Subgroups — C₄₁×#20007 #23796208

Order 10496.

570 conjugacy classes of subgroups.

The subgroup lattice has 374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₁×#3395	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄₁×#3381	C₂	1	2	yes	maximal
3	C₄₁×#3338	C₂	1	1	yes	maximal, characteristic
4	C₄₁×#1707	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₁×#1676	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄₁×#1672	C₂	1	2	yes	maximal, complemented
7	C₄₁×#1669	C₂	1	1	yes	maximal, characteristic
8	C₄₁×#1644	C₂	1	2	yes	maximal
9	C₄₁×#1636	C₂	1	2	yes	maximal, complemented
10	C₈×Q₁₆×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈×SD₁₆×C₄₁	C₂	1	1	yes	maximal, characteristic
12	C₄₁×#557	C₂²	1	2	yes	—
13	C₄₁×#554	C₂²	1	2	yes	—
14	C₄₁×#500	C₂²	1	1	yes	characteristic
15	C₄₁×#499	—	2	2	no	—
16	C₄₁×#498	C₂²	1	2	yes	—
17	C₄₁×#494	—	2	1	no	—
18	C₄₁×#494	C₂²	1	1	yes	characteristic
19	C₄₁×#487	C₂²	1	2	yes	—
20	C₄₁×#484	—	2	2	no	—
21	C₄₁×#479	—	2	2	no	—
22	C₄₁×#478	—	2	2	no	—
23	C₄₁×#477	C₂²	1	2	yes	—
24	C₄₁×#477	C₂²	1	2	yes	—
25	C₄₁×#474	C₂²	1	2	yes	—
26	C₄₁×#467	—	2	1	no	—
27	C₄₁×#462	—	2	2	no	—
28	C₄₁×#462	C₂²	1	2	yes	—
29	C₈×Q₈×C₄₁	C₂²	1	1	yes	characteristic
30	C₈×Q₈×C₄₁	C₂²	1	2	yes	—
31	C₄×Q₁₆×C₄₁	—	2	1	no	—
32	C₄×Q₁₆×C₄₁	C₂²	1	1	yes	characteristic
33	C₄×SD₁₆×C₄₁	—	2	2	no	—
34	C₄×SD₁₆×C₄₁	C₂²	1	1	yes	characteristic
35	C₈×D₄×C₄₁	C₂²	1	1	yes	characteristic
36	C₂×#107×C₄₁	—	2	1	no	—
37	C₄₁×#335	C₂²	1	1	yes	characteristic
38	C₄₁×#334	C₂²	1	1	yes	characteristic
39	C₄₁×#333	C₂²	1	2	yes	—
40	C₄₁×#332	C₂²	1	2	yes	—
41	C₄₁×Q₈⋊C₈	C₂²	1	1	yes	characteristic
42	C₄₁×Q₈⋊C₈	C₂²	1	2	yes	—
43	C₄₁×D₄⋊C₈	C₂²	1	1	yes	characteristic
44	C₈²×C₄₁	C₂²	1	1	yes	characteristic
45	C₂×Q₁₆×C₄₁	—	2	2	no	—
46	C₂×Q₁₆×C₄₁	—	2	1	no	—
47	C₂×Q₁₆×C₄₁	—	2	1	no	—
48	C₂×Q₁₆×C₄₁	D₄	1	1	yes	characteristic
49	C₂×SD₁₆×C₄₁	D₄	1	1	yes	characteristic
50	C₂²×C₈×C₄₁	—	2	1	no	—
51	C₄⋊Q₈×C₄₁	—	2	2	no	—
52	C₄⋊Q₈×C₄₁	C₂³	1	2	yes	—
53	C₄⋊Q₈×C₄₁	C₂³	1	2	yes	—
54	#125×C₄₁	—	2	2	no	—
55	#125×C₄₁	—	2	2	no	—
56	#125×C₄₁	—	4	2	no	—
57	C₂²⋊Q₈×C₄₁	—	2	2	no	—
58	C₂²⋊Q₈×C₄₁	—	4	2	no	—
59	C₄×Q₈×C₄₁	—	2	2	no	—
60	C₄×Q₈×C₄₁	—	2	2	no	—
61	C₄×Q₈×C₄₁	C₂³	1	2	yes	—
62	C₄×Q₈×C₄₁	C₂³	1	1	yes	characteristic
63	C₄×D₄×C₄₁	—	2	2	no	—
64	C₄×D₄×C₄₁	C₂³	1	1	yes	characteristic
65	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
66	#107×C₄₁	—	2	1	no	—
67	#107×C₄₁	—	2	1	no	—
68	#107×C₄₁	—	2	2	no	—
69	#107×C₄₁	—	2	2	no	—
70	#107×C₄₁	—	2	2	no	—
71	#107×C₄₁	D₄	1	1	yes	characteristic
72	#106×C₄₁	—	2	2	no	—
73	#106×C₄₁	—	2	2	no	—
74	#106×C₄₁	D₄	1	1	yes	characteristic
75	C₄⋊C₈×C₄₁	—	2	1	no	—
76	C₄⋊C₈×C₄₁	—	2	2	no	—
77	C₄⋊C₈×C₄₁	C₂³	1	1	yes	characteristic
78	C₄⋊C₈×C₄₁	C₂³	1	1	yes	characteristic
79	C₄⋊C₈×C₄₁	C₂³	1	2	yes	—
80	#103×C₄₁	—	2	2	no	—
81	#103×C₄₁	—	2	2	no	—
82	#103×C₄₁	—	2	2	no	—
83	#103×C₄₁	—	4	2	no	—
84	#103×C₄₁	D₄	1	1	yes	characteristic
85	#103×C₄₁	D₄	1	2	yes	—
86	#102×C₄₁	—	2	2	no	—
87	#102×C₄₁	D₄	1	1	yes	characteristic
88	C₂²⋊C₈×C₄₁	—	2	1	no	—
89	C₄×C₈×C₄₁	—	2	2	no	—
90	C₄×C₈×C₄₁	—	2	1	no	—
91	C₄×C₈×C₄₁	C₂³	1	1	yes	characteristic
92	C₄×C₈×C₄₁	C₂³	1	1	yes	characteristic
93	C₄×C₈×C₄₁	C₂³	1	1	yes	characteristic
94	C₂×Q₈×C₄₁	—	2	2	no	—
95	C₂×Q₈×C₄₁	—	2	2	no	—
96	C₂×Q₈×C₄₁	C₂×D₄	1	2	yes	—
97	C₂×Q₈×C₄₁	C₂×D₄	1	1	yes	characteristic
98	C₂×D₄×C₄₁	C₂×D₄	1	1	yes	characteristic
99	C₂²×C₄×C₄₁	—	2	1	no	—
100	C₂²×C₄×C₄₁	—	4	2	no	—
101	Q₁₆×C₄₁	—	2	2	no	—
102	Q₁₆×C₄₁	—	4	2	no	—
103	Q₁₆×C₄₁	—	8	1	no	—
104	Q₁₆×C₄₁	—	8	2	no	—
105	SD₁₆×C₄₁	Q₁₆	1	4	yes	complemented
106	C₂×C₈×C₄₁	—	2	2	no	—
107	C₂×C₈×C₄₁	—	2	1	no	—
108	C₂×C₈×C₄₁	—	2	1	no	—
109	C₂×C₈×C₄₁	—	2	1	no	—
110	C₂×C₈×C₄₁	—	4	2	no	—
111	C₂×C₈×C₄₁	C₂×D₄	1	1	yes	characteristic
112	C₂×C₈×C₄₁	C₂×D₄	1	1	yes	characteristic
113	C₂×C₈×C₄₁	C₂×D₄	1	1	yes	characteristic
114	C₂×C₈×C₄₁	C₂×D₄	1	1	yes	characteristic
115	C₄⋊C₄×C₄₁	—	2	2	no	—
116	C₄⋊C₄×C₄₁	—	2	1	no	—
117	C₄⋊C₄×C₄₁	—	2	2	no	—
118	C₄⋊C₄×C₄₁	—	2	2	no	—
119	C₄⋊C₄×C₄₁	—	2	2	no	—
120	C₄⋊C₄×C₄₁	—	2	2	no	—
121	C₄⋊C₄×C₄₁	—	4	2	no	—
122	C₄⋊C₄×C₄₁	—	4	2	no	—
123	C₄⋊C₄×C₄₁	—	4	2	no	—
124	C₄⋊C₄×C₄₁	—	4	2	no	—
125	C₄⋊C₄×C₄₁	—	4	2	no	—
126	C₄⋊C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
127	C₄⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
128	C₄⋊C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
129	C₂²⋊C₄×C₄₁	—	2	1	no	—
130	C₂²⋊C₄×C₄₁	—	4	2	no	—
131	C₄²×C₄₁	—	2	2	no	—
132	C₄²×C₄₁	—	2	1	no	—
133	C₄²×C₄₁	—	4	2	no	—
134	C₄²×C₄₁	C₂⁴	1	1	yes	characteristic
135	C₂³×C₄₁	—	2	1	no	—
136	Q₈×C₄₁	—	2	1	no	—
137	Q₈×C₄₁	—	2	2	no	—
138	Q₈×C₄₁	—	2	2	no	—
139	Q₈×C₄₁	—	4	2	no	—
140	Q₈×C₄₁	—	4	2	no	—
141	Q₈×C₄₁	—	8	2	no	—
142	Q₈×C₄₁	C₂×Q₁₆	1	2	yes	—
143	D₄×C₄₁	—	2	1	no	—
144	D₄×C₄₁	C₂×Q₁₆	1	2	yes	—
145	C₂×C₄×C₄₁	—	2	1	no	—
146	C₂×C₄×C₄₁	—	2	2	no	—
147	C₂×C₄×C₄₁	—	2	2	no	—
148	C₂×C₄×C₄₁	—	2	1	no	—
149	C₂×C₄×C₄₁	—	2	1	no	—
150	C₂×C₄×C₄₁	—	4	1	no	—
151	C₂×C₄×C₄₁	—	4	1	no	—
152	C₂×C₄×C₄₁	—	4	2	no	—
153	C₂×C₄×C₄₁	—	4	2	no	—
154	C₂×C₄×C₄₁	—	16	2	no	—
155	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
156	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
157	C₂×C₄×C₄₁	H(5,𝔽₂)	1	1	yes	characteristic
158	C₈×C₄₁	—	2	1	no	—
159	C₈×C₄₁	—	2	1	no	—
160	C₈×C₄₁	—	4	1	no	—
161	C₈×C₄₁	—	4	1	no	—
162	C₈×C₄₁	—	4	1	no	—
163	C₈×C₄₁	—	4	2	no	—
164	C₈×C₄₁	C₂×Q₁₆	1	2	yes	—
165	C₈×C₄₁	#135	1	2	yes	—
166	#20007	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
167	C₂²×C₄₁	—	2	2	no	—
168	C₂²×C₄₁	—	4	1	no	—
169	C₂²×C₄₁	—	4	1	no	—
170	C₂²×C₄₁	D₄²	1	1	yes	characteristic
171	C₄×C₄₁	—	2	2	no	—
172	C₄×C₄₁	—	2	1	no	—
173	C₄×C₄₁	—	4	1	no	—
174	C₄×C₄₁	—	4	2	no	—
175	C₄×C₄₁	—	4	1	no	—
176	C₄×C₄₁	—	4	2	no	—
177	C₄×C₄₁	—	8	2	no	—
178	C₄×C₄₁	—	8	2	no	—
179	C₄×C₄₁	C₂²×Q₁₆	1	1	yes	characteristic
180	C₄×C₄₁	C₂×#135	1	1	yes	characteristic
181	C₄×C₄₁	#577	1	1	yes	characteristic
182	C₄×C₄₁	#578	1	1	yes	characteristic
183	#3395	C₂×C₄₁	1	1	yes	characteristic, complemented
184	#3381	C₂×C₄₁	1	2	yes	—
185	#3338	C₂×C₄₁	1	1	yes	characteristic
186	#1707	C₂×C₄₁	1	1	yes	characteristic, complemented
187	#1676	C₂×C₄₁	1	1	yes	characteristic, complemented
188	#1672	C₂×C₄₁	1	2	yes	complemented
189	#1669	C₂×C₄₁	1	1	yes	characteristic
190	#1644	C₂×C₄₁	1	2	yes	—
191	#1636	C₂×C₄₁	1	2	yes	complemented
192	C₈×Q₁₆	C₂×C₄₁	1	1	yes	characteristic, complemented
193	C₈×SD₁₆	C₂×C₄₁	1	1	yes	characteristic
194	C₂×C₄₁	—	4	2	no	—
195	C₂×C₄₁	#3284	1	1	yes	characteristic
196	C₂×C₄₁	D₄×Q₁₆	1	1	yes	characteristic
197	C₂×C₄₁	#3290	1	1	yes	characteristic
198	#557	C₂²×C₄₁	1	2	yes	—
199	#554	C₂²×C₄₁	1	2	yes	—
200	#500	C₂²×C₄₁	1	1	yes	characteristic
201	#499	—	2	2	no	—
202	#498	C₂²×C₄₁	1	2	yes	—
203	#494	—	2	1	no	—
204	#494	C₂²×C₄₁	1	1	yes	characteristic
205	#487	C₂²×C₄₁	1	2	yes	—
206	#484	—	2	2	no	—
207	#479	—	2	2	no	—
208	#478	—	2	2	no	—
209	#477	C₂²×C₄₁	1	2	yes	—
210	#477	C₂²×C₄₁	1	2	yes	—
211	#474	C₂²×C₄₁	1	2	yes	—
212	#467	—	2	1	no	—
213	#462	—	2	2	no	—
214	#462	C₂²×C₄₁	1	2	yes	—
215	C₈×Q₈	C₂²×C₄₁	1	1	yes	characteristic
216	C₈×Q₈	C₂²×C₄₁	1	2	yes	—
217	C₄×Q₁₆	—	2	1	no	—
218	C₄×Q₁₆	C₂²×C₄₁	1	1	yes	characteristic
219	C₄×SD₁₆	—	2	2	no	—
220	C₄×SD₁₆	C₂²×C₄₁	1	1	yes	characteristic
221	C₈×D₄	C₂²×C₄₁	1	1	yes	characteristic
222	C₂×#107	—	2	1	no	—
223	#335	C₂²×C₄₁	1	1	yes	characteristic
224	#334	C₂²×C₄₁	1	1	yes	characteristic
225	#333	C₂²×C₄₁	1	2	yes	—
226	#332	C₂²×C₄₁	1	2	yes	—
227	Q₈⋊C₈	C₂²×C₄₁	1	1	yes	characteristic
228	Q₈⋊C₈	C₂²×C₄₁	1	2	yes	—
229	D₄⋊C₈	C₂²×C₄₁	1	1	yes	characteristic
230	C₈²	C₂²×C₄₁	1	1	yes	characteristic
231	C₄₁	#20007	1	1	yes	characteristic, direct product factor, Sylow
232	C₂×Q₁₆	—	2	2	no	—
233	C₂×Q₁₆	—	2	1	no	—
234	C₂×Q₁₆	—	2	1	no	—
235	C₂×Q₁₆	D₄×C₄₁	1	1	yes	characteristic
236	C₂×SD₁₆	D₄×C₄₁	1	1	yes	characteristic
237	C₂²×C₈	—	2	1	no	—
238	C₄⋊Q₈	—	2	2	no	—
239	C₄⋊Q₈	C₂³×C₄₁	1	2	yes	—
240	C₄⋊Q₈	C₂³×C₄₁	1	2	yes	—
241	#125	—	2	2	no	—
242	#125	—	2	2	no	—
243	#125	—	4	2	no	—
244	C₂²⋊Q₈	—	2	2	no	—
245	C₂²⋊Q₈	—	4	2	no	—
246	C₄×Q₈	—	2	2	no	—
247	C₄×Q₈	—	2	2	no	—
248	C₄×Q₈	C₂³×C₄₁	1	2	yes	—
249	C₄×Q₈	C₂³×C₄₁	1	1	yes	characteristic
250	C₄×D₄	—	2	2	no	—
251	C₄×D₄	C₂³×C₄₁	1	1	yes	characteristic
252	C₂×C₄⋊C₄	—	2	2	no	—
253	#107	—	2	1	no	—
254	#107	—	2	1	no	—
255	#107	—	2	2	no	—
256	#107	—	2	2	no	—
257	#107	—	2	2	no	—
258	#107	D₄×C₄₁	1	1	yes	characteristic
259	#106	—	2	2	no	—
260	#106	—	2	2	no	—
261	#106	D₄×C₄₁	1	1	yes	characteristic
262	C₄⋊C₈	—	2	1	no	—
263	C₄⋊C₈	—	2	2	no	—
264	C₄⋊C₈	C₂³×C₄₁	1	1	yes	characteristic
265	C₄⋊C₈	C₂³×C₄₁	1	1	yes	characteristic
266	C₄⋊C₈	C₂³×C₄₁	1	2	yes	—
267	#103	—	2	2	no	—
268	#103	—	2	2	no	—
269	#103	—	2	2	no	—
270	#103	—	4	2	no	—
271	#103	D₄×C₄₁	1	1	yes	characteristic
272	#103	D₄×C₄₁	1	2	yes	—
273	#102	—	2	2	no	—
274	#102	D₄×C₄₁	1	1	yes	characteristic
275	C₂²⋊C₈	—	2	1	no	—
276	C₄×C₈	—	2	2	no	—
277	C₄×C₈	—	2	1	no	—
278	C₄×C₈	C₂³×C₄₁	1	1	yes	characteristic
279	C₄×C₈	C₂³×C₄₁	1	1	yes	characteristic
280	C₄×C₈	C₂³×C₄₁	1	1	yes	characteristic
281	C₂×Q₈	—	2	2	no	—
282	C₂×Q₈	—	2	2	no	—
283	C₂×Q₈	C₂×D₄×C₄₁	1	2	yes	—
284	C₂×Q₈	C₂×D₄×C₄₁	1	1	yes	characteristic
285	C₂×D₄	C₂×D₄×C₄₁	1	1	yes	characteristic
286	C₂²×C₄	—	2	1	no	—
287	C₂²×C₄	—	4	2	no	—
288	Q₁₆	—	2	2	no	—
289	Q₁₆	—	4	2	no	—
290	Q₁₆	—	8	1	no	—
291	Q₁₆	—	8	2	no	—
292	SD₁₆	Q₁₆×C₄₁	1	4	yes	complemented
293	C₂×C₈	—	2	2	no	—
294	C₂×C₈	—	2	1	no	—
295	C₂×C₈	—	2	1	no	—
296	C₂×C₈	—	2	1	no	—
297	C₂×C₈	—	4	2	no	—
298	C₂×C₈	C₂×D₄×C₄₁	1	1	yes	characteristic
299	C₂×C₈	C₂×D₄×C₄₁	1	1	yes	characteristic
300	C₂×C₈	C₂×D₄×C₄₁	1	1	yes	characteristic
301	C₂×C₈	C₂×D₄×C₄₁	1	1	yes	characteristic
302	C₄⋊C₄	—	2	2	no	—
303	C₄⋊C₄	—	2	1	no	—
304	C₄⋊C₄	—	2	2	no	—
305	C₄⋊C₄	—	2	2	no	—
306	C₄⋊C₄	—	2	2	no	—
307	C₄⋊C₄	—	2	2	no	—
308	C₄⋊C₄	—	4	2	no	—
309	C₄⋊C₄	—	4	2	no	—
310	C₄⋊C₄	—	4	2	no	—
311	C₄⋊C₄	—	4	2	no	—
312	C₄⋊C₄	—	4	2	no	—
313	C₄⋊C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
314	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
315	C₄⋊C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
316	C₂²⋊C₄	—	2	1	no	—
317	C₂²⋊C₄	—	4	2	no	—
318	C₄²	—	2	2	no	—
319	C₄²	—	2	1	no	—
320	C₄²	—	4	2	no	—
321	C₄²	C₂⁴×C₄₁	1	1	yes	characteristic
322	C₂³	—	2	1	no	—
323	Q₈	—	2	1	no	—
324	Q₈	—	2	2	no	—
325	Q₈	—	2	2	no	—
326	Q₈	—	4	2	no	—
327	Q₈	—	4	2	no	—
328	Q₈	—	8	2	no	—
329	Q₈	C₂×Q₁₆×C₄₁	1	2	yes	—
330	D₄	—	2	1	no	—
331	D₄	C₂×Q₁₆×C₄₁	1	2	yes	—
332	C₂×C₄	—	2	1	no	—
333	C₂×C₄	—	2	2	no	—
334	C₂×C₄	—	2	2	no	—
335	C₂×C₄	—	2	1	no	—
336	C₂×C₄	—	2	1	no	—
337	C₂×C₄	—	4	1	no	—
338	C₂×C₄	—	4	1	no	—
339	C₂×C₄	—	4	2	no	—
340	C₂×C₄	—	4	2	no	—
341	C₂×C₄	—	16	2	no	—
342	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
343	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
344	C₂×C₄	H(5,𝔽₂)×C₄₁	1	1	yes	characteristic
345	C₈	—	2	1	no	—
346	C₈	—	2	1	no	—
347	C₈	—	4	1	no	—
348	C₈	—	4	1	no	—
349	C₈	—	4	1	no	—
350	C₈	—	4	2	no	—
351	C₈	C₂×Q₁₆×C₄₁	1	2	yes	—
352	C₈	#135×C₄₁	1	2	yes	—
353	C₂²	—	2	2	no	—
354	C₂²	—	4	1	no	—
355	C₂²	—	4	1	no	—
356	C₂²	D₄²×C₄₁	1	1	yes	characteristic
357	C₄	—	2	2	no	—
358	C₄	—	2	1	no	—
359	C₄	—	4	1	no	—
360	C₄	—	4	2	no	—
361	C₄	—	4	2	no	—
362	C₄	—	4	1	no	—
363	C₄	—	8	2	no	—
364	C₄	—	8	2	no	—
365	C₄	C₂²×Q₁₆×C₄₁	1	1	yes	characteristic
366	C₄	C₂×#135×C₄₁	1	1	yes	characteristic
367	C₄	C₄₁×#577	1	1	yes	characteristic
368	C₄	C₄₁×#578	1	1	yes	characteristic
369	C₂	—	4	2	no	—
370	C₂	C₄₁×#3284	1	1	yes	characteristic
371	C₂	D₄×Q₁₆×C₄₁	1	1	yes	characteristic
372	C₂	C₄₁×#3290	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₄₁	D₄²
commutator, Frattini, cosocle	C₄²	C₂⁴×C₄₁
prime radical	C₂×D₄×C₄₁	C₂×D₄
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₄₁ ◁ C₄²×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₄₁×#3395	C₂	semidirect
4. C₄₁×#1707	C₂	semidirect
5. C₄₁×#1676	C₂	semidirect
6. C₄₁×#1672	C₂	semidirect
9. C₄₁×#1636	C₂	semidirect
10. C₈×Q₁₆×C₄₁	C₂	semidirect
105. SD₁₆×C₄₁	Q₁₆	semidirect
166. #20007	C₄₁	direct (N × H)
183. #3395	C₂×C₄₁	semidirect
186. #1707	C₂×C₄₁	semidirect
187. #1676	C₂×C₄₁	semidirect
188. #1672	C₂×C₄₁	semidirect
191. #1636	C₂×C₄₁	semidirect
192. C₈×Q₁₆	C₂×C₄₁	semidirect
231. C₄₁	#20007	direct (N × H)
292. SD₁₆	Q₁₆×C₄₁	semidirect

Maximal subgroups

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

subgroup	index
C₄₁×#3395	2
C₄₁×#3381	2
C₄₁×#3338	2
C₄₁×#1707	2
C₄₁×#1676	2
C₄₁×#1672	2
C₄₁×#1669	2
C₄₁×#1644	2
C₄₁×#1636	2
C₈×Q₁₆×C₄₁	2
C₈×SD₁₆×C₄₁	2
#20007	41

Subgroups — C41×#20007 #23796208

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#20007 #23796208