Subgroups — C₄₁×#33859 #23810060

Order 10496.

646 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₁×#3417	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄₁×#3415	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₁×#3290	C₂	1	2	yes	maximal, complemented
4	C₄₁×#2249	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₁×#2222	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄₁×#2221	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₁×#2212	C₂	1	2	yes	maximal, complemented
8	C₄₁×#2194	C₂	1	2	yes	maximal, complemented
9	C₄₁×#2193	C₂	1	2	yes	maximal, complemented
10	C₄₁×#2178	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₁×#2170	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄₁×#578	C₂²	1	2	yes	complemented
13	C₄₁×#577	—	2	2	no	—
14	C₄₁×#576	C₂²	1	2	yes	—
15	C₄₁×#510	—	2	2	no	—
16	C₄₁×#510	C₂²	1	2	yes	complemented
17	C₄₁×#509	—	2	2	no	—
18	C₄₁×#509	C₂²	1	2	yes	—
19	C₄₁×#508	—	2	1	no	—
20	C₄₁×#508	—	2	1	no	—
21	C₄₁×#508	C₂²	1	1	yes	characteristic
22	C₂×Q₃₂×C₄₁	—	2	1	no	—
23	C₂×Q₃₂×C₄₁	C₂²	1	1	yes	characteristic, complemented
24	C₂×SD₃₂×C₄₁	C₂²	1	2	yes	complemented
25	C₂×D₁₆×C₄₁	—	2	1	no	—
26	C₂×D₁₆×C₄₁	C₂²	1	1	yes	characteristic
27	C₄₁×#504	C₂²	1	1	yes	characteristic
28	C₄₁×#504	C₂²	1	1	yes	characteristic, complemented
29	C₄₁×#495	C₂²	1	2	yes	complemented
30	C₄₁×#473	C₂²	1	2	yes	—
31	C₄₁×#472	C₂²	1	2	yes	complemented
32	C₄₁×#471	—	2	2	no	—
33	C₄₁×#455	—	2	2	no	—
34	C₄₁×#454	—	2	2	no	—
35	C₄₁×#443	C₂²	1	1	yes	characteristic
36	C₄₁×#443	C₂²	1	2	yes	complemented
37	C₄₁×#368	C₂²	1	1	yes	characteristic, complemented
38	C₄₁×#364	C₂²	1	1	yes	characteristic, complemented
39	C₄₁×#362	C₂²	1	2	yes	complemented
40	C₄₁×#361	C₂²	1	2	yes	complemented
41	C₄₁×#359	C₂²	1	2	yes	complemented
42	C₄₁×#350	C₂²	1	1	yes	characteristic
43	C₄₁×#350	C₂²	1	1	yes	characteristic, complemented
44	C₄×C₁₆×C₄₁	C₂²	1	1	yes	characteristic, complemented
45	2₋¹⁺⁴×C₄₁	—	2	2	no	—
46	H(5,𝔽₂)×C₄₁	—	2	2	no	—
47	#137×C₄₁	—	2	2	no	—
48	#137×C₄₁	—	2	2	no	—
49	#137×C₄₁	—	4	2	no	—
50	#137×C₄₁	—	4	2	no	—
51	AGL(1,ℤ/8)×C₄₁	—	2	2	no	—
52	AGL(1,ℤ/8)×C₄₁	—	2	2	no	—
53	AGL(1,ℤ/8)×C₄₁	—	4	2	no	—
54	AGL(1,ℤ/8)×C₄₁	—	4	2	no	—
55	#135×C₄₁	—	2	2	no	—
56	#135×C₄₁	—	2	2	no	—
57	#135×C₄₁	—	4	2	no	—
58	#135×C₄₁	D₄	1	1	yes	characteristic
59	#135×C₄₁	C₂³	1	2	yes	—
60	C₂×Q₁₆×C₄₁	—	2	2	no	—
61	C₂×Q₁₆×C₄₁	C₂³	1	2	yes	—
62	C₂×SD₁₆×C₄₁	—	2	2	no	—
63	C₂×SD₁₆×C₄₁	—	4	2	no	—
64	C₂×D₈×C₄₁	—	2	2	no	—
65	C₂×D₈×C₄₁	C₂³	1	2	yes	—
66	#131×C₄₁	—	2	2	no	—
67	#131×C₄₁	C₂³	1	1	yes	characteristic
68	#131×C₄₁	C₂³	1	1	yes	characteristic
69	#124×C₄₁	—	2	2	no	—
70	Q₃₂×C₄₁	—	2	2	no	—
71	Q₃₂×C₄₁	—	2	1	no	—
72	Q₃₂×C₄₁	—	2	1	no	—
73	Q₃₂×C₄₁	D₄	1	1	yes	characteristic
74	SD₃₂×C₄₁	—	2	2	no	—
75	SD₃₂×C₄₁	—	2	2	no	—
76	SD₃₂×C₄₁	—	4	2	no	—
77	SD₃₂×C₄₁	D₄	1	2	yes	—
78	D₁₆×C₄₁	—	2	2	no	—
79	D₁₆×C₄₁	—	2	1	no	—
80	D₁₆×C₄₁	—	2	1	no	—
81	D₁₆×C₄₁	D₄	1	1	yes	characteristic
82	M₃₂×C₄₁	—	2	1	no	—
83	M₃₂×C₄₁	—	2	1	no	—
84	M₃₂×C₄₁	C₂³	1	1	yes	characteristic
85	M₃₂×C₄₁	C₂³	1	1	yes	characteristic
86	C₂×C₁₆×C₄₁	—	2	1	no	—
87	C₂×C₁₆×C₄₁	—	2	1	no	—
88	C₂×C₁₆×C₄₁	C₂³	1	1	yes	characteristic
89	C₂×C₁₆×C₄₁	C₂³	1	1	yes	characteristic
90	#108×C₄₁	D₄	1	1	yes	characteristic
91	#108×C₄₁	C₂³	1	2	yes	—
92	#104×C₄₁	—	2	2	no	—
93	#104×C₄₁	D₄	1	1	yes	characteristic
94	#104×C₄₁	D₄	1	1	yes	characteristic
95	#101×C₄₁	—	2	2	no	—
96	#100×C₄₁	—	2	2	no	—
97	C₄×C₈×C₄₁	C₂³	1	1	yes	characteristic
98	#41×C₄₁	—	2	2	no	—
99	#41×C₄₁	—	4	2	no	—
100	#41×C₄₁	—	4	2	no	—
101	#41×C₄₁	—	4	2	no	—
102	#41×C₄₁	—	4	2	no	—
103	#41×C₄₁	—	8	2	no	—
104	#41×C₄₁	C₂×D₄	1	1	yes	characteristic
105	#41×C₄₁	C₂×D₄	1	1	yes	characteristic
106	C₂×Q₈×C₄₁	—	2	2	no	—
107	C₂×Q₈×C₄₁	—	4	2	no	—
108	C₂×Q₈×C₄₁	—	4	2	no	—
109	C₂×D₄×C₄₁	—	2	2	no	—
110	C₂×D₄×C₄₁	—	4	2	no	—
111	C₂×D₄×C₄₁	—	4	2	no	—
112	C₂×D₄×C₄₁	—	8	2	no	—
113	Q₁₆×C₄₁	—	2	2	no	—
114	Q₁₆×C₄₁	—	2	2	no	—
115	Q₁₆×C₄₁	—	4	2	no	—
116	Q₁₆×C₄₁	—	4	2	no	—
117	Q₁₆×C₄₁	D₈	1	1	yes	characteristic
118	Q₁₆×C₄₁	C₂×D₄	1	2	yes	—
119	SD₁₆×C₄₁	—	2	2	no	—
120	SD₁₆×C₄₁	—	4	2	no	—
121	SD₁₆×C₄₁	—	4	2	no	—
122	SD₁₆×C₄₁	—	4	2	no	—
123	SD₁₆×C₄₁	—	4	2	no	—
124	SD₁₆×C₄₁	—	4	2	no	—
125	SD₁₆×C₄₁	—	4	2	no	—
126	SD₁₆×C₄₁	D₈	1	1	yes	characteristic
127	SD₁₆×C₄₁	D₈	1	1	yes	characteristic
128	D₈×C₄₁	—	2	2	no	—
129	D₈×C₄₁	—	2	2	no	—
130	D₈×C₄₁	—	4	2	no	—
131	D₈×C₄₁	—	4	2	no	—
132	D₈×C₄₁	D₈	1	1	yes	characteristic
133	D₈×C₄₁	C₂×D₄	1	2	yes	—
134	M₁₆×C₄₁	—	2	1	no	—
135	M₁₆×C₄₁	—	2	1	no	—
136	M₁₆×C₄₁	—	2	2	no	—
137	M₁₆×C₄₁	—	4	2	no	—
138	M₁₆×C₄₁	C₂×D₄	1	1	yes	characteristic
139	M₁₆×C₄₁	C₂×D₄	1	1	yes	characteristic
140	C₂×C₈×C₄₁	—	2	1	no	—
141	C₂×C₈×C₄₁	—	2	1	no	—
142	C₂×C₈×C₄₁	—	4	2	no	—
143	C₂×C₈×C₄₁	C₂×D₄	1	1	yes	characteristic
144	C₂×C₈×C₄₁	C₂⁴	1	1	yes	characteristic
145	C₂²⋊C₄×C₄₁	—	8	2	no	—
146	C₄²×C₄₁	C₂×D₄	1	1	yes	characteristic
147	C₁₆×C₄₁	—	2	1	no	—
148	C₁₆×C₄₁	—	2	1	no	—
149	C₁₆×C₄₁	—	2	1	no	—
150	C₁₆×C₄₁	C₂×D₄	1	1	yes	characteristic
151	C₁₆×C₄₁	C₂×D₄	1	1	yes	characteristic
152	C₂³×C₄₁	—	4	2	no	—
153	C₂³×C₄₁	—	8	2	no	—
154	Q₈×C₄₁	—	2	2	no	—
155	Q₈×C₄₁	—	4	2	no	—
156	Q₈×C₄₁	—	4	2	no	—
157	Q₈×C₄₁	—	8	2	no	—
158	Q₈×C₄₁	C₂×D₈	1	1	yes	characteristic
159	Q₈×C₄₁	C₂×D₈	1	1	yes	characteristic
160	D₄×C₄₁	—	2	1	no	—
161	D₄×C₄₁	—	2	1	no	—
162	D₄×C₄₁	—	2	2	no	—
163	D₄×C₄₁	—	4	2	no	—
164	D₄×C₄₁	—	4	2	no	—
165	D₄×C₄₁	—	4	2	no	—
166	D₄×C₄₁	—	8	2	no	—
167	D₄×C₄₁	—	8	2	no	—
168	D₄×C₄₁	—	8	2	no	—
169	D₄×C₄₁	C₂×D₈	1	1	yes	characteristic
170	D₄×C₄₁	C₂×D₈	1	1	yes	characteristic
171	C₂×C₄×C₄₁	—	2	1	no	—
172	C₂×C₄×C₄₁	—	2	1	no	—
173	C₂×C₄×C₄₁	—	2	1	no	—
174	C₂×C₄×C₄₁	—	4	2	no	—
175	C₂×C₄×C₄₁	—	4	2	no	—
176	C₂×C₄×C₄₁	—	8	2	no	—
177	C₂×C₄×C₄₁	—	8	2	no	—
178	C₂×C₄×C₄₁	—	8	2	no	—
179	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
180	C₈×C₄₁	—	2	1	no	—
181	C₈×C₄₁	—	2	1	no	—
182	C₈×C₄₁	—	4	2	no	—
183	C₈×C₄₁	C₂×D₈	1	1	yes	characteristic
184	C₈×C₄₁	C₂×D₈	1	1	yes	characteristic
185	C₈×C₄₁	C₂²×D₄	1	1	yes	characteristic
186	C₈×C₄₁	H(5,𝔽₂)	1	1	yes	characteristic
187	#33859	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
188	C₂²×C₄₁	—	2	1	no	—
189	C₂²×C₄₁	—	2	1	no	—
190	C₂²×C₄₁	—	4	2	no	—
191	C₂²×C₄₁	—	8	2	no	—
192	C₂²×C₄₁	—	16	2	no	—
193	C₂²×C₄₁	—	32	2	no	—
194	C₂²×C₄₁	#576	1	1	yes	characteristic
195	C₄×C₄₁	—	2	1	no	—
196	C₄×C₄₁	—	2	1	no	—
197	C₄×C₄₁	—	4	1	no	—
198	C₄×C₄₁	—	4	2	no	—
199	C₄×C₄₁	—	8	2	no	—
200	C₄×C₄₁	D₄²	1	1	yes	characteristic
201	C₄×C₄₁	C₂²×D₈	1	1	yes	characteristic
202	#3417	C₂×C₄₁	1	1	yes	characteristic, complemented
203	#3415	C₂×C₄₁	1	1	yes	characteristic, complemented
204	#3290	C₂×C₄₁	1	2	yes	complemented
205	#2249	C₂×C₄₁	1	1	yes	characteristic, complemented
206	#2222	C₂×C₄₁	1	1	yes	characteristic, complemented
207	#2221	C₂×C₄₁	1	1	yes	characteristic, complemented
208	#2212	C₂×C₄₁	1	2	yes	complemented
209	#2194	C₂×C₄₁	1	2	yes	complemented
210	#2193	C₂×C₄₁	1	2	yes	complemented
211	#2178	C₂×C₄₁	1	1	yes	characteristic, complemented
212	#2170	C₂×C₄₁	1	1	yes	characteristic, complemented
213	C₂×C₄₁	—	2	1	no	—
214	C₂×C₄₁	—	4	1	no	—
215	C₂×C₄₁	—	4	1	no	—
216	C₂×C₄₁	—	8	2	no	—
217	C₂×C₄₁	—	16	2	no	—
218	C₂×C₄₁	D₄×D₈	1	1	yes	characteristic
219	#578	C₂²×C₄₁	1	2	yes	complemented
220	#577	—	2	2	no	—
221	#576	C₂²×C₄₁	1	2	yes	—
222	#510	—	2	2	no	—
223	#510	C₂²×C₄₁	1	2	yes	complemented
224	#509	—	2	2	no	—
225	#509	C₂²×C₄₁	1	2	yes	—
226	#508	—	2	1	no	—
227	#508	—	2	1	no	—
228	#508	C₂²×C₄₁	1	1	yes	characteristic
229	C₂×Q₃₂	—	2	1	no	—
230	C₂×Q₃₂	C₂²×C₄₁	1	1	yes	characteristic, complemented
231	C₂×SD₃₂	C₂²×C₄₁	1	2	yes	complemented
232	C₂×D₁₆	—	2	1	no	—
233	C₂×D₁₆	C₂²×C₄₁	1	1	yes	characteristic
234	#504	C₂²×C₄₁	1	1	yes	characteristic
235	#504	C₂²×C₄₁	1	1	yes	characteristic, complemented
236	#495	C₂²×C₄₁	1	2	yes	complemented
237	#473	C₂²×C₄₁	1	2	yes	—
238	#472	C₂²×C₄₁	1	2	yes	complemented
239	#471	—	2	2	no	—
240	#455	—	2	2	no	—
241	#454	—	2	2	no	—
242	#443	C₂²×C₄₁	1	1	yes	characteristic
243	#443	C₂²×C₄₁	1	2	yes	complemented
244	#368	C₂²×C₄₁	1	1	yes	characteristic, complemented
245	#364	C₂²×C₄₁	1	1	yes	characteristic, complemented
246	#362	C₂²×C₄₁	1	2	yes	complemented
247	#361	C₂²×C₄₁	1	2	yes	complemented
248	#359	C₂²×C₄₁	1	2	yes	complemented
249	#350	C₂²×C₄₁	1	1	yes	characteristic
250	#350	C₂²×C₄₁	1	1	yes	characteristic, complemented
251	C₄×C₁₆	C₂²×C₄₁	1	1	yes	characteristic, complemented
252	C₄₁	#33859	1	1	yes	characteristic, direct product factor, Sylow
253	2₋¹⁺⁴	—	2	2	no	—
254	H(5,𝔽₂)	—	2	2	no	—
255	#137	—	2	2	no	—
256	#137	—	2	2	no	—
257	#137	—	4	2	no	—
258	#137	—	4	2	no	—
259	AGL(1,ℤ/8)	—	2	2	no	—
260	AGL(1,ℤ/8)	—	2	2	no	—
261	AGL(1,ℤ/8)	—	4	2	no	—
262	AGL(1,ℤ/8)	—	4	2	no	—
263	#135	—	2	2	no	—
264	#135	—	2	2	no	—
265	#135	—	4	2	no	—
266	#135	D₄×C₄₁	1	1	yes	characteristic
267	#135	C₂³×C₄₁	1	2	yes	—
268	C₂×Q₁₆	—	2	2	no	—
269	C₂×Q₁₆	C₂³×C₄₁	1	2	yes	—
270	C₂×SD₁₆	—	2	2	no	—
271	C₂×SD₁₆	—	4	2	no	—
272	C₂×D₈	—	2	2	no	—
273	C₂×D₈	C₂³×C₄₁	1	2	yes	—
274	#131	—	2	2	no	—
275	#131	C₂³×C₄₁	1	1	yes	characteristic
276	#131	C₂³×C₄₁	1	1	yes	characteristic
277	#124	—	2	2	no	—
278	Q₃₂	—	2	2	no	—
279	Q₃₂	—	2	1	no	—
280	Q₃₂	—	2	1	no	—
281	Q₃₂	D₄×C₄₁	1	1	yes	characteristic
282	SD₃₂	—	2	2	no	—
283	SD₃₂	—	2	2	no	—
284	SD₃₂	—	4	2	no	—
285	SD₃₂	D₄×C₄₁	1	2	yes	—
286	D₁₆	—	2	2	no	—
287	D₁₆	—	2	1	no	—
288	D₁₆	—	2	1	no	—
289	D₁₆	D₄×C₄₁	1	1	yes	characteristic
290	M₃₂	—	2	1	no	—
291	M₃₂	—	2	1	no	—
292	M₃₂	C₂³×C₄₁	1	1	yes	characteristic
293	M₃₂	C₂³×C₄₁	1	1	yes	characteristic
294	C₂×C₁₆	—	2	1	no	—
295	C₂×C₁₆	—	2	1	no	—
296	C₂×C₁₆	C₂³×C₄₁	1	1	yes	characteristic
297	C₂×C₁₆	C₂³×C₄₁	1	1	yes	characteristic
298	#108	D₄×C₄₁	1	1	yes	characteristic
299	#108	C₂³×C₄₁	1	2	yes	—
300	#104	—	2	2	no	—
301	#104	D₄×C₄₁	1	1	yes	characteristic
302	#104	D₄×C₄₁	1	1	yes	characteristic
303	#101	—	2	2	no	—
304	#100	—	2	2	no	—
305	C₄×C₈	C₂³×C₄₁	1	1	yes	characteristic
306	#41	—	2	2	no	—
307	#41	—	4	2	no	—
308	#41	—	4	2	no	—
309	#41	—	4	2	no	—
310	#41	—	4	2	no	—
311	#41	—	8	2	no	—
312	#41	C₂×D₄×C₄₁	1	1	yes	characteristic
313	#41	C₂×D₄×C₄₁	1	1	yes	characteristic
314	C₂×Q₈	—	2	2	no	—
315	C₂×Q₈	—	4	2	no	—
316	C₂×Q₈	—	4	2	no	—
317	C₂×D₄	—	2	2	no	—
318	C₂×D₄	—	4	2	no	—
319	C₂×D₄	—	4	2	no	—
320	C₂×D₄	—	8	2	no	—
321	Q₁₆	—	2	2	no	—
322	Q₁₆	—	2	2	no	—
323	Q₁₆	—	4	2	no	—
324	Q₁₆	—	4	2	no	—
325	Q₁₆	D₈×C₄₁	1	1	yes	characteristic
326	Q₁₆	C₂×D₄×C₄₁	1	2	yes	—
327	SD₁₆	—	2	2	no	—
328	SD₁₆	—	4	2	no	—
329	SD₁₆	—	4	2	no	—
330	SD₁₆	—	4	2	no	—
331	SD₁₆	—	4	2	no	—
332	SD₁₆	—	4	2	no	—
333	SD₁₆	—	4	2	no	—
334	SD₁₆	D₈×C₄₁	1	1	yes	characteristic
335	SD₁₆	D₈×C₄₁	1	1	yes	characteristic
336	D₈	—	2	2	no	—
337	D₈	—	2	2	no	—
338	D₈	—	4	2	no	—
339	D₈	—	4	2	no	—
340	D₈	D₈×C₄₁	1	1	yes	characteristic
341	D₈	C₂×D₄×C₄₁	1	2	yes	—
342	M₁₆	—	2	1	no	—
343	M₁₆	—	2	1	no	—
344	M₁₆	—	2	2	no	—
345	M₁₆	—	4	2	no	—
346	M₁₆	C₂×D₄×C₄₁	1	1	yes	characteristic
347	M₁₆	C₂×D₄×C₄₁	1	1	yes	characteristic
348	C₂×C₈	—	2	1	no	—
349	C₂×C₈	—	2	1	no	—
350	C₂×C₈	—	4	2	no	—
351	C₂×C₈	C₂×D₄×C₄₁	1	1	yes	characteristic
352	C₂×C₈	C₂⁴×C₄₁	1	1	yes	characteristic
353	C₂²⋊C₄	—	8	2	no	—
354	C₄²	C₂×D₄×C₄₁	1	1	yes	characteristic
355	C₁₆	—	2	1	no	—
356	C₁₆	—	2	1	no	—
357	C₁₆	—	2	1	no	—
358	C₁₆	C₂×D₄×C₄₁	1	1	yes	characteristic
359	C₁₆	C₂×D₄×C₄₁	1	1	yes	characteristic
360	C₂³	—	4	2	no	—
361	C₂³	—	8	2	no	—
362	Q₈	—	2	2	no	—
363	Q₈	—	4	2	no	—
364	Q₈	—	4	2	no	—
365	Q₈	—	8	2	no	—
366	Q₈	C₂×D₈×C₄₁	1	1	yes	characteristic
367	Q₈	C₂×D₈×C₄₁	1	1	yes	characteristic
368	D₄	—	2	1	no	—
369	D₄	—	2	1	no	—
370	D₄	—	2	2	no	—
371	D₄	—	4	2	no	—
372	D₄	—	4	2	no	—
373	D₄	—	4	2	no	—
374	D₄	—	8	2	no	—
375	D₄	—	8	2	no	—
376	D₄	—	8	2	no	—
377	D₄	C₂×D₈×C₄₁	1	1	yes	characteristic
378	D₄	C₂×D₈×C₄₁	1	1	yes	characteristic
379	C₂×C₄	—	2	1	no	—
380	C₂×C₄	—	2	1	no	—
381	C₂×C₄	—	2	1	no	—
382	C₂×C₄	—	4	2	no	—
383	C₂×C₄	—	4	2	no	—
384	C₂×C₄	—	8	2	no	—
385	C₂×C₄	—	8	2	no	—
386	C₂×C₄	—	8	2	no	—
387	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
388	C₈	—	2	1	no	—
389	C₈	—	2	1	no	—
390	C₈	—	4	2	no	—
391	C₈	C₂×D₈×C₄₁	1	1	yes	characteristic
392	C₈	C₂×D₈×C₄₁	1	1	yes	characteristic
393	C₈	C₂²×D₄×C₄₁	1	1	yes	characteristic
394	C₈	H(5,𝔽₂)×C₄₁	1	1	yes	characteristic
395	C₂²	—	2	1	no	—
396	C₂²	—	2	1	no	—
397	C₂²	—	4	2	no	—
398	C₂²	—	8	2	no	—
399	C₂²	—	16	2	no	—
400	C₂²	—	32	2	no	—
401	C₂²	C₄₁×#576	1	1	yes	characteristic
402	C₄	—	2	1	no	—
403	C₄	—	2	1	no	—
404	C₄	—	4	1	no	—
405	C₄	—	4	2	no	—
406	C₄	—	8	2	no	—
407	C₄	D₄²×C₄₁	1	1	yes	characteristic
408	C₄	C₂²×D₈×C₄₁	1	1	yes	characteristic
409	C₂	—	2	1	no	—
410	C₂	—	4	1	no	—
411	C₂	—	4	1	no	—
412	C₂	—	8	2	no	—
413	C₂	—	16	2	no	—
414	C₂	D₄×D₈×C₄₁	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₄₁	D₄×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₄₁
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄₁ ◁ C₂×C₄×C₄₁ ◁ C₄₁×#443 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₄₁×#3417	C₂	semidirect
2. C₄₁×#3415	C₂	semidirect
3. C₄₁×#3290	C₂	semidirect
4. C₄₁×#2249	C₂	semidirect
5. C₄₁×#2222	C₂	semidirect
6. C₄₁×#2221	C₂	semidirect
7. C₄₁×#2212	C₂	semidirect
8. C₄₁×#2194	C₂	semidirect
9. C₄₁×#2193	C₂	semidirect
10. C₄₁×#2178	C₂	semidirect
11. C₄₁×#2170	C₂	semidirect
12. C₄₁×#578	C₂²	semidirect
16. C₄₁×#510	C₂²	semidirect
23. C₂×Q₃₂×C₄₁	C₂²	semidirect
24. C₂×SD₃₂×C₄₁	C₂²	semidirect
28. C₄₁×#504	C₂²	semidirect
29. C₄₁×#495	C₂²	semidirect
31. C₄₁×#472	C₂²	semidirect
36. C₄₁×#443	C₂²	semidirect
37. C₄₁×#368	C₂²	semidirect
38. C₄₁×#364	C₂²	semidirect
39. C₄₁×#362	C₂²	semidirect
40. C₄₁×#361	C₂²	semidirect
41. C₄₁×#359	C₂²	semidirect
43. C₄₁×#350	C₂²	semidirect
44. C₄×C₁₆×C₄₁	C₂²	semidirect
187. #33859	C₄₁	direct (N × H)
202. #3417	C₂×C₄₁	semidirect
203. #3415	C₂×C₄₁	semidirect
204. #3290	C₂×C₄₁	semidirect
205. #2249	C₂×C₄₁	semidirect
206. #2222	C₂×C₄₁	semidirect
207. #2221	C₂×C₄₁	semidirect
208. #2212	C₂×C₄₁	semidirect
209. #2194	C₂×C₄₁	semidirect
210. #2193	C₂×C₄₁	semidirect
211. #2178	C₂×C₄₁	semidirect
212. #2170	C₂×C₄₁	semidirect
219. #578	C₂²×C₄₁	semidirect
223. #510	C₂²×C₄₁	semidirect
230. C₂×Q₃₂	C₂²×C₄₁	semidirect
231. C₂×SD₃₂	C₂²×C₄₁	semidirect
235. #504	C₂²×C₄₁	semidirect
236. #495	C₂²×C₄₁	semidirect
238. #472	C₂²×C₄₁	semidirect
243. #443	C₂²×C₄₁	semidirect
244. #368	C₂²×C₄₁	semidirect
245. #364	C₂²×C₄₁	semidirect
246. #362	C₂²×C₄₁	semidirect
247. #361	C₂²×C₄₁	semidirect
248. #359	C₂²×C₄₁	semidirect
250. #350	C₂²×C₄₁	semidirect
251. C₄×C₁₆	C₂²×C₄₁	semidirect
252. C₄₁	#33859	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×#3417	2
C₄₁×#3415	2
C₄₁×#3290	2
C₄₁×#2249	2
C₄₁×#2222	2
C₄₁×#2221	2
C₄₁×#2212	2
C₄₁×#2194	2
C₄₁×#2193	2
C₄₁×#2178	2
C₄₁×#2170	2
#33859	41

Subgroups — C41×#33859 #23810060

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#33859 #23810060