Subgroups — C₂×C₄₁×#2184 #23809711

Order 10496.

1434 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×D₈×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×D₁₆×C₄₁	C₂	1	2	yes	maximal, complemented
3	C₂×C₄₁×#466	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₁×#2184	C₂	1	8	yes	maximal, direct product factor
5	C₂×C₄₁×#357	C₂	1	2	yes	maximal, complemented
6	C₂×C₄₁×C₂²⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂³×D₄×C₄₁	—	2	1	no	—
8	C₂²×D₈×C₄₁	—	2	8	no	—
9	C₂²×D₈×C₄₁	—	2	1	no	—
10	C₂²×D₈×C₄₁	—	2	2	no	—
11	C₂²×D₈×C₄₁	C₂²	1	2	yes	—
12	C₂²×D₈×C₄₁	C₂²	1	4	yes	complemented
13	C₂²×D₈×C₄₁	C₂²	1	1	yes	characteristic, complemented
14	C₂³×C₈×C₄₁	C₂²	1	1	yes	characteristic
15	C₂×#121×C₄₁	—	2	1	no	—
16	C₂×D₁₆×C₄₁	—	2	8	no	—
17	C₂×D₁₆×C₄₁	C₂²	1	8	yes	complemented
18	C₂²×C₁₆×C₄₁	C₂²	1	2	yes	complemented
19	C₄₁×#466	—	2	2	no	—
20	C₄₁×#466	C₂²	1	4	yes	complemented
21	C₂×#107×C₄₁	C₂²	1	1	yes	characteristic, complemented
22	C₂×#102×C₄₁	—	2	1	no	—
23	C₄₁×#357	C₂²	1	8	yes	complemented
24	C₄₁×C₂²⋊C₁₆	C₂²	1	4	yes	complemented
25	C₂⁵×C₄₁	—	4	1	no	—
26	C₂²×D₄×C₄₁	—	2	8	no	—
27	C₂²×D₄×C₄₁	—	2	2	no	—
28	C₂²×D₄×C₄₁	—	2	4	no	—
29	C₂²×D₄×C₄₁	—	2	1	no	—
30	C₂²×D₄×C₄₁	—	4	4	no	—
31	C₂²×D₄×C₄₁	—	4	1	no	—
32	C₂²×D₄×C₄₁	—	4	2	no	—
33	C₂²×D₄×C₄₁	—	4	1	no	—
34	C₂³×C₄×C₄₁	D₄	1	1	yes	characteristic
35	C₂×D₈×C₄₁	—	2	8	no	—
36	C₂×D₈×C₄₁	—	2	16	no	—
37	C₂×D₈×C₄₁	—	2	16	no	—
38	C₂×D₈×C₄₁	—	2	2	no	—
39	C₂×D₈×C₄₁	—	2	4	no	—
40	C₂×D₈×C₄₁	—	2	4	no	—
41	C₂×D₈×C₄₁	—	2	4	no	—
42	C₂×D₈×C₄₁	—	2	1	no	—
43	C₂×D₈×C₄₁	D₄	1	8	yes	complemented
44	C₂×D₈×C₄₁	C₂³	1	4	yes	—
45	C₂×D₈×C₄₁	C₂³	1	2	yes	complemented
46	C₂²×C₈×C₄₁	—	2	4	no	—
47	C₂²×C₈×C₄₁	D₄	1	1	yes	characteristic
48	C₂²×C₈×C₄₁	D₄	1	2	yes	—
49	C₂²×C₈×C₄₁	C₂³	1	2	yes	—
50	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
51	#121×C₄₁	—	2	4	no	—
52	#121×C₄₁	—	4	2	no	—
53	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
54	C₂×C₂²⋊C₄×C₄₁	—	4	1	no	—
55	D₁₆×C₄₁	—	2	16	no	—
56	C₂×C₁₆×C₄₁	—	2	4	no	—
57	C₂×C₁₆×C₄₁	C₂³	1	4	yes	complemented
58	#107×C₄₁	—	2	1	no	—
59	#107×C₄₁	C₂³	1	2	yes	complemented
60	#102×C₄₁	—	2	4	no	—
61	C₂⁴×C₄₁	—	4	8	no	—
62	C₂⁴×C₄₁	—	4	4	no	—
63	C₂⁴×C₄₁	—	4	2	no	—
64	C₂⁴×C₄₁	—	4	1	no	—
65	C₂⁴×C₄₁	—	8	4	no	—
66	C₂⁴×C₄₁	—	8	4	no	—
67	C₂⁴×C₄₁	D₈	1	1	yes	characteristic
68	C₂×D₄×C₄₁	—	2	16	no	—
69	C₂×D₄×C₄₁	—	2	8	no	—
70	C₂×D₄×C₄₁	—	2	4	no	—
71	C₂×D₄×C₄₁	—	2	2	no	—
72	C₂×D₄×C₄₁	—	4	8	no	—
73	C₂×D₄×C₄₁	—	4	8	no	—
74	C₂×D₄×C₄₁	—	4	16	no	—
75	C₂×D₄×C₄₁	—	4	4	no	—
76	C₂×D₄×C₄₁	—	4	2	no	—
77	C₂×D₄×C₄₁	—	4	4	no	—
78	C₂×D₄×C₄₁	—	4	2	no	—
79	C₂×D₄×C₄₁	—	4	1	no	—
80	C₂×D₄×C₄₁	—	4	4	no	—
81	C₂×D₄×C₄₁	—	4	2	no	—
82	C₂×D₄×C₄₁	—	8	4	no	—
83	C₂²×C₄×C₄₁	—	2	2	no	—
84	C₂²×C₄×C₄₁	—	2	2	no	—
85	C₂²×C₄×C₄₁	—	4	1	no	—
86	C₂²×C₄×C₄₁	D₈	1	2	yes	—
87	C₂²×C₄×C₄₁	D₈	1	1	yes	characteristic
88	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
89	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
90	D₈×C₄₁	—	2	16	no	—
91	D₈×C₄₁	—	2	8	no	—
92	D₈×C₄₁	—	2	4	no	—
93	D₈×C₄₁	—	2	4	no	—
94	D₈×C₄₁	—	4	2	no	—
95	D₈×C₄₁	C₂×D₄	1	8	yes	complemented
96	C₂×C₈×C₄₁	—	2	2	no	—
97	C₂×C₈×C₄₁	—	2	4	no	—
98	C₂×C₈×C₄₁	—	2	4	no	—
99	C₂×C₈×C₄₁	C₂×D₄	1	2	yes	—
100	C₂×C₈×C₄₁	C₂×D₄	1	1	yes	characteristic
101	C₂×C₈×C₄₁	C₂×D₄	1	4	yes	—
102	C₂×C₈×C₄₁	C₂⁴	1	1	yes	characteristic
103	C₄⋊C₄×C₄₁	—	2	2	no	—
104	C₄⋊C₄×C₄₁	—	4	1	no	—
105	C₂²⋊C₄×C₄₁	—	4	4	no	—
106	C₁₆×C₄₁	—	2	4	no	—
107	C₂³×C₄₁	—	2	2	no	—
108	C₂³×C₄₁	—	2	2	no	—
109	C₂³×C₄₁	—	4	16	no	—
110	C₂³×C₄₁	—	4	4	no	—
111	C₂³×C₄₁	—	4	8	no	—
112	C₂³×C₄₁	—	4	2	no	—
113	C₂³×C₄₁	—	8	8	no	—
114	C₂³×C₄₁	—	8	32	no	—
115	C₂³×C₄₁	—	8	4	no	—
116	C₂³×C₄₁	—	8	8	no	—
117	C₂³×C₄₁	—	8	4	no	—
118	C₂³×C₄₁	—	8	2	no	—
119	C₂³×C₄₁	—	8	2	no	—
120	C₂³×C₄₁	—	8	2	no	—
121	C₂³×C₄₁	D₁₆	1	4	yes	complemented
122	C₂³×C₄₁	C₂×D₈	1	2	yes	—
123	C₂³×C₄₁	C₂×D₈	1	1	yes	characteristic
124	D₄×C₄₁	—	2	8	no	—
125	D₄×C₄₁	—	4	16	no	—
126	D₄×C₄₁	—	4	2	no	—
127	D₄×C₄₁	—	4	4	no	—
128	D₄×C₄₁	—	4	2	no	—
129	D₄×C₄₁	—	4	8	no	—
130	D₄×C₄₁	—	8	8	no	—
131	D₄×C₄₁	—	8	2	no	—
132	C₂×C₄×C₄₁	—	2	2	no	—
133	C₂×C₄×C₄₁	—	2	2	no	—
134	C₂×C₄×C₄₁	—	2	2	no	—
135	C₂×C₄×C₄₁	—	2	4	no	—
136	C₂×C₄×C₄₁	—	4	2	no	—
137	C₂×C₄×C₄₁	—	8	2	no	—
138	C₂×C₄×C₄₁	#120	1	2	yes	—
139	C₂×C₄×C₄₁	C₂×D₈	1	2	yes	—
140	C₂×C₄×C₄₁	C₂×D₈	1	1	yes	characteristic
141	C₂×C₄×C₄₁	AGL(1,ℤ/8)	1	2	yes	—
142	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
143	C₈×C₄₁	—	2	2	no	—
144	C₈×C₄₁	#120	1	2	yes	—
145	C₈×C₄₁	C₂²×D₄	1	2	yes	—
146	C₂×#2184	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
147	C₂²×C₄₁	—	2	2	no	—
148	C₂²×C₄₁	—	2	8	no	—
149	C₂²×C₄₁	—	2	2	no	—
150	C₂²×C₄₁	—	4	8	no	—
151	C₂²×C₄₁	—	8	32	no	—
152	C₂²×C₄₁	—	8	4	no	—
153	C₂²×C₄₁	—	8	4	no	—
154	C₂²×C₄₁	—	8	16	no	—
155	C₂²×C₄₁	—	8	2	no	—
156	C₂²×C₄₁	—	8	2	no	—
157	C₂²×C₄₁	—	8	2	no	—
158	C₂²×C₄₁	—	16	4	no	—
159	C₂²×C₄₁	#447	1	2	yes	—
160	C₂²×C₄₁	C₂×D₁₆	1	2	yes	—
161	C₂²×C₄₁	C₂×D₁₆	1	4	yes	complemented
162	C₂²×C₄₁	#509	1	2	yes	—
163	C₂²×C₄₁	C₂²×D₈	1	1	yes	characteristic
164	C₄×C₄₁	—	2	2	no	—
165	C₄×C₄₁	—	8	2	no	—
166	C₄×C₄₁	#447	1	2	yes	—
167	C₄×C₄₁	C₂×#120	1	1	yes	characteristic
168	C₄×C₄₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
169	C₂³×D₈	C₂×C₄₁	1	1	yes	characteristic, complemented
170	C₂²×D₁₆	C₂×C₄₁	1	2	yes	complemented
171	C₂×#466	C₂×C₄₁	1	1	yes	characteristic, complemented
172	#2184	C₂×C₄₁	1	8	yes	direct product factor
173	C₂×#357	C₂×C₄₁	1	2	yes	complemented
174	C₂×C₂²⋊C₁₆	C₂×C₄₁	1	1	yes	characteristic, complemented
175	C₂×C₄₁	—	2	4	no	—
176	C₂×C₄₁	—	8	8	no	—
177	C₂×C₄₁	—	16	2	no	—
178	C₂×C₄₁	#2184	1	4	yes	direct product factor
179	C₂×C₄₁	C₂×#447	1	1	yes	characteristic
180	C₂×C₄₁	C₂²×D₁₆	1	1	yes	characteristic
181	C₂×C₄₁	C₂×#509	1	1	yes	characteristic
182	C₂³×D₄	—	2	1	no	—
183	C₂²×D₈	—	2	8	no	—
184	C₂²×D₈	—	2	1	no	—
185	C₂²×D₈	—	2	2	no	—
186	C₂²×D₈	C₂²×C₄₁	1	2	yes	—
187	C₂²×D₈	C₂²×C₄₁	1	4	yes	complemented
188	C₂²×D₈	C₂²×C₄₁	1	1	yes	characteristic, complemented
189	C₂³×C₈	C₂²×C₄₁	1	1	yes	characteristic
190	C₂×#121	—	2	1	no	—
191	C₂×D₁₆	—	2	8	no	—
192	C₂×D₁₆	C₂²×C₄₁	1	8	yes	complemented
193	C₂²×C₁₆	C₂²×C₄₁	1	2	yes	complemented
194	#466	—	2	2	no	—
195	#466	C₂²×C₄₁	1	4	yes	complemented
196	C₂×#107	C₂²×C₄₁	1	1	yes	characteristic, complemented
197	C₂×#102	—	2	1	no	—
198	#357	C₂²×C₄₁	1	8	yes	complemented
199	C₂²⋊C₁₆	C₂²×C₄₁	1	4	yes	complemented
200	C₄₁	C₂×#2184	1	1	yes	characteristic, direct product factor, Sylow
201	C₂⁵	—	4	1	no	—
202	C₂²×D₄	—	2	8	no	—
203	C₂²×D₄	—	2	2	no	—
204	C₂²×D₄	—	2	4	no	—
205	C₂²×D₄	—	2	1	no	—
206	C₂²×D₄	—	4	4	no	—
207	C₂²×D₄	—	4	1	no	—
208	C₂²×D₄	—	4	1	no	—
209	C₂²×D₄	—	4	2	no	—
210	C₂³×C₄	D₄×C₄₁	1	1	yes	characteristic
211	C₂×D₈	—	2	8	no	—
212	C₂×D₈	—	2	16	no	—
213	C₂×D₈	—	2	16	no	—
214	C₂×D₈	—	2	2	no	—
215	C₂×D₈	—	2	4	no	—
216	C₂×D₈	—	2	4	no	—
217	C₂×D₈	—	2	4	no	—
218	C₂×D₈	—	2	1	no	—
219	C₂×D₈	D₄×C₄₁	1	8	yes	complemented
220	C₂×D₈	C₂³×C₄₁	1	4	yes	—
221	C₂×D₈	C₂³×C₄₁	1	2	yes	complemented
222	C₂²×C₈	—	2	4	no	—
223	C₂²×C₈	D₄×C₄₁	1	1	yes	characteristic
224	C₂²×C₈	D₄×C₄₁	1	2	yes	—
225	C₂²×C₈	C₂³×C₄₁	1	2	yes	—
226	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
227	#121	—	2	4	no	—
228	#121	—	4	2	no	—
229	C₂×C₄⋊C₄	—	2	1	no	—
230	C₂×C₂²⋊C₄	—	4	1	no	—
231	D₁₆	—	2	16	no	—
232	C₂×C₁₆	—	2	4	no	—
233	C₂×C₁₆	C₂³×C₄₁	1	4	yes	complemented
234	#107	—	2	1	no	—
235	#107	C₂³×C₄₁	1	2	yes	complemented
236	#102	—	2	4	no	—
237	C₂⁴	—	4	8	no	—
238	C₂⁴	—	4	4	no	—
239	C₂⁴	—	4	2	no	—
240	C₂⁴	—	4	1	no	—
241	C₂⁴	—	8	4	no	—
242	C₂⁴	—	8	4	no	—
243	C₂⁴	D₈×C₄₁	1	1	yes	characteristic
244	C₂×D₄	—	2	16	no	—
245	C₂×D₄	—	2	8	no	—
246	C₂×D₄	—	2	4	no	—
247	C₂×D₄	—	2	2	no	—
248	C₂×D₄	—	4	8	no	—
249	C₂×D₄	—	4	8	no	—
250	C₂×D₄	—	4	16	no	—
251	C₂×D₄	—	4	4	no	—
252	C₂×D₄	—	4	2	no	—
253	C₂×D₄	—	4	4	no	—
254	C₂×D₄	—	4	2	no	—
255	C₂×D₄	—	4	1	no	—
256	C₂×D₄	—	4	4	no	—
257	C₂×D₄	—	4	2	no	—
258	C₂×D₄	—	8	4	no	—
259	C₂²×C₄	—	2	2	no	—
260	C₂²×C₄	—	2	2	no	—
261	C₂²×C₄	—	4	1	no	—
262	C₂²×C₄	D₈×C₄₁	1	1	yes	characteristic
263	C₂²×C₄	D₈×C₄₁	1	2	yes	—
264	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
265	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
266	D₈	—	2	16	no	—
267	D₈	—	2	8	no	—
268	D₈	—	2	4	no	—
269	D₈	—	2	4	no	—
270	D₈	—	4	2	no	—
271	D₈	C₂×D₄×C₄₁	1	8	yes	complemented
272	C₂×C₈	—	2	2	no	—
273	C₂×C₈	—	2	4	no	—
274	C₂×C₈	—	2	4	no	—
275	C₂×C₈	C₂×D₄×C₄₁	1	2	yes	—
276	C₂×C₈	C₂×D₄×C₄₁	1	1	yes	characteristic
277	C₂×C₈	C₂×D₄×C₄₁	1	4	yes	—
278	C₂×C₈	C₂⁴×C₄₁	1	1	yes	characteristic
279	C₄⋊C₄	—	2	2	no	—
280	C₄⋊C₄	—	4	1	no	—
281	C₂²⋊C₄	—	4	4	no	—
282	C₁₆	—	2	4	no	—
283	C₂³	—	2	2	no	—
284	C₂³	—	2	2	no	—
285	C₂³	—	4	16	no	—
286	C₂³	—	4	4	no	—
287	C₂³	—	4	8	no	—
288	C₂³	—	4	2	no	—
289	C₂³	—	8	8	no	—
290	C₂³	—	8	32	no	—
291	C₂³	—	8	4	no	—
292	C₂³	—	8	8	no	—
293	C₂³	—	8	4	no	—
294	C₂³	—	8	2	no	—
295	C₂³	—	8	2	no	—
296	C₂³	—	8	2	no	—
297	C₂³	D₁₆×C₄₁	1	4	yes	complemented
298	C₂³	C₂×D₈×C₄₁	1	2	yes	—
299	C₂³	C₂×D₈×C₄₁	1	1	yes	characteristic
300	D₄	—	2	8	no	—
301	D₄	—	4	16	no	—
302	D₄	—	4	2	no	—
303	D₄	—	4	4	no	—
304	D₄	—	4	2	no	—
305	D₄	—	4	8	no	—
306	D₄	—	8	8	no	—
307	D₄	—	8	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	—	4	2	no	—
313	C₂×C₄	—	8	2	no	—
314	C₂×C₄	#120×C₄₁	1	2	yes	—
315	C₂×C₄	C₂×D₈×C₄₁	1	2	yes	—
316	C₂×C₄	C₂×D₈×C₄₁	1	1	yes	characteristic
317	C₂×C₄	AGL(1,ℤ/8)×C₄₁	1	2	yes	—
318	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
319	C₈	—	2	2	no	—
320	C₈	#120×C₄₁	1	2	yes	—
321	C₈	C₂²×D₄×C₄₁	1	2	yes	—
322	C₂²	—	2	2	no	—
323	C₂²	—	2	8	no	—
324	C₂²	—	2	2	no	—
325	C₂²	—	4	8	no	—
326	C₂²	—	8	32	no	—
327	C₂²	—	8	4	no	—
328	C₂²	—	8	4	no	—
329	C₂²	—	8	16	no	—
330	C₂²	—	8	2	no	—
331	C₂²	—	8	2	no	—
332	C₂²	—	8	2	no	—
333	C₂²	—	16	4	no	—
334	C₂²	C₄₁×#447	1	2	yes	—
335	C₂²	C₂×D₁₆×C₄₁	1	2	yes	—
336	C₂²	C₂×D₁₆×C₄₁	1	4	yes	complemented
337	C₂²	C₄₁×#509	1	2	yes	—
338	C₂²	C₂²×D₈×C₄₁	1	1	yes	characteristic
339	C₄	—	2	2	no	—
340	C₄	—	8	2	no	—
341	C₄	C₄₁×#447	1	2	yes	—
342	C₄	C₂×#120×C₄₁	1	1	yes	characteristic
343	C₄	C₂×AGL(1,ℤ/8)×C₄₁	1	1	yes	characteristic
344	C₂	—	2	4	no	—
345	C₂	—	8	8	no	—
346	C₂	—	16	2	no	—
347	C₂	C₄₁×#2184	1	4	yes	direct product factor
348	C₂	C₂×C₄₁×#447	1	1	yes	characteristic
349	C₂	C₂²×D₁₆×C₄₁	1	1	yes	characteristic
350	C₂	C₂×C₄₁×#509	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₄₁	C₂×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₄₁
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₄₁ ◁ C₂³×C₄×C₄₁ ◁ C₂³×C₈×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂³×D₈×C₄₁	C₂	semidirect
2. C₂²×D₁₆×C₄₁	C₂	semidirect
3. C₂×C₄₁×#466	C₂	semidirect
4. C₄₁×#2184	C₂	direct (N × H)
5. C₂×C₄₁×#357	C₂	semidirect
6. C₂×C₄₁×C₂²⋊C₁₆	C₂	semidirect
12. C₂²×D₈×C₄₁	C₂²	semidirect
13. C₂²×D₈×C₄₁	C₂²	semidirect
17. C₂×D₁₆×C₄₁	C₂²	semidirect
18. C₂²×C₁₆×C₄₁	C₂²	semidirect
20. C₄₁×#466	C₂²	semidirect
21. C₂×#107×C₄₁	C₂²	semidirect
23. C₄₁×#357	C₂²	semidirect
24. C₄₁×C₂²⋊C₁₆	C₂²	semidirect
43. C₂×D₈×C₄₁	D₄	semidirect
45. C₂×D₈×C₄₁	C₂³	semidirect
57. C₂×C₁₆×C₄₁	C₂³	semidirect
59. #107×C₄₁	C₂³	semidirect
95. D₈×C₄₁	C₂×D₄	semidirect
121. C₂³×C₄₁	D₁₆	semidirect
146. C₂×#2184	C₄₁	direct (N × H)
161. C₂²×C₄₁	C₂×D₁₆	semidirect
169. C₂³×D₈	C₂×C₄₁	semidirect
170. C₂²×D₁₆	C₂×C₄₁	semidirect
171. C₂×#466	C₂×C₄₁	semidirect
172. #2184	C₂×C₄₁	direct (N × H)
173. C₂×#357	C₂×C₄₁	semidirect
174. C₂×C₂²⋊C₁₆	C₂×C₄₁	semidirect
178. C₂×C₄₁	#2184	direct (N × H)
187. C₂²×D₈	C₂²×C₄₁	semidirect
188. C₂²×D₈	C₂²×C₄₁	semidirect
192. C₂×D₁₆	C₂²×C₄₁	semidirect
193. C₂²×C₁₆	C₂²×C₄₁	semidirect
195. #466	C₂²×C₄₁	semidirect
196. C₂×#107	C₂²×C₄₁	semidirect
198. #357	C₂²×C₄₁	semidirect
199. C₂²⋊C₁₆	C₂²×C₄₁	semidirect
200. C₄₁	C₂×#2184	direct (N × H)
219. C₂×D₈	D₄×C₄₁	semidirect
221. C₂×D₈	C₂³×C₄₁	semidirect
233. C₂×C₁₆	C₂³×C₄₁	semidirect
235. #107	C₂³×C₄₁	semidirect
271. D₈	C₂×D₄×C₄₁	semidirect
297. C₂³	D₁₆×C₄₁	semidirect
336. C₂²	C₂×D₁₆×C₄₁	semidirect
347. C₂	C₄₁×#2184	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×D₈×C₄₁	2
C₂²×D₁₆×C₄₁	2
C₂×C₄₁×#466	2
C₄₁×#2184	2
C₂×C₄₁×#357	2
C₂×C₄₁×C₂²⋊C₁₆	2
C₂×#2184	41

Subgroups — C2×C41×#2184 #23809711

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄₁×#2184 #23809711