Subgroups — C₄₁×#9133 #23785334

Order 10496.

784 conjugacy classes of subgroups.

The subgroup lattice has 436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄⋊C₈×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄₁×#2856	C₂	1	1	yes	maximal, characteristic
3	C₄₁×#1797	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₄₁×#331	C₂	1	2	yes	maximal, complemented
5	C₄₁×#1296	C₂	1	2	yes	maximal, complemented
6	C₂³×C₈×C₄₁	—	2	1	no	—
7	C₂×#127×C₄₁	C₂²	1	1	yes	characteristic
8	C₂×#121×C₄₁	—	2	1	no	—
9	C₂×#121×C₄₁	—	2	1	no	—
10	C₂×#121×C₄₁	C₄	1	2	yes	—
11	C₂²×C₄²×C₄₁	C₂²	1	1	yes	characteristic
12	C₂×C₄⋊C₈×C₄₁	—	2	1	no	—
13	C₂×C₄⋊C₈×C₄₁	—	2	4	no	—
14	C₂×C₄⋊C₈×C₄₁	C₂²	1	2	yes	—
15	C₂×C₄⋊C₈×C₄₁	C₂²	1	2	yes	—
16	C₂×C₂²⋊C₈×C₄₁	—	2	1	no	—
17	C₄₁×#390	—	2	1	no	—
18	C₄₁×#390	—	2	1	no	—
19	C₄₁×#390	C₄	1	2	yes	—
20	C₄₁×#384	C₂²	1	1	yes	characteristic
21	C₄₁×#336	—	2	1	no	—
22	C₄₁×#331	—	2	4	no	—
23	C₂²×D₄×C₄₁	—	2	2	no	—
24	C₂²×D₄×C₄₁	—	2	1	no	—
25	C₂²×D₄×C₄₁	—	2	1	no	—
26	C₂²×D₄×C₄₁	C₂×C₄	1	2	yes	—
27	C₂³×C₄×C₄₁	C₂×C₄	1	1	yes	characteristic
28	C₂³×C₄×C₄₁	D₄	1	1	yes	characteristic
29	C₂³×C₄×C₄₁	D₄	1	1	yes	characteristic
30	C₂²×C₈×C₄₁	—	2	4	no	—
31	C₂²×C₈×C₄₁	—	2	2	no	—
32	C₂²×C₈×C₄₁	—	2	2	no	—
33	C₂²×C₈×C₄₁	—	4	2	no	—
34	C₂²×C₈×C₄₁	—	4	2	no	—
35	#127×C₄₁	—	2	2	no	—
36	#127×C₄₁	—	2	2	no	—
37	#121×C₄₁	—	4	4	no	—
38	#121×C₄₁	—	4	2	no	—
39	#121×C₄₁	—	4	2	no	—
40	#121×C₄₁	—	4	2	no	—
41	#121×C₄₁	—	4	2	no	—
42	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
43	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
44	C₂×C₄⋊C₄×C₄₁	C₂×C₄	1	2	yes	—
45	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
46	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
47	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
48	C₂×C₄²×C₄₁	—	2	2	no	—
49	C₂×C₄²×C₄₁	—	2	2	no	—
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	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
54	C₄⋊C₈×C₄₁	—	2	4	no	—
55	C₄⋊C₈×C₄₁	—	2	2	no	—
56	C₄⋊C₈×C₄₁	—	2	2	no	—
57	C₄⋊C₈×C₄₁	—	2	2	no	—
58	C₄⋊C₈×C₄₁	D₄	1	4	yes	complemented
59	C₂²⋊C₈×C₄₁	—	4	2	no	—
60	C₂⁴×C₄₁	—	2	2	no	—
61	C₂⁴×C₄₁	C₂²⋊C₄	1	1	yes	characteristic
62	C₂×D₄×C₄₁	—	2	4	no	—
63	C₂×D₄×C₄₁	—	4	2	no	—
64	C₂×D₄×C₄₁	—	4	2	no	—
65	C₂×D₄×C₄₁	—	4	4	no	—
66	C₂×D₄×C₄₁	—	4	4	no	—
67	C₂×D₄×C₄₁	—	4	4	no	—
68	C₂×D₄×C₄₁	—	4	1	no	—
69	C₂×D₄×C₄₁	—	4	2	no	—
70	C₂×D₄×C₄₁	—	4	1	no	—
71	C₂×D₄×C₄₁	—	4	1	no	—
72	C₂×D₄×C₄₁	—	4	1	no	—
73	C₂×D₄×C₄₁	—	4	1	no	—
74	C₂×D₄×C₄₁	—	4	1	no	—
75	C₂×D₄×C₄₁	—	4	2	no	—
76	C₂×D₄×C₄₁	—	4	1	no	—
77	C₂×D₄×C₄₁	—	4	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	2	no	—
82	C₂²×C₄×C₄₁	—	2	1	no	—
83	C₂²×C₄×C₄₁	—	2	1	no	—
84	C₂²×C₄×C₄₁	—	2	2	no	—
85	C₂²×C₄×C₄₁	—	2	2	no	—
86	C₂²×C₄×C₄₁	—	2	2	no	—
87	C₂²×C₄×C₄₁	—	4	1	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	D₈	1	2	yes	—
92	C₂²×C₄×C₄₁	D₈	1	2	yes	—
93	C₂²×C₄×C₄₁	SD₁₆	1	2	yes	—
94	C₂²×C₄×C₄₁	SD₁₆	1	2	yes	—
95	C₂²×C₄×C₄₁	C₂²×C₄	1	1	yes	characteristic
96	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
97	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
98	C₂×C₈×C₄₁	—	2	4	no	—
99	C₂×C₈×C₄₁	—	4	8	no	—
100	C₂×C₈×C₄₁	—	4	2	no	—
101	C₂×C₈×C₄₁	—	4	2	no	—
102	C₂×C₈×C₄₁	—	4	2	no	—
103	C₂×C₈×C₄₁	—	4	2	no	—
104	C₂×C₈×C₄₁	—	4	2	no	—
105	C₄⋊C₄×C₄₁	—	4	2	no	—
106	C₄⋊C₄×C₄₁	—	4	1	no	—
107	C₄⋊C₄×C₄₁	—	4	1	no	—
108	C₄⋊C₄×C₄₁	—	4	1	no	—
109	C₄⋊C₄×C₄₁	—	4	1	no	—
110	C₂²⋊C₄×C₄₁	—	4	4	no	—
111	C₂²⋊C₄×C₄₁	—	4	4	no	—
112	C₂²⋊C₄×C₄₁	—	4	4	no	—
113	C₄²×C₄₁	—	2	2	no	—
114	C₄²×C₄₁	—	2	1	no	—
115	C₄²×C₄₁	—	2	2	no	—
116	C₄²×C₄₁	—	2	1	no	—
117	C₄²×C₄₁	C₂×D₄	1	2	yes	—
118	C₄²×C₄₁	#41	1	2	yes	—
119	C₂³×C₄₁	—	2	1	no	—
120	C₂³×C₄₁	—	2	1	no	—
121	C₂³×C₄₁	—	2	1	no	—
122	C₂³×C₄₁	—	2	1	no	—
123	C₂³×C₄₁	—	4	2	no	—
124	C₂³×C₄₁	—	4	2	no	—
125	C₂³×C₄₁	—	4	2	no	—
126	C₂³×C₄₁	—	4	2	no	—
127	C₂³×C₄₁	—	4	2	no	—
128	C₂³×C₄₁	—	4	2	no	—
129	C₂³×C₄₁	—	4	2	no	—
130	C₂³×C₄₁	#100	1	2	yes	—
131	C₂³×C₄₁	#102	1	2	yes	—
132	C₂³×C₄₁	#102	1	2	yes	—
133	C₂³×C₄₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
134	D₄×C₄₁	—	8	4	no	—
135	D₄×C₄₁	—	8	8	no	—
136	D₄×C₄₁	—	8	1	no	—
137	D₄×C₄₁	—	8	1	no	—
138	D₄×C₄₁	—	8	2	no	—
139	D₄×C₄₁	—	8	2	no	—
140	D₄×C₄₁	—	8	1	no	—
141	D₄×C₄₁	—	8	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	2	no	—
149	C₂×C₄×C₄₁	—	2	2	no	—
150	C₂×C₄×C₄₁	—	2	4	no	—
151	C₂×C₄×C₄₁	—	2	4	no	—
152	C₂×C₄×C₄₁	—	2	2	no	—
153	C₂×C₄×C₄₁	—	2	2	no	—
154	C₂×C₄×C₄₁	—	2	1	no	—
155	C₂×C₄×C₄₁	—	2	1	no	—
156	C₂×C₄×C₄₁	—	2	1	no	—
157	C₂×C₄×C₄₁	—	4	4	no	—
158	C₂×C₄×C₄₁	—	4	2	no	—
159	C₂×C₄×C₄₁	—	4	2	no	—
160	C₂×C₄×C₄₁	—	4	2	no	—
161	C₂×C₄×C₄₁	#102	1	2	yes	—
162	C₂×C₄×C₄₁	#102	1	2	yes	—
163	C₂×C₄×C₄₁	C₄×D₄	1	2	yes	—
164	C₂×C₄×C₄₁	#120	1	1	yes	characteristic
165	C₂×C₄×C₄₁	#121	1	2	yes	—
166	C₂×C₄×C₄₁	#123	1	1	yes	characteristic
167	C₂×C₄×C₄₁	C₂×D₈	1	1	yes	characteristic
168	C₂×C₄×C₄₁	C₂×D₈	1	1	yes	characteristic
169	C₂×C₄×C₄₁	C₂×SD₁₆	1	1	yes	characteristic
170	C₂×C₄×C₄₁	C₂×SD₁₆	1	1	yes	characteristic
171	C₂×C₄×C₄₁	#135	1	2	yes	—
172	C₂×C₄×C₄₁	AGL(1,ℤ/8)	1	1	yes	characteristic
173	C₂×C₄×C₄₁	#137	1	1	yes	characteristic
174	C₈×C₄₁	—	4	4	no	—
175	C₈×C₄₁	—	8	2	no	—
176	#9133	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
177	C₂²×C₄₁	—	2	2	no	—
178	C₂²×C₄₁	—	2	2	no	—
179	C₂²×C₄₁	—	2	2	no	—
180	C₂²×C₄₁	—	2	2	no	—
181	C₂²×C₄₁	—	2	2	no	—
182	C₂²×C₄₁	—	2	2	no	—
183	C₂²×C₄₁	—	8	2	no	—
184	C₂²×C₄₁	—	8	2	no	—
185	C₂²×C₄₁	—	8	2	no	—
186	C₂²×C₄₁	—	8	2	no	—
187	C₂²×C₄₁	—	8	2	no	—
188	C₂²×C₄₁	—	8	2	no	—
189	C₂²×C₄₁	—	8	2	no	—
190	C₂²×C₄₁	#331	1	4	yes	complemented
191	C₂²×C₄₁	#386	1	1	yes	characteristic
192	C₂²×C₄₁	C₂×#100	1	1	yes	characteristic
193	C₂²×C₄₁	#413	1	1	yes	characteristic
194	C₂²×C₄₁	C₂×#102	1	1	yes	characteristic
195	C₂²×C₄₁	C₂×#102	1	1	yes	characteristic
196	C₂²×C₄₁	#416	1	1	yes	characteristic
197	C₂²×C₄₁	#417	1	1	yes	characteristic
198	C₄×C₄₁	—	2	2	no	—
199	C₄×C₄₁	—	2	2	no	—
200	C₄×C₄₁	—	2	2	no	—
201	C₄×C₄₁	—	4	1	no	—
202	C₄×C₄₁	—	8	2	no	—
203	C₄×C₄₁	#447	1	1	yes	characteristic
204	C₄×C₄₁	#448	1	1	yes	characteristic
205	C₄×C₄₁	#465	1	2	yes	—
206	C₄×C₄₁	#466	1	2	yes	—
207	C₄×C₄₁	#480	1	1	yes	characteristic
208	C₄×C₄₁	#481	1	1	yes	characteristic
209	C₂²×C₄⋊C₈	C₂×C₄₁	1	1	yes	characteristic, complemented
210	#2856	C₂×C₄₁	1	1	yes	characteristic
211	#1797	C₂×C₄₁	1	1	yes	characteristic, complemented
212	C₂×#331	C₂×C₄₁	1	2	yes	complemented
213	#1296	C₂×C₄₁	1	2	yes	complemented
214	C₂×C₄₁	—	2	4	no	—
215	C₂×C₄₁	—	16	2	no	—
216	C₂×C₄₁	C₂×#331	1	1	yes	characteristic
217	C₂×C₄₁	#1540	1	1	yes	characteristic
218	C₂×C₄₁	#1547	1	1	yes	characteristic
219	C₂×C₄₁	#1551	1	1	yes	characteristic
220	C₂×C₄₁	#1874	1	1	yes	characteristic
221	C₂×C₄₁	#1893	1	1	yes	characteristic
222	C₂×C₄₁	#1900	1	1	yes	characteristic
223	C₂³×C₈	—	2	1	no	—
224	C₂×#127	C₂²×C₄₁	1	1	yes	characteristic
225	C₂×#121	—	2	1	no	—
226	C₂×#121	—	2	1	no	—
227	C₂×#121	C₄×C₄₁	1	2	yes	—
228	C₂²×C₄²	C₂²×C₄₁	1	1	yes	characteristic
229	C₂×C₄⋊C₈	—	2	1	no	—
230	C₂×C₄⋊C₈	—	2	4	no	—
231	C₂×C₄⋊C₈	C₂²×C₄₁	1	2	yes	—
232	C₂×C₄⋊C₈	C₂²×C₄₁	1	2	yes	—
233	C₂×C₂²⋊C₈	—	2	1	no	—
234	#390	—	2	1	no	—
235	#390	—	2	1	no	—
236	#390	C₄×C₄₁	1	2	yes	—
237	#384	C₂²×C₄₁	1	1	yes	characteristic
238	#336	—	2	1	no	—
239	#331	—	2	4	no	—
240	C₄₁	#9133	1	1	yes	characteristic, direct product factor, Sylow
241	C₂²×D₄	—	2	2	no	—
242	C₂²×D₄	—	2	1	no	—
243	C₂²×D₄	—	2	1	no	—
244	C₂²×D₄	C₂×C₄×C₄₁	1	2	yes	—
245	C₂³×C₄	C₂×C₄×C₄₁	1	1	yes	characteristic
246	C₂³×C₄	D₄×C₄₁	1	1	yes	characteristic
247	C₂³×C₄	D₄×C₄₁	1	1	yes	characteristic
248	C₂²×C₈	—	2	4	no	—
249	C₂²×C₈	—	2	2	no	—
250	C₂²×C₈	—	2	2	no	—
251	C₂²×C₈	—	4	2	no	—
252	C₂²×C₈	—	4	2	no	—
253	#127	—	2	2	no	—
254	#127	—	2	2	no	—
255	#121	—	4	4	no	—
256	#121	—	4	2	no	—
257	#121	—	4	2	no	—
258	#121	—	4	2	no	—
259	#121	—	4	2	no	—
260	C₂×C₄⋊C₄	—	2	1	no	—
261	C₂×C₄⋊C₄	—	2	1	no	—
262	C₂×C₄⋊C₄	C₂×C₄×C₄₁	1	2	yes	—
263	C₂×C₂²⋊C₄	—	2	2	no	—
264	C₂×C₂²⋊C₄	—	2	2	no	—
265	C₂×C₂²⋊C₄	—	2	2	no	—
266	C₂×C₄²	—	2	2	no	—
267	C₂×C₄²	—	2	2	no	—
268	C₂×C₄²	C₂×C₄×C₄₁	1	1	yes	characteristic
269	C₂×C₄²	D₄×C₄₁	1	1	yes	characteristic
270	C₂×C₄²	D₄×C₄₁	1	1	yes	characteristic
271	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
272	C₄⋊C₈	—	2	4	no	—
273	C₄⋊C₈	—	2	2	no	—
274	C₄⋊C₈	—	2	2	no	—
275	C₄⋊C₈	—	2	2	no	—
276	C₄⋊C₈	D₄×C₄₁	1	4	yes	complemented
277	C₂²⋊C₈	—	4	2	no	—
278	C₂⁴	—	2	2	no	—
279	C₂⁴	C₂²⋊C₄×C₄₁	1	1	yes	characteristic
280	C₂×D₄	—	2	4	no	—
281	C₂×D₄	—	4	2	no	—
282	C₂×D₄	—	4	2	no	—
283	C₂×D₄	—	4	4	no	—
284	C₂×D₄	—	4	4	no	—
285	C₂×D₄	—	4	4	no	—
286	C₂×D₄	—	4	1	no	—
287	C₂×D₄	—	4	2	no	—
288	C₂×D₄	—	4	1	no	—
289	C₂×D₄	—	4	1	no	—
290	C₂×D₄	—	4	1	no	—
291	C₂×D₄	—	4	1	no	—
292	C₂×D₄	—	4	1	no	—
293	C₂×D₄	—	4	2	no	—
294	C₂×D₄	—	4	1	no	—
295	C₂×D₄	—	4	1	no	—
296	C₂²×C₄	—	2	1	no	—
297	C₂²×C₄	—	2	2	no	—
298	C₂²×C₄	—	2	1	no	—
299	C₂²×C₄	—	2	2	no	—
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	2	no	—
305	C₂²×C₄	—	4	1	no	—
306	C₂²×C₄	C₂²⋊C₄×C₄₁	1	1	yes	characteristic
307	C₂²×C₄	C₂²⋊C₄×C₄₁	1	1	yes	characteristic
308	C₂²×C₄	C₂²⋊C₄×C₄₁	1	1	yes	characteristic
309	C₂²×C₄	D₈×C₄₁	1	2	yes	—
310	C₂²×C₄	D₈×C₄₁	1	2	yes	—
311	C₂²×C₄	SD₁₆×C₄₁	1	2	yes	—
312	C₂²×C₄	SD₁₆×C₄₁	1	2	yes	—
313	C₂²×C₄	C₂²×C₄×C₄₁	1	1	yes	characteristic
314	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
315	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
316	C₂×C₈	—	2	4	no	—
317	C₂×C₈	—	4	8	no	—
318	C₂×C₈	—	4	2	no	—
319	C₂×C₈	—	4	2	no	—
320	C₂×C₈	—	4	2	no	—
321	C₂×C₈	—	4	2	no	—
322	C₂×C₈	—	4	2	no	—
323	C₄⋊C₄	—	4	2	no	—
324	C₄⋊C₄	—	4	1	no	—
325	C₄⋊C₄	—	4	1	no	—
326	C₄⋊C₄	—	4	1	no	—
327	C₄⋊C₄	—	4	1	no	—
328	C₂²⋊C₄	—	4	4	no	—
329	C₂²⋊C₄	—	4	4	no	—
330	C₂²⋊C₄	—	4	4	no	—
331	C₄²	—	2	2	no	—
332	C₄²	—	2	1	no	—
333	C₄²	—	2	2	no	—
334	C₄²	—	2	1	no	—
335	C₄²	C₂×D₄×C₄₁	1	2	yes	—
336	C₄²	#41×C₄₁	1	2	yes	—
337	C₂³	—	2	1	no	—
338	C₂³	—	2	1	no	—
339	C₂³	—	2	1	no	—
340	C₂³	—	2	1	no	—
341	C₂³	—	4	2	no	—
342	C₂³	—	4	2	no	—
343	C₂³	—	4	2	no	—
344	C₂³	—	4	2	no	—
345	C₂³	—	4	2	no	—
346	C₂³	—	4	2	no	—
347	C₂³	—	4	2	no	—
348	C₂³	#100×C₄₁	1	2	yes	—
349	C₂³	#102×C₄₁	1	2	yes	—
350	C₂³	#102×C₄₁	1	2	yes	—
351	C₂³	C₂×C₂²⋊C₄×C₄₁	1	1	yes	characteristic
352	D₄	—	8	4	no	—
353	D₄	—	8	8	no	—
354	D₄	—	8	1	no	—
355	D₄	—	8	1	no	—
356	D₄	—	8	2	no	—
357	D₄	—	8	2	no	—
358	D₄	—	8	1	no	—
359	D₄	—	8	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	1	no	—
366	C₂×C₄	—	2	2	no	—
367	C₂×C₄	—	2	2	no	—
368	C₂×C₄	—	2	4	no	—
369	C₂×C₄	—	2	4	no	—
370	C₂×C₄	—	2	2	no	—
371	C₂×C₄	—	2	2	no	—
372	C₂×C₄	—	2	1	no	—
373	C₂×C₄	—	2	1	no	—
374	C₂×C₄	—	2	1	no	—
375	C₂×C₄	—	4	4	no	—
376	C₂×C₄	—	4	2	no	—
377	C₂×C₄	—	4	2	no	—
378	C₂×C₄	—	4	2	no	—
379	C₂×C₄	#102×C₄₁	1	2	yes	—
380	C₂×C₄	#102×C₄₁	1	2	yes	—
381	C₂×C₄	C₄×D₄×C₄₁	1	2	yes	—
382	C₂×C₄	#120×C₄₁	1	1	yes	characteristic
383	C₂×C₄	#121×C₄₁	1	2	yes	—
384	C₂×C₄	#123×C₄₁	1	1	yes	characteristic
385	C₂×C₄	C₂×D₈×C₄₁	1	1	yes	characteristic
386	C₂×C₄	C₂×D₈×C₄₁	1	1	yes	characteristic
387	C₂×C₄	C₂×SD₁₆×C₄₁	1	1	yes	characteristic
388	C₂×C₄	C₂×SD₁₆×C₄₁	1	1	yes	characteristic
389	C₂×C₄	#135×C₄₁	1	2	yes	—
390	C₂×C₄	AGL(1,ℤ/8)×C₄₁	1	1	yes	characteristic
391	C₂×C₄	#137×C₄₁	1	1	yes	characteristic
392	C₈	—	4	4	no	—
393	C₈	—	8	2	no	—
394	C₂²	—	2	2	no	—
395	C₂²	—	2	2	no	—
396	C₂²	—	2	2	no	—
397	C₂²	—	2	2	no	—
398	C₂²	—	2	2	no	—
399	C₂²	—	2	2	no	—
400	C₂²	—	8	2	no	—
401	C₂²	—	8	2	no	—
402	C₂²	—	8	2	no	—
403	C₂²	—	8	2	no	—
404	C₂²	—	8	2	no	—
405	C₂²	—	8	2	no	—
406	C₂²	—	8	2	no	—
407	C₂²	C₄₁×#331	1	4	yes	complemented
408	C₂²	C₄₁×#386	1	1	yes	characteristic
409	C₂²	C₂×#100×C₄₁	1	1	yes	characteristic
410	C₂²	C₄₁×#413	1	1	yes	characteristic
411	C₂²	C₂×#102×C₄₁	1	1	yes	characteristic
412	C₂²	C₂×#102×C₄₁	1	1	yes	characteristic
413	C₂²	C₄₁×#416	1	1	yes	characteristic
414	C₂²	C₄₁×#417	1	1	yes	characteristic
415	C₄	—	2	2	no	—
416	C₄	—	2	2	no	—
417	C₄	—	2	2	no	—
418	C₄	—	4	1	no	—
419	C₄	—	8	2	no	—
420	C₄	C₄₁×#447	1	1	yes	characteristic
421	C₄	C₄₁×#448	1	1	yes	characteristic
422	C₄	C₄₁×#465	1	2	yes	—
423	C₄	C₄₁×#466	1	2	yes	—
424	C₄	C₄₁×#480	1	1	yes	characteristic
425	C₄	C₄₁×#481	1	1	yes	characteristic
426	C₂	—	2	4	no	—
427	C₂	—	16	2	no	—
428	C₂	C₂×C₄₁×#331	1	1	yes	characteristic
429	C₂	C₄₁×#1540	1	1	yes	characteristic
430	C₂	C₄₁×#1547	1	1	yes	characteristic
431	C₂	C₄₁×#1551	1	1	yes	characteristic
432	C₂	C₄₁×#1874	1	1	yes	characteristic
433	C₂	C₄₁×#1893	1	1	yes	characteristic
434	C₂	C₄₁×#1900	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₄₁	C₂×C₂²⋊C₄
commutator	C₂²×C₄	C₂²×C₄×C₄₁
Frattini, cosocle	C₂×C₄²	C₂³×C₄₁
prime radical	C₄₁×#2856	C₂
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
1. C₂²×C₄⋊C₈×C₄₁	C₂	semidirect
3. C₄₁×#1797	C₂	semidirect
4. C₂×C₄₁×#331	C₂	semidirect
5. C₄₁×#1296	C₂	semidirect
58. C₄⋊C₈×C₄₁	D₄	semidirect
176. #9133	C₄₁	direct (N × H)
190. C₂²×C₄₁	#331	semidirect
209. C₂²×C₄⋊C₈	C₂×C₄₁	semidirect
211. #1797	C₂×C₄₁	semidirect
212. C₂×#331	C₂×C₄₁	semidirect
213. #1296	C₂×C₄₁	semidirect
240. C₄₁	#9133	direct (N × H)
276. C₄⋊C₈	D₄×C₄₁	semidirect
407. C₂²	C₄₁×#331	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₄⋊C₈×C₄₁	2
C₄₁×#2856	2
C₄₁×#1797	2
C₂×C₄₁×#331	2
C₄₁×#1296	2
#9133	41

Subgroups — C41×#9133 #23785334

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#9133 #23785334