Subgroups — C₄₁×#10884 #23787085

Order 10496.

986 conjugacy classes of subgroups.

The subgroup lattice has 446 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₁×#389	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×C₄⋊C₄×C₄₁	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄₁×#340	C₂	1	2	yes	maximal
4	C₂×C₄₁×#340	C₂	1	2	yes	maximal
5	C₂×C₄₁×#336	C₂	1	1	yes	maximal, characteristic
6	C₂³×C₈×C₄₁	C₂²	1	2	yes	—
7	C₂²×C₄⋊C₄×C₄₁	—	2	1	no	—
8	C₂²×C₄⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
9	C₂²×C₄⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
10	C₂²×C₄⋊C₄×C₄₁	C₂²	1	2	yes	—
11	C₂²×C₄²×C₄₁	—	2	1	no	—
12	C₂²×C₄²×C₄₁	C₂²	1	1	yes	characteristic
13	C₄₁×#389	—	2	2	no	—
14	C₄₁×#389	C₄	1	4	yes	complemented
15	C₄×C₄⋊C₄×C₄₁	—	2	4	no	—
16	C₂×#95×C₄₁	—	2	1	no	—
17	C₂×#95×C₄₁	—	2	1	no	—
18	C₄₁×#340	—	2	4	no	—
19	C₄₁×#340	C₄	1	8	yes	complemented
20	C₄₁×#336	—	2	2	no	—
21	C₂³×C₄×C₄₁	—	2	2	no	—
22	C₂³×C₄×C₄₁	—	2	1	no	—
23	C₂³×C₄×C₄₁	—	2	1	no	—
24	C₂³×C₄×C₄₁	D₄	1	1	yes	characteristic
25	C₂³×C₄×C₄₁	D₄	1	1	yes	characteristic
26	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
27	C₂²×C₈×C₄₁	—	2	2	no	—
28	C₂²×C₈×C₄₁	—	2	2	no	—
29	C₂²×C₈×C₄₁	—	2	2	no	—
30	C₂²×C₈×C₄₁	—	2	2	no	—
31	C₂²×C₈×C₄₁	—	2	2	no	—
32	C₂²×C₈×C₄₁	—	2	2	no	—
33	C₂²×C₈×C₄₁	C₂×C₄	1	4	yes	—
34	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
35	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
36	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
37	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
38	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
39	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
40	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
41	C₂×C₄⋊C₄×C₄₁	—	2	4	no	—
42	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
43	C₂×C₄⋊C₄×C₄₁	—	4	2	no	—
44	C₂×C₄⋊C₄×C₄₁	—	4	2	no	—
45	C₂×C₄⋊C₄×C₄₁	C₂×C₄	1	2	yes	—
46	C₂×C₄⋊C₄×C₄₁	C₂×C₄	1	4	yes	—
47	C₂×C₄⋊C₄×C₄₁	C₂×C₄	1	2	yes	—
48	C₂×C₄⋊C₄×C₄₁	C₂×C₄	1	4	yes	—
49	C₂×C₄⋊C₄×C₄₁	D₄	1	4	yes	—
50	C₂×C₄⋊C₄×C₄₁	Q₈	1	4	yes	—
51	C₂×C₄²×C₄₁	—	2	2	no	—
52	C₂×C₄²×C₄₁	—	2	2	no	—
53	C₂×C₄²×C₄₁	—	2	4	no	—
54	C₂×C₄²×C₄₁	—	4	2	no	—
55	C₂×C₄²×C₄₁	—	4	2	no	—
56	C₂×C₄²×C₄₁	C₂×C₄	1	2	yes	—
57	C₂×C₄²×C₄₁	D₄	1	2	yes	—
58	#95×C₄₁	—	2	4	no	—
59	#95×C₄₁	—	2	4	no	—
60	C₂⁴×C₄₁	C₂×D₄	1	1	yes	characteristic
61	C₂²×C₄×C₄₁	—	2	1	no	—
62	C₂²×C₄×C₄₁	—	2	1	no	—
63	C₂²×C₄×C₄₁	—	2	1	no	—
64	C₂²×C₄×C₄₁	—	2	1	no	—
65	C₂²×C₄×C₄₁	—	2	2	no	—
66	C₂²×C₄×C₄₁	—	2	4	no	—
67	C₂²×C₄×C₄₁	—	2	4	no	—
68	C₂²×C₄×C₄₁	—	2	1	no	—
69	C₂²×C₄×C₄₁	—	2	4	no	—
70	C₂²×C₄×C₄₁	—	2	4	no	—
71	C₂²×C₄×C₄₁	—	2	1	no	—
72	C₂²×C₄×C₄₁	—	2	2	no	—
73	C₂²×C₄×C₄₁	—	2	2	no	—
74	C₂²×C₄×C₄₁	—	2	2	no	—
75	C₂²×C₄×C₄₁	—	4	2	no	—
76	C₂²×C₄×C₄₁	—	4	1	no	—
77	C₂²×C₄×C₄₁	—	4	1	no	—
78	C₂²×C₄×C₄₁	—	4	2	no	—
79	C₂²×C₄×C₄₁	—	4	2	no	—
80	C₂²×C₄×C₄₁	—	4	2	no	—
81	C₂²×C₄×C₄₁	—	4	2	no	—
82	C₂²×C₄×C₄₁	—	4	1	no	—
83	C₂²×C₄×C₄₁	—	4	1	no	—
84	C₂²×C₄×C₄₁	—	4	1	no	—
85	C₂²×C₄×C₄₁	—	4	1	no	—
86	C₂²×C₄×C₄₁	—	4	1	no	—
87	C₂²×C₄×C₄₁	—	4	1	no	—
88	C₂²×C₄×C₄₁	C₂²⋊C₄	1	2	yes	—
89	C₂²×C₄×C₄₁	C₂²⋊C₄	1	2	yes	—
90	C₂²×C₄×C₄₁	D₈	1	2	yes	—
91	C₂²×C₄×C₄₁	SD₁₆	1	2	yes	—
92	C₂²×C₄×C₄₁	C₂²×C₄	1	2	yes	—
93	C₂²×C₄×C₄₁	C₂²×C₄	1	1	yes	characteristic
94	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
95	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
96	C₂²×C₄×C₄₁	C₂×Q₈	1	2	yes	—
97	C₂²×C₄×C₄₁	#41	1	2	yes	—
98	C₂²×C₄×C₄₁	#41	1	2	yes	—
99	C₂²×C₄×C₄₁	#41	1	2	yes	—
100	C₂×C₈×C₄₁	—	2	4	no	—
101	C₂×C₈×C₄₁	—	2	4	no	—
102	C₂×C₈×C₄₁	—	2	4	no	—
103	C₂×C₈×C₄₁	—	4	2	no	—
104	C₂×C₈×C₄₁	—	4	2	no	—
105	C₂×C₈×C₄₁	—	4	2	no	—
106	C₂×C₈×C₄₁	—	4	2	no	—
107	C₄⋊C₄×C₄₁	—	2	2	no	—
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	—	2	4	no	—
113	C₄⋊C₄×C₄₁	—	4	8	no	—
114	C₄⋊C₄×C₄₁	—	4	2	no	—
115	C₄⋊C₄×C₄₁	C₄²	1	4	yes	complemented
116	C₄⋊C₄×C₄₁	C₄⋊C₄	1	8	yes	complemented
117	C₄²×C₄₁	—	2	4	no	—
118	C₄²×C₄₁	—	2	4	no	—
119	C₄²×C₄₁	—	4	8	no	—
120	C₂³×C₄₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
121	C₂³×C₄₁	C₄×D₄	1	2	yes	—
122	C₂³×C₄₁	#120	1	1	yes	characteristic
123	C₂³×C₄₁	C₂²⋊Q₈	1	2	yes	—
124	C₂³×C₄₁	#123	1	1	yes	characteristic
125	C₂³×C₄₁	C₂×D₈	1	1	yes	characteristic
126	C₂³×C₄₁	C₂×SD₁₆	1	1	yes	characteristic
127	C₂³×C₄₁	#135	1	2	yes	—
128	C₂³×C₄₁	AGL(1,ℤ/8)	1	1	yes	characteristic
129	C₂³×C₄₁	#137	1	1	yes	characteristic
130	C₂³×C₄₁	#137	1	2	yes	—
131	C₂×C₄×C₄₁	—	2	2	no	—
132	C₂×C₄×C₄₁	—	2	2	no	—
133	C₂×C₄×C₄₁	—	2	2	no	—
134	C₂×C₄×C₄₁	—	2	2	no	—
135	C₂×C₄×C₄₁	—	2	2	no	—
136	C₂×C₄×C₄₁	—	2	2	no	—
137	C₂×C₄×C₄₁	—	2	4	no	—
138	C₂×C₄×C₄₁	—	2	8	no	—
139	C₂×C₄×C₄₁	—	2	2	no	—
140	C₂×C₄×C₄₁	—	2	2	no	—
141	C₂×C₄×C₄₁	—	2	2	no	—
142	C₂×C₄×C₄₁	—	4	2	no	—
143	C₂×C₄×C₄₁	—	4	2	no	—
144	C₂×C₄×C₄₁	—	4	4	no	—
145	C₂×C₄×C₄₁	—	4	4	no	—
146	C₂×C₄×C₄₁	—	4	4	no	—
147	C₂×C₄×C₄₁	—	4	4	no	—
148	C₂×C₄×C₄₁	—	4	4	no	—
149	C₂×C₄×C₄₁	—	4	2	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	2	no	—
156	C₂×C₄×C₄₁	—	4	2	no	—
157	C₂×C₄×C₄₁	—	8	1	no	—
158	C₂×C₄×C₄₁	—	8	1	no	—
159	C₂×C₄×C₄₁	—	8	1	no	—
160	C₂×C₄×C₄₁	—	8	1	no	—
161	C₂×C₄×C₄₁	#102	1	4	yes	—
162	C₂×C₄×C₄₁	C₂×C₄²	1	1	yes	characteristic
163	C₂×C₄×C₄₁	C₂×C₄⋊C₄	1	2	yes	—
164	C₂×C₄×C₄₁	#117	1	2	yes	—
165	C₂×C₄×C₄₁	#117	1	1	yes	characteristic
166	C₂×C₄×C₄₁	C₄×D₄	1	2	yes	—
167	C₂×C₄×C₄₁	C₄×D₄	1	2	yes	—
168	C₂×C₄×C₄₁	C₄×D₄	1	2	yes	—
169	C₂×C₄×C₄₁	C₄×Q₈	1	2	yes	—
170	C₂×C₄×C₄₁	C₄×Q₈	1	2	yes	—
171	C₂×C₄×C₄₁	#121	1	2	yes	—
172	C₂×C₄×C₄₁	C₂²⋊Q₈	1	2	yes	—
173	C₂×C₄×C₄₁	#123	1	2	yes	—
174	C₂×C₄×C₄₁	#124	1	1	yes	characteristic
175	C₂×C₄×C₄₁	#125	1	2	yes	—
176	C₂×C₄×C₄₁	#126	1	2	yes	—
177	C₂×C₄×C₄₁	C₄⋊Q₈	1	1	yes	characteristic
178	C₈×C₄₁	—	4	4	no	—
179	#10884	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
180	C₂²×C₄₁	C₄×C₂²⋊C₄	1	1	yes	characteristic
181	C₂²×C₄₁	#385	1	2	yes	—
182	C₂²×C₄₁	#386	1	1	yes	characteristic
183	C₂²×C₄₁	#387	1	2	yes	—
184	C₂²×C₄₁	#391	1	1	yes	characteristic
185	C₂²×C₄₁	C₂×#102	1	1	yes	characteristic
186	C₂²×C₄₁	#416	1	1	yes	characteristic
187	C₂²×C₄₁	#417	1	1	yes	characteristic
188	C₂²×C₄₁	#419	1	1	yes	characteristic
189	C₂²×C₄₁	C₄×D₈	1	2	yes	—
190	C₂²×C₄₁	C₄×SD₁₆	1	2	yes	—
191	C₂²×C₄₁	#440	1	2	yes	—
192	C₂²×C₄₁	#441	1	2	yes	—
193	C₂²×C₄₁	#447	1	1	yes	characteristic
194	C₂²×C₄₁	#448	1	1	yes	characteristic
195	C₂²×C₄₁	#452	1	2	yes	—
196	C₂²×C₄₁	#474	1	2	yes	—
197	C₂²×C₄₁	#475	1	2	yes	—
198	C₂²×C₄₁	#478	1	2	yes	—
199	C₂²×C₄₁	#479	1	2	yes	—
200	C₂²×C₄₁	#480	1	1	yes	characteristic
201	C₂²×C₄₁	#481	1	1	yes	characteristic
202	C₂²×C₄₁	#485	1	2	yes	—
203	C₄×C₄₁	—	2	4	no	—
204	C₄×C₄₁	—	4	8	no	—
205	C₄×C₄₁	—	4	2	no	—
206	C₄×C₄₁	—	4	4	no	—
207	C₄×C₄₁	—	8	2	no	—
208	C₄×C₄₁	C₄×C₄⋊C₄	1	2	yes	—
209	C₄×C₄₁	#387	1	2	yes	—
210	C₄×C₄₁	#388	1	2	yes	—
211	C₄×C₄₁	#389	1	2	yes	—
212	C₂×#389	C₂×C₄₁	1	1	yes	characteristic
213	C₂×C₄×C₄⋊C₄	C₂×C₄₁	1	1	yes	characteristic
214	C₂×#340	C₂×C₄₁	1	2	yes	—
215	C₂×#340	C₂×C₄₁	1	2	yes	—
216	C₂×#336	C₂×C₄₁	1	1	yes	characteristic
217	C₂×C₄₁	#1436	1	1	yes	characteristic
218	C₂×C₄₁	C₄×#102	1	1	yes	characteristic
219	C₂×C₄₁	#1763	1	1	yes	characteristic
220	C₂×C₄₁	#1862	1	2	yes	—
221	C₂×C₄₁	#1865	1	2	yes	—
222	C₂×C₄₁	#1873	1	1	yes	characteristic
223	C₂×C₄₁	#1874	1	1	yes	characteristic
224	C₂×C₄₁	#1918	1	2	yes	—
225	C₂×C₄₁	#1919	1	2	yes	—
226	C₂×C₄₁	#1988	1	1	yes	characteristic
227	C₂×C₄₁	#1989	1	1	yes	characteristic
228	C₂³×C₈	C₂²×C₄₁	1	2	yes	—
229	C₂²×C₄⋊C₄	—	2	1	no	—
230	C₂²×C₄⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
231	C₂²×C₄⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
232	C₂²×C₄⋊C₄	C₂²×C₄₁	1	2	yes	—
233	C₂²×C₄²	—	2	1	no	—
234	C₂²×C₄²	C₂²×C₄₁	1	1	yes	characteristic
235	#389	—	2	2	no	—
236	#389	C₄×C₄₁	1	4	yes	complemented
237	C₄×C₄⋊C₄	—	2	4	no	—
238	C₂×#95	—	2	1	no	—
239	C₂×#95	—	2	1	no	—
240	#340	—	2	4	no	—
241	#340	C₄×C₄₁	1	8	yes	complemented
242	#336	—	2	2	no	—
243	C₄₁	#10884	1	1	yes	characteristic, direct product factor, Sylow
244	C₂³×C₄	—	2	1	no	—
245	C₂³×C₄	—	2	2	no	—
246	C₂³×C₄	—	2	1	no	—
247	C₂³×C₄	D₄×C₄₁	1	1	yes	characteristic
248	C₂³×C₄	D₄×C₄₁	1	1	yes	characteristic
249	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
250	C₂²×C₈	—	2	2	no	—
251	C₂²×C₈	—	2	2	no	—
252	C₂²×C₈	—	2	2	no	—
253	C₂²×C₈	—	2	2	no	—
254	C₂²×C₈	—	2	2	no	—
255	C₂²×C₈	—	2	2	no	—
256	C₂²×C₈	C₂×C₄×C₄₁	1	4	yes	—
257	C₂×C₄⋊C₄	—	2	2	no	—
258	C₂×C₄⋊C₄	—	2	1	no	—
259	C₂×C₄⋊C₄	—	2	2	no	—
260	C₂×C₄⋊C₄	—	2	2	no	—
261	C₂×C₄⋊C₄	—	2	2	no	—
262	C₂×C₄⋊C₄	—	2	2	no	—
263	C₂×C₄⋊C₄	—	2	2	no	—
264	C₂×C₄⋊C₄	—	2	4	no	—
265	C₂×C₄⋊C₄	—	2	1	no	—
266	C₂×C₄⋊C₄	—	4	2	no	—
267	C₂×C₄⋊C₄	—	4	2	no	—
268	C₂×C₄⋊C₄	C₂×C₄×C₄₁	1	2	yes	—
269	C₂×C₄⋊C₄	C₂×C₄×C₄₁	1	4	yes	—
270	C₂×C₄⋊C₄	C₂×C₄×C₄₁	1	2	yes	—
271	C₂×C₄⋊C₄	C₂×C₄×C₄₁	1	4	yes	—
272	C₂×C₄⋊C₄	D₄×C₄₁	1	4	yes	—
273	C₂×C₄⋊C₄	Q₈×C₄₁	1	4	yes	—
274	C₂×C₄²	—	2	2	no	—
275	C₂×C₄²	—	2	2	no	—
276	C₂×C₄²	—	2	4	no	—
277	C₂×C₄²	—	4	2	no	—
278	C₂×C₄²	—	4	2	no	—
279	C₂×C₄²	C₂×C₄×C₄₁	1	2	yes	—
280	C₂×C₄²	D₄×C₄₁	1	2	yes	—
281	#95	—	2	4	no	—
282	#95	—	2	4	no	—
283	C₂⁴	C₂×D₄×C₄₁	1	1	yes	characteristic
284	C₂²×C₄	—	2	1	no	—
285	C₂²×C₄	—	2	1	no	—
286	C₂²×C₄	—	2	1	no	—
287	C₂²×C₄	—	2	1	no	—
288	C₂²×C₄	—	2	2	no	—
289	C₂²×C₄	—	2	4	no	—
290	C₂²×C₄	—	2	4	no	—
291	C₂²×C₄	—	2	1	no	—
292	C₂²×C₄	—	2	4	no	—
293	C₂²×C₄	—	2	4	no	—
294	C₂²×C₄	—	2	1	no	—
295	C₂²×C₄	—	2	2	no	—
296	C₂²×C₄	—	2	2	no	—
297	C₂²×C₄	—	2	2	no	—
298	C₂²×C₄	—	4	2	no	—
299	C₂²×C₄	—	4	1	no	—
300	C₂²×C₄	—	4	1	no	—
301	C₂²×C₄	—	4	2	no	—
302	C₂²×C₄	—	4	2	no	—
303	C₂²×C₄	—	4	2	no	—
304	C₂²×C₄	—	4	2	no	—
305	C₂²×C₄	—	4	1	no	—
306	C₂²×C₄	—	4	1	no	—
307	C₂²×C₄	—	4	1	no	—
308	C₂²×C₄	—	4	1	no	—
309	C₂²×C₄	—	4	1	no	—
310	C₂²×C₄	—	4	1	no	—
311	C₂²×C₄	C₂²⋊C₄×C₄₁	1	2	yes	—
312	C₂²×C₄	C₂²⋊C₄×C₄₁	1	2	yes	—
313	C₂²×C₄	D₈×C₄₁	1	2	yes	—
314	C₂²×C₄	SD₁₆×C₄₁	1	2	yes	—
315	C₂²×C₄	C₂²×C₄×C₄₁	1	2	yes	—
316	C₂²×C₄	C₂²×C₄×C₄₁	1	1	yes	characteristic
317	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
318	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
319	C₂²×C₄	C₂×Q₈×C₄₁	1	2	yes	—
320	C₂²×C₄	#41×C₄₁	1	2	yes	—
321	C₂²×C₄	#41×C₄₁	1	2	yes	—
322	C₂²×C₄	#41×C₄₁	1	2	yes	—
323	C₂×C₈	—	2	4	no	—
324	C₂×C₈	—	2	4	no	—
325	C₂×C₈	—	2	4	no	—
326	C₂×C₈	—	4	2	no	—
327	C₂×C₈	—	4	2	no	—
328	C₂×C₈	—	4	2	no	—
329	C₂×C₈	—	4	2	no	—
330	C₄⋊C₄	—	2	2	no	—
331	C₄⋊C₄	—	2	4	no	—
332	C₄⋊C₄	—	2	4	no	—
333	C₄⋊C₄	—	2	4	no	—
334	C₄⋊C₄	—	2	4	no	—
335	C₄⋊C₄	—	2	4	no	—
336	C₄⋊C₄	—	4	8	no	—
337	C₄⋊C₄	—	4	2	no	—
338	C₄⋊C₄	C₄²×C₄₁	1	4	yes	complemented
339	C₄⋊C₄	C₄⋊C₄×C₄₁	1	8	yes	complemented
340	C₄²	—	2	4	no	—
341	C₄²	—	2	4	no	—
342	C₄²	—	4	8	no	—
343	C₂³	C₂×C₂²⋊C₄×C₄₁	1	1	yes	characteristic
344	C₂³	C₄×D₄×C₄₁	1	2	yes	—
345	C₂³	#120×C₄₁	1	1	yes	characteristic
346	C₂³	C₂²⋊Q₈×C₄₁	1	2	yes	—
347	C₂³	#123×C₄₁	1	1	yes	characteristic
348	C₂³	C₂×D₈×C₄₁	1	1	yes	characteristic
349	C₂³	C₂×SD₁₆×C₄₁	1	1	yes	characteristic
350	C₂³	#135×C₄₁	1	2	yes	—
351	C₂³	AGL(1,ℤ/8)×C₄₁	1	1	yes	characteristic
352	C₂³	#137×C₄₁	1	1	yes	characteristic
353	C₂³	#137×C₄₁	1	2	yes	—
354	C₂×C₄	—	2	2	no	—
355	C₂×C₄	—	2	2	no	—
356	C₂×C₄	—	2	2	no	—
357	C₂×C₄	—	2	2	no	—
358	C₂×C₄	—	2	2	no	—
359	C₂×C₄	—	2	2	no	—
360	C₂×C₄	—	2	4	no	—
361	C₂×C₄	—	2	8	no	—
362	C₂×C₄	—	2	2	no	—
363	C₂×C₄	—	2	2	no	—
364	C₂×C₄	—	2	2	no	—
365	C₂×C₄	—	4	2	no	—
366	C₂×C₄	—	4	2	no	—
367	C₂×C₄	—	4	4	no	—
368	C₂×C₄	—	4	4	no	—
369	C₂×C₄	—	4	4	no	—
370	C₂×C₄	—	4	4	no	—
371	C₂×C₄	—	4	4	no	—
372	C₂×C₄	—	4	2	no	—
373	C₂×C₄	—	4	4	no	—
374	C₂×C₄	—	4	4	no	—
375	C₂×C₄	—	4	4	no	—
376	C₂×C₄	—	4	2	no	—
377	C₂×C₄	—	4	2	no	—
378	C₂×C₄	—	4	2	no	—
379	C₂×C₄	—	4	2	no	—
380	C₂×C₄	—	8	1	no	—
381	C₂×C₄	—	8	1	no	—
382	C₂×C₄	—	8	1	no	—
383	C₂×C₄	—	8	1	no	—
384	C₂×C₄	#102×C₄₁	1	4	yes	—
385	C₂×C₄	C₂×C₄²×C₄₁	1	1	yes	characteristic
386	C₂×C₄	C₂×C₄⋊C₄×C₄₁	1	2	yes	—
387	C₂×C₄	#117×C₄₁	1	2	yes	—
388	C₂×C₄	#117×C₄₁	1	1	yes	characteristic
389	C₂×C₄	C₄×D₄×C₄₁	1	2	yes	—
390	C₂×C₄	C₄×D₄×C₄₁	1	2	yes	—
391	C₂×C₄	C₄×D₄×C₄₁	1	2	yes	—
392	C₂×C₄	C₄×Q₈×C₄₁	1	2	yes	—
393	C₂×C₄	C₄×Q₈×C₄₁	1	2	yes	—
394	C₂×C₄	#121×C₄₁	1	2	yes	—
395	C₂×C₄	C₂²⋊Q₈×C₄₁	1	2	yes	—
396	C₂×C₄	#123×C₄₁	1	2	yes	—
397	C₂×C₄	#124×C₄₁	1	1	yes	characteristic
398	C₂×C₄	#125×C₄₁	1	2	yes	—
399	C₂×C₄	#126×C₄₁	1	2	yes	—
400	C₂×C₄	C₄⋊Q₈×C₄₁	1	1	yes	characteristic
401	C₈	—	4	4	no	—
402	C₂²	C₄×C₂²⋊C₄×C₄₁	1	1	yes	characteristic
403	C₂²	C₄₁×#385	1	2	yes	—
404	C₂²	C₄₁×#386	1	1	yes	characteristic
405	C₂²	C₄₁×#387	1	2	yes	—
406	C₂²	C₄₁×#391	1	1	yes	characteristic
407	C₂²	C₂×#102×C₄₁	1	1	yes	characteristic
408	C₂²	C₄₁×#416	1	1	yes	characteristic
409	C₂²	C₄₁×#417	1	1	yes	characteristic
410	C₂²	C₄₁×#419	1	1	yes	characteristic
411	C₂²	C₄×D₈×C₄₁	1	2	yes	—
412	C₂²	C₄×SD₁₆×C₄₁	1	2	yes	—
413	C₂²	C₄₁×#440	1	2	yes	—
414	C₂²	C₄₁×#441	1	2	yes	—
415	C₂²	C₄₁×#447	1	1	yes	characteristic
416	C₂²	C₄₁×#448	1	1	yes	characteristic
417	C₂²	C₄₁×#452	1	2	yes	—
418	C₂²	C₄₁×#474	1	2	yes	—
419	C₂²	C₄₁×#475	1	2	yes	—
420	C₂²	C₄₁×#478	1	2	yes	—
421	C₂²	C₄₁×#479	1	2	yes	—
422	C₂²	C₄₁×#480	1	1	yes	characteristic
423	C₂²	C₄₁×#481	1	1	yes	characteristic
424	C₂²	C₄₁×#485	1	2	yes	—
425	C₄	—	2	4	no	—
426	C₄	—	4	4	no	—
427	C₄	—	4	8	no	—
428	C₄	—	4	2	no	—
429	C₄	—	8	2	no	—
430	C₄	C₄×C₄⋊C₄×C₄₁	1	2	yes	—
431	C₄	C₄₁×#387	1	2	yes	—
432	C₄	C₄₁×#388	1	2	yes	—
433	C₄	C₄₁×#389	1	2	yes	—
434	C₂	C₄₁×#1436	1	1	yes	characteristic
435	C₂	C₄×#102×C₄₁	1	1	yes	characteristic
436	C₂	C₄₁×#1763	1	1	yes	characteristic
437	C₂	C₄₁×#1862	1	2	yes	—
438	C₂	C₄₁×#1865	1	2	yes	—
439	C₂	C₄₁×#1873	1	1	yes	characteristic
440	C₂	C₄₁×#1874	1	1	yes	characteristic
441	C₂	C₄₁×#1918	1	2	yes	—
442	C₂	C₄₁×#1919	1	2	yes	—
443	C₂	C₄₁×#1988	1	1	yes	characteristic
444	C₂	C₄₁×#1989	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
14. C₄₁×#389	C₄	semidirect
19. C₄₁×#340	C₄	semidirect
115. C₄⋊C₄×C₄₁	C₄²	semidirect
116. C₄⋊C₄×C₄₁	C₄⋊C₄	semidirect
179. #10884	C₄₁	direct (N × H)
236. #389	C₄×C₄₁	semidirect
241. #340	C₄×C₄₁	semidirect
243. C₄₁	#10884	direct (N × H)
338. C₄⋊C₄	C₄²×C₄₁	semidirect
339. C₄⋊C₄	C₄⋊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×#389	2
C₂×C₄×C₄⋊C₄×C₄₁	2
C₂×C₄₁×#340	2
C₂×C₄₁×#336	2
#10884	41

Subgroups — C41×#10884 #23787085

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#10884 #23787085