Subgroups — C₄₁×#21392 #23797593

Order 10496.

1150 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₁×#533	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄₁×#432	C₂	1	1	yes	maximal, characteristic
3	C₄×#117×C₄₁	C₂	1	1	yes	maximal, characteristic
4	C₄₁×#1987	C₂	1	2	yes	maximal, complemented
5	C₄₁×#1981	C₂	1	2	yes	maximal, complemented
6	C₄₁×#1873	C₂	1	4	yes	maximal
7	C₄₁×#1763	C₂	1	4	yes	maximal, complemented
8	C₄₁×#533	—	2	4	no	—
9	C₄₁×#533	C₄	1	8	yes	complemented
10	C₂×C₄⋊Q₈×C₄₁	C₂²	1	1	yes	characteristic
11	C₂×C₄⋊Q₈×C₄₁	C₂²	1	1	yes	characteristic
12	C₂×#125×C₄₁	—	2	1	no	—
13	C₂×C₂²⋊Q₈×C₄₁	—	2	1	no	—
14	C₂×C₂²⋊Q₈×C₄₁	C₂²	1	2	yes	—
15	C₂×C₄×Q₈×C₄₁	—	2	1	no	—
16	C₂×C₄×Q₈×C₄₁	C₂²	1	2	yes	—
17	C₂×#117×C₄₁	—	2	1	no	—
18	C₂×#117×C₄₁	C₂²	1	2	yes	—
19	C₂²×C₄²×C₄₁	C₂²	1	1	yes	characteristic
20	C₄₁×#432	—	2	4	no	—
21	C₂×C₄⋊C₈×C₄₁	C₂²	1	2	yes	—
22	C₂×#103×C₄₁	C₂²	1	8	yes	—
23	C₂×C₂²⋊C₈×C₄₁	C₂²	1	2	yes	—
24	C₂×#97×C₄₁	C₂²	1	2	yes	—
25	C₄×C₄⋊C₄×C₄₁	C₂²	1	2	yes	—
26	C₄×C₄⋊C₄×C₄₁	C₂²	1	2	yes	—
27	C₄×C₂²⋊C₄×C₄₁	—	2	1	no	—
28	C₄×C₂²⋊C₄×C₄₁	—	2	1	no	—
29	C₄₁×#376	—	2	1	no	—
30	C₄³×C₄₁	—	2	1	no	—
31	C₄₁×#340	C₂²	1	8	yes	—
32	C₂²×Q₈×C₄₁	—	2	1	no	—
33	C₂²×Q₈×C₄₁	C₂³	1	2	yes	—
34	C₂³×C₄×C₄₁	D₄	1	1	yes	characteristic
35	C₂³×C₄×C₄₁	D₄	1	1	yes	characteristic
36	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
37	C₂²×C₈×C₄₁	C₂³	1	4	yes	—
38	C₄⋊Q₈×C₄₁	—	2	2	no	—
39	C₄⋊Q₈×C₄₁	—	2	2	no	—
40	C₄⋊Q₈×C₄₁	C₂×C₄	1	4	yes	—
41	C₄⋊Q₈×C₄₁	C₂×C₄	1	4	yes	—
42	#125×C₄₁	—	2	8	no	—
43	C₂²⋊Q₈×C₄₁	—	2	8	no	—
44	C₂²⋊Q₈×C₄₁	—	2	4	no	—
45	C₂²⋊Q₈×C₄₁	C₂×C₄	1	8	yes	—
46	C₄×Q₈×C₄₁	—	2	8	no	—
47	C₄×Q₈×C₄₁	—	2	4	no	—
48	C₄×Q₈×C₄₁	C₂×C₄	1	8	yes	—
49	#117×C₄₁	—	2	8	no	—
50	#117×C₄₁	—	2	8	no	—
51	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
52	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
53	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
54	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
55	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
56	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
57	C₂×C₄⋊C₄×C₄₁	C₂³	1	4	yes	—
58	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
59	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
60	C₂×C₄²×C₄₁	—	2	2	no	—
61	C₂×C₄²×C₄₁	—	2	2	no	—
62	C₂×C₄²×C₄₁	—	2	2	no	—
63	C₂×C₄²×C₄₁	—	2	2	no	—
64	C₂×C₄²×C₄₁	C₂×C₄	1	4	yes	—
65	C₂×C₄²×C₄₁	D₄	1	1	yes	characteristic
66	C₂×C₄²×C₄₁	D₄	1	1	yes	characteristic
67	C₂×C₄²×C₄₁	D₄	1	4	yes	—
68	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
69	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
70	C₄⋊C₈×C₄₁	—	2	4	no	—
71	#103×C₄₁	—	2	16	no	—
72	C₂²⋊C₈×C₄₁	—	2	4	no	—
73	#97×C₄₁	—	2	4	no	—
74	#95×C₄₁	—	2	2	no	—
75	#95×C₄₁	—	2	2	no	—
76	C₂⁴×C₄₁	C₂×D₄	1	1	yes	characteristic
77	C₂×Q₈×C₄₁	—	2	4	no	—
78	C₂×Q₈×C₄₁	—	2	2	no	—
79	C₂×Q₈×C₄₁	—	2	8	no	—
80	C₂×Q₈×C₄₁	—	4	4	no	—
81	C₂×Q₈×C₄₁	C₂²×C₄	1	4	yes	—
82	C₂²×C₄×C₄₁	—	2	4	no	—
83	C₂²×C₄×C₄₁	—	2	4	no	—
84	C₂²×C₄×C₄₁	—	2	4	no	—
85	C₂²×C₄×C₄₁	—	2	2	no	—
86	C₂²×C₄×C₄₁	—	2	2	no	—
87	C₂²×C₄×C₄₁	—	4	2	no	—
88	C₂²×C₄×C₄₁	C₂²⋊C₄	1	4	yes	—
89	C₂²×C₄×C₄₁	C₂²⋊C₄	1	4	yes	—
90	C₂²×C₄×C₄₁	C₂²×C₄	1	2	yes	—
91	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
92	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
93	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
94	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
95	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
96	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
97	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
98	C₂×C₈×C₄₁	—	2	4	no	—
99	C₂×C₈×C₄₁	—	2	8	no	—
100	C₄⋊C₄×C₄₁	—	2	4	no	—
101	C₄⋊C₄×C₄₁	—	2	4	no	—
102	C₄⋊C₄×C₄₁	—	2	4	no	—
103	C₄⋊C₄×C₄₁	—	2	8	no	—
104	C₄⋊C₄×C₄₁	—	2	8	no	—
105	C₄⋊C₄×C₄₁	—	2	2	no	—
106	C₄⋊C₄×C₄₁	—	2	4	no	—
107	C₄⋊C₄×C₄₁	C₂²×C₄	1	4	yes	—
108	C₄⋊C₄×C₄₁	#41	1	8	yes	—
109	C₂²⋊C₄×C₄₁	—	2	8	no	—
110	C₂²⋊C₄×C₄₁	—	2	8	no	—
111	C₄²×C₄₁	—	2	8	no	—
112	C₄²×C₄₁	—	2	8	no	—
113	C₄²×C₄₁	—	4	4	no	—
114	C₄²×C₄₁	—	4	4	no	—
115	C₄²×C₄₁	C₂²⋊C₄	1	4	yes	—
116	C₄²×C₄₁	C₂²⋊C₄	1	4	yes	—
117	C₄²×C₄₁	C₂²×C₄	1	2	yes	—
118	C₄²×C₄₁	C₂²×C₄	1	2	yes	—
119	C₄²×C₄₁	C₂×D₄	1	2	yes	—
120	C₄²×C₄₁	C₂×D₄	1	2	yes	—
121	C₂³×C₄₁	—	2	2	no	—
122	C₂³×C₄₁	—	2	2	no	—
123	C₂³×C₄₁	—	2	2	no	—
124	C₂³×C₄₁	C₂×C₂²⋊C₄	1	2	yes	—
125	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
126	Q₈×C₄₁	—	2	8	no	—
127	Q₈×C₄₁	—	4	8	no	—
128	Q₈×C₄₁	—	4	4	no	—
129	C₂×C₄×C₄₁	—	2	2	no	—
130	C₂×C₄×C₄₁	—	2	2	no	—
131	C₂×C₄×C₄₁	—	2	2	no	—
132	C₂×C₄×C₄₁	—	2	2	no	—
133	C₂×C₄×C₄₁	—	2	4	no	—
134	C₂×C₄×C₄₁	—	2	4	no	—
135	C₂×C₄×C₄₁	—	2	8	no	—
136	C₂×C₄×C₄₁	—	2	4	no	—
137	C₂×C₄×C₄₁	—	2	4	no	—
138	C₂×C₄×C₄₁	—	2	8	no	—
139	C₂×C₄×C₄₁	—	4	4	no	—
140	C₂×C₄×C₄₁	—	4	4	no	—
141	C₂×C₄×C₄₁	—	4	4	no	—
142	C₂×C₄×C₄₁	—	4	4	no	—
143	C₂×C₄×C₄₁	—	4	4	no	—
144	C₂×C₄×C₄₁	C₂×C₂²⋊C₄	1	2	yes	—
145	C₂×C₄×C₄₁	C₂×C₂²⋊C₄	1	2	yes	—
146	C₂×C₄×C₄₁	C₂×C₂²⋊C₄	1	2	yes	—
147	C₂×C₄×C₄₁	C₂×C₂²⋊C₄	1	2	yes	—
148	C₂×C₄×C₄₁	C₂×C₂²⋊C₄	1	2	yes	—
149	C₂×C₄×C₄₁	#137	1	4	yes	—
150	C₂×C₄×C₄₁	C₂³×C₄	1	1	yes	characteristic
151	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
152	C₂×C₄×C₄₁	C₂×#41	1	4	yes	—
153	C₈×C₄₁	—	4	4	no	—
154	#21392	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
155	C₂²×C₄₁	—	2	2	no	—
156	C₂²×C₄₁	—	2	2	no	—
157	C₂²×C₄₁	—	2	2	no	—
158	C₂²×C₄₁	—	4	4	no	—
159	C₂²×C₄₁	C₂²×C₂²⋊C₄	1	1	yes	characteristic
160	C₂²×C₄₁	#525	1	2	yes	—
161	C₂²×C₄₁	C₂×#137	1	2	yes	—
162	C₂²×C₄₁	#575	1	2	yes	—
163	C₄×C₄₁	—	2	2	no	—
164	C₄×C₄₁	—	2	2	no	—
165	C₄×C₄₁	—	2	2	no	—
166	C₄×C₄₁	—	2	2	no	—
167	C₄×C₄₁	—	4	8	no	—
168	C₄×C₄₁	—	4	4	no	—
169	C₄×C₄₁	—	4	4	no	—
170	C₄×C₄₁	#419	1	4	yes	—
171	C₄×C₄₁	C₄×#41	1	2	yes	—
172	C₄×C₄₁	#532	1	2	yes	—
173	C₂×#533	C₂×C₄₁	1	1	yes	characteristic
174	C₂×#432	C₂×C₄₁	1	1	yes	characteristic
175	C₄×#117	C₂×C₄₁	1	1	yes	characteristic
176	#1987	C₂×C₄₁	1	2	yes	complemented
177	#1981	C₂×C₄₁	1	2	yes	complemented
178	#1873	C₂×C₄₁	1	4	yes	—
179	#1763	C₂×C₄₁	1	4	yes	complemented
180	C₂×C₄₁	—	4	2	no	—
181	C₂×C₄₁	#2297	1	1	yes	characteristic
182	C₂×C₄₁	C₂×#419	1	1	yes	characteristic
183	C₂×C₄₁	#2896	1	1	yes	characteristic
184	C₂×C₄₁	#3116	1	4	yes	—
185	#533	—	2	4	no	—
186	#533	C₄×C₄₁	1	8	yes	complemented
187	C₂×C₄⋊Q₈	C₂²×C₄₁	1	1	yes	characteristic
188	C₂×C₄⋊Q₈	C₂²×C₄₁	1	1	yes	characteristic
189	C₂×#125	—	2	1	no	—
190	C₂×C₂²⋊Q₈	—	2	1	no	—
191	C₂×C₂²⋊Q₈	C₂²×C₄₁	1	2	yes	—
192	C₂×C₄×Q₈	—	2	1	no	—
193	C₂×C₄×Q₈	C₂²×C₄₁	1	2	yes	—
194	C₂×#117	—	2	1	no	—
195	C₂×#117	C₂²×C₄₁	1	2	yes	—
196	C₂²×C₄²	C₂²×C₄₁	1	1	yes	characteristic
197	#432	—	2	4	no	—
198	C₂×C₄⋊C₈	C₂²×C₄₁	1	2	yes	—
199	C₂×#103	C₂²×C₄₁	1	8	yes	—
200	C₂×C₂²⋊C₈	C₂²×C₄₁	1	2	yes	—
201	C₂×#97	C₂²×C₄₁	1	2	yes	—
202	C₄×C₄⋊C₄	C₂²×C₄₁	1	2	yes	—
203	C₄×C₄⋊C₄	C₂²×C₄₁	1	2	yes	—
204	C₄×C₂²⋊C₄	—	2	1	no	—
205	C₄×C₂²⋊C₄	—	2	1	no	—
206	#376	—	2	1	no	—
207	C₄³	—	2	1	no	—
208	#340	C₂²×C₄₁	1	8	yes	—
209	C₄₁	#21392	1	1	yes	characteristic, direct product factor, Sylow
210	C₂²×Q₈	—	2	1	no	—
211	C₂²×Q₈	C₂³×C₄₁	1	2	yes	—
212	C₂³×C₄	D₄×C₄₁	1	1	yes	characteristic
213	C₂³×C₄	D₄×C₄₁	1	1	yes	characteristic
214	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
215	C₂²×C₈	C₂³×C₄₁	1	4	yes	—
216	C₄⋊Q₈	—	2	2	no	—
217	C₄⋊Q₈	—	2	2	no	—
218	C₄⋊Q₈	C₂×C₄×C₄₁	1	4	yes	—
219	C₄⋊Q₈	C₂×C₄×C₄₁	1	4	yes	—
220	#125	—	2	8	no	—
221	C₂²⋊Q₈	—	2	8	no	—
222	C₂²⋊Q₈	—	2	4	no	—
223	C₂²⋊Q₈	C₂×C₄×C₄₁	1	8	yes	—
224	C₄×Q₈	—	2	8	no	—
225	C₄×Q₈	—	2	4	no	—
226	C₄×Q₈	C₂×C₄×C₄₁	1	8	yes	—
227	#117	—	2	8	no	—
228	#117	—	2	8	no	—
229	C₂×C₄⋊C₄	—	2	1	no	—
230	C₂×C₄⋊C₄	—	2	1	no	—
231	C₂×C₄⋊C₄	—	2	1	no	—
232	C₂×C₄⋊C₄	—	2	2	no	—
233	C₂×C₄⋊C₄	—	2	2	no	—
234	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
235	C₂×C₄⋊C₄	C₂³×C₄₁	1	4	yes	—
236	C₂×C₂²⋊C₄	—	2	2	no	—
237	C₂×C₂²⋊C₄	—	2	2	no	—
238	C₂×C₄²	—	2	2	no	—
239	C₂×C₄²	—	2	2	no	—
240	C₂×C₄²	—	2	2	no	—
241	C₂×C₄²	—	2	2	no	—
242	C₂×C₄²	C₂×C₄×C₄₁	1	4	yes	—
243	C₂×C₄²	D₄×C₄₁	1	1	yes	characteristic
244	C₂×C₄²	D₄×C₄₁	1	1	yes	characteristic
245	C₂×C₄²	D₄×C₄₁	1	4	yes	—
246	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
247	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
248	C₄⋊C₈	—	2	4	no	—
249	#103	—	2	16	no	—
250	C₂²⋊C₈	—	2	4	no	—
251	#97	—	2	4	no	—
252	#95	—	2	2	no	—
253	#95	—	2	2	no	—
254	C₂⁴	C₂×D₄×C₄₁	1	1	yes	characteristic
255	C₂×Q₈	—	2	4	no	—
256	C₂×Q₈	—	2	2	no	—
257	C₂×Q₈	—	2	8	no	—
258	C₂×Q₈	—	4	4	no	—
259	C₂×Q₈	C₂²×C₄×C₄₁	1	4	yes	—
260	C₂²×C₄	—	2	4	no	—
261	C₂²×C₄	—	2	4	no	—
262	C₂²×C₄	—	2	4	no	—
263	C₂²×C₄	—	2	2	no	—
264	C₂²×C₄	—	2	2	no	—
265	C₂²×C₄	—	4	2	no	—
266	C₂²×C₄	C₂²⋊C₄×C₄₁	1	4	yes	—
267	C₂²×C₄	C₂²⋊C₄×C₄₁	1	4	yes	—
268	C₂²×C₄	C₂²×C₄×C₄₁	1	2	yes	—
269	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
270	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
271	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
272	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
273	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
274	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
275	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
276	C₂×C₈	—	2	4	no	—
277	C₂×C₈	—	2	8	no	—
278	C₄⋊C₄	—	2	4	no	—
279	C₄⋊C₄	—	2	4	no	—
280	C₄⋊C₄	—	2	4	no	—
281	C₄⋊C₄	—	2	8	no	—
282	C₄⋊C₄	—	2	8	no	—
283	C₄⋊C₄	—	2	2	no	—
284	C₄⋊C₄	—	2	4	no	—
285	C₄⋊C₄	C₂²×C₄×C₄₁	1	4	yes	—
286	C₄⋊C₄	#41×C₄₁	1	8	yes	—
287	C₂²⋊C₄	—	2	8	no	—
288	C₂²⋊C₄	—	2	8	no	—
289	C₄²	—	2	8	no	—
290	C₄²	—	2	8	no	—
291	C₄²	—	4	4	no	—
292	C₄²	—	4	4	no	—
293	C₄²	C₂²⋊C₄×C₄₁	1	4	yes	—
294	C₄²	C₂²⋊C₄×C₄₁	1	4	yes	—
295	C₄²	C₂²×C₄×C₄₁	1	2	yes	—
296	C₄²	C₂²×C₄×C₄₁	1	2	yes	—
297	C₄²	C₂×D₄×C₄₁	1	2	yes	—
298	C₄²	C₂×D₄×C₄₁	1	2	yes	—
299	C₂³	—	2	2	no	—
300	C₂³	—	2	2	no	—
301	C₂³	—	2	2	no	—
302	C₂³	C₂×C₂²⋊C₄×C₄₁	1	2	yes	—
303	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
304	Q₈	—	2	8	no	—
305	Q₈	—	4	8	no	—
306	Q₈	—	4	4	no	—
307	C₂×C₄	—	2	2	no	—
308	C₂×C₄	—	2	2	no	—
309	C₂×C₄	—	2	2	no	—
310	C₂×C₄	—	2	2	no	—
311	C₂×C₄	—	2	4	no	—
312	C₂×C₄	—	2	4	no	—
313	C₂×C₄	—	2	8	no	—
314	C₂×C₄	—	2	4	no	—
315	C₂×C₄	—	2	4	no	—
316	C₂×C₄	—	2	8	no	—
317	C₂×C₄	—	4	4	no	—
318	C₂×C₄	—	4	4	no	—
319	C₂×C₄	—	4	4	no	—
320	C₂×C₄	—	4	4	no	—
321	C₂×C₄	—	4	4	no	—
322	C₂×C₄	C₂×C₂²⋊C₄×C₄₁	1	2	yes	—
323	C₂×C₄	C₂×C₂²⋊C₄×C₄₁	1	2	yes	—
324	C₂×C₄	C₂×C₂²⋊C₄×C₄₁	1	2	yes	—
325	C₂×C₄	C₂×C₂²⋊C₄×C₄₁	1	2	yes	—
326	C₂×C₄	C₂×C₂²⋊C₄×C₄₁	1	2	yes	—
327	C₂×C₄	#137×C₄₁	1	4	yes	—
328	C₂×C₄	C₂³×C₄×C₄₁	1	1	yes	characteristic
329	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
330	C₂×C₄	C₂×#41×C₄₁	1	4	yes	—
331	C₈	—	4	4	no	—
332	C₂²	—	2	2	no	—
333	C₂²	—	2	2	no	—
334	C₂²	—	2	2	no	—
335	C₂²	—	4	4	no	—
336	C₂²	C₂²×C₂²⋊C₄×C₄₁	1	1	yes	characteristic
337	C₂²	C₄₁×#525	1	2	yes	—
338	C₂²	C₂×#137×C₄₁	1	2	yes	—
339	C₂²	C₄₁×#575	1	2	yes	—
340	C₄	—	2	2	no	—
341	C₄	—	2	2	no	—
342	C₄	—	2	2	no	—
343	C₄	—	2	2	no	—
344	C₄	—	4	4	no	—
345	C₄	—	4	8	no	—
346	C₄	—	4	4	no	—
347	C₄	C₄₁×#419	1	4	yes	—
348	C₄	C₄×#41×C₄₁	1	2	yes	—
349	C₄	C₄₁×#532	1	2	yes	—
350	C₂	—	4	2	no	—
351	C₂	C₄₁×#2297	1	1	yes	characteristic
352	C₂	C₂×C₄₁×#419	1	1	yes	characteristic
353	C₂	C₄₁×#2896	1	1	yes	characteristic
354	C₂	C₄₁×#3116	1	4	yes	—

	subgroup	G/H
center, socle	C₂³×C₄₁	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₄₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₁
prime radical	C₂⁴×C₄₁	C₂×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₄₁ ◁ C₂²×C₄²×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₄₁×#1987	C₂	semidirect
5. C₄₁×#1981	C₂	semidirect
7. C₄₁×#1763	C₂	semidirect
9. C₄₁×#533	C₄	semidirect
154. #21392	C₄₁	direct (N × H)
176. #1987	C₂×C₄₁	semidirect
177. #1981	C₂×C₄₁	semidirect
179. #1763	C₂×C₄₁	semidirect
186. #533	C₄×C₄₁	semidirect
209. C₄₁	#21392	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₄₁×#533	2
C₂×C₄₁×#432	2
C₄×#117×C₄₁	2
C₄₁×#1987	2
C₄₁×#1981	2
C₄₁×#1873	2
C₄₁×#1763	2
#21392	41

Subgroups — C41×#21392 #23797593

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#21392 #23797593