Subgroups — C₄₁×#23183 #23799384

Order 10496.

1038 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₁×#495	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×SD₁₆×C₄₁	C₂	1	2	yes	maximal, complemented
3	C₄₁×#2367	C₂	1	2	yes	maximal, complemented
4	C₄₁×#1983	C₂	1	2	yes	maximal, complemented
5	C₄₁×#1968	C₂	1	2	yes	maximal, complemented
6	C₄₁×#1879	C₂	1	2	yes	maximal
7	C₄₁×#1878	C₂	1	2	yes	maximal, complemented
8	C₄×#106×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
9	C₈×C₄⋊C₄×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×Q₁₆×C₄₁	C₂²	1	1	yes	characteristic
11	C₂²×SD₁₆×C₄₁	C₂²	1	2	yes	—
12	C₂²×D₈×C₄₁	C₂²	1	1	yes	characteristic
13	C₂×#124×C₄₁	C₂²	1	2	yes	—
14	C₂×C₄×Q₈×C₄₁	C₂²	1	2	yes	—
15	C₂×C₄×D₄×C₄₁	C₂²	1	2	yes	—
16	C₄₁×#495	C₄	1	8	yes	complemented
17	C₄×SD₁₆×C₄₁	—	2	8	no	—
18	C₂×#106×C₄₁	C₂²	1	1	yes	characteristic
19	C₂×#106×C₄₁	C₂²	1	1	yes	characteristic
20	C₂×C₄⋊C₈×C₄₁	C₂²	1	1	yes	characteristic
21	C₂×#103×C₄₁	C₂²	1	2	yes	—
22	C₂×#103×C₄₁	C₂²	1	2	yes	—
23	C₂×#102×C₄₁	C₂²	1	2	yes	—
24	C₂×#102×C₄₁	C₂²	1	2	yes	—
25	C₂×C₄×C₈×C₄₁	C₂²	1	2	yes	—
26	C₂×C₄×C₈×C₄₁	C₂²	1	1	yes	characteristic
27	C₄₁×#391	C₂²	1	2	yes	—
28	C₄₁×#390	C₂²	1	2	yes	—
29	C₄₁×#388	—	2	2	no	—
30	C₄₁×#388	—	2	2	no	—
31	C₄₁×#385	—	2	2	no	—
32	C₄×C₄⋊C₄×C₄₁	C₂²	1	2	yes	—
33	C₄×C₄⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
34	C₄×C₂²⋊C₄×C₄₁	—	2	2	no	—
35	C₄₁×#340	C₂²	1	2	yes	—
36	C₄₁×#336	C₂²	1	2	yes	—
37	C₂²×Q₈×C₄₁	C₂³	1	2	yes	—
38	C₂²×D₄×C₄₁	C₂³	1	2	yes	—
39	C₂³×C₄×C₄₁	—	2	2	no	—
40	C₂×Q₁₆×C₄₁	—	4	1	no	—
41	C₂×Q₁₆×C₄₁	—	4	1	no	—
42	C₂×Q₁₆×C₄₁	C₂×C₄	1	4	yes	complemented
43	C₂×SD₁₆×C₄₁	—	2	4	no	—
44	C₂×SD₁₆×C₄₁	—	2	4	no	—
45	C₂×SD₁₆×C₄₁	C₂×C₄	1	8	yes	complemented
46	C₂×D₈×C₄₁	—	4	1	no	—
47	C₂×D₈×C₄₁	—	4	1	no	—
48	C₂×D₈×C₄₁	C₂×C₄	1	4	yes	—
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	#124×C₄₁	—	2	4	no	—
53	#124×C₄₁	C₂×C₄	1	8	yes	complemented
54	C₄×Q₈×C₄₁	—	2	4	no	—
55	C₄×Q₈×C₄₁	—	4	2	no	—
56	C₄×D₄×C₄₁	—	2	4	no	—
57	C₄×D₄×C₄₁	—	4	2	no	—
58	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
59	C₂×C₄⋊C₄×C₄₁	D₄	1	2	yes	—
60	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
61	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
62	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
63	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
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×C₄²×C₄₁	—	2	2	no	—
68	C₂×C₄²×C₄₁	—	2	2	no	—
69	C₂×C₄²×C₄₁	C₂³	1	2	yes	—
70	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
71	#106×C₄₁	—	2	2	no	—
72	#106×C₄₁	D₄	1	4	yes	—
73	C₄⋊C₈×C₄₁	—	2	2	no	—
74	#103×C₄₁	—	2	4	no	—
75	#103×C₄₁	—	4	2	no	—
76	#102×C₄₁	—	2	4	no	—
77	#102×C₄₁	—	4	2	no	—
78	C₄×C₈×C₄₁	—	2	4	no	—
79	C₄×C₈×C₄₁	C₂×C₄	1	4	yes	complemented
80	#95×C₄₁	—	2	2	no	—
81	#95×C₄₁	—	2	2	no	—
82	#95×C₄₁	—	2	2	no	—
83	#95×C₄₁	D₄	1	1	yes	characteristic
84	#95×C₄₁	D₄	1	1	yes	characteristic
85	C₂⁴×C₄₁	—	2	2	no	—
86	C₂×Q₈×C₄₁	—	2	2	no	—
87	C₂×Q₈×C₄₁	—	2	2	no	—
88	C₂×Q₈×C₄₁	—	2	2	no	—
89	C₂×Q₈×C₄₁	—	2	2	no	—
90	C₂×Q₈×C₄₁	—	2	2	no	—
91	C₂×Q₈×C₄₁	C₂²×C₄	1	4	yes	—
92	C₂×D₄×C₄₁	—	2	2	no	—
93	C₂×D₄×C₄₁	—	2	2	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	C₂²×C₄	1	4	yes	—
98	C₂²×C₄×C₄₁	—	2	2	no	—
99	C₂²×C₄×C₄₁	—	2	2	no	—
100	C₂²×C₄×C₄₁	—	2	2	no	—
101	C₂²×C₄×C₄₁	—	4	4	no	—
102	C₂²×C₄×C₄₁	—	4	4	no	—
103	C₂²×C₄×C₄₁	—	8	2	no	—
104	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
105	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
106	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
107	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
108	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
109	Q₁₆×C₄₁	—	4	4	no	—
110	SD₁₆×C₄₁	—	2	16	no	—
111	D₈×C₄₁	—	4	4	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	C₂²×C₄	1	2	yes	—
118	C₂×C₈×C₄₁	C₂²×C₄	1	2	yes	—
119	C₂×C₈×C₄₁	C₂×D₄	1	2	yes	—
120	C₂×C₈×C₄₁	#41	1	2	yes	—
121	C₄⋊C₄×C₄₁	—	2	4	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	4	no	—
126	C₄⋊C₄×C₄₁	C₂×D₄	1	4	yes	—
127	C₂²⋊C₄×C₄₁	—	2	8	no	—
128	C₂²⋊C₄×C₄₁	—	2	8	no	—
129	C₂²⋊C₄×C₄₁	—	4	4	no	—
130	C₂²⋊C₄×C₄₁	—	4	4	no	—
131	C₂²⋊C₄×C₄₁	—	8	2	no	—
132	C₄²×C₄₁	—	2	2	no	—
133	C₄²×C₄₁	—	2	2	no	—
134	C₄²×C₄₁	—	4	4	no	—
135	C₄²×C₄₁	—	8	2	no	—
136	C₄²×C₄₁	C₂²×C₄	1	2	yes	—
137	C₄²×C₄₁	#41	1	2	yes	—
138	C₂³×C₄₁	—	2	4	no	—
139	C₂³×C₄₁	—	4	2	no	—
140	C₂³×C₄₁	—	4	2	no	—
141	C₂³×C₄₁	—	4	2	no	—
142	C₂³×C₄₁	—	4	2	no	—
143	C₂³×C₄₁	—	4	2	no	—
144	C₂³×C₄₁	—	4	2	no	—
145	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
146	Q₈×C₄₁	—	2	4	no	—
147	Q₈×C₄₁	—	2	4	no	—
148	Q₈×C₄₁	—	4	2	no	—
149	Q₈×C₄₁	—	4	2	no	—
150	D₄×C₄₁	—	2	4	no	—
151	D₄×C₄₁	—	2	4	no	—
152	D₄×C₄₁	—	4	2	no	—
153	D₄×C₄₁	—	4	2	no	—
154	C₂×C₄×C₄₁	—	2	2	no	—
155	C₂×C₄×C₄₁	—	2	2	no	—
156	C₂×C₄×C₄₁	—	2	2	no	—
157	C₂×C₄×C₄₁	—	2	2	no	—
158	C₂×C₄×C₄₁	—	2	4	no	—
159	C₂×C₄×C₄₁	—	2	2	no	—
160	C₂×C₄×C₄₁	—	2	4	no	—
161	C₂×C₄×C₄₁	—	2	2	no	—
162	C₂×C₄×C₄₁	—	2	2	no	—
163	C₂×C₄×C₄₁	—	4	2	no	—
164	C₂×C₄×C₄₁	—	4	2	no	—
165	C₂×C₄×C₄₁	—	4	2	no	—
166	C₂×C₄×C₄₁	—	4	2	no	—
167	C₂×C₄×C₄₁	—	4	2	no	—
168	C₂×C₄×C₄₁	—	4	2	no	—
169	C₂×C₄×C₄₁	—	4	2	no	—
170	C₂×C₄×C₄₁	—	8	8	no	—
171	C₂×C₄×C₄₁	C₄×D₄	1	2	yes	—
172	C₂×C₄×C₄₁	C₄×D₄	1	2	yes	—
173	C₂×C₄×C₄₁	#135	1	4	yes	—
174	C₂×C₄×C₄₁	C₂³×C₄	1	1	yes	characteristic
175	C₂×C₄×C₄₁	C₂²×D₄	1	1	yes	characteristic
176	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
177	C₂×C₄×C₄₁	C₂×#41	1	1	yes	characteristic
178	C₂×C₄×C₄₁	H(5,𝔽₂)	1	1	yes	characteristic
179	C₂×C₄×C₄₁	H(5,𝔽₂)	1	1	yes	characteristic
180	C₈×C₄₁	—	2	2	no	—
181	C₈×C₄₁	—	4	2	no	—
182	C₈×C₄₁	C₄×D₄	1	4	yes	—
183	#23183	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
184	C₂²×C₄₁	—	4	4	no	—
185	C₂²×C₄₁	—	4	4	no	—
186	C₂²×C₄₁	—	4	4	no	—
187	C₂²×C₄₁	—	8	2	no	—
188	C₂²×C₄₁	—	8	2	no	—
189	C₂²×C₄₁	—	8	2	no	—
190	C₂²×C₄₁	—	8	2	no	—
191	C₂²×C₄₁	C₂×C₄×D₄	1	1	yes	characteristic
192	C₂²×C₄₁	D₄²	1	1	yes	characteristic
193	C₂²×C₄₁	#550	1	1	yes	characteristic
194	C₂²×C₄₁	C₂×#135	1	2	yes	—
195	C₂²×C₄₁	#577	1	2	yes	—
196	C₄×C₄₁	—	2	2	no	—
197	C₄×C₄₁	—	2	2	no	—
198	C₄×C₄₁	—	2	4	no	—
199	C₄×C₄₁	—	4	4	no	—
200	C₄×C₄₁	—	4	2	no	—
201	C₄×C₄₁	—	4	4	no	—
202	C₄×C₄₁	—	8	2	no	—
203	C₄×C₄₁	C₂×C₄×D₄	1	1	yes	characteristic
204	C₄×C₄₁	#518	1	1	yes	characteristic
205	C₄×C₄₁	#550	1	1	yes	characteristic
206	C₄×C₄₁	#559	1	1	yes	characteristic
207	C₂×#495	C₂×C₄₁	1	1	yes	characteristic
208	C₂×C₄×SD₁₆	C₂×C₄₁	1	2	yes	complemented
209	#2367	C₂×C₄₁	1	2	yes	complemented
210	#1983	C₂×C₄₁	1	2	yes	complemented
211	#1968	C₂×C₄₁	1	2	yes	complemented
212	#1879	C₂×C₄₁	1	2	yes	—
213	#1878	C₂×C₄₁	1	2	yes	complemented
214	C₄×#106	C₂×C₄₁	1	1	yes	characteristic, complemented
215	C₈×C₄⋊C₄	C₂×C₄₁	1	1	yes	characteristic, complemented
216	C₂×C₄₁	—	8	4	no	—
217	C₂×C₄₁	#2366	1	1	yes	characteristic
218	C₂×C₄₁	C₄×#135	1	1	yes	characteristic
219	C₂×C₄₁	#2952	1	1	yes	characteristic
220	C₂×C₄₁	#3282	1	2	yes	—
221	C₂×C₄₁	#3394	1	2	yes	—
222	C₂²×Q₁₆	C₂²×C₄₁	1	1	yes	characteristic
223	C₂²×SD₁₆	C₂²×C₄₁	1	2	yes	—
224	C₂²×D₈	C₂²×C₄₁	1	1	yes	characteristic
225	C₂×#124	C₂²×C₄₁	1	2	yes	—
226	C₂×C₄×Q₈	C₂²×C₄₁	1	2	yes	—
227	C₂×C₄×D₄	C₂²×C₄₁	1	2	yes	—
228	#495	C₄×C₄₁	1	8	yes	complemented
229	C₄×SD₁₆	—	2	8	no	—
230	C₂×#106	C₂²×C₄₁	1	1	yes	characteristic
231	C₂×#106	C₂²×C₄₁	1	1	yes	characteristic
232	C₂×C₄⋊C₈	C₂²×C₄₁	1	1	yes	characteristic
233	C₂×#103	C₂²×C₄₁	1	2	yes	—
234	C₂×#103	C₂²×C₄₁	1	2	yes	—
235	C₂×#102	C₂²×C₄₁	1	2	yes	—
236	C₂×#102	C₂²×C₄₁	1	2	yes	—
237	C₂×C₄×C₈	C₂²×C₄₁	1	2	yes	—
238	C₂×C₄×C₈	C₂²×C₄₁	1	1	yes	characteristic
239	#391	C₂²×C₄₁	1	2	yes	—
240	#390	C₂²×C₄₁	1	2	yes	—
241	#388	—	2	2	no	—
242	#388	—	2	2	no	—
243	#385	—	2	2	no	—
244	C₄×C₄⋊C₄	C₂²×C₄₁	1	2	yes	—
245	C₄×C₄⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
246	C₄×C₂²⋊C₄	—	2	2	no	—
247	#340	C₂²×C₄₁	1	2	yes	—
248	#336	C₂²×C₄₁	1	2	yes	—
249	C₄₁	#23183	1	1	yes	characteristic, direct product factor, Sylow
250	C₂²×Q₈	C₂³×C₄₁	1	2	yes	—
251	C₂²×D₄	C₂³×C₄₁	1	2	yes	—
252	C₂³×C₄	—	2	2	no	—
253	C₂×Q₁₆	—	4	1	no	—
254	C₂×Q₁₆	—	4	1	no	—
255	C₂×Q₁₆	C₂×C₄×C₄₁	1	4	yes	complemented
256	C₂×SD₁₆	—	2	4	no	—
257	C₂×SD₁₆	—	2	4	no	—
258	C₂×SD₁₆	C₂×C₄×C₄₁	1	8	yes	complemented
259	C₂×D₈	—	4	1	no	—
260	C₂×D₈	—	4	1	no	—
261	C₂×D₈	C₂×C₄×C₄₁	1	4	yes	—
262	C₂²×C₈	C₂³×C₄₁	1	2	yes	—
263	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
264	C₂²×C₈	C₂³×C₄₁	1	1	yes	characteristic
265	#124	—	2	4	no	—
266	#124	C₂×C₄×C₄₁	1	8	yes	complemented
267	C₄×Q₈	—	2	4	no	—
268	C₄×Q₈	—	4	2	no	—
269	C₄×D₄	—	2	4	no	—
270	C₄×D₄	—	4	2	no	—
271	C₂×C₄⋊C₄	—	2	2	no	—
272	C₂×C₄⋊C₄	D₄×C₄₁	1	2	yes	—
273	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
274	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
275	C₂×C₂²⋊C₄	—	2	2	no	—
276	C₂×C₂²⋊C₄	—	2	2	no	—
277	C₂×C₂²⋊C₄	—	2	2	no	—
278	C₂×C₂²⋊C₄	—	2	2	no	—
279	C₂×C₂²⋊C₄	—	2	2	no	—
280	C₂×C₄²	—	2	2	no	—
281	C₂×C₄²	—	2	2	no	—
282	C₂×C₄²	C₂³×C₄₁	1	2	yes	—
283	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
284	#106	—	2	2	no	—
285	#106	D₄×C₄₁	1	4	yes	—
286	C₄⋊C₈	—	2	2	no	—
287	#103	—	2	4	no	—
288	#103	—	4	2	no	—
289	#102	—	2	4	no	—
290	#102	—	4	2	no	—
291	C₄×C₈	—	2	4	no	—
292	C₄×C₈	C₂×C₄×C₄₁	1	4	yes	complemented
293	#95	—	2	2	no	—
294	#95	—	2	2	no	—
295	#95	—	2	2	no	—
296	#95	D₄×C₄₁	1	1	yes	characteristic
297	#95	D₄×C₄₁	1	1	yes	characteristic
298	C₂⁴	—	2	2	no	—
299	C₂×Q₈	—	2	2	no	—
300	C₂×Q₈	—	2	2	no	—
301	C₂×Q₈	—	2	2	no	—
302	C₂×Q₈	—	2	2	no	—
303	C₂×Q₈	—	2	2	no	—
304	C₂×Q₈	C₂²×C₄×C₄₁	1	4	yes	—
305	C₂×D₄	—	2	2	no	—
306	C₂×D₄	—	2	2	no	—
307	C₂×D₄	—	2	2	no	—
308	C₂×D₄	—	2	2	no	—
309	C₂×D₄	—	2	2	no	—
310	C₂×D₄	C₂²×C₄×C₄₁	1	4	yes	—
311	C₂²×C₄	—	2	2	no	—
312	C₂²×C₄	—	2	2	no	—
313	C₂²×C₄	—	2	2	no	—
314	C₂²×C₄	—	4	4	no	—
315	C₂²×C₄	—	4	4	no	—
316	C₂²×C₄	—	8	2	no	—
317	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
318	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
319	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
320	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
321	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
322	Q₁₆	—	4	4	no	—
323	SD₁₆	—	2	16	no	—
324	D₈	—	4	4	no	—
325	C₂×C₈	—	2	1	no	—
326	C₂×C₈	—	2	1	no	—
327	C₂×C₈	—	2	2	no	—
328	C₂×C₈	—	2	2	no	—
329	C₂×C₈	—	2	2	no	—
330	C₂×C₈	C₂²×C₄×C₄₁	1	2	yes	—
331	C₂×C₈	C₂²×C₄×C₄₁	1	2	yes	—
332	C₂×C₈	C₂×D₄×C₄₁	1	2	yes	—
333	C₂×C₈	#41×C₄₁	1	2	yes	—
334	C₄⋊C₄	—	2	4	no	—
335	C₄⋊C₄	—	2	2	no	—
336	C₄⋊C₄	—	2	2	no	—
337	C₄⋊C₄	—	2	2	no	—
338	C₄⋊C₄	—	4	4	no	—
339	C₄⋊C₄	C₂×D₄×C₄₁	1	4	yes	—
340	C₂²⋊C₄	—	2	8	no	—
341	C₂²⋊C₄	—	2	8	no	—
342	C₂²⋊C₄	—	4	4	no	—
343	C₂²⋊C₄	—	4	4	no	—
344	C₂²⋊C₄	—	8	2	no	—
345	C₄²	—	2	2	no	—
346	C₄²	—	2	2	no	—
347	C₄²	—	4	4	no	—
348	C₄²	—	8	2	no	—
349	C₄²	C₂²×C₄×C₄₁	1	2	yes	—
350	C₄²	#41×C₄₁	1	2	yes	—
351	C₂³	—	2	4	no	—
352	C₂³	—	4	2	no	—
353	C₂³	—	4	2	no	—
354	C₂³	—	4	2	no	—
355	C₂³	—	4	2	no	—
356	C₂³	—	4	2	no	—
357	C₂³	—	4	2	no	—
358	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
359	Q₈	—	2	4	no	—
360	Q₈	—	2	4	no	—
361	Q₈	—	4	2	no	—
362	Q₈	—	4	2	no	—
363	D₄	—	2	4	no	—
364	D₄	—	2	4	no	—
365	D₄	—	4	2	no	—
366	D₄	—	4	2	no	—
367	C₂×C₄	—	2	2	no	—
368	C₂×C₄	—	2	2	no	—
369	C₂×C₄	—	2	2	no	—
370	C₂×C₄	—	2	2	no	—
371	C₂×C₄	—	2	4	no	—
372	C₂×C₄	—	2	2	no	—
373	C₂×C₄	—	2	4	no	—
374	C₂×C₄	—	2	2	no	—
375	C₂×C₄	—	2	2	no	—
376	C₂×C₄	—	4	2	no	—
377	C₂×C₄	—	4	2	no	—
378	C₂×C₄	—	4	2	no	—
379	C₂×C₄	—	4	2	no	—
380	C₂×C₄	—	4	2	no	—
381	C₂×C₄	—	4	2	no	—
382	C₂×C₄	—	4	2	no	—
383	C₂×C₄	—	8	8	no	—
384	C₂×C₄	C₄×D₄×C₄₁	1	2	yes	—
385	C₂×C₄	C₄×D₄×C₄₁	1	2	yes	—
386	C₂×C₄	#135×C₄₁	1	4	yes	—
387	C₂×C₄	C₂³×C₄×C₄₁	1	1	yes	characteristic
388	C₂×C₄	C₂²×D₄×C₄₁	1	1	yes	characteristic
389	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
390	C₂×C₄	C₂×#41×C₄₁	1	1	yes	characteristic
391	C₂×C₄	H(5,𝔽₂)×C₄₁	1	1	yes	characteristic
392	C₂×C₄	H(5,𝔽₂)×C₄₁	1	1	yes	characteristic
393	C₈	—	2	2	no	—
394	C₈	—	4	2	no	—
395	C₈	C₄×D₄×C₄₁	1	4	yes	—
396	C₂²	—	4	4	no	—
397	C₂²	—	4	4	no	—
398	C₂²	—	4	4	no	—
399	C₂²	—	8	2	no	—
400	C₂²	—	8	2	no	—
401	C₂²	—	8	2	no	—
402	C₂²	—	8	2	no	—
403	C₂²	C₂×C₄×D₄×C₄₁	1	1	yes	characteristic
404	C₂²	D₄²×C₄₁	1	1	yes	characteristic
405	C₂²	C₄₁×#550	1	1	yes	characteristic
406	C₂²	C₂×#135×C₄₁	1	2	yes	—
407	C₂²	C₄₁×#577	1	2	yes	—
408	C₄	—	2	2	no	—
409	C₄	—	2	2	no	—
410	C₄	—	2	4	no	—
411	C₄	—	4	4	no	—
412	C₄	—	4	2	no	—
413	C₄	—	4	4	no	—
414	C₄	—	8	2	no	—
415	C₄	C₂×C₄×D₄×C₄₁	1	1	yes	characteristic
416	C₄	C₄₁×#518	1	1	yes	characteristic
417	C₄	C₄₁×#550	1	1	yes	characteristic
418	C₄	C₄₁×#559	1	1	yes	characteristic
419	C₂	—	8	4	no	—
420	C₂	C₄₁×#2366	1	1	yes	characteristic
421	C₂	C₄×#135×C₄₁	1	1	yes	characteristic
422	C₂	C₄₁×#2952	1	1	yes	characteristic
423	C₂	C₄₁×#3282	1	2	yes	—
424	C₂	C₄₁×#3394	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₄₁	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₄₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₁
prime radical	C₂²×D₈×C₄₁	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₄₁ ◁ C₄×C₄⋊C₄×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₄×SD₁₆×C₄₁	C₂	semidirect
3. C₄₁×#2367	C₂	semidirect
4. C₄₁×#1983	C₂	semidirect
5. C₄₁×#1968	C₂	semidirect
7. C₄₁×#1878	C₂	semidirect
8. C₄×#106×C₄₁	C₂	semidirect
9. C₈×C₄⋊C₄×C₄₁	C₂	semidirect
16. C₄₁×#495	C₄	semidirect
42. C₂×Q₁₆×C₄₁	C₂×C₄	semidirect
45. C₂×SD₁₆×C₄₁	C₂×C₄	semidirect
53. #124×C₄₁	C₂×C₄	semidirect
79. C₄×C₈×C₄₁	C₂×C₄	semidirect
183. #23183	C₄₁	direct (N × H)
208. C₂×C₄×SD₁₆	C₂×C₄₁	semidirect
209. #2367	C₂×C₄₁	semidirect
210. #1983	C₂×C₄₁	semidirect
211. #1968	C₂×C₄₁	semidirect
213. #1878	C₂×C₄₁	semidirect
214. C₄×#106	C₂×C₄₁	semidirect
215. C₈×C₄⋊C₄	C₂×C₄₁	semidirect
228. #495	C₄×C₄₁	semidirect
249. C₄₁	#23183	direct (N × H)
255. C₂×Q₁₆	C₂×C₄×C₄₁	semidirect
258. C₂×SD₁₆	C₂×C₄×C₄₁	semidirect
266. #124	C₂×C₄×C₄₁	semidirect
292. C₄×C₈	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×#495	2
C₂×C₄×SD₁₆×C₄₁	2
C₄₁×#2367	2
C₄₁×#1983	2
C₄₁×#1968	2
C₄₁×#1879	2
C₄₁×#1878	2
C₄×#106×C₄₁	2
C₈×C₄⋊C₄×C₄₁	2
#23183	41

Subgroups — C41×#23183 #23799384

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#23183 #23799384