Subgroups — C₄₁×#20310 #23796511

Order 10496.

754 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₁×#3399	C₂	1	2	yes	maximal, complemented
2	C₄₁×#3274	C₂	1	2	yes	maximal, complemented
3	C₄₁×#1712	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₁×#1688	C₂	1	2	yes	maximal, complemented
5	C₄₁×#1687	C₂	1	2	yes	maximal, complemented
6	C₄₁×#1621	C₂	1	2	yes	maximal, complemented
7	C₄₁×#1620	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄₁×#1619	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄₁×#1590	C₂	1	2	yes	maximal, complemented
10	C₂×AGL(1,ℤ/8)×C₄₁	—	2	2	no	—
11	C₄₁×#559	C₂²	1	1	yes	characteristic, complemented
12	C₄₁×#550	C₂²	1	2	yes	—
13	D₄²×C₄₁	C₂²	1	1	yes	characteristic
14	C₄₁×#496	—	2	2	no	—
15	C₄₁×#493	C₂²	1	2	yes	—
16	C₄₁×#493	C₂²	1	1	yes	characteristic
17	C₄₁×#493	C₂²	1	2	yes	complemented
18	C₄₁×#493	C₂²	1	1	yes	characteristic, complemented
19	C₄₁×#469	—	2	2	no	—
20	C₄₁×#463	—	2	2	no	—
21	C₄₁×#460	C₂²	1	2	yes	—
22	C₄₁×#460	C₂²	1	2	yes	complemented
23	C₄₁×#459	—	2	2	no	—
24	C₄₁×#459	C₂²	1	2	yes	—
25	C₄₁×#459	C₂²	1	2	yes	—
26	C₄₁×#449	—	2	2	no	—
27	C₄₁×#447	—	2	2	no	—
28	C₄₁×#446	C₂²	1	2	yes	complemented
29	C₄₁×#442	—	2	2	no	—
30	C₄×SD₁₆×C₄₁	C₂²	1	2	yes	—
31	C₄₁×#436	C₂²	1	2	yes	—
32	C₄₁×#334	C₂²	1	2	yes	complemented
33	C₄₁×#331	C₂²	1	1	yes	characteristic
34	C₄₁×#331	C₂²	1	1	yes	characteristic, complemented
35	C₄₁×#331	C₂²	1	2	yes	complemented
36	C₄₁×Q₈⋊C₈	C₂²	1	2	yes	complemented
37	C₄₁×D₄⋊C₈	C₂²	1	2	yes	—
38	C₈²×C₄₁	C₂²	1	1	yes	characteristic, complemented
39	C₂×#41×C₄₁	—	2	2	no	—
40	C₂²×D₄×C₄₁	—	2	2	no	—
41	AGL(1,ℤ/8)×C₄₁	—	4	8	no	—
42	C₂×SD₁₆×C₄₁	—	2	2	no	—
43	C₂×SD₁₆×C₄₁	—	2	2	no	—
44	C₂×SD₁₆×C₄₁	D₄	1	2	yes	—
45	C₂×D₈×C₄₁	—	2	2	no	—
46	C₂×D₈×C₄₁	—	2	2	no	—
47	C₂×D₈×C₄₁	—	2	2	no	—
48	C₂×D₈×C₄₁	—	2	2	no	—
49	C₂×D₈×C₄₁	—	2	2	no	—
50	C₂×D₈×C₄₁	—	2	2	no	—
51	C₂×D₈×C₄₁	—	4	1	no	—
52	C₂×D₈×C₄₁	—	4	1	no	—
53	C₂×M₁₆×C₄₁	—	2	2	no	—
54	#127×C₄₁	—	2	2	no	—
55	#127×C₄₁	C₂³	1	1	yes	characteristic
56	#127×C₄₁	C₂³	1	2	yes	—
57	#127×C₄₁	C₂³	1	1	yes	characteristic
58	#124×C₄₁	—	2	2	no	—
59	#123×C₄₁	—	4	1	no	—
60	#121×C₄₁	—	2	2	no	—
61	#121×C₄₁	—	2	2	no	—
62	#121×C₄₁	—	4	2	no	—
63	#120×C₄₁	—	4	1	no	—
64	C₄×Q₈×C₄₁	C₂³	1	2	yes	—
65	C₄×D₄×C₄₁	—	2	2	no	—
66	C₄×D₄×C₄₁	—	2	2	no	—
67	C₄×D₄×C₄₁	C₂³	1	2	yes	—
68	#106×C₄₁	D₄	1	2	yes	—
69	C₄⋊C₈×C₄₁	—	2	2	no	—
70	C₄⋊C₈×C₄₁	C₂³	1	2	yes	—
71	C₄⋊C₈×C₄₁	C₂³	1	2	yes	—
72	#103×C₄₁	D₄	1	2	yes	—
73	#102×C₄₁	—	2	2	no	—
74	#102×C₄₁	—	2	2	no	—
75	#102×C₄₁	—	2	2	no	—
76	#102×C₄₁	—	2	2	no	—
77	#102×C₄₁	D₄	1	2	yes	—
78	C₂²⋊C₈×C₄₁	—	2	2	no	—
79	#97×C₄₁	—	2	2	no	—
80	C₄×C₈×C₄₁	C₂³	1	1	yes	characteristic
81	C₄×C₈×C₄₁	C₂³	1	2	yes	—
82	C₂⁴×C₄₁	—	4	1	no	—
83	#41×C₄₁	—	4	4	no	—
84	#41×C₄₁	—	8	2	no	—
85	C₂×Q₈×C₄₁	C₂×D₄	1	2	yes	—
86	C₂×D₄×C₄₁	—	2	2	no	—
87	C₂×D₄×C₄₁	—	2	2	no	—
88	C₂×D₄×C₄₁	—	2	2	no	—
89	C₂×D₄×C₄₁	—	2	2	no	—
90	C₂×D₄×C₄₁	—	2	1	no	—
91	C₂×D₄×C₄₁	—	2	2	no	—
92	C₂×D₄×C₄₁	—	2	1	no	—
93	C₂×D₄×C₄₁	—	4	2	no	—
94	C₂×D₄×C₄₁	—	4	2	no	—
95	C₂×D₄×C₄₁	—	4	2	no	—
96	C₂×D₄×C₄₁	—	4	4	no	—
97	C₂×D₄×C₄₁	—	8	2	no	—
98	C₂×D₄×C₄₁	C₂×D₄	1	2	yes	—
99	C₂²×C₄×C₄₁	—	2	2	no	—
100	C₂²×C₄×C₄₁	—	4	2	no	—
101	C₂²×C₄×C₄₁	—	4	1	no	—
102	SD₁₆×C₄₁	—	2	4	no	—
103	SD₁₆×C₄₁	—	4	4	no	—
104	SD₁₆×C₄₁	—	8	2	no	—
105	D₈×C₄₁	—	4	4	no	—
106	D₈×C₄₁	—	4	4	no	—
107	D₈×C₄₁	—	4	4	no	—
108	D₈×C₄₁	—	8	2	no	—
109	D₈×C₄₁	—	8	2	no	—
110	D₈×C₄₁	—	8	2	no	—
111	D₈×C₄₁	—	8	2	no	—
112	D₈×C₄₁	—	8	2	no	—
113	M₁₆×C₄₁	—	4	4	no	—
114	C₂×C₈×C₄₁	—	2	1	no	—
115	C₂×C₈×C₄₁	—	2	2	no	—
116	C₂×C₈×C₄₁	—	2	2	no	—
117	C₂×C₈×C₄₁	C₂×D₄	1	2	yes	—
118	C₂×C₈×C₄₁	C₂×D₄	1	2	yes	—
119	C₄⋊C₄×C₄₁	—	2	2	no	—
120	C₄⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
121	C₄⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
122	C₂²⋊C₄×C₄₁	—	2	2	no	—
123	C₂²⋊C₄×C₄₁	—	4	2	no	—
124	C₂²⋊C₄×C₄₁	—	4	2	no	—
125	C₂²⋊C₄×C₄₁	—	4	1	no	—
126	C₂²⋊C₄×C₄₁	—	4	1	no	—
127	C₄²×C₄₁	—	2	2	no	—
128	C₄²×C₄₁	C₂⁴	1	1	yes	characteristic
129	C₂³×C₄₁	—	2	2	no	—
130	C₂³×C₄₁	—	4	1	no	—
131	C₂³×C₄₁	—	4	2	no	—
132	C₂³×C₄₁	—	4	1	no	—
133	C₂³×C₄₁	—	8	4	no	—
134	C₂³×C₄₁	—	16	1	no	—
135	Q₈×C₄₁	—	2	2	no	—
136	Q₈×C₄₁	—	2	2	no	—
137	D₄×C₄₁	—	2	2	no	—
138	D₄×C₄₁	—	2	2	no	—
139	D₄×C₄₁	—	4	2	no	—
140	D₄×C₄₁	—	4	2	no	—
141	D₄×C₄₁	—	4	2	no	—
142	D₄×C₄₁	—	4	2	no	—
143	D₄×C₄₁	—	4	2	no	—
144	D₄×C₄₁	—	4	2	no	—
145	D₄×C₄₁	—	4	2	no	—
146	D₄×C₄₁	—	4	2	no	—
147	D₄×C₄₁	—	8	1	no	—
148	D₄×C₄₁	—	8	2	no	—
149	D₄×C₄₁	—	8	1	no	—
150	D₄×C₄₁	—	8	4	no	—
151	D₄×C₄₁	—	8	4	no	—
152	D₄×C₄₁	—	16	2	no	—
153	C₂×C₄×C₄₁	—	2	2	no	—
154	C₂×C₄×C₄₁	—	2	2	no	—
155	C₂×C₄×C₄₁	—	2	2	no	—
156	C₂×C₄×C₄₁	—	4	2	no	—
157	C₂×C₄×C₄₁	—	4	2	no	—
158	C₂×C₄×C₄₁	—	8	4	no	—
159	C₂×C₄×C₄₁	—	16	1	no	—
160	C₂×C₄×C₄₁	C₂²×D₄	1	2	yes	—
161	C₂×C₄×C₄₁	H(5,𝔽₂)	1	1	yes	characteristic
162	C₈×C₄₁	—	2	2	no	—
163	C₈×C₄₁	—	2	2	no	—
164	C₈×C₄₁	—	4	2	no	—
165	C₈×C₄₁	—	4	2	no	—
166	C₈×C₄₁	AGL(1,ℤ/8)	1	4	yes	complemented
167	#20310	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
168	C₂²×C₄₁	—	4	2	no	—
169	C₂²×C₄₁	—	4	2	no	—
170	C₂²×C₄₁	—	4	2	no	—
171	C₂²×C₄₁	—	8	2	no	—
172	C₂²×C₄₁	—	8	2	no	—
173	C₂²×C₄₁	—	8	2	no	—
174	C₂²×C₄₁	—	8	2	no	—
175	C₂²×C₄₁	—	8	1	no	—
176	C₂²×C₄₁	—	8	2	no	—
177	C₂²×C₄₁	—	8	1	no	—
178	C₂²×C₄₁	—	16	4	no	—
179	C₂²×C₄₁	D₄²	1	1	yes	characteristic
180	C₄×C₄₁	—	2	1	no	—
181	C₄×C₄₁	—	4	2	no	—
182	C₄×C₄₁	—	4	2	no	—
183	C₄×C₄₁	—	4	2	no	—
184	C₄×C₄₁	C₂×AGL(1,ℤ/8)	1	2	yes	—
185	C₄×C₄₁	#576	1	2	yes	—
186	#3399	C₂×C₄₁	1	2	yes	complemented
187	#3274	C₂×C₄₁	1	2	yes	complemented
188	#1712	C₂×C₄₁	1	1	yes	characteristic, complemented
189	#1688	C₂×C₄₁	1	2	yes	complemented
190	#1687	C₂×C₄₁	1	2	yes	complemented
191	#1621	C₂×C₄₁	1	2	yes	complemented
192	#1620	C₂×C₄₁	1	1	yes	characteristic, complemented
193	#1619	C₂×C₄₁	1	1	yes	characteristic, complemented
194	#1590	C₂×C₄₁	1	2	yes	complemented
195	C₂×C₄₁	—	8	2	no	—
196	C₂×C₄₁	—	16	2	no	—
197	C₂×C₄₁	—	16	1	no	—
198	C₂×C₄₁	—	16	1	no	—
199	C₂×C₄₁	#3274	1	2	yes	—
200	C₂×C₄₁	#3292	1	1	yes	characteristic
201	C₂×AGL(1,ℤ/8)	—	2	2	no	—
202	#559	C₂²×C₄₁	1	1	yes	characteristic, complemented
203	#550	C₂²×C₄₁	1	2	yes	—
204	D₄²	C₂²×C₄₁	1	1	yes	characteristic
205	#496	—	2	2	no	—
206	#493	C₂²×C₄₁	1	2	yes	—
207	#493	C₂²×C₄₁	1	1	yes	characteristic
208	#493	C₂²×C₄₁	1	2	yes	complemented
209	#493	C₂²×C₄₁	1	1	yes	characteristic, complemented
210	#469	—	2	2	no	—
211	#463	—	2	2	no	—
212	#460	C₂²×C₄₁	1	2	yes	—
213	#460	C₂²×C₄₁	1	2	yes	complemented
214	#459	—	2	2	no	—
215	#459	C₂²×C₄₁	1	2	yes	—
216	#459	C₂²×C₄₁	1	2	yes	—
217	#449	—	2	2	no	—
218	#447	—	2	2	no	—
219	#446	C₂²×C₄₁	1	2	yes	complemented
220	#442	—	2	2	no	—
221	C₄×SD₁₆	C₂²×C₄₁	1	2	yes	—
222	#436	C₂²×C₄₁	1	2	yes	—
223	#334	C₂²×C₄₁	1	2	yes	complemented
224	#331	C₂²×C₄₁	1	1	yes	characteristic
225	#331	C₂²×C₄₁	1	1	yes	characteristic, complemented
226	#331	C₂²×C₄₁	1	2	yes	complemented
227	Q₈⋊C₈	C₂²×C₄₁	1	2	yes	complemented
228	D₄⋊C₈	C₂²×C₄₁	1	2	yes	—
229	C₈²	C₂²×C₄₁	1	1	yes	characteristic, complemented
230	C₄₁	#20310	1	1	yes	characteristic, direct product factor, Sylow
231	C₂×#41	—	2	2	no	—
232	C₂²×D₄	—	2	2	no	—
233	AGL(1,ℤ/8)	—	4	8	no	—
234	C₂×SD₁₆	—	2	2	no	—
235	C₂×SD₁₆	—	2	2	no	—
236	C₂×SD₁₆	D₄×C₄₁	1	2	yes	—
237	C₂×D₈	—	2	2	no	—
238	C₂×D₈	—	2	2	no	—
239	C₂×D₈	—	2	2	no	—
240	C₂×D₈	—	2	2	no	—
241	C₂×D₈	—	2	2	no	—
242	C₂×D₈	—	2	2	no	—
243	C₂×D₈	—	4	1	no	—
244	C₂×D₈	—	4	1	no	—
245	C₂×M₁₆	—	2	2	no	—
246	#127	—	2	2	no	—
247	#127	C₂³×C₄₁	1	1	yes	characteristic
248	#127	C₂³×C₄₁	1	2	yes	—
249	#127	C₂³×C₄₁	1	1	yes	characteristic
250	#124	—	2	2	no	—
251	#123	—	4	1	no	—
252	#121	—	2	2	no	—
253	#121	—	2	2	no	—
254	#121	—	4	2	no	—
255	#120	—	4	1	no	—
256	C₄×Q₈	C₂³×C₄₁	1	2	yes	—
257	C₄×D₄	—	2	2	no	—
258	C₄×D₄	—	2	2	no	—
259	C₄×D₄	C₂³×C₄₁	1	2	yes	—
260	#106	D₄×C₄₁	1	2	yes	—
261	C₄⋊C₈	—	2	2	no	—
262	C₄⋊C₈	C₂³×C₄₁	1	2	yes	—
263	C₄⋊C₈	C₂³×C₄₁	1	2	yes	—
264	#103	D₄×C₄₁	1	2	yes	—
265	#102	—	2	2	no	—
266	#102	—	2	2	no	—
267	#102	—	2	2	no	—
268	#102	—	2	2	no	—
269	#102	D₄×C₄₁	1	2	yes	—
270	C₂²⋊C₈	—	2	2	no	—
271	#97	—	2	2	no	—
272	C₄×C₈	C₂³×C₄₁	1	1	yes	characteristic
273	C₄×C₈	C₂³×C₄₁	1	2	yes	—
274	C₂⁴	—	4	1	no	—
275	#41	—	4	4	no	—
276	#41	—	8	2	no	—
277	C₂×Q₈	C₂×D₄×C₄₁	1	2	yes	—
278	C₂×D₄	—	2	2	no	—
279	C₂×D₄	—	2	2	no	—
280	C₂×D₄	—	2	2	no	—
281	C₂×D₄	—	2	2	no	—
282	C₂×D₄	—	2	1	no	—
283	C₂×D₄	—	2	2	no	—
284	C₂×D₄	—	2	1	no	—
285	C₂×D₄	—	4	2	no	—
286	C₂×D₄	—	4	2	no	—
287	C₂×D₄	—	4	2	no	—
288	C₂×D₄	—	4	4	no	—
289	C₂×D₄	—	8	2	no	—
290	C₂×D₄	C₂×D₄×C₄₁	1	2	yes	—
291	C₂²×C₄	—	2	2	no	—
292	C₂²×C₄	—	4	2	no	—
293	C₂²×C₄	—	4	1	no	—
294	SD₁₆	—	2	4	no	—
295	SD₁₆	—	4	4	no	—
296	SD₁₆	—	8	2	no	—
297	D₈	—	4	4	no	—
298	D₈	—	4	4	no	—
299	D₈	—	4	4	no	—
300	D₈	—	8	2	no	—
301	D₈	—	8	2	no	—
302	D₈	—	8	2	no	—
303	D₈	—	8	2	no	—
304	D₈	—	8	2	no	—
305	M₁₆	—	4	4	no	—
306	C₂×C₈	—	2	1	no	—
307	C₂×C₈	—	2	2	no	—
308	C₂×C₈	—	2	2	no	—
309	C₂×C₈	C₂×D₄×C₄₁	1	2	yes	—
310	C₂×C₈	C₂×D₄×C₄₁	1	2	yes	—
311	C₄⋊C₄	—	2	2	no	—
312	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
313	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
314	C₂²⋊C₄	—	2	2	no	—
315	C₂²⋊C₄	—	4	2	no	—
316	C₂²⋊C₄	—	4	2	no	—
317	C₂²⋊C₄	—	4	1	no	—
318	C₂²⋊C₄	—	4	1	no	—
319	C₄²	—	2	2	no	—
320	C₄²	C₂⁴×C₄₁	1	1	yes	characteristic
321	C₂³	—	2	2	no	—
322	C₂³	—	4	1	no	—
323	C₂³	—	4	2	no	—
324	C₂³	—	4	1	no	—
325	C₂³	—	8	4	no	—
326	C₂³	—	16	1	no	—
327	Q₈	—	2	2	no	—
328	Q₈	—	2	2	no	—
329	D₄	—	2	2	no	—
330	D₄	—	2	2	no	—
331	D₄	—	4	2	no	—
332	D₄	—	4	2	no	—
333	D₄	—	4	2	no	—
334	D₄	—	4	2	no	—
335	D₄	—	4	2	no	—
336	D₄	—	4	2	no	—
337	D₄	—	4	2	no	—
338	D₄	—	4	2	no	—
339	D₄	—	8	1	no	—
340	D₄	—	8	2	no	—
341	D₄	—	8	1	no	—
342	D₄	—	8	4	no	—
343	D₄	—	8	4	no	—
344	D₄	—	16	2	no	—
345	C₂×C₄	—	2	2	no	—
346	C₂×C₄	—	2	2	no	—
347	C₂×C₄	—	2	2	no	—
348	C₂×C₄	—	4	2	no	—
349	C₂×C₄	—	4	2	no	—
350	C₂×C₄	—	8	4	no	—
351	C₂×C₄	—	16	1	no	—
352	C₂×C₄	C₂²×D₄×C₄₁	1	2	yes	—
353	C₂×C₄	H(5,𝔽₂)×C₄₁	1	1	yes	characteristic
354	C₈	—	2	2	no	—
355	C₈	—	2	2	no	—
356	C₈	—	4	2	no	—
357	C₈	—	4	2	no	—
358	C₈	AGL(1,ℤ/8)×C₄₁	1	4	yes	complemented
359	C₂²	—	4	2	no	—
360	C₂²	—	4	2	no	—
361	C₂²	—	4	2	no	—
362	C₂²	—	8	1	no	—
363	C₂²	—	8	2	no	—
364	C₂²	—	8	1	no	—
365	C₂²	—	8	2	no	—
366	C₂²	—	8	2	no	—
367	C₂²	—	8	2	no	—
368	C₂²	—	8	2	no	—
369	C₂²	—	16	4	no	—
370	C₂²	D₄²×C₄₁	1	1	yes	characteristic
371	C₄	—	2	1	no	—
372	C₄	—	4	2	no	—
373	C₄	—	4	2	no	—
374	C₄	—	4	2	no	—
375	C₄	C₂×AGL(1,ℤ/8)×C₄₁	1	2	yes	—
376	C₄	C₄₁×#576	1	2	yes	—
377	C₂	—	8	2	no	—
378	C₂	—	16	1	no	—
379	C₂	—	16	1	no	—
380	C₂	—	16	2	no	—
381	C₂	C₄₁×#3274	1	2	yes	—
382	C₂	C₄₁×#3292	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₄₁	D₄²
commutator, Frattini, cosocle	C₄²	C₂⁴×C₄₁
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×#3399	C₂	semidirect
2. C₄₁×#3274	C₂	semidirect
3. C₄₁×#1712	C₂	semidirect
4. C₄₁×#1688	C₂	semidirect
5. C₄₁×#1687	C₂	semidirect
6. C₄₁×#1621	C₂	semidirect
7. C₄₁×#1620	C₂	semidirect
8. C₄₁×#1619	C₂	semidirect
9. C₄₁×#1590	C₂	semidirect
11. C₄₁×#559	C₂²	semidirect
17. C₄₁×#493	C₂²	semidirect
18. C₄₁×#493	C₂²	semidirect
22. C₄₁×#460	C₂²	semidirect
28. C₄₁×#446	C₂²	semidirect
32. C₄₁×#334	C₂²	semidirect
34. C₄₁×#331	C₂²	semidirect
35. C₄₁×#331	C₂²	semidirect
36. C₄₁×Q₈⋊C₈	C₂²	semidirect
38. C₈²×C₄₁	C₂²	semidirect
166. C₈×C₄₁	AGL(1,ℤ/8)	semidirect
167. #20310	C₄₁	direct (N × H)
186. #3399	C₂×C₄₁	semidirect
187. #3274	C₂×C₄₁	semidirect
188. #1712	C₂×C₄₁	semidirect
189. #1688	C₂×C₄₁	semidirect
190. #1687	C₂×C₄₁	semidirect
191. #1621	C₂×C₄₁	semidirect
192. #1620	C₂×C₄₁	semidirect
193. #1619	C₂×C₄₁	semidirect
194. #1590	C₂×C₄₁	semidirect
202. #559	C₂²×C₄₁	semidirect
208. #493	C₂²×C₄₁	semidirect
209. #493	C₂²×C₄₁	semidirect
213. #460	C₂²×C₄₁	semidirect
219. #446	C₂²×C₄₁	semidirect
223. #334	C₂²×C₄₁	semidirect
225. #331	C₂²×C₄₁	semidirect
226. #331	C₂²×C₄₁	semidirect
227. Q₈⋊C₈	C₂²×C₄₁	semidirect
229. C₈²	C₂²×C₄₁	semidirect
230. C₄₁	#20310	direct (N × H)
358. C₈	AGL(1,ℤ/8)×C₄₁	semidirect

Maximal subgroups

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

subgroup	index
C₄₁×#3399	2
C₄₁×#3274	2
C₄₁×#1712	2
C₄₁×#1688	2
C₄₁×#1687	2
C₄₁×#1621	2
C₄₁×#1620	2
C₄₁×#1619	2
C₄₁×#1590	2
#20310	41

Subgroups — C41×#20310 #23796511

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#20310 #23796511