Subgroups — C₄₁×#22196 #23798397

Order 10496.

934 conjugacy classes of subgroups.

The subgroup lattice has 462 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₁×#466	C₂	1	1	yes	maximal, characteristic
2	C₄₁×#2324	C₂	1	2	yes	maximal, complemented
3	C₄₁×#1925	C₂	1	2	yes	maximal, complemented
4	C₄₁×#1921	C₂	1	2	yes	maximal, complemented
5	C₄₁×#1895	C₂	1	2	yes	maximal, complemented
6	C₄₁×#1879	C₂	1	2	yes	maximal, complemented
7	C₄₁×#1862	C₂	1	2	yes	maximal, complemented
8	C₄₁×#1808	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄₁×#1729	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×D₈×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×#121×C₄₁	C₂²	1	2	yes	—
14	C₂×C₄×D₄×C₄₁	C₂²	1	2	yes	—
15	C₂×#117×C₄₁	C₂²	1	1	yes	characteristic
16	C₄₁×#466	C₄	1	8	yes	complemented
17	C₂×#107×C₄₁	C₂²	1	1	yes	characteristic
18	C₂×#107×C₄₁	C₂²	1	1	yes	characteristic
19	C₂×#107×C₄₁	C₂²	1	1	yes	characteristic
20	C₂×#102×C₄₁	C₂²	1	2	yes	—
21	C₂×#102×C₄₁	C₂²	1	2	yes	—
22	C₂×#102×C₄₁	C₂²	1	2	yes	—
23	C₄₁×#390	—	2	2	no	—
24	C₄₁×#390	C₂²	1	2	yes	—
25	C₄₁×#389	C₂²	1	2	yes	—
26	C₄₁×#388	—	2	2	no	—
27	C₄₁×#386	—	2	2	no	—
28	C₄₁×#385	—	2	2	no	—
29	C₄₁×#380	C₂²	1	2	yes	—
30	C₄×C₄⋊C₄×C₄₁	C₂²	1	2	yes	—
31	C₄₁×#340	C₂²	1	2	yes	—
32	C₄₁×#340	C₂²	1	2	yes	—
33	C₄₁×#340	C₂²	1	2	yes	—
34	C₄₁×#336	C₂²	1	2	yes	—
35	C₄₁×#336	C₂²	1	2	yes	—
36	C₂²×D₄×C₄₁	—	2	2	no	—
37	C₂²×D₄×C₄₁	C₂³	1	2	yes	—
38	C₂³×C₄×C₄₁	—	2	2	no	—
39	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
40	C₂×D₈×C₄₁	—	4	1	no	—
41	C₂×D₈×C₄₁	—	4	1	no	—
42	C₂×D₈×C₄₁	C₂×C₄	1	4	yes	—
43	C₂×M₁₆×C₄₁	—	2	2	no	—
44	C₂×M₁₆×C₄₁	—	4	1	no	—
45	C₂×M₁₆×C₄₁	—	4	1	no	—
46	C₂²×C₈×C₄₁	—	4	1	no	—
47	C₂²×C₈×C₄₁	—	4	1	no	—
48	C₂²×C₈×C₄₁	C₂×C₄	1	4	yes	complemented
49	C₂²×C₈×C₄₁	C₂³	1	2	yes	—
50	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
51	C₂²×C₈×C₄₁	C₂³	1	1	yes	characteristic
52	#121×C₄₁	—	2	4	no	—
53	#121×C₄₁	C₂×C₄	1	8	yes	complemented
54	C₄×D₄×C₄₁	—	4	2	no	—
55	C₄×D₄×C₄₁	—	4	2	no	—
56	#117×C₄₁	—	4	1	no	—
57	#117×C₄₁	—	4	1	no	—
58	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
59	C₂×C₄⋊C₄×C₄₁	D₄	1	1	yes	characteristic
60	C₂×C₄⋊C₄×C₄₁	D₄	1	1	yes	characteristic
61	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
62	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
63	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
64	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
65	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
66	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
67	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
68	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
69	C₂×C₂²⋊C₄×C₄₁	D₄	1	2	yes	—
70	C₂×C₄²×C₄₁	—	2	2	no	—
71	C₂×C₄²×C₄₁	C₂³	1	2	yes	—
72	#107×C₄₁	—	4	1	no	—
73	#107×C₄₁	—	4	1	no	—
74	#107×C₄₁	C₂×C₄	1	4	yes	complemented
75	#102×C₄₁	—	4	2	no	—
76	#102×C₄₁	—	4	2	no	—
77	#102×C₄₁	C₂×C₄	1	8	yes	complemented
78	#95×C₄₁	—	2	2	no	—
79	#95×C₄₁	—	2	2	no	—
80	#95×C₄₁	—	2	2	no	—
81	C₂⁴×C₄₁	—	2	2	no	—
82	C₂⁴×C₄₁	C₂×D₄	1	1	yes	characteristic
83	C₂×D₄×C₄₁	—	2	8	no	—
84	C₂×D₄×C₄₁	—	2	2	no	—
85	C₂×D₄×C₄₁	—	2	2	no	—
86	C₂×D₄×C₄₁	—	2	2	no	—
87	C₂×D₄×C₄₁	—	2	2	no	—
88	C₂×D₄×C₄₁	—	2	2	no	—
89	C₂×D₄×C₄₁	—	8	2	no	—
90	C₂×D₄×C₄₁	—	8	2	no	—
91	C₂×D₄×C₄₁	C₂²×C₄	1	4	yes	—
92	C₂²×C₄×C₄₁	—	2	1	no	—
93	C₂²×C₄×C₄₁	—	2	1	no	—
94	C₂²×C₄×C₄₁	—	2	1	no	—
95	C₂²×C₄×C₄₁	—	2	1	no	—
96	C₂²×C₄×C₄₁	—	2	2	no	—
97	C₂²×C₄×C₄₁	—	2	2	no	—
98	C₂²×C₄×C₄₁	—	2	2	no	—
99	C₂²×C₄×C₄₁	—	4	4	no	—
100	C₂²×C₄×C₄₁	—	8	2	no	—
101	C₂²×C₄×C₄₁	—	8	2	no	—
102	C₂²×C₄×C₄₁	C₂²×C₄	1	2	yes	—
103	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
104	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
105	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
106	C₂²×C₄×C₄₁	#41	1	2	yes	—
107	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
108	D₈×C₄₁	—	4	4	no	—
109	M₁₆×C₄₁	—	4	4	no	—
110	C₂×C₈×C₄₁	—	2	1	no	—
111	C₂×C₈×C₄₁	—	2	1	no	—
112	C₂×C₈×C₄₁	—	2	1	no	—
113	C₂×C₈×C₄₁	—	2	1	no	—
114	C₂×C₈×C₄₁	—	2	2	no	—
115	C₂×C₈×C₄₁	—	2	2	no	—
116	C₂×C₈×C₄₁	—	2	2	no	—
117	C₂×C₈×C₄₁	—	4	4	no	—
118	C₂×C₈×C₄₁	C₂²×C₄	1	2	yes	—
119	C₂×C₈×C₄₁	C₂²×C₄	1	2	yes	—
120	C₄⋊C₄×C₄₁	—	2	2	no	—
121	C₄⋊C₄×C₄₁	—	2	2	no	—
122	C₄⋊C₄×C₄₁	—	2	2	no	—
123	C₄⋊C₄×C₄₁	—	2	2	no	—
124	C₄⋊C₄×C₄₁	—	2	2	no	—
125	C₄⋊C₄×C₄₁	—	4	1	no	—
126	C₄⋊C₄×C₄₁	—	4	1	no	—
127	C₄⋊C₄×C₄₁	—	8	2	no	—
128	C₄⋊C₄×C₄₁	C₂²×C₄	1	4	yes	—
129	C₂²⋊C₄×C₄₁	—	2	8	no	—
130	C₂²⋊C₄×C₄₁	—	4	2	no	—
131	C₂²⋊C₄×C₄₁	—	4	4	no	—
132	C₂²⋊C₄×C₄₁	—	8	2	no	—
133	C₂²⋊C₄×C₄₁	—	8	2	no	—
134	C₂²⋊C₄×C₄₁	—	8	2	no	—
135	C₄²×C₄₁	—	2	2	no	—
136	C₄²×C₄₁	—	2	2	no	—
137	C₄²×C₄₁	—	8	2	no	—
138	C₂³×C₄₁	—	2	1	no	—
139	C₂³×C₄₁	—	2	1	no	—
140	C₂³×C₄₁	—	2	1	no	—
141	C₂³×C₄₁	—	2	1	no	—
142	C₂³×C₄₁	—	2	1	no	—
143	C₂³×C₄₁	—	2	1	no	—
144	C₂³×C₄₁	—	2	4	no	—
145	C₂³×C₄₁	—	4	2	no	—
146	C₂³×C₄₁	—	4	2	no	—
147	C₂³×C₄₁	—	4	2	no	—
148	C₂³×C₄₁	—	4	2	no	—
149	C₂³×C₄₁	—	4	2	no	—
150	C₂³×C₄₁	—	4	2	no	—
151	C₂³×C₄₁	C₄×D₄	1	2	yes	—
152	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
153	D₄×C₄₁	—	2	4	no	—
154	D₄×C₄₁	—	2	4	no	—
155	D₄×C₄₁	—	4	2	no	—
156	D₄×C₄₁	—	4	2	no	—
157	D₄×C₄₁	—	8	8	no	—
158	C₂×C₄×C₄₁	—	2	1	no	—
159	C₂×C₄×C₄₁	—	2	1	no	—
160	C₂×C₄×C₄₁	—	2	2	no	—
161	C₂×C₄×C₄₁	—	2	2	no	—
162	C₂×C₄×C₄₁	—	2	2	no	—
163	C₂×C₄×C₄₁	—	2	2	no	—
164	C₂×C₄×C₄₁	—	2	4	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	—	2	2	no	—
169	C₂×C₄×C₄₁	—	2	2	no	—
170	C₂×C₄×C₄₁	—	2	2	no	—
171	C₂×C₄×C₄₁	—	4	2	no	—
172	C₂×C₄×C₄₁	—	4	2	no	—
173	C₂×C₄×C₄₁	—	4	2	no	—
174	C₂×C₄×C₄₁	—	4	2	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	—	8	8	no	—
180	C₂×C₄×C₄₁	C₄×D₄	1	2	yes	—
181	C₂×C₄×C₄₁	C₂³×C₄	1	1	yes	characteristic
182	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
183	C₂×C₄×C₄₁	H(5,𝔽₂)	1	1	yes	characteristic
184	C₂×C₄×C₄₁	H(5,𝔽₂)	1	1	yes	characteristic
185	C₂×C₄×C₄₁	H(5,𝔽₂)	1	1	yes	characteristic
186	C₂×C₄×C₄₁	2₋¹⁺⁴	1	1	yes	characteristic
187	C₈×C₄₁	—	2	2	no	—
188	C₈×C₄₁	—	2	2	no	—
189	C₈×C₄₁	—	4	2	no	—
190	#22196	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
191	C₂²×C₄₁	—	2	2	no	—
192	C₂²×C₄₁	—	2	2	no	—
193	C₂²×C₄₁	—	2	2	no	—
194	C₂²×C₄₁	—	4	1	no	—
195	C₂²×C₄₁	—	4	1	no	—
196	C₂²×C₄₁	—	4	1	no	—
197	C₂²×C₄₁	—	4	1	no	—
198	C₂²×C₄₁	—	4	4	no	—
199	C₂²×C₄₁	—	4	4	no	—
200	C₂²×C₄₁	—	4	4	no	—
201	C₂²×C₄₁	—	8	2	no	—
202	C₂²×C₄₁	—	8	2	no	—
203	C₂²×C₄₁	—	8	2	no	—
204	C₂²×C₄₁	—	8	2	no	—
205	C₂²×C₄₁	C₂×C₄×D₄	1	1	yes	characteristic
206	C₂²×C₄₁	#534	1	1	yes	characteristic
207	C₂²×C₄₁	#537	1	1	yes	characteristic
208	C₂²×C₄₁	#576	1	1	yes	characteristic
209	C₂²×C₄₁	#576	1	1	yes	characteristic
210	C₂²×C₄₁	#576	1	1	yes	characteristic
211	C₂²×C₄₁	#578	1	1	yes	characteristic
212	C₄×C₄₁	—	2	2	no	—
213	C₄×C₄₁	—	4	2	no	—
214	C₄×C₄₁	—	4	2	no	—
215	C₄×C₄₁	—	4	4	no	—
216	C₄×C₄₁	—	8	2	no	—
217	C₄×C₄₁	—	8	2	no	—
218	C₄×C₄₁	#518	1	1	yes	characteristic
219	C₄×C₄₁	#520	1	1	yes	characteristic
220	C₄×C₄₁	#538	1	1	yes	characteristic
221	C₄×C₄₁	#539	1	1	yes	characteristic
222	C₂×#466	C₂×C₄₁	1	1	yes	characteristic
223	#2324	C₂×C₄₁	1	2	yes	complemented
224	#1925	C₂×C₄₁	1	2	yes	complemented
225	#1921	C₂×C₄₁	1	2	yes	complemented
226	#1895	C₂×C₄₁	1	2	yes	complemented
227	#1879	C₂×C₄₁	1	2	yes	complemented
228	#1862	C₂×C₄₁	1	2	yes	complemented
229	#1808	C₂×C₄₁	1	1	yes	characteristic, complemented
230	#1729	C₂×C₄₁	1	1	yes	characteristic, complemented
231	C₂×C₄₁	—	4	2	no	—
232	C₂×C₄₁	—	8	4	no	—
233	C₂×C₄₁	#2325	1	1	yes	characteristic
234	C₂×C₄₁	#2948	1	1	yes	characteristic
235	C₂×C₄₁	#2951	1	1	yes	characteristic
236	C₂×C₄₁	#3199	1	1	yes	characteristic
237	C₂×C₄₁	#3203	1	1	yes	characteristic
238	C₂×C₄₁	#3259	1	1	yes	characteristic
239	C₂×C₄₁	#3262	1	1	yes	characteristic
240	C₂²×D₈	C₂²×C₄₁	1	1	yes	characteristic
241	C₂²×M₁₆	C₂²×C₄₁	1	1	yes	characteristic
242	C₂³×C₈	C₂²×C₄₁	1	1	yes	characteristic
243	C₂×#121	C₂²×C₄₁	1	2	yes	—
244	C₂×C₄×D₄	C₂²×C₄₁	1	2	yes	—
245	C₂×#117	C₂²×C₄₁	1	1	yes	characteristic
246	#466	C₄×C₄₁	1	8	yes	complemented
247	C₂×#107	C₂²×C₄₁	1	1	yes	characteristic
248	C₂×#107	C₂²×C₄₁	1	1	yes	characteristic
249	C₂×#107	C₂²×C₄₁	1	1	yes	characteristic
250	C₂×#102	C₂²×C₄₁	1	2	yes	—
251	C₂×#102	C₂²×C₄₁	1	2	yes	—
252	C₂×#102	C₂²×C₄₁	1	2	yes	—
253	#390	—	2	2	no	—
254	#390	C₂²×C₄₁	1	2	yes	—
255	#389	C₂²×C₄₁	1	2	yes	—
256	#388	—	2	2	no	—
257	#386	—	2	2	no	—
258	#385	—	2	2	no	—
259	#380	C₂²×C₄₁	1	2	yes	—
260	C₄×C₄⋊C₄	C₂²×C₄₁	1	2	yes	—
261	#340	C₂²×C₄₁	1	2	yes	—
262	#340	C₂²×C₄₁	1	2	yes	—
263	#340	C₂²×C₄₁	1	2	yes	—
264	#336	C₂²×C₄₁	1	2	yes	—
265	#336	C₂²×C₄₁	1	2	yes	—
266	C₄₁	#22196	1	1	yes	characteristic, direct product factor, Sylow
267	C₂²×D₄	—	2	2	no	—
268	C₂²×D₄	C₂³×C₄₁	1	2	yes	—
269	C₂³×C₄	—	2	2	no	—
270	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
271	C₂×D₈	—	4	1	no	—
272	C₂×D₈	—	4	1	no	—
273	C₂×D₈	C₂×C₄×C₄₁	1	4	yes	—
274	C₂×M₁₆	—	2	2	no	—
275	C₂×M₁₆	—	4	1	no	—
276	C₂×M₁₆	—	4	1	no	—
277	C₂²×C₈	—	4	1	no	—
278	C₂²×C₈	—	4	1	no	—
279	C₂²×C₈	C₂×C₄×C₄₁	1	4	yes	complemented
280	C₂²×C₈	C₂³×C₄₁	1	2	yes	—
281	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
282	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
283	#121	—	2	4	no	—
284	#121	C₂×C₄×C₄₁	1	8	yes	complemented
285	C₄×D₄	—	4	2	no	—
286	C₄×D₄	—	4	2	no	—
287	#117	—	4	1	no	—
288	#117	—	4	1	no	—
289	C₂×C₄⋊C₄	—	2	2	no	—
290	C₂×C₄⋊C₄	D₄×C₄₁	1	1	yes	characteristic
291	C₂×C₄⋊C₄	D₄×C₄₁	1	1	yes	characteristic
292	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
293	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
294	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
295	C₂×C₂²⋊C₄	—	2	2	no	—
296	C₂×C₂²⋊C₄	—	2	2	no	—
297	C₂×C₂²⋊C₄	—	2	2	no	—
298	C₂×C₂²⋊C₄	—	2	2	no	—
299	C₂×C₂²⋊C₄	—	2	2	no	—
300	C₂×C₂²⋊C₄	D₄×C₄₁	1	2	yes	—
301	C₂×C₄²	—	2	2	no	—
302	C₂×C₄²	C₂³×C₄₁	1	2	yes	—
303	#107	—	4	1	no	—
304	#107	—	4	1	no	—
305	#107	C₂×C₄×C₄₁	1	4	yes	complemented
306	#102	—	4	2	no	—
307	#102	—	4	2	no	—
308	#102	C₂×C₄×C₄₁	1	8	yes	complemented
309	#95	—	2	2	no	—
310	#95	—	2	2	no	—
311	#95	—	2	2	no	—
312	C₂⁴	—	2	2	no	—
313	C₂⁴	C₂×D₄×C₄₁	1	1	yes	characteristic
314	C₂×D₄	—	2	8	no	—
315	C₂×D₄	—	2	2	no	—
316	C₂×D₄	—	2	2	no	—
317	C₂×D₄	—	2	2	no	—
318	C₂×D₄	—	2	2	no	—
319	C₂×D₄	—	2	2	no	—
320	C₂×D₄	—	8	2	no	—
321	C₂×D₄	—	8	2	no	—
322	C₂×D₄	C₂²×C₄×C₄₁	1	4	yes	—
323	C₂²×C₄	—	2	1	no	—
324	C₂²×C₄	—	2	1	no	—
325	C₂²×C₄	—	2	1	no	—
326	C₂²×C₄	—	2	1	no	—
327	C₂²×C₄	—	2	2	no	—
328	C₂²×C₄	—	2	2	no	—
329	C₂²×C₄	—	2	2	no	—
330	C₂²×C₄	—	4	4	no	—
331	C₂²×C₄	—	8	2	no	—
332	C₂²×C₄	—	8	2	no	—
333	C₂²×C₄	C₂²×C₄×C₄₁	1	2	yes	—
334	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
335	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
336	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
337	C₂²×C₄	#41×C₄₁	1	2	yes	—
338	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
339	D₈	—	4	4	no	—
340	M₁₆	—	4	4	no	—
341	C₂×C₈	—	2	1	no	—
342	C₂×C₈	—	2	1	no	—
343	C₂×C₈	—	2	1	no	—
344	C₂×C₈	—	2	1	no	—
345	C₂×C₈	—	2	2	no	—
346	C₂×C₈	—	2	2	no	—
347	C₂×C₈	—	2	2	no	—
348	C₂×C₈	—	4	4	no	—
349	C₂×C₈	C₂²×C₄×C₄₁	1	2	yes	—
350	C₂×C₈	C₂²×C₄×C₄₁	1	2	yes	—
351	C₄⋊C₄	—	2	2	no	—
352	C₄⋊C₄	—	2	2	no	—
353	C₄⋊C₄	—	2	2	no	—
354	C₄⋊C₄	—	2	2	no	—
355	C₄⋊C₄	—	2	2	no	—
356	C₄⋊C₄	—	4	1	no	—
357	C₄⋊C₄	—	4	1	no	—
358	C₄⋊C₄	—	8	2	no	—
359	C₄⋊C₄	C₂²×C₄×C₄₁	1	4	yes	—
360	C₂²⋊C₄	—	2	8	no	—
361	C₂²⋊C₄	—	4	2	no	—
362	C₂²⋊C₄	—	4	4	no	—
363	C₂²⋊C₄	—	8	2	no	—
364	C₂²⋊C₄	—	8	2	no	—
365	C₂²⋊C₄	—	8	2	no	—
366	C₄²	—	2	2	no	—
367	C₄²	—	2	2	no	—
368	C₄²	—	8	2	no	—
369	C₂³	—	2	1	no	—
370	C₂³	—	2	1	no	—
371	C₂³	—	2	1	no	—
372	C₂³	—	2	1	no	—
373	C₂³	—	2	1	no	—
374	C₂³	—	2	1	no	—
375	C₂³	—	2	4	no	—
376	C₂³	—	4	2	no	—
377	C₂³	—	4	2	no	—
378	C₂³	—	4	2	no	—
379	C₂³	—	4	2	no	—
380	C₂³	—	4	2	no	—
381	C₂³	—	4	2	no	—
382	C₂³	C₄×D₄×C₄₁	1	2	yes	—
383	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
384	D₄	—	2	4	no	—
385	D₄	—	2	4	no	—
386	D₄	—	4	2	no	—
387	D₄	—	4	2	no	—
388	D₄	—	8	8	no	—
389	C₂×C₄	—	2	1	no	—
390	C₂×C₄	—	2	1	no	—
391	C₂×C₄	—	2	2	no	—
392	C₂×C₄	—	2	2	no	—
393	C₂×C₄	—	2	2	no	—
394	C₂×C₄	—	2	2	no	—
395	C₂×C₄	—	2	4	no	—
396	C₂×C₄	—	2	2	no	—
397	C₂×C₄	—	2	2	no	—
398	C₂×C₄	—	2	2	no	—
399	C₂×C₄	—	2	2	no	—
400	C₂×C₄	—	2	2	no	—
401	C₂×C₄	—	2	2	no	—
402	C₂×C₄	—	4	2	no	—
403	C₂×C₄	—	4	2	no	—
404	C₂×C₄	—	4	2	no	—
405	C₂×C₄	—	4	2	no	—
406	C₂×C₄	—	4	2	no	—
407	C₂×C₄	—	4	2	no	—
408	C₂×C₄	—	4	2	no	—
409	C₂×C₄	—	4	2	no	—
410	C₂×C₄	—	8	8	no	—
411	C₂×C₄	C₄×D₄×C₄₁	1	2	yes	—
412	C₂×C₄	C₂³×C₄×C₄₁	1	1	yes	characteristic
413	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
414	C₂×C₄	H(5,𝔽₂)×C₄₁	1	1	yes	characteristic
415	C₂×C₄	H(5,𝔽₂)×C₄₁	1	1	yes	characteristic
416	C₂×C₄	H(5,𝔽₂)×C₄₁	1	1	yes	characteristic
417	C₂×C₄	2₋¹⁺⁴×C₄₁	1	1	yes	characteristic
418	C₈	—	2	2	no	—
419	C₈	—	2	2	no	—
420	C₈	—	4	2	no	—
421	C₂²	—	2	2	no	—
422	C₂²	—	2	2	no	—
423	C₂²	—	2	2	no	—
424	C₂²	—	4	1	no	—
425	C₂²	—	4	1	no	—
426	C₂²	—	4	1	no	—
427	C₂²	—	4	1	no	—
428	C₂²	—	4	4	no	—
429	C₂²	—	4	4	no	—
430	C₂²	—	4	4	no	—
431	C₂²	—	8	2	no	—
432	C₂²	—	8	2	no	—
433	C₂²	—	8	2	no	—
434	C₂²	—	8	2	no	—
435	C₂²	C₂×C₄×D₄×C₄₁	1	1	yes	characteristic
436	C₂²	C₄₁×#534	1	1	yes	characteristic
437	C₂²	C₄₁×#537	1	1	yes	characteristic
438	C₂²	C₄₁×#576	1	1	yes	characteristic
439	C₂²	C₄₁×#576	1	1	yes	characteristic
440	C₂²	C₄₁×#576	1	1	yes	characteristic
441	C₂²	C₄₁×#578	1	1	yes	characteristic
442	C₄	—	2	2	no	—
443	C₄	—	4	2	no	—
444	C₄	—	4	2	no	—
445	C₄	—	4	4	no	—
446	C₄	—	8	2	no	—
447	C₄	—	8	2	no	—
448	C₄	C₄₁×#518	1	1	yes	characteristic
449	C₄	C₄₁×#520	1	1	yes	characteristic
450	C₄	C₄₁×#538	1	1	yes	characteristic
451	C₄	C₄₁×#539	1	1	yes	characteristic
452	C₂	—	4	2	no	—
453	C₂	—	8	4	no	—
454	C₂	C₄₁×#2325	1	1	yes	characteristic
455	C₂	C₄₁×#2948	1	1	yes	characteristic
456	C₂	C₄₁×#2951	1	1	yes	characteristic
457	C₂	C₄₁×#3199	1	1	yes	characteristic
458	C₂	C₄₁×#3203	1	1	yes	characteristic
459	C₂	C₄₁×#3259	1	1	yes	characteristic
460	C₂	C₄₁×#3262	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	C₂×C₄₁×#466	C₂
LCS	G ▷ C₂×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
2. C₄₁×#2324	C₂	semidirect
3. C₄₁×#1925	C₂	semidirect
4. C₄₁×#1921	C₂	semidirect
5. C₄₁×#1895	C₂	semidirect
6. C₄₁×#1879	C₂	semidirect
7. C₄₁×#1862	C₂	semidirect
8. C₄₁×#1808	C₂	semidirect
9. C₄₁×#1729	C₂	semidirect
16. C₄₁×#466	C₄	semidirect
48. C₂²×C₈×C₄₁	C₂×C₄	semidirect
53. #121×C₄₁	C₂×C₄	semidirect
74. #107×C₄₁	C₂×C₄	semidirect
77. #102×C₄₁	C₂×C₄	semidirect
190. #22196	C₄₁	direct (N × H)
223. #2324	C₂×C₄₁	semidirect
224. #1925	C₂×C₄₁	semidirect
225. #1921	C₂×C₄₁	semidirect
226. #1895	C₂×C₄₁	semidirect
227. #1879	C₂×C₄₁	semidirect
228. #1862	C₂×C₄₁	semidirect
229. #1808	C₂×C₄₁	semidirect
230. #1729	C₂×C₄₁	semidirect
246. #466	C₄×C₄₁	semidirect
266. C₄₁	#22196	direct (N × H)
279. C₂²×C₈	C₂×C₄×C₄₁	semidirect
284. #121	C₂×C₄×C₄₁	semidirect
305. #107	C₂×C₄×C₄₁	semidirect
308. #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×#466	2
C₄₁×#2324	2
C₄₁×#1925	2
C₄₁×#1921	2
C₄₁×#1895	2
C₄₁×#1879	2
C₄₁×#1862	2
C₄₁×#1808	2
C₄₁×#1729	2
#22196	41

Subgroups — C41×#22196 #23798397

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#22196 #23798397