Subgroups — C₄₁×#23613 #23799814

Order 10496.

1054 conjugacy classes of subgroups.

The subgroup lattice has 442 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₁×#427	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄₁×#424	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄₁×#419	C₂	1	1	yes	maximal, characteristic
4	C₂²×#103×C₄₁	C₂	1	1	yes	maximal, characteristic
5	C₄₁×#2317	C₂	1	1	yes	maximal, characteristic
6	C₄₁×#2310	C₂	1	1	yes	maximal, characteristic
7	C₄₁×#2068	C₂	1	4	yes	maximal, complemented
8	C₄₁×#2066	C₂	1	4	yes	maximal, complemented
9	C₄₁×#1736	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	C₂³×C₈×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	C₂×#117×C₄₁	C₂²	1	1	yes	characteristic
16	C₂²×C₄⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
17	C₄₁×#427	—	2	4	no	—
18	C₂×#107×C₄₁	C₂²	1	2	yes	—
19	C₂×#106×C₄₁	C₂²	1	2	yes	—
20	C₄₁×#424	—	2	4	no	—
21	C₂×C₄⋊C₈×C₄₁	C₂²	1	2	yes	—
22	C₂×C₄⋊C₈×C₄₁	C₂²	1	2	yes	—
23	C₄₁×#419	—	2	4	no	—
24	C₂×#103×C₄₁	—	2	4	no	—
25	C₂×#103×C₄₁	C₂²	1	2	yes	—
26	C₂×#103×C₄₁	C₂²	1	4	yes	—
27	C₂×#103×C₄₁	C₂²	1	2	yes	—
28	C₄₁×#391	—	2	1	no	—
29	C₄₁×#391	—	2	1	no	—
30	C₄₁×#391	C₂²	1	4	yes	—
31	C₄₁×#389	C₂²	1	4	yes	—
32	C₄₁×#385	—	2	2	no	—
33	C₄₁×#384	—	2	1	no	—
34	C₄₁×#382	—	2	1	no	—
35	C₄₁×#381	—	2	2	no	—
36	C₄₁×#340	C₂²	1	4	yes	—
37	C₂²×Q₈×C₄₁	—	2	1	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	—	2	2	no	—
43	C₂²×Q₈×C₄₁	Q₈	1	4	yes	—
44	C₂²×Q₈×C₄₁	C₂³	1	2	yes	—
45	C₂³×C₄×C₄₁	—	2	1	no	—
46	C₂³×C₄×C₄₁	—	2	1	no	—
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	C₂²×C₈×C₄₁	—	2	2	no	—
52	C₂²×C₈×C₄₁	—	2	2	no	—
53	C₂²×C₈×C₄₁	D₄	1	4	yes	—
54	C₂²×C₈×C₄₁	C₂³	1	2	yes	—
55	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
56	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
57	#117×C₄₁	—	2	2	no	—
58	#117×C₄₁	—	2	2	no	—
59	#117×C₄₁	—	2	2	no	—
60	#117×C₄₁	—	2	2	no	—
61	#117×C₄₁	—	2	2	no	—
62	#117×C₄₁	D₄	1	4	yes	—
63	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
64	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
65	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
66	C₂×C₄⋊C₄×C₄₁	—	2	4	no	—
67	C₂×C₄⋊C₄×C₄₁	D₄	1	1	yes	characteristic
68	C₂×C₄⋊C₄×C₄₁	D₄	1	1	yes	characteristic
69	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
70	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
71	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
72	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
73	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
74	C₂×C₂²⋊C₄×C₄₁	D₄	1	2	yes	—
75	C₂×C₄²×C₄₁	—	2	1	no	—
76	C₂×C₄²×C₄₁	—	2	1	no	—
77	C₂×C₄²×C₄₁	C₂³	1	2	yes	—
78	#107×C₄₁	—	2	4	no	—
79	#106×C₄₁	—	2	4	no	—
80	C₄⋊C₈×C₄₁	—	2	4	no	—
81	C₄⋊C₈×C₄₁	—	2	4	no	—
82	#103×C₄₁	—	2	4	no	—
83	#103×C₄₁	—	2	4	no	—
84	#103×C₄₁	—	2	8	no	—
85	#95×C₄₁	—	2	4	no	—
86	#95×C₄₁	—	2	4	no	—
87	#95×C₄₁	—	2	4	no	—
88	C₂⁴×C₄₁	C₂×D₄	1	1	yes	characteristic
89	C₂×Q₈×C₄₁	—	2	4	no	—
90	C₂×Q₈×C₄₁	—	2	2	no	—
91	C₂×Q₈×C₄₁	—	2	8	no	—
92	C₂×Q₈×C₄₁	—	2	8	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	—	2	2	no	—
97	C₂×Q₈×C₄₁	—	4	2	no	—
98	C₂×Q₈×C₄₁	—	4	2	no	—
99	C₂×Q₈×C₄₁	—	4	4	no	—
100	C₂×Q₈×C₄₁	—	4	4	no	—
101	C₂×Q₈×C₄₁	C₂×Q₈	1	4	yes	—
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	2	no	—
106	C₂²×C₄×C₄₁	—	2	2	no	—
107	C₂²×C₄×C₄₁	—	4	2	no	—
108	C₂²×C₄×C₄₁	—	4	2	no	—
109	C₂²×C₄×C₄₁	—	4	2	no	—
110	C₂²×C₄×C₄₁	—	8	2	no	—
111	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
112	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
113	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
114	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
115	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
116	C₂²×C₄×C₄₁	C₂×Q₈	1	2	yes	—
117	C₂²×C₄×C₄₁	#41	1	2	yes	—
118	C₂²×C₄×C₄₁	#41	1	2	yes	—
119	C₂²×C₄×C₄₁	#41	1	2	yes	—
120	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
121	M₁₆×C₄₁	—	4	4	no	—
122	C₂×C₈×C₄₁	—	2	8	no	—
123	C₂×C₈×C₄₁	—	2	1	no	—
124	C₂×C₈×C₄₁	—	2	1	no	—
125	C₂×C₈×C₄₁	—	2	1	no	—
126	C₂×C₈×C₄₁	—	2	1	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	C₂×D₄	1	2	yes	—
131	C₂×C₈×C₄₁	C₂×D₄	1	2	yes	—
132	C₄⋊C₄×C₄₁	—	2	2	no	—
133	C₄⋊C₄×C₄₁	—	2	2	no	—
134	C₄⋊C₄×C₄₁	—	2	2	no	—
135	C₄⋊C₄×C₄₁	—	2	2	no	—
136	C₄⋊C₄×C₄₁	—	2	2	no	—
137	C₄⋊C₄×C₄₁	—	2	2	no	—
138	C₄⋊C₄×C₄₁	—	2	2	no	—
139	C₄⋊C₄×C₄₁	—	4	2	no	—
140	C₄⋊C₄×C₄₁	—	8	4	no	—
141	C₄⋊C₄×C₄₁	C₂×D₄	1	4	yes	—
142	C₂²⋊C₄×C₄₁	—	2	4	no	—
143	C₂²⋊C₄×C₄₁	—	2	4	no	—
144	C₂²⋊C₄×C₄₁	—	4	2	no	—
145	C₄²×C₄₁	—	2	4	no	—
146	C₄²×C₄₁	—	2	2	no	—
147	C₄²×C₄₁	—	2	2	no	—
148	C₄²×C₄₁	—	4	2	no	—
149	C₂³×C₄₁	—	2	2	no	—
150	C₂³×C₄₁	—	2	2	no	—
151	C₂³×C₄₁	#121	1	2	yes	—
152	C₂³×C₄₁	#121	1	2	yes	—
153	C₂³×C₄₁	C₂²⋊Q₈	1	2	yes	—
154	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
155	Q₈×C₄₁	—	2	4	no	—
156	Q₈×C₄₁	—	2	4	no	—
157	Q₈×C₄₁	—	4	2	no	—
158	Q₈×C₄₁	—	4	2	no	—
159	Q₈×C₄₁	—	4	8	no	—
160	C₂×C₄×C₄₁	—	2	2	no	—
161	C₂×C₄×C₄₁	—	2	2	no	—
162	C₂×C₄×C₄₁	—	2	4	no	—
163	C₂×C₄×C₄₁	—	2	4	no	—
164	C₂×C₄×C₄₁	—	2	4	no	—
165	C₂×C₄×C₄₁	—	2	4	no	—
166	C₂×C₄×C₄₁	—	4	2	no	—
167	C₂×C₄×C₄₁	—	4	2	no	—
168	C₂×C₄×C₄₁	—	4	2	no	—
169	C₂×C₄×C₄₁	—	4	2	no	—
170	C₂×C₄×C₄₁	—	4	8	no	—
171	C₂×C₄×C₄₁	—	4	2	no	—
172	C₂×C₄×C₄₁	—	4	2	no	—
173	C₂×C₄×C₄₁	—	4	4	no	—
174	C₂×C₄×C₄₁	—	4	2	no	—
175	C₂×C₄×C₄₁	—	4	2	no	—
176	C₂×C₄×C₄₁	—	8	4	no	—
177	C₂×C₄×C₄₁	#121	1	4	yes	—
178	C₂×C₄×C₄₁	#121	1	2	yes	—
179	C₂×C₄×C₄₁	#121	1	2	yes	—
180	C₂×C₄×C₄₁	C₂²⋊Q₈	1	4	yes	—
181	C₂×C₄×C₄₁	C₂²⋊Q₈	1	4	yes	—
182	C₂×C₄×C₄₁	C₂²⋊Q₈	1	2	yes	—
183	C₂×C₄×C₄₁	#126	1	4	yes	—
184	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
185	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
186	C₂×C₄×C₄₁	C₂²×Q₈	1	1	yes	characteristic
187	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
188	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
189	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
190	C₈×C₄₁	—	2	2	no	—
191	C₈×C₄₁	—	2	2	no	—
192	C₈×C₄₁	—	4	2	no	—
193	#23613	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
194	C₂²×C₄₁	—	2	4	no	—
195	C₂²×C₄₁	—	2	4	no	—
196	C₂²×C₄₁	—	2	2	no	—
197	C₂²×C₄₁	—	2	2	no	—
198	C₂²×C₄₁	#396	1	4	yes	—
199	C₂²×C₄₁	C₂×#121	1	1	yes	characteristic
200	C₂²×C₄₁	C₂×#121	1	1	yes	characteristic
201	C₂²×C₄₁	C₂×C₂²⋊Q₈	1	1	yes	characteristic
202	C₂²×C₄₁	#577	1	2	yes	—
203	C₂²×C₄₁	#578	1	2	yes	—
204	C₄×C₄₁	—	4	4	no	—
205	C₄×C₄₁	—	4	4	no	—
206	C₄×C₄₁	—	4	2	no	—
207	C₄×C₄₁	—	4	2	no	—
208	C₄×C₄₁	—	8	2	no	—
209	C₄×C₄₁	—	8	2	no	—
210	C₄×C₄₁	#396	1	4	yes	—
211	C₄×C₄₁	C₂×#121	1	1	yes	characteristic
212	C₄×C₄₁	C₂×C₂²⋊Q₈	1	1	yes	characteristic
213	C₄×C₄₁	C₂×C₂²⋊Q₈	1	1	yes	characteristic
214	C₄×C₄₁	C₂×#126	1	1	yes	characteristic
215	C₂×#427	C₂×C₄₁	1	1	yes	characteristic
216	C₂×#424	C₂×C₄₁	1	1	yes	characteristic
217	C₂×#419	C₂×C₄₁	1	1	yes	characteristic
218	C₂²×#103	C₂×C₄₁	1	1	yes	characteristic
219	#2317	C₂×C₄₁	1	1	yes	characteristic
220	#2310	C₂×C₄₁	1	1	yes	characteristic
221	#2068	C₂×C₄₁	1	4	yes	complemented
222	#2066	C₂×C₄₁	1	4	yes	complemented
223	#1736	C₂×C₄₁	1	1	yes	characteristic
224	C₂×C₄₁	—	2	4	no	—
225	C₂×C₄₁	C₂×#396	1	1	yes	characteristic
226	C₂×C₄₁	#3046	1	2	yes	—
227	C₂×C₄₁	#3057	1	1	yes	characteristic
228	C₂×C₄₁	#3059	1	1	yes	characteristic
229	C₂×C₄₁	#3082	1	2	yes	—
230	C₂³×Q₈	C₂²×C₄₁	1	1	yes	characteristic
231	C₂²×M₁₆	C₂²×C₄₁	1	1	yes	characteristic
232	C₂³×C₈	C₂²×C₄₁	1	1	yes	characteristic
233	C₂×#117	C₂²×C₄₁	1	1	yes	characteristic
234	C₂×#117	C₂²×C₄₁	1	1	yes	characteristic
235	C₂×#117	C₂²×C₄₁	1	1	yes	characteristic
236	C₂²×C₄⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
237	#427	—	2	4	no	—
238	C₂×#107	C₂²×C₄₁	1	2	yes	—
239	C₂×#106	C₂²×C₄₁	1	2	yes	—
240	#424	—	2	4	no	—
241	C₂×C₄⋊C₈	C₂²×C₄₁	1	2	yes	—
242	C₂×C₄⋊C₈	C₂²×C₄₁	1	2	yes	—
243	#419	—	2	4	no	—
244	C₂×#103	—	2	4	no	—
245	C₂×#103	C₂²×C₄₁	1	2	yes	—
246	C₂×#103	C₂²×C₄₁	1	4	yes	—
247	C₂×#103	C₂²×C₄₁	1	2	yes	—
248	#391	—	2	1	no	—
249	#391	—	2	1	no	—
250	#391	C₂²×C₄₁	1	4	yes	—
251	#389	C₂²×C₄₁	1	4	yes	—
252	#385	—	2	2	no	—
253	#384	—	2	1	no	—
254	#382	—	2	1	no	—
255	#381	—	2	2	no	—
256	#340	C₂²×C₄₁	1	4	yes	—
257	C₄₁	#23613	1	1	yes	characteristic, direct product factor, Sylow
258	C₂²×Q₈	—	2	1	no	—
259	C₂²×Q₈	—	2	2	no	—
260	C₂²×Q₈	—	2	2	no	—
261	C₂²×Q₈	—	2	2	no	—
262	C₂²×Q₈	—	2	2	no	—
263	C₂²×Q₈	—	2	2	no	—
264	C₂²×Q₈	Q₈×C₄₁	1	4	yes	—
265	C₂²×Q₈	C₂³×C₄₁	1	2	yes	—
266	C₂³×C₄	—	2	1	no	—
267	C₂³×C₄	—	2	1	no	—
268	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
269	C₂×M₁₆	—	2	2	no	—
270	C₂×M₁₆	—	2	2	no	—
271	C₂×M₁₆	—	2	2	no	—
272	C₂²×C₈	—	2	2	no	—
273	C₂²×C₈	—	2	2	no	—
274	C₂²×C₈	D₄×C₄₁	1	4	yes	—
275	C₂²×C₈	C₂³×C₄₁	1	2	yes	—
276	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
277	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
278	#117	—	2	2	no	—
279	#117	—	2	2	no	—
280	#117	—	2	2	no	—
281	#117	—	2	2	no	—
282	#117	—	2	2	no	—
283	#117	D₄×C₄₁	1	4	yes	—
284	C₂×C₄⋊C₄	—	2	2	no	—
285	C₂×C₄⋊C₄	—	2	2	no	—
286	C₂×C₄⋊C₄	—	2	1	no	—
287	C₂×C₄⋊C₄	—	2	4	no	—
288	C₂×C₄⋊C₄	D₄×C₄₁	1	1	yes	characteristic
289	C₂×C₄⋊C₄	D₄×C₄₁	1	1	yes	characteristic
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	2	yes	—
293	C₂×C₂²⋊C₄	—	2	1	no	—
294	C₂×C₂²⋊C₄	—	2	1	no	—
295	C₂×C₂²⋊C₄	D₄×C₄₁	1	2	yes	—
296	C₂×C₄²	—	2	1	no	—
297	C₂×C₄²	—	2	1	no	—
298	C₂×C₄²	C₂³×C₄₁	1	2	yes	—
299	#107	—	2	4	no	—
300	#106	—	2	4	no	—
301	C₄⋊C₈	—	2	4	no	—
302	C₄⋊C₈	—	2	4	no	—
303	#103	—	2	4	no	—
304	#103	—	2	4	no	—
305	#103	—	2	8	no	—
306	#95	—	2	4	no	—
307	#95	—	2	4	no	—
308	#95	—	2	4	no	—
309	C₂⁴	C₂×D₄×C₄₁	1	1	yes	characteristic
310	C₂×Q₈	—	2	4	no	—
311	C₂×Q₈	—	2	2	no	—
312	C₂×Q₈	—	2	8	no	—
313	C₂×Q₈	—	2	8	no	—
314	C₂×Q₈	—	2	2	no	—
315	C₂×Q₈	—	2	2	no	—
316	C₂×Q₈	—	2	2	no	—
317	C₂×Q₈	—	2	2	no	—
318	C₂×Q₈	—	4	2	no	—
319	C₂×Q₈	—	4	2	no	—
320	C₂×Q₈	—	4	4	no	—
321	C₂×Q₈	—	4	4	no	—
322	C₂×Q₈	C₂×Q₈×C₄₁	1	4	yes	—
323	C₂²×C₄	—	2	4	no	—
324	C₂²×C₄	—	2	2	no	—
325	C₂²×C₄	—	2	2	no	—
326	C₂²×C₄	—	2	2	no	—
327	C₂²×C₄	—	2	2	no	—
328	C₂²×C₄	—	4	2	no	—
329	C₂²×C₄	—	4	2	no	—
330	C₂²×C₄	—	4	2	no	—
331	C₂²×C₄	—	8	2	no	—
332	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
333	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
334	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
335	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
336	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
337	C₂²×C₄	C₂×Q₈×C₄₁	1	2	yes	—
338	C₂²×C₄	#41×C₄₁	1	2	yes	—
339	C₂²×C₄	#41×C₄₁	1	2	yes	—
340	C₂²×C₄	#41×C₄₁	1	2	yes	—
341	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
342	M₁₆	—	4	4	no	—
343	C₂×C₈	—	2	8	no	—
344	C₂×C₈	—	2	1	no	—
345	C₂×C₈	—	2	1	no	—
346	C₂×C₈	—	2	1	no	—
347	C₂×C₈	—	2	1	no	—
348	C₂×C₈	—	2	2	no	—
349	C₂×C₈	—	2	2	no	—
350	C₂×C₈	—	2	2	no	—
351	C₂×C₈	C₂×D₄×C₄₁	1	2	yes	—
352	C₂×C₈	C₂×D₄×C₄₁	1	2	yes	—
353	C₄⋊C₄	—	2	2	no	—
354	C₄⋊C₄	—	2	2	no	—
355	C₄⋊C₄	—	2	2	no	—
356	C₄⋊C₄	—	2	2	no	—
357	C₄⋊C₄	—	2	2	no	—
358	C₄⋊C₄	—	2	2	no	—
359	C₄⋊C₄	—	2	2	no	—
360	C₄⋊C₄	—	4	2	no	—
361	C₄⋊C₄	—	8	4	no	—
362	C₄⋊C₄	C₂×D₄×C₄₁	1	4	yes	—
363	C₂²⋊C₄	—	2	4	no	—
364	C₂²⋊C₄	—	2	4	no	—
365	C₂²⋊C₄	—	4	2	no	—
366	C₄²	—	2	4	no	—
367	C₄²	—	2	2	no	—
368	C₄²	—	2	2	no	—
369	C₄²	—	4	2	no	—
370	C₂³	—	2	2	no	—
371	C₂³	—	2	2	no	—
372	C₂³	#121×C₄₁	1	2	yes	—
373	C₂³	#121×C₄₁	1	2	yes	—
374	C₂³	C₂²⋊Q₈×C₄₁	1	2	yes	—
375	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
376	Q₈	—	2	4	no	—
377	Q₈	—	2	4	no	—
378	Q₈	—	4	2	no	—
379	Q₈	—	4	2	no	—
380	Q₈	—	4	8	no	—
381	C₂×C₄	—	2	2	no	—
382	C₂×C₄	—	2	2	no	—
383	C₂×C₄	—	2	4	no	—
384	C₂×C₄	—	2	4	no	—
385	C₂×C₄	—	2	4	no	—
386	C₂×C₄	—	2	4	no	—
387	C₂×C₄	—	4	2	no	—
388	C₂×C₄	—	4	2	no	—
389	C₂×C₄	—	4	2	no	—
390	C₂×C₄	—	4	2	no	—
391	C₂×C₄	—	4	8	no	—
392	C₂×C₄	—	4	2	no	—
393	C₂×C₄	—	4	2	no	—
394	C₂×C₄	—	4	4	no	—
395	C₂×C₄	—	4	2	no	—
396	C₂×C₄	—	4	2	no	—
397	C₂×C₄	—	8	4	no	—
398	C₂×C₄	#121×C₄₁	1	4	yes	—
399	C₂×C₄	#121×C₄₁	1	2	yes	—
400	C₂×C₄	#121×C₄₁	1	2	yes	—
401	C₂×C₄	C₂²⋊Q₈×C₄₁	1	4	yes	—
402	C₂×C₄	C₂²⋊Q₈×C₄₁	1	4	yes	—
403	C₂×C₄	C₂²⋊Q₈×C₄₁	1	2	yes	—
404	C₂×C₄	#126×C₄₁	1	4	yes	—
405	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
406	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
407	C₂×C₄	C₂²×Q₈×C₄₁	1	1	yes	characteristic
408	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
409	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
410	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
411	C₈	—	2	2	no	—
412	C₈	—	2	2	no	—
413	C₈	—	4	2	no	—
414	C₂²	—	2	4	no	—
415	C₂²	—	2	2	no	—
416	C₂²	—	2	2	no	—
417	C₂²	—	2	4	no	—
418	C₂²	C₄₁×#396	1	4	yes	—
419	C₂²	C₂×#121×C₄₁	1	1	yes	characteristic
420	C₂²	C₂×#121×C₄₁	1	1	yes	characteristic
421	C₂²	C₂×C₂²⋊Q₈×C₄₁	1	1	yes	characteristic
422	C₂²	C₄₁×#577	1	2	yes	—
423	C₂²	C₄₁×#578	1	2	yes	—
424	C₄	—	4	4	no	—
425	C₄	—	4	2	no	—
426	C₄	—	4	2	no	—
427	C₄	—	4	4	no	—
428	C₄	—	8	2	no	—
429	C₄	—	8	2	no	—
430	C₄	C₄₁×#396	1	4	yes	—
431	C₄	C₂×#121×C₄₁	1	1	yes	characteristic
432	C₄	C₂×C₂²⋊Q₈×C₄₁	1	1	yes	characteristic
433	C₄	C₂×C₂²⋊Q₈×C₄₁	1	1	yes	characteristic
434	C₄	C₂×#126×C₄₁	1	1	yes	characteristic
435	C₂	—	2	4	no	—
436	C₂	C₂×C₄₁×#396	1	1	yes	characteristic
437	C₂	C₄₁×#3046	1	2	yes	—
438	C₂	C₄₁×#3057	1	1	yes	characteristic
439	C₂	C₄₁×#3059	1	1	yes	characteristic
440	C₂	C₄₁×#3082	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₄₁	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₁
prime radical	C₂⁴×C₄₁	C₂×D₄
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₄₁ ◁ C₂×#117×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
7. C₄₁×#2068	C₂	semidirect
8. C₄₁×#2066	C₂	semidirect
193. #23613	C₄₁	direct (N × H)
221. #2068	C₂×C₄₁	semidirect
222. #2066	C₂×C₄₁	semidirect
257. C₄₁	#23613	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₄₁×#427	2
C₂×C₄₁×#424	2
C₂×C₄₁×#419	2
C₂²×#103×C₄₁	2
C₄₁×#2317	2
C₄₁×#2310	2
C₄₁×#2068	2
C₄₁×#2066	2
C₄₁×#1736	2
#23613	41

Subgroups — C41×#23613 #23799814

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#23613 #23799814