Subgroups — C₄₁×#19902 #23796103

Order 10496.

672 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₁×#3334	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄₁×#3330	C₂	1	2	yes	maximal, complemented
3	C₄₁×#3283	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₁×#1707	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₁×#1699	C₂	1	2	yes	maximal, complemented
6	C₄₁×#1673	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₁×#1669	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄₁×#1654	C₂	1	2	yes	maximal, complemented
9	C₄₁×#1654	C₂	1	2	yes	maximal, complemented
10	C₄₁×#1589	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈×D₈×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#135×C₄₁	—	2	1	no	—
13	C₄₁×#547	C₂²	1	2	yes	—
14	C₄₁×#547	C₂²	1	2	yes	—
15	C₄₁×#500	C₂²	1	1	yes	characteristic
16	C₄₁×#498	C₂²	1	2	yes	—
17	C₄₁×#494	C₂²	1	1	yes	characteristic
18	C₄₁×#487	C₂²	1	2	yes	—
19	C₄₁×#484	—	2	2	no	—
20	C₄₁×#480	—	2	2	no	—
21	C₄₁×#474	C₂²	1	2	yes	—
22	C₄₁×#474	C₂²	1	2	yes	—
23	C₄₁×#468	—	2	2	no	—
24	C₄₁×#467	—	2	1	no	—
25	C₄₁×#466	—	2	1	no	—
26	C₄₁×#461	C₂²	1	2	yes	—
27	C₄₁×#461	C₂²	1	2	yes	—
28	C₄₁×#452	—	2	2	no	—
29	C₄₁×#449	—	2	2	no	—
30	C₄×D₈×C₄₁	C₂²	1	1	yes	characteristic
31	C₄×D₈×C₄₁	C₂²	1	1	yes	characteristic
32	C₄₁×#436	C₂²	1	2	yes	—
33	C₈×D₄×C₄₁	C₂²	1	1	yes	characteristic
34	C₈×D₄×C₄₁	C₂²	1	1	yes	characteristic
35	C₂×#107×C₄₁	—	2	1	no	—
36	C₄₁×#417	—	2	2	no	—
37	C₄₁×#335	C₂²	1	1	yes	characteristic
38	C₄₁×#335	C₂²	1	1	yes	characteristic
39	C₄₁×#332	C₂²	1	2	yes	—
40	C₄₁×#332	C₂²	1	2	yes	—
41	C₄₁×D₄⋊C₈	C₂²	1	1	yes	characteristic
42	C₄₁×D₄⋊C₈	C₂²	1	1	yes	characteristic
43	C₄₁×D₄⋊C₈	C₂²	1	2	yes	—
44	C₈²×C₄₁	C₂²	1	1	yes	characteristic
45	C₂×#41×C₄₁	—	2	2	no	—
46	C₂×#41×C₄₁	—	2	2	no	—
47	#135×C₄₁	—	4	4	no	—
48	C₂×Q₁₆×C₄₁	—	2	1	no	—
49	C₂×Q₁₆×C₄₁	—	2	1	no	—
50	C₂×SD₁₆×C₄₁	—	2	2	no	—
51	C₂×SD₁₆×C₄₁	—	2	2	no	—
52	C₂×D₈×C₄₁	D₄	1	1	yes	characteristic
53	C₂×D₈×C₄₁	D₄	1	1	yes	characteristic
54	C₂×M₁₆×C₄₁	—	2	2	no	—
55	C₂²×C₈×C₄₁	—	2	1	no	—
56	C₂²×C₈×C₄₁	—	2	1	no	—
57	C₄⋊Q₈×C₄₁	C₂³	1	2	yes	—
58	C₄⋊Q₈×C₄₁	C₂³	1	2	yes	—
59	#123×C₄₁	—	4	2	no	—
60	#123×C₄₁	—	4	2	no	—
61	C₂²⋊Q₈×C₄₁	—	2	2	no	—
62	C₂²⋊Q₈×C₄₁	—	2	2	no	—
63	#121×C₄₁	—	2	2	no	—
64	#121×C₄₁	—	2	2	no	—
65	C₄×D₄×C₄₁	C₂³	1	1	yes	characteristic
66	C₄×D₄×C₄₁	C₂³	1	1	yes	characteristic
67	C₄×D₄×C₄₁	C₂³	1	2	yes	—
68	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
69	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
70	#107×C₄₁	—	2	1	no	—
71	#107×C₄₁	—	2	1	no	—
72	#107×C₄₁	—	2	2	no	—
73	#107×C₄₁	—	2	2	no	—
74	#107×C₄₁	D₄	1	1	yes	characteristic
75	#107×C₄₁	D₄	1	1	yes	characteristic
76	#106×C₄₁	—	4	2	no	—
77	C₄⋊C₈×C₄₁	C₂³	1	1	yes	characteristic
78	C₄⋊C₈×C₄₁	C₂³	1	1	yes	characteristic
79	C₄⋊C₈×C₄₁	C₂³	1	2	yes	—
80	#103×C₄₁	—	2	2	no	—
81	#103×C₄₁	—	2	2	no	—
82	#103×C₄₁	—	2	2	no	—
83	#103×C₄₁	—	2	2	no	—
84	#102×C₄₁	—	2	2	no	—
85	#102×C₄₁	—	2	2	no	—
86	#102×C₄₁	D₄	1	1	yes	characteristic
87	#102×C₄₁	D₄	1	2	yes	—
88	#102×C₄₁	D₄	1	1	yes	characteristic
89	C₂²⋊C₈×C₄₁	—	2	1	no	—
90	C₂²⋊C₈×C₄₁	—	2	1	no	—
91	C₂²⋊C₈×C₄₁	—	2	2	no	—
92	C₄×C₈×C₄₁	C₂³	1	1	yes	characteristic
93	C₄×C₈×C₄₁	C₂³	1	1	yes	characteristic
94	C₄×C₈×C₄₁	C₂³	1	1	yes	characteristic
95	#41×C₄₁	—	4	4	no	—
96	#41×C₄₁	—	4	4	no	—
97	#41×C₄₁	—	8	2	no	—
98	#41×C₄₁	—	8	2	no	—
99	C₂×Q₈×C₄₁	—	2	2	no	—
100	C₂×Q₈×C₄₁	—	2	2	no	—
101	C₂×D₄×C₄₁	—	4	2	no	—
102	C₂×D₄×C₄₁	—	4	2	no	—
103	C₂×D₄×C₄₁	C₂×D₄	1	2	yes	—
104	C₂×D₄×C₄₁	C₂×D₄	1	1	yes	characteristic
105	C₂×D₄×C₄₁	C₂×D₄	1	1	yes	characteristic
106	C₂²×C₄×C₄₁	—	2	1	no	—
107	C₂²×C₄×C₄₁	—	2	2	no	—
108	C₂²×C₄×C₄₁	—	2	1	no	—
109	C₂²×C₄×C₄₁	—	4	2	no	—
110	C₂²×C₄×C₄₁	—	4	2	no	—
111	Q₁₆×C₄₁	—	4	2	no	—
112	Q₁₆×C₄₁	—	8	1	no	—
113	SD₁₆×C₄₁	—	4	4	no	—
114	SD₁₆×C₄₁	—	8	2	no	—
115	D₈×C₄₁	—	2	2	no	—
116	D₈×C₄₁	—	2	2	no	—
117	M₁₆×C₄₁	—	8	2	no	—
118	C₂×C₈×C₄₁	—	2	1	no	—
119	C₂×C₈×C₄₁	—	2	1	no	—
120	C₂×C₈×C₄₁	—	2	2	no	—
121	C₂×C₈×C₄₁	—	2	1	no	—
122	C₂×C₈×C₄₁	—	4	2	no	—
123	C₂×C₈×C₄₁	—	4	2	no	—
124	C₂×C₈×C₄₁	C₂×D₄	1	1	yes	characteristic
125	C₂×C₈×C₄₁	C₂×D₄	1	1	yes	characteristic
126	C₂×C₈×C₄₁	C₂×D₄	1	1	yes	characteristic
127	C₂×C₈×C₄₁	C₂×D₄	1	1	yes	characteristic
128	C₄⋊C₄×C₄₁	—	2	2	no	—
129	C₄⋊C₄×C₄₁	—	2	2	no	—
130	C₄⋊C₄×C₄₁	—	2	2	no	—
131	C₄⋊C₄×C₄₁	—	2	2	no	—
132	C₄⋊C₄×C₄₁	—	4	2	no	—
133	C₄⋊C₄×C₄₁	—	4	2	no	—
134	C₄⋊C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
135	C₄⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
136	C₄⋊C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
137	C₂²⋊C₄×C₄₁	—	2	1	no	—
138	C₂²⋊C₄×C₄₁	—	2	2	no	—
139	C₂²⋊C₄×C₄₁	—	2	1	no	—
140	C₂²⋊C₄×C₄₁	—	4	2	no	—
141	C₂²⋊C₄×C₄₁	—	4	2	no	—
142	C₄²×C₄₁	C₂⁴	1	1	yes	characteristic
143	C₂³×C₄₁	—	2	1	no	—
144	C₂³×C₄₁	—	2	1	no	—
145	C₂³×C₄₁	—	2	2	no	—
146	Q₈×C₄₁	—	4	2	no	—
147	Q₈×C₄₁	—	4	2	no	—
148	Q₈×C₄₁	—	4	2	no	—
149	Q₈×C₄₁	—	4	2	no	—
150	D₄×C₄₁	—	2	1	no	—
151	D₄×C₄₁	—	2	2	no	—
152	D₄×C₄₁	—	2	1	no	—
153	D₄×C₄₁	—	2	1	no	—
154	D₄×C₄₁	—	2	2	no	—
155	D₄×C₄₁	—	8	4	no	—
156	D₄×C₄₁	—	8	4	no	—
157	D₄×C₄₁	#135	1	2	yes	complemented
158	C₂×C₄×C₄₁	—	2	1	no	—
159	C₂×C₄×C₄₁	—	2	2	no	—
160	C₂×C₄×C₄₁	—	2	1	no	—
161	C₂×C₄×C₄₁	—	4	2	no	—
162	C₂×C₄×C₄₁	—	4	1	no	—
163	C₂×C₄×C₄₁	—	4	1	no	—
164	C₂×C₄×C₄₁	—	4	2	no	—
165	C₂×C₄×C₄₁	—	4	1	no	—
166	C₂×C₄×C₄₁	—	4	1	no	—
167	C₂×C₄×C₄₁	—	4	2	no	—
168	C₂×C₄×C₄₁	—	4	2	no	—
169	C₂×C₄×C₄₁	—	8	4	no	—
170	C₂×C₄×C₄₁	—	8	4	no	—
171	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
172	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
173	C₂×C₄×C₄₁	H(5,𝔽₂)	1	1	yes	characteristic
174	C₈×C₄₁	—	2	2	no	—
175	C₈×C₄₁	—	2	1	no	—
176	C₈×C₄₁	—	2	1	no	—
177	C₈×C₄₁	—	2	1	no	—
178	C₈×C₄₁	—	4	1	no	—
179	C₈×C₄₁	—	4	1	no	—
180	C₈×C₄₁	—	4	2	no	—
181	C₈×C₄₁	AGL(1,ℤ/8)	1	2	yes	—
182	#19902	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
183	C₂²×C₄₁	—	2	2	no	—
184	C₂²×C₄₁	—	4	1	no	—
185	C₂²×C₄₁	—	4	1	no	—
186	C₂²×C₄₁	—	4	1	no	—
187	C₂²×C₄₁	—	4	2	no	—
188	C₂²×C₄₁	—	4	2	no	—
189	C₂²×C₄₁	—	4	1	no	—
190	C₂²×C₄₁	—	4	1	no	—
191	C₂²×C₄₁	—	4	2	no	—
192	C₂²×C₄₁	D₄²	1	1	yes	characteristic
193	C₄×C₄₁	—	2	1	no	—
194	C₄×C₄₁	—	4	1	no	—
195	C₄×C₄₁	—	4	1	no	—
196	C₄×C₄₁	—	4	2	no	—
197	C₄×C₄₁	—	8	2	no	—
198	C₄×C₄₁	—	8	2	no	—
199	C₄×C₄₁	C₂×#135	1	1	yes	characteristic
200	C₄×C₄₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
201	C₄×C₄₁	#576	1	1	yes	characteristic
202	C₄×C₄₁	#577	1	1	yes	characteristic
203	#3334	C₂×C₄₁	1	1	yes	characteristic, complemented
204	#3330	C₂×C₄₁	1	2	yes	complemented
205	#3283	C₂×C₄₁	1	1	yes	characteristic, complemented
206	#1707	C₂×C₄₁	1	1	yes	characteristic, complemented
207	#1699	C₂×C₄₁	1	2	yes	complemented
208	#1673	C₂×C₄₁	1	1	yes	characteristic, complemented
209	#1669	C₂×C₄₁	1	1	yes	characteristic, complemented
210	#1654	C₂×C₄₁	1	2	yes	complemented
211	#1654	C₂×C₄₁	1	2	yes	complemented
212	#1589	C₂×C₄₁	1	1	yes	characteristic, complemented
213	C₈×D₈	C₂×C₄₁	1	1	yes	characteristic, complemented
214	C₂×C₄₁	—	4	2	no	—
215	C₂×C₄₁	—	8	1	no	—
216	C₂×C₄₁	—	8	2	no	—
217	C₂×C₄₁	#3272	1	1	yes	characteristic
218	C₂×C₄₁	#3280	1	1	yes	characteristic
219	C₂×C₄₁	#3293	1	1	yes	characteristic
220	C₂×#135	—	2	1	no	—
221	#547	C₂²×C₄₁	1	2	yes	—
222	#547	C₂²×C₄₁	1	2	yes	—
223	#500	C₂²×C₄₁	1	1	yes	characteristic
224	#498	C₂²×C₄₁	1	2	yes	—
225	#494	C₂²×C₄₁	1	1	yes	characteristic
226	#487	C₂²×C₄₁	1	2	yes	—
227	#484	—	2	2	no	—
228	#480	—	2	2	no	—
229	#474	C₂²×C₄₁	1	2	yes	—
230	#474	C₂²×C₄₁	1	2	yes	—
231	#468	—	2	2	no	—
232	#467	—	2	1	no	—
233	#466	—	2	1	no	—
234	#461	C₂²×C₄₁	1	2	yes	—
235	#461	C₂²×C₄₁	1	2	yes	—
236	#452	—	2	2	no	—
237	#449	—	2	2	no	—
238	C₄×D₈	C₂²×C₄₁	1	1	yes	characteristic
239	C₄×D₈	C₂²×C₄₁	1	1	yes	characteristic
240	#436	C₂²×C₄₁	1	2	yes	—
241	C₈×D₄	C₂²×C₄₁	1	1	yes	characteristic
242	C₈×D₄	C₂²×C₄₁	1	1	yes	characteristic
243	C₂×#107	—	2	1	no	—
244	#417	—	2	2	no	—
245	#335	C₂²×C₄₁	1	1	yes	characteristic
246	#335	C₂²×C₄₁	1	1	yes	characteristic
247	#332	C₂²×C₄₁	1	2	yes	—
248	#332	C₂²×C₄₁	1	2	yes	—
249	D₄⋊C₈	C₂²×C₄₁	1	1	yes	characteristic
250	D₄⋊C₈	C₂²×C₄₁	1	1	yes	characteristic
251	D₄⋊C₈	C₂²×C₄₁	1	2	yes	—
252	C₈²	C₂²×C₄₁	1	1	yes	characteristic
253	C₄₁	#19902	1	1	yes	characteristic, direct product factor, Sylow
254	C₂×#41	—	2	2	no	—
255	C₂×#41	—	2	2	no	—
256	#135	—	4	4	no	—
257	C₂×Q₁₆	—	2	1	no	—
258	C₂×Q₁₆	—	2	1	no	—
259	C₂×SD₁₆	—	2	2	no	—
260	C₂×SD₁₆	—	2	2	no	—
261	C₂×D₈	D₄×C₄₁	1	1	yes	characteristic
262	C₂×D₈	D₄×C₄₁	1	1	yes	characteristic
263	C₂×M₁₆	—	2	2	no	—
264	C₂²×C₈	—	2	1	no	—
265	C₂²×C₈	—	2	1	no	—
266	C₄⋊Q₈	C₂³×C₄₁	1	2	yes	—
267	C₄⋊Q₈	C₂³×C₄₁	1	2	yes	—
268	#123	—	4	2	no	—
269	#123	—	4	2	no	—
270	C₂²⋊Q₈	—	2	2	no	—
271	C₂²⋊Q₈	—	2	2	no	—
272	#121	—	2	2	no	—
273	#121	—	2	2	no	—
274	C₄×D₄	C₂³×C₄₁	1	1	yes	characteristic
275	C₄×D₄	C₂³×C₄₁	1	1	yes	characteristic
276	C₄×D₄	C₂³×C₄₁	1	2	yes	—
277	C₂×C₄⋊C₄	—	2	2	no	—
278	C₂×C₄⋊C₄	—	2	2	no	—
279	#107	—	2	1	no	—
280	#107	—	2	1	no	—
281	#107	—	2	2	no	—
282	#107	—	2	2	no	—
283	#107	D₄×C₄₁	1	1	yes	characteristic
284	#107	D₄×C₄₁	1	1	yes	characteristic
285	#106	—	4	2	no	—
286	C₄⋊C₈	C₂³×C₄₁	1	1	yes	characteristic
287	C₄⋊C₈	C₂³×C₄₁	1	1	yes	characteristic
288	C₄⋊C₈	C₂³×C₄₁	1	2	yes	—
289	#103	—	2	2	no	—
290	#103	—	2	2	no	—
291	#103	—	2	2	no	—
292	#103	—	2	2	no	—
293	#102	—	2	2	no	—
294	#102	—	2	2	no	—
295	#102	D₄×C₄₁	1	1	yes	characteristic
296	#102	D₄×C₄₁	1	2	yes	—
297	#102	D₄×C₄₁	1	1	yes	characteristic
298	C₂²⋊C₈	—	2	1	no	—
299	C₂²⋊C₈	—	2	1	no	—
300	C₂²⋊C₈	—	2	2	no	—
301	C₄×C₈	C₂³×C₄₁	1	1	yes	characteristic
302	C₄×C₈	C₂³×C₄₁	1	1	yes	characteristic
303	C₄×C₈	C₂³×C₄₁	1	1	yes	characteristic
304	#41	—	4	4	no	—
305	#41	—	4	4	no	—
306	#41	—	8	2	no	—
307	#41	—	8	2	no	—
308	C₂×Q₈	—	2	2	no	—
309	C₂×Q₈	—	2	2	no	—
310	C₂×D₄	—	4	2	no	—
311	C₂×D₄	—	4	2	no	—
312	C₂×D₄	C₂×D₄×C₄₁	1	2	yes	—
313	C₂×D₄	C₂×D₄×C₄₁	1	1	yes	characteristic
314	C₂×D₄	C₂×D₄×C₄₁	1	1	yes	characteristic
315	C₂²×C₄	—	2	1	no	—
316	C₂²×C₄	—	2	2	no	—
317	C₂²×C₄	—	2	1	no	—
318	C₂²×C₄	—	4	2	no	—
319	C₂²×C₄	—	4	2	no	—
320	Q₁₆	—	4	2	no	—
321	Q₁₆	—	8	1	no	—
322	SD₁₆	—	4	4	no	—
323	SD₁₆	—	8	2	no	—
324	D₈	—	2	2	no	—
325	D₈	—	2	2	no	—
326	M₁₆	—	8	2	no	—
327	C₂×C₈	—	2	1	no	—
328	C₂×C₈	—	2	1	no	—
329	C₂×C₈	—	2	2	no	—
330	C₂×C₈	—	2	1	no	—
331	C₂×C₈	—	4	2	no	—
332	C₂×C₈	—	4	2	no	—
333	C₂×C₈	C₂×D₄×C₄₁	1	1	yes	characteristic
334	C₂×C₈	C₂×D₄×C₄₁	1	1	yes	characteristic
335	C₂×C₈	C₂×D₄×C₄₁	1	1	yes	characteristic
336	C₂×C₈	C₂×D₄×C₄₁	1	1	yes	characteristic
337	C₄⋊C₄	—	2	2	no	—
338	C₄⋊C₄	—	2	2	no	—
339	C₄⋊C₄	—	2	2	no	—
340	C₄⋊C₄	—	2	2	no	—
341	C₄⋊C₄	—	4	2	no	—
342	C₄⋊C₄	—	4	2	no	—
343	C₄⋊C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
344	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
345	C₄⋊C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
346	C₂²⋊C₄	—	2	1	no	—
347	C₂²⋊C₄	—	2	2	no	—
348	C₂²⋊C₄	—	2	1	no	—
349	C₂²⋊C₄	—	4	2	no	—
350	C₂²⋊C₄	—	4	2	no	—
351	C₄²	C₂⁴×C₄₁	1	1	yes	characteristic
352	C₂³	—	2	1	no	—
353	C₂³	—	2	1	no	—
354	C₂³	—	2	2	no	—
355	Q₈	—	4	2	no	—
356	Q₈	—	4	2	no	—
357	Q₈	—	4	2	no	—
358	Q₈	—	4	2	no	—
359	D₄	—	2	1	no	—
360	D₄	—	2	2	no	—
361	D₄	—	2	1	no	—
362	D₄	—	2	1	no	—
363	D₄	—	2	2	no	—
364	D₄	—	8	4	no	—
365	D₄	—	8	4	no	—
366	D₄	#135×C₄₁	1	2	yes	complemented
367	C₂×C₄	—	2	1	no	—
368	C₂×C₄	—	2	2	no	—
369	C₂×C₄	—	2	1	no	—
370	C₂×C₄	—	4	2	no	—
371	C₂×C₄	—	4	1	no	—
372	C₂×C₄	—	4	1	no	—
373	C₂×C₄	—	4	2	no	—
374	C₂×C₄	—	4	1	no	—
375	C₂×C₄	—	4	1	no	—
376	C₂×C₄	—	4	2	no	—
377	C₂×C₄	—	4	2	no	—
378	C₂×C₄	—	8	4	no	—
379	C₂×C₄	—	8	4	no	—
380	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
381	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
382	C₂×C₄	H(5,𝔽₂)×C₄₁	1	1	yes	characteristic
383	C₈	—	2	2	no	—
384	C₈	—	2	1	no	—
385	C₈	—	2	1	no	—
386	C₈	—	2	1	no	—
387	C₈	—	4	1	no	—
388	C₈	—	4	1	no	—
389	C₈	—	4	2	no	—
390	C₈	AGL(1,ℤ/8)×C₄₁	1	2	yes	—
391	C₂²	—	2	2	no	—
392	C₂²	—	4	1	no	—
393	C₂²	—	4	1	no	—
394	C₂²	—	4	1	no	—
395	C₂²	—	4	2	no	—
396	C₂²	—	4	1	no	—
397	C₂²	—	4	2	no	—
398	C₂²	—	4	2	no	—
399	C₂²	—	4	1	no	—
400	C₂²	D₄²×C₄₁	1	1	yes	characteristic
401	C₄	—	2	1	no	—
402	C₄	—	4	1	no	—
403	C₄	—	4	1	no	—
404	C₄	—	4	2	no	—
405	C₄	—	8	2	no	—
406	C₄	—	8	2	no	—
407	C₄	C₂×#135×C₄₁	1	1	yes	characteristic
408	C₄	C₂×AGL(1,ℤ/8)×C₄₁	1	1	yes	characteristic
409	C₄	C₄₁×#576	1	1	yes	characteristic
410	C₄	C₄₁×#577	1	1	yes	characteristic
411	C₂	—	4	2	no	—
412	C₂	—	8	1	no	—
413	C₂	—	8	2	no	—
414	C₂	C₄₁×#3272	1	1	yes	characteristic
415	C₂	C₄₁×#3280	1	1	yes	characteristic
416	C₂	C₄₁×#3293	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×#3334	C₂	semidirect
2. C₄₁×#3330	C₂	semidirect
3. C₄₁×#3283	C₂	semidirect
4. C₄₁×#1707	C₂	semidirect
5. C₄₁×#1699	C₂	semidirect
6. C₄₁×#1673	C₂	semidirect
7. C₄₁×#1669	C₂	semidirect
8. C₄₁×#1654	C₂	semidirect
9. C₄₁×#1654	C₂	semidirect
10. C₄₁×#1589	C₂	semidirect
11. C₈×D₈×C₄₁	C₂	semidirect
157. D₄×C₄₁	#135	semidirect
182. #19902	C₄₁	direct (N × H)
203. #3334	C₂×C₄₁	semidirect
204. #3330	C₂×C₄₁	semidirect
205. #3283	C₂×C₄₁	semidirect
206. #1707	C₂×C₄₁	semidirect
207. #1699	C₂×C₄₁	semidirect
208. #1673	C₂×C₄₁	semidirect
209. #1669	C₂×C₄₁	semidirect
210. #1654	C₂×C₄₁	semidirect
211. #1654	C₂×C₄₁	semidirect
212. #1589	C₂×C₄₁	semidirect
213. C₈×D₈	C₂×C₄₁	semidirect
253. C₄₁	#19902	direct (N × H)
366. D₄	#135×C₄₁	semidirect

Maximal subgroups

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

subgroup	index
C₄₁×#3334	2
C₄₁×#3330	2
C₄₁×#3283	2
C₄₁×#1707	2
C₄₁×#1699	2
C₄₁×#1673	2
C₄₁×#1669	2
C₄₁×#1654	2
C₄₁×#1589	2
C₈×D₈×C₄₁	2
#19902	41

Subgroups — C41×#19902 #23796103

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#19902 #23796103