Subgroups — C₄₁×#23934 #23800135

Order 10496.

1272 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₁×#533	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄₁×#451	C₂	1	2	yes	maximal
3	C₂×C₄₁×#391	C₂	1	1	yes	maximal, characteristic
4	C₄₁×#2024	C₂	1	2	yes	maximal, complemented
5	C₄₁×#2016	C₂	1	2	yes	maximal, complemented
6	C₄₁×#1878	C₂	1	4	yes	maximal, complemented
7	C₄₁×#1872	C₂	1	2	yes	maximal
8	C₄₁×#1817	C₂	1	1	yes	maximal, characteristic
9	C₂³×Q₈×C₄₁	C₂²	1	1	yes	characteristic
10	C₂²×Q₁₆×C₄₁	C₂²	1	4	yes	—
11	C₄₁×#533	—	2	8	no	—
12	C₂×C₄⋊Q₈×C₄₁	C₂²	1	1	yes	characteristic
13	C₂×C₄⋊Q₈×C₄₁	C₂²	1	1	yes	characteristic
14	C₂×#125×C₄₁	—	2	1	no	—
15	C₂×C₂²⋊Q₈×C₄₁	—	2	1	no	—
16	C₂×C₂²⋊Q₈×C₄₁	C₂²	1	2	yes	—
17	C₂×C₄×Q₈×C₄₁	—	2	1	no	—
18	C₂×C₄×Q₈×C₄₁	C₂²	1	2	yes	—
19	C₂×#117×C₄₁	—	2	1	no	—
20	C₂²×C₄⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
21	C₂²×C₄²×C₄₁	C₂²	1	1	yes	characteristic
22	C₄₁×#451	—	2	8	no	—
23	C₂×#103×C₄₁	C₂²	1	4	yes	—
24	C₂×#103×C₄₁	C₂²	1	4	yes	—
25	C₂×C₂²⋊C₈×C₄₁	C₂²	1	2	yes	—
26	C₄₁×#391	—	2	1	no	—
27	C₄₁×#391	—	2	1	no	—
28	C₄₁×#391	C₂²	1	2	yes	—
29	C₄₁×#391	C₂²	1	2	yes	—
30	C₂×#95×C₄₁	—	2	1	no	—
31	C₂×#95×C₄₁	—	2	1	no	—
32	C₄₁×#340	C₂²	1	4	yes	—
33	C₄₁×#336	C₂²	1	2	yes	—
34	C₄₁×#336	C₂²	1	2	yes	—
35	C₂²×Q₈×C₄₁	—	2	4	no	—
36	C₂²×Q₈×C₄₁	—	2	1	no	—
37	C₂²×Q₈×C₄₁	—	2	1	no	—
38	C₂²×Q₈×C₄₁	—	2	4	no	—
39	C₂²×Q₈×C₄₁	—	4	2	no	—
40	C₂²×Q₈×C₄₁	C₂³	1	2	yes	—
41	C₂²×Q₈×C₄₁	C₂³	1	2	yes	—
42	C₂³×C₄×C₄₁	—	2	1	no	—
43	C₂³×C₄×C₄₁	—	2	1	no	—
44	C₂³×C₄×C₄₁	D₄	1	1	yes	characteristic
45	C₂³×C₄×C₄₁	D₄	1	1	yes	characteristic
46	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
47	C₂×Q₁₆×C₄₁	—	2	8	no	—
48	C₂×Q₁₆×C₄₁	—	2	8	no	—
49	C₂×Q₁₆×C₄₁	—	4	4	no	—
50	C₂²×C₈×C₄₁	C₂³	1	4	yes	—
51	C₄⋊Q₈×C₄₁	—	2	4	no	—
52	C₄⋊Q₈×C₄₁	—	2	4	no	—
53	#125×C₄₁	—	2	8	no	—
54	C₂²⋊Q₈×C₄₁	—	2	8	no	—
55	C₂²⋊Q₈×C₄₁	—	2	4	no	—
56	C₂²⋊Q₈×C₄₁	D₄	1	8	yes	—
57	C₄×Q₈×C₄₁	—	2	8	no	—
58	C₄×Q₈×C₄₁	—	2	4	no	—
59	C₄×Q₈×C₄₁	—	2	4	no	—
60	#117×C₄₁	—	2	8	no	—
61	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
62	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
63	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
64	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
65	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
66	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
67	C₂×C₄⋊C₄×C₄₁	—	4	2	no	—
68	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
69	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
70	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
71	C₂×C₄²×C₄₁	—	2	4	no	—
72	C₂×C₄²×C₄₁	—	2	2	no	—
73	C₂×C₄²×C₄₁	D₄	1	1	yes	characteristic
74	C₂×C₄²×C₄₁	D₄	1	1	yes	characteristic
75	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
76	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
77	#103×C₄₁	—	2	8	no	—
78	#103×C₄₁	—	4	4	no	—
79	C₂²⋊C₈×C₄₁	—	2	4	no	—
80	#95×C₄₁	—	2	2	no	—
81	#95×C₄₁	—	2	2	no	—
82	#95×C₄₁	—	2	2	no	—
83	#95×C₄₁	—	2	2	no	—
84	C₂⁴×C₄₁	C₂×D₄	1	1	yes	characteristic
85	C₂×Q₈×C₄₁	—	2	4	no	—
86	C₂×Q₈×C₄₁	—	2	4	no	—
87	C₂×Q₈×C₄₁	—	2	2	no	—
88	C₂×Q₈×C₄₁	—	2	2	no	—
89	C₂×Q₈×C₄₁	—	2	4	no	—
90	C₂×Q₈×C₄₁	—	2	4	no	—
91	C₂×Q₈×C₄₁	—	2	4	no	—
92	C₂×Q₈×C₄₁	—	2	4	no	—
93	C₂×Q₈×C₄₁	—	4	16	no	—
94	C₂×Q₈×C₄₁	—	4	2	no	—
95	C₂×Q₈×C₄₁	—	4	2	no	—
96	C₂×Q₈×C₄₁	—	4	2	no	—
97	C₂×Q₈×C₄₁	—	4	2	no	—
98	C₂×Q₈×C₄₁	C₂×D₄	1	4	yes	—
99	C₂×Q₈×C₄₁	#41	1	4	yes	—
100	C₂²×C₄×C₄₁	—	2	2	no	—
101	C₂²×C₄×C₄₁	—	2	2	no	—
102	C₂²×C₄×C₄₁	—	2	2	no	—
103	C₂²×C₄×C₄₁	—	2	2	no	—
104	C₂²×C₄×C₄₁	—	2	4	no	—
105	C₂²×C₄×C₄₁	—	2	2	no	—
106	C₂²×C₄×C₄₁	—	2	2	no	—
107	C₂²×C₄×C₄₁	—	2	2	no	—
108	C₂²×C₄×C₄₁	—	2	2	no	—
109	C₂²×C₄×C₄₁	—	2	2	no	—
110	C₂²×C₄×C₄₁	—	2	2	no	—
111	C₂²×C₄×C₄₁	—	4	1	no	—
112	C₂²×C₄×C₄₁	—	4	2	no	—
113	C₂²×C₄×C₄₁	—	4	2	no	—
114	C₂²×C₄×C₄₁	—	4	2	no	—
115	C₂²×C₄×C₄₁	—	4	2	no	—
116	C₂²×C₄×C₄₁	—	4	2	no	—
117	C₂²×C₄×C₄₁	Q₁₆	1	4	yes	complemented
118	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
119	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
120	C₂²×C₄×C₄₁	C₂×D₄	1	4	yes	—
121	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
122	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
123	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
124	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
125	Q₁₆×C₄₁	—	4	16	no	—
126	C₂×C₈×C₄₁	—	2	4	no	—
127	C₂×C₈×C₄₁	—	2	4	no	—
128	C₂×C₈×C₄₁	—	2	4	no	—
129	C₄⋊C₄×C₄₁	—	2	4	no	—
130	C₄⋊C₄×C₄₁	—	2	4	no	—
131	C₄⋊C₄×C₄₁	—	2	8	no	—
132	C₄⋊C₄×C₄₁	—	2	4	no	—
133	C₄⋊C₄×C₄₁	—	2	8	no	—
134	C₄⋊C₄×C₄₁	—	2	2	no	—
135	C₄⋊C₄×C₄₁	—	2	4	no	—
136	C₄⋊C₄×C₄₁	—	4	2	no	—
137	C₄⋊C₄×C₄₁	C₂×D₄	1	4	yes	—
138	C₂²⋊C₄×C₄₁	—	2	8	no	—
139	C₄²×C₄₁	—	2	8	no	—
140	C₄²×C₄₁	—	2	2	no	—
141	C₄²×C₄₁	—	2	2	no	—
142	C₄²×C₄₁	—	2	2	no	—
143	C₄²×C₄₁	—	2	2	no	—
144	C₂³×C₄₁	—	2	1	no	—
145	C₂³×C₄₁	—	2	1	no	—
146	C₂³×C₄₁	—	2	1	no	—
147	C₂³×C₄₁	—	2	1	no	—
148	C₂³×C₄₁	#120	1	2	yes	—
149	C₂³×C₄₁	C₂×Q₁₆	1	2	yes	—
150	C₂³×C₄₁	#137	1	2	yes	—
151	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
152	Q₈×C₄₁	—	2	8	no	—
153	Q₈×C₄₁	—	2	8	no	—
154	Q₈×C₄₁	—	4	8	no	—
155	Q₈×C₄₁	—	4	8	no	—
156	Q₈×C₄₁	—	4	4	no	—
157	Q₈×C₄₁	—	4	4	no	—
158	C₂×C₄×C₄₁	—	2	1	no	—
159	C₂×C₄×C₄₁	—	2	1	no	—
160	C₂×C₄×C₄₁	—	2	1	no	—
161	C₂×C₄×C₄₁	—	2	1	no	—
162	C₂×C₄×C₄₁	—	2	1	no	—
163	C₂×C₄×C₄₁	—	2	1	no	—
164	C₂×C₄×C₄₁	—	2	1	no	—
165	C₂×C₄×C₄₁	—	2	1	no	—
166	C₂×C₄×C₄₁	—	2	8	no	—
167	C₂×C₄×C₄₁	—	2	8	no	—
168	C₂×C₄×C₄₁	—	2	1	no	—
169	C₂×C₄×C₄₁	—	2	4	no	—
170	C₂×C₄×C₄₁	—	2	4	no	—
171	C₂×C₄×C₄₁	—	2	4	no	—
172	C₂×C₄×C₄₁	—	2	1	no	—
173	C₂×C₄×C₄₁	—	2	1	no	—
174	C₂×C₄×C₄₁	—	4	4	no	—
175	C₂×C₄×C₄₁	—	4	8	no	—
176	C₂×C₄×C₄₁	—	4	2	no	—
177	C₂×C₄×C₄₁	—	4	2	no	—
178	C₂×C₄×C₄₁	—	4	2	no	—
179	C₂×C₄×C₄₁	—	4	2	no	—
180	C₂×C₄×C₄₁	—	4	2	no	—
181	C₂×C₄×C₄₁	—	4	2	no	—
182	C₂×C₄×C₄₁	—	4	2	no	—
183	C₂×C₄×C₄₁	—	4	2	no	—
184	C₂×C₄×C₄₁	—	4	2	no	—
185	C₂×C₄×C₄₁	—	8	4	no	—
186	C₂×C₄×C₄₁	#120	1	2	yes	—
187	C₂×C₄×C₄₁	C₂×Q₁₆	1	2	yes	—
188	C₂×C₄×C₄₁	C₂×Q₁₆	1	2	yes	—
189	C₂×C₄×C₄₁	#137	1	2	yes	—
190	C₂×C₄×C₄₁	C₂²×D₄	1	2	yes	—
191	C₂×C₄×C₄₁	C₂×#41	1	2	yes	—
192	C₂×C₄×C₄₁	H(5,𝔽₂)	1	2	yes	—
193	C₈×C₄₁	—	4	4	no	—
194	#23934	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
195	C₂²×C₄₁	—	2	2	no	—
196	C₂²×C₄₁	—	2	2	no	—
197	C₂²×C₄₁	—	2	2	no	—
198	C₂²×C₄₁	—	2	2	no	—
199	C₂²×C₄₁	—	2	2	no	—
200	C₂²×C₄₁	—	2	2	no	—
201	C₂²×C₄₁	#451	1	4	yes	—
202	C₂²×C₄₁	C₂×#120	1	1	yes	characteristic
203	C₂²×C₄₁	#525	1	1	yes	characteristic
204	C₂²×C₄₁	#535	1	1	yes	characteristic
205	C₂²×C₄₁	C₂²×Q₁₆	1	1	yes	characteristic
206	C₂²×C₄₁	C₂×#137	1	1	yes	characteristic
207	C₂²×C₄₁	C₂×#137	1	1	yes	characteristic
208	C₂²×C₄₁	#575	1	1	yes	characteristic
209	C₄×C₄₁	—	2	2	no	—
210	C₄×C₄₁	—	2	2	no	—
211	C₄×C₄₁	—	2	2	no	—
212	C₄×C₄₁	—	2	2	no	—
213	C₄×C₄₁	—	4	4	no	—
214	C₄×C₄₁	—	4	4	no	—
215	C₄×C₄₁	—	4	1	no	—
216	C₄×C₄₁	—	4	4	no	—
217	C₄×C₄₁	—	8	2	no	—
218	C₄×C₄₁	#546	1	4	yes	—
219	C₂×#533	C₂×C₄₁	1	1	yes	characteristic
220	C₂×#451	C₂×C₄₁	1	2	yes	—
221	C₂×#391	C₂×C₄₁	1	1	yes	characteristic
222	#2024	C₂×C₄₁	1	2	yes	complemented
223	#2016	C₂×C₄₁	1	2	yes	complemented
224	#1878	C₂×C₄₁	1	4	yes	complemented
225	#1872	C₂×C₄₁	1	2	yes	—
226	#1817	C₂×C₄₁	1	1	yes	characteristic
227	C₂×C₄₁	—	2	4	no	—
228	C₂×C₄₁	#2404	1	1	yes	characteristic
229	C₂×C₄₁	C₂×#451	1	1	yes	characteristic
230	C₂×C₄₁	#3007	1	1	yes	characteristic
231	C₂×C₄₁	#3104	1	1	yes	characteristic
232	C₂×C₄₁	#3113	1	1	yes	characteristic
233	C₂×C₄₁	#3209	1	1	yes	characteristic
234	C₂×C₄₁	#3215	1	1	yes	characteristic
235	C₂³×Q₈	C₂²×C₄₁	1	1	yes	characteristic
236	C₂²×Q₁₆	C₂²×C₄₁	1	4	yes	—
237	#533	—	2	8	no	—
238	C₂×C₄⋊Q₈	C₂²×C₄₁	1	1	yes	characteristic
239	C₂×C₄⋊Q₈	C₂²×C₄₁	1	1	yes	characteristic
240	C₂×#125	—	2	1	no	—
241	C₂×C₂²⋊Q₈	—	2	1	no	—
242	C₂×C₂²⋊Q₈	C₂²×C₄₁	1	2	yes	—
243	C₂×C₄×Q₈	—	2	1	no	—
244	C₂×C₄×Q₈	C₂²×C₄₁	1	2	yes	—
245	C₂×#117	—	2	1	no	—
246	C₂²×C₄⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
247	C₂²×C₄²	C₂²×C₄₁	1	1	yes	characteristic
248	#451	—	2	8	no	—
249	C₂×#103	C₂²×C₄₁	1	4	yes	—
250	C₂×#103	C₂²×C₄₁	1	4	yes	—
251	C₂×C₂²⋊C₈	C₂²×C₄₁	1	2	yes	—
252	#391	—	2	1	no	—
253	#391	—	2	1	no	—
254	#391	C₂²×C₄₁	1	2	yes	—
255	#391	C₂²×C₄₁	1	2	yes	—
256	C₂×#95	—	2	1	no	—
257	C₂×#95	—	2	1	no	—
258	#340	C₂²×C₄₁	1	4	yes	—
259	#336	C₂²×C₄₁	1	2	yes	—
260	#336	C₂²×C₄₁	1	2	yes	—
261	C₄₁	#23934	1	1	yes	characteristic, direct product factor, Sylow
262	C₂²×Q₈	—	2	4	no	—
263	C₂²×Q₈	—	2	1	no	—
264	C₂²×Q₈	—	2	1	no	—
265	C₂²×Q₈	—	2	4	no	—
266	C₂²×Q₈	—	4	2	no	—
267	C₂²×Q₈	C₂³×C₄₁	1	2	yes	—
268	C₂²×Q₈	C₂³×C₄₁	1	2	yes	—
269	C₂³×C₄	—	2	1	no	—
270	C₂³×C₄	—	2	1	no	—
271	C₂³×C₄	D₄×C₄₁	1	1	yes	characteristic
272	C₂³×C₄	D₄×C₄₁	1	1	yes	characteristic
273	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
274	C₂×Q₁₆	—	2	8	no	—
275	C₂×Q₁₆	—	2	8	no	—
276	C₂×Q₁₆	—	4	4	no	—
277	C₂²×C₈	C₂³×C₄₁	1	4	yes	—
278	C₄⋊Q₈	—	2	4	no	—
279	C₄⋊Q₈	—	2	4	no	—
280	#125	—	2	8	no	—
281	C₂²⋊Q₈	—	2	8	no	—
282	C₂²⋊Q₈	—	2	4	no	—
283	C₂²⋊Q₈	D₄×C₄₁	1	8	yes	—
284	C₄×Q₈	—	2	8	no	—
285	C₄×Q₈	—	2	4	no	—
286	C₄×Q₈	—	2	4	no	—
287	#117	—	2	8	no	—
288	C₂×C₄⋊C₄	—	2	1	no	—
289	C₂×C₄⋊C₄	—	2	1	no	—
290	C₂×C₄⋊C₄	—	2	1	no	—
291	C₂×C₄⋊C₄	—	2	2	no	—
292	C₂×C₄⋊C₄	—	2	2	no	—
293	C₂×C₄⋊C₄	—	2	1	no	—
294	C₂×C₄⋊C₄	—	4	2	no	—
295	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
296	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
297	C₂×C₂²⋊C₄	—	2	2	no	—
298	C₂×C₄²	—	2	2	no	—
299	C₂×C₄²	—	2	4	no	—
300	C₂×C₄²	D₄×C₄₁	1	1	yes	characteristic
301	C₂×C₄²	D₄×C₄₁	1	1	yes	characteristic
302	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
303	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
304	#103	—	2	8	no	—
305	#103	—	4	4	no	—
306	C₂²⋊C₈	—	2	4	no	—
307	#95	—	2	2	no	—
308	#95	—	2	2	no	—
309	#95	—	2	2	no	—
310	#95	—	2	2	no	—
311	C₂⁴	C₂×D₄×C₄₁	1	1	yes	characteristic
312	C₂×Q₈	—	2	4	no	—
313	C₂×Q₈	—	2	4	no	—
314	C₂×Q₈	—	2	2	no	—
315	C₂×Q₈	—	2	2	no	—
316	C₂×Q₈	—	2	4	no	—
317	C₂×Q₈	—	2	4	no	—
318	C₂×Q₈	—	2	4	no	—
319	C₂×Q₈	—	2	4	no	—
320	C₂×Q₈	—	4	16	no	—
321	C₂×Q₈	—	4	2	no	—
322	C₂×Q₈	—	4	2	no	—
323	C₂×Q₈	—	4	2	no	—
324	C₂×Q₈	—	4	2	no	—
325	C₂×Q₈	C₂×D₄×C₄₁	1	4	yes	—
326	C₂×Q₈	#41×C₄₁	1	4	yes	—
327	C₂²×C₄	—	2	2	no	—
328	C₂²×C₄	—	2	2	no	—
329	C₂²×C₄	—	2	2	no	—
330	C₂²×C₄	—	2	2	no	—
331	C₂²×C₄	—	2	4	no	—
332	C₂²×C₄	—	2	2	no	—
333	C₂²×C₄	—	2	2	no	—
334	C₂²×C₄	—	2	2	no	—
335	C₂²×C₄	—	2	2	no	—
336	C₂²×C₄	—	2	2	no	—
337	C₂²×C₄	—	2	2	no	—
338	C₂²×C₄	—	4	1	no	—
339	C₂²×C₄	—	4	2	no	—
340	C₂²×C₄	—	4	2	no	—
341	C₂²×C₄	—	4	2	no	—
342	C₂²×C₄	—	4	2	no	—
343	C₂²×C₄	—	4	2	no	—
344	C₂²×C₄	Q₁₆×C₄₁	1	4	yes	complemented
345	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
346	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
347	C₂²×C₄	C₂×D₄×C₄₁	1	4	yes	—
348	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
349	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
350	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
351	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
352	Q₁₆	—	4	16	no	—
353	C₂×C₈	—	2	4	no	—
354	C₂×C₈	—	2	4	no	—
355	C₂×C₈	—	2	4	no	—
356	C₄⋊C₄	—	2	4	no	—
357	C₄⋊C₄	—	2	4	no	—
358	C₄⋊C₄	—	2	8	no	—
359	C₄⋊C₄	—	2	4	no	—
360	C₄⋊C₄	—	2	8	no	—
361	C₄⋊C₄	—	2	2	no	—
362	C₄⋊C₄	—	2	4	no	—
363	C₄⋊C₄	—	4	2	no	—
364	C₄⋊C₄	C₂×D₄×C₄₁	1	4	yes	—
365	C₂²⋊C₄	—	2	8	no	—
366	C₄²	—	2	8	no	—
367	C₄²	—	2	2	no	—
368	C₄²	—	2	2	no	—
369	C₄²	—	2	2	no	—
370	C₄²	—	2	2	no	—
371	C₂³	—	2	1	no	—
372	C₂³	—	2	1	no	—
373	C₂³	—	2	1	no	—
374	C₂³	—	2	1	no	—
375	C₂³	#120×C₄₁	1	2	yes	—
376	C₂³	C₂×Q₁₆×C₄₁	1	2	yes	—
377	C₂³	#137×C₄₁	1	2	yes	—
378	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
379	Q₈	—	2	8	no	—
380	Q₈	—	2	8	no	—
381	Q₈	—	4	8	no	—
382	Q₈	—	4	8	no	—
383	Q₈	—	4	4	no	—
384	Q₈	—	4	4	no	—
385	C₂×C₄	—	2	1	no	—
386	C₂×C₄	—	2	1	no	—
387	C₂×C₄	—	2	1	no	—
388	C₂×C₄	—	2	1	no	—
389	C₂×C₄	—	2	1	no	—
390	C₂×C₄	—	2	1	no	—
391	C₂×C₄	—	2	1	no	—
392	C₂×C₄	—	2	1	no	—
393	C₂×C₄	—	2	8	no	—
394	C₂×C₄	—	2	8	no	—
395	C₂×C₄	—	2	1	no	—
396	C₂×C₄	—	2	4	no	—
397	C₂×C₄	—	2	4	no	—
398	C₂×C₄	—	2	4	no	—
399	C₂×C₄	—	2	1	no	—
400	C₂×C₄	—	2	1	no	—
401	C₂×C₄	—	4	4	no	—
402	C₂×C₄	—	4	8	no	—
403	C₂×C₄	—	4	2	no	—
404	C₂×C₄	—	4	2	no	—
405	C₂×C₄	—	4	2	no	—
406	C₂×C₄	—	4	2	no	—
407	C₂×C₄	—	4	2	no	—
408	C₂×C₄	—	4	2	no	—
409	C₂×C₄	—	4	2	no	—
410	C₂×C₄	—	4	2	no	—
411	C₂×C₄	—	4	2	no	—
412	C₂×C₄	—	8	4	no	—
413	C₂×C₄	#120×C₄₁	1	2	yes	—
414	C₂×C₄	C₂×Q₁₆×C₄₁	1	2	yes	—
415	C₂×C₄	C₂×Q₁₆×C₄₁	1	2	yes	—
416	C₂×C₄	#137×C₄₁	1	2	yes	—
417	C₂×C₄	C₂²×D₄×C₄₁	1	2	yes	—
418	C₂×C₄	C₂×#41×C₄₁	1	2	yes	—
419	C₂×C₄	H(5,𝔽₂)×C₄₁	1	2	yes	—
420	C₈	—	4	4	no	—
421	C₂²	—	2	2	no	—
422	C₂²	—	2	2	no	—
423	C₂²	—	2	2	no	—
424	C₂²	—	2	2	no	—
425	C₂²	—	2	2	no	—
426	C₂²	—	2	2	no	—
427	C₂²	C₄₁×#451	1	4	yes	—
428	C₂²	C₂×#120×C₄₁	1	1	yes	characteristic
429	C₂²	C₄₁×#525	1	1	yes	characteristic
430	C₂²	C₄₁×#535	1	1	yes	characteristic
431	C₂²	C₂²×Q₁₆×C₄₁	1	1	yes	characteristic
432	C₂²	C₂×#137×C₄₁	1	1	yes	characteristic
433	C₂²	C₂×#137×C₄₁	1	1	yes	characteristic
434	C₂²	C₄₁×#575	1	1	yes	characteristic
435	C₄	—	2	2	no	—
436	C₄	—	2	2	no	—
437	C₄	—	2	2	no	—
438	C₄	—	2	2	no	—
439	C₄	—	4	4	no	—
440	C₄	—	4	4	no	—
441	C₄	—	4	1	no	—
442	C₄	—	4	4	no	—
443	C₄	—	8	2	no	—
444	C₄	C₄₁×#546	1	4	yes	—
445	C₂	—	2	4	no	—
446	C₂	C₄₁×#2404	1	1	yes	characteristic
447	C₂	C₂×C₄₁×#451	1	1	yes	characteristic
448	C₂	C₄₁×#3007	1	1	yes	characteristic
449	C₂	C₄₁×#3104	1	1	yes	characteristic
450	C₂	C₄₁×#3113	1	1	yes	characteristic
451	C₂	C₄₁×#3209	1	1	yes	characteristic
452	C₂	C₄₁×#3215	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₄₁	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₁
prime radical	C₂⁴×C₄₁	C₂×D₄
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₄₁ ◁ C₂²×C₄²×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₄₁×#2024	C₂	semidirect
5. C₄₁×#2016	C₂	semidirect
6. C₄₁×#1878	C₂	semidirect
117. C₂²×C₄×C₄₁	Q₁₆	semidirect
194. #23934	C₄₁	direct (N × H)
222. #2024	C₂×C₄₁	semidirect
223. #2016	C₂×C₄₁	semidirect
224. #1878	C₂×C₄₁	semidirect
261. C₄₁	#23934	direct (N × H)
344. C₂²×C₄	Q₁₆×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×#533	2
C₂×C₄₁×#451	2
C₂×C₄₁×#391	2
C₄₁×#2024	2
C₄₁×#2016	2
C₄₁×#1878	2
C₄₁×#1872	2
C₄₁×#1817	2
#23934	41

Subgroups — C41×#23934 #23800135

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#23934 #23800135