Subgroups — C₄₁×#21972 #23798173

Order 10496.

946 conjugacy classes of subgroups.

The subgroup lattice has 328 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₁×#431	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₄⋊C₈×C₄₁	C₂	1	1	yes	maximal, characteristic
3	C₄×#117×C₄₁	C₂	1	1	yes	maximal, characteristic
4	C₄₁×#1939	C₂	1	4	yes	maximal, complemented
5	C₄₁×#1850	C₂	1	4	yes	maximal
6	C₄₁×#1842	C₂	1	2	yes	maximal, complemented
7	C₄₁×#1831	C₂	1	2	yes	maximal, complemented
8	C₂³×C₈×C₄₁	C₂²	1	2	yes	—
9	C₂×#117×C₄₁	C₄	1	1	yes	characteristic
10	C₂×#117×C₄₁	C₄	1	1	yes	characteristic
11	C₂²×C₄²×C₄₁	C₂²	1	1	yes	characteristic
12	C₄₁×#431	—	2	4	no	—
13	C₂×C₄⋊C₈×C₄₁	—	2	4	no	—
14	C₂×C₄⋊C₈×C₄₁	C₂²	1	1	yes	characteristic
15	C₂×C₄⋊C₈×C₄₁	C₂²	1	2	yes	—
16	C₂×C₄⋊C₈×C₄₁	C₂²	1	1	yes	characteristic
17	C₂×C₄⋊C₈×C₄₁	C₂²	1	2	yes	—
18	C₂×C₄⋊C₈×C₄₁	C₂²	1	8	yes	—
19	C₂×C₂²⋊C₈×C₄₁	C₂²	1	2	yes	—
20	C₂×C₄×C₈×C₄₁	C₂²	1	2	yes	—
21	C₄×C₄⋊C₄×C₄₁	C₄	1	2	yes	—
22	C₄×C₄⋊C₄×C₄₁	C₂²	1	2	yes	—
23	C₄×C₂²⋊C₄×C₄₁	C₄	1	2	yes	—
24	C₄×C₂²⋊C₄×C₄₁	C₂²	1	2	yes	—
25	C₄₁×#376	C₄	1	2	yes	—
26	C₄³×C₄₁	C₂²	1	2	yes	—
27	C₄₁×#336	C₂²	1	8	yes	—
28	C₂³×C₄×C₄₁	C₂×C₄	1	1	yes	characteristic
29	C₂³×C₄×C₄₁	C₂×C₄	1	1	yes	characteristic
30	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
31	C₂²×C₈×C₄₁	—	2	4	no	—
32	C₂²×C₈×C₄₁	—	4	4	no	—
33	C₂²×C₈×C₄₁	C₂³	1	4	yes	—
34	C₂²×C₈×C₄₁	C₂³	1	2	yes	—
35	C₂²×C₈×C₄₁	C₂³	1	2	yes	—
36	#117×C₄₁	—	2	4	no	—
37	#117×C₄₁	C₈	1	8	yes	complemented
38	C₂×C₄⋊C₄×C₄₁	C₂×C₄	1	2	yes	—
39	C₂×C₄⋊C₄×C₄₁	C₂×C₄	1	2	yes	—
40	C₂×C₂²⋊C₄×C₄₁	C₂×C₄	1	2	yes	—
41	C₂×C₂²⋊C₄×C₄₁	C₂×C₄	1	2	yes	—
42	C₂×C₄²×C₄₁	C₂×C₄	1	2	yes	—
43	C₂×C₄²×C₄₁	C₂×C₄	1	4	yes	—
44	C₂×C₄²×C₄₁	C₂×C₄	1	1	yes	characteristic
45	C₂×C₄²×C₄₁	C₂×C₄	1	1	yes	characteristic
46	C₂×C₄²×C₄₁	C₂×C₄	1	2	yes	—
47	C₂×C₄²×C₄₁	D₄	1	4	yes	—
48	C₂×C₄²×C₄₁	Q₈	1	4	yes	—
49	C₂×C₄²×C₄₁	C₂³	1	4	yes	—
50	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
51	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
52	C₄⋊C₈×C₄₁	—	2	4	no	—
53	C₄⋊C₈×C₄₁	—	2	4	no	—
54	C₄⋊C₈×C₄₁	—	2	2	no	—
55	C₄⋊C₈×C₄₁	—	2	2	no	—
56	C₄⋊C₈×C₄₁	—	4	8	no	—
57	C₂²⋊C₈×C₄₁	—	2	4	no	—
58	C₄×C₈×C₄₁	—	2	4	no	—
59	#95×C₄₁	C₂×C₄	1	4	yes	—
60	#95×C₄₁	C₂×C₄	1	4	yes	—
61	C₂⁴×C₄₁	C₂²×C₄	1	1	yes	characteristic
62	C₂²×C₄×C₄₁	—	2	2	no	—
63	C₂²×C₄×C₄₁	—	2	2	no	—
64	C₂²×C₄×C₄₁	—	4	2	no	—
65	C₂²×C₄×C₄₁	C₄⋊C₄	1	4	yes	—
66	C₂²×C₄×C₄₁	C₄⋊C₄	1	4	yes	—
67	C₂²×C₄×C₄₁	C₂×C₈	1	4	yes	—
68	C₂²×C₄×C₄₁	M₁₆	1	4	yes	—
69	C₂²×C₄×C₄₁	C₂²×C₄	1	4	yes	—
70	C₂²×C₄×C₄₁	C₂²×C₄	1	1	yes	characteristic
71	C₂²×C₄×C₄₁	C₂²×C₄	1	1	yes	characteristic
72	C₂²×C₄×C₄₁	C₂²×C₄	1	1	yes	characteristic
73	C₂²×C₄×C₄₁	C₂²×C₄	1	4	yes	—
74	C₂²×C₄×C₄₁	C₂²×C₄	1	1	yes	characteristic
75	C₂²×C₄×C₄₁	C₂²×C₄	1	1	yes	characteristic
76	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
77	C₂²×C₄×C₄₁	C₂×Q₈	1	2	yes	—
78	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
79	C₂×C₈×C₄₁	—	2	2	no	—
80	C₂×C₈×C₄₁	—	2	2	no	—
81	C₂×C₈×C₄₁	—	2	4	no	—
82	C₂×C₈×C₄₁	—	2	4	no	—
83	C₂×C₈×C₄₁	—	2	8	no	—
84	C₂×C₈×C₄₁	—	2	4	no	—
85	C₂×C₈×C₄₁	—	4	8	no	—
86	C₄⋊C₄×C₄₁	—	2	4	no	—
87	C₄⋊C₄×C₄₁	C₂×C₈	1	8	yes	complemented
88	C₂²⋊C₄×C₄₁	—	2	4	no	—
89	C₂²⋊C₄×C₄₁	C₂×C₈	1	8	yes	—
90	C₄²×C₄₁	—	2	4	no	—
91	C₄²×C₄₁	—	2	4	no	—
92	C₄²×C₄₁	—	2	4	no	—
93	C₄²×C₄₁	—	4	4	no	—
94	C₄²×C₄₁	C₄⋊C₄	1	4	yes	—
95	C₄²×C₄₁	C₄⋊C₄	1	4	yes	—
96	C₄²×C₄₁	C₂×C₈	1	8	yes	complemented
97	C₄²×C₄₁	C₂×D₄	1	2	yes	—
98	C₄²×C₄₁	C₂×D₄	1	2	yes	—
99	C₄²×C₄₁	C₂×Q₈	1	2	yes	—
100	C₄²×C₄₁	C₂×Q₈	1	2	yes	—
101	C₂³×C₄₁	—	2	2	no	—
102	C₂³×C₄₁	—	2	2	no	—
103	C₂³×C₄₁	C₂×C₄⋊C₄	1	2	yes	—
104	C₂³×C₄₁	C₂²×C₈	1	2	yes	—
105	C₂³×C₄₁	C₂×M₁₆	1	2	yes	—
106	C₂³×C₄₁	C₂³×C₄	1	1	yes	characteristic
107	C₂×C₄×C₄₁	—	2	4	no	—
108	C₂×C₄×C₄₁	—	2	2	no	—
109	C₂×C₄×C₄₁	—	2	2	no	—
110	C₂×C₄×C₄₁	—	2	4	no	—
111	C₂×C₄×C₄₁	—	2	2	no	—
112	C₂×C₄×C₄₁	—	2	2	no	—
113	C₂×C₄×C₄₁	—	2	2	no	—
114	C₂×C₄×C₄₁	—	2	4	no	—
115	C₂×C₄×C₄₁	—	2	4	no	—
116	C₂×C₄×C₄₁	—	2	4	no	—
117	C₂×C₄×C₄₁	—	2	4	no	—
118	C₂×C₄×C₄₁	—	4	4	no	—
119	C₂×C₄×C₄₁	C₄⋊C₈	1	16	yes	complemented
120	C₂×C₄×C₄₁	C₂×C₄⋊C₄	1	2	yes	—
121	C₂×C₄×C₄₁	C₂×C₄⋊C₄	1	2	yes	—
122	C₂×C₄×C₄₁	C₂×C₄⋊C₄	1	2	yes	—
123	C₂×C₄×C₄₁	C₂×C₄⋊C₄	1	2	yes	—
124	C₂×C₄×C₄₁	C₂×C₄⋊C₄	1	2	yes	—
125	C₂×C₄×C₄₁	C₂²×C₈	1	8	yes	—
126	C₂×C₄×C₄₁	C₂²×C₈	1	2	yes	—
127	C₂×C₄×C₄₁	C₂²×C₈	1	2	yes	—
128	C₂×C₄×C₄₁	C₂×M₁₆	1	2	yes	—
129	C₂×C₄×C₄₁	C₂×M₁₆	1	2	yes	—
130	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
131	C₂×C₄×C₄₁	C₂²×Q₈	1	1	yes	characteristic
132	C₂×C₄×C₄₁	H(5,𝔽₂)	1	2	yes	—
133	C₂×C₄×C₄₁	2₋¹⁺⁴	1	2	yes	—
134	C₈×C₄₁	—	4	2	no	—
135	C₈×C₄₁	—	4	4	no	—
136	C₈×C₄₁	—	4	2	no	—
137	#21972	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
138	C₂²×C₄₁	—	2	2	no	—
139	C₂²×C₄₁	—	2	2	no	—
140	C₂²×C₄₁	—	2	4	no	—
141	C₂²×C₄₁	—	2	4	no	—
142	C₂²×C₄₁	C₂×C₄⋊C₈	1	4	yes	—
143	C₂²×C₄₁	C₂²×C₄⋊C₄	1	1	yes	characteristic
144	C₂²×C₄₁	#520	1	2	yes	—
145	C₂²×C₄₁	C₂³×C₈	1	1	yes	characteristic
146	C₂²×C₄₁	C₂²×M₁₆	1	1	yes	characteristic
147	C₂²×C₄₁	#568	1	2	yes	—
148	C₄×C₄₁	—	2	2	no	—
149	C₄×C₄₁	—	2	2	no	—
150	C₄×C₄₁	—	2	2	no	—
151	C₄×C₄₁	—	2	8	no	—
152	C₄×C₄₁	—	4	4	no	—
153	C₄×C₄₁	C₂×C₄⋊C₈	1	4	yes	—
154	C₄×C₄₁	C₂×C₄⋊C₈	1	4	yes	—
155	C₄×C₄₁	#535	1	1	yes	characteristic
156	C₄×C₄₁	#536	1	1	yes	characteristic
157	C₄×C₄₁	#544	1	2	yes	—
158	C₂×#431	C₂×C₄₁	1	1	yes	characteristic
159	C₂²×C₄⋊C₈	C₂×C₄₁	1	1	yes	characteristic
160	C₄×#117	C₂×C₄₁	1	1	yes	characteristic
161	#1939	C₂×C₄₁	1	4	yes	complemented
162	#1850	C₂×C₄₁	1	4	yes	—
163	#1842	C₂×C₄₁	1	2	yes	complemented
164	#1831	C₂×C₄₁	1	2	yes	complemented
165	C₂×C₄₁	—	2	4	no	—
166	C₂×C₄₁	#2317	1	1	yes	characteristic
167	C₂×C₄₁	C₂²×C₄⋊C₈	1	1	yes	characteristic
168	C₂×C₄₁	#2905	1	1	yes	characteristic
169	C₂×C₄₁	#2988	1	2	yes	—
170	C₂×C₄₁	#2989	1	2	yes	—
171	C₂³×C₈	C₂²×C₄₁	1	2	yes	—
172	C₂×#117	C₄×C₄₁	1	1	yes	characteristic
173	C₂×#117	C₄×C₄₁	1	1	yes	characteristic
174	C₂²×C₄²	C₂²×C₄₁	1	1	yes	characteristic
175	#431	—	2	4	no	—
176	C₂×C₄⋊C₈	—	2	4	no	—
177	C₂×C₄⋊C₈	C₂²×C₄₁	1	1	yes	characteristic
178	C₂×C₄⋊C₈	C₂²×C₄₁	1	2	yes	—
179	C₂×C₄⋊C₈	C₂²×C₄₁	1	1	yes	characteristic
180	C₂×C₄⋊C₈	C₂²×C₄₁	1	2	yes	—
181	C₂×C₄⋊C₈	C₂²×C₄₁	1	8	yes	—
182	C₂×C₂²⋊C₈	C₂²×C₄₁	1	2	yes	—
183	C₂×C₄×C₈	C₂²×C₄₁	1	2	yes	—
184	C₄×C₄⋊C₄	C₄×C₄₁	1	2	yes	—
185	C₄×C₄⋊C₄	C₂²×C₄₁	1	2	yes	—
186	C₄×C₂²⋊C₄	C₄×C₄₁	1	2	yes	—
187	C₄×C₂²⋊C₄	C₂²×C₄₁	1	2	yes	—
188	#376	C₄×C₄₁	1	2	yes	—
189	C₄³	C₂²×C₄₁	1	2	yes	—
190	#336	C₂²×C₄₁	1	8	yes	—
191	C₄₁	#21972	1	1	yes	characteristic, direct product factor, Sylow
192	C₂³×C₄	C₂×C₄×C₄₁	1	1	yes	characteristic
193	C₂³×C₄	C₂×C₄×C₄₁	1	1	yes	characteristic
194	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
195	C₂²×C₈	—	2	4	no	—
196	C₂²×C₈	—	4	4	no	—
197	C₂²×C₈	C₂³×C₄₁	1	4	yes	—
198	C₂²×C₈	C₂³×C₄₁	1	2	yes	—
199	C₂²×C₈	C₂³×C₄₁	1	2	yes	—
200	#117	—	2	4	no	—
201	#117	C₈×C₄₁	1	8	yes	complemented
202	C₂×C₄⋊C₄	C₂×C₄×C₄₁	1	2	yes	—
203	C₂×C₄⋊C₄	C₂×C₄×C₄₁	1	2	yes	—
204	C₂×C₂²⋊C₄	C₂×C₄×C₄₁	1	2	yes	—
205	C₂×C₂²⋊C₄	C₂×C₄×C₄₁	1	2	yes	—
206	C₂×C₄²	C₂×C₄×C₄₁	1	2	yes	—
207	C₂×C₄²	C₂×C₄×C₄₁	1	4	yes	—
208	C₂×C₄²	C₂×C₄×C₄₁	1	1	yes	characteristic
209	C₂×C₄²	C₂×C₄×C₄₁	1	1	yes	characteristic
210	C₂×C₄²	C₂×C₄×C₄₁	1	2	yes	—
211	C₂×C₄²	D₄×C₄₁	1	4	yes	—
212	C₂×C₄²	Q₈×C₄₁	1	4	yes	—
213	C₂×C₄²	C₂³×C₄₁	1	4	yes	—
214	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
215	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
216	C₄⋊C₈	—	2	4	no	—
217	C₄⋊C₈	—	2	4	no	—
218	C₄⋊C₈	—	2	2	no	—
219	C₄⋊C₈	—	2	2	no	—
220	C₄⋊C₈	—	4	8	no	—
221	C₂²⋊C₈	—	2	4	no	—
222	C₄×C₈	—	2	4	no	—
223	#95	C₂×C₄×C₄₁	1	4	yes	—
224	#95	C₂×C₄×C₄₁	1	4	yes	—
225	C₂⁴	C₂²×C₄×C₄₁	1	1	yes	characteristic
226	C₂²×C₄	—	2	2	no	—
227	C₂²×C₄	—	2	2	no	—
228	C₂²×C₄	—	4	2	no	—
229	C₂²×C₄	C₄⋊C₄×C₄₁	1	4	yes	—
230	C₂²×C₄	C₄⋊C₄×C₄₁	1	4	yes	—
231	C₂²×C₄	C₂×C₈×C₄₁	1	4	yes	—
232	C₂²×C₄	M₁₆×C₄₁	1	4	yes	—
233	C₂²×C₄	C₂²×C₄×C₄₁	1	4	yes	—
234	C₂²×C₄	C₂²×C₄×C₄₁	1	1	yes	characteristic
235	C₂²×C₄	C₂²×C₄×C₄₁	1	1	yes	characteristic
236	C₂²×C₄	C₂²×C₄×C₄₁	1	1	yes	characteristic
237	C₂²×C₄	C₂²×C₄×C₄₁	1	4	yes	—
238	C₂²×C₄	C₂²×C₄×C₄₁	1	1	yes	characteristic
239	C₂²×C₄	C₂²×C₄×C₄₁	1	1	yes	characteristic
240	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
241	C₂²×C₄	C₂×Q₈×C₄₁	1	2	yes	—
242	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
243	C₂×C₈	—	2	2	no	—
244	C₂×C₈	—	2	2	no	—
245	C₂×C₈	—	2	4	no	—
246	C₂×C₈	—	2	4	no	—
247	C₂×C₈	—	2	8	no	—
248	C₂×C₈	—	2	4	no	—
249	C₂×C₈	—	4	8	no	—
250	C₄⋊C₄	—	2	4	no	—
251	C₄⋊C₄	C₂×C₈×C₄₁	1	8	yes	complemented
252	C₂²⋊C₄	—	2	4	no	—
253	C₂²⋊C₄	C₂×C₈×C₄₁	1	8	yes	—
254	C₄²	—	2	4	no	—
255	C₄²	—	2	4	no	—
256	C₄²	—	2	4	no	—
257	C₄²	—	4	4	no	—
258	C₄²	C₄⋊C₄×C₄₁	1	4	yes	—
259	C₄²	C₄⋊C₄×C₄₁	1	4	yes	—
260	C₄²	C₂×C₈×C₄₁	1	8	yes	complemented
261	C₄²	C₂×D₄×C₄₁	1	2	yes	—
262	C₄²	C₂×D₄×C₄₁	1	2	yes	—
263	C₄²	C₂×Q₈×C₄₁	1	2	yes	—
264	C₄²	C₂×Q₈×C₄₁	1	2	yes	—
265	C₂³	—	2	2	no	—
266	C₂³	—	2	2	no	—
267	C₂³	C₂×C₄⋊C₄×C₄₁	1	2	yes	—
268	C₂³	C₂²×C₈×C₄₁	1	2	yes	—
269	C₂³	C₂×M₁₆×C₄₁	1	2	yes	—
270	C₂³	C₂³×C₄×C₄₁	1	1	yes	characteristic
271	C₂×C₄	—	2	4	no	—
272	C₂×C₄	—	2	2	no	—
273	C₂×C₄	—	2	2	no	—
274	C₂×C₄	—	2	4	no	—
275	C₂×C₄	—	2	2	no	—
276	C₂×C₄	—	2	2	no	—
277	C₂×C₄	—	2	2	no	—
278	C₂×C₄	—	2	4	no	—
279	C₂×C₄	—	2	4	no	—
280	C₂×C₄	—	2	4	no	—
281	C₂×C₄	—	2	4	no	—
282	C₂×C₄	—	4	4	no	—
283	C₂×C₄	C₄⋊C₈×C₄₁	1	16	yes	complemented
284	C₂×C₄	C₂×C₄⋊C₄×C₄₁	1	2	yes	—
285	C₂×C₄	C₂×C₄⋊C₄×C₄₁	1	2	yes	—
286	C₂×C₄	C₂×C₄⋊C₄×C₄₁	1	2	yes	—
287	C₂×C₄	C₂×C₄⋊C₄×C₄₁	1	2	yes	—
288	C₂×C₄	C₂×C₄⋊C₄×C₄₁	1	2	yes	—
289	C₂×C₄	C₂²×C₈×C₄₁	1	8	yes	—
290	C₂×C₄	C₂²×C₈×C₄₁	1	2	yes	—
291	C₂×C₄	C₂²×C₈×C₄₁	1	2	yes	—
292	C₂×C₄	C₂×M₁₆×C₄₁	1	2	yes	—
293	C₂×C₄	C₂×M₁₆×C₄₁	1	2	yes	—
294	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
295	C₂×C₄	C₂²×Q₈×C₄₁	1	1	yes	characteristic
296	C₂×C₄	H(5,𝔽₂)×C₄₁	1	2	yes	—
297	C₂×C₄	2₋¹⁺⁴×C₄₁	1	2	yes	—
298	C₈	—	4	4	no	—
299	C₈	—	4	2	no	—
300	C₈	—	4	2	no	—
301	C₂²	—	2	2	no	—
302	C₂²	—	2	2	no	—
303	C₂²	—	2	4	no	—
304	C₂²	—	2	4	no	—
305	C₂²	C₂×C₄⋊C₈×C₄₁	1	4	yes	—
306	C₂²	C₂²×C₄⋊C₄×C₄₁	1	1	yes	characteristic
307	C₂²	C₄₁×#520	1	2	yes	—
308	C₂²	C₂³×C₈×C₄₁	1	1	yes	characteristic
309	C₂²	C₂²×M₁₆×C₄₁	1	1	yes	characteristic
310	C₂²	C₄₁×#568	1	2	yes	—
311	C₄	—	2	2	no	—
312	C₄	—	2	2	no	—
313	C₄	—	2	2	no	—
314	C₄	—	2	8	no	—
315	C₄	—	4	4	no	—
316	C₄	C₂×C₄⋊C₈×C₄₁	1	4	yes	—
317	C₄	C₂×C₄⋊C₈×C₄₁	1	4	yes	—
318	C₄	C₄₁×#535	1	1	yes	characteristic
319	C₄	C₄₁×#536	1	1	yes	characteristic
320	C₄	C₄₁×#544	1	2	yes	—
321	C₂	—	2	4	no	—
322	C₂	C₄₁×#2317	1	1	yes	characteristic
323	C₂	C₂²×C₄⋊C₈×C₄₁	1	1	yes	characteristic
324	C₂	C₄₁×#2905	1	1	yes	characteristic
325	C₂	C₄₁×#2988	1	2	yes	—
326	C₂	C₄₁×#2989	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄×C₄₁	C₂⁴
commutator	C₂²	C₂³×C₈×C₄₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₁
socle	C₂³×C₄₁	C₂³×C₄
prime radical	C₂⁴×C₄₁	C₂²×C₄
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₄₁×#1939	C₂	semidirect
6. C₄₁×#1842	C₂	semidirect
7. C₄₁×#1831	C₂	semidirect
37. #117×C₄₁	C₈	semidirect
87. C₄⋊C₄×C₄₁	C₂×C₈	semidirect
96. C₄²×C₄₁	C₂×C₈	semidirect
119. C₂×C₄×C₄₁	C₄⋊C₈	semidirect
137. #21972	C₄₁	direct (N × H)
161. #1939	C₂×C₄₁	semidirect
163. #1842	C₂×C₄₁	semidirect
164. #1831	C₂×C₄₁	semidirect
191. C₄₁	#21972	direct (N × H)
201. #117	C₈×C₄₁	semidirect
251. C₄⋊C₄	C₂×C₈×C₄₁	semidirect
260. C₄²	C₂×C₈×C₄₁	semidirect
283. C₂×C₄	C₄⋊C₈×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×#431	2
C₂²×C₄⋊C₈×C₄₁	2
C₄×#117×C₄₁	2
C₄₁×#1939	2
C₄₁×#1850	2
C₄₁×#1842	2
C₄₁×#1831	2
#21972	41

Subgroups — C41×#21972 #23798173

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#21972 #23798173