Subgroups — C₄₁×#21061 #23797262

Order 10496.

1126 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₁×#428	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄₁×#419	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄₁×#419	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄₁×#391	C₂	1	1	yes	maximal, characteristic
5	C₄×#117×C₄₁	C₂	1	1	yes	maximal, characteristic
6	C₄₁×#1928	C₂	1	4	yes	maximal, complemented
7	C₄₁×#1927	C₂	1	4	yes	maximal, complemented
8	C₄₁×#1736	C₂	1	1	yes	maximal, characteristic
9	C₄₁×#1728	C₂	1	1	yes	maximal, characteristic
10	C₂³×Q₈×C₄₁	C₂²	1	1	yes	characteristic
11	C₂²×M₁₆×C₄₁	C₂²	1	1	yes	characteristic
12	C₂²×M₁₆×C₄₁	C₂²	1	1	yes	characteristic
13	C₂×#117×C₄₁	C₂²	1	1	yes	characteristic
14	C₂×#117×C₄₁	C₂²	1	1	yes	characteristic
15	C₂²×C₄⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
16	C₂²×C₄²×C₄₁	C₂²	1	1	yes	characteristic
17	C₄₁×#428	—	2	4	no	—
18	C₂×#107×C₄₁	C₂²	1	2	yes	—
19	C₂×#106×C₄₁	C₂²	1	2	yes	—
20	C₄₁×#419	—	2	4	no	—
21	C₄₁×#419	C₄	1	8	yes	complemented
22	C₂×#103×C₄₁	C₂²	1	2	yes	—
23	C₂×#103×C₄₁	C₂²	1	2	yes	—
24	C₂×#103×C₄₁	C₂²	1	4	yes	—
25	C₄₁×#391	—	2	1	no	—
26	C₄₁×#391	—	2	1	no	—
27	C₄₁×#391	C₂²	1	4	yes	—
28	C₄×C₄⋊C₄×C₄₁	C₂²	1	2	yes	—
29	C₄×C₄⋊C₄×C₄₁	C₂²	1	2	yes	—
30	C₄×C₂²⋊C₄×C₄₁	—	2	2	no	—
31	C₄₁×#376	—	2	1	no	—
32	C₂×#95×C₄₁	—	2	2	no	—
33	C₄³×C₄₁	—	2	1	no	—
34	C₄₁×#340	C₂²	1	4	yes	—
35	C₄₁×#336	C₂²	1	4	yes	—
36	C₂²×Q₈×C₄₁	—	2	1	no	—
37	C₂²×Q₈×C₄₁	—	2	2	no	—
38	C₂²×Q₈×C₄₁	—	2	2	no	—
39	C₂²×Q₈×C₄₁	—	2	2	no	—
40	C₂²×Q₈×C₄₁	—	2	2	no	—
41	C₂²×Q₈×C₄₁	—	2	2	no	—
42	C₂²×Q₈×C₄₁	C₂×C₄	1	4	yes	—
43	C₂²×Q₈×C₄₁	C₂³	1	2	yes	—
44	C₂³×C₄×C₄₁	—	2	1	no	—
45	C₂³×C₄×C₄₁	—	2	1	no	—
46	C₂³×C₄×C₄₁	D₄	1	2	yes	—
47	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
48	C₂×M₁₆×C₄₁	—	2	2	no	—
49	C₂×M₁₆×C₄₁	—	2	2	no	—
50	C₂×M₁₆×C₄₁	—	2	2	no	—
51	C₂×M₁₆×C₄₁	—	2	2	no	—
52	C₂×M₁₆×C₄₁	—	2	2	no	—
53	C₂×M₁₆×C₄₁	C₂×C₄	1	4	yes	—
54	C₂²×C₈×C₄₁	C₂³	1	2	yes	—
55	C₂²×C₈×C₄₁	C₂³	1	2	yes	—
56	#117×C₄₁	—	2	2	no	—
57	#117×C₄₁	—	2	2	no	—
58	#117×C₄₁	C₂×C₄	1	4	yes	—
59	#117×C₄₁	D₄	1	4	yes	—
60	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
61	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
62	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
63	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
64	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
65	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
66	C₂×C₄⋊C₄×C₄₁	C₂³	1	1	yes	characteristic
67	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
68	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
69	C₂×C₄²×C₄₁	—	2	1	no	—
70	C₂×C₄²×C₄₁	—	2	1	no	—
71	C₂×C₄²×C₄₁	—	2	2	no	—
72	C₂×C₄²×C₄₁	—	2	2	no	—
73	C₂×C₄²×C₄₁	—	2	2	no	—
74	C₂×C₄²×C₄₁	—	2	2	no	—
75	C₂×C₄²×C₄₁	D₄	1	1	yes	characteristic
76	C₂×C₄²×C₄₁	D₄	1	1	yes	characteristic
77	C₂×C₄²×C₄₁	C₂³	1	2	yes	—
78	#107×C₄₁	—	2	4	no	—
79	#106×C₄₁	—	2	4	no	—
80	#103×C₄₁	—	2	4	no	—
81	#103×C₄₁	—	2	4	no	—
82	#103×C₄₁	C₂×C₄	1	16	yes	complemented
83	#95×C₄₁	—	2	4	no	—
84	#95×C₄₁	—	2	4	no	—
85	#95×C₄₁	—	2	2	no	—
86	#95×C₄₁	—	2	2	no	—
87	C₂⁴×C₄₁	C₂×D₄	1	1	yes	characteristic
88	C₂×Q₈×C₄₁	—	2	4	no	—
89	C₂×Q₈×C₄₁	—	2	2	no	—
90	C₂×Q₈×C₄₁	—	2	8	no	—
91	C₂×Q₈×C₄₁	—	2	8	no	—
92	C₂×Q₈×C₄₁	—	2	2	no	—
93	C₂×Q₈×C₄₁	—	2	2	no	—
94	C₂×Q₈×C₄₁	—	2	2	no	—
95	C₂×Q₈×C₄₁	—	2	2	no	—
96	C₂×Q₈×C₄₁	—	4	2	no	—
97	C₂×Q₈×C₄₁	—	4	2	no	—
98	C₂×Q₈×C₄₁	—	4	4	no	—
99	C₂×Q₈×C₄₁	—	4	4	no	—
100	C₂×Q₈×C₄₁	C₂²×C₄	1	4	yes	—
101	C₂²×C₄×C₄₁	—	2	4	no	—
102	C₂²×C₄×C₄₁	—	2	4	no	—
103	C₂²×C₄×C₄₁	—	2	2	no	—
104	C₂²×C₄×C₄₁	—	2	2	no	—
105	C₂²×C₄×C₄₁	—	2	1	no	—
106	C₂²×C₄×C₄₁	—	2	1	no	—
107	C₂²×C₄×C₄₁	—	2	4	no	—
108	C₂²×C₄×C₄₁	—	2	2	no	—
109	C₂²×C₄×C₄₁	—	4	2	no	—
110	C₂²×C₄×C₄₁	—	4	2	no	—
111	C₂²×C₄×C₄₁	—	4	2	no	—
112	C₂²×C₄×C₄₁	—	4	4	no	—
113	C₂²×C₄×C₄₁	—	4	2	no	—
114	C₂²×C₄×C₄₁	C₂²×C₄	1	2	yes	—
115	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
116	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
117	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
118	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
119	C₂²×C₄×C₄₁	#41	1	2	yes	—
120	C₂²×C₄×C₄₁	#41	1	2	yes	—
121	C₂²×C₄×C₄₁	#41	1	2	yes	—
122	C₂²×C₄×C₄₁	#41	1	2	yes	—
123	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
124	M₁₆×C₄₁	—	2	8	no	—
125	M₁₆×C₄₁	—	4	4	no	—
126	C₂×C₈×C₄₁	—	2	2	no	—
127	C₂×C₈×C₄₁	—	2	2	no	—
128	C₂×C₈×C₄₁	—	2	2	no	—
129	C₂×C₈×C₄₁	—	2	2	no	—
130	C₂×C₈×C₄₁	—	2	2	no	—
131	C₂×C₈×C₄₁	C₂²×C₄	1	4	yes	—
132	C₄⋊C₄×C₄₁	—	2	2	no	—
133	C₄⋊C₄×C₄₁	—	2	1	no	—
134	C₄⋊C₄×C₄₁	—	2	1	no	—
135	C₄⋊C₄×C₄₁	—	2	2	no	—
136	C₄⋊C₄×C₄₁	—	2	2	no	—
137	C₄⋊C₄×C₄₁	—	4	2	no	—
138	C₄⋊C₄×C₄₁	C₂²×C₄	1	4	yes	—
139	C₄⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
140	C₄⋊C₄×C₄₁	C₂×D₄	1	2	yes	—
141	C₂²⋊C₄×C₄₁	—	2	4	no	—
142	C₂²⋊C₄×C₄₁	—	2	4	no	—
143	C₄²×C₄₁	—	2	4	no	—
144	C₄²×C₄₁	—	2	4	no	—
145	C₄²×C₄₁	—	2	2	no	—
146	C₄²×C₄₁	—	2	2	no	—
147	C₄²×C₄₁	—	2	2	no	—
148	C₄²×C₄₁	—	2	2	no	—
149	C₄²×C₄₁	—	4	4	no	—
150	C₄²×C₄₁	—	4	4	no	—
151	C₂³×C₄₁	—	2	2	no	—
152	C₂³×C₄₁	—	2	2	no	—
153	C₂³×C₄₁	C₄×D₄	1	2	yes	—
154	C₂³×C₄₁	#121	1	2	yes	—
155	C₂³×C₄₁	#123	1	2	yes	—
156	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
157	Q₈×C₄₁	—	2	4	no	—
158	Q₈×C₄₁	—	2	4	no	—
159	Q₈×C₄₁	—	4	2	no	—
160	Q₈×C₄₁	—	4	2	no	—
161	Q₈×C₄₁	—	4	8	no	—
162	C₂×C₄×C₄₁	—	2	2	no	—
163	C₂×C₄×C₄₁	—	2	2	no	—
164	C₂×C₄×C₄₁	—	2	4	no	—
165	C₂×C₄×C₄₁	—	2	4	no	—
166	C₂×C₄×C₄₁	—	2	2	no	—
167	C₂×C₄×C₄₁	—	2	2	no	—
168	C₂×C₄×C₄₁	—	2	2	no	—
169	C₂×C₄×C₄₁	—	2	2	no	—
170	C₂×C₄×C₄₁	—	2	2	no	—
171	C₂×C₄×C₄₁	—	4	8	no	—
172	C₂×C₄×C₄₁	—	4	2	no	—
173	C₂×C₄×C₄₁	—	4	2	no	—
174	C₂×C₄×C₄₁	—	4	2	no	—
175	C₂×C₄×C₄₁	—	4	2	no	—
176	C₂×C₄×C₄₁	—	4	2	no	—
177	C₂×C₄×C₄₁	—	4	2	no	—
178	C₂×C₄×C₄₁	—	4	8	no	—
179	C₂×C₄×C₄₁	—	4	2	no	—
180	C₂×C₄×C₄₁	—	4	4	no	—
181	C₂×C₄×C₄₁	—	8	4	no	—
182	C₂×C₄×C₄₁	#117	1	4	yes	—
183	C₂×C₄×C₄₁	C₄×D₄	1	4	yes	—
184	C₂×C₄×C₄₁	C₄×D₄	1	2	yes	—
185	C₂×C₄×C₄₁	#121	1	2	yes	—
186	C₂×C₄×C₄₁	#123	1	2	yes	—
187	C₂×C₄×C₄₁	#124	1	4	yes	—
188	C₂×C₄×C₄₁	#126	1	4	yes	—
189	C₂×C₄×C₄₁	#137	1	4	yes	—
190	C₂×C₄×C₄₁	C₂³×C₄	1	1	yes	characteristic
191	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
192	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
193	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
194	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
195	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
196	C₈×C₄₁	—	2	4	no	—
197	C₈×C₄₁	—	4	2	no	—
198	#21061	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
199	C₂²×C₄₁	—	2	4	no	—
200	C₂²×C₄₁	—	2	4	no	—
201	C₂²×C₄₁	—	2	2	no	—
202	C₂²×C₄₁	—	2	2	no	—
203	C₂²×C₄₁	#388	1	4	yes	—
204	C₂²×C₄₁	C₂×C₄×D₄	1	1	yes	characteristic
205	C₂²×C₄₁	C₂×#121	1	1	yes	characteristic
206	C₂²×C₄₁	C₂×#123	1	1	yes	characteristic
207	C₂²×C₄₁	C₂×#137	1	2	yes	—
208	C₂²×C₄₁	#575	1	2	yes	—
209	C₄×C₄₁	—	2	4	no	—
210	C₄×C₄₁	—	4	2	no	—
211	C₄×C₄₁	—	4	4	no	—
212	C₄×C₄₁	—	4	2	no	—
213	C₄×C₄₁	—	4	2	no	—
214	C₄×C₄₁	—	4	4	no	—
215	C₄×C₄₁	—	8	2	no	—
216	C₄×C₄₁	#388	1	4	yes	—
217	C₄×C₄₁	C₂×#117	1	1	yes	characteristic
218	C₄×C₄₁	C₂×C₄×D₄	1	1	yes	characteristic
219	C₄×C₄₁	C₂×#124	1	1	yes	characteristic
220	C₄×C₄₁	C₂×#126	1	1	yes	characteristic
221	C₂×#428	C₂×C₄₁	1	1	yes	characteristic
222	C₂×#419	C₂×C₄₁	1	1	yes	characteristic
223	C₂×#419	C₂×C₄₁	1	1	yes	characteristic
224	C₂×#391	C₂×C₄₁	1	1	yes	characteristic
225	C₄×#117	C₂×C₄₁	1	1	yes	characteristic
226	#1928	C₂×C₄₁	1	4	yes	complemented
227	#1927	C₂×C₄₁	1	4	yes	complemented
228	#1736	C₂×C₄₁	1	1	yes	characteristic
229	#1728	C₂×C₄₁	1	1	yes	characteristic
230	C₂×C₄₁	—	2	4	no	—
231	C₂×C₄₁	C₂×#388	1	1	yes	characteristic
232	C₂×C₄₁	C₄×#137	1	2	yes	—
233	C₂×C₄₁	#3039	1	1	yes	characteristic
234	C₂×C₄₁	#3040	1	1	yes	characteristic
235	C₂×C₄₁	#3095	1	2	yes	—
236	C₂³×Q₈	C₂²×C₄₁	1	1	yes	characteristic
237	C₂²×M₁₆	C₂²×C₄₁	1	1	yes	characteristic
238	C₂²×M₁₆	C₂²×C₄₁	1	1	yes	characteristic
239	C₂×#117	C₂²×C₄₁	1	1	yes	characteristic
240	C₂×#117	C₂²×C₄₁	1	1	yes	characteristic
241	C₂²×C₄⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
242	C₂²×C₄²	C₂²×C₄₁	1	1	yes	characteristic
243	#428	—	2	4	no	—
244	C₂×#107	C₂²×C₄₁	1	2	yes	—
245	C₂×#106	C₂²×C₄₁	1	2	yes	—
246	#419	—	2	4	no	—
247	#419	C₄×C₄₁	1	8	yes	complemented
248	C₂×#103	C₂²×C₄₁	1	2	yes	—
249	C₂×#103	C₂²×C₄₁	1	2	yes	—
250	C₂×#103	C₂²×C₄₁	1	4	yes	—
251	#391	—	2	1	no	—
252	#391	—	2	1	no	—
253	#391	C₂²×C₄₁	1	4	yes	—
254	C₄×C₄⋊C₄	C₂²×C₄₁	1	2	yes	—
255	C₄×C₄⋊C₄	C₂²×C₄₁	1	2	yes	—
256	C₄×C₂²⋊C₄	—	2	2	no	—
257	#376	—	2	1	no	—
258	C₂×#95	—	2	2	no	—
259	C₄³	—	2	1	no	—
260	#340	C₂²×C₄₁	1	4	yes	—
261	#336	C₂²×C₄₁	1	4	yes	—
262	C₄₁	#21061	1	1	yes	characteristic, direct product factor, Sylow
263	C₂²×Q₈	—	2	1	no	—
264	C₂²×Q₈	—	2	2	no	—
265	C₂²×Q₈	—	2	2	no	—
266	C₂²×Q₈	—	2	2	no	—
267	C₂²×Q₈	—	2	2	no	—
268	C₂²×Q₈	—	2	2	no	—
269	C₂²×Q₈	C₂×C₄×C₄₁	1	4	yes	—
270	C₂²×Q₈	C₂³×C₄₁	1	2	yes	—
271	C₂³×C₄	—	2	1	no	—
272	C₂³×C₄	—	2	1	no	—
273	C₂³×C₄	D₄×C₄₁	1	2	yes	—
274	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
275	C₂×M₁₆	—	2	2	no	—
276	C₂×M₁₆	—	2	2	no	—
277	C₂×M₁₆	—	2	2	no	—
278	C₂×M₁₆	—	2	2	no	—
279	C₂×M₁₆	—	2	2	no	—
280	C₂×M₁₆	C₂×C₄×C₄₁	1	4	yes	—
281	C₂²×C₈	C₂³×C₄₁	1	2	yes	—
282	C₂²×C₈	C₂³×C₄₁	1	2	yes	—
283	#117	—	2	2	no	—
284	#117	—	2	2	no	—
285	#117	C₂×C₄×C₄₁	1	4	yes	—
286	#117	D₄×C₄₁	1	4	yes	—
287	C₂×C₄⋊C₄	—	2	2	no	—
288	C₂×C₄⋊C₄	—	2	2	no	—
289	C₂×C₄⋊C₄	—	2	1	no	—
290	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
291	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
292	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
293	C₂×C₄⋊C₄	C₂³×C₄₁	1	1	yes	characteristic
294	C₂×C₂²⋊C₄	—	2	1	no	—
295	C₂×C₂²⋊C₄	—	2	1	no	—
296	C₂×C₄²	—	2	1	no	—
297	C₂×C₄²	—	2	1	no	—
298	C₂×C₄²	—	2	2	no	—
299	C₂×C₄²	—	2	2	no	—
300	C₂×C₄²	—	2	2	no	—
301	C₂×C₄²	—	2	2	no	—
302	C₂×C₄²	D₄×C₄₁	1	1	yes	characteristic
303	C₂×C₄²	D₄×C₄₁	1	1	yes	characteristic
304	C₂×C₄²	C₂³×C₄₁	1	2	yes	—
305	#107	—	2	4	no	—
306	#106	—	2	4	no	—
307	#103	—	2	4	no	—
308	#103	—	2	4	no	—
309	#103	C₂×C₄×C₄₁	1	16	yes	complemented
310	#95	—	2	4	no	—
311	#95	—	2	4	no	—
312	#95	—	2	2	no	—
313	#95	—	2	2	no	—
314	C₂⁴	C₂×D₄×C₄₁	1	1	yes	characteristic
315	C₂×Q₈	—	2	4	no	—
316	C₂×Q₈	—	2	2	no	—
317	C₂×Q₈	—	2	8	no	—
318	C₂×Q₈	—	2	8	no	—
319	C₂×Q₈	—	2	2	no	—
320	C₂×Q₈	—	2	2	no	—
321	C₂×Q₈	—	2	2	no	—
322	C₂×Q₈	—	2	2	no	—
323	C₂×Q₈	—	4	2	no	—
324	C₂×Q₈	—	4	2	no	—
325	C₂×Q₈	—	4	4	no	—
326	C₂×Q₈	—	4	4	no	—
327	C₂×Q₈	C₂²×C₄×C₄₁	1	4	yes	—
328	C₂²×C₄	—	2	4	no	—
329	C₂²×C₄	—	2	4	no	—
330	C₂²×C₄	—	2	2	no	—
331	C₂²×C₄	—	2	2	no	—
332	C₂²×C₄	—	2	1	no	—
333	C₂²×C₄	—	2	1	no	—
334	C₂²×C₄	—	2	4	no	—
335	C₂²×C₄	—	2	2	no	—
336	C₂²×C₄	—	4	2	no	—
337	C₂²×C₄	—	4	2	no	—
338	C₂²×C₄	—	4	2	no	—
339	C₂²×C₄	—	4	4	no	—
340	C₂²×C₄	—	4	2	no	—
341	C₂²×C₄	C₂²×C₄×C₄₁	1	2	yes	—
342	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
343	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
344	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
345	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
346	C₂²×C₄	#41×C₄₁	1	2	yes	—
347	C₂²×C₄	#41×C₄₁	1	2	yes	—
348	C₂²×C₄	#41×C₄₁	1	2	yes	—
349	C₂²×C₄	#41×C₄₁	1	2	yes	—
350	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
351	M₁₆	—	2	8	no	—
352	M₁₆	—	4	4	no	—
353	C₂×C₈	—	2	2	no	—
354	C₂×C₈	—	2	2	no	—
355	C₂×C₈	—	2	2	no	—
356	C₂×C₈	—	2	2	no	—
357	C₂×C₈	—	2	2	no	—
358	C₂×C₈	C₂²×C₄×C₄₁	1	4	yes	—
359	C₄⋊C₄	—	2	2	no	—
360	C₄⋊C₄	—	2	1	no	—
361	C₄⋊C₄	—	2	1	no	—
362	C₄⋊C₄	—	2	2	no	—
363	C₄⋊C₄	—	2	2	no	—
364	C₄⋊C₄	—	4	2	no	—
365	C₄⋊C₄	C₂²×C₄×C₄₁	1	4	yes	—
366	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
367	C₄⋊C₄	C₂×D₄×C₄₁	1	2	yes	—
368	C₂²⋊C₄	—	2	4	no	—
369	C₂²⋊C₄	—	2	4	no	—
370	C₄²	—	2	4	no	—
371	C₄²	—	2	4	no	—
372	C₄²	—	2	2	no	—
373	C₄²	—	2	2	no	—
374	C₄²	—	2	2	no	—
375	C₄²	—	2	2	no	—
376	C₄²	—	4	4	no	—
377	C₄²	—	4	4	no	—
378	C₂³	—	2	2	no	—
379	C₂³	—	2	2	no	—
380	C₂³	C₄×D₄×C₄₁	1	2	yes	—
381	C₂³	#121×C₄₁	1	2	yes	—
382	C₂³	#123×C₄₁	1	2	yes	—
383	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
384	Q₈	—	2	4	no	—
385	Q₈	—	2	4	no	—
386	Q₈	—	4	2	no	—
387	Q₈	—	4	2	no	—
388	Q₈	—	4	8	no	—
389	C₂×C₄	—	2	2	no	—
390	C₂×C₄	—	2	2	no	—
391	C₂×C₄	—	2	4	no	—
392	C₂×C₄	—	2	4	no	—
393	C₂×C₄	—	2	2	no	—
394	C₂×C₄	—	2	2	no	—
395	C₂×C₄	—	2	2	no	—
396	C₂×C₄	—	2	2	no	—
397	C₂×C₄	—	2	2	no	—
398	C₂×C₄	—	4	8	no	—
399	C₂×C₄	—	4	2	no	—
400	C₂×C₄	—	4	2	no	—
401	C₂×C₄	—	4	2	no	—
402	C₂×C₄	—	4	2	no	—
403	C₂×C₄	—	4	2	no	—
404	C₂×C₄	—	4	2	no	—
405	C₂×C₄	—	4	8	no	—
406	C₂×C₄	—	4	2	no	—
407	C₂×C₄	—	4	4	no	—
408	C₂×C₄	—	8	4	no	—
409	C₂×C₄	#117×C₄₁	1	4	yes	—
410	C₂×C₄	C₄×D₄×C₄₁	1	4	yes	—
411	C₂×C₄	C₄×D₄×C₄₁	1	2	yes	—
412	C₂×C₄	#121×C₄₁	1	2	yes	—
413	C₂×C₄	#123×C₄₁	1	2	yes	—
414	C₂×C₄	#124×C₄₁	1	4	yes	—
415	C₂×C₄	#126×C₄₁	1	4	yes	—
416	C₂×C₄	#137×C₄₁	1	4	yes	—
417	C₂×C₄	C₂³×C₄×C₄₁	1	1	yes	characteristic
418	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
419	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
420	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
421	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
422	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
423	C₈	—	2	4	no	—
424	C₈	—	4	2	no	—
425	C₂²	—	2	2	no	—
426	C₂²	—	2	2	no	—
427	C₂²	—	2	4	no	—
428	C₂²	—	2	4	no	—
429	C₂²	C₄₁×#388	1	4	yes	—
430	C₂²	C₂×C₄×D₄×C₄₁	1	1	yes	characteristic
431	C₂²	C₂×#121×C₄₁	1	1	yes	characteristic
432	C₂²	C₂×#123×C₄₁	1	1	yes	characteristic
433	C₂²	C₂×#137×C₄₁	1	2	yes	—
434	C₂²	C₄₁×#575	1	2	yes	—
435	C₄	—	2	4	no	—
436	C₄	—	4	2	no	—
437	C₄	—	4	2	no	—
438	C₄	—	4	4	no	—
439	C₄	—	4	2	no	—
440	C₄	—	4	4	no	—
441	C₄	—	8	2	no	—
442	C₄	C₄₁×#388	1	4	yes	—
443	C₄	C₂×#117×C₄₁	1	1	yes	characteristic
444	C₄	C₂×C₄×D₄×C₄₁	1	1	yes	characteristic
445	C₄	C₂×#124×C₄₁	1	1	yes	characteristic
446	C₄	C₂×#126×C₄₁	1	1	yes	characteristic
447	C₂	—	2	4	no	—
448	C₂	C₂×C₄₁×#388	1	1	yes	characteristic
449	C₂	C₄×#137×C₄₁	1	2	yes	—
450	C₂	C₄₁×#3039	1	1	yes	characteristic
451	C₂	C₄₁×#3040	1	1	yes	characteristic
452	C₂	C₄₁×#3095	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	C₂⁴×C₄₁	C₂×D₄
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
6. C₄₁×#1928	C₂	semidirect
7. C₄₁×#1927	C₂	semidirect
21. C₄₁×#419	C₄	semidirect
82. #103×C₄₁	C₂×C₄	semidirect
198. #21061	C₄₁	direct (N × H)
226. #1928	C₂×C₄₁	semidirect
227. #1927	C₂×C₄₁	semidirect
247. #419	C₄×C₄₁	semidirect
262. C₄₁	#21061	direct (N × H)
309. #103	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×#428	2
C₂×C₄₁×#419	2
C₂×C₄₁×#391	2
C₄×#117×C₄₁	2
C₄₁×#1928	2
C₄₁×#1927	2
C₄₁×#1736	2
C₄₁×#1728	2
#21061	41

Subgroups — C41×#21061 #23797262

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#21061 #23797262