Subgroups — C₄₁×#21806 #23798007

Order 10496.

1450 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#124×C₄₁	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄₁×#431	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₁×#2283	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₁×#1983	C₂	1	4	yes	maximal, complemented
5	C₄₁×#1958	C₂	1	4	yes	maximal, complemented
6	C₄₁×#1787	C₂	1	2	yes	maximal, complemented
7	C₄₁×#1786	C₂	1	2	yes	maximal
8	C₂³×Q₈×C₄₁	C₂²	1	1	yes	characteristic
9	C₂³×D₄×C₄₁	C₂²	1	1	yes	characteristic
10	C₂×#124×C₄₁	—	2	1	no	—
11	C₂×#124×C₄₁	—	2	1	no	—
12	C₂×#124×C₄₁	—	2	4	no	—
13	C₂×#124×C₄₁	C₄	1	8	yes	complemented
14	C₂×#124×C₄₁	C₂²	1	2	yes	—
15	C₂×#124×C₄₁	C₂²	1	2	yes	—
16	C₂²×C₂²⋊C₄×C₄₁	—	2	1	no	—
17	C₂²×C₂²⋊C₄×C₄₁	—	2	1	no	—
18	C₂²×C₄²×C₄₁	C₂²	1	1	yes	characteristic
19	C₄₁×#431	—	2	4	no	—
20	C₂×C₄⋊C₈×C₄₁	C₂²	1	2	yes	complemented
21	C₂×#103×C₄₁	C₂²	1	8	yes	complemented
22	C₂×#102×C₄₁	C₂²	1	8	yes	—
23	C₂×C₂²⋊C₈×C₄₁	C₂²	1	2	yes	—
24	C₂×C₄×C₈×C₄₁	C₂²	1	2	yes	complemented
25	C₄₁×#383	—	2	1	no	—
26	C₄₁×#382	C₂²	1	2	yes	complemented
27	C₄₁×#381	—	2	1	no	—
28	C₄₁×#380	C₂²	1	2	yes	—
29	C₄×C₄⋊C₄×C₄₁	C₂²	1	2	yes	complemented
30	C₄×C₂²⋊C₄×C₄₁	—	2	1	no	—
31	C₄₁×#376	—	2	1	no	—
32	C₂⁵×C₄₁	—	2	1	no	—
33	C₂²×Q₈×C₄₁	—	2	2	no	—
34	C₂²×Q₈×C₄₁	—	2	1	no	—
35	C₂²×Q₈×C₄₁	—	4	4	no	—
36	C₂²×Q₈×C₄₁	C₂×C₄	1	4	yes	—
37	C₂²×Q₈×C₄₁	C₂³	1	2	yes	—
38	C₂²×D₄×C₄₁	—	2	1	no	—
39	C₂²×D₄×C₄₁	—	2	2	no	—
40	C₂²×D₄×C₄₁	—	4	4	no	—
41	C₂²×D₄×C₄₁	C₂×C₄	1	4	yes	—
42	C₂²×D₄×C₄₁	C₂³	1	2	yes	—
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	C₂²×C₈×C₄₁	C₂³	1	4	yes	—
48	#124×C₄₁	—	2	8	no	—
49	#124×C₄₁	—	2	8	no	—
50	#124×C₄₁	—	2	4	no	—
51	#124×C₄₁	—	2	4	no	—
52	#124×C₄₁	C₂×C₄	1	8	yes	—
53	#124×C₄₁	C₂×C₄	1	8	yes	—
54	C₂×C₄⋊C₄×C₄₁	C₂³	1	4	yes	—
55	C₂×C₂²⋊C₄×C₄₁	—	2	8	no	—
56	C₂×C₂²⋊C₄×C₄₁	—	2	8	no	—
57	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
58	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
59	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
60	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
61	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
62	C₂×C₄²×C₄₁	—	2	2	no	—
63	C₂×C₄²×C₄₁	C₂×C₄	1	4	yes	—
64	C₂×C₄²×C₄₁	D₄	1	1	yes	characteristic
65	C₂×C₄²×C₄₁	D₄	1	1	yes	characteristic
66	C₂×C₄²×C₄₁	D₄	1	4	yes	—
67	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
68	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
69	C₄⋊C₈×C₄₁	—	2	4	no	—
70	#103×C₄₁	—	4	8	no	—
71	#102×C₄₁	—	4	8	no	—
72	C₂²⋊C₈×C₄₁	—	2	4	no	—
73	C₄×C₈×C₄₁	—	2	4	no	—
74	#95×C₄₁	—	2	2	no	—
75	#95×C₄₁	—	2	2	no	—
76	#95×C₄₁	—	2	2	no	—
77	#95×C₄₁	—	2	2	no	—
78	C₂⁴×C₄₁	—	2	4	no	—
79	C₂⁴×C₄₁	—	2	2	no	—
80	C₂⁴×C₄₁	—	4	4	no	—
81	C₂⁴×C₄₁	—	4	4	no	—
82	C₂⁴×C₄₁	—	4	4	no	—
83	C₂⁴×C₄₁	C₂×D₄	1	1	yes	characteristic
84	C₂×Q₈×C₄₁	—	2	4	no	—
85	C₂×Q₈×C₄₁	—	2	2	no	—
86	C₂×Q₈×C₄₁	—	2	8	no	—
87	C₂×Q₈×C₄₁	—	4	8	no	—
88	C₂×Q₈×C₄₁	—	4	4	no	—
89	C₂×Q₈×C₄₁	—	4	8	no	—
90	C₂×Q₈×C₄₁	C₂²×C₄	1	4	yes	—
91	C₂×D₄×C₄₁	—	2	4	no	—
92	C₂×D₄×C₄₁	—	2	2	no	—
93	C₂×D₄×C₄₁	—	2	8	no	—
94	C₂×D₄×C₄₁	—	4	8	no	—
95	C₂×D₄×C₄₁	—	4	4	no	—
96	C₂×D₄×C₄₁	—	4	8	no	—
97	C₂×D₄×C₄₁	C₂²×C₄	1	4	yes	—
98	C₂²×C₄×C₄₁	—	2	4	no	—
99	C₂²×C₄×C₄₁	—	2	4	no	—
100	C₂²×C₄×C₄₁	—	2	4	no	—
101	C₂²×C₄×C₄₁	—	2	2	no	—
102	C₂²×C₄×C₄₁	—	2	4	no	—
103	C₂²×C₄×C₄₁	—	4	2	no	—
104	C₂²×C₄×C₄₁	—	4	4	no	—
105	C₂²×C₄×C₄₁	C₂²⋊C₄	1	4	yes	—
106	C₂²×C₄×C₄₁	C₂²⋊C₄	1	4	yes	—
107	C₂²×C₄×C₄₁	C₂²×C₄	1	2	yes	—
108	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
109	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
110	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
111	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
112	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
113	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
114	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
115	C₂×C₈×C₄₁	—	2	4	no	—
116	C₂×C₈×C₄₁	—	2	8	no	—
117	C₄⋊C₄×C₄₁	—	2	8	no	—
118	C₂²⋊C₄×C₄₁	—	2	8	no	—
119	C₂²⋊C₄×C₄₁	—	2	8	no	—
120	C₂²⋊C₄×C₄₁	—	2	8	no	—
121	C₂²⋊C₄×C₄₁	—	2	8	no	—
122	C₂²⋊C₄×C₄₁	—	4	4	no	—
123	C₄²×C₄₁	—	4	4	no	—
124	C₄²×C₄₁	C₂²⋊C₄	1	4	yes	—
125	C₄²×C₄₁	C₂²⋊C₄	1	4	yes	—
126	C₄²×C₄₁	C₂²×C₄	1	2	yes	—
127	C₄²×C₄₁	C₂²×C₄	1	2	yes	—
128	C₄²×C₄₁	C₂×D₄	1	2	yes	—
129	C₄²×C₄₁	C₂×D₄	1	2	yes	—
130	C₂³×C₄₁	—	2	2	no	—
131	C₂³×C₄₁	—	2	2	no	—
132	C₂³×C₄₁	—	2	4	no	—
133	C₂³×C₄₁	—	4	8	no	—
134	C₂³×C₄₁	—	4	8	no	—
135	C₂³×C₄₁	—	4	4	no	—
136	C₂³×C₄₁	—	4	4	no	—
137	C₂³×C₄₁	—	4	4	no	—
138	C₂³×C₄₁	—	4	8	no	—
139	C₂³×C₄₁	—	8	16	no	—
140	C₂³×C₄₁	C₂×C₂²⋊C₄	1	2	yes	—
141	C₂³×C₄₁	#135	1	4	yes	—
142	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
143	Q₈×C₄₁	—	2	8	no	—
144	Q₈×C₄₁	—	4	8	no	—
145	Q₈×C₄₁	—	4	4	no	—
146	D₄×C₄₁	—	2	8	no	—
147	D₄×C₄₁	—	4	8	no	—
148	D₄×C₄₁	—	4	4	no	—
149	C₂×C₄×C₄₁	—	2	2	no	—
150	C₂×C₄×C₄₁	—	2	2	no	—
151	C₂×C₄×C₄₁	—	2	2	no	—
152	C₂×C₄×C₄₁	—	2	2	no	—
153	C₂×C₄×C₄₁	—	2	2	no	—
154	C₂×C₄×C₄₁	—	2	8	no	—
155	C₂×C₄×C₄₁	—	2	4	no	—
156	C₂×C₄×C₄₁	—	2	4	no	—
157	C₂×C₄×C₄₁	—	2	4	no	—
158	C₂×C₄×C₄₁	—	4	4	no	—
159	C₂×C₄×C₄₁	—	4	8	no	—
160	C₂×C₄×C₄₁	—	4	4	no	—
161	C₂×C₄×C₄₁	—	4	4	no	—
162	C₂×C₄×C₄₁	—	4	4	no	—
163	C₂×C₄×C₄₁	—	4	4	no	—
164	C₂×C₄×C₄₁	C₂×C₂²⋊C₄	1	2	yes	—
165	C₂×C₄×C₄₁	C₂×C₂²⋊C₄	1	2	yes	—
166	C₂×C₄×C₄₁	C₂×C₂²⋊C₄	1	2	yes	—
167	C₂×C₄×C₄₁	C₂×C₂²⋊C₄	1	2	yes	—
168	C₂×C₄×C₄₁	C₂×C₂²⋊C₄	1	2	yes	—
169	C₂×C₄×C₄₁	C₂³×C₄	1	1	yes	characteristic
170	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
171	C₂×C₄×C₄₁	H(5,𝔽₂)	1	4	yes	—
172	C₈×C₄₁	—	4	4	no	—
173	#21806	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
174	C₂²×C₄₁	—	2	2	no	—
175	C₂²×C₄₁	—	2	2	no	—
176	C₂²×C₄₁	—	2	8	no	—
177	C₂²×C₄₁	—	4	4	no	—
178	C₂²×C₄₁	—	4	4	no	—
179	C₂²×C₄₁	—	4	4	no	—
180	C₂²×C₄₁	—	8	16	no	—
181	C₂²×C₄₁	—	8	8	no	—
182	C₂²×C₄₁	#416	1	4	yes	—
183	C₂²×C₄₁	C₂²×C₂²⋊C₄	1	1	yes	characteristic
184	C₂²×C₄₁	#535	1	2	yes	—
185	C₂²×C₄₁	C₂×#135	1	2	yes	—
186	C₂²×C₄₁	#575	1	2	yes	—
187	C₄×C₄₁	—	2	2	no	—
188	C₄×C₄₁	—	2	2	no	—
189	C₄×C₄₁	—	2	2	no	—
190	C₄×C₄₁	—	2	2	no	—
191	C₄×C₄₁	—	2	2	no	—
192	C₄×C₄₁	—	4	4	no	—
193	C₄×C₄₁	—	8	4	no	—
194	C₄×C₄₁	#518	1	2	yes	—
195	C₄×C₄₁	#535	1	2	yes	—
196	C₂²×#124	C₂×C₄₁	1	1	yes	characteristic
197	C₂×#431	C₂×C₄₁	1	1	yes	characteristic, complemented
198	#2283	C₂×C₄₁	1	1	yes	characteristic, complemented
199	#1983	C₂×C₄₁	1	4	yes	complemented
200	#1958	C₂×C₄₁	1	4	yes	complemented
201	#1787	C₂×C₄₁	1	2	yes	complemented
202	#1786	C₂×C₄₁	1	2	yes	—
203	C₂×C₄₁	—	2	4	no	—
204	C₂×C₄₁	—	8	4	no	—
205	C₂×C₄₁	#2309	1	1	yes	characteristic
206	C₂×C₄₁	C₂×#416	1	1	yes	characteristic
207	C₂×C₄₁	#2896	1	1	yes	characteristic
208	C₂×C₄₁	#3211	1	4	yes	—
209	C₂³×Q₈	C₂²×C₄₁	1	1	yes	characteristic
210	C₂³×D₄	C₂²×C₄₁	1	1	yes	characteristic
211	C₂×#124	—	2	1	no	—
212	C₂×#124	—	2	1	no	—
213	C₂×#124	—	2	4	no	—
214	C₂×#124	C₄×C₄₁	1	8	yes	complemented
215	C₂×#124	C₂²×C₄₁	1	2	yes	—
216	C₂×#124	C₂²×C₄₁	1	2	yes	—
217	C₂²×C₂²⋊C₄	—	2	1	no	—
218	C₂²×C₂²⋊C₄	—	2	1	no	—
219	C₂²×C₄²	C₂²×C₄₁	1	1	yes	characteristic
220	#431	—	2	4	no	—
221	C₂×C₄⋊C₈	C₂²×C₄₁	1	2	yes	complemented
222	C₂×#103	C₂²×C₄₁	1	8	yes	complemented
223	C₂×#102	C₂²×C₄₁	1	8	yes	—
224	C₂×C₂²⋊C₈	C₂²×C₄₁	1	2	yes	—
225	C₂×C₄×C₈	C₂²×C₄₁	1	2	yes	complemented
226	#383	—	2	1	no	—
227	#382	C₂²×C₄₁	1	2	yes	complemented
228	#381	—	2	1	no	—
229	#380	C₂²×C₄₁	1	2	yes	—
230	C₄×C₄⋊C₄	C₂²×C₄₁	1	2	yes	complemented
231	C₄×C₂²⋊C₄	—	2	1	no	—
232	#376	—	2	1	no	—
233	C₄₁	#21806	1	1	yes	characteristic, direct product factor, Sylow
234	C₂⁵	—	2	1	no	—
235	C₂²×Q₈	—	2	2	no	—
236	C₂²×Q₈	—	2	1	no	—
237	C₂²×Q₈	—	4	4	no	—
238	C₂²×Q₈	C₂×C₄×C₄₁	1	4	yes	—
239	C₂²×Q₈	C₂³×C₄₁	1	2	yes	—
240	C₂²×D₄	—	2	1	no	—
241	C₂²×D₄	—	2	2	no	—
242	C₂²×D₄	—	4	4	no	—
243	C₂²×D₄	C₂×C₄×C₄₁	1	4	yes	—
244	C₂²×D₄	C₂³×C₄₁	1	2	yes	—
245	C₂³×C₄	—	2	1	no	—
246	C₂³×C₄	D₄×C₄₁	1	1	yes	characteristic
247	C₂³×C₄	D₄×C₄₁	1	1	yes	characteristic
248	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
249	C₂²×C₈	C₂³×C₄₁	1	4	yes	—
250	#124	—	2	8	no	—
251	#124	—	2	8	no	—
252	#124	—	2	4	no	—
253	#124	—	2	4	no	—
254	#124	C₂×C₄×C₄₁	1	8	yes	—
255	#124	C₂×C₄×C₄₁	1	8	yes	—
256	C₂×C₄⋊C₄	C₂³×C₄₁	1	4	yes	—
257	C₂×C₂²⋊C₄	—	2	8	no	—
258	C₂×C₂²⋊C₄	—	2	8	no	—
259	C₂×C₂²⋊C₄	—	2	2	no	—
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×C₄²	—	2	2	no	—
265	C₂×C₄²	C₂×C₄×C₄₁	1	4	yes	—
266	C₂×C₄²	D₄×C₄₁	1	1	yes	characteristic
267	C₂×C₄²	D₄×C₄₁	1	1	yes	characteristic
268	C₂×C₄²	D₄×C₄₁	1	4	yes	—
269	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
270	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
271	C₄⋊C₈	—	2	4	no	—
272	#103	—	4	8	no	—
273	#102	—	4	8	no	—
274	C₂²⋊C₈	—	2	4	no	—
275	C₄×C₈	—	2	4	no	—
276	#95	—	2	2	no	—
277	#95	—	2	2	no	—
278	#95	—	2	2	no	—
279	#95	—	2	2	no	—
280	C₂⁴	—	2	4	no	—
281	C₂⁴	—	2	2	no	—
282	C₂⁴	—	4	4	no	—
283	C₂⁴	—	4	4	no	—
284	C₂⁴	—	4	4	no	—
285	C₂⁴	C₂×D₄×C₄₁	1	1	yes	characteristic
286	C₂×Q₈	—	2	4	no	—
287	C₂×Q₈	—	2	2	no	—
288	C₂×Q₈	—	2	8	no	—
289	C₂×Q₈	—	4	8	no	—
290	C₂×Q₈	—	4	4	no	—
291	C₂×Q₈	—	4	8	no	—
292	C₂×Q₈	C₂²×C₄×C₄₁	1	4	yes	—
293	C₂×D₄	—	2	4	no	—
294	C₂×D₄	—	2	2	no	—
295	C₂×D₄	—	2	8	no	—
296	C₂×D₄	—	4	8	no	—
297	C₂×D₄	—	4	4	no	—
298	C₂×D₄	—	4	8	no	—
299	C₂×D₄	C₂²×C₄×C₄₁	1	4	yes	—
300	C₂²×C₄	—	2	4	no	—
301	C₂²×C₄	—	2	4	no	—
302	C₂²×C₄	—	2	4	no	—
303	C₂²×C₄	—	2	2	no	—
304	C₂²×C₄	—	2	4	no	—
305	C₂²×C₄	—	4	2	no	—
306	C₂²×C₄	—	4	4	no	—
307	C₂²×C₄	C₂²⋊C₄×C₄₁	1	4	yes	—
308	C₂²×C₄	C₂²⋊C₄×C₄₁	1	4	yes	—
309	C₂²×C₄	C₂²×C₄×C₄₁	1	2	yes	—
310	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
311	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
312	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
313	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
314	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
315	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
316	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
317	C₂×C₈	—	2	4	no	—
318	C₂×C₈	—	2	8	no	—
319	C₄⋊C₄	—	2	8	no	—
320	C₂²⋊C₄	—	2	8	no	—
321	C₂²⋊C₄	—	2	8	no	—
322	C₂²⋊C₄	—	2	8	no	—
323	C₂²⋊C₄	—	2	8	no	—
324	C₂²⋊C₄	—	4	4	no	—
325	C₄²	—	4	4	no	—
326	C₄²	C₂²⋊C₄×C₄₁	1	4	yes	—
327	C₄²	C₂²⋊C₄×C₄₁	1	4	yes	—
328	C₄²	C₂²×C₄×C₄₁	1	2	yes	—
329	C₄²	C₂²×C₄×C₄₁	1	2	yes	—
330	C₄²	C₂×D₄×C₄₁	1	2	yes	—
331	C₄²	C₂×D₄×C₄₁	1	2	yes	—
332	C₂³	—	2	2	no	—
333	C₂³	—	2	2	no	—
334	C₂³	—	2	4	no	—
335	C₂³	—	4	8	no	—
336	C₂³	—	4	8	no	—
337	C₂³	—	4	4	no	—
338	C₂³	—	4	4	no	—
339	C₂³	—	4	4	no	—
340	C₂³	—	4	8	no	—
341	C₂³	—	8	16	no	—
342	C₂³	C₂×C₂²⋊C₄×C₄₁	1	2	yes	—
343	C₂³	#135×C₄₁	1	4	yes	—
344	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
345	Q₈	—	2	8	no	—
346	Q₈	—	4	8	no	—
347	Q₈	—	4	4	no	—
348	D₄	—	2	8	no	—
349	D₄	—	4	8	no	—
350	D₄	—	4	4	no	—
351	C₂×C₄	—	2	2	no	—
352	C₂×C₄	—	2	2	no	—
353	C₂×C₄	—	2	2	no	—
354	C₂×C₄	—	2	2	no	—
355	C₂×C₄	—	2	2	no	—
356	C₂×C₄	—	2	8	no	—
357	C₂×C₄	—	2	4	no	—
358	C₂×C₄	—	2	4	no	—
359	C₂×C₄	—	2	4	no	—
360	C₂×C₄	—	4	4	no	—
361	C₂×C₄	—	4	8	no	—
362	C₂×C₄	—	4	4	no	—
363	C₂×C₄	—	4	4	no	—
364	C₂×C₄	—	4	4	no	—
365	C₂×C₄	—	4	4	no	—
366	C₂×C₄	C₂×C₂²⋊C₄×C₄₁	1	2	yes	—
367	C₂×C₄	C₂×C₂²⋊C₄×C₄₁	1	2	yes	—
368	C₂×C₄	C₂×C₂²⋊C₄×C₄₁	1	2	yes	—
369	C₂×C₄	C₂×C₂²⋊C₄×C₄₁	1	2	yes	—
370	C₂×C₄	C₂×C₂²⋊C₄×C₄₁	1	2	yes	—
371	C₂×C₄	C₂³×C₄×C₄₁	1	1	yes	characteristic
372	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
373	C₂×C₄	H(5,𝔽₂)×C₄₁	1	4	yes	—
374	C₈	—	4	4	no	—
375	C₂²	—	2	2	no	—
376	C₂²	—	2	2	no	—
377	C₂²	—	2	8	no	—
378	C₂²	—	4	4	no	—
379	C₂²	—	4	4	no	—
380	C₂²	—	4	4	no	—
381	C₂²	—	8	16	no	—
382	C₂²	—	8	8	no	—
383	C₂²	C₄₁×#416	1	4	yes	—
384	C₂²	C₂²×C₂²⋊C₄×C₄₁	1	1	yes	characteristic
385	C₂²	C₄₁×#535	1	2	yes	—
386	C₂²	C₂×#135×C₄₁	1	2	yes	—
387	C₂²	C₄₁×#575	1	2	yes	—
388	C₄	—	2	2	no	—
389	C₄	—	2	2	no	—
390	C₄	—	2	2	no	—
391	C₄	—	2	2	no	—
392	C₄	—	2	2	no	—
393	C₄	—	4	4	no	—
394	C₄	—	8	4	no	—
395	C₄	C₄₁×#518	1	2	yes	—
396	C₄	C₄₁×#535	1	2	yes	—
397	C₂	—	2	4	no	—
398	C₂	—	8	4	no	—
399	C₂	C₄₁×#2309	1	1	yes	characteristic
400	C₂	C₂×C₄₁×#416	1	1	yes	characteristic
401	C₂	C₄₁×#2896	1	1	yes	characteristic
402	C₂	C₄₁×#3211	1	4	yes	—

	subgroup	G/H
center, socle	C₂³×C₄₁	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₄₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₁
prime radical	C₂³×D₄×C₄₁	C₂²
LCS	G ▷ C₂×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
2. C₂×C₄₁×#431	C₂	semidirect
3. C₄₁×#2283	C₂	semidirect
4. C₄₁×#1983	C₂	semidirect
5. C₄₁×#1958	C₂	semidirect
6. C₄₁×#1787	C₂	semidirect
13. C₂×#124×C₄₁	C₄	semidirect
20. C₂×C₄⋊C₈×C₄₁	C₂²	semidirect
21. C₂×#103×C₄₁	C₂²	semidirect
24. C₂×C₄×C₈×C₄₁	C₂²	semidirect
26. C₄₁×#382	C₂²	semidirect
29. C₄×C₄⋊C₄×C₄₁	C₂²	semidirect
173. #21806	C₄₁	direct (N × H)
197. C₂×#431	C₂×C₄₁	semidirect
198. #2283	C₂×C₄₁	semidirect
199. #1983	C₂×C₄₁	semidirect
200. #1958	C₂×C₄₁	semidirect
201. #1787	C₂×C₄₁	semidirect
214. C₂×#124	C₄×C₄₁	semidirect
221. C₂×C₄⋊C₈	C₂²×C₄₁	semidirect
222. C₂×#103	C₂²×C₄₁	semidirect
225. C₂×C₄×C₈	C₂²×C₄₁	semidirect
227. #382	C₂²×C₄₁	semidirect
230. C₄×C₄⋊C₄	C₂²×C₄₁	semidirect
233. C₄₁	#21806	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂²×#124×C₄₁	2
C₂×C₄₁×#431	2
C₄₁×#2283	2
C₄₁×#1983	2
C₄₁×#1958	2
C₄₁×#1787	2
C₄₁×#1786	2
#21806	41

Subgroups — C41×#21806 #23798007

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#21806 #23798007