Subgroups — C₄₁×#33522 #23809723

Order 10496.

1170 conjugacy classes of subgroups.

The subgroup lattice has 448 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₁×#576	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄₁×#509	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×D₁₆×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₁×#3058	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₁×#2186	C₂	1	4	yes	maximal, complemented
6	C₄₁×#2184	C₂	1	4	yes	maximal, complemented
7	C₄₁×#2140	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄₁×#2138	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄₁×#2113	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×H(5,𝔽₂)×C₄₁	—	2	1	no	—
11	C₄₁×#576	—	2	4	no	—
12	C₄₁×#576	—	2	4	no	—
13	C₂×AGL(1,ℤ/8)×C₄₁	—	2	1	no	—
14	C₂×AGL(1,ℤ/8)×C₄₁	—	2	2	no	—
15	C₂×#135×C₄₁	C₂²	1	1	yes	characteristic
16	C₂×#135×C₄₁	C₂²	1	2	yes	complemented
17	C₂²×D₈×C₄₁	C₂²	1	1	yes	characteristic
18	C₂²×D₈×C₄₁	C₂²	1	1	yes	characteristic, complemented
19	C₂²×D₈×C₄₁	C₂²	1	2	yes	complemented
20	C₂×#131×C₄₁	C₂²	1	1	yes	characteristic
21	C₄₁×#535	—	2	1	no	—
22	C₄₁×#509	—	2	4	no	—
23	C₂×SD₃₂×C₄₁	C₂²	1	2	yes	complemented
24	C₂×D₁₆×C₄₁	—	2	4	no	—
25	C₂×D₁₆×C₄₁	C₂²	1	4	yes	complemented
26	C₂×D₁₆×C₄₁	C₂²	1	2	yes	complemented
27	C₂×M₃₂×C₄₁	C₂²	1	1	yes	characteristic, complemented
28	C₂²×C₁₆×C₄₁	C₂²	1	1	yes	characteristic, complemented
29	C₄₁×#469	—	2	2	no	—
30	C₄₁×#466	C₂²	1	4	yes	complemented
31	C₄₁×#427	C₂²	1	1	yes	characteristic, complemented
32	C₄₁×#418	—	2	1	no	—
33	C₄₁×#358	C₂²	1	2	yes	complemented
34	C₄₁×#357	C₂²	1	2	yes	complemented
35	C₄₁×#357	C₂²	1	4	yes	complemented
36	C₄₁×C₂²⋊C₁₆	C₂²	1	4	yes	complemented
37	H(5,𝔽₂)×C₄₁	—	2	8	no	—
38	H(5,𝔽₂)×C₄₁	—	4	4	no	—
39	C₂×#41×C₄₁	—	2	1	no	—
40	C₂×#41×C₄₁	—	2	2	no	—
41	C₂×#41×C₄₁	—	4	1	no	—
42	C₂×#41×C₄₁	D₄	1	1	yes	characteristic
43	C₂²×D₄×C₄₁	—	2	1	no	—
44	C₂²×D₄×C₄₁	—	2	2	no	—
45	C₂²×D₄×C₄₁	—	2	1	no	—
46	C₂²×D₄×C₄₁	—	4	2	no	—
47	C₂²×D₄×C₄₁	—	4	1	no	—
48	AGL(1,ℤ/8)×C₄₁	—	2	8	no	—
49	AGL(1,ℤ/8)×C₄₁	—	2	16	no	—
50	#135×C₄₁	—	2	4	no	—
51	#135×C₄₁	—	2	4	no	—
52	#135×C₄₁	—	2	2	no	—
53	#135×C₄₁	D₄	1	4	yes	complemented
54	C₂×Q₁₆×C₄₁	C₂³	1	1	yes	characteristic
55	C₂×SD₁₆×C₄₁	—	2	1	no	—
56	C₂×SD₁₆×C₄₁	—	2	2	no	—
57	C₂×D₈×C₄₁	—	2	4	no	—
58	C₂×D₈×C₄₁	—	2	4	no	—
59	C₂×D₈×C₄₁	—	2	1	no	—
60	C₂×D₈×C₄₁	—	2	2	no	—
61	C₂×D₈×C₄₁	—	2	2	no	—
62	C₂×D₈×C₄₁	—	2	2	no	—
63	C₂×D₈×C₄₁	—	2	2	no	—
64	C₂×D₈×C₄₁	—	2	1	no	—
65	C₂×D₈×C₄₁	D₄	1	4	yes	complemented
66	C₂×D₈×C₄₁	C₂³	1	2	yes	—
67	C₂×D₈×C₄₁	C₂³	1	2	yes	—
68	C₂×D₈×C₄₁	C₂³	1	1	yes	characteristic
69	#131×C₄₁	—	2	2	no	—
70	#131×C₄₁	—	2	2	no	—
71	C₂×M₁₆×C₄₁	D₄	1	1	yes	characteristic
72	C₂×M₁₆×C₄₁	D₄	1	2	yes	—
73	C₂²×C₈×C₄₁	C₂³	1	2	yes	—
74	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
75	#127×C₄₁	—	4	1	no	—
76	#124×C₄₁	—	4	1	no	—
77	#121×C₄₁	—	2	4	no	—
78	#120×C₄₁	—	4	2	no	—
79	#117×C₄₁	—	2	1	no	—
80	SD₃₂×C₄₁	—	2	4	no	—
81	D₁₆×C₄₁	—	2	8	no	—
82	D₁₆×C₄₁	—	2	4	no	—
83	M₃₂×C₄₁	—	2	2	no	—
84	C₂×C₁₆×C₄₁	—	2	2	no	—
85	C₂×C₁₆×C₄₁	C₂³	1	2	yes	—
86	C₂×C₁₆×C₄₁	C₂³	1	2	yes	—
87	#107×C₄₁	C₂³	1	2	yes	—
88	#106×C₄₁	—	2	1	no	—
89	#102×C₄₁	—	2	4	no	—
90	C₂⁴×C₄₁	—	4	2	no	—
91	C₂⁴×C₄₁	—	4	1	no	—
92	C₂⁴×C₄₁	—	4	1	no	—
93	#41×C₄₁	—	2	2	no	—
94	#41×C₄₁	—	2	2	no	—
95	#41×C₄₁	—	2	8	no	—
96	#41×C₄₁	—	2	4	no	—
97	#41×C₄₁	—	4	4	no	—
98	#41×C₄₁	—	4	8	no	—
99	#41×C₄₁	—	4	2	no	—
100	C₂×Q₈×C₄₁	—	2	1	no	—
101	C₂×Q₈×C₄₁	D₈	1	1	yes	characteristic
102	C₂×D₄×C₄₁	—	2	8	no	—
103	C₂×D₄×C₄₁	—	2	4	no	—
104	C₂×D₄×C₄₁	—	2	2	no	—
105	C₂×D₄×C₄₁	—	2	1	no	—
106	C₂×D₄×C₄₁	—	2	2	no	—
107	C₂×D₄×C₄₁	—	4	4	no	—
108	C₂×D₄×C₄₁	—	4	16	no	—
109	C₂×D₄×C₄₁	—	4	8	no	—
110	C₂×D₄×C₄₁	—	4	2	no	—
111	C₂×D₄×C₄₁	—	4	1	no	—
112	C₂×D₄×C₄₁	—	4	4	no	—
113	C₂×D₄×C₄₁	—	4	2	no	—
114	C₂×D₄×C₄₁	—	4	2	no	—
115	C₂×D₄×C₄₁	—	4	1	no	—
116	C₂×D₄×C₄₁	—	4	1	no	—
117	C₂×D₄×C₄₁	—	4	2	no	—
118	C₂×D₄×C₄₁	—	4	2	no	—
119	C₂×D₄×C₄₁	D₈	1	2	yes	—
120	C₂×D₄×C₄₁	D₈	1	1	yes	characteristic
121	C₂²×C₄×C₄₁	—	4	2	no	—
122	C₂²×C₄×C₄₁	—	4	1	no	—
123	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
124	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
125	Q₁₆×C₄₁	—	2	1	no	—
126	Q₁₆×C₄₁	C₂×D₄	1	2	yes	—
127	SD₁₆×C₄₁	—	2	8	no	—
128	SD₁₆×C₄₁	—	2	4	no	—
129	D₈×C₄₁	—	2	8	no	—
130	D₈×C₄₁	—	2	4	no	—
131	D₈×C₄₁	—	2	2	no	—
132	D₈×C₄₁	—	2	1	no	—
133	D₈×C₄₁	—	2	2	no	—
134	D₈×C₄₁	—	2	2	no	—
135	D₈×C₄₁	—	4	2	no	—
136	D₈×C₄₁	C₂×D₄	1	2	yes	—
137	D₈×C₄₁	C₂×D₄	1	4	yes	—
138	M₁₆×C₄₁	—	2	2	no	—
139	M₁₆×C₄₁	—	2	4	no	—
140	C₂×C₈×C₄₁	—	2	2	no	—
141	C₂×C₈×C₄₁	—	2	2	no	—
142	C₂×C₈×C₄₁	C₂×D₄	1	2	yes	—
143	C₂×C₈×C₄₁	C₂×D₄	1	1	yes	characteristic
144	C₂×C₈×C₄₁	C₂×D₄	1	2	yes	—
145	C₂×C₈×C₄₁	C₂×D₄	1	2	yes	—
146	C₂×C₈×C₄₁	C₂⁴	1	1	yes	characteristic
147	C₄⋊C₄×C₄₁	—	2	2	no	—
148	C₂²⋊C₄×C₄₁	—	4	1	no	—
149	C₂²⋊C₄×C₄₁	—	4	4	no	—
150	C₄²×C₄₁	—	4	1	no	—
151	C₁₆×C₄₁	—	2	2	no	—
152	C₁₆×C₄₁	—	2	2	no	—
153	C₂³×C₄₁	—	4	8	no	—
154	C₂³×C₄₁	—	4	2	no	—
155	C₂³×C₄₁	—	4	1	no	—
156	C₂³×C₄₁	—	4	4	no	—
157	C₂³×C₄₁	—	4	2	no	—
158	C₂³×C₄₁	—	8	2	no	—
159	C₂³×C₄₁	—	16	2	no	—
160	C₂³×C₄₁	—	16	2	no	—
161	C₂³×C₄₁	—	16	4	no	—
162	C₂³×C₄₁	C₂×D₈	1	2	yes	—
163	C₂³×C₄₁	C₂×D₈	1	1	yes	characteristic
164	Q₈×C₄₁	—	2	2	no	—
165	Q₈×C₄₁	—	2	2	no	—
166	Q₈×C₄₁	—	4	1	no	—
167	D₄×C₄₁	—	2	4	no	—
168	D₄×C₄₁	—	2	2	no	—
169	D₄×C₄₁	—	2	4	no	—
170	D₄×C₄₁	—	2	2	no	—
171	D₄×C₄₁	—	4	8	no	—
172	D₄×C₄₁	—	4	8	no	—
173	D₄×C₄₁	—	4	4	no	—
174	D₄×C₄₁	—	4	2	no	—
175	D₄×C₄₁	—	4	1	no	—
176	D₄×C₄₁	—	4	2	no	—
177	D₄×C₄₁	—	4	2	no	—
178	D₄×C₄₁	—	4	4	no	—
179	D₄×C₄₁	—	8	2	no	—
180	D₄×C₄₁	—	16	4	no	—
181	C₂×C₄×C₄₁	—	2	2	no	—
182	C₂×C₄×C₄₁	—	2	2	no	—
183	C₂×C₄×C₄₁	—	4	8	no	—
184	C₂×C₄×C₄₁	—	4	1	no	—
185	C₂×C₄×C₄₁	—	4	4	no	—
186	C₂×C₄×C₄₁	—	4	2	no	—
187	C₂×C₄×C₄₁	#120	1	2	yes	—
188	C₂×C₄×C₄₁	C₂×D₈	1	2	yes	—
189	C₂×C₄×C₄₁	C₂×D₈	1	1	yes	characteristic
190	C₂×C₄×C₄₁	AGL(1,ℤ/8)	1	2	yes	—
191	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
192	C₈×C₄₁	—	2	2	no	—
193	C₈×C₄₁	#120	1	2	yes	—
194	C₈×C₄₁	C₂²×D₄	1	1	yes	characteristic
195	C₈×C₄₁	C₂²×D₄	1	1	yes	characteristic
196	#33522	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
197	C₂²×C₄₁	—	2	2	no	—
198	C₂²×C₄₁	—	2	4	no	—
199	C₂²×C₄₁	—	2	2	no	—
200	C₂²×C₄₁	—	4	4	no	—
201	C₂²×C₄₁	—	4	2	no	—
202	C₂²×C₄₁	—	8	4	no	—
203	C₂²×C₄₁	—	8	2	no	—
204	C₂²×C₄₁	—	8	4	no	—
205	C₂²×C₄₁	—	8	2	no	—
206	C₂²×C₄₁	—	16	4	no	—
207	C₂²×C₄₁	—	16	4	no	—
208	C₂²×C₄₁	—	16	8	no	—
209	C₂²×C₄₁	#447	1	2	yes	—
210	C₂²×C₄₁	C₂²×D₈	1	1	yes	characteristic
211	C₄×C₄₁	—	2	2	no	—
212	C₄×C₄₁	—	4	2	no	—
213	C₄×C₄₁	—	8	2	no	—
214	C₄×C₄₁	#447	1	2	yes	—
215	C₄×C₄₁	C₂×#120	1	1	yes	characteristic
216	C₄×C₄₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
217	C₂×#576	C₂×C₄₁	1	1	yes	characteristic, complemented
218	C₂×#509	C₂×C₄₁	1	1	yes	characteristic, complemented
219	C₂²×D₁₆	C₂×C₄₁	1	1	yes	characteristic, complemented
220	#3058	C₂×C₄₁	1	1	yes	characteristic, complemented
221	#2186	C₂×C₄₁	1	4	yes	complemented
222	#2184	C₂×C₄₁	1	4	yes	complemented
223	#2140	C₂×C₄₁	1	1	yes	characteristic, complemented
224	#2138	C₂×C₄₁	1	1	yes	characteristic, complemented
225	#2113	C₂×C₄₁	1	1	yes	characteristic, complemented
226	C₂×C₄₁	—	2	2	no	—
227	C₂×C₄₁	—	4	2	no	—
228	C₂×C₄₁	—	8	4	no	—
229	C₂×C₄₁	—	8	2	no	—
230	C₂×C₄₁	—	16	2	no	—
231	C₂×C₄₁	C₂×#447	1	1	yes	characteristic
232	C₂×C₄₁	#3415	1	2	yes	—
233	C₂×H(5,𝔽₂)	—	2	1	no	—
234	#576	—	2	4	no	—
235	#576	—	2	4	no	—
236	C₂×AGL(1,ℤ/8)	—	2	1	no	—
237	C₂×AGL(1,ℤ/8)	—	2	2	no	—
238	C₂×#135	C₂²×C₄₁	1	1	yes	characteristic
239	C₂×#135	C₂²×C₄₁	1	2	yes	complemented
240	C₂²×D₈	C₂²×C₄₁	1	1	yes	characteristic
241	C₂²×D₈	C₂²×C₄₁	1	1	yes	characteristic, complemented
242	C₂²×D₈	C₂²×C₄₁	1	2	yes	complemented
243	C₂×#131	C₂²×C₄₁	1	1	yes	characteristic
244	#535	—	2	1	no	—
245	#509	—	2	4	no	—
246	C₂×SD₃₂	C₂²×C₄₁	1	2	yes	complemented
247	C₂×D₁₆	—	2	4	no	—
248	C₂×D₁₆	C₂²×C₄₁	1	4	yes	complemented
249	C₂×D₁₆	C₂²×C₄₁	1	2	yes	complemented
250	C₂×M₃₂	C₂²×C₄₁	1	1	yes	characteristic, complemented
251	C₂²×C₁₆	C₂²×C₄₁	1	1	yes	characteristic, complemented
252	#469	—	2	2	no	—
253	#466	C₂²×C₄₁	1	4	yes	complemented
254	#427	C₂²×C₄₁	1	1	yes	characteristic, complemented
255	#418	—	2	1	no	—
256	#358	C₂²×C₄₁	1	2	yes	complemented
257	#357	C₂²×C₄₁	1	2	yes	complemented
258	#357	C₂²×C₄₁	1	4	yes	complemented
259	C₂²⋊C₁₆	C₂²×C₄₁	1	4	yes	complemented
260	C₄₁	#33522	1	1	yes	characteristic, direct product factor, Sylow
261	H(5,𝔽₂)	—	2	8	no	—
262	H(5,𝔽₂)	—	4	4	no	—
263	C₂×#41	—	2	1	no	—
264	C₂×#41	—	2	2	no	—
265	C₂×#41	—	4	1	no	—
266	C₂×#41	D₄×C₄₁	1	1	yes	characteristic
267	C₂²×D₄	—	2	1	no	—
268	C₂²×D₄	—	2	2	no	—
269	C₂²×D₄	—	2	1	no	—
270	C₂²×D₄	—	4	2	no	—
271	C₂²×D₄	—	4	1	no	—
272	AGL(1,ℤ/8)	—	2	8	no	—
273	AGL(1,ℤ/8)	—	2	16	no	—
274	#135	—	2	4	no	—
275	#135	—	2	4	no	—
276	#135	—	2	2	no	—
277	#135	D₄×C₄₁	1	4	yes	complemented
278	C₂×Q₁₆	C₂³×C₄₁	1	1	yes	characteristic
279	C₂×SD₁₆	—	2	1	no	—
280	C₂×SD₁₆	—	2	2	no	—
281	C₂×D₈	—	2	4	no	—
282	C₂×D₈	—	2	4	no	—
283	C₂×D₈	—	2	1	no	—
284	C₂×D₈	—	2	2	no	—
285	C₂×D₈	—	2	2	no	—
286	C₂×D₈	—	2	2	no	—
287	C₂×D₈	—	2	2	no	—
288	C₂×D₈	—	2	1	no	—
289	C₂×D₈	D₄×C₄₁	1	4	yes	complemented
290	C₂×D₈	C₂³×C₄₁	1	2	yes	—
291	C₂×D₈	C₂³×C₄₁	1	2	yes	—
292	C₂×D₈	C₂³×C₄₁	1	1	yes	characteristic
293	#131	—	2	2	no	—
294	#131	—	2	2	no	—
295	C₂×M₁₆	D₄×C₄₁	1	1	yes	characteristic
296	C₂×M₁₆	D₄×C₄₁	1	2	yes	—
297	C₂²×C₈	C₂³×C₄₁	1	2	yes	—
298	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
299	#127	—	4	1	no	—
300	#124	—	4	1	no	—
301	#121	—	2	4	no	—
302	#120	—	4	2	no	—
303	#117	—	2	1	no	—
304	SD₃₂	—	2	4	no	—
305	D₁₆	—	2	8	no	—
306	D₁₆	—	2	4	no	—
307	M₃₂	—	2	2	no	—
308	C₂×C₁₆	—	2	2	no	—
309	C₂×C₁₆	C₂³×C₄₁	1	2	yes	—
310	C₂×C₁₆	C₂³×C₄₁	1	2	yes	—
311	#107	C₂³×C₄₁	1	2	yes	—
312	#106	—	2	1	no	—
313	#102	—	2	4	no	—
314	C₂⁴	—	4	2	no	—
315	C₂⁴	—	4	1	no	—
316	C₂⁴	—	4	1	no	—
317	#41	—	2	2	no	—
318	#41	—	2	2	no	—
319	#41	—	2	8	no	—
320	#41	—	2	4	no	—
321	#41	—	4	4	no	—
322	#41	—	4	8	no	—
323	#41	—	4	2	no	—
324	C₂×Q₈	—	2	1	no	—
325	C₂×Q₈	D₈×C₄₁	1	1	yes	characteristic
326	C₂×D₄	—	2	8	no	—
327	C₂×D₄	—	2	4	no	—
328	C₂×D₄	—	2	2	no	—
329	C₂×D₄	—	2	1	no	—
330	C₂×D₄	—	2	2	no	—
331	C₂×D₄	—	4	4	no	—
332	C₂×D₄	—	4	16	no	—
333	C₂×D₄	—	4	8	no	—
334	C₂×D₄	—	4	2	no	—
335	C₂×D₄	—	4	1	no	—
336	C₂×D₄	—	4	4	no	—
337	C₂×D₄	—	4	2	no	—
338	C₂×D₄	—	4	2	no	—
339	C₂×D₄	—	4	1	no	—
340	C₂×D₄	—	4	1	no	—
341	C₂×D₄	—	4	2	no	—
342	C₂×D₄	—	4	2	no	—
343	C₂×D₄	D₈×C₄₁	1	2	yes	—
344	C₂×D₄	D₈×C₄₁	1	1	yes	characteristic
345	C₂²×C₄	—	4	2	no	—
346	C₂²×C₄	—	4	1	no	—
347	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
348	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
349	Q₁₆	—	2	1	no	—
350	Q₁₆	C₂×D₄×C₄₁	1	2	yes	—
351	SD₁₆	—	2	8	no	—
352	SD₁₆	—	2	4	no	—
353	D₈	—	2	8	no	—
354	D₈	—	2	4	no	—
355	D₈	—	2	2	no	—
356	D₈	—	2	1	no	—
357	D₈	—	2	2	no	—
358	D₈	—	2	2	no	—
359	D₈	—	4	2	no	—
360	D₈	C₂×D₄×C₄₁	1	2	yes	—
361	D₈	C₂×D₄×C₄₁	1	4	yes	—
362	M₁₆	—	2	2	no	—
363	M₁₆	—	2	4	no	—
364	C₂×C₈	—	2	2	no	—
365	C₂×C₈	—	2	2	no	—
366	C₂×C₈	C₂×D₄×C₄₁	1	2	yes	—
367	C₂×C₈	C₂×D₄×C₄₁	1	1	yes	characteristic
368	C₂×C₈	C₂×D₄×C₄₁	1	2	yes	—
369	C₂×C₈	C₂×D₄×C₄₁	1	2	yes	—
370	C₂×C₈	C₂⁴×C₄₁	1	1	yes	characteristic
371	C₄⋊C₄	—	2	2	no	—
372	C₂²⋊C₄	—	4	1	no	—
373	C₂²⋊C₄	—	4	4	no	—
374	C₄²	—	4	1	no	—
375	C₁₆	—	2	2	no	—
376	C₁₆	—	2	2	no	—
377	C₂³	—	4	8	no	—
378	C₂³	—	4	2	no	—
379	C₂³	—	4	1	no	—
380	C₂³	—	4	4	no	—
381	C₂³	—	4	2	no	—
382	C₂³	—	8	2	no	—
383	C₂³	—	16	2	no	—
384	C₂³	—	16	2	no	—
385	C₂³	—	16	4	no	—
386	C₂³	C₂×D₈×C₄₁	1	2	yes	—
387	C₂³	C₂×D₈×C₄₁	1	1	yes	characteristic
388	Q₈	—	2	2	no	—
389	Q₈	—	2	2	no	—
390	Q₈	—	4	1	no	—
391	D₄	—	2	4	no	—
392	D₄	—	2	2	no	—
393	D₄	—	2	4	no	—
394	D₄	—	2	2	no	—
395	D₄	—	4	8	no	—
396	D₄	—	4	8	no	—
397	D₄	—	4	4	no	—
398	D₄	—	4	2	no	—
399	D₄	—	4	1	no	—
400	D₄	—	4	2	no	—
401	D₄	—	4	2	no	—
402	D₄	—	4	4	no	—
403	D₄	—	8	2	no	—
404	D₄	—	16	4	no	—
405	C₂×C₄	—	2	2	no	—
406	C₂×C₄	—	2	2	no	—
407	C₂×C₄	—	4	8	no	—
408	C₂×C₄	—	4	1	no	—
409	C₂×C₄	—	4	4	no	—
410	C₂×C₄	—	4	2	no	—
411	C₂×C₄	#120×C₄₁	1	2	yes	—
412	C₂×C₄	C₂×D₈×C₄₁	1	2	yes	—
413	C₂×C₄	C₂×D₈×C₄₁	1	1	yes	characteristic
414	C₂×C₄	AGL(1,ℤ/8)×C₄₁	1	2	yes	—
415	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
416	C₈	—	2	2	no	—
417	C₈	#120×C₄₁	1	2	yes	—
418	C₈	C₂²×D₄×C₄₁	1	1	yes	characteristic
419	C₈	C₂²×D₄×C₄₁	1	1	yes	characteristic
420	C₂²	—	2	2	no	—
421	C₂²	—	2	4	no	—
422	C₂²	—	2	2	no	—
423	C₂²	—	4	4	no	—
424	C₂²	—	4	2	no	—
425	C₂²	—	8	4	no	—
426	C₂²	—	8	2	no	—
427	C₂²	—	8	4	no	—
428	C₂²	—	8	2	no	—
429	C₂²	—	16	4	no	—
430	C₂²	—	16	4	no	—
431	C₂²	—	16	8	no	—
432	C₂²	C₄₁×#447	1	2	yes	—
433	C₂²	C₂²×D₈×C₄₁	1	1	yes	characteristic
434	C₄	—	2	2	no	—
435	C₄	—	4	2	no	—
436	C₄	—	8	2	no	—
437	C₄	C₄₁×#447	1	2	yes	—
438	C₄	C₂×#120×C₄₁	1	1	yes	characteristic
439	C₄	C₂×AGL(1,ℤ/8)×C₄₁	1	1	yes	characteristic
440	C₂	—	2	2	no	—
441	C₂	—	4	2	no	—
442	C₂	—	8	4	no	—
443	C₂	—	8	2	no	—
444	C₂	—	16	2	no	—
445	C₂	C₂×C₄₁×#447	1	1	yes	characteristic
446	C₂	C₄₁×#3415	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₄₁	C₂²×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₄₁
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄₁ ◁ C₂×#41×C₄₁ ◁ C₂×#131×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₄₁×#576	C₂	semidirect
2. C₂×C₄₁×#509	C₂	semidirect
3. C₂²×D₁₆×C₄₁	C₂	semidirect
4. C₄₁×#3058	C₂	semidirect
5. C₄₁×#2186	C₂	semidirect
6. C₄₁×#2184	C₂	semidirect
7. C₄₁×#2140	C₂	semidirect
8. C₄₁×#2138	C₂	semidirect
9. C₄₁×#2113	C₂	semidirect
16. C₂×#135×C₄₁	C₂²	semidirect
18. C₂²×D₈×C₄₁	C₂²	semidirect
19. C₂²×D₈×C₄₁	C₂²	semidirect
23. C₂×SD₃₂×C₄₁	C₂²	semidirect
25. C₂×D₁₆×C₄₁	C₂²	semidirect
26. C₂×D₁₆×C₄₁	C₂²	semidirect
27. C₂×M₃₂×C₄₁	C₂²	semidirect
28. C₂²×C₁₆×C₄₁	C₂²	semidirect
30. C₄₁×#466	C₂²	semidirect
31. C₄₁×#427	C₂²	semidirect
33. C₄₁×#358	C₂²	semidirect
34. C₄₁×#357	C₂²	semidirect
35. C₄₁×#357	C₂²	semidirect
36. C₄₁×C₂²⋊C₁₆	C₂²	semidirect
53. #135×C₄₁	D₄	semidirect
65. C₂×D₈×C₄₁	D₄	semidirect
196. #33522	C₄₁	direct (N × H)
217. C₂×#576	C₂×C₄₁	semidirect
218. C₂×#509	C₂×C₄₁	semidirect
219. C₂²×D₁₆	C₂×C₄₁	semidirect
220. #3058	C₂×C₄₁	semidirect
221. #2186	C₂×C₄₁	semidirect
222. #2184	C₂×C₄₁	semidirect
223. #2140	C₂×C₄₁	semidirect
224. #2138	C₂×C₄₁	semidirect
225. #2113	C₂×C₄₁	semidirect
239. C₂×#135	C₂²×C₄₁	semidirect
241. C₂²×D₈	C₂²×C₄₁	semidirect
242. C₂²×D₈	C₂²×C₄₁	semidirect
246. C₂×SD₃₂	C₂²×C₄₁	semidirect
248. C₂×D₁₆	C₂²×C₄₁	semidirect
249. C₂×D₁₆	C₂²×C₄₁	semidirect
250. C₂×M₃₂	C₂²×C₄₁	semidirect
251. C₂²×C₁₆	C₂²×C₄₁	semidirect
253. #466	C₂²×C₄₁	semidirect
254. #427	C₂²×C₄₁	semidirect
256. #358	C₂²×C₄₁	semidirect
257. #357	C₂²×C₄₁	semidirect
258. #357	C₂²×C₄₁	semidirect
259. C₂²⋊C₁₆	C₂²×C₄₁	semidirect
260. C₄₁	#33522	direct (N × H)
277. #135	D₄×C₄₁	semidirect
289. C₂×D₈	D₄×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×#576	2
C₂×C₄₁×#509	2
C₂²×D₁₆×C₄₁	2
C₄₁×#3058	2
C₄₁×#2186	2
C₄₁×#2184	2
C₄₁×#2140	2
C₄₁×#2138	2
C₄₁×#2113	2
#33522	41

Subgroups — C41×#33522 #23809723

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#33522 #23809723