Subgroups — C₄₁×#33788 #23809989

Order 10496.

594 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₁×#3177	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄₁×#3155	C₂	1	1	yes	maximal, characteristic
3	C₄₁×#2251	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₁×#2248	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₁×#2244	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄₁×#2242	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₁×#2211	C₂	1	2	yes	maximal, complemented
8	C₄₁×#2207	C₂	1	2	yes	maximal, complemented
9	C₄₁×#2189	C₂	1	2	yes	maximal, complemented
10	C₄₁×#2187	C₂	1	2	yes	maximal, complemented
11	C₄₁×#2164	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×AGL(1,ℤ/8)×C₄₁	—	2	1	no	—
13	C₂×#135×C₄₁	C₂²	1	1	yes	characteristic
14	C₂²×D₈×C₄₁	C₂²	1	1	yes	characteristic
15	C₄₁×#541	—	2	1	no	—
16	C₄₁×#535	—	2	1	no	—
17	C₂×Q₃₂×C₄₁	C₂²	1	2	yes	complemented
18	C₂×SD₃₂×C₄₁	C₂²	1	2	yes	—
19	C₂×SD₃₂×C₄₁	C₂²	1	2	yes	—
20	C₂×SD₃₂×C₄₁	C₂²	1	2	yes	complemented
21	C₄₁×#499	C₂²	1	1	yes	characteristic, complemented
22	C₄₁×#496	—	2	1	no	—
23	C₄₁×#496	—	2	1	no	—
24	C₄₁×#495	C₂²	1	1	yes	characteristic
25	C₄₁×#495	C₂²	1	1	yes	characteristic
26	C₄₁×#494	C₂²	1	1	yes	characteristic, complemented
27	C₄₁×#493	C₂²	1	1	yes	characteristic
28	C₄₁×#493	C₂²	1	1	yes	characteristic
29	C₄₁×#491	—	2	1	no	—
30	C₄₁×#470	—	2	1	no	—
31	C₄₁×#467	C₂²	1	2	yes	—
32	C₄₁×#441	—	2	1	no	—
33	C₄×Q₁₆×C₄₁	C₂²	1	2	yes	complemented
34	C₄₁×#405	C₂²	1	1	yes	characteristic
35	C₄₁×C₄⋊C₁₆	C₂²	1	2	yes	complemented
36	C₄₁×#358	C₂²	1	2	yes	complemented
37	C₄₁×#357	C₂²	1	2	yes	—
38	C₄₁×#357	C₂²	1	2	yes	—
39	C₄₁×#357	C₂²	1	2	yes	complemented
40	C₄₁×C₂²⋊C₁₆	C₂²	1	2	yes	—
41	C₄₁×#346	C₂²	1	1	yes	characteristic, complemented
42	C₄×C₁₆×C₄₁	C₂²	1	1	yes	characteristic, complemented
43	C₂×#41×C₄₁	—	2	1	no	—
44	C₂²×D₄×C₄₁	—	2	1	no	—
45	AGL(1,ℤ/8)×C₄₁	—	4	4	no	—
46	#135×C₄₁	—	4	2	no	—
47	C₂×Q₁₆×C₄₁	—	2	1	no	—
48	C₂×Q₁₆×C₄₁	C₂³	1	2	yes	—
49	C₂×Q₁₆×C₄₁	C₂³	1	1	yes	characteristic
50	C₂×SD₁₆×C₄₁	—	2	1	no	—
51	C₂×SD₁₆×C₄₁	—	2	1	no	—
52	C₂×SD₁₆×C₄₁	—	2	1	no	—
53	C₂×D₈×C₄₁	—	2	1	no	—
54	C₂×D₈×C₄₁	—	2	1	no	—
55	C₂×D₈×C₄₁	—	2	1	no	—
56	C₂×D₈×C₄₁	—	4	2	no	—
57	C₂×D₈×C₄₁	C₂³	1	1	yes	characteristic
58	C₂×D₈×C₄₁	C₂³	1	1	yes	characteristic
59	C₂×D₈×C₄₁	C₂³	1	1	yes	characteristic
60	C₂×M₁₆×C₄₁	D₄	1	1	yes	characteristic
61	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
62	C₄⋊Q₈×C₄₁	—	2	1	no	—
63	#127×C₄₁	—	2	1	no	—
64	#127×C₄₁	—	2	1	no	—
65	#126×C₄₁	—	4	2	no	—
66	#125×C₄₁	—	2	1	no	—
67	#125×C₄₁	—	4	2	no	—
68	#124×C₄₁	—	2	1	no	—
69	#124×C₄₁	—	2	1	no	—
70	C₂²⋊Q₈×C₄₁	—	2	2	no	—
71	#121×C₄₁	—	4	2	no	—
72	#120×C₄₁	—	4	2	no	—
73	C₄×Q₈×C₄₁	—	2	2	no	—
74	#117×C₄₁	D₄	1	1	yes	characteristic
75	Q₃₂×C₄₁	—	4	2	no	—
76	SD₃₂×C₄₁	—	4	2	no	—
77	SD₃₂×C₄₁	—	4	2	no	—
78	SD₃₂×C₄₁	—	4	2	no	—
79	C₂×C₁₆×C₄₁	C₂³	1	2	yes	—
80	C₂×C₁₆×C₄₁	C₂³	1	2	yes	—
81	#107×C₄₁	C₂³	1	2	yes	—
82	#106×C₄₁	—	2	1	no	—
83	#103×C₄₁	—	2	2	no	—
84	#103×C₄₁	—	2	2	no	—
85	#97×C₄₁	D₄	1	1	yes	characteristic
86	#97×C₄₁	D₄	1	1	yes	characteristic
87	C₄×C₈×C₄₁	C₂³	1	1	yes	characteristic
88	C₄×C₈×C₄₁	C₂³	1	1	yes	characteristic
89	C₂⁴×C₄₁	—	4	1	no	—
90	#41×C₄₁	—	4	2	no	—
91	#41×C₄₁	—	4	2	no	—
92	C₂×Q₈×C₄₁	—	2	2	no	—
93	C₂×Q₈×C₄₁	—	2	1	no	—
94	C₂×D₄×C₄₁	—	2	1	no	—
95	C₂×D₄×C₄₁	—	2	1	no	—
96	C₂×D₄×C₄₁	—	2	1	no	—
97	C₂×D₄×C₄₁	—	4	2	no	—
98	C₂×D₄×C₄₁	—	4	2	no	—
99	C₂×D₄×C₄₁	—	4	1	no	—
100	C₂×D₄×C₄₁	—	4	1	no	—
101	C₂×D₄×C₄₁	—	4	2	no	—
102	C₂×D₄×C₄₁	—	4	2	no	—
103	C₂²×C₄×C₄₁	—	4	1	no	—
104	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
105	Q₁₆×C₄₁	—	2	2	no	—
106	Q₁₆×C₄₁	—	2	2	no	—
107	Q₁₆×C₄₁	—	2	2	no	—
108	Q₁₆×C₄₁	—	4	2	no	—
109	SD₁₆×C₄₁	—	4	2	no	—
110	SD₁₆×C₄₁	—	4	2	no	—
111	SD₁₆×C₄₁	—	4	2	no	—
112	D₈×C₄₁	—	2	2	no	—
113	D₈×C₄₁	—	2	2	no	—
114	D₈×C₄₁	—	2	2	no	—
115	D₈×C₄₁	—	4	2	no	—
116	D₈×C₄₁	—	4	2	no	—
117	D₈×C₄₁	—	4	2	no	—
118	M₁₆×C₄₁	—	2	2	no	—
119	C₂×C₈×C₄₁	—	2	2	no	—
120	C₂×C₈×C₄₁	C₂×D₄	1	1	yes	characteristic
121	C₂×C₈×C₄₁	C₂×D₄	1	1	yes	characteristic
122	C₂×C₈×C₄₁	C₂×D₄	1	1	yes	characteristic
123	C₂×C₈×C₄₁	C₂⁴	1	1	yes	characteristic
124	C₄⋊C₄×C₄₁	—	2	2	no	—
125	C₄⋊C₄×C₄₁	—	4	2	no	—
126	C₄⋊C₄×C₄₁	—	4	2	no	—
127	C₄⋊C₄×C₄₁	—	4	2	no	—
128	C₄⋊C₄×C₄₁	—	4	2	no	—
129	C₄⋊C₄×C₄₁	D₈	1	2	yes	—
130	C₂²⋊C₄×C₄₁	—	4	2	no	—
131	C₂²⋊C₄×C₄₁	—	4	2	no	—
132	C₂²⋊C₄×C₄₁	—	4	2	no	—
133	C₂²⋊C₄×C₄₁	D₈	1	2	yes	—
134	C₄²×C₄₁	—	4	2	no	—
135	C₄²×C₄₁	C₂×D₄	1	1	yes	characteristic
136	C₄²×C₄₁	C₂×D₄	1	1	yes	characteristic
137	C₁₆×C₄₁	—	2	2	no	—
138	C₁₆×C₄₁	—	2	2	no	—
139	C₂³×C₄₁	—	4	1	no	—
140	C₂³×C₄₁	—	4	1	no	—
141	C₂³×C₄₁	—	4	1	no	—
142	C₂³×C₄₁	—	8	2	no	—
143	C₂³×C₄₁	—	16	2	no	—
144	C₂³×C₄₁	C₂×D₈	1	1	yes	characteristic
145	Q₈×C₄₁	—	4	1	no	—
146	Q₈×C₄₁	—	4	2	no	—
147	Q₈×C₄₁	—	4	1	no	—
148	Q₈×C₄₁	—	4	2	no	—
149	D₄×C₄₁	—	4	1	no	—
150	D₄×C₄₁	—	4	1	no	—
151	D₄×C₄₁	—	4	1	no	—
152	D₄×C₄₁	—	4	1	no	—
153	D₄×C₄₁	—	4	1	no	—
154	D₄×C₄₁	—	4	1	no	—
155	D₄×C₄₁	—	8	2	no	—
156	D₄×C₄₁	—	8	2	no	—
157	D₄×C₄₁	—	16	2	no	—
158	D₄×C₄₁	—	16	2	no	—
159	C₂×C₄×C₄₁	—	2	1	no	—
160	C₂×C₄×C₄₁	—	2	1	no	—
161	C₂×C₄×C₄₁	—	4	2	no	—
162	C₂×C₄×C₄₁	—	4	2	no	—
163	C₂×C₄×C₄₁	—	4	1	no	—
164	C₂×C₄×C₄₁	—	8	2	no	—
165	C₂×C₄×C₄₁	C₂×D₈	1	2	yes	—
166	C₂×C₄×C₄₁	C₂×D₈	1	2	yes	—
167	C₂×C₄×C₄₁	C₂×D₈	1	1	yes	characteristic
168	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
169	C₈×C₄₁	—	2	1	no	—
170	C₈×C₄₁	—	2	1	no	—
171	C₈×C₄₁	AGL(1,ℤ/8)	1	2	yes	—
172	C₈×C₄₁	H(5,𝔽₂)	1	2	yes	—
173	#33788	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
174	C₂²×C₄₁	—	2	2	no	—
175	C₂²×C₄₁	—	2	1	no	—
176	C₂²×C₄₁	—	8	2	no	—
177	C₂²×C₄₁	—	8	2	no	—
178	C₂²×C₄₁	—	8	2	no	—
179	C₂²×C₄₁	—	8	1	no	—
180	C₂²×C₄₁	—	8	1	no	—
181	C₂²×C₄₁	—	8	1	no	—
182	C₂²×C₄₁	—	16	4	no	—
183	C₂²×C₄₁	C₂²×D₈	1	1	yes	characteristic
184	C₄×C₄₁	—	2	2	no	—
185	C₄×C₄₁	—	2	2	no	—
186	C₄×C₄₁	—	2	1	no	—
187	C₄×C₄₁	—	8	2	no	—
188	C₄×C₄₁	—	8	1	no	—
189	C₄×C₄₁	—	8	2	no	—
190	C₄×C₄₁	#535	1	1	yes	characteristic
191	C₄×C₄₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
192	#3177	C₂×C₄₁	1	1	yes	characteristic, complemented
193	#3155	C₂×C₄₁	1	1	yes	characteristic
194	#2251	C₂×C₄₁	1	1	yes	characteristic, complemented
195	#2248	C₂×C₄₁	1	1	yes	characteristic, complemented
196	#2244	C₂×C₄₁	1	1	yes	characteristic, complemented
197	#2242	C₂×C₄₁	1	1	yes	characteristic, complemented
198	#2211	C₂×C₄₁	1	2	yes	complemented
199	#2207	C₂×C₄₁	1	2	yes	complemented
200	#2189	C₂×C₄₁	1	2	yes	complemented
201	#2187	C₂×C₄₁	1	2	yes	complemented
202	#2164	C₂×C₄₁	1	1	yes	characteristic, complemented
203	C₂×C₄₁	—	4	1	no	—
204	C₂×C₄₁	—	16	1	no	—
205	C₂×C₄₁	—	16	1	no	—
206	C₂×C₄₁	—	16	1	no	—
207	C₂×C₄₁	#3205	1	1	yes	characteristic
208	C₂×C₄₁	#3416	1	2	yes	—
209	C₂×AGL(1,ℤ/8)	—	2	1	no	—
210	C₂×#135	C₂²×C₄₁	1	1	yes	characteristic
211	C₂²×D₈	C₂²×C₄₁	1	1	yes	characteristic
212	#541	—	2	1	no	—
213	#535	—	2	1	no	—
214	C₂×Q₃₂	C₂²×C₄₁	1	2	yes	complemented
215	C₂×SD₃₂	C₂²×C₄₁	1	2	yes	—
216	C₂×SD₃₂	C₂²×C₄₁	1	2	yes	—
217	C₂×SD₃₂	C₂²×C₄₁	1	2	yes	complemented
218	#499	C₂²×C₄₁	1	1	yes	characteristic, complemented
219	#496	—	2	1	no	—
220	#496	—	2	1	no	—
221	#495	C₂²×C₄₁	1	1	yes	characteristic
222	#495	C₂²×C₄₁	1	1	yes	characteristic
223	#494	C₂²×C₄₁	1	1	yes	characteristic, complemented
224	#493	C₂²×C₄₁	1	1	yes	characteristic
225	#493	C₂²×C₄₁	1	1	yes	characteristic
226	#491	—	2	1	no	—
227	#470	—	2	1	no	—
228	#467	C₂²×C₄₁	1	2	yes	—
229	#441	—	2	1	no	—
230	C₄×Q₁₆	C₂²×C₄₁	1	2	yes	complemented
231	#405	C₂²×C₄₁	1	1	yes	characteristic
232	C₄⋊C₁₆	C₂²×C₄₁	1	2	yes	complemented
233	#358	C₂²×C₄₁	1	2	yes	complemented
234	#357	C₂²×C₄₁	1	2	yes	—
235	#357	C₂²×C₄₁	1	2	yes	—
236	#357	C₂²×C₄₁	1	2	yes	complemented
237	C₂²⋊C₁₆	C₂²×C₄₁	1	2	yes	—
238	#346	C₂²×C₄₁	1	1	yes	characteristic, complemented
239	C₄×C₁₆	C₂²×C₄₁	1	1	yes	characteristic, complemented
240	C₄₁	#33788	1	1	yes	characteristic, direct product factor, Sylow
241	C₂×#41	—	2	1	no	—
242	C₂²×D₄	—	2	1	no	—
243	AGL(1,ℤ/8)	—	4	4	no	—
244	#135	—	4	2	no	—
245	C₂×Q₁₆	—	2	1	no	—
246	C₂×Q₁₆	C₂³×C₄₁	1	1	yes	characteristic
247	C₂×Q₁₆	C₂³×C₄₁	1	2	yes	—
248	C₂×SD₁₆	—	2	1	no	—
249	C₂×SD₁₆	—	2	1	no	—
250	C₂×SD₁₆	—	2	1	no	—
251	C₂×D₈	—	2	1	no	—
252	C₂×D₈	—	2	1	no	—
253	C₂×D₈	—	2	1	no	—
254	C₂×D₈	—	4	2	no	—
255	C₂×D₈	C₂³×C₄₁	1	1	yes	characteristic
256	C₂×D₈	C₂³×C₄₁	1	1	yes	characteristic
257	C₂×D₈	C₂³×C₄₁	1	1	yes	characteristic
258	C₂×M₁₆	D₄×C₄₁	1	1	yes	characteristic
259	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
260	C₄⋊Q₈	—	2	1	no	—
261	#127	—	2	1	no	—
262	#127	—	2	1	no	—
263	#126	—	4	2	no	—
264	#125	—	2	1	no	—
265	#125	—	4	2	no	—
266	#124	—	2	1	no	—
267	#124	—	2	1	no	—
268	C₂²⋊Q₈	—	2	2	no	—
269	#121	—	4	2	no	—
270	#120	—	4	2	no	—
271	C₄×Q₈	—	2	2	no	—
272	#117	D₄×C₄₁	1	1	yes	characteristic
273	Q₃₂	—	4	2	no	—
274	SD₃₂	—	4	2	no	—
275	SD₃₂	—	4	2	no	—
276	SD₃₂	—	4	2	no	—
277	C₂×C₁₆	C₂³×C₄₁	1	2	yes	—
278	C₂×C₁₆	C₂³×C₄₁	1	2	yes	—
279	#107	C₂³×C₄₁	1	2	yes	—
280	#106	—	2	1	no	—
281	#103	—	2	2	no	—
282	#103	—	2	2	no	—
283	#97	D₄×C₄₁	1	1	yes	characteristic
284	#97	D₄×C₄₁	1	1	yes	characteristic
285	C₄×C₈	C₂³×C₄₁	1	1	yes	characteristic
286	C₄×C₈	C₂³×C₄₁	1	1	yes	characteristic
287	C₂⁴	—	4	1	no	—
288	#41	—	4	2	no	—
289	#41	—	4	2	no	—
290	C₂×Q₈	—	2	2	no	—
291	C₂×Q₈	—	2	1	no	—
292	C₂×D₄	—	2	1	no	—
293	C₂×D₄	—	2	1	no	—
294	C₂×D₄	—	2	1	no	—
295	C₂×D₄	—	4	2	no	—
296	C₂×D₄	—	4	2	no	—
297	C₂×D₄	—	4	1	no	—
298	C₂×D₄	—	4	1	no	—
299	C₂×D₄	—	4	2	no	—
300	C₂×D₄	—	4	2	no	—
301	C₂²×C₄	—	4	1	no	—
302	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
303	Q₁₆	—	2	2	no	—
304	Q₁₆	—	2	2	no	—
305	Q₁₆	—	2	2	no	—
306	Q₁₆	—	4	2	no	—
307	SD₁₆	—	4	2	no	—
308	SD₁₆	—	4	2	no	—
309	SD₁₆	—	4	2	no	—
310	D₈	—	2	2	no	—
311	D₈	—	2	2	no	—
312	D₈	—	2	2	no	—
313	D₈	—	4	2	no	—
314	D₈	—	4	2	no	—
315	D₈	—	4	2	no	—
316	M₁₆	—	2	2	no	—
317	C₂×C₈	—	2	2	no	—
318	C₂×C₈	C₂×D₄×C₄₁	1	1	yes	characteristic
319	C₂×C₈	C₂×D₄×C₄₁	1	1	yes	characteristic
320	C₂×C₈	C₂×D₄×C₄₁	1	1	yes	characteristic
321	C₂×C₈	C₂⁴×C₄₁	1	1	yes	characteristic
322	C₄⋊C₄	—	2	2	no	—
323	C₄⋊C₄	—	4	2	no	—
324	C₄⋊C₄	—	4	2	no	—
325	C₄⋊C₄	—	4	2	no	—
326	C₄⋊C₄	—	4	2	no	—
327	C₄⋊C₄	D₈×C₄₁	1	2	yes	—
328	C₂²⋊C₄	—	4	2	no	—
329	C₂²⋊C₄	—	4	2	no	—
330	C₂²⋊C₄	—	4	2	no	—
331	C₂²⋊C₄	D₈×C₄₁	1	2	yes	—
332	C₄²	—	4	2	no	—
333	C₄²	C₂×D₄×C₄₁	1	1	yes	characteristic
334	C₄²	C₂×D₄×C₄₁	1	1	yes	characteristic
335	C₁₆	—	2	2	no	—
336	C₁₆	—	2	2	no	—
337	C₂³	—	4	1	no	—
338	C₂³	—	4	1	no	—
339	C₂³	—	4	1	no	—
340	C₂³	—	8	2	no	—
341	C₂³	—	16	2	no	—
342	C₂³	C₂×D₈×C₄₁	1	1	yes	characteristic
343	Q₈	—	4	1	no	—
344	Q₈	—	4	2	no	—
345	Q₈	—	4	1	no	—
346	Q₈	—	4	2	no	—
347	D₄	—	4	1	no	—
348	D₄	—	4	1	no	—
349	D₄	—	4	1	no	—
350	D₄	—	4	1	no	—
351	D₄	—	4	1	no	—
352	D₄	—	4	1	no	—
353	D₄	—	8	2	no	—
354	D₄	—	8	2	no	—
355	D₄	—	16	2	no	—
356	D₄	—	16	2	no	—
357	C₂×C₄	—	2	1	no	—
358	C₂×C₄	—	2	1	no	—
359	C₂×C₄	—	4	2	no	—
360	C₂×C₄	—	4	2	no	—
361	C₂×C₄	—	4	1	no	—
362	C₂×C₄	—	8	2	no	—
363	C₂×C₄	C₂×D₈×C₄₁	1	2	yes	—
364	C₂×C₄	C₂×D₈×C₄₁	1	2	yes	—
365	C₂×C₄	C₂×D₈×C₄₁	1	1	yes	characteristic
366	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
367	C₈	—	2	1	no	—
368	C₈	—	2	1	no	—
369	C₈	AGL(1,ℤ/8)×C₄₁	1	2	yes	—
370	C₈	H(5,𝔽₂)×C₄₁	1	2	yes	—
371	C₂²	—	2	2	no	—
372	C₂²	—	2	1	no	—
373	C₂²	—	8	2	no	—
374	C₂²	—	8	2	no	—
375	C₂²	—	8	2	no	—
376	C₂²	—	8	1	no	—
377	C₂²	—	8	1	no	—
378	C₂²	—	8	1	no	—
379	C₂²	—	16	4	no	—
380	C₂²	C₂²×D₈×C₄₁	1	1	yes	characteristic
381	C₄	—	2	2	no	—
382	C₄	—	2	2	no	—
383	C₄	—	2	1	no	—
384	C₄	—	8	2	no	—
385	C₄	—	8	1	no	—
386	C₄	—	8	2	no	—
387	C₄	C₄₁×#535	1	1	yes	characteristic
388	C₄	C₂×AGL(1,ℤ/8)×C₄₁	1	1	yes	characteristic
389	C₂	—	4	1	no	—
390	C₂	—	16	1	no	—
391	C₂	—	16	1	no	—
392	C₂	—	16	1	no	—
393	C₂	C₄₁×#3205	1	1	yes	characteristic
394	C₂	C₄₁×#3416	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₄₁	C₂²×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₄₁
prime radical	C₄₁×#3155	C₂
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄₁ ◁ #117×C₄₁ ◁ C₄₁×#405 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₄₁×#3177	C₂	semidirect
3. C₄₁×#2251	C₂	semidirect
4. C₄₁×#2248	C₂	semidirect
5. C₄₁×#2244	C₂	semidirect
6. C₄₁×#2242	C₂	semidirect
7. C₄₁×#2211	C₂	semidirect
8. C₄₁×#2207	C₂	semidirect
9. C₄₁×#2189	C₂	semidirect
10. C₄₁×#2187	C₂	semidirect
11. C₄₁×#2164	C₂	semidirect
17. C₂×Q₃₂×C₄₁	C₂²	semidirect
20. C₂×SD₃₂×C₄₁	C₂²	semidirect
21. C₄₁×#499	C₂²	semidirect
26. C₄₁×#494	C₂²	semidirect
33. C₄×Q₁₆×C₄₁	C₂²	semidirect
35. C₄₁×C₄⋊C₁₆	C₂²	semidirect
36. C₄₁×#358	C₂²	semidirect
39. C₄₁×#357	C₂²	semidirect
41. C₄₁×#346	C₂²	semidirect
42. C₄×C₁₆×C₄₁	C₂²	semidirect
173. #33788	C₄₁	direct (N × H)
192. #3177	C₂×C₄₁	semidirect
194. #2251	C₂×C₄₁	semidirect
195. #2248	C₂×C₄₁	semidirect
196. #2244	C₂×C₄₁	semidirect
197. #2242	C₂×C₄₁	semidirect
198. #2211	C₂×C₄₁	semidirect
199. #2207	C₂×C₄₁	semidirect
200. #2189	C₂×C₄₁	semidirect
201. #2187	C₂×C₄₁	semidirect
202. #2164	C₂×C₄₁	semidirect
214. C₂×Q₃₂	C₂²×C₄₁	semidirect
217. C₂×SD₃₂	C₂²×C₄₁	semidirect
218. #499	C₂²×C₄₁	semidirect
223. #494	C₂²×C₄₁	semidirect
230. C₄×Q₁₆	C₂²×C₄₁	semidirect
232. C₄⋊C₁₆	C₂²×C₄₁	semidirect
233. #358	C₂²×C₄₁	semidirect
236. #357	C₂²×C₄₁	semidirect
238. #346	C₂²×C₄₁	semidirect
239. C₄×C₁₆	C₂²×C₄₁	semidirect
240. C₄₁	#33788	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×#3177	2
C₄₁×#3155	2
C₄₁×#2251	2
C₄₁×#2248	2
C₄₁×#2244	2
C₄₁×#2242	2
C₄₁×#2211	2
C₄₁×#2207	2
C₄₁×#2189	2
C₄₁×#2187	2
C₄₁×#2164	2
#33788	41

Subgroups — C41×#33788 #23809989

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#33788 #23809989