Subgroups — C₄₁×#11053 #23787254

Order 10496.

1070 conjugacy classes of subgroups.

The subgroup lattice has 482 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₁×#423	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×#104×C₄₁	C₂	1	2	yes	maximal
3	C₄₁×#2297	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄₁×#339	C₂	1	2	yes	maximal, complemented
5	C₄×#95×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×#41×C₄₁	C₂²	1	1	yes	characteristic
7	C₂²×M₁₆×C₄₁	C₂²	1	2	yes	—
8	C₂×#117×C₄₁	C₂²	1	1	yes	characteristic
9	C₂²×C₄²×C₄₁	C₂²	1	2	yes	—
10	C₂²×C₄²×C₄₁	C₂²	1	1	yes	characteristic
11	C₄₁×#423	—	2	4	no	—
12	C₂×C₄⋊C₈×C₄₁	—	2	2	no	—
13	C₂×#104×C₄₁	—	2	4	no	—
14	C₂×#104×C₄₁	—	2	4	no	—
15	C₂×#104×C₄₁	—	2	4	no	—
16	C₄₁×#391	C₄	1	1	yes	characteristic, complemented
17	C₄₁×#391	C₄	1	1	yes	characteristic, complemented
18	C₄₁×#390	C₄	1	1	yes	characteristic, complemented
19	C₄₁×#390	C₄	1	1	yes	characteristic, complemented
20	C₄₁×#386	—	2	2	no	—
21	C₄×C₂²⋊C₄×C₄₁	—	2	2	no	—
22	C₂×#95×C₄₁	—	2	2	no	—
23	C₄₁×#339	—	2	4	no	—
24	C₂×#41×C₄₁	—	2	1	no	—
25	C₂×#41×C₄₁	—	2	1	no	—
26	C₂×#41×C₄₁	—	2	2	no	—
27	C₂×#41×C₄₁	—	2	2	no	—
28	C₂×#41×C₄₁	—	2	2	no	—
29	C₂×#41×C₄₁	—	2	2	no	—
30	C₂×#41×C₄₁	D₄	1	2	yes	—
31	C₂×#41×C₄₁	Q₈	1	2	yes	—
32	C₂²×Q₈×C₄₁	C₂×C₄	1	1	yes	characteristic
33	C₂²×D₄×C₄₁	—	2	1	no	—
34	C₂²×D₄×C₄₁	C₂×C₄	1	1	yes	characteristic
35	C₂³×C₄×C₄₁	—	2	2	no	—
36	C₂³×C₄×C₄₁	—	2	1	no	—
37	C₂³×C₄×C₄₁	D₄	1	2	yes	—
38	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
39	C₂×M₁₆×C₄₁	—	2	2	no	—
40	C₂×M₁₆×C₄₁	—	2	2	no	—
41	C₂×M₁₆×C₄₁	—	2	2	no	—
42	C₂×M₁₆×C₄₁	—	2	2	no	—
43	C₂×M₁₆×C₄₁	—	2	2	no	—
44	C₂×M₁₆×C₄₁	D₄	1	4	yes	—
45	C₂²×C₈×C₄₁	—	2	2	no	—
46	#117×C₄₁	—	2	2	no	—
47	#117×C₄₁	—	2	2	no	—
48	C₂×C₄⋊C₄×C₄₁	C₂×C₄	1	1	yes	characteristic
49	C₂×C₄⋊C₄×C₄₁	C₂×C₄	1	1	yes	characteristic
50	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
51	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
52	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
53	C₂×C₄²×C₄₁	—	2	2	no	—
54	C₂×C₄²×C₄₁	—	2	2	no	—
55	C₂×C₄²×C₄₁	—	2	2	no	—
56	C₂×C₄²×C₄₁	—	2	2	no	—
57	C₂×C₄²×C₄₁	—	2	2	no	—
58	C₂×C₄²×C₄₁	—	2	2	no	—
59	C₂×C₄²×C₄₁	—	2	1	no	—
60	C₂×C₄²×C₄₁	—	2	2	no	—
61	C₂×C₄²×C₄₁	C₂×C₄	1	1	yes	characteristic
62	C₂×C₄²×C₄₁	C₂×C₄	1	1	yes	characteristic
63	C₂×C₄²×C₄₁	D₄	1	4	yes	—
64	C₂×C₄²×C₄₁	D₄	1	2	yes	—
65	C₄⋊C₈×C₄₁	—	2	8	no	—
66	#104×C₄₁	—	2	16	no	—
67	#95×C₄₁	—	2	8	no	—
68	#95×C₄₁	—	2	2	no	—
69	#95×C₄₁	—	2	2	no	—
70	C₂⁴×C₄₁	—	2	1	no	—
71	C₂⁴×C₄₁	C₂×D₄	1	1	yes	characteristic
72	#41×C₄₁	—	2	4	no	—
73	#41×C₄₁	—	2	4	no	—
74	#41×C₄₁	—	2	4	no	—
75	#41×C₄₁	—	2	4	no	—
76	#41×C₄₁	—	4	2	no	—
77	#41×C₄₁	—	4	2	no	—
78	#41×C₄₁	—	4	2	no	—
79	#41×C₄₁	—	4	2	no	—
80	C₂×Q₈×C₄₁	—	2	1	no	—
81	C₂×Q₈×C₄₁	—	2	2	no	—
82	C₂×Q₈×C₄₁	—	2	2	no	—
83	C₂×Q₈×C₄₁	C₄⋊C₄	1	2	yes	—
84	C₂×D₄×C₄₁	—	2	2	no	—
85	C₂×D₄×C₄₁	—	2	2	no	—
86	C₂×D₄×C₄₁	—	2	1	no	—
87	C₂×D₄×C₄₁	—	2	2	no	—
88	C₂×D₄×C₄₁	—	2	2	no	—
89	C₂×D₄×C₄₁	—	4	2	no	—
90	C₂×D₄×C₄₁	—	4	2	no	—
91	C₂×D₄×C₄₁	C₄⋊C₄	1	2	yes	—
92	C₂²×C₄×C₄₁	—	2	8	no	—
93	C₂²×C₄×C₄₁	—	2	1	no	—
94	C₂²×C₄×C₄₁	—	2	4	no	—
95	C₂²×C₄×C₄₁	—	2	4	no	—
96	C₂²×C₄×C₄₁	—	2	4	no	—
97	C₂²×C₄×C₄₁	—	2	2	no	—
98	C₂²×C₄×C₄₁	—	2	2	no	—
99	C₂²×C₄×C₄₁	—	2	1	no	—
100	C₂²×C₄×C₄₁	—	2	1	no	—
101	C₂²×C₄×C₄₁	—	4	2	no	—
102	C₂²×C₄×C₄₁	—	4	4	no	—
103	C₂²×C₄×C₄₁	—	4	2	no	—
104	C₂²×C₄×C₄₁	—	4	2	no	—
105	C₂²×C₄×C₄₁	—	4	1	no	—
106	C₂²×C₄×C₄₁	—	4	1	no	—
107	C₂²×C₄×C₄₁	—	4	1	no	—
108	C₂²×C₄×C₄₁	—	4	1	no	—
109	C₂²×C₄×C₄₁	C₂²⋊C₄	1	2	yes	—
110	C₂²×C₄×C₄₁	C₂²⋊C₄	1	2	yes	—
111	C₂²×C₄×C₄₁	C₂²×C₄	1	1	yes	characteristic
112	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
113	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
114	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
115	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
116	C₂²×C₄×C₄₁	C₂×Q₈	1	1	yes	characteristic
117	C₂²×C₄×C₄₁	#41	1	1	yes	characteristic
118	C₂²×C₄×C₄₁	#41	1	1	yes	characteristic
119	C₂²×C₄×C₄₁	#41	1	2	yes	—
120	C₂²×C₄×C₄₁	#41	1	2	yes	—
121	M₁₆×C₄₁	—	2	4	no	—
122	M₁₆×C₄₁	—	2	4	no	—
123	M₁₆×C₄₁	—	4	2	no	—
124	M₁₆×C₄₁	—	4	2	no	—
125	C₂×C₈×C₄₁	—	2	4	no	—
126	C₂×C₈×C₄₁	—	4	2	no	—
127	C₂×C₈×C₄₁	—	4	2	no	—
128	C₄⋊C₄×C₄₁	—	2	2	no	—
129	C₄⋊C₄×C₄₁	—	2	2	no	—
130	C₂²⋊C₄×C₄₁	—	4	4	no	—
131	C₂²⋊C₄×C₄₁	—	4	2	no	—
132	C₂²⋊C₄×C₄₁	—	4	4	no	—
133	C₄²×C₄₁	—	2	2	no	—
134	C₄²×C₄₁	—	2	2	no	—
135	C₄²×C₄₁	—	2	2	no	—
136	C₄²×C₄₁	—	2	2	no	—
137	C₄²×C₄₁	—	2	4	no	—
138	C₄²×C₄₁	—	2	4	no	—
139	C₄²×C₄₁	—	4	2	no	—
140	C₄²×C₄₁	—	4	2	no	—
141	C₄²×C₄₁	—	4	1	no	—
142	C₄²×C₄₁	—	4	1	no	—
143	C₂³×C₄₁	—	2	2	no	—
144	C₂³×C₄₁	—	2	2	no	—
145	C₂³×C₄₁	—	2	2	no	—
146	C₂³×C₄₁	—	4	1	no	—
147	C₂³×C₄₁	—	4	1	no	—
148	C₂³×C₄₁	—	4	2	no	—
149	C₂³×C₄₁	—	4	2	no	—
150	C₂³×C₄₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
151	C₂³×C₄₁	#121	1	1	yes	characteristic
152	C₂³×C₄₁	#121	1	2	yes	—
153	C₂³×C₄₁	#121	1	2	yes	—
154	C₂³×C₄₁	C₂²⋊Q₈	1	1	yes	characteristic
155	Q₈×C₄₁	—	2	4	no	—
156	Q₈×C₄₁	—	4	2	no	—
157	D₄×C₄₁	—	2	4	no	—
158	D₄×C₄₁	—	4	4	no	—
159	D₄×C₄₁	—	4	4	no	—
160	D₄×C₄₁	—	4	2	no	—
161	C₂×C₄×C₄₁	—	2	2	no	—
162	C₂×C₄×C₄₁	—	2	2	no	—
163	C₂×C₄×C₄₁	—	2	8	no	—
164	C₂×C₄×C₄₁	—	2	2	no	—
165	C₂×C₄×C₄₁	—	2	2	no	—
166	C₂×C₄×C₄₁	—	2	2	no	—
167	C₂×C₄×C₄₁	—	2	2	no	—
168	C₂×C₄×C₄₁	—	4	8	no	—
169	C₂×C₄×C₄₁	—	4	8	no	—
170	C₂×C₄×C₄₁	—	4	8	no	—
171	C₂×C₄×C₄₁	—	4	4	no	—
172	C₂×C₄×C₄₁	—	4	1	no	—
173	C₂×C₄×C₄₁	—	4	1	no	—
174	C₂×C₄×C₄₁	—	4	4	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	2	no	—
179	C₂×C₄×C₄₁	—	4	1	no	—
180	C₂×C₄×C₄₁	—	4	1	no	—
181	C₂×C₄×C₄₁	—	4	2	no	—
182	C₂×C₄×C₄₁	—	4	2	no	—
183	C₂×C₄×C₄₁	#104	1	4	yes	complemented
184	C₂×C₄×C₄₁	C₂×C₄⋊C₄	1	1	yes	characteristic
185	C₂×C₄×C₄₁	#117	1	1	yes	characteristic
186	C₂×C₄×C₄₁	C₄×D₄	1	2	yes	—
187	C₂×C₄×C₄₁	C₄×D₄	1	2	yes	—
188	C₂×C₄×C₄₁	#120	1	2	yes	—
189	C₂×C₄×C₄₁	#120	1	1	yes	characteristic
190	C₂×C₄×C₄₁	#121	1	2	yes	—
191	C₂×C₄×C₄₁	#121	1	1	yes	characteristic
192	C₂×C₄×C₄₁	C₂²⋊Q₈	1	2	yes	—
193	C₂×C₄×C₄₁	C₂²⋊Q₈	1	2	yes	—
194	C₂×C₄×C₄₁	C₂²⋊Q₈	1	1	yes	characteristic
195	C₂×C₄×C₄₁	#123	1	2	yes	—
196	C₂×C₄×C₄₁	#123	1	2	yes	—
197	C₂×C₄×C₄₁	#123	1	1	yes	characteristic
198	C₂×C₄×C₄₁	#124	1	2	yes	—
199	C₂×C₄×C₄₁	#124	1	1	yes	characteristic
200	C₂×C₄×C₄₁	#126	1	2	yes	—
201	C₂×C₄×C₄₁	#127	1	1	yes	characteristic
202	C₈×C₄₁	—	4	4	no	—
203	#11053	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
204	C₂²×C₄₁	—	2	2	no	—
205	C₂²×C₄₁	—	2	2	no	—
206	C₂²×C₄₁	—	2	4	no	—
207	C₂²×C₄₁	—	2	2	no	—
208	C₂²×C₄₁	—	2	2	no	—
209	C₂²×C₄₁	—	4	4	no	—
210	C₂²×C₄₁	—	4	2	no	—
211	C₂²×C₄₁	—	8	2	no	—
212	C₂²×C₄₁	—	8	1	no	—
213	C₂²×C₄₁	—	8	1	no	—
214	C₂²×C₄₁	#380	1	1	yes	characteristic
215	C₂²×C₄₁	#386	1	1	yes	characteristic
216	C₂²×C₄₁	#390	1	1	yes	characteristic
217	C₂²×C₄₁	#394	1	2	yes	—
218	C₂²×C₄₁	#396	1	2	yes	—
219	C₂²×C₄₁	C₂×#104	1	2	yes	—
220	C₂²×C₄₁	#421	1	2	yes	—
221	C₄×C₄₁	—	2	4	no	—
222	C₄×C₄₁	—	4	8	no	—
223	C₄×C₄₁	—	4	2	no	—
224	C₄×C₄₁	—	4	2	no	—
225	C₄×C₄₁	—	8	1	no	—
226	C₄×C₄₁	—	8	1	no	—
227	C₄×C₄₁	#385	1	2	yes	—
228	C₄×C₄₁	#388	1	2	yes	—
229	C₄×C₄₁	#392	1	1	yes	characteristic
230	C₄×C₄₁	#393	1	1	yes	characteristic
231	C₄×C₄₁	#397	1	1	yes	characteristic
232	C₄×C₄₁	#399	1	1	yes	characteristic
233	C₂×#423	C₂×C₄₁	1	1	yes	characteristic, complemented
234	C₂²×#104	C₂×C₄₁	1	2	yes	—
235	#2297	C₂×C₄₁	1	1	yes	characteristic
236	C₂×#339	C₂×C₄₁	1	2	yes	complemented
237	C₄×#95	C₂×C₄₁	1	1	yes	characteristic, complemented
238	C₂×C₄₁	—	2	2	no	—
239	C₂×C₄₁	—	2	2	no	—
240	C₂×C₄₁	—	8	2	no	—
241	C₂×C₄₁	#1439	1	1	yes	characteristic
242	C₂×C₄₁	#1806	1	2	yes	—
243	C₂×C₄₁	#1871	1	2	yes	—
244	C₂×C₄₁	#1962	1	1	yes	characteristic
245	C₂×C₄₁	#1963	1	1	yes	characteristic
246	C₂²×#41	C₂²×C₄₁	1	1	yes	characteristic
247	C₂²×M₁₆	C₂²×C₄₁	1	2	yes	—
248	C₂×#117	C₂²×C₄₁	1	1	yes	characteristic
249	C₂²×C₄²	C₂²×C₄₁	1	2	yes	—
250	C₂²×C₄²	C₂²×C₄₁	1	1	yes	characteristic
251	#423	—	2	4	no	—
252	C₂×C₄⋊C₈	—	2	2	no	—
253	C₂×#104	—	2	4	no	—
254	C₂×#104	—	2	4	no	—
255	C₂×#104	—	2	4	no	—
256	#391	C₄×C₄₁	1	1	yes	characteristic, complemented
257	#391	C₄×C₄₁	1	1	yes	characteristic, complemented
258	#390	C₄×C₄₁	1	1	yes	characteristic, complemented
259	#390	C₄×C₄₁	1	1	yes	characteristic, complemented
260	#386	—	2	2	no	—
261	C₄×C₂²⋊C₄	—	2	2	no	—
262	C₂×#95	—	2	2	no	—
263	#339	—	2	4	no	—
264	C₄₁	#11053	1	1	yes	characteristic, direct product factor, Sylow
265	C₂×#41	—	2	1	no	—
266	C₂×#41	—	2	1	no	—
267	C₂×#41	—	2	2	no	—
268	C₂×#41	—	2	2	no	—
269	C₂×#41	—	2	2	no	—
270	C₂×#41	—	2	2	no	—
271	C₂×#41	D₄×C₄₁	1	2	yes	—
272	C₂×#41	Q₈×C₄₁	1	2	yes	—
273	C₂²×Q₈	C₂×C₄×C₄₁	1	1	yes	characteristic
274	C₂²×D₄	—	2	1	no	—
275	C₂²×D₄	C₂×C₄×C₄₁	1	1	yes	characteristic
276	C₂³×C₄	—	2	2	no	—
277	C₂³×C₄	—	2	1	no	—
278	C₂³×C₄	D₄×C₄₁	1	2	yes	—
279	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
280	C₂×M₁₆	—	2	2	no	—
281	C₂×M₁₆	—	2	2	no	—
282	C₂×M₁₆	—	2	2	no	—
283	C₂×M₁₆	—	2	2	no	—
284	C₂×M₁₆	—	2	2	no	—
285	C₂×M₁₆	D₄×C₄₁	1	4	yes	—
286	C₂²×C₈	—	2	2	no	—
287	#117	—	2	2	no	—
288	#117	—	2	2	no	—
289	C₂×C₄⋊C₄	C₂×C₄×C₄₁	1	1	yes	characteristic
290	C₂×C₄⋊C₄	C₂×C₄×C₄₁	1	1	yes	characteristic
291	C₂×C₂²⋊C₄	—	2	1	no	—
292	C₂×C₂²⋊C₄	—	2	2	no	—
293	C₂×C₂²⋊C₄	—	2	2	no	—
294	C₂×C₄²	—	2	2	no	—
295	C₂×C₄²	—	2	2	no	—
296	C₂×C₄²	—	2	2	no	—
297	C₂×C₄²	—	2	2	no	—
298	C₂×C₄²	—	2	2	no	—
299	C₂×C₄²	—	2	2	no	—
300	C₂×C₄²	—	2	1	no	—
301	C₂×C₄²	—	2	2	no	—
302	C₂×C₄²	C₂×C₄×C₄₁	1	1	yes	characteristic
303	C₂×C₄²	C₂×C₄×C₄₁	1	1	yes	characteristic
304	C₂×C₄²	D₄×C₄₁	1	4	yes	—
305	C₂×C₄²	D₄×C₄₁	1	2	yes	—
306	C₄⋊C₈	—	2	8	no	—
307	#104	—	2	16	no	—
308	#95	—	2	8	no	—
309	#95	—	2	2	no	—
310	#95	—	2	2	no	—
311	C₂⁴	—	2	1	no	—
312	C₂⁴	C₂×D₄×C₄₁	1	1	yes	characteristic
313	#41	—	2	4	no	—
314	#41	—	2	4	no	—
315	#41	—	2	4	no	—
316	#41	—	2	4	no	—
317	#41	—	4	2	no	—
318	#41	—	4	2	no	—
319	#41	—	4	2	no	—
320	#41	—	4	2	no	—
321	C₂×Q₈	—	2	1	no	—
322	C₂×Q₈	—	2	2	no	—
323	C₂×Q₈	—	2	2	no	—
324	C₂×Q₈	C₄⋊C₄×C₄₁	1	2	yes	—
325	C₂×D₄	—	2	2	no	—
326	C₂×D₄	—	2	2	no	—
327	C₂×D₄	—	2	1	no	—
328	C₂×D₄	—	2	2	no	—
329	C₂×D₄	—	2	2	no	—
330	C₂×D₄	—	4	2	no	—
331	C₂×D₄	—	4	2	no	—
332	C₂×D₄	C₄⋊C₄×C₄₁	1	2	yes	—
333	C₂²×C₄	—	2	8	no	—
334	C₂²×C₄	—	2	1	no	—
335	C₂²×C₄	—	2	4	no	—
336	C₂²×C₄	—	2	4	no	—
337	C₂²×C₄	—	2	4	no	—
338	C₂²×C₄	—	2	2	no	—
339	C₂²×C₄	—	2	2	no	—
340	C₂²×C₄	—	2	1	no	—
341	C₂²×C₄	—	2	1	no	—
342	C₂²×C₄	—	4	2	no	—
343	C₂²×C₄	—	4	4	no	—
344	C₂²×C₄	—	4	2	no	—
345	C₂²×C₄	—	4	2	no	—
346	C₂²×C₄	—	4	1	no	—
347	C₂²×C₄	—	4	1	no	—
348	C₂²×C₄	—	4	1	no	—
349	C₂²×C₄	—	4	1	no	—
350	C₂²×C₄	C₂²⋊C₄×C₄₁	1	2	yes	—
351	C₂²×C₄	C₂²⋊C₄×C₄₁	1	2	yes	—
352	C₂²×C₄	C₂²×C₄×C₄₁	1	1	yes	characteristic
353	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
354	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
355	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
356	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
357	C₂²×C₄	C₂×Q₈×C₄₁	1	1	yes	characteristic
358	C₂²×C₄	#41×C₄₁	1	1	yes	characteristic
359	C₂²×C₄	#41×C₄₁	1	1	yes	characteristic
360	C₂²×C₄	#41×C₄₁	1	2	yes	—
361	C₂²×C₄	#41×C₄₁	1	2	yes	—
362	M₁₆	—	2	4	no	—
363	M₁₆	—	2	4	no	—
364	M₁₆	—	4	2	no	—
365	M₁₆	—	4	2	no	—
366	C₂×C₈	—	2	4	no	—
367	C₂×C₈	—	4	2	no	—
368	C₂×C₈	—	4	2	no	—
369	C₄⋊C₄	—	2	2	no	—
370	C₄⋊C₄	—	2	2	no	—
371	C₂²⋊C₄	—	4	4	no	—
372	C₂²⋊C₄	—	4	2	no	—
373	C₂²⋊C₄	—	4	4	no	—
374	C₄²	—	2	2	no	—
375	C₄²	—	2	2	no	—
376	C₄²	—	2	2	no	—
377	C₄²	—	2	2	no	—
378	C₄²	—	2	4	no	—
379	C₄²	—	2	4	no	—
380	C₄²	—	4	2	no	—
381	C₄²	—	4	2	no	—
382	C₄²	—	4	1	no	—
383	C₄²	—	4	1	no	—
384	C₂³	—	2	2	no	—
385	C₂³	—	2	2	no	—
386	C₂³	—	2	2	no	—
387	C₂³	—	4	1	no	—
388	C₂³	—	4	1	no	—
389	C₂³	—	4	2	no	—
390	C₂³	—	4	2	no	—
391	C₂³	C₂×C₂²⋊C₄×C₄₁	1	1	yes	characteristic
392	C₂³	#121×C₄₁	1	1	yes	characteristic
393	C₂³	#121×C₄₁	1	2	yes	—
394	C₂³	#121×C₄₁	1	2	yes	—
395	C₂³	C₂²⋊Q₈×C₄₁	1	1	yes	characteristic
396	Q₈	—	2	4	no	—
397	Q₈	—	4	2	no	—
398	D₄	—	2	4	no	—
399	D₄	—	4	4	no	—
400	D₄	—	4	4	no	—
401	D₄	—	4	2	no	—
402	C₂×C₄	—	2	2	no	—
403	C₂×C₄	—	2	2	no	—
404	C₂×C₄	—	2	8	no	—
405	C₂×C₄	—	2	2	no	—
406	C₂×C₄	—	2	2	no	—
407	C₂×C₄	—	2	2	no	—
408	C₂×C₄	—	2	2	no	—
409	C₂×C₄	—	4	8	no	—
410	C₂×C₄	—	4	8	no	—
411	C₂×C₄	—	4	8	no	—
412	C₂×C₄	—	4	4	no	—
413	C₂×C₄	—	4	1	no	—
414	C₂×C₄	—	4	1	no	—
415	C₂×C₄	—	4	4	no	—
416	C₂×C₄	—	4	2	no	—
417	C₂×C₄	—	4	2	no	—
418	C₂×C₄	—	4	2	no	—
419	C₂×C₄	—	4	2	no	—
420	C₂×C₄	—	4	1	no	—
421	C₂×C₄	—	4	1	no	—
422	C₂×C₄	—	4	2	no	—
423	C₂×C₄	—	4	2	no	—
424	C₂×C₄	#104×C₄₁	1	4	yes	complemented
425	C₂×C₄	C₂×C₄⋊C₄×C₄₁	1	1	yes	characteristic
426	C₂×C₄	#117×C₄₁	1	1	yes	characteristic
427	C₂×C₄	C₄×D₄×C₄₁	1	2	yes	—
428	C₂×C₄	C₄×D₄×C₄₁	1	2	yes	—
429	C₂×C₄	#120×C₄₁	1	2	yes	—
430	C₂×C₄	#120×C₄₁	1	1	yes	characteristic
431	C₂×C₄	#121×C₄₁	1	2	yes	—
432	C₂×C₄	#121×C₄₁	1	1	yes	characteristic
433	C₂×C₄	C₂²⋊Q₈×C₄₁	1	2	yes	—
434	C₂×C₄	C₂²⋊Q₈×C₄₁	1	2	yes	—
435	C₂×C₄	C₂²⋊Q₈×C₄₁	1	1	yes	characteristic
436	C₂×C₄	#123×C₄₁	1	2	yes	—
437	C₂×C₄	#123×C₄₁	1	2	yes	—
438	C₂×C₄	#123×C₄₁	1	1	yes	characteristic
439	C₂×C₄	#124×C₄₁	1	2	yes	—
440	C₂×C₄	#124×C₄₁	1	1	yes	characteristic
441	C₂×C₄	#126×C₄₁	1	2	yes	—
442	C₂×C₄	#127×C₄₁	1	1	yes	characteristic
443	C₈	—	4	4	no	—
444	C₂²	—	2	2	no	—
445	C₂²	—	2	2	no	—
446	C₂²	—	2	4	no	—
447	C₂²	—	2	2	no	—
448	C₂²	—	2	2	no	—
449	C₂²	—	4	4	no	—
450	C₂²	—	4	2	no	—
451	C₂²	—	8	2	no	—
452	C₂²	—	8	1	no	—
453	C₂²	—	8	1	no	—
454	C₂²	C₄₁×#380	1	1	yes	characteristic
455	C₂²	C₄₁×#386	1	1	yes	characteristic
456	C₂²	C₄₁×#390	1	1	yes	characteristic
457	C₂²	C₄₁×#394	1	2	yes	—
458	C₂²	C₄₁×#396	1	2	yes	—
459	C₂²	C₂×#104×C₄₁	1	2	yes	—
460	C₂²	C₄₁×#421	1	2	yes	—
461	C₄	—	2	4	no	—
462	C₄	—	4	8	no	—
463	C₄	—	4	2	no	—
464	C₄	—	4	2	no	—
465	C₄	—	8	1	no	—
466	C₄	—	8	1	no	—
467	C₄	C₄₁×#385	1	2	yes	—
468	C₄	C₄₁×#388	1	2	yes	—
469	C₄	C₄₁×#392	1	1	yes	characteristic
470	C₄	C₄₁×#393	1	1	yes	characteristic
471	C₄	C₄₁×#397	1	1	yes	characteristic
472	C₄	C₄₁×#399	1	1	yes	characteristic
473	C₂	—	2	2	no	—
474	C₂	—	2	2	no	—
475	C₂	—	8	2	no	—
476	C₂	C₄₁×#1439	1	1	yes	characteristic
477	C₂	C₄₁×#1806	1	2	yes	—
478	C₂	C₄₁×#1871	1	2	yes	—
479	C₂	C₄₁×#1962	1	1	yes	characteristic
480	C₂	C₄₁×#1963	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₄₁	C₂×D₄
commutator	C₂²×C₄	C₂²×C₄×C₄₁
Frattini, cosocle	C₂³×C₄	C₂³×C₄₁
socle	C₂³×C₄₁	C₂×C₂²⋊C₄
prime radical	C₂²×#41×C₄₁	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₄₁ ◁ C₂²×C₄²×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₄₁×#423	C₂	semidirect
4. C₂×C₄₁×#339	C₂	semidirect
5. C₄×#95×C₄₁	C₂	semidirect
16. C₄₁×#391	C₄	semidirect
17. C₄₁×#391	C₄	semidirect
18. C₄₁×#390	C₄	semidirect
19. C₄₁×#390	C₄	semidirect
183. C₂×C₄×C₄₁	#104	semidirect
203. #11053	C₄₁	direct (N × H)
233. C₂×#423	C₂×C₄₁	semidirect
236. C₂×#339	C₂×C₄₁	semidirect
237. C₄×#95	C₂×C₄₁	semidirect
256. #391	C₄×C₄₁	semidirect
257. #391	C₄×C₄₁	semidirect
258. #390	C₄×C₄₁	semidirect
259. #390	C₄×C₄₁	semidirect
264. C₄₁	#11053	direct (N × H)
424. C₂×C₄	#104×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×#423	2
C₂²×#104×C₄₁	2
C₄₁×#2297	2
C₂×C₄₁×#339	2
C₄×#95×C₄₁	2
#11053	41

Subgroups — C41×#11053 #23787254

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#11053 #23787254