Subgroups — C₄₁×#21095 #23797296

Order 10496.

1338 conjugacy classes of subgroups.

The subgroup lattice has 472 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₁×#418	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄₁×#418	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×M₁₆×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₁×#2296	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₄₁×#390	C₂	1	1	yes	maximal, characteristic
6	C₄₁×#1936	C₂	1	4	yes	maximal, complemented
7	C₄₁×#1934	C₂	1	4	yes	maximal, complemented
8	C₄₁×#1736	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄₁×#1736	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂³×D₄×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×C₂²⋊C₄×C₄₁	—	2	2	no	—
17	C₂²×C₄²×C₄₁	C₂²	1	1	yes	characteristic
18	C₄₁×#418	—	2	4	no	—
19	C₄₁×#418	C₄	1	8	yes	complemented
20	C₂×#102×C₄₁	C₂²	1	4	yes	—
21	C₂×#102×C₄₁	C₂²	1	4	yes	—
22	C₄×M₁₆×C₄₁	—	2	4	no	—
23	C₂×#97×C₄₁	C₂²	1	2	yes	complemented
24	C₂×C₄×C₈×C₄₁	C₂²	1	2	yes	complemented
25	C₄₁×#390	—	2	2	no	—
26	C₄₁×#390	C₂²	1	2	yes	—
27	C₄₁×#390	C₂²	1	2	yes	—
28	C₄₁×#389	C₂²	1	2	yes	complemented
29	C₄₁×#389	C₂²	1	2	yes	complemented
30	C₄₁×#385	—	2	2	no	—
31	C₄×C₄⋊C₄×C₄₁	—	2	2	no	—
32	C₄₁×#340	C₂²	1	4	yes	complemented
33	C₄₁×#340	C₂²	1	4	yes	complemented
34	C₂⁵×C₄₁	—	2	1	no	—
35	C₂²×D₄×C₄₁	—	2	2	no	—
36	C₂²×D₄×C₄₁	—	2	1	no	—
37	C₂²×D₄×C₄₁	—	2	2	no	—
38	C₂²×D₄×C₄₁	—	2	2	no	—
39	C₂²×D₄×C₄₁	—	2	2	no	—
40	C₂²×D₄×C₄₁	—	2	2	no	—
41	C₂²×D₄×C₄₁	C₂×C₄	1	4	yes	—
42	C₂²×D₄×C₄₁	C₂³	1	2	yes	—
43	C₂³×C₄×C₄₁	—	2	1	no	—
44	C₂³×C₄×C₄₁	D₄	1	2	yes	—
45	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
46	C₂×M₁₆×C₄₁	—	2	2	no	—
47	C₂×M₁₆×C₄₁	—	2	2	no	—
48	C₂×M₁₆×C₄₁	—	2	2	no	—
49	C₂×M₁₆×C₄₁	—	2	2	no	—
50	C₂×M₁₆×C₄₁	C₂×C₄	1	4	yes	—
51	C₂×M₁₆×C₄₁	D₄	1	4	yes	—
52	C₂²×C₈×C₄₁	C₂³	1	2	yes	—
53	C₂²×C₈×C₄₁	C₂³	1	2	yes	—
54	#117×C₄₁	—	2	2	no	—
55	#117×C₄₁	—	2	2	no	—
56	#117×C₄₁	—	2	2	no	—
57	#117×C₄₁	C₂×C₄	1	4	yes	—
58	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
59	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
60	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
61	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
62	C₂×C₄⋊C₄×C₄₁	—	2	2	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	2	yes	—
66	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
67	C₂×C₂²⋊C₄×C₄₁	—	2	1	no	—
68	C₂×C₂²⋊C₄×C₄₁	—	2	4	no	—
69	C₂×C₂²⋊C₄×C₄₁	—	2	4	no	—
70	C₂×C₂²⋊C₄×C₄₁	—	4	8	no	—
71	C₂×C₄²×C₄₁	—	2	2	no	—
72	C₂×C₄²×C₄₁	—	2	1	no	—
73	C₂×C₄²×C₄₁	—	2	2	no	—
74	C₂×C₄²×C₄₁	—	2	1	no	—
75	C₂×C₄²×C₄₁	D₄	1	2	yes	—
76	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
77	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
78	#102×C₄₁	—	2	8	no	—
79	#102×C₄₁	C₂×C₄	1	16	yes	complemented
80	#97×C₄₁	—	2	4	no	—
81	C₄×C₈×C₄₁	—	2	4	no	—
82	#95×C₄₁	—	2	2	no	—
83	#95×C₄₁	—	2	2	no	—
84	C₂⁴×C₄₁	—	2	4	no	—
85	C₂⁴×C₄₁	—	2	2	no	—
86	C₂⁴×C₄₁	—	4	4	no	—
87	C₂⁴×C₄₁	—	4	4	no	—
88	C₂⁴×C₄₁	—	4	2	no	—
89	C₂⁴×C₄₁	—	4	2	no	—
90	C₂⁴×C₄₁	C₂×D₄	1	1	yes	characteristic
91	C₂×D₄×C₄₁	—	2	8	no	—
92	C₂×D₄×C₄₁	—	2	8	no	—
93	C₂×D₄×C₄₁	—	2	4	no	—
94	C₂×D₄×C₄₁	—	2	2	no	—
95	C₂×D₄×C₄₁	—	2	2	no	—
96	C₂×D₄×C₄₁	—	2	2	no	—
97	C₂×D₄×C₄₁	—	2	2	no	—
98	C₂×D₄×C₄₁	—	2	2	no	—
99	C₂×D₄×C₄₁	—	4	2	no	—
100	C₂×D₄×C₄₁	—	4	4	no	—
101	C₂×D₄×C₄₁	—	4	2	no	—
102	C₂×D₄×C₄₁	—	4	4	no	—
103	C₂×D₄×C₄₁	C₂²×C₄	1	4	yes	—
104	C₂²×C₄×C₄₁	—	2	4	no	—
105	C₂²×C₄×C₄₁	—	2	2	no	—
106	C₂²×C₄×C₄₁	—	2	4	no	—
107	C₂²×C₄×C₄₁	—	2	2	no	—
108	C₂²×C₄×C₄₁	—	2	2	no	—
109	C₂²×C₄×C₄₁	—	4	2	no	—
110	C₂²×C₄×C₄₁	—	4	4	no	—
111	C₂²×C₄×C₄₁	—	4	2	no	—
112	C₂²×C₄×C₄₁	C₂²×C₄	1	2	yes	—
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×D₄	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	#41	1	2	yes	—
121	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
122	M₁₆×C₄₁	—	2	8	no	—
123	M₁₆×C₄₁	—	2	8	no	—
124	C₂×C₈×C₄₁	—	2	2	no	—
125	C₂×C₈×C₄₁	—	2	2	no	—
126	C₂×C₈×C₄₁	—	2	2	no	—
127	C₂×C₈×C₄₁	—	2	2	no	—
128	C₂×C₈×C₄₁	C₂²×C₄	1	4	yes	—
129	C₂×C₈×C₄₁	C₂×D₄	1	4	yes	—
130	C₄⋊C₄×C₄₁	—	2	2	no	—
131	C₄⋊C₄×C₄₁	—	2	2	no	—
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	—	4	4	no	—
136	C₄⋊C₄×C₄₁	—	4	2	no	—
137	C₄⋊C₄×C₄₁	—	4	4	no	—
138	C₄⋊C₄×C₄₁	C₂²×C₄	1	4	yes	—
139	C₂²⋊C₄×C₄₁	—	2	4	no	—
140	C₂²⋊C₄×C₄₁	—	4	8	no	—
141	C₂²⋊C₄×C₄₁	—	4	2	no	—
142	C₂²⋊C₄×C₄₁	—	4	8	no	—
143	C₄²×C₄₁	—	2	4	no	—
144	C₄²×C₄₁	—	2	4	no	—
145	C₄²×C₄₁	—	2	1	no	—
146	C₄²×C₄₁	—	2	1	no	—
147	C₄²×C₄₁	—	2	1	no	—
148	C₄²×C₄₁	—	2	1	no	—
149	C₄²×C₄₁	—	4	2	no	—
150	C₂³×C₄₁	—	2	2	no	—
151	C₂³×C₄₁	—	2	2	no	—
152	C₂³×C₄₁	—	2	4	no	—
153	C₂³×C₄₁	—	4	16	no	—
154	C₂³×C₄₁	—	4	2	no	—
155	C₂³×C₄₁	—	4	2	no	—
156	C₂³×C₄₁	—	4	4	no	—
157	C₂³×C₄₁	—	4	4	no	—
158	C₂³×C₄₁	—	4	8	no	—
159	C₂³×C₄₁	—	8	4	no	—
160	C₂³×C₄₁	—	8	4	no	—
161	C₂³×C₄₁	—	8	8	no	—
162	C₂³×C₄₁	C₄×D₄	1	2	yes	—
163	C₂³×C₄₁	#121	1	2	yes	—
164	C₂³×C₄₁	#124	1	2	yes	—
165	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
166	D₄×C₄₁	—	2	4	no	—
167	D₄×C₄₁	—	2	4	no	—
168	D₄×C₄₁	—	4	2	no	—
169	D₄×C₄₁	—	4	2	no	—
170	D₄×C₄₁	—	4	8	no	—
171	C₂×C₄×C₄₁	—	2	2	no	—
172	C₂×C₄×C₄₁	—	2	2	no	—
173	C₂×C₄×C₄₁	—	2	4	no	—
174	C₂×C₄×C₄₁	—	2	2	no	—
175	C₂×C₄×C₄₁	—	2	2	no	—
176	C₂×C₄×C₄₁	—	2	2	no	—
177	C₂×C₄×C₄₁	—	4	8	no	—
178	C₂×C₄×C₄₁	—	4	2	no	—
179	C₂×C₄×C₄₁	—	4	2	no	—
180	C₂×C₄×C₄₁	—	4	2	no	—
181	C₂×C₄×C₄₁	—	4	2	no	—
182	C₂×C₄×C₄₁	—	4	4	no	—
183	C₂×C₄×C₄₁	—	4	2	no	—
184	C₂×C₄×C₄₁	—	4	2	no	—
185	C₂×C₄×C₄₁	—	8	4	no	—
186	C₂×C₄×C₄₁	#117	1	4	yes	—
187	C₂×C₄×C₄₁	C₄×D₄	1	4	yes	—
188	C₂×C₄×C₄₁	C₄×D₄	1	2	yes	—
189	C₂×C₄×C₄₁	#121	1	2	yes	—
190	C₂×C₄×C₄₁	#123	1	4	yes	—
191	C₂×C₄×C₄₁	#124	1	2	yes	—
192	C₂×C₄×C₄₁	#126	1	4	yes	—
193	C₂×C₄×C₄₁	AGL(1,ℤ/8)	1	4	yes	—
194	C₂×C₄×C₄₁	C₂³×C₄	1	1	yes	characteristic
195	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
196	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
197	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
198	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
199	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
200	C₈×C₄₁	—	2	4	no	—
201	C₈×C₄₁	—	2	4	no	—
202	#21095	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
203	C₂²×C₄₁	—	2	2	no	—
204	C₂²×C₄₁	—	2	2	no	—
205	C₂²×C₄₁	—	2	4	no	—
206	C₂²×C₄₁	—	2	4	no	—
207	C₂²×C₄₁	—	4	8	no	—
208	C₂²×C₄₁	—	4	4	no	—
209	C₂²×C₄₁	—	8	16	no	—
210	C₂²×C₄₁	—	8	2	no	—
211	C₂²×C₄₁	—	8	2	no	—
212	C₂²×C₄₁	—	8	4	no	—
213	C₂²×C₄₁	#388	1	4	yes	—
214	C₂²×C₄₁	C₂×C₄×D₄	1	1	yes	characteristic
215	C₂²×C₄₁	C₂×#121	1	1	yes	characteristic
216	C₂²×C₄₁	C₂×#124	1	1	yes	characteristic
217	C₂²×C₄₁	C₂×AGL(1,ℤ/8)	1	2	yes	—
218	C₂²×C₄₁	#575	1	2	yes	—
219	C₄×C₄₁	—	2	4	no	—
220	C₄×C₄₁	—	4	4	no	—
221	C₄×C₄₁	—	4	2	no	—
222	C₄×C₄₁	—	8	2	no	—
223	C₄×C₄₁	—	8	2	no	—
224	C₄×C₄₁	#388	1	4	yes	—
225	C₄×C₄₁	C₂×#117	1	1	yes	characteristic
226	C₄×C₄₁	C₂×C₄×D₄	1	1	yes	characteristic
227	C₄×C₄₁	C₂×#123	1	1	yes	characteristic
228	C₄×C₄₁	C₂×#126	1	1	yes	characteristic
229	C₂×#418	C₂×C₄₁	1	1	yes	characteristic
230	C₂×#418	C₂×C₄₁	1	1	yes	characteristic
231	C₂×C₄×M₁₆	C₂×C₄₁	1	1	yes	characteristic, complemented
232	#2296	C₂×C₄₁	1	1	yes	characteristic, complemented
233	C₂×#390	C₂×C₄₁	1	1	yes	characteristic
234	#1936	C₂×C₄₁	1	4	yes	complemented
235	#1934	C₂×C₄₁	1	4	yes	complemented
236	#1736	C₂×C₄₁	1	1	yes	characteristic, complemented
237	#1736	C₂×C₄₁	1	1	yes	characteristic, complemented
238	C₂×C₄₁	—	2	4	no	—
239	C₂×C₄₁	—	8	4	no	—
240	C₂×C₄₁	C₂×#388	1	1	yes	characteristic
241	C₂×C₄₁	C₄×AGL(1,ℤ/8)	1	2	yes	—
242	C₂×C₄₁	#3055	1	2	yes	—
243	C₂×C₄₁	#3138	1	1	yes	characteristic
244	C₂×C₄₁	#3140	1	1	yes	characteristic
245	C₂³×D₄	C₂²×C₄₁	1	1	yes	characteristic
246	C₂²×M₁₆	C₂²×C₄₁	1	1	yes	characteristic
247	C₂²×M₁₆	C₂²×C₄₁	1	1	yes	characteristic
248	C₂×#117	C₂²×C₄₁	1	1	yes	characteristic
249	C₂×#117	C₂²×C₄₁	1	1	yes	characteristic
250	C₂²×C₄⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
251	C₂²×C₂²⋊C₄	—	2	2	no	—
252	C₂²×C₄²	C₂²×C₄₁	1	1	yes	characteristic
253	#418	—	2	4	no	—
254	#418	C₄×C₄₁	1	8	yes	complemented
255	C₂×#102	C₂²×C₄₁	1	4	yes	—
256	C₂×#102	C₂²×C₄₁	1	4	yes	—
257	C₄×M₁₆	—	2	4	no	—
258	C₂×#97	C₂²×C₄₁	1	2	yes	complemented
259	C₂×C₄×C₈	C₂²×C₄₁	1	2	yes	complemented
260	#390	—	2	2	no	—
261	#390	C₂²×C₄₁	1	2	yes	—
262	#390	C₂²×C₄₁	1	2	yes	—
263	#389	C₂²×C₄₁	1	2	yes	complemented
264	#389	C₂²×C₄₁	1	2	yes	complemented
265	#385	—	2	2	no	—
266	C₄×C₄⋊C₄	—	2	2	no	—
267	#340	C₂²×C₄₁	1	4	yes	complemented
268	#340	C₂²×C₄₁	1	4	yes	complemented
269	C₄₁	#21095	1	1	yes	characteristic, direct product factor, Sylow
270	C₂⁵	—	2	1	no	—
271	C₂²×D₄	—	2	2	no	—
272	C₂²×D₄	—	2	1	no	—
273	C₂²×D₄	—	2	2	no	—
274	C₂²×D₄	—	2	2	no	—
275	C₂²×D₄	—	2	2	no	—
276	C₂²×D₄	—	2	2	no	—
277	C₂²×D₄	C₂×C₄×C₄₁	1	4	yes	—
278	C₂²×D₄	C₂³×C₄₁	1	2	yes	—
279	C₂³×C₄	—	2	1	no	—
280	C₂³×C₄	D₄×C₄₁	1	2	yes	—
281	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
282	C₂×M₁₆	—	2	2	no	—
283	C₂×M₁₆	—	2	2	no	—
284	C₂×M₁₆	—	2	2	no	—
285	C₂×M₁₆	—	2	2	no	—
286	C₂×M₁₆	C₂×C₄×C₄₁	1	4	yes	—
287	C₂×M₁₆	D₄×C₄₁	1	4	yes	—
288	C₂²×C₈	C₂³×C₄₁	1	2	yes	—
289	C₂²×C₈	C₂³×C₄₁	1	2	yes	—
290	#117	—	2	2	no	—
291	#117	—	2	2	no	—
292	#117	—	2	2	no	—
293	#117	C₂×C₄×C₄₁	1	4	yes	—
294	C₂×C₄⋊C₄	—	2	2	no	—
295	C₂×C₄⋊C₄	—	2	2	no	—
296	C₂×C₄⋊C₄	—	2	1	no	—
297	C₂×C₄⋊C₄	—	2	2	no	—
298	C₂×C₄⋊C₄	—	2	2	no	—
299	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
300	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
301	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
302	C₂×C₂²⋊C₄	—	2	1	no	—
303	C₂×C₂²⋊C₄	—	2	1	no	—
304	C₂×C₂²⋊C₄	—	2	4	no	—
305	C₂×C₂²⋊C₄	—	2	4	no	—
306	C₂×C₂²⋊C₄	—	4	8	no	—
307	C₂×C₄²	—	2	1	no	—
308	C₂×C₄²	—	2	2	no	—
309	C₂×C₄²	—	2	2	no	—
310	C₂×C₄²	—	2	1	no	—
311	C₂×C₄²	D₄×C₄₁	1	2	yes	—
312	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
313	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
314	#102	—	2	8	no	—
315	#102	C₂×C₄×C₄₁	1	16	yes	complemented
316	#97	—	2	4	no	—
317	C₄×C₈	—	2	4	no	—
318	#95	—	2	2	no	—
319	#95	—	2	2	no	—
320	C₂⁴	—	2	4	no	—
321	C₂⁴	—	2	2	no	—
322	C₂⁴	—	4	4	no	—
323	C₂⁴	—	4	4	no	—
324	C₂⁴	—	4	2	no	—
325	C₂⁴	—	4	2	no	—
326	C₂⁴	C₂×D₄×C₄₁	1	1	yes	characteristic
327	C₂×D₄	—	2	8	no	—
328	C₂×D₄	—	2	8	no	—
329	C₂×D₄	—	2	4	no	—
330	C₂×D₄	—	2	2	no	—
331	C₂×D₄	—	2	2	no	—
332	C₂×D₄	—	2	2	no	—
333	C₂×D₄	—	2	2	no	—
334	C₂×D₄	—	2	2	no	—
335	C₂×D₄	—	4	2	no	—
336	C₂×D₄	—	4	4	no	—
337	C₂×D₄	—	4	2	no	—
338	C₂×D₄	—	4	4	no	—
339	C₂×D₄	C₂²×C₄×C₄₁	1	4	yes	—
340	C₂²×C₄	—	2	4	no	—
341	C₂²×C₄	—	2	2	no	—
342	C₂²×C₄	—	2	4	no	—
343	C₂²×C₄	—	2	2	no	—
344	C₂²×C₄	—	2	2	no	—
345	C₂²×C₄	—	4	2	no	—
346	C₂²×C₄	—	4	4	no	—
347	C₂²×C₄	—	4	2	no	—
348	C₂²×C₄	C₂²×C₄×C₄₁	1	2	yes	—
349	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
350	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
351	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
352	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
353	C₂²×C₄	#41×C₄₁	1	2	yes	—
354	C₂²×C₄	#41×C₄₁	1	2	yes	—
355	C₂²×C₄	#41×C₄₁	1	2	yes	—
356	C₂²×C₄	#41×C₄₁	1	2	yes	—
357	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
358	M₁₆	—	2	8	no	—
359	M₁₆	—	2	8	no	—
360	C₂×C₈	—	2	2	no	—
361	C₂×C₈	—	2	2	no	—
362	C₂×C₈	—	2	2	no	—
363	C₂×C₈	—	2	2	no	—
364	C₂×C₈	C₂²×C₄×C₄₁	1	4	yes	—
365	C₂×C₈	C₂×D₄×C₄₁	1	4	yes	—
366	C₄⋊C₄	—	2	2	no	—
367	C₄⋊C₄	—	2	2	no	—
368	C₄⋊C₄	—	2	2	no	—
369	C₄⋊C₄	—	2	2	no	—
370	C₄⋊C₄	—	2	2	no	—
371	C₄⋊C₄	—	4	4	no	—
372	C₄⋊C₄	—	4	2	no	—
373	C₄⋊C₄	—	4	4	no	—
374	C₄⋊C₄	C₂²×C₄×C₄₁	1	4	yes	—
375	C₂²⋊C₄	—	2	4	no	—
376	C₂²⋊C₄	—	4	8	no	—
377	C₂²⋊C₄	—	4	2	no	—
378	C₂²⋊C₄	—	4	8	no	—
379	C₄²	—	2	4	no	—
380	C₄²	—	2	4	no	—
381	C₄²	—	2	1	no	—
382	C₄²	—	2	1	no	—
383	C₄²	—	2	1	no	—
384	C₄²	—	2	1	no	—
385	C₄²	—	4	2	no	—
386	C₂³	—	2	2	no	—
387	C₂³	—	2	2	no	—
388	C₂³	—	2	4	no	—
389	C₂³	—	4	16	no	—
390	C₂³	—	4	2	no	—
391	C₂³	—	4	2	no	—
392	C₂³	—	4	4	no	—
393	C₂³	—	4	4	no	—
394	C₂³	—	4	8	no	—
395	C₂³	—	8	8	no	—
396	C₂³	—	8	4	no	—
397	C₂³	—	8	4	no	—
398	C₂³	C₄×D₄×C₄₁	1	2	yes	—
399	C₂³	#121×C₄₁	1	2	yes	—
400	C₂³	#124×C₄₁	1	2	yes	—
401	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
402	D₄	—	2	4	no	—
403	D₄	—	2	4	no	—
404	D₄	—	4	2	no	—
405	D₄	—	4	2	no	—
406	D₄	—	4	8	no	—
407	C₂×C₄	—	2	2	no	—
408	C₂×C₄	—	2	2	no	—
409	C₂×C₄	—	2	4	no	—
410	C₂×C₄	—	2	2	no	—
411	C₂×C₄	—	2	2	no	—
412	C₂×C₄	—	2	2	no	—
413	C₂×C₄	—	4	8	no	—
414	C₂×C₄	—	4	2	no	—
415	C₂×C₄	—	4	2	no	—
416	C₂×C₄	—	4	2	no	—
417	C₂×C₄	—	4	2	no	—
418	C₂×C₄	—	4	4	no	—
419	C₂×C₄	—	4	2	no	—
420	C₂×C₄	—	4	2	no	—
421	C₂×C₄	—	8	4	no	—
422	C₂×C₄	#117×C₄₁	1	4	yes	—
423	C₂×C₄	C₄×D₄×C₄₁	1	4	yes	—
424	C₂×C₄	C₄×D₄×C₄₁	1	2	yes	—
425	C₂×C₄	#121×C₄₁	1	2	yes	—
426	C₂×C₄	#123×C₄₁	1	4	yes	—
427	C₂×C₄	#124×C₄₁	1	2	yes	—
428	C₂×C₄	#126×C₄₁	1	4	yes	—
429	C₂×C₄	AGL(1,ℤ/8)×C₄₁	1	4	yes	—
430	C₂×C₄	C₂³×C₄×C₄₁	1	1	yes	characteristic
431	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
432	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
433	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
434	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
435	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
436	C₈	—	2	4	no	—
437	C₈	—	2	4	no	—
438	C₂²	—	2	4	no	—
439	C₂²	—	2	2	no	—
440	C₂²	—	2	2	no	—
441	C₂²	—	2	4	no	—
442	C₂²	—	4	4	no	—
443	C₂²	—	4	8	no	—
444	C₂²	—	8	16	no	—
445	C₂²	—	8	4	no	—
446	C₂²	—	8	2	no	—
447	C₂²	—	8	2	no	—
448	C₂²	C₄₁×#388	1	4	yes	—
449	C₂²	C₂×C₄×D₄×C₄₁	1	1	yes	characteristic
450	C₂²	C₂×#121×C₄₁	1	1	yes	characteristic
451	C₂²	C₂×#124×C₄₁	1	1	yes	characteristic
452	C₂²	C₂×AGL(1,ℤ/8)×C₄₁	1	2	yes	—
453	C₂²	C₄₁×#575	1	2	yes	—
454	C₄	—	2	4	no	—
455	C₄	—	4	2	no	—
456	C₄	—	4	4	no	—
457	C₄	—	8	2	no	—
458	C₄	—	8	2	no	—
459	C₄	C₄₁×#388	1	4	yes	—
460	C₄	C₂×#117×C₄₁	1	1	yes	characteristic
461	C₄	C₂×C₄×D₄×C₄₁	1	1	yes	characteristic
462	C₄	C₂×#123×C₄₁	1	1	yes	characteristic
463	C₄	C₂×#126×C₄₁	1	1	yes	characteristic
464	C₂	—	2	4	no	—
465	C₂	—	8	4	no	—
466	C₂	C₂×C₄₁×#388	1	1	yes	characteristic
467	C₂	C₄×AGL(1,ℤ/8)×C₄₁	1	2	yes	—
468	C₂	C₄₁×#3055	1	2	yes	—
469	C₂	C₄₁×#3138	1	1	yes	characteristic
470	C₂	C₄₁×#3140	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₄₁	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₄₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₁
prime radical	C₂³×D₄×C₄₁	C₂²
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
3. C₂×C₄×M₁₆×C₄₁	C₂	semidirect
4. C₄₁×#2296	C₂	semidirect
6. C₄₁×#1936	C₂	semidirect
7. C₄₁×#1934	C₂	semidirect
8. C₄₁×#1736	C₂	semidirect
9. C₄₁×#1736	C₂	semidirect
19. C₄₁×#418	C₄	semidirect
23. C₂×#97×C₄₁	C₂²	semidirect
24. C₂×C₄×C₈×C₄₁	C₂²	semidirect
28. C₄₁×#389	C₂²	semidirect
29. C₄₁×#389	C₂²	semidirect
32. C₄₁×#340	C₂²	semidirect
33. C₄₁×#340	C₂²	semidirect
79. #102×C₄₁	C₂×C₄	semidirect
202. #21095	C₄₁	direct (N × H)
231. C₂×C₄×M₁₆	C₂×C₄₁	semidirect
232. #2296	C₂×C₄₁	semidirect
234. #1936	C₂×C₄₁	semidirect
235. #1934	C₂×C₄₁	semidirect
236. #1736	C₂×C₄₁	semidirect
237. #1736	C₂×C₄₁	semidirect
254. #418	C₄×C₄₁	semidirect
258. C₂×#97	C₂²×C₄₁	semidirect
259. C₂×C₄×C₈	C₂²×C₄₁	semidirect
263. #389	C₂²×C₄₁	semidirect
264. #389	C₂²×C₄₁	semidirect
267. #340	C₂²×C₄₁	semidirect
268. #340	C₂²×C₄₁	semidirect
269. C₄₁	#21095	direct (N × H)
315. #102	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×#418	2
C₂×C₄×M₁₆×C₄₁	2
C₄₁×#2296	2
C₂×C₄₁×#390	2
C₄₁×#1936	2
C₄₁×#1934	2
C₄₁×#1736	2
#21095	41

Subgroups — C41×#21095 #23797296

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#21095 #23797296