Subgroups — C₄₁×#20512 #23796713

Order 10496.

1014 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₁×#444	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄₁×#443	C₂	1	1	yes	maximal, characteristic
3	C₄₁×#2943	C₂	1	1	yes	maximal, characteristic
4	C₄₁×#2875	C₂	1	2	yes	maximal, complemented
5	C₄₁×#1778	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄₁×#1773	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₁×#1772	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄₁×#1765	C₂	1	2	yes	maximal, complemented
9	C₄₁×#1764	C₂	1	2	yes	maximal, complemented
10	C₄×#104×C₄₁	C₂	1	2	yes	maximal, complemented
11	C₄×#97×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#135×C₄₁	C₂²	1	1	yes	characteristic
13	C₂×#131×C₄₁	C₂²	1	2	yes	—
14	C₂×#131×C₄₁	C₂²	1	2	yes	—
15	C₄×#41×C₄₁	C₂²	1	2	yes	—
16	C₄₁×#444	C₄	1	8	yes	complemented
17	C₄₁×#443	C₄	1	8	yes	complemented
18	C₄₁×#442	C₄	1	2	yes	complemented
19	C₄₁×#441	C₄	1	2	yes	complemented
20	C₄₁×#440	C₄	1	4	yes	complemented
21	C₂×#108×C₄₁	C₂²	1	1	yes	characteristic
22	C₂×#108×C₄₁	C₂²	1	1	yes	characteristic
23	C₄₁×#427	C₂²	1	1	yes	characteristic
24	C₂×#104×C₄₁	C₂²	1	2	yes	—
25	C₂×#104×C₄₁	C₂²	1	2	yes	—
26	C₄₁×#416	C₂²	1	2	yes	—
27	C₄₁×#405	—	2	2	no	—
28	C₄₁×#405	—	2	2	no	—
29	C₄₁×#405	C₂²	1	2	yes	—
30	C₄₁×#405	C₂²	1	2	yes	—
31	C₄×M₁₆×C₄₁	—	2	2	no	—
32	C₄×M₁₆×C₄₁	C₂²	1	2	yes	—
33	C₂×#97×C₄₁	—	2	2	no	—
34	C₂×#97×C₄₁	C₂²	1	1	yes	characteristic
35	C₂×#97×C₄₁	C₂²	1	1	yes	characteristic
36	C₂×#97×C₄₁	C₂²	1	1	yes	characteristic
37	C₂×#97×C₄₁	C₂²	1	1	yes	characteristic
38	C₂×C₄×C₈×C₄₁	C₂²	1	1	yes	characteristic
39	C₂×C₄×C₈×C₄₁	C₂²	1	1	yes	characteristic
40	C₄³×C₄₁	C₂²	1	1	yes	characteristic
41	C₄₁×#341	C₂²	1	2	yes	—
42	C₄₁×#339	C₂²	1	2	yes	—
43	C₄₁×#339	C₂²	1	2	yes	—
44	C₂×#41×C₄₁	C₂³	1	2	yes	—
45	#135×C₄₁	C₂×C₄	1	4	yes	—
46	#135×C₄₁	C₂×C₄	1	4	yes	—
47	C₂×Q₁₆×C₄₁	C₂×C₄	1	1	yes	characteristic
48	C₂×SD₁₆×C₄₁	C₂×C₄	1	2	yes	—
49	C₂×D₈×C₄₁	C₂×C₄	1	1	yes	characteristic
50	#131×C₄₁	—	2	4	no	—
51	#131×C₄₁	—	2	4	no	—
52	#131×C₄₁	C₂×C₄	1	8	yes	complemented
53	#131×C₄₁	C₂×C₄	1	8	yes	complemented
54	C₂×M₁₆×C₄₁	—	2	2	no	—
55	C₂×M₁₆×C₄₁	—	2	2	no	—
56	C₂×M₁₆×C₄₁	C₂³	1	2	yes	—
57	C₂×M₁₆×C₄₁	C₂³	1	2	yes	—
58	C₂²×C₈×C₄₁	—	2	2	no	—
59	C₂²×C₈×C₄₁	—	2	2	no	—
60	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
61	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
62	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
63	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
64	C₄×Q₈×C₄₁	C₂×C₄	1	4	yes	—
65	C₄×D₄×C₄₁	—	2	4	no	—
66	C₄×D₄×C₄₁	C₂×C₄	1	4	yes	—
67	#117×C₄₁	—	2	2	no	—
68	#117×C₄₁	C₂³	1	2	yes	—
69	C₂×C₄²×C₄₁	—	2	2	no	—
70	C₂×C₄²×C₄₁	—	2	2	no	—
71	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
72	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
73	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
74	#108×C₄₁	C₂×C₄	1	4	yes	complemented
75	#108×C₄₁	C₂×C₄	1	4	yes	complemented
76	#107×C₄₁	C₂×C₄	1	2	yes	—
77	#106×C₄₁	C₂×C₄	1	2	yes	—
78	#104×C₄₁	C₂×C₄	1	8	yes	complemented
79	#104×C₄₁	C₂×C₄	1	8	yes	complemented
80	#103×C₄₁	C₂×C₄	1	4	yes	—
81	#102×C₄₁	C₂×C₄	1	4	yes	—
82	#97×C₄₁	—	2	2	no	—
83	#97×C₄₁	—	2	2	no	—
84	#97×C₄₁	—	2	2	no	—
85	#97×C₄₁	—	2	2	no	—
86	#97×C₄₁	C₂×C₄	1	2	yes	—
87	#97×C₄₁	C₂×C₄	1	2	yes	—
88	#97×C₄₁	C₂×C₄	1	4	yes	complemented
89	#97×C₄₁	D₄	1	2	yes	—
90	#97×C₄₁	D₄	1	2	yes	—
91	C₄×C₈×C₄₁	—	2	2	no	—
92	C₄×C₈×C₄₁	—	2	2	no	—
93	C₄×C₈×C₄₁	—	2	2	no	—
94	C₄×C₈×C₄₁	—	2	2	no	—
95	C₄×C₈×C₄₁	C₂×C₄	1	4	yes	complemented
96	#41×C₄₁	—	2	2	no	—
97	#41×C₄₁	—	2	2	no	—
98	#41×C₄₁	C₂²×C₄	1	4	yes	—
99	#41×C₄₁	C₂²×C₄	1	4	yes	—
100	C₂×Q₈×C₄₁	C₂²×C₄	1	2	yes	—
101	C₂×D₄×C₄₁	—	2	2	no	—
102	C₂×D₄×C₄₁	C₂²×C₄	1	2	yes	—
103	C₂²×C₄×C₄₁	—	2	1	no	—
104	C₂²×C₄×C₄₁	—	2	2	no	—
105	C₂²×C₄×C₄₁	—	2	1	no	—
106	C₂²×C₄×C₄₁	—	2	4	no	—
107	C₂²×C₄×C₄₁	#41	1	2	yes	—
108	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
109	Q₁₆×C₄₁	C₄²	1	4	yes	complemented
110	SD₁₆×C₄₁	C₄²	1	8	yes	complemented
111	D₈×C₄₁	C₄²	1	4	yes	complemented
112	M₁₆×C₄₁	—	2	2	no	—
113	M₁₆×C₄₁	—	2	2	no	—
114	M₁₆×C₄₁	—	2	8	no	—
115	M₁₆×C₄₁	—	2	8	no	—
116	M₁₆×C₄₁	C₂²×C₄	1	4	yes	—
117	M₁₆×C₄₁	C₂²×C₄	1	4	yes	—
118	C₂×C₈×C₄₁	—	2	2	no	—
119	C₂×C₈×C₄₁	—	2	2	no	—
120	C₂×C₈×C₄₁	—	2	1	no	—
121	C₂×C₈×C₄₁	—	2	1	no	—
122	C₂×C₈×C₄₁	—	2	8	no	—
123	C₂×C₈×C₄₁	—	2	8	no	—
124	C₂×C₈×C₄₁	C₂²×C₄	1	2	yes	—
125	C₂×C₈×C₄₁	C₂²×C₄	1	2	yes	—
126	C₂×C₈×C₄₁	C₂²×C₄	1	1	yes	characteristic
127	C₂×C₈×C₄₁	C₂²×C₄	1	1	yes	characteristic
128	C₂×C₈×C₄₁	C₂²×C₄	1	2	yes	—
129	C₂×C₈×C₄₁	C₂²×C₄	1	2	yes	—
130	C₂×C₈×C₄₁	C₂²×C₄	1	2	yes	—
131	C₂×C₈×C₄₁	C₂×D₄	1	1	yes	characteristic
132	C₂×C₈×C₄₁	C₂×D₄	1	2	yes	—
133	C₂×C₈×C₄₁	C₂×D₄	1	1	yes	characteristic
134	C₂×C₈×C₄₁	#41	1	2	yes	—
135	C₂×C₈×C₄₁	#41	1	2	yes	—
136	C₄⋊C₄×C₄₁	—	2	4	no	—
137	C₄⋊C₄×C₄₁	C₂²×C₄	1	4	yes	—
138	C₂²⋊C₄×C₄₁	—	2	2	no	—
139	C₂²⋊C₄×C₄₁	—	2	4	no	—
140	C₄²×C₄₁	—	2	4	no	—
141	C₄²×C₄₁	—	2	2	no	—
142	C₄²×C₄₁	—	2	1	no	—
143	C₄²×C₄₁	—	2	1	no	—
144	C₄²×C₄₁	—	4	4	no	—
145	C₄²×C₄₁	C₂²×C₄	1	2	yes	—
146	C₄²×C₄₁	C₂²×C₄	1	2	yes	—
147	C₄²×C₄₁	C₂²×C₄	1	2	yes	—
148	C₄²×C₄₁	C₂×D₄	1	2	yes	—
149	C₂³×C₄₁	—	2	2	no	—
150	C₂³×C₄₁	C₂×#41	1	1	yes	characteristic
151	Q₈×C₄₁	—	2	2	no	—
152	Q₈×C₄₁	C₂×C₄²	1	4	yes	—
153	D₄×C₄₁	—	2	4	no	—
154	D₄×C₄₁	—	2	4	no	—
155	D₄×C₄₁	—	2	2	no	—
156	D₄×C₄₁	C₂×C₄²	1	4	yes	—
157	C₂×C₄×C₄₁	—	2	4	no	—
158	C₂×C₄×C₄₁	—	2	2	no	—
159	C₂×C₄×C₄₁	—	2	2	no	—
160	C₂×C₄×C₄₁	—	2	4	no	—
161	C₂×C₄×C₄₁	—	2	4	no	—
162	C₂×C₄×C₄₁	—	2	4	no	—
163	C₂×C₄×C₄₁	—	2	2	no	—
164	C₂×C₄×C₄₁	—	4	2	no	—
165	C₂×C₄×C₄₁	—	4	2	no	—
166	C₂×C₄×C₄₁	—	8	4	no	—
167	C₂×C₄×C₄₁	C₄×D₄	1	4	yes	—
168	C₂×C₄×C₄₁	C₂³×C₄	1	1	yes	characteristic
169	C₂×C₄×C₄₁	C₂³×C₄	1	1	yes	characteristic
170	C₂×C₄×C₄₁	C₂³×C₄	1	1	yes	characteristic
171	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
172	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
173	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
174	C₈×C₄₁	—	2	4	no	—
175	C₈×C₄₁	—	2	4	no	—
176	C₈×C₄₁	—	2	2	no	—
177	C₈×C₄₁	C₂×C₄²	1	2	yes	—
178	C₈×C₄₁	C₂×C₄²	1	2	yes	—
179	C₈×C₄₁	C₄×D₄	1	2	yes	—
180	C₈×C₄₁	C₄×D₄	1	4	yes	—
181	C₈×C₄₁	C₄×D₄	1	2	yes	—
182	#20512	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
183	C₂²×C₄₁	—	2	2	no	—
184	C₂²×C₄₁	—	2	4	no	—
185	C₂²×C₄₁	—	4	4	no	—
186	C₂²×C₄₁	C₂×C₄×D₄	1	1	yes	characteristic
187	C₂²×C₄₁	C₄×#41	1	1	yes	characteristic
188	C₂²×C₄₁	C₄×#41	1	1	yes	characteristic
189	C₄×C₄₁	—	2	4	no	—
190	C₄×C₄₁	—	2	4	no	—
191	C₄×C₄₁	—	2	4	no	—
192	C₄×C₄₁	—	4	2	no	—
193	C₄×C₄₁	—	4	4	no	—
194	C₄×C₄₁	C₂²×C₄²	1	1	yes	characteristic
195	C₄×C₄₁	C₂×C₄×D₄	1	1	yes	characteristic
196	C₄×C₄₁	C₂×C₄×D₄	1	1	yes	characteristic
197	C₄×C₄₁	C₄×#41	1	1	yes	characteristic
198	C₂×#444	C₂×C₄₁	1	1	yes	characteristic
199	C₂×#443	C₂×C₄₁	1	1	yes	characteristic
200	#2943	C₂×C₄₁	1	1	yes	characteristic
201	#2875	C₂×C₄₁	1	2	yes	complemented
202	#1778	C₂×C₄₁	1	1	yes	characteristic, complemented
203	#1773	C₂×C₄₁	1	1	yes	characteristic, complemented
204	#1772	C₂×C₄₁	1	1	yes	characteristic, complemented
205	#1765	C₂×C₄₁	1	2	yes	complemented
206	#1764	C₂×C₄₁	1	2	yes	complemented
207	C₄×#104	C₂×C₄₁	1	2	yes	complemented
208	C₄×#97	C₂×C₄₁	1	1	yes	characteristic, complemented
209	C₂×C₄₁	—	2	1	no	—
210	C₂×C₄₁	—	2	1	no	—
211	C₂×C₄₁	—	4	4	no	—
212	C₂×C₄₁	C₄²×D₄	1	1	yes	characteristic
213	C₂×C₄₁	#2956	1	2	yes	—
214	C₂×#135	C₂²×C₄₁	1	1	yes	characteristic
215	C₂×#131	C₂²×C₄₁	1	2	yes	—
216	C₂×#131	C₂²×C₄₁	1	2	yes	—
217	C₄×#41	C₂²×C₄₁	1	2	yes	—
218	#444	C₄×C₄₁	1	8	yes	complemented
219	#443	C₄×C₄₁	1	8	yes	complemented
220	#442	C₄×C₄₁	1	2	yes	complemented
221	#441	C₄×C₄₁	1	2	yes	complemented
222	#440	C₄×C₄₁	1	4	yes	complemented
223	C₂×#108	C₂²×C₄₁	1	1	yes	characteristic
224	C₂×#108	C₂²×C₄₁	1	1	yes	characteristic
225	#427	C₂²×C₄₁	1	1	yes	characteristic
226	C₂×#104	C₂²×C₄₁	1	2	yes	—
227	C₂×#104	C₂²×C₄₁	1	2	yes	—
228	#416	C₂²×C₄₁	1	2	yes	—
229	#405	—	2	2	no	—
230	#405	—	2	2	no	—
231	#405	C₂²×C₄₁	1	2	yes	—
232	#405	C₂²×C₄₁	1	2	yes	—
233	C₄×M₁₆	—	2	2	no	—
234	C₄×M₁₆	C₂²×C₄₁	1	2	yes	—
235	C₂×#97	—	2	2	no	—
236	C₂×#97	C₂²×C₄₁	1	1	yes	characteristic
237	C₂×#97	C₂²×C₄₁	1	1	yes	characteristic
238	C₂×#97	C₂²×C₄₁	1	1	yes	characteristic
239	C₂×#97	C₂²×C₄₁	1	1	yes	characteristic
240	C₂×C₄×C₈	C₂²×C₄₁	1	1	yes	characteristic
241	C₂×C₄×C₈	C₂²×C₄₁	1	1	yes	characteristic
242	C₄³	C₂²×C₄₁	1	1	yes	characteristic
243	#341	C₂²×C₄₁	1	2	yes	—
244	#339	C₂²×C₄₁	1	2	yes	—
245	#339	C₂²×C₄₁	1	2	yes	—
246	C₄₁	#20512	1	1	yes	characteristic, direct product factor, Sylow
247	C₂×#41	C₂³×C₄₁	1	2	yes	—
248	#135	C₂×C₄×C₄₁	1	4	yes	—
249	#135	C₂×C₄×C₄₁	1	4	yes	—
250	C₂×Q₁₆	C₂×C₄×C₄₁	1	1	yes	characteristic
251	C₂×SD₁₆	C₂×C₄×C₄₁	1	2	yes	—
252	C₂×D₈	C₂×C₄×C₄₁	1	1	yes	characteristic
253	#131	—	2	4	no	—
254	#131	—	2	4	no	—
255	#131	C₂×C₄×C₄₁	1	8	yes	complemented
256	#131	C₂×C₄×C₄₁	1	8	yes	complemented
257	C₂×M₁₆	—	2	2	no	—
258	C₂×M₁₆	—	2	2	no	—
259	C₂×M₁₆	C₂³×C₄₁	1	2	yes	—
260	C₂×M₁₆	C₂³×C₄₁	1	2	yes	—
261	C₂²×C₈	—	2	2	no	—
262	C₂²×C₈	—	2	2	no	—
263	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
264	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
265	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
266	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
267	C₄×Q₈	C₂×C₄×C₄₁	1	4	yes	—
268	C₄×D₄	—	2	4	no	—
269	C₄×D₄	C₂×C₄×C₄₁	1	4	yes	—
270	#117	—	2	2	no	—
271	#117	C₂³×C₄₁	1	2	yes	—
272	C₂×C₄²	—	2	2	no	—
273	C₂×C₄²	—	2	2	no	—
274	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
275	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
276	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
277	#108	C₂×C₄×C₄₁	1	4	yes	complemented
278	#108	C₂×C₄×C₄₁	1	4	yes	complemented
279	#107	C₂×C₄×C₄₁	1	2	yes	—
280	#106	C₂×C₄×C₄₁	1	2	yes	—
281	#104	C₂×C₄×C₄₁	1	8	yes	complemented
282	#104	C₂×C₄×C₄₁	1	8	yes	complemented
283	#103	C₂×C₄×C₄₁	1	4	yes	—
284	#102	C₂×C₄×C₄₁	1	4	yes	—
285	#97	—	2	2	no	—
286	#97	—	2	2	no	—
287	#97	—	2	2	no	—
288	#97	—	2	2	no	—
289	#97	C₂×C₄×C₄₁	1	2	yes	—
290	#97	C₂×C₄×C₄₁	1	2	yes	—
291	#97	C₂×C₄×C₄₁	1	4	yes	complemented
292	#97	D₄×C₄₁	1	2	yes	—
293	#97	D₄×C₄₁	1	2	yes	—
294	C₄×C₈	—	2	2	no	—
295	C₄×C₈	—	2	2	no	—
296	C₄×C₈	—	2	2	no	—
297	C₄×C₈	—	2	2	no	—
298	C₄×C₈	C₂×C₄×C₄₁	1	4	yes	complemented
299	#41	—	2	2	no	—
300	#41	—	2	2	no	—
301	#41	C₂²×C₄×C₄₁	1	4	yes	—
302	#41	C₂²×C₄×C₄₁	1	4	yes	—
303	C₂×Q₈	C₂²×C₄×C₄₁	1	2	yes	—
304	C₂×D₄	—	2	2	no	—
305	C₂×D₄	C₂²×C₄×C₄₁	1	2	yes	—
306	C₂²×C₄	—	2	1	no	—
307	C₂²×C₄	—	2	2	no	—
308	C₂²×C₄	—	2	1	no	—
309	C₂²×C₄	—	2	4	no	—
310	C₂²×C₄	#41×C₄₁	1	2	yes	—
311	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
312	Q₁₆	C₄²×C₄₁	1	4	yes	complemented
313	SD₁₆	C₄²×C₄₁	1	8	yes	complemented
314	D₈	C₄²×C₄₁	1	4	yes	complemented
315	M₁₆	—	2	2	no	—
316	M₁₆	—	2	2	no	—
317	M₁₆	—	2	8	no	—
318	M₁₆	—	2	8	no	—
319	M₁₆	C₂²×C₄×C₄₁	1	4	yes	—
320	M₁₆	C₂²×C₄×C₄₁	1	4	yes	—
321	C₂×C₈	—	2	2	no	—
322	C₂×C₈	—	2	2	no	—
323	C₂×C₈	—	2	1	no	—
324	C₂×C₈	—	2	1	no	—
325	C₂×C₈	—	2	8	no	—
326	C₂×C₈	—	2	8	no	—
327	C₂×C₈	C₂²×C₄×C₄₁	1	2	yes	—
328	C₂×C₈	C₂²×C₄×C₄₁	1	2	yes	—
329	C₂×C₈	C₂²×C₄×C₄₁	1	1	yes	characteristic
330	C₂×C₈	C₂²×C₄×C₄₁	1	1	yes	characteristic
331	C₂×C₈	C₂²×C₄×C₄₁	1	2	yes	—
332	C₂×C₈	C₂²×C₄×C₄₁	1	2	yes	—
333	C₂×C₈	C₂²×C₄×C₄₁	1	2	yes	—
334	C₂×C₈	C₂×D₄×C₄₁	1	1	yes	characteristic
335	C₂×C₈	C₂×D₄×C₄₁	1	2	yes	—
336	C₂×C₈	C₂×D₄×C₄₁	1	1	yes	characteristic
337	C₂×C₈	#41×C₄₁	1	2	yes	—
338	C₂×C₈	#41×C₄₁	1	2	yes	—
339	C₄⋊C₄	—	2	4	no	—
340	C₄⋊C₄	C₂²×C₄×C₄₁	1	4	yes	—
341	C₂²⋊C₄	—	2	2	no	—
342	C₂²⋊C₄	—	2	4	no	—
343	C₄²	—	2	4	no	—
344	C₄²	—	2	2	no	—
345	C₄²	—	2	1	no	—
346	C₄²	—	2	1	no	—
347	C₄²	—	4	4	no	—
348	C₄²	C₂²×C₄×C₄₁	1	2	yes	—
349	C₄²	C₂²×C₄×C₄₁	1	2	yes	—
350	C₄²	C₂²×C₄×C₄₁	1	2	yes	—
351	C₄²	C₂×D₄×C₄₁	1	2	yes	—
352	C₂³	—	2	2	no	—
353	C₂³	C₂×#41×C₄₁	1	1	yes	characteristic
354	Q₈	—	2	2	no	—
355	Q₈	C₂×C₄²×C₄₁	1	4	yes	—
356	D₄	—	2	4	no	—
357	D₄	—	2	4	no	—
358	D₄	—	2	2	no	—
359	D₄	C₂×C₄²×C₄₁	1	4	yes	—
360	C₂×C₄	—	2	4	no	—
361	C₂×C₄	—	2	2	no	—
362	C₂×C₄	—	2	2	no	—
363	C₂×C₄	—	2	4	no	—
364	C₂×C₄	—	2	4	no	—
365	C₂×C₄	—	2	4	no	—
366	C₂×C₄	—	2	2	no	—
367	C₂×C₄	—	4	2	no	—
368	C₂×C₄	—	4	2	no	—
369	C₂×C₄	—	8	4	no	—
370	C₂×C₄	C₄×D₄×C₄₁	1	4	yes	—
371	C₂×C₄	C₂³×C₄×C₄₁	1	1	yes	characteristic
372	C₂×C₄	C₂³×C₄×C₄₁	1	1	yes	characteristic
373	C₂×C₄	C₂³×C₄×C₄₁	1	1	yes	characteristic
374	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
375	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
376	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
377	C₈	—	2	4	no	—
378	C₈	—	2	4	no	—
379	C₈	—	2	2	no	—
380	C₈	C₂×C₄²×C₄₁	1	2	yes	—
381	C₈	C₂×C₄²×C₄₁	1	2	yes	—
382	C₈	C₄×D₄×C₄₁	1	2	yes	—
383	C₈	C₄×D₄×C₄₁	1	4	yes	—
384	C₈	C₄×D₄×C₄₁	1	2	yes	—
385	C₂²	—	2	2	no	—
386	C₂²	—	2	4	no	—
387	C₂²	—	4	4	no	—
388	C₂²	C₂×C₄×D₄×C₄₁	1	1	yes	characteristic
389	C₂²	C₄×#41×C₄₁	1	1	yes	characteristic
390	C₂²	C₄×#41×C₄₁	1	1	yes	characteristic
391	C₄	—	2	4	no	—
392	C₄	—	2	4	no	—
393	C₄	—	2	4	no	—
394	C₄	—	4	2	no	—
395	C₄	—	4	4	no	—
396	C₄	C₂²×C₄²×C₄₁	1	1	yes	characteristic
397	C₄	C₂×C₄×D₄×C₄₁	1	1	yes	characteristic
398	C₄	C₂×C₄×D₄×C₄₁	1	1	yes	characteristic
399	C₄	C₄×#41×C₄₁	1	1	yes	characteristic
400	C₂	—	2	1	no	—
401	C₂	—	2	1	no	—
402	C₂	—	4	4	no	—
403	C₂	C₄²×D₄×C₄₁	1	1	yes	characteristic
404	C₂	C₄₁×#2956	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₄₁	C₂²×D₄
commutator	C₄	C₂²×C₄²×C₄₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₁
socle	C₂²×C₄₁	C₂×C₄×D₄
prime radical	C₂×#135×C₄₁	C₂²
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₄₁ ◁ C₂×#97×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₄₁×#2875	C₂	semidirect
5. C₄₁×#1778	C₂	semidirect
6. C₄₁×#1773	C₂	semidirect
7. C₄₁×#1772	C₂	semidirect
8. C₄₁×#1765	C₂	semidirect
9. C₄₁×#1764	C₂	semidirect
10. C₄×#104×C₄₁	C₂	semidirect
11. C₄×#97×C₄₁	C₂	semidirect
16. C₄₁×#444	C₄	semidirect
17. C₄₁×#443	C₄	semidirect
18. C₄₁×#442	C₄	semidirect
19. C₄₁×#441	C₄	semidirect
20. C₄₁×#440	C₄	semidirect
52. #131×C₄₁	C₂×C₄	semidirect
53. #131×C₄₁	C₂×C₄	semidirect
74. #108×C₄₁	C₂×C₄	semidirect
75. #108×C₄₁	C₂×C₄	semidirect
78. #104×C₄₁	C₂×C₄	semidirect
79. #104×C₄₁	C₂×C₄	semidirect
88. #97×C₄₁	C₂×C₄	semidirect
95. C₄×C₈×C₄₁	C₂×C₄	semidirect
109. Q₁₆×C₄₁	C₄²	semidirect
110. SD₁₆×C₄₁	C₄²	semidirect
111. D₈×C₄₁	C₄²	semidirect
182. #20512	C₄₁	direct (N × H)
201. #2875	C₂×C₄₁	semidirect
202. #1778	C₂×C₄₁	semidirect
203. #1773	C₂×C₄₁	semidirect
204. #1772	C₂×C₄₁	semidirect
205. #1765	C₂×C₄₁	semidirect
206. #1764	C₂×C₄₁	semidirect
207. C₄×#104	C₂×C₄₁	semidirect
208. C₄×#97	C₂×C₄₁	semidirect
218. #444	C₄×C₄₁	semidirect
219. #443	C₄×C₄₁	semidirect
220. #442	C₄×C₄₁	semidirect
221. #441	C₄×C₄₁	semidirect
222. #440	C₄×C₄₁	semidirect
246. C₄₁	#20512	direct (N × H)
255. #131	C₂×C₄×C₄₁	semidirect
256. #131	C₂×C₄×C₄₁	semidirect
277. #108	C₂×C₄×C₄₁	semidirect
278. #108	C₂×C₄×C₄₁	semidirect
281. #104	C₂×C₄×C₄₁	semidirect
282. #104	C₂×C₄×C₄₁	semidirect
291. #97	C₂×C₄×C₄₁	semidirect
298. C₄×C₈	C₂×C₄×C₄₁	semidirect
312. Q₁₆	C₄²×C₄₁	semidirect
313. SD₁₆	C₄²×C₄₁	semidirect
314. D₈	C₄²×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×#444	2
C₂×C₄₁×#443	2
C₄₁×#2943	2
C₄₁×#2875	2
C₄₁×#1778	2
C₄₁×#1773	2
C₄₁×#1772	2
C₄₁×#1765	2
C₄₁×#1764	2
C₄×#104×C₄₁	2
C₄×#97×C₄₁	2
#20512	41

Subgroups — C41×#20512 #23796713

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#20512 #23796713