Subgroups — C₄₁×#33524 #23809725

Order 10496.

1118 conjugacy classes of subgroups.

The subgroup lattice has 436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₁×#578	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄₁×#509	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×SD₃₂×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×#2185	C₂	1	4	yes	maximal, complemented
7	C₄₁×#2141	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	C₂×2₋¹⁺⁴×C₄₁	—	2	1	no	—
11	C₄₁×#578	—	2	4	no	—
12	C₄₁×#578	—	2	4	no	—
13	C₂×#137×C₄₁	—	2	1	no	—
14	C₂×#137×C₄₁	—	2	2	no	—
15	C₂×#135×C₄₁	C₂²	1	1	yes	characteristic
16	C₂×#135×C₄₁	C₂²	1	2	yes	complemented
17	C₂²×Q₁₆×C₄₁	C₂²	1	1	yes	characteristic
18	C₂²×Q₁₆×C₄₁	C₂²	1	2	yes	complemented
19	C₂²×D₈×C₄₁	C₂²	1	1	yes	characteristic
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	—	2	4	no	—
24	C₂×SD₃₂×C₄₁	C₂²	1	4	yes	—
25	C₂×SD₃₂×C₄₁	C₂²	1	2	yes	—
26	C₂×D₁₆×C₄₁	C₂²	1	2	yes	—
27	C₂×M₃₂×C₄₁	C₂²	1	1	yes	characteristic
28	C₂²×C₁₆×C₄₁	C₂²	1	1	yes	characteristic
29	C₄₁×#469	—	2	2	no	—
30	C₄₁×#466	C₂²	1	4	yes	—
31	C₄₁×#427	C₂²	1	1	yes	characteristic
32	C₄₁×#418	—	2	1	no	—
33	C₄₁×#358	C₂²	1	2	yes	complemented
34	C₄₁×#358	C₂²	1	4	yes	complemented
35	C₄₁×#357	C₂²	1	2	yes	complemented
36	C₄₁×C₂²⋊C₁₆	C₂²	1	4	yes	complemented
37	2₋¹⁺⁴×C₄₁	—	2	8	no	—
38	2₋¹⁺⁴×C₄₁	—	4	4	no	—
39	C₂×#41×C₄₁	—	2	1	no	—
40	C₂×#41×C₄₁	—	2	2	no	—
41	C₂×#41×C₄₁	—	4	2	no	—
42	C₂×#41×C₄₁	—	4	1	no	—
43	C₂×#41×C₄₁	D₄	1	1	yes	characteristic
44	C₂²×Q₈×C₄₁	—	2	1	no	—
45	C₂²×Q₈×C₄₁	—	2	2	no	—
46	C₂²×Q₈×C₄₁	—	4	1	no	—
47	C₂²×D₄×C₄₁	—	2	1	no	—
48	#137×C₄₁	—	2	8	no	—
49	#137×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	—	2	4	no	—
55	C₂×Q₁₆×C₄₁	—	2	4	no	—
56	C₂×Q₁₆×C₄₁	—	2	1	no	—
57	C₂×Q₁₆×C₄₁	—	2	2	no	—
58	C₂×Q₁₆×C₄₁	—	2	2	no	—
59	C₂×Q₁₆×C₄₁	D₄	1	4	yes	complemented
60	C₂×Q₁₆×C₄₁	C₂³	1	2	yes	—
61	C₂×Q₁₆×C₄₁	C₂³	1	1	yes	characteristic
62	C₂×SD₁₆×C₄₁	—	2	1	no	—
63	C₂×SD₁₆×C₄₁	—	2	2	no	—
64	C₂×D₈×C₄₁	—	2	2	no	—
65	C₂×D₈×C₄₁	—	2	2	no	—
66	C₂×D₈×C₄₁	—	2	1	no	—
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	8	no	—
81	SD₃₂×C₄₁	—	2	4	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	1	no	—
91	#41×C₄₁	—	2	2	no	—
92	#41×C₄₁	—	2	2	no	—
93	#41×C₄₁	—	2	8	no	—
94	#41×C₄₁	—	2	4	no	—
95	#41×C₄₁	—	4	4	no	—
96	#41×C₄₁	—	4	16	no	—
97	#41×C₄₁	—	4	8	no	—
98	#41×C₄₁	—	4	2	no	—
99	C₂×Q₈×C₄₁	—	2	8	no	—
100	C₂×Q₈×C₄₁	—	2	4	no	—
101	C₂×Q₈×C₄₁	—	2	1	no	—
102	C₂×Q₈×C₄₁	—	2	2	no	—
103	C₂×Q₈×C₄₁	—	4	4	no	—
104	C₂×Q₈×C₄₁	—	4	8	no	—
105	C₂×Q₈×C₄₁	—	4	2	no	—
106	C₂×Q₈×C₄₁	—	4	1	no	—
107	C₂×Q₈×C₄₁	—	4	2	no	—
108	C₂×Q₈×C₄₁	D₈	1	1	yes	characteristic
109	C₂×D₄×C₄₁	—	2	1	no	—
110	C₂×D₄×C₄₁	—	2	2	no	—
111	C₂×D₄×C₄₁	—	4	2	no	—
112	C₂×D₄×C₄₁	—	4	1	no	—
113	C₂×D₄×C₄₁	—	4	4	no	—
114	C₂×D₄×C₄₁	—	4	2	no	—
115	C₂×D₄×C₄₁	—	4	1	no	—
116	C₂×D₄×C₄₁	—	4	2	no	—
117	C₂×D₄×C₄₁	D₈	1	2	yes	—
118	C₂×D₄×C₄₁	D₈	1	1	yes	characteristic
119	C₂²×C₄×C₄₁	—	4	2	no	—
120	C₂²×C₄×C₄₁	—	4	1	no	—
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	8	no	—
126	Q₁₆×C₄₁	—	2	4	no	—
127	Q₁₆×C₄₁	—	2	1	no	—
128	Q₁₆×C₄₁	—	2	2	no	—
129	Q₁₆×C₄₁	C₂×D₄	1	2	yes	—
130	Q₁₆×C₄₁	C₂×D₄	1	4	yes	—
131	SD₁₆×C₄₁	—	2	8	no	—
132	SD₁₆×C₄₁	—	2	4	no	—
133	D₈×C₄₁	—	2	1	no	—
134	D₈×C₄₁	—	2	2	no	—
135	D₈×C₄₁	—	2	2	no	—
136	D₈×C₄₁	—	4	2	no	—
137	D₈×C₄₁	C₂×D₄	1	2	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	1	no	—
154	C₂³×C₄₁	—	4	2	no	—
155	C₂³×C₄₁	—	8	2	no	—
156	C₂³×C₄₁	—	16	2	no	—
157	C₂³×C₄₁	C₂×D₈	1	2	yes	—
158	C₂³×C₄₁	C₂×D₈	1	1	yes	characteristic
159	Q₈×C₄₁	—	2	2	no	—
160	Q₈×C₄₁	—	2	4	no	—
161	Q₈×C₄₁	—	2	2	no	—
162	Q₈×C₄₁	—	4	8	no	—
163	Q₈×C₄₁	—	4	1	no	—
164	Q₈×C₄₁	—	4	2	no	—
165	Q₈×C₄₁	—	4	4	no	—
166	D₄×C₄₁	—	2	4	no	—
167	D₄×C₄₁	—	2	2	no	—
168	D₄×C₄₁	—	2	2	no	—
169	D₄×C₄₁	—	4	8	no	—
170	D₄×C₄₁	—	4	4	no	—
171	D₄×C₄₁	—	4	2	no	—
172	D₄×C₄₁	—	4	1	no	—
173	D₄×C₄₁	—	4	2	no	—
174	D₄×C₄₁	—	8	2	no	—
175	D₄×C₄₁	—	16	4	no	—
176	C₂×C₄×C₄₁	—	2	2	no	—
177	C₂×C₄×C₄₁	—	2	2	no	—
178	C₂×C₄×C₄₁	—	4	8	no	—
179	C₂×C₄×C₄₁	—	4	8	no	—
180	C₂×C₄×C₄₁	—	4	2	no	—
181	C₂×C₄×C₄₁	—	4	1	no	—
182	C₂×C₄×C₄₁	—	4	4	no	—
183	C₂×C₄×C₄₁	—	4	4	no	—
184	C₂×C₄×C₄₁	—	4	2	no	—
185	C₂×C₄×C₄₁	#120	1	2	yes	—
186	C₂×C₄×C₄₁	C₂×D₈	1	2	yes	—
187	C₂×C₄×C₄₁	C₂×D₈	1	1	yes	characteristic
188	C₂×C₄×C₄₁	AGL(1,ℤ/8)	1	2	yes	—
189	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
190	C₈×C₄₁	—	2	2	no	—
191	C₈×C₄₁	#120	1	2	yes	—
192	C₈×C₄₁	C₂²×D₄	1	1	yes	characteristic
193	C₈×C₄₁	C₂²×D₄	1	1	yes	characteristic
194	#33524	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
195	C₂²×C₄₁	—	2	2	no	—
196	C₂²×C₄₁	—	2	4	no	—
197	C₂²×C₄₁	—	2	2	no	—
198	C₂²×C₄₁	—	4	2	no	—
199	C₂²×C₄₁	—	8	2	no	—
200	C₂²×C₄₁	—	8	4	no	—
201	C₂²×C₄₁	—	8	2	no	—
202	C₂²×C₄₁	—	16	4	no	—
203	C₂²×C₄₁	#447	1	2	yes	—
204	C₂²×C₄₁	C₂²×D₈	1	1	yes	characteristic
205	C₄×C₄₁	—	2	2	no	—
206	C₄×C₄₁	—	4	4	no	—
207	C₄×C₄₁	—	4	2	no	—
208	C₄×C₄₁	—	8	2	no	—
209	C₄×C₄₁	#447	1	2	yes	—
210	C₄×C₄₁	C₂×#120	1	1	yes	characteristic
211	C₄×C₄₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
212	C₂×#578	C₂×C₄₁	1	1	yes	characteristic, complemented
213	C₂×#509	C₂×C₄₁	1	1	yes	characteristic, complemented
214	C₂²×SD₃₂	C₂×C₄₁	1	1	yes	characteristic, complemented
215	#3058	C₂×C₄₁	1	1	yes	characteristic, complemented
216	#2186	C₂×C₄₁	1	4	yes	complemented
217	#2185	C₂×C₄₁	1	4	yes	complemented
218	#2141	C₂×C₄₁	1	1	yes	characteristic, complemented
219	#2138	C₂×C₄₁	1	1	yes	characteristic, complemented
220	#2113	C₂×C₄₁	1	1	yes	characteristic, complemented
221	C₂×C₄₁	—	2	2	no	—
222	C₂×C₄₁	—	4	2	no	—
223	C₂×C₄₁	—	8	2	no	—
224	C₂×C₄₁	—	16	2	no	—
225	C₂×C₄₁	C₂×#447	1	1	yes	characteristic
226	C₂×C₄₁	#3416	1	2	yes	—
227	C₂×2₋¹⁺⁴	—	2	1	no	—
228	#578	—	2	4	no	—
229	#578	—	2	4	no	—
230	C₂×#137	—	2	1	no	—
231	C₂×#137	—	2	2	no	—
232	C₂×#135	C₂²×C₄₁	1	1	yes	characteristic
233	C₂×#135	C₂²×C₄₁	1	2	yes	complemented
234	C₂²×Q₁₆	C₂²×C₄₁	1	1	yes	characteristic
235	C₂²×Q₁₆	C₂²×C₄₁	1	2	yes	complemented
236	C₂²×D₈	C₂²×C₄₁	1	1	yes	characteristic
237	C₂×#131	C₂²×C₄₁	1	1	yes	characteristic
238	#535	—	2	1	no	—
239	#509	—	2	4	no	—
240	C₂×SD₃₂	—	2	4	no	—
241	C₂×SD₃₂	C₂²×C₄₁	1	4	yes	—
242	C₂×SD₃₂	C₂²×C₄₁	1	2	yes	—
243	C₂×D₁₆	C₂²×C₄₁	1	2	yes	—
244	C₂×M₃₂	C₂²×C₄₁	1	1	yes	characteristic
245	C₂²×C₁₆	C₂²×C₄₁	1	1	yes	characteristic
246	#469	—	2	2	no	—
247	#466	C₂²×C₄₁	1	4	yes	—
248	#427	C₂²×C₄₁	1	1	yes	characteristic
249	#418	—	2	1	no	—
250	#358	C₂²×C₄₁	1	2	yes	complemented
251	#358	C₂²×C₄₁	1	4	yes	complemented
252	#357	C₂²×C₄₁	1	2	yes	complemented
253	C₂²⋊C₁₆	C₂²×C₄₁	1	4	yes	complemented
254	C₄₁	#33524	1	1	yes	characteristic, direct product factor, Sylow
255	2₋¹⁺⁴	—	2	8	no	—
256	2₋¹⁺⁴	—	4	4	no	—
257	C₂×#41	—	2	1	no	—
258	C₂×#41	—	2	2	no	—
259	C₂×#41	—	4	2	no	—
260	C₂×#41	—	4	1	no	—
261	C₂×#41	D₄×C₄₁	1	1	yes	characteristic
262	C₂²×Q₈	—	2	1	no	—
263	C₂²×Q₈	—	2	2	no	—
264	C₂²×Q₈	—	4	1	no	—
265	C₂²×D₄	—	2	1	no	—
266	#137	—	2	8	no	—
267	#137	—	2	16	no	—
268	#135	—	2	4	no	—
269	#135	—	2	4	no	—
270	#135	—	2	2	no	—
271	#135	D₄×C₄₁	1	4	yes	complemented
272	C₂×Q₁₆	—	2	4	no	—
273	C₂×Q₁₆	—	2	4	no	—
274	C₂×Q₁₆	—	2	1	no	—
275	C₂×Q₁₆	—	2	2	no	—
276	C₂×Q₁₆	—	2	2	no	—
277	C₂×Q₁₆	D₄×C₄₁	1	4	yes	complemented
278	C₂×Q₁₆	C₂³×C₄₁	1	2	yes	—
279	C₂×Q₁₆	C₂³×C₄₁	1	1	yes	characteristic
280	C₂×SD₁₆	—	2	1	no	—
281	C₂×SD₁₆	—	2	2	no	—
282	C₂×D₈	—	2	2	no	—
283	C₂×D₈	—	2	2	no	—
284	C₂×D₈	—	2	1	no	—
285	C₂×D₈	C₂³×C₄₁	1	2	yes	—
286	C₂×D₈	C₂³×C₄₁	1	1	yes	characteristic
287	#131	—	2	2	no	—
288	#131	—	2	2	no	—
289	C₂×M₁₆	D₄×C₄₁	1	1	yes	characteristic
290	C₂×M₁₆	D₄×C₄₁	1	2	yes	—
291	C₂²×C₈	C₂³×C₄₁	1	2	yes	—
292	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
293	#127	—	4	1	no	—
294	#124	—	4	1	no	—
295	#121	—	2	4	no	—
296	#120	—	4	2	no	—
297	#117	—	2	1	no	—
298	SD₃₂	—	2	8	no	—
299	SD₃₂	—	2	4	no	—
300	D₁₆	—	2	4	no	—
301	M₃₂	—	2	2	no	—
302	C₂×C₁₆	—	2	2	no	—
303	C₂×C₁₆	C₂³×C₄₁	1	2	yes	—
304	C₂×C₁₆	C₂³×C₄₁	1	2	yes	—
305	#107	C₂³×C₄₁	1	2	yes	—
306	#106	—	2	1	no	—
307	#102	—	2	4	no	—
308	C₂⁴	—	4	1	no	—
309	#41	—	2	2	no	—
310	#41	—	2	2	no	—
311	#41	—	2	8	no	—
312	#41	—	2	4	no	—
313	#41	—	4	4	no	—
314	#41	—	4	16	no	—
315	#41	—	4	8	no	—
316	#41	—	4	2	no	—
317	C₂×Q₈	—	2	8	no	—
318	C₂×Q₈	—	2	4	no	—
319	C₂×Q₈	—	2	1	no	—
320	C₂×Q₈	—	2	2	no	—
321	C₂×Q₈	—	4	4	no	—
322	C₂×Q₈	—	4	8	no	—
323	C₂×Q₈	—	4	2	no	—
324	C₂×Q₈	—	4	1	no	—
325	C₂×Q₈	—	4	2	no	—
326	C₂×Q₈	D₈×C₄₁	1	1	yes	characteristic
327	C₂×D₄	—	2	1	no	—
328	C₂×D₄	—	2	2	no	—
329	C₂×D₄	—	4	2	no	—
330	C₂×D₄	—	4	1	no	—
331	C₂×D₄	—	4	4	no	—
332	C₂×D₄	—	4	2	no	—
333	C₂×D₄	—	4	1	no	—
334	C₂×D₄	—	4	2	no	—
335	C₂×D₄	D₈×C₄₁	1	2	yes	—
336	C₂×D₄	D₈×C₄₁	1	1	yes	characteristic
337	C₂²×C₄	—	4	2	no	—
338	C₂²×C₄	—	4	1	no	—
339	C₂²×C₄	—	4	2	no	—
340	C₂²×C₄	—	4	1	no	—
341	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
342	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
343	Q₁₆	—	2	8	no	—
344	Q₁₆	—	2	4	no	—
345	Q₁₆	—	2	1	no	—
346	Q₁₆	—	2	2	no	—
347	Q₁₆	C₂×D₄×C₄₁	1	2	yes	—
348	Q₁₆	C₂×D₄×C₄₁	1	4	yes	—
349	SD₁₆	—	2	8	no	—
350	SD₁₆	—	2	4	no	—
351	D₈	—	2	1	no	—
352	D₈	—	2	2	no	—
353	D₈	—	2	2	no	—
354	D₈	—	4	2	no	—
355	D₈	C₂×D₄×C₄₁	1	2	yes	—
356	M₁₆	—	2	2	no	—
357	M₁₆	—	2	4	no	—
358	C₂×C₈	—	2	2	no	—
359	C₂×C₈	—	2	2	no	—
360	C₂×C₈	C₂×D₄×C₄₁	1	2	yes	—
361	C₂×C₈	C₂×D₄×C₄₁	1	1	yes	characteristic
362	C₂×C₈	C₂×D₄×C₄₁	1	2	yes	—
363	C₂×C₈	C₂×D₄×C₄₁	1	2	yes	—
364	C₂×C₈	C₂⁴×C₄₁	1	1	yes	characteristic
365	C₄⋊C₄	—	2	2	no	—
366	C₂²⋊C₄	—	4	1	no	—
367	C₂²⋊C₄	—	4	4	no	—
368	C₄²	—	4	1	no	—
369	C₁₆	—	2	2	no	—
370	C₁₆	—	2	2	no	—
371	C₂³	—	4	1	no	—
372	C₂³	—	4	2	no	—
373	C₂³	—	8	2	no	—
374	C₂³	—	16	2	no	—
375	C₂³	C₂×D₈×C₄₁	1	2	yes	—
376	C₂³	C₂×D₈×C₄₁	1	1	yes	characteristic
377	Q₈	—	2	2	no	—
378	Q₈	—	2	4	no	—
379	Q₈	—	2	2	no	—
380	Q₈	—	4	8	no	—
381	Q₈	—	4	1	no	—
382	Q₈	—	4	2	no	—
383	Q₈	—	4	4	no	—
384	D₄	—	2	4	no	—
385	D₄	—	2	2	no	—
386	D₄	—	2	2	no	—
387	D₄	—	4	8	no	—
388	D₄	—	4	4	no	—
389	D₄	—	4	2	no	—
390	D₄	—	4	1	no	—
391	D₄	—	4	2	no	—
392	D₄	—	8	2	no	—
393	D₄	—	16	4	no	—
394	C₂×C₄	—	2	2	no	—
395	C₂×C₄	—	2	2	no	—
396	C₂×C₄	—	4	8	no	—
397	C₂×C₄	—	4	8	no	—
398	C₂×C₄	—	4	2	no	—
399	C₂×C₄	—	4	1	no	—
400	C₂×C₄	—	4	4	no	—
401	C₂×C₄	—	4	4	no	—
402	C₂×C₄	—	4	2	no	—
403	C₂×C₄	#120×C₄₁	1	2	yes	—
404	C₂×C₄	C₂×D₈×C₄₁	1	2	yes	—
405	C₂×C₄	C₂×D₈×C₄₁	1	1	yes	characteristic
406	C₂×C₄	AGL(1,ℤ/8)×C₄₁	1	2	yes	—
407	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
408	C₈	—	2	2	no	—
409	C₈	#120×C₄₁	1	2	yes	—
410	C₈	C₂²×D₄×C₄₁	1	1	yes	characteristic
411	C₈	C₂²×D₄×C₄₁	1	1	yes	characteristic
412	C₂²	—	2	2	no	—
413	C₂²	—	2	4	no	—
414	C₂²	—	2	2	no	—
415	C₂²	—	4	2	no	—
416	C₂²	—	8	2	no	—
417	C₂²	—	8	4	no	—
418	C₂²	—	8	2	no	—
419	C₂²	—	16	4	no	—
420	C₂²	C₄₁×#447	1	2	yes	—
421	C₂²	C₂²×D₈×C₄₁	1	1	yes	characteristic
422	C₄	—	2	2	no	—
423	C₄	—	4	4	no	—
424	C₄	—	4	2	no	—
425	C₄	—	8	2	no	—
426	C₄	C₄₁×#447	1	2	yes	—
427	C₄	C₂×#120×C₄₁	1	1	yes	characteristic
428	C₄	C₂×AGL(1,ℤ/8)×C₄₁	1	1	yes	characteristic
429	C₂	—	2	2	no	—
430	C₂	—	4	2	no	—
431	C₂	—	8	2	no	—
432	C₂	—	16	2	no	—
433	C₂	C₂×C₄₁×#447	1	1	yes	characteristic
434	C₂	C₄₁×#3416	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×#578	C₂	semidirect
2. C₂×C₄₁×#509	C₂	semidirect
3. C₂²×SD₃₂×C₄₁	C₂	semidirect
4. C₄₁×#3058	C₂	semidirect
5. C₄₁×#2186	C₂	semidirect
6. C₄₁×#2185	C₂	semidirect
7. C₄₁×#2141	C₂	semidirect
8. C₄₁×#2138	C₂	semidirect
9. C₄₁×#2113	C₂	semidirect
16. C₂×#135×C₄₁	C₂²	semidirect
18. C₂²×Q₁₆×C₄₁	C₂²	semidirect
33. C₄₁×#358	C₂²	semidirect
34. C₄₁×#358	C₂²	semidirect
35. C₄₁×#357	C₂²	semidirect
36. C₄₁×C₂²⋊C₁₆	C₂²	semidirect
53. #135×C₄₁	D₄	semidirect
59. C₂×Q₁₆×C₄₁	D₄	semidirect
194. #33524	C₄₁	direct (N × H)
212. C₂×#578	C₂×C₄₁	semidirect
213. C₂×#509	C₂×C₄₁	semidirect
214. C₂²×SD₃₂	C₂×C₄₁	semidirect
215. #3058	C₂×C₄₁	semidirect
216. #2186	C₂×C₄₁	semidirect
217. #2185	C₂×C₄₁	semidirect
218. #2141	C₂×C₄₁	semidirect
219. #2138	C₂×C₄₁	semidirect
220. #2113	C₂×C₄₁	semidirect
233. C₂×#135	C₂²×C₄₁	semidirect
235. C₂²×Q₁₆	C₂²×C₄₁	semidirect
250. #358	C₂²×C₄₁	semidirect
251. #358	C₂²×C₄₁	semidirect
252. #357	C₂²×C₄₁	semidirect
253. C₂²⋊C₁₆	C₂²×C₄₁	semidirect
254. C₄₁	#33524	direct (N × H)
271. #135	D₄×C₄₁	semidirect
277. C₂×Q₁₆	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×#578	2
C₂×C₄₁×#509	2
C₂²×SD₃₂×C₄₁	2
C₄₁×#3058	2
C₄₁×#2186	2
C₄₁×#2185	2
C₄₁×#2141	2
C₄₁×#2138	2
C₄₁×#2113	2
#33524	41

Subgroups — C41×#33524 #23809725

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#33524 #23809725