×C₄	—	4	1	no	—
341	C₂×C₄	—	4	2	no	—
342	C₂×C₄	—	8	2	no	—
343	C₂×C₄	—	8	1	no	—
344	C₂×C₄	—	8	2	no	—
345	C₂×C₄	#121×C₄₁	1	1	yes	characteristic
346	C₂×C₄	#121×C₄₁	1	1	yes	characteristic
347	C₂×C₄	#121×C₄₁	1	1	yes	characteristic
348	C₂×C₄	C₂×SD₁₆×C₄₁	1	2	yes	—
349	C₂×C₄	#135×C₄₁	1	2	yes	—
350	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
351	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
352	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
353	C₈	—	2	4	no	—
354	C₈	—	4	2	no	—
355	C₈	—	4	2	no	—
356	C₈	—	4	2	no	—
357	C₂²	—	2	1	no	—
358	C₂²	—	2	1	no	—
359	C₂²	—	2	4	no	—
360	C₂²	—	4	2	no	—
361	C₂²	—	4	2	no	—
362	C₂²	—	8	4	no	—
363	C₂²	C₄₁×#465	1	2	yes	—
364	C₂²	C₂×#121×C₄₁	1	1	yes	characteristic
365	C₄	—	2	1	no	—
366	C₄	—	2	1	no	—
367	C₄	—	2	1	no	—
368	C₄	—	4	2	no	—
369	C₄	—	8	1	no	—
370	C₄	—	8	2	no	—
371	C₄	—	8	1	no	—
372	C₄	C₄₁×#465	1	2	yes	—
373	C₄	C₂²×SD₁₆×C₄₁	1	1	yes	characteristic
374	C₄	C₂×#135×C₄₁	1	1	yes	characteristic
375	C₄	C₄₁×#577	1	2	yes	—
376	C₂	—	2	2	no	—
377	C₂	—	4	4	no	—
378	C₂	C₄₁×#3042	1	1	yes	characteristic
379	C₂	C₂×C₄₁×#465	1	1	yes	characteristic
380	C₂	C₄₁×#3069	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₄₁	C₂×#121
commutator, Frattini, cosocle	C₄²	C₂⁴×C₄₁
prime radical	C₂²×D₄×C₄₁	D₄
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₄₁ ◁ C₂×C₄²×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₄₁×#3229	C₂	semidirect
5. C₄₁×#1679	C₂	semidirect
6. C₄₁×#1671	C₂	semidirect
7. C₄₁×#1570	C₂	semidirect
8. C₄₁×#1546	C₂	semidirect
9. C₄₁×#1542	C₂	semidirect
14. C₄₁×#498	C₂²	semidirect
15. C₄₁×#487	C₂²	semidirect
33. C₄₁×#334	C₂²	semidirect
34. C₄₁×#333	C₂²	semidirect
35. C₄₁×#332	C₂²	semidirect
36. C₄₁×#332	C₂²	semidirect
166. #19390	C₄₁	direct (N × H)
186. #3229	C₂×C₄₁	semidirect
190. #1679	C₂×C₄₁	semidirect
191. #1671	C₂×C₄₁	semidirect
192. #1570	C₂×C₄₁	semidirect
193. #1546	C₂×C₄₁	semidirect
194. #1542	C₂×C₄₁	semidirect
204. #498	C₂²×C₄₁	semidirect
205. #487	C₂²×C₄₁	semidirect
223. #334	C₂²×C₄₁	semidirect
224. #333	C₂²×C₄₁	semidirect
225. #332	C₂²×C₄₁	semidirect
226. #332	C₂²×C₄₁	semidirect
227. C₄₁	#19390	direct (N × H)

Maximal subgroups

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

subgroup	index
C₄₁×#3229	2
C₄₁×#3077	2
C₂×C₄₁×#461	2
C₄₁×#2972	2
C₄₁×#1679	2
C₄₁×#1671	2
C₄₁×#1570	2
C₄₁×#1546	2
C₄₁×#1542	2
#19390	41

Subgroups — C41×#19390 #23795591

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#19390 #23795591