Subgroups — C₄₁×#7578 #23783779

Order 10496.

708 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₁×#2297	C₂	1	1	yes	maximal, characteristic
2	C₄₁×#1817	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄₁×#336	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₁×#1272	C₂	1	2	yes	maximal, complemented
5	C₄₁×#1270	C₂	1	2	yes	maximal, complemented
6	C₂²×#41×C₄₁	C₄	1	1	yes	characteristic
7	C₂³×C₈×C₄₁	—	2	1	no	—
8	C₂×#117×C₄₁	C₄	1	1	yes	characteristic
9	C₂²×C₄²×C₄₁	C₂²	1	1	yes	characteristic
10	C₂×C₂²⋊C₈×C₄₁	—	2	1	no	—
11	C₄₁×#391	C₄	1	1	yes	characteristic
12	C₄₁×#391	C₂²	1	1	yes	characteristic
13	C₄₁×#390	C₄	1	1	yes	characteristic
14	C₄₁×#390	C₂²	1	1	yes	characteristic
15	C₄₁×#386	—	2	1	no	—
16	C₄₁×#386	—	2	1	no	—
17	C₄×C₂²⋊C₄×C₄₁	—	2	1	no	—
18	C₄×C₂²⋊C₄×C₄₁	—	2	1	no	—
19	C₄₁×#336	—	2	1	no	—
20	C₄₁×#336	—	2	1	no	—
21	C₄₁×#336	C₂²	1	2	yes	—
22	C₄₁×#336	C₂²	1	2	yes	—
23	C₂×#41×C₄₁	—	2	2	no	—
24	C₂×#41×C₄₁	—	4	2	no	—
25	C₂×#41×C₄₁	—	4	2	no	—
26	C₂×#41×C₄₁	C₈	1	4	yes	complemented
27	C₂²×Q₈×C₄₁	C₂×C₄	1	1	yes	characteristic
28	C₂²×D₄×C₄₁	—	2	1	no	—
29	C₂²×D₄×C₄₁	C₂×C₄	1	1	yes	characteristic
30	C₂³×C₄×C₄₁	—	2	1	no	—
31	C₂³×C₄×C₄₁	C₂×C₄	1	1	yes	characteristic
32	C₂³×C₄×C₄₁	D₄	1	1	yes	characteristic
33	C₂³×C₄×C₄₁	D₄	1	1	yes	characteristic
34	C₂²×C₈×C₄₁	—	2	4	no	—
35	C₂²×C₈×C₄₁	—	2	2	no	—
36	C₂²×C₈×C₄₁	—	2	2	no	—
37	C₂²×C₈×C₄₁	—	4	2	no	—
38	C₂²×C₈×C₄₁	—	4	2	no	—
39	#117×C₄₁	—	4	2	no	—
40	C₂×C₄⋊C₄×C₄₁	C₂×C₄	1	1	yes	characteristic
41	C₂×C₄⋊C₄×C₄₁	C₂×C₄	1	1	yes	characteristic
42	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
43	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
44	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
45	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
46	C₂×C₂²⋊C₄×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	D₄	1	1	yes	characteristic
51	C₂×C₄²×C₄₁	D₄	1	1	yes	characteristic
52	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
53	C₂²⋊C₈×C₄₁	—	4	2	no	—
54	#95×C₄₁	—	2	1	no	—
55	#95×C₄₁	—	2	1	no	—
56	#95×C₄₁	—	2	1	no	—
57	#95×C₄₁	—	2	1	no	—
58	C₂⁴×C₄₁	—	2	1	no	—
59	C₂⁴×C₄₁	C₂²⋊C₄	1	1	yes	characteristic
60	#41×C₄₁	—	4	8	no	—
61	#41×C₄₁	—	4	8	no	—
62	C₂×Q₈×C₄₁	—	2	1	no	—
63	C₂×Q₈×C₄₁	—	4	1	no	—
64	C₂×Q₈×C₄₁	—	4	1	no	—
65	C₂×Q₈×C₄₁	C₂×C₈	1	2	yes	complemented
66	C₂×D₄×C₄₁	—	2	4	no	—
67	C₂×D₄×C₄₁	—	2	1	no	—
68	C₂×D₄×C₄₁	—	4	1	no	—
69	C₂×D₄×C₄₁	—	4	1	no	—
70	C₂×D₄×C₄₁	—	4	2	no	—
71	C₂×D₄×C₄₁	—	4	2	no	—
72	C₂×D₄×C₄₁	C₂×C₈	1	2	yes	complemented
73	C₂²×C₄×C₄₁	—	2	2	no	—
74	C₂²×C₄×C₄₁	—	2	2	no	—
75	C₂²×C₄×C₄₁	—	2	2	no	—
76	C₂²×C₄×C₄₁	—	2	2	no	—
77	C₂²×C₄×C₄₁	—	2	1	no	—
78	C₂²×C₄×C₄₁	—	2	1	no	—
79	C₂²×C₄×C₄₁	—	2	2	no	—
80	C₂²×C₄×C₄₁	—	2	1	no	—
81	C₂²×C₄×C₄₁	—	2	4	no	—
82	C₂²×C₄×C₄₁	—	2	2	no	—
83	C₂²×C₄×C₄₁	—	2	1	no	—
84	C₂²×C₄×C₄₁	—	2	1	no	—
85	C₂²×C₄×C₄₁	—	4	1	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	C₂×C₈	1	2	yes	—
92	C₂²×C₄×C₄₁	M₁₆	1	2	yes	—
93	C₂²×C₄×C₄₁	C₂²×C₄	1	1	yes	characteristic
94	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
95	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
96	C₂×C₈×C₄₁	—	2	4	no	—
97	C₂×C₈×C₄₁	—	4	8	no	—
98	C₂×C₈×C₄₁	—	4	2	no	—
99	C₂×C₈×C₄₁	—	4	2	no	—
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	—	4	1	no	—
104	C₄⋊C₄×C₄₁	—	4	1	no	—
105	C₂²⋊C₄×C₄₁	—	4	2	no	—
106	C₂²⋊C₄×C₄₁	—	4	2	no	—
107	C₂²⋊C₄×C₄₁	—	4	2	no	—
108	C₂²⋊C₄×C₄₁	—	4	2	no	—
109	C₂²⋊C₄×C₄₁	—	4	1	no	—
110	C₂²⋊C₄×C₄₁	—	4	1	no	—
111	C₄²×C₄₁	—	4	1	no	—
112	C₄²×C₄₁	—	4	1	no	—
113	C₄²×C₄₁	—	4	1	no	—
114	C₄²×C₄₁	—	4	1	no	—
115	C₄²×C₄₁	—	4	2	no	—
116	C₂³×C₄₁	—	2	1	no	—
117	C₂³×C₄₁	—	2	1	no	—
118	C₂³×C₄₁	—	2	1	no	—
119	C₂³×C₄₁	—	2	1	no	—
120	C₂³×C₄₁	—	2	2	no	—
121	C₂³×C₄₁	—	4	1	no	—
122	C₂³×C₄₁	—	4	1	no	—
123	C₂³×C₄₁	—	4	1	no	—
124	C₂³×C₄₁	—	4	1	no	—
125	C₂³×C₄₁	—	4	1	no	—
126	C₂³×C₄₁	—	4	1	no	—
127	C₂³×C₄₁	C₂²⋊C₈	1	2	yes	—
128	C₂³×C₄₁	#99	1	2	yes	—
129	C₂³×C₄₁	#100	1	2	yes	—
130	C₂³×C₄₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
131	Q₈×C₄₁	—	4	2	no	—
132	Q₈×C₄₁	—	4	2	no	—
133	D₄×C₄₁	—	4	2	no	—
134	D₄×C₄₁	—	4	2	no	—
135	D₄×C₄₁	—	4	8	no	—
136	C₂×C₄×C₄₁	—	2	4	no	—
137	C₂×C₄×C₄₁	—	2	4	no	—
138	C₂×C₄×C₄₁	—	2	4	no	—
139	C₂×C₄×C₄₁	—	2	4	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	1	no	—
150	C₂×C₄×C₄₁	—	2	2	no	—
151	C₂×C₄×C₄₁	—	2	1	no	—
152	C₂×C₄×C₄₁	—	2	1	no	—
153	C₂×C₄×C₄₁	—	2	1	no	—
154	C₂×C₄×C₄₁	—	4	4	no	—
155	C₂×C₄×C₄₁	—	4	8	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	1	no	—
162	C₂×C₄×C₄₁	—	4	1	no	—
163	C₂×C₄×C₄₁	—	4	1	no	—
164	C₂×C₄×C₄₁	C₂²⋊C₈	1	2	yes	—
165	C₂×C₄×C₄₁	#104	1	2	yes	—
166	C₂×C₄×C₄₁	C₂²×C₈	1	1	yes	characteristic
167	C₂×C₄×C₄₁	C₂×M₁₆	1	1	yes	characteristic
168	C₂×C₄×C₄₁	#135	1	2	yes	—
169	C₂×C₄×C₄₁	AGL(1,ℤ/8)	1	1	yes	characteristic
170	C₂×C₄×C₄₁	#137	1	1	yes	characteristic
171	C₈×C₄₁	—	4	4	no	—
172	C₈×C₄₁	—	8	2	no	—
173	#7578	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
174	C₂²×C₄₁	—	2	2	no	—
175	C₂²×C₄₁	—	2	2	no	—
176	C₂²×C₄₁	—	2	2	no	—
177	C₂²×C₄₁	—	2	2	no	—
178	C₂²×C₄₁	—	2	2	no	—
179	C₂²×C₄₁	—	2	2	no	—
180	C₂²×C₄₁	—	4	2	no	—
181	C₂²×C₄₁	—	4	2	no	—
182	C₂²×C₄₁	—	4	2	no	—
183	C₂²×C₄₁	—	8	1	no	—
184	C₂²×C₄₁	—	8	1	no	—
185	C₂²×C₄₁	—	8	1	no	—
186	C₂²×C₄₁	—	8	1	no	—
187	C₂²×C₄₁	#323	1	4	yes	—
188	C₂²×C₄₁	C₂×C₂²⋊C₈	1	1	yes	characteristic
189	C₂²×C₄₁	C₂×#99	1	1	yes	characteristic
190	C₂²×C₄₁	C₂×#100	1	1	yes	characteristic
191	C₂²×C₄₁	#416	1	1	yes	characteristic
192	C₂²×C₄₁	#417	1	1	yes	characteristic
193	C₂²×C₄₁	C₂×#104	1	1	yes	characteristic
194	C₂²×C₄₁	#421	1	1	yes	characteristic
195	C₄×C₄₁	—	2	2	no	—
196	C₄×C₄₁	—	2	1	no	—
197	C₄×C₄₁	—	2	1	no	—
198	C₄×C₄₁	—	2	1	no	—
199	C₄×C₄₁	—	2	2	no	—
200	C₄×C₄₁	—	2	1	no	—
201	C₄×C₄₁	—	2	2	no	—
202	C₄×C₄₁	—	4	2	no	—
203	C₄×C₄₁	—	4	1	no	—
204	C₄×C₄₁	—	8	1	no	—
205	C₄×C₄₁	—	8	1	no	—
206	#2297	C₂×C₄₁	1	1	yes	characteristic
207	#1817	C₂×C₄₁	1	1	yes	characteristic, complemented
208	C₂×#336	C₂×C₄₁	1	1	yes	characteristic, complemented
209	#1272	C₂×C₄₁	1	2	yes	complemented
210	#1270	C₂×C₄₁	1	2	yes	complemented
211	C₂×C₄₁	—	2	4	no	—
212	C₂×C₄₁	—	8	2	no	—
213	C₂×C₄₁	C₂×#323	1	1	yes	characteristic
214	C₂×C₄₁	#1476	1	1	yes	characteristic
215	C₂×C₄₁	#1477	1	1	yes	characteristic
216	C₂×C₄₁	#1504	1	1	yes	characteristic
217	C₂×C₄₁	#1516	1	1	yes	characteristic
218	C₂×C₄₁	#1530	1	1	yes	characteristic
219	C₂×C₄₁	#1551	1	1	yes	characteristic
220	C₂²×#41	C₄×C₄₁	1	1	yes	characteristic
221	C₂³×C₈	—	2	1	no	—
222	C₂×#117	C₄×C₄₁	1	1	yes	characteristic
223	C₂²×C₄²	C₂²×C₄₁	1	1	yes	characteristic
224	C₂×C₂²⋊C₈	—	2	1	no	—
225	#391	C₄×C₄₁	1	1	yes	characteristic
226	#391	C₂²×C₄₁	1	1	yes	characteristic
227	#390	C₄×C₄₁	1	1	yes	characteristic
228	#390	C₂²×C₄₁	1	1	yes	characteristic
229	#386	—	2	1	no	—
230	#386	—	2	1	no	—
231	C₄×C₂²⋊C₄	—	2	1	no	—
232	C₄×C₂²⋊C₄	—	2	1	no	—
233	#336	—	2	1	no	—
234	#336	—	2	1	no	—
235	#336	C₂²×C₄₁	1	2	yes	—
236	#336	C₂²×C₄₁	1	2	yes	—
237	C₄₁	#7578	1	1	yes	characteristic, direct product factor, Sylow
238	C₂×#41	—	2	2	no	—
239	C₂×#41	—	4	2	no	—
240	C₂×#41	—	4	2	no	—
241	C₂×#41	C₈×C₄₁	1	4	yes	complemented
242	C₂²×Q₈	C₂×C₄×C₄₁	1	1	yes	characteristic
243	C₂²×D₄	—	2	1	no	—
244	C₂²×D₄	C₂×C₄×C₄₁	1	1	yes	characteristic
245	C₂³×C₄	—	2	1	no	—
246	C₂³×C₄	C₂×C₄×C₄₁	1	1	yes	characteristic
247	C₂³×C₄	D₄×C₄₁	1	1	yes	characteristic
248	C₂³×C₄	D₄×C₄₁	1	1	yes	characteristic
249	C₂²×C₈	—	2	4	no	—
250	C₂²×C₈	—	2	2	no	—
251	C₂²×C₈	—	2	2	no	—
252	C₂²×C₈	—	4	2	no	—
253	C₂²×C₈	—	4	2	no	—
254	#117	—	4	2	no	—
255	C₂×C₄⋊C₄	C₂×C₄×C₄₁	1	1	yes	characteristic
256	C₂×C₄⋊C₄	C₂×C₄×C₄₁	1	1	yes	characteristic
257	C₂×C₂²⋊C₄	—	2	1	no	—
258	C₂×C₂²⋊C₄	—	2	1	no	—
259	C₂×C₂²⋊C₄	—	2	1	no	—
260	C₂×C₂²⋊C₄	—	2	1	no	—
261	C₂×C₂²⋊C₄	—	2	1	no	—
262	C₂×C₄²	—	2	1	no	—
263	C₂×C₄²	—	4	2	no	—
264	C₂×C₄²	C₂×C₄×C₄₁	1	1	yes	characteristic
265	C₂×C₄²	D₄×C₄₁	1	1	yes	characteristic
266	C₂×C₄²	D₄×C₄₁	1	1	yes	characteristic
267	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
268	C₂²⋊C₈	—	4	2	no	—
269	#95	—	2	1	no	—
270	#95	—	2	1	no	—
271	#95	—	2	1	no	—
272	#95	—	2	1	no	—
273	C₂⁴	—	2	1	no	—
274	C₂⁴	C₂²⋊C₄×C₄₁	1	1	yes	characteristic
275	#41	—	4	8	no	—
276	#41	—	4	8	no	—
277	C₂×Q₈	—	2	1	no	—
278	C₂×Q₈	—	4	1	no	—
279	C₂×Q₈	—	4	1	no	—
280	C₂×Q₈	C₂×C₈×C₄₁	1	2	yes	complemented
281	C₂×D₄	—	2	4	no	—
282	C₂×D₄	—	2	1	no	—
283	C₂×D₄	—	4	1	no	—
284	C₂×D₄	—	4	1	no	—
285	C₂×D₄	—	4	2	no	—
286	C₂×D₄	—	4	2	no	—
287	C₂×D₄	C₂×C₈×C₄₁	1	2	yes	complemented
288	C₂²×C₄	—	2	2	no	—
289	C₂²×C₄	—	2	2	no	—
290	C₂²×C₄	—	2	2	no	—
291	C₂²×C₄	—	2	2	no	—
292	C₂²×C₄	—	2	1	no	—
293	C₂²×C₄	—	2	1	no	—
294	C₂²×C₄	—	2	2	no	—
295	C₂²×C₄	—	2	1	no	—
296	C₂²×C₄	—	2	4	no	—
297	C₂²×C₄	—	2	2	no	—
298	C₂²×C₄	—	2	1	no	—
299	C₂²×C₄	—	2	1	no	—
300	C₂²×C₄	—	4	1	no	—
301	C₂²×C₄	—	4	2	no	—
302	C₂²×C₄	—	4	2	no	—
303	C₂²×C₄	C₂²⋊C₄×C₄₁	1	1	yes	characteristic
304	C₂²×C₄	C₂²⋊C₄×C₄₁	1	1	yes	characteristic
305	C₂²×C₄	C₂²⋊C₄×C₄₁	1	1	yes	characteristic
306	C₂²×C₄	C₂×C₈×C₄₁	1	2	yes	—
307	C₂²×C₄	M₁₆×C₄₁	1	2	yes	—
308	C₂²×C₄	C₂²×C₄×C₄₁	1	1	yes	characteristic
309	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
310	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
311	C₂×C₈	—	2	4	no	—
312	C₂×C₈	—	4	8	no	—
313	C₂×C₈	—	4	2	no	—
314	C₂×C₈	—	4	2	no	—
315	C₂×C₈	—	4	2	no	—
316	C₂×C₈	—	4	2	no	—
317	C₂×C₈	—	4	2	no	—
318	C₄⋊C₄	—	4	1	no	—
319	C₄⋊C₄	—	4	1	no	—
320	C₂²⋊C₄	—	4	2	no	—
321	C₂²⋊C₄	—	4	2	no	—
322	C₂²⋊C₄	—	4	2	no	—
323	C₂²⋊C₄	—	4	2	no	—
324	C₂²⋊C₄	—	4	1	no	—
325	C₂²⋊C₄	—	4	1	no	—
326	C₄²	—	4	1	no	—
327	C₄²	—	4	1	no	—
328	C₄²	—	4	1	no	—
329	C₄²	—	4	1	no	—
330	C₄²	—	4	2	no	—
331	C₂³	—	2	1	no	—
332	C₂³	—	2	1	no	—
333	C₂³	—	2	1	no	—
334	C₂³	—	2	1	no	—
335	C₂³	—	2	2	no	—
336	C₂³	—	4	1	no	—
337	C₂³	—	4	1	no	—
338	C₂³	—	4	1	no	—
339	C₂³	—	4	1	no	—
340	C₂³	—	4	1	no	—
341	C₂³	—	4	1	no	—
342	C₂³	C₂²⋊C₈×C₄₁	1	2	yes	—
343	C₂³	#99×C₄₁	1	2	yes	—
344	C₂³	#100×C₄₁	1	2	yes	—
345	C₂³	C₂×C₂²⋊C₄×C₄₁	1	1	yes	characteristic
346	Q₈	—	4	2	no	—
347	Q₈	—	4	2	no	—
348	D₄	—	4	2	no	—
349	D₄	—	4	2	no	—
350	D₄	—	4	8	no	—
351	C₂×C₄	—	2	4	no	—
352	C₂×C₄	—	2	4	no	—
353	C₂×C₄	—	2	4	no	—
354	C₂×C₄	—	2	4	no	—
355	C₂×C₄	—	2	1	no	—
356	C₂×C₄	—	2	1	no	—
357	C₂×C₄	—	2	1	no	—
358	C₂×C₄	—	2	1	no	—
359	C₂×C₄	—	2	1	no	—
360	C₂×C₄	—	2	1	no	—
361	C₂×C₄	—	2	1	no	—
362	C₂×C₄	—	2	1	no	—
363	C₂×C₄	—	2	1	no	—
364	C₂×C₄	—	2	1	no	—
365	C₂×C₄	—	2	2	no	—
366	C₂×C₄	—	2	1	no	—
367	C₂×C₄	—	2	1	no	—
368	C₂×C₄	—	2	1	no	—
369	C₂×C₄	—	4	4	no	—
370	C₂×C₄	—	4	8	no	—
371	C₂×C₄	—	4	1	no	—
372	C₂×C₄	—	4	1	no	—
373	C₂×C₄	—	4	1	no	—
374	C₂×C₄	—	4	1	no	—
375	C₂×C₄	—	4	1	no	—
376	C₂×C₄	—	4	1	no	—
377	C₂×C₄	—	4	1	no	—
378	C₂×C₄	—	4	1	no	—
379	C₂×C₄	C₂²⋊C₈×C₄₁	1	2	yes	—
380	C₂×C₄	#104×C₄₁	1	2	yes	—
381	C₂×C₄	C₂²×C₈×C₄₁	1	1	yes	characteristic
382	C₂×C₄	C₂×M₁₆×C₄₁	1	1	yes	characteristic
383	C₂×C₄	#135×C₄₁	1	2	yes	—
384	C₂×C₄	AGL(1,ℤ/8)×C₄₁	1	1	yes	characteristic
385	C₂×C₄	#137×C₄₁	1	1	yes	characteristic
386	C₈	—	4	4	no	—
387	C₈	—	8	2	no	—
388	C₂²	—	2	2	no	—
389	C₂²	—	2	2	no	—
390	C₂²	—	2	2	no	—
391	C₂²	—	2	2	no	—
392	C₂²	—	2	2	no	—
393	C₂²	—	2	2	no	—
394	C₂²	—	4	2	no	—
395	C₂²	—	4	2	no	—
396	C₂²	—	4	2	no	—
397	C₂²	—	8	1	no	—
398	C₂²	—	8	1	no	—
399	C₂²	—	8	1	no	—
400	C₂²	—	8	1	no	—
401	C₂²	C₄₁×#323	1	4	yes	—
402	C₂²	C₂×C₂²⋊C₈×C₄₁	1	1	yes	characteristic
403	C₂²	C₂×#99×C₄₁	1	1	yes	characteristic
404	C₂²	C₂×#100×C₄₁	1	1	yes	characteristic
405	C₂²	C₄₁×#416	1	1	yes	characteristic
406	C₂²	C₄₁×#417	1	1	yes	characteristic
407	C₂²	C₂×#104×C₄₁	1	1	yes	characteristic
408	C₂²	C₄₁×#421	1	1	yes	characteristic
409	C₄	—	2	1	no	—
410	C₄	—	2	2	no	—
411	C₄	—	2	1	no	—
412	C₄	—	2	2	no	—
413	C₄	—	2	2	no	—
414	C₄	—	2	1	no	—
415	C₄	—	2	1	no	—
416	C₄	—	4	1	no	—
417	C₄	—	4	2	no	—
418	C₄	—	8	1	no	—
419	C₄	—	8	1	no	—
420	C₂	—	2	4	no	—
421	C₂	—	8	2	no	—
422	C₂	C₂×C₄₁×#323	1	1	yes	characteristic
423	C₂	C₄₁×#1476	1	1	yes	characteristic
424	C₂	C₄₁×#1477	1	1	yes	characteristic
425	C₂	C₄₁×#1504	1	1	yes	characteristic
426	C₂	C₄₁×#1516	1	1	yes	characteristic
427	C₂	C₄₁×#1530	1	1	yes	characteristic
428	C₂	C₄₁×#1551	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₄₁	C₂×C₂²⋊C₄
commutator	C₂×C₄	C₂²×C₈×C₄₁
Frattini, cosocle	C₂×C₄²	C₂³×C₄₁
prime radical	C₂²×#41×C₄₁	C₄
LCS	G ▷ C₂×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
2. C₄₁×#1817	C₂	semidirect
3. C₂×C₄₁×#336	C₂	semidirect
4. C₄₁×#1272	C₂	semidirect
5. C₄₁×#1270	C₂	semidirect
26. C₂×#41×C₄₁	C₈	semidirect
65. C₂×Q₈×C₄₁	C₂×C₈	semidirect
72. C₂×D₄×C₄₁	C₂×C₈	semidirect
173. #7578	C₄₁	direct (N × H)
207. #1817	C₂×C₄₁	semidirect
208. C₂×#336	C₂×C₄₁	semidirect
209. #1272	C₂×C₄₁	semidirect
210. #1270	C₂×C₄₁	semidirect
237. C₄₁	#7578	direct (N × H)
241. C₂×#41	C₈×C₄₁	semidirect
280. C₂×Q₈	C₂×C₈×C₄₁	semidirect
287. C₂×D₄	C₂×C₈×C₄₁	semidirect

Maximal subgroups

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

subgroup	index
C₄₁×#2297	2
C₄₁×#1817	2
C₂×C₄₁×#336	2
C₄₁×#1272	2
C₄₁×#1270	2
#7578	41

Subgroups — C41×#7578 #23783779

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#7578 #23783779