Subgroups — C₄₁×#8578 #23784779

Order 10496.

658 conjugacy classes of subgroups.

The subgroup lattice has 462 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₂²⋊Q₈×C₄₁	C₂	1	1	yes	maximal, characteristic
2	C₄₁×#1797	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄₁×#328	C₂	1	2	yes	maximal
4	C₄₁×C₄⋊#95	C₂	1	1	yes	maximal, characteristic
5	C₄₁×#1294	C₂	1	2	yes	maximal
6	C₂×C₂²⋊Q₈×C₄₁	C₂²	1	1	yes	characteristic
7	C₂×C₄×Q₈×C₄₁	C₄	1	1	yes	characteristic, complemented
8	C₂²×C₄⋊C₄×C₄₁	—	2	1	no	—
9	C₂²×C₄²×C₄₁	C₂²	1	1	yes	characteristic
10	C₂×C₄⋊C₈×C₄₁	—	2	1	no	—
11	C₂×C₂²⋊C₈×C₄₁	C₂²	1	2	yes	—
12	C₄₁×#391	C₄	1	1	yes	characteristic, complemented
13	C₄₁×#389	C₄	1	1	yes	characteristic, complemented
14	C₄₁×#387	—	2	1	no	—
15	C₄₁×#385	—	2	1	no	—
16	C₄₁×#380	C₂²	1	1	yes	characteristic
17	C₄×C₄⋊C₄×C₄₁	—	2	1	no	—
18	C₄×C₄⋊C₄×C₄₁	C₄	1	1	yes	characteristic, complemented
19	C₄×C₂²⋊C₄×C₄₁	—	2	1	no	—
20	C₂×#95×C₄₁	—	2	1	no	—
21	C₂×#95×C₄₁	C₂²	1	2	yes	—
22	C₄₁×#336	—	2	1	no	—
23	C₄₁×#328	—	2	4	no	—
24	C₂²×Q₈×C₄₁	C₂×C₄	1	1	yes	characteristic
25	C₂³×C₄×C₄₁	—	2	2	no	—
26	C₂³×C₄×C₄₁	D₄	1	1	yes	characteristic
27	C₂³×C₄×C₄₁	D₄	1	1	yes	characteristic
28	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
29	C₂²×C₈×C₄₁	—	2	2	no	—
30	C₂²⋊Q₈×C₄₁	—	2	1	no	—
31	C₂²⋊Q₈×C₄₁	—	2	1	no	—
32	C₂²⋊Q₈×C₄₁	D₄	1	2	yes	—
33	C₂²⋊Q₈×C₄₁	Q₈	1	2	yes	—
34	C₄×Q₈×C₄₁	—	4	2	no	—
35	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
36	C₂×C₄⋊C₄×C₄₁	—	2	4	no	—
37	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
38	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
39	C₂×C₄⋊C₄×C₄₁	—	4	2	no	—
40	C₂×C₄⋊C₄×C₄₁	—	4	2	no	—
41	C₂×C₄⋊C₄×C₄₁	C₂×C₄	1	1	yes	characteristic
42	C₂×C₄⋊C₄×C₄₁	C₂×C₄	1	1	yes	characteristic
43	C₂×C₄⋊C₄×C₄₁	C₂×C₄	1	1	yes	characteristic
44	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
45	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
46	C₂×C₄²×C₄₁	—	2	1	no	—
47	C₂×C₄²×C₄₁	—	2	1	no	—
48	C₂×C₄²×C₄₁	—	4	2	no	—
49	C₂×C₄²×C₄₁	C₂×C₄	1	1	yes	characteristic
50	C₂×C₄²×C₄₁	C₂×C₄	1	1	yes	characteristic
51	C₂×C₄²×C₄₁	D₄	1	1	yes	characteristic
52	C₂×C₄²×C₄₁	D₄	1	1	yes	characteristic
53	C₄⋊C₈×C₄₁	—	4	2	no	—
54	C₂²⋊C₈×C₄₁	—	2	2	no	—
55	C₂²⋊C₈×C₄₁	—	2	2	no	—
56	#95×C₄₁	—	2	1	no	—
57	#95×C₄₁	—	2	1	no	—
58	#95×C₄₁	—	2	1	no	—
59	#95×C₄₁	—	2	1	no	—
60	#95×C₄₁	—	2	1	no	—
61	#95×C₄₁	—	2	2	no	—
62	#95×C₄₁	—	2	2	no	—
63	#95×C₄₁	—	4	2	no	—
64	C₂⁴×C₄₁	C₂×D₄	1	1	yes	characteristic
65	C₂×Q₈×C₄₁	—	2	1	no	—
66	C₂×Q₈×C₄₁	—	4	1	no	—
67	C₂×Q₈×C₄₁	—	4	1	no	—
68	C₂×Q₈×C₄₁	C₄⋊C₄	1	2	yes	complemented
69	C₂²×C₄×C₄₁	—	2	1	no	—
70	C₂²×C₄×C₄₁	—	2	1	no	—
71	C₂²×C₄×C₄₁	—	2	2	no	—
72	C₂²×C₄×C₄₁	—	2	2	no	—
73	C₂²×C₄×C₄₁	—	2	1	no	—
74	C₂²×C₄×C₄₁	—	2	1	no	—
75	C₂²×C₄×C₄₁	—	2	4	no	—
76	C₂²×C₄×C₄₁	—	2	1	no	—
77	C₂²×C₄×C₄₁	—	2	1	no	—
78	C₂²×C₄×C₄₁	—	4	1	no	—
79	C₂²×C₄×C₄₁	—	4	1	no	—
80	C₂²×C₄×C₄₁	—	4	1	no	—
81	C₂²×C₄×C₄₁	—	4	1	no	—
82	C₂²×C₄×C₄₁	—	4	2	no	—
83	C₂²×C₄×C₄₁	—	4	2	no	—
84	C₂²×C₄×C₄₁	—	4	2	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	C₂²⋊C₄	1	1	yes	characteristic
89	C₂²×C₄×C₄₁	C₂²⋊C₄	1	1	yes	characteristic
90	C₂²×C₄×C₄₁	C₂²⋊C₄	1	1	yes	characteristic
91	C₂²×C₄×C₄₁	C₂²⋊C₄	1	1	yes	characteristic
92	C₂²×C₄×C₄₁	SD₁₆	1	2	yes	—
93	C₂²×C₄×C₄₁	Q₁₆	1	2	yes	—
94	C₂²×C₄×C₄₁	C₂²×C₄	1	1	yes	characteristic
95	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
96	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
97	C₂²×C₄×C₄₁	C₂×Q₈	1	1	yes	characteristic
98	C₂²×C₄×C₄₁	#41	1	1	yes	characteristic
99	C₂²×C₄×C₄₁	#41	1	1	yes	characteristic
100	C₂×C₈×C₄₁	—	4	2	no	—
101	C₂×C₈×C₄₁	—	4	2	no	—
102	C₂×C₈×C₄₁	—	4	2	no	—
103	C₄⋊C₄×C₄₁	—	2	1	no	—
104	C₄⋊C₄×C₄₁	—	2	2	no	—
105	C₄⋊C₄×C₄₁	—	2	2	no	—
106	C₄⋊C₄×C₄₁	—	4	1	no	—
107	C₄⋊C₄×C₄₁	—	4	1	no	—
108	C₄⋊C₄×C₄₁	—	4	8	no	—
109	C₄⋊C₄×C₄₁	—	4	2	no	—
110	C₄⋊C₄×C₄₁	—	4	2	no	—
111	C₄⋊C₄×C₄₁	C₄⋊C₄	1	2	yes	complemented
112	C₂²⋊C₄×C₄₁	—	2	2	no	—
113	C₂²⋊C₄×C₄₁	—	2	2	no	—
114	C₂²⋊C₄×C₄₁	—	4	1	no	—
115	C₂²⋊C₄×C₄₁	—	4	1	no	—
116	C₄²×C₄₁	—	2	2	no	—
117	C₄²×C₄₁	—	2	2	no	—
118	C₄²×C₄₁	—	4	1	no	—
119	C₄²×C₄₁	—	4	1	no	—
120	C₄²×C₄₁	—	4	2	no	—
121	C₄²×C₄₁	—	4	2	no	—
122	C₂³×C₄₁	—	2	1	no	—
123	C₂³×C₄₁	—	2	1	no	—
124	C₂³×C₄₁	—	2	1	no	—
125	C₂³×C₄₁	—	2	1	no	—
126	C₂³×C₄₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
127	C₂³×C₄₁	#121	1	1	yes	characteristic
128	C₂³×C₄₁	C₂²⋊Q₈	1	1	yes	characteristic
129	C₂³×C₄₁	C₂×SD₁₆	1	1	yes	characteristic
130	C₂³×C₄₁	C₂×Q₁₆	1	1	yes	characteristic
131	C₂³×C₄₁	AGL(1,ℤ/8)	1	1	yes	characteristic
132	C₂³×C₄₁	#137	1	1	yes	characteristic
133	Q₈×C₄₁	—	4	2	no	—
134	Q₈×C₄₁	—	4	2	no	—
135	C₂×C₄×C₄₁	—	2	4	no	—
136	C₂×C₄×C₄₁	—	2	4	no	—
137	C₂×C₄×C₄₁	—	2	1	no	—
138	C₂×C₄×C₄₁	—	2	1	no	—
139	C₂×C₄×C₄₁	—	2	1	no	—
140	C₂×C₄×C₄₁	—	2	1	no	—
141	C₂×C₄×C₄₁	—	2	1	no	—
142	C₂×C₄×C₄₁	—	2	1	no	—
143	C₂×C₄×C₄₁	—	2	1	no	—
144	C₂×C₄×C₄₁	—	2	1	no	—
145	C₂×C₄×C₄₁	—	2	1	no	—
146	C₂×C₄×C₄₁	—	2	1	no	—
147	C₂×C₄×C₄₁	—	2	1	no	—
148	C₂×C₄×C₄₁	—	2	1	no	—
149	C₂×C₄×C₄₁	—	2	2	no	—
150	C₂×C₄×C₄₁	—	2	2	no	—
151	C₂×C₄×C₄₁	—	4	2	no	—
152	C₂×C₄×C₄₁	—	4	2	no	—
153	C₂×C₄×C₄₁	—	4	1	no	—
154	C₂×C₄×C₄₁	—	4	1	no	—
155	C₂×C₄×C₄₁	—	4	1	no	—
156	C₂×C₄×C₄₁	—	4	1	no	—
157	C₂×C₄×C₄₁	—	4	1	no	—
158	C₂×C₄×C₄₁	—	4	1	no	—
159	C₂×C₄×C₄₁	—	4	1	no	—
160	C₂×C₄×C₄₁	—	4	1	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	—	4	1	no	—
165	C₂×C₄×C₄₁	—	4	1	no	—
166	C₂×C₄×C₄₁	—	4	1	no	—
167	C₂×C₄×C₄₁	—	4	1	no	—
168	C₂×C₄×C₄₁	—	4	1	no	—
169	C₂×C₄×C₄₁	—	4	1	no	—
170	C₂×C₄×C₄₁	—	8	2	no	—
171	C₂×C₄×C₄₁	—	8	2	no	—
172	C₂×C₄×C₄₁	—	8	2	no	—
173	C₂×C₄×C₄₁	—	8	2	no	—
174	C₂×C₄×C₄₁	#99	1	2	yes	—
175	C₂×C₄×C₄₁	#103	1	2	yes	—
176	C₂×C₄×C₄₁	#103	1	2	yes	—
177	C₂×C₄×C₄₁	#104	1	2	yes	—
178	C₂×C₄×C₄₁	C₂×C₄⋊C₄	1	1	yes	characteristic
179	C₂×C₄×C₄₁	#117	1	1	yes	characteristic
180	C₂×C₄×C₄₁	#121	1	1	yes	characteristic
181	C₂×C₄×C₄₁	C₂²⋊Q₈	1	1	yes	characteristic
182	C₈×C₄₁	—	8	2	no	—
183	#8578	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
184	C₂²×C₄₁	—	2	1	no	—
185	C₂²×C₄₁	—	2	1	no	—
186	C₂²×C₄₁	—	2	1	no	—
187	C₂²×C₄₁	—	2	1	no	—
188	C₂²×C₄₁	—	2	1	no	—
189	C₂²×C₄₁	—	2	1	no	—
190	C₂²×C₄₁	—	2	1	no	—
191	C₂²×C₄₁	—	2	1	no	—
192	C₂²×C₄₁	—	2	1	no	—
193	C₂²×C₄₁	—	2	1	no	—
194	C₂²×C₄₁	—	2	1	no	—
195	C₂²×C₄₁	—	2	1	no	—
196	C₂²×C₄₁	#380	1	1	yes	characteristic
197	C₂²×C₄₁	C₂×#99	1	1	yes	characteristic
198	C₂²×C₄₁	#410	1	1	yes	characteristic
199	C₂²×C₄₁	C₂×#103	1	1	yes	characteristic
200	C₂²×C₄₁	#417	1	1	yes	characteristic
201	C₂²×C₄₁	C₂×#104	1	1	yes	characteristic
202	C₂²×C₄₁	#421	1	1	yes	characteristic
203	C₂²×C₄₁	#460	1	1	yes	characteristic
204	C₂²×C₄₁	#462	1	1	yes	characteristic
205	C₂²×C₄₁	#475	1	1	yes	characteristic
206	C₂²×C₄₁	#477	1	1	yes	characteristic
207	C₄×C₄₁	—	2	1	no	—
208	C₄×C₄₁	—	2	1	no	—
209	C₄×C₄₁	—	2	1	no	—
210	C₄×C₄₁	—	2	1	no	—
211	C₄×C₄₁	—	2	2	no	—
212	C₄×C₄₁	—	2	2	no	—
213	C₄×C₄₁	—	2	2	no	—
214	C₄×C₄₁	—	2	2	no	—
215	C₄×C₄₁	—	4	2	no	—
216	C₄×C₄₁	—	4	2	no	—
217	C₄×C₄₁	—	8	4	no	—
218	C₄×C₄₁	—	8	1	no	—
219	C₄×C₄₁	—	8	1	no	—
220	C₄×C₂²⋊Q₈	C₂×C₄₁	1	1	yes	characteristic
221	#1797	C₂×C₄₁	1	1	yes	characteristic
222	C₂×#328	C₂×C₄₁	1	2	yes	—
223	C₄⋊#95	C₂×C₄₁	1	1	yes	characteristic
224	#1294	C₂×C₄₁	1	2	yes	—
225	C₂×C₄₁	—	2	1	no	—
226	C₂×C₄₁	—	2	1	no	—
227	C₂×C₄₁	—	2	1	no	—
228	C₂×C₄₁	—	2	1	no	—
229	C₂×C₄₁	#1503	1	1	yes	characteristic
230	C₂×C₄₁	#1504	1	1	yes	characteristic
231	C₂×C₄₁	#1512	1	1	yes	characteristic
232	C₂×C₄₁	#1520	1	1	yes	characteristic
233	C₂×C₄₁	#1799	1	1	yes	characteristic
234	C₂×C₄₁	#1803	1	1	yes	characteristic
235	C₂×C₄₁	#1806	1	1	yes	characteristic
236	C₂×C₂²⋊Q₈	C₂²×C₄₁	1	1	yes	characteristic
237	C₂×C₄×Q₈	C₄×C₄₁	1	1	yes	characteristic, complemented
238	C₂²×C₄⋊C₄	—	2	1	no	—
239	C₂²×C₄²	C₂²×C₄₁	1	1	yes	characteristic
240	C₂×C₄⋊C₈	—	2	1	no	—
241	C₂×C₂²⋊C₈	C₂²×C₄₁	1	2	yes	—
242	#391	C₄×C₄₁	1	1	yes	characteristic, complemented
243	#389	C₄×C₄₁	1	1	yes	characteristic, complemented
244	#387	—	2	1	no	—
245	#385	—	2	1	no	—
246	#380	C₂²×C₄₁	1	1	yes	characteristic
247	C₄×C₄⋊C₄	—	2	1	no	—
248	C₄×C₄⋊C₄	C₄×C₄₁	1	1	yes	characteristic, complemented
249	C₄×C₂²⋊C₄	—	2	1	no	—
250	C₂×#95	—	2	1	no	—
251	C₂×#95	C₂²×C₄₁	1	2	yes	—
252	#336	—	2	1	no	—
253	#328	—	2	4	no	—
254	C₄₁	#8578	1	1	yes	characteristic, direct product factor, Sylow
255	C₂²×Q₈	C₂×C₄×C₄₁	1	1	yes	characteristic
256	C₂³×C₄	—	2	2	no	—
257	C₂³×C₄	D₄×C₄₁	1	1	yes	characteristic
258	C₂³×C₄	D₄×C₄₁	1	1	yes	characteristic
259	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
260	C₂²×C₈	—	2	2	no	—
261	C₂²⋊Q₈	—	2	1	no	—
262	C₂²⋊Q₈	—	2	1	no	—
263	C₂²⋊Q₈	D₄×C₄₁	1	2	yes	—
264	C₂²⋊Q₈	Q₈×C₄₁	1	2	yes	—
265	C₄×Q₈	—	4	2	no	—
266	C₂×C₄⋊C₄	—	2	1	no	—
267	C₂×C₄⋊C₄	—	2	4	no	—
268	C₂×C₄⋊C₄	—	2	1	no	—
269	C₂×C₄⋊C₄	—	2	1	no	—
270	C₂×C₄⋊C₄	—	4	2	no	—
271	C₂×C₄⋊C₄	—	4	2	no	—
272	C₂×C₄⋊C₄	C₂×C₄×C₄₁	1	1	yes	characteristic
273	C₂×C₄⋊C₄	C₂×C₄×C₄₁	1	1	yes	characteristic
274	C₂×C₄⋊C₄	C₂×C₄×C₄₁	1	1	yes	characteristic
275	C₂×C₂²⋊C₄	—	2	1	no	—
276	C₂×C₂²⋊C₄	—	2	1	no	—
277	C₂×C₄²	—	2	1	no	—
278	C₂×C₄²	—	2	1	no	—
279	C₂×C₄²	—	4	2	no	—
280	C₂×C₄²	C₂×C₄×C₄₁	1	1	yes	characteristic
281	C₂×C₄²	C₂×C₄×C₄₁	1	1	yes	characteristic
282	C₂×C₄²	D₄×C₄₁	1	1	yes	characteristic
283	C₂×C₄²	D₄×C₄₁	1	1	yes	characteristic
284	C₄⋊C₈	—	4	2	no	—
285	C₂²⋊C₈	—	2	2	no	—
286	C₂²⋊C₈	—	2	2	no	—
287	#95	—	2	1	no	—
288	#95	—	2	1	no	—
289	#95	—	2	1	no	—
290	#95	—	2	1	no	—
291	#95	—	2	1	no	—
292	#95	—	2	2	no	—
293	#95	—	2	2	no	—
294	#95	—	4	2	no	—
295	C₂⁴	C₂×D₄×C₄₁	1	1	yes	characteristic
296	C₂×Q₈	—	2	1	no	—
297	C₂×Q₈	—	4	1	no	—
298	C₂×Q₈	—	4	1	no	—
299	C₂×Q₈	C₄⋊C₄×C₄₁	1	2	yes	complemented
300	C₂²×C₄	—	2	1	no	—
301	C₂²×C₄	—	2	1	no	—
302	C₂²×C₄	—	2	2	no	—
303	C₂²×C₄	—	2	2	no	—
304	C₂²×C₄	—	2	1	no	—
305	C₂²×C₄	—	2	1	no	—
306	C₂²×C₄	—	2	4	no	—
307	C₂²×C₄	—	2	1	no	—
308	C₂²×C₄	—	2	1	no	—
309	C₂²×C₄	—	4	1	no	—
310	C₂²×C₄	—	4	1	no	—
311	C₂²×C₄	—	4	1	no	—
312	C₂²×C₄	—	4	1	no	—
313	C₂²×C₄	—	4	2	no	—
314	C₂²×C₄	—	4	2	no	—
315	C₂²×C₄	—	4	2	no	—
316	C₂²×C₄	—	4	2	no	—
317	C₂²×C₄	—	4	2	no	—
318	C₂²×C₄	—	4	2	no	—
319	C₂²×C₄	C₂²⋊C₄×C₄₁	1	1	yes	characteristic
320	C₂²×C₄	C₂²⋊C₄×C₄₁	1	1	yes	characteristic
321	C₂²×C₄	C₂²⋊C₄×C₄₁	1	1	yes	characteristic
322	C₂²×C₄	C₂²⋊C₄×C₄₁	1	1	yes	characteristic
323	C₂²×C₄	SD₁₆×C₄₁	1	2	yes	—
324	C₂²×C₄	Q₁₆×C₄₁	1	2	yes	—
325	C₂²×C₄	C₂²×C₄×C₄₁	1	1	yes	characteristic
326	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
327	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
328	C₂²×C₄	C₂×Q₈×C₄₁	1	1	yes	characteristic
329	C₂²×C₄	#41×C₄₁	1	1	yes	characteristic
330	C₂²×C₄	#41×C₄₁	1	1	yes	characteristic
331	C₂×C₈	—	4	2	no	—
332	C₂×C₈	—	4	2	no	—
333	C₂×C₈	—	4	2	no	—
334	C₄⋊C₄	—	2	1	no	—
335	C₄⋊C₄	—	2	2	no	—
336	C₄⋊C₄	—	2	2	no	—
337	C₄⋊C₄	—	4	1	no	—
338	C₄⋊C₄	—	4	1	no	—
339	C₄⋊C₄	—	4	8	no	—
340	C₄⋊C₄	—	4	2	no	—
341	C₄⋊C₄	—	4	2	no	—
342	C₄⋊C₄	C₄⋊C₄×C₄₁	1	2	yes	complemented
343	C₂²⋊C₄	—	2	2	no	—
344	C₂²⋊C₄	—	2	2	no	—
345	C₂²⋊C₄	—	4	1	no	—
346	C₂²⋊C₄	—	4	1	no	—
347	C₄²	—	2	2	no	—
348	C₄²	—	2	2	no	—
349	C₄²	—	4	1	no	—
350	C₄²	—	4	1	no	—
351	C₄²	—	4	2	no	—
352	C₄²	—	4	2	no	—
353	C₂³	—	2	1	no	—
354	C₂³	—	2	1	no	—
355	C₂³	—	2	1	no	—
356	C₂³	—	2	1	no	—
357	C₂³	C₂×C₂²⋊C₄×C₄₁	1	1	yes	characteristic
358	C₂³	#121×C₄₁	1	1	yes	characteristic
359	C₂³	C₂²⋊Q₈×C₄₁	1	1	yes	characteristic
360	C₂³	C₂×SD₁₆×C₄₁	1	1	yes	characteristic
361	C₂³	C₂×Q₁₆×C₄₁	1	1	yes	characteristic
362	C₂³	AGL(1,ℤ/8)×C₄₁	1	1	yes	characteristic
363	C₂³	#137×C₄₁	1	1	yes	characteristic
364	Q₈	—	4	2	no	—
365	Q₈	—	4	2	no	—
366	C₂×C₄	—	2	4	no	—
367	C₂×C₄	—	2	4	no	—
368	C₂×C₄	—	2	1	no	—
369	C₂×C₄	—	2	1	no	—
370	C₂×C₄	—	2	1	no	—
371	C₂×C₄	—	2	1	no	—
372	C₂×C₄	—	2	1	no	—
373	C₂×C₄	—	2	1	no	—
374	C₂×C₄	—	2	1	no	—
375	C₂×C₄	—	2	1	no	—
376	C₂×C₄	—	2	1	no	—
377	C₂×C₄	—	2	1	no	—
378	C₂×C₄	—	2	1	no	—
379	C₂×C₄	—	2	1	no	—
380	C₂×C₄	—	2	2	no	—
381	C₂×C₄	—	2	2	no	—
382	C₂×C₄	—	4	2	no	—
383	C₂×C₄	—	4	2	no	—
384	C₂×C₄	—	4	1	no	—
385	C₂×C₄	—	4	1	no	—
386	C₂×C₄	—	4	1	no	—
387	C₂×C₄	—	4	1	no	—
388	C₂×C₄	—	4	1	no	—
389	C₂×C₄	—	4	1	no	—
390	C₂×C₄	—	4	1	no	—
391	C₂×C₄	—	4	1	no	—
392	C₂×C₄	—	4	4	no	—
393	C₂×C₄	—	4	4	no	—
394	C₂×C₄	—	4	4	no	—
395	C₂×C₄	—	4	1	no	—
396	C₂×C₄	—	4	1	no	—
397	C₂×C₄	—	4	1	no	—
398	C₂×C₄	—	4	1	no	—
399	C₂×C₄	—	4	1	no	—
400	C₂×C₄	—	4	1	no	—
401	C₂×C₄	—	8	2	no	—
402	C₂×C₄	—	8	2	no	—
403	C₂×C₄	—	8	2	no	—
404	C₂×C₄	—	8	2	no	—
405	C₂×C₄	#99×C₄₁	1	2	yes	—
406	C₂×C₄	#103×C₄₁	1	2	yes	—
407	C₂×C₄	#103×C₄₁	1	2	yes	—
408	C₂×C₄	#104×C₄₁	1	2	yes	—
409	C₂×C₄	C₂×C₄⋊C₄×C₄₁	1	1	yes	characteristic
410	C₂×C₄	#117×C₄₁	1	1	yes	characteristic
411	C₂×C₄	#121×C₄₁	1	1	yes	characteristic
412	C₂×C₄	C₂²⋊Q₈×C₄₁	1	1	yes	characteristic
413	C₈	—	8	2	no	—
414	C₂²	—	2	1	no	—
415	C₂²	—	2	1	no	—
416	C₂²	—	2	1	no	—
417	C₂²	—	2	1	no	—
418	C₂²	—	2	1	no	—
419	C₂²	—	2	1	no	—
420	C₂²	—	2	1	no	—
421	C₂²	—	2	1	no	—
422	C₂²	—	2	1	no	—
423	C₂²	—	2	1	no	—
424	C₂²	—	2	1	no	—
425	C₂²	—	2	1	no	—
426	C₂²	C₄₁×#380	1	1	yes	characteristic
427	C₂²	C₂×#99×C₄₁	1	1	yes	characteristic
428	C₂²	C₄₁×#410	1	1	yes	characteristic
429	C₂²	C₂×#103×C₄₁	1	1	yes	characteristic
430	C₂²	C₄₁×#417	1	1	yes	characteristic
431	C₂²	C₂×#104×C₄₁	1	1	yes	characteristic
432	C₂²	C₄₁×#421	1	1	yes	characteristic
433	C₂²	C₄₁×#460	1	1	yes	characteristic
434	C₂²	C₄₁×#462	1	1	yes	characteristic
435	C₂²	C₄₁×#475	1	1	yes	characteristic
436	C₂²	C₄₁×#477	1	1	yes	characteristic
437	C₄	—	2	2	no	—
438	C₄	—	2	2	no	—
439	C₄	—	2	2	no	—
440	C₄	—	2	2	no	—
441	C₄	—	2	1	no	—
442	C₄	—	2	1	no	—
443	C₄	—	2	1	no	—
444	C₄	—	2	1	no	—
445	C₄	—	4	2	no	—
446	C₄	—	4	2	no	—
447	C₄	—	8	4	no	—
448	C₄	—	8	1	no	—
449	C₄	—	8	1	no	—
450	C₂	—	2	1	no	—
451	C₂	—	2	1	no	—
452	C₂	—	2	1	no	—
453	C₂	—	2	1	no	—
454	C₂	C₄₁×#1503	1	1	yes	characteristic
455	C₂	C₄₁×#1504	1	1	yes	characteristic
456	C₂	C₄₁×#1512	1	1	yes	characteristic
457	C₂	C₄₁×#1520	1	1	yes	characteristic
458	C₂	C₄₁×#1799	1	1	yes	characteristic
459	C₂	C₄₁×#1803	1	1	yes	characteristic
460	C₂	C₄₁×#1806	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₄₁	C₂×C₂²⋊C₄
commutator	C₂²×C₄	C₂²×C₄×C₄₁
Frattini, cosocle	C₂³×C₄	C₂³×C₄₁
prime radical	C₂⁴×C₄₁	C₂×D₄
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ 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
7. C₂×C₄×Q₈×C₄₁	C₄	semidirect
12. C₄₁×#391	C₄	semidirect
13. C₄₁×#389	C₄	semidirect
18. C₄×C₄⋊C₄×C₄₁	C₄	semidirect
68. C₂×Q₈×C₄₁	C₄⋊C₄	semidirect
111. C₄⋊C₄×C₄₁	C₄⋊C₄	semidirect
183. #8578	C₄₁	direct (N × H)
237. C₂×C₄×Q₈	C₄×C₄₁	semidirect
242. #391	C₄×C₄₁	semidirect
243. #389	C₄×C₄₁	semidirect
248. C₄×C₄⋊C₄	C₄×C₄₁	semidirect
254. C₄₁	#8578	direct (N × H)
299. C₂×Q₈	C₄⋊C₄×C₄₁	semidirect
342. 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
C₄×C₂²⋊Q₈×C₄₁	2
C₄₁×#1797	2
C₂×C₄₁×#328	2
C₄₁×C₄⋊#95	2
C₄₁×#1294	2
#8578	41

Subgroups — C41×#8578 #23784779

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#8578 #23784779