Subgroups — C₄₁×#21944 #23798145

Order 10496.

1162 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	C₂×C₄₁×#407	C₂	1	1	yes	maximal, characteristic
2	C₄₁×#2280	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄₁×#380	C₂	1	1	yes	maximal, characteristic
4	C₄₁×#1854	C₂	1	4	yes	maximal, complemented
5	C₄₁×#1853	C₂	1	2	yes	maximal, complemented
6	C₄₁×#1852	C₂	1	2	yes	maximal, complemented
7	C₄₁×#1809	C₂	1	4	yes	maximal, complemented
8	C₂⁴×C₄×C₄₁	C₂²	1	1	yes	characteristic
9	C₂²×M₁₆×C₄₁	C₂²	1	2	yes	—
10	C₂×#117×C₄₁	C₂²	1	2	yes	—
11	C₂²×C₄⋊C₄×C₄₁	C₂²	1	2	yes	—
12	C₂²×C₂²⋊C₄×C₄₁	—	2	1	no	—
13	C₂×#107×C₄₁	C₂²	1	4	yes	complemented
14	C₂×#106×C₄₁	C₂²	1	4	yes	complemented
15	C₄₁×#407	C₄	1	8	yes	complemented
16	C₂×C₂²⋊C₈×C₄₁	C₂²	1	2	yes	—
17	C₂×C₂²⋊C₈×C₄₁	C₂²	1	2	yes	—
18	C₄₁×#381	—	2	1	no	—
19	C₄₁×#380	—	2	1	no	—
20	C₄₁×#380	—	2	1	no	—
21	C₄₁×#380	C₂²	1	2	yes	—
22	C₄₁×#380	C₂²	1	2	yes	—
23	C₄₁×#380	C₂²	1	2	yes	—
24	C₄₁×#380	C₂²	1	1	yes	characteristic
25	C₄₁×#380	C₂²	1	1	yes	characteristic
26	C₄₁×#379	—	2	1	no	—
27	C₄×C₂²⋊C₄×C₄₁	—	2	1	no	—
28	C₄×C₂²⋊C₄×C₄₁	—	2	1	no	—
29	C₂×#95×C₄₁	—	2	1	no	—
30	C₄₁×#340	C₂²	1	4	yes	complemented
31	C₄₁×#340	C₂²	1	4	yes	complemented
32	C₂⁵×C₄₁	D₄	1	1	yes	characteristic
33	C₂³×C₄×C₄₁	—	2	2	no	—
34	C₂³×C₄×C₄₁	—	4	4	no	—
35	C₂³×C₄×C₄₁	C₂×C₄	1	4	yes	—
36	C₂³×C₄×C₄₁	D₄	1	1	yes	characteristic
37	C₂³×C₄×C₄₁	D₄	1	1	yes	characteristic
38	C₂³×C₄×C₄₁	D₄	1	1	yes	characteristic
39	C₂³×C₄×C₄₁	Q₈	1	4	yes	—
40	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
41	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
42	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
43	C₂×M₁₆×C₄₁	—	4	4	no	—
44	C₂×M₁₆×C₄₁	C₂×C₄	1	8	yes	complemented
45	C₂²×C₈×C₄₁	C₂³	1	4	yes	—
46	#117×C₄₁	—	4	4	no	—
47	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
48	C₂×C₄⋊C₄×C₄₁	—	4	4	no	—
49	C₂×C₄⋊C₄×C₄₁	C₂³	1	4	yes	—
50	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
51	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
52	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
53	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
54	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
55	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
56	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
57	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
58	C₂×C₂²⋊C₄×C₄₁	—	4	4	no	—
59	C₂×C₄²×C₄₁	—	2	2	no	—
60	#107×C₄₁	—	4	4	no	—
61	#106×C₄₁	—	4	4	no	—
62	C₂²⋊C₈×C₄₁	C₂×C₄	1	8	yes	—
63	C₂²⋊C₈×C₄₁	C₂×C₄	1	8	yes	complemented
64	#95×C₄₁	—	2	2	no	—
65	#95×C₄₁	—	2	2	no	—
66	#95×C₄₁	—	2	2	no	—
67	#95×C₄₁	—	2	1	no	—
68	#95×C₄₁	—	2	1	no	—
69	C₂⁴×C₄₁	—	2	2	no	—
70	C₂⁴×C₄₁	—	2	2	no	—
71	C₂⁴×C₄₁	—	4	2	no	—
72	C₂⁴×C₄₁	—	4	2	no	—
73	C₂⁴×C₄₁	C₄⋊C₄	1	4	yes	—
74	C₂⁴×C₄₁	C₂×D₄	1	1	yes	characteristic
75	C₂⁴×C₄₁	C₂×D₄	1	1	yes	characteristic
76	C₂⁴×C₄₁	C₂×D₄	1	1	yes	characteristic
77	C₂²×C₄×C₄₁	—	2	4	no	—
78	C₂²×C₄×C₄₁	—	2	4	no	—
79	C₂²×C₄×C₄₁	—	2	4	no	—
80	C₂²×C₄×C₄₁	—	2	2	no	—
81	C₂²×C₄×C₄₁	—	2	2	no	—
82	C₂²×C₄×C₄₁	—	2	4	no	—
83	C₂²×C₄×C₄₁	—	4	8	no	—
84	C₂²×C₄×C₄₁	—	4	8	no	—
85	C₂²×C₄×C₄₁	—	4	2	no	—
86	C₂²×C₄×C₄₁	—	4	2	no	—
87	C₂²×C₄×C₄₁	—	4	2	no	—
88	C₂²×C₄×C₄₁	—	4	4	no	—
89	C₂²×C₄×C₄₁	—	4	4	no	—
90	C₂²×C₄×C₄₁	—	4	4	no	—
91	C₂²×C₄×C₄₁	C₄⋊C₄	1	4	yes	—
92	C₂²×C₄×C₄₁	C₄⋊C₄	1	4	yes	—
93	C₂²×C₄×C₄₁	C₄⋊C₄	1	4	yes	—
94	C₂²×C₄×C₄₁	C₂²×C₄	1	2	yes	—
95	C₂²×C₄×C₄₁	C₂²×C₄	1	2	yes	—
96	C₂²×C₄×C₄₁	C₂²×C₄	1	2	yes	—
97	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
98	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
99	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
100	C₂²×C₄×C₄₁	C₂×Q₈	1	2	yes	—
101	C₂²×C₄×C₄₁	C₂×Q₈	1	2	yes	—
102	C₂²×C₄×C₄₁	C₂×Q₈	1	2	yes	—
103	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
104	M₁₆×C₄₁	—	4	8	no	—
105	C₂×C₈×C₄₁	—	2	4	no	—
106	C₂×C₈×C₄₁	—	2	4	no	—
107	C₂×C₈×C₄₁	C₂²×C₄	1	8	yes	—
108	C₄⋊C₄×C₄₁	—	2	4	no	—
109	C₄⋊C₄×C₄₁	—	2	4	no	—
110	C₄⋊C₄×C₄₁	—	2	4	no	—
111	C₄⋊C₄×C₄₁	—	2	4	no	—
112	C₄⋊C₄×C₄₁	—	4	4	no	—
113	C₂²⋊C₄×C₄₁	—	4	4	no	—
114	C₂²⋊C₄×C₄₁	—	4	4	no	—
115	C₂²⋊C₄×C₄₁	—	4	4	no	—
116	C₂²⋊C₄×C₄₁	—	4	4	no	—
117	C₂²⋊C₄×C₄₁	—	4	2	no	—
118	C₂²⋊C₄×C₄₁	—	4	2	no	—
119	C₄²×C₄₁	—	4	4	no	—
120	C₂³×C₄₁	—	2	2	no	—
121	C₂³×C₄₁	—	2	2	no	—
122	C₂³×C₄₁	—	2	2	no	—
123	C₂³×C₄₁	—	2	2	no	—
124	C₂³×C₄₁	—	2	1	no	—
125	C₂³×C₄₁	—	2	1	no	—
126	C₂³×C₄₁	—	2	1	no	—
127	C₂³×C₄₁	—	2	1	no	—
128	C₂³×C₄₁	—	2	2	no	—
129	C₂³×C₄₁	—	2	2	no	—
130	C₂³×C₄₁	—	2	8	no	—
131	C₂³×C₄₁	—	4	4	no	—
132	C₂³×C₄₁	—	4	4	no	—
133	C₂³×C₄₁	—	4	8	no	—
134	C₂³×C₄₁	—	4	8	no	—
135	C₂³×C₄₁	C₂×C₄⋊C₄	1	2	yes	—
136	C₂³×C₄₁	C₂×C₄⋊C₄	1	2	yes	—
137	C₂³×C₄₁	C₂×C₄⋊C₄	1	2	yes	—
138	C₂³×C₄₁	AGL(1,ℤ/8)	1	2	yes	—
139	C₂³×C₄₁	#137	1	2	yes	—
140	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
141	C₂×C₄×C₄₁	—	2	2	no	—
142	C₂×C₄×C₄₁	—	2	2	no	—
143	C₂×C₄×C₄₁	—	2	2	no	—
144	C₂×C₄×C₄₁	—	2	4	no	—
145	C₂×C₄×C₄₁	—	2	4	no	—
146	C₂×C₄×C₄₁	—	2	4	no	—
147	C₂×C₄×C₄₁	—	2	4	no	—
148	C₂×C₄×C₄₁	—	2	4	no	—
149	C₂×C₄×C₄₁	—	2	4	no	—
150	C₂×C₄×C₄₁	—	4	4	no	—
151	C₂×C₄×C₄₁	—	4	4	no	—
152	C₂×C₄×C₄₁	—	4	4	no	—
153	C₂×C₄×C₄₁	—	4	2	no	—
154	C₂×C₄×C₄₁	—	4	2	no	—
155	C₂×C₄×C₄₁	—	4	4	no	—
156	C₂×C₄×C₄₁	—	4	4	no	—
157	C₂×C₄×C₄₁	—	4	2	no	—
158	C₂×C₄×C₄₁	—	4	2	no	—
159	C₂×C₄×C₄₁	—	4	2	no	—
160	C₂×C₄×C₄₁	—	4	2	no	—
161	C₂×C₄×C₄₁	—	4	4	no	—
162	C₂×C₄×C₄₁	—	8	8	no	—
163	C₂×C₄×C₄₁	C₂×C₄⋊C₄	1	2	yes	—
164	C₂×C₄×C₄₁	C₂×C₄⋊C₄	1	2	yes	—
165	C₂×C₄×C₄₁	C₂×C₄⋊C₄	1	2	yes	—
166	C₂×C₄×C₄₁	C₂³×C₄	1	1	yes	characteristic
167	C₂×C₄×C₄₁	C₂²×Q₈	1	1	yes	characteristic
168	C₂×C₄×C₄₁	H(5,𝔽₂)	1	4	yes	—
169	C₈×C₄₁	—	2	8	no	—
170	#21944	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
171	C₂²×C₄₁	—	2	2	no	—
172	C₂²×C₄₁	—	2	2	no	—
173	C₂²×C₄₁	—	2	4	no	—
174	C₂²×C₄₁	—	2	4	no	—
175	C₂²×C₄₁	—	2	2	no	—
176	C₂²×C₄₁	—	2	2	no	—
177	C₂²×C₄₁	—	2	2	no	—
178	C₂²×C₄₁	—	2	2	no	—
179	C₂²×C₄₁	—	2	2	no	—
180	C₂²×C₄₁	—	2	2	no	—
181	C₂²×C₄₁	—	4	16	no	—
182	C₂²×C₄₁	—	4	2	no	—
183	C₂²×C₄₁	—	4	2	no	—
184	C₂²×C₄₁	—	4	2	no	—
185	C₂²×C₄₁	—	4	2	no	—
186	C₂²×C₄₁	#428	1	4	yes	—
187	C₂²×C₄₁	C₂²×C₄⋊C₄	1	1	yes	characteristic
188	C₂²×C₄₁	#534	1	2	yes	—
189	C₂²×C₄₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
190	C₂²×C₄₁	C₂×#137	1	1	yes	characteristic
191	C₂²×C₄₁	#575	1	2	yes	—
192	C₄×C₄₁	—	2	2	no	—
193	C₄×C₄₁	—	2	2	no	—
194	C₄×C₄₁	—	2	2	no	—
195	C₄×C₄₁	—	8	2	no	—
196	C₄×C₄₁	—	8	4	no	—
197	C₄×C₄₁	—	8	2	no	—
198	C₄×C₄₁	#518	1	2	yes	—
199	C₄×C₄₁	#543	1	2	yes	—
200	C₂×#407	C₂×C₄₁	1	1	yes	characteristic
201	#2280	C₂×C₄₁	1	1	yes	characteristic
202	C₂×#380	C₂×C₄₁	1	1	yes	characteristic
203	#1854	C₂×C₄₁	1	4	yes	complemented
204	#1853	C₂×C₄₁	1	2	yes	complemented
205	#1852	C₂×C₄₁	1	2	yes	complemented
206	#1809	C₂×C₄₁	1	4	yes	complemented
207	C₂×C₄₁	—	2	4	no	—
208	C₂×C₄₁	—	4	2	no	—
209	C₂×C₄₁	—	4	2	no	—
210	C₂×C₄₁	#2315	1	1	yes	characteristic
211	C₂×C₄₁	C₂×#428	1	1	yes	characteristic
212	C₂×C₄₁	#2911	1	1	yes	characteristic
213	C₂×C₄₁	#3194	1	2	yes	—
214	C₂×C₄₁	#3196	1	2	yes	—
215	C₂⁴×C₄	C₂²×C₄₁	1	1	yes	characteristic
216	C₂²×M₁₆	C₂²×C₄₁	1	2	yes	—
217	C₂×#117	C₂²×C₄₁	1	2	yes	—
218	C₂²×C₄⋊C₄	C₂²×C₄₁	1	2	yes	—
219	C₂²×C₂²⋊C₄	—	2	1	no	—
220	C₂×#107	C₂²×C₄₁	1	4	yes	complemented
221	C₂×#106	C₂²×C₄₁	1	4	yes	complemented
222	#407	C₄×C₄₁	1	8	yes	complemented
223	C₂×C₂²⋊C₈	C₂²×C₄₁	1	2	yes	—
224	C₂×C₂²⋊C₈	C₂²×C₄₁	1	2	yes	—
225	#381	—	2	1	no	—
226	#380	—	2	1	no	—
227	#380	—	2	1	no	—
228	#380	C₂²×C₄₁	1	2	yes	—
229	#380	C₂²×C₄₁	1	2	yes	—
230	#380	C₂²×C₄₁	1	1	yes	characteristic
231	#380	C₂²×C₄₁	1	1	yes	characteristic
232	#380	C₂²×C₄₁	1	2	yes	—
233	#379	—	2	1	no	—
234	C₄×C₂²⋊C₄	—	2	1	no	—
235	C₄×C₂²⋊C₄	—	2	1	no	—
236	C₂×#95	—	2	1	no	—
237	#340	C₂²×C₄₁	1	4	yes	complemented
238	#340	C₂²×C₄₁	1	4	yes	complemented
239	C₄₁	#21944	1	1	yes	characteristic, direct product factor, Sylow
240	C₂⁵	D₄×C₄₁	1	1	yes	characteristic
241	C₂³×C₄	—	2	2	no	—
242	C₂³×C₄	—	4	4	no	—
243	C₂³×C₄	C₂×C₄×C₄₁	1	4	yes	—
244	C₂³×C₄	D₄×C₄₁	1	1	yes	characteristic
245	C₂³×C₄	D₄×C₄₁	1	1	yes	characteristic
246	C₂³×C₄	D₄×C₄₁	1	1	yes	characteristic
247	C₂³×C₄	Q₈×C₄₁	1	4	yes	—
248	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
249	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
250	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
251	C₂×M₁₆	—	4	4	no	—
252	C₂×M₁₆	C₂×C₄×C₄₁	1	8	yes	complemented
253	C₂²×C₈	C₂³×C₄₁	1	4	yes	—
254	#117	—	4	4	no	—
255	C₂×C₄⋊C₄	—	2	2	no	—
256	C₂×C₄⋊C₄	—	4	4	no	—
257	C₂×C₄⋊C₄	C₂³×C₄₁	1	4	yes	—
258	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
259	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
260	C₂×C₂²⋊C₄	—	2	2	no	—
261	C₂×C₂²⋊C₄	—	2	2	no	—
262	C₂×C₂²⋊C₄	—	2	2	no	—
263	C₂×C₂²⋊C₄	—	2	2	no	—
264	C₂×C₂²⋊C₄	—	2	1	no	—
265	C₂×C₂²⋊C₄	—	2	1	no	—
266	C₂×C₂²⋊C₄	—	4	4	no	—
267	C₂×C₄²	—	2	2	no	—
268	#107	—	4	4	no	—
269	#106	—	4	4	no	—
270	C₂²⋊C₈	C₂×C₄×C₄₁	1	8	yes	—
271	C₂²⋊C₈	C₂×C₄×C₄₁	1	8	yes	complemented
272	#95	—	2	2	no	—
273	#95	—	2	2	no	—
274	#95	—	2	2	no	—
275	#95	—	2	1	no	—
276	#95	—	2	1	no	—
277	C₂⁴	—	2	2	no	—
278	C₂⁴	—	2	2	no	—
279	C₂⁴	—	4	2	no	—
280	C₂⁴	—	4	2	no	—
281	C₂⁴	C₄⋊C₄×C₄₁	1	4	yes	—
282	C₂⁴	C₂×D₄×C₄₁	1	1	yes	characteristic
283	C₂⁴	C₂×D₄×C₄₁	1	1	yes	characteristic
284	C₂⁴	C₂×D₄×C₄₁	1	1	yes	characteristic
285	C₂²×C₄	—	2	4	no	—
286	C₂²×C₄	—	2	4	no	—
287	C₂²×C₄	—	2	4	no	—
288	C₂²×C₄	—	2	2	no	—
289	C₂²×C₄	—	2	2	no	—
290	C₂²×C₄	—	2	4	no	—
291	C₂²×C₄	—	4	8	no	—
292	C₂²×C₄	—	4	8	no	—
293	C₂²×C₄	—	4	2	no	—
294	C₂²×C₄	—	4	2	no	—
295	C₂²×C₄	—	4	2	no	—
296	C₂²×C₄	—	4	4	no	—
297	C₂²×C₄	—	4	4	no	—
298	C₂²×C₄	—	4	4	no	—
299	C₂²×C₄	C₄⋊C₄×C₄₁	1	4	yes	—
300	C₂²×C₄	C₄⋊C₄×C₄₁	1	4	yes	—
301	C₂²×C₄	C₄⋊C₄×C₄₁	1	4	yes	—
302	C₂²×C₄	C₂²×C₄×C₄₁	1	2	yes	—
303	C₂²×C₄	C₂²×C₄×C₄₁	1	2	yes	—
304	C₂²×C₄	C₂²×C₄×C₄₁	1	2	yes	—
305	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
306	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
307	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
308	C₂²×C₄	C₂×Q₈×C₄₁	1	2	yes	—
309	C₂²×C₄	C₂×Q₈×C₄₁	1	2	yes	—
310	C₂²×C₄	C₂×Q₈×C₄₁	1	2	yes	—
311	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
312	M₁₆	—	4	8	no	—
313	C₂×C₈	—	2	4	no	—
314	C₂×C₈	—	2	4	no	—
315	C₂×C₈	C₂²×C₄×C₄₁	1	8	yes	—
316	C₄⋊C₄	—	2	4	no	—
317	C₄⋊C₄	—	2	4	no	—
318	C₄⋊C₄	—	2	4	no	—
319	C₄⋊C₄	—	2	4	no	—
320	C₄⋊C₄	—	4	4	no	—
321	C₂²⋊C₄	—	4	4	no	—
322	C₂²⋊C₄	—	4	4	no	—
323	C₂²⋊C₄	—	4	4	no	—
324	C₂²⋊C₄	—	4	4	no	—
325	C₂²⋊C₄	—	4	2	no	—
326	C₂²⋊C₄	—	4	2	no	—
327	C₄²	—	4	4	no	—
328	C₂³	—	2	2	no	—
329	C₂³	—	2	2	no	—
330	C₂³	—	2	2	no	—
331	C₂³	—	2	2	no	—
332	C₂³	—	2	1	no	—
333	C₂³	—	2	1	no	—
334	C₂³	—	2	1	no	—
335	C₂³	—	2	1	no	—
336	C₂³	—	2	2	no	—
337	C₂³	—	2	2	no	—
338	C₂³	—	2	8	no	—
339	C₂³	—	4	4	no	—
340	C₂³	—	4	4	no	—
341	C₂³	—	4	8	no	—
342	C₂³	—	4	8	no	—
343	C₂³	C₂×C₄⋊C₄×C₄₁	1	2	yes	—
344	C₂³	C₂×C₄⋊C₄×C₄₁	1	2	yes	—
345	C₂³	C₂×C₄⋊C₄×C₄₁	1	2	yes	—
346	C₂³	AGL(1,ℤ/8)×C₄₁	1	2	yes	—
347	C₂³	#137×C₄₁	1	2	yes	—
348	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
349	C₂×C₄	—	2	2	no	—
350	C₂×C₄	—	2	2	no	—
351	C₂×C₄	—	2	2	no	—
352	C₂×C₄	—	2	4	no	—
353	C₂×C₄	—	2	4	no	—
354	C₂×C₄	—	2	4	no	—
355	C₂×C₄	—	2	4	no	—
356	C₂×C₄	—	2	4	no	—
357	C₂×C₄	—	2	4	no	—
358	C₂×C₄	—	4	4	no	—
359	C₂×C₄	—	4	4	no	—
360	C₂×C₄	—	4	4	no	—
361	C₂×C₄	—	4	2	no	—
362	C₂×C₄	—	4	2	no	—
363	C₂×C₄	—	4	4	no	—
364	C₂×C₄	—	4	4	no	—
365	C₂×C₄	—	4	2	no	—
366	C₂×C₄	—	4	2	no	—
367	C₂×C₄	—	4	2	no	—
368	C₂×C₄	—	4	2	no	—
369	C₂×C₄	—	4	4	no	—
370	C₂×C₄	—	8	8	no	—
371	C₂×C₄	C₂×C₄⋊C₄×C₄₁	1	2	yes	—
372	C₂×C₄	C₂×C₄⋊C₄×C₄₁	1	2	yes	—
373	C₂×C₄	C₂×C₄⋊C₄×C₄₁	1	2	yes	—
374	C₂×C₄	C₂³×C₄×C₄₁	1	1	yes	characteristic
375	C₂×C₄	C₂²×Q₈×C₄₁	1	1	yes	characteristic
376	C₂×C₄	H(5,𝔽₂)×C₄₁	1	4	yes	—
377	C₈	—	2	8	no	—
378	C₂²	—	2	2	no	—
379	C₂²	—	2	2	no	—
380	C₂²	—	2	4	no	—
381	C₂²	—	2	4	no	—
382	C₂²	—	2	2	no	—
383	C₂²	—	2	2	no	—
384	C₂²	—	2	2	no	—
385	C₂²	—	2	2	no	—
386	C₂²	—	2	2	no	—
387	C₂²	—	2	2	no	—
388	C₂²	—	4	16	no	—
389	C₂²	—	4	2	no	—
390	C₂²	—	4	2	no	—
391	C₂²	—	4	2	no	—
392	C₂²	—	4	2	no	—
393	C₂²	C₄₁×#428	1	4	yes	—
394	C₂²	C₂²×C₄⋊C₄×C₄₁	1	1	yes	characteristic
395	C₂²	C₄₁×#534	1	2	yes	—
396	C₂²	C₂×AGL(1,ℤ/8)×C₄₁	1	1	yes	characteristic
397	C₂²	C₂×#137×C₄₁	1	1	yes	characteristic
398	C₂²	C₄₁×#575	1	2	yes	—
399	C₄	—	2	2	no	—
400	C₄	—	2	2	no	—
401	C₄	—	2	2	no	—
402	C₄	—	8	4	no	—
403	C₄	—	8	2	no	—
404	C₄	—	8	2	no	—
405	C₄	C₄₁×#518	1	2	yes	—
406	C₄	C₄₁×#543	1	2	yes	—
407	C₂	—	2	4	no	—
408	C₂	—	4	2	no	—
409	C₂	—	4	2	no	—
410	C₂	C₄₁×#2315	1	1	yes	characteristic
411	C₂	C₂×C₄₁×#428	1	1	yes	characteristic
412	C₂	C₄₁×#2911	1	1	yes	characteristic
413	C₂	C₄₁×#3194	1	2	yes	—
414	C₂	C₄₁×#3196	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₄₁	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₄₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₁
prime radical	C₂⁵×C₄₁	D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₄₁ ◁ C₂⁴×C₄×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₄₁×#1854	C₂	semidirect
5. C₄₁×#1853	C₂	semidirect
6. C₄₁×#1852	C₂	semidirect
7. C₄₁×#1809	C₂	semidirect
13. C₂×#107×C₄₁	C₂²	semidirect
14. C₂×#106×C₄₁	C₂²	semidirect
15. C₄₁×#407	C₄	semidirect
30. C₄₁×#340	C₂²	semidirect
31. C₄₁×#340	C₂²	semidirect
44. C₂×M₁₆×C₄₁	C₂×C₄	semidirect
63. C₂²⋊C₈×C₄₁	C₂×C₄	semidirect
170. #21944	C₄₁	direct (N × H)
203. #1854	C₂×C₄₁	semidirect
204. #1853	C₂×C₄₁	semidirect
205. #1852	C₂×C₄₁	semidirect
206. #1809	C₂×C₄₁	semidirect
220. C₂×#107	C₂²×C₄₁	semidirect
221. C₂×#106	C₂²×C₄₁	semidirect
222. #407	C₄×C₄₁	semidirect
237. #340	C₂²×C₄₁	semidirect
238. #340	C₂²×C₄₁	semidirect
239. C₄₁	#21944	direct (N × H)
252. C₂×M₁₆	C₂×C₄×C₄₁	semidirect
271. C₂²⋊C₈	C₂×C₄×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×#407	2
C₄₁×#2280	2
C₂×C₄₁×#380	2
C₄₁×#1854	2
C₄₁×#1853	2
C₄₁×#1852	2
C₄₁×#1809	2
#21944	41

Subgroups — C41×#21944 #23798145

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#21944 #23798145